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 | 641.4 | ||
Root | \(0.793353 - 0.608761i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.641 |
Dual form | 1024.2.g.g.385.4 |
$q$-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 | 0.985754 | − | 0.168194i | \(-0.0537936\pi\) |
0.578102 | + | 0.815965i | \(0.303794\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.151613 | + | 0.366025i | 0.0678033 | + | 0.163692i | 0.954149 | − | 0.299333i | \(-0.0967642\pi\) |
−0.886345 | + | 0.463025i | \(0.846764\pi\) | |||||||
\(6\) | 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 | −0.859242 | − | 0.511569i | \(-0.829064\pi\) |
−0.245842 | + | 0.969310i | \(0.579064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.780239 | − | 1.88366i | 0.216399 | − | 0.522434i | −0.777983 | − | 0.628286i | \(-0.783757\pi\) |
0.994382 | + | 0.105852i | \(0.0337568\pi\) | |||||||
\(14\) | 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 | −0.896437 | − | 0.443172i | \(-0.853853\pi\) |
0.947246 | + | 0.320507i | \(0.103853\pi\) | |||||||
\(20\) | 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 | −0.104461 | − | 0.994529i | \(-0.533312\pi\) |
−0.777103 | + | 0.629373i | \(0.783312\pi\) | |||||||
\(30\) | 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 | 0.894358 | − | 0.447353i | \(-0.147633\pi\) |
−0.948732 | + | 0.316080i | \(0.897633\pi\) | |||||||
\(38\) | 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 | −0.219284 | − | 0.975661i | \(-0.570372\pi\) |
0.534839 | + | 0.844954i | \(0.320372\pi\) | |||||||
\(44\) | 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 | −0.944907 | − | 0.327339i | \(-0.893848\pi\) |
−0.436687 | + | 0.899614i | \(0.643848\pi\) | |||||||
\(54\) | 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 | \(0.0438026\pi\) |
−0.603424 | + | 0.797420i | \(0.706197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.72911 | − | 4.02993i | −1.24568 | − | 0.515979i | −0.340198 | − | 0.940354i | \(-0.610494\pi\) |
−0.905487 | + | 0.424375i | \(0.860494\pi\) | |||||||
\(62\) | 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 | 0.792259 | − | 0.610185i | \(-0.208905\pi\) |
0.128746 | + | 0.991678i | \(0.458905\pi\) | |||||||
\(68\) | 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 | −0.981033 | − | 0.193840i | \(-0.937906\pi\) |
0.830761 | + | 0.556630i | \(0.187906\pi\) | |||||||
\(84\) | 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 | \(-0.861874\pi\) |
0.344271 | − | 0.938870i | \(-0.388126\pi\) | |||||||
\(102\) | 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 | −0.719716 | − | 0.694269i | \(-0.755728\pi\) |
−0.0179938 | + | 0.999838i | \(0.505728\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.01996 | + | 2.46240i | −0.0976945 | + | 0.235855i | −0.965169 | − | 0.261625i | \(-0.915741\pi\) |
0.867475 | + | 0.497481i | \(0.165741\pi\) | |||||||
\(110\) | 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 | 0.762613 | − | 0.646855i | \(-0.223916\pi\) |
0.0818527 | + | 0.996644i | \(0.473916\pi\) | |||||||
\(132\) | 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 | −0.656567 | − | 0.754268i | \(-0.727992\pi\) |
0.0690854 | + | 0.997611i | \(0.477992\pi\) | |||||||
\(140\) | 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 | −0.609154 | − | 0.793052i | \(-0.708491\pi\) |
0.130035 | + | 0.991509i | \(0.458491\pi\) | |||||||
\(150\) | 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 | 0.662459 | − | 0.749098i | \(-0.269513\pi\) |
−0.0612635 | + | 0.998122i | \(0.519513\pi\) | |||||||
\(158\) | 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 | 0.587752 | − | 0.809041i | \(-0.300013\pi\) |
−0.156475 | + | 0.987682i | \(0.550013\pi\) | |||||||
\(164\) | 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 | \(-0.645982\pi\) |
0.947081 | − | 0.320996i | \(-0.104018\pi\) | |||||||
\(174\) | 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 | −0.999440 | − | 0.0334535i | \(-0.989349\pi\) |
0.730366 | + | 0.683056i | \(0.239349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.666847 | + | 0.276217i | −0.0495663 | + | 0.0205310i | −0.407329 | − | 0.913282i | \(-0.633540\pi\) |
