Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(577,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.s (of order \(3\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1873.1 | ||
Root | \(-1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2736.1873 |
Dual form | 2736.2.s.u.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −0.822876 | + | 1.42526i | −0.368001 | + | 0.637397i | −0.989253 | − | 0.146214i | \(-0.953291\pi\) |
0.621252 | + | 0.783611i | \(0.286624\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.645751 | 0.244071 | 0.122036 | − | 0.992526i | \(-0.461058\pi\) | ||||
0.122036 | + | 0.992526i | \(0.461058\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.64575 | 1.70226 | 0.851129 | − | 0.524957i | \(-0.175918\pi\) | ||||
0.851129 | + | 0.524957i | \(0.175918\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.14575 | − | 5.44860i | −0.872474 | − | 1.51117i | −0.859429 | − | 0.511255i | \(-0.829181\pi\) |
−0.0130455 | − | 0.999915i | \(-0.504153\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.64575 | − | 6.31463i | 0.884225 | − | 1.53152i | 0.0376247 | − | 0.999292i | \(-0.488021\pi\) |
0.846600 | − | 0.532230i | \(-0.178646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.64575 | + | 3.46410i | −0.606977 | + | 0.794719i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.177124 | + | 0.306788i | 0.0369330 | + | 0.0639698i | 0.883901 | − | 0.467674i | \(-0.154908\pi\) |
−0.846968 | + | 0.531644i | \(0.821575\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.14575 | + | 1.98450i | 0.229150 | + | 0.396900i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.64575 | − | 2.85052i | −0.305608 | − | 0.529329i | 0.671788 | − | 0.740743i | \(-0.265526\pi\) |
−0.977397 | + | 0.211414i | \(0.932193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.64575 | −0.834402 | −0.417201 | − | 0.908814i | \(-0.636989\pi\) | ||||
−0.417201 | + | 0.908814i | \(0.636989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.531373 | + | 0.920365i | −0.0898184 | + | 0.155570i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.00000 | −0.821995 | −0.410997 | − | 0.911636i | \(-0.634819\pi\) | ||||
−0.410997 | + | 0.911636i | \(0.634819\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | − | 3.46410i | 0.312348 | − | 0.541002i | −0.666523 | − | 0.745485i | \(-0.732218\pi\) |
0.978870 | + | 0.204483i | \(0.0655513\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.32288 | − | 9.21949i | 0.811731 | − | 1.40596i | −0.0999207 | − | 0.994995i | \(-0.531859\pi\) |
0.911652 | − | 0.410964i | \(-0.134808\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.64575 | + | 4.58258i | 0.385922 | + | 0.668437i | 0.991897 | − | 0.127047i | \(-0.0405499\pi\) |
−0.605974 | + | 0.795484i | \(0.707217\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.58301 | −0.940429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.46863 | − | 7.73989i | −0.613813 | − | 1.06316i | −0.990591 | − | 0.136852i | \(-0.956301\pi\) |
0.376778 | − | 0.926303i | \(-0.377032\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.64575 | + | 8.04668i | −0.626433 | + | 1.08501i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.17712 | + | 2.03884i | −0.153249 | + | 0.265434i | −0.932420 | − | 0.361377i | \(-0.882307\pi\) |
0.779171 | + | 0.626811i | \(0.215640\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.50000 | − | 4.33013i | −0.320092 | − | 0.554416i | 0.660415 | − | 0.750901i | \(-0.270381\pi\) |
−0.980507 | + | 0.196485i | \(0.937047\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.3542 | 1.28429 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.968627 | − | 1.67771i | −0.118337 | − | 0.204965i | 0.800772 | − | 0.598969i | \(-0.204423\pi\) |
−0.919109 | + | 0.394004i | \(0.871090\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.00000 | − | 8.66025i | 0.593391 | − | 1.02778i | −0.400381 | − | 0.916349i | \(-0.631122\pi\) |
0.993772 | − | 0.111434i | \(-0.0355445\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.14575 | + | 3.71655i | −0.251141 | + | 0.434989i | −0.963840 | − | 0.266481i | \(-0.914139\pi\) |
0.712699 | + | 0.701470i | \(0.247473\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.64575 | 0.415472 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.32288 | − | 7.48744i | 0.486362 | − | 0.842403i | −0.513516 | − | 0.858080i | \(-0.671657\pi\) |
0.999877 | + | 0.0156774i | \(0.00499048\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.70850 | 0.516825 | 0.258412 | − | 0.966035i | \(-0.416801\pi\) | ||||
0.258412 | + | 0.966035i | \(0.416801\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | + | 10.3923i | 0.650791 | + | 1.12720i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.17712 | + | 7.23499i | 0.442774 | + | 0.766908i | 0.997894 | − | 0.0648628i | \(-0.0206610\pi\) |
−0.555120 | + | 0.831770i | \(0.687328\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.03137 | − | 3.51844i | −0.212946 | − | 0.368833i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.76013 | − | 6.62141i | −0.283183 | − | 0.679343i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.29150 | − | 9.16515i | 0.537271 | − | 0.930580i | −0.461779 | − | 0.886995i | \(-0.652789\pi\) |
0.999050 | − | 0.0435851i | \(-0.0138780\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.93725 | + | 10.2836i | 0.590779 | + | 1.02326i | 0.994128 | + | 0.108213i | \(0.0345128\pi\) |
−0.403349 | + | 0.915046i | \(0.632154\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.93725 | 0.782081 | 0.391040 | − | 0.920373i | \(-0.372115\pi\) | ||||
0.391040 | + | 0.920373i | \(0.372115\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.0000 | 1.35343 | 0.676716 | − | 0.736245i | \(-0.263403\pi\) | ||||
