Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1024,2,Mod(129,1024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1024, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1024.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1024 = 2^{10} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1024.g (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.17668116698\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 641.1 | ||
Root | \(-0.793353 + 0.608761i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.641 |
Dual form | 1024.2.g.d.385.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.70868 | − | 1.12197i | −1.56386 | − | 0.647770i | −0.578102 | − | 0.815965i | \(-0.696206\pi\) |
−0.985754 | + | 0.168194i | \(0.946206\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.151613 | − | 0.366025i | −0.0678033 | − | 0.163692i | 0.886345 | − | 0.463025i | \(-0.153236\pi\) |
−0.954149 | + | 0.299333i | \(0.903236\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.06528 | − | 3.06528i | 1.15857 | − | 1.15857i | 0.173784 | − | 0.984784i | \(-0.444401\pi\) |
0.984784 | − | 0.173784i | \(-0.0555994\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.95680 | + | 3.95680i | 1.31893 | + | 1.31893i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.66515 | − | 1.51815i | 1.10508 | − | 0.457741i | 0.245842 | − | 0.969310i | \(-0.420936\pi\) |
0.859242 | + | 0.511569i | \(0.170936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.780239 | + | 1.88366i | −0.216399 | + | 0.522434i | −0.994382 | − | 0.105852i | \(-0.966243\pi\) |
0.777983 | + | 0.628286i | \(0.216243\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.16155i | 0.299911i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.54587i | 1.10253i | 0.834329 | + | 0.551267i | \(0.185856\pi\) | ||||
−0.834329 | + | 0.551267i | \(0.814144\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.221474 | + | 0.534684i | −0.0508095 | + | 0.122665i | −0.947246 | − | 0.320507i | \(-0.896147\pi\) |
0.896437 | + | 0.443172i | \(0.146147\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.7420 | + | 4.86370i | −2.56232 | + | 1.06135i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.41794 | + | 4.41794i | 0.921203 | + | 0.921203i | 0.997115 | − | 0.0759114i | \(-0.0241866\pi\) |
−0.0759114 | + | 0.997115i | \(0.524187\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.42455 | − | 3.42455i | 0.684909 | − | 0.684909i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.91236 | − | 7.03106i | −0.560484 | − | 1.35313i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.74737 | + | 1.96642i | 0.881564 | + | 0.365156i | 0.777103 | − | 0.629373i | \(-0.216688\pi\) |
0.104461 | + | 0.994529i | \(0.466688\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0539984 | 0.00969841 | 0.00484920 | − | 0.999988i | \(-0.498456\pi\) | ||||
0.00484920 | + | 0.999988i | \(0.498456\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −11.6310 | −2.02470 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.58671 | − | 0.657235i | −0.268202 | − | 0.111093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.330749 | + | 0.798499i | 0.0543748 | + | 0.131272i | 0.948732 | − | 0.316080i | \(-0.102367\pi\) |
−0.894358 | + | 0.447353i | \(0.852367\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.22683 | − | 4.22683i | 0.676835 | − | 0.676835i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.621063 | + | 0.621063i | 0.0969937 | + | 0.0969937i | 0.753939 | − | 0.656945i | \(-0.228152\pi\) |
−0.656945 | + | 0.753939i | \(0.728152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.06923 | + | 0.857104i | −0.315555 | + | 0.130707i | −0.534839 | − | 0.844954i | \(-0.679628\pi\) |
0.219284 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.848387 | − | 2.04819i | 0.126470 | − | 0.305326i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 9.44387i | − | 1.37753i | −0.724984 | − | 0.688765i | \(-0.758153\pi\) | ||
0.724984 | − | 0.688765i | \(-0.241847\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 11.7919i | − | 1.68456i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.10033 | − | 12.3133i | 0.714189 | − | 1.72420i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0582 | − | 4.16622i | 1.38159 | − | 0.572275i | 0.436687 | − | 0.899614i | \(-0.356152\pi\) |
0.944907 | + | 0.327339i | \(0.106152\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.11137 | − | 1.11137i | −0.149857 | − | 0.149857i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.19980 | − | 1.19980i | 0.158918 | − | 0.158918i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.97354 | − | 7.17877i | −0.387123 | − | 0.934596i | −0.990547 | − | 0.137176i | \(-0.956197\pi\) |
0.603424 | − | 0.797420i | \(-0.293803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.72911 | + | 4.02993i | 1.24568 | + | 0.515979i | 0.905487 | − | 0.424375i | \(-0.139506\pi\) |
0.340198 | + | 0.940354i | \(0.389506\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 24.2574 | 3.05614 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.807763 | 0.100191 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.53875 | − | 3.12265i | −0.921004 | − | 0.381493i | −0.128746 | − | 0.991678i | \(-0.541095\pi\) |
−0.792259 | + | 0.610185i | \(0.791095\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.00997 | − | 16.9236i | −0.843901 | − | 2.03736i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.99152 | + | 2.99152i | −0.355028 | + | 0.355028i | −0.861976 | − | 0.506948i | \(-0.830773\pi\) |
0.506948 | + | 0.861976i | \(0.330773\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.91724 | − | 2.91724i | −0.341437 | − | 0.341437i | 0.515470 | − | 0.856907i | \(-0.327617\pi\) |
−0.856907 | + | 0.515470i | \(0.827617\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.1182 | + | 5.43375i | −1.51476 | + | 0.627435i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.58114 | − | 15.8883i | 0.749991 | − | 1.81064i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.74836i | 0.646741i | 0.946272 | + | 0.323370i | \(0.104816\pi\) | ||||
−0.946272 | + | 0.323370i | \(0.895184\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.52520i | 0.613911i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.36905 | − | 3.30517i | 0.150272 | − | 0.362790i | −0.830761 | − | 0.556630i | \(-0.812094\pi\) |
0.981033 | + | 0.193840i | \(0.0620942\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.66390 | − | 0.689211i | 0.180476 | − | 0.0747554i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.6528 | − | 10.6528i | −1.14210 | − | 1.14210i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.38134 | − | 2.38134i | 0.252422 | − | 0.252422i | −0.569541 | − | 0.821963i | \(-0.692879\pi\) |
0.821963 | + | 0.569541i | \(0.192879\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.38231 | + | 8.16561i | 0.354562 | + | 0.855989i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.146264 | − | 0.0605847i | −0.0151669 | − | 0.00628234i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.229286 | 0.0235243 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2672 | −1.34708 | −0.673541 | − | 0.739150i | \(-0.735228\pi\) | ||||
−0.673541 | + | 0.739150i | \(0.735228\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 20.5093 | + | 8.49522i | 2.06126 | + | 0.853801i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.65855 | + | 13.6610i | 0.563047 | + | 1.35932i | 0.907318 | + | 0.420446i | \(0.138126\pi\) |
−0.344271 | + | 0.938870i | \(0.611874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.66978 | + | 4.66978i | −0.460127 | + | 0.460127i | −0.898697 | − | 0.438570i | \(-0.855485\pi\) |
0.438570 | + | 0.898697i | \(0.355485\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.56048 | + | 3.56048i | 0.347467 | + | 0.347467i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.63093 | − | 3.16083i | 0.737710 | − | 0.305569i | 0.0179938 | − | 0.999838i | \(-0.494272\pi\) |
0.719716 | + | 0.694269i | \(0.244272\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.01996 | − | 2.46240i | 0.0976945 | − | 0.235855i | −0.867475 | − | 0.497481i | \(-0.834259\pi\) |
