Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,2,Mod(703,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.703");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.bl (of order \(6\), degree \(2\), not 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: | \(10.7318940317\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.562828176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1279.4 | ||
Root | \(0.856419 + 1.12541i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.1279 |
Dual form | 1344.2.bl.i.703.4 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.33878 | + | 1.92764i | 1.49315 | + | 0.862069i | 0.999969 | − | 0.00785986i | \(-0.00250190\pi\) |
0.493178 | + | 0.869929i | \(0.335835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.59285 | + | 2.11254i | −0.602040 | + | 0.798466i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.17975 | − | 0.681127i | 0.355707 | − | 0.205367i | −0.311489 | − | 0.950250i | \(-0.600828\pi\) |
0.667196 | + | 0.744882i | \(0.267494\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.369798i | 0.102563i | 0.998684 | + | 0.0512817i | \(0.0163306\pi\) | ||||
−0.998684 | + | 0.0512817i | \(0.983669\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.85529i | − | 0.995431i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.89853 | − | 2.25082i | 0.945533 | − | 0.545904i | 0.0538425 | − | 0.998549i | \(-0.482853\pi\) |
0.891690 | + | 0.452646i | \(0.149520\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0330925 | − | 0.0573178i | 0.00759193 | − | 0.0131496i | −0.862204 | − | 0.506560i | \(-0.830917\pi\) |
0.869796 | + | 0.493411i | \(0.164250\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.62594 | + | 0.323174i | 0.573027 | + | 0.0705224i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.77902 | − | 1.60447i | −0.579466 | − | 0.334555i | 0.181455 | − | 0.983399i | \(-0.441919\pi\) |
−0.760921 | + | 0.648844i | \(0.775253\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.93162 | + | 8.54182i | 0.986325 | + | 1.70836i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.11951 | 0.579278 | 0.289639 | − | 0.957136i | \(-0.406465\pi\) | ||||
0.289639 | + | 0.957136i | \(0.406465\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.01852 | + | 5.22824i | 0.542143 | + | 0.939019i | 0.998781 | + | 0.0493663i | \(0.0157202\pi\) |
−0.456638 | + | 0.889653i | \(0.650946\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.17975 | − | 0.681127i | −0.205367 | − | 0.118569i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.39039 | + | 3.98287i | −1.58727 | + | 0.673228i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.74593 | + | 4.75609i | −0.451428 | + | 0.781897i | −0.998475 | − | 0.0552054i | \(-0.982419\pi\) |
0.547047 | + | 0.837102i | \(0.315752\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.320254 | − | 0.184899i | 0.0512817 | − | 0.0296075i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.45017i | 1.31970i | 0.751399 | + | 0.659848i | \(0.229379\pi\) | ||||
−0.751399 | + | 0.659848i | \(0.770621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.30324i | 0.961236i | 0.876930 | + | 0.480618i | \(0.159588\pi\) | ||||
−0.876930 | + | 0.480618i | \(0.840412\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.33878 | + | 1.92764i | −0.497716 | + | 0.287356i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.712838 | − | 1.23467i | 0.103978 | − | 0.180095i | −0.809342 | − | 0.587338i | \(-0.800176\pi\) |
0.913320 | + | 0.407242i | \(0.133509\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.92568 | − | 6.72992i | −0.275097 | − | 0.961417i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.89853 | − | 2.25082i | −0.545904 | − | 0.315178i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.27259 | − | 2.20420i | −0.174804 | − | 0.302770i | 0.765289 | − | 0.643686i | \(-0.222596\pi\) |
−0.940093 | + | 0.340917i | \(0.889263\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.25188 | 0.708163 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0661849 | −0.00876641 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.71879 | + | 2.97703i | 0.223767 | + | 0.387576i | 0.955949 | − | 0.293533i | \(-0.0948312\pi\) |
−0.732182 | + | 0.681109i | \(0.761498\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.23998 | − | 0.715904i | −0.158763 | − | 0.0916621i | 0.418513 | − | 0.908211i | \(-0.362551\pi\) |
−0.577277 | + | 0.816549i | \(0.695885\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.03309 | − | 2.43572i | −0.130157 | − | 0.306872i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.712838 | + | 1.23467i | −0.0884167 | + | 0.153142i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.45877 | − | 4.88367i | 1.03340 | − | 0.596636i | 0.115445 | − | 0.993314i | \(-0.463170\pi\) |
0.917958 | + | 0.396678i | \(0.129837\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.20894i | 0.386311i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9518i | 1.53710i | 0.639792 | + | 0.768549i | \(0.279021\pi\) | ||||
−0.639792 | + | 0.768549i | \(0.720979\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.56024 | + | 0.900803i | −0.182612 | + | 0.105431i | −0.588519 | − | 0.808483i | \(-0.700289\pi\) |
0.405907 | + | 0.913914i | \(0.366956\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.93162 | − | 8.54182i | 0.569455 | − | 0.986325i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.440245 | + | 3.57719i | −0.0501706 | + | 0.407659i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8156 | − | 6.24438i | −1.21685 | − | 0.702548i | −0.252606 | − | 0.967569i | \(-0.581288\pi\) |
−0.964243 | + | 0.265021i | \(0.914621\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.2889 | 1.34888 | 0.674442 | − | 0.738327i | \(-0.264384\pi\) | ||||
0.674442 | + | 0.738327i | \(0.264384\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.3551 | 1.88243 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.55975 | − | 2.70157i | −0.167223 | − | 0.289639i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.11951 | + | 0.646349i | 0.118668 | + | 0.0685128i | 0.558159 | − | 0.829734i | \(-0.311508\pi\) |
−0.439491 | + | 0.898247i | \(0.644841\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.781213 | − | 0.589031i | −0.0818934 | − | 0.0617472i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.01852 | − | 5.22824i | 0.313006 | − | 0.542143i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.220977 | − | 0.127581i | 0.0226717 | − | 0.0130895i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.88422i | − | 0.292848i | −0.989222 | − | 0.146424i | \(-0.953224\pi\) | ||
0.989222 | − | 0.146424i | \(-0.0467764\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.36225i | 0.136912i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.35949 | + | 3.09430i | −0.533289 | + | 0.307895i | −0.742355 | − | 0.670007i | \(-0.766291\pi\) |
0.209066 | + | 0.977902i | \(0.432958\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.89634 | − | 15.4089i | 0.876583 | − | 1.51829i | 0.0215154 | − | 0.999769i | \(-0.493151\pi\) |
0.855067 | − | 0.518517i | \(-0.173516\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.14446 | + | 6.14088i | 0.794818 | + | 0.599289i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.27683 | − | 3.04658i | −0.510131 | − | 0.294524i | 0.222757 | − | 0.974874i | \(-0.428494\pi\) |
−0.732887 | + | 0.680350i | \(0.761828\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.93162 | + | 6.80977i | 0.376581 | + | 0.652258i | 0.990562 | − | 0.137063i | \(-0.0437662\pi\) |
−0.613981 | + | 0.789321i | \(0.710433\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.49186 | 0.521264 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.70669 | 0.442768 | 0.221384 | − | 0.975187i | \(-0.428943\pi\) | ||||