0.676716 | + | 0.736245i | \(0.263403\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.64575 | − | 16.7069i | 0.923895 | − | 1.60023i | 0.130567 | − | 0.991439i | \(-0.458320\pi\) |
0.793328 | − | 0.608794i | \(-0.208347\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.354249 | 0.0333249 | 0.0166625 | − | 0.999861i | \(-0.494696\pi\) | ||||
0.0166625 | + | 0.999861i | \(0.494696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.583005 | −0.0543655 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.35425 | − | 4.07768i | 0.215814 | − | 0.373800i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.8745 | 1.89768 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.64575 | + | 6.31463i | 0.323508 | + | 0.560332i | 0.981209 | − | 0.192946i | \(-0.0618044\pi\) |
−0.657701 | + | 0.753279i | \(0.728471\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | + | 5.19615i | −0.262111 | + | 0.453990i | −0.966803 | − | 0.255524i | \(-0.917752\pi\) |
0.704692 | + | 0.709514i | \(0.251085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.70850 | + | 2.23695i | −0.148146 | + | 0.193968i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.35425 | + | 2.34563i | 0.115701 | + | 0.200400i | 0.918060 | − | 0.396442i | \(-0.129755\pi\) |
−0.802359 | + | 0.596842i | \(0.796422\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.322876 | + | 0.559237i | 0.0273860 | + | 0.0474339i | 0.879394 | − | 0.476096i | \(-0.157948\pi\) |
−0.852008 | + | 0.523529i | \(0.824615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.7601 | − | 30.7614i | −1.48518 | − | 2.57240i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.41699 | 0.449857 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.82288 | − | 3.15731i | 0.149336 | − | 0.258657i | −0.781646 | − | 0.623722i | \(-0.785620\pi\) |
0.930982 | + | 0.365065i | \(0.118953\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.2915 | 0.918889 | 0.459445 | − | 0.888206i | \(-0.348048\pi\) | ||||
0.459445 | + | 0.888206i | \(0.348048\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.82288 | − | 6.62141i | 0.307061 | − | 0.531845i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.145751 | − | 0.252449i | 0.0116322 | − | 0.0201476i | −0.860151 | − | 0.510040i | \(-0.829631\pi\) |
0.871783 | + | 0.489892i | \(0.162964\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.114378 | + | 0.198109i | 0.00901427 | + | 0.0156132i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −15.9373 | −1.24830 | −0.624151 | − | 0.781304i | \(-0.714555\pi\) | ||||
−0.624151 | + | 0.781304i | \(0.714555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.46863 | − | 14.6681i | −0.655322 | − | 1.13505i | −0.981813 | − | 0.189851i | \(-0.939200\pi\) |
0.326491 | − | 0.945200i | \(-0.394134\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.2915 | + | 23.0216i | −1.02242 | + | 1.77089i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9373 | − | 18.9439i | 0.831544 | − | 1.44028i | −0.0652695 | − | 0.997868i | \(-0.520791\pi\) |
0.896813 | − | 0.442409i | \(-0.145876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.739870 | + | 1.28149i | 0.0559289 | + | 0.0968718i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.6458 | −1.16942 | −0.584709 | − | 0.811243i | \(-0.698791\pi\) | ||||
−0.584709 | + | 0.811243i | \(0.698791\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.70850 | + | 4.69126i | 0.201321 | + | 0.348698i | 0.948954 | − | 0.315414i | \(-0.102143\pi\) |
−0.747633 | + | 0.664112i | \(0.768810\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.11438 | − | 7.12631i | 0.302495 | − | 0.523937i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 20.5830 | − | 35.6508i | 1.50518 | − | 2.60705i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9373 | 1.08082 | 0.540411 | − | 0.841401i | \(-0.318269\pi\) | ||||
0.540411 | + | 0.841401i | \(0.318269\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0830 | − | 17.4643i | 0.725791 | − | 1.25711i | −0.232857 | − | 0.972511i | \(-0.574807\pi\) |
0.958648 | − | 0.284595i | \(-0.0918592\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.3542 | 0.880204 | 0.440102 | − | 0.897948i | \(-0.354942\pi\) | ||||
0.440102 | + | 0.897948i | \(0.354942\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.96863 | + | 3.40976i | 0.139552 | + | 0.241712i | 0.927327 | − | 0.374252i | \(-0.122100\pi\) |
−0.787775 | + | 0.615963i | \(0.788767\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.06275 | − | 1.84073i | −0.0745902 | − | 0.129194i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.29150 | + | 5.70105i | 0.229889 | + | 0.398179i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.9373 | + | 19.5575i | −1.03323 | + | 1.35282i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.67712 | − | 4.63692i | 0.184301 | − | 0.319218i | −0.759040 | − | 0.651044i | \(-0.774331\pi\) |
0.943341 | + | 0.331826i | \(0.107665\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.76013 | + | 15.1730i | 0.597436 | + | 1.03479i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −45.8745 | −3.08585 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.32288 | + | 9.21949i | −0.356446 | + | 0.617383i | −0.987364 | − | 0.158467i | \(-0.949345\pi\) |
0.630918 | + | 0.775849i | \(0.282678\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.5203 | −1.42835 | −0.714175 | − | 0.699967i | \(-0.753198\pi\) | ||||
−0.714175 | + | 0.699967i | \(0.753198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.2915 | −1.34090 | −0.670450 | − | 0.741955i | \(-0.733899\pi\) | ||||
−0.670450 | + | 0.741955i | \(0.733899\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.9373 | − | 24.1400i | 0.913060 | − | 1.58147i | 0.103343 | − | 0.994646i | \(-0.467046\pi\) |
0.809717 | − | 0.586820i | \(-0.199620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.70850 | −0.568080 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.9373 | −0.707472 | −0.353736 | − | 0.935345i | \(-0.615089\pi\) | ||||
