Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(35,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.v (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 35.9 | ||
Character | \(\chi\) | \(=\) | 432.35 |
Dual form | 432.2.v.a.395.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.378412 | + | 1.36265i | −0.267578 | + | 0.963536i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.71361 | − | 1.03128i | −0.856804 | − | 0.515642i | ||||
\(5\) | −1.00059 | + | 3.73424i | −0.447476 | + | 1.67000i | 0.261839 | + | 0.965111i | \(0.415671\pi\) |
−0.709315 | + | 0.704891i | \(0.750996\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.68236 | + | 2.91393i | −0.635872 | + | 1.10136i | 0.350457 | + | 0.936579i | \(0.386026\pi\) |
−0.986330 | + | 0.164785i | \(0.947307\pi\) | |||||||
\(8\) | 2.05372 | − | 1.94479i | 0.726101 | − | 0.687588i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.70981 | − | 2.77653i | −1.48937 | − | 0.878015i | ||||
\(11\) | −0.0566521 | − | 0.211428i | −0.0170812 | − | 0.0637480i | 0.956859 | − | 0.290552i | \(-0.0938390\pi\) |
−0.973940 | + | 0.226804i | \(0.927172\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.727551 | − | 2.71526i | 0.201786 | − | 0.753076i | −0.788619 | − | 0.614882i | \(-0.789204\pi\) |
0.990405 | − | 0.138194i | \(-0.0441298\pi\) | |||||||
\(14\) | −3.33403 | − | 3.39513i | −0.891058 | − | 0.907386i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.87291 | + | 3.53443i | 0.468227 | + | 0.883608i | ||||
\(17\) | − | 4.23937i | − | 1.02820i | −0.857731 | − | 0.514100i | \(-0.828126\pi\) | ||
0.857731 | − | 0.514100i | \(-0.171874\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.12365 | + | 1.12365i | −0.257782 | + | 0.257782i | −0.824152 | − | 0.566369i | \(-0.808348\pi\) |
0.566369 | + | 0.824152i | \(0.308348\pi\) | |||||||
\(20\) | 5.56567 | − | 5.36714i | 1.24452 | − | 1.20013i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.309540 | + | 0.00281033i | 0.0659941 | + | 0.000599165i | ||||
\(23\) | −3.33369 | + | 1.92471i | −0.695123 | + | 0.401329i | −0.805528 | − | 0.592557i | \(-0.798118\pi\) |
0.110405 | + | 0.993887i | \(0.464785\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.61325 | − | 4.97286i | −1.72265 | − | 0.994572i | ||||
\(26\) | 3.42462 | + | 2.01888i | 0.671623 | + | 0.395935i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.88800 | − | 3.25835i | 1.11273 | − | 0.615771i | ||||
\(29\) | −0.545635 | − | 2.03634i | −0.101322 | − | 0.378138i | 0.896580 | − | 0.442882i | \(-0.146044\pi\) |
−0.997902 | + | 0.0647434i | \(0.979377\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.21206 | + | 4.16388i | −1.29532 | + | 0.747856i | −0.979593 | − | 0.200993i | \(-0.935583\pi\) |
−0.315731 | + | 0.948849i | \(0.602250\pi\) | |||||||
\(32\) | −5.52491 | + | 1.21464i | −0.976676 | + | 0.214720i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.77677 | + | 1.60423i | 0.990707 | + | 0.275123i | ||||
\(35\) | −9.19798 | − | 9.19798i | −1.55474 | − | 1.55474i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.66564 | + | 2.66564i | −0.438229 | + | 0.438229i | −0.891416 | − | 0.453187i | \(-0.850287\pi\) |
0.453187 | + | 0.891416i | \(0.350287\pi\) | |||||||
\(38\) | −1.10593 | − | 1.95634i | −0.179406 | − | 0.317359i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.20739 | + | 9.61503i | 0.823361 | + | 1.52027i | ||||
\(41\) | 1.70386 | + | 2.95117i | 0.266098 | + | 0.460895i | 0.967851 | − | 0.251526i | \(-0.0809323\pi\) |
−0.701753 | + | 0.712420i | \(0.747599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.68985 | − | 1.25664i | 0.715195 | − | 0.191636i | 0.117168 | − | 0.993112i | \(-0.462618\pi\) |
0.598027 | + | 0.801476i | \(0.295952\pi\) | |||||||
\(44\) | −0.120963 | + | 0.420730i | −0.0182359 | + | 0.0634274i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.36119 | − | 5.27098i | −0.200696 | − | 0.777163i | ||||
\(47\) | −2.34998 | + | 4.07028i | −0.342779 | + | 0.593711i | −0.984948 | − | 0.172852i | \(-0.944702\pi\) |
0.642168 | + | 0.766564i | \(0.278035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.16067 | − | 3.74239i | −0.308667 | − | 0.534628i | ||||
\(50\) | 10.0356 | − | 9.85502i | 1.41925 | − | 1.39371i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.04693 | + | 3.90257i | −0.561209 | + | 0.541190i | ||||
\(53\) | 7.58271 | + | 7.58271i | 1.04157 | + | 1.04157i | 0.999098 | + | 0.0424680i | \(0.0135220\pi\) |
0.0424680 | + | 0.999098i | \(0.486478\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.846209 | 0.114103 | ||||||||
\(56\) | 2.21189 | + | 9.25626i | 0.295576 | + | 1.23692i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.98128 | + | 0.0270672i | 0.391461 | + | 0.00355410i | ||||
\(59\) | 5.34305 | + | 1.43167i | 0.695605 | + | 0.186387i | 0.589261 | − | 0.807942i | \(-0.299419\pi\) |
0.106344 | + | 0.994329i | \(0.466085\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.69958 | − | 2.33105i | 1.11387 | − | 0.298460i | 0.345468 | − | 0.938431i | \(-0.387720\pi\) |
0.768399 | + | 0.639971i | \(0.221054\pi\) | |||||||
\(62\) | −2.94477 | − | 11.4031i | −0.373986 | − | 1.44820i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.435568 | − | 7.98813i | 0.0544460 | − | 0.998517i | ||||
\(65\) | 9.41144 | + | 5.43370i | 1.16735 | + | 0.673967i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.17504 | − | 1.38665i | −0.632231 | − | 0.169406i | −0.0715493 | − | 0.997437i | \(-0.522794\pi\) |
−0.560682 | + | 0.828031i | \(0.689461\pi\) | |||||||
\(68\) | −4.37200 | + | 7.26463i | −0.530182 | + | 0.880965i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 16.0142 | − | 9.05296i | 1.91406 | − | 1.08204i | ||||
\(71\) | 7.53614i | 0.894375i | 0.894440 | + | 0.447187i | \(0.147574\pi\) | ||||
−0.894440 | + | 0.447187i | \(0.852426\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.22646i | − | 0.377629i | −0.982013 | − | 0.188814i | \(-0.939536\pi\) | ||
0.982013 | − | 0.188814i | \(-0.0604644\pi\) | |||||||
\(74\) | −2.62362 | − | 4.64104i | −0.304989 | − | 0.539510i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.08429 | − | 0.766693i | 0.353792 | − | 0.0879457i | ||||
\(77\) | 0.711397 | + | 0.190618i | 0.0810712 | + | 0.0217230i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.98587 | − | 2.87859i | −0.560954 | − | 0.323867i | 0.192574 | − | 0.981282i | \(-0.438316\pi\) |
−0.753528 | + | 0.657415i | \(0.771650\pi\) | |||||||
\(80\) | −15.0724 | + | 3.45739i | −1.68515 | + | 0.386548i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.66616 | + | 1.20500i | −0.515291 | + | 0.133070i | ||||
\(83\) | −4.50604 | + | 1.20739i | −0.494602 | + | 0.132528i | −0.497494 | − | 0.867468i | \(-0.665746\pi\) |
0.00289160 | + | 0.999996i | \(0.499080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.8308 | + | 4.24186i | 1.71710 | + | 0.460094i | ||||
\(86\) | −0.0623381 | + | 6.86613i | −0.00672209 | + | 0.740394i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.527532 | − | 0.324039i | −0.0562351 | − | 0.0345427i | ||||
\(89\) | 2.96157 | 0.313926 | 0.156963 | − | 0.987605i | \(-0.449830\pi\) | ||||
0.156963 | + | 0.987605i | \(0.449830\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.68807 | + | 6.68807i | 0.701100 | + | 0.701100i | ||||
\(92\) | 7.69756 | + | 0.139785i | 0.802527 | + | 0.0145736i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.65709 | − | 4.74243i | −0.480342 | − | 0.489144i | ||||
\(95\) | −3.07166 | − | 5.32027i | −0.315146 | − | 0.545849i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.63883 | + | 13.2308i | −0.775606 | + | 1.34339i | 0.158848 | + | 0.987303i | \(0.449222\pi\) |
−0.934453 | + | 0.356085i | \(0.884111\pi\) | |||||||
\(98\) | 5.91718 | − | 1.52806i | 0.597726 | − | 0.154358i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.63131 | + | 17.4042i | 0.963131 | + | 1.74042i | ||||
\(101\) | −0.129684 | + | 0.0347486i | −0.0129040 | + | 0.00345762i | −0.265265 | − | 0.964175i | \(-0.585460\pi\) |
0.252361 | + | 0.967633i | \(0.418793\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.09117 | − | 7.08611i | −0.403115 | − | 0.698215i | 0.590985 | − | 0.806682i | \(-0.298739\pi\) |
−0.994100 | + | 0.108467i | \(0.965406\pi\) | |||||||
\(104\) | −3.78642 | − | 6.99132i | −0.371289 | − | 0.685555i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.2019 | + | 7.46316i | −1.28229 | + | 0.724887i | ||||
\(107\) | −8.28837 | + | 8.28837i | −0.801267 | + | 0.801267i | −0.983294 | − | 0.182027i | \(-0.941734\pi\) |
0.182027 | + | 0.983294i | \(0.441734\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.31291 | + | 6.31291i | 0.604667 | + | 0.604667i | 0.941547 | − | 0.336881i | \(-0.109372\pi\) |
−0.336881 | + | 0.941547i | \(0.609372\pi\) | |||||||
\(110\) | −0.320216 | + | 1.15308i | −0.0305314 | + | 0.109942i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.4500 | − | 0.488655i | −1.27091 | − | 0.0461736i | ||||
\(113\) | −14.6562 | + | 8.46178i | −1.37874 | + | 0.796017i | −0.992008 | − | 0.126174i | \(-0.959730\pi\) |
