Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(361,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.g (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: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 882.361 |
Dual form | 882.2.g.e.667.1 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.50000 | + | 2.59808i | 0.670820 | + | 1.16190i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.50000 | − | 2.59808i | 0.474342 | − | 0.821584i | ||||
\(11\) | 1.50000 | − | 2.59808i | 0.452267 | − | 0.783349i | −0.546259 | − | 0.837616i | \(-0.683949\pi\) |
0.998526 | + | 0.0542666i | \(0.0172821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.00000 | −0.554700 | −0.277350 | − | 0.960769i | \(-0.589456\pi\) | ||||
−0.277350 | + | 0.960769i | \(0.589456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | −3.00000 | −0.670820 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 1.00000 | + | 1.73205i | 0.196116 | + | 0.339683i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.00000 | 1.67126 | 0.835629 | − | 0.549294i | \(-0.185103\pi\) | ||||
0.835629 | + | 0.549294i | \(0.185103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50000 | + | 6.06218i | −0.628619 | + | 1.08880i | 0.359211 | + | 0.933257i | \(0.383046\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | + | 8.66025i | 0.821995 | + | 1.42374i | 0.904194 | + | 0.427121i | \(0.140472\pi\) |
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 1.00000 | − | 1.73205i | 0.162221 | − | 0.280976i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.50000 | + | 2.59808i | 0.237171 | + | 0.410792i | ||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | − | 5.19615i | 0.442326 | − | 0.766131i | ||||
\(47\) | 6.00000 | + | 10.3923i | 0.875190 | + | 1.51587i | 0.856560 | + | 0.516047i | \(0.172597\pi\) |
0.0186297 | + | 0.999826i | \(0.494070\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.00000 | 0.565685 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.00000 | − | 1.73205i | 0.138675 | − | 0.240192i | ||||
\(53\) | 1.50000 | − | 2.59808i | 0.206041 | − | 0.356873i | −0.744423 | − | 0.667708i | \(-0.767275\pi\) |
0.950464 | + | 0.310835i | \(0.100609\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000 | 1.21356 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.50000 | − | 7.79423i | −0.590879 | − | 1.02343i | ||||
\(59\) | −1.50000 | + | 2.59808i | −0.195283 | + | 0.338241i | −0.946993 | − | 0.321253i | \(-0.895896\pi\) |
0.751710 | + | 0.659494i | \(0.229229\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | − | 3.46410i | −0.256074 | − | 0.443533i | 0.709113 | − | 0.705095i | \(-0.249096\pi\) |
−0.965187 | + | 0.261562i | \(0.915762\pi\) | |||||||
\(62\) | 7.00000 | 0.889001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.00000 | − | 5.19615i | −0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | + | 1.73205i | −0.122169 | + | 0.211604i | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | 3.00000 | + | 5.19615i | 0.363803 | + | 0.630126i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.00000 | − | 1.73205i | 0.117041 | − | 0.202721i | −0.801553 | − | 0.597924i | \(-0.795992\pi\) |
0.918594 | + | 0.395203i | \(0.129326\pi\) | |||||||
\(74\) | 5.00000 | − | 8.66025i | 0.581238 | − | 1.00673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.50000 | − | 4.33013i | −0.281272 | − | 0.487177i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.971698 | + | 0.236225i | \(0.924090\pi\) | |||||||
\(80\) | 1.50000 | − | 2.59808i | 0.167705 | − | 0.290474i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.00000 | −0.987878 | −0.493939 | − | 0.869496i | \(-0.664443\pi\) | ||||
−0.493939 | + | 0.869496i | \(0.664443\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.0000 | 1.95237 | ||||||||
\(86\) | 2.00000 | + | 3.46410i | 0.215666 | + | 0.373544i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −3.00000 | − | 5.19615i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980071 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00000 | − | 10.3923i | 0.618853 | − | 1.07188i | ||||
\(95\) | −3.00000 | + | 5.19615i | −0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.0000 | 1.31995 | 0.659975 | − | 0.751288i | \(-0.270567\pi\) | ||||
0.659975 | + | 0.751288i | \(0.270567\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | − | 3.46410i | −0.200000 | − | 0.346410i | ||||
\(101\) | 3.00000 | − | 5.19615i | 0.298511 | − | 0.517036i | −0.677284 | − | 0.735721i | \(-0.736843\pi\) |
0.975796 | + | 0.218685i | \(0.0701767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.00000 | − | 13.8564i | −0.788263 | − | 1.36531i | −0.927030 | − | 0.374987i | \(-0.877647\pi\) |
0.138767 | − | 0.990325i | \(-0.455686\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.00000 | −0.291386 | ||||||||
\(107\) | −1.50000 | − | 2.59808i | −0.145010 | − | 0.251166i | 0.784366 | − | 0.620298i | \(-0.212988\pi\) |
−0.929377 | + | 0.369132i | \(0.879655\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.00000 | − | 8.66025i | 0.478913 | − | 0.829502i | −0.520794 | − | 0.853682i | \(-0.674364\pi\) |
0.999708 | + | 0.0241802i | \(0.00769755\pi\) | |||||||
\(110\) | −4.50000 | − | 7.79423i | −0.429058 | − | 0.743151i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.00000 | + | 15.5885i | −0.839254 | + | 1.45363i | ||||
\(116\) | −4.50000 | + | 7.79423i | −0.417815 | + | 0.723676i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.00000 | 0.276172 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | −2.00000 | + | 3.46410i | −0.181071 | + | 0.313625i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.50000 | − | 6.06218i | −0.314309 | − | 0.544400i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | −0.0443678 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443678 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | + | 5.19615i | −0.263117 | + | 0.455733i | ||||
\(131\) | −7.50000 | − | 12.9904i | −0.655278 | − | 1.13497i | −0.981824 | − | 0.189794i | \(-0.939218\pi\) |
0.326546 | − | 0.945181i | \(-0.394115\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | − | 5.19615i | 0.257248 | − | 0.445566i | ||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.00000 | + | 5.19615i | −0.250873 | + | 0.434524i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.5000 | + | 23.3827i | 1.12111 | + | 1.94183i | ||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.0000 | −0.821995 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.0000 | −1.68676 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | + | 3.46410i | −0.159617 | + | 0.276465i | −0.934731 | − | 0.355357i | \(-0.884359\pi\) |
