Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(257,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bs (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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 257.6 | ||
Character | \(\chi\) | \(=\) | 504.257 |
Dual form | 504.2.bs.a.353.6 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −1.32026 | − | 1.12112i | −0.762255 | − | 0.647277i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.38468 | + | 2.39834i | 0.619249 | + | 1.07257i | 0.989623 | + | 0.143688i | \(0.0458962\pi\) |
−0.370374 | + | 0.928883i | \(0.620770\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.42373 | − | 2.23002i | −0.538119 | − | 0.842869i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.486198 | + | 2.96034i | 0.162066 | + | 0.986780i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.09513 | + | 1.20962i | 0.631704 | + | 0.364715i | 0.781412 | − | 0.624016i | \(-0.214500\pi\) |
−0.149707 | + | 0.988730i | \(0.547833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0461613 | − | 0.0266512i | −0.0128028 | − | 0.00739172i | 0.493585 | − | 0.869698i | \(-0.335686\pi\) |
−0.506388 | + | 0.862306i | \(0.669020\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.860670 | − | 4.71884i | 0.222224 | − | 1.21840i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.79727 | + | 3.11297i | 0.435903 | + | 0.755006i | 0.997369 | − | 0.0724940i | \(-0.0230958\pi\) |
−0.561466 | + | 0.827500i | \(0.689762\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.96978 | + | 2.29195i | 0.910730 | + | 0.525810i | 0.880666 | − | 0.473738i | \(-0.157096\pi\) |
0.0300639 | + | 0.999548i | \(0.490429\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.620412 | + | 4.54038i | −0.135385 | + | 0.990793i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0925928 | − | 0.0534585i | 0.0193069 | − | 0.0111469i | −0.490315 | − | 0.871545i | \(-0.663118\pi\) |
0.509622 | + | 0.860398i | \(0.329785\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.33469 | + | 2.31176i | −0.266939 | + | 0.462351i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.67697 | − | 4.45352i | 0.515184 | − | 0.857080i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.57376 | − | 3.79536i | 1.22072 | − | 0.704781i | 0.255646 | − | 0.966770i | \(-0.417712\pi\) |
0.965071 | + | 0.261989i | \(0.0843785\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.81563i | 1.22412i | 0.790810 | + | 0.612062i | \(0.209660\pi\) | ||||
−0.790810 | + | 0.612062i | \(0.790340\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.41000 | − | 3.94590i | −0.245449 | − | 0.686893i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.37694 | − | 6.50246i | 0.570807 | − | 1.09912i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.06198 | − | 3.57146i | 0.338988 | − | 0.587144i | −0.645255 | − | 0.763967i | \(-0.723249\pi\) |
0.984243 | + | 0.176823i | \(0.0565821\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0310660 | + | 0.0869389i | 0.00497454 | + | 0.0139214i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.838974 | + | 1.45315i | −0.131026 | + | 0.226943i | −0.924072 | − | 0.382218i | \(-0.875160\pi\) |
0.793047 | + | 0.609161i | \(0.208494\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.74347 | + | 3.01978i | 0.265877 | + | 0.460513i | 0.967793 | − | 0.251747i | \(-0.0810051\pi\) |
−0.701916 | + | 0.712260i | \(0.747672\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.42667 | + | 5.26520i | −0.958032 | + | 0.784890i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.1940 | 1.92454 | 0.962268 | − | 0.272104i | \(-0.0877196\pi\) | ||||
0.962268 | + | 0.272104i | \(0.0877196\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.94599 | + | 6.34989i | −0.420855 | + | 0.907128i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.11712 | − | 6.12489i | 0.156428 | − | 0.857657i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.27512 | − | 3.04559i | 0.724593 | − | 0.418344i | −0.0918477 | − | 0.995773i | \(-0.529277\pi\) |
0.816441 | + | 0.577429i | \(0.195944\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.69977i | 0.903397i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.67161 | − | 7.47657i | −0.353864 | − | 0.990295i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.44833 | −1.23007 | −0.615034 | − | 0.788500i | \(-0.710858\pi\) | ||||
−0.615034 | + | 0.788500i | \(0.710858\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.65498i | 0.339935i | 0.985450 | + | 0.169967i | \(0.0543663\pi\) | ||||
−0.985450 | + | 0.169967i | \(0.945634\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.90941 | − | 5.29896i | 0.744515 | − | 0.667606i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.147614i | − | 0.0183093i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.1871 | −1.73323 | −0.866616 | − | 0.498975i | \(-0.833710\pi\) | ||||
−0.866616 | + | 0.498975i | \(0.833710\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.182180 | − | 0.0332279i | −0.0219319 | − | 0.00400017i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.40262i | − | 0.166460i | −0.996530 | − | 0.0832300i | \(-0.973476\pi\) | ||
0.996530 | − | 0.0832300i | \(-0.0265236\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.54168 | − | 3.19949i | 0.648605 | − | 0.374472i | −0.139317 | − | 0.990248i | \(-0.544491\pi\) |
0.787921 | + | 0.615776i | \(0.211157\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.35390 | − | 1.55579i | 0.502745 | − | 0.179647i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.285412 | − | 6.39435i | −0.0325257 | − | 0.728704i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.22133 | 0.474937 | 0.237469 | − | 0.971395i | \(-0.423682\pi\) | ||||
0.237469 | + | 0.971395i | \(0.423682\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.52722 | + | 2.87862i | −0.947469 | + | 0.319847i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.86670 | − | 11.8935i | −0.753719 | − | 1.30548i | −0.946009 | − | 0.324141i | \(-0.894925\pi\) |
0.192290 | − | 0.981338i | \(-0.438409\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.97731 | + | 8.62095i | −0.539865 | + | 0.935073i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.9341 | − | 2.35907i | −1.38669 | − | 0.252918i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.71724 | + | 9.90254i | −0.606026 | + | 1.04967i | 0.385863 | + | 0.922556i | \(0.373904\pi\) |
−0.991888 | + | 0.127111i | \(0.959429\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.00628839 | + | 0.140885i | 0.000659203 | + | 0.0147687i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.64111 | − | 8.99843i | 0.792346 | − | 0.933094i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.6945i | 1.30243i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.3549 | + | 8.28778i | −1.45751 | + | 0.841496i | −0.998889 | − | 0.0471333i | \(-0.984991\pi\) |
−0.458626 | + | 0.888630i | \(0.651658\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.56224 | + | 6.79040i | −0.257515 | + | 0.682461i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.25000 | + | 9.09326i | −0.522394 | + | 0.904813i | 0.477266 | + | 0.878759i | \(0.341628\pi\) |
−0.999661 | + | 0.0260545i | \(0.991706\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.3602 | + | 7.71349i | −1.31642 | + | 0.760033i | −0.983150 | − | 0.182800i | \(-0.941484\pi\) |
−0.333266 | + | 0.942833i | \(0.608151\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.7485 | + | 4.79903i | −1.14653 | + | 0.468338i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.76426 | − | 5.63740i | −0.943946 | − | 0.544988i | −0.0527511 | − | 0.998608i | \(-0.516799\pi\) |
−0.891195 | + | 0.453620i | \(0.850132\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.06307 | − | 13.9657i | −0.772302 | − | 1.33767i | −0.936298 | − | 0.351206i | \(-0.885772\pi\) |
0.163996 | − | 0.986461i | \(-0.447562\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.72638 | + | 2.40355i | −0.638440 | + | 0.228135i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.7542 | + | 6.78629i | 1.10574 | + | 0.638400i | 0.937723 | − | 0.347384i | \(-0.112930\pi\) |
