Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5600,2,Mod(1,5600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5600, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5600.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5600 = 2^{5} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5600.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: | \(44.7162251319\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.504568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 3x^{2} + 7x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1120) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.28447\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5600.1 |
$q$-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 | ||||||||
\(3\) | 1.63460 | 0.943739 | 0.471869 | − | 0.881668i | \(-0.343579\pi\) | ||||
0.471869 | + | 0.881668i | \(0.343579\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.328072 | −0.109357 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.24087 | −0.374137 | −0.187069 | − | 0.982347i | \(-0.559899\pi\) | ||||
−0.187069 | + | 0.982347i | \(0.559899\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.20355 | −1.16585 | −0.582927 | − | 0.812524i | \(-0.698093\pi\) | ||||
−0.582927 | + | 0.812524i | \(0.698093\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.39596 | 0.823641 | 0.411821 | − | 0.911265i | \(-0.364893\pi\) | ||||
0.411821 | + | 0.911265i | \(0.364893\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.46162 | −1.48240 | −0.741198 | − | 0.671286i | \(-0.765742\pi\) | ||||
−0.741198 | + | 0.671286i | \(0.765742\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.63460 | 0.356700 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.15509 | −0.449367 | −0.224683 | − | 0.974432i | \(-0.572135\pi\) | ||||
−0.224683 | + | 0.974432i | \(0.572135\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.44008 | −1.04694 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.96490 | 0.736264 | 0.368132 | − | 0.929773i | \(-0.379997\pi\) | ||||
0.368132 | + | 0.929773i | \(0.379997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0611 | 1.80703 | 0.903516 | − | 0.428555i | \(-0.140977\pi\) | ||||
0.903516 | + | 0.428555i | \(0.140977\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.02833 | −0.353088 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.76815 | −1.11268 | −0.556338 | − | 0.830956i | \(-0.687794\pi\) | ||||
−0.556338 | + | 0.830956i | \(0.687794\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.87113 | −1.10026 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.131318 | −0.0205084 | −0.0102542 | − | 0.999947i | \(-0.503264\pi\) | ||||
−0.0102542 | + | 0.999947i | \(0.503264\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.40498 | 1.12925 | 0.564625 | − | 0.825348i | \(-0.309021\pi\) | ||||
0.564625 | + | 0.825348i | \(0.309021\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.82702 | 0.704093 | 0.352046 | − | 0.935983i | \(-0.385486\pi\) | ||||
0.352046 | + | 0.935983i | \(0.385486\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.55105 | 0.777302 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.0374 | −1.37874 | −0.689368 | − | 0.724411i | \(-0.742112\pi\) | ||||
−0.689368 | + | 0.724411i | \(0.742112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.5622 | −1.39900 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.9864 | −1.43031 | −0.715157 | − | 0.698964i | \(-0.753645\pi\) | ||||
−0.715157 | + | 0.698964i | \(0.753645\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.33030 | −0.810512 | −0.405256 | − | 0.914203i | \(-0.632818\pi\) | ||||
−0.405256 | + | 0.914203i | \(0.632818\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.328072 | −0.0413332 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.65614 | 0.324500 | 0.162250 | − | 0.986750i | \(-0.448125\pi\) | ||||
0.162250 | + | 0.986750i | \(0.448125\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.52271 | −0.424085 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.754563 | −0.0895501 | −0.0447751 | − | 0.998997i | \(-0.514257\pi\) | ||||
−0.0447751 | + | 0.998997i | \(0.514257\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.03736 | −0.706619 | −0.353310 | − | 0.935506i | \(-0.614944\pi\) | ||||
−0.353310 | + | 0.935506i | \(0.614944\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.24087 | −0.141411 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.6652 | −1.64996 | −0.824980 | − | 0.565162i | \(-0.808814\pi\) | ||||
−0.824980 | + | 0.565162i | \(0.808814\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.90815 | −0.878684 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.0813 | −1.54562 | −0.772809 | − | 0.634639i | \(-0.781149\pi\) | ||||
−0.772809 | + | 0.634639i | \(0.781149\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.48105 | 0.694841 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.6742 | −1.34346 | −0.671731 | − | 0.740795i | \(-0.734449\pi\) | ||||
−0.671731 | + | 0.740795i | \(0.734449\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.20355 | −0.440652 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.4459 | 1.70537 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.914215 | −0.0928244 | −0.0464122 | − | 0.998922i | \(-0.514779\pi\) | ||||
−0.0464122 | + | 0.998922i | \(0.514779\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.407096 | 0.0409146 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.4818 | 1.34149 | 0.670743 | − | 0.741689i | \(-0.265975\pi\) | ||||
0.670743 | + | 0.741689i | \(0.265975\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.516841 | 0.0509258 | 0.0254629 | − | 0.999676i | \(-0.491894\pi\) | ||||
