Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [392,3,Mod(117,392)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(392, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("392.117");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 392 = 2^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 392.j (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: | \(10.6812263629\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 325.1 | ||
Character | \(\chi\) | \(=\) | 392.325 |
Dual form | 392.3.j.e.117.1 |
$q$-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 \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(297\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97030 | − | 0.343404i | −0.985149 | − | 0.171702i | ||||
\(3\) | 1.94818 | − | 3.37434i | 0.649392 | − | 1.12478i | −0.333876 | − | 0.942617i | \(-0.608357\pi\) |
0.983268 | − | 0.182163i | \(-0.0583098\pi\) | |||||||
\(4\) | 3.76415 | + | 1.35322i | 0.941037 | + | 0.338304i | ||||
\(5\) | 4.42985 | + | 7.67272i | 0.885969 | + | 1.53454i | 0.844599 | + | 0.535400i | \(0.179839\pi\) |
0.0413705 | + | 0.999144i | \(0.486828\pi\) | |||||||
\(6\) | −4.99725 | + | 5.97944i | −0.832875 | + | 0.996574i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −6.95179 | − | 3.95886i | −0.868974 | − | 0.494858i | ||||
\(9\) | −3.09078 | − | 5.35338i | −0.343420 | − | 0.594820i | ||||
\(10\) | −6.09327 | − | 16.6388i | −0.609327 | − | 1.66388i | ||||
\(11\) | −3.15749 | − | 1.82298i | −0.287045 | − | 0.165725i | 0.349564 | − | 0.936913i | \(-0.386330\pi\) |
−0.636608 | + | 0.771187i | \(0.719663\pi\) | |||||||
\(12\) | 11.8994 | − | 10.0652i | 0.991619 | − | 0.838767i | ||||
\(13\) | 7.79378 | 0.599522 | 0.299761 | − | 0.954014i | \(-0.403093\pi\) | ||||
0.299761 | + | 0.954014i | \(0.403093\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 34.5205 | 2.30136 | ||||||||
\(16\) | 12.3376 | + | 10.1874i | 0.771101 | + | 0.636713i | ||||
\(17\) | 9.07152 | + | 5.23744i | 0.533619 | + | 0.308085i | 0.742489 | − | 0.669858i | \(-0.233645\pi\) |
−0.208870 | + | 0.977943i | \(0.566979\pi\) | |||||||
\(18\) | 4.25138 | + | 11.6091i | 0.236188 | + | 0.644952i | ||||
\(19\) | −5.39264 | − | 9.34032i | −0.283823 | − | 0.491596i | 0.688500 | − | 0.725236i | \(-0.258269\pi\) |
−0.972323 | + | 0.233640i | \(0.924936\pi\) | |||||||
\(20\) | 6.29174 | + | 34.8758i | 0.314587 | + | 1.74379i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.59518 | + | 4.67610i | 0.254326 | + | 0.212550i | ||||
\(23\) | 6.45553 | + | 11.1813i | 0.280675 | + | 0.486144i | 0.971551 | − | 0.236829i | \(-0.0761083\pi\) |
−0.690876 | + | 0.722973i | \(0.742775\pi\) | |||||||
\(24\) | −26.9019 | + | 15.7451i | −1.12091 | + | 0.656047i | ||||
\(25\) | −26.7471 | + | 46.3273i | −1.06988 | + | 1.85309i | ||||
\(26\) | −15.3561 | − | 2.67642i | −0.590618 | − | 0.102939i | ||||
\(27\) | 10.9817 | 0.406728 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17.2327i | 0.594231i | 0.954842 | + | 0.297115i | \(0.0960246\pi\) | ||||
−0.954842 | + | 0.297115i | \(0.903975\pi\) | |||||||
\(30\) | −68.0156 | − | 11.8545i | −2.26719 | − | 0.395149i | ||||
\(31\) | 26.1797 | + | 15.1148i | 0.844505 | + | 0.487575i | 0.858793 | − | 0.512323i | \(-0.171215\pi\) |
−0.0142878 | + | 0.999898i | \(0.504548\pi\) | |||||||
\(32\) | −20.8104 | − | 24.3090i | −0.650324 | − | 0.759657i | ||||
\(33\) | −12.3027 | + | 7.10296i | −0.372809 | + | 0.215241i | ||||
\(34\) | −16.0750 | − | 13.4345i | −0.472795 | − | 0.395133i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.38985 | − | 24.3334i | −0.121940 | − | 0.675928i | ||||
\(37\) | 34.2810 | − | 19.7922i | 0.926515 | − | 0.534924i | 0.0408071 | − | 0.999167i | \(-0.487007\pi\) |
0.885708 | + | 0.464244i | \(0.153674\pi\) | |||||||
\(38\) | 7.41760 | + | 20.2551i | 0.195200 | + | 0.533028i | ||||
\(39\) | 15.1837 | − | 26.2989i | 0.389324 | − | 0.674330i | ||||
\(40\) | −0.420114 | − | 70.8763i | −0.0105029 | − | 1.77191i | ||||
\(41\) | 73.6801i | 1.79707i | 0.438897 | + | 0.898537i | \(0.355369\pi\) | ||||
−0.438897 | + | 0.898537i | \(0.644631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 40.8501i | − | 0.950002i | −0.879985 | − | 0.475001i | \(-0.842448\pi\) | ||
0.879985 | − | 0.475001i | \(-0.157552\pi\) | |||||||
\(44\) | −9.41837 | − | 11.1347i | −0.214054 | − | 0.253062i | ||||
\(45\) | 27.3833 | − | 47.4293i | 0.608518 | − | 1.05398i | ||||
\(46\) | −8.87961 | − | 24.2474i | −0.193035 | − | 0.527117i | ||||
\(47\) | 36.2025 | − | 20.9015i | 0.770266 | − | 0.444713i | −0.0627038 | − | 0.998032i | \(-0.519972\pi\) |
0.832969 | + | 0.553319i | \(0.186639\pi\) | |||||||
\(48\) | 58.4116 | − | 21.7844i | 1.21691 | − | 0.453842i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 68.6087 | − | 82.0935i | 1.37217 | − | 1.64187i | ||||
\(51\) | 35.3458 | − | 20.4069i | 0.693055 | − | 0.400136i | ||||
\(52\) | 29.3369 | + | 10.5467i | 0.564172 | + | 0.202821i | ||||
\(53\) | −5.55272 | − | 3.20586i | −0.104768 | − | 0.0604880i | 0.446700 | − | 0.894684i | \(-0.352599\pi\) |
−0.551469 | + | 0.834196i | \(0.685932\pi\) | |||||||
\(54\) | −21.6371 | − | 3.77115i | −0.400688 | − | 0.0698361i | ||||
\(55\) | − | 32.3020i | − | 0.587310i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −42.0232 | −0.737249 | ||||||||
\(58\) | 5.91778 | − | 33.9535i | 0.102031 | − | 0.585406i | ||||
\(59\) | 7.95742 | − | 13.7827i | 0.134871 | − | 0.233604i | −0.790677 | − | 0.612234i | \(-0.790271\pi\) |
0.925548 | + | 0.378629i | \(0.123605\pi\) | |||||||
\(60\) | 129.940 | + | 46.7137i | 2.16567 | + | 0.778561i | ||||
\(61\) | 6.07848 | + | 10.5282i | 0.0996472 | + | 0.172594i | 0.911539 | − | 0.411214i | \(-0.134895\pi\) |
−0.811891 | + | 0.583808i | \(0.801562\pi\) | |||||||
\(62\) | −46.3912 | − | 38.7709i | −0.748246 | − | 0.625338i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 32.6548 | + | 55.0424i | 0.510231 | + | 0.860037i | ||||
\(65\) | 34.5253 | + | 59.7995i | 0.531158 | + | 0.919992i | ||||
\(66\) | 26.6792 | − | 9.77016i | 0.404230 | − | 0.148033i | ||||
\(67\) | 6.75274 | + | 3.89870i | 0.100787 | + | 0.0581895i | 0.549546 | − | 0.835463i | \(-0.314801\pi\) |
−0.448759 | + | 0.893653i | \(0.648134\pi\) | |||||||
\(68\) | 27.0591 | + | 31.9902i | 0.397928 | + | 0.470445i | ||||
\(69\) | 50.3060 | 0.729073 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −41.3627 | −0.582574 | −0.291287 | − | 0.956636i | \(-0.594083\pi\) | ||||
−0.291287 | + | 0.956636i | \(0.594083\pi\) | |||||||
\(72\) | 0.293120 | + | 49.4516i | 0.00407112 | + | 0.686827i | ||||
\(73\) | −77.6038 | − | 44.8046i | −1.06307 | − | 0.613761i | −0.136787 | − | 0.990601i | \(-0.543678\pi\) |
−0.926279 | + | 0.376839i | \(0.877011\pi\) | |||||||
\(74\) | −74.3406 | + | 27.2242i | −1.00460 | + | 0.367895i | ||||
\(75\) | 104.216 | + | 180.507i | 1.38955 | + | 2.40677i | ||||
\(76\) | −7.65920 | − | 42.4557i | −0.100779 | − | 0.558628i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −38.9475 | + | 46.6025i | −0.499326 | + | 0.597467i | ||||
\(79\) | −35.3975 | − | 61.3103i | −0.448070 | − | 0.776080i | 0.550191 | − | 0.835039i | \(-0.314555\pi\) |
−0.998260 | + | 0.0589594i | \(0.981222\pi\) | |||||||
\(80\) | −23.5115 | + | 139.792i | −0.293893 | + | 1.74740i | ||||
\(81\) | 49.2112 | − | 85.2363i | 0.607546 | − | 1.05230i | ||||
\(82\) | 25.3020 | − | 145.172i | 0.308561 | − | 1.77039i | ||||
\(83\) | 60.8673 | 0.733341 | 0.366671 | − | 0.930351i | \(-0.380498\pi\) | ||||
0.366671 | + | 0.930351i | \(0.380498\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 92.8043i | 1.09182i | ||||||||
\(86\) | −14.0281 | + | 80.4868i | −0.163117 | + | 0.935894i | ||||
\(87\) | 58.1489 | + | 33.5723i | 0.668379 | + | 0.385889i | ||||
\(88\) | 14.7333 | + | 25.1730i | 0.167424 | + | 0.286057i | ||||
\(89\) | 23.4004 | − | 13.5102i | 0.262926 | − | 0.151800i | −0.362743 | − | 0.931889i | \(-0.618160\pi\) |
0.625668 | + | 0.780089i | \(0.284826\pi\) | |||||||
\(90\) | −70.2407 | + | 84.0463i | −0.780453 | + | 0.933848i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.16883 | + | 50.8238i | 0.0996612 | + | 0.552433i | ||||
\(93\) | 102.005 | − | 58.8927i | 1.09683 | − | 0.633255i | ||||
\(94\) | −78.5073 | + | 28.7501i | −0.835184 | + | 0.305852i | ||||
\(95\) | 47.7771 | − | 82.7524i | 0.502917 | − | 0.871078i | ||||
\(96\) | −122.569 | + | 22.8630i | −1.27676 | + | 0.238156i | ||||
\(97\) | − | 3.26608i | − | 0.0336710i | −0.999858 | − | 0.0168355i | \(-0.994641\pi\) | ||
0.999858 | − | 0.0168355i | \(-0.00535916\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 22.5377i | 0.227653i | ||||||||
\(100\) | −163.371 | + | 138.188i | −1.63371 | + | 1.38188i | ||||
\(101\) | 68.8571 | − | 119.264i | 0.681754 | − | 1.18083i | −0.292691 | − | 0.956207i | \(-0.594551\pi\) |
0.974445 | − | 0.224625i | \(-0.0721158\pi\) | |||||||
\(102\) | −76.6496 | + | 28.0698i | −0.751467 | + | 0.275194i | ||||
\(103\) | −86.3243 | + | 49.8393i | −0.838100 | + | 0.483877i | −0.856618 | − | 0.515952i | \(-0.827438\pi\) |
0.0185182 | + | 0.999829i | \(0.494105\pi\) | |||||||
\(104\) | −54.1807 | − | 30.8545i | −0.520969 | − | 0.296678i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.83960 | + | 8.22333i | 0.0928265 | + | 0.0775786i | ||||
\(107\) | −81.4157 | + | 47.0054i | −0.760894 | + | 0.439302i | −0.829617 | − | 0.558333i | \(-0.811441\pi\) |
0.0687226 | + | 0.997636i | \(0.478108\pi\) | |||||||
\(108\) | 41.3366 | + | 14.8606i | 0.382746 | + | 0.137598i | ||||
\(109\) | −169.697 | − | 97.9745i | −1.55685 | − | 0.898849i | −0.997555 | − | 0.0698815i | \(-0.977738\pi\) |
−0.559297 | − | 0.828967i | \(-0.688929\pi\) | |||||||
\(110\) | −11.0927 | + | 63.6446i | −0.100842 | + | 0.578588i | ||||