0.168018 | + | 0.985784i | \(0.446263\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.256423 | + | 0.148046i | 0.0239116 | + | 0.0138054i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0564532 | − | 0.149611i | 0.00521910 | − | 0.0138315i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.38315 | − | 8.43998i | 0.401803 | − | 0.773692i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.57363 | − | 4.45766i | −0.233966 | − | 0.405242i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.73681 | − | 0.977949i | 0.246770 | − | 0.0881787i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.45432 | 0.577292 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.23056 | −0.819080 | −0.409540 | − | 0.912292i | \(-0.634311\pi\) | ||||
−0.409540 | + | 0.912292i | \(0.634311\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.08368 | − | 5.94155i | 0.0954129 | − | 0.523124i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.59440 | − | 2.76158i | −0.139303 | − | 0.241280i | 0.787930 | − | 0.615765i | \(-0.211153\pi\) |
−0.927233 | + | 0.374485i | \(0.877820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.540789 | − | 12.1158i | −0.0468924 | − | 1.05057i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 14.3878 | + | 0.253588i | 1.23831 | + | 0.0218254i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.87507 | + | 2.81462i | 0.416505 | + | 0.240470i | 0.693581 | − | 0.720379i | \(-0.256032\pi\) |
−0.277076 | + | 0.960848i | \(0.589365\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.6739 | + | 10.7814i | 1.58390 | + | 0.914467i | 0.994282 | + | 0.106786i | \(0.0340560\pi\) |
0.589620 | + | 0.807680i | \(0.299277\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.4195 | − | 14.7919i | −1.46699 | − | 1.24571i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.0644758 | − | 0.111675i | −0.00539174 | − | 0.00933877i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.2052 | + | 10.5107i | 1.51186 | + | 0.872870i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.0085 | − | 5.08075i | 0.907962 | − | 0.419053i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.5674 | − | 9.56517i | 1.35725 | − | 0.783609i | 0.367998 | − | 0.929826i | \(-0.380043\pi\) |
0.989252 | + | 0.146217i | \(0.0467099\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.94050 | − | 6.82515i | 0.320673 | − | 0.555423i | −0.659954 | − | 0.751306i | \(-0.729424\pi\) |
0.980627 | + | 0.195884i | \(0.0627575\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.34161 | + | 6.83406i | −0.674380 | + | 0.552501i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.3462 | + | 9.43748i | −1.31296 | + | 0.758037i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 19.9593i | − | 1.59293i | −0.604687 | − | 0.796463i | \(-0.706702\pi\) | ||
0.604687 | − | 0.796463i | \(-0.293298\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.3790 | − | 1.89303i | −0.823109 | − | 0.150127i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.251041 | − | 0.130373i | −0.0197848 | − | 0.0102749i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0423 | − | 20.8578i | 0.943223 | − | 1.63371i | 0.183951 | − | 0.982935i | \(-0.441111\pi\) |
0.759271 | − | 0.650774i | \(-0.225556\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.51122 | − | 8.84547i | 0.584748 | − | 0.688619i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.793686 | + | 1.37470i | −0.0614172 | + | 0.106378i | −0.895099 | − | 0.445867i | \(-0.852895\pi\) |
0.833682 | + | 0.552245i | \(0.186229\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.49858 | − | 11.2559i | −0.499891 | − | 0.865836i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.85486 | + | 12.8662i | −0.371260 | + | 0.983906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.23711 | 0.322142 | 0.161071 | − | 0.986943i | \(-0.448505\pi\) | ||||
0.161071 | + | 0.986943i | \(0.448505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.05551 | − | 0.314923i | 0.533346 | − | 0.0238059i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.4743 | + | 10.5927i | 0.937626 | + | 0.796194i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.38034 | − | 1.95164i | 0.252658 | − | 0.145872i | −0.368323 | − | 0.929698i | \(-0.620068\pi\) |
0.620981 | + | 0.783826i | \(0.286734\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.3685i | 1.14233i | 0.820835 | + | 0.571166i | \(0.193509\pi\) | ||||
−0.820835 | + | 0.571166i | \(0.806491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.97654 | − | 3.50527i | 0.220032 | − | 0.259117i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.4208 | 0.839671 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.69608i | 0.635921i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.7427 | + | 0.370896i | −0.999636 | + | 0.0269787i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.63751i | 0.190844i | 0.995437 | + | 0.0954219i | \(0.0304200\pi\) | ||||
−0.995437 | + | 0.0954219i | \(0.969580\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.45930 | −0.536932 | −0.268466 | − | 0.963289i | \(-0.586517\pi\) | ||||
−0.268466 | + | 0.963289i | \(0.586517\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.165492 | + | 0.194890i | −0.0118512 | + | 0.0139563i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 2.77770i | − | 0.197903i | −0.995092 | − | 0.0989515i | \(-0.968451\pi\) | ||
0.995092 | − | 0.0989515i | \(-0.0315489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.49892 | + | 2.02010i | −0.248032 | + | 0.143201i | −0.618863 | − | 0.785499i | \(-0.712406\pi\) |
0.370831 | + | 0.928700i | \(0.379073\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.7308 | + | 15.9054i | 1.32117 | + | 1.12188i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.8230 | − | 9.25606i | −1.25093 | − | 0.649648i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.64685 | −0.324550 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.203274 | + | 0.248115i | 0.0141285 | + | 0.0172452i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.54479 | + | 9.60386i | 0.383541 | + | 0.664313i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4855 | + | 18.1614i | −0.721849 | + | 1.25028i | 0.238409 | + | 0.971165i | \(0.423374\pi\) |
−0.960258 | + | 0.279115i | \(0.909959\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.57250 | + | 1.85183i | −0.107746 | + | 0.126885i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.82831 | + | 8.36289i | −0.329288 | + | 0.570344i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.1990 | − | 9.70361i | 1.03178 | − | 0.658724i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.9035 | − | 1.98869i | −0.736789 | − | 0.134383i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.191598i | − | 0.0128883i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.82344 | − | 5.09421i | 0.590861 | − | 0.341134i | −0.174577 | − | 0.984644i | \(-0.555856\pi\) |
0.765438 | + | 0.643510i | \(0.222522\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.49251 | − | 2.82717i | −0.499501 | − | 0.188478i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.03151 | + | 8.71483i | −0.333953 | + | 0.578424i | −0.983283 | − | 0.182083i | \(-0.941716\pi\) |
0.649330 | + | 0.760507i | \(0.275049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.9518 | − | 7.47775i | 0.855882 | − | 0.494144i | −0.00674926 | − | 0.999977i | \(-0.502148\pi\) |
0.862631 | + | 0.505834i | \(0.168815\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.79199 | + | 8.76221i | −0.446880 | + | 0.576511i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.3200 | − | 8.26764i | −0.938133 | − | 0.541631i | −0.0487581 | − | 0.998811i | \(-0.515526\pi\) |
−0.889374 | + | 0.457180i | \(0.848860\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.2694 | + | 31.6436i | 1.19177 | + | 2.06420i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.57328 | − | 4.73260i | −0.362023 | − | 0.307416i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.02155 | + | 5.20859i | 0.583555 | + | 0.336916i | 0.762545 | − | 0.646935i | \(-0.223950\pi\) |
