Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,3,Mod(15,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, 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("128.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.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: | \(3.48774738381\) |
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 | 15.5 | ||
Character | \(\chi\) | \(=\) | 128.15 |
Dual form | 128.3.h.a.111.5 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) |
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 | −0.141940 | − | 0.989875i | \(-0.545334\pi\) |
0.599580 | + | 0.800315i | \(0.295334\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.28872 | + | 0.948019i | 0.457744 | + | 0.189604i | 0.599627 | − | 0.800280i | \(-0.295316\pi\) |
−0.141883 | + | 0.989883i | \(0.545316\pi\) | |||||||
\(6\) | 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 | 0.462843 | − | 0.886440i | \(-0.346829\pi\) |
−0.299529 | + | 0.954087i | \(0.596829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16.7036 | − | 6.91888i | 1.28490 | − | 0.532221i | 0.367436 | − | 0.930049i | \(-0.380236\pi\) |
0.917460 | + | 0.397827i | \(0.130236\pi\) | |||||||
\(14\) | 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 | \(0.0737375\pi\) |
−0.525876 | + | 0.850561i | \(0.676262\pi\) | |||||||
\(20\) | 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 | \(0.102984\pi\) |
−0.445618 | + | 0.895223i | \(0.647016\pi\) | |||||||
\(30\) | 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 | −0.0626629 | − | 0.998035i | \(-0.519959\pi\) |
−0.750027 | + | 0.661408i | \(0.769959\pi\) | |||||||
\(38\) | 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 | −0.355310 | − | 0.934748i | \(-0.615625\pi\) |
−0.912209 | + | 0.409724i | \(0.865625\pi\) | |||||||
\(44\) | 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 | −0.882462 | − | 0.470384i | \(-0.844115\pi\) |
0.956606 | + | 0.291383i | \(0.0941154\pi\) | |||||||
\(54\) | 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 | −0.983375 | − | 0.181586i | \(-0.941877\pi\) |
0.823752 | + | 0.566951i | \(0.191877\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00467 | + | 7.25391i | 0.0492568 | + | 0.118916i | 0.946593 | − | 0.322432i | \(-0.104500\pi\) |
−0.897336 | + | 0.441348i | \(0.854500\pi\) | |||||||
\(62\) | 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 | 0.0757497 | − | 0.997127i | \(-0.475865\pi\) |
0.758638 | + | 0.651512i | \(0.225865\pi\) | |||||||
\(68\) | 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 | 0.931138 | − | 0.364666i | \(-0.118817\pi\) |
−0.916272 | + | 0.400556i | \(0.868817\pi\) | |||||||
\(84\) | 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 | 0.281020 | − | 0.959702i | \(-0.409327\pi\) |
−0.479901 | + | 0.877323i | \(0.659327\pi\) | |||||||
\(102\) | 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 | 0.612080 | − | 0.790795i | \(-0.290333\pi\) |
−0.126371 | + | 0.991983i | \(0.540333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −49.8054 | + | 20.6301i | −0.456931 | + | 0.189267i | −0.599263 | − | 0.800552i | \(-0.704540\pi\) |
0.142333 | + | 0.989819i | \(0.454540\pi\) | |||||||
\(110\) | 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 | −0.694823 | − | 0.719181i | \(-0.744517\pi\) |
0.0172241 | + | 0.999852i | \(0.494517\pi\) | |||||||
\(132\) | 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 | 0.891072 | − | 0.453861i | \(-0.149954\pi\) |
0.309155 | + | 0.951012i | \(0.399954\pi\) | |||||||
\(140\) | 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 | −0.851877 | − | 0.523742i | \(-0.824536\pi\) |
0.972709 | + | 0.232027i | \(0.0745357\pi\) | |||||||
\(150\) | 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 | \(-0.911916\pi\) |
0.487020 | − | 0.873391i | \(-0.338084\pi\) | |||||||
\(158\) | 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 | −0.996175 | − | 0.0873756i | \(-0.972152\pi\) |
