Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6498,2,Mod(1,6498)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6498, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6498.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6498 = 2 \cdot 3^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6498.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: | \(51.8867912334\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 722) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.17557\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6498.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.45965 | 1.09999 | 0.549994 | − | 0.835168i | \(-0.314630\pi\) | ||||
0.549994 | + | 0.835168i | \(0.314630\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.79360 | −1.05588 | −0.527942 | − | 0.849281i | \(-0.677036\pi\) | ||||
−0.527942 | + | 0.849281i | \(0.677036\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.45965 | 0.777809 | ||||||||
\(11\) | 1.67853 | 0.506096 | 0.253048 | − | 0.967454i | \(-0.418567\pi\) | ||||
0.253048 | + | 0.967454i | \(0.418567\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.34458 | −1.75967 | −0.879834 | − | 0.475280i | \(-0.842347\pi\) | ||||
−0.879834 | + | 0.475280i | \(0.842347\pi\) | |||||||
\(14\) | −2.79360 | −0.746622 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.96917 | −1.20520 | −0.602601 | − | 0.798043i | \(-0.705869\pi\) | ||||
−0.602601 | + | 0.798043i | \(0.705869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.45965 | 0.549994 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.67853 | 0.357864 | ||||||||
\(23\) | 2.49890 | 0.521057 | 0.260529 | − | 0.965466i | \(-0.416103\pi\) | ||||
0.260529 | + | 0.965466i | \(0.416103\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.04988 | 0.209975 | ||||||||
\(26\) | −6.34458 | −1.24427 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.79360 | −0.527942 | ||||||||
\(29\) | 5.93179 | 1.10150 | 0.550752 | − | 0.834669i | \(-0.314341\pi\) | ||||
0.550752 | + | 0.834669i | \(0.314341\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.28408 | −1.30826 | −0.654130 | − | 0.756382i | \(-0.726965\pi\) | ||||
−0.654130 | + | 0.756382i | \(0.726965\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.96917 | −0.852206 | ||||||||
\(35\) | −6.87129 | −1.16146 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.550972 | −0.0905792 | −0.0452896 | − | 0.998974i | \(-0.514421\pi\) | ||||
−0.0452896 | + | 0.998974i | \(0.514421\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.45965 | 0.388905 | ||||||||
\(41\) | −2.60741 | −0.407209 | −0.203605 | − | 0.979053i | \(-0.565266\pi\) | ||||
−0.203605 | + | 0.979053i | \(0.565266\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.87129 | 0.437867 | 0.218934 | − | 0.975740i | \(-0.429742\pi\) | ||||
0.218934 | + | 0.975740i | \(0.429742\pi\) | |||||||
\(44\) | 1.67853 | 0.253048 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.49890 | 0.368443 | ||||||||
\(47\) | −0.745593 | −0.108756 | −0.0543780 | − | 0.998520i | \(-0.517318\pi\) | ||||
−0.0543780 | + | 0.998520i | \(0.517318\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.804226 | 0.114889 | ||||||||
\(50\) | 1.04988 | 0.148475 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.34458 | −0.879834 | ||||||||
\(53\) | −1.47027 | −0.201957 | −0.100979 | − | 0.994889i | \(-0.532197\pi\) | ||||
−0.100979 | + | 0.994889i | \(0.532197\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.12860 | 0.556700 | ||||||||
\(56\) | −2.79360 | −0.373311 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.93179 | 0.778882 | ||||||||
\(59\) | −4.96261 | −0.646077 | −0.323038 | − | 0.946386i | \(-0.604704\pi\) | ||||
−0.323038 | + | 0.946386i | \(0.604704\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.33686 | 1.19546 | 0.597731 | − | 0.801697i | \(-0.296069\pi\) | ||||
0.597731 | + | 0.801697i | \(0.296069\pi\) | |||||||
\(62\) | −7.28408 | −0.925079 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −15.6054 | −1.93562 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.5604 | −1.41233 | −0.706166 | − | 0.708046i | \(-0.749577\pi\) | ||||
−0.706166 | + | 0.708046i | \(0.749577\pi\) | |||||||
\(68\) | −4.96917 | −0.602601 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.87129 | −0.821276 | ||||||||
\(71\) | −6.99698 | −0.830389 | −0.415195 | − | 0.909733i | \(-0.636286\pi\) | ||||
−0.415195 | + | 0.909733i | \(0.636286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.18619 | −0.724039 | −0.362020 | − | 0.932171i | \(-0.617913\pi\) | ||||
−0.362020 | + | 0.932171i | \(0.617913\pi\) | |||||||
\(74\) | −0.550972 | −0.0640492 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.68915 | −0.534379 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.91158 | 0.665105 | 0.332552 | − | 0.943085i | \(-0.392090\pi\) | ||||
0.332552 | + | 0.943085i | \(0.392090\pi\) | |||||||
\(80\) | 2.45965 | 0.274997 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.60741 | −0.287941 | ||||||||
\(83\) | −15.1773 | −1.66593 | −0.832964 | − | 0.553328i | \(-0.813358\pi\) | ||||
−0.832964 | + | 0.553328i | \(0.813358\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.2224 | −1.32571 | ||||||||
\(86\) | 2.87129 | 0.309619 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.67853 | 0.178932 | ||||||||
\(89\) | 6.90502 | 0.731930 | 0.365965 | − | 0.930629i | \(-0.380739\pi\) | ||||
0.365965 | + | 0.930629i | \(0.380739\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.7242 | 1.85800 | ||||||||
\(92\) | 2.49890 | 0.260529 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.745593 | −0.0769021 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.3874 | −1.46082 | −0.730408 | − | 0.683011i | \(-0.760670\pi\) | ||||
−0.730408 | + | 0.683011i | \(0.760670\pi\) | |||||||
\(98\) | 0.804226 | 0.0812391 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.04988 | 0.104988 | ||||||||
\(101\) | −11.2829 | −1.12269 | −0.561347 | − | 0.827581i | \(-0.689717\pi\) | ||||
−0.561347 | + | 0.827581i | \(0.689717\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.8280 | −1.46104 | −0.730522 | − | 0.682889i | \(-0.760723\pi\) | ||||
−0.730522 | + | 0.682889i | \(0.760723\pi\) | |||||||
\(104\) | −6.34458 | −0.622137 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.47027 | −0.142805 | ||||||||
\(107\) | −2.82849 | −0.273440 | −0.136720 | − | 0.990610i | \(-0.543656\pi\) | ||||
−0.136720 | + | 0.990610i | \(0.543656\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.72539 | −0.165262 | −0.0826312 | − | 0.996580i | \(-0.526332\pi\) | ||||
−0.0826312 | + | 0.996580i | \(0.526332\pi\) | |||||||
\(110\) | 4.12860 | 0.393646 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.79360 | −0.263971 | ||||||||
