Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3600,2,Mod(593,3600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3600.593");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3600 = 2^{4} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3600.w (of order \(4\), degree \(2\), 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: | \(28.7461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 450) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.1 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3600.1457 |
Dual form | 3600.2.w.h.593.2 |
$q$-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 \(\left(\mathbb{Z}/3600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(2801\) | \(3151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | + | 3.00000i | 1.13389 | + | 1.13389i | 0.989524 | + | 0.144370i | \(0.0461154\pi\) |
0.144370 | + | 0.989524i | \(0.453885\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 4.24264i | − | 1.27920i | −0.768706 | − | 0.639602i | \(-0.779099\pi\) | ||
0.768706 | − | 0.639602i | \(-0.220901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 3.00000i | −0.832050 | + | 0.832050i | −0.987797 | − | 0.155747i | \(-0.950222\pi\) |
0.155747 | + | 0.987797i | \(0.450222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.24264 | + | 4.24264i | −1.02899 | + | 1.02899i | −0.0294245 | + | 0.999567i | \(0.509367\pi\) |
−0.999567 | + | 0.0294245i | \(0.990633\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.00000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.24264 | − | 4.24264i | −0.884652 | − | 0.884652i | 0.109351 | − | 0.994003i | \(-0.465123\pi\) |
−0.994003 | + | 0.109351i | \(0.965123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.48528 | −1.57568 | −0.787839 | − | 0.615882i | \(-0.788800\pi\) | ||||
−0.787839 | + | 0.615882i | \(0.788800\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | − | 3.00000i | −0.493197 | − | 0.493197i | 0.416115 | − | 0.909312i | \(-0.363391\pi\) |
−0.909312 | + | 0.416115i | \(0.863391\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.24264i | − | 0.662589i | −0.943527 | − | 0.331295i | \(-0.892515\pi\) | ||
0.943527 | − | 0.331295i | \(-0.107485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.0000i | 1.57143i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.24264 | − | 4.24264i | −0.582772 | − | 0.582772i | 0.352892 | − | 0.935664i | \(-0.385198\pi\) |
−0.935664 | + | 0.352892i | \(0.885198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.24264 | 0.552345 | 0.276172 | − | 0.961108i | \(-0.410934\pi\) | ||||
0.276172 | + | 0.961108i | \(0.410934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0000 | −1.28037 | −0.640184 | − | 0.768221i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768221i | \(0.721142\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.00000 | − | 6.00000i | −0.733017 | − | 0.733017i | 0.238200 | − | 0.971216i | \(-0.423443\pi\) |
−0.971216 | + | 0.238200i | \(0.923443\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.48528i | − | 1.00702i | −0.863990 | − | 0.503509i | \(-0.832042\pi\) | ||
0.863990 | − | 0.503509i | \(-0.167958\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000 | − | 6.00000i | 0.702247 | − | 0.702247i | −0.262646 | − | 0.964892i | \(-0.584595\pi\) |
0.964892 | + | 0.262646i | \(0.0845950\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.7279 | − | 12.7279i | 1.45048 | − | 1.45048i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000i | 0.900070i | 0.893011 | + | 0.450035i | \(0.148589\pi\) | ||||
−0.893011 | + | 0.450035i | \(0.851411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.48528 | + | 8.48528i | 0.931381 | + | 0.931381i | 0.997792 | − | 0.0664117i | \(-0.0211551\pi\) |
−0.0664117 | + | 0.997792i | \(0.521155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.24264 | −0.449719 | −0.224860 | − | 0.974391i | \(-0.572192\pi\) | ||||
−0.224860 | + | 0.974391i | \(0.572192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.0000 | −1.88691 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000 | + | 12.0000i | 1.21842 | + | 1.21842i | 0.968187 | + | 0.250229i | \(0.0805058\pi\) |
0.250229 | + | 0.968187i | \(0.419494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.48528i | − | 0.844317i | −0.906522 | − | 0.422159i | \(-0.861273\pi\) | ||
