Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(1,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5184.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.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: | \(41.3944484078\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2592) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.18890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.64575 | 1.18322 | 0.591608 | − | 0.806226i | \(-0.298493\pi\) | ||||
0.591608 | + | 0.806226i | \(0.298493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.913701 | −0.345346 | −0.172673 | − | 0.984979i | \(-0.555240\pi\) | ||||
−0.172673 | + | 0.984979i | \(0.555240\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.58258 | −1.68321 | −0.841605 | − | 0.540094i | \(-0.818389\pi\) | ||||
−0.841605 | + | 0.540094i | \(0.818389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.58258 | −0.716278 | −0.358139 | − | 0.933668i | \(-0.616589\pi\) | ||||
−0.358139 | + | 0.933668i | \(0.616589\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73205 | 0.420084 | 0.210042 | − | 0.977692i | \(-0.432640\pi\) | ||||
0.210042 | + | 0.977692i | \(0.432640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.84190 | 1.79906 | 0.899528 | − | 0.436863i | \(-0.143911\pi\) | ||||
0.899528 | + | 0.436863i | \(0.143911\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.58258 | −0.329990 | −0.164995 | − | 0.986294i | \(-0.552761\pi\) | ||||
−0.164995 | + | 0.986294i | \(0.552761\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.818350 | −0.151964 | −0.0759819 | − | 0.997109i | \(-0.524209\pi\) | ||||
−0.0759819 | + | 0.997109i | \(0.524209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.82740 | −0.328211 | −0.164105 | − | 0.986443i | \(-0.552474\pi\) | ||||
−0.164105 | + | 0.986443i | \(0.552474\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.41742 | −0.408619 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.58258 | 1.08217 | 0.541084 | − | 0.840968i | \(-0.318014\pi\) | ||||
0.541084 | + | 0.840968i | \(0.318014\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.75560 | 1.36740 | 0.683698 | − | 0.729765i | \(-0.260371\pi\) | ||||
0.683698 | + | 0.729765i | \(0.260371\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.84190 | −1.19588 | −0.597940 | − | 0.801541i | \(-0.704014\pi\) | ||||
−0.597940 | + | 0.801541i | \(0.704014\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.16515 | −0.880736 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.75560 | 1.20267 | 0.601337 | − | 0.798995i | \(-0.294635\pi\) | ||||
0.601337 | + | 0.798995i | \(0.294635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.7701 | −1.99160 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.5826 | 1.35496 | 0.677480 | − | 0.735541i | \(-0.263072\pi\) | ||||
0.677480 | + | 0.735541i | \(0.263072\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.83285 | −0.847511 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.84190 | −0.958041 | −0.479021 | − | 0.877804i | \(-0.659008\pi\) | ||||
−0.479021 | + | 0.877804i | \(0.659008\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.58258 | 1.13724 | 0.568621 | − | 0.822599i | \(-0.307477\pi\) | ||||
0.568621 | + | 0.822599i | \(0.307477\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.1652 | 1.42382 | 0.711912 | − | 0.702269i | \(-0.247830\pi\) | ||||
0.711912 | + | 0.702269i | \(0.247830\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.10080 | 0.581290 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7701 | 1.66177 | 0.830883 | − | 0.556447i | \(-0.187836\pi\) | ||||
0.830883 | + | 0.556447i | \(0.187836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.16515 | 0.347421 | 0.173710 | − | 0.984797i | \(-0.444424\pi\) | ||||
0.173710 | + | 0.984797i | \(0.444424\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.58258 | 0.497050 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.85095 | 0.938199 | 0.469100 | − | 0.883145i | \(-0.344579\pi\) | ||||
0.469100 | + | 0.883145i | \(0.344579\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.35970 | 0.247364 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.7477 | 2.12867 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1652 | 1.33672 | 0.668359 | − | 0.743839i | \(-0.266997\pi\) | ||||
0.668359 | + | 0.743839i | \(0.266997\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.8564 | −1.37876 | −0.689382 | − | 0.724398i | \(-0.742118\pi\) | ||||
−0.689382 | + | 0.724398i | \(0.742118\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.3386 | 1.90549 | 0.952745 | − | 0.303772i | \(-0.0982460\pi\) | ||||
0.952745 | + | 0.303772i | \(0.0982460\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.1652 | −1.07938 | −0.539688 | − | 0.841865i | \(-0.681458\pi\) | ||||
−0.539688 | + | 0.841865i | \(0.681458\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.41742 | 0.518895 | 0.259448 | − | 0.965757i | \(-0.416460\pi\) | ||||
