Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.a (trivial) |
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: | yes |
Analytic conductor: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2x^{5} - 12x^{4} + 28x^{3} + 16x^{2} - 60x + 27 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 836) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.24102\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3344.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | 1.24102 | 0.716505 | 0.358252 | − | 0.933625i | \(-0.383373\pi\) | ||||
0.358252 | + | 0.933625i | \(0.383373\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.83235 | 1.26666 | 0.633332 | − | 0.773880i | \(-0.281687\pi\) | ||||
0.633332 | + | 0.773880i | \(0.281687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.46564 | 1.68785 | 0.843926 | − | 0.536460i | \(-0.180239\pi\) | ||||
0.843926 | + | 0.536460i | \(0.180239\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.45986 | −0.486621 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.14252 | 0.594229 | 0.297114 | − | 0.954842i | \(-0.403976\pi\) | ||||
0.297114 | + | 0.954842i | \(0.403976\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.51500 | 0.907570 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.81594 | 1.89564 | 0.947822 | − | 0.318801i | \(-0.103280\pi\) | ||||
0.947822 | + | 0.318801i | \(0.103280\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.54196 | 1.20935 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.81016 | −0.794474 | −0.397237 | − | 0.917716i | \(-0.630031\pi\) | ||||
−0.397237 | + | 0.917716i | \(0.630031\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.02218 | 0.604436 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.53479 | −1.06517 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.86854 | 0.346979 | 0.173490 | − | 0.984836i | \(-0.444496\pi\) | ||||
0.173490 | + | 0.984836i | \(0.444496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.22996 | 0.220907 | 0.110454 | − | 0.993881i | \(-0.464770\pi\) | ||||
0.110454 | + | 0.993881i | \(0.464770\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.24102 | −0.216034 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 12.6482 | 2.13794 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.10815 | −1.33297 | −0.666485 | − | 0.745518i | \(-0.732202\pi\) | ||||
−0.666485 | + | 0.745518i | \(0.732202\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.65892 | 0.425768 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9225 | 1.70582 | 0.852908 | − | 0.522062i | \(-0.174837\pi\) | ||||
0.852908 | + | 0.522062i | \(0.174837\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.97782 | −0.454113 | −0.227057 | − | 0.973882i | \(-0.572910\pi\) | ||||
−0.227057 | + | 0.973882i | \(0.572910\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.13484 | −0.616385 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.28504 | −0.916768 | −0.458384 | − | 0.888754i | \(-0.651572\pi\) | ||||
−0.458384 | + | 0.888754i | \(0.651572\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.9419 | 1.84884 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.69975 | 1.35824 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.43768 | 0.884284 | 0.442142 | − | 0.896945i | \(-0.354219\pi\) | ||||
0.442142 | + | 0.896945i | \(0.354219\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.83235 | −0.381913 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.24102 | −0.164377 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.40754 | −0.964380 | −0.482190 | − | 0.876067i | \(-0.660159\pi\) | ||||
−0.482190 | + | 0.876067i | \(0.660159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.83806 | −1.25963 | −0.629817 | − | 0.776743i | \(-0.716870\pi\) | ||||
−0.629817 | + | 0.776743i | \(0.716870\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.51922 | −0.821344 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.06836 | 0.752688 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.7013 | 1.67388 | 0.836941 | − | 0.547293i | \(-0.184342\pi\) | ||||
0.836941 | + | 0.547293i | \(0.184342\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.72850 | −0.569244 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.27693 | 0.270222 | 0.135111 | − | 0.990830i | \(-0.456861\pi\) | ||||
0.135111 | + | 0.990830i | \(0.456861\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.77299 | 0.324554 | 0.162277 | − | 0.986745i | \(-0.448116\pi\) | ||||
0.162277 | + | 0.986745i | \(0.448116\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.75060 | 0.433081 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.46564 | −0.508906 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.9183 | −1.79095 | −0.895475 | − | 0.445112i | \(-0.853164\pi\) | ||||
−0.895475 | + | 0.445112i | \(0.853164\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.48921 | −0.276579 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.37820 | −0.700098 | −0.350049 | − | 0.936731i | \(-0.613835\pi\) | ||||
−0.350049 | + | 0.936731i | \(0.613835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 22.1374 | 2.40114 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.31890 | 0.248612 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.65892 | 0.175845 | 0.0879225 | − | 0.996127i | \(-0.471977\pi\) | ||||
0.0879225 | + | 0.996127i | \(0.471977\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.56772 | 1.00297 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.52641 | 0.158281 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.83235 | −0.290593 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.99423 | −0.608622 | −0.304311 | − | 0.952573i | \(-0.598426\pi\) | ||||
−0.304311 | + | 0.952573i | \(0.598426\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.45986 | 0.146722 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.9627 | 1.19033 | 0.595165 | − | 0.803603i | \(-0.297087\pi\) | ||||
0.595165 | + | 0.803603i | \(0.297087\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.753204 | 0.0742154 | 0.0371077 | − | 0.999311i | \(-0.488186\pi\) | ||||
0.0371077 | + | 0.999311i | \(0.488186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.6967 | 1.53184 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.05803 | 0.102284 | 0.0511420 | − | 0.998691i | \(-0.483714\pi\) | ||||
0.0511420 | + | 0.998691i | \(0.483714\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.10240 | 0.680286 | 0.340143 | − | 0.940374i | \(-0.389524\pi\) | ||||
