Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3072,2,Mod(1,3072)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3072, 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("3072.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3072 = 2^{10} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3072.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: | \(24.5300435009\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 768) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.93185\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3072.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.86370 | −1.72790 | −0.863950 | − | 0.503577i | \(-0.832017\pi\) | ||||
−0.863950 | + | 0.503577i | \(0.832017\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | −0.925820 | −0.462910 | − | 0.886405i | \(-0.653195\pi\) | ||||
−0.462910 | + | 0.886405i | \(0.653195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.46410 | 0.441443 | 0.220722 | − | 0.975337i | \(-0.429159\pi\) | ||||
0.220722 | + | 0.975337i | \(0.429159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.24264 | −1.17670 | −0.588348 | − | 0.808608i | \(-0.700222\pi\) | ||||
−0.588348 | + | 0.808608i | \(0.700222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.86370 | 0.997604 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.46410 | −1.71238 | −0.856191 | − | 0.516659i | \(-0.827175\pi\) | ||||
−0.856191 | + | 0.516659i | \(0.827175\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.44949 | 0.534522 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.82843 | −0.589768 | −0.294884 | − | 0.955533i | \(-0.595281\pi\) | ||||
−0.294884 | + | 0.955533i | \(0.595281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.92820 | 1.98564 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.76268 | −1.62719 | −0.813595 | − | 0.581432i | \(-0.802492\pi\) | ||||
−0.813595 | + | 0.581432i | \(0.802492\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.34847 | −1.31982 | −0.659912 | − | 0.751343i | \(-0.729406\pi\) | ||||
−0.659912 | + | 0.751343i | \(0.729406\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.46410 | −0.254867 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.46410 | 1.59973 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.656339 | −0.107901 | −0.0539507 | − | 0.998544i | \(-0.517181\pi\) | ||||
−0.0539507 | + | 0.998544i | \(0.517181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.24264 | 0.679366 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.53590 | 0.708388 | 0.354194 | − | 0.935172i | \(-0.384755\pi\) | ||||
0.354194 | + | 0.935172i | \(0.384755\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.46410 | 0.528271 | 0.264135 | − | 0.964486i | \(-0.414913\pi\) | ||||
0.264135 | + | 0.964486i | \(0.414913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.86370 | −0.575967 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.46410 | 0.485071 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.62158 | 0.634823 | 0.317411 | − | 0.948288i | \(-0.397186\pi\) | ||||
0.317411 | + | 0.948288i | \(0.397186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.65685 | −0.762770 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.46410 | 0.988644 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.8564 | −1.80395 | −0.901975 | − | 0.431788i | \(-0.857883\pi\) | ||||
−0.901975 | + | 0.431788i | \(0.857883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.656339 | 0.0840356 | 0.0420178 | − | 0.999117i | \(-0.486621\pi\) | ||||
0.0420178 | + | 0.999117i | \(0.486621\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.44949 | −0.308607 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16.3923 | 2.03322 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.9282 | −1.82377 | −0.911885 | − | 0.410445i | \(-0.865373\pi\) | ||||
−0.911885 | + | 0.410445i | \(0.865373\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.82843 | 0.340503 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.41473 | −0.761288 | −0.380644 | − | 0.924722i | \(-0.624298\pi\) | ||||
−0.380644 | + | 0.924722i | \(0.624298\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.92820 | −1.14641 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.58630 | −0.408697 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.44949 | 0.275589 | 0.137795 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137795 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.46410 | −0.599763 | −0.299882 | − | 0.953976i | \(-0.596947\pi\) | ||||
−0.299882 | + | 0.953976i | \(0.596947\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.3843 | 1.45173 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.76268 | 0.939458 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.92820 | −0.522388 | −0.261194 | − | 0.965286i | \(-0.584116\pi\) | ||||
−0.261194 | + | 0.965286i | \(0.584116\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3923 | 1.08941 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.34847 | 0.762001 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 28.8391 | 2.95883 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.07180 | 0.108824 | 0.0544122 | − | 0.998519i | \(-0.482671\pi\) | ||||
0.0544122 | + | 0.998519i | \(0.482671\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.46410 | 0.147148 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.4195 | 1.43480 | 0.717399 | − | 0.696663i | \(-0.245333\pi\) | ||||
0.717399 | + | 0.696663i | \(0.245333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.20736 | 0.316031 | 0.158016 | − | 0.987437i | \(-0.449490\pi\) | ||||
0.158016 | + | 0.987437i | \(0.449490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.46410 | −0.923602 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.00000 | 0.386695 | 0.193347 | − | 0.981130i | \(-0.438066\pi\) | ||||
0.193347 | + | 0.981130i | \(0.438066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.41421 | −0.135457 | −0.0677285 | − | 0.997704i | \(-0.521575\pi\) | ||||
−0.0677285 | + | 0.997704i | \(0.521575\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.656339 | 0.0622969 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 18.0000 | 1.69330 | 0.846649 | − | 0.532152i | \(-0.178617\pi\) | ||||
