Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 143.5 | ||
Character | \(\chi\) | \(=\) | 1152.143 |
Dual form | 1152.2.w.a.1007.5 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0963530 | + | 0.232617i | −0.0430904 | + | 0.104029i | −0.943959 | − | 0.330062i | \(-0.892930\pi\) |
0.900869 | + | 0.434091i | \(0.142930\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.617536 | + | 0.617536i | −0.233407 | + | 0.233407i | −0.814113 | − | 0.580706i | \(-0.802776\pi\) |
0.580706 | + | 0.814113i | \(0.302776\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.505112 | + | 1.21945i | −0.152297 | + | 0.367677i | −0.981553 | − | 0.191192i | \(-0.938765\pi\) |
0.829256 | + | 0.558869i | \(0.188765\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41575 | − | 1.41485i | 0.947358 | − | 0.392408i | 0.145121 | − | 0.989414i | \(-0.453643\pi\) |
0.802237 | + | 0.597006i | \(0.203643\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.76109 | 0.669662 | 0.334831 | − | 0.942278i | \(-0.391321\pi\) | ||||
0.334831 | + | 0.942278i | \(0.391321\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.189895 | − | 0.458448i | −0.0435650 | − | 0.105175i | 0.900599 | − | 0.434651i | \(-0.143128\pi\) |
−0.944164 | + | 0.329475i | \(0.893128\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.46959 | + | 4.46959i | −0.931975 | + | 0.931975i | −0.997829 | − | 0.0658547i | \(-0.979023\pi\) |
0.0658547 | + | 0.997829i | \(0.479023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.49071 | + | 3.49071i | 0.698141 | + | 0.698141i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.0101033 | + | 0.00418494i | −0.00187614 | + | 0.000777123i | −0.383621 | − | 0.923490i | \(-0.625323\pi\) |
0.381745 | + | 0.924268i | \(0.375323\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.03370i | − | 0.724474i | −0.932086 | − | 0.362237i | \(-0.882013\pi\) | ||
0.932086 | − | 0.362237i | \(-0.117987\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0841477 | − | 0.203151i | −0.0142236 | − | 0.0343387i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.30586 | + | 2.61197i | 1.03668 | + | 0.429406i | 0.835118 | − | 0.550071i | \(-0.185399\pi\) |
0.201559 | + | 0.979476i | \(0.435399\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.34633 | + | 5.34633i | 0.834957 | + | 0.834957i | 0.988190 | − | 0.153233i | \(-0.0489686\pi\) |
−0.153233 | + | 0.988190i | \(0.548969\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1719 | + | 4.21336i | 1.55121 | + | 0.642531i | 0.983534 | − | 0.180724i | \(-0.0578440\pi\) |
0.567673 | + | 0.823254i | \(0.307844\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.5870i | 1.69013i | 0.534660 | + | 0.845067i | \(0.320440\pi\) | ||||
−0.534660 | + | 0.845067i | \(0.679560\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.23730i | 0.891043i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.04956 | − | 3.74845i | −1.24305 | − | 0.514889i | −0.338385 | − | 0.941008i | \(-0.609881\pi\) |
−0.904667 | + | 0.426119i | \(0.859881\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.234995 | − | 0.234995i | −0.0316867 | − | 0.0316867i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.939369 | − | 0.389099i | −0.122295 | − | 0.0506564i | 0.320697 | − | 0.947182i | \(-0.396083\pi\) |
−0.442992 | + | 0.896526i | \(0.646083\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.97084 | − | 7.17223i | −0.380377 | − | 0.918311i | −0.991893 | − | 0.127078i | \(-0.959440\pi\) |
0.611516 | − | 0.791232i | \(-0.290560\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.930884i | 0.115462i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.40244 | − | 3.06619i | 0.904352 | − | 0.374595i | 0.118460 | − | 0.992959i | \(-0.462204\pi\) |
0.785892 | + | 0.618364i | \(0.212204\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.20890 | + | 1.20890i | 0.143470 | + | 0.143470i | 0.775194 | − | 0.631724i | \(-0.217652\pi\) |
−0.631724 | + | 0.775194i | \(0.717652\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.73875 | − | 3.73875i | 0.437588 | − | 0.437588i | −0.453612 | − | 0.891199i | \(-0.649865\pi\) |
0.891199 | + | 0.453612i | \(0.149865\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.441128 | − | 1.06498i | −0.0502712 | − | 0.121366i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.22016 | 0.812331 | 0.406166 | − | 0.913800i | \(-0.366866\pi\) | ||||
0.406166 | + | 0.913800i | \(0.366866\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.2970 | − | 4.67935i | 1.24000 | − | 0.513626i | 0.336287 | − | 0.941760i | \(-0.390829\pi\) |
0.903715 | + | 0.428134i | \(0.140829\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.266039 | + | 0.642275i | −0.0288560 | + | 0.0696645i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.70197 | + | 3.70197i | −0.392408 | + | 0.392408i | −0.875545 | − | 0.483137i | \(-0.839497\pi\) |
0.483137 | + | 0.875545i | \(0.339497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.23563 | + | 2.98307i | −0.129529 | + | 0.312710i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.124940 | 0.0128185 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0257 | −1.42409 | −0.712046 | − | 0.702133i | \(-0.752231\pi\) | ||||
−0.712046 | + | 0.702133i | \(0.752231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.26734 | + | 10.3023i | −0.424616 | + | 1.02511i | 0.556352 | + | 0.830947i | \(0.312201\pi\) |
−0.980968 | + | 0.194168i | \(0.937799\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.34273 | + | 8.34273i | −0.822034 | + | 0.822034i | −0.986399 | − | 0.164366i | \(-0.947442\pi\) |
0.164366 | + | 0.986399i | \(0.447442\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.28476 | − | 3.10168i | 0.124202 | − | 0.299850i | −0.849533 | − | 0.527536i | \(-0.823116\pi\) |
0.973735 | + | 0.227686i | \(0.0731159\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.00684 | − | 3.31654i | 0.766916 | − | 0.317667i | 0.0352935 | − | 0.999377i | \(-0.488763\pi\) |
