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 | 195.1 | ||
Root | \(-0.581861 - 1.28897i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.195 |
Dual form | 224.2.x.a.139.1 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{8}\right)\) |
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 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(4\) | −1.32288 | + | 1.50000i | −0.661438 | + | 0.750000i | ||||
\(5\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | −2.18914 | − | 5.28504i | −0.660049 | − | 1.59350i | −0.797724 | − | 0.603023i | \(-0.793963\pi\) |
0.137675 | − | 0.990478i | \(-0.456037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(14\) | −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 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.53848 | + | 5.89689i | −1.18081 | + | 1.25722i | ||||
\(23\) | 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 | ||||
\(29\) | 8.32605 | + | 3.44876i | 1.54611 | + | 0.640419i | 0.982607 | − | 0.185695i | \(-0.0594537\pi\) |
0.563502 | + | 0.826115i | \(0.309454\pi\) | |||||||
\(30\) | 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 | ||||
\(37\) | −0.571475 | − | 1.37966i | −0.0939499 | − | 0.226815i | 0.869918 | − | 0.493197i | \(-0.164172\pi\) |
−0.963868 | + | 0.266382i | \(0.914172\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | −3.62819 | − | 8.75922i | −0.553293 | − | 1.33577i | −0.914991 | − | 0.403473i | \(-0.867803\pi\) |
0.361698 | − | 0.932295i | \(-0.382197\pi\) | |||||||
\(44\) | 10.8235 | + | 3.70775i | 1.63171 | + | 0.558964i | ||||
\(45\) | 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 | ||||||||
\(53\) | 12.2772 | − | 5.08538i | 1.68640 | − | 0.698531i | 0.686803 | − | 0.726844i | \(-0.259014\pi\) |
0.999599 | + | 0.0283132i | \(0.00901359\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.50000 | − | 6.61438i | −0.467707 | − | 0.883883i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.399260 | − | 12.7387i | −0.0524253 | − | 1.67268i | ||||
\(59\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.93725i | 1.00000i | ||||||||
\(64\) | 6.61438 | + | 4.50000i | 0.826797 | + | 0.562500i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.19827 | − | 14.9640i | 0.757240 | − | 1.82814i | 0.244339 | − | 0.969690i | \(-0.421429\pi\) |
0.512901 | − | 0.858448i | \(-0.328571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3137 | + | 11.3137i | 1.34269 | + | 1.34269i | 0.893372 | + | 0.449319i | \(0.148333\pi\) |
0.449319 | + | 0.893372i | \(0.351667\pi\) | |||||||
\(72\) | −3.96863 | − | 7.50000i | −0.467707 | − | 0.883883i | ||||
\(73\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(74\) | −1.44582 | + | 1.53938i | −0.168073 | + | 0.178950i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.79191 | + | 13.9829i | −0.660049 | + | 1.59350i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.8818 | −1.89935 | −0.949677 | − | 0.313231i | \(-0.898589\pi\) | ||||
−0.949677 | + | 0.313231i | \(0.898589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000i | 1.00000i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.17925 | + | 9.77327i | −0.989824 | + | 1.05388i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.51861 | − | 16.1086i | −0.161885 | − | 1.71718i | ||||
\(89\) | 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 | ||||
\(99\) | −6.56741 | + | 15.8551i | −0.660049 | + | 1.59350i | ||||
\(100\) | −0.626229 | − | 9.98037i | −0.0626229 | − | 0.998037i | ||||
\(101\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(102\) | 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 | ||||||||
\(106\) | −13.6985 | − | 12.8659i | −1.33052 | − | 1.24965i | ||||
\(107\) | −1.05810 | − | 2.55449i | −0.102291 | − | 0.246952i | 0.864446 | − | 0.502726i | \(-0.167670\pi\) |
−0.966736 | + | 0.255774i | \(0.917670\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.10562 | − | 2.66920i | 0.105899 | − | 0.255663i | −0.862044 | − | 0.506834i | \(-0.830816\pi\) |
0.967943 | + | 0.251171i | \(0.0808157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.48921 | + | 8.36004i | −0.613172 | + | 0.789949i | ||||
