Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(55,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.f (of order \(6\), degree \(2\), 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: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.207360000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 55.1 | ||
Root | \(0.437016 - 0.756934i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.55 |
Dual form | 324.3.f.o.271.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.85123 | − | 0.756934i | −0.925615 | − | 0.378467i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.85410 | + | 2.80252i | 0.713525 | + | 0.700629i | ||||
\(5\) | −3.70246 | − | 6.41285i | −0.740492 | − | 1.28257i | −0.952272 | − | 0.305252i | \(-0.901259\pi\) |
0.211780 | − | 0.977317i | \(-0.432074\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.20820 | − | 4.73901i | −1.17260 | − | 0.677001i | −0.218309 | − | 0.975880i | \(-0.570054\pi\) |
−0.954291 | + | 0.298878i | \(0.903388\pi\) | |||||||
\(8\) | −3.16228 | − | 7.34847i | −0.395285 | − | 0.918559i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000 | + | 14.6742i | 0.200000 | + | 1.46742i | ||||
\(11\) | −5.86319 | − | 3.38511i | −0.533017 | − | 0.307737i | 0.209227 | − | 0.977867i | \(-0.432905\pi\) |
−0.742244 | + | 0.670130i | \(0.766238\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.20820 | + | 12.4850i | 0.554477 | + | 0.960383i | 0.997944 | + | 0.0640919i | \(0.0204151\pi\) |
−0.443467 | + | 0.896291i | \(0.646252\pi\) | |||||||
\(14\) | 11.6082 | + | 14.9861i | 0.829154 | + | 1.07043i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.291796 | + | 15.9973i | 0.0182373 | + | 0.999834i | ||||
\(17\) | 17.8933 | 1.05255 | 0.526274 | − | 0.850315i | \(-0.323589\pi\) | ||||
0.526274 | + | 0.850315i | \(0.323589\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.19615i | − | 0.273482i | −0.990607 | − | 0.136741i | \(-0.956337\pi\) | ||
0.990607 | − | 0.136741i | \(-0.0436628\pi\) | |||||||
\(20\) | 7.40492 | − | 28.6791i | 0.370246 | − | 1.43396i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.29180 | + | 10.7047i | 0.376900 | + | 0.486576i | ||||
\(23\) | −21.5958 | + | 12.4683i | −0.938946 | + | 0.542101i | −0.889630 | − | 0.456682i | \(-0.849038\pi\) |
−0.0493164 | + | 0.998783i | \(0.515704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −14.9164 | + | 25.8360i | −0.596656 | + | 1.03344i | ||||
\(26\) | −3.89374 | − | 28.5687i | −0.149759 | − | 1.09880i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.1459 | − | 36.5292i | −0.362354 | − | 1.30462i | ||||
\(29\) | −14.8098 | + | 25.6514i | −0.510684 | + | 0.884531i | 0.489239 | + | 0.872150i | \(0.337274\pi\) |
−0.999923 | + | 0.0123811i | \(0.996059\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −14.8328 | + | 8.56373i | −0.478478 | + | 0.276249i | −0.719782 | − | 0.694200i | \(-0.755758\pi\) |
0.241304 | + | 0.970450i | \(0.422425\pi\) | |||||||
\(32\) | 11.5687 | − | 29.8356i | 0.361523 | − | 0.932363i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −33.1246 | − | 13.5440i | −0.974253 | − | 0.398354i | ||||
\(35\) | 70.1839i | 2.00526i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.41641 | 0.173416 | 0.0867082 | − | 0.996234i | \(-0.472365\pi\) | ||||
0.0867082 | + | 0.996234i | \(0.472365\pi\) | |||||||
\(38\) | −3.93314 | + | 9.61927i | −0.103504 | + | 0.253139i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −35.4164 | + | 47.4866i | −0.885410 | + | 1.18717i | ||||
\(41\) | −4.32145 | − | 7.48497i | −0.105401 | − | 0.182560i | 0.808501 | − | 0.588495i | \(-0.200279\pi\) |
−0.913902 | + | 0.405935i | \(0.866946\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.4164 | + | 25.0665i | 1.00968 | + | 0.582941i | 0.911099 | − | 0.412187i | \(-0.135235\pi\) |
0.0985848 | + | 0.995129i | \(0.468568\pi\) | |||||||
\(44\) | −7.24730 | − | 26.0931i | −0.164711 | − | 0.593026i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 49.4164 | − | 6.73516i | 1.07427 | − | 0.146416i | ||||
\(47\) | 45.0485 | + | 26.0088i | 0.958479 | + | 0.553378i | 0.895705 | − | 0.444650i | \(-0.146672\pi\) |
0.0627743 | + | 0.998028i | \(0.480005\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.4164 | + | 35.3623i | 0.416661 | + | 0.721679i | ||||
\(50\) | 47.1698 | − | 36.5376i | 0.943396 | − | 0.730752i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14.4164 | + | 55.8345i | −0.277239 | + | 1.07374i | ||||
\(53\) | −82.6921 | −1.56023 | −0.780114 | − | 0.625637i | \(-0.784839\pi\) | ||||
−0.780114 | + | 0.625637i | \(0.784839\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 50.1329i | 0.911508i | ||||||||
\(56\) | −8.86784 | + | 75.3038i | −0.158354 | + | 1.34471i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 46.8328 | − | 36.2765i | 0.807462 | − | 0.625458i | ||||
\(59\) | −72.5075 | + | 41.8622i | −1.22894 | + | 0.709529i | −0.966808 | − | 0.255503i | \(-0.917759\pi\) |
−0.262132 | + | 0.965032i | \(0.584425\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.20820 | − | 7.28882i | 0.0689869 | − | 0.119489i | −0.829469 | − | 0.558553i | \(-0.811357\pi\) |
0.898456 | + | 0.439064i | \(0.144690\pi\) | |||||||
\(62\) | 33.9411 | − | 4.62597i | 0.547438 | − | 0.0746124i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −44.0000 | + | 46.4758i | −0.687500 | + | 0.726184i | ||||
\(65\) | 53.3762 | − | 92.4502i | 0.821172 | − | 1.42231i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25.1656 | − | 14.5294i | 0.375606 | − | 0.216856i | −0.300299 | − | 0.953845i | \(-0.597086\pi\) |
0.675905 | + | 0.736989i | \(0.263753\pi\) | |||||||
\(68\) | 51.0693 | + | 50.1463i | 0.751019 | + | 0.737445i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 53.1246 | − | 129.927i | 0.758923 | − | 1.85609i | ||||
\(71\) | 113.287i | 1.59559i | 0.602928 | + | 0.797796i | \(0.294001\pi\) | ||||
−0.602928 | + | 0.797796i | \(0.705999\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.16718 | 0.0296875 | 0.0148437 | − | 0.999890i | \(-0.495275\pi\) | ||||
0.0148437 | + | 0.999890i | \(0.495275\pi\) | |||||||
\(74\) | −11.8782 | − | 4.85680i | −0.160517 | − | 0.0656324i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14.5623 | − | 14.8303i | 0.191609 | − | 0.195136i | ||||
\(77\) | 32.0841 | + | 55.5714i | 0.416677 | + | 0.721706i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −129.457 | − | 74.7423i | −1.63870 | − | 0.946105i | −0.981281 | − | 0.192581i | \(-0.938314\pi\) |
−0.657421 | − | 0.753524i | \(-0.728352\pi\) | |||||||
\(80\) | 101.508 | − | 61.1007i | 1.26885 | − | 0.763759i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.33437 | + | 17.1275i | 0.0284679 | + | 0.208871i | ||||
\(83\) | 11.7264 | + | 6.77022i | 0.141282 | + | 0.0815690i | 0.568975 | − | 0.822355i | \(-0.307340\pi\) |
−0.427693 | + | 0.903924i | \(0.640674\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −66.2492 | − | 114.747i | −0.779403 | − | 1.34996i | ||||
\(86\) | −61.4001 | − | 79.2672i | −0.713954 | − | 0.921711i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −6.33437 | + | 53.7901i | −0.0719815 | + | 0.611251i | ||||
\(89\) | 17.8933 | 0.201048 | 0.100524 | − | 0.994935i | \(-0.467948\pi\) | ||||
0.100524 | + | 0.994935i | \(0.467948\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 136.639i | − | 1.50153i | ||||||
\(92\) | −96.5792 | − | 24.9366i | −1.04977 | − | 0.271050i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −63.7082 | − | 82.2469i | −0.677747 | − | 0.874967i | ||||
\(95\) | −33.3221 | + | 19.2385i | −0.350759 | + | 0.202511i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 69.1656 | − | 119.798i | 0.713048 | − | 1.23503i | −0.250660 | − | 0.968075i | \(-0.580648\pi\) |
0.963708 | − | 0.266960i | \(-0.0860191\pi\) | |||||||
\(98\) | −11.0286 | − | 80.9175i | −0.112536 | − | 0.825689i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −114.979 | + | 31.9350i | −1.14979 | + | 0.319350i | ||||
\(101\) | −48.7510 | + | 84.4391i | −0.482683 | + | 0.836031i | −0.999802 | − | 0.0198821i | \(-0.993671\pi\) |
0.517120 | + | 0.855913i | \(0.327004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 36.7918 | − | 21.2418i | 0.357202 | − | 0.206231i | −0.310651 | − | 0.950524i | \(-0.600547\pi\) |
0.667853 | + | 0.744294i | \(0.267214\pi\) | |||||||
\(104\) | 68.9511 | − | 92.4502i | 0.662991 | − | 0.888944i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 153.082 | + | 62.5924i | 1.44417 | + | 0.590495i | ||||
\(107\) | − | 97.2648i | − | 0.909017i | −0.890742 | − | 0.454509i | \(-0.849815\pi\) | ||
0.890742 | − | 0.454509i | \(-0.150185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −96.8328 | −0.888374 | −0.444187 | − | 0.895934i | \(-0.646507\pi\) | ||||
−0.444187 | + | 0.895934i | \(0.646507\pi\) | |||||||
\(110\) | 37.9473 | − | 92.8076i | 0.344976 | − | 0.843705i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 73.4164 | − | 132.692i | 0.655504 | − | 1.18475i | ||||
