Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(143,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.w (of order \(8\), degree \(4\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 288) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 143.3 | ||
Character | \(\chi\) | \(=\) | 1152.143 |
Dual form | 1152.2.w.b.1007.3 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.739921 | + | 1.78633i | −0.330903 | + | 0.798870i | 0.667618 | + | 0.744504i | \(0.267314\pi\) |
−0.998521 | + | 0.0543661i | \(0.982686\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.385417 | + | 0.385417i | −0.145674 | + | 0.145674i | −0.776182 | − | 0.630509i | \(-0.782846\pi\) |
0.630509 | + | 0.776182i | \(0.282846\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.36398 | − | 5.70716i | 0.712767 | − | 1.72077i | 0.0197998 | − | 0.999804i | \(-0.493697\pi\) |
0.692968 | − | 0.720969i | \(-0.256303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.30916 | + | 0.956485i | −0.640446 | + | 0.265281i | −0.679184 | − | 0.733968i | \(-0.737666\pi\) |
0.0387383 | + | 0.999249i | \(0.487666\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.05518 | 1.22606 | 0.613031 | − | 0.790059i | \(-0.289950\pi\) | ||||
0.613031 | + | 0.790059i | \(0.289950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.27305 | + | 3.07341i | 0.292057 | + | 0.705089i | 0.999999 | − | 0.00118164i | \(-0.000376129\pi\) |
−0.707942 | + | 0.706271i | \(0.750376\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.28291 | − | 2.28291i | 0.476020 | − | 0.476020i | −0.427837 | − | 0.903856i | \(-0.640724\pi\) |
0.903856 | + | 0.427837i | \(0.140724\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.892052 | + | 0.892052i | 0.178410 | + | 0.178410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.735171 | − | 0.304518i | 0.136518 | − | 0.0565475i | −0.313379 | − | 0.949628i | \(-0.601461\pi\) |
0.449896 | + | 0.893081i | \(0.351461\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.40740i | 0.611988i | 0.952033 | + | 0.305994i | \(0.0989887\pi\) | ||||
−0.952033 | + | 0.305994i | \(0.901011\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.403302 | − | 0.973658i | −0.0681705 | − | 0.164578i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.56094 | + | 3.96027i | 1.57181 | + | 0.651065i | 0.987089 | − | 0.160170i | \(-0.0512043\pi\) |
0.584720 | + | 0.811235i | \(0.301204\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.27801 | + | 5.27801i | 0.824287 | + | 0.824287i | 0.986720 | − | 0.162432i | \(-0.0519340\pi\) |
−0.162432 | + | 0.986720i | \(0.551934\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.53597 | − | 1.05043i | −0.386732 | − | 0.160190i | 0.180842 | − | 0.983512i | \(-0.442118\pi\) |
−0.567574 | + | 0.823323i | \(0.692118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.85609i | 1.00006i | 0.866007 | + | 0.500031i | \(0.166678\pi\) | ||||
−0.866007 | + | 0.500031i | \(0.833322\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.70291i | 0.957558i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.45793 | − | 3.08917i | −1.02442 | − | 0.424331i | −0.193728 | − | 0.981055i | \(-0.562058\pi\) |
−0.830697 | + | 0.556725i | \(0.812058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.44569 | + | 8.44569i | 1.13882 | + | 1.13882i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.14066 | − | 2.54355i | −0.799446 | − | 0.331142i | −0.0547117 | − | 0.998502i | \(-0.517424\pi\) |
−0.744735 | + | 0.667361i | \(0.767424\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.67989 | + | 6.46983i | 0.343125 | + | 0.828376i | 0.997396 | + | 0.0721165i | \(0.0229753\pi\) |
−0.654272 | + | 0.756260i | \(0.727025\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4.83264i | − | 0.599415i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.2890 | + | 4.26184i | −1.25700 | + | 0.520666i | −0.908987 | − | 0.416824i | \(-0.863143\pi\) |
−0.348012 | + | 0.937490i | \(0.613143\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.37064 | + | 6.37064i | 0.756056 | + | 0.756056i | 0.975602 | − | 0.219546i | \(-0.0704577\pi\) |
−0.219546 | + | 0.975602i | \(0.570458\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.03739 | − | 9.03739i | 1.05775 | − | 1.05775i | 0.0595198 | − | 0.998227i | \(-0.481043\pi\) |
0.998227 | − | 0.0595198i | \(-0.0189570\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.28852 | + | 3.11075i | 0.146840 | + | 0.354503i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.22095 | −0.137367 | −0.0686837 | − | 0.997638i | \(-0.521880\pi\) | ||||
−0.0686837 | + | 0.997638i | \(0.521880\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.8416 | − | 6.14761i | 1.62908 | − | 0.674788i | 0.633953 | − | 0.773372i | \(-0.281431\pi\) |
0.995129 | + | 0.0985841i | \(0.0314314\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.74043 | + | 9.03021i | −0.405707 | + | 0.979464i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.97492 | − | 4.97492i | 0.527340 | − | 0.527340i | −0.392438 | − | 0.919778i | \(-0.628368\pi\) |
0.919778 | + | 0.392438i | \(0.128368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.521343 | − | 1.25863i | 0.0546516 | − | 0.131941i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.43208 | −0.659917 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.23680 | 0.125579 | 0.0627893 | − | 0.998027i | \(-0.480000\pi\) | ||||
0.0627893 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.61006 | − | 13.5439i | 0.558222 | − | 1.34767i | −0.352950 | − | 0.935642i | \(-0.614821\pi\) |
0.911172 | − | 0.412025i | \(-0.135179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0799 | − | 13.0799i | 1.28880 | − | 1.28880i | 0.353279 | − | 0.935518i | \(-0.385067\pi\) |
0.935518 | − | 0.353279i | \(-0.114933\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.16330 | − | 2.80844i | 0.112460 | − | 0.271502i | −0.857622 | − | 0.514281i | \(-0.828059\pi\) |