0.731623 | + | 0.681710i | \(0.238763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.12115 | 0.481757 | 0.240879 | − | 0.970555i | \(-0.422564\pi\) | ||||
0.240879 | + | 0.970555i | \(0.422564\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.609043 | − | 1.47036i | −0.0567936 | − | 0.137112i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.70507 | + | 1.70507i | −0.156304 | + | 0.156304i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.54626 | + | 6.54626i | 0.595114 | + | 0.595114i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.31142 | + | 0.957421i | −0.206740 | + | 0.0856344i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.28564i | − | 0.735232i | −0.929978 | − | 0.367616i | \(-0.880174\pi\) | ||
0.929978 | − | 0.367616i | \(-0.119826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.82244 | − | 18.8850i | −0.683450 | − | 1.64999i | −0.757578 | − | 0.652745i | \(-0.773617\pi\) |
0.0741279 | − | 0.997249i | \(-0.476383\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.400375 | + | 0.165841i | 0.0347169 | + | 0.0143802i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.3963 | + | 13.3963i | 1.14452 | + | 1.14452i | 0.987613 | + | 0.156906i | \(0.0501521\pi\) |
0.156906 | + | 0.987613i | \(0.449848\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.0954 | + | 7.49538i | 1.53484 | + | 0.635750i | 0.980496 | − | 0.196540i | \(-0.0629706\pi\) |
0.554340 | + | 0.832290i | \(0.312971\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.87998i | 0.408085i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.00275343i | − | 0.000228660i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.0938 | − | 5.83786i | −1.15461 | − | 0.478256i | −0.278535 | − | 0.960426i | \(-0.589849\pi\) |
−0.876078 | + | 0.482170i | \(0.839849\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.91247 | − | 3.91247i | −0.318392 | − | 0.318392i | 0.529757 | − | 0.848149i | \(-0.322283\pi\) |
−0.848149 | + | 0.529757i | \(0.822283\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.938306 | + | 0.388659i | 0.0753665 | + | 0.0312178i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.38756 | − | 17.8351i | −0.589591 | − | 1.42340i | −0.883894 | − | 0.467687i | \(-0.845088\pi\) |
0.294303 | − | 0.955712i | \(-0.404912\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 5.52027i | − | 0.435058i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.9611 | + | 7.43971i | −1.40682 | + | 0.582723i | −0.951512 | − | 0.307611i | \(-0.900470\pi\) |
−0.455307 | + | 0.890335i | \(0.650470\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.9383 | − | 13.9383i | −1.07858 | − | 1.07858i | −0.996637 | − | 0.0819391i | \(-0.973889\pi\) |
−0.0819391 | − | 0.996637i | \(-0.526111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.473139 | − | 0.473139i | 0.0363953 | − | 0.0363953i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.06460 | − | 2.57018i | −0.0809402 | − | 0.195407i | 0.878229 | − | 0.478241i | \(-0.158725\pi\) |
−0.959169 | + | 0.282834i | \(0.908725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.31128 | −0.325902 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.3931 | − | 5.96183i | 1.07579 | − | 0.445608i | 0.226761 | − | 0.973950i | \(-0.427186\pi\) |
0.849031 | + | 0.528342i | \(0.177186\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.56470 | + | 6.19174i | −0.190633 | + | 0.460229i | −0.990079 | − | 0.140509i | \(-0.955126\pi\) |
0.799446 | + | 0.600737i | \(0.205126\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.21518 | + | 1.21518i | −0.0893415 | + | 0.0893415i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.39466 | + | 3.36700i | −0.101988 | + | 0.246220i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.0419 | 1.08840 | 0.544198 | − | 0.838957i | \(-0.316834\pi\) | ||||
0.544198 | + | 0.838957i | \(0.316834\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.6537 | −1.41470 | −0.707352 | − | 0.706861i | \(-0.750111\pi\) | ||||
−0.707352 | + | 0.706861i | \(0.750111\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.28693 | − | 7.93534i | 0.234184 | − | 0.565370i | −0.762478 | − | 0.647015i | \(-0.776017\pi\) |
0.996661 | + | 0.0816448i | \(0.0260173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.6374 | + | 14.6374i | −1.03761 | + | 1.03761i | −0.0383500 | + | 0.999264i | \(0.512210\pi\) |
−0.999264 | + | 0.0383500i | \(0.987790\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.00365482 | − | 0.00882352i | 0.000256518 | − | 0.000619290i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.75878 | + | 0.728511i | −0.122839 | + | 0.0508814i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.654971 | 0.0453053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.76173 | − | 16.3243i | −0.465497 | − | 1.12381i | −0.966108 | − | 0.258137i | \(-0.916891\pi\) |
0.500612 | − | 0.865672i | \(-0.333109\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.96019 | + | 1.96019i | −0.133684 | + | 0.133684i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.49096 | + | 2.49096i | 0.169097 | + | 0.169097i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.43118 | − | 3.90652i | 0.634410 | − | 0.262781i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 15.8618i | − | 1.06219i | −0.847313 | − | 0.531093i | \(-0.821781\pi\) | ||
0.847313 | − | 0.531093i | \(-0.178219\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.50806 | + | 6.05500i | 0.166466 | + | 0.401884i | 0.984995 | − | 0.172580i | \(-0.0552104\pi\) |
−0.818530 | + | 0.574464i | \(0.805210\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.60466 | − | 3.14995i | −0.502530 | − | 0.208155i | 0.116994 | − | 0.993133i | \(-0.462674\pi\) |
−0.619524 | + | 0.784978i | \(0.712674\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.99464 | − | 5.99464i | −0.392722 | − | 0.392722i | 0.482935 | − | 0.875656i | \(-0.339571\pi\) |
