Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,3,Mod(31,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.h (of order \(8\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.97549476762\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Character | \(\chi\) | \(=\) | 256.31 |
Dual form | 256.3.h.a.223.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.37292 | + | 0.568682i | −0.457640 | + | 0.189561i | −0.599580 | − | 0.800315i | \(-0.704666\pi\) |
0.141940 | + | 0.989875i | \(0.454666\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.28872 | − | 0.948019i | −0.457744 | − | 0.189604i | 0.141883 | − | 0.989883i | \(-0.454684\pi\) |
−0.599627 | + | 0.800280i | \(0.704684\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.37744 | − | 6.37744i | 0.911063 | − | 0.911063i | −0.0852929 | − | 0.996356i | \(-0.527183\pi\) |
0.996356 | + | 0.0852929i | \(0.0271826\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.80245 | + | 4.80245i | −0.533606 | + | 0.533606i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.79646 | − | 0.744117i | −0.163314 | − | 0.0676470i | 0.299529 | − | 0.954087i | \(-0.403171\pi\) |
−0.462843 | + | 0.886440i | \(0.653171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −16.7036 | + | 6.91888i | −1.28490 | + | 0.532221i | −0.917460 | − | 0.397827i | \(-0.869764\pi\) |
−0.367436 | + | 0.930049i | \(0.619764\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.68135 | 0.245423 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.19811i | − | 0.364595i | −0.983243 | − | 0.182297i | \(-0.941647\pi\) | ||
0.983243 | − | 0.182297i | \(-0.0583533\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.50083 | − | 20.5228i | −0.447412 | − | 1.08015i | −0.973288 | − | 0.229587i | \(-0.926262\pi\) |
0.525876 | − | 0.850561i | \(-0.323738\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.12898 | + | 12.3825i | −0.244237 | + | 0.589641i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.6476 | − | 23.6476i | −1.02815 | − | 1.02815i | −0.999592 | − | 0.0285625i | \(-0.990907\pi\) |
−0.0285625 | − | 0.999592i | \(-0.509093\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.3382 | − | 13.3382i | −0.533527 | − | 0.533527i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.98045 | − | 21.6807i | 0.332609 | − | 0.802990i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −14.5725 | − | 35.1811i | −0.502500 | − | 1.21314i | −0.948118 | − | 0.317919i | \(-0.897016\pi\) |
0.445618 | − | 0.895223i | \(-0.352984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 14.1609i | 0.456803i | 0.973567 | + | 0.228401i | \(0.0733498\pi\) | ||||
−0.973567 | + | 0.228401i | \(0.926650\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.88956 | 0.0875623 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −20.6421 | + | 8.55025i | −0.589775 | + | 0.244293i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.0695 | + | 12.4552i | 0.812689 | + | 0.336627i | 0.750027 | − | 0.661408i | \(-0.230041\pi\) |
0.0626629 | + | 0.998035i | \(0.480041\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 18.9981 | − | 18.9981i | 0.487131 | − | 0.487131i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −56.9700 | + | 56.9700i | −1.38951 | + | 1.38951i | −0.563170 | + | 0.826341i | \(0.690418\pi\) |
−0.826341 | + | 0.563170i | \(0.809582\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 54.5034 | + | 22.5760i | 1.26752 | + | 0.525024i | 0.912209 | − | 0.409724i | \(-0.134375\pi\) |
0.355310 | + | 0.934748i | \(0.384375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 15.5443 | − | 6.43866i | 0.345429 | − | 0.143081i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −34.8047 | −0.740525 | −0.370263 | − | 0.928927i | \(-0.620732\pi\) | ||||
−0.370263 | + | 0.928927i | \(0.620732\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 32.3435i | − | 0.660072i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.52475 | + | 8.50951i | 0.0691128 | + | 0.166853i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.92967 | + | 9.48706i | −0.0741447 | + | 0.179001i | −0.956606 | − | 0.291383i | \(-0.905885\pi\) |
0.882462 | + | 0.470384i | \(0.155885\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.40615 | + | 3.40615i | 0.0619300 | + | 0.0619300i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 23.3419 | + | 23.3419i | 0.409507 | + | 0.409507i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.41777 | − | 22.7365i | 0.159623 | − | 0.385365i | −0.823752 | − | 0.566951i | \(-0.808123\pi\) |
0.983375 | + | 0.181586i | \(0.0581230\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00467 | − | 7.25391i | −0.0492568 | − | 0.118916i | 0.897336 | − | 0.441348i | \(-0.145500\pi\) |
−0.946593 | + | 0.322432i | \(0.895500\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 61.2547i | 0.972297i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 44.7892 | 0.689065 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −55.9040 | + | 23.1562i | −0.834388 | + | 0.345615i | −0.758638 | − | 0.651512i | \(-0.774135\pi\) |
−0.0757497 | + | 0.997127i | \(0.524135\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 45.9141 | + | 19.0183i | 0.665422 | + | 0.275627i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.27499 | + | 6.27499i | −0.0883801 | + | 0.0883801i | −0.749915 | − | 0.661535i | \(-0.769905\pi\) |
0.661535 | + | 0.749915i | \(0.269905\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 66.4597 | − | 66.4597i | 0.910406 | − | 0.910406i | −0.0858977 | − | 0.996304i | \(-0.527376\pi\) |
0.996304 | + | 0.0858977i | \(0.0273758\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 25.8974 | + | 10.7271i | 0.345299 | + | 0.143027i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.2024 | + | 6.71124i | −0.210420 | + | 0.0871589i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 75.8508 | 0.960136 | 0.480068 | − | 0.877231i | \(-0.340612\pi\) | ||||
0.480068 | + | 0.877231i | \(0.340612\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 26.2523i | − | 0.324103i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.23390 | − | 2.97891i | −0.0148663 | − | 0.0358905i | 0.916272 | − | 0.400556i | \(-0.131183\pi\) |
−0.931138 | + | 0.364666i | \(0.881183\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.87593 | + | 14.1857i | −0.0691286 | + | 0.166891i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 40.0138 | + | 40.0138i | 0.459928 | + | 0.459928i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 36.7030 | + | 36.7030i | 0.412393 | + | 0.412393i | 0.882572 | − | 0.470178i | \(-0.155810\pi\) |
−0.470178 | + | 0.882572i | \(0.655810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −62.4018 | + | 150.651i | −0.685734 | + | 1.65551i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.05304 | − | 19.4417i | −0.0865918 | − | 0.209051i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 55.0300i | 0.579263i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 90.0528 | 0.928379 | 0.464189 | − | 0.885736i | \(-0.346346\pi\) | ||||
0.464189 | + | 0.885736i | \(0.346346\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.2010 | − | 5.05381i | 0.123242 | − | 0.0510486i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 20.0870 | + | 8.32031i | 0.198881 | + | 0.0823793i | 0.479901 | − | 0.877323i | \(-0.340673\pi\) |
−0.281020 | + | 0.959702i | \(0.590673\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.88882 | + | 4.88882i | −0.0474642 | + | 0.0474642i | −0.730441 | − | 0.682976i | \(-0.760685\pi\) |
0.682976 | + | 0.730441i | \(0.260685\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 23.4776 | − | 23.4776i | 0.223596 | − | 0.223596i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −51.9710 | − | 21.5271i | −0.485710 | − | 0.201188i | 0.126371 | − | 0.991983i | \(-0.459667\pi\) |
−0.612080 | + | 0.790795i | \(0.709667\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 49.8054 | − | 20.6301i | 0.456931 | − | 0.189267i | −0.142333 | − | 0.989819i | \(-0.545460\pi\) |
