Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9200,2,Mod(1,9200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9200, 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("9200.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9200.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: | \(73.4623698596\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3x^{6} - 7x^{5} + 24x^{4} + x^{3} - 35x^{2} + 17x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 920) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.40334\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9200.1 |
$q$-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 | ||||||||
\(3\) | 1.40334 | 0.810221 | 0.405110 | − | 0.914268i | \(-0.367233\pi\) | ||||
0.405110 | + | 0.914268i | \(0.367233\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.57117 | −0.593846 | −0.296923 | − | 0.954901i | \(-0.595960\pi\) | ||||
−0.296923 | + | 0.954901i | \(0.595960\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.03063 | −0.343543 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.35401 | −1.31278 | −0.656391 | − | 0.754421i | \(-0.727918\pi\) | ||||
−0.656391 | + | 0.754421i | \(0.727918\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.964590 | 0.267529 | 0.133765 | − | 0.991013i | \(-0.457293\pi\) | ||||
0.133765 | + | 0.991013i | \(0.457293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.300242 | −0.0728193 | −0.0364096 | − | 0.999337i | \(-0.511592\pi\) | ||||
−0.0364096 | + | 0.999337i | \(0.511592\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.62443 | 1.97858 | 0.989290 | − | 0.145963i | \(-0.0466280\pi\) | ||||
0.989290 | + | 0.145963i | \(0.0466280\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.20489 | −0.481146 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.65635 | −1.08857 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.76644 | 0.885106 | 0.442553 | − | 0.896742i | \(-0.354073\pi\) | ||||
0.442553 | + | 0.896742i | \(0.354073\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.59148 | 1.00426 | 0.502129 | − | 0.864792i | \(-0.332550\pi\) | ||||
0.502129 | + | 0.864792i | \(0.332550\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.11017 | −1.06364 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.38462 | −0.720827 | −0.360413 | − | 0.932793i | \(-0.617364\pi\) | ||||
−0.360413 | + | 0.932793i | \(0.617364\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.35365 | 0.216758 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.62014 | −1.03389 | −0.516946 | − | 0.856018i | \(-0.672931\pi\) | ||||
−0.516946 | + | 0.856018i | \(0.672931\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.72988 | 0.263804 | 0.131902 | − | 0.991263i | \(-0.457892\pi\) | ||||
0.131902 | + | 0.991263i | \(0.457892\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.687333 | 0.100258 | 0.0501289 | − | 0.998743i | \(-0.484037\pi\) | ||||
0.0501289 | + | 0.998743i | \(0.484037\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.53143 | −0.647347 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.421342 | −0.0589997 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.05208 | 1.10604 | 0.553019 | − | 0.833168i | \(-0.313476\pi\) | ||||
0.553019 | + | 0.833168i | \(0.313476\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12.1030 | 1.60309 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.74620 | −0.748091 | −0.374046 | − | 0.927410i | \(-0.622030\pi\) | ||||
−0.374046 | + | 0.927410i | \(0.622030\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.6547 | −1.74831 | −0.874153 | − | 0.485651i | \(-0.838583\pi\) | ||||
−0.874153 | + | 0.485651i | \(0.838583\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.61929 | 0.204011 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.49053 | −0.792945 | −0.396472 | − | 0.918047i | \(-0.629766\pi\) | ||||
−0.396472 | + | 0.918047i | \(0.629766\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.40334 | 0.168943 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.89977 | −1.17489 | −0.587443 | − | 0.809265i | \(-0.699866\pi\) | ||||
−0.587443 | + | 0.809265i | \(0.699866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.35994 | 0.744375 | 0.372187 | − | 0.928158i | \(-0.378608\pi\) | ||||
0.372187 | + | 0.928158i | \(0.378608\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.84088 | 0.779591 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.95266 | 0.782236 | 0.391118 | − | 0.920341i | \(-0.372088\pi\) | ||||
0.391118 | + | 0.920341i | \(0.372088\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.84592 | −0.538436 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.185320 | 0.0203415 | 0.0101707 | − | 0.999948i | \(-0.496762\pi\) | ||||
0.0101707 | + | 0.999948i | \(0.496762\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.68895 | 0.717131 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.64878 | −0.174770 | −0.0873852 | − | 0.996175i | \(-0.527851\pi\) | ||||
−0.0873852 | + | 0.996175i | \(0.527851\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.51553 | −0.158871 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.84676 | 0.813671 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.21689 | −0.935834 | −0.467917 | − | 0.883773i | \(-0.654995\pi\) | ||||
−0.467917 | + | 0.883773i | \(0.654995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.48736 | 0.450997 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.719780 | −0.0716208 | −0.0358104 | − | 0.999359i | \(-0.511401\pi\) | ||||
−0.0358104 | + | 0.999359i | \(0.511401\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.16137 | −0.902696 | −0.451348 | − | 0.892348i | \(-0.649057\pi\) | ||||