0.965169 | + | 0.261625i | \(0.0842585\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.53397i | − | 0.240514i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 4.96472i | − | 0.467042i | −0.972352 | − | 0.233521i | \(-0.924975\pi\) | ||
0.972352 | − | 0.233521i | \(-0.0750247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.947262 | − | 2.28689i | 0.0883326 | − | 0.213254i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.5405 | + | 4.36603i | −0.974471 | + | 0.403639i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.9344 | + | 13.9344i | 1.27736 | + | 1.27736i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.35034 | − | 3.35034i | 0.304577 | − | 0.304577i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.985444 | − | 2.37907i | −0.0888545 | − | 0.214514i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.60280 | − | 1.49233i | −0.322244 | − | 0.133478i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4530 | −1.37123 | −0.685614 | − | 0.727965i | \(-0.740466\pi\) | ||||
−0.685614 | + | 0.727965i | \(0.740466\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.56653 | 0.578151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.66535 | − | 4.00352i | −0.844465 | − | 0.349789i | −0.0818527 | − | 0.996644i | \(-0.526084\pi\) |
−0.762613 | + | 0.646855i | \(0.776084\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.960080 | + | 2.31784i | 0.0832495 | + | 0.200982i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.13200 | + | 2.13200i | −0.183493 | + | 0.183493i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.4887 | − | 11.4887i | −0.981544 | − | 0.981544i | 0.0182885 | − | 0.999833i | \(-0.494178\pi\) |
−0.999833 | + | 0.0182885i | \(0.994178\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.92630 | − | 2.86897i | 0.587481 | − | 0.243343i | −0.0690854 | − | 0.997611i | \(-0.522008\pi\) |
0.656567 | + | 0.754268i | \(0.272008\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.5958 | + | 25.5804i | −0.892323 | + | 2.15426i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.08843i | 0.676388i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2.03579i | − | 0.169063i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.2302 | + | 31.9405i | −1.09121 | + | 2.63441i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.84839 | − | 2.42248i | 0.479119 | − | 0.198457i | −0.130035 | − | 0.991509i | \(-0.541509\pi\) |
0.609154 | + | 0.793052i | \(0.291509\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.57293 | + | 7.57293i | 0.616276 | + | 0.616276i | 0.944574 | − | 0.328298i | \(-0.106475\pi\) |
−0.328298 | + | 0.944574i | \(0.606475\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.9871 | + | 17.9871i | −1.45417 | + | 1.45417i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.00818685 | − | 0.0197648i | −0.000657583 | − | 0.00158755i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.53295 | − | 3.12025i | −0.601195 | − | 0.249023i | 0.0612635 | − | 0.998122i | \(-0.480487\pi\) |
−0.662459 | + | 0.749098i | \(0.730487\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −31.9187 | −2.53132 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.0844 | 2.13455 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50617 | − | 2.28073i | −0.431276 | − | 0.178640i | 0.156475 | − | 0.987682i | \(-0.449987\pi\) |
−0.587752 | + | 0.809041i | \(0.699987\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.76341 | + | 4.25725i | 0.137281 | + | 0.331427i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.4145 | − | 14.4145i | 1.11543 | − | 1.11543i | 0.123021 | − | 0.992404i | \(-0.460742\pi\) |
0.992404 | − | 0.123021i | \(-0.0392583\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.25297 | + | 6.25297i | 0.480998 | + | 0.480998i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.99196 | + | 1.23931i | −0.228801 | + | 0.0947725i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.63397 | + | 16.0158i | −0.504372 | + | 1.21766i | 0.442709 | + | 0.896665i | \(0.354018\pi\) |
−0.947081 | + | 0.320996i | \(0.895982\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 20.9944i | − | 1.58703i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.7812i | 1.71234i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.59997 | − | 8.69109i | 0.269074 | − | 0.649602i | −0.730366 | − | 0.683056i | \(-0.760651\pi\) |
0.999440 | + | 0.0334535i | \(0.0106506\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.666847 | − | 0.276217i | 0.0495663 | − | 0.0205310i | −0.357763 | − | 0.933813i | \(-0.616460\pi\) |
0.407329 | + | 0.913282i | \(0.366460\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.8316 | − | 21.8316i | −1.61383 | − | 1.61383i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.242125 | − | 0.242125i | 0.0178014 | − | 0.0178014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.90133 | + | 16.6613i | 0.504675 | + | 1.21839i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −30.4794 | − | 12.6250i | −2.21705 | − | 0.918332i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1746 | 0.736209 | 0.368105 | − | 0.929784i | \(-0.380007\pi\) | ||||
0.368105 | + | 0.929784i | \(0.380007\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7515 | 0.845889 | 0.422945 | − | 0.906156i | \(-0.360996\pi\) | ||||
0.422945 | + | 0.906156i | \(0.360996\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.18797 | − | 0.906286i | −0.156684 | − | 0.0649005i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.00875 | + | 14.5064i | 0.428106 | + | 1.03354i | 0.979888 | + | 0.199550i | \(0.0639480\pi\) |
−0.551782 | + | 0.833988i | \(0.686052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.32691 | − | 2.32691i | 0.164951 | − | 0.164951i | −0.619805 | − | 0.784756i | \(-0.712788\pi\) |
0.784756 | + | 0.619805i | \(0.212788\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.9165 | + | 16.9165i | 1.19320 | + | 1.19320i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.5797 | − | 8.52437i | 1.44441 | − | 0.598294i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.133164 | − | 0.321486i | 0.00930056 | − | 0.0224535i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 34.9617i | 2.43001i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.29593i | 0.158813i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.00267 | + | 16.9059i | −0.482083 | + | 1.16385i | 0.476534 | + | 0.879156i | \(0.341893\pi\) |
−0.958618 | + | 0.284696i | \(0.908107\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.4595 | − | 4.74666i | 0.785189 | − | 0.325236i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.627444 | + | 0.627444i | 0.0427913 | + | 0.0427913i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.165520 | − | 0.165520i | 0.0112363 | − | 0.0112363i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.62880 | + | 11.1749i | 0.312786 | + | 0.755131i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.56288 | − | 3.54686i | −0.576002 | − | 0.238588i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.6471 | −1.44959 | −0.724797 | − | 0.688962i | \(-0.758066\pi\) | ||||
−0.724797 | + | 0.688962i | \(0.758066\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 27.1005 | 1.80670 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.86440 | + | 3.67176i | 0.588351 | + | 0.243703i | 0.656941 | − | 0.753942i | \(-0.271850\pi\) |
−0.0685901 | + | 0.997645i | \(0.521850\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0093 | − | 26.5787i | −0.727513 | − | 1.75637i | −0.650712 | − | 0.759324i | \(-0.725530\pi\) |
−0.0768003 | − | 0.997046i | \(-0.524470\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −35.6524 | + | 35.6524i | −2.34575 | + | 2.34575i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0722 | − | 18.0722i | −1.18395 | − | 1.18395i | −0.978712 | − | 0.205239i | \(-0.934203\pi\) |
−0.205239 | − | 0.978712i | \(-0.565797\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.45670 | + | 1.43181i | −0.225490 | + | 0.0934011i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.44949 | − | 15.5704i | 0.418939 | − | 1.01141i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0765i | 1.55738i | 0.627409 | + | 0.778690i | \(0.284116\pi\) | ||||
