Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4923,2,Mod(1,4923)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4923, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4923.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4923 = 3^{2} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4923.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: | \(39.3103529151\) |
Analytic rank: | \(0\) |
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: | \( x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} + \cdots + 328 \) |
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 | 1.14 | ||
Root | \(1.74487\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4923.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.74487 | 1.23381 | 0.616903 | − | 0.787039i | \(-0.288387\pi\) | ||||
0.616903 | + | 0.787039i | \(0.288387\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.04455 | 0.522277 | ||||||||
\(5\) | 3.61409 | 1.61627 | 0.808135 | − | 0.588997i | \(-0.200477\pi\) | ||||
0.808135 | + | 0.588997i | \(0.200477\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.28084 | 1.61801 | 0.809003 | − | 0.587804i | \(-0.200008\pi\) | ||||
0.809003 | + | 0.587804i | \(0.200008\pi\) | |||||||
\(8\) | −1.66712 | −0.589417 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.30610 | 1.99416 | ||||||||
\(11\) | 1.82207 | 0.549376 | 0.274688 | − | 0.961533i | \(-0.411425\pi\) | ||||
0.274688 | + | 0.961533i | \(0.411425\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.54763 | 0.429236 | 0.214618 | − | 0.976698i | \(-0.431149\pi\) | ||||
0.214618 | + | 0.976698i | \(0.431149\pi\) | |||||||
\(14\) | 7.46949 | 1.99631 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.99801 | −1.24950 | ||||||||
\(17\) | −5.89804 | −1.43048 | −0.715242 | − | 0.698877i | \(-0.753684\pi\) | ||||
−0.715242 | + | 0.698877i | \(0.753684\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.77207 | 1.32420 | 0.662102 | − | 0.749414i | \(-0.269664\pi\) | ||||
0.662102 | + | 0.749414i | \(0.269664\pi\) | |||||||
\(20\) | 3.77512 | 0.844142 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.17927 | 0.677824 | ||||||||
\(23\) | 7.36494 | 1.53570 | 0.767848 | − | 0.640632i | \(-0.221327\pi\) | ||||
0.767848 | + | 0.640632i | \(0.221327\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.06166 | 1.61233 | ||||||||
\(26\) | 2.70041 | 0.529594 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.47157 | 0.845048 | ||||||||
\(29\) | 4.20778 | 0.781365 | 0.390683 | − | 0.920525i | \(-0.372239\pi\) | ||||
0.390683 | + | 0.920525i | \(0.372239\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.68625 | −1.56010 | −0.780049 | − | 0.625719i | \(-0.784806\pi\) | ||||
−0.780049 | + | 0.625719i | \(0.784806\pi\) | |||||||
\(32\) | −5.38662 | −0.952228 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.2913 | −1.76494 | ||||||||
\(35\) | 15.4714 | 2.61514 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.26711 | −1.52350 | −0.761752 | − | 0.647869i | \(-0.775660\pi\) | ||||
−0.761752 | + | 0.647869i | \(0.775660\pi\) | |||||||
\(38\) | 10.0715 | 1.63381 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.02514 | −0.952658 | ||||||||
\(41\) | −8.29157 | −1.29493 | −0.647463 | − | 0.762097i | \(-0.724170\pi\) | ||||
−0.647463 | + | 0.762097i | \(0.724170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.50047 | −0.381319 | −0.190659 | − | 0.981656i | \(-0.561063\pi\) | ||||
−0.190659 | + | 0.981656i | \(0.561063\pi\) | |||||||
\(44\) | 1.90326 | 0.286927 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.8508 | 1.89475 | ||||||||
\(47\) | 6.07577 | 0.886242 | 0.443121 | − | 0.896462i | \(-0.353871\pi\) | ||||
0.443121 | + | 0.896462i | \(0.353871\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.3256 | 1.61794 | ||||||||
\(50\) | 14.0665 | 1.98930 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.61659 | 0.224180 | ||||||||
\(53\) | 4.35174 | 0.597757 | 0.298879 | − | 0.954291i | \(-0.403387\pi\) | ||||
0.298879 | + | 0.954291i | \(0.403387\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.58514 | 0.887941 | ||||||||
\(56\) | −7.13669 | −0.953680 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.34201 | 0.964053 | ||||||||
\(59\) | 13.6982 | 1.78336 | 0.891680 | − | 0.452667i | \(-0.149527\pi\) | ||||
0.891680 | + | 0.452667i | \(0.149527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.67314 | −1.23852 | −0.619259 | − | 0.785186i | \(-0.712567\pi\) | ||||
−0.619259 | + | 0.785186i | \(0.712567\pi\) | |||||||
\(62\) | −15.1563 | −1.92486 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.597111 | 0.0746389 | ||||||||
\(65\) | 5.59329 | 0.693762 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.67729 | −0.449253 | −0.224626 | − | 0.974445i | \(-0.572116\pi\) | ||||
−0.224626 | + | 0.974445i | \(0.572116\pi\) | |||||||
\(68\) | −6.16082 | −0.747110 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 26.9954 | 3.22657 | ||||||||
\(71\) | −6.92649 | −0.822023 | −0.411012 | − | 0.911630i | \(-0.634824\pi\) | ||||
−0.411012 | + | 0.911630i | \(0.634824\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.36768 | 0.277116 | 0.138558 | − | 0.990354i | \(-0.455753\pi\) | ||||
0.138558 | + | 0.990354i | \(0.455753\pi\) | |||||||
\(74\) | −16.1699 | −1.87971 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.02925 | 0.691602 | ||||||||
\(77\) | 7.80001 | 0.888894 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.27816 | 0.706348 | 0.353174 | − | 0.935558i | \(-0.385102\pi\) | ||||
0.353174 | + | 0.935558i | \(0.385102\pi\) | |||||||
\(80\) | −18.0633 | −2.01954 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.4677 | −1.59769 | ||||||||
\(83\) | 2.57942 | 0.283128 | 0.141564 | − | 0.989929i | \(-0.454787\pi\) | ||||
0.141564 | + | 0.989929i | \(0.454787\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −21.3161 | −2.31205 | ||||||||
\(86\) | −4.36299 | −0.470473 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.03762 | −0.323812 | ||||||||
\(89\) | −8.45581 | −0.896314 | −0.448157 | − | 0.893955i | \(-0.647919\pi\) | ||||
−0.448157 | + | 0.893955i | \(0.647919\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.62517 | 0.694507 | ||||||||
\(92\) | 7.69309 | 0.802060 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.6014 | 1.09345 | ||||||||
\(95\) | 20.8608 | 2.14027 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.0935 | −1.12637 | −0.563187 | − | 0.826329i | \(-0.690425\pi\) | ||||
−0.563187 | + | 0.826329i | \(0.690425\pi\) | |||||||
\(98\) | 19.7617 | 1.99623 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.42084 | 0.842084 | ||||||||
\(101\) | 12.1254 | 1.20652 | 0.603259 | − | 0.797545i | \(-0.293869\pi\) | ||||
