Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(897,1792)]
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([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.897");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.b (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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 896) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 897.3 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.897 |
Dual form | 1792.2.b.n.897.2 |
$q$-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 | ||||||||
\(3\) | 0.732051i | 0.422650i | 0.977416 | + | 0.211325i | \(0.0677778\pi\) | ||||
−0.977416 | + | 0.211325i | \(0.932222\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 2.73205i | − 1.22181i | −0.791704 | − | 0.610905i | \(-0.790806\pi\) | ||||
0.791704 | − | 0.610905i | \(-0.209194\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.46410 | 0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.46410i | − 0.441443i | −0.975337 | − | 0.220722i | \(-0.929159\pi\) | ||||
0.975337 | − | 0.220722i | \(-0.0708412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.73205i | 0.757735i | 0.925451 | + | 0.378867i | \(0.123686\pi\) | ||||
−0.925451 | + | 0.378867i | \(0.876314\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | 0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.46410 | 1.81031 | 0.905155 | − | 0.425081i | \(-0.139754\pi\) | ||||
0.905155 | + | 0.425081i | \(0.139754\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 6.19615i | − 1.42149i | −0.703447 | − | 0.710747i | \(-0.748357\pi\) | ||||
0.703447 | − | 0.710747i | \(-0.251643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.732051i | 0.159747i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.92820 | −1.86166 | −0.930830 | − | 0.365454i | \(-0.880914\pi\) | ||||
−0.930830 | + | 0.365454i | \(0.880914\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.46410 | −0.492820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000i | 0.769800i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.46410i | 0.643268i | 0.946864 | + | 0.321634i | \(0.104232\pi\) | ||||
−0.946864 | + | 0.321634i | \(0.895768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.53590 | 0.455461 | 0.227730 | − | 0.973724i | \(-0.426870\pi\) | ||||
0.227730 | + | 0.973724i | \(0.426870\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.07180 | 0.186576 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.73205i | − 0.461801i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 4.53590i | − 0.745697i | −0.927892 | − | 0.372849i | \(-0.878381\pi\) | ||||
0.927892 | − | 0.372849i | \(-0.121619\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.00000 | −0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410 | 0.541002 | 0.270501 | − | 0.962720i | \(-0.412811\pi\) | ||||
0.270501 | + | 0.962720i | \(0.412811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.53590i | 0.386721i | 0.981128 | + | 0.193360i | \(0.0619387\pi\) | ||||
−0.981128 | + | 0.193360i | \(0.938061\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 6.73205i | − 1.00355i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.46410 | −0.213561 | −0.106781 | − | 0.994283i | \(-0.534054\pi\) | ||||
−0.106781 | + | 0.994283i | \(0.534054\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.46410i | 0.765127i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 6.00000i | − 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.53590 | 0.600794 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.19615i | 0.806670i | 0.915052 | + | 0.403335i | \(0.132149\pi\) | ||||
−0.915052 | + | 0.403335i | \(0.867851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 11.1244i | − 1.42433i | −0.702013 | − | 0.712164i | \(-0.747715\pi\) | ||||
0.702013 | − | 0.712164i | \(-0.252285\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.46410 | 0.310448 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.46410 | 0.925808 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 14.9282i | − 1.82377i | −0.410445 | − | 0.911885i | \(-0.634627\pi\) | ||||
0.410445 | − | 0.911885i | \(-0.365373\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 6.53590i | − 0.786830i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8564 | 1.64445 | 0.822226 | − | 0.569160i | \(-0.192732\pi\) | ||||
0.822226 | + | 0.569160i | \(0.192732\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.92820 | −1.04497 | −0.522484 | − | 0.852649i | \(-0.674994\pi\) | ||||
−0.522484 | + | 0.852649i | \(0.674994\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 1.80385i | − 0.208290i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.46410i | − 0.166850i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.26795i | 0.797761i | 0.917003 | + | 0.398881i | \(0.130601\pi\) | ||||
−0.917003 | + | 0.398881i | \(0.869399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 20.3923i | − 2.21186i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.53590 | −0.271877 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.92820 | −0.522388 | −0.261194 | − | 0.965286i | \(-0.584116\pi\) | ||||
−0.261194 | + | 0.965286i | \(0.584116\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.73205i | 0.286397i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.85641i | 0.192500i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.9282 | −1.73680 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.535898 | 0.0544122 | 0.0272061 | − | 0.999630i | \(-0.491339\pi\) | ||||
0.0272061 | + | 0.999630i | \(0.491339\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 3.60770i | − 0.362587i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.80385i | 0.378497i | 0.981929 | + | 0.189248i | \(0.0606052\pi\) | ||||
−0.981929 | + | 0.189248i | \(0.939395\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.39230 | −0.826918 | −0.413459 | − | 0.910523i | \(-0.635680\pi\) | ||||
−0.413459 | + | 0.910523i | \(0.635680\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 16.0000i | − 1.54678i | −0.633932 | − | 0.773389i | \(-0.718560\pi\) | ||||
0.633932 | − | 0.773389i | \(-0.281440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 3.46410i | − 0.331801i | −0.986143 | − | 0.165900i | \(-0.946947\pi\) | ||||
0.986143 | − | 0.165900i | \(-0.0530530\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.32051 | 0.315169 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.392305 | 0.0369049 | 0.0184525 | − | 0.999830i | \(-0.494126\pi\) | ||||