\(111\) | − | 154.234i | − | 1.38950i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 101.873 | 0.901527 | 0.450763 | − | 0.892643i | \(-0.351152\pi\) | ||||
0.450763 | + | 0.892643i | \(0.351152\pi\) | |||||||
\(114\) | 82.7982 | + | 14.4309i | 0.726300 | + | 0.126587i | ||||
\(115\) | −57.1940 | + | 99.0629i | −0.497339 | + | 0.861417i | ||||
\(116\) | −23.3196 | + | 64.8664i | −0.201031 | + | 0.559193i | ||||
\(117\) | −24.0888 | − | 41.7231i | −0.205887 | − | 0.356608i | ||||
\(118\) | −20.4115 | + | 24.4233i | −0.172979 | + | 0.206977i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −239.979 | − | 136.662i | −1.99983 | − | 1.13885i | ||||
\(121\) | −53.8535 | − | 93.2770i | −0.445070 | − | 0.770884i | ||||
\(122\) | −8.36098 | − | 22.8311i | −0.0685326 | − | 0.187140i | ||||
\(123\) | 248.622 | + | 143.542i | 2.02131 | + | 1.16701i | ||||
\(124\) | 78.0905 | + | 92.3212i | 0.629762 | + | 0.744526i | ||||
\(125\) | −252.449 | −2.01960 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −139.079 | −1.09511 | −0.547554 | − | 0.836770i | \(-0.684441\pi\) | ||||
−0.547554 | + | 0.836770i | \(0.684441\pi\) | |||||||
\(128\) | −45.4379 | − | 119.664i | −0.354983 | − | 0.934873i | ||||
\(129\) | −137.842 | − | 79.5831i | −1.06854 | − | 0.616924i | ||||
\(130\) | −47.4896 | − | 129.679i | −0.365305 | − | 0.997530i | ||||
\(131\) | −45.8526 | − | 79.4190i | −0.350020 | − | 0.606252i | 0.636233 | − | 0.771497i | \(-0.280492\pi\) |
−0.986252 | + | 0.165245i | \(0.947158\pi\) | |||||||
\(132\) | −55.9210 | + | 10.0884i | −0.423644 | + | 0.0764272i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.9661 | − | 10.0005i | −0.0892991 | − | 0.0746307i | ||||
\(135\) | 48.6471 | + | 84.2592i | 0.360349 | + | 0.624142i | ||||
\(136\) | −42.3290 | − | 72.3225i | −0.311242 | − | 0.531783i | ||||
\(137\) | −99.7904 | + | 172.842i | −0.728397 | + | 1.26162i | 0.229163 | + | 0.973388i | \(0.426401\pi\) |
−0.957560 | + | 0.288233i | \(0.906932\pi\) | |||||||
\(138\) | −99.1179 | − | 17.2753i | −0.718245 | − | 0.125183i | ||||
\(139\) | 39.4768 | 0.284006 | 0.142003 | − | 0.989866i | \(-0.454646\pi\) | ||||
0.142003 | + | 0.989866i | \(0.454646\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 162.879i | − | 1.15517i | ||||||
\(142\) | 81.4969 | + | 14.2041i | 0.573922 | + | 0.100029i | ||||
\(143\) | −24.6088 | − | 14.2079i | −0.172089 | − | 0.0993559i | ||||
\(144\) | 16.4043 | − | 97.5349i | 0.113919 | − | 0.677326i | ||||
\(145\) | −132.222 | + | 76.3382i | −0.911873 | + | 0.526470i | ||||
\(146\) | 137.516 | + | 114.928i | 0.941894 | + | 0.787177i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 155.822 | − | 28.1110i | 1.05285 | − | 0.189939i | ||||
\(149\) | 82.0846 | − | 47.3916i | 0.550903 | − | 0.318064i | −0.198583 | − | 0.980084i | \(-0.563634\pi\) |
0.749486 | + | 0.662020i | \(0.230301\pi\) | |||||||
\(150\) | −143.350 | − | 391.442i | −0.955664 | − | 2.60961i | ||||
\(151\) | −33.2843 | + | 57.6501i | −0.220426 | + | 0.381789i | −0.954937 | − | 0.296807i | \(-0.904078\pi\) |
0.734511 | + | 0.678596i | \(0.237411\pi\) | |||||||
\(152\) | 0.511422 | + | 86.2807i | 0.00336462 | + | 0.567636i | ||||
\(153\) | − | 64.7511i | − | 0.423210i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 267.826i | 1.72791i | ||||||||
\(156\) | 92.7416 | − | 78.4460i | 0.594497 | − | 0.502859i | ||||
\(157\) | 12.7597 | − | 22.1004i | 0.0812720 | − | 0.140767i | −0.822525 | − | 0.568730i | \(-0.807435\pi\) |
0.903797 | + | 0.427962i | \(0.140768\pi\) | |||||||
\(158\) | 48.6894 | + | 132.955i | 0.308161 | + | 0.841489i | ||||
\(159\) | −21.6353 | + | 12.4912i | −0.136071 | + | 0.0785608i | ||||
\(160\) | 94.3296 | − | 267.357i | 0.589560 | − | 1.67098i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −126.231 | + | 151.042i | −0.779205 | + | 0.932355i | ||||
\(163\) | 166.364 | − | 96.0504i | 1.02064 | − | 0.589267i | 0.106350 | − | 0.994329i | \(-0.466083\pi\) |
0.914289 | + | 0.405062i | \(0.132750\pi\) | |||||||
\(164\) | −99.7051 | + | 277.343i | −0.607958 | + | 1.69111i | ||||
\(165\) | −108.998 | − | 62.9301i | −0.660594 | − | 0.381394i | ||||
\(166\) | −119.927 | − | 20.9021i | −0.722450 | − | 0.125916i | ||||
\(167\) | 184.150i | 1.10269i | 0.834276 | + | 0.551346i | \(0.185886\pi\) | ||||
−0.834276 | + | 0.551346i | \(0.814114\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −108.257 | −0.640574 | ||||||||
\(170\) | 31.8694 | − | 182.852i | 0.187467 | − | 1.07560i | ||||
\(171\) | −33.3349 | + | 57.7377i | −0.194941 | + | 0.337647i | ||||
\(172\) | 55.2790 | − | 153.766i | 0.321390 | − | 0.893987i | ||||
\(173\) | 34.9519 | + | 60.5384i | 0.202034 | + | 0.349933i | 0.949184 | − | 0.314723i | \(-0.101912\pi\) |
−0.747150 | + | 0.664656i | \(0.768578\pi\) | |||||||
\(174\) | −103.042 | − | 86.1160i | −0.592195 | − | 0.494920i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −20.3844 | − | 54.6578i | −0.115821 | − | 0.310556i | ||||
\(177\) | −31.0049 | − | 53.7021i | −0.175169 | − | 0.303401i | ||||
\(178\) | −50.7452 | + | 18.5834i | −0.285085 | + | 0.104401i | ||||
\(179\) | −207.251 | − | 119.657i | −1.15783 | − | 0.668473i | −0.207047 | − | 0.978331i | \(-0.566385\pi\) |
−0.950783 | + | 0.309858i | \(0.899719\pi\) | |||||||
\(180\) | 167.257 | − | 141.475i | 0.929206 | − | 0.785974i | ||||
\(181\) | −36.2834 | −0.200461 | −0.100230 | − | 0.994964i | \(-0.531958\pi\) | ||||
−0.100230 | + | 0.994964i | \(0.531958\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 47.3678 | 0.258840 | ||||||||
\(184\) | −0.612224 | − | 103.287i | −0.00332731 | − | 0.561341i | ||||
\(185\) | 303.720 | + | 175.353i | 1.64173 | + | 0.947852i | ||||
\(186\) | −221.205 | + | 81.0072i | −1.18927 | + | 0.435522i | ||||
\(187\) | −19.0955 | − | 33.0744i | −0.102115 | − | 0.176868i | ||||
\(188\) | 164.556 | − | 29.6866i | 0.875296 | − | 0.157907i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −122.553 | + | 146.640i | −0.645014 | + | 0.771789i | ||||
\(191\) | 162.622 | + | 281.669i | 0.851422 | + | 1.47471i | 0.879925 | + | 0.475113i | \(0.157593\pi\) |
−0.0285024 | + | 0.999594i | \(0.509074\pi\) | |||||||
\(192\) | 249.349 | − | 2.95610i | 1.29869 | − | 0.0153964i | ||||
\(193\) | −99.8198 | + | 172.893i | −0.517201 | + | 0.895818i | 0.482599 | + | 0.875841i | \(0.339693\pi\) |
−0.999800 | + | 0.0199772i | \(0.993641\pi\) | |||||||
\(194\) | −1.12159 | + | 6.43516i | −0.00578138 | + | 0.0331709i | ||||
\(195\) | 269.045 | 1.37972 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5053i | 0.0787071i | 0.999225 | + | 0.0393536i | \(0.0125299\pi\) | ||||
−0.999225 | + | 0.0393536i | \(0.987470\pi\) | |||||||
\(198\) | 7.73953 | − | 44.4059i | 0.0390885 | − | 0.224272i | ||||
\(199\) | 48.6375 | + | 28.0809i | 0.244409 | + | 0.141110i | 0.617202 | − | 0.786805i | \(-0.288266\pi\) |
−0.372792 | + | 0.927915i | \(0.621600\pi\) | |||||||
\(200\) | 369.344 | − | 216.170i | 1.84672 | − | 1.08085i | ||||
\(201\) | 26.3110 | − | 15.1907i | 0.130901 | − | 0.0755756i | ||||
\(202\) | −176.625 | + | 211.340i | −0.874380 | + | 1.04624i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 160.662 | − | 28.9841i | 0.787558 | − | 0.142079i | ||||
\(205\) | −565.326 | + | 326.391i | −2.75769 | + | 1.59215i | ||||
\(206\) | 187.200 | − | 68.5542i | 0.908736 | − | 0.332787i | ||||
\(207\) | 39.9052 | − | 69.1178i | 0.192779 | − | 0.333903i | ||||
\(208\) | 96.1566 | + | 79.3985i | 0.462291 | + | 0.381723i | ||||
\(209\) | 39.3226i | 0.188147i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 370.470i | − | 1.75578i | −0.478859 | − | 0.877892i | \(-0.658949\pi\) | ||
0.478859 | − | 0.877892i | \(-0.341051\pi\) | |||||||
\(212\) | −16.5630 | − | 19.5814i | −0.0781275 | − | 0.0923650i | ||||
\(213\) | −80.5819 | + | 139.572i | −0.378319 | + | 0.655267i | ||||
\(214\) | 176.555 | − | 64.6561i | 0.825023 | − | 0.302131i | ||||
\(215\) | 313.431 | − | 180.960i | 1.45782 | − | 0.841673i | ||||
\(216\) | −76.3422 | − | 43.4749i | −0.353436 | − | 0.201273i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 300.709 | + | 251.314i | 1.37940 | + | 1.15281i | ||||
\(219\) | −302.372 | + | 174.574i | −1.38069 | + | 0.797143i | ||||
\(220\) | 43.7117 | − | 121.590i | 0.198689 | − | 0.552680i | ||||
\(221\) | 70.7014 | + | 40.8195i | 0.319916 | + | 0.184704i | ||||
\(222\) | −52.9648 | + | 303.888i | −0.238580 | + | 1.36886i | ||||
\(223\) | 6.78533i | 0.0304275i | 0.999884 | + | 0.0152137i | \(0.00484287\pi\) | ||||
−0.999884 | + | 0.0152137i | \(0.995157\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 330.677 | 1.46968 | ||||||||
\(226\) | −200.719 | − | 34.9834i | −0.888138 | − | 0.154794i | ||||
\(227\) | −148.309 | + | 256.879i | −0.653344 | + | 1.13163i | 0.328962 | + | 0.944343i | \(0.393301\pi\) |
−0.982306 | + | 0.187282i | \(0.940032\pi\) | |||||||
\(228\) | −158.182 | − | 56.8665i | −0.693779 | − | 0.249415i | ||||
\(229\) | −89.0964 | − | 154.320i | −0.389067 | − | 0.673885i | 0.603257 | − | 0.797547i | \(-0.293869\pi\) |
−0.992324 | + | 0.123662i | \(0.960536\pi\) | |||||||
\(230\) | 146.708 | − | 175.543i | 0.637860 | − | 0.763230i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 68.2219 | − | 119.798i | 0.294060 | − | 0.516371i | ||||
\(233\) | −58.9011 | − | 102.020i | −0.252795 | − | 0.437853i | 0.711500 | − | 0.702687i | \(-0.248016\pi\) |
−0.964294 | + | 0.264833i | \(0.914683\pi\) | |||||||
\(234\) | 33.1343 | + | 90.4791i | 0.141600 | + | 0.386663i | ||||
\(235\) | 320.743 | + | 185.181i | 1.36486 | + | 0.788004i | ||||
\(236\) | 48.6038 | − | 41.1118i | 0.205948 | − | 0.174203i | ||||
\(237\) | −275.842 | −1.16389 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 46.3543 | 0.193951 | 0.0969755 | − | 0.995287i | \(-0.469083\pi\) | ||||
