Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,2,Mod(65,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, 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("224.65");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.i (of order \(3\), degree \(2\), 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: | \(4\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 65.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.65 |
Dual form | 224.2.i.d.193.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.20711 | + | 2.09077i | 0.696923 | + | 1.20711i | 0.969528 | + | 0.244981i | \(0.0787816\pi\) |
−0.272605 | + | 0.962126i | \(0.587885\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.91421 | + | 3.31552i | −0.856062 | + | 1.48274i | 0.0195936 | + | 0.999808i | \(0.493763\pi\) |
−0.875656 | + | 0.482935i | \(0.839571\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | 0.207107 | + | 0.358719i | 0.0624450 | + | 0.108158i | 0.895558 | − | 0.444945i | \(-0.146777\pi\) |
−0.833113 | + | 0.553103i | \(0.813444\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −9.24264 | −2.38644 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.91421 | + | 5.04757i | 0.706801 | + | 1.22421i | 0.966038 | + | 0.258401i | \(0.0831955\pi\) |
−0.259237 | + | 0.965814i | \(0.583471\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.79289 | − | 3.10538i | 0.411318 | − | 0.712424i | −0.583716 | − | 0.811958i | \(-0.698402\pi\) |
0.995034 | + | 0.0995342i | \(0.0317353\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.32843 | − | 0.866025i | 1.38098 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.62132 | − | 2.80821i | 0.338069 | − | 0.585552i | −0.646001 | − | 0.763337i | \(-0.723560\pi\) |
0.984069 | + | 0.177785i | \(0.0568931\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.82843 | − | 8.36308i | −0.965685 | − | 1.67262i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414214 | 0.0797154 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843 | 0.525226 | 0.262613 | − | 0.964901i | \(-0.415416\pi\) | ||||
0.262613 | + | 0.964901i | \(0.415416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.20711 | + | 7.28692i | 0.755619 | + | 1.30877i | 0.945066 | + | 0.326879i | \(0.105997\pi\) |
−0.189447 | + | 0.981891i | \(0.560670\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.500000 | + | 0.866025i | −0.0870388 | + | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.20711 | + | 8.00436i | 1.04919 | + | 1.35298i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.32843 | − | 2.30090i | 0.218392 | − | 0.378266i | −0.735924 | − | 0.677064i | \(-0.763252\pi\) |
0.954317 | + | 0.298797i | \(0.0965855\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.41421 | − | 5.91359i | −0.546712 | − | 0.946932i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.17157 | −0.182969 | −0.0914845 | − | 0.995807i | \(-0.529161\pi\) | ||||
−0.0914845 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.65685 | 0.252668 | 0.126334 | − | 0.991988i | \(-0.459679\pi\) | ||||
0.126334 | + | 0.991988i | \(0.459679\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.41421 | − | 9.37769i | −0.807103 | − | 1.39794i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.79289 | − | 6.56948i | 0.553250 | − | 0.958258i | −0.444787 | − | 0.895636i | \(-0.646721\pi\) |
0.998037 | − | 0.0626213i | \(-0.0199460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.03553 | + | 12.1859i | −0.985172 | + | 1.70637i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.500000 | + | 0.866025i | 0.0686803 | + | 0.118958i | 0.898321 | − | 0.439340i | \(-0.144788\pi\) |
−0.829640 | + | 0.558298i | \(0.811454\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.58579 | −0.213827 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.65685 | 1.14663 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.44975 | − | 7.70719i | −0.579308 | − | 1.00339i | −0.995559 | − | 0.0941408i | \(-0.969990\pi\) |
0.416251 | − | 0.909250i | \(-0.363344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.32843 | − | 2.30090i | 0.170088 | − | 0.294600i | −0.768363 | − | 0.640015i | \(-0.778928\pi\) |
0.938450 | + | 0.345414i | \(0.112262\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.58579 | + | 5.91359i | 0.577755 | + | 0.745042i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.41421 | − | 9.37769i | 0.671551 | − | 1.16316i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.62132 | − | 9.73641i | −0.686754 | − | 1.18949i | −0.972882 | − | 0.231301i | \(-0.925702\pi\) |
0.286129 | − | 0.958191i | \(-0.407632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.82843 | 0.942432 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.34315 | −0.278080 | −0.139040 | − | 0.990287i | \(-0.544402\pi\) | ||||
−0.139040 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.67157 | + | 2.89525i | 0.195643 | + | 0.338863i | 0.947111 | − | 0.320906i | \(-0.103987\pi\) |
−0.751468 | + | 0.659769i | \(0.770654\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.6569 | − | 20.1903i | 1.34602 | − | 2.33137i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.08579 | − | 0.148586i | 0.123737 | − | 0.0169330i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.03553 | + | 6.98975i | −0.454033 | + | 0.786408i | −0.998632 | − | 0.0522883i | \(-0.983349\pi\) |
0.544599 | + | 0.838697i | \(0.316682\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.74264 | + | 8.21449i | 0.526960 | + | 0.912722i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.3137 | −1.68090 | −0.840449 | − | 0.541891i | \(-0.817709\pi\) | ||||
−0.840449 | + | 0.541891i | \(0.817709\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22.3137 | −2.42026 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.41421 | + | 5.91359i | 0.366042 | + | 0.634004i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.50000 | − | 7.79423i | 0.476999 | − | 0.826187i | −0.522654 | − | 0.852545i | \(-0.675058\pi\) |
0.999653 | + | 0.0263586i | \(0.00839118\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82843 | + | 6.92820i | −0.296500 | + | 0.726273i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.1569 | + | 17.5922i | −1.05322 | + | 1.82422i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.86396 | + | 11.8887i | 0.704228 | + | 1.21976i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.82843 | −0.693322 | −0.346661 | − | 0.937991i | \(-0.612685\pi\) | ||||
−0.346661 | + | 0.937991i | \(0.612685\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.17157 | −0.117748 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.74264 | + | 3.01834i | 0.173399 | + | 0.300336i | 0.939606 | − | 0.342258i | \(-0.111192\pi\) |
−0.766207 | + | 0.642594i | \(0.777858\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.79289 | − | 4.83743i | 0.275192 | − | 0.476646i | −0.694992 | − | 0.719018i | \(-0.744592\pi\) |
0.970184 | + | 0.242371i | \(0.0779253\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.24264 | + | 22.6398i | −0.901989 | + | 2.20941i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.44975 | − | 5.97514i | 0.333500 | − | 0.577638i | −0.649696 | − | 0.760194i | \(-0.725104\pi\) |
0.983195 | + | 0.182556i | \(0.0584371\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.91421 | + | 11.9758i | 0.662262 | + | 1.14707i | 0.980020 | + | 0.198899i | \(0.0637366\pi\) |
−0.317758 | + | 0.948172i | \(0.602930\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.41421 | 0.608810 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1421 | −0.954092 | −0.477046 | − | 0.878878i | \(-0.658292\pi\) | ||||