0.0184525 | + | 0.999830i | \(0.494126\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 24.3923i | 2.27459i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.73205i | 0.622378i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.46410 | 0.684233 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.85641 | 0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.53590i | 0.228654i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 6.92820i | − 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.85641 | −0.163447 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.19615i | 0.191879i | 0.995387 | + | 0.0959394i | \(0.0305855\pi\) | ||||
−0.995387 | + | 0.0959394i | \(0.969415\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 6.19615i | − 0.537275i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.9282 | 0.940550 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 20.9282 | 1.78802 | 0.894009 | − | 0.448050i | \(-0.147881\pi\) | ||||
0.894009 | + | 0.448050i | \(0.147881\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.6603i | 1.32829i | 0.747606 | + | 0.664143i | \(0.231203\pi\) | ||||
−0.747606 | + | 0.664143i | \(0.768797\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 1.07180i | − 0.0902616i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.00000 | 0.334497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.46410 | 0.785951 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.732051i | 0.0603785i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.8564i | 1.62670i | 0.581775 | + | 0.813350i | \(0.302359\pi\) | ||||
−0.581775 | + | 0.813350i | \(0.697641\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.3923 | 1.48693 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 6.92820i | − 0.556487i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 13.2679i | − 1.05890i | −0.848342 | − | 0.529449i | \(-0.822399\pi\) | ||||
0.848342 | − | 0.529449i | \(-0.177601\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.39230 | 0.348332 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.92820 | −0.703641 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 20.3923i | − 1.59725i | −0.601830 | − | 0.798624i | \(-0.705561\pi\) | ||||
0.601830 | − | 0.798624i | \(-0.294439\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 2.92820i | − 0.227960i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.53590 | 0.505763 | 0.252882 | − | 0.967497i | \(-0.418622\pi\) | ||||
0.252882 | + | 0.967497i | \(0.418622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.53590 | 0.425838 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 15.2679i | − 1.16757i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.66025i | 0.430341i | 0.976576 | + | 0.215171i | \(0.0690307\pi\) | ||||
−0.976576 | + | 0.215171i | \(0.930969\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.46410 | −0.186269 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.53590 | −0.340939 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000i | 0.896922i | 0.893802 | + | 0.448461i | \(0.148028\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.66025i | 0.123406i | 0.998095 | + | 0.0617029i | \(0.0196531\pi\) | ||||
−0.998095 | + | 0.0617029i | \(0.980347\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.14359 | 0.601992 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.3923 | −0.911100 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 10.9282i | − 0.799149i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.00000i | 0.290957i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.9282 | 0.790737 | 0.395369 | − | 0.918523i | \(-0.370617\pi\) | ||||
0.395369 | + | 0.918523i | \(0.370617\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.3923 | −0.892018 | −0.446009 | − | 0.895029i | \(-0.647155\pi\) | ||||
−0.446009 | + | 0.895029i | \(0.647155\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.46410i | 0.391292i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.8564i | 1.69970i | 0.527026 | + | 0.849849i | \(0.323307\pi\) | ||||
−0.527026 | + | 0.849849i | \(0.676693\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.5359 | −1.31397 | −0.656987 | − | 0.753901i | \(-0.728170\pi\) | ||||
−0.656987 | + | 0.753901i | \(0.728170\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.9282 | 0.770816 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.46410i | 0.243132i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 9.46410i | − 0.661002i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.0000 | −1.52911 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.07180 | −0.627509 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 4.00000i | − 0.275371i | −0.990476 | − | 0.137686i | \(-0.956034\pi\) | ||||
0.990476 | − | 0.137686i | \(-0.0439664\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.1436i | 0.695028i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.92820 | 0.472500 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.53590 | 0.172148 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 6.53590i | − 0.441655i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 20.3923i | 1.37173i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.8564 | −1.73147 | −0.865737 | − | 0.500500i | \(-0.833150\pi\) | ||||
−0.865737 | + | 0.500500i | \(0.833150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.07180 | −0.404786 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.80385i | 0.650704i | 0.945593 | + | 0.325352i | \(0.105483\pi\) | ||||
−0.945593 | + | 0.325352i | \(0.894517\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.196152i | 0.0129621i | 0.999979 | + | 0.00648106i | \(0.00206300\pi\) | ||||
−0.999979 | + | 0.00648106i | \(0.997937\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.07180 | 0.0705191 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000i | 0.260931i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.85641i | 0.380414i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.9282 | −0.836256 | −0.418128 | − | 0.908388i | \(-0.637314\pi\) | ||||
−0.418128 | + | 0.908388i | \(0.637314\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4641 | 1.25379 | 0.626897 | − | 0.779103i | \(-0.284325\pi\) | ||||
0.626897 | + | 0.779103i | \(0.284325\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.2679i | 0.979439i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 2.73205i | − 0.174544i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.9282 | 1.07712 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.32051 | −0.337173 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.1962i | 1.65349i | 0.562579 | + | 0.826743i | \(0.309809\pi\) | ||||