0.0969755 | + | 0.995287i | \(0.469083\pi\) | |||||||
\(240\) | 425.900 | + | 351.674i | 1.77458 | + | 1.46531i | ||||
\(241\) | −317.501 | − | 183.309i | −1.31743 | − | 0.760619i | −0.334115 | − | 0.942532i | \(-0.608438\pi\) |
−0.983315 | + | 0.181914i | \(0.941771\pi\) | |||||||
\(242\) | 74.0757 | + | 202.277i | 0.306098 | + | 0.835855i | ||||
\(243\) | −142.327 | − | 246.517i | −0.585706 | − | 1.01447i | ||||
\(244\) | 8.63331 | + | 47.8553i | 0.0353824 | + | 0.196128i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −440.566 | − | 368.198i | −1.79092 | − | 1.49674i | ||||
\(247\) | −42.0290 | − | 72.7964i | −0.170158 | − | 0.294722i | ||||
\(248\) | −122.158 | − | 208.717i | −0.492572 | − | 0.841600i | ||||
\(249\) | 118.580 | − | 205.387i | 0.476226 | − | 0.824847i | ||||
\(250\) | 497.400 | + | 86.6922i | 1.98960 | + | 0.346769i | ||||
\(251\) | −129.896 | −0.517513 | −0.258756 | − | 0.965943i | \(-0.583313\pi\) | ||||
−0.258756 | + | 0.965943i | \(0.583313\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 47.0732i | − | 0.186060i | ||||||
\(254\) | 274.027 | + | 47.7602i | 1.07884 | + | 0.188032i | ||||
\(255\) | 313.153 | + | 180.799i | 1.22805 | + | 0.709016i | ||||
\(256\) | 48.4332 | + | 251.377i | 0.189192 | + | 0.981940i | ||||
\(257\) | −232.394 | + | 134.173i | −0.904256 | + | 0.522073i | −0.878579 | − | 0.477598i | \(-0.841508\pi\) |
−0.0256776 | + | 0.999670i | \(0.508174\pi\) | |||||||
\(258\) | 244.261 | + | 204.138i | 0.946747 | + | 0.791233i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 49.0365 | + | 271.814i | 0.188602 | + | 1.04544i | ||||
\(261\) | 92.2532 | − | 53.2624i | 0.353460 | − | 0.204070i | ||||
\(262\) | 63.0704 | + | 172.225i | 0.240727 | + | 0.657347i | ||||
\(263\) | 117.691 | − | 203.847i | 0.447495 | − | 0.775085i | −0.550727 | − | 0.834685i | \(-0.685649\pi\) |
0.998222 | + | 0.0596008i | \(0.0189828\pi\) | |||||||
\(264\) | 113.645 | − | 0.673625i | 0.430475 | − | 0.00255161i | ||||
\(265\) | − | 56.8059i | − | 0.214362i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 105.281i | − | 0.394311i | ||||||
\(268\) | 20.1425 | + | 23.8132i | 0.0751587 | + | 0.0888552i | ||||
\(269\) | 177.348 | − | 307.175i | 0.659285 | − | 1.14192i | −0.321516 | − | 0.946904i | \(-0.604192\pi\) |
0.980801 | − | 0.195011i | \(-0.0624743\pi\) | |||||||
\(270\) | −66.9143 | − | 182.721i | −0.247831 | − | 0.676746i | ||||
\(271\) | 365.350 | − | 210.935i | 1.34816 | − | 0.778358i | 0.360168 | − | 0.932888i | \(-0.382719\pi\) |
0.987988 | + | 0.154529i | \(0.0493861\pi\) | |||||||
\(272\) | 58.5648 | + | 157.033i | 0.215312 | + | 0.577327i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 255.972 | − | 306.282i | 0.934203 | − | 1.11782i | ||||
\(275\) | 168.907 | − | 97.5186i | 0.614208 | − | 0.354613i | ||||
\(276\) | 189.359 | + | 68.0750i | 0.686084 | + | 0.246648i | ||||
\(277\) | 319.155 | + | 184.264i | 1.15218 | + | 0.665214i | 0.949419 | − | 0.314013i | \(-0.101674\pi\) |
0.202766 | + | 0.979227i | \(0.435007\pi\) | |||||||
\(278\) | −77.7810 | − | 13.5565i | −0.279788 | − | 0.0487644i | ||||
\(279\) | − | 186.866i | − | 0.669772i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −35.2868 | −0.125576 | −0.0627879 | − | 0.998027i | \(-0.519999\pi\) | ||||
−0.0627879 | + | 0.998027i | \(0.519999\pi\) | |||||||
\(282\) | −55.9334 | + | 320.921i | −0.198345 | + | 1.13802i | ||||
\(283\) | −98.3087 | + | 170.276i | −0.347380 | + | 0.601681i | −0.985783 | − | 0.168022i | \(-0.946262\pi\) |
0.638403 | + | 0.769702i | \(0.279595\pi\) | |||||||
\(284\) | −155.695 | − | 55.9728i | −0.548223 | − | 0.197087i | ||||
\(285\) | −186.156 | − | 322.432i | −0.653180 | − | 1.13134i | ||||
\(286\) | 43.6076 | + | 36.4445i | 0.152474 | + | 0.127428i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −65.8153 | + | 186.540i | −0.228525 | + | 0.647707i | ||||
\(289\) | −89.6384 | − | 155.258i | −0.310167 | − | 0.537226i | ||||
\(290\) | 286.731 | − | 105.003i | 0.988727 | − | 0.362081i | ||||
\(291\) | −11.0209 | − | 6.36291i | −0.0378724 | − | 0.0218657i | ||||
\(292\) | −231.482 | − | 273.666i | −0.792746 | − | 0.937211i | ||||
\(293\) | 317.573 | 1.08387 | 0.541933 | − | 0.840421i | \(-0.317693\pi\) | ||||
0.541933 | + | 0.840421i | \(0.317693\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 141.001 | 0.477968 | ||||||||
\(296\) | −316.669 | + | 1.87703i | −1.06983 | + | 0.00634133i | ||||
\(297\) | −34.6745 | − | 20.0193i | −0.116749 | − | 0.0674051i | ||||
\(298\) | −178.006 | + | 65.1873i | −0.597334 | + | 0.218749i | ||||
\(299\) | 50.3130 | + | 87.1447i | 0.168271 | + | 0.291454i | ||||
\(300\) | 148.019 | + | 820.483i | 0.493396 | + | 2.73494i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 85.3773 | − | 102.158i | 0.282706 | − | 0.338271i | ||||
\(303\) | −268.292 | − | 464.695i | −0.885451 | − | 1.53365i | ||||
\(304\) | 28.6215 | − | 170.174i | 0.0941496 | − | 0.559784i | ||||
\(305\) | −53.8535 | + | 93.2769i | −0.176569 | + | 0.305826i | ||||
\(306\) | −22.2358 | + | 127.579i | −0.0726660 | + | 0.416924i | ||||
\(307\) | −132.193 | −0.430596 | −0.215298 | − | 0.976548i | \(-0.569072\pi\) | ||||
−0.215298 | + | 0.976548i | \(0.569072\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 388.383i | 1.25690i | ||||||||
\(310\) | 91.9724 | − | 527.696i | 0.296685 | − | 1.70225i | ||||
\(311\) | −400.453 | − | 231.202i | −1.28763 | − | 0.743414i | −0.309400 | − | 0.950932i | \(-0.600128\pi\) |
−0.978231 | + | 0.207518i | \(0.933462\pi\) | |||||||
\(312\) | −209.667 | + | 122.714i | −0.672010 | + | 0.393315i | ||||
\(313\) | 490.206 | − | 283.021i | 1.56615 | − | 0.904220i | 0.569544 | − | 0.821961i | \(-0.307120\pi\) |
0.996611 | − | 0.0822589i | \(-0.0262134\pi\) | |||||||
\(314\) | −32.7298 | + | 39.1627i | −0.104235 | + | 0.124722i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −50.2753 | − | 278.682i | −0.159099 | − | 0.881904i | ||||
\(317\) | 153.315 | − | 88.5163i | 0.483643 | − | 0.279231i | −0.238291 | − | 0.971194i | \(-0.576587\pi\) |
0.721933 | + | 0.691963i | \(0.243254\pi\) | |||||||
\(318\) | 46.9176 | − | 17.1817i | 0.147540 | − | 0.0540304i | ||||
\(319\) | 31.4148 | − | 54.4120i | 0.0984790 | − | 0.170571i | ||||
\(320\) | −277.669 | + | 494.380i | −0.867716 | + | 1.54494i | ||||
\(321\) | 366.299i | 1.14112i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 112.975i | − | 0.349766i | ||||||
\(324\) | 300.581 | − | 254.248i | 0.927720 | − | 0.784718i | ||||
\(325\) | −208.461 | + | 361.065i | −0.641418 | + | 1.11097i | ||||
\(326\) | −360.771 | + | 132.118i | −1.10666 | + | 0.405269i | ||||
\(327\) | −661.199 | + | 381.743i | −2.02201 | + | 1.16741i | ||||
\(328\) | 291.689 | − | 512.208i | 0.889297 | − | 1.56161i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 193.148 | + | 161.421i | 0.585298 | + | 0.489156i | ||||
\(331\) | −429.688 | + | 248.080i | −1.29815 | + | 0.749487i | −0.980084 | − | 0.198582i | \(-0.936366\pi\) |
−0.318065 | + | 0.948069i | \(0.603033\pi\) | |||||||
\(332\) | 229.114 | + | 82.3667i | 0.690101 | + | 0.248092i | ||||
\(333\) | −211.910 | − | 122.346i | −0.636367 | − | 0.367406i | ||||
\(334\) | 63.2378 | − | 362.830i | 0.189335 | − | 1.08632i | ||||
\(335\) | 69.0825i | 0.206216i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −206.191 | −0.611843 | −0.305922 | − | 0.952057i | \(-0.598965\pi\) | ||||
−0.305922 | + | 0.952057i | \(0.598965\pi\) | |||||||
\(338\) | 213.298 | + | 37.1759i | 0.631061 | + | 0.109988i | ||||
\(339\) | 198.466 | − | 343.752i | 0.585444 | − | 1.01402i | ||||
\(340\) | −125.584 | + | 349.329i | −0.369366 | + | 1.02744i | ||||
\(341\) | −55.1080 | − | 95.4499i | −0.161607 | − | 0.279912i | ||||
\(342\) | 85.5070 | − | 102.313i | 0.250020 | − | 0.299161i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −161.720 | + | 283.981i | −0.470116 | + | 0.825527i | ||||
\(345\) | 222.848 | + | 385.984i | 0.645936 | + | 1.11879i | ||||
\(346\) | −48.0764 | − | 131.281i | −0.138949 | − | 0.379426i | ||||
\(347\) | −524.976 | − | 303.095i | −1.51290 | − | 0.873472i | −0.999886 | − | 0.0150913i | \(-0.995196\pi\) |
−0.513013 | − | 0.858381i | \(-0.671471\pi\) | |||||||
\(348\) | 173.451 | + | 205.059i | 0.498421 | + | 0.589251i | ||||
\(349\) | 136.343 | 0.390669 | 0.195335 | − | 0.980737i | \(-0.437421\pi\) | ||||
0.195335 | + | 0.980737i | \(0.437421\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 85.5887 | 0.243842 | ||||||||
\(352\) | 21.3937 | + | 114.692i | 0.0607775 | + | 0.325831i | ||||
\(353\) | 8.72457 | + | 5.03713i | 0.0247155 | + | 0.0142695i | 0.512307 | − | 0.858802i | \(-0.328791\pi\) |
−0.487591 | + | 0.873072i | \(0.662124\pi\) | |||||||
\(354\) | 42.6474 | + | 116.456i | 0.120473 | + | 0.328972i | ||||
\(355\) | −183.231 | − | 317.365i | −0.516143 | − | 0.893985i | ||||
\(356\) | 106.365 | − | 19.1887i | 0.298777 | − | 0.0539007i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 367.257 | + | 306.930i | 1.02586 | + | 0.857347i | ||||
\(359\) | −197.808 | − | 342.613i | −0.550997 | − | 0.954354i | −0.998203 | − | 0.0599236i | \(-0.980914\pi\) |
0.447206 | − | 0.894431i | \(-0.352419\pi\) | |||||||
\(360\) | −378.129 | + | 221.312i | −1.05036 | + | 0.614755i | ||||
\(361\) | 122.339 | − | 211.897i | 0.338889 | − | 0.586973i | ||||
\(362\) | 71.4890 | + | 12.4599i | 0.197483 | + | 0.0344195i | ||||
\(363\) | −419.664 | −1.15610 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 793.909i | − | 2.17509i | ||||||
\(366\) | −93.3286 | − | 16.2663i | −0.254996 | − | 0.0444434i | ||||
\(367\) | −164.486 | − | 94.9661i | −0.448191 | − | 0.258763i | 0.258875 | − | 0.965911i | \(-0.416648\pi\) |
−0.707066 | + | 0.707148i | \(0.749982\pi\) | |||||||
\(368\) | −34.2628 | + | 203.716i | −0.0931055 | + | 0.553575i | ||||
