Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [512,2,Mod(129,512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(512, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("512.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 512 = 2^{9} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 512.e (of order \(4\), degree \(2\), 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: | \(4.08834058349\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(-0.382683 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 512.129 |
Dual form | 512.2.e.j.385.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/512\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.84776 | − | 1.84776i | −1.06680 | − | 1.06680i | −0.997603 | − | 0.0692015i | \(-0.977955\pi\) |
−0.0692015 | − | 0.997603i | \(-0.522045\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.41421 | − | 2.41421i | 1.07967 | − | 1.07967i | 0.0831305 | − | 0.996539i | \(-0.473508\pi\) |
0.996539 | − | 0.0831305i | \(-0.0264918\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.53073i | − | 0.578563i | −0.957244 | − | 0.289281i | \(-0.906584\pi\) | ||
0.957244 | − | 0.289281i | \(-0.0934164\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.82843i | 1.27614i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.37849 | − | 3.37849i | 1.01865 | − | 1.01865i | 0.0188312 | − | 0.999823i | \(-0.494005\pi\) |
0.999823 | − | 0.0188312i | \(-0.00599452\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.414214 | + | 0.414214i | 0.114882 | + | 0.114882i | 0.762211 | − | 0.647329i | \(-0.224114\pi\) |
−0.647329 | + | 0.762211i | \(0.724114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −8.92177 | −2.30359 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.82843 | 0.685994 | 0.342997 | − | 0.939336i | \(-0.388558\pi\) | ||||
0.342997 | + | 0.939336i | \(0.388558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.317025 | − | 0.317025i | −0.0727306 | − | 0.0727306i | 0.669806 | − | 0.742536i | \(-0.266377\pi\) |
−0.742536 | + | 0.669806i | \(0.766377\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.82843 | + | 2.82843i | −0.617213 | + | 0.617213i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.86030i | 1.22196i | 0.791647 | + | 0.610979i | \(0.209224\pi\) | ||||
−0.791647 | + | 0.610979i | \(0.790776\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 6.65685i | − | 1.33137i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.53073 | − | 1.53073i | 0.294590 | − | 0.294590i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.24264 | − | 3.24264i | −0.602143 | − | 0.602143i | 0.338738 | − | 0.940881i | \(-0.390000\pi\) |
−0.940881 | + | 0.338738i | \(0.890000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.39104 | −1.32747 | −0.663735 | − | 0.747968i | \(-0.731030\pi\) | ||||
−0.663735 | + | 0.747968i | \(0.731030\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.4853 | −2.17341 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.69552 | − | 3.69552i | −0.624657 | − | 0.624657i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.58579 | + | 3.58579i | −0.589500 | + | 0.589500i | −0.937496 | − | 0.347996i | \(-0.886862\pi\) |
0.347996 | + | 0.937496i | \(0.386862\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.53073i | − | 0.245114i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.00000i | − | 0.624695i | −0.949968 | − | 0.312348i | \(-0.898885\pi\) | ||
0.949968 | − | 0.312348i | \(-0.101115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.84776 | − | 1.84776i | 0.281781 | − | 0.281781i | −0.552038 | − | 0.833819i | \(-0.686150\pi\) |
0.833819 | + | 0.552038i | \(0.186150\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.24264 | + | 9.24264i | 1.37781 | + | 1.37781i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.39104 | 1.07809 | 0.539047 | − | 0.842276i | \(-0.318785\pi\) | ||||
0.539047 | + | 0.842276i | \(0.318785\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.65685 | 0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.22625 | − | 5.22625i | −0.731822 | − | 0.731822i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.24264 | + | 5.24264i | −0.720132 | + | 0.720132i | −0.968632 | − | 0.248500i | \(-0.920062\pi\) |
0.248500 | + | 0.968632i | \(0.420062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 16.3128i | − | 2.19962i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17157i | 0.155179i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.84776 | − | 1.84776i | 0.240558 | − | 0.240558i | −0.576523 | − | 0.817081i | \(-0.695591\pi\) |
0.817081 | + | 0.576523i | \(0.195591\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.24264 | − | 9.24264i | −1.18340 | − | 1.18340i | −0.978858 | − | 0.204541i | \(-0.934430\pi\) |
−0.204541 | − | 0.978858i | \(-0.565570\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.86030 | 0.738329 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.07401 | + | 7.07401i | 0.864228 | + | 0.864228i | 0.991826 | − | 0.127598i | \(-0.0407267\pi\) |
−0.127598 | + | 0.991826i | \(0.540727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.8284 | − | 10.8284i | 1.30359 | − | 1.30359i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9832i | 1.42215i | 0.703117 | + | 0.711074i | \(0.251791\pi\) | ||||
−0.703117 | + | 0.711074i | \(0.748209\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4853i | 1.22721i | 0.789613 | + | 0.613605i | \(0.210281\pi\) | ||||
−0.789613 | + | 0.613605i | \(0.789719\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.3003 | + | 12.3003i | −1.42031 | + | 1.42031i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.17157 | − | 5.17157i | −0.589355 | − | 0.589355i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.12293 | 0.688884 | 0.344442 | − | 0.938808i | \(-0.388068\pi\) | ||||
0.344442 | + | 0.938808i | \(0.388068\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.82843 | 0.647603 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.48181 | + | 2.48181i | 0.272414 | + | 0.272414i | 0.830071 | − | 0.557657i | \(-0.188300\pi\) |
−0.557657 | + | 0.830071i | \(0.688300\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.82843 | − | 6.82843i | 0.740647 | − | 0.740647i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.9832i | 1.28474i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.828427i | 0.0878131i | 0.999036 | + | 0.0439065i | \(0.0139804\pi\) | ||||
−0.999036 | + | 0.0439065i | \(0.986020\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.634051 | − | 0.634051i | 0.0664666 | − | 0.0664666i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 13.6569 | + | 13.6569i | 1.41615 | + | 1.41615i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.53073 | −0.157050 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8284 | 1.09946 | 0.549730 | − | 0.835342i | \(-0.314731\pi\) | ||||
0.549730 | + | 0.835342i | \(0.314731\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.9343 | + | 12.9343i | 1.29995 | + | 1.29995i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.07107 | − | 2.07107i | 0.206079 | − | 0.206079i | −0.596520 | − | 0.802599i | \(-0.703450\pi\) |
0.802599 | + | 0.596520i | \(0.203450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.79884i | − | 0.275777i | −0.990448 | − | 0.137889i | \(-0.955968\pi\) | ||
0.990448 | − | 0.137889i | \(-0.0440316\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.6569i | 1.33277i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.07401 | + | 7.07401i | −0.683870 | + | 0.683870i | −0.960870 | − | 0.277000i | \(-0.910660\pi\) |
0.277000 | + | 0.960870i | \(0.410660\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.757359 | + | 0.757359i | 0.0725419 | + | 0.0725419i | 0.742447 | − | 0.669905i | \(-0.233665\pi\) |