\(113\) | −0.427785 | −0.0402426 | −0.0201213 | − | 0.999798i | \(-0.506405\pi\) | ||||
−0.0201213 | + | 0.999798i | \(0.506405\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.14643 | 0.573157 | ||||||||
\(116\) | 5.93179 | 0.550752 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.96261 | −0.456845 | ||||||||
\(119\) | 13.8819 | 1.27255 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.18253 | −0.743867 | ||||||||
\(122\) | 9.33686 | 0.845320 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.28408 | −0.654130 | ||||||||
\(125\) | −9.71592 | −0.869018 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.13632 | 0.100832 | 0.0504159 | − | 0.998728i | \(-0.483945\pi\) | ||||
0.0504159 | + | 0.998728i | \(0.483945\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −15.6054 | −1.36869 | ||||||||
\(131\) | 17.8415 | 1.55882 | 0.779410 | − | 0.626515i | \(-0.215519\pi\) | ||||
0.779410 | + | 0.626515i | \(0.215519\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.5604 | −0.998670 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.96917 | −0.426103 | ||||||||
\(137\) | 15.9156 | 1.35976 | 0.679882 | − | 0.733321i | \(-0.262031\pi\) | ||||
0.679882 | + | 0.733321i | \(0.262031\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.1202 | 0.858382 | 0.429191 | − | 0.903214i | \(-0.358799\pi\) | ||||
0.429191 | + | 0.903214i | \(0.358799\pi\) | |||||||
\(140\) | −6.87129 | −0.580730 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.99698 | −0.587174 | ||||||||
\(143\) | −10.6496 | −0.890562 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.5901 | 1.21164 | ||||||||
\(146\) | −6.18619 | −0.511973 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.550972 | −0.0452896 | ||||||||
\(149\) | −9.39851 | −0.769956 | −0.384978 | − | 0.922926i | \(-0.625791\pi\) | ||||
−0.384978 | + | 0.922926i | \(0.625791\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2632 | 0.835210 | 0.417605 | − | 0.908629i | \(-0.362870\pi\) | ||||
0.417605 | + | 0.908629i | \(0.362870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.68915 | −0.377863 | ||||||||
\(155\) | −17.9163 | −1.43907 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.97387 | 0.237341 | 0.118671 | − | 0.992934i | \(-0.462137\pi\) | ||||
0.118671 | + | 0.992934i | \(0.462137\pi\) | |||||||
\(158\) | 5.91158 | 0.470300 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.45965 | 0.194452 | ||||||||
\(161\) | −6.98095 | −0.550176 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.59191 | 0.437992 | 0.218996 | − | 0.975726i | \(-0.429722\pi\) | ||||
0.218996 | + | 0.975726i | \(0.429722\pi\) | |||||||
\(164\) | −2.60741 | −0.203605 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.1773 | −1.17799 | ||||||||
\(167\) | −7.08361 | −0.548146 | −0.274073 | − | 0.961709i | \(-0.588371\pi\) | ||||
−0.274073 | + | 0.961709i | \(0.588371\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.2537 | 2.09643 | ||||||||
\(170\) | −12.2224 | −0.937418 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.87129 | 0.218934 | ||||||||
\(173\) | −23.0208 | −1.75024 | −0.875120 | − | 0.483907i | \(-0.839217\pi\) | ||||
−0.875120 | + | 0.483907i | \(0.839217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.93294 | −0.221709 | ||||||||
\(176\) | 1.67853 | 0.126524 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.90502 | 0.517553 | ||||||||
\(179\) | 8.21471 | 0.613996 | 0.306998 | − | 0.951710i | \(-0.400675\pi\) | ||||
0.306998 | + | 0.951710i | \(0.400675\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9999 | 0.966274 | 0.483137 | − | 0.875545i | \(-0.339497\pi\) | ||||
0.483137 | + | 0.875545i | \(0.339497\pi\) | |||||||
\(182\) | 17.7242 | 1.31381 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.49890 | 0.184222 | ||||||||
\(185\) | −1.35520 | −0.0996361 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.34092 | −0.609948 | ||||||||
\(188\) | −0.745593 | −0.0543780 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.57479 | −0.475735 | −0.237868 | − | 0.971298i | \(-0.576448\pi\) | ||||
−0.237868 | + | 0.971298i | \(0.576448\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.8826 | −1.93505 | −0.967527 | − | 0.252769i | \(-0.918659\pi\) | ||||
−0.967527 | + | 0.252769i | \(0.918659\pi\) | |||||||
\(194\) | −14.3874 | −1.03295 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.804226 | 0.0574447 | ||||||||
\(197\) | 9.84940 | 0.701741 | 0.350870 | − | 0.936424i | \(-0.385886\pi\) | ||||
0.350870 | + | 0.936424i | \(0.385886\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.4661 | −1.45080 | −0.725402 | − | 0.688326i | \(-0.758346\pi\) | ||||
−0.725402 | + | 0.688326i | \(0.758346\pi\) | |||||||
\(200\) | 1.04988 | 0.0742374 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.2829 | −0.793864 | ||||||||
\(203\) | −16.5711 | −1.16306 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.41332 | −0.447926 | ||||||||
\(206\) | −14.8280 | −1.03311 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.34458 | −0.439917 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.11630 | −0.558749 | −0.279374 | − | 0.960182i | \(-0.590127\pi\) | ||||
−0.279374 | + | 0.960182i | \(0.590127\pi\) | |||||||
\(212\) | −1.47027 | −0.100979 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.82849 | −0.193351 | ||||||||
\(215\) | 7.06236 | 0.481649 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.3488 | 1.38137 | ||||||||
\(218\) | −1.72539 | −0.116858 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.12860 | 0.278350 | ||||||||
\(221\) | 31.5273 | 2.12076 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.7540 | −0.720143 | −0.360071 | − | 0.932925i | \(-0.617248\pi\) | ||||
−0.360071 | + | 0.932925i | \(0.617248\pi\) | |||||||
\(224\) | −2.79360 | −0.186656 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.427785 | −0.0284558 | ||||||||
\(227\) | 27.0936 | 1.79827 | 0.899133 | − | 0.437676i | \(-0.144198\pi\) | ||||
0.899133 | + | 0.437676i | \(0.144198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.46557 | 0.625503 | 0.312751 | − | 0.949835i | \(-0.398749\pi\) | ||||
0.312751 | + | 0.949835i | \(0.398749\pi\) | |||||||
\(230\) | 6.14643 | 0.405283 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.93179 | 0.389441 | ||||||||
\(233\) | −22.8621 | −1.49775 | −0.748873 | − | 0.662713i | \(-0.769405\pi\) | ||||
−0.748873 | + | 0.662713i | \(0.769405\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.83390 | −0.119630 | ||||||||
\(236\) | −4.96261 | −0.323038 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 13.8819 | 0.899831 | ||||||||
\(239\) | −8.66611 | −0.560564 | −0.280282 | − | 0.959918i | \(-0.590428\pi\) | ||||
