Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(65,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 193.1 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.193 |
Dual form | 448.2.i.j.65.1 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.207107 | + | 0.358719i | −0.119573 | + | 0.207107i | −0.919599 | − | 0.392859i | \(-0.871486\pi\) |
0.800025 | + | 0.599966i | \(0.204819\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.914214 | − | 1.58346i | −0.408849 | − | 0.708147i | 0.585912 | − | 0.810374i | \(-0.300736\pi\) |
−0.994761 | + | 0.102228i | \(0.967403\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 2.44949i | −0.377964 | + | 0.925820i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41421 | + | 2.44949i | 0.471405 | + | 0.816497i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.20711 | + | 2.09077i | −0.363956 | + | 0.630391i | −0.988608 | − | 0.150513i | \(-0.951908\pi\) |
0.624652 | + | 0.780903i | \(0.285241\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.757359 | 0.195549 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0857864 | − | 0.148586i | 0.0208063 | − | 0.0360375i | −0.855435 | − | 0.517911i | \(-0.826710\pi\) |
0.876241 | + | 0.481873i | \(0.160043\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.20711 | + | 5.55487i | 0.735761 | + | 1.27438i | 0.954389 | + | 0.298567i | \(0.0965085\pi\) |
−0.218628 | + | 0.975808i | \(0.570158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.671573 | − | 0.866025i | −0.146549 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.62132 | + | 4.54026i | 0.546583 | + | 0.946710i | 0.998505 | + | 0.0546524i | \(0.0174051\pi\) |
−0.451922 | + | 0.892057i | \(0.649262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.828427 | − | 1.43488i | 0.165685 | − | 0.286976i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.41421 | −0.464616 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.79289 | + | 4.83743i | −0.501618 | + | 0.868829i | 0.498380 | + | 0.866959i | \(0.333929\pi\) |
−0.999998 | + | 0.00186981i | \(0.999405\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.79289 | − | 0.655892i | 0.810147 | − | 0.110866i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.32843 | + | 7.49706i | 0.711589 | + | 1.23251i | 0.964260 | + | 0.264956i | \(0.0853575\pi\) |
−0.252671 | + | 0.967552i | \(0.581309\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.585786 | − | 1.01461i | 0.0938009 | − | 0.162468i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.82843 | −1.06642 | −0.533211 | − | 0.845983i | \(-0.679015\pi\) | ||||
−0.533211 | + | 0.845983i | \(0.679015\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.65685 | −1.47266 | −0.736328 | − | 0.676625i | \(-0.763442\pi\) | ||||
−0.736328 | + | 0.676625i | \(0.763442\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.58579 | − | 4.47871i | 0.385466 | − | 0.667647i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.20711 | − | 9.01897i | −0.759535 | − | 1.31555i | −0.943088 | − | 0.332543i | \(-0.892093\pi\) |
0.183554 | − | 0.983010i | \(-0.441240\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0355339 | + | 0.0615465i | 0.00497574 | + | 0.00861824i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.500000 | + | 0.866025i | −0.0686803 | + | 0.118958i | −0.898321 | − | 0.439340i | \(-0.855212\pi\) |
0.829640 | + | 0.558298i | \(0.188546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.41421 | 0.595212 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.65685 | −0.351909 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.44975 | − | 9.43924i | 0.709497 | − | 1.22888i | −0.255547 | − | 0.966797i | \(-0.582256\pi\) |
0.965044 | − | 0.262088i | \(-0.0844110\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.32843 | + | 7.49706i | 0.554198 | + | 0.959900i | 0.997965 | + | 0.0637575i | \(0.0203084\pi\) |
−0.443767 | + | 0.896142i | \(0.646358\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.41421 | + | 1.01461i | −0.934103 | + | 0.127829i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.58579 | + | 4.47871i | 0.320727 | + | 0.555516i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.37868 | + | 2.38794i | −0.168433 | + | 0.291734i | −0.937869 | − | 0.346990i | \(-0.887204\pi\) |
0.769436 | + | 0.638723i | \(0.220537\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.17157 | −0.261427 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.6569 | 1.62077 | 0.810385 | − | 0.585897i | \(-0.199258\pi\) | ||||
0.810385 | + | 0.585897i | \(0.199258\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.32843 | − | 12.6932i | 0.857728 | − | 1.48563i | −0.0163639 | − | 0.999866i | \(-0.505209\pi\) |
0.874091 | − | 0.485762i | \(-0.161458\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.343146 | + | 0.594346i | 0.0396231 | + | 0.0686292i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.91421 | − | 5.04757i | −0.446066 | − | 0.575224i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.03553 | − | 5.25770i | −0.341524 | − | 0.591537i | 0.643192 | − | 0.765705i | \(-0.277610\pi\) |
−0.984716 | + | 0.174168i | \(0.944276\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.74264 | + | 6.48244i | −0.415849 | + | 0.720272i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.31371 | 0.802784 | 0.401392 | − | 0.915906i | \(-0.368527\pi\) | ||||
0.401392 | + | 0.915906i | \(0.368527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.313708 | −0.0340265 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.585786 | + | 1.01461i | −0.0628029 | + | 0.108778i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.50000 | + | 7.79423i | 0.476999 | + | 0.826187i | 0.999653 | − | 0.0263586i | \(-0.00839118\pi\) |
−0.522654 | + | 0.852545i | \(0.675058\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.82843 | − | 6.92820i | 0.296500 | − | 0.726273i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.15685 | − | 2.00373i | −0.119960 | − | 0.207777i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.86396 | − | 10.1567i | 0.601630 | − | 1.04205i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.17157 | −0.118955 | −0.0594776 | − | 0.998230i | \(-0.518943\pi\) | ||||
−0.0594776 | + | 0.998230i | \(0.518943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.82843 | −0.686283 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.74264 | − | 11.6786i | 0.670918 | − | 1.16206i | −0.306726 | − | 0.951798i | \(-0.599234\pi\) |
0.977644 | − | 0.210266i | \(-0.0674330\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.20711 | − | 7.28692i | −0.414539 | − | 0.718002i | 0.580841 | − | 0.814017i | \(-0.302724\pi\) |
−0.995380 | + | 0.0960150i | \(0.969390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.757359 | + | 1.85514i | −0.0739107 | + | 0.181044i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.44975 | − | 11.1713i | −0.623521 | − | 1.07997i | −0.988825 | − | 0.149081i | \(-0.952368\pi\) |
0.365304 | − | 0.930888i | \(-0.380965\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.08579 | + | 7.07679i | −0.391347 | + | 0.677834i | −0.992628 | − | 0.121205i | \(-0.961324\pi\) |
0.601280 | + | 0.799038i | \(0.294658\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.58579 | −0.340348 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.1421 | 1.70667 | 0.853334 | − | 0.521364i | \(-0.174577\pi\) | ||||
0.853334 | + | 0.521364i | \(0.174577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.79289 | − | 8.30153i | 0.446940 | − | 0.774122i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.00000 | − | 6.92820i | −0.369800 | − | 0.640513i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.278175 | + | 0.358719i | 0.0255002 | + | 0.0328838i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.58579 | + | 4.47871i | 0.235071 | + | 0.407156i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.41421 | − | 2.44949i | 0.127515 | − | 0.220863i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1716 | −1.08866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.65685 | −0.501965 | −0.250982 | − | 0.967992i | \(-0.580754\pi\) | ||||