−0.627409 | + | 0.778690i | \(0.715884\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3823i | 0.668785i | 0.942434 | + | 0.334393i | \(0.108531\pi\) | ||||
−0.942434 | + | 0.334393i | \(0.891469\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.53797 | + | 6.12719i | −0.162811 | + | 0.393060i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.31614 | + | 1.78780i | −0.275748 | + | 0.114219i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.834363 | − | 0.834363i | −0.0530893 | − | 0.0530893i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.41662 | + | 7.41662i | −0.470009 | + | 0.470009i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.54203 | + | 23.0365i | 0.602288 | + | 1.45405i | 0.871221 | + | 0.490892i | \(0.163329\pi\) |
−0.268933 | + | 0.963159i | \(0.586671\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.8995 | + | 9.48528i | 1.43968 | + | 0.596335i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.28025 | −0.330662 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.7121 | −1.16723 | −0.583613 | − | 0.812032i | \(-0.698362\pi\) | ||||
−0.583613 | + | 0.812032i | \(0.698362\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.46146 | + | 1.43379i | 0.215085 | + | 0.0890911i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.0036 | + | 26.5651i | 0.681107 | + | 1.64434i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.884682 | − | 0.884682i | 0.0545518 | − | 0.0545518i | −0.679305 | − | 0.733856i | \(-0.737718\pi\) |
0.733856 | + | 0.679305i | \(0.237718\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.04989 | − | 3.04989i | −0.187353 | − | 0.187353i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.12208 | + | 3.77849i | −0.558262 | + | 0.231240i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.44363 | − | 13.1421i | 0.331904 | − | 0.801286i | −0.666537 | − | 0.745472i | \(-0.732224\pi\) |
0.998441 | − | 0.0558149i | \(-0.0177757\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 17.5598i | − | 1.06668i | −0.845900 | − | 0.533341i | \(-0.820936\pi\) | ||
0.845900 | − | 0.533341i | \(-0.179064\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 25.9129i | − | 1.56832i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.35248 | − | 17.7505i | 0.443371 | − | 1.07039i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.3747 | − | 10.0964i | 1.46454 | − | 0.606631i | 0.498931 | − | 0.866642i | \(-0.333726\pi\) |
0.965606 | + | 0.260011i | \(0.0837261\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.213661 | + | 0.213661i | 0.0127915 | + | 0.0127915i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.9764 | − | 16.9764i | 1.01273 | − | 1.01273i | 0.0128071 | − | 0.999918i | \(-0.495923\pi\) |
0.999918 | − | 0.0128071i | \(-0.00407675\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.34744 | − | 3.25301i | −0.0800972 | − | 0.193372i | 0.878758 | − | 0.477268i | \(-0.158373\pi\) |
−0.958855 | + | 0.283896i | \(0.908373\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.621063 | − | 0.257253i | −0.0367886 | − | 0.0152383i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.80746 | 0.224747 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.66490 | −0.215582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 35.9366 | + | 14.8854i | 2.10664 | + | 0.872600i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.19545 | + | 2.88607i | 0.0698388 | + | 0.168606i | 0.954945 | − | 0.296784i | \(-0.0959141\pi\) |
−0.885106 | + | 0.465390i | \(0.845914\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.17679 | + | 2.17679i | −0.126737 | + | 0.126737i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.3485 | − | 21.3485i | −1.23876 | − | 1.23876i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.7689 | + | 4.87486i | −0.680616 | + | 0.281920i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.71552 | + | 8.97005i | −0.214159 | + | 0.517025i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 43.3519i | − | 2.49050i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 4.17209i | − | 0.238893i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.26318 | + | 7.87800i | −0.186239 | + | 0.449621i | −0.989230 | − | 0.146370i | \(-0.953241\pi\) |
0.802991 | + | 0.595992i | \(0.203241\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.8883 | − | 7.40957i | 1.01763 | − | 0.421516i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.38586 | + | 3.38586i | 0.191995 | + | 0.191995i | 0.796557 | − | 0.604563i | \(-0.206652\pi\) |
−0.604563 | + | 0.796557i | \(0.706652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.0698 | + | 21.0698i | −1.19094 | + | 1.19094i | −0.214132 | + | 0.976805i | \(0.568692\pi\) |
−0.976805 | + | 0.214132i | \(0.931308\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.67773 | − | 8.87882i | −0.207216 | − | 0.500265i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.0404 | − | 10.7863i | −1.46258 | − | 0.605818i | −0.497423 | − | 0.867508i | \(-0.665720\pi\) |
−0.965152 | + | 0.261690i | \(0.915720\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.3851 | 1.14135 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.2161 | −1.35161 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.43060 | − | 1.00679i | −0.135242 | − | 0.0560192i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.77873 | + | 9.12266i | 0.209606 | + | 0.506034i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.52549 | + | 5.52549i | −0.305560 | + | 0.305560i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.9481 | − | 28.9481i | −1.59596 | − | 1.59596i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.9852 | + | 12.0060i | −1.59317 | + | 0.659912i | −0.990429 | − | 0.138026i | \(-0.955924\pi\) |
−0.602740 | + | 0.797938i | \(0.705924\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.85079 | + | 4.46821i | −0.101423 | + | 0.244856i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.23281i | 0.176627i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 35.6957i | − | 1.94447i | −0.234010 | − | 0.972234i | \(-0.575185\pi\) | ||
0.234010 | − | 0.972234i | \(-0.424815\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.57028 | + | 13.4478i | −0.302536 | + | 0.730386i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.197912 | − | 0.0819780i | 0.0107176 | − | 0.00443935i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.6885 | − | 14.6885i | −0.793107 | − | 0.793107i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.13165 | + | 5.13165i | −0.276279 | + | 0.276279i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.8129 | − | 26.1047i | −0.580468 | − | 1.40137i | −0.892389 | − | 0.451266i | \(-0.850973\pi\) |
0.311921 | − | 0.950108i | \(-0.399027\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0652 | + | 4.99757i | 0.645836 | + | 0.267514i | 0.681464 | − | 0.731851i | \(-0.261343\pi\) |
−0.0356289 | + | 0.999365i | \(0.511343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.5165 | 0.828209 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.4488 | 0.875479 | 0.437740 | − | 0.899102i | \(-0.355779\pi\) | ||||
0.437740 | + | 0.899102i | \(0.355779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.54852 | + | 0.641420i | 0.0821871 | + | 0.0340430i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −22.1097 | − | 53.3776i | −1.17017 | − | 2.82504i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.92378 | − | 3.92378i | 0.207089 | − | 0.207089i | −0.595940 | − | 0.803029i | \(-0.703220\pi\) |
0.803029 | + | 0.595940i | \(0.203220\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.1982 | + | 13.1982i | 0.694642 | + | 0.694642i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.8340 | + | 5.31601i | −0.673610 | + | 0.279018i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.625493 | + | 1.51007i | −0.0327398 | + | 0.0790409i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.9285i | 0.988061i | 0.869444 | + | 0.494031i | \(0.164477\pi\) | ||||