−0.280282 | + | 0.959918i | \(0.590428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.65826 | −0.364480 | −0.182240 | − | 0.983254i | \(-0.558335\pi\) | ||||
−0.182240 | + | 0.983254i | \(0.558335\pi\) | |||||||
\(242\) | −8.18253 | −0.525993 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.33686 | 0.597731 | ||||||||
\(245\) | 1.97811 | 0.126377 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −7.28408 | −0.462539 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.71592 | −0.614489 | ||||||||
\(251\) | 13.5552 | 0.855599 | 0.427799 | − | 0.903874i | \(-0.359289\pi\) | ||||
0.427799 | + | 0.903874i | \(0.359289\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.19449 | 0.263705 | ||||||||
\(254\) | 1.13632 | 0.0712988 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.0393 | 0.626231 | 0.313116 | − | 0.949715i | \(-0.398627\pi\) | ||||
0.313116 | + | 0.949715i | \(0.398627\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.53920 | 0.0956411 | ||||||||
\(260\) | −15.6054 | −0.967808 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.8415 | 1.10225 | ||||||||
\(263\) | 18.8262 | 1.16087 | 0.580436 | − | 0.814306i | \(-0.302882\pi\) | ||||
0.580436 | + | 0.814306i | \(0.302882\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.61635 | −0.222151 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.5604 | −0.706166 | ||||||||
\(269\) | −16.3827 | −0.998870 | −0.499435 | − | 0.866351i | \(-0.666459\pi\) | ||||
−0.499435 | + | 0.866351i | \(0.666459\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.76684 | −0.168073 | −0.0840367 | − | 0.996463i | \(-0.526781\pi\) | ||||
−0.0840367 | + | 0.996463i | \(0.526781\pi\) | |||||||
\(272\) | −4.96917 | −0.301300 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.9156 | 0.961499 | ||||||||
\(275\) | 1.76225 | 0.106268 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.5321 | 1.47399 | 0.736996 | − | 0.675897i | \(-0.236244\pi\) | ||||
0.736996 | + | 0.675897i | \(0.236244\pi\) | |||||||
\(278\) | 10.1202 | 0.606967 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.87129 | −0.410638 | ||||||||
\(281\) | 10.1704 | 0.606713 | 0.303356 | − | 0.952877i | \(-0.401893\pi\) | ||||
0.303356 | + | 0.952877i | \(0.401893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.6678 | 1.64468 | 0.822340 | − | 0.568997i | \(-0.192668\pi\) | ||||
0.822340 | + | 0.568997i | \(0.192668\pi\) | |||||||
\(284\) | −6.99698 | −0.415195 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.6496 | −0.629722 | ||||||||
\(287\) | 7.28408 | 0.429966 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.69270 | 0.452512 | ||||||||
\(290\) | 14.5901 | 0.856761 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.18619 | −0.362020 | ||||||||
\(293\) | 23.8386 | 1.39267 | 0.696333 | − | 0.717719i | \(-0.254814\pi\) | ||||
0.696333 | + | 0.717719i | \(0.254814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2063 | −0.710677 | ||||||||
\(296\) | −0.550972 | −0.0320246 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.39851 | −0.544441 | ||||||||
\(299\) | −15.8545 | −0.916889 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.02124 | −0.462337 | ||||||||
\(302\) | 10.2632 | 0.590583 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 22.9654 | 1.31500 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.9884 | −1.48324 | −0.741619 | − | 0.670821i | \(-0.765942\pi\) | ||||
−0.741619 | + | 0.670821i | \(0.765942\pi\) | |||||||
\(308\) | −4.68915 | −0.267189 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.9163 | −1.01758 | ||||||||
\(311\) | 23.1043 | 1.31013 | 0.655063 | − | 0.755574i | \(-0.272642\pi\) | ||||
0.655063 | + | 0.755574i | \(0.272642\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.2647 | 0.693242 | 0.346621 | − | 0.938005i | \(-0.387329\pi\) | ||||
0.346621 | + | 0.938005i | \(0.387329\pi\) | |||||||
\(314\) | 2.97387 | 0.167825 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.91158 | 0.332552 | ||||||||
\(317\) | −0.272305 | −0.0152942 | −0.00764708 | − | 0.999971i | \(-0.502434\pi\) | ||||
−0.00764708 | + | 0.999971i | \(0.502434\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.95669 | 0.557468 | ||||||||
\(320\) | 2.45965 | 0.137499 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.98095 | −0.389033 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.66102 | −0.369487 | ||||||||
\(326\) | 5.59191 | 0.309707 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.60741 | −0.143970 | ||||||||
\(329\) | 2.08289 | 0.114834 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.9930 | 1.09891 | 0.549457 | − | 0.835522i | \(-0.314835\pi\) | ||||
0.549457 | + | 0.835522i | \(0.314835\pi\) | |||||||
\(332\) | −15.1773 | −0.832964 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −7.08361 | −0.387598 | ||||||||
\(335\) | −28.4346 | −1.55355 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.2824 | 0.941433 | 0.470717 | − | 0.882284i | \(-0.343995\pi\) | ||||
0.470717 | + | 0.882284i | \(0.343995\pi\) | |||||||
\(338\) | 27.2537 | 1.48240 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −12.2224 | −0.662854 | ||||||||
\(341\) | −12.2266 | −0.662105 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.3085 | 0.934573 | ||||||||
\(344\) | 2.87129 | 0.154809 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.0208 | −1.23761 | ||||||||
\(347\) | 18.5456 | 0.995579 | 0.497789 | − | 0.867298i | \(-0.334145\pi\) | ||||
0.497789 | + | 0.867298i | \(0.334145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.1210 | −1.07705 | −0.538527 | − | 0.842609i | \(-0.681019\pi\) | ||||
−0.538527 | + | 0.842609i | \(0.681019\pi\) | |||||||
\(350\) | −2.93294 | −0.156772 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.67853 | 0.0894660 | ||||||||
\(353\) | −24.0557 | −1.28035 | −0.640177 | − | 0.768227i | \(-0.721139\pi\) | ||||
−0.640177 | + | 0.768227i | \(0.721139\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17.2101 | −0.913419 | ||||||||
\(356\) | 6.90502 | 0.365965 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.21471 | 0.434161 | ||||||||
\(359\) | 10.8535 | 0.572824 | 0.286412 | − | 0.958107i | \(-0.407537\pi\) | ||||
0.286412 | + | 0.958107i | \(0.407537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 12.9999 | 0.683259 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.7242 | 0.929002 | ||||||||
\(365\) | −15.2159 | −0.796435 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −32.6121 | −1.70234 | −0.851168 | − | 0.524893i | \(-0.824105\pi\) | ||||
−0.851168 | + | 0.524893i | \(0.824105\pi\) | |||||||
\(368\) | 2.49890 | 0.130264 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.35520 | −0.0704534 | ||||||||
