Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(3905,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.3905");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.k (of order \(2\), degree \(1\), 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: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | 16.0.101415451701035401216.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 18x^{12} + 145x^{8} - 72x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{26}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 2016) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3905.13 | ||
Root | \(0.752908 - 0.137538i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.3905 |
Dual form | 4032.2.k.h.3905.14 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.36028 | 1.50276 | 0.751382 | − | 0.659867i | \(-0.229388\pi\) | ||||
0.751382 | + | 0.659867i | \(0.229388\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.57794 | − | 0.595188i | −0.974368 | − | 0.224960i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.64575i | − | 0.496213i | −0.968733 | − | 0.248106i | \(-0.920192\pi\) | ||
0.968733 | − | 0.248106i | \(-0.0798082\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.06871i | − | 0.851108i | −0.904933 | − | 0.425554i | \(-0.860079\pi\) | ||
0.904933 | − | 0.425554i | \(-0.139921\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.36028 | −0.814988 | −0.407494 | − | 0.913208i | \(-0.633597\pi\) | ||||
−0.407494 | + | 0.913208i | \(0.633597\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.53019i | − | 1.26871i | −0.773041 | − | 0.634356i | \(-0.781265\pi\) | ||
0.773041 | − | 0.634356i | \(-0.218735\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.64575i | − | 0.343163i | −0.985170 | − | 0.171581i | \(-0.945112\pi\) | ||
0.985170 | − | 0.171581i | \(-0.0548877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.29150 | 1.25830 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.06910i | 1.12700i | 0.826115 | + | 0.563502i | \(0.190546\pi\) | ||||
−0.826115 | + | 0.563502i | \(0.809454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.33981i | − | 0.779454i | −0.920931 | − | 0.389727i | \(-0.872569\pi\) | ||
0.920931 | − | 0.389727i | \(-0.127431\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.66259 | − | 2.00000i | −1.46425 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.29150 | −1.19872 | −0.599358 | − | 0.800481i | \(-0.704577\pi\) | ||||
−0.599358 | + | 0.800481i | \(0.704577\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.979531 | 0.152977 | 0.0764885 | − | 0.997070i | \(-0.475629\pi\) | ||||
0.0764885 | + | 0.997070i | \(0.475629\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.15587 | −0.786263 | −0.393131 | − | 0.919482i | \(-0.628608\pi\) | ||||
−0.393131 | + | 0.919482i | \(0.628608\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.1878 | −1.63190 | −0.815951 | − | 0.578121i | \(-0.803786\pi\) | ||||
−0.815951 | + | 0.578121i | \(0.803786\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.29150 | + | 3.06871i | 0.898786 | + | 0.438387i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.24264i | 0.582772i | 0.956606 | + | 0.291386i | \(0.0941163\pi\) | ||||
−0.956606 | + | 0.291386i | \(0.905884\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.53019i | − | 0.745691i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.13742 | 0.799025 | 0.399512 | − | 0.916728i | \(-0.369179\pi\) | ||||
0.399512 | + | 0.916728i | \(0.369179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1878i | 1.43245i | 0.697871 | + | 0.716223i | \(0.254131\pi\) | ||||
−0.697871 | + | 0.716223i | \(0.745869\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10.3117i | − | 1.27901i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.48528 | −1.03664 | −0.518321 | − | 0.855186i | \(-0.673443\pi\) | ||||
−0.518321 | + | 0.855186i | \(0.673443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.64575i | − | 0.670027i | −0.942213 | − | 0.335014i | \(-0.891259\pi\) | ||
0.942213 | − | 0.335014i | \(-0.108741\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.11905i | − | 0.950263i | −0.879915 | − | 0.475131i | \(-0.842401\pi\) | ||
0.879915 | − | 0.475131i | \(-0.157599\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.979531 | + | 4.24264i | −0.111628 | + | 0.483494i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.1878 | −1.22802 | −0.614008 | − | 0.789300i | \(-0.710444\pi\) | ||||
−0.614008 | + | 0.789300i | \(0.710444\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.2915 | −1.22474 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.70010 | 0.816209 | 0.408104 | − | 0.912935i | \(-0.366190\pi\) | ||||
0.408104 | + | 0.912935i | \(0.366190\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.82646 | + | 7.91094i | −0.191465 | + | 0.829292i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 18.5830i | − | 1.90658i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 14.2565i | − | 1.44753i | −0.690049 | − | 0.723763i | \(-0.742411\pi\) | ||
0.690049 | − | 0.723763i | \(-0.257589\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0399 | −1.19802 | −0.599008 | − | 0.800743i | \(-0.704438\pi\) | ||||
−0.599008 | + | 0.800743i | \(0.704438\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 20.1617i | 1.98659i | 0.115602 | + | 0.993296i | \(0.463120\pi\) | ||||