\(113\) | − | 16.3808i | − | 1.54098i | −0.637452 | − | 0.770490i | \(-0.720012\pi\) | ||
0.637452 | − | 0.770490i | \(-0.279988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −16.1875 | + | 7.92679i | −1.50297 | + | 0.735984i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.3612 | + | 15.3612i | −1.39647 | + | 1.39647i | ||||
\(122\) | 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 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −22.8946 | + | 0.717567i | −1.97779 | + | 0.0619884i | ||||
\(135\) | 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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(140\) | 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 | ||||||||
\(148\) | 2.82548 | + | 0.967910i | 0.232253 | + | 0.0795617i | ||||
\(149\) | 15.0365 | − | 6.22833i | 1.23184 | − | 0.510245i | 0.330684 | − | 0.943741i | \(-0.392720\pi\) |
0.901155 | + | 0.433497i | \(0.142720\pi\) | |||||||
\(150\) | 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 | ||||||||
\(154\) | 21.3936 | − | 0.670523i | 1.72395 | − | 0.0540323i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(158\) | 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 | ||||
\(163\) | −4.74630 | + | 11.4586i | −0.371759 | + | 0.897505i | 0.621694 | + | 0.783260i | \(0.286445\pi\) |
−0.993453 | + | 0.114245i | \(0.963555\pi\) | |||||||
\(164\) | 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 | ||||||||
\(172\) | 17.9385 | + | 6.14508i | 1.36780 | + | 0.468558i | ||||
\(173\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.2288 | 1.00000 | ||||||||
\(176\) | −19.8798 | + | 11.3304i | −1.49850 | + | 0.854060i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.1687 | + | 8.76836i | 1.58222 | + | 0.655378i | 0.988764 | − | 0.149487i | \(-0.0477622\pi\) |
0.593458 | + | 0.804865i | \(0.297762\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(182\) | 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 | \(0.156534\pi\) | ||||
−0.881500 | + | 0.472184i | \(0.843466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.6946 | 1.99350 | 0.996749 | − | 0.0805728i | \(-0.0256750\pi\) | ||||
0.996749 | + | 0.0805728i | \(0.0256750\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.5000 | − | 9.26013i | −0.750000 | − | 0.661438i | ||||
\(197\) | −10.7422 | − | 25.9340i | −0.765352 | − | 1.84772i | −0.388348 | − | 0.921513i | \(-0.626954\pi\) |
−0.377004 | − | 0.926212i | \(-0.623046\pi\) | |||||||
\(198\) | 24.2581 | − | 0.760301i | 1.72395 | − | 0.0540323i | ||||
\(199\) | 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 | ||||||||
\(203\) | −9.12457 | − | 22.0287i | −0.640419 | − | 1.54611i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.74559 | −0.399346 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.888497 | + | 0.368028i | 0.0611667 | + | 0.0253361i | 0.413057 | − | 0.910705i | \(-0.364461\pi\) |
−0.351890 | + | 0.936041i | \(0.614461\pi\) | |||||||
\(212\) | −8.61313 | + | 25.1431i | −0.591552 | + | 1.72684i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.67698 | + | 2.85022i | −0.182995 | + | 0.194837i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.08383 | + | 0.127996i | −0.276592 | + | 0.00866900i | ||||
\(219\) | 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 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.6362 | + | 16.2528i | 1.28918 | + | 1.06705i | ||||
\(233\) | −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 | \(0.5\pi\) | |||||||||
\(242\) | 28.7381 | + | 10.8620i | 1.84736 | + | 0.698235i | ||||
\(243\) | 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 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(252\) | −11.9059 | − | 10.5000i | −0.750000 | − | 0.661438i | ||||
\(253\) | −10.1219 | − | 4.19263i | −0.636358 | − | 0.263588i | ||||
\(254\) | 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 | ||||||||
\(259\) | −1.51198 | + | 3.65025i | −0.0939499 | + | 0.226815i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.3463 | − | 24.9782i | −0.640419 | − | 1.54611i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.74166 | + | 3.74166i | 0.230720 | + | 0.230720i | 0.812993 | − | 0.582273i | \(-0.197836\pi\) |