0.221384 | + | 0.975187i | \(0.428943\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.18569 | − | 10.7139i | −0.576819 | − | 0.999080i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.320254 | − | 0.184899i | −0.0296075 | − | 0.0170939i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.45481 | + | 11.8210i | −0.133363 | + | 1.08363i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.57213 | + | 7.91917i | −0.415648 | + | 0.719924i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.31806 | − | 4.22509i | 0.659848 | − | 0.380963i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 18.7492i | 1.67698i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.70312i | 0.239863i | 0.992782 | + | 0.119931i | \(0.0382675\pi\) | ||||
−0.992782 | + | 0.119931i | \(0.961733\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.45877 | − | 3.15162i | 0.480618 | − | 0.277485i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.88644 | + | 6.73151i | −0.339560 | + | 0.588135i | −0.984350 | − | 0.176225i | \(-0.943611\pi\) |
0.644790 | + | 0.764360i | \(0.276945\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0683751 | + | 0.161208i | 0.00592888 | + | 0.0139785i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.33878 | + | 1.92764i | 0.287356 | + | 0.165905i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.42568 | − | 2.46934i | −0.121804 | − | 0.210970i | 0.798675 | − | 0.601762i | \(-0.205535\pi\) |
−0.920479 | + | 0.390792i | \(0.872201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.15656 | −0.607011 | −0.303506 | − | 0.952830i | \(-0.598157\pi\) | ||||
−0.303506 | + | 0.952830i | \(0.598157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.42568 | −0.120064 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.251879 | + | 0.436267i | 0.0210632 | + | 0.0364825i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.4153 | + | 6.01330i | 0.864948 | + | 0.499378i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.86544 | + | 5.03264i | −0.401295 | + | 0.415085i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6776 | − | 18.4941i | 0.874739 | − | 1.51509i | 0.0176994 | − | 0.999843i | \(-0.494366\pi\) |
0.857040 | − | 0.515250i | \(-0.172301\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2373 | − | 11.1067i | 1.56551 | − | 0.903848i | 0.568828 | − | 0.822457i | \(-0.307397\pi\) |
0.996682 | − | 0.0813911i | \(-0.0259363\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.50164i | 0.363936i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.2746i | 1.86946i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.71898 | − | 2.72451i | 0.376616 | − | 0.217439i | −0.299729 | − | 0.954024i | \(-0.596896\pi\) |
0.676345 | + | 0.736585i | \(0.263563\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.27259 | + | 2.20420i | −0.100923 | + | 0.174804i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.81607 | − | 3.31513i | 0.615993 | − | 0.261269i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.11951 | + | 2.37840i | 0.322665 | + | 0.186291i | 0.652580 | − | 0.757720i | \(-0.273687\pi\) |
−0.329915 | + | 0.944011i | \(0.607020\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.62594 | − | 4.54826i | −0.204429 | − | 0.354082i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.0618 | −1.08814 | −0.544068 | − | 0.839041i | \(-0.683116\pi\) | ||||
−0.544068 | + | 0.839041i | \(0.683116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8632 | 0.989481 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.0330925 | + | 0.0573178i | 0.00253064 | + | 0.00438320i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.53904 | − | 0.888566i | −0.117011 | − | 0.0675564i | 0.440352 | − | 0.897825i | \(-0.354854\pi\) |
−0.557363 | + | 0.830269i | \(0.688187\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −25.9003 | − | 3.18755i | −1.95788 | − | 0.240956i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.71879 | − | 2.97703i | 0.129192 | − | 0.223767i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.81607 | + | 1.62586i | −0.210483 | + | 0.121522i | −0.601536 | − | 0.798846i | \(-0.705444\pi\) |
0.391053 | + | 0.920368i | \(0.372111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.5015i | − | 1.74685i | −0.486954 | − | 0.873427i | \(-0.661892\pi\) | ||
0.486954 | − | 0.873427i | \(-0.338108\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.43181i | 0.105842i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.3361 | + | 10.5864i | −1.34810 | + | 0.778324i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.06618 | − | 5.31079i | 0.224222 | − | 0.388363i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.59285 | + | 2.11254i | −0.115863 | + | 0.153665i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.6956 | + | 11.9486i | 1.49748 | + | 0.864571i | 0.999996 | − | 0.00290157i | \(-0.000923599\pi\) |
0.497485 | + | 0.867473i | \(0.334257\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.93757 | − | 17.2124i | −0.715322 | − | 1.23897i | −0.962835 | − | 0.270090i | \(-0.912947\pi\) |
0.247513 | − | 0.968885i | \(-0.420387\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.42568 | 0.102095 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.0198 | −1.35511 | −0.677553 | − | 0.735474i | \(-0.736959\pi\) | ||||
−0.677553 | + | 0.735474i | \(0.736959\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.42568 | − | 12.8616i | −0.526392 | − | 0.911738i | −0.999527 | − | 0.0307481i | \(-0.990211\pi\) |
0.473135 | − | 0.880990i | \(-0.343122\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.45877 | − | 4.88367i | −0.596636 | − | 0.344468i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.96890 | + | 6.59010i | −0.348748 | + | 0.462534i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.2889 | + | 28.2132i | −1.13767 | + | 1.97050i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.77902 | − | 1.60447i | 0.193155 | − | 0.111518i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 0.0901606i | − | 0.00623654i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 19.6676i | − | 1.35398i | −0.735994 | − | 0.676988i | \(-0.763285\pi\) | ||
0.735994 | − | 0.676988i | \(-0.236715\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.2166 | − | 6.47590i | 0.768549 | − | 0.443722i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.1504 | + | 21.0451i | −0.828651 | + | 1.43527i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.8529 | − | 1.95102i | −1.07617 | − | 0.132444i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.56024 | + | 0.900803i | 0.105431 | + | 0.0608706i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.832347 | + | 1.44167i | 0.0559897 | + | 0.0969771i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.10323 | 0.542633 | 0.271316 | − | 0.962490i | \(-0.412541\pi\) | ||||
0.271316 | + | 0.962490i | \(0.412541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.86325 | −0.657550 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.04300 | + | 10.4668i | 0.401088 | + | 0.694704i | 0.993857 | − | 0.110668i | \(-0.0352989\pi\) |
−0.592770 | + | 0.805372i | \(0.701966\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.5963 | − | 11.8913i | −1.36104 | − | 0.785799i | −0.371280 | − | 0.928521i | \(-0.621081\pi\) |
−0.989763 | + | 0.142722i | \(0.954414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.31806 | − | 1.40733i | 0.218313 | − | 0.0925957i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.96472 | − | 17.2594i | 0.652810 | − | 1.13070i | −0.329628 | − | 0.944111i | \(-0.606923\pi\) |
0.982438 | − | 0.186590i | \(-0.0597435\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.76002 | − | 2.74820i | 0.310509 | − | 0.179273i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.4888i | 0.811233i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.60993i | 0.621615i | 0.950473 | + | 0.310807i | \(0.100599\pi\) | ||||
−0.950473 | + | 0.310807i | \(0.899401\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.01386 | + | 5.20415i | −0.580634 | + | 0.335229i | −0.761385 | − | 0.648300i | \(-0.775480\pi\) |