0.775113 | + | 0.631822i | \(0.217693\pi\) | |||||||
\(158\) | −2.50000 | + | 4.33013i | −0.198889 | + | 0.344486i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.00000 | −0.237171 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.00000 | + | 8.66025i | 0.391630 | + | 0.678323i | 0.992665 | − | 0.120900i | \(-0.0385779\pi\) |
−0.601035 | + | 0.799223i | \(0.705245\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.50000 | + | 7.79423i | 0.349268 | + | 0.604949i | ||||
\(167\) | 18.0000 | 1.39288 | 0.696441 | − | 0.717614i | \(-0.254766\pi\) | ||||
0.696441 | + | 0.717614i | \(0.254766\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | −9.00000 | − | 15.5885i | −0.690268 | − | 1.19558i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | − | 3.46410i | 0.152499 | − | 0.264135i | ||||
\(173\) | −3.00000 | − | 5.19615i | −0.228086 | − | 0.395056i | 0.729155 | − | 0.684349i | \(-0.239913\pi\) |
−0.957241 | + | 0.289292i | \(0.906580\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | 6.00000 | − | 10.3923i | 0.448461 | − | 0.776757i | −0.549825 | − | 0.835280i | \(-0.685306\pi\) |
0.998286 | + | 0.0585225i | \(0.0186389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.00000 | + | 5.19615i | 0.221163 | + | 0.383065i | ||||
\(185\) | −15.0000 | + | 25.9808i | −1.10282 | + | 1.91014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | − | 15.5885i | −0.658145 | − | 1.13994i | ||||
\(188\) | −12.0000 | −0.875190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | −6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | \(-0.309616\pi\) |
−0.997225 | + | 0.0744412i | \(0.976283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.50000 | − | 6.06218i | 0.251936 | − | 0.436365i | −0.712123 | − | 0.702055i | \(-0.752266\pi\) |
0.964059 | + | 0.265689i | \(0.0855996\pi\) | |||||||
\(194\) | −6.50000 | − | 11.2583i | −0.466673 | − | 0.808301i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.00000 | − | 6.92820i | 0.283552 | − | 0.491127i | −0.688705 | − | 0.725042i | \(-0.741820\pi\) |
0.972257 | + | 0.233915i | \(0.0751537\pi\) | |||||||
\(200\) | −2.00000 | + | 3.46410i | −0.141421 | + | 0.244949i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.00000 | −0.422159 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | + | 13.8564i | −0.557386 | + | 0.965422i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.00000 | + | 1.73205i | 0.0693375 | + | 0.120096i | ||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0000 | −1.10149 | −0.550743 | − | 0.834675i | \(-0.685655\pi\) | ||||
−0.550743 | + | 0.834675i | \(0.685655\pi\) | |||||||
\(212\) | 1.50000 | + | 2.59808i | 0.103020 | + | 0.178437i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.50000 | + | 2.59808i | −0.102538 | + | 0.177601i | ||||
\(215\) | −6.00000 | − | 10.3923i | −0.409197 | − | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.50000 | + | 7.79423i | −0.303390 | + | 0.525487i | ||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | 0.0669650 | 0.0334825 | − | 0.999439i | \(-0.489340\pi\) | ||||
0.0334825 | + | 0.999439i | \(0.489340\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.50000 | − | 12.9904i | 0.497792 | − | 0.862202i | −0.502204 | − | 0.864749i | \(-0.667477\pi\) |
0.999997 | + | 0.00254715i | \(0.000810783\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | + | 17.3205i | 0.660819 | + | 1.14457i | 0.980401 | + | 0.197013i | \(0.0631241\pi\) |
−0.319582 | + | 0.947559i | \(0.603543\pi\) | |||||||
\(230\) | 18.0000 | 1.18688 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.00000 | 0.590879 | ||||||||
\(233\) | 3.00000 | + | 5.19615i | 0.196537 | + | 0.340411i | 0.947403 | − | 0.320043i | \(-0.103697\pi\) |
−0.750867 | + | 0.660454i | \(0.770364\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0000 | + | 31.1769i | −1.17419 | + | 2.03376i | ||||
\(236\) | −1.50000 | − | 2.59808i | −0.0976417 | − | 0.169120i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5000 | − | 19.9186i | 0.740780 | − | 1.28307i | −0.211360 | − | 0.977408i | \(-0.567789\pi\) |
0.952141 | − | 0.305661i | \(-0.0988773\pi\) | |||||||
\(242\) | 1.00000 | − | 1.73205i | 0.0642824 | − | 0.111340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.00000 | 0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | − | 3.46410i | −0.127257 | − | 0.220416i | ||||
\(248\) | −3.50000 | + | 6.06218i | −0.222250 | + | 0.384949i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.50000 | − | 2.59808i | −0.0948683 | − | 0.164317i | ||||
\(251\) | −9.00000 | −0.568075 | −0.284037 | − | 0.958813i | \(-0.591674\pi\) | ||||
−0.284037 | + | 0.958813i | \(0.591674\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | 0.500000 | + | 0.866025i | 0.0313728 | + | 0.0543393i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.50000 | + | 12.9904i | −0.463352 | + | 0.802548i | ||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.00000 | − | 1.73205i | −0.0610847 | − | 0.105802i | ||||
\(269\) | −1.50000 | + | 2.59808i | −0.0914566 | + | 0.158408i | −0.908124 | − | 0.418701i | \(-0.862486\pi\) |
0.816668 | + | 0.577108i | \(0.195819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.50000 | − | 16.4545i | −0.577084 | − | 0.999539i | −0.995812 | − | 0.0914269i | \(-0.970857\pi\) |
0.418728 | − | 0.908112i | \(-0.362476\pi\) | |||||||
\(272\) | −6.00000 | −0.363803 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 6.00000 | + | 10.3923i | 0.361814 | + | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | − | 3.46410i | 0.120168 | − | 0.208138i | −0.799666 | − | 0.600446i | \(-0.794990\pi\) |
0.919834 | + | 0.392308i | \(0.128323\pi\) | |||||||
\(278\) | 1.00000 | + | 1.73205i | 0.0599760 | + | 0.103882i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.0000 | − | 17.3205i | 0.594438 | − | 1.02960i | −0.399188 | − | 0.916869i | \(-0.630708\pi\) |
0.993626 | − | 0.112728i | \(-0.0359589\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.00000 | 0.354787 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | 13.5000 | − | 23.3827i | 0.792747 | − | 1.37308i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.00000 | + | 1.73205i | 0.0585206 | + | 0.101361i | ||||