0.846649 | + | 0.532152i | \(0.178617\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.9282 | 1.01906 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.24264 | −0.392232 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.48528 | 0.777844 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.85641 | −0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.53590 | −0.408988 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −19.0411 | −1.70309 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5211 | −1.28854 | −0.644268 | − | 0.764799i | \(-0.722838\pi\) | ||||
−0.644268 | + | 0.764799i | \(0.722838\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.46410 | −0.304997 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.9282 | 1.30428 | 0.652142 | − | 0.758097i | \(-0.273871\pi\) | ||||
0.652142 | + | 0.758097i | \(0.273871\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.2832 | 1.58536 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.86370 | 0.332535 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.3923 | 1.22962 | 0.614809 | − | 0.788676i | \(-0.289233\pi\) | ||||
0.614809 | + | 0.788676i | \(0.289233\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.82843 | −0.238197 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.21166 | −0.519445 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 33.8564 | 2.81162 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.37945 | 0.440702 | 0.220351 | − | 0.975421i | \(-0.429280\pi\) | ||||
0.220351 | + | 0.975421i | \(0.429280\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.59059 | −0.536335 | −0.268167 | − | 0.963372i | \(-0.586418\pi\) | ||||
−0.268167 | + | 0.963372i | \(0.586418\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.46410 | −0.280056 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 28.3923 | 2.28052 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.17209 | −0.173352 | −0.0866758 | − | 0.996237i | \(-0.527624\pi\) | ||||
−0.0866758 | + | 0.996237i | \(0.527624\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.62158 | −0.366515 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.53590 | −0.355279 | −0.177639 | − | 0.984096i | \(-0.556846\pi\) | ||||
−0.177639 | + | 0.984096i | \(0.556846\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.65685 | 0.440386 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.72741 | 0.597965 | 0.298982 | − | 0.954259i | \(-0.403353\pi\) | ||||
0.298982 | + | 0.954259i | \(0.403353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | 0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.46410 | −0.570794 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.2480 | 1.31134 | 0.655669 | − | 0.755048i | \(-0.272387\pi\) | ||||
0.655669 | + | 0.755048i | \(0.272387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.3190 | −1.83835 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.8564 | 1.04151 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.9282 | 1.41476 | 0.707380 | − | 0.706833i | \(-0.249877\pi\) | ||||
0.707380 | + | 0.706833i | \(0.249877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.07107 | −0.525588 | −0.262794 | − | 0.964852i | \(-0.584644\pi\) | ||||
−0.262794 | + | 0.964852i | \(0.584644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.656339 | −0.0485180 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.53590 | 0.186443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.07180 | −0.370887 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.44949 | 0.178174 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.72741 | 0.559136 | 0.279568 | − | 0.960126i | \(-0.409809\pi\) | ||||
0.279568 | + | 0.960126i | \(0.409809\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.3923 | −1.17388 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.76268 | 0.624315 | 0.312158 | − | 0.950030i | \(-0.398948\pi\) | ||||
0.312158 | + | 0.950030i | \(0.398948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.6622 | −1.32293 | −0.661463 | − | 0.749977i | \(-0.730064\pi\) | ||||
−0.661463 | + | 0.749977i | \(0.730064\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.9282 | 1.05295 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.4641 | 1.50648 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.5254 | −1.22402 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.82843 | −0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.9282 | −0.755920 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.92820 | −0.476957 | −0.238479 | − | 0.971148i | \(-0.576649\pi\) | ||||
−0.238479 | + | 0.971148i | \(0.576649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.41473 | 0.439530 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −13.3843 | −0.912799 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.0000 | 1.22192 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.6969 | 0.988623 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.5211 | 0.972403 | 0.486201 | − | 0.873847i | \(-0.338382\pi\) | ||||
0.486201 | + | 0.873847i | \(0.338382\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.92820 | 0.661880 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.3205 | −0.751369 | −0.375684 | − | 0.926748i | \(-0.622592\pi\) | ||||
−0.375684 | + | 0.926748i | \(0.622592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.8690 | 1.11474 | 0.557368 | − | 0.830265i | \(-0.311811\pi\) | ||||
0.557368 | + | 0.830265i | \(0.311811\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.58630 | 0.235961 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.9282 | 0.846955 | 0.423477 | − | 0.905907i | \(-0.360809\pi\) | ||||
0.423477 | + | 0.905907i | \(0.360809\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9282 | −0.712877 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.44949 | −0.159111 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.72741 | −0.499844 | −0.249922 | − | 0.968266i | \(-0.580405\pi\) | ||||
−0.249922 | + | 0.968266i | \(0.580405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.7846 | −1.72535 | −0.862674 | − | 0.505760i | \(-0.831212\pi\) | ||||
−0.862674 | + | 0.505760i | \(0.831212\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.86370 | 0.246843 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 31.6675 | 2.01495 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.46410 | 0.346273 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.53590 | 0.412542 | 0.206271 | − | 0.978495i | \(-0.433867\pi\) | ||||
0.206271 | + | 0.978495i | \(0.433867\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.14110 | −0.260349 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.3843 | −0.838155 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.7846 | −1.42126 | −0.710632 | − | 0.703563i | \(-0.751591\pi\) | ||||