0.180752 | + | 0.983529i | \(0.442147\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.54348 | − | 26.1817i | 0.418047 | − | 1.67269i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0211960 | + | 0.0122375i | 0.00134867 | + | 0.000778654i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.14446 | − | 10.6425i | −0.389390 | − | 0.674442i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.6860 | −1.30569 | −0.652846 | − | 0.757491i | \(-0.726425\pi\) | ||||
−0.652846 | + | 0.757491i | \(0.726425\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.37139 | −0.274827 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.67756 | − | 15.0300i | −0.543410 | − | 0.941213i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.3732 | − | 8.87569i | −0.958951 | − | 0.553651i | −0.0631009 | − | 0.998007i | \(-0.520099\pi\) |
−0.895850 | + | 0.444357i | \(0.853432\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.67360 | − | 13.3766i | −0.352540 | − | 0.831183i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.55975 | + | 2.70157i | −0.0965464 | + | 0.167223i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.80241 | − | 1.04062i | 0.111141 | − | 0.0641675i | −0.443399 | − | 0.896324i | \(-0.646227\pi\) |
0.554540 | + | 0.832157i | \(0.312894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.81243i | − | 0.602773i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 1.29270i | − | 0.0791118i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.08075 | + | 1.77867i | −0.187837 | + | 0.108448i | −0.590970 | − | 0.806694i | \(-0.701255\pi\) |
0.403133 | + | 0.915142i | \(0.367921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.18399 | + | 10.7110i | −0.375650 | + | 0.650646i | −0.990424 | − | 0.138058i | \(-0.955914\pi\) |
0.614774 | + | 0.788704i | \(0.289247\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.119509 | + | 0.971066i | −0.00723302 | + | 0.0587716i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.6361 | + | 6.71812i | 0.701685 | + | 0.405118i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.93162 | − | 10.2739i | −0.356397 | − | 0.617297i | 0.630959 | − | 0.775816i | \(-0.282662\pi\) |
−0.987356 | + | 0.158519i | \(0.949328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.03705 | −0.361429 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.3428 | −1.15390 | −0.576948 | − | 0.816781i | \(-0.695756\pi\) | ||||
−0.576948 | + | 0.816781i | \(0.695756\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4707 | − | 21.5998i | −0.741304 | − | 1.28398i | −0.951902 | − | 0.306404i | \(-0.900874\pi\) |
0.210598 | − | 0.977573i | \(-0.432459\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.220977 | − | 0.127581i | −0.0130895 | − | 0.00755725i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.8514 | − | 13.4598i | −1.05373 | − | 0.794509i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.63237 | − | 2.82735i | 0.0960218 | − | 0.166315i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.49781 | + | 1.44211i | −0.146424 | + | 0.0845381i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.88234i | − | 0.402071i | −0.979584 | − | 0.201035i | \(-0.935569\pi\) | ||
0.979584 | − | 0.201035i | \(-0.0644306\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 13.2528i | 0.771610i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.17975 | − | 0.681127i | 0.0684558 | − | 0.0395230i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.593329 | − | 1.02768i | 0.0343131 | − | 0.0594321i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.3159 | − | 10.0401i | −0.767514 | − | 0.578702i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.35949 | + | 3.09430i | 0.307895 | + | 0.177763i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.76002 | − | 4.78049i | −0.158038 | − | 0.273730i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.4213 | 0.994286 | 0.497143 | − | 0.867669i | \(-0.334382\pi\) | ||||
0.497143 | + | 0.867669i | \(0.334382\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.7927 | −1.01219 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.5580 | − | 21.7512i | −0.712101 | − | 1.23340i | −0.964067 | − | 0.265660i | \(-0.914410\pi\) |
0.251965 | − | 0.967736i | \(-0.418923\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.1361 | − | 11.0482i | −1.08164 | − | 0.624484i | −0.150300 | − | 0.988640i | \(-0.548024\pi\) |
−0.931338 | + | 0.364156i | \(0.881357\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.24593 | − | 10.1238i | 0.0702002 | − | 0.570409i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.811634 | + | 1.40579i | −0.0455859 | + | 0.0789571i | −0.887918 | − | 0.460002i | \(-0.847849\pi\) |
0.842332 | + | 0.538959i | \(0.181182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.68023 | − | 2.12478i | 0.206053 | − | 0.118965i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.09316i | 0.340087i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 0.297941i | − | 0.0165779i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.15875 | + | 1.82370i | −0.175216 | + | 0.101161i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.93162 | − | 6.80977i | 0.217419 | − | 0.376581i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.47286 | + | 3.47255i | 0.0812012 | + | 0.191448i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.0949 | + | 13.3338i | 1.26941 | + | 0.732894i | 0.974876 | − | 0.222747i | \(-0.0715023\pi\) |
0.294534 | + | 0.955641i | \(0.404836\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.74593 | − | 4.75609i | −0.150476 | − | 0.260632i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 37.6559 | 2.05736 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.8426 | 1.62563 | 0.812815 | − | 0.582522i | \(-0.197934\pi\) | ||||
0.812815 | + | 0.582522i | \(0.197934\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.35335 | − | 4.07612i | −0.127816 | − | 0.221384i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.12218 | + | 4.11199i | 0.385688 | + | 0.222677i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.2845 | + | 6.65165i | 0.933278 | + | 0.359155i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.18569 | + | 10.7139i | −0.333027 | + | 0.576819i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.820451 | − | 0.473688i | 0.0440441 | − | 0.0254289i | −0.477816 | − | 0.878460i | \(-0.658572\pi\) |
0.521860 | + | 0.853031i | \(0.325238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 6.41788i | − | 0.343541i | −0.985137 | − | 0.171771i | \(-0.945051\pi\) | ||
0.985137 | − | 0.171771i | \(-0.0549488\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.369798i | 0.0197383i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0146 | − | 6.93665i | 0.639474 | − | 0.369200i | −0.144938 | − | 0.989441i | \(-0.546298\pi\) |
0.784412 | + | 0.620240i | \(0.212965\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.9665 | + | 43.2432i | −1.32508 | + | 2.29511i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.9647 | − | 4.65061i | 0.580314 | − | 0.246136i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.00000 | − | 3.46410i | −0.316668 | − | 0.182828i | 0.333238 | − | 0.942843i | \(-0.391859\pi\) |
−0.649906 | + | 0.760014i | \(0.725192\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49781 | + | 16.4507i | 0.499885 | + | 0.865826i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.14427 | 0.479950 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.94571 | −0.363555 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.65903 | − | 16.7299i | −0.504197 | − | 0.873295i | −0.999988 | − | 0.00485350i | \(-0.998455\pi\) |
0.495791 | − | 0.868442i | \(-0.334878\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.31806 | − | 4.22509i | −0.380963 | − | 0.219949i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.68350 | + | 0.822539i | 0.346990 | + | 0.0427041i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.63832 | − | 9.76585i | 0.291941 | − | 0.505657i | −0.682328 | − | 0.731047i | \(-0.739032\pi\) |