−0.353736 | + | 0.935345i | \(0.615089\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.4373 | + | 18.0779i | 0.672323 | + | 1.16450i | 0.977244 | + | 0.212119i | \(0.0680366\pi\) |
−0.304921 | + | 0.952378i | \(0.598630\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.41699 | − | 9.38251i | 0.346079 | − | 0.599427i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.1974 | + | 3.51844i | 1.73053 | + | 0.223873i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.35425 | + | 2.34563i | 0.0854794 | + | 0.148055i | 0.905595 | − | 0.424143i | \(-0.139424\pi\) |
−0.820116 | + | 0.572197i | \(0.806091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00000 | + | 1.73205i | 0.0628695 | + | 0.108893i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.17712 | + | 8.96704i | 0.322940 | + | 0.559349i | 0.981093 | − | 0.193535i | \(-0.0619954\pi\) |
−0.658153 | + | 0.752884i | \(0.728662\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.22876 | −0.200625 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.00000 | + | 15.5885i | −0.554964 | + | 0.961225i | 0.442943 | + | 0.896550i | \(0.353935\pi\) |
−0.997906 | + | 0.0646755i | \(0.979399\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.7085 | 0.903536 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.17712 | + | 7.23499i | −0.254684 | + | 0.441125i | −0.964810 | − | 0.262950i | \(-0.915305\pi\) |
0.710126 | + | 0.704075i | \(0.248638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.29150 | + | 9.16515i | −0.321436 | + | 0.556743i | −0.980785 | − | 0.195094i | \(-0.937499\pi\) |
0.659349 | + | 0.751837i | \(0.270832\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.46863 | + | 11.2040i | 0.390073 | + | 0.675626i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.00000 | −0.480673 | −0.240337 | − | 0.970690i | \(-0.577258\pi\) | ||||
−0.240337 | + | 0.970690i | \(0.577258\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.46863 | + | 7.73989i | 0.266576 | + | 0.461723i | 0.967975 | − | 0.251045i | \(-0.0807744\pi\) |
−0.701399 | + | 0.712768i | \(0.747441\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.2915 | + | 23.0216i | −0.790098 | + | 1.36849i | 0.135808 | + | 0.990735i | \(0.456637\pi\) |
−0.925906 | + | 0.377754i | \(0.876696\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.29150 | − | 2.23695i | 0.0762350 | − | 0.132043i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −18.0830 | − | 31.3207i | −1.06371 | − | 1.84239i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.41699 | 0.199623 | 0.0998115 | − | 0.995006i | \(-0.468176\pi\) | ||||
0.0998115 | + | 0.995006i | \(0.468176\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.93725 | − | 3.35542i | −0.112791 | − | 0.195360i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.11438 | − | 1.93016i | 0.0644462 | − | 0.111624i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.43725 | − | 5.95350i | 0.198120 | − | 0.343154i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.22876 | 0.471177 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.93725 | − | 3.35542i | 0.110565 | − | 0.191504i | −0.805433 | − | 0.592686i | \(-0.798067\pi\) |
0.915998 | + | 0.401182i | \(0.131401\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.9373 | 1.86770 | 0.933850 | − | 0.357664i | \(-0.116427\pi\) | ||||
0.933850 | + | 0.357664i | \(0.116427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.35425 | + | 7.54178i | 0.246117 | + | 0.426287i | 0.962445 | − | 0.271477i | \(-0.0875120\pi\) |
−0.716328 | + | 0.697763i | \(0.754179\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.46863 | + | 4.27579i | 0.138652 | + | 0.240152i | 0.926987 | − | 0.375095i | \(-0.122390\pi\) |
−0.788335 | + | 0.615247i | \(0.789056\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.29150 | − | 16.0934i | −0.520224 | − | 0.901055i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.2288 | + | 29.3362i | 0.680426 | + | 1.63231i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.20850 | − | 12.4855i | 0.399855 | − | 0.692570i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.70850 | + | 2.95920i | 0.0941925 | + | 0.163146i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.22876 | −0.287398 | −0.143699 | − | 0.989621i | \(-0.545900\pi\) | ||||
−0.143699 | + | 0.989621i | \(0.545900\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.18824 | 0.174192 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.85425 | − | 8.40781i | 0.264428 | − | 0.458002i | −0.702986 | − | 0.711204i | \(-0.748150\pi\) |
0.967414 | + | 0.253202i | \(0.0814836\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.2288 | −1.42037 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.77124 | −0.473603 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.4059 | − | 24.9517i | 0.773348 | − | 1.33948i | −0.162370 | − | 0.986730i | \(-0.551914\pi\) |
0.935718 | − | 0.352748i | \(-0.114753\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.8745 | −1.11739 | −0.558693 | − | 0.829374i | \(-0.688697\pi\) | ||||
−0.558693 | + | 0.829374i | \(0.688697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.93725 | −0.262784 | −0.131392 | − | 0.991331i | \(-0.541945\pi\) | ||||
−0.131392 | + | 0.991331i | \(0.541945\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.22876 | + | 14.2526i | 0.436737 | + | 0.756451i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0000 | + | 20.7846i | −0.633336 | + | 1.09697i | 0.353529 | + | 0.935423i | \(0.384981\pi\) |
−0.986865 | + | 0.161546i | \(0.948352\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | − | 18.3303i | −0.263158 | − | 0.964753i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.53137 | − | 6.11652i | −0.184841 | − | 0.320153i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.61438 | + | 11.4564i | 0.345268 | + | 0.598021i | 0.985402 | − | 0.170241i | \(-0.0544548\pi\) |
