Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,3,Mod(65,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 13]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.65");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.bc (of order \(18\), degree \(6\), 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: | \(11.7711474204\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 27) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 353.3 | ||
Character | \(\chi\) | \(=\) | 432.353 |
Dual form | 432.3.bc.a.257.3 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{18}\right)\) |
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 | ||||||||
\(3\) | −1.10490 | − | 2.78912i | −0.368300 | − | 0.929707i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.46013 | − | 4.12362i | −0.692026 | − | 0.824724i | 0.299574 | − | 0.954073i | \(-0.403156\pi\) |
−0.991599 | + | 0.129349i | \(0.958711\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.89907 | + | 3.60297i | −1.41415 | + | 0.514709i | −0.932346 | − | 0.361568i | \(-0.882241\pi\) |
−0.481807 | + | 0.876278i | \(0.660019\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.55839 | + | 6.16340i | −0.728710 | + | 0.684822i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.54888 | − | 8.99640i | 0.686262 | − | 0.817855i | −0.304636 | − | 0.952469i | \(-0.598535\pi\) |
0.990898 | + | 0.134614i | \(0.0429794\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.95057 | + | 11.0622i | 0.150044 | + | 0.850940i | 0.963178 | + | 0.268864i | \(0.0866482\pi\) |
−0.813134 | + | 0.582076i | \(0.802241\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.67818 | + | 14.2069i | −0.511879 | + | 0.947127i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.73630 | − | 1.57980i | 0.160959 | − | 0.0929296i | −0.417357 | − | 0.908743i | \(-0.637044\pi\) |
0.578316 | + | 0.815813i | \(0.303710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.26051 | + | 3.91532i | −0.118974 | + | 0.206069i | −0.919361 | − | 0.393414i | \(-0.871294\pi\) |
0.800387 | + | 0.599483i | \(0.204627\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 20.9866 | + | 23.6288i | 0.999361 | + | 1.12518i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.80880 | + | 18.7070i | −0.296035 | + | 0.813349i | 0.699118 | + | 0.715007i | \(0.253576\pi\) |
−0.995153 | + | 0.0983427i | \(0.968646\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.690550 | + | 3.91630i | −0.0276220 | + | 0.156652i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 24.4368 | + | 11.4822i | 0.905068 | + | 0.425267i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 24.9744 | + | 4.40366i | 0.861187 | + | 0.151851i | 0.586763 | − | 0.809758i | \(-0.300402\pi\) |
0.274424 | + | 0.961609i | \(0.411513\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.7874 | + | 7.56598i | 0.670560 | + | 0.244064i | 0.654789 | − | 0.755812i | \(-0.272757\pi\) |
0.0157712 | + | 0.999876i | \(0.494980\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −33.4328 | − | 11.1146i | −1.01312 | − | 0.336807i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 49.1093 | + | 28.3533i | 1.40312 | + | 0.810093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.82807 | − | 15.2907i | −0.238596 | − | 0.413261i | 0.721715 | − | 0.692190i | \(-0.243354\pi\) |
−0.960312 | + | 0.278929i | \(0.910021\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 28.6987 | − | 17.6630i | 0.735864 | − | 0.452898i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.2557 | + | 2.16101i | −0.298920 | + | 0.0527076i | −0.321096 | − | 0.947046i | \(-0.604051\pi\) |
0.0221770 | + | 0.999754i | \(0.492940\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −27.9211 | − | 23.4286i | −0.649329 | − | 0.544851i | 0.257539 | − | 0.966268i | \(-0.417089\pi\) |
−0.906867 | + | 0.421417i | \(0.861533\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 48.1084 | + | 5.71818i | 1.06908 | + | 0.127071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.24091 | + | 11.6518i | 0.0902320 | + | 0.247910i | 0.976597 | − | 0.215076i | \(-0.0690000\pi\) |
−0.886365 | + | 0.462987i | \(0.846778\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 47.4740 | − | 39.8354i | 0.968857 | − | 0.812967i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.42960 | − | 5.88634i | −0.145678 | − | 0.115419i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 84.6210i | 1.59662i | 0.602245 | + | 0.798311i | \(0.294273\pi\) | ||||
−0.602245 | + | 0.798311i | \(0.705727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −63.2178 | −1.14942 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.4179 | + | 1.97880i | 0.235402 | + | 0.0347158i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 43.8854 | + | 52.3006i | 0.743820 | + | 0.886451i | 0.996711 | − | 0.0810443i | \(-0.0258255\pi\) |
−0.252890 | + | 0.967495i | \(0.581381\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −73.3637 | + | 26.7022i | −1.20268 | + | 0.437741i | −0.864160 | − | 0.503217i | \(-0.832150\pi\) |
−0.338523 | + | 0.940958i | \(0.609927\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 42.7155 | − | 84.6415i | 0.678023 | − | 1.34352i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 38.8672 | − | 46.3201i | 0.597956 | − | 0.712617i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 16.8654 | + | 95.6483i | 0.251722 | + | 1.42759i | 0.804349 | + | 0.594157i | \(0.202514\pi\) |
−0.552627 | + | 0.833429i | \(0.686375\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 59.6992 | − | 1.67882i | 0.865206 | − | 0.0243307i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −105.364 | + | 60.8322i | −1.48401 | + | 0.856791i | −0.999835 | − | 0.0181820i | \(-0.994212\pi\) |
−0.484171 | + | 0.874973i | \(0.660879\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −45.5705 | + | 78.9304i | −0.624254 | + | 1.08124i | 0.364431 | + | 0.931230i | \(0.381263\pi\) |
−0.988685 | + | 0.150009i | \(0.952070\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.6860 | − | 2.40109i | 0.155814 | − | 0.0320146i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −42.3131 | + | 116.254i | −0.549521 | + | 1.50980i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.54032 | − | 20.0781i | 0.0448142 | − | 0.254154i | −0.954167 | − | 0.299273i | \(-0.903256\pi\) |
0.998982 | + | 0.0451196i | \(0.0143669\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.02506 | − | 80.8440i | 0.0620378 | − | 0.998074i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −31.1219 | − | 5.48763i | −0.374963 | − | 0.0661161i | −0.0170090 | − | 0.999855i | \(-0.505414\pi\) |
−0.357954 | + | 0.933739i | \(0.616526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.9824 | − | 5.81713i | −0.188029 | − | 0.0684369i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −15.3119 | − | 74.5223i | −0.175999 | − | 0.856578i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 59.7756 | + | 34.5114i | 0.671636 | + | 0.387769i | 0.796696 | − | 0.604380i | \(-0.206579\pi\) |
−0.125060 | + | 0.992149i | \(0.539912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −59.1656 | − | 102.478i | −0.650171 | − | 1.12613i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.86551 | − | 66.3381i | −0.0200592 | − | 0.713313i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 23.9669 | − | 4.22602i | 0.252283 | − | 0.0444844i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −61.1335 | − | 51.2971i | −0.630243 | − | 0.528836i | 0.270762 | − | 0.962646i | \(-0.412724\pi\) |
−0.901004 | + | 0.433810i | \(0.857169\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.93989 | + | 105.529i | 0.0599989 | + | 1.06595i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.63372 | − | 4.48862i | −0.0161755 | − | 0.0444417i | 0.931342 | − | 0.364145i | \(-0.118639\pi\) |
−0.947518 | + | 0.319704i | \(0.896417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 55.3795 | − | 46.4689i | 0.537665 | − | 0.451154i | −0.333074 | − | 0.942901i | \(-0.608086\pi\) |
0.870738 | + | 0.491746i | \(0.163641\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 24.8199 | − | 168.299i | 0.236380 | − | 1.60285i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 158.133i | − | 1.47788i | −0.673773 | − | 0.738938i | \(-0.735328\pi\) | ||
0.673773 | − | 0.738938i | \(-0.264672\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.5788 | −0.170448 | −0.0852240 | − | 0.996362i | \(-0.527161\pi\) | ||||
