Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, 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("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.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: | \(48.2935231425\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.25808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.46810\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-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 | ||||||||
\(5\) | 1.34410 | 0.601101 | 0.300551 | − | 0.953766i | \(-0.402830\pi\) | ||||
0.300551 | + | 0.953766i | \(0.402830\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.28030 | 1.89358 | 0.946791 | − | 0.321848i | \(-0.104304\pi\) | ||||
0.946791 | + | 0.321848i | \(0.104304\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.43102 | −1.22894 | −0.614472 | − | 0.788939i | \(-0.710631\pi\) | ||||
−0.614472 | + | 0.788939i | \(0.710631\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.505178 | 0.122524 | 0.0612619 | − | 0.998122i | \(-0.480488\pi\) | ||||
0.0612619 | + | 0.998122i | \(0.480488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.19339 | −1.42086 | −0.710430 | − | 0.703768i | \(-0.751500\pi\) | ||||
−0.710430 | + | 0.703768i | \(0.751500\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.84928 | −1.21966 | −0.609830 | − | 0.792532i | \(-0.708762\pi\) | ||||
−0.609830 | + | 0.792532i | \(0.708762\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.19339 | −0.638677 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.43102 | 0.822820 | 0.411410 | − | 0.911450i | \(-0.365036\pi\) | ||||
0.411410 | + | 0.911450i | \(0.365036\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.62441 | −1.18978 | −0.594889 | − | 0.803808i | \(-0.702804\pi\) | ||||
−0.594889 | + | 0.803808i | \(0.702804\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.34410 | 0.227195 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.44138 | −1.38775 | −0.693877 | − | 0.720094i | \(-0.744099\pi\) | ||||
−0.693877 | + | 0.720094i | \(0.744099\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.77512 | −0.901923 | −0.450961 | − | 0.892543i | \(-0.648919\pi\) | ||||
−0.450961 | + | 0.892543i | \(0.648919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.44138 | 1.13480 | 0.567400 | − | 0.823443i | \(-0.307949\pi\) | ||||
0.567400 | + | 0.823443i | \(0.307949\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1296 | −1.76928 | −0.884641 | − | 0.466273i | \(-0.845596\pi\) | ||||
−0.884641 | + | 0.466273i | \(0.845596\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −13.8724 | −1.90552 | −0.952760 | − | 0.303724i | \(-0.901770\pi\) | ||||
−0.952760 | + | 0.303724i | \(0.901770\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.44138 | 1.13824 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.25719 | −0.814616 | −0.407308 | − | 0.913291i | \(-0.633532\pi\) | ||||
−0.407308 | + | 0.913291i | \(0.633532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.01036 | 0.129363 | 0.0646815 | − | 0.997906i | \(-0.479397\pi\) | ||||
0.0646815 | + | 0.997906i | \(0.479397\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.95575 | −0.738720 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.8178 | −1.81028 | −0.905141 | − | 0.425112i | \(-0.860235\pi\) | ||||
−0.905141 | + | 0.425112i | \(0.860235\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.35446 | 0.279423 | 0.139712 | − | 0.990192i | \(-0.455382\pi\) | ||||
0.139712 | + | 0.990192i | \(0.455382\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.8074 | 1.38196 | 0.690978 | − | 0.722876i | \(-0.257180\pi\) | ||||
0.690978 | + | 0.722876i | \(0.257180\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.28030 | 0.715707 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.3034 | 1.38424 | 0.692121 | − | 0.721781i | \(-0.256676\pi\) | ||||
0.692121 | + | 0.721781i | \(0.256676\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.43102 | −0.925425 | −0.462712 | − | 0.886508i | \(-0.653124\pi\) | ||||
−0.462712 | + | 0.886508i | \(0.653124\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.679012 | 0.0736492 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.91308 | −0.520786 | −0.260393 | − | 0.965503i | \(-0.583852\pi\) | ||||
−0.260393 | + | 0.965503i | \(0.583852\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.43102 | −0.464497 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.32455 | −0.854081 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.37641 | −0.545892 | −0.272946 | − | 0.962029i | \(-0.587998\pi\) | ||||
−0.272946 | + | 0.962029i | \(0.587998\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.88159 | 0.983255 | 0.491628 | − | 0.870806i | \(-0.336402\pi\) | ||||
0.491628 | + | 0.870806i | \(0.336402\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −15.4864 | −1.52592 | −0.762962 | − | 0.646443i | \(-0.776256\pi\) | ||||
