Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 9x^{8} + 14x^{7} + 27x^{6} - 27x^{5} - 34x^{4} + 14x^{3} + 17x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 503) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.489003\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | 1.48900 | 0.859676 | 0.429838 | − | 0.902906i | \(-0.358571\pi\) | ||||
0.429838 | + | 0.902906i | \(0.358571\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.79865 | −0.804380 | −0.402190 | − | 0.915556i | \(-0.631751\pi\) | ||||
−0.402190 | + | 0.915556i | \(0.631751\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.552233 | −0.208724 | −0.104362 | − | 0.994539i | \(-0.533280\pi\) | ||||
−0.104362 | + | 0.994539i | \(0.533280\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.782869 | −0.260956 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.33718 | −1.30771 | −0.653854 | − | 0.756620i | \(-0.726849\pi\) | ||||
−0.653854 | + | 0.756620i | \(0.726849\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.54873 | 0.706891 | 0.353445 | − | 0.935455i | \(-0.385010\pi\) | ||||
0.353445 | + | 0.935455i | \(0.385010\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.67819 | −0.691507 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.52304 | 0.611928 | 0.305964 | − | 0.952043i | \(-0.401021\pi\) | ||||
0.305964 | + | 0.952043i | \(0.401021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.11893 | 1.17436 | 0.587181 | − | 0.809455i | \(-0.300238\pi\) | ||||
0.587181 | + | 0.809455i | \(0.300238\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.822276 | −0.179435 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.78409 | 0.789036 | 0.394518 | − | 0.918888i | \(-0.370912\pi\) | ||||
0.394518 | + | 0.918888i | \(0.370912\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.76486 | −0.352972 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.63270 | −1.08401 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.907287 | 0.168479 | 0.0842395 | − | 0.996446i | \(-0.473154\pi\) | ||||
0.0842395 | + | 0.996446i | \(0.473154\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.380820 | −0.0683972 | −0.0341986 | − | 0.999415i | \(-0.510888\pi\) | ||||
−0.0341986 | + | 0.999415i | \(0.510888\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.45807 | −1.12421 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.993273 | 0.167894 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.43266 | −0.893124 | −0.446562 | − | 0.894753i | \(-0.647352\pi\) | ||||
−0.446562 | + | 0.894753i | \(0.647352\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.79507 | 0.607697 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.72459 | 0.894031 | 0.447015 | − | 0.894526i | \(-0.352487\pi\) | ||||
0.447015 | + | 0.894526i | \(0.352487\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.21553 | 1.40536 | 0.702678 | − | 0.711508i | \(-0.251988\pi\) | ||||
0.702678 | + | 0.711508i | \(0.251988\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.40811 | 0.209908 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.81077 | 1.28518 | 0.642592 | − | 0.766209i | \(-0.277859\pi\) | ||||
0.642592 | + | 0.766209i | \(0.277859\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.69504 | −0.956434 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.75682 | 0.526060 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.46357 | −0.887840 | −0.443920 | − | 0.896066i | \(-0.646413\pi\) | ||||
−0.443920 | + | 0.896066i | \(0.646413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.80106 | 1.05190 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.62210 | 1.00957 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.40568 | −0.443381 | −0.221691 | − | 0.975117i | \(-0.571157\pi\) | ||||
−0.221691 | + | 0.975117i | \(0.571157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.06109 | −0.135859 | −0.0679294 | − | 0.997690i | \(-0.521639\pi\) | ||||
−0.0679294 | + | 0.997690i | \(0.521639\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.432326 | 0.0544679 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.58427 | −0.568609 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.253929 | 0.0310223 | 0.0155112 | − | 0.999880i | \(-0.495062\pi\) | ||||
0.0155112 | + | 0.999880i | \(0.495062\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.63451 | 0.678316 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7311 | −1.39222 | −0.696112 | − | 0.717933i | \(-0.745088\pi\) | ||||
−0.696112 | + | 0.717933i | \(0.745088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.1271 | −1.88753 | −0.943765 | − | 0.330617i | \(-0.892743\pi\) | ||||
−0.943765 | + | 0.330617i | \(0.892743\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.62789 | −0.303442 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.39513 | 0.272951 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.76447 | −0.873571 | −0.436785 | − | 0.899566i | \(-0.643883\pi\) | ||||
−0.436785 | + | 0.899566i | \(0.643883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.03851 | −0.670945 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.3846 | 1.79844 | 0.899222 | − | 0.437492i | \(-0.144133\pi\) | ||||
0.899222 | + | 0.437492i | \(0.144133\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.53807 | −0.492223 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.35095 | 0.144837 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.09992 | −0.328590 | −0.164295 | − | 0.986411i | \(-0.552535\pi\) | ||||
−0.164295 | + | 0.986411i | \(0.552535\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.40749 | −0.147545 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.567042 | −0.0587995 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9.20715 | −0.944634 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.28605 | −0.435183 | −0.217591 | − | 0.976040i | \(-0.569820\pi\) | ||||
−0.217591 | + | 0.976040i | \(0.569820\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.39544 | 0.341255 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.73446 | −0.371592 | −0.185796 | − | 0.982588i | \(-0.559486\pi\) | ||||
−0.185796 | + | 0.982588i | \(0.559486\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.83220 | −0.279065 | −0.139533 | − | 0.990217i | \(-0.544560\pi\) | ||||
−0.139533 | + | 0.990217i | \(0.544560\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.47899 | 0.144334 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.0994 | −0.976343 | −0.488172 | − | 0.872748i | \(-0.662336\pi\) | ||||