−0.250982 | + | 0.967992i | \(0.580754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.86396 | + | 6.69258i | 0.337596 | + | 0.584733i | 0.983980 | − | 0.178279i | \(-0.0570530\pi\) |
−0.646384 | + | 0.763012i | \(0.723720\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −16.8137 | + | 2.30090i | −1.45793 | + | 0.199514i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.20711 | + | 3.82282i | 0.189958 | + | 0.329016i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.57107 | + | 9.64937i | −0.475968 | + | 0.824402i | −0.999621 | − | 0.0275304i | \(-0.991236\pi\) |
0.523653 | + | 0.851932i | \(0.324569\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.3137 | −1.29889 | −0.649446 | − | 0.760408i | \(-0.724999\pi\) | ||||
−0.649446 | + | 0.760408i | \(0.724999\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.31371 | 0.363280 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.41421 | − | 5.91359i | 0.285511 | − | 0.494519i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.58579 | − | 4.47871i | −0.214738 | − | 0.371937i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.79289 | − | 0.778985i | 0.230354 | − | 0.0642496i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.08579 | + | 5.34474i | 0.252797 | + | 0.437858i | 0.964295 | − | 0.264831i | \(-0.0853160\pi\) |
−0.711497 | + | 0.702689i | \(0.751983\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.449747 | + | 0.778985i | −0.0365999 | + | 0.0633929i | −0.883745 | − | 0.467969i | \(-0.844986\pi\) |
0.847145 | + | 0.531361i | \(0.178319\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.485281 | 0.0392327 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2132 | 0.820344 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.67157 | − | 8.09140i | 0.372832 | − | 0.645764i | −0.617168 | − | 0.786831i | \(-0.711720\pi\) |
0.990000 | + | 0.141067i | \(0.0450534\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.207107 | − | 0.358719i | −0.0164246 | − | 0.0284483i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.7426 | + | 1.88064i | −1.08307 | + | 0.148215i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.37868 | + | 5.85204i | 0.264639 | + | 0.458368i | 0.967469 | − | 0.252990i | \(-0.0814140\pi\) |
−0.702830 | + | 0.711358i | \(0.748081\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.914214 | + | 1.58346i | −0.0711714 | + | 0.123273i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.00000 | 0.154765 | 0.0773823 | − | 0.997001i | \(-0.475344\pi\) | ||||
0.0773823 | + | 0.997001i | \(0.475344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.07107 | + | 15.7116i | −0.693682 | + | 1.20149i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.50000 | + | 9.52628i | 0.418157 | + | 0.724270i | 0.995754 | − | 0.0920525i | \(-0.0293428\pi\) |
−0.577597 | + | 0.816322i | \(0.696009\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.68629 | + | 3.46410i | 0.203065 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.25736 | + | 3.90986i | 0.169674 | + | 0.293883i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.79289 | − | 4.83743i | 0.208751 | − | 0.361567i | −0.742571 | − | 0.669768i | \(-0.766394\pi\) |
0.951321 | + | 0.308201i | \(0.0997270\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.31371 | 0.692283 | 0.346141 | − | 0.938182i | \(-0.387492\pi\) | ||||
0.346141 | + | 0.938182i | \(0.387492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.58579 | −0.265069 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.91421 | − | 13.7078i | 0.581865 | − | 1.00782i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.207107 | + | 0.358719i | 0.0151451 | + | 0.0262322i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.41421 | − | 5.91359i | 0.175608 | − | 0.430150i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.44975 | + | 7.70719i | 0.321972 | + | 0.557673i | 0.980895 | − | 0.194538i | \(-0.0623208\pi\) |
−0.658923 | + | 0.752211i | \(0.728987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.57107 | − | 7.91732i | 0.329033 | − | 0.569901i | −0.653288 | − | 0.757110i | \(-0.726611\pi\) |
0.982320 | + | 0.187209i | \(0.0599440\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.14214 | −0.153402 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.8284 | 1.34147 | 0.670735 | − | 0.741697i | \(-0.265979\pi\) | ||||
0.670735 | + | 0.741697i | \(0.265979\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.62132 | + | 9.73641i | −0.398485 | + | 0.690196i | −0.993539 | − | 0.113489i | \(-0.963797\pi\) |
0.595054 | + | 0.803685i | \(0.297131\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.571068 | − | 0.989118i | −0.0402800 | − | 0.0697670i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.82843 | + | 6.92820i | −0.198517 | + | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.24264 | + | 10.8126i | 0.436005 | + | 0.755183i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.41421 | + | 12.8418i | −0.515323 | + | 0.892566i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.4853 | −1.07114 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.82843 | + | 4.89898i | −0.193801 | + | 0.335673i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.82843 | + | 15.2913i | 0.602094 | + | 1.04286i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.05635 | − | 11.6786i | −0.614785 | − | 0.792795i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.03553 | + | 5.25770i | 0.205122 | + | 0.355282i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.242641 | + | 0.420266i | −0.0163218 | + | 0.0282702i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.34315 | 0.156909 | 0.0784543 | − | 0.996918i | \(-0.475002\pi\) | ||||
0.0784543 | + | 0.996918i | \(0.475002\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.68629 | 0.312419 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.03553 | + | 13.9180i | −0.533337 | + | 0.923767i | 0.465905 | + | 0.884835i | \(0.345729\pi\) |
−0.999242 | + | 0.0389321i | \(0.987604\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.08579 | − | 3.61269i | −0.137833 | − | 0.238733i | 0.788843 | − | 0.614594i | \(-0.210680\pi\) |
−0.926676 | + | 0.375861i | \(0.877347\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.62132 | − | 0.358719i | 0.172470 | − | 0.0236020i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.08579 | − | 1.88064i | −0.0711322 | − | 0.123205i | 0.828266 | − | 0.560336i | \(-0.189328\pi\) |
−0.899398 | + | 0.437131i | \(0.855995\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.52082 | + | 16.4905i | −0.621070 | + | 1.07572i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.51472 | 0.163349 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.31371 | 0.0849767 | 0.0424884 | − | 0.999097i | \(-0.486471\pi\) | ||||
0.0424884 | + | 0.999097i | \(0.486471\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.15685 | + | 8.93193i | −0.332182 | + | 0.575356i | −0.982939 | − | 0.183929i | \(-0.941118\pi\) |
0.650757 | + | 0.759286i | \(0.274452\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.17157 | − | 8.95743i | −0.331757 | − | 0.574619i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.18629 | + | 12.3960i | −0.203565 | + | 0.791954i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.07107 | − | 15.7116i | −0.577178 | − | 0.999702i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.51472 | + | 2.62357i | −0.0959914 | + | 0.166262i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.9706 | 1.95484 | 0.977422 | − | 0.211295i | \(-0.0677681\pi\) | ||||