0.0254629 | + | 0.999676i | \(0.491894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.8486 | −1.82216 | −0.911081 | − | 0.412228i | \(-0.864751\pi\) | ||||
−0.911081 | + | 0.412228i | \(0.864751\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.345270 | 0.0330709 | 0.0165354 | − | 0.999863i | \(-0.494736\pi\) | ||||
0.0165354 | + | 0.999863i | \(0.494736\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.0632 | −1.05008 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.77026 | −0.354677 | −0.177338 | − | 0.984150i | \(-0.556749\pi\) | ||||
−0.177338 | + | 0.984150i | \(0.556749\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.37907 | 0.127495 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.39596 | 0.311307 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.46024 | −0.860021 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.214652 | −0.0193545 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.63895 | 0.500376 | 0.250188 | − | 0.968197i | \(-0.419508\pi\) | ||||
0.250188 | + | 0.968197i | \(0.419508\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.1042 | 1.06572 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5183 | −0.918987 | −0.459493 | − | 0.888181i | \(-0.651969\pi\) | ||||
−0.459493 | + | 0.888181i | \(0.651969\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.46162 | −0.560293 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.96632 | 0.595173 | 0.297586 | − | 0.954695i | \(-0.403818\pi\) | ||||
0.297586 | + | 0.954695i | \(0.403818\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.3258 | −0.875827 | −0.437913 | − | 0.899017i | \(-0.644282\pi\) | ||||
−0.437913 | + | 0.899017i | \(0.644282\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.89025 | 0.664479 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.21607 | 0.436189 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.63460 | 0.134820 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.773875 | −0.0633983 | −0.0316992 | − | 0.999497i | \(-0.510092\pi\) | ||||
−0.0316992 | + | 0.999497i | \(0.510092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.14607 | −0.500160 | −0.250080 | − | 0.968225i | \(-0.580457\pi\) | ||||
−0.250080 | + | 0.968225i | \(0.580457\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.11412 | −0.0900712 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.5421 | 1.47982 | 0.739909 | − | 0.672707i | \(-0.234869\pi\) | ||||
0.739909 | + | 0.672707i | \(0.234869\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.4071 | −1.30117 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.15509 | −0.169845 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.993429 | −0.0778113 | −0.0389057 | − | 0.999243i | \(-0.512387\pi\) | ||||
−0.0389057 | + | 0.999243i | \(0.512387\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.22052 | −0.249212 | −0.124606 | − | 0.992206i | \(-0.539767\pi\) | ||||
−0.124606 | + | 0.992206i | \(0.539767\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.66981 | 0.359216 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.11988 | 0.162111 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.9187 | −1.21028 | −0.605138 | − | 0.796120i | \(-0.706882\pi\) | ||||
−0.605138 | + | 0.796120i | \(0.706882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.9585 | −1.34984 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.84647 | 0.735960 | 0.367980 | − | 0.929834i | \(-0.380049\pi\) | ||||
0.367980 | + | 0.929834i | \(0.380049\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.6562 | 1.60969 | 0.804845 | − | 0.593484i | \(-0.202248\pi\) | ||||
0.804845 | + | 0.593484i | \(0.202248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.3475 | −0.764911 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.21395 | −0.308155 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.44008 | −0.395707 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7197 | −1.28215 | −0.641077 | − | 0.767477i | \(-0.721512\pi\) | ||||
−0.641077 | + | 0.767477i | \(0.721512\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0238 | −0.865490 | −0.432745 | − | 0.901516i | \(-0.642455\pi\) | ||||
−0.432745 | + | 0.901516i | \(0.642455\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.12069 | 0.293587 | 0.146794 | − | 0.989167i | \(-0.453105\pi\) | ||||
0.146794 | + | 0.989167i | \(0.453105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.86868 | −0.699572 | −0.349786 | − | 0.936830i | \(-0.613746\pi\) | ||||
−0.349786 | + | 0.936830i | \(0.613746\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.34174 | 0.306243 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.96490 | 0.278282 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.707024 | 0.0491416 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.01804 | 0.554620 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.93076 | 0.477133 | 0.238567 | − | 0.971126i | \(-0.423322\pi\) | ||||
0.238567 | + | 0.971126i | \(0.423322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.23341 | −0.0845119 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.0611 | 0.682994 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.86868 | −0.666864 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.2751 | −0.960246 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.0625 | 1.54438 | 0.772191 | − | 0.635391i | \(-0.219161\pi\) | ||||
0.772191 | + | 0.635391i | \(0.219161\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.86073 | 0.189873 | 0.0949366 | − | 0.995483i | \(-0.469735\pi\) | ||||
0.0949366 | + | 0.995483i | \(0.469735\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.5227 | 1.22402 | 0.612009 | − | 0.790851i | \(-0.290362\pi\) | ||||