−0.875656 | + | 0.482935i | \(0.839571\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.69532 | − | 1.11644i | −0.175824 | − | 0.0728285i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.11236i | 0.0719527i | 0.999353 | + | 0.0359763i | \(0.0114541\pi\) | ||||
−0.999353 | + | 0.0359763i | \(0.988546\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.709331i | 0.0456920i | 0.999739 | + | 0.0228460i | \(0.00727274\pi\) | ||||
−0.999739 | + | 0.0228460i | \(0.992727\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.45090 | − | 0.600982i | −0.0926946 | − | 0.0383953i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.29727 | − | 1.29727i | −0.0825432 | − | 0.0825432i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.3657 | − | 4.29361i | −0.654276 | − | 0.271010i | 0.0307514 | − | 0.999527i | \(-0.490210\pi\) |
−0.685028 | + | 0.728517i | \(0.740210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.19279 | − | 7.70808i | −0.200729 | − | 0.484603i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 29.1264i | − | 1.81686i | −0.418042 | − | 0.908428i | \(-0.637284\pi\) | ||
0.418042 | − | 0.908428i | \(-0.362716\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.50708 | + | 2.28111i | −0.342194 | + | 0.141741i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.87052 | + | 1.87052i | 0.115341 | + | 0.115341i | 0.762422 | − | 0.647080i | \(-0.224010\pi\) |
−0.647080 | + | 0.762422i | \(0.724010\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.74390 | − | 1.74390i | 0.107127 | − | 0.107127i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.63828 | − | 3.95517i | −0.0998879 | − | 0.241151i | 0.866034 | − | 0.499986i | \(-0.166661\pi\) |
−0.965922 | + | 0.258835i | \(0.916661\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.865193 | −0.0525567 | −0.0262784 | − | 0.999655i | \(-0.508366\pi\) | ||||
−0.0262784 | + | 0.999655i | \(0.508366\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.01993 | + | 2.49354i | −0.363016 | + | 0.150366i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.8442 | + | 26.1801i | −0.651563 | + | 1.57301i | 0.158948 | + | 0.987287i | \(0.449190\pi\) |
−0.810510 | + | 0.585724i | \(0.800810\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.20552 | − | 3.20552i | 0.191225 | − | 0.191225i | −0.605000 | − | 0.796225i | \(-0.706827\pi\) |
0.796225 | + | 0.605000i | \(0.206827\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.808604 | − | 1.95214i | 0.0480665 | − | 0.116043i | −0.898023 | − | 0.439949i | \(-0.854996\pi\) |
0.946089 | + | 0.323907i | \(0.104996\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.60311 | −0.389769 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.37639 | −0.551552 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.84084 | − | 6.85839i | 0.165964 | − | 0.400671i | −0.818916 | − | 0.573914i | \(-0.805424\pi\) |
0.984879 | + | 0.173242i | \(0.0554244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.181022 | − | 0.181022i | 0.0105395 | − | 0.0105395i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.94320 | + | 21.5908i | −0.517199 | + | 1.24863i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.88344 | + | 3.67964i | −0.512033 | + | 0.212091i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.95463 | 0.111922 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.75328 | − | 13.8897i | −0.328357 | − | 0.792724i | −0.998715 | − | 0.0506860i | \(-0.983859\pi\) |
0.670357 | − | 0.742038i | \(-0.266141\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.92757 | − | 9.92757i | 0.562941 | − | 0.562941i | −0.367201 | − | 0.930142i | \(-0.619684\pi\) |
0.930142 | + | 0.367201i | \(0.119684\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.07029 | − | 6.07029i | −0.343113 | − | 0.343113i | 0.514423 | − | 0.857536i | \(-0.328006\pi\) |
−0.857536 | + | 0.514423i | \(0.828006\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.8754 | − | 11.9606i | 1.62180 | − | 0.671773i | 0.627525 | − | 0.778596i | \(-0.284068\pi\) |
0.994278 | + | 0.106823i | \(0.0340678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.0144343i | − | 0.000808168i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.524318 | − | 1.26581i | −0.0291738 | − | 0.0704318i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.8622 | + | 6.98455i | 0.935346 | + | 0.387433i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.15538 | − | 7.15538i | −0.394489 | − | 0.394489i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.5735 | − | 5.62233i | −0.746067 | − | 0.309031i | −0.0229312 | − | 0.999737i | \(-0.507300\pi\) |
−0.723136 | + | 0.690706i | \(0.757300\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.01737i | 0.110221i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.22397i | 0.393515i | 0.980452 | + | 0.196757i | \(0.0630411\pi\) | ||||
−0.980452 | + | 0.196757i | \(0.936959\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.91889 | + | 2.03747i | 0.266373 | + | 0.110335i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.17451 | − | 8.17451i | −0.441382 | − | 0.441382i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.78836 | − | 2.81183i | −0.364418 | − | 0.150947i | 0.192958 | − | 0.981207i | \(-0.438192\pi\) |
−0.557376 | + | 0.830260i | \(0.688192\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0989263 | + | 0.238829i | 0.00529540 | + | 0.0127842i | 0.926505 | − | 0.376282i | \(-0.122798\pi\) |
−0.921210 | + | 0.389066i | \(0.872798\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 1.04908i | − | 0.0558369i | −0.999610 | − | 0.0279184i | \(-0.991112\pi\) | ||
0.999610 | − | 0.0279184i | \(-0.00888787\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.397691 | + | 0.164729i | −0.0211072 | + | 0.00874290i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.9586 | − | 10.9586i | −0.578375 | − | 0.578375i | 0.356080 | − | 0.934455i | \(-0.384113\pi\) |