−0.669905 | + | 0.742447i | \(0.733665\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.2513 | 1.25776 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.65685 | −0.344008 | −0.172004 | − | 0.985096i | \(-0.555024\pi\) | ||||
−0.172004 | + | 0.985096i | \(0.555024\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.1480 | + | 14.1480i | 1.31931 | + | 1.31931i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.58579 | + | 1.58579i | −0.146606 | + | 0.146606i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.32957i | − | 0.396891i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 11.8284i | − | 1.07531i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.39104 | + | 7.39104i | −0.666427 | + | 0.666427i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.00000 | − | 4.00000i | −0.357771 | − | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.5140 | 1.19917 | 0.599586 | − | 0.800311i | \(-0.295332\pi\) | ||||
0.599586 | + | 0.800311i | \(0.295332\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.82843 | −0.601209 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.43996 | − | 6.43996i | −0.562662 | − | 0.562662i | 0.367401 | − | 0.930063i | \(-0.380248\pi\) |
−0.930063 | + | 0.367401i | \(0.880248\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.485281 | + | 0.485281i | −0.0420792 | + | 0.0420792i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 7.39104i | − | 0.636119i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 20.9706i | − | 1.79164i | −0.444421 | − | 0.895818i | \(-0.646591\pi\) | ||
0.444421 | − | 0.895818i | \(-0.353409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.5684 | − | 13.5684i | 1.15085 | − | 1.15085i | 0.164472 | − | 0.986382i | \(-0.447408\pi\) |
0.986382 | − | 0.164472i | \(-0.0525920\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.6569 | − | 13.6569i | −1.15011 | − | 1.15011i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.79884 | 0.234050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.6569 | −1.30023 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.60474 | − | 8.60474i | −0.709707 | − | 0.709707i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.24264 | + | 7.24264i | −0.593340 | + | 0.593340i | −0.938532 | − | 0.345192i | \(-0.887814\pi\) |
0.345192 | + | 0.938532i | \(0.387814\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.92177i | − | 0.726043i | −0.931781 | − | 0.363022i | \(-0.881745\pi\) | ||
0.931781 | − | 0.363022i | \(-0.118255\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.8284i | 0.875426i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −17.8435 | + | 17.8435i | −1.43323 | + | 1.43323i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.41421 | + | 4.41421i | 0.352293 | + | 0.352293i | 0.860962 | − | 0.508669i | \(-0.169862\pi\) |
−0.508669 | + | 0.860962i | \(0.669862\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.3743 | 1.53648 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.97056 | 0.706979 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.23880 | − | 9.23880i | −0.723638 | − | 0.723638i | 0.245706 | − | 0.969344i | \(-0.420980\pi\) |
−0.969344 | + | 0.245706i | \(0.920980\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −30.1421 | + | 30.1421i | −2.34656 | + | 2.34656i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 1.53073i | − | 0.118452i | −0.998245 | − | 0.0592259i | \(-0.981137\pi\) | ||
0.998245 | − | 0.0592259i | \(-0.0188632\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.6569i | − | 0.973604i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.21371 | − | 1.21371i | 0.0928146 | − | 0.0928146i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.4142 | + | 16.4142i | 1.24795 | + | 1.24795i | 0.956624 | + | 0.291326i | \(0.0940963\pi\) |
0.291326 | + | 0.956624i | \(0.405904\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.1899 | −0.770282 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.82843 | −0.513256 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.21371 | + | 1.21371i | 0.0907168 | + | 0.0907168i | 0.751009 | − | 0.660292i | \(-0.229568\pi\) |
−0.660292 | + | 0.751009i | \(0.729568\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.07107 | − | 4.07107i | 0.302600 | − | 0.302600i | −0.539430 | − | 0.842030i | \(-0.681360\pi\) |
0.842030 | + | 0.539430i | \(0.181360\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 34.1563i | 2.52491i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.3137i | 1.27293i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.55582 | − | 9.55582i | 0.698791 | − | 0.698791i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.34315 | − | 2.34315i | −0.170439 | − | 0.170439i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5140 | −0.977837 | −0.488918 | − | 0.872330i | \(-0.662608\pi\) | ||||
−0.488918 | + | 0.872330i | \(0.662608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.4853 | −1.18664 | −0.593318 | − | 0.804968i | \(-0.702182\pi\) | ||||
−0.593318 | + | 0.804968i | \(0.702182\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.69552 | − | 3.69552i | −0.264642 | − | 0.264642i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.4142 | − | 10.4142i | 0.741982 | − | 0.741982i | −0.230977 | − | 0.972959i | \(-0.574192\pi\) |
0.972959 | + | 0.230977i | \(0.0741923\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.4357i | − | 1.59043i | −0.606329 | − | 0.795214i | \(-0.707359\pi\) | ||
0.606329 | − | 0.795214i | \(-0.292641\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 26.1421i | − | 1.84392i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.96362 | + | 4.96362i | −0.348378 | + | 0.348378i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.65685 | − | 9.65685i | −0.674464 | − | 0.674464i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.4357 | −1.55939 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.14214 | −0.148175 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0572 | + | 19.0572i | 1.31196 | + | 1.31196i | 0.919973 | + | 0.391982i | \(0.128211\pi\) |
0.391982 | + | 0.919973i | \(0.371789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.1421 | − | 22.1421i | 1.51715 | − | 1.51715i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.92177i | − | 0.608460i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.3137i | 0.768025i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.3743 | − | 19.3743i | 1.30919 | − | 1.30919i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.17157 | + | 1.17157i | 0.0788085 | + | 0.0788085i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.39104 | −0.494940 | −0.247470 | − | 0.968896i | \(-0.579599\pi\) | ||||
−0.247470 | + | 0.968896i | \(0.579599\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 25.4853 | 1.69902 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.84776 | − | 1.84776i | −0.122640 | − | 0.122640i | 0.643123 | − | 0.765763i | \(-0.277638\pi\) |
−0.765763 | + | 0.643123i | \(0.777638\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.2426 | + | 11.2426i | −0.742935 | + | 0.742935i | −0.973142 | − | 0.230207i | \(-0.926060\pi\) |
0.230207 | + | 0.973142i | \(0.426060\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 19.1116i | 1.25745i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1716i | 0.993923i | 0.867773 | + | 0.496961i | \(0.165551\pi\) | ||||
−0.867773 | + | 0.496961i | \(0.834449\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.8435 | − | 17.8435i | 1.16398 | − | 1.16398i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.3137 | − | 11.3137i | −0.734904 | − | 0.734904i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −29.5641 | −1.91235 | −0.956173 | − | 0.292803i | \(-0.905412\pi\) | ||||