0.970082 | + | 0.242779i | \(0.0780588\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5958 | + | 5.63158i | −1.30225 | + | 0.539408i | −0.922612 | − | 0.385729i | \(-0.873950\pi\) |
−0.379634 | + | 0.925137i | \(0.623950\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.6829 | 1.28718 | 0.643591 | − | 0.765369i | \(-0.277444\pi\) | ||||
0.643591 | + | 0.765369i | \(0.277444\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.38885 | + | 5.76720i | 0.222761 | + | 0.537794i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.94835 | + | 1.94835i | −0.178605 | + | 0.178605i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.2051 | − | 19.2051i | −1.74591 | − | 1.74591i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1852 | + | 4.63305i | −1.00043 | + | 0.414393i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.19707i | − | 0.727372i | −0.931522 | − | 0.363686i | \(-0.881518\pi\) | ||
0.931522 | − | 0.363686i | \(-0.118482\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.61003 | + | 3.88695i | 0.140669 | + | 0.339604i | 0.978476 | − | 0.206362i | \(-0.0661626\pi\) |
−0.837807 | + | 0.545967i | \(0.816163\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.67520 | − | 0.693890i | −0.145258 | − | 0.0601679i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.79006 | − | 6.79006i | −0.580114 | − | 0.580114i | 0.354821 | − | 0.934934i | \(-0.384542\pi\) |
−0.934934 | + | 0.354821i | \(0.884542\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.08589 | + | 1.27822i | 0.261742 | + | 0.108417i | 0.509695 | − | 0.860355i | \(-0.329758\pi\) |
−0.247954 | + | 0.968772i | \(0.579758\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.4399i | 1.29115i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.53857i | 0.127772i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.40712 | − | 3.48234i | −0.688738 | − | 0.285285i | 0.0107364 | − | 0.999942i | \(-0.496582\pi\) |
−0.699474 | + | 0.714658i | \(0.746582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.7649 | + | 13.7649i | 1.12017 | + | 1.12017i | 0.991715 | + | 0.128459i | \(0.0410032\pi\) |
0.128459 | + | 0.991715i | \(0.458997\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.08674 | − | 2.52121i | −0.488899 | − | 0.202508i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.16741 | + | 2.81838i | 0.0931694 | + | 0.224931i | 0.963593 | − | 0.267372i | \(-0.0861553\pi\) |
−0.870424 | + | 0.492303i | \(0.836155\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.75974i | 0.138687i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.1679 | + | 4.62591i | −0.874740 | + | 0.362329i | −0.774455 | − | 0.632630i | \(-0.781976\pi\) |
−0.100285 | + | 0.994959i | \(0.531976\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.51551 | − | 2.51551i | −0.194656 | − | 0.194656i | 0.603049 | − | 0.797704i | \(-0.293952\pi\) |
−0.797704 | + | 0.603049i | \(0.793952\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.77503 | + | 4.77503i | −0.367310 | + | 0.367310i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.737563 | + | 1.78063i | 0.0560759 | + | 0.135379i | 0.949434 | − | 0.313965i | \(-0.101658\pi\) |
−0.893359 | + | 0.449344i | \(0.851658\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.687623 | −0.0519794 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.47042 | + | 3.92278i | −0.707852 | + | 0.293202i | −0.707416 | − | 0.706798i | \(-0.750139\pi\) |
−0.000436715 | 1.00000i | \(0.500139\pi\) | ||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.91984 | − | 23.9486i | 0.737336 | − | 1.78009i | 0.120927 | − | 0.992661i | \(-0.461413\pi\) |
0.616410 | − | 0.787426i | \(-0.288587\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.1487 | + | 14.1487i | −1.04023 | + | 1.04023i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.9504 | − | 28.8507i | 0.873897 | − | 2.10977i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.03200 | 0.219388 | 0.109694 | − | 0.993965i | \(-0.465013\pi\) | ||||
0.109694 | + | 0.993965i | \(0.465013\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.75813 | 0.342498 | 0.171249 | − | 0.985228i | \(-0.445220\pi\) | ||||
0.171249 | + | 0.985228i | \(0.445220\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.20309 | + | 7.73295i | −0.228211 | + | 0.550950i | −0.995960 | − | 0.0898012i | \(-0.971377\pi\) |
0.767749 | + | 0.640751i | \(0.221377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.9060 | + | 15.9060i | −1.12755 | + | 1.12755i | −0.136973 | + | 0.990575i | \(0.543737\pi\) |
−0.990575 | + | 0.136973i | \(0.956263\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.165981 | + | 0.400713i | −0.0116496 | + | 0.0281245i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.3336 | + | 5.52295i | −0.931257 | + | 0.385739i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 20.5499 | 1.42147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.38241 | − | 5.75165i | −0.164012 | − | 0.395960i | 0.820412 | − | 0.571773i | \(-0.193744\pi\) |
−0.984423 | + | 0.175814i | \(0.943744\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.75284 | − | 3.75284i | 0.255941 | − | 0.255941i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.31327 | − | 1.31327i | −0.0891506 | − | 0.0891506i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.6732 | + | 4.83521i | −0.785226 | + | 0.325251i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 24.2829i | − | 1.62611i | −0.582190 | − | 0.813053i | \(-0.697804\pi\) | ||
0.582190 | − | 0.813053i | \(-0.302196\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.57334 | − | 8.62682i | −0.237171 | − | 0.572582i | 0.759817 | − | 0.650137i | \(-0.225289\pi\) |
−0.996988 | + | 0.0775552i | \(0.975289\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.4317 | + | 5.97779i | 0.953672 | + | 0.395024i | 0.804610 | − | 0.593804i | \(-0.202375\pi\) |