−0.762962 | + | 0.646443i | \(0.776256\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.80661 | −0.464673 | −0.232336 | − | 0.972635i | \(-0.574637\pi\) | ||||
−0.232336 | + | 0.972635i | \(0.574637\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.62441 | 0.634503 | 0.317252 | − | 0.948341i | \(-0.397240\pi\) | ||||
0.317252 | + | 0.948341i | \(0.397240\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.31179 | 0.875980 | 0.437990 | − | 0.898980i | \(-0.355691\pi\) | ||||
0.437990 | + | 0.898980i | \(0.355691\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.86204 | −0.733139 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.505178 | 0.0463096 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.4422 | 2.58565 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.0128 | −0.985011 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.44138 | −0.482844 | −0.241422 | − | 0.970420i | \(-0.577614\pi\) | ||||
−0.241422 | + | 0.970420i | \(0.577614\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1192 | −1.32097 | −0.660487 | − | 0.750838i | \(-0.729650\pi\) | ||||
−0.660487 | + | 0.750838i | \(0.729650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.19339 | −0.537035 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.8281 | 1.69403 | 0.847017 | − | 0.531567i | \(-0.178396\pi\) | ||||
0.847017 | + | 0.531567i | \(0.178396\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.2488 | 1.63266 | 0.816331 | − | 0.577584i | \(-0.196004\pi\) | ||||
0.816331 | + | 0.577584i | \(0.196004\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.8281 | −2.32711 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.95575 | 0.494598 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.5502 | 1.27393 | 0.636963 | − | 0.770894i | \(-0.280190\pi\) | ||||
0.636963 | + | 0.770894i | \(0.280190\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.01036 | −0.570495 | −0.285247 | − | 0.958454i | \(-0.592076\pi\) | ||||
−0.285247 | + | 0.958454i | \(0.592076\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.90389 | −0.715177 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.06496 | −0.324419 | −0.162210 | − | 0.986756i | \(-0.551862\pi\) | ||||
−0.162210 | + | 0.986756i | \(0.551862\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.84928 | −0.460988 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.6902 | 1.62058 | 0.810290 | − | 0.586029i | \(-0.199309\pi\) | ||||
0.810290 | + | 0.586029i | \(0.199309\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.93702 | 0.768950 | 0.384475 | − | 0.923135i | \(-0.374383\pi\) | ||||
0.384475 | + | 0.923135i | \(0.374383\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.63394 | 0.510303 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.84928 | 0.444713 | 0.222356 | − | 0.974965i | \(-0.428625\pi\) | ||||
0.222356 | + | 0.974965i | \(0.428625\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.19339 | −0.241397 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.2037 | −0.912151 | −0.456075 | − | 0.889941i | \(-0.650745\pi\) | ||||
−0.456075 | + | 0.889941i | \(0.650745\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.1212 | 1.71859 | 0.859293 | − | 0.511484i | \(-0.170904\pi\) | ||||
0.859293 | + | 0.511484i | \(0.170904\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.3461 | −0.834181 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.17267 | 0.232009 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.33491 | 0.0965906 | 0.0482953 | − | 0.998833i | \(-0.484621\pi\) | ||||
0.0482953 | + | 0.998833i | \(0.484621\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.24881 | −0.665744 | −0.332872 | − | 0.942972i | \(-0.608018\pi\) | ||||
−0.332872 | + | 0.942972i | \(0.608018\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.5502 | 0.822921 | 0.411461 | − | 0.911428i | \(-0.365019\pi\) | ||||
0.411461 | + | 0.911428i | \(0.365019\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.42066 | 0.596925 | 0.298463 | − | 0.954421i | \(-0.403526\pi\) | ||||
0.298463 | + | 0.954421i | \(0.403526\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.43102 | 0.310997 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.76237 | −0.542147 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −38.8963 | −2.69052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2385 | 1.11790 | 0.558951 | − | 0.829201i | \(-0.311204\pi\) | ||||
0.558951 | + | 0.829201i | \(0.311204\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0020 | 0.682129 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.62441 | −0.449694 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.23846 | −0.150575 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.4414 | −0.699206 | −0.349603 | − | 0.936898i | \(-0.613684\pi\) | ||||
−0.349603 | + | 0.936898i | \(0.613684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.5502 | −1.03211 | −0.516053 | − | 0.856557i | \(-0.672599\pi\) | ||||
