Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 13x^{6} + 24x^{5} + 48x^{4} - 68x^{3} - 62x^{2} + 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.932340\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 0.579017 | 0.334296 | 0.167148 | − | 0.985932i | \(-0.446544\pi\) | ||||
0.167148 | + | 0.985932i | \(0.446544\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.10882 | −0.943091 | −0.471546 | − | 0.881842i | \(-0.656304\pi\) | ||||
−0.471546 | + | 0.881842i | \(0.656304\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.73436 | −1.03349 | −0.516745 | − | 0.856140i | \(-0.672856\pi\) | ||||
−0.516745 | + | 0.856140i | \(0.672856\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.66474 | −0.888246 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.66474 | −1.40647 | −0.703236 | − | 0.710957i | \(-0.748262\pi\) | ||||
−0.703236 | + | 0.710957i | \(0.748262\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.47791 | −1.24195 | −0.620974 | − | 0.783831i | \(-0.713263\pi\) | ||||
−0.620974 | + | 0.783831i | \(0.713263\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.22104 | −0.315271 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.85237 | −1.66194 | −0.830972 | − | 0.556314i | \(-0.812215\pi\) | ||||
−0.830972 | + | 0.556314i | \(0.812215\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.58324 | −0.345491 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.20416 | −0.251085 | −0.125543 | − | 0.992088i | \(-0.540067\pi\) | ||||
−0.125543 | + | 0.992088i | \(0.540067\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.552894 | −0.110579 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.27998 | −0.631233 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.57484 | 1.77800 | 0.889002 | − | 0.457904i | \(-0.151400\pi\) | ||||
0.889002 | + | 0.457904i | \(0.151400\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.35842 | 0.962400 | 0.481200 | − | 0.876611i | \(-0.340201\pi\) | ||||
0.481200 | + | 0.876611i | \(0.340201\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.70096 | −0.470178 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.76625 | 0.974675 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.09693 | 0.180335 | 0.0901674 | − | 0.995927i | \(-0.471260\pi\) | ||||
0.0901674 | + | 0.995927i | \(0.471260\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.59279 | −0.415178 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.33797 | −1.14600 | −0.573000 | − | 0.819556i | \(-0.694220\pi\) | ||||
−0.573000 | + | 0.819556i | \(0.694220\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.64408 | −1.16571 | −0.582856 | − | 0.812576i | \(-0.698065\pi\) | ||||
−0.582856 | + | 0.812576i | \(0.698065\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.61945 | 0.837697 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.56486 | −1.10345 | −0.551724 | − | 0.834027i | \(-0.686030\pi\) | ||||
−0.551724 | + | 0.834027i | \(0.686030\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.476702 | 0.0681003 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.96764 | −0.555581 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.11949 | 0.428495 | 0.214248 | − | 0.976779i | \(-0.431270\pi\) | ||||
0.214248 | + | 0.976779i | \(0.431270\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.83708 | 1.32643 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.579017 | −0.0766927 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.2442 | 1.33368 | 0.666840 | − | 0.745201i | \(-0.267646\pi\) | ||||
0.666840 | + | 0.745201i | \(0.267646\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.722061 | −0.0924504 | −0.0462252 | − | 0.998931i | \(-0.514719\pi\) | ||||
−0.0462252 | + | 0.998931i | \(0.514719\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.28634 | 0.917993 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.44309 | 1.17127 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.13698 | −0.749752 | −0.374876 | − | 0.927075i | \(-0.622315\pi\) | ||||
−0.374876 | + | 0.927075i | \(0.622315\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.697232 | −0.0839368 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.62247 | 0.548587 | 0.274293 | − | 0.961646i | \(-0.411556\pi\) | ||||
0.274293 | + | 0.961646i | \(0.411556\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.19270 | 0.724801 | 0.362400 | − | 0.932022i | \(-0.381957\pi\) | ||||
0.362400 | + | 0.932022i | \(0.381957\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.320135 | −0.0369660 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.7551 | 1.45357 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.26723 | 0.367592 | 0.183796 | − | 0.982964i | \(-0.441161\pi\) | ||||
0.183796 | + | 0.982964i | \(0.441161\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.09505 | 0.677228 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.97934 | −0.985611 | −0.492805 | − | 0.870140i | \(-0.664029\pi\) | ||||
−0.492805 | + | 0.870140i | \(0.664029\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4504 | 1.56736 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.54400 | 0.594379 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.620707 | −0.0657948 | −0.0328974 | − | 0.999459i | \(-0.510473\pi\) | ||||
−0.0328974 | + | 0.999459i | \(0.510473\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2442 | 1.28354 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.10262 | 0.321726 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.10882 | 0.216360 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.67284 | −0.169851 | −0.0849257 | − | 0.996387i | \(-0.527065\pi\) | ||||
−0.0849257 | + | 0.996387i | \(0.527065\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.4303 | 1.24929 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.30571 | 0.726946 | 0.363473 | − | 0.931605i | \(-0.381591\pi\) | ||||
0.363473 | + | 0.931605i | \(0.381591\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.77332 | −0.864461 | −0.432231 | − | 0.901763i | \(-0.642273\pi\) | ||||
−0.432231 | + | 0.901763i | \(0.642273\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.33876 | 0.325830 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.91355 | 0.958379 | 0.479190 | − | 0.877711i | \(-0.340931\pi\) | ||||
0.479190 | + | 0.877711i | \(0.340931\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.84589 | −0.272587 | −0.136293 | − | 0.990669i | \(-0.543519\pi\) | ||||
