Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.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: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 30 x^{17} + 132 x^{16} + 332 x^{15} - 1714 x^{14} - 1598 x^{13} + 11179 x^{12} + 2544 x^{11} - 38897 x^{10} + 3416 x^{9} + 71354 x^{8} - 10941 x^{7} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-0.346400\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 | ||||||||
\(3\) | 0.346400 | 0.199994 | 0.0999970 | − | 0.994988i | \(-0.468117\pi\) | ||||
0.0999970 | + | 0.994988i | \(0.468117\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.720634 | 0.322277 | 0.161139 | − | 0.986932i | \(-0.448483\pi\) | ||||
0.161139 | + | 0.986932i | \(0.448483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.22237 | −0.839976 | −0.419988 | − | 0.907530i | \(-0.637966\pi\) | ||||
−0.419988 | + | 0.907530i | \(0.637966\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.88001 | −0.960002 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.78340 | 0.839226 | 0.419613 | − | 0.907703i | \(-0.362166\pi\) | ||||
0.419613 | + | 0.907703i | \(0.362166\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.24197 | 0.899161 | 0.449580 | − | 0.893240i | \(-0.351574\pi\) | ||||
0.449580 | + | 0.893240i | \(0.351574\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.249627 | 0.0644535 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.710604 | −0.172347 | −0.0861734 | − | 0.996280i | \(-0.527464\pi\) | ||||
−0.0861734 | + | 0.996280i | \(0.527464\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.769828 | −0.167990 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.68771 | 0.351912 | 0.175956 | − | 0.984398i | \(-0.443698\pi\) | ||||
0.175956 | + | 0.984398i | \(0.443698\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.48069 | −0.896137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.03683 | −0.391989 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.75104 | −1.43933 | −0.719666 | − | 0.694320i | \(-0.755705\pi\) | ||||
−0.719666 | + | 0.694320i | \(0.755705\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25896 | 0.226116 | 0.113058 | − | 0.993588i | \(-0.463935\pi\) | ||||
0.113058 | + | 0.993588i | \(0.463935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.964168 | 0.167840 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.60151 | −0.270705 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.09938 | 0.345137 | 0.172568 | − | 0.984998i | \(-0.444793\pi\) | ||||
0.172568 | + | 0.984998i | \(0.444793\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.12302 | 0.179827 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.36373 | −0.369153 | −0.184576 | − | 0.982818i | \(-0.559091\pi\) | ||||
−0.184576 | + | 0.982818i | \(0.559091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.0964 | −1.53969 | −0.769843 | − | 0.638234i | \(-0.779665\pi\) | ||||
−0.769843 | + | 0.638234i | \(0.779665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.07543 | −0.309387 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.417239 | 0.0608606 | 0.0304303 | − | 0.999537i | \(-0.490312\pi\) | ||||
0.0304303 | + | 0.999537i | \(0.490312\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.06108 | −0.294440 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.246153 | −0.0344683 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00581 | 0.270463 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.346400 | −0.0458818 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.65806 | 0.476239 | 0.238120 | − | 0.971236i | \(-0.423469\pi\) | ||||
0.238120 | + | 0.971236i | \(0.423469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.5228 | 1.73142 | 0.865710 | − | 0.500545i | \(-0.166867\pi\) | ||||
0.865710 | + | 0.500545i | \(0.166867\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.40044 | 0.806379 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.33627 | 0.289779 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.76347 | 1.07063 | 0.535314 | − | 0.844653i | \(-0.320193\pi\) | ||||
0.535314 | + | 0.844653i | \(0.320193\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.584623 | 0.0703803 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.98537 | −0.354298 | −0.177149 | − | 0.984184i | \(-0.556688\pi\) | ||||
−0.177149 | + | 0.984184i | \(0.556688\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.93629 | −0.811832 | −0.405916 | − | 0.913910i | \(-0.633047\pi\) | ||||
−0.405916 | + | 0.913910i | \(0.633047\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.55211 | −0.179222 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.18573 | −0.704930 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.08026 | −0.909100 | −0.454550 | − | 0.890721i | \(-0.650200\pi\) | ||||
−0.454550 | + | 0.890721i | \(0.650200\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.93446 | 0.881607 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.16898 | −0.567369 | −0.283684 | − | 0.958918i | \(-0.591557\pi\) | ||||
−0.283684 | + | 0.958918i | \(0.591557\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.512086 | −0.0555435 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.68496 | −0.287858 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.0222 | −1.16835 | −0.584174 | − | 0.811628i | \(-0.698582\pi\) | ||||
−0.584174 | + | 0.811628i | \(0.698582\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.20485 | −0.755274 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.436103 | 0.0452218 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.720634 | −0.0739355 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.60335 | −0.772004 | −0.386002 | − | 0.922498i | \(-0.626144\pi\) | ||||
−0.386002 | + | 0.922498i | \(0.626144\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.01620 | −0.805659 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.30523 | −0.229379 | −0.114689 | − | 0.993401i | \(-0.536587\pi\) | ||||
−0.114689 | + | 0.993401i | \(0.536587\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.0290 | −1.87499 | −0.937493 | − | 0.348005i | \(-0.886859\pi\) | ||||
−0.937493 | + | 0.348005i | \(0.886859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.554764 | −0.0541394 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.2535 | −1.28126 | −0.640632 | − | 0.767848i | \(-0.721327\pi\) | ||||