0.599263 | + | 0.800552i | \(0.295460\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −48.3661 | −0.435730 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 62.0870i | 0.549442i | 0.961524 | + | 0.274721i | \(0.0885855\pi\) | ||||
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31.7043 | + | 76.5410i | 0.275690 | + | 0.665574i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 46.9909 | − | 113.446i | 0.401632 | − | 0.969624i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −39.5281 | − | 39.5281i | −0.332169 | − | 0.332169i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −82.8864 | − | 82.8864i | −0.685011 | − | 0.685011i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 45.8174 | − | 110.613i | 0.372499 | − | 0.899292i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 41.5830 | + | 100.390i | 0.332664 | + | 0.803122i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 177.045i | − | 1.39406i | −0.717043 | − | 0.697029i | \(-0.754505\pi\) | ||
0.717043 | − | 0.697029i | \(-0.245495\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −87.6673 | −0.679592 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 88.7654 | − | 36.7678i | 0.677598 | − | 0.280670i | −0.0172241 | − | 0.999852i | \(-0.505483\pi\) |
0.694823 | + | 0.719181i | \(0.255483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −185.097 | − | 76.6695i | −1.39170 | − | 0.576462i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −41.1075 | + | 41.1075i | −0.304500 | + | 0.304500i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −58.5583 | + | 58.5583i | −0.427433 | + | 0.427433i | −0.887753 | − | 0.460320i | \(-0.847735\pi\) |
0.460320 | + | 0.887753i | \(0.347735\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −166.832 | − | 69.1039i | −1.20023 | − | 0.497151i | −0.309155 | − | 0.951012i | \(-0.600046\pi\) |
−0.891072 | + | 0.453861i | \(0.850046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 47.7840 | − | 19.7928i | 0.338894 | − | 0.140374i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 35.1558 | 0.245845 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 94.3348i | 0.650585i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18.3932 | + | 44.4050i | 0.125124 | + | 0.302075i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.0040 | + | 43.4655i | −0.120832 | + | 0.291715i | −0.972709 | − | 0.232027i | \(-0.925464\pi\) |
0.851877 | + | 0.523742i | \(0.175464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 68.3596 | + | 68.3596i | 0.452713 | + | 0.452713i | 0.896254 | − | 0.443541i | \(-0.146278\pi\) |
−0.443541 | + | 0.896254i | \(0.646278\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.7661 | + | 29.7661i | 0.194550 | + | 0.194550i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.4248 | − | 32.4103i | 0.0866115 | − | 0.209099i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 74.5650 | + | 180.016i | 0.474936 | + | 1.14660i | 0.961956 | + | 0.273206i | \(0.0880840\pi\) |
−0.487020 | + | 0.873391i | \(0.661916\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 15.2597i | − | 0.0959730i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −301.622 | −1.87343 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 267.123 | − | 110.646i | 1.63879 | − | 0.678811i | 0.642619 | − | 0.766186i | \(-0.277848\pi\) |
0.996175 | + | 0.0873756i | \(0.0278480\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.61339 | − | 2.73936i | −0.0400812 | − | 0.0166022i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −99.3059 | + | 99.3059i | −0.594646 | + | 0.594646i | −0.938883 | − | 0.344237i | \(-0.888138\pi\) |
0.344237 | + | 0.938883i | \(0.388138\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 111.640 | − | 111.640i | 0.660592 | − | 0.660592i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 139.385 | + | 57.7350i | 0.815115 | + | 0.337632i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −187.259 | + | 77.5652i | −1.08242 | + | 0.448354i | −0.851358 | − | 0.524585i | \(-0.824220\pi\) |
−0.231063 | + | 0.972939i | \(0.574220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −170.127 | −0.972153 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 36.5711i | 0.206617i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −101.230 | − | 244.390i | −0.565528 | − | 1.36531i | −0.905290 | − | 0.424795i | \(-0.860346\pi\) |
0.339761 | − | 0.940512i | \(-0.389654\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.07796 | + | 14.6735i | −0.0335799 | + | 0.0810690i | −0.939780 | − | 0.341780i | \(-0.888970\pi\) |
0.906200 | + | 0.422849i | \(0.138970\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.25033 | + | 8.25033i | 0.0450838 | + | 0.0450838i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −57.0130 | − | 57.0130i | −0.308178 | − | 0.308178i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.61212 | + | 11.1346i | −0.0246637 | + | 0.0595435i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −80.9953 | − | 195.540i | −0.428546 | − | 1.03460i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 370.577i | − | 1.94019i | −0.242716 | − | 0.970097i | \(-0.578038\pi\) | ||
0.242716 | − | 0.970097i | \(-0.421962\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −132.679 | −0.687456 | −0.343728 | − | 0.939069i | \(-0.611690\pi\) | ||||
−0.343728 | + | 0.939069i | \(0.611690\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −61.4920 | + | 25.4708i | −0.315344 | + | 0.130620i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −116.390 | − | 48.2104i | −0.590814 | − | 0.244723i | 0.0671870 | − | 0.997740i | \(-0.478598\pi\) |
−0.658001 | + | 0.753017i | \(0.728598\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 89.9950 | − | 89.9950i | 0.452236 | − | 0.452236i | −0.443860 | − | 0.896096i | \(-0.646391\pi\) |
0.896096 | + | 0.443860i | \(0.146391\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 63.5832 | − | 63.5832i | 0.316334 | − | 0.316334i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −317.301 | − | 131.430i | −1.56306 | − | 0.647440i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 184.397 | − | 76.3797i | 0.899498 | − | 0.372584i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 227.132 | 1.09726 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 43.1940i | 0.206670i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.9287 | + | 50.5264i | 0.0991883 | + | 0.239462i | 0.965683 | − | 0.259725i | \(-0.0836321\pi\) |
−0.866494 | + | 0.499187i | \(0.833632\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.04658 | − | 12.1835i | 0.0236929 | − | 0.0571996i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −103.340 | − | 103.340i | −0.480653 | − | 0.480653i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 90.3102 | + | 90.3102i | 0.416176 | + | 0.416176i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −53.4494 | + | 129.038i | −0.244061 | + | 0.589215i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 42.8840 | + | 103.531i | 0.194045 | + | 0.468466i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 52.7540i | 0.236565i | 0.992980 | + | 0.118283i | \(0.0377388\pi\) | ||||
−0.992980 | + | 0.118283i | \(0.962261\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 128.112 | 0.569386 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −327.101 | + | 135.490i | −1.44097 | + | 0.596871i | −0.960034 | − | 0.279883i | \(-0.909704\pi\) |
−0.480939 | + | 0.876754i | \(0.659704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −245.430 | − | 101.660i | −1.07175 | − | 0.443932i | −0.224139 | − | 0.974557i | \(-0.571957\pi\) |
−0.847606 | + | 0.530625i | \(0.821957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.4280 | − | 18.4280i | 0.0797748 | − | 0.0797748i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −31.8772 | + | 31.8772i | −0.136812 | + | 0.136812i | −0.772196 | − | 0.635384i | \(-0.780842\pi\) |
0.635384 | + | 0.772196i | \(0.280842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 79.6582 | + | 32.9955i | 0.338971 | + | 0.140406i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −104.137 | + | 43.1350i | −0.439397 | + | 0.182004i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −90.0511 | −0.376783 | −0.188391 | − | 0.982094i | \(-0.560327\pi\) | ||||
