Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(367,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 4, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cz (of order \(6\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 607.15 | ||
Character | \(\chi\) | \(=\) | 1008.607 |
Dual form | 1008.2.cz.i.367.15 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.69998 | − | 0.331769i | 0.981483 | − | 0.191547i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.535741 | + | 0.309310i | −0.239591 | + | 0.138328i | −0.614989 | − | 0.788536i | \(-0.710839\pi\) |
0.375398 | + | 0.926864i | \(0.377506\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.62638 | + | 0.319613i | 0.992677 | + | 0.120802i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.77986 | − | 1.12800i | 0.926619 | − | 0.376001i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.58062 | − | 1.48992i | −0.778085 | − | 0.449228i | 0.0576660 | − | 0.998336i | \(-0.481634\pi\) |
−0.835751 | + | 0.549108i | \(0.814967\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.64842 | + | 0.951716i | 0.457190 | + | 0.263959i | 0.710862 | − | 0.703332i | \(-0.248305\pi\) |
−0.253672 | + | 0.967290i | \(0.581638\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.808129 | + | 0.703564i | −0.208658 | + | 0.181659i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.92194 | − | 1.68698i | 0.708675 | − | 0.409154i | −0.101895 | − | 0.994795i | \(-0.532491\pi\) |
0.810570 | + | 0.585641i | \(0.199157\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.13454 | + | 1.96509i | −0.260282 | + | 0.450822i | −0.966317 | − | 0.257355i | \(-0.917149\pi\) |
0.706034 | + | 0.708177i | \(0.250482\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.57082 | − | 0.328016i | 0.997435 | − | 0.0715790i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.84046 | − | 3.37199i | 1.21782 | − | 0.703109i | 0.253369 | − | 0.967370i | \(-0.418461\pi\) |
0.964451 | + | 0.264260i | \(0.0851278\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.30865 | + | 3.99871i | −0.461731 | + | 0.799741i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.35146 | − | 2.83985i | 0.837440 | − | 0.546530i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.74898 | − | 3.02933i | −0.324778 | − | 0.562532i | 0.656689 | − | 0.754161i | \(-0.271956\pi\) |
−0.981467 | + | 0.191629i | \(0.938623\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.35193 | 1.32045 | 0.660223 | − | 0.751070i | \(-0.270462\pi\) | ||||
0.660223 | + | 0.751070i | \(0.270462\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.88130 | − | 1.67666i | −0.849726 | − | 0.291870i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.50592 | + | 0.641135i | −0.254546 | + | 0.108372i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.25230 | + | 5.63315i | −0.534675 | + | 0.926085i | 0.464504 | + | 0.885571i | \(0.346233\pi\) |
−0.999179 | + | 0.0405136i | \(0.987101\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.11803 | + | 1.07100i | 0.499285 | + | 0.171498i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.09363 | − | 5.25021i | −1.42019 | − | 0.819945i | −0.423872 | − | 0.905722i | \(-0.639330\pi\) |
−0.996314 | + | 0.0857766i | \(0.972663\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.48652 | + | 1.43559i | −0.379191 | + | 0.218926i | −0.677466 | − | 0.735554i | \(-0.736922\pi\) |
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.14038 | + | 1.46416i | −0.169998 | + | 0.218264i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.60907 | 0.818167 | 0.409083 | − | 0.912497i | \(-0.365848\pi\) | ||||
0.409083 | + | 0.912497i | \(0.365848\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.79570 | + | 1.67885i | 0.970814 | + | 0.239835i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.40755 | − | 3.83725i | 0.617181 | − | 0.537322i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.50765 | + | 4.34338i | 0.344452 | + | 0.596609i | 0.985254 | − | 0.171097i | \(-0.0547313\pi\) |
−0.640802 | + | 0.767706i | \(0.721398\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.84339 | 0.248563 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.27675 | + | 3.71702i | −0.169109 | + | 0.492331i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.34188 | 0.565265 | 0.282632 | − | 0.959228i | \(-0.408792\pi\) | ||||
0.282632 | + | 0.959228i | \(0.408792\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.63138i | − | 0.464951i | −0.972602 | − | 0.232475i | \(-0.925318\pi\) | ||
0.972602 | − | 0.232475i | \(-0.0746825\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.66147 | − | 2.07408i | 0.965255 | − | 0.261309i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.17750 | −0.146051 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 5.01617i | − | 0.612822i | −0.951899 | − | 0.306411i | \(-0.900872\pi\) | ||
0.951899 | − | 0.306411i | \(-0.0991282\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.80994 | − | 7.67000i | 1.06059 | − | 0.923360i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.18857i | 0.734448i | 0.930132 | + | 0.367224i | \(0.119692\pi\) | ||||
−0.930132 | + | 0.367224i | \(0.880308\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.5278 | + | 7.23291i | −1.46626 | + | 0.846548i | −0.999288 | − | 0.0377215i | \(-0.987990\pi\) |
−0.466976 | + | 0.884270i | \(0.654657\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.59802 | + | 7.56366i | −0.299993 | + | 0.873376i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.30147 | − | 4.73789i | −0.718119 | − | 0.539932i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.0606i | − | 1.35693i | −0.734635 | − | 0.678463i | \(-0.762646\pi\) | ||
0.734635 | − | 0.678463i | \(-0.237354\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.45522 | − | 6.27137i | 0.717247 | − | 0.696819i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.48427 | + | 9.49903i | 0.601977 | + | 1.04265i | 0.992521 | + | 0.122070i | \(0.0389533\pi\) |
−0.390545 | + | 0.920584i | \(0.627713\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.04360 | + | 1.80757i | −0.113195 | + | 0.196059i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.97828 | − | 4.56954i | −0.426516 | − | 0.489906i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.03976 | − | 3.48706i | −0.640213 | − | 0.369627i | 0.144483 | − | 0.989507i | \(-0.453848\pi\) |
−0.784697 | + | 0.619880i | \(0.787181\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.02519 | + | 3.02642i | 0.421955 | + | 0.317255i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 12.4981 | − | 2.43915i | 1.29600 | − | 0.252928i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1.40371i | − | 0.144017i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.71311 | + | 1.56642i | −0.275475 | + | 0.159045i | −0.631373 | − | 0.775479i | \(-0.717508\pi\) |
0.355898 | + | 0.934525i | \(0.384175\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.85438 | − | 1.23082i | −0.889899 | − | 0.123702i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1962 | − | 6.46415i | −1.11407 | − | 0.643207i | −0.174187 | − | 0.984713i | \(-0.555730\pi\) |
−0.939880 | + | 0.341505i | \(0.889063\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.52663 | − | 6.10830i | −0.347489 | − | 0.601869i | 0.638314 | − | 0.769776i | \(-0.279632\pi\) |
−0.985803 | + | 0.167907i | \(0.946299\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.34732 | + | 1.58953i | −0.229075 | + | 0.155123i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.44421 | − | 1.98852i | −0.332964 | − | 0.192237i | 0.324192 | − | 0.945991i | \(-0.394908\pi\) |
−0.657156 | + | 0.753754i | \(0.728241\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.60818 | + | 13.1778i | 0.728731 | + | 1.26220i | 0.957420 | + | 0.288700i | \(0.0932230\pi\) |
−0.228688 | + | 0.973500i | \(0.573444\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.65994 | + | 10.6553i | −0.347386 | + | 1.01135i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.44699 | + | 2.50626i | −0.136121 | + | 0.235769i | −0.926025 | − | 0.377462i | \(-0.876797\pi\) |