−0.582273 | + | 0.812993i | \(0.697836\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.2464 | + | 29.0929i | 0.870237 | + | 1.77713i | ||||
\(269\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(270\) | 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 | ||||
\(275\) | 26.4252 | + | 10.9457i | 1.59350 | + | 0.660049i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.6350 | + | 12.6894i | −1.84068 | + | 0.762434i | −0.886873 | + | 0.462014i | \(0.847127\pi\) |
−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 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(284\) | −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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.396435 | − | 4.20515i | −0.0230423 | − | 0.244419i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.7773 | − | 15.7576i | −0.971882 | − | 0.912811i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.59928 | + | 23.1747i | −0.553293 | + | 1.33577i | ||||
\(302\) | −27.3997 | − | 10.3561i | −1.57668 | − | 0.595927i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(308\) | −13.3124 | − | 27.1855i | −0.758544 | − | 1.54904i | ||||
\(309\) | 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 | ||||
\(317\) | 2.98766 | + | 1.23753i | 0.167803 | + | 0.0695065i | 0.465004 | − | 0.885309i | \(-0.346053\pi\) |
−0.297200 | + | 0.954815i | \(0.596053\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 51.5534i | − | 2.88643i | ||||||
\(320\) | 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 | ||||||||
\(326\) | 17.5314 | − | 0.549474i | 0.970976 | − | 0.0304325i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5028 | + | 32.5988i | 0.742183 | + | 1.79179i | 0.596760 | + | 0.802420i | \(0.296455\pi\) |
0.145424 | + | 0.989369i | \(0.453545\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.71443 | + | 4.13899i | −0.0939499 | + | 0.226815i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.24657i | − | 0.340273i | −0.985421 | − | 0.170136i | \(-0.945579\pi\) | ||
0.985421 | − | 0.170136i | \(-0.0544208\pi\) | |||||||
\(338\) | −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 | ||||
\(344\) | −2.51689 | − | 26.6977i | −0.135702 | − | 1.43944i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.68159 | + | 4.01024i | −0.519735 | + | 0.215281i | −0.627100 | − | 0.778938i | \(-0.715758\pi\) |
0.107366 | + | 0.994220i | \(0.465758\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(350\) | −7.69730 | − | 17.0514i | −0.411438 | − | 0.911438i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 26.1718 | + | 19.0317i | 1.39496 | + | 1.01439i | ||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.01510 | − | 32.3877i | −0.0536499 | − | 1.71174i | ||||
\(359\) | −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 | ||||||||
\(371\) | −32.4824 | − | 13.4546i | −1.68640 | − | 0.698531i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.3213 | − | 8.00315i | 1.00042 | − | 0.414387i | 0.178468 | − | 0.983946i | \(-0.442886\pi\) |
0.821951 | + | 0.569558i | \(0.192886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.3734 | + | 11.3384i | −1.40608 | + | 0.582417i | −0.951322 | − | 0.308199i | \(-0.900274\pi\) |
−0.454756 | + | 0.890616i | \(0.650274\pi\) | |||||||
\(380\) | 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 | ||||
\(387\) | −10.8846 | + | 26.2777i | −0.553293 | + | 1.33577i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.8852 | + | 28.6934i | 0.602603 | + | 1.45481i | 0.870893 | + | 0.491473i | \(0.163542\pi\) |
−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 | ||||||||
\(394\) | −27.1777 | + | 28.9364i | −1.36919 | + | 1.45779i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −15.0948 | − | 30.8255i | −0.758544 | − | 1.54904i | ||||
\(397\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.7990 | + | 12.2634i | 0.789949 | + | 0.613172i | ||||
\(401\) | 39.0083i | 1.94798i | 0.226592 | + | 0.973990i | \(0.427242\pi\) | ||||
−0.226592 | + | 0.973990i | \(0.572758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −23.0850 | + | 24.5789i | −1.14569 | + | 1.21983i | ||||
\(407\) | −6.04054 | + | 6.04054i | −0.299418 | + | 0.299418i | ||||
