Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(1791,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.f (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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 896) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.4 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1791 |
Dual form | 1792.2.f.h.1791.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 2.73205 | 1.57735 | 0.788675 | − | 0.614810i | \(-0.210767\pi\) | ||||
0.788675 | + | 0.614810i | \(0.210767\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.732051i | 0.327383i | 0.986512 | + | 0.163692i | \(0.0523402\pi\) | ||||
−0.986512 | + | 0.163692i | \(0.947660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.46410 | 1.48803 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.46410i | − | 1.64749i | −0.566961 | − | 0.823744i | \(-0.691881\pi\) | ||
0.566961 | − | 0.823744i | \(-0.308119\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.73205i | 1.31243i | 0.754572 | + | 0.656217i | \(0.227845\pi\) | ||||
−0.754572 | + | 0.656217i | \(0.772155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000i | 0.516398i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.00000i | − | 0.970143i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.26795 | 0.290887 | 0.145444 | − | 0.989367i | \(-0.453539\pi\) | ||||
0.145444 | + | 0.989367i | \(0.453539\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.46410 | − | 4.73205i | −1.19236 | − | 1.03262i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.46410i | − | 1.13934i | −0.821872 | − | 0.569672i | \(-0.807070\pi\) | ||
0.821872 | − | 0.569672i | \(-0.192930\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.46410 | 0.892820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.92820 | 1.28654 | 0.643268 | − | 0.765641i | \(-0.277578\pi\) | ||||
0.643268 | + | 0.765641i | \(0.277578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92820 | 1.24434 | 0.622171 | − | 0.782881i | \(-0.286251\pi\) | ||||
0.622171 | + | 0.782881i | \(0.286251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 14.9282i | − | 2.59867i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.26795 | − | 1.46410i | 0.214323 | − | 0.247478i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.9282i | 2.07017i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.92820i | − | 0.457309i | −0.973508 | − | 0.228654i | \(-0.926567\pi\) | ||
0.973508 | − | 0.228654i | \(-0.0734325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.53590i | 0.386721i | 0.981128 | + | 0.193360i | \(0.0619387\pi\) | ||||
−0.981128 | + | 0.193360i | \(0.938061\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.26795i | 0.487157i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.92820 | −1.01058 | −0.505291 | − | 0.862949i | \(-0.668615\pi\) | ||||
−0.505291 | + | 0.862949i | \(0.668615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 10.9282i | − | 1.53025i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.92820 | −0.951662 | −0.475831 | − | 0.879537i | \(-0.657853\pi\) | ||||
−0.475831 | + | 0.879537i | \(0.657853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.46410 | 0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.80385 | 0.495219 | 0.247609 | − | 0.968860i | \(-0.420355\pi\) | ||||
0.247609 | + | 0.968860i | \(0.420355\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 11.6603i | − | 1.49294i | −0.665418 | − | 0.746471i | \(-0.731747\pi\) | ||
0.665418 | − | 0.746471i | \(-0.268253\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.92820 | − | 7.73205i | −1.12485 | − | 0.974147i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.53590i | 0.309809i | 0.987929 | + | 0.154905i | \(0.0495070\pi\) | ||||
−0.987929 | + | 0.154905i | \(0.950493\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 14.9282i | − | 1.79714i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.53590i | − | 0.538312i | −0.963097 | − | 0.269156i | \(-0.913255\pi\) | ||
0.963097 | − | 0.269156i | \(-0.0867447\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.1962 | 1.40829 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9.46410 | + | 10.9282i | −1.07853 | + | 1.24538i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.46410i | − | 0.389742i | −0.980829 | − | 0.194871i | \(-0.937571\pi\) | ||
0.980829 | − | 0.194871i | \(-0.0624288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.7321 | 1.17800 | 0.588998 | − | 0.808135i | \(-0.299523\pi\) | ||||
0.588998 | + | 0.808135i | \(0.299523\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.92820 | 0.317608 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 18.9282 | 2.02932 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.9282i | 1.58239i | 0.611566 | + | 0.791193i | \(0.290540\pi\) | ||||
−0.611566 | + | 0.791193i | \(0.709460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.19615 | − | 9.46410i | 0.859190 | − | 0.992107i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.9282 | 1.96276 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.928203i | 0.0952316i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000i | 1.21842i | 0.793011 | + | 0.609208i | \(0.208512\pi\) | ||||
−0.793011 | + | 0.609208i | \(0.791488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 24.3923i | − | 2.45152i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.19615i | 0.616540i | 0.951299 | + | 0.308270i | \(0.0997501\pi\) | ||||
−0.951299 | + | 0.308270i | \(0.900250\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.9282 | −1.86505 | −0.932526 | − | 0.361104i | \(-0.882400\pi\) | ||||
−0.932526 | + | 0.361104i | \(0.882400\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.46410 | − | 4.00000i | 0.338062 | − | 0.390360i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 8.39230i | − | 0.811315i | −0.914025 | − | 0.405657i | \(-0.867043\pi\) | ||
0.914025 | − | 0.405657i | \(-0.132957\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.92820 | −0.663602 | −0.331801 | − | 0.943349i | \(-0.607656\pi\) | ||||
−0.331801 | + | 0.943349i | \(0.607656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.9282 | 1.03726 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.46410 | −0.890308 | −0.445154 | − | 0.895454i | \(-0.646851\pi\) | ||||
−0.445154 | + | 0.895454i | \(0.646851\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 21.1244i | 1.95295i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.92820 | + | 8.00000i | −0.635107 | + | 0.733359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.8564 | −1.71422 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.00000i | − | 0.721336i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.4641i | 1.90463i | 0.305115 | + | 0.952316i | \(0.401305\pi\) | ||||