0.259448 | + | 0.965757i | \(0.416460\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.92275 | −0.180877 | −0.0904386 | − | 0.995902i | \(-0.528827\pi\) | ||||
−0.0904386 | + | 0.995902i | \(0.528827\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.18710 | −0.390449 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.58258 | −0.145074 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.1652 | 1.83320 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.93725 | −0.709930 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.9427 | −1.14848 | −0.574240 | − | 0.818687i | \(-0.694702\pi\) | ||||
−0.574240 | + | 0.818687i | \(0.694702\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.58258 | −0.487752 | −0.243876 | − | 0.969806i | \(-0.578419\pi\) | ||||
−0.243876 | + | 0.969806i | \(0.578419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.16515 | −0.621297 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.66025 | −0.739895 | −0.369948 | − | 0.929053i | \(-0.620624\pi\) | ||||
−0.369948 | + | 0.929053i | \(0.620624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.82740 | 0.154998 | 0.0774991 | − | 0.996992i | \(-0.475307\pi\) | ||||
0.0774991 | + | 0.996992i | \(0.475307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.4174 | 1.20565 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.16515 | −0.179806 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.8655 | 1.21783 | 0.608913 | − | 0.793237i | \(-0.291606\pi\) | ||||
0.608913 | + | 0.793237i | \(0.291606\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.3386 | 1.57375 | 0.786877 | − | 0.617110i | \(-0.211697\pi\) | ||||
0.786877 | + | 0.617110i | \(0.211697\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.83485 | −0.388344 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.4174 | 0.911210 | 0.455605 | − | 0.890182i | \(-0.349423\pi\) | ||||
0.455605 | + | 0.890182i | \(0.349423\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.44600 | 0.113961 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.5112 | 1.37158 | 0.685792 | − | 0.727798i | \(-0.259456\pi\) | ||||
0.685792 | + | 0.727798i | \(0.259456\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.41742 | 0.496595 | 0.248298 | − | 0.968684i | \(-0.420129\pi\) | ||||
0.248298 | + | 0.968684i | \(0.420129\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.33030 | −0.486946 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.3296 | −1.39357 | −0.696785 | − | 0.717280i | \(-0.745387\pi\) | ||||
−0.696785 | + | 0.717280i | \(0.745387\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.82740 | −0.138139 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 17.4159 | 1.28044 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.66930 | −0.707090 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.58258 | 0.114511 | 0.0572556 | − | 0.998360i | \(-0.481765\pi\) | ||||
0.0572556 | + | 0.998360i | \(0.481765\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.16515 | 0.443777 | 0.221889 | − | 0.975072i | \(-0.428778\pi\) | ||||
0.221889 | + | 0.975072i | \(0.428778\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.9663 | 1.42254 | 0.711269 | − | 0.702920i | \(-0.248121\pi\) | ||||
0.711269 | + | 0.702920i | \(0.248121\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.65480 | 0.259082 | 0.129541 | − | 0.991574i | \(-0.458650\pi\) | ||||
0.129541 | + | 0.991574i | \(0.458650\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.747727 | 0.0524802 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.1652 | 1.61792 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −43.7780 | −3.02819 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.01450 | −0.414055 | −0.207028 | − | 0.978335i | \(-0.566379\pi\) | ||||
−0.207028 | + | 0.978335i | \(0.566379\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.7477 | −1.41498 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.66970 | 0.113346 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.47315 | −0.300897 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.2523 | −1.35619 | −0.678097 | − | 0.734972i | \(-0.737195\pi\) | ||||
−0.678097 | + | 0.734972i | \(0.737195\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.7477 | −1.11159 | −0.555793 | − | 0.831321i | \(-0.687585\pi\) | ||||
−0.555793 | + | 0.831321i | \(0.687585\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.7477 | 1.56929 | 0.784647 | − | 0.619943i | \(-0.212844\pi\) | ||||
0.784647 | + | 0.619943i | \(0.212844\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.0707 | −1.38038 | −0.690192 | − | 0.723626i | \(-0.742474\pi\) | ||||
−0.690192 | + | 0.723626i | \(0.742474\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.1660 | 1.38072 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.1652 | −1.75717 | −0.878584 | − | 0.477588i | \(-0.841511\pi\) | ||||
−0.878584 | + | 0.477588i | \(0.841511\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | 0.0322078 | − | 0.999481i | \(-0.489746\pi\) | ||||