0.974269 | + | 0.225390i | \(0.0723656\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.2373 | − | 9.37462i | 0.838491 | − | 0.484103i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.15359i | 0.0594128i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.1457i | 1.29165i | 0.763486 | + | 0.645824i | \(0.223486\pi\) | ||||
−0.763486 | + | 0.645824i | \(0.776514\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.34097 | − | 1.35156i | 0.119931 | − | 0.0692424i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.88226 | + | 15.3845i | −0.453862 | + | 0.786112i | −0.998622 | − | 0.0524799i | \(-0.983287\pi\) |
0.544760 | + | 0.838592i | \(0.316621\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.36544 | + | 11.0948i | −0.426342 | + | 0.565444i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.45877 | − | 3.15162i | −0.277485 | − | 0.160206i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.07233 | + | 12.2496i | 0.358581 | + | 0.621081i | 0.987724 | − | 0.156209i | \(-0.0499272\pi\) |
−0.629143 | + | 0.777290i | \(0.716594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.4455 | −0.730539 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.77288 | 0.392090 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −24.0739 | − | 41.6972i | −1.21129 | − | 2.09801i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.9558 | + | 6.32534i | 0.549856 | + | 0.317460i | 0.749064 | − | 0.662498i | \(-0.230503\pi\) |
−0.199208 | + | 0.979957i | \(0.563837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.105422 | − | 0.139819i | 0.00527772 | − | 0.00699968i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.3904 | − | 21.4608i | 0.618747 | − | 1.07170i | −0.370968 | − | 0.928646i | \(-0.620974\pi\) |
0.989715 | − | 0.143055i | \(-0.0456926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.93339 | + | 1.11624i | −0.0963090 | + | 0.0556040i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 3.85529i | − | 0.191571i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.48131i | 0.370835i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.02003 | + | 2.89832i | −0.248225 | + | 0.143313i | −0.618951 | − | 0.785430i | \(-0.712442\pi\) |
0.370726 | + | 0.928742i | \(0.379109\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.42568 | + | 2.46934i | −0.0703234 | + | 0.121804i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.02686 | − | 1.11094i | −0.444183 | − | 0.0546656i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.0300 | + | 23.6887i | 2.01408 | + | 1.16283i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.57828 | + | 6.19776i | 0.175229 | + | 0.303506i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.42966 | 0.118697 | 0.0593484 | − | 0.998237i | \(-0.481098\pi\) | ||||
0.0593484 | + | 0.998237i | \(0.481098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.9373 | 1.26411 | 0.632054 | − | 0.774924i | \(-0.282212\pi\) | ||||
0.632054 | + | 0.774924i | \(0.282212\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.712838 | + | 1.23467i | 0.0346594 | + | 0.0600318i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38.4522 | + | 22.2004i | 1.86521 | + | 1.07688i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.48748 | − | 1.47919i | 0.168771 | − | 0.0715830i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.251879 | − | 0.436267i | 0.0121608 | − | 0.0210632i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.7781 | − | 7.37742i | 0.615497 | − | 0.355358i | −0.159616 | − | 0.987179i | \(-0.551026\pi\) |
0.775114 | + | 0.631821i | \(0.217692\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 35.7396i | − | 1.71754i | −0.512364 | − | 0.858769i | \(-0.671230\pi\) | ||
0.512364 | − | 0.858769i | \(-0.328770\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 12.0266i | − | 0.576632i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.183929 | + | 0.106192i | −0.00879854 | + | 0.00507984i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.91925 | + | 17.1806i | −0.473420 | + | 0.819987i | −0.999537 | − | 0.0304249i | \(-0.990314\pi\) |
0.526117 | + | 0.850412i | \(0.323647\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.79112 | + | 1.69727i | 0.323387 | + | 0.0808225i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.4378 | + | 9.49035i | 0.780982 | + | 0.450900i | 0.836778 | − | 0.547542i | \(-0.184436\pi\) |
−0.0557962 | + | 0.998442i | \(0.517770\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.49186 | + | 4.31603i | 0.118126 | + | 0.204599i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −21.3551 | −1.01006 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.2845 | −1.19325 | −0.596626 | − | 0.802520i | \(-0.703492\pi\) | ||||
−0.596626 | + | 0.802520i | \(0.703492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.75564 | + | 9.96906i | 0.271022 | + | 0.469425i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −19.2373 | − | 11.1067i | −0.903848 | − | 0.521837i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.47286 | − | 3.47255i | −0.0690485 | − | 0.162795i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.4837 | + | 19.8904i | −0.537186 | + | 0.930433i | 0.461868 | + | 0.886949i | \(0.347179\pi\) |
−0.999054 | + | 0.0434847i | \(0.986154\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.89853 | − | 2.25082i | 0.181968 | − | 0.105059i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.95838i | 0.137786i | 0.997624 | + | 0.0688928i | \(0.0219466\pi\) | ||||
−0.997624 | + | 0.0688928i | \(0.978053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.30669i | 0.153675i | 0.997044 | + | 0.0768374i | \(0.0244822\pi\) | ||||
−0.997044 | + | 0.0768374i | \(0.975518\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.1564 | − | 11.6373i | 0.934729 | − | 0.539666i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.95282 | + | 10.3106i | −0.275464 | + | 0.477117i | −0.970252 | − | 0.242097i | \(-0.922165\pi\) |
0.694788 | + | 0.719214i | \(0.255498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.15656 | + | 25.6485i | −0.145756 | + | 1.18434i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.71898 | − | 2.72451i | −0.217439 | − | 0.125539i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.29331 | + | 7.43623i | 0.197406 | + | 0.341918i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.652798 | 0.0299524 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.54519 | 0.116536 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.95186 | − | 10.3089i | −0.271947 | − | 0.471026i | 0.697413 | − | 0.716669i | \(-0.254334\pi\) |
−0.969360 | + | 0.245643i | \(0.921001\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.75879 | − | 1.01544i | −0.0801940 | − | 0.0463000i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.77902 | − | 5.11135i | −0.308456 | − | 0.232574i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.55975 | − | 9.62978i | 0.252455 | − | 0.437266i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.50151 | − | 3.75365i | 0.294612 | − | 0.170094i | −0.345408 | − | 0.938453i | \(-0.612260\pi\) |
0.640020 | + | 0.768358i | \(0.278926\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 4.75680i | − | 0.215110i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.0031i | 0.992988i | 0.868040 | + | 0.496494i | \(0.165380\pi\) | ||||
−0.868040 | + | 0.496494i | \(0.834620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.1615 | − | 7.02145i | 0.547727 | − | 0.316230i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.62594 | + | 4.54826i | −0.118027 | + | 0.204429i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −27.3613 | − | 20.6303i | −1.22732 | − | 0.925393i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.22277 | − | 0.705968i | −0.0547389 | − | 0.0316035i | 0.472381 | − | 0.881395i | \(-0.343395\pi\) |
−0.527120 | + | 0.849791i | \(0.676728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.03090 | + | 12.1779i | 0.314118 | + | 0.544068i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −26.2303 | −1.16955 | −0.584775 | − | 0.811196i | \(-0.698817\pi\) | ||||