−0.0852240 | + | 0.996362i | \(0.527161\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −32.8934 | + | 41.5172i | −0.296337 | + | 0.374029i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.5806 | − | 13.8012i | −0.102483 | − | 0.122134i | 0.712365 | − | 0.701809i | \(-0.247624\pi\) |
−0.814848 | + | 0.579675i | \(0.803180\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 100.700 | − | 36.6518i | 0.875652 | − | 0.318711i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −80.9734 | − | 60.5283i | −0.692081 | − | 0.517336i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −21.3948 | + | 25.4974i | −0.179788 | + | 0.214264i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.93828 | − | 16.6638i | −0.0242833 | − | 0.137717i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.5686 | + | 31.7949i | 0.159095 | + | 0.258495i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −98.0067 | + | 56.5842i | −0.784054 | + | 0.452674i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −78.1067 | + | 135.285i | −0.615013 | + | 1.06523i | 0.375369 | + | 0.926876i | \(0.377516\pi\) |
−0.990382 | + | 0.138359i | \(0.955817\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −34.4952 | + | 103.762i | −0.267405 | + | 0.804354i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −33.6955 | + | 92.5776i | −0.257217 | + | 0.706699i | 0.742119 | + | 0.670268i | \(0.233821\pi\) |
−0.999336 | + | 0.0364307i | \(0.988401\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.27018 | − | 46.9025i | 0.0621818 | − | 0.352651i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −37.2062 | − | 140.498i | −0.275602 | − | 1.04073i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −64.6590 | − | 11.4011i | −0.471963 | − | 0.0832199i | −0.0673925 | − | 0.997727i | \(-0.521468\pi\) |
−0.404571 | + | 0.914507i | \(0.632579\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −117.744 | − | 42.8553i | −0.847080 | − | 0.308312i | −0.118231 | − | 0.992986i | \(-0.537722\pi\) |
−0.728849 | + | 0.684674i | \(0.759944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 27.8125 | − | 24.7025i | 0.197252 | − | 0.175195i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 114.245 | + | 65.9593i | 0.798915 | + | 0.461254i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −68.2557 | − | 118.222i | −0.470729 | − | 0.815326i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −163.560 | − | 88.3966i | −1.11265 | − | 0.601337i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 198.691 | − | 35.0346i | 1.33350 | − | 0.235132i | 0.538953 | − | 0.842336i | \(-0.318820\pi\) |
0.794546 | + | 0.607204i | \(0.207709\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −98.1613 | − | 82.3671i | −0.650075 | − | 0.545478i | 0.257019 | − | 0.966406i | \(-0.417260\pi\) |
−0.907094 | + | 0.420929i | \(0.861704\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.20877 | + | 27.2259i | −0.0536521 | + | 0.177947i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −40.7277 | − | 111.898i | −0.262759 | − | 0.721926i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −106.439 | + | 89.3129i | −0.677955 | + | 0.568872i | −0.915408 | − | 0.402527i | \(-0.868132\pi\) |
0.237453 | + | 0.971399i | \(0.423687\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 236.018 | − | 93.4977i | 1.48439 | − | 0.588036i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 209.714i | − | 1.30257i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −39.8569 | −0.244521 | −0.122261 | − | 0.992498i | \(-0.539014\pi\) | ||||
−0.122261 | + | 0.992498i | \(0.539014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 69.8494 | + | 176.322i | 0.423329 | + | 1.06862i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 106.672 | + | 127.127i | 0.638757 | + | 0.761241i | 0.984173 | − | 0.177208i | \(-0.0567067\pi\) |
−0.345416 | + | 0.938450i | \(0.612262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 40.2401 | − | 14.6462i | 0.238107 | − | 0.0866639i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.30634 | − | 39.6106i | −0.0544231 | − | 0.231641i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.00006 | + | 8.34234i | −0.0404628 | + | 0.0482216i | −0.785896 | − | 0.618358i | \(-0.787798\pi\) |
0.745434 | + | 0.666580i | \(0.232243\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.27451 | − | 41.2558i | −0.0415686 | − | 0.235747i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 97.3837 | − | 180.189i | 0.550191 | − | 1.01801i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 244.720 | − | 141.289i | 1.36715 | − | 0.789326i | 0.376590 | − | 0.926380i | \(-0.377097\pi\) |
0.990564 | + | 0.137054i | \(0.0437633\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 54.3996 | − | 94.2228i | 0.300550 | − | 0.520568i | −0.675711 | − | 0.737167i | \(-0.736163\pi\) |
0.976261 | + | 0.216599i | \(0.0694964\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 155.535 | + | 175.117i | 0.849919 | + | 0.956923i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −32.5066 | + | 89.3112i | −0.175711 | + | 0.482763i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.44344 | − | 36.5426i | 0.0344569 | − | 0.195415i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −283.272 | − | 25.6182i | −1.49879 | − | 0.135546i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −106.979 | − | 18.8633i | −0.560100 | − | 0.0987607i | −0.113571 | − | 0.993530i | \(-0.536229\pi\) |
−0.446529 | + | 0.894769i | \(0.647340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −188.040 | − | 68.4410i | −0.974301 | − | 0.354617i | −0.194679 | − | 0.980867i | \(-0.562367\pi\) |
−0.779622 | + | 0.626250i | \(0.784589\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −172.137 | − | 57.2262i | −0.882752 | − | 0.293468i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 253.494 | + | 146.355i | 1.28677 | + | 0.742918i | 0.978077 | − | 0.208243i | \(-0.0667746\pi\) |
0.308694 | + | 0.951161i | \(0.400108\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −41.1548 | − | 71.2822i | −0.206808 | − | 0.358202i | 0.743899 | − | 0.668292i | \(-0.232974\pi\) |
−0.950707 | + | 0.310090i | \(0.899641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 248.140 | − | 152.721i | 1.23453 | − | 0.759807i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −263.090 | + | 46.3898i | −1.29601 | + | 0.228521i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 51.3175 | + | 43.0605i | 0.250329 | + | 0.210051i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −70.6441 | − | 164.653i | −0.341276 | − | 0.795427i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.1595 | + | 49.8927i | 0.0868874 | + | 0.238721i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −88.7425 | + | 74.4638i | −0.420581 | + | 0.352909i | −0.828384 | − | 0.560161i | \(-0.810739\pi\) |
0.407803 | + | 0.913070i | \(0.366295\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 286.085 | + | 226.661i | 1.34312 | + | 1.06413i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 196.202i | 0.912568i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −233.036 | −1.07390 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 270.497 | + | 39.8915i | 1.23515 | + | 0.182153i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.8135 | + | 27.1880i | 0.103228 | + | 0.123023i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −186.281 | + | 67.8007i | −0.835341 | + | 0.304039i | −0.724049 | − | 0.689749i | \(-0.757721\pi\) |
−0.111292 | + | 0.993788i | \(0.535499\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.6088 | − | 29.9408i | −0.0871504 | − | 0.133070i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.31155 | − | 3.94655i | 0.0145883 | − | 0.0173857i | −0.758701 | − | 0.651439i | \(-0.774166\pi\) |
0.773289 | + | 0.634053i | \(0.218610\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 61.3581 | + | 347.979i | 0.267939 | + | 1.51956i | 0.760533 | + | 0.649299i | \(0.224938\pi\) |
−0.492594 | + | 0.870259i | \(0.663951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 370.999 | − | 10.4330i | 1.60606 | − | 0.0451643i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 121.729 | − | 70.2803i | 0.522442 | − | 0.301632i | −0.215491 | − | 0.976506i | \(-0.569135\pi\) |
0.737933 | + | 0.674874i | \(0.235802\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 33.3735 | − | 57.8046i | 0.142015 | − | 0.245977i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −59.9121 | + | 12.3100i | −0.252794 | + | 0.0519407i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 50.5074 | − | 138.768i | 0.211328 | − | 0.580619i | −0.788060 | − | 0.615598i | \(-0.788914\pi\) |