−0.386735 | + | 0.922191i | \(0.626397\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.85167 | − | 14.3746i | −0.359171 | − | 1.34044i | ||||
\(116\) | −1.16504 | + | 4.05219i | −0.108171 | + | 0.376236i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.97273 | + | 6.73892i | −0.365719 | + | 0.620368i | ||||
\(119\) | 12.3533 | + | 7.13215i | 1.13242 | + | 0.653803i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.48479 | − | 5.47604i | 0.862253 | − | 0.497822i | ||||
\(122\) | −0.115636 | + | 12.7365i | −0.0104692 | + | 1.15311i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 16.6528 | + | 0.302408i | 1.49546 | + | 0.0271571i | ||||
\(125\) | 13.5199 | − | 13.5199i | 1.20926 | − | 1.20926i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4028i | 1.18931i | 0.803981 | + | 0.594654i | \(0.202711\pi\) | ||||
−0.803981 | + | 0.594654i | \(0.797289\pi\) | |||||||
\(128\) | 10.7202 | + | 3.61633i | 0.947539 | + | 0.319641i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.9656 | + | 10.7683i | −0.961747 | + | 0.944441i | ||||
\(131\) | −0.169534 | + | 0.632708i | −0.0148122 | + | 0.0552800i | −0.972936 | − | 0.231073i | \(-0.925776\pi\) |
0.958124 | + | 0.286353i | \(0.0924430\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.38385 | − | 5.16461i | −0.119995 | − | 0.447829i | ||||
\(134\) | 3.84781 | − | 6.52702i | 0.332400 | − | 0.563849i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.24470 | − | 8.70650i | −0.706977 | − | 0.746577i | ||||
\(137\) | −10.5230 | + | 18.2263i | −0.899037 | + | 1.55718i | −0.0703095 | + | 0.997525i | \(0.522399\pi\) |
−0.828727 | + | 0.559652i | \(0.810935\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.72666 | + | 6.44400i | −0.146454 | + | 0.546573i | 0.853233 | + | 0.521530i | \(0.174639\pi\) |
−0.999686 | + | 0.0250423i | \(0.992028\pi\) | |||||||
\(140\) | 6.27601 | + | 25.2475i | 0.530420 | + | 2.13380i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.2691 | − | 2.85176i | −0.861763 | − | 0.239315i | ||||
\(143\) | −0.615299 | −0.0514539 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.15012 | 0.676831 | ||||||||
\(146\) | 4.39652 | + | 1.22093i | 0.363859 | + | 0.101045i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.31691 | − | 1.81884i | 0.601446 | − | 0.149507i | ||||
\(149\) | 5.78161 | − | 21.5773i | 0.473648 | − | 1.76768i | −0.152844 | − | 0.988250i | \(-0.548843\pi\) |
0.626492 | − | 0.779428i | \(-0.284490\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.97506 | + | 17.2773i | −0.811759 | + | 1.40601i | 0.0998734 | + | 0.995000i | \(0.468156\pi\) |
−0.911632 | + | 0.411007i | \(0.865177\pi\) | |||||||
\(152\) | −0.122401 | + | 4.49292i | −0.00992807 | + | 0.364424i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.528947 | + | 0.897250i | −0.0426237 | + | 0.0723025i | ||||
\(155\) | −8.33265 | − | 31.0979i | −0.669295 | − | 2.49784i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.85693 | − | 14.3943i | 0.307817 | − | 1.14879i | −0.622677 | − | 0.782479i | \(-0.713955\pi\) |
0.930494 | − | 0.366308i | \(-0.119378\pi\) | |||||||
\(158\) | 5.80922 | − | 5.70468i | 0.462157 | − | 0.453840i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.992392 | − | 21.8467i | 0.0784555 | − | 1.72713i | ||||
\(161\) | − | 12.9522i | − | 1.02078i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.35766 | + | 4.35766i | −0.341318 | + | 0.341318i | −0.856863 | − | 0.515545i | \(-0.827590\pi\) |
0.515545 | + | 0.856863i | \(0.327590\pi\) | |||||||
\(164\) | 0.123745 | − | 6.81430i | 0.00966288 | − | 0.532108i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0598948 | − | 6.59703i | 0.00464874 | − | 0.512029i | ||||
\(167\) | 11.8952 | − | 6.86770i | 0.920479 | − | 0.531439i | 0.0366910 | − | 0.999327i | \(-0.488318\pi\) |
0.883788 | + | 0.467888i | \(0.154985\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.41505 | + | 2.54903i | 0.339619 | + | 0.196079i | ||||
\(170\) | −11.7707 | + | 19.9667i | −0.902774 | + | 1.53137i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.33252 | − | 2.68317i | −0.711598 | − | 0.204590i | ||||
\(173\) | −1.40497 | − | 5.24342i | −0.106818 | − | 0.398650i | 0.891727 | − | 0.452573i | \(-0.149494\pi\) |
−0.998545 | + | 0.0539235i | \(0.982827\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28.9812 | − | 16.7323i | 2.19077 | − | 1.26484i | ||||
\(176\) | 0.641175 | − | 0.596219i | 0.0483304 | − | 0.0449417i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.12069 | + | 4.03557i | −0.0839995 | + | 0.302479i | ||||
\(179\) | −0.380130 | − | 0.380130i | −0.0284123 | − | 0.0284123i | 0.692758 | − | 0.721170i | \(-0.256395\pi\) |
−0.721170 | + | 0.692758i | \(0.756395\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.98992 | + | 4.98992i | −0.370898 | + | 0.370898i | −0.867804 | − | 0.496906i | \(-0.834469\pi\) |
0.496906 | + | 0.867804i | \(0.334469\pi\) | |||||||
\(182\) | −11.6443 | + | 6.58263i | −0.863134 | + | 0.487937i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.10333 | + | 10.4362i | −0.228780 | + | 0.769364i | ||||
\(185\) | −7.28695 | − | 12.6214i | −0.535747 | − | 0.927941i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.896324 | + | 0.240169i | −0.0655457 | + | 0.0175629i | ||||
\(188\) | 8.22455 | − | 4.55137i | 0.599837 | − | 0.331943i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.41200 | − | 2.17233i | 0.610271 | − | 0.157598i | ||||
\(191\) | 5.40555 | − | 9.36269i | 0.391132 | − | 0.677461i | −0.601467 | − | 0.798898i | \(-0.705417\pi\) |
0.992599 | + | 0.121437i | \(0.0387502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.60044 | + | 4.50410i | 0.187184 | + | 0.324212i | 0.944310 | − | 0.329056i | \(-0.106731\pi\) |
−0.757126 | + | 0.653268i | \(0.773397\pi\) | |||||||
\(194\) | −15.1383 | − | 15.4157i | −1.08687 | − | 1.10679i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.156922 | + | 8.64126i | −0.0112087 | + | 0.617233i | ||||
\(197\) | 2.94550 | + | 2.94550i | 0.209858 | + | 0.209858i | 0.804207 | − | 0.594349i | \(-0.202590\pi\) |
−0.594349 | + | 0.804207i | \(0.702590\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.57285 | 0.182384 | 0.0911921 | − | 0.995833i | \(-0.470932\pi\) | ||||
0.0911921 | + | 0.995833i | \(0.470932\pi\) | |||||||
\(200\) | −27.3604 | + | 6.53809i | −1.93467 | + | 0.462313i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.00172377 | − | 0.189862i | 0.000121284 | − | 0.0133587i | ||||
\(203\) | 6.85170 | + | 1.83591i | 0.480895 | + | 0.128856i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.7252 | + | 3.40971i | −0.888768 | + | 0.238145i | ||||
\(206\) | 11.2040 | − | 2.89334i | 0.780620 | − | 0.201589i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.9595 | − | 2.51395i | 0.759906 | − | 0.174311i | ||||
\(209\) | 0.301228 | + | 0.173914i | 0.0208364 | + | 0.0120299i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.5700 | + | 4.70786i | 1.20957 | + | 0.324103i | 0.806592 | − | 0.591108i | \(-0.201309\pi\) |
0.402975 | + | 0.915211i | \(0.367976\pi\) | |||||||
\(212\) | −5.17388 | − | 20.8137i | −0.355343 | − | 1.42949i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.15769 | − | 14.4305i | −0.557648 | − | 0.986451i | ||||
\(215\) | 18.7704i | 1.28013i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 28.0206i | − | 1.90216i | ||||||
\(218\) | −10.9911 | + | 6.21338i | −0.744414 | + | 0.420823i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.45007 | − | 0.872682i | −0.0977638 | − | 0.0588362i | ||||
\(221\) | −11.5110 | − | 3.08436i | −0.774312 | − | 0.207476i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.82059 | + | 1.62847i | 0.188881 | + | 0.109050i | 0.591458 | − | 0.806336i | \(-0.298552\pi\) |
−0.402578 | + | 0.915386i | \(0.631886\pi\) | |||||||
\(224\) | 5.75551 | − | 18.1427i | 0.384556 | − | 1.21221i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.98432 | − | 23.1733i | −0.398071 | − | 1.54147i | ||||
\(227\) | 8.83238 | − | 2.36663i | 0.586226 | − | 0.157079i | 0.0464979 | − | 0.998918i | \(-0.485194\pi\) |
0.539728 | + | 0.841840i | \(0.318527\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.07755 | − | 1.36053i | −0.335534 | − | 0.0899061i | 0.0871183 | − | 0.996198i | \(-0.472234\pi\) |
−0.422652 | + | 0.906292i | \(0.638901\pi\) | |||||||
\(230\) | 21.0451 | + | 0.191070i | 1.38767 | + | 0.0125988i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.08083 | − | 3.12093i | −0.333573 | − | 0.204899i | ||||
\(233\) | −14.1506 | −0.927034 | −0.463517 | − | 0.886088i | \(-0.653413\pi\) | ||||
−0.463517 | + | 0.886088i | \(0.653413\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.8480 | − | 12.8480i | −0.838114 | − | 0.838114i | ||||
\(236\) | −7.67944 | − | 7.96351i | −0.499889 | − | 0.518380i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.3932 | + | 14.1342i | −0.932974 | + | 0.916185i | ||||
\(239\) | 7.51536 | + | 13.0170i | 0.486128 | + | 0.841999i | 0.999873 | − | 0.0159444i | \(-0.00507546\pi\) |