\(408\) | 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 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.0326 | + | 36.2919i | 0.732643 | + | 1.76876i | 0.633581 | + | 0.773676i | \(0.281584\pi\) |
0.0990621 | + | 0.995081i | \(0.468416\pi\) | |||||||
\(422\) | −0.0426061 | − | 1.35939i | −0.00207403 | − | 0.0661738i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 37.4203 | − | 3.52775i | 1.81729 | − | 0.171323i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.23147 | + | 1.79211i | 0.252873 | + | 0.0866251i | ||||
\(429\) | 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 | ||||||||
\(436\) | 2.54120 | + | 5.18945i | 0.121702 | + | 0.248529i | ||||
\(437\) | 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 | ||||||||
\(443\) | 38.6871 | − | 16.0247i | 1.83808 | − | 0.761358i | 0.879924 | − | 0.475114i | \(-0.157593\pi\) |
0.958157 | − | 0.286244i | \(-0.0924067\pi\) | |||||||
\(444\) | 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 | \(0.205182\pi\) |
0.600878 | + | 0.799341i | \(0.294818\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.5092 | 1.83615 | 0.918075 | − | 0.396406i | \(-0.129743\pi\) | ||||
0.918075 | + | 0.396406i | \(0.129743\pi\) | |||||||
\(464\) | 9.52383 | − | 34.7674i | 0.442133 | − | 1.61404i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.294860 | + | 0.780126i | −0.0136591 | + | 0.0361386i | ||||
\(467\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.5909 | + | 16.3991i | −1.82814 | + | 0.757240i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −38.3503 | + | 38.3503i | −1.76335 | + | 1.76335i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −36.8316 | − | 15.2561i | −1.68640 | − | 0.698531i | ||||
\(478\) | 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 | ||||||||
\(484\) | −2.72084 | − | 43.3627i | −0.123674 | − | 1.97103i | ||||
\(485\) | 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 | ||||||||
\(491\) | 8.31448 | + | 20.0729i | 0.375227 | + | 0.905879i | 0.992846 | + | 0.119401i | \(0.0380974\pi\) |
−0.617619 | + | 0.786478i | \(0.711903\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 42.3320i | − | 1.89885i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.85498 | − | 4.08207i | −0.441169 | − | 0.182738i | 0.151031 | − | 0.988529i | \(-0.451741\pi\) |
−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 | ||||||||
\(506\) | 0.485376 | + | 15.4863i | 0.0215776 | + | 0.688451i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −24.0000 | − | 21.1660i | −1.06483 | − | 0.939090i | ||||
\(509\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(510\) | 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 | ||||||||
\(518\) | 5.58481 | − | 0.175040i | 0.245383 | − | 0.00769083i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(522\) | −26.1759 | + | 27.8699i | −1.14569 | + | 1.21983i | ||||
\(523\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(524\) | 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 | ||||||||
\(536\) | 29.2103 | − | 35.2911i | 1.26169 | − | 1.52434i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.9953 | − | 15.3240i | 1.59350 | − | 0.660049i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.7958 | + | 7.37128i | 0.765103 | + | 0.316916i | 0.730887 | − | 0.682498i | \(-0.239107\pi\) |
0.0342160 | + | 0.999414i | \(0.489107\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.8811 | − | 43.1688i | 0.764541 | − | 1.84577i | 0.339372 | − | 0.940652i | \(-0.389785\pi\) |
0.425169 | − | 0.905114i | \(-0.360215\pi\) | |||||||
\(548\) | 43.9889 | − | 2.76013i | 1.87911 | − | 0.117907i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.26717 | − | 40.4301i | −0.0540323 | − | 1.72395i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 31.5830 | + | 31.5830i | 1.34305 | + | 1.34305i | ||||
\(554\) | 34.1816 | + | 32.1041i | 1.45224 | + | 1.36397i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.4782 | − | 25.2966i | 0.443976 | − | 1.07185i | −0.530566 | − | 0.847644i | \(-0.678020\pi\) |
0.974541 | − | 0.224208i | \(-0.0719796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −44.1198 | − | 16.6757i | −1.86108 | − | 0.703422i | ||||