−0.640135 | + | 0.768263i | \(0.721121\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.88562 | − | 4.99804i | −0.149814 | − | 0.259485i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.00000 | −0.207112 | −0.103556 | − | 0.994624i | \(-0.533022\pi\) | ||||
−0.103556 | + | 0.994624i | \(0.533022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.3542 | + | 17.9341i | −0.533271 | + | 0.923652i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.5203 | −1.46499 | −0.732494 | − | 0.680774i | \(-0.761644\pi\) | ||||
−0.732494 | + | 0.680774i | \(0.761644\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.17712 | + | 5.50294i | −0.162343 | + | 0.281187i | −0.935709 | − | 0.352774i | \(-0.885239\pi\) |
0.773365 | + | 0.633961i | \(0.218572\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.00000 | + | 5.19615i | −0.152894 | + | 0.264820i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.1144 | − | 31.3750i | −0.918435 | − | 1.59078i | −0.801792 | − | 0.597603i | \(-0.796120\pi\) |
−0.116643 | − | 0.993174i | \(-0.537213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58301 | 0.130628 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.11438 | + | 12.3225i | 0.357963 | + | 0.620010i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.85425 | − | 10.1399i | 0.293816 | − | 0.508905i | −0.680893 | − | 0.732383i | \(-0.738408\pi\) |
0.974709 | + | 0.223479i | \(0.0717413\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.82288 | − | 17.0137i | 0.490531 | − | 0.849625i | −0.509410 | − | 0.860524i | \(-0.670136\pi\) |
0.999941 | + | 0.0108996i | \(0.00346951\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.6144 | + | 25.3128i | 0.727994 | + | 1.26092i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.2288 | −1.39925 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.64575 | + | 13.2428i | 0.378058 | + | 0.654816i | 0.990780 | − | 0.135483i | \(-0.0432586\pi\) |
−0.612722 | + | 0.790299i | \(0.709925\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.760130 | + | 1.31658i | −0.0374035 | + | 0.0647848i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.87451 | + | 6.71084i | −0.190192 | + | 0.329422i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.06275 | 0.345038 | 0.172519 | − | 0.985006i | \(-0.444809\pi\) | ||||
0.172519 | + | 0.985006i | \(0.444809\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.2288 | + | 28.1090i | −0.790941 | + | 1.36995i | 0.134444 | + | 0.990921i | \(0.457075\pi\) |
−0.925385 | + | 0.379029i | \(0.876258\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.7085 | 0.810481 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.61438 | − | 2.79619i | −0.0781252 | − | 0.135317i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.22876 | − | 15.9847i | −0.444534 | − | 0.769955i | 0.553486 | − | 0.832858i | \(-0.313297\pi\) |
−0.998020 | + | 0.0629037i | \(0.979964\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.145751 | − | 0.252449i | −0.00700436 | − | 0.0121319i | 0.862502 | − | 0.506054i | \(-0.168896\pi\) |
−0.869506 | + | 0.493922i | \(0.835563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.53137 | − | 0.198109i | −0.0732555 | − | 0.00947684i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.26013 | − | 16.0390i | 0.441962 | − | 0.765500i | −0.555873 | − | 0.831267i | \(-0.687616\pi\) |
0.997835 | + | 0.0657667i | \(0.0209493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.35425 | − | 7.54178i | −0.206877 | − | 0.358321i | 0.743852 | − | 0.668344i | \(-0.232997\pi\) |
−0.950729 | + | 0.310023i | \(0.899663\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.7490 | −0.651766 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.29150 | 0.155336 | 0.0776678 | − | 0.996979i | \(-0.475253\pi\) | ||||
0.0776678 | + | 0.996979i | \(0.475253\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.2915 | − | 19.5575i | 0.531696 | − | 0.920925i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.68627 | 0.313457 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.12549 | −0.146204 | −0.0731022 | − | 0.997324i | \(-0.523290\pi\) | ||||
−0.0731022 | + | 0.997324i | \(0.523290\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.7601 | + | 35.9576i | −0.966896 | + | 1.67471i | −0.262462 | + | 0.964942i | \(0.584535\pi\) |
−0.704433 | + | 0.709770i | \(0.748799\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.77124 | −0.314686 | −0.157343 | − | 0.987544i | \(-0.550293\pi\) | ||||
−0.157343 | + | 0.987544i | \(0.550293\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.1660 | 1.53474 | 0.767370 | − | 0.641205i | \(-0.221565\pi\) | ||||
0.767370 | + | 0.641205i | \(0.221565\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.625492 | − | 1.08338i | −0.0288825 | − | 0.0500260i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.0516 | − | 52.0510i | 1.38178 | − | 2.39331i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.90588 | − | 1.28149i | −0.454513 | − | 0.0587989i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.5830 | + | 37.3829i | 0.986153 | + | 1.70807i | 0.636698 | + | 0.771113i | \(0.280300\pi\) |
0.349455 | + | 0.936953i | \(0.386367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7288 | + | 27.2430i | 0.717170 | + | 1.24217i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.70850 | + | 15.0836i | 0.395432 | + | 0.684909i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.2915 | −0.511667 | −0.255833 | − | 0.966721i | \(-0.582350\pi\) | ||||
−0.255833 | + | 0.966721i | \(0.582350\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.58301 | + | 16.5983i | −0.432475 | + | 0.749069i | −0.997086 | − | 0.0762887i | \(-0.975693\pi\) |