0.149062 | + | 0.988828i | \(0.452375\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.50138 | − | 6.50138i | −0.425920 | − | 0.425920i | 0.461316 | − | 0.887236i | \(-0.347377\pi\) |
−0.887236 | + | 0.461316i | \(0.847377\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.2472 | − | 5.07296i | −0.798920 | − | 0.330923i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.9787i | 1.29232i | 0.763203 | + | 0.646159i | \(0.223626\pi\) | ||||
−0.763203 | + | 0.646159i | \(0.776374\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 0.606349i | − | 0.0390584i | −0.999809 | − | 0.0195292i | \(-0.993783\pi\) | ||
0.999809 | − | 0.0195292i | \(-0.00621673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.9736 | − | 4.95962i | −0.764964 | − | 0.316859i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.87935 | − | 5.87935i | −0.374094 | − | 0.374094i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.5988 | − | 6.04703i | −0.921470 | − | 0.381685i | −0.129034 | − | 0.991640i | \(-0.541187\pi\) |
−0.792436 | + | 0.609955i | \(0.791187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.63217 | − | 18.4257i | −0.479830 | − | 1.15841i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.5962i | 0.660974i | 0.943811 | + | 0.330487i | \(0.107213\pi\) | ||||
−0.943811 | + | 0.330487i | \(0.892787\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.21130 | + | 2.15859i | −0.323815 | + | 0.134128i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.2991 | − | 19.2991i | −1.19004 | − | 1.19004i | −0.977057 | − | 0.212979i | \(-0.931683\pi\) |
−0.212979 | − | 0.977057i | \(-0.568317\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.0366 | − | 11.0366i | 0.677970 | − | 0.677970i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.57782 | + | 11.0518i | 0.279114 | + | 0.673842i | 0.999812 | − | 0.0194081i | \(-0.00617818\pi\) |
−0.720697 | + | 0.693250i | \(0.756178\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.0069 | −1.76204 | −0.881022 | − | 0.473075i | \(-0.843144\pi\) | ||||
−0.881022 | + | 0.473075i | \(0.843144\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.19988 | − | 2.98229i | 0.434169 | − | 0.179839i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.29625 | − | 7.95785i | 0.198053 | − | 0.478141i | −0.793385 | − | 0.608720i | \(-0.791683\pi\) |
0.991438 | + | 0.130578i | \(0.0416834\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.61069 | + | 6.61069i | −0.394361 | + | 0.394361i | −0.876238 | − | 0.481878i | \(-0.839955\pi\) |
0.481878 | + | 0.876238i | \(0.339955\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.300555 | − | 0.725605i | 0.0178662 | − | 0.0431327i | −0.914695 | − | 0.404146i | \(-0.867569\pi\) |
0.932561 | + | 0.361013i | \(0.117569\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.06847 | −0.240154 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.55486 | 0.503227 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.400806 | − | 0.967632i | 0.0234154 | − | 0.0565297i | −0.911739 | − | 0.410769i | \(-0.865260\pi\) |
0.935155 | + | 0.354239i | \(0.115260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.08721 | − | 9.08721i | 0.529078 | − | 0.529078i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.08803 | + | 7.45517i | −0.178586 | + | 0.431144i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.38226 | − | 0.572551i | 0.0796721 | − | 0.0330013i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.5401 | −0.775306 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.22266 | + | 7.78018i | 0.183927 | + | 0.444038i | 0.988769 | − | 0.149450i | \(-0.0477503\pi\) |
−0.804843 | + | 0.593488i | \(0.797750\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.17660 | + | 7.17660i | −0.406948 | + | 0.406948i | −0.880673 | − | 0.473725i | \(-0.842909\pi\) |
0.473725 | + | 0.880673i | \(0.342909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.108611 | + | 0.108611i | 0.00613907 | + | 0.00613907i | 0.710170 | − | 0.704031i | \(-0.248618\pi\) |
−0.704031 | + | 0.710170i | \(0.748618\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.89983 | − | 4.10065i | 0.556030 | − | 0.230315i | −0.0869307 | − | 0.996214i | \(-0.527706\pi\) |
0.642961 | + | 0.765899i | \(0.277706\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.91561i | − | 0.275221i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.43549 | + | 15.5367i | 0.358080 | + | 0.864483i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.91312 | − | 1.20666i | −0.161591 | − | 0.0669332i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.64245 | − | 2.64245i | −0.145683 | − | 0.145683i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7254 | + | 6.09946i | 0.809381 | + | 0.335257i | 0.748707 | − | 0.662901i | \(-0.230675\pi\) |
0.0606740 | + | 0.998158i | \(0.480675\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 21.5329i | − | 1.17647i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5033i | 0.844517i | 0.906475 | + | 0.422259i | \(0.138763\pi\) | ||||
−0.906475 | + | 0.422259i | \(0.861237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.4466 | + | 8.05504i | 1.05309 | + | 0.436205i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.28133 | − | 5.28133i | −0.285165 | − | 0.285165i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.714667 | − | 0.296025i | −0.0383654 | − | 0.0158914i | 0.363418 | − | 0.931626i | \(-0.381610\pi\) |
−0.401784 | + | 0.915735i | \(0.631610\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.21246 | − | 7.75558i | −0.171959 | − | 0.415146i | 0.814280 | − | 0.580473i | \(-0.197132\pi\) |
−0.986239 | + | 0.165326i | \(0.947132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 11.9668i | − | 0.636927i | −0.947935 | − | 0.318463i | \(-0.896833\pi\) | ||
0.947935 | − | 0.318463i | \(-0.103167\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0938 | + | 6.66628i | −0.854171 | + | 0.353809i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0179 | + | 10.0179i | 0.528723 | + | 0.528723i | 0.920191 | − | 0.391469i | \(-0.128033\pi\) |