\(563\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(564\) | 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 | \(-0.402561\pi\) |
0.953512 | − | 0.301356i | \(-0.0974392\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2517 | + | 8.38852i | −0.847506 | + | 0.351049i | −0.763809 | − | 0.645443i | \(-0.776673\pi\) |
−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 | ||||||||
\(583\) | −53.7529 | − | 53.7529i | −2.22622 | − | 2.22622i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.18963 | + | 2.95780i | −0.213292 | + | 0.121565i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.5489 | + | 30.7941i | −0.432102 | + | 1.26137i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.1916 | + | 26.1916i | −1.07016 | + | 1.07016i | −0.0728143 | + | 0.997346i | \(0.523198\pi\) |
−0.997346 | + | 0.0728143i | \(0.976802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(602\) | 35.4569 | − | 1.11130i | 1.44512 | − | 0.0452931i | ||||
\(603\) | −44.8919 | + | 18.5948i | −1.82814 | + | 0.757240i | ||||
\(604\) | 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 | ||||||||
\(613\) | 5.66000 | + | 13.6645i | 0.228605 | + | 0.551902i | 0.996008 | − | 0.0892633i | \(-0.0284513\pi\) |
−0.767403 | + | 0.641165i | \(0.778451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −27.2953 | + | 32.9774i | −1.09976 | + | 1.32870i | ||||
\(617\) | −29.9333 | − | 29.9333i | −1.20507 | − | 1.20507i | −0.972605 | − | 0.232462i | \(-0.925322\pi\) |
−0.232462 | − | 0.972605i | \(-0.574678\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(620\) | 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 | \(-0.853171\pi\) |
0.445093 | + | 0.895484i | \(0.353171\pi\) | |||||||
\(632\) | −45.6346 | − | 14.0516i | −1.81525 | − | 0.558944i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.143267 | − | 4.57106i | −0.00568987 | − | 0.181540i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −66.4506 | + | 29.9969i | −2.63081 | + | 1.18759i | ||||
\(639\) | − | 48.0000i | − | 1.89885i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.5603 | −0.693589 | −0.346795 | − | 0.937941i | \(-0.612730\pi\) | ||||
−0.346795 | + | 0.937941i | \(0.612730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(644\) | 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 | ||||||||
\(652\) | −10.9091 | − | 22.2777i | −0.427234 | − | 0.872463i | ||||
\(653\) | 3.58067 | − | 8.64451i | 0.140123 | − | 0.338286i | −0.838203 | − | 0.545358i | \(-0.816394\pi\) |
0.978326 | + | 0.207072i | \(0.0663936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −28.2022 | − | 11.6817i | −1.09860 | − | 0.455056i | −0.241604 | − | 0.970375i | \(-0.577673\pi\) |
−0.856998 | + | 0.515319i | \(0.827673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(662\) | 34.1620 | − | 36.3727i | 1.32774 | − | 1.41366i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.33258 | − | 0.198477i | 0.245383 | − | 0.00769083i | ||||
\(667\) | 15.9460 | − | 6.60506i | 0.617433 | − | 0.255749i | ||||
\(668\) | 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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.74439 | + | 13.8682i | 0.219803 | + | 0.530652i | 0.994862 | − | 0.101237i | \(-0.0322800\pi\) |
−0.775059 | + | 0.631889i | \(0.782280\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.5000 | − | 9.26013i | −0.935414 | − | 0.353553i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −32.9480 | + | 18.7785i | −1.25613 | + | 0.715925i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 41.9487 | − | 17.3757i | 1.59350 | − | 0.660049i | ||||
\(694\) | 10.8024 | + | 10.1458i | 0.410054 | + | 0.385131i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.5000 | + | 19.8431i | −0.661438 | + | 0.750000i | ||||
\(701\) | 20.4154 | + | 8.45633i | 0.771079 | + | 0.319391i | 0.733309 | − | 0.679895i | \(-0.237975\pi\) |
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 9.30292 | − | 44.8084i | 0.350617 | − | 1.68878i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.5870 | − | 47.2871i | −0.735604 | − | 1.77591i | −0.622937 | − | 0.782272i | \(-0.714061\pi\) |