\(369\) | 394.438 | − | 227.729i | 1.06894 | − | 0.617151i | ||||
\(370\) | −538.201 | − | 449.795i | −1.45460 | − | 1.21566i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 463.657 | − | 83.6457i | 1.24639 | − | 0.224854i | ||||
\(373\) | 311.859 | − | 180.052i | 0.836083 | − | 0.482713i | −0.0198479 | − | 0.999803i | \(-0.506318\pi\) |
0.855931 | + | 0.517090i | \(0.172985\pi\) | |||||||
\(374\) | 26.2659 | + | 71.7238i | 0.0702298 | + | 0.191775i | ||||
\(375\) | −491.816 | + | 851.850i | −1.31151 | + | 2.27160i | ||||
\(376\) | −334.418 | + | 1.98224i | −0.889410 | + | 0.00527192i | ||||
\(377\) | 134.308i | 0.356254i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2929i | 0.0297966i | 0.999889 | + | 0.0148983i | \(0.00474246\pi\) | ||||
−0.999889 | + | 0.0148983i | \(0.995258\pi\) | |||||||
\(380\) | 291.822 | − | 246.839i | 0.767952 | − | 0.649577i | ||||
\(381\) | −270.950 | + | 469.299i | −0.711154 | + | 1.23176i | ||||
\(382\) | −223.687 | − | 610.817i | −0.585568 | − | 1.59900i | ||||
\(383\) | −376.075 | + | 217.127i | −0.981918 | + | 0.566910i | −0.902849 | − | 0.429959i | \(-0.858528\pi\) |
−0.0790692 | + | 0.996869i | \(0.525195\pi\) | |||||||
\(384\) | −492.307 | − | 79.8031i | −1.28205 | − | 0.207820i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 256.047 | − | 306.372i | 0.663334 | − | 0.793710i | ||||
\(387\) | −218.686 | + | 126.258i | −0.565080 | + | 0.326249i | ||||
\(388\) | 4.41972 | − | 12.2940i | 0.0113910 | − | 0.0316856i | ||||
\(389\) | −37.3803 | − | 21.5816i | −0.0960934 | − | 0.0554796i | 0.451183 | − | 0.892431i | \(-0.351002\pi\) |
−0.547277 | + | 0.836952i | \(0.684335\pi\) | |||||||
\(390\) | −530.099 | − | 92.3912i | −1.35923 | − | 0.236900i | ||||
\(391\) | 135.242i | 0.345887i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −357.315 | −0.909199 | ||||||||
\(394\) | 5.32458 | − | 30.5501i | 0.0135142 | − | 0.0775382i | ||||
\(395\) | 313.611 | − | 543.190i | 0.793952 | − | 1.37517i | ||||
\(396\) | −30.4984 | + | 84.8351i | −0.0770160 | + | 0.214230i | ||||
\(397\) | 243.395 | + | 421.573i | 0.613086 | + | 1.06190i | 0.990717 | + | 0.135940i | \(0.0434053\pi\) |
−0.377631 | + | 0.925956i | \(0.623261\pi\) | |||||||
\(398\) | −86.1872 | − | 72.0300i | −0.216551 | − | 0.180980i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −801.950 | + | 299.084i | −2.00488 | + | 0.747711i | ||||
\(401\) | 273.457 | + | 473.641i | 0.681938 | + | 1.18115i | 0.974389 | + | 0.224870i | \(0.0721958\pi\) |
−0.292451 | + | 0.956280i | \(0.594471\pi\) | |||||||
\(402\) | −57.0571 | + | 20.8949i | −0.141933 | + | 0.0519773i | ||||
\(403\) | 204.039 | + | 117.802i | 0.506299 | + | 0.292312i | ||||
\(404\) | 420.579 | − | 355.749i | 1.04104 | − | 0.880566i | ||||
\(405\) | 871.992 | 2.15307 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −144.323 | −0.354601 | ||||||||
\(408\) | −326.505 | + | 1.93533i | −0.800257 | + | 0.00474347i | ||||
\(409\) | −57.8217 | − | 33.3834i | −0.141373 | − | 0.0816220i | 0.427645 | − | 0.903947i | \(-0.359343\pi\) |
−0.569018 | + | 0.822325i | \(0.692677\pi\) | |||||||
\(410\) | 1225.95 | − | 448.953i | 2.99011 | − | 1.09501i | ||||
\(411\) | 388.819 | + | 673.453i | 0.946030 | + | 1.63857i | ||||
\(412\) | −392.381 | + | 70.7871i | −0.952380 | + | 0.171813i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −102.360 | + | 122.479i | −0.247248 | + | 0.295843i | ||||
\(415\) | 269.633 | + | 467.018i | 0.649718 | + | 1.12534i | ||||
\(416\) | −162.191 | − | 189.459i | −0.389883 | − | 0.455431i | ||||
\(417\) | 76.9077 | − | 133.208i | 0.184431 | − | 0.319444i | ||||
\(418\) | 13.5036 | − | 77.4773i | 0.0323052 | − | 0.185352i | ||||
\(419\) | −550.169 | −1.31305 | −0.656527 | − | 0.754303i | \(-0.727975\pi\) | ||||
−0.656527 | + | 0.754303i | \(0.727975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 579.599i | 1.37672i | 0.725369 | + | 0.688360i | \(0.241669\pi\) | ||||
−0.725369 | + | 0.688360i | \(0.758331\pi\) | |||||||
\(422\) | −127.221 | + | 729.937i | −0.301472 | + | 1.72971i | ||||
\(423\) | −223.788 | − | 129.204i | −0.529049 | − | 0.305446i | ||||
\(424\) | 25.9098 | + | 44.2690i | 0.0611079 | + | 0.104408i | ||||
\(425\) | −485.273 | + | 280.173i | −1.14182 | + | 0.659230i | ||||
\(426\) | 206.700 | − | 247.326i | 0.485211 | − | 0.580578i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −370.069 | + | 66.7620i | −0.864647 | + | 0.155986i | ||||
\(429\) | −95.8845 | + | 55.3589i | −0.223507 | + | 0.129042i | ||||
\(430\) | −679.695 | + | 248.911i | −1.58069 | + | 0.578862i | ||||
\(431\) | 215.935 | − | 374.010i | 0.501009 | − | 0.867773i | −0.498990 | − | 0.866607i | \(-0.666296\pi\) |
0.999999 | − | 0.00116534i | \(-0.000370939\pi\) | |||||||
\(432\) | 135.487 | + | 111.875i | 0.313628 | + | 0.258969i | ||||
\(433\) | 0.143463i | 0.000331322i | 1.00000 | 0.000165661i | \(5.27316e-5\pi\) | |||||
−1.00000 | 0.000165661i | \(0.999947\pi\) | ||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 594.881i | 1.36754i | ||||||||
\(436\) | −506.183 | − | 598.427i | −1.16097 | − | 1.37254i | ||||
\(437\) | 69.6247 | − | 120.593i | 0.159324 | − | 0.275958i | ||||
\(438\) | 655.712 | − | 240.128i | 1.49706 | − | 0.548237i | ||||
\(439\) | 165.713 | − | 95.6744i | 0.377478 | − | 0.217937i | −0.299242 | − | 0.954177i | \(-0.596734\pi\) |
0.676721 | + | 0.736240i | \(0.263401\pi\) | |||||||
\(440\) | −127.879 | + | 224.557i | −0.290635 | + | 0.510357i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −125.285 | − | 104.706i | −0.283451 | − | 0.236891i | ||||
\(443\) | 340.782 | − | 196.751i | 0.769260 | − | 0.444133i | −0.0633505 | − | 0.997991i | \(-0.520179\pi\) |
0.832611 | + | 0.553859i | \(0.186845\pi\) | |||||||
\(444\) | 208.713 | − | 580.561i | 0.470074 | − | 1.30757i | ||||
\(445\) | 207.320 | + | 119.696i | 0.465888 | + | 0.268981i | ||||
\(446\) | 2.33011 | − | 13.3691i | 0.00522446 | − | 0.0299756i | ||||
\(447\) | − | 369.308i | − | 0.826193i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −725.831 | −1.61655 | −0.808275 | − | 0.588805i | \(-0.799598\pi\) | ||||
−0.808275 | + | 0.588805i | \(0.799598\pi\) | |||||||
\(450\) | −651.532 | − | 113.556i | −1.44785 | − | 0.252346i | ||||
\(451\) | 134.317 | − | 232.644i | 0.297821 | − | 0.515841i | ||||
\(452\) | 383.463 | + | 137.856i | 0.848370 | + | 0.304990i | ||||
\(453\) | 129.687 | + | 224.625i | 0.286286 | + | 0.495861i | ||||
\(454\) | 380.427 | − | 455.198i | 0.837944 | − | 1.00264i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 292.137 | + | 166.364i | 0.640650 | + | 0.364834i | ||||
\(457\) | 34.6713 | + | 60.0525i | 0.0758673 | + | 0.131406i | 0.901463 | − | 0.432856i | \(-0.142494\pi\) |
−0.825596 | + | 0.564262i | \(0.809161\pi\) | |||||||
\(458\) | 122.553 | + | 334.652i | 0.267582 | + | 0.730680i | ||||
\(459\) | 99.6203 | + | 57.5158i | 0.217038 | + | 0.125307i | ||||
\(460\) | −349.340 | + | 295.492i | −0.759436 | + | 0.642373i | ||||
\(461\) | −768.006 | −1.66596 | −0.832978 | − | 0.553306i | \(-0.813366\pi\) | ||||
−0.832978 | + | 0.553306i | \(0.813366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 215.717 | 0.465911 | 0.232956 | − | 0.972487i | \(-0.425160\pi\) | ||||
0.232956 | + | 0.972487i | \(0.425160\pi\) | |||||||
\(464\) | −175.557 | + | 212.610i | −0.378355 | + | 0.458212i | ||||
\(465\) | 903.734 | + | 521.771i | 1.94351 | + | 1.12209i | ||||
\(466\) | 81.0188 | + | 221.236i | 0.173860 | + | 0.474756i | ||||
\(467\) | −14.4688 | − | 25.0607i | −0.0309824 | − | 0.0536631i | 0.850118 | − | 0.526592i | \(-0.176530\pi\) |
−0.881101 | + | 0.472928i | \(0.843197\pi\) | |||||||
\(468\) | −34.2135 | − | 189.649i | −0.0731058 | − | 0.405233i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −568.367 | − | 475.006i | −1.20929 | − | 1.01065i | ||||
\(471\) | −49.7163 | − | 86.1111i | −0.105555 | − | 0.182826i | ||||
\(472\) | −109.882 | + | 64.3118i | −0.232801 | + | 0.136254i | ||||
\(473\) | −74.4688 | + | 128.984i | −0.157439 | + | 0.272693i | ||||
\(474\) | 543.492 | + | 94.7254i | 1.14661 | + | 0.199843i | ||||
\(475\) | 576.949 | 1.21463 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 39.6344i | 0.0830911i | ||||||||
\(478\) | −91.3317 | − | 15.9183i | −0.191071 | − | 0.0333018i | ||||
\(479\) | 695.377 | + | 401.476i | 1.45173 | + | 0.838154i | 0.998580 | − | 0.0532818i | \(-0.0169682\pi\) |
0.453146 | + | 0.891436i | \(0.350302\pi\) | |||||||
\(480\) | −718.384 | − | 839.159i | −1.49663 | − | 1.74825i | ||||
\(481\) | 267.179 | − | 154.256i | 0.555466 | − | 0.320698i | ||||
\(482\) | 562.622 | + | 470.205i | 1.16726 | + | 0.975528i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −76.4885 | − | 423.984i | −0.158034 | − | 0.876000i | ||||
\(485\) | 25.0598 | − | 14.4683i | 0.0516696 | − | 0.0298315i | ||||
\(486\) | 195.771 | + | 534.587i | 0.402821 | + | 1.09997i | ||||
\(487\) | −9.96197 | + | 17.2546i | −0.0204558 | + | 0.0354305i | −0.876072 | − | 0.482180i | \(-0.839845\pi\) |
0.855616 | + | 0.517611i | \(0.173178\pi\) | |||||||
\(488\) | −0.576466 | − | 97.2540i | −0.00118128 | − | 0.199291i | ||||
\(489\) | − | 748.493i | − | 1.53066i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 76.2017i | 0.155197i | 0.996985 | + | 0.0775985i | \(0.0247252\pi\) | ||||
−0.996985 | + | 0.0775985i | \(0.975275\pi\) | |||||||
\(492\) | 741.605 | + | 876.751i | 1.50733 | + | 1.78201i | ||||
\(493\) | −90.2552 | + | 156.327i | −0.183073 | + | 0.317093i | ||||
\(494\) | 57.8111 | + | 157.864i | 0.117027 | + | 0.319562i | ||||
\(495\) | −172.925 | + | 99.8384i | −0.349344 | + | 0.201694i | ||||
\(496\) | 169.013 | + | 453.184i | 0.340753 | + | 0.913677i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −304.169 | + | 363.953i | −0.610781 | + | 0.730828i | ||||