−0.562579 | + | 0.826743i | \(0.690191\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.0718i | 0.821817i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.9282 | 0.934840 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.9282 | −1.55498 | −0.777489 | − | 0.628896i | \(-0.783507\pi\) | ||||
−0.777489 | + | 0.628896i | \(0.783507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 4.53590i | − 0.281847i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.53590i | 0.528359i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.8564 | −0.854423 | −0.427211 | − | 0.904152i | \(-0.640504\pi\) | ||||
−0.427211 | + | 0.904152i | \(0.640504\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.3923 | −1.00697 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 3.60770i | − 0.220787i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 14.0526i | − 0.856800i | −0.903589 | − | 0.428400i | \(-0.859077\pi\) | ||||
0.903589 | − | 0.428400i | \(-0.140923\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.07180 | 0.551072 | 0.275536 | − | 0.961291i | \(-0.411145\pi\) | ||||
0.275536 | + | 0.961291i | \(0.411145\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.60770i | 0.217552i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 12.9282i | − 0.776780i | −0.921495 | − | 0.388390i | \(-0.873031\pi\) | ||||
0.921495 | − | 0.388390i | \(-0.126969\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.24871 | 0.374101 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.85641 | 0.468674 | 0.234337 | − | 0.972155i | \(-0.424708\pi\) | ||||
0.234337 | + | 0.972155i | \(0.424708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 16.0526i | − 0.954226i | −0.878842 | − | 0.477113i | \(-0.841683\pi\) | ||||
0.878842 | − | 0.477113i | \(-0.158317\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 12.3923i | − 0.734057i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.46410 | 0.204479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 38.7128 | 2.27722 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.392305i | 0.0229973i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.7321i | 0.860656i | 0.902673 | + | 0.430328i | \(0.141602\pi\) | ||||
−0.902673 | + | 0.430328i | \(0.858398\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.9282 | 0.985598 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.85641 | 0.339823 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 24.3923i | − 1.41064i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.53590i | 0.146167i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.78461 | −0.159972 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.3923 | −1.74026 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.1962i | 1.49509i | 0.664209 | + | 0.747547i | \(0.268768\pi\) | ||||
−0.664209 | + | 0.747547i | \(0.731232\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 6.14359i | − 0.349497i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.9282 | −0.619682 | −0.309841 | − | 0.950788i | \(-0.600276\pi\) | ||||
−0.309841 | + | 0.950788i | \(0.600276\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.5359 | −0.708571 | −0.354285 | − | 0.935137i | \(-0.615276\pi\) | ||||
−0.354285 | + | 0.935137i | \(0.615276\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 6.73205i | − 0.379308i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 12.9282i | − 0.726120i | −0.931766 | − | 0.363060i | \(-0.881732\pi\) | ||||
0.931766 | − | 0.363060i | \(-0.118268\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.07180 | 0.283966 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.7128 | 0.653745 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 46.2487i | − 2.57335i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 6.73205i | − 0.373427i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.53590 | 0.140236 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.46410 | −0.0807185 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 5.46410i | − 0.300334i | −0.988661 | − | 0.150167i | \(-0.952019\pi\) | ||||
0.988661 | − | 0.150167i | \(-0.0479812\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 11.1769i | − 0.612491i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −40.7846 | −2.22830 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −26.2487 | −1.42986 | −0.714929 | − | 0.699197i | \(-0.753541\pi\) | ||||
−0.714929 | + | 0.699197i | \(0.753541\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.287187i | 0.0155979i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3.71281i | − 0.201060i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −17.8564 | −0.961357 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.4641i | 1.15225i | 0.817360 | + | 0.576127i | \(0.195437\pi\) | ||||
−0.817360 | + | 0.576127i | \(0.804563\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1244i | 1.23782i | 0.785463 | + | 0.618909i | \(0.212425\pi\) | ||||
−0.785463 | + | 0.618909i | \(0.787575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.9282 | −0.583304 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9282 | −0.688099 | −0.344049 | − | 0.938952i | \(-0.611799\pi\) | ||||
−0.344049 | + | 0.938952i | \(0.611799\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 37.8564i | − 2.00921i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.46410i | 0.289191i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.8564 | −0.625757 | −0.312879 | − | 0.949793i | \(-0.601293\pi\) | ||||
−0.312879 | + | 0.949793i | \(0.601293\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.3923 | −1.02065 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.48334i | 0.340287i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.3923i | 1.27675i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.7846 | 1.50254 | 0.751272 | − | 0.659992i | \(-0.229441\pi\) | ||||
0.751272 | + | 0.659992i | \(0.229441\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.53590 | 0.444361 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 6.00000i | − 0.311504i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.8564i | 0.613901i | 0.951725 | + | 0.306951i | \(0.0993087\pi\) | ||||
−0.951725 | + | 0.306951i | \(0.900691\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.07180 | 0.261906 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.46410 | −0.487426 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.2487i | 1.96470i | 0.187041 | + | 0.982352i | \(0.440110\pi\) | ||||