−0.188391 | + | 0.982094i | \(0.560327\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.9972i | − | 0.0871252i | −0.999051 | − | 0.0435626i | \(-0.986129\pi\) | ||
0.999051 | − | 0.0435626i | \(-0.0138708\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 95.7533 | + | 231.169i | 0.394046 | + | 0.951312i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −30.6623 | + | 74.0253i | −0.125152 | + | 0.302144i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 283.990 | + | 283.990i | 1.14976 | + | 1.14976i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.38810 | + | 3.38810i | 0.0136068 | + | 0.0136068i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 105.207 | − | 253.991i | 0.419150 | − | 1.01192i | −0.563444 | − | 0.826154i | \(-0.690524\pi\) |
0.982594 | − | 0.185764i | \(-0.0594759\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.8853 | + | 60.0783i | 0.0983607 | + | 0.237464i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 22.8174i | − | 0.0894801i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 236.584 | 0.920561 | 0.460281 | − | 0.887773i | \(-0.347749\pi\) | ||||
0.460281 | + | 0.887773i | \(0.347749\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 271.199 | − | 112.334i | 1.04710 | − | 0.433723i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 238.939 | + | 98.9720i | 0.915477 | + | 0.379203i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −32.0070 | + | 32.0070i | −0.121700 | + | 0.121700i | −0.765334 | − | 0.643634i | \(-0.777426\pi\) |
0.643634 | + | 0.765334i | \(0.277426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.9878 | − | 17.9878i | 0.0678786 | − | 0.0678786i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −71.2626 | − | 29.5179i | −0.266901 | − | 0.110554i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −115.344 | + | 47.7769i | −0.428787 | + | 0.177609i | −0.586630 | − | 0.809855i | \(-0.699546\pi\) |
0.157844 | + | 0.987464i | \(0.449546\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 55.4325 | 0.204548 | 0.102274 | − | 0.994756i | \(-0.467388\pi\) | ||||
0.102274 | + | 0.994756i | \(0.467388\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 242.319i | − | 0.887615i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.0363 | + | 33.8866i | 0.0510410 | + | 0.123224i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 35.7881 | − | 86.4001i | 0.129199 | − | 0.311914i | −0.846022 | − | 0.533148i | \(-0.821009\pi\) |
0.975221 | + | 0.221235i | \(0.0710087\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −68.0069 | − | 68.0069i | −0.243752 | − | 0.243752i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.8509 | + | 13.8509i | 0.0492914 | + | 0.0492914i | 0.731323 | − | 0.682031i | \(-0.238903\pi\) |
−0.682031 | + | 0.731323i | \(0.738903\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −135.615 | + | 327.403i | −0.479205 | + | 1.15690i | 0.480778 | + | 0.876843i | \(0.340354\pi\) |
−0.959982 | + | 0.280060i | \(0.909646\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −31.2945 | − | 75.5517i | −0.109805 | − | 0.265094i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 726.645i | 2.53186i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 250.583 | 0.867071 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −123.635 | + | 51.2114i | −0.424863 | + | 0.175984i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 412.791 | + | 170.984i | 1.40884 | + | 0.583562i | 0.952031 | − | 0.306002i | \(-0.0989914\pi\) |
0.456811 | + | 0.889564i | \(0.348991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −43.1093 | + | 43.1093i | −0.146133 | + | 0.146133i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −32.2660 | + | 32.2660i | −0.108640 | + | 0.108640i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 558.615 | + | 231.386i | 1.86828 | + | 0.773866i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 491.569 | − | 203.615i | 1.63312 | − | 0.676461i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −32.3094 | −0.106632 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.4507i | 0.0637726i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −42.3557 | − | 102.256i | −0.137967 | − | 0.333081i | 0.839762 | − | 0.542955i | \(-0.182695\pi\) |
−0.977728 | + | 0.209874i | \(0.932695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.93177 | − | 9.49213i | 0.0127242 | − | 0.0307189i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −337.326 | − | 337.326i | −1.08465 | − | 1.08465i | −0.996069 | − | 0.0885790i | \(-0.971767\pi\) |
−0.0885790 | − | 0.996069i | \(-0.528233\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −70.0735 | − | 70.0735i | −0.223877 | − | 0.223877i | 0.586252 | − | 0.810129i | \(-0.300603\pi\) |
−0.810129 | + | 0.586252i | \(0.800603\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 58.0707 | − | 140.195i | 0.184351 | − | 0.445063i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.8632 | − | 79.3388i | −0.103669 | − | 0.250280i | 0.863530 | − | 0.504297i | \(-0.168248\pi\) |
−0.967200 | + | 0.254017i | \(0.918248\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 74.0450i | 0.232116i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 83.5940 | 0.260417 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −127.203 | + | 52.6891i | −0.393816 | + | 0.163124i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 315.081 | + | 130.511i | 0.969480 | + | 0.401572i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −56.6469 | + | 56.6469i | −0.173232 | + | 0.173232i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −221.965 | + | 221.965i | −0.674665 | + | 0.674665i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 124.865 | + | 51.7206i | 0.377234 | + | 0.156256i | 0.563240 | − | 0.826293i | \(-0.309554\pi\) |
−0.186006 | + | 0.982549i | \(0.559554\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −204.223 | + | 84.5919i | −0.613282 | + | 0.254030i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 149.901 | 0.447466 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 323.529i | 0.960027i | 0.877261 | + | 0.480014i | \(0.159368\pi\) | ||||
−0.877261 | + | 0.480014i | \(0.840632\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −35.3077 | − | 85.2404i | −0.104153 | − | 0.251447i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.5373 | − | 25.4394i | 0.0309013 | − | 0.0746024i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 106.226 | + | 106.226i | 0.309696 | + | 0.309696i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −87.0550 | − | 87.0550i | −0.252333 | − | 0.252333i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −135.065 | + | 326.076i | −0.389236 | + | 0.939700i | 0.600866 | + | 0.799350i | \(0.294823\pi\) |
−0.990102 | + | 0.140350i | \(0.955177\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −187.869 | − | 453.555i | −0.538305 | − | 1.29958i | −0.925905 | − | 0.377756i | \(-0.876696\pi\) |
0.387600 | − | 0.921828i | \(-0.373304\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 424.282i | 1.20878i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −70.5556 | −0.199874 | −0.0999372 | − | 0.994994i | \(-0.531864\pi\) | ||||
−0.0999372 | + | 0.994994i | \(0.531864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.3105 | − | 8.41289i | 0.0572127 | − | 0.0236983i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 76.7478 | + | 31.7900i | 0.214980 | + | 0.0890475i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 409.567 | − | 409.567i | 1.14086 | − | 1.14086i | 0.152561 | − | 0.988294i | \(-0.451248\pi\) |
0.988294 | − | 0.152561i | \(-0.0487522\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −93.6563 | + | 93.6563i | −0.259436 | + | 0.259436i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 160.932 | + | 66.6604i | 0.443340 | + | 0.183637i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −215.113 | + | 89.1026i | −0.589350 | + | 0.244117i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −513.680 | −1.39967 | −0.699837 | − | 0.714303i | \(-0.746744\pi\) | ||||
