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: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8x^{14} + 32x^{12} - 64x^{10} + 127x^{8} - 576x^{6} + 2592x^{4} - 5832x^{2} + 6561 \) |
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 | 129.4 | ||
Root | \(-1.59056 - 0.685641i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1024.129 |
Dual form | 1024.2.g.c.897.4 |
$q$-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 \(\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(1023\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.942835 | − | 2.27621i | 0.544346 | − | 1.31417i | −0.377284 | − | 0.926098i | \(-0.623142\pi\) |
0.921630 | − | 0.388070i | \(-0.126858\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.49877 | − | 1.03503i | 1.11749 | − | 0.462878i | 0.253976 | − | 0.967211i | \(-0.418262\pi\) |
0.863509 | + | 0.504333i | \(0.168262\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.37128 | − | 1.37128i | 0.518296 | − | 0.518296i | −0.398760 | − | 0.917056i | \(-0.630559\pi\) |
0.917056 | + | 0.398760i | \(0.130559\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.17085 | − | 2.17085i | −0.723618 | − | 0.723618i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.70820 | + | 4.12396i | 0.515042 | + | 1.24342i | 0.940916 | + | 0.338640i | \(0.109967\pi\) |
−0.425874 | + | 0.904783i | \(0.640033\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.86345 | − | 2.01451i | −1.34888 | − | 0.558724i | −0.412899 | − | 0.910777i | \(-0.635484\pi\) |
−0.935980 | + | 0.352053i | \(0.885484\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.66358i | − | 1.72053i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.31269i | − | 1.53105i | −0.643405 | − | 0.765526i | \(-0.722479\pi\) | ||
0.643405 | − | 0.765526i | \(-0.277521\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.72988 | + | 1.95918i | 1.08511 | + | 0.449467i | 0.852299 | − | 0.523055i | \(-0.175208\pi\) |
0.232810 | + | 0.972522i | \(0.425208\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.82843 | − | 4.41421i | −0.398996 | − | 0.963260i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.288890 | − | 0.288890i | −0.0602377 | − | 0.0602377i | 0.676346 | − | 0.736584i | \(-0.263562\pi\) |
−0.736584 | + | 0.676346i | \(0.763562\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.63706 | − | 1.63706i | 0.327411 | − | 0.327411i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.159452 | + | 0.0660470i | −0.0306865 | + | 0.0127108i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.428722 | + | 1.03503i | −0.0796116 | + | 0.192199i | −0.958674 | − | 0.284508i | \(-0.908170\pi\) |
0.879062 | + | 0.476707i | \(0.158170\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.69552 | 0.663735 | 0.331867 | − | 0.943326i | \(-0.392321\pi\) | ||||
0.331867 | + | 0.943326i | \(0.392321\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.9975 | 1.91443 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00721 | − | 4.84584i | 0.339281 | − | 0.819096i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4468 | + | 4.32720i | −1.71744 | + | 0.711387i | −0.717552 | + | 0.696505i | \(0.754737\pi\) |
−0.999889 | + | 0.0148821i | \(0.995263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.17087 | + | 9.17087i | −1.46851 | + | 1.46851i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.68485 | + | 1.68485i | 0.263130 | + | 0.263130i | 0.826324 | − | 0.563194i | \(-0.190428\pi\) |
−0.563194 | + | 0.826324i | \(0.690428\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.67029 | + | 4.03244i | 0.254717 | + | 0.614941i | 0.998573 | − | 0.0533985i | \(-0.0170053\pi\) |
−0.743856 | + | 0.668340i | \(0.767005\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.67136 | − | 3.17758i | −1.14358 | − | 0.473686i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.83153i | − | 0.704750i | −0.935859 | − | 0.352375i | \(-0.885374\pi\) | ||
0.935859 | − | 0.352375i | \(-0.114626\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.23917i | 0.462739i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −14.3690 | − | 5.95183i | −2.01206 | − | 0.833423i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.207615 | − | 0.501227i | −0.0285181 | − | 0.0688488i | 0.908979 | − | 0.416842i | \(-0.136863\pi\) |
−0.937497 | + | 0.347993i | \(0.886863\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.53682 | + | 8.53682i | 1.15110 | + | 1.15110i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.91900 | − | 8.91900i | 1.18135 | − | 1.18135i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.25148 | + | 3.00366i | −0.944062 | + | 0.391043i | −0.800996 | − | 0.598670i | \(-0.795696\pi\) |
−0.143066 | + | 0.989713i | \(0.545696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.40820 | − | 3.39971i | 0.180302 | − | 0.435288i | −0.807727 | − | 0.589557i | \(-0.799302\pi\) |
0.988029 | + | 0.154269i | \(0.0493023\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.95371 | −0.750097 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.2377 | −1.76597 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.123853 | + | 0.299008i | −0.0151311 | + | 0.0365297i | −0.931265 | − | 0.364344i | \(-0.881293\pi\) |
0.916133 | + | 0.400873i | \(0.131293\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.929949 | + | 0.385197i | −0.111953 | + | 0.0463723i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.54392 | + | 6.54392i | −0.776620 | + | 0.776620i | −0.979255 | − | 0.202634i | \(-0.935050\pi\) |
0.202634 | + | 0.979255i | \(0.435050\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.53380 | + | 5.53380i | 0.647682 | + | 0.647682i | 0.952432 | − | 0.304750i | \(-0.0985730\pi\) |
−0.304750 | + | 0.952432i | \(0.598573\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.18280 | − | 5.26975i | −0.252048 | − | 0.608498i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.99755 | + | 3.31269i | 0.911405 | + | 0.377516i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 0.877131i | − | 0.0986849i | −0.998782 | − | 0.0493425i | \(-0.984287\pi\) | ||
0.998782 | − | 0.0493425i | \(-0.0157126\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 8.78494i | − | 0.976104i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.42652 | + | 1.41931i | 0.376110 | + | 0.155790i | 0.562727 | − | 0.826643i | \(-0.309752\pi\) |
−0.186617 | + | 0.982433i | \(0.559752\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.53380 | − | 15.7740i | −0.708690 | − | 1.71093i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.95172 | + | 1.95172i | 0.209246 | + | 0.209246i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.46129 | − | 6.46129i | 0.684896 | − | 0.684896i | −0.276203 | − | 0.961099i | \(-0.589076\pi\) |
0.961099 | + | 0.276203i | \(0.0890764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.43162 | + | 3.90671i | −0.988703 | + | 0.409534i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.48427 | − | 8.41176i | 0.361301 | − | 0.872259i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.8467 | 1.42064 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.58333 | −0.363832 | −0.181916 | − | 0.983314i | \(-0.558230\pi\) | ||||
−0.181916 | + | 0.983314i | \(0.558230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.24427 | − | 12.6608i | 0.527069 | − | 1.27246i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.20761 | + | 2.57128i | −0.617681 | + | 0.255852i | −0.669509 | − | 0.742804i | \(-0.733495\pi\) |
0.0518279 | + | 0.998656i | \(0.483495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.9244 | − | 10.9244i | 1.07642 | − | 1.07642i | 0.0795901 | − | 0.996828i | \(-0.474639\pi\) |
0.996828 | − | 0.0795901i | \(-0.0253611\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.13765 | − | 9.13765i | −0.891743 | − | 0.891743i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.94753 | + | 4.70174i | 0.188274 | + | 0.454535i | 0.989628 | − | 0.143657i | \(-0.0458861\pi\) |
−0.801353 | + | 0.598192i | \(0.795886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.32720 | + | 2.20660i | 0.510253 | + | 0.211354i | 0.622930 | − | 0.782278i | \(-0.285942\pi\) |