−0.640632 | + | 0.767848i | \(0.721327\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0744 | 1.25230 | 0.626149 | − | 0.779704i | \(-0.284630\pi\) | ||||
0.626149 | + | 0.779704i | \(0.284630\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.727226 | 0.0690252 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.3979 | 1.26037 | 0.630185 | − | 0.776445i | \(-0.282979\pi\) | ||||
0.630185 | + | 0.776445i | \(0.282979\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.21622 | 0.113413 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.33690 | −0.863197 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.57922 | 0.144767 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.25270 | −0.295700 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.818795 | −0.0738283 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.83211 | −0.611082 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.173674 | 0.0154111 | 0.00770555 | − | 0.999970i | \(-0.497547\pi\) | ||||
0.00770555 | + | 0.999970i | \(0.497547\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.49739 | −0.307928 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.6921 | 1.02154 | 0.510772 | − | 0.859716i | \(-0.329360\pi\) | ||||
0.510772 | + | 0.859716i | \(0.329360\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.22237 | 0.192704 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.46781 | −0.126329 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00319 | −0.512887 | −0.256444 | − | 0.966559i | \(-0.582551\pi\) | ||||
−0.256444 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.0859 | −0.855475 | −0.427737 | − | 0.903903i | \(-0.640689\pi\) | ||||
−0.427737 | + | 0.903903i | \(0.640689\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.144532 | 0.0121718 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.02369 | 0.754599 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.58566 | −0.463864 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.713958 | −0.0588863 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.5191 | −1.10753 | −0.553765 | − | 0.832673i | \(-0.686810\pi\) | ||||
−0.553765 | + | 0.832673i | \(0.686810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0696 | −0.900833 | −0.450417 | − | 0.892819i | \(-0.648725\pi\) | ||||
−0.450417 | + | 0.892819i | \(0.648725\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.04655 | 0.165453 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.907249 | 0.0728720 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 23.3388 | 1.86264 | 0.931318 | − | 0.364206i | \(-0.118660\pi\) | ||||
0.931318 | + | 0.364206i | \(0.118660\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.346400 | 0.0274713 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.75072 | −0.295598 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.42979 | −0.581946 | −0.290973 | − | 0.956731i | \(-0.593979\pi\) | ||||
−0.290973 | + | 0.956731i | \(0.593979\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.694812 | 0.0540911 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −21.8387 | −1.68993 | −0.844964 | − | 0.534823i | \(-0.820378\pi\) | ||||
−0.844964 | + | 0.534823i | \(0.820378\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.48963 | −0.191510 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.88001 | 0.220240 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.6928 | −1.72530 | −0.862652 | − | 0.505798i | \(-0.831198\pi\) | ||||
−0.862652 | + | 0.505798i | \(0.831198\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.95773 | 0.752734 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.26715 | 0.0952449 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −23.5535 | −1.76047 | −0.880235 | − | 0.474539i | \(-0.842615\pi\) | ||||
−0.880235 | + | 0.474539i | \(0.842615\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.56883 | −0.339598 | −0.169799 | − | 0.985479i | \(-0.554312\pi\) | ||||
−0.169799 | + | 0.985479i | \(0.554312\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.68430 | 0.346274 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.51289 | 0.111230 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.97789 | −0.144638 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.52659 | 0.329261 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.0357 | −1.52209 | −0.761044 | − | 0.648700i | \(-0.775313\pi\) | ||||
−0.761044 | + | 0.648700i | \(0.775313\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.44441 | −0.463879 | −0.231939 | − | 0.972730i | \(-0.574507\pi\) | ||||
−0.231939 | + | 0.972730i | \(0.574507\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.809285 | 0.0579541 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.5334 | 0.892967 | 0.446484 | − | 0.894792i | \(-0.352676\pi\) | ||||
0.446484 | + | 0.894792i | \(0.352676\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.7391 | −1.25749 | −0.628744 | − | 0.777612i | \(-0.716431\pi\) | ||||
−0.628744 | + | 0.777612i | \(0.716431\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.03566 | 0.214119 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.2257 | 1.20900 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.70338 | −0.118970 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.86062 | −0.337836 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.78340 | −0.192532 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9787 | 1.16886 | 0.584430 | − | 0.811444i | \(-0.301318\pi\) | ||||
0.584430 | + | 0.811444i | \(0.301318\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.03413 | −0.0708575 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.27580 | −0.496206 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.79787 | −0.189932 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.40273 | −0.162361 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.30376 | −0.154968 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.56648 | −0.372759 | −0.186379 | − | 0.982478i | \(-0.559675\pi\) | ||||
−0.186379 | + | 0.982478i | \(0.559675\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.9044 | 0.860294 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7367 | 0.911737 | 0.455868 | − | 0.890047i | \(-0.349329\pi\) | ||||
0.455868 | + | 0.890047i | \(0.349329\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.5539 | 0.763500 | 0.381750 | − | 0.924266i | \(-0.375322\pi\) | ||||