−0.699837 | + | 0.714303i | \(0.746744\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 547.191i | − | 1.48290i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 35.4419 | + | 85.5644i | 0.0955308 | + | 0.230632i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 46.5164 | − | 112.301i | 0.124709 | − | 0.301074i | −0.849178 | − | 0.528106i | \(-0.822902\pi\) |
0.973887 | + | 0.227032i | \(0.0729023\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −114.180 | − | 114.180i | −0.304481 | − | 0.304481i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 486.828 | + | 486.828i | 1.29132 | + | 1.29132i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 172.090 | − | 415.462i | 0.454064 | − | 1.09621i | −0.516699 | − | 0.856167i | \(-0.672840\pi\) |
0.970763 | − | 0.240040i | \(-0.0771604\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 100.683 | + | 243.069i | 0.264259 | + | 0.637977i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 430.627i | − | 1.12435i | −0.827017 | − | 0.562177i | \(-0.809964\pi\) | ||
0.827017 | − | 0.562177i | \(-0.190036\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 43.4451 | 0.112844 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −370.170 | + | 153.329i | −0.956512 | + | 0.396200i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −55.8615 | − | 23.1386i | −0.143603 | − | 0.0594823i | 0.309725 | − | 0.950826i | \(-0.399763\pi\) |
−0.453327 | + | 0.891344i | \(0.649763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −146.570 | + | 146.570i | −0.374860 | + | 0.374860i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −100.959 | + | 100.959i | −0.256892 | + | 0.256892i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −173.601 | − | 71.9080i | −0.439497 | − | 0.182046i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 67.6641 | − | 28.0274i | 0.170439 | − | 0.0705979i | −0.295833 | − | 0.955240i | \(-0.595597\pi\) |
0.466271 | + | 0.884642i | \(0.345597\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 297.723 | 0.746174 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 536.024i | − | 1.33672i | −0.743839 | − | 0.668359i | \(-0.766997\pi\) | ||
0.743839 | − | 0.668359i | \(-0.233003\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −97.9774 | − | 236.538i | −0.243120 | − | 0.586944i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −24.8877 | + | 60.0842i | −0.0614511 | + | 0.148356i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −44.7505 | − | 44.7505i | −0.109952 | − | 0.109952i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −540.379 | − | 540.379i | −1.32122 | − | 1.32122i | −0.912790 | − | 0.408430i | \(-0.866077\pi\) |
−0.408430 | − | 0.912790i | \(-0.633923\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 47.0948 | − | 113.697i | 0.114586 | − | 0.276635i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −84.9395 | − | 205.062i | −0.205665 | − | 0.496518i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.98765i | 0.0192474i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 268.345 | 0.643512 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −341.184 | + | 141.323i | −0.814281 | + | 0.337286i | −0.750661 | − | 0.660688i | \(-0.770265\pi\) |
−0.0636205 | + | 0.997974i | \(0.520265\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −339.196 | − | 140.500i | −0.805692 | − | 0.333728i | −0.0584581 | − | 0.998290i | \(-0.518618\pi\) |
−0.747234 | + | 0.664561i | \(0.768618\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 167.148 | − | 167.148i | 0.395149 | − | 0.395149i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −82.6714 | + | 82.6714i | −0.194521 | + | 0.194521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −65.4234 | − | 27.0993i | −0.153216 | − | 0.0634643i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −48.2661 | + | 19.9925i | −0.112508 | + | 0.0466025i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −154.504 | −0.358478 | −0.179239 | − | 0.983806i | \(-0.557363\pi\) | ||||
−0.179239 | + | 0.983806i | \(0.557363\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 506.808i | 1.17046i | 0.810868 | + | 0.585228i | \(0.198995\pi\) | ||||
−0.810868 | + | 0.585228i | \(0.801005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −53.6465 | − | 129.514i | −0.123325 | − | 0.297734i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −284.291 | + | 686.338i | −0.650550 | + | 1.57057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 144.746 | + | 144.746i | 0.329718 | + | 0.329718i | 0.852479 | − | 0.522761i | \(-0.175098\pi\) |
−0.522761 | + | 0.852479i | \(0.675098\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 155.328 | + | 155.328i | 0.352218 | + | 0.352218i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 230.959 | − | 557.584i | 0.521351 | − | 1.25865i | −0.415713 | − | 0.909496i | \(-0.636468\pi\) |
0.937064 | − | 0.349158i | \(-0.113532\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −49.2078 | − | 118.798i | −0.110579 | − | 0.266962i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 69.9132i | − | 0.156405i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.201052 | −0.000447778 | −0.000223889 | − | 1.00000i | \(-0.500071\pi\) | ||||
−0.000223889 | 1.00000i | \(0.500071\pi\) | ||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 144.736 | − | 59.9518i | 0.320923 | − | 0.132931i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −132.727 | − | 54.9774i | −0.292996 | − | 0.121363i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 285.641 | − | 285.641i | 0.627782 | − | 0.627782i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 226.835 | − | 226.835i | 0.496358 | − | 0.496358i | −0.413944 | − | 0.910302i | \(-0.635849\pi\) |
0.910302 | + | 0.413944i | \(0.135849\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −134.379 | − | 55.6618i | −0.292766 | − | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −496.600 | + | 205.699i | −1.07722 | + | 0.446201i | −0.849535 | − | 0.527533i | \(-0.823117\pi\) |
−0.227690 | + | 0.973734i | \(0.573117\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 520.019 | 1.12315 | 0.561576 | − | 0.827425i | \(-0.310195\pi\) | ||||
0.561576 | + | 0.827425i | \(0.310195\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 52.1312i | 0.112110i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.4966 | + | 85.6964i | 0.0760099 | + | 0.183504i | 0.957317 | − | 0.289040i | \(-0.0933359\pi\) |
−0.881307 | + | 0.472544i | \(0.843336\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −208.847 | + | 504.202i | −0.445303 | + | 1.07506i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −204.743 | − | 204.743i | −0.434699 | − | 0.434699i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −81.1137 | − | 81.1137i | −0.171488 | − | 0.171488i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −160.351 | + | 387.122i | −0.337582 | + | 0.814994i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.6891 | − | 64.4332i | −0.0559520 | − | 0.135080i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 163.116i | − | 0.340535i | −0.985398 | − | 0.170268i | \(-0.945537\pi\) | ||
0.985398 | − | 0.170268i | \(-0.0544632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −588.447 | −1.22338 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 414.102 | − | 171.527i | 0.857355 | − | 0.355128i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −206.106 | − | 85.3718i | −0.424960 | − | 0.176024i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −371.724 | + | 371.724i | −0.763294 | + | 0.763294i | −0.976916 | − | 0.213622i | \(-0.931474\pi\) |
0.213622 | + | 0.976916i | \(0.431474\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −303.817 | + | 303.817i | −0.621302 | + | 0.621302i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 281.201 | + | 116.477i | 0.572710 | + | 0.237224i | 0.650193 | − | 0.759769i | \(-0.274688\pi\) |