−0.112667 | − | 0.993633i | \(-0.535939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 35.8118 | + | 35.8118i | 1.34305 | + | 1.34305i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −41.1561 | + | 20.1536i | −1.53807 | + | 0.753175i | ||||
\(717\) | 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 | ||||||||
\(725\) | −41.6303 | + | 17.2438i | −1.54611 | + | 0.640419i | ||||
\(726\) | 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 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.53357 | + | 10.5336i | −0.0933885 | + | 0.388273i | ||||
\(737\) | −92.6540 | −3.41295 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.0600 | − | 38.7723i | 0.590777 | − | 1.42626i | −0.291977 | − | 0.956425i | \(-0.594313\pi\) |
0.882754 | − | 0.469836i | \(-0.155687\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.55763 | + | 49.6975i | 0.0571824 | + | 1.82445i | ||||
\(743\) | 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 | ||||||||
\(746\) | −21.5581 | − | 20.2478i | −0.789299 | − | 0.741325i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.79948 | + | 6.75854i | −0.102291 | + | 0.246952i | ||||
\(750\) | 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 | ||||||||
\(757\) | −42.3502 | + | 17.5420i | −1.53925 | + | 0.637576i | −0.981332 | − | 0.192323i | \(-0.938398\pi\) |
−0.557913 | + | 0.829899i | \(0.688398\pi\) | |||||||
\(758\) | 30.5424 | + | 28.6861i | 1.10935 | + | 1.04192i | ||||
\(759\) | 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 | ||||||||
\(763\) | −7.06204 | + | 2.92519i | −0.255663 | + | 0.105899i | ||||
\(764\) | −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 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(774\) | 40.2044 | − | 1.26009i | 1.44512 | − | 0.0452931i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 30.0693 | − | 32.0152i | 1.07804 | − | 1.14780i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.0262 | − | 84.5607i | 1.25334 | − | 3.02582i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.7804 | − | 3.50000i | 0.992157 | − | 0.125000i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(788\) | 53.1117 | + | 18.1942i | 1.89203 | + | 0.648140i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.6458 | + | 30.6458i | −1.08964 | + | 1.08964i | ||||
\(792\) | −30.9500 | + | 37.3929i | −1.09976 | + | 1.32870i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(798\) | 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 | \(-0.982851\pi\) |
−0.0538482 | − | 0.998549i | \(-0.517149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(812\) | 45.1137 | + | 15.4543i | 1.58318 | + | 0.542341i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.3008 | + | 4.27131i | 0.396093 | + | 0.149709i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.9440 | − | 21.9301i | 1.84776 | − | 0.765366i | 0.923374 | − | 0.383903i | \(-0.125420\pi\) |
0.924384 | − | 0.381464i | \(-0.124580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33.6749 | + | 33.6749i | −1.17383 | + | 1.17383i | −0.192546 | + | 0.981288i | \(0.561674\pi\) |
−0.981288 | + | 0.192546i | \(0.938326\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.0597 | − | 6.65215i | 0.558451 | − | 0.231318i | −0.0855616 | − | 0.996333i | \(-0.527268\pi\) |
0.644013 | + | 0.765015i | \(0.277268\pi\) | |||||||
\(828\) | 7.60070 | − | 8.61839i | 0.264143 | − | 0.299510i | ||||
\(829\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(830\) | 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 | ||||||||
\(841\) | 36.9231 | + | 36.9231i | 1.27321 | + | 1.27321i | ||||
\(842\) | 38.0322 | − | 40.4933i | 1.31068 | − | 1.39549i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.72741 | + | 0.845891i | −0.0594600 | + | 0.0291168i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 57.4763 | 1.97491 | ||||||||
\(848\) | −26.3206 | − | 46.1809i | −0.903852 | − | 1.58586i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.64233 | − | 1.09449i | −0.0905778 | − | 0.0375185i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.734011 | − | 7.78596i | −0.0250880 | − | 0.266119i | ||||
\(857\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.3946 | + | 34.1029i | 0.524342 | + | 1.16155i | ||||
