Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [232,2,Mod(9,232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(232, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("232.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 232 = 2^{3} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 232.q (of order \(14\), degree \(6\), 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: | \(1.85252932689\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{14})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{14}]$ |
Embedding invariants
Embedding label | 209.3 | ||
Character | \(\chi\) | \(=\) | 232.209 |
Dual form | 232.2.q.a.121.3 |
$q$-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 \(\left(\mathbb{Z}/232\mathbb{Z}\right)^\times\).
\(n\) | \(89\) | \(117\) | \(175\) |
\(\chi(n)\) | \(e\left(\frac{3}{14}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.18604 | − | 0.270705i | −0.684759 | − | 0.156292i | −0.134032 | − | 0.990977i | \(-0.542792\pi\) |
−0.550727 | + | 0.834685i | \(0.685650\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.84749 | − | 2.31668i | 0.826221 | − | 1.03605i | −0.172476 | − | 0.985014i | \(-0.555177\pi\) |
0.998697 | − | 0.0510348i | \(-0.0162519\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.161250 | + | 0.706484i | −0.0609469 | + | 0.267026i | −0.996216 | − | 0.0869115i | \(-0.972300\pi\) |
0.935269 | + | 0.353937i | \(0.115157\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.36950 | − | 0.659517i | −0.456501 | − | 0.219839i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.22355 | − | 2.54073i | −0.368914 | − | 0.766058i | 0.631039 | − | 0.775751i | \(-0.282629\pi\) |
−0.999953 | + | 0.00969294i | \(0.996915\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.17169 | − | 1.52740i | 0.879668 | − | 0.423626i | 0.0611648 | − | 0.998128i | \(-0.480518\pi\) |
0.818503 | + | 0.574502i | \(0.194804\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.81833 | + | 2.24754i | −0.727689 | + | 0.580312i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.89842i | − | 1.18804i | −0.804450 | − | 0.594020i | \(-0.797540\pi\) | ||
0.804450 | − | 0.594020i | \(-0.202460\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.80988 | − | 0.869580i | 0.874046 | − | 0.199495i | 0.238111 | − | 0.971238i | \(-0.423472\pi\) |
0.635935 | + | 0.771743i | \(0.280615\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.382498 | − | 0.794266i | 0.0834679 | − | 0.173323i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.27957 | − | 1.60454i | −0.266810 | − | 0.334569i | 0.630320 | − | 0.776335i | \(-0.282923\pi\) |
−0.897130 | + | 0.441766i | \(0.854352\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.841172 | − | 3.68541i | −0.168234 | − | 0.737083i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.29913 | + | 3.42844i | 0.827368 | + | 0.659804i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.02298 | + | 5.28711i | 0.189963 | + | 0.981791i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.13218 | − | 0.902887i | −0.203346 | − | 0.162163i | 0.516522 | − | 0.856274i | \(-0.327226\pi\) |
−0.719868 | + | 0.694111i | \(0.755798\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.763388 | + | 3.34462i | 0.132889 | + | 0.582224i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.33879 | + | 1.67878i | 0.226296 | + | 0.283766i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.92038 | + | 3.98772i | −0.315709 | + | 0.655577i | −0.997080 | − | 0.0763612i | \(-0.975670\pi\) |
0.681371 | + | 0.731938i | \(0.261384\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.17522 | + | 0.952967i | −0.668570 | + | 0.152597i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.63260i | 1.03584i | 0.855429 | + | 0.517919i | \(0.173293\pi\) | ||||
−0.855429 | + | 0.517919i | \(0.826707\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.57251 | + | 7.63382i | −1.45979 | + | 1.16415i | −0.506446 | + | 0.862272i | \(0.669041\pi\) |
−0.953348 | + | 0.301875i | \(0.902387\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.05802 | + | 1.95424i | −0.604934 | + | 0.291321i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.65877 | − | 3.44448i | −0.241957 | − | 0.502429i | 0.744259 | − | 0.667891i | \(-0.232803\pi\) |
−0.986216 | + | 0.165462i | \(0.947088\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.83366 | + | 2.80934i | 0.833381 | + | 0.401335i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.32603 | + | 5.80971i | −0.185681 | + | 0.813522i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.21277 | − | 2.77473i | 0.303948 | − | 0.381138i | −0.606277 | − | 0.795254i | \(-0.707338\pi\) |
0.910224 | + | 0.414116i | \(0.135909\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.14653 | − | 1.85939i | −1.09848 | − | 0.250721i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.75406 | −0.629691 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.0729 | 1.44157 | 0.720784 | − | 0.693160i | \(-0.243782\pi\) | ||||
0.720784 | + | 0.693160i | \(0.243782\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.36693 | + | 0.540237i | 0.303055 | + | 0.0691702i | 0.371344 | − | 0.928495i | \(-0.378897\pi\) |
−0.0682895 | + | 0.997666i | \(0.521754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.686771 | − | 0.861184i | 0.0865250 | − | 0.108499i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.32115 | − | 10.1696i | 0.287903 | − | 1.26139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.82946 | + | 4.73362i | 1.20086 | + | 0.578304i | 0.923921 | − | 0.382584i | \(-0.124966\pi\) |
0.276939 | + | 0.960888i | \(0.410680\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.08327 | + | 2.24943i | 0.130410 | + | 0.270799i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.16682 | − | 2.48821i | 0.613189 | − | 0.295296i | −0.101395 | − | 0.994846i | \(-0.532330\pi\) |
0.714584 | + | 0.699550i | \(0.246616\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.5229 | + | 9.98665i | −1.46569 | + | 1.16885i | −0.515617 | + | 0.856819i | \(0.672437\pi\) |
−0.950072 | + | 0.312029i | \(0.898991\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.59875i | 0.531018i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.99228 | − | 0.454725i | 0.227042 | − | 0.0518208i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.83014 | − | 5.87684i | 0.318415 | − | 0.661196i | −0.678915 | − | 0.734217i | \(-0.737550\pi\) |
0.997330 | + | 0.0730206i | \(0.0232639\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.32766 | − | 1.66484i | −0.147518 | − | 0.184982i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.25710 | − | 9.88900i | −0.247749 | − | 1.08546i | −0.933769 | − | 0.357876i | \(-0.883501\pi\) |
0.686020 | − | 0.727582i | \(-0.259356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.3480 | − | 9.04976i | −1.23087 | − | 0.981584i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.217955 | − | 6.54764i | 0.0233672 | − | 0.701980i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.08526 | + | 4.05536i | 0.539036 | + | 0.429867i | 0.854790 | − | 0.518974i | \(-0.173686\pi\) |
−0.315754 | + | 0.948841i | \(0.602257\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.567651 | + | 2.48704i | 0.0595060 | + | 0.260713i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.09840 | + | 1.37735i | 0.113899 | + | 0.142824i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.02417 | − | 10.4328i | 0.515468 | − | 1.07038i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.88891 | − | 0.659375i | 0.293324 | − | 0.0669494i | −0.0733265 | − | 0.997308i | \(-0.523362\pi\) |
0.366651 | + | 0.930359i | \(0.380504\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.28648i | 0.430808i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.45601 | + | 2.75608i | −0.343886 | + | 0.274240i | −0.780168 | − | 0.625570i | \(-0.784866\pi\) |
0.436282 | + | 0.899810i | \(0.356295\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6113 | + | 6.55485i | −1.34116 | + | 0.645869i | −0.960353 | − | 0.278786i | \(-0.910068\pi\) |