0.789904 | + | 0.613231i | \(0.210130\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.08598 | + | 3.61303i | −0.194519 | + | 0.336917i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.65592 | + | 0.786214i | 0.522890 | + | 0.0726855i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.21330 | − | 3.49676i | 0.752912 | − | 0.320548i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.06028 | − | 1.83646i | −0.0963889 | − | 0.166951i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.2008 | − | 5.90826i | −1.55095 | − | 0.532730i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.94947i | − | 0.532136i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.01268i | 0.178596i | 0.996005 | + | 0.0892982i | \(0.0284624\pi\) | ||||
−0.996005 | + | 0.0892982i | \(0.971538\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.75075 | + | 3.26543i | −0.330235 | + | 0.287505i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.03856 | − | 15.6553i | −0.789703 | − | 1.36781i | −0.926149 | − | 0.377158i | \(-0.876901\pi\) |
0.136446 | − | 0.990648i | \(-0.456432\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.60781 | + | 4.79845i | −0.312837 | + | 0.416078i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.45286 | + | 2.86738i | −0.125043 | + | 0.246785i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3621 | + | 17.9477i | −0.885297 | + | 1.53338i | −0.0399235 | + | 0.999203i | \(0.512711\pi\) |
−0.845373 | + | 0.534176i | \(0.820622\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.98194 | + | 6.89693i | −0.337744 | + | 0.584990i | −0.984008 | − | 0.178124i | \(-0.942997\pi\) |
0.646264 | + | 0.763114i | \(0.276330\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.53530 | − | 1.86092i | 0.803017 | − | 0.156718i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.83596 | − | 4.91203i | −0.237155 | − | 0.410765i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.87401 | + | 1.08196i | 0.155628 | + | 0.0898517i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.1095 | + | 0.599400i | 0.998777 | + | 0.0494377i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5029 | − | 18.1915i | −0.860427 | − | 1.49030i | −0.871517 | − | 0.490365i | \(-0.836864\pi\) |
0.0110903 | − | 0.999939i | \(-0.496470\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.8560 | + | 7.42241i | 1.04621 | + | 0.604027i | 0.921585 | − | 0.388177i | \(-0.126895\pi\) |
0.124621 | + | 0.992204i | \(0.460228\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.21966 | − | 7.98553i | 0.502830 | − | 0.645592i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.93873 | + | 2.27403i | −0.316367 | + | 0.182654i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.0499i | 1.67996i | 0.542614 | + | 0.839982i | \(0.317435\pi\) | ||||
−0.542614 | + | 0.839982i | \(0.682565\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.70396 | + | 6.55169i | 0.452353 | + | 0.519583i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.4170 | − | 6.98943i | 1.29384 | − | 0.550844i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.53261 | − | 0.884855i | −0.120044 | − | 0.0693072i | 0.438776 | − | 0.898597i | \(-0.355412\pi\) |
−0.558819 | + | 0.829289i | \(0.688746\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.13373 | − | 0.611581i | 0.243960 | − | 0.0476115i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.50736 | + | 4.34288i | −0.194025 | + | 0.336062i | −0.946581 | − | 0.322467i | \(-0.895488\pi\) |
0.752555 | + | 0.658529i | \(0.228821\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.68847 | − | 8.12067i | −0.360652 | − | 0.624667i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.937249 | + | 6.74244i | −0.0716732 | + | 0.515607i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.13008i | 0.237976i | 0.992896 | + | 0.118988i | \(0.0379650\pi\) | ||||
−0.992896 | + | 0.118988i | \(0.962035\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.34143 | + | 9.76423i | −0.554960 | + | 0.738106i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.38110 | − | 1.44050i | 0.554798 | − | 0.108275i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.1505 | + | 8.74714i | −1.13240 | + | 0.653792i | −0.944538 | − | 0.328404i | \(-0.893489\pi\) |
−0.187863 | + | 0.982195i | \(0.560156\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.76258i | 0.354000i | 0.984211 | + | 0.177000i | \(0.0566392\pi\) | ||||
−0.984211 | + | 0.177000i | \(0.943361\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.20478 | − | 6.17327i | −0.0890600 | − | 0.456341i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4.02388i | − | 0.295842i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0539 | −0.735213 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.3362 | − | 6.06773i | 0.897329 | − | 0.441363i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.60774i | 0.695191i | 0.937645 | + | 0.347596i | \(0.113002\pi\) | ||||
−0.937645 | + | 0.347596i | \(0.886998\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.1521 | 1.09067 | 0.545336 | − | 0.838218i | \(-0.316402\pi\) | ||||
0.545336 | + | 0.838218i | \(0.316402\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.00173 | + | 0.390660i | −0.143347 | + | 0.0279757i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.93656 | −0.351715 | −0.175858 | − | 0.984416i | \(-0.556270\pi\) | ||||
−0.175858 | + | 0.984416i | \(0.556270\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.3771 | − | 19.7058i | −0.806503 | − | 1.39690i | −0.915272 | − | 0.402837i | \(-0.868024\pi\) |
0.108769 | − | 0.994067i | \(-0.465309\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.66421 | − | 8.52738i | −0.117384 | − | 0.601475i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.62528 | − | 8.51516i | −0.254445 | − | 0.597647i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.49578 | 0.453685 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.4320 | − | 15.9617i | 0.864087 | − | 1.10942i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.85565 | − | 3.38076i | 0.405044 | − | 0.233852i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.10815 | − | 1.79449i | −0.213974 | − | 0.123538i | 0.389183 | − | 0.921160i | \(-0.372757\pi\) |
−0.603157 | + | 0.797623i | \(0.706091\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.05318 | + | 10.5204i | 0.140682 | + | 0.720849i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.888088 | − | 1.53821i | 0.0605671 | − | 0.104905i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.3089 | + | 2.34977i | 1.31078 | + | 0.159513i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.8973 | + | 16.4521i | −1.27696 | + | 1.11173i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.42212 | 0.431999 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.12744 | + | 8.88098i | 0.343358 | + | 0.594714i | 0.985054 | − | 0.172245i | \(-0.0551021\pi\) |
−0.641696 | + | 0.766959i | \(0.721769\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.90718 | + | 13.7200i | −0.127145 | + | 0.914667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.19572 | + | 12.4634i | −0.477597 | + | 0.827222i | −0.999670 | − | 0.0256788i | \(-0.991825\pi\) |
0.522074 | + | 0.852900i | \(0.325159\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.35284 | + | 1.93576i | −0.221562 | + | 0.127919i | −0.606673 | − | 0.794951i | \(-0.707496\pi\) |
0.385111 | + | 0.922870i | \(0.374163\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.2843 | − | 5.96367i | −0.808245 | − | 0.392381i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.84465 | − | 10.1232i | 0.382896 | − | 0.663195i | −0.608579 | − | 0.793493i | \(-0.708260\pi\) |
0.991475 | + | 0.130298i | \(0.0415935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00501 | + | 1.73494i | −0.196025 | + | 0.113175i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.00134 | − | 20.5028i | −0.259915 | − | 1.33180i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.38726 | − | 3.11033i | −0.348473 | − | 0.201191i | 0.315540 | − | 0.948912i | \(-0.397814\pi\) |
−0.664012 | + | 0.747722i | \(0.731148\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.7081 | − | 8.49173i | −0.947433 | − | 0.547001i | −0.0551504 | − | 0.998478i | \(-0.517564\pi\) |