0.977422 | + | 0.211295i | \(0.0677681\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.6569 | −0.795730 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.0649712 | − | 0.112533i | 0.00406865 | − | 0.00704711i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.25736 | − | 3.90986i | −0.140810 | − | 0.243890i | 0.786992 | − | 0.616964i | \(-0.211637\pi\) |
−0.927802 | + | 0.373073i | \(0.878304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.6924 | + | 3.10538i | −1.41004 | + | 0.192959i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | + | 6.92820i | 0.247594 | + | 0.428845i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.44975 | + | 9.43924i | −0.336046 | + | 0.582048i | −0.983685 | − | 0.179899i | \(-0.942423\pi\) |
0.647639 | + | 0.761947i | \(0.275756\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.82843 | 0.112319 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.72792 | −0.228145 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.32843 | − | 10.9612i | 0.385851 | − | 0.668314i | −0.606036 | − | 0.795437i | \(-0.707241\pi\) |
0.991887 | + | 0.127124i | \(0.0405745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1066 | + | 26.1654i | 0.917661 | + | 1.58943i | 0.802958 | + | 0.596035i | \(0.203258\pi\) |
0.114702 | + | 0.993400i | \(0.463409\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.89949 | + | 2.44949i | 0.114963 | + | 0.148250i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | + | 3.46410i | 0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.15685 | − | 8.93193i | 0.309845 | − | 0.536668i | −0.668483 | − | 0.743727i | \(-0.733056\pi\) |
0.978328 | + | 0.207060i | \(0.0663894\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.7990 | −0.945861 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.4853 | −0.744809 | −0.372405 | − | 0.928070i | \(-0.621467\pi\) | ||||
−0.372405 | + | 0.928070i | \(0.621467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.79289 | − | 4.83743i | 0.166020 | − | 0.287556i | −0.770997 | − | 0.636839i | \(-0.780242\pi\) |
0.937017 | + | 0.349283i | \(0.113575\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.42893 | + | 4.20703i | 0.143878 | + | 0.249203i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.82843 | − | 16.7262i | 0.403069 | − | 0.987314i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.48528 | + | 14.6969i | 0.499134 | + | 0.864526i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.242641 | − | 0.420266i | 0.0142238 | − | 0.0246364i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.6274 | −1.67243 | −0.836216 | − | 0.548401i | \(-0.815237\pi\) | ||||
−0.836216 | + | 0.548401i | \(0.815237\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.9289 | −1.16031 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.91421 | − | 5.04757i | 0.169100 | − | 0.292889i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.41421 | − | 12.8418i | −0.428775 | − | 0.742660i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.65685 | − | 23.6544i | 0.556612 | − | 1.36341i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.79289 | + | 4.83743i | 0.160448 | + | 0.277903i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.91421 | − | 13.7078i | 0.453167 | − | 0.784907i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.3431 | −0.818607 | −0.409303 | − | 0.912398i | \(-0.634228\pi\) | ||||
−0.409303 | + | 0.912398i | \(0.634228\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.48528 | 0.198271 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.37868 | − | 16.2443i | 0.531816 | − | 0.921133i | −0.467494 | − | 0.883996i | \(-0.654843\pi\) |
0.999310 | − | 0.0371364i | \(-0.0118236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6421 | + | 25.3609i | 0.827622 | + | 1.43348i | 0.899898 | + | 0.436099i | \(0.143640\pi\) |
−0.0722760 | + | 0.997385i | \(0.523026\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.38478 | + | 10.8126i | 0.472429 | + | 0.609219i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.84315 | − | 8.38857i | −0.272018 | − | 0.471149i | 0.697360 | − | 0.716721i | \(-0.254358\pi\) |
−0.969379 | + | 0.245571i | \(0.921024\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.41421 | + | 5.91359i | −0.191159 | + | 0.331098i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.34315 | 0.298225 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.10051 | 0.0612337 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.34315 | + | 4.05845i | −0.129974 | + | 0.225122i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.69239 | − | 2.93130i | −0.0935893 | − | 0.162101i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.2990 | − | 3.73578i | 1.50504 | − | 0.205960i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.2071 | + | 24.6074i | 0.780893 | + | 1.35255i | 0.931422 | + | 0.363941i | \(0.118569\pi\) |
−0.150529 | + | 0.988606i | \(0.548098\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12.2426 | + | 21.2049i | −0.670893 | + | 1.16202i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.04163 | 0.275454 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.17157 | 0.499607 | 0.249804 | − | 0.968296i | \(-0.419634\pi\) | ||||
0.249804 | + | 0.968296i | \(0.419634\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.75736 | + | 6.50794i | −0.204072 | + | 0.353463i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.74264 | − | 11.6786i | −0.365134 | − | 0.632431i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | − | 7.34847i | 0.917914 | − | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.98528 | + | 3.43861i | 0.106884 | + | 0.185128i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4497 | − | 30.2238i | 0.936752 | − | 1.62250i | 0.165271 | − | 0.986248i | \(-0.447150\pi\) |
0.771480 | − | 0.636253i | \(-0.219517\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.17157 | −0.276828 | −0.138414 | − | 0.990374i | \(-0.544200\pi\) | ||||
−0.138414 | + | 0.990374i | \(0.544200\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.82843 | 0.364474 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.08579 | + | 1.88064i | −0.0577906 | + | 0.100096i | −0.893473 | − | 0.449116i | \(-0.851739\pi\) |
0.835683 | + | 0.549212i | \(0.185072\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.4853 | − | 21.6251i | −0.662650 | − | 1.14774i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.186292 | + | 0.0254934i | −0.00985959 | + | 0.00134925i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.69239 | − | 9.85951i | −0.300433 | − | 0.520365i | 0.675801 | − | 0.737084i | \(-0.263798\pi\) |
−0.976234 | + | 0.216719i | \(0.930464\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.0711 | + | 19.1757i | −0.582688 | + | 1.00924i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.14214 | −0.112433 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.7990 | −1.40272 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.13604 | + | 3.69973i | −0.111500 | + | 0.193124i | −0.916375 | − | 0.400320i | \(-0.868899\pi\) |
0.804875 | + | 0.593444i | \(0.202232\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.65685 | − | 16.7262i | −0.502716 | − | 0.870729i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.62132 | − | 2.09077i | −0.0841748 | − | 0.108547i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.15685 | − | 7.19988i | −0.215234 | − | 0.372796i | 0.738111 | − | 0.674679i | \(-0.235718\pi\) |
−0.953345 | + | 0.301883i | \(0.902385\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.52082 | − | 4.36618i | 0.130174 | − | 0.225469i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.9706 | 1.79632 | 0.898159 | − | 0.439672i | \(-0.144905\pi\) | ||||
0.898159 | + | 0.439672i | \(0.144905\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.17157 | − | 2.02922i | 0.0600215 | − | 0.103960i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.62132 | + | 9.73641i | 0.287236 | + | 0.497507i | 0.973149 | − | 0.230176i | \(-0.0739303\pi\) |