0.340143 | + | 0.940374i | \(0.389524\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.0624 | −0.955080 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.8752 | −1.96378 | −0.981888 | − | 0.189460i | \(-0.939326\pi\) | ||||
−0.981888 | + | 0.189460i | \(0.939326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.7917 | −1.00633 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.12779 | −0.289164 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 34.9031 | 3.19956 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 13.5551 | 1.22222 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.60187 | −0.501046 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.9848 | 1.77336 | 0.886682 | − | 0.462380i | \(-0.153004\pi\) | ||||
0.886682 | + | 0.462380i | \(0.153004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.69554 | −0.325374 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.5666 | −1.27269 | −0.636346 | − | 0.771404i | \(-0.719555\pi\) | ||||
−0.636346 | + | 0.771404i | \(0.719555\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.46564 | −0.387220 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −15.6764 | −1.34921 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.89754 | 0.247554 | 0.123777 | − | 0.992310i | \(-0.460499\pi\) | ||||
0.123777 | + | 0.992310i | \(0.460499\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −18.2399 | −1.54709 | −0.773544 | − | 0.633743i | \(-0.781518\pi\) | ||||
−0.773544 | + | 0.633743i | \(0.781518\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.79988 | −0.656868 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.14252 | −0.179167 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.29235 | 0.439506 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 16.0612 | 1.32471 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.3109 | −1.50009 | −0.750044 | − | 0.661387i | \(-0.769968\pi\) | ||||
−0.750044 | + | 0.661387i | \(0.769968\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.3574 | 1.24977 | 0.624884 | − | 0.780718i | \(-0.285146\pi\) | ||||
0.624884 | + | 0.780718i | \(0.285146\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.4102 | −0.922460 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.48367 | 0.279815 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.81022 | −0.224280 | −0.112140 | − | 0.993692i | \(-0.535771\pi\) | ||||
−0.112140 | + | 0.993692i | \(0.535771\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.98931 | 0.633593 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −17.0148 | −1.34095 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.73427 | 0.527469 | 0.263734 | − | 0.964595i | \(-0.415046\pi\) | ||||
0.263734 | + | 0.964595i | \(0.415046\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.51500 | −0.273643 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.27586 | 0.640405 | 0.320203 | − | 0.947349i | \(-0.396249\pi\) | ||||
0.320203 | + | 0.947349i | \(0.396249\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.40960 | −0.646892 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.45986 | 0.111639 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.83263 | −0.367418 | −0.183709 | − | 0.982981i | \(-0.558810\pi\) | ||||
−0.183709 | + | 0.982981i | \(0.558810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.4960 | 1.02020 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.19293 | −0.690983 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 7.19714 | 0.537940 | 0.268970 | − | 0.963149i | \(-0.413317\pi\) | ||||
0.268970 | + | 0.963149i | \(0.413317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.75664 | 0.204899 | 0.102450 | − | 0.994738i | \(-0.467332\pi\) | ||||
0.102450 | + | 0.994738i | \(0.467332\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.2093 | −0.902534 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.9651 | −1.68843 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.81594 | −0.571558 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −24.7164 | −1.79785 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.9906 | −1.01232 | −0.506161 | − | 0.862439i | \(-0.668936\pi\) | ||||
−0.506161 | + | 0.862439i | \(0.668936\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.78688 | −0.488530 | −0.244265 | − | 0.969709i | \(-0.578547\pi\) | ||||
−0.244265 | + | 0.969709i | \(0.578547\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.53098 | 0.539304 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.99861 | −0.142395 | −0.0711975 | − | 0.997462i | \(-0.522682\pi\) | ||||
−0.0711975 | + | 0.997462i | \(0.522682\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.31094 | −0.0929304 | −0.0464652 | − | 0.998920i | \(-0.514796\pi\) | ||||
−0.0464652 | + | 0.998920i | \(0.514796\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.0036 | 1.19934 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.34422 | 0.585649 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 30.9364 | 2.16069 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.56232 | 0.386608 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.31644 | −0.503685 | −0.251842 | − | 0.967768i | \(-0.581036\pi\) | ||||
−0.251842 | + | 0.967768i | \(0.581036\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.82572 | 0.193615 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.43421 | −0.575208 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.49255 | 0.372859 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.44134 | 0.232544 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.7458 | 1.12645 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.69849 | 0.515529 | 0.257765 | − | 0.966208i | \(-0.417014\pi\) | ||||
0.257765 | + | 0.966208i | \(0.417014\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.41197 | −0.294131 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.61894 | −0.638431 | −0.319216 | − | 0.947682i | \(-0.603419\pi\) | ||||
−0.319216 | + | 0.947682i | \(0.603419\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.1361 | 0.801976 | 0.400988 | − | 0.916083i | \(-0.368667\pi\) | ||||
0.400988 | + | 0.916083i | \(0.368667\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.54196 | −0.364634 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.5356 | −0.886745 | −0.443372 | − | 0.896338i | \(-0.646218\pi\) | ||||