−0.584775 | + | 0.811196i | \(0.698817\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.8589 | −1.06171 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.43162 | − | 11.1399i | −0.285638 | − | 0.494740i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.38419 | + | 2.53121i | 0.194326 | + | 0.112194i | 0.594006 | − | 0.804461i | \(-0.297545\pi\) |
−0.399680 | + | 0.916655i | \(0.630879\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.582233 | − | 4.73091i | 0.0257565 | − | 0.209283i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.0330925 | − | 0.0573178i | 0.00146107 | − | 0.00253064i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 59.4058 | − | 34.2980i | 2.61773 | − | 1.51135i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.94213i | − | 0.0854149i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.77713i | 0.0780074i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.60044 | + | 4.96547i | −0.376792 | + | 0.217541i | −0.676422 | − | 0.736515i | \(-0.736470\pi\) |
0.299630 | + | 0.954056i | \(0.403137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.6686 | − | 27.1389i | 0.685142 | − | 1.18670i | −0.288250 | − | 0.957555i | \(-0.593073\pi\) |
0.973392 | − | 0.229146i | \(-0.0735933\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 10.1896 | + | 24.0241i | 0.444713 | + | 1.04850i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.5356 | + | 13.5883i | 1.02523 | + | 0.591916i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.35135 | − | 11.0009i | −0.276146 | − | 0.478299i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.43757 | −0.149178 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.12485 | −0.135352 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.7454 | − | 20.3437i | −0.507800 | − | 0.879535i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.81607 | + | 1.62586i | 0.121522 | + | 0.0701610i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.85573 | − | 6.62796i | −0.295297 | − | 0.285486i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.09313 | + | 3.62541i | −0.0899908 | + | 0.155869i | −0.907507 | − | 0.420037i | \(-0.862017\pi\) |
0.817516 | + | 0.575906i | \(0.195350\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.3529 | + | 11.7508i | −0.873427 | + | 0.504274i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.3151i | 1.29856i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.4674i | 0.533067i | 0.963826 | + | 0.266533i | \(0.0858782\pi\) | ||||
−0.963826 | + | 0.266533i | \(0.914122\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.23998 | − | 0.715904i | 0.0529212 | − | 0.0305540i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.103232 | − | 0.178803i | 0.00439784 | − | 0.00761728i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.4191 | − | 12.9020i | 1.29355 | − | 0.548651i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 18.3361 | + | 10.5864i | 0.778324 | + | 0.449366i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.2744 | − | 31.6521i | −0.774309 | − | 1.34114i | −0.935182 | − | 0.354168i | \(-0.884764\pi\) |
0.160872 | − | 0.986975i | \(-0.448569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.33092 | −0.0985876 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.13237 | −0.258909 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.3672 | − | 37.0091i | −0.900520 | − | 1.55975i | −0.826820 | − | 0.562466i | \(-0.809853\pi\) |
−0.0737002 | − | 0.997280i | \(-0.523481\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.7146 | + | 9.07283i | 0.661118 | + | 0.381697i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.62594 | + | 0.323174i | 0.110279 | + | 0.0135721i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.7265 | + | 18.5788i | −0.449678 | + | 0.778866i | −0.998365 | − | 0.0571625i | \(-0.981795\pi\) |
0.548687 | + | 0.836028i | \(0.315128\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3349 | − | 10.5856i | 0.767291 | − | 0.442996i | −0.0646165 | − | 0.997910i | \(-0.520582\pi\) |
0.831907 | + | 0.554915i | \(0.187249\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 23.8972i | − | 0.998321i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 31.6506i | − | 1.31992i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.10289 | − | 2.36880i | 0.170806 | − | 0.0986146i | −0.412160 | − | 0.911111i | \(-0.635226\pi\) |
0.582966 | + | 0.812497i | \(0.301892\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.93757 | + | 17.2124i | −0.412991 | + | 0.715322i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −19.5744 | + | 25.9609i | −0.812082 | + | 1.07704i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.00267 | − | 1.73359i | −0.124358 | − | 0.0717981i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.712838 | − | 1.23467i | −0.0294722 | − | 0.0510474i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.8450 | −1.23184 | −0.615918 | − | 0.787810i | \(-0.711215\pi\) | ||||
−0.615918 | + | 0.787810i | \(0.711215\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.399562 | 0.0164636 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.50990 | + | 16.4716i | 0.391185 | + | 0.677553i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.9586 | + | 13.2551i | 0.942796 | + | 0.544323i | 0.890836 | − | 0.454326i | \(-0.150120\pi\) |
0.0519600 | + | 0.998649i | \(0.483453\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.6440 | + | 36.6634i | −1.13330 | + | 1.50305i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.42568 | + | 12.8616i | −0.303913 | + | 0.526392i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.0000 | − | 10.3923i | 0.735460 | − | 0.424618i | −0.0849563 | − | 0.996385i | \(-0.527075\pi\) |
0.820416 | + | 0.571767i | \(0.193742\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.8255i | 0.441581i | 0.975321 | + | 0.220790i | \(0.0708637\pi\) | ||||
−0.975321 | + | 0.220790i | \(0.929136\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.76735i | 0.397757i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −30.5307 | + | 17.6269i | −1.24125 | + | 0.716635i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.95330 | − | 12.0435i | 0.282226 | − | 0.488830i | −0.689707 | − | 0.724089i | \(-0.742261\pi\) |
0.971933 | + | 0.235259i | \(0.0755939\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 8.19164 | + | 1.00815i | 0.331942 | + | 0.0408521i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.456579 | + | 0.263606i | 0.0184712 | + | 0.0106644i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.322444 | + | 0.558490i | 0.0130234 | + | 0.0225572i | 0.872464 | − | 0.488679i | \(-0.162521\pi\) |
−0.859440 | + | 0.511236i | \(0.829188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 32.5779 | 1.31367 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.3626 | 0.497701 | 0.248850 | − | 0.968542i | \(-0.419947\pi\) | ||||
0.248850 | + | 0.968542i | \(0.419947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.69875 | − | 9.87053i | −0.229052 | − | 0.396730i | 0.728475 | − | 0.685072i | \(-0.240229\pi\) |
−0.957527 | + | 0.288342i | \(0.906896\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.77902 | − | 1.60447i | −0.111518 | − | 0.0643852i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.14865 | + | 1.33548i | −0.126148 | + | 0.0535047i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.4837 | + | 19.8904i | −0.459349 | + | 0.795616i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0780814 | + | 0.0450803i | −0.00311827 | + | 0.00180033i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.7224i | 0.985745i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.8050i | 0.430140i | 0.976599 | + | 0.215070i | \(0.0689979\pi\) | ||||
−0.976599 | + | 0.215070i | \(0.931002\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.0327 | + | 9.83381i | −0.676988 | + | 0.390859i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.21065 | + | 9.02511i | −0.206778 | + | 0.358150i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.48871 | − | 0.712111i | 0.0986062 | − | 0.0282149i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.2166 | − | 6.47590i | −0.443722 | − | 0.256183i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.12662 | − | 1.95136i | −0.0444988 | − | 0.0770741i | 0.842918 | − | 0.538042i | \(-0.180836\pi\) |