−0.115602 | + | 0.993296i | \(0.536880\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 20.2288i | − | 1.95559i | −0.209569 | − | 0.977794i | \(-0.567206\pi\) | ||
0.209569 | − | 0.977794i | \(-0.432794\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.5830 | −1.01367 | −0.506834 | − | 0.862044i | \(-0.669184\pi\) | ||||
−0.506834 | + | 0.862044i | \(0.669184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.5544i | − | 1.36916i | −0.728937 | − | 0.684581i | \(-0.759985\pi\) | ||
0.728937 | − | 0.684581i | \(-0.240015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.53019i | − | 0.515693i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.66259 | + | 2.00000i | 0.794099 | + | 0.183340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.29150 | 0.753773 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.33981 | 0.388165 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.1382 | −1.07709 | −0.538546 | − | 0.842596i | \(-0.681026\pi\) | ||||
−0.538546 | + | 0.842596i | \(0.681026\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.3252 | 1.51371 | 0.756854 | − | 0.653584i | \(-0.226735\pi\) | ||||
0.756854 | + | 0.653584i | \(0.226735\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.29150 | + | 14.2565i | −0.285409 | + | 1.23619i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.06910i | − | 0.518518i | −0.965808 | − | 0.259259i | \(-0.916522\pi\) | ||
0.965808 | − | 0.259259i | \(-0.0834784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.8219i | 1.34199i | 0.741460 | + | 0.670997i | \(0.234134\pi\) | ||||
−0.741460 | + | 0.670997i | \(0.765866\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.05034 | −0.422330 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.3939i | 1.69362i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.06910i | 0.497200i | 0.968606 | + | 0.248600i | \(0.0799705\pi\) | ||||
−0.968606 | + | 0.248600i | \(0.920030\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8147 | 0.961466 | 0.480733 | − | 0.876867i | \(-0.340371\pi\) | ||||
0.480733 | + | 0.876867i | \(0.340371\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 14.5830i | − | 1.17134i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 17.3252i | − | 1.38270i | −0.722520 | − | 0.691350i | \(-0.757016\pi\) | ||
0.722520 | − | 0.691350i | \(-0.242984\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.979531 | + | 4.24264i | −0.0771979 | + | 0.334367i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.48528 | 0.664619 | 0.332309 | − | 0.943170i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943170i | \(0.392172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.4626 | 1.81559 | 0.907796 | − | 0.419413i | \(-0.137764\pi\) | ||||
0.907796 | + | 0.419413i | \(0.137764\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.58301 | 0.275616 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.4616 | 0.947438 | 0.473719 | − | 0.880676i | \(-0.342911\pi\) | ||||
0.473719 | + | 0.880676i | \(0.342911\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.2191 | − | 3.74463i | −1.22605 | − | 0.283067i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.06275i | 0.228920i | 0.993428 | + | 0.114460i | \(0.0365138\pi\) | ||||
−0.993428 | + | 0.114460i | \(0.963486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.06871i | − | 0.228096i | −0.993475 | − | 0.114048i | \(-0.963618\pi\) | ||
0.993475 | − | 0.114048i | \(-0.0363817\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −24.5015 | −1.80139 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.53019i | 0.404408i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.5203i | − | 0.833577i | −0.909004 | − | 0.416788i | \(-0.863156\pi\) | ||
0.909004 | − | 0.416788i | \(-0.136844\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.70850 | 0.338925 | 0.169463 | − | 0.985537i | \(-0.445797\pi\) | ||||
0.169463 | + | 0.985537i | \(0.445797\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 24.8661i | − | 1.77164i | −0.464031 | − | 0.885819i | \(-0.653597\pi\) | ||
0.464031 | − | 0.885819i | \(-0.346403\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.3111i | 1.65248i | 0.563316 | + | 0.826241i | \(0.309525\pi\) | ||||
−0.563316 | + | 0.826241i | \(0.690475\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.61226 | − | 15.6458i | 0.253531 | − | 1.09812i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.29150 | 0.229889 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.10132 | −0.629551 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.4676 | −1.06483 | −0.532417 | − | 0.846482i | \(-0.678716\pi\) | ||||
−0.532417 | + | 0.846482i | \(0.678716\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.3252 | −1.18157 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.58301 | + | 11.1878i | −0.175346 | + | 0.759475i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3117i | 0.693643i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.19038i | 0.0797135i | 0.999205 | + | 0.0398567i | \(0.0126902\pi\) | ||||
−0.999205 | + | 0.0398567i | \(0.987310\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.13742 | −0.407355 | −0.203678 | − | 0.979038i | \(-0.565289\pi\) | ||||
−0.203678 | + | 0.979038i | \(0.565289\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3.06871i | − | 0.202786i | −0.994846 | − | 0.101393i | \(-0.967670\pi\) | ||