−0.869444 | + | 0.494031i | \(0.835523\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.91484i | 0.255856i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.0604 | − | 43.6017i | 0.937651 | − | 2.26369i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.2960 | + | 5.92159i | −0.740218 | + | 0.306608i | −0.720743 | − | 0.693202i | \(-0.756199\pi\) |
−0.0194748 | + | 0.999810i | \(0.506199\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.08448 | + | 8.08448i | 0.417481 | + | 0.417481i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.40816 | + | 7.40816i | −0.381540 | + | 0.381540i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.23798 | − | 19.8882i | −0.423157 | − | 1.02159i | −0.981411 | − | 0.191920i | \(-0.938529\pi\) |
0.558254 | − | 0.829670i | \(-0.311471\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 41.8571 | + | 17.3378i | 2.14440 | + | 0.888241i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.8953 | 0.761113 | 0.380556 | − | 0.924758i | \(-0.375732\pi\) | ||||
0.380556 | + | 0.924758i | \(0.375732\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.81330 | −0.347238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.5789 | − | 4.79614i | −0.588589 | − | 0.243802i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.61723 | + | 18.3896i | 0.386209 | + | 0.932390i | 0.990736 | + | 0.135805i | \(0.0433622\pi\) |
−0.604527 | + | 0.796585i | \(0.706638\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.0833 | + | 20.0833i | −1.01566 | + | 1.01566i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.6885 | + | 21.6885i | 1.09404 | + | 1.09404i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.10404 | − | 0.871524i | 0.105866 | − | 0.0438511i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.23072 | − | 15.0423i | 0.312711 | − | 0.754951i | −0.686891 | − | 0.726760i | \(-0.741025\pi\) |
0.999603 | − | 0.0281913i | \(-0.00897477\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 7.35546i | − | 0.368233i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.1297i | 1.30485i | 0.757852 | + | 0.652427i | \(0.226249\pi\) | ||||
−0.757852 | + | 0.652427i | \(0.773751\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0421317 | + | 0.101715i | −0.00209873 | + | 0.00506678i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.02236 | − | 0.837691i | 0.100492 | − | 0.0416252i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.42449 | + | 2.42449i | 0.120177 | + | 0.120177i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.4495 | − | 15.4495i | 0.763928 | − | 0.763928i | −0.213102 | − | 0.977030i | \(-0.568357\pi\) |
0.977030 | + | 0.213102i | \(0.0683566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.2292 | + | 44.0091i | 0.899179 | + | 2.17081i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.1197 | − | 12.8902i | −1.53130 | − | 0.634286i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.41734 | −0.0695746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.9800 | −1.07637 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.2918 | − | 4.26299i | −0.502786 | − | 0.208261i | 0.116851 | − | 0.993149i | \(-0.462720\pi\) |
−0.619637 | + | 0.784889i | \(0.712720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0453 | + | 24.2514i | 0.489576 | + | 1.18194i | 0.954934 | + | 0.296819i | \(0.0959259\pi\) |
−0.465357 | + | 0.885123i | \(0.654074\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 37.3675 | − | 37.3675i | 1.81687 | − | 1.81687i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.5675 | + | 15.5675i | 0.755136 | + | 0.755136i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 42.1753 | − | 17.4696i | 2.04101 | − | 0.845413i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.07498 | − | 21.9089i | 0.438144 | − | 1.05777i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.4592i | 0.551972i | 0.961162 | + | 0.275986i | \(0.0890043\pi\) | ||||
−0.961162 | + | 0.275986i | \(0.910996\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.0019i | 0.720946i | 0.932770 | + | 0.360473i | \(0.117385\pi\) | ||||
−0.932770 | + | 0.360473i | \(0.882615\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.28410 | + | 5.51430i | −0.109514 | + | 0.264391i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.34066 | + | 1.38375i | −0.159805 | + | 0.0661935i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.9503 | − | 13.9503i | −0.665812 | − | 0.665812i | 0.290932 | − | 0.956744i | \(-0.406035\pi\) |
−0.956744 | + | 0.290932i | \(0.906035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 46.6582 | − | 46.6582i | 2.22182 | − | 2.22182i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.47872 | − | 10.8126i | −0.212791 | − | 0.513722i | 0.781059 | − | 0.624457i | \(-0.214680\pi\) |
−0.993850 | + | 0.110735i | \(0.964680\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.23267 | − | 0.510590i | −0.0584343 | − | 0.0242043i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −18.5594 | −0.877827 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.74061 | 0.223723 | 0.111862 | − | 0.993724i | \(-0.464319\pi\) | ||||
0.111862 | + | 0.993724i | \(0.464319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.21916 | + | 1.33342i | 0.151584 | + | 0.0627882i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.0160 | − | 29.0092i | −0.564562 | − | 1.36297i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.47602 | − | 2.47602i | 0.116078 | − | 0.116078i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1910 | + | 15.1910i | 0.710605 | + | 0.710605i | 0.966662 | − | 0.256057i | \(-0.0824235\pi\) |
−0.256057 | + | 0.966662i | \(0.582423\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 31.9623 | − | 13.2392i | 1.49187 | − | 0.617953i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.16815 | − | 14.8912i | 0.287279 | − | 0.693554i | −0.712689 | − | 0.701480i | \(-0.752523\pi\) |
0.999969 | + | 0.00792626i | \(0.00252303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4145i | 0.530477i | 0.964183 | + | 0.265238i | \(0.0854506\pi\) | ||||
−0.964183 | + | 0.265238i | \(0.914549\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0627219i | 0.00290866i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.64610 | − | 6.38825i | 0.122447 | − | 0.295613i | −0.850756 | − | 0.525561i | \(-0.823856\pi\) |
0.973203 | + | 0.229948i | \(0.0738556\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.6802 | + | 13.5366i | −1.50903 | + | 0.625061i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.9035 | + | 16.9035i | 0.778873 | + | 0.778873i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.28283 | + | 6.28283i | −0.288885 | + | 0.288885i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.07260 | + | 2.58950i | 0.0492145 | + | 0.118814i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 56.2830 | + | 23.3132i | 2.57702 | + | 1.06744i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.2733 | 0.743545 | 0.371772 | − | 0.928324i | \(-0.378750\pi\) | ||||
0.371772 | + | 0.928324i | \(0.378750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.76217 | −0.0803479 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −73.3630 | − | 30.3880i | −3.33813 | − | 1.38270i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.01148 | + | 4.85614i | 0.0913366 | + | 0.220506i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.0573 | − | 13.0573i | 0.591683 | − | 0.591683i | −0.346403 | − | 0.938086i | \(-0.612597\pi\) |
0.938086 | + | 0.346403i | \(0.112597\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12.3555 | + | 12.3555i | 0.558736 | + | 0.558736i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.2438 | − | 5.48577i | 0.597686 | − | 0.247569i | −0.0632676 | − | 0.997997i | \(-0.520152\pi\) |
0.660953 | + | 0.750427i | \(0.270152\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.93910 | + | 21.5809i | −0.402597 | + | 0.971955i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 8.79490i | − | 0.395301i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.3397i | 0.822648i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9.43511 | + | 22.7784i | −0.422374 | + | 1.01970i | 0.559272 | + | 0.828984i | \(0.311081\pi\) |