\(293\) | −9.00000 | −0.525786 | −0.262893 | − | 0.964825i | \(-0.584677\pi\) | ||||
−0.262893 | + | 0.964825i | \(0.584677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.00000 | −0.524000 | ||||||||
\(296\) | 5.00000 | + | 8.66025i | 0.290619 | + | 0.503367i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | −6.00000 | − | 10.3923i | −0.346989 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.00000 | 0.287718 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | − | 1.73205i | 0.0573539 | − | 0.0993399i | ||||
\(305\) | 6.00000 | − | 10.3923i | 0.343559 | − | 0.595062i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.0000 | −1.48390 | −0.741949 | − | 0.670456i | \(-0.766098\pi\) | ||||
−0.741949 | + | 0.670456i | \(0.766098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.5000 | + | 18.1865i | 0.596360 | + | 1.03293i | ||||
\(311\) | −6.00000 | + | 10.3923i | −0.340229 | + | 0.589294i | −0.984475 | − | 0.175525i | \(-0.943838\pi\) |
0.644246 | + | 0.764818i | \(0.277171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.00000 | 0.281272 | ||||||||
\(317\) | −10.5000 | − | 18.1865i | −0.589739 | − | 1.02146i | −0.994266 | − | 0.106932i | \(-0.965897\pi\) |
0.404528 | − | 0.914526i | \(-0.367436\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.5000 | − | 23.3827i | 0.755855 | − | 1.30918i | ||||
\(320\) | 1.50000 | + | 2.59808i | 0.0838525 | + | 0.145237i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.00000 | − | 6.92820i | 0.221880 | − | 0.384308i | ||||
\(326\) | 5.00000 | − | 8.66025i | 0.276924 | − | 0.479647i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | − | 6.92820i | −0.219860 | − | 0.380808i | 0.734905 | − | 0.678170i | \(-0.237227\pi\) |
−0.954765 | + | 0.297361i | \(0.903893\pi\) | |||||||
\(332\) | 4.50000 | − | 7.79423i | 0.246970 | − | 0.427764i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.00000 | − | 15.5885i | −0.492458 | − | 0.852962i | ||||
\(335\) | −6.00000 | −0.327815 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.00000 | + | 15.5885i | −0.488094 | + | 0.845403i | ||||
\(341\) | 10.5000 | + | 18.1865i | 0.568607 | + | 0.984856i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | 6.00000 | − | 10.3923i | 0.322097 | − | 0.557888i | −0.658824 | − | 0.752297i | \(-0.728946\pi\) |
0.980921 | + | 0.194409i | \(0.0622790\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.50000 | + | 2.59808i | 0.0799503 | + | 0.138478i | ||||
\(353\) | 12.0000 | − | 20.7846i | 0.638696 | − | 1.10625i | −0.347024 | − | 0.937856i | \(-0.612808\pi\) |
0.985719 | − | 0.168397i | \(-0.0538590\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −15.0000 | − | 25.9808i | −0.791670 | − | 1.37121i | −0.924932 | − | 0.380131i | \(-0.875879\pi\) |
0.133263 | − | 0.991081i | \(-0.457455\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 10.0000 | + | 17.3205i | 0.525588 | + | 0.910346i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.5000 | + | 32.0429i | −0.965692 | + | 1.67263i | −0.257948 | + | 0.966159i | \(0.583046\pi\) |
−0.707744 | + | 0.706469i | \(0.750287\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 30.0000 | 1.55963 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | −9.00000 | + | 15.5885i | −0.465379 | + | 0.806060i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | + | 10.3923i | 0.309426 | + | 0.535942i | ||||
\(377\) | −18.0000 | −0.927047 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | −3.00000 | − | 5.19615i | −0.153897 | − | 0.266557i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.00000 | + | 10.3923i | −0.306987 | + | 0.531717i | ||||
\(383\) | 15.0000 | + | 25.9808i | 0.766464 | + | 1.32755i | 0.939469 | + | 0.342634i | \(0.111319\pi\) |
−0.173005 | + | 0.984921i | \(0.555348\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.00000 | −0.356291 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.50000 | + | 11.2583i | −0.329988 | + | 0.571555i | ||||
\(389\) | 15.0000 | − | 25.9808i | 0.760530 | − | 1.31728i | −0.182047 | − | 0.983290i | \(-0.558272\pi\) |
0.942578 | − | 0.333987i | \(-0.108394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.0000 | 1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.00000 | + | 15.5885i | 0.453413 | + | 0.785335i | ||||
\(395\) | 7.50000 | − | 12.9904i | 0.377366 | − | 0.653617i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00000 | + | 6.92820i | 0.200754 | + | 0.347717i | 0.948772 | − | 0.315963i | \(-0.102327\pi\) |
−0.748017 | + | 0.663679i | \(0.768994\pi\) | |||||||
\(398\) | −8.00000 | −0.401004 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | 12.0000 | + | 20.7846i | 0.599251 | + | 1.03793i | 0.992932 | + | 0.118686i | \(0.0378683\pi\) |
−0.393680 | + | 0.919247i | \(0.628798\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.00000 | − | 12.1244i | 0.348695 | − | 0.603957i | ||||
\(404\) | 3.00000 | + | 5.19615i | 0.149256 | + | 0.258518i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.0000 | 1.48704 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.50000 | − | 9.52628i | 0.271957 | − | 0.471044i | −0.697406 | − | 0.716677i | \(-0.745662\pi\) |
0.969363 | + | 0.245633i | \(0.0789957\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.0000 | 0.788263 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.5000 | − | 23.3827i | −0.662689 | − | 1.14781i | ||||
\(416\) | 1.00000 | − | 1.73205i | 0.0490290 | − | 0.0849208i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.00000 | − | 5.19615i | −0.146735 | − | 0.254152i | ||||
\(419\) | 36.0000 | 1.75872 | 0.879358 | − | 0.476162i | \(-0.157972\pi\) | ||||
0.879358 | + | 0.476162i | \(0.157972\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.00000 | 0.389896 | 0.194948 | − | 0.980814i | \(-0.437546\pi\) | ||||
0.194948 | + | 0.980814i | \(0.437546\pi\) | |||||||
\(422\) | 8.00000 | + | 13.8564i | 0.389434 | + | 0.674519i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.50000 | − | 2.59808i | 0.0728464 | − | 0.126174i | ||||
\(425\) | 12.0000 | + | 20.7846i | 0.582086 | + | 1.00820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.00000 | 0.145010 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.00000 | + | 10.3923i | −0.289346 | + | 0.501161i | ||||
\(431\) | −12.0000 | + | 20.7846i | −0.578020 | + | 1.00116i | 0.417687 | + | 0.908591i | \(0.362841\pi\) |