0.994846 | − | 0.101393i | \(-0.0323300\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.3808i | 1.07314i | 0.843854 | + | 0.536572i | \(0.180281\pi\) | ||||
−0.843854 | + | 0.536572i | \(0.819719\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −37.5940 | −2.45237 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.9373i | − | 1.35432i | −0.735837 | − | 0.677159i | \(-0.763211\pi\) | ||
0.735837 | − | 0.677159i | \(-0.236789\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.3939i | − | 1.31369i | −0.754027 | − | 0.656843i | \(-0.771891\pi\) | ||
0.754027 | − | 0.656843i | \(-0.228109\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 21.1412 | + | 10.3117i | 1.35066 | + | 0.658793i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.9706 | −1.07981 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.05034 | −0.318774 | −0.159387 | − | 0.987216i | \(-0.550952\pi\) | ||||
−0.159387 | + | 0.987216i | \(0.550952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.70850 | −0.170282 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.4616 | 0.777333 | 0.388667 | − | 0.921378i | \(-0.372936\pi\) | ||||
0.388667 | + | 0.921378i | \(0.372936\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.7970 | + | 4.33981i | 1.16799 | + | 0.269663i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 15.0627i | − | 0.928809i | −0.885623 | − | 0.464404i | \(-0.846268\pi\) | ||
0.885623 | − | 0.464404i | \(-0.153732\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.2565i | 0.875768i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.5025 | −0.640351 | −0.320176 | − | 0.947358i | \(-0.603742\pi\) | ||||
−0.320176 | + | 0.947358i | \(0.603742\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.0194i | − | 0.790875i | −0.918493 | − | 0.395437i | \(-0.870593\pi\) | ||
0.918493 | − | 0.395437i | \(-0.129407\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 10.3542i | − | 0.624385i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.8745 | 1.67482 | 0.837408 | − | 0.546578i | \(-0.184070\pi\) | ||||
0.837408 | + | 0.546578i | \(0.184070\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 10.9015i | − | 0.650327i | −0.945658 | − | 0.325163i | \(-0.894581\pi\) | ||
0.945658 | − | 0.325163i | \(-0.105419\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.6724i | 0.753299i | 0.926356 | + | 0.376649i | \(0.122924\pi\) | ||||
−0.926356 | + | 0.376649i | \(0.877076\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.52517 | − | 0.583005i | −0.149056 | − | 0.0344137i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.70850 | −0.335794 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.70010 | −0.449845 | −0.224922 | − | 0.974377i | \(-0.572213\pi\) | ||||
−0.224922 | + | 0.974377i | \(0.572213\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.6235 | 1.20075 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.05034 | −0.292069 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.2915 | + | 3.06871i | 0.766109 | + | 0.176878i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 37.5940i | 2.15263i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.53019i | − | 0.315625i | −0.987469 | − | 0.157812i | \(-0.949556\pi\) | ||
0.987469 | − | 0.157812i | \(-0.0504441\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.13742 | −0.348021 | −0.174011 | − | 0.984744i | \(-0.555673\pi\) | ||||
−0.174011 | + | 0.984744i | \(0.555673\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 12.2748i | − | 0.693815i | −0.937899 | − | 0.346908i | \(-0.887232\pi\) | ||
0.937899 | − | 0.346908i | \(-0.112768\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6.06910i | − | 0.340875i | −0.985369 | − | 0.170437i | \(-0.945482\pi\) | ||
0.985369 | − | 0.170437i | \(-0.0545180\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.98823 | 0.559234 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.5830i | 1.03399i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 19.3068i | − | 1.07095i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 28.8413 | + | 6.65882i | 1.59007 | + | 0.367113i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.8147 | 0.649394 | 0.324697 | − | 0.945818i | \(-0.394738\pi\) | ||||
0.324697 | + | 0.945818i | \(0.394738\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28.5129 | −1.55783 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.5830 | −1.66596 | −0.832981 | − | 0.553301i | \(-0.813368\pi\) | ||||
−0.832981 | + | 0.553301i | \(0.813368\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.14226 | −0.386775 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.3926 | − | 11.6556i | −0.777129 | − | 0.629342i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.06275i | 0.164417i | 0.996615 | + | 0.0822084i | \(0.0261973\pi\) | ||||
−0.996615 | + | 0.0822084i | \(0.973803\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.05034i | − | 0.270338i | −0.990823 | − | 0.135169i | \(-0.956842\pi\) | ||
0.990823 | − | 0.135169i | \(-0.0431578\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.3797 | 0.871805 | 0.435902 | − | 0.899994i | \(-0.356429\pi\) | ||||
0.435902 | + | 0.899994i | \(0.356429\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 18.9713i | − | 1.00689i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.2288i | 1.48986i | 0.667144 | + | 0.744928i | \(0.267516\pi\) | ||||