−0.981645 | + | 0.190716i | \(0.938919\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −55.2168 | + | 22.8715i | −2.46690 | + | 1.02182i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.0166 | + | 29.0166i | 1.29378 | + | 1.29378i | 0.932428 | + | 0.361357i | \(0.117686\pi\) |
0.361357 | + | 0.932428i | \(0.382314\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.14235 | − | 4.14235i | 0.184332 | − | 0.184332i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.92163 | − | 23.9529i | −0.440635 | − | 1.06379i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.240941 | + | 0.0998009i | 0.0106795 | + | 0.00442360i | 0.388017 | − | 0.921652i | \(-0.373160\pi\) |
−0.377337 | + | 0.926076i | \(0.623160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −17.8843 | −0.791156 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.40441 | 0.194459 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.41726 | + | 1.00126i | 0.106517 | + | 0.0441208i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.3373 | − | 34.6132i | −0.630552 | − | 1.52229i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.9386 | − | 35.9386i | 1.57753 | − | 1.57753i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.59451 | + | 6.59451i | 0.288911 | + | 0.288911i | 0.836649 | − | 0.547739i | \(-0.184511\pi\) |
−0.547739 | + | 0.836649i | \(0.684511\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.1535 | + | 12.4900i | −1.31852 | + | 0.546148i | −0.927358 | − | 0.374174i | \(-0.877926\pi\) |
−0.391160 | + | 0.920323i | \(0.627926\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −23.5551 | + | 56.8671i | −1.02803 | + | 2.48188i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.245470i | 0.0106928i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.0363i | 0.697231i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 16.6392 | − | 40.1706i | 0.722081 | − | 1.74326i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.65445 | + | 0.685296i | −0.0716622 | + | 0.0296835i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.31389 | − | 2.31389i | −0.100038 | − | 0.100038i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.5023 | + | 19.5023i | −0.841586 | + | 0.841586i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.9019 | − | 43.2191i | −0.771091 | − | 1.86158i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.1850 | − | 5.46141i | −0.566867 | − | 0.234804i | 0.0807961 | − | 0.996731i | \(-0.474254\pi\) |
−0.647664 | + | 0.761926i | \(0.724254\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.11618 | −0.0908140 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.05594 | −0.0452315 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.8546 | + | 9.46669i | 0.977192 | + | 0.404766i | 0.813385 | − | 0.581726i | \(-0.197622\pi\) |
0.163807 | + | 0.986492i | \(0.447622\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 22.5505 | + | 54.4417i | 0.962431 | + | 2.32351i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.10283 | + | 2.10283i | −0.0895837 | + | 0.0895837i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.6203 | + | 17.6203i | 0.749293 | + | 0.749293i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.927497 | + | 0.384182i | −0.0393700 | + | 0.0163076i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.31400 | + | 17.6576i | −0.309904 | + | 0.748175i | 0.689804 | + | 0.723997i | \(0.257697\pi\) |
−0.999708 | + | 0.0241782i | \(0.992303\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.56648i | − | 0.193142i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 52.8731i | − | 2.23230i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.0464 | + | 29.0826i | −0.507695 | + | 1.22568i | 0.437512 | + | 0.899213i | \(0.355860\pi\) |
−0.945207 | + | 0.326472i | \(0.894140\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.81722 | + | 0.752715i | −0.0764508 | + | 0.0316670i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.9363 | + | 16.9363i | 0.711258 | + | 0.711258i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.1317 | + | 18.1317i | −0.760118 | + | 0.760118i | −0.976344 | − | 0.216225i | \(-0.930625\pi\) |
0.216225 | + | 0.976344i | \(0.430625\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.21852 | − | 7.77020i | −0.134691 | − | 0.325173i | 0.842115 | − | 0.539297i | \(-0.181310\pi\) |
−0.976806 | + | 0.214125i | \(0.931310\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −27.5597 | − | 11.4156i | −1.15133 | − | 0.476894i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.2588 | 1.26188 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.2275 | −0.550669 | −0.275335 | − | 0.961348i | \(-0.588789\pi\) | ||||
−0.275335 | + | 0.961348i | \(0.588789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.8309 | − | 13.1848i | −1.32285 | − | 0.547942i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.93477 | − | 14.3278i | −0.246216 | − | 0.594418i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 30.5397 | − | 30.5397i | 1.26482 | − | 1.26482i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.19615 | + | 3.19615i | 0.132145 | + | 0.132145i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.0438 | − | 13.2730i | 1.32259 | − | 0.547835i | 0.394058 | − | 0.919086i | \(-0.371071\pi\) |
0.928533 | + | 0.371251i | \(0.121071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0119592 | + | 0.0288721i | −0.000492771 | + | 0.00118966i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 46.0348i | − | 1.89362i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.4869i | 1.53940i | 0.638405 | + | 0.769700i | \(0.279594\pi\) | ||||
−0.638405 | + | 0.769700i | \(0.720406\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.98770 | − | 7.21296i | 0.122484 | − | 0.295702i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.91359 | + | 3.69213i | −0.364809 | + | 0.151109i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.05549 | − | 4.05549i | −0.165703 | − | 0.165703i | 0.619385 | − | 0.785088i | \(-0.287382\pi\) |
−0.785088 | + | 0.619385i | \(0.787382\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.796070 | − | 0.796070i | 0.0324724 | − | 0.0324724i | −0.690684 | − | 0.723157i | \(-0.742691\pi\) |
0.723157 | + | 0.690684i | \(0.242691\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.4736 | − | 42.1850i | −0.711579 | − | 1.71790i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.73427 | − | 0.718357i | −0.0705079 | − | 0.0292053i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.8854 | 0.563591 | 0.281795 | − | 0.959475i | \(-0.409070\pi\) | ||||
0.281795 | + | 0.959475i | \(0.409070\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −65.3078 | −2.64640 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.7891 | + | 7.36848i | 0.719669 | + | 0.298097i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.91967 | − | 9.46292i | −0.158314 | − | 0.382204i | 0.824742 | − | 0.565509i | \(-0.191320\pi\) |
−0.983056 | + | 0.183305i | \(0.941320\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.721395 | + | 0.721395i | −0.0290895 | + | 0.0290895i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.39736 | + | 5.39736i | 0.217290 | + | 0.217290i | 0.807355 | − | 0.590066i | \(-0.200898\pi\) |
−0.590066 | + | 0.807355i | \(0.700898\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.2161 | + | 12.9301i | −1.25468 | + | 0.519706i | −0.908273 | − | 0.418379i | \(-0.862599\pi\) |
−0.346408 | + | 0.938084i | \(0.612599\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.1962 | − | 43.9294i | 0.730186 | − | 1.76283i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 14.5990i | − | 0.584895i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 22.6702i | − | 0.906809i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.57597 | − | 6.21893i | 0.102874 | − | 0.248360i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3.62987 | + | 1.50354i | −0.144732 | + | 0.0599501i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.8697 | − | 21.8697i | −0.870620 | − | 0.870620i | 0.121920 | − | 0.992540i | \(-0.461095\pi\) |