0.381750 | + | 0.924266i | \(0.375322\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.14274 | −0.140982 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.8863 | 0.713188 | 0.356594 | − | 0.934259i | \(-0.383938\pi\) | ||||
0.356594 | + | 0.934259i | \(0.383938\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.300677 | 0.0196140 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.79900 | −0.181815 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.4246 | 1.12710 | 0.563550 | − | 0.826082i | \(-0.309435\pi\) | ||||
0.563550 | + | 0.826082i | \(0.309435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.99167 | 0.257126 | 0.128563 | − | 0.991701i | \(-0.458964\pi\) | ||||
0.128563 | + | 0.991701i | \(0.458964\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.85899 | 0.568305 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.48529 | −0.0948914 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.24197 | −0.206282 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.79053 | −0.113470 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.80686 | −0.366526 | −0.183263 | − | 0.983064i | \(-0.558666\pi\) | ||||
−0.183263 | + | 0.983064i | \(0.558666\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.69757 | 0.295334 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.177386 | −0.0111084 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.93977 | 0.432891 | 0.216446 | − | 0.976295i | \(-0.430554\pi\) | ||||
0.216446 | + | 0.976295i | \(0.430554\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.66560 | −0.289906 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.3231 | 1.38176 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.45091 | 0.336118 | 0.168059 | − | 0.985777i | \(-0.446250\pi\) | ||||
0.168059 | + | 0.985777i | \(0.446250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.720634 | 0.0442682 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.81808 | −0.233663 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.39226 | −0.511685 | −0.255842 | − | 0.966718i | \(-0.582353\pi\) | ||||
−0.255842 | + | 0.966718i | \(0.582353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.92172 | 0.420465 | 0.210232 | − | 0.977651i | \(-0.432578\pi\) | ||||
0.210232 | + | 0.977651i | \(0.432578\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.49576 | −0.151050 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.4715 | −0.752062 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.9822 | 1.44095 | 0.720475 | − | 0.693481i | \(-0.243924\pi\) | ||||
0.720475 | + | 0.693481i | \(0.243924\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.62581 | −0.217072 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.8257 | 1.48097 | 0.740487 | − | 0.672070i | \(-0.234595\pi\) | ||||
0.740487 | + | 0.672070i | \(0.234595\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0293 | −0.774514 | −0.387257 | − | 0.921972i | \(-0.626577\pi\) | ||||
−0.387257 | + | 0.921972i | \(0.626577\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.249627 | −0.0147867 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.25308 | 0.310079 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4950 | −0.970297 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.63380 | −0.154396 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.98307 | 0.174273 | 0.0871363 | − | 0.996196i | \(-0.472228\pi\) | ||||
0.0871363 | + | 0.996196i | \(0.472228\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.63612 | 0.153481 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.66932 | −0.328967 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.47151 | 0.316426 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 22.4379 | 1.29330 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.798531 | −0.0458744 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.74501 | 0.557998 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.7305 | 1.58266 | 0.791331 | − | 0.611388i | \(-0.209388\pi\) | ||||
0.791331 | + | 0.611388i | \(0.209388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.59165 | −0.374986 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.2006 | −0.975356 | −0.487678 | − | 0.873023i | \(-0.662156\pi\) | ||||
−0.487678 | + | 0.873023i | \(0.662156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.6078 | −1.39091 | −0.695457 | − | 0.718568i | \(-0.744798\pi\) | ||||
−0.695457 | + | 0.718568i | \(0.744798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.61237 | 0.259878 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.6548 | −0.654600 | −0.327300 | − | 0.944920i | \(-0.606139\pi\) | ||||
−0.327300 | + | 0.944920i | \(0.606139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.5742 | −1.20792 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.59101 | −0.256245 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.710604 | 0.0395391 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.5263 | −0.805772 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.52896 | 0.250452 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.927259 | −0.0511215 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9.23557 | −0.507633 | −0.253816 | − | 0.967252i | \(-0.581686\pi\) | ||||
−0.253816 | + | 0.967252i | \(0.581686\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.04624 | −0.331332 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.31525 | 0.345039 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.5639 | −0.575451 | −0.287725 | − | 0.957713i | \(-0.592899\pi\) | ||||
−0.287725 | + | 0.957713i | \(0.592899\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.64104 | 0.252066 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.50418 | 0.189762 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1371 | 1.08730 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.421299 | 0.0226820 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.2507 | 1.19448 | 0.597241 | − | 0.802062i | \(-0.296264\pi\) | ||||
0.597241 | + | 0.802062i | \(0.296264\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.6577 | −1.58754 | −0.793771 | − | 0.608217i | \(-0.791885\pi\) | ||||
−0.793771 | + | 0.608217i | \(0.791885\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.60335 | −0.352461 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.59015 | 0.0846349 | 0.0423175 | − | 0.999104i | \(-0.486526\pi\) | ||||
0.0423175 | + | 0.999104i | \(0.486526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.15136 | −0.114182 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.547043 | 0.0289526 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0570 | −0.530790 | −0.265395 | − | 0.964140i | \(-0.585502\pi\) | ||||