−0.0774824 | + | 0.996994i | \(0.524688\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −218.056 | + | 90.3220i | −0.442305 | + | 0.183209i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −32.7158 | −0.0660924 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 80.0367i | 0.161040i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −236.126 | − | 570.059i | −0.473199 | − | 1.14240i | −0.962741 | − | 0.270424i | \(-0.912836\pi\) |
0.489542 | − | 0.871980i | \(-0.337164\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 79.8656 | − | 192.813i | 0.159412 | − | 0.384855i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.8902 | − | 12.8902i | −0.0256266 | − | 0.0256266i | 0.694177 | − | 0.719804i | \(-0.255768\pi\) |
−0.719804 | + | 0.694177i | \(0.755768\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −38.0857 | − | 38.0857i | −0.0754173 | − | 0.0754173i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −89.7851 | + | 216.760i | −0.177091 | + | 0.427535i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −59.1272 | − | 142.746i | −0.116163 | − | 0.280443i | 0.855095 | − | 0.518472i | \(-0.173499\pi\) |
−0.971258 | + | 0.238028i | \(0.923499\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 847.685i | − | 1.65888i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −521.291 | −1.01616 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.8238 | − | 6.55444i | 0.0307259 | − | 0.0127271i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 62.5251 | + | 25.8988i | 0.120938 | + | 0.0500943i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 212.982 | − | 212.982i | 0.410369 | − | 0.410369i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 119.838 | − | 119.838i | 0.230015 | − | 0.230015i | −0.582684 | − | 0.812699i | \(-0.697997\pi\) |
0.812699 | + | 0.582684i | \(0.197997\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −689.004 | − | 285.395i | −1.31741 | − | 0.545688i | −0.390370 | − | 0.920658i | \(-0.627653\pi\) |
−0.927037 | + | 0.374970i | \(0.877653\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 233.570 | − | 96.7480i | 0.444896 | − | 0.184282i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 87.7707 | 0.166548 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 589.413i | 1.11420i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 63.9626 | + | 154.419i | 0.120457 | + | 0.290809i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 557.438 | − | 1345.77i | 1.04585 | − | 2.52490i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 98.5390 | + | 98.5390i | 0.184185 | + | 0.184185i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 277.960 | + | 277.960i | 0.517617 | + | 0.517617i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.0673 | + | 58.1037i | −0.0446519 | + | 0.107799i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 294.810 | + | 711.735i | 0.544936 | + | 1.31559i | 0.921204 | + | 0.389081i | \(0.127207\pi\) |
−0.376267 | + | 0.926511i | \(0.622793\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 23.6020i | − | 0.0434658i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −133.549 | −0.245043 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 518.930 | − | 214.948i | 0.948683 | − | 0.392957i | 0.145948 | − | 0.989292i | \(-0.453377\pi\) |
0.802736 | + | 0.596335i | \(0.203377\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 49.2663 | + | 20.4068i | 0.0897382 | + | 0.0371708i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −598.138 | + | 598.138i | −1.08555 | + | 1.08555i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 483.734 | − | 483.734i | 0.874745 | − | 0.874745i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 110.696 | + | 45.8520i | 0.199453 | + | 0.0826162i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 883.511 | − | 365.962i | 1.58620 | − | 0.657024i | 0.596816 | − | 0.802378i | \(-0.296432\pi\) |
0.989380 | + | 0.145355i | \(0.0464323\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1066.61 | −1.90806 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 17.9098i | − | 0.0319248i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 385.055 | + | 929.606i | 0.683935 | + | 1.65117i | 0.756656 | + | 0.653813i | \(0.226832\pi\) |
−0.0727214 | + | 0.997352i | \(0.523168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 58.8596 | − | 142.100i | 0.104176 | − | 0.251504i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −167.423 | − | 167.423i | −0.295278 | − | 0.295278i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −503.029 | − | 503.029i | −0.884058 | − | 0.884058i | 0.109886 | − | 0.993944i | \(-0.464951\pi\) |
−0.993944 | + | 0.109886i | \(0.964951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −48.1525 | + | 116.250i | −0.0843301 | + | 0.203591i | −0.960419 | − | 0.278558i | \(-0.910144\pi\) |
0.876089 | + | 0.482149i | \(0.160144\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 210.741 | + | 508.773i | 0.367785 | + | 0.887910i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 630.830i | 1.09710i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.8629 | −0.0205595 | −0.0102798 | − | 0.999947i | \(-0.503272\pi\) | ||||
−0.0102798 | + | 0.999947i | \(0.503272\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 182.158 | − | 75.4522i | 0.314607 | − | 0.130315i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.8670 | − | 11.1287i | −0.0462426 | − | 0.0191543i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.1190 | − | 14.1190i | 0.0242178 | − | 0.0242178i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −215.098 | + | 215.098i | −0.367689 | + | 0.367689i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −496.631 | − | 205.711i | −0.846049 | − | 0.350445i | −0.0828132 | − | 0.996565i | \(-0.526390\pi\) |
−0.763236 | + | 0.646120i | \(0.776390\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 290.621 | − | 120.379i | 0.493414 | − | 0.204379i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 187.211 | 0.316770 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 410.471i | − | 0.692193i | −0.938199 | − | 0.346097i | \(-0.887507\pi\) | ||
0.938199 | − | 0.346097i | \(-0.112493\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 52.9954 | + | 127.942i | 0.0890678 | + | 0.215029i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −72.3774 | + | 174.735i | −0.121235 | + | 0.292688i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 565.778 | + | 565.778i | 0.944537 | + | 0.944537i | 0.998541 | − | 0.0540033i | \(-0.0171982\pi\) |
−0.0540033 | + | 0.998541i | \(0.517198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 224.391 | + | 224.391i | 0.373362 | + | 0.373362i | 0.868700 | − | 0.495338i | \(-0.164956\pi\) |
−0.495338 | + | 0.868700i | \(0.664956\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 157.270 | − | 379.683i | 0.260812 | − | 0.629656i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 111.126 | + | 268.282i | 0.183679 | + | 0.443441i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 19.8654i | − | 0.0327271i | −0.999866 | − | 0.0163636i | \(-0.994791\pi\) | ||
0.999866 | − | 0.0163636i | \(-0.00520892\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 510.371 | 0.838047 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 581.365 | − | 240.809i | 0.951498 | − | 0.394123i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −905.460 | − | 375.054i | −1.47710 | − | 0.611833i | −0.508631 | − | 0.860985i | \(-0.669848\pi\) |
−0.968464 | + | 0.249152i | \(0.919848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −209.726 | + | 209.726i | −0.341019 | + | 0.341019i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 673.907 | − | 673.907i | 1.09223 | − | 1.09223i | 0.0969409 | − | 0.995290i | \(-0.469094\pi\) |
0.995290 | − | 0.0969409i | \(-0.0309058\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 354.963 | + | 147.030i | 0.573446 | + | 0.237529i | 0.650511 | − | 0.759497i | \(-0.274555\pi\) |
