Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8752,2,Mod(1,8752)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8752, 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("8752.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8752 = 2^{4} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8752.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: | \(69.8850718490\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} - 137 x^{10} - 7703 x^{9} + 2068 x^{8} + 11068 x^{7} - 4274 x^{6} - 9021 x^{5} + \cdots + 328 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 547) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-1.87675\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8752.1 |
$q$-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 | ||||||||
\(3\) | 1.13919 | 0.657712 | 0.328856 | − | 0.944380i | \(-0.393337\pi\) | ||||
0.328856 | + | 0.944380i | \(0.393337\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.30620 | −0.584152 | −0.292076 | − | 0.956395i | \(-0.594346\pi\) | ||||
−0.292076 | + | 0.956395i | \(0.594346\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.71403 | 0.647843 | 0.323922 | − | 0.946084i | \(-0.394999\pi\) | ||||
0.323922 | + | 0.946084i | \(0.394999\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.70224 | −0.567415 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.30835 | 1.60053 | 0.800263 | − | 0.599649i | \(-0.204693\pi\) | ||||
0.800263 | + | 0.599649i | \(0.204693\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.18823 | 0.606905 | 0.303452 | − | 0.952847i | \(-0.401861\pi\) | ||||
0.303452 | + | 0.952847i | \(0.401861\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.48801 | −0.384204 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.392924 | 0.0952980 | 0.0476490 | − | 0.998864i | \(-0.484827\pi\) | ||||
0.0476490 | + | 0.998864i | \(0.484827\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.498929 | −0.114462 | −0.0572311 | − | 0.998361i | \(-0.518227\pi\) | ||||
−0.0572311 | + | 0.998361i | \(0.518227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.95261 | 0.426094 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.33591 | −1.73816 | −0.869079 | − | 0.494674i | \(-0.835287\pi\) | ||||
−0.869079 | + | 0.494674i | \(0.835287\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.29383 | −0.658767 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.35675 | −1.03091 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.50948 | −0.837389 | −0.418695 | − | 0.908127i | \(-0.637512\pi\) | ||||
−0.418695 | + | 0.908127i | \(0.637512\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.96386 | 0.532324 | 0.266162 | − | 0.963928i | \(-0.414244\pi\) | ||||
0.266162 | + | 0.963928i | \(0.414244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.04722 | 1.05269 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.23887 | −0.378439 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.06843 | 0.504447 | 0.252223 | − | 0.967669i | \(-0.418838\pi\) | ||||
0.252223 | + | 0.967669i | \(0.418838\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.49281 | 0.399169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0885 | −1.57556 | −0.787780 | − | 0.615957i | \(-0.788770\pi\) | ||||
−0.787780 | + | 0.615957i | \(0.788770\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.93284 | −1.51474 | −0.757372 | − | 0.652984i | \(-0.773517\pi\) | ||||
−0.757372 | + | 0.652984i | \(0.773517\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.22348 | 0.331456 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.714605 | −0.104236 | −0.0521179 | − | 0.998641i | \(-0.516597\pi\) | ||||
−0.0521179 | + | 0.998641i | \(0.516597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.06209 | −0.580299 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.447615 | 0.0626787 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3693 | −1.42433 | −0.712165 | − | 0.702012i | \(-0.752285\pi\) | ||||
−0.712165 | + | 0.702012i | \(0.752285\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.93378 | −0.934950 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.568376 | −0.0752832 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.58293 | 0.857024 | 0.428512 | − | 0.903536i | \(-0.359038\pi\) | ||||
0.428512 | + | 0.903536i | \(0.359038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.889139 | −0.113843 | −0.0569213 | − | 0.998379i | \(-0.518128\pi\) | ||||
−0.0569213 | + | 0.998379i | \(0.518128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.91770 | −0.367596 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.85827 | −0.354524 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.67997 | −0.571750 | −0.285875 | − | 0.958267i | \(-0.592284\pi\) | ||||
−0.285875 | + | 0.958267i | \(0.592284\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.49619 | −1.14321 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.4239 | −1.35577 | −0.677886 | − | 0.735167i | \(-0.737104\pi\) | ||||
−0.677886 | + | 0.735167i | \(0.737104\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.35047 | 0.626225 | 0.313113 | − | 0.949716i | \(-0.398628\pi\) | ||||
0.313113 | + | 0.949716i | \(0.398628\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.75231 | −0.433279 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.09868 | 1.03689 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.79987 | 0.877554 | 0.438777 | − | 0.898596i | \(-0.355412\pi\) | ||||
0.438777 | + | 0.898596i | \(0.355412\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.995634 | −0.110626 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 17.9975 | 1.97548 | 0.987740 | − | 0.156107i | \(-0.0498946\pi\) | ||||
0.987740 | + | 0.156107i | \(0.0498946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.513238 | −0.0556685 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.13716 | −0.550761 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.3683 | 1.41704 | 0.708519 | − | 0.705691i | \(-0.249363\pi\) | ||||
0.708519 | + | 0.705691i | \(0.249363\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.75069 | 0.393179 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.37640 | 0.350116 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.651703 | 0.0668633 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2660 | −1.34696 | −0.673480 | − | 0.739206i | \(-0.735201\pi\) | ||||
−0.673480 | + | 0.739206i | \(0.735201\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.03610 | −0.908162 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.06820 | −0.504305 | −0.252152 | − | 0.967688i | \(-0.581138\pi\) | ||||