−0.516053 | + | 0.856557i | \(0.672599\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.0104 | −1.12408 | −0.562038 | − | 0.827111i | \(-0.689983\pi\) | ||||
−0.562038 | + | 0.827111i | \(0.689983\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.9474 | 0.979235 | 0.489618 | − | 0.871937i | \(-0.337136\pi\) | ||||
0.489618 | + | 0.871937i | \(0.337136\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.3034 | −1.06352 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.33134 | −0.409541 | −0.204770 | − | 0.978810i | \(-0.565645\pi\) | ||||
−0.204770 | + | 0.978810i | \(0.565645\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.06496 | −0.133016 | −0.0665080 | − | 0.997786i | \(-0.521186\pi\) | ||||
−0.0665080 | + | 0.997786i | \(0.521186\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.34410 | 0.0858716 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 27.4430 | 1.74616 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.7632 | −1.24744 | −0.623721 | − | 0.781647i | \(-0.714380\pi\) | ||||
−0.623721 | + | 0.781647i | \(0.714380\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36.7353 | −2.30953 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.1423 | 0.944553 | 0.472277 | − | 0.881450i | \(-0.343432\pi\) | ||||
0.472277 | + | 0.881450i | \(0.343432\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.44138 | −0.524522 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.88516 | 0.301232 | 0.150616 | − | 0.988592i | \(-0.451874\pi\) | ||||
0.150616 | + | 0.988592i | \(0.451874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.6459 | −1.14541 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.3637 | −0.631883 | −0.315942 | − | 0.948779i | \(-0.602320\pi\) | ||||
−0.315942 | + | 0.948779i | \(0.602320\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.52473 | 0.335603 | 0.167802 | − | 0.985821i | \(-0.446333\pi\) | ||||
0.167802 | + | 0.985821i | \(0.446333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −20.0554 | −1.20939 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −27.1942 | −1.63394 | −0.816971 | − | 0.576679i | \(-0.804348\pi\) | ||||
−0.816971 | + | 0.576679i | \(0.804348\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.1192 | 1.14056 | 0.570279 | − | 0.821451i | \(-0.306835\pi\) | ||||
0.570279 | + | 0.821451i | \(0.306835\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8620 | −0.764569 | −0.382284 | − | 0.924045i | \(-0.624863\pi\) | ||||
−0.382284 | + | 0.924045i | \(0.624863\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.77512 | −0.340895 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.7448 | −0.984988 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 25.1304 | 1.46813 | 0.734067 | − | 0.679077i | \(-0.237620\pi\) | ||||
0.734067 | + | 0.679077i | \(0.237620\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.41031 | −0.489667 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 25.9183 | 1.49889 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.44138 | 0.428914 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.35802 | 0.0777602 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.80661 | −0.217255 | −0.108627 | − | 0.994083i | \(-0.534646\pi\) | ||||
−0.108627 | + | 0.994083i | \(0.534646\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.1838 | 0.860997 | 0.430499 | − | 0.902591i | \(-0.358338\pi\) | ||||
0.430499 | + | 0.902591i | \(0.358338\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.4310 | 1.38092 | 0.690461 | − | 0.723369i | \(-0.257408\pi\) | ||||
0.690461 | + | 0.723369i | \(0.257408\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −34.3680 | −1.93030 | −0.965151 | − | 0.261695i | \(-0.915719\pi\) | ||||
−0.965151 | + | 0.261695i | \(0.915719\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.8281 | 1.55808 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.12876 | −0.174089 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.1500 | 0.784898 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.1296 | −0.668726 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.751188 | 0.0412890 | 0.0206445 | − | 0.999787i | \(-0.493428\pi\) | ||||
0.0206445 | + | 0.999787i | \(0.493428\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.9166 | −1.08816 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.86204 | −0.319326 | −0.159663 | − | 0.987172i | \(-0.551041\pi\) | ||||
−0.159663 | + | 0.987172i | \(0.551041\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −41.6033 | −2.25294 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −36.8756 | −1.97959 | −0.989794 | − | 0.142509i | \(-0.954483\pi\) | ||||
−0.989794 | + | 0.142509i | \(0.954483\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.86204 | −0.367317 | −0.183658 | − | 0.982990i | \(-0.558794\pi\) | ||||
−0.183658 | + | 0.982990i | \(0.558794\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.9234 | 0.741070 | 0.370535 | − | 0.928819i | \(-0.379174\pi\) | ||||