−0.187041 | + | 0.982352i | \(0.559890\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.46410i | 0.0750082i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.4641 | 1.70994 | 0.854968 | − | 0.518681i | \(-0.173577\pi\) | ||||
0.854968 | + | 0.518681i | \(0.173577\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.24871i | 0.317640i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.535898i | 0.0271711i | 0.999908 | + | 0.0135856i | \(0.00432455\pi\) | ||||
−0.999908 | + | 0.0135856i | \(0.995675\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −66.6410 | −3.37018 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.60770 | −0.0810975 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 21.8564i | − 1.09972i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.9808i | 1.45450i | 0.686371 | + | 0.727251i | \(0.259203\pi\) | ||||
−0.686371 | + | 0.727251i | \(0.740797\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.53590 | 0.227079 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.2487 | −1.51055 | −0.755274 | − | 0.655409i | \(-0.772496\pi\) | ||||
−0.755274 | + | 0.655409i | \(0.772496\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.92820i | 0.345118i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 12.1962i | − 0.606032i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.64102 | −0.329183 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −24.5359 | −1.21322 | −0.606611 | − | 0.794999i | \(-0.707471\pi\) | ||||
−0.606611 | + | 0.794999i | \(0.707471\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.3205i | 0.755705i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.19615i | 0.304893i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.8564 | 0.974713 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.4641 | −0.561399 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 18.1962i | − 0.888940i | −0.895794 | − | 0.444470i | \(-0.853392\pi\) | ||||
0.895794 | − | 0.444470i | \(-0.146608\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 20.9282i | − 1.01998i | −0.860181 | − | 0.509989i | \(-0.829649\pi\) | ||||
0.860181 | − | 0.509989i | \(-0.170351\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.60770 | −0.175412 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.3923 | −0.892158 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 11.1244i | − 0.538345i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.92820i | 0.141375i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.7846 | 0.519476 | 0.259738 | − | 0.965679i | \(-0.416364\pi\) | ||||
0.259738 | + | 0.965679i | \(0.416364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.2487 | −0.588636 | −0.294318 | − | 0.955708i | \(-0.595092\pi\) | ||||
−0.294318 | + | 0.955708i | \(0.595092\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.92820i | 0.332182i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 55.3205i | 2.64634i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.7128 | 0.749932 | 0.374966 | − | 0.927039i | \(-0.377654\pi\) | ||||
0.374966 | + | 0.927039i | \(0.377654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.46410 | 0.117338 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.92820i | − 0.329169i | −0.986363 | − | 0.164584i | \(-0.947372\pi\) | ||||
0.986363 | − | 0.164584i | \(-0.0526283\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.4641i | 0.638260i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.5359 | −0.687524 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000 | 0.0943858 | 0.0471929 | − | 0.998886i | \(-0.484972\pi\) | ||||
0.0471929 | + | 0.998886i | \(0.484972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 5.07180i | − 0.238822i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 1.46410i | − 0.0687895i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 7.46410 | 0.349922 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.46410 | −0.442712 | −0.221356 | − | 0.975193i | \(-0.571048\pi\) | ||||
−0.221356 | + | 0.975193i | \(0.571048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 29.8564i | 1.39358i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.3397i | 0.667869i | 0.942596 | + | 0.333934i | \(0.108376\pi\) | ||||
−0.942596 | + | 0.333934i | \(0.891624\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.7128 | 1.65972 | 0.829858 | − | 0.557975i | \(-0.188422\pi\) | ||||
0.829858 | + | 0.557975i | \(0.188422\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.07180 | 0.235199 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 24.4449i | 1.13117i | 0.824689 | + | 0.565587i | \(0.191350\pi\) | ||||
−0.824689 | + | 0.565587i | \(0.808650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 14.9282i | − 0.689320i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.71281 | 0.447543 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.71281 | 0.170715 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.2679i | 0.700542i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 14.7846i | − 0.676941i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.3923 | −0.748984 | −0.374492 | − | 0.927230i | \(-0.622183\pi\) | ||||
−0.374492 | + | 0.927230i | \(0.622183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.3923 | 0.565040 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 6.53590i | − 0.297394i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.46410i | − 0.0664814i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 32.6410 | 1.47911 | 0.739553 | − | 0.673099i | \(-0.235037\pi\) | ||||
0.739553 | + | 0.673099i | \(0.235037\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 14.9282 | 0.675077 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 20.0000i | − 0.902587i | −0.892375 | − | 0.451294i | \(-0.850963\pi\) | ||||
0.892375 | − | 0.451294i | \(-0.149037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.8564i | 1.16451i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.85641 | −0.443013 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.8564 | 0.621545 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 16.0000i | − 0.716258i | −0.933672 | − | 0.358129i | \(-0.883415\pi\) | ||||
0.933672 | − | 0.358129i | \(-0.116585\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.78461i | 0.213761i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.07180 | −0.404491 | −0.202246 | − | 0.979335i | \(-0.564824\pi\) | ||||