−0.710632 | + | 0.703563i | \(0.751591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.60770 | 0.0998973 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.76268 | −0.542396 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.6274 | −1.39527 | −0.697633 | − | 0.716455i | \(-0.745763\pi\) | ||||
−0.697633 | + | 0.716455i | \(0.745763\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.8564 | −1.09691 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.92820 | 0.301601 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.2784 | −0.626687 | −0.313344 | − | 0.949640i | \(-0.601449\pi\) | ||||
−0.313344 | + | 0.949640i | \(0.601449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.20736 | 0.194834 | 0.0974168 | − | 0.995244i | \(-0.468942\pi\) | ||||
0.0974168 | + | 0.995244i | \(0.468942\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.3923 | −0.628971 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.5359 | 0.876548 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.5249 | −0.752545 | −0.376273 | − | 0.926509i | \(-0.622794\pi\) | ||||
−0.376273 | + | 0.926509i | \(0.622794\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.34847 | −0.439941 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.928203 | 0.0553720 | 0.0276860 | − | 0.999617i | \(-0.491186\pi\) | ||||
0.0276860 | + | 0.999617i | \(0.491186\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.85641 | −0.585903 | −0.292951 | − | 0.956127i | \(-0.594637\pi\) | ||||
−0.292951 | + | 0.956127i | \(0.594637\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −28.8391 | −1.70828 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.1106 | −0.655840 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.07180 | −0.0628298 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.8332 | −0.632884 | −0.316442 | − | 0.948612i | \(-0.602488\pi\) | ||||
−0.316442 | + | 0.948612i | \(0.602488\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 53.5370 | 3.11705 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.46410 | −0.0849558 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.0000 | 0.693978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.48528 | −0.489083 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.4195 | −0.828381 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.53590 | −0.145205 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.9282 | −1.30858 | −0.654291 | − | 0.756243i | \(-0.727033\pi\) | ||||
−0.654291 | + | 0.756243i | \(0.727033\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.20736 | −0.182461 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.4254 | −1.83867 | −0.919337 | − | 0.393471i | \(-0.871274\pi\) | ||||
−0.919337 | + | 0.393471i | \(0.871274\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.85641 | 0.217977 | 0.108988 | − | 0.994043i | \(-0.465239\pi\) | ||||
0.108988 | + | 0.994043i | \(0.465239\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.46410 | 0.533242 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.69213 | −0.375867 | −0.187934 | − | 0.982182i | \(-0.560179\pi\) | ||||
−0.187934 | + | 0.982182i | \(0.560179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.8295 | −0.718312 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.8564 | 1.43869 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −42.1218 | −2.33650 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.41421 | 0.0782062 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.92820 | −0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.07180 | −0.0589113 | −0.0294556 | − | 0.999566i | \(-0.509377\pi\) | ||||
−0.0294556 | + | 0.999566i | \(0.509377\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.656339 | −0.0359671 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 57.6781 | 3.15129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.85641 | 0.536913 | 0.268456 | − | 0.963292i | \(-0.413486\pi\) | ||||
0.268456 | + | 0.963292i | \(0.413486\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.0000 | −0.977626 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.7589 | −0.582627 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.5959 | 1.05808 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.9282 | −0.588355 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.53590 | −0.136134 | −0.0680671 | − | 0.997681i | \(-0.521683\pi\) | ||||
−0.0680671 | + | 0.997681i | \(0.521683\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.4249 | −1.46802 | −0.734010 | − | 0.679139i | \(-0.762353\pi\) | ||||
−0.734010 | + | 0.679139i | \(0.762353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.24264 | 0.226455 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.928203 | −0.0494033 | −0.0247016 | − | 0.999695i | \(-0.507864\pi\) | ||||
−0.0247016 | + | 0.999695i | \(0.507864\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.7846 | 1.31543 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.48528 | −0.449089 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.8380 | −0.994234 | −0.497117 | − | 0.867684i | \(-0.665608\pi\) | ||||
−0.497117 | + | 0.867684i | \(0.665608\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.7128 | 1.93225 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.85641 | 0.464841 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.4548 | −0.808942 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.3886 | 0.855476 | 0.427738 | − | 0.903903i | \(-0.359311\pi\) | ||||
0.427738 | + | 0.903903i | \(0.359311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.53590 | 0.236129 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.3205 | −0.587731 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.2827 | 0.687753 | 0.343877 | − | 0.939015i | \(-0.388260\pi\) | ||||
0.343877 | + | 0.939015i | \(0.388260\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.0411 | 0.983279 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 37.1769 | 1.91471 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.3205 | −0.684229 | −0.342114 | − | 0.939658i | \(-0.611143\pi\) | ||||
−0.342114 | + | 0.939658i | \(0.611143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.5211 | 0.743937 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.8391 | −1.47361 | −0.736804 | − | 0.676106i | \(-0.763666\pi\) | ||||