−0.513745 | + | 0.857943i | \(0.671742\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.18920 | − | 12.4521i | 0.463097 | − | 0.802108i | −0.536016 | − | 0.844208i | \(-0.680071\pi\) |
0.999113 | + | 0.0420996i | \(0.0134047\pi\) | |||||||
\(242\) | 3.87275 | + | 14.9966i | 0.248950 | + | 0.964019i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −17.3116 | − | 4.97723i | −1.10826 | − | 0.318635i | ||||
\(245\) | 16.1369 | − | 4.32388i | 1.03095 | − | 0.276242i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.23348 | + | 3.86850i | 0.142113 | + | 0.246147i | ||||
\(248\) | −6.71369 | + | 22.5774i | −0.426320 | + | 1.43367i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.3067 | + | 23.5389i | 0.841592 | + | 1.48873i | ||||
\(251\) | 3.59758 | − | 3.59758i | 0.227077 | − | 0.227077i | −0.584393 | − | 0.811471i | \(-0.698667\pi\) |
0.811471 | + | 0.584393i | \(0.198667\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.595798 | + | 0.595798i | 0.0374575 | + | 0.0374575i | ||||
\(254\) | −18.2633 | − | 5.07179i | −1.14594 | − | 0.318233i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.98442 | + | 13.2393i | −0.561526 | + | 0.827459i | ||||
\(257\) | 4.92640 | − | 2.84426i | 0.307300 | − | 0.177420i | −0.338418 | − | 0.940996i | \(-0.609892\pi\) |
0.645718 | + | 0.763576i | \(0.276558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.28294 | − | 12.2521i | −0.203992 | − | 0.761307i | ||||
\(260\) | −10.5238 | − | 19.0171i | −0.652661 | − | 1.17939i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.798004 | − | 0.470439i | −0.0493008 | − | 0.0290638i | ||||
\(263\) | −18.8392 | − | 10.8768i | −1.16167 | − | 0.670693i | −0.209970 | − | 0.977708i | \(-0.567337\pi\) |
−0.951705 | + | 0.307015i | \(0.900670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −35.9028 | + | 20.7285i | −2.20549 | + | 1.27334i | ||||
\(266\) | 7.56121 | + | 0.0686487i | 0.463607 | + | 0.00420912i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.43796 | + | 7.71310i | 0.454346 | + | 0.471153i | ||||
\(269\) | 7.43467 | − | 7.43467i | 0.453300 | − | 0.453300i | −0.443148 | − | 0.896448i | \(-0.646139\pi\) |
0.896448 | + | 0.443148i | \(0.146139\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.8875i | 0.722111i | 0.932544 | + | 0.361056i | \(0.117584\pi\) | ||||
−0.932544 | + | 0.361056i | \(0.882416\pi\) | |||||||
\(272\) | 14.9838 | − | 7.93996i | 0.908525 | − | 0.481431i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.8540 | − | 21.2361i | −1.25983 | − | 1.28292i | ||||
\(275\) | −0.563445 | + | 2.10281i | −0.0339770 | + | 0.126804i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.68166 | + | 10.0081i | 0.161126 | + | 0.601329i | 0.998503 | + | 0.0547032i | \(0.0174213\pi\) |
−0.837377 | + | 0.546626i | \(0.815912\pi\) | |||||||
\(278\) | −8.12750 | − | 4.79132i | −0.487455 | − | 0.287364i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −36.7783 | − | 1.00196i | −2.19792 | − | 0.0598784i | ||||
\(281\) | 7.05630 | − | 12.2219i | 0.420944 | − | 0.729096i | −0.575088 | − | 0.818091i | \(-0.695032\pi\) |
0.996032 | + | 0.0889955i | \(0.0283657\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.42843 | − | 12.7951i | 0.203799 | − | 0.760588i | −0.786013 | − | 0.618209i | \(-0.787858\pi\) |
0.989812 | − | 0.142378i | \(-0.0454749\pi\) | |||||||
\(284\) | 7.77189 | − | 12.9140i | 0.461177 | − | 0.766304i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.232837 | − | 0.838435i | 0.0137679 | − | 0.0495777i | ||||
\(287\) | −11.4660 | −0.676817 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.972286 | −0.0571933 | ||||||||
\(290\) | −3.08411 | + | 11.1057i | −0.181105 | + | 0.652151i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.32739 | + | 5.52889i | −0.194721 | + | 0.323554i | ||||
\(293\) | −7.96005 | + | 29.7073i | −0.465031 | + | 1.73552i | 0.191756 | + | 0.981443i | \(0.438582\pi\) |
−0.656787 | + | 0.754077i | \(0.728085\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.6924 | + | 18.5197i | −0.622533 | + | 1.07826i | ||||
\(296\) | −0.290375 | + | 10.6586i | −0.0168777 | + | 0.619520i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 27.2143 | + | 16.0434i | 1.57648 | + | 0.929368i | ||||
\(299\) | 2.80065 | + | 10.4522i | 0.161965 | + | 0.604463i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.22825 | + | 15.7800i | −0.243712 | + | 0.909546i | ||||
\(302\) | −19.7682 | − | 20.1304i | −1.13753 | − | 1.15838i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.07594 | − | 1.86697i | −0.348479 | − | 0.107078i | ||||
\(305\) | 34.8187i | 1.99371i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.8109 | − | 23.8109i | 1.35896 | − | 1.35896i | 0.483758 | − | 0.875202i | \(-0.339272\pi\) |
0.875202 | − | 0.483758i | \(-0.160728\pi\) | |||||||
\(308\) | −1.02247 | − | 1.06030i | −0.0582609 | − | 0.0604160i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 45.5286 | + | 0.413357i | 2.58585 | + | 0.0234771i | ||||
\(311\) | 9.20941 | − | 5.31706i | 0.522218 | − | 0.301503i | −0.215624 | − | 0.976477i | \(-0.569178\pi\) |
0.737842 | + | 0.674974i | \(0.235845\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.4634 | + | 9.50514i | 0.930565 | + | 0.537262i | 0.886990 | − | 0.461788i | \(-0.152792\pi\) |
0.0435750 | + | 0.999050i | \(0.486125\pi\) | |||||||
\(314\) | 18.1548 | + | 10.7026i | 1.02453 | + | 0.603982i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.57519 | + | 10.0746i | 0.313629 | + | 0.566742i | ||||
\(317\) | 3.18193 | + | 11.8751i | 0.178715 | + | 0.666972i | 0.995889 | + | 0.0905818i | \(0.0288727\pi\) |
−0.817174 | + | 0.576391i | \(0.804461\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.399628 | + | 0.230725i | −0.0223749 | + | 0.0129181i | ||||
\(320\) | 29.3938 | + | 9.61933i | 1.64316 | + | 0.537737i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.6493 | + | 4.90127i | 0.983556 | + | 0.273137i | ||||
\(323\) | 4.76356 | + | 4.76356i | 0.265052 | + | 0.265052i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.7692 | + | 19.7692i | −1.09660 | + | 1.09660i | ||||
\(326\) | −4.28896 | − | 7.58694i | −0.237543 | − | 0.420202i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.23866 | + | 2.74724i | 0.510119 | + | 0.151691i | ||||
\(329\) | −7.90701 | − | 13.6953i | −0.435928 | − | 0.755049i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.3960 | − | 8.94844i | 1.83561 | − | 0.491851i | 0.837134 | − | 0.546998i | \(-0.184229\pi\) |
0.998478 | + | 0.0551468i | \(0.0175627\pi\) | |||||||
\(332\) | 8.96675 | + | 2.57801i | 0.492114 | + | 0.141487i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.85696 | + | 18.8078i | 0.265761 | + | 1.02912i | ||||
\(335\) | 10.3561 | − | 17.9374i | 0.565817 | − | 0.980023i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.3693 | − | 24.8884i | −0.782746 | − | 1.35576i | −0.930336 | − | 0.366707i | \(-0.880485\pi\) |
0.147591 | − | 0.989049i | \(-0.452848\pi\) | |||||||
\(338\) | −5.14413 | + | 5.05156i | −0.279804 | + | 0.274769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −22.7533 | − | 23.5950i | −1.23397 | − | 1.27962i | ||||
\(341\) | 1.28894 | + | 1.28894i | 0.0698001 | + | 0.0698001i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.01293 | −0.486653 | ||||||||
\(344\) | 7.18775 | − | 11.7016i | 0.387538 | − | 0.630907i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.67659 | + | 0.0696962i | 0.412696 | + | 0.00374689i | ||||
\(347\) | 10.9346 | + | 2.92992i | 0.587002 | + | 0.157287i | 0.540082 | − | 0.841612i | \(-0.318393\pi\) |
0.0469191 | + | 0.998899i | \(0.485060\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.8496 | − | 2.90715i | 0.580767 | − | 0.155616i | 0.0435372 | − | 0.999052i | \(-0.486137\pi\) |
0.537230 | + | 0.843436i | \(0.319471\pi\) | |||||||
\(350\) | 11.8334 | + | 45.8228i | 0.632520 | + | 2.44933i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.569807 | + | 1.09931i | 0.0303708 | + | 0.0585935i | ||||
\(353\) | −1.85946 | − | 1.07356i | −0.0989689 | − | 0.0571397i | 0.449699 | − | 0.893180i | \(-0.351531\pi\) |
−0.548668 | + | 0.836041i | \(0.684865\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −28.1417 | − | 7.54056i | −1.49361 | − | 0.400211i | ||||
\(356\) | −5.07497 | − | 3.05422i | −0.268973 | − | 0.161873i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.661829 | − | 0.374137i | 0.0349787 | − | 0.0197738i | ||||
\(359\) | − | 11.0166i | − | 0.581435i | −0.956809 | − | 0.290718i | \(-0.906106\pi\) | ||
0.956809 | − | 0.290718i | \(-0.0938941\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.4748i | 0.867097i | ||||||||
\(362\) | −4.91125 | − | 8.68775i | −0.258130 | − | 0.456618i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.56344 | − | 18.3580i | −0.239189 | − | 0.962222i | ||||
\(365\) | 12.0484 | + | 3.22835i | 0.630641 | + | 0.168980i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.1365 | − | 11.6258i | −1.05112 | − | 0.606863i | −0.128156 | − | 0.991754i | \(-0.540906\pi\) |
−0.922962 | + | 0.384891i | \(0.874239\pi\) | |||||||
\(368\) | −13.0465 | − | 8.17791i | −0.680094 | − | 0.426303i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19.9559 | − | 5.15345i | 1.03746 | − | 0.267915i | ||||