\(499\) | 452.819 | − | 261.435i | 0.907454 | − | 0.523919i | 0.0278428 | − | 0.999612i | \(-0.491136\pi\) |
0.879611 | + | 0.475694i | \(0.157803\pi\) | |||||||
\(500\) | −950.257 | − | 341.619i | −1.90051 | − | 0.683238i | ||||
\(501\) | 621.384 | + | 358.756i | 1.24029 | + | 0.716080i | ||||
\(502\) | 255.933 | + | 44.6067i | 0.509827 | + | 0.0888581i | ||||
\(503\) | 132.060i | 0.262545i | 0.991346 | + | 0.131273i | \(0.0419064\pi\) | ||||
−0.991346 | + | 0.131273i | \(0.958094\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1220.11 | 2.41605 | ||||||||
\(506\) | −16.1651 | + | 92.7481i | −0.0319469 | + | 0.183297i | ||||
\(507\) | −210.904 | + | 365.296i | −0.415983 | + | 0.720504i | ||||
\(508\) | −523.513 | − | 188.204i | −1.03054 | − | 0.370480i | ||||
\(509\) | 155.079 | + | 268.604i | 0.304673 | + | 0.527709i | 0.977189 | − | 0.212374i | \(-0.0681194\pi\) |
−0.672515 | + | 0.740083i | \(0.734786\pi\) | |||||||
\(510\) | −554.918 | − | 463.766i | −1.08807 | − | 0.909345i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −9.10394 | − | 511.919i | −0.0177811 | − | 0.999842i | ||||
\(513\) | −59.2201 | − | 102.572i | −0.115439 | − | 0.199946i | ||||
\(514\) | 503.961 | − | 184.555i | 0.980468 | − | 0.359057i | ||||
\(515\) | −764.806 | − | 441.561i | −1.48506 | − | 0.857400i | ||||
\(516\) | −411.165 | − | 486.093i | −0.796830 | − | 0.942040i | ||||
\(517\) | −152.412 | −0.294801 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 272.369 | 0.524797 | ||||||||
\(520\) | −3.27428 | − | 552.394i | −0.00629669 | − | 1.06230i | ||||
\(521\) | −52.9121 | − | 30.5488i | −0.101559 | − | 0.0586349i | 0.448360 | − | 0.893853i | \(-0.352008\pi\) |
−0.549919 | + | 0.835218i | \(0.685341\pi\) | |||||||
\(522\) | −200.057 | + | 73.2626i | −0.383250 | + | 0.140350i | ||||
\(523\) | −256.923 | − | 445.004i | −0.491249 | − | 0.850868i | 0.508701 | − | 0.860944i | \(-0.330126\pi\) |
−0.999949 | + | 0.0100759i | \(0.996793\pi\) | |||||||
\(524\) | −65.1247 | − | 360.993i | −0.124284 | − | 0.688918i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −301.889 | + | 361.224i | −0.573933 | + | 0.686738i | ||||
\(527\) | 158.326 | + | 274.229i | 0.300429 | + | 0.520359i | ||||
\(528\) | −224.147 | − | 37.6991i | −0.424520 | − | 0.0713997i | ||||
\(529\) | 181.152 | − | 313.765i | 0.342443 | − | 0.593128i | ||||
\(530\) | −19.5074 | + | 111.925i | −0.0368064 | + | 0.211179i | ||||
\(531\) | −98.3784 | −0.185270 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 574.246i | 1.07739i | ||||||||
\(534\) | −36.1540 | + | 207.435i | −0.0677041 | + | 0.388455i | ||||
\(535\) | −721.318 | − | 416.453i | −1.34826 | − | 0.778417i | ||||
\(536\) | −31.5092 | − | 53.8361i | −0.0587859 | − | 0.100440i | ||||
\(537\) | −807.525 | + | 466.225i | −1.50377 | + | 0.868202i | ||||
\(538\) | −454.913 | + | 544.325i | −0.845563 | + | 1.01176i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 69.0938 | + | 382.994i | 0.127951 | + | 0.709248i | ||||
\(541\) | −92.7322 | + | 53.5390i | −0.171409 | + | 0.0989630i | −0.583250 | − | 0.812293i | \(-0.698219\pi\) |
0.411841 | + | 0.911256i | \(0.364886\pi\) | |||||||
\(542\) | −792.285 | + | 290.142i | −1.46178 | + | 0.535318i | ||||
\(543\) | −70.6863 | + | 122.432i | −0.130177 | + | 0.225474i | ||||
\(544\) | −61.4644 | − | 329.513i | −0.112986 | − | 0.605722i | ||||
\(545\) | − | 1736.05i | − | 3.18541i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 43.3240i | − | 0.0792030i | −0.999216 | − | 0.0396015i | \(-0.987391\pi\) | ||
0.999216 | − | 0.0396015i | \(-0.0126088\pi\) | |||||||
\(548\) | −609.519 | + | 515.565i | −1.11226 | + | 0.940812i | ||||
\(549\) | 37.5744 | − | 65.0808i | 0.0684416 | − | 0.118544i | ||||
\(550\) | −366.286 | + | 134.137i | −0.665974 | + | 0.243886i | ||||
\(551\) | 160.959 | − | 92.9296i | 0.292121 | − | 0.168656i | ||||
\(552\) | −349.717 | − | 199.155i | −0.633545 | − | 0.360788i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −565.553 | − | 472.655i | −1.02085 | − | 0.853167i | ||||
\(555\) | 1183.40 | − | 683.235i | 2.13225 | − | 1.23105i | ||||
\(556\) | 148.596 | + | 53.4207i | 0.267260 | + | 0.0960803i | ||||
\(557\) | −62.7878 | − | 36.2506i | −0.112725 | − | 0.0650818i | 0.442577 | − | 0.896730i | \(-0.354064\pi\) |
−0.555302 | + | 0.831648i | \(0.687397\pi\) | |||||||
\(558\) | −64.1707 | + | 368.182i | −0.115001 | + | 0.659825i | ||||
\(559\) | − | 318.377i | − | 0.569547i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −148.805 | −0.265250 | ||||||||
\(562\) | 69.5255 | + | 12.1176i | 0.123711 | + | 0.0215616i | ||||
\(563\) | 292.471 | − | 506.575i | 0.519487 | − | 0.899779i | −0.480256 | − | 0.877128i | \(-0.659456\pi\) |
0.999743 | − | 0.0226503i | \(-0.00721043\pi\) | |||||||
\(564\) | 220.411 | − | 613.102i | 0.390800 | − | 1.08706i | ||||
\(565\) | 451.280 | + | 781.639i | 0.798725 | + | 1.38343i | ||||
\(566\) | 252.171 | − | 301.734i | 0.445531 | − | 0.533099i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 287.545 | + | 163.749i | 0.506241 | + | 0.288291i | ||||
\(569\) | −371.765 | − | 643.915i | −0.653365 | − | 1.13166i | −0.982301 | − | 0.187309i | \(-0.940023\pi\) |
0.328936 | − | 0.944352i | \(-0.393310\pi\) | |||||||
\(570\) | 256.059 | + | 699.215i | 0.449226 | + | 1.22669i | ||||
\(571\) | −893.793 | − | 516.031i | −1.56531 | − | 0.903733i | −0.996704 | − | 0.0811234i | \(-0.974149\pi\) |
−0.568607 | − | 0.822609i | \(-0.692517\pi\) | |||||||
\(572\) | −73.4047 | − | 86.7816i | −0.128330 | − | 0.151716i | ||||
\(573\) | 1267.26 | 2.21163 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −690.666 | −1.20116 | ||||||||
\(576\) | 193.734 | − | 344.937i | 0.336344 | − | 0.598849i | ||||
\(577\) | 825.404 | + | 476.547i | 1.43051 | + | 0.825905i | 0.997159 | − | 0.0753213i | \(-0.0239982\pi\) |
0.433350 | + | 0.901226i | \(0.357332\pi\) | |||||||
\(578\) | 123.298 | + | 336.687i | 0.213318 | + | 0.582504i | ||||
\(579\) | 388.933 | + | 673.652i | 0.671732 | + | 1.16347i | ||||
\(580\) | −601.004 | + | 108.424i | −1.03621 | + | 0.186937i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 19.5294 | + | 16.3214i | 0.0335556 | + | 0.0280437i | ||||
\(583\) | 11.6884 | + | 20.2450i | 0.0200488 | + | 0.0347255i | ||||
\(584\) | 362.110 | + | 618.695i | 0.620051 | + | 1.05941i | ||||
\(585\) | 213.420 | − | 369.654i | 0.364820 | − | 0.631887i | ||||
\(586\) | −625.713 | − | 109.056i | −1.06777 | − | 0.186102i | ||||
\(587\) | −96.2876 | −0.164033 | −0.0820167 | − | 0.996631i | \(-0.526136\pi\) | ||||
−0.0820167 | + | 0.996631i | \(0.526136\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 326.035i | − | 0.553540i | ||||||
\(590\) | −277.813 | − | 48.4202i | −0.470870 | − | 0.0820681i | ||||
\(591\) | 52.3201 | + | 30.2071i | 0.0885282 | + | 0.0511118i | ||||
\(592\) | 624.577 | + | 105.047i | 1.05503 | + | 0.177445i | ||||
\(593\) | −44.1840 | + | 25.5096i | −0.0745092 | + | 0.0430179i | −0.536792 | − | 0.843715i | \(-0.680364\pi\) |
0.462283 | + | 0.886733i | \(0.347031\pi\) | |||||||
\(594\) | 61.4443 | + | 51.3514i | 0.103442 | + | 0.0864501i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 373.109 | − | 67.3105i | 0.626023 | − | 0.112937i | ||||
\(597\) | 189.509 | − | 109.413i | 0.317435 | − | 0.183271i | ||||
\(598\) | −69.2058 | − | 188.979i | −0.115729 | − | 0.316018i | ||||
\(599\) | −451.118 | + | 781.359i | −0.753119 | + | 1.30444i | 0.193186 | + | 0.981162i | \(0.438118\pi\) |
−0.946304 | + | 0.323277i | \(0.895215\pi\) | |||||||
\(600\) | −9.88355 | − | 1667.43i | −0.0164726 | − | 2.77904i | ||||
\(601\) | 903.595i | 1.50349i | 0.659456 | + | 0.751743i | \(0.270787\pi\) | ||||
−0.659456 | + | 0.751743i | \(0.729213\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 48.2000i | − | 0.0799337i | ||||||
\(604\) | −203.300 | + | 171.963i | −0.336590 | + | 0.284706i | ||||
\(605\) | 477.125 | − | 826.406i | 0.788637 | − | 1.36596i | ||||
\(606\) | 369.036 | + | 1007.72i | 0.608971 | + | 1.66290i | ||||
\(607\) | 306.928 | − | 177.205i | 0.505648 | − | 0.291936i | −0.225395 | − | 0.974267i | \(-0.572367\pi\) |
0.731043 | + | 0.682332i | \(0.239034\pi\) | |||||||
\(608\) | −114.831 | + | 325.465i | −0.188867 | + | 0.535305i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 138.139 | − | 165.290i | 0.226457 | − | 0.270967i | ||||
\(611\) | 282.154 | − | 162.902i | 0.461791 | − | 0.266615i | ||||
\(612\) | 87.6222 | − | 243.733i | 0.143174 | − | 0.398256i | ||||
\(613\) | 290.984 | + | 168.000i | 0.474688 | + | 0.274061i | 0.718200 | − | 0.695837i | \(-0.244966\pi\) |
−0.243512 | + | 0.969898i | \(0.578300\pi\) | |||||||
\(614\) | 260.460 | + | 45.3956i | 0.424201 | + | 0.0739342i | ||||
\(615\) | 2543.47i | 4.13573i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 223.359 | 0.362008 | 0.181004 | − | 0.983482i | \(-0.442065\pi\) | ||||
0.181004 | + | 0.983482i | \(0.442065\pi\) | |||||||
\(618\) | 133.372 | − | 765.230i | 0.215813 | − | 1.23824i | ||||
\(619\) | 363.026 | − | 628.780i | 0.586472 | − | 1.01580i | −0.408218 | − | 0.912885i | \(-0.633850\pi\) |
0.994690 | − | 0.102915i | \(-0.0328170\pi\) | |||||||
\(620\) | −362.426 | + | 1008.13i | −0.584558 | + | 1.62602i | ||||
\(621\) | 70.8925 | + | 122.789i | 0.114159 | + | 0.197728i | ||||
\(622\) | 709.617 | + | 593.054i | 1.14086 | + | 0.953463i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 455.247 | − | 169.783i | 0.729563 | − | 0.272088i | ||||
\(625\) | −449.635 | − | 778.791i | −0.719416 | − | 1.24607i | ||||
\(626\) | −1063.04 | + | 389.296i | −1.69815 | + | 0.621879i | ||||
\(627\) | 132.688 | + | 76.6074i | 0.211623 | + | 0.122181i | ||||
\(628\) | 77.9361 | − | 65.9227i | 0.124102 | − | 0.104972i | ||||