0.0322078 | + | 0.999481i | \(0.489746\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.3115 | −1.04210 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.2523 | −1.28862 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.5826 | −0.857325 | −0.428662 | − | 0.903465i | \(-0.641015\pi\) | ||||
−0.428662 | + | 0.903465i | \(0.641015\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.83485 | 0.555442 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.02355 | 0.438117 | 0.219059 | − | 0.975712i | \(-0.429701\pi\) | ||||
0.219059 | + | 0.975712i | \(0.429701\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.01450 | −0.373723 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 30.3303 | 1.87025 | 0.935123 | − | 0.354322i | \(-0.115288\pi\) | ||||
0.935123 | + | 0.354322i | \(0.115288\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 23.1652 | 1.42302 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.7937 | −1.32878 | −0.664391 | − | 0.747385i | \(-0.731309\pi\) | ||||
−0.664391 | + | 0.747385i | \(0.731309\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.74110 | −0.166510 | −0.0832550 | − | 0.996528i | \(-0.526532\pi\) | ||||
−0.0832550 | + | 0.996528i | \(0.526532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.1652 | −0.673284 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3303 | −0.981193 | −0.490596 | − | 0.871387i | \(-0.663221\pi\) | ||||
−0.490596 | + | 0.871387i | \(0.663221\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.21425 | 0.430366 | 0.215183 | − | 0.976574i | \(-0.430965\pi\) | ||||
0.215183 | + | 0.976574i | \(0.430965\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.65480 | −0.217255 | −0.108628 | − | 0.994083i | \(-0.534646\pi\) | ||||
−0.108628 | + | 0.994083i | \(0.534646\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.00905 | −0.0589494 | −0.0294747 | − | 0.999566i | \(-0.509383\pi\) | ||||
−0.0294747 | + | 0.999566i | \(0.509383\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.1660 | −1.23233 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.08712 | 0.236364 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.16515 | 0.412992 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.9989 | 1.60321 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.3386 | −1.10371 | −0.551856 | − | 0.833939i | \(-0.686080\pi\) | ||||
−0.551856 | + | 0.833939i | \(0.686080\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.16515 | −0.179479 | −0.0897396 | − | 0.995965i | \(-0.528603\pi\) | ||||
−0.0897396 | + | 0.995965i | \(0.528603\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0000 | 1.07394 | 0.536972 | − | 0.843600i | \(-0.319568\pi\) | ||||
0.536972 | + | 0.843600i | \(0.319568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.3477 | −1.14284 | −0.571419 | − | 0.820658i | \(-0.693607\pi\) | ||||
−0.571419 | + | 0.820658i | \(0.693607\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.56850 | 0.255787 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.5826 | 0.755755 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.16515 | −0.286511 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.30960 | −0.402992 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.3531 | 1.39353 | 0.696767 | − | 0.717298i | \(-0.254621\pi\) | ||||
0.696767 | + | 0.717298i | \(0.254621\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −20.7477 | −1.13357 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.16515 | −0.0634698 | −0.0317349 | − | 0.999496i | \(-0.510103\pi\) | ||||
−0.0317349 | + | 0.999496i | \(0.510103\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.2016 | 0.552448 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.0290 | 0.649505 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.4174 | 1.41816 | 0.709081 | − | 0.705127i | \(-0.249110\pi\) | ||||
0.709081 | + | 0.705127i | \(0.249110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.1652 | 0.918829 | 0.459415 | − | 0.888222i | \(-0.348059\pi\) | ||||
0.459415 | + | 0.888222i | \(0.348059\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.2016 | −0.542977 | −0.271488 | − | 0.962442i | \(-0.587516\pi\) | ||||
−0.271488 | + | 0.962442i | \(0.587516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.3531 | 1.34560 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.9129 | 1.26207 | 0.631037 | − | 0.775753i | \(-0.282630\pi\) | ||||
0.631037 | + | 0.775753i | \(0.282630\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 42.4955 | 2.23660 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.1860 | 1.68469 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.48220 | 0.286169 | 0.143084 | − | 0.989710i | \(-0.454298\pi\) | ||||
0.143084 | + | 0.989710i | \(0.454298\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.00000 | −0.415339 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.0000 | −0.724893 | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||||