−0.477046 | + | 0.878878i | \(0.658292\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.20711 | + | 10.7510i | 0.578816 | + | 1.00254i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.00000 | − | 6.92820i | 0.369800 | − | 0.640513i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.2782 | − | 2.09077i | 1.40055 | − | 0.191661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.41421 | − | 9.37769i | 0.492201 | − | 0.852518i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.41421 | − | 2.44949i | −0.127515 | − | 0.220863i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 17.8284 | 1.59462 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | −8.86396 | + | 15.3528i | −0.774448 | + | 1.34138i | 0.160656 | + | 0.987010i | \(0.448639\pi\) |
−0.935104 | + | 0.354373i | \(0.884694\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.81371 | − | 7.49706i | −0.504112 | − | 0.650077i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.792893 | + | 1.37333i | −0.0682414 | + | 0.118198i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.57107 | + | 14.8455i | 0.732276 | + | 1.26834i | 0.955908 | + | 0.293665i | \(0.0948751\pi\) |
−0.223633 | + | 0.974674i | \(0.571792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.31371 | 0.620341 | 0.310170 | − | 0.950681i | \(-0.399614\pi\) | ||||
0.310170 | + | 0.950681i | \(0.399614\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.3137 | 1.54229 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.585786 | − | 1.01461i | −0.0489859 | − | 0.0848461i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.41421 | + | 9.37769i | −0.449626 | + | 0.778775i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.20711 | − | 16.3674i | 0.346996 | − | 1.34996i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.91421 | + | 10.2437i | −0.484511 | + | 0.839198i | −0.999842 | − | 0.0177935i | \(-0.994336\pi\) |
0.515330 | + | 0.856992i | \(0.327669\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.44975 | − | 16.3674i | −0.769010 | − | 1.33196i | −0.938101 | − | 0.346363i | \(-0.887417\pi\) |
0.169091 | − | 0.985600i | \(-0.445917\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −16.4853 | −1.33276 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −32.2132 | −2.58743 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3284 | − | 17.8894i | −0.824298 | − | 1.42773i | −0.902454 | − | 0.430785i | \(-0.858237\pi\) |
0.0781562 | − | 0.996941i | \(-0.475097\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.20711 | + | 2.09077i | −0.0957298 | + | 0.165809i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.25736 | − | 6.77962i | −0.414338 | − | 0.534309i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.62132 | − | 13.2005i | 0.596948 | − | 1.03394i | −0.396321 | − | 0.918112i | \(-0.629713\pi\) |
0.993269 | − | 0.115832i | \(-0.0369534\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.91421 | − | 3.31552i | −0.149021 | − | 0.258113i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.00000 | −0.154765 | −0.0773823 | − | 0.997001i | \(-0.524656\pi\) | ||||
−0.0773823 | + | 0.997001i | \(0.524656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.07107 | + | 8.78335i | 0.387794 | + | 0.671679i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.50000 | + | 9.52628i | −0.418157 | + | 0.724270i | −0.995754 | − | 0.0920525i | \(-0.970657\pi\) |
0.577597 | + | 0.816322i | \(0.303991\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −25.3137 | + | 3.46410i | −1.91354 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.7426 | − | 18.6068i | 0.807466 | − | 1.39857i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.20711 | + | 7.28692i | 0.314454 | + | 0.544650i | 0.979321 | − | 0.202311i | \(-0.0648453\pi\) |
−0.664867 | + | 0.746961i | \(0.731512\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.3137 | 0.989600 | 0.494800 | − | 0.869007i | \(-0.335241\pi\) | ||||
0.494800 | + | 0.869007i | \(0.335241\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.41421 | 0.474152 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.08579 | + | 8.80884i | 0.373914 | + | 0.647639i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.20711 | + | 2.09077i | −0.0882724 | + | 0.152892i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.414214 | − | 1.01461i | 0.0301296 | − | 0.0738022i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.44975 | − | 9.43924i | 0.394330 | − | 0.682999i | −0.598686 | − | 0.800984i | \(-0.704310\pi\) |
0.993015 | + | 0.117985i | \(0.0376434\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.57107 | − | 16.5776i | −0.688941 | − | 1.19328i | −0.972181 | − | 0.234231i | \(-0.924743\pi\) |
0.283240 | − | 0.959049i | \(-0.408591\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 26.1421 | 1.87208 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.1716 | −0.938436 | −0.469218 | − | 0.883082i | \(-0.655464\pi\) | ||||
−0.469218 | + | 0.883082i | \(0.655464\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.37868 | + | 2.38794i | 0.0977320 | + | 0.169277i | 0.910746 | − | 0.412968i | \(-0.135508\pi\) |
−0.813014 | + | 0.582245i | \(0.802175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.5711 | − | 23.5058i | 0.957229 | − | 1.65797i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.82843 | − | 6.92820i | 0.198517 | − | 0.486265i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.24264 | − | 3.88437i | 0.156633 | − | 0.271296i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.58579 | + | 7.94282i | 0.318734 | + | 0.552064i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.48528 | 0.102739 | ||||||||
\(210\) | 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 | ||||||||
\(215\) | −3.17157 | + | 5.49333i | −0.216299 | + | 0.374642i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 22.0563 | − | 3.01834i | 1.49728 | − | 0.204898i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.03553 | + | 6.98975i | −0.272696 | + | 0.472324i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.24264 | − | 14.2767i | −0.554460 | − | 0.960353i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6569 | −0.914531 | −0.457265 | − | 0.889330i | \(-0.651171\pi\) | ||||
−0.457265 | + | 0.889330i | \(0.651171\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 27.3137 | 1.82091 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.964466 | − | 1.67050i | −0.0640139 | − | 0.110875i | 0.832242 | − | 0.554412i | \(-0.187057\pi\) |
−0.896256 | + | 0.443537i | \(0.853724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.91421 | − | 8.51167i | 0.324740 | − | 0.562467i | −0.656719 | − | 0.754135i | \(-0.728056\pi\) |
0.981460 | + | 0.191668i | \(0.0613897\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.62132 | + | 2.09077i | 0.106675 | + | 0.137563i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.91421 | + | 6.77962i | −0.256429 | + | 0.444147i | −0.965283 | − | 0.261208i | \(-0.915879\pi\) |
0.708854 | + | 0.705355i | \(0.249213\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.5208 | + | 25.1508i | 0.947234 | + | 1.64066i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.4853 | −1.26571 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.3137 | 1.37867 | 0.689335 | − | 0.724443i | \(-0.257903\pi\) | ||||
0.689335 | + | 0.724443i | \(0.257903\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.15685 | + | 10.6640i | 0.396598 | + | 0.686928i | 0.993304 | − | 0.115532i | \(-0.0368574\pi\) |
−0.596706 | + | 0.802460i | \(0.703524\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.8284 | + | 18.7554i | −0.694644 | + | 1.20316i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.8137 | − | 7.19988i | 1.64918 | − | 0.459984i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.07107 | + | 8.78335i | −0.322664 | + | 0.558871i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.4853 | − | 32.0174i | −1.17146 | − | 2.02902i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.97056 | −0.187500 | −0.0937501 | − | 0.995596i | \(-0.529885\pi\) | ||||
