Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(47,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.bh (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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 47.18 | ||
Character | \(\chi\) | \(=\) | 864.47 |
Dual form | 864.2.bh.b.239.18 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{18}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.166515 | − | 1.72403i | 0.0961374 | − | 0.995368i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.135936 | + | 0.770931i | 0.0607924 | + | 0.344771i | 0.999999 | + | 0.00141816i | \(0.000451416\pi\) |
−0.939207 | + | 0.343352i | \(0.888437\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.51012 | + | 2.99144i | −0.948735 | + | 1.13066i | 0.0425722 | + | 0.999093i | \(0.486445\pi\) |
−0.991308 | + | 0.131565i | \(0.958000\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.94455 | − | 0.574153i | −0.981515 | − | 0.191384i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00834 | + | 0.706778i | 1.20856 | + | 0.213101i | 0.741395 | − | 0.671069i | \(-0.234165\pi\) |
0.467164 | + | 0.884171i | \(0.345276\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.688932 | − | 1.89283i | 0.191075 | − | 0.524976i | −0.806750 | − | 0.590894i | \(-0.798775\pi\) |
0.997825 | + | 0.0659179i | \(0.0209976\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.35174 | − | 0.105986i | 0.349018 | − | 0.0273654i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.24509 | − | 1.87355i | 0.787049 | − | 0.454403i | −0.0518736 | − | 0.998654i | \(-0.516519\pi\) |
0.838923 | + | 0.544251i | \(0.183186\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.03521 | − | 3.52509i | 0.466909 | − | 0.808711i | −0.532376 | − | 0.846508i | \(-0.678701\pi\) |
0.999285 | + | 0.0377971i | \(0.0120341\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.73936 | + | 4.82563i | 1.03421 | + | 1.05304i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.29440 | − | 1.08613i | 0.269901 | − | 0.226474i | −0.497784 | − | 0.867301i | \(-0.665853\pi\) |
0.767685 | + | 0.640827i | \(0.221409\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.12261 | − | 1.50051i | 0.824522 | − | 0.300101i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.48017 | + | 4.98087i | −0.284858 | + | 0.958570i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.97408 | − | 1.44645i | 0.737968 | − | 0.268598i | 0.0544344 | − | 0.998517i | \(-0.482664\pi\) |
0.683534 | + | 0.729919i | \(0.260442\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.62062 | + | 6.69839i | 1.00949 | + | 1.20307i | 0.979069 | + | 0.203530i | \(0.0652414\pi\) |
0.0304242 | + | 0.999537i | \(0.490314\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.88595 | − | 6.79279i | 0.328302 | − | 1.18247i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.64741 | − | 1.52848i | −0.447494 | − | 0.258361i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.04670 | − | 5.22312i | 1.48727 | − | 0.858675i | 0.487374 | − | 0.873193i | \(-0.337955\pi\) |
0.999895 | + | 0.0145181i | \(0.00462140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.14857 | − | 1.50292i | −0.504174 | − | 0.240660i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.48236 | + | 9.56770i | −0.543853 | + | 1.49422i | 0.298026 | + | 0.954558i | \(0.403672\pi\) |
−0.841879 | + | 0.539666i | \(0.818550\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.751767 | − | 4.26348i | 0.114643 | − | 0.650175i | −0.872283 | − | 0.489002i | \(-0.837361\pi\) |
0.986926 | − | 0.161173i | \(-0.0515277\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0423626 | − | 2.34809i | 0.00631505 | − | 0.350032i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.29698 | + | 1.08829i | 0.189184 | + | 0.158744i | 0.732460 | − | 0.680810i | \(-0.238372\pi\) |
−0.543276 | + | 0.839554i | \(0.682816\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.43250 | − | 8.12409i | −0.204642 | − | 1.16058i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.68970 | − | 5.90659i | −0.376633 | − | 0.827089i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.8358 | −1.48841 | −0.744203 | − | 0.667954i | \(-0.767170\pi\) | ||||
−0.744203 | + | 0.667954i | \(0.767170\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.18622i | 0.429630i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.73846 | − | 4.09574i | −0.760078 | − | 0.542494i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.48911 | + | 0.438898i | −0.324055 | + | 0.0571396i | −0.333309 | − | 0.942818i | \(-0.608165\pi\) |
0.00925433 | + | 0.999957i | \(0.497054\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.41745 | + | 2.88100i | −0.309523 | + | 0.368875i | −0.898271 | − | 0.439442i | \(-0.855176\pi\) |
0.588749 | + | 0.808316i | \(0.299621\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.10870 | − | 7.36725i | 1.14759 | − | 0.928186i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.55289 | + | 0.273816i | 0.192612 | + | 0.0339627i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.89251 | + | 1.05279i | 0.353376 | + | 0.128618i | 0.512608 | − | 0.858623i | \(-0.328680\pi\) |
−0.159232 | + | 0.987241i | \(0.550902\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.65698 | − | 2.41244i | −0.199477 | − | 0.290423i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.46797 | − | 6.00671i | −0.411573 | − | 0.712865i | 0.583489 | − | 0.812121i | \(-0.301687\pi\) |
−0.995062 | + | 0.0992558i | \(0.968354\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.963671 | − | 1.66913i | 0.112789 | − | 0.195356i | −0.804105 | − | 0.594488i | \(-0.797355\pi\) |
0.916894 | + | 0.399131i | \(0.130688\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.90044 | − | 7.35735i | −0.219444 | − | 0.849553i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.1757 | + | 10.2166i | −1.38755 | + | 1.16429i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.21520 | + | 6.08622i | 0.249230 | + | 0.684753i | 0.999715 | + | 0.0238663i | \(0.00759760\pi\) |
−0.750485 | + | 0.660887i | \(0.770180\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.34070 | + | 3.38124i | 0.926744 | + | 0.375693i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.31513 | − | 3.61329i | −0.144354 | − | 0.396610i | 0.846353 | − | 0.532623i | \(-0.178793\pi\) |
−0.990707 | + | 0.136013i | \(0.956571\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.88550 | + | 2.24705i | 0.204511 | + | 0.243727i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.83197 | − | 7.09228i | −0.196408 | − | 0.760372i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.55395 | − | 3.78393i | −0.694718 | − | 0.401095i | 0.110659 | − | 0.993858i | \(-0.464704\pi\) |
−0.805377 | + | 0.592763i | \(0.798037\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.93298 | + | 6.81212i | 0.412288 | + | 0.714104i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.4841 | − | 8.57472i | 1.29454 | − | 0.889157i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.99426 | + | 1.08982i | 0.307204 | + | 0.111813i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.481780 | + | 2.73231i | −0.0489174 | + | 0.277424i | −0.999449 | − | 0.0332049i | \(-0.989429\pi\) |
0.950531 | + | 0.310629i | \(0.100540\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.3969 | − | 4.38254i | −1.14543 | − | 0.440461i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.17833 | − | 0.988733i | −0.117248 | − | 0.0983826i | 0.582279 | − | 0.812989i | \(-0.302161\pi\) |
−0.699527 | + | 0.714607i | \(0.746606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.3730 | − | 3.23966i | 1.81035 | − | 0.319213i | 0.836766 | − | 0.547561i | \(-0.184444\pi\) |
0.973580 | + | 0.228348i | \(0.0733325\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.07598 | + | 4.30969i | −0.300185 | + | 0.420583i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.25626i | 0.701489i | 0.936471 | + | 0.350745i | \(0.114071\pi\) | ||||
−0.936471 | + | 0.350745i | \(0.885929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.50798i | 0.431786i | 0.976417 | + | 0.215893i | \(0.0692663\pi\) | ||||
−0.976417 | + | 0.215893i | \(0.930734\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.49839 | − | 16.4665i | −0.711716 | − | 1.56293i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.23012 | − | 0.569558i | 0.303864 | − | 0.0535795i | −0.0196371 | − | 0.999807i | \(-0.506251\pi\) |