\(113\) | −19.4350 | − | 33.6625i | −0.171991 | − | 0.297898i | 0.767125 | − | 0.641498i | \(-0.221687\pi\) |
−0.939116 | + | 0.343600i | \(0.888353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 159.915 | + | 92.3269i | 1.39056 | + | 0.802842i | ||||
\(116\) | −114.157 | + | 31.7069i | −0.984114 | + | 0.273335i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 165.915 | − | 22.6132i | 1.40606 | − | 0.191637i | ||||
\(119\) | −146.872 | − | 84.7965i | −1.23422 | − | 0.712576i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −37.5820 | − | 65.0940i | −0.310595 | − | 0.537967i | ||||
\(122\) | −13.3075 | + | 10.3080i | −0.109078 | + | 0.0844914i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −66.3344 | − | 17.1275i | −0.534955 | − | 0.138125i | ||||
\(125\) | 35.7866 | 0.286293 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 99.0165i | 0.779657i | 0.920887 | + | 0.389829i | \(0.127466\pi\) | ||||
−0.920887 | + | 0.389829i | \(0.872534\pi\) | |||||||
\(128\) | 116.633 | − | 52.7323i | 0.911197 | − | 0.411971i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −168.790 | + | 130.744i | −1.29839 | + | 1.00573i | ||||
\(131\) | 46.9055 | − | 27.0809i | 0.358057 | − | 0.206724i | −0.310171 | − | 0.950681i | \(-0.600386\pi\) |
0.668228 | + | 0.743956i | \(0.267053\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.6246 | + | 42.6511i | −0.185147 | + | 0.320685i | ||||
\(134\) | −57.5851 | + | 7.84850i | −0.429740 | + | 0.0585709i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −56.5836 | − | 131.488i | −0.416056 | − | 0.966826i | ||||
\(137\) | 2.77972 | − | 4.81461i | 0.0202899 | − | 0.0351432i | −0.855702 | − | 0.517469i | \(-0.826874\pi\) |
0.875992 | + | 0.482325i | \(0.160208\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −132.084 | + | 76.2585i | −0.950242 | + | 0.548622i | −0.893156 | − | 0.449747i | \(-0.851514\pi\) |
−0.0570857 | + | 0.998369i | \(0.518181\pi\) | |||||||
\(140\) | −196.692 | + | 200.312i | −1.40494 | + | 1.43080i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 85.7508 | − | 209.720i | 0.603879 | − | 1.47690i | ||||
\(143\) | − | 97.6023i | − | 0.682534i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 219.331 | 1.51263 | ||||||||
\(146\) | −4.01196 | − | 1.64042i | −0.0274791 | − | 0.0112357i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.3131 | + | 17.9821i | 0.123737 | + | 0.121501i | ||||
\(149\) | −68.4897 | − | 118.628i | −0.459663 | − | 0.796159i | 0.539280 | − | 0.842126i | \(-0.318696\pi\) |
−0.998943 | + | 0.0459672i | \(0.985363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 67.5395 | + | 38.9939i | 0.447281 | + | 0.258238i | 0.706681 | − | 0.707532i | \(-0.250191\pi\) |
−0.259400 | + | 0.965770i | \(0.583525\pi\) | |||||||
\(152\) | −38.1838 | + | 16.4317i | −0.251209 | + | 0.108103i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −17.3313 | − | 127.161i | −0.112541 | − | 0.825720i | ||||
\(155\) | 109.836 | + | 63.4137i | 0.708618 | + | 0.409121i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 36.0820 | + | 62.4959i | 0.229822 | + | 0.398063i | 0.957755 | − | 0.287585i | \(-0.0928523\pi\) |
−0.727933 | + | 0.685648i | \(0.759519\pi\) | |||||||
\(158\) | 183.080 | + | 236.356i | 1.15874 | + | 1.49592i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −234.164 | + | 36.2765i | −1.46353 | + | 0.226728i | ||||
\(161\) | 236.350 | 1.46801 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 56.5785i | 0.347108i | 0.984824 | + | 0.173554i | \(0.0555250\pi\) | ||||
−0.984824 | + | 0.173554i | \(0.944475\pi\) | |||||||
\(164\) | 8.64290 | − | 33.4738i | 0.0527006 | − | 0.204109i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.5836 | − | 21.4093i | −0.0999012 | − | 0.128972i | ||||
\(167\) | 174.623 | − | 100.819i | 1.04565 | − | 0.603705i | 0.124220 | − | 0.992255i | \(-0.460357\pi\) |
0.921428 | + | 0.388550i | \(0.127024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −19.4164 | + | 33.6302i | −0.114890 | + | 0.198995i | ||||
\(170\) | 35.7866 | + | 262.569i | 0.210509 | + | 1.54453i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 53.6656 | + | 193.217i | 0.312009 | + | 1.12336i | ||||
\(173\) | −46.2750 | + | 80.1506i | −0.267485 | + | 0.463298i | −0.968212 | − | 0.250132i | \(-0.919526\pi\) |
0.700726 | + | 0.713430i | \(0.252859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 244.874 | − | 141.378i | 1.39928 | − | 0.807874i | ||||
\(176\) | 52.4419 | − | 94.7831i | 0.297965 | − | 0.538540i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −33.1246 | − | 13.5440i | −0.186093 | − | 0.0760902i | ||||
\(179\) | 4.28851i | 0.0239581i | 0.999928 | + | 0.0119791i | \(0.00381315\pi\) | ||||
−0.999928 | + | 0.0119791i | \(0.996187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −289.748 | −1.60082 | −0.800408 | − | 0.599456i | \(-0.795384\pi\) | ||||
−0.800408 | + | 0.599456i | \(0.795384\pi\) | |||||||
\(182\) | −103.427 | + | 252.950i | −0.568278 | + | 1.38984i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 159.915 | + | 119.268i | 0.869102 | + | 0.648193i | ||||
\(185\) | −23.7565 | − | 41.1474i | −0.128413 | − | 0.222419i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −104.912 | − | 60.5708i | −0.561025 | − | 0.323908i | ||||
\(188\) | 55.6830 | + | 200.481i | 0.296186 | + | 1.06639i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 76.2492 | − | 10.3923i | 0.401312 | − | 0.0546963i | ||||
\(191\) | 80.2276 | + | 46.3194i | 0.420040 | + | 0.242510i | 0.695094 | − | 0.718919i | \(-0.255363\pi\) |
−0.275055 | + | 0.961429i | \(0.588696\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 121.582 | + | 210.586i | 0.629959 | + | 1.09112i | 0.987559 | + | 0.157246i | \(0.0502616\pi\) |
−0.357601 | + | 0.933875i | \(0.616405\pi\) | |||||||
\(194\) | −218.721 | + | 169.421i | −1.12743 | + | 0.873302i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −40.8328 | + | 158.145i | −0.208331 | + | 0.806861i | ||||
\(197\) | −139.432 | −0.707779 | −0.353890 | − | 0.935287i | \(-0.615141\pi\) | ||||
−0.353890 | + | 0.935287i | \(0.615141\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 110.993i | 0.557756i | 0.960327 | + | 0.278878i | \(0.0899624\pi\) | ||||
−0.960327 | + | 0.278878i | \(0.910038\pi\) | |||||||
\(200\) | 237.025 | + | 27.9122i | 1.18512 | + | 0.139561i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 154.164 | − | 119.415i | 0.763189 | − | 0.591163i | ||||
\(203\) | 243.124 | − | 140.368i | 1.19766 | − | 0.691467i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.0000 | + | 55.4256i | −0.156098 | + | 0.270369i | ||||
\(206\) | −84.1887 | + | 11.4744i | −0.408683 | + | 0.0557010i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −197.623 | + | 118.955i | −0.950111 | + | 0.571900i | ||||
\(209\) | −17.5896 | + | 30.4660i | −0.0841606 | + | 0.145770i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −229.579 | + | 132.547i | −1.08805 | + | 0.628187i | −0.933057 | − | 0.359728i | \(-0.882869\pi\) |
−0.154995 | + | 0.987915i | \(0.549536\pi\) | |||||||
\(212\) | −236.012 | − | 231.746i | −1.11326 | − | 1.09314i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −73.6231 | + | 180.060i | −0.344033 | + | 0.841400i | ||||
\(215\) | − | 371.230i | − | 1.72665i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 162.334 | 0.748085 | ||||||||
\(218\) | 179.260 | + | 73.2960i | 0.822293 | + | 0.336220i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −140.498 | + | 143.085i | −0.638629 | + | 0.650384i | ||||
\(221\) | 128.979 | + | 223.397i | 0.583613 | + | 1.01085i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −275.331 | − | 158.963i | −1.23467 | − | 0.712837i | −0.266670 | − | 0.963788i | \(-0.585923\pi\) |
−0.968000 | + | 0.250951i | \(0.919257\pi\) | |||||||
\(224\) | −236.350 | + | 190.072i | −1.05513 | + | 0.848538i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.4984 | + | 77.0280i | 0.0464533 | + | 0.340832i | ||||
\(227\) | −215.958 | − | 124.683i | −0.951355 | − | 0.549265i | −0.0578535 | − | 0.998325i | \(-0.518426\pi\) |
−0.893502 | + | 0.449060i | \(0.851759\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −76.1672 | − | 131.925i | −0.332608 | − | 0.576094i | 0.650415 | − | 0.759579i | \(-0.274595\pi\) |
−0.983022 | + | 0.183486i | \(0.941262\pi\) | |||||||
\(230\) | −226.154 | − | 291.963i | −0.983277 | − | 1.26941i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 235.331 | + | 27.7128i | 1.01436 | + | 0.119452i | ||||
\(233\) | −346.793 | −1.48838 | −0.744191 | − | 0.667966i | \(-0.767165\pi\) | ||||
−0.744191 | + | 0.667966i | \(0.767165\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 385.186i | − | 1.63909i | ||||||
\(236\) | −324.263 | − | 83.7244i | −1.37400 | − | 0.354764i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 207.708 | + | 268.150i | 0.872724 | + | 1.12668i | ||||