\(371\) | −34.8524 | + | 9.33867i | −1.80945 | + | 0.484839i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.93021 | + | 2.66079i | 0.514167 | + | 0.137771i | 0.506567 | − | 0.862201i | \(-0.330914\pi\) |
0.00759967 | + | 0.999971i | \(0.497581\pi\) | |||||||
\(374\) | 0.0119140 | − | 1.31225i | 0.000616061 | − | 0.0678551i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.08964 | + | 12.9294i | 0.159336 | + | 0.666785i | ||||
\(377\) | −5.92615 | −0.305212 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.14819 | − | 6.14819i | −0.315811 | − | 0.315811i | 0.531345 | − | 0.847156i | \(-0.321687\pi\) |
−0.847156 | + | 0.531345i | \(0.821687\pi\) | |||||||
\(380\) | −0.223084 | + | 12.2846i | −0.0114440 | + | 0.630188i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.7125 | + | 10.9088i | 0.548100 | + | 0.558143i | ||||
\(383\) | 1.40170 | + | 2.42782i | 0.0716238 | + | 0.124056i | 0.899613 | − | 0.436688i | \(-0.143849\pi\) |
−0.827989 | + | 0.560744i | \(0.810515\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.42363 | + | 2.46580i | −0.0725548 | + | 0.125669i | ||||
\(386\) | −7.12153 | + | 1.83908i | −0.362476 | + | 0.0936066i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 26.7347 | − | 14.7947i | 1.35725 | − | 0.751086i | ||||
\(389\) | −29.1977 | + | 7.82350i | −1.48038 | + | 0.396667i | −0.906477 | − | 0.422255i | \(-0.861239\pi\) |
−0.573905 | + | 0.818922i | \(0.694572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.15956 | + | 14.1328i | 0.412647 | + | 0.714725i | ||||
\(392\) | −11.7156 | − | 3.48379i | −0.591727 | − | 0.175958i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.12828 | + | 2.89906i | −0.258359 | + | 0.146052i | ||||
\(395\) | 15.7382 | − | 15.7382i | 0.791873 | − | 0.791873i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.95789 | + | 1.95789i | 0.0982636 | + | 0.0982636i | 0.754530 | − | 0.656266i | \(-0.227865\pi\) |
−0.656266 | + | 0.754530i | \(0.727865\pi\) | |||||||
\(398\) | −0.973596 | + | 3.50588i | −0.0488020 | + | 0.175734i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.44441 | − | 39.7567i | 0.0722204 | − | 1.98783i | ||||
\(401\) | 28.7356 | − | 16.5905i | 1.43499 | − | 0.828489i | 0.437490 | − | 0.899223i | \(-0.355867\pi\) |
0.997495 | + | 0.0707337i | \(0.0225340\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.05887 | + | 22.6120i | 0.301814 | + | 1.12638i | ||||
\(404\) | 0.258063 | + | 0.0741950i | 0.0128391 | + | 0.00369134i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.09446 | + | 8.64172i | −0.252834 | + | 0.428881i | ||||
\(407\) | 0.714607 | + | 0.412578i | 0.0354217 | + | 0.0204508i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.8959 | + | 13.2190i | −1.13213 | + | 0.653636i | −0.944470 | − | 0.328598i | \(-0.893424\pi\) |
−0.187660 | + | 0.982234i | \(0.560090\pi\) | |||||||
\(410\) | 0.169145 | − | 18.6302i | 0.00835349 | − | 0.920082i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.297127 | + | 16.3620i | −0.0146384 | + | 0.806097i | ||||
\(413\) | −13.1607 | + | 13.1607i | −0.647596 | + | 0.647596i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 18.0347i | − | 0.885290i | ||||||
\(416\) | −0.721592 | + | 15.8853i | −0.0353790 | + | 0.778839i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.350971 | + | 0.344656i | −0.0171666 | + | 0.0168577i | ||||
\(419\) | 0.133835 | − | 0.499479i | 0.00653827 | − | 0.0244012i | −0.962580 | − | 0.270999i | \(-0.912646\pi\) |
0.969118 | + | 0.246598i | \(0.0793127\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.44352 | − | 12.8514i | −0.167827 | − | 0.626339i | −0.997663 | − | 0.0683313i | \(-0.978233\pi\) |
0.829836 | − | 0.558008i | \(-0.188434\pi\) | |||||||
\(422\) | −13.0638 | + | 22.1601i | −0.635938 | + | 1.07874i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 30.3196 | + | 0.826002i | 1.47245 | + | 0.0401142i | ||||
\(425\) | −21.0818 | + | 36.5148i | −1.02262 | + | 1.77123i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.84332 | + | 29.2717i | −0.379565 | + | 1.41655i | ||||
\(428\) | 22.7507 | − | 5.65536i | 1.09970 | − | 0.273362i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.5774 | − | 7.10295i | −1.23345 | − | 0.342534i | ||||
\(431\) | −8.61129 | −0.414791 | −0.207396 | − | 0.978257i | \(-0.566499\pi\) | ||||
−0.207396 | + | 0.978257i | \(0.566499\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.43973 | 0.309474 | 0.154737 | − | 0.987956i | \(-0.450547\pi\) | ||||
0.154737 | + | 0.987956i | \(0.450547\pi\) | |||||||
\(434\) | 38.1822 | + | 10.6033i | 1.83280 | + | 0.508976i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.30746 | − | 17.3282i | −0.206290 | − | 0.829873i | ||||
\(437\) | 1.58320 | − | 5.90859i | 0.0757348 | − | 0.282646i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4510 | − | 25.0298i | 0.689707 | − | 1.19461i | −0.282225 | − | 0.959348i | \(-0.591073\pi\) |
0.971933 | − | 0.235260i | \(-0.0755941\pi\) | |||||||
\(440\) | 1.73788 | − | 1.64570i | 0.0828502 | − | 0.0784557i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.55878 | − | 14.5182i | 0.407100 | − | 0.690562i | ||||
\(443\) | 8.35627 | + | 31.1860i | 0.397018 | + | 1.48169i | 0.818315 | + | 0.574770i | \(0.194908\pi\) |
−0.421297 | + | 0.906923i | \(0.638425\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.96330 | + | 11.0592i | −0.140474 | + | 0.524257i | ||||
\(446\) | −3.28637 | + | 3.22723i | −0.155614 | + | 0.152814i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 22.5441 | + | 14.7081i | 1.06511 | + | 0.694894i | ||||
\(449\) | − | 10.7097i | − | 0.505423i | −0.967542 | − | 0.252711i | \(-0.918678\pi\) | ||
0.967542 | − | 0.252711i | \(-0.0813223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.527433 | − | 0.527433i | 0.0248359 | − | 0.0248359i | ||||
\(452\) | 33.8415 | + | 0.614550i | 1.59177 | + | 0.0289060i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.117401 | + | 12.9310i | −0.00550991 | + | 0.606880i | ||||
\(455\) | −31.6669 | + | 18.2829i | −1.48457 | + | 0.857114i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1358 | − | 7.58393i | −0.614465 | − | 0.354761i | 0.160246 | − | 0.987077i | \(-0.448771\pi\) |
−0.774711 | + | 0.632316i | \(0.782105\pi\) | |||||||
\(458\) | 3.77532 | − | 6.40406i | 0.176409 | − | 0.299242i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.22407 | + | 28.6047i | −0.383449 | + | 1.33370i | ||||
\(461\) | 3.10006 | + | 11.5696i | 0.144384 | + | 0.538849i | 0.999782 | + | 0.0208774i | \(0.00664596\pi\) |
−0.855398 | + | 0.517971i | \(0.826687\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.03363 | − | 1.17412i | 0.0945107 | − | 0.0545658i | −0.452000 | − | 0.892018i | \(-0.649289\pi\) |
0.546510 | + | 0.837452i | \(0.315956\pi\) | |||||||
\(464\) | 6.17537 | − | 5.74238i | 0.286684 | − | 0.266583i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.35474 | − | 19.2822i | 0.248054 | − | 0.893231i | ||||
\(467\) | 24.1509 | + | 24.1509i | 1.11757 | + | 1.11757i | 0.992097 | + | 0.125473i | \(0.0400449\pi\) |
0.125473 | + | 0.992097i | \(0.459955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.7469 | − | 12.7469i | 0.588596 | − | 0.588596i | ||||
\(470\) | 22.3692 | − | 12.6455i | 1.03181 | − | 0.583292i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.7574 | − | 7.45087i | 0.633237 | − | 0.342954i | ||||
\(473\) | −0.531379 | − | 0.920376i | −0.0244328 | − | 0.0423189i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.2660 | − | 4.09051i | 0.700452 | − | 0.187685i | ||||
\(476\) | −13.8134 | − | 24.9614i | −0.633135 | − | 1.14410i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.5814 | + | 5.31499i | −0.941373 | + | 0.243102i | ||||
\(479\) | −2.40917 | + | 4.17281i | −0.110078 | + | 0.190660i | −0.915801 | − | 0.401631i | \(-0.868443\pi\) |
0.805724 | + | 0.592292i | \(0.201777\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.29851 | + | 9.17730i | 0.241591 | + | 0.418449i | ||||
\(482\) | 14.2473 | + | 14.5084i | 0.648946 | + | 0.660837i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.9006 | − | 0.397706i | −0.995480 | − | 0.0180775i | ||||
\(485\) | −41.7638 | − | 41.7638i | −1.89640 | − | 1.89640i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 37.5042 | 1.69948 | 0.849739 | − | 0.527204i | \(-0.176760\pi\) | ||||
0.849739 | + | 0.527204i | \(0.176760\pi\) | |||||||
\(488\) | 13.3331 | − | 21.7062i | 0.603563 | − | 0.982593i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.214494 | + | 23.6251i | −0.00968986 | + | 1.06727i | ||||
\(491\) | 1.88310 | + | 0.504576i | 0.0849832 | + | 0.0227712i | 0.301060 | − | 0.953605i | \(-0.402660\pi\) |
−0.216077 | + | 0.976376i | \(0.569326\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.63279 | + | 2.31315i | −0.388801 | + | 0.104179i | ||||
\(494\) | −6.11657 | + | 1.57955i | −0.275198 | + | 0.0710675i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −28.2245 | − | 17.6920i | −1.26732 | − | 0.794392i | ||||