0.323501 | + | 0.946228i | \(0.395140\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.01328 | + | 0.850247i | 0.0944893 | + | 0.0792859i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.11536 | + | 5.17796i | −0.288016 | + | 0.478703i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.54093 | + | 14.4103i | −0.232927 | + | 1.32099i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.23060 | + | 1.90378i | 0.475509 | + | 0.173071i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.9151 | + | 7.59685i | 1.43502 | + | 0.684985i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.67425 | + | 6.36400i | 0.328635 | + | 0.569213i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1332 | − | 9.89185i | −1.52033 | − | 0.877760i | −0.999713 | − | 0.0239670i | \(-0.992370\pi\) |
−0.520612 | − | 0.853793i | \(-0.674296\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.22518 | − | 2.00600i | −0.636142 | − | 0.176618i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.3636 | + | 13.5426i | 0.992843 | + | 1.18322i | 0.983062 | + | 0.183272i | \(0.0586688\pi\) |
0.00978049 | + | 0.999952i | \(0.496887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.43648 | + | 14.9366i | 0.471403 | + | 1.29517i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.04112 | − | 0.464026i | −0.347804 | − | 0.0399370i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.87855 | + | 13.4037i | 0.416803 | + | 1.14516i | 0.953503 | + | 0.301383i | \(0.0974483\pi\) |
−0.536701 | + | 0.843773i | \(0.680329\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.9256 | − | 11.6849i | 1.18115 | − | 0.991104i | 0.181181 | − | 0.983450i | \(-0.442008\pi\) |
0.999971 | − | 0.00765422i | \(-0.00243644\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.09222 | − | 2.05481i | 0.176196 | − | 0.173046i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.09928 | − | 7.10016i | 0.342799 | − | 0.593745i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.65533 | + | 2.86712i | 0.137468 | + | 0.238101i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.2447 | + | 1.11688i | −1.17488 | + | 0.0921188i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.3251 | − | 6.66979i | −1.50125 | − | 0.546411i | −0.544867 | − | 0.838522i | \(-0.683420\pi\) |
−0.956384 | + | 0.292112i | \(0.905642\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.07581 | − | 1.42398i | −0.657200 | − | 0.115882i | −0.164904 | − | 0.986310i | \(-0.552731\pi\) |
−0.492296 | + | 0.870428i | \(0.663842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.6310 | + | 3.65358i | −0.859466 | + | 0.295375i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.39995 | + | 5.24366i | −0.353413 | + | 0.421181i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3569 | + | 2.35518i | −1.06600 | + | 0.187964i | −0.679015 | − | 0.734124i | \(-0.737593\pi\) |
−0.386981 | + | 0.922088i | \(0.626482\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.80432 | + | 18.6811i | −0.143091 | + | 1.48151i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.59843i | 0.520029i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.2904 | −1.04098 | −0.520492 | − | 0.853867i | \(-0.674251\pi\) | ||||
−0.520492 | + | 0.853867i | \(0.674251\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.49314 | + | 0.530554i | 0.427640 | + | 0.0413036i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.24589 | − | 7.06577i | −0.0964095 | − | 0.546765i | −0.994306 | − | 0.106559i | \(-0.966017\pi\) |
0.897897 | − | 0.440206i | \(-0.145095\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.85041 | + | 5.74818i | 0.526955 | + | 0.442168i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.01671 | + | 9.21126i | −0.613053 | + | 0.704403i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.595900 | − | 3.37951i | 0.0453054 | − | 0.256940i | −0.953740 | − | 0.300634i | \(-0.902802\pi\) |
0.999045 | + | 0.0436944i | \(0.0139128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.85955 | + | 16.0990i | −0.442941 | + | 1.21697i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.342198 | + | 4.36438i | 0.0257212 | + | 0.328047i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.0731 | + | 6.39304i | −0.827641 | + | 0.477838i | −0.853044 | − | 0.521839i | \(-0.825246\pi\) |
0.0254036 | + | 0.999677i | \(0.491913\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.359928 | − | 0.207804i | −0.0267532 | − | 0.0154460i | 0.486564 | − | 0.873645i | \(-0.338250\pi\) |
−0.513317 | + | 0.858199i | \(0.671583\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.56439 | + | 4.64748i | 0.337409 | + | 0.343551i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.25643 | + | 6.26437i | 0.386461 | + | 0.460566i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.3316 | − | 5.21627i | 1.04803 | − | 0.381451i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.1846 | − | 16.9304i | −0.813560 | − | 1.23151i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.9508 | + | 9.08136i | −1.80538 | + | 0.657104i | −0.807656 | + | 0.589654i | \(0.799264\pi\) |
−0.997723 | + | 0.0674507i | \(0.978513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.97492 | − | 7.53086i | 0.646029 | − | 0.542083i | −0.259834 | − | 0.965653i | \(-0.583668\pi\) |
0.905863 | + | 0.423570i | \(0.139223\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.730646 | − | 2.63163i | 0.0523226 | − | 0.188455i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.8898 | − | 18.8617i | 0.775866 | − | 1.34384i | −0.158440 | − | 0.987369i | \(-0.550646\pi\) |
0.934306 | − | 0.356471i | \(-0.116020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.674947 | + | 0.389681i | −0.0478457 | + | 0.0276237i | −0.523732 | − | 0.851883i | \(-0.675461\pi\) |
0.475886 | + | 0.879507i | \(0.342127\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.29668 | − | 4.81146i | 0.161995 | − | 0.339374i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.64845 | + | 15.5190i | −0.396443 | + | 1.08922i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.84941 | − | 1.38406i | −0.548227 | − | 0.0966672i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.43502 | + | 2.45497i | −0.308255 | + | 0.170632i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 10.6493 | − | 12.6913i | 0.736625 | − | 0.877875i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.44923 | − | 8.21900i | −0.0997692 | − | 0.565819i | −0.993181 | − | 0.116581i | \(-0.962807\pi\) |
0.893412 | − | 0.449238i | \(-0.148305\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.9332 | + | 4.97868i | −0.749131 | + | 0.341133i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.38904 | 0.231131 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −34.1463 | −2.31800 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.71716 | − | 1.93933i | −0.183608 | − | 0.131048i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.31066 | − | 7.43314i | −0.0881647 | − | 0.500007i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.5510 | − | 16.1495i | 0.907444 | − | 1.08145i | −0.0889020 | − | 0.996040i | \(-0.528336\pi\) |
0.996346 | − | 0.0854092i | \(-0.0272198\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0007 | + | 2.05130i | −0.866715 | + | 0.136754i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 11.9451 | + | 2.10624i | 0.792824 | + | 0.139796i | 0.555371 | − | 0.831603i | \(-0.312576\pi\) |
0.237453 | + | 0.971399i | \(0.423687\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.11109 | − | 14.0426i | 0.337751 | − | 0.927962i | −0.648281 | − | 0.761401i | \(-0.724512\pi\) |
0.986031 | − | 0.166560i | \(-0.0532661\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.5863 | + | 22.6924i | 1.02550 | + | 1.49305i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.7082 | + | 8.49179i | −0.963567 | + | 0.556315i | −0.897269 | − | 0.441484i | \(-0.854452\pi\) |
−0.0662977 | + | 0.997800i | \(0.521119\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.662693 | + | 1.14782i | −0.0432293 | + | 0.0748754i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.8617 | − | 2.80563i | 0.705542 | − | 0.182245i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.41696 | + | 7.90177i | −0.609132 | + | 0.511123i | −0.894366 | − | 0.447335i | \(-0.852373\pi\) |