\(863\) | 46.8151i | 1.59360i | 0.604240 | + | 0.796802i | \(0.293477\pi\) | ||||
−0.604240 | + | 0.796802i | \(0.706523\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.9566 | + | 89.2212i | 1.25367 | + | 3.02662i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 5.21040 | − | 6.29506i | 0.176446 | − | 0.213178i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.0281 | − | 31.4527i | 0.439929 | − | 1.06208i | −0.536044 | − | 0.844190i | \(-0.680082\pi\) |
0.975973 | − | 0.217892i | \(-0.0699181\pi\) | |||||||
\(878\) | 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 | ||||
\(883\) | −30.8218 | − | 12.7668i | −1.03723 | − | 0.429637i | −0.201916 | − | 0.979403i | \(-0.564717\pi\) |
−0.835319 | + | 0.549766i | \(0.814717\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −43.1659 | − | 40.5423i | −1.45019 | − | 1.36204i | ||||
\(887\) | 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 | ||||||||
\(891\) | 47.5654 | − | 19.7022i | 1.59350 | − | 0.660049i | ||||
\(892\) | 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 | ||||||||
\(907\) | 20.4383 | + | 49.3424i | 0.678642 | + | 1.63839i | 0.766493 | + | 0.642253i | \(0.222000\pi\) |
−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 | \(0.540797\pi\) |
−0.991798 | + | 0.127817i | \(0.959203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.89831 | + | 2.85738i | 0.226815 | + | 0.0939499i | ||||
\(926\) | −22.9889 | − | 50.9261i | −0.755462 | − | 1.67354i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −50.3556 | + | 7.95387i | −1.65300 | + | 0.261099i | ||||
\(929\) | 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 | \(0.250000\pi\) | |||||||
\(938\) | 44.1743 | + | 41.4894i | 1.44234 | + | 1.35468i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 71.7468 | + | 27.1177i | 2.33269 | + | 0.881673i | ||||
\(947\) | 3.50805 | + | 1.45308i | 0.113996 | + | 0.0472188i | 0.438953 | − | 0.898510i | \(-0.355350\pi\) |
−0.324956 | + | 0.945729i | \(0.605350\pi\) | |||||||
\(948\) | 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 | \(0.888619\pi\) | |||||||
\(954\) | 1.76619 | + | 56.3517i | 0.0571824 | + | 1.82445i | ||||
\(955\) | 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 | ||||||||
\(963\) | −3.17431 | + | 7.66346i | −0.102291 | + | 0.246952i | ||||
\(964\) | 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 | \(0.722376\pi\) | |||||||
\(968\) | −54.3100 | + | 28.7381i | −1.74559 | + | 0.923679i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(972\) | 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 | ||||||||
\(981\) | −8.00760 | + | 3.31686i | −0.255663 | + | 0.105899i | ||||
\(982\) | 21.0355 | − | 22.3967i | 0.671269 | − | 0.714709i | ||||
\(983\) | 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 | ||||||||
\(989\) | −16.7756 | − | 6.94869i | −0.533434 | − | 0.220956i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24.1877i | − | 0.768347i | −0.923261 | − | 0.384173i | \(-0.874487\pi\) | ||
0.923261 | − | 0.384173i | \(-0.125513\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −54.5646 | + | 24.6314i | −1.73068 | + | 0.781259i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(998\) | 0.472576 | + | 15.0779i | 0.0149591 | + | 0.477284i | ||||
\(999\) | 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.195.1 | yes | 8 | |
4.3 | odd | 2 | 896.2.x.a.559.2 | 8 | |||
7.6 | odd | 2 | CM | 224.2.x.a.195.1 | yes | 8 | |
28.27 | even | 2 | 896.2.x.a.559.2 | 8 | |||
32.11 | odd | 8 | inner | 224.2.x.a.139.1 | ✓ | 8 | |
32.21 | even | 8 | 896.2.x.a.335.2 | 8 | |||
224.139 | even | 8 | inner | 224.2.x.a.139.1 | ✓ | 8 | |
224.181 | odd | 8 | 896.2.x.a.335.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.x.a.139.1 | ✓ | 8 | 32.11 | odd | 8 | inner | |
224.2.x.a.139.1 | ✓ | 8 | 224.139 | even | 8 | inner | |
224.2.x.a.195.1 | yes | 8 | 1.1 | even | 1 | trivial | |
224.2.x.a.195.1 | yes | 8 | 7.6 | odd | 2 | CM | |
896.2.x.a.335.2 | 8 | 32.21 | even | 8 | |||
896.2.x.a.335.2 | 8 | 224.181 | odd | 8 | |||
896.2.x.a.559.2 | 8 | 4.3 | odd | 2 | |||
896.2.x.a.559.2 | 8 | 28.27 | even | 2 |