\(371\) | 4.10736 | 0.213243 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.30198 | 0.274526 | 0.137263 | − | 0.990535i | \(-0.456169\pi\) | ||||
0.137263 | + | 0.990535i | \(0.456169\pi\) | |||||||
\(374\) | −8.34092 | −0.431299 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.745593 | −0.0384510 | ||||||||
\(377\) | −37.6347 | −1.93828 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.6656 | −1.26699 | −0.633494 | − | 0.773748i | \(-0.718380\pi\) | ||||
−0.633494 | + | 0.773748i | \(0.718380\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.57479 | −0.336396 | ||||||||
\(383\) | 3.64416 | 0.186208 | 0.0931039 | − | 0.995656i | \(-0.470321\pi\) | ||||
0.0931039 | + | 0.995656i | \(0.470321\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.5337 | −0.587810 | ||||||||
\(386\) | −26.8826 | −1.36829 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −14.3874 | −0.730408 | ||||||||
\(389\) | −2.79353 | −0.141638 | −0.0708189 | − | 0.997489i | \(-0.522561\pi\) | ||||
−0.0708189 | + | 0.997489i | \(0.522561\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.4175 | −0.627979 | ||||||||
\(392\) | 0.804226 | 0.0406196 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.84940 | 0.496206 | ||||||||
\(395\) | 14.5404 | 0.731608 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39.5101 | −1.98296 | −0.991478 | − | 0.130273i | \(-0.958415\pi\) | ||||
−0.991478 | + | 0.130273i | \(0.958415\pi\) | |||||||
\(398\) | −20.4661 | −1.02587 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.04988 | 0.0524938 | ||||||||
\(401\) | −18.6215 | −0.929912 | −0.464956 | − | 0.885334i | \(-0.653930\pi\) | ||||
−0.464956 | + | 0.885334i | \(0.653930\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 46.2144 | 2.30210 | ||||||||
\(404\) | −11.2829 | −0.561347 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.5711 | −0.822408 | ||||||||
\(407\) | −0.924824 | −0.0458418 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.1433 | 0.847681 | 0.423840 | − | 0.905737i | \(-0.360682\pi\) | ||||
0.423840 | + | 0.905737i | \(0.360682\pi\) | |||||||
\(410\) | −6.41332 | −0.316731 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.8280 | −0.730522 | ||||||||
\(413\) | 13.8636 | 0.682182 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.3309 | −1.83250 | ||||||||
\(416\) | −6.34458 | −0.311068 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.5042 | 0.903989 | 0.451995 | − | 0.892021i | \(-0.350713\pi\) | ||||
0.451995 | + | 0.892021i | \(0.350713\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.1996 | 0.789520 | 0.394760 | − | 0.918784i | \(-0.370828\pi\) | ||||
0.394760 | + | 0.918784i | \(0.370828\pi\) | |||||||
\(422\) | −8.11630 | −0.395095 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.47027 | −0.0714027 | ||||||||
\(425\) | −5.21702 | −0.253062 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −26.0835 | −1.26227 | ||||||||
\(428\) | −2.82849 | −0.136720 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.06236 | 0.340577 | ||||||||
\(431\) | 12.6997 | 0.611721 | 0.305861 | − | 0.952076i | \(-0.401056\pi\) | ||||
0.305861 | + | 0.952076i | \(0.401056\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.2350 | −0.684092 | −0.342046 | − | 0.939683i | \(-0.611120\pi\) | ||||
−0.342046 | + | 0.939683i | \(0.611120\pi\) | |||||||
\(434\) | 20.3488 | 0.976775 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.72539 | −0.0826312 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −28.1900 | −1.34544 | −0.672718 | − | 0.739899i | \(-0.734873\pi\) | ||||
−0.672718 | + | 0.739899i | \(0.734873\pi\) | |||||||
\(440\) | 4.12860 | 0.196823 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.5273 | 1.49960 | ||||||||
\(443\) | 32.9944 | 1.56761 | 0.783805 | − | 0.621007i | \(-0.213276\pi\) | ||||
0.783805 | + | 0.621007i | \(0.213276\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.9839 | 0.805115 | ||||||||
\(446\) | −10.7540 | −0.509218 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.79360 | −0.131985 | ||||||||
\(449\) | −17.1975 | −0.811601 | −0.405801 | − | 0.913962i | \(-0.633007\pi\) | ||||
−0.405801 | + | 0.913962i | \(0.633007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.37662 | −0.206087 | ||||||||
\(452\) | −0.427785 | −0.0201213 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 27.0936 | 1.27157 | ||||||||
\(455\) | 43.5954 | 2.04378 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.1517 | −1.45722 | −0.728608 | − | 0.684931i | \(-0.759832\pi\) | ||||
−0.728608 | + | 0.684931i | \(0.759832\pi\) | |||||||
\(458\) | 9.46557 | 0.442297 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.14643 | 0.286579 | ||||||||
\(461\) | −15.5410 | −0.723816 | −0.361908 | − | 0.932214i | \(-0.617875\pi\) | ||||
−0.361908 | + | 0.932214i | \(0.617875\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.6648 | 0.960374 | 0.480187 | − | 0.877166i | \(-0.340569\pi\) | ||||
0.480187 | + | 0.877166i | \(0.340569\pi\) | |||||||
\(464\) | 5.93179 | 0.275376 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.8621 | −1.05907 | ||||||||
\(467\) | 28.4830 | 1.31803 | 0.659017 | − | 0.752128i | \(-0.270972\pi\) | ||||
0.659017 | + | 0.752128i | \(0.270972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.2953 | 1.49126 | ||||||||
\(470\) | −1.83390 | −0.0845914 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.96261 | −0.228423 | ||||||||
\(473\) | 4.81955 | 0.221603 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 13.8819 | 0.636276 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.66611 | −0.396379 | ||||||||
\(479\) | 10.4726 | 0.478507 | 0.239254 | − | 0.970957i | \(-0.423097\pi\) | ||||
0.239254 | + | 0.970957i | \(0.423097\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.49568 | 0.159389 | ||||||||
\(482\) | −5.65826 | −0.257727 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.18253 | −0.371933 | ||||||||
\(485\) | −35.3879 | −1.60688 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.29894 | −0.104175 | −0.0520875 | − | 0.998643i | \(-0.516587\pi\) | ||||
−0.0520875 | + | 0.998643i | \(0.516587\pi\) | |||||||
\(488\) | 9.33686 | 0.422660 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.97811 | 0.0893621 | ||||||||
\(491\) | −12.1612 | −0.548826 | −0.274413 | − | 0.961612i | \(-0.588484\pi\) | ||||
−0.274413 | + | 0.961612i | \(0.588484\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.4761 | −1.32754 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.28408 | −0.327065 | ||||||||
\(497\) | 19.5468 | 0.876794 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.1348 | 0.677528 | 0.338764 | − | 0.940871i | \(-0.389991\pi\) | ||||
0.338764 | + | 0.940871i | \(0.389991\pi\) | |||||||