−0.362446 | + | 0.932005i | \(0.618058\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.11345 | 0.108848 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.6838 | −0.805623 | −0.402812 | − | 0.915283i | \(-0.631967\pi\) | ||||
−0.402812 | + | 0.915283i | \(0.631967\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.41742 | 0.327915 | 0.163958 | − | 0.986467i | \(-0.447574\pi\) | ||||
0.163958 | + | 0.986467i | \(0.447574\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.4955 | 0.687792 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.44600 | −0.0733151 | −0.0366576 | − | 0.999328i | \(-0.511671\pi\) | ||||
−0.0366576 | + | 0.999328i | \(0.511671\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.74110 | −0.138623 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 39.0780 | 1.96623 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.74773 | 0.489224 | 0.244612 | − | 0.969621i | \(-0.421339\pi\) | ||||
0.244612 | + | 0.969621i | \(0.421339\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4877 | −0.523729 | −0.261864 | − | 0.965105i | \(-0.584337\pi\) | ||||
−0.261864 | + | 0.965105i | \(0.584337\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.71940 | 0.235090 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −36.7477 | −1.82152 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.16515 | −0.107060 | −0.0535299 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535299 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.30960 | 0.359682 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.37420 | 0.411073 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.1652 | 0.545453 | 0.272727 | − | 0.962092i | \(-0.412075\pi\) | ||||
0.272727 | + | 0.962092i | \(0.412075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.58258 | 0.418289 | 0.209145 | − | 0.977885i | \(-0.432932\pi\) | ||||
0.209145 | + | 0.977885i | \(0.432932\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.66930 | −0.467930 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.8348 | −1.00358 | −0.501790 | − | 0.864990i | \(-0.667325\pi\) | ||||
−0.501790 | + | 0.864990i | \(0.667325\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.3303 | 0.640613 | 0.320307 | − | 0.947314i | \(-0.396214\pi\) | ||||
0.320307 | + | 0.947314i | \(0.396214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.4104 | −0.593670 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1660 | 1.01020 | 0.505099 | − | 0.863061i | \(-0.331456\pi\) | ||||
0.505099 | + | 0.863061i | \(0.331456\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.6606 | 1.74180 | 0.870899 | − | 0.491462i | \(-0.163537\pi\) | ||||
0.870899 | + | 0.491462i | \(0.163537\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.4174 | 1.11009 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.9572 | 0.894646 | 0.447323 | − | 0.894372i | \(-0.352377\pi\) | ||||
0.447323 | + | 0.894372i | \(0.352377\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −48.8788 | −2.30161 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.24318 | 0.292685 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.1652 | −0.475506 | −0.237753 | − | 0.971326i | \(-0.576411\pi\) | ||||
−0.237753 | + | 0.971326i | \(0.576411\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.2668 | 1.22337 | 0.611684 | − | 0.791102i | \(-0.290493\pi\) | ||||
0.611684 | + | 0.791102i | \(0.290493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.5112 | 0.813815 | 0.406907 | − | 0.913469i | \(-0.366607\pi\) | ||||
0.406907 | + | 0.913469i | \(0.366607\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.1652 | −0.886857 | −0.443429 | − | 0.896310i | \(-0.646238\pi\) | ||||
−0.443429 | + | 0.896310i | \(0.646238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.16515 | 0.330856 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 43.7780 | 2.01292 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.6838 | 0.719622 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.74773 | −0.216929 | −0.108465 | − | 0.994100i | \(-0.534593\pi\) | ||||
−0.108465 | + | 0.994100i | \(0.534593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.0000 | −0.775133 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 34.8317 | 1.58163 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.5402 | 1.33859 | 0.669297 | − | 0.742995i | \(-0.266595\pi\) | ||||
0.669297 | + | 0.742995i | \(0.266595\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.58258 | −0.251938 | −0.125969 | − | 0.992034i | \(-0.540204\pi\) | ||||
−0.125969 | + | 0.992034i | \(0.540204\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.41742 | −0.0638376 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.75560 | −0.392743 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0435 | 0.807738 | 0.403869 | − | 0.914817i | \(-0.367665\pi\) | ||||
0.403869 | + | 0.914817i | \(0.367665\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.16515 | 0.141127 | 0.0705636 | − | 0.997507i | \(-0.477520\pi\) | ||||