−0.136293 | + | 0.990669i | \(0.543519\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.635143 | 0.0602851 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.58487 | −0.149092 | −0.0745462 | − | 0.997218i | \(-0.523751\pi\) | ||||
−0.0745462 | + | 0.997218i | \(0.523751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.53936 | 0.236797 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.9325 | 1.10316 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18.7368 | 1.71760 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.7598 | 0.978163 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.24881 | −0.383103 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7100 | 1.04738 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.2933 | −1.26833 | −0.634163 | − | 0.773199i | \(-0.718655\pi\) | ||||
−0.634163 | + | 0.773199i | \(0.718655\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.42605 | −0.389692 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.609006 | −0.0532091 | −0.0266046 | − | 0.999646i | \(-0.508469\pi\) | ||||
−0.0266046 | + | 0.999646i | \(0.508469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.73436 | 0.237099 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.91688 | 0.595310 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.1589 | −1.55142 | −0.775710 | − | 0.631089i | \(-0.782608\pi\) | ||||
−0.775710 | + | 0.631089i | \(0.782608\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.93421 | −0.164058 | −0.0820289 | − | 0.996630i | \(-0.526140\pi\) | ||||
−0.0820289 | + | 0.996630i | \(0.526140\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.38018 | −0.368878 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.8883 | 1.74677 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.1916 | −1.67682 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.276019 | 0.0227656 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.5775 | 1.27616 | 0.638080 | − | 0.769970i | \(-0.279729\pi\) | ||||
0.638080 | + | 0.769970i | \(0.279729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.9746 | −1.62551 | −0.812756 | − | 0.582605i | \(-0.802034\pi\) | ||||
−0.812756 | + | 0.582605i | \(0.802034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.2598 | 1.47622 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.2999 | −0.907631 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.8872 | −1.66698 | −0.833489 | − | 0.552536i | \(-0.813660\pi\) | ||||
−0.833489 | + | 0.552536i | \(0.813660\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.80624 | 0.143244 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.29261 | 0.259494 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.54835 | 0.199602 | 0.0998010 | − | 0.995007i | \(-0.468179\pi\) | ||||
0.0998010 | + | 0.995007i | \(0.468179\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.69584 | 0.443420 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.6644 | −1.44429 | −0.722146 | − | 0.691740i | \(-0.756844\pi\) | ||||
−0.722146 | + | 0.691740i | \(0.756844\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.05167 | 0.542436 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.66474 | 0.203778 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.42370 | −0.640442 | −0.320221 | − | 0.947343i | \(-0.603757\pi\) | ||||
−0.320221 | + | 0.947343i | \(0.603757\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.51181 | 0.114282 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.93157 | 0.445844 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.6809 | −1.24679 | −0.623394 | − | 0.781908i | \(-0.714247\pi\) | ||||
−0.623394 | + | 0.781908i | \(0.714247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.65888 | 0.346292 | 0.173146 | − | 0.984896i | \(-0.444607\pi\) | ||||
0.173146 | + | 0.984896i | \(0.444607\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.418086 | −0.0309058 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.31323 | −0.170072 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 31.9645 | 2.33748 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.96864 | 0.652372 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.0609 | −1.45155 | −0.725777 | − | 0.687930i | \(-0.758520\pi\) | ||||
−0.725777 | + | 0.687930i | \(0.758520\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.85117 | 0.133250 | 0.0666251 | − | 0.997778i | \(-0.478777\pi\) | ||||
0.0666251 | + | 0.997778i | \(0.478777\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.46771 | 0.391551 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.224883 | 0.0160222 | 0.00801112 | − | 0.999968i | \(-0.497450\pi\) | ||||
0.00801112 | + | 0.999968i | \(0.497450\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.77685 | −0.125957 | −0.0629787 | − | 0.998015i | \(-0.520060\pi\) | ||||
−0.0629787 | + | 0.998015i | \(0.520060\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.55342 | −0.250639 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26.1810 | −1.83755 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.4744 | 1.08078 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.20878 | 0.223026 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.66474 | 0.322667 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.0194 | 1.17166 | 0.585831 | − | 0.810433i | \(-0.300768\pi\) | ||||
0.585831 | + | 0.810433i | \(0.300768\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.67649 | 0.183390 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 16.1200 | 1.09937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.6518 | −0.994630 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.58568 | 0.242298 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.6843 | 2.06405 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6634 | −0.914971 | −0.457486 | − | 0.889217i | \(-0.651250\pi\) | ||||
−0.457486 | + | 0.889217i | \(0.651250\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.47332 | 0.0982212 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.46152 | −0.362494 | −0.181247 | − | 0.983438i | \(-0.558013\pi\) | ||||
−0.181247 | + | 0.983438i | \(0.558013\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.22791 | 0.213306 | 0.106653 | − | 0.994296i | \(-0.465987\pi\) | ||||
0.106653 | + | 0.994296i | \(0.465987\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.38540 | 0.485923 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.8344 | 1.16837 | 0.584185 | − | 0.811621i | \(-0.301414\pi\) | ||||
0.584185 | + | 0.811621i | \(0.301414\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.9529 | 1.04065 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.89178 | 0.122884 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.82556 | −0.118086 | −0.0590428 | − | 0.998255i | \(-0.518805\pi\) | ||||