−0.0937501 | + | 0.995596i | \(0.529885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.34315 | 0.0844428 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −26.9350 | − | 46.6528i | −1.68674 | − | 2.92151i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.7426 | + | 18.6068i | −0.670108 | + | 1.16066i | 0.307766 | + | 0.951462i | \(0.400419\pi\) |
−0.977873 | + | 0.209198i | \(0.932915\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.30761 | − | 5.55487i | −0.267662 | − | 0.345163i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.00000 | + | 6.92820i | −0.247594 | + | 0.428845i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.44975 | − | 7.70719i | −0.274383 | − | 0.475246i | 0.695596 | − | 0.718433i | \(-0.255140\pi\) |
−0.969979 | + | 0.243187i | \(0.921807\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.82843 | −0.235178 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.7279 | 1.32973 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.671573 | − | 1.16320i | −0.0409465 | − | 0.0709215i | 0.844826 | − | 0.535041i | \(-0.179704\pi\) |
−0.885772 | + | 0.464120i | \(0.846371\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.10660 | − | 10.5769i | 0.370950 | − | 0.642504i | −0.618762 | − | 0.785578i | \(-0.712366\pi\) |
0.989712 | + | 0.143075i | \(0.0456989\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.8995 | + | 2.44949i | −1.08333 | + | 0.148250i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | − | 3.46410i | 0.120605 | − | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.15685 | + | 10.6640i | 0.369930 | + | 0.640737i | 0.989554 | − | 0.144162i | \(-0.0460485\pi\) |
−0.619625 | + | 0.784898i | \(0.712715\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.7990 | −1.42481 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.48528 | 0.267569 | 0.133785 | − | 0.991010i | \(-0.457287\pi\) | ||||
0.133785 | + | 0.991010i | \(0.457287\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.20711 | + | 7.28692i | 0.250087 | + | 0.433163i | 0.963549 | − | 0.267530i | \(-0.0862076\pi\) |
−0.713463 | + | 0.700693i | \(0.752874\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −16.5711 | + | 28.7019i | −0.981585 | + | 1.70016i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.17157 | + | 2.86976i | −0.0691558 | + | 0.169396i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.48528 | + | 14.6969i | −0.499134 | + | 0.864526i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.24264 | − | 14.2767i | −0.483192 | − | 0.836913i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.6274 | −0.971384 | −0.485692 | − | 0.874130i | \(-0.661432\pi\) | ||||
−0.485692 | + | 0.874130i | \(0.661432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.0711 | 1.98369 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.0857864 | + | 0.148586i | 0.00497783 | + | 0.00862186i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.58579 | + | 7.94282i | −0.265203 | + | 0.459345i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.65685 | − | 4.05845i | 0.0954995 | − | 0.233925i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.20711 | + | 7.28692i | −0.241692 | + | 0.418623i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.08579 | + | 8.80884i | 0.291211 | + | 0.504393i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.6569 | −1.46431 | −0.732157 | − | 0.681136i | \(-0.761486\pi\) | ||||
−0.732157 | + | 0.681136i | \(0.761486\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.4853 | 0.767151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.6213 | − | 23.5928i | −0.772394 | − | 1.33783i | −0.936247 | − | 0.351341i | \(-0.885726\pi\) |
0.163853 | − | 0.986485i | \(-0.447608\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.6421 | + | 23.6289i | −0.771099 | + | 1.33558i | 0.165862 | + | 0.986149i | \(0.446959\pi\) |
−0.936961 | + | 0.349434i | \(0.886374\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.3848 | + | 3.88437i | −1.59930 | + | 0.218859i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.1569 | − | 27.9845i | 0.907459 | − | 1.57177i | 0.0898778 | − | 0.995953i | \(-0.471352\pi\) |
0.817582 | − | 0.575813i | \(-0.195314\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.585786 | + | 1.01461i | 0.0327977 | + | 0.0568074i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 16.6569 | 0.929695 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.8995 | 1.16288 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.6569 | + | 23.6544i | 0.757546 | + | 1.31211i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.6924 | + | 28.9121i | −0.923091 | + | 1.59884i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.2990 | − | 15.8601i | −0.678065 | − | 0.874398i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.7929 | − | 22.1579i | 0.703161 | − | 1.21791i | −0.264190 | − | 0.964471i | \(-0.585105\pi\) |
0.967351 | − | 0.253440i | \(-0.0815620\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.75736 | + | 6.50794i | 0.205902 | + | 0.356633i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 43.0416 | 2.35162 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.8284 | 0.807756 | 0.403878 | − | 0.914813i | \(-0.367662\pi\) | ||||
0.403878 | + | 0.914813i | \(0.367662\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.2426 | − | 21.2049i | −0.664929 | − | 1.15169i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.74264 | + | 3.01834i | −0.0943693 | + | 0.163452i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.9853 | + | 25.9553i | −0.806780 | + | 1.39738i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.55025 | + | 13.0774i | 0.405319 | + | 0.702033i | 0.994359 | − | 0.106071i | \(-0.0338272\pi\) |
−0.589040 | + | 0.808104i | \(0.700494\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.8284 | 0.579632 | 0.289816 | − | 0.957082i | \(-0.406406\pi\) | ||||
0.289816 | + | 0.957082i | \(0.406406\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.17157 | −0.0625339 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.91421 | − | 6.77962i | −0.208333 | − | 0.360843i | 0.742857 | − | 0.669450i | \(-0.233470\pi\) |
−0.951189 | + | 0.308608i | \(0.900137\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.48528 | − | 7.76874i | 0.238054 | − | 0.412322i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 22.8137 | + | 29.4194i | 1.20743 | + | 1.55704i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.6924 | + | 21.9839i | −0.669879 | + | 1.16026i | 0.308059 | + | 0.951367i | \(0.400321\pi\) |
−0.977938 | + | 0.208897i | \(0.933013\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.07107 | + | 5.31925i | 0.161635 | + | 0.279960i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 26.1421 | 1.37211 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.7990 | −0.669930 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.8640 | + | 25.7451i | 0.775892 | + | 1.34389i | 0.934292 | + | 0.356510i | \(0.116033\pi\) |
−0.158399 | + | 0.987375i | \(0.550633\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.65685 | − | 2.86976i | 0.0862524 | − | 0.149394i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.62132 | − | 0.358719i | 0.136092 | − | 0.0186238i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.15685 | + | 12.3960i | −0.370568 | + | 0.641842i | −0.989653 | − | 0.143482i | \(-0.954170\pi\) |
0.619085 | + | 0.785324i | \(0.287504\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.5208 | + | 37.2751i | 1.11133 | + | 1.92488i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.00000 | −0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.02944 | 0.0528786 | 0.0264393 | − | 0.999650i | \(-0.491583\pi\) | ||||