−0.252152 | + | 0.967688i | \(0.581138\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.26789 | 0.124929 | 0.0624644 | − | 0.998047i | \(-0.480104\pi\) | ||||
0.0624644 | + | 0.998047i | \(0.480104\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.55050 | −0.248904 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.5228 | −1.11395 | −0.556974 | − | 0.830530i | \(-0.688038\pi\) | ||||
−0.556974 | + | 0.830530i | \(0.688038\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.84704 | 0.176914 | 0.0884570 | − | 0.996080i | \(-0.471806\pi\) | ||||
0.0884570 | + | 0.996080i | \(0.471806\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.49553 | 0.331781 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.8186 | −1.01773 | −0.508865 | − | 0.860846i | \(-0.669935\pi\) | ||||
−0.508865 | + | 0.860846i | \(0.669935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.8884 | 1.01535 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.72489 | −0.344367 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.673484 | 0.0617382 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.1786 | 1.56169 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.4927 | −1.03626 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.8334 | 0.968971 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9759 | −1.50637 | −0.753185 | − | 0.657809i | \(-0.771483\pi\) | ||||
−0.753185 | + | 0.657809i | \(0.771483\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.3154 | −0.996266 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.273878 | −0.0239289 | −0.0119644 | − | 0.999928i | \(-0.503808\pi\) | ||||
−0.0119644 | + | 0.999928i | \(0.503808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.855181 | −0.0741536 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.99701 | 0.602206 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.63213 | −0.481185 | −0.240593 | − | 0.970626i | \(-0.577342\pi\) | ||||
−0.240593 | + | 0.970626i | \(0.577342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.7017 | 1.92553 | 0.962767 | − | 0.270333i | \(-0.0871337\pi\) | ||||
0.962767 | + | 0.270333i | \(0.0871337\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.814072 | −0.0685572 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.6159 | 0.971367 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.89029 | 0.489162 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.62750 | −0.381670 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.23862 | −0.265318 | −0.132659 | − | 0.991162i | \(-0.542352\pi\) | ||||
−0.132659 | + | 0.991162i | \(0.542352\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.3287 | −1.49157 | −0.745783 | − | 0.666189i | \(-0.767924\pi\) | ||||
−0.745783 | + | 0.666189i | \(0.767924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.668852 | −0.0540735 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.87140 | −0.310958 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.10134 | −0.167705 | −0.0838527 | − | 0.996478i | \(-0.526723\pi\) | ||||
−0.0838527 | + | 0.996478i | \(0.526723\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.8126 | −0.936799 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.2880 | −1.12605 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.0706 | 1.80703 | 0.903514 | − | 0.428558i | \(-0.140978\pi\) | ||||
0.903514 | + | 0.428558i | \(0.140978\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.89890 | −0.614928 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.3441 | 0.877832 | 0.438916 | − | 0.898528i | \(-0.355363\pi\) | ||||
0.438916 | + | 0.898528i | \(0.355363\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.21167 | −0.631667 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.849299 | 0.0649476 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.2109 | −1.30852 | −0.654259 | − | 0.756271i | \(-0.727019\pi\) | ||||
−0.654259 | + | 0.756271i | \(0.727019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.64574 | −0.426778 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.49921 | 0.563675 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.9899 | 0.896168 | 0.448084 | − | 0.893991i | \(-0.352107\pi\) | ||||
0.448084 | + | 0.893991i | \(0.352107\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.09690 | 0.0815319 | 0.0407660 | − | 0.999169i | \(-0.487020\pi\) | ||||
0.0407660 | + | 0.999169i | \(0.487020\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.01290 | −0.0748756 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.00799 | −0.294673 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.08578 | 0.152527 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.18165 | −0.667867 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.44468 | −0.104533 | −0.0522667 | − | 0.998633i | \(-0.516645\pi\) | ||||
−0.0522667 | + | 0.998633i | \(0.516645\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.41359 | 0.101753 | 0.0508763 | − | 0.998705i | \(-0.483799\pi\) | ||||
0.0508763 | + | 0.998705i | \(0.483799\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.25611 | −0.233175 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.14237 | −0.366379 | −0.183189 | − | 0.983078i | \(-0.558642\pi\) | ||||
−0.183189 | + | 0.983078i | \(0.558642\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7502 | 1.18739 | 0.593695 | − | 0.804690i | \(-0.297668\pi\) | ||||
0.593695 | + | 0.804690i | \(0.297668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.33139 | −0.376047 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.72939 | −0.542497 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 13.1776 | 0.920366 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.1897 | 0.986256 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.64849 | −0.183200 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7475 | 0.808734 | 0.404367 | − | 0.914597i | \(-0.367492\pi\) | ||||
0.404367 | + | 0.914597i | \(0.367492\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.0141 | −0.891708 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.9743 | 0.884840 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.08014 | 0.344863 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.09521 | 0.411876 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.859806 | 0.0578368 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.9958 | −1.80778 | −0.903888 | − | 0.427770i | \(-0.859299\pi\) | ||||