−0.956173 | + | 0.292803i | \(0.905412\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8284 | 1.21285 | 0.606423 | − | 0.795142i | \(-0.292604\pi\) | ||||
0.606423 | + | 0.795142i | \(0.292604\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.3617 | − | 15.3617i | −0.985455 | − | 0.985455i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.2426 | − | 11.2426i | 0.718266 | − | 0.718266i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.262632i | − | 0.0167109i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 9.17157i | − | 0.581225i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.87285 | + | 9.87285i | −0.623169 | + | 0.623169i | −0.946340 | − | 0.323172i | \(-0.895251\pi\) |
0.323172 | + | 0.946340i | \(0.395251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.7990 | + | 19.7990i | 1.24475 | + | 1.24475i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −25.2346 | −1.58025 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.9706 | 1.18335 | 0.591676 | − | 0.806176i | \(-0.298467\pi\) | ||||
0.591676 | + | 0.806176i | \(0.298467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.48888 | + | 5.48888i | 0.341063 | + | 0.341063i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.4142 | − | 12.4142i | 0.768421 | − | 0.768421i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.6424i | 1.27286i | 0.771333 | + | 0.636432i | \(0.219590\pi\) | ||||
−0.771333 | + | 0.636432i | \(0.780410\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.3137i | 1.55501i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.53073 | − | 1.53073i | 0.0936794 | − | 0.0936794i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.92893 | − | 3.92893i | −0.239551 | − | 0.239551i | 0.577113 | − | 0.816664i | \(-0.304179\pi\) |
−0.816664 | + | 0.577113i | \(0.804179\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.2960 | 1.71886 | 0.859431 | − | 0.511252i | \(-0.170818\pi\) | ||||
0.859431 | + | 0.511252i | \(0.170818\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.34315 | −0.141814 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.4901 | − | 22.4901i | −1.35621 | − | 1.35621i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.414214 | − | 0.414214i | 0.0248877 | − | 0.0248877i | −0.694553 | − | 0.719441i | \(-0.744398\pi\) |
0.719441 | + | 0.694553i | \(0.244398\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 28.2960i | − | 1.69404i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.7990i | 1.30042i | 0.759755 | + | 0.650209i | \(0.225319\pi\) | ||||
−0.759755 | + | 0.650209i | \(0.774681\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.43996 | − | 6.43996i | 0.382816 | − | 0.382816i | −0.489300 | − | 0.872116i | \(-0.662748\pi\) |
0.872116 | + | 0.489300i | \(0.162748\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.82843 | + | 2.82843i | 0.167542 | + | 0.167542i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.12293 | −0.361425 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.00000 | −0.529412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.0083 | − | 20.0083i | −1.17291 | − | 1.17291i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.41421 | − | 2.41421i | 0.141040 | − | 0.141040i | −0.633062 | − | 0.774101i | \(-0.718202\pi\) |
0.774101 | + | 0.633062i | \(0.218202\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8.92177i | − | 0.519446i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 10.3431i | − | 0.600170i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.42742 | + | 2.42742i | −0.140381 | + | 0.140381i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.82843 | − | 2.82843i | −0.163028 | − | 0.163028i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.65367 | −0.439692 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −44.6274 | −2.55536 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.1606 | − | 18.1606i | −1.03648 | − | 1.03648i | −0.999309 | − | 0.0371692i | \(-0.988166\pi\) |
−0.0371692 | − | 0.999309i | \(-0.511834\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.17157 | + | 5.17157i | −0.294201 | + | 0.294201i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.12840i | 0.404215i | 0.979363 | + | 0.202107i | \(0.0647790\pi\) | ||||
−0.979363 | + | 0.202107i | \(0.935221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.68629i | 0.490978i | 0.969399 | + | 0.245489i | \(0.0789486\pi\) | ||||
−0.969399 | + | 0.245489i | \(0.921051\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 14.1480 | − | 14.1480i | 0.797151 | − | 0.797151i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.89949 | − | 8.89949i | −0.499845 | − | 0.499845i | 0.411544 | − | 0.911390i | \(-0.364990\pi\) |
−0.911390 | + | 0.411544i | \(0.864990\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.9105 | −1.22675 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.1421 | 1.45911 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.896683 | − | 0.896683i | −0.0498928 | − | 0.0498928i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.75736 | − | 2.75736i | 0.152951 | − | 0.152951i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 2.79884i | − | 0.154776i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 11.3137i | − | 0.623745i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.01254 | + | 4.01254i | −0.220549 | + | 0.220549i | −0.808730 | − | 0.588180i | \(-0.799844\pi\) |
0.588180 | + | 0.808730i | \(0.299844\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.7279 | − | 13.7279i | −0.752285 | − | 0.752285i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.1563 | 1.86616 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000 | 0.326841 | 0.163420 | − | 0.986557i | \(-0.447747\pi\) | ||||
0.163420 | + | 0.986557i | \(0.447747\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.75699 | + | 6.75699i | 0.366989 | + | 0.366989i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.9706 | + | 24.9706i | −1.35223 | + | 1.35223i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 17.8435i | − | 0.963461i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 52.2843i | − | 2.81489i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.3617 | − | 15.3617i | 0.824661 | − | 0.824661i | −0.162112 | − | 0.986772i | \(-0.551830\pi\) |
0.986772 | + | 0.162112i | \(0.0518304\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.0711 | + | 16.0711i | 0.860265 | + | 0.860265i | 0.991369 | − | 0.131104i | \(-0.0418522\pi\) |
−0.131104 | + | 0.991369i | \(0.541852\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.26810 | 0.0676862 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.9706 | −0.583904 | −0.291952 | − | 0.956433i | \(-0.594305\pi\) | ||||
−0.291952 | + | 0.956433i | \(0.594305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.9301 | + | 28.9301i | 1.53545 | + | 1.53545i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.00000 | + | 8.00000i | −0.423405 | + | 0.423405i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 8.92177i | − | 0.470873i | −0.971890 | − | 0.235437i | \(-0.924348\pi\) | ||
0.971890 | − | 0.235437i | \(-0.0756520\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 18.7990i | − | 0.989421i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −21.8561 | + | 21.8561i | −1.14715 | + | 1.14715i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 25.3137 | + | 25.3137i | 1.32498 | + | 1.32498i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.1731 | −1.15743 | −0.578713 | − | 0.815531i | \(-0.696445\pi\) | ||||