0.357763 | + | 0.933813i | \(0.383540\pi\) | |||||||
\(182\) | 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 | \(-0.936052\pi\) |
0.551782 | − | 0.833988i | \(-0.313948\pi\) | |||||||
\(198\) | 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 | \(-0.658107\pi\) |
0.958618 | − | 0.284696i | \(-0.0918928\pi\) | |||||||
\(212\) | 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 | 0.0685901 | − | 0.997645i | \(-0.478150\pi\) |
−0.656941 | + | 0.753942i | \(0.728150\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.0093 | + | 26.5787i | 0.727513 | + | 1.75637i | 0.650712 | + | 0.759324i | \(0.274470\pi\) |
0.0768003 | + | 0.997046i | \(0.475530\pi\) | |||||||
\(230\) | 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 | \(-0.836671\pi\) |
0.268933 | − | 0.963159i | \(-0.413329\pi\) | |||||||
\(252\) | 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 | \(0.267776\pi\) |
−0.998441 | + | 0.0558149i | \(0.982224\pi\) | |||||||
\(270\) | 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 | −0.965606 | − | 0.260011i | \(-0.916274\pi\) |
−0.498931 | + | 0.866642i | \(0.666274\pi\) | |||||||
\(278\) | 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 | 0.958855 | − | 0.283896i | \(-0.0916271\pi\) |
−0.878758 | + | 0.477268i | \(0.841627\pi\) | |||||||
\(284\) | 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 | 0.885106 | − | 0.465390i | \(-0.154086\pi\) |
−0.954945 | + | 0.296784i | \(0.904086\pi\) | |||||||
\(294\) | 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 | −0.802991 | − | 0.595992i | \(-0.796759\pi\) |
0.989230 | + | 0.146370i | \(0.0467591\pi\) | |||||||
\(308\) | 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 | 0.965152 | − | 0.261690i | \(-0.0842797\pi\) |
0.497423 | + | 0.867508i | \(0.334280\pi\) | |||||||
\(318\) | 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 | 0.602740 | − | 0.797938i | \(-0.294076\pi\) |
0.990429 | + | 0.138026i | \(0.0440756\pi\) | |||||||
\(332\) | 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 | \(0.149027\pi\) |
−0.311921 | + | 0.950108i | \(0.600973\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.0652 | − | 4.99757i | −0.645836 | − | 0.267514i | 0.0356289 | − | 0.999365i | \(-0.488657\pi\) |
−0.681464 | + | 0.731851i | \(0.738657\pi\) | |||||||
\(350\) | 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 | 0.0194748 | − | 0.999810i | \(-0.493801\pi\) |
0.720743 | + | 0.693202i | \(0.243801\pi\) | |||||||
\(374\) | 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 | \(0.0614715\pi\) |
−0.558254 | + | 0.829670i | \(0.688529\pi\) | |||||||
\(380\) | 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 | \(-0.956638\pi\) |
0.604527 | − | 0.796585i | \(-0.293362\pi\) | |||||||
\(390\) | 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 | \(0.258975\pi\) |
−0.999603 | + | 0.0281913i | \(0.991025\pi\) | |||||||
\(398\) | 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 | 0.619637 | − | 0.784889i | \(-0.287280\pi\) |
−0.116851 | + | 0.993149i | \(0.537280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.0453 | − | 24.2514i | −0.489576 | − | 1.18194i | −0.954934 | − | 0.296819i | \(-0.904074\pi\) |
0.465357 | − | 0.885123i | \(-0.345926\pi\) | |||||||
\(422\) | 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 | 0.993850 | − | 0.110735i | \(-0.0353204\pi\) |
−0.781059 | + | 0.624457i | \(0.785320\pi\) | |||||||
\(444\) | 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 | −0.999969 | − | 0.00792626i | \(-0.997477\pi\) |
0.712689 | + | 0.701480i | \(0.247477\pi\) | |||||||
\(462\) | 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 | −0.973203 | − | 0.229948i | \(-0.926144\pi\) |
0.850756 | + | 0.525561i | \(0.176144\pi\) | |||||||
\(468\) | 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 | −0.660953 | − | 0.750427i | \(-0.729848\pi\) |
0.0632676 | + | 0.997997i | \(0.479848\pi\) | |||||||
\(492\) | 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 | \(-0.688919\pi\) |
0.981645 | − | 0.190716i | \(-0.0610808\pi\) | |||||||
\(500\) | 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 | 0.377337 | − | 0.926076i | \(-0.376840\pi\) |
