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 | 27.1 | ||
Root | \(-1.28897 + 0.581861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.27 |
Dual form | 224.2.x.a.83.1 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28897 | + | 0.581861i | −0.911438 | + | 0.411438i | ||||
\(3\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(4\) | 1.32288 | − | 1.50000i | 0.661438 | − | 0.750000i | ||||
\(5\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.87083 | + | 1.87083i | −0.707107 | + | 0.707107i | ||||
\(8\) | −0.832353 | + | 2.70318i | −0.294281 | + | 0.955719i | ||||
\(9\) | 2.12132 | − | 2.12132i | 0.707107 | − | 0.707107i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.93079 | + | 2.45662i | 1.78820 | + | 0.740697i | 0.990478 | + | 0.137675i | \(0.0439628\pi\) |
0.797724 | + | 0.603023i | \(0.206037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(14\) | 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 | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.07401 | + | 0.284400i | −1.93459 | + | 0.0606342i | ||||
\(23\) | 6.64575 | + | 6.64575i | 1.38573 | + | 1.38573i | 0.834058 | + | 0.551677i | \(0.186012\pi\) |
0.551677 | + | 0.834058i | \(0.313988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.53553 | + | 3.53553i | 0.707107 | + | 0.707107i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.331369 | + | 5.28112i | 0.0626229 | + | 0.998037i | ||||
\(29\) | −0.842738 | − | 2.03455i | −0.156493 | − | 0.377807i | 0.826115 | − | 0.563502i | \(-0.190546\pi\) |
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 2.95367 | + | 4.82450i | 0.522141 | + | 0.852859i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.375737 | − | 5.98822i | −0.0626229 | − | 0.998037i | ||||
\(37\) | −6.91184 | − | 2.86298i | −1.13630 | − | 0.470671i | −0.266382 | − | 0.963868i | \(-0.585828\pi\) |
−0.869918 | + | 0.493197i | \(0.835828\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1135 | − | 5.01756i | −1.84729 | − | 0.765171i | −0.932295 | − | 0.361698i | \(-0.882197\pi\) |
−0.914991 | − | 0.403473i | \(-0.867803\pi\) | |||||||
\(44\) | 11.5306 | − | 5.64639i | 1.73831 | − | 0.851226i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.4331 | − | 4.69926i | −1.83316 | − | 0.692867i | ||||
\(47\) | 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 | ||||||||
\(53\) | 5.20612 | − | 12.5687i | 0.715116 | − | 1.72644i | 0.0283132 | − | 0.999599i | \(-0.490986\pi\) |
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 | ||||||||
\(58\) | 2.27009 | + | 2.13211i | 0.298077 | + | 0.279960i | ||||
\(59\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.93725i | 1.00000i | ||||||||
\(64\) | −6.61438 | − | 4.50000i | −0.826797 | − | 0.562500i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.02670 | − | 3.73898i | 1.10279 | − | 0.456789i | 0.244339 | − | 0.969690i | \(-0.421429\pi\) |
0.858448 | + | 0.512901i | \(0.171429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3137 | + | 11.3137i | −1.34269 | + | 1.34269i | −0.449319 | + | 0.893372i | \(0.648333\pi\) |
−0.893372 | + | 0.449319i | \(0.851667\pi\) | |||||||
\(72\) | 3.96863 | + | 7.50000i | 0.467707 | + | 0.883883i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | 10.5750 | − | 0.331444i | 1.22932 | − | 0.0385295i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −15.6914 | + | 6.49959i | −1.78820 | + | 0.740697i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.56812 | −0.626462 | −0.313231 | − | 0.949677i | \(-0.601411\pi\) | ||||
−0.313231 | + | 0.949677i | \(0.601411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 9.00000i | − | 1.00000i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 18.5334 | − | 0.580878i | 1.99851 | − | 0.0626376i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −11.5772 | + | 13.9872i | −1.23413 | + | 1.49104i | ||||
\(89\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 18.7601 | − | 1.17712i | 1.95588 | − | 0.122724i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 4.07303 | + | 9.02277i | 0.411438 | + | 0.911438i | ||||
\(99\) | 17.7924 | − | 7.36985i | 1.78820 | − | 0.740697i | ||||
\(100\) | 9.98037 | − | 0.626229i | 0.998037 | − | 0.0626229i | ||||
\(101\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.602707 | + | 19.2299i | 0.0585401 | + | 1.86777i | ||||
\(107\) | −15.2002 | − | 6.29615i | −1.46946 | − | 0.608671i | −0.502726 | − | 0.864446i | \(-0.667670\pi\) |