0.0264393 | + | 0.999650i | \(0.491583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.82843 | − | 11.8272i | −0.349831 | − | 0.605925i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.37868 | + | 2.38794i | −0.0704472 | + | 0.122018i | −0.899097 | − | 0.437749i | \(-0.855776\pi\) |
0.828650 | + | 0.559767i | \(0.189109\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.58579 | + | 3.88437i | −0.0808192 | + | 0.197966i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.34315 | + | 4.05845i | −0.119109 | + | 0.206302i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.9142 | − | 20.6360i | −0.604075 | − | 1.04629i | −0.992197 | − | 0.124680i | \(-0.960210\pi\) |
0.388122 | − | 0.921608i | \(-0.373124\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.8995 | 0.955789 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −42.7990 | −2.15892 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.4497 | − | 26.7597i | −0.777361 | − | 1.34643i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.91421 | − | 8.51167i | 0.246637 | − | 0.427188i | −0.715953 | − | 0.698148i | \(-0.754008\pi\) |
0.962591 | + | 0.270960i | \(0.0873410\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.65685 | − | 21.2049i | 0.433385 | − | 1.06157i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.08579 | + | 1.88064i | −0.0542216 | + | 0.0939145i | −0.891862 | − | 0.452307i | \(-0.850601\pi\) |
0.837641 | + | 0.546222i | \(0.183934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.8995 | − | 20.6105i | −0.592756 | − | 1.02668i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −36.3137 | −1.80444 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.10051 | 0.0545500 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.2279 | + | 31.5717i | 0.901313 | + | 1.56112i | 0.825792 | + | 0.563975i | \(0.190729\pi\) |
0.0755210 | + | 0.997144i | \(0.475938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.6924 | + | 35.8403i | −1.02068 | + | 1.76787i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −23.3284 | + | 3.19242i | −1.14792 | + | 0.157089i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 29.3137 | − | 50.7728i | 1.43895 | − | 2.49234i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.82843 | + | 15.2913i | 0.432330 | + | 0.748817i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.65685 | 0.0809426 | 0.0404713 | − | 0.999181i | \(-0.487114\pi\) | ||||
0.0404713 | + | 0.999181i | \(0.487114\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.485281 | 0.0236512 | 0.0118256 | − | 0.999930i | \(-0.496236\pi\) | ||||
0.0118256 | + | 0.999930i | \(0.496236\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.7279 | + | 18.5813i | 0.521609 | + | 0.903454i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 28.1421 | − | 48.7436i | 1.36509 | − | 2.36441i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.30761 | − | 5.55487i | −0.208460 | − | 0.268819i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.41421 | − | 2.44949i | 0.0682789 | − | 0.118262i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.6213 | − | 18.3967i | −0.511611 | − | 0.886136i | −0.999909 | − | 0.0134595i | \(-0.995716\pi\) |
0.488298 | − | 0.872677i | \(-0.337618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.4853 | 1.36892 | 0.684458 | − | 0.729053i | \(-0.260039\pi\) | ||||
0.684458 | + | 0.729053i | \(0.260039\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −26.1421 | −1.25342 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.81371 | − | 10.0696i | −0.278107 | − | 0.481696i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.3492 | + | 31.7818i | −0.875762 | + | 1.51686i | −0.0198123 | + | 0.999804i | \(0.506307\pi\) |
−0.855949 | + | 0.517060i | \(0.827026\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.0711 | − | 5.31925i | 0.908146 | − | 0.253297i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.0355 | + | 22.5782i | −0.619337 | + | 1.07272i | 0.370270 | + | 0.928924i | \(0.379265\pi\) |
−0.989607 | + | 0.143799i | \(0.954068\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.2279 | + | 29.8396i | 0.816682 | + | 1.41453i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −28.5563 | −1.35067 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.82843 | 0.322253 | 0.161127 | − | 0.986934i | \(-0.448487\pi\) | ||||
0.161127 | + | 0.986934i | \(0.448487\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.242641 | − | 0.420266i | −0.0114255 | − | 0.0197896i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.8137 | − | 39.5145i | 1.07188 | − | 1.85655i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.5563 | − | 22.6398i | −0.823054 | − | 1.06137i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.6421 | − | 32.2891i | 0.872042 | − | 1.51042i | 0.0121619 | − | 0.999926i | \(-0.496129\pi\) |
0.859880 | − | 0.510496i | \(-0.170538\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.20711 | + | 2.09077i | 0.0563429 | + | 0.0975888i | ||||
\(460\) | 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 | ||||||||
\(465\) | −38.8848 | − | 67.3504i | −1.80324 | − | 3.12330i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.27817 | − | 16.0703i | 0.429343 | − | 0.743643i | −0.567472 | − | 0.823393i | \(-0.692079\pi\) |
0.996815 | + | 0.0797491i | \(0.0254119\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −29.4706 | + | 4.03295i | −1.36082 | + | 0.186225i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.9350 | − | 43.1887i | 1.14895 | − | 1.99003i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.343146 | + | 0.594346i | 0.0157779 | + | 0.0273281i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.6274 | −1.58881 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.82843 | −0.129505 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.3492 | + | 26.5857i | 0.701325 | + | 1.21473i | 0.968002 | + | 0.250944i | \(0.0807410\pi\) |
−0.266677 | + | 0.963786i | \(0.585926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.75736 | + | 6.50794i | −0.171321 | + | 0.296736i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 7.82843 | − | 19.1757i | 0.356206 | − | 0.872522i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.0711 | − | 22.6398i | 0.593527 | − | 1.02802i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.86396 | + | 11.8887i | 0.311036 | + | 0.538730i | 0.978587 | − | 0.205834i | \(-0.0659908\pi\) |
−0.667551 | + | 0.744564i | \(0.732657\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 36.7990 | 1.66411 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.65685 | 0.345549 | 0.172774 | − | 0.984961i | \(-0.444727\pi\) | ||||
0.172774 | + | 0.984961i | \(0.444727\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.24264 | + | 14.2767i | 0.371230 | + | 0.642989i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.24264 | − | 3.88437i | 0.100799 | − | 0.174589i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.34315 | + | 5.73951i | −0.105104 | + | 0.257452i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.2782 | − | 22.9985i | 0.594413 | − | 1.02955i | −0.399217 | − | 0.916857i | \(-0.630718\pi\) |
0.993629 | − | 0.112696i | \(-0.0359488\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.41421 | − | 4.18154i | −0.107859 | − | 0.186817i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.6569 | 0.965631 | 0.482816 | − | 0.875722i | \(-0.339614\pi\) | ||||
0.482816 | + | 0.875722i | \(0.339614\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.3431 | −0.593762 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.03553 | − | 10.4539i | −0.268047 | − | 0.464272i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.2574 | + | 21.2304i | −0.543298 | + | 0.941020i | 0.455414 | + | 0.890280i | \(0.349491\pi\) |
