Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 21 x^{10} + 116 x^{9} + 106 x^{8} - 774 x^{7} - 63 x^{6} + 2013 x^{5} - 417 x^{4} + \cdots - 375 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.17050\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.17050 | 0.523463 | 0.261732 | − | 0.965141i | \(-0.415706\pi\) | ||||
0.261732 | + | 0.965141i | \(0.415706\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.506529 | 0.191450 | 0.0957249 | − | 0.995408i | \(-0.469483\pi\) | ||||
0.0957249 | + | 0.995408i | \(0.469483\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.17050 | 0.370144 | ||||||||
\(11\) | 3.88070 | 1.17008 | 0.585038 | − | 0.811006i | \(-0.301080\pi\) | ||||
0.585038 | + | 0.811006i | \(0.301080\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.61369 | −1.00226 | −0.501129 | − | 0.865372i | \(-0.667082\pi\) | ||||
−0.501129 | + | 0.865372i | \(0.667082\pi\) | |||||||
\(14\) | 0.506529 | 0.135375 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.95227 | −1.68617 | −0.843087 | − | 0.537777i | \(-0.819264\pi\) | ||||
−0.843087 | + | 0.537777i | \(0.819264\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.33695 | −0.536133 | −0.268066 | − | 0.963400i | \(-0.586385\pi\) | ||||
−0.268066 | + | 0.963400i | \(0.586385\pi\) | |||||||
\(20\) | 1.17050 | 0.261732 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.88070 | 0.827369 | ||||||||
\(23\) | 1.72649 | 0.359997 | 0.179999 | − | 0.983667i | \(-0.442391\pi\) | ||||
0.179999 | + | 0.983667i | \(0.442391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.62993 | −0.725986 | ||||||||
\(26\) | −3.61369 | −0.708704 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.506529 | 0.0957249 | ||||||||
\(29\) | −4.21919 | −0.783483 | −0.391742 | − | 0.920075i | \(-0.628127\pi\) | ||||
−0.391742 | + | 0.920075i | \(0.628127\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.29279 | −0.591403 | −0.295702 | − | 0.955280i | \(-0.595553\pi\) | ||||
−0.295702 | + | 0.955280i | \(0.595553\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.95227 | −1.19231 | ||||||||
\(35\) | 0.592892 | 0.100217 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.04259 | −1.15779 | −0.578897 | − | 0.815400i | \(-0.696517\pi\) | ||||
−0.578897 | + | 0.815400i | \(0.696517\pi\) | |||||||
\(38\) | −2.33695 | −0.379103 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.17050 | 0.185072 | ||||||||
\(41\) | −10.5485 | −1.64740 | −0.823700 | − | 0.567026i | \(-0.808094\pi\) | ||||
−0.823700 | + | 0.567026i | \(0.808094\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.84084 | −1.04322 | −0.521609 | − | 0.853184i | \(-0.674668\pi\) | ||||
−0.521609 | + | 0.853184i | \(0.674668\pi\) | |||||||
\(44\) | 3.88070 | 0.585038 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.72649 | 0.254557 | ||||||||
\(47\) | 4.17683 | 0.609253 | 0.304627 | − | 0.952472i | \(-0.401468\pi\) | ||||
0.304627 | + | 0.952472i | \(0.401468\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.74343 | −0.963347 | ||||||||
\(50\) | −3.62993 | −0.513350 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.61369 | −0.501129 | ||||||||
\(53\) | −12.8841 | −1.76976 | −0.884880 | − | 0.465819i | \(-0.845760\pi\) | ||||
−0.884880 | + | 0.465819i | \(0.845760\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.54236 | 0.612492 | ||||||||
\(56\) | 0.506529 | 0.0676877 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.21919 | −0.554006 | ||||||||
\(59\) | 7.05273 | 0.918188 | 0.459094 | − | 0.888388i | \(-0.348174\pi\) | ||||
0.459094 | + | 0.888388i | \(0.348174\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.2400 | 1.43913 | 0.719566 | − | 0.694424i | \(-0.244341\pi\) | ||||
0.719566 | + | 0.694424i | \(0.244341\pi\) | |||||||