−0.391469 | + | 0.920191i | \(0.628033\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.60982 | − | 5.60982i | 0.295254 | − | 0.295254i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.45679 | + | 22.8307i | 0.494991 | + | 1.19501i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.0524 | −1.35992 | −0.679961 | − | 0.733248i | \(-0.738004\pi\) | ||||
−0.679961 | + | 0.733248i | \(0.738004\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.06503 | − | 1.68379i | 0.211046 | − | 0.0874180i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.11398 | − | 2.68939i | 0.0576797 | − | 0.139251i | −0.892412 | − | 0.451221i | \(-0.850989\pi\) |
0.950092 | + | 0.311970i | \(0.100989\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.40636 | + | 1.40636i | −0.0724312 | + | 0.0724312i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.87476 | − | 6.94029i | 0.147667 | − | 0.356499i | −0.832688 | − | 0.553743i | \(-0.813199\pi\) |
0.980354 | + | 0.197244i | \(0.0631991\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.2355 | −0.931792 | −0.465896 | − | 0.884839i | \(-0.654268\pi\) | ||||
−0.465896 | + | 0.884839i | \(0.654268\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.51022 | −0.331791 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.18501 | − | 22.1746i | 0.465699 | − | 1.12430i | −0.500324 | − | 0.865838i | \(-0.666786\pi\) |
0.966023 | − | 0.258458i | \(-0.0832143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 11.5405 | − | 11.5405i | 0.583629 | − | 0.583629i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.903405 | − | 2.18101i | 0.0454552 | − | 0.109739i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.77144 | − | 1.56218i | 0.189283 | − | 0.0784037i | −0.286029 | − | 0.958221i | \(-0.592335\pi\) |
0.475312 | + | 0.879817i | \(0.342335\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −32.5110 | −1.62352 | −0.811761 | − | 0.583990i | \(-0.801491\pi\) | ||||
−0.811761 | + | 0.583990i | \(0.801491\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.25913 | − | 7.86824i | −0.162349 | − | 0.391945i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.2038 | − | 45.2038i | 2.24067 | − | 2.24067i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0850 | − | 15.0850i | −0.745903 | − | 0.745903i | 0.227804 | − | 0.973707i | \(-0.426845\pi\) |
−0.973707 | + | 0.227804i | \(0.926845\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.34704 | − | 1.38639i | 0.164697 | − | 0.0682197i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31.0608i | 1.52471i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.41529 | + | 15.4879i | 0.313407 | + | 0.756632i | 0.999574 | + | 0.0291878i | \(0.00929208\pi\) |
−0.686167 | + | 0.727444i | \(0.740708\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8675 | − | 5.74412i | −0.675863 | − | 0.279951i | 0.0182335 | − | 0.999834i | \(-0.494196\pi\) |
−0.694096 | + | 0.719882i | \(0.744196\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.50948 | + | 4.50948i | 0.218742 | + | 0.218742i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.52645 | − | 1.46070i | −0.170657 | − | 0.0706884i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 39.1679i | − | 1.88665i | −0.331870 | − | 0.943325i | \(-0.607680\pi\) | ||
0.331870 | − | 0.943325i | \(-0.392320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.6897i | 0.994283i | 0.867669 | + | 0.497142i | \(0.165617\pi\) | ||||
−0.867669 | + | 0.497142i | \(0.834383\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.92258 | + | 4.11007i | 0.474661 | + | 0.196611i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.49686 | + | 7.49686i | 0.357805 | + | 0.357805i | 0.863003 | − | 0.505198i | \(-0.168581\pi\) |
−0.505198 | + | 0.863003i | \(0.668581\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.58792 | − | 2.31459i | −0.265490 | − | 0.109970i | 0.245968 | − | 0.969278i | \(-0.420894\pi\) |
−0.511458 | + | 0.859308i | \(0.670894\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.20579 | + | 12.5679i | 0.246778 | + | 0.595775i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.22927i | 0.435556i | 0.975998 | + | 0.217778i | \(0.0698809\pi\) | ||||
−0.975998 | + | 0.217778i | \(0.930119\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 42.5996 | − | 17.6453i | 2.00594 | − | 0.830886i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.86258 | + | 1.86258i | 0.0873190 | + | 0.0873190i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0540 | + | 15.0540i | −0.704197 | + | 0.704197i | −0.965309 | − | 0.261112i | \(-0.915911\pi\) |
0.261112 | + | 0.965309i | \(0.415911\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.11682 | − | 5.11046i | −0.0985902 | − | 0.238018i | 0.866887 | − | 0.498504i | \(-0.166117\pi\) |
−0.965478 | + | 0.260486i | \(0.916117\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.2844 | 1.40743 | 0.703717 | − | 0.710481i | \(-0.251522\pi\) | ||||
0.703717 | + | 0.710481i | \(0.251522\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.9725 | + | 5.37338i | −0.600295 | + | 0.248650i | −0.662073 | − | 0.749439i | \(-0.730323\pi\) |
0.0617775 | + | 0.998090i | \(0.480323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.32296 | − | 5.60813i | 0.107264 | − | 0.258959i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.9900 | + | 11.9900i | −0.551300 | + | 0.551300i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.60602 | + | 3.87727i | −0.0736891 | + | 0.177901i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.51607 | 0.114962 | 0.0574810 | − | 0.998347i | \(-0.481693\pi\) | ||||
0.0574810 | + | 0.998347i | \(0.481693\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.8657 | −1.17937 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.915138 | + | 2.20934i | −0.0415543 | + | 0.100321i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.66386 | + | 1.66386i | −0.0753965 | + | 0.0753965i | −0.743799 | − | 0.668403i | \(-0.766978\pi\) |