0.906522 | − | 0.422159i | \(-0.138727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.00000 | + | 3.00000i | −0.295599 | + | 0.295599i | −0.839287 | − | 0.543688i | \(-0.817027\pi\) |
0.543688 | + | 0.839287i | \(0.317027\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.00000i | − | 0.191565i | −0.995402 | − | 0.0957826i | \(-0.969465\pi\) | ||
0.995402 | − | 0.0957826i | \(-0.0305354\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.7279 | + | 12.7279i | 1.19734 | + | 1.19734i | 0.974959 | + | 0.222383i | \(0.0713835\pi\) |
0.222383 | + | 0.974959i | \(0.428617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −25.4558 | −2.33353 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.00000 | − | 9.00000i | −0.798621 | − | 0.798621i | 0.184257 | − | 0.982878i | \(-0.441012\pi\) |
−0.982878 | + | 0.184257i | \(0.941012\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 21.2132i | − | 1.85341i | −0.375794 | − | 0.926703i | \(-0.622630\pi\) | ||
0.375794 | − | 0.926703i | \(-0.377370\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | − | 6.00000i | 0.520266 | − | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.24264 | + | 4.24264i | −0.362473 | + | 0.362473i | −0.864723 | − | 0.502249i | \(-0.832506\pi\) |
0.502249 | + | 0.864723i | \(0.332506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.7279 | + | 12.7279i | 1.06436 | + | 1.06436i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | − | 9.00000i | −0.718278 | − | 0.718278i | 0.249974 | − | 0.968252i | \(-0.419578\pi\) |
−0.968252 | + | 0.249974i | \(0.919578\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 25.4558i | − | 2.00620i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000 | − | 6.00000i | 0.469956 | − | 0.469956i | −0.431944 | − | 0.901900i | \(-0.642172\pi\) |
0.901900 | + | 0.431944i | \(0.142172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.24264 | + | 4.24264i | −0.328305 | + | 0.328305i | −0.851942 | − | 0.523636i | \(-0.824575\pi\) |
0.523636 | + | 0.851942i | \(0.324575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.00000i | − | 0.384615i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.24264 | − | 4.24264i | −0.322562 | − | 0.322562i | 0.527187 | − | 0.849749i | \(-0.323247\pi\) |
−0.849749 | + | 0.527187i | \(0.823247\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.24264 | −0.317110 | −0.158555 | − | 0.987350i | \(-0.550683\pi\) | ||||
−0.158555 | + | 0.987350i | \(0.550683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | + | 18.0000i | 1.31629 | + | 1.31629i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.48528i | 0.613973i | 0.951714 | + | 0.306987i | \(0.0993207\pi\) | ||||
−0.951714 | + | 0.306987i | \(0.900679\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.00000 | + | 6.00000i | −0.431889 | + | 0.431889i | −0.889271 | − | 0.457381i | \(-0.848787\pi\) |
0.457381 | + | 0.889271i | \(0.348787\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.48528 | + | 8.48528i | −0.604551 | + | 0.604551i | −0.941517 | − | 0.336966i | \(-0.890599\pi\) |
0.336966 | + | 0.941517i | \(0.390599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.0000i | 1.41776i | 0.705328 | + | 0.708881i | \(0.250800\pi\) | ||||
−0.705328 | + | 0.708881i | \(0.749200\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −25.4558 | − | 25.4558i | −1.78665 | − | 1.78665i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.48528 | −0.586939 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.0000 | − | 12.0000i | −0.814613 | − | 0.814613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 25.4558i | − | 1.71235i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.00000 | − | 9.00000i | 0.602685 | − | 0.602685i | −0.338340 | − | 0.941024i | \(-0.609865\pi\) |
0.941024 | + | 0.338340i | \(0.109865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.48528 | − | 8.48528i | 0.563188 | − | 0.563188i | −0.367024 | − | 0.930212i | \(-0.619623\pi\) |
0.930212 | + | 0.367024i | \(0.119623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.0000i | 0.925146i | 0.886581 | + | 0.462573i | \(0.153074\pi\) | ||||
−0.886581 | + | 0.462573i | \(0.846926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7279 | − | 12.7279i | −0.833834 | − | 0.833834i | 0.154205 | − | 0.988039i | \(-0.450718\pi\) |
−0.988039 | + | 0.154205i | \(0.950718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.4558 | −1.64660 | −0.823301 | − | 0.567605i | \(-0.807870\pi\) | ||||