−0.642619 | + | 0.766186i | \(0.722152\pi\) | |||||||
\(164\) | 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 | 0.231063 | − | 0.972939i | \(-0.425780\pi\) |
0.851358 | + | 0.524585i | \(0.175780\pi\) | |||||||
\(174\) | 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 | \(0.139654\pi\) |
−0.339761 | + | 0.940512i | \(0.610346\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.07796 | − | 14.6735i | 0.0335799 | − | 0.0810690i | −0.906200 | − | 0.422849i | \(-0.861030\pi\) |
0.939780 | + | 0.341780i | \(0.111030\pi\) | |||||||
\(182\) | 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 | 0.658001 | − | 0.753017i | \(-0.271402\pi\) |
−0.0671870 | + | 0.997740i | \(0.521402\pi\) | |||||||
\(198\) | 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 | 0.866494 | − | 0.499187i | \(-0.166368\pi\) |
−0.965683 | + | 0.259725i | \(0.916368\pi\) | |||||||
\(212\) | 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 | 0.480939 | − | 0.876754i | \(-0.340296\pi\) |
0.960034 | + | 0.279883i | \(0.0902957\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 245.430 | + | 101.660i | 1.07175 | + | 0.443932i | 0.847606 | − | 0.530625i | \(-0.178043\pi\) |
0.224139 | + | 0.974557i | \(0.428043\pi\) | |||||||
\(230\) | 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 | \(0.309476\pi\) |
−0.982594 | + | 0.185764i | \(0.940524\pi\) | |||||||
\(252\) | 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 | −0.157844 | − | 0.987464i | \(-0.550454\pi\) |
0.586630 | + | 0.809855i | \(0.300454\pi\) | |||||||
\(270\) | 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 | −0.975221 | − | 0.221235i | \(-0.928991\pi\) |
0.846022 | + | 0.533148i | \(0.178991\pi\) | |||||||
\(278\) | 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 | \(-0.659646\pi\) |
0.959982 | − | 0.280060i | \(-0.0903544\pi\) | |||||||
\(284\) | 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 | −0.456811 | − | 0.889564i | \(-0.651009\pi\) |
−0.952031 | + | 0.306002i | \(0.901009\pi\) | |||||||
\(294\) | 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 | 0.977728 | − | 0.209874i | \(-0.0673054\pi\) |
−0.839762 | + | 0.542955i | \(0.817305\pi\) | |||||||
\(308\) | 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 | 0.967200 | − | 0.254017i | \(-0.0817518\pi\) |
−0.863530 | + | 0.504297i | \(0.831752\pi\) | |||||||
\(318\) | 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 | 0.186006 | − | 0.982549i | \(-0.440446\pi\) |
−0.563240 | + | 0.826293i | \(0.690446\pi\) | |||||||
\(332\) | 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 | \(-0.705177\pi\) |
0.990102 | − | 0.140350i | \(-0.0448226\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 187.869 | + | 453.555i | 0.538305 | + | 1.29958i | 0.925905 | + | 0.377756i | \(0.123304\pi\) |
−0.387600 | + | 0.921828i | \(0.626696\pi\) | |||||||
\(350\) | 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 | −0.973887 | − | 0.227032i | \(-0.927098\pi\) |
0.849178 | + | 0.528106i | \(0.177098\pi\) | |||||||
\(374\) | 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 | \(0.327160\pi\) |
−0.970763 | + | 0.240040i | \(0.922840\pi\) | |||||||
\(380\) | 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 | 0.453327 | − | 0.891344i | \(-0.350237\pi\) |
−0.309725 | + | 0.950826i | \(0.600237\pi\) | |||||||
\(390\) | 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 | −0.466271 | − | 0.884642i | \(-0.654403\pi\) |
0.295833 | + | 0.955240i | \(0.404403\pi\) | |||||||
\(398\) | 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 | 0.0636205 | − | 0.997974i | \(-0.479735\pi\) |
0.750661 | + | 0.660688i | \(0.229735\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 339.196 | + | 140.500i | 0.805692 | + | 0.333728i | 0.747234 | − | 0.664561i | \(-0.231382\pi\) |
0.0584581 | + | 0.998290i | \(0.481382\pi\) | |||||||