−0.736804 | + | 0.676106i | \(0.763666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.8564 | 0.706188 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.46410 | 0.176090 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.52056 | −0.482711 | −0.241356 | − | 0.970437i | \(-0.577592\pi\) | ||||
−0.241356 | + | 0.970437i | \(0.577592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.79796 | 0.495504 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.9282 | −0.753028 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −9.46410 | −0.476191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.0807 | 1.15839 | 0.579193 | − | 0.815190i | \(-0.303368\pi\) | ||||
0.579193 | + | 0.815190i | \(0.303368\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.2832 | −0.915307 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.3923 | −0.918468 | −0.459234 | − | 0.888315i | \(-0.651876\pi\) | ||||
−0.459234 | + | 0.888315i | \(0.651876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 31.1769 | 1.55303 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.86370 | −0.191989 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.960947 | −0.0476324 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.07180 | −0.448571 | −0.224286 | − | 0.974523i | \(-0.572005\pi\) | ||||
−0.224286 | + | 0.974523i | \(0.572005\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −14.3923 | −0.709920 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.9411 | 1.67013 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 21.1117 | 1.03633 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.92820 | 0.339276 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.392305 | −0.0191653 | −0.00958267 | − | 0.999954i | \(-0.503050\pi\) | ||||
−0.00958267 | + | 0.999954i | \(0.503050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.6975 | −0.959995 | −0.479998 | − | 0.877270i | \(-0.659362\pi\) | ||||
−0.479998 | + | 0.877270i | \(0.659362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843 | 0.137523 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.3923 | −1.66827 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.60770 | −0.0778018 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.21166 | 0.299902 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.34418 | −0.209252 | −0.104626 | − | 0.994512i | \(-0.533364\pi\) | ||||
−0.104626 | + | 0.994512i | \(0.533364\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.8564 | −1.43481 | −0.717404 | − | 0.696658i | \(-0.754670\pi\) | ||||
−0.717404 | + | 0.696658i | \(0.754670\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −33.8564 | −1.62329 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.1117 | 1.00991 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.83272 | −0.278381 | −0.139190 | − | 0.990266i | \(-0.544450\pi\) | ||||
−0.139190 | + | 0.990266i | \(0.544450\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.3205 | 1.67813 | 0.839064 | − | 0.544033i | \(-0.183103\pi\) | ||||
0.839064 | + | 0.544033i | \(0.183103\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 19.0411 | 0.902635 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.37945 | −0.254439 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.39230 | −0.301672 | −0.150836 | − | 0.988559i | \(-0.548196\pi\) | ||||
−0.150836 | + | 0.988559i | \(0.548196\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.64102 | 0.312713 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.59059 | 0.309653 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −40.1528 | −1.88239 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.7846 | −0.972263 | −0.486132 | − | 0.873886i | \(-0.661592\pi\) | ||||
−0.486132 | + | 0.873886i | \(0.661592\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.46410 | 0.161690 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.1870 | −1.45252 | −0.726262 | − | 0.687418i | \(-0.758744\pi\) | ||||
−0.726262 | + | 0.687418i | \(0.758744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.2180 | 1.35788 | 0.678938 | − | 0.734196i | \(-0.262440\pi\) | ||||
0.678938 | + | 0.734196i | \(0.262440\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −28.3923 | −1.31666 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.2487 | 1.39974 | 0.699872 | − | 0.714269i | \(-0.253240\pi\) | ||||
0.699872 | + | 0.714269i | \(0.253240\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.5665 | 1.68848 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.17209 | 0.100085 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.07180 | 0.233201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −74.1051 | −3.40018 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.62158 | 0.211608 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.0421 | 1.32697 | 0.663485 | − | 0.748190i | \(-0.269077\pi\) | ||||
0.663485 | + | 0.748190i | \(0.269077\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.78461 | 0.126967 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.92820 | −0.315244 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.14110 | −0.188038 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.4896 | −0.520642 | −0.260321 | − | 0.965522i | \(-0.583828\pi\) | ||||
−0.260321 | + | 0.965522i | \(0.583828\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.53590 | 0.205120 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.85641 | −0.264296 | −0.132148 | − | 0.991230i | \(-0.542187\pi\) | ||||
−0.132148 | + | 0.991230i | \(0.542187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.3548 | 1.36711 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.65685 | −0.254257 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.7128 | 0.704816 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.00000 | −0.179065 | −0.0895323 | − | 0.995984i | \(-0.528537\pi\) | ||||
−0.0895323 | + | 0.995984i | \(0.528537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.72741 | −0.345235 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.3853 | −1.04270 | −0.521349 | − | 0.853343i | \(-0.674571\pi\) | ||||
−0.521349 | + | 0.853343i | \(0.674571\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −55.7128 | −2.47919 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.00000 | −0.222058 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.24693 | 0.321215 | 0.160607 | − | 0.987018i | \(-0.448655\pi\) | ||||