0.0705636 | + | 0.997507i | \(0.477520\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.6606 | −1.63138 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.44600 | −0.0640928 | −0.0320464 | − | 0.999486i | \(-0.510202\pi\) | ||||
−0.0320464 | + | 0.999486i | \(0.510202\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1153 | −0.491712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 51.1652 | 2.25461 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44.6606 | −1.96417 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.2668 | −1.15077 | −0.575385 | − | 0.817883i | \(-0.695148\pi\) | ||||
−0.575385 | + | 0.817883i | \(0.695148\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −37.3821 | −1.63461 | −0.817303 | − | 0.576208i | \(-0.804532\pi\) | ||||
−0.817303 | + | 0.576208i | \(0.804532\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.16515 | −0.137876 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.4955 | −0.891107 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.6120 | −0.979435 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.5402 | −1.27713 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 34.4174 | 1.48246 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.9129 | 1.84497 | 0.922484 | − | 0.386034i | \(-0.126155\pi\) | ||||
0.922484 | + | 0.386034i | \(0.126155\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.3332 | 0.613965 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8564 | 0.592457 | 0.296229 | − | 0.955117i | \(-0.404271\pi\) | ||||
0.296229 | + | 0.955117i | \(0.404271\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.41742 | −0.273391 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.4955 | −0.573885 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.5312 | −1.20890 | −0.604452 | − | 0.796641i | \(-0.706608\pi\) | ||||
−0.604452 | + | 0.796641i | \(0.706608\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.2523 | 0.856581 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.0000 | 1.01148 | 0.505740 | − | 0.862686i | \(-0.331220\pi\) | ||||
0.505740 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.08712 | −0.214017 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 31.2723 | 1.31100 | 0.655501 | − | 0.755195i | \(-0.272458\pi\) | ||||
0.655501 | + | 0.755195i | \(0.272458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.1660 | −0.885770 | −0.442885 | − | 0.896578i | \(-0.646045\pi\) | ||||
−0.442885 | + | 0.896578i | \(0.646045\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.16515 | −0.131996 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.165151 | −0.00687534 | −0.00343767 | − | 0.999994i | \(-0.501094\pi\) | ||||
−0.00343767 | + | 0.999994i | \(0.501094\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.89200 | −0.119980 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −48.8788 | −2.02435 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.5826 | −0.560613 | −0.280306 | − | 0.959911i | \(-0.590436\pi\) | ||||
−0.280306 | + | 0.959911i | \(0.590436\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.3303 | −0.590470 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.1244 | 0.497888 | 0.248944 | − | 0.968518i | \(-0.419917\pi\) | ||||
0.248944 | + | 0.968518i | \(0.419917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.18710 | −0.171654 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.8348 | −0.524418 | −0.262209 | − | 0.965011i | \(-0.584451\pi\) | ||||
−0.262209 | + | 0.965011i | \(0.584451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.4955 | 1.65184 | 0.825922 | − | 0.563784i | \(-0.190655\pi\) | ||||
0.825922 | + | 0.563784i | \(0.190655\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 53.3520 | 2.16907 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.39590 | 0.259602 | 0.129801 | − | 0.991540i | \(-0.458566\pi\) | ||||
0.129801 | + | 0.991540i | \(0.458566\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.6606 | −0.835839 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.0000 | −1.21169 | −0.605844 | − | 0.795583i | \(-0.707165\pi\) | ||||
−0.605844 | + | 0.795583i | \(0.707165\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.0707 | −0.848273 | −0.424136 | − | 0.905598i | \(-0.639422\pi\) | ||||
−0.424136 | + | 0.905598i | \(0.639422\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.37420 | −0.336588 | −0.168294 | − | 0.985737i | \(-0.553826\pi\) | ||||
−0.168294 | + | 0.985737i | \(0.553826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.08712 | −0.324004 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.4014 | 0.454602 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0290 | 0.478867 | 0.239434 | − | 0.970913i | \(-0.423038\pi\) | ||||
0.239434 | + | 0.970913i | \(0.423038\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −34.2432 | −1.35890 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.9220 | 0.630851 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.92275 | 0.0759441 | 0.0379721 | − | 0.999279i | \(-0.487910\pi\) | ||||