−0.685913 | + | 0.727684i | \(0.740597\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.41421 | + | 10.8126i | −0.224969 | + | 0.551060i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −13.6569 | − | 23.6544i | −0.694217 | − | 1.20242i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.08579 | − | 15.7370i | 0.460668 | − | 0.797900i | −0.538327 | − | 0.842736i | \(-0.680943\pi\) |
0.998994 | + | 0.0448365i | \(0.0142767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.899495 | 0.0454894 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.20101 | −0.161470 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.55025 | + | 9.61332i | −0.279264 | + | 0.483699i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.08579 | − | 3.61269i | −0.104683 | − | 0.181316i | 0.808926 | − | 0.587911i | \(-0.200049\pi\) |
−0.913608 | + | 0.406595i | \(0.866716\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.65685 | − | 6.50794i | 0.133009 | − | 0.325804i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.91421 | − | 6.77962i | −0.195466 | − | 0.338558i | 0.751587 | − | 0.659634i | \(-0.229289\pi\) |
−0.947053 | + | 0.321076i | \(0.895955\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.89949 | − | 13.6823i | 0.393502 | − | 0.681565i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.6863 | 0.680077 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −20.8995 | −1.03595 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.22792 | + | 12.5191i | −0.357398 | + | 0.619031i | −0.987525 | − | 0.157461i | \(-0.949669\pi\) |
0.630128 | + | 0.776492i | \(0.283003\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.30761 | − | 3.99690i | −0.113826 | − | 0.197153i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.6716 | + | 22.7883i | 0.869561 | + | 1.12134i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.68629 | − | 11.5810i | −0.328217 | − | 0.568489i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.17157 | − | 5.49333i | 0.155313 | − | 0.269009i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.65685 | −0.471768 | −0.235884 | − | 0.971781i | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.4853 | 0.803443 | 0.401722 | − | 0.915762i | \(-0.368412\pi\) | ||||
0.401722 | + | 0.915762i | \(0.368412\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 14.7279 | − | 25.5095i | 0.716096 | − | 1.24031i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.142136 | − | 0.246186i | −0.00689459 | − | 0.0119418i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.6924 | + | 3.10538i | −1.09816 | + | 0.150280i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.41421 | + | 2.44949i | 0.0682789 | + | 0.118262i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.37868 | − | 11.0482i | 0.307250 | − | 0.532173i | −0.670510 | − | 0.741901i | \(-0.733924\pi\) |
0.977760 | + | 0.209728i | \(0.0672578\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.5147 | 0.553362 | 0.276681 | − | 0.960962i | \(-0.410765\pi\) | ||||
0.276681 | + | 0.960962i | \(0.410765\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.14214 | 0.102708 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.8137 | + | 29.1222i | −0.804309 | + | 1.39310i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.3492 | − | 19.6575i | −0.541670 | − | 0.938200i | −0.998808 | − | 0.0488041i | \(-0.984459\pi\) |
0.457139 | − | 0.889395i | \(-0.348874\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.92893 | − | 19.1757i | 0.234711 | − | 0.913126i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.96447 | − | 10.3308i | −0.283380 | − | 0.490829i | 0.688835 | − | 0.724918i | \(-0.258123\pi\) |
−0.972215 | + | 0.234089i | \(0.924789\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.22792 | − | 14.2512i | 0.390041 | − | 0.675571i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.55635 | −0.120911 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.17157 | 0.0552899 | 0.0276450 | − | 0.999618i | \(-0.491199\pi\) | ||||
0.0276450 | + | 0.999618i | \(0.491199\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.24264 | − | 14.2767i | 0.388131 | − | 0.672262i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.186292 | − | 0.322666i | −0.00875274 | − | 0.0151602i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −13.5563 | + | 1.85514i | −0.635531 | + | 0.0869705i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.64214 | − | 16.7007i | −0.451040 | − | 0.781224i | 0.547411 | − | 0.836864i | \(-0.315614\pi\) |
−0.998451 | + | 0.0556397i | \(0.982280\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.207107 | + | 0.358719i | −0.00966692 | + | 0.0167436i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.4558 | 1.18560 | 0.592798 | − | 0.805351i | \(-0.298023\pi\) | ||||
0.592798 | + | 0.805351i | \(0.298023\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.3137 | −0.525793 | −0.262896 | − | 0.964824i | \(-0.584678\pi\) | ||||
−0.262896 | + | 0.964824i | \(0.584678\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.11522 | + | 3.66367i | −0.0980911 | + | 0.169899i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.27817 | − | 10.8741i | −0.290519 | − | 0.503194i | 0.683413 | − | 0.730032i | \(-0.260495\pi\) |
−0.973933 | + | 0.226837i | \(0.927161\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.47056 | − | 5.76500i | −0.206431 | − | 0.266203i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.93503 | + | 3.35157i | 0.0891614 | + | 0.154432i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.6569 | − | 20.1903i | 0.535983 | − | 0.928349i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.6274 | 0.487619 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.82843 | −0.129505 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.3492 | − | 24.8536i | 0.655634 | − | 1.13559i | −0.326101 | − | 0.945335i | \(-0.605735\pi\) |
0.981735 | − | 0.190256i | \(-0.0609317\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.2426 | − | 21.2049i | −0.558216 | − | 0.966859i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.17157 | − | 5.31925i | 0.0988100 | − | 0.242034i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.07107 | + | 1.85514i | 0.0486347 | + | 0.0842377i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.86396 | − | 10.1567i | 0.265721 | − | 0.460243i | −0.702031 | − | 0.712146i | \(-0.747723\pi\) |
0.967752 | + | 0.251903i | \(0.0810565\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.79899 | −0.126575 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.65685 | −0.165032 | −0.0825158 | − | 0.996590i | \(-0.526295\pi\) | ||||
−0.0825158 | + | 0.996590i | \(0.526295\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.242641 | − | 0.420266i | 0.0109280 | − | 0.0189278i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.24264 | + | 10.8126i | 0.280586 | + | 0.485989i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.6569 | + | 33.4523i | −0.612594 | + | 1.50054i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.27817 | − | 3.94591i | −0.101985 | − | 0.176643i | 0.810517 | − | 0.585715i | \(-0.199186\pi\) |
−0.912502 | + | 0.409071i | \(0.865853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.414214 | + | 0.717439i | −0.0185057 | + | 0.0320528i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.3431 | −0.461178 | −0.230589 | − | 0.973051i | \(-0.574065\pi\) | ||||
−0.230589 | + | 0.973051i | \(0.574065\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.6569 | −1.09722 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.03553 | − | 1.79360i | 0.0459897 | − | 0.0796565i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 20.7426 | + | 35.9273i | 0.919401 | + | 1.59245i | 0.800326 | + | 0.599565i | \(0.204660\pi\) |