−0.305115 | + | 0.952316i | \(0.598695\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.92820i | 0.609994i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7321 | 0.937664 | 0.468832 | − | 0.883287i | \(-0.344675\pi\) | ||||
0.468832 | + | 0.883287i | \(0.344675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.53590 | − | 2.19615i | −0.219890 | − | 0.190431i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.92820i | 0.252020i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.8564 | −1.69645 | −0.848224 | − | 0.529638i | \(-0.822328\pi\) | ||||
−0.848224 | + | 0.529638i | \(0.822328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.19615 | −0.355913 | −0.177957 | − | 0.984038i | \(-0.556949\pi\) | ||||
−0.177957 | + | 0.984038i | \(0.556949\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.9282 | −1.59404 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 25.8564 | 2.16222 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.07180i | 0.421190i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.73205 | + | 18.9282i | 0.225336 | + | 1.56117i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.0000 | 0.983078 | 0.491539 | − | 0.870855i | \(-0.336434\pi\) | ||||
0.491539 | + | 0.870855i | \(0.336434\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.3205i | − | 0.921250i | −0.887595 | − | 0.460625i | \(-0.847625\pi\) | ||
0.887595 | − | 0.460625i | \(-0.152375\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 17.8564i | − | 1.44360i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.07180i | 0.407377i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.2679i | − | 1.53775i | −0.639399 | − | 0.768875i | \(-0.720817\pi\) | ||
0.639399 | − | 0.768875i | \(-0.279183\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.9282 | −1.50110 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.46410 | + | 10.9282i | −0.745876 | + | 0.861263i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.3923i | 1.28394i | 0.766728 | + | 0.641972i | \(0.221884\pi\) | ||||
−0.766728 | + | 0.641972i | \(0.778116\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.9282 | 0.850759 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.07180 | −0.392467 | −0.196234 | − | 0.980557i | \(-0.562871\pi\) | ||||
−0.196234 | + | 0.980557i | \(0.562871\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.39230 | −0.722485 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.66025 | 0.432850 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3.26795i | − | 0.248458i | −0.992254 | − | 0.124229i | \(-0.960354\pi\) | ||
0.992254 | − | 0.124229i | \(-0.0396457\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.92820 | − | 7.73205i | −0.674909 | − | 0.584488i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3923 | 0.781133 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 0.392305i | − | 0.0293222i | −0.999893 | − | 0.0146611i | \(-0.995333\pi\) | ||
0.999893 | − | 0.0146611i | \(-0.00466695\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7321i | 1.24368i | 0.783143 | + | 0.621842i | \(0.213615\pi\) | ||||
−0.783143 | + | 0.621842i | \(0.786385\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 31.8564i | − | 2.35489i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.92820i | 0.215286i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.8564 | −1.59830 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.00000 | − | 6.92820i | −0.581914 | − | 0.503953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.4641i | 0.829513i | 0.909932 | + | 0.414757i | \(0.136133\pi\) | ||||
−0.909932 | + | 0.414757i | \(0.863867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.39230 | 0.316165 | 0.158083 | − | 0.987426i | \(-0.449469\pi\) | ||||
0.158083 | + | 0.987426i | \(0.449469\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.46410 | −0.677738 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7846 | 1.18983 | 0.594915 | − | 0.803789i | \(-0.297186\pi\) | ||||
0.594915 | + | 0.803789i | \(0.297186\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.92820i | 0.488678i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.8564 | − | 12.0000i | −0.972529 | − | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.14359 | 0.149715 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 24.3923i | − | 1.69538i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.92820i | − | 0.479234i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.60770i | − | 0.523735i | −0.965104 | − | 0.261868i | \(-0.915662\pi\) | ||
0.965104 | − | 0.261868i | \(-0.0843384\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 12.3923i | − | 0.849107i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.85641 | −0.126606 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.8564 | − | 12.0000i | −0.940634 | − | 0.814613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.9282i | 1.27905i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.9282 | 1.27325 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.00000 | −0.535720 | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||||
−0.267860 | + | 0.963458i | \(0.586316\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.9282 | 1.32855 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.26795 | 0.0841567 | 0.0420784 | − | 0.999114i | \(-0.486602\pi\) | ||||
0.0420784 | + | 0.999114i | \(0.486602\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.339746i | 0.0224510i | 0.999937 | + | 0.0112255i | \(0.00357327\pi\) | ||||
−0.999937 | + | 0.0112255i | \(0.996427\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −25.8564 | + | 29.8564i | −1.70123 | + | 1.96441i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.8564 | 1.30084 | 0.650418 | − | 0.759576i | \(-0.274594\pi\) | ||||
0.650418 | + | 0.759576i | \(0.274594\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 5.07180i | − | 0.330848i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 9.46410i | − | 0.614759i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 0.392305i | − | 0.0253761i | −0.999920 | − | 0.0126880i | \(-0.995961\pi\) | ||
0.999920 | − | 0.0126880i | \(-0.00403884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0000i | 0.772988i | 0.922292 | + | 0.386494i | \(0.126314\pi\) | ||||