−0.380807 | + | 0.924655i | \(0.624354\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.13340 | − | 2.35352i | −0.110608 | − | 0.229680i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.5245 | + | 6.51305i | 1.30746 | + | 0.629641i | 0.952300 | − | 0.305164i | \(-0.0987112\pi\) |
0.355163 | + | 0.934805i | \(0.384426\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0382839 | + | 0.167733i | −0.00366693 | + | 0.0160659i | −0.976728 | − | 0.214480i | \(-0.931194\pi\) |
0.973061 | + | 0.230546i | \(0.0740513\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.35715 | − | 4.20973i | 0.318646 | − | 0.399570i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.7922 | − | 2.46324i | −1.01524 | − | 0.231722i | −0.317643 | − | 0.948211i | \(-0.602891\pi\) |
−0.697599 | + | 0.716488i | \(0.745748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.08118 | −0.567073 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.35098 | −0.494699 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.46065 | + | 0.789872i | 0.317238 | + | 0.0724074i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.90016 | − | 2.38273i | 0.172742 | − | 0.216612i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.79548 | − | 7.86652i | 0.161893 | − | 0.709300i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.25652 | + | 1.56826i | 0.291272 | + | 0.140269i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.78650 | − | 12.0158i | −0.513469 | − | 1.06623i | −0.983050 | − | 0.183339i | \(-0.941309\pi\) |
0.469581 | − | 0.882889i | \(-0.344405\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.4199 | − | 6.46267i | 1.18155 | − | 0.569006i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.7547 | − | 10.9690i | 1.20175 | − | 0.958366i | 0.201974 | − | 0.979391i | \(-0.435264\pi\) |
0.999779 | + | 0.0210245i | \(0.00669279\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.83184i | 0.245552i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.8852 | − | 3.62569i | 1.36718 | − | 0.312050i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.72107 | + | 5.65036i | −0.232477 | + | 0.482743i | −0.984273 | − | 0.176652i | \(-0.943473\pi\) |
0.751797 | + | 0.659395i | \(0.229187\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.72668 | + | 7.18103i | 0.485731 | + | 0.609087i | 0.962944 | − | 0.269700i | \(-0.0869246\pi\) |
−0.477214 | + | 0.878787i | \(0.658353\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.03493 | + | 4.53432i | 0.0871567 | + | 0.381859i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.76144 | − | 6.18954i | −0.649044 | − | 0.517596i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.1385 | + | 7.39795i | 1.17413 | + | 0.614366i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.15844 | − | 4.91119i | −0.507940 | − | 0.405068i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.27767 | − | 23.1230i | −0.432363 | − | 1.89431i | −0.447232 | − | 0.894418i | \(-0.647590\pi\) |
0.0148685 | − | 0.999889i | \(-0.495267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.05791 | − | 6.34241i | −0.411607 | − | 0.516138i | 0.532208 | − | 0.846614i | \(-0.321362\pi\) |
−0.943815 | + | 0.330475i | \(0.892791\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.23059 | + | 6.70839i | −0.261178 | + | 0.542341i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.18339 | + | 0.954832i | −0.336018 | + | 0.0766939i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.65786i | − | 0.132312i | −0.997809 | − | 0.0661559i | \(-0.978927\pi\) | ||
0.997809 | − | 0.0661559i | \(-0.0210735\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.37557 | + | 2.69192i | −0.267700 | + | 0.213483i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.33991 | − | 0.645267i | 0.105600 | − | 0.0508542i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.522746 | + | 1.08549i | 0.0409446 | + | 0.0850224i | 0.920438 | − | 0.390889i | \(-0.127832\pi\) |
−0.879493 | + | 0.475912i | \(0.842118\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.15875 | + | 4.41062i | 0.713008 | + | 0.343366i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.89624 | + | 17.0706i | −0.301500 | + | 1.32096i | 0.566363 | + | 0.824156i | \(0.308350\pi\) |
−0.867863 | + | 0.496803i | \(0.834507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.378725 | + | 0.474906i | −0.0291327 | + | 0.0365312i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.79114 | − | 1.32179i | −0.442859 | − | 0.101080i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −23.7453 | −1.80532 | −0.902661 | − | 0.430351i | \(-0.858390\pi\) | ||||
−0.902661 | + | 0.430351i | \(0.858390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.73933 | 0.207074 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −13.1329 | − | 2.99749i | −0.987127 | − | 0.225305i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.5274 | − | 18.2168i | 1.08583 | − | 1.36159i | 0.158495 | − | 0.987360i | \(-0.449336\pi\) |
0.927336 | − | 0.374229i | \(-0.122093\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.923443 | − | 4.04587i | 0.0686390 | − | 0.300727i | −0.928943 | − | 0.370222i | \(-0.879282\pi\) |
0.997582 | + | 0.0694949i | \(0.0221388\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.66103 | − | 1.28148i | −0.196709 | − | 0.0947299i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.69037 | + | 11.8162i | 0.418364 | + | 0.868742i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.4455 | + | 5.99346i | −0.910109 | + | 0.438285i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.11538 | + | 2.48443i | −0.226610 | + | 0.180716i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.2057i | 1.10025i | 0.835084 | + | 0.550123i | \(0.185419\pi\) | ||||
−0.835084 | + | 0.550123i | \(0.814581\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.1816 | − | 4.14983i | 1.30874 | − | 0.298711i | 0.489419 | − | 0.872049i | \(-0.337209\pi\) |
0.819319 | + | 0.573337i | \(0.194352\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.50595 | + | 11.4332i | −0.394289 | + | 0.818750i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.33808 | + | 5.43978i | 0.309075 | + | 0.387568i | 0.911973 | − | 0.410250i | \(-0.134559\pi\) |
−0.602898 | + | 0.797819i | \(0.705987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.623047 | + | 2.72975i | 0.0441666 | + | 0.193507i | 0.992198 | − | 0.124669i | \(-0.0397869\pi\) |
−0.948032 | + | 0.318176i | \(0.896930\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.3767 | − | 8.27514i | −0.731916 | − | 0.583683i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.90021 | − | 0.129829i | −0.273741 | − | 0.00911218i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.3656 | + | 12.2536i | 1.07318 | + | 0.855832i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.694161 | + | 3.04132i | 0.0482475 | + | 0.211386i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.87094 | − | 8.61589i | −0.475273 | − | 0.595974i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0820 | + | 23.0121i | −0.762919 | + | 1.58422i | 0.0478528 | + | 0.998854i | \(0.484762\pi\) |
−0.810772 | + | 0.585363i | \(0.800952\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.80162 | + | 1.55243i | −0.466039 | + | 0.106370i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 36.2798i | 2.47426i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.820441 | − | 0.654280i | 0.0556951 | − | 0.0444154i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.5560 | − | 8.45454i | 1.18633 | − | 0.571305i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.48187 | − | 15.5363i | −0.503285 | − | 1.04508i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.89915 | − | 3.32246i | −0.462002 | − | 0.222488i | 0.188380 | − | 0.982096i | \(-0.439676\pi\) |
−0.650381 | + | 0.759608i | \(0.725391\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.27861 | + | 5.60195i | −0.0852405 | + | 0.373463i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.08040 | − | 2.60874i | 0.138081 | − | 0.173148i | −0.707983 | − | 0.706230i | \(-0.750395\pi\) |
0.846064 | + | 0.533081i | \(0.178966\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.7547 | + | 5.87834i | 1.70192 | + | 0.388451i | 0.959549 | − | 0.281541i | \(-0.0908457\pi\) |