−0.903888 | + | 0.427770i | \(0.859299\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.60691 | 0.373794 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.16279 | 0.409039 | 0.204519 | − | 0.978863i | \(-0.434437\pi\) | ||||
0.204519 | + | 0.978863i | \(0.434437\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.04203 | 0.333187 | 0.166593 | − | 0.986026i | \(-0.446723\pi\) | ||||
0.166593 | + | 0.986026i | \(0.446723\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.3651 | 0.681975 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.21008 | −0.537860 | −0.268930 | − | 0.963160i | \(-0.586670\pi\) | ||||
−0.268930 | + | 0.963160i | \(0.586670\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.933419 | 0.0608896 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.88554 | 0.577178 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.4229 | −1.64447 | −0.822235 | − | 0.569148i | \(-0.807273\pi\) | ||||
−0.822235 | + | 0.569148i | \(0.807273\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.7739 | 1.72466 | 0.862328 | − | 0.506350i | \(-0.169006\pi\) | ||||
0.862328 | + | 0.506350i | \(0.169006\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.9360 | 0.958148 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.30592 | 0.338983 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.09177 | −0.0694677 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20.5026 | 1.29930 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7572 | −1.49954 | −0.749770 | − | 0.661699i | \(-0.769836\pi\) | ||||
−0.749770 | + | 0.661699i | \(0.769836\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −44.2499 | −2.78197 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.584676 | −0.0366138 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.92184 | −0.431773 | −0.215886 | − | 0.976418i | \(-0.569264\pi\) | ||||
−0.215886 | + | 0.976418i | \(0.569264\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.25939 | 0.326802 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.67623 | 0.475147 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.02135 | 0.556281 | 0.278140 | − | 0.960540i | \(-0.410282\pi\) | ||||
0.278140 | + | 0.960540i | \(0.410282\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.5444 | 0.832025 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.2291 | 0.932004 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.43191 | 0.453131 | 0.226566 | − | 0.973996i | \(-0.427250\pi\) | ||||
0.226566 | + | 0.973996i | \(0.427250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.3754 | −1.48070 | −0.740351 | − | 0.672220i | \(-0.765341\pi\) | ||||
−0.740351 | + | 0.672220i | \(0.765341\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.27275 | 0.258599 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.4848 | −1.05437 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8453 | 0.952052 | 0.476026 | − | 0.879431i | \(-0.342077\pi\) | ||||
0.476026 | + | 0.879431i | \(0.342077\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.04520 | −0.302049 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.55329 | 0.331281 | 0.165641 | − | 0.986186i | \(-0.447031\pi\) | ||||
0.165641 | + | 0.986186i | \(0.447031\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.5322 | 1.27996 | 0.639978 | − | 0.768394i | \(-0.278944\pi\) | ||||
0.639978 | + | 0.768394i | \(0.278944\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.742414 | 0.0439768 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.2920 | −1.02072 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8456 | −0.990918 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.1125 | −0.885912 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −23.9442 | −1.39884 | −0.699418 | − | 0.714713i | \(-0.746557\pi\) | ||||
−0.699418 | + | 0.714713i | \(0.746557\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.59863 | −0.500632 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −28.4355 | −1.65000 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.2408 | −1.05490 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.0252 | −0.981316 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.77365 | −0.331687 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.16140 | 0.0665013 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.31760 | −0.0751996 | −0.0375998 | − | 0.999293i | \(-0.511971\pi\) | ||||
−0.0375998 | + | 0.999293i | \(0.511971\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.44437 | 0.0821672 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.9974 | 1.24736 | 0.623679 | − | 0.781680i | \(-0.285637\pi\) | ||||
0.623679 | + | 0.781680i | \(0.285637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.891821 | −0.0504087 | −0.0252044 | − | 0.999682i | \(-0.508024\pi\) | ||||
−0.0252044 | + | 0.999682i | \(0.508024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.81111 | 0.214732 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.3281 | −1.36640 | −0.683202 | − | 0.730229i | \(-0.739413\pi\) | ||||
−0.683202 | + | 0.730229i | \(0.739413\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.9379 | −1.34026 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.1266 | −0.732657 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.196041 | −0.0109080 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.20765 | −0.399809 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.10413 | 0.116359 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.22486 | −0.0675285 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.7538 | −1.52549 | −0.762745 | − | 0.646700i | \(-0.776149\pi\) | ||||
−0.762745 | + | 0.646700i | \(0.776149\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.22322 | −0.286231 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.11300 | 0.333989 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.10740 | 0.332691 | 0.166346 | − | 0.986068i | \(-0.446803\pi\) | ||||
0.166346 | + | 0.986068i | \(0.446803\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.3245 | −0.669374 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7332 | 0.851999 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.9608 | −1.02379 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 12.4040 | 0.667806 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.7441 | −1.48938 | −0.744691 | − | 0.667409i | \(-0.767403\pi\) | ||||
−0.744691 | + | 0.667409i | \(0.767403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.3589 | −0.768616 | −0.384308 | − | 0.923205i | \(-0.625560\pi\) | ||||