−0.112676 | + | 0.993632i | \(0.535942\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27.8589i | 2.64425i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.06760i | − | 0.100431i | −0.998738 | − | 0.0502156i | \(-0.984009\pi\) | ||
0.998738 | − | 0.0502156i | \(-0.0159908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.02088 | − | 0.422862i | −0.0951974 | − | 0.0394321i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.18464 | + | 14.9311i | 0.571771 | + | 1.38038i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.65648 | − | 8.65648i | −0.793538 | − | 0.793538i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.31096 | + | 6.31096i | −0.573723 | + | 0.573723i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.42362 | − | 2.24653i | 0.489031 | − | 0.202563i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.77889 | + | 6.70884i | −0.248552 | + | 0.600057i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.7979 | −1.93425 | −0.967127 | − | 0.254294i | \(-0.918157\pi\) | ||||
−0.967127 | + | 0.254294i | \(0.918157\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.7535 | 0.946790 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.53973 | + | 15.7883i | −0.571379 | + | 1.37943i | 0.329003 | + | 0.944329i | \(0.393287\pi\) |
−0.900382 | + | 0.435101i | \(0.856713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.17259 | − | 3.79941i | 0.795364 | − | 0.329451i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.330073 | + | 0.330073i | −0.0284082 | + | 0.0284082i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.85744 | − | 3.85744i | −0.329564 | − | 0.329564i | 0.522857 | − | 0.852420i | \(-0.324866\pi\) |
−0.852420 | + | 0.522857i | \(0.824866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.16568 | + | 2.81420i | 0.0988715 | + | 0.238697i | 0.965574 | − | 0.260128i | \(-0.0837649\pi\) |
−0.866703 | + | 0.498825i | \(0.833765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.9975 | − | 4.55533i | −0.926160 | − | 0.383628i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 23.4979i | − | 1.96499i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.03003i | 0.251631i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.37302 | + | 3.05400i | 0.608116 | + | 0.251890i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.57128 | + | 13.4503i | 0.456417 | + | 1.10189i | 0.969838 | + | 0.243751i | \(0.0783780\pi\) |
−0.513421 | + | 0.858137i | \(0.671622\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.87718 | − | 3.87718i | −0.315520 | − | 0.315520i | 0.531523 | − | 0.847044i | \(-0.321620\pi\) |
−0.847044 | + | 0.531523i | \(0.821620\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.7039 | + | 13.7039i | −1.10790 | + | 1.10790i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.23426 | − | 3.82496i | 0.741714 | − | 0.307228i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.82140 | + | 4.39725i | −0.145364 | + | 0.350939i | −0.979745 | − | 0.200248i | \(-0.935825\pi\) |
0.834381 | + | 0.551187i | \(0.185825\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.33664 | −0.106003 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.792299 | −0.0624419 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.494494 | − | 1.19381i | 0.0387317 | − | 0.0935067i | −0.903330 | − | 0.428946i | \(-0.858885\pi\) |
0.942062 | + | 0.335440i | \(0.108885\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 27.4804 | − | 11.3827i | 2.13934 | − | 0.886145i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.53607 | − | 3.53607i | 0.273629 | − | 0.273629i | −0.556930 | − | 0.830559i | \(-0.688021\pi\) |
0.830559 | + | 0.556930i | \(0.188021\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.4025 | + | 10.4025i | 0.800196 | + | 0.800196i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.01479 | − | 14.5210i | −0.459962 | − | 1.11045i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.1376 | + | 4.19912i | 0.770745 | + | 0.319253i | 0.733174 | − | 0.680041i | \(-0.238038\pi\) |
0.0375707 | + | 0.999294i | \(0.488038\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.48973i | − | 0.339392i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 19.3378i | 1.45352i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.2386 | + | 5.48359i | 0.989497 | + | 0.409863i | 0.817935 | − | 0.575310i | \(-0.195119\pi\) |
0.171562 | + | 0.985173i | \(0.445119\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.21510 | − | 10.1761i | −0.313306 | − | 0.756387i | −0.999578 | − | 0.0290424i | \(-0.990754\pi\) |
0.686272 | − | 0.727345i | \(-0.259246\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.41072 | − | 6.41072i | −0.473894 | − | 0.473894i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.6254 | + | 21.6254i | −1.58993 | + | 1.58993i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 26.0333 | − | 10.7834i | 1.90374 | − | 0.788557i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.128084 | + | 0.309222i | −0.00931674 | + | 0.0224926i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.0607 | 1.66862 | 0.834308 | − | 0.551299i | \(-0.185868\pi\) | ||||
0.834308 | + | 0.551299i | \(0.185868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.24019 | 0.665123 | 0.332562 | − | 0.943082i | \(-0.392087\pi\) | ||||
0.332562 | + | 0.943082i | \(0.392087\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.4238 | + | 32.4080i | −0.961301 | + | 2.32079i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.8815 | + | 4.50727i | −0.775276 | + | 0.321130i | −0.735007 | − | 0.678059i | \(-0.762821\pi\) |
−0.0402686 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5468 | − | 14.5468i | 1.03120 | − | 1.03120i | 0.0316976 | − | 0.999498i | \(-0.489909\pi\) |
0.999498 | − | 0.0316976i | \(-0.0100914\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.563832 | + | 0.563832i | 0.0397696 | + | 0.0397696i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.831414 | + | 2.00721i | 0.0583538 | + | 0.140879i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.95394 | + | 2.46620i | 0.415841 | + | 0.172247i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.25428i | 0.0871782i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.8525i | 1.58074i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.68155 | + | 4.01023i | 0.666506 | + | 0.276076i | 0.690173 | − | 0.723644i | \(-0.257534\pi\) |
−0.0236676 | + | 0.999720i | \(0.507534\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.72547 | + | 21.0651i | 0.597859 | + | 1.44336i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.34735 | + | 8.34735i | 0.569285 | + | 0.569285i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.06760 | − | 5.06760i | 0.344011 | − | 0.344011i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.8135 | − | 7.37860i | 1.20373 | − | 0.498600i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.7170 | + | 30.7015i | −0.855436 | + | 2.06521i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6174 | 0.911892 | 0.455946 | − | 0.890008i | \(-0.349301\pi\) | ||||
0.455946 | + | 0.890008i | \(0.349301\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.10762 | −0.473841 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.17300 | − | 17.3172i | 0.476089 | − | 1.14938i | −0.485340 | − | 0.874326i | \(-0.661304\pi\) |
0.961429 | − | 0.275054i | \(-0.0886959\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.67035 | − | 0.691880i | 0.110380 | − | 0.0457207i | −0.326810 | − | 0.945090i | \(-0.605974\pi\) |
0.437190 | + | 0.899369i | \(0.355974\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.0807 | − | 15.0807i | 0.992240 | − | 0.992240i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.606304 | + | 0.606304i | 0.0397203 | + | 0.0397203i | 0.726688 | − | 0.686968i | \(-0.241059\pi\) |
−0.686968 | + | 0.726688i | \(0.741059\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.00075 | − | 12.0729i | −0.326213 | − | 0.787548i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.99653 | − | 0.826990i | −0.129689 | − | 0.0537188i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.5680i | 1.52449i | 0.647291 | + | 0.762243i | \(0.275902\pi\) | ||||