0.119075 | + | 0.992885i | \(0.462007\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.7635 | + | 30.6441i | 1.05123 | + | 1.35562i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.74264 | − | 13.4106i | −0.341846 | − | 0.592095i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.69239 | + | 13.3236i | −0.338967 | + | 0.587108i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.1421 | 1.10575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.55635 | −0.200002 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.50000 | + | 6.06218i | −0.153338 | + | 0.265589i | −0.932453 | − | 0.361293i | \(-0.882336\pi\) |
0.779115 | + | 0.626881i | \(0.215669\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.86396 | + | 15.3528i | 0.387594 | + | 0.671332i | 0.992125 | − | 0.125249i | \(-0.0399729\pi\) |
−0.604531 | + | 0.796581i | \(0.706640\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.79899 | + | 0.246186i | −0.0785144 | + | 0.0107444i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.479185 | + | 0.829972i | 0.0208736 | + | 0.0361542i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.24264 | + | 3.88437i | −0.0975061 | + | 0.168886i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 30.8284 | 1.33784 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.3137 | 0.836570 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.7929 | + | 20.4259i | −0.509851 | + | 0.883088i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.15685 | + | 2.00373i | 0.0499219 | + | 0.0864673i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.2782 | − | 4.54026i | 0.701151 | − | 0.195563i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.9142 | − | 22.3681i | −0.555225 | − | 0.961679i | −0.997886 | − | 0.0649894i | \(-0.979299\pi\) |
0.442661 | − | 0.896689i | \(-0.354035\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.92893 | + | 3.34101i | −0.0827784 | + | 0.143376i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.9411 | 0.640007 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.9706 | −0.469067 | −0.234534 | − | 0.972108i | \(-0.575356\pi\) | ||||
−0.234534 | + | 0.972108i | \(0.575356\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.2426 | + | 21.2049i | −0.522503 | + | 0.905002i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.07107 | + | 15.7116i | 0.386440 | + | 0.669335i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15.9142 | − | 2.17781i | 0.676741 | − | 0.0926099i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.27817 | + | 5.67796i | 0.139151 | + | 0.241016i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.0857864 | + | 0.148586i | −0.00363489 | + | 0.00629581i | −0.867837 | − | 0.496849i | \(-0.834490\pi\) |
0.864202 | + | 0.503145i | \(0.167824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.3137 | 1.15525 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.171573 | −0.00724381 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.03553 | + | 12.1859i | −0.296512 | + | 0.513575i | −0.975336 | − | 0.220727i | \(-0.929157\pi\) |
0.678823 | + | 0.734302i | \(0.262490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.5858 | − | 28.7274i | −0.697769 | − | 1.20857i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.1360 | − | 15.6500i | −0.509666 | − | 0.657238i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.3284 | − | 31.7458i | −0.768368 | − | 1.33085i | −0.938448 | − | 0.345422i | \(-0.887736\pi\) |
0.170080 | − | 0.985430i | \(-0.445597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.20711 | + | 15.9472i | −0.385305 | + | 0.667369i | −0.991812 | − | 0.127710i | \(-0.959237\pi\) |
0.606506 | + | 0.795079i | \(0.292571\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.68629 | −0.153997 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.68629 | 0.362243 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.5000 | + | 33.7750i | −0.811796 | + | 1.40607i | 0.0998105 | + | 0.995006i | \(0.468176\pi\) |
−0.911606 | + | 0.411065i | \(0.865157\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.89340 | + | 3.27946i | 0.0786869 | + | 0.136290i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.31371 | + | 17.9149i | −0.303424 | + | 0.743233i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.20711 | − | 2.09077i | −0.0499933 | − | 0.0865909i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.31371 | + | 12.6677i | −0.302385 | + | 0.523746i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.9706 | −1.19574 | −0.597872 | − | 0.801592i | \(-0.703987\pi\) | ||||
−0.597872 | + | 0.801592i | \(0.703987\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.8284 | −1.47628 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.89949 | + | 6.75412i | −0.160404 | + | 0.277828i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.74264 | − | 4.75039i | −0.112627 | − | 0.195075i | 0.804202 | − | 0.594356i | \(-0.202593\pi\) |
−0.916829 | + | 0.399281i | \(0.869260\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.313708 | − | 0.768426i | 0.0128608 | − | 0.0315024i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.32843 | − | 4.03295i | −0.0952962 | − | 0.165058i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.9350 | + | 31.0644i | −0.732805 | + | 1.26926i | 0.222874 | + | 0.974847i | \(0.428456\pi\) |
−0.955680 | + | 0.294409i | \(0.904877\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.1421 | 1.06636 | 0.533180 | − | 0.846002i | \(-0.320997\pi\) | ||||
0.533180 | + | 0.846002i | \(0.320997\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.79899 | −0.317599 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.72792 | − | 8.18900i | 0.192217 | − | 0.332930i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.6924 | − | 30.6441i | −0.718112 | − | 1.24381i | −0.961747 | − | 0.273939i | \(-0.911673\pi\) |
0.243635 | − | 0.969867i | \(-0.421660\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.89949 | − | 2.44949i | −0.0769714 | − | 0.0992583i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.7279 | + | 25.5095i | 0.595828 | + | 1.03200i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.25736 | − | 3.90986i | 0.0911739 | − | 0.157918i | −0.816831 | − | 0.576876i | \(-0.804271\pi\) |
0.908005 | + | 0.418959i | \(0.137605\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.17157 | −0.208538 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.1127 | 0.769448 | 0.384724 | − | 0.923032i | \(-0.374297\pi\) | ||||
0.384724 | + | 0.923032i | \(0.374297\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.96447 | − | 15.5269i | 0.360312 | − | 0.624079i | −0.627700 | − | 0.778455i | \(-0.716003\pi\) |
0.988012 | + | 0.154376i | \(0.0493368\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.32843 | − | 10.9612i | −0.253951 | − | 0.439856i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −23.5919 | + | 3.22848i | −0.945189 | + | 0.129346i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.98528 | + | 12.0989i | 0.279411 | + | 0.483954i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.20711 | − | 5.55487i | 0.128080 | − | 0.221840i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.48528 | 0.0592220 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6569 | 1.18062 | 0.590310 | − | 0.807176i | \(-0.299005\pi\) | ||||
0.590310 | + | 0.807176i | \(0.299005\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.48528 | + | 4.30463i | −0.0987811 | + | 0.171094i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.17157 | + | 8.95743i | 0.205228 | + | 0.355465i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.1421 | + | 13.8564i | 0.560332 | + | 0.549011i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.3137 | + | 33.4523i | 0.764038 | + | 1.32335i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.50000 | − | 14.7224i | 0.335730 | − | 0.581501i | −0.647895 | − | 0.761730i | \(-0.724350\pi\) |