0.603259 | + | 0.797545i | \(0.293869\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8356 | −1.06767 | −0.533833 | − | 0.845590i | \(-0.679249\pi\) | ||||
−0.533833 | + | 0.845590i | \(0.679249\pi\) | |||||||
\(104\) | −2.58010 | −0.252999 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.59320 | 0.737517 | ||||||||
\(107\) | −15.7365 | −1.52130 | −0.760652 | − | 0.649160i | \(-0.775121\pi\) | ||||
−0.760652 | + | 0.649160i | \(0.775121\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.74111 | −0.741464 | −0.370732 | − | 0.928740i | \(-0.620893\pi\) | ||||
−0.370732 | + | 0.928740i | \(0.620893\pi\) | |||||||
\(110\) | 11.4902 | 1.09555 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −21.3957 | −2.02170 | ||||||||
\(113\) | 0.0433232 | 0.00407550 | 0.00203775 | − | 0.999998i | \(-0.499351\pi\) | ||||
0.00203775 | + | 0.999998i | \(0.499351\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.6176 | 2.48210 | ||||||||
\(116\) | 4.39526 | 0.408089 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 23.9016 | 2.20032 | ||||||||
\(119\) | −25.2486 | −2.31453 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.68004 | −0.698186 | ||||||||
\(122\) | −16.8783 | −1.52809 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.07327 | −0.814803 | ||||||||
\(125\) | 11.0651 | 0.989694 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.557420 | 0.0494630 | 0.0247315 | − | 0.999694i | \(-0.492127\pi\) | ||||
0.0247315 | + | 0.999694i | \(0.492127\pi\) | |||||||
\(128\) | 11.8151 | 1.04432 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.75954 | 0.855968 | ||||||||
\(131\) | 4.31192 | 0.376735 | 0.188367 | − | 0.982099i | \(-0.439680\pi\) | ||||
0.188367 | + | 0.982099i | \(0.439680\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 24.7093 | 2.14257 | ||||||||
\(134\) | −6.41638 | −0.554291 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.83276 | 0.843152 | ||||||||
\(137\) | 9.86688 | 0.842985 | 0.421492 | − | 0.906832i | \(-0.361506\pi\) | ||||
0.421492 | + | 0.906832i | \(0.361506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3673 | 0.964163 | 0.482082 | − | 0.876126i | \(-0.339881\pi\) | ||||
0.482082 | + | 0.876126i | \(0.339881\pi\) | |||||||
\(140\) | 16.1607 | 1.36583 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.0858 | −1.01422 | ||||||||
\(143\) | 2.81990 | 0.235812 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 15.2073 | 1.26290 | ||||||||
\(146\) | 4.13128 | 0.341907 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.68001 | −0.795692 | ||||||||
\(149\) | −14.2550 | −1.16781 | −0.583907 | − | 0.811821i | \(-0.698477\pi\) | ||||
−0.583907 | + | 0.811821i | \(0.698477\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5151 | 1.42536 | 0.712680 | − | 0.701489i | \(-0.247481\pi\) | ||||
0.712680 | + | 0.701489i | \(0.247481\pi\) | |||||||
\(152\) | −9.62276 | −0.780509 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.6100 | 1.09672 | ||||||||
\(155\) | −31.3929 | −2.52154 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.960703 | −0.0766725 | −0.0383362 | − | 0.999265i | \(-0.512206\pi\) | ||||
−0.0383362 | + | 0.999265i | \(0.512206\pi\) | |||||||
\(158\) | 10.9545 | 0.871497 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −19.4677 | −1.53906 | ||||||||
\(161\) | 31.5282 | 2.48477 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.10300 | −0.634676 | −0.317338 | − | 0.948313i | \(-0.602789\pi\) | ||||
−0.317338 | + | 0.948313i | \(0.602789\pi\) | |||||||
\(164\) | −8.66100 | −0.676311 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.50074 | 0.349325 | ||||||||
\(167\) | 12.7559 | 0.987083 | 0.493541 | − | 0.869722i | \(-0.335702\pi\) | ||||
0.493541 | + | 0.869722i | \(0.335702\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.6048 | −0.815756 | ||||||||
\(170\) | −37.1936 | −2.85262 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.61188 | −0.199154 | ||||||||
\(173\) | 6.36016 | 0.483554 | 0.241777 | − | 0.970332i | \(-0.422270\pi\) | ||||
0.241777 | + | 0.970332i | \(0.422270\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 34.5107 | 2.60876 | ||||||||
\(176\) | −9.10675 | −0.686447 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.7542 | −1.10588 | ||||||||
\(179\) | −15.6282 | −1.16811 | −0.584055 | − | 0.811714i | \(-0.698535\pi\) | ||||
−0.584055 | + | 0.811714i | \(0.698535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0567 | −0.896164 | −0.448082 | − | 0.893992i | \(-0.647893\pi\) | ||||
−0.448082 | + | 0.893992i | \(0.647893\pi\) | |||||||
\(182\) | 11.5600 | 0.856887 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.2783 | −0.905166 | ||||||||
\(185\) | −33.4922 | −2.46240 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.7467 | −0.785874 | ||||||||
\(188\) | 6.34648 | 0.462864 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 36.3993 | 2.64068 | ||||||||
\(191\) | 15.1622 | 1.09710 | 0.548550 | − | 0.836118i | \(-0.315180\pi\) | ||||
0.548550 | + | 0.836118i | \(0.315180\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.95522 | −0.500648 | −0.250324 | − | 0.968162i | \(-0.580537\pi\) | ||||
−0.250324 | + | 0.968162i | \(0.580537\pi\) | |||||||
\(194\) | −19.3567 | −1.38973 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.8302 | 0.845015 | ||||||||
\(197\) | 14.5377 | 1.03577 | 0.517884 | − | 0.855451i | \(-0.326720\pi\) | ||||
0.517884 | + | 0.855451i | \(0.326720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.94365 | −0.421334 | −0.210667 | − | 0.977558i | \(-0.567564\pi\) | ||||
−0.210667 | + | 0.977558i | \(0.567564\pi\) | |||||||
\(200\) | −13.4398 | −0.950336 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 21.1571 | 1.48861 | ||||||||
\(203\) | 18.0128 | 1.26425 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29.9665 | −2.09295 | ||||||||
\(206\) | −18.9067 | −1.31729 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7.73509 | −0.536332 | ||||||||
\(209\) | 10.5171 | 0.727486 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −27.1667 | −1.87024 | −0.935118 | − | 0.354337i | \(-0.884707\pi\) | ||||
−0.935118 | + | 0.354337i | \(0.884707\pi\) | |||||||
\(212\) | 4.54563 | 0.312195 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −27.4581 | −1.87699 | ||||||||
\(215\) | −9.03694 | −0.616314 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37.1845 | −2.52425 | ||||||||
\(218\) | −13.5072 | −0.914823 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.87854 | 0.463751 | ||||||||
\(221\) | −9.12800 | −0.614016 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.41548 | 0.228717 | 0.114359 | − | 0.993440i | \(-0.463519\pi\) | ||||
0.114359 | + | 0.993440i | \(0.463519\pi\) | |||||||
\(224\) | −23.0592 | −1.54071 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.0755931 | 0.00502838 | ||||||||