\(422\) | 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 | \(0.363532\pi\) |
−0.937064 | + | 0.349158i | \(0.886468\pi\) | |||||||
\(444\) | 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 | 0.227690 | − | 0.973734i | \(-0.426883\pi\) |
0.849535 | + | 0.527533i | \(0.176883\pi\) | |||||||
\(462\) | 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 | 0.881307 | − | 0.472544i | \(-0.156664\pi\) |
−0.957317 | + | 0.289040i | \(0.906664\pi\) | |||||||
\(468\) | 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 | 0.0774824 | − | 0.996994i | \(-0.475312\pi\) |
−0.650193 | + | 0.759769i | \(0.725312\pi\) | |||||||
\(492\) | 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 | \(0.0871639\pi\) |
−0.489542 | + | 0.871980i | \(0.662836\pi\) | |||||||
\(500\) | 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 | 0.971258 | − | 0.238028i | \(-0.0765011\pi\) |
−0.855095 | + | 0.518472i | \(0.826501\pi\) | |||||||
\(510\) | 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 | 0.927037 | − | 0.374970i | \(-0.122347\pi\) |
0.390370 | + | 0.920658i | \(0.372347\pi\) | |||||||
\(524\) | 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 | \(-0.872793\pi\) |
0.376267 | − | 0.926511i | \(-0.377207\pi\) | |||||||
\(542\) | 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 | −0.802736 | − | 0.596335i | \(-0.796623\pi\) |
−0.145948 | + | 0.989292i | \(0.546623\pi\) | |||||||
\(548\) | 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 | −0.989380 | − | 0.145355i | \(-0.953568\pi\) |
−0.596816 | + | 0.802378i | \(0.703568\pi\) | |||||||
\(558\) | 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 | \(-0.773168\pi\) |
0.0727214 | − | 0.997352i | \(-0.476832\pi\) | |||||||
\(564\) | 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 | −0.876089 | − | 0.482149i | \(-0.839856\pi\) |
0.960419 | + | 0.278558i | \(0.0898564\pi\) | |||||||
\(572\) | 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 | 0.763236 | − | 0.646120i | \(-0.223610\pi\) |
0.0828132 | + | 0.996565i | \(0.473610\pi\) | |||||||
\(588\) | 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 | 0.968464 | − | 0.249152i | \(-0.0801518\pi\) |
0.508631 | + | 0.860985i | \(0.330152\pi\) | |||||||
\(614\) | 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 | 0.0770649 | − | 0.997026i | \(-0.475445\pi\) |
−0.650511 | + | 0.759497i | \(0.725445\pi\) | |||||||
\(620\) | 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 | −0.212479 | − | 0.977166i | \(-0.568154\pi\) |
0.540715 | + | 0.841206i | \(0.318154\pi\) | |||||||
\(644\) | 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 | −0.799082 | − | 0.601222i | \(-0.794681\pi\) |
−0.139909 | + | 0.990164i | \(0.544681\pi\) | |||||||
\(654\) | 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 | 0.937962 | − | 0.346738i | \(-0.112711\pi\) |
−0.908420 | + | 0.418058i | \(0.862711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.1458 | − | 111.406i | 0.0698122 | − | 0.168541i | −0.885122 | − | 0.465359i | \(-0.845925\pi\) |
0.954934 | + | 0.296817i | \(0.0959253\pi\) | |||||||
\(662\) | 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 | \(-0.984035\pi\) |
−0.741669 | − | 0.670766i | \(-0.765965\pi\) | |||||||
\(678\) | 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 | 0.664861 | − | 0.746967i | \(-0.268491\pi\) |
−0.0580582 | + | 0.998313i | \(0.518491\pi\) | |||||||
\(684\) | 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 | \(-0.955356\pi\) |
0.601314 | − | 0.799012i | \(-0.294644\pi\) | |||||||
\(692\) | 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 | \(0.208026\pi\) |
−0.131484 | + | 0.991318i | \(0.541974\pi\) | |||||||
\(702\) | 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 | 0.758863 | − | 0.651250i | \(-0.225755\pi\) |
0.0760937 | + | 0.997101i | \(0.475755\pi\) | |||||||
\(710\) | 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 | 0.776811 | − | 0.629734i | \(-0.216836\pi\) |