0.983625 | + | 0.180229i | \(0.0576838\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.0294 | −0.434959 | −0.217479 | − | 0.976065i | \(-0.569783\pi\) | ||||
−0.217479 | + | 0.976065i | \(0.569783\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.31371 | −0.287977 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.9350 | + | 24.1362i | −0.547843 | + | 0.948891i | 0.450580 | + | 0.892736i | \(0.351217\pi\) |
−0.998422 | + | 0.0561548i | \(0.982116\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.1569 | + | 22.7883i | 0.516452 | + | 0.894521i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.06497 | − | 0.829972i | 0.237705 | − | 0.0325292i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.4706 | − | 33.7240i | −0.761942 | − | 1.31972i | −0.941848 | − | 0.336038i | \(-0.890913\pi\) |
0.179906 | − | 0.983684i | \(-0.442421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.06497 | − | 12.2369i | 0.276051 | − | 0.478135i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41.4558 | 1.61735 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.6274 | −1.34889 | −0.674446 | − | 0.738324i | \(-0.735618\pi\) | ||||
−0.674446 | + | 0.738324i | \(0.735618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.3284 | + | 26.5496i | −0.596207 | + | 1.03266i | 0.397169 | + | 0.917746i | \(0.369993\pi\) |
−0.993375 | + | 0.114915i | \(0.963341\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.100505 | − | 0.174080i | −0.00390329 | − | 0.00676070i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.0147 | + | 24.5204i | 0.737359 | + | 0.950860i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.41421 | + | 12.8418i | 0.287079 | + | 0.497236i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.485281 | + | 0.840532i | −0.0187621 | + | 0.0324968i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.8995 | −0.806816 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.14214 | −0.0825733 | −0.0412866 | − | 0.999147i | \(-0.513146\pi\) | ||||
−0.0412866 | + | 0.999147i | \(0.513146\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.00000 | + | 3.46410i | −0.0769800 | + | 0.133333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.39949 | − | 16.2804i | −0.361252 | − | 0.625707i | 0.626915 | − | 0.779087i | \(-0.284317\pi\) |
−0.988167 | + | 0.153381i | \(0.950984\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.17157 | − | 2.86976i | 0.0449608 | − | 0.110131i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.32843 | − | 5.76500i | −0.127546 | − | 0.220915i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.72183 | + | 15.1066i | −0.333731 | + | 0.578040i | −0.983240 | − | 0.182314i | \(-0.941641\pi\) |
0.649509 | + | 0.760354i | \(0.274975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.3726 | 0.778396 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.72792 | 0.0659243 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.41421 | − | 2.44949i | 0.0538772 | − | 0.0933181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.5208 | + | 23.4187i | 0.514356 | + | 0.890891i | 0.999861 | + | 0.0166570i | \(0.00530235\pi\) |
−0.485505 | + | 0.874234i | \(0.661364\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.82843 | − | 16.7262i | 0.259390 | − | 0.635374i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.0000 | + | 24.2487i | 0.531050 | + | 0.919806i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.585786 | + | 1.01461i | −0.0221882 | + | 0.0384312i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.899495 | 0.0340220 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.0000 | −0.528773 | −0.264386 | − | 0.964417i | \(-0.585169\pi\) | ||||
−0.264386 | + | 0.964417i | \(0.585169\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.7635 | + | 48.0877i | −1.04712 | + | 1.81366i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.94365 | − | 6.83060i | −0.148526 | − | 0.257255i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.8640 | + | 28.1946i | 0.822279 | + | 1.06037i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.2990 | − | 31.6948i | −0.687233 | − | 1.19032i | −0.972729 | − | 0.231943i | \(-0.925492\pi\) |
0.285496 | − | 0.958380i | \(-0.407842\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.58579 | − | 14.8710i | 0.321992 | − | 0.557707i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −29.2843 | −1.09670 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.4853 | −0.466923 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.272078 | + | 0.471253i | −0.0101609 | + | 0.0175993i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.5208 | − | 26.8828i | −0.578829 | − | 1.00256i | −0.995614 | − | 0.0935558i | \(-0.970177\pi\) |
0.416785 | − | 0.909005i | \(-0.363157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.0563 | − | 3.01834i | 0.821421 | − | 0.112409i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.13604 | − | 3.69973i | −0.0794401 | − | 0.137594i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.34315 | − | 4.05845i | 0.0870222 | − | 0.150727i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.3431 | 1.27372 | 0.636858 | − | 0.770981i | \(-0.280234\pi\) | ||||
0.636858 | + | 0.770981i | \(0.280234\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18.1716 | −0.673021 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.828427 | + | 1.43488i | −0.0306405 | + | 0.0530709i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.8431 | + | 20.5129i | 0.437437 | + | 0.757662i | 0.997491 | − | 0.0707935i | \(-0.0225531\pi\) |
−0.560054 | + | 0.828456i | \(0.689220\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.78680 | − | 3.71029i | −0.139678 | − | 0.136856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.32843 | − | 5.76500i | −0.122604 | − | 0.212357i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.34924 | + | 5.80106i | −0.123204 | + | 0.213395i | −0.921029 | − | 0.389493i | \(-0.872650\pi\) |
0.797826 | + | 0.602888i | \(0.205984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.51472 | 0.276060 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.3431 | 0.966436 | 0.483218 | − | 0.875500i | \(-0.339468\pi\) | ||||
0.483218 | + | 0.875500i | \(0.339468\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.64214 | − | 9.77247i | 0.206712 | − | 0.358035i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.3431 | + | 17.9149i | 0.378436 | + | 0.655470i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 33.8137 | − | 4.62730i | 1.23553 | − | 0.169078i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8640 | − | 18.8169i | −0.396432 | − | 0.686640i | 0.596851 | − | 0.802352i | \(-0.296418\pi\) |
−0.993283 | + | 0.115712i | \(0.963085\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.41421 | + | 11.1097i | −0.233747 | + | 0.404862i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.64466 | 0.0598553 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.14214 | 0.223240 | 0.111620 | − | 0.993751i | \(-0.464396\pi\) | ||||
0.111620 | + | 0.993751i | \(0.464396\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.62132 | − | 4.54026i | 0.0951479 | − | 0.164801i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.0563 | + | 36.4707i | 0.763292 | + | 1.32206i | 0.941145 | + | 0.338004i | \(0.109752\pi\) |
−0.177853 | + | 0.984057i | \(0.556915\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.2487 | − | 17.0849i | −0.479636 | − | 0.618514i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.443651 | − | 0.768426i | −0.0160402 | − | 0.0277825i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.4142 | + | 26.6982i | −0.556575 | + | 0.964016i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.8579 | 0.499727 | 0.249864 | − | 0.968281i | \(-0.419614\pi\) | ||||