−0.384308 | + | 0.923205i | \(0.625560\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.7218 | −0.625663 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.89459 | 0.100839 | 0.0504194 | − | 0.998728i | \(-0.483944\pi\) | ||||
0.0504194 | + | 0.998728i | \(0.483944\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.9220 | 0.791977 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.767227 | 0.0406060 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.0371 | −0.529740 | −0.264870 | − | 0.964284i | \(-0.585329\pi\) | ||||
−0.264870 | + | 0.964284i | \(0.585329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7511 | −0.986898 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.5697 | 1.02714 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.98880 | −0.365810 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.02023 | −0.262054 | −0.131027 | − | 0.991379i | \(-0.541827\pi\) | ||||
−0.131027 | + | 0.991379i | \(0.541827\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.1731 | 0.893996 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.7733 | −0.922742 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.12699 | −0.161910 | −0.0809548 | − | 0.996718i | \(-0.525797\pi\) | ||||
−0.0809548 | + | 0.996718i | \(0.525797\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.3413 | 0.637304 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.86776 | −0.508215 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.8372 | −0.864867 | −0.432433 | − | 0.901666i | \(-0.642345\pi\) | ||||
−0.432433 | + | 0.901666i | \(0.642345\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −19.3388 | −0.990757 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.31954 | 0.169621 | 0.0848104 | − | 0.996397i | \(-0.472972\pi\) | ||||
0.0848104 | + | 0.996397i | \(0.472972\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.8847 | −0.605701 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.9081 | 0.859488 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.8035 | −0.699867 | −0.349933 | − | 0.936775i | \(-0.613796\pi\) | ||||
−0.349933 | + | 0.936775i | \(0.613796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.27538 | −0.165643 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.312000 | −0.0157383 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.1882 | −0.512625 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.6460 | 0.684875 | 0.342438 | − | 0.939541i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939541i | \(0.388747\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.974214 | −0.0487717 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.21927 | −0.210700 | −0.105350 | − | 0.994435i | \(-0.533596\pi\) | ||||
−0.105350 | + | 0.994435i | \(0.533596\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.48558 | 0.323070 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.30050 | 0.0646224 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.2883 | 0.807381 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.32926 | 0.164621 | 0.0823105 | − | 0.996607i | \(-0.473770\pi\) | ||||
0.0823105 | + | 0.996607i | \(0.473770\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.41607 | −0.316481 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.2833 | 0.555217 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −23.5084 | −1.15398 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.8616 | 1.26645 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.2091 | 0.840718 | 0.420359 | − | 0.907358i | \(-0.361904\pi\) | ||||
0.420359 | + | 0.907358i | \(0.361904\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.90690 | 0.287884 | 0.143942 | − | 0.989586i | \(-0.454022\pi\) | ||||
0.143942 | + | 0.989586i | \(0.454022\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.21643 | 0.0591450 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.29423 | −0.0627792 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.52401 | −0.0737521 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.2327 | 0.638880 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.0646 | 1.30366 | 0.651829 | − | 0.758366i | \(-0.274002\pi\) | ||||
0.651829 | + | 0.758366i | \(0.274002\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.65104 | −0.271571 | −0.135786 | − | 0.990738i | \(-0.543356\pi\) | ||||
−0.135786 | + | 0.990738i | \(0.543356\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.71017 | 0.321728 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.15903 | 0.198953 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.7713 | 1.27772 | 0.638861 | − | 0.769322i | \(-0.279406\pi\) | ||||
0.638861 | + | 0.769322i | \(0.279406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.91468 | 0.329270 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.1995 | −1.62487 | −0.812435 | − | 0.583052i | \(-0.801858\pi\) | ||||
−0.812435 | + | 0.583052i | \(0.801858\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.4617 | −0.827765 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.68940 | −0.174503 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.11797 | −0.335918 | −0.167959 | − | 0.985794i | \(-0.553718\pi\) | ||||
−0.167959 | + | 0.985794i | \(0.553718\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −53.5533 | −2.52173 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.8799 | −0.981021 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.89916 | −0.229676 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.8336 | 1.20845 | 0.604223 | − | 0.796815i | \(-0.293484\pi\) | ||||
0.604223 | + | 0.796815i | \(0.293484\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.10480 | −0.0982435 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.8134 | −1.80772 | −0.903860 | − | 0.427829i | \(-0.859279\pi\) | ||||
−0.903860 | + | 0.427829i | \(0.859279\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.8908 | −1.06383 | −0.531913 | − | 0.846799i | \(-0.678527\pi\) | ||||
−0.531913 | + | 0.846799i | \(0.678527\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.41026 | −0.204521 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.1901 | 0.564089 | 0.282045 | − | 0.959401i | \(-0.408987\pi\) | ||||
0.282045 | + | 0.959401i | \(0.408987\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.02163 | −0.370404 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.39383 | −0.110302 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −52.7270 | −2.42439 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.64339 | 0.0754039 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.6510 | 0.808186 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 35.1228 | 1.60480 | 0.802400 | − | 0.596786i | \(-0.203556\pi\) | ||||