0.999388 | + | 0.0349794i | \(0.0111366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 52.8609 | − | 299.789i | 0.219340 | − | 1.24394i | −0.653875 | − | 0.756602i | \(-0.726858\pi\) |
0.873215 | − | 0.487335i | \(-0.162031\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −231.036 | + | 75.3090i | −0.950765 | + | 0.309913i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −328.532 | − | 57.9291i | −1.34095 | − | 0.236445i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −47.7214 | − | 17.3692i | −0.193204 | − | 0.0703205i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.0809 | + | 92.8661i | 0.0766302 | + | 0.372956i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 108.072 | + | 62.3955i | 0.430567 | + | 0.248588i | 0.699588 | − | 0.714546i | \(-0.253367\pi\) |
−0.269021 | + | 0.963134i | \(0.586700\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 116.897 | + | 202.472i | 0.462044 | + | 0.800284i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.43430 | + | 51.0043i | 0.00562472 | + | 0.200017i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −450.088 | + | 79.3627i | −1.75132 | + | 0.308804i | −0.955116 | − | 0.296231i | \(-0.904270\pi\) |
−0.796199 | + | 0.605035i | \(0.793159\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 142.481 | + | 119.556i | 0.550121 | + | 0.461606i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −190.934 | + | 125.046i | −0.731547 | + | 0.479105i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 160.047 | + | 439.726i | 0.608545 | + | 1.67196i | 0.733408 | + | 0.679789i | \(0.237929\pi\) |
−0.124863 | + | 0.992174i | \(0.539849\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 348.945 | − | 292.799i | 1.31677 | − | 1.10490i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.2106 | − | 204.853i | 0.113148 | − | 0.767240i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 317.049i | − | 1.17862i | −0.807907 | − | 0.589310i | \(-0.799399\pi\) | ||
0.807907 | − | 0.589310i | \(-0.200601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −115.698 | −0.426931 | −0.213465 | − | 0.976951i | \(-0.568475\pi\) | ||||
−0.213465 | + | 0.976951i | \(0.568475\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −220.451 | + | 278.248i | −0.807513 | + | 1.01922i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.0198 | + | 35.7762i | 0.109163 | + | 0.130095i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 108.352 | − | 39.4370i | 0.391163 | − | 0.142372i | −0.138949 | − | 0.990300i | \(-0.544372\pi\) |
0.530112 | + | 0.847928i | \(0.322150\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −182.964 | + | 78.5001i | −0.655785 | + | 0.281362i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −52.4463 | + | 62.5031i | −0.186642 | + | 0.222431i | −0.851249 | − | 0.524762i | \(-0.824154\pi\) |
0.664607 | + | 0.747193i | \(0.268599\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 72.4355 | + | 410.802i | 0.255956 | + | 1.45160i | 0.793608 | + | 0.608430i | \(0.208200\pi\) |
−0.537652 | + | 0.843167i | \(0.680689\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −38.2679 | − | 62.1773i | −0.134273 | − | 0.218166i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 113.534 | − | 65.5489i | 0.395589 | − | 0.228393i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −139.508 | + | 241.636i | −0.482728 | + | 0.836110i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −75.5275 | + | 227.187i | −0.259545 | + | 0.780712i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −118.282 | + | 324.977i | −0.403693 | + | 1.10914i | 0.556755 | + | 0.830676i | \(0.312046\pi\) |
−0.960448 | + | 0.278460i | \(0.910176\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 63.8186 | − | 361.933i | 0.216334 | − | 1.22689i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 287.769 | − | 133.166i | 0.968920 | − | 0.448369i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −220.222 | − | 38.8311i | −0.736529 | − | 0.129870i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 360.806 | + | 131.323i | 1.19869 | + | 0.436287i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.7142 | + | 9.51612i | −0.0353604 | + | 0.0314063i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 363.957 | + | 210.131i | 1.19330 | + | 0.688954i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 288.668 | + | 499.988i | 0.940286 | + | 1.62862i | 0.764925 | + | 0.644120i | \(0.222776\pi\) |
0.175362 | + | 0.984504i | \(0.443890\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −190.796 | − | 103.117i | −0.617463 | − | 0.333711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −442.280 | + | 77.9859i | −1.42212 | + | 0.250759i | −0.831202 | − | 0.555971i | \(-0.812347\pi\) |
−0.590921 | + | 0.806730i | \(0.701235\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.30206 | + | 6.96625i | 0.0265241 | + | 0.0222564i | 0.655953 | − | 0.754801i | \(-0.272267\pi\) |
−0.629429 | + | 0.777058i | \(0.716711\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −496.830 | + | 116.728i | −1.57724 | + | 0.370566i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −74.6402 | − | 205.072i | −0.235458 | − | 0.646916i | −0.999997 | − | 0.00233841i | \(-0.999256\pi\) |
0.764539 | − | 0.644577i | \(-0.222967\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 228.146 | − | 191.437i | 0.715191 | − | 0.600117i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −441.051 | + | 174.721i | −1.37399 | + | 0.544302i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.2846i | 0.0442249i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −44.6700 | −0.137446 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.5277 | + | 51.8186i | 0.0627760 | + | 0.158467i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −83.9620 | − | 100.062i | −0.255204 | − | 0.304140i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 564.453 | − | 205.444i | 1.70530 | − | 0.620677i | 0.708885 | − | 0.705324i | \(-0.249198\pi\) |
0.996411 | + | 0.0846470i | \(0.0269763\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 152.140 | + | 45.8713i | 0.456878 | + | 0.137752i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 336.061 | − | 400.502i | 1.00317 | − | 1.19553i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 78.0147 | + | 442.443i | 0.231498 | + | 1.31289i | 0.849865 | + | 0.527000i | \(0.176683\pi\) |
−0.618368 | + | 0.785889i | \(0.712206\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.6978 | + | 47.5485i | −0.0758047 | + | 0.140261i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 224.988 | − | 129.897i | 0.659789 | − | 0.380929i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −68.3305 | + | 118.352i | −0.199214 | + | 0.345049i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −213.490 | − | 240.368i | −0.618811 | − | 0.696719i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 80.7717 | − | 221.918i | 0.232771 | − | 0.639534i | −0.767227 | − | 0.641376i | \(-0.778364\pi\) |
0.999998 | + | 0.00184170i | \(0.000586231\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 41.6381 | − | 236.141i | 0.119307 | − | 0.676622i | −0.865221 | − | 0.501391i | \(-0.832822\pi\) |
0.984527 | − | 0.175231i | \(-0.0560672\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −79.3531 | + | 292.722i | −0.226077 | + | 0.833967i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.2020 | + | 4.44379i | 0.0713937 | + | 0.0125886i | 0.209231 | − | 0.977866i | \(-0.432904\pi\) |
−0.137837 | + | 0.990455i | \(0.544015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 615.423 | + | 223.996i | 1.73359 | + | 0.630974i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 94.7544 | + | 31.5007i | 0.265418 | + | 0.0882374i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.7796 | − | 9.68773i | −0.0467399 | − | 0.0269853i | 0.476448 | − | 0.879203i | \(-0.341924\pi\) |
−0.523188 | + | 0.852217i | \(0.675257\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 170.280 | + | 294.934i | 0.471690 | + | 0.816992i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −43.2308 | + | 26.6070i | −0.119093 | + | 0.0732976i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 483.159 | − | 85.1939i | 1.32372 | − | 0.233408i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −299.305 | − | 251.147i | −0.815545 | − | 0.684324i | 0.136379 | − | 0.990657i | \(-0.456453\pi\) |