0.160607 | + | 0.987018i | \(0.448655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.79796 | −0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.46410 | 0.329548 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.3923 | −0.546070 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.14110 | 0.182126 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.2480 | −0.757102 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.3205 | −0.934068 | −0.467034 | − | 0.884239i | \(-0.654678\pi\) | ||||
−0.467034 | + | 0.884239i | \(0.654678\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.4641 | −1.37583 | −0.687915 | − | 0.725792i | \(-0.741474\pi\) | ||||
−0.687915 | + | 0.725792i | \(0.741474\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24.3190 | 1.06137 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.4558 | 1.10887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.8564 | −0.601317 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.2442 | −0.833558 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.4548 | −0.668170 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −18.9282 | −0.816812 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.46410 | −0.0630633 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.1827 | 1.21167 | 0.605835 | − | 0.795590i | \(-0.292839\pi\) | ||||
0.605835 | + | 0.795590i | \(0.292839\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.07107 | 0.303449 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.46410 | 0.234056 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.1769 | −0.990973 | −0.495487 | − | 0.868616i | \(-0.665010\pi\) | ||||
−0.495487 | + | 0.868616i | \(0.665010\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.656339 | 0.0280119 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 65.4056 | 2.78637 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | −0.255146 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.53590 | −0.107643 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.0069 | 1.18669 | 0.593345 | − | 0.804949i | \(-0.297807\pi\) | ||||
0.593345 | + | 0.804949i | \(0.297807\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.6969 | −0.621614 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.07180 | 0.214131 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.46410 | −0.0617045 | −0.0308523 | − | 0.999524i | \(-0.509822\pi\) | ||||
−0.0308523 | + | 0.999524i | \(0.509822\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −69.5467 | −2.92585 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.44949 | −0.102869 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.46410 | −0.145223 | −0.0726113 | − | 0.997360i | \(-0.523133\pi\) | ||||
−0.0726113 | + | 0.997360i | \(0.523133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.7128 | 1.32714 | 0.663570 | − | 0.748114i | \(-0.269041\pi\) | ||||
0.663570 | + | 0.748114i | \(0.269041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.72741 | −0.322817 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.0812 | −1.17107 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.8564 | −0.909894 | −0.454947 | − | 0.890518i | \(-0.650342\pi\) | ||||
−0.454947 | + | 0.890518i | \(0.650342\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −6.00000 | −0.249351 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.3843 | 0.555273 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.76646 | 0.280238 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 16.3923 | 0.677738 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.9282 | 1.77184 | 0.885918 | − | 0.463841i | \(-0.153529\pi\) | ||||
0.885918 | + | 0.463841i | \(0.153529\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 54.8497 | 2.26004 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.76268 | −0.360449 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.7128 | 1.54868 | 0.774340 | − | 0.632770i | \(-0.218082\pi\) | ||||
0.774340 | + | 0.632770i | \(0.218082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −32.7846 | −1.34404 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.6622 | 0.763792 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.96953 | −0.284767 | −0.142384 | − | 0.989812i | \(-0.545477\pi\) | ||||
−0.142384 | + | 0.989812i | \(0.545477\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.7128 | 0.804102 | 0.402051 | − | 0.915617i | \(-0.368297\pi\) | ||||
0.402051 | + | 0.915617i | \(0.368297\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −14.9282 | −0.607923 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 34.2185 | 1.39118 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.8434 | 1.29248 | 0.646241 | − | 0.763133i | \(-0.276340\pi\) | ||||
0.646241 | + | 0.763133i | \(0.276340\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.4641 | −0.869769 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | −0.485468 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.11012 | 0.246785 | 0.123393 | − | 0.992358i | \(-0.460623\pi\) | ||||
0.123393 | + | 0.992358i | \(0.460623\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 17.5254 | 0.706691 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.8564 | −1.60456 | −0.802279 | − | 0.596949i | \(-0.796379\pi\) | ||||
−0.802279 | + | 0.596949i | \(0.796379\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000 | 0.482321 | 0.241160 | − | 0.970485i | \(-0.422472\pi\) | ||||
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.82843 | 0.113501 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.0716 | 0.483638 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9282 | 0.957128 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.9282 | 0.436430 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.27362 | 0.0906553 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5612 | 0.937955 | 0.468977 | − | 0.883210i | \(-0.344623\pi\) | ||||
0.468977 | + | 0.883210i | \(0.344623\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.92820 | 0.275371 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 56.1051 | 2.22646 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.24264 | 0.168100 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.41473 | −0.253763 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.6077 | −1.01144 | −0.505722 | − | 0.862697i | \(-0.668774\pi\) | ||||
−0.505722 | + | 0.862697i | \(0.668774\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.5359 | 1.12535 | 0.562673 | − | 0.826680i | \(-0.309773\pi\) | ||||
0.562673 | + | 0.826680i | \(0.309773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.3843 | 0.527005 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.9107 | −1.60836 | −0.804182 | − | 0.594383i | \(-0.797396\pi\) | ||||