−0.0590428 | + | 0.998255i | \(0.518805\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.47608 | 0.417161 | 0.208581 | − | 0.978005i | \(-0.433116\pi\) | ||||
0.208581 | + | 0.978005i | \(0.433116\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.3691 | 0.857627 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00528 | −0.0642248 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.47791 | 0.284923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.19919 | −0.329485 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.10899 | −0.196238 | −0.0981189 | − | 0.995175i | \(-0.531283\pi\) | ||||
−0.0981189 | + | 0.995175i | \(0.531283\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.61711 | 0.353145 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.36702 | 0.523963 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.75606 | 0.359053 | 0.179526 | − | 0.983753i | \(-0.442543\pi\) | ||||
0.179526 | + | 0.983753i | \(0.442543\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.99941 | −0.186374 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −25.5145 | −1.57931 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.58595 | −0.282782 | −0.141391 | − | 0.989954i | \(-0.545157\pi\) | ||||
−0.141391 | + | 0.989954i | \(0.545157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.57844 | −0.404110 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.359400 | −0.0219949 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.3913 | 0.694542 | 0.347271 | − | 0.937765i | \(-0.387108\pi\) | ||||
0.347271 | + | 0.937765i | \(0.387108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.1252 | −1.52625 | −0.763124 | − | 0.646252i | \(-0.776336\pi\) | ||||
−0.763124 | + | 0.646252i | \(0.776336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.08960 | 0.429082 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.57910 | 0.155526 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.2998 | 1.09953 | 0.549763 | − | 0.835321i | \(-0.314718\pi\) | ||||
0.549763 | + | 0.835321i | \(0.314718\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.2788 | −0.854848 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0708 | 1.07802 | 0.539008 | − | 0.842301i | \(-0.318799\pi\) | ||||
0.539008 | + | 0.842301i | \(0.318799\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.3972 | −0.915269 | −0.457634 | − | 0.889140i | \(-0.651303\pi\) | ||||
−0.457634 | + | 0.889140i | \(0.651303\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.22104 | 0.0723282 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0646 | 1.18438 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.9550 | 1.76206 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.968605 | −0.0567806 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.4407 | 0.668374 | 0.334187 | − | 0.942507i | \(-0.391538\pi\) | ||||
0.334187 | + | 0.942507i | \(0.391538\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.6031 | −1.25778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.3003 | 0.887811 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.39214 | 0.311835 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.9016 | 1.20475 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.23013 | 0.243015 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.52269 | 0.0871892 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.3453 | −1.21824 | −0.609122 | − | 0.793077i | \(-0.708478\pi\) | ||||
−0.609122 | + | 0.793077i | \(0.708478\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.07991 | −0.288986 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.7295 | −1.23216 | −0.616082 | − | 0.787682i | \(-0.711281\pi\) | ||||
−0.616082 | + | 0.787682i | \(0.711281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.1009 | −1.92750 | −0.963748 | − | 0.266814i | \(-0.914029\pi\) | ||||
−0.963748 | + | 0.266814i | \(0.914029\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −15.3656 | −0.865751 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.2281 | 1.24845 | 0.624226 | − | 0.781244i | \(-0.285414\pi\) | ||||
0.624226 | + | 0.781244i | \(0.285414\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −44.6641 | −2.50071 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.74012 | 0.320382 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.85237 | 0.381276 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.47581 | 0.137333 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.64782 | −0.0911245 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.6850 | 1.14040 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.1969 | −1.32998 | −0.664991 | − | 0.746852i | \(-0.731564\pi\) | ||||
−0.664991 | + | 0.746852i | \(0.731564\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.92304 | −0.160182 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.9418 | 0.707084 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −34.2735 | −1.86700 | −0.933498 | − | 0.358583i | \(-0.883260\pi\) | ||||
−0.933498 | + | 0.358583i | \(0.883260\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.917670 | −0.0498410 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.9956 | −1.35359 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8370 | 0.963108 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.47033 | 0.0791601 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.9233 | −1.44532 | −0.722658 | − | 0.691206i | \(-0.757080\pi\) | ||||
−0.722658 | + | 0.691206i | \(0.757080\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.65769 | −0.463436 | −0.231718 | − | 0.972783i | \(-0.574435\pi\) | ||||
−0.231718 | + | 0.972783i | \(0.574435\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.6875 | 0.783959 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9.11265 | −0.485018 | −0.242509 | − | 0.970149i | \(-0.577970\pi\) | ||||
−0.242509 | + | 0.970149i | \(0.577970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.74795 | −0.517367 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.8489 | 0.574187 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.29978 | 0.226934 | 0.113467 | − | 0.993542i | \(-0.463804\pi\) | ||||
0.113467 | + | 0.993542i | \(0.463804\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.23010 | 0.326996 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.0593 | −0.683553 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.2873 | 1.11119 | 0.555594 | − | 0.831454i | \(-0.312491\pi\) | ||||