−0.887417 | + | 0.460968i | \(0.847502\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.0574 | −0.869860 | −0.434930 | − | 0.900464i | \(-0.643227\pi\) | ||||
−0.434930 | + | 0.900464i | \(0.643227\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 24.3008 | 0.956844 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.26417 | + | 3.92166i | 0.0890137 | + | 0.154176i | 0.907094 | − | 0.420927i | \(-0.138295\pi\) |
−0.818081 | + | 0.575103i | \(0.804962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.05546 | + | 2.34142i | 0.159191 | + | 0.0919089i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.23683 | + | 14.7045i | 0.244441 | + | 0.576316i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.6749 | − | 35.8099i | 0.809071 | − | 1.40135i | −0.104438 | − | 0.994531i | \(-0.533304\pi\) |
0.913508 | − | 0.406820i | \(-0.133362\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.9519 | + | 14.9833i | −1.01403 | + | 0.585448i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.80161i | − | 0.0702874i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 10.6413i | − | 0.414526i | −0.978285 | − | 0.207263i | \(-0.933544\pi\) | ||
0.978285 | − | 0.207263i | \(-0.0664556\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.7871 | + | 24.1258i | −1.62533 | + | 0.938384i | −0.639867 | + | 0.768485i | \(0.721011\pi\) |
−0.985462 | + | 0.169899i | \(0.945656\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.832347 | − | 1.44167i | 0.0323257 | − | 0.0559897i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0824618 | + | 0.670040i | −0.00319773 | + | 0.0259830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.66919 | − | 5.00516i | −0.335672 | − | 0.193801i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.05162 | − | 7.01760i | −0.156645 | − | 0.271316i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.95049 | −0.0752977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −0.148647 | −0.00572991 | −0.00286496 | − | 0.999996i | \(-0.500912\pi\) | ||||
−0.00286496 | + | 0.999996i | \(0.500912\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.93162 | + | 8.54182i | 0.189818 | + | 0.328775i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.3935 | + | 19.8571i | 1.32185 | + | 0.763170i | 0.984023 | − | 0.178039i | \(-0.0569754\pi\) |
0.337825 | + | 0.941209i | \(0.390309\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.09304 | + | 4.59412i | 0.233830 | + | 0.176306i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.04300 | − | 10.4668i | 0.231568 | − | 0.401088i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.9070 | + | 21.3083i | −1.41221 | + | 0.815339i | −0.995596 | − | 0.0937450i | \(-0.970116\pi\) |
−0.416613 | + | 0.909084i | \(0.636783\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 10.9928i | − | 0.420013i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.7826i | 0.907362i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.815106 | − | 0.470602i | 0.0310531 | − | 0.0179285i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.22317 | + | 3.85064i | −0.0845733 | + | 0.146485i | −0.905209 | − | 0.424966i | \(-0.860286\pi\) |
0.820636 | + | 0.571451i | \(0.193619\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.87782 | − | 2.16986i | −0.109319 | − | 0.0824262i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.8942 | − | 13.7953i | −0.906357 | − | 0.523285i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0198 | + | 32.9433i | 0.720427 | + | 1.24782i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.9294 | −0.753800 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.9907 | 0.943885 | 0.471942 | − | 0.881629i | \(-0.343553\pi\) | ||||
0.471942 | + | 0.881629i | \(0.343553\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.181739 | + | 0.314782i | 0.00685442 | + | 0.0118722i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.76002 | − | 2.74820i | −0.179273 | − | 0.103503i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.00000 | − | 16.2509i | 0.0752177 | − | 0.611178i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.07409 | − | 15.7168i | 0.340785 | − | 0.590257i | −0.643794 | − | 0.765199i | \(-0.722641\pi\) |
0.984579 | + | 0.174942i | \(0.0559739\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.8156 | − | 6.24438i | 0.405616 | − | 0.234183i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 19.3725i | − | 0.725507i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.94213i | 0.0726316i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8.32244 | − | 4.80497i | 0.310807 | − | 0.179445i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.5818 | − | 35.6488i | 0.767573 | − | 1.32948i | −0.171302 | − | 0.985219i | \(-0.554797\pi\) |
0.938875 | − | 0.344257i | \(-0.111869\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.3815 | + | 43.3380i | 0.684562 | + | 1.61399i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.01386 | + | 5.20415i | 0.335229 | + | 0.193545i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.3842 | + | 26.6463i | 0.571357 | + | 0.989619i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.77231 | 0.214083 | 0.107042 | − | 0.994255i | \(-0.465862\pi\) | ||||
0.107042 | + | 0.994255i | \(0.465862\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.1875 | + | 24.5734i | 0.524742 | + | 0.908880i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.63928 | + | 3.83319i | 0.245227 | + | 0.141582i | 0.617577 | − | 0.786510i | \(-0.288114\pi\) |
−0.372350 | + | 0.928093i | \(0.621448\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −25.9458 | + | 7.42404i | −0.957024 | + | 0.273840i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.65280 | − | 11.5230i | 0.245059 | − | 0.424455i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.3753 | − | 10.0317i | 0.639162 | − | 0.369021i | −0.145129 | − | 0.989413i | \(-0.546360\pi\) |
0.784292 | + | 0.620392i | \(0.213027\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.0244750i | − | 0.000899113i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.26368i | 0.303165i | 0.988445 | + | 0.151583i | \(0.0484369\pi\) | ||||
−0.988445 | + | 0.151583i | \(0.951563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 71.3000 | − | 41.1651i | 2.61223 | − | 1.50817i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.14446 | + | 10.6425i | −0.224814 | + | 0.389390i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.8412 | − | 6.29480i | 0.542286 | − | 0.230007i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −23.4113 | − | 13.5165i | −0.854289 | − | 0.493224i | 0.00780684 | − | 0.999970i | \(-0.497515\pi\) |
−0.862096 | + | 0.506746i | \(0.830848\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.3430 | + | 17.9146i | 0.376921 | + | 0.652846i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 85.6388 | 3.11672 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.9417 | −0.797486 | −0.398743 | − | 0.917063i | \(-0.630553\pi\) | ||||
−0.398743 | + | 0.917063i | \(0.630553\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.18569 | + | 3.78573i | 0.0793357 | + | 0.137413i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.02680 | + | 0.592825i | 0.0372216 | + | 0.0214899i | 0.518495 | − | 0.855080i | \(-0.326492\pi\) |
−0.481274 | + | 0.876570i | \(0.659826\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.6484 | − | 2.54120i | −0.747523 | − | 0.0919977i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.67756 | + | 15.0300i | −0.313738 | + | 0.543410i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.10090 | + | 0.635603i | −0.0397511 | + | 0.0229503i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.0892i | 0.688373i | 0.938901 | + | 0.344186i | \(0.111845\pi\) | ||||