−0.922292 | + | 0.386494i | \(0.873686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.7321 | −1.20166 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.07180 | + | 0.732051i | −0.324025 | + | 0.0467690i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000i | 0.381771i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 29.3205 | 1.85811 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.0526 | 1.39195 | 0.695973 | − | 0.718068i | \(-0.254973\pi\) | ||||
0.695973 | + | 0.718068i | \(0.254973\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −29.8564 | −1.87706 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.00000 | 0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.8564i | 1.36337i | 0.731648 | + | 0.681683i | \(0.238751\pi\) | ||||
−0.731648 | + | 0.681683i | \(0.761249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | − | 6.92820i | −0.497096 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 30.9282 | 1.91441 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.4641i | 0.706907i | 0.935452 | + | 0.353453i | \(0.114993\pi\) | ||||
−0.935452 | + | 0.353453i | \(0.885007\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 5.07180i | − | 0.311558i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 40.7846i | 2.49598i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.12436i | − | 0.0685532i | −0.999412 | − | 0.0342766i | \(-0.989087\pi\) | ||
0.999412 | − | 0.0342766i | \(-0.0109127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.3923 | − | 25.8564i | 1.35524 | − | 1.56490i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 24.3923i | − | 1.47091i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.7846 | 1.72950 | 0.864750 | − | 0.502203i | \(-0.167477\pi\) | ||||
0.864750 | + | 0.502203i | \(0.167477\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.9282 | 1.85162 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.8038 | −0.939441 | −0.469721 | − | 0.882815i | \(-0.655645\pi\) | ||||
−0.469721 | + | 0.882815i | \(0.655645\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.53590i | 0.150214i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.07180 | + | 5.85641i | −0.299379 | + | 0.345693i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 32.7846i | 1.92187i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.80385i | − | 0.105382i | −0.998611 | − | 0.0526910i | \(-0.983220\pi\) | ||
0.998611 | − | 0.0526910i | \(-0.0167798\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.78461i | 0.162126i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 21.8564i | − | 1.26824i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.8564 | 1.49531 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.39230 | − | 5.07180i | 0.253168 | − | 0.292334i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.9282i | 0.972500i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.53590 | 0.488764 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.2679 | −0.757242 | −0.378621 | − | 0.925552i | \(-0.623602\pi\) | ||||
−0.378621 | + | 0.925552i | \(0.623602\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −51.7128 | −2.94184 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.8564 | 1.46618 | 0.733091 | − | 0.680130i | \(-0.238077\pi\) | ||||
0.733091 | + | 0.680130i | \(0.238077\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 32.7846i | − | 1.85310i | −0.376177 | − | 0.926548i | \(-0.622762\pi\) | ||
0.376177 | − | 0.926548i | \(-0.377238\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.66025 | − | 6.53590i | 0.318919 | − | 0.368256i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.85641 | −0.104266 | −0.0521331 | − | 0.998640i | \(-0.516602\pi\) | ||||
−0.0521331 | + | 0.998640i | \(0.516602\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 37.8564i | − | 2.11955i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 22.9282i | − | 1.27973i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.07180i | − | 0.282202i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.1244i | 1.17177i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.9282 | −1.04673 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.8564 | + | 12.0000i | 0.763928 | + | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3205i | 0.622231i | 0.950372 | + | 0.311116i | \(0.100703\pi\) | ||||
−0.950372 | + | 0.311116i | \(0.899297\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.8564 | 0.978525 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.85641 | −0.101426 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.60770 | −0.196524 | −0.0982618 | − | 0.995161i | \(-0.531328\pi\) | ||||
−0.0982618 | + | 0.995161i | \(0.531328\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.8564 | −1.40433 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 37.8564i | − | 2.05004i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 10.9282 | 0.588355 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 13.4641i | − | 0.722791i | −0.932413 | − | 0.361395i | \(-0.882300\pi\) | ||
0.932413 | − | 0.361395i | \(-0.117700\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11.6603i | − | 0.624159i | −0.950056 | − | 0.312080i | \(-0.898974\pi\) | ||
0.950056 | − | 0.312080i | \(-0.101026\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.9282i | 1.01031i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 29.8564i | − | 1.58910i | −0.607201 | − | 0.794548i | \(-0.707708\pi\) | ||
0.607201 | − | 0.794548i | \(-0.292292\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.32051 | 0.176234 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −18.9282 | + | 21.8564i | −1.00179 | + | 1.15676i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.392305i | 0.0207051i | 0.999946 | + | 0.0103525i | \(0.00329537\pi\) | ||||
−0.999946 | + | 0.0103525i | \(0.996705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3923 | −0.915384 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −51.5167 | −2.70392 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.07180 | −0.265470 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 13.0718i | − | 0.680491i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.8564 | + | 12.0000i | 0.719389 | + | 0.623009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.0718 | 0.883944 | 0.441972 | − | 0.897029i | \(-0.354279\pi\) | ||||
0.441972 | + | 0.897029i | \(0.354279\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.9282i | 0.977448i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 32.7846i | 1.68849i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.4641i | 1.10254i | 0.834328 | + | 0.551268i | \(0.185856\pi\) | ||||
−0.834328 | + | 0.551268i | \(0.814144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 58.6410i | 3.00427i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.92820 | −0.354015 | −0.177007 | − | 0.984210i | \(-0.556642\pi\) | ||||