0.285234 | + | 0.958458i | \(0.407929\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.2458 | − | 8.82476i | 1.56181 | − | 0.568453i | 0.590661 | − | 0.806920i | \(-0.298867\pi\) |
0.971151 | + | 0.238467i | \(0.0766448\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.21820 | − | 13.8166i | 0.463048 | − | 0.886333i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.06838 | − | 2.20871i | 0.387695 | − | 0.141109i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.27026 | − | 6.28085i | −0.335339 | − | 0.399641i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.44840 | + | 1.66565i | −0.408651 | + | 0.105556i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.90919 | − | 5.72107i | −0.625463 | − | 0.361111i | 0.153530 | − | 0.988144i | \(-0.450936\pi\) |
−0.778993 | + | 0.627033i | \(0.784269\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.95603 | − | 3.43872i | 0.374453 | − | 0.216190i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.18795 | − | 2.87649i | 0.262259 | − | 0.180133i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.38303 | + | 6.54733i | −0.148650 | + | 0.408411i | −0.991561 | − | 0.129641i | \(-0.958618\pi\) |
0.842911 | + | 0.538052i | \(0.180840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.08364 | + | 40.1733i | −0.440156 | + | 2.49625i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.5323 | + | 1.97740i | −0.775732 | + | 0.122398i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.78611 | + | 8.21152i | 0.603437 | + | 0.506344i | 0.892548 | − | 0.450952i | \(-0.148915\pi\) |
−0.289111 | + | 0.957296i | \(0.593360\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.47297 | − | 8.35361i | −0.0904837 | − | 0.513158i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.61493 | + | 10.6691i | −0.466026 | + | 0.652939i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.2970 | 0.749762 | 0.374881 | − | 0.927073i | \(-0.377684\pi\) | ||||
0.374881 | + | 0.927073i | \(0.377684\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0290908i | 0.00176714i | 1.00000 | 0.000883569i | \(0.000281249\pi\) | |||||
−1.00000 | 0.000883569i | \(0.999719\pi\) | ||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 12.3992 | − | 5.64625i | 0.750433 | − | 0.341726i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.5853 | − | 3.10077i | 1.06043 | − | 0.186983i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.42372 | + | 10.0390i | −0.506133 | + | 0.603185i | −0.957244 | − | 0.289282i | \(-0.906583\pi\) |
0.451111 | + | 0.892468i | \(0.351028\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.7043 | − | 22.9508i | −0.760585 | − | 1.37403i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.87063 | − | 1.03515i | −0.350213 | − | 0.0617519i | −0.00422519 | − | 0.999991i | \(-0.501345\pi\) |
−0.345987 | + | 0.938239i | \(0.612456\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.2795 | − | 7.38115i | −1.20549 | − | 0.438764i | −0.340355 | − | 0.940297i | \(-0.610547\pi\) |
−0.865139 | + | 0.501533i | \(0.832770\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.37747 | − | 4.98071i | 0.140829 | − | 0.295032i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −19.8801 | − | 34.4333i | −1.17348 | − | 2.03254i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.47961 | + | 2.56276i | −0.0870359 | + | 0.150751i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.63036 | + | 1.28557i | 0.271437 | + | 0.0753617i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.243742 | + | 0.204524i | −0.0142396 | + | 0.0119484i | −0.649880 | − | 0.760037i | \(-0.725181\pi\) |
0.635640 | + | 0.771986i | \(0.280736\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.676719 | − | 1.85927i | −0.0394001 | − | 0.108251i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.45337 | + | 18.9189i | −0.548540 | + | 1.09778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.16410 | − | 3.19834i | −0.0673217 | − | 0.184965i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8669 | + | 12.9507i | 0.626360 | + | 0.746466i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.90081 | + | 1.86683i | −0.109199 | + | 0.107247i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.54967 | − | 1.47205i | −0.145994 | − | 0.0842895i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.67206 | − | 6.36020i | −0.209576 | − | 0.362996i | 0.742005 | − | 0.670394i | \(-0.233875\pi\) |
−0.951581 | + | 0.307398i | \(0.900542\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.52588 | − | 32.2150i | −0.143692 | − | 1.83265i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.8000 | − | 6.47869i | −1.00935 | − | 0.367373i | −0.216166 | − | 0.976357i | \(-0.569355\pi\) |
−0.793183 | + | 0.608984i | \(0.791577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.61511 | + | 26.1736i | −0.260861 | + | 1.47942i | 0.519705 | + | 0.854346i | \(0.326042\pi\) |
−0.780566 | + | 0.625073i | \(0.785069\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.91783 | + | 6.02070i | 0.389776 | + | 0.339228i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.1863 | + | 10.2255i | 0.684450 | + | 0.574322i | 0.917303 | − | 0.398190i | \(-0.130361\pi\) |
−0.232853 | + | 0.972512i | \(0.574806\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.9518 | − | 2.98905i | 0.949116 | − | 0.167355i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.5100 | + | 1.20828i | 0.698240 | + | 0.0674394i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 15.2523i | − | 0.848660i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 8.83713i | − | 0.490196i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.77188 | + | 0.750646i | 0.429786 | + | 0.0415108i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.51114 | + | 1.14809i | −0.358971 | + | 0.0632962i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.81198 | + | 3.19863i | 0.209525 | + | 0.175813i | 0.741511 | − | 0.670941i | \(-0.234110\pi\) |
−0.531986 | + | 0.846753i | \(0.678554\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −29.6373 | + | 10.1855i | −1.62411 | + | 0.558163i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.418430 | + | 2.37303i | −0.0228613 | + | 0.129653i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.29261 | + | 1.56238i | 0.233834 | + | 0.0851085i | 0.456279 | − | 0.889837i | \(-0.349182\pi\) |
−0.222446 | + | 0.974945i | \(0.571404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.444070 | − | 5.66366i | −0.0241186 | − | 0.307608i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.7950 | + | 30.8219i | 0.963656 | + | 1.66910i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.22536 | + | 2.43951i | 0.228148 | + | 0.131721i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.63458 | − | 1.60535i | 0.0880027 | − | 0.0864293i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.1321 | − | 19.2255i | −0.866018 | − | 1.03208i | −0.999160 | − | 0.0409830i | \(-0.986951\pi\) |
0.133142 | − | 0.991097i | \(-0.457493\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.75352 | + | 21.3026i | 0.415036 | + | 1.14030i | 0.954478 | + | 0.298280i | \(0.0964130\pi\) |
−0.539442 | + | 0.842023i | \(0.681365\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.40820 | + | 6.23318i | 0.448796 | + | 0.332703i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.8634 | − | 32.5944i | −0.631425 | − | 1.73482i | −0.677123 | − | 0.735869i | \(-0.736774\pi\) |
0.0456988 | − | 0.998955i | \(-0.485449\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.15933 | − | 3.49009i | 0.220754 | − | 0.185235i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.4207 | + | 6.78017i | 1.29248 | + | 0.358844i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.5606 | + | 23.4877i | −0.715702 | + | 1.23963i | 0.246986 | + | 0.969019i | \(0.420560\pi\) |
−0.962688 | + | 0.270613i | \(0.912774\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.21583 | + | 2.10588i | 0.0639911 | + | 0.110836i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.15315 | − | 8.70069i | 0.217984 | − | 0.456668i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.41778 | + | 0.516029i | 0.0742099 | + | 0.0270102i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.46503 | − | 1.13996i | −0.337472 | − | 0.0595054i | 0.00234427 | − | 0.999997i | \(-0.499254\pi\) |