−0.938901 | + | 0.344186i | \(0.888155\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.7514i | 0.639301i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.7887 | − | 17.7759i | 1.10739 | − | 0.639353i | 0.169240 | − | 0.985575i | \(-0.445869\pi\) |
0.938153 | + | 0.346222i | \(0.112535\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.7725 | + | 51.5674i | −1.06946 | + | 1.85236i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.74770 | + | 11.6018i | −0.313822 | + | 0.416212i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.484346 | + | 0.279637i | 0.0173535 | + | 0.0100190i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.82182 | + | 15.2798i | 0.315670 | + | 0.546756i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.11951 | 0.111482 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.0075 | 0.749790 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.3018 | − | 36.8958i | −0.759327 | − | 1.31519i | −0.943194 | − | 0.332241i | \(-0.892195\pi\) |
0.183868 | − | 0.982951i | \(-0.441138\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.80241 | − | 1.04062i | −0.0641675 | − | 0.0370471i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.49704 | + | 9.94309i | −0.266564 | + | 0.353536i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.264740 | − | 0.458543i | 0.00940118 | − | 0.0162833i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.49781 | + | 4.90621i | −0.301386 | + | 0.174005i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.1179i | 0.818879i | 0.912337 | + | 0.409440i | \(0.134276\pi\) | ||||
−0.912337 | + | 0.409440i | \(0.865724\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.41788i | − | 0.227048i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.11951 | + | 0.646349i | −0.0395559 | + | 0.0228376i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.22712 | + | 2.12544i | −0.0433042 | + | 0.0750051i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.4865 | + | 3.99812i | 1.14500 | + | 0.140915i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.08075 | + | 1.77867i | 0.108448 | + | 0.0626123i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.0852 | + | 27.8604i | 0.565525 | + | 0.979518i | 0.997001 | + | 0.0773937i | \(0.0246598\pi\) |
−0.431475 | + | 0.902125i | \(0.642007\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.0797 | 1.44250 | 0.721251 | − | 0.692673i | \(-0.243567\pi\) | ||||
0.721251 | + | 0.692673i | \(0.243567\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.3680 | 0.433764 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.16942 | + | 15.8819i | 0.321191 | + | 0.556319i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.361288 | + | 0.208590i | 0.0126399 | + | 0.00729764i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.900723 | − | 0.382035i | 0.0314738 | − | 0.0133494i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.6233 | + | 25.3283i | −0.510358 | + | 0.883965i | 0.489570 | + | 0.871964i | \(0.337154\pi\) |
−0.999928 | + | 0.0120014i | \(0.996180\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.0790 | − | 9.86059i | 0.595338 | − | 0.343719i | −0.171867 | − | 0.985120i | \(-0.554980\pi\) |
0.767205 | + | 0.641401i | \(0.221647\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 13.4362i | − | 0.467790i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 16.1125i | − | 0.560286i | −0.959958 | − | 0.280143i | \(-0.909618\pi\) | ||
0.959958 | − | 0.280143i | \(-0.0903819\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 40.9056 | − | 23.6169i | 1.42071 | − | 0.820248i | 0.424351 | − | 0.905498i | \(-0.360502\pi\) |
0.996360 | + | 0.0852497i | \(0.0271688\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.93162 | + | 10.2739i | −0.205766 | + | 0.356397i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −22.6551 | − | 21.9024i | −0.784954 | − | 0.758875i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −46.9492 | − | 27.1062i | −1.62475 | − | 0.938047i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.01852 | + | 5.22824i | 0.104335 | + | 0.180714i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.3551 | 0.875356 | 0.437678 | − | 0.899132i | \(-0.355801\pi\) | ||||
0.437678 | + | 0.899132i | \(0.355801\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.2687 | −0.664437 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.67141 | + | 16.7514i | 0.333101 | + | 0.576948i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 42.9475 | + | 24.7958i | 1.47744 | + | 0.853000i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.44687 | − | 22.2728i | −0.324598 | − | 0.765304i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.4707 | + | 21.5998i | −0.427992 | + | 0.741304i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.2620 | − | 8.81153i | 0.523175 | − | 0.302055i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.3802i | 0.834763i | 0.908731 | + | 0.417382i | \(0.137052\pi\) | ||||
−0.908731 | + | 0.417382i | \(0.862948\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.255162i | 0.00872636i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.4742 | + | 12.9755i | −0.767705 | + | 0.443235i | −0.832055 | − | 0.554693i | \(-0.812836\pi\) |
0.0643503 | + | 0.997927i | \(0.479502\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.4213 | − | 49.2271i | 0.969722 | − | 1.67961i | 0.273368 | − | 0.961909i | \(-0.411862\pi\) |
0.696354 | − | 0.717698i | \(-0.254804\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.73088 | + | 22.1896i | −0.0930681 | + | 0.756221i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.3044 | − | 8.83597i | −0.520966 | − | 0.300780i | 0.216364 | − | 0.976313i | \(-0.430580\pi\) |
−0.737330 | + | 0.675533i | \(0.763914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.42568 | − | 5.93345i | −0.116476 | − | 0.201743i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.26474 | −0.110876 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.0129 | −0.577122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.80597 | + | 3.12803i | 0.0611930 | + | 0.105989i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.49781 | + | 1.44211i | 0.0845381 | + | 0.0488081i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −39.6086 | − | 29.8647i | −1.33901 | − | 1.00961i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.17283 | + | 10.6917i | −0.208442 | + | 0.361032i | −0.951224 | − | 0.308502i | \(-0.900173\pi\) |
0.742782 | + | 0.669533i | \(0.233506\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.96028 | + | 3.44117i | −0.201035 | + | 0.116068i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.0442i | 1.11329i | 0.830751 | + | 0.556644i | \(0.187911\pi\) | ||||
−0.830751 | + | 0.556644i | \(0.812089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.2680i | 1.32147i | 0.750618 | + | 0.660737i | \(0.229756\pi\) | ||||
−0.750618 | + | 0.660737i | \(0.770244\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.4773 | − | 6.62642i | 0.385805 | − | 0.222745i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.7517 | − | 34.2109i | 0.663196 | − | 1.14869i | −0.316576 | − | 0.948567i | \(-0.602533\pi\) |
0.979771 | − | 0.200121i | \(-0.0641335\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.71045 | − | 4.30565i | −0.191522 | − | 0.144407i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.17975 | − | 0.681127i | −0.0395230 | − | 0.0228186i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.0471792 | − | 0.0817167i | −0.00157879 | − | 0.00273454i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.5363 | −0.419043 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.18666 | −0.0396214 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.41631 | + | 16.3095i | 0.314052 | + | 0.543953i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.92249 | − | 5.72875i | −0.330566 | − | 0.190852i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.03705 | + | 16.5519i | −0.0677887 | + | 0.550814i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 45.3026 | − | 78.4664i | 1.50591 | − | 2.60831i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.46372 | + | 2.57713i | −0.148215 | + | 0.0855722i | −0.572274 | − | 0.820063i | \(-0.693938\pi\) |