−0.804182 | + | 0.594383i | \(0.797396\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −20.2872 | −0.796342 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.0000 | −0.705476 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.9754 | 0.977362 | 0.488681 | − | 0.872463i | \(-0.337478\pi\) | ||||
0.488681 | + | 0.872463i | \(0.337478\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57.6781 | −2.25367 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.0000 | 0.934907 | 0.467454 | − | 0.884018i | \(-0.345171\pi\) | ||||
0.467454 | + | 0.884018i | \(0.345171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.51626 | −0.253453 | −0.126727 | − | 0.991938i | \(-0.540447\pi\) | ||||
−0.126727 | + | 0.991938i | \(0.540447\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.6969 | −0.570782 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −70.6410 | −2.73934 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.7846 | 0.959664 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.5211 | −0.561417 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.960947 | 0.0370969 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.00000 | 0.308377 | 0.154189 | − | 0.988041i | \(-0.450724\pi\) | ||||
0.154189 | + | 0.988041i | \(0.450724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.92820 | −0.382137 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.30890 | −0.127171 | −0.0635857 | − | 0.997976i | \(-0.520254\pi\) | ||||
−0.0635857 | + | 0.997976i | \(0.520254\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.62536 | −0.100752 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.3205 | 0.433803 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.1769 | −0.963368 | −0.481684 | − | 0.876345i | \(-0.659975\pi\) | ||||
−0.481684 | + | 0.876345i | \(0.659975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55.6076 | −2.12466 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.8690 | −0.643594 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −19.6077 | −0.746994 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.3923 | −1.00401 | −0.502005 | − | 0.864865i | \(-0.667404\pi\) | ||||
−0.502005 | + | 0.864865i | \(0.667404\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.58630 | −0.136232 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 26.7685 | 1.01539 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.7128 | −0.595165 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.9282 | −0.488990 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.9743 | 0.565573 | 0.282787 | − | 0.959183i | \(-0.408741\pi\) | ||||
0.282787 | + | 0.959183i | \(0.408741\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89898 | 0.184769 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.9282 | 0.411580 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.3205 | −1.32836 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.0913 | 1.84366 | 0.921832 | − | 0.387590i | \(-0.126692\pi\) | ||||
0.921832 | + | 0.387590i | \(0.126692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.44949 | 0.0918630 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7846 | 0.778390 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | 0.897549 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.72741 | 0.288585 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.27362 | 0.0847919 | 0.0423959 | − | 0.999101i | \(-0.486501\pi\) | ||||
0.0423959 | + | 0.999101i | \(0.486501\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.85641 | −0.292588 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.7846 | 0.996130 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −86.9977 | −3.23101 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.10634 | 0.300648 | 0.150324 | − | 0.988637i | \(-0.451968\pi\) | ||||
0.150324 | + | 0.988637i | \(0.451968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.0000 | −0.443836 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.07107 | −0.261176 | −0.130588 | − | 0.991437i | \(-0.541686\pi\) | ||||
−0.130588 | + | 0.991437i | \(0.541686\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.86370 | −0.142515 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.8564 | −0.805091 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.0000 | −1.32428 | −0.662141 | − | 0.749380i | \(-0.730352\pi\) | ||||
−0.662141 | + | 0.749380i | \(0.730352\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31.6675 | −1.16333 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.3233 | −1.00240 | −0.501198 | − | 0.865333i | \(-0.667107\pi\) | ||||
−0.501198 | + | 0.865333i | \(0.667107\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.7846 | −0.761489 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.46410 | −0.199921 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.79796 | −0.358010 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −46.1886 | −1.68545 | −0.842723 | − | 0.538348i | \(-0.819049\pi\) | ||||
−0.842723 | + | 0.538348i | \(0.819049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.53590 | −0.238181 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.4641 | 0.926734 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.6365 | 1.22254 | 0.611270 | − | 0.791422i | \(-0.290659\pi\) | ||||
0.611270 | + | 0.791422i | \(0.290659\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.14110 | 0.150313 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −52.2487 | −1.89401 | −0.947007 | − | 0.321212i | \(-0.895910\pi\) | ||||
−0.947007 | + | 0.321212i | \(0.895910\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.46410 | 0.125409 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.3843 | 0.483909 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 58.7878 | 2.12270 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.7846 | 0.820568 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −48.9155 | −1.75937 | −0.879684 | − | 0.475560i | \(-0.842246\pi\) | ||||
−0.879684 | + | 0.475560i | \(0.842246\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −72.9571 | −2.62070 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.60770 | −0.0576757 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.8564 | −1.21303 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.39182 | −0.336066 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.76268 | 0.313153 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.39230 | 0.299534 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.4641 | 0.836405 | 0.418202 | − | 0.908354i | \(-0.362660\pi\) | ||||