−0.951924 | + | 0.306333i | \(0.900898\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 67.0585 | − | 89.7095i | 0.181730 | − | 0.243115i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −304.886 | − | 837.669i | −0.821796 | − | 2.25787i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −136.986 | + | 114.945i | −0.367255 | + | 0.308164i | −0.807675 | − | 0.589628i | \(-0.799274\pi\) |
0.440419 | + | 0.897792i | \(0.354830\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 266.108 | + | 210.833i | 0.709621 | + | 0.562221i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 284.862i | 0.755603i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.48118 | −0.00918518 | −0.00459259 | − | 0.999989i | \(-0.501462\pi\) | ||||
−0.00459259 | + | 0.999989i | \(0.501462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 463.626 | + | 68.3730i | 1.21687 | + | 0.179457i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.0730 | − | 13.1963i | −0.0289112 | − | 0.0344550i | 0.751395 | − | 0.659853i | \(-0.229381\pi\) |
−0.780306 | + | 0.625398i | \(0.784937\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 625.797 | − | 227.772i | 1.62545 | − | 0.591615i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 327.518 | − | 18.4350i | 0.846299 | − | 0.0476356i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 203.618 | − | 242.662i | 0.523439 | − | 0.623810i | −0.437952 | − | 0.898999i | \(-0.644296\pi\) |
0.961390 | + | 0.275189i | \(0.0887403\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.9225 | + | 61.9446i | 0.0279348 | + | 0.158426i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 295.440 | − | 8.30814i | 0.751756 | − | 0.0211403i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −95.0446 | + | 54.8740i | −0.240619 | + | 0.138922i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −134.041 | + | 232.165i | −0.337634 | + | 0.584800i | −0.983987 | − | 0.178239i | \(-0.942960\pi\) |
0.646353 | + | 0.763039i | \(0.276293\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −139.955 | + | 28.7560i | −0.350763 | + | 0.0720703i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.3356 | − | 91.5887i | 0.0831311 | − | 0.228401i | −0.891162 | − | 0.453685i | \(-0.850109\pi\) |
0.974293 | + | 0.225285i | \(0.0723312\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.1494 | + | 244.712i | −0.107070 | + | 0.607227i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −350.757 | + | 259.009i | −0.866067 | + | 0.639528i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −204.203 | − | 36.0065i | −0.501727 | − | 0.0884680i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 380.898 | + | 138.636i | 0.931292 | + | 0.338962i | 0.762721 | − | 0.646727i | \(-0.223863\pi\) |
0.168570 | + | 0.985690i | \(0.446085\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 39.6426 | + | 192.939i | 0.0964539 | + | 0.469437i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −622.862 | − | 359.609i | −1.50814 | − | 0.870725i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 85.0569 | + | 147.323i | 0.204956 | + | 0.354995i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.5666 | + | 375.753i | 0.0253397 | + | 0.901087i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −115.552 | + | 20.3750i | −0.275781 | + | 0.0486277i | −0.309828 | − | 0.950793i | \(-0.600272\pi\) |
0.0340470 | + | 0.999420i | \(0.489160\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −399.365 | − | 335.107i | −0.948610 | − | 0.795979i | 0.0304527 | − | 0.999536i | \(-0.490305\pi\) |
−0.979063 | + | 0.203558i | \(0.934750\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −99.6282 | − | 50.2787i | −0.235528 | − | 0.118862i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.29744 | + | 11.8071i | 0.0101116 | + | 0.0277814i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 630.025 | − | 528.654i | 1.47547 | − | 1.23806i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 57.7393 | − | 391.521i | 0.134591 | − | 0.912636i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 263.580i | 0.611555i | 0.952103 | + | 0.305777i | \(0.0989163\pi\) | ||||
−0.952103 | + | 0.305777i | \(0.901084\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −702.013 | −1.62128 | −0.810639 | − | 0.585547i | \(-0.800880\pi\) | ||||
−0.810639 | + | 0.585547i | \(0.800880\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −254.321 | + | 320.997i | −0.584645 | + | 0.737924i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −57.8526 | − | 68.9461i | −0.132386 | − | 0.157771i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −416.204 | + | 151.486i | −0.948073 | + | 0.345070i | −0.769349 | − | 0.638829i | \(-0.779419\pi\) |
−0.178724 | + | 0.983899i | \(0.557197\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −65.8317 | + | 553.857i | −0.149278 | + | 1.25591i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 390.071 | − | 464.868i | 0.880520 | − | 1.04936i | −0.117891 | − | 0.993026i | \(-0.537613\pi\) |
0.998412 | − | 0.0563369i | \(-0.0179421\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −64.5191 | − | 365.906i | −0.144987 | − | 0.822260i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −317.250 | − | 515.464i | −0.709731 | − | 1.15316i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 347.745 | − | 200.771i | 0.774488 | − | 0.447151i | −0.0599853 | − | 0.998199i | \(-0.519105\pi\) |
0.834473 | + | 0.551048i | \(0.185772\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −73.0755 | + | 126.570i | −0.162030 | + | 0.280644i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −121.274 | + | 364.791i | −0.267712 | + | 0.805279i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −217.859 | + | 598.563i | −0.478811 | + | 1.31552i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.5458 | + | 144.878i | −0.0558990 | + | 0.317019i | −0.999917 | − | 0.0128747i | \(-0.995902\pi\) |
0.944018 | + | 0.329894i | \(0.107013\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 85.0061 | − | 7.18658i | 0.185198 | − | 0.0156570i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −773.480 | − | 136.385i | −1.67783 | − | 0.295847i | −0.747963 | − | 0.663740i | \(-0.768968\pi\) |
−0.929868 | + | 0.367893i | \(0.880079\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −336.835 | − | 122.598i | −0.727506 | − | 0.264791i | −0.0483975 | − | 0.998828i | \(-0.515411\pi\) |
−0.679109 | + | 0.734037i | \(0.737634\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −267.098 | + | 237.231i | −0.574405 | + | 0.510174i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 88.2727 | + | 50.9643i | 0.189021 | + | 0.109131i | 0.591524 | − | 0.806287i | \(-0.298526\pi\) |
−0.402503 | + | 0.915419i | \(0.631860\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −511.569 | − | 886.063i | −1.09077 | − | 1.88926i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 366.709 | + | 198.189i | 0.778575 | + | 0.420784i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −421.547 | + | 74.3300i | −0.891219 | + | 0.157146i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.7726 | − | 11.5566i | −0.0289949 | − | 0.0243296i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −521.553 | − | 554.978i | −1.09340 | − | 1.16348i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −43.2210 | − | 118.749i | −0.0902318 | − | 0.247910i | 0.886365 | − | 0.462986i | \(-0.153222\pi\) |
−0.976597 | + | 0.215077i | \(0.931000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 151.929 | − | 127.483i | 0.315860 | − | 0.265038i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −584.918 | + | 231.713i | −1.21101 | + | 0.479737i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 429.586i | 0.885745i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −454.010 | −0.932258 | −0.466129 | − | 0.884717i | \(-0.654352\pi\) | ||||
−0.466129 | + | 0.884717i | \(0.654352\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 44.0379 | + | 111.166i | 0.0900571 | + | 0.227333i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −203.177 | − | 242.137i | −0.413803 | − | 0.493151i | 0.518374 | − | 0.855154i | \(-0.326537\pi\) |