0.742368 | + | 0.669993i | \(0.233703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.48602 | −0.163568 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.1059 | 0.727574 | 0.363787 | − | 0.931482i | \(-0.381484\pi\) | ||||
0.363787 | + | 0.931482i | \(0.381484\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0443 | − | 2.52079i | −0.720450 | − | 0.164438i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.94754 | + | 6.20402i | −0.321377 | + | 0.402995i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.18885 | + | 22.7339i | −0.335639 | + | 1.47053i | 0.472391 | + | 0.881389i | \(0.343391\pi\) |
−0.808030 | + | 0.589142i | \(0.799466\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.65248 | + | 0.795790i | 0.106445 | + | 0.0512614i | 0.486349 | − | 0.873765i | \(-0.338328\pi\) |
−0.379903 | + | 0.925026i | \(0.624043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.03354 | − | 12.5288i | −0.387052 | − | 0.803721i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.2860 | − | 8.32448i | 1.10436 | − | 0.531831i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.7555 | − | 8.57726i | 0.684359 | − | 0.545758i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.3397i | 0.781999i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.33943 | + | 2.13166i | −0.589500 | + | 0.134549i | −0.506857 | − | 0.862030i | \(-0.669193\pi\) |
−0.0826421 | + | 0.996579i | \(0.526336\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.51107 | + | 5.21428i | −0.157869 | + | 0.327819i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.0094 | + | 13.8053i | 0.689435 | + | 0.864524i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.806692 | − | 3.53435i | −0.0503200 | − | 0.220467i | 0.943516 | − | 0.331327i | \(-0.107496\pi\) |
−0.993836 | + | 0.110861i | \(0.964639\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50760 | − | 1.99974i | −0.155815 | − | 0.124258i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.08597 | − | 7.91538i | 0.129118 | − | 0.489950i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.44179 | − | 7.52958i | −0.582206 | − | 0.464294i | 0.287557 | − | 0.957763i | \(-0.407157\pi\) |
−0.869763 | + | 0.493470i | \(0.835728\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.34008 | − | 10.2525i | −0.143750 | − | 0.629809i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.93350 | − | 6.18641i | −0.301925 | − | 0.378602i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.54750 | + | 17.7491i | −0.521151 | + | 1.08218i | 0.459818 | + | 0.888013i | \(0.347915\pi\) |
−0.980968 | + | 0.194167i | \(0.937800\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.9096 | + | 7.05491i | −1.87762 | + | 0.428556i | −0.998817 | − | 0.0486215i | \(-0.984517\pi\) |
−0.878807 | + | 0.477177i | \(0.841660\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 3.10339i | − | 0.187826i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.33442 | + | 6.64648i | −0.502584 | + | 0.400798i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.7140 | − | 8.53060i | 1.06433 | − | 0.512554i | 0.182055 | − | 0.983288i | \(-0.441725\pi\) |
0.882275 | + | 0.470734i | \(0.156011\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.955059 | + | 1.98320i | 0.0571779 | + | 0.118731i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.38898 | − | 3.07677i | −0.381135 | − | 0.183545i | 0.233500 | − | 0.972357i | \(-0.424982\pi\) |
−0.614635 | + | 0.788812i | \(0.710697\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.804064 | + | 3.52283i | −0.0477966 | + | 0.209411i | −0.993187 | − | 0.116529i | \(-0.962823\pi\) |
0.945391 | + | 0.325939i | \(0.105680\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.78306 | + | 11.0136i | −0.520264 | + | 0.652390i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.68583 | − | 1.06951i | −0.276596 | − | 0.0631312i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.99449 | −0.411441 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.60485 | −0.211320 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.0660 | + | 4.80817i | 1.23069 | + | 0.280897i | 0.787941 | − | 0.615750i | \(-0.211147\pi\) |
0.442747 | + | 0.896647i | \(0.354004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.4570 | − | 25.6523i | 1.19105 | − | 1.49353i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.45054 | − | 15.1178i | 0.200221 | − | 0.877224i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.50919 | − | 3.13466i | −0.376436 | − | 0.181282i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.84960 | − | 7.99378i | −0.221887 | − | 0.460754i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.84505 | − | 2.33325i | 0.278341 | − | 0.134042i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.62443 | − | 4.48533i | 0.322054 | − | 0.256829i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3962i | 1.27822i | 0.769116 | + | 0.639109i | \(0.220697\pi\) | ||||
−0.769116 | + | 0.639109i | \(0.779303\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.9179 | − | 4.08965i | 1.01932 | − | 0.232652i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0436 | − | 20.8558i | 0.569521 | − | 1.18262i | −0.395016 | − | 0.918674i | \(-0.629261\pi\) |
0.964537 | − | 0.263948i | \(-0.0850246\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1241 | + | 12.6952i | 0.572246 | + | 0.717574i | 0.980769 | − | 0.195175i | \(-0.0625273\pi\) |
−0.408523 | + | 0.912748i | \(0.633956\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.726282 | − | 3.18205i | −0.0409214 | − | 0.179288i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.9730 | − | 15.9279i | −1.12180 | − | 0.894602i | −0.126546 | − | 0.991961i | \(-0.540389\pi\) |
−0.995249 | + | 0.0973583i | \(0.968961\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.1814 | − | 9.06816i | 0.682029 | − | 0.507719i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.2774 | − | 11.3859i | −0.796889 | − | 0.635498i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.25956 | − | 18.6624i | −0.237009 | − | 1.03840i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.29705 | − | 10.4042i | −0.460238 | − | 0.577120i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.0908124 | − | 0.188574i | 0.00502193 | − | 0.0104282i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.70095 | − | 0.616473i | 0.148908 | − | 0.0339873i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10.1111i | − | 0.555755i | −0.960617 | − | 0.277877i | \(-0.910369\pi\) | ||
0.960617 | − | 0.277877i | \(-0.0896309\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.25994 | − | 4.19466i | 0.288243 | − | 0.229866i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 29.1261 | − | 14.0264i | 1.59133 | − | 0.766342i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.74139 | − | 18.1517i | −0.476174 | − | 0.988785i | −0.991294 | − | 0.131667i | \(-0.957967\pi\) |
0.515120 | − | 0.857118i | \(-0.327747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 12.1331 | + | 5.84300i | 0.658980 | + | 0.317348i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.908706 | + | 3.98130i | −0.0492092 | + | 0.215600i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.08813 | + | 7.63428i | −0.328728 | + | 0.412212i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.21252 | + | 1.64621i | 0.388309 | + | 0.0886290i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.8444 | −0.957938 | −0.478969 | − | 0.877832i | \(-0.658989\pi\) | ||||
−0.478969 | + | 0.877832i | \(0.658989\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.19398 | −0.385085 | −0.192543 | − | 0.981289i | \(-0.561673\pi\) | ||||
−0.192543 | + | 0.981289i | \(0.561673\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.8721 | + | 4.30744i | 1.00732 | + | 0.229914i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0858 | + | 15.1551i | −0.643260 | + | 0.806623i | −0.991407 | − | 0.130817i | \(-0.958240\pi\) |
0.348146 | + | 0.937440i | \(0.386811\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.78126 | − | 16.5668i | 0.200688 | − | 0.879274i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.89064 | − | 1.87364i | −0.205915 | − | 0.0991633i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.44636 | + | 3.00339i | 0.0763358 | + | 0.158513i | 0.935644 | − | 0.352945i | \(-0.114820\pi\) |