−0.388017 | + | 0.921652i | \(0.626840\pi\) | |||||||
\(510\) | 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 | 0.391160 | − | 0.920323i | \(-0.372074\pi\) |
0.927358 | + | 0.374174i | \(0.122074\pi\) | |||||||
\(524\) | 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 | 0.647664 | − | 0.761926i | \(-0.275746\pi\) |
−0.0807961 | + | 0.996731i | \(0.525746\pi\) | |||||||
\(542\) | 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 | −0.163807 | − | 0.986492i | \(-0.552378\pi\) |
−0.813385 | + | 0.581726i | \(0.802378\pi\) | |||||||
\(548\) | 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 | \(-0.742303\pi\) |
0.999708 | − | 0.0241782i | \(-0.00769690\pi\) | |||||||
\(558\) | 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 | \(-0.644140\pi\) |
0.945207 | − | 0.326472i | \(-0.105860\pi\) | |||||||
\(564\) | 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 | 0.976806 | − | 0.214125i | \(-0.0686899\pi\) |
−0.842115 | + | 0.539297i | \(0.818690\pi\) | |||||||
\(572\) | 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 | −0.928533 | − | 0.371251i | \(-0.878929\pi\) |
−0.394058 | + | 0.919086i | \(0.628929\pi\) | |||||||
\(588\) | 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 | 0.983056 | − | 0.183305i | \(-0.0586797\pi\) |
−0.824742 | + | 0.565509i | \(0.808680\pi\) | |||||||
\(614\) | 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 | 0.346408 | − | 0.938084i | \(-0.387401\pi\) |
0.908273 | + | 0.418379i | \(0.137401\pi\) | |||||||
\(620\) | 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 | 0.189380 | − | 0.981904i | \(-0.439352\pi\) |
−0.560399 | + | 0.828223i | \(0.689352\pi\) | |||||||
\(644\) | 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 | −0.998864 | − | 0.0476419i | \(-0.984829\pi\) |
0.739992 | + | 0.672616i | \(0.234829\pi\) | |||||||
\(654\) | 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 | −0.896692 | − | 0.442656i | \(-0.854036\pi\) |
0.947062 | + | 0.321052i | \(0.104036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.9077 | − | 17.7729i | 1.66892 | − | 0.691287i | 0.670211 | − | 0.742171i | \(-0.266204\pi\) |
0.998705 | + | 0.0508836i | \(0.0162037\pi\) | |||||||
\(662\) | 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 | 0.821069 | − | 0.570829i | \(-0.193378\pi\) |
−0.984220 | + | 0.176947i | \(0.943378\pi\) | |||||||
\(678\) | 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 | 0.157638 | − | 0.987497i | \(-0.449612\pi\) |
0.809733 | + | 0.586799i | \(0.199612\pi\) | |||||||
\(684\) | 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 | \(0.321144\pi\) |
−0.975127 | + | 0.221648i | \(0.928856\pi\) | |||||||
\(692\) | 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 | −0.150317 | − | 0.988638i | \(-0.548029\pi\) |
−0.805363 | + | 0.592783i | \(0.798029\pi\) | |||||||
\(702\) | 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 | \(0.228195\pi\) |
−0.0684496 | + | 0.997655i | \(0.521805\pi\) | |||||||
\(710\) | 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 | 0.995774 | − | 0.0918368i | \(-0.0292738\pi\) |
0.639180 | + | 0.769057i | \(0.279274\pi\) | |||||||
\(734\) | 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 | 0.650020 | − | 0.759917i | \(-0.274760\pi\) |
−0.0777085 | + | 0.996976i | \(0.524760\pi\) | |||||||
\(740\) | 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 | −0.750137 | − | 0.661282i | \(-0.770013\pi\) |
−0.0628304 | + | 0.998024i | \(0.520013\pi\) | |||||||
\(758\) | 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 | 0.789068 | − | 0.614305i | \(-0.210564\pi\) |
−0.992335 | + | 0.123576i | \(0.960564\pi\) | |||||||
\(774\) | 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 | −0.976563 | − | 0.215231i | \(-0.930949\pi\) |
0.842726 | + | 0.538343i | \(0.180949\pi\) | |||||||
\(788\) | 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 | 0.901421 | − | 0.432943i | \(-0.142525\pi\) |
0.331264 | + | 0.943538i | \(0.392525\pi\) | |||||||
\(798\) | 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 | 0.189922 | − | 0.981799i | \(-0.439177\pi\) |
0.828532 | + | 0.559942i | \(0.189177\pi\) | |||||||