−0.178990 | + | 0.983851i | \(0.557283\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.97668 | − | 5.18269i | −0.578239 | − | 0.333846i | 0.182194 | − | 0.983263i | \(-0.441680\pi\) |
−0.760433 | + | 0.649416i | \(0.775013\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.4855 | + | 5.75946i | 0.929243 | + | 0.369470i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.3085 | + | 1.72711i | −1.23357 | + | 0.110341i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.122167 | − | 0.211599i | −0.00777328 | − | 0.0134637i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.26810 | + | 23.4009i | −0.270480 | + | 1.48297i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 13.1006 | 0.826903 | 0.413452 | − | 0.910526i | \(-0.364323\pi\) | ||||
0.413452 | + | 0.910526i | \(0.364323\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.258658 | 0.0162617 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16.2364 | − | 5.80180i | 1.01677 | − | 0.363323i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.443415 | + | 0.768018i | 0.0276595 | + | 0.0479076i | 0.879524 | − | 0.475855i | \(-0.157861\pi\) |
−0.851864 | + | 0.523763i | \(0.824528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.9001 | + | 0.486527i | −0.677301 | + | 0.0302313i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.4317 | + | 17.6153i | 0.893301 | + | 1.09036i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.17036 | + | 3.56246i | 0.380481 | + | 0.219671i | 0.678028 | − | 0.735037i | \(-0.262835\pi\) |
−0.297547 | + | 0.954707i | \(0.596168\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.6087 | + | 8.43436i | 0.897407 | + | 0.518118i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.6502 | − | 6.66429i | 1.14137 | − | 0.407848i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.7987 | − | 27.3641i | −0.963261 | − | 1.66842i | −0.714216 | − | 0.699925i | \(-0.753217\pi\) |
−0.249045 | − | 0.968492i | \(-0.580117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.8215 | − | 9.13455i | −0.961088 | − | 0.554884i | −0.0645803 | − | 0.997913i | \(-0.520571\pi\) |
−0.896508 | + | 0.443028i | \(0.853904\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.149646 | − | 0.193055i | 0.00905698 | − | 0.0116842i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.59270 | + | 3.22895i | −0.337253 | + | 0.194713i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.2845 | − | 26.4735i | 0.918357 | − | 1.59064i | 0.116447 | − | 0.993197i | \(-0.462850\pi\) |
0.801910 | − | 0.597444i | \(-0.203817\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.1766 | + | 3.31375i | −1.20794 | + | 0.198389i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.92237 | − | 2.26458i | 0.233989 | − | 0.135094i | −0.378422 | − | 0.925633i | \(-0.623533\pi\) |
0.612411 | + | 0.790540i | \(0.290200\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.36150i | 0.556484i | 0.960511 | + | 0.278242i | \(0.0897517\pi\) | ||||
−0.960511 | + | 0.278242i | \(0.910248\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.2320 | − | 16.7601i | 0.843032 | − | 0.992784i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.43502 | − | 0.197957i | 0.261791 | − | 0.0116850i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.03962 | − | 3.53272i | 0.119977 | − | 0.207807i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.2438 | + | 5.15139i | 1.65568 | + | 0.301980i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.17267 | − | 14.1555i | 0.477452 | − | 0.826972i | −0.522214 | − | 0.852815i | \(-0.674894\pi\) |
0.999666 | + | 0.0258430i | \(0.00822701\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.0829 | − | 22.6603i | −0.761719 | − | 1.31934i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.9957 | − | 6.09255i | 0.638033 | − | 0.353526i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.00569894 | −0.000329578 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.25195 | − | 8.18734i | 0.245078 | − | 0.471910i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 17.1260 | − | 6.11966i | 0.983862 | − | 0.351565i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.36754 | + | 3.67630i | −0.364604 | + | 0.210504i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.985041i | 0.0562193i | 0.999605 | + | 0.0281096i | \(0.00894875\pi\) | ||||
−0.999605 | + | 0.0281096i | \(0.991051\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.2867 | + | 4.79444i | 1.49540 | + | 0.272746i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.2604 | −1.48909 | −0.744545 | − | 0.667573i | \(-0.767333\pi\) | ||||
−0.744545 | + | 0.667573i | \(0.767333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 14.5329i | − | 0.821446i | −0.911760 | − | 0.410723i | \(-0.865276\pi\) | ||
0.911760 | − | 0.410723i | \(-0.134724\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.8914 | + | 6.83540i | 1.17709 | + | 0.385131i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.4620i | 1.65475i | 0.561649 | + | 0.827375i | \(0.310167\pi\) | ||||
−0.561649 | + | 0.827375i | \(0.689833\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.3638 | 1.02818 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.57123 | + | 18.3897i | 0.366770 | + | 1.02641i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.4771i | 0.916808i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.123222 | − | 0.0711425i | 0.00683515 | − | 0.00394627i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.01172 | + | 27.4780i | −0.277149 | + | 1.51954i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.7846 | − | 29.4228i | −1.03563 | − | 1.62213i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.82030 | −0.319913 | −0.159956 | − | 0.987124i | \(-0.551135\pi\) | ||||
−0.159956 | + | 0.987124i | \(0.551135\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.5753 | + | 4.36773i | 0.634320 | + | 0.239350i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.6447 | − | 34.0255i | −1.07330 | − | 1.85901i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.4909 | + | 19.9028i | −0.625950 | + | 1.08418i | 0.362407 | + | 0.932020i | \(0.381955\pi\) |
−0.988356 | + | 0.152157i | \(0.951378\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.91043 | − | 22.1375i | −0.429636 | − | 1.20234i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.24433 | + | 14.2796i | −0.446456 | + | 0.773284i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3547 | − | 2.47092i | 0.991060 | − | 0.133417i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.172570 | − | 0.482940i | −0.00929085 | − | 0.0260006i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.9459i | 0.802336i | 0.916005 | + | 0.401168i | \(0.131396\pi\) | ||||
−0.916005 | + | 0.401168i | \(0.868604\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.768588 | − | 0.443744i | 0.0411416 | − | 0.0237531i | −0.479288 | − | 0.877658i | \(-0.659105\pi\) |
0.520430 | + | 0.853905i | \(0.325772\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.242264 | + | 0.134235i | −0.0129311 | + | 0.00716496i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.52498 | − | 4.37339i | 0.134391 | − | 0.232772i | −0.790974 | − | 0.611850i | \(-0.790426\pi\) |
0.925365 | + | 0.379078i | \(0.123759\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.36395 | − | 1.94218i | 0.178540 | − | 0.103080i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.2491 | + | 6.22899i | −0.807069 | + | 0.329673i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.2467 | + | 17.4629i | 1.59636 | + | 0.921659i | 0.992181 | + | 0.124810i | \(0.0398322\pi\) |
0.604179 | + | 0.796848i | \(0.293501\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00610 | + | 1.74261i | 0.0529524 | + | 0.0917163i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.59968 | + | 8.77063i | −0.0839614 | + | 0.460339i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.3469 | + | 8.86056i | 0.803296 | + | 0.463783i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.9959 | − | 11.5446i | −1.04378 | − | 0.602625i | −0.122876 | − | 0.992422i | \(-0.539212\pi\) |