\(227\) | 22.1539 | 1.47041 | 0.735204 | − | 0.677846i | \(-0.237086\pi\) | ||||
0.735204 | + | 0.677846i | \(0.237086\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.65658 | 0.109470 | 0.0547350 | − | 0.998501i | \(-0.482569\pi\) | ||||
0.0547350 | + | 0.998501i | \(0.482569\pi\) | |||||||
\(230\) | 46.4441 | 3.06243 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.01489 | −0.460550 | ||||||||
\(233\) | −9.45846 | −0.619644 | −0.309822 | − | 0.950795i | \(-0.600269\pi\) | ||||
−0.309822 | + | 0.950795i | \(0.600269\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.9584 | 1.43241 | ||||||||
\(236\) | 14.3086 | 0.931408 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −44.0554 | −2.85568 | ||||||||
\(239\) | 20.2498 | 1.30985 | 0.654926 | − | 0.755693i | \(-0.272700\pi\) | ||||
0.654926 | + | 0.755693i | \(0.272700\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.5021 | 0.805328 | 0.402664 | − | 0.915348i | \(-0.368084\pi\) | ||||
0.402664 | + | 0.915348i | \(0.368084\pi\) | |||||||
\(242\) | −13.4006 | −0.861426 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.1041 | −0.646850 | ||||||||
\(245\) | 40.9318 | 2.61504 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.93305 | 0.568397 | ||||||||
\(248\) | 14.4811 | 0.919548 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.3071 | 1.22109 | ||||||||
\(251\) | −15.4087 | −0.972590 | −0.486295 | − | 0.873795i | \(-0.661652\pi\) | ||||
−0.486295 | + | 0.873795i | \(0.661652\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.4195 | 0.843675 | ||||||||
\(254\) | 0.972622 | 0.0610277 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 19.4216 | 1.21385 | ||||||||
\(257\) | 5.96426 | 0.372040 | 0.186020 | − | 0.982546i | \(-0.440441\pi\) | ||||
0.186020 | + | 0.982546i | \(0.440441\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −39.6710 | −2.46504 | ||||||||
\(260\) | 5.84250 | 0.362336 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.52373 | 0.464817 | ||||||||
\(263\) | −22.1233 | −1.36418 | −0.682089 | − | 0.731269i | \(-0.738928\pi\) | ||||
−0.682089 | + | 0.731269i | \(0.738928\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.7276 | 0.966138 | ||||||||
\(266\) | 43.1144 | 2.64352 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.84113 | −0.234635 | ||||||||
\(269\) | 8.96149 | 0.546391 | 0.273196 | − | 0.961958i | \(-0.411919\pi\) | ||||
0.273196 | + | 0.961958i | \(0.411919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.25602 | 0.137043 | 0.0685217 | − | 0.997650i | \(-0.478172\pi\) | ||||
0.0685217 | + | 0.997650i | \(0.478172\pi\) | |||||||
\(272\) | 29.4785 | 1.78740 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.2164 | 1.04008 | ||||||||
\(275\) | 14.6889 | 0.885777 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.2849 | −0.738128 | −0.369064 | − | 0.929404i | \(-0.620322\pi\) | ||||
−0.369064 | + | 0.929404i | \(0.620322\pi\) | |||||||
\(278\) | 19.8344 | 1.18959 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −25.7927 | −1.54141 | ||||||||
\(281\) | 31.3296 | 1.86897 | 0.934484 | − | 0.356005i | \(-0.115861\pi\) | ||||
0.934484 | + | 0.356005i | \(0.115861\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.8312 | 1.59495 | 0.797474 | − | 0.603353i | \(-0.206169\pi\) | ||||
0.797474 | + | 0.603353i | \(0.206169\pi\) | |||||||
\(284\) | −7.23510 | −0.429324 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.92035 | 0.290946 | ||||||||
\(287\) | −35.4949 | −2.09520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.7869 | 1.04629 | ||||||||
\(290\) | 26.5347 | 1.55817 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.47317 | 0.144731 | ||||||||
\(293\) | −8.91567 | −0.520859 | −0.260430 | − | 0.965493i | \(-0.583864\pi\) | ||||
−0.260430 | + | 0.965493i | \(0.583864\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 49.5067 | 2.88239 | ||||||||
\(296\) | 15.4494 | 0.897979 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.8730 | −1.44086 | ||||||||
\(299\) | 11.3982 | 0.659177 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.7041 | −0.616976 | ||||||||
\(302\) | 30.5615 | 1.75862 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −28.8489 | −1.65460 | ||||||||
\(305\) | −34.9596 | −2.00178 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.6821 | −1.18039 | −0.590195 | − | 0.807260i | \(-0.700949\pi\) | ||||
−0.590195 | + | 0.807260i | \(0.700949\pi\) | |||||||
\(308\) | 8.14754 | 0.464249 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −54.7764 | −3.11109 | ||||||||
\(311\) | −9.54165 | −0.541057 | −0.270529 | − | 0.962712i | \(-0.587198\pi\) | ||||
−0.270529 | + | 0.962712i | \(0.587198\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.8618 | −1.12265 | −0.561327 | − | 0.827594i | \(-0.689709\pi\) | ||||
−0.561327 | + | 0.827594i | \(0.689709\pi\) | |||||||
\(314\) | −1.67630 | −0.0945989 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.55788 | 0.368910 | ||||||||
\(317\) | 12.6386 | 0.709857 | 0.354929 | − | 0.934893i | \(-0.384505\pi\) | ||||
0.354929 | + | 0.934893i | \(0.384505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.66689 | 0.429263 | ||||||||
\(320\) | 2.15802 | 0.120637 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 55.0124 | 3.06572 | ||||||||
\(323\) | −34.0439 | −1.89425 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.4765 | 0.692071 | ||||||||
\(326\) | −14.1386 | −0.783067 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 13.8231 | 0.763252 | ||||||||
\(329\) | 26.0094 | 1.43395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.8621 | 0.981790 | 0.490895 | − | 0.871219i | \(-0.336670\pi\) | ||||
0.490895 | + | 0.871219i | \(0.336670\pi\) | |||||||
\(332\) | 2.69434 | 0.147871 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.2574 | 1.21787 | ||||||||
\(335\) | −13.2901 | −0.726114 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1406 | 0.606865 | 0.303432 | − | 0.952853i | \(-0.401867\pi\) | ||||
0.303432 | + | 0.952853i | \(0.401867\pi\) | |||||||
\(338\) | −18.5040 | −1.00648 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −22.2658 | −1.20753 | ||||||||
\(341\) | −15.8270 | −0.857080 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.5172 | 0.999836 | ||||||||
\(344\) | 4.16860 | 0.224756 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 11.0976 | 0.596612 | ||||||||
\(347\) | 0.533400 | 0.0286344 | 0.0143172 | − | 0.999898i | \(-0.495443\pi\) | ||||
0.0143172 | + | 0.999898i | \(0.495443\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6600 | 1.42708 | 0.713539 | − | 0.700616i | \(-0.247091\pi\) | ||||
0.713539 | + | 0.700616i | \(0.247091\pi\) | |||||||
