Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,2,Mod(27,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.27");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.x (of order \(8\), degree \(4\), 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: | \(1.78864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{8})\) |
Coefficient field: | 8.0.157351936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{8}]$ |
Embedding invariants
Embedding label | 83.2 | ||
Root | \(0.581861 + 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.83 |
Dual form | 224.2.x.a.27.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.581861 | + | 1.28897i | 0.411438 | + | 0.911438i | ||||
\(3\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(4\) | −1.32288 | + | 1.50000i | −0.661438 | + | 0.750000i | ||||
\(5\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.87083 | + | 1.87083i | 0.707107 | + | 0.707107i | ||||
\(8\) | −2.70318 | − | 0.832353i | −0.955719 | − | 0.294281i | ||||
\(9\) | 2.12132 | + | 2.12132i | 0.707107 | + | 0.707107i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.10237 | + | 1.28504i | −0.935399 | + | 0.387455i | −0.797724 | − | 0.603023i | \(-0.793963\pi\) |
−0.137675 | + | 0.990478i | \(0.543963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(14\) | −1.32288 | + | 3.50000i | −0.353553 | + | 0.935414i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 3.96863i | −0.125000 | − | 0.992157i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −1.50000 | + | 3.96863i | −0.353553 | + | 0.935414i | ||||
\(19\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.46152 | − | 3.25113i | −0.737999 | − | 0.693144i | ||||
\(23\) | 1.35425 | − | 1.35425i | 0.282380 | − | 0.282380i | −0.551677 | − | 0.834058i | \(-0.686012\pi\) |
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.53553 | − | 3.53553i | 0.707107 | − | 0.707107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −5.28112 | + | 0.331369i | −0.998037 | + | 0.0626229i | ||||
\(29\) | 2.25695 | − | 5.44876i | 0.419105 | − | 1.01181i | −0.563502 | − | 0.826115i | \(-0.690546\pi\) |
0.982607 | − | 0.185695i | \(-0.0594537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 4.82450 | − | 2.95367i | 0.852859 | − | 0.522141i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.98822 | + | 0.375737i | −0.998037 | + | 0.0626229i | ||||
\(37\) | 11.1545 | − | 4.62034i | 1.83379 | − | 0.759579i | 0.869918 | − | 0.493197i | \(-0.164172\pi\) |
0.963868 | − | 0.266382i | \(-0.0858282\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.37181 | + | 3.46772i | −1.27669 | + | 0.528822i | −0.914991 | − | 0.403473i | \(-0.867803\pi\) |
−0.361698 | + | 0.932295i | \(0.617803\pi\) | |||||||
\(44\) | 2.17648 | − | 6.35350i | 0.328117 | − | 0.957826i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.53357 | + | 0.957598i | 0.373554 | + | 0.141190i | ||||
\(47\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 6.61438 | + | 2.50000i | 0.935414 | + | 0.353553i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.27719 | − | 5.49763i | −0.312796 | − | 0.755157i | −0.999599 | − | 0.0283132i | \(-0.990986\pi\) |
0.686803 | − | 0.726844i | \(-0.259014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.50000 | − | 6.61438i | −0.467707 | − | 0.883883i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.33651 | − | 0.261285i | 1.09464 | − | 0.0343084i | ||||
\(59\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.93725i | 1.00000i | ||||||||
\(64\) | 6.61438 | + | 4.50000i | 0.826797 | + | 0.562500i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.19827 | − | 0.910554i | −0.268562 | − | 0.111242i | 0.244339 | − | 0.969690i | \(-0.421429\pi\) |
−0.512901 | + | 0.858448i | \(0.671429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | − | 11.3137i | −1.34269 | − | 1.34269i | −0.893372 | − | 0.449319i | \(-0.851667\pi\) |
−0.449319 | − | 0.893372i | \(-0.648333\pi\) | |||||||
\(72\) | −3.96863 | − | 7.50000i | −0.467707 | − | 0.883883i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | 12.4458 | + | 11.6894i | 1.44680 | + | 1.35886i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.20809 | − | 3.39990i | −0.935399 | − | 0.387455i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.8818 | 1.89935 | 0.949677 | − | 0.313231i | \(-0.101411\pi\) | ||||
0.949677 | + | 0.313231i | \(0.101411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000i | 1.00000i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.34101 | − | 8.77327i | −1.00727 | − | 0.946046i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.45587 | − | 0.891439i | 1.00800 | − | 0.0950278i | ||||