0.612009 | + | 0.790851i | \(0.290362\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.02833 | −0.133455 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.1112 | 1.51407 | 0.757033 | − | 0.653376i | \(-0.226648\pi\) | ||||
0.757033 | + | 0.653376i | \(0.226648\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −23.9717 | −1.55713 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.01270 | 0.582983 | 0.291491 | − | 0.956573i | \(-0.405849\pi\) | ||||
0.291491 | + | 0.956573i | \(0.405849\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4415 | −0.801427 | −0.400713 | − | 0.916203i | \(-0.631238\pi\) | ||||
−0.400713 | + | 0.916203i | \(0.631238\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.39354 | 0.217696 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.1617 | 1.72826 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.0173 | −1.45866 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.3984 | −1.35066 | −0.675329 | − | 0.737517i | \(-0.735998\pi\) | ||||
−0.675329 | + | 0.737517i | \(0.735998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.67419 | 0.168125 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.5737 | 1.72000 | 0.859999 | − | 0.510296i | \(-0.170464\pi\) | ||||
0.859999 | + | 0.510296i | \(0.170464\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.76815 | −0.420552 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.30077 | −0.0805159 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.77388 | 0.417695 | 0.208848 | − | 0.977948i | \(-0.433029\pi\) | ||||
0.208848 | + | 0.977948i | \(0.433029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −20.7173 | −1.26788 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.5794 | −0.888922 | −0.444461 | − | 0.895798i | \(-0.646605\pi\) | ||||
−0.444461 | + | 0.895798i | \(0.646605\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.3842 | −1.42049 | −0.710244 | − | 0.703956i | \(-0.751415\pi\) | ||||
−0.710244 | + | 0.703956i | \(0.751415\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.87113 | −0.415860 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.57577 | 0.515268 | 0.257634 | − | 0.966243i | \(-0.417057\pi\) | ||||
0.257634 | + | 0.966243i | \(0.417057\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.30077 | −0.197612 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.49675 | −0.208598 | −0.104299 | − | 0.994546i | \(-0.533260\pi\) | ||||
−0.104299 | + | 0.994546i | \(0.533260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.2952 | −1.08754 | −0.543769 | − | 0.839235i | \(-0.683003\pi\) | ||||
−0.543769 | + | 0.839235i | \(0.683003\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.131318 | −0.00775143 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.46746 | −0.321615 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.49438 | −0.0876020 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.4752 | 1.78038 | 0.890189 | − | 0.455592i | \(-0.150572\pi\) | ||||
0.890189 | + | 0.455592i | \(0.150572\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.75044 | 0.391700 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.05901 | 0.523896 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.40498 | 0.426816 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 22.0374 | 1.26601 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.8725 | 1.41955 | 0.709773 | − | 0.704430i | \(-0.248797\pi\) | ||||
0.709773 | + | 0.704430i | \(0.248797\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.844830 | 0.0480607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.42579 | −0.421078 | −0.210539 | − | 0.977585i | \(-0.567522\pi\) | ||||
−0.210539 | + | 0.977585i | \(0.567522\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.10594 | 0.458175 | 0.229088 | − | 0.973406i | \(-0.426426\pi\) | ||||
0.229088 | + | 0.973406i | \(0.426426\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.6010 | −0.820076 | −0.410038 | − | 0.912068i | \(-0.634485\pi\) | ||||
−0.410038 | + | 0.912068i | \(0.634485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.91994 | −0.275464 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.8100 | −1.71964 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.9434 | −1.22096 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.564380 | 0.0312103 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.82702 | 0.266122 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.7374 | −1.63452 | −0.817258 | − | 0.576271i | \(-0.804507\pi\) | ||||
−0.817258 | + | 0.576271i | \(0.804507\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.22044 | 0.121679 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.88799 | −0.429686 | −0.214843 | − | 0.976649i | \(-0.568924\pi\) | ||||
−0.214843 | + | 0.976649i | \(0.568924\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.16289 | −0.334722 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.4846 | −0.676078 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.28725 | 0.176469 | 0.0882344 | − | 0.996100i | \(-0.471878\pi\) | ||||
0.0882344 | + | 0.996100i | \(0.471878\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.68073 | 0.357611 | 0.178806 | − | 0.983884i | \(-0.442777\pi\) | ||||
0.178806 | + | 0.983884i | \(0.442777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.8676 | 1.22058 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 26.3234 | 1.40105 | 0.700527 | − | 0.713626i | \(-0.252948\pi\) | ||||
0.700527 | + | 0.713626i | \(0.252948\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.55105 | 0.293793 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.27155 | 0.436556 | 0.218278 | − | 0.975887i | \(-0.429956\pi\) | ||||