0.370535 | + | 0.928819i | \(0.379174\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.16464 | 0.167962 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.0658 | −1.32292 | −0.661461 | − | 0.749980i | \(-0.730063\pi\) | ||||
−0.661461 | + | 0.749980i | \(0.730063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.3580 | 1.01884 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.8704 | 0.830696 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.05461 | −0.107250 | −0.0536248 | − | 0.998561i | \(-0.517077\pi\) | ||||
−0.0536248 | + | 0.998561i | \(0.517077\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8724 | −0.720219 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.01118 | 0.259469 | 0.129734 | − | 0.991549i | \(-0.458588\pi\) | ||||
0.129734 | + | 0.991549i | \(0.458588\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −19.6339 | −1.01120 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.57934 | −0.132492 | −0.0662458 | − | 0.997803i | \(-0.521102\pi\) | ||||
−0.0662458 | + | 0.997803i | \(0.521102\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.1738 | −0.519859 | −0.259929 | − | 0.965628i | \(-0.583699\pi\) | ||||
−0.259929 | + | 0.965628i | \(0.583699\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.44138 | 0.430212 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.1316 | −1.12211 | −0.561057 | − | 0.827777i | \(-0.689605\pi\) | ||||
−0.561057 | + | 0.827777i | \(0.689605\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.95493 | −0.149437 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.5371 | 0.832070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.4075 | −0.723091 | −0.361545 | − | 0.932354i | \(-0.617751\pi\) | ||||
−0.361545 | + | 0.932354i | \(0.617751\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.96611 | 0.347871 | 0.173935 | − | 0.984757i | \(-0.444352\pi\) | ||||
0.173935 | + | 0.984757i | \(0.444352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.3529 | 1.46217 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −53.0144 | −2.62783 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.3425 | 1.69813 | 0.849064 | − | 0.528290i | \(-0.177166\pi\) | ||||
0.849064 | + | 0.528290i | \(0.177166\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.25719 | −0.307896 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.3322 | −0.556274 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.66982 | 0.325842 | 0.162921 | − | 0.986639i | \(-0.447908\pi\) | ||||
0.162921 | + | 0.986639i | \(0.447908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.9454 | −0.972079 | −0.486040 | − | 0.873937i | \(-0.661559\pi\) | ||||
−0.486040 | + | 0.873937i | \(0.661559\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.61323 | −0.0782531 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.01036 | 0.0488946 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.84928 | 0.281750 | 0.140875 | − | 0.990027i | \(-0.455008\pi\) | ||||
0.140875 | + | 0.990027i | \(0.455008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.5626 | 1.66097 | 0.830486 | − | 0.557040i | \(-0.188063\pi\) | ||||
0.830486 | + | 0.557040i | \(0.188063\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.2269 | 1.73297 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.7448 | −1.32419 | −0.662093 | − | 0.749421i | \(-0.730332\pi\) | ||||
−0.662093 | + | 0.749421i | \(0.730332\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.47253 | 0.212496 | 0.106248 | − | 0.994340i | \(-0.466116\pi\) | ||||
0.106248 | + | 0.994340i | \(0.466116\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.60369 | −0.313045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.03587 | −0.332043 | −0.166022 | − | 0.986122i | \(-0.553092\pi\) | ||||
−0.166022 | + | 0.986122i | \(0.553092\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.2695 | −1.70787 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.95575 | −0.279210 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.7528 | 1.11111 | 0.555555 | − | 0.831480i | \(-0.312506\pi\) | ||||
0.555555 | + | 0.831480i | \(0.312506\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.0693 | 0.562126 | 0.281063 | − | 0.959689i | \(-0.409313\pi\) | ||||
0.281063 | + | 0.959689i | \(0.409313\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.86204 | 0.133010 | 0.0665052 | − | 0.997786i | \(-0.478815\pi\) | ||||
0.0665052 | + | 0.997786i | \(0.478815\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.4773 | −1.31777 | −0.658885 | − | 0.752244i | \(-0.728972\pi\) | ||||
−0.658885 | + | 0.752244i | \(0.728972\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.8178 | −0.684222 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 46.7341 | 2.14884 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.7779 | 0.907471 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.3971 | 1.06904 | 0.534521 | − | 0.845155i | \(-0.320492\pi\) | ||||