0.0379721 | + | 0.999279i | \(0.487910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.48220 | 0.216197 | 0.108098 | − | 0.994140i | \(-0.465524\pi\) | ||||
0.108098 | + | 0.994140i | \(0.465524\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.9129 | −1.25462 | −0.627312 | − | 0.778768i | \(-0.715845\pi\) | ||||
−0.627312 | + | 0.778768i | \(0.715845\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 44.6606 | 1.75308 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.4684 | 1.42712 | 0.713560 | − | 0.700594i | \(-0.247082\pi\) | ||||
0.713560 | + | 0.700594i | \(0.247082\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.7701 | −0.577116 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.25227 | 0.282508 | 0.141254 | − | 0.989973i | \(-0.454887\pi\) | ||||
0.141254 | + | 0.989973i | \(0.454887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −15.7477 | −0.612516 | −0.306258 | − | 0.951949i | \(-0.599077\pi\) | ||||
−0.306258 | + | 0.951949i | \(0.599077\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.9572 | −0.735129 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.29510 | 0.0501465 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −59.0780 | −2.28068 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.1652 | −1.54825 | −0.774126 | − | 0.633031i | \(-0.781811\pi\) | ||||
−0.774126 | + | 0.633031i | \(0.781811\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.0652 | −0.617436 | −0.308718 | − | 0.951154i | \(-0.599900\pi\) | ||||
−0.308718 | + | 0.951154i | \(0.599900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0290 | −0.461631 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0000 | −0.918334 | −0.459167 | − | 0.888350i | \(-0.651852\pi\) | ||||
−0.459167 | + | 0.888350i | \(0.651852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.9129 | −0.875456 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.6120 | −0.861449 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.6983 | 0.825443 | 0.412721 | − | 0.910857i | \(-0.364578\pi\) | ||||
0.412721 | + | 0.910857i | \(0.364578\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.83485 | 0.183396 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.1652 | 0.574421 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.3477 | −0.768521 | −0.384260 | − | 0.923225i | \(-0.625543\pi\) | ||||
−0.384260 | + | 0.923225i | \(0.625543\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 51.6199 | 1.94688 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.6606 | 0.476151 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.25227 | −0.309921 | −0.154960 | − | 0.987921i | \(-0.549525\pi\) | ||||
−0.154960 | + | 0.987921i | \(0.549525\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.89200 | 0.108306 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.1449 | 1.42654 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −47.9129 | −1.78685 | −0.893424 | − | 0.449214i | \(-0.851704\pi\) | ||||
−0.893424 | + | 0.449214i | \(0.851704\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.6697 | −0.658054 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.63670 | −0.0607855 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.5975 | −0.615567 | −0.307784 | − | 0.951456i | \(-0.599587\pi\) | ||||
−0.307784 | + | 0.951456i | \(0.599587\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.5826 | −0.502370 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.33030 | 0.159943 | 0.0799717 | − | 0.996797i | \(-0.474517\pi\) | ||||
0.0799717 | + | 0.996797i | \(0.474517\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.7780 | 1.61258 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.3320 | 1.55721 | 0.778604 | − | 0.627515i | \(-0.215928\pi\) | ||||
0.778604 | + | 0.627515i | \(0.215928\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.33030 | −0.232236 | −0.116118 | − | 0.993235i | \(-0.537045\pi\) | ||||
−0.116118 | + | 0.993235i | \(0.537045\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.3303 | 1.44095 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.2016 | 0.372759 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.7635 | −1.37801 | −0.689005 | − | 0.724756i | \(-0.741952\pi\) | ||||
−0.689005 | + | 0.724756i | \(0.741952\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51.1652 | 1.86209 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0000 | −0.654221 | −0.327111 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.5167 | −0.816228 | −0.408114 | − | 0.912931i | \(-0.633813\pi\) | ||||
−0.408114 | + | 0.912931i | \(0.633813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.94990 | −0.179199 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.6606 | 0.746011 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.1652 | 0.799296 | 0.399648 | − | 0.916669i | \(-0.369132\pi\) | ||||