−0.892283 | + | 0.451477i | \(0.850897\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.89309 | − | 12.8028i | 0.570492 | − | 0.821303i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.16002 | + | 1.20255i | −0.265774 | + | 0.0768282i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.74042 | + | 2.15953i | −0.237997 | + | 0.137408i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.4746 | + | 14.3286i | 0.790548 | + | 0.908041i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.3406 | −1.72572 | −0.862861 | − | 0.505442i | \(-0.831330\pi\) | ||||
−0.862861 | + | 0.505442i | \(0.831330\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0960 | −1.26342 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.17441 | + | 3.41907i | −0.0735442 | + | 0.214111i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0373645 | + | 0.0215724i | −0.00233074 | + | 0.00134565i | −0.501165 | − | 0.865352i | \(-0.667095\pi\) |
0.498834 | + | 0.866697i | \(0.333762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.3422 | + | 13.7553i | −0.642633 | + | 0.854713i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.27902 | − | 6.44825i | −0.512458 | − | 0.399137i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.4150 | + | 7.74514i | 0.827203 | + | 0.477586i | 0.852894 | − | 0.522084i | \(-0.174845\pi\) |
−0.0256913 | + | 0.999670i | \(0.508179\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.68690 | − | 1.55129i | −0.165055 | − | 0.0952947i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.4244 | − | 3.92412i | −0.699160 | − | 0.240152i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.9814 | + | 14.4230i | −1.52314 | + | 0.879385i | −0.523515 | + | 0.852017i | \(0.675380\pi\) |
−0.999625 | + | 0.0273690i | \(0.991287\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.16925 | + | 12.4175i | −0.435501 | + | 0.754310i | −0.997336 | − | 0.0729394i | \(-0.976762\pi\) |
0.561836 | + | 0.827249i | \(0.310095\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.84682 | + | 3.80942i | 0.474911 | + | 0.230556i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.9155 | − | 6.87942i | 0.718532 | − | 0.414845i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.30158 | + | 12.6467i | −0.438709 | + | 0.759867i | −0.997590 | − | 0.0693811i | \(-0.977898\pi\) |
0.558881 | + | 0.829248i | \(0.311231\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.4373 | − | 8.29299i | 1.22355 | − | 0.496489i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.04644 | + | 1.81248i | 0.0624251 | + | 0.108123i | 0.895549 | − | 0.444963i | \(-0.146783\pi\) |
−0.833124 | + | 0.553087i | \(0.813450\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.81783 | −0.226946 | −0.113473 | − | 0.993541i | \(-0.536198\pi\) | ||||
−0.113473 | + | 0.993541i | \(0.536198\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.465707 | − | 2.38627i | −0.0275861 | − | 0.141350i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.2053 | − | 16.6955i | −1.31073 | − | 0.985502i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.80817 | + | 4.86389i | −0.165186 | + | 0.286111i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.09255 | + | 3.56300i | −0.239909 | + | 0.208867i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.7432 | − | 6.77992i | −0.686043 | − | 0.396087i | 0.116085 | − | 0.993239i | \(-0.462966\pi\) |
−0.802128 | + | 0.597152i | \(0.796299\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.32612 | + | 1.34299i | −0.135432 | + | 0.0781918i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −15.4606 | + | 0.845237i | −0.897116 | + | 0.0490456i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.8367 | 0.742367 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.98937 | + | 2.97568i | −0.402861 | + | 0.171516i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.1780 | − | 7.27435i | −1.21664 | − | 0.417901i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.12322 | + | 1.94548i | 0.0643156 | + | 0.111398i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.0932072 | 0.00531961 | 0.00265981 | − | 0.999996i | \(-0.499153\pi\) | ||||
0.00265981 | + | 0.999996i | \(0.499153\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.02175 | − | 9.21396i | −0.456341 | − | 0.524164i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.00835538 | −0.000473790 | −0.000236895 | − | 1.00000i | \(-0.500075\pi\) | ||||
−0.000236895 | 1.00000i | \(0.500075\pi\) | ||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0547355i | 0.00309383i | 0.999999 | + | 0.00154692i | \(0.000492399\pi\) | ||||
−0.999999 | + | 0.00154692i | \(0.999508\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.46303 | + | 3.48094i | −0.195120 | + | 0.196129i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.5118 | −0.590401 | −0.295201 | − | 0.955435i | \(-0.595386\pi\) | ||||
−0.295201 | + | 0.955435i | \(0.595386\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.4234i | 0.583598i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.51482 | − | 2.23775i | −0.363622 | − | 0.124899i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.65584i | 0.425982i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.61127 | + | 4.39437i | −0.422197 | + | 0.243756i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.3057 | + | 19.8777i | 0.957008 | + | 1.09924i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 14.7315 | + | 1.79273i | 0.812175 | + | 0.0988364i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 26.7610i | − | 1.47092i | −0.677569 | − | 0.735459i | \(-0.736967\pi\) | ||
0.677569 | − | 0.735459i | \(-0.263033\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.68673 | + | 19.3280i | −0.147232 | + | 1.05917i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.55155 | + | 2.68737i | 0.0847703 | + | 0.146827i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.90313 | − | 10.2245i | 0.321564 | − | 0.556965i | −0.659247 | − | 0.751927i | \(-0.729125\pi\) |
0.980811 | + | 0.194961i | \(0.0624581\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.62835 | + | 4.74066i | −0.0884399 | + | 0.257477i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.9725 | − | 10.9538i | −1.02742 | − | 0.593181i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.3115 | + | 6.58127i | 0.934731 | + | 0.355355i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.34744 | + | 6.83414i | −0.126382 | + | 0.367938i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2.11386i | − | 0.113478i | −0.998389 | − | 0.0567390i | \(-0.981930\pi\) | ||
0.998389 | − | 0.0567390i | \(-0.0180703\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.9624 | − | 10.9480i | 1.01504 | − | 0.586031i | 0.102373 | − | 0.994746i | \(-0.467356\pi\) |
0.912662 | + | 0.408715i | \(0.134023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.87578 | − | 0.539912i | 0.527130 | − | 0.0288184i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.95031 | + | 4.59011i | 0.423152 | + | 0.244307i | 0.696425 | − | 0.717630i | \(-0.254773\pi\) |
−0.273273 | + | 0.961937i | \(0.588106\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.91419 | − | 3.31547i | −0.101595 | − | 0.175967i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.8023 | − | 8.66935i | 0.677571 | − | 0.458831i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.1651 | + | 15.1064i | 1.38094 | + | 0.797286i | 0.992271 | − | 0.124091i | \(-0.0396015\pi\) |
0.388669 | + | 0.921377i | \(0.372935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.92562 | + | 11.9955i | 0.364506 | + | 0.631343i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.41173 | − | 2.77017i | −0.126583 | − | 0.145396i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.47443 | − | 7.74994i | 0.234202 | − | 0.405650i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.42672 | − | 4.20320i | 0.126674 | − | 0.219405i | −0.795712 | − | 0.605675i | \(-0.792903\pi\) |