−0.0770649 | + | 0.997026i | \(0.524555\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −725.062 | + | 300.330i | −1.16757 | + | 0.483624i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 468.143 | 0.751433 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 202.389i | 0.323822i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.5636 | − | 59.3018i | −0.0391764 | − | 0.0945803i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 77.1987 | − | 186.374i | 0.122732 | − | 0.296302i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 494.698 | + | 494.698i | 0.783991 | + | 0.783991i | 0.980502 | − | 0.196511i | \(-0.0629611\pi\) |
−0.196511 | + | 0.980502i | \(0.562961\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −57.4669 | − | 57.4669i | −0.0907850 | − | 0.0907850i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −167.843 | + | 405.208i | −0.264319 | + | 0.638122i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 223.781 | + | 540.255i | 0.351304 | + | 0.848124i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 60.2706i | − | 0.0943202i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 440.457 | 0.687141 | 0.343571 | − | 0.939127i | \(-0.388364\pi\) | ||||
0.343571 | + | 0.939127i | \(0.388364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −211.055 | + | 87.4220i | −0.328235 | + | 0.135960i | −0.540715 | − | 0.841206i | \(-0.681846\pi\) |
0.212479 | + | 0.977166i | \(0.431846\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 200.646 | + | 83.1103i | 0.311079 | + | 0.128853i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −515.935 | + | 515.935i | −0.797426 | + | 0.797426i | −0.982689 | − | 0.185263i | \(-0.940686\pi\) |
0.185263 | + | 0.982689i | \(0.440686\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.8372 | + | 33.8372i | −0.0521375 | + | 0.0521375i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −175.346 | − | 72.6309i | −0.269349 | − | 0.111568i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 613.161 | − | 253.980i | 0.938991 | − | 0.388943i | 0.139909 | − | 0.990164i | \(-0.455319\pi\) |
0.799082 | + | 0.601222i | \(0.205319\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −238.016 | −0.363383 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 638.339i | 0.971596i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.4679 | − | 46.9996i | −0.0295416 | − | 0.0713196i | 0.908420 | − | 0.418058i | \(-0.137289\pi\) |
−0.937962 | + | 0.346738i | \(0.887289\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.1458 | + | 111.406i | −0.0698122 | + | 0.168541i | −0.954934 | − | 0.296817i | \(-0.904075\pi\) |
0.885122 | + | 0.465359i | \(0.154075\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −117.752 | − | 117.752i | −0.177606 | − | 0.177606i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 350.950 | + | 350.950i | 0.527745 | + | 0.527745i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −487.344 | + | 1176.55i | −0.730650 | + | 1.76395i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.0002 | − | 72.4270i | −0.0448434 | − | 0.108262i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.2672i | 0.0227528i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −352.344 | −0.523542 | −0.261771 | − | 0.965130i | \(-0.584306\pi\) | ||||
−0.261771 | + | 0.965130i | \(0.584306\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −408.964 | + | 169.398i | −0.605872 | + | 0.250961i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1178.26 | + | 488.051i | 1.74041 | + | 0.720902i | 0.998742 | + | 0.0501357i | \(0.0159654\pi\) |
0.741669 | + | 0.670766i | \(0.234035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 574.306 | − | 574.306i | 0.845812 | − | 0.845812i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 372.033 | − | 372.033i | 0.546304 | − | 0.546304i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −414.446 | − | 171.669i | −0.606802 | − | 0.251346i | 0.0580582 | − | 0.998313i | \(-0.481509\pi\) |
−0.664861 | + | 0.746967i | \(0.731509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 189.538 | − | 78.5093i | 0.276698 | − | 0.114612i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 394.768 | 0.574626 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 185.657i | − | 0.269459i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 268.707 | + | 648.715i | 0.388866 | + | 0.938806i | 0.990181 | + | 0.139794i | \(0.0446439\pi\) |
−0.601314 | + | 0.799012i | \(0.705356\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 45.5807 | − | 110.041i | 0.0657729 | − | 0.158790i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 316.319 | + | 316.319i | 0.455136 | + | 0.455136i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 353.106 | + | 353.106i | 0.506608 | + | 0.506608i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 25.6368 | − | 61.8927i | 0.0366764 | − | 0.0885447i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −464.382 | − | 1121.12i | −0.662457 | − | 1.59931i | −0.793941 | − | 0.607995i | \(-0.791974\pi\) |
0.131484 | − | 0.991318i | \(-0.458026\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 722.990i | − | 1.02844i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −128.128 | −0.181742 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 181.166 | − | 75.0414i | 0.256246 | − | 0.106141i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −591.984 | − | 245.208i | −0.834957 | − | 0.345850i | −0.0760937 | − | 0.997101i | \(-0.524245\pi\) |
−0.758863 | + | 0.651250i | \(0.774245\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −364.270 | + | 364.270i | −0.512334 | + | 0.512334i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 334.870 | − | 334.870i | 0.469664 | − | 0.469664i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −80.4619 | − | 33.3284i | −0.112534 | − | 0.0466132i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 123.633 | − | 51.2104i | 0.172431 | − | 0.0714232i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 906.230 | 1.26040 | 0.630202 | − | 0.776432i | \(-0.282972\pi\) | ||||
0.630202 | + | 0.776432i | \(0.282972\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 62.3563i | 0.0864858i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.9407 | + | 28.8274i | 0.0165155 | + | 0.0398720i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −274.881 | + | 663.622i | −0.379147 | + | 0.915341i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −317.957 | − | 317.957i | −0.437355 | − | 0.437355i | 0.453766 | − | 0.891121i | \(-0.350080\pi\) |
−0.891121 | + | 0.453766i | \(0.850080\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −95.8544 | − | 95.8544i | −0.131488 | − | 0.131488i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 139.929 | − | 337.818i | 0.191421 | − | 0.462131i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 159.623 | + | 385.363i | 0.217766 | + | 0.525734i | 0.994577 | − | 0.103999i | \(-0.0331640\pi\) |
−0.776811 | + | 0.629734i | \(0.783164\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 119.068i | − | 0.161997i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 117.660 | 0.159647 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −380.514 | + | 157.614i | −0.514904 | + | 0.213280i | −0.624977 | − | 0.780643i | \(-0.714892\pi\) |
0.110073 | + | 0.993924i | \(0.464892\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −551.395 | − | 228.395i | −0.744123 | − | 0.308226i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.76228 | + | 5.76228i | −0.00775542 | + | 0.00775542i | −0.710974 | − | 0.703218i | \(-0.751746\pi\) |
0.703218 | + | 0.710974i | \(0.251746\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 82.4123 | − | 82.4123i | 0.110620 | − | 0.110620i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.2318 | + | 8.38030i | 0.0270841 | + | 0.0112186i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −468.729 | + | 194.154i | −0.625807 | + | 0.259218i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 302.377 | 0.402632 | 0.201316 | − | 0.979526i | \(-0.435478\pi\) | ||||