−0.202246 | + | 0.979335i | \(0.564824\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.3923 | 0.462451 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.05256i | 0.179980i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.26795i | 0.410795i | 0.978679 | + | 0.205397i | \(0.0658487\pi\) | ||||
−0.978679 | + | 0.205397i | \(0.934151\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.92820 | −0.394960 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.7846 | 1.09427 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.9282i | 1.01034i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.14359i | 0.0942751i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.14359 | −0.181884 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.3923 | −1.33151 | −0.665756 | − | 0.746170i | \(-0.731891\pi\) | ||||
−0.665756 | + | 0.746170i | \(0.731891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2.58846i | − 0.113185i | −0.998397 | − | 0.0565927i | \(-0.981976\pi\) | ||||
0.998397 | − | 0.0565927i | \(-0.0180236\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 1.80385i | − 0.0787264i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 18.9282 | 0.824525 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.7128 | 2.46577 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.2679i | 0.662573i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.46410i | 0.409936i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −43.7128 | −1.88987 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.78461 | −0.379084 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.46410i | − 0.0630633i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.7846i | 1.49551i | 0.663976 | + | 0.747754i | \(0.268868\pi\) | ||||
−0.663976 | + | 0.747754i | \(0.731132\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.21539 | −0.0521574 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.46410 | −0.405398 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 3.60770i | − 0.154254i | −0.997021 | − | 0.0771270i | \(-0.975425\pi\) | ||||
0.997021 | − | 0.0771270i | \(-0.0245747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 27.4115i | − 1.16990i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.4641 | 0.914401 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.00000 | 0.340195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 9.07180i | − 0.385076i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.7128i | 1.08949i | 0.838603 | + | 0.544743i | \(0.183373\pi\) | ||||
−0.838603 | + | 0.544743i | \(0.816627\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.92820 | −0.293032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.12436i | 0.384546i | 0.981342 | + | 0.192273i | \(0.0615859\pi\) | ||||
−0.981342 | + | 0.192273i | \(0.938414\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 1.07180i | − 0.0450908i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.46410 | 0.187475 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.2487 | 0.932714 | 0.466357 | − | 0.884596i | \(-0.345566\pi\) | ||||
0.466357 | + | 0.884596i | \(0.345566\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.3923i | 1.35558i | 0.735257 | + | 0.677788i | \(0.237061\pi\) | ||||
−0.735257 | + | 0.677788i | \(0.762939\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000i | 0.334205i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.0000 | 0.917463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.92820 | 0.371686 | 0.185843 | − | 0.982579i | \(-0.440498\pi\) | ||||
0.185843 | + | 0.982579i | \(0.440498\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 9.07180i | − 0.377011i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.26795i | 0.301525i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.78461 | −0.363821 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 18.3923 | 0.760428 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.5885i | 0.437032i | 0.975833 | + | 0.218516i | \(0.0701217\pi\) | ||||
−0.975833 | + | 0.218516i | \(0.929878\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 15.7128i | − 0.647435i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.4641 | −0.718377 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.85641 | 0.322624 | 0.161312 | − | 0.986903i | \(-0.448427\pi\) | ||||
0.161312 | + | 0.986903i | \(0.448427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 20.3923i | − 0.836003i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 13.5692i | − 0.555351i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.928203 | 0.0378622 | 0.0189311 | − | 0.999821i | \(-0.493974\pi\) | ||||
0.0189311 | + | 0.999821i | \(0.493974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 36.7846i | − 1.49799i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 24.1962i | − 0.983713i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.9282 | −1.09298 | −0.546491 | − | 0.837465i | \(-0.684037\pi\) | ||||
−0.546491 | + | 0.837465i | \(0.684037\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.53590 | −0.102760 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 4.00000i | − 0.161823i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.3205i | 0.861127i | 0.902560 | + | 0.430564i | \(0.141685\pi\) | ||||
−0.902560 | + | 0.430564i | \(0.858315\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.92820 | 0.279372 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.3205 | −0.616780 | −0.308390 | − | 0.951260i | \(-0.599790\pi\) | ||||
−0.308390 | + | 0.951260i | \(0.599790\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.3731i | 1.90408i | 0.305967 | + | 0.952042i | \(0.401020\pi\) | ||||
−0.305967 | + | 0.952042i | \(0.598980\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 35.7128i | − 1.43311i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.92820 | −0.197444 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 6.64102i | − 0.265217i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 33.8564i | − 1.34994i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.0718 | 0.838855 | 0.419427 | − | 0.907789i | \(-0.362231\pi\) | ||||
0.419427 | + | 0.907789i | \(0.362231\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.92820 | 0.116386 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 5.46410i | − 0.216836i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.73205i | 0.108248i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34.1436 | 1.35070 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.6795 | −0.500810 | −0.250405 | − | 0.968141i | \(-0.580564\pi\) | ||||