\(89\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.239870 | + | 3.82288i | 0.0250082 | + | 0.398562i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | −9.02277 | + | 4.07303i | −0.911438 | + | 0.411438i | ||||
\(99\) | −9.30710 | − | 3.85513i | −0.935399 | − | 0.387455i | ||||
\(100\) | 0.626229 | + | 9.98037i | 0.0626229 | + | 0.998037i | ||||
\(101\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.76125 | − | 6.13408i | 0.559582 | − | 0.595795i | ||||
\(107\) | −18.9419 | + | 7.84599i | −1.83118 | + | 0.758501i | −0.864446 | + | 0.502726i | \(0.832330\pi\) |
−0.966736 | + | 0.255774i | \(0.917670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.1056 | − | 7.91381i | −1.82999 | − | 0.758005i | −0.967943 | − | 0.251171i | \(-0.919184\pi\) |
−0.862044 | − | 0.506834i | \(-0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.48921 | − | 8.36004i | 0.613172 | − | 0.789949i | ||||
\(113\) | 16.3808i | 1.54098i | 0.637452 | + | 0.770490i | \(0.279988\pi\) | ||||
−0.637452 | + | 0.770490i | \(0.720012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.18748 | + | 10.5935i | 0.481645 | + | 0.983579i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.195169 | − | 0.195169i | 0.0177427 | − | 0.0177427i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −10.2309 | + | 4.61838i | −0.911438 | + | 0.411438i | ||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | −1.95171 | + | 11.1441i | −0.172508 | + | 0.985008i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.105414 | − | 3.36332i | −0.00910637 | − | 0.290546i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.5830 | − | 15.5830i | −1.33135 | − | 1.33135i | −0.904167 | − | 0.427179i | \(-0.859507\pi\) |
−0.427179 | − | 0.904167i | \(-0.640493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.00000 | − | 21.1660i | 0.671345 | − | 1.77621i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.35807 | − | 9.47939i | 0.613172 | − | 0.789949i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.82548 | + | 22.8439i | −0.643251 | + | 1.87775i | ||||
\(149\) | 6.96348 | + | 16.8113i | 0.570471 | + | 1.37724i | 0.901155 | + | 0.433497i | \(0.142720\pi\) |
−0.330684 | + | 0.943741i | \(0.607280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.6458 | − | 14.6458i | 1.19185 | − | 1.19185i | 0.215308 | − | 0.976546i | \(-0.430924\pi\) |
0.976546 | − | 0.215308i | \(-0.0690756\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.393603 | − | 12.5582i | −0.0317174 | − | 1.01197i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(158\) | 9.82288 | + | 21.7601i | 0.781466 | + | 1.73114i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.06713 | 0.399346 | ||||||||
\(162\) | −11.6007 | + | 5.23675i | −0.911438 | + | 0.411438i | ||||
\(163\) | 20.6208 | + | 8.54142i | 1.61515 | + | 0.669016i | 0.993453 | − | 0.114245i | \(-0.0364449\pi\) |
0.621694 | + | 0.783260i | \(0.286445\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.19239 | + | 9.19239i | 0.707107 | + | 0.707107i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.87329 | − | 17.1451i | 0.447834 | − | 1.30730i | ||||
\(173\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.2288 | 1.00000 | ||||||||
\(176\) | 6.65104 | + | 11.6696i | 0.501341 | + | 0.879630i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.28883 | − | 12.7684i | 0.395305 | − | 0.954352i | −0.593458 | − | 0.804865i | \(-0.702238\pi\) |
0.988764 | − | 0.149487i | \(-0.0477622\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.78799 | + | 2.53357i | −0.352975 | + | 0.186777i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 13.0514i | − | 0.944369i | −0.881500 | − | 0.472184i | \(-0.843466\pi\) | ||
0.881500 | − | 0.472184i | \(-0.156534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −27.6946 | −1.99350 | −0.996749 | − | 0.0805728i | \(-0.974325\pi\) | ||||
−0.996749 | + | 0.0805728i | \(0.974325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.5000 | − | 9.26013i | −0.750000 | − | 0.661438i | ||||
\(197\) | 0.159228 | − | 0.0659545i | 0.0113445 | − | 0.00469906i | −0.377004 | − | 0.926212i | \(-0.623046\pi\) |
0.388348 | + | 0.921513i | \(0.373046\pi\) | |||||||
\(198\) | −0.446304 | − | 14.2397i | −0.0317174 | − | 1.01197i | ||||
\(199\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(200\) | −12.5000 | + | 6.61438i | −0.883883 | + | 0.467707i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 14.4161 | − | 5.97133i | 1.01181 | − | 0.419105i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.74559 | 0.399346 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.1115 | − | 26.8255i | 0.764947 | − | 1.84675i | 0.351890 | − | 0.936041i | \(-0.385539\pi\) |