−0.823301 | + | 0.567605i | \(0.807870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.0000 | −1.80364 | −0.901819 | − | 0.432113i | \(-0.857768\pi\) | ||||
−0.901819 | + | 0.432113i | \(0.857768\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000 | + | 6.00000i | 0.381771 | + | 0.381771i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 12.7279i | − | 0.803379i | −0.915776 | − | 0.401690i | \(-0.868423\pi\) | ||
0.915776 | − | 0.401690i | \(-0.131577\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.0000 | + | 18.0000i | −1.13165 | + | 1.13165i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.24264 | + | 4.24264i | −0.264649 | + | 0.264649i | −0.826940 | − | 0.562291i | \(-0.809920\pi\) |
0.562291 | + | 0.826940i | \(0.309920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 18.0000i | − | 1.11847i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7279 | − | 12.7279i | −0.784837 | − | 0.784837i | 0.195805 | − | 0.980643i | \(-0.437268\pi\) |
−0.980643 | + | 0.195805i | \(0.937268\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.48528 | 0.517357 | 0.258678 | − | 0.965964i | \(-0.416713\pi\) | ||||
0.258678 | + | 0.965964i | \(0.416713\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.0000 | −1.21491 | −0.607457 | − | 0.794353i | \(-0.707810\pi\) | ||||
−0.607457 | + | 0.794353i | \(0.707810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.00000 | + | 9.00000i | 0.540758 | + | 0.540758i | 0.923751 | − | 0.382993i | \(-0.125107\pi\) |
−0.382993 | + | 0.923751i | \(0.625107\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7279i | 0.759284i | 0.925133 | + | 0.379642i | \(0.123953\pi\) | ||||
−0.925133 | + | 0.379642i | \(0.876047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0000 | + | 18.0000i | −1.06999 | + | 1.06999i | −0.0726300 | + | 0.997359i | \(0.523139\pi\) |
−0.997359 | + | 0.0726300i | \(0.976861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.7279 | − | 12.7279i | 0.751305 | − | 0.751305i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 19.0000i | − | 1.11765i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.48528 | + | 8.48528i | 0.495715 | + | 0.495715i | 0.910101 | − | 0.414386i | \(-0.136004\pi\) |
−0.414386 | + | 0.910101i | \(0.636004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.4558 | 1.47215 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.48528i | 0.481156i | 0.970630 | + | 0.240578i | \(0.0773370\pi\) | ||||
−0.970630 | + | 0.240578i | \(0.922663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | + | 6.00000i | −0.339140 | + | 0.339140i | −0.856044 | − | 0.516904i | \(-0.827085\pi\) |
0.516904 | + | 0.856044i | \(0.327085\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.48528 | + | 8.48528i | −0.476581 | + | 0.476581i | −0.904036 | − | 0.427456i | \(-0.859410\pi\) |
0.427456 | + | 0.904036i | \(0.359410\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.0000i | 2.01561i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.48528 | + | 8.48528i | 0.472134 | + | 0.472134i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.0000 | −1.42909 | −0.714545 | − | 0.699590i | \(-0.753366\pi\) | ||||
−0.714545 | + | 0.699590i | \(0.753366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00000 | − | 6.00000i | −0.326841 | − | 0.326841i | 0.524543 | − | 0.851384i | \(-0.324236\pi\) |
−0.851384 | + | 0.524543i | \(0.824236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706i | 0.919007i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | + | 12.0000i | −0.647939 | + | 0.647939i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.4558 | + | 25.4558i | −1.36654 | + | 1.36654i | −0.501223 | + | 0.865318i | \(0.667117\pi\) |
−0.865318 | + | 0.501223i | \(0.832883\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0000i | 1.39175i | 0.718164 | + | 0.695874i | \(0.244983\pi\) | ||||
−0.718164 | + | 0.695874i | \(0.755017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.7279 | − | 12.7279i | −0.677439 | − | 0.677439i | 0.281981 | − | 0.959420i | \(-0.409008\pi\) |
−0.959420 | + | 0.281981i | \(0.909008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.9706 | −0.895672 | −0.447836 | − | 0.894116i | \(-0.647805\pi\) | ||||
−0.447836 | + | 0.894116i | \(0.647805\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.00000 | − | 3.00000i | −0.156599 | − | 0.156599i | 0.624459 | − | 0.781058i | \(-0.285320\pi\) |