−0.488172 | + | 0.872748i | \(0.662336\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.86764 | −0.657800 | −0.328900 | − | 0.944365i | \(-0.606678\pi\) | ||||
−0.328900 | + | 0.944365i | \(0.606678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.08925 | −0.767798 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.80558 | 0.263927 | 0.131963 | − | 0.991255i | \(-0.457872\pi\) | ||||
0.131963 | + | 0.991255i | \(0.457872\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.80624 | −0.634685 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.99532 | −0.184468 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.39331 | −0.127724 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.81112 | 0.710102 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.52393 | 0.768577 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1676 | 1.08830 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.9147 | 1.32347 | 0.661734 | − | 0.749739i | \(-0.269821\pi\) | ||||
0.661734 | + | 0.749739i | \(0.269821\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.7220 | 1.20815 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.5207 | −1.18131 | −0.590654 | − | 0.806925i | \(-0.701130\pi\) | ||||
−0.590654 | + | 0.806925i | \(0.701130\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.82684 | −0.245118 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.1313 | 0.871960 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.4479 | −1.06350 | −0.531750 | − | 0.846901i | \(-0.678465\pi\) | ||||
−0.531750 | + | 0.846901i | \(0.678465\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.15443 | −0.182736 | −0.0913681 | − | 0.995817i | \(-0.529124\pi\) | ||||
−0.0913681 | + | 0.995817i | \(0.529124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.1193 | 1.10484 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.0543 | −0.924407 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.63189 | −0.135521 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.96894 | −0.822224 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.59253 | −0.703927 | −0.351964 | − | 0.936014i | \(-0.614486\pi\) | ||||
−0.351964 | + | 0.936014i | \(0.614486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.527862 | −0.0429568 | −0.0214784 | − | 0.999769i | \(-0.506837\pi\) | ||||
−0.0214784 | + | 0.999769i | \(0.506837\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.97521 | −0.159687 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.684961 | 0.0550174 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.1711 | 0.891554 | 0.445777 | − | 0.895144i | \(-0.352927\pi\) | ||||
0.445777 | + | 0.895144i | \(0.352927\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.62428 | −0.763255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.08970 | −0.164691 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.0109 | −1.56738 | −0.783689 | − | 0.621153i | \(-0.786664\pi\) | ||||
−0.783689 | + | 0.621153i | \(0.786664\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.6158 | 0.904289 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.9520 | 0.924877 | 0.462439 | − | 0.886651i | \(-0.346975\pi\) | ||||
0.462439 | + | 0.886651i | \(0.346975\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.50397 | −0.500305 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00745 | −0.306457 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.14561 | 0.239156 | 0.119578 | − | 0.992825i | \(-0.461846\pi\) | ||||
0.119578 | + | 0.992825i | \(0.461846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.974615 | 0.0736739 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.07106 | −0.381164 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.02096 | 0.450028 | 0.225014 | − | 0.974356i | \(-0.427757\pi\) | ||||
0.225014 | + | 0.974356i | \(0.427757\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0475 | −1.71311 | −0.856553 | − | 0.516059i | \(-0.827398\pi\) | ||||
−0.856553 | + | 0.516059i | \(0.827398\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.57997 | −0.116795 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.77145 | 0.718412 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.9429 | −0.800224 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.11056 | 0.226260 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.9774 | 1.30080 | 0.650398 | − | 0.759594i | \(-0.274602\pi\) | ||||
0.650398 | + | 0.759594i | \(0.274602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.4429 | −0.751697 | −0.375848 | − | 0.926681i | \(-0.622649\pi\) | ||||
−0.375848 | + | 0.926681i | \(0.622649\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.82600 | −0.488820 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.36026 | −0.310656 | −0.155328 | − | 0.987863i | \(-0.549643\pi\) | ||||
−0.155328 | + | 0.987863i | \(0.549643\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0205 | −0.993888 | −0.496944 | − | 0.867783i | \(-0.665545\pi\) | ||||
−0.496944 | + | 0.867783i | \(0.665545\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.378101 | 0.0266692 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.501034 | −0.0351657 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.2965 | −0.719141 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.96244 | −0.205904 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.2017 | −1.53572 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0580 | 0.761265 | 0.380633 | − | 0.924726i | \(-0.375706\pi\) | ||||
0.380633 | + | 0.924726i | \(0.375706\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17.4676 | −1.19686 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −16.5755 | −1.13044 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.210301 | 0.0142762 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.0133 | −1.62267 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.43056 | 0.432566 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.5502 | 1.04132 | 0.520658 | − | 0.853765i | \(-0.325687\pi\) | ||||
0.520658 | + | 0.853765i | \(0.325687\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.38166 | 0.0921104 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.27577 | −0.0846759 | −0.0423379 | − | 0.999103i | \(-0.513481\pi\) | ||||
−0.0423379 | + | 0.999103i | \(0.513481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.5232 | −1.02580 | −0.512901 | − | 0.858448i | \(-0.671429\pi\) | ||||