−0.451348 | + | 0.892348i | \(0.649057\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.7486 | 1.23245 | 0.616226 | − | 0.787570i | \(-0.288661\pi\) | ||||
0.616226 | + | 0.787570i | \(0.288661\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.38019 | −0.323763 | −0.161882 | − | 0.986810i | \(-0.551756\pi\) | ||||
−0.161882 | + | 0.986810i | \(0.551756\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.15312 | −0.584029 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.8547 | −1.49148 | −0.745741 | − | 0.666237i | \(-0.767904\pi\) | ||||
−0.745741 | + | 0.666237i | \(0.767904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.994133 | −0.0919076 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.471730 | 0.0432434 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.95739 | 0.723399 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.29032 | −0.837680 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.2222 | −1.35075 | −0.675377 | − | 0.737473i | \(-0.736019\pi\) | ||||
−0.675377 | + | 0.737473i | \(0.736019\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.42762 | 0.213740 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.8695 | 1.12441 | 0.562207 | − | 0.826997i | \(-0.309953\pi\) | ||||
0.562207 | + | 0.826997i | \(0.309953\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5504 | −1.17497 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.7433 | 1.43048 | 0.715238 | − | 0.698881i | \(-0.246318\pi\) | ||||
0.715238 | + | 0.698881i | \(0.246318\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.8293 | 1.00335 | 0.501676 | − | 0.865056i | \(-0.332717\pi\) | ||||
0.501676 | + | 0.865056i | \(0.332717\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.964565 | 0.0812310 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.19983 | −0.351208 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.35915 | −0.524494 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.46021 | 0.119625 | 0.0598125 | − | 0.998210i | \(-0.480950\pi\) | ||||
0.0598125 | + | 0.998210i | \(0.480950\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7897 | −1.44771 | −0.723854 | − | 0.689953i | \(-0.757631\pi\) | ||||
−0.723854 | + | 0.689953i | \(0.757631\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.309437 | 0.0250165 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0359 | −1.59904 | −0.799518 | − | 0.600642i | \(-0.794912\pi\) | ||||
−0.799518 | + | 0.600642i | \(0.794912\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 11.2998 | 0.896135 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.57117 | −0.123825 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.9076 | −1.79426 | −0.897130 | − | 0.441766i | \(-0.854352\pi\) | ||||
−0.897130 | + | 0.441766i | \(0.854352\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.826887 | 0.0639864 | 0.0319932 | − | 0.999488i | \(-0.489815\pi\) | ||||
0.0319932 | + | 0.999488i | \(0.489815\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0696 | −0.928428 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.88858 | −0.679727 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.03904 | −0.611197 | −0.305599 | − | 0.952160i | \(-0.598857\pi\) | ||||
−0.305599 | + | 0.952160i | \(0.598857\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.06389 | −0.606119 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 21.6941 | 1.62149 | 0.810747 | − | 0.585397i | \(-0.199061\pi\) | ||||
0.810747 | + | 0.585397i | \(0.199061\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.9499 | −1.11122 | −0.555609 | − | 0.831444i | \(-0.687515\pi\) | ||||
−0.555609 | + | 0.831444i | \(0.687515\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.1622 | −1.41651 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.30725 | 0.0955959 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.88709 | 0.646441 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.86406 | 0.569024 | 0.284512 | − | 0.958673i | \(-0.408169\pi\) | ||||
0.284512 | + | 0.958673i | \(0.408169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.1864 | 1.09314 | 0.546571 | − | 0.837413i | \(-0.315933\pi\) | ||||
0.546571 | + | 0.837413i | \(0.315933\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2911 | −0.875707 | −0.437853 | − | 0.899046i | \(-0.644261\pi\) | ||||
−0.437853 | + | 0.899046i | \(0.644261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.37123 | 0.309869 | 0.154934 | − | 0.987925i | \(-0.450483\pi\) | ||||
0.154934 | + | 0.987925i | \(0.450483\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.10845 | −0.642460 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.48888 | −0.525617 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.03063 | −0.0716336 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −37.5508 | −2.59745 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.93960 | 0.615427 | 0.307714 | − | 0.951479i | \(-0.400436\pi\) | ||||
0.307714 | + | 0.951479i | \(0.400436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.8928 | −0.951917 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.78516 | −0.596375 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.92518 | 0.603108 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.289610 | −0.0194813 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.9586 | −0.800806 | −0.400403 | − | 0.916339i | \(-0.631130\pi\) | ||||
−0.400403 | + | 0.916339i | \(0.631130\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.85445 | 0.123084 | 0.0615419 | − | 0.998104i | \(-0.480398\pi\) | ||||