−0.966736 | + | 0.255774i | \(0.917670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.6223 | + | 4.81412i | −1.11321 | + | 0.461109i | −0.862044 | − | 0.506834i | \(-0.830816\pi\) |
−0.251171 | + | 0.967943i | \(0.580816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.36004 | + | 6.48921i | 0.789949 | + | 0.613172i | ||||
\(113\) | 13.5524i | 1.27490i | 0.770490 | + | 0.637452i | \(0.220012\pi\) | ||||
−0.770490 | + | 0.637452i | \(0.779988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.16666 | − | 1.42735i | −0.386865 | − | 0.132526i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.3612 | + | 21.3612i | 1.94193 | + | 1.94193i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.61838 | − | 10.2309i | −0.411438 | − | 0.911438i | ||||
\(127\) | − | 16.0000i | − | 1.41977i | −0.704317 | − | 0.709885i | \(-0.748747\pi\) | ||
0.704317 | − | 0.709885i | \(-0.251253\pi\) | |||||||
\(128\) | 11.1441 | + | 1.95171i | 0.985008 | + | 0.172508i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.45956 | + | 10.0717i | −0.817181 | + | 0.870063i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.58301 | − | 5.58301i | 0.476988 | − | 0.476988i | −0.427179 | − | 0.904167i | \(-0.640493\pi\) |
0.904167 | + | 0.427179i | \(0.140493\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.00000 | − | 21.1660i | 0.671345 | − | 1.77621i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −9.47939 | − | 7.35807i | −0.789949 | − | 0.613172i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −13.4380 | + | 6.58040i | −1.10459 | + | 0.540905i | ||||
\(149\) | −0.519832 | + | 1.25499i | −0.0425863 | + | 0.102812i | −0.943741 | − | 0.330684i | \(-0.892720\pi\) |
0.901155 | + | 0.433497i | \(0.142720\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.35425 | + | 9.35425i | 0.761238 | + | 0.761238i | 0.976546 | − | 0.215308i | \(-0.0690756\pi\) |
−0.215308 | + | 0.976546i | \(0.569076\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.4439 | − | 17.5080i | 1.32508 | − | 1.41083i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(158\) | 7.17712 | − | 3.23987i | 0.570981 | − | 0.257750i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.8661 | −1.95973 | ||||||||
\(162\) | 5.23675 | + | 11.6007i | 0.411438 | + | 0.911438i | ||||
\(163\) | −6.47867 | + | 2.68355i | −0.507449 | + | 0.210192i | −0.621694 | − | 0.783260i | \(-0.713555\pi\) |
0.114245 | + | 0.993453i | \(0.463555\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.19239 | − | 9.19239i | 0.707107 | − | 0.707107i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −23.5510 | + | 11.5326i | −1.79574 | + | 0.879352i | ||||
\(173\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.2288 | −1.00000 | ||||||||
\(176\) | 6.78399 | − | 24.7654i | 0.511363 | − | 1.86676i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.46040 | − | 5.93993i | −0.183899 | − | 0.443971i | 0.804865 | − | 0.593458i | \(-0.202238\pi\) |
−0.988764 | + | 0.149487i | \(0.952238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −23.4963 | + | 12.4331i | −1.73217 | + | 0.916578i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.3651i | − | 1.76300i | −0.472184 | − | 0.881500i | \(-0.656534\pi\) | ||
0.472184 | − | 0.881500i | \(-0.343466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23871 | 0.161146 | 0.0805728 | − | 0.996749i | \(-0.474325\pi\) | ||||
0.0805728 | + | 0.996749i | \(0.474325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.5000 | − | 9.26013i | −0.750000 | − | 0.661438i | ||||
\(197\) | 18.2255 | + | 7.54927i | 1.29852 | + | 0.537863i | 0.921513 | − | 0.388348i | \(-0.126954\pi\) |
0.377004 | + | 0.926212i | \(0.376954\pi\) | |||||||
\(198\) | −18.6456 | + | 19.8522i | −1.32508 | + | 1.41083i | ||||
\(199\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(200\) | −12.5000 | + | 6.61438i | −0.883883 | + | 0.467707i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.38291 | + | 2.22968i | 0.377807 | + | 0.156493i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 28.1955 | 1.95973 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.59678 | − | 18.3403i | −0.522984 | − | 1.26260i | −0.936041 | − | 0.351890i | \(-0.885539\pi\) |
0.413057 | − | 0.910705i | \(-0.364461\pi\) | |||||||
\(212\) | −11.9660 | − | 24.4360i | −0.821827 | − | 1.67827i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.2561 | − | 0.728898i | 1.58975 | − | 0.0498264i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 12.1796 | − | 12.9678i | 0.824909 | − | 0.878291i | ||||