−0.667144 | + | 0.744928i | \(0.732484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.5830 | −0.609632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 27.2823i | − | 1.42802i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.19038i | 0.0621371i | 0.999517 | + | 0.0310686i | \(0.00989102\pi\) | ||||
−0.999517 | + | 0.0310686i | \(0.990109\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.52517 | − | 10.9373i | 0.131100 | − | 0.567834i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5830 | 0.651523 | 0.325762 | − | 0.945452i | \(-0.394379\pi\) | ||||
0.325762 | + | 0.945452i | \(0.394379\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.6243 | 0.959202 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.8147 | −0.606880 | −0.303440 | − | 0.952851i | \(-0.598135\pi\) | ||||
−0.303440 | + | 0.952851i | \(0.598135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.6000 | 1.51249 | 0.756246 | − | 0.654288i | \(-0.227032\pi\) | ||||
0.756246 | + | 0.654288i | \(0.227032\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.29150 | + | 14.2565i | −0.167751 | + | 0.726577i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 21.2132i | 1.07555i | 0.843088 | + | 0.537776i | \(0.180735\pi\) | ||||
−0.843088 | + | 0.537776i | \(0.819265\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.53019i | 0.279674i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −28.5129 | −1.43464 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.7375i | 1.79361i | 0.442424 | + | 0.896806i | \(0.354119\pi\) | ||||
−0.442424 | + | 0.896806i | \(0.645881\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 2.41618i | − | 0.120658i | −0.998179 | − | 0.0603291i | \(-0.980785\pi\) | ||
0.998179 | − | 0.0603291i | \(-0.0192150\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.3176 | −0.663399 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.0000i | 0.594818i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.3939i | − | 1.00841i | −0.863583 | − | 0.504207i | \(-0.831785\pi\) | ||
0.863583 | − | 0.504207i | \(-0.168215\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.8219 | − | 3.65292i | −0.778544 | − | 0.179748i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.5940 | −1.84542 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1007 | 0.493450 | 0.246725 | − | 0.969086i | \(-0.420646\pi\) | ||||
0.246725 | + | 0.969086i | \(0.420646\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.29150 | 0.0629440 | 0.0314720 | − | 0.999505i | \(-0.489980\pi\) | ||||
0.0314720 | + | 0.999505i | \(0.489980\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.1412 | −1.02550 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.65882 | − | 28.8413i | 0.322243 | − | 1.39573i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 35.5203i | − | 1.71095i | −0.517844 | − | 0.855475i | \(-0.673265\pi\) | ||
0.517844 | − | 0.855475i | \(-0.326735\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.13742i | − | 0.294946i | −0.989066 | − | 0.147473i | \(-0.952886\pi\) | ||
0.989066 | − | 0.147473i | \(-0.0471139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.10132 | −0.435375 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 32.8341i | − | 1.56709i | −0.621336 | − | 0.783544i | \(-0.713410\pi\) | ||
0.621336 | − | 0.783544i | \(-0.286590\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 24.9373i | − | 1.18480i | −0.805642 | − | 0.592402i | \(-0.798180\pi\) | ||
0.805642 | − | 0.592402i | \(-0.201820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 25.8745 | 1.22657 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.72202i | 0.458811i | 0.973331 | + | 0.229405i | \(0.0736781\pi\) | ||||
−0.973331 | + | 0.229405i | \(0.926322\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.61206i | − | 0.0759092i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.13742 | + | 26.5830i | −0.287727 | + | 1.24623i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.7490 | −1.67227 | −0.836134 | − | 0.548525i | \(-0.815190\pi\) | ||||
−0.836134 | + | 0.548525i | \(0.815190\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.4810 | −1.18677 | −0.593385 | − | 0.804919i | \(-0.702209\pi\) | ||||
−0.593385 | + | 0.804919i | \(0.702209\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.1382 | −0.564110 | −0.282055 | − | 0.959398i | \(-0.591016\pi\) | ||||
−0.282055 | + | 0.959398i | \(0.591016\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.3252 | −0.801714 | −0.400857 | − | 0.916141i | \(-0.631288\pi\) | ||||
−0.400857 | + | 0.916141i | \(0.631288\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.8745 | + | 5.05034i | 1.01007 | + | 0.233203i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.48528i | 0.390154i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 34.7932i | − | 1.59642i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.3755i | 1.02024i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 47.9058i | − | 2.17529i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.0970 | 1.77165 | 0.885827 | − | 0.464016i | \(-0.153592\pi\) | ||||
0.885827 | + | 0.464016i | \(0.153592\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 10.8118i | − | 0.487928i | −0.969784 | − | 0.243964i | \(-0.921552\pi\) | ||