0.0615419 | + | 0.998104i | \(0.480398\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.5190 | −1.09161 | −0.545804 | − | 0.837913i | \(-0.683776\pi\) | ||||
−0.545804 | + | 0.837913i | \(0.683776\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.60011 | 0.631641 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −24.5906 | −1.61099 | −0.805493 | − | 0.592606i | \(-0.798099\pi\) | ||||
−0.805493 | + | 0.592606i | \(0.798099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.75697 | 0.633783 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.1169 | −1.75405 | −0.877025 | − | 0.480446i | \(-0.840475\pi\) | ||||
−0.877025 | + | 0.480446i | \(0.840475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8855 | −0.830030 | −0.415015 | − | 0.909815i | \(-0.636224\pi\) | ||||
−0.415015 | + | 0.909815i | \(0.636224\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.1686 | 0.652314 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.31904 | 0.529328 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.260067 | 0.0164811 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.4610 | 0.786533 | 0.393267 | − | 0.919424i | \(-0.371345\pi\) | ||||
0.393267 | + | 0.919424i | \(0.371345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.35401 | −0.273734 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.5073 | −0.842564 | −0.421282 | − | 0.906930i | \(-0.638420\pi\) | ||||
−0.421282 | + | 0.906930i | \(0.638420\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.88898 | 0.428060 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.91243 | −0.304072 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 27.2579 | 1.68080 | 0.840399 | − | 0.541969i | \(-0.182321\pi\) | ||||
0.840399 | + | 0.541969i | \(0.182321\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.31380 | −0.141603 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.8409 | −1.08778 | −0.543889 | − | 0.839157i | \(-0.683049\pi\) | ||||
−0.543889 | + | 0.839157i | \(0.683049\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.31906 | −0.140873 | −0.0704364 | − | 0.997516i | \(-0.522439\pi\) | ||||
−0.0704364 | + | 0.997516i | \(0.522439\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.12681 | −0.128721 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.0762 | −1.92727 | −0.963637 | − | 0.267215i | \(-0.913897\pi\) | ||||
−0.963637 | + | 0.267215i | \(0.913897\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.76273 | −0.345006 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.9448 | 0.772221 | 0.386110 | − | 0.922453i | \(-0.373818\pi\) | ||||
0.386110 | + | 0.922453i | \(0.373818\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.6070 | −1.34385 | −0.671923 | − | 0.740621i | \(-0.734532\pi\) | ||||
−0.671923 | + | 0.740621i | \(0.734532\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.4014 | 0.613972 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9099 | −0.994697 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.9345 | −0.758232 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.61612 | −0.328097 | −0.164049 | − | 0.986452i | \(-0.552455\pi\) | ||||
−0.164049 | + | 0.986452i | \(0.552455\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.6278 | 1.42905 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.964590 | 0.0557837 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.71794 | −0.156659 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.01010 | −0.0580286 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.42467 | 0.138383 | 0.0691915 | − | 0.997603i | \(-0.477958\pi\) | ||||
0.0691915 | + | 0.997603i | \(0.477958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.8565 | −0.731383 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.57886 | −0.202938 | −0.101469 | − | 0.994839i | \(-0.532354\pi\) | ||||
−0.101469 | + | 0.994839i | \(0.532354\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.51000 | 0.311443 | 0.155722 | − | 0.987801i | \(-0.450230\pi\) | ||||
0.155722 | + | 0.987801i | \(0.450230\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.88368 | −0.330461 | −0.165230 | − | 0.986255i | \(-0.552837\pi\) | ||||
−0.165230 | + | 0.986255i | \(0.552837\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.7531 | −1.16195 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.8906 | 0.998558 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.58941 | −0.144079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.74356 | −0.262320 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.07992 | −0.0595377 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.6138 | 1.02311 | 0.511553 | − | 0.859252i | \(-0.329070\pi\) | ||||
0.511553 | + | 0.859252i | \(0.329070\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.51891 | 0.247635 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.9571 | −1.63187 | −0.815933 | − | 0.578146i | \(-0.803776\pi\) | ||||
−0.815933 | + | 0.578146i | \(0.803776\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −22.2495 | −1.20843 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.3453 | −1.31837 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.1178 | 0.978270 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.7363 | −1.43528 | −0.717640 | − | 0.696415i | \(-0.754778\pi\) | ||||
−0.717640 | + | 0.696415i | \(0.754778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.7392 | 1.53837 | 0.769186 | − | 0.639025i | \(-0.220662\pi\) | ||||
0.769186 | + | 0.639025i | \(0.220662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.45606 | −0.291223 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.662874 | 0.0352812 | 0.0176406 | − | 0.999844i | \(-0.494385\pi\) | ||||