\(219\) | 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 | ||||||||
\(226\) | −7.88562 | − | 17.4686i | −0.524544 | − | 1.16200i | ||||
\(227\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.20121 | − | 0.584611i | 0.407130 | − | 0.0383816i | ||||
\(233\) | −21.5830 | + | 21.5830i | −1.41395 | + | 1.41395i | −0.693316 | + | 0.720634i | \(0.743851\pi\) |
−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 | \(0.5\pi\) | |||||||||
\(242\) | −39.9631 | − | 15.1046i | −2.56893 | − | 0.970963i | ||||
\(243\) | 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 | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(252\) | 11.9059 | + | 10.5000i | 0.750000 | + | 0.661438i | ||||
\(253\) | 23.0885 | + | 55.7406i | 1.45156 | + | 3.50438i | ||||
\(254\) | 9.30978 | + | 20.6235i | 0.584147 | + | 1.29403i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5000 | + | 3.96863i | −0.968750 | + | 0.248039i | ||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.2870 | − | 7.57473i | 1.13630 | − | 0.470671i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.10365 | − | 2.52822i | −0.377807 | − | 0.156493i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.74166 | − | 3.74166i | 0.230720 | − | 0.230720i | −0.582273 | − | 0.812993i | \(-0.697836\pi\) |
0.812993 | + | 0.582273i | \(0.197836\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6.33273 | − | 18.4863i | 0.386833 | − | 1.12923i | ||||
\(269\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.94778 | + | 10.4448i | −0.238494 | + | 0.630996i | ||||
\(275\) | 12.2831 | + | 29.6540i | 0.740697 | + | 1.78820i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.18507 | − | 19.7605i | 0.491793 | − | 1.18729i | −0.462014 | − | 0.886873i | \(-0.652873\pi\) |
0.953807 | − | 0.300421i | \(-0.0971271\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.41699 | + | 2.41699i | 0.144186 | + | 0.144186i | 0.775515 | − | 0.631329i | \(-0.217490\pi\) |
−0.631329 | + | 0.775515i | \(0.717490\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(284\) | 2.00393 | + | 31.9372i | 0.118912 | + | 1.89512i | ||||
\(285\) | 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 | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.4922 | − | 16.3009i | 0.784220 | − | 0.947473i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.0601804 | − | 1.92011i | −0.00348615 | − | 0.111229i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.0492 | − | 13.2752i | 1.84729 | − | 0.765171i | ||||
\(302\) | −17.5002 | − | 6.61445i | −1.00702 | − | 0.380619i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(308\) | −11.0084 | + | 32.1353i | −0.627261 | + | 1.83108i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.36593 | + | 8.35218i | −0.414366 | + | 0.469847i | ||||
\(317\) | −10.4710 | − | 25.2792i | −0.588108 | − | 1.41982i | −0.885309 | − | 0.465004i | \(-0.846053\pi\) |
0.297200 | − | 0.954815i | \(-0.403947\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 14.1368i | − | 0.791508i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 32.0516 | − | 14.4686i | 1.78617 | − | 0.806305i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −13.5000 | − | 11.9059i | −0.750000 | − | 0.661438i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.78934 | − | 7.22870i | 0.376027 | − | 0.400361i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.2445 | − | 7.14291i | −0.947844 | − | 0.392610i | −0.145424 | − | 0.989369i | \(-0.546455\pi\) |
−0.802420 | + | 0.596760i | \(0.796455\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.7355 | + | 8.58893i | −1.13630 | + | 0.470671i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 36.1798i | − | 1.97084i | −0.170136 | − | 0.985421i | \(-0.554421\pi\) | ||
0.170136 | − | 0.985421i | \(-0.445579\pi\) | |||||||
\(338\) | −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 | ||||
\(344\) | 23.6461 | − | 28.5685i | 1.27491 | − | 1.54031i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.5100 | + | 30.2018i | −0.671573 | + | 1.62132i | 0.107366 | + | 0.994220i | \(0.465758\pi\) |
−0.778938 | + | 0.627100i | \(0.784242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(350\) | 17.0514 | − | 7.69730i | 0.911438 | − | 0.411438i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.66568 | + | 35.8692i | 0.301982 | + | 1.91183i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.62759 | + | 6.22477i | 0.350279 | + | 0.328989i | ||||