0.201316 | + | 0.979526i | \(0.435478\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 408.539i | 0.542548i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −91.6499 | − | 221.262i | −0.121391 | − | 0.293063i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.31627 | − | 22.4915i | 0.0123068 | − | 0.0297113i | −0.917607 | − | 0.397490i | \(-0.869881\pi\) |
0.929914 | + | 0.367778i | \(0.119881\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −68.3309 | − | 68.3309i | −0.0900276 | − | 0.0900276i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −163.034 | − | 163.034i | −0.214236 | − | 0.214236i | 0.591828 | − | 0.806064i | \(-0.298406\pi\) |
−0.806064 | + | 0.591828i | \(0.798406\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 186.064 | − | 449.198i | 0.243859 | − | 0.588727i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −39.9075 | − | 96.3452i | −0.0521667 | − | 0.125941i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 444.943i | 0.580109i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 180.205 | 0.234337 | 0.117168 | − | 0.993112i | \(-0.462618\pi\) | ||||
0.117168 | + | 0.993112i | \(0.462618\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −324.811 | + | 134.541i | −0.421286 | + | 0.174502i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −196.725 | − | 81.4860i | −0.254495 | − | 0.105415i | 0.251789 | − | 0.967782i | \(-0.418981\pi\) |
−0.506284 | + | 0.862367i | \(0.668981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 188.880 | − | 188.880i | 0.243716 | − | 0.243716i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −308.452 | + | 308.452i | −0.396978 | + | 0.396978i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1653.48 | + | 684.892i | 2.12256 | + | 0.879194i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.9421 | − | 6.60342i | 0.0204124 | − | 0.00845508i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −893.620 | −1.14128 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 482.695i | − | 0.614898i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 80.6847 | + | 194.790i | 0.102522 | + | 0.247510i | 0.966814 | − | 0.255480i | \(-0.0822334\pi\) |
−0.864293 | + | 0.502990i | \(0.832233\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.7412 | − | 62.1448i | 0.0326251 | − | 0.0787640i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 395.956 | + | 395.956i | 0.500576 | + | 0.500576i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 100.378 | + | 100.378i | 0.126580 | + | 0.126580i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.4665 | + | 34.9252i | −0.0181969 | + | 0.0439311i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 256.509 | + | 619.268i | 0.321843 | + | 0.776999i | 0.999147 | + | 0.0412950i | \(0.0131483\pi\) |
−0.677304 | + | 0.735704i | \(0.736852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 215.723i | 0.269992i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −352.529 | −0.440111 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −168.846 | + | 69.9382i | −0.210269 | + | 0.0870961i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 690.328 | + | 285.943i | 0.857551 | + | 0.355209i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 131.188 | − | 131.188i | 0.162562 | − | 0.162562i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1008.10 | + | 1008.10i | −1.24611 | + | 1.24611i | −0.288683 | + | 0.957425i | \(0.593217\pi\) |
−0.957425 | + | 0.288683i | \(0.906783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1271.85 | − | 526.816i | −1.56825 | − | 0.649588i | −0.581748 | − | 0.813369i | \(-0.697631\pi\) |
−0.986497 | + | 0.163780i | \(0.947631\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −76.1044 | + | 31.5235i | −0.0936094 | + | 0.0387743i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −716.266 | −0.878854 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1310.48i | − | 1.60401i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −423.814 | − | 1023.18i | −0.517477 | − | 1.24930i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 119.922 | − | 289.516i | 0.146068 | − | 0.352639i | −0.833865 | − | 0.551969i | \(-0.813877\pi\) |
0.979932 | + | 0.199330i | \(0.0638767\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −607.735 | − | 607.735i | −0.738439 | − | 0.738439i | 0.233837 | − | 0.972276i | \(-0.424872\pi\) |
−0.972276 | + | 0.233837i | \(0.924872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −38.5414 | − | 38.5414i | −0.0467168 | − | 0.0467168i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 246.520 | − | 595.152i | 0.298090 | − | 0.719652i | −0.701883 | − | 0.712292i | \(-0.747657\pi\) |
0.999973 | − | 0.00736012i | \(-0.00234282\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −393.211 | − | 949.295i | −0.474319 | − | 1.14511i | −0.962236 | − | 0.272218i | \(-0.912243\pi\) |
0.487916 | − | 0.872890i | \(-0.337757\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 138.972i | 0.167235i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −200.469 | −0.240659 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 321.428 | − | 133.140i | 0.384943 | − | 0.159449i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 307.018 | + | 127.171i | 0.366808 | + | 0.151937i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 575.067 | − | 575.067i | 0.685420 | − | 0.685420i | −0.275796 | − | 0.961216i | \(-0.588941\pi\) |
0.961216 | + | 0.275796i | \(0.0889415\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −430.678 | + | 430.678i | −0.512102 | + | 0.512102i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.8929 | − | 11.1394i | −0.0319015 | − | 0.0132140i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −361.350 | + | 149.676i | −0.427633 | + | 0.177131i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1057.21 | −1.24818 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 526.620i | − | 0.620283i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −416.535 | − | 1005.61i | −0.489466 | − | 1.18167i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −304.017 | + | 733.961i | −0.356409 | + | 0.860447i | 0.639390 | + | 0.768882i | \(0.279187\pi\) |
−0.995799 | + | 0.0915645i | \(0.970813\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −264.279 | − | 264.279i | −0.309098 | − | 0.309098i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −241.394 | − | 241.394i | −0.281673 | − | 0.281673i | 0.552103 | − | 0.833776i | \(-0.313826\pi\) |
−0.833776 | + | 0.552103i | \(0.813826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 443.212 | − | 1070.01i | 0.515963 | − | 1.24564i | −0.424401 | − | 0.905474i | \(-0.639515\pi\) |
0.940364 | − | 0.340170i | \(-0.110485\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −413.230 | − | 997.625i | −0.479942 | − | 1.15868i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 167.859i | − | 0.194507i | −0.995260 | − | 0.0972533i | \(-0.968994\pi\) | ||
0.995260 | − | 0.0972533i | \(-0.0310057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 502.117 | 0.580482 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −344.031 | + | 142.502i | −0.396806 | + | 0.164363i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −136.263 | − | 56.4418i | −0.156804 | − | 0.0649503i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 773.586 | − | 773.586i | 0.888158 | − | 0.888158i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −432.474 | + | 432.474i | −0.495388 | + | 0.495388i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 905.426 | + | 375.040i | 1.03477 | + | 0.428617i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −659.079 | + | 272.999i | −0.751515 | + | 0.311288i | −0.725360 | − | 0.688370i | \(-0.758326\pi\) |
−0.0261554 | + | 0.999658i | \(0.508326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −663.964 | −0.755363 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 806.984i | 0.915987i | 0.888956 | + | 0.457993i | \(0.151432\pi\) | ||||
−0.888956 | + | 0.457993i | \(0.848568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −118.704 | − | 286.577i | −0.134433 | − | 0.324549i | 0.842300 | − | 0.539009i | \(-0.181201\pi\) |