−0.265395 | + | 0.964140i | \(0.585502\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.12673 | −0.0591382 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.99853 | −0.261635 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6349 | −0.763934 | −0.381967 | − | 0.924176i | \(-0.624753\pi\) | ||||
−0.381967 | + | 0.924176i | \(0.624753\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.80756 | 0.354387 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.22237 | −0.115380 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.00123 | −0.362510 | −0.181255 | − | 0.983436i | \(-0.558016\pi\) | ||||
−0.181255 | + | 0.983436i | \(0.558016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.36664 | −0.122213 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −25.1286 | −1.29419 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.88858 | 0.251110 | 0.125555 | − | 0.992087i | \(-0.459929\pi\) | ||||
0.125555 | + | 0.992087i | \(0.459929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0601607 | 0.00308213 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −11.8258 | −0.604272 | −0.302136 | − | 0.953265i | \(-0.597700\pi\) | ||||
−0.302136 | + | 0.953265i | \(0.597700\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.45765 | −0.227183 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.0777 | 1.47810 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.6778 | 0.693489 | 0.346745 | − | 0.937960i | \(-0.387287\pi\) | ||||
0.346745 | + | 0.937960i | \(0.387287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.19929 | −0.0606509 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.05014 | 0.204303 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.82291 | −0.292982 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.4367 | 1.47739 | 0.738694 | − | 0.674041i | \(-0.235443\pi\) | ||||
0.738694 | + | 0.674041i | \(0.235443\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.769828 | 0.0385396 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.4277 | −0.520736 | −0.260368 | − | 0.965510i | \(-0.583844\pi\) | ||||
−0.260368 | + | 0.965510i | \(0.583844\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.08151 | 0.203314 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.71784 | 0.284122 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.84342 | 0.289648 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.9306 | 1.28219 | 0.641093 | − | 0.767463i | \(-0.278481\pi\) | ||||
0.641093 | + | 0.767463i | \(0.278481\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.07950 | −0.102574 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.12956 | −0.400029 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.72494 | −0.182850 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.49375 | −0.171090 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.2995 | 1.28482 | 0.642408 | − | 0.766363i | \(-0.277935\pi\) | ||||
0.642408 | + | 0.766363i | \(0.277935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.3871 | 1.82214 | 0.911068 | − | 0.412256i | \(-0.135259\pi\) | ||||
0.911068 | + | 0.412256i | \(0.135259\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.20165 | −0.0584263 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.18399 | 0.154446 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.0527 | −1.45435 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.12580 | 0.150915 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.23482 | 0.155816 | 0.0779080 | − | 0.996961i | \(-0.475176\pi\) | ||||
0.0779080 | + | 0.996961i | \(0.475176\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.62682 | 0.270408 | 0.135204 | − | 0.990818i | \(-0.456831\pi\) | ||||
0.135204 | + | 0.990818i | \(0.456831\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.93487 | −0.0927700 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.68771 | −0.0807342 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.0845 | −1.53131 | −0.765654 | − | 0.643252i | \(-0.777585\pi\) | ||||
−0.765654 | + | 0.643252i | \(0.777585\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.93593 | 0.282663 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.29854 | −0.346764 | −0.173382 | − | 0.984855i | \(-0.555470\pi\) | ||||
−0.173382 | + | 0.984855i | \(0.555470\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.94296 | −0.376532 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.68302 | −0.221499 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.1789 | −0.716336 | −0.358168 | − | 0.933657i | \(-0.616598\pi\) | ||||
−0.358168 | + | 0.933657i | \(0.616598\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.57920 | −0.309802 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.83451 | −0.180161 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.19206 | −0.243408 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.3934 | 1.32819 | 0.664094 | − | 0.747649i | \(-0.268818\pi\) | ||||
0.664094 | + | 0.747649i | \(0.268818\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.44738 | 0.0675580 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.3896 | 0.903061 | 0.451531 | − | 0.892256i | \(-0.350878\pi\) | ||||
0.451531 | + | 0.892256i | \(0.350878\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.9603 | −1.53180 | −0.765898 | − | 0.642962i | \(-0.777705\pi\) | ||||
−0.765898 | + | 0.642962i | \(0.777705\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.314271 | 0.0145740 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.22530 | −0.195524 | −0.0977618 | − | 0.995210i | \(-0.531168\pi\) | ||||
−0.0977618 | + | 0.995210i | \(0.531168\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.4756 | −0.899302 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.08454 | 0.372516 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −28.1023 | −1.29214 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.48069 | 0.205588 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.88001 | −0.131866 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −35.3560 | −1.61546 | −0.807728 | − | 0.589556i | \(-0.799303\pi\) | ||||