−0.920901 | + | 0.389797i | \(0.872545\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.70971 | − | 1.77713i | −0.245178 | − | 0.0925137i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.3021 | − | 7.42753i | −0.742527 | − | 0.385618i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.899257 | − | 1.55756i | −0.0465617 | − | 0.0806473i | 0.841805 | − | 0.539781i | \(-0.181493\pi\) |
−0.888367 | + | 0.459134i | \(0.848160\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.52141 | − | 7.23604i | −0.440044 | − | 0.373668i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.404605 | −0.0208382 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.34605 | −0.171875 | −0.0859375 | − | 0.996301i | \(-0.527389\pi\) | ||||
−0.0859375 | + | 0.996301i | \(0.527389\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.1868 | + | 10.3485i | 0.624348 | + | 0.530171i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.989164 | + | 1.71328i | 0.0505439 | + | 0.0875447i | 0.890190 | − | 0.455589i | \(-0.150571\pi\) |
−0.839647 | + | 0.543133i | \(0.817238\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.9406 | − | 9.53866i | 0.761445 | − | 0.486135i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.09191 | + | 6.62949i | −0.411335 | + | 0.336996i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.2325 | − | 17.4547i | −1.53285 | − | 0.884990i | −0.999229 | − | 0.0392657i | \(-0.987498\pi\) |
−0.533619 | − | 0.845725i | \(-0.679169\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.332829 | + | 0.192159i | 0.0168319 | + | 0.00971789i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.991021 | + | 5.43352i | −0.0499904 | + | 0.274085i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.84521 | + | 10.1242i | 0.294104 | + | 0.509404i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.73751 | + | 1.58050i | 0.137392 | + | 0.0793231i | 0.567120 | − | 0.823635i | \(-0.308057\pi\) |
−0.429729 | + | 0.902958i | \(0.641391\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.8692 | + | 16.6024i | −0.644268 | + | 0.831158i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.6041 | + | 16.5146i | −1.42842 | + | 0.824698i | −0.996996 | − | 0.0774514i | \(-0.975322\pi\) |
−0.431423 | + | 0.902150i | \(0.641988\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.181645 | − | 0.314618i | 0.00904838 | − | 0.0156723i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.7114 | − | 16.4652i | −0.929778 | − | 0.818163i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.64023 | − | 4.98844i | 0.428280 | − | 0.247268i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.07813i | − | 0.0533099i | −0.999645 | − | 0.0266549i | \(-0.991514\pi\) | ||
0.999645 | − | 0.0266549i | \(-0.00848553\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.28087 | − | 9.18157i | −0.161833 | − | 0.452893i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 13.4519 | + | 21.0700i | 0.661923 | + | 1.03679i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.0164 | − | 32.9374i | 0.933479 | − | 1.61683i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.5673 | − | 35.1699i | −0.615425 | − | 1.72228i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.2799 | − | 23.0015i | 0.648768 | − | 1.12370i | −0.334650 | − | 0.942343i | \(-0.608618\pi\) |
0.983418 | − | 0.181356i | \(-0.0580486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.32791 | + | 5.76411i | 0.162192 | + | 0.280925i | 0.935655 | − | 0.352917i | \(-0.114810\pi\) |
−0.773462 | + | 0.633842i | \(0.781477\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.41487 | + | 39.0586i | 0.311902 | + | 1.89909i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.59524 | −0.465437 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.92065 | − | 3.77997i | 0.286521 | − | 0.182926i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0400759 | + | 0.219726i | −0.00193488 | + | 0.0106085i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.2930 | + | 7.67471i | −0.640300 | + | 0.369678i | −0.784730 | − | 0.619837i | \(-0.787199\pi\) |
0.144430 | + | 0.989515i | \(0.453865\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 15.9407i | − | 0.766060i | −0.923736 | − | 0.383030i | \(-0.874881\pi\) | ||
0.923736 | − | 0.383030i | \(-0.125119\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.2519 | − | 34.2871i | −0.587431 | − | 1.64394i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.490097 | 0.0234445 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 20.6424i | − | 0.985207i | −0.870254 | − | 0.492603i | \(-0.836045\pi\) | ||
0.870254 | − | 0.492603i | \(-0.163955\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.2302 | − | 5.63382i | −0.963342 | − | 0.268277i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.45354i | − | 0.0690595i | −0.999404 | − | 0.0345298i | \(-0.989007\pi\) | ||
0.999404 | − | 0.0345298i | \(-0.0109934\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −31.6662 | −1.50112 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.5970 | − | 5.94537i | −1.54178 | − | 0.281207i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.09933i | 0.429424i | 0.976677 | + | 0.214712i | \(0.0688813\pi\) | ||||
−0.976677 | + | 0.214712i | \(0.931119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.51551 | + | 2.02968i | −0.165539 | + | 0.0955740i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.8543 | + | 4.59324i | −0.603947 | + | 0.215809i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.329182 | + | 0.210163i | −0.0154323 | + | 0.00985257i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.4642 | −0.676606 | −0.338303 | − | 0.941037i | \(-0.609853\pi\) | ||||
−0.338303 | + | 0.941037i | \(0.609853\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.6749 | + | 0.329149i | 0.871670 | + | 0.0153634i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.2769 | + | 22.9963i | 0.618369 | + | 1.07105i | 0.989783 | + | 0.142579i | \(0.0455395\pi\) |
−0.371415 | + | 0.928467i | \(0.621127\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.4968 | − | 26.8412i | 0.720196 | − | 1.24742i | −0.240725 | − | 0.970593i | \(-0.577385\pi\) |
0.960921 | − | 0.276823i | \(-0.0892816\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 32.1618 | + | 5.86601i | 1.49147 | + | 0.272030i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.1348 | − | 17.5541i | 0.468985 | − | 0.812306i | −0.530387 | − | 0.847756i | \(-0.677953\pi\) |
0.999371 | + | 0.0354503i | \(0.0112865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.1986 | + | 31.6376i | 0.932686 | + | 1.46089i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −22.3767 | + | 26.3516i | −1.03106 | + | 1.21422i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.43577i | 0.387877i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.5969 | + | 6.11811i | −0.486218 | + | 0.280718i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 11.5807 | + | 14.1354i | 0.530245 | + | 0.647215i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.01288 | − | 13.8787i | 0.366118 | − | 0.634135i | −0.622837 | − | 0.782352i | \(-0.714020\pi\) |
0.988955 | + | 0.148217i | \(0.0473533\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.190368 | + | 0.109909i | −0.00868001 | + | 0.00501141i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.185276 | + | 0.453573i | 0.00843036 | + | 0.0206383i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −39.7538 | − | 22.9519i | −1.80513 | − | 1.04219i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.54048 | + | 14.7925i | 0.387006 | + | 0.670314i | 0.992045 | − | 0.125881i | \(-0.0401759\pi\) |
−0.605039 | + | 0.796196i | \(0.706843\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −39.2830 | + | 14.0371i | −1.77644 | + | 0.634778i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.9745 | + | 7.49082i | 0.585530 | + | 0.338056i | 0.763328 | − | 0.646011i | \(-0.223564\pi\) |
−0.177798 | + | 0.984067i | \(0.556897\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.6297 | + | 13.6426i | 1.06423 | + | 0.614432i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.8336 | + | 3.25742i | −0.891454 | + | 0.146410i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.12787 | + | 1.99695i | −0.140304 | + | 0.0895753i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.6638 | − | 21.9343i | −0.566910 | − | 0.981916i | −0.996869 | − | 0.0790682i | \(-0.974806\pi\) |