−0.992540 | + | 0.121920i | \(0.961095\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 37.9359 | − | 37.9359i | 1.50782 | − | 1.50782i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.34286 | + | 5.65618i | 0.0929737 | + | 0.224458i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 22.2120 | + | 9.20050i | 0.880071 | + | 0.364537i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −23.6737 | −0.936515 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.0037 | 1.34307 | 0.671533 | − | 0.740975i | \(-0.265636\pi\) | ||||
0.671533 | + | 0.740975i | \(0.265636\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.40811 | + | 3.89697i | 0.371020 | + | 0.153681i | 0.560399 | − | 0.828223i | \(-0.310648\pi\) |
−0.189380 | + | 0.981904i | \(0.560648\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.995569 | − | 2.40352i | −0.0392005 | − | 0.0946384i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.9528 | + | 11.9528i | −0.469914 | + | 0.469914i | −0.901887 | − | 0.431973i | \(-0.857818\pi\) |
0.431973 | + | 0.901887i | \(0.357818\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.7970 | − | 21.7970i | −0.855606 | − | 0.855606i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.634051 | + | 0.262632i | −0.0248504 | + | 0.0102934i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.61520 | − | 15.9705i | 0.258873 | − | 0.624974i | −0.739992 | − | 0.672616i | \(-0.765171\pi\) |
0.998864 | + | 0.0476419i | \(0.0151706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.14475i | 0.161949i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 23.0858i | − | 0.900665i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.29305 | + | 3.12170i | −0.0503701 | + | 0.121604i | −0.947062 | − | 0.321052i | \(-0.895964\pi\) |
0.896692 | + | 0.442656i | \(0.145964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.9077 | + | 17.7729i | −1.66892 | + | 0.691287i | −0.998705 | − | 0.0508836i | \(-0.983796\pi\) |
−0.670211 | + | 0.742171i | \(0.733796\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19.2146 | + | 19.2146i | 0.746234 | + | 0.746234i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.702827 | − | 0.702827i | 0.0272545 | − | 0.0272545i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.2860 | + | 29.6611i | 0.475717 | + | 1.14848i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 58.6349 | + | 24.2874i | 2.26696 | + | 0.939004i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 41.7767 | 1.61277 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.107425 | −0.00414091 | −0.00207046 | − | 0.999998i | \(-0.500659\pi\) | ||||
−0.00207046 | + | 0.999998i | \(0.500659\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −34.0517 | − | 14.1047i | −1.31065 | − | 0.542889i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.24507 | + | 10.2485i | 0.163151 | + | 0.393882i | 0.984220 | − | 0.176947i | \(-0.0566220\pi\) |
−0.821069 | + | 0.570829i | \(0.806622\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −40.6678 | + | 40.6678i | −1.56069 | + | 1.56069i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −19.8912 | − | 19.8912i | −0.762233 | − | 0.762233i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.2815 | + | 10.4720i | −0.967371 | + | 0.400698i | −0.809733 | − | 0.586799i | \(-0.800388\pi\) |
−0.157638 | + | 0.987497i | \(0.550388\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.46332 | + | 5.94698i | −0.0941186 | + | 0.227222i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 84.3452i | 3.21797i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22.1968i | 0.845632i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11.6277 | − | 28.0716i | 0.442337 | − | 1.06790i | −0.532790 | − | 0.846248i | \(-0.678856\pi\) |
0.975127 | − | 0.221648i | \(-0.0711436\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 88.9069 | − | 36.8265i | 3.37729 | − | 1.39892i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.10023 | − | 2.10023i | −0.0796663 | − | 0.0796663i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.82327 | + | 2.82327i | −0.106939 | + | 0.106939i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 28.6753 | + | 69.2284i | 1.08460 | + | 2.61846i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.3030 | + | 10.4808i | 0.955679 | + | 0.395855i | 0.805363 | − | 0.592783i | \(-0.201971\pi\) |
0.150317 | + | 0.988638i | \(0.451971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.500197 | −0.0188653 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.9695 | 0.413136 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 59.2198 | + | 24.5296i | 2.22719 | + | 0.922531i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.2502 | − | 44.0598i | −0.685400 | − | 1.65470i | −0.753850 | − | 0.657047i | \(-0.771805\pi\) |
0.0684496 | − | 0.997655i | \(-0.478195\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.7451 | + | 22.7451i | −0.853007 | + | 0.853007i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.238562 | + | 0.238562i | 0.00893420 | + | 0.00893420i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.96057 | − | 1.22631i | 0.110719 | − | 0.0458613i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 27.0132 | − | 65.2155i | 1.00882 | − | 2.43552i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 20.5621i | − | 0.766835i | −0.923575 | − | 0.383418i | \(-0.874747\pi\) | ||
0.923575 | − | 0.383418i | \(-0.125253\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.6284i | 1.06618i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6487 | − | 28.1224i | 0.433219 | − | 1.04588i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 22.9917 | − | 9.52347i | 0.853890 | − | 0.353693i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.98129 | + | 2.98129i | 0.110570 | + | 0.110570i | 0.760227 | − | 0.649657i | \(-0.225088\pi\) |
−0.649657 | + | 0.760227i | \(0.725088\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.4698 | − | 25.4698i | 0.943326 | − | 0.943326i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.89628 | − | 9.40645i | −0.144109 | − | 0.347910i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −44.2647 | − | 18.3350i | −1.63495 | − | 0.677220i | −0.639180 | − | 0.769057i | \(-0.720726\pi\) |
−0.995774 | + | 0.0918368i | \(0.970726\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.6969 | 0.505217 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −32.3713 | −1.19241 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.5580 | − | 6.44435i | −0.572312 | − | 0.237059i | 0.0777085 | − | 0.996976i | \(-0.475240\pi\) |
−0.650020 | + | 0.759917i | \(0.725240\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.32389 | + | 3.19615i | 0.0486343 | + | 0.117414i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.2184 | − | 15.2184i | 0.558309 | − | 0.558309i | −0.370516 | − | 0.928826i | \(-0.620819\pi\) |
0.928826 | + | 0.370516i | \(0.120819\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.77338 | − | 1.77338i | −0.0649716 | − | 0.0649716i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.4949 | − | 7.66085i | 0.676694 | − | 0.280296i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.7021 | − | 33.0798i | 0.500664 | − | 1.20871i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.40389i | 0.160700i | 0.996767 | + | 0.0803501i | \(0.0256038\pi\) | ||||
−0.996767 | + | 0.0803501i | \(0.974396\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 73.1043i | − | 2.66407i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.62373 | − | 3.92004i | 0.0590937 | − | 0.142665i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.3677 | − | 9.26500i | 0.812968 | − | 0.336742i | 0.0628304 | − | 0.998024i | \(-0.479987\pi\) |
0.750137 | + | 0.661282i | \(0.229987\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −51.3851 | − | 51.3851i | −1.86516 | − | 1.86516i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.81382 | + | 6.81382i | −0.247001 | + | 0.247001i | −0.819739 | − | 0.572738i | \(-0.805881\pi\) |
0.572738 | + | 0.819739i | \(0.305881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.42149 | − | 10.6744i | −0.160069 | − | 0.386440i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.31079 | + | 3.85666i | 0.336632 | + | 0.139438i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.8425 | 0.572038 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.7366 | −0.603538 | −0.301769 | − | 0.953381i | \(-0.597577\pi\) | ||||