\(359\) | 14.5203 | − | 14.5203i | 0.766350 | − | 0.766350i | −0.211112 | − | 0.977462i | \(-0.567708\pi\) |
0.977462 | + | 0.211112i | \(0.0677085\pi\) | |||||||
\(360\) | 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 | \(\pi\) | |||||||||
\(368\) | 23.0516 | − | 29.6974i | 1.20165 | − | 1.54808i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.7741 | + | 33.2536i | 0.715116 | + | 1.72644i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.12864 | − | 7.55320i | 0.161995 | − | 0.391090i | −0.821951 | − | 0.569558i | \(-0.807114\pi\) |
0.983946 | + | 0.178468i | \(0.0571142\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.18182 | − | 2.85316i | 0.0607059 | − | 0.146557i | −0.890616 | − | 0.454756i | \(-0.849726\pi\) |
0.951322 | + | 0.308199i | \(0.0997264\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.1771 | + | 31.4059i | 0.725365 | + | 1.60686i | ||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.88562 | + | 1.30262i | −0.146874 | + | 0.0663014i | ||||
\(387\) | −36.3404 | + | 15.0527i | −1.84729 | + | 0.765171i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.40187 | − | 1.82331i | −0.223184 | − | 0.0924457i | 0.268290 | − | 0.963338i | \(-0.413542\pi\) |
−0.491473 | + | 0.870893i | \(0.663542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 18.9223 | + | 5.82647i | 0.955719 | + | 0.294281i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −27.8848 | + | 0.873970i | −1.40481 | + | 0.0440300i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.4823 | − | 36.4380i | 0.627261 | − | 1.83108i | ||||
\(397\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.2634 | − | 15.7990i | 0.613172 | − | 0.789949i | ||||
\(401\) | 9.07500i | 0.453184i | 0.973990 | + | 0.226592i | \(0.0727584\pi\) | ||||
−0.973990 | + | 0.226592i | \(0.927242\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.23577 | + | 0.258127i | −0.408734 | + | 0.0128106i | ||||
\(407\) | −33.9595 | − | 33.9595i | −1.68331 | − | 1.68331i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −36.3431 | + | 16.4059i | −1.78617 | + | 0.806305i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.4174 | + | 13.8419i | 1.62866 | + | 0.674614i | 0.995081 | − | 0.0990621i | \(-0.0315842\pi\) |
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | 20.4635 | + | 19.2197i | 0.996147 | + | 0.935602i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 29.6421 | + | 24.5347i | 1.43955 | + | 1.19151i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −29.5522 | + | 14.4713i | −1.42846 | + | 0.699499i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.4575 | 1.27441 | 0.637207 | − | 0.770693i | \(-0.280090\pi\) | ||||
0.637207 | + | 0.770693i | \(0.280090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.15369 | + | 23.8019i | −0.390491 | + | 1.13991i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.8492 | − | 14.8492i | −0.707107 | − | 0.707107i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.4955 | + | 30.1669i | −0.593680 | + | 1.43327i | 0.286244 | + | 0.958157i | \(0.407593\pi\) |
−0.879924 | + | 0.475114i | \(0.842407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.7931 | − | 3.95564i | 0.982382 | − | 0.186886i | ||||
\(449\) | −42.3320 | −1.99777 | −0.998886 | − | 0.0471929i | \(-0.984972\pi\) | ||||
−0.998886 | + | 0.0471929i | \(0.984972\pi\) | |||||||
\(450\) | −19.3345 | + | 8.72791i | −0.911438 | + | 0.411438i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 20.3286 | + | 17.9282i | 0.956178 | + | 0.843270i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.9333 | − | 29.9333i | 1.40022 | − | 1.40022i | 0.600878 | − | 0.799341i | \(-0.294818\pi\) |
0.799341 | − | 0.600878i | \(-0.205182\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.0593 | −0.792813 | −0.396406 | − | 0.918075i | \(-0.629743\pi\) | ||||
−0.396406 | + | 0.918075i | \(0.629743\pi\) | |||||||
\(464\) | −7.65300 | + | 4.36179i | −0.355282 | + | 0.202491i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.2615 | − | 40.3781i | 0.706975 | − | 1.87048i | ||||
\(467\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.89241 | + | 23.8824i | −0.456789 | + | 1.10279i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −59.5163 | − | 59.5163i | −2.73656 | − | 2.73656i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.6184 | − | 37.7061i | −0.715116 | − | 1.72644i | ||||