0.413057 | − | 0.910705i | \(-0.364461\pi\) | |||||||
\(212\) | 11.2589 | + | 3.85689i | 0.773263 | + | 0.264892i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −21.1348 | − | 19.8502i | −1.44474 | − | 1.35693i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −0.916172 | − | 29.2313i | −0.0620510 | − | 1.97979i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 14.5516 | + | 3.50000i | 0.972272 | + | 0.233854i | ||||
\(225\) | 15.0000 | 1.00000 | ||||||||
\(226\) | −21.1144 | + | 9.53137i | −1.40451 | + | 0.634018i | ||||
\(227\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.6362 | + | 12.8504i | −0.698304 | + | 0.843671i | ||||
\(233\) | −0.416995 | − | 0.416995i | −0.0273182 | − | 0.0273182i | 0.693316 | − | 0.720634i | \(-0.256149\pi\) |
−0.720634 | + | 0.693316i | \(0.756149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0.365128 | + | 0.138006i | 0.0234713 | + | 0.00887133i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(252\) | −11.9059 | − | 10.5000i | −0.750000 | − | 0.661438i | ||||
\(253\) | −2.46111 | + | 5.94164i | −0.154729 | + | 0.373548i | ||||
\(254\) | −20.6235 | + | 9.30978i | −1.29403 | + | 0.584147i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5000 | + | 3.96863i | −0.968750 | + | 0.248039i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29.5120 | + | 12.2243i | 1.83379 | + | 0.759579i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 16.3463 | − | 6.77086i | 1.01181 | − | 0.419105i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.74166 | − | 3.74166i | −0.230720 | − | 0.230720i | 0.582273 | − | 0.812993i | \(-0.302164\pi\) |
−0.812993 | + | 0.582273i | \(0.802164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.27387 | − | 2.09286i | 0.261068 | − | 0.127842i | ||||
\(269\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.0188 | − | 29.1531i | 0.665673 | − | 1.76121i | ||||
\(275\) | −6.42521 | + | 15.5118i | −0.387455 | + | 0.935399i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.11400 | − | 2.68944i | −0.0669339 | − | 0.161593i | 0.886873 | − | 0.462014i | \(-0.152873\pi\) |
−0.953807 | + | 0.300421i | \(0.902873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.5830 | − | 23.5830i | 1.40684 | − | 1.40684i | 0.631329 | − | 0.775515i | \(-0.282510\pi\) |
0.775515 | − | 0.631329i | \(-0.217490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(284\) | 31.9372 | − | 2.00393i | 1.89512 | − | 0.118912i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 16.5000 | + | 3.96863i | 0.972272 | + | 0.233854i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −33.9983 | + | 3.20515i | −1.97611 | + | 0.186295i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.6175 | + | 18.7576i | −1.02055 | + | 1.08660i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.1497 | − | 9.17472i | −1.27669 | − | 0.528822i | ||||
\(302\) | 27.3997 | + | 10.3561i | 1.57668 | + | 0.595927i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(308\) | 15.9581 | − | 7.81449i | 0.909299 | − | 0.445272i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.3326 | + | 25.3227i | −1.25630 | + | 1.42452i | ||||
\(317\) | −13.5707 | + | 32.7625i | −0.762204 | + | 1.84012i | −0.297200 | + | 0.954815i | \(0.596053\pi\) |
−0.465004 | + | 0.885309i | \(0.653947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.8043i | 1.10883i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.94837 | + | 6.53137i | 0.164306 | + | 0.363979i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −13.5000 | − | 11.9059i | −0.750000 | − | 0.661438i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.988830 | + | 31.5495i | 0.0547662 | + | 1.74736i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.21134 | + | 3.40125i | −0.451336 | + | 0.186950i | −0.596760 | − | 0.802420i | \(-0.703545\pi\) |
0.145424 | + | 0.989369i | \(0.453545\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 33.4634 | + | 13.8610i | 1.83379 | + | 0.759579i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.24657i | 0.340273i | 0.985421 | + | 0.170136i | \(0.0544208\pi\) | ||||
−0.985421 | + | 0.170136i | \(0.945579\pi\) | |||||||
\(338\) | −6.50000 | + | 17.1974i | −0.353553 | + | 0.935414i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0958 | + | 13.0958i | −0.707107 | + | 0.707107i | ||||
\(344\) | 25.5169 | − | 2.40557i | 1.37578 | − | 0.129700i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.6816 | + | 33.0303i | 0.734466 | + | 1.77316i | 0.627100 | + | 0.778938i | \(0.284242\pi\) |