0.429960 | − | 0.902848i | \(-0.358528\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.58908 | − | 0.925160i | 0.115671 | − | 0.0413331i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.95401 | 0.443827 | 0.221914 | − | 0.975066i | \(-0.428770\pi\) | ||||
0.221914 | + | 0.975066i | \(0.428770\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −29.0783 | −1.29397 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.03929 | + | 22.1464i | −0.179391 | + | 0.983556i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.82977 | − | 10.0975i | −0.258400 | − | 0.447562i | 0.707413 | − | 0.706800i | \(-0.249862\pi\) |
−0.965813 | + | 0.259238i | \(0.916529\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0248 | − | 7.80285i | −0.664657 | − | 0.345178i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.8342 | − | 11.5440i | 0.919854 | − | 0.509679i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −36.9992 | − | 21.3615i | −1.63038 | − | 0.941300i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 27.6430 | + | 15.9597i | 1.21574 | + | 0.701906i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.59411 | − | 4.75029i | −0.245554 | − | 0.208515i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.59307 | + | 14.8836i | 0.376469 | + | 0.652064i | 0.990546 | − | 0.137183i | \(-0.0438048\pi\) |
−0.614077 | + | 0.789246i | \(0.710471\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.1175 | − | 22.0071i | −1.66676 | − | 0.962305i | −0.969367 | − | 0.245616i | \(-0.921010\pi\) |
−0.697394 | − | 0.716688i | \(-0.745657\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.66821 | − | 7.49426i | −0.421955 | − | 0.327076i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.2168 | + | 12.2495i | −0.924220 | + | 0.533599i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4943 | + | 19.9087i | −0.499751 | + | 0.865595i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.59376 | − | 27.9703i | −0.199352 | − | 1.21381i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0774562 | − | 0.0447194i | 0.00335500 | − | 0.00193701i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 31.2240i | − | 1.34993i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.65095 | − | 1.21307i | −0.287010 | − | 0.0523478i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.8532 | + | 9.74030i | −0.596699 | + | 0.419544i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.06580 | + | 8.77423i | −0.217796 | + | 0.377234i | −0.954134 | − | 0.299380i | \(-0.903220\pi\) |
0.736338 | + | 0.676614i | \(0.236553\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.2299 | − | 20.2905i | 0.739405 | − | 0.870749i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 22.3296 | − | 38.6760i | 0.956495 | − | 1.65670i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0000 | + | 29.4449i | 0.726869 | + | 1.25897i | 0.958200 | + | 0.286099i | \(0.0923585\pi\) |
−0.231331 | + | 0.972875i | \(0.574308\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.85963 | + | 1.29084i | −0.335441 | + | 0.0550919i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.7952 | 1.48232 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.01004 | − | 9.41366i | −0.255573 | − | 0.400310i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.0784 | − | 12.8040i | −0.640044 | − | 0.543500i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.88366 | + | 1.08753i | −0.0798133 | + | 0.0460802i | −0.539376 | − | 0.842065i | \(-0.681340\pi\) |
0.459562 | + | 0.888146i | \(0.348006\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.185863i | − | 0.00786116i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.74932 | − | 11.4811i | 0.411617 | − | 0.484734i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.49555 | −0.189465 | −0.0947324 | − | 0.995503i | \(-0.530200\pi\) | ||||
−0.0947324 | + | 0.995503i | \(0.530200\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.5874i | 1.58131i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.5599 | + | 14.9175i | 0.779440 | + | 0.626476i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 6.12306i | − | 0.256692i | −0.991729 | − | 0.128346i | \(-0.959033\pi\) | ||
0.991729 | − | 0.128346i | \(-0.0409668\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.3658 | −1.35447 | −0.677233 | − | 0.735769i | \(-0.736821\pi\) | ||||
−0.677233 | + | 0.735769i | \(0.736821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.95696 | − | 3.48222i | 0.123529 | − | 0.145472i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.285403i | 0.0119021i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.2034 | + | 19.7473i | −1.42390 | + | 0.822092i | −0.996630 | − | 0.0820304i | \(-0.973860\pi\) |
−0.427274 | + | 0.904122i | \(0.640526\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.84825 | + | 8.36274i | 0.409279 | + | 0.347544i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.7464 | + | 32.2460i | −0.694757 | + | 1.33779i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.7361 | 0.610305 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.436988 | − | 0.0717697i | 0.0180672 | − | 0.00296731i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.129711 | − | 0.224667i | −0.00535376 | − | 0.00927298i | 0.863336 | − | 0.504629i | \(-0.168371\pi\) |
−0.868690 | + | 0.495356i | \(0.835037\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.6211 | + | 27.0565i | −0.643656 | + | 1.11485i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.11412 | + | 3.66730i | −0.128098 | + | 0.150853i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.13549 | + | 5.43083i | −0.128759 | + | 0.223017i | −0.923196 | − | 0.384329i | \(-0.874433\pi\) |
0.794437 | + | 0.607347i | \(0.207766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.3112 | − | 1.17440i | 1.07866 | − | 0.0481458i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.88427 | + | 1.25563i | 0.281754 | + | 0.0513893i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.37396i | 0.260433i | 0.991486 | + | 0.130217i | \(0.0415672\pi\) | ||||
−0.991486 | + | 0.130217i | \(0.958433\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0862 | − | 8.71001i | 0.615378 | − | 0.355289i | −0.159689 | − | 0.987167i | \(-0.551049\pi\) |
0.775067 | + | 0.631879i | \(0.217716\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.89775 | − | 41.9987i | −0.280898 | − | 1.71032i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.12732 | − | 12.3449i | 0.289767 | − | 0.501891i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.56183 | − | 0.901722i | 0.0633927 | − | 0.0365998i | −0.467969 | − | 0.883745i | \(-0.655014\pi\) |
0.531361 | + | 0.847145i | \(0.321681\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.1540 | + | 32.2021i | 0.533026 | + | 1.30489i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.609050 | − | 0.351635i | −0.0246395 | − | 0.0142256i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.6290 | − | 30.5343i | −0.712028 | − | 1.23327i | −0.964095 | − | 0.265559i | \(-0.914443\pi\) |
0.252066 | − | 0.967710i | \(-0.418890\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.13507 | + | 5.20966i | 0.247390 | + | 0.210074i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.73458 | − | 4.46556i | −0.311383 | − | 0.179777i | 0.336162 | − | 0.941804i | \(-0.390871\pi\) |
−0.647545 | + | 0.762027i | \(0.724204\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.3546 | + | 19.2573i | 1.34064 | + | 0.774016i | 0.986901 | − | 0.161330i | \(-0.0515782\pi\) |
0.353735 | + | 0.935346i | \(0.384912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.00979028 | − | 0.555470i | 0.000392870 | − | 0.0222903i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.2227 | − | 1.34899i | 1.21085 | − | 0.0540461i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6107 | + | 27.0384i | 0.624426 | + | 1.08154i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.44645 | − | 18.8960i | 0.137638 | − | 0.754633i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 14.8238 | 0.591063 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.5826 | −0.978616 | −0.489308 | − | 0.872111i | \(-0.662751\pi\) | ||||