−0.934455 | + | 0.356080i | \(0.884113\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.2609 | − | 13.2609i | 0.697943 | − | 0.697943i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.509456 | + | 1.22994i | 0.0266662 | + | 0.0643778i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.0919 | 0.735589 | 0.367795 | − | 0.929907i | \(-0.380113\pi\) | ||||
0.367795 | + | 0.929907i | \(0.380113\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.90323 | − | 3.27363i | 0.410315 | − | 0.169958i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.973904 | − | 2.35121i | 0.0504268 | − | 0.121741i | −0.896659 | − | 0.442723i | \(-0.854013\pi\) |
0.947086 | + | 0.320981i | \(0.104013\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.0285894 | + | 0.0285894i | −0.00147243 | + | 0.00147243i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.22577 | + | 17.4446i | −0.371163 | + | 0.896067i | 0.622391 | + | 0.782707i | \(0.286161\pi\) |
−0.993554 | + | 0.113360i | \(0.963839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.91841 | 0.251319 | 0.125660 | − | 0.992073i | \(-0.459895\pi\) | ||||
0.125660 | + | 0.992073i | \(0.459895\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.290236 | 0.0147918 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.57039 | + | 15.8623i | −0.333132 | + | 0.804252i | 0.665208 | + | 0.746658i | \(0.268343\pi\) |
−0.998340 | + | 0.0575939i | \(0.981657\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.3409 | + | 12.3409i | −0.624108 | + | 0.624108i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.695683 | + | 1.67953i | −0.0350036 | + | 0.0845062i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.49381 | − | 0.618757i | 0.0749723 | − | 0.0310545i | −0.344882 | − | 0.938646i | \(-0.612081\pi\) |
0.419854 | + | 0.907591i | \(0.362081\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.8271 | −1.48949 | −0.744747 | − | 0.667347i | \(-0.767430\pi\) | ||||
−0.744747 | + | 0.667347i | \(0.767430\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.70708 | − | 13.7781i | −0.284290 | − | 0.686336i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.37033 | + | 6.37033i | −0.315765 | + | 0.315765i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.09883 | + | 9.09883i | 0.449908 | + | 0.449908i | 0.895324 | − | 0.445416i | \(-0.146944\pi\) |
−0.445416 | + | 0.895324i | \(0.646944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.820377 | − | 0.339811i | 0.0403681 | − | 0.0167210i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.07873i | 0.151129i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.94681 | + | 9.52845i | 0.192814 | + | 0.465495i | 0.990489 | − | 0.137593i | \(-0.0439366\pi\) |
−0.797674 | + | 0.603088i | \(0.793937\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.91334 | + | 1.20674i | 0.141987 | + | 0.0588131i | 0.452546 | − | 0.891741i | \(-0.350516\pi\) |
−0.310558 | + | 0.950554i | \(0.600516\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.63815 | + | 9.63815i | 0.467519 | + | 0.467519i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.26371 | + | 2.59451i | 0.303122 | + | 0.125557i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 23.1792i | − | 1.11650i | −0.829672 | − | 0.558252i | \(-0.811472\pi\) | ||
0.829672 | − | 0.558252i | \(-0.188528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.2987i | − | 1.21578i | −0.794023 | − | 0.607888i | \(-0.792017\pi\) | ||
0.794023 | − | 0.607888i | \(-0.207983\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.89783 | + | 1.20032i | 0.138622 | + | 0.0574191i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.3833 | + | 28.3833i | 1.35466 | + | 1.35466i | 0.880365 | + | 0.474297i | \(0.157298\pi\) |
0.474297 | + | 0.880365i | \(0.342702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.8722 | + | 8.23132i | 0.944155 | + | 0.391082i | 0.801031 | − | 0.598623i | \(-0.204285\pi\) |
0.143124 | + | 0.989705i | \(0.454285\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.504444 | − | 1.21784i | −0.0239130 | − | 0.0577310i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12.5843i | 0.593889i | 0.954895 | + | 0.296944i | \(0.0959676\pi\) | ||||
−0.954895 | + | 0.296944i | \(0.904032\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.22007 | + | 3.81908i | −0.434156 | + | 0.179833i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.574855 | − | 0.574855i | −0.0269496 | − | 0.0269496i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.93449 | − | 8.93449i | 0.417938 | − | 0.417938i | −0.466554 | − | 0.884492i | \(-0.654505\pi\) |
0.884492 | + | 0.466554i | \(0.154505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9213 | + | 31.1949i | 0.601807 | + | 1.45289i | 0.871720 | + | 0.490005i | \(0.163005\pi\) |
−0.269913 | + | 0.962885i | \(0.586995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.78637 | 0.0830196 | 0.0415098 | − | 0.999138i | \(-0.486783\pi\) | ||||
0.0415098 | + | 0.999138i | \(0.486783\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −37.9374 | + | 15.7142i | −1.75553 | + | 0.727166i | −0.758376 | + | 0.651818i | \(0.774007\pi\) |
−0.997157 | + | 0.0753479i | \(0.975993\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.67779 | + | 6.46476i | −0.123649 | + | 0.298515i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.2759 | + | 10.2759i | −0.472488 | + | 0.472488i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.937438 | − | 2.26318i | 0.0430126 | − | 0.103842i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.3196 | 1.38534 | 0.692669 | − | 0.721256i | \(-0.256435\pi\) | ||||
0.692669 | + | 0.721256i | \(0.256435\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.2348 | 1.15061 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.35142 | − | 3.26260i | 0.0613646 | − | 0.148147i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2907 | − | 23.2907i | 1.05540 | − | 1.05540i | 0.0570287 | − | 0.998373i | \(-0.481837\pi\) |