0.534521 | + | 0.845155i | \(0.320492\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.4039 | 1.70547 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.22646 | −0.328137 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.2931 | 1.23677 | 0.618383 | − | 0.785877i | \(-0.287788\pi\) | ||||
0.618383 | + | 0.785877i | \(0.287788\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.9490 | 0.539249 | 0.269624 | − | 0.962966i | \(-0.413100\pi\) | ||||
0.269624 | + | 0.962966i | \(0.413100\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.23846 | 0.100815 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.35446 | 0.105612 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.4598 | 0.513010 | 0.256505 | − | 0.966543i | \(-0.417429\pi\) | ||||
0.256505 | + | 0.966543i | \(0.417429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.0649626 | −0.00289654 | −0.00144827 | − | 0.999999i | \(-0.500461\pi\) | ||||
−0.00144827 | + | 0.999999i | \(0.500461\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.2819 | 0.591036 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.1200 | −1.06910 | −0.534551 | − | 0.845136i | \(-0.679519\pi\) | ||||
−0.534551 | + | 0.845136i | \(0.679519\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.8074 | 0.522330 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.8154 | −0.917236 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −76.1775 | −3.35028 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.1734 | −1.49716 | −0.748582 | − | 0.663042i | \(-0.769265\pi\) | ||||
−0.748582 | + | 0.663042i | \(0.769265\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.2695 | 0.623963 | 0.311981 | − | 0.950088i | \(-0.399007\pi\) | ||||
0.311981 | + | 0.950088i | \(0.399007\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.34651 | −0.145776 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2141 | 0.487570 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.5897 | 1.10841 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.46059 | −0.279316 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.28030 | 0.270512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.82815 | 0.379552 | 0.189776 | − | 0.981827i | \(-0.439224\pi\) | ||||
0.189776 | + | 0.981827i | \(0.439224\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.90389 | 0.381401 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.6356 | −0.583015 | −0.291508 | − | 0.956568i | \(-0.594157\pi\) | ||||
−0.291508 | + | 0.956568i | \(0.594157\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.4430 | −1.16911 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.3034 | 0.523195 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.31179 | −0.225068 | −0.112534 | − | 0.993648i | \(-0.535897\pi\) | ||||
−0.112534 | + | 0.993648i | \(0.535897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.9729 | −1.39460 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.91665 | 0.165067 | 0.0825335 | − | 0.996588i | \(-0.473699\pi\) | ||||
0.0825335 | + | 0.996588i | \(0.473699\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.5160 | 0.526553 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.91631 | 0.331869 | 0.165934 | − | 0.986137i | \(-0.446936\pi\) | ||||
0.165934 | + | 0.986137i | \(0.446936\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.5144 | −0.607408 | −0.303704 | − | 0.952766i | \(-0.598223\pi\) | ||||
−0.303704 | + | 0.952766i | \(0.598223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.6790 | 0.778969 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.475270 | 0.0197857 | 0.00989287 | − | 0.999951i | \(-0.496851\pi\) | ||||
0.00989287 | + | 0.999951i | \(0.496851\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.43102 | −0.349778 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −87.1229 | −3.60826 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.0646 | −0.828156 | −0.414078 | − | 0.910242i | \(-0.635896\pi\) | ||||
−0.414078 | + | 0.910242i | \(0.635896\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.0275 | 1.69051 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.2699 | −1.53049 | −0.765247 | − | 0.643737i | \(-0.777383\pi\) | ||||
−0.765247 | + | 0.643737i | \(0.777383\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.679012 | 0.0278368 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.9059 | −0.935908 | −0.467954 | − | 0.883753i | \(-0.655009\pi\) | ||||
−0.467954 | + | 0.883753i | \(0.655009\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.55862 | 0.267532 | 0.133766 | − | 0.991013i | \(-0.457293\pi\) | ||||
0.133766 | + | 0.991013i | \(0.457293\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 38.2293 | 1.55424 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4960 | 0.994261 | 0.497131 | − | 0.867676i | \(-0.334387\pi\) | ||||
0.497131 | + | 0.867676i | \(0.334387\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.7464 | 2.17435 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20.6037 | −0.832175 | −0.416088 | − | 0.909325i | \(-0.636599\pi\) | ||||