\(62\) | −3.29279 | −0.418185 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.22983 | −0.524646 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00991 | −0.612058 | −0.306029 | − | 0.952022i | \(-0.599000\pi\) | ||||
−0.306029 | + | 0.952022i | \(0.599000\pi\) | |||||||
\(68\) | −6.95227 | −0.843087 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.592892 | 0.0708641 | ||||||||
\(71\) | 0.923816 | 0.109637 | 0.0548184 | − | 0.998496i | \(-0.482542\pi\) | ||||
0.0548184 | + | 0.998496i | \(0.482542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.46929 | 0.289009 | 0.144505 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144505 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(74\) | −7.04259 | −0.818685 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.33695 | −0.268066 | ||||||||
\(77\) | 1.96569 | 0.224011 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.80783 | −0.878450 | −0.439225 | − | 0.898377i | \(-0.644747\pi\) | ||||
−0.439225 | + | 0.898377i | \(0.644747\pi\) | |||||||
\(80\) | 1.17050 | 0.130866 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.5485 | −1.16489 | ||||||||
\(83\) | 8.00835 | 0.879030 | 0.439515 | − | 0.898235i | \(-0.355150\pi\) | ||||
0.439515 | + | 0.898235i | \(0.355150\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.13763 | −0.882650 | ||||||||
\(86\) | −6.84084 | −0.737667 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.88070 | 0.413684 | ||||||||
\(89\) | −15.6581 | −1.65975 | −0.829877 | − | 0.557946i | \(-0.811590\pi\) | ||||
−0.829877 | + | 0.557946i | \(0.811590\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.83044 | −0.191882 | ||||||||
\(92\) | 1.72649 | 0.179999 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.17683 | 0.430807 | ||||||||
\(95\) | −2.73540 | −0.280646 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.02168 | 0.103736 | 0.0518681 | − | 0.998654i | \(-0.483482\pi\) | ||||
0.0518681 | + | 0.998654i | \(0.483482\pi\) | |||||||
\(98\) | −6.74343 | −0.681189 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.62993 | −0.362993 | ||||||||
\(101\) | 4.32214 | 0.430069 | 0.215035 | − | 0.976606i | \(-0.431014\pi\) | ||||
0.215035 | + | 0.976606i | \(0.431014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.94103 | 0.683920 | 0.341960 | − | 0.939715i | \(-0.388909\pi\) | ||||
0.341960 | + | 0.939715i | \(0.388909\pi\) | |||||||
\(104\) | −3.61369 | −0.354352 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −12.8841 | −1.25141 | ||||||||
\(107\) | 14.3087 | 1.38327 | 0.691636 | − | 0.722246i | \(-0.256890\pi\) | ||||
0.691636 | + | 0.722246i | \(0.256890\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.75669 | −0.742957 | −0.371478 | − | 0.928442i | \(-0.621149\pi\) | ||||
−0.371478 | + | 0.928442i | \(0.621149\pi\) | |||||||
\(110\) | 4.54236 | 0.433097 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.506529 | 0.0478625 | ||||||||
\(113\) | 1.71654 | 0.161479 | 0.0807393 | − | 0.996735i | \(-0.474272\pi\) | ||||
0.0807393 | + | 0.996735i | \(0.474272\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.02085 | 0.188445 | ||||||||
\(116\) | −4.21919 | −0.391742 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.05273 | 0.649257 | ||||||||
\(119\) | −3.52153 | −0.322818 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.05985 | 0.369077 | ||||||||
\(122\) | 11.2400 | 1.01762 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.29279 | −0.295702 | ||||||||
\(125\) | −10.1013 | −0.903490 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.86129 | 0.342634 | 0.171317 | − | 0.985216i | \(-0.445198\pi\) | ||||
0.171317 | + | 0.985216i | \(0.445198\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.22983 | −0.370980 | ||||||||
\(131\) | 7.45036 | 0.650941 | 0.325470 | − | 0.945552i | \(-0.394477\pi\) | ||||