\(497\) | −21.9598 | − | 12.6785i | −0.985032 | − | 0.568708i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.8793 | + | 2.91509i | 0.487023 | + | 0.130497i | 0.493971 | − | 0.869478i | \(-0.335545\pi\) |
−0.00694794 | + | 0.999976i | \(0.502212\pi\) | |||||||
\(500\) | −37.1106 | + | 9.22496i | −1.65964 | + | 0.412553i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.54086 | + | 6.26360i | 0.158036 | + | 0.279558i | ||||
\(503\) | 15.3339i | 0.683706i | 0.939753 | + | 0.341853i | \(0.111055\pi\) | ||||
−0.939753 | + | 0.341853i | \(0.888945\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.519039i | − | 0.0230969i | ||||||
\(506\) | −1.03732 | + | 0.586405i | −0.0461145 | + | 0.0260689i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.8221 | − | 22.9672i | 0.613257 | − | 1.01900i | ||||
\(509\) | −32.0866 | − | 8.59758i | −1.42221 | − | 0.381081i | −0.535945 | − | 0.844253i | \(-0.680045\pi\) |
−0.886269 | + | 0.463172i | \(0.846711\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.40169 | + | 5.42807i | 0.415906 | + | 0.240124i | ||||
\(512\) | −14.6407 | − | 17.2525i | −0.647035 | − | 0.762461i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.01151 | + | 7.78924i | 0.0887238 | + | 0.343568i | ||||
\(515\) | 30.5548 | − | 8.18713i | 1.34641 | − | 0.360768i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.993703 | + | 0.266262i | 0.0437030 | + | 0.0117102i | ||||
\(518\) | 17.9376 | + | 0.162856i | 0.788131 | + | 0.00715549i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 29.8959 | − | 7.14398i | 1.31102 | − | 0.313284i | ||||
\(521\) | 20.5032 | 0.898262 | 0.449131 | − | 0.893466i | \(-0.351734\pi\) | ||||
0.449131 | + | 0.893466i | \(0.351734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.2406 | − | 29.2406i | −1.27860 | − | 1.27860i | −0.941451 | − | 0.337151i | \(-0.890537\pi\) |
−0.337151 | − | 0.941451i | \(-0.609463\pi\) | |||||||
\(524\) | 0.943016 | − | 0.909377i | 0.0411958 | − | 0.0397263i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.9502 | − | 21.5552i | 0.957076 | − | 0.939853i | ||||
\(527\) | 17.6523 | + | 30.5746i | 0.768944 | + | 1.33185i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.09099 | + | 7.08581i | −0.177869 | + | 0.308079i | ||||
\(530\) | −14.6596 | − | 56.7668i | −0.636771 | − | 2.46579i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.95479 | + | 10.2773i | −0.128107 | + | 0.445576i | ||||
\(533\) | 9.25281 | − | 2.47928i | 0.400784 | − | 0.107390i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −22.6575 | − | 39.2440i | −0.979570 | − | 1.69667i | ||||
\(536\) | −13.3248 | + | 7.21658i | −0.575545 | + | 0.311709i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.31746 | + | 12.9442i | 0.315478 | + | 0.558064i | ||||
\(539\) | −0.668841 | + | 0.668841i | −0.0288090 | + | 0.0288090i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.5836 | + | 20.5836i | 0.884956 | + | 0.884956i | 0.994033 | − | 0.109077i | \(-0.0347895\pi\) |
−0.109077 | + | 0.994033i | \(0.534790\pi\) | |||||||
\(542\) | −16.1984 | − | 4.49836i | −0.695780 | − | 0.193221i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.14932 | + | 23.4222i | 0.220775 | + | 1.00422i | ||||
\(545\) | −29.8905 | + | 17.2573i | −1.28037 | + | 0.739221i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.2029 | + | 38.0779i | 0.436246 | + | 1.62809i | 0.738067 | + | 0.674728i | \(0.235739\pi\) |
−0.301821 | + | 0.953365i | \(0.597594\pi\) | |||||||
\(548\) | 36.8287 | − | 20.3806i | 1.57324 | − | 0.870616i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.65217 | − | 1.56350i | −0.113089 | − | 0.0666680i | ||||
\(551\) | 2.90122 | + | 1.67502i | 0.123596 | + | 0.0713584i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.7761 | − | 9.68566i | 0.713391 | − | 0.411876i | ||||
\(554\) | −14.6523 | − | 0.133029i | −0.622516 | − | 0.00565186i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.60441 | − | 9.26181i | 0.407318 | − | 0.392788i | ||||
\(557\) | 1.52288 | − | 1.52288i | 0.0645265 | − | 0.0645265i | −0.674107 | − | 0.738634i | \(-0.735471\pi\) |
0.738634 | + | 0.674107i | \(0.235471\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 13.6484i | − | 0.577266i | ||||||
\(560\) | 15.2827 | − | 49.7366i | 0.645810 | − | 2.10176i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.9839 | + | 14.2401i | 0.589875 | + | 0.600684i | ||||
\(563\) | 1.30147 | − | 4.85715i | 0.0548504 | − | 0.204705i | −0.933063 | − | 0.359714i | \(-0.882874\pi\) |
0.987913 | + | 0.155010i | \(0.0495409\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.9335 | − | 63.1966i | −0.712397 | − | 2.65870i | ||||
\(566\) | 16.1378 | + | 9.51354i | 0.678322 | + | 0.399884i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.6562 | + | 15.4771i | 0.614961 | + | 0.649407i | ||||
\(569\) | 17.4710 | − | 30.2606i | 0.732421 | − | 1.26859i | −0.223425 | − | 0.974721i | \(-0.571724\pi\) |
0.955846 | − | 0.293869i | \(-0.0949430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.16034 | + | 34.1869i | −0.383348 | + | 1.43068i | 0.457406 | + | 0.889258i | \(0.348779\pi\) |
−0.840754 | + | 0.541417i | \(0.817888\pi\) | |||||||
\(572\) | 1.05438 | + | 0.634548i | 0.0440859 | + | 0.0265318i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.33887 | − | 15.6241i | 0.181101 | − | 0.652137i | ||||
\(575\) | 38.2852 | 1.59660 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.4865 | −0.727972 | −0.363986 | − | 0.931404i | \(-0.618584\pi\) | ||||
−0.363986 | + | 0.931404i | \(0.618584\pi\) | |||||||
\(578\) | 0.367925 | − | 1.32488i | 0.0153037 | − | 0.0551078i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13.9661 | − | 8.40509i | −0.579912 | − | 0.349002i | ||||
\(581\) | 4.06253 | − | 15.1616i | 0.168542 | − | 0.629008i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17362 | − | 2.03278i | 0.0486065 | − | 0.0841890i | ||||
\(584\) | −6.27479 | − | 6.62626i | −0.259653 | − | 0.274197i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −37.4684 | − | 22.0883i | −1.54780 | − | 0.912461i | ||||
\(587\) | −3.31081 | − | 12.3561i | −0.136652 | − | 0.509991i | −0.999986 | − | 0.00535825i | \(-0.998294\pi\) |
0.863334 | − | 0.504633i | \(-0.168372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.42507 | − | 12.7825i | 0.141128 | − | 0.526696i | ||||
\(590\) | −21.1897 | − | 21.5780i | −0.872366 | − | 0.888352i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.4140 | − | 4.42903i | −0.592414 | − | 0.182032i | ||||
\(593\) | − | 25.7816i | − | 1.05872i | −0.848397 | − | 0.529361i | \(-0.822432\pi\) | ||
0.848397 | − | 0.529361i | \(-0.177568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −38.9937 | + | 38.9937i | −1.59858 | + | 1.59858i | ||||
\(596\) | −32.1597 | + | 31.0125i | −1.31731 | + | 1.27032i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.3024 | − | 0.138931i | −0.625761 | − | 0.00568132i | ||||
\(599\) | 27.3647 | − | 15.7990i | 1.11809 | − | 0.645531i | 0.177180 | − | 0.984179i | \(-0.443303\pi\) |
0.940913 | + | 0.338647i | \(0.109969\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.3729 | + | 13.4944i | 0.953401 | + | 0.550447i | 0.894136 | − | 0.447796i | \(-0.147791\pi\) |
0.0592656 | + | 0.998242i | \(0.481124\pi\) | |||||||
\(602\) | −19.9026 | − | 11.7330i | −0.811169 | − | 0.478200i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 34.9111 | − | 19.3194i | 1.42051 | − | 0.786097i | ||||
\(605\) | 10.9585 | + | 40.8977i | 0.445527 | + | 1.66273i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.2314 | + | 12.2579i | −0.861755 | + | 0.497534i | −0.864600 | − | 0.502462i | \(-0.832428\pi\) |
0.00284471 | + | 0.999996i | \(0.499095\pi\) | |||||||
\(608\) | 4.84322 | − | 7.57288i | 0.196419 | − | 0.307121i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −47.4456 | − | 13.1758i | −1.92102 | − | 0.533474i | ||||
\(611\) | 9.34212 | + | 9.34212i | 0.377942 | + | 0.377942i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.3894 | + | 30.3894i | −1.22742 | + | 1.22742i | −0.262481 | + | 0.964937i | \(0.584541\pi\) |
−0.964937 | + | 0.262481i | \(0.915459\pi\) | |||||||
\(614\) | 23.4355 | + | 41.4562i | 0.945780 | + | 1.67303i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.83173 | − | 0.992042i | 0.0738024 | − | 0.0399705i | ||||
\(617\) | 15.8393 | + | 27.4345i | 0.637668 | + | 1.10447i | 0.985943 | + | 0.167081i | \(0.0534341\pi\) |
−0.348275 | + | 0.937392i | \(0.613233\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.1312 | + | 5.39413i | −0.809141 | + | 0.216809i | −0.639593 | − | 0.768713i | \(-0.720897\pi\) |
−0.169547 | + | 0.985522i | \(0.554231\pi\) | |||||||
\(620\) | −17.7918 | + | 61.8829i | −0.714537 | + | 2.48528i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.76031 | + | 14.5612i | 0.150775 | + | 0.583851i | ||||
\(623\) | −4.98242 | + | 8.62981i | −0.199617 | + | 0.345746i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.0944 | + | 20.9481i | 0.483775 | + | 0.837923i | ||||
\(626\) | −19.1821 | + | 18.8369i | −0.766670 | + | 0.752874i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.4538 | + | 20.6885i | −0.856101 | + | 0.825563i | ||||