\(239\) | −90.0970 | + | 52.0175i | −0.376975 | + | 0.217647i | −0.676501 | − | 0.736441i | \(-0.736505\pi\) |
0.299526 | + | 0.954088i | \(0.403171\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −140.913 | + | 244.069i | −0.584702 | + | 1.01273i | 0.410210 | + | 0.911991i | \(0.365455\pi\) |
−0.994912 | + | 0.100743i | \(0.967878\pi\) | |||||||
\(242\) | 20.3011 | + | 148.951i | 0.0838889 | + | 0.615500i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 32.4377 | − | 9.00948i | 0.132941 | − | 0.0369241i | ||||
\(245\) | 151.182 | − | 261.855i | 0.617069 | − | 1.06879i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 64.8738 | − | 37.4549i | 0.262647 | − | 0.151639i | ||||
\(248\) | 109.836 | + | 81.9176i | 0.442886 | + | 0.330313i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −66.2492 | − | 27.0881i | −0.264997 | − | 0.108352i | ||||
\(251\) | − | 271.484i | − | 1.08161i | −0.841148 | − | 0.540804i | \(-0.818120\pi\) | ||
0.841148 | − | 0.540804i | \(-0.181880\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 168.827 | 0.667299 | ||||||||
\(254\) | 74.9489 | − | 183.302i | 0.295075 | − | 0.721662i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −255.830 | + | 9.33592i | −0.999335 | + | 0.0364684i | ||||
\(257\) | 229.552 | + | 397.597i | 0.893200 | + | 1.54707i | 0.836016 | + | 0.548705i | \(0.184879\pi\) |
0.0571840 | + | 0.998364i | \(0.481788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −52.6672 | − | 30.4074i | −0.203348 | − | 0.117403i | ||||
\(260\) | 411.434 | − | 114.275i | 1.58244 | − | 0.439518i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −107.331 | + | 14.6286i | −0.409661 | + | 0.0558343i | ||||
\(263\) | 176.480 | + | 101.891i | 0.671027 | + | 0.387418i | 0.796466 | − | 0.604684i | \(-0.206701\pi\) |
−0.125439 | + | 0.992101i | \(0.540034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 306.164 | + | 530.292i | 1.15534 | + | 2.00110i | ||||
\(266\) | 77.8699 | − | 60.3177i | 0.292744 | − | 0.226758i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 112.544 | + | 29.0588i | 0.419941 | + | 0.108428i | ||||
\(269\) | 323.363 | 1.20209 | 0.601047 | − | 0.799213i | \(-0.294750\pi\) | ||||
0.601047 | + | 0.799213i | \(0.294750\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 104.928i | − | 0.387190i | −0.981082 | − | 0.193595i | \(-0.937985\pi\) | ||
0.981082 | − | 0.193595i | \(-0.0620148\pi\) | |||||||
\(272\) | 5.22120 | + | 286.245i | 0.0191956 | + | 1.05237i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.79024 | + | 6.80889i | −0.0320812 | + | 0.0248500i | ||||
\(275\) | 174.915 | − | 100.987i | 0.636056 | − | 0.367227i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.4164 | − | 42.2905i | 0.0881459 | − | 0.152673i | −0.818582 | − | 0.574390i | \(-0.805239\pi\) |
0.906727 | + | 0.421717i | \(0.138573\pi\) | |||||||
\(278\) | 302.240 | − | 41.1934i | 1.08719 | − | 0.148178i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 515.745 | − | 221.941i | 1.84194 | − | 0.792647i | ||||
\(281\) | −14.8098 | + | 25.6514i | −0.0527040 | + | 0.0912861i | −0.891174 | − | 0.453662i | \(-0.850117\pi\) |
0.838470 | + | 0.544948i | \(0.183451\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −333.580 | + | 192.593i | −1.17873 | + | 0.680540i | −0.955720 | − | 0.294276i | \(-0.904921\pi\) |
−0.223009 | + | 0.974816i | \(0.571588\pi\) | |||||||
\(284\) | −317.489 | + | 323.333i | −1.11792 | + | 1.13850i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −73.8785 | + | 180.684i | −0.258316 | + | 0.631763i | ||||
\(287\) | 81.9176i | 0.285427i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.1703 | 0.107856 | ||||||||
\(290\) | −406.033 | − | 166.019i | −1.40011 | − | 0.572480i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.18536 | + | 6.07357i | 0.0211828 | + | 0.0207999i | ||||
\(293\) | −140.705 | − | 243.708i | −0.480222 | − | 0.831768i | 0.519521 | − | 0.854458i | \(-0.326110\pi\) |
−0.999743 | + | 0.0226894i | \(0.992777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 536.912 | + | 309.986i | 1.82004 | + | 1.05080i | ||||
\(296\) | −20.2905 | − | 47.1508i | −0.0685489 | − | 0.159293i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 36.9969 | + | 271.449i | 0.124151 | + | 0.910904i | ||||
\(299\) | −311.333 | − | 179.748i | −1.04125 | − | 0.601165i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −237.580 | − | 411.501i | −0.789304 | − | 1.36711i | ||||
\(302\) | −95.5152 | − | 123.310i | −0.316276 | − | 0.408310i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 83.1246 | − | 1.51622i | 0.273436 | − | 0.00498756i | ||||
\(305\) | −62.3228 | −0.204337 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 553.961i | 1.80443i | 0.431282 | + | 0.902217i | \(0.358061\pi\) | ||||
−0.431282 | + | 0.902217i | \(0.641939\pi\) | |||||||
\(308\) | −64.1683 | + | 248.523i | −0.208339 | + | 0.806892i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −155.331 | − | 200.532i | −0.501069 | − | 0.646877i | ||||
\(311\) | 13.5833 | − | 7.84235i | 0.0436764 | − | 0.0252166i | −0.478003 | − | 0.878358i | \(-0.658639\pi\) |
0.521679 | + | 0.853142i | \(0.325306\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 154.080 | − | 266.875i | 0.492270 | − | 0.852637i | −0.507690 | − | 0.861540i | \(-0.669501\pi\) |
0.999960 | + | 0.00890304i | \(0.00283396\pi\) | |||||||
\(314\) | −19.4909 | − | 143.006i | −0.0620728 | − | 0.455433i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −160.018 | − | 576.129i | −0.506387 | − | 1.82319i | ||||
\(317\) | 248.053 | − | 429.641i | 0.782502 | − | 1.35533i | −0.147977 | − | 0.988991i | \(-0.547276\pi\) |
0.930480 | − | 0.366343i | \(-0.119390\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 173.666 | − | 100.266i | 0.544406 | − | 0.314313i | ||||
\(320\) | 460.950 | + | 110.091i | 1.44047 | + | 0.344033i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −437.538 | − | 178.901i | −1.35881 | − | 0.555594i | ||||
\(323\) | − | 92.9763i | − | 0.287852i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −430.082 | −1.32333 | ||||||||
\(326\) | 42.8262 | − | 104.740i | 0.131369 | − | 0.321288i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −41.3375 | + | 55.4256i | −0.126029 | + | 0.168981i | ||||
\(329\) | −246.512 | − | 426.970i | −0.749275 | − | 1.29778i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 74.9164 | + | 43.2530i | 0.226334 | + | 0.130674i | 0.608879 | − | 0.793263i | \(-0.291619\pi\) |
−0.382546 | + | 0.923936i | \(0.624953\pi\) | |||||||
\(332\) | 14.4946 | + | 52.1863i | 0.0436584 | + | 0.157188i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −399.580 | + | 54.4604i | −1.19635 | + | 0.163055i | ||||
\(335\) | −186.349 | − | 107.589i | −0.556267 | − | 0.321161i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −160.330 | − | 277.699i | −0.475756 | − | 0.824033i | 0.523858 | − | 0.851805i | \(-0.324492\pi\) |
−0.999614 | + | 0.0277721i | \(0.991159\pi\) | |||||||
\(338\) | 61.4001 | − | 47.5603i | 0.181657 | − | 0.140711i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 132.498 | − | 513.164i | 0.389701 | − | 1.50931i | ||||
\(341\) | 115.957 | 0.340049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 77.4087i | 0.225681i | ||||||||
\(344\) | 46.9055 | − | 398.311i | 0.136353 | − | 1.15788i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 146.334 | − | 113.350i | 0.422932 | − | 0.327601i | ||||
\(347\) | −584.358 | + | 337.379i | −1.68403 | + | 0.972275i | −0.725093 | + | 0.688650i | \(0.758203\pi\) |
−0.958936 | + | 0.283624i | \(0.908463\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −76.9590 | + | 133.297i | −0.220513 | + | 0.381939i | −0.954964 | − | 0.296722i | \(-0.904106\pi\) |
0.734451 | + | 0.678662i | \(0.237440\pi\) | |||||||
\(350\) | −560.331 | + | 76.3698i | −1.60095 | + | 0.218199i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −168.827 | + | 135.770i | −0.479621 | + | 0.385711i | ||||
\(353\) | −311.614 | + | 539.731i | −0.882759 | + | 1.52898i | −0.0344990 | + | 0.999405i | \(0.510984\pi\) |
−0.848260 | + | 0.529579i | \(0.822350\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 726.492 | − | 419.440i | 2.04646 | − | 1.18152i | ||||
\(356\) | 51.0693 | + | 50.1463i | 0.143453 | + | 0.140860i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.24612 | − | 7.93901i | 0.00906737 | − | 0.0221760i | ||||
\(359\) | 160.341i | 0.446633i | 0.974746 | + | 0.223316i | \(0.0716883\pi\) | ||||
−0.974746 | + | 0.223316i | \(0.928312\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 334.000 | 0.925208 | ||||||||
\(362\) | 536.389 | + | 219.320i | 1.48174 | + | 0.605856i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 382.933 | − | 389.982i | 1.05201 | − | 1.07138i | ||||
\(365\) | −8.02391 | − | 13.8978i | −0.0219833 | − | 0.0380762i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −246.457 | − | 142.292i | −0.671546 | − | 0.387717i | 0.125116 | − | 0.992142i | \(-0.460070\pi\) |