−0.250405 | + | 0.968141i | \(0.580564\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.2679i | 0.759854i | 0.925017 | + | 0.379927i | \(0.124051\pi\) | ||||
−0.925017 | + | 0.379927i | \(0.875949\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.07180i | 0.199702i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.3205 | 0.445055 | 0.222528 | − | 0.974926i | \(-0.428569\pi\) | ||||
0.222528 | + | 0.974926i | \(0.428569\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.07180 | 0.356099 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.85641i | 0.0727583i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.4641i | 1.07475i | 0.843342 | + | 0.537377i | \(0.180585\pi\) | ||||
−0.843342 | + | 0.537377i | \(0.819415\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | 0.234439 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.0000 | −0.858302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 23.3205i | − 0.908438i | −0.890890 | − | 0.454219i | \(-0.849918\pi\) | ||||
0.890890 | − | 0.454219i | \(-0.150082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.5885i | 1.11196i | 0.831195 | + | 0.555981i | \(0.187657\pi\) | ||||
−0.831195 | + | 0.555981i | \(0.812343\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.9282 | −0.579763 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −16.9282 | −0.656448 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 30.9282i | − 1.19754i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 18.9282i | − 0.731807i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.2872 | −0.628760 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.07180 | 0.118409 | 0.0592045 | − | 0.998246i | \(-0.481144\pi\) | ||||
0.0592045 | + | 0.998246i | \(0.481144\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 9.85641i | − 0.379373i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 39.5167i | 1.51875i | 0.650654 | + | 0.759374i | \(0.274495\pi\) | ||||
−0.650654 | + | 0.759374i | \(0.725505\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.535898 | 0.0205659 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.17691 | −0.275020 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.8564i | 0.530201i | 0.964221 | + | 0.265100i | \(0.0854051\pi\) | ||||
−0.964221 | + | 0.265100i | \(0.914595\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 57.1769i | − 2.18462i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.143594 | −0.00547844 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.3923 | 0.624497 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.19615i | 0.0835456i | 0.999127 | + | 0.0417728i | \(0.0133006\pi\) | ||||
−0.999127 | + | 0.0417728i | \(0.986699\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3.60770i | − 0.137045i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 42.7846 | 1.62291 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.8564 | 0.979381 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 13.1769i | − 0.498397i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.535898i | 0.0202406i | 0.999949 | + | 0.0101203i | \(0.00322145\pi\) | ||||
−0.999949 | + | 0.0101203i | \(0.996779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.1051 | −1.06000 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.92820 | −0.110283 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.80385i | 0.143058i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 36.5359i | − 1.37213i | −0.727538 | − | 0.686067i | \(-0.759336\pi\) | ||||
0.727538 | − | 0.686067i | \(-0.240664\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 19.7128 | 0.739288 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.6410 | −0.847913 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 10.9282i | − 0.408692i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 9.46410i | − 0.353443i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 42.2487 | 1.57561 | 0.787806 | − | 0.615924i | \(-0.211217\pi\) | ||||
0.787806 | + | 0.615924i | \(0.211217\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.39230 | −0.312546 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 14.2487i | 0.529915i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 8.53590i | − 0.317015i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.5359 | −1.42922 | −0.714609 | − | 0.699524i | \(-0.753395\pi\) | ||||
−0.714609 | + | 0.699524i | \(0.753395\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.21539 | 0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.9282i | 0.700085i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.588457i | 0.0217352i | 0.999941 | + | 0.0108676i | \(0.00345933\pi\) | ||||
−0.999941 | + | 0.0108676i | \(0.996541\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.00000 | 0.0737711 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.8564 | −0.805091 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.3205i | 0.857859i | 0.903338 | + | 0.428929i | \(0.141109\pi\) | ||||
−0.903338 | + | 0.428929i | \(0.858891\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.3923i | 0.455243i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.7128 | 1.09006 | 0.545029 | − | 0.838417i | \(-0.316519\pi\) | ||||
0.545029 | + | 0.838417i | \(0.316519\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 54.2487 | 1.98752 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.9090i | 0.655255i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 16.0000i | − 0.584627i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.92820 | 0.179833 | 0.0899163 | − | 0.995949i | \(-0.471340\pi\) | ||||
0.0899163 | + | 0.995949i | \(0.471340\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.1769 | −0.698846 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.46410i | 0.198859i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 0.535898i | − 0.0194776i | −0.999953 | − | 0.00973878i | \(-0.996900\pi\) | ||||
0.999953 | − | 0.00973878i | \(-0.00310000\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.56922 | −0.347341 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.32051 | 0.0478684 | 0.0239342 | − | 0.999714i | \(-0.492381\pi\) | ||||
0.0239342 | + | 0.999714i | \(0.492381\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 3.46410i | − 0.125409i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 50.2487i | − 1.81675i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.9282 | −0.611242 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.5359 | 1.46176 | 0.730881 | − | 0.682505i | \(-0.239109\pi\) | ||||