−0.859308 | + | 0.511458i | \(0.829106\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.35941 | + | 1.61780i | −0.176811 | + | 0.0851476i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.89868 | + | 2.31162i | −0.152141 | + | 0.121329i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 47.4616i | 2.48425i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.9680 | − | 7.52474i | 1.72092 | − | 0.392788i | 0.755840 | − | 0.654756i | \(-0.227229\pi\) |
0.965077 | + | 0.261968i | \(0.0843714\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.37432 | − | 9.08336i | 0.227718 | − | 0.472861i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.60349 | + | 2.01071i | 0.0832491 | + | 0.104391i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.33564 | − | 36.5208i | −0.431603 | − | 1.89098i | −0.453577 | − | 0.891217i | \(-0.649852\pi\) |
0.0219744 | − | 0.999759i | \(-0.493005\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.43782 | − | 2.74157i | −0.177528 | − | 0.141574i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.3201 | + | 15.2066i | 0.583016 | + | 0.783177i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.74439 | + | 7.77089i | 0.500535 | + | 0.399164i | 0.840951 | − | 0.541111i | \(-0.181996\pi\) |
−0.340415 | + | 0.940275i | \(0.610568\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.61027 | + | 15.8176i | 0.184960 | + | 0.810361i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.70818 | − | 7.15783i | −0.291674 | − | 0.365748i | 0.614306 | − | 0.789068i | \(-0.289436\pi\) |
−0.905980 | + | 0.423320i | \(0.860865\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.62726 | − | 5.45557i | 0.133898 | − | 0.278042i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 18.1442 | − | 4.14130i | 0.922322 | − | 0.210514i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 14.6428i | − | 0.742417i | −0.928549 | − | 0.371209i | \(-0.878943\pi\) | ||
0.928549 | − | 0.371209i | \(-0.121057\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.85968 | + | 6.26789i | −0.397481 | + | 0.316981i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.2830 | + | 9.28618i | −0.972697 | + | 0.468426i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.38609 | − | 17.4139i | −0.421950 | − | 0.876188i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.83610 | − | 0.884217i | −0.0921510 | − | 0.0443776i | 0.387240 | − | 0.921979i | \(-0.373428\pi\) |
−0.479392 | + | 0.877601i | \(0.659143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.766594 | − | 3.35867i | 0.0383777 | − | 0.168144i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11.6940 | + | 14.6638i | −0.583972 | + | 0.732277i | −0.982785 | − | 0.184755i | \(-0.940851\pi\) |
0.398813 | + | 0.917032i | \(0.369422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.97001 | − | 1.13437i | −0.247574 | − | 0.0565071i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.30972 | −0.313533 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.4814 | 0.618680 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.6171 | + | 2.65153i | 0.574430 | + | 0.131110i | 0.499861 | − | 0.866106i | \(-0.333385\pi\) |
0.0745695 | + | 0.997216i | \(0.476242\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.75687 | − | 5.96493i | 0.234639 | − | 0.294228i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.78551 | + | 7.82282i | −0.0878591 | + | 0.384936i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.0796 | − | 13.0408i | −1.32928 | − | 0.640149i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.84812 | − | 10.0672i | −0.237413 | − | 0.492994i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.8835 | + | 5.72278i | −0.580546 | + | 0.279576i | −0.701021 | − | 0.713140i | \(-0.747272\pi\) |
0.120476 | + | 0.992716i | \(0.461558\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.1448 | + | 9.68512i | −0.591899 | + | 0.472024i | −0.873044 | − | 0.487642i | \(-0.837857\pi\) |
0.281145 | + | 0.959665i | \(0.409286\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.81121i | 0.282551i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.0527 | + | 4.12041i | −0.875684 | + | 0.199869i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.763337 | + | 1.58509i | −0.0369405 | + | 0.0767077i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7.52982 | + | 9.44210i | 0.363543 | + | 0.455869i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.31072 | + | 36.4116i | 0.400313 | + | 1.75389i | 0.626131 | + | 0.779718i | \(0.284637\pi\) |
−0.225818 | + | 0.974169i | \(0.572506\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.1813 | − | 14.4991i | −0.873739 | − | 0.696784i | 0.0802018 | − | 0.996779i | \(-0.474444\pi\) |
−0.953941 | + | 0.299995i | \(0.903015\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.7661 | − | 12.6016i | −0.707979 | − | 0.604201i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.27029 | − | 5.00039i | −0.299949 | − | 0.239201i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.08084 | + | 22.2606i | 0.242495 | + | 1.06244i | 0.938737 | + | 0.344634i | \(0.111997\pi\) |
−0.696242 | + | 0.717807i | \(0.745146\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.13640 | − | 7.69481i | −0.292210 | − | 0.366419i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.245308 | − | 0.509388i | 0.0116550 | − | 0.0242018i | −0.895060 | − | 0.445945i | \(-0.852868\pi\) |
0.906715 | + | 0.421744i | \(0.138582\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.7899 | − | 4.28867i | 0.890726 | − | 0.203302i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 28.8534i | 1.36472i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.4023 | − | 18.6627i | 1.10442 | − | 0.880746i | 0.110836 | − | 0.993839i | \(-0.464647\pi\) |
0.993584 | + | 0.113093i | \(0.0360757\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.8516 | − | 8.11532i | 0.793513 | − | 0.382136i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.28194 | + | 8.89155i | 0.201183 | + | 0.417761i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.81040 | + | 3.27971i | 0.319276 | + | 0.153755i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.85881 | + | 25.6691i | −0.274063 | + | 1.20075i | 0.631105 | + | 0.775697i | \(0.282602\pi\) |
−0.905168 | + | 0.425053i | \(0.860255\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.7939 | − | 21.0589i | 0.783874 | − | 0.982947i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.06162 | − | 0.927038i | −0.189168 | − | 0.0431765i | 0.126887 | − | 0.991917i | \(-0.459501\pi\) |
−0.316055 | + | 0.948741i | \(0.602359\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.39217 | 0.157648 | 0.0788239 | − | 0.996889i | \(-0.474884\pi\) | ||||
0.0788239 | + | 0.996889i | \(0.474884\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.22014 | 0.242078 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.1904 | − | 6.89076i | −1.39704 | − | 0.318866i | −0.543291 | − | 0.839544i | \(-0.682822\pi\) |
−0.853753 | + | 0.520678i | \(0.825679\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.92923 | + | 6.18106i | −0.227611 | + | 0.285415i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.448792 | + | 1.96629i | −0.0206793 | + | 0.0906017i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.1079 | + | 14.9808i | 1.43034 | + | 0.688817i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.40952 | − | 13.3095i | −0.294089 | − | 0.610682i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.86038 | + | 2.34063i | −0.222541 | + | 0.107170i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.50897 | − | 5.98820i | 0.343094 | − | 0.273608i | −0.436749 | − | 0.899583i | \(-0.643870\pi\) |
0.779843 | + | 0.625975i | \(0.215299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.5810i | 0.710433i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.76386 | + | 0.402590i | −0.0802585 | + | 0.0183185i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.80966 | − | 7.91085i | 0.172988 | − | 0.359213i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.3438 | − | 20.4944i | −0.740607 | − | 0.928692i | 0.258698 | − | 0.965958i | \(-0.416706\pi\) |