−0.932177 | + | 0.362003i | \(0.882093\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 75.2944 | − | 27.4049i | 0.152727 | − | 0.0555881i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 414.607 | − | 389.637i | 0.837591 | − | 0.787145i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 823.833 | − | 981.806i | 1.65761 | − | 1.97547i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.2323 | − | 120.414i | −0.0425497 | − | 0.241312i | 0.956114 | − | 0.292996i | \(-0.0946522\pi\) |
−0.998663 | + | 0.0516842i | \(0.983541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 236.711 | − | 437.985i | 0.472477 | − | 0.874222i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 391.041 | − | 225.768i | 0.777418 | − | 0.448843i | −0.0580963 | − | 0.998311i | \(-0.518503\pi\) |
0.835515 | + | 0.549468i | \(0.185170\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.8565 | + | 22.2680i | −0.0254583 | + | 0.0440951i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −85.3113 | − | 96.0519i | −0.168267 | − | 0.189452i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −170.911 | + | 469.573i | −0.335778 | + | 0.922541i | 0.650800 | + | 0.759249i | \(0.274434\pi\) |
−0.986578 | + | 0.163292i | \(0.947789\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 166.722 | − | 945.527i | 0.326266 | − | 1.85035i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −100.196 | + | 69.7223i | −0.195314 | + | 0.135911i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −383.240 | − | 67.5756i | −0.744156 | − | 0.131215i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 136.838 | + | 49.8051i | 0.264678 | + | 0.0963348i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.0022 | + | 10.3066i | 0.0597344 | + | 0.0198585i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −595.632 | − | 343.888i | −1.14325 | − | 0.660054i | −0.196015 | − | 0.980601i | \(-0.562800\pi\) |
−0.947233 | + | 0.320546i | \(0.896133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −260.218 | − | 450.711i | −0.497549 | − | 0.861780i | 0.502447 | − | 0.864608i | \(-0.332433\pi\) |
−0.999996 | + | 0.00282784i | \(0.999100\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −107.030 | + | 65.8730i | −0.203866 | + | 0.125472i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 68.8332 | − | 12.1372i | 0.130613 | − | 0.0230306i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 101.644 | + | 85.2896i | 0.192144 | + | 0.161228i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −610.167 | − | 72.5247i | −1.14909 | − | 0.136581i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −47.8111 | − | 131.360i | −0.0897020 | − | 0.246454i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −652.079 | + | 547.160i | −1.21884 | + | 1.02273i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −664.465 | − | 526.444i | −1.23736 | − | 0.980343i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 727.808i | − | 1.35029i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 803.120 | 1.48451 | 0.742255 | − | 0.670117i | \(-0.233756\pi\) | ||||
0.742255 | + | 0.670117i | \(0.233756\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −322.905 | − | 47.6203i | −0.594668 | − | 0.0876984i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 64.2851 | + | 76.6120i | 0.117954 | + | 0.140572i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −64.5461 | + | 23.4929i | −0.118000 | + | 0.0429486i | −0.400345 | − | 0.916364i | \(-0.631110\pi\) |
0.282345 | + | 0.959313i | \(0.408888\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 316.572 | − | 627.293i | 0.576633 | − | 1.14261i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −73.6967 | + | 87.8283i | −0.133751 | + | 0.159398i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 37.2950 | + | 211.511i | 0.0674412 | + | 0.382478i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 285.016 | − | 8.01501i | 0.513543 | − | 0.0144415i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 575.120 | − | 332.045i | 1.03253 | − | 0.596132i | 0.114822 | − | 0.993386i | \(-0.463370\pi\) |
0.917709 | + | 0.397254i | \(0.130037\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 204.710 | − | 354.569i | 0.366208 | − | 0.634291i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −109.041 | + | 22.4043i | −0.194369 | + | 0.0399364i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 118.905 | − | 326.689i | 0.211199 | − | 0.580264i | −0.788182 | − | 0.615442i | \(-0.788978\pi\) |
0.999381 | + | 0.0351778i | \(0.0111997\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.8406 | + | 95.5076i | −0.0298063 | + | 0.169040i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 241.535 | + | 818.385i | 0.425987 | + | 1.44336i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −385.078 | − | 67.8997i | −0.676763 | − | 0.119332i | −0.175306 | − | 0.984514i | \(-0.556091\pi\) |
−0.501457 | + | 0.865182i | \(0.667203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 804.118 | + | 292.675i | 1.40826 | + | 0.512566i | 0.930620 | − | 0.365988i | \(-0.119269\pi\) |
0.477644 | + | 0.878554i | \(0.341491\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 65.5891 | + | 319.219i | 0.114466 | + | 0.557102i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −68.5606 | − | 39.5835i | −0.119236 | − | 0.0688408i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 313.746 | + | 543.423i | 0.543753 | + | 0.941808i | 0.998684 | + | 0.0512815i | \(0.0163306\pi\) |
−0.454931 | + | 0.890527i | \(0.650336\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 16.8752 | + | 600.087i | 0.0291454 | + | 1.03642i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 327.850 | − | 57.8088i | 0.564285 | − | 0.0994987i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 761.285 | + | 638.794i | 1.30581 | + | 1.09570i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 30.5829 | + | 543.339i | 0.0522785 | + | 0.928785i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 254.654 | + | 699.655i | 0.433822 | + | 1.19192i | 0.943448 | + | 0.331520i | \(0.107561\pi\) |
−0.509626 | + | 0.860396i | \(0.670216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −76.6133 | + | 64.2862i | −0.130073 | + | 0.109145i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 128.116 | − | 868.733i | 0.216778 | − | 1.46994i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 625.722i | 1.05518i | 0.849499 | + | 0.527591i | \(0.176904\pi\) | ||||
−0.849499 | + | 0.527591i | \(0.823096\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 179.170 | 0.301126 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −153.343 | + | 193.546i | −0.256856 | + | 0.324197i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 368.344 | + | 438.975i | 0.614932 | + | 0.732847i | 0.980190 | − | 0.198059i | \(-0.0634638\pi\) |
−0.365258 | + | 0.930906i | \(0.619019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1063.24 | + | 386.989i | −1.76912 | + | 0.643908i | −0.769134 | + | 0.639088i | \(0.779312\pi\) |
−0.999988 | + | 0.00482034i | \(0.998466\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −700.128 | − | 523.351i | −1.16107 | − | 0.867912i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −58.5483 | + | 69.7752i | −0.0967741 | + | 0.115331i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.3687 | + | 228.942i | 0.0665052 | + | 0.377170i | 0.999835 | + | 0.0181503i | \(0.00577772\pi\) |
−0.933330 | + | 0.359019i | \(0.883111\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 420.075 | + | 682.533i | 0.689778 | + | 1.12074i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −120.623 | + | 69.6414i | −0.197418 | + | 0.113979i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 533.889 | − | 924.724i | 0.870945 | − | 1.50852i | 0.00992514 | − | 0.999951i | \(-0.496841\pi\) |
0.861020 | − | 0.508571i | \(-0.169826\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 63.4002 | − | 190.708i | 0.103090 | − | 0.310095i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 144.247 | − | 396.317i | 0.233788 | − | 0.642328i | −0.766212 | − | 0.642588i | \(-0.777861\pi\) |
1.00000 | 0.000260046i | \(8.27751e-5\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −104.335 | + | 591.711i | −0.168554 | + | 0.955915i | 0.776771 | + | 0.629783i | \(0.216856\pi\) |
−0.945324 | + | 0.326131i | \(0.894255\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −381.184 | + | 378.960i | −0.613823 | + | 0.610242i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −716.066 | − | 126.262i | −1.14938 | − | 0.202667i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 665.870 | + | 242.357i | 1.06539 | + | 0.387771i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 119.092 | − | 105.775i | 0.189940 | − | 0.168701i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −48.3124 | − | 27.8932i | −0.0768083 | − | 0.0443453i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −554.621 | − | 960.632i | −0.878956 | − | 1.52240i | −0.852488 | − | 0.522747i | \(-0.824907\pi\) |