−0.489308 | + | 0.872111i | \(0.662751\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.2046 | − | 12.2224i | 1.35951 | − | 0.485796i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.7814 | − | 22.1380i | −0.507214 | − | 0.878521i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.305223 | − | 0.214605i | 0.0120934 | − | 0.00850297i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.15222 | − | 0.681950i | 0.164259 | − | 0.0269775i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.1635 | + | 16.8376i | 1.15189 | + | 0.665044i | 0.949347 | − | 0.314229i | \(-0.101746\pi\) |
0.202543 | + | 0.979273i | \(0.435079\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.02496 | − | 1.16911i | −0.0798567 | − | 0.0461053i | 0.459540 | − | 0.888157i | \(-0.348014\pi\) |
−0.539397 | + | 0.842052i | \(0.681348\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.7504 | − | 5.62812i | 0.620172 | − | 0.221607i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.89769 | − | 3.28689i | −0.0746059 | − | 0.129221i | 0.826309 | − | 0.563217i | \(-0.190437\pi\) |
−0.900915 | + | 0.433996i | \(0.857103\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.7955 | − | 11.4289i | −0.777040 | − | 0.448624i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30.9456 | − | 4.22850i | −1.21285 | − | 0.165728i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.1456 | − | 5.85755i | 0.397027 | − | 0.229224i | −0.288173 | − | 0.957578i | \(-0.593048\pi\) |
0.685200 | + | 0.728355i | \(0.259715\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.41547 | − | 7.64782i | 0.172527 | − | 0.298825i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.1659 | + | 14.8497i | 0.474638 | + | 0.579341i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.4962 | − | 12.9882i | 0.876329 | − | 0.505949i | 0.00688257 | − | 0.999976i | \(-0.497809\pi\) |
0.869446 | + | 0.494028i | \(0.164476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 6.86096i | − | 0.266860i | −0.991058 | − | 0.133430i | \(-0.957401\pi\) | ||
0.991058 | − | 0.133430i | \(-0.0425992\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.214804 | + | 0.252960i | −0.00834229 | + | 0.00982417i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.3090 | − | 18.0736i | 1.09778 | − | 0.700862i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.405789 | − | 0.702846i | 0.0157122 | − | 0.0272143i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.3605 | − | 3.16639i | −0.671195 | − | 0.122420i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.21152 | + | 5.56251i | −0.123979 | + | 0.214738i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.652179 | − | 1.12961i | −0.0251397 | − | 0.0435432i | 0.853182 | − | 0.521614i | \(-0.174670\pi\) |
−0.878322 | + | 0.478070i | \(0.841336\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.72251 | + | 12.1326i | 0.258749 | + | 0.466984i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.2303 | −0.508483 | −0.254241 | − | 0.967141i | \(-0.581826\pi\) | ||||
−0.254241 | + | 0.967141i | \(0.581826\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.9193 | + | 20.2121i | 1.49359 | + | 0.775668i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 16.4133 | − | 5.86498i | 0.628958 | − | 0.224747i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.49949 | − | 0.865733i | 0.0573765 | − | 0.0331264i | −0.471037 | − | 0.882113i | \(-0.656120\pi\) |
0.528414 | + | 0.848987i | \(0.322787\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5894i | 0.595642i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −25.4833 | − | 4.64791i | −0.972248 | − | 0.177329i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.324675 | −0.0123691 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.40092i | − | 0.319586i | −0.987151 | − | 0.159793i | \(-0.948917\pi\) | ||
0.987151 | − | 0.159793i | \(-0.0510827\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.7907 | − | 3.95384i | 0.713799 | − | 0.150194i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 59.7153i | 2.26513i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.03146 | −0.228458 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.63717 | + | 26.9698i | 0.364511 | + | 1.02009i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 21.3493i | − | 0.806353i | −0.915122 | − | 0.403176i | \(-0.867906\pi\) | ||
0.915122 | − | 0.403176i | \(-0.132094\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.3712 | − | 9.45193i | 0.617452 | − | 0.356486i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 11.3556 | − | 62.2601i | 0.427678 | − | 2.34485i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 27.7527 | − | 1.23874i | 1.04375 | − | 0.0465877i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.2617 | −0.723390 | −0.361695 | − | 0.932296i | \(-0.617802\pi\) | ||||
−0.361695 | + | 0.932296i | \(0.617802\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.05240 | + | 12.4966i | 0.0769712 | + | 0.468658i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.364353 | + | 0.631078i | 0.0136451 | + | 0.0236341i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.178557 | − | 0.309270i | 0.00667766 | − | 0.0115660i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.07139 | − | 16.9909i | −0.226740 | − | 0.634538i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.39920 | − | 9.35168i | 0.201356 | − | 0.348759i | −0.747610 | − | 0.664138i | \(-0.768799\pi\) |
0.948966 | + | 0.315380i | \(0.102132\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.2225 | + | 18.8115i | 1.34900 | + | 0.700577i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.04120 | + | 16.9064i | 0.224675 | + | 0.628757i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.2626i | 0.752534i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9316 | + | 14.9716i | −0.961751 | + | 0.555267i | −0.896711 | − | 0.442616i | \(-0.854051\pi\) |
−0.0650393 | + | 0.997883i | \(0.520717\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.6676 | − | 23.8439i | −0.469171 | − | 0.883107i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.26700 | + | 10.8548i | −0.231793 | + | 0.401478i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.8872 | + | 8.01776i | −0.512934 | + | 0.296143i | −0.734039 | − | 0.679107i | \(-0.762367\pi\) |
0.221105 | + | 0.975250i | \(0.429034\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 27.4286 | + | 19.3668i | 1.01172 | + | 0.714355i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.7238 | − | 17.1610i | −1.09489 | − | 0.632135i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.5186 | + | 19.9508i | 0.423719 | + | 0.733903i | 0.996300 | − | 0.0859453i | \(-0.0273910\pi\) |
−0.572581 | + | 0.819848i | \(0.694058\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0759346 | + | 0.416330i | −0.00278953 | + | 0.0152943i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 37.2352 | + | 21.4978i | 1.36603 | + | 0.788676i | 0.990418 | − | 0.138102i | \(-0.0441001\pi\) |
0.375609 | + | 0.926778i | \(0.377433\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.8811 | + | 26.4895i | 1.68095 | + | 0.970498i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31.8702 | − | 26.1104i | 1.16607 | − | 0.955328i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.33015 | + | 29.8006i | 0.0486026 | + | 1.08889i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.6900 | − | 30.6400i | −0.645518 | − | 1.11807i | −0.984182 | − | 0.177162i | \(-0.943308\pi\) |
0.338664 | − | 0.940907i | \(-0.390025\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.2963 | − | 14.6873i | −0.630311 | − | 0.535235i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.8254 | 0.794307 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.6138 | −0.894604 | −0.447302 | − | 0.894383i | \(-0.647615\pi\) | ||||
−0.447302 | + | 0.894383i | \(0.647615\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.341497 | − | 0.289986i | −0.0123956 | − | 0.0105258i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.89264 | + | 11.9384i | 0.249858 | + | 0.432766i | 0.963486 | − | 0.267758i | \(-0.0862828\pi\) |