−0.416088 | + | 0.909325i | \(0.636599\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.2572 | 1.05707 | 0.528537 | − | 0.848910i | \(-0.322741\pi\) | ||||
0.528537 | + | 0.848910i | \(0.322741\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.9729 | 1.12433 | 0.562163 | − | 0.827027i | \(-0.309969\pi\) | ||||
0.562163 | + | 0.827027i | \(0.309969\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.91308 | −0.196839 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.16464 | 0.0465855 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.26440 | −0.170033 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5690 | 0.540173 | 0.270086 | − | 0.962836i | \(-0.412948\pi\) | ||||
0.270086 | + | 0.962836i | \(0.412948\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.31377 | −0.290238 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.43102 | −0.175563 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.53989 | 0.258310 | 0.129155 | − | 0.991624i | \(-0.458773\pi\) | ||||
0.129155 | + | 0.991624i | \(0.458773\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.2755 | −0.996768 | −0.498384 | − | 0.866956i | \(-0.666073\pi\) | ||||
−0.498384 | + | 0.866956i | \(0.666073\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.3664 | −0.486173 | −0.243087 | − | 0.970005i | \(-0.578160\pi\) | ||||
−0.243087 | + | 0.970005i | \(0.578160\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.2970 | −1.54254 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −40.4996 | −1.58487 | −0.792436 | − | 0.609955i | \(-0.791187\pi\) | ||||
−0.792436 | + | 0.609955i | \(0.791187\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −20.3218 | −0.794039 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.4015 | 0.911593 | 0.455797 | − | 0.890084i | \(-0.349354\pi\) | ||||
0.455797 | + | 0.890084i | \(0.349354\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1926 | −0.396445 | −0.198222 | − | 0.980157i | \(-0.563517\pi\) | ||||
−0.198222 | + | 0.980157i | \(0.563517\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.32455 | −0.322812 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.9183 | −1.00356 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.34534 | 0.244959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.2281 | 0.587000 | 0.293500 | − | 0.955959i | \(-0.405180\pi\) | ||||
0.293500 | + | 0.955959i | \(0.405180\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.0993 | −1.46427 | −0.732137 | − | 0.681158i | \(-0.761477\pi\) | ||||
−0.732137 | + | 0.681158i | \(0.761477\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.37641 | −0.206328 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.8329 | 1.37111 | 0.685553 | − | 0.728022i | \(-0.259560\pi\) | ||||
0.685553 | + | 0.728022i | \(0.259560\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.6511 | 1.01829 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 61.4689 | 2.34178 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.8844 | 1.85965 | 0.929825 | − | 0.368002i | \(-0.119958\pi\) | ||||
0.929825 | + | 0.368002i | \(0.119958\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.8724 | 0.981396 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.91747 | −0.110507 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.0857 | 0.532009 | 0.266004 | − | 0.963972i | \(-0.414296\pi\) | ||||
0.266004 | + | 0.963972i | \(0.414296\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.2807 | 1.97180 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.88159 | 0.371636 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.85086 | −0.144622 | −0.0723111 | − | 0.997382i | \(-0.523037\pi\) | ||||
−0.0723111 | + | 0.997382i | \(0.523037\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 38.7480 | 1.45112 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.4039 | −1.39883 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.792273 | −0.0295468 | −0.0147734 | − | 0.999891i | \(-0.504703\pi\) | ||||
−0.0147734 | + | 0.999891i | \(0.504703\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.4864 | −0.576745 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.1500 | −0.525516 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.11725 | −0.189788 | −0.0948941 | − | 0.995487i | \(-0.530251\pi\) | ||||
−0.0948941 | + | 0.995487i | \(0.530251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.75922 | 0.139040 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.71730 | 0.0634297 | 0.0317149 | − | 0.999497i | \(-0.489903\pi\) | ||||
0.0317149 | + | 0.999497i | \(0.489903\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −93.0602 | −3.42792 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.1276 | −0.593263 | −0.296632 | − | 0.954992i | \(-0.595863\pi\) | ||||
−0.296632 | + | 0.954992i | \(0.595863\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.10565 | 0.113935 | 0.0569676 | − | 0.998376i | \(-0.481857\pi\) | ||||