0.418202 | + | 0.908354i | \(0.362660\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.6274 | 0.805557 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −44.0908 | −1.56769 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.78461 | −0.0988844 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.8564 | 0.633301 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −21.9439 | −0.777292 | −0.388646 | − | 0.921387i | \(-0.627057\pi\) | ||||
−0.388646 | + | 0.921387i | \(0.627057\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.79796 | −0.346627 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.92820 | −0.174129 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.85641 | 0.206668 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −26.7685 | −0.943466 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.2784 | 0.361818 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.67949 | −0.234838 | −0.117419 | − | 0.993082i | \(-0.537462\pi\) | ||||
−0.117419 | + | 0.993082i | \(0.537462\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −54.3923 | −1.90997 | −0.954986 | − | 0.296651i | \(-0.904130\pi\) | ||||
−0.954986 | + | 0.296651i | \(0.904130\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.20736 | −0.112487 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.5254 | 0.613887 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.8564 | −0.904601 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3923 | 0.363137 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.1784 | 0.878734 | 0.439367 | − | 0.898308i | \(-0.355203\pi\) | ||||
0.439367 | + | 0.898308i | \(0.355203\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.97382 | −0.347666 | −0.173833 | − | 0.984775i | \(-0.555615\pi\) | ||||
−0.173833 | + | 0.984775i | \(0.555615\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14.5359 | −0.506075 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.7846 | −1.55731 | −0.778657 | − | 0.627450i | \(-0.784099\pi\) | ||||
−0.778657 | + | 0.627450i | \(0.784099\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.61729 | 0.0561706 | 0.0280853 | − | 0.999606i | \(-0.491059\pi\) | ||||
0.0280853 | + | 0.999606i | \(0.491059\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.5249 | 0.434482 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.8564 | −1.03322 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.34847 | 0.254000 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.0106 | 0.897987 | 0.448994 | − | 0.893535i | \(-0.351783\pi\) | ||||
0.448994 | + | 0.893535i | \(0.351783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47.7846 | 1.64775 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.928203 | −0.0319690 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.3185 | −0.664577 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.6937 | 0.745404 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.85641 | 0.338271 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.85641 | 0.0636368 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.0208 | −1.60996 | −0.804980 | − | 0.593301i | \(-0.797824\pi\) | ||||
−0.804980 | + | 0.593301i | \(0.797824\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 28.8391 | 0.986276 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.1769 | 1.47490 | 0.737448 | − | 0.675404i | \(-0.236031\pi\) | ||||
0.737448 | + | 0.675404i | \(0.236031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.2487 | 1.10031 | 0.550156 | − | 0.835062i | \(-0.314568\pi\) | ||||
0.550156 | + | 0.835062i | \(0.314568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.1106 | 0.378649 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.1213 | 1.26362 | 0.631812 | − | 0.775122i | \(-0.282312\pi\) | ||||
0.631812 | + | 0.775122i | \(0.282312\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −66.6410 | −2.26586 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.00000 | 0.169809 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.58630 | 0.121657 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 63.3350 | 2.14602 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.07180 | 0.0362748 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 46.6410 | 1.57675 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.7071 | 1.20574 | 0.602871 | − | 0.797839i | \(-0.294023\pi\) | ||||
0.602871 | + | 0.797839i | \(0.294023\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.8332 | 0.365396 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.6410 | −1.23447 | −0.617234 | − | 0.786780i | \(-0.711747\pi\) | ||||
−0.617234 | + | 0.786780i | \(0.711747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.60770 | 0.188714 | 0.0943570 | − | 0.995538i | \(-0.469920\pi\) | ||||
0.0943570 | + | 0.995538i | \(0.469920\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −53.5370 | −1.79963 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.5665 | 1.22778 | 0.613891 | − | 0.789391i | \(-0.289603\pi\) | ||||
0.613891 | + | 0.789391i | \(0.289603\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.5692 | 1.19295 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.46410 | 0.0490492 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −21.1117 | −0.706475 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −73.1330 | −2.44457 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.0000 | −0.400668 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 64.3923 | 2.14760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0096 | −0.533358 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.48528 | 0.282372 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 27.3205 | 0.908164 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.3923 | 1.40761 | 0.703807 | − | 0.710392i | \(-0.251482\pi\) | ||||
0.703807 | + | 0.710392i | \(0.251482\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14.4195 | 0.478266 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.0726 | −0.731298 | −0.365649 | − | 0.930753i | \(-0.619153\pi\) | ||||
−0.365649 | + | 0.930753i | \(0.619153\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | −0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.53590 | 0.0838342 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.5665 | −1.20753 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.582009 | −0.0191987 | −0.00959936 | − | 0.999954i | \(-0.503056\pi\) | ||||