\(629\) | 414.642 | 0.659208 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −326.157 | −0.516888 | −0.258444 | − | 0.966026i | \(-0.583210\pi\) | ||||
−0.258444 | + | 0.966026i | \(0.583210\pi\) | |||||||
\(632\) | 3.35700 | + | 566.350i | 0.00531171 | + | 0.896124i | ||||
\(633\) | −1250.09 | − | 721.741i | −1.97487 | − | 1.14019i | ||||
\(634\) | −332.473 | + | 121.755i | −0.524405 | + | 0.192042i | ||||
\(635\) | −616.097 | − | 1067.11i | −0.970232 | − | 1.68049i | ||||
\(636\) | −98.3419 | + | 17.7413i | −0.154626 | + | 0.0278951i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −80.5818 | + | 96.4200i | −0.126304 | + | 0.151128i | ||||
\(639\) | 127.843 | + | 221.431i | 0.200067 | + | 0.346527i | ||||
\(640\) | 716.863 | − | 878.724i | 1.12010 | − | 1.37301i | ||||
\(641\) | 299.187 | − | 518.208i | 0.466751 | − | 0.808436i | −0.532528 | − | 0.846413i | \(-0.678758\pi\) |
0.999279 | + | 0.0379764i | \(0.0120912\pi\) | |||||||
\(642\) | 125.788 | − | 721.718i | 0.195932 | − | 1.12417i | ||||
\(643\) | 1008.20 | 1.56796 | 0.783979 | − | 0.620787i | \(-0.213187\pi\) | ||||
0.783979 | + | 0.620787i | \(0.213187\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1410.16i | − | 2.18630i | ||||||
\(646\) | −38.7959 | + | 222.593i | −0.0600556 | + | 0.344572i | ||||
\(647\) | −574.378 | − | 331.617i | −0.887756 | − | 0.512546i | −0.0145481 | − | 0.999894i | \(-0.504631\pi\) |
−0.873208 | + | 0.487348i | \(0.837964\pi\) | |||||||
\(648\) | −679.545 | + | 397.724i | −1.04868 | + | 0.613772i | ||||
\(649\) | −50.2509 | + | 29.0124i | −0.0774283 | + | 0.0447032i | ||||
\(650\) | 534.721 | − | 639.819i | 0.822648 | − | 0.984337i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 756.197 | − | 136.421i | 1.15981 | − | 0.209235i | ||||
\(653\) | −857.892 | + | 495.304i | −1.31377 | + | 0.758506i | −0.982718 | − | 0.185107i | \(-0.940737\pi\) |
−0.331052 | + | 0.943612i | \(0.607404\pi\) | |||||||
\(654\) | 1433.85 | − | 525.089i | 2.19243 | − | 0.802889i | ||||
\(655\) | 406.240 | − | 703.628i | 0.620213 | − | 1.07424i | ||||
\(656\) | −750.609 | + | 909.036i | −1.14422 | + | 1.38573i | ||||
\(657\) | 553.924i | 0.843110i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 82.2318i | 0.124783i | 0.998052 | + | 0.0623914i | \(0.0198727\pi\) | ||||
−0.998052 | + | 0.0623914i | \(0.980127\pi\) | |||||||
\(660\) | −325.127 | − | 384.376i | −0.492616 | − | 0.582388i | ||||
\(661\) | −313.110 | + | 542.322i | −0.473691 | + | 0.820457i | −0.999546 | − | 0.0301171i | \(-0.990412\pi\) |
0.525855 | + | 0.850574i | \(0.323745\pi\) | |||||||
\(662\) | 931.804 | − | 341.235i | 1.40756 | − | 0.515461i | ||||
\(663\) | 275.478 | − | 159.047i | 0.415502 | − | 0.239890i | ||||
\(664\) | −423.137 | − | 240.965i | −0.637254 | − | 0.362900i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 375.512 | + | 313.830i | 0.563831 | + | 0.471216i | ||||
\(667\) | −192.684 | + | 111.246i | −0.288882 | + | 0.166786i | ||||
\(668\) | −249.195 | + | 693.167i | −0.373046 | + | 1.03767i | ||||
\(669\) | 22.8960 | + | 13.2190i | 0.0342242 | + | 0.0197594i | ||||
\(670\) | 23.7232 | − | 136.113i | 0.0354078 | − | 0.203154i | ||||
\(671\) | − | 44.3237i | − | 0.0660562i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −150.211 | −0.223196 | −0.111598 | − | 0.993753i | \(-0.535597\pi\) | ||||
−0.111598 | + | 0.993753i | \(0.535597\pi\) | |||||||
\(674\) | 406.258 | + | 70.8069i | 0.602757 | + | 0.105055i | ||||
\(675\) | −293.727 | + | 508.751i | −0.435152 | + | 0.753705i | ||||
\(676\) | −407.495 | − | 146.495i | −0.602804 | − | 0.216709i | ||||
\(677\) | −278.207 | − | 481.869i | −0.410941 | − | 0.711771i | 0.584052 | − | 0.811716i | \(-0.301467\pi\) |
−0.994993 | + | 0.0999455i | \(0.968133\pi\) | |||||||
\(678\) | −509.082 | + | 609.141i | −0.750859 | + | 0.898438i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 367.400 | − | 645.156i | 0.540293 | − | 0.948759i | ||||
\(681\) | 577.865 | + | 1000.89i | 0.848553 | + | 1.46974i | ||||
\(682\) | 75.8013 | + | 206.989i | 0.111146 | + | 0.303503i | ||||
\(683\) | 685.334 | + | 395.678i | 1.00342 | + | 0.579323i | 0.909258 | − | 0.416234i | \(-0.136650\pi\) |
0.0941597 | + | 0.995557i | \(0.469984\pi\) | |||||||
\(684\) | −203.609 | + | 172.224i | −0.297674 | + | 0.251789i | ||||
\(685\) | −1768.22 | −2.58135 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −694.302 | −1.01063 | ||||||||
\(688\) | 416.157 | − | 503.992i | 0.604879 | − | 0.732547i | ||||
\(689\) | −43.2767 | − | 24.9858i | −0.0628109 | − | 0.0362639i | ||||
\(690\) | −306.528 | − | 837.030i | −0.444244 | − | 1.21309i | ||||
\(691\) | 488.267 | + | 845.703i | 0.706609 | + | 1.22388i | 0.966108 | + | 0.258139i | \(0.0831093\pi\) |
−0.259499 | + | 0.965743i | \(0.583557\pi\) | |||||||
\(692\) | 49.6424 | + | 275.173i | 0.0717375 | + | 0.397649i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 930.275 | + | 777.466i | 1.34045 | + | 1.12027i | ||||
\(695\) | 174.876 | + | 302.894i | 0.251620 | + | 0.435819i | ||||
\(696\) | −271.331 | − | 463.591i | −0.389843 | − | 0.666080i | ||||
\(697\) | −385.895 | + | 668.390i | −0.553652 | + | 0.958953i | ||||
\(698\) | −268.637 | − | 46.8209i | −0.384867 | − | 0.0670787i | ||||
\(699\) | −458.999 | −0.656651 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 855.098i | 1.21983i | 0.792468 | + | 0.609913i | \(0.208796\pi\) | ||||
−0.792468 | + | 0.609913i | \(0.791204\pi\) | |||||||
\(702\) | −168.635 | − | 29.3915i | −0.240221 | − | 0.0418682i | ||||
\(703\) | −369.730 | − | 213.464i | −0.525932 | − | 0.303647i | ||||
\(704\) | −2.76613 | − | 233.325i | −0.00392916 | − | 0.331427i | ||||
\(705\) | 1249.73 | − | 721.530i | 1.77266 | − | 1.02345i | ||||
\(706\) | −15.4602 | − | 12.9207i | −0.0218983 | − | 0.0183013i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −44.0365 | − | 244.099i | −0.0621984 | − | 0.344772i | ||||
\(709\) | 288.794 | − | 166.735i | 0.407326 | − | 0.235170i | −0.282314 | − | 0.959322i | \(-0.591102\pi\) |
0.689640 | + | 0.724152i | \(0.257769\pi\) | |||||||
\(710\) | 252.035 | + | 688.225i | 0.354978 | + | 0.969331i | ||||
\(711\) | −218.812 | + | 378.993i | −0.307752 | + | 0.533042i | ||||
\(712\) | −216.160 | + | 1.28127i | −0.303595 | + | 0.00179954i | ||||
\(713\) | 390.297i | 0.547401i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 251.755i | − | 0.352105i | ||||||
\(716\) | −618.204 | − | 730.862i | −0.863413 | − | 1.02076i | ||||
\(717\) | 90.3063 | − | 156.415i | 0.125950 | − | 0.218152i | ||||
\(718\) | 272.086 | + | 742.978i | 0.378949 | + | 1.03479i | ||||
\(719\) | 34.4877 | − | 19.9115i | 0.0479662 | − | 0.0276933i | −0.475825 | − | 0.879540i | \(-0.657850\pi\) |
0.523791 | + | 0.851847i | \(0.324517\pi\) | |||||||
\(720\) | 821.027 | − | 306.199i | 1.14032 | − | 0.425276i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −313.811 | + | 375.489i | −0.434641 | + | 0.520068i | ||||
\(723\) | −1237.09 | + | 714.237i | −1.71106 | + | 0.987879i | ||||
\(724\) | −136.576 | − | 49.0992i | −0.188641 | − | 0.0678166i | ||||
\(725\) | −798.344 | − | 460.924i | −1.10116 | − | 0.635757i | ||||
\(726\) | 826.864 | + | 144.114i | 1.13893 | + | 0.198505i | ||||
\(727\) | − | 489.402i | − | 0.673180i | −0.941651 | − | 0.336590i | \(-0.890726\pi\) | ||
0.941651 | − | 0.336590i | \(-0.109274\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −223.307 | −0.306320 | ||||||||
\(730\) | −272.632 | + | 1564.24i | −0.373468 | + | 2.14279i | ||||
\(731\) | 213.950 | − | 370.572i | 0.292681 | − | 0.506939i | ||||
\(732\) | 178.299 | + | 64.0989i | 0.243578 | + | 0.0875668i | ||||
\(733\) | 89.1592 | + | 154.428i | 0.121636 | + | 0.210680i | 0.920413 | − | 0.390948i | \(-0.127853\pi\) |
−0.798777 | + | 0.601627i | \(0.794519\pi\) | |||||||
\(734\) | 291.475 | + | 243.597i | 0.397105 | + | 0.331876i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 137.465 | − | 389.615i | 0.186773 | − | 0.529368i | ||||
\(737\) | −14.2145 | − | 24.6202i | −0.0192869 | − | 0.0334060i | ||||
\(738\) | −855.362 | + | 313.242i | −1.15903 | + | 0.424447i | ||||
\(739\) | 764.182 | + | 441.200i | 1.03408 | + | 0.597024i | 0.918149 | − | 0.396234i | \(-0.129683\pi\) |
0.115926 | + | 0.993258i | \(0.463017\pi\) | |||||||
\(740\) | 905.955 | + | 1071.05i | 1.22426 | + | 1.44737i | ||||
\(741\) | −327.520 | −0.441997 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1404.00 | 1.88964 | 0.944819 | − | 0.327591i | \(-0.106237\pi\) | ||||
0.944819 | + | 0.327591i | \(0.106237\pi\) | |||||||
\(744\) | −942.267 | + | 5.58522i | −1.26649 | + | 0.00750701i | ||||
\(745\) | 727.244 | + | 419.875i | 0.976167 | + | 0.563590i | ||||
\(746\) | −676.286 | + | 247.662i | −0.906549 | + | 0.331987i | ||||
\(747\) | −188.127 | − | 325.846i | −0.251844 | − | 0.436206i | ||||
\(748\) | −27.1215 | − | 150.337i | −0.0362586 | − | 0.200985i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1261.55 | − | 1509.51i | 1.68207 | − | 2.01268i | ||||
\(751\) | −102.840 | − | 178.124i | −0.136938 | − | 0.237183i | 0.789398 | − | 0.613881i | \(-0.210393\pi\) |
−0.926336 | + | 0.376698i | \(0.877059\pi\) | |||||||
\(752\) | 659.584 | + | 110.935i | 0.877107 | + | 0.147520i | ||||
\(753\) | −253.060 | + | 438.312i | −0.336069 | + | 0.582088i | ||||
\(754\) | 46.1219 | − | 264.626i | 0.0611696 | − | 0.350963i | ||||
\(755\) | −589.777 | −0.781162 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0345i | 0.0198606i | 0.999951 | + | 0.00993032i | \(0.00316097\pi\) | ||||
−0.999951 | + | 0.00993032i | \(0.996839\pi\) | |||||||
\(758\) | 3.87804 | − | 22.2504i | 0.00511614 | − | 0.0293541i | ||||
\(759\) | −158.841 | − | 91.7068i | −0.209276 | − | 0.120826i | ||||
\(760\) | −659.742 | + | 386.134i | −0.868081 | + | 0.508071i | ||||