\(350\) | 60.2165 | 3.21871 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −9.81481 | −0.523131 | ||||||||
\(353\) | 2.12890 | 0.113310 | 0.0566548 | − | 0.998394i | \(-0.481957\pi\) | ||||
0.0566548 | + | 0.998394i | \(0.481957\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.0330 | −1.32861 | ||||||||
\(356\) | −8.83255 | −0.468124 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −27.2692 | −1.44122 | ||||||||
\(359\) | −1.54866 | −0.0817353 | −0.0408677 | − | 0.999165i | \(-0.513012\pi\) | ||||
−0.0408677 | + | 0.999165i | \(0.513012\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.3168 | 0.753517 | ||||||||
\(362\) | −21.0372 | −1.10569 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 6.92036 | 0.362725 | ||||||||
\(365\) | 8.55700 | 0.447894 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.10473 | 0.423064 | 0.211532 | − | 0.977371i | \(-0.432155\pi\) | ||||
0.211532 | + | 0.977371i | \(0.432155\pi\) | |||||||
\(368\) | −36.8101 | −1.91886 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −58.4394 | −3.03812 | ||||||||
\(371\) | 18.6291 | 0.967175 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 36.4059 | 1.88503 | 0.942514 | − | 0.334167i | \(-0.108455\pi\) | ||||
0.942514 | + | 0.334167i | \(0.108455\pi\) | |||||||
\(374\) | −18.7515 | −0.969616 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.1291 | −0.522366 | ||||||||
\(377\) | 6.51210 | 0.335390 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.17841 | −0.0605309 | −0.0302655 | − | 0.999542i | \(-0.509635\pi\) | ||||
−0.0302655 | + | 0.999542i | \(0.509635\pi\) | |||||||
\(380\) | 21.7902 | 1.11782 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 26.4560 | 1.35361 | ||||||||
\(383\) | −3.86230 | −0.197355 | −0.0986773 | − | 0.995119i | \(-0.531461\pi\) | ||||
−0.0986773 | + | 0.995119i | \(0.531461\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 28.1900 | 1.43669 | ||||||||
\(386\) | −12.1359 | −0.617702 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −11.5878 | −0.588280 | ||||||||
\(389\) | 9.33318 | 0.473211 | 0.236605 | − | 0.971606i | \(-0.423965\pi\) | ||||
0.236605 | + | 0.971606i | \(0.423965\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −43.4387 | −2.19679 | ||||||||
\(392\) | −18.8812 | −0.953644 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.3663 | 1.27794 | ||||||||
\(395\) | 22.6898 | 1.14165 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.7948 | −1.49536 | −0.747680 | − | 0.664059i | \(-0.768832\pi\) | ||||
−0.747680 | + | 0.664059i | \(0.768832\pi\) | |||||||
\(398\) | −10.3709 | −0.519844 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −40.2923 | −2.01461 | ||||||||
\(401\) | −5.34757 | −0.267045 | −0.133522 | − | 0.991046i | \(-0.542629\pi\) | ||||
−0.133522 | + | 0.991046i | \(0.542629\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.4431 | −0.669650 | ||||||||
\(404\) | 12.6656 | 0.630137 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 31.4300 | 1.55984 | ||||||||
\(407\) | −16.8854 | −0.836977 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.05618 | −0.299459 | −0.149729 | − | 0.988727i | \(-0.547840\pi\) | ||||
−0.149729 | + | 0.988727i | \(0.547840\pi\) | |||||||
\(410\) | −52.2875 | −2.58230 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.3184 | −0.557617 | ||||||||
\(413\) | 58.6400 | 2.88549 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.32226 | 0.457612 | ||||||||
\(416\) | −8.33651 | −0.408731 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.3510 | 0.897577 | ||||||||
\(419\) | −8.84901 | −0.432303 | −0.216151 | − | 0.976360i | \(-0.569350\pi\) | ||||
−0.216151 | + | 0.976360i | \(0.569350\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.4589 | −0.899631 | −0.449816 | − | 0.893121i | \(-0.648510\pi\) | ||||
−0.449816 | + | 0.893121i | \(0.648510\pi\) | |||||||
\(422\) | −47.4023 | −2.30751 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.25489 | −0.352328 | ||||||||
\(425\) | −47.5480 | −2.30642 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −41.4092 | −2.00393 | ||||||||
\(428\) | −16.4376 | −0.794543 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.7682 | −0.760413 | ||||||||
\(431\) | −17.9207 | −0.863212 | −0.431606 | − | 0.902062i | \(-0.642053\pi\) | ||||
−0.431606 | + | 0.902062i | \(0.642053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −39.6184 | −1.90394 | −0.951969 | − | 0.306193i | \(-0.900945\pi\) | ||||
−0.951969 | + | 0.306193i | \(0.900945\pi\) | |||||||
\(434\) | −64.8819 | −3.11443 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.08602 | −0.387250 | ||||||||
\(437\) | 42.5110 | 2.03358 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0915 | 0.672553 | 0.336276 | − | 0.941763i | \(-0.390832\pi\) | ||||
0.336276 | + | 0.941763i | \(0.390832\pi\) | |||||||
\(440\) | −10.9782 | −0.523367 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −15.9271 | −0.757576 | ||||||||
\(443\) | 24.4089 | 1.15970 | 0.579850 | − | 0.814723i | \(-0.303111\pi\) | ||||
0.579850 | + | 0.814723i | \(0.303111\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.5601 | −1.44869 | ||||||||
\(446\) | 5.95955 | 0.282193 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.55614 | 0.120766 | ||||||||
\(449\) | −25.2207 | −1.19024 | −0.595120 | − | 0.803637i | \(-0.702895\pi\) | ||||
−0.595120 | + | 0.803637i | \(0.702895\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.1079 | −0.711401 | ||||||||
\(452\) | 0.0452534 | 0.00212854 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 38.6556 | 1.81420 | ||||||||
\(455\) | 23.9440 | 1.12251 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.5255 | 1.56826 | 0.784128 | − | 0.620599i | \(-0.213111\pi\) | ||||
0.784128 | + | 0.620599i | \(0.213111\pi\) | |||||||
\(458\) | 2.89051 | 0.135065 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 27.8035 | 1.29635 | ||||||||
\(461\) | −8.70385 | −0.405379 | −0.202689 | − | 0.979243i | \(-0.564968\pi\) | ||||
−0.202689 | + | 0.979243i | \(0.564968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.2456 | 0.754997 | 0.377498 | − | 0.926010i | \(-0.376784\pi\) | ||||
0.377498 | + | 0.926010i | \(0.376784\pi\) | |||||||
\(464\) | −21.0306 | −0.976319 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.5037 | −0.764521 | ||||||||
\(467\) | −13.7642 | −0.636932 | −0.318466 | − | 0.947934i | \(-0.603168\pi\) | ||||
−0.318466 | + | 0.947934i | \(0.603168\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.7419 | −0.726894 | ||||||||
\(470\) | 38.3144 | 1.76731 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −22.8367 | −1.05114 | ||||||||
\(473\) | −4.55605 | −0.209487 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 46.5325 | 2.13506 | ||||||||
\(476\) | −26.3735 | −1.20883 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 35.3332 | 1.61610 | ||||||||