−0.781058 | + | 0.624459i | \(0.785320\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 25.4558i | − | 1.32160i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0000 | − | 15.0000i | 0.776671 | − | 0.776671i | −0.202593 | − | 0.979263i | \(-0.564937\pi\) |
0.979263 | + | 0.202593i | \(0.0649367\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 25.4558 | − | 25.4558i | 1.31104 | − | 1.31104i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 20.0000i | − | 1.02733i | −0.857991 | − | 0.513665i | \(-0.828287\pi\) | ||
0.857991 | − | 0.513665i | \(-0.171713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.9706 | + | 16.9706i | 0.867155 | + | 0.867155i | 0.992157 | − | 0.125001i | \(-0.0398935\pi\) |
−0.125001 | + | 0.992157i | \(0.539894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0000 | 1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.0000 | + | 27.0000i | 1.35509 | + | 1.35509i | 0.879862 | + | 0.475229i | \(0.157635\pi\) |
0.475229 | + | 0.879862i | \(0.342365\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.7279i | 0.635602i | 0.948157 | + | 0.317801i | \(0.102944\pi\) | ||||
−0.948157 | + | 0.317801i | \(0.897056\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0000 | − | 12.0000i | 0.597763 | − | 0.597763i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.7279 | + | 12.7279i | −0.630900 | + | 0.630900i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000i | 0.692255i | 0.938187 | + | 0.346128i | \(0.112504\pi\) | ||||
−0.938187 | + | 0.346128i | \(0.887496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.7279 | + | 12.7279i | 0.626300 | + | 0.626300i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.1838 | 1.86540 | 0.932700 | − | 0.360654i | \(-0.117447\pi\) | ||||
0.932700 | + | 0.360654i | \(0.117447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.0000 | − | 30.0000i | −1.45180 | − | 1.45180i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.9706i | 0.817443i | 0.912659 | + | 0.408722i | \(0.134025\pi\) | ||||
−0.912659 | + | 0.408722i | \(0.865975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.0000 | − | 18.0000i | 0.865025 | − | 0.865025i | −0.126892 | − | 0.991917i | \(-0.540500\pi\) |
0.991917 | + | 0.126892i | \(0.0405001\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.48528 | + | 8.48528i | −0.405906 | + | 0.405906i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 28.0000i | − | 1.33637i | −0.743996 | − | 0.668184i | \(-0.767072\pi\) | ||
0.743996 | − | 0.668184i | \(-0.232928\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.9706 | + | 16.9706i | 0.806296 | + | 0.806296i | 0.984071 | − | 0.177775i | \(-0.0568900\pi\) |
−0.177775 | + | 0.984071i | \(0.556890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.6985 | −1.40156 | −0.700779 | − | 0.713378i | \(-0.747164\pi\) | ||||
−0.700779 | + | 0.713378i | \(0.747164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 16.9706i | − | 0.790398i | −0.918596 | − | 0.395199i | \(-0.870676\pi\) | ||
0.918596 | − | 0.395199i | \(-0.129324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.0000 | − | 21.0000i | 0.975953 | − | 0.975953i | −0.0237648 | − | 0.999718i | \(-0.507565\pi\) |
0.999718 | + | 0.0237648i | \(0.00756529\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.48528 | − | 8.48528i | 0.392652 | − | 0.392652i | −0.482980 | − | 0.875632i | \(-0.660445\pi\) |
0.875632 | + | 0.482980i | \(0.160445\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 36.0000i | − | 1.66233i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.48528 | −0.387702 | −0.193851 | − | 0.981031i | \(-0.562098\pi\) | ||||
−0.193851 | + | 0.981031i | \(0.562098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.0000 | 0.820729 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.00000 | + | 3.00000i | 0.135943 | + | 0.135943i | 0.771804 | − | 0.635861i | \(-0.219355\pi\) |
−0.635861 | + | 0.771804i | \(0.719355\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.24264i | 0.191468i | 0.995407 | + | 0.0957338i | \(0.0305198\pi\) | ||||
−0.995407 | + | 0.0957338i | \(0.969480\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.0000 | − | 36.0000i | 1.62136 | − | 1.62136i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 25.4558 | − | 25.4558i | 1.14185 | − | 1.14185i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 22.0000i | − | 0.984855i | −0.870353 | − | 0.492428i | \(-0.836110\pi\) | ||