−0.578713 | + | 0.815531i | \(0.696445\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 15.3137 | 0.797200 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.02509 | + | 8.02509i | 0.416642 | + | 0.416642i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.2426 | + | 13.2426i | −0.685678 | + | 0.685678i | −0.961274 | − | 0.275596i | \(-0.911125\pi\) |
0.275596 | + | 0.961274i | \(0.411125\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.7821i | 0.763343i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.68629i | − | 0.138351i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.11586 | − | 3.11586i | 0.160051 | − | 0.160051i | −0.622538 | − | 0.782589i | \(-0.713899\pi\) |
0.782589 | + | 0.622538i | \(0.213899\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.9706 | − | 24.9706i | −1.27928 | − | 1.27928i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.65914 | 0.442461 | 0.221231 | − | 0.975222i | \(-0.428993\pi\) | ||||
0.221231 | + | 0.975222i | \(0.428993\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.9706 | −1.27262 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.07401 | + | 7.07401i | 0.359592 | + | 0.359592i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.5858 | + | 11.5858i | −0.587423 | + | 0.587423i | −0.936933 | − | 0.349510i | \(-0.886348\pi\) |
0.349510 | + | 0.936933i | \(0.386348\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.5754i | 0.838256i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 23.7990i | 1.20050i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 14.7821 | − | 14.7821i | 0.743767 | − | 0.743767i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.41421 | + | 6.41421i | 0.321920 | + | 0.321920i | 0.849503 | − | 0.527583i | \(-0.176902\pi\) |
−0.527583 | + | 0.849503i | \(0.676902\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.79337 | 0.0897806 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.4853 | −1.22274 | −0.611368 | − | 0.791346i | \(-0.709381\pi\) | ||||
−0.611368 | + | 0.791346i | \(0.709381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.06147 | − | 3.06147i | −0.152503 | − | 0.152503i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 14.0711 | − | 14.0711i | 0.699197 | − | 0.699197i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.2291i | 1.20099i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.68629i | 0.429509i | 0.976668 | + | 0.214755i | \(0.0688952\pi\) | ||||
−0.976668 | + | 0.214755i | \(0.931105\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −38.7485 | + | 38.7485i | −1.91132 | + | 1.91132i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.82843 | − | 2.82843i | −0.139178 | − | 0.139178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.9832 | 0.588234 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −50.1421 | −2.45547 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1355 | + | 10.1355i | 0.495151 | + | 0.495151i | 0.909924 | − | 0.414774i | \(-0.136139\pi\) |
−0.414774 | + | 0.909924i | \(0.636139\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.07107 | − | 8.07107i | 0.393360 | − | 0.393360i | −0.482523 | − | 0.875883i | \(-0.660280\pi\) |
0.875883 | + | 0.482523i | \(0.160280\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28.2960i | 1.37580i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 18.8284i | − | 0.913313i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.1480 | + | 14.1480i | −0.684671 | + | 0.684671i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.17157 | − | 5.17157i | −0.249686 | − | 0.249686i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.4558 | 1.22333 | 0.611665 | − | 0.791117i | \(-0.290500\pi\) | ||||
0.611665 | + | 0.791117i | \(0.290500\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 28.9301 | + | 28.9301i | 1.38709 | + | 1.38709i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.85786 | − | 1.85786i | 0.0888737 | − | 0.0888737i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 18.8490i | − | 0.899614i | −0.893126 | − | 0.449807i | \(-0.851493\pi\) | ||
0.893126 | − | 0.449807i | \(-0.148507\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.8284i | 0.848973i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.07401 | + | 7.07401i | −0.336096 | + | 0.336096i | −0.854896 | − | 0.518800i | \(-0.826379\pi\) |
0.518800 | + | 0.854896i | \(0.326379\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.00000 | + | 2.00000i | 0.0948091 | + | 0.0948091i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.7653 | 1.26596 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.1421 | 1.04495 | 0.522476 | − | 0.852654i | \(-0.325008\pi\) | ||||
0.522476 | + | 0.852654i | \(0.325008\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.5140 | − | 13.5140i | −0.636348 | − | 0.636348i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.4853 | + | 16.4853i | −0.774546 | + | 0.774546i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 3.06147i | − | 0.143524i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6274i | 0.871354i | 0.900103 | + | 0.435677i | \(0.143491\pi\) | ||||
−0.900103 | + | 0.435677i | \(0.856509\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.32957 | − | 4.32957i | 0.202087 | − | 0.202087i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.0416 | + | 21.0416i | 0.980006 | + | 0.980006i | 0.999804 | − | 0.0197976i | \(-0.00630217\pi\) |
−0.0197976 | + | 0.999804i | \(0.506302\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.53620 | 0.117867 | 0.0589337 | − | 0.998262i | \(-0.481230\pi\) | ||||
0.0589337 | + | 0.998262i | \(0.481230\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 65.9411 | 3.05795 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6717 | + | 12.6717i | 0.586375 | + | 0.586375i | 0.936648 | − | 0.350272i | \(-0.113911\pi\) |
−0.350272 | + | 0.936648i | \(0.613911\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.8284 | − | 10.8284i | 0.500010 | − | 0.500010i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 16.3128i | − | 0.751654i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 12.4853i | − | 0.574074i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.11039 | + | 2.11039i | −0.0968314 | + | 0.0968314i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.0711 | − | 20.0711i | −0.918991 | − | 0.918991i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.5419 | 1.85241 | 0.926204 | − | 0.377024i | \(-0.123052\pi\) | ||||
0.926204 | + | 0.377024i | \(0.123052\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.97056 | −0.135446 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.5754 | − | 16.5754i | −0.754209 | − | 0.754209i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.1421 | − | 26.1421i | 1.18705 | − | 1.18705i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 37.2178i | − | 1.68650i | −0.537521 | − | 0.843250i | \(-0.680639\pi\) | ||
0.537521 | − | 0.843250i | \(-0.319361\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.1421i | 1.54396i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.3003 | − | 12.3003i | 0.555103 | − | 0.555103i | −0.372806 | − | 0.927909i | \(-0.621604\pi\) |
0.927909 | + | 0.372806i | \(0.121604\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.17157 | − | 9.17157i | −0.413067 | − | 0.413067i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 62.4524 | 2.80703 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.3431 | 0.822803 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.6662 | + | 11.6662i | 0.522251 | + | 0.522251i | 0.918251 | − | 0.395999i | \(-0.129602\pi\) |
−0.395999 | + | 0.918251i | \(0.629602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.82843 | + | 2.82843i | −0.126365 | + | 0.126365i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.1062i | 0.807314i | 0.914910 | + | 0.403657i | \(0.132261\pi\) | ||||