\(629\) | 11.3007 | + | 11.3007i | 0.450587 | + | 0.450587i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.9953 | −0.796002 | −0.398001 | − | 0.917385i | \(-0.630296\pi\) | ||||
−0.398001 | + | 0.917385i | \(0.630296\pi\) | |||||||
\(632\) | −15.8379 | + | 3.78464i | −0.629997 | + | 0.150545i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.3856 | − | 0.157845i | −0.690472 | − | 0.00626884i | ||||
\(635\) | −50.0494 | − | 13.4107i | −1.98615 | − | 0.532187i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.7335 | + | 3.14400i | −0.464900 | + | 0.124570i | ||||
\(638\) | −0.163173 | − | 0.631861i | −0.00646008 | − | 0.0250156i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.2307 | + | 36.4133i | −0.957803 | + | 1.43936i | ||||
\(641\) | −12.6976 | − | 7.33098i | −0.501526 | − | 0.289556i | 0.227818 | − | 0.973704i | \(-0.426841\pi\) |
−0.729344 | + | 0.684148i | \(0.760174\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.8777 | + | 3.45056i | 0.507846 | + | 0.136077i | 0.503639 | − | 0.863914i | \(-0.331994\pi\) |
0.00420705 | + | 0.999991i | \(0.498661\pi\) | |||||||
\(644\) | −13.3574 | + | 22.1950i | −0.526355 | + | 0.874606i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.29363 | + | 4.68846i | −0.326309 | + | 0.184465i | ||||
\(647\) | − | 30.5078i | − | 1.19939i | −0.800231 | − | 0.599693i | \(-0.795290\pi\) | ||
0.800231 | − | 0.599693i | \(-0.204710\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.21078i | − | 0.0475272i | ||||||
\(650\) | −19.4575 | − | 34.4193i | −0.763185 | − | 1.35003i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.9613 | − | 2.97334i | 0.468441 | − | 0.116445i | ||||
\(653\) | −20.1465 | − | 5.39824i | −0.788394 | − | 0.211249i | −0.157912 | − | 0.987453i | \(-0.550476\pi\) |
−0.630482 | + | 0.776204i | \(0.717143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.19305 | − | 1.26616i | −0.0856896 | − | 0.0494729i | ||||
\(656\) | −7.23953 | + | 11.5494i | −0.282656 | + | 0.450930i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.6540 | − | 5.59198i | 0.844162 | − | 0.217998i | ||||
\(659\) | 14.5728 | − | 3.90477i | 0.567676 | − | 0.152108i | 0.0364452 | − | 0.999336i | \(-0.488397\pi\) |
0.531230 | + | 0.847227i | \(0.321730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.11835 | − | 2.44325i | −0.354663 | − | 0.0950316i | 0.0770887 | − | 0.997024i | \(-0.475438\pi\) |
−0.431751 | + | 0.901993i | \(0.642104\pi\) | |||||||
\(662\) | −0.443904 | + | 48.8932i | −0.0172528 | + | 1.90029i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.90604 | + | 11.2430i | −0.268006 | + | 0.436311i | ||||
\(665\) | 20.6706 | 0.801570 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.73833 | + | 5.73833i | 0.222189 | + | 0.222189i | ||||
\(668\) | −27.4663 | − | 0.498777i | −1.06270 | − | 0.0192983i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 20.5234 | + | 20.8995i | 0.792888 | + | 0.807417i | ||||
\(671\) | −0.985698 | − | 1.70728i | −0.0380525 | − | 0.0659088i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.1140 | + | 27.9103i | −0.621149 | + | 1.07586i | 0.368123 | + | 0.929777i | \(0.380001\pi\) |
−0.989272 | + | 0.146085i | \(0.953333\pi\) | |||||||
\(674\) | 39.3516 | − | 10.1622i | 1.51577 | − | 0.391434i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.93689 | − | 8.92120i | −0.189880 | − | 0.343123i | ||||
\(677\) | 15.5364 | − | 4.16296i | 0.597111 | − | 0.159996i | 0.0524101 | − | 0.998626i | \(-0.483310\pi\) |
0.544701 | + | 0.838630i | \(0.316643\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −25.7025 | − | 44.5181i | −0.986372 | − | 1.70845i | ||||
\(680\) | 40.7617 | − | 22.0761i | 1.56314 | − | 0.846579i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.24412 | + | 1.26862i | −0.0859318 | + | 0.0485779i | ||||
\(683\) | −28.6734 | + | 28.6734i | −1.09716 | + | 1.09716i | −0.102416 | + | 0.994742i | \(0.532657\pi\) |
−0.994742 | + | 0.102416i | \(0.967343\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −57.5322 | − | 57.5322i | −2.19819 | − | 2.19819i | ||||
\(686\) | 3.41060 | − | 12.2814i | 0.130217 | − | 0.468907i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.2252 | + | 14.2224i | 0.504205 | + | 0.542223i | ||||
\(689\) | 26.1058 | − | 15.0722i | 0.994552 | − | 0.574205i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.8033 | − | 44.0504i | −0.449017 | − | 1.67575i | −0.705106 | − | 0.709102i | \(-0.749101\pi\) |
0.256089 | − | 0.966653i | \(-0.417566\pi\) | |||||||
\(692\) | −2.99988 | + | 10.4341i | −0.114038 | + | 0.396645i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.13025 | + | 13.7913i | −0.308620 | + | 0.523511i | ||||
\(695\) | −22.3358 | − | 12.8956i | −0.847243 | − | 0.489156i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.5111 | − | 7.22328i | 0.473892 | − | 0.273601i | ||||
\(698\) | −0.144215 | + | 15.8843i | −0.00545861 | + | 0.601230i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −66.9181 | − | 1.21521i | −2.52927 | − | 0.0459305i | ||||
\(701\) | −13.0178 | + | 13.0178i | −0.491676 | + | 0.491676i | −0.908834 | − | 0.417158i | \(-0.863026\pi\) |
0.417158 | + | 0.908834i | \(0.363026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.99049i | − | 0.225935i | ||||||
\(704\) | −1.71359 | + | 0.360453i | −0.0645835 | + | 0.0135851i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.16652 | − | 2.12753i | 0.0815380 | − | 0.0800708i | ||||
\(707\) | 0.116919 | − | 0.436349i | 0.00439721 | − | 0.0164106i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.39011 | + | 16.3841i | 0.164874 | + | 0.615319i | 0.998056 | + | 0.0623199i | \(0.0198499\pi\) |
−0.833182 | + | 0.552999i | \(0.813483\pi\) | |||||||
\(710\) | 20.9243 | − | 35.4938i | 0.785274 | − | 1.33206i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.08224 | − | 5.75963i | 0.227942 | − | 0.215851i | ||||
\(713\) | 16.0285 | − | 27.7622i | 0.600273 | − | 1.03970i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.615660 | − | 2.29767i | 0.0230244 | − | 0.0859282i | ||||
\(716\) | 0.259372 | + | 1.04342i | 0.00969320 | + | 0.0389943i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.0118 | + | 4.16883i | 0.560234 | + | 0.155579i | ||||
\(719\) | −43.0731 | −1.60635 | −0.803177 | − | 0.595740i | \(-0.796859\pi\) | ||||
−0.803177 | + | 0.595740i | \(0.796859\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.5313 | 1.02532 | ||||||||
\(722\) | −22.4494 | − | 6.23428i | −0.835479 | − | 0.232016i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.6968 | − | 3.40475i | 0.509038 | − | 0.126537i | ||||
\(725\) | −5.42673 | + | 20.2528i | −0.201544 | + | 0.752171i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.3101 | − | 26.5179i | 0.567821 | − | 0.983495i | −0.428960 | − | 0.903324i | \(-0.641120\pi\) |
0.996781 | − | 0.0801716i | \(-0.0255468\pi\) | |||||||
\(728\) | 26.7424 | + | 0.728547i | 0.991138 | + | 0.0270017i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.95835 | + | 15.1960i | −0.331563 | + | 0.562430i | ||||
\(731\) | −5.32737 | − | 19.8820i | −0.197040 | − | 0.735363i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.679676 | − | 2.53658i | 0.0251044 | − | 0.0936909i | −0.952237 | − | 0.305360i | \(-0.901223\pi\) |
0.977341 | + | 0.211669i | \(0.0678899\pi\) | |||||||
\(734\) | 23.4618 | − | 23.0396i | 0.865990 | − | 0.850407i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0805 | − | 14.6831i | 0.592736 | − | 0.541226i | ||||
\(737\) | 1.17271i | 0.0431972i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.1402 | − | 13.1402i | 0.483370 | − | 0.483370i | −0.422836 | − | 0.906206i | \(-0.638965\pi\) |
0.906206 | + | 0.422836i | \(0.138965\pi\) | |||||||
\(740\) | −0.529226 | + | 29.1430i | −0.0194547 | + | 1.07132i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.463262 | − | 51.0253i | 0.0170069 | − | 1.87320i | ||||
\(743\) | 1.79055 | − | 1.03378i | 0.0656890 | − | 0.0379255i | −0.466796 | − | 0.884365i | \(-0.654592\pi\) |
0.532485 | + | 0.846440i | \(0.321258\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 74.7897 | + | 43.1798i | 2.74008 | + | 1.58199i | ||||
\(746\) | −7.38343 | + | 12.5245i | −0.270327 | + | 0.458554i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.78363 | + | 0.512808i | 0.0652160 | + | 0.0187501i | ||||
\(749\) | −10.2077 | − | 38.0958i | −0.372982 | − | 1.39199i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.86676 | + | 4.54188i | −0.287062 | + | 0.165735i | −0.636616 | − | 0.771181i | \(-0.719666\pi\) |
0.349554 | + | 0.936916i | \(0.386333\pi\) | |||||||
\(752\) | −18.7874 | − | 0.682570i | −0.685107 | − | 0.0248908i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.24253 | − | 8.07525i | 0.0816680 | − | 0.294083i | ||||
\(755\) | −54.5367 | − | 54.5367i | −1.98479 | − | 1.98479i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.3910 | − | 18.3910i | 0.668433 | − | 0.668433i | −0.288920 | − | 0.957353i | \(-0.593296\pi\) |
0.957353 | + | 0.288920i | \(0.0932961\pi\) | |||||||