\(478\) | 20.6235 | − | 9.30978i | 0.943296 | − | 0.425819i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 60.3000 | − | 3.78358i | 2.74091 | − | 0.171981i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.5203 | + | 30.5203i | −1.38300 | + | 1.38300i | −0.543772 | + | 0.839233i | \(0.683004\pi\) |
−0.839233 | + | 0.543772i | \(0.816996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.4272 | + | 16.3313i | 1.77932 | + | 0.737020i | 0.992846 | + | 0.119401i | \(0.0380974\pi\) |
0.786478 | + | 0.617619i | \(0.211903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 42.3320i | − | 1.89885i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.85331 | − | 21.3738i | −0.396329 | − | 0.956822i | −0.988529 | − | 0.151031i | \(-0.951741\pi\) |
0.592200 | − | 0.805791i | \(-0.298259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(504\) | −21.4558 | − | 6.60659i | −0.955719 | − | 0.294281i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −62.1937 | − | 58.4136i | −2.76485 | − | 2.59680i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −24.0000 | − | 21.1660i | −1.06483 | − | 0.939090i | ||||
\(509\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 17.6698 | − | 14.1343i | 0.780903 | − | 0.624653i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −19.1639 | + | 20.4041i | −0.842015 | + | 0.896504i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(522\) | 9.33848 | − | 0.292689i | 0.408734 | − | 0.0128106i | ||||
\(523\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.64575 | + | 7.00000i | −0.115360 | + | 0.305215i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 65.3320i | 2.84052i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.59375 | + | 27.5130i | 0.112033 | + | 1.18838i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.1963 | − | 41.5156i | 0.740697 | − | 1.78820i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.24579 | − | 15.0787i | −0.268527 | − | 0.648282i | 0.730887 | − | 0.682498i | \(-0.239107\pi\) |
−0.999414 | + | 0.0342160i | \(0.989107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.1061 | + | 12.0561i | −1.24449 | + | 0.515483i | −0.905114 | − | 0.425169i | \(-0.860215\pi\) |
−0.339372 | + | 0.940652i | \(0.610215\pi\) | |||||||
\(548\) | −0.988886 | − | 15.7601i | −0.0422431 | − | 0.673239i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −33.0870 | − | 31.0760i | −1.41083 | − | 1.32508i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.4170 | − | 10.4170i | 0.442976 | − | 0.442976i | ||||
\(554\) | 0.947576 | + | 30.2332i | 0.0402587 | + | 1.28449i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 43.0051 | − | 17.8133i | 1.82219 | − | 0.754774i | 0.847644 | − | 0.530566i | \(-0.178020\pi\) |
0.974541 | − | 0.224208i | \(-0.0719796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.52178 | − | 1.70907i | −0.190740 | − | 0.0720929i | ||||
\(563\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(564\) | 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 | 0.953512 | + | 0.301356i | \(0.0974392\pi\) |
0.301356 | + | 0.953512i | \(0.402561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.4232 | + | 42.0634i | −0.729140 | + | 1.76030i | −0.0836974 | + | 0.996491i | \(0.526673\pi\) |
−0.645443 | + | 0.763809i | \(0.723327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 46.9926i | 1.95973i | ||||||||
\(576\) | −23.5772 | + | 4.48527i | −0.982382 | + | 0.186886i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 21.9125 | − | 9.89164i | 0.911438 | − | 0.411438i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 61.7529 | − | 61.7529i | 2.55754 | − | 2.55754i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.90617 | + | 28.8620i | −0.324942 | + | 1.18622i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.19481 | + | 2.43994i | 0.0489411 | + | 0.0999437i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.1916 | − | 26.1916i | −1.07016 | − | 1.07016i | −0.997346 | − | 0.0728143i | \(-0.976802\pi\) |
−0.0728143 | − | 0.997346i | \(-0.523198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(602\) | −33.5861 | + | 35.7595i | −1.36887 | + | 1.45745i | ||||
\(603\) | 11.2169 | − | 27.0801i | 0.456789 | − | 1.10279i | ||||
\(604\) | 26.4059 | − | 1.65687i | 1.07444 | − | 0.0674169i | ||||
\(605\) | 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 | ||||||||