0.249864 | + | 0.968281i | \(0.419614\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.87006 | 0.0673485 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.57107 | + | 7.91732i | −0.164410 | + | 0.284766i | −0.936446 | − | 0.350813i | \(-0.885905\pi\) |
0.772036 | + | 0.635579i | \(0.219239\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.62742 | + | 8.01492i | 0.166222 | + | 0.287904i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.58579 | − | 8.78335i | 0.128639 | − | 0.315101i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.8995 | − | 37.9310i | −0.784631 | − | 1.35902i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.4853 | + | 28.5533i | −0.589890 | + | 1.02172i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.82843 | −0.244028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.0833 | −0.609728 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.1066 | − | 40.0218i | 0.823661 | − | 1.42662i | −0.0792766 | − | 0.996853i | \(-0.525261\pi\) |
0.902938 | − | 0.429771i | \(-0.141406\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.25736 | − | 3.90986i | −0.0803641 | − | 0.139195i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.1421 | + | 44.4390i | −0.645060 | + | 1.58007i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.2426 | − | 21.2049i | −0.434749 | − | 0.753007i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.378680 | + | 0.655892i | −0.0134304 | + | 0.0232621i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −47.1127 | −1.66882 | −0.834409 | − | 0.551146i | \(-0.814191\pi\) | ||||
−0.834409 | + | 0.551146i | \(0.814191\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.78680 | −0.0632123 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.7279 | + | 22.0454i | −0.449719 | + | 0.778936i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.6924 | + | 30.6441i | 0.624351 | + | 1.08141i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.5416 | + | 20.0417i | 0.547771 | + | 0.706376i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.62132 | + | 4.54026i | 0.0922748 | + | 0.159825i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.98528 | − | 15.5630i | 0.315906 | − | 0.547165i | −0.663724 | − | 0.747978i | \(-0.731025\pi\) |
0.979630 | + | 0.200813i | \(0.0643584\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.6569 | 0.620016 | 0.310008 | − | 0.950734i | \(-0.399668\pi\) | ||||
0.310008 | + | 0.950734i | \(0.399668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −12.5147 | −0.438910 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.17767 | − | 10.7000i | 0.216394 | − | 0.374806i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −30.9706 | − | 53.6426i | −1.08352 | − | 1.87672i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.9706 | − | 2.86976i | 0.732771 | − | 0.100277i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.57107 | + | 13.1135i | 0.264232 | + | 0.457663i | 0.967362 | − | 0.253398i | \(-0.0815482\pi\) |
−0.703130 | + | 0.711061i | \(0.748215\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0061 | − | 41.5798i | 0.836800 | − | 1.44938i | −0.0557566 | − | 0.998444i | \(-0.517757\pi\) |
0.892556 | − | 0.450936i | \(-0.148910\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.65685 | −0.0576843 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.6569 | −1.44855 | −0.724275 | − | 0.689511i | \(-0.757826\pi\) | ||||
−0.724275 | + | 0.689511i | \(0.757826\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.600505 | − | 1.04011i | 0.0208564 | − | 0.0361243i | −0.855409 | − | 0.517953i | \(-0.826694\pi\) |
0.876265 | + | 0.481829i | \(0.160027\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.13604 | + | 3.69973i | 0.0740984 | + | 0.128342i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.15685 | + | 0.322666i | −0.0400826 | + | 0.0111797i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.82843 | − | 3.16693i | −0.0632753 | − | 0.109596i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.74264 | − | 11.6786i | 0.233060 | − | 0.403671i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.31371 | −0.114402 | −0.0572010 | − | 0.998363i | \(-0.518218\pi\) | ||||
−0.0572010 | + | 0.998363i | \(0.518218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.58579 | − | 4.47871i | 0.0890592 | − | 0.154255i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.57107 | + | 7.91732i | 0.157250 | + | 0.272364i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.5563 | + | 1.85514i | −0.465802 | + | 0.0637435i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.15685 | + | 2.00373i | 0.0397031 | + | 0.0687678i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.6924 | + | 39.3044i | −0.777885 | + | 1.34734i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40.4853 | 1.38619 | 0.693095 | − | 0.720846i | \(-0.256247\pi\) | ||||
0.693095 | + | 0.720846i | \(0.256247\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33.1716 | 1.13444 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.6716 | + | 21.9478i | −0.432853 | + | 0.749723i | −0.997118 | − | 0.0758709i | \(-0.975826\pi\) |
0.564265 | + | 0.825594i | \(0.309160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.72183 | + | 4.71434i | 0.0928675 | + | 0.160851i | 0.908717 | − | 0.417414i | \(-0.137063\pi\) |
−0.815849 | + | 0.578265i | \(0.803730\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.58579 | + | 5.91359i | 0.156283 | + | 0.201535i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.6924 | − | 28.9121i | −0.568216 | − | 0.984178i | −0.996743 | − | 0.0806492i | \(-0.974301\pi\) |
0.428527 | − | 0.903529i | \(-0.359033\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.0563 | − | 17.4181i | 0.341926 | − | 0.592233i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.02944 | −0.238732 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.6569 | 0.497200 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.89949 | − | 6.75412i | 0.132129 | − | 0.228855i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.65685 | − | 2.86976i | −0.0560760 | − | 0.0971265i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.1716 | − | 29.8141i | 0.411474 | − | 1.00790i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.7132 | + | 44.5366i | 0.868273 | + | 1.50389i | 0.863760 | + | 0.503903i | \(0.168103\pi\) |
0.00451320 | + | 0.999990i | \(0.498563\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.92893 | − | 10.2692i | 0.199978 | − | 0.346372i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.0000 | −0.875962 | −0.437981 | − | 0.898984i | \(-0.644306\pi\) | ||||
−0.437981 | + | 0.898984i | \(0.644306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 41.2548 | 1.38834 | 0.694168 | − | 0.719813i | \(-0.255773\pi\) | ||||
0.694168 | + | 0.719813i | \(0.255773\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.12742 | − | 7.14890i | 0.138742 | − | 0.240308i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.5503 | − | 26.9338i | −0.522126 | − | 0.904349i | −0.999669 | − | 0.0257406i | \(-0.991806\pi\) |
0.477542 | − | 0.878609i | \(-0.341528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.65685 | − | 13.8564i | 0.189725 | − | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.03553 | − | 15.6500i | −0.302702 | − | 0.524295i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 33.3995 | − | 57.8496i | 1.11767 | − | 1.93586i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.2132 | −0.341390 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.14214 | 0.205080 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.89949 | + | 13.6823i | −0.263463 | + | 0.456331i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.0857864 | + | 0.148586i | 0.00285796 | + | 0.00495013i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.48528 | + | 8.36308i | 0.215817 | + | 0.278306i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.51472 | − | 14.7479i | −0.283039 | − | 0.490238i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.7635 | − | 22.1070i | 0.423804 | − | 0.734049i | −0.572504 | − | 0.819902i | \(-0.694028\pi\) |