0.399648 | + | 0.916669i | \(0.369132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.95536 | −0.358069 | −0.179035 | − | 0.983843i | \(-0.557297\pi\) | ||||
−0.179035 | + | 0.983843i | \(0.557297\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.65480 | −0.131284 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 68.6606 | 2.46002 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.4955 | −1.91422 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 30.2077 | 1.07816 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.1515 | −0.540093 | −0.270046 | − | 0.962847i | \(-0.587039\pi\) | ||||
−0.270046 | + | 0.962847i | \(0.587039\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.75682 | 0.0624653 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.3303 | −0.970528 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.5964 | −1.57968 | −0.789842 | − | 0.613310i | \(-0.789838\pi\) | ||||
−0.789842 | + | 0.613310i | \(0.789838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.8564 | 0.490204 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −67.9129 | −2.39659 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.82576 | 0.134840 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.1287 | −1.58664 | −0.793320 | − | 0.608805i | \(-0.791649\pi\) | ||||
−0.793320 | + | 0.608805i | \(0.791649\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.65480 | 0.128337 | 0.0641687 | − | 0.997939i | \(-0.479560\pi\) | ||||
0.0641687 | + | 0.997939i | \(0.479560\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 46.3303 | 1.62288 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −61.4955 | −2.15145 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.76465 | −0.340789 | −0.170394 | − | 0.985376i | \(-0.554504\pi\) | ||||
−0.170394 | + | 0.985376i | \(0.554504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0580 | 0.838610 | 0.419305 | − | 0.907846i | \(-0.362274\pi\) | ||||
0.419305 | + | 0.907846i | \(0.362274\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.74773 | −0.304188 | −0.152094 | − | 0.988366i | \(-0.548602\pi\) | ||||
−0.152094 | + | 0.988366i | \(0.548602\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.33030 | −0.289323 | −0.144662 | − | 0.989481i | \(-0.546209\pi\) | ||||
−0.144662 | + | 0.989481i | \(0.546209\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.6784 | −0.369983 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.9789 | 0.587579 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.7477 | −1.54486 | −0.772432 | − | 0.635098i | \(-0.780960\pi\) | ||||
−0.772432 | + | 0.635098i | \(0.780960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3303 | −0.976907 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.7484 | −0.576163 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.4249 | −0.633087 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.4174 | −0.357105 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.330303 | 0.0113094 | 0.00565468 | − | 0.999984i | \(-0.498200\pi\) | ||||
0.00565468 | + | 0.999984i | \(0.498200\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.1534 | 0.825063 | 0.412532 | − | 0.910943i | \(-0.364645\pi\) | ||||
0.412532 | + | 0.910943i | \(0.364645\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.8788 | 1.66772 | 0.833862 | − | 0.551973i | \(-0.186125\pi\) | ||||
0.833862 | + | 0.551973i | \(0.186125\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.4083 | 1.68188 | 0.840940 | − | 0.541129i | \(-0.182003\pi\) | ||||
0.840940 | + | 0.541129i | \(0.182003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −48.4955 | −1.64889 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −82.4552 | −2.79710 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.2523 | 0.686223 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 7.25227 | 0.245172 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.0780 | 1.35334 | 0.676669 | − | 0.736287i | \(-0.263423\pi\) | ||||
0.676669 | + | 0.736287i | \(0.263423\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.44600 | 0.0487170 | 0.0243585 | − | 0.999703i | \(-0.492246\pi\) | ||||
0.0243585 | + | 0.999703i | \(0.492246\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.13701 | −0.307485 | −0.153742 | − | 0.988111i | \(-0.549133\pi\) | ||||
−0.153742 | + | 0.988111i | \(0.549133\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.5826 | −0.858979 | −0.429489 | − | 0.903072i | \(-0.641306\pi\) | ||||
−0.429489 | + | 0.903072i | \(0.641306\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.8258 | 0.396623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 62.7352 | 2.09935 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.49545 | 0.0498762 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.1652 | 0.505224 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.29150 | −0.175895 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.9934 | 0.763484 | 0.381742 | − | 0.924269i | \(-0.375324\pi\) | ||||