−0.713628 | + | 0.700525i | \(0.752949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −19.6641 | + | 37.8641i | −0.711887 | + | 1.37077i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.9409 | − | 10.5430i | −1.01021 | − | 0.381184i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.436147 | + | 0.251810i | 0.0157484 | + | 0.00909233i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.0352 | + | 11.5673i | 0.722486 | + | 0.417128i | 0.815667 | − | 0.578522i | \(-0.196370\pi\) |
−0.0931808 | + | 0.995649i | \(0.529703\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.275611 | − | 1.51111i | 0.00992591 | − | 0.0544212i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.5072 | − | 45.9118i | −0.953398 | − | 1.65133i | −0.737993 | − | 0.674808i | \(-0.764226\pi\) |
−0.215405 | − | 0.976525i | \(-0.569107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.7561 | − | 9.09678i | −0.565975 | − | 0.326766i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 14.9365 | + | 11.5780i | 0.535844 | + | 0.415357i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.66108 | + | 3.84578i | −0.238658 | + | 0.137789i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.69664 | − | 2.93866i | 0.0607104 | − | 0.105154i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.695075 | − | 39.4364i | 0.0248400 | − | 1.40934i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.8693 | − | 27.6373i | 1.70853 | − | 0.986418i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 5.96329i | − | 0.212568i | −0.994336 | − | 0.106284i | \(-0.966105\pi\) | ||
0.994336 | − | 0.106284i | \(-0.0338953\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.15258 | − | 11.6211i | −0.147836 | − | 0.413722i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.60123 | − | 35.8739i | −0.0569333 | − | 1.27553i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0707584 | − | 0.122557i | 0.00251271 | − | 0.00435213i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.83150 | − | 27.5137i | −0.348688 | − | 0.975809i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −5.28758 | + | 9.15836i | −0.187296 | + | 0.324406i | −0.944348 | − | 0.328949i | \(-0.893306\pi\) |
0.757052 | + | 0.653355i | \(0.226639\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7131 | + | 41.0724i | 0.838910 | + | 1.45304i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.0946 | − | 12.1104i | −1.13401 | − | 0.427899i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.4807 | 0.546302 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0349316 | − | 0.782607i | −0.00123118 | − | 0.0275833i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.81989 | + | 53.8400i | −0.345677 | + | 1.89526i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.1452 | − | 18.5591i | 1.13017 | − | 0.652501i | 0.186189 | − | 0.982514i | \(-0.440386\pi\) |
0.943977 | + | 0.330012i | \(0.107053\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.02945i | 0.246837i | 0.992355 | + | 0.123419i | \(0.0393858\pi\) | ||||
−0.992355 | + | 0.123419i | \(0.960614\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.6477 | + | 29.7978i | 0.373431 | + | 1.04505i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 66.6989 | 2.33636 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.9838i | 0.559203i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.414010 | + | 0.0871137i | −0.0144667 | + | 0.00304400i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 21.4378i | − | 0.748184i | −0.927392 | − | 0.374092i | \(-0.877954\pi\) | ||
0.927392 | − | 0.374092i | \(-0.122046\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.4491 | −0.677953 | −0.338977 | − | 0.940795i | \(-0.610081\pi\) | ||||
−0.338977 | + | 0.940795i | \(0.610081\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.0039 | + | 2.00700i | 0.383106 | + | 0.0698748i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.3789i | 0.569549i | 0.958595 | + | 0.284774i | \(0.0919187\pi\) | ||||
−0.958595 | + | 0.284774i | \(0.908081\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.5517 | + | 7.82408i | −0.470670 | + | 0.271741i | −0.716520 | − | 0.697566i | \(-0.754266\pi\) |
0.245850 | + | 0.969308i | \(0.420933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −49.8595 | + | 17.8164i | −1.72961 | + | 0.618043i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −25.0618 | + | 2.24173i | −0.868339 | + | 0.0776713i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.39601 | −0.152130 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30.3535 | + | 18.2453i | 1.04917 | + | 0.630648i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.260756 | − | 0.451642i | −0.00900229 | − | 0.0155924i | 0.861489 | − | 0.507776i | \(-0.169532\pi\) |
−0.870491 | + | 0.492184i | \(0.836199\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.3096 | − | 24.7849i | 0.493433 | − | 0.854652i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.71742 | − | 1.40758i | −0.265802 | − | 0.0484798i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.9969 | − | 31.1716i | 0.619114 | − | 1.07234i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.27652 | + | 12.0858i | −0.215664 | + | 0.415271i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.4953 | − | 12.3597i | 0.360199 | − | 0.424183i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 0.440921i | − | 0.0151146i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3460 | + | 8.85999i | −0.525436 | + | 0.303360i | −0.739156 | − | 0.673535i | \(-0.764775\pi\) |
0.213720 | + | 0.976895i | \(0.431442\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −37.5801 | + | 6.17205i | −1.28521 | + | 0.211080i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.41363 | + | 2.44849i | −0.0482888 | + | 0.0836387i | −0.889160 | − | 0.457597i | \(-0.848710\pi\) |
0.840871 | + | 0.541236i | \(0.182043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.97741 | − | 4.60576i | 0.272186 | − | 0.157147i | −0.357695 | − | 0.933839i | \(-0.616437\pi\) |
0.629881 | + | 0.776692i | \(0.283104\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.07733 | − | 4.71081i | −0.207115 | − | 0.160544i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.7016 | + | 9.06534i | 0.534490 | + | 0.308588i | 0.742843 | − | 0.669466i | \(-0.233477\pi\) |
−0.208353 | + | 0.978054i | \(0.566810\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.86705 | + | 10.1620i | 0.199486 | + | 0.345520i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.65342 | + | 2.37748i | −0.225962 | + | 0.0807434i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.84423 | + | 5.10622i | 0.300020 | + | 0.173217i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.654896 | + | 0.378104i | 0.0221903 | + | 0.0128116i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.5139 | − | 38.4657i | −1.06659 | − | 1.30187i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.18921 | − | 14.3933i | −0.310652 | − | 0.486581i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.10432 | − | 12.3050i | −0.239896 | − | 0.415512i | 0.720788 | − | 0.693155i | \(-0.243780\pi\) |
−0.960684 | + | 0.277643i | \(0.910447\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.6600 | + | 9.52647i | −0.899220 | + | 0.321320i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.0649 | −1.55197 | −0.775984 | − | 0.630753i | \(-0.782746\pi\) | ||||
−0.775984 | + | 0.630753i | \(0.782746\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.16154 | 0.274658 | 0.137329 | − | 0.990526i | \(-0.456148\pi\) | ||||
0.137329 | + | 0.990526i | \(0.456148\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.13190 | + | 44.5851i | −0.273351 | + | 1.49871i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.5643 | + | 23.4941i | 0.455446 | + | 0.788856i | 0.998714 | − | 0.0507036i | \(-0.0161464\pi\) |