0.0176406 | + | 0.999844i | \(0.494385\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.661999 | 0.0350367 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.0576 | 0.847485 | 0.423743 | − | 0.905783i | \(-0.360716\pi\) | ||||
0.423743 | + | 0.905783i | \(0.360716\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 55.3808 | 2.91478 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.1669 | 0.586113 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −27.5855 | −1.43995 | −0.719976 | − | 0.693999i | \(-0.755847\pi\) | ||||
−0.719976 | + | 0.693999i | \(0.755847\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.82290 | 0.355186 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.6512 | −0.656817 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.1014 | −1.71393 | −0.856964 | − | 0.515376i | \(-0.827652\pi\) | ||||
−0.856964 | + | 0.515376i | \(0.827652\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.59766 | 0.236791 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.17121 | −0.111527 | −0.0557637 | − | 0.998444i | \(-0.517759\pi\) | ||||
−0.0557637 | + | 0.998444i | \(0.517759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.3620 | −1.09441 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.52673 | 0.282403 | 0.141201 | − | 0.989981i | \(-0.454903\pi\) | ||||
0.141201 | + | 0.989981i | \(0.454903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.78286 | −0.0906281 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.1036 | 0.867185 | 0.433593 | − | 0.901109i | \(-0.357246\pi\) | ||||
0.433593 | + | 0.901109i | \(0.357246\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.300242 | −0.0151839 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.0603 | 0.911023 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.7419 | 0.639497 | 0.319748 | − | 0.947503i | \(-0.396402\pi\) | ||||
0.319748 | + | 0.947503i | \(0.396402\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.0159 | −0.951987 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1997 | 0.709098 | 0.354549 | − | 0.935038i | \(-0.384634\pi\) | ||||
0.354549 | + | 0.935038i | \(0.384634\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.39348 | 0.268668 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 19.0907 | 0.946289 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.0235143 | −0.00116271 | −0.000581354 | − | 1.00000i | \(-0.500185\pi\) | ||||
−0.000581354 | 1.00000i | \(0.500185\pi\) | ||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 23.4966 | 1.15900 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.02825 | 0.444251 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.6006 | 0.812936 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.2763 | 0.990562 | 0.495281 | − | 0.868733i | \(-0.335065\pi\) | ||||
0.495281 | + | 0.868733i | \(0.335065\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.5320 | 0.610771 | 0.305386 | − | 0.952229i | \(-0.401215\pi\) | ||||
0.305386 | + | 0.952229i | \(0.401215\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.708385 | −0.0344429 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.4539 | 1.03822 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.89380 | −0.284556 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.8635 | 1.10130 | 0.550648 | − | 0.834737i | \(-0.314381\pi\) | ||||
0.550648 | + | 0.834737i | \(0.314381\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.7997 | −1.14374 | −0.571871 | − | 0.820343i | \(-0.693782\pi\) | ||||
−0.571871 | + | 0.820343i | \(0.693782\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.62443 | 0.412562 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.66686 | −0.222737 | −0.111368 | − | 0.993779i | \(-0.535523\pi\) | ||||
−0.111368 | + | 0.993779i | \(0.535523\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.67022 | 0.222391 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.6616 | 0.649082 | 0.324541 | − | 0.945872i | \(-0.394790\pi\) | ||||
0.324541 | + | 0.945872i | \(0.394790\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.04917 | 0.0969226 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.8921 | −1.22192 | −0.610961 | − | 0.791661i | \(-0.709217\pi\) | ||||
−0.610961 | + | 0.791661i | \(0.709217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.8241 | 1.35727 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −24.9651 | −1.17296 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.6856 | 0.593405 | 0.296703 | − | 0.954970i | \(-0.404113\pi\) | ||||
0.296703 | + | 0.954970i | \(0.404113\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.69827 | 0.0792686 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 26.5769 | 1.23781 | 0.618904 | − | 0.785466i | \(-0.287577\pi\) | ||||
0.618904 | + | 0.785466i | \(0.287577\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.6461 | −0.680664 | −0.340332 | − | 0.940305i | \(-0.610539\pi\) | ||||
−0.340332 | + | 0.940305i | \(0.610539\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.7601 | −0.590467 | −0.295233 | − | 0.955425i | \(-0.595397\pi\) | ||||
−0.295233 | + | 0.955425i | \(0.595397\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.1977 | 0.470887 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.1172 | −1.29557 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.53192 | −0.346318 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.29870 | −0.379971 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2315 | −0.467488 | −0.233744 | − | 0.972298i | \(-0.575098\pi\) | ||||