0.922386 | + | 0.386269i | \(0.126237\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −31.2013 | − | 4.33721i | −1.62427 | − | 0.225786i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.19783 | + | 12.2088i | 0.269858 | + | 0.633850i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.26478 | + | 3.92271i | 0.117266 | + | 0.203110i | 0.918683 | − | 0.394995i | \(-0.129254\pi\) |
−0.801418 | + | 0.598105i | \(0.795920\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.97385 | − | 10.1140i | −0.101929 | − | 0.522283i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.65815i | − | 0.342912i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 27.9107i | − | 1.43368i | −0.697239 | − | 0.716838i | \(-0.745589\pi\) | ||
0.697239 | − | 0.716838i | \(-0.254411\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.667745 | + | 3.42151i | 0.0342096 | + | 0.175289i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.7050 | − | 18.5416i | −0.547000 | − | 0.947432i | −0.998478 | − | 0.0551495i | \(-0.982436\pi\) |
0.451478 | − | 0.892282i | \(-0.350897\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.84144 | + | 0.589171i | 0.246742 | + | 0.0300269i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.29282 | + | 6.79555i | −0.269049 | + | 0.345437i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.13605 | − | 12.3600i | 0.361812 | − | 0.626677i | −0.626447 | − | 0.779464i | \(-0.715492\pi\) |
0.988259 | + | 0.152787i | \(0.0488249\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.3770 | − | 19.7055i | 0.575360 | − | 0.996552i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.5593 | − | 23.6149i | −1.03708 | − | 1.19121i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.73047 | + | 6.46137i | 0.187701 | + | 0.325107i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.2084 | − | 7.62586i | −0.662909 | − | 0.382731i | 0.130475 | − | 0.991452i | \(-0.458350\pi\) |
−0.793385 | + | 0.608721i | \(0.791683\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.54122 | + | 9.35422i | −0.227345 | + | 0.468297i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.3931 | + | 30.1257i | 0.868569 | + | 1.50440i | 0.863460 | + | 0.504418i | \(0.168293\pi\) |
0.00510899 | + | 0.999987i | \(0.498374\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.1191 | + | 6.99695i | 0.603694 | + | 0.348543i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.51853 | + | 5.35650i | −0.0754563 | + | 0.266167i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.7859 | − | 9.69134i | 0.832046 | − | 0.480382i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 27.7719i | − | 1.37323i | −0.727019 | − | 0.686617i | \(-0.759095\pi\) | ||
0.727019 | − | 0.686617i | \(-0.240905\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.6609 | + | 33.9486i | −0.575190 | + | 1.67456i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.4034 | + | 1.38772i | 0.561125 | + | 0.0682852i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.87630 | − | 3.39268i | −0.288456 | − | 0.166540i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.48103 | + | 13.0457i | −0.219437 | + | 0.638852i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7876 | − | 34.2732i | 0.966689 | − | 1.67436i | 0.261684 | − | 0.965154i | \(-0.415722\pi\) |
0.705006 | − | 0.709202i | \(-0.250944\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.5960 | + | 33.9413i | 0.955050 | + | 1.65420i | 0.734253 | + | 0.678876i | \(0.237533\pi\) |
0.220798 | + | 0.975320i | \(0.429134\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 15.5924 | − | 6.32704i | 0.758129 | − | 0.307631i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.5787i | 0.755676i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.16064 | − | 9.53737i | 0.0561671 | − | 0.461546i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.45074 | − | 7.40946i | −0.311445 | − | 0.357732i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.3367 | + | 18.0923i | −1.50944 | + | 0.871474i | −0.509497 | + | 0.860472i | \(0.670168\pi\) |
−0.999939 | + | 0.0110011i | \(0.996498\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 36.6472i | − | 1.76115i | −0.473904 | − | 0.880577i | \(-0.657156\pi\) | ||
0.473904 | − | 0.880577i | \(-0.342844\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.54473 | + | 1.21757i | 0.169957 | + | 0.0583779i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.3027i | 0.732028i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.52279 | −0.359043 | −0.179522 | − | 0.983754i | \(-0.557455\pi\) | ||||
−0.179522 | + | 0.983754i | \(0.557455\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.7848 | − | 2.99860i | 0.989753 | − | 0.142791i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.0670i | 1.61857i | 0.587416 | + | 0.809285i | \(0.300145\pi\) | ||||
−0.587416 | + | 0.809285i | \(0.699855\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.31433 | 0.204519 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −23.8900 | − | 27.4406i | −1.12996 | − | 1.29790i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.4345 | 1.10594 | 0.552972 | − | 0.833200i | \(-0.313494\pi\) | ||||
0.552972 | + | 0.833200i | \(0.313494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.6448 | + | 27.0976i | 0.736684 | + | 1.27597i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.3175 | + | 8.35272i | 1.14253 | + | 0.392445i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.09257 | − | 0.376345i | −0.144982 | − | 0.0176433i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.96087 | −0.232060 | −0.116030 | − | 0.993246i | \(-0.537017\pi\) | ||||
−0.116030 | + | 0.993246i | \(0.537017\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.92394 | − | 15.6387i | 0.369858 | − | 0.729954i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.2217 | − | 10.5203i | 0.848671 | − | 0.489981i | −0.0115310 | − | 0.999934i | \(-0.503671\pi\) |
0.860202 | + | 0.509953i | \(0.170337\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0110 | + | 13.8627i | 1.11589 | + | 0.644257i | 0.940347 | − | 0.340216i | \(-0.110500\pi\) |
0.175538 | + | 0.984473i | \(0.443834\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.94131 | + | 5.17255i | −0.275522 | + | 0.239871i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.0302 | − | 27.7652i | 0.741791 | − | 1.28482i | −0.209887 | − | 0.977726i | \(-0.567310\pi\) |
0.951679 | − | 0.307095i | \(-0.0993569\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.60323 | − | 13.1743i | 0.0740303 | − | 0.608334i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.98371 | + | 35.7844i | 0.321792 | + | 1.64886i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.55568 | 0.393390 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.23854 | − | 9.07342i | −0.240361 | − | 0.416317i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.8703 | + | 9.24534i | 0.543502 | + | 0.423315i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.30666 | − | 12.6555i | 0.333850 | − | 0.578245i | −0.649414 | − | 0.760435i | \(-0.724986\pi\) |
0.983263 | + | 0.182191i | \(0.0583189\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.7223 | + | 6.19054i | −0.488896 | + | 0.282264i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 25.5896 | − | 17.3285i | 1.16437 | − | 0.788476i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.969018 | − | 1.67839i | 0.0440008 | − | 0.0762117i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9705 | − | 16.7261i | 1.31278 | − | 0.757932i | 0.330222 | − | 0.943903i | \(-0.392877\pi\) |
0.982555 | + | 0.185971i | \(0.0595432\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.89898 | − | 0.995761i | −0.131096 | − | 0.0450299i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 35.7574 | + | 20.6445i | 1.61371 | + | 0.931675i | 0.988501 | + | 0.151217i | \(0.0483192\pi\) |
0.625208 | + | 0.780458i | \(0.285014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2209 | − | 5.90102i | −0.460325 | − | 0.265769i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.12436 | − | 2.07935i | 0.230323 | − | 0.0934598i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.97795 | + | 16.2535i | −0.0887230 | + | 0.729070i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.0288 | − | 9.25425i | 0.717549 | − | 0.414277i | −0.0963011 | − | 0.995352i | \(-0.530701\pi\) |