0.668403 | + | 0.743799i | \(0.266978\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.2708 | + | 29.6244i | −0.553775 | + | 1.33693i | 0.360849 | + | 0.932624i | \(0.382487\pi\) |
−0.914624 | + | 0.404306i | \(0.867513\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.71642 | − | 1.53939i | 0.167379 | − | 0.0693307i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.91070 | −0.220275 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.7034 | + | 33.0830i | 0.613450 | + | 1.48100i | 0.859186 | + | 0.511663i | \(0.170971\pi\) |
−0.245736 | + | 0.969337i | \(0.579029\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.6161 | + | 23.6161i | −1.05299 | + | 1.05299i | −0.0544742 | + | 0.998515i | \(0.517348\pi\) |
−0.998515 | + | 0.0544742i | \(0.982652\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.0428 | + | 20.0428i | 0.891894 | + | 0.891894i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.8424 | − | 14.0180i | 1.50004 | − | 0.621336i | 0.526565 | − | 0.850135i | \(-0.323480\pi\) |
0.973474 | + | 0.228798i | \(0.0734797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.96632i | 0.308172i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.6868 | + | 33.0430i | 0.603115 | + | 1.45605i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.1288 | + | 16.2077i | 1.72088 | + | 0.712812i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.30745 | + | 1.30745i | 0.0572804 | + | 0.0572804i | 0.735167 | − | 0.677886i | \(-0.237104\pi\) |
−0.677886 | + | 0.735167i | \(0.737104\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.7896 | + | 9.02554i | 0.952792 | + | 0.394660i | 0.804280 | − | 0.594251i | \(-0.202551\pi\) |
0.148513 | + | 0.988911i | \(0.452551\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.2250i | 0.750335i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.5766i | 0.546811i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.2361 | − | 7.13943i | −0.746579 | − | 0.309243i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.15605 | + | 4.15605i | 0.179682 | + | 0.179682i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 38.2546 | + | 15.8456i | 1.64774 | + | 0.682516i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.04512 | − | 7.35157i | −0.130920 | − | 0.316069i | 0.844803 | − | 0.535078i | \(-0.179718\pi\) |
−0.975723 | + | 0.219009i | \(0.929718\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 28.4536i | − | 1.21882i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.38090 | + | 2.22884i | −0.230071 | + | 0.0952984i | −0.494741 | − | 0.869041i | \(-0.664737\pi\) |
0.264670 | + | 0.964339i | \(0.414737\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.87182 | + | 1.87182i | 0.0797421 | + | 0.0797421i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.470574 | − | 0.470574i | 0.0200108 | − | 0.0200108i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.63425 | − | 20.8449i | −0.365845 | − | 0.883228i | −0.994421 | − | 0.105480i | \(-0.966362\pi\) |
0.628576 | − | 0.777748i | \(-0.283638\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.86069 | 0.290176 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.1318 | + | 7.09624i | −0.722021 | + | 0.299071i | −0.713268 | − | 0.700891i | \(-0.752786\pi\) |
−0.00875227 | + | 0.999962i | \(0.502786\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1243 | + | 24.4422i | −0.425932 | + | 1.02829i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.5020 | − | 15.5020i | 0.649877 | − | 0.649877i | −0.303086 | − | 0.952963i | \(-0.598017\pi\) |
0.952963 | + | 0.303086i | \(0.0980169\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.3574 | + | 27.4193i | −0.475294 | + | 1.14746i | 0.486499 | + | 0.873681i | \(0.338274\pi\) |
−0.961793 | + | 0.273779i | \(0.911726\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.07295 | 0.169854 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.6105 | 0.816396 | 0.408198 | − | 0.912893i | \(-0.366157\pi\) | ||||
0.408198 | + | 0.912893i | \(0.366157\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.35082 | + | 8.08960i | −0.139016 | + | 0.335613i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.2608 | + | 35.2608i | −1.46035 | + | 1.46035i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.56890 | − | 15.8587i | 0.271128 | − | 0.654560i | −0.728404 | − | 0.685147i | \(-0.759738\pi\) |
0.999532 | + | 0.0305874i | \(0.00973779\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.4724 | + | 4.33779i | −0.431506 | + | 0.178736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.287201 | 0.0117939 | 0.00589697 | − | 0.999983i | \(-0.498123\pi\) | ||||
0.00589697 | + | 0.999983i | \(0.498123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.03877 | − | 4.92202i | −0.0835813 | − | 0.201783i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.5596 | − | 12.5596i | 0.513170 | − | 0.513170i | −0.402326 | − | 0.915496i | \(-0.631798\pi\) |
0.915496 | + | 0.402326i | \(0.131798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.9708 | + | 23.9708i | 0.977791 | + | 0.977791i | 0.999759 | − | 0.0219673i | \(-0.00699298\pi\) |
−0.0219673 | + | 0.999759i | \(0.506993\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 48.5168 | − | 20.0963i | 1.97249 | − | 0.817031i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 27.9757i | − | 1.13550i | −0.823202 | − | 0.567749i | \(-0.807815\pi\) | ||
0.823202 | − | 0.567749i | \(-0.192185\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.55774 | − | 15.8318i | −0.265298 | − | 0.640486i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.2175 | − | 12.5165i | −1.22047 | − | 0.505537i | −0.322913 | − | 0.946429i | \(-0.604662\pi\) |
−0.897560 | + | 0.440892i | \(0.854662\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.4695 | − | 23.4695i | −0.944848 | − | 0.944848i | 0.0537086 | − | 0.998557i | \(-0.482896\pi\) |