−0.177007 | + | 0.984210i | \(0.556642\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | − | 6.92820i | −0.407718 | − | 0.353094i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.3205i | 0.575454i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.85641 | −0.0941235 | −0.0470618 | − | 0.998892i | \(-0.514986\pi\) | ||||
−0.0470618 | + | 0.998892i | \(0.514986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.8564 | −1.10533 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.3205 | 1.47902 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.53590 | 0.127595 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.9090i | 1.50109i | 0.660821 | + | 0.750544i | \(0.270208\pi\) | ||||
−0.660821 | + | 0.750544i | \(0.729792\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | − | 6.00000i | −0.346844 | − | 0.300376i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.3205 | −1.16457 | −0.582285 | − | 0.812985i | \(-0.697841\pi\) | ||||
−0.582285 | + | 0.812985i | \(0.697841\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.7846i | 1.63312i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 1.80385i | − | 0.0896339i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 21.8564i | − | 1.08338i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.07180i | 0.250784i | 0.992107 | + | 0.125392i | \(0.0400189\pi\) | ||||
−0.992107 | + | 0.125392i | \(0.959981\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −54.2487 | −2.67589 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.60770 | − | 6.58846i | −0.374350 | − | 0.324197i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.85641i | 0.385656i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.4641 | −0.561399 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.12436 | −0.152635 | −0.0763174 | − | 0.997084i | \(-0.524316\pi\) | ||||
−0.0763174 | + | 0.997084i | \(0.524316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.9282 | −1.50378 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 17.8564i | − | 0.866163i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.1962 | + | 23.3205i | −0.977360 | + | 1.12856i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 70.6410 | 3.41058 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.46410i | 0.263197i | 0.991303 | + | 0.131598i | \(0.0420109\pi\) | ||||
−0.991303 | + | 0.131598i | \(0.957989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.85641i | 0.0892132i | 0.999005 | + | 0.0446066i | \(0.0142034\pi\) | ||||
−0.999005 | + | 0.0446066i | \(0.985797\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.8564i | 0.664364i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.92820i | − | 0.331421i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.00000 | 0.190910 | 0.0954548 | − | 0.995434i | \(-0.469569\pi\) | ||||
0.0954548 | + | 0.995434i | \(0.469569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.46410 | + | 30.9282i | 0.212576 | + | 1.47277i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.46410i | 0.259607i | 0.991540 | + | 0.129804i | \(0.0414347\pi\) | ||||
−0.991540 | + | 0.129804i | \(0.958565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.9282 | −0.518047 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 32.7846 | 1.55066 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.14359 | 0.195548 | 0.0977741 | − | 0.995209i | \(-0.468828\pi\) | ||||
0.0977741 | + | 0.995209i | \(0.468828\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.0000 | −0.753411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 30.9282i | − | 1.45313i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.92820 | + | 6.00000i | 0.324799 | + | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.3923 | −0.579688 | −0.289844 | − | 0.957074i | \(-0.593603\pi\) | ||||
−0.289844 | + | 0.957074i | \(0.593603\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 16.0000i | − | 0.746816i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.5167i | − | 0.815832i | −0.913019 | − | 0.407916i | \(-0.866256\pi\) | ||
0.913019 | − | 0.407916i | \(-0.133744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.4641i | 1.27637i | 0.769885 | + | 0.638183i | \(0.220313\pi\) | ||||
−0.769885 | + | 0.638183i | \(0.779687\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.8564i | 0.642575i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.5885 | −0.582524 | −0.291262 | − | 0.956643i | \(-0.594075\pi\) | ||||
−0.291262 | + | 0.956643i | \(0.594075\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.39230 | − | 5.07180i | 0.202818 | − | 0.234194i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 52.6410i | − | 2.42557i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 13.8564 | 0.637118 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.66025 | 0.259710 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −30.9282 | −1.41611 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0718 | −0.780030 | −0.390015 | − | 0.920808i | \(-0.627530\pi\) | ||||
−0.390015 | + | 0.920808i | \(0.627530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.9282i | 0.863052i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −25.8564 | + | 29.8564i | −1.17651 | + | 1.35851i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.78461 | −0.398889 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.3923i | 0.742806i | 0.928472 | + | 0.371403i | \(0.121123\pi\) | ||||
−0.928472 | + | 0.371403i | \(0.878877\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 44.7846i | 2.02523i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.3205i | − | 0.871922i | −0.899965 | − | 0.435961i | \(-0.856409\pi\) | ||
0.899965 | − | 0.435961i | \(-0.143591\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 27.7128i | − | 1.24812i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.8564 | 0.802586 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.85641 | + | 9.07180i | −0.352408 | + | 0.406926i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.3923i | 0.733820i | 0.930256 | + | 0.366910i | \(0.119584\pi\) | ||||
−0.930256 | + | 0.366910i | \(0.880416\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.8564 | −0.619059 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.53590 | −0.201845 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.6603 | −1.13961 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 42.1962i | 1.87031i | 0.354237 | + | 0.935156i | \(0.384741\pi\) | ||||