\(500\) | −9.71592 | −0.434509 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.5552 | 0.605000 | ||||||||
\(503\) | 0.573683 | 0.0255793 | 0.0127896 | − | 0.999918i | \(-0.495929\pi\) | ||||
0.0127896 | + | 0.999918i | \(0.495929\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.7520 | −1.23495 | ||||||||
\(506\) | 4.19449 | 0.186468 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.13632 | 0.0504159 | ||||||||
\(509\) | −26.2163 | −1.16202 | −0.581008 | − | 0.813898i | \(-0.697341\pi\) | ||||
−0.581008 | + | 0.813898i | \(0.697341\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.2818 | 0.764501 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.0393 | 0.442813 | ||||||||
\(515\) | −36.4716 | −1.60713 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.25150 | −0.0550410 | ||||||||
\(518\) | 1.53920 | 0.0676285 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −15.6054 | −0.684344 | ||||||||
\(521\) | −12.9637 | −0.567948 | −0.283974 | − | 0.958832i | \(-0.591653\pi\) | ||||
−0.283974 | + | 0.958832i | \(0.591653\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.7793 | −0.777432 | −0.388716 | − | 0.921358i | \(-0.627081\pi\) | ||||
−0.388716 | + | 0.921358i | \(0.627081\pi\) | |||||||
\(524\) | 17.8415 | 0.779410 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.8262 | 0.820861 | ||||||||
\(527\) | 36.1959 | 1.57672 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.7555 | −0.728499 | ||||||||
\(530\) | −3.61635 | −0.157084 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.5429 | 0.716554 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.95709 | −0.300781 | ||||||||
\(536\) | −11.5604 | −0.499335 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.3827 | −0.706307 | ||||||||
\(539\) | 1.34992 | 0.0581451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.34418 | −0.229764 | −0.114882 | − | 0.993379i | \(-0.536649\pi\) | ||||
−0.114882 | + | 0.993379i | \(0.536649\pi\) | |||||||
\(542\) | −2.76684 | −0.118846 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.96917 | −0.213052 | ||||||||
\(545\) | −4.24385 | −0.181787 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.10112 | −0.218108 | −0.109054 | − | 0.994036i | \(-0.534782\pi\) | ||||
−0.109054 | + | 0.994036i | \(0.534782\pi\) | |||||||
\(548\) | 15.9156 | 0.679882 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.76225 | 0.0751426 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.5146 | −0.702273 | ||||||||
\(554\) | 24.5321 | 1.04227 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.1202 | 0.429191 | ||||||||
\(557\) | 10.7235 | 0.454370 | 0.227185 | − | 0.973852i | \(-0.427048\pi\) | ||||
0.227185 | + | 0.973852i | \(0.427048\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.2171 | −0.770502 | ||||||||
\(560\) | −6.87129 | −0.290365 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.1704 | 0.429011 | ||||||||
\(563\) | 9.76285 | 0.411455 | 0.205728 | − | 0.978609i | \(-0.434044\pi\) | ||||
0.205728 | + | 0.978609i | \(0.434044\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.05220 | −0.0442664 | ||||||||
\(566\) | 27.6678 | 1.16296 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.99698 | −0.293587 | ||||||||
\(569\) | −8.84194 | −0.370674 | −0.185337 | − | 0.982675i | \(-0.559338\pi\) | ||||
−0.185337 | + | 0.982675i | \(0.559338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.8411 | 0.955871 | 0.477935 | − | 0.878395i | \(-0.341385\pi\) | ||||
0.477935 | + | 0.878395i | \(0.341385\pi\) | |||||||
\(572\) | −10.6496 | −0.445281 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.28408 | 0.304032 | ||||||||
\(575\) | 2.62354 | 0.109409 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.0176 | −0.583560 | −0.291780 | − | 0.956486i | \(-0.594247\pi\) | ||||
−0.291780 | + | 0.956486i | \(0.594247\pi\) | |||||||
\(578\) | 7.69270 | 0.319974 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.5901 | 0.605821 | ||||||||
\(581\) | 42.3994 | 1.75903 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.46790 | −0.102210 | ||||||||
\(584\) | −6.18619 | −0.255986 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 23.8386 | 0.984763 | ||||||||
\(587\) | −21.0356 | −0.868232 | −0.434116 | − | 0.900857i | \(-0.642939\pi\) | ||||
−0.434116 | + | 0.900857i | \(0.642939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −12.2063 | −0.502525 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.550972 | −0.0226448 | ||||||||
\(593\) | 34.9193 | 1.43396 | 0.716981 | − | 0.697093i | \(-0.245523\pi\) | ||||
0.716981 | + | 0.697093i | \(0.245523\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34.1446 | 1.39979 | ||||||||
\(596\) | −9.39851 | −0.384978 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.8545 | −0.648338 | ||||||||
\(599\) | 21.5106 | 0.878901 | 0.439450 | − | 0.898267i | \(-0.355173\pi\) | ||||
0.439450 | + | 0.898267i | \(0.355173\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.3417 | 0.585012 | 0.292506 | − | 0.956264i | \(-0.405511\pi\) | ||||
0.292506 | + | 0.956264i | \(0.405511\pi\) | |||||||
\(602\) | −8.02124 | −0.326921 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.2632 | 0.417605 | ||||||||
\(605\) | −20.1262 | −0.818245 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.3488 | 0.420046 | 0.210023 | − | 0.977696i | \(-0.432646\pi\) | ||||
0.210023 | + | 0.977696i | \(0.432646\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.9654 | 0.929842 | ||||||||
\(611\) | 4.73047 | 0.191375 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5674 | 0.790320 | 0.395160 | − | 0.918612i | \(-0.370689\pi\) | ||||
0.395160 | + | 0.918612i | \(0.370689\pi\) | |||||||
\(614\) | −25.9884 | −1.04881 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.68915 | −0.188931 | ||||||||
\(617\) | 5.92522 | 0.238540 | 0.119270 | − | 0.992862i | \(-0.461945\pi\) | ||||
0.119270 | + | 0.992862i | \(0.461945\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.03958 | 0.323138 | 0.161569 | − | 0.986861i | \(-0.448345\pi\) | ||||
0.161569 | + | 0.986861i | \(0.448345\pi\) | |||||||
\(620\) | −17.9163 | −0.719535 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 23.1043 | 0.926400 | ||||||||
\(623\) | −19.2899 | −0.772833 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.1471 | −1.16589 | ||||||||
\(626\) | 12.2647 | 0.490196 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.97387 | 0.118671 | ||||||||
\(629\) | 2.73788 | 0.109166 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.9006 | −0.513567 | −0.256783 | − | 0.966469i | \(-0.582663\pi\) | ||||
−0.256783 | + | 0.966469i | \(0.582663\pi\) | |||||||
\(632\) | 5.91158 | 0.235150 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.272305 | −0.0108146 | ||||||||