−0.512901 | + | 0.858448i | \(0.671429\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.56636 | 0.234649 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −27.8010 | −1.82130 | −0.910651 | − | 0.413177i | \(-0.864419\pi\) | ||||
−0.910651 | + | 0.413177i | \(0.864419\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.8475 | −1.03378 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.5613 | −0.750988 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.20369 | −0.0778601 | −0.0389301 | − | 0.999242i | \(-0.512395\pi\) | ||||
−0.0389301 | + | 0.999242i | \(0.512395\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.6025 | −1.64920 | −0.824602 | − | 0.565713i | \(-0.808601\pi\) | ||||
−0.824602 | + | 0.565713i | \(0.808601\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.90676 | 0.507219 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.0420 | 0.769337 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.0468 | 0.830146 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 24.3967 | 1.54608 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.2638 | −0.837205 | −0.418603 | − | 0.908170i | \(-0.637480\pi\) | ||||
−0.418603 | + | 0.908170i | \(0.637480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.4123 | −1.03183 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.75720 | −0.423152 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −16.1006 | −1.00433 | −0.502163 | − | 0.864773i | \(-0.667462\pi\) | ||||
−0.502163 | + | 0.864773i | \(0.667462\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.00009 | 0.186417 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.710288 | −0.0439657 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.77336 | −0.417663 | −0.208832 | − | 0.977952i | \(-0.566966\pi\) | ||||
−0.208832 | + | 0.977952i | \(0.566966\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 11.6257 | 0.714161 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.61579 | −0.282481 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.4853 | 1.43192 | 0.715962 | − | 0.698139i | \(-0.245988\pi\) | ||||
0.715962 | + | 0.698139i | \(0.245988\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.5886 | −1.06843 | −0.534216 | − | 0.845348i | \(-0.679393\pi\) | ||||
−0.534216 | + | 0.845348i | \(0.679393\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.09576 | −0.126841 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.65452 | 0.461585 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.3448 | −0.681645 | −0.340823 | − | 0.940128i | \(-0.610706\pi\) | ||||
−0.340823 | + | 0.940128i | \(0.610706\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.298132 | 0.0178487 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.36752 | −0.558820 | −0.279410 | − | 0.960172i | \(-0.590139\pi\) | ||||
−0.279410 | + | 0.960172i | \(0.590139\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.8789 | −1.59778 | −0.798892 | − | 0.601474i | \(-0.794580\pi\) | ||||
−0.798892 | + | 0.601474i | \(0.794580\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.7095 | −0.812080 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.16131 | −0.186606 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.6342 | −0.625544 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.38195 | −0.374117 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 17.2365 | 1.00697 | 0.503485 | − | 0.864004i | \(-0.332051\pi\) | ||||
0.503485 | + | 0.864004i | \(0.332051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.12561 | 0.356647 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 24.4301 | 1.41758 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.64462 | 0.557763 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.08912 | −0.293332 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.56062 | −0.319449 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.90853 | 0.109282 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.0001 | −1.65512 | −0.827561 | − | 0.561376i | \(-0.810272\pi\) | ||||
−0.827561 | + | 0.561376i | \(0.810272\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.21716 | −0.239906 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.2312 | −1.54414 | −0.772071 | − | 0.635536i | \(-0.780779\pi\) | ||||
−0.772071 | + | 0.635536i | \(0.780779\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.53059 | 0.312607 | 0.156304 | − | 0.987709i | \(-0.450042\pi\) | ||||
0.156304 | + | 0.987709i | \(0.450042\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.777603 | −0.0438129 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.2030 | 1.75253 | 0.876267 | − | 0.481826i | \(-0.160026\pi\) | ||||
0.876267 | + | 0.481826i | \(0.160026\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.93507 | −0.220322 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0380 | −0.839339 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.9153 | 0.718626 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.49816 | −0.249513 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.2259 | −0.565495 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.86560 | −0.268249 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.8025 | −0.923551 | −0.461775 | − | 0.886997i | \(-0.652787\pi\) | ||||
−0.461775 | + | 0.886997i | \(0.652787\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.25307 | 0.233067 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.456729 | −0.0249538 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.57943 | 0.412878 | 0.206439 | − | 0.978459i | \(-0.433813\pi\) | ||||
0.206439 | + | 0.978459i | \(0.433813\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.17752 | 0.226892 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.65168 | 0.0894437 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.56285 | 0.408355 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.1345 | −0.545624 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.0855 | 1.50771 | 0.753853 | − | 0.657043i | \(-0.228193\pi\) | ||||
0.753853 | + | 0.657043i | \(0.228193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.6230 | 0.622164 | 0.311082 | − | 0.950383i | \(-0.399309\pi\) | ||||
0.311082 | + | 0.950383i | \(0.399309\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.3563 | −0.766280 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.16556 | −0.328160 | −0.164080 | − | 0.986447i | \(-0.552465\pi\) | ||||