0.870353 | − | 0.492428i | \(-0.163890\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.9706 | − | 16.9706i | −0.756680 | − | 0.756680i | 0.219037 | − | 0.975717i | \(-0.429709\pi\) |
−0.975717 | + | 0.219037i | \(0.929709\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.4558 | −1.12831 | −0.564155 | − | 0.825669i | \(-0.690798\pi\) | ||||
−0.564155 | + | 0.825669i | \(0.690798\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.0000 | 1.59255 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.7279i | 0.557620i | 0.960346 | + | 0.278810i | \(0.0899400\pi\) | ||||
−0.960346 | + | 0.278810i | \(0.910060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.00000 | + | 6.00000i | −0.262362 | + | 0.262362i | −0.826013 | − | 0.563651i | \(-0.809396\pi\) |
0.563651 | + | 0.826013i | \(0.309396\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.9706 | − | 16.9706i | 0.739249 | − | 0.739249i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000i | 0.565217i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.7279 | + | 12.7279i | 0.551308 | + | 0.551308i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 46.6690 | 2.01018 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | − | 12.0000i | −0.513083 | − | 0.513083i | 0.402387 | − | 0.915470i | \(-0.368181\pi\) |
−0.915470 | + | 0.402387i | \(0.868181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9706i | 0.722970i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.0000 | + | 24.0000i | −1.02058 | + | 1.02058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.7279 | + | 12.7279i | −0.539299 | + | 0.539299i | −0.923323 | − | 0.384024i | \(-0.874538\pi\) |
0.384024 | + | 0.923323i | \(0.374538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.4558 | + | 25.4558i | 1.07284 | + | 1.07284i | 0.997130 | + | 0.0757057i | \(0.0241210\pi\) |
0.0757057 | + | 0.997130i | \(0.475879\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 46.6690 | 1.95647 | 0.978234 | − | 0.207504i | \(-0.0665341\pi\) | ||||
0.978234 | + | 0.207504i | \(0.0665341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0000 | 0.920671 | 0.460336 | − | 0.887745i | \(-0.347729\pi\) | ||||
0.460336 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.0000 | − | 24.0000i | −0.999133 | − | 0.999133i | 0.000866551 | − | 1.00000i | \(-0.499724\pi\) |
−1.00000 | 0.000866551i | \(0.999724\pi\) | ||||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.9117i | 2.11217i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | + | 18.0000i | −0.745484 | + | 0.745484i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.9706 | − | 16.9706i | 0.700450 | − | 0.700450i | −0.264057 | − | 0.964507i | \(-0.585061\pi\) |
0.964507 | + | 0.264057i | \(0.0850607\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000i | 0.329634i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.24264 | + | 4.24264i | 0.174224 | + | 0.174224i | 0.788833 | − | 0.614608i | \(-0.210686\pi\) |
−0.614608 | + | 0.788833i | \(0.710686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.9706 | −0.693398 | −0.346699 | − | 0.937976i | \(-0.612698\pi\) | ||||
−0.346699 | + | 0.937976i | \(0.612698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 28.0000 | 1.14214 | 0.571072 | − | 0.820900i | \(-0.306528\pi\) | ||||
0.571072 | + | 0.820900i | \(0.306528\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.0000 | + | 21.0000i | 0.852364 | + | 0.852364i | 0.990424 | − | 0.138060i | \(-0.0440867\pi\) |
−0.138060 | + | 0.990424i | \(0.544087\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.0000 | + | 33.0000i | −1.33286 | + | 1.33286i | −0.430055 | + | 0.902803i | \(0.641506\pi\) |
−0.902803 | + | 0.430055i | \(0.858494\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.24264 | + | 4.24264i | −0.170802 | + | 0.170802i | −0.787332 | − | 0.616530i | \(-0.788538\pi\) |
0.616530 | + | 0.787332i | \(0.288538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.0000i | − | 1.12542i | −0.826656 | − | 0.562708i | \(-0.809760\pi\) | ||
0.826656 | − | 0.562708i | \(-0.190240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.7279 | − | 12.7279i | −0.509933 | − | 0.509933i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 25.4558 | 1.01499 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −33.0000 | − | 33.0000i | −1.30751 | − | 1.30751i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.24264i | − | 0.167574i | −0.996484 | − | 0.0837871i | \(-0.973298\pi\) | ||