0.218278 | + | 0.975887i | \(0.429956\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.7525 | 1.19750 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.4637 | −0.811635 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −33.7548 | −1.76198 | −0.880992 | − | 0.473130i | \(-0.843124\pi\) | ||||
−0.880992 | + | 0.473130i | \(0.843124\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.0430816 | 0.00224274 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.0374 | −0.521114 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.0582 | 1.45280 | 0.726400 | − | 0.687272i | \(-0.241192\pi\) | ||||
0.726400 | + | 0.687272i | \(0.241192\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.6667 | −0.858377 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6585 | −0.804322 | −0.402161 | − | 0.915569i | \(-0.631741\pi\) | ||||
−0.402161 | + | 0.915569i | \(0.631741\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.21744 | 0.472224 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.6950 | 0.955270 | 0.477635 | − | 0.878558i | \(-0.341494\pi\) | ||||
0.477635 | + | 0.878558i | \(0.341494\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.42937 | −0.123492 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.7798 | 1.71270 | 0.856352 | − | 0.516392i | \(-0.172725\pi\) | ||||
0.856352 | + | 0.516392i | \(0.172725\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.31859 | −0.370117 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −17.1932 | −0.867284 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.466183 | 0.0233971 | 0.0116985 | − | 0.999932i | \(-0.496276\pi\) | ||||
0.0116985 | + | 0.999932i | \(0.496276\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.5622 | −0.528771 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.2221 | 1.65903 | 0.829516 | − | 0.558483i | \(-0.188616\pi\) | ||||
0.829516 | + | 0.558483i | \(0.188616\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −42.2924 | −2.10674 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.39841 | 0.416294 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.4588 | −0.764390 | −0.382195 | − | 0.924082i | \(-0.624832\pi\) | ||||
−0.382195 | + | 0.924082i | \(0.624832\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.3872 | 0.561688 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.9864 | −0.540608 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.8787 | −0.826551 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.0268 | −1.41805 | −0.709025 | − | 0.705183i | \(-0.750865\pi\) | ||||
−0.709025 | + | 0.705183i | \(0.750865\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.31745 | −0.259156 | −0.129578 | − | 0.991569i | \(-0.541362\pi\) | ||||
−0.129578 | + | 0.991569i | \(0.541362\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.58361 | −0.0769977 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.33030 | −0.306345 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.52620 | 0.411649 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.6480 | 0.850073 | 0.425036 | − | 0.905176i | \(-0.360261\pi\) | ||||
0.425036 | + | 0.905176i | \(0.360261\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5011 | 0.889107 | 0.444554 | − | 0.895752i | \(-0.353362\pi\) | ||||
0.444554 | + | 0.895752i | \(0.353362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.9254 | 0.666140 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.7444 | −0.703711 | −0.351855 | − | 0.936054i | \(-0.614449\pi\) | ||||
−0.351855 | + | 0.936054i | \(0.614449\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.328072 | −0.0156225 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0223 | −0.856264 | −0.428132 | − | 0.903716i | \(-0.640828\pi\) | ||||
−0.428132 | + | 0.903716i | \(0.640828\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.26498 | −0.0598314 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.46746 | −0.116447 | −0.0582233 | − | 0.998304i | \(-0.518544\pi\) | ||||
−0.0582233 | + | 0.998304i | \(0.518544\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.162948 | 0.00767294 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.0464 | −0.472020 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.73587 | 0.0812004 | 0.0406002 | − | 0.999175i | \(-0.487073\pi\) | ||||
0.0406002 | + | 0.999175i | \(0.487073\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.4743 | −0.862306 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.00725 | 0.419510 | 0.209755 | − | 0.977754i | \(-0.432733\pi\) | ||||
0.209755 | + | 0.977754i | \(0.432733\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.1293 | 1.81849 | 0.909246 | − | 0.416260i | \(-0.136659\pi\) | ||||
0.909246 | + | 0.416260i | \(0.136659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.47873 | 0.299800 | 0.149900 | − | 0.988701i | \(-0.452105\pi\) | ||||
0.149900 | + | 0.988701i | \(0.452105\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.65614 | 0.122649 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.3089 | 1.39656 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.18864 | −0.422494 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.29298 | 0.150775 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.5651 | 1.03103 | 0.515514 | − | 0.856881i | \(-0.327601\pi\) | ||||
0.515514 | + | 0.856881i | \(0.327601\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.4502 | 1.29722 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.52271 | −0.160289 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −39.2500 | −1.77859 | −0.889293 | − | 0.457339i | \(-0.848803\pi\) | ||||