−0.914910 | + | 0.403657i | \(0.867739\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.0000i | − | 0.444994i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −23.3868 | + | 23.3868i | −1.03865 | + | 1.03865i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.5563 | − | 12.5563i | −0.556550 | − | 0.556550i | 0.371773 | − | 0.928324i | \(-0.378750\pi\) |
−0.928324 | + | 0.371773i | \(0.878750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0502 | 0.710018 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.970563 | −0.0428514 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.75699 | − | 6.75699i | −0.297748 | − | 0.297748i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.9706 | − | 24.9706i | 1.09820 | − | 1.09820i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 60.6590i | − | 2.66264i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.6569i | 0.773561i | 0.922172 | + | 0.386780i | \(0.126413\pi\) | ||||
−0.922172 | + | 0.386780i | \(0.873587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.9790 | + | 27.9790i | −1.22344 | + | 1.22344i | −0.257035 | + | 0.966402i | \(0.582746\pi\) |
−0.966402 | + | 0.257035i | \(0.917254\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.8284 | + | 18.8284i | 0.821740 | + | 0.821740i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.9050 | −0.910636 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3431 | −0.493180 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.07401 | + | 7.07401i | 0.306986 | + | 0.306986i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.65685 | − | 1.65685i | 0.0717663 | − | 0.0717663i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.1563i | 1.47671i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 4.48528i | − | 0.193554i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.7331 | − | 15.7331i | 0.677675 | − | 0.677675i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.24264 | − | 1.24264i | −0.0534253 | − | 0.0534253i | 0.679889 | − | 0.733315i | \(-0.262028\pi\) |
−0.733315 | + | 0.679889i | \(0.762028\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −15.0447 | −0.645630 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.65685 | 0.156642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.951076 | + | 0.951076i | 0.0406651 | + | 0.0406651i | 0.727147 | − | 0.686482i | \(-0.240846\pi\) |
−0.686482 | + | 0.727147i | \(0.740846\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 35.3848 | − | 35.3848i | 1.51019 | − | 1.51019i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.05600i | 0.0875885i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9.37258i | − | 0.398563i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 31.9916 | − | 31.9916i | 1.35797 | − | 1.35797i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.07107 | + | 6.07107i | 0.257239 | + | 0.257239i | 0.823930 | − | 0.566691i | \(-0.191777\pi\) |
−0.566691 | + | 0.823930i | \(0.691777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.53073 | 0.0647431 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −35.3137 | −1.49095 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.0991 | − | 15.0991i | −0.636351 | − | 0.636351i | 0.313302 | − | 0.949653i | \(-0.398565\pi\) |
−0.949653 | + | 0.313302i | \(0.898565\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.82843 | + | 8.82843i | −0.371415 | + | 0.371415i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 8.92177i | − | 0.374679i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.3431i | 0.601296i | 0.953735 | + | 0.300648i | \(0.0972029\pi\) | ||||
−0.953735 | + | 0.300648i | \(0.902797\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.7331 | + | 15.7331i | −0.658412 | + | 0.658412i | −0.955004 | − | 0.296592i | \(-0.904150\pi\) |
0.296592 | + | 0.955004i | \(0.404150\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 24.9706 | + | 24.9706i | 1.04316 | + | 1.04316i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 39.0112 | 1.62688 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.31371 | −0.221213 | −0.110606 | − | 0.993864i | \(-0.535279\pi\) | ||||
−0.110606 | + | 0.993864i | \(0.535279\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 30.4608 | + | 30.4608i | 1.26591 | + | 1.26591i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.79899 | − | 3.79899i | 0.157609 | − | 0.157609i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.4244i | 1.46713i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 7.65685i | 0.316572i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.5880 | + | 20.5880i | −0.849757 | + | 0.849757i | −0.990103 | − | 0.140346i | \(-0.955179\pi\) |
0.140346 | + | 0.990103i | \(0.455179\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.34315 | + | 2.34315i | 0.0965476 | + | 0.0965476i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −38.4859 | −1.58310 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.3137 | 0.546728 | 0.273364 | − | 0.961911i | \(-0.411864\pi\) | ||||
0.273364 | + | 0.961911i | \(0.411864\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.4525 | − | 10.4525i | −0.428511 | − | 0.428511i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −41.4558 | + | 41.4558i | −1.69667 | + | 1.69667i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.7875i | 0.645061i | 0.946559 | + | 0.322531i | \(0.104534\pi\) | ||||
−0.946559 | + | 0.322531i | \(0.895466\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15.1716i | − | 0.618861i | −0.950922 | − | 0.309431i | \(-0.899862\pi\) | ||
0.950922 | − | 0.309431i | \(-0.100138\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −27.0823 | + | 27.0823i | −1.10288 | + | 1.10288i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −28.5563 | − | 28.5563i | −1.16098 | − | 1.16098i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 18.3431 | 0.743302 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.06147 | + | 3.06147i | 0.123854 | + | 0.123854i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.8701 | + | 25.8701i | −1.04488 | + | 1.04488i | −0.0459375 | + | 0.998944i | \(0.514627\pi\) |
−0.998944 | + | 0.0459375i | \(0.985373\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 35.6871i | 1.43904i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.5147i | 0.866150i | 0.901358 | + | 0.433075i | \(0.142571\pi\) | ||||
−0.901358 | + | 0.433075i | \(0.857429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.37849 | − | 3.37849i | 0.135793 | − | 0.135793i | −0.635943 | − | 0.771736i | \(-0.719389\pi\) |
0.771736 | + | 0.635943i | \(0.219389\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.97056 | + | 8.97056i | 0.359976 | + | 0.359976i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.26810 | 0.0508054 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.9706 | 0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.95815 | + | 3.95815i | 0.158073 | + | 0.158073i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.1421 | + | 10.1421i | −0.404393 | + | 0.404393i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.79884i | − | 0.111420i | −0.998447 | − | 0.0557099i | \(-0.982258\pi\) | ||
0.998447 | − | 0.0557099i | \(-0.0177422\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 70.4264i | − | 2.79920i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 32.6256 | − | 32.6256i | 1.29471 | − | 1.29471i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.92893 | + | 1.92893i | 0.0764271 | + | 0.0764271i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −45.8770 | −1.81486 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.85786 | −0.389362 | −0.194681 | − | 0.980867i | \(-0.562367\pi\) | ||||