−0.647291 | + | 0.762243i | \(0.724098\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 25.6775i | − | 1.65403i | −0.562178 | − | 0.827016i | \(-0.690036\pi\) | ||
0.562178 | − | 0.827016i | \(-0.309964\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20.4747 | − | 8.48089i | −1.31345 | − | 0.544049i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.35263 | + | 8.09395i | 0.214191 | + | 0.517104i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −19.0568 | − | 19.0568i | −1.21255 | − | 1.21255i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.46129 | − | 6.46129i | 0.409468 | − | 0.409468i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.5723 | + | 11.4208i | −1.74035 | + | 0.720876i | −0.741600 | + | 0.670842i | \(0.765933\pi\) |
−0.998748 | + | 0.0500337i | \(0.984067\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.697889 | − | 1.68485i | 0.0438759 | − | 0.105926i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −42.0651 | −2.63422 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.5578 | −1.09522 | −0.547612 | − | 0.836732i | \(-0.684463\pi\) | ||||
−0.547612 | + | 0.836732i | \(0.684463\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.39168 | + | 20.2593i | −0.521433 | + | 1.25885i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.17758 | − | 1.31620i | 0.196687 | − | 0.0814706i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.89551 | + | 8.89551i | −0.548521 | + | 0.548521i | −0.926013 | − | 0.377492i | \(-0.876787\pi\) |
0.377492 | + | 0.926013i | \(0.376787\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.03757 | − | 1.03757i | −0.0637371 | − | 0.0637371i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.61530 | − | 20.7992i | −0.527248 | − | 1.27289i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.8791 | + | 6.57732i | 0.968164 | + | 0.401026i | 0.810028 | − | 0.586391i | \(-0.199452\pi\) |
0.158135 | + | 0.987417i | \(0.449452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.9379i | 1.45412i | 0.686573 | + | 0.727061i | \(0.259114\pi\) | ||||
−0.686573 | + | 0.727061i | \(0.740886\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.1517i | 1.52225i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.54758 | + | 3.95474i | 0.575741 | + | 0.238480i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.99154 | + | 12.0506i | 0.299912 | + | 0.724053i | 0.999951 | + | 0.00994710i | \(0.00316631\pi\) |
−0.700038 | + | 0.714105i | \(0.746834\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.02243 | − | 8.02243i | −0.480290 | − | 0.480290i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.0761 | + | 15.0761i | −0.899365 | + | 0.899365i | −0.995380 | − | 0.0960153i | \(-0.969390\pi\) |
0.0960153 | + | 0.995380i | \(0.469390\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.37563 | + | 0.984018i | −0.141217 | + | 0.0584938i | −0.452172 | − | 0.891931i | \(-0.649351\pi\) |
0.310956 | + | 0.950424i | \(0.399351\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.0552 | − | 31.5179i | 0.773321 | − | 1.86696i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.62082 | 0.272758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −22.8501 | −1.34412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.37849 | + | 8.15640i | −0.198051 | + | 0.478137i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.3017 | − | 5.50973i | 0.777091 | − | 0.321882i | 0.0413500 | − | 0.999145i | \(-0.486834\pi\) |
0.735741 | + | 0.677263i | \(0.236834\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.0109 | + | 15.0109i | −0.873970 | + | 0.873970i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.544751 | − | 0.544751i | −0.0316097 | − | 0.0316097i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.823031 | + | 1.98697i | 0.0475971 | + | 0.114910i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.82005 | + | 3.23917i | 0.450740 | + | 0.186703i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.5541i | 0.951008i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 9.95262i | − | 0.569885i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.1975 | − | 7.12343i | −0.981513 | − | 0.406556i | −0.166527 | − | 0.986037i | \(-0.553255\pi\) |
−0.814986 | + | 0.579481i | \(0.803255\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.5663 | − | 35.1662i | −0.828650 | − | 2.00054i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.1862 | + | 19.1862i | 1.08795 | + | 1.08795i | 0.995740 | + | 0.0922102i | \(0.0293932\pi\) |
0.0922102 | + | 0.995740i | \(0.470607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.7525 | − | 14.7525i | 0.833858 | − | 0.833858i | −0.154184 | − | 0.988042i | \(-0.549275\pi\) |
0.988042 | + | 0.154184i | \(0.0492749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.8770 | + | 6.16224i | −0.838222 | + | 0.347203i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.4663 | − | 25.2679i | 0.587845 | − | 1.41918i | −0.297713 | − | 0.954655i | \(-0.596224\pi\) |
0.885558 | − | 0.464529i | \(-0.153776\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.00075 | −0.279988 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.5383 | 0.699822 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.3677 | − | 29.8583i | 0.688157 | − | 1.66136i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.2596 | + | 4.66388i | −0.624570 | + | 0.258706i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0453 | − | 10.0453i | 0.555509 | − | 0.555509i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.62538 | − | 6.62538i | −0.365269 | − | 0.365269i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.33960 | + | 5.64829i | 0.128596 | + | 0.310458i | 0.975043 | − | 0.222014i | \(-0.0712631\pi\) |
−0.846448 | + | 0.532472i | \(0.821263\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 32.0722 | + | 13.2847i | 1.75754 | + | 0.727999i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.875346i | 0.0478253i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.82843i | 0.154074i | 0.997028 | + | 0.0770371i | \(0.0245460\pi\) | ||||
−0.997028 | + | 0.0770371i | \(0.975454\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.43007 | − | 1.00657i | −0.131983 | − | 0.0546693i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.31269 | + | 15.2402i | 0.341851 | + | 0.825302i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.0408 | + | 14.0408i | 0.758131 | + | 0.758131i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.92504 | + | 1.92504i | −0.103641 | + | 0.103641i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0909 | + | 6.25084i | −0.810120 | + | 0.335563i | −0.749002 | − | 0.662568i | \(-0.769467\pi\) |
−0.0611179 | + | 0.998131i | \(0.519467\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.28515 | − | 15.1737i | 0.336436 | − | 0.812229i | −0.661616 | − | 0.749843i | \(-0.730129\pi\) |
0.998052 | − | 0.0623861i | \(-0.0198710\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.908538 | 0.0484942 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.5234 | −1.73105 | −0.865524 | − | 0.500867i | \(-0.833014\pi\) | ||||
−0.865524 | + | 0.500867i | \(0.833014\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.57864 | + | 23.1249i | −0.508382 | + | 1.22734i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −27.8656 | + | 11.5423i | −1.47480 | + | 0.610883i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.30331 | + | 4.30331i | −0.227120 | + | 0.227120i | −0.811488 | − | 0.584368i | \(-0.801342\pi\) |
0.584368 | + | 0.811488i | \(0.301342\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.09835 | + | 5.09835i | 0.268334 | + | 0.268334i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.41484 | + | 20.3152i | 0.441665 | + | 1.06627i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.5553 | + | 8.10008i | 1.02357 | + | 0.423978i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.45619i | 0.180412i | 0.995923 | + | 0.0902059i | \(0.0287525\pi\) | ||||