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(350\) | 7.69730 | + | 17.0514i | 0.411438 | + | 0.911438i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11.1718 | + | 15.3631i | −0.595458 | + | 0.818854i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.5354 | − | 0.612282i | 1.03248 | − | 0.0323601i | ||||
\(359\) | −22.5203 | − | 22.5203i | −1.18857 | − | 1.18857i | −0.977462 | − | 0.211112i | \(-0.932292\pi\) |
−0.211112 | − | 0.977462i | \(-0.567708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.4350 | − | 13.4350i | −0.707107 | − | 0.707107i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | −6.05163 | − | 4.69738i | −0.315463 | − | 0.244868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.02488 | − | 14.5454i | 0.312796 | − | 0.755157i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.4277 | + | 30.0031i | 0.643482 | + | 1.55350i | 0.821951 | + | 0.569558i | \(0.192886\pi\) |
−0.178468 | + | 0.983946i | \(0.557114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.66710 | − | 23.3384i | −0.496566 | − | 1.19882i | −0.951322 | − | 0.308199i | \(-0.900274\pi\) |
0.454756 | − | 0.890616i | \(-0.349726\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.8229 | − | 7.59412i | 0.860733 | − | 0.388549i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.1144 | − | 35.6974i | −0.820200 | − | 1.81695i | ||||
\(387\) | −25.1154 | − | 10.4032i | −1.27669 | − | 0.528822i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.4682 | + | 9.30663i | −1.13918 | + | 0.471865i | −0.870893 | − | 0.491473i | \(-0.836458\pi\) |
−0.268290 | + | 0.963338i | \(0.586458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.82647 | − | 18.9223i | 0.294281 | − | 0.955719i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.177662 | + | 0.166864i | 0.00895047 | + | 0.00840647i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 18.0948 | − | 8.86080i | 0.909299 | − | 0.445272i | ||||
\(397\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −15.7990 | − | 12.2634i | −0.789949 | − | 0.613172i | ||||
\(401\) | − | 39.0083i | − | 1.94798i | −0.226592 | − | 0.973990i | \(-0.572758\pi\) | ||
0.226592 | − | 0.973990i | \(-0.427242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.0850 | + | 15.1074i | 0.798286 | + | 0.749766i | ||||
\(407\) | −28.6680 | + | 28.6680i | −1.42102 | + | 1.42102i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.34313 | + | 7.40588i | 0.164306 | + | 0.363979i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.9674 | − | 4.54285i | 0.534519 | − | 0.221405i | −0.0990621 | − | 0.995081i | \(-0.531584\pi\) |
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | 41.0426 | − | 1.28637i | 1.99792 | − | 0.0626193i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.57970 | + | 16.7565i | 0.0767169 | + | 0.813768i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.2888 | − | 38.7921i | 0.642338 | − | 1.87509i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.4575 | −1.27441 | −0.637207 | − | 0.770693i | \(-0.719910\pi\) | ||||
−0.637207 | + | 0.770693i | \(0.719910\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 37.1451 | − | 18.1894i | 1.77893 | − | 0.871116i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.8492 | + | 14.8492i | −0.707107 | + | 0.707107i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.64661 | − | 3.97527i | −0.0782328 | − | 0.188871i | 0.879924 | − | 0.475114i | \(-0.157593\pi\) |
−0.958157 | + | 0.286244i | \(0.907593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.95564 | + | 20.7931i | 0.186886 | + | 0.982382i | ||||
\(449\) | 42.3320 | 1.99777 | 0.998886 | − | 0.0471929i | \(-0.0150276\pi\) | ||||
0.998886 | + | 0.0471929i | \(0.0150276\pi\) | |||||||
\(450\) | 8.72791 | + | 19.3345i | 0.411438 | + | 0.911438i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −24.5713 | − | 21.6698i | −1.15574 | − | 1.01926i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.9333 | − | 29.9333i | −1.40022 | − | 1.40022i | −0.799341 | − | 0.600878i | \(-0.794818\pi\) |
−0.600878 | − | 0.799341i | \(-0.705182\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.5092 | −1.83615 | −0.918075 | − | 0.396406i | \(-0.870257\pi\) | ||||
−0.918075 | + | 0.396406i | \(0.870257\pi\) | |||||||
\(464\) | −22.7526 | − | 6.23262i | −1.05626 | − | 0.289342i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.294860 | − | 0.780126i | 0.0136591 | − | 0.0361386i | ||||
\(467\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.40910 | − | 5.81608i | −0.111242 | − | 0.268562i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.5163 | − | 21.5163i | 0.989319 | − | 0.989319i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.83157 | − | 16.4929i | 0.312796 | − | 0.755157i | ||||