0.998373 | − | 0.0570287i | \(-0.0181627\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.68275 | + | 11.3052i | −0.211330 | + | 0.510195i | −0.993628 | − | 0.112709i | \(-0.964047\pi\) |
0.782298 | + | 0.622904i | \(0.214047\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0278962 | + | 0.0115550i | −0.00125638 | + | 0.000520410i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.49308 | −0.0669736 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.69892 | + | 21.0011i | 0.389417 | + | 0.940136i | 0.990063 | + | 0.140621i | \(0.0449100\pi\) |
−0.600646 | + | 0.799515i | \(0.705090\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.4548 | − | 27.4548i | 1.22415 | − | 1.22415i | 0.258004 | − | 0.966144i | \(-0.416935\pi\) |
0.966144 | − | 0.258004i | \(-0.0830649\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.98531 | − | 1.98531i | −0.0883451 | − | 0.0883451i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.5641 | + | 6.86109i | −0.734193 | + | 0.304113i | −0.718274 | − | 0.695761i | \(-0.755067\pi\) |
−0.0159191 | + | 0.999873i | \(0.505067\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.61763i | 0.204272i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.13681 | − | 2.74451i | −0.0500939 | − | 0.120937i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.1297 | − | 5.85272i | −0.621424 | − | 0.257402i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.2903 | − | 24.2903i | −1.06418 | − | 1.06418i | −0.997794 | − | 0.0663854i | \(-0.978853\pi\) |
−0.0663854 | − | 0.997794i | \(-0.521147\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.09598 | − | 1.28240i | −0.135378 | − | 0.0560753i | 0.313966 | − | 0.949434i | \(-0.398342\pi\) |
−0.449344 | + | 0.893359i | \(0.648342\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 11.1374i | − | 0.485153i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 16.9545i | − | 0.737153i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.8260 | + | 10.6975i | 1.11865 | + | 0.463359i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.597711 | + | 0.597711i | 0.0258413 | + | 0.0258413i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.60606 | − | 3.15053i | −0.327616 | − | 0.135703i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.7340 | + | 30.7426i | 0.547477 | + | 1.32173i | 0.919349 | + | 0.393443i | \(0.128716\pi\) |
−0.371872 | + | 0.928284i | \(0.621284\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.18208i | 0.0934701i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.08569 | + | 0.449709i | −0.0464209 | + | 0.0192282i | −0.405773 | − | 0.913974i | \(-0.632998\pi\) |
0.359352 | + | 0.933202i | \(0.382998\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.00383715 | + | 0.00383715i | 0.000163468 | + | 0.000163468i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.45871 | + | 4.45871i | −0.189604 | + | 0.189604i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.36569 | + | 22.6108i | 0.396837 | + | 0.958049i | 0.988411 | + | 0.151799i | \(0.0485066\pi\) |
−0.591574 | + | 0.806250i | \(0.701493\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.7060 | 1.72168 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.1131 | − | 10.4022i | 1.05839 | − | 0.438400i | 0.215511 | − | 0.976501i | \(-0.430858\pi\) |
0.842880 | + | 0.538101i | \(0.180858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.493438 | + | 1.19126i | −0.0207591 | + | 0.0501169i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.7622 | + | 21.7622i | −0.912319 | + | 0.912319i | −0.996454 | − | 0.0841358i | \(-0.973187\pi\) |
0.0841358 | + | 0.996454i | \(0.473187\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.7421 | − | 30.7622i | 0.533241 | − | 1.28736i | −0.396124 | − | 0.918197i | \(-0.629645\pi\) |
0.929365 | − | 0.369161i | \(-0.120355\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.2041 | −1.30130 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.17163 | 0.381820 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.08661 | + | 9.86595i | −0.169541 | + | 0.409308i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.14208 | − | 9.14208i | 0.378626 | − | 0.378626i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.6350 | + | 25.6751i | −0.438953 | + | 1.05973i | 0.537359 | + | 0.843354i | \(0.319422\pi\) |
−0.976311 | + | 0.216371i | \(0.930578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.84924 | + | 0.765981i | −0.0761966 | + | 0.0315617i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.8973 | 0.447497 | 0.223748 | − | 0.974647i | \(-0.428171\pi\) | ||||
0.223748 | + | 0.974647i | \(0.428171\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.232339 | − | 0.560917i | −0.00952498 | − | 0.0229953i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.15470 | + | 7.15470i | −0.292333 | + | 0.292333i | −0.838001 | − | 0.545668i | \(-0.816276\pi\) |
0.545668 | + | 0.838001i | \(0.316276\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.0354 | − | 16.0354i | −0.654098 | − | 0.654098i | 0.299879 | − | 0.953977i | \(-0.403054\pi\) |
−0.953977 | + | 0.299879i | \(0.903054\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.15352 | + | 0.892017i | −0.0875530 | + | 0.0362657i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.1378i | 1.06090i | 0.847716 | + | 0.530450i | \(0.177977\pi\) | ||||
−0.847716 | + | 0.530450i | \(0.822023\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.3938 | + | 39.5782i | 0.663223 | + | 1.60116i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.264513 | − | 0.109565i | −0.0106836 | − | 0.00442529i | 0.377335 | − | 0.926077i | \(-0.376840\pi\) |
−0.388019 | + | 0.921651i | \(0.626840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.11322 | − | 9.11322i | −0.366884 | − | 0.366884i | 0.499455 | − | 0.866340i | \(-0.333533\pi\) |