−0.796662 | + | 0.604425i | \(0.793403\pi\) | |||||||
\(368\) | −205.761 | − | 341.837i | −0.559134 | − | 0.928904i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12.8328 | + | 94.1555i | 0.0346833 | + | 0.254474i | ||||
\(371\) | 678.754 | + | 391.879i | 1.82952 | + | 1.05628i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −150.710 | − | 261.037i | −0.404048 | − | 0.699831i | 0.590163 | − | 0.807284i | \(-0.299064\pi\) |
−0.994210 | + | 0.107453i | \(0.965730\pi\) | |||||||
\(374\) | 148.368 | + | 191.542i | 0.396705 | + | 0.512144i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 48.6687 | − | 413.284i | 0.129438 | − | 1.09916i | ||||
\(377\) | −427.009 | −1.13265 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 248.547i | − | 0.655796i | −0.944713 | − | 0.327898i | \(-0.893660\pi\) | ||
0.944713 | − | 0.327898i | \(-0.106340\pi\) | |||||||
\(380\) | −149.021 | − | 38.4771i | −0.392161 | − | 0.101255i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −113.459 | − | 146.475i | −0.297013 | − | 0.383442i | ||||
\(383\) | 422.734 | − | 244.065i | 1.10374 | − | 0.637247i | 0.166542 | − | 0.986034i | \(-0.446740\pi\) |
0.937202 | + | 0.348788i | \(0.113407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 237.580 | − | 411.501i | 0.617092 | − | 1.06883i | ||||
\(386\) | −65.6764 | − | 481.873i | −0.170146 | − | 1.24838i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 533.143 | − | 148.079i | 1.37408 | − | 0.381647i | ||||
\(389\) | −207.934 | + | 360.152i | −0.534534 | + | 0.925840i | 0.464652 | + | 0.885493i | \(0.346180\pi\) |
−0.999186 | + | 0.0403465i | \(0.987154\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −386.420 | + | 223.099i | −0.988285 | + | 0.570587i | ||||
\(392\) | 195.296 | − | 261.855i | 0.498204 | − | 0.667996i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 258.122 | + | 105.541i | 0.655131 | + | 0.267871i | ||||
\(395\) | 1106.92i | 2.80233i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −670.827 | −1.68974 | −0.844870 | − | 0.534972i | \(-0.820322\pi\) | ||||
−0.844870 | + | 0.534972i | \(0.820322\pi\) | |||||||
\(398\) | 84.0146 | − | 205.474i | 0.211092 | − | 0.516267i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −417.659 | − | 231.084i | −1.04415 | − | 0.577710i | ||||
\(401\) | 57.3709 | + | 99.3693i | 0.143070 | + | 0.247804i | 0.928651 | − | 0.370955i | \(-0.120969\pi\) |
−0.785582 | + | 0.618758i | \(0.787636\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −213.836 | − | 123.458i | −0.530610 | − | 0.306348i | ||||
\(404\) | −375.782 | + | 104.373i | −0.930154 | + | 0.258348i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −556.328 | + | 75.8241i | −1.37027 | + | 0.186759i | ||||
\(407\) | −37.6206 | − | 21.7203i | −0.0924339 | − | 0.0533667i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 73.3359 | + | 127.022i | 0.179305 | + | 0.310566i | 0.941643 | − | 0.336614i | \(-0.109282\pi\) |
−0.762337 | + | 0.647180i | \(0.775948\pi\) | |||||||
\(410\) | 101.193 | − | 78.3837i | 0.246812 | − | 0.191180i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 164.538 | + | 42.4835i | 0.399364 | + | 0.103115i | ||||
\(413\) | 793.541 | 1.92141 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 100.266i | − | 0.241605i | ||||||
\(416\) | 455.887 | − | 70.6257i | 1.09588 | − | 0.169773i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 55.6231 | − | 43.0854i | 0.133070 | − | 0.103075i | ||||
\(419\) | −464.945 | + | 268.436i | −1.10965 | + | 0.640659i | −0.938740 | − | 0.344627i | \(-0.888005\pi\) |
−0.170914 | + | 0.985286i | \(0.554672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 183.707 | − | 318.189i | 0.436358 | − | 0.755794i | −0.561048 | − | 0.827784i | \(-0.689602\pi\) |
0.997405 | + | 0.0719896i | \(0.0229349\pi\) | |||||||
\(422\) | 525.333 | − | 71.5997i | 1.24486 | − | 0.169668i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 261.495 | + | 607.660i | 0.616734 | + | 1.43316i | ||||
\(425\) | −266.904 | + | 462.291i | −0.628009 | + | 1.08774i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −69.0836 | + | 39.8854i | −0.161788 | + | 0.0934085i | ||||
\(428\) | 272.586 | − | 277.604i | 0.636884 | − | 0.648607i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −280.997 | + | 687.233i | −0.653481 | + | 1.59822i | ||||
\(431\) | 735.353i | 1.70616i | 0.521784 | + | 0.853078i | \(0.325267\pi\) | ||||
−0.521784 | + | 0.853078i | \(0.674733\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 765.161 | 1.76712 | 0.883558 | − | 0.468322i | \(-0.155141\pi\) | ||||
0.883558 | + | 0.468322i | \(0.155141\pi\) | |||||||
\(434\) | −300.518 | − | 122.876i | −0.692438 | − | 0.283125i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −276.371 | − | 271.376i | −0.633878 | − | 0.622421i | ||||
\(437\) | 64.7873 | + | 112.215i | 0.148255 | + | 0.256785i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 40.1703 | + | 23.1923i | 0.0915041 | + | 0.0528299i | 0.545054 | − | 0.838401i | \(-0.316509\pi\) |
−0.453550 | + | 0.891231i | \(0.649843\pi\) | |||||||
\(440\) | 368.400 | − | 158.534i | 0.837274 | − | 0.360305i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −69.6718 | − | 511.188i | −0.157629 | − | 1.15653i | ||||
\(443\) | 120.978 | + | 69.8465i | 0.273087 | + | 0.157667i | 0.630290 | − | 0.776360i | \(-0.282936\pi\) |
−0.357203 | + | 0.934027i | \(0.616269\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −66.2492 | − | 114.747i | −0.148875 | − | 0.257858i | ||||
\(446\) | 389.377 | + | 502.684i | 0.873043 | + | 1.12709i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 581.410 | − | 172.966i | 1.29779 | − | 0.386086i | ||||
\(449\) | 267.139 | 0.594963 | 0.297482 | − | 0.954728i | \(-0.403853\pi\) | ||||
0.297482 | + | 0.954728i | \(0.403853\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 58.5144i | 0.129744i | ||||||||
\(452\) | 38.8701 | − | 150.543i | 0.0859957 | − | 0.333060i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 305.410 | + | 394.283i | 0.672710 | + | 0.868464i | ||||
\(455\) | −876.245 | + | 505.900i | −1.92581 | + | 1.11187i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −118.915 | + | 205.967i | −0.260208 | + | 0.450693i | −0.966297 | − | 0.257430i | \(-0.917124\pi\) |
0.706089 | + | 0.708123i | \(0.250458\pi\) | |||||||
\(458\) | 41.1441 | + | 301.878i | 0.0898343 | + | 0.659122i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 197.666 | + | 711.674i | 0.429708 | + | 1.54712i | ||||
\(461\) | 149.325 | − | 258.638i | 0.323915 | − | 0.561037i | −0.657377 | − | 0.753562i | \(-0.728334\pi\) |
0.981292 | + | 0.192524i | \(0.0616675\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −423.950 | + | 244.767i | −0.915658 | + | 0.528655i | −0.882247 | − | 0.470786i | \(-0.843970\pi\) |
−0.0334107 | + | 0.999442i | \(0.510637\pi\) | |||||||
\(464\) | −414.675 | − | 229.433i | −0.893697 | − | 0.494468i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 641.994 | + | 262.500i | 1.37767 | + | 0.563304i | ||||
\(467\) | − | 454.280i | − | 0.972762i | −0.873747 | − | 0.486381i | \(-0.838317\pi\) | ||
0.873747 | − | 0.486381i | \(-0.161683\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −275.420 | −0.587248 | ||||||||
\(470\) | −291.560 | + | 713.067i | −0.620341 | + | 1.51716i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 536.912 | + | 400.439i | 1.13752 | + | 0.848387i | ||||
\(473\) | −169.706 | − | 293.939i | −0.358786 | − | 0.621435i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 134.248 | + | 77.5079i | 0.282627 | + | 0.163175i | ||||
\(476\) | −181.544 | − | 653.629i | −0.381394 | − | 1.37317i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 206.164 | − | 28.0989i | 0.431306 | − | 0.0587843i | ||||
\(479\) | −3.12946 | − | 1.80679i | −0.00653332 | − | 0.00377201i | 0.496730 | − | 0.867905i | \(-0.334534\pi\) |
−0.503263 | + | 0.864133i | \(0.667867\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 46.2508 | + | 80.1087i | 0.0961555 | + | 0.166546i | ||||
\(482\) | 445.607 | − | 345.166i | 0.924496 | − | 0.716111i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 75.1641 | − | 291.109i | 0.155298 | − | 0.601465i | ||||
\(485\) | −1024.33 | −2.11202 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 874.538i | − | 1.79577i | −0.440234 | − | 0.897883i | \(-0.645104\pi\) | ||
0.440234 | − | 0.897883i | \(-0.354896\pi\) | |||||||
\(488\) | −66.8692 | − | 7.87457i | −0.137027 | − | 0.0161364i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −478.079 | + | 370.318i | −0.975671 | + | 0.755752i | ||||
\(491\) | 558.756 | − | 322.598i | 1.13800 | − | 0.657022i | 0.192063 | − | 0.981383i | \(-0.438482\pi\) |
0.945934 | + | 0.324360i | \(0.105149\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −264.997 | + | 458.988i | −0.537519 | + | 0.931010i | ||||
\(494\) | −148.447 | + | 20.2325i | −0.300501 | + | 0.0409564i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −141.325 | − | 234.787i | −0.284930 | − | 0.473360i | ||||