\(478\) | −9.30978 | − | 20.6235i | −0.425819 | − | 0.943296i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0345692 | + | 0.550939i | 0.00157133 | + | 0.0250427i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.52026 | + | 6.52026i | 0.295461 | + | 0.295461i | 0.839233 | − | 0.543772i | \(-0.183004\pi\) |
−0.543772 | + | 0.839233i | \(0.683004\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.6855 | − | 14.7814i | 1.61046 | − | 0.667076i | 0.617619 | − | 0.786478i | \(-0.288097\pi\) |
0.992846 | + | 0.119401i | \(0.0380974\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 42.3320i | − | 1.89885i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6025 | + | 40.0821i | −0.743232 | + | 1.79432i | −0.151031 | + | 0.988529i | \(0.548259\pi\) |
−0.592200 | + | 0.805791i | \(0.701741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(504\) | 6.60659 | − | 21.4558i | 0.294281 | − | 0.955719i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.09061 | + | 0.284920i | −0.404127 | + | 0.0126662i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −24.0000 | − | 21.1660i | −1.06483 | − | 0.939090i | ||||
\(509\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −14.1343 | − | 17.6698i | −0.624653 | − | 0.780903i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.41519 | + | 45.1528i | 0.0621798 | + | 1.98390i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(522\) | 18.2387 | + | 17.1301i | 0.798286 | + | 0.749766i | ||||
\(523\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.64575 | − | 7.00000i | 0.115360 | − | 0.305215i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.3320i | 0.840523i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.18443 | + | 4.29113i | 0.223933 | + | 0.185349i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.99530 | − | 21.7166i | −0.387455 | − | 0.935399i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.2042 | − | 39.1203i | 0.696671 | − | 1.68191i | −0.0342160 | − | 0.999414i | \(-0.510893\pi\) |
0.730887 | − | 0.682498i | \(-0.239107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00661 | − | 0.831165i | −0.0857964 | − | 0.0355380i | 0.339372 | − | 0.940652i | \(-0.389785\pi\) |
−0.425169 | + | 0.905114i | \(0.639785\pi\) | |||||||
\(548\) | 43.9889 | − | 2.76013i | 1.87911 | − | 0.117907i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23.7328 | + | 0.743839i | −1.01197 | + | 0.0317174i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.5830 | + | 31.5830i | 1.34305 | + | 1.34305i | ||||
\(554\) | 2.81840 | − | 3.00079i | 0.119743 | − | 0.127491i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.5218 | + | 14.7136i | 1.50511 | + | 0.623436i | 0.974541 | − | 0.224208i | \(-0.0719796\pi\) |
0.530566 | + | 0.847644i | \(0.321980\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 44.1198 | + | 16.6757i | 1.86108 | + | 0.703422i | ||||
\(563\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.8375 | + | 16.8375i | −0.707107 | + | 0.707107i | ||||
\(568\) | 21.1660 | + | 40.0000i | 0.888106 | + | 1.67836i | ||||
\(569\) | −29.9333 | + | 29.9333i | −1.25487 | + | 1.25487i | −0.301356 | + | 0.953512i | \(0.597439\pi\) |
−0.953512 | + | 0.301356i | \(0.902561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2517 | + | 39.2350i | 0.680111 | + | 1.64193i | 0.763809 | + | 0.645443i | \(0.223327\pi\) |
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 9.57598i | − | 0.399346i | ||||||
\(576\) | 4.48527 | + | 23.5772i | 0.186886 | + | 0.982382i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −9.89164 | − | 21.9125i | −0.411438 | − | 0.911438i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.1294 | + | 14.1294i | 0.585178 | + | 0.585178i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −23.9136 | − | 41.9578i | −0.982844 | − | 1.72446i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −34.4288 | − | 11.7941i | −1.41026 | − | 0.483104i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.1916 | − | 26.1916i | 1.07016 | − | 1.07016i | 0.0728143 | − | 0.997346i | \(-0.476802\pi\) |
0.997346 | − | 0.0728143i | \(-0.0231980\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(602\) | −1.06215 | − | 33.8887i | −0.0432899 | − | 1.38120i | ||||
\(603\) | −2.73166 | − | 6.59482i | −0.111242 | − | 0.268562i | ||||
\(604\) | 2.59412 | + | 41.3431i | 0.105553 | + | 1.68223i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −43.6600 | + | 18.0846i | −1.76341 | + | 0.730429i | −0.767403 | + | 0.641165i | \(0.778451\pi\) |