−0.995923 | + | 0.0902059i | \(0.971247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 7.31515i | − | 0.380811i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.972022 | − | 0.402625i | −0.0504649 | − | 0.0209032i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00601 | + | 4.84294i | 0.103867 | + | 0.250758i | 0.967266 | − | 0.253764i | \(-0.0816688\pi\) |
−0.863399 | + | 0.504522i | \(0.831669\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.6507 | + | 12.6507i | 0.653278 | + | 0.653278i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.17014 | − | 4.17014i | 0.214773 | − | 0.214773i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.9167 | − | 10.3208i | 1.27989 | − | 0.530146i | 0.363931 | − | 0.931426i | \(-0.381435\pi\) |
0.915956 | + | 0.401280i | \(0.131435\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.5519 | + | 49.6166i | −1.05290 | + | 2.54193i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.16870 | −0.161913 | −0.0809564 | − | 0.996718i | \(-0.525797\pi\) | ||||
−0.0809564 | + | 0.996718i | \(0.525797\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 23.4128 | 1.19323 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.12788 | − | 12.3798i | 0.260665 | − | 0.629300i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.3428 | + | 5.94099i | −0.727209 | + | 0.301220i | −0.715405 | − | 0.698710i | \(-0.753758\pi\) |
−0.0118047 | + | 0.999930i | \(0.503758\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.82367 | + | 1.82367i | −0.0922271 | + | 0.0922271i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 29.7715 | + | 29.7715i | 1.50178 | + | 1.50178i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.907853 | − | 2.19175i | −0.0456790 | − | 0.110279i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −36.0551 | − | 14.9345i | −1.80955 | − | 0.749542i | −0.982194 | − | 0.187872i | \(-0.939841\pi\) |
−0.827361 | − | 0.561670i | \(-0.810159\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 24.4609i | − | 1.22458i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9.14806i | − | 0.456832i | −0.973564 | − | 0.228416i | \(-0.926645\pi\) | ||
0.973564 | − | 0.228416i | \(-0.0733547\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.9730 | − | 7.44465i | −0.895298 | − | 0.370844i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.09264 | − | 21.9516i | −0.451817 | − | 1.09078i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.6904 | − | 35.6904i | −1.76911 | − | 1.76911i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.4503 | − | 22.4503i | 1.11010 | − | 1.11010i | 0.116961 | − | 0.993136i | \(-0.462685\pi\) |
0.993136 | − | 0.116961i | \(-0.0373154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.4173 | + | 5.14340i | −0.612499 | + | 0.253705i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.82496 | + | 14.0627i | −0.286627 | + | 0.691980i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.0311 | 0.492409 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.50473 | 0.367508 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.47620 | − | 18.0491i | 0.365236 | − | 0.881758i | −0.629280 | − | 0.777178i | \(-0.716650\pi\) |
0.994516 | − | 0.104580i | \(-0.0333498\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.7751 | − | 12.3332i | 1.45115 | − | 0.601086i | 0.488677 | − | 0.872465i | \(-0.337480\pi\) |
0.962472 | + | 0.271379i | \(0.0874798\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −10.4885 | + | 10.4885i | −0.509970 | + | 0.509970i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.3342 | − | 10.3342i | −0.501284 | − | 0.501284i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.73091 | − | 6.59300i | −0.132158 | − | 0.319058i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −53.4860 | − | 22.1546i | −2.58233 | − | 1.06964i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 20.3993i | − | 0.982599i | −0.870991 | − | 0.491300i | \(-0.836522\pi\) | ||
0.870991 | − | 0.491300i | \(-0.163478\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.8560i | 0.521706i | 0.965378 | + | 0.260853i | \(0.0840038\pi\) | ||||
−0.965378 | + | 0.260853i | \(0.915996\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.89698 | + | 2.85682i | 0.330685 | + | 0.136974i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.800427 | − | 1.93240i | −0.0382896 | − | 0.0924393i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.44342 | + | 8.44342i | 0.402982 | + | 0.402982i | 0.879283 | − | 0.476300i | \(-0.158023\pi\) |
−0.476300 | + | 0.879283i | \(0.658023\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.03177 | − | 7.03177i | 0.334846 | − | 0.334846i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.74286 | + | 2.37877i | −0.272852 | + | 0.113019i | −0.514914 | − | 0.857242i | \(-0.672176\pi\) |
0.242062 | + | 0.970261i | \(0.422176\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.45770 | − | 22.8329i | 0.448338 | − | 1.08238i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 35.8683 | 1.69651 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.69940 | 0.363357 | 0.181679 | − | 0.983358i | \(-0.441847\pi\) | ||||
0.181679 | + | 0.983358i | \(0.441847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.07021 | + | 9.82635i | −0.191659 | + | 0.462705i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.4808 | + | 5.16971i | −0.586399 | + | 0.242894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −19.5239 | + | 19.5239i | −0.915297 | + | 0.915297i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.0976 | − | 21.0976i | −0.986906 | − | 0.986906i | 0.0130098 | − | 0.999915i | \(-0.495859\pi\) |
−0.999915 | + | 0.0130098i | \(0.995859\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.416935 | + | 1.00657i | 0.0194608 | + | 0.0469826i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −37.1844 | − | 15.4023i | −1.73185 | − | 0.717356i | −0.999330 | − | 0.0366105i | \(-0.988344\pi\) |
−0.732520 | − | 0.680745i | \(-0.761656\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.4608i | − | 1.09031i | −0.838334 | − | 0.545157i | \(-0.816470\pi\) | ||
0.838334 | − | 0.545157i | \(-0.183530\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 24.6254i | − | 1.14197i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 33.2562 | + | 13.7752i | 1.53891 | + | 0.637438i | 0.981269 | − | 0.192642i | \(-0.0617057\pi\) |
0.557643 | + | 0.830081i | \(0.311706\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.240187 | + | 0.579863i | 0.0110908 | + | 0.0267756i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.29177 | + | 8.29177i | 0.382065 | + | 0.382065i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.7764 | + | 13.7764i | −0.633441 | + | 0.633441i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.9504 | − | 4.53579i | 0.502437 | − | 0.208116i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.637389 | + | 1.53879i | −0.0291840 | + | 0.0704565i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.55206 | −0.436445 | −0.218222 | − | 0.975899i | \(-0.570026\pi\) | ||||
−0.218222 | + | 0.975899i | \(0.570026\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 59.5246 | 2.71409 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.747008 | + | 1.80344i | −0.0339900 | + | 0.0820592i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.95394 | + | 3.70884i | −0.406577 | + | 0.168410i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.14134 | + | 3.14134i | −0.142348 | + | 0.142348i | −0.774690 | − | 0.632342i | \(-0.782094\pi\) |
0.632342 | + | 0.774690i | \(0.282094\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.25114 | − | 2.25114i | −0.101800 | − | 0.101800i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.17829 | − | 14.9157i | −0.278822 | − | 0.673136i | 0.720981 | − | 0.692954i | \(-0.243691\pi\) |
−0.999804 | + | 0.0198181i | \(0.993691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.53380 | + | 2.70639i | 0.294268 | + | 0.121890i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 37.0644i | − | 1.66592i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.9471i | 0.805038i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.94503 | − | 3.70515i | −0.400435 | − | 0.165865i | 0.173372 | − | 0.984856i | \(-0.444534\pi\) |