0.813850 | + | 0.581075i | \(0.197368\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.82163 | + | 8.21466i | −0.126061 | + | 0.367004i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.4055 | −0.731483 | −0.365742 | − | 0.930716i | \(-0.619185\pi\) | ||||
−0.365742 | + | 0.930716i | \(0.619185\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.99772 | 0.355894 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.6645 | − | 12.2495i | −0.473627 | − | 0.544018i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.5541 | − | 11.2896i | 0.866721 | − | 0.500401i | 0.000463610 | − | 1.00000i | \(-0.499852\pi\) |
0.866257 | + | 0.499598i | \(0.166519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.2144 | + | 14.9923i | −1.55779 | + | 0.663221i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.643632 | + | 11.7730i | 0.0284170 | + | 0.519789i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.77872 | + | 2.18165i | 0.166510 | + | 0.0961348i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.4749 | − | 8.35706i | −0.636604 | − | 0.367543i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.03847 | + | 5.32107i | 0.0455836 | + | 0.233569i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.6511 | + | 14.2323i | −1.07998 | + | 0.623529i | −0.930892 | − | 0.365294i | \(-0.880968\pi\) |
−0.149092 | + | 0.988823i | \(0.547635\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.2249 | + | 21.1742i | −0.534558 | + | 0.925882i | 0.464627 | + | 0.885507i | \(0.346189\pi\) |
−0.999185 | + | 0.0403749i | \(0.987145\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.24081 | + | 19.0346i | −0.403302 | + | 0.830740i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.4819 | − | 12.4026i | 0.935767 | − | 0.540265i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2407 | − | 19.4694i | 0.488725 | − | 0.846496i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0698 | − | 4.89765i | 0.523785 | − | 0.212540i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.99343 | − | 17.3091i | −0.432863 | − | 0.749741i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.46027 | 0.106367 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.8535 | + | 19.8964i | −0.986200 | + | 0.858594i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.0357 | − | 14.4575i | −0.647635 | − | 0.622729i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.2501 | − | 36.8062i | 0.913613 | − | 1.58242i | 0.104693 | − | 0.994505i | \(-0.466614\pi\) |
0.808920 | − | 0.587919i | \(-0.200053\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.58008 | + | 8.09628i | 0.0678076 | + | 0.347445i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.15203 | − | 4.70658i | −0.349195 | − | 0.201608i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 40.0427 | − | 23.1187i | 1.71210 | − | 0.988483i | 0.780386 | − | 0.625298i | \(-0.215022\pi\) |
0.931717 | − | 0.363185i | \(-0.118311\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.09621 | − | 10.0947i | −0.174822 | − | 0.430832i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.93721 | 0.338136 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.85473 | − | 31.6757i | 0.163920 | − | 1.34699i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.33500 | − | 6.84052i | −0.0566677 | − | 0.290364i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8064 | + | 25.6454i | 0.627365 | + | 1.08663i | 0.988078 | + | 0.153952i | \(0.0492000\pi\) |
−0.360713 | + | 0.932677i | \(0.617467\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.46511 | −0.231150 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −17.0914 | + | 3.33557i | −0.721599 | + | 0.140828i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.6407 | 0.448453 | 0.224226 | − | 0.974537i | \(-0.428015\pi\) | ||||
0.224226 | + | 0.974537i | \(0.428015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.79028i | − | 0.0753175i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.9582 | − | 14.4078i | 0.796172 | − | 0.605071i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 40.1154 | 1.68173 | 0.840863 | − | 0.541249i | \(-0.182048\pi\) | ||||
0.840863 | + | 0.541249i | \(0.182048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.9281i | 1.16875i | 0.811483 | + | 0.584376i | \(0.198661\pi\) | ||||
−0.811483 | + | 0.584376i | \(0.801339\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.18755 | + | 16.3330i | 0.133162 | + | 0.682319i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.1391i | 1.29859i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.5370 | − | 11.8571i | 0.854969 | − | 0.493616i | −0.00735564 | − | 0.999973i | \(-0.502341\pi\) |
0.862324 | + | 0.506357i | \(0.169008\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.7582 | − | 5.02700i | 1.07048 | − | 0.208915i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.3677 | + | 26.7009i | 0.471613 | + | 1.10774i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 14.9448i | − | 0.618950i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.27329 | + | 1.32823i | −0.135334 | + | 0.0549154i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.00010 | − | 3.46427i | −0.0825530 | − | 0.142986i | 0.821793 | − | 0.569786i | \(-0.192974\pi\) |
−0.904346 | + | 0.426800i | \(0.859641\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.34110 | + | 14.4472i | −0.343689 | + | 0.595287i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.39205 | + | 1.63780i | −0.345203 | + | 0.0673701i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.2297 | + | 7.63817i | 0.543279 | + | 0.313662i | 0.746407 | − | 0.665490i | \(-0.231777\pi\) |
−0.203128 | + | 0.979152i | \(0.565111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.31862 | + | 4.41382i | −0.136050 | + | 0.180949i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.8786 | − | 29.7248i | −1.05914 | − | 1.21655i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 18.2542i | − | 0.745848i | −0.927862 | − | 0.372924i | \(-0.878355\pi\) | ||
0.927862 | − | 0.372924i | \(-0.121645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.833186 | + | 0.481040i | −0.0339863 | + | 0.0196220i | −0.516897 | − | 0.856048i | \(-0.672913\pi\) |
0.482911 | + | 0.875670i | \(0.339580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.65825 | − | 13.9442i | −0.230422 | − | 0.567853i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.13607 | + | 0.655910i | 0.0461878 | + | 0.0266665i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.1758 | − | 17.6249i | −0.413021 | − | 0.715374i | 0.582197 | − | 0.813048i | \(-0.302193\pi\) |
−0.995218 | + | 0.0976738i | \(0.968860\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.98796 | − | 13.2728i | −0.364211 | − | 0.537842i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.24611 | + | 5.33824i | 0.374058 | + | 0.215962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.545611 | − | 0.945026i | −0.0220370 | − | 0.0381692i | 0.854797 | − | 0.518963i | \(-0.173682\pi\) |
−0.876834 | + | 0.480794i | \(0.840348\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.0427 | − | 2.15510i | 0.445284 | − | 0.0869021i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.9190 | + | 34.5008i | −0.801911 | + | 1.38895i | 0.116446 | + | 0.993197i | \(0.462850\pi\) |
−0.918357 | + | 0.395753i | \(0.870484\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.72902 | − | 8.19091i | 0.190075 | − | 0.329220i | −0.755200 | − | 0.655495i | \(-0.772460\pi\) |
0.945275 | + | 0.326275i | \(0.105793\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.8386 | − | 31.2592i | 0.635581 | − | 1.25439i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.7482 | − | 11.0887i | −0.590873 | − | 0.444260i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.70304 | − | 16.8062i | −0.388122 | − | 0.672246i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.83285 | − | 7.68995i | 0.352750 | − | 0.307107i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.9463i | 0.875058i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.9236i | 0.872765i | 0.899761 | + | 0.436382i | \(0.143741\pi\) | ||||