−0.301769 | + | 0.953381i | \(0.597577\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 50.6850 | + | 20.9944i | 1.82537 | + | 0.756095i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.65140 | + | 13.6437i | 0.203267 | + | 0.490730i | 0.992335 | − | 0.123576i | \(-0.0394363\pi\) |
−0.789068 | + | 0.614305i | \(0.789436\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.184920 | − | 0.184920i | 0.00664253 | − | 0.00664253i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.76733 | − | 7.76733i | −0.278651 | − | 0.278651i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.469621 | + | 0.194524i | −0.0168259 | + | 0.00696953i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.42277 | + | 15.5059i | −0.229825 | + | 0.554846i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 39.1060i | − | 1.39753i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.23032i | 0.115295i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.75460 | − | 9.06441i | 0.133837 | − | 0.323111i | −0.842726 | − | 0.538343i | \(-0.819051\pi\) |
0.976563 | + | 0.215231i | \(0.0690506\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.38891 | + | 1.40373i | −0.120648 | + | 0.0499741i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.2183 | − | 15.2183i | −0.541100 | − | 0.541100i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.1821 | + | 15.1821i | −0.539131 | + | 0.539131i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.83928 | + | 11.6830i | 0.171631 | + | 0.414355i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −34.8002 | − | 14.4147i | −1.23269 | − | 0.510595i | −0.331264 | − | 0.943538i | \(-0.607475\pi\) |
−0.901421 | + | 0.432943i | \(0.857475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.9306 | 1.51878 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.8450 | 0.665854 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.1209 | − | 6.26330i | −0.533606 | − | 0.221027i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.10634 | − | 9.91359i | −0.144730 | − | 0.349408i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −29.4901 | + | 29.4901i | −1.03810 | + | 1.03810i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.59383 | − | 6.59383i | −0.231827 | − | 0.231827i | 0.581628 | − | 0.813455i | \(-0.302416\pi\) |
−0.813455 | + | 0.581628i | \(0.802416\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.0036 | + | 12.0137i | −1.01845 | + | 0.421857i | −0.828532 | − | 0.559942i | \(-0.810823\pi\) |
−0.189922 | + | 0.981799i | \(0.560823\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −19.7016 | + | 47.5638i | −0.690965 | + | 1.66814i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.36118i | 0.0827087i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.29621i | − | 0.0453487i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.9266 | + | 45.6928i | −0.661348 | + | 1.59663i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 26.9988 | − | 11.1833i | 0.942265 | − | 0.390299i | 0.141947 | − | 0.989874i | \(-0.454664\pi\) |
0.800318 | + | 0.599575i | \(0.204664\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.497968 | + | 0.497968i | 0.0173581 | + | 0.0173581i | 0.715733 | − | 0.698374i | \(-0.246093\pi\) |
−0.698374 | + | 0.715733i | \(0.746093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −39.8310 | + | 39.8310i | −1.38674 | + | 1.38674i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.1468 | − | 43.8102i | −0.631025 | − | 1.52343i | −0.838336 | − | 0.545154i | \(-0.816471\pi\) |
0.207311 | − | 0.978275i | \(-0.433529\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −29.0154 | − | 12.0186i | −1.00774 | − | 0.417422i | −0.183113 | − | 0.983092i | \(-0.558618\pi\) |
−0.824632 | + | 0.565670i | \(0.808618\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −77.3512 | −2.68328 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 53.6044 | 1.85728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.46148 | − | 3.09065i | −0.258215 | − | 0.106956i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.157263 | − | 0.379666i | −0.00543580 | − | 0.0131232i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.1636 | + | 28.1636i | −0.972317 | + | 0.972317i | −0.999627 | − | 0.0273102i | \(-0.991306\pi\) |
0.0273102 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.83543 | − | 1.83543i | −0.0632906 | − | 0.0632906i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −65.0305 | + | 26.9365i | −2.23977 | + | 0.927743i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.34072 | − | 3.23678i | 0.0461221 | − | 0.111349i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 20.5395i | − | 0.705746i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.3232i | 0.354290i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.06649 | + | 4.98895i | −0.0708383 | + | 0.171019i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.62203 | − | 3.15715i | 0.260973 | − | 0.108099i | −0.248361 | − | 0.968668i | \(-0.579892\pi\) |
0.509334 | + | 0.860569i | \(0.329892\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.907239 | + | 0.907239i | 0.0310269 | + | 0.0310269i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.53805 | − | 8.53805i | 0.291654 | − | 0.291654i | −0.546079 | − | 0.837734i | \(-0.683880\pi\) |
0.837734 | + | 0.546079i | \(0.183880\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.77131 | + | 9.10474i | 0.128675 | + | 0.310650i | 0.975067 | − | 0.221912i | \(-0.0712296\pi\) |
−0.846392 | + | 0.532561i | \(0.821230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.3132 | − | 4.27186i | −0.351473 | − | 0.145585i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.7816 | −0.605294 | −0.302647 | − | 0.953103i | \(-0.597870\pi\) | ||||
−0.302647 | + | 0.953103i | \(0.597870\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.86800 | 0.233519 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.92703 | + | 4.11191i | 0.337140 | + | 0.139648i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.72689 | + | 21.0686i | 0.296040 | + | 0.714703i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.7640 | − | 11.7640i | 0.398610 | − | 0.398610i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −52.4957 | − | 52.4957i | −1.77671 | − | 1.77671i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15.6180 | + | 6.46919i | −0.527985 | + | 0.218699i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.87297 | + | 21.4212i | −0.299619 | + | 0.723344i | 0.700336 | + | 0.713814i | \(0.253034\pi\) |
−0.999955 | + | 0.00953022i | \(0.996966\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 9.15869i | − | 0.308915i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.5225i | 0.725113i | 0.931962 | + | 0.362557i | \(0.118096\pi\) | ||||
−0.931962 | + | 0.362557i | \(0.881904\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.5351 | + | 27.8481i | −0.388186 | + | 0.937165i | 0.602138 | + | 0.798392i | \(0.294316\pi\) |
−0.990324 | + | 0.138773i | \(0.955684\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.33850 | − | 3.45392i | 0.280296 | − | 0.116102i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 25.2963 | + | 25.2963i | 0.849368 | + | 0.849368i | 0.990054 | − | 0.140686i | \(-0.0449309\pi\) |
−0.140686 | + | 0.990054i | \(0.544931\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −47.3677 | + | 47.3677i | −1.58866 | + | 1.58866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.38811 | + | 20.2507i | 0.281012 | + | 0.678423i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.04949 | + | 2.09157i | 0.168975 | + | 0.0699917i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.72696 | −0.124579 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37.3477 | 1.24700 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.256350 | + | 0.106184i | 0.00854976 | + | 0.00354143i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.9391 | + | 45.7230i | 0.630953 | + | 1.52325i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.1283 | − | 20.1283i | 0.669827 | − | 0.669827i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.202205 | − | 0.202205i | −0.00672152 | − | 0.00672152i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5718 | − | 7.69269i | 0.616666 | − | 0.255432i | −0.0524095 | − | 0.998626i | \(-0.516690\pi\) |