0.424058 | + | 0.905635i | \(0.360605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 6.18861i | − | 0.205263i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.8365i | 0.856002i | 0.903778 | + | 0.428001i | \(0.140782\pi\) | ||||
−0.903778 | + | 0.428001i | \(0.859218\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.4978 | − | 8.37031i | 0.479807 | − | 0.277017i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.76002 | + | 4.78049i | −0.0912434 | + | 0.158038i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.03010 | − | 18.9325i | −0.265177 | − | 0.625207i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.6881 | + | 17.7178i | 1.01231 | + | 0.584455i | 0.911866 | − | 0.410488i | \(-0.134642\pi\) |
0.100440 | + | 0.994943i | \(0.467975\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.71065 | − | 15.0873i | −0.287026 | − | 0.497143i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.78955 | −0.157650 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −54.1676 | −1.78102 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.89634 | + | 15.4089i | 0.292194 | + | 0.506095i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.6452 | + | 27.5080i | 1.56319 | + | 0.902508i | 0.996931 | + | 0.0782797i | \(0.0249427\pi\) |
0.566258 | + | 0.824228i | \(0.308391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.449470 | − | 0.112334i | −0.0147308 | − | 0.00368159i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.5580 | + | 21.7512i | −0.411132 | + | 0.712101i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.4746 | − | 11.8210i | 0.669592 | − | 0.386589i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.90001i | 0.225414i | 0.993628 | + | 0.112707i | \(0.0359521\pi\) | ||||
−0.993628 | + | 0.112707i | \(0.964048\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.0965i | 0.721092i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −16.2597 | + | 9.38756i | −0.530052 | + | 0.306026i | −0.741038 | − | 0.671463i | \(-0.765666\pi\) |
0.210986 | + | 0.977489i | \(0.432333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.5580 | − | 23.4832i | 0.441511 | − | 0.764719i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.39039 | + | 3.98287i | −0.305470 | + | 0.129563i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.7931 | − | 14.8916i | −0.838162 | − | 0.483913i | 0.0184768 | − | 0.999829i | \(-0.494118\pi\) |
−0.856639 | + | 0.515916i | \(0.827452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.333115 | − | 0.576972i | −0.0108134 | − | 0.0187293i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.62327 | 0.0526380 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.2676 | −0.753711 | −0.376856 | − | 0.926272i | \(-0.622995\pi\) | ||||
−0.376856 | + | 0.926272i | \(0.622995\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 46.0653 | + | 79.7875i | 1.49064 | + | 2.58186i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.68023 | − | 2.12478i | −0.118965 | − | 0.0686844i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.48748 | + | 0.921485i | 0.241783 | + | 0.0297563i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.72297 | + | 4.71632i | −0.0878377 | + | 0.152139i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.27683 | − | 3.04658i | 0.170044 | − | 0.0981747i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 76.6244i | − | 2.46663i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 16.9691i | − | 0.545690i | −0.962058 | − | 0.272845i | \(-0.912035\pi\) | ||
0.962058 | − | 0.272845i | \(-0.0879646\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.258024 | + | 0.148970i | −0.00828893 | + | 0.00478561i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.8349 | − | 39.5512i | 0.732806 | − | 1.26926i | −0.222873 | − | 0.974847i | \(-0.571544\pi\) |
0.955679 | − | 0.294410i | \(-0.0951231\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.3993 | − | 15.1185i | 0.365445 | − | 0.484678i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.15875 | + | 1.82370i | 0.101161 | + | 0.0584052i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.7102 | + | 41.0673i | 0.758557 | + | 1.31386i | 0.943586 | + | 0.331127i | \(0.107429\pi\) |
−0.185029 | + | 0.982733i | \(0.559238\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.76098 | 0.0562812 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.86325 | −0.251054 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.6956 | − | 30.6497i | −0.564402 | − | 0.977573i | −0.997105 | − | 0.0760363i | \(-0.975774\pi\) |
0.432703 | − | 0.901536i | \(-0.357560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −63.5029 | − | 36.6634i | −2.02337 | − | 1.16819i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.27088 | − | 3.01180i | 0.0722831 | − | 0.0958668i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.1134 | − | 17.5169i | 0.321586 | − | 0.557004i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.0136 | − | 5.78134i | 0.318092 | − | 0.183650i | −0.332450 | − | 0.943121i | \(-0.607875\pi\) |
0.650542 | + | 0.759471i | \(0.274542\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 26.6677i | − | 0.846274i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 57.2563i | − | 1.81515i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.6832 | − | 6.16793i | 0.338339 | − | 0.195340i | −0.321198 | − | 0.947012i | \(-0.604086\pi\) |
0.659537 | + | 0.751672i | \(0.270752\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.74593 | + | 4.75609i | −0.0868774 | + | 0.150476i |
(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 | 1344.2.bl.i.1279.4 | 8 | ||
4.3 | odd | 2 | 1344.2.bl.j.1279.4 | 8 | |||
7.3 | odd | 6 | 1344.2.bl.j.703.4 | 8 | |||
8.3 | odd | 2 | 84.2.o.a.19.2 | ✓ | 8 | ||
8.5 | even | 2 | 84.2.o.b.19.4 | yes | 8 | ||
24.5 | odd | 2 | 252.2.bf.f.19.1 | 8 | |||
24.11 | even | 2 | 252.2.bf.g.19.3 | 8 | |||
28.3 | even | 6 | inner | 1344.2.bl.i.703.4 | 8 | ||
56.3 | even | 6 | 84.2.o.b.31.4 | yes | 8 | ||
56.5 | odd | 6 | 588.2.b.b.391.3 | 8 | |||
56.11 | odd | 6 | 588.2.o.b.31.4 | 8 | |||
56.13 | odd | 2 | 588.2.o.b.19.4 | 8 | |||
56.19 | even | 6 | 588.2.b.a.391.4 | 8 | |||
56.27 | even | 2 | 588.2.o.d.19.2 | 8 | |||
56.37 | even | 6 | 588.2.b.a.391.3 | 8 | |||
56.45 | odd | 6 | 84.2.o.a.31.2 | yes | 8 | ||
56.51 | odd | 6 | 588.2.b.b.391.4 | 8 | |||
56.53 | even | 6 | 588.2.o.d.31.2 | 8 | |||
168.5 | even | 6 | 1764.2.b.i.1567.6 | 8 | |||
168.59 | odd | 6 | 252.2.bf.f.199.1 | 8 | |||
168.101 | even | 6 | 252.2.bf.g.199.3 | 8 | |||
168.107 | even | 6 | 1764.2.b.i.1567.5 | 8 | |||
168.131 | odd | 6 | 1764.2.b.j.1567.5 | 8 | |||
168.149 | odd | 6 | 1764.2.b.j.1567.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.o.a.19.2 | ✓ | 8 | 8.3 | odd | 2 | ||
84.2.o.a.31.2 | yes | 8 | 56.45 | odd | 6 | ||
84.2.o.b.19.4 | yes | 8 | 8.5 | even | 2 | ||
84.2.o.b.31.4 | yes | 8 | 56.3 | even | 6 | ||
252.2.bf.f.19.1 | 8 | 24.5 | odd | 2 | |||
252.2.bf.f.199.1 | 8 | 168.59 | odd | 6 | |||
252.2.bf.g.19.3 | 8 | 24.11 | even | 2 | |||
252.2.bf.g.199.3 | 8 | 168.101 | even | 6 | |||
588.2.b.a.391.3 | 8 | 56.37 | even | 6 | |||
588.2.b.a.391.4 | 8 | 56.19 | even | 6 | |||
588.2.b.b.391.3 | 8 | 56.5 | odd | 6 | |||
588.2.b.b.391.4 | 8 | 56.51 | odd | 6 | |||
588.2.o.b.19.4 | 8 | 56.13 | odd | 2 | |||
588.2.o.b.31.4 | 8 | 56.11 | odd | 6 | |||
588.2.o.d.19.2 | 8 | 56.27 | even | 2 | |||
588.2.o.d.31.2 | 8 | 56.53 | even | 6 | |||
1344.2.bl.i.703.4 | 8 | 28.3 | even | 6 | inner | ||
1344.2.bl.i.1279.4 | 8 | 1.1 | even | 1 | trivial | ||
1344.2.bl.j.703.4 | 8 | 7.3 | odd | 6 | |||
1344.2.bl.j.1279.4 | 8 | 4.3 | odd | 2 | |||
1764.2.b.i.1567.5 | 8 | 168.107 | even | 6 | |||
1764.2.b.i.1567.6 | 8 | 168.5 | even | 6 | |||
1764.2.b.j.1567.5 | 8 | 168.131 | odd | 6 | |||
1764.2.b.j.1567.6 | 8 | 168.149 | odd | 6 |