0.0569676 | + | 0.998376i | \(0.481857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.9011 | 0.765759 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.80661 | −0.175630 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.9581 | −0.801261 | −0.400631 | − | 0.916240i | \(-0.631209\pi\) | ||||
−0.400631 | + | 0.916240i | \(0.631209\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.42265 | −0.342925 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −53.3597 | −1.93939 | −0.969695 | − | 0.244319i | \(-0.921436\pi\) | ||||
−0.969695 | + | 0.244319i | \(0.921436\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.34883 | −0.338895 | −0.169447 | − | 0.985539i | \(-0.554198\pi\) | ||||
−0.169447 | + | 0.985539i | \(0.554198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.62441 | 0.239820 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.7257 | 1.00112 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.22131 | 0.260407 | 0.130204 | − | 0.991487i | \(-0.458437\pi\) | ||||
0.130204 | + | 0.991487i | \(0.458437\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.69177 | −0.204719 | −0.102359 | − | 0.994747i | \(-0.532639\pi\) | ||||
−0.102359 | + | 0.994747i | \(0.532639\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.1543 | 0.759884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.7676 | 1.28151 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.7867 | 0.529111 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.46373 | −0.195009 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.3787 | 0.548193 | 0.274096 | − | 0.961702i | \(-0.411621\pi\) | ||||
0.274096 | + | 0.961702i | \(0.411621\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.31179 | 0.331089 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.47691 | −0.158980 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.0211 | −1.24051 | −0.620256 | − | 0.784400i | \(-0.712971\pi\) | ||||
−0.620256 | + | 0.784400i | \(0.712971\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.12760 | −0.216779 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 74.1543 | 2.61685 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.86204 | −0.277101 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.6591 | −0.620862 | −0.310431 | − | 0.950596i | \(-0.600473\pi\) | ||||
−0.310431 | + | 0.950596i | \(0.600473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.91150 | −0.172466 | −0.0862331 | − | 0.996275i | \(-0.527483\pi\) | ||||
−0.0862331 | + | 0.996275i | \(0.527483\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 27.8098 | 0.974133 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.0873 | −1.61239 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.6359 | 0.475897 | 0.237949 | − | 0.971278i | \(-0.423525\pi\) | ||||
0.237949 | + | 0.971278i | \(0.423525\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.77354 | −0.236111 | −0.118055 | − | 0.993007i | \(-0.537666\pi\) | ||||
−0.118055 | + | 0.993007i | \(0.537666\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −51.7161 | −1.79835 | −0.899173 | − | 0.437594i | \(-0.855831\pi\) | ||||
−0.899173 | + | 0.437594i | \(0.855831\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.2046 | −0.944854 | −0.472427 | − | 0.881370i | \(-0.656622\pi\) | ||||
−0.472427 | + | 0.881370i | \(0.656622\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.505178 | 0.0175034 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.3564 | 0.462217 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.431020 | −0.0148805 | −0.00744024 | − | 0.999972i | \(-0.502368\pi\) | ||||
−0.00744024 | + | 0.999972i | \(0.502368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.36606 | −0.322968 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.91671 | 0.306744 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 28.4422 | 0.977285 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49.3760 | 1.69259 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.3971 | −0.801102 | −0.400551 | − | 0.916274i | \(-0.631181\pi\) | ||||
−0.400551 | + | 0.916274i | \(0.631181\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.23523 | 0.110513 | 0.0552567 | − | 0.998472i | \(-0.482402\pi\) | ||||
0.0552567 | + | 0.998472i | \(0.482402\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −54.3042 | −1.85284 | −0.926418 | − | 0.376496i | \(-0.877129\pi\) | ||||
−0.926418 | + | 0.376496i | \(0.877129\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.5611 | −1.55092 | −0.775459 | − | 0.631398i | \(-0.782481\pi\) | ||||
−0.775459 | + | 0.631398i | \(0.782481\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.86204 | 0.267317 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 77.2692 | 2.62118 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 65.6579 | 2.22473 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0128 | −0.372299 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.3661 | 0.620178 | 0.310089 | − | 0.950708i | \(-0.399641\pi\) | ||||