−0.976733 | + | 0.214459i | \(0.931201\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 34.6701 | − | 83.7011i | 0.0391753 | − | 0.0945776i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −727.865 | − | 727.865i | −0.820592 | − | 0.820592i | 0.165601 | − | 0.986193i | \(-0.447044\pi\) |
−0.986193 | + | 0.165601i | \(0.947044\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1129.10 | − | 1129.10i | −1.27008 | − | 1.27008i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.5348 | + | 47.1611i | −0.0219246 | + | 0.0529306i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 295.869 | + | 714.290i | 0.331320 | + | 0.799877i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 655.308i | 0.732188i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −898.518 | −1.00169 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 498.196 | − | 206.359i | 0.554167 | − | 0.229543i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.8018 | + | 24.3565i | 0.0652628 | + | 0.0270328i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −559.093 | + | 559.093i | −0.619151 | + | 0.619151i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.8215 | − | 27.8215i | 0.0307420 | − | 0.0307420i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 711.116 | + | 294.554i | 0.784031 | + | 0.324756i | 0.738541 | − | 0.674209i | \(-0.235515\pi\) |
0.0454897 | + | 0.998965i | \(0.485515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −136.425 | + | 56.5090i | −0.150082 | + | 0.0621661i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 758.696 | 0.832817 | 0.416409 | − | 0.909178i | \(-0.363289\pi\) | ||||
0.416409 | + | 0.909178i | \(0.363289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.26965i | 0.00686708i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.0612 | − | 26.7042i | −0.0120888 | − | 0.0291849i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 331.611 | − | 800.581i | 0.361626 | − | 0.873043i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −949.647 | − | 949.647i | −1.03335 | − | 1.03335i | −0.999424 | − | 0.0339243i | \(-0.989199\pi\) |
−0.0339243 | − | 0.999424i | \(-0.510801\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 116.302 | + | 116.302i | 0.126278 | + | 0.126278i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 61.3993 | − | 148.231i | 0.0665215 | − | 0.160597i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −234.943 | − | 567.202i | −0.253992 | − | 0.613191i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 46.9566i | − | 0.0506544i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 222.645 | 0.239661 | 0.119830 | − | 0.992794i | \(-0.461765\pi\) | ||||
0.119830 | + | 0.992794i | \(0.461765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −663.780 | + | 274.947i | −0.712975 | + | 0.295324i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 654.952 | + | 271.290i | 0.701985 | + | 0.290772i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.1117 | − | 21.1117i | 0.0225794 | − | 0.0225794i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1027.40 | + | 1027.40i | −1.09648 | + | 1.09648i | −0.101659 | + | 0.994819i | \(0.532415\pi\) |
−0.994819 | + | 0.101659i | \(0.967585\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 136.055 | + | 56.3558i | 0.144893 | + | 0.0600168i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 892.441 | − | 369.661i | 0.948397 | − | 0.392839i | 0.145769 | − | 0.989319i | \(-0.453434\pi\) |
0.802628 | + | 0.596480i | \(0.203434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2694.40 | 2.85726 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 524.321i | 0.554837i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 385.441 | + | 930.536i | 0.407012 | + | 0.982615i | 0.985919 | + | 0.167221i | \(0.0534795\pi\) |
−0.578907 | + | 0.815394i | \(0.696521\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −650.293 | + | 1569.95i | −0.685240 | + | 1.65432i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 90.2371 | + | 90.2371i | 0.0948865 | + | 0.0948865i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 648.910 | + | 648.910i | 0.680913 | + | 0.680913i | 0.960206 | − | 0.279293i | \(-0.0901001\pi\) |
−0.279293 | + | 0.960206i | \(0.590100\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −351.314 | + | 848.148i | −0.367868 | + | 0.888113i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −42.1081 | − | 101.658i | −0.0440001 | − | 0.106226i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 746.905i | 0.778837i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 760.470 | 0.791331 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 352.971 | − | 146.205i | 0.366532 | − | 0.151823i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 303.665 | + | 125.782i | 0.314679 | + | 0.130344i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.2757 | − | 41.2757i | 0.0426842 | − | 0.0426842i | −0.685443 | − | 0.728127i | \(-0.740391\pi\) |
0.728127 | + | 0.685443i | \(0.240391\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 144.676 | − | 144.676i | 0.149304 | − | 0.149304i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −213.816 | − | 88.5653i | −0.220201 | − | 0.0912104i | 0.269856 | − | 0.962901i | \(-0.413024\pi\) |
−0.490057 | + | 0.871690i | \(0.663024\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1504.67 | + | 623.253i | −1.54642 | + | 0.640547i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −506.800 | −0.519795 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 314.091i | 0.321485i | 0.986996 | + | 0.160742i | \(0.0513888\pi\) | ||||
−0.986996 | + | 0.160742i | \(0.948611\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −38.6240 | − | 93.2467i | −0.0394526 | − | 0.0952469i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −140.113 | + | 338.263i | −0.142827 | + | 0.344815i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.50847 | + | 8.50847i | 0.00865562 | + | 0.00865562i | 0.711421 | − | 0.702766i | \(-0.248052\pi\) |
−0.702766 | + | 0.711421i | \(0.748052\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 220.680 | + | 220.680i | 0.224041 | + | 0.224041i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 178.513 | − | 430.967i | 0.180864 | − | 0.436644i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −755.003 | − | 1822.74i | −0.763400 | − | 1.84301i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 93.7233i | 0.0945745i | 0.998881 | + | 0.0472872i | \(0.0150576\pi\) | ||||
−0.998881 | + | 0.0472872i | \(0.984942\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −200.842 | −0.202257 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −291.291 | + | 120.657i | −0.292754 | + | 0.121263i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 287.749 | + | 119.189i | 0.288614 | + | 0.119548i | 0.522294 | − | 0.852766i | \(-0.325077\pi\) |
−0.233679 | + | 0.972314i | \(0.575077\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 540.075 | − | 540.075i | 0.540616 | − | 0.540616i |
(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 | 256.3.h.a.31.3 | 28 | ||
4.3 | odd | 2 | 256.3.h.b.31.5 | 28 | |||
8.3 | odd | 2 | 32.3.h.a.27.6 | yes | 28 | ||
8.5 | even | 2 | 128.3.h.a.15.5 | 28 | |||
24.11 | even | 2 | 288.3.u.a.91.2 | 28 | |||
32.3 | odd | 8 | 128.3.h.a.111.5 | 28 | |||
32.13 | even | 8 | 256.3.h.b.223.5 | 28 | |||
32.19 | odd | 8 | inner | 256.3.h.a.223.3 | 28 | ||
32.29 | even | 8 | 32.3.h.a.19.6 | ✓ | 28 | ||
96.29 | odd | 8 | 288.3.u.a.19.2 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.6 | ✓ | 28 | 32.29 | even | 8 | ||
32.3.h.a.27.6 | yes | 28 | 8.3 | odd | 2 | ||
128.3.h.a.15.5 | 28 | 8.5 | even | 2 | |||
128.3.h.a.111.5 | 28 | 32.3 | odd | 8 | |||
256.3.h.a.31.3 | 28 | 1.1 | even | 1 | trivial | ||
256.3.h.a.223.3 | 28 | 32.19 | odd | 8 | inner | ||
256.3.h.b.31.5 | 28 | 4.3 | odd | 2 | |||
256.3.h.b.223.5 | 28 | 32.13 | even | 8 | |||
288.3.u.a.19.2 | 28 | 96.29 | odd | 8 | |||
288.3.u.a.91.2 | 28 | 24.11 | even | 2 |