\(635\) | 2.79494 | 0.110914 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.10247 | −0.202167 | ||||||||
\(638\) | 9.95669 | 0.394189 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.45965 | 0.0972262 | ||||||||
\(641\) | −28.8639 | −1.14006 | −0.570028 | − | 0.821625i | \(-0.693068\pi\) | ||||
−0.570028 | + | 0.821625i | \(0.693068\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.3394 | 1.03873 | 0.519363 | − | 0.854554i | \(-0.326169\pi\) | ||||
0.519363 | + | 0.854554i | \(0.326169\pi\) | |||||||
\(644\) | −6.98095 | −0.275088 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.04601 | 0.119751 | 0.0598756 | − | 0.998206i | \(-0.480930\pi\) | ||||
0.0598756 | + | 0.998206i | \(0.480930\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.32990 | −0.326977 | ||||||||
\(650\) | −6.66102 | −0.261267 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.59191 | 0.218996 | ||||||||
\(653\) | 15.1973 | 0.594717 | 0.297359 | − | 0.954766i | \(-0.403894\pi\) | ||||
0.297359 | + | 0.954766i | \(0.403894\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.8838 | 1.71468 | ||||||||
\(656\) | −2.60741 | −0.101802 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.08289 | 0.0811996 | ||||||||
\(659\) | 17.8741 | 0.696275 | 0.348138 | − | 0.937443i | \(-0.386814\pi\) | ||||
0.348138 | + | 0.937443i | \(0.386814\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.8525 | −1.47229 | −0.736146 | − | 0.676823i | \(-0.763356\pi\) | ||||
−0.736146 | + | 0.676823i | \(0.763356\pi\) | |||||||
\(662\) | 19.9930 | 0.777050 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.1773 | −0.588994 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.8230 | 0.573947 | ||||||||
\(668\) | −7.08361 | −0.274073 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −28.4346 | −1.09853 | ||||||||
\(671\) | 15.6722 | 0.605019 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.28461 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(674\) | 17.2824 | 0.665694 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 27.2537 | 1.04822 | ||||||||
\(677\) | −18.3233 | −0.704223 | −0.352111 | − | 0.935958i | \(-0.614536\pi\) | ||||
−0.352111 | + | 0.935958i | \(0.614536\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.1926 | 1.54245 | ||||||||
\(680\) | −12.2224 | −0.468709 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.2266 | −0.468179 | ||||||||
\(683\) | −49.2217 | −1.88342 | −0.941709 | − | 0.336429i | \(-0.890781\pi\) | ||||
−0.941709 | + | 0.336429i | \(0.890781\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 39.1469 | 1.49573 | ||||||||
\(686\) | 17.3085 | 0.660843 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.87129 | 0.109467 | ||||||||
\(689\) | 9.32825 | 0.355378 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6779 | 0.634458 | 0.317229 | − | 0.948349i | \(-0.397248\pi\) | ||||
0.317229 | + | 0.948349i | \(0.397248\pi\) | |||||||
\(692\) | −23.0208 | −0.875120 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.5456 | 0.703981 | ||||||||
\(695\) | 24.8921 | 0.944210 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.9567 | 0.490770 | ||||||||
\(698\) | −20.1210 | −0.761592 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.93294 | −0.110855 | ||||||||
\(701\) | 30.9066 | 1.16733 | 0.583663 | − | 0.811996i | \(-0.301619\pi\) | ||||
0.583663 | + | 0.811996i | \(0.301619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.67853 | 0.0632620 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24.0557 | −0.905348 | ||||||||
\(707\) | 31.5200 | 1.18543 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.1056 | 1.50620 | 0.753098 | − | 0.657908i | \(-0.228558\pi\) | ||||
0.753098 | + | 0.657908i | \(0.228558\pi\) | |||||||
\(710\) | −17.2101 | −0.645884 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.90502 | 0.258776 | ||||||||
\(713\) | −18.2022 | −0.681678 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.1942 | −0.979608 | ||||||||
\(716\) | 8.21471 | 0.306998 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.8535 | 0.405048 | ||||||||
\(719\) | 45.6529 | 1.70256 | 0.851282 | − | 0.524708i | \(-0.175825\pi\) | ||||
0.851282 | + | 0.524708i | \(0.175825\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.4235 | 1.54269 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.9999 | 0.483137 | ||||||||
\(725\) | 6.22764 | 0.231289 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.1811 | −0.563034 | −0.281517 | − | 0.959556i | \(-0.590838\pi\) | ||||
−0.281517 | + | 0.959556i | \(0.590838\pi\) | |||||||
\(728\) | 17.7242 | 0.656904 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.2159 | −0.563164 | ||||||||
\(731\) | −14.2679 | −0.527719 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.9986 | −0.997217 | −0.498608 | − | 0.866827i | \(-0.666155\pi\) | ||||
−0.498608 | + | 0.866827i | \(0.666155\pi\) | |||||||
\(734\) | −32.6121 | −1.20373 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.49890 | 0.0921108 | ||||||||
\(737\) | −19.4046 | −0.714776 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.20782 | −0.191573 | −0.0957864 | − | 0.995402i | \(-0.530537\pi\) | ||||
−0.0957864 | + | 0.995402i | \(0.530537\pi\) | |||||||
\(740\) | −1.35520 | −0.0498181 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.10736 | 0.150786 | ||||||||
\(743\) | 22.1079 | 0.811059 | 0.405529 | − | 0.914082i | \(-0.367087\pi\) | ||||
0.405529 | + | 0.914082i | \(0.367087\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.1170 | −0.846943 | ||||||||
\(746\) | 5.30198 | 0.194119 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.34092 | −0.304974 | ||||||||
\(749\) | 7.90167 | 0.288721 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.4960 | 0.455984 | 0.227992 | − | 0.973663i | \(-0.426784\pi\) | ||||
0.227992 | + | 0.973663i | \(0.426784\pi\) | |||||||
\(752\) | −0.745593 | −0.0271890 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −37.6347 | −1.37057 | ||||||||
\(755\) | 25.2440 | 0.918722 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.9988 | −1.12667 | −0.563336 | − | 0.826228i | \(-0.690482\pi\) | ||||
−0.563336 | + | 0.826228i | \(0.690482\pi\) | |||||||
\(758\) | −24.6656 | −0.895895 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.96398 | −0.0711941 | −0.0355971 | − | 0.999366i | \(-0.511333\pi\) | ||||
−0.0355971 | + | 0.999366i | \(0.511333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.82006 | 0.174498 | ||||||||
\(764\) | −6.57479 | −0.237868 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.64416 | 0.131669 | ||||||||
\(767\) | 31.4857 | 1.13688 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.3322 | −0.805318 | −0.402659 | − | 0.915350i | \(-0.631914\pi\) | ||||