0.555594 | + | 0.831454i | \(0.312491\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.5538 | 1.01793 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.52980 | −0.442845 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1076 | −0.575129 | −0.287565 | − | 0.957761i | \(-0.592846\pi\) | ||||
−0.287565 | + | 0.957761i | \(0.592846\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.78031 | 0.350134 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −42.8753 | −2.20819 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.6908 | 1.06281 | 0.531407 | − | 0.847117i | \(-0.321664\pi\) | ||||
0.531407 | + | 0.847117i | \(0.321664\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.27608 | −0.423996 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.1869 | 0.622720 | 0.311360 | − | 0.950292i | \(-0.399215\pi\) | ||||
0.311360 | + | 0.950292i | \(0.399215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −26.8981 | −1.37085 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.3695 | 1.03544 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.1769 | 1.32722 | 0.663611 | − | 0.748078i | \(-0.269023\pi\) | ||||
0.663611 | + | 0.748078i | \(0.269023\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.25137 | 0.417290 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.352625 | −0.0177876 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.88999 | −0.346673 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.8451 | 0.745055 | 0.372528 | − | 0.928021i | \(-0.378491\pi\) | ||||
0.372528 | + | 0.928021i | \(0.378491\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.58324 | 0.0792611 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.4111 | 1.71841 | 0.859205 | − | 0.511632i | \(-0.170959\pi\) | ||||
0.859205 | + | 0.511632i | \(0.170959\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −23.9945 | −1.19525 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −12.8533 | −0.638688 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.11691 | −0.253636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.43283 | −0.0708487 | −0.0354243 | − | 0.999372i | \(-0.511278\pi\) | ||||
−0.0354243 | + | 0.999372i | \(0.511278\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.5143 | −0.518633 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.0113 | −1.37834 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.9358 | 0.929521 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.11994 | −0.0548438 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.6886 | 1.64579 | 0.822897 | − | 0.568190i | \(-0.192356\pi\) | ||||
0.822897 | + | 0.568190i | \(0.192356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.237430 | 0.0115716 | 0.00578582 | − | 0.999983i | \(-0.498158\pi\) | ||||
0.00578582 | + | 0.999983i | \(0.498158\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 20.1584 | 0.980134 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.78863 | 0.183776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.97437 | 0.0955465 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.0947 | 0.583936 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0743 | −0.629766 | −0.314883 | − | 0.949130i | \(-0.601965\pi\) | ||||
−0.314883 | + | 0.949130i | \(0.601965\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.67718 | −0.465056 | −0.232528 | − | 0.972590i | \(-0.574700\pi\) | ||||
−0.232528 | + | 0.972590i | \(0.574700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.6913 | −0.560554 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.20416 | 0.0576030 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.7983 | 0.849468 | 0.424734 | − | 0.905318i | \(-0.360368\pi\) | ||||
0.424734 | + | 0.905318i | \(0.360368\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.27029 | −0.0604898 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.30468 | 0.157010 | 0.0785050 | − | 0.996914i | \(-0.474985\pi\) | ||||
0.0785050 | + | 0.996914i | \(0.474985\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.30896 | 0.0620505 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.01966 | 0.426615 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.6543 | −1.39947 | −0.699735 | − | 0.714402i | \(-0.746699\pi\) | ||||
−0.699735 | + | 0.714402i | \(0.746699\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 34.2297 | 1.61182 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −11.5656 | −0.543402 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25.8208 | −1.21050 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.2310 | 0.946368 | 0.473184 | − | 0.880964i | \(-0.343105\pi\) | ||||
0.473184 | + | 0.880964i | \(0.343105\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 22.4756 | 1.04907 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 41.2429 | 1.92087 | 0.960436 | − | 0.278502i | \(-0.0898377\pi\) | ||||
0.960436 | + | 0.278502i | \(0.0898377\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.5232 | 0.767896 | 0.383948 | − | 0.923355i | \(-0.374564\pi\) | ||||
0.383948 | + | 0.923355i | \(0.374564\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.54285 | −0.303417 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.9967 | −1.15671 | −0.578355 | − | 0.815786i | \(-0.696305\pi\) | ||||
−0.578355 | + | 0.815786i | \(0.696305\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.7807 | 0.774860 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.0940 | −0.557264 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.6576 | 1.63954 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.552894 | 0.0253685 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.31263 | −0.380609 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.0298 | −0.458273 | −0.229137 | − | 0.973394i | \(-0.573590\pi\) | ||||
−0.229137 | + | 0.973394i | \(0.573590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.91197 | −0.223966 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.90648 | 0.0867478 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.52772 | 0.160185 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.6248 | 1.88620 | 0.943101 | − | 0.332508i | \(-0.107895\pi\) | ||||
0.943101 | + | 0.332508i | \(0.107895\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.47554 | 0.0667261 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.6939 | −1.56572 | −0.782858 | − | 0.622200i | \(-0.786239\pi\) | ||||