0.564611 | + | 0.825357i | \(0.309026\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.0000 | −1.08091 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.22876 | − | 5.59237i | 0.144830 | − | 0.250852i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.5516 | − | 30.4003i | 0.785719 | − | 1.36091i | −0.142850 | − | 0.989744i | \(-0.545627\pi\) |
0.928569 | − | 0.371161i | \(-0.121040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6458 | − | 27.0992i | −0.697610 | − | 1.20830i | −0.969293 | − | 0.245909i | \(-0.920914\pi\) |
0.271683 | − | 0.962387i | \(-0.412420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −19.5425 | −0.869629 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.1660 | + | 34.9286i | 0.893843 | + | 1.54818i | 0.835230 | + | 0.549900i | \(0.185334\pi\) |
0.0586123 | + | 0.998281i | \(0.481332\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.38562 | + | 2.39997i | −0.0612963 | + | 0.106168i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.53137 | + | 11.3127i | −0.287807 | + | 0.498496i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.9373 | + | 25.8721i | 0.656940 | + | 1.13785i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.3542 | 0.541249 | 0.270625 | − | 0.962685i | \(-0.412770\pi\) | ||||
0.270625 | + | 0.962685i | \(0.412770\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.1974 | + | 29.7867i | 0.751989 | + | 1.30248i | 0.946857 | + | 0.321654i | \(0.104239\pi\) |
−0.194868 | + | 0.980829i | \(0.562428\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.9373 | + | 29.3362i | −0.737798 | + | 1.27790i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4373 | − | 19.8099i | 0.497272 | − | 0.861300i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −25.1660 | −1.09006 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.5203 | + | 19.9537i | −0.498064 | + | 0.862673i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.1660 | −1.60085 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.43725 | + | 4.22145i | 0.104786 | + | 0.181494i | 0.913651 | − | 0.406500i | \(-0.133251\pi\) |
−0.808865 | + | 0.587995i | \(0.799918\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.8745 | + | 27.4955i | 0.679989 | + | 1.17778i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.6144 | + | 21.8487i | 0.539352 | + | 0.934185i | 0.998939 | + | 0.0460522i | \(0.0146640\pi\) |
−0.459587 | + | 0.888133i | \(0.652003\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.2288 | + | 1.84073i | 0.606165 | + | 0.0784177i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.79150 | − | 4.83502i | 0.118707 | − | 0.205606i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.06275 | − | 3.57278i | −0.0874014 | − | 0.151384i | 0.819011 | − | 0.573778i | \(-0.194523\pi\) |
−0.906412 | + | 0.422395i | \(0.861190\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −66.9778 | −2.83286 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.00000 | 0.252870 | 0.126435 | − | 0.991975i | \(-0.459647\pi\) | ||||
0.126435 | + | 0.991975i | \(0.459647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.291503 | + | 0.504897i | −0.0122636 | + | 0.0212412i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.16601 | 0.0488817 | 0.0244409 | − | 0.999701i | \(-0.492219\pi\) | ||||
0.0244409 | + | 0.999701i | \(0.492219\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.9373 | 0.499559 | 0.249779 | − | 0.968303i | \(-0.419642\pi\) | ||||
0.249779 | + | 0.968303i | \(0.419642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.405881 | + | 0.703006i | −0.0169264 | + | 0.0293174i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.2915 | −0.470071 | −0.235036 | − | 0.971987i | \(-0.575521\pi\) | ||||
−0.235036 | + | 0.971987i | \(0.575521\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.04052 | 0.126142 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −25.2288 | − | 43.6975i | −1.04487 | − | 1.80977i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.114378 | + | 0.198109i | −0.00472090 | + | 0.00817683i | −0.868376 | − | 0.495906i | \(-0.834836\pi\) |
0.863655 | + | 0.504083i | \(0.168169\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2915 | − | 16.0934i | 0.506463 | − | 0.663115i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.46863 | − | 6.00784i | −0.142439 | − | 0.246712i | 0.785975 | − | 0.618258i | \(-0.212161\pi\) |
−0.928415 | + | 0.371546i | \(0.878828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.87451 | + | 6.71084i | 0.158839 | + | 0.275118i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.17712 | + | 2.03884i | 0.0480960 | + | 0.0833047i | 0.889071 | − | 0.457769i | \(-0.151351\pi\) |
−0.840975 | + | 0.541074i | \(0.818018\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.2915 | −1.23562 | −0.617808 | − | 0.786329i | \(-0.711979\pi\) | ||||
−0.617808 | + | 0.786329i | \(0.711979\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.1771 | + | 29.7517i | −0.698349 | + | 1.20958i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0627 | 0.814322 | 0.407161 | − | 0.913356i | \(-0.366519\pi\) | ||||
0.407161 | + | 0.913356i | \(0.366519\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.6458 | − | 28.8313i | 0.673415 | − | 1.16639i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.5830 | + | 28.7226i | −0.669781 | + | 1.16010i | 0.308184 | + | 0.951327i | \(0.400279\pi\) |
−0.977965 | + | 0.208768i | \(0.933055\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.4686 | + | 30.2565i | 0.703260 | + | 1.21808i | 0.967316 | + | 0.253575i | \(0.0816065\pi\) |
−0.264055 | + | 0.964508i | \(0.585060\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.06275 | −0.324069 | −0.162035 | − | 0.986785i | \(-0.551806\pi\) | ||||