\(479\) | −5.69599 | −0.260256 | −0.130128 | − | 0.991497i | \(-0.541539\pi\) | ||||
−0.130128 | + | 0.991497i | \(0.541539\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.3421 | −0.653943 | ||||||||
\(482\) | 21.8144 | 0.993619 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.02223 | −0.364647 | ||||||||
\(485\) | −40.0930 | −1.82053 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.3309 | 1.01191 | 0.505954 | − | 0.862560i | \(-0.331140\pi\) | ||||
0.505954 | + | 0.862560i | \(0.331140\pi\) | |||||||
\(488\) | 16.1263 | 0.730004 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 71.4204 | 3.22645 | ||||||||
\(491\) | −27.1853 | −1.22686 | −0.613429 | − | 0.789750i | \(-0.710210\pi\) | ||||
−0.613429 | + | 0.789750i | \(0.710210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.8177 | −1.11773 | ||||||||
\(494\) | 15.5870 | 0.701291 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 43.4140 | 1.94935 | ||||||||
\(497\) | −29.6512 | −1.33004 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.0533 | 0.852941 | 0.426470 | − | 0.904502i | \(-0.359757\pi\) | ||||
0.426470 | + | 0.904502i | \(0.359757\pi\) | |||||||
\(500\) | 11.5581 | 0.516895 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.8861 | −1.19999 | ||||||||
\(503\) | 8.63613 | 0.385066 | 0.192533 | − | 0.981290i | \(-0.438330\pi\) | ||||
0.192533 | + | 0.981290i | \(0.438330\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 43.8222 | 1.95006 | ||||||||
\(506\) | 23.4152 | 1.04093 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.582255 | 0.0258334 | ||||||||
\(509\) | −25.5400 | −1.13204 | −0.566020 | − | 0.824392i | \(-0.691517\pi\) | ||||
−0.566020 | + | 0.824392i | \(0.691517\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.1356 | 0.448375 | ||||||||
\(512\) | 10.2578 | 0.453334 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.4068 | 0.459025 | ||||||||
\(515\) | −39.1609 | −1.72564 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0705 | 0.486880 | ||||||||
\(518\) | −69.2206 | −3.04138 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.32470 | −0.408915 | ||||||||
\(521\) | 39.4866 | 1.72994 | 0.864970 | − | 0.501824i | \(-0.167337\pi\) | ||||
0.864970 | + | 0.501824i | \(0.167337\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.3341 | −0.757967 | −0.378984 | − | 0.925403i | \(-0.623726\pi\) | ||||
−0.378984 | + | 0.925403i | \(0.623726\pi\) | |||||||
\(524\) | 4.50404 | 0.196760 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −38.6021 | −1.68313 | ||||||||
\(527\) | 51.2319 | 2.23169 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.2424 | 1.35837 | ||||||||
\(530\) | 27.4425 | 1.19203 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 25.8102 | 1.11902 | ||||||||
\(533\) | −12.8323 | −0.555829 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −56.8731 | −2.45884 | ||||||||
\(536\) | 6.13050 | 0.264797 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.6366 | 0.674141 | ||||||||
\(539\) | 20.6361 | 0.888859 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.4300 | −1.13632 | −0.568158 | − | 0.822919i | \(-0.692344\pi\) | ||||
−0.568158 | + | 0.822919i | \(0.692344\pi\) | |||||||
\(542\) | 3.93645 | 0.169085 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 31.7705 | 1.36215 | ||||||||
\(545\) | −27.9771 | −1.19841 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | 10.3065 | 0.440272 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.6302 | 1.09288 | ||||||||
\(551\) | 24.2876 | 1.03469 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.8758 | 1.14288 | ||||||||
\(554\) | −21.4355 | −0.910706 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.8738 | 0.503561 | ||||||||
\(557\) | −1.27168 | −0.0538829 | −0.0269414 | − | 0.999637i | \(-0.508577\pi\) | ||||
−0.0269414 | + | 0.999637i | \(0.508577\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.86982 | −0.163676 | ||||||||
\(560\) | −77.3261 | −3.26762 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 54.6660 | 2.30594 | ||||||||
\(563\) | 3.96838 | 0.167247 | 0.0836237 | − | 0.996497i | \(-0.473351\pi\) | ||||
0.0836237 | + | 0.996497i | \(0.473351\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.156574 | 0.00658711 | ||||||||
\(566\) | 46.8168 | 1.96786 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.5473 | 0.484515 | ||||||||
\(569\) | −16.1671 | −0.677761 | −0.338881 | − | 0.940829i | \(-0.610048\pi\) | ||||
−0.338881 | + | 0.940829i | \(0.610048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9457 | 0.751005 | 0.375503 | − | 0.926821i | \(-0.377470\pi\) | ||||
0.375503 | + | 0.926821i | \(0.377470\pi\) | |||||||
\(572\) | 2.94554 | 0.123159 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −61.9338 | −2.58507 | ||||||||
\(575\) | 59.3737 | 2.47605 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.6268 | 0.692184 | 0.346092 | − | 0.938200i | \(-0.387508\pi\) | ||||
0.346092 | + | 0.938200i | \(0.387508\pi\) | |||||||
\(578\) | 31.0357 | 1.29091 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.8849 | 0.659583 | ||||||||
\(581\) | 11.0421 | 0.458103 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.92919 | 0.328394 | ||||||||
\(584\) | −3.94721 | −0.163337 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.5566 | −0.642639 | ||||||||
\(587\) | −33.9183 | −1.39996 | −0.699979 | − | 0.714163i | \(-0.746807\pi\) | ||||
−0.699979 | + | 0.714163i | \(0.746807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −50.1377 | −2.06589 | ||||||||
\(590\) | 86.3825 | 3.55631 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 46.3172 | 1.90362 | ||||||||
\(593\) | −23.7489 | −0.975252 | −0.487626 | − | 0.873053i | \(-0.662137\pi\) | ||||
−0.487626 | + | 0.873053i | \(0.662137\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −91.2506 | −3.74091 | ||||||||
\(596\) | −14.8901 | −0.609922 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.8884 | 0.813296 | ||||||||
\(599\) | −35.6788 | −1.45779 | −0.728897 | − | 0.684623i | \(-0.759967\pi\) | ||||
−0.728897 | + | 0.684623i | \(0.759967\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.46392 | −0.304460 | −0.152230 | − | 0.988345i | \(-0.548645\pi\) | ||||
−0.152230 | + | 0.988345i | \(0.548645\pi\) | |||||||
\(602\) | −18.6773 | −0.761229 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.2955 | 0.744433 | ||||||||
\(605\) | −27.7564 | −1.12846 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.18262 | −0.129179 | −0.0645893 | − | 0.997912i | \(-0.520574\pi\) | ||||
−0.0645893 | + | 0.997912i | \(0.520574\pi\) | |||||||
\(608\) | −31.0919 | −1.26094 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −60.9998 | −2.46981 | ||||||||