\(758\) | 10.7043 | − | 6.05125i | 0.388799 | − | 0.219791i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −16.6552 | − | 4.95263i | −0.604147 | − | 0.179651i | ||||
\(761\) | 14.1080 | + | 24.4358i | 0.511415 | + | 0.885797i | 0.999912 | + | 0.0132318i | \(0.00421194\pi\) |
−0.488497 | + | 0.872565i | \(0.662455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.0160 | + | 7.77481i | −1.05045 | + | 0.281467i | ||||
\(764\) | −18.9186 | + | 10.4693i | −0.684451 | + | 0.378767i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.83869 | + | 0.991310i | −0.138697 | + | 0.0358175i | ||||
\(767\) | 7.77467 | − | 13.4661i | 0.280727 | − | 0.486234i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.6064 | − | 25.2991i | −0.526722 | − | 0.912309i | −0.999515 | − | 0.0311354i | \(-0.990088\pi\) |
0.472794 | − | 0.881173i | \(-0.343246\pi\) | |||||||
\(770\) | −2.82129 | − | 2.87299i | −0.101672 | − | 0.103535i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.188861 | − | 10.4001i | 0.00679726 | − | 0.374306i | ||||
\(773\) | 10.5491 | + | 10.5491i | 0.379425 | + | 0.379425i | 0.870895 | − | 0.491470i | \(-0.163540\pi\) |
−0.491470 | + | 0.870895i | \(0.663540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 82.8256 | 2.97518 | ||||||||
\(776\) | 10.0432 | + | 42.0284i | 0.360529 | + | 1.50873i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.388099 | − | 42.7466i | 0.0139140 | − | 1.53254i | ||||
\(779\) | −5.23060 | − | 1.40154i | −0.187406 | − | 0.0502152i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.59335 | − | 0.426938i | 0.0570146 | − | 0.0152770i | ||||
\(782\) | −22.3456 | + | 5.77058i | −0.799078 | + | 0.206356i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.18049 | − | 14.6459i | 0.327875 | − | 0.523068i | ||||
\(785\) | 49.8924 | + | 28.8054i | 1.78074 | + | 1.02811i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.8023 | + | 9.05729i | 1.20492 | + | 0.322857i | 0.804767 | − | 0.593591i | \(-0.202290\pi\) |
0.400153 | + | 0.916448i | \(0.368957\pi\) | |||||||
\(788\) | −2.00979 | − | 8.08507i | −0.0715957 | − | 0.288019i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.4900 | + | 27.4010i | 0.551110 | + | 0.974885i | ||||
\(791\) | − | 56.9431i | − | 2.02466i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 25.3175i | − | 0.899052i | ||||||
\(794\) | −3.40880 | + | 1.92702i | −0.120974 | + | 0.0683874i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.40885 | − | 2.65333i | −0.156268 | − | 0.0940449i | ||||
\(797\) | 27.6668 | + | 7.41329i | 0.980007 | + | 0.262592i | 0.713048 | − | 0.701116i | \(-0.247314\pi\) |
0.266959 | + | 0.963708i | \(0.413981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.2554 | + | 9.96243i | 0.610453 | + | 0.352445i | ||||
\(800\) | 53.6277 | + | 17.0126i | 1.89602 | + | 0.601487i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.7331 | + | 45.4344i | 0.414309 | + | 1.60435i | ||||
\(803\) | −0.682165 | + | 0.182786i | −0.0240731 | + | 0.00645036i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 48.3667 | + | 12.9598i | 1.70470 | + | 0.456773i | ||||
\(806\) | −33.1049 | − | 0.300562i | −1.16607 | − | 0.0105868i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.198756 | + | 0.323572i | −0.00699220 | + | 0.0113832i | ||||
\(809\) | 39.9831 | 1.40573 | 0.702865 | − | 0.711323i | \(-0.251904\pi\) | ||||
0.702865 | + | 0.711323i | \(0.251904\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.5121 | − | 33.5121i | −1.17677 | − | 1.17677i | −0.980563 | − | 0.196204i | \(-0.937138\pi\) |
−0.196204 | − | 0.980563i | \(-0.562862\pi\) | |||||||
\(812\) | −9.84780 | − | 10.2121i | −0.345590 | − | 0.358374i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.832614 | + | 0.817632i | −0.0291831 | + | 0.0286580i | ||||
\(815\) | −11.9123 | − | 20.6328i | −0.417271 | − | 0.722734i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.85771 | + | 6.68176i | −0.134964 | + | 0.233765i | ||||
\(818\) | −9.34868 | − | 36.2012i | −0.326869 | − | 1.26575i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 25.3224 | + | 7.28039i | 0.884297 | + | 0.254242i | ||||
\(821\) | 10.8942 | − | 2.91908i | 0.380209 | − | 0.101877i | −0.0636527 | − | 0.997972i | \(-0.520275\pi\) |
0.443861 | + | 0.896096i | \(0.353608\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.4702 | + | 47.5798i | 0.957551 | + | 1.65853i | 0.728420 | + | 0.685131i | \(0.240255\pi\) |
0.229131 | + | 0.973396i | \(0.426412\pi\) | |||||||
\(824\) | −22.1831 | − | 6.59645i | −0.772786 | − | 0.229798i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.9532 | − | 22.9136i | −0.450700 | − | 0.797265i | ||||
\(827\) | −14.2104 | + | 14.2104i | −0.494144 | + | 0.494144i | −0.909609 | − | 0.415465i | \(-0.863619\pi\) |
0.415465 | + | 0.909609i | \(0.363619\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.15512 | + | 6.15512i | 0.213776 | + | 0.213776i | 0.805869 | − | 0.592093i | \(-0.201698\pi\) |
−0.592093 | + | 0.805869i | \(0.701698\pi\) | |||||||
\(830\) | 24.5750 | + | 6.82456i | 0.853009 | + | 0.236884i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −21.3729 | − | 6.99445i | −0.740973 | − | 0.242489i | ||||
\(833\) | −15.8654 | + | 9.15989i | −0.549704 | + | 0.317371i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.7435 | + | 51.2913i | 0.475612 | + | 1.77501i | ||||
\(836\) | −0.336832 | − | 0.608672i | −0.0116496 | − | 0.0210513i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.629969 | + | 0.371379i | 0.0217619 | + | 0.0128291i | ||||
\(839\) | 21.5384 | + | 12.4352i | 0.743590 | + | 0.429312i | 0.823373 | − | 0.567500i | \(-0.192089\pi\) |
−0.0797833 | + | 0.996812i | \(0.525423\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.2658 | − | 12.2778i | 0.733303 | − | 0.423373i | ||||
\(842\) | 18.8150 | + | 0.170822i | 0.648407 | + | 0.00588693i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −25.2529 | − | 26.1871i | −0.869242 | − | 0.901396i | ||||
\(845\) | −13.9363 | + | 13.9363i | −0.479424 | + | 0.479424i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.8507i | 1.26621i | ||||||||
\(848\) | −12.5989 | + | 41.0023i | −0.432646 | + | 1.40803i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −41.7791 | − | 42.5447i | −1.43301 | − | 1.45927i | ||||
\(851\) | 3.75585 | − | 14.0170i | 0.128749 | − | 0.480497i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.05023 | − | 18.8477i | −0.172917 | − | 0.645334i | −0.996897 | − | 0.0787157i | \(-0.974918\pi\) |
0.823980 | − | 0.566618i | \(-0.191749\pi\) | |||||||
\(854\) | −36.9189 | − | 21.7644i | −1.26334 | − | 0.744763i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.902871 | + | 33.1412i | −0.0308595 | + | 1.13274i | ||||
\(857\) | 18.6982 | − | 32.3862i | 0.638717 | − | 1.10629i | −0.346998 | − | 0.937866i | \(-0.612799\pi\) |
0.985715 | − | 0.168424i | \(-0.0538679\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.10549 | + | 26.5180i | −0.242436 | + | 0.904784i | 0.732219 | + | 0.681070i | \(0.238485\pi\) |
−0.974655 | + | 0.223714i | \(0.928182\pi\) | |||||||
\(860\) | 19.3576 | − | 32.1651i | 0.660089 | − | 1.09682i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.25862 | − | 11.7341i | 0.110989 | − | 0.399667i | ||||
\(863\) | 10.1797 | 0.346520 | 0.173260 | − | 0.984876i | \(-0.444570\pi\) | ||||
0.173260 | + | 0.984876i | \(0.444570\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.9860 | 0.713545 | ||||||||
\(866\) | −2.43687 | + | 8.77507i | −0.0828082 | + | 0.298189i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −28.8972 | + | 48.0164i | −0.980834 | + | 1.62978i | ||||
\(869\) | −0.326156 | + | 1.21723i | −0.0110641 | + | 0.0412918i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.53020 | + | 13.0427i | −0.255151 | + | 0.441935i | ||||
\(872\) | 25.2423 | + | 0.687680i | 0.854811 | + | 0.0232878i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.45221 | + | 4.39322i | 0.252075 | + | 0.148603i | ||||
\(875\) | 16.6507 | + | 62.1414i | 0.562897 | + | 2.10076i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.90717 | + | 25.7779i | −0.233239 | + | 0.870458i | 0.745696 | + | 0.666286i | \(0.232117\pi\) |
−0.978935 | + | 0.204172i | \(0.934550\pi\) | |||||||
\(878\) | 28.6384 | + | 29.1631i | 0.966498 | + | 0.984208i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.58487 | + | 2.99087i | 0.0534261 | + | 0.100822i | ||||
\(881\) | 30.7798i | 1.03700i | 0.855078 | + | 0.518499i | \(0.173509\pi\) | ||||
−0.855078 | + | 0.518499i | \(0.826491\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.8089 | + | 19.8089i | −0.666622 | + | 0.666622i | −0.956933 | − | 0.290310i | \(-0.906241\pi\) |
0.290310 | + | 0.956933i | \(0.406241\pi\) | |||||||
\(884\) | 16.5445 | + | 17.1565i | 0.556451 | + | 0.577034i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −45.6576 | − | 0.414528i | −1.53390 | − | 0.0139264i | ||||
\(887\) | −21.0940 | + | 12.1786i | −0.708266 | + | 0.408918i | −0.810419 | − | 0.585851i | \(-0.800760\pi\) |