−0.995706 | + | 0.0925683i | \(0.970492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.0000 | −1.24948 | −0.624740 | − | 0.780833i | \(-0.714795\pi\) | ||||
−0.624740 | + | 0.780833i | \(0.714795\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | + | 8.66025i | 0.239457 | + | 0.414751i | ||||
\(437\) | −6.00000 | + | 10.3923i | −0.287019 | + | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.50000 | − | 16.4545i | −0.453410 | − | 0.785330i | 0.545185 | − | 0.838316i | \(-0.316459\pi\) |
−0.998595 | + | 0.0529862i | \(0.983126\pi\) | |||||||
\(440\) | 9.00000 | 0.429058 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.0000 | 0.570782 | ||||||||
\(443\) | 7.50000 | + | 12.9904i | 0.356336 | + | 0.617192i | 0.987346 | − | 0.158583i | \(-0.0506926\pi\) |
−0.631010 | + | 0.775775i | \(0.717359\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.00000 | − | 15.5885i | 0.426641 | − | 0.738964i | ||||
\(446\) | −0.500000 | − | 0.866025i | −0.0236757 | − | 0.0410075i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.0000 | −0.703985 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.50000 | + | 11.2583i | 0.304057 | + | 0.526642i | 0.977051 | − | 0.213006i | \(-0.0683253\pi\) |
−0.672994 | + | 0.739648i | \(0.734992\pi\) | |||||||
\(458\) | 10.0000 | − | 17.3205i | 0.467269 | − | 0.809334i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.00000 | − | 15.5885i | −0.419627 | − | 0.726816i | ||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | −0.185896 | −0.0929479 | − | 0.995671i | \(-0.529629\pi\) | ||||
−0.0929479 | + | 0.995671i | \(0.529629\pi\) | |||||||
\(464\) | −4.50000 | − | 7.79423i | −0.208907 | − | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.00000 | − | 5.19615i | 0.138972 | − | 0.240707i | ||||
\(467\) | 6.00000 | + | 10.3923i | 0.277647 | + | 0.480899i | 0.970799 | − | 0.239892i | \(-0.0771121\pi\) |
−0.693153 | + | 0.720791i | \(0.743779\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 36.0000 | 1.66056 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.50000 | + | 2.59808i | −0.0690431 | + | 0.119586i | ||||
\(473\) | −6.00000 | + | 10.3923i | −0.275880 | + | 0.477839i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.00000 | −0.367065 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.00000 | − | 15.5885i | −0.411650 | − | 0.712999i | ||||
\(479\) | 12.0000 | − | 20.7846i | 0.548294 | − | 0.949673i | −0.450098 | − | 0.892979i | \(-0.648611\pi\) |
0.998392 | − | 0.0566937i | \(-0.0180558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.0000 | − | 17.3205i | −0.455961 | − | 0.789747i | ||||
\(482\) | −23.0000 | −1.04762 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00000 | −0.0909091 | ||||||||
\(485\) | 19.5000 | + | 33.7750i | 0.885449 | + | 1.53364i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.50000 | + | 9.52628i | −0.249229 | + | 0.431677i | −0.963312 | − | 0.268384i | \(-0.913510\pi\) |
0.714083 | + | 0.700061i | \(0.246844\pi\) | |||||||
\(488\) | −2.00000 | − | 3.46410i | −0.0905357 | − | 0.156813i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.00000 | 0.406164 | 0.203082 | − | 0.979162i | \(-0.434904\pi\) | ||||
0.203082 | + | 0.979162i | \(0.434904\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.0000 | − | 46.7654i | 1.21602 | − | 2.10621i | ||||
\(494\) | −2.00000 | + | 3.46410i | −0.0899843 | + | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.00000 | 0.314309 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.0000 | − | 32.9090i | −0.850557 | − | 1.47321i | −0.880707 | − | 0.473662i | \(-0.842932\pi\) |
0.0301498 | − | 0.999545i | \(-0.490402\pi\) | |||||||
\(500\) | −1.50000 | + | 2.59808i | −0.0670820 | + | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.50000 | + | 7.79423i | 0.200845 | + | 0.347873i | ||||
\(503\) | −18.0000 | −0.802580 | −0.401290 | − | 0.915951i | \(-0.631438\pi\) | ||||
−0.401290 | + | 0.915951i | \(0.631438\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | −9.00000 | − | 15.5885i | −0.400099 | − | 0.692991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.500000 | − | 0.866025i | 0.0221839 | − | 0.0384237i | ||||
\(509\) | −7.50000 | − | 12.9904i | −0.332432 | − | 0.575789i | 0.650556 | − | 0.759458i | \(-0.274536\pi\) |
−0.982988 | + | 0.183669i | \(0.941202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.00000 | + | 5.19615i | −0.132324 | + | 0.229192i | ||||
\(515\) | 24.0000 | − | 41.5692i | 1.05757 | − | 1.83176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.0000 | 1.58328 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.00000 | − | 5.19615i | −0.131559 | − | 0.227866i | ||||
\(521\) | 12.0000 | − | 20.7846i | 0.525730 | − | 0.910590i | −0.473821 | − | 0.880621i | \(-0.657126\pi\) |
0.999551 | − | 0.0299693i | \(-0.00954094\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.0000 | + | 22.5167i | 0.568450 | + | 0.984585i | 0.996719 | + | 0.0809336i | \(0.0257902\pi\) |
−0.428269 | + | 0.903651i | \(0.640876\pi\) | |||||||
\(524\) | 15.0000 | 0.655278 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 21.0000 | + | 36.3731i | 0.914774 | + | 1.58444i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | −4.50000 | − | 7.79423i | −0.195468 | − | 0.338560i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.50000 | − | 7.79423i | 0.194552 | − | 0.336974i | ||||
\(536\) | −1.00000 | + | 1.73205i | −0.0431934 | + | 0.0748132i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.00000 | 0.129339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | + | 13.8564i | 0.343947 | + | 0.595733i | 0.985162 | − | 0.171628i | \(-0.0549027\pi\) |
−0.641215 | + | 0.767361i | \(0.721569\pi\) | |||||||
\(542\) | −9.50000 | + | 16.4545i | −0.408060 | + | 0.706781i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.00000 | + | 5.19615i | 0.128624 | + | 0.222783i | ||||
\(545\) | 30.0000 | 1.28506 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | 0.598597 | 0.299298 | − | 0.954160i | \(-0.403247\pi\) | ||||
0.299298 | + | 0.954160i | \(0.403247\pi\) | |||||||
\(548\) | −3.00000 | − | 5.19615i | −0.128154 | − | 0.221969i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.00000 | − | 10.3923i | 0.255841 | − | 0.443129i | ||||
\(551\) | 9.00000 | + | 15.5885i | 0.383413 | + | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −4.00000 | −0.169944 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.00000 | − | 1.73205i | 0.0424094 | − | 0.0734553i | ||||