−0.164080 | + | 0.986447i | \(0.552465\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.1001 | 1.11988 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.07464 | −0.109802 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.3896 | 0.548344 | 0.274172 | − | 0.961681i | \(-0.411596\pi\) | ||||
0.274172 | + | 0.961681i | \(0.411596\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.20342 | 0.379127 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.6308 | 0.610458 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.0069 | 1.51829 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.571294 | −0.0298213 | −0.0149107 | − | 0.999889i | \(-0.504746\pi\) | ||||
−0.0149107 | + | 0.999889i | \(0.504746\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.48161 | −0.233303 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.56940 | 0.185314 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.95332 | 0.152917 | 0.0764586 | − | 0.997073i | \(-0.475639\pi\) | ||||
0.0764586 | + | 0.997073i | \(0.475639\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.1176 | 0.935590 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.31243 | 0.119096 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.2705 | 1.34942 | 0.674711 | − | 0.738082i | \(-0.264268\pi\) | ||||
0.674711 | + | 0.738082i | \(0.264268\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.2081 | 1.13775 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.44503 | −0.176033 | −0.0880164 | − | 0.996119i | \(-0.528053\pi\) | ||||
−0.0880164 | + | 0.996119i | \(0.528053\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.30800 | −0.219556 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.21456 | −0.366736 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.95150 | −0.403157 | −0.201578 | − | 0.979472i | \(-0.564607\pi\) | ||||
−0.201578 | + | 0.979472i | \(0.564607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.54742 | 0.482834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.1323 | −1.01554 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.9656 | 0.702683 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.7255 | 1.09037 | 0.545186 | − | 0.838315i | \(-0.316459\pi\) | ||||
0.545186 | + | 0.838315i | \(0.316459\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.20917 | −0.210722 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1072 | 0.704481 | 0.352241 | − | 0.935909i | \(-0.385420\pi\) | ||||
0.352241 | + | 0.935909i | \(0.385420\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.970607 | −0.0483494 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.8612 | 0.539695 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 23.5624 | 1.16795 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.2905 | −0.508834 | −0.254417 | − | 0.967095i | \(-0.581884\pi\) | ||||
−0.254417 | + | 0.967095i | \(0.581884\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.5350 | −0.914266 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.88072 | 0.0925444 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −29.4702 | −1.44663 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.20795 | −0.157094 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.0965 | −0.932925 | −0.466463 | − | 0.884541i | \(-0.654472\pi\) | ||||
−0.466463 | + | 0.884541i | \(0.654472\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.3025 | 1.28191 | 0.640953 | − | 0.767580i | \(-0.278539\pi\) | ||||
0.640953 | + | 0.767580i | \(0.278539\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.89768 | −0.335377 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.45283 | −0.215994 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.585969 | 0.0283570 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.4599 | −0.794691 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.5246 | 0.795963 | 0.397982 | − | 0.917393i | \(-0.369711\pi\) | ||||
0.397982 | + | 0.917393i | \(0.369711\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.52467 | 0.217442 | 0.108721 | − | 0.994072i | \(-0.465325\pi\) | ||||
0.108721 | + | 0.994072i | \(0.465325\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.42989 | −0.116504 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.3705 | 0.926615 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.06783 | 0.432784 | 0.216392 | − | 0.976307i | \(-0.430571\pi\) | ||||
0.216392 | + | 0.976307i | \(0.430571\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.24134 | 0.249588 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.6542 | 0.601219 | 0.300609 | − | 0.953747i | \(-0.402810\pi\) | ||||
0.300609 | + | 0.953747i | \(0.402810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.57566 | 0.264312 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.7943 | −0.605150 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.8336 | 1.64390 | 0.821950 | − | 0.569560i | \(-0.192886\pi\) | ||||
0.821950 | + | 0.569560i | \(0.192886\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.8286 | −1.16913 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.785988 | −0.0369290 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.53158 | 0.118683 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3718 | −0.672283 | −0.336141 | − | 0.941812i | \(-0.609122\pi\) | ||||
−0.336141 | + | 0.941812i | \(0.609122\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.2116 | −0.663339 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.9323 | −0.974914 | −0.487457 | − | 0.873147i | \(-0.662075\pi\) | ||||
−0.487457 | + | 0.873147i | \(0.662075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.4204 | −0.902541 | −0.451271 | − | 0.892387i | \(-0.649029\pi\) | ||||
−0.451271 | + | 0.892387i | \(0.649029\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.01991 | 0.0472971 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.0847 | −1.02196 | −0.510980 | − | 0.859593i | \(-0.670717\pi\) | ||||
−0.510980 | + | 0.859593i | \(0.670717\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.140228 | −0.00647512 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 16.6339 | 0.766448 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −39.9694 | −1.83780 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.03420 | −0.414518 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.06013 | 0.231688 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.4118 | −1.16109 | −0.580547 | − | 0.814227i | \(-0.697161\pi\) | ||||