\(761\) | 544.290 | − | 314.246i | 0.715229 | − | 0.412938i | −0.0977649 | − | 0.995210i | \(-0.531169\pi\) |
0.812994 | + | 0.582272i | \(0.197836\pi\) | |||||||
\(762\) | 695.011 | − | 831.613i | 0.912088 | − | 1.09136i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 230.973 | + | 1280.31i | 0.302320 | + | 1.67579i | ||||
\(765\) | 496.817 | − | 286.837i | 0.649434 | − | 0.374951i | ||||
\(766\) | 815.541 | − | 298.659i | 1.06467 | − | 0.389894i | ||||
\(767\) | 62.0184 | − | 107.419i | 0.0808584 | − | 0.140051i | ||||
\(768\) | 942.586 | + | 326.296i | 1.22733 | + | 0.424865i | ||||
\(769\) | 442.918i | 0.575967i | 0.957635 | + | 0.287983i | \(0.0929848\pi\) | ||||
−0.957635 | + | 0.287983i | \(0.907015\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1045.57i | 1.35612i | ||||||||
\(772\) | −609.698 | + | 515.717i | −0.789764 | + | 0.668027i | ||||
\(773\) | −84.5990 | + | 146.530i | −0.109442 | + | 0.189560i | −0.915545 | − | 0.402217i | \(-0.868240\pi\) |
0.806102 | + | 0.591777i | \(0.201573\pi\) | |||||||
\(774\) | 474.234 | − | 173.669i | 0.612706 | − | 0.224379i | ||||
\(775\) | −1400.46 | + | 808.555i | −1.80704 | + | 1.04330i | ||||
\(776\) | −12.9300 | + | 22.7051i | −0.0166624 | + | 0.0292592i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 66.2392 | + | 55.3586i | 0.0851404 | + | 0.0711551i | ||||
\(779\) | 688.196 | − | 397.330i | 0.883435 | − | 0.510051i | ||||
\(780\) | 1012.73 | + | 364.076i | 1.29837 | + | 0.466764i | ||||
\(781\) | 130.602 | + | 75.4034i | 0.167225 | + | 0.0965472i | ||||
\(782\) | 46.4426 | − | 266.467i | 0.0593896 | − | 0.340750i | ||||
\(783\) | 189.244i | 0.241690i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 226.094 | 0.288018 | ||||||||
\(786\) | 704.018 | + | 122.704i | 0.895697 | + | 0.156111i | ||||
\(787\) | −23.2437 | + | 40.2593i | −0.0295346 | + | 0.0511554i | −0.880415 | − | 0.474204i | \(-0.842736\pi\) |
0.850880 | + | 0.525360i | \(0.176069\pi\) | |||||||
\(788\) | −20.9820 | + | 58.3642i | −0.0266269 | + | 0.0740663i | ||||
\(789\) | −458.567 | − | 794.261i | −0.581200 | − | 1.00667i | ||||
\(790\) | −804.441 | + | 962.551i | −1.01828 | + | 1.21842i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 89.2236 | − | 156.677i | 0.112656 | − | 0.197825i | ||||
\(793\) | 47.3743 | + | 82.0548i | 0.0597407 | + | 0.103474i | ||||
\(794\) | −334.791 | − | 914.206i | −0.421651 | − | 1.15139i | ||||
\(795\) | −191.683 | − | 110.668i | −0.241110 | − | 0.139205i | ||||
\(796\) | 145.079 | + | 171.518i | 0.182260 | + | 0.215474i | ||||
\(797\) | 1351.86 | 1.69618 | 0.848092 | − | 0.529850i | \(-0.177752\pi\) | ||||
0.848092 | + | 0.529850i | \(0.177752\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 437.882 | 0.548038 | ||||||||
\(800\) | 1682.79 | − | 313.892i | 2.10348 | − | 0.392365i | ||||
\(801\) | −144.651 | − | 83.5141i | −0.180588 | − | 0.104262i | ||||
\(802\) | −376.141 | − | 1027.12i | −0.469004 | − | 1.28070i | ||||
\(803\) | 163.355 | + | 282.940i | 0.203431 | + | 0.352354i | ||||
\(804\) | 119.595 | − | 21.5754i | 0.148750 | − | 0.0268351i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −361.563 | − | 302.172i | −0.448590 | − | 0.374903i | ||||
\(807\) | −691.009 | − | 1196.86i | −0.856269 | − | 1.48310i | ||||
\(808\) | −950.831 | + | 556.503i | −1.17677 | + | 0.688741i | ||||
\(809\) | 701.563 | − | 1215.14i | 0.867198 | − | 1.50203i | 0.00235012 | − | 0.999997i | \(-0.499252\pi\) |
0.864848 | − | 0.502034i | \(-0.167415\pi\) | |||||||
\(810\) | −1718.08 | − | 299.446i | −2.12109 | − | 0.369686i | ||||
\(811\) | 689.037 | 0.849614 | 0.424807 | − | 0.905284i | \(-0.360342\pi\) | ||||
0.424807 | + | 0.905284i | \(0.360342\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1643.75i | − | 2.02184i | ||||||
\(814\) | 284.359 | + | 49.5610i | 0.349335 | + | 0.0608858i | ||||
\(815\) | 1473.94 | + | 850.977i | 1.80851 | + | 1.04414i | ||||
\(816\) | 643.977 | + | 108.310i | 0.789187 | + | 0.132733i | ||||
\(817\) | −381.553 | + | 220.290i | −0.467017 | + | 0.269632i | ||||
\(818\) | 102.462 | + | 85.6314i | 0.125259 | + | 0.104684i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2569.65 | + | 463.576i | −3.13372 | + | 0.565336i | ||||
\(821\) | 19.3490 | − | 11.1711i | 0.0235675 | − | 0.0136067i | −0.488170 | − | 0.872749i | \(-0.662335\pi\) |
0.511737 | + | 0.859142i | \(0.329002\pi\) | |||||||
\(822\) | −534.822 | − | 1460.43i | −0.650635 | − | 1.77667i | ||||
\(823\) | −512.111 | + | 887.003i | −0.622249 | + | 1.07777i | 0.366816 | + | 0.930293i | \(0.380448\pi\) |
−0.989066 | + | 0.147474i | \(0.952886\pi\) | |||||||
\(824\) | 797.415 | − | 4.72662i | 0.967737 | − | 0.00573619i | ||||
\(825\) | − | 759.934i | − | 0.921132i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 466.377i | 0.563938i | 0.959424 | + | 0.281969i | \(0.0909875\pi\) | ||||
−0.959424 | + | 0.281969i | \(0.909012\pi\) | |||||||
\(828\) | 243.741 | − | 206.169i | 0.294373 | − | 0.248997i | ||||
\(829\) | −750.350 | + | 1299.64i | −0.905126 | + | 1.56773i | −0.0843791 | + | 0.996434i | \(0.526891\pi\) |
−0.820747 | + | 0.571291i | \(0.806443\pi\) | |||||||
\(830\) | −370.881 | − | 1012.76i | −0.446845 | − | 1.22019i | ||||
\(831\) | 1243.54 | − | 717.958i | 1.49644 | − | 0.863969i | ||||
\(832\) | 254.504 | + | 428.988i | 0.305895 | + | 0.515611i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −197.275 | + | 236.049i | −0.236541 | + | 0.283033i | ||||
\(835\) | −1412.93 | + | 815.755i | −1.69213 | + | 0.976952i | ||||
\(836\) | −53.2120 | + | 148.016i | −0.0636508 | + | 0.177053i | ||||
\(837\) | 287.496 | + | 165.986i | 0.343484 | + | 0.198311i | ||||
\(838\) | 1084.00 | + | 188.930i | 1.29355 | + | 0.225454i | ||||
\(839\) | − | 1068.18i | − | 1.27316i | −0.771212 | − | 0.636579i | \(-0.780349\pi\) | ||
0.771212 | − | 0.636579i | \(-0.219651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 544.034 | 0.646890 | ||||||||
\(842\) | 199.037 | − | 1141.98i | 0.236386 | − | 1.35627i | ||||
\(843\) | −68.7449 | + | 119.070i | −0.0815479 | + | 0.141245i | ||||
\(844\) | 501.327 | − | 1394.51i | 0.593989 | − | 1.65226i | ||||
\(845\) | −479.562 | − | 830.625i | −0.567529 | − | 0.982988i | ||||
\(846\) | 396.559 | + | 331.420i | 0.468746 | + | 0.391749i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −35.8478 | − | 96.1206i | −0.0422734 | − | 0.113350i | ||||
\(849\) | 383.045 | + | 663.453i | 0.451172 | + | 0.781453i | ||||
\(850\) | 1052.35 | − | 385.379i | 1.23805 | − | 0.453387i | ||||
\(851\) | 442.605 | + | 255.538i | 0.520100 | + | 0.300280i | ||||
\(852\) | −492.193 | + | 416.325i | −0.577692 | + | 0.488644i | ||||
\(853\) | 918.640 | 1.07695 | 0.538476 | − | 0.842641i | \(-0.319000\pi\) | ||||
0.538476 | + | 0.842641i | \(0.319000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −590.673 | −0.690846 | ||||||||
\(856\) | 752.072 | − | 4.45785i | 0.878589 | − | 0.00520777i | ||||
\(857\) | 438.167 | + | 252.976i | 0.511280 | + | 0.295188i | 0.733360 | − | 0.679841i | \(-0.237951\pi\) |
−0.222080 | + | 0.975029i | \(0.571284\pi\) | |||||||
\(858\) | 207.931 | − | 76.1465i | 0.242344 | − | 0.0887488i | ||||
\(859\) | −688.516 | − | 1192.54i | −0.801532 | − | 1.38829i | −0.918607 | − | 0.395171i | \(-0.870685\pi\) |
0.117075 | − | 0.993123i | \(-0.462648\pi\) | |||||||
\(860\) | 1424.68 | − | 257.018i | 1.65660 | − | 0.298858i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −553.893 | + | 662.758i | −0.642567 | + | 0.768861i | ||||
\(863\) | −458.817 | − | 794.695i | −0.531654 | − | 0.920852i | −0.999317 | − | 0.0369450i | \(-0.988237\pi\) |
0.467663 | − | 0.883907i | \(-0.345096\pi\) | |||||||
\(864\) | −228.532 | − | 266.953i | −0.264505 | − | 0.308974i | ||||
\(865\) | −309.663 | + | 536.352i | −0.357992 | + | 0.620060i | ||||
\(866\) | 0.0492657 | − | 0.282664i | 5.68888e−5 | − | 0.000326402i | ||||
\(867\) | −698.525 | −0.805681 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 258.116i | 0.297026i | ||||||||
\(870\) | 204.284 | − | 1172.09i | 0.234810 | − | 1.34723i | ||||
\(871\) | 52.6294 | + | 30.3856i | 0.0604241 | + | 0.0348859i | ||||
\(872\) | 791.829 | + | 1352.91i | 0.908061 | + | 1.55150i | ||||
\(873\) | −17.4846 | + | 10.0947i | −0.0200282 | + | 0.0115633i | ||||
\(874\) | −178.594 | + | 213.696i | −0.204341 | + | 0.244503i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1374.41 | + | 247.949i | −1.56896 | + | 0.283047i | ||||
\(877\) | 606.173 | − | 349.974i | 0.691189 | − | 0.399058i | −0.112868 | − | 0.993610i | \(-0.536004\pi\) |
0.804057 | + | 0.594552i | \(0.202671\pi\) | |||||||
\(878\) | −359.359 | + | 131.601i | −0.409293 | + | 0.149887i | ||||
\(879\) | 618.688 | − | 1071.60i | 0.703854 | − | 1.21911i | ||||
\(880\) | 329.074 | − | 398.530i | 0.373948 | − | 0.452875i | ||||
\(881\) | − | 6.37652i | − | 0.00723783i | −0.999993 | − | 0.00361891i | \(-0.998848\pi\) | ||
0.999993 | − | 0.00361891i | \(-0.00115194\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1548.35i | − | 1.75351i | −0.480935 | − | 0.876756i | \(-0.659703\pi\) | ||
0.480935 | − | 0.876756i | \(-0.340297\pi\) | |||||||
\(884\) | 210.893 | + | 249.325i | 0.238567 | + | 0.282042i | ||||
\(885\) | 274.694 | − | 475.784i | 0.310389 | − | 0.537609i | ||||
\(886\) | −739.008 | + | 270.631i | −0.834094 | + | 0.305453i | ||||
\(887\) | −634.250 | + | 366.185i | −0.715051 | + | 0.412835i | −0.812928 | − | 0.582364i | \(-0.802128\pi\) |
0.0978774 | + | 0.995198i | \(0.468795\pi\) | |||||||
\(888\) | −610.593 | + | 1072.21i | −0.687605 | + | 1.20744i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −367.378 | − | 307.032i | −0.412785 | − | 0.344980i | ||||
\(891\) | −310.768 | + | 179.422i | −0.348785 | + | 0.201371i | ||||