\(497\) | 536.868 | − | 929.883i | 1.08022 | − | 1.87099i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 489.167 | − | 282.421i | 0.980295 | − | 0.565974i | 0.0779358 | − | 0.996958i | \(-0.475167\pi\) |
0.902359 | + | 0.430985i | \(0.141834\pi\) | |||||||
\(500\) | 102.139 | + | 100.293i | 0.204277 | + | 0.200585i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −205.495 | + | 502.579i | −0.409353 | + | 1.00115i | ||||
\(503\) | 483.048i | 0.960334i | 0.877177 | + | 0.480167i | \(0.159424\pi\) | ||||
−0.877177 | + | 0.480167i | \(0.840576\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 721.994 | 1.42969 | ||||||||
\(506\) | −312.537 | − | 127.791i | −0.617662 | − | 0.252551i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −277.495 | + | 282.603i | −0.546251 | + | 0.556305i | ||||
\(509\) | −108.002 | − | 187.065i | −0.212184 | − | 0.367514i | 0.740214 | − | 0.672372i | \(-0.234724\pi\) |
−0.952398 | + | 0.304858i | \(0.901391\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.7887 | − | 10.2703i | −0.0348115 | − | 0.0200984i | ||||
\(512\) | 480.666 | + | 176.363i | 0.938801 | + | 0.344459i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −124.000 | − | 909.799i | −0.241245 | − | 1.77004i | ||||
\(515\) | −272.440 | − | 157.293i | −0.529010 | − | 0.305424i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −176.085 | − | 304.988i | −0.340590 | − | 0.589920i | ||||
\(518\) | 74.4826 | + | 96.1567i | 0.143789 | + | 0.185631i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −848.158 | − | 99.8798i | −1.63107 | − | 0.192077i | ||||
\(521\) | −454.806 | −0.872949 | −0.436475 | − | 0.899717i | \(-0.643773\pi\) | ||||
−0.436475 | + | 0.899717i | \(0.643773\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 325.041i | 0.621493i | 0.950493 | + | 0.310747i | \(0.100579\pi\) | ||||
−0.950493 | + | 0.310747i | \(0.899421\pi\) | |||||||
\(524\) | 209.768 | + | 54.1618i | 0.400320 | + | 0.103362i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −249.580 | − | 322.207i | −0.474488 | − | 0.612561i | ||||
\(527\) | −265.408 | + | 153.233i | −0.503621 | + | 0.290765i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.4180 | − | 80.3983i | 0.0877466 | − | 0.151982i | ||||
\(530\) | −165.384 | − | 1213.44i | −0.312046 | − | 2.28951i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −189.812 | + | 52.7196i | −0.356789 | + | 0.0990971i | ||||
\(533\) | 62.2998 | − | 107.906i | 0.116885 | − | 0.202451i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −623.745 | + | 360.119i | −1.16588 | + | 0.673120i | ||||
\(536\) | −186.349 | − | 138.983i | −0.347667 | − | 0.259296i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −598.620 | − | 244.765i | −1.11268 | − | 0.454953i | ||||
\(539\) | − | 276.447i | − | 0.512889i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −962.574 | −1.77925 | −0.889625 | − | 0.456692i | \(-0.849034\pi\) | ||||
−0.889625 | + | 0.456692i | \(0.849034\pi\) | |||||||
\(542\) | −79.4239 | + | 194.247i | −0.146539 | + | 0.358389i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 207.003 | − | 533.858i | 0.380520 | − | 0.981356i | ||||
\(545\) | 358.520 | + | 620.974i | 0.657834 | + | 1.13940i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −115.588 | − | 66.7349i | −0.211313 | − | 0.122002i | 0.390608 | − | 0.920557i | \(-0.372265\pi\) |
−0.601921 | + | 0.798555i | \(0.705598\pi\) | |||||||
\(548\) | 21.4266 | − | 5.95119i | 0.0390997 | − | 0.0108598i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −400.249 | + | 54.5515i | −0.727726 | + | 0.0991846i | ||||
\(551\) | 133.289 | + | 76.9542i | 0.241903 | + | 0.139663i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 708.409 | + | 1227.00i | 1.28103 | + | 2.21881i | ||||
\(554\) | −77.2115 | + | 59.8077i | −0.139371 | + | 0.107956i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −590.696 | − | 152.517i | −1.06240 | − | 0.274311i | ||||
\(557\) | −413.437 | −0.742258 | −0.371129 | − | 0.928581i | \(-0.621029\pi\) | ||||
−0.371129 | + | 0.928581i | \(0.621029\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 722.737i | 1.29291i | ||||||||
\(560\) | −1122.76 | + | 20.4794i | −2.00492 | + | 0.0365704i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 46.8328 | − | 36.2765i | 0.0833324 | − | 0.0645490i | ||||
\(563\) | −447.356 | + | 258.281i | −0.794592 | + | 0.458758i | −0.841577 | − | 0.540137i | \(-0.818372\pi\) |
0.0469843 | + | 0.998896i | \(0.485039\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −143.915 | + | 249.268i | −0.254717 | + | 0.441182i | ||||
\(566\) | 763.314 | − | 104.035i | 1.34861 | − | 0.183808i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 832.486 | − | 358.245i | 1.46564 | − | 0.630713i | ||||
\(569\) | 234.178 | − | 405.608i | 0.411560 | − | 0.712843i | −0.583500 | − | 0.812113i | \(-0.698317\pi\) |
0.995061 | + | 0.0992699i | \(0.0316507\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 585.409 | − | 337.986i | 1.02523 | − | 0.591919i | 0.109618 | − | 0.993974i | \(-0.465037\pi\) |
0.915616 | + | 0.402055i | \(0.131704\pi\) | |||||||
\(572\) | 273.532 | − | 278.567i | 0.478203 | − | 0.487005i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 62.0062 | − | 151.648i | 0.108025 | − | 0.264196i | ||||
\(575\) | − | 743.930i | − | 1.29379i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −354.823 | −0.614945 | −0.307473 | − | 0.951557i | \(-0.599483\pi\) | ||||
−0.307473 | + | 0.951557i | \(0.599483\pi\) | |||||||
\(578\) | −57.7034 | − | 23.5939i | −0.0998328 | − | 0.0408198i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 625.994 | + | 614.680i | 1.07930 | + | 1.05979i | ||||
\(581\) | −64.1683 | − | 111.143i | −0.110445 | − | 0.191296i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 484.839 | + | 279.922i | 0.831628 | + | 0.480141i | ||||
\(584\) | −6.85324 | − | 15.9255i | −0.0117350 | − | 0.0272697i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 76.0062 | + | 557.664i | 0.129703 | + | 0.951645i | ||||
\(587\) | −190.940 | − | 110.239i | −0.325281 | − | 0.187801i | 0.328463 | − | 0.944517i | \(-0.393469\pi\) |
−0.653744 | + | 0.756716i | \(0.726803\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 44.4984 | + | 77.0736i | 0.0755491 | + | 0.130855i | ||||
\(590\) | −759.308 | − | 980.262i | −1.28696 | − | 1.66146i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.87228 | + | 102.645i | 0.00316264 | + | 0.173388i | ||||
\(593\) | 993.520 | 1.67541 | 0.837707 | − | 0.546121i | \(-0.183896\pi\) | ||||
0.837707 | + | 0.546121i | \(0.183896\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1255.82i | 2.11063i | ||||||||
\(596\) | 136.979 | − | 530.519i | 0.229831 | − | 0.890133i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 440.292 | + | 568.414i | 0.736274 | + | 0.950526i | ||||
\(599\) | 243.124 | − | 140.368i | 0.405884 | − | 0.234337i | −0.283136 | − | 0.959080i | \(-0.591375\pi\) |
0.689020 | + | 0.724743i | \(0.258041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −280.915 | + | 486.559i | −0.467412 | + | 0.809582i | −0.999307 | − | 0.0372287i | \(-0.988147\pi\) |
0.531894 | + | 0.846811i | \(0.321480\pi\) | |||||||
\(602\) | 128.337 | + | 941.616i | 0.213184 | + | 1.56415i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 83.4834 | + | 300.573i | 0.138218 | + | 0.497638i | ||||
\(605\) | −278.292 | + | 482.016i | −0.459987 | + | 0.796720i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 72.7918 | − | 42.0264i | 0.119921 | − | 0.0692362i | −0.438840 | − | 0.898565i | \(-0.644610\pi\) |
0.558760 | + | 0.829329i | \(0.311277\pi\) | |||||||
\(608\) | −155.030 | − | 60.1130i | −0.254984 | − | 0.0988700i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 115.374 | + | 47.1743i | 0.189137 | + | 0.0773348i | ||||
\(611\) | 749.906i | 1.22734i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 730.234 | 1.19125 | 0.595623 | − | 0.803264i | \(-0.296905\pi\) | ||||
0.595623 | + | 0.803264i | \(0.296905\pi\) | |||||||
\(614\) | 419.312 | − | 1025.51i | 0.682919 | − | 1.67021i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 306.906 | − | 411.501i | 0.498223 | − | 0.668022i | ||||
\(617\) | 274.893 | + | 476.129i | 0.445532 | + | 0.771684i | 0.998089 | − | 0.0617910i | \(-0.0196812\pi\) |
−0.552557 | + | 0.833475i | \(0.686348\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −63.3297 | − | 36.5634i | −0.102310 | − | 0.0590685i | 0.447972 | − | 0.894048i | \(-0.352146\pi\) |
−0.550282 | + | 0.834979i | \(0.685480\pi\) | |||||||
\(620\) | 135.765 | + | 488.806i | 0.218975 | + | 0.788397i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.0820 | + | 4.23629i | −0.0499711 | + | 0.00681076i | ||||
\(623\) | −146.872 | − | 84.7965i | −0.235749 | − | 0.136110i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 240.412 | + | 416.405i | 0.384659 | + | 0.666249i | ||||