0.969784 | − | 0.243964i | \(-0.0784479\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 20.3939i | − | 0.918495i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.36028 | + | 14.5544i | −0.150729 | + | 0.652853i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.4735 | 0.826988 | 0.413494 | − | 0.910507i | \(-0.364308\pi\) | ||||
0.413494 | + | 0.910507i | \(0.364308\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.7375 | −1.59345 | −0.796727 | − | 0.604339i | \(-0.793437\pi\) | ||||
−0.796727 | + | 0.604339i | \(0.793437\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.4575 | −1.80034 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.12179 | 0.359992 | 0.179996 | − | 0.983667i | \(-0.442392\pi\) | ||||
0.179996 | + | 0.983667i | \(0.442392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.83236 | + | 20.9304i | −0.213771 | + | 0.925906i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 67.7490i | 2.98538i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.4123i | 0.809771i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.9990 | −0.613306 | −0.306653 | − | 0.951821i | \(-0.599209\pi\) | ||||
−0.306653 | + | 0.951821i | \(0.599209\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.9641i | 1.00415i | 0.864824 | + | 0.502076i | \(0.167430\pi\) | ||||
−0.864824 | + | 0.502076i | \(0.832570\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.5830i | 0.635246i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.2915 | 0.882239 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.00590i | − | 0.130200i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 67.9743i | − | 2.93879i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.05034 | − | 10.3542i | 0.217533 | − | 0.445989i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.29150 | −0.0555260 | −0.0277630 | − | 0.999615i | \(-0.508838\pi\) | ||||
−0.0277630 | + | 0.999615i | \(0.508838\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −35.5619 | −1.52330 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.7617 | 1.40079 | 0.700394 | − | 0.713756i | \(-0.253008\pi\) | ||||
0.700394 | + | 0.713756i | \(0.253008\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.5633 | 1.42984 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.8745 | + | 5.05034i | 0.930199 | + | 0.214762i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 38.8308i | − | 1.64531i | −0.568539 | − | 0.822657i | \(-0.692491\pi\) | ||
0.568539 | − | 0.822657i | \(-0.307509\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8219i | 0.669194i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.4626 | 0.988831 | 0.494416 | − | 0.869226i | \(-0.335382\pi\) | ||||
0.494416 | + | 0.869226i | \(0.335382\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 48.9068i | − | 2.05753i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 28.5190i | − | 1.19558i | −0.801653 | − | 0.597790i | \(-0.796046\pi\) | ||
0.801653 | − | 0.597790i | \(-0.203954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −46.0793 | −1.92836 | −0.964180 | − | 0.265249i | \(-0.914546\pi\) | ||||
−0.964180 | + | 0.265249i | \(0.914546\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 10.3542i | − | 0.431802i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.2381i | 0.676001i | 0.941146 | + | 0.338000i | \(0.109751\pi\) | ||||
−0.941146 | + | 0.338000i | \(0.890249\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.8413 | + | 6.65882i | 1.19654 | + | 0.276254i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.98233 | 0.289179 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.4626 | 0.968406 | 0.484203 | − | 0.874956i | \(-0.339110\pi\) | ||||
0.484203 | + | 0.874956i | \(0.339110\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0000 | −0.988903 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.6039 | 0.805034 | 0.402517 | − | 0.915413i | \(-0.368135\pi\) | ||||
0.402517 | + | 0.915413i | \(0.368135\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 29.1088 | + | 6.72057i | 1.19334 | + | 0.275516i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.8118i | 0.768628i | 0.923202 | + | 0.384314i | \(0.125562\pi\) | ||||
−0.923202 | + | 0.384314i | \(0.874438\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.7878i | 1.66377i | 0.554949 | + | 0.831884i | \(0.312738\pi\) | ||||
−0.554949 | + | 0.831884i | \(0.687262\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 27.8618 | 1.13274 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.6919i | 1.04280i | 0.853312 | + | 0.521401i | \(0.174590\pi\) | ||||
−0.853312 | + | 0.521401i | \(0.825410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.3320i | 1.38892i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.4170 | 0.461128 | 0.230564 | − | 0.973057i | \(-0.425943\pi\) | ||||
0.230564 | + | 0.973057i | \(0.425943\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 31.5249i | − | 1.26915i | −0.772863 | − | 0.634573i | \(-0.781176\pi\) | ||
0.772863 | − | 0.634573i | \(-0.218824\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.14226i | − | 0.287071i | −0.989645 | − | 0.143536i | \(-0.954153\pi\) | ||
0.989645 | − | 0.143536i | \(-0.0458472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.8504 | − | 4.58301i | −0.795288 | − | 0.183614i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.8745 | −0.674980 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.5015 | 0.976939 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.7617 | 1.30422 | 0.652111 | − | 0.758123i | \(-0.273884\pi\) | ||||