0.996484 | − | 0.0837871i | \(-0.0267016\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0000 | − | 18.0000i | 0.709851 | − | 0.709851i | −0.256653 | − | 0.966504i | \(-0.582620\pi\) |
0.966504 | + | 0.256653i | \(0.0826197\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.9706 | + | 16.9706i | −0.667182 | + | 0.667182i | −0.957063 | − | 0.289881i | \(-0.906384\pi\) |
0.289881 | + | 0.957063i | \(0.406384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 18.0000i | − | 0.706562i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.9706 | − | 16.9706i | −0.664109 | − | 0.664109i | 0.292237 | − | 0.956346i | \(-0.405601\pi\) |
−0.956346 | + | 0.292237i | \(0.905601\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.1838 | 1.48743 | 0.743714 | − | 0.668498i | \(-0.233062\pi\) | ||||
0.743714 | + | 0.668498i | \(0.233062\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.0000 | + | 36.0000i | 1.39393 | + | 1.39393i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.4264i | 1.63785i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.0000 | + | 30.0000i | −1.15642 | + | 1.15642i | −0.171174 | + | 0.985241i | \(0.554756\pi\) |
−0.985241 | + | 0.171174i | \(0.945244\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 72.0000i | 2.76311i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9411 | − | 33.9411i | −1.29872 | − | 1.29872i | −0.929237 | − | 0.369484i | \(-0.879534\pi\) |
−0.369484 | − | 0.929237i | \(-0.620466\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.4558 | 0.969790 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.0000 | −0.380418 | −0.190209 | − | 0.981744i | \(-0.560917\pi\) | ||||
−0.190209 | + | 0.981744i | \(0.560917\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | + | 18.0000i | 0.681799 | + | 0.681799i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.4264i | 1.60242i | 0.598381 | + | 0.801212i | \(0.295811\pi\) | ||||
−0.598381 | + | 0.801212i | \(0.704189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | + | 6.00000i | −0.226294 | + | 0.226294i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.4558 | − | 25.4558i | 0.957366 | − | 0.957366i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 46.0000i | − | 1.72757i | −0.503864 | − | 0.863783i | \(-0.668089\pi\) | ||
0.503864 | − | 0.863783i | \(-0.331911\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.9706 | + | 16.9706i | 0.635553 | + | 0.635553i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.9411 | −1.26579 | −0.632895 | − | 0.774237i | \(-0.718134\pi\) | ||||
−0.632895 | + | 0.774237i | \(0.718134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.0000 | −0.670355 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.00000 | − | 9.00000i | −0.333792 | − | 0.333792i | 0.520233 | − | 0.854024i | \(-0.325845\pi\) |
−0.854024 | + | 0.520233i | \(0.825845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.00000 | − | 9.00000i | 0.332423 | − | 0.332423i | −0.521083 | − | 0.853506i | \(-0.674472\pi\) |
0.853506 | + | 0.521083i | \(0.174472\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.4558 | + | 25.4558i | −0.937678 | + | 0.937678i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 38.0000i | − | 1.39785i | −0.715194 | − | 0.698926i | \(-0.753662\pi\) | ||
0.715194 | − | 0.698926i | \(-0.246338\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0000 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.0000 | + | 15.0000i | 0.545184 | + | 0.545184i | 0.925044 | − | 0.379860i | \(-0.124028\pi\) |
−0.379860 | + | 0.925044i | \(0.624028\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.6985i | 1.07657i | 0.842763 | + | 0.538285i | \(0.180927\pi\) | ||||
−0.842763 | + | 0.538285i | \(0.819073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.00000 | − | 6.00000i | 0.217215 | − | 0.217215i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −12.7279 | + | 12.7279i | −0.459579 | + | 0.459579i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.0000i | 1.44244i | 0.692708 | + | 0.721218i | \(0.256418\pi\) | ||||
−0.692708 | + | 0.721218i | \(0.743582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.48528 | − | 8.48528i | −0.305194 | − | 0.305194i | 0.537848 | − | 0.843042i | \(-0.319238\pi\) |