−0.0264679 | − | 0.999650i | \(-0.508426\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 305.740 | + | 165.239i | 0.483002 | + | 0.261040i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 828.122 | − | 146.020i | 1.30413 | − | 0.229953i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 533.269 | + | 447.466i | 0.837157 | + | 0.702458i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 316.089 | − | 1048.36i | 0.494661 | − | 1.64063i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −56.5257 | − | 155.303i | −0.0881837 | − | 0.242283i | 0.887760 | − | 0.460308i | \(-0.152261\pi\) |
−0.975943 | + | 0.218025i | \(0.930039\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −608.717 | + | 510.774i | −0.946683 | + | 0.794361i | −0.978736 | − | 0.205125i | \(-0.934240\pi\) |
0.0320527 | + | 0.999486i | \(0.489796\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 547.231 | − | 216.784i | 0.848421 | − | 0.336099i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 222.504i | − | 0.343900i | −0.985106 | − | 0.171950i | \(-0.944993\pi\) | ||
0.985106 | − | 0.171950i | \(-0.0550068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 801.803 | 1.23544 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 257.481 | + | 649.964i | 0.395516 | + | 0.998409i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −299.851 | − | 357.348i | −0.459190 | − | 0.547241i | 0.485916 | − | 0.874006i | \(-0.338486\pi\) |
−0.945106 | + | 0.326764i | \(0.894042\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 498.345 | − | 181.383i | 0.760833 | − | 0.276920i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −187.610 | − | 798.526i | −0.285556 | − | 1.21541i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 133.876 | − | 159.547i | 0.203150 | − | 0.242104i | −0.654845 | − | 0.755764i | \(-0.727266\pi\) |
0.857994 | + | 0.513659i | \(0.171710\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −110.055 | − | 624.153i | −0.166498 | − | 0.944256i | −0.947507 | − | 0.319736i | \(-0.896406\pi\) |
0.781009 | − | 0.624520i | \(-0.214705\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 50.6241 | − | 93.6695i | 0.0763561 | − | 0.141281i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −222.024 | + | 128.186i | −0.333871 | + | 0.192760i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −252.425 | + | 437.214i | −0.378449 | + | 0.655493i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 394.926 | + | 444.647i | 0.590323 | + | 0.664645i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −313.590 | + | 861.581i | −0.467347 | + | 1.28403i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.1049 | − | 108.349i | 0.0283877 | − | 0.160994i | −0.967319 | − | 0.253564i | \(-0.918397\pi\) |
0.995706 | + | 0.0925699i | \(0.0295082\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −61.8427 | + | 87.7730i | −0.0916188 | + | 0.130034i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −140.866 | − | 24.8384i | −0.208073 | − | 0.0366890i | 0.0686398 | − | 0.997642i | \(-0.478134\pi\) |
−0.276713 | + | 0.960953i | \(0.589245\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 789.987 | + | 287.532i | 1.16346 | + | 0.423463i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.6663 | − | 4.87577i | −0.0215365 | − | 0.00715972i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −784.050 | − | 452.671i | −1.14795 | − | 0.662769i | −0.199563 | − | 0.979885i | \(-0.563952\pi\) |
−0.948387 | + | 0.317116i | \(0.897286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 176.714 | + | 306.078i | 0.257977 | + | 0.446830i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 902.761 | − | 555.617i | 1.31406 | − | 0.808758i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −936.096 | + | 165.059i | −1.35863 | + | 0.239563i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −407.543 | − | 341.969i | −0.589788 | − | 0.494891i | 0.298357 | − | 0.954454i | \(-0.403561\pi\) |
−0.888145 | + | 0.459564i | \(0.848006\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −439.016 | − | 1023.23i | −0.633500 | − | 1.47653i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 230.690 | + | 633.817i | 0.331929 | + | 0.911967i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.1213 | + | 25.2748i | −0.0432156 | + | 0.0362622i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −330.519 | − | 261.864i | −0.472845 | − | 0.374627i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 905.026i | − | 1.29105i | −0.763739 | − | 0.645525i | \(-0.776639\pi\) | ||
0.763739 | − | 0.645525i | \(-0.223361\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 79.8237 | 0.113547 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −198.098 | − | 29.2144i | −0.280991 | − | 0.0414389i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 32.3447 | + | 38.5469i | 0.0457492 | + | 0.0545217i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 341.922 | − | 124.450i | 0.482260 | − | 0.175528i | −0.0894380 | − | 0.995992i | \(-0.528507\pi\) |
0.571698 | + | 0.820464i | \(0.306285\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 100.531 | + | 153.501i | 0.141393 | + | 0.215894i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −283.074 | + | 337.355i | −0.397019 | + | 0.473148i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −123.311 | − | 699.329i | −0.172462 | − | 0.978083i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −442.846 | + | 12.4534i | −0.617638 | + | 0.0173687i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 389.328 | − | 224.778i | 0.541485 | − | 0.312626i | −0.204196 | − | 0.978930i | \(-0.565458\pi\) |
0.745680 | + | 0.666304i | \(0.232125\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −380.779 | + | 659.529i | −0.528127 | + | 0.914742i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −894.553 | + | 183.801i | −1.23728 | + | 0.254220i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −34.4922 | + | 94.7665i | −0.0475754 | + | 0.130712i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −100.606 | + | 570.564i | −0.138385 | + | 0.784820i | 0.834058 | + | 0.551677i | \(0.186012\pi\) |
−0.972443 | + | 0.233142i | \(0.925099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 465.317 | + | 561.178i | 0.638295 | + | 0.769792i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −113.413 | − | 19.9978i | −0.155148 | − | 0.0273568i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −879.854 | − | 320.241i | −1.20035 | − | 0.436891i | −0.337002 | − | 0.941504i | \(-0.609413\pi\) |
−0.863345 | + | 0.504613i | \(0.831635\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 201.424 | + | 980.321i | 0.274046 | + | 1.33377i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 987.805 | + | 570.310i | 1.34031 | + | 0.773826i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 263.918 | + | 457.119i | 0.357128 | + | 0.618564i | 0.987480 | − | 0.157746i | \(-0.0504227\pi\) |
−0.630352 | + | 0.776310i | \(0.717089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.28263 | + | 152.292i | 0.00577953 | + | 0.205522i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.2725 | − | 6.39582i | 0.0488190 | − | 0.00860811i | −0.149185 | − | 0.988809i | \(-0.547665\pi\) |
0.198004 | + | 0.980201i | \(0.436554\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −831.967 | − | 698.103i | −1.11673 | − | 0.937051i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 237.932 | − | 155.827i | 0.318517 | − | 0.208603i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 569.747 | + | 1565.37i | 0.760677 | + | 2.08994i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −75.4565 | + | 63.3155i | −0.100475 | + | 0.0843082i | −0.691641 | − | 0.722241i | \(-0.743112\pi\) |
0.591167 | + | 0.806550i | \(0.298668\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 54.6197 | − | 370.367i | 0.0725362 | − | 0.491856i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 689.781i | 0.913617i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1385.09 | −1.82971 | −0.914857 | − | 0.403779i | \(-0.867697\pi\) | ||||