−0.194681 | + | 0.980867i | \(0.562367\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.951076 | + | 0.951076i | 0.0375068 | + | 0.0375068i | 0.725611 | − | 0.688105i | \(-0.241557\pi\) |
−0.688105 | + | 0.725611i | \(0.741557\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.4853 | + | 16.4853i | −0.649107 | + | 0.649107i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 0.262632i | − | 0.0103251i | −0.999987 | − | 0.00516257i | \(-0.998357\pi\) | ||
0.999987 | − | 0.00516257i | \(-0.00164331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.4853i | − | 0.490090i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.9050 | − | 20.9050i | 0.819332 | − | 0.819332i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.5563 | − | 26.5563i | −1.03923 | − | 1.03923i | −0.999198 | − | 0.0400318i | \(-0.987254\pi\) |
−0.0400318 | − | 0.999198i | \(-0.512746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −31.0949 | −1.21498 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −40.1421 | −1.56609 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.3868 | + | 23.3868i | 0.911021 | + | 0.911021i | 0.996353 | − | 0.0853316i | \(-0.0271950\pi\) |
−0.0853316 | + | 0.996353i | \(0.527195\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.5563 | + | 10.5563i | −0.410594 | + | 0.410594i | −0.881946 | − | 0.471351i | \(-0.843766\pi\) |
0.471351 | + | 0.881946i | \(0.343766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 4.32957i | − | 0.168147i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.34315i | 0.0908633i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19.0029 | − | 19.0029i | 0.735794 | − | 0.735794i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.6569 | + | 13.6569i | 0.528004 | + | 0.528004i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −62.4524 | −2.41095 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.1716 | −0.816104 | −0.408052 | − | 0.912959i | \(-0.633792\pi\) | ||||
−0.408052 | + | 0.912959i | \(0.633792\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −10.1899 | − | 10.1899i | −0.392208 | − | 0.392208i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.4142 | − | 12.4142i | 0.477117 | − | 0.477117i | −0.427091 | − | 0.904208i | \(-0.640462\pi\) |
0.904208 | + | 0.427091i | \(0.140462\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 16.5754i | − | 0.636107i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.82843i | 0.261666i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.2024 | + | 14.2024i | −0.543440 | + | 0.543440i | −0.924536 | − | 0.381095i | \(-0.875547\pi\) |
0.381095 | + | 0.924536i | \(0.375547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −50.6274 | − | 50.6274i | −1.93437 | − | 1.93437i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 41.5474 | 1.58513 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.34315 | −0.165461 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.0936 | − | 14.0936i | −0.536147 | − | 0.536147i | 0.386248 | − | 0.922395i | \(-0.373771\pi\) |
−0.922395 | + | 0.386248i | \(0.873771\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.7990 | − | 19.7990i | 0.752101 | − | 0.752101i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 65.5139i | − | 2.48508i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 11.3137i | − | 0.428537i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.0334 | − | 28.0334i | 1.06032 | − | 1.06032i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.4142 | + | 20.4142i | 0.771034 | + | 0.771034i | 0.978287 | − | 0.207253i | \(-0.0664524\pi\) |
−0.207253 | + | 0.978287i | \(0.566452\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.27357 | 0.0857493 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −65.9411 | −2.48349 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.17025 | − | 3.17025i | −0.119230 | − | 0.119230i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.2426 | + | 25.2426i | −0.948007 | + | 0.948007i | −0.998714 | − | 0.0507063i | \(-0.983853\pi\) |
0.0507063 | + | 0.998714i | \(0.483853\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.4412i | 0.879114i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 43.3137i | − | 1.62211i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.75699 | − | 6.75699i | 0.252697 | − | 0.252697i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 54.6274 | + | 54.6274i | 2.04010 | + | 2.04010i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.2459 | 0.456694 | 0.228347 | − | 0.973580i | \(-0.426668\pi\) | ||||
0.228347 | + | 0.973580i | \(0.426668\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.28427 | −0.159555 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −34.7904 | − | 34.7904i | −1.29387 | − | 1.29387i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.5858 | + | 21.5858i | −0.801676 | + | 0.801676i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.8155i | 1.58794i | 0.607958 | + | 0.793969i | \(0.291989\pi\) | ||||
−0.607958 | + | 0.793969i | \(0.708011\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 39.2843i | 1.45497i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.22625 | − | 5.22625i | 0.193300 | − | 0.193300i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.8995 | − | 32.8995i | −1.21517 | − | 1.21517i | −0.969304 | − | 0.245867i | \(-0.920927\pi\) |
−0.245867 | − | 0.969304i | \(-0.579073\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −41.5474 | −1.53250 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 47.7990 | 1.76070 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.2275 | − | 22.2275i | −0.817652 | − | 0.817652i | 0.168115 | − | 0.985767i | \(-0.446232\pi\) |
−0.985767 | + | 0.168115i | \(0.946232\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.485281 | + | 0.485281i | −0.0178273 | + | 0.0178273i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28.5587i | − | 1.04772i | −0.851806 | − | 0.523858i | \(-0.824492\pi\) | ||
0.851806 | − | 0.523858i | \(-0.175508\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 34.9706i | 1.28122i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.50143 | + | 9.50143i | −0.347639 | + | 0.347639i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.8284 | + | 10.8284i | 0.395662 | + | 0.395662i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.12293 | −0.223429 | −0.111715 | − | 0.993740i | \(-0.535634\pi\) | ||||
−0.111715 | + | 0.993740i | \(0.535634\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.4853 | 1.32960 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.5391 | − | 21.5391i | −0.783887 | − | 0.783887i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.3848 | − | 23.3848i | 0.849934 | − | 0.849934i | −0.140190 | − | 0.990125i | \(-0.544771\pi\) |
0.990125 | + | 0.140190i | \(0.0447715\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 73.1675i | − | 2.65581i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.6274i | 0.385244i | 0.981273 | + | 0.192622i | \(0.0616990\pi\) | ||||
−0.981273 | + | 0.192622i | \(0.938301\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.15932 | − | 1.15932i | 0.0419700 | − | 0.0419700i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 26.1421 | + | 26.1421i | 0.945171 | + | 0.945171i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.53073 | 0.0552716 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8284 | 0.390483 | 0.195242 | − | 0.980755i | \(-0.437451\pi\) | ||||
0.195242 | + | 0.980755i | \(0.437451\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.0530 | − | 35.0530i | −1.26240 | − | 1.26240i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.9289 | + | 13.9289i | −0.500989 | + | 0.500989i | −0.911745 | − | 0.410756i | \(-0.865265\pi\) |