0.802400 | + | 0.596786i | \(0.203556\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.71442 | 0.306151 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.2768 | −0.740619 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.3281 | 0.786828 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.59211 | −0.344031 | −0.172016 | − | 0.985094i | \(-0.555028\pi\) | ||||
−0.172016 | + | 0.985094i | \(0.555028\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.2818 | 1.18850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.2927 | −0.825537 | −0.412768 | − | 0.910836i | \(-0.635438\pi\) | ||||
−0.412768 | + | 0.910836i | \(0.635438\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.77188 | −0.0798015 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.8030 | 0.530504 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −19.5810 | −0.878328 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.76535 | −0.258093 | −0.129046 | − | 0.991639i | \(-0.541192\pi\) | ||||
−0.129046 | + | 0.991639i | \(0.541192\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12.9231 | 0.577361 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.1805 | 0.944394 | 0.472197 | − | 0.881493i | \(-0.343461\pi\) | ||||
0.472197 | + | 0.881493i | \(0.343461\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.62010 | 0.294590 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.35466 | −0.415455 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.1907 | 0.806289 | 0.403145 | − | 0.915136i | \(-0.367917\pi\) | ||||
0.403145 | + | 0.915136i | \(0.367917\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.17088 | 0.405696 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.67264 | 0.118000 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.65612 | −0.0729773 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.79337 | −0.166832 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −19.6065 | −0.860628 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.4553 | 0.939976 | 0.469988 | − | 0.882673i | \(-0.344258\pi\) | ||||
0.469988 | + | 0.882673i | \(0.344258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.6184 | −0.508038 | −0.254019 | − | 0.967199i | \(-0.581753\pi\) | ||||
−0.254019 | + | 0.967199i | \(0.581753\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.43157 | −0.280697 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.16457 | 0.0507294 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.4874 | 2.02119 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.2057 | −0.486288 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −22.0759 | −0.956214 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.0511 | 0.650714 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.6588 | 0.589421 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.5630 | −0.928785 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.8443 | 0.681198 | 0.340599 | − | 0.940209i | \(-0.389370\pi\) | ||||
0.340599 | + | 0.940209i | \(0.389370\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.24958 | 0.0536245 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.41260 | −0.103345 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.51353 | 0.0645959 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.24991 | 0.0958495 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3692 | 0.568517 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.56587 | −0.193810 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.0799 | 0.469471 | 0.234735 | − | 0.972059i | \(-0.424578\pi\) | ||||
0.234735 | + | 0.972059i | \(0.424578\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.7353 | −0.919305 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.37610 | 0.100319 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −41.1603 | −1.73470 | −0.867351 | − | 0.497697i | \(-0.834179\pi\) | ||||
−0.867351 | + | 0.497697i | \(0.834179\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.1313 | 0.594509 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.70655 | −0.0716683 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.52628 | −0.399363 | −0.199681 | − | 0.979861i | \(-0.563991\pi\) | ||||
−0.199681 | + | 0.979861i | \(0.563991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.76393 | −0.199364 | −0.0996822 | − | 0.995019i | \(-0.531783\pi\) | ||||
−0.0996822 | + | 0.995019i | \(0.531783\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.64577 | −0.0687530 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 27.4571 | 1.14504 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.8345 | 1.40855 | 0.704274 | − | 0.709929i | \(-0.251273\pi\) | ||||
0.704274 | + | 0.709929i | \(0.251273\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.61035 | 0.0669240 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.8483 | 1.27980 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −55.0437 | −2.27968 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.86547 | 0.201162 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2101 | 0.503964 | 0.251982 | − | 0.967732i | \(-0.418918\pi\) | ||||
0.251982 | + | 0.967732i | \(0.418918\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.47875 | −0.0609310 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.85814 | −0.240972 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.7830 | 1.34624 | 0.673118 | − | 0.739535i | \(-0.264954\pi\) | ||||
0.673118 | + | 0.739535i | \(0.264954\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.879707 | −0.0360645 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.0817 | 0.780961 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.1846 | 1.06987 | 0.534936 | − | 0.844892i | \(-0.320336\pi\) | ||||
0.534936 | + | 0.844892i | \(0.320336\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.1011 | −0.575196 | −0.287598 | − | 0.957751i | \(-0.592857\pi\) | ||||
−0.287598 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.96646 | 0.324419 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −22.4387 | −0.912262 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.3651 | −0.664239 | −0.332120 | − | 0.943237i | \(-0.607764\pi\) | ||||