−0.573806 | + | 0.818991i | \(0.694534\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.71489 | − | 11.3827i | −0.210646 | − | 0.508543i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.3899 | + | 15.3899i | 0.686200 | + | 0.686200i | 0.961390 | − | 0.275190i | \(-0.0887407\pi\) |
−0.275190 | + | 0.961390i | \(0.588741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.8501 | + | 12.8501i | −0.571821 | + | 0.571821i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.4862 | − | 13.8704i | 1.48717 | − | 0.616008i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.59281 | + | 23.1591i | −0.425194 | + | 1.02651i | 0.555598 | + | 0.831451i | \(0.312489\pi\) |
−0.980792 | + | 0.195058i | \(0.937511\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.1768 | 0.671382 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.883585 | −0.0390112 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.9906 | − | 38.6048i | 0.704631 | − | 1.70113i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.9250 | − | 8.25322i | 0.876302 | − | 0.362976i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 19.1161 | − | 19.1161i | 0.839104 | − | 0.839104i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.9005 | − | 23.9005i | −1.04710 | − | 1.04710i | −0.998835 | − | 0.0482659i | \(-0.984631\pi\) |
−0.0482659 | − | 0.998835i | \(-0.515369\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5373 | + | 37.5104i | 0.679400 | + | 1.64022i | 0.765113 | + | 0.643896i | \(0.222683\pi\) |
−0.0857135 | + | 0.996320i | \(0.527317\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.2195 | − | 4.23308i | −0.446018 | − | 0.184747i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 23.3287i | − | 1.01621i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 22.8331i | − | 0.992743i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.2624 | + | 9.22139i | 0.966107 | + | 0.400174i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.80006 | − | 11.5884i | −0.207914 | − | 0.501948i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.73285 | + | 9.73285i | 0.420788 | + | 0.420788i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.9636 | − | 24.9636i | 1.07726 | − | 1.07726i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.3582 | + | 5.53316i | −0.575380 | + | 0.238330i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.06548 | + | 9.81494i | −0.174789 | + | 0.421977i | −0.986859 | − | 0.161582i | \(-0.948340\pi\) |
0.812071 | + | 0.583559i | \(0.198340\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −27.1371 | −1.16457 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15.5954 | 0.668031 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.76275 | − | 21.1552i | 0.374668 | − | 0.904529i | −0.618277 | − | 0.785960i | \(-0.712169\pi\) |
0.992946 | − | 0.118569i | \(-0.0378308\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.4373 | + | 4.32326i | −0.445452 | + | 0.184512i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.05560 | + | 4.05560i | −0.172775 | + | 0.172775i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.20279 | − | 1.20279i | −0.0511480 | − | 0.0511480i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 28.8346 | + | 69.6130i | 1.22396 | + | 2.95491i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.62530 | − | 3.15850i | −0.323094 | − | 0.133830i | 0.215241 | − | 0.976561i | \(-0.430946\pi\) |
−0.538335 | + | 0.842731i | \(0.680946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 22.9764i | − | 0.971798i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 69.4241i | − | 2.93109i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.80767 | − | 2.81983i | −0.286909 | − | 0.118842i | 0.234587 | − | 0.972095i | \(-0.424626\pi\) |
−0.521497 | + | 0.853253i | \(0.674626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.10499 | − | 2.66768i | −0.0464873 | − | 0.112230i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.0466 | − | 12.0466i | −0.505911 | − | 0.505911i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.9201 | + | 14.9201i | −0.625485 | + | 0.625485i | −0.946929 | − | 0.321444i | \(-0.895832\pi\) |
0.321444 | + | 0.946929i | \(0.395832\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.1982 | + | 9.19481i | −0.928968 | + | 0.384791i | −0.795287 | − | 0.606233i | \(-0.792680\pi\) |
−0.133681 | + | 0.991024i | \(0.542680\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.7425 | − | 52.4910i | 0.908305 | − | 2.19284i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.945857 | −0.0394450 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.71236 | −0.196178 | −0.0980891 | − | 0.995178i | \(-0.531273\pi\) | ||||
−0.0980891 | + | 0.995178i | \(0.531273\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.71197 | − | 21.0326i | 0.362057 | − | 0.874084i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.64501 | − | 2.75245i | 0.275681 | − | 0.114191i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.71239 | − | 1.71239i | 0.0709201 | − | 0.0709201i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 30.9080 | + | 30.9080i | 1.27789 | + | 1.27789i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.5321 | + | 27.8409i | 0.475981 | + | 1.14912i | 0.961478 | + | 0.274881i | \(0.0886384\pi\) |
−0.485498 | + | 0.874238i | \(0.661362\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.4794 | + | 7.24019i | 0.720224 | + | 0.298327i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.0182i | 1.19365i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.4902i | 0.430780i | 0.976528 | + | 0.215390i | \(0.0691023\pi\) | ||||
−0.976528 | + | 0.215390i | \(0.930898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.5903 | − | 12.6709i | −1.25408 | − | 0.519456i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.3963 | − | 46.8267i | −0.793837 | − | 1.91649i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.7913 | − | 17.7913i | −0.726934 | − | 0.726934i | 0.243074 | − | 0.970008i | \(-0.421844\pi\) |
−0.970008 | + | 0.243074i | \(0.921844\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.81138 | − | 8.81138i | 0.359424 | − | 0.359424i | −0.504177 | − | 0.863600i | \(-0.668204\pi\) |
0.863600 | + | 0.504177i | \(0.168204\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.917971 | − | 0.380236i | 0.0373827 | − | 0.0154844i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.23765 | + | 22.3017i | −0.375564 | + | 0.906691i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.9547 | −0.769347 | −0.384673 | − | 0.923053i | \(-0.625686\pi\) | ||||
−0.384673 | + | 0.923053i | \(0.625686\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.35271 | 0.216903 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.73315 | + | 23.4979i | −0.393761 | + | 0.950623i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.94446 | + | 1.21963i | −0.118925 | + | 0.0492605i | −0.441353 | − | 0.897334i | \(-0.645501\pi\) |
0.322427 | + | 0.946594i | \(0.395501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 11.2272 | − | 11.2272i | 0.452723 | − | 0.452723i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.36121 | + | 7.36121i | 0.296351 | + | 0.296351i | 0.839583 | − | 0.543232i | \(-0.182799\pi\) |
−0.543232 | + | 0.839583i | \(0.682799\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.41098 | − | 10.6490i | −0.177292 | − | 0.428021i | 0.810105 | − | 0.586285i | \(-0.199410\pi\) |
−0.987397 | + | 0.158264i | \(0.949410\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.0651443 | + | 0.0269836i | 0.00261415 | + | 0.00108282i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 17.7205i | − | 0.709957i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 31.2158i | 1.24863i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 52.0171 | + | 21.5462i | 2.07736 | + | 0.860471i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 27.3163 | + | 65.9473i | 1.08917 | + | 2.62949i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.1664 | − | 22.1664i | −0.882431 | − | 0.882431i | 0.111351 | − | 0.993781i | \(-0.464482\pi\) |