−0.782858 | + | 0.622200i | \(0.786239\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −65.6104 | −2.95494 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −26.2132 | −1.17820 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.6395 | −0.566959 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.1270 | −0.632413 | −0.316207 | − | 0.948690i | \(-0.602409\pi\) | ||||
−0.316207 | + | 0.948690i | \(0.602409\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.8070 | −0.482821 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.01157 | 0.134279 | 0.0671395 | − | 0.997744i | \(-0.478613\pi\) | ||||
0.0671395 | + | 0.997744i | \(0.478613\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.4064 | −0.685576 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.08304 | 0.181334 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.38122 | 0.105546 | 0.0527730 | − | 0.998607i | \(-0.483194\pi\) | ||||
0.0527730 | + | 0.998607i | \(0.483194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.9330 | −0.749074 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.27998 | 0.144815 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.5013 | 0.815266 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 35.2881 | 1.55197 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.87747 | −0.214097 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.9133 | −0.784798 | −0.392399 | − | 0.919795i | \(-0.628355\pi\) | ||||
−0.392399 | + | 0.919795i | \(0.628355\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.9602 | 0.829071 | 0.414536 | − | 0.910033i | \(-0.363944\pi\) | ||||
0.414536 | + | 0.910033i | \(0.363944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.875363 | 0.0382040 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −36.7178 | −1.59945 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.5500 | −0.936956 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.2981 | −1.18464 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.8588 | 1.42327 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.9059 | −0.903839 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.65852 | −0.416796 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.22369 | −0.0957811 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.2027 | 1.47049 | 0.735245 | − | 0.677802i | \(-0.237067\pi\) | ||||
0.735245 | + | 0.677802i | \(0.237067\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.69757 | 0.115764 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00145 | 0.257074 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.645113 | −0.0275830 | −0.0137915 | − | 0.999905i | \(-0.504390\pi\) | ||||
−0.0137915 | + | 0.999905i | \(0.504390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.92410 | 0.0821187 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.57484 | −0.407902 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.93377 | −0.379903 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.33940 | −0.0568544 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.2596 | −0.434714 | −0.217357 | − | 0.976092i | \(-0.569744\pi\) | ||||
−0.217357 | + | 0.976092i | \(0.569744\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.2295 | 1.44775 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.5080 | 0.781409 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −12.9293 | −0.544906 | −0.272453 | − | 0.962169i | \(-0.587835\pi\) | ||||
−0.272453 | + | 0.962169i | \(0.587835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.34221 | 0.140608 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −16.6660 | −0.699908 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.32637 | −0.265215 | −0.132608 | − | 0.991169i | \(-0.542335\pi\) | ||||
−0.132608 | + | 0.991169i | \(0.542335\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.1997 | 1.30566 | 0.652832 | − | 0.757502i | \(-0.273581\pi\) | ||||
0.652832 | + | 0.757502i | \(0.273581\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.6156 | −0.485248 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.665774 | 0.0277647 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.48996 | 0.228550 | 0.114275 | − | 0.993449i | \(-0.463545\pi\) | ||||
0.114275 | + | 0.993449i | \(0.463545\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.07186 | 0.0445450 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.5527 | 1.01862 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14.5516 | −0.602666 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.1634 | −1.04038 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.4576 | 0.720552 | 0.360276 | − | 0.932846i | \(-0.382683\pi\) | ||||
0.360276 | + | 0.932846i | \(0.382683\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.35842 | −0.220790 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.130211 | 0.00535617 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.7657 | −0.688486 | −0.344243 | − | 0.938881i | \(-0.611864\pi\) | ||||
−0.344243 | + | 0.938881i | \(0.611864\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.5125 | −1.61985 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.02883 | −0.0421070 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.357982 | −0.0146267 | −0.00731337 | − | 0.999973i | \(-0.502328\pi\) | ||||
−0.00731337 | + | 0.999973i | \(0.502328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.8949 | −0.933903 | −0.466952 | − | 0.884283i | \(-0.654648\pi\) | ||||
−0.466952 | + | 0.884283i | \(0.654648\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.3535 | 0.665964 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.6904 | −0.922497 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.33917 | −0.0543551 | −0.0271775 | − | 0.999631i | \(-0.508652\pi\) | ||||
−0.0271775 | + | 0.999631i | \(0.508652\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.1593 | −0.614284 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 33.8747 | 1.37043 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.8667 | −1.20631 | −0.603153 | − | 0.797625i | \(-0.706089\pi\) | ||||
−0.603153 | + | 0.797625i | \(0.706089\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.95997 | 0.361301 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.4935 | 1.46917 | 0.734587 | − | 0.678514i | \(-0.237376\pi\) | ||||
0.734587 | + | 0.678514i | \(0.237376\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.88669 | 0.357186 | 0.178593 | − | 0.983923i | \(-0.442845\pi\) | ||||