−0.580547 | + | 0.814227i | \(0.697161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.8464 | −0.631342 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.11156 | −0.141581 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.70911 | 0.350053 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.7671 | 1.66608 | 0.833039 | − | 0.553214i | \(-0.186599\pi\) | ||||
0.833039 | + | 0.553214i | \(0.186599\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −29.7964 | −1.34744 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.6572 | 0.571212 | 0.285606 | − | 0.958347i | \(-0.407805\pi\) | ||||
0.285606 | + | 0.958347i | \(0.407805\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.28913 | 0.103097 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.10721 | −0.274499 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.47829 | 0.290591 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.39500 | −0.107215 | −0.0536074 | − | 0.998562i | \(-0.517072\pi\) | ||||
−0.0536074 | + | 0.998562i | \(0.517072\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.7966 | 0.795095 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.71697 | 0.298901 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.68443 | −0.430101 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.46329 | 0.286480 | 0.143240 | − | 0.989688i | \(-0.454248\pi\) | ||||
0.143240 | + | 0.989688i | \(0.454248\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.90589 | 0.393973 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.8334 | −1.27303 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.09414 | 0.224475 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −38.2139 | −1.68065 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.68382 | 0.205597 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.3036 | 1.50287 | 0.751434 | − | 0.659808i | \(-0.229363\pi\) | ||||
0.751434 | + | 0.659808i | \(0.229363\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.3662 | −1.32782 | −0.663910 | − | 0.747812i | \(-0.731104\pi\) | ||||
−0.663910 | + | 0.747812i | \(0.731104\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.45120 | 0.0633357 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.960825 | −0.0418542 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.68070 | −0.377422 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.66620 | 0.115703 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.5904 | 0.631982 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.1652 | 0.785351 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.96523 | 0.386878 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 29.0376 | 1.25074 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.1371 | 1.68263 | 0.841317 | − | 0.540542i | \(-0.181781\pi\) | ||||
0.841317 | + | 0.540542i | \(0.181781\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −34.3178 | −1.47272 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.3525 | 0.529121 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −24.0487 | −1.02825 | −0.514125 | − | 0.857715i | \(-0.671883\pi\) | ||||
−0.514125 | + | 0.857715i | \(0.671883\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.830696 | 0.0354532 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.64434 | 0.197855 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.28779 | 0.182335 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.5497 | 0.617602 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.2987 | −0.732971 | −0.366486 | − | 0.930424i | \(-0.619439\pi\) | ||||
−0.366486 | + | 0.930424i | \(0.619439\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 23.4879 | 0.993433 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.2940 | −0.687934 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.63944 | −0.237674 | −0.118837 | − | 0.992914i | \(-0.537917\pi\) | ||||
−0.118837 | + | 0.992914i | \(0.537917\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.04626 | −0.212298 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.33466 | 0.140043 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.0350 | −0.504535 | −0.252268 | − | 0.967658i | \(-0.581176\pi\) | ||||
−0.252268 | + | 0.967658i | \(0.581176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.9404 | −1.25297 | −0.626484 | − | 0.779434i | \(-0.715507\pi\) | ||||
−0.626484 | + | 0.779434i | \(0.715507\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 26.7683 | 1.11826 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.67839 | −0.278508 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6080 | 0.733032 | 0.366516 | − | 0.930412i | \(-0.380551\pi\) | ||||
0.366516 | + | 0.930412i | \(0.380551\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.5495 | −0.646216 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.04811 | −0.375379 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.0337 | 1.16104 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.58889 | 0.148382 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.2268 | 0.876125 | 0.438062 | − | 0.898945i | \(-0.355665\pi\) | ||||
0.438062 | + | 0.898945i | \(0.355665\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.94939 | −0.0803231 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.49244 | −0.267063 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.78783 | 0.0734175 | 0.0367087 | − | 0.999326i | \(-0.488313\pi\) | ||||
0.0367087 | + | 0.999326i | \(0.488313\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.50607 | 0.102739 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −20.8766 | −0.854422 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.15199 | 0.169646 | 0.0848228 | − | 0.996396i | \(-0.472968\pi\) | ||||
0.0848228 | + | 0.996396i | \(0.472968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.87221 | −0.198742 | −0.0993708 | − | 0.995050i | \(-0.531683\pi\) | ||||
−0.0993708 | + | 0.995050i | \(0.531683\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.198793 | −0.00809548 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.0495 | −0.571192 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.0579 | 0.895303 | 0.447652 | − | 0.894208i | \(-0.352261\pi\) | ||||
0.447652 | + | 0.894208i | \(0.352261\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.746041 | −0.0302311 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.4563 | 0.908484 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0369 | −0.768895 | −0.384447 | − | 0.923147i | \(-0.625608\pi\) | ||||