−0.899761 | + | 0.436382i | \(0.856259\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.87915 | − | 2.01941i | −0.233675 | − | 0.0802643i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.622543 | − | 1.07828i | −0.0247049 | − | 0.0427901i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.60438 | + | 9.23502i | 0.380540 | + | 0.365905i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.98072 | + | 17.2034i | 0.276153 | + | 0.680554i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.830084 | + | 1.43775i | −0.0327863 | + | 0.0567876i | −0.881953 | − | 0.471337i | \(-0.843771\pi\) |
0.849167 | + | 0.528125i | \(0.177105\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.32745 | + | 12.6915i | −0.288966 | + | 0.500504i | −0.973563 | − | 0.228418i | \(-0.926645\pi\) |
0.684597 | + | 0.728922i | \(0.259978\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.999399 | − | 2.90957i | 0.0393513 | − | 0.114564i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.70627 | + | 13.3477i | 0.302965 | + | 0.524750i | 0.976806 | − | 0.214126i | \(-0.0686902\pi\) |
−0.673841 | + | 0.738876i | \(0.735357\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.2047 | − | 6.46905i | −0.439824 | − | 0.253933i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.6044 | − | 2.41155i | 1.31706 | − | 0.0945161i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.694964 | − | 1.20371i | −0.0271960 | − | 0.0471049i | 0.852107 | − | 0.523368i | \(-0.175324\pi\) |
−0.879303 | + | 0.476263i | \(0.841991\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.68466 | + | 5.59144i | 0.378411 | + | 0.218476i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26.6667 | + | 34.2378i | −1.04037 | + | 1.33574i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.58496 | − | 3.80183i | 0.256514 | − | 0.148098i | −0.366230 | − | 0.930525i | \(-0.619352\pi\) |
0.622743 | + | 0.782426i | \(0.286018\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.3951i | 1.41561i | 0.706410 | + | 0.707803i | \(0.250314\pi\) | ||||
−0.706410 | + | 0.707803i | \(0.749686\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.9175 | − | 2.13066i | 0.424000 | − | 0.0827481i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.448642 | − | 3.68666i | 0.0173976 | − | 0.142962i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.4298 | − | 11.7951i | −0.791043 | − | 0.456709i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.6630 | + | 13.3964i | 0.450916 | + | 0.517933i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.41047 | + | 9.37120i | −0.208869 | + | 0.361771i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.1537 | − | 22.7829i | −0.507038 | − | 0.878216i | −0.999967 | − | 0.00814606i | \(-0.997407\pi\) |
0.492929 | − | 0.870070i | \(-0.335926\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.30971 | + | 23.9565i | 0.0504107 | + | 0.922085i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 36.4345i | − | 1.40029i | −0.714001 | − | 0.700145i | \(-0.753119\pi\) | ||
0.714001 | − | 0.700145i | \(-0.246881\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.62630 | + | 3.24685i | −0.292670 | + | 0.124603i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.09761 | + | 23.5748i | −0.310301 | + | 0.903387i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −42.8648 | + | 24.7480i | −1.64017 | + | 0.946955i | −0.659405 | + | 0.751788i | \(0.729192\pi\) |
−0.980770 | + | 0.195167i | \(0.937475\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12.8205i | − | 0.489845i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.05753 | + | 4.40313i | −0.192957 | + | 0.167990i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.54629i | 0.363685i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.5566 | −1.46676 | −0.733381 | − | 0.679818i | \(-0.762059\pi\) | ||||
−0.733381 | + | 0.679818i | \(0.762059\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.8615 | − | 6.06258i | −0.868438 | − | 0.230298i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 4.92662i | − | 0.186877i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.4281 | −1.34193 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.57720 | − | 19.1484i | 0.248773 | − | 0.724257i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.2585 | −0.387458 | −0.193729 | − | 0.981055i | \(-0.562058\pi\) | ||||
−0.193729 | + | 0.981055i | \(0.562058\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.37977 | − | 12.7821i | −0.278333 | − | 0.482087i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.53285 | + | 3.94634i | −0.170717 | + | 0.148628i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −27.3395 | − | 20.5557i | −1.02821 | − | 0.773078i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1248 | 0.417799 | 0.208900 | − | 0.977937i | \(-0.433012\pi\) | ||||
0.208900 | + | 0.977937i | \(0.433012\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.6044 | − | 33.5268i | −0.510205 | − | 1.25735i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 42.9387 | − | 24.7907i | 1.60807 | − | 0.928417i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.03868 | + | 1.75439i | 0.113640 | + | 0.0656103i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.1901 | − | 3.50018i | −0.380558 | − | 0.130716i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.64721 | − | 16.7095i | 0.359780 | − | 0.623158i | −0.628144 | − | 0.778097i | \(-0.716185\pi\) |
0.987924 | + | 0.154940i | \(0.0495183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.30996 | − | 17.1699i | −0.272237 | − | 0.639439i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −27.8208 | − | 9.55607i | −1.03467 | − | 0.355394i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.1512 | 0.599841 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.0702 | + | 22.6382i | 0.484747 | + | 0.839606i | 0.999846 | − | 0.0175243i | \(-0.00557846\pi\) |
−0.515100 | + | 0.857130i | \(0.672245\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.8705 | − | 24.7150i | 0.402610 | − | 0.915371i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.84365 | + | 8.38944i | −0.179149 | + | 0.310295i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.1392 | − | 9.89531i | 0.633050 | − | 0.365492i | −0.148882 | − | 0.988855i | \(-0.547567\pi\) |
0.781932 | + | 0.623363i | \(0.214234\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.67298 | + | 3.42448i | −0.246136 | + | 0.126314i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.47368 | + | 12.9448i | −0.275297 | + | 0.476828i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 38.3346 | − | 22.1325i | 1.41016 | − | 0.814158i | 0.414759 | − | 0.909931i | \(-0.363866\pi\) |
0.995403 | + | 0.0957737i | \(0.0305325\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.64216 | + | 4.91211i | −0.207270 | + | 0.180451i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.3816 | − | 18.6955i | −1.18797 | − | 0.685873i | −0.230123 | − | 0.973162i | \(-0.573913\pi\) |
−0.957844 | + | 0.287289i | \(0.907246\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.2536 | + | 6.49728i | 0.412301 | + | 0.238042i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.9604 | + | 20.2197i | 0.949842 | + | 0.739800i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.41024 | − | 6.32340i | −0.307303 | − | 0.231052i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.04602 | − | 1.18127i | 0.0746603 | − | 0.0431052i | −0.462205 | − | 0.886773i | \(-0.652942\pi\) |
0.536865 | + | 0.843668i | \(0.319608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −46.4784 | + | 9.07076i | −1.69377 | + | 0.330557i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.18332 | −0.334215 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.6132 | 0.494779 | 0.247389 | − | 0.968916i | \(-0.420427\pi\) | ||||
0.247389 | + | 0.968916i | \(0.420427\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.1628 | + | 6.66724i | −1.24003 | + | 0.242005i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.0200 | + | 10.4039i | −0.653225 | + | 0.377140i | −0.789691 | − | 0.613505i | \(-0.789759\pi\) |