−0.402659 | + | 0.915350i | \(0.631914\pi\) | |||||||
\(770\) | −11.5337 | −0.415645 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −26.8826 | −0.967527 | ||||||||
\(773\) | 27.3553 | 0.983901 | 0.491951 | − | 0.870623i | \(-0.336284\pi\) | ||||
0.491951 | + | 0.870623i | \(0.336284\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.64738 | −0.274702 | ||||||||
\(776\) | −14.3874 | −0.516477 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.79353 | −0.100153 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.7447 | −0.420257 | ||||||||
\(782\) | −12.4175 | −0.444049 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.804226 | 0.0287224 | ||||||||
\(785\) | 7.31469 | 0.261072 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.78962 | −0.277670 | −0.138835 | − | 0.990316i | \(-0.544336\pi\) | ||||
−0.138835 | + | 0.990316i | \(0.544336\pi\) | |||||||
\(788\) | 9.84940 | 0.350870 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 14.5404 | 0.517325 | ||||||||
\(791\) | 1.19506 | 0.0424915 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −59.2384 | −2.10362 | ||||||||
\(794\) | −39.5101 | −1.40216 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.4661 | −0.725402 | ||||||||
\(797\) | −6.09655 | −0.215951 | −0.107975 | − | 0.994154i | \(-0.534437\pi\) | ||||
−0.107975 | + | 0.994154i | \(0.534437\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.70498 | 0.131073 | ||||||||
\(800\) | 1.04988 | 0.0371187 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.6215 | −0.657547 | ||||||||
\(803\) | −10.3837 | −0.366433 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.1707 | −0.605187 | ||||||||
\(806\) | 46.2144 | 1.62783 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.2829 | −0.396932 | ||||||||
\(809\) | −56.8455 | −1.99858 | −0.999291 | − | 0.0376413i | \(-0.988016\pi\) | ||||
−0.999291 | + | 0.0376413i | \(0.988016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.9209 | 0.734631 | 0.367316 | − | 0.930096i | \(-0.380277\pi\) | ||||
0.367316 | + | 0.930096i | \(0.380277\pi\) | |||||||
\(812\) | −16.5711 | −0.581530 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.924824 | −0.0324151 | ||||||||
\(815\) | 13.7541 | 0.481786 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 17.1433 | 0.599401 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.41332 | −0.223963 | ||||||||
\(821\) | −16.2582 | −0.567416 | −0.283708 | − | 0.958911i | \(-0.591565\pi\) | ||||
−0.283708 | + | 0.958911i | \(0.591565\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.5328 | −0.611157 | −0.305578 | − | 0.952167i | \(-0.598850\pi\) | ||||
−0.305578 | + | 0.952167i | \(0.598850\pi\) | |||||||
\(824\) | −14.8280 | −0.516557 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.8636 | 0.482375 | ||||||||
\(827\) | −17.0254 | −0.592030 | −0.296015 | − | 0.955183i | \(-0.595658\pi\) | ||||
−0.296015 | + | 0.955183i | \(0.595658\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.76207 | 0.200125 | 0.100062 | − | 0.994981i | \(-0.468096\pi\) | ||||
0.100062 | + | 0.994981i | \(0.468096\pi\) | |||||||
\(830\) | −37.3309 | −1.29577 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.34458 | −0.219959 | ||||||||
\(833\) | −3.99634 | −0.138465 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.4232 | −0.602954 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 18.5042 | 0.639217 | ||||||||
\(839\) | 8.89954 | 0.307246 | 0.153623 | − | 0.988130i | \(-0.450906\pi\) | ||||
0.153623 | + | 0.988130i | \(0.450906\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.18608 | 0.213313 | ||||||||
\(842\) | 16.1996 | 0.558275 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.11630 | −0.279374 | ||||||||
\(845\) | 67.0344 | 2.30605 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.8588 | 0.785436 | ||||||||
\(848\) | −1.47027 | −0.0504893 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.21702 | −0.178942 | ||||||||
\(851\) | −1.37683 | −0.0471970 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.78915 | 0.0954987 | 0.0477493 | − | 0.998859i | \(-0.484795\pi\) | ||||
0.0477493 | + | 0.998859i | \(0.484795\pi\) | |||||||
\(854\) | −26.0835 | −0.892559 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.82849 | −0.0966757 | ||||||||
\(857\) | 16.3945 | 0.560025 | 0.280012 | − | 0.959996i | \(-0.409661\pi\) | ||||
0.280012 | + | 0.959996i | \(0.409661\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.52505 | 0.324990 | 0.162495 | − | 0.986709i | \(-0.448046\pi\) | ||||
0.162495 | + | 0.986709i | \(0.448046\pi\) | |||||||
\(860\) | 7.06236 | 0.240825 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.6997 | 0.432552 | ||||||||
\(863\) | −50.6764 | −1.72505 | −0.862523 | − | 0.506018i | \(-0.831117\pi\) | ||||
−0.862523 | + | 0.506018i | \(0.831117\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −56.6231 | −1.92524 | ||||||||
\(866\) | −14.2350 | −0.483726 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.3488 | 0.690684 | ||||||||
\(869\) | 9.92278 | 0.336607 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 73.3461 | 2.48524 | ||||||||
\(872\) | −1.72539 | −0.0584291 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.1424 | 0.917582 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.2578 | −0.650291 | −0.325146 | − | 0.945664i | \(-0.605413\pi\) | ||||
−0.325146 | + | 0.945664i | \(0.605413\pi\) | |||||||
\(878\) | −28.1900 | −0.951367 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.12860 | 0.139175 | ||||||||
\(881\) | −19.1076 | −0.643750 | −0.321875 | − | 0.946782i | \(-0.604313\pi\) | ||||
−0.321875 | + | 0.946782i | \(0.604313\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 49.9980 | 1.68257 | 0.841283 | − | 0.540595i | \(-0.181801\pi\) | ||||
0.841283 | + | 0.540595i | \(0.181801\pi\) | |||||||
\(884\) | 31.5273 | 1.06038 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.9944 | 1.10847 | ||||||||
\(887\) | 39.6195 | 1.33029 | 0.665146 | − | 0.746713i | \(-0.268369\pi\) | ||||
0.665146 | + | 0.746713i | \(0.268369\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.17442 | −0.106467 | ||||||||
\(890\) | 16.9839 | 0.569302 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.7540 | −0.360071 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.2053 | 0.675389 | ||||||||
\(896\) | −2.79360 | −0.0933278 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.1975 | −0.573889 | ||||||||
\(899\) | −43.2076 | −1.44105 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.30603 | 0.243399 | ||||||||
\(902\) | −4.37662 | −0.145726 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.427785 | −0.0142279 | ||||||||
\(905\) | 31.9752 | 1.06289 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.2545 | −1.83470 | −0.917348 | − | 0.398087i | \(-0.869674\pi\) | ||||