−0.866340 | + | 0.499455i | \(0.833533\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.31772 | + | 1.78846i | 0.173544 | + | 0.0718842i | 0.467764 | − | 0.883854i | \(-0.345060\pi\) |
−0.294220 | + | 0.955738i | \(0.595060\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 4.57221i | − | 0.183182i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0531i | 0.962124i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.4110 | + | 7.21189i | 0.694223 | + | 0.287557i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.3839 | + | 24.3839i | 0.970707 | + | 0.970707i | 0.999583 | − | 0.0288764i | \(-0.00919293\pi\) |
−0.0288764 | + | 0.999583i | \(0.509193\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.92738 | + | 0.798346i | 0.0764856 | + | 0.0316814i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.82483 | + | 21.3050i | 0.349653 | + | 0.844136i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.45729i | 0.334043i | 0.985953 | + | 0.167022i | \(0.0534149\pi\) | ||||
−0.985953 | + | 0.167022i | \(0.946585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.7117 | − | 14.3781i | 1.36890 | − | 0.567015i | 0.427407 | − | 0.904059i | \(-0.359427\pi\) |
0.941489 | + | 0.337044i | \(0.109427\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.4083 | + | 26.4083i | 1.03822 | + | 1.03822i | 0.999240 | + | 0.0389780i | \(0.0124102\pi\) |
0.0389780 | + | 0.999240i | \(0.487590\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.948973 | − | 0.948973i | 0.0372504 | − | 0.0372504i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.3223 | − | 27.3345i | −0.443076 | − | 1.06968i | −0.974864 | − | 0.222802i | \(-0.928480\pi\) |
0.531788 | − | 0.846878i | \(-0.321520\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.14669 | 0.201098 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −35.5774 | + | 14.7366i | −1.38590 | + | 0.574058i | −0.946052 | − | 0.324015i | \(-0.894967\pi\) |
−0.439847 | + | 0.898073i | \(0.644967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.9242 | − | 28.7874i | 0.463796 | − | 1.11970i | −0.503031 | − | 0.864268i | \(-0.667782\pi\) |
0.966827 | − | 0.255434i | \(-0.0822182\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0771547 | + | 0.0771547i | −0.00299193 | + | 0.00299193i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0264528 | − | 0.0638627i | 0.00102426 | − | 0.00247278i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.2468 | 0.395572 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.89312 | 0.188616 | 0.0943080 | − | 0.995543i | \(-0.469936\pi\) | ||||
0.0943080 | + | 0.995543i | \(0.469936\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.36496 | + | 8.12372i | −0.129326 | + | 0.312220i | −0.975258 | − | 0.221071i | \(-0.929045\pi\) |
0.845932 | + | 0.533291i | \(0.179045\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.66136 | − | 8.66136i | 0.332392 | − | 0.332392i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.0545 | − | 31.5165i | 0.499518 | − | 1.20594i | −0.450225 | − | 0.892915i | \(-0.648656\pi\) |
0.949744 | − | 0.313029i | \(-0.101344\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.40696 | + | 1.82542i | −0.168381 | + | 0.0697459i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.2145 | −1.37966 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.7784 | + | 33.2640i | 0.524155 | + | 1.26542i | 0.935301 | + | 0.353853i | \(0.115129\pi\) |
−0.411146 | + | 0.911569i | \(0.634871\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.48710 | + | 3.48710i | −0.132273 | + | 0.132273i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.7617 | + | 14.7617i | 0.559139 | + | 0.559139i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9772 | + | 8.27483i | −0.754529 | + | 0.312536i | −0.726588 | − | 0.687073i | \(-0.758895\pi\) |
−0.0279411 | + | 0.999610i | \(0.508895\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.38691i | − | 0.127740i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.72679 | − | 8.99726i | −0.140160 | − | 0.338377i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.4355 | + | 6.80779i | 0.617246 | + | 0.255672i | 0.669323 | − | 0.742971i | \(-0.266584\pi\) |
−0.0520769 | + | 0.998643i | \(0.516584\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.0290 | + | 18.0290i | 0.675191 | + | 0.675191i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.13516 | − | 0.470201i | −0.0424528 | − | 0.0175845i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 13.9143i | 0.518917i | 0.965754 | + | 0.259458i | \(0.0835440\pi\) | ||||
−0.965754 | + | 0.259458i | \(0.916456\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 10.3039i | − | 0.383736i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.0498762 | − | 0.0206594i | −0.00185235 | − | 0.000767270i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.4548 | − | 21.4548i | −0.795713 | − | 0.795713i | 0.186703 | − | 0.982416i | \(-0.440220\pi\) |
−0.982416 | + | 0.186703i | \(0.940220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.0856 | + | 11.6334i | 1.03878 | + | 0.430279i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.82805 | − | 16.4844i | −0.252200 | − | 0.608864i | 0.746181 | − | 0.665743i | \(-0.231885\pi\) |
−0.998381 | + | 0.0568787i | \(0.981885\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.5757i | 0.389559i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.45405 | + | 2.67336i | −0.237416 | + | 0.0983410i | −0.498219 | − | 0.867051i | \(-0.666013\pi\) |
0.260803 | + | 0.965392i | \(0.416013\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.5864 | − | 15.5864i | −0.571811 | − | 0.571811i | 0.360823 | − | 0.932634i | \(-0.382496\pi\) |
−0.932634 | + | 0.360823i | \(0.882496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.71597 | − | 2.71597i | 0.0995053 | − | 0.0995053i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.12201 | + | 2.70878i | 0.0409975 | + | 0.0989767i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.0270 | −1.53359 | −0.766793 | − | 0.641894i | \(-0.778149\pi\) | ||||