−0.996008 | + | 0.0892633i | \(0.971549\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.3580 | + | 16.0226i | 0.779958 | + | 0.645568i | ||||
\(617\) | 29.9333 | + | 29.9333i | 1.20507 | + | 1.20507i | 0.972605 | + | 0.232462i | \(0.0746782\pi\) |
0.232462 | + | 0.972605i | \(0.425322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 25.0000i | − | 1.00000i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.3137 | − | 11.3137i | 0.450392 | − | 0.450392i | −0.445093 | − | 0.895484i | \(-0.646829\pi\) |
0.895484 | + | 0.445093i | \(0.146829\pi\) | |||||||
\(632\) | −45.6346 | − | 14.0516i | −1.81525 | − | 0.558944i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −50.1260 | + | 1.57106i | −1.99076 | + | 0.0623948i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.5272 | + | 11.5234i | −1.01063 | + | 0.456215i | ||||
\(639\) | − | 48.0000i | − | 1.89885i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.5603 | 0.693589 | 0.346795 | − | 0.937941i | \(-0.387270\pi\) | ||||
0.346795 | + | 0.937941i | \(0.387270\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(644\) | −6.70319 | + | 7.60070i | −0.264143 | + | 0.299510i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(648\) | 7.49117 | − | 24.3286i | 0.294281 | − | 0.955719i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −40.0909 | + | 19.6320i | −1.57008 | + | 0.768848i | ||||
\(653\) | 46.4193 | + | 19.2275i | 1.81653 | + | 0.752431i | 0.978326 | + | 0.207072i | \(0.0663936\pi\) |
0.838203 | + | 0.545358i | \(0.183606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −15.7978 | + | 38.1392i | −0.615395 | + | 1.48569i | 0.241604 | + | 0.970375i | \(0.422327\pi\) |
−0.856998 | + | 0.515319i | \(0.827673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(662\) | −9.16196 | − | 8.60510i | −0.356090 | − | 0.334447i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.60467 | + | 51.1985i | 0.0621798 | + | 1.98390i | ||||
\(667\) | −4.32251 | − | 10.4355i | −0.167368 | − | 0.404062i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −42.3320 | −1.63178 | −0.815890 | − | 0.578208i | \(-0.803752\pi\) | ||||
−0.815890 | + | 0.578208i | \(0.803752\pi\) | |||||||
\(674\) | −8.05163 | + | 3.63464i | −0.310137 | + | 0.140001i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.9490 | + | 1.62820i | −0.998037 | + | 0.0626229i | ||||
\(677\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 46.2556 | − | 19.1597i | 1.76992 | − | 0.733126i | 0.775059 | − | 0.631889i | \(-0.217720\pi\) |
0.994862 | − | 0.101237i | \(-0.0322800\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.5000 | − | 9.26013i | −0.935414 | − | 0.353553i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.9480 | + | 31.4907i | 0.684261 | + | 1.20057i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.1997 | − | 24.6243i | −0.387455 | − | 0.935399i | ||||
\(694\) | −34.6142 | + | 36.8542i | −1.31394 | + | 1.39896i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.5000 | + | 19.8431i | −0.661438 | + | 0.750000i | ||||
\(701\) | −18.4154 | + | 44.4587i | −0.695540 | + | 1.67918i | 0.0377695 | + | 0.999286i | \(0.487975\pi\) |
−0.733309 | + | 0.679895i | \(0.762025\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −26.3029 | − | 5.46089i | −0.991328 | − | 0.205815i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5870 | − | 5.62791i | 0.510269 | − | 0.211360i | −0.112667 | − | 0.993633i | \(-0.535939\pi\) |
0.622937 | + | 0.782272i | \(0.285939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 35.8118 | + | 35.8118i | 1.34305 | + | 1.34305i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.1561 | + | 24.8242i | 0.454294 | + | 0.927723i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.9242 | − | 42.1315i | 0.594287 | − | 1.57234i | ||||
\(719\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.50000 | − | 25.1346i | 0.353553 | − | 0.935414i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −11.2848 | − | 27.2438i | −0.419105 | − | 1.01181i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.0919 | + | 19.0919i | −0.707107 | + | 0.707107i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.53357 | − | 10.5336i | 0.0933885 | − | 0.388273i | ||||
\(737\) | 7.98995 | 0.294314 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.9345 | − | 13.2277i | −1.17473 | − | 0.486589i | −0.291977 | − | 0.956425i | \(-0.594313\pi\) |
−0.882754 | + | 0.469836i | \(0.844313\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.2541 | − | 0.697494i | 0.816975 | − | 0.0256058i | ||||
\(743\) | 38.5203 | + | 38.5203i | 1.41317 | + | 1.41317i | 0.733729 | + | 0.679442i | \(0.237778\pi\) |