−0.443372 | + | 0.896338i | \(0.646218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.8014 | −1.16124 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.7550 | −1.28322 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.0084 | −1.16487 | −0.582433 | − | 0.812879i | \(-0.697899\pi\) | ||||
−0.582433 | + | 0.812879i | \(0.697899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.4331 | 1.57387 | 0.786936 | − | 0.617034i | \(-0.211666\pi\) | ||||
0.786936 | + | 0.617034i | \(0.211666\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5152 | 0.867001 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 36.6560 | 2.34186 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.14252 | −0.136325 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.91549 | −0.501624 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.0408 | 1.70680 | 0.853400 | − | 0.521256i | \(-0.174536\pi\) | ||||
0.853400 | + | 0.521256i | \(0.174536\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.81016 | 0.239543 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 27.4731 | 1.72043 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −26.1689 | −1.63237 | −0.816184 | − | 0.577792i | \(-0.803915\pi\) | ||||
−0.816184 | + | 0.577792i | \(0.803915\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −36.2080 | −2.24986 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.72781 | −0.168847 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.1061 | −0.746494 | −0.373247 | − | 0.927732i | \(-0.621756\pi\) | ||||
−0.373247 | + | 0.927732i | \(0.621756\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.2337 | 1.12009 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.05875 | 0.125994 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 27.5041 | 1.67696 | 0.838479 | − | 0.544934i | \(-0.183445\pi\) | ||||
0.838479 | + | 0.544934i | \(0.183445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.45270 | 0.270482 | 0.135241 | − | 0.990813i | \(-0.456819\pi\) | ||||
0.135241 | + | 0.990813i | \(0.456819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.8738 | 0.718633 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.02218 | −0.182244 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0559 | 0.844538 | 0.422269 | − | 0.906471i | \(-0.361234\pi\) | ||||
0.422269 | + | 0.906471i | \(0.361234\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.79557 | −0.107498 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0282 | −0.717543 | −0.358772 | − | 0.933425i | \(-0.616804\pi\) | ||||
−0.358772 | + | 0.933425i | \(0.616804\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.1496 | 1.13833 | 0.569164 | − | 0.822224i | \(-0.307267\pi\) | ||||
0.569164 | + | 0.822224i | \(0.307267\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.51500 | −0.208211 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 48.7761 | 2.87916 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.0889 | 2.59346 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.43897 | −0.436080 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.3732 | 1.01495 | 0.507476 | − | 0.861666i | \(-0.330579\pi\) | ||||
0.507476 | + | 0.861666i | \(0.330579\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.9807 | −1.22155 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.53479 | 0.321161 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.16336 | −0.472099 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.2979 | −0.766476 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.8459 | 0.852877 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −27.8648 | −1.59553 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4419 | 1.45205 | 0.726023 | − | 0.687670i | \(-0.241366\pi\) | ||||
0.726023 | + | 0.687670i | \(0.241366\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.934744 | 0.0531757 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.22913 | 0.353222 | 0.176611 | − | 0.984281i | \(-0.443487\pi\) | ||||
0.176611 | + | 0.984281i | \(0.443487\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.4024 | 1.32278 | 0.661392 | − | 0.750041i | \(-0.269966\pi\) | ||||
0.661392 | + | 0.750041i | \(0.269966\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −18.4647 | −1.04037 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.9440 | −0.783171 | −0.391585 | − | 0.920142i | \(-0.628073\pi\) | ||||
−0.391585 | + | 0.920142i | \(0.628073\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.86854 | −0.104618 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.31304 | 0.0732870 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.81594 | −0.434890 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.47509 | 0.359173 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.81424 | 0.487428 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.0667 | −1.54737 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.96372 | −0.492691 | −0.246345 | − | 0.969182i | \(-0.579230\pi\) | ||||
−0.246345 | + | 0.969182i | \(0.579230\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 11.8368 | 0.648652 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 38.8069 | 2.12024 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.52217 | 0.409759 | 0.204879 | − | 0.978787i | \(-0.434320\pi\) | ||||
0.204879 | + | 0.978787i | \(0.434320\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.9066 | −1.40706 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.22996 | −0.0666061 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 26.5344 | 1.43272 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −13.3927 | −0.721041 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.09789 | 0.381035 | 0.190517 | − | 0.981684i | \(-0.438983\pi\) | ||||
0.190517 | + | 0.981684i | \(0.438983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.8496 | −1.65134 | −0.825670 | − | 0.564153i | \(-0.809203\pi\) | ||||
−0.825670 | + | 0.564153i | \(0.809203\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.8584 | −0.632955 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.7894 | 1.74521 | 0.872603 | − | 0.488430i | \(-0.162430\pi\) | ||||
0.872603 | + | 0.488430i | \(0.162430\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.44906 | 0.342281 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 43.3156 | 2.29250 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.72206 | −0.513111 | −0.256555 | − | 0.966530i | \(-0.582588\pi\) | ||||