−0.807728 | + | 0.589556i | \(0.799303\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.80614 | 0.310333 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.29925 | −0.0591178 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.47924 | −0.248799 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.79732 | −0.398645 | −0.199322 | − | 0.979934i | \(-0.563874\pi\) | ||||
−0.199322 | + | 0.979934i | \(0.563874\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.57368 | −0.116386 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.37429 | 0.152280 | 0.0761398 | − | 0.997097i | \(-0.475740\pi\) | ||||
0.0761398 | + | 0.997097i | \(0.475740\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.50792 | 0.248064 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.77675 | −0.259646 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.63459 | 0.297602 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.6930 | 0.747281 | 0.373640 | − | 0.927574i | \(-0.378109\pi\) | ||||
0.373640 | + | 0.927574i | \(0.378109\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.56492 | −0.337976 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.3813 | −0.596641 | −0.298321 | − | 0.954466i | \(-0.596426\pi\) | ||||
−0.298321 | + | 0.954466i | \(0.596426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.66123 | −0.0739236 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.862406 | −0.0383008 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.34006 | 0.369667 | 0.184833 | − | 0.982770i | \(-0.440825\pi\) | ||||
0.184833 | + | 0.982770i | \(0.440825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.4150 | 0.681919 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.03683 | 0.0899284 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.7130 | −0.604265 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.16134 | 0.0510758 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −7.86079 | −0.345050 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.6310 | −0.465755 | −0.232877 | − | 0.972506i | \(-0.574814\pi\) | ||||
−0.232877 | + | 0.972506i | \(0.574814\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.3580 | −1.06510 | −0.532550 | − | 0.846399i | \(-0.678766\pi\) | ||||
−0.532550 | + | 0.846399i | \(0.678766\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.44936 | 0.150542 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.894622 | −0.0389703 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1516 | −0.876158 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.5352 | −0.457191 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.66314 | −0.331928 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.55092 | −0.412922 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.15892 | −0.352083 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.73681 | −0.247102 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.0282 | 1.89292 | 0.946460 | − | 0.322820i | \(-0.104631\pi\) | ||||
0.946460 | + | 0.322820i | \(0.104631\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.58264 | −0.0679176 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.42184 | 0.403587 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.5917 | 1.05146 | 0.525732 | − | 0.850650i | \(-0.323791\pi\) | ||||
0.525732 | + | 0.850650i | \(0.323791\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −38.9458 | −1.66217 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.75104 | 0.330205 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.9573 | 0.763623 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.524064 | 0.0222453 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.4790 | 0.655866 | 0.327933 | − | 0.944701i | \(-0.393648\pi\) | ||||
0.327933 | + | 0.944701i | \(0.393648\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −32.7322 | −1.38442 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.685142 | −0.0289267 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.6618 | 1.84013 | 0.920063 | − | 0.391771i | \(-0.128137\pi\) | ||||
0.920063 | + | 0.391771i | \(0.128137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.65500 | 0.406189 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.6333 | −0.740529 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.6225 | 1.24184 | 0.620920 | − | 0.783874i | \(-0.286759\pi\) | ||||
0.620920 | + | 0.783874i | \(0.286759\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.16244 | −0.299739 | −0.149869 | − | 0.988706i | \(-0.547885\pi\) | ||||
−0.149869 | + | 0.988706i | \(0.547885\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.28676 | −0.304409 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.56211 | −0.315362 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.7602 | −0.822629 | −0.411314 | − | 0.911494i | \(-0.634930\pi\) | ||||
−0.411314 | + | 0.911494i | \(0.634930\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.23234 | −0.0927730 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.4874 | 0.476576 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.78340 | 0.115277 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.72849 | −0.278189 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.4507 | 0.802817 | 0.401408 | − | 0.915899i | \(-0.368521\pi\) | ||||
0.401408 | + | 0.915899i | \(0.368521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.25896 | −0.0518745 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.34156 | 0.178588 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.0325528 | −0.00133678 | −0.000668392 | − | 1.00000i | \(-0.500213\pi\) | ||||
−0.000668392 | 1.00000i | \(0.500213\pi\) | ||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.13804 | 0.0466552 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.14480 | −0.251490 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.8235 | 1.74972 | 0.874861 | − | 0.484375i | \(-0.160953\pi\) | ||||
0.874861 | + | 0.484375i | \(0.160953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.4942 | 0.795183 | 0.397592 | − | 0.917562i | \(-0.369846\pi\) | ||||
0.397592 | + | 0.917562i | \(0.369846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.2388 | −1.02781 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.34401 | −0.0952974 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −44.3556 | −1.80034 | −0.900169 | − | 0.435540i | \(-0.856557\pi\) | ||||
−0.900169 | + | 0.435540i | \(0.856557\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.96696 | 0.241794 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.35268 | 0.0547235 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.5469 | −0.951050 | −0.475525 | − | 0.879702i | \(-0.657742\pi\) | ||||