0.102153 | + | 0.994769i | \(0.467427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −39.0550 | − | 22.5484i | −1.30986 | − | 0.756249i | ||||
\(890\) | −13.9484 | − | 8.22287i | −0.467552 | − | 0.275631i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.15397 | − | 5.69938i | −0.105603 | − | 0.190829i | ||||
\(893\) | −1.93301 | − | 7.21410i | −0.0646858 | − | 0.241411i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.79985 | − | 1.03914i | 0.0601624 | − | 0.0347348i | ||||
\(896\) | −28.5729 | + | 25.1539i | −0.954555 | + | 0.840333i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.5935 | + | 4.05268i | 0.486993 | + | 0.135240i | ||||
\(899\) | 12.4142 | + | 12.4142i | 0.414037 | + | 0.414037i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 32.1460 | − | 32.1460i | 1.07094 | − | 1.07094i | ||||
\(902\) | 0.519118 | + | 0.918292i | 0.0172847 | + | 0.0305758i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.6435 | + | 45.8815i | −0.453775 | + | 1.52600i | ||||
\(905\) | −13.6407 | − | 23.6264i | −0.453433 | − | 0.785369i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.0698 | − | 15.0239i | 1.86177 | − | 0.498859i | 0.861802 | − | 0.507245i | \(-0.169336\pi\) |
0.999965 | + | 0.00838605i | \(0.00266939\pi\) | |||||||
\(908\) | −17.5759 | − | 5.05321i | −0.583277 | − | 0.167697i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.9300 | − | 50.0692i | −0.428624 | − | 1.65978i | ||||
\(911\) | −11.9347 | + | 20.6715i | −0.395414 | + | 0.684877i | −0.993154 | − | 0.116813i | \(-0.962732\pi\) |
0.597740 | + | 0.801690i | \(0.296066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.510553 | + | 0.884303i | 0.0168968 | + | 0.0292662i | ||||
\(914\) | 15.3049 | − | 15.0295i | 0.506242 | − | 0.497133i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.29785 | + | 7.56780i | 0.241128 | + | 0.250047i | ||||
\(917\) | −1.55845 | − | 1.55845i | −0.0514646 | − | 0.0514646i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.7779 | −0.520466 | −0.260233 | − | 0.965546i | \(-0.583799\pi\) | ||||
−0.260233 | + | 0.965546i | \(0.583799\pi\) | |||||||
\(920\) | −35.8660 | − | 22.0309i | −1.18247 | − | 0.726336i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.9383 | − | 0.153784i | −0.557834 | − | 0.00506461i | ||||
\(923\) | 20.4625 | + | 5.48292i | 0.673533 | + | 0.180473i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.2157 | − | 9.70397i | 1.19077 | − | 0.319065i | ||||
\(926\) | 0.830355 | + | 3.21541i | 0.0272872 | + | 0.105665i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.48800 | + | 10.5878i | 0.180152 | + | 0.347563i | ||||
\(929\) | −14.3132 | − | 8.26371i | −0.469600 | − | 0.271123i | 0.246472 | − | 0.969150i | \(-0.420729\pi\) |
−0.716072 | + | 0.698026i | \(0.754062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.63296 | + | 1.77730i | 0.217387 | + | 0.0582485i | ||||
\(932\) | 24.2485 | + | 14.5932i | 0.794287 | + | 0.478017i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −42.0481 | + | 23.7701i | −1.37586 | + | 0.777783i | ||||
\(935\) | − | 3.58740i | − | 0.117320i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.92940i | 0.193705i | 0.995299 | + | 0.0968526i | \(0.0308775\pi\) | ||||
−0.995299 | + | 0.0968526i | \(0.969122\pi\) | |||||||
\(938\) | 12.5459 | + | 22.1930i | 0.409638 | + | 0.724629i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.76654 | + | 35.2665i | 0.285933 | + | 1.15027i | ||||
\(941\) | 20.6096 | + | 5.52232i | 0.671853 | + | 0.180022i | 0.578589 | − | 0.815619i | \(-0.303603\pi\) |
0.0932635 | + | 0.995641i | \(0.470270\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.3603 | − | 6.55886i | −0.369941 | − | 0.213586i | ||||
\(944\) | 4.94692 | + | 21.5660i | 0.161008 | + | 0.701914i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.45523 | − | 0.375800i | 0.0473135 | − | 0.0122183i | ||||
\(947\) | 31.9863 | − | 8.57071i | 1.03942 | − | 0.278511i | 0.301545 | − | 0.953452i | \(-0.402498\pi\) |
0.737871 | + | 0.674941i | \(0.235831\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.76066 | − | 2.34741i | −0.284383 | − | 0.0762002i | ||||
\(950\) | −0.202917 | + | 22.3500i | −0.00658351 | + | 0.725131i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 39.2407 | − | 9.37703i | 1.27180 | − | 0.303911i | ||||
\(953\) | 0.546564 | 0.0177049 | 0.00885247 | − | 0.999961i | \(-0.497182\pi\) | ||||
0.00885247 | + | 0.999961i | \(0.497182\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.5538 | + | 29.5538i | 0.956339 | + | 0.956339i | ||||
\(956\) | 0.545814 | − | 30.0565i | 0.0176529 | − | 0.972096i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.77440 | − | 4.86189i | −0.154254 | − | 0.157080i | ||||
\(959\) | −35.4068 | − | 61.3264i | −1.14335 | − | 1.98033i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.1758 | − | 33.2135i | 0.618576 | − | 1.07140i | ||||
\(962\) | −14.5104 | + | 3.74720i | −0.467835 | + | 0.120815i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.1611 | + | 13.9239i | −0.810384 | + | 0.448457i | ||||
\(965\) | −19.4213 | + | 5.20393i | −0.625195 | + | 0.167521i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.49046 | − | 12.9739i | −0.240877 | − | 0.417211i | 0.720087 | − | 0.693883i | \(-0.244102\pi\) |
−0.960964 | + | 0.276672i | \(0.910768\pi\) | |||||||
\(968\) | 8.82937 | − | 29.6922i | 0.283787 | − | 0.954344i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 72.7133 | − | 41.1054i | 2.33468 | − | 1.31981i | ||||
\(971\) | 29.4725 | − | 29.4725i | 0.945816 | − | 0.945816i | −0.0527896 | − | 0.998606i | \(-0.516811\pi\) |
0.998606 | + | 0.0527896i | \(0.0168113\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.8725 | − | 15.8725i | −0.508849 | − | 0.508849i | ||||
\(974\) | −14.1920 | + | 51.1049i | −0.454742 | + | 1.63751i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24.5324 | + | 26.3822i | 0.785264 | + | 0.844475i | ||||
\(977\) | −2.02199 | + | 1.16740i | −0.0646892 | + | 0.0373483i | −0.531996 | − | 0.846747i | \(-0.678558\pi\) |
0.467307 | + | 0.884095i | \(0.345224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.167779 | − | 0.626159i | −0.00536224 | − | 0.0200121i | ||||
\(980\) | −32.1115 | − | 9.23231i | −1.02577 | − | 0.294915i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.40015 | + | 2.37506i | −0.0446805 | + | 0.0757913i | ||||
\(983\) | −21.5089 | − | 12.4182i | −0.686029 | − | 0.396079i | 0.116094 | − | 0.993238i | \(-0.462963\pi\) |
−0.802123 | + | 0.597159i | \(0.796296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.9464 | + | 8.05197i | −0.444370 | + | 0.256557i | ||||
\(986\) | 0.114748 | − | 12.6388i | 0.00365433 | − | 0.402500i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.162210 | − | 8.93244i | 0.00516058 | − | 0.284179i | ||||
\(989\) | −13.2158 | + | 13.2158i | −0.420240 | + | 0.420240i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.12527i | 0.226342i | 0.993576 | + | 0.113171i | \(0.0361008\pi\) | ||||
−0.993576 | + | 0.113171i | \(0.963899\pi\) | |||||||
\(992\) | 34.7884 | − | 31.7651i | 1.10453 | − | 1.00854i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.5862 | − | 25.1257i | 0.811544 | − | 0.796940i | ||||
\(995\) | −2.57436 | + | 9.60763i | −0.0816126 | + | 0.304582i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.7516 | + | 47.5897i | 0.403848 | + | 1.50718i | 0.806170 | + | 0.591684i | \(0.201537\pi\) |
−0.402322 | + | 0.915498i | \(0.631797\pi\) | |||||||
\(998\) | −8.08908 | + | 13.7215i | −0.256055 | + | 0.434346i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.2.v.a.35.9 | 88 | ||
3.2 | odd | 2 | 144.2.u.a.83.14 | yes | 88 | ||
4.3 | odd | 2 | 1728.2.z.a.1007.1 | 88 | |||
9.4 | even | 3 | 144.2.u.a.131.7 | yes | 88 | ||
9.5 | odd | 6 | inner | 432.2.v.a.179.16 | 88 | ||
12.11 | even | 2 | 576.2.y.a.47.3 | 88 | |||
16.5 | even | 4 | 1728.2.z.a.143.1 | 88 | |||
16.11 | odd | 4 | inner | 432.2.v.a.251.16 | 88 | ||
36.23 | even | 6 | 1728.2.z.a.1583.1 | 88 | |||
36.31 | odd | 6 | 576.2.y.a.239.15 | 88 | |||
48.5 | odd | 4 | 576.2.y.a.335.15 | 88 | |||
48.11 | even | 4 | 144.2.u.a.11.7 | ✓ | 88 | ||
144.5 | odd | 12 | 1728.2.z.a.719.1 | 88 | |||
144.59 | even | 12 | inner | 432.2.v.a.395.9 | 88 | ||
144.85 | even | 12 | 576.2.y.a.527.3 | 88 | |||
144.139 | odd | 12 | 144.2.u.a.59.14 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.u.a.11.7 | ✓ | 88 | 48.11 | even | 4 | ||
144.2.u.a.59.14 | yes | 88 | 144.139 | odd | 12 | ||
144.2.u.a.83.14 | yes | 88 | 3.2 | odd | 2 | ||
144.2.u.a.131.7 | yes | 88 | 9.4 | even | 3 | ||
432.2.v.a.35.9 | 88 | 1.1 | even | 1 | trivial | ||
432.2.v.a.179.16 | 88 | 9.5 | odd | 6 | inner | ||
432.2.v.a.251.16 | 88 | 16.11 | odd | 4 | inner | ||
432.2.v.a.395.9 | 88 | 144.59 | even | 12 | inner | ||
576.2.y.a.47.3 | 88 | 12.11 | even | 2 | |||
576.2.y.a.239.15 | 88 | 36.31 | odd | 6 | |||
576.2.y.a.335.15 | 88 | 48.5 | odd | 4 | |||
576.2.y.a.527.3 | 88 | 144.85 | even | 12 | |||
1728.2.z.a.143.1 | 88 | 16.5 | even | 4 | |||
1728.2.z.a.719.1 | 88 | 144.5 | odd | 12 | |||
1728.2.z.a.1007.1 | 88 | 4.3 | odd | 2 | |||
1728.2.z.a.1583.1 | 88 | 36.23 | even | 6 |