−0.339816 | + | 0.940492i | \(0.610365\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.7473 | − | 26.1731i | 0.819771 | − | 1.36252i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.1990 | − | 32.4145i | 1.41210 | − | 1.68288i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.6886 | − | 1.88468i | 0.553432 | − | 0.0975850i | 0.110064 | − | 0.993925i | \(-0.464894\pi\) |
0.443368 | + | 0.896339i | \(0.353783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.5835 | − | 5.27482i | 0.598171 | − | 0.272390i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.51875i | − | 0.438738i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.56361 | −0.337150 | −0.168575 | − | 0.985689i | \(-0.553917\pi\) | ||||
−0.168575 | + | 0.985689i | \(0.553917\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.9068 | + | 27.8910i | −1.01985 | + | 1.42890i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.26029 | + | 12.8188i | 0.115496 | + | 0.655008i | 0.986504 | + | 0.163739i | \(0.0523556\pi\) |
−0.871008 | + | 0.491269i | \(0.836533\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.53140 | − | 7.99780i | −0.485765 | − | 0.407606i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.66150 | + | 12.1224i | −0.236957 | + | 0.616215i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.53930 | + | 8.72982i | −0.0780458 | + | 0.442620i | 0.920596 | + | 0.390516i | \(0.127704\pi\) |
−0.998642 | + | 0.0521031i | \(0.983408\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.16551 | − | 5.94970i | 0.109515 | − | 0.300889i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.2401 | − | 17.3361i | 1.27319 | − | 0.874492i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.39093 | + | 2.53510i | −0.220932 | + | 0.127555i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.3068 | − | 7.68271i | −0.667852 | − | 0.385584i | 0.127411 | − | 0.991850i | \(-0.459333\pi\) |
−0.795262 | + | 0.606266i | \(0.792667\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 26.6564 | − | 6.88548i | 1.33449 | − | 0.344705i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4543 | + | 17.2260i | 0.721813 | + | 0.860224i | 0.994806 | − | 0.101792i | \(-0.0324578\pi\) |
−0.272992 | + | 0.962016i | \(0.588013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.5511 | − | 6.02412i | 0.824470 | − | 0.300083i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.47290 | + | 6.88973i | −0.0731890 | + | 0.342353i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.9538 | − | 14.5420i | 1.98044 | − | 0.720820i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.1785 | + | 12.7363i | −0.750530 | + | 0.629769i | −0.935643 | − | 0.352948i | \(-0.885179\pi\) |
0.185113 | + | 0.982717i | \(0.440735\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.9207 | − | 6.17884i | 1.17992 | − | 0.304780i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.93503 | − | 8.54772i | 0.242837 | − | 0.420606i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.60682 | − | 1.50505i | 0.127964 | − | 0.0738799i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.8264 | − | 25.9538i | −0.872960 | − | 1.27096i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.96698 | + | 10.8992i | −0.193800 | + | 0.532460i | −0.998090 | − | 0.0617762i | \(-0.980323\pi\) |
0.804290 | + | 0.594237i | \(0.202546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.4892 | − | 4.84709i | −1.33974 | − | 0.236233i | −0.542584 | − | 0.840002i | \(-0.682554\pi\) |
−0.797159 | + | 0.603769i | \(0.793665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.19417 | − | 3.94920i | −0.155306 | − | 0.192016i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.5669 | − | 12.5932i | 0.512572 | − | 0.610859i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.55027 | − | 14.4633i | −0.123416 | − | 0.699929i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.5583 | − | 8.24956i | −0.558039 | − | 0.398292i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.5855 | 1.85860 | 0.929298 | − | 0.369330i | \(-0.120413\pi\) | ||||
0.929298 | + | 0.369330i | \(0.120413\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.4071 | 1.31710 | 0.658551 | − | 0.752536i | \(-0.271170\pi\) | ||||
0.658551 | + | 0.752536i | \(0.271170\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.21862 | − | 2.37642i | 0.250214 | − | 0.113941i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.19433 | − | 6.77337i | −0.0571325 | − | 0.324014i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.90532 | + | 3.46242i | −0.138663 | + | 0.165252i | −0.830907 | − | 0.556411i | \(-0.812178\pi\) |
0.692244 | + | 0.721664i | \(0.256622\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.446419 | + | 24.7442i | −0.0212580 | + | 1.17830i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.65023 | − | 1.34894i | −0.363473 | − | 0.0640902i | −0.0110709 | − | 0.999939i | \(-0.503524\pi\) |
−0.352402 | + | 0.935849i | \(0.614635\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.02623 | − | 5.56701i | 0.0960524 | − | 0.263902i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.5503 | + | 30.4824i | −0.688206 | + | 1.44177i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.99255 | − | 3.45980i | 0.282806 | − | 0.163278i | −0.351887 | − | 0.936042i | \(-0.614460\pi\) |
0.634693 | + | 0.772764i | \(0.281127\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.7207 | + | 35.8893i | −0.975700 | + | 1.68996i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.79973 | + | 13.6858i | −0.178527 | + | 0.643015i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.71704 | + | 3.95806i | −0.221138 | + | 0.185557i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.03870 | − | 0.742024i | 0.0953661 | − | 0.0347104i | −0.293896 | − | 0.955837i | \(-0.594952\pi\) |
0.389263 | + | 0.921127i | \(0.372730\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.52866 | + | 18.9365i | 0.211380 | + | 0.883882i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.55121 | − | 1.29254i | 0.165396 | − | 0.0601994i | −0.257995 | − | 0.966146i | \(-0.583062\pi\) |
0.423391 | + | 0.905947i | \(0.360840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.61147 | + | 3.11222i | 0.121365 | + | 0.144637i | 0.823306 | − | 0.567598i | \(-0.192127\pi\) |
−0.701941 | + | 0.712235i | \(0.747683\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.30756 | + | 8.45879i | 0.385254 | + | 0.392267i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.2451 | + | 7.06974i | 0.566638 | + | 0.327148i | 0.755805 | − | 0.654796i | \(-0.227246\pi\) |
−0.189168 | + | 0.981945i | \(0.560579\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.4099 | + | 6.01015i | −0.480684 | + | 0.277523i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.83627 | + | 23.4198i | 0.0846111 | + | 1.07913i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.02667 | − | 16.5581i | 0.277106 | − | 0.761344i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.10096 | − | 17.5864i | 0.142282 | − | 0.806920i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 31.9064 | + | 6.22138i | 1.46089 | + | 0.284857i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.17960 | + | 5.18530i | 0.282353 | + | 0.236922i | 0.772954 | − | 0.634462i | \(-0.218778\pi\) |
−0.490601 | + | 0.871384i | \(0.663223\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.65389 | − | 20.7222i | −0.166603 | − | 0.944852i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.3759 | + | 1.09874i | 0.517620 | + | 0.0499943i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.17191 | −0.0986216 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.8287i | − | 0.717266i | −0.933479 | − | 0.358633i | \(-0.883243\pi\) | ||
0.933479 | − | 0.358633i | \(-0.116757\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.21305 | + | 22.9130i | −0.100078 | + | 1.03616i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.3135 | + | 3.93448i | −1.00700 | + | 0.177561i | −0.652735 | − | 0.757586i | \(-0.726379\pi\) |