−0.475525 | + | 0.879702i | \(0.657742\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.590052 | −0.0237932 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.64021 | −0.106291 | −0.0531454 | − | 0.998587i | \(-0.516925\pi\) | ||||
−0.0531454 | + | 0.998587i | \(0.516925\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.1575 | 0.970973 | 0.485486 | − | 0.874244i | \(-0.338643\pi\) | ||||
0.485486 | + | 0.874244i | \(0.338643\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.43759 | −0.137946 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 24.4953 | 0.981385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.4800 | 0.699199 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.964168 | −0.0385052 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.49183 | −0.0594832 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5486 | 0.897647 | 0.448823 | − | 0.893620i | \(-0.351843\pi\) | ||||
0.448823 | + | 0.893620i | \(0.351843\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.88141 | 0.233765 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.125156 | 0.00496665 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.68197 | −0.264749 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.59789 | 0.340127 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.0639 | 0.555490 | 0.277745 | − | 0.960655i | \(-0.410413\pi\) | ||||
0.277745 | + | 0.960655i | \(0.410413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.54719 | −0.337068 | −0.168534 | − | 0.985696i | \(-0.553903\pi\) | ||||
−0.168534 | + | 0.985696i | \(0.553903\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.52034 | −0.0992381 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.2190 | −0.676948 | −0.338474 | − | 0.940976i | \(-0.609911\pi\) | ||||
−0.338474 | + | 0.940976i | \(0.609911\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1818 | 0.399672 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.969181 | −0.0379852 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 42.1998 | 1.65141 | 0.825704 | − | 0.564104i | \(-0.190778\pi\) | ||||
0.825704 | + | 0.564104i | \(0.190778\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.42573 | 0.329220 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.9766 | 0.779360 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −32.4581 | −1.26439 | −0.632195 | − | 0.774809i | \(-0.717846\pi\) | ||||
−0.632195 | + | 0.774809i | \(0.717846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.3667 | 0.558801 | 0.279400 | − | 0.960175i | \(-0.409864\pi\) | ||||
0.279400 | + | 0.960175i | \(0.409864\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.798021 | −0.0309926 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.60151 | 0.0621040 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.0815 | −0.506518 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.92823 | −0.0745495 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 37.6394 | 1.45305 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.6634 | −1.79874 | −0.899371 | − | 0.437186i | \(-0.855975\pi\) | ||||
−0.899371 | + | 0.437186i | \(0.855975\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.12641 | 0.351276 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.6579 | 0.909247 | 0.454624 | − | 0.890684i | \(-0.349774\pi\) | ||||
0.454624 | + | 0.890684i | \(0.349774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8974 | 0.648465 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.75839 | 0.182342 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.4841 | 1.24297 | 0.621484 | − | 0.783427i | \(-0.286530\pi\) | ||||
0.621484 | + | 0.783427i | \(0.286530\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.32610 | −0.165292 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.00225 | 0.152695 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.24197 | 0.123509 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.1576 | −1.60375 | −0.801875 | − | 0.597491i | \(-0.796164\pi\) | ||||
−0.801875 | + | 0.597491i | \(0.796164\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 17.8150 | 0.676734 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.26824 | −0.275700 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.67968 | 0.0636223 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.77103 | 0.142633 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.1908 | −0.535979 | −0.267990 | − | 0.963422i | \(-0.586359\pi\) | ||||
−0.267990 | + | 0.963422i | \(0.586359\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.09938 | −0.0791798 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.104154 | 0.00392268 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.12307 | 0.192673 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.5555 | 0.771978 | 0.385989 | − | 0.922503i | \(-0.373860\pi\) | ||||
0.385989 | + | 0.922503i | \(0.373860\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.2712 | 0.872739 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.12476 | 0.0795729 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.50278 | 0.243190 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.03586 | 0.225413 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.3223 | 1.35459 | 0.677296 | − | 0.735710i | \(-0.263151\pi\) | ||||
0.677296 | + | 0.735710i | \(0.263151\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42.2895 | 1.57494 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.38271 | 0.0514236 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.7300 | 1.28984 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 35.0925 | 1.30151 | 0.650755 | − | 0.759288i | \(-0.274452\pi\) | ||||
0.650755 | + | 0.759288i | \(0.274452\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.7346 | −0.767950 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.17454 | 0.265360 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.8515 | 0.770168 | 0.385084 | − | 0.922882i | \(-0.374172\pi\) | ||||
0.385084 | + | 0.922882i | \(0.374172\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.514503 | −0.0189777 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.3922 | 0.898499 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.3770 | 1.15422 | 0.577110 | − | 0.816666i | \(-0.304180\pi\) | ||||