−0.998557 | + | 0.0537086i | \(0.982896\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.2802 | + | 6.74349i | 0.654357 | + | 0.271044i | 0.685062 | − | 0.728485i | \(-0.259775\pi\) |
−0.0307046 | + | 0.999529i | \(0.509775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.83483i | 0.153639i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 17.1007i | − | 0.684029i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.3323 | + | 20.0199i | 1.92714 | + | 0.798246i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.7206 | − | 18.7206i | −0.745256 | − | 0.745256i | 0.228328 | − | 0.973584i | \(-0.426674\pi\) |
−0.973584 | + | 0.228328i | \(0.926674\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.6426 | + | 6.06518i | 0.581076 | + | 0.240689i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.41123 | − | 15.4781i | −0.254022 | − | 0.613264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 39.5671i | − | 1.56281i | −0.624026 | − | 0.781404i | \(-0.714504\pi\) | ||
0.624026 | − | 0.781404i | \(-0.285496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.9323 | − | 13.6410i | 1.29872 | − | 0.537949i | 0.377149 | − | 0.926153i | \(-0.376904\pi\) |
0.921573 | + | 0.388204i | \(0.126904\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.1226 | − | 15.1226i | −0.594532 | − | 0.594532i | 0.344320 | − | 0.938852i | \(-0.388109\pi\) |
−0.938852 | + | 0.344320i | \(0.888109\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.0328 | + | 29.0328i | −1.13964 | + | 1.13964i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.76633 | − | 13.9212i | −0.225654 | − | 0.544777i | 0.769985 | − | 0.638061i | \(-0.220263\pi\) |
−0.995640 | + | 0.0932843i | \(0.970263\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.13465 | −0.317847 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.9719 | − | 9.10108i | 0.855905 | − | 0.354528i | 0.0888005 | − | 0.996049i | \(-0.471697\pi\) |
0.767105 | + | 0.641522i | \(0.221697\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.04221 | − | 14.5872i | 0.235015 | − | 0.567376i | −0.761739 | − | 0.647884i | \(-0.775654\pi\) |
0.996754 | + | 0.0805079i | \(0.0256542\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.47903 | − | 2.47903i | 0.0961326 | − | 0.0961326i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.983142 | − | 2.37351i | 0.0380674 | − | 0.0919029i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 43.2595 | 1.67002 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.2501 | 0.896225 | 0.448113 | − | 0.893977i | \(-0.352096\pi\) | ||||
0.448113 | + | 0.893977i | \(0.352096\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.28073 | + | 19.9914i | −0.318254 | + | 0.768333i | 0.681093 | + | 0.732197i | \(0.261505\pi\) |
−0.999347 | + | 0.0361363i | \(0.988495\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.476685 | + | 0.476685i | −0.0182935 | + | 0.0182935i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.09927 | − | 14.7249i | 0.233382 | − | 0.563434i | −0.763189 | − | 0.646175i | \(-0.776367\pi\) |
0.996571 | + | 0.0827411i | \(0.0263674\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.1534 | − | 7.10516i | 0.655397 | − | 0.271474i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.1763 | 0.768655 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.28104 | + | 15.1638i | 0.238942 | + | 0.576857i | 0.997174 | − | 0.0751281i | \(-0.0239366\pi\) |
−0.758232 | + | 0.651985i | \(0.773937\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.56663 | + | 4.56663i | −0.173222 | + | 0.173222i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.6813 | + | 26.6813i | 1.01063 | + | 1.01063i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.6746 | + | 10.2205i | −0.931946 | + | 0.386025i | −0.796416 | − | 0.604749i | \(-0.793274\pi\) |
−0.135529 | + | 0.990773i | \(0.543274\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.4263i | 1.29841i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.05783 | + | 7.38225i | 0.115001 | + | 0.277638i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.4821 | − | 4.75606i | −0.431221 | − | 0.178617i | 0.156506 | − | 0.987677i | \(-0.449977\pi\) |
−0.587727 | + | 0.809060i | \(0.699977\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.77879 | + | 7.77879i | 0.291318 | + | 0.291318i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.5806 | − | 11.4243i | −1.03146 | − | 0.427243i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 24.1182i | − | 0.899455i | −0.893166 | − | 0.449728i | \(-0.851521\pi\) | ||
0.893166 | − | 0.449728i | \(-0.148479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0824i | 0.375488i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.927456 | + | 0.384165i | 0.0344449 | + | 0.0142675i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.8328 | − | 23.8328i | −0.883909 | − | 0.883909i | 0.110020 | − | 0.993929i | \(-0.464908\pi\) |
−0.993929 | + | 0.110020i | \(0.964908\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.8198 | − | 5.31013i | −0.474157 | − | 0.196402i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.22918 | + | 17.4528i | 0.267016 | + | 0.644633i | 0.999340 | − | 0.0363227i | \(-0.0115644\pi\) |
−0.732324 | + | 0.680956i | \(0.761564\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 68.7958i | 2.53412i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.37240 | + | 0.982682i | −0.0872703 | + | 0.0361485i | −0.425892 | − | 0.904774i | \(-0.640039\pi\) |
0.338621 | + | 0.940923i | \(0.390039\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.84906 | + | 9.84906i | 0.361327 | + | 0.361327i | 0.864301 | − | 0.502974i | \(-0.167761\pi\) |
−0.502974 | + | 0.864301i | \(0.667761\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.4412 | − | 12.4412i | 0.455810 | − | 0.455810i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.634067 | + | 1.53077i | 0.0231683 | + | 0.0559333i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.4324 | 0.526644 | 0.263322 | − | 0.964708i | \(-0.415182\pi\) | ||||