−0.162035 | + | 0.986785i | \(0.551806\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.69738 | + | 4.67201i | 0.108068 | + | 0.187180i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.14575 | − | 7.18065i | 0.165830 | − | 0.287226i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.2288 | + | 31.5731i | −0.726828 | + | 1.25890i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.03137 | − | 1.78639i | −0.0410583 | − | 0.0711151i | 0.844766 | − | 0.535136i | \(-0.179740\pi\) |
−0.885824 | + | 0.464021i | \(0.846406\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.0000 | −0.476205 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.7085 | + | 35.8682i | 0.820501 | + | 1.42115i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.2915 | + | 17.8254i | −0.406490 | + | 0.704061i | −0.994494 | − | 0.104797i | \(-0.966581\pi\) |
0.588004 | + | 0.808858i | \(0.299914\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.0314 | + | 26.0351i | −0.592779 | + | 1.02672i | 0.401077 | + | 0.916045i | \(0.368636\pi\) |
−0.993856 | + | 0.110680i | \(0.964697\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.2915 | 1.07294 | 0.536470 | − | 0.843919i | \(-0.319758\pi\) | ||||
0.536470 | + | 0.843919i | \(0.319758\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.64575 | + | 11.5108i | −0.260869 | + | 0.451838i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.12549 | 0.317975 | 0.158988 | − | 0.987281i | \(-0.449177\pi\) | ||||
0.158988 | + | 0.987281i | \(0.449177\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.93725 | − | 8.55157i | −0.192914 | − | 0.334138i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.88562 | − | 6.73009i | −0.151362 | − | 0.262167i | 0.780366 | − | 0.625323i | \(-0.215033\pi\) |
−0.931729 | + | 0.363156i | \(0.881699\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.00000 | + | 1.73205i | 0.0388955 | + | 0.0673690i | 0.884818 | − | 0.465937i | \(-0.154283\pi\) |
−0.845922 | + | 0.533306i | \(0.820949\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.78236 | − | 4.27579i | −0.0691169 | − | 0.165808i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.583005 | − | 1.00979i | 0.0225741 | − | 0.0390994i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1144 | − | 24.4468i | −0.544880 | − | 0.943759i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.8745 | 1.49850 | 0.749251 | − | 0.662286i | \(-0.230414\pi\) | ||||
0.749251 | + | 0.662286i | \(0.230414\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.1660 | 0.736610 | 0.368305 | − | 0.929705i | \(-0.379938\pi\) | ||||
0.368305 | + | 0.929705i | \(0.379938\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.41699 | − | 5.91841i | 0.131132 | − | 0.227128i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.2288 | −1.00362 | −0.501808 | − | 0.864979i | \(-0.667332\pi\) | ||||
−0.501808 | + | 0.864979i | \(0.667332\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.45751 | −0.170313 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.1144 | + | 48.6955i | −1.07107 | + | 1.85515i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.1660 | −1.10953 | −0.554764 | − | 0.832008i | \(-0.687191\pi\) | ||||
−0.554764 | + | 0.832008i | \(0.687191\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.06275 | −0.0403123 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.5830 | − | 25.2585i | −0.552371 | − | 0.956734i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.05163 | + | 12.2138i | −0.266336 | + | 0.461308i | −0.967913 | − | 0.251286i | \(-0.919147\pi\) |
0.701576 | + | 0.712594i | \(0.252480\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.2288 | − | 17.3205i | 0.498932 | − | 0.653255i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.83399 | + | 6.64066i | 0.144192 | + | 0.249748i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.79150 | − | 15.2273i | −0.330172 | − | 0.571874i | 0.652374 | − | 0.757898i | \(-0.273773\pi\) |
−0.982545 | + | 0.186023i | \(0.940440\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.822876 | − | 1.42526i | −0.0308169 | − | 0.0533765i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 58.4575 | 2.18619 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.46863 | + | 12.9360i | −0.278533 | + | 0.482433i | −0.971020 | − | 0.238997i | \(-0.923181\pi\) |
0.692488 | + | 0.721430i | \(0.256515\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.12549 | 0.190883 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.77124 | − | 6.53199i | 0.140060 | − | 0.242592i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.26013 | + | 10.8429i | −0.232175 | + | 0.402140i | −0.958448 | − | 0.285267i | \(-0.907918\pi\) |
0.726273 | + | 0.687407i | \(0.241251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.8118 | − | 67.2239i | −1.43550 | − | 2.48637i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.1660 | 1.07727 | 0.538636 | − | 0.842539i | \(-0.318940\pi\) | ||||
0.538636 | + | 0.842539i | \(0.318940\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.46863 | − | 9.47194i | −0.201439 | − | 0.348903i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.6771 | + | 23.6895i | −0.503121 | + | 0.871431i | 0.496872 | + | 0.867824i | \(0.334482\pi\) |
−0.999993 | + | 0.00360775i | \(0.998852\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.1144 | + | 17.5186i | −0.371061 | + | 0.642696i | −0.989729 | − | 0.142956i | \(-0.954339\pi\) |
0.618668 | + | 0.785652i | \(0.287672\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.00000 | + | 5.19615i | 0.109911 | + | 0.190372i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.04052 | 0.330333 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.32288 | + | 2.29129i | 0.0482724 | + | 0.0836103i | 0.889152 | − | 0.457612i | \(-0.151295\pi\) |