−0.354237 | + | 0.935156i | \(0.615259\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | − | 13.8564i | 0.530849 | − | 0.612971i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.07180 | 0.223925 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 13.8564i | − | 0.610586i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.8564i | 1.66492i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 8.92820i | − | 0.391905i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.0718i | 0.572686i | 0.958127 | + | 0.286343i | \(0.0924397\pi\) | ||||
−0.958127 | + | 0.286343i | \(0.907560\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.3731 | 1.28439 | 0.642197 | − | 0.766539i | \(-0.278023\pi\) | ||||
0.642197 | + | 0.766539i | \(0.278023\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −24.3923 | − | 21.1244i | −1.06457 | − | 0.921942i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 27.7128i | − | 1.20719i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.85641 | −0.298105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.9808 | 0.736902 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.8564 | 0.600188 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.14359 | 0.265611 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 1.07180i | − | 0.0462514i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.8564 | − | 5.46410i | 1.63059 | − | 0.235356i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.0000 | 1.20381 | 0.601907 | − | 0.798566i | \(-0.294408\pi\) | ||||
0.601907 | + | 0.798566i | \(0.294408\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 45.7128i | 1.96172i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 5.07180i | − | 0.217252i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 21.4641i | − | 0.917739i | −0.888504 | − | 0.458869i | \(-0.848255\pi\) | ||
0.888504 | − | 0.458869i | \(-0.151745\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 52.0526i | − | 2.22155i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.78461 | 0.374237 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | + | 6.92820i | −0.255146 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.00000i | 0.339581i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.9282 | 1.31047 | 0.655235 | − | 0.755425i | \(-0.272570\pi\) | ||||
0.655235 | + | 0.755425i | \(0.272570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.0000 | −0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −59.7128 | −2.52108 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.9808 | 1.22139 | 0.610697 | − | 0.791865i | \(-0.290889\pi\) | ||||
0.610697 | + | 0.791865i | \(0.290889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.92820i | − | 0.291472i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.92820 | + | 4.26795i | 0.206965 | + | 0.179237i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.3923 | −1.19027 | −0.595134 | − | 0.803627i | \(-0.702901\pi\) | ||||
−0.595134 | + | 0.803627i | \(0.702901\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.2487i | 1.26587i | 0.774205 | + | 0.632935i | \(0.218150\pi\) | ||||
−0.774205 | + | 0.632935i | \(0.781850\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.3205i | 1.30843i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 24.3923i | − | 1.01723i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.1436i | 0.422283i | 0.977455 | + | 0.211142i | \(0.0677181\pi\) | ||||
−0.977455 | + | 0.211142i | \(0.932282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0000 | 0.498703 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.4641 | − | 18.5885i | −0.890481 | − | 0.771179i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 37.8564i | 1.56785i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.4641 | −0.639362 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.80385 | 0.157002 | 0.0785008 | − | 0.996914i | \(-0.474987\pi\) | ||||
0.0785008 | + | 0.996914i | \(0.474987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.78461 | 0.361964 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −32.7846 | −1.34858 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.7128i | 0.809508i | 0.914426 | + | 0.404754i | \(0.132643\pi\) | ||||
−0.914426 | + | 0.404754i | \(0.867357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.85641 | − | 5.07180i | −0.240089 | − | 0.207923i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 45.8564 | 1.87678 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.5359i | 0.512203i | 0.966650 | + | 0.256101i | \(0.0824381\pi\) | ||||
−0.966650 | + | 0.256101i | \(0.917562\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 34.6410i | 1.41304i | 0.707695 | + | 0.706518i | \(0.249735\pi\) | ||||
−0.707695 | + | 0.706518i | \(0.750265\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3205i | 0.461007i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 13.8038i | − | 0.561206i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.00000 | −0.324710 | −0.162355 | − | 0.986732i | \(-0.551909\pi\) | ||||
−0.162355 | + | 0.986732i | \(0.551909\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −37.8564 | − | 32.7846i | −1.53402 | − | 1.32850i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 32.7846i | − | 1.32632i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.8564 | −1.04433 | −0.522165 | − | 0.852844i | \(-0.674876\pi\) | ||||
−0.522165 | + | 0.852844i | \(0.674876\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.85641 | 0.236153 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.39230 | −0.176828 | −0.0884138 | − | 0.996084i | \(-0.528180\pi\) | ||||
−0.0884138 | + | 0.996084i | \(0.528180\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.1962 | 0.972525 | 0.486263 | − | 0.873813i | \(-0.338360\pi\) | ||||
0.486263 | + | 0.873813i | \(0.338360\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 21.8564i | − | 0.877067i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 25.8564 | − | 29.8564i | 1.03592 | − | 1.19617i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 18.9282i | − | 0.755920i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 16.0000i | − | 0.637962i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.2487i | 0.965326i | 0.875806 | + | 0.482663i | \(0.160330\pi\) | ||||
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 20.7846i | − | 0.826114i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.7128 | −0.623544 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.7846 | + | 4.73205i | −1.29897 | + | 0.187491i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 20.2487i | − | 0.801027i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.4641 | −1.32175 | −0.660876 | − | 0.750495i | \(-0.729815\pi\) | ||||