−0.256555 | + | 0.966530i | \(0.582588\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.24102 | 0.0651368 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.85407 | 0.411101 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.3115 | −0.694856 | −0.347428 | − | 0.937707i | \(-0.612945\pi\) | ||||
−0.347428 | + | 0.937707i | \(0.612945\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.9454 | −0.830086 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.7483 | 1.49254 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.88925 | −0.356712 | −0.178356 | − | 0.983966i | \(-0.557078\pi\) | ||||
−0.178356 | + | 0.983966i | \(0.557078\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.95204 | −0.359002 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.00339 | 0.206185 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6685 | −0.804837 | −0.402418 | − | 0.915456i | \(-0.631830\pi\) | ||||
−0.402418 | + | 0.915456i | \(0.631830\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.8016 | 1.27062 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 38.2914 | 1.95660 | 0.978299 | − | 0.207198i | \(-0.0664346\pi\) | ||||
0.978299 | + | 0.207198i | \(0.0664346\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.6482 | −0.644613 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.34721 | 0.220981 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.4533 | 0.682108 | 0.341054 | − | 0.940044i | \(-0.389216\pi\) | ||||
0.341054 | + | 0.940044i | \(0.389216\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.7800 | −1.50604 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.0775 | −0.911889 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −45.0862 | −2.26853 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.5925 | −1.53539 | −0.767697 | − | 0.640813i | \(-0.778597\pi\) | ||||
−0.767697 | + | 0.640813i | \(0.778597\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5.54196 | −0.277445 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.2750 | −0.762798 | −0.381399 | − | 0.924411i | \(-0.624558\pi\) | ||||
−0.381399 | + | 0.924411i | \(0.624558\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.63522 | 0.131270 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.05030 | −0.350332 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.10815 | 0.401906 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.3255 | −0.757799 | −0.378900 | − | 0.925438i | \(-0.623697\pi\) | ||||
−0.378900 | + | 0.925438i | \(0.623697\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.59592 | 0.177374 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −33.0794 | −1.62773 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.0653 | −0.886789 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.6361 | −1.10850 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.42923 | −0.265235 | −0.132618 | − | 0.991167i | \(-0.542338\pi\) | ||||
−0.132618 | + | 0.991167i | \(0.542338\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.4074 | −0.653437 | −0.326719 | − | 0.945122i | \(-0.605943\pi\) | ||||
−0.326719 | + | 0.945122i | \(0.605943\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.17531 | 0.446119 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 23.6212 | 1.14580 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −43.9332 | −2.12608 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.65892 | −0.128374 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.96718 | 0.480102 | 0.240051 | − | 0.970760i | \(-0.422836\pi\) | ||||
0.240051 | + | 0.970760i | \(0.422836\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.3082 | 1.12012 | 0.560061 | − | 0.828451i | \(-0.310778\pi\) | ||||
0.560061 | + | 0.828451i | \(0.310778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.56793 | 0.314908 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.81016 | 0.182265 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.5107 | 0.549374 | 0.274687 | − | 0.961534i | \(-0.411426\pi\) | ||||
0.274687 | + | 0.961534i | \(0.411426\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.8934 | −0.899686 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −31.2930 | −1.48678 | −0.743389 | − | 0.668860i | \(-0.766783\pi\) | ||||
−0.743389 | + | 0.668860i | \(0.766783\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.69863 | 0.222736 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.7243 | −1.07482 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.4750 | −1.62697 | −0.813487 | − | 0.581583i | \(-0.802434\pi\) | ||||
−0.813487 | + | 0.581583i | \(0.802434\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.9225 | −0.514323 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.0589 | 0.895465 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.0991 | 1.27043 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.2398 | 1.36778 | 0.683891 | − | 0.729584i | \(-0.260286\pi\) | ||||
0.683891 | + | 0.729584i | \(0.260286\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −43.2596 | −2.01918 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.66554 | 0.450169 | 0.225085 | − | 0.974339i | \(-0.427734\pi\) | ||||
0.225085 | + | 0.974339i | \(0.427734\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.41991 | 0.344833 | 0.172416 | − | 0.985024i | \(-0.444843\pi\) | ||||
0.172416 | + | 0.985024i | \(0.444843\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.32332 | 0.200489 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.09212 | 0.143086 | 0.0715430 | − | 0.997438i | \(-0.477208\pi\) | ||||
0.0715430 | + | 0.997438i | \(0.477208\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 61.1851 | 2.82526 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.48755 | −0.160698 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.97782 | 0.136920 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.02218 | −0.138667 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.39813 | −0.430311 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.3725 | −1.38776 | −0.693879 | − | 0.720092i | \(-0.744100\pi\) | ||||
−0.693879 | + | 0.720092i | \(0.744100\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.3719 | −0.792090 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.1158 | −0.960800 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.9777 | −0.770919 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.6521 | 1.66086 | 0.830432 | − | 0.557120i | \(-0.188094\pi\) | ||||