0.679442 | + | 0.733729i | \(0.262222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −31.4419 | + | 33.4766i | −1.15117 | + | 1.22566i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −50.1155 | − | 20.7585i | −1.83118 | − | 0.758501i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.0000 | 1.75154 | 0.875772 | − | 0.482724i | \(-0.160353\pi\) | ||||
0.875772 | + | 0.482724i | \(0.160353\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.6498 | − | 28.1250i | −0.423418 | − | 1.02222i | −0.981332 | − | 0.192323i | \(-0.938398\pi\) |
0.557913 | − | 0.829899i | \(-0.311602\pi\) | |||||||
\(758\) | 24.4576 | − | 26.0403i | 0.888340 | − | 0.945827i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.9380 | − | 50.5487i | −0.758005 | − | 1.82999i | ||||
\(764\) | 19.5771 | + | 17.2654i | 0.708276 | + | 0.624641i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 36.6364 | − | 41.5418i | 1.31857 | − | 1.49512i | ||||
\(773\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(774\) | −1.20436 | − | 38.4262i | −0.0432899 | − | 1.38120i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25.0693 | − | 23.5456i | −0.898778 | − | 0.844151i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.6379 | + | 20.5607i | 1.77618 | + | 0.735719i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.7804 | − | 3.50000i | 0.992157 | − | 0.125000i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(788\) | −0.111707 | + | 0.326092i | −0.00397941 | + | 0.0116165i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.6458 | + | 30.6458i | −1.08964 | + | 1.08964i | ||||
\(792\) | 21.9500 | + | 18.1679i | 0.779958 | + | 0.645568i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 6.61438 | − | 27.5000i | 0.233854 | − | 0.972272i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 50.2804 | − | 22.6974i | 1.77546 | − | 0.801472i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.9333 | + | 29.9333i | 1.05240 | + | 1.05240i | 0.998549 | + | 0.0538482i | \(0.0171487\pi\) |
0.0538482 | + | 0.998549i | \(0.482851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(812\) | −10.1137 | + | 29.5234i | −0.354920 | + | 1.03607i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −53.6328 | − | 20.2713i | −1.87983 | − | 0.710509i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.0289484 | − | 0.0698877i | −0.00101031 | − | 0.00243910i | 0.923374 | − | 0.383903i | \(-0.125420\pi\) |
−0.924384 | + | 0.381464i | \(0.875420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 33.6749 | − | 33.6749i | 1.17383 | − | 1.17383i | 0.192546 | − | 0.981288i | \(-0.438326\pi\) |
0.981288 | − | 0.192546i | \(-0.0616744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.9808 | + | 50.6522i | 0.729574 | + | 1.76135i | 0.644013 | + | 0.765015i | \(0.277268\pi\) |
0.0855616 | + | 0.996333i | \(0.472732\pi\) | |||||||
\(828\) | −7.60070 | + | 8.61839i | −0.264143 | + | 0.299510i | ||||
\(829\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.08910 | − | 4.08910i | −0.141004 | − | 0.141004i | ||||
\(842\) | 12.2371 | + | 11.4933i | 0.421718 | + | 0.396087i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 25.5392 | + | 52.1541i | 0.879095 | + | 1.79522i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.730257 | 0.0250919 | ||||||||
\(848\) | −20.6794 | + | 11.7861i | −0.710135 | + | 0.404738i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.84886 | − | 21.3630i | 0.303335 | − | 0.732315i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 57.7340 | − | 5.44280i | 1.97331 | − | 0.186031i | ||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.3946 | − | 34.1029i | −0.524342 | − | 1.16155i | ||||
\(863\) | − | 46.8151i | − | 1.59360i | −0.604240 | − | 0.796802i | \(-0.706523\pi\) | ||
0.604240 | − | 0.796802i | \(-0.293477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −52.3736 | + | 21.6939i | −1.77665 | + | 0.735914i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 45.0589 | + | 37.2951i | 1.52589 | + | 1.26297i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.7771 | − | 18.5473i | −1.51202 | − | 0.626298i | −0.536044 | − | 0.844190i | \(-0.680082\pi\) |
−0.975973 | + | 0.217892i | \(0.930082\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | −27.7804 | − | 10.5000i | −0.935414 | − | 0.353553i | ||||
\(883\) | 18.8218 | − | 45.4397i | 0.633403 | − | 1.52917i | −0.201916 | − | 0.979403i | \(-0.564717\pi\) |
0.835319 | − | 0.549766i | \(-0.185283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.16589 | − | 4.43548i | 0.139956 | − | 0.149013i | ||||