−0.889293 | + | 0.457339i | \(0.848803\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.62386 | −0.0734336 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.7793 | 1.52444 | 0.762220 | − | 0.647318i | \(-0.224109\pi\) | ||||
0.762220 | + | 0.647318i | \(0.224109\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.4647 | 0.606418 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.754563 | −0.0338468 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.6529 | −0.521654 | −0.260827 | − | 0.965386i | \(-0.583995\pi\) | ||||
−0.260827 | + | 0.965386i | \(0.583995\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.26428 | −0.235191 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.0639 | 0.671668 | 0.335834 | − | 0.941921i | \(-0.390982\pi\) | ||||
0.335834 | + | 0.941921i | \(0.390982\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.63329 | 0.339006 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.8458 | −0.879649 | −0.439825 | − | 0.898084i | \(-0.644959\pi\) | ||||
−0.439825 | + | 0.898084i | \(0.644959\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.03736 | −0.267077 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 35.1517 | 1.55199 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.98971 | −0.263427 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.0208 | −1.14218 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.7964 | −0.823484 | −0.411742 | − | 0.911300i | \(-0.635080\pi\) | ||||
−0.411742 | + | 0.911300i | \(0.635080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −31.0907 | −1.35950 | −0.679750 | − | 0.733444i | \(-0.737912\pi\) | ||||
−0.679750 | + | 0.733444i | \(0.737912\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 34.1672 | 1.48835 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3556 | −0.798070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.60435 | 0.156415 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.552000 | 0.0239098 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.0951 | 0.694554 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.24087 | −0.0534482 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −35.8816 | −1.54267 | −0.771336 | − | 0.636428i | \(-0.780411\pi\) | ||||
−0.771336 | + | 0.636428i | \(0.780411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 35.3993 | 1.51913 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.4869 | 1.08974 | 0.544871 | − | 0.838520i | \(-0.316579\pi\) | ||||
0.544871 | + | 0.838520i | \(0.316579\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.07679 | 0.0886354 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.6197 | −1.09144 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.6652 | −0.623626 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.5917 | 0.999612 | 0.499806 | − | 0.866137i | \(-0.333405\pi\) | ||||
0.499806 | + | 0.866137i | \(0.333405\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −31.1272 | −1.31654 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.88814 | −0.290818 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.25815 | −0.0530245 | −0.0265123 | − | 0.999648i | \(-0.508440\pi\) | ||||
−0.0265123 | + | 0.999648i | \(0.508440\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.90815 | −0.332111 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.4899 | 0.984747 | 0.492373 | − | 0.870384i | \(-0.336129\pi\) | ||||
0.492373 | + | 0.870384i | \(0.336129\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.0476 | 0.755269 | 0.377634 | − | 0.925955i | \(-0.376738\pi\) | ||||
0.377634 | + | 0.925955i | \(0.376738\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −28.9647 | −1.21002 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.4141 | 1.89061 | 0.945306 | − | 0.326184i | \(-0.105763\pi\) | ||||
0.945306 | + | 0.326184i | \(0.105763\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.6541 | −0.816796 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.0813 | −0.584189 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.4551 | 0.515837 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −38.1946 | −1.57646 | −0.788230 | − | 0.615381i | \(-0.789002\pi\) | ||||
−0.788230 | + | 0.615381i | \(0.789002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −65.0112 | −2.67874 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.73569 | 0.277069 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −11.0544 | −0.453952 | −0.226976 | − | 0.973900i | \(-0.572884\pi\) | ||||
−0.226976 | + | 0.973900i | \(0.572884\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −16.1314 | −0.660213 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.4206 | −0.425773 | −0.212887 | − | 0.977077i | \(-0.568286\pi\) | ||||
−0.212887 | + | 0.977077i | \(0.568286\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.5047 | −1.28510 | −0.642552 | − | 0.766242i | \(-0.722125\pi\) | ||||
−0.642552 | + | 0.766242i | \(0.722125\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.871407 | −0.0354864 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.9493 | −1.41855 | −0.709275 | − | 0.704932i | \(-0.750977\pi\) | ||||
−0.709275 | + | 0.704932i | \(0.750977\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.48105 | 0.262625 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.2906 | −0.820869 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.9464 | −1.53264 | −0.766319 | − | 0.642460i | \(-0.777914\pi\) | ||||
−0.766319 | + | 0.642460i | \(0.777914\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.0081 | −1.08731 | −0.543653 | − | 0.839310i | \(-0.682959\pi\) | ||||
−0.543653 | + | 0.839310i | \(0.682959\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.0656 | 1.16825 | 0.584123 | − | 0.811665i | \(-0.301439\pi\) | ||||