−0.843042 | + | 0.537848i | \(0.819238\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.48528 | −0.304017 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.0000 | −1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.0000 | + | 30.0000i | 1.06938 | + | 1.06938i | 0.997406 | + | 0.0719783i | \(0.0229312\pi\) |
0.0719783 | + | 0.997406i | \(0.477069\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 76.3675i | 2.71532i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.0000 | − | 30.0000i | 1.06533 | − | 1.06533i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.2132 | + | 21.2132i | −0.751410 | + | 0.751410i | −0.974742 | − | 0.223332i | \(-0.928307\pi\) |
0.223332 | + | 0.974742i | \(0.428307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.4558 | − | 25.4558i | −0.898317 | − | 0.898317i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.6985 | 1.04414 | 0.522072 | − | 0.852902i | \(-0.325159\pi\) | ||||
0.522072 | + | 0.852902i | \(0.325159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.48528i | 0.296138i | 0.988977 | + | 0.148069i | \(0.0473058\pi\) | ||||
−0.988977 | + | 0.148069i | \(0.952694\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.00000 | + | 3.00000i | −0.104573 | + | 0.104573i | −0.757458 | − | 0.652884i | \(-0.773559\pi\) |
0.652884 | + | 0.757458i | \(0.273559\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.9411 | + | 33.9411i | −1.18025 | + | 1.18025i | −0.200569 | + | 0.979680i | \(0.564279\pi\) |
−0.979680 | + | 0.200569i | \(0.935721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 34.0000i | − | 1.18087i | −0.807086 | − | 0.590434i | \(-0.798956\pi\) | ||
0.807086 | − | 0.590434i | \(-0.201044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −46.6690 | − | 46.6690i | −1.61699 | − | 1.61699i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.9706 | 0.585889 | 0.292944 | − | 0.956129i | \(-0.405365\pi\) | ||||
0.292944 | + | 0.956129i | \(0.405365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.0000 | 1.48276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0000 | − | 21.0000i | −0.721569 | − | 0.721569i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25.4558i | 0.872615i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.0000 | + | 21.0000i | −0.719026 | + | 0.719026i | −0.968406 | − | 0.249380i | \(-0.919773\pi\) |
0.249380 | + | 0.968406i | \(0.419773\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.6985 | + | 29.6985i | −1.01448 | + | 1.01448i | −0.0145873 | + | 0.999894i | \(0.504643\pi\) |
−0.999894 | + | 0.0145873i | \(0.995357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 4.00000i | − | 0.136478i | −0.997669 | − | 0.0682391i | \(-0.978262\pi\) | ||
0.997669 | − | 0.0682391i | \(-0.0217381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.24264 | + | 4.24264i | 0.144421 | + | 0.144421i | 0.775621 | − | 0.631199i | \(-0.217437\pi\) |
−0.631199 | + | 0.775621i | \(0.717437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.9411 | 1.15137 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 36.0000 | 1.21981 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.0000 | + | 15.0000i | 0.506514 | + | 0.506514i | 0.913455 | − | 0.406941i | \(-0.133404\pi\) |
−0.406941 | + | 0.913455i | \(0.633404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 46.6690i | − | 1.57232i | −0.618023 | − | 0.786160i | \(-0.712066\pi\) | ||
0.618023 | − | 0.786160i | \(-0.287934\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.00000 | + | 6.00000i | −0.201916 | + | 0.201916i | −0.800821 | − | 0.598904i | \(-0.795603\pi\) |
0.598904 | + | 0.800821i | \(0.295603\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.24264 | − | 4.24264i | 0.142454 | − | 0.142454i | −0.632283 | − | 0.774737i | \(-0.717882\pi\) |
0.774737 | + | 0.632283i | \(0.217882\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 54.0000i | − | 1.81110i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 33.9411 | 1.13200 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.0000 | − | 24.0000i | −0.796907 | − | 0.796907i | 0.185700 | − | 0.982607i | \(-0.440545\pi\) |
−0.982607 | + | 0.185700i | \(0.940545\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.9706i | 0.562260i | 0.959670 | + | 0.281130i | \(0.0907092\pi\) | ||||