\(812\) | 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 | −0.800318 | − | 0.599575i | \(-0.795336\pi\) |
−0.141947 | + | 0.989874i | \(0.545336\pi\) | |||||||
\(822\) | 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 | \(0.183529\pi\) |
−0.207311 | + | 0.978275i | \(0.566471\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.0154 | + | 12.0186i | 1.00774 | + | 0.417422i | 0.824632 | − | 0.565670i | \(-0.191382\pi\) |
0.183113 | + | 0.983092i | \(0.441382\pi\) | |||||||
\(830\) | 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 | −0.509334 | − | 0.860569i | \(-0.670108\pi\) |
0.248361 | + | 0.968668i | \(0.420108\pi\) | |||||||
\(854\) | 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 | 0.846392 | − | 0.532561i | \(-0.178770\pi\) |
−0.975067 | + | 0.221912i | \(0.928770\pi\) | |||||||
\(860\) | 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 | \(-0.746966\pi\) |
0.999955 | − | 0.00953022i | \(-0.00303361\pi\) | |||||||
\(878\) | 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 | \(-0.705684\pi\) |
0.990324 | − | 0.138773i | \(-0.0443157\pi\) | |||||||
\(884\) | 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 | −0.669076 | − | 0.743194i | \(-0.733310\pi\) |
0.0524095 | + | 0.998626i | \(0.483310\pi\) | |||||||
\(908\) | 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 | −0.904250 | − | 0.427004i | \(-0.859569\pi\) |
0.941339 | + | 0.337464i | \(0.109569\pi\) | |||||||
\(942\) | 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 | −0.707643 | − | 0.706570i | \(-0.750242\pi\) |
1.00000 | 0.000758845i | \(0.000241548\pi\) | ||||||||
\(948\) | 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 | −0.966860 | − | 0.255308i | \(-0.917823\pi\) |
−0.503143 | + | 0.864203i | \(0.667823\pi\) | |||||||
\(972\) | 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 | \(-0.950048\pi\) |
0.587907 | − | 0.808928i | \(-0.299952\pi\) | |||||||
\(998\) | 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.g.641.4 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.g.641.1 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.d.641.4 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.d.641.1 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.a.129.4 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.f.129.4 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.f.129.1 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.a.129.1 | ✓ | 16 | ||
32.3 | odd | 8 | 1024.2.g.f.897.1 | yes | 16 | ||
32.5 | even | 8 | 1024.2.g.d.385.1 | yes | 16 | ||
32.11 | odd | 8 | inner | 1024.2.g.g.385.1 | yes | 16 | |
32.13 | even | 8 | 1024.2.g.a.897.1 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.a.897.4 | yes | 16 | ||
32.21 | even | 8 | inner | 1024.2.g.g.385.4 | yes | 16 | |
32.27 | odd | 8 | 1024.2.g.d.385.4 | yes | 16 | ||
32.29 | even | 8 | 1024.2.g.f.897.4 | yes | 16 | ||
64.11 | odd | 16 | 4096.2.a.i.1.1 | 8 | |||
64.21 | even | 16 | 4096.2.a.i.1.2 | 8 | |||
64.43 | odd | 16 | 4096.2.a.s.1.8 | 8 | |||
64.53 | even | 16 | 4096.2.a.s.1.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.a.129.1 | ✓ | 16 | 16.13 | even | 4 | ||
1024.2.g.a.129.4 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.a.897.1 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.a.897.4 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.d.385.1 | yes | 16 | 32.5 | even | 8 | ||
1024.2.g.d.385.4 | yes | 16 | 32.27 | odd | 8 | ||
1024.2.g.d.641.1 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.d.641.4 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.f.129.1 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.f.129.4 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.f.897.1 | yes | 16 | 32.3 | odd | 8 | ||
1024.2.g.f.897.4 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.g.385.1 | yes | 16 | 32.11 | odd | 8 | inner | |
1024.2.g.g.385.4 | yes | 16 | 32.21 | even | 8 | inner | |
1024.2.g.g.641.1 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.g.641.4 | yes | 16 | 1.1 | even | 1 | trivial | |
4096.2.a.i.1.1 | 8 | 64.11 | odd | 16 | |||
4096.2.a.i.1.2 | 8 | 64.21 | even | 16 | |||
4096.2.a.s.1.7 | 8 | 64.53 | even | 16 | |||
4096.2.a.s.1.8 | 8 | 64.43 | odd | 16 |