−0.332120 | + | 0.943237i | \(0.607764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.80525 | −0.356807 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.56372 | −0.0632612 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.3441 | −0.538961 | −0.269481 | − | 0.963006i | \(-0.586852\pi\) | ||||
−0.269481 | + | 0.963006i | \(0.586852\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.0118 | 0.605336 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.5802 | 1.39215 | 0.696074 | − | 0.717971i | \(-0.254929\pi\) | ||||
0.696074 | + | 0.717971i | \(0.254929\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.0240 | 0.804832 | 0.402416 | − | 0.915457i | \(-0.368171\pi\) | ||||
0.402416 | + | 0.915457i | \(0.368171\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.6534 | 1.79188 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 22.9137 | 0.918019 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.31852 | 0.0927408 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.01714 | −0.120493 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.20566 | 0.0480728 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.64737 | 0.0655808 | 0.0327904 | − | 0.999462i | \(-0.489561\pi\) | ||||
0.0327904 | + | 0.999462i | \(0.489561\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.3827 | 0.531914 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.1740 | 0.879948 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.88878 | −0.352186 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19.4463 | 0.769285 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.9733 | 1.22337 | 0.611686 | − | 0.791100i | \(-0.290491\pi\) | ||||
0.611686 | + | 0.791100i | \(0.290491\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.8226 | −0.978907 | −0.489454 | − | 0.872029i | \(-0.662804\pi\) | ||||
−0.489454 | + | 0.872029i | \(0.662804\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.7802 | 0.581970 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −36.5122 | −1.43544 | −0.717721 | − | 0.696331i | \(-0.754815\pi\) | ||||
−0.717721 | + | 0.696331i | \(0.754815\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 34.9445 | 1.37169 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.78725 | 0.226820 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.5164 | −1.03767 | −0.518834 | − | 0.854875i | \(-0.673634\pi\) | ||||
−0.518834 | + | 0.854875i | \(0.673634\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.357740 | 0.0139781 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.10781 | −0.355329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.7938 | 1.00478 | 0.502391 | − | 0.864641i | \(-0.332454\pi\) | ||||
0.502391 | + | 0.864641i | \(0.332454\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.9540 | −1.63182 | −0.815910 | − | 0.578179i | \(-0.803764\pi\) | ||||
−0.815910 | + | 0.578179i | \(0.803764\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.979483 | 0.0380400 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.11704 | 0.0433169 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 37.5906 | 1.45551 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −30.7534 | −1.18900 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.71986 | −0.182208 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.20648 | −0.123601 | −0.0618003 | − | 0.998089i | \(-0.519684\pi\) | ||||
−0.0618003 | + | 0.998089i | \(0.519684\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17.6443 | 0.679128 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.84844 | 0.186341 | 0.0931704 | − | 0.995650i | \(-0.470300\pi\) | ||||
0.0931704 | + | 0.995650i | \(0.470300\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.7384 | −0.872618 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.02059 | 0.269030 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.3263 | 1.23693 | 0.618466 | − | 0.785812i | \(-0.287755\pi\) | ||||
0.618466 | + | 0.785812i | \(0.287755\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.35670 | 0.281085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.74384 | 0.219141 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −22.6903 | −0.864432 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.59431 | 0.364985 | 0.182492 | − | 0.983207i | \(-0.441584\pi\) | ||||
0.182492 | + | 0.983207i | \(0.441584\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.4882 | −0.588347 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.6530 | −1.12480 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.96401 | −0.150148 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.35285 | −0.353757 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −48.0675 | −1.81549 | −0.907743 | − | 0.419527i | \(-0.862196\pi\) | ||||
−0.907743 | + | 0.419527i | \(0.862196\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.53093 | −0.0577401 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.06334 | 0.0400478 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.68706 | −0.326710 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.6771 | 0.476099 | 0.238049 | − | 0.971253i | \(-0.423492\pi\) | ||||
0.238049 | + | 0.971253i | \(0.423492\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.2773 | −0.497937 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.7064 | −0.925263 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.1727 | −0.567426 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28.9615 | −1.08159 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.9369 | −0.557053 | −0.278526 | − | 0.960429i | \(-0.589846\pi\) | ||||
−0.278526 | + | 0.960429i | \(0.589846\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.17320 | 0.0809343 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.5005 | 1.13433 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.8535 | 0.551644 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9039 | 0.626932 | 0.313466 | − | 0.949599i | \(-0.398510\pi\) | ||||
0.313466 | + | 0.949599i | \(0.398510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0019 | 0.740811 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.90285 | −0.144352 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.0731 | 0.630609 | 0.315305 | − | 0.948991i | \(-0.397893\pi\) | ||||
0.315305 | + | 0.948991i | \(0.397893\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.04445 | 0.222953 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.8429 | −0.915101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.313121 | 0.0115183 | 0.00575917 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00575917 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.24373 | −0.0456897 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.0657 | 0.699451 | 0.349726 | − | 0.936852i | \(-0.386275\pi\) | ||||