\(613\) | −21.2101 | − | 8.78549i | −0.856666 | − | 0.354843i | −0.0892633 | − | 0.996008i | \(-0.528451\pi\) |
−0.767403 | + | 0.641165i | \(0.778451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.50880 | − | 47.8267i | −0.181665 | − | 1.92699i | ||||
\(617\) | −29.9333 | + | 29.9333i | −1.20507 | + | 1.20507i | −0.232462 | + | 0.972605i | \(0.574678\pi\) |
−0.972605 | + | 0.232462i | \(0.925322\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(620\) | 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 | 0.895484 | − | 0.445093i | \(-0.146829\pi\) |
−0.445093 | + | 0.895484i | \(0.646829\pi\) | |||||||
\(632\) | 4.63464 | − | 15.0516i | 0.184356 | − | 0.598722i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 28.2057 | + | 26.4914i | 1.12019 | + | 1.05211i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8.22564 | + | 18.2219i | 0.325656 | + | 0.721410i | ||||
\(639\) | 48.0000i | 1.89885i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 47.4935 | 1.87588 | 0.937941 | − | 0.346795i | \(-0.112730\pi\) | ||||
0.937941 | + | 0.346795i | \(0.112730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(644\) | −32.8948 | + | 37.2992i | −1.29624 | + | 1.46979i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(648\) | 24.3286 | + | 7.49117i | 0.955719 | + | 0.294281i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.54515 | + | 13.2680i | −0.178002 | + | 0.519616i | ||||
\(653\) | 38.9360 | − | 16.1278i | 1.52368 | − | 0.631131i | 0.545358 | − | 0.838203i | \(-0.316394\pi\) |
0.978326 | + | 0.207072i | \(0.0663936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.91049 | + | 7.02655i | 0.113377 | + | 0.273716i | 0.970375 | − | 0.241604i | \(-0.0776734\pi\) |
−0.856998 | + | 0.515319i | \(0.827673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(662\) | 26.3838 | − | 0.826926i | 1.02543 | − | 0.0321394i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.7299 | − | 23.1360i | 0.842015 | − | 0.896504i | ||||
\(667\) | 7.92049 | − | 19.1217i | 0.306682 | − | 0.740397i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.3320 | 1.63178 | 0.815890 | − | 0.578208i | \(-0.196248\pi\) | ||||
0.815890 | + | 0.578208i | \(0.196248\pi\) | |||||||
\(674\) | 21.0516 | + | 46.6346i | 0.810879 | + | 1.79630i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.62820 | − | 25.9490i | −0.0626229 | − | 0.998037i | ||||
\(677\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.5139 | + | 17.6099i | 1.62675 | + | 0.673822i | 0.994862 | − | 0.101237i | \(-0.0322800\pi\) |
0.631889 | + | 0.775059i | \(0.282280\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.5000 | − | 9.26013i | −0.935414 | − | 0.353553i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.8561 | + | 50.5826i | −0.528259 | + | 1.92844i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.4988 | + | 47.0742i | −0.740697 | + | 1.78820i | ||||
\(694\) | −1.44827 | − | 46.2083i | −0.0549756 | − | 1.75404i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.5000 | + | 19.8431i | −0.661438 | + | 0.750000i | ||||
\(701\) | 19.0012 | + | 45.8729i | 0.717665 | + | 1.73260i | 0.679895 | + | 0.733309i | \(0.262025\pi\) |
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −28.1737 | − | 42.9376i | −1.06184 | − | 1.61827i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.8296 | − | 9.87055i | −0.894940 | − | 0.370696i | −0.112667 | − | 0.993633i | \(-0.535939\pi\) |
−0.782272 | + | 0.622937i | \(0.785939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.8118 | + | 11.8118i | −0.442976 | + | 0.442976i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.1647 | − | 4.16719i | −0.454616 | − | 0.155735i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.2674 | + | 27.1649i | −0.383175 | + | 1.01379i | ||||
\(719\) | 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 | ||||||||
\(725\) | 4.21369 | − | 10.1728i | 0.156493 | − | 0.377807i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(728\) | 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 | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −12.4331 | + | 51.6918i | −0.458289 | + | 1.90539i | ||||
\(737\) | 62.7207 | 2.31035 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.83504 | + | 2.00274i | −0.177860 | + | 0.0736719i | −0.469836 | − | 0.882754i | \(-0.655687\pi\) |
0.291977 | + | 0.956425i | \(0.405687\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −37.1034 | − | 34.8483i | −1.36211 | − | 1.27932i | ||||