−0.384447 | + | 0.923147i | \(0.625608\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −15.3316 | −0.618228 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.0697 | −0.888494 | −0.444247 | − | 0.895904i | \(-0.646529\pi\) | ||||
−0.444247 | + | 0.895904i | \(0.646529\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.69372 | 0.228850 | 0.114425 | − | 0.993432i | \(-0.463497\pi\) | ||||
0.114425 | + | 0.993432i | \(0.463497\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.3146 | −0.855327 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.71187 | 0.0685848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.0609 | −0.522438 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −33.0584 | −1.32023 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.7069 | −0.546528 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.6327 | −1.49813 | −0.749067 | − | 0.662494i | \(-0.769498\pi\) | ||||
−0.749067 | + | 0.662494i | \(0.769498\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.4654 | 0.654442 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −26.8263 | −1.06457 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.0639 | −0.676095 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.18391 | 0.363310 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.63550 | 0.262086 | 0.131043 | − | 0.991377i | \(-0.458167\pi\) | ||||
0.131043 | + | 0.991377i | \(0.458167\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.4970 | 1.16325 | 0.581625 | − | 0.813457i | \(-0.302417\pi\) | ||||
0.581625 | + | 0.813457i | \(0.302417\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.6810 | −0.971813 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 45.6726 | 1.79558 | 0.897788 | − | 0.440427i | \(-0.145173\pi\) | ||||
0.897788 | + | 0.440427i | \(0.145173\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.7710 | 0.579813 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.313139 | 0.0122729 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.6691 | −1.23931 | −0.619655 | − | 0.784875i | \(-0.712727\pi\) | ||||
−0.619655 | + | 0.784875i | \(0.712727\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.3190 | 0.950220 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 12.6254 | 0.492563 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.73186 | −0.379099 | −0.189550 | − | 0.981871i | \(-0.560703\pi\) | ||||
−0.189550 | + | 0.981871i | \(0.560703\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.5544 | −0.566100 | −0.283050 | − | 0.959105i | \(-0.591346\pi\) | ||||
−0.283050 | + | 0.959105i | \(0.591346\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.57513 | 0.371867 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.08449 | 0.197168 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.43325 | 0.132936 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.1542 | 0.895195 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.60214 | 0.177664 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.1914 | −1.78055 | −0.890273 | − | 0.455427i | \(-0.849486\pi\) | ||||
−0.890273 | + | 0.455427i | \(0.849486\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.94095 | 0.382627 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.6087 | −0.407725 | −0.203863 | − | 0.978999i | \(-0.565350\pi\) | ||||
−0.203863 | + | 0.978999i | \(0.565350\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.36690 | 0.0908333 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.89963 | −0.0727939 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.9985 | 1.37745 | 0.688723 | − | 0.725025i | \(-0.258172\pi\) | ||||
0.688723 | + | 0.725025i | \(0.258172\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.3895 | 0.855458 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.1141 | −0.881858 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.4739 | −0.627606 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.7115 | −0.940070 | −0.470035 | − | 0.882648i | \(-0.655759\pi\) | ||||
−0.470035 | + | 0.882648i | \(0.655759\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.87508 | −0.0712282 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.87506 | 0.146989 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.4434 | 0.547083 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −41.3957 | −1.56573 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.8712 | 1.09045 | 0.545225 | − | 0.838290i | \(-0.316444\pi\) | ||||
0.545225 | + | 0.838290i | \(0.316444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.8094 | −1.04885 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −23.5970 | −0.888713 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.06229 | 0.0775603 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.6656 | −1.18923 | −0.594614 | − | 0.804012i | \(-0.702695\pi\) | ||||
−0.594614 | + | 0.804012i | \(0.702695\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.07856 | 0.227964 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.44105 | −0.0539679 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.8828 | 0.743575 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.79230 | −0.0669345 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.1524 | −1.12449 | −0.562247 | − | 0.826969i | \(-0.690063\pi\) | ||||
−0.562247 | + | 0.826969i | \(0.690063\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.56403 | 0.0582477 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −38.1222 | −1.41778 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.60124 | −0.0594685 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.1905 | −0.563384 | −0.281692 | − | 0.959505i | \(-0.590896\pi\) | ||||
−0.281692 | + | 0.959505i | \(0.590896\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.8887 | 1.10699 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.2512 | 0.859977 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.8270 | 1.47104 | 0.735522 | − | 0.677501i | \(-0.236937\pi\) | ||||
0.735522 | + | 0.677501i | \(0.236937\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.9306 | 0.661381 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.10134 | −0.0405682 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.4367 | 0.972489 | 0.486245 | − | 0.873823i | \(-0.338366\pi\) | ||||
0.486245 | + | 0.873823i | \(0.338366\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 19.4267 | 0.713657 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.5745 | 0.974923 | 0.487462 | − | 0.873144i | \(-0.337923\pi\) | ||||