−0.840880 | + | 0.541222i | \(0.817962\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.29150 | + | 16.0934i | −0.338152 | + | 0.585697i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.79150 | − | 6.56708i | 0.137805 | − | 0.238684i | −0.788861 | − | 0.614572i | \(-0.789329\pi\) |
0.926665 | + | 0.375888i | \(0.122662\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.52026 | −0.0551094 | −0.0275547 | − | 0.999620i | \(-0.508772\pi\) | ||||
−0.0275547 | + | 0.999620i | \(0.508772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.22876 | − | 10.7885i | 0.225496 | − | 0.390571i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.8118 | 0.534822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.79150 | − | 8.29913i | −0.172786 | − | 0.299274i | 0.766607 | − | 0.642117i | \(-0.221944\pi\) |
−0.939393 | + | 0.342843i | \(0.888610\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.8745 | − | 22.2993i | −0.463064 | − | 0.802050i | 0.536048 | − | 0.844188i | \(-0.319917\pi\) |
−0.999112 | + | 0.0421374i | \(0.986583\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.32288 | − | 9.21949i | −0.191203 | − | 0.331174i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.70850 | + | 16.0934i | 0.240357 | + | 0.576604i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.2288 | − | 48.8936i | 1.01010 | − | 1.74955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.239870 | + | 0.415468i | 0.00856134 | + | 0.0148287i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.8118 | −0.991382 | −0.495691 | − | 0.868499i | \(-0.665085\pi\) | ||||
−0.495691 | + | 0.868499i | \(0.665085\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.228757 | 0.00813365 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.7288 | + | 27.2430i | −0.558545 | + | 0.967427i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.7085 | −1.22944 | −0.614719 | − | 0.788746i | \(-0.710731\pi\) | ||||
−0.614719 | + | 0.788746i | \(0.710731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.5830 | 1.36497 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.1144 | + | 20.9827i | −0.427507 | + | 0.740464i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.376476 | −0.0132690 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.93725 | −0.173585 | −0.0867923 | − | 0.996226i | \(-0.527662\pi\) | ||||
−0.0867923 | + | 0.996226i | \(0.527662\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.2288 | − | 41.9654i | −0.850787 | − | 1.47361i | −0.880499 | − | 0.474047i | \(-0.842793\pi\) |
0.0297126 | − | 0.999558i | \(-0.490541\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.1144 | − | 22.7148i | 0.459377 | − | 0.795664i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.8542 | + | 42.8315i | 0.624641 | + | 1.49848i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.9373 | − | 39.7285i | −0.800516 | − | 1.38653i | −0.919277 | − | 0.393611i | \(-0.871226\pi\) |
0.118761 | − | 0.992923i | \(-0.462108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.3542 | + | 21.3982i | 0.430642 | + | 0.745894i | 0.996929 | − | 0.0783145i | \(-0.0249538\pi\) |
−0.566287 | + | 0.824208i | \(0.691620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.6458 | − | 23.6351i | −0.474509 | − | 0.821874i | 0.525065 | − | 0.851062i | \(-0.324041\pi\) |
−0.999574 | + | 0.0291882i | \(0.990708\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.4170 | −1.05643 | −0.528213 | − | 0.849112i | \(-0.677138\pi\) | ||||
−0.528213 | + | 0.849112i | \(0.677138\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −24.0000 | + | 41.5692i | −0.831551 | + | 1.44029i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.8745 | 0.964637 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.17712 | + | 3.77089i | −0.0751627 | + | 0.130186i | −0.901157 | − | 0.433493i | \(-0.857281\pi\) |
0.825994 | + | 0.563678i | \(0.190614\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.08301 | − | 15.7322i | 0.313207 | − | 0.542491i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.8745 | − | 37.8878i | −0.752506 | − | 1.30338i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.4797 | 0.463169 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.885622 | − | 1.53394i | −0.0303587 | − | 0.0525828i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.3745 | − | 24.8974i | 0.492174 | − | 0.852470i | −0.507786 | − | 0.861483i | \(-0.669536\pi\) |
0.999959 | + | 0.00901349i | \(0.00286912\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | − | 36.3731i | 0.717346 | − | 1.24248i | −0.244701 | − | 0.969599i | \(-0.578690\pi\) |
0.962048 | − | 0.272882i | \(-0.0879768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.9686 | − | 18.9982i | −0.374245 | − | 0.648211i | 0.615969 | − | 0.787770i | \(-0.288765\pi\) |
−0.990214 | + | 0.139560i | \(0.955431\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.2915 | −1.26942 | −0.634709 | − | 0.772751i | \(-0.718880\pi\) | ||||
−0.634709 | + | 0.772751i | \(0.718880\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0000 | + | 31.1769i | 0.612018 | + | 1.06005i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.4059 | − | 42.2722i | 0.827913 | − | 1.43399i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.09412 | + | 10.5553i | −0.206491 | + | 0.357654i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.74902 | −0.261965 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12.0830 | + | 20.9284i | −0.408014 | + | 0.706701i | −0.994667 | − | 0.103137i | \(-0.967112\pi\) |
0.586653 | + | 0.809838i | \(0.300445\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.6863 | 1.64028 | 0.820141 | − | 0.572161i | \(-0.193895\pi\) | ||||
0.820141 | + | 0.572161i | \(0.193895\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 11.3229 | + | 19.6118i | 0.381045 | + | 0.659989i | 0.991212 | − | 0.132283i | \(-0.0422309\pi\) |