0.830432 | + | 0.557120i | \(0.188094\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.35738 | 0.377934 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.8522 | −0.670270 | −0.335135 | − | 0.942170i | \(-0.608782\pi\) | ||||
−0.335135 | + | 0.942170i | \(0.608782\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.6044 | 0.657749 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.13484 | 0.185847 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.1680 | 0.456095 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.9369 | −1.25063 | −0.625314 | − | 0.780374i | \(-0.715029\pi\) | ||||
−0.625314 | + | 0.780374i | \(0.715029\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.2705 | 0.458853 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.65406 | −0.385865 | −0.192933 | − | 0.981212i | \(-0.561800\pi\) | ||||
−0.192933 | + | 0.981212i | \(0.561800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 33.8824 | 1.50775 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.4365 | −0.463501 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.6016 | −1.17910 | −0.589548 | − | 0.807733i | \(-0.700694\pi\) | ||||
−0.589548 | + | 0.807733i | \(0.700694\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.3832 | 0.547799 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.53479 | 0.244367 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.13334 | 0.0940060 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.28504 | 0.276416 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.99740 | −0.263257 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.17685 | 0.182991 | 0.0914955 | − | 0.995805i | \(-0.470835\pi\) | ||||
0.0914955 | + | 0.995805i | \(0.470835\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.07716 | −0.134555 | −0.0672773 | − | 0.997734i | \(-0.521431\pi\) | ||||
−0.0672773 | + | 0.997734i | \(0.521431\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.7488 | 0.730977 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.61329 | 0.418762 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.48265 | −0.368811 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.8140 | 0.469288 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 23.4018 | 1.01364 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.99672 | 0.129560 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.93182 | 0.385436 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.9419 | −0.557447 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.9766 | −1.71873 | −0.859365 | − | 0.511363i | \(-0.829141\pi\) | ||||
−0.859365 | + | 0.511363i | \(0.829141\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.42105 | 0.146811 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.1164 | 0.861694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.7551 | −0.588125 | −0.294063 | − | 0.955786i | \(-0.595007\pi\) | ||||
−0.294063 | + | 0.955786i | \(0.595007\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.3622 | 0.612965 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.86854 | −0.0796025 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −71.0854 | −3.02286 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −28.5002 | −1.20976 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.37375 | 0.142950 | 0.0714751 | − | 0.997442i | \(-0.477229\pi\) | ||||
0.0714751 | + | 0.997442i | \(0.477229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.38004 | −0.269847 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.69975 | −0.409524 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −32.4119 | −1.36600 | −0.682999 | − | 0.730419i | \(-0.739325\pi\) | ||||
−0.682999 | + | 0.730419i | \(0.739325\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −59.1259 | −2.48744 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −11.1159 | −0.466824 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.7569 | 1.24748 | 0.623738 | − | 0.781633i | \(-0.285613\pi\) | ||||
0.623738 | + | 0.781633i | \(0.285613\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.9446 | −0.499865 | −0.249933 | − | 0.968263i | \(-0.580409\pi\) | ||||
−0.249933 | + | 0.968263i | \(0.580409\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.3626 | −0.725334 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.5150 | −0.480209 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.05443 | −0.168788 | −0.0843941 | − | 0.996432i | \(-0.526895\pi\) | ||||
−0.0843941 | + | 0.996432i | \(0.526895\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.42266 | −0.350034 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.4827 | −1.18166 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.43768 | −0.266622 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.85898 | −0.366274 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.7020 | −0.730640 | −0.365320 | − | 0.930882i | \(-0.619040\pi\) | ||||
−0.365320 | + | 0.930882i | \(0.619040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.22996 | −0.0506796 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.48032 | −0.102027 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.42897 | 0.387201 | 0.193601 | − | 0.981080i | \(-0.437983\pi\) | ||||
0.193601 | + | 0.981080i | \(0.437983\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 98.8577 | 4.05277 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.62691 | −0.0665851 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.75320 | −0.112493 | −0.0562464 | − | 0.998417i | \(-0.517913\pi\) | ||||
−0.0562464 | + | 0.998417i | \(0.517913\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −45.2029 | −1.84386 | −0.921932 | − | 0.387351i | \(-0.873390\pi\) | ||||
−0.921932 | + | 0.387351i | \(0.873390\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −20.0020 | −0.814546 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.83235 | 0.115151 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.2093 | 1.55087 | 0.775433 | − | 0.631430i | \(-0.217532\pi\) | ||||
0.775433 | + | 0.631430i | \(0.217532\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.3554 | 0.419621 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.4658 | −0.544770 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.78003 | −0.112284 | −0.0561421 | − | 0.998423i | \(-0.517880\pi\) | ||||