−0.354261 | + | 0.935147i | \(0.615268\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.1862 | − | 12.1395i | 0.458765 | − | 0.546735i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.82938 | − | 9.38198i | 0.0822245 | − | 0.421689i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.6737 | + | 4.70330i | 1.19648 | + | 0.210972i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.80455 | + | 1.74871i | 0.215081 | + | 0.0782832i | 0.447314 | − | 0.894377i | \(-0.352381\pi\) |
−0.232232 | + | 0.972660i | \(0.574603\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.3890 | + | 0.971385i | −0.553501 | + | 0.0433983i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.79569 | − | 10.0384i | −0.258417 | − | 0.447592i | 0.707401 | − | 0.706812i | \(-0.249868\pi\) |
−0.965818 | + | 0.259221i | \(0.916534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.602068 | − | 1.04281i | 0.0267917 | − | 0.0464045i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.0507 | − | 10.8531i | 0.490780 | − | 0.482005i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.52773 | + | 1.28192i | −0.0677153 | + | 0.0568199i | −0.676017 | − | 0.736886i | \(-0.736295\pi\) |
0.608302 | + | 0.793706i | \(0.291851\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.57417 | + | 7.07247i | 0.113874 | + | 0.312868i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.5456 | + | 15.3548i | 0.642203 | + | 0.677933i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.99510 | + | 13.7239i | 0.220110 | + | 0.604748i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.42954 | + | 5.27892i | 0.194811 | + | 0.232167i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.72715 | − | 1.59009i | −0.251394 | − | 0.0697971i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.0614 | − | 13.3145i | −1.01034 | − | 0.583319i | −0.0990474 | − | 0.995083i | \(-0.531580\pi\) |
−0.911291 | + | 0.411764i | \(0.864913\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.5145 | − | 21.6758i | −0.547223 | − | 0.947818i | −0.998463 | − | 0.0554155i | \(-0.982352\pi\) |
0.451240 | − | 0.892402i | \(-0.350982\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26.7794 | + | 12.7828i | 1.16875 | + | 0.557885i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 30.7892 | + | 11.2063i | 1.34120 | + | 0.488156i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.49812 | + | 19.8388i | −0.152092 | + | 0.862557i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.58130 | + | 0.136777i | 0.329000 | + | 0.00593561i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.7109 | + | 13.1830i | 0.680514 | + | 0.571019i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.59407 | + | 0.986386i | −0.241853 | + | 0.0426452i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.17795 | + | 20.1548i | 0.396058 | + | 0.869745i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 33.5765i | − | 1.44624i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 41.3952i | − | 1.77972i | −0.456233 | − | 0.889860i | \(-0.650802\pi\) | ||
0.456233 | − | 0.889860i | \(-0.349198\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.418194 | + | 0.585923i | −0.0179464 | + | 0.0251443i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.47534 | + | 0.612796i | −0.148867 | + | 0.0262493i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.3233 | − | 11.1795i | −0.569662 | − | 0.478003i | 0.311872 | − | 0.950124i | \(-0.399044\pi\) |
−0.881534 | + | 0.472121i | \(0.843488\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.77242 | − | 7.09526i | 0.374398 | − | 0.302818i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.98924 | − | 16.9528i | 0.127346 | − | 0.722214i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.7670 | − | 8.65048i | −1.01068 | − | 0.367856i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.6752 | − | 8.01912i | 0.495586 | − | 0.340393i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.0747 | − | 36.5024i | −0.892963 | − | 1.54666i | −0.836306 | − | 0.548263i | \(-0.815289\pi\) |
−0.0566567 | − | 0.998394i | \(-0.518044\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.55211 | − | 4.36021i | −0.319420 | − | 0.184417i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.60657 | − | 25.5766i | −0.278930 | − | 1.07985i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.76403 | + | 2.10229i | 0.0743450 | + | 0.0886009i | 0.801935 | − | 0.597411i | \(-0.203804\pi\) |
−0.727590 | + | 0.686012i | \(0.759360\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.878179 | + | 2.41278i | 0.0369453 | + | 0.101506i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −31.0509 | + | 16.4634i | −1.30402 | + | 0.691398i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.717043 | − | 1.97006i | −0.0300600 | − | 0.0825892i | 0.923755 | − | 0.382984i | \(-0.125104\pi\) |
−0.953815 | + | 0.300395i | \(0.902881\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.63316 | − | 2.20949i | 0.110194 | − | 0.0924641i | −0.586026 | − | 0.810293i | \(-0.699308\pi\) |
0.696220 | + | 0.717828i | \(0.254864\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.5018 | + | 44.5281i | 0.480496 | + | 1.86019i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.70655 | − | 6.41994i | 0.154574 | − | 0.267730i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7440 | − | 23.8053i | −0.572171 | − | 0.991029i | −0.996343 | − | 0.0854469i | \(-0.972768\pi\) |
0.424172 | − | 0.905582i | \(-0.360565\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.4889 | − | 16.7270i | −0.477464 | − | 0.695151i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.1101 | + | 5.13565i | 0.585384 | + | 0.213062i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −43.4333 | − | 7.65847i | −1.79883 | − | 0.317181i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.41534 | − | 1.69786i | −0.182552 | − | 0.0701978i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.95898 | + | 2.33462i | −0.0808557 | + | 0.0963600i | −0.804956 | − | 0.593335i | \(-0.797811\pi\) |
0.724100 | + | 0.689695i | \(0.242255\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.0516 | − | 6.18054i | 1.44428 | − | 0.254665i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.7048 | − | 21.9151i | −1.26303 | − | 0.901466i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.4432i | − | 1.45548i | −0.685854 | − | 0.727740i | \(-0.740571\pi\) | ||
0.685854 | − | 0.727740i | \(-0.259429\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.4548 | −0.469599 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.559432 | + | 1.22852i | 0.0228960 | + | 0.0502798i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0.864787 | + | 4.90445i | 0.0353342 | + | 0.200390i | 0.997365 | − | 0.0725519i | \(-0.0231143\pi\) |
−0.962030 | + | 0.272942i | \(0.912003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.85816 | − | 7.43288i | −0.361332 | − | 0.303193i | 0.443989 | − | 0.896032i | \(-0.353563\pi\) |
−0.805321 | + | 0.592839i | \(0.798007\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.91265 | − | 4.76072i | −0.322228 | − | 0.193871i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.756658 | + | 4.29122i | −0.0307625 | + | 0.174463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0821746 | − | 0.225773i | 0.00333536 | − | 0.00916384i | −0.938014 | − | 0.346598i | \(-0.887337\pi\) |
0.941349 | + | 0.337434i | \(0.109559\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.8146 | + | 12.3222i | 1.04606 | + | 0.499322i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.95348 | − | 1.70519i | 0.119485 | − | 0.0689848i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.5946 | − | 13.0450i | −0.912588 | − | 0.526883i | −0.0313252 | − | 0.999509i | \(-0.509973\pi\) |
−0.881263 | + | 0.472626i | \(0.843306\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.69321 | + | 13.3021i | −0.148925 | + | 0.536394i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.53125 | − | 11.3589i | −0.383714 | − | 0.457292i | 0.539269 | − | 0.842134i | \(-0.318701\pi\) |
−0.922983 | + | 0.384841i | \(0.874256\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.2206 | − | 4.08396i | 0.450993 | − | 0.164148i | −0.106530 | − | 0.994309i | \(-0.533974\pi\) |