0.349726 | + | 0.936852i | \(0.386275\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.23029 | 0.154986 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −30.6361 | −1.12092 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.7504 | −0.721663 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.1901 | 0.517803 | 0.258901 | − | 0.965904i | \(-0.416640\pi\) | ||||
0.258901 | + | 0.965904i | \(0.416640\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.0640 | −0.986266 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.9410 | 0.871301 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.0979 | −1.16662 | −0.583309 | − | 0.812250i | \(-0.698242\pi\) | ||||
−0.583309 | + | 0.812250i | \(0.698242\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −50.4091 | −1.82973 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.3107 | 0.990013 | 0.495006 | − | 0.868889i | \(-0.335166\pi\) | ||||
0.495006 | + | 0.868889i | \(0.335166\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.16588 | 0.114613 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.873656 | 0.0315871 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 14.4049 | 0.520132 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.5549 | 0.560923 | 0.280461 | − | 0.959865i | \(-0.409513\pi\) | ||||
0.280461 | + | 0.959865i | \(0.409513\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.88530 | −0.283982 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −49.6932 | −1.78734 | −0.893670 | − | 0.448724i | \(-0.851878\pi\) | ||||
−0.893670 | + | 0.448724i | \(0.851878\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.76245 | −0.350678 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.99145 | 0.214942 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.03345 | 0.180342 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.6423 | −2.16995 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.1562 | 0.863271 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.74478 | 0.0979654 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.9449 | 0.532729 | 0.266365 | − | 0.963872i | \(-0.414177\pi\) | ||||
0.266365 | + | 0.963872i | \(0.414177\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.2770 | 0.365873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.5435 | −0.659330 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.94564 | −0.0690916 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.4296 | 0.547233 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.1154 | −0.464573 | −0.232286 | − | 0.972647i | \(-0.574621\pi\) | ||||
−0.232286 | + | 0.972647i | \(0.574621\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.280785 | −0.00993347 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.7561 | −0.804049 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.4022 | 1.00229 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.6630 | 0.657786 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.46636 | 0.298030 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.4909 | −0.685262 | −0.342631 | − | 0.939470i | \(-0.611318\pi\) | ||||
−0.342631 | + | 0.939470i | \(0.611318\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.5367 | −0.650912 | −0.325456 | − | 0.945557i | \(-0.605518\pi\) | ||||
−0.325456 | + | 0.945557i | \(0.605518\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.7683 | −0.973876 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −30.1349 | −1.05558 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.95579 | 0.173381 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.38459 | −0.223095 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.1526 | −0.424130 | −0.212065 | − | 0.977256i | \(-0.568019\pi\) | ||||
−0.212065 | + | 0.977256i | \(0.568019\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.5837 | −0.543214 | −0.271607 | − | 0.962408i | \(-0.587555\pi\) | ||||
−0.271607 | + | 0.962408i | \(0.587555\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.9185 | −0.693475 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.2481 | −0.495456 | −0.247728 | − | 0.968830i | \(-0.579684\pi\) | ||||
−0.247728 | + | 0.968830i | \(0.579684\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.8914 | 1.83700 | 0.918498 | − | 0.395426i | \(-0.129403\pi\) | ||||
0.918498 | + | 0.395426i | \(0.129403\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.0508 | 0.626176 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.59609 | −0.0553014 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.8177 | −0.512787 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.8766 | −0.548777 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.6169 | 0.884395 | 0.442198 | − | 0.896918i | \(-0.354199\pi\) | ||||
0.442198 | + | 0.896918i | \(0.354199\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.66460 | −0.298779 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.32625 | 0.217888 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.7261 | 0.368989 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.4446 | 1.01173 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 24.5293 | 0.841842 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.5782 | −0.876808 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.7883 | 0.814498 | 0.407249 | − | 0.913317i | \(-0.366488\pi\) | ||||
0.407249 | + | 0.913317i | \(0.366488\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.10936 | −0.0379392 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.27557 | −0.0435727 | −0.0217863 | − | 0.999763i | \(-0.506935\pi\) | ||||
−0.0217863 | + | 0.999763i | \(0.506935\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.6456 | 1.31857 | 0.659285 | − | 0.751893i | \(-0.270859\pi\) | ||||
0.659285 | + | 0.751893i | \(0.270859\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.6989 | −0.671337 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.3344 | −0.453908 | −0.226954 | − | 0.973905i | \(-0.572877\pi\) | ||||
−0.226954 | + | 0.973905i | \(0.572877\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.4809 | 0.764373 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −19.1904 | −0.651739 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41.4044 | 1.40455 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.2408 | −0.346998 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.5820 | 0.764284 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 18.5688 | 0.627741 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.39699 | −0.182244 | −0.0911218 | − | 0.995840i | \(-0.529045\pi\) | ||||