−0.999305 | + | 0.0372663i | \(0.988135\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.326148 | − | 1.42895i | −0.0147489 | − | 0.0646192i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.7516 | + | 9.37162i | 0.530344 | + | 0.422935i | 0.851705 | − | 0.524022i | \(-0.175569\pi\) |
−0.321361 | + | 0.946957i | \(0.604140\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.8985 | − | 5.01099i | 1.16641 | − | 0.225683i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.93039 | + | 7.91922i | 0.446338 | + | 0.355943i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.924729 | + | 4.05150i | 0.0414798 | + | 0.181735i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.34886 | − | 6.70725i | −0.239448 | − | 0.300258i | 0.647558 | − | 0.762016i | \(-0.275790\pi\) |
−0.887006 | + | 0.461758i | \(0.847219\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.24218 | − | 19.1916i | 0.412910 | − | 0.857417i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.3227 | + | 4.63853i | −0.906145 | + | 0.206822i | −0.650105 | − | 0.759844i | \(-0.725275\pi\) |
−0.256040 | + | 0.966666i | \(0.582418\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0983i | 0.582866i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.577741 | − | 0.460733i | 0.0256584 | − | 0.0204619i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.7769 | + | 16.2661i | −1.49713 | + | 0.720982i | −0.990024 | − | 0.140900i | \(-0.955001\pi\) |
−0.507110 | + | 0.861881i | \(0.669286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.03609 | − | 10.4575i | −0.222784 | − | 0.462615i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19.3605 | + | 9.32351i | 0.854786 | + | 0.411643i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.96122 | + | 43.6429i | −0.438944 | + | 1.92314i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.72189 | + | 8.42898i | −0.295628 | + | 0.370706i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 28.1628 | + | 6.42799i | 1.23621 | + | 0.282157i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −38.5983 | −1.69102 | −0.845512 | − | 0.533957i | \(-0.820704\pi\) | ||||
−0.845512 | + | 0.533957i | \(0.820704\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.47374 | −0.283077 | −0.141538 | − | 0.989933i | \(-0.545205\pi\) | ||||
−0.141538 | + | 0.989933i | \(0.545205\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.24894 | − | 0.741550i | −0.141796 | − | 0.0323639i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.42272 | + | 5.54591i | −0.192657 | + | 0.241584i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.18076 | − | 18.3171i | 0.181772 | − | 0.796395i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.1643 | − | 7.30277i | −0.658077 | − | 0.316913i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.1307 | + | 21.0366i | 0.438808 | + | 0.911194i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 40.0750 | − | 19.2991i | 1.73259 | − | 0.834372i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.1615 | + | 17.6732i | −0.956338 | + | 0.762654i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 18.2591i | − | 0.786476i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.7696 | + | 6.56646i | −1.23690 | + | 0.282314i | −0.790468 | − | 0.612503i | \(-0.790163\pi\) |
−0.446432 | + | 0.894818i | \(0.647305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.19048 | + | 4.54857i | −0.0940024 | + | 0.195198i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.317853 | + | 0.398575i | 0.0136153 | + | 0.0170731i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.09123 | + | 31.0687i | 0.303199 | + | 1.32840i | 0.865267 | + | 0.501311i | \(0.167149\pi\) |
−0.562068 | + | 0.827091i | \(0.689994\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.88522 | − | 2.30089i | −0.123138 | − | 0.0981995i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.49499 | + | 19.2537i | 0.361899 | + | 0.820234i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.69553 | + | 2.94709i | 0.157150 | + | 0.125323i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.55029 | − | 15.5548i | −0.150701 | − | 0.660266i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.31590 | − | 11.6818i | −0.394728 | − | 0.494973i | 0.544263 | − | 0.838914i | \(-0.316809\pi\) |
−0.938991 | + | 0.343942i | \(0.888238\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.7011 | + | 38.8332i | −0.790971 | + | 1.64247i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16.3834 | − | 3.73939i | 0.691706 | − | 0.157877i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 4.93691i | − | 0.208066i | −0.994574 | − | 0.104033i | \(-0.966825\pi\) | ||
0.994574 | − | 0.104033i | \(-0.0331748\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.6449 | + | 20.4511i | −1.07889 | + | 0.860386i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.39027 | − | 0.669517i | 0.0583857 | − | 0.0281171i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.879472 | + | 1.82624i | 0.0368694 | + | 0.0765600i | 0.918590 | − | 0.395212i | \(-0.129329\pi\) |
−0.881721 | + | 0.471772i | \(0.843615\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.4906 | + | 19.4992i | 1.69448 | + | 0.816017i | 0.994833 | + | 0.101526i | \(0.0323726\pi\) |
0.699645 | + | 0.714491i | \(0.253342\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.11627 | − | 18.0345i | 0.171959 | − | 0.753404i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.83704 | + | 6.06545i | −0.201718 | + | 0.252947i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.98664 | + | 0.453438i | 0.0827050 | + | 0.0188769i | 0.263673 | − | 0.964612i | \(-0.415066\pi\) |
−0.180968 | + | 0.983489i | \(0.557923\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.6874 | −0.942857 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.35038 | 0.304945 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9.75727 | − | 2.22703i | −0.404105 | − | 0.0922343i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.88587 | + | 12.3965i | −0.408730 | + | 0.512532i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.42398 | − | 6.23888i | 0.0587741 | − | 0.257506i | −0.937002 | − | 0.349325i | \(-0.886411\pi\) |
0.995776 | + | 0.0918188i | \(0.0292681\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.09862 | − | 2.45536i | −0.210085 | − | 0.101172i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.67255 | − | 7.62613i | −0.151069 | − | 0.313697i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.5222 | + | 9.40139i | −0.801680 | + | 0.386069i | −0.789418 | − | 0.613856i | \(-0.789618\pi\) |
−0.0122621 | + | 0.999925i | \(0.503903\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.22339 | − | 6.55793i | 0.337126 | − | 0.268849i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 3.40625i | − | 0.139408i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.55712 | + | 1.49662i | −0.267917 | + | 0.0611502i | −0.354369 | − | 0.935106i | \(-0.615304\pi\) |
0.0864521 | + | 0.996256i | \(0.472447\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.84283 | − | 14.2093i | 0.279125 | − | 0.579609i | −0.713525 | − | 0.700630i | \(-0.752903\pi\) |
0.992650 | + | 0.121021i | \(0.0386168\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.3396 | − | 12.9654i | −0.421059 | − | 0.527992i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.00948 | − | 8.80412i | −0.0816971 | − | 0.357938i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.9488 | + | 30.2632i | 1.54029 | + | 1.22834i | 0.877535 | + | 0.479512i | \(0.159186\pi\) |
0.662759 | + | 0.748832i | \(0.269385\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.59066 | + | 1.20979i | 0.186023 | + | 0.0490232i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.5222 | − | 8.39119i | −0.425683 | − | 0.339471i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.77215 | + | 20.9082i | 0.192745 | + | 0.844473i | 0.975122 | + | 0.221668i | \(0.0711500\pi\) |