0.577110 | + | 0.816666i | \(0.304180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.12302 | −0.0412551 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.35265 | 0.343116 | 0.171558 | − | 0.985174i | \(-0.445120\pi\) | ||||
0.171558 | + | 0.985174i | \(0.445120\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.74235 | −0.356932 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.8867 | 0.544675 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.4541 | 1.07623 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.20700 | 0.335968 | 0.167984 | − | 0.985790i | \(-0.446274\pi\) | ||||
0.167984 | + | 0.985790i | \(0.446274\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.01149 | −0.0733029 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.97715 | −0.290318 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.3581 | −1.06704 | −0.533519 | − | 0.845788i | \(-0.679131\pi\) | ||||
−0.533519 | + | 0.845788i | \(0.679131\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.62724 | 0.0590650 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 54.0730 | 1.96015 | 0.980073 | − | 0.198639i | \(-0.0636522\pi\) | ||||
0.980073 | + | 0.198639i | \(0.0636522\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.0561 | −1.05190 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.47481 | 0.0533219 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.8593 | 0.428215 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.26019 | −0.261809 | −0.130905 | − | 0.991395i | \(-0.541788\pi\) | ||||
−0.130905 | + | 0.991395i | \(0.541788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.40394 | 0.0865756 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.8109 | −0.424810 | −0.212405 | − | 0.977182i | \(-0.568130\pi\) | ||||
−0.212405 | + | 0.977182i | \(0.568130\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.64100 | −0.202631 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.61616 | −0.0579796 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.36373 | 0.0846894 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.30948 | −0.297336 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.7876 | 0.564202 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 16.8187 | 0.600286 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.5851 | 0.662488 | 0.331244 | − | 0.943545i | \(-0.392532\pi\) | ||||
0.331244 | + | 0.943545i | \(0.392532\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.88819 | 0.0672215 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −29.7751 | −1.05868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 43.8406 | 1.55683 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.249627 | 0.00885337 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.5975 | −0.552493 | −0.276246 | − | 0.961087i | \(-0.589091\pi\) | ||||
−0.276246 | + | 0.961087i | \(0.589091\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.296492 | −0.0104891 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.7440 | 1.12162 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.3065 | −0.681310 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.70289 | −0.0952645 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.90708 | −0.102334 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.11526 | −0.109527 | −0.0547634 | − | 0.998499i | \(-0.517440\pi\) | ||||
−0.0547634 | + | 0.998499i | \(0.517440\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −51.2793 | −1.80066 | −0.900330 | − | 0.435208i | \(-0.856675\pi\) | ||||
−0.900330 | + | 0.435208i | \(0.856675\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.39768 | 0.0840904 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.35416 | −0.187548 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0964 | 0.353228 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 20.7500 | 0.725065 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −54.8738 | −1.91511 | −0.957555 | − | 0.288250i | \(-0.906927\pi\) | ||||
−0.957555 | + | 0.288250i | \(0.906927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.5407 | −0.541714 | −0.270857 | − | 0.962620i | \(-0.587307\pi\) | ||||
−0.270857 | + | 0.962620i | \(0.587307\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.32014 | −0.150408 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.2172 | 1.36372 | 0.681858 | − | 0.731485i | \(-0.261172\pi\) | ||||
0.681858 | + | 0.731485i | \(0.261172\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0077 | −0.382312 | −0.191156 | − | 0.981560i | \(-0.561224\pi\) | ||||
−0.191156 | + | 0.981560i | \(0.561224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.30742 | 0.288181 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.46461 | 0.0507458 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.7377 | −0.544626 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.56429 | −0.0886348 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −44.4047 | −1.53302 | −0.766510 | − | 0.642233i | \(-0.778008\pi\) | ||||
−0.766510 | + | 0.642233i | \(0.778008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.0786 | 1.07168 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.59960 | 0.296186 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.79411 | −0.0617192 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.22869 | 0.248381 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.51336 | −0.154898 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.54315 | 0.121458 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.69793 | 0.263572 | 0.131786 | − | 0.991278i | \(-0.457929\pi\) | ||||
0.131786 | + | 0.991278i | \(0.457929\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.07543 | 0.0709783 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.0258 | −1.43557 | −0.717787 | − | 0.696263i | \(-0.754845\pi\) | ||||
−0.717787 | + | 0.696263i | \(0.754845\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.0136 | 1.22877 | 0.614384 | − | 0.789007i | \(-0.289404\pi\) | ||||
0.614384 | + | 0.789007i | \(0.289404\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.81966 | 0.0620140 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 44.2147 | 1.50509 | 0.752543 | − | 0.658544i | \(-0.228827\pi\) | ||||
0.752543 | + | 0.658544i | \(0.228827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.3532 | −0.556026 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.71388 | −0.194053 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22.4906 | −0.762941 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28.4109 | 0.962667 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.8977 | 0.741125 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.1835 | 0.513294 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.2047 | −1.32385 | −0.661923 | − | 0.749571i | \(-0.730260\pi\) | ||||