−0.0911218 | + | 0.995840i | \(0.529045\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.2770 | −0.920031 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.04786 | −0.170067 | −0.0850333 | − | 0.996378i | \(-0.527100\pi\) | ||||
−0.0850333 | + | 0.996378i | \(0.527100\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.4145 | 1.22545 | 0.612723 | − | 0.790298i | \(-0.290074\pi\) | ||||
0.612723 | + | 0.790298i | \(0.290074\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.79549 | −0.329272 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.9346 | 0.837224 | 0.418612 | − | 0.908165i | \(-0.362517\pi\) | ||||
0.418612 | + | 0.908165i | \(0.362517\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29.0973 | −0.975891 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.28517 | −0.177060 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.356538 | 0.0119311 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.6613 | −0.523498 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −20.7798 | −0.693818 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.3654 | −0.445763 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.07434 | −0.135736 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −19.3950 | −0.645424 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.43277 | −0.0476270 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.1951 | 0.903000 | 0.451500 | − | 0.892271i | \(-0.350889\pi\) | ||||
0.451500 | + | 0.892271i | \(0.350889\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.62731 | 0.286150 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.9588 | 1.58895 | 0.794473 | − | 0.607299i | \(-0.207747\pi\) | ||||
0.794473 | + | 0.607299i | \(0.207747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 95.5369 | 3.16181 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.32305 | 0.0437387 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.469436 | −0.0155021 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.3674 | 0.671857 | 0.335928 | − | 0.941887i | \(-0.390950\pi\) | ||||
0.335928 | + | 0.941887i | \(0.390950\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.50100 | −0.0494597 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.9982 | −0.822825 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.1069 | −0.332313 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.15826 | −0.0708864 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.43001 | 0.112535 | 0.0562675 | − | 0.998416i | \(-0.482080\pi\) | ||||
0.0562675 | + | 0.998416i | \(0.482080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.02670 | 0.0664224 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25.0593 | 0.820403 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.72445 | −0.0890989 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55.8441 | −1.82435 | −0.912173 | − | 0.409805i | \(-0.865597\pi\) | ||||
−0.912173 | + | 0.409805i | \(0.865597\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.01595 | −0.0331544 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.2757 | −1.14996 | −0.574978 | − | 0.818169i | \(-0.694989\pi\) | ||||
−0.574978 | + | 0.818169i | \(0.694989\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 84.0969 | 2.73857 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 11.9931 | 0.390135 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.2546 | 1.47058 | 0.735289 | − | 0.677754i | \(-0.237046\pi\) | ||||
0.735289 | + | 0.677754i | \(0.237046\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.7080 | 0.380059 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −27.7144 | −0.898701 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.0690 | 1.26557 | 0.632784 | − | 0.774328i | \(-0.281912\pi\) | ||||
0.632784 | + | 0.774328i | \(0.281912\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.88705 | 0.0610634 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −27.2698 | −0.881508 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.65365 | −0.311733 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2156 | −0.716631 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 19.6146 | 0.632070 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.84644 | −0.0594390 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.8771 | −0.381942 | −0.190971 | − | 0.981596i | \(-0.561164\pi\) | ||||
−0.190971 | + | 0.981596i | \(0.561164\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.223328 | −0.00717434 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.3430 | 1.39094 | 0.695471 | − | 0.718554i | \(-0.255196\pi\) | ||||
0.695471 | + | 0.718554i | \(0.255196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.9115 | 1.24744 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.21089 | −0.262959 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.9084 | 0.988846 | 0.494423 | − | 0.869221i | \(-0.335379\pi\) | ||||
0.494423 | + | 0.869221i | \(0.335379\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 70.9637 | 2.26801 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.14411 | −0.100384 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.0128 | −1.11673 | −0.558367 | − | 0.829594i | \(-0.688572\pi\) | ||||
−0.558367 | + | 0.829594i | \(0.688572\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.71698 | 0.214021 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.39535 | −0.0444143 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 82.7992 | 2.63286 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.7329 | 0.722135 | 0.361067 | − | 0.932540i | \(-0.382412\pi\) | ||||
0.361067 | + | 0.932540i | \(0.382412\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −31.6169 | −1.00333 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.8792 | −0.693616 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.6754 | −0.338095 | −0.169047 | − | 0.985608i | \(-0.554069\pi\) | ||||
−0.169047 | + | 0.985608i | \(0.554069\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.4368 | −0.520038 |
(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 | 8752.2.a.s.1.11 | 18 | ||
4.3 | odd | 2 | 547.2.a.b.1.16 | ✓ | 18 | ||
12.11 | even | 2 | 4923.2.a.l.1.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.b.1.16 | ✓ | 18 | 4.3 | odd | 2 | ||
4923.2.a.l.1.3 | 18 | 12.11 | even | 2 | |||
8752.2.a.s.1.11 | 18 | 1.1 | even | 1 | trivial |