0.652111 | + | 0.758123i | \(0.273884\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.7878 | −1.61861 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.41699 | − | 19.3068i | 0.373115 | − | 0.764964i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.07500i | 0.358441i | 0.983809 | + | 0.179220i | \(0.0573576\pi\) | ||||
−0.983809 | + | 0.179220i | \(0.942642\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.8894i | 0.902672i | 0.892354 | + | 0.451336i | \(0.149052\pi\) | ||||
−0.892354 | + | 0.451336i | \(0.850948\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.2381 | 0.638386 | 0.319193 | − | 0.947690i | \(-0.396588\pi\) | ||||
0.319193 | + | 0.947690i | \(0.396588\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10.1007i | − | 0.396486i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16.3808i | 0.641032i | 0.947243 | + | 0.320516i | \(0.103856\pi\) | ||||
−0.947243 | + | 0.320516i | \(0.896144\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 58.2175 | 2.27475 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8118i | 0.732802i | 0.930457 | + | 0.366401i | \(0.119410\pi\) | ||||
−0.930457 | + | 0.366401i | \(0.880590\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.3252i | 0.673872i | 0.941528 | + | 0.336936i | \(0.109391\pi\) | ||||
−0.941528 | + | 0.336936i | \(0.890609\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.0604 | + | 47.9058i | −0.428903 | + | 1.85771i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.98823 | 0.386746 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.4123 | 0.710798 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.70850 | −0.181499 | −0.0907496 | − | 0.995874i | \(-0.528926\pi\) | ||||
−0.0907496 | + | 0.995874i | \(0.528926\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.1412 | −0.812523 | −0.406262 | − | 0.913757i | \(-0.633168\pi\) | ||||
−0.406262 | + | 0.913757i | \(0.633168\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.48528 | + | 36.7523i | −0.325635 | + | 1.41042i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.77124i | 0.144303i | 0.997394 | + | 0.0721513i | \(0.0229864\pi\) | ||||
−0.997394 | + | 0.0721513i | \(0.977014\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 20.3939i | − | 0.779211i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.0194 | 0.496001 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.8608i | 1.59246i | 0.604995 | + | 0.796229i | \(0.293175\pi\) | ||||
−0.604995 | + | 0.796229i | \(0.706825\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.1660i | 2.01670i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.29150 | −0.124675 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 48.4955i | − | 1.83165i | −0.401578 | − | 0.915825i | \(-0.631538\pi\) | ||
0.401578 | − | 0.915825i | \(-0.368462\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 40.3234i | 1.52083i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.0381 | + | 7.16601i | 1.16731 | + | 0.269506i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.0000 | −1.05156 | −0.525781 | − | 0.850620i | \(-0.676227\pi\) | ||||
−0.525781 | + | 0.850620i | \(0.676227\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.14226 | −0.267480 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.9706 | −0.634663 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.3755 | 0.834466 | 0.417233 | − | 0.908800i | \(-0.363000\pi\) | ||||
0.417233 | + | 0.908800i | \(0.363000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | − | 51.9756i | 0.446903 | − | 1.93567i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.1838i | 1.41811i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.80244i | − | 0.103937i | −0.998649 | − | 0.0519684i | \(-0.983450\pi\) | ||
0.998649 | − | 0.0519684i | \(-0.0165495\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.3252 | 0.640795 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.3068i | 0.713113i | 0.934274 | + | 0.356557i | \(0.116049\pi\) | ||||
−0.934274 | + | 0.356557i | \(0.883951\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.9647i | 0.514395i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.7911 | 0.580886 | 0.290443 | − | 0.956892i | \(-0.406197\pi\) | ||||
0.290443 | + | 0.956892i | \(0.406197\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.22876i | 0.301884i | 0.988543 | + | 0.150942i | \(0.0482306\pi\) | ||||
−0.988543 | + | 0.150942i | \(0.951769\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.3939i | 0.747175i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0399 | + | 52.1484i | −0.439929 | + | 1.90546i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0911 | −1.31698 | −0.658491 | − | 0.752588i | \(-0.728805\pi\) | ||||
−0.658491 | + | 0.752588i | \(0.728805\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 39.7007 | 1.44486 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.16601 | 0.0423794 | 0.0211897 | − | 0.999775i | \(-0.493255\pi\) | ||||
0.0211897 | + | 0.999775i | \(0.493255\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.51690 | 0.0912377 | 0.0456189 | − | 0.998959i | \(-0.485474\pi\) | ||||