0.178593 | + | 0.983923i | \(0.442845\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.94963 | 0.158493 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.69723 | 0.0679982 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.9298 | −0.877194 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.70096 | 0.107866 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.51659 | −0.299706 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.1724 | −1.12153 | −0.560763 | − | 0.827977i | \(-0.689492\pi\) | ||||
−0.560763 | + | 0.827977i | \(0.689492\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.85452 | 0.391682 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.1420 | 1.19615 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.13463 | −0.0845771 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.3177 | −0.487280 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.58435 | 0.141573 | 0.0707867 | − | 0.997491i | \(-0.477449\pi\) | ||||
0.0707867 | + | 0.997491i | \(0.477449\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.8837 | 0.784137 | 0.392069 | − | 0.919936i | \(-0.371760\pi\) | ||||
0.392069 | + | 0.919936i | \(0.371760\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.33373 | 0.367515 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.7712 | 1.40631 | 0.703156 | − | 0.711036i | \(-0.251774\pi\) | ||||
0.703156 | + | 0.711036i | \(0.251774\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.7865 | −1.87578 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.48365 | −0.332501 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.57378 | 0.335518 | 0.167759 | − | 0.985828i | \(-0.446347\pi\) | ||||
0.167759 | + | 0.985828i | \(0.446347\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.28428 | 0.0501810 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.5019 | −0.643802 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.9993 | −0.895927 | −0.447964 | − | 0.894052i | \(-0.647851\pi\) | ||||
−0.447964 | + | 0.894052i | \(0.647851\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.4720 | −1.10743 | −0.553716 | − | 0.832706i | \(-0.686791\pi\) | ||||
−0.553716 | + | 0.832706i | \(0.686791\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.7667 | 0.690003 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.76625 | −0.223606 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.5297 | −0.446431 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.91136 | −0.305871 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.36822 | 0.130029 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.63685 | 0.255832 | 0.127916 | − | 0.991785i | \(-0.459171\pi\) | ||||
0.127916 | + | 0.991785i | \(0.459171\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.81348 | 0.0698009 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.0823 | 1.11772 | 0.558862 | − | 0.829261i | \(-0.311238\pi\) | ||||
0.558862 | + | 0.829261i | \(0.311238\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.57415 | 0.175540 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.16231 | −0.121180 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.63939 | −0.177521 | −0.0887607 | − | 0.996053i | \(-0.528291\pi\) | ||||
−0.0887607 | + | 0.996053i | \(0.528291\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.2938 | 1.46313 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.86902 | 0.0713074 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.9688 | −0.532169 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.11245 | 0.194487 | 0.0972434 | − | 0.995261i | \(-0.468997\pi\) | ||||
0.0972434 | + | 0.995261i | \(0.468997\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −33.9889 | −1.29113 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.07890 | 0.154721 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 50.2825 | 1.90459 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.3264 | 0.390581 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.27938 | −0.199399 | −0.0996997 | − | 0.995018i | \(-0.531788\pi\) | ||||
−0.0996997 | + | 0.995018i | \(0.531788\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.09693 | −0.0413716 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.23700 | 0.347886 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.9764 | −0.751290 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.1441 | −1.05697 | −0.528486 | − | 0.848942i | \(-0.677240\pi\) | ||||
−0.528486 | + | 0.848942i | \(0.677240\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.70632 | −0.326512 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.45241 | −0.241645 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −44.0495 | −1.64736 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.05703 | −0.0394755 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.51160 | −0.354723 | −0.177361 | − | 0.984146i | \(-0.556756\pi\) | ||||
−0.177361 | + | 0.984146i | \(0.556756\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.9894 | 0.893412 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.74976 | 0.139455 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.29387 | −0.196609 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.06196 | 0.261914 | 0.130957 | − | 0.991388i | \(-0.458195\pi\) | ||||
0.130957 | + | 0.991388i | \(0.458195\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.5442 | −0.390527 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 52.3801 | 1.93735 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.62443 | −0.281615 | −0.140807 | − | 0.990037i | \(-0.544970\pi\) | ||||
−0.140807 | + | 0.990037i | \(0.544970\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.582073 | −0.0214701 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.6274 | 1.05450 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.0131 | 1.65583 | 0.827917 | − | 0.560851i | \(-0.189526\pi\) | ||||
0.827917 | + | 0.560851i | \(0.189526\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.59279 | 0.0952484 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.3137 | 0.561805 | 0.280903 | − | 0.959736i | \(-0.409366\pi\) | ||||
0.280903 | + | 0.959736i | \(0.409366\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.8501 | −1.20354 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 23.9276 | 0.875465 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −27.1072 | −0.990475 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.09580 | −0.149458 | −0.0747290 | − | 0.997204i | \(-0.523809\pi\) | ||||
−0.0747290 | + | 0.997204i | \(0.523809\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.80016 | −0.0656015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42.1228 | 1.53301 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.51720 | −0.345909 | −0.172954 | − | 0.984930i | \(-0.555331\pi\) | ||||