−0.993781 | + | 0.111351i | \(0.964482\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.2562 | − | 18.2562i | 0.725620 | − | 0.725620i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −54.4681 | + | 22.5614i | −2.16150 | + | 0.895323i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.52534 | − | 15.7536i | 0.258543 | − | 0.624179i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 28.4118 | 1.12395 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.2598 | −0.958205 | −0.479102 | − | 0.877759i | \(-0.659038\pi\) | ||||
−0.479102 | + | 0.877759i | \(0.659038\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.7001 | − | 25.8323i | 0.421970 | − | 1.01872i | −0.559796 | − | 0.828630i | \(-0.689121\pi\) |
0.981766 | − | 0.190094i | \(-0.0608794\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 26.8705 | − | 11.1301i | 1.05802 | − | 0.438248i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.2804 | + | 25.2804i | −0.993875 | + | 0.993875i | −0.999981 | − | 0.00610682i | \(-0.998056\pi\) |
0.00610682 | + | 0.999981i | \(0.498056\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.7740 | − | 24.7740i | −0.972464 | − | 0.972464i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.75699 | − | 16.3128i | −0.264827 | − | 0.639349i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.8766 | − | 8.64737i | −0.816965 | − | 0.338398i | −0.0652357 | − | 0.997870i | \(-0.520780\pi\) |
−0.751729 | + | 0.659472i | \(0.770780\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 46.2202i | 1.80597i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 24.0261i | − | 0.937349i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −43.7800 | − | 18.1343i | −1.70543 | − | 0.706410i | −0.705428 | − | 0.708781i | \(-0.749245\pi\) |
−0.999997 | + | 0.00237069i | \(0.999245\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.7510 | − | 28.3694i | −0.457060 | − | 1.10344i | −0.969582 | − | 0.244767i | \(-0.921289\pi\) |
0.512522 | − | 0.858674i | \(-0.328711\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 57.8929 | + | 57.8929i | 2.24837 | + | 2.24837i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 18.9877 | − | 18.9877i | 0.736313 | − | 0.736313i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.422862 | − | 0.175155i | 0.0163733 | − | 0.00678203i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.8390 | − | 30.9961i | 0.496385 | − | 1.19838i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.4258 | 0.634110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.36607 | 0.206847 | 0.103423 | − | 0.994637i | \(-0.467020\pi\) | ||||
0.103423 | + | 0.994637i | \(0.467020\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.152908 | + | 0.369154i | −0.00588545 | + | 0.0142087i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.0626 | + | 7.48178i | −0.694202 | + | 0.287548i | −0.701750 | − | 0.712424i | \(-0.747598\pi\) |
0.00754748 | + | 0.999972i | \(0.497598\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.91376 | + | 4.91376i | −0.188573 | + | 0.188573i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −32.6545 | − | 32.6545i | −1.25132 | − | 1.25132i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.4845 | − | 34.9686i | −0.554232 | − | 1.33804i | −0.914273 | − | 0.405099i | \(-0.867237\pi\) |
0.360041 | − | 0.932937i | \(-0.382763\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.6314 | − | 5.64632i | −0.520830 | − | 0.215735i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4.45438i | − | 0.169945i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.85593i | 0.108802i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.1342 | + | 8.75408i | 0.803983 | + | 0.333021i | 0.746551 | − | 0.665329i | \(-0.231709\pi\) |
0.0574327 | + | 0.998349i | \(0.481709\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.1701 | − | 24.5529i | −0.386332 | − | 0.932687i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.82553 | + | 5.82553i | 0.220975 | + | 0.220975i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.6360 | − | 10.6360i | 0.402866 | − | 0.402866i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.95172 | − | 0.808428i | 0.0738207 | − | 0.0305776i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.28579 | + | 12.7610i | −0.199642 | + | 0.481978i | −0.991716 | − | 0.128446i | \(-0.959001\pi\) |
0.792075 | + | 0.610424i | \(0.209001\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −57.8898 | −2.18336 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32.1953 | −1.21254 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.98644 | + | 12.0383i | −0.187535 | + | 0.452748i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.6145 | + | 14.3378i | −1.29997 | + | 0.538467i | −0.921943 | − | 0.387326i | \(-0.873399\pi\) |
−0.378031 | + | 0.925793i | \(0.623399\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.90412 | + | 1.90412i | −0.0714102 | + | 0.0714102i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.06760 | − | 1.06760i | −0.0399819 | − | 0.0399819i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.3209 | − | 58.7159i | −0.909551 | − | 2.19585i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 53.6456 | + | 22.2207i | 2.00343 | + | 0.829849i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 17.6095i | 0.656725i | 0.944552 | + | 0.328362i | \(0.106497\pi\) | ||||
−0.944552 | + | 0.328362i | \(0.893503\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 29.9610i | − | 1.11581i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −58.4473 | − | 24.2096i | −2.17368 | − | 0.900366i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.992553 | + | 2.39624i | 0.0368625 | + | 0.0889940i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.0431541 | + | 0.0431541i | 0.00160050 | + | 0.00160050i | 0.707907 | − | 0.706306i | \(-0.249640\pi\) |
−0.706306 | + | 0.707907i | \(0.749640\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.9728 | + | 19.9728i | −0.739735 | + | 0.739735i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.4555 | − | 10.5440i | 0.941507 | − | 0.389985i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.0530897 | + | 0.128170i | −0.00196091 | + | 0.00473407i | −0.924857 | − | 0.380315i | \(-0.875816\pi\) |
0.922896 | + | 0.385049i | \(0.125816\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.5845 | 0.796155 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.44467 | −0.0532150 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.74164 | − | 6.61892i | 0.100853 | − | 0.243481i | −0.865397 | − | 0.501087i | \(-0.832934\pi\) |
0.966250 | + | 0.257606i | \(0.0829337\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −61.3445 | + | 25.4097i | −2.25355 | + | 0.933450i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −28.5981 | + | 28.5981i | −1.04916 | + | 1.04916i | −0.0504342 | + | 0.998727i | \(0.516061\pi\) |
−0.998727 | + | 0.0504342i | \(0.983939\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.8427 | + | 27.8427i | 1.02008 | + | 1.02008i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.35736 | − | 10.5196i | −0.159428 | − | 0.384892i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.11803 | + | 3.77681i | 0.333165 | + | 0.138002i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.5222i | 0.967810i | 0.875121 | + | 0.483905i | \(0.160782\pi\) | ||||
−0.875121 | + | 0.483905i | \(0.839218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 73.5282i | 2.67952i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.7012 | − | 5.67521i | −0.498637 | − | 0.206542i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.87542 | + | 9.35610i | 0.140855 | + | 0.340053i | 0.978527 | − | 0.206121i | \(-0.0660839\pi\) |
−0.837672 | + | 0.546174i | \(0.816084\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.17708 | − | 3.17708i | −0.115321 | − | 0.115321i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5904 | − | 10.5904i | 0.383903 | − | 0.383903i | −0.488603 | − | 0.872506i | \(-0.662493\pi\) |