0.263322 | + | 0.964708i | \(0.415182\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.7736 | + | 14.4037i | −1.26554 | + | 0.524205i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.5839 | + | 30.3803i | −0.457371 | + | 1.10419i | 0.512088 | + | 0.858933i | \(0.328872\pi\) |
−0.969458 | + | 0.245257i | \(0.921128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.8012 | − | 10.8012i | 0.391543 | − | 0.391543i | −0.483694 | − | 0.875237i | \(-0.660705\pi\) |
0.875237 | + | 0.483694i | \(0.160705\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.06956 | − | 7.41057i | 0.111125 | − | 0.268281i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.6126 | 0.599848 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.6614 | −1.14174 | −0.570869 | − | 0.821041i | \(-0.693394\pi\) | ||||
−0.570869 | + | 0.821041i | \(0.693394\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.73399 | − | 18.6715i | 0.278172 | − | 0.671567i | −0.721613 | − | 0.692297i | \(-0.756599\pi\) |
0.999785 | + | 0.0207297i | \(0.00659894\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.03958 | + | 3.03958i | −0.109185 | + | 0.109185i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.50234 | + | 22.9407i | −0.340457 | + | 0.821935i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.4183 | − | 21.2982i | 1.83989 | − | 0.762108i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.89833 | −0.210520 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.03017 | − | 16.9723i | −0.250598 | − | 0.604998i | 0.747654 | − | 0.664088i | \(-0.231180\pi\) |
−0.998253 | + | 0.0590900i | \(0.981180\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.27363 | + | 5.27363i | −0.187509 | + | 0.187509i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.3766 | − | 12.3766i | −0.439505 | − | 0.439505i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −43.7568 | + | 18.1246i | −1.54994 | + | 0.642008i | −0.983306 | − | 0.181959i | \(-0.941756\pi\) |
−0.566638 | + | 0.823967i | \(0.691756\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.6588i | 1.22614i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −30.2136 | − | 72.9421i | −1.06621 | − | 2.57407i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.14348 | − | 1.30207i | −0.110793 | − | 0.0458919i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.34143 | + | 6.34143i | 0.222953 | + | 0.222953i | 0.809741 | − | 0.586788i | \(-0.199608\pi\) |
−0.586788 | + | 0.809741i | \(0.699608\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.8711 | + | 5.33139i | 0.451966 | + | 0.187210i | 0.597042 | − | 0.802210i | \(-0.296343\pi\) |
−0.145076 | + | 0.989421i | \(0.546343\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 23.3724i | − | 0.818699i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 9.13134i | − | 0.319465i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.6767 | + | 5.25088i | 0.442421 | + | 0.183257i | 0.592763 | − | 0.805377i | \(-0.298037\pi\) |
−0.150341 | + | 0.988634i | \(0.548037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.6528 | + | 21.6528i | 0.754770 | + | 0.754770i | 0.975365 | − | 0.220596i | \(-0.0708002\pi\) |
−0.220596 | + | 0.975365i | \(0.570800\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.0418 | + | 10.7869i | 0.905563 | + | 0.375096i | 0.786356 | − | 0.617773i | \(-0.211965\pi\) |
0.119206 | + | 0.992869i | \(0.461965\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.29036 | + | 12.7721i | 0.183742 | + | 0.443592i | 0.988732 | − | 0.149696i | \(-0.0478295\pi\) |
−0.804990 | + | 0.593288i | \(0.797830\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.8844i | 1.17403i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.35479 | − | 2.63224i | 0.219917 | − | 0.0910924i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.9362 | − | 14.9362i | −0.515654 | − | 0.515654i | 0.400600 | − | 0.916253i | \(-0.368802\pi\) |
−0.916253 | + | 0.400600i | \(0.868802\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0584 | + | 20.0584i | −0.691667 | + | 0.691667i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.99663 | − | 12.0629i | −0.171889 | − | 0.414977i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.8039 | 0.508668 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.8677 | − | 12.7858i | 1.05813 | − | 0.438292i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.9239 | − | 26.3725i | 0.374026 | − | 0.902978i | −0.619034 | − | 0.785364i | \(-0.712476\pi\) |
0.993059 | − | 0.117613i | \(-0.0375243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.77666 | + | 2.77666i | −0.0948488 | + | 0.0948488i | −0.752939 | − | 0.658090i | \(-0.771365\pi\) |
0.658090 | + | 0.752939i | \(0.271365\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.8775 | + | 52.8170i | −0.746452 | + | 1.80209i | −0.169100 | + | 0.985599i | \(0.554086\pi\) |
−0.577352 | + | 0.816495i | \(0.695914\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −35.8729 | −1.22113 | −0.610564 | − | 0.791967i | \(-0.709057\pi\) | ||||
−0.610564 | + | 0.791967i | \(0.709057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.72653 | −0.126706 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.88630 | + | 6.96814i | −0.0979110 | + | 0.236378i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.6825 | − | 19.6825i | 0.666917 | − | 0.666917i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.52530 | − | 6.09661i | 0.0853707 | − | 0.206103i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.2190 | − | 5.88971i | 0.480142 | − | 0.198882i | −0.129466 | − | 0.991584i | \(-0.541326\pi\) |
0.609609 | + | 0.792702i | \(0.291326\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −51.9652 | −1.75075 | −0.875377 | − | 0.483442i | \(-0.839386\pi\) | ||||
−0.875377 | + | 0.483442i | \(0.839386\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.6623 | − | 49.8832i | −0.695342 | − | 1.67870i | −0.733731 | − | 0.679440i | \(-0.762223\pi\) |