−0.766793 | + | 0.641894i | \(0.778149\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.28708 | − | 0.533128i | 0.0468418 | − | 0.0194025i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.05779 | + | 17.0390i | −0.256520 | + | 0.619294i | −0.998704 | − | 0.0509027i | \(-0.983790\pi\) |
0.742184 | + | 0.670196i | \(0.233790\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.7062 | − | 26.7062i | 0.968098 | − | 0.968098i | −0.0314086 | − | 0.999507i | \(-0.509999\pi\) |
0.999507 | + | 0.0314086i | \(0.00999931\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.89643 | + | 6.99260i | −0.104858 | + | 0.253149i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.75916 | −0.135735 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.3834 | 1.60051 | 0.800253 | − | 0.599662i | \(-0.204698\pi\) | ||||
0.800253 | + | 0.599662i | \(0.204698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.1152 | − | 34.0770i | 0.507687 | − | 1.22566i | −0.437525 | − | 0.899206i | \(-0.644145\pi\) |
0.945212 | − | 0.326458i | \(-0.105855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.0805 | − | 14.0805i | 0.505785 | − | 0.505785i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.43577 | − | 3.46626i | 0.0514418 | − | 0.124191i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.08482 | + | 0.863560i | −0.0746006 | + | 0.0309006i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.86056 | 0.173481 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.82978 | − | 14.0743i | −0.207809 | − | 0.501696i | 0.785269 | − | 0.619155i | \(-0.212525\pi\) |
−0.993078 | + | 0.117460i | \(0.962525\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.16250 | + | 3.16250i | −0.112445 | + | 0.112445i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.2953 | − | 20.2953i | −0.720705 | − | 0.720705i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.7102 | − | 7.33581i | 0.627328 | − | 0.259848i | −0.0462892 | − | 0.998928i | \(-0.514740\pi\) |
0.673617 | + | 0.739080i | \(0.264740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.9927i | 1.13182i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.67073 | + | 6.44770i | 0.0942479 | + | 0.227535i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.28411 | + | 0.531894i | 0.0452588 | + | 0.0187468i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.6456 | − | 15.6456i | −0.550069 | − | 0.550069i | 0.376391 | − | 0.926461i | \(-0.377165\pi\) |
−0.926461 | + | 0.376391i | \(0.877165\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.2382 | − | 18.3241i | −1.55341 | − | 0.643445i | −0.569484 | − | 0.822003i | \(-0.692857\pi\) |
−0.983929 | + | 0.178558i | \(0.942857\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 4.89488i | − | 0.171460i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5.46340i | − | 0.191140i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.06690 | + | 3.75563i | 0.316437 | + | 0.131072i | 0.535248 | − | 0.844695i | \(-0.320218\pi\) |
−0.218812 | + | 0.975767i | \(0.570218\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.6440 | − | 21.6440i | −0.754461 | − | 0.754461i | 0.220847 | − | 0.975308i | \(-0.429118\pi\) |
−0.975308 | + | 0.220847i | \(0.929118\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.2211 | − | 15.8317i | −1.32908 | − | 0.550522i | −0.398685 | − | 0.917088i | \(-0.630533\pi\) |
−0.930392 | + | 0.366566i | \(0.880533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.2172 | + | 34.3234i | 0.493784 | + | 1.19210i | 0.952780 | + | 0.303661i | \(0.0982091\pi\) |
−0.458996 | + | 0.888438i | \(0.651791\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17.2217i | 0.596698i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.58527 | − | 1.89928i | 0.158680 | − | 0.0657273i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.0743 | + | 25.0743i | 0.865660 | + | 0.865660i | 0.991988 | − | 0.126329i | \(-0.0403194\pi\) |
−0.126329 | + | 0.991988i | \(0.540319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5060 | + | 20.5060i | −0.707104 | + | 0.707104i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.0644717 | + | 0.155648i | 0.00221789 | + | 0.00535447i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.08510 | −0.277807 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −39.8591 | + | 16.5102i | −1.36635 | + | 0.565961i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.6749 | − | 47.4993i | 0.673655 | − | 1.62635i | −0.101696 | − | 0.994816i | \(-0.532427\pi\) |
0.775351 | − | 0.631531i | \(-0.217573\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0148 | − | 21.0148i | 0.717851 | − | 0.717851i | −0.250314 | − | 0.968165i | \(-0.580534\pi\) |
0.968165 | + | 0.250314i | \(0.0805339\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.592319 | + | 1.42998i | −0.0202097 | + | 0.0487905i | −0.933662 | − | 0.358155i | \(-0.883406\pi\) |
0.913453 | + | 0.406945i | \(0.133406\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.0354 | −1.56706 | −0.783531 | − | 0.621352i | \(-0.786584\pi\) | ||||
−0.783531 | + | 0.621352i | \(0.786584\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.700443 | 0.0238158 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.64699 | + | 8.80461i | −0.123716 | + | 0.298676i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.9467 | − | 20.9467i | 0.709750 | − | 0.709750i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.836143 | − | 2.01863i | 0.0282668 | − | 0.0682421i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.47725 | − | 2.26875i | 0.184954 | − | 0.0766103i | −0.288285 | − | 0.957545i | \(-0.593085\pi\) |
0.473238 | + | 0.880934i | \(0.343085\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.4957 | 0.926355 | 0.463178 | − | 0.886265i | \(-0.346709\pi\) | ||||
0.463178 | + | 0.886265i | \(0.346709\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.6048 | + | 25.6023i | 0.356880 | + | 0.861585i | 0.995735 | + | 0.0922578i | \(0.0294084\pi\) |