0.136466 | + | 0.990645i | \(0.456426\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 15.7702 | + | 37.0414i | 0.570918 | + | 1.34099i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.862122 | + | 6.20199i | −0.0311701 | + | 0.224233i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.15725 | + | 4.13224i | 0.258433 | + | 0.149206i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.5703 | − | 6.10279i | −0.381176 | − | 0.220072i | 0.297154 | − | 0.954830i | \(-0.403963\pi\) |
−0.678330 | + | 0.734757i | \(0.737296\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.0563618 | + | 0.0490691i | −0.00202982 | + | 0.00176718i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.16232 | − | 1.82577i | 0.113741 | − | 0.0656683i | −0.442050 | − | 0.896990i | \(-0.645749\pi\) |
0.555791 | + | 0.831322i | \(0.312415\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −16.9731 | + | 29.3982i | −0.609691 | + | 1.05601i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.0179 | + | 26.8149i | −0.467016 | + | 0.961981i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.6343 | − | 11.9132i | 0.739299 | − | 0.426835i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.22048 | − | 15.9703i | 0.329935 | − | 0.571463i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.2135 | − | 8.21516i | −0.579423 | − | 0.293586i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.51095 | − | 11.2773i | −0.232386 | − | 0.402504i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.32993 | 0.296930 | 0.148465 | − | 0.988918i | \(-0.452567\pi\) | ||||
0.148465 | + | 0.988918i | \(0.452567\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.3748 | + | 8.71589i | 0.903366 | + | 0.310294i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.60137 | + | 6.11990i | −0.163606 | + | 0.217599i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.45604 | − | 5.98605i | 0.122728 | − | 0.212571i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.08235 | − | 1.74572i | −0.180252 | − | 0.0619143i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.3707 | + | 15.8025i | 0.969520 | + | 0.559753i | 0.899090 | − | 0.437764i | \(-0.144229\pi\) |
0.0704305 | + | 0.997517i | \(0.477563\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3894 | − | 9.46241i | 0.579815 | − | 0.334756i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.7231 | − | 2.88066i | −0.732214 | − | 0.101783i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 43.1058 | 1.52117 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.63335 | + | 8.82247i | −0.233795 | + | 0.310951i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −37.6827 | + | 32.8068i | −1.32649 | + | 1.15486i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.15525 | − | 10.6612i | −0.216407 | − | 0.374828i | 0.737300 | − | 0.675566i | \(-0.236100\pi\) |
−0.953707 | + | 0.300738i | \(0.902767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.741828 | −0.0260491 | −0.0130245 | − | 0.999915i | \(-0.504146\pi\) | ||||
−0.0130245 | + | 0.999915i | \(0.504146\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.06783 | + | 23.4880i | −0.282951 | + | 0.823761i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.09478 | 0.0383485 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.51498i | − | 0.227930i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.6033 | + | 3.87260i | 0.510280 | + | 0.135319i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5572 | −0.438250 | −0.219125 | − | 0.975697i | \(-0.570320\pi\) | ||||
−0.219125 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.95398i | − | 0.0681113i | −0.999420 | − | 0.0340557i | \(-0.989158\pi\) | ||
0.999420 | − | 0.0340557i | \(-0.0108424\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.9737 | − | 15.6481i | 0.625765 | − | 0.544796i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 26.2468i | − | 0.912692i | −0.889802 | − | 0.456346i | \(-0.849158\pi\) | ||
0.889802 | − | 0.456346i | \(-0.150842\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.405249 | + | 0.233970i | −0.0140749 | + | 0.00812613i | −0.507021 | − | 0.861934i | \(-0.669253\pi\) |
0.492946 | + | 0.870060i | \(0.335920\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.21674 | + | 23.9216i | −0.285036 | + | 0.829830i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.6888 | − | 6.55874i | 0.786121 | − | 0.227247i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.10221i | − | 0.107356i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.9917 | − | 20.8784i | 1.10579 | − | 0.721663i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.54979 | + | 11.3446i | 0.226124 | + | 0.391658i | 0.956656 | − | 0.291220i | \(-0.0940613\pi\) |
−0.730532 | + | 0.682878i | \(0.760728\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.38211 | − | 14.5182i | 0.289038 | − | 0.500629i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.38024 | + | 2.73400i | 0.0819799 | + | 0.0941640i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.02362 | + | 2.90039i | 0.172818 | + | 0.0997763i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.19773 | − | 5.16210i | −0.0755150 | − | 0.177372i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.49023 | + | 1.26664i | −0.222744 | + | 0.0434709i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 43.8670i | 1.50374i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.5601 | + | 7.25157i | −0.430049 | + | 0.248289i | −0.699368 | − | 0.714762i | \(-0.746535\pi\) |
0.269318 | + | 0.963051i | \(0.413202\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.58338 | − | 3.90210i | −0.0541506 | − | 0.133449i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 26.9380 | + | 15.5527i | 0.920186 | + | 0.531269i | 0.883694 | − | 0.468065i | \(-0.155049\pi\) |
0.0364913 | + | 0.999334i | \(0.488382\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.0019 | − | 22.5200i | −0.443619 | − | 0.768371i | 0.554335 | − | 0.832293i | \(-0.312972\pi\) |
−0.997955 | + | 0.0639219i | \(0.979639\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −43.2875 | − | 21.0149i | −1.47523 | − | 0.716187i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.1288 | + | 15.0854i | 0.889433 | + | 0.513515i | 0.873757 | − | 0.486363i | \(-0.161677\pi\) |
0.0156763 | + | 0.999877i | \(0.495010\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.968167 | − | 1.67691i | −0.0329187 | − | 0.0570168i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.16014 | + | 9.20017i | −0.107324 | + | 0.312454i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.9694 | + | 31.1238i | −0.609569 | + | 1.05580i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.77397 | − | 8.26875i | 0.161760 | − | 0.280176i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.77515 | + | 7.41481i | −0.195459 | + | 0.250953i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.90153 | − | 15.6255i | 0.0642833 | − | 0.528239i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.57800 | − | 13.1255i | −0.255891 | − | 0.443216i | 0.709246 | − | 0.704961i | \(-0.249035\pi\) |
−0.965137 | + | 0.261745i | \(0.915702\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.2125 | − | 7.62970i | −0.749210 | − | 0.257344i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.0172i | 1.55036i | 0.631741 | + | 0.775180i | \(0.282341\pi\) | ||||
−0.631741 | + | 0.775180i | \(0.717659\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.3035i | − | 0.683267i | −0.939833 | − | 0.341633i | \(-0.889020\pi\) | ||
0.939833 | − | 0.341633i | \(-0.110980\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.50880 | + | 3.05479i | −0.117947 | + | 0.102686i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19.5332 | − | 33.8325i | −0.655861 | − | 1.13598i | −0.981677 | − | 0.190551i | \(-0.938973\pi\) |