\(892\) | −9.18203 | + | 25.5410i | −0.0102938 | + | 0.0286334i | ||||
\(893\) | −390.454 | − | 225.429i | −0.437238 | − | 0.252440i | ||||
\(894\) | −126.822 | + | 727.647i | −0.141859 | + | 0.813923i | ||||
\(895\) | − | 2120.24i | − | 2.36899i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 392.074 | 0.437095 | ||||||||
\(898\) | 1430.10 | + | 249.253i | 1.59254 | + | 0.277565i | ||||
\(899\) | −260.469 | + | 451.146i | −0.289732 | + | 0.501831i | ||||
\(900\) | 1244.72 | + | 447.478i | 1.38302 | + | 0.497197i | ||||
\(901\) | −33.5811 | − | 58.1641i | −0.0372709 | − | 0.0645551i | ||||
\(902\) | −344.536 | + | 412.253i | −0.381969 | + | 0.457043i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −708.197 | − | 403.299i | −0.783403 | − | 0.446128i | ||||
\(905\) | −160.730 | − | 278.392i | −0.177602 | − | 0.307615i | ||||
\(906\) | −178.386 | − | 487.113i | −0.196894 | − | 0.537653i | ||||
\(907\) | −626.862 | − | 361.919i | −0.691138 | − | 0.399029i | 0.112900 | − | 0.993606i | \(-0.463986\pi\) |
−0.804038 | + | 0.594578i | \(0.797319\pi\) | |||||||
\(908\) | −905.870 | + | 766.236i | −0.997655 | + | 0.843872i | ||||
\(909\) | −851.288 | −0.936511 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1600.04 | 1.75636 | 0.878179 | − | 0.478332i | \(-0.158758\pi\) | ||||
0.878179 | + | 0.478332i | \(0.158758\pi\) | |||||||
\(912\) | −518.466 | − | 428.108i | −0.568493 | − | 0.469417i | ||||
\(913\) | −192.188 | − | 110.960i | −0.210502 | − | 0.121533i | ||||
\(914\) | −47.6906 | − | 130.228i | −0.0521779 | − | 0.142481i | ||||
\(915\) | 209.832 | + | 363.440i | 0.229325 | + | 0.397202i | ||||
\(916\) | −126.544 | − | 701.448i | −0.138149 | − | 0.765773i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −176.531 | − | 147.533i | −0.192299 | − | 0.160712i | ||||
\(919\) | 262.042 | + | 453.871i | 0.285139 | + | 0.493875i | 0.972643 | − | 0.232306i | \(-0.0746270\pi\) |
−0.687504 | + | 0.726180i | \(0.741294\pi\) | |||||||
\(920\) | 789.778 | − | 462.242i | 0.858454 | − | 0.502436i | ||||
\(921\) | −257.535 | + | 446.064i | −0.279626 | + | 0.484326i | ||||
\(922\) | 1513.20 | + | 263.736i | 1.64122 | + | 0.286048i | ||||
\(923\) | −322.372 | −0.349266 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2117.53i | 2.28922i | ||||||||
\(926\) | −425.027 | − | 74.0781i | −0.458992 | − | 0.0799980i | ||||
\(927\) | 533.618 | + | 308.084i | 0.575640 | + | 0.332346i | ||||
\(928\) | 418.910 | − | 358.618i | 0.451412 | − | 0.386442i | ||||
\(929\) | −551.791 | + | 318.577i | −0.593962 | + | 0.342924i | −0.766663 | − | 0.642050i | \(-0.778084\pi\) |
0.172700 | + | 0.984974i | \(0.444751\pi\) | |||||||
\(930\) | −1601.45 | − | 1338.39i | −1.72199 | − | 1.43913i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −83.6577 | − | 463.723i | −0.0897615 | − | 0.497557i | ||||
\(933\) | −1560.31 | + | 900.844i | −1.67235 | + | 0.965534i | ||||
\(934\) | 19.9019 | + | 54.3456i | 0.0213082 | + | 0.0581859i | ||||
\(935\) | 169.180 | − | 293.029i | 0.180941 | − | 0.313400i | ||||
\(936\) | 2.28452 | + | 385.415i | 0.00244072 | + | 0.411768i | ||||
\(937\) | − | 383.587i | − | 0.409378i | −0.978827 | − | 0.204689i | \(-0.934382\pi\) | ||
0.978827 | − | 0.204689i | \(-0.0656182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 2205.50i | − | 2.34877i | ||||||
\(940\) | 956.733 | + | 1131.08i | 1.01780 | + | 1.20328i | ||||
\(941\) | −130.295 | + | 225.678i | −0.138465 | + | 0.239828i | −0.926916 | − | 0.375270i | \(-0.877550\pi\) |
0.788451 | + | 0.615098i | \(0.210883\pi\) | |||||||
\(942\) | 68.3850 | + | 186.737i | 0.0725955 | + | 0.198235i | ||||
\(943\) | −823.840 | + | 475.644i | −0.873637 | + | 0.504394i | ||||
\(944\) | 238.585 | − | 88.9794i | 0.252738 | − | 0.0942579i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 191.019 | − | 228.564i | 0.201923 | − | 0.241610i | ||||
\(947\) | −851.444 | + | 491.581i | −0.899096 | + | 0.519093i | −0.876907 | − | 0.480660i | \(-0.840397\pi\) |
−0.0221894 | + | 0.999754i | \(0.507064\pi\) | |||||||
\(948\) | −1038.31 | − | 373.274i | −1.09526 | − | 0.393749i | ||||
\(949\) | −604.827 | − | 349.197i | −0.637331 | − | 0.367963i | ||||
\(950\) | −1136.76 | − | 198.127i | −1.19659 | − | 0.208554i | ||||
\(951\) | − | 689.781i | − | 0.725322i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1137.60 | −1.19370 | −0.596851 | − | 0.802352i | \(-0.703582\pi\) | ||||
−0.596851 | + | 0.802352i | \(0.703582\pi\) | |||||||
\(954\) | 13.6106 | − | 78.0916i | 0.0142669 | − | 0.0818571i | ||||
\(955\) | −1440.78 | + | 2495.50i | −1.50867 | + | 2.61309i | ||||
\(956\) | 174.484 | + | 62.7274i | 0.182515 | + | 0.0656144i | ||||
\(957\) | −122.403 | − | 212.008i | −0.127903 | − | 0.221534i | ||||
\(958\) | −1232.23 | − | 1029.82i | −1.28625 | − | 1.07497i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1127.26 | + | 1900.09i | 1.17423 | + | 1.97926i | ||||
\(961\) | −23.5835 | − | 40.8479i | −0.0245406 | − | 0.0425056i | ||||
\(962\) | −579.394 | + | 212.180i | −0.602281 | + | 0.220561i | ||||
\(963\) | 503.275 | + | 290.566i | 0.522612 | + | 0.301730i | ||||
\(964\) | −947.062 | − | 1119.65i | −0.982430 | − | 1.16146i | ||||
\(965\) | −1768.75 | −1.83290 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1296.35 | −1.34059 | −0.670297 | − | 0.742093i | \(-0.733833\pi\) | ||||
−0.670297 | + | 0.742093i | \(0.733833\pi\) | |||||||
\(968\) | 5.10731 | + | 861.641i | 0.00527615 | + | 0.890125i | ||||
\(969\) | −381.214 | − | 220.094i | −0.393410 | − | 0.227135i | ||||
\(970\) | −54.3436 | + | 19.9011i | −0.0560244 | + | 0.0205166i | ||||
\(971\) | 665.237 | + | 1152.22i | 0.685105 | + | 1.18664i | 0.973404 | + | 0.229096i | \(0.0735768\pi\) |
−0.288299 | + | 0.957540i | \(0.593090\pi\) | |||||||
\(972\) | −202.147 | − | 1120.52i | −0.207971 | − | 1.15280i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 25.5534 | − | 30.5758i | 0.0262355 | − | 0.0313920i | ||||
\(975\) | 812.237 | + | 1406.84i | 0.833063 | + | 1.44291i | ||||
\(976\) | −32.2616 | + | 191.817i | −0.0330549 | + | 0.196534i | ||||
\(977\) | −693.081 | + | 1200.45i | −0.709397 | + | 1.22871i | 0.255684 | + | 0.966760i | \(0.417699\pi\) |
−0.965081 | + | 0.261952i | \(0.915634\pi\) | |||||||
\(978\) | −257.035 | + | 1474.75i | −0.262817 | + | 1.50793i | ||||
\(979\) | −98.5153 | −0.100629 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1211.27i | 1.23473i | ||||||||
\(982\) | 26.1680 | − | 150.140i | 0.0266476 | − | 0.152892i | ||||
\(983\) | 601.161 | + | 347.081i | 0.611558 | + | 0.353083i | 0.773575 | − | 0.633705i | \(-0.218467\pi\) |
−0.162017 | + | 0.986788i | \(0.551800\pi\) | |||||||
\(984\) | −1160.10 | − | 1982.13i | −1.17897 | − | 2.01436i | ||||
\(985\) | −118.968 | + | 68.6861i | −0.120780 | + | 0.0697321i | ||||
\(986\) | 231.513 | − | 277.016i | 0.234800 | − | 0.280949i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −59.6941 | − | 330.891i | −0.0604192 | − | 0.334910i | ||||
\(989\) | 456.757 | − | 263.709i | 0.461838 | − | 0.266642i | ||||
\(990\) | 374.999 | − | 137.328i | 0.378787 | − | 0.138715i | ||||
\(991\) | 467.257 | − | 809.312i | 0.471500 | − | 0.816662i | −0.527968 | − | 0.849264i | \(-0.677046\pi\) |
0.999468 | + | 0.0326018i | \(0.0103793\pi\) | |||||||
\(992\) | −177.381 | − | 950.947i | −0.178812 | − | 0.958616i | ||||
\(993\) | 1933.22i | 1.94684i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 497.576i | 0.500076i | ||||||||
\(996\) | 724.287 | − | 612.642i | 0.727195 | − | 0.615102i | ||||
\(997\) | 769.103 | − | 1332.12i | 0.771417 | − | 1.33613i | −0.165370 | − | 0.986232i | \(-0.552882\pi\) |
0.936786 | − | 0.349902i | \(-0.113785\pi\) | |||||||
\(998\) | −981.967 | + | 359.606i | −0.983935 | + | 0.360326i | ||||
\(999\) | 376.463 | − | 217.351i | 0.376840 | − | 0.217568i |
(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 | 392.3.j.e.325.1 | 28 | ||
7.2 | even | 3 | 56.3.j.a.5.10 | yes | 28 | ||
7.3 | odd | 6 | 392.3.h.a.293.18 | 28 | |||
7.4 | even | 3 | 392.3.h.a.293.17 | 28 | |||
7.5 | odd | 6 | inner | 392.3.j.e.117.10 | 28 | ||
7.6 | odd | 2 | 56.3.j.a.45.1 | yes | 28 | ||
8.5 | even | 2 | inner | 392.3.j.e.325.10 | 28 | ||
28.3 | even | 6 | 1568.3.h.a.881.3 | 28 | |||
28.11 | odd | 6 | 1568.3.h.a.881.25 | 28 | |||
28.23 | odd | 6 | 224.3.n.a.145.2 | 28 | |||
28.27 | even | 2 | 224.3.n.a.17.13 | 28 | |||
56.3 | even | 6 | 1568.3.h.a.881.26 | 28 | |||
56.5 | odd | 6 | inner | 392.3.j.e.117.1 | 28 | ||
56.11 | odd | 6 | 1568.3.h.a.881.4 | 28 | |||
56.13 | odd | 2 | 56.3.j.a.45.10 | yes | 28 | ||
56.27 | even | 2 | 224.3.n.a.17.2 | 28 | |||
56.37 | even | 6 | 56.3.j.a.5.1 | ✓ | 28 | ||
56.45 | odd | 6 | 392.3.h.a.293.19 | 28 | |||
56.51 | odd | 6 | 224.3.n.a.145.13 | 28 | |||
56.53 | even | 6 | 392.3.h.a.293.20 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.1 | ✓ | 28 | 56.37 | even | 6 | ||
56.3.j.a.5.10 | yes | 28 | 7.2 | even | 3 | ||
56.3.j.a.45.1 | yes | 28 | 7.6 | odd | 2 | ||
56.3.j.a.45.10 | yes | 28 | 56.13 | odd | 2 | ||
224.3.n.a.17.2 | 28 | 56.27 | even | 2 | |||
224.3.n.a.17.13 | 28 | 28.27 | even | 2 | |||
224.3.n.a.145.2 | 28 | 28.23 | odd | 6 | |||
224.3.n.a.145.13 | 28 | 56.51 | odd | 6 | |||
392.3.h.a.293.17 | 28 | 7.4 | even | 3 | |||
392.3.h.a.293.18 | 28 | 7.3 | odd | 6 | |||
392.3.h.a.293.19 | 28 | 56.45 | odd | 6 | |||
392.3.h.a.293.20 | 28 | 56.53 | even | 6 | |||
392.3.j.e.117.1 | 28 | 56.5 | odd | 6 | inner | ||
392.3.j.e.117.10 | 28 | 7.5 | odd | 6 | inner | ||
392.3.j.e.325.1 | 28 | 1.1 | even | 1 | trivial | ||
392.3.j.e.325.10 | 28 | 8.5 | even | 2 | inner | ||
1568.3.h.a.881.3 | 28 | 28.3 | even | 6 | |||
1568.3.h.a.881.4 | 28 | 56.11 | odd | 6 | |||
1568.3.h.a.881.25 | 28 | 28.11 | odd | 6 | |||
1568.3.h.a.881.26 | 28 | 56.3 | even | 6 |