0.557523 | + | 0.830161i | \(0.311752\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.49395 | + | 8.05488i | 0.140207 | + | 0.323231i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.7706 | − | 10.1077i | 1.11261 | − | 0.404955i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.3972 | − | 10.4025i | 0.495887 | − | 0.416098i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −20.1069 | − | 20.4729i | −0.802992 | − | 0.817610i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.5716 | − | 33.8989i | 0.780369 | − | 1.35164i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.14304 | − | 1.81464i | 0.125122 | − | 0.0722395i | −0.436132 | − | 0.899882i | \(-0.643652\pi\) |
0.561255 | + | 0.827643i | \(0.310319\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.4111 | + | 1.12993i | −0.572790 | + | 0.0449106i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.29692 | − | 14.5532i | 0.210202 | − | 0.577525i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.3644 | − | 2.88548i | −0.648380 | − | 0.114327i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.76284 | + | 19.6782i | 0.267534 | + | 0.778457i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.6906 | + | 17.5075i | −0.580242 | + | 0.691506i | −0.973699 | − | 0.227837i | \(-0.926835\pi\) |
0.393457 | + | 0.919343i | \(0.371279\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.40620 | + | 42.0026i | 0.292072 | + | 1.65642i | 0.678871 | + | 0.734258i | \(0.262470\pi\) |
−0.386799 | + | 0.922164i | \(0.626419\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.564326 | − | 5.84280i | 0.0222203 | − | 0.230060i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.8902 | 0.899906 | 0.449953 | − | 0.893052i | \(-0.351441\pi\) | ||||
0.449953 | + | 0.893052i | \(0.351441\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.2874 | −0.403816 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.68586 | + | 58.8691i | −0.222847 | + | 2.30726i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.77297 | + | 15.7263i | 0.108515 | + | 0.615418i | 0.989758 | + | 0.142755i | \(0.0455961\pi\) |
−0.881243 | + | 0.472663i | \(0.843293\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.89570 | + | 10.6015i | −0.347584 | + | 0.414234i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.79591 | + | 4.36152i | −0.148092 | + | 0.170159i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.3500 | + | 2.17764i | 0.481089 | + | 0.0848289i | 0.408933 | − | 0.912564i | \(-0.365901\pi\) |
0.0721558 | + | 0.997393i | \(0.477012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.07399 | + | 16.6881i | −0.236251 | + | 0.649093i | 0.763743 | + | 0.645521i | \(0.223360\pi\) |
−0.999994 | + | 0.00357294i | \(0.998863\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.0332 | + | 1.02189i | −0.506167 | + | 0.0396869i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.7761 | + | 6.22157i | −0.417878 | + | 0.241262i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.57301 | − | 6.18864i | 0.138348 | − | 0.239625i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.5857 | − | 26.0515i | −0.989201 | − | 1.00721i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.7262 | + | 9.83943i | −0.452684 | + | 0.379847i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.2988 | + | 11.3918i | −1.20648 | + | 0.439122i | −0.865481 | − | 0.500942i | \(-0.832987\pi\) |
−0.340997 | + | 0.940064i | \(0.610765\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.37169 | + | 22.7552i | 0.0527963 | + | 0.875848i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.5846 | + | 9.31202i | −0.983295 | + | 0.357890i | −0.783120 | − | 0.621870i | \(-0.786373\pi\) |
−0.200175 | + | 0.979760i | \(0.564151\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.96423 | − | 8.29964i | −0.267263 | − | 0.318511i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.62026 | − | 20.2430i | 0.215369 | − | 0.775712i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.0275 | − | 19.6458i | −1.30203 | − | 0.751725i | −0.321275 | − | 0.946986i | \(-0.604111\pi\) |
−0.980751 | + | 0.195261i | \(0.937445\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.67016 | + | 5.58307i | −0.369478 | + | 0.213318i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.3588 | − | 11.1500i | −0.891193 | − | 0.425398i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.46510 | + | 20.5102i | −0.284398 | + | 0.781377i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.24693 | + | 41.0994i | −0.275686 | + | 1.56349i | 0.461087 | + | 0.887355i | \(0.347460\pi\) |
−0.736773 | + | 0.676140i | \(0.763652\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 41.7177 | − | 23.0926i | 1.58473 | − | 0.877214i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.9013 | + | 9.14725i | 0.413509 | + | 0.346975i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.62503 | + | 37.5724i | 0.250941 | + | 1.42316i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.1909 | + | 26.7714i | 0.461104 | + | 1.01259i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.6358 | −1.34594 | −0.672972 | − | 0.739668i | \(-0.734983\pi\) | ||||
−0.672972 | + | 0.739668i | \(0.734983\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 42.5206i | − | 1.60369i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.86852 | + | 1.33363i | 0.0703726 | + | 0.0502274i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.91548 | − | 1.04306i | 0.222474 | − | 0.0392282i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.4298 | − | 14.8132i | 0.466810 | − | 0.556322i | −0.480353 | − | 0.877075i | \(-0.659491\pi\) |
0.947163 | + | 0.320753i | \(0.103936\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.02835 | − | 19.1930i | −0.113572 | − | 0.719795i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 14.5506 | + | 2.56567i | 0.544926 | + | 0.0960851i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.03097 | + | 2.19509i | 0.225545 | + | 0.0820918i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0548 | + | 17.5509i | 0.450195 | + | 0.655449i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.38435 | + | 7.59391i | 0.163509 | + | 0.283205i | 0.936125 | − | 0.351668i | \(-0.114386\pi\) |
−0.772616 | + | 0.634873i | \(0.781052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.4271 | + | 63.0937i | −1.35662 | + | 2.34973i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −11.1768 | − | 43.2700i | −0.415671 | − | 1.60923i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.2132 | − | 11.9263i | 0.527864 | − | 0.442930i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.7683 | + | 48.8179i | 0.658988 | + | 1.81055i | 0.581477 | + | 0.813563i | \(0.302475\pi\) |
0.0775114 | + | 0.996991i | \(0.475303\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.6182 | − | 14.7450i | −0.837712 | − | 0.546113i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.54830 | − | 15.2438i | −0.205211 | − | 0.563814i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.92115 | − | 4.67304i | −0.144831 | − | 0.172603i | 0.688752 | − | 0.724997i | \(-0.258159\pi\) |
−0.833583 | + | 0.552394i | \(0.813714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.79740 | − | 10.8298i | −0.103184 | − | 0.399465i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.8500 | + | 6.26428i | 0.399667 | + | 0.230748i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.5953 | + | 30.4760i | 0.647255 | + | 1.12108i | 0.983776 | + | 0.179402i | \(0.0574164\pi\) |
−0.336521 | + | 0.941676i | \(0.609250\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.7059 | + | 8.04022i | −0.430028 | + | 0.295365i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.6151 | − | 8.95918i | −0.903042 | − | 0.328681i | −0.151571 | − | 0.988446i | \(-0.548433\pi\) |
−0.751471 | + | 0.659766i | \(0.770655\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.65091 | − | 15.0340i | 0.0971218 | − | 0.550805i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.79788 | + | 11.3946i | 0.0657809 | + | 0.416906i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −21.7067 | − | 18.2141i | −0.793145 | − | 0.665527i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.0395 | + | 5.82576i | −1.20563 | + | 0.212585i | −0.740130 | − | 0.672464i | \(-0.765236\pi\) |
−0.465499 | + | 0.885049i | \(0.654125\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.5133 | + | 16.1311i | −0.419569 | + | 0.587849i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 6.41946i | − | 0.233628i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 24.5635i | − | 0.892774i | −0.894840 | − | 0.446387i | \(-0.852711\pi\) | ||