−0.00959936 | + | 0.999954i | \(0.503056\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.9282 | 0.755510 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.2154 | 0.895805 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.51626 | −0.214253 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3.20736 | 0.105344 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.3205 | −1.48692 | −0.743459 | − | 0.668782i | \(-0.766816\pi\) | ||||
−0.743459 | + | 0.668782i | \(0.766816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.46410 | 0.244626 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 32.4254 | 1.06156 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5959 | 0.640855 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.85641 | −0.125849 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.2891 | 1.18299 | 0.591495 | − | 0.806309i | \(-0.298538\pi\) | ||||
0.591495 | + | 0.806309i | \(0.298538\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.8295 | −0.417785 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.46410 | −0.307867 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.0718 | −0.944706 | −0.472353 | − | 0.881409i | \(-0.656595\pi\) | ||||
−0.472353 | + | 0.881409i | \(0.656595\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.9706 | −0.550888 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.69213 | 0.217007 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.3923 | 1.50279 | 0.751397 | − | 0.659850i | \(-0.229380\pi\) | ||||
0.751397 | + | 0.659850i | \(0.229380\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.8564 | −0.966131 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.8295 | 0.414717 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −35.2538 | −1.13840 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.0000 | 0.741935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000 | 0.128898 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.1822 | −0.746262 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3800 | 0.333797 | 0.166899 | − | 0.985974i | \(-0.446625\pi\) | ||||
0.166899 | + | 0.985974i | \(0.446625\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25.8564 | −0.830627 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.2487 | −0.713995 | −0.356998 | − | 0.934105i | \(-0.616200\pi\) | ||||
−0.356998 | + | 0.934105i | \(0.616200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.9706 | 0.544051 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 42.1218 | 1.34898 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.1769 | −1.12541 | −0.562705 | − | 0.826658i | \(-0.690239\pi\) | ||||
−0.562705 | + | 0.826658i | \(0.690239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.21539 | −0.230605 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.41421 | −0.0451524 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.7370 | 0.757093 | 0.378547 | − | 0.925582i | \(-0.376424\pi\) | ||||
0.378547 | + | 0.925582i | \(0.376424\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.8564 | −1.07875 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.92820 | 0.220527 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.79796 | −0.311557 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.2474 | −0.389053 | −0.194527 | − | 0.980897i | \(-0.562317\pi\) | ||||
−0.194527 | + | 0.980897i | \(0.562317\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.07180 | 0.0340124 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 72.1051 | 2.28589 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.6269 | −0.558250 | −0.279125 | − | 0.960255i | \(-0.590044\pi\) | ||||
−0.279125 | + | 0.960255i | \(0.590044\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.656339 | 0.0207656 |
(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 | 3072.2.a.l.1.1 | 4 | ||
3.2 | odd | 2 | 9216.2.a.bi.1.4 | 4 | |||
4.3 | odd | 2 | 3072.2.a.r.1.1 | 4 | |||
8.3 | odd | 2 | inner | 3072.2.a.l.1.4 | 4 | ||
8.5 | even | 2 | 3072.2.a.r.1.4 | 4 | |||
12.11 | even | 2 | 9216.2.a.bc.1.4 | 4 | |||
16.3 | odd | 4 | 3072.2.d.h.1537.8 | 8 | |||
16.5 | even | 4 | 3072.2.d.h.1537.5 | 8 | |||
16.11 | odd | 4 | 3072.2.d.h.1537.1 | 8 | |||
16.13 | even | 4 | 3072.2.d.h.1537.4 | 8 | |||
24.5 | odd | 2 | 9216.2.a.bc.1.1 | 4 | |||
24.11 | even | 2 | 9216.2.a.bi.1.1 | 4 | |||
32.3 | odd | 8 | 768.2.j.f.577.4 | yes | 8 | ||
32.5 | even | 8 | 768.2.j.e.193.3 | yes | 8 | ||
32.11 | odd | 8 | 768.2.j.f.193.4 | yes | 8 | ||
32.13 | even | 8 | 768.2.j.e.577.3 | yes | 8 | ||
32.19 | odd | 8 | 768.2.j.e.577.1 | yes | 8 | ||
32.21 | even | 8 | 768.2.j.f.193.2 | yes | 8 | ||
32.27 | odd | 8 | 768.2.j.e.193.1 | ✓ | 8 | ||
32.29 | even | 8 | 768.2.j.f.577.2 | yes | 8 | ||
96.5 | odd | 8 | 2304.2.k.l.1729.3 | 8 | |||
96.11 | even | 8 | 2304.2.k.e.1729.2 | 8 | |||
96.29 | odd | 8 | 2304.2.k.e.577.2 | 8 | |||
96.35 | even | 8 | 2304.2.k.e.577.1 | 8 | |||
96.53 | odd | 8 | 2304.2.k.e.1729.1 | 8 | |||
96.59 | even | 8 | 2304.2.k.l.1729.4 | 8 | |||
96.77 | odd | 8 | 2304.2.k.l.577.4 | 8 | |||
96.83 | even | 8 | 2304.2.k.l.577.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.2.j.e.193.1 | ✓ | 8 | 32.27 | odd | 8 | ||
768.2.j.e.193.3 | yes | 8 | 32.5 | even | 8 | ||
768.2.j.e.577.1 | yes | 8 | 32.19 | odd | 8 | ||
768.2.j.e.577.3 | yes | 8 | 32.13 | even | 8 | ||
768.2.j.f.193.2 | yes | 8 | 32.21 | even | 8 | ||
768.2.j.f.193.4 | yes | 8 | 32.11 | odd | 8 | ||
768.2.j.f.577.2 | yes | 8 | 32.29 | even | 8 | ||
768.2.j.f.577.4 | yes | 8 | 32.3 | odd | 8 | ||
2304.2.k.e.577.1 | 8 | 96.35 | even | 8 | |||
2304.2.k.e.577.2 | 8 | 96.29 | odd | 8 | |||
2304.2.k.e.1729.1 | 8 | 96.53 | odd | 8 | |||
2304.2.k.e.1729.2 | 8 | 96.11 | even | 8 | |||
2304.2.k.l.577.3 | 8 | 96.83 | even | 8 | |||
2304.2.k.l.577.4 | 8 | 96.77 | odd | 8 | |||
2304.2.k.l.1729.3 | 8 | 96.5 | odd | 8 | |||
2304.2.k.l.1729.4 | 8 | 96.59 | even | 8 | |||
3072.2.a.l.1.1 | 4 | 1.1 | even | 1 | trivial | ||
3072.2.a.l.1.4 | 4 | 8.3 | odd | 2 | inner | ||
3072.2.a.r.1.1 | 4 | 4.3 | odd | 2 | |||
3072.2.a.r.1.4 | 4 | 8.5 | even | 2 | |||
3072.2.d.h.1537.1 | 8 | 16.11 | odd | 4 | |||
3072.2.d.h.1537.4 | 8 | 16.13 | even | 4 | |||
3072.2.d.h.1537.5 | 8 | 16.5 | even | 4 | |||
3072.2.d.h.1537.8 | 8 | 16.3 | odd | 4 | |||
9216.2.a.bc.1.1 | 4 | 24.5 | odd | 2 | |||
9216.2.a.bc.1.4 | 4 | 12.11 | even | 2 | |||
9216.2.a.bi.1.1 | 4 | 24.11 | even | 2 | |||
9216.2.a.bi.1.4 | 4 | 3.2 | odd | 2 |