−0.172954 | + | 0.984930i | \(0.555331\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.25240 | 0.118055 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 38.4841 | 1.39505 | 0.697523 | − | 0.716562i | \(-0.254285\pi\) | ||||
0.697523 | + | 0.716562i | \(0.254285\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.78167 | 0.281715 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −38.5065 | −1.39221 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45.8726 | −1.65636 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0210 | 0.541670 | 0.270835 | − | 0.962626i | \(-0.412700\pi\) | ||||
0.270835 | + | 0.962626i | \(0.412700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.33286 | 0.120030 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −38.4471 | −1.38285 | −0.691423 | − | 0.722451i | \(-0.743016\pi\) | ||||
−0.691423 | + | 0.722451i | \(0.743016\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.96263 | −0.106421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.73671 | −0.0623040 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.33797 | 0.262910 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −21.5626 | −0.771572 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −31.4053 | −1.12233 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 44.0472 | 1.57211 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.8457 | −1.09953 | −0.549765 | − | 0.835319i | \(-0.685283\pi\) | ||||
−0.549765 | + | 0.835319i | \(0.685283\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.65535 | −0.0945328 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.33361 | 0.154085 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.23332 | 0.114819 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.80903 | −0.135092 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 34.1285 | 1.20889 | 0.604446 | − | 0.796646i | \(-0.293394\pi\) | ||||
0.604446 | + | 0.796646i | \(0.293394\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.8372 | 1.83387 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.65402 | 0.0584420 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.8873 | −1.01941 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.94351 | −0.244727 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.59578 | 0.232182 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.9170 | 0.911192 | 0.455596 | − | 0.890187i | \(-0.349426\pi\) | ||||
0.455596 | + | 0.890187i | \(0.349426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.7874 | −1.18644 | −0.593219 | − | 0.805041i | \(-0.702143\pi\) | ||||
−0.593219 | + | 0.805041i | \(0.702143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14.5479 | −0.510218 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.37400 | −0.188243 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.64408 | 0.267432 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −32.6276 | −1.14010 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.6475 | −0.964903 | −0.482451 | − | 0.875923i | \(-0.660254\pi\) | ||||
−0.482451 | + | 0.875923i | \(0.660254\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.4983 | −0.435665 | −0.217832 | − | 0.975986i | \(-0.569899\pi\) | ||||
−0.217832 | + | 0.975986i | \(0.569899\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.49335 | 0.0519916 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.03084 | −0.314033 | −0.157017 | − | 0.987596i | \(-0.550188\pi\) | ||||
−0.157017 | + | 0.987596i | \(0.550188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −55.7684 | −1.93692 | −0.968458 | − | 0.249175i | \(-0.919841\pi\) | ||||
−0.968458 | + | 0.249175i | \(0.919841\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.5959 | 0.367567 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.26654 | −0.113179 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.3597 | 1.36210 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.5755 | −0.607498 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.3128 | −0.494134 | −0.247067 | − | 0.968998i | \(-0.579467\pi\) | ||||
−0.247067 | + | 0.968998i | \(0.579467\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.6776 | 2.16130 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.4633 | 0.360376 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.8707 | −0.511567 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29.4211 | −1.01092 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.91525 | −0.305971 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.32089 | −0.0452794 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −38.0325 | −1.30221 | −0.651105 | − | 0.758988i | \(-0.725694\pi\) | ||||
−0.651105 | + | 0.758988i | \(0.725694\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.61945 | −0.192181 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.1869 | 0.792048 | 0.396024 | − | 0.918240i | \(-0.370390\pi\) | ||||
0.396024 | + | 0.918240i | \(0.370390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.5870 | −1.58953 | −0.794764 | − | 0.606919i | \(-0.792405\pi\) | ||||
−0.794764 | + | 0.606919i | \(0.792405\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.6178 | 0.395933 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.3149 | 1.84890 | 0.924451 | − | 0.381301i | \(-0.124524\pi\) | ||||
0.924451 | + | 0.381301i | \(0.124524\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 17.7640 | 0.603995 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.3444 | 0.589048 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.2408 | −0.517008 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.4808 | 0.931153 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.45769 | 0.150870 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −32.0194 | −1.08245 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.80324 | −0.0608910 | −0.0304455 | − | 0.999536i | \(-0.509693\pi\) | ||||
−0.0304455 | + | 0.999536i | \(0.509693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.62438 | 0.223435 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.6372 | 0.425759 | 0.212880 | − | 0.977078i | \(-0.431716\pi\) | ||||
0.212880 | + | 0.977078i | \(0.431716\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.9276 | 1.34367 | 0.671835 | − | 0.740700i | \(-0.265506\pi\) | ||||
0.671835 | + | 0.740700i | \(0.265506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.5086 | −0.420471 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.3642 | −0.482304 | −0.241152 | − | 0.970487i | \(-0.577525\pi\) | ||||