\(557\) | −7.50000 | + | 12.9904i | −0.317785 | + | 0.550420i | −0.980026 | − | 0.198871i | \(-0.936272\pi\) |
0.662240 | + | 0.749291i | \(0.269606\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.00000 | 0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.00000 | + | 15.5885i | 0.379642 | + | 0.657559i | ||||
\(563\) | −1.50000 | + | 2.59808i | −0.0632175 | + | 0.109496i | −0.895902 | − | 0.444252i | \(-0.853470\pi\) |
0.832684 | + | 0.553748i | \(0.186803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.0000 | − | 25.9808i | −0.628833 | − | 1.08917i | −0.987786 | − | 0.155815i | \(-0.950200\pi\) |
0.358954 | − | 0.933355i | \(-0.383134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | −3.00000 | − | 5.19615i | −0.125436 | − | 0.217262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24.0000 | −1.00087 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.500000 | + | 0.866025i | −0.0208153 | + | 0.0360531i | −0.876245 | − | 0.481865i | \(-0.839960\pi\) |
0.855430 | + | 0.517918i | \(0.173293\pi\) | |||||||
\(578\) | −9.50000 | + | 16.4545i | −0.395148 | + | 0.684416i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −27.0000 | −1.12111 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.50000 | − | 7.79423i | −0.186371 | − | 0.322804i | ||||
\(584\) | 1.00000 | − | 1.73205i | 0.0413803 | − | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.50000 | + | 7.79423i | 0.185893 | + | 0.321977i | ||||
\(587\) | −27.0000 | −1.11441 | −0.557205 | − | 0.830375i | \(-0.688126\pi\) | ||||
−0.557205 | + | 0.830375i | \(0.688126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.0000 | −0.576860 | ||||||||
\(590\) | 4.50000 | + | 7.79423i | 0.185262 | + | 0.320883i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.00000 | − | 8.66025i | 0.205499 | − | 0.355934i | ||||
\(593\) | 15.0000 | + | 25.9808i | 0.615976 | + | 1.06690i | 0.990212 | + | 0.139569i | \(0.0445716\pi\) |
−0.374236 | + | 0.927333i | \(0.622095\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.00000 | + | 10.3923i | −0.245358 | + | 0.424973i | ||||
\(599\) | 15.0000 | − | 25.9808i | 0.612883 | − | 1.06155i | −0.377869 | − | 0.925859i | \(-0.623343\pi\) |
0.990752 | − | 0.135686i | \(-0.0433238\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.0000 | −0.938190 | −0.469095 | − | 0.883148i | \(-0.655420\pi\) | ||||
−0.469095 | + | 0.883148i | \(0.655420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.50000 | − | 4.33013i | −0.101724 | − | 0.176190i | ||||
\(605\) | −3.00000 | + | 5.19615i | −0.121967 | + | 0.211254i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.50000 | − | 11.2583i | −0.263827 | − | 0.456962i | 0.703429 | − | 0.710766i | \(-0.251651\pi\) |
−0.967256 | + | 0.253804i | \(0.918318\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | −0.485866 | ||||||||
\(611\) | −12.0000 | − | 20.7846i | −0.485468 | − | 0.840855i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0000 | + | 22.5167i | −0.525065 | + | 0.909439i | 0.474509 | + | 0.880251i | \(0.342626\pi\) |
−0.999574 | + | 0.0291886i | \(0.990708\pi\) | |||||||
\(614\) | 13.0000 | + | 22.5167i | 0.524637 | + | 0.908698i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.0000 | 1.44931 | 0.724653 | − | 0.689114i | \(-0.242000\pi\) | ||||
0.724653 | + | 0.689114i | \(0.242000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.00000 | + | 3.46410i | −0.0803868 | + | 0.139234i | −0.903416 | − | 0.428765i | \(-0.858949\pi\) |
0.823029 | + | 0.567999i | \(0.192282\pi\) | |||||||
\(620\) | 10.5000 | − | 18.1865i | 0.421690 | − | 0.730389i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.0000 | 0.481156 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 8.50000 | − | 14.7224i | 0.339728 | − | 0.588427i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.00000 | − | 3.46410i | −0.0798087 | − | 0.138233i | ||||
\(629\) | 60.0000 | 2.39236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.0000 | −1.47295 | −0.736473 | − | 0.676467i | \(-0.763510\pi\) | ||||
−0.736473 | + | 0.676467i | \(0.763510\pi\) | |||||||
\(632\) | −2.50000 | − | 4.33013i | −0.0994447 | − | 0.172243i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.5000 | + | 18.1865i | −0.417008 | + | 0.722280i | ||||
\(635\) | −1.50000 | − | 2.59808i | −0.0595257 | − | 0.103102i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −27.0000 | −1.06894 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.50000 | − | 2.59808i | 0.0592927 | − | 0.102698i | ||||
\(641\) | 6.00000 | − | 10.3923i | 0.236986 | − | 0.410471i | −0.722862 | − | 0.690992i | \(-0.757174\pi\) |
0.959848 | + | 0.280521i | \(0.0905072\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −38.0000 | −1.49857 | −0.749287 | − | 0.662246i | \(-0.769604\pi\) | ||||
−0.749287 | + | 0.662246i | \(0.769604\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | −6.00000 | + | 10.3923i | −0.235884 | + | 0.408564i | −0.959529 | − | 0.281609i | \(-0.909132\pi\) |
0.723645 | + | 0.690172i | \(0.242465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.50000 | + | 7.79423i | 0.176640 | + | 0.305950i | ||||
\(650\) | −8.00000 | −0.313786 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.0000 | −0.391630 | ||||||||
\(653\) | −19.5000 | − | 33.7750i | −0.763094 | − | 1.32172i | −0.941248 | − | 0.337715i | \(-0.890346\pi\) |
0.178154 | − | 0.984003i | \(-0.442987\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.5000 | − | 38.9711i | 0.879148 | − | 1.52273i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0000 | + | 34.6410i | −0.777910 | + | 1.34738i | 0.155235 | + | 0.987878i | \(0.450387\pi\) |
−0.933144 | + | 0.359502i | \(0.882947\pi\) | |||||||
\(662\) | −4.00000 | + | 6.92820i | −0.155464 | + | 0.269272i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.00000 | −0.349268 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.0000 | + | 46.7654i | 1.04544 | + | 1.81076i | ||||
\(668\) | −9.00000 | + | 15.5885i | −0.348220 | + | 0.603136i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.00000 | + | 5.19615i | 0.115900 | + | 0.200745i | ||||
\(671\) | −12.0000 | −0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.0000 | 0.655302 | 0.327651 | − | 0.944799i | \(-0.393743\pi\) | ||||
0.327651 | + | 0.944799i | \(0.393743\pi\) | |||||||
\(674\) | −2.50000 | − | 4.33013i | −0.0962964 | − | 0.166790i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | − | 7.79423i | 0.173077 | − | 0.299778i | ||||