\(611\) | 9.40307 | 0.380407 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.7245 | −0.877446 | −0.438723 | − | 0.898622i | \(-0.644569\pi\) | ||||
−0.438723 | + | 0.898622i | \(0.644569\pi\) | |||||||
\(614\) | −36.0875 | −1.45637 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −13.0036 | −0.523929 | ||||||||
\(617\) | 6.04399 | 0.243322 | 0.121661 | − | 0.992572i | \(-0.461178\pi\) | ||||
0.121661 | + | 0.992572i | \(0.461178\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.9041 | −0.438272 | −0.219136 | − | 0.975694i | \(-0.570324\pi\) | ||||
−0.219136 | + | 0.975694i | \(0.570324\pi\) | |||||||
\(620\) | −32.7916 | −1.31694 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16.6489 | −0.667559 | ||||||||
\(623\) | −36.1980 | −1.45024 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.317943 | −0.0127177 | ||||||||
\(626\) | −34.6561 | −1.38514 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.00351 | −0.0400443 | ||||||||
\(629\) | 54.6578 | 2.17935 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.17161 | −0.245688 | −0.122844 | − | 0.992426i | \(-0.539201\pi\) | ||||
−0.122844 | + | 0.992426i | \(0.539201\pi\) | |||||||
\(632\) | −10.4665 | −0.416334 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.0527 | 0.875826 | ||||||||
\(635\) | 2.01457 | 0.0799456 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.5279 | 0.694480 | ||||||||
\(638\) | 13.3777 | 0.529628 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 42.7009 | 1.68790 | ||||||||
\(641\) | 4.63006 | 0.182876 | 0.0914382 | − | 0.995811i | \(-0.470854\pi\) | ||||
0.0914382 | + | 0.995811i | \(0.470854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.9357 | −1.02281 | −0.511403 | − | 0.859341i | \(-0.670874\pi\) | ||||
−0.511403 | + | 0.859341i | \(0.670874\pi\) | |||||||
\(644\) | 32.9329 | 1.29774 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −59.4020 | −2.33714 | ||||||||
\(647\) | 18.9502 | 0.745009 | 0.372505 | − | 0.928030i | \(-0.378499\pi\) | ||||
0.372505 | + | 0.928030i | \(0.378499\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.9592 | 0.979735 | ||||||||
\(650\) | 21.7698 | 0.853882 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.46403 | −0.331477 | ||||||||
\(653\) | 21.2753 | 0.832568 | 0.416284 | − | 0.909235i | \(-0.363332\pi\) | ||||
0.416284 | + | 0.909235i | \(0.363332\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.5837 | 0.608905 | ||||||||
\(656\) | 41.4414 | 1.61802 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 45.3829 | 1.76921 | ||||||||
\(659\) | −2.22303 | −0.0865968 | −0.0432984 | − | 0.999062i | \(-0.513787\pi\) | ||||
−0.0432984 | + | 0.999062i | \(0.513787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.9111 | −1.16341 | −0.581704 | − | 0.813401i | \(-0.697614\pi\) | ||||
−0.581704 | + | 0.813401i | \(0.697614\pi\) | |||||||
\(662\) | 31.1670 | 1.21134 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.30021 | −0.166881 | ||||||||
\(665\) | 89.3018 | 3.46297 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.9901 | 1.19994 | ||||||||
\(668\) | 13.3243 | 0.515531 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −23.1894 | −0.895884 | ||||||||
\(671\) | −17.6252 | −0.680413 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.14161 | −0.0825530 | −0.0412765 | − | 0.999148i | \(-0.513142\pi\) | ||||
−0.0412765 | + | 0.999148i | \(0.513142\pi\) | |||||||
\(674\) | 19.4388 | 0.748754 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0773 | −0.426051 | ||||||||
\(677\) | −46.7475 | −1.79665 | −0.898326 | − | 0.439329i | \(-0.855216\pi\) | ||||
−0.898326 | + | 0.439329i | \(0.855216\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −47.4895 | −1.82248 | ||||||||
\(680\) | 35.5365 | 1.36276 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.6160 | −1.05747 | ||||||||
\(683\) | −43.9641 | −1.68224 | −0.841119 | − | 0.540850i | \(-0.818103\pi\) | ||||
−0.841119 | + | 0.540850i | \(0.818103\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.6598 | 1.36249 | ||||||||
\(686\) | 32.3101 | 1.23360 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.4974 | 0.476459 | ||||||||
\(689\) | 6.73490 | 0.256579 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.2320 | 0.541412 | 0.270706 | − | 0.962662i | \(-0.412743\pi\) | ||||
0.270706 | + | 0.962662i | \(0.412743\pi\) | |||||||
\(692\) | 6.64354 | 0.252549 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.930711 | 0.0353293 | ||||||||
\(695\) | 41.0825 | 1.55835 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.9040 | 1.85237 | ||||||||
\(698\) | 46.5181 | 1.76074 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 36.0483 | 1.36250 | ||||||||
\(701\) | −25.9017 | −0.978293 | −0.489147 | − | 0.872202i | \(-0.662692\pi\) | ||||
−0.489147 | + | 0.872202i | \(0.662692\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −53.4904 | −2.01743 | ||||||||
\(704\) | 1.08798 | 0.0410048 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.71464 | 0.139802 | ||||||||
\(707\) | 51.9067 | 1.95215 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.1752 | 1.09570 | 0.547849 | − | 0.836577i | \(-0.315447\pi\) | ||||
0.547849 | + | 0.836577i | \(0.315447\pi\) | |||||||
\(710\) | −43.6792 | −1.63925 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.0969 | 0.528303 | ||||||||
\(713\) | −63.9738 | −2.39584 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.1914 | 0.381136 | ||||||||
\(716\) | −16.3246 | −0.610077 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.70221 | −0.100846 | ||||||||
\(719\) | 29.1591 | 1.08745 | 0.543725 | − | 0.839263i | \(-0.317013\pi\) | ||||
0.543725 | + | 0.839263i | \(0.317013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46.3856 | −1.72749 | ||||||||
\(722\) | 24.9809 | 0.929694 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.5938 | −0.468046 | ||||||||
\(725\) | 33.9217 | 1.25982 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.6294 | −0.913456 | −0.456728 | − | 0.889606i | \(-0.650979\pi\) | ||||
−0.456728 | + | 0.889606i | \(0.650979\pi\) | |||||||
\(728\) | −11.0450 | −0.409354 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.9308 | 0.552614 | ||||||||
\(731\) | 14.7479 | 0.545471 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.1022 | −0.816362 | −0.408181 | − | 0.912901i | \(-0.633837\pi\) | ||||
−0.408181 | + | 0.912901i | \(0.633837\pi\) | |||||||
\(734\) | 14.1417 | 0.521978 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −39.6721 | −1.46233 | ||||||||
\(737\) | −6.70030 | −0.246809 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.16477 | −0.337131 | −0.168566 | − | 0.985690i | \(-0.553914\pi\) | ||||
−0.168566 | + | 0.985690i | \(0.553914\pi\) | |||||||