0.894840 | − | 0.446387i | \(-0.147289\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.93668 | − | 10.8410i | −0.179190 | − | 0.393502i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.6026 | − | 5.57238i | 1.14559 | − | 0.201999i | 0.431542 | − | 0.902093i | \(-0.357970\pi\) |
0.714050 | + | 0.700094i | \(0.246859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.4854 | − | 11.3156i | −0.488203 | − | 0.409651i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.26179 | − | 7.69912i | −0.154085 | − | 0.278362i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.884074 | + | 5.01383i | −0.0319220 | + | 0.181039i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.6669 | + | 4.97435i | 0.492842 | + | 0.179380i | 0.576472 | − | 0.817117i | \(-0.304429\pi\) |
−0.0836298 | + | 0.996497i | \(0.526651\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8910 | + | 5.19865i | 0.392229 | + | 0.187225i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.4834 | + | 21.6219i | 0.448997 | + | 0.777686i | 0.998321 | − | 0.0579237i | \(-0.0184480\pi\) |
−0.549324 | + | 0.835609i | \(0.685115\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.2226 | + | 19.1811i | 1.19339 | + | 0.689004i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 68.0804 | + | 18.9019i | 2.44237 | + | 0.678100i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.6397 | + | 31.7479i | 0.954465 | + | 1.13749i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.65540 | − | 26.5280i | −0.345497 | − | 0.949246i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.32227 | + | 21.9354i | 0.0472541 | + | 0.783906i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.63136 | − | 9.97708i | −0.129609 | − | 0.356097i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.8410 | + | 16.6486i | −0.707257 | + | 0.593459i | −0.923828 | − | 0.382808i | \(-0.874957\pi\) |
0.216571 | + | 0.976267i | \(0.430513\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.7864 | − | 15.5042i | 0.562011 | − | 0.551964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.40419 | + | 11.0924i | −0.227707 | + | 0.394400i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.78778 | + | 6.56063i | 0.134508 | + | 0.232975i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.6471 | + | 1.14844i | −0.519480 | + | 0.0407308i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.36086 | − | 1.58722i | −0.154469 | − | 0.0562223i | 0.263628 | − | 0.964624i | \(-0.415081\pi\) |
−0.418098 | + | 0.908402i | \(0.637303\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.24778 | + | 1.10165i | 0.221031 | + | 0.0389737i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.1259 | + | 14.9049i | 0.605113 | + | 0.526639i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.04242 | − | 6.00932i | 0.177943 | − | 0.212064i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.08693 | + | 0.896963i | −0.179291 | + | 0.0316138i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.04763 | − | 21.2004i | 0.0720802 | − | 0.746289i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.2974i | 0.924566i | 0.886732 | + | 0.462283i | \(0.152970\pi\) | ||||
−0.886732 | + | 0.462283i | \(0.847030\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.3273 | 0.678674 | 0.339337 | − | 0.940665i | \(-0.389797\pi\) | ||||
0.339337 | + | 0.940665i | \(0.389797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0501533 | + | 0.00484405i | 0.00175895 | + | 0.000169888i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.80664 | − | 10.2460i | −0.0632839 | − | 0.358901i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.4991 | − | 11.3271i | −0.472275 | − | 0.396286i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.66964 | − | 22.3167i | −0.267999 | − | 0.779809i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.65700 | + | 20.7399i | −0.127630 | + | 0.723826i | 0.852081 | + | 0.523410i | \(0.175340\pi\) |
−0.979711 | + | 0.200416i | \(0.935771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.88857 | − | 7.93629i | 0.100689 | − | 0.276642i | −0.879112 | − | 0.476615i | \(-0.841863\pi\) |
0.979801 | + | 0.199974i | \(0.0640857\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.41759 | − | 30.8339i | −0.0841697 | − | 1.07350i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.5829 | + | 16.5024i | −0.993926 | + | 0.573843i | −0.906445 | − | 0.422323i | \(-0.861215\pi\) |
−0.0874801 | + | 0.996166i | \(0.527881\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.1395 | + | 20.2878i | 1.22045 | + | 0.704624i | 0.965013 | − | 0.262202i | \(-0.0844488\pi\) |
0.255432 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.9048 | + | 16.1944i | 0.551733 | + | 0.561777i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.8695 | − | 23.6795i | −0.688436 | − | 0.820446i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.27785 | − | 1.92098i | 0.182648 | − | 0.0664783i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −41.6833 | + | 18.0809i | −1.44079 | + | 0.624966i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.0300 | + | 6.56238i | −0.622464 | + | 0.226558i | −0.633948 | − | 0.773376i | \(-0.718567\pi\) |
0.0114838 | + | 0.999934i | \(0.496345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.51418 | + | 7.14425i | −0.293593 | + | 0.246353i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.76218 | + | 9.94877i | −0.0951345 | + | 0.342654i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.50023 | + | 6.06258i | −0.120412 | + | 0.208559i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.8245 | + | 10.8683i | −0.646816 | + | 0.373440i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −16.1022 | + | 33.7334i | −0.552625 | + | 1.15773i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.03706 | − | 16.5867i | 0.206948 | − | 0.568584i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.315761 | + | 0.0556772i | 0.0108114 | + | 0.00190635i | 0.179051 | − | 0.983840i | \(-0.442697\pi\) |
−0.168240 | + | 0.985746i | \(0.553808\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.19100 | − | 4.92819i | −0.280126 | − | 0.168540i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −13.5508 | + | 16.1492i | −0.462887 | + | 0.551647i | −0.946108 | − | 0.323851i | \(-0.895022\pi\) |
0.483221 | + | 0.875498i | \(0.339467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.24367 | − | 41.0809i | −0.247151 | − | 1.40166i | −0.815444 | − | 0.578836i | \(-0.803507\pi\) |
0.568293 | − | 0.822826i | \(-0.307604\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −62.6744 | + | 28.5402i | −2.13594 | + | 0.972647i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.7867 | 0.401223 | 0.200611 | − | 0.979671i | \(-0.435707\pi\) | ||||
0.200611 | + | 0.979671i | \(0.435707\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.68637 | 0.0913395 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.17189 | + | 2.97763i | 0.141685 | + | 0.101126i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.57767 | + | 25.9613i | 0.155287 | + | 0.880676i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.98548 | − | 4.74971i | 0.135043 | − | 0.160938i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.98739 | − | 7.76880i | 0.101108 | − | 0.262934i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −28.2603 | − | 4.98306i | −0.955374 | − | 0.168458i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.87782 | − | 10.6542i | 0.130945 | − | 0.359768i | −0.856842 | − | 0.515579i | \(-0.827577\pi\) |
0.987787 | + | 0.155811i | \(0.0497992\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.312019 | + | 0.454275i | 0.0105241 | + | 0.0153223i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.5990 | − | 14.2023i | 0.828763 | − | 0.478486i | −0.0246662 | − | 0.999696i | \(-0.507852\pi\) |
0.853429 | + | 0.521209i | \(0.174519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.49495 | + | 6.05343i | −0.117614 | + | 0.203714i | −0.918822 | − | 0.394673i | \(-0.870858\pi\) |
0.801207 | + | 0.598387i | \(0.204191\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.31812 | + | 0.857087i | −0.111537 | + | 0.0288107i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.6087 | − | 24.0056i | 0.960587 | − | 0.806028i | −0.0204617 | − | 0.999791i | \(-0.506514\pi\) |