0.381742 | + | 0.924269i | \(0.375324\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 22.4174 | 0.742722 | 0.371361 | − | 0.928488i | \(-0.378891\pi\) | ||||
0.371361 | + | 0.928488i | \(0.378891\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.6697 | −0.584782 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.10080 | 0.168443 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.4539 | −1.00458 | −0.502291 | − | 0.864699i | \(-0.667509\pi\) | ||||
−0.502291 | + | 0.864699i | \(0.667509\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.7477 | −0.814581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.1652 | 0.432868 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.5885 | 0.511441 | 0.255720 | − | 0.966751i | \(-0.417687\pi\) | ||||
0.255720 | + | 0.966751i | \(0.417687\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.3465 | −1.58449 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.5826 | −0.836640 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.16515 | 0.0707324 | 0.0353662 | − | 0.999374i | \(-0.488740\pi\) | ||||
0.0353662 | + | 0.999374i | \(0.488740\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.12795 | −0.264964 | −0.132482 | − | 0.991185i | \(-0.542295\pi\) | ||||
−0.132482 | + | 0.991185i | \(0.542295\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.8564 | −0.451227 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.0780 | 1.52983 | 0.764915 | − | 0.644131i | \(-0.222781\pi\) | ||||
0.764915 | + | 0.644131i | \(0.222781\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.4174 | −1.01985 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.7835 | −1.58025 | −0.790126 | − | 0.612945i | \(-0.789985\pi\) | ||||
−0.790126 | + | 0.612945i | \(0.789985\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.18710 | 0.135491 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.91288 | 0.255520 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.6606 | −0.892278 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.3115 | 0.525084 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.4539 | 0.979332 | 0.489666 | − | 0.871910i | \(-0.337119\pi\) | ||||
0.489666 | + | 0.871910i | \(0.337119\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.747727 | 0.0239957 | 0.0119979 | − | 0.999928i | \(-0.496181\pi\) | ||||
0.0119979 | + | 0.999928i | \(0.496181\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.66970 | −0.0535280 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.9572 | −0.606495 | −0.303247 | − | 0.952912i | \(-0.598071\pi\) | ||||
−0.303247 | + | 0.952912i | \(0.598071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49.4111 | −1.57919 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.4955 | 1.83382 | 0.916910 | − | 0.399094i | \(-0.130675\pi\) | ||||
0.916910 | + | 0.399094i | \(0.130675\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.8258 | 1.68317 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.4104 | 0.394628 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9427 | −0.411139 | −0.205569 | − | 0.978643i | \(-0.565905\pi\) | ||||
−0.205569 | + | 0.978643i | \(0.565905\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.66970 | 0.306550 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.2523 | −0.324693 | −0.162346 | − | 0.986734i | \(-0.551906\pi\) | ||||
−0.162346 | + | 0.986734i | \(0.551906\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 5184.2.a.cd.1.4 | 4 | ||
3.2 | odd | 2 | 5184.2.a.ce.1.2 | 4 | |||
4.3 | odd | 2 | 5184.2.a.ce.1.3 | 4 | |||
8.3 | odd | 2 | 2592.2.a.v.1.1 | ✓ | 4 | ||
8.5 | even | 2 | 2592.2.a.w.1.2 | yes | 4 | ||
12.11 | even | 2 | inner | 5184.2.a.cd.1.1 | 4 | ||
24.5 | odd | 2 | 2592.2.a.v.1.4 | yes | 4 | ||
24.11 | even | 2 | 2592.2.a.w.1.3 | yes | 4 | ||
72.5 | odd | 6 | 2592.2.i.bh.865.1 | 8 | |||
72.11 | even | 6 | 2592.2.i.bg.1729.2 | 8 | |||
72.13 | even | 6 | 2592.2.i.bg.865.3 | 8 | |||
72.29 | odd | 6 | 2592.2.i.bh.1729.1 | 8 | |||
72.43 | odd | 6 | 2592.2.i.bh.1729.4 | 8 | |||
72.59 | even | 6 | 2592.2.i.bg.865.2 | 8 | |||
72.61 | even | 6 | 2592.2.i.bg.1729.3 | 8 | |||
72.67 | odd | 6 | 2592.2.i.bh.865.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2592.2.a.v.1.1 | ✓ | 4 | 8.3 | odd | 2 | ||
2592.2.a.v.1.4 | yes | 4 | 24.5 | odd | 2 | ||
2592.2.a.w.1.2 | yes | 4 | 8.5 | even | 2 | ||
2592.2.a.w.1.3 | yes | 4 | 24.11 | even | 2 | ||
2592.2.i.bg.865.2 | 8 | 72.59 | even | 6 | |||
2592.2.i.bg.865.3 | 8 | 72.13 | even | 6 | |||
2592.2.i.bg.1729.2 | 8 | 72.11 | even | 6 | |||
2592.2.i.bg.1729.3 | 8 | 72.61 | even | 6 | |||
2592.2.i.bh.865.1 | 8 | 72.5 | odd | 6 | |||
2592.2.i.bh.865.4 | 8 | 72.67 | odd | 6 | |||
2592.2.i.bh.1729.1 | 8 | 72.29 | odd | 6 | |||
2592.2.i.bh.1729.4 | 8 | 72.43 | odd | 6 | |||
5184.2.a.cd.1.1 | 4 | 12.11 | even | 2 | inner | ||
5184.2.a.cd.1.4 | 4 | 1.1 | even | 1 | trivial | ||
5184.2.a.ce.1.2 | 4 | 3.2 | odd | 2 | |||
5184.2.a.ce.1.3 | 4 | 4.3 | odd | 2 |