−0.782377 | + | 0.622805i | \(0.785993\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −14.9070 | − | 18.6928i | −0.601110 | − | 0.753768i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.23374 | − | 8.79145i | 0.170444 | − | 0.353930i | −0.798197 | − | 0.602397i | \(-0.794212\pi\) |
0.968640 | + | 0.248467i | \(0.0799267\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.4871 | − | 3.76306i | 0.662671 | − | 0.151250i | 0.122060 | − | 0.992523i | \(-0.461050\pi\) |
0.540611 | + | 0.841272i | \(0.318193\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 11.2851i | − | 0.452854i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.68504 | + | 2.93872i | −0.147638 | + | 0.117737i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 26.6787 | − | 12.8478i | 1.06715 | − | 0.513911i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.81683 | + | 12.0788i | 0.232302 | + | 0.482380i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.5335 | + | 9.40685i | 0.778852 | + | 0.375076i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.13194 | + | 9.34066i | −0.0848713 | + | 0.371846i | −0.999471 | − | 0.0325143i | \(-0.989649\pi\) |
0.914600 | + | 0.404360i | \(0.132506\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.3732 | − | 24.2932i | 0.770016 | − | 0.965570i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.5272 | − | 8.79357i | −1.52890 | − | 0.348962i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.7936 | 0.903114 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.71699 | −0.344839 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.79740 | + | 2.23619i | 0.386974 | + | 0.0883243i | 0.411582 | − | 0.911373i | \(-0.364977\pi\) |
−0.0246077 | + | 0.999697i | \(0.507834\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.7819 | − | 37.3453i | 1.17448 | − | 1.47275i | 0.324544 | − | 0.945871i | \(-0.394789\pi\) |
0.849938 | − | 0.526883i | \(-0.176639\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.82113 | − | 43.0292i | 0.386707 | − | 1.69427i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.0796 | − | 6.78036i | −0.553525 | − | 0.266563i | 0.136143 | − | 0.990689i | \(-0.456529\pi\) |
−0.689668 | + | 0.724126i | \(0.742243\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.5482 | − | 28.1332i | −0.531815 | − | 1.10433i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.15019 | + | 0.553903i | −0.0450795 | + | 0.0217092i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.04580 | − | 2.42894i | 0.119191 | − | 0.0950520i | −0.562080 | − | 0.827083i | \(-0.689999\pi\) |
0.681272 | + | 0.732031i | \(0.261427\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 52.1303i | − | 2.03690i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.7364 | − | 5.41769i | 0.926047 | − | 0.211364i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.96607 | + | 14.4652i | −0.271360 | + | 0.563484i | −0.991464 | − | 0.130382i | \(-0.958380\pi\) |
0.720104 | + | 0.693866i | \(0.244094\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.5993 | − | 35.8624i | −1.11239 | − | 1.39489i | −0.909510 | − | 0.415683i | \(-0.863543\pi\) |
−0.202876 | − | 0.979204i | \(-0.565029\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.66803 | + | 20.4520i | 0.181291 | + | 0.794289i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.56045 | + | 5.23178i | 0.254403 | + | 0.202880i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.17437 | − | 8.40666i | 0.277793 | − | 0.325507i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.28325 | + | 5.80820i | 0.281587 | + | 0.224558i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.52347 | − | 6.67474i | −0.0588127 | − | 0.257675i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.8371 | + | 24.8750i | 0.764665 | + | 0.958860i | 0.999915 | − | 0.0130749i | \(-0.00416200\pi\) |
−0.235249 | + | 0.971935i | \(0.575591\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.01892 | − | 18.7280i | 0.347139 | − | 0.720841i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.6226 | + | 3.56575i | −0.600424 | + | 0.137043i | −0.511920 | − | 0.859033i | \(-0.671066\pi\) |
−0.0885039 | + | 0.996076i | \(0.528209\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.14729i | 0.0824055i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.17363 | + | 2.53089i | −0.121614 | + | 0.0969838i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11.3892 | + | 5.48473i | −0.435794 | + | 0.209867i | −0.638901 | − | 0.769289i | \(-0.720611\pi\) |
0.203107 | + | 0.979157i | \(0.434896\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.06290 | + | 16.7428i | 0.308068 | + | 0.639709i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −28.9547 | − | 13.9439i | −1.10469 | − | 0.531991i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.78009 | − | 12.1804i | 0.105913 | − | 0.464035i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.55072 | − | 1.94455i | 0.0589923 | − | 0.0739740i | −0.751460 | − | 0.659779i | \(-0.770650\pi\) |
0.810452 | + | 0.585805i | \(0.199221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.02833 | − | 0.691197i | −0.115037 | − | 0.0262564i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 27.2161 | 1.03236 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.4893 | 1.23062 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.1721 | − | 3.00644i | −0.498213 | − | 0.113714i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1761 | − | 29.0619i | 0.875350 | − | 1.09765i | −0.119146 | − | 0.992877i | \(-0.538016\pi\) |
0.994496 | − | 0.104777i | \(-0.0334130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.84879 | + | 16.8627i | −0.145160 | + | 0.635987i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.4166 | + | 5.97950i | 0.467635 | + | 0.225201i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.38984 | − | 2.88604i | −0.0522704 | − | 0.108541i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.97970 | + | 0.953374i | −0.0743493 | + | 0.0358047i | −0.470689 | − | 0.882299i | \(-0.655995\pi\) |
0.396340 | + | 0.918104i | \(0.370280\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.75176 | + | 6.18182i | −0.290714 | + | 0.231836i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.97194i | 0.111300i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.6783 | + | 6.54564i | −1.07251 | + | 0.244793i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.3084 | − | 25.5586i | 0.459664 | − | 0.954502i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.7919 | − | 16.0406i | −0.477059 | − | 0.598213i | 0.483825 | − | 0.875165i | \(-0.339247\pi\) |
−0.960884 | + | 0.276952i | \(0.910676\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.43607 | − | 10.6731i | −0.0907241 | − | 0.397488i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.74447 | − | 1.39117i | −0.0648777 | − | 0.0517382i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.6247 | − | 8.21747i | 0.691703 | − | 0.305189i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.6619 | − | 27.6419i | −1.28554 | − | 1.02518i | −0.997719 | − | 0.0674968i | \(-0.978499\pi\) |
−0.287818 | − | 0.957685i | \(-0.592930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.18591 | + | 22.7210i | 0.192071 | + | 0.841517i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.3936 | + | 46.8901i | 1.38305 | + | 1.73429i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.753825 | + | 1.56533i | −0.0278431 | + | 0.0578169i | −0.914427 | − | 0.404752i | \(-0.867358\pi\) |
0.886583 | + | 0.462569i | \(0.153072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −22.7553 | + | 5.19374i | −0.839341 | + | 0.191574i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 30.7658i | − | 1.13327i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.56036 | + | 6.82666i | −0.314898 | + | 0.251123i | −0.768165 | − | 0.640252i | \(-0.778830\pi\) |
0.453267 | + | 0.891375i | \(0.350258\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.0784 | + | 7.26137i | −0.553919 | + | 0.266753i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.2649 | − | 21.3152i | −0.376581 | − | 0.781979i | −1.00000 | 9.08456e-5i | \(-0.999971\pi\) | |