0.584123 | + | 0.811665i | \(0.301439\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.7238 | 0.470462 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.6742 | −0.507781 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.1063 | 0.523416 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.9844 | −0.916447 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.8146 | 1.54518 | 0.772592 | − | 0.634903i | \(-0.218960\pi\) | ||||
0.772592 | + | 0.634903i | \(0.218960\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.3290 | 0.450289 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.20355 | −0.166551 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.247551 | 0.00979297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.2837 | 1.59111 | 0.795555 | − | 0.605881i | \(-0.207179\pi\) | ||||
0.795555 | + | 0.605881i | \(0.207179\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.02226 | −0.0797500 | −0.0398750 | − | 0.999205i | \(-0.512696\pi\) | ||||
−0.0398750 | + | 0.999205i | \(0.512696\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.08779 | 0.317964 | 0.158982 | − | 0.987281i | \(-0.449179\pi\) | ||||
0.158982 | + | 0.987281i | \(0.449179\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.6328 | 0.535133 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.4459 | 0.644568 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.0259 | 0.979338 | 0.489669 | − | 0.871908i | \(-0.337118\pi\) | ||||
0.489669 | + | 0.871908i | \(0.337118\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.98069 | 0.0772740 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.1054 | 1.36751 | 0.683756 | − | 0.729711i | \(-0.260345\pi\) | ||||
0.683756 | + | 0.729711i | \(0.260345\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.69197 | −0.299183 | −0.149592 | − | 0.988748i | \(-0.547796\pi\) | ||||
−0.149592 | + | 0.988748i | \(0.547796\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.3341 | −0.906221 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.54471 | −0.330853 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 37.6981 | 1.45749 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.85510 | 0.303243 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.07019 | −0.156894 | −0.0784472 | − | 0.996918i | \(-0.524996\pi\) | ||||
−0.0784472 | + | 0.996918i | \(0.524996\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.6451 | 1.25465 | 0.627327 | − | 0.778756i | \(-0.284149\pi\) | ||||
0.627327 | + | 0.778756i | \(0.284149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.914215 | −0.0350843 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.67616 | 0.179191 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.7284 | 1.36711 | 0.683554 | − | 0.729900i | \(-0.260433\pi\) | ||||
0.683554 | + | 0.729900i | \(0.260433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 30.2773 | 1.15515 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 42.1925 | 1.60741 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.9663 | −1.06389 | −0.531945 | − | 0.846779i | \(-0.678539\pi\) | ||||
−0.531945 | + | 0.846779i | \(0.678539\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.407096 | 0.0154643 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.445949 | −0.0168915 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 37.7777 | 1.42888 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.7996 | −0.747822 | −0.373911 | − | 0.927465i | \(-0.621983\pi\) | ||||
−0.373911 | + | 0.927465i | \(0.621983\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.7332 | 1.64943 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.4818 | 0.507034 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.46892 | 0.318057 | 0.159029 | − | 0.987274i | \(-0.449164\pi\) | ||||
0.159029 | + | 0.987274i | \(0.449164\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.81123 | 0.180435 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.6826 | −0.812020 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.7322 | 0.550183 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.2512 | 0.419598 | 0.209799 | − | 0.977745i | \(-0.432719\pi\) | ||||
0.209799 | + | 0.977745i | \(0.432719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.516841 | 0.0192482 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.3369 | −0.756338 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.2716 | 0.974360 | 0.487180 | − | 0.873302i | \(-0.338026\pi\) | ||||
0.487180 | + | 0.873302i | \(0.338026\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.2716 | 1.08413 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.1470 | 0.930096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.7804 | 1.80175 | 0.900873 | − | 0.434082i | \(-0.142927\pi\) | ||||
0.900873 | + | 0.434082i | \(0.142927\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.29594 | −0.121407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −37.5871 | −1.38267 | −0.691333 | − | 0.722537i | \(-0.742976\pi\) | ||||
−0.691333 | + | 0.722537i | \(0.742976\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 44.3986 | 1.63102 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.2572 | 1.07334 | 0.536671 | − | 0.843792i | \(-0.319682\pi\) | ||||
0.536671 | + | 0.843792i | \(0.319682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.61967 | 0.169025 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −18.8486 | −0.688712 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.4125 | −1.51116 | −0.755582 | − | 0.655054i | \(-0.772646\pi\) | ||||
−0.755582 | + | 0.655054i | \(0.772646\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −34.9780 | −1.27467 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.1411 | −1.20453 | −0.602266 | − | 0.798295i | \(-0.705736\pi\) | ||||