−0.998712 | + | 0.0507398i | \(0.983842\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.76346 | − | 1.19925i | 0.387672 | − | 0.0530518i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.742641 | − | 1.28629i | 0.0327884 | − | 0.0567912i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.6924 | + | 18.5198i | 0.471163 | + | 0.816078i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.14214 | 0.138191 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.5563 | −1.16569 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.50000 | − | 6.06218i | −0.153338 | − | 0.265589i | 0.779115 | − | 0.626881i | \(-0.215669\pi\) |
−0.932453 | + | 0.361293i | \(0.882336\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.86396 | + | 6.69258i | −0.168959 | + | 0.292646i | −0.938054 | − | 0.346489i | \(-0.887374\pi\) |
0.769095 | + | 0.639134i | \(0.220707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −37.7990 | − | 48.7436i | −1.64968 | − | 2.12735i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −24.5208 | + | 42.4713i | −1.06814 | + | 1.85008i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.24264 | + | 10.8126i | 0.271419 | + | 0.470112i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.1716 | 1.09235 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.31371 | 0.143533 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2071 | + | 22.8754i | 0.570993 | + | 0.988989i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10.1569 | + | 17.5922i | −0.438301 | + | 0.759159i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.721825 | − | 2.80821i | 0.0310912 | − | 0.120958i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0858 | − | 17.4691i | 0.433622 | − | 0.751055i | −0.563560 | − | 0.826075i | \(-0.690569\pi\) |
0.997182 | + | 0.0750200i | \(0.0239021\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.0711 | + | 27.8359i | 0.689676 | + | 1.19455i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −52.9411 | −2.26775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9706 | 0.982150 | 0.491075 | − | 0.871117i | \(-0.336604\pi\) | ||||
0.491075 | + | 0.871117i | \(0.336604\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.75736 | + | 6.50794i | 0.160360 | + | 0.277752i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.07107 | − | 8.78335i | 0.216035 | − | 0.374183i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.0858 | + | 16.8747i | 0.556464 | + | 0.717587i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.2782 | + | 21.2664i | −0.521179 | + | 0.902709i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.91421 | + | 5.04757i | 0.123479 | + | 0.213872i | 0.921137 | − | 0.389237i | \(-0.127261\pi\) |
−0.797658 | + | 0.603110i | \(0.793928\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.68629 | −0.198209 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.82843 | −0.246076 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.0355339 | + | 0.0615465i | 0.00149758 | + | 0.00259388i | 0.866773 | − | 0.498703i | \(-0.166190\pi\) |
−0.865276 | + | 0.501296i | \(0.832857\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.4142 | − | 33.6264i | 0.816762 | − | 1.41467i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 24.8640 | − | 3.40256i | 1.04419 | − | 0.142894i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.6716 | + | 21.9478i | −0.531220 | + | 0.920100i | 0.468116 | + | 0.883667i | \(0.344933\pi\) |
−0.999336 | + | 0.0364330i | \(0.988400\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.79289 | − | 13.4977i | −0.326122 | − | 0.564861i | 0.655616 | − | 0.755094i | \(-0.272409\pi\) |
−0.981739 | + | 0.190233i | \(0.939076\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.3137 | 1.09927 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.3137 | −1.30587 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.5000 | − | 33.7750i | −0.811796 | − | 1.40607i | −0.911606 | − | 0.411065i | \(-0.865157\pi\) |
0.0998105 | − | 0.995006i | \(-0.468176\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 23.1066 | − | 40.0218i | 0.960278 | − | 1.66325i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.3137 | + | 37.5108i | −0.635320 | + | 1.55621i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.207107 | + | 0.358719i | −0.00857749 | + | 0.0148566i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.3137 | + | 26.5241i | 0.633144 | + | 1.09664i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.97056 | 0.205157 | 0.102579 | − | 0.994725i | \(-0.467291\pi\) | ||||
0.102579 | + | 0.994725i | \(0.467291\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.1716 | 1.24320 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.8995 | − | 27.5387i | −0.654018 | − | 1.13279i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.74264 | − | 9.94655i | 0.235822 | − | 0.408456i | −0.723689 | − | 0.690126i | \(-0.757555\pi\) |
0.959511 | + | 0.281670i | \(0.0908884\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22.3137 | + | 54.6572i | −0.914773 | + | 2.24073i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.32843 | + | 5.76500i | −0.136223 | + | 0.235946i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.93503 | − | 15.4759i | −0.365075 | − | 0.632329i | 0.623713 | − | 0.781654i | \(-0.285623\pi\) |
−0.988788 | + | 0.149324i | \(0.952290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.14214 | −0.0873795 | −0.0436898 | − | 0.999045i | \(-0.513911\pi\) | ||||
−0.0436898 | + | 0.999045i | \(0.513911\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 31.7990 | 1.29495 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.7279 | + | 35.9018i | 0.842710 | + | 1.45962i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.692388 | + | 1.19925i | −0.0281032 | + | 0.0486761i | −0.879735 | − | 0.475464i | \(-0.842280\pi\) |
0.851632 | + | 0.524141i | \(0.175613\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.8995 | − | 2.44949i | 0.725324 | − | 0.0992583i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.7279 | + | 18.5813i | −0.434005 | + | 0.751719i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.7426 | − | 18.6068i | −0.433891 | − | 0.751522i | 0.563313 | − | 0.826243i | \(-0.309526\pi\) |
−0.997204 | + | 0.0747219i | \(0.976193\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.8284 | 0.436644 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.1127 | −1.73565 | −0.867826 | − | 0.496868i | \(-0.834483\pi\) | ||||
−0.867826 | + | 0.496868i | \(0.834483\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.0355 | + | 27.7744i | 0.644523 | + | 1.11635i | 0.984412 | + | 0.175880i | \(0.0562771\pi\) |
−0.339889 | + | 0.940466i | \(0.610390\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.671573 | − | 1.16320i | 0.0269493 | − | 0.0466775i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.5919 | − | 18.8169i | −0.584611 | − | 0.753884i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.98528 | + | 17.2950i | −0.399411 | + | 0.691801i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.79289 | + | 3.10538i | 0.0716013 | + | 0.124017i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.4853 | 0.617439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.3431 | −0.730229 | −0.365115 | − | 0.930963i | \(-0.618970\pi\) | ||||
−0.365115 | + | 0.930963i | \(0.618970\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.4853 | + | 25.0892i | 0.575738 | + | 0.997208i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.8284 | − | 18.7554i | 0.429713 | − | 0.744285i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.1421 | + | 13.8564i | 0.560332 | + | 0.549011i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.31371 | − | 5.73951i | 0.131088 | − | 0.227052i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.50000 | + | 14.7224i | 0.335730 | + | 0.581501i | 0.983625 | − | 0.180229i | \(-0.0576838\pi\) |
−0.647895 | + | 0.761730i | \(0.724350\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −44.9706 | −1.77347 | −0.886733 | − | 0.462282i | \(-0.847031\pi\) | ||||