0.623419 | − | 0.781888i | \(-0.285743\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −63.3188 | − | 30.4927i | −2.31982 | − | 1.11717i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.43086 | + | 15.0316i | −0.125529 | + | 0.549977i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.78220 | + | 8.50461i | −0.247816 | + | 0.310752i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.40435 | + | 0.777021i | 0.124227 | + | 0.0283539i | 0.284182 | − | 0.958770i | \(-0.408278\pi\) |
−0.159956 | + | 0.987124i | \(0.551135\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.6540 | 0.424694 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.0377 | −0.874822 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.29672 | − | 0.980698i | −0.156167 | − | 0.0356441i | 0.143723 | − | 0.989618i | \(-0.454093\pi\) |
−0.299890 | + | 0.953974i | \(0.596950\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.38975 | − | 5.50458i | 0.159338 | − | 0.199803i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.40630 | − | 6.16139i | 0.0509782 | − | 0.223350i | −0.943022 | − | 0.332731i | \(-0.892030\pi\) |
0.994000 | + | 0.109381i | \(0.0348869\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.112327 | − | 0.0540940i | −0.00406652 | − | 0.00195833i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.57269 | + | 19.8779i | 0.346101 | + | 0.718687i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 35.1198 | − | 16.9128i | 1.26810 | − | 0.610685i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.60924 | − | 6.06816i | 0.274396 | − | 0.218824i | −0.476617 | − | 0.879111i | \(-0.658137\pi\) |
0.751013 | + | 0.660288i | \(0.229566\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.41025i | 0.158831i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.0031 | + | 2.28313i | −0.359785 | + | 0.0821186i | −0.398593 | − | 0.917128i | \(-0.630501\pi\) |
0.0388074 | + | 0.999247i | \(0.487644\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.37515 | + | 4.93205i | −0.0853179 | + | 0.177165i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.43277 | + | 3.05059i | 0.0872750 | + | 0.109439i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.76758 | + | 25.2694i | 0.206645 | + | 0.905371i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6437 | − | 10.0830i | −0.452428 | − | 0.360800i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.7286 | + | 26.2372i | −0.490621 | + | 0.937641i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.84073 | − | 3.06288i | −0.137081 | − | 0.109319i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.21319 | + | 22.8405i | 0.185830 | + | 0.814176i | 0.978784 | + | 0.204894i | \(0.0656850\pi\) |
−0.792954 | + | 0.609282i | \(0.791458\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.16002 | + | 11.4863i | 0.326105 | + | 0.408923i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.48048 | − | 7.22730i | 0.123752 | − | 0.256973i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.33233 | − | 1.90180i | 0.295890 | − | 0.0675349i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.7934i | 0.453734i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.38598 | − | 6.68760i | 0.297047 | − | 0.236887i | −0.463613 | − | 0.886038i | \(-0.653447\pi\) |
0.760660 | + | 0.649151i | \(0.224876\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.8725 | + | 8.12536i | −0.596906 | + | 0.287455i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.28969 | − | 8.90763i | −0.151569 | − | 0.314736i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 40.6957 | + | 19.5980i | 1.43612 | + | 0.691599i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.980593 | − | 4.29626i | 0.0345614 | − | 0.151423i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.9424 | − | 18.7372i | 0.525999 | − | 0.659581i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.9505 | − | 4.09708i | −0.631106 | − | 0.144046i | −0.105010 | − | 0.994471i | \(-0.533487\pi\) |
−0.526096 | + | 0.850425i | \(0.676345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.8805 | 0.908789 | 0.454394 | − | 0.890801i | \(-0.349856\pi\) | ||||
0.454394 | + | 0.890801i | \(0.349856\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 38.5698 | 1.35270 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.48050 | + | 0.794402i | 0.121917 | + | 0.0278267i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.8319 | + | 37.4080i | −1.04369 | + | 1.30874i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.862848 | − | 3.78038i | 0.0301504 | − | 0.132097i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.4099 | + | 19.4604i | 1.41032 | + | 0.679173i | 0.975225 | − | 0.221214i | \(-0.0710018\pi\) |
0.435091 | + | 0.900386i | \(0.356716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.3181 | − | 25.5788i | −0.429382 | − | 0.891622i | −0.997633 | − | 0.0687661i | \(-0.978094\pi\) |
0.568250 | − | 0.822856i | \(-0.307620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.6842 | − | 5.62680i | 0.406791 | − | 0.195900i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.96266 | + | 7.94496i | −0.346436 | + | 0.276273i | −0.781213 | − | 0.624265i | \(-0.785399\pi\) |
0.434777 | + | 0.900538i | \(0.356827\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.79481i | 0.131799i | 0.997826 | + | 0.0658996i | \(0.0209917\pi\) | ||||
−0.997826 | + | 0.0658996i | \(0.979008\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −23.3187 | + | 5.32235i | −0.808918 | + | 0.184630i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.7613 | − | 28.5757i | 0.476802 | − | 0.990090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.3487 | + | 40.5640i | 1.11947 | + | 1.40377i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.77191 | − | 7.76326i | −0.0612463 | − | 0.268338i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.43121 | + | 1.93883i | 0.0839348 | + | 0.0669358i | 0.664558 | − | 0.747236i | \(-0.268620\pi\) |
−0.580623 | + | 0.814172i | \(0.697191\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9070 | + | 10.8172i | −0.927828 | + | 0.373008i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.74468 | + | 5.37870i | 0.232299 | + | 0.185252i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.400513 | + | 1.75476i | 0.0137781 | + | 0.0603657i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.37696 | + | 1.72665i | 0.0473128 | + | 0.0593284i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.90730 | − | 3.96055i | 0.0654584 | − | 0.135926i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.85571 | − | 2.02126i | 0.303570 | − | 0.0692879i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.125350i | 0.00429189i | 0.999998 | + | 0.00214594i | \(0.000683076\pi\) | ||||
−0.999998 | + | 0.00214594i | \(0.999317\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −13.7612 | + | 10.9742i | −0.470623 | + | 0.375310i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.1606 | + | 7.30095i | −0.517875 | + | 0.249396i | −0.674516 | − | 0.738260i | \(-0.735648\pi\) |
0.156641 | + | 0.987656i | \(0.449933\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.35394 | + | 17.3471i | 0.285033 | + | 0.591877i | 0.993495 | − | 0.113871i | \(-0.0363252\pi\) |
−0.708463 | + | 0.705748i | \(0.750611\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.26805 | + | 2.53696i | 0.179535 | + | 0.0864593i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.00175 | − | 21.9141i | 0.170262 | − | 0.745964i | −0.815629 | − | 0.578575i | \(-0.803609\pi\) |
0.985891 | − | 0.167390i | \(-0.0535338\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.8692 | + | 55.0102i | −1.49160 | + | 1.87040i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.29573 | + | 1.89345i | 0.281738 | + | 0.0643048i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.3943 | −0.623983 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.4061 | 1.30134 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.39124 | − | 1.00227i | −0.148621 | − | 0.0339217i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.63306 | + | 2.04780i | −0.0552076 | + | 0.0692282i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.91217 | + | 17.1403i | −0.132105 | + | 0.578788i | 0.864934 | + | 0.501886i | \(0.167360\pi\) |