−0.914857 | + | 0.403779i | \(0.867697\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 435.559 | − | 549.752i | 0.573859 | − | 0.724310i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 935.204 | + | 1114.53i | 1.22891 | + | 1.46456i | 0.839374 | + | 0.543555i | \(0.182922\pi\) |
0.389541 | + | 0.921009i | \(0.372634\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 183.913 | − | 66.9389i | 0.241039 | − | 0.0877312i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 140.672 | − | 60.3551i | 0.183886 | − | 0.0788956i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −492.959 | + | 587.486i | −0.642711 | + | 0.765953i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.3763 | − | 98.5458i | −0.0225959 | − | 0.128148i | 0.971423 | − | 0.237354i | \(-0.0762802\pi\) |
−0.994019 | + | 0.109206i | \(0.965169\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 718.654 | + | 1167.66i | 0.932106 | + | 1.51448i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −547.928 | + | 316.347i | −0.708834 | + | 0.409245i | −0.810629 | − | 0.585560i | \(-0.800875\pi\) |
0.101795 | + | 0.994805i | \(0.467541\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −43.9854 | + | 76.1850i | −0.0567554 | + | 0.0983032i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 176.029 | − | 529.495i | 0.226549 | − | 0.681461i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.2431 | − | 52.8699i | 0.0247023 | − | 0.0678690i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −248.112 | + | 1407.12i | −0.317686 | + | 1.80168i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 559.732 | + | 394.373i | 0.714856 | + | 0.503670i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 736.585 | + | 129.880i | 0.938325 | + | 0.165452i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −766.476 | − | 278.974i | −0.973921 | − | 0.354478i | −0.194447 | − | 0.980913i | \(-0.562291\pi\) |
−0.779474 | + | 0.626435i | \(0.784513\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1049.61 | − | 932.244i | 1.33031 | − | 1.18155i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 164.362 | + | 94.8944i | 0.207790 | + | 0.119968i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −438.486 | − | 759.481i | −0.552946 | − | 0.957731i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1202.20 | − | 649.735i | −1.51220 | − | 0.817277i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1233.67 | − | 217.529i | 1.54789 | − | 0.272934i | 0.666564 | − | 0.745448i | \(-0.267764\pi\) |
0.881323 | + | 0.472514i | \(0.156653\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.0119 | + | 25.1830i | 0.0375618 | + | 0.0315181i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −604.740 | + | 142.081i | −0.754981 | + | 0.177380i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 366.084 | + | 1005.81i | 0.455895 | + | 1.25256i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −864.781 | + | 725.637i | −1.07426 | + | 0.901413i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −884.288 | + | 350.307i | −1.09577 | + | 0.434086i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1021.88i | 1.26313i | 0.775321 | + | 0.631567i | \(0.217588\pi\) | ||||
−0.775321 | + | 0.631567i | \(0.782412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 365.788 | 0.451034 | 0.225517 | − | 0.974239i | \(-0.427593\pi\) | ||||
0.225517 | + | 0.974239i | \(0.427593\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 127.835 | + | 322.696i | 0.157239 | + | 0.396921i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 137.910 | + | 164.355i | 0.169215 | + | 0.201662i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 154.846 | − | 56.3595i | 0.189531 | − | 0.0689835i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1019.64 | + | 307.429i | 1.24498 | + | 0.375371i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.23245 | + | 7.42755i | −0.00759129 | + | 0.00904695i | −0.769827 | − | 0.638253i | \(-0.779657\pi\) |
0.762235 | + | 0.647300i | \(0.224102\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.155222 | − | 0.880308i | −0.000188605 | − | 0.00106963i | 0.984713 | − | 0.174183i | \(-0.0557284\pi\) |
−0.984902 | + | 0.173113i | \(0.944617\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 66.6153 | − | 123.258i | 0.0807458 | − | 0.149403i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 583.611 | − | 336.948i | 0.705696 | − | 0.407434i | −0.103769 | − | 0.994601i | \(-0.533090\pi\) |
0.809465 | + | 0.587168i | \(0.199757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.4804 | + | 25.0808i | −0.0174673 | + | 0.0302542i | −0.874627 | − | 0.484797i | \(-0.838894\pi\) |
0.857160 | + | 0.515051i | \(0.172227\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −229.713 | − | 258.633i | −0.276429 | − | 0.311231i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 66.9709 | − | 184.001i | 0.0803972 | − | 0.220890i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 155.124 | − | 879.753i | 0.185778 | − | 1.05360i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 421.103 | + | 423.574i | 0.503110 | + | 0.506062i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −629.012 | − | 110.912i | −0.749716 | − | 0.132195i | −0.214282 | − | 0.976772i | \(-0.568741\pi\) |
−0.535434 | + | 0.844577i | \(0.679852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −185.952 | − | 67.6809i | −0.221108 | − | 0.0804767i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 232.277 | + | 77.2195i | 0.275536 | + | 0.0916008i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −199.631 | − | 115.257i | −0.236250 | − | 0.136399i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 89.1253 | + | 154.370i | 0.105225 | + | 0.182254i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1065.74 | − | 655.926i | 1.25529 | − | 0.772587i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 346.151 | − | 61.0358i | 0.406758 | − | 0.0717225i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 595.279 | + | 499.498i | 0.697865 | + | 0.585578i | 0.921165 | − | 0.389171i | \(-0.127239\pi\) |
−0.223300 | + | 0.974750i | \(0.571683\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −131.138 | + | 175.434i | −0.153378 | + | 0.205185i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 368.296 | + | 1011.88i | 0.429750 | + | 1.18073i | 0.945965 | + | 0.324269i | \(0.105118\pi\) |
−0.516215 | + | 0.856459i | \(0.672659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 62.0374 | − | 52.0556i | 0.0722205 | − | 0.0606002i | −0.605963 | − | 0.795493i | \(-0.707212\pi\) |
0.678183 | + | 0.734893i | \(0.262768\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −308.267 | − | 244.235i | −0.358034 | − | 0.283664i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1599.17i | 1.85304i | 0.376244 | + | 0.926520i | \(0.377215\pi\) | ||||
−0.376244 | + | 0.926520i | \(0.622785\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 58.6217 | 0.0677708 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 828.094 | + | 122.123i | 0.955126 | + | 0.140857i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −153.906 | − | 183.418i | −0.177107 | − | 0.211067i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1025.19 | + | 373.137i | −1.17702 | + | 0.428400i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 717.103 | − | 40.3635i | 0.821423 | − | 0.0462354i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 766.304 | − | 913.245i | 0.875776 | − | 1.04371i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −65.7402 | − | 372.831i | −0.0749603 | − | 0.425121i | −0.999075 | − | 0.0430055i | \(-0.986307\pi\) |
0.924115 | − | 0.382116i | \(-0.124804\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1037.09 | − | 29.1642i | 1.17985 | − | 0.0331789i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1046.81 | + | 604.374i | −1.18820 | + | 0.686009i | −0.957898 | − | 0.287109i | \(-0.907306\pi\) |
−0.230305 | + | 0.973119i | \(0.573972\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −298.144 | + | 516.401i | −0.337649 | + | 0.584826i | −0.983990 | − | 0.178223i | \(-0.942965\pi\) |
0.646341 | + | 0.763049i | \(0.276298\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1079.99 | + | 221.902i | −1.22033 | + | 0.250737i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34.7360 | + | 95.4364i | −0.0391612 | + | 0.107595i | −0.957732 | − | 0.287662i | \(-0.907122\pi\) |