−0.886733 | + | 0.462282i | \(0.847031\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −15.3137 | −0.602977 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.9350 | − | 22.4041i | −0.508528 | − | 0.880797i | −0.999951 | − | 0.00987597i | \(-0.996856\pi\) |
0.491423 | − | 0.870921i | \(-0.336477\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.84315 | − | 3.19242i | 0.0723498 | − | 0.125314i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 32.9350 | + | 42.4713i | 1.29083 | + | 1.66458i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.4706 | + | 25.0637i | −0.566277 | + | 0.980820i | 0.430653 | + | 0.902518i | \(0.358283\pi\) |
−0.996930 | + | 0.0783026i | \(0.975050\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −33.9350 | − | 58.7772i | −1.32595 | − | 2.29662i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.45584 | −0.368908 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.6274 | 0.413985 | 0.206993 | − | 0.978342i | \(-0.433632\pi\) | ||||
0.206993 | + | 0.978342i | \(0.433632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.67157 | + | 16.7517i | 0.376181 | + | 0.651564i | 0.990503 | − | 0.137491i | \(-0.0439039\pi\) |
−0.614322 | + | 0.789055i | \(0.710571\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.8995 | − | 34.4669i | 0.772832 | − | 1.33858i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 35.9853 | − | 4.92447i | 1.39545 | − | 0.190963i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.58579 | − | 7.94282i | 0.177562 | − | 0.307547i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.4853 | − | 28.5533i | −0.637358 | − | 1.10394i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.10051 | 0.0424845 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.1421 | 1.00771 | 0.503853 | − | 0.863790i | \(-0.331915\pi\) | ||||
0.503853 | + | 0.863790i | \(0.331915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.00000 | − | 3.46410i | −0.0769800 | − | 0.133333i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.3995 | + | 18.0125i | −0.399685 | + | 0.692275i | −0.993687 | − | 0.112189i | \(-0.964214\pi\) |
0.594002 | + | 0.804464i | \(0.297547\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.82843 | + | 16.7262i | −0.262051 | + | 0.641891i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.32843 | − | 4.03295i | 0.0892255 | − | 0.154543i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.2782 | − | 42.0510i | −0.928979 | − | 1.60904i | −0.785034 | − | 0.619452i | \(-0.787355\pi\) |
−0.143944 | − | 0.989586i | \(-0.545979\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −65.6274 | −2.50749 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.7279 | 0.905277 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.41421 | − | 2.44949i | −0.0538772 | − | 0.0933181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.5208 | + | 18.2226i | −0.400231 | + | 0.693220i | −0.993754 | − | 0.111597i | \(-0.964403\pi\) |
0.593523 | + | 0.804817i | \(0.297737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.17157 | + | 2.86976i | −0.0445044 | + | 0.109013i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.0000 | + | 24.2487i | −0.531050 | + | 0.919806i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.41421 | − | 5.91359i | −0.129323 | − | 0.223993i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.8995 | −0.714845 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.0000 | 0.528773 | 0.264386 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264386 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.76346 | − | 8.25055i | −0.179657 | − | 0.311175i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −35.0563 | + | 60.7194i | −1.32030 | + | 2.28682i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.13604 | − | 1.25024i | 0.343596 | − | 0.0470200i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.2990 | + | 36.8909i | −0.799900 | + | 1.38547i | 0.119780 | + | 0.992800i | \(0.461781\pi\) |
−0.919680 | + | 0.392668i | \(0.871552\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.4142 | − | 19.7700i | −0.428066 | − | 0.741433i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 27.2843 | 1.02180 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.48528 | 0.167740 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 25.7279 | + | 44.5621i | 0.960827 | + | 1.66420i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.52082 | + | 14.7585i | −0.317773 | + | 0.550399i | −0.980023 | − | 0.198884i | \(-0.936268\pi\) |
0.662250 | + | 0.749283i | \(0.269602\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.05635 | − | 11.6786i | −0.337276 | − | 0.434934i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.8640 | + | 25.7451i | −0.552797 | + | 0.957472i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.6569 | − | 23.6544i | −0.507203 | − | 0.878501i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.6569 | −1.69332 | −0.846659 | − | 0.532135i | \(-0.821390\pi\) | ||||
−0.846659 | + | 0.532135i | \(0.821390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8284 | −0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.82843 | + | 8.36308i | 0.178586 | + | 0.309320i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.1569 | + | 40.1088i | −0.855318 | + | 1.48145i | 0.0210318 | + | 0.999779i | \(0.493305\pi\) |
−0.876350 | + | 0.481675i | \(0.840028\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 46.2132 | + | 45.2795i | 1.70460 | + | 1.67016i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.32843 | − | 4.03295i | 0.0857687 | − | 0.148556i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.3492 | + | 45.6382i | 0.969273 | + | 1.67883i | 0.697669 | + | 0.716420i | \(0.254221\pi\) |
0.271603 | + | 0.962409i | \(0.412446\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.4853 | −0.899489 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.6569 | −1.38150 | −0.690748 | − | 0.723096i | \(-0.742719\pi\) | ||||
−0.690748 | + | 0.723096i | \(0.742719\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.6421 | − | 39.2173i | −0.829544 | − | 1.43681i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 21.6569 | − | 37.5108i | 0.792383 | − | 1.37245i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −11.1863 | − | 14.4253i | −0.408738 | − | 0.527087i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.86396 | + | 3.22848i | −0.0680169 | + | 0.117809i | −0.898028 | − | 0.439938i | \(-0.855001\pi\) |
0.830011 | + | 0.557746i | \(0.188334\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.58579 | − | 6.21076i | −0.130673 | − | 0.226333i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 72.3553 | 2.63328 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.1421 | 0.804770 | 0.402385 | − | 0.915471i | \(-0.368181\pi\) | ||||
0.402385 | + | 0.915471i | \(0.368181\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.62132 | + | 2.80821i | 0.0588502 | + | 0.101932i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0563 | + | 17.4181i | −0.364542 | + | 0.631406i | −0.988703 | − | 0.149890i | \(-0.952108\pi\) |
0.624160 | + | 0.781296i | \(0.285441\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.2487 | − | 4.96053i | 1.31229 | − | 0.179583i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 31.5563 | − | 54.6572i | 1.14092 | − | 1.97614i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.5858 | + | 21.7992i | 0.454446 | + | 0.787124i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.1421 | 1.51968 | 0.759842 | − | 0.650108i | \(-0.225276\pi\) | ||||
0.759842 | + | 0.650108i | \(0.225276\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −51.8701 | −1.86805 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.57107 | − | 16.5776i | −0.344247 | − | 0.596254i | 0.640969 | − | 0.767566i | \(-0.278533\pi\) |