−0.994577 | + | 0.103999i | \(0.966836\pi\) | |||||||
\(734\) | 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 | −0.110073 | − | 0.993924i | \(-0.535108\pi\) |
0.624977 | + | 0.780643i | \(0.285108\pi\) | |||||||
\(740\) | 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 | −0.929914 | − | 0.367778i | \(-0.880119\pi\) |
0.917607 | + | 0.397490i | \(0.130119\pi\) | |||||||
\(758\) | 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 | 0.506284 | − | 0.862367i | \(-0.331019\pi\) |
−0.251789 | + | 0.967782i | \(0.581019\pi\) | |||||||
\(774\) | 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 | 0.864293 | − | 0.502990i | \(-0.167767\pi\) |
−0.966814 | + | 0.255480i | \(0.917767\pi\) | |||||||
\(788\) | 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 | \(-0.986852\pi\) |
0.677304 | − | 0.735704i | \(-0.263148\pi\) | |||||||
\(798\) | 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 | 0.986497 | − | 0.163780i | \(-0.0523688\pi\) |
0.581748 | + | 0.813369i | \(0.302369\pi\) | |||||||
\(812\) | 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 | −0.979932 | − | 0.199330i | \(-0.936123\pi\) |
0.833865 | + | 0.551969i | \(0.186123\pi\) | |||||||
\(822\) | 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 | \(0.252343\pi\) |
−0.999973 | + | 0.00736012i | \(0.997657\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 393.211 | + | 949.295i | 0.474319 | + | 1.14511i | 0.962236 | + | 0.272218i | \(0.0877571\pi\) |
−0.487916 | + | 0.872890i | \(0.662243\pi\) | |||||||
\(830\) | 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 | \(-0.720813\pi\) |
0.995799 | − | 0.0915645i | \(-0.0291868\pi\) | |||||||
\(854\) | 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 | \(0.360485\pi\) |
−0.940364 | + | 0.340170i | \(0.889515\pi\) | |||||||
\(860\) | 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 | 0.0261554 | − | 0.999658i | \(-0.491674\pi\) |
0.725360 | + | 0.688370i | \(0.241674\pi\) | |||||||
\(878\) | 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 | 0.976733 | − | 0.214459i | \(-0.0687989\pi\) |
−0.842300 | + | 0.539009i | \(0.818799\pi\) | |||||||
\(884\) | 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 | −0.0454897 | − | 0.998965i | \(-0.514485\pi\) |
−0.738541 | + | 0.674209i | \(0.764485\pi\) | |||||||
\(908\) | 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 | −0.802628 | − | 0.596480i | \(-0.796566\pi\) |
−0.145769 | + | 0.989319i | \(0.546566\pi\) | |||||||
\(942\) | 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 | \(-0.946521\pi\) |
0.578907 | − | 0.815394i | \(-0.303479\pi\) | |||||||
\(948\) | 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 | 0.490057 | − | 0.871690i | \(-0.336976\pi\) |
−0.269856 | + | 0.962901i | \(0.586976\pi\) | |||||||
\(972\) | 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 | 0.233679 | − | 0.972314i | \(-0.424923\pi\) |
−0.522294 | + | 0.852766i | \(0.674923\pi\) | |||||||
\(998\) | 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 | 128.3.h.a.15.5 | 28 | ||
4.3 | odd | 2 | 32.3.h.a.27.6 | yes | 28 | ||
8.3 | odd | 2 | 256.3.h.b.31.5 | 28 | |||
8.5 | even | 2 | 256.3.h.a.31.3 | 28 | |||
12.11 | even | 2 | 288.3.u.a.91.2 | 28 | |||
32.3 | odd | 8 | 256.3.h.a.223.3 | 28 | |||
32.13 | even | 8 | 32.3.h.a.19.6 | ✓ | 28 | ||
32.19 | odd | 8 | inner | 128.3.h.a.111.5 | 28 | ||
32.29 | even | 8 | 256.3.h.b.223.5 | 28 | |||
96.77 | 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 | 32.13 | even | 8 | ||
32.3.h.a.27.6 | yes | 28 | 4.3 | odd | 2 | ||
128.3.h.a.15.5 | 28 | 1.1 | even | 1 | trivial | ||
128.3.h.a.111.5 | 28 | 32.19 | odd | 8 | inner | ||
256.3.h.a.31.3 | 28 | 8.5 | even | 2 | |||
256.3.h.a.223.3 | 28 | 32.3 | odd | 8 | |||
256.3.h.b.31.5 | 28 | 8.3 | odd | 2 | |||
256.3.h.b.223.5 | 28 | 32.29 | even | 8 | |||
288.3.u.a.19.2 | 28 | 96.77 | odd | 8 | |||
288.3.u.a.91.2 | 28 | 12.11 | even | 2 |