\(677\) | −16.5000 | − | 28.5788i | −0.634147 | − | 1.09837i | −0.986695 | − | 0.162581i | \(-0.948018\pi\) |
0.352549 | − | 0.935793i | \(-0.385315\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 18.0000 | 0.690268 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.5000 | − | 18.1865i | 0.402066 | − | 0.696398i | ||||
\(683\) | −25.5000 | + | 44.1673i | −0.975730 | + | 1.69001i | −0.298227 | + | 0.954495i | \(0.596395\pi\) |
−0.677503 | + | 0.735520i | \(0.736938\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | −0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | −3.00000 | + | 5.19615i | −0.114291 | + | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.0000 | + | 27.7128i | 0.608669 | + | 1.05425i | 0.991460 | + | 0.130410i | \(0.0416295\pi\) |
−0.382791 | + | 0.923835i | \(0.625037\pi\) | |||||||
\(692\) | 6.00000 | 0.228086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | −3.00000 | − | 5.19615i | −0.113796 | − | 0.197101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 7.00000 | + | 12.1244i | 0.264954 | + | 0.458914i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.00000 | 0.339925 | 0.169963 | − | 0.985451i | \(-0.445635\pi\) | ||||
0.169963 | + | 0.985451i | \(0.445635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0000 | + | 17.3205i | −0.377157 | + | 0.653255i | ||||
\(704\) | 1.50000 | − | 2.59808i | 0.0565334 | − | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.0000 | −0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.00000 | − | 12.1244i | −0.262891 | − | 0.455340i | 0.704118 | − | 0.710083i | \(-0.251342\pi\) |
−0.967009 | + | 0.254743i | \(0.918009\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | − | 5.19615i | −0.112430 | − | 0.194734i | ||||
\(713\) | −42.0000 | −1.57291 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0000 | −0.673162 | ||||||||
\(716\) | 6.00000 | + | 10.3923i | 0.224231 | + | 0.388379i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.0000 | + | 25.9808i | −0.559795 | + | 0.969593i | ||||
\(719\) | −21.0000 | − | 36.3731i | −0.783168 | − | 1.35649i | −0.930087 | − | 0.367338i | \(-0.880269\pi\) |
0.146920 | − | 0.989148i | \(-0.453064\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.0000 | − | 17.3205i | 0.371647 | − | 0.643712i | ||||
\(725\) | −18.0000 | + | 31.1769i | −0.668503 | + | 1.15788i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.0000 | 1.14973 | 0.574863 | − | 0.818250i | \(-0.305055\pi\) | ||||
0.574863 | + | 0.818250i | \(0.305055\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.00000 | − | 5.19615i | −0.111035 | − | 0.192318i | ||||
\(731\) | −12.0000 | + | 20.7846i | −0.443836 | + | 0.768747i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.0000 | + | 17.3205i | 0.369358 | + | 0.639748i | 0.989465 | − | 0.144770i | \(-0.0462441\pi\) |
−0.620107 | + | 0.784517i | \(0.712911\pi\) | |||||||
\(734\) | 37.0000 | 1.36569 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 3.00000 | + | 5.19615i | 0.110506 | + | 0.191403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.0000 | + | 22.5167i | −0.478213 | + | 0.828289i | −0.999688 | − | 0.0249776i | \(-0.992049\pi\) |
0.521475 | + | 0.853266i | \(0.325382\pi\) | |||||||
\(740\) | −15.0000 | − | 25.9808i | −0.551411 | − | 0.955072i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −54.0000 | −1.98107 | −0.990534 | − | 0.137268i | \(-0.956168\pi\) | ||||
−0.990534 | + | 0.137268i | \(0.956168\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.00000 | + | 15.5885i | −0.329734 | + | 0.571117i | ||||
\(746\) | 2.00000 | − | 3.46410i | 0.0732252 | − | 0.126830i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 18.0000 | 0.658145 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.5000 | − | 19.9186i | −0.419641 | − | 0.726839i | 0.576262 | − | 0.817265i | \(-0.304511\pi\) |
−0.995903 | + | 0.0904254i | \(0.971177\pi\) | |||||||
\(752\) | 6.00000 | − | 10.3923i | 0.218797 | − | 0.378968i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 9.00000 | + | 15.5885i | 0.327761 | + | 0.567698i | ||||
\(755\) | −15.0000 | −0.545906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −28.0000 | −1.01768 | −0.508839 | − | 0.860862i | \(-0.669925\pi\) | ||||
−0.508839 | + | 0.860862i | \(0.669925\pi\) | |||||||
\(758\) | 14.0000 | + | 24.2487i | 0.508503 | + | 0.880753i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.00000 | + | 5.19615i | −0.108821 | + | 0.188484i | ||||
\(761\) | −21.0000 | − | 36.3731i | −0.761249 | − | 1.31852i | −0.942207 | − | 0.335032i | \(-0.891253\pi\) |
0.180957 | − | 0.983491i | \(-0.442080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.0000 | − | 25.9808i | 0.541972 | − | 0.938723i | ||||
\(767\) | 3.00000 | − | 5.19615i | 0.108324 | − | 0.187622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.50000 | + | 6.06218i | 0.125968 | + | 0.218183i | ||||
\(773\) | 3.00000 | − | 5.19615i | 0.107903 | − | 0.186893i | −0.807018 | − | 0.590527i | \(-0.798920\pi\) |
0.914920 | + | 0.403634i | \(0.132253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.0000 | − | 24.2487i | −0.502895 | − | 0.871039i | ||||
\(776\) | 13.0000 | 0.466673 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −30.0000 | −1.07555 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −18.0000 | − | 31.1769i | −0.643679 | − | 1.11488i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.0000 | −0.428298 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.00000 | + | 13.8564i | −0.285169 | + | 0.493928i | −0.972650 | − | 0.232275i | \(-0.925383\pi\) |
0.687481 | + | 0.726202i | \(0.258716\pi\) | |||||||
\(788\) | 9.00000 | − | 15.5885i | 0.320612 | − | 0.555316i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.0000 | −0.533676 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | + | 6.92820i | 0.142044 | + | 0.246028i | ||||
\(794\) | 4.00000 | − | 6.92820i | 0.141955 | − | 0.245873i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.00000 | + | 6.92820i | 0.141776 | + | 0.245564i | ||||
\(797\) | −27.0000 | −0.956389 | −0.478195 | − | 0.878254i | \(-0.658709\pi\) | ||||
−0.478195 | + | 0.878254i | \(0.658709\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 72.0000 | 2.54718 | ||||||||
\(800\) | −2.00000 | − | 3.46410i | −0.0707107 | − | 0.122474i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.0000 | − | 20.7846i | 0.423735 | − | 0.733930i | ||||