0.410756 | + | 0.911745i | \(0.365265\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 49.2011i | 1.76735i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 20.2843i | − | 0.727694i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.26810 | + | 1.26810i | −0.0454344 | + | 0.0454344i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.4853 | + | 40.4853i | 1.44868 | + | 1.44868i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.92724 | −0.354771 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.3137 | 0.760719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.4734 | − | 34.4734i | −1.22884 | − | 1.22884i | −0.964402 | − | 0.264441i | \(-0.914813\pi\) |
−0.264441 | − | 0.964402i | \(-0.585187\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38.1421 | − | 38.1421i | 1.35790 | − | 1.35790i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.59767i | 0.199030i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.65685i | − | 0.271903i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 46.7736 | − | 46.7736i | 1.65889 | − | 1.65889i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.9289 | − | 13.9289i | −0.493388 | − | 0.493388i | 0.415984 | − | 0.909372i | \(-0.363437\pi\) |
−0.909372 | + | 0.415984i | \(0.863437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.9050 | 0.739566 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.17157 | −0.112062 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.4244 | + | 35.4244i | 1.25010 | + | 1.25010i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.6569 | − | 21.6569i | 0.763304 | − | 0.763304i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.5194i | 0.511108i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 47.3137i | − | 1.66346i | −0.555179 | − | 0.831731i | \(-0.687350\pi\) | ||
0.555179 | − | 0.831731i | \(-0.312650\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.4650 | + | 14.4650i | −0.507937 | + | 0.507937i | −0.913893 | − | 0.405956i | \(-0.866939\pi\) |
0.405956 | + | 0.913893i | \(0.366939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −52.2843 | − | 52.2843i | −1.83369 | − | 1.83369i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −44.6088 | −1.56258 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.17157 | −0.0409881 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.42742 | + | 2.42742i | 0.0848208 | + | 0.0848208i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.7574 | − | 18.7574i | 0.654636 | − | 0.654636i | −0.299470 | − | 0.954106i | \(-0.596810\pi\) |
0.954106 | + | 0.299470i | \(0.0968097\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.8155i | 1.49245i | 0.665692 | + | 0.746227i | \(0.268137\pi\) | ||||
−0.665692 | + | 0.746227i | \(0.731863\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 83.1127i | 2.89361i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.5880 | + | 20.5880i | −0.715914 | + | 0.715914i | −0.967766 | − | 0.251852i | \(-0.918961\pi\) |
0.251852 | + | 0.967766i | \(0.418961\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.2426 | − | 17.2426i | −0.598862 | − | 0.598862i | 0.341148 | − | 0.940010i | \(-0.389184\pi\) |
−0.940010 | + | 0.341148i | \(0.889184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.53073 | −0.0531006 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.1716 | 0.456368 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.69552 | − | 3.69552i | −0.127889 | − | 0.127889i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.3137 | + | 11.3137i | −0.391059 | + | 0.391059i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 39.7540i | − | 1.37246i | −0.727384 | − | 0.686231i | \(-0.759264\pi\) | ||
0.727384 | − | 0.686231i | \(-0.240736\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 7.97056i | − | 0.274847i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 40.2793 | − | 40.2793i | 1.38729 | − | 1.38729i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −30.5563 | − | 30.5563i | −1.05117 | − | 1.05117i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.1062 | −0.622135 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.7990 | −0.816779 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.0138 | − | 21.0138i | −0.720344 | − | 0.720344i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.6985 | − | 36.6985i | 1.25653 | − | 1.25653i | 0.303795 | − | 0.952738i | \(-0.401746\pi\) |
0.952738 | − | 0.303795i | \(-0.0982537\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 5.86030i | − | 0.200418i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32.2843i | 1.10281i | 0.834238 | + | 0.551405i | \(0.185908\pi\) | ||||
−0.834238 | + | 0.551405i | \(0.814092\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.3253 | + | 20.3253i | −0.693492 | + | 0.693492i | −0.962999 | − | 0.269507i | \(-0.913139\pi\) |
0.269507 | + | 0.962999i | \(0.413139\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.3137 | + | 11.3137i | 0.385570 | + | 0.385570i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −43.0781 | −1.46640 | −0.733198 | − | 0.680015i | \(-0.761973\pi\) | ||||
−0.733198 | + | 0.680015i | \(0.761973\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 79.2548 | 2.69475 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.6298 | + | 16.6298i | 0.564779 | + | 0.564779i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.6863 | − | 20.6863i | 0.701734 | − | 0.701734i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.86030i | 0.198569i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 41.4558i | 1.40307i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.12293 | + | 6.12293i | −0.206993 | + | 0.206993i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.0416 | + | 13.0416i | 0.440385 | + | 0.440385i | 0.892141 | − | 0.451757i | \(-0.149202\pi\) |
−0.451757 | + | 0.892141i | \(0.649202\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −8.92177 | −0.300924 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.9411 | −0.941360 | −0.470680 | − | 0.882304i | \(-0.655991\pi\) | ||||
−0.470680 | + | 0.882304i | \(0.655991\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.11039 | − | 2.11039i | −0.0710203 | − | 0.0710203i | 0.670704 | − | 0.741725i | \(-0.265992\pi\) |
−0.741725 | + | 0.670704i | \(0.765992\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.4853 | + | 16.4853i | −0.554147 | + | 0.554147i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 10.1899i | − | 0.342142i | −0.985259 | − | 0.171071i | \(-0.945277\pi\) | ||
0.985259 | − | 0.171071i | \(-0.0547228\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 20.6863i | − | 0.693796i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.6913 | − | 19.6913i | 0.659683 | − | 0.659683i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.34315 | − | 2.34315i | −0.0784104 | − | 0.0784104i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.86030 | 0.195888 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.97056 | 0.299518 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23.9665 | + | 23.9665i | 0.799327 | + | 0.799327i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.8284 | + | 14.8284i | −0.494007 | + | 0.494007i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.4525i | 0.347838i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 19.6569i | − | 0.653416i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.70259 | − | 6.70259i | 0.222556 | − | 0.222556i | −0.587018 | − | 0.809574i | \(-0.699698\pi\) |
0.809574 | + | 0.587018i | \(0.199698\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.92893 | + | 7.92893i | 0.262986 | + | 0.262986i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0502 | 0.531766 | 0.265883 | − | 0.964005i | \(-0.414337\pi\) | ||||