−0.233744 | + | 0.972298i | \(0.575098\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.22936 | −0.192842 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.20489 | −0.100326 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.8299 | 0.989207 | 0.494603 | − | 0.869119i | \(-0.335313\pi\) | ||||
0.494603 | + | 0.869119i | \(0.335313\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −32.1472 | −1.45375 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.1315 | 1.72085 | 0.860426 | − | 0.509575i | \(-0.170198\pi\) | ||||
0.860426 | + | 0.509575i | \(0.170198\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.43108 | −0.0644527 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.5542 | 0.697702 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.36523 | −0.284947 | −0.142474 | − | 0.989799i | \(-0.545506\pi\) | ||||
−0.142474 | + | 0.989799i | \(0.545506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.16041 | 0.0518431 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.3160 | 0.950433 | 0.475217 | − | 0.879869i | \(-0.342370\pi\) | ||||
0.475217 | + | 0.879869i | \(0.342370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.9377 | −0.752232 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.5122 | −1.13081 | −0.565405 | − | 0.824814i | \(-0.691280\pi\) | ||||
−0.565405 | + | 0.824814i | \(0.691280\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.99254 | −0.442044 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −48.7828 | −2.15381 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.99266 | −0.131617 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.2815 | −0.495205 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.7247 | −1.78418 | −0.892091 | − | 0.451856i | \(-0.850762\pi\) | ||||
−0.892091 | + | 0.451856i | \(0.850762\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.3437 | −1.02075 | −0.510374 | − | 0.859953i | \(-0.670493\pi\) | ||||
−0.510374 | + | 0.859953i | \(0.670493\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.67879 | −0.0731294 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.92219 | 0.257001 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.38571 | −0.276596 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.4443 | 1.31377 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.7299 | 0.849826 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.23303 | 0.0530123 | 0.0265061 | − | 0.999649i | \(-0.491562\pi\) | ||||
0.0265061 | + | 0.999649i | \(0.491562\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −20.9798 | −0.900331 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.56470 | 0.0669018 | 0.0334509 | − | 0.999440i | \(-0.489350\pi\) | ||||
0.0334509 | + | 0.999440i | \(0.489350\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.0729 | 0.600618 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.1078 | 1.75125 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.9238 | −0.464528 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.4857 | 0.952749 | 0.476375 | − | 0.879242i | \(-0.341951\pi\) | ||||
0.476375 | + | 0.879242i | \(0.341951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.66863 | 0.0705753 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.83453 | 0.0774537 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.68774 | −0.324000 | −0.162000 | − | 0.986791i | \(-0.551794\pi\) | ||||
−0.162000 | + | 0.986791i | \(0.551794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.61376 | 0.319748 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 28.1828 | 1.18149 | 0.590743 | − | 0.806860i | \(-0.298835\pi\) | ||||
0.590743 | + | 0.806860i | \(0.298835\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.1444 | −1.30335 | −0.651676 | − | 0.758497i | \(-0.725934\pi\) | ||||
−0.651676 | + | 0.758497i | \(0.725934\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.0360 | 0.461035 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.20837 | −0.0503051 | −0.0251525 | − | 0.999684i | \(-0.508007\pi\) | ||||
−0.0251525 | + | 0.999684i | \(0.508007\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.3118 | 0.885687 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.291168 | −0.0120797 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.0588 | −1.45199 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.4162 | 0.553746 | 0.276873 | − | 0.960906i | \(-0.410702\pi\) | ||||
0.276873 | + | 0.960906i | \(0.410702\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.2233 | 1.98701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.2487 | −0.709516 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.37465 | −0.220711 | −0.110355 | − | 0.993892i | \(-0.535199\pi\) | ||||
−0.110355 | + | 0.993892i | \(0.535199\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.13434 | 0.251062 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.7001 | 0.764064 | 0.382032 | − | 0.924149i | \(-0.375224\pi\) | ||||
0.382032 | + | 0.924149i | \(0.375224\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.4418 | 0.752255 | 0.376128 | − | 0.926568i | \(-0.377255\pi\) | ||||
0.376128 | + | 0.926568i | \(0.377255\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.68932 | 0.272410 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.6501 | 0.635218 | 0.317609 | − | 0.948222i | \(-0.397120\pi\) | ||||
0.317609 | + | 0.948222i | \(0.397120\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.5095 | −0.425865 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.662995 | 0.0268219 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.18552 | 0.0882725 | 0.0441363 | − | 0.999026i | \(-0.485946\pi\) | ||||
0.0441363 | + | 0.999026i | \(0.485946\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.07539 | 0.164069 | 0.0820346 | − | 0.996629i | \(-0.473858\pi\) | ||||