\(743\) | 1.47974 | − | 1.47974i | 0.0542864 | − | 0.0542864i | −0.679442 | − | 0.733729i | \(-0.737778\pi\) |
0.733729 | + | 0.679442i | \(0.237778\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.362199 | + | 11.5563i | 0.0132610 | + | 0.423105i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 40.2161 | − | 16.6580i | 1.46946 | − | 0.608671i | ||||
\(750\) | 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 | ||||||||
\(757\) | −4.16646 | + | 10.0587i | −0.151433 | + | 0.365591i | −0.981332 | − | 0.192323i | \(-0.938398\pi\) |
0.829899 | + | 0.557913i | \(0.188398\pi\) | |||||||
\(758\) | 0.136818 | + | 4.36528i | 0.00496944 | + | 0.158554i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.7370 | − | 30.7497i | 0.461109 | − | 1.11321i | ||||
\(764\) | −36.5477 | − | 32.2321i | −1.32225 | − | 1.16611i | ||||
\(765\) | 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 | ||||||||
\(772\) | 2.96153 | − | 3.35806i | 0.106588 | − | 0.120859i | ||||
\(773\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(774\) | 38.0830 | − | 40.5475i | 1.36887 | − | 1.45745i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.73478 | − | 0.211083i | 0.241454 | − | 0.00756769i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −94.8927 | + | 39.3058i | −3.39553 | + | 1.40647i | ||||
\(782\) | 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 | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(788\) | 35.4340 | − | 17.3516i | 1.26229 | − | 0.618124i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.3542 | − | 25.3542i | −0.901493 | − | 0.901493i | ||||
\(792\) | 5.11249 | + | 54.2303i | 0.181665 | + | 1.92699i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −6.61438 | + | 27.5000i | −0.233854 | + | 0.972272i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.28039 | − | 11.6974i | −0.186457 | − | 0.413049i | ||||
\(803\) | 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 | −0.0538482 | + | 0.998549i | \(0.517149\pi\) |
−0.998549 | + | 0.0538482i | \(0.982851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(812\) | 10.4654 | − | 5.12479i | 0.367265 | − | 0.179845i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 63.5323 | + | 24.0130i | 2.22681 | + | 0.841654i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.5274 | + | 37.4865i | −0.541910 | + | 1.30829i | 0.381464 | + | 0.924384i | \(0.375420\pi\) |
−0.923374 | + | 0.383903i | \(0.874580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.6749 | − | 33.6749i | −1.17383 | − | 1.17383i | −0.981288 | − | 0.192546i | \(-0.938326\pi\) |
−0.192546 | − | 0.981288i | \(-0.561674\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.1319 | − | 24.4605i | 0.352320 | − | 0.850577i | −0.644013 | − | 0.765015i | \(-0.722732\pi\) |
0.996333 | − | 0.0855616i | \(-0.0272685\pi\) | |||||||
\(828\) | 37.2992 | − | 42.2933i | 1.29624 | − | 1.46979i | ||||
\(829\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(830\) | 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 | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0769 | − | 17.0769i | 0.588859 | − | 0.588859i | ||||
\(842\) | −51.1280 | + | 1.60246i | −1.76199 | + | 0.0552246i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −37.5600 | − | 12.8667i | −1.29287 | − | 0.442890i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −79.9262 | −2.74630 | ||||||||
\(848\) | −52.4835 | − | 14.3768i | −1.80229 | − | 0.493702i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.9077 | − | 64.9610i | −0.922385 | − | 2.22683i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.6716 | − | 35.8484i | 1.01415 | − | 1.22527i | ||||
\(857\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34.1029 | + | 15.3946i | −1.16155 | + | 0.524342i | ||||
\(863\) | − | 35.5014i | − | 1.20848i | −0.796802 | − | 0.604240i | \(-0.793477\pi\) | ||
0.796802 | − | 0.604240i | \(-0.206523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −33.0234 | − | 13.6787i | −1.12024 | − | 0.464019i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −3.33957 | − | 35.4242i | −0.113092 | − | 1.19962i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.42181 | − | 3.90264i | 0.318152 | − | 0.131783i | −0.217892 | − | 0.975973i | \(-0.569918\pi\) |
0.536044 | + | 0.844190i | \(0.319918\pi\) | |||||||
\(878\) | 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 | ||||