−0.997039 | + | 0.0769025i | \(0.975497\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.6835 | − | 11.4054i | −0.798823 | − | 0.384693i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.0183 | + | 41.5684i | 0.674434 | + | 1.40048i | 0.904148 | + | 0.427218i | \(0.140506\pi\) |
−0.229715 | + | 0.973258i | \(0.573779\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30.1751 | + | 14.5316i | −1.01547 | + | 0.489027i | −0.866162 | − | 0.499763i | \(-0.833420\pi\) |
−0.149312 | + | 0.988790i | \(0.547706\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −31.2070 | + | 24.8868i | −1.04901 | + | 0.836560i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 12.7174i | − | 0.427007i | −0.976942 | − | 0.213504i | \(-0.931512\pi\) | ||
0.976942 | − | 0.213504i | \(-0.0684875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.42204 | − | 2.15052i | 0.316005 | − | 0.0721261i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.60543 | + | 5.41024i | −0.0872853 | + | 0.181250i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.31497 | − | 11.6806i | −0.311714 | − | 0.390876i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.3632 | − | 67.3107i | −0.513536 | − | 2.24995i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.87157 | + | 5.47990i | 0.229435 | + | 0.182968i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.61546 | − | 6.90962i | 0.120582 | − | 0.230449i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.5918 | − | 10.8391i | −0.452808 | − | 0.361102i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.40181 | + | 10.5230i | 0.0799274 | + | 0.350185i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.66692 | − | 9.61401i | −0.254857 | − | 0.319580i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.8072 | + | 30.7474i | −0.491664 | + | 1.02095i | 0.496570 | + | 0.867997i | \(0.334593\pi\) |
−0.988233 | + | 0.152953i | \(0.951122\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.55070 | − | 1.49515i | 0.217273 | − | 0.0495911i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 22.9200i | − | 0.759372i | −0.925115 | − | 0.379686i | \(-0.876032\pi\) | ||
0.925115 | − | 0.379686i | \(-0.123968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.3636 | + | 17.8344i | −0.740126 | + | 0.590231i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.88499 | + | 3.79721i | −0.260670 | + | 0.125532i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.53148 | + | 11.4862i | 0.182665 | + | 0.379309i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.0233 | − | 18.7926i | −1.28726 | − | 0.619912i | −0.340015 | − | 0.940420i | \(-0.610432\pi\) |
−0.947246 | + | 0.320508i | \(0.896146\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.06277 | − | 26.5627i | 0.199775 | − | 0.875272i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.5870 | − | 15.7837i | 0.414308 | − | 0.519525i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.3118 | + | 3.72305i | 0.536328 | + | 0.122413i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 22.9637 | 0.754228 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −42.9957 | −1.41064 | −0.705321 | − | 0.708888i | \(-0.749197\pi\) | ||||
−0.705321 | + | 0.708888i | \(0.749197\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.6685 | + | 5.63042i | 0.808477 | + | 0.184530i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.5579 | + | 22.0169i | −0.574819 | + | 0.720800i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.10808 | + | 39.9051i | −0.297866 | + | 1.30504i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.4992 | + | 7.94560i | 0.539006 | + | 0.259571i | 0.683521 | − | 0.729931i | \(-0.260448\pi\) |
−0.144515 | + | 0.989503i | \(0.546162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.57087 | − | 17.7976i | −0.279700 | − | 0.580803i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.16806 | + | 2.00723i | −0.135875 | + | 0.0654339i | −0.500586 | − | 0.865687i | \(-0.666882\pi\) |
0.364711 | + | 0.931121i | \(0.381168\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6423 | − | 8.48691i | 0.346559 | − | 0.276372i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.8073i | 0.384091i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.7036 | − | 5.41018i | 0.770262 | − | 0.175807i | 0.180709 | − | 0.983537i | \(-0.442161\pi\) |
0.589554 | + | 0.807729i | \(0.299304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.4650 | + | 50.8020i | −0.794166 | + | 1.64910i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.3770 | + | 24.2979i | 0.628341 | + | 0.787915i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.259391 | + | 1.13647i | 0.00840250 | + | 0.0368138i | 0.978955 | − | 0.204074i | \(-0.0654184\pi\) |
−0.970553 | + | 0.240888i | \(0.922561\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 35.2267 | + | 28.0923i | 1.13991 | + | 0.909046i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.9024 | + | 7.45760i | −0.546378 | + | 0.241070i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.55311 | − | 2.83351i | −0.114736 | − | 0.0914989i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.43151 | − | 28.1783i | −0.207468 | − | 0.908977i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.2264 | − | 17.8393i | −0.458438 | − | 0.574863i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.9764 | − | 49.7876i | 0.771829 | − | 1.60272i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.6836 | + | 5.63387i | −0.793770 | + | 0.181173i | −0.600133 | − | 0.799900i | \(-0.704886\pi\) |
−0.193637 | + | 0.981073i | \(0.562029\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.2874i | 0.748098i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.1810 | − | 15.2963i | 0.615547 | − | 0.490882i | −0.265374 | − | 0.964145i | \(-0.585496\pi\) |
0.880921 | + | 0.473263i | \(0.156924\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.99671 | + | 2.88786i | −0.192246 | + | 0.0925807i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.02415 | + | 14.5858i | 0.224953 | + | 0.467120i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.2888 | − | 6.39953i | −0.425145 | − | 0.204739i | 0.209062 | − | 0.977902i | \(-0.432959\pi\) |
−0.634207 | + | 0.773163i | \(0.718673\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.08149 | − | 17.8822i | 0.130445 | − | 0.571517i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.163053 | − | 0.204461i | 0.00520587 | − | 0.00652795i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.1635 | − | 5.74340i | −0.802590 | − | 0.183186i | −0.198499 | − | 0.980101i | \(-0.563607\pi\) |
−0.604091 | + | 0.796915i | \(0.706464\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.6168 | 0.656904 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.37031 | −0.107278 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.4975 | + | 5.59139i | 0.778974 | + | 0.177796i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.9358 | + | 19.9829i | −0.506217 | + | 0.634776i | −0.967619 | − | 0.252415i | \(-0.918775\pi\) |
0.461402 | + | 0.887191i | \(0.347347\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.73712 | + | 11.9921i | −0.0868599 | + | 0.380558i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.47501 | + | 3.59978i | 0.236974 | + | 0.114121i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.3639 | + | 36.0564i | 0.549919 | + | 1.14192i | 0.971918 | + | 0.235322i | \(0.0756144\pi\) |
−0.421999 | + | 0.906596i | \(0.638671\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −21.9277 | + | 10.5598i | −0.693760 | + | 0.334097i |
(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 | 232.2.q.a.209.3 | yes | 48 | |
4.3 | odd | 2 | 464.2.y.e.209.6 | 48 | |||
29.5 | even | 14 | inner | 232.2.q.a.121.3 | ✓ | 48 | |
29.11 | odd | 28 | 6728.2.a.bf.1.16 | 24 | |||
29.18 | odd | 28 | 6728.2.a.be.1.9 | 24 | |||
116.63 | odd | 14 | 464.2.y.e.353.6 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
232.2.q.a.121.3 | ✓ | 48 | 29.5 | even | 14 | inner | |
232.2.q.a.209.3 | yes | 48 | 1.1 | even | 1 | trivial | |
464.2.y.e.209.6 | 48 | 4.3 | odd | 2 | |||
464.2.y.e.353.6 | 48 | 116.63 | odd | 14 | |||
6728.2.a.be.1.9 | 24 | 29.18 | odd | 28 | |||
6728.2.a.bf.1.16 | 24 | 29.11 | odd | 28 |