\(803\) | −3.00000 | − | 5.19615i | −0.105868 | − | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.0000 | −0.493129 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.00000 | − | 5.19615i | 0.105540 | − | 0.182800i | ||||
\(809\) | 6.00000 | − | 10.3923i | 0.210949 | − | 0.365374i | −0.741063 | − | 0.671436i | \(-0.765678\pi\) |
0.952012 | + | 0.306062i | \(0.0990113\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.00000 | −0.0702295 | −0.0351147 | − | 0.999383i | \(-0.511180\pi\) | ||||
−0.0351147 | + | 0.999383i | \(0.511180\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −15.0000 | − | 25.9808i | −0.525750 | − | 0.910625i | ||||
\(815\) | −15.0000 | + | 25.9808i | −0.525427 | + | 0.910066i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.00000 | − | 6.92820i | −0.139942 | − | 0.242387i | ||||
\(818\) | −11.0000 | −0.384606 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | −8.00000 | − | 13.8564i | −0.278693 | − | 0.482711i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.00000 | 0.312961 | 0.156480 | − | 0.987681i | \(-0.449985\pi\) | ||||
0.156480 | + | 0.987681i | \(0.449985\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.00000 | − | 1.73205i | 0.0347314 | − | 0.0601566i | −0.848137 | − | 0.529777i | \(-0.822276\pi\) |
0.882869 | + | 0.469620i | \(0.155609\pi\) | |||||||
\(830\) | −13.5000 | + | 23.3827i | −0.468592 | + | 0.811625i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.00000 | −0.0693375 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.0000 | + | 46.7654i | 0.934374 | + | 1.61838i | ||||
\(836\) | −3.00000 | + | 5.19615i | −0.103757 | + | 0.179713i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.0000 | − | 31.1769i | −0.621800 | − | 1.07699i | ||||
\(839\) | 54.0000 | 1.86429 | 0.932144 | − | 0.362089i | \(-0.117936\pi\) | ||||
0.932144 | + | 0.362089i | \(0.117936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | −4.00000 | − | 6.92820i | −0.137849 | − | 0.238762i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.00000 | − | 13.8564i | 0.275371 | − | 0.476957i | ||||
\(845\) | −13.5000 | − | 23.3827i | −0.464414 | − | 0.804389i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.0000 | − | 20.7846i | 0.411597 | − | 0.712906i | ||||
\(851\) | −30.0000 | + | 51.9615i | −1.02839 | + | 1.78122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.0000 | 1.57501 | 0.787505 | − | 0.616308i | \(-0.211372\pi\) | ||||
0.787505 | + | 0.616308i | \(0.211372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50000 | − | 2.59808i | −0.0512689 | − | 0.0888004i | ||||
\(857\) | −6.00000 | + | 10.3923i | −0.204956 | + | 0.354994i | −0.950119 | − | 0.311888i | \(-0.899038\pi\) |
0.745163 | + | 0.666883i | \(0.232372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.00000 | − | 13.8564i | −0.272956 | − | 0.472774i | 0.696661 | − | 0.717400i | \(-0.254668\pi\) |
−0.969618 | + | 0.244626i | \(0.921335\pi\) | |||||||
\(860\) | 12.0000 | 0.409197 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.0000 | 0.817443 | ||||||||
\(863\) | 3.00000 | + | 5.19615i | 0.102121 | + | 0.176879i | 0.912558 | − | 0.408946i | \(-0.134104\pi\) |
−0.810437 | + | 0.585826i | \(0.800770\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | − | 15.5885i | 0.306009 | − | 0.530023i | ||||
\(866\) | 13.0000 | + | 22.5167i | 0.441758 | + | 0.765147i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.0000 | −0.508840 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | − | 3.46410i | 0.0677674 | − | 0.117377i | ||||
\(872\) | 5.00000 | − | 8.66025i | 0.169321 | − | 0.293273i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 12.0000 | 0.405906 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.0000 | − | 48.4974i | −0.945493 | − | 1.63764i | −0.754761 | − | 0.655999i | \(-0.772247\pi\) |
−0.190731 | − | 0.981642i | \(-0.561086\pi\) | |||||||
\(878\) | −9.50000 | + | 16.4545i | −0.320609 | + | 0.555312i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.50000 | − | 7.79423i | −0.151695 | − | 0.262743i | ||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | −6.00000 | − | 10.3923i | −0.201802 | − | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.50000 | − | 12.9904i | 0.251967 | − | 0.436420i | ||||
\(887\) | −3.00000 | − | 5.19615i | −0.100730 | − | 0.174470i | 0.811256 | − | 0.584692i | \(-0.198785\pi\) |
−0.911986 | + | 0.410222i | \(0.865451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −18.0000 | −0.603361 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.500000 | + | 0.866025i | −0.0167412 | + | 0.0289967i | ||||
\(893\) | −12.0000 | + | 20.7846i | −0.401565 | + | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0000 | 1.20335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.00000 | − | 15.5885i | −0.300334 | − | 0.520194i | ||||
\(899\) | −31.5000 | + | 54.5596i | −1.05058 | + | 1.81966i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.00000 | − | 15.5885i | −0.299833 | − | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.0000 | − | 51.9615i | −0.997234 | − | 1.72726i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.0000 | + | 43.3013i | −0.830111 | + | 1.43780i | 0.0678380 | + | 0.997696i | \(0.478390\pi\) |
−0.897949 | + | 0.440099i | \(0.854943\pi\) | |||||||
\(908\) | 7.50000 | + | 12.9904i | 0.248896 | + | 0.431101i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.5000 | + | 23.3827i | −0.446785 | + | 0.773854i | ||||
\(914\) | 6.50000 | − | 11.2583i | 0.215001 | − | 0.372392i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.0000 | −0.660819 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.0000 | + | 24.2487i | 0.461817 | + | 0.799891i | 0.999052 | − | 0.0435419i | \(-0.0138642\pi\) |
−0.537234 | + | 0.843433i | \(0.680531\pi\) | |||||||
\(920\) | −9.00000 | + | 15.5885i | −0.296721 | + | 0.513936i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.00000 | + | 15.5885i | 0.296399 | + | 0.513378i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.0000 | −1.31519 | ||||||||
\(926\) | 2.00000 | + | 3.46410i | 0.0657241 | + | 0.113837i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.50000 | + | 7.79423i | −0.147720 | + | 0.255858i | ||||
\(929\) | −12.0000 | − | 20.7846i | −0.393707 | − | 0.681921i | 0.599228 | − | 0.800578i | \(-0.295474\pi\) |