0.0820346 | + | 0.996629i | \(0.473858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0289543 | 0.00116377 | 0.000581885 | − | 1.00000i | \(-0.499815\pi\) | ||||
0.000581885 | 1.00000i | \(0.499815\pi\) | ||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.65635 | −0.226982 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.59051 | 0.103787 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −52.6967 | −2.10450 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.31644 | 0.0524901 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.3679 | −1.32836 | −0.664178 | − | 0.747575i | \(-0.731218\pi\) | ||||
−0.664178 | + | 0.747575i | \(0.731218\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.5453 | 0.498632 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.37097 | −0.173184 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.2030 | 0.403624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.56295 | 0.0617327 | 0.0308663 | − | 0.999524i | \(-0.490173\pi\) | ||||
0.0308663 | + | 0.999524i | \(0.490173\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.3037 | 1.31337 | 0.656684 | − | 0.754166i | \(-0.271958\pi\) | ||||
0.656684 | + | 0.754166i | \(0.271958\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.54230 | −0.0606343 | −0.0303171 | − | 0.999540i | \(-0.509652\pi\) | ||||
−0.0303171 | + | 0.999540i | \(0.509652\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.0190 | 0.982081 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.3286 | −0.483195 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.1195 | −0.513407 | −0.256703 | − | 0.966490i | \(-0.582636\pi\) | ||||
−0.256703 | + | 0.966490i | \(0.582636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.55473 | −0.255724 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.38016 | −0.287490 | −0.143745 | − | 0.989615i | \(-0.545915\pi\) | ||||
−0.143745 | + | 0.989615i | \(0.545915\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.0266 | −0.973421 | −0.486710 | − | 0.873563i | \(-0.661803\pi\) | ||||
−0.486710 | + | 0.873563i | \(0.661803\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.406422 | −0.0157841 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.76644 | 0.184557 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.7820 | −0.648830 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 59.4527 | 2.29515 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.2500 | 1.35879 | 0.679395 | − | 0.733773i | \(-0.262243\pi\) | ||||
0.679395 | + | 0.733773i | \(0.262243\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.04850 | −0.232463 | −0.116231 | − | 0.993222i | \(-0.537081\pi\) | ||||
−0.116231 | + | 0.993222i | \(0.537081\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.4813 | 0.555741 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.60242 | 0.0997251 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −32.9347 | −1.26021 | −0.630105 | − | 0.776510i | \(-0.716988\pi\) | ||||
−0.630105 | + | 0.776510i | \(0.716988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.1819 | −0.884443 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.76696 | 0.295897 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.7152 | −0.445668 | −0.222834 | − | 0.974856i | \(-0.571531\pi\) | ||||
−0.222834 | + | 0.974856i | \(0.571531\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.05040 | −0.267823 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.98764 | 0.0752872 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −34.5091 | −1.30525 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.8861 | 1.65756 | 0.828779 | − | 0.559577i | \(-0.189036\pi\) | ||||
0.828779 | + | 0.559577i | \(0.189036\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37.8148 | −1.42621 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.13090 | 0.0425317 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.2394 | 1.13567 | 0.567833 | − | 0.823144i | \(-0.307782\pi\) | ||||
0.567833 | + | 0.823144i | \(0.307782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.16561 | −0.268731 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.59148 | 0.209402 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −38.0544 | −1.42117 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27.5338 | −1.02684 | −0.513419 | − | 0.858138i | \(-0.671621\pi\) | ||||
−0.513419 | + | 0.858138i | \(0.671621\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3941 | 0.536063 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.0828 | −0.672507 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.7995 | −1.25356 | −0.626778 | − | 0.779198i | \(-0.715627\pi\) | ||||
−0.626778 | + | 0.779198i | \(0.715627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.8078 | 1.06695 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.519382 | −0.0192100 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.3133 | 1.78449 | 0.892246 | − | 0.451550i | \(-0.149129\pi\) | ||||
0.892246 | + | 0.451550i | \(0.149129\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.2598 | 1.04096 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.7004 | 0.835048 | 0.417524 | − | 0.908666i | \(-0.362898\pi\) | ||||
0.417524 | + | 0.908666i | \(0.362898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.6745 | 0.428872 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.9953 | −0.770242 | −0.385121 | − | 0.922866i | \(-0.625840\pi\) | ||||
−0.385121 | + | 0.922866i | \(0.625840\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.190995 | −0.00698816 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.0302 | −0.731887 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3909 | 0.780565 | 0.390283 | − | 0.920695i | \(-0.372377\pi\) | ||||