0.0383892 | − | 0.999263i | \(-0.487777\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.4215 | + | 24.4215i | −0.819994 | + | 0.819994i | −0.986107 | − | 0.166112i | \(-0.946879\pi\) |
0.166112 | + | 0.986107i | \(0.446879\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.15928 | + | 3.15928i | 0.105959 | + | 0.105959i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.0716 | + | 8.72813i | −0.705133 | + | 0.292076i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 19.8198i | − | 0.662503i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.03761 | + | 2.50502i | 0.0346064 | + | 0.0835472i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.7012 | − | 15.6163i | −1.25601 | − | 0.520256i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 35.4402 | + | 35.4402i | 1.17807 | + | 1.17807i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.89537 | + | 0.785090i | 0.0629349 | + | 0.0260685i | 0.413929 | − | 0.910309i | \(-0.364156\pi\) |
−0.350994 | + | 0.936378i | \(0.614156\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.10306i | − | 0.0365460i | −0.999833 | − | 0.0182730i | \(-0.994183\pi\) | ||
0.999833 | − | 0.0182730i | \(-0.00581679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 99.2364i | − | 3.28425i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.11862 | − | 0.877563i | −0.0699632 | − | 0.0289797i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.1448 | − | 21.1448i | −0.697501 | − | 0.697501i | 0.266370 | − | 0.963871i | \(-0.414176\pi\) |
−0.963871 | + | 0.266370i | \(0.914176\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.8042 | − | 8.61740i | −0.684780 | − | 0.283645i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.99609 | + | 12.0616i | 0.164270 | + | 0.396584i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.59550i | − | 0.282009i | −0.990009 | − | 0.141005i | \(-0.954967\pi\) | ||
0.990009 | − | 0.141005i | \(-0.0450332\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.6008 | + | 8.53313i | −0.675164 | + | 0.279662i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 42.6945 | + | 42.6945i | 1.39626 | + | 1.39626i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.50940 | − | 5.50940i | 0.179984 | − | 0.179984i | −0.611365 | − | 0.791349i | \(-0.709379\pi\) |
0.791349 | + | 0.611365i | \(0.209379\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.60686 | + | 18.3646i | 0.247977 | + | 0.598669i | 0.998032 | − | 0.0627064i | \(-0.0199732\pi\) |
−0.750055 | + | 0.661375i | \(0.769973\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0985 | 0.784754 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.912836 | − | 0.378109i | 0.0296632 | − | 0.0122869i | −0.367803 | − | 0.929904i | \(-0.619890\pi\) |
0.397466 | + | 0.917617i | \(0.369890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.2247 | + | 29.5129i | −0.396829 | + | 0.958030i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.2689 | − | 32.2689i | 1.04529 | − | 1.04529i | 0.0463673 | − | 0.998924i | \(-0.485236\pi\) |
0.998924 | − | 0.0463673i | \(-0.0147645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.24344 | + | 5.41614i | −0.0725960 | + | 0.175262i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.23400 | 0.169015 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.3896 | 0.625471 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.52064 | + | 8.49958i | −0.113334 | + | 0.273611i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.4056 | + | 13.4056i | −0.431097 | + | 0.431097i | −0.889001 | − | 0.457905i | \(-0.848600\pi\) |
0.457905 | + | 0.889001i | \(0.348600\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.93498 | + | 19.1567i | −0.254645 | + | 0.614769i | −0.998568 | − | 0.0534973i | \(-0.982963\pi\) |
0.743923 | + | 0.668266i | \(0.232963\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.68200 | + | 0.696707i | −0.0539224 | + | 0.0223354i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.52723 | −0.176832 | −0.0884159 | − | 0.996084i | \(-0.528180\pi\) | ||||
−0.0884159 | + | 0.996084i | \(0.528180\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.6320 | − | 40.1533i | −0.531562 | − | 1.28330i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.1493 | + | 28.1493i | −0.897822 | + | 0.897822i | −0.995243 | − | 0.0974212i | \(-0.968941\pi\) |
0.0974212 | + | 0.995243i | \(0.468941\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.4435 | − | 11.4435i | −0.364622 | − | 0.364622i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.18744 | + | 3.39135i | −0.260345 | + | 0.107839i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 24.7160i | − | 0.785131i | −0.919724 | − | 0.392565i | \(-0.871588\pi\) | ||
0.919724 | − | 0.392565i | \(-0.128412\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.6442 | − | 40.1825i | −0.527655 | − | 1.27387i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.8087 | − | 11.1045i | −0.849039 | − | 0.351684i | −0.0846280 | − | 0.996413i | \(-0.526970\pi\) |
−0.764411 | + | 0.644729i | \(0.776970\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1152.2.w.b.143.3 | 32 | ||
3.2 | odd | 2 | 1152.2.w.a.143.6 | 32 | |||
4.3 | odd | 2 | 288.2.w.a.251.6 | yes | 32 | ||
12.11 | even | 2 | 288.2.w.b.251.3 | yes | 32 | ||
32.13 | even | 8 | 288.2.w.b.179.3 | yes | 32 | ||
32.19 | odd | 8 | 1152.2.w.a.1007.6 | 32 | |||
96.77 | odd | 8 | 288.2.w.a.179.6 | ✓ | 32 | ||
96.83 | even | 8 | inner | 1152.2.w.b.1007.3 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.179.6 | ✓ | 32 | 96.77 | odd | 8 | ||
288.2.w.a.251.6 | yes | 32 | 4.3 | odd | 2 | ||
288.2.w.b.179.3 | yes | 32 | 32.13 | even | 8 | ||
288.2.w.b.251.3 | yes | 32 | 12.11 | even | 2 | ||
1152.2.w.a.143.6 | 32 | 3.2 | odd | 2 | |||
1152.2.w.a.1007.6 | 32 | 32.19 | odd | 8 | |||
1152.2.w.b.143.3 | 32 | 1.1 | even | 1 | trivial | ||
1152.2.w.b.1007.3 | 32 | 96.83 | even | 8 | inner |