−0.992935 | + | 0.118657i | \(0.962141\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −6.00000 | −0.196537 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.00000 | − | 10.3923i | 0.196326 | − | 0.340047i | ||||
\(935\) | 27.0000 | − | 46.7654i | 0.882994 | − | 1.52939i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.0000 | 1.20874 | 0.604369 | − | 0.796705i | \(-0.293425\pi\) | ||||
0.604369 | + | 0.796705i | \(0.293425\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.0000 | − | 31.1769i | −0.587095 | − | 1.01688i | ||||
\(941\) | 7.50000 | − | 12.9904i | 0.244493 | − | 0.423474i | −0.717496 | − | 0.696563i | \(-0.754712\pi\) |
0.961989 | + | 0.273088i | \(0.0880451\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 3.00000 | 0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.0000 | 0.390154 | ||||||||
\(947\) | −6.00000 | − | 10.3923i | −0.194974 | − | 0.337705i | 0.751918 | − | 0.659256i | \(-0.229129\pi\) |
−0.946892 | + | 0.321552i | \(0.895796\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | ||||
\(950\) | 4.00000 | + | 6.92820i | 0.129777 | + | 0.224781i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36.0000 | −1.16615 | −0.583077 | − | 0.812417i | \(-0.698151\pi\) | ||||
−0.583077 | + | 0.812417i | \(0.698151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.0000 | − | 31.1769i | 0.582466 | − | 1.00886i | ||||
\(956\) | −9.00000 | + | 15.5885i | −0.291081 | + | 0.504167i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.0000 | −0.775405 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | − | 15.5885i | −0.290323 | − | 0.502853i | ||||
\(962\) | −10.0000 | + | 17.3205i | −0.322413 | + | 0.558436i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.5000 | + | 19.9186i | 0.370390 | + | 0.641534i | ||||
\(965\) | 21.0000 | 0.676014 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.0000 | 0.932577 | 0.466289 | − | 0.884633i | \(-0.345591\pi\) | ||||
0.466289 | + | 0.884633i | \(0.345591\pi\) | |||||||
\(968\) | 1.00000 | + | 1.73205i | 0.0321412 | + | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.5000 | − | 33.7750i | 0.626107 | − | 1.08445i | ||||
\(971\) | 19.5000 | + | 33.7750i | 0.625785 | + | 1.08389i | 0.988389 | + | 0.151948i | \(0.0485545\pi\) |
−0.362604 | + | 0.931943i | \(0.618112\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.0000 | 0.352463 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | + | 3.46410i | −0.0640184 | + | 0.110883i | ||||
\(977\) | 6.00000 | − | 10.3923i | 0.191957 | − | 0.332479i | −0.753942 | − | 0.656941i | \(-0.771850\pi\) |
0.945899 | + | 0.324462i | \(0.105183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.0000 | −0.575282 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.50000 | − | 7.79423i | −0.143601 | − | 0.248724i | ||||
\(983\) | 12.0000 | − | 20.7846i | 0.382741 | − | 0.662926i | −0.608712 | − | 0.793391i | \(-0.708314\pi\) |
0.991453 | + | 0.130465i | \(0.0416470\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.0000 | − | 46.7654i | −0.860292 | − | 1.49007i | ||||
\(986\) | −54.0000 | −1.71971 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | 0.127257 | ||||||||
\(989\) | −12.0000 | − | 20.7846i | −0.381578 | − | 0.660912i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.50000 | − | 16.4545i | 0.301777 | − | 0.522694i | −0.674761 | − | 0.738036i | \(-0.735753\pi\) |
0.976539 | + | 0.215342i | \(0.0690867\pi\) | |||||||
\(992\) | −3.50000 | − | 6.06218i | −0.111125 | − | 0.192474i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000 | 0.760851 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.0000 | + | 19.0526i | −0.348373 | + | 0.603401i | −0.985961 | − | 0.166978i | \(-0.946599\pi\) |
0.637587 | + | 0.770378i | \(0.279933\pi\) | |||||||
\(998\) | −19.0000 | + | 32.9090i | −0.601434 | + | 1.04172i | ||||
\(999\) | 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 | 882.2.g.e.361.1 | 2 | ||
3.2 | odd | 2 | 882.2.g.g.361.1 | 2 | |||
7.2 | even | 3 | inner | 882.2.g.e.667.1 | 2 | ||
7.3 | odd | 6 | 882.2.a.j.1.1 | 1 | |||
7.4 | even | 3 | 882.2.a.h.1.1 | 1 | |||
7.5 | odd | 6 | 126.2.g.a.37.1 | ✓ | 2 | ||
7.6 | odd | 2 | 126.2.g.a.109.1 | yes | 2 | ||
21.2 | odd | 6 | 882.2.g.g.667.1 | 2 | |||
21.5 | even | 6 | 126.2.g.d.37.1 | yes | 2 | ||
21.11 | odd | 6 | 882.2.a.e.1.1 | 1 | |||
21.17 | even | 6 | 882.2.a.a.1.1 | 1 | |||
21.20 | even | 2 | 126.2.g.d.109.1 | yes | 2 | ||
28.3 | even | 6 | 7056.2.a.by.1.1 | 1 | |||
28.11 | odd | 6 | 7056.2.a.h.1.1 | 1 | |||
28.19 | even | 6 | 1008.2.s.b.289.1 | 2 | |||
28.27 | even | 2 | 1008.2.s.b.865.1 | 2 | |||
63.5 | even | 6 | 1134.2.h.j.541.1 | 2 | |||
63.13 | odd | 6 | 1134.2.e.k.865.1 | 2 | |||
63.20 | even | 6 | 1134.2.h.j.109.1 | 2 | |||
63.34 | odd | 6 | 1134.2.h.f.109.1 | 2 | |||
63.40 | odd | 6 | 1134.2.h.f.541.1 | 2 | |||
63.41 | even | 6 | 1134.2.e.g.865.1 | 2 | |||
63.47 | even | 6 | 1134.2.e.g.919.1 | 2 | |||
63.61 | odd | 6 | 1134.2.e.k.919.1 | 2 | |||
84.11 | even | 6 | 7056.2.a.bx.1.1 | 1 | |||
84.47 | odd | 6 | 1008.2.s.o.289.1 | 2 | |||
84.59 | odd | 6 | 7056.2.a.e.1.1 | 1 | |||
84.83 | odd | 2 | 1008.2.s.o.865.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.2.g.a.37.1 | ✓ | 2 | 7.5 | odd | 6 | ||
126.2.g.a.109.1 | yes | 2 | 7.6 | odd | 2 | ||
126.2.g.d.37.1 | yes | 2 | 21.5 | even | 6 | ||
126.2.g.d.109.1 | yes | 2 | 21.20 | even | 2 | ||
882.2.a.a.1.1 | 1 | 21.17 | even | 6 | |||
882.2.a.e.1.1 | 1 | 21.11 | odd | 6 | |||
882.2.a.h.1.1 | 1 | 7.4 | even | 3 | |||
882.2.a.j.1.1 | 1 | 7.3 | odd | 6 | |||
882.2.g.e.361.1 | 2 | 1.1 | even | 1 | trivial | ||
882.2.g.e.667.1 | 2 | 7.2 | even | 3 | inner | ||
882.2.g.g.361.1 | 2 | 3.2 | odd | 2 | |||
882.2.g.g.667.1 | 2 | 21.2 | odd | 6 | |||
1008.2.s.b.289.1 | 2 | 28.19 | even | 6 | |||
1008.2.s.b.865.1 | 2 | 28.27 | even | 2 | |||
1008.2.s.o.289.1 | 2 | 84.47 | odd | 6 | |||
1008.2.s.o.865.1 | 2 | 84.83 | odd | 2 | |||
1134.2.e.g.865.1 | 2 | 63.41 | even | 6 | |||
1134.2.e.g.919.1 | 2 | 63.47 | even | 6 | |||
1134.2.e.k.865.1 | 2 | 63.13 | odd | 6 | |||
1134.2.e.k.919.1 | 2 | 63.61 | odd | 6 | |||
1134.2.h.f.109.1 | 2 | 63.34 | odd | 6 | |||
1134.2.h.f.541.1 | 2 | 63.40 | odd | 6 | |||
1134.2.h.j.109.1 | 2 | 63.20 | even | 6 | |||
1134.2.h.j.541.1 | 2 | 63.5 | even | 6 | |||
7056.2.a.e.1.1 | 1 | 84.59 | odd | 6 | |||
7056.2.a.h.1.1 | 1 | 28.11 | odd | 6 | |||
7056.2.a.bx.1.1 | 1 | 84.11 | even | 6 | |||
7056.2.a.by.1.1 | 1 | 28.3 | even | 6 |