0.487462 | + | 0.873144i | \(0.337923\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.4549 | 0.566225 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.8270 | −0.469316 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.57720 | 0.203787 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.1977 | 1.10193 | 0.550964 | − | 0.834529i | \(-0.314260\pi\) | ||||
0.550964 | + | 0.834529i | \(0.314260\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19.7499 | −0.719725 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.949439 | 0.0345536 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.3606 | 1.13982 | 0.569911 | − | 0.821706i | \(-0.306978\pi\) | ||||
0.569911 | + | 0.821706i | \(0.306978\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.4379 | −0.887040 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 40.3426 | 1.46242 | 0.731210 | − | 0.682153i | \(-0.238956\pi\) | ||||
0.731210 | + | 0.682153i | \(0.238956\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.79253 | 0.137299 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.55272 | 0.128449 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.68015 | −0.313422 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −20.4304 | −0.736739 | −0.368369 | − | 0.929680i | \(-0.620084\pi\) | ||||
−0.368369 | + | 0.929680i | \(0.620084\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.9738 | −0.863395 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.6859 | 1.64321 | 0.821605 | − | 0.570058i | \(-0.193079\pi\) | ||||
0.821605 | + | 0.570058i | \(0.193079\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.672094 | 0.0241423 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.46715 | 0.160258 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 29.3038 | 1.04992 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 50.8798 | 1.82062 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.11048 | −0.182634 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.0930 | −0.717149 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.1038 | −0.538392 | −0.269196 | − | 0.963085i | \(-0.586758\pi\) | ||||
−0.269196 | + | 0.963085i | \(0.586758\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.0856 | −0.359055 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.54933 | −0.0550880 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.70444 | −0.0960373 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.3107 | 0.613947 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.0697 | 0.462954 | 0.231477 | − | 0.972840i | \(-0.425644\pi\) | ||||
0.231477 | + | 0.972840i | \(0.425644\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.2300 | 0.786440 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.42683 | 0.0857478 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 69.9460 | 2.46834 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.75863 | 0.132474 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 34.9697 | 1.23099 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.0282 | −0.668996 | −0.334498 | − | 0.942396i | \(-0.608567\pi\) | ||||
−0.334498 | + | 0.942396i | \(0.608567\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.0749 | −0.740042 | −0.370021 | − | 0.929023i | \(-0.620649\pi\) | ||||
−0.370021 | + | 0.929023i | \(0.620649\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.1895 | −0.918506 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 35.9927 | 1.26077 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 47.1736 | 1.65040 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.10188 | 0.0385029 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5704 | 0.368909 | 0.184454 | − | 0.982841i | \(-0.440948\pi\) | ||||
0.184454 | + | 0.982841i | \(0.440948\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −40.5293 | −1.41276 | −0.706381 | − | 0.707832i | \(-0.749673\pi\) | ||||
−0.706381 | + | 0.707832i | \(0.749673\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.3976 | 0.396814 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.1057 | 1.63803 | 0.819013 | − | 0.573775i | \(-0.194522\pi\) | ||||
0.819013 | + | 0.573775i | \(0.194522\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.69487 | −0.336717 | −0.168358 | − | 0.985726i | \(-0.553847\pi\) | ||||
−0.168358 | + | 0.985726i | \(0.553847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.8925 | −0.585994 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −16.8919 | −0.585269 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.4975 | −0.743953 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.14504 | 0.0741436 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.2517 | −1.00988 | −0.504940 | − | 0.863154i | \(-0.668485\pi\) | ||||
−0.504940 | + | 0.863154i | \(0.668485\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.1768 | −0.971615 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.9483 | −0.480404 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.6984 | 0.402436 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.31356 | −0.148216 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −40.0228 | −1.37358 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.5577 | −0.704708 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.0610 | −1.06351 | −0.531754 | − | 0.846899i | \(-0.678467\pi\) | ||||
−0.531754 | + | 0.846899i | \(0.678467\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.20800 | 0.246508 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.3567 | −0.934486 | −0.467243 | − | 0.884129i | \(-0.654753\pi\) | ||||
−0.467243 | + | 0.884129i | \(0.654753\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.0124 | 1.26285 | 0.631424 | − | 0.775438i | \(-0.282471\pi\) | ||||
0.631424 | + | 0.775438i | \(0.282471\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.70719 | −0.160421 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.6253 | 1.28078 | 0.640389 | − | 0.768051i | \(-0.278773\pi\) | ||||
0.640389 | + | 0.768051i | \(0.278773\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.65785 | −0.192373 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.8344 | −0.537765 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.6759 | 1.14238 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.647196 | 0.0219294 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.35542 | 0.113564 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.71935 | −0.227156 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.6727 | 1.20458 | 0.602291 | − | 0.798277i | \(-0.294255\pi\) | ||||