−0.241152 | + | 0.970487i | \(0.577525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 39.0830 | 1.31080 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −28.4318 | −0.952502 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.56486 | 0.253148 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.1769 | 1.17584 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.12214 | 0.104245 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 51.3060 | 1.71115 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.3759 | −0.712135 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.1024 | 0.402743 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.82473 | −0.326585 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.32787 | 0.110500 | 0.0552501 | − | 0.998473i | \(-0.482404\pi\) | ||||
0.0552501 | + | 0.998473i | \(0.482404\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −19.4678 | −0.645707 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.8252 | 1.18694 | 0.593471 | − | 0.804855i | \(-0.297757\pi\) | ||||
0.593471 | + | 0.804855i | \(0.297757\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 41.8863 | 1.38623 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.881666 | 0.0291470 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.66524 | 0.0549910 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.3186 | −1.59388 | −0.796942 | − | 0.604055i | \(-0.793551\pi\) | ||||
−0.796942 | + | 0.604055i | \(0.793551\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.3593 | −0.407254 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −20.6990 | −0.681316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.606487 | −0.0199412 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23.3786 | 0.767855 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.2127 | −0.761585 | −0.380792 | − | 0.924661i | \(-0.624349\pi\) | ||||
−0.380792 | + | 0.924661i | \(0.624349\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.476702 | −0.0156233 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.5817 | −0.411908 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −67.4073 | −2.20445 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.10467 | −0.232099 | −0.116050 | − | 0.993243i | \(-0.537023\pi\) | ||||
−0.116050 | + | 0.993243i | \(0.537023\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.7450 | −0.644354 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −55.5352 | −1.81040 | −0.905199 | − | 0.424989i | \(-0.860278\pi\) | ||||
−0.905199 | + | 0.424989i | \(0.860278\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.83612 | 0.287744 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.9132 | −0.615247 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.5988 | −0.506894 | −0.253447 | − | 0.967349i | \(-0.581564\pi\) | ||||
−0.253447 | + | 0.967349i | \(0.581564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.7304 | −0.900165 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.8704 | 0.417352 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.1243 | −0.684282 | −0.342141 | − | 0.939649i | \(-0.611152\pi\) | ||||
−0.342141 | + | 0.939649i | \(0.611152\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.3047 | 1.36895 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25.8613 | −0.835977 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.6529 | 1.60338 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.28738 | −0.0737863 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −26.4170 | −0.851277 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.90378 | −0.125667 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.1207 | 1.48314 | 0.741570 | − | 0.670875i | \(-0.234081\pi\) | ||||
0.741570 | + | 0.670875i | \(0.234081\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.96764 | 0.127459 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.3253 | −0.716454 | −0.358227 | − | 0.933635i | \(-0.616619\pi\) | ||||
−0.358227 | + | 0.933635i | \(0.616619\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.28882 | 0.169552 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.43354 | 0.0459099 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.2650 | 0.456379 | 0.228190 | − | 0.973617i | \(-0.426719\pi\) | ||||
0.228190 | + | 0.973617i | \(0.426719\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.89544 | 0.0925385 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.58355 | 0.242124 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.7242 | 0.405838 | 0.202919 | − | 0.979196i | \(-0.434957\pi\) | ||||
0.202919 | + | 0.979196i | \(0.434957\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.474237 | −0.0151104 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.9770 | 0.381232 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.20472 | 0.292693 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8169 | 0.343611 | 0.171806 | − | 0.985131i | \(-0.445040\pi\) | ||||
0.171806 | + | 0.985131i | \(0.445040\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.0104 | −0.444607 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.74705 | 0.118789 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.39134 | 0.170746 | 0.0853728 | − | 0.996349i | \(-0.472792\pi\) | ||||
0.0853728 | + | 0.996349i | \(0.472792\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.59792 | −0.113833 |
(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 | 4864.2.a.bp.1.5 | 8 | ||
4.3 | odd | 2 | 4864.2.a.bq.1.4 | 8 | |||
8.3 | odd | 2 | 4864.2.a.bo.1.5 | 8 | |||
8.5 | even | 2 | 4864.2.a.bn.1.4 | 8 | |||
16.3 | odd | 4 | 152.2.c.b.77.16 | yes | 16 | ||
16.5 | even | 4 | 608.2.c.b.305.8 | 16 | |||
16.11 | odd | 4 | 152.2.c.b.77.15 | ✓ | 16 | ||
16.13 | even | 4 | 608.2.c.b.305.9 | 16 | |||
48.5 | odd | 4 | 5472.2.g.b.2737.12 | 16 | |||
48.11 | even | 4 | 1368.2.g.b.685.2 | 16 | |||
48.29 | odd | 4 | 5472.2.g.b.2737.5 | 16 | |||
48.35 | even | 4 | 1368.2.g.b.685.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.2.c.b.77.15 | ✓ | 16 | 16.11 | odd | 4 | ||
152.2.c.b.77.16 | yes | 16 | 16.3 | odd | 4 | ||
608.2.c.b.305.8 | 16 | 16.5 | even | 4 | |||
608.2.c.b.305.9 | 16 | 16.13 | even | 4 | |||
1368.2.g.b.685.1 | 16 | 48.35 | even | 4 | |||
1368.2.g.b.685.2 | 16 | 48.11 | even | 4 | |||
4864.2.a.bn.1.4 | 8 | 8.5 | even | 2 | |||
4864.2.a.bo.1.5 | 8 | 8.3 | odd | 2 | |||
4864.2.a.bp.1.5 | 8 | 1.1 | even | 1 | trivial | ||
4864.2.a.bq.1.4 | 8 | 4.3 | odd | 2 | |||
5472.2.g.b.2737.5 | 16 | 48.29 | odd | 4 | |||
5472.2.g.b.2737.12 | 16 | 48.5 | odd | 4 |