\(883\) | −22.3365 | − | 53.9250i | −0.751682 | − | 1.81472i | −0.549766 | − | 0.835319i | \(-0.685283\pi\) |
−0.201916 | − | 0.979403i | \(-0.564717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.44659 | − | 46.1548i | −0.0485992 | − | 1.55060i | ||||
\(887\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29.9333 | + | 29.9333i | 1.00393 | + | 1.00393i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.1095 | − | 53.3771i | 0.740697 | − | 1.78820i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −24.5000 | + | 17.1974i | −0.818488 | + | 0.574524i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 54.5646 | − | 24.6314i | 1.82084 | − | 0.821959i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 19.8431 | − | 22.5000i | 0.661438 | − | 0.750000i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −36.6346 | − | 11.2804i | −1.21845 | − | 0.375180i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.6966 | − | 6.91597i | −0.554402 | − | 0.229641i | 0.0878507 | − | 0.996134i | \(-0.472000\pi\) |
−0.642253 | + | 0.766493i | \(0.722000\pi\) | |||||||
\(908\) | 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 | 0.991798 | + | 0.127817i | \(0.0407969\pi\) |
0.127817 | + | 0.991798i | \(0.459203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.3149 | − | 34.5592i | −0.470671 | − | 1.13630i | ||||
\(926\) | 21.9889 | − | 9.92614i | 0.722600 | − | 0.326193i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.32652 | − | 10.0752i | 0.240505 | − | 0.330734i | ||||
\(929\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.82288 | + | 60.9261i | 0.125222 | + | 1.99570i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(938\) | −1.14523 | − | 36.5397i | −0.0373932 | − | 1.19306i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 111.345 | + | 42.0844i | 3.62013 | + | 1.36828i | ||||
\(947\) | 17.6502 | + | 42.6113i | 0.573554 | + | 1.38468i | 0.898510 | + | 0.438953i | \(0.144650\pi\) |
−0.324956 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.4170 | − | 18.4170i | −0.596585 | − | 0.596585i | 0.342817 | − | 0.939402i | \(-0.388619\pi\) |
−0.939402 | + | 0.342817i | \(0.888619\pi\) | |||||||
\(954\) | 42.0713 | + | 39.5142i | 1.36211 | + | 1.27932i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −21.1660 | + | 24.0000i | −0.684558 | + | 0.776215i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.8897i | 0.674563i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −45.6007 | + | 18.8884i | −1.46946 | + | 0.608671i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.8118 | + | 43.8118i | −1.40889 | + | 1.40889i | −0.643157 | + | 0.765735i | \(0.722376\pi\) |
−0.765735 | + | 0.643157i | \(0.777624\pi\) | |||||||
\(968\) | −75.5232 | + | 39.9631i | −2.42741 | + | 1.28446i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 21.5811 | − | 57.0982i | 0.691502 | − | 1.82954i | ||||
\(975\) | 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 | ||||||||
\(981\) | −14.4423 | + | 34.8669i | −0.461109 | + | 1.11321i | ||||
\(982\) | −60.3229 | + | 1.89065i | −1.92498 | + | 0.0603332i | ||||
\(983\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −47.1576 | − | 113.849i | −1.49953 | − | 3.62017i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.1288i | 1.84652i | 0.384173 | + | 0.923261i | \(0.374487\pi\) | ||||
−0.384173 | + | 0.923261i | \(0.625513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.6314 | + | 54.5646i | 0.781259 | + | 1.73068i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(998\) | 23.8482 | + | 22.3987i | 0.754901 | + | 0.709019i | ||||
\(999\) | 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.27.1 | ✓ | 8 | |
4.3 | odd | 2 | 896.2.x.a.783.2 | 8 | |||
7.6 | odd | 2 | CM | 224.2.x.a.27.1 | ✓ | 8 | |
28.27 | even | 2 | 896.2.x.a.783.2 | 8 | |||
32.13 | even | 8 | 896.2.x.a.111.2 | 8 | |||
32.19 | odd | 8 | inner | 224.2.x.a.83.1 | yes | 8 | |
224.13 | odd | 8 | 896.2.x.a.111.2 | 8 | |||
224.83 | even | 8 | inner | 224.2.x.a.83.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.x.a.27.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
224.2.x.a.27.1 | ✓ | 8 | 7.6 | odd | 2 | CM | |
224.2.x.a.83.1 | yes | 8 | 32.19 | odd | 8 | inner | |
224.2.x.a.83.1 | yes | 8 | 224.83 | even | 8 | inner | |
896.2.x.a.111.2 | 8 | 32.13 | even | 8 | |||
896.2.x.a.111.2 | 8 | 224.13 | odd | 8 | |||
896.2.x.a.783.2 | 8 | 4.3 | odd | 2 | |||
896.2.x.a.783.2 | 8 | 28.27 | even | 2 |