0.602291 | + | 0.798277i | \(0.294255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.6653 | 0.865668 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.3930 | −1.02397 | −0.511984 | − | 0.858995i | \(-0.671089\pi\) | ||||
−0.511984 | + | 0.858995i | \(0.671089\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.6017 | −0.794260 | −0.397130 | − | 0.917762i | \(-0.629994\pi\) | ||||
−0.397130 | + | 0.917762i | \(0.629994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.12106 | 0.306601 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.1804 | 0.610437 | 0.305219 | − | 0.952282i | \(-0.401270\pi\) | ||||
0.305219 | + | 0.952282i | \(0.401270\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.23639 | −0.276240 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.1901 | 0.877401 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.1017 | 1.50927 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.8296 | −0.361993 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.3609 | 0.479495 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.345513 | −0.0115235 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.3079 | −0.543294 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.57771 | −0.252170 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 41.4543 | 1.37799 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.8615 | 0.891921 | 0.445961 | − | 0.895053i | \(-0.352862\pi\) | ||||
0.445961 | + | 0.895053i | \(0.352862\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.92359 | 0.0969694 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.7019 | −1.41478 | −0.707388 | − | 0.706825i | \(-0.750127\pi\) | ||||
−0.707388 | + | 0.706825i | \(0.750127\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −71.0630 | −2.35184 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.84181 | 0.0939473 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.46656 | 0.246568 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.59767 | 0.250624 | 0.125312 | − | 0.992117i | \(-0.460007\pi\) | ||||
0.125312 | + | 0.992117i | \(0.460007\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −43.1812 | −1.42287 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −29.8994 | −0.984151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.58790 | 0.315248 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.21724 | 0.0728239 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.5765 | −1.13442 | −0.567210 | − | 0.823574i | \(-0.691977\pi\) | ||||
−0.567210 | + | 0.823574i | \(0.691977\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.2714 | −1.12320 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −40.5474 | −1.32746 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.6824 | 0.643684 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.4353 | 1.32096 | 0.660482 | − | 0.750842i | \(-0.270352\pi\) | ||||
0.660482 | + | 0.750842i | \(0.270352\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.23506 | 0.268741 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.3193 | −0.727587 | −0.363794 | − | 0.931480i | \(-0.618519\pi\) | ||||
−0.363794 | + | 0.931480i | \(0.618519\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.6623 | 0.705423 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.59481 | −0.181999 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.0277 | 1.30073 | 0.650363 | − | 0.759623i | \(-0.274617\pi\) | ||||
0.650363 | + | 0.759623i | \(0.274617\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.1036 | −1.33428 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 46.4613 | 1.50661 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.33099 | −0.205081 | −0.102540 | − | 0.994729i | \(-0.532697\pi\) | ||||
−0.102540 | + | 0.994729i | \(0.532697\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.3349 | −1.04633 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.85933 | −0.189405 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.87416 | 0.221978 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8550 | −0.995322 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.90649 | 0.254783 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 18.7831 | 0.604650 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8388 | 0.412867 | 0.206433 | − | 0.978461i | \(-0.433814\pi\) | ||||
0.206433 | + | 0.978461i | \(0.433814\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.2309 | 0.617785 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.1505 | −0.710842 | −0.355421 | − | 0.934706i | \(-0.615662\pi\) | ||||
−0.355421 | + | 0.934706i | \(0.615662\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.18975 | 0.0381415 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.69778 | −0.214500 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.0297 | 1.31266 | 0.656328 | − | 0.754475i | \(-0.272109\pi\) | ||||
0.656328 | + | 0.754475i | \(0.272109\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.4449 | 0.429701 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.37646 | 0.171657 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.9691 | −1.40240 | −0.701199 | − | 0.712966i | \(-0.747351\pi\) | ||||
−0.701199 | + | 0.712966i | \(0.747351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.84258 | 0.249885 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.24489 | −0.230607 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.8724 | 1.10888 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.6965 | −0.657446 | −0.328723 | − | 0.944426i | \(-0.606618\pi\) | ||||
−0.328723 | + | 0.944426i | \(0.606618\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.0190 | −0.793955 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.2180 | 0.799464 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 52.9018 | 1.67542 | 0.837709 | − | 0.546117i | \(-0.183895\pi\) | ||||
0.837709 | + | 0.546117i | \(0.183895\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.6006 | 0.968160 |
(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 | 8048.2.a.p.1.6 | 10 | ||
4.3 | odd | 2 | 503.2.a.e.1.3 | ✓ | 10 | ||
12.11 | even | 2 | 4527.2.a.k.1.8 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
503.2.a.e.1.3 | ✓ | 10 | 4.3 | odd | 2 | ||
4527.2.a.k.1.8 | 10 | 12.11 | even | 2 | |||
8048.2.a.p.1.6 | 10 | 1.1 | even | 1 | trivial |