0.996308 | + | 0.0858524i | \(0.0273613\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 38.1421 | 1.26509 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.82843 | + | 15.2913i | −0.292178 | + | 0.506068i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.27817 | + | 5.67796i | 0.108373 | + | 0.187708i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.2574 | + | 2.77216i | −0.668957 | + | 0.0915447i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.27817 | + | 5.67796i | 0.108137 | + | 0.187299i | 0.915016 | − | 0.403419i | \(-0.132178\pi\) |
−0.806879 | + | 0.590717i | \(0.798845\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.97056 | − | 5.14517i | 0.0978834 | − | 0.169539i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38.6274 | −1.27144 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.3431 | 0.471600 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.8995 | − | 20.6105i | 0.390831 | − | 0.676939i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.67157 | + | 16.7517i | 0.317314 | + | 0.549604i | 0.979927 | − | 0.199358i | \(-0.0638857\pi\) |
−0.662613 | + | 0.748962i | \(0.730552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.1777 | − | 43.4859i | 0.366333 | − | 1.42519i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.88478 | + | 6.72863i | 0.127182 | + | 0.220285i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.378680 | − | 0.655892i | 0.0123841 | − | 0.0214500i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 16.6274 | 0.543194 | 0.271597 | − | 0.962411i | \(-0.412448\pi\) | ||||
0.271597 | + | 0.962411i | \(0.412448\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.1299 | −0.395846 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.1274 | + | 33.1297i | −0.623536 | + | 1.08000i | 0.365286 | + | 0.930895i | \(0.380971\pi\) |
−0.988822 | + | 0.149101i | \(0.952362\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −17.8995 | − | 31.0028i | −0.582888 | − | 1.00959i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.5711 | + | 1.58346i | −0.376407 | + | 0.0515101i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.10660 | − | 15.7731i | −0.295925 | − | 0.512557i | 0.679275 | − | 0.733884i | \(-0.262294\pi\) |
−0.975200 | + | 0.221327i | \(0.928961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −20.7279 | + | 35.9018i | −0.672857 | + | 1.16542i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.01219 | 0.130104 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.1127 | −0.878266 | −0.439133 | − | 0.898422i | \(-0.644714\pi\) | ||||
−0.439133 | + | 0.898422i | \(0.644714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.13604 | − | 14.0920i | 0.263276 | − | 0.456007i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.41421 | − | 2.44949i | −0.0457150 | − | 0.0791808i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.0650 | − | 23.2956i | −0.583348 | − | 0.752256i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.100505 | − | 0.174080i | −0.00324210 | − | 0.00561548i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.2426 | − | 31.5972i | 0.587861 | − | 1.01820i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.7157 | −0.538098 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.3431 | −0.589876 | −0.294938 | − | 0.955516i | \(-0.595299\pi\) | ||||
−0.294938 | + | 0.955516i | \(0.595299\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.227922 | + | 0.394773i | −0.00732191 | + | 0.0126819i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.7929 | − | 30.8182i | −0.571001 | − | 0.989003i | −0.996463 | − | 0.0840268i | \(-0.973222\pi\) |
0.425462 | − | 0.904976i | \(-0.360111\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.3137 | − | 37.5108i | 0.490935 | − | 1.20254i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.970563 | − | 1.68106i | −0.0310829 | − | 0.0538371i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.2574 | − | 29.8906i | 0.552112 | − | 0.956286i | −0.446010 | − | 0.895028i | \(-0.647155\pi\) |
0.998122 | − | 0.0612578i | \(-0.0195112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.7279 | −0.694427 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.1127 | −0.737932 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.4203 | + | 23.2447i | −0.428041 | + | 0.741389i | −0.996699 | − | 0.0811848i | \(-0.974130\pi\) |
0.568658 | + | 0.822574i | \(0.307463\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.2132 | − | 29.8141i | −0.548458 | − | 0.949958i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.31371 | + | 10.5664i | −0.137307 | + | 0.336332i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.3137 | − | 43.8446i | −0.804929 | − | 1.39418i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.3492 | − | 38.7100i | 0.709947 | − | 1.22966i | −0.254929 | − | 0.966960i | \(-0.582052\pi\) |
0.964876 | − | 0.262705i | \(-0.0846145\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.7696 | −0.373495 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.5563 | 0.651680 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.6421 | + | 39.2173i | −0.717084 | + | 1.24203i | 0.245067 | + | 0.969506i | \(0.421190\pi\) |
−0.962150 | + | 0.272519i | \(0.912143\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.4497 | − | 18.0995i | −0.330615 | − | 0.572643i |
(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 | 448.2.i.j.193.1 | 4 | ||
4.3 | odd | 2 | 448.2.i.g.193.2 | 4 | |||
7.2 | even | 3 | inner | 448.2.i.j.65.1 | 4 | ||
7.3 | odd | 6 | 3136.2.a.bx.1.1 | 2 | |||
7.4 | even | 3 | 3136.2.a.bd.1.2 | 2 | |||
8.3 | odd | 2 | 224.2.i.d.193.1 | yes | 4 | ||
8.5 | even | 2 | 224.2.i.a.193.2 | yes | 4 | ||
24.5 | odd | 2 | 2016.2.s.q.865.1 | 4 | |||
24.11 | even | 2 | 2016.2.s.s.865.1 | 4 | |||
28.3 | even | 6 | 3136.2.a.be.1.2 | 2 | |||
28.11 | odd | 6 | 3136.2.a.bw.1.1 | 2 | |||
28.23 | odd | 6 | 448.2.i.g.65.2 | 4 | |||
56.3 | even | 6 | 1568.2.a.u.1.1 | 2 | |||
56.5 | odd | 6 | 1568.2.i.x.961.1 | 4 | |||
56.11 | odd | 6 | 1568.2.a.l.1.2 | 2 | |||
56.13 | odd | 2 | 1568.2.i.x.1537.1 | 4 | |||
56.19 | even | 6 | 1568.2.i.o.961.2 | 4 | |||
56.27 | even | 2 | 1568.2.i.o.1537.2 | 4 | |||
56.37 | even | 6 | 224.2.i.a.65.2 | ✓ | 4 | ||
56.45 | odd | 6 | 1568.2.a.j.1.2 | 2 | |||
56.51 | odd | 6 | 224.2.i.d.65.1 | yes | 4 | ||
56.53 | even | 6 | 1568.2.a.w.1.1 | 2 | |||
168.107 | even | 6 | 2016.2.s.s.289.1 | 4 | |||
168.149 | odd | 6 | 2016.2.s.q.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.i.a.65.2 | ✓ | 4 | 56.37 | even | 6 | ||
224.2.i.a.193.2 | yes | 4 | 8.5 | even | 2 | ||
224.2.i.d.65.1 | yes | 4 | 56.51 | odd | 6 | ||
224.2.i.d.193.1 | yes | 4 | 8.3 | odd | 2 | ||
448.2.i.g.65.2 | 4 | 28.23 | odd | 6 | |||
448.2.i.g.193.2 | 4 | 4.3 | odd | 2 | |||
448.2.i.j.65.1 | 4 | 7.2 | even | 3 | inner | ||
448.2.i.j.193.1 | 4 | 1.1 | even | 1 | trivial | ||
1568.2.a.j.1.2 | 2 | 56.45 | odd | 6 | |||
1568.2.a.l.1.2 | 2 | 56.11 | odd | 6 | |||
1568.2.a.u.1.1 | 2 | 56.3 | even | 6 | |||
1568.2.a.w.1.1 | 2 | 56.53 | even | 6 | |||
1568.2.i.o.961.2 | 4 | 56.19 | even | 6 | |||
1568.2.i.o.1537.2 | 4 | 56.27 | even | 2 | |||
1568.2.i.x.961.1 | 4 | 56.5 | odd | 6 | |||
1568.2.i.x.1537.1 | 4 | 56.13 | odd | 2 | |||
2016.2.s.q.289.1 | 4 | 168.149 | odd | 6 | |||
2016.2.s.q.865.1 | 4 | 24.5 | odd | 2 | |||
2016.2.s.s.289.1 | 4 | 168.107 | even | 6 | |||
2016.2.s.s.865.1 | 4 | 24.11 | even | 2 | |||
3136.2.a.bd.1.2 | 2 | 7.4 | even | 3 | |||
3136.2.a.be.1.2 | 2 | 28.3 | even | 6 | |||
3136.2.a.bw.1.1 | 2 | 28.11 | odd | 6 | |||
3136.2.a.bx.1.1 | 2 | 7.3 | odd | 6 |