\(626\) | −487.245 | + | 377.419i | −0.778347 | + | 0.602905i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −72.1641 | + | 279.490i | −0.114911 | + | 0.445048i | ||||
\(629\) | 114.811 | 0.182529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 779.849i | − | 1.23589i | −0.786220 | − | 0.617947i | \(-0.787965\pi\) | ||
0.786220 | − | 0.617947i | \(-0.212035\pi\) | |||||||
\(632\) | −139.861 | + | 1187.67i | −0.221299 | + | 1.87922i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −784.413 | + | 607.604i | −1.23724 | + | 0.958366i | ||||
\(635\) | 634.977 | − | 366.604i | 0.999965 | − | 0.577330i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −294.331 | + | 509.797i | −0.462058 | + | 0.800309i | ||||
\(638\) | −397.390 | + | 54.1618i | −0.622868 | + | 0.0848931i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −769.994 | − | 552.712i | −1.20312 | − | 0.863612i | ||||
\(641\) | −222.171 | + | 384.811i | −0.346600 | + | 0.600329i | −0.985643 | − | 0.168842i | \(-0.945997\pi\) |
0.639043 | + | 0.769171i | \(0.279331\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 386.420 | − | 223.099i | 0.600963 | − | 0.346966i | −0.168457 | − | 0.985709i | \(-0.553878\pi\) |
0.769421 | + | 0.638743i | \(0.220545\pi\) | |||||||
\(644\) | 674.567 | + | 662.375i | 1.04746 | + | 1.02853i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −70.3769 | + | 172.121i | −0.108943 | + | 0.266440i | ||||
\(647\) | − | 861.386i | − | 1.33135i | −0.746240 | − | 0.665677i | \(-0.768143\pi\) | ||
0.746240 | − | 0.665677i | \(-0.231857\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 566.833 | 0.873394 | ||||||||
\(650\) | 796.181 | + | 325.544i | 1.22489 | + | 0.500836i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −158.562 | + | 161.481i | −0.243194 | + | 0.247670i | ||||
\(653\) | 438.151 | + | 758.900i | 0.670982 | + | 1.16217i | 0.977626 | + | 0.210350i | \(0.0674605\pi\) |
−0.306644 | + | 0.951824i | \(0.599206\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −347.331 | − | 200.532i | −0.530277 | − | 0.306155i | ||||
\(656\) | 118.479 | − | 71.3158i | 0.180608 | − | 0.108713i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 133.161 | + | 977.013i | 0.202372 | + | 1.48482i | ||||
\(659\) | −489.963 | − | 282.880i | −0.743494 | − | 0.429257i | 0.0798443 | − | 0.996807i | \(-0.474558\pi\) |
−0.823338 | + | 0.567551i | \(0.807891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −316.290 | − | 547.831i | −0.478503 | − | 0.828791i | 0.521194 | − | 0.853438i | \(-0.325487\pi\) |
−0.999696 | + | 0.0246476i | \(0.992154\pi\) | |||||||
\(662\) | −105.948 | − | 136.778i | −0.160042 | − | 0.206613i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.6687 | − | 107.580i | 0.0190794 | − | 0.162018i | ||||
\(665\) | 364.686 | 0.548401 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 738.615i | − | 1.10737i | ||||||
\(668\) | 780.938 | + | 201.637i | 1.16907 | + | 0.301852i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 263.538 | + | 340.226i | 0.393340 | + | 0.507800i | ||||
\(671\) | −49.3470 | + | 28.4905i | −0.0735424 | + | 0.0424597i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 536.330 | − | 928.950i | 0.796924 | − | 1.38031i | −0.124687 | − | 0.992196i | \(-0.539793\pi\) |
0.921610 | − | 0.388116i | \(-0.126874\pi\) | |||||||
\(674\) | 86.6071 | + | 635.444i | 0.128497 | + | 0.942795i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −149.666 | + | 41.5692i | −0.221399 | + | 0.0614929i | ||||
\(677\) | −239.399 | + | 414.651i | −0.353617 | + | 0.612483i | −0.986880 | − | 0.161454i | \(-0.948382\pi\) |
0.633263 | + | 0.773937i | \(0.281715\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1135.45 | + | 655.553i | −1.67224 | + | 0.965468i | ||||
\(680\) | −633.717 | + | 849.692i | −0.931936 | + | 1.24955i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −214.663 | − | 87.7716i | −0.314754 | − | 0.128697i | ||||
\(683\) | − | 318.418i | − | 0.466206i | −0.972452 | − | 0.233103i | \(-0.925112\pi\) | ||
0.972452 | − | 0.233103i | \(-0.0748879\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −41.1672 | −0.0600981 | ||||||||
\(686\) | 58.5933 | − | 143.301i | 0.0854130 | − | 0.208894i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −388.328 | + | 701.861i | −0.564430 | + | 1.02015i | ||||
\(689\) | −596.061 | − | 1032.41i | −0.865111 | − | 1.49842i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −971.076 | − | 560.651i | −1.40532 | − | 0.811362i | −0.410388 | − | 0.911911i | \(-0.634607\pi\) |
−0.994932 | + | 0.100550i | \(0.967940\pi\) | |||||||
\(692\) | −356.697 | + | 99.0716i | −0.515458 | + | 0.143167i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1337.15 | − | 182.246i | 1.92674 | − | 0.262602i | ||||
\(695\) | 978.068 | + | 564.688i | 1.40729 | + | 0.812501i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −77.3251 | − | 133.931i | −0.110940 | − | 0.192153i | ||||
\(698\) | 243.366 | − | 188.510i | 0.348661 | − | 0.270072i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1095.11 | + | 282.756i | 1.56444 | + | 0.403937i | ||||
\(701\) | −413.437 | −0.589782 | −0.294891 | − | 0.955531i | \(-0.595283\pi\) | ||||
−0.294891 | + | 0.955531i | \(0.595283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 33.3406i | − | 0.0474262i | ||||||
\(704\) | 415.306 | − | 123.551i | 0.589923 | − | 0.175499i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 985.410 | − | 763.295i | 1.39577 | − | 1.08116i | ||||
\(707\) | 800.316 | − | 462.062i | 1.13199 | − | 0.653554i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 341.457 | − | 591.422i | 0.481604 | − | 0.834163i | −0.518173 | − | 0.855276i | \(-0.673388\pi\) |
0.999777 | + | 0.0211129i | \(0.00672093\pi\) | |||||||
\(710\) | −1662.39 | + | 226.574i | −2.34140 | + | 0.319118i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −56.5836 | − | 131.488i | −0.0794713 | − | 0.184675i | ||||
\(713\) | 213.551 | − | 369.881i | 0.299510 | − | 0.518767i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −625.909 | + | 361.369i | −0.875397 | + | 0.505411i | ||||
\(716\) | −12.0186 | + | 12.2398i | −0.0167858 | + | 0.0170948i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 121.368 | − | 296.828i | 0.169036 | − | 0.413410i | ||||
\(719\) | − | 286.374i | − | 0.398295i | −0.979970 | − | 0.199148i | \(-0.936183\pi\) | ||
0.979970 | − | 0.199148i | \(-0.0638173\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −402.659 | −0.558474 | ||||||||
\(722\) | −618.311 | − | 252.816i | −0.856386 | − | 0.350161i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −826.969 | − | 812.023i | −1.14222 | − | 1.12158i | ||||
\(725\) | −441.819 | − | 765.253i | −0.609406 | − | 1.05552i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 279.659 | + | 161.461i | 0.384676 | + | 0.222093i | 0.679851 | − | 0.733351i | \(-0.262045\pi\) |
−0.295175 | + | 0.955443i | \(0.595378\pi\) | |||||||
\(728\) | −1004.09 | + | 432.090i | −1.37924 | + | 0.593531i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 4.33437 | + | 31.8016i | 0.00593749 | + | 0.0435639i | ||||
\(731\) | 776.863 | + | 448.522i | 1.06274 | + | 0.613573i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 260.915 | + | 451.918i | 0.355955 | + | 0.616532i | 0.987281 | − | 0.158986i | \(-0.0508224\pi\) |
−0.631326 | + | 0.775517i | \(0.717489\pi\) | |||||||
\(734\) | 348.543 | + | 449.968i | 0.474855 | + | 0.613035i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 122.164 | + | 788.566i | 0.165984 | + | 1.07142i | ||||
\(737\) | −196.734 | −0.266939 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 965.020i | − | 1.30585i | −0.757424 | − | 0.652923i | \(-0.773542\pi\) | ||
0.757424 | − | 0.652923i | \(-0.226458\pi\) | |||||||
\(740\) | 47.5130 | − | 184.017i | 0.0642067 | − | 0.248672i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −959.902 | − | 1239.23i | −1.29367 | − | 1.67012i | ||||
\(743\) | 950.317 | − | 548.666i | 1.27903 | − | 0.738447i | 0.302357 | − | 0.953195i | \(-0.402226\pi\) |
0.976669 | + | 0.214748i | \(0.0688930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −507.161 | + | 878.429i | −0.680753 | + | 1.17910i | ||||
\(746\) | 81.4106 | + | 597.317i | 0.109130 | + | 0.800693i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −129.678 | − | 466.892i | −0.173366 | − | 0.624188i | ||||
\(749\) | −460.939 | + | 798.370i | −0.615406 | + | 1.06591i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1196.02 | − | 690.524i | 1.59257 | − | 0.919472i | 0.599709 | − | 0.800218i | \(-0.295283\pi\) |
0.992864 | − | 0.119255i | \(-0.0380505\pi\) | |||||||
\(752\) | −402.926 | + | 728.245i | −0.535806 | + | 0.968411i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 790.492 | + | 323.218i | 1.04840 | + | 0.428671i | ||||
\(755\) | − | 577.494i | − | 0.764892i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −516.252 | −0.681971 | −0.340986 | − | 0.940068i | \(-0.610761\pi\) | ||||