−0.959670 | + | 0.281130i | \(0.909291\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.0000 | − | 36.0000i | 1.19143 | − | 1.19143i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 63.6396 | − | 63.6396i | 2.10157 | − | 2.10157i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 20.0000i | − | 0.659739i | −0.944027 | − | 0.329870i | \(-0.892995\pi\) | ||
0.944027 | − | 0.329870i | \(-0.107005\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.4558 | + | 25.4558i | 0.837889 | + | 0.837889i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.24264 | 0.139197 | 0.0695983 | − | 0.997575i | \(-0.477828\pi\) | ||||
0.0695983 | + | 0.997575i | \(0.477828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.0000 | 0.721021 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.0000 | + | 24.0000i | 0.784046 | + | 0.784046i | 0.980511 | − | 0.196465i | \(-0.0629462\pi\) |
−0.196465 | + | 0.980511i | \(0.562946\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 50.9117i | − | 1.65967i | −0.558006 | − | 0.829837i | \(-0.688433\pi\) | ||
0.558006 | − | 0.829837i | \(-0.311567\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | + | 18.0000i | −0.586161 | + | 0.586161i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.9411 | + | 33.9411i | −1.10294 | + | 1.10294i | −0.108884 | + | 0.994054i | \(0.534728\pi\) |
−0.994054 | + | 0.108884i | \(0.965272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.0000i | 1.16861i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38.1838 | + | 38.1838i | 1.23689 | + | 1.23689i | 0.961264 | + | 0.275630i | \(0.0888863\pi\) |
0.275630 | + | 0.961264i | \(0.411114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.4558 | −0.822012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.0000 | − | 15.0000i | −0.482367 | − | 0.482367i | 0.423520 | − | 0.905887i | \(-0.360795\pi\) |
−0.905887 | + | 0.423520i | \(0.860795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 29.6985i | − | 0.953070i | −0.879156 | − | 0.476535i | \(-0.841893\pi\) | ||
0.879156 | − | 0.476535i | \(-0.158107\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.0000 | + | 12.0000i | −0.384702 | + | 0.384702i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.7279 | − | 12.7279i | 0.407202 | − | 0.407202i | −0.473560 | − | 0.880762i | \(-0.657031\pi\) |
0.880762 | + | 0.473560i | \(0.157031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000i | 0.575282i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.9411 | + | 33.9411i | 1.08255 | + | 1.08255i | 0.996271 | + | 0.0862831i | \(0.0274990\pi\) |
0.0862831 | + | 0.996271i | \(0.472501\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 52.0000 | 1.65183 | 0.825917 | − | 0.563791i | \(-0.190658\pi\) | ||||
0.825917 | + | 0.563791i | \(0.190658\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.0000 | − | 27.0000i | −0.855099 | − | 0.855099i | 0.135657 | − | 0.990756i | \(-0.456685\pi\) |
−0.990756 | + | 0.135657i | \(0.956685\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3600.2.w.h.1457.1 | 4 | ||
3.2 | odd | 2 | inner | 3600.2.w.h.1457.2 | 4 | ||
4.3 | odd | 2 | 450.2.f.a.107.1 | ✓ | 4 | ||
5.2 | odd | 4 | 3600.2.w.a.593.1 | 4 | |||
5.3 | odd | 4 | inner | 3600.2.w.h.593.1 | 4 | ||
5.4 | even | 2 | 3600.2.w.a.1457.1 | 4 | |||
12.11 | even | 2 | 450.2.f.a.107.2 | yes | 4 | ||
15.2 | even | 4 | 3600.2.w.a.593.2 | 4 | |||
15.8 | even | 4 | inner | 3600.2.w.h.593.2 | 4 | ||
15.14 | odd | 2 | 3600.2.w.a.1457.2 | 4 | |||
20.3 | even | 4 | 450.2.f.a.143.2 | yes | 4 | ||
20.7 | even | 4 | 450.2.f.c.143.1 | yes | 4 | ||
20.19 | odd | 2 | 450.2.f.c.107.2 | yes | 4 | ||
60.23 | odd | 4 | 450.2.f.a.143.1 | yes | 4 | ||
60.47 | odd | 4 | 450.2.f.c.143.2 | yes | 4 | ||
60.59 | even | 2 | 450.2.f.c.107.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.f.a.107.1 | ✓ | 4 | 4.3 | odd | 2 | ||
450.2.f.a.107.2 | yes | 4 | 12.11 | even | 2 | ||
450.2.f.a.143.1 | yes | 4 | 60.23 | odd | 4 | ||
450.2.f.a.143.2 | yes | 4 | 20.3 | even | 4 | ||
450.2.f.c.107.1 | yes | 4 | 60.59 | even | 2 | ||
450.2.f.c.107.2 | yes | 4 | 20.19 | odd | 2 | ||
450.2.f.c.143.1 | yes | 4 | 20.7 | even | 4 | ||
450.2.f.c.143.2 | yes | 4 | 60.47 | odd | 4 | ||
3600.2.w.a.593.1 | 4 | 5.2 | odd | 4 | |||
3600.2.w.a.593.2 | 4 | 15.2 | even | 4 | |||
3600.2.w.a.1457.1 | 4 | 5.4 | even | 2 | |||
3600.2.w.a.1457.2 | 4 | 15.14 | odd | 2 | |||
3600.2.w.h.593.1 | 4 | 5.3 | odd | 4 | inner | ||
3600.2.w.h.593.2 | 4 | 15.8 | even | 4 | inner | ||
3600.2.w.h.1457.1 | 4 | 1.1 | even | 1 | trivial | ||
3600.2.w.h.1457.2 | 4 | 3.2 | odd | 2 | inner |