−0.602266 | + | 0.798295i | \(0.705736\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.37124 | 0.158666 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.08166 | 0.256710 | 0.128355 | − | 0.991728i | \(-0.459030\pi\) | ||||
0.128355 | + | 0.991728i | \(0.459030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.345270 | 0.0124996 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 46.1820 | 1.66754 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.8844 | 0.753112 | 0.376556 | − | 0.926394i | \(-0.377108\pi\) | ||||
0.376556 | + | 0.926394i | \(0.377108\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 45.0720 | 1.62323 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.0409 | 1.79985 | 0.899923 | − | 0.436049i | \(-0.143623\pi\) | ||||
0.899923 | + | 0.436049i | \(0.143623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.0632 | −0.396892 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.848524 | 0.0304015 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.936316 | 0.0335040 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.5694 | −0.770827 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0831 | 0.822824 | 0.411412 | − | 0.911449i | \(-0.365036\pi\) | ||||
0.411412 | + | 0.911449i | \(0.365036\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.0726 | 0.394195 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.77026 | −0.134055 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.6097 | 0.944939 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.553975 | 0.0196228 | 0.00981140 | − | 0.999952i | \(-0.496877\pi\) | ||||
0.00981140 | + | 0.999952i | \(0.496877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.3923 | 0.579920 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.15805 | 0.146917 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.49159 | 0.264372 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.8316 | −0.838910 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.8647 | −1.50704 | −0.753521 | − | 0.657424i | \(-0.771646\pi\) | ||||
−0.753521 | + | 0.657424i | \(0.771646\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.28042 | −0.115191 | −0.0575955 | − | 0.998340i | \(-0.518343\pi\) | ||||
−0.0575955 | + | 0.998340i | \(0.518343\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −38.2238 | −1.34057 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.8482 | −1.67400 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.37907 | 0.0481885 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.73361 | −0.269905 | −0.134952 | − | 0.990852i | \(-0.543088\pi\) | ||||
−0.134952 | + | 0.990852i | \(0.543088\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.9368 | −0.799527 | −0.399764 | − | 0.916618i | \(-0.630908\pi\) | ||||
−0.399764 | + | 0.916618i | \(0.630908\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −48.4640 | −1.68526 | −0.842629 | − | 0.538494i | \(-0.818993\pi\) | ||||
−0.842629 | + | 0.538494i | \(0.818993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.4482 | −1.19643 | −0.598217 | − | 0.801334i | \(-0.704124\pi\) | ||||
−0.598217 | + | 0.801334i | \(0.704124\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.0180 | 0.486278 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.39596 | 0.117663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −54.7333 | −1.89186 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.81974 | 0.339015 | 0.169508 | − | 0.985529i | \(-0.445782\pi\) | ||||
0.169508 | + | 0.985529i | \(0.445782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2795 | −0.457915 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.71579 | −0.196862 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.46024 | −0.325058 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.9054 | −1.02635 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.5860 | 0.500000 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.3139 | −1.44880 | −0.724400 | − | 0.689380i | \(-0.757883\pi\) | ||||
−0.724400 | + | 0.689380i | \(0.757883\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.54342 | 0.0527224 | 0.0263612 | − | 0.999652i | \(-0.491608\pi\) | ||||
0.0263612 | + | 0.999652i | \(0.491608\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.41854 | −0.150759 | −0.0753793 | − | 0.997155i | \(-0.524017\pi\) | ||||
−0.0753793 | + | 0.997155i | \(0.524017\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.214652 | −0.00731533 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.91388 | 0.167270 | 0.0836352 | − | 0.996496i | \(-0.473347\pi\) | ||||
0.0836352 | + | 0.996496i | \(0.473347\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.93713 | −0.303521 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 18.1976 | 0.617311 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.1652 | −0.378319 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.299928 | 0.0101510 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7021 | 0.395153 | 0.197577 | − | 0.980287i | \(-0.436693\pi\) | ||||
0.197577 | + | 0.980287i | \(0.436693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 49.8148 | 1.68021 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.8823 | −1.00676 | −0.503380 | − | 0.864065i | \(-0.667910\pi\) | ||||
−0.503380 | + | 0.864065i | \(0.667910\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.6829 | −1.50370 | −0.751850 | − | 0.659334i | \(-0.770838\pi\) | ||||
−0.751850 | + | 0.659334i | \(0.770838\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15.8523 | −0.532269 | −0.266135 | − | 0.963936i | \(-0.585747\pi\) | ||||