0.0456189 | + | 0.998959i | \(0.485474\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.2823 | + | 6.29888i | 0.987686 | + | 0.228035i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 18.8340i | − | 0.680056i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 50.8885i | − | 1.83509i | −0.397637 | − | 0.917543i | \(-0.630170\pi\) | ||
0.397637 | − | 0.917543i | \(-0.369830\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.8014 | −0.604305 | −0.302152 | − | 0.953260i | \(-0.597705\pi\) | ||||
−0.302152 | + | 0.953260i | \(0.597705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 27.3040i | − | 0.980787i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 5.41699i | − | 0.194084i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.29150 | −0.332476 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 58.2175i | − | 2.07787i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.6438i | 1.12798i | 0.825782 | + | 0.563989i | \(0.190734\pi\) | ||||
−0.825782 | + | 0.563989i | \(0.809266\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.66259 | + | 37.5203i | −0.308006 | + | 1.33407i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.3320 | 1.21917 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.4616 | −0.441413 | −0.220706 | − | 0.975340i | \(-0.570836\pi\) | ||||
−0.220706 | + | 0.975340i | \(0.570836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 37.5940 | 1.32998 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.3619 | −0.471532 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.29150 | + | 14.2565i | −0.116010 | + | 0.502475i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.5190i | 1.00268i | 0.865251 | + | 0.501338i | \(0.167159\pi\) | ||||
−0.865251 | + | 0.501338i | \(0.832841\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 17.3593i | − | 0.609566i | −0.952422 | − | 0.304783i | \(-0.901416\pi\) | ||
0.952422 | − | 0.304783i | \(-0.0985839\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.5129 | 0.998765 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.5129i | 0.997542i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.3808i | 0.571695i | 0.958275 | + | 0.285848i | \(0.0922751\pi\) | ||||
−0.958275 | + | 0.285848i | \(0.907725\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4558 | 0.887335 | 0.443667 | − | 0.896191i | \(-0.353677\pi\) | ||||
0.443667 | + | 0.896191i | \(0.353677\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.6458i | 0.613603i | 0.951774 | + | 0.306801i | \(0.0992588\pi\) | ||||
−0.951774 | + | 0.306801i | \(0.900741\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.8198i | 1.66085i | 0.557131 | + | 0.830424i | \(0.311902\pi\) | ||||
−0.557131 | + | 0.830424i | \(0.688098\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.1412 | − | 10.3117i | −0.732500 | − | 0.357281i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 78.8410 | 2.72841 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.4259 | 0.946846 | 0.473423 | − | 0.880835i | \(-0.343018\pi\) | ||||
0.473423 | + | 0.880835i | \(0.343018\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.83399 | −0.270138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.0399 | 0.414186 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.3750 | − | 4.93500i | −0.734452 | − | 0.169569i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000i | 0.411355i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.5633i | 1.14918i | 0.818440 | + | 0.574592i | \(0.194839\pi\) | ||||
−0.818440 | + | 0.574592i | \(0.805161\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.4810 | 0.870416 | 0.435208 | − | 0.900330i | \(-0.356675\pi\) | ||||
0.435208 | + | 0.900330i | \(0.356675\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.6724i | − | 0.432378i | −0.976352 | − | 0.216189i | \(-0.930637\pi\) | ||
0.976352 | − | 0.216189i | \(-0.0693628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.64575i | − | 0.0560220i | −0.999608 | − | 0.0280110i | \(-0.991083\pi\) | ||
0.999608 | − | 0.0280110i | \(-0.00891735\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 41.8745 | 1.42378 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.9647i | 0.473719i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 26.0389i | 0.882294i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.1878 | − | 2.58301i | −0.378215 | − | 0.0873215i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 52.3633 | 1.76416 | 0.882082 | − | 0.471095i | \(-0.156141\pi\) | ||||
0.882082 | + | 0.471095i | \(0.156141\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.80879 | −0.296439 | −0.148220 | − | 0.988954i | \(-0.547354\pi\) | ||||
−0.148220 | + | 0.988954i | \(0.547354\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.3619 | −0.448650 | −0.224325 | − | 0.974514i | \(-0.572018\pi\) | ||||
−0.224325 | + | 0.974514i | \(0.572018\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.2915 | + | 7.22451i | 1.04948 | + | 0.242302i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 61.8705i | 2.07042i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 10.2917i | 0.344013i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.3388 | 0.878447 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 14.2565i | − | 0.474952i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 10.3117i | − | 0.342774i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.50295 | −0.0499046 | −0.0249523 | − | 0.999689i | \(-0.507943\pi\) | ||||