\(740\) | −34.9844 | −1.28605 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 32.5053 | 1.19331 | ||||||||
\(743\) | −32.0802 | −1.17691 | −0.588454 | − | 0.808531i | \(-0.700263\pi\) | ||||
−0.588454 | + | 0.808531i | \(0.700263\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −51.5188 | −1.88750 | ||||||||
\(746\) | 63.5234 | 2.32576 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −11.2255 | −0.410444 | ||||||||
\(749\) | −67.3654 | −2.46148 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.3094 | −0.704611 | −0.352305 | − | 0.935885i | \(-0.614602\pi\) | ||||
−0.352305 | + | 0.935885i | \(0.614602\pi\) | |||||||
\(752\) | −30.3668 | −1.10736 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.3627 | 0.413807 | ||||||||
\(755\) | 63.3012 | 2.30377 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.52491 | 0.346189 | 0.173094 | − | 0.984905i | \(-0.444623\pi\) | ||||
0.173094 | + | 0.984905i | \(0.444623\pi\) | |||||||
\(758\) | −2.05617 | −0.0746834 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −34.7775 | −1.26151 | ||||||||
\(761\) | −26.1744 | −0.948823 | −0.474411 | − | 0.880303i | \(-0.657339\pi\) | ||||
−0.474411 | + | 0.880303i | \(0.657339\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.1385 | −1.19969 | ||||||||
\(764\) | 15.8378 | 0.572991 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.73920 | −0.243497 | ||||||||
\(767\) | 21.1999 | 0.765483 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.8856 | 1.04164 | 0.520820 | − | 0.853666i | \(-0.325626\pi\) | ||||
0.520820 | + | 0.853666i | \(0.325626\pi\) | |||||||
\(770\) | 49.1877 | 1.77260 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.26511 | −0.261477 | ||||||||
\(773\) | 4.07993 | 0.146745 | 0.0733725 | − | 0.997305i | \(-0.476624\pi\) | ||||
0.0733725 | + | 0.997305i | \(0.476624\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −70.0256 | −2.51539 | ||||||||
\(776\) | 18.4942 | 0.663905 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.2851 | 0.583851 | ||||||||
\(779\) | −47.8596 | −1.71475 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6206 | −0.451600 | ||||||||
\(782\) | −75.7947 | −2.71041 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −56.6055 | −2.02163 | ||||||||
\(785\) | −3.47207 | −0.123923 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.4800 | −0.409219 | −0.204609 | − | 0.978844i | \(-0.565592\pi\) | ||||
−0.204609 | + | 0.978844i | \(0.565592\pi\) | |||||||
\(788\) | 15.1854 | 0.540958 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 39.5907 | 1.40857 | ||||||||
\(791\) | 0.185460 | 0.00659418 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.9705 | −0.531617 | ||||||||
\(794\) | −51.9880 | −1.84498 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.20846 | −0.220053 | ||||||||
\(797\) | 22.6786 | 0.803316 | 0.401658 | − | 0.915790i | \(-0.368434\pi\) | ||||
0.401658 | + | 0.915790i | \(0.368434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.8351 | −1.26776 | ||||||||
\(800\) | −43.4251 | −1.53531 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.33079 | −0.329482 | ||||||||
\(803\) | 4.31408 | 0.152241 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 113.946 | 4.01606 | ||||||||
\(806\) | −23.4565 | −0.826219 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −20.2145 | −0.711142 | ||||||||
\(809\) | 8.43197 | 0.296452 | 0.148226 | − | 0.988953i | \(-0.452644\pi\) | ||||
0.148226 | + | 0.988953i | \(0.452644\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.0503 | −0.879637 | −0.439818 | − | 0.898087i | \(-0.644957\pi\) | ||||
−0.439818 | + | 0.898087i | \(0.644957\pi\) | |||||||
\(812\) | 18.8154 | 0.660291 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −29.4627 | −1.03267 | ||||||||
\(815\) | −29.2850 | −1.02581 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.4329 | −0.504944 | ||||||||
\(818\) | −10.5672 | −0.369474 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −31.3017 | −1.09310 | ||||||||
\(821\) | −3.90486 | −0.136280 | −0.0681402 | − | 0.997676i | \(-0.521707\pi\) | ||||
−0.0681402 | + | 0.997676i | \(0.521707\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.1872 | −0.668825 | −0.334412 | − | 0.942427i | \(-0.608538\pi\) | ||||
−0.334412 | + | 0.942427i | \(0.608538\pi\) | |||||||
\(824\) | 18.0643 | 0.629300 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 102.319 | 3.56013 | ||||||||
\(827\) | 32.9961 | 1.14739 | 0.573694 | − | 0.819070i | \(-0.305510\pi\) | ||||
0.573694 | + | 0.819070i | \(0.305510\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.64456 | −0.334969 | −0.167485 | − | 0.985875i | \(-0.553564\pi\) | ||||
−0.167485 | + | 0.985875i | \(0.553564\pi\) | |||||||
\(830\) | 16.2661 | 0.564604 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.924109 | 0.0320377 | ||||||||
\(833\) | −66.7989 | −2.31444 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 46.1011 | 1.59539 | ||||||||
\(836\) | 10.9857 | 0.379950 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15.4403 | −0.533378 | ||||||||
\(839\) | −49.6031 | −1.71249 | −0.856244 | − | 0.516572i | \(-0.827208\pi\) | ||||
−0.856244 | + | 0.516572i | \(0.827208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.2946 | −0.389468 | ||||||||
\(842\) | −32.2083 | −1.10997 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −28.3771 | −0.976782 | ||||||||
\(845\) | −38.3268 | −1.31848 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −32.8771 | −1.12967 | ||||||||
\(848\) | −21.7501 | −0.746900 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −82.9648 | −2.84567 | ||||||||
\(851\) | −68.2518 | −2.33964 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.9174 | 0.613480 | 0.306740 | − | 0.951793i | \(-0.400762\pi\) | ||||
0.306740 | + | 0.951793i | \(0.400762\pi\) | |||||||
\(854\) | −72.2535 | −2.47246 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 26.2347 | 0.896683 | ||||||||
\(857\) | 2.42086 | 0.0826950 | 0.0413475 | − | 0.999145i | \(-0.486835\pi\) | ||||
0.0413475 | + | 0.999145i | \(0.486835\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.6676 | −0.568692 | −0.284346 | − | 0.958722i | \(-0.591776\pi\) | ||||
−0.284346 | + | 0.958722i | \(0.591776\pi\) | |||||||
\(860\) | −9.43958 | −0.321887 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −31.2693 | −1.06504 | ||||||||
\(863\) | −34.8647 | −1.18681 | −0.593404 | − | 0.804905i | \(-0.702216\pi\) | ||||
−0.593404 | + | 0.804905i | \(0.702216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.9862 | 0.781554 | ||||||||
\(866\) | −69.1288 | −2.34909 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −38.8412 | −1.31836 | ||||||||
\(869\) | 11.4393 | 0.388051 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.69110 | −0.192836 | ||||||||