0.669076 | + | 0.743194i | \(0.266690\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −31.6639 | + | 76.4434i | −1.05022 | + | 2.53547i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 57.0332i | 1.88960i | 0.327655 | + | 0.944798i | \(0.393742\pi\) | ||||
−0.327655 | + | 0.944798i | \(0.606258\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 14.1924i | − | 0.469699i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.68096 | + | 11.3008i | −0.154748 | + | 0.373594i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −41.8989 | + | 17.3551i | −1.38362 | + | 0.573116i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7.18487 | − | 7.18487i | −0.237007 | − | 0.237007i | 0.578603 | − | 0.815610i | \(-0.303598\pi\) |
−0.815610 | + | 0.578603i | \(0.803598\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.6778 | − | 17.6778i | 0.582503 | − | 0.582503i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.30092 | − | 7.96911i | −0.108651 | − | 0.262307i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.86716 | + | 1.60183i | 0.127152 | + | 0.0526679i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −36.9547 | −1.21375 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.2751 | −0.763630 | −0.381815 | − | 0.924239i | \(-0.624701\pi\) | ||||
−0.381815 | + | 0.924239i | \(0.624701\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.30495 | + | 2.61160i | 0.206636 | + | 0.0855916i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.37237 | − | 12.9700i | −0.175883 | − | 0.424620i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.05212 | − | 5.05212i | 0.165222 | − | 0.165222i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.60456 | + | 7.60456i | 0.248430 | + | 0.248430i | 0.820326 | − | 0.571896i | \(-0.193792\pi\) |
−0.571896 | + | 0.820326i | \(0.693792\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 80.7111 | − | 33.4316i | 2.63391 | − | 1.09100i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.13773 | + | 2.74672i | −0.0370889 | + | 0.0895406i | −0.941339 | − | 0.337464i | \(-0.890431\pi\) |
0.904250 | + | 0.427004i | \(0.140431\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.48763i | 0.178702i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.0703i | 0.425178i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.99679 | + | 21.7202i | −0.292357 | + | 0.705811i | −1.00000 | 0.000758845i | \(-0.999758\pi\) | |
0.707643 | + | 0.706570i | \(0.249758\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.77124 | − | 3.21895i | 0.252265 | − | 0.104492i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 58.4332 | + | 58.4332i | 1.89483 | + | 1.89483i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.594510 | + | 0.594510i | −0.0192581 | + | 0.0192581i | −0.716670 | − | 0.697412i | \(-0.754335\pi\) |
0.697412 | + | 0.716670i | \(0.254335\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.54260 | − | 3.72417i | −0.0499174 | − | 0.120511i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −55.2168 | − | 22.8715i | −1.78490 | − | 0.739332i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −70.4321 | −2.27437 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9971 | −0.999906 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.7008 | + | 17.6872i | 1.37601 | + | 0.569964i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.78167 | − | 4.30134i | −0.0573541 | − | 0.138465i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.28012 | + | 5.28012i | −0.169797 | + | 0.169797i | −0.786890 | − | 0.617093i | \(-0.788310\pi\) |
0.617093 | + | 0.786890i | \(0.288310\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.45413 | + | 5.45413i | 0.175212 | + | 0.175212i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45.8066 | − | 18.9737i | 1.47000 | − | 0.608895i | 0.503143 | − | 0.864203i | \(-0.332177\pi\) |
0.966860 | + | 0.255308i | \(0.0821770\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.4369 | − | 30.0253i | 0.398708 | − | 0.962566i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 28.9500i | − | 0.927141i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 27.5870i | − | 0.882586i | −0.897363 | − | 0.441293i | \(-0.854520\pi\) | ||
0.897363 | − | 0.441293i | \(-0.145480\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.11273 | − | 12.3432i | 0.163403 | − | 0.394491i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.7790 | − | 5.70745i | 0.439929 | − | 0.182225i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.4856 | − | 32.4856i | −1.03613 | − | 1.03613i | −0.999322 | − | 0.0368067i | \(-0.988281\pi\) |
−0.0368067 | − | 0.999322i | \(-0.511719\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.39871 | − | 4.39871i | 0.140155 | − | 0.140155i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 45.9322 | + | 110.890i | 1.46204 | + | 3.52967i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.9284 | − | 5.35510i | −0.411098 | − | 0.170282i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.6148 | −1.38547 | −0.692735 | − | 0.721192i | \(-0.743595\pi\) | ||||
−0.692735 | + | 0.721192i | \(0.743595\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 91.9819 | 2.91896 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.20450 | − | 0.498920i | −0.0381852 | − | 0.0158168i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.6240 | + | 30.4769i | 0.399805 | + | 0.965214i | 0.987712 | + | 0.156286i | \(0.0499520\pi\) |
−0.587907 | + | 0.808928i | \(0.700048\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.65104 | − | 4.65104i | 0.147152 | − | 0.147152i |
(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 | 1024.2.g.d.641.1 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.d.641.4 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.g.641.1 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.g.641.4 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.f.129.1 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.a.129.1 | ✓ | 16 | ||
16.11 | odd | 4 | 1024.2.g.a.129.4 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.f.129.4 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.a.897.4 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.g.385.4 | yes | 16 | ||
32.11 | odd | 8 | inner | 1024.2.g.d.385.4 | yes | 16 | |
32.13 | even | 8 | 1024.2.g.f.897.4 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.f.897.1 | yes | 16 | ||
32.21 | even | 8 | inner | 1024.2.g.d.385.1 | yes | 16 | |
32.27 | odd | 8 | 1024.2.g.g.385.1 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.a.897.1 | yes | 16 | ||
64.11 | odd | 16 | 4096.2.a.s.1.8 | 8 | |||
64.21 | even | 16 | 4096.2.a.s.1.7 | 8 | |||
64.43 | odd | 16 | 4096.2.a.i.1.1 | 8 | |||
64.53 | even | 16 | 4096.2.a.i.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.a.129.1 | ✓ | 16 | 16.5 | even | 4 | ||
1024.2.g.a.129.4 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.a.897.1 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.a.897.4 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.d.385.1 | yes | 16 | 32.21 | even | 8 | inner | |
1024.2.g.d.385.4 | yes | 16 | 32.11 | odd | 8 | inner | |
1024.2.g.d.641.1 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.d.641.4 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.f.129.1 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.f.129.4 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.f.897.1 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.f.897.4 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.g.385.1 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.g.385.4 | yes | 16 | 32.5 | even | 8 | ||
1024.2.g.g.641.1 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.g.641.4 | yes | 16 | 8.5 | even | 2 | ||
4096.2.a.i.1.1 | 8 | 64.43 | odd | 16 | |||
4096.2.a.i.1.2 | 8 | 64.53 | even | 16 | |||
4096.2.a.s.1.7 | 8 | 64.21 | even | 16 | |||
4096.2.a.s.1.8 | 8 | 64.11 | odd | 16 |