−0.660876 | + | 0.750495i | \(0.729815\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.7321 | −0.896465 | −0.448232 | − | 0.893917i | \(-0.647946\pi\) | ||||
−0.448232 | + | 0.893917i | \(0.647946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.07180 | −0.199702 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.6410 | −0.890110 | −0.445055 | − | 0.895503i | \(-0.646816\pi\) | ||||
−0.445055 | + | 0.895503i | \(0.646816\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 20.7846i | − | 0.815867i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −37.8564 | − | 32.7846i | −1.48371 | − | 1.28493i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.0000 | 0.469596 | 0.234798 | − | 0.972044i | \(-0.424557\pi\) | ||||
0.234798 | + | 0.972044i | \(0.424557\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.85641i | 0.306975i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 30.9282i | 1.20662i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 36.1051i | − | 1.40646i | −0.710965 | − | 0.703228i | \(-0.751741\pi\) | ||
0.710965 | − | 0.703228i | \(-0.248259\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.1962i | 0.552166i | 0.961134 | + | 0.276083i | \(0.0890365\pi\) | ||||
−0.961134 | + | 0.276083i | \(0.910963\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 51.7128 | 2.00836 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.60770 | − | 1.85641i | 0.0623437 | − | 0.0719884i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 37.8564i | − | 1.46581i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −21.8564 | −0.845017 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −63.7128 | −2.45961 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0000 | 1.15642 | 0.578208 | − | 0.815890i | \(-0.303752\pi\) | ||||
0.578208 | + | 0.815890i | \(0.303752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.8564 | 0.687293 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.8756i | 0.725450i | 0.931896 | + | 0.362725i | \(0.118154\pi\) | ||||
−0.931896 | + | 0.362725i | \(0.881846\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.7846 | − | 24.0000i | 0.797640 | − | 0.921035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.46410 | 0.132745 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.4641i | 1.12741i | 0.825975 | + | 0.563706i | \(0.190625\pi\) | ||||
−0.825975 | + | 0.563706i | \(0.809375\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 14.5359i | − | 0.555388i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.928203i | 0.0354132i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 32.7846i | − | 1.24899i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.9808 | −1.25465 | −0.627324 | − | 0.778759i | \(-0.715850\pi\) | ||||
−0.627324 | + | 0.778759i | \(0.715850\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −42.2487 | + | 48.7846i | −1.60490 | + | 1.85317i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3.07180i | − | 0.116520i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.7128 | −0.443654 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 54.2487 | 2.05187 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.85641 | 0.0701155 | 0.0350578 | − | 0.999385i | \(-0.488838\pi\) | ||||
0.0350578 | + | 0.999385i | \(0.488838\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.07180 | 0.191286 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 13.8564i | − | 0.521862i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.7321 | − | 12.3923i | 0.403620 | − | 0.466061i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.9282 | 1.16153 | 0.580767 | − | 0.814070i | \(-0.302753\pi\) | ||||
0.580767 | + | 0.814070i | \(0.302753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 15.4641i | − | 0.579949i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 37.8564i | − | 1.41773i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.9282i | 0.707875i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 1.07180i | − | 0.0400270i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.0718 | 0.636671 | 0.318335 | − | 0.947978i | \(-0.396876\pi\) | ||||
0.318335 | + | 0.947978i | \(0.396876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.8564 | + | 32.7846i | 1.40985 | + | 1.22096i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 32.7846i | 1.21927i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.9282 | 1.14864 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.78461 | −0.325803 | −0.162902 | − | 0.986642i | \(-0.552085\pi\) | ||||
−0.162902 | + | 0.986642i | \(0.552085\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.7846 | −1.62165 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.1436 | 0.375174 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.19615i | 0.0811167i | 0.999177 | + | 0.0405584i | \(0.0129137\pi\) | ||||
−0.999177 | + | 0.0405584i | \(0.987086\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.8564 | + | 2.00000i | −0.511101 | + | 0.0737711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.8564 | 0.510407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 11.3205i | − | 0.416432i | −0.978083 | − | 0.208216i | \(-0.933234\pi\) | ||
0.978083 | − | 0.208216i | \(-0.0667656\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.3923i | 0.602186i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.5359i | 0.386525i | 0.981147 | + | 0.193262i | \(0.0619068\pi\) | ||||
−0.981147 | + | 0.193262i | \(0.938093\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.78461i | 0.321843i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 47.9090 | 1.75290 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.5359 | + | 16.7846i | −0.531130 | + | 0.613296i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 26.5359i | − | 0.968309i | −0.874983 | − | 0.484154i | \(-0.839127\pi\) | ||
0.874983 | − | 0.484154i | \(-0.160873\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 60.2487 | 2.19559 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.28719 | 0.301602 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.5692 | 1.07471 | 0.537356 | − | 0.843356i | \(-0.319423\pi\) | ||||
0.537356 | + | 0.843356i | \(0.319423\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −81.5692 | −2.96078 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.7846i | 0.608442i | 0.952602 | + | 0.304221i | \(0.0983961\pi\) | ||||
−0.952602 | + | 0.304221i | \(0.901604\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.8564 | + | 12.0000i | 0.501636 | + | 0.434429i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.0718 | 0.472612 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.0000i | 0.649942i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.85641i | 0.0669437i | 0.999440 | + | 0.0334719i | \(0.0106564\pi\) | ||||