0.265883 | + | 0.964005i | \(0.414337\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.7696 | 0.554991 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 82.4607 | + | 82.4607i | 2.72607 | + | 2.72607i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.85786 | + | 9.85786i | −0.325535 | + | 0.325535i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4244i | 1.16854i | 0.811558 | + | 0.584272i | \(0.198620\pi\) | ||||
−0.811558 | + | 0.584272i | \(0.801380\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 67.1127i | 2.21144i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.96362 | + | 4.96362i | −0.163380 | + | 0.163380i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.8701 | + | 23.8701i | 0.784843 | + | 0.784843i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.7151 | 0.351931 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −37.1716 | −1.21956 | −0.609780 | − | 0.792571i | \(-0.708742\pi\) | ||||
−0.609780 | + | 0.792571i | \(0.708742\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.47634 | − | 1.47634i | −0.0483851 | − | 0.0483851i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.1716 | − | 13.1716i | 0.431218 | − | 0.431218i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 46.1396i | − | 1.50893i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.45584i | − | 0.243572i | −0.992556 | − | 0.121786i | \(-0.961138\pi\) | ||
0.992556 | − | 0.121786i | \(-0.0388621\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.0502 | − | 16.0502i | 0.523778 | − | 0.523778i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0711 | + | 12.0711i | 0.393506 | + | 0.393506i | 0.875935 | − | 0.482429i | \(-0.160245\pi\) |
−0.482429 | + | 0.875935i | \(0.660245\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.4412 | 0.763351 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.3137 | −0.368035 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.1857 | + | 26.1857i | 0.850919 | + | 0.850919i | 0.990246 | − | 0.139327i | \(-0.0444939\pi\) |
−0.139327 | + | 0.990246i | \(0.544494\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.34315 | + | 4.34315i | −0.140984 | + | 0.140984i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.8882i | 1.06647i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44.9706i | − | 1.45674i | −0.685184 | − | 0.728370i | \(-0.740278\pi\) | ||
0.685184 | − | 0.728370i | \(-0.259722\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.6256 | + | 32.6256i | −1.05574 | + | 1.05574i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.4853 | + | 40.4853i | 1.30870 | + | 1.30870i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.1003 | −1.03657 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.6274 | 0.762175 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −27.0823 | − | 27.0823i | −0.872716 | − | 0.872716i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.7990 | + | 39.7990i | −1.28117 | + | 1.28117i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.59220i | 0.147675i | 0.997270 | + | 0.0738376i | \(0.0235247\pi\) | ||||
−0.997270 | + | 0.0738376i | \(0.976475\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.31371i | 0.106452i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.06854 | + | 6.06854i | −0.194749 | + | 0.194749i | −0.797744 | − | 0.602996i | \(-0.793974\pi\) |
0.602996 | + | 0.797744i | \(0.293974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −20.7696 | − | 20.7696i | −0.665841 | − | 0.665841i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.1899 | −0.326337 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.1127 | −0.483498 | −0.241749 | − | 0.970339i | \(-0.577721\pi\) | ||||
−0.241749 | + | 0.970339i | \(0.577721\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.79884 | + | 2.79884i | 0.0894512 | + | 0.0894512i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.89949 | + | 2.89949i | −0.0925737 | + | 0.0925737i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.05600i | 0.0655762i | 0.999462 | + | 0.0327881i | \(0.0104386\pi\) | ||||
−0.999462 | + | 0.0327881i | \(0.989561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 50.2843i | − | 1.60219i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.9050 | + | 20.9050i | −0.665414 | + | 0.665414i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.8284 | + | 10.8284i | 0.344324 | + | 0.344324i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.4412 | 0.744635 | 0.372317 | − | 0.928106i | \(-0.378563\pi\) | ||||
0.372317 | + | 0.928106i | \(0.378563\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.8284 | 0.470566 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −54.1647 | − | 54.1647i | −1.71714 | − | 1.71714i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.92893 | + | 5.92893i | −0.187771 | + | 0.187771i | −0.794732 | − | 0.606961i | \(-0.792389\pi\) |
0.606961 | + | 0.794732i | \(0.292389\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.9778i | 0.347321i |
(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 | 512.2.e.j.129.1 | yes | 8 | |
3.2 | odd | 2 | 4608.2.k.bd.1153.1 | 8 | |||
4.3 | odd | 2 | inner | 512.2.e.j.129.4 | yes | 8 | |
8.3 | odd | 2 | 512.2.e.i.129.1 | ✓ | 8 | ||
8.5 | even | 2 | 512.2.e.i.129.4 | yes | 8 | ||
12.11 | even | 2 | 4608.2.k.bd.1153.2 | 8 | |||
16.3 | odd | 4 | 512.2.e.i.385.1 | yes | 8 | ||
16.5 | even | 4 | inner | 512.2.e.j.385.1 | yes | 8 | |
16.11 | odd | 4 | inner | 512.2.e.j.385.4 | yes | 8 | |
16.13 | even | 4 | 512.2.e.i.385.4 | yes | 8 | ||
24.5 | odd | 2 | 4608.2.k.bi.1153.3 | 8 | |||
24.11 | even | 2 | 4608.2.k.bi.1153.4 | 8 | |||
32.3 | odd | 8 | 1024.2.b.g.513.8 | 8 | |||
32.5 | even | 8 | 1024.2.a.i.1.4 | 4 | |||
32.11 | odd | 8 | 1024.2.a.h.1.4 | 4 | |||
32.13 | even | 8 | 1024.2.b.g.513.7 | 8 | |||
32.19 | odd | 8 | 1024.2.b.g.513.1 | 8 | |||
32.21 | even | 8 | 1024.2.a.h.1.1 | 4 | |||
32.27 | odd | 8 | 1024.2.a.i.1.1 | 4 | |||
32.29 | even | 8 | 1024.2.b.g.513.2 | 8 | |||
48.5 | odd | 4 | 4608.2.k.bd.3457.2 | 8 | |||
48.11 | even | 4 | 4608.2.k.bd.3457.1 | 8 | |||
48.29 | odd | 4 | 4608.2.k.bi.3457.4 | 8 | |||
48.35 | even | 4 | 4608.2.k.bi.3457.3 | 8 | |||
96.5 | odd | 8 | 9216.2.a.w.1.2 | 4 | |||
96.11 | even | 8 | 9216.2.a.bp.1.3 | 4 | |||
96.53 | odd | 8 | 9216.2.a.bp.1.4 | 4 | |||
96.59 | even | 8 | 9216.2.a.w.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
512.2.e.i.129.1 | ✓ | 8 | 8.3 | odd | 2 | ||
512.2.e.i.129.4 | yes | 8 | 8.5 | even | 2 | ||
512.2.e.i.385.1 | yes | 8 | 16.3 | odd | 4 | ||
512.2.e.i.385.4 | yes | 8 | 16.13 | even | 4 | ||
512.2.e.j.129.1 | yes | 8 | 1.1 | even | 1 | trivial | |
512.2.e.j.129.4 | yes | 8 | 4.3 | odd | 2 | inner | |
512.2.e.j.385.1 | yes | 8 | 16.5 | even | 4 | inner | |
512.2.e.j.385.4 | yes | 8 | 16.11 | odd | 4 | inner | |
1024.2.a.h.1.1 | 4 | 32.21 | even | 8 | |||
1024.2.a.h.1.4 | 4 | 32.11 | odd | 8 | |||
1024.2.a.i.1.1 | 4 | 32.27 | odd | 8 | |||
1024.2.a.i.1.4 | 4 | 32.5 | even | 8 | |||
1024.2.b.g.513.1 | 8 | 32.19 | odd | 8 | |||
1024.2.b.g.513.2 | 8 | 32.29 | even | 8 | |||
1024.2.b.g.513.7 | 8 | 32.13 | even | 8 | |||
1024.2.b.g.513.8 | 8 | 32.3 | odd | 8 | |||
4608.2.k.bd.1153.1 | 8 | 3.2 | odd | 2 | |||
4608.2.k.bd.1153.2 | 8 | 12.11 | even | 2 | |||
4608.2.k.bd.3457.1 | 8 | 48.11 | even | 4 | |||
4608.2.k.bd.3457.2 | 8 | 48.5 | odd | 4 | |||
4608.2.k.bi.1153.3 | 8 | 24.5 | odd | 2 | |||
4608.2.k.bi.1153.4 | 8 | 24.11 | even | 2 | |||
4608.2.k.bi.3457.3 | 8 | 48.35 | even | 4 | |||
4608.2.k.bi.3457.4 | 8 | 48.29 | odd | 4 | |||
9216.2.a.w.1.1 | 4 | 96.59 | even | 8 | |||
9216.2.a.w.1.2 | 4 | 96.5 | odd | 8 | |||
9216.2.a.bp.1.3 | 4 | 96.11 | even | 8 | |||
9216.2.a.bp.1.4 | 4 | 96.53 | odd | 8 |