−0.340986 | + | 0.940068i | \(0.610761\pi\) | |||||||
\(758\) | −188.133 | + | 460.117i | −0.248197 | + | 0.607014i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 246.748 | + | 184.029i | 0.324668 | + | 0.242143i | ||||
\(761\) | −608.092 | − | 1053.25i | −0.799069 | − | 1.38403i | −0.920223 | − | 0.391394i | \(-0.871993\pi\) |
0.121154 | − | 0.992634i | \(-0.461341\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 794.823 | + | 458.892i | 1.04171 | + | 0.601431i | ||||
\(764\) | 99.1668 | + | 357.040i | 0.129799 | + | 0.467329i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −967.319 | + | 131.840i | −1.26282 | + | 0.172114i | ||||
\(767\) | −1045.30 | − | 603.502i | −1.36284 | − | 0.786835i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −502.163 | − | 869.771i | −0.653007 | − | 1.13104i | −0.982389 | − | 0.186845i | \(-0.940174\pi\) |
0.329382 | − | 0.944197i | \(-0.393160\pi\) | |||||||
\(770\) | −751.295 | + | 581.951i | −0.975708 | + | 0.755780i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −243.164 | + | 941.770i | −0.314979 | + | 1.21991i | ||||
\(773\) | 382.580 | 0.494929 | 0.247464 | − | 0.968897i | \(-0.420403\pi\) | ||||
0.247464 | + | 0.968897i | \(0.420403\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 510.960i | − | 0.659304i | ||||||
\(776\) | −1099.06 | − | 129.426i | −1.41631 | − | 0.166786i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 657.544 | − | 509.331i | 0.845172 | − | 0.654668i | ||||
\(779\) | −38.8931 | + | 22.4549i | −0.0499269 | + | 0.0288253i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 383.489 | − | 664.223i | 0.491023 | − | 0.850477i | ||||
\(782\) | 884.223 | − | 120.514i | 1.13072 | − | 0.154110i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −559.745 | + | 336.927i | −0.713960 | + | 0.429754i | ||||
\(785\) | 267.185 | − | 462.777i | 0.340362 | − | 0.589525i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −413.327 | + | 238.634i | −0.525193 | + | 0.303220i | −0.739057 | − | 0.673643i | \(-0.764728\pi\) |
0.213864 | + | 0.976863i | \(0.431395\pi\) | |||||||
\(788\) | −397.954 | − | 390.762i | −0.505018 | − | 0.495891i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 837.866 | − | 2049.16i | 1.06059 | − | 2.59388i | ||||
\(791\) | 368.411i | 0.465754i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 121.334 | 0.153007 | ||||||||
\(794\) | 1241.85 | + | 507.771i | 1.56405 | + | 0.639511i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −311.061 | + | 316.786i | −0.390780 | + | 0.397973i | ||||
\(797\) | 257.304 | + | 445.663i | 0.322840 | + | 0.559176i | 0.981073 | − | 0.193639i | \(-0.0620290\pi\) |
−0.658233 | + | 0.752815i | \(0.728696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 806.067 | + | 465.383i | 1.00884 | + | 0.582456i | ||||
\(800\) | 598.268 | + | 743.930i | 0.747835 | + | 0.929913i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.9907 | − | 227.381i | −0.0386417 | − | 0.283518i | ||||
\(803\) | −12.7066 | − | 7.33616i | −0.0158239 | − | 0.00913594i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −875.076 | − | 1515.68i | −1.08705 | − | 1.88283i | ||||
\(806\) | 302.410 | + | 390.409i | 0.375198 | + | 0.484379i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 774.663 | + | 91.2249i | 0.958741 | + | 0.112902i | ||||
\(809\) | 1463.74 | 1.80932 | 0.904662 | − | 0.426129i | \(-0.140123\pi\) | ||||
0.904662 | + | 0.426129i | \(0.140123\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1163.05i | 1.43410i | 0.697023 | + | 0.717049i | \(0.254508\pi\) | ||||
−0.697023 | + | 0.717049i | \(0.745492\pi\) | |||||||
\(812\) | 1087.29 | + | 280.736i | 1.33902 | + | 0.345734i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 53.2035 | + | 68.6855i | 0.0653606 | + | 0.0843802i | ||||
\(815\) | 362.830 | − | 209.480i | 0.445190 | − | 0.257030i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 130.249 | − | 225.598i | 0.159424 | − | 0.276130i | ||||
\(818\) | −39.6147 | − | 290.656i | −0.0484287 | − | 0.355326i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −246.663 | + | 68.5098i | −0.300808 | + | 0.0835486i | ||||
\(821\) | −196.276 | + | 339.961i | −0.239070 | + | 0.414081i | −0.960448 | − | 0.278461i | \(-0.910176\pi\) |
0.721378 | + | 0.692542i | \(0.243509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1081.53 | − | 624.422i | 1.31413 | − | 0.758714i | 0.331354 | − | 0.943507i | \(-0.392495\pi\) |
0.982778 | + | 0.184792i | \(0.0591613\pi\) | |||||||
\(824\) | −272.440 | − | 203.191i | −0.330631 | − | 0.246591i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1469.03 | − | 600.658i | −1.77848 | − | 0.727189i | ||||
\(827\) | − | 1369.15i | − | 1.65557i | −0.561049 | − | 0.827783i | \(-0.689602\pi\) | ||
0.561049 | − | 0.827783i | \(-0.310398\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −73.7477 | −0.0889598 | −0.0444799 | − | 0.999010i | \(-0.514163\pi\) | ||||
−0.0444799 | + | 0.999010i | \(0.514163\pi\) | |||||||
\(830\) | −75.8947 | + | 185.615i | −0.0914394 | + | 0.223633i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −897.410 | − | 214.332i | −1.07862 | − | 0.257610i | ||||
\(833\) | 365.317 | + | 632.748i | 0.438556 | + | 0.759601i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1293.07 | − | 746.554i | −1.54859 | − | 0.894077i | ||||
\(836\) | −135.584 | + | 37.6581i | −0.162182 | + | 0.0450455i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1063.91 | − | 145.004i | 1.26958 | − | 0.173036i | ||||
\(839\) | −1039.73 | − | 600.286i | −1.23924 | − | 0.715478i | −0.270305 | − | 0.962775i | \(-0.587124\pi\) |
−0.968940 | + | 0.247297i | \(0.920458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.1625 | − | 31.4584i | −0.0215963 | − | 0.0374060i | ||||
\(842\) | −580.931 | + | 449.988i | −0.689942 | + | 0.534427i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1026.71 | − | 265.095i | −1.21648 | − | 0.314094i | ||||
\(845\) | 287.554 | 0.340300 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 712.406i | 0.841094i | ||||||||
\(848\) | −24.1292 | − | 1322.85i | −0.0284543 | − | 1.55997i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 844.024 | − | 653.778i | 0.992969 | − | 0.769151i | ||||
\(851\) | −138.567 | + | 80.0018i | −0.162829 | + | 0.0940092i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 219.539 | − | 380.254i | 0.257373 | − | 0.445784i | −0.708164 | − | 0.706048i | \(-0.750476\pi\) |
0.965537 | + | 0.260264i | \(0.0838097\pi\) | |||||||
\(854\) | 158.080 | − | 21.5454i | 0.185106 | − | 0.0252288i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −714.748 | + | 307.578i | −0.834986 | + | 0.359321i | ||||
\(857\) | 255.481 | − | 442.506i | 0.298111 | − | 0.516344i | −0.677593 | − | 0.735437i | \(-0.736977\pi\) |
0.975704 | + | 0.219094i | \(0.0703101\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −153.093 | + | 88.3882i | −0.178222 | + | 0.102897i | −0.586457 | − | 0.809980i | \(-0.699478\pi\) |
0.408235 | + | 0.912877i | \(0.366144\pi\) | |||||||
\(860\) | 1040.38 | − | 1059.53i | 1.20974 | − | 1.23201i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 556.614 | − | 1361.31i | 0.645724 | − | 1.57924i | ||||
\(863\) | − | 1028.28i | − | 1.19152i | −0.803163 | − | 0.595759i | \(-0.796851\pi\) | ||
0.803163 | − | 0.595759i | \(-0.203149\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 685.325 | 0.792283 | ||||||||
\(866\) | −1416.49 | − | 579.176i | −1.63567 | − | 0.668795i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 463.319 | + | 454.945i | 0.533777 | + | 0.524130i | ||||
\(869\) | 506.022 | + | 876.456i | 0.582304 | + | 1.00858i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 362.798 | + | 209.462i | 0.416530 | + | 0.240484i | ||||
\(872\) | 306.212 | + | 711.573i | 0.351161 | + | 0.816024i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34.9969 | − | 256.775i | −0.0400422 | − | 0.293793i | ||||
\(875\) | −293.744 | − | 169.593i | −0.335707 | − | 0.193821i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 470.457 | + | 814.856i | 0.536439 | + | 0.929140i | 0.999092 | + | 0.0426008i | \(0.0135644\pi\) |
−0.462653 | + | 0.886540i | \(0.653102\pi\) | |||||||
\(878\) | −56.8094 | − | 73.3406i | −0.0647032 | − | 0.0835314i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −801.994 | + | 14.6286i | −0.911357 | + | 0.0166234i | ||||
\(881\) | −1065.75 | −1.20970 | −0.604851 | − | 0.796339i | \(-0.706767\pi\) | ||||
−0.604851 | + | 0.796339i | \(0.706767\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1001.97i | 1.13474i | 0.823464 | + | 0.567368i | \(0.192038\pi\) | ||||
−0.823464 | + | 0.567368i | \(0.807962\pi\) | |||||||
\(884\) | −257.957 | + | 999.064i | −0.291807 | + | 1.13016i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −171.088 | − | 220.874i | −0.193102 | − | 0.249293i | ||||
\(887\) | 583.774 | − | 337.042i | 0.658144 | − | 0.379980i | −0.133426 | − | 0.991059i | \(-0.542598\pi\) |