−0.999440 | + | 0.0334719i | \(0.989344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 59.7128i | 2.15050i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.4449i | 1.31083i | 0.755269 | + | 0.655415i | \(0.227506\pi\) | ||||
−0.755269 | + | 0.655415i | \(0.772494\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.9282 | 1.11097 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −21.8564 | − | 18.9282i | −0.784094 | − | 0.679046i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 3.71281i | − | 0.133025i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.7846 | −0.886863 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.7128 | 0.990375 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.1051 | 0.503433 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.5885 | −0.733899 | −0.366950 | − | 0.930241i | \(-0.619598\pi\) | ||||
−0.366950 | + | 0.930241i | \(0.619598\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.3205i | 1.11504i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.9282 | + | 16.3923i | 0.673009 | + | 0.582843i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 55.1769 | 1.95939 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 13.8564i | − | 0.491436i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 41.1244i | − | 1.45670i | −0.685206 | − | 0.728350i | \(-0.740288\pi\) | ||
0.685206 | − | 0.728350i | \(-0.259712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.7128i | 0.980409i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 66.6410i | 2.35464i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 37.8564 | 1.33592 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.00000 | − | 6.92820i | −0.281963 | − | 0.244187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 3.07180i | − | 0.108132i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.1769 | 1.30707 | 0.653535 | − | 0.756896i | \(-0.273285\pi\) | ||||
0.653535 | + | 0.756896i | \(0.273285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −49.3731 | −1.73372 | −0.866861 | − | 0.498549i | \(-0.833866\pi\) | ||||
−0.866861 | + | 0.498549i | \(0.833866\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.0000 | −0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.21539i | 0.112492i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 36.5885 | − | 42.2487i | 1.27850 | − | 1.47629i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.92820 | 0.241796 | 0.120898 | − | 0.992665i | \(-0.461423\pi\) | ||||
0.120898 | + | 0.992665i | \(0.461423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 20.5359i | − | 0.715836i | −0.933753 | − | 0.357918i | \(-0.883487\pi\) | ||
0.933753 | − | 0.357918i | \(-0.116513\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 66.6410i | − | 2.32014i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 43.3205i | − | 1.50640i | −0.657791 | − | 0.753201i | \(-0.728509\pi\) | ||
0.657791 | − | 0.753201i | \(-0.271491\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.19615i | 0.0762755i | 0.999272 | + | 0.0381378i | \(0.0121426\pi\) | ||||
−0.999272 | + | 0.0381378i | \(0.987857\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 78.6410 | 2.72803 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 27.7128 | − | 4.00000i | 0.960192 | − | 0.138592i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.71281i | − | 0.128487i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.7128 | 0.957895 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.07180 | 0.175098 | 0.0875489 | − | 0.996160i | \(-0.472097\pi\) | ||||
0.0875489 | + | 0.996160i | \(0.472097\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −16.3923 | −0.564581 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 6.87564i | − | 0.236529i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.7128 | + | 32.6603i | 1.29583 | + | 1.12222i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −43.1769 | −1.48183 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 21.8564i | − | 0.749228i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 51.3731i | − | 1.75898i | −0.475917 | − | 0.879490i | \(-0.657884\pi\) | ||
0.475917 | − | 0.879490i | \(-0.342116\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.14359i | 0.141708i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 21.0718i | − | 0.719799i | −0.932991 | − | 0.359899i | \(-0.882811\pi\) | ||
0.932991 | − | 0.359899i | \(-0.117189\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.5167 | −0.665900 | −0.332950 | − | 0.942945i | \(-0.608044\pi\) | ||||
−0.332950 | + | 0.942945i | \(0.608044\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.8564 | + | 16.0000i | −0.472225 | + | 0.545279i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.1769i | 1.33360i | 0.745238 | + | 0.666799i | \(0.232336\pi\) | ||||
−0.745238 | + | 0.666799i | \(0.767664\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.39230 | 0.0813408 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.73205 | 0.0927853 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −18.9282 | −0.642095 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0000 | −0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 53.5692i | 1.81304i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0000 | − | 13.8564i | 0.405674 | − | 0.468432i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.5692 | −0.998482 | −0.499241 | − | 0.866463i | \(-0.666388\pi\) | ||||
−0.499241 | + | 0.866463i | \(0.666388\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 4.92820i | − | 0.166224i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 35.7128i | − | 1.20320i | −0.798799 | − | 0.601598i | \(-0.794531\pi\) | ||
0.798799 | − | 0.601598i | \(-0.205469\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.53590i | − | 0.0853398i | −0.999089 | − | 0.0426699i | \(-0.986414\pi\) | ||
0.999089 | − | 0.0426699i | \(-0.0135864\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.60770i | 0.255730i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.0718 | −0.976135 | −0.488068 | − | 0.872806i | \(-0.662298\pi\) | ||||
−0.488068 | + | 0.872806i | \(0.662298\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.1769 | − | 42.9282i | 1.24687 | − | 1.43977i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.4641i | 0.451064i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.78461 | −0.293966 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.287187 | 0.00959961 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 70.6410 | 2.35863 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.0000 | 1.60089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.7128i | 0.923248i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.0000 | − | 13.8564i | 0.399335 | − | 0.461112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.2487 | −0.407161 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 44.1051i | − | 1.46449i | −0.681043 | − | 0.732243i | \(-0.738473\pi\) | ||