−0.266135 | + | 0.963936i | \(0.585747\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.63895 | 0.189124 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.81301 | 0.328748 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31.1903 | −1.04374 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.8079 | 0.494421 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 39.8914 | 1.33045 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.0865 | −1.13558 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 12.1042 | 0.402803 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.5453 | −0.881421 | −0.440710 | − | 0.897649i | \(-0.645273\pi\) | ||||
−0.440710 | + | 0.897649i | \(0.645273\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.42299 | −0.146701 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.855810 | −0.0283543 | −0.0141771 | − | 0.999899i | \(-0.504513\pi\) | ||||
−0.0141771 | + | 0.999899i | \(0.504513\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.4730 | 0.578273 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.5183 | −0.347344 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.6925 | 0.451675 | 0.225838 | − | 0.974165i | \(-0.427488\pi\) | ||||
0.225838 | + | 0.974165i | \(0.427488\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.6566 | 1.33968 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.17184 | 0.104402 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.169561 | −0.00556911 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.2648 | 0.828912 | 0.414456 | − | 0.910069i | \(-0.363972\pi\) | ||||
0.414456 | + | 0.910069i | \(0.363972\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.46162 | −0.211771 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.1382 | −0.397388 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.8534 | 0.942599 | 0.471299 | − | 0.881973i | \(-0.343785\pi\) | ||||
0.471299 | + | 0.881973i | \(0.343785\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.2500 | 0.432397 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.28998 | 0.139850 | 0.0699248 | − | 0.997552i | \(-0.477724\pi\) | ||||
0.0699248 | + | 0.997552i | \(0.477724\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.283001 | 0.00921578 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −48.2836 | −1.56901 | −0.784503 | − | 0.620126i | \(-0.787082\pi\) | ||||
−0.784503 | + | 0.620126i | \(0.787082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 25.3783 | 0.823815 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.8669 | −0.773937 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.2147 | −1.10832 | −0.554162 | − | 0.832409i | \(-0.686961\pi\) | ||||
−0.554162 | + | 0.832409i | \(0.686961\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.04215 | −0.259966 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.96632 | 0.224954 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.2263 | 2.26536 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.18369 | 0.199267 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49.1870 | −1.58175 | −0.790873 | − | 0.611980i | \(-0.790373\pi\) | ||||
−0.790873 | + | 0.611980i | \(0.790373\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.8687 | −1.15227 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.2107 | −0.809051 | −0.404526 | − | 0.914527i | \(-0.632563\pi\) | ||||
−0.404526 | + | 0.914527i | \(0.632563\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.3258 | −0.331031 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0389 | 0.577116 | 0.288558 | − | 0.957462i | \(-0.406824\pi\) | ||||
0.288558 | + | 0.957462i | \(0.406824\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.7271 | 0.502639 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.113274 | −0.00361654 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.6099 | −1.64610 | −0.823051 | − | 0.567968i | \(-0.807730\pi\) | ||||
−0.823051 | + | 0.567968i | \(0.807730\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.89025 | 0.251150 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.9584 | −0.507447 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.4063 | 0.489398 | 0.244699 | − | 0.969599i | \(-0.421311\pi\) | ||||
0.244699 | + | 0.969599i | \(0.421311\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −48.6089 | −1.54256 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.6176 | 0.431274 | 0.215637 | − | 0.976474i | \(-0.430817\pi\) | ||||
0.215637 | + | 0.976474i | \(0.430817\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.8193 | 1.16491 |
(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 | 5600.2.a.bu.1.4 | 5 | ||
4.3 | odd | 2 | 5600.2.a.bx.1.2 | 5 | |||
5.2 | odd | 4 | 1120.2.g.b.449.4 | ✓ | 10 | ||
5.3 | odd | 4 | 1120.2.g.b.449.7 | yes | 10 | ||
5.4 | even | 2 | 5600.2.a.bw.1.2 | 5 | |||
20.3 | even | 4 | 1120.2.g.c.449.4 | yes | 10 | ||
20.7 | even | 4 | 1120.2.g.c.449.7 | yes | 10 | ||
20.19 | odd | 2 | 5600.2.a.bv.1.4 | 5 | |||
40.3 | even | 4 | 2240.2.g.n.449.7 | 10 | |||
40.13 | odd | 4 | 2240.2.g.o.449.4 | 10 | |||
40.27 | even | 4 | 2240.2.g.n.449.4 | 10 | |||
40.37 | odd | 4 | 2240.2.g.o.449.7 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1120.2.g.b.449.4 | ✓ | 10 | 5.2 | odd | 4 | ||
1120.2.g.b.449.7 | yes | 10 | 5.3 | odd | 4 | ||
1120.2.g.c.449.4 | yes | 10 | 20.3 | even | 4 | ||
1120.2.g.c.449.7 | yes | 10 | 20.7 | even | 4 | ||
2240.2.g.n.449.4 | 10 | 40.27 | even | 4 | |||
2240.2.g.n.449.7 | 10 | 40.3 | even | 4 | |||
2240.2.g.o.449.4 | 10 | 40.13 | odd | 4 | |||
2240.2.g.o.449.7 | 10 | 40.37 | odd | 4 | |||
5600.2.a.bu.1.4 | 5 | 1.1 | even | 1 | trivial | ||
5600.2.a.bv.1.4 | 5 | 20.19 | odd | 2 | |||
5600.2.a.bw.1.2 | 5 | 5.4 | even | 2 | |||
5600.2.a.bx.1.2 | 5 | 4.3 | odd | 2 |