−0.985217 | + | 0.171313i | \(0.945199\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.6274 | − | 70.3688i | 1.45938 | − | 2.52772i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.41421 | − | 15.7116i | 0.230109 | − | 0.563649i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.10051 | + | 3.63818i | −0.0752584 | + | 0.130351i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.485281 | − | 0.840532i | −0.0173647 | − | 0.0300766i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.17157 | 0.0418686 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 79.0833 | 2.82260 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.89340 | + | 3.27946i | 0.0674924 | + | 0.116900i | 0.897797 | − | 0.440410i | \(-0.145167\pi\) |
−0.830305 | + | 0.557310i | \(0.811834\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.7426 | − | 18.6068i | 0.382448 | − | 0.662420i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.1421 | + | 24.8431i | −0.360613 | + | 0.883317i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.75736 | + | 6.50794i | −0.133428 | + | 0.231104i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.62132 | − | 8.00436i | −0.163901 | − | 0.283885i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.1127 | −0.535319 | −0.267660 | − | 0.963514i | \(-0.586250\pi\) | ||||
−0.267660 | + | 0.963514i | \(0.586250\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44.2132 | 1.56415 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.7279 | + | 22.0454i | 0.449719 | + | 0.778936i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.692388 | + | 1.19925i | −0.0244338 | + | 0.0423207i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.5416 | − | 4.45322i | 1.14694 | − | 0.156955i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.62132 | − | 2.80821i | 0.0570732 | − | 0.0988536i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.98528 | − | 13.8309i | −0.280748 | − | 0.486269i | 0.690822 | − | 0.723025i | \(-0.257249\pi\) |
−0.971569 | + | 0.236756i | \(0.923916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.34315 | 0.222738 | 0.111369 | − | 0.993779i | \(-0.464476\pi\) | ||||
0.111369 | + | 0.993779i | \(0.464476\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.4853 | 1.03409 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29.1777 | + | 50.5372i | 1.02205 | + | 1.77024i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.97056 | − | 5.14517i | 0.103927 | − | 0.180007i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.9706 | − | 16.7262i | −0.453228 | − | 0.584459i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.57107 | − | 11.3814i | 0.229332 | − | 0.397214i | −0.728278 | − | 0.685281i | \(-0.759679\pi\) |
0.957610 | + | 0.288067i | \(0.0930126\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0061 | + | 29.4554i | 0.592795 | + | 1.02675i | 0.993854 | + | 0.110699i | \(0.0353090\pi\) |
−0.401059 | + | 0.916052i | \(0.631358\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.65685 | 0.336209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.3431 | −1.05513 | −0.527567 | − | 0.849513i | \(-0.676896\pi\) | ||||
−0.527567 | + | 0.849513i | \(0.676896\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.3995 | − | 35.3330i | −0.708504 | − | 1.22716i | −0.965412 | − | 0.260729i | \(-0.916037\pi\) |
0.256908 | − | 0.966436i | \(-0.417296\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.8640 | + | 25.7451i | −0.515625 | + | 0.893089i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.1569 | − | 39.5145i | 0.351914 | − | 1.36910i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.82843 | − | 6.63103i | 0.132488 | − | 0.229476i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.74264 | + | 3.01834i | 0.0602345 | + | 0.104329i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.3137 | −0.666783 | −0.333392 | − | 0.942788i | \(-0.608193\pi\) | ||||
−0.333392 | + | 0.942788i | \(0.608193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.0000 | −0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.41421 | + | 9.37769i | 0.186475 | + | 0.322985i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.57107 | − | 16.5776i | 0.329255 | − | 0.570286i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.5563 | − | 22.6398i | −0.603243 | − | 0.777911i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.1569 | + | 17.5922i | −0.348582 | + | 0.603762i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.30761 | − | 7.46100i | −0.147663 | − | 0.255760i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.5147 | −0.805129 | −0.402564 | − | 0.915392i | \(-0.631881\pi\) | ||||
−0.402564 | + | 0.915392i | \(0.631881\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −38.8284 | −1.32790 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.3284 | − | 31.7458i | −0.626087 | − | 1.08441i | −0.988330 | − | 0.152331i | \(-0.951322\pi\) |
0.362242 | − | 0.932084i | \(-0.382011\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.2782 | − | 31.6587i | 0.623643 | − | 1.08018i | −0.365158 | − | 0.930945i | \(-0.618985\pi\) |
0.988802 | − | 0.149236i | \(-0.0476815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.41421 | + | 1.01461i | −0.252676 | + | 0.0345779i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.69239 | + | 2.93130i | −0.0576096 | + | 0.0997827i | −0.893392 | − | 0.449278i | \(-0.851681\pi\) |
0.835782 | + | 0.549061i | \(0.185015\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0563 | − | 36.4707i | −0.715937 | − | 1.24004i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −40.9706 | −1.39143 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.34315 | −0.113408 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.8995 | + | 27.5387i | 0.538734 | + | 0.933114i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.65685 | − | 16.7262i | 0.326835 | − | 0.566095i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17.8284 | − | 43.6705i | 0.602711 | − | 1.47633i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.7132 | − | 28.9481i | 0.564365 | − | 0.977508i | −0.432744 | − | 0.901517i | \(-0.642454\pi\) |
0.997108 | − | 0.0759915i | \(-0.0242122\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.0711 | − | 34.7641i | −0.676980 | − | 1.17256i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.0000 | −0.875962 | −0.437981 | − | 0.898984i | \(-0.644306\pi\) | ||||
−0.437981 | + | 0.898984i | \(0.644306\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.2548 | −1.65756 | −0.828779 | − | 0.559577i | \(-0.810964\pi\) | ||||
−0.828779 | + | 0.559577i | \(0.810964\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 41.1274 | + | 71.2348i | 1.38248 | + | 2.39453i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.4497 | − | 44.0803i | 0.854519 | − | 1.48007i | −0.0225717 | − | 0.999745i | \(-0.507185\pi\) |
0.877091 | − | 0.480325i | \(-0.159481\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.65685 | + | 13.8564i | −0.189725 | + | 0.464729i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.96447 | + | 3.40256i | −0.0658121 | + | 0.113990i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.6005 | − | 23.5568i | −0.455124 | − | 0.788297i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.2132 | −1.07677 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.1421 | −0.739304 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.8995 | + | 20.6105i | 0.396870 | + | 0.687400i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.91421 | + | 5.04757i | −0.0970865 | + | 0.168159i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.4853 | − | 1.43488i | 0.348928 | − | 0.0477497i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.4853 | + | 44.1418i | −0.847159 | + | 1.46732i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.7635 | − | 34.2313i | −0.656235 | − | 1.13663i | −0.981583 | − | 0.191038i | \(-0.938815\pi\) |