0.981048 | + | 0.193763i | \(0.0620692\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 72.5972 | − | 26.4232i | 2.43483 | − | 0.886207i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.0425 | + | 19.4482i | 1.03996 | + | 0.651538i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.47596 | − | 2.35706i | 0.216710 | − | 0.0788759i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.43382 | − | 7.66753i | −0.215059 | − | 0.256297i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.70787 | + | 1.47437i | −0.190580 | + | 0.0492278i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.0257 | + | 18.4900i | 1.06812 | + | 0.616677i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −35.1630 | + | 20.3013i | −1.17145 | + | 0.676336i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.1369 | − | 16.5784i | 0.803225 | − | 0.551695i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.111276 | − | 0.305727i | 0.00369893 | − | 0.0101627i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.78756 | + | 44.1654i | −0.258582 | + | 1.46649i | 0.528127 | + | 0.849165i | \(0.322894\pi\) |
−0.786709 | + | 0.617324i | \(0.788217\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.90195 | + | 3.58791i | 0.0962517 | + | 0.119003i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.0561 | − | 27.7374i | −1.09520 | − | 0.918981i | −0.0981060 | − | 0.995176i | \(-0.531278\pi\) |
−0.997093 | + | 0.0761949i | \(0.975723\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.71769 | − | 15.4128i | −0.0899423 | − | 0.510088i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.96242 | + | 4.15058i | −0.0979345 | + | 0.137214i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −69.0359 | −2.27977 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.21294i | 0.171959i | 0.996297 | + | 0.0859796i | \(0.0274020\pi\) | ||||
−0.996297 | + | 0.0859796i | \(0.972598\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.5766 | + | 5.27167i | −0.381462 | + | 0.173707i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.7589 | + | 2.42606i | −0.452878 | + | 0.0798547i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.4587 | − | 35.1075i | 0.968596 | − | 1.15433i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −55.9602 | − | 1.00960i | −1.83797 | − | 0.0331595i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.0093 | − | 3.52818i | −0.656484 | − | 0.115756i | −0.164523 | − | 0.986373i | \(-0.552609\pi\) |
−0.491961 | + | 0.870617i | \(0.663720\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.5536 | − | 11.4846i | −1.03413 | − | 0.376391i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.1334 | + | 29.6090i | −0.462707 | + | 0.969355i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.96955 | + | 10.3396i | 0.195225 | + | 0.338140i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.65752 | − | 14.9953i | 0.282829 | − | 0.489874i | −0.689251 | − | 0.724522i | \(-0.742060\pi\) |
0.972080 | + | 0.234648i | \(0.0753938\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 44.3555 | + | 12.3149i | 1.44749 | + | 0.401881i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.65680 | − | 8.10302i | 0.314803 | − | 0.264151i | −0.471671 | − | 0.881775i | \(-0.656349\pi\) |
0.786474 | + | 0.617624i | \(0.211905\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.88420 | + | 16.1667i | 0.191616 | + | 0.526460i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.5318 | − | 10.9240i | 0.375129 | − | 0.355358i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.904890 | + | 2.48616i | 0.0294050 | + | 0.0807895i | 0.953526 | − | 0.301309i | \(-0.0974236\pi\) |
−0.924122 | + | 0.382099i | \(0.875201\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.49546 | − | 2.97398i | −0.0810061 | − | 0.0965394i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.6583 | − | 19.3068i | 0.637463 | − | 0.626066i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.5984 | − | 6.69633i | −0.375708 | − | 0.216915i | 0.300241 | − | 0.953863i | \(-0.402933\pi\) |
−0.675949 | + | 0.736948i | \(0.736266\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.3928 | − | 18.0009i | −0.336303 | − | 0.582495i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.33049 | − | 29.7230i | −0.0753340 | − | 0.960809i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −52.3421 | − | 19.0510i | −1.69022 | − | 0.615188i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.89401 | + | 44.7692i | −0.254646 | + | 1.44417i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.16620 | − | 21.3664i | 0.134254 | − | 0.688522i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.02578 | + | 5.89533i | 0.226168 | + | 0.189777i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.36499 | − | 0.769665i | 0.140369 | − | 0.0247508i | −0.103022 | − | 0.994679i | \(-0.532851\pi\) |
0.243391 | + | 0.969928i | \(0.421740\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −26.2954 | − | 2.53973i | −0.844729 | − | 0.0815880i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.6830i | 1.33767i | 0.743411 | + | 0.668835i | \(0.233207\pi\) | ||||
−0.743411 | + | 0.668835i | \(0.766793\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 70.9881i | 2.27577i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.2355 | − | 1.47151i | −0.487925 | − | 0.0471262i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.5330 | + | 7.14705i | −1.29676 | + | 0.228655i | −0.779084 | − | 0.626920i | \(-0.784315\pi\) |
−0.517680 | + | 0.855574i | \(0.673204\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.5960 | − | 19.7994i | −0.754133 | − | 0.632793i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.58827 | − | 13.2740i | 0.0826371 | − | 0.423805i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.36427 | − | 13.4084i | 0.0754085 | − | 0.427663i | −0.923609 | − | 0.383337i | \(-0.874775\pi\) |
0.999017 | − | 0.0443262i | \(-0.0141141\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0214 | + | 5.83130i | 0.510483 | + | 0.185801i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.895136 | + | 11.4166i | 0.0284925 | + | 0.363393i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.65760 | − | 6.33516i | −0.116305 | − | 0.201446i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.9495 | + | 12.0952i | 0.665484 | + | 0.384218i | 0.794363 | − | 0.607443i | \(-0.207805\pi\) |
−0.128879 | + | 0.991660i | \(0.541138\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.14928 | − | 6.03934i | 0.195141 | − | 0.191653i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.392166 | − | 0.467366i | −0.0124325 | − | 0.0148165i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.22417 | − | 6.11086i | −0.0704402 | − | 0.193533i | 0.899477 | − | 0.436968i | \(-0.143948\pi\) |
−0.969917 | + | 0.243435i | \(0.921726\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.6251 | + | 52.7916i | 0.399439 | + | 1.67025i |
(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 | 864.2.bh.b.47.18 | 192 | ||
4.3 | odd | 2 | 216.2.v.b.155.27 | yes | 192 | ||
8.3 | odd | 2 | inner | 864.2.bh.b.47.17 | 192 | ||
8.5 | even | 2 | 216.2.v.b.155.13 | yes | 192 | ||
12.11 | even | 2 | 648.2.v.b.467.6 | 192 | |||
24.5 | odd | 2 | 648.2.v.b.467.20 | 192 | |||
27.23 | odd | 18 | inner | 864.2.bh.b.239.17 | 192 | ||
108.23 | even | 18 | 216.2.v.b.131.13 | ✓ | 192 | ||
108.31 | odd | 18 | 648.2.v.b.179.20 | 192 | |||
216.77 | odd | 18 | 216.2.v.b.131.27 | yes | 192 | ||
216.85 | even | 18 | 648.2.v.b.179.6 | 192 | |||
216.131 | even | 18 | inner | 864.2.bh.b.239.18 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.v.b.131.13 | ✓ | 192 | 108.23 | even | 18 | ||
216.2.v.b.131.27 | yes | 192 | 216.77 | odd | 18 | ||
216.2.v.b.155.13 | yes | 192 | 8.5 | even | 2 | ||
216.2.v.b.155.27 | yes | 192 | 4.3 | odd | 2 | ||
648.2.v.b.179.6 | 192 | 216.85 | even | 18 | |||
648.2.v.b.179.20 | 192 | 108.31 | odd | 18 | |||
648.2.v.b.467.6 | 192 | 12.11 | even | 2 | |||
648.2.v.b.467.20 | 192 | 24.5 | odd | 2 | |||
864.2.bh.b.47.17 | 192 | 8.3 | odd | 2 | inner | ||
864.2.bh.b.47.18 | 192 | 1.1 | even | 1 | trivial | ||
864.2.bh.b.239.17 | 192 | 27.23 | odd | 18 | inner | ||
864.2.bh.b.239.18 | 192 | 216.131 | even | 18 | inner |