0.730881 | + | 0.682505i | \(0.239109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 18.2487i | − 0.657211i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 43.5167i | − 1.56519i | −0.622534 | − | 0.782593i | \(-0.713897\pi\) | ||||
0.622534 | − | 0.782593i | \(-0.286103\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.24871 | −0.224460 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.32051 | 0.119123 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 21.4641i | − 0.769031i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 20.2872i | − 0.725933i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.8564 | −0.495188 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.2487 | −1.29377 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7321i | 0.453849i | 0.973912 | + | 0.226924i | \(0.0728670\pi\) | ||||
−0.973912 | + | 0.226924i | \(0.927133\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 10.1436i | − 0.361121i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.392305 | 0.0139488 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.3923 | 1.07926 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 12.0000i | − 0.425596i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.66025i | 0.200496i | 0.994962 | + | 0.100248i | \(0.0319637\pi\) | ||||
−0.994962 | + | 0.100248i | \(0.968036\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.9282 | −0.386612 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.1436 | −0.429073 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.0718i | 0.461294i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.3923i | 0.859716i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.2872 | 0.362126 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.46410 | −0.332740 | −0.166370 | − | 0.986063i | \(-0.553205\pi\) | ||||
−0.166370 | + | 0.986063i | \(0.553205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 34.9808i | − 1.22834i | −0.789173 | − | 0.614170i | \(-0.789491\pi\) | ||||
0.789173 | − | 0.614170i | \(-0.210509\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.64102i | 0.232911i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −55.7128 | −1.95153 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.7128 | 0.549722 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.73205i | 0.235237i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 5.71281i | − 0.199379i | −0.995019 | − | 0.0996893i | \(-0.968215\pi\) | ||||
0.995019 | − | 0.0996893i | \(-0.0317849\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.784610 | −0.0273498 | −0.0136749 | − | 0.999906i | \(-0.504353\pi\) | ||||
−0.0136749 | + | 0.999906i | \(0.504353\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.64102 | −0.0919484 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 34.9282i | − 1.21457i | −0.794483 | − | 0.607286i | \(-0.792258\pi\) | ||||
0.794483 | − | 0.607286i | \(-0.207742\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 29.2679i | − 1.01652i | −0.861204 | − | 0.508259i | \(-0.830289\pi\) | ||||
0.861204 | − | 0.508259i | \(-0.169711\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.46410 | 0.328306 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.46410 | 0.258616 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 17.8564i | − 0.617946i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.1436i | 0.350614i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.53590 | 0.0875489 | 0.0437745 | − | 0.999041i | \(-0.486062\pi\) | ||||
0.0437745 | + | 0.999041i | \(0.486062\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0000 | 0.586207 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.75129i | 0.198085i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 15.1244i | − 0.520294i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.85641 | 0.304310 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.7513 | 0.403303 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.4974i | 1.38823i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 11.5167i | − 0.394323i | −0.980371 | − | 0.197161i | \(-0.936828\pi\) | ||||
0.980371 | − | 0.197161i | \(-0.0631723\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −41.7128 | −1.42655 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.5359 | 0.701493 | 0.350746 | − | 0.936470i | \(-0.385928\pi\) | ||||
0.350746 | + | 0.936470i | \(0.385928\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 3.66025i | − 0.124886i | −0.998049 | − | 0.0624431i | \(-0.980111\pi\) | ||||
0.998049 | − | 0.0624431i | \(-0.0198892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.53590i | 0.0864232i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.0718 | −0.717292 | −0.358646 | − | 0.933474i | \(-0.616762\pi\) | ||||
−0.358646 | + | 0.933474i | \(0.616762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.4641 | 0.525795 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 28.3397i | 0.962468i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 11.7128i | − 0.397330i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.7846 | 1.38193 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.32051 | 0.0446924 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 6.92820i | − 0.234216i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 34.1051i | − 1.15165i | −0.817574 | − | 0.575824i | \(-0.804681\pi\) | ||||
0.817574 | − | 0.575824i | \(-0.195319\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.7846 | −0.363756 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.7128 | −0.461996 | −0.230998 | − | 0.972954i | \(-0.574199\pi\) | ||||
−0.230998 | + | 0.972954i | \(0.574199\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 8.00000i | − 0.269221i | −0.990899 | − | 0.134611i | \(-0.957022\pi\) | ||||
0.990899 | − | 0.134611i | \(-0.0429784\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12.3923i | 0.416563i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 33.4641 | 1.12361 | 0.561807 | − | 0.827268i | \(-0.310106\pi\) | ||||