0.325348 | − | 0.945594i | \(-0.394519\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.85786 | −0.326965 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.00000 | −0.265052 | −0.132526 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132526 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.17157 | − | 5.49333i | −0.104964 | − | 0.181803i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.2782 | + | 21.2664i | −0.405904 | + | 0.703046i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.7426 | + | 37.0650i | 0.949166 | + | 1.22399i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.2782 | − | 21.2664i | 0.405020 | − | 0.701515i | −0.589304 | − | 0.807911i | \(-0.700598\pi\) |
0.994324 | + | 0.106397i | \(0.0339314\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −30.9706 | − | 53.6426i | −1.02051 | − | 1.76758i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.62742 | 0.218144 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.6569 | −0.843592 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.89949 | + | 13.6823i | 0.259453 | + | 0.449387i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.3284 | − | 26.5496i | 0.502909 | − | 0.871065i | −0.497085 | − | 0.867702i | \(-0.665596\pi\) |
0.999994 | − | 0.00336273i | \(-0.00107039\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.1777 | + | 6.74356i | −0.792391 | + | 0.221011i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.8848 | − | 56.9581i | 1.07660 | − | 1.86472i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.62132 | − | 8.00436i | −0.151133 | − | 0.261771i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.6274 | −0.935217 | −0.467608 | − | 0.883936i | \(-0.654884\pi\) | ||||
−0.467608 | + | 0.883936i | \(0.654884\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −65.8701 | −2.14959 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.1274 | − | 45.2540i | −0.851729 | − | 1.47524i | −0.879646 | − | 0.475628i | \(-0.842221\pi\) |
0.0279168 | − | 0.999610i | \(-0.491113\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.89949 | + | 3.29002i | −0.0618561 | + | 0.107138i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.57107 | + | 3.31552i | 0.0836368 | + | 0.107854i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.1066 | − | 20.9692i | 0.393412 | − | 0.681409i | −0.599485 | − | 0.800386i | \(-0.704628\pi\) |
0.992897 | + | 0.118977i | \(0.0379614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.72792 | − | 8.18900i | −0.153475 | − | 0.265826i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 78.0122 | 2.52972 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.1127 | 1.13741 | 0.568706 | − | 0.822541i | \(-0.307444\pi\) | ||||
0.568706 | + | 0.822541i | \(0.307444\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.8640 | + | 36.1374i | 0.675142 | + | 1.16938i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.41421 | + | 2.44949i | −0.0457150 | + | 0.0791808i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 44.9350 | − | 6.14922i | 1.45103 | − | 0.198569i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.8995 | + | 34.4669i | −0.641919 | + | 1.11184i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.75736 | + | 16.9002i | 0.314427 | + | 0.544603i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 73.2843 | 2.35910 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.6569 | 0.953700 | 0.476850 | − | 0.878985i | \(-0.341778\pi\) | ||||
0.476850 | + | 0.878985i | \(0.341778\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.2279 | + | 43.6960i | 0.810438 | + | 1.40372i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2071 | + | 33.2677i | −0.616385 | + | 1.06761i | 0.373754 | + | 0.927528i | \(0.378070\pi\) |
−0.990140 | + | 0.140083i | \(0.955263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.31371 | − | 17.9149i | 0.234467 | − | 0.574324i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −32.9706 | + | 57.1067i | −1.05590 | + | 1.82888i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.7426 | + | 44.5876i | 0.823580 | + | 1.42648i | 0.903000 | + | 0.429641i | \(0.141360\pi\) |
−0.0794196 | + | 0.996841i | \(0.525307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.72792 | 0.119145 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39.1127 | −1.24877 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.4203 | − | 52.6895i | −0.970257 | − | 1.68053i | −0.694773 | − | 0.719229i | \(-0.744495\pi\) |
−0.275484 | − | 0.961306i | \(-0.588838\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.2132 | − | 43.6705i | 0.803359 | − | 1.39146i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 18.3137 | − | 44.8592i | 0.582932 | − | 1.42789i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.68629 | − | 4.65279i | 0.0854191 | − | 0.147950i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.34924 | + | 12.7293i | 0.233456 | + | 0.404358i | 0.958823 | − | 0.284004i | \(-0.0916631\pi\) |
−0.725367 | + | 0.688363i | \(0.758330\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 61.7696 | 1.96020 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.5563 | −0.334659 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.64214 | − | 9.77247i | −0.178688 | − | 0.309497i | 0.762743 | − | 0.646701i | \(-0.223852\pi\) |
−0.941431 | + | 0.337204i | \(0.890519\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.550253 | − | 0.953065i | 0.0174092 | − | 0.0301537i |
(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.i.d.65.2 | yes | 4 | |
3.2 | odd | 2 | 2016.2.s.s.289.2 | 4 | |||
4.3 | odd | 2 | 224.2.i.a.65.1 | ✓ | 4 | ||
7.2 | even | 3 | 1568.2.a.l.1.1 | 2 | |||
7.3 | odd | 6 | 1568.2.i.o.1537.1 | 4 | |||
7.4 | even | 3 | inner | 224.2.i.d.193.2 | yes | 4 | |
7.5 | odd | 6 | 1568.2.a.u.1.2 | 2 | |||
7.6 | odd | 2 | 1568.2.i.o.961.1 | 4 | |||
8.3 | odd | 2 | 448.2.i.j.65.2 | 4 | |||
8.5 | even | 2 | 448.2.i.g.65.1 | 4 | |||
12.11 | even | 2 | 2016.2.s.q.289.2 | 4 | |||
21.11 | odd | 6 | 2016.2.s.s.865.2 | 4 | |||
28.3 | even | 6 | 1568.2.i.x.1537.2 | 4 | |||
28.11 | odd | 6 | 224.2.i.a.193.1 | yes | 4 | ||
28.19 | even | 6 | 1568.2.a.j.1.1 | 2 | |||
28.23 | odd | 6 | 1568.2.a.w.1.2 | 2 | |||
28.27 | even | 2 | 1568.2.i.x.961.2 | 4 | |||
56.5 | odd | 6 | 3136.2.a.be.1.1 | 2 | |||
56.11 | odd | 6 | 448.2.i.j.193.2 | 4 | |||
56.19 | even | 6 | 3136.2.a.bx.1.2 | 2 | |||
56.37 | even | 6 | 3136.2.a.bw.1.2 | 2 | |||
56.51 | odd | 6 | 3136.2.a.bd.1.1 | 2 | |||
56.53 | even | 6 | 448.2.i.g.193.1 | 4 | |||
84.11 | even | 6 | 2016.2.s.q.865.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.2.i.a.65.1 | ✓ | 4 | 4.3 | odd | 2 | ||
224.2.i.a.193.1 | yes | 4 | 28.11 | odd | 6 | ||
224.2.i.d.65.2 | yes | 4 | 1.1 | even | 1 | trivial | |
224.2.i.d.193.2 | yes | 4 | 7.4 | even | 3 | inner | |
448.2.i.g.65.1 | 4 | 8.5 | even | 2 | |||
448.2.i.g.193.1 | 4 | 56.53 | even | 6 | |||
448.2.i.j.65.2 | 4 | 8.3 | odd | 2 | |||
448.2.i.j.193.2 | 4 | 56.11 | odd | 6 | |||
1568.2.a.j.1.1 | 2 | 28.19 | even | 6 | |||
1568.2.a.l.1.1 | 2 | 7.2 | even | 3 | |||
1568.2.a.u.1.2 | 2 | 7.5 | odd | 6 | |||
1568.2.a.w.1.2 | 2 | 28.23 | odd | 6 | |||
1568.2.i.o.961.1 | 4 | 7.6 | odd | 2 | |||
1568.2.i.o.1537.1 | 4 | 7.3 | odd | 6 | |||
1568.2.i.x.961.2 | 4 | 28.27 | even | 2 | |||
1568.2.i.x.1537.2 | 4 | 28.3 | even | 6 | |||
2016.2.s.q.289.2 | 4 | 12.11 | even | 2 | |||
2016.2.s.q.865.2 | 4 | 84.11 | even | 6 | |||
2016.2.s.s.289.2 | 4 | 3.2 | odd | 2 | |||
2016.2.s.s.865.2 | 4 | 21.11 | odd | 6 | |||
3136.2.a.bd.1.1 | 2 | 56.51 | odd | 6 | |||
3136.2.a.be.1.1 | 2 | 56.5 | odd | 6 | |||
3136.2.a.bw.1.2 | 2 | 56.37 | even | 6 | |||
3136.2.a.bx.1.2 | 2 | 56.19 | even | 6 |