0.872506 | + | 0.488603i | \(0.162493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.3310 | − | 4.27923i | 0.374006 | − | 0.154918i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −20.0591 | + | 48.4269i | −0.725238 | + | 1.75088i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 41.3181 | 1.49191 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.3754 | −1.13143 | −0.565713 | − | 0.824602i | \(-0.691399\pi\) | ||||
−0.565713 | + | 0.824602i | \(0.691399\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.5541 | + | 39.9651i | −0.596181 | + | 1.43931i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 41.9982 | − | 17.3962i | 1.51057 | − | 0.625699i | 0.534896 | − | 0.844918i | \(-0.320351\pi\) |
0.975676 | + | 0.219219i | \(0.0703509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.04977 | − | 6.04977i | 0.217314 | − | 0.217314i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 38.2024 | + | 38.2024i | 1.37050 | + | 1.37050i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.66822 | + | 11.2701i | 0.167257 | + | 0.403793i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.1652 | − | 15.8086i | −1.36566 | − | 0.565675i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 0.193352i | − | 0.00690985i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.8729i | 0.459455i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.8929 | − | 5.75461i | −0.495227 | − | 0.205130i | 0.121070 | − | 0.992644i | \(-0.461368\pi\) |
−0.616296 | + | 0.787514i | \(0.711368\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.8610 | + | 28.6350i | 0.422263 | + | 1.01943i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.46398 | − | 1.46398i | −0.0520531 | − | 0.0520531i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.6975 | + | 13.6975i | −0.486411 | + | 0.486411i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.33997 | + | 1.38346i | −0.118456 | + | 0.0490662i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.80297 | − | 23.6665i | 0.347239 | − | 0.838309i | −0.649705 | − | 0.760187i | \(-0.725108\pi\) |
0.996944 | − | 0.0781223i | \(-0.0248925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.4999 | −1.07901 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −28.0531 | −0.991206 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.3683 | + | 32.2740i | −0.471759 | + | 1.13893i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.97978 | + | 0.820050i | −0.0697779 | + | 0.0289030i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 29.9427 | − | 29.9427i | 1.05403 | − | 1.05403i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.9526 | + | 24.9526i | 0.877287 | + | 0.877287i | 0.993253 | − | 0.115966i | \(-0.0369963\pi\) |
−0.115966 | + | 0.993253i | \(0.536996\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.46443 | − | 8.36388i | −0.121653 | − | 0.293696i | 0.851308 | − | 0.524666i | \(-0.175810\pi\) |
−0.972961 | + | 0.230971i | \(0.925810\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 54.4875 | + | 22.5695i | 1.91096 | + | 0.791545i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 3.49488i | − | 0.122420i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.3454i | 0.781765i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.9556 | + | 11.9938i | 1.01179 | + | 0.419097i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.05202 | − | 4.95402i | −0.0716161 | − | 0.172897i | 0.884018 | − | 0.467453i | \(-0.154828\pi\) |
−0.955634 | + | 0.294556i | \(0.904828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.6645 | − | 10.6645i | −0.371740 | − | 0.371740i | 0.496371 | − | 0.868111i | \(-0.334666\pi\) |
−0.868111 | + | 0.496371i | \(0.834666\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.0036 | − | 18.0036i | 0.626805 | − | 0.626805i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.97690 | + | 2.88993i | −0.242611 | + | 0.100493i | −0.500676 | − | 0.865635i | \(-0.666915\pi\) |
0.258065 | + | 0.966128i | \(0.416915\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.79382 | + | 13.9875i | −0.201228 | + | 0.485807i | −0.991990 | − | 0.126317i | \(-0.959684\pi\) |
0.790762 | + | 0.612123i | \(0.209684\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 32.1359 | 1.11478 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.4479 | 0.708477 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.17591 | − | 12.4957i | 0.179120 | − | 0.432433i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.589256 | + | 0.244078i | −0.0203677 | + | 0.00843657i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.3549 | + | 22.3549i | −0.771777 | + | 0.771777i | −0.978417 | − | 0.206640i | \(-0.933747\pi\) |
0.206640 | + | 0.978417i | \(0.433747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.6186 | + | 19.6186i | 0.676504 | + | 0.676504i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.1020 | + | 48.5306i | 0.692350 | + | 1.67148i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.7605 | + | 15.2267i | 1.26460 | + | 0.523814i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.3082i | 0.594717i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.33519i | 0.217423i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.26806 | + | 1.76789i | 0.146307 | + | 0.0606024i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.79442 | + | 4.33211i | 0.0614397 | + | 0.148329i | 0.951618 | − | 0.307284i | \(-0.0994202\pi\) |
−0.890178 | + | 0.455613i | \(0.849420\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −30.0592 | − | 30.0592i | −1.02800 | − | 1.02800i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.4779 | + | 14.4779i | −0.494556 | + | 0.494556i | −0.909738 | − | 0.415182i | \(-0.863718\pi\) |
0.415182 | + | 0.909738i | \(0.363718\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.1502 | + | 12.0744i | −0.994593 | + | 0.411974i | −0.819812 | − | 0.572633i | \(-0.805922\pi\) |
−0.174781 | + | 0.984607i | \(0.555922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.35667 | − | 10.5179i | 0.148475 | − | 0.358450i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.2601 | −1.67683 | −0.838417 | − | 0.545030i | \(-0.816518\pi\) | ||||
−0.838417 | + | 0.545030i | \(0.816518\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.6777 | 1.00907 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.5439 | + | 52.0115i | −0.731668 | + | 1.76640i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.61726 | − | 1.49832i | 0.122707 | − | 0.0508269i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.20471 | − | 1.20471i | 0.0408200 | − | 0.0408200i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.77889 | + | 7.77889i | 0.263276 | + | 0.263276i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.38907 | + | 13.0104i | 0.182184 | + | 0.439830i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.42178 | − | 1.83156i | −0.149313 | − | 0.0618475i | 0.306775 | − | 0.951782i | \(-0.400750\pi\) |
−0.456088 | + | 0.889934i | \(0.650750\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 35.4721i | − | 1.19644i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.99509i | 0.336743i | 0.985724 | + | 0.168372i | \(0.0538509\pi\) | ||||
−0.985724 | + | 0.168372i | \(0.946149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.6233 | + | 11.4420i | 0.929600 | + | 0.385053i | 0.795527 | − | 0.605919i | \(-0.207194\pi\) |
0.134073 | + | 0.990971i | \(0.457194\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.0151 | + | 48.3208i | 0.672802 | + | 1.62429i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.4541 | + | 19.4541i | 0.653206 | + | 0.653206i | 0.953764 | − | 0.300557i | \(-0.0971727\pi\) |
−0.300557 | + | 0.953764i | \(0.597173\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.8911 | + | 29.8911i | −1.00252 | + | 1.00252i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.2288 | − | 15.0065i | 1.21371 | − | 0.502735i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.46583 | − | 22.8525i | 0.316762 | − | 0.764731i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.7558 | 1.29546 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.29874 | 0.176920 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.58435 | + | 3.82496i | −0.0528410 | + | 0.127569i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.16409 | + | 1.31061i | −0.105411 | + | 0.0436627i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.7460 | − | 14.7460i | 0.490717 | − | 0.490717i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.0651 | − | 21.0651i | −0.700229 | − | 0.700229i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.8478 | − | 52.7454i | −0.725446 | − | 1.75138i | −0.657205 | − | 0.753712i | \(-0.728261\pi\) |