0.561807 | + | 0.827268i | \(0.310106\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | 0.0670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 6.53590i | − 0.218961i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.07180i | 0.303576i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.7846 | 1.09587 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.8564 | 0.596208 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.78461i | 0.292983i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 44.7846i | − 1.49199i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.85641 | −0.0617773 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.53590 | 0.150778 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 42.6410i | − 1.41587i | −0.706277 | − | 0.707936i | \(-0.749627\pi\) | ||||
0.706277 | − | 0.707936i | \(-0.250373\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.37307i | 0.310885i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.00000 | 0.198789 | 0.0993944 | − | 0.995048i | \(-0.468309\pi\) | ||||
0.0993944 | + | 0.995048i | \(0.468309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6410 | 0.352166 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 22.2487i | − 0.735520i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.19615i | 0.0725233i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.78461 | −0.289778 | −0.144889 | − | 0.989448i | \(-0.546282\pi\) | ||||
−0.144889 | + | 0.989448i | \(0.546282\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.1769 | −0.631901 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37.8564i | 1.24606i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.1769i | 0.367495i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −20.6795 | −0.679204 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.46410 | −0.113653 | −0.0568267 | − | 0.998384i | \(-0.518098\pi\) | ||||
−0.0568267 | + | 0.998384i | \(0.518098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 6.19615i | − 0.203071i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 8.00000i | − 0.261908i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −29.8564 | −0.976409 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.5692 | 1.42334 | 0.711672 | − | 0.702512i | \(-0.247938\pi\) | ||||
0.711672 | + | 0.702512i | \(0.247938\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 9.17691i | − 0.299477i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 55.9090i | 1.82258i | 0.411765 | + | 0.911290i | \(0.364912\pi\) | ||||
−0.411765 | + | 0.911290i | \(0.635088\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −30.9282 | −1.00716 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.9282 | 0.355494 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 7.32051i | − 0.237885i | −0.992901 | − | 0.118942i | \(-0.962050\pi\) | ||||
0.992901 | − | 0.118942i | \(-0.0379503\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 24.3923i | − 0.791808i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.46410 | 0.306895 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.0000 | −1.10137 | −0.550684 | − | 0.834714i | \(-0.685633\pi\) | ||||
−0.550684 | + | 0.834714i | \(0.685633\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 29.8564i | − 0.966131i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.71281i | 0.120018i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.9282 | 0.675807 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.5692 | −0.792555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 39.4256i | − 1.27047i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.8564i | 1.08988i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32.6410 | 1.04966 | 0.524832 | − | 0.851206i | \(-0.324128\pi\) | ||||
0.524832 | + | 0.851206i | \(0.324128\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.8564 | 1.08762 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 17.8038i | − 0.571353i | −0.958326 | − | 0.285676i | \(-0.907782\pi\) | ||||
0.958326 | − | 0.285676i | \(-0.0922182\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.6603i | 0.502045i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.92820 | 0.157829 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.6410 | 0.532393 | 0.266197 | − | 0.963919i | \(-0.414233\pi\) | ||||
0.266197 | + | 0.963919i | \(0.414233\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.21539i | 0.230605i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 8.53590i | − 0.272530i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.392305 | 0.0125126 | 0.00625629 | − | 0.999980i | \(-0.498009\pi\) | ||||
0.00625629 | + | 0.999980i | \(0.498009\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 65.1769 | 2.07671 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 1.07180i | − 0.0341157i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 22.6410i | − 0.719942i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.9282 | −0.347146 | −0.173573 | − | 0.984821i | \(-0.555531\pi\) | ||||
−0.173573 | + | 0.984821i | \(0.555531\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 50.6410i | 1.60543i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 53.6603i | − 1.69944i | −0.527236 | − | 0.849719i | \(-0.676772\pi\) | ||||
0.527236 | − | 0.849719i | \(-0.323228\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 18.1436 | 0.574038 |
(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.b.n.897.3 | 4 | ||
4.3 | odd | 2 | 1792.2.b.l.897.2 | 4 | |||
8.3 | odd | 2 | 1792.2.b.l.897.3 | 4 | |||
8.5 | even | 2 | inner | 1792.2.b.n.897.2 | 4 | ||
16.3 | odd | 4 | 896.2.a.e.1.2 | ✓ | 2 | ||
16.5 | even | 4 | 896.2.a.f.1.2 | yes | 2 | ||
16.11 | odd | 4 | 896.2.a.h.1.1 | yes | 2 | ||
16.13 | even | 4 | 896.2.a.g.1.1 | yes | 2 | ||
48.5 | odd | 4 | 8064.2.a.be.1.1 | 2 | |||
48.11 | even | 4 | 8064.2.a.bf.1.1 | 2 | |||
48.29 | odd | 4 | 8064.2.a.bm.1.2 | 2 | |||
48.35 | even | 4 | 8064.2.a.br.1.2 | 2 | |||
112.13 | odd | 4 | 6272.2.a.j.1.2 | 2 | |||
112.27 | even | 4 | 6272.2.a.i.1.2 | 2 | |||
112.69 | odd | 4 | 6272.2.a.s.1.1 | 2 | |||
112.83 | even | 4 | 6272.2.a.t.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.a.e.1.2 | ✓ | 2 | 16.3 | odd | 4 | ||
896.2.a.f.1.2 | yes | 2 | 16.5 | even | 4 | ||
896.2.a.g.1.1 | yes | 2 | 16.13 | even | 4 | ||
896.2.a.h.1.1 | yes | 2 | 16.11 | odd | 4 | ||
1792.2.b.l.897.2 | 4 | 4.3 | odd | 2 | |||
1792.2.b.l.897.3 | 4 | 8.3 | odd | 2 | |||
1792.2.b.n.897.2 | 4 | 8.5 | even | 2 | inner | ||
1792.2.b.n.897.3 | 4 | 1.1 | even | 1 | trivial | ||
6272.2.a.i.1.2 | 2 | 112.27 | even | 4 | |||
6272.2.a.j.1.2 | 2 | 112.13 | odd | 4 | |||
6272.2.a.s.1.1 | 2 | 112.69 | odd | 4 | |||
6272.2.a.t.1.1 | 2 | 112.83 | even | 4 | |||
8064.2.a.be.1.1 | 2 | 48.5 | odd | 4 | |||
8064.2.a.bf.1.1 | 2 | 48.11 | even | 4 | |||
8064.2.a.bm.1.2 | 2 | 48.29 | odd | 4 | |||
8064.2.a.br.1.2 | 2 | 48.35 | even | 4 |