−0.0561421 | + | 0.998423i | \(0.517880\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 38.3928 | 1.54815 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.4168 | 0.862207 | 0.431104 | − | 0.902302i | \(-0.358124\pi\) | ||||
0.431104 | + | 0.902302i | \(0.358124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.63033 | −0.226302 | −0.113151 | − | 0.993578i | \(-0.536094\pi\) | ||||
−0.113151 | + | 0.993578i | \(0.536094\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.0885 | 0.846251 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.40813 | 0.296800 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9773 | −1.23909 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.24102 | 0.0495617 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −63.3728 | −2.52684 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 47.0442 | 1.87280 | 0.936400 | − | 0.350935i | \(-0.114136\pi\) | ||||
0.936400 | + | 0.350935i | \(0.114136\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.07987 | −0.360893 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 56.6039 | 2.24626 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 27.7283 | 1.09864 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.32401 | −0.131496 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.26926 | −0.168626 | −0.0843128 | − | 0.996439i | \(-0.526870\pi\) | ||||
−0.0843128 | + | 0.996439i | \(0.526870\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.72241 | −0.383414 | −0.191707 | − | 0.981452i | \(-0.561402\pi\) | ||||
−0.191707 | + | 0.981452i | \(0.561402\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.4670 | −0.412139 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −30.8738 | −1.21377 | −0.606887 | − | 0.794788i | \(-0.707582\pi\) | ||||
−0.606887 | + | 0.794788i | \(0.707582\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.40754 | 0.290772 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.81638 | 0.267155 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.21765 | −0.0867832 | −0.0433916 | − | 0.999058i | \(-0.513816\pi\) | ||||
−0.0433916 | + | 0.999058i | \(0.513816\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −41.2577 | −1.61207 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.04819 | −0.157935 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.82521 | −0.343781 | −0.171891 | − | 0.985116i | \(-0.554988\pi\) | ||||
−0.171891 | + | 0.985116i | \(0.554988\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.0328 | 1.82937 | 0.914683 | − | 0.404173i | \(-0.132441\pi\) | ||||
0.914683 | + | 0.404173i | \(0.132441\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.7819 | 0.807104 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.6482 | −0.490477 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.11944 | −0.275666 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.55400 | 0.369379 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.83806 | 0.379794 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.0771 | 0.889556 | 0.444778 | − | 0.895641i | \(-0.353283\pi\) | ||||
0.444778 | + | 0.895641i | \(0.353283\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.7271 | −0.643828 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.34225 | 0.243753 | 0.121876 | − | 0.992545i | \(-0.461109\pi\) | ||||
0.121876 | + | 0.992545i | \(0.461109\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.7680 | −1.02726 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.9373 | −0.457439 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.29657 | −0.126140 | −0.0630698 | − | 0.998009i | \(-0.520089\pi\) | ||||
−0.0630698 | + | 0.998009i | \(0.520089\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.20685 | 0.313568 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 15.0612 | 0.574620 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.7929 | 0.525467 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.7705 | 0.599937 | 0.299969 | − | 0.953949i | \(-0.403024\pi\) | ||||
0.299969 | + | 0.953949i | \(0.403024\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.51922 | 0.247645 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −51.6617 | −1.95964 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 85.3700 | 3.23362 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.7979 | −0.635357 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.1060 | −0.683855 | −0.341927 | − | 0.939726i | \(-0.611080\pi\) | ||||
−0.341927 | + | 0.939726i | \(0.611080\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.10815 | 0.305805 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.0920 | −0.832031 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 53.4209 | 2.00910 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.6798 | −0.964426 | −0.482213 | − | 0.876054i | \(-0.660167\pi\) | ||||
−0.482213 | + | 0.876054i | \(0.660167\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.2386 | 0.871514 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.68635 | −0.175505 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.06836 | −0.226944 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.3488 | −0.834632 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27.8775 | 1.03966 | 0.519828 | − | 0.854271i | \(-0.325996\pi\) | ||||
0.519828 | + | 0.854271i | \(0.325996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.36354 | 0.125265 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.3220 | 1.12769 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.64707 | 0.209727 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.7941 | 1.55006 | 0.775029 | − | 0.631925i | \(-0.217735\pi\) | ||||
0.775029 | + | 0.631925i | \(0.217735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.2403 | 0.897789 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −23.2744 | −0.860836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.36881 | 0.346045 | 0.173022 | − | 0.984918i | \(-0.444647\pi\) | ||||
0.173022 | + | 0.984918i | \(0.444647\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 45.4909 | 1.67796 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.7013 | −0.504694 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34.2879 | −1.26130 | −0.630650 | − | 0.776067i | \(-0.717212\pi\) | ||||
−0.630650 | + | 0.776067i | \(0.717212\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.65892 | −0.0976778 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.3459 | −0.929851 | −0.464925 | − | 0.885350i | \(-0.653919\pi\) | ||||