−0.661923 | + | 0.749571i | \(0.730260\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.03333 | 0.0348535 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.2309 | −0.614215 | −0.307108 | − | 0.951675i | \(-0.599361\pi\) | ||||
−0.307108 | + | 0.951675i | \(0.599361\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.2739 | −0.850536 | −0.425268 | − | 0.905068i | \(-0.639820\pi\) | ||||
−0.425268 | + | 0.905068i | \(0.639820\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.913152 | 0.0306953 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.0379 | −0.471348 | −0.235674 | − | 0.971832i | \(-0.575730\pi\) | ||||
−0.235674 | + | 0.971832i | \(0.575730\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.385968 | −0.0129450 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.0848 | 0.739867 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.417239 | −0.0139624 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.9734 | −0.567359 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.89533 | 0.0632832 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.75824 | −0.325456 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.710604 | −0.0236737 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.77248 | 0.258652 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.29245 | −0.109445 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.7739 | 0.390947 | 0.195473 | − | 0.980709i | \(-0.437376\pi\) | ||||
0.195473 | + | 0.980709i | \(0.437376\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.63908 | 0.220204 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.1967 | −0.602884 | −0.301442 | − | 0.953484i | \(-0.597468\pi\) | ||||
−0.301442 | + | 0.953484i | \(0.597468\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.3873 | −0.476151 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.37567 | 0.111596 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.9842 | −0.858072 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.1207 | −0.366837 | −0.183418 | − | 0.983035i | \(-0.558716\pi\) | ||||
−0.183418 | + | 0.983035i | \(0.558716\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.60583 | 0.316523 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.67849 | −0.318571 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.40668 | −0.309290 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 54.8037 | 1.79999 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 59.0155 | 1.93624 | 0.968119 | − | 0.250492i | \(-0.0805924\pi\) | ||||
0.968119 | + | 0.250492i | \(0.0805924\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.06108 | 0.0675492 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.95828 | −0.195065 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.42534 | −0.0466135 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.7877 | −0.973122 | −0.486561 | − | 0.873647i | \(-0.661749\pi\) | ||||
−0.486561 | + | 0.873647i | \(0.661749\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.52413 | −0.278174 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 56.2456 | 1.83355 | 0.916777 | − | 0.399400i | \(-0.130781\pi\) | ||||
0.916777 | + | 0.399400i | \(0.130781\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.98929 | −0.129909 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.26202 | 0.106113 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.0743 | 0.424856 | 0.212428 | − | 0.977177i | \(-0.431863\pi\) | ||||
0.212428 | + | 0.977177i | \(0.431863\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.4873 | −0.729967 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.03723 | −0.130916 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.1537 | 0.555661 | 0.277831 | − | 0.960630i | \(-0.410385\pi\) | ||||
0.277831 | + | 0.960630i | \(0.410385\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.1590 | −0.490535 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.47331 | −0.241578 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.3413 | 0.430813 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4150 | −0.948872 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 38.1702 | 1.23002 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.64406 | −0.149498 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.0857 | −0.581596 | −0.290798 | − | 0.956785i | \(-0.593921\pi\) | ||||
−0.290798 | + | 0.956785i | \(0.593921\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.246153 | 0.00790758 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 52.5054 | 1.68498 | 0.842489 | − | 0.538713i | \(-0.181089\pi\) | ||||
0.842489 | + | 0.538713i | \(0.181089\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.4146 | 0.718578 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.03189 | −0.161149 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 37.1839 | 1.18962 | 0.594810 | − | 0.803866i | \(-0.297227\pi\) | ||||
0.594810 | + | 0.803866i | \(0.297227\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.6791 | −0.980508 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.6543 | −1.20221 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.7298 | 0.916339 | 0.458170 | − | 0.888865i | \(-0.348505\pi\) | ||||
0.458170 | + | 0.888865i | \(0.348505\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.03199 | 0.287783 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.321202 | −0.0102240 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.0398 | −0.541834 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.59860 | −0.209611 | −0.104806 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104806 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.19920 | −0.101524 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.7834 | −0.405260 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.2232 | −0.925507 | −0.462754 | − | 0.886487i | \(-0.653139\pi\) | ||||
−0.462754 | + | 0.886487i | \(0.653139\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.27609 | −0.135290 |
(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 | 4028.2.a.d.1.11 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.d.1.11 | ✓ | 19 | 1.1 | even | 1 | trivial |