−0.543267 | + | 0.839560i | \(0.682813\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.1418 | + | 20.5843i | 0.440763 | + | 0.690377i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.3477 | − | 4.28364i | −0.715173 | − | 0.143507i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 52.3771 | + | 30.2399i | 1.75273 | + | 1.01194i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.36139 | + | 5.40480i | 0.312917 | + | 0.180662i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.00752410 | + | 0.00638917i | 0.000251223 | + | 0.000213328i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.8678 | + | 44.8043i | 0.862739 | + | 1.49431i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.9617 | + | 10.9475i | 0.631704 | + | 0.364715i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.7927 | + | 6.04253i | −0.492269 | + | 0.201083i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.8589 | + | 21.2805i | −1.22523 | + | 0.707388i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.7926 | − | 22.1574i | 0.424770 | − | 0.735724i | −0.571629 | − | 0.820512i | \(-0.693688\pi\) |
0.996399 | + | 0.0847887i | \(0.0270215\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −29.4717 | − | 11.1206i | −0.977514 | − | 0.368849i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.57426 | − | 2.64095i | 0.151552 | − | 0.0874986i | −0.422306 | − | 0.906453i | \(-0.638779\pi\) |
0.573858 | + | 0.818955i | \(0.305446\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 33.2245i | − | 1.09957i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.5284 | + | 2.28506i | 0.414176 | + | 0.0755418i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.88838 | + | 7.48728i | −0.128406 | + | 0.247252i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.7214 | + | 48.0149i | −0.914445 | + | 1.58387i | −0.106733 | + | 0.994288i | \(0.534039\pi\) |
−0.807712 | + | 0.589578i | \(0.799294\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.10435 | − | 1.30051i | 0.0363894 | − | 0.0428534i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0373815 | + | 0.0647466i | −0.00123043 | + | 0.00213116i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.50423 | + | 9.53360i | 0.180978 | + | 0.313463i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.3303 | − | 35.8003i | −0.963332 | − | 1.17584i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.2009 | −1.15490 | −0.577452 | − | 0.816425i | \(-0.695953\pi\) | ||||
−0.577452 | + | 0.816425i | \(0.695953\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.2486 | + | 18.4556i | −0.860262 | + | 0.604858i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.6706 | + | 29.4409i | 1.13507 | + | 0.963853i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.8562 | + | 12.0413i | −0.682070 | + | 0.393793i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 47.6315i | − | 1.55605i | −0.628231 | − | 0.778027i | \(-0.716221\pi\) | ||
0.628231 | − | 0.778027i | \(-0.283779\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.2930 | + | 19.1872i | −0.531702 | + | 0.626151i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.7603 | 0.676767 | 0.338384 | − | 0.941008i | \(-0.390120\pi\) | ||||
0.338384 | + | 0.941008i | \(0.390120\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.179401i | 0.00584210i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −19.9188 | − | 32.4462i | −0.647960 | − | 1.05547i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.51326i | 0.244148i | 0.992521 | + | 0.122074i | \(0.0389545\pi\) | ||||
−0.992521 | + | 0.122074i | \(0.961045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.341082 | −0.0110720 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.0303 | − | 38.8976i | 1.07108 | − | 1.26134i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 53.6047i | 1.73643i | 0.496192 | + | 0.868213i | \(0.334731\pi\) | ||||
−0.496192 | + | 0.868213i | \(0.665269\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.32566 | + | 3.65212i | −0.204694 | + | 0.118180i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −24.2451 | − | 20.5880i | −0.783733 | − | 0.665514i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.664114 | − | 14.8788i | −0.0214454 | − | 0.480461i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.4528 | −0.498477 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.9412 | − | 31.6464i | 0.384801 | − | 1.01979i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.3288 | − | 17.8899i | −0.332495 | − | 0.575898i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.72860 | + | 9.92223i | −0.184220 | + | 0.319078i | −0.943313 | − | 0.331904i | \(-0.892309\pi\) |
0.759094 | + | 0.650981i | \(0.225642\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.4727 | − | 21.7541i | 0.593429 | − | 0.698842i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.02601 | − | 6.97326i | 0.129201 | − | 0.223782i | −0.794166 | − | 0.607700i | \(-0.792092\pi\) |
0.923367 | + | 0.383918i | \(0.125425\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.54388 | − | 56.9931i | −0.0815532 | − | 1.82711i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.242445 | − | 0.0442197i | −0.00776446 | − | 0.00141616i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 47.8756i | − | 1.53168i | −0.643034 | − | 0.765838i | \(-0.722324\pi\) | ||
0.643034 | − | 0.765838i | \(-0.277676\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.9567 | + | 13.8314i | −0.765658 | + | 0.442053i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.4228 | − | 30.6595i | 1.19482 | − | 0.978883i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.18090 | − | 2.04538i | 0.0376648 | − | 0.0652374i | −0.846578 | − | 0.532264i | \(-0.821341\pi\) |
0.884243 | + | 0.467027i | \(0.154675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.66187 | − | 3.84623i | 0.212265 | − | 0.122551i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.18568 | + | 59.9056i | −0.260553 | + | 1.90682i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.322866 | + | 0.186407i | 0.0102665 | + | 0.00592739i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.8241 | − | 20.4800i | −0.375606 | − | 0.650568i | 0.614812 | − | 0.788674i | \(-0.289232\pi\) |
−0.990417 | + | 0.138106i | \(0.955899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.68434 | + | 6.52523i | 0.243855 | + | 0.207072i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.68979 | − | 5.59440i | −0.307187 | − | 0.177355i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.7446 | + | 21.2145i | 1.16371 | + | 0.671869i | 0.952191 | − | 0.305504i | \(-0.0988250\pi\) |
0.211521 | + | 0.977373i | \(0.432158\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.3857 | − | 18.7438i | −0.328588 | − | 0.593027i |
(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 | 504.2.bs.a.257.6 | ✓ | 48 | |
3.2 | odd | 2 | 1512.2.bs.a.1097.4 | 48 | |||
4.3 | odd | 2 | 1008.2.ca.e.257.19 | 48 | |||
7.3 | odd | 6 | 504.2.cx.a.185.14 | yes | 48 | ||
9.2 | odd | 6 | 504.2.cx.a.425.14 | yes | 48 | ||
9.7 | even | 3 | 1512.2.cx.a.89.4 | 48 | |||
12.11 | even | 2 | 3024.2.ca.e.2609.4 | 48 | |||
21.17 | even | 6 | 1512.2.cx.a.17.4 | 48 | |||
28.3 | even | 6 | 1008.2.df.e.689.11 | 48 | |||
36.7 | odd | 6 | 3024.2.df.e.1601.4 | 48 | |||
36.11 | even | 6 | 1008.2.df.e.929.11 | 48 | |||
63.38 | even | 6 | inner | 504.2.bs.a.353.6 | yes | 48 | |
63.52 | odd | 6 | 1512.2.bs.a.521.4 | 48 | |||
84.59 | odd | 6 | 3024.2.df.e.17.4 | 48 | |||
252.115 | even | 6 | 3024.2.ca.e.2033.4 | 48 | |||
252.227 | odd | 6 | 1008.2.ca.e.353.19 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bs.a.257.6 | ✓ | 48 | 1.1 | even | 1 | trivial | |
504.2.bs.a.353.6 | yes | 48 | 63.38 | even | 6 | inner | |
504.2.cx.a.185.14 | yes | 48 | 7.3 | odd | 6 | ||
504.2.cx.a.425.14 | yes | 48 | 9.2 | odd | 6 | ||
1008.2.ca.e.257.19 | 48 | 4.3 | odd | 2 | |||
1008.2.ca.e.353.19 | 48 | 252.227 | odd | 6 | |||
1008.2.df.e.689.11 | 48 | 28.3 | even | 6 | |||
1008.2.df.e.929.11 | 48 | 36.11 | even | 6 | |||
1512.2.bs.a.521.4 | 48 | 63.52 | odd | 6 | |||
1512.2.bs.a.1097.4 | 48 | 3.2 | odd | 2 | |||
1512.2.cx.a.17.4 | 48 | 21.17 | even | 6 | |||
1512.2.cx.a.89.4 | 48 | 9.7 | even | 3 | |||
3024.2.ca.e.2033.4 | 48 | 252.115 | even | 6 | |||
3024.2.ca.e.2609.4 | 48 | 12.11 | even | 2 | |||
3024.2.df.e.17.4 | 48 | 84.59 | odd | 6 | |||
3024.2.df.e.1601.4 | 48 | 36.7 | odd | 6 |