−0.464925 | + | 0.885350i | \(0.653919\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −51.8629 | −1.90011 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.31130 | 0.340683 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.72480 | 0.172640 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.2198 | −1.32168 | −0.660840 | − | 0.750527i | \(-0.729800\pi\) | ||||
−0.660840 | + | 0.750527i | \(0.729800\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.5583 | 1.22293 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 43.4975 | 1.58304 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.7822 | −1.22784 | −0.613918 | − | 0.789370i | \(-0.710407\pi\) | ||||
−0.613918 | + | 0.789370i | \(0.710407\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.72850 | 0.171634 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.9369 | −0.903963 | −0.451981 | − | 0.892027i | \(-0.649283\pi\) | ||||
−0.451981 | + | 0.892027i | \(0.649283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.7167 | 1.14822 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −32.3176 | −1.16845 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.8708 | −0.573062 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.4936 | 0.486592 | 0.243296 | − | 0.969952i | \(-0.421771\pi\) | ||||
0.243296 | + | 0.969952i | \(0.421771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.4761 | −1.16960 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.4133 | −0.410509 | −0.205254 | − | 0.978709i | \(-0.565802\pi\) | ||||
−0.205254 | + | 0.978709i | \(0.565802\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.71716 | 0.133524 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −44.9350 | −1.61203 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.9225 | −0.391341 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.27693 | −0.0814751 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.3420 | −0.369592 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.95952 | −0.284087 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.7206 | −0.738609 | −0.369304 | − | 0.929308i | \(-0.620404\pi\) | ||||
−0.369304 | + | 0.929308i | \(0.620404\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.0239 | −0.534866 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −93.2212 | −3.31456 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.0783 | −0.748511 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.6285 | 0.802549 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.4629 | 0.795675 | 0.397838 | − | 0.917456i | \(-0.369761\pi\) | ||||
0.397838 | + | 0.917456i | \(0.369761\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.1235 | −1.73786 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.42179 | −0.0855699 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.77299 | −0.0978567 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48.1918 | −1.69854 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.1333 | 1.20155 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.49572 | 0.0525866 | 0.0262933 | − | 0.999654i | \(-0.491630\pi\) | ||||
0.0262933 | + | 0.999654i | \(0.491630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.8558 | 1.68044 | 0.840222 | − | 0.542243i | \(-0.182425\pi\) | ||||
0.840222 | + | 0.542243i | \(0.182425\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.52590 | 0.193802 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.0738 | 0.668126 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.97782 | 0.104181 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.9676 | −0.488066 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.4124 | −1.51510 | −0.757552 | − | 0.652774i | \(-0.773605\pi\) | ||||
−0.757552 | + | 0.652774i | \(0.773605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.7858 | −0.410826 | −0.205413 | − | 0.978675i | \(-0.565854\pi\) | ||||
−0.205413 | + | 0.978675i | \(0.565854\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.75060 | −0.130579 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −42.6416 | −1.48279 | −0.741397 | − | 0.671067i | \(-0.765836\pi\) | ||||
−0.741397 | + | 0.671067i | \(0.765836\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −56.4118 | −1.95926 | −0.979631 | − | 0.200808i | \(-0.935643\pi\) | ||||
−0.979631 | + | 0.200808i | \(0.935643\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.4437 | 0.605115 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 101.153 | 3.50475 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.4401 | 0.811178 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.80757 | −0.235304 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.6179 | 0.953474 | 0.476737 | − | 0.879046i | \(-0.341819\pi\) | ||||
0.476737 | + | 0.879046i | \(0.341819\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.5086 | −0.879605 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.9273 | −0.514123 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.8189 | −0.819395 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.46564 | 0.153441 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.7651 | 0.815617 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.8934 | 1.05901 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2378 | 0.761409 | 0.380705 | − | 0.924697i | \(-0.375681\pi\) | ||||
0.380705 | + | 0.924697i | \(0.375681\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.13484 | 0.141408 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.2312 | −0.520289 | −0.260144 | − | 0.965570i | \(-0.583770\pi\) | ||||
−0.260144 | + | 0.965570i | \(0.583770\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.9212 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 60.5323 | 2.06293 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.2896 | 0.452384 | 0.226192 | − | 0.974083i | \(-0.427372\pi\) | ||||
0.226192 | + | 0.974083i | \(0.427372\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.6877 | −0.465395 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 54.7153 | 1.85823 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.9183 | 0.539992 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.3554 | 0.994669 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.75075 | 0.296168 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25.0159 | −0.845692 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.3501 | 0.585872 | 0.292936 | − | 0.956132i | \(-0.405368\pi\) | ||||