\(887\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.9333 | + | 29.9333i | −1.00393 | + | 1.00393i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.5654 | − | 27.9213i | −0.387455 | − | 0.935399i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −24.5000 | + | 17.1974i | −0.818488 | + | 0.574524i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.6314 | + | 54.5646i | 0.821959 | + | 1.82084i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −19.8431 | + | 22.5000i | −0.661438 | + | 0.750000i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.6346 | − | 44.2804i | 0.453481 | − | 1.47274i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.7298 | + | 10.6576i | −0.854343 | + | 0.353881i | −0.766493 | − | 0.642253i | \(-0.778000\pi\) |
−0.0878507 | + | 0.996134i | \(0.528000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.0000 | 0.530104 | 0.265052 | − | 0.964234i | \(-0.414611\pi\) | ||||
0.265052 | + | 0.964234i | \(0.414611\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 21.1660 | − | 56.0000i | 0.700109 | − | 1.85232i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.9411 | − | 33.9411i | 1.11961 | − | 1.11961i | 0.127817 | − | 0.991798i | \(-0.459203\pi\) |
0.991798 | − | 0.127817i | \(-0.0407969\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 23.1017 | − | 55.7724i | 0.759579 | − | 1.83379i | ||||
\(926\) | −22.9889 | − | 50.9261i | −0.755462 | − | 1.67354i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.20520 | − | 32.9539i | −0.170869 | − | 1.08176i | ||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.17712 | − | 0.0738599i | 0.0385580 | − | 0.00241936i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(938\) | 6.09498 | − | 6.48940i | 0.199008 | − | 0.211887i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.2532 | + | 15.2143i | 1.30875 | + | 0.494659i | ||||
\(947\) | −23.5080 | + | 56.7534i | −0.763909 | + | 1.84424i | −0.324956 | + | 0.945729i | \(0.605350\pi\) |
−0.438953 | + | 0.898510i | \(0.644650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.5830 | + | 39.5830i | −1.28222 | + | 1.28222i | −0.342817 | + | 0.939402i | \(0.611381\pi\) |
−0.939402 | + | 0.342817i | \(0.888619\pi\) | |||||||
\(954\) | 25.2338 | − | 0.790884i | 0.816975 | − | 0.0256058i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21.1660 | − | 24.0000i | 0.684558 | − | 0.776215i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 58.3063i | − | 1.88281i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −56.8257 | − | 23.5380i | −1.83118 | − | 0.758501i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.81176 | + | 3.81176i | 0.122578 | + | 0.122578i | 0.765735 | − | 0.643157i | \(-0.222376\pi\) |
−0.643157 | + | 0.765735i | \(0.722376\pi\) | |||||||
\(968\) | −0.690028 | + | 0.365128i | −0.0221783 | + | 0.0117357i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.61052 | + | 12.1983i | −0.147731 | + | 0.390858i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 42.3320i | 1.35432i | 0.735835 | + | 0.677161i | \(0.236790\pi\) | ||||
−0.735835 | + | 0.677161i | \(0.763210\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.7414 | − | 57.3169i | −0.758005 | − | 1.82999i | ||||
\(982\) | 39.8168 | + | 37.3967i | 1.27060 | + | 1.19338i | ||||
\(983\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.64136 | + | 16.0337i | −0.211183 | + | 0.509841i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.1877i | 0.768347i | 0.923261 | + | 0.384173i | \(0.125513\pi\) | ||||
−0.923261 | + | 0.384173i | \(0.874487\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 54.5646 | − | 24.6314i | 1.73068 | − | 0.781259i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(998\) | −61.3249 | + | 1.92206i | −1.94120 | + | 0.0608416i | ||||
\(999\) | 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 | 224.2.x.a.83.2 | yes | 8 | |
4.3 | odd | 2 | 896.2.x.a.111.1 | 8 | |||
7.6 | odd | 2 | CM | 224.2.x.a.83.2 | yes | 8 | |
28.27 | even | 2 | 896.2.x.a.111.1 | 8 | |||
32.5 | even | 8 | 896.2.x.a.783.1 | 8 | |||
32.27 | odd | 8 | inner | 224.2.x.a.27.2 | ✓ | 8 | |
224.27 | even | 8 | inner | 224.2.x.a.27.2 | ✓ | 8 | |
224.69 | odd | 8 | 896.2.x.a.783.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.x.a.27.2 | ✓ | 8 | 32.27 | odd | 8 | inner | |
224.2.x.a.27.2 | ✓ | 8 | 224.27 | even | 8 | inner | |
224.2.x.a.83.2 | yes | 8 | 1.1 | even | 1 | trivial | |
224.2.x.a.83.2 | yes | 8 | 7.6 | odd | 2 | CM | |
896.2.x.a.111.1 | 8 | 4.3 | odd | 2 | |||
896.2.x.a.111.1 | 8 | 28.27 | even | 2 | |||
896.2.x.a.783.1 | 8 | 32.5 | even | 8 | |||
896.2.x.a.783.1 | 8 | 224.69 | odd | 8 |