0.918571 | + | 0.395256i | \(0.129344\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 285.757 | − | 1620.61i | 0.321436 | − | 1.82296i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −689.371 | − | 655.489i | −0.773705 | − | 0.735678i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −55.2071 | − | 9.73450i | −0.0618220 | − | 0.0109009i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1429.39 | − | 520.255i | −1.59708 | − | 0.581290i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 135.019 | + | 657.131i | 0.150523 | + | 0.732588i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 485.835 | + | 280.497i | 0.540417 | + | 0.312010i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 133.684 | + | 231.548i | 0.148373 | + | 0.256990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −32.3796 | − | 1151.43i | −0.0358578 | − | 1.27511i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −576.769 | + | 101.700i | −0.637313 | + | 0.112376i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1321.91 | − | 1109.21i | −1.45745 | − | 1.22295i | −0.926906 | − | 0.375293i | \(-0.877542\pi\) |
−0.530547 | − | 0.847656i | \(-0.678013\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 38.3797 | + | 19.3688i | 0.0422219 | + | 0.0213078i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −106.953 | − | 293.850i | −0.117401 | − | 0.322558i | 0.867048 | − | 0.498224i | \(-0.166014\pi\) |
−0.984450 | + | 0.175666i | \(0.943792\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −284.305 | + | 238.560i | −0.311396 | + | 0.261292i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 183.944 | − | 1247.30i | 0.201032 | − | 1.36316i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1037.84i | − | 1.13177i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −198.504 | −0.216000 | −0.108000 | − | 0.994151i | \(-0.534445\pi\) | ||||
−0.108000 | + | 0.994151i | \(0.534445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1075.58 | − | 1357.57i | 1.16784 | − | 1.47401i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −878.459 | − | 1046.91i | −0.951743 | − | 1.13424i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 65.9791 | − | 24.0144i | 0.0713287 | − | 0.0259615i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −76.7941 | + | 646.087i | −0.0828416 | + | 0.696966i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 854.746 | − | 1018.65i | 0.920071 | − | 1.09650i | −0.0749849 | − | 0.997185i | \(-0.523891\pi\) |
0.995056 | − | 0.0993136i | \(-0.0316647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48.6528 | + | 275.924i | 0.0522587 | + | 0.296374i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 706.187 | + | 1147.41i | 0.756899 | + | 1.22980i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −172.983 | + | 99.8717i | −0.185008 | + | 0.106815i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −675.671 | + | 1170.30i | −0.721100 | + | 1.24898i | 0.239459 | + | 0.970906i | \(0.423030\pi\) |
−0.960559 | + | 0.278076i | \(0.910303\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.2568 | − | 30.8524i | 0.0109231 | − | 0.0328567i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 265.840 | − | 730.391i | 0.282508 | − | 0.776186i | −0.714553 | − | 0.699581i | \(-0.753370\pi\) |
0.997062 | − | 0.0766044i | \(-0.0244078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.0206 | − | 243.982i | 0.0456210 | − | 0.258729i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 874.517 | + | 1256.75i | 0.925415 | + | 1.32989i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 270.124 | + | 47.6301i | 0.285242 | + | 0.0502958i | 0.314438 | − | 0.949278i | \(-0.398184\pi\) |
−0.0291967 | + | 0.999574i | \(0.509295\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −962.034 | − | 350.152i | −1.01373 | − | 0.368969i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −489.501 | + | 434.765i | −0.514723 | + | 0.457166i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 858.313 | + | 495.548i | 0.900644 | + | 0.519987i | 0.877409 | − | 0.479743i | \(-0.159270\pi\) |
0.0232347 | + | 0.999730i | \(0.492603\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 292.376 | + | 506.410i | 0.306153 | + | 0.530272i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −786.020 | − | 424.808i | −0.821338 | − | 0.443896i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 681.141 | − | 120.104i | 0.710262 | − | 0.125238i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −361.298 | − | 303.165i | −0.375961 | − | 0.315468i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 974.635 | + | 1037.10i | 1.01208 | + | 1.07694i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 368.418 | + | 1012.22i | 0.381780 | + | 1.04893i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −239.352 | + | 200.840i | −0.247520 | + | 0.207694i | −0.758104 | − | 0.652134i | \(-0.773874\pi\) |
0.510583 | + | 0.859828i | \(0.329429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 39.8416 | − | 15.7831i | 0.0411162 | − | 0.0162880i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 487.838i | − | 0.502407i | −0.967934 | − | 0.251204i | \(-0.919174\pi\) | ||
0.967934 | − | 0.251204i | \(-0.0808264\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1319.96 | 1.35659 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 49.3558 | + | 124.590i | 0.0506214 | + | 0.127785i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −413.839 | − | 493.194i | −0.423582 | − | 0.504805i | 0.511478 | − | 0.859297i | \(-0.329098\pi\) |
−0.935059 | + | 0.354492i | \(0.884654\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 761.718 | − | 277.243i | 0.778057 | − | 0.283190i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 121.847 | − | 114.509i | 0.124207 | − | 0.116726i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 989.779 | − | 1179.57i | 1.00690 | − | 1.19997i | 0.0271699 | − | 0.999631i | \(-0.491350\pi\) |
0.979726 | − | 0.200341i | \(-0.0642051\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −273.610 | − | 1551.72i | −0.277777 | − | 1.57535i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −186.316 | + | 344.739i | −0.188770 | + | 0.349279i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 628.389 | − | 362.801i | 0.635378 | − | 0.366836i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 155.571 | − | 269.456i | 0.156984 | − | 0.271903i | −0.776796 | − | 0.629752i | \(-0.783156\pi\) |
0.933780 | + | 0.357849i | \(0.116490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1196.67 | − | 1347.33i | −1.20511 | − | 1.35683i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −151.540 | + | 416.352i | −0.152301 | + | 0.418445i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.37502 | + | 47.4971i | −0.00840022 | + | 0.0476400i | −0.988720 | − | 0.149777i | \(-0.952144\pi\) |
0.980320 | + | 0.197417i | \(0.0632554\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.1592 | − | 475.021i | −0.0401994 | − | 0.475496i |
(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 | 432.3.bc.a.353.3 | 30 | ||
4.3 | odd | 2 | 27.3.f.a.2.4 | ✓ | 30 | ||
12.11 | even | 2 | 81.3.f.a.8.2 | 30 | |||
27.14 | odd | 18 | inner | 432.3.bc.a.257.3 | 30 | ||
36.7 | odd | 6 | 243.3.f.c.188.2 | 30 | |||
36.11 | even | 6 | 243.3.f.b.188.4 | 30 | |||
36.23 | even | 6 | 243.3.f.a.107.4 | 30 | |||
36.31 | odd | 6 | 243.3.f.d.107.2 | 30 | |||
108.11 | even | 18 | 729.3.b.a.728.12 | 30 | |||
108.23 | even | 18 | 243.3.f.d.134.2 | 30 | |||
108.31 | odd | 18 | 243.3.f.a.134.4 | 30 | |||
108.43 | odd | 18 | 729.3.b.a.728.19 | 30 | |||
108.59 | even | 18 | 243.3.f.c.53.2 | 30 | |||
108.67 | odd | 18 | 81.3.f.a.71.2 | 30 | |||
108.95 | even | 18 | 27.3.f.a.14.4 | yes | 30 | ||
108.103 | odd | 18 | 243.3.f.b.53.4 | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
27.3.f.a.2.4 | ✓ | 30 | 4.3 | odd | 2 | ||
27.3.f.a.14.4 | yes | 30 | 108.95 | even | 18 | ||
81.3.f.a.8.2 | 30 | 12.11 | even | 2 | |||
81.3.f.a.71.2 | 30 | 108.67 | odd | 18 | |||
243.3.f.a.107.4 | 30 | 36.23 | even | 6 | |||
243.3.f.a.134.4 | 30 | 108.31 | odd | 18 | |||
243.3.f.b.53.4 | 30 | 108.103 | odd | 18 | |||
243.3.f.b.188.4 | 30 | 36.11 | even | 6 | |||
243.3.f.c.53.2 | 30 | 108.59 | even | 18 | |||
243.3.f.c.188.2 | 30 | 36.7 | odd | 6 | |||
243.3.f.d.107.2 | 30 | 36.31 | odd | 6 | |||
243.3.f.d.134.2 | 30 | 108.23 | even | 18 | |||
432.3.bc.a.257.3 | 30 | 27.14 | odd | 18 | inner | ||
432.3.bc.a.353.3 | 30 | 1.1 | even | 1 | trivial | ||
729.3.b.a.728.12 | 30 | 108.11 | even | 18 | |||
729.3.b.a.728.19 | 30 | 108.43 | odd | 18 |