0.390283 | + | 0.920695i | \(0.372377\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.4871 | 0.637266 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −54.7364 | −1.98943 | −0.994715 | − | 0.102676i | \(-0.967260\pi\) | ||||
−0.994715 | + | 0.102676i | \(0.967260\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.11017 | −0.221785 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.87321 | 0.285404 | 0.142702 | − | 0.989766i | \(-0.454421\pi\) | ||||
0.142702 | + | 0.989766i | \(0.454421\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.31084 | 0.192265 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.54272 | −0.200136 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.7134 | 1.17968 | 0.589838 | − | 0.807522i | \(-0.299192\pi\) | ||||
0.589838 | + | 0.807522i | \(0.299192\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9554 | −0.682663 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.88974 | 0.103937 | 0.0519684 | − | 0.998649i | \(-0.483450\pi\) | ||||
0.0519684 | + | 0.998649i | \(0.483450\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.66760 | 0.346823 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −57.0949 | −2.04564 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.1037 | 1.54237 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.9607 | −0.963496 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.4472 | 1.65566 | 0.827832 | − | 0.560976i | \(-0.189574\pi\) | ||||
0.827832 | + | 0.560976i | \(0.189574\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 38.2523 | 1.36182 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.9104 | 0.885710 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.1712 | −0.467723 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −45.6713 | −1.61776 | −0.808880 | − | 0.587974i | \(-0.799926\pi\) | ||||
−0.808880 | + | 0.587974i | \(0.799926\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.206366 | −0.00730070 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.69928 | 0.0600411 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −27.6912 | −0.977202 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.0369 | −0.881340 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.7080 | 1.32574 | 0.662872 | − | 0.748733i | \(-0.269337\pi\) | ||||
0.662872 | + | 0.748733i | \(0.269337\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.02541 | −0.316925 | −0.158462 | − | 0.987365i | \(-0.550654\pi\) | ||||
−0.158462 | + | 0.987365i | \(0.550654\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.25444 | −0.114138 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.9192 | 0.521958 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.56195 | 0.0545790 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.2481 | −1.19527 | −0.597634 | − | 0.801769i | \(-0.703892\pi\) | ||||
−0.597634 | + | 0.801769i | \(0.703892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.1842 | 0.354999 | 0.177499 | − | 0.984121i | \(-0.443199\pi\) | ||||
0.177499 | + | 0.984121i | \(0.443199\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.0710 | 1.18477 | 0.592383 | − | 0.805656i | \(-0.298187\pi\) | ||||
0.592383 | + | 0.805656i | \(0.298187\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.5131 | −0.851376 | −0.425688 | − | 0.904870i | \(-0.639968\pi\) | ||||
−0.425688 | + | 0.904870i | \(0.639968\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −45.0140 | −1.56152 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.36052 | 0.0471393 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.6274 | −1.09320 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.2362 | −0.664107 | −0.332053 | − | 0.943261i | \(-0.607741\pi\) | ||||
−0.332053 | + | 0.943261i | \(0.607741\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.28105 | −0.216588 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 18.1660 | 0.625669 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.5024 | −0.429588 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −31.7254 | −1.08881 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.38462 | −0.150303 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.8964 | −1.19483 | −0.597415 | − | 0.801932i | \(-0.703805\pi\) | ||||
−0.597415 | + | 0.801932i | \(0.703805\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.9040 | −1.43141 | −0.715706 | − | 0.698401i | \(-0.753895\pi\) | ||||
−0.715706 | + | 0.698401i | \(0.753895\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.1286 | 0.652658 | 0.326329 | − | 0.945256i | \(-0.394188\pi\) | ||||
0.326329 | + | 0.945256i | \(0.394188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.5967 | 0.497453 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.509621 | −0.0173477 | −0.00867385 | − | 0.999962i | \(-0.502761\pi\) | ||||
−0.00867385 | + | 0.999962i | \(0.502761\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.7303 | −0.805924 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.2719 | −1.02691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.26070 | −0.212136 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.49919 | 0.321499 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.6710 | −0.529171 | −0.264586 | − | 0.964362i | \(-0.585235\pi\) | ||||
−0.264586 | + | 0.964362i | \(0.585235\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.88135 | −0.265831 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.00846 | −0.0676667 | −0.0338333 | − | 0.999427i | \(-0.510772\pi\) | ||||