0.791569 | + | 0.611079i | \(0.209264\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 469.240 | − | 812.747i | 0.527829 | − | 0.914227i | ||||
\(890\) | 35.7866 | + | 262.569i | 0.0402097 | + | 0.295022i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −340.328 | − | 1225.32i | −0.381534 | − | 1.37367i | ||||
\(893\) | 135.146 | − | 234.079i | 0.151339 | − | 0.262126i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.5016 | − | 15.8780i | 0.0307280 | − | 0.0177408i | ||||
\(896\) | −1207.25 | − | 119.888i | −1.34737 | − | 0.133804i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −494.535 | − | 202.206i | −0.550707 | − | 0.225174i | ||||
\(899\) | − | 507.310i | − | 0.564305i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1479.63 | −1.64221 | ||||||||
\(902\) | 44.2915 | − | 108.324i | 0.0491037 | − | 0.120093i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −185.909 | + | 249.268i | −0.205651 | + | 0.275739i | ||||
\(905\) | 1072.78 | + | 1858.11i | 1.18539 | + | 2.05316i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1023.16 | + | 590.723i | 1.12807 | + | 0.651293i | 0.943450 | − | 0.331516i | \(-0.107560\pi\) |
0.184624 | + | 0.982809i | \(0.440893\pi\) | |||||||
\(908\) | −266.938 | − | 961.083i | −0.293985 | − | 1.05846i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2005.06 | − | 273.278i | 2.20337 | − | 0.300305i | ||||
\(911\) | 1207.61 | + | 697.213i | 1.32559 | + | 0.765328i | 0.984614 | − | 0.174746i | \(-0.0559103\pi\) |
0.340973 | + | 0.940073i | \(0.389244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.8359 | − | 79.3901i | −0.0502036 | − | 0.0869553i | ||||
\(914\) | 376.042 | − | 291.281i | 0.411424 | − | 0.318688i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 152.334 | − | 589.988i | 0.166304 | − | 0.644092i | ||||
\(917\) | −513.346 | −0.559811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 210.163i | 0.228686i | 0.993441 | + | 0.114343i | \(0.0364763\pi\) | ||||
−0.993441 | + | 0.114343i | \(0.963524\pi\) | |||||||
\(920\) | 172.766 | − | 1467.09i | 0.187789 | − | 1.59467i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −472.207 | + | 365.770i | −0.512155 | + | 0.396713i | ||||
\(923\) | −1414.39 | + | 816.596i | −1.53238 | + | 0.884719i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −95.7098 | + | 165.774i | −0.103470 | + | 0.179215i | ||||
\(926\) | 970.101 | − | 132.219i | 1.04763 | − | 0.142785i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 593.994 | + | 738.615i | 0.640080 | + | 0.795921i | ||||
\(929\) | 83.2996 | − | 144.279i | 0.0896659 | − | 0.155306i | −0.817704 | − | 0.575639i | \(-0.804753\pi\) |
0.907370 | + | 0.420333i | \(0.138087\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 183.748 | − | 106.087i | 0.197366 | − | 0.113949i | ||||
\(932\) | −989.783 | − | 971.894i | −1.06200 | − | 1.04280i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −343.860 | + | 840.976i | −0.368158 | + | 0.900403i | ||||
\(935\) | 897.044i | 0.959405i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 251.158 | 0.268045 | 0.134022 | − | 0.990978i | \(-0.457211\pi\) | ||||
0.134022 | + | 0.990978i | \(0.457211\pi\) | |||||||
\(938\) | 509.865 | + | 208.474i | 0.543566 | + | 0.222254i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1079.49 | − | 1099.36i | 1.14839 | − | 1.16953i | ||||
\(941\) | −407.282 | − | 705.433i | −0.432818 | − | 0.749663i | 0.564296 | − | 0.825572i | \(-0.309147\pi\) |
−0.997115 | + | 0.0759090i | \(0.975814\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 186.650 | + | 107.762i | 0.197932 | + | 0.114276i | ||||
\(944\) | −690.841 | − | 1147.71i | −0.731823 | − | 1.21580i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 91.6718 | + | 672.604i | 0.0969047 | + | 0.710998i | ||||
\(947\) | −513.020 | − | 296.192i | −0.541731 | − | 0.312769i | 0.204049 | − | 0.978961i | \(-0.434590\pi\) |
−0.745780 | + | 0.666192i | \(0.767923\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6215 | + | 27.0572i | 0.0164610 | + | 0.0285113i | ||||
\(950\) | −189.855 | − | 245.102i | −0.199847 | − | 0.258002i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −158.675 | + | 1347.43i | −0.166675 | + | 1.41537i | ||||
\(953\) | −844.768 | −0.886430 | −0.443215 | − | 0.896415i | \(-0.646162\pi\) | ||||
−0.443215 | + | 0.896415i | \(0.646162\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 685.983i | − | 0.718307i | ||||||
\(956\) | −402.926 | − | 104.035i | −0.421471 | − | 0.108823i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.42572 | + | 5.71359i | 0.00461975 | + | 0.00596408i | ||||
\(959\) | −45.6330 | + | 26.3462i | −0.0475839 | + | 0.0274726i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −333.825 | + | 578.202i | −0.347373 | + | 0.601667i | ||||
\(962\) | −24.9838 | − | 183.308i | −0.0259707 | − | 0.190549i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1086.19 | + | 301.686i | −1.12675 | + | 0.312952i | ||||
\(965\) | 900.305 | − | 1559.37i | 0.932959 | − | 1.61593i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 156.035 | − | 90.0867i | 0.161360 | − | 0.0931611i | −0.417146 | − | 0.908840i | \(-0.636970\pi\) |
0.578505 | + | 0.815679i | \(0.303636\pi\) | |||||||
\(968\) | −359.496 | + | 482.016i | −0.371381 | + | 0.497950i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1896.27 | + | 775.351i | 1.95492 | + | 0.799331i | ||||
\(971\) | 411.395i | 0.423682i | 0.977304 | + | 0.211841i | \(0.0679458\pi\) | ||||
−0.977304 | + | 0.211841i | \(0.932054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1445.56 | 1.48567 | ||||||||
\(974\) | −661.968 | + | 1618.97i | −0.679638 | + | 1.66219i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 117.830 | + | 65.1932i | 0.120727 | + | 0.0667963i | ||||
\(977\) | −878.125 | − | 1520.96i | −0.898797 | − | 1.55676i | −0.829034 | − | 0.559199i | \(-0.811109\pi\) |
−0.0697635 | − | 0.997564i | \(-0.522224\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −104.912 | − | 60.5708i | −0.107162 | − | 0.0618701i | ||||
\(980\) | 1165.34 | − | 323.670i | 1.18912 | − | 0.330276i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1278.57 | + | 174.261i | −1.30201 | + | 0.177456i | ||||
\(983\) | −695.466 | − | 401.528i | −0.707494 | − | 0.408472i | 0.102639 | − | 0.994719i | \(-0.467271\pi\) |
−0.810132 | + | 0.586247i | \(0.800605\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 516.243 | + | 894.159i | 0.524105 | + | 0.907776i | ||||
\(986\) | 837.994 | − | 649.107i | 0.849892 | − | 0.658324i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 290.125 | + | 74.9099i | 0.293648 | + | 0.0758197i | ||||
\(989\) | −1250.15 | −1.26405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 338.466i | 0.341540i | 0.985311 | + | 0.170770i | \(0.0546254\pi\) | ||||
−0.985311 | + | 0.170770i | \(0.945375\pi\) | |||||||
\(992\) | 83.9071 | + | 541.618i | 0.0845837 | + | 0.545986i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1697.73 | + | 1315.05i | −1.70797 | + | 1.32299i | ||||
\(995\) | 711.783 | − | 410.948i | 0.715360 | − | 0.413013i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −295.906 | + | 512.523i | −0.296796 | + | 0.514066i | −0.975401 | − | 0.220438i | \(-0.929251\pi\) |
0.678605 | + | 0.734503i | \(0.262585\pi\) | |||||||
\(998\) | −1119.33 | + | 152.558i | −1.12158 | + | 0.152864i | ||||
\(999\) | 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 | 324.3.f.o.55.1 | 8 | ||
3.2 | odd | 2 | inner | 324.3.f.o.55.4 | 8 | ||
4.3 | odd | 2 | 324.3.f.p.55.4 | 8 | |||
9.2 | odd | 6 | 108.3.d.d.55.3 | ✓ | 8 | ||
9.4 | even | 3 | 324.3.f.p.271.3 | 8 | |||
9.5 | odd | 6 | 324.3.f.p.271.2 | 8 | |||
9.7 | even | 3 | 108.3.d.d.55.6 | yes | 8 | ||
12.11 | even | 2 | 324.3.f.p.55.1 | 8 | |||
36.7 | odd | 6 | 108.3.d.d.55.5 | yes | 8 | ||
36.11 | even | 6 | 108.3.d.d.55.4 | yes | 8 | ||
36.23 | even | 6 | inner | 324.3.f.o.271.4 | 8 | ||
36.31 | odd | 6 | inner | 324.3.f.o.271.1 | 8 | ||
72.11 | even | 6 | 1728.3.g.l.703.7 | 8 | |||
72.29 | odd | 6 | 1728.3.g.l.703.8 | 8 | |||
72.43 | odd | 6 | 1728.3.g.l.703.1 | 8 | |||
72.61 | even | 6 | 1728.3.g.l.703.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.d.d.55.3 | ✓ | 8 | 9.2 | odd | 6 | ||
108.3.d.d.55.4 | yes | 8 | 36.11 | even | 6 | ||
108.3.d.d.55.5 | yes | 8 | 36.7 | odd | 6 | ||
108.3.d.d.55.6 | yes | 8 | 9.7 | even | 3 | ||
324.3.f.o.55.1 | 8 | 1.1 | even | 1 | trivial | ||
324.3.f.o.55.4 | 8 | 3.2 | odd | 2 | inner | ||
324.3.f.o.271.1 | 8 | 36.31 | odd | 6 | inner | ||
324.3.f.o.271.4 | 8 | 36.23 | even | 6 | inner | ||
324.3.f.p.55.1 | 8 | 12.11 | even | 2 | |||
324.3.f.p.55.4 | 8 | 4.3 | odd | 2 | |||
324.3.f.p.271.2 | 8 | 9.5 | odd | 6 | |||
324.3.f.p.271.3 | 8 | 9.4 | even | 3 | |||
1728.3.g.l.703.1 | 8 | 72.43 | odd | 6 | |||
1728.3.g.l.703.2 | 8 | 72.61 | even | 6 | |||
1728.3.g.l.703.7 | 8 | 72.11 | even | 6 | |||
1728.3.g.l.703.8 | 8 | 72.29 | odd | 6 |