−0.917348 | + | 0.398087i | \(0.869674\pi\) | |||||||
\(908\) | 27.0936 | 0.899133 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 43.5954 | 1.44517 | ||||||||
\(911\) | 27.7087 | 0.918031 | 0.459015 | − | 0.888428i | \(-0.348202\pi\) | ||||
0.459015 | + | 0.888428i | \(0.348202\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.4756 | −0.843120 | ||||||||
\(914\) | −31.1517 | −1.03041 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.46557 | 0.312751 | ||||||||
\(917\) | −49.8421 | −1.64593 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27.2500 | 0.898894 | 0.449447 | − | 0.893307i | \(-0.351621\pi\) | ||||
0.449447 | + | 0.893307i | \(0.351621\pi\) | |||||||
\(920\) | 6.14643 | 0.202642 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.5410 | −0.511815 | ||||||||
\(923\) | 44.3929 | 1.46121 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.578452 | −0.0190194 | ||||||||
\(926\) | 20.6648 | 0.679087 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.93179 | 0.194720 | ||||||||
\(929\) | −44.4410 | −1.45806 | −0.729031 | − | 0.684481i | \(-0.760029\pi\) | ||||
−0.729031 | + | 0.684481i | \(0.760029\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −22.8621 | −0.748873 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 28.4830 | 0.931991 | ||||||||
\(935\) | −20.5157 | −0.670936 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.2097 | −0.594885 | −0.297442 | − | 0.954740i | \(-0.596134\pi\) | ||||
−0.297442 | + | 0.954740i | \(0.596134\pi\) | |||||||
\(938\) | 32.2953 | 1.05448 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.83390 | −0.0598152 | ||||||||
\(941\) | −40.2680 | −1.31270 | −0.656350 | − | 0.754457i | \(-0.727901\pi\) | ||||
−0.656350 | + | 0.754457i | \(0.727901\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.51567 | −0.212180 | ||||||||
\(944\) | −4.96261 | −0.161519 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.81955 | 0.156697 | ||||||||
\(947\) | −6.36561 | −0.206854 | −0.103427 | − | 0.994637i | \(-0.532981\pi\) | ||||
−0.103427 | + | 0.994637i | \(0.532981\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39.2488 | 1.27407 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 13.8819 | 0.449915 | ||||||||
\(953\) | −32.6944 | −1.05907 | −0.529537 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529537 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.1717 | −0.523303 | ||||||||
\(956\) | −8.66611 | −0.280282 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.4726 | 0.338356 | ||||||||
\(959\) | −44.4620 | −1.43575 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.0578 | 0.711542 | ||||||||
\(962\) | 3.49568 | 0.112705 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.65826 | −0.182240 | ||||||||
\(965\) | −66.1218 | −2.12854 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.55936 | 0.275250 | 0.137625 | − | 0.990484i | \(-0.456053\pi\) | ||||
0.137625 | + | 0.990484i | \(0.456053\pi\) | |||||||
\(968\) | −8.18253 | −0.262997 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −35.3879 | −1.13624 | ||||||||
\(971\) | −41.8789 | −1.34396 | −0.671978 | − | 0.740571i | \(-0.734555\pi\) | ||||
−0.671978 | + | 0.740571i | \(0.734555\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.2718 | −0.906351 | ||||||||
\(974\) | −2.29894 | −0.0736628 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.33686 | 0.298866 | ||||||||
\(977\) | −6.18021 | −0.197722 | −0.0988612 | − | 0.995101i | \(-0.531520\pi\) | ||||
−0.0988612 | + | 0.995101i | \(0.531520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.5903 | 0.370427 | ||||||||
\(980\) | 1.97811 | 0.0631885 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.1612 | −0.388079 | ||||||||
\(983\) | 33.5742 | 1.07085 | 0.535425 | − | 0.844583i | \(-0.320152\pi\) | ||||
0.535425 | + | 0.844583i | \(0.320152\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.2261 | 0.771907 | ||||||||
\(986\) | −29.4761 | −0.938710 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.17507 | 0.228154 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46.1746 | 1.46679 | 0.733393 | − | 0.679805i | \(-0.237936\pi\) | ||||
0.733393 | + | 0.679805i | \(0.237936\pi\) | |||||||
\(992\) | −7.28408 | −0.231270 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.5468 | 0.619987 | ||||||||
\(995\) | −50.3394 | −1.59587 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.819130 | −0.0259421 | −0.0129711 | − | 0.999916i | \(-0.504129\pi\) | ||||
−0.0129711 | + | 0.999916i | \(0.504129\pi\) | |||||||
\(998\) | 15.1348 | 0.479085 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6498.2.a.ca.1.4 | 4 | ||
3.2 | odd | 2 | 722.2.a.m.1.4 | ✓ | 4 | ||
12.11 | even | 2 | 5776.2.a.bv.1.1 | 4 | |||
19.18 | odd | 2 | 6498.2.a.bx.1.4 | 4 | |||
57.2 | even | 18 | 722.2.e.r.99.1 | 24 | |||
57.5 | odd | 18 | 722.2.e.s.595.1 | 24 | |||
57.8 | even | 6 | 722.2.c.m.653.4 | 8 | |||
57.11 | odd | 6 | 722.2.c.n.653.1 | 8 | |||
57.14 | even | 18 | 722.2.e.r.595.4 | 24 | |||
57.17 | odd | 18 | 722.2.e.s.99.4 | 24 | |||
57.23 | odd | 18 | 722.2.e.s.415.1 | 24 | |||
57.26 | odd | 6 | 722.2.c.n.429.1 | 8 | |||
57.29 | even | 18 | 722.2.e.r.423.1 | 24 | |||
57.32 | even | 18 | 722.2.e.r.245.1 | 24 | |||
57.35 | odd | 18 | 722.2.e.s.389.4 | 24 | |||
57.41 | even | 18 | 722.2.e.r.389.1 | 24 | |||
57.44 | odd | 18 | 722.2.e.s.245.4 | 24 | |||
57.47 | odd | 18 | 722.2.e.s.423.4 | 24 | |||
57.50 | even | 6 | 722.2.c.m.429.4 | 8 | |||
57.53 | even | 18 | 722.2.e.r.415.4 | 24 | |||
57.56 | even | 2 | 722.2.a.n.1.1 | yes | 4 | ||
228.227 | odd | 2 | 5776.2.a.bt.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
722.2.a.m.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
722.2.a.n.1.1 | yes | 4 | 57.56 | even | 2 | ||
722.2.c.m.429.4 | 8 | 57.50 | even | 6 | |||
722.2.c.m.653.4 | 8 | 57.8 | even | 6 | |||
722.2.c.n.429.1 | 8 | 57.26 | odd | 6 | |||
722.2.c.n.653.1 | 8 | 57.11 | odd | 6 | |||
722.2.e.r.99.1 | 24 | 57.2 | even | 18 | |||
722.2.e.r.245.1 | 24 | 57.32 | even | 18 | |||
722.2.e.r.389.1 | 24 | 57.41 | even | 18 | |||
722.2.e.r.415.4 | 24 | 57.53 | even | 18 | |||
722.2.e.r.423.1 | 24 | 57.29 | even | 18 | |||
722.2.e.r.595.4 | 24 | 57.14 | even | 18 | |||
722.2.e.s.99.4 | 24 | 57.17 | odd | 18 | |||
722.2.e.s.245.4 | 24 | 57.44 | odd | 18 | |||
722.2.e.s.389.4 | 24 | 57.35 | odd | 18 | |||
722.2.e.s.415.1 | 24 | 57.23 | odd | 18 | |||
722.2.e.s.423.4 | 24 | 57.47 | odd | 18 | |||
722.2.e.s.595.1 | 24 | 57.5 | odd | 18 | |||
5776.2.a.bt.1.4 | 4 | 228.227 | odd | 2 | |||
5776.2.a.bv.1.1 | 4 | 12.11 | even | 2 | |||
6498.2.a.bx.1.4 | 4 | 19.18 | odd | 2 | |||
6498.2.a.ca.1.4 | 4 | 1.1 | even | 1 | trivial |