0.292936 | + | 0.956132i | \(0.405368\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.5605 | 0.727217 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.6924 | −0.831907 | −0.415954 | − | 0.909386i | \(-0.636552\pi\) | ||||
−0.415954 | + | 0.909386i | \(0.636552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −14.7443 | −0.496185 | −0.248092 | − | 0.968736i | \(-0.579804\pi\) | ||||
−0.248092 | + | 0.968736i | \(0.579804\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −26.0376 | −0.875243 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.0908 | 0.741737 | 0.370869 | − | 0.928685i | \(-0.379060\pi\) | ||||
0.370869 | + | 0.928685i | \(0.379060\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 89.2448 | 2.99318 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.48921 | 0.0833917 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.28504 | 0.210321 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.3848 | 0.681389 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.1309 | −0.338261 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.29823 | 0.0766503 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.3165 | 1.67629 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.5029 | −0.549183 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.80775 | 0.259539 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.1803 | 1.23455 | 0.617275 | − | 0.786747i | \(-0.288236\pi\) | ||||
0.617275 | + | 0.786747i | \(0.288236\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.4639 | −0.579240 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.79211 | −0.225033 | −0.112516 | − | 0.993650i | \(-0.535891\pi\) | ||||
−0.112516 | + | 0.993650i | \(0.535891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.37820 | 0.211088 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −34.5808 | −1.14321 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −65.0492 | −2.14811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.7646 | 1.11379 | 0.556896 | − | 0.830582i | \(-0.311992\pi\) | ||||
0.556896 | + | 0.830582i | \(0.311992\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.5740 | 1.04040 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.87838 | 0.160574 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −24.5043 | −0.805696 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.09958 | −0.0361148 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.77431 | 0.156640 | 0.0783200 | − | 0.996928i | \(-0.475044\pi\) | ||||
0.0783200 | + | 0.996928i | \(0.475044\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.9419 | −0.424154 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.73050 | 0.253085 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.1374 | −0.723972 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −52.6610 | −1.72036 | −0.860180 | − | 0.509990i | \(-0.829649\pi\) | ||||
−0.860180 | + | 0.509990i | \(0.829649\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.0429 | 0.947781 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6960 | −0.870264 | −0.435132 | − | 0.900367i | \(-0.643298\pi\) | ||||
−0.435132 | + | 0.900367i | \(0.643298\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.6167 | −1.35523 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −70.0053 | −2.27727 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −49.0764 | −1.59477 | −0.797384 | − | 0.603472i | \(-0.793783\pi\) | ||||
−0.797384 | + | 0.603472i | \(0.793783\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.94119 | 0.192859 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.3048 | −0.561146 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −47.8969 | −1.55153 | −0.775767 | − | 0.631020i | \(-0.782637\pi\) | ||||
−0.775767 | + | 0.631020i | \(0.782637\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −39.6261 | −1.28227 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.31890 | −0.0749594 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12.9394 | 0.417834 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4872 | −0.951200 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.54459 | −0.0497736 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.2228 | −0.618803 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.0737 | 1.06358 | 0.531789 | − | 0.846877i | \(-0.321520\pi\) | ||||
0.531789 | + | 0.846877i | \(0.321520\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.69975 | −0.311601 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.21427 | 0.0710593 | 0.0355296 | − | 0.999369i | \(-0.488688\pi\) | ||||
0.0355296 | + | 0.999369i | \(0.488688\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −81.4527 | −2.61125 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.03573 | 0.257349 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.6454 | −1.04442 | −0.522210 | − | 0.852817i | \(-0.674892\pi\) | ||||
−0.522210 | + | 0.852817i | \(0.674892\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.65892 | −0.0530193 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.3685 | −0.331042 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 47.4633 | 1.51385 | 0.756923 | − | 0.653505i | \(-0.226702\pi\) | ||||
0.756923 | + | 0.653505i | \(0.226702\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.66075 | −0.180366 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −34.8314 | −1.10870 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.3460 | 0.360781 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.0157 | −1.39821 | −0.699103 | − | 0.715021i | \(-0.746417\pi\) | ||||
−0.699103 | + | 0.715021i | \(0.746417\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.1242 | −0.353015 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.71305 | −0.117712 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.1273 | 0.764120 | 0.382060 | − | 0.924138i | \(-0.375215\pi\) | ||||
0.382060 | + | 0.924138i | \(0.375215\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 44.8769 | 1.41984 |
(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 | 3344.2.a.x.1.4 | 6 | ||
4.3 | odd | 2 | 836.2.a.d.1.3 | ✓ | 6 | ||
12.11 | even | 2 | 7524.2.a.r.1.2 | 6 | |||
44.43 | even | 2 | 9196.2.a.k.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
836.2.a.d.1.3 | ✓ | 6 | 4.3 | odd | 2 | ||
3344.2.a.x.1.4 | 6 | 1.1 | even | 1 | trivial | ||
7524.2.a.r.1.2 | 6 | 12.11 | even | 2 | |||
9196.2.a.k.1.3 | 6 | 44.43 | even | 2 |