−0.0338333 | + | 0.999427i | \(0.510772\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.7848 | 0.564854 | 0.282427 | − | 0.959289i | \(-0.408861\pi\) | ||||
0.282427 | + | 0.959289i | \(0.408861\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −51.7294 | −1.73690 | −0.868452 | − | 0.495774i | \(-0.834884\pi\) | ||||
−0.868452 | + | 0.495774i | \(0.834884\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.9167 | 0.802140 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.0992 | 0.706849 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.92786 | 0.198368 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.35365 | 0.0451971 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.6514 | 0.888875 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.41757 | −0.0805409 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.81420 | −0.126929 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.0849 | 0.965747 | 0.482874 | − | 0.875690i | \(-0.339593\pi\) | ||||
0.482874 | + | 0.875690i | \(0.339593\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.741825 | 0.0246048 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.3517 | −0.873070 | −0.436535 | − | 0.899687i | \(-0.643795\pi\) | ||||
−0.436535 | + | 0.899687i | \(0.643795\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.806883 | −0.0267039 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.2202 | −0.667728 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.0148 | 1.51789 | 0.758945 | − | 0.651155i | \(-0.225715\pi\) | ||||
0.758945 | + | 0.651155i | \(0.225715\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.40264 | 0.112121 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.54922 | −0.314316 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.44196 | 0.310115 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.1770 | 0.858838 | 0.429419 | − | 0.903105i | \(-0.358718\pi\) | ||||
0.429419 | + | 0.903105i | \(0.358718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.0810 | −1.28083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.02237 | −0.164425 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.4429 | 1.45189 | 0.725944 | − | 0.687754i | \(-0.241403\pi\) | ||||
0.725944 | + | 0.687754i | \(0.241403\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.73242 | 0.252338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 7.07346 | 0.230588 | 0.115294 | − | 0.993331i | \(-0.463219\pi\) | ||||
0.115294 | + | 0.993331i | \(0.463219\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.62014 | −0.215581 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.4533 | −0.469670 | −0.234835 | − | 0.972035i | \(-0.575455\pi\) | ||||
−0.234835 | + | 0.972035i | \(0.575455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.13473 | 0.199142 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.25683 | −0.267746 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 32.3773 | 1.04880 | 0.524402 | − | 0.851471i | \(-0.324289\pi\) | ||||
0.524402 | + | 0.851471i | \(0.324289\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −29.1237 | −0.941437 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −26.3065 | −0.849482 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.264608 | 0.00853575 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.1390 | −0.423400 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.8993 | −0.832865 | −0.416433 | − | 0.909167i | \(-0.636720\pi\) | ||||
−0.416433 | + | 0.909167i | \(0.636720\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.63383 | −0.116736 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.2153 | 0.809197 | 0.404599 | − | 0.914494i | \(-0.367411\pi\) | ||||
0.404599 | + | 0.914494i | \(0.367411\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.5859 | −0.595837 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.64235 | 0.180515 | 0.0902573 | − | 0.995918i | \(-0.471231\pi\) | ||||
0.0902573 | + | 0.995918i | \(0.471231\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.17880 | 0.229436 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.48371 | 0.111226 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −37.0322 | −1.18114 | −0.590571 | − | 0.806986i | \(-0.701097\pi\) | ||||
−0.590571 | + | 0.806986i | \(0.701097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.51549 | −0.0482387 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.72988 | 0.0550070 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.14822 | −0.227071 | −0.113535 | − | 0.993534i | \(-0.536218\pi\) | ||||
−0.113535 | + | 0.993534i | \(0.536218\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.1215 | 0.828942 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.96521 | −0.157250 | −0.0786249 | − | 0.996904i | \(-0.525053\pi\) | ||||
−0.0786249 | + | 0.996904i | \(0.525053\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.8010 | 0.784667 |
(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 | 9200.2.a.cz.1.6 | 7 | ||
4.3 | odd | 2 | 4600.2.a.bi.1.2 | 7 | |||
5.2 | odd | 4 | 1840.2.e.g.369.5 | 14 | |||
5.3 | odd | 4 | 1840.2.e.g.369.10 | 14 | |||
5.4 | even | 2 | 9200.2.a.dc.1.2 | 7 | |||
20.3 | even | 4 | 920.2.e.b.369.5 | ✓ | 14 | ||
20.7 | even | 4 | 920.2.e.b.369.10 | yes | 14 | ||
20.19 | odd | 2 | 4600.2.a.bh.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.b.369.5 | ✓ | 14 | 20.3 | even | 4 | ||
920.2.e.b.369.10 | yes | 14 | 20.7 | even | 4 | ||
1840.2.e.g.369.5 | 14 | 5.2 | odd | 4 | |||
1840.2.e.g.369.10 | 14 | 5.3 | odd | 4 | |||
4600.2.a.bh.1.6 | 7 | 20.19 | odd | 2 | |||
4600.2.a.bi.1.2 | 7 | 4.3 | odd | 2 | |||
9200.2.a.cz.1.6 | 7 | 1.1 | even | 1 | trivial | ||
9200.2.a.dc.1.2 | 7 | 5.4 | even | 2 |