−0.0249523 | + | 0.999689i | \(0.507943\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.3542i | 0.608103i | 0.952656 | + | 0.304052i | \(0.0983396\pi\) | ||||
−0.952656 | + | 0.304052i | \(0.901660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.4123i | 0.609357i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −44.6632 | − | 10.3117i | −1.47491 | − | 0.340524i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.4617 | 0.411074 | 0.205537 | − | 0.978649i | \(-0.434106\pi\) | ||||
0.205537 | + | 0.978649i | \(0.434106\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −17.3252 | −0.570265 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −45.8745 | −1.50834 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.82291 | −0.0598077 | −0.0299039 | − | 0.999553i | \(-0.509520\pi\) | ||||
−0.0299039 | + | 0.999553i | \(0.509520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.9706 | − | 34.7932i | 0.556188 | − | 1.14030i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.5830i | 0.607729i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 24.5497i | − | 0.802004i | −0.916077 | − | 0.401002i | \(-0.868662\pi\) | ||
0.916077 | − | 0.401002i | \(-0.131338\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.9846 | 0.716678 | 0.358339 | − | 0.933592i | \(-0.383343\pi\) | ||||
0.358339 | + | 0.933592i | \(0.383343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.61206i | − | 0.0524961i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 16.2288i | − | 0.527364i | −0.964610 | − | 0.263682i | \(-0.915063\pi\) | ||
0.964610 | − | 0.263682i | \(-0.0849369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.9150 | −0.808776 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 40.0102i | − | 1.29606i | −0.761616 | − | 0.648029i | \(-0.775593\pi\) | ||
0.761616 | − | 0.648029i | \(-0.224407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 38.7113i | − | 1.25267i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.61226 | + | 15.6458i | −0.116646 | + | 0.505228i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.1660 | 0.392452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.8219 | 0.509324 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.48528 | 0.272868 | 0.136434 | − | 0.990649i | \(-0.456436\pi\) | ||||
0.136434 | + | 0.990649i | \(0.456436\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.4123 | 0.590878 | 0.295439 | − | 0.955362i | \(-0.404534\pi\) | ||||
0.295439 | + | 0.955362i | \(0.404534\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.41699 | − | 40.7878i | 0.301895 | − | 1.30760i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.7338i | 0.503370i | 0.967809 | + | 0.251685i | \(0.0809846\pi\) | ||||
−0.967809 | + | 0.251685i | \(0.919015\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12.6724i | − | 0.405013i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.4626 | 0.748341 | 0.374171 | − | 0.927360i | \(-0.377927\pi\) | ||||
0.374171 | + | 0.927360i | \(0.377927\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 83.5572i | − | 2.66235i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.48528i | 0.269816i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.4617 | −0.395859 | −0.197930 | − | 0.980216i | \(-0.563422\pi\) | ||||
−0.197930 | + | 0.980216i | \(0.563422\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 78.3320i | 2.48329i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.1878i | 0.354320i | 0.984182 | + | 0.177160i | \(0.0566910\pi\) | ||||
−0.984182 | + | 0.177160i | \(0.943309\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4032.2.k.h.3905.13 | 16 | ||
3.2 | odd | 2 | inner | 4032.2.k.h.3905.1 | 16 | ||
4.3 | odd | 2 | inner | 4032.2.k.h.3905.16 | 16 | ||
7.6 | odd | 2 | inner | 4032.2.k.h.3905.2 | 16 | ||
8.3 | odd | 2 | 2016.2.k.b.1889.4 | yes | 16 | ||
8.5 | even | 2 | 2016.2.k.b.1889.1 | ✓ | 16 | ||
12.11 | even | 2 | inner | 4032.2.k.h.3905.4 | 16 | ||
21.20 | even | 2 | inner | 4032.2.k.h.3905.14 | 16 | ||
24.5 | odd | 2 | 2016.2.k.b.1889.13 | yes | 16 | ||
24.11 | even | 2 | 2016.2.k.b.1889.16 | yes | 16 | ||
28.27 | even | 2 | inner | 4032.2.k.h.3905.3 | 16 | ||
56.13 | odd | 2 | 2016.2.k.b.1889.14 | yes | 16 | ||
56.27 | even | 2 | 2016.2.k.b.1889.15 | yes | 16 | ||
84.83 | odd | 2 | inner | 4032.2.k.h.3905.15 | 16 | ||
168.83 | odd | 2 | 2016.2.k.b.1889.3 | yes | 16 | ||
168.125 | even | 2 | 2016.2.k.b.1889.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2016.2.k.b.1889.1 | ✓ | 16 | 8.5 | even | 2 | ||
2016.2.k.b.1889.2 | yes | 16 | 168.125 | even | 2 | ||
2016.2.k.b.1889.3 | yes | 16 | 168.83 | odd | 2 | ||
2016.2.k.b.1889.4 | yes | 16 | 8.3 | odd | 2 | ||
2016.2.k.b.1889.13 | yes | 16 | 24.5 | odd | 2 | ||
2016.2.k.b.1889.14 | yes | 16 | 56.13 | odd | 2 | ||
2016.2.k.b.1889.15 | yes | 16 | 56.27 | even | 2 | ||
2016.2.k.b.1889.16 | yes | 16 | 24.11 | even | 2 | ||
4032.2.k.h.3905.1 | 16 | 3.2 | odd | 2 | inner | ||
4032.2.k.h.3905.2 | 16 | 7.6 | odd | 2 | inner | ||
4032.2.k.h.3905.3 | 16 | 28.27 | even | 2 | inner | ||
4032.2.k.h.3905.4 | 16 | 12.11 | even | 2 | inner | ||
4032.2.k.h.3905.13 | 16 | 1.1 | even | 1 | trivial | ||
4032.2.k.h.3905.14 | 16 | 21.20 | even | 2 | inner | ||
4032.2.k.h.3905.15 | 16 | 84.83 | odd | 2 | inner | ||
4032.2.k.h.3905.16 | 16 | 4.3 | odd | 2 | inner |