−0.638855 | + | 0.769327i | \(0.720592\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.2715 | − | 10.2715i | 0.344883 | − | 0.344883i | −0.513316 | − | 0.858199i | \(-0.671583\pi\) |
0.858199 | + | 0.513316i | \(0.171583\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.11668 | + | 5.11668i | 0.171608 | + | 0.171608i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.31202 | − | 2.20031i | 0.177760 | − | 0.0736306i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.92252i | 0.131115i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.0168808 | + | 0.0407538i | 0.000563006 | + | 0.00135922i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.9866 | − | 10.3498i | −0.832425 | − | 0.344802i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.19319 | − | 1.19319i | −0.0396628 | − | 0.0396628i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.7977 | − | 16.4847i | −1.32146 | − | 0.547367i | −0.393253 | − | 0.919430i | \(-0.628650\pi\) |
−0.928207 | + | 0.372064i | \(0.878650\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12.4103i | − | 0.411171i | −0.978639 | − | 0.205585i | \(-0.934090\pi\) | ||
0.978639 | − | 0.205585i | \(-0.0659098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.1396i | 0.534144i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.4928 | + | 6.83156i | 0.544641 | + | 0.225598i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.07058 | + | 1.07058i | 0.0353151 | + | 0.0353151i | 0.724544 | − | 0.689229i | \(-0.242050\pi\) |
−0.689229 | + | 0.724544i | \(0.742050\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.83970 | + | 2.41888i | 0.192216 | + | 0.0796185i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.8943 | + | 31.1295i | 0.423961 | + | 1.02353i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 7.00180i | − | 0.229722i | −0.993382 | − | 0.114861i | \(-0.963358\pi\) | ||
0.993382 | − | 0.114861i | \(-0.0366422\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.85947 | − | 1.18443i | 0.0937155 | − | 0.0388182i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.648842 | − | 0.648842i | −0.0212194 | − | 0.0212194i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.5015 | + | 18.5015i | −0.604417 | + | 0.604417i | −0.941481 | − | 0.337065i | \(-0.890566\pi\) |
0.337065 | + | 0.941481i | \(0.390566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.8709 | − | 35.9014i | −0.484776 | − | 1.17035i | −0.957316 | − | 0.289044i | \(-0.906663\pi\) |
0.472540 | − | 0.881309i | \(-0.343337\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −47.7918 | −1.55632 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.6795 | − | 11.0510i | 0.866969 | − | 0.359110i | 0.0955398 | − | 0.995426i | \(-0.469542\pi\) |
0.771429 | + | 0.636315i | \(0.219542\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.48086 | − | 18.0604i | 0.242839 | − | 0.586265i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.5517 | − | 12.5517i | 0.406591 | − | 0.406591i | −0.473957 | − | 0.880548i | \(-0.657175\pi\) |
0.880548 | + | 0.473957i | \(0.157175\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.44933 | + | 3.49900i | −0.0468993 | + | 0.113225i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.5454 | −0.534277 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.7293 | 0.475137 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.89369 | − | 4.57178i | 0.0609601 | − | 0.147171i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.7248 | + | 33.7248i | −1.08452 | + | 1.08452i | −0.0884351 | + | 0.996082i | \(0.528187\pi\) |
−0.996082 | + | 0.0884351i | \(0.971813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.5211 | − | 44.7139i | 0.594371 | − | 1.43494i | −0.284873 | − | 0.958565i | \(-0.591951\pi\) |
0.879243 | − | 0.476373i | \(-0.158049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.8033 | + | 6.54593i | −0.506629 | + | 0.209853i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.3998 | 1.29250 | 0.646252 | − | 0.763124i | \(-0.276336\pi\) | ||||
0.646252 | + | 0.763124i | \(0.276336\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.64445 | − | 6.38428i | −0.0845171 | − | 0.204042i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.1712 | + | 39.1712i | −1.24937 | + | 1.24937i | −0.293369 | + | 0.955999i | \(0.594776\pi\) |
−0.955999 | + | 0.293369i | \(0.905224\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.52919 | + | 1.52919i | 0.0487240 | + | 0.0487240i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −64.2964 | + | 26.6325i | −2.04451 | + | 0.846863i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 16.6218i | − | 0.528007i | −0.964522 | − | 0.264004i | \(-0.914957\pi\) | ||
0.964522 | − | 0.264004i | \(-0.0850431\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.99454 | − | 4.81524i | −0.0632311 | − | 0.152653i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9978 | − | 7.45495i | −0.569997 | − | 0.236101i | 0.0790217 | − | 0.996873i | \(-0.474820\pi\) |
−0.649019 | + | 0.760772i | \(0.724820\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1152.2.w.a.143.5 | 32 | ||
3.2 | odd | 2 | 1152.2.w.b.143.4 | 32 | |||
4.3 | odd | 2 | 288.2.w.b.251.2 | yes | 32 | ||
12.11 | even | 2 | 288.2.w.a.251.7 | yes | 32 | ||
32.13 | even | 8 | 288.2.w.a.179.7 | ✓ | 32 | ||
32.19 | odd | 8 | 1152.2.w.b.1007.4 | 32 | |||
96.77 | odd | 8 | 288.2.w.b.179.2 | yes | 32 | ||
96.83 | even | 8 | inner | 1152.2.w.a.1007.5 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.179.7 | ✓ | 32 | 32.13 | even | 8 | ||
288.2.w.a.251.7 | yes | 32 | 12.11 | even | 2 | ||
288.2.w.b.179.2 | yes | 32 | 96.77 | odd | 8 | ||
288.2.w.b.251.2 | yes | 32 | 4.3 | odd | 2 | ||
1152.2.w.a.143.5 | 32 | 1.1 | even | 1 | trivial | ||
1152.2.w.a.1007.5 | 32 | 96.83 | even | 8 | inner | ||
1152.2.w.b.143.4 | 32 | 3.2 | odd | 2 | |||
1152.2.w.b.1007.4 | 32 | 32.19 | odd | 8 |