−0.0682409 | − | 0.997669i | \(-0.521739\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.0577 | + | 7.89396i | 0.632104 | + | 0.261826i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.1777i | 1.62933i | 0.579931 | + | 0.814666i | \(0.303080\pi\) | ||||
−0.579931 | + | 0.814666i | \(0.696920\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.5553i | 0.547902i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −22.6542 | − | 9.38368i | −0.748925 | − | 0.310215i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.6824 | + | 30.6180i | 0.418810 | + | 1.01110i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.6738 | + | 23.6738i | 0.780928 | + | 0.780928i | 0.979987 | − | 0.199060i | \(-0.0637888\pi\) |
−0.199060 | + | 0.979987i | \(0.563789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.4288 | + | 32.4288i | −1.06857 | + | 1.06857i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 45.0088 | − | 18.6433i | 1.48148 | − | 0.613650i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0181 | + | 24.1858i | −0.329393 | + | 0.795225i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −47.4308 | −1.55783 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.4698 | −0.474738 | −0.237369 | − | 0.971419i | \(-0.576285\pi\) | ||||
−0.237369 | + | 0.971419i | \(0.576285\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.34612 | + | 15.3209i | −0.207986 | + | 0.502122i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 61.7612 | − | 25.5823i | 2.02197 | − | 0.837527i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 53.8903 | − | 53.8903i | 1.76240 | − | 1.76240i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.4154 | − | 36.4154i | −1.18964 | − | 1.18964i | −0.977168 | − | 0.212470i | \(-0.931849\pi\) |
−0.212470 | − | 0.977168i | \(-0.568151\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.6705 | − | 47.4888i | −0.641922 | − | 1.54974i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.9189 | − | 7.00804i | −0.551541 | − | 0.228456i | 0.0894674 | − | 0.995990i | \(-0.471484\pi\) |
−0.641008 | + | 0.767534i | \(0.721484\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 0.973475i | − | 0.0317007i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.905247i | 0.0294477i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.0505 | + | 9.96206i | 0.781537 | + | 0.323723i | 0.737536 | − | 0.675308i | \(-0.235989\pi\) |
0.0440017 | + | 0.999031i | \(0.485989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.7655 | − | 38.0613i | −0.511769 | − | 1.23552i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −47.6468 | − | 47.6468i | −1.54505 | − | 1.54505i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −40.0406 | + | 40.0406i | −1.29704 | + | 1.29704i | −0.366706 | + | 0.930337i | \(0.619514\pi\) |
−0.930337 | + | 0.366706i | \(0.880486\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 57.6235 | − | 23.8684i | 1.86465 | − | 0.772365i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.71489 | + | 11.3827i | −0.152411 | + | 0.367952i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.5793 | −0.341623 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3431 | −0.559456 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.97901 | − | 14.4346i | 0.192671 | − | 0.465148i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.0891 | − | 9.56383i | 0.743265 | − | 0.307871i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.12949 | − | 3.12949i | 0.100637 | − | 0.100637i | −0.654995 | − | 0.755633i | \(-0.727329\pi\) |
0.755633 | + | 0.654995i | \(0.227329\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −56.3029 | − | 56.3029i | −1.80871 | − | 1.80871i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.51674 | − | 15.7328i | −0.209132 | − | 0.504890i | 0.784155 | − | 0.620565i | \(-0.213097\pi\) |
−0.993287 | + | 0.115675i | \(0.963097\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.45753 | + | 2.26058i | 0.174960 | + | 0.0724710i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.0264i | 0.961616i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 29.3535i | − | 0.939101i | −0.882906 | − | 0.469550i | \(-0.844416\pi\) | ||
0.882906 | − | 0.469550i | \(-0.155584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 37.6833 | + | 15.6090i | 1.20436 | + | 0.498864i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.77437 | − | 16.3548i | −0.216289 | − | 0.522168i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.2452 | − | 24.2452i | −0.773302 | − | 0.773302i | 0.205380 | − | 0.978682i | \(-0.434157\pi\) |
−0.978682 | + | 0.205380i | \(0.934157\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −22.5253 | + | 22.5253i | −0.717716 | + | 0.717716i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −21.3274 | + | 8.83409i | −0.678858 | + | 0.281192i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.682401 | − | 1.64746i | 0.0216991 | − | 0.0523862i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.7200 | −1.03939 | −0.519693 | − | 0.854353i | \(-0.673954\pi\) | ||||
−0.519693 | + | 0.854353i | \(0.673954\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.0625 | 0.477995 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.2928 | − | 51.4055i | 0.675028 | − | 1.62966i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.78155 | − | 1.15216i | 0.0880927 | − | 0.0364892i | −0.338202 | − | 0.941074i | \(-0.609819\pi\) |
0.426295 | + | 0.904584i | \(0.359819\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.37996 | − | 1.37996i | 0.0436599 | − | 0.0436599i |
(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.c.129.4 | yes | 16 | |
4.3 | odd | 2 | inner | 1024.2.g.c.129.1 | yes | 16 | |
8.3 | odd | 2 | 1024.2.g.h.129.4 | yes | 16 | ||
8.5 | even | 2 | 1024.2.g.h.129.1 | yes | 16 | ||
16.3 | odd | 4 | 1024.2.g.b.641.1 | yes | 16 | ||
16.5 | even | 4 | 1024.2.g.e.641.1 | yes | 16 | ||
16.11 | odd | 4 | 1024.2.g.e.641.4 | yes | 16 | ||
16.13 | even | 4 | 1024.2.g.b.641.4 | yes | 16 | ||
32.3 | odd | 8 | 1024.2.g.b.385.1 | ✓ | 16 | ||
32.5 | even | 8 | inner | 1024.2.g.c.897.4 | yes | 16 | |
32.11 | odd | 8 | 1024.2.g.h.897.4 | yes | 16 | ||
32.13 | even | 8 | 1024.2.g.e.385.1 | yes | 16 | ||
32.19 | odd | 8 | 1024.2.g.e.385.4 | yes | 16 | ||
32.21 | even | 8 | 1024.2.g.h.897.1 | yes | 16 | ||
32.27 | odd | 8 | inner | 1024.2.g.c.897.1 | yes | 16 | |
32.29 | even | 8 | 1024.2.g.b.385.4 | yes | 16 | ||
64.5 | even | 16 | 4096.2.a.n.1.8 | 8 | |||
64.27 | odd | 16 | 4096.2.a.n.1.7 | 8 | |||
64.37 | even | 16 | 4096.2.a.o.1.1 | 8 | |||
64.59 | odd | 16 | 4096.2.a.o.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1024.2.g.b.385.1 | ✓ | 16 | 32.3 | odd | 8 | ||
1024.2.g.b.385.4 | yes | 16 | 32.29 | even | 8 | ||
1024.2.g.b.641.1 | yes | 16 | 16.3 | odd | 4 | ||
1024.2.g.b.641.4 | yes | 16 | 16.13 | even | 4 | ||
1024.2.g.c.129.1 | yes | 16 | 4.3 | odd | 2 | inner | |
1024.2.g.c.129.4 | yes | 16 | 1.1 | even | 1 | trivial | |
1024.2.g.c.897.1 | yes | 16 | 32.27 | odd | 8 | inner | |
1024.2.g.c.897.4 | yes | 16 | 32.5 | even | 8 | inner | |
1024.2.g.e.385.1 | yes | 16 | 32.13 | even | 8 | ||
1024.2.g.e.385.4 | yes | 16 | 32.19 | odd | 8 | ||
1024.2.g.e.641.1 | yes | 16 | 16.5 | even | 4 | ||
1024.2.g.e.641.4 | yes | 16 | 16.11 | odd | 4 | ||
1024.2.g.h.129.1 | yes | 16 | 8.5 | even | 2 | ||
1024.2.g.h.129.4 | yes | 16 | 8.3 | odd | 2 | ||
1024.2.g.h.897.1 | yes | 16 | 32.21 | even | 8 | ||
1024.2.g.h.897.4 | yes | 16 | 32.11 | odd | 8 | ||
4096.2.a.n.1.7 | 8 | 64.27 | odd | 16 | |||
4096.2.a.n.1.8 | 8 | 64.5 | even | 16 | |||
4096.2.a.o.1.1 | 8 | 64.37 | even | 16 | |||
4096.2.a.o.1.2 | 8 | 64.59 | odd | 16 |