\(872\) | 12.9054 | 0.437032 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 74.1760 | 2.50904 | ||||||||
\(875\) | 47.3680 | 1.60133 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.48932 | −0.219129 | −0.109564 | − | 0.993980i | \(-0.534946\pi\) | ||||
−0.109564 | + | 0.993980i | \(0.534946\pi\) | |||||||
\(878\) | 24.5879 | 0.829800 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −32.9126 | −1.10949 | ||||||||
\(881\) | 57.2243 | 1.92794 | 0.963968 | − | 0.266020i | \(-0.0857087\pi\) | ||||
0.963968 | + | 0.266020i | \(0.0857087\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.1168 | −0.811595 | −0.405797 | − | 0.913963i | \(-0.633006\pi\) | ||||
−0.405797 | + | 0.913963i | \(0.633006\pi\) | |||||||
\(884\) | −9.53470 | −0.320687 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.5902 | 1.43084 | ||||||||
\(887\) | −42.1176 | −1.41417 | −0.707086 | − | 0.707128i | \(-0.749990\pi\) | ||||
−0.707086 | + | 0.707128i | \(0.749990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.38622 | 0.0800314 | ||||||||
\(890\) | −53.3232 | −1.78740 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.56765 | 0.119454 | ||||||||
\(893\) | 35.0698 | 1.17357 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56.4819 | −1.88798 | ||||||||
\(896\) | 50.5786 | 1.68971 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −44.0068 | −1.46852 | ||||||||
\(899\) | −36.5499 | −1.21901 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.6667 | −0.855083 | ||||||||
\(902\) | −26.3612 | −0.877731 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.0722250 | −0.00240217 | ||||||||
\(905\) | −43.5739 | −1.44844 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.8210 | 0.857371 | 0.428686 | − | 0.903454i | \(-0.358977\pi\) | ||||
0.428686 | + | 0.903454i | \(0.358977\pi\) | |||||||
\(908\) | 23.1410 | 0.767960 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41.7790 | 1.38496 | ||||||||
\(911\) | 20.3911 | 0.675587 | 0.337794 | − | 0.941220i | \(-0.390319\pi\) | ||||
0.337794 | + | 0.941220i | \(0.390319\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.69989 | 0.155544 | ||||||||
\(914\) | 58.4974 | 1.93492 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.73039 | 0.0571737 | ||||||||
\(917\) | 18.4587 | 0.609559 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.0410 | −0.760054 | −0.380027 | − | 0.924975i | \(-0.624085\pi\) | ||||
−0.380027 | + | 0.924975i | \(0.624085\pi\) | |||||||
\(920\) | −44.3748 | −1.46299 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.1870 | −0.500159 | ||||||||
\(923\) | −10.7197 | −0.352842 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −74.7083 | −2.45639 | ||||||||
\(926\) | 28.3464 | 0.931520 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −22.6657 | −0.744038 | ||||||||
\(929\) | 24.2154 | 0.794483 | 0.397241 | − | 0.917714i | \(-0.369968\pi\) | ||||
0.397241 | + | 0.917714i | \(0.369968\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 65.3722 | 2.14249 | ||||||||
\(932\) | −9.87987 | −0.323626 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.0167 | −0.785850 | ||||||||
\(935\) | −38.8394 | −1.27019 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.7273 | 0.938479 | 0.469239 | − | 0.883071i | \(-0.344528\pi\) | ||||
0.469239 | + | 0.883071i | \(0.344528\pi\) | |||||||
\(938\) | −27.4675 | −0.896846 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 22.9367 | 0.748114 | ||||||||
\(941\) | 36.9396 | 1.20420 | 0.602098 | − | 0.798422i | \(-0.294331\pi\) | ||||
0.602098 | + | 0.798422i | \(0.294331\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.0670 | −1.98861 | ||||||||
\(944\) | −68.4640 | −2.22831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.94969 | −0.258467 | ||||||||
\(947\) | 56.3251 | 1.83032 | 0.915160 | − | 0.403090i | \(-0.132064\pi\) | ||||
0.915160 | + | 0.403090i | \(0.132064\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.66430 | 0.118948 | ||||||||
\(950\) | 81.1929 | 2.63425 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 42.0925 | 1.36423 | ||||||||
\(953\) | 10.9066 | 0.353298 | 0.176649 | − | 0.984274i | \(-0.443474\pi\) | ||||
0.176649 | + | 0.984274i | \(0.443474\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 54.7977 | 1.77321 | ||||||||
\(956\) | 21.1520 | 0.684106 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.93873 | −0.321106 | ||||||||
\(959\) | 42.2386 | 1.36395 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.4510 | 1.43390 | ||||||||
\(962\) | −25.0250 | −0.806839 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.0591 | 0.420605 | ||||||||
\(965\) | −25.1368 | −0.809182 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0179 | 0.515100 | 0.257550 | − | 0.966265i | \(-0.417085\pi\) | ||||
0.257550 | + | 0.966265i | \(0.417085\pi\) | |||||||
\(968\) | 12.8036 | 0.411523 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −69.9568 | −2.24618 | ||||||||
\(971\) | −24.3509 | −0.781457 | −0.390728 | − | 0.920506i | \(-0.627777\pi\) | ||||
−0.390728 | + | 0.920506i | \(0.627777\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.6617 | 1.56002 | ||||||||
\(974\) | 38.9644 | 1.24850 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 48.3465 | 1.54753 | ||||||||
\(977\) | 9.25929 | 0.296231 | 0.148115 | − | 0.988970i | \(-0.452679\pi\) | ||||
0.148115 | + | 0.988970i | \(0.452679\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.4071 | −0.492413 | ||||||||
\(980\) | 42.7555 | 1.36577 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −47.4348 | −1.51370 | ||||||||
\(983\) | 50.2659 | 1.60323 | 0.801617 | − | 0.597839i | \(-0.203974\pi\) | ||||
0.801617 | + | 0.597839i | \(0.203974\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.5405 | 1.67408 | ||||||||
\(986\) | −43.3035 | −1.37906 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.33106 | 0.296861 | ||||||||
\(989\) | −18.4159 | −0.585590 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.3702 | −1.18711 | −0.593553 | − | 0.804795i | \(-0.702275\pi\) | ||||
−0.593553 | + | 0.804795i | \(0.702275\pi\) | |||||||
\(992\) | 46.7895 | 1.48557 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −51.7374 | −1.64101 | ||||||||
\(995\) | −21.4809 | −0.680990 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.1667 | −1.20875 | −0.604375 | − | 0.796700i | \(-0.706577\pi\) | ||||
−0.604375 | + | 0.796700i | \(0.706577\pi\) | |||||||
\(998\) | 33.2454 | 1.05236 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4923.2.a.l.1.14 | 18 | ||
3.2 | odd | 2 | 547.2.a.b.1.5 | ✓ | 18 | ||
12.11 | even | 2 | 8752.2.a.s.1.12 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.b.1.5 | ✓ | 18 | 3.2 | odd | 2 | ||
4923.2.a.l.1.14 | 18 | 1.1 | even | 1 | trivial | ||
8752.2.a.s.1.12 | 18 | 12.11 | even | 2 |