0.325817 | − | 0.945433i | \(-0.394361\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.643278 | + | 5.28605i | −0.0215749 | + | 0.177288i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26.0023 | + | 6.56624i | −0.871110 | + | 0.219977i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.36374 | + | 11.0223i | −0.212954 | + | 0.368848i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.41116 | − | 9.37240i | 0.180875 | − | 0.313285i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 21.8222 | − | 4.25883i | 0.728621 | − | 0.142198i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.8584 | − | 22.2714i | −0.428852 | − | 0.742794i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.6544 | + | 8.46074i | 0.488210 | + | 0.281868i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.8945 | + | 7.37746i | −0.362548 | + | 0.245506i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.47311 | − | 2.55151i | −0.0489680 | − | 0.0848150i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.0468 | + | 14.4608i | 0.831667 | + | 0.480163i | 0.854423 | − | 0.519578i | \(-0.173911\pi\) |
−0.0227563 | + | 0.999741i | \(0.507244\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −38.4155 | − | 5.34004i | −1.27416 | − | 0.177118i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −50.0777 | + | 28.9124i | −1.65915 | + | 0.957910i | −0.686039 | + | 0.727565i | \(0.740652\pi\) |
−0.973109 | + | 0.230345i | \(0.926015\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 32.6845i | − | 1.08170i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.55491 | + | 2.93463i | 0.0844626 | + | 0.0970157i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −18.7350 | − | 44.0054i | −0.618686 | − | 1.45319i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.0466 | − | 21.3889i | −1.22205 | − | 0.705554i | −0.256699 | − | 0.966491i | \(-0.582635\pi\) |
−0.965356 | + | 0.260938i | \(0.915968\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.158450 | − | 0.0309233i | 0.00522111 | − | 0.00101896i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.88977 | + | 10.2014i | −0.193864 | + | 0.335782i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.0169 | − | 26.0100i | −0.493752 | − | 0.855204i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.6937 | − | 13.0022i | −0.548293 | − | 0.427047i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.2840i | 1.02639i | 0.858271 | + | 0.513197i | \(0.171539\pi\) | ||||
−0.858271 | + | 0.513197i | \(0.828461\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.0091 | + | 11.4494i | −0.360809 | + | 0.375240i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.0142040 | + | 0.00277206i | −0.000465017 | + | 9.07531e-5i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.38628 | − | 3.10977i | 0.176150 | − | 0.101700i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.2887i | 0.401454i | 0.979647 | + | 0.200727i | \(0.0643305\pi\) | ||||
−0.979647 | + | 0.200727i | \(0.935670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.0181596 | + | 0.0930492i | 0.000592615 | + | 0.00303655i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 15.5977i | − | 0.508469i | −0.967143 | − | 0.254235i | \(-0.918176\pi\) | ||
0.967143 | − | 0.254235i | \(-0.0818236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −70.8147 | −2.30604 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.73222 | + | 7.06646i | −0.153939 | + | 0.229872i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.4755i | 1.31528i | 0.753334 | + | 0.657639i | \(0.228445\pi\) | ||||
−0.753334 | + | 0.657639i | \(0.771555\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.5347 | −0.893815 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.8698 | + | 3.48749i | −0.579469 | + | 0.113090i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.9759 | 1.55409 | 0.777046 | − | 0.629444i | \(-0.216717\pi\) | ||||
0.777046 | + | 0.629444i | \(0.216717\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.97177 | − | 5.14726i | −0.0961643 | − | 0.166561i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.45816 | + | 17.7195i | 0.111786 | + | 0.572791i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −32.9512 | + | 43.8256i | −1.06405 | + | 1.41520i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0509 | 0.743577 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −11.8175 | − | 1.64272i | −0.380813 | − | 0.0529358i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −8.11760 | + | 4.68670i | −0.261315 | + | 0.150870i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.0636 | − | 23.7081i | −1.32052 | − | 0.762401i | −0.336707 | − | 0.941610i | \(-0.609313\pi\) |
−0.983811 | + | 0.179208i | \(0.942646\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.53997 | + | 13.0148i | 0.0815957 | + | 0.418094i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.0930 | − | 22.6777i | 0.420173 | − | 0.727761i | −0.575783 | − | 0.817602i | \(-0.695303\pi\) |
0.995956 | + | 0.0898415i | \(0.0286361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.6624 | + | 16.8412i | −0.405939 | + | 0.539905i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.4811 | + | 9.99552i | −0.367689 | + | 0.320113i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 26.8970 | 0.860513 | 0.430256 | − | 0.902707i | \(-0.358423\pi\) | ||||
0.430256 | + | 0.902707i | \(0.358423\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3909 | + | 17.9975i | 0.332094 | + | 0.575203i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 36.0142 | + | 28.0502i | 1.14984 | + | 0.895575i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.46289 | + | 12.9261i | −0.238029 | + | 0.412279i | −0.960149 | − | 0.279490i | \(-0.909835\pi\) |
0.722119 | + | 0.691768i | \(0.243168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.64472 | − | 1.52693i | 0.0842677 | − | 0.0486520i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 25.6381 | − | 1.83986i | 0.816068 | − | 0.0585635i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.68162 | + | 16.7691i | −0.307858 | + | 0.533225i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.6509 | + | 19.4284i | −1.06896 | + | 0.617163i | −0.927896 | − | 0.372838i | \(-0.878385\pi\) |
−0.141061 | + | 0.990001i | \(0.545051\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.87849 | − | 45.4932i | −0.281750 | − | 1.44368i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.1904 | + | 7.03812i | 0.386461 | + | 0.223124i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.5019 | + | 18.7650i | 1.02935 | + | 0.594293i | 0.916797 | − | 0.399353i | \(-0.130765\pi\) |
0.112549 | + | 0.993646i | \(0.464099\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.84504 | + | 33.7485i | 0.0583746 | + | 1.06776i |
(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 | 1008.2.cz.i.607.15 | yes | 32 | |
3.2 | odd | 2 | 3024.2.cz.i.1279.9 | 32 | |||
4.3 | odd | 2 | inner | 1008.2.cz.i.607.2 | yes | 32 | |
7.3 | odd | 6 | 1008.2.bf.i.31.12 | yes | 32 | ||
9.2 | odd | 6 | 3024.2.bf.i.2287.9 | 32 | |||
9.7 | even | 3 | 1008.2.bf.i.943.5 | yes | 32 | ||
12.11 | even | 2 | 3024.2.cz.i.1279.10 | 32 | |||
21.17 | even | 6 | 3024.2.bf.i.1711.7 | 32 | |||
28.3 | even | 6 | 1008.2.bf.i.31.5 | ✓ | 32 | ||
36.7 | odd | 6 | 1008.2.bf.i.943.12 | yes | 32 | ||
36.11 | even | 6 | 3024.2.bf.i.2287.10 | 32 | |||
63.38 | even | 6 | 3024.2.cz.i.2719.10 | 32 | |||
63.52 | odd | 6 | inner | 1008.2.cz.i.367.2 | yes | 32 | |
84.59 | odd | 6 | 3024.2.bf.i.1711.8 | 32 | |||
252.115 | even | 6 | inner | 1008.2.cz.i.367.15 | yes | 32 | |
252.227 | odd | 6 | 3024.2.cz.i.2719.9 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1008.2.bf.i.31.5 | ✓ | 32 | 28.3 | even | 6 | ||
1008.2.bf.i.31.12 | yes | 32 | 7.3 | odd | 6 | ||
1008.2.bf.i.943.5 | yes | 32 | 9.7 | even | 3 | ||
1008.2.bf.i.943.12 | yes | 32 | 36.7 | odd | 6 | ||
1008.2.cz.i.367.2 | yes | 32 | 63.52 | odd | 6 | inner | |
1008.2.cz.i.367.15 | yes | 32 | 252.115 | even | 6 | inner | |
1008.2.cz.i.607.2 | yes | 32 | 4.3 | odd | 2 | inner | |
1008.2.cz.i.607.15 | yes | 32 | 1.1 | even | 1 | trivial | |
3024.2.bf.i.1711.7 | 32 | 21.17 | even | 6 | |||
3024.2.bf.i.1711.8 | 32 | 84.59 | odd | 6 | |||
3024.2.bf.i.2287.9 | 32 | 9.2 | odd | 6 | |||
3024.2.bf.i.2287.10 | 32 | 36.11 | even | 6 | |||
3024.2.cz.i.1279.9 | 32 | 3.2 | odd | 2 | |||
3024.2.cz.i.1279.10 | 32 | 12.11 | even | 2 | |||
3024.2.cz.i.2719.9 | 32 | 252.227 | odd | 6 | |||
3024.2.cz.i.2719.10 | 32 | 63.38 | even | 6 |