0.681043 | − | 0.732243i | \(-0.261527\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.6603i | 0.917433i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.3923i | − | 1.07320i | −0.843835 | − | 0.536602i | \(-0.819707\pi\) | ||
0.843835 | − | 0.536602i | \(-0.180293\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 58.6410i | − | 1.94073i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.3205 | 0.770952 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.4641 | − | 18.5885i | −0.708807 | − | 0.613845i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.4641i | 0.905957i | 0.891521 | + | 0.452979i | \(0.149639\pi\) | ||||
−0.891521 | + | 0.452979i | \(0.850361\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.2487 | −1.19444 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.4641 | 0.706500 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.8564 | 0.587115 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −84.4974 | −2.77526 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.00000i | 0.131236i | 0.997845 | + | 0.0656179i | \(0.0209018\pi\) | ||||
−0.997845 | + | 0.0656179i | \(0.979098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.26795 | + | 8.78461i | 0.0415554 | + | 0.287904i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 70.6410 | 2.31268 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 16.0000i | − | 0.523256i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 30.9282i | − | 1.01038i | −0.863008 | − | 0.505190i | \(-0.831422\pi\) | ||
0.863008 | − | 0.505190i | \(-0.168578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 89.5692i | − | 2.92298i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 17.1244i | − | 0.558238i | −0.960257 | − | 0.279119i | \(-0.909958\pi\) | ||
0.960257 | − | 0.279119i | \(-0.0900424\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.07180 | − | 5.85641i | 0.164986 | − | 0.190509i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.4641i | 0.437525i | 0.975778 | + | 0.218762i | \(0.0702019\pi\) | ||||
−0.975778 | + | 0.218762i | \(0.929798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.7846 | −1.06423 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.07180 | −0.164464 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.7128 | 1.09207 | 0.546033 | − | 0.837764i | \(-0.316137\pi\) | ||||
0.546033 | + | 0.837764i | \(0.316137\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.39230 | −0.271569 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 103.426i | − | 3.34328i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.7128 | + | 34.3923i | 1.28239 | + | 1.11059i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 37.4641i | − | 1.20726i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.21539i | 0.103507i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 11.3205i | − | 0.364043i | −0.983295 | − | 0.182021i | \(-0.941736\pi\) | ||
0.983295 | − | 0.182021i | \(-0.0582640\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 13.8564i | − | 0.445132i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 55.5167 | 1.78161 | 0.890807 | − | 0.454381i | \(-0.150140\pi\) | ||||
0.890807 | + | 0.454381i | \(0.150140\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.39230 | + | 7.26795i | 0.269045 | + | 0.233000i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 57.7128i | 1.84829i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.8564 | 1.01918 | 0.509588 | − | 0.860418i | \(-0.329798\pi\) | ||||
0.509588 | + | 0.860418i | \(0.329798\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 81.5692 | 2.60696 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.9282 | −0.987462 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.07180 | −0.161765 | −0.0808826 | − | 0.996724i | \(-0.525774\pi\) | ||||
−0.0808826 | + | 0.996724i | \(0.525774\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 8.78461i | − | 0.279901i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 37.8564 | + | 32.7846i | 1.20498 | + | 1.04355i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.8564 | 0.440608 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 31.1769i | − | 0.990367i | −0.868788 | − | 0.495184i | \(-0.835101\pi\) | ||
0.868788 | − | 0.495184i | \(-0.164899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.9282i | 0.981477i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.2872i | 0.389530i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.87564i | 0.0910726i | 0.998963 | + | 0.0455363i | \(0.0144997\pi\) | ||||
−0.998963 | + | 0.0455363i | \(0.985500\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.0000 | 0.506218 |
(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 | 1792.2.f.h.1791.4 | 4 | ||
4.3 | odd | 2 | 1792.2.f.b.1791.2 | 4 | |||
7.6 | odd | 2 | 1792.2.f.b.1791.1 | 4 | |||
8.3 | odd | 2 | 1792.2.f.i.1791.3 | 4 | |||
8.5 | even | 2 | 1792.2.f.a.1791.1 | 4 | |||
16.3 | odd | 4 | 896.2.e.a.447.1 | ✓ | 4 | ||
16.5 | even | 4 | 896.2.e.f.447.1 | yes | 4 | ||
16.11 | odd | 4 | 896.2.e.e.447.4 | yes | 4 | ||
16.13 | even | 4 | 896.2.e.b.447.4 | yes | 4 | ||
28.27 | even | 2 | inner | 1792.2.f.h.1791.3 | 4 | ||
56.13 | odd | 2 | 1792.2.f.i.1791.4 | 4 | |||
56.27 | even | 2 | 1792.2.f.a.1791.2 | 4 | |||
112.13 | odd | 4 | 896.2.e.e.447.1 | yes | 4 | ||
112.27 | even | 4 | 896.2.e.b.447.1 | yes | 4 | ||
112.69 | odd | 4 | 896.2.e.a.447.4 | yes | 4 | ||
112.83 | even | 4 | 896.2.e.f.447.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.e.a.447.1 | ✓ | 4 | 16.3 | odd | 4 | ||
896.2.e.a.447.4 | yes | 4 | 112.69 | odd | 4 | ||
896.2.e.b.447.1 | yes | 4 | 112.27 | even | 4 | ||
896.2.e.b.447.4 | yes | 4 | 16.13 | even | 4 | ||
896.2.e.e.447.1 | yes | 4 | 112.13 | odd | 4 | ||
896.2.e.e.447.4 | yes | 4 | 16.11 | odd | 4 | ||
896.2.e.f.447.1 | yes | 4 | 16.5 | even | 4 | ||
896.2.e.f.447.4 | yes | 4 | 112.83 | even | 4 | ||
1792.2.f.a.1791.1 | 4 | 8.5 | even | 2 | |||
1792.2.f.a.1791.2 | 4 | 56.27 | even | 2 | |||
1792.2.f.b.1791.1 | 4 | 7.6 | odd | 2 | |||
1792.2.f.b.1791.2 | 4 | 4.3 | odd | 2 | |||
1792.2.f.h.1791.3 | 4 | 28.27 | even | 2 | inner | ||
1792.2.f.h.1791.4 | 4 | 1.1 | even | 1 | trivial | ||
1792.2.f.i.1791.3 | 4 | 8.3 | odd | 2 | |||
1792.2.f.i.1791.4 | 4 | 56.13 | odd | 2 |