−0.610167 | + | 0.792273i | \(0.708898\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.0516 | + | 36.4625i | 0.706845 | + | 1.22429i | 0.966022 | + | 0.258461i | \(0.0832153\pi\) |
−0.259177 | + | 0.965830i | \(0.583451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.35425 | + | 4.07768i | 0.0789590 | + | 0.136761i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.8745 | − | 2.95920i | −0.765466 | − | 0.0990260i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.8745 | − | 22.2993i | 0.430347 | − | 0.745383i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.64575 | + | 13.2428i | 0.255000 | + | 0.441673i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −65.1660 | −2.17099 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.91503 | −0.296345 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.5830 | + | 39.1149i | −0.749856 | + | 1.29879i | 0.198035 | + | 0.980195i | \(0.436544\pi\) |
−0.947891 | + | 0.318594i | \(0.896789\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.7490 | −0.654314 | −0.327157 | − | 0.944970i | \(-0.606091\pi\) | ||||
−0.327157 | + | 0.944970i | \(0.606091\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.5830 | 0.879769 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.93725 | + | 3.35542i | −0.0639738 | + | 0.110806i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.2288 | 0.832220 | 0.416110 | − | 0.909314i | \(-0.363393\pi\) | ||||
0.416110 | + | 0.909314i | \(0.363393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −62.9150 | −2.07087 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.72876 | − | 9.92250i | −0.188360 | − | 0.326250i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.239870 | − | 0.415468i | 0.00786989 | − | 0.0136311i | −0.862064 | − | 0.506800i | \(-0.830828\pi\) |
0.869934 | + | 0.493169i | \(0.164162\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.4170 | − | 22.8042i | 0.570819 | − | 0.747377i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.8745 | + | 58.6724i | 1.10781 | + | 1.91879i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.50000 | + | 6.06218i | 0.114340 | + | 0.198043i | 0.917516 | − | 0.397699i | \(-0.130191\pi\) |
−0.803176 | + | 0.595742i | \(0.796858\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.8745 | + | 20.5673i | 0.387098 | + | 0.670473i | 0.992058 | − | 0.125783i | \(-0.0401442\pi\) |
−0.604960 | + | 0.796256i | \(0.706811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.41699 | 0.0461437 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.1660 | − | 24.5362i | 0.460333 | − | 0.797321i | −0.538644 | − | 0.842534i | \(-0.681063\pi\) |
0.998977 | + | 0.0452125i | \(0.0143965\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.0000 | 0.876457 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.23987 | − | 5.61162i | 0.104950 | − | 0.181778i | −0.808768 | − | 0.588128i | \(-0.799865\pi\) |
0.913718 | + | 0.406350i | \(0.133199\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.2915 | + | 21.2895i | −0.397744 | + | 0.688912i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.874508 | + | 1.51469i | 0.0282393 | + | 0.0489120i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.41699 | −0.303774 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.5941 | + | 28.7419i | 0.534184 | + | 0.925233i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.968627 | − | 1.67771i | 0.0311489 | − | 0.0539516i | −0.850031 | − | 0.526733i | \(-0.823417\pi\) |
0.881180 | + | 0.472782i | \(0.156750\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.5203 | + | 25.1498i | −0.465977 | + | 0.807096i | −0.999245 | − | 0.0388502i | \(-0.987630\pi\) |
0.533268 | + | 0.845947i | \(0.320964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.208497 | + | 0.361128i | 0.00668412 | + | 0.0115772i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −50.9150 | −1.62892 | −0.814458 | − | 0.580223i | \(-0.802966\pi\) | ||||
−0.814458 | + | 0.580223i | \(0.802966\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.5830 | + | 40.8470i | 0.753716 | + | 1.30547i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.5314 | + | 37.2934i | −0.686744 | + | 1.18948i | 0.286141 | + | 0.958187i | \(0.407627\pi\) |
−0.972885 | + | 0.231288i | \(0.925706\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.1660 | + | 17.6080i | −0.323916 | + | 0.561039i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.77124 | 0.119919 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.96863 | + | 3.40976i | −0.0625355 | + | 0.108315i | −0.895598 | − | 0.444864i | \(-0.853252\pi\) |
0.833063 | + | 0.553179i | \(0.186585\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.47974 | −0.205422 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.0203 | − | 39.8723i | −0.729059 | − | 1.26277i | −0.957281 | − | 0.289158i | \(-0.906625\pi\) |
0.228222 | − | 0.973609i | \(-0.426709\pi\) | |||||||
\(998\) | 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 | 2736.2.s.u.1873.1 | 4 | ||
3.2 | odd | 2 | 912.2.q.g.49.2 | 4 | |||
4.3 | odd | 2 | 684.2.k.g.505.1 | 4 | |||
12.11 | even | 2 | 228.2.i.b.49.2 | ✓ | 4 | ||
19.7 | even | 3 | inner | 2736.2.s.u.577.1 | 4 | ||
57.26 | odd | 6 | 912.2.q.g.577.2 | 4 | |||
76.7 | odd | 6 | 684.2.k.g.577.1 | 4 | |||
228.11 | even | 6 | 4332.2.a.h.1.1 | 2 | |||
228.83 | even | 6 | 228.2.i.b.121.2 | yes | 4 | ||
228.179 | odd | 6 | 4332.2.a.m.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.2.i.b.49.2 | ✓ | 4 | 12.11 | even | 2 | ||
228.2.i.b.121.2 | yes | 4 | 228.83 | even | 6 | ||
684.2.k.g.505.1 | 4 | 4.3 | odd | 2 | |||
684.2.k.g.577.1 | 4 | 76.7 | odd | 6 | |||
912.2.q.g.49.2 | 4 | 3.2 | odd | 2 | |||
912.2.q.g.577.2 | 4 | 57.26 | odd | 6 | |||
2736.2.s.u.577.1 | 4 | 19.7 | even | 3 | inner | ||
2736.2.s.u.1873.1 | 4 | 1.1 | even | 1 | trivial | ||
4332.2.a.h.1.1 | 2 | 228.11 | even | 6 | |||
4332.2.a.m.1.1 | 2 | 228.179 | odd | 6 |