0.310089 | + | 0.950708i | \(0.399641\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.02394 | 0.169261 | 0.0846304 | − | 0.996412i | \(-0.473029\pi\) | ||||
0.0846304 | + | 0.996412i | \(0.473029\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.7344 | 0.495853 | 0.247927 | − | 0.968779i | \(-0.420251\pi\) | ||||
0.247927 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.4621 | 0.384859 | 0.192430 | − | 0.981311i | \(-0.438363\pi\) | ||||
0.192430 | + | 0.981311i | \(0.438363\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.44138 | −0.182498 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 75.1232 | 2.51390 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.4031 | −0.548295 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −29.3529 | −0.978973 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.00803 | −0.233471 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 31.0773 | 1.03304 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.9809 | 0.729865 | 0.364932 | − | 0.931034i | \(-0.381092\pi\) | ||||
0.364932 | + | 0.931034i | \(0.381092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.676689 | 0.0224197 | 0.0112099 | − | 0.999937i | \(-0.496432\pi\) | ||||
0.0112099 | + | 0.999937i | \(0.496432\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.9494 | −1.75237 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15.1192 | −0.499281 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −22.0717 | −0.728080 | −0.364040 | − | 0.931383i | \(-0.618603\pi\) | ||||
−0.364040 | + | 0.931383i | \(0.618603\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.4327 | −0.343395 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.9566 | 0.886327 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.5091 | 0.935355 | 0.467677 | − | 0.883899i | \(-0.345091\pi\) | ||||
0.467677 | + | 0.883899i | \(0.345091\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.19339 | −0.202980 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.26440 | 0.139461 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.8046 | 1.03901 | 0.519506 | − | 0.854467i | \(-0.326116\pi\) | ||||
0.519506 | + | 0.854467i | \(0.326116\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.6320 | 1.12897 | 0.564486 | − | 0.825443i | \(-0.309074\pi\) | ||||
0.564486 | + | 0.825443i | \(0.309074\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 33.7803 | 1.10004 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.9920 | −1.10459 | −0.552296 | − | 0.833648i | \(-0.686248\pi\) | ||||
−0.552296 | + | 0.833648i | \(0.686248\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −52.3190 | −1.69835 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.41031 | 0.207650 | 0.103825 | − | 0.994596i | \(-0.466892\pi\) | ||||
0.103825 | + | 0.994596i | \(0.466892\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.79426 | 0.0580607 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.8281 | 0.640284 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.8828 | 0.415573 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.4314 | −0.400180 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −31.1028 | −1.00020 | −0.500100 | − | 0.865968i | \(-0.666703\pi\) | ||||
−0.500100 | + | 0.865968i | \(0.666703\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.9701 | −1.25061 | −0.625305 | − | 0.780381i | \(-0.715025\pi\) | ||||
−0.625305 | + | 0.780381i | \(0.715025\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.2488 | 0.617089 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.6356 | 1.46001 | 0.730006 | − | 0.683441i | \(-0.239517\pi\) | ||||
0.730006 | + | 0.683441i | \(0.239517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.8556 | −0.986151 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 30.1089 | 0.960324 | 0.480162 | − | 0.877180i | \(-0.340578\pi\) | ||||
0.480162 | + | 0.877180i | \(0.340578\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.5247 | 0.494659 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43.5267 | −1.38407 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.927003 | −0.0294472 | −0.0147236 | − | 0.999892i | \(-0.504687\pi\) | ||||
−0.0147236 | + | 0.999892i | \(0.504687\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.3182 | 0.358812 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.7735 | 0.847927 | 0.423963 | − | 0.905679i | \(-0.360639\pi\) | ||||
0.423963 | + | 0.905679i | \(0.360639\pi\) | |||||||
\(998\) | 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 | 6048.2.a.bn.1.3 | yes | 4 | |
3.2 | odd | 2 | 6048.2.a.bu.1.2 | yes | 4 | ||
4.3 | odd | 2 | 6048.2.a.bl.1.3 | ✓ | 4 | ||
12.11 | even | 2 | 6048.2.a.bq.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bl.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
6048.2.a.bn.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
6048.2.a.bq.1.2 | yes | 4 | 12.11 | even | 2 | ||
6048.2.a.bu.1.2 | yes | 4 | 3.2 | odd | 2 |