0.325470 | + | 0.945552i | \(0.394477\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.18373 | −0.102642 | ||||||||
\(134\) | −5.00991 | −0.432790 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.95227 | −0.596153 | ||||||||
\(137\) | 11.7309 | 1.00223 | 0.501117 | − | 0.865379i | \(-0.332923\pi\) | ||||
0.501117 | + | 0.865379i | \(0.332923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.614537 | −0.0521244 | −0.0260622 | − | 0.999660i | \(-0.508297\pi\) | ||||
−0.0260622 | + | 0.999660i | \(0.508297\pi\) | |||||||
\(140\) | 0.592892 | 0.0501085 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.923816 | 0.0775249 | ||||||||
\(143\) | −14.0237 | −1.17272 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.93855 | −0.410125 | ||||||||
\(146\) | 2.46929 | 0.204360 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.04259 | −0.578897 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.5323 | 1.42676 | 0.713378 | − | 0.700779i | \(-0.247164\pi\) | ||||
0.713378 | + | 0.700779i | \(0.247164\pi\) | |||||||
\(152\) | −2.33695 | −0.189551 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.96569 | 0.158400 | ||||||||
\(155\) | −3.85422 | −0.309578 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.2770 | 1.77790 | 0.888950 | − | 0.458005i | \(-0.151436\pi\) | ||||
0.888950 | + | 0.458005i | \(0.151436\pi\) | |||||||
\(158\) | −7.80783 | −0.621158 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.17050 | 0.0925361 | ||||||||
\(161\) | 0.874515 | 0.0689214 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4831 | 1.05608 | 0.528038 | − | 0.849221i | \(-0.322928\pi\) | ||||
0.528038 | + | 0.849221i | \(0.322928\pi\) | |||||||
\(164\) | −10.5485 | −0.823700 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.00835 | 0.621568 | ||||||||
\(167\) | −12.6208 | −0.976625 | −0.488313 | − | 0.872669i | \(-0.662387\pi\) | ||||
−0.488313 | + | 0.872669i | \(0.662387\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.0587896 | 0.00452227 | ||||||||
\(170\) | −8.13763 | −0.624128 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.84084 | −0.521609 | ||||||||
\(173\) | −13.5303 | −1.02869 | −0.514346 | − | 0.857583i | \(-0.671965\pi\) | ||||
−0.514346 | + | 0.857583i | \(0.671965\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.83866 | −0.138990 | ||||||||
\(176\) | 3.88070 | 0.292519 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.6581 | −1.17362 | ||||||||
\(179\) | 7.23353 | 0.540659 | 0.270330 | − | 0.962768i | \(-0.412867\pi\) | ||||
0.270330 | + | 0.962768i | \(0.412867\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.30723 | 0.245824 | 0.122912 | − | 0.992418i | \(-0.460777\pi\) | ||||
0.122912 | + | 0.992418i | \(0.460777\pi\) | |||||||
\(182\) | −1.83044 | −0.135681 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.72649 | 0.127278 | ||||||||
\(185\) | −8.24335 | −0.606063 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.9797 | −1.97295 | ||||||||
\(188\) | 4.17683 | 0.304627 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.73540 | −0.198446 | ||||||||
\(191\) | −12.7158 | −0.920083 | −0.460042 | − | 0.887897i | \(-0.652165\pi\) | ||||
−0.460042 | + | 0.887897i | \(0.652165\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.36901 | −0.242507 | −0.121253 | − | 0.992622i | \(-0.538691\pi\) | ||||
−0.121253 | + | 0.992622i | \(0.538691\pi\) | |||||||
\(194\) | 1.02168 | 0.0733526 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.74343 | −0.481673 | ||||||||
\(197\) | 0.815685 | 0.0581151 | 0.0290576 | − | 0.999578i | \(-0.490749\pi\) | ||||
0.0290576 | + | 0.999578i | \(0.490749\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.35685 | 0.379737 | 0.189868 | − | 0.981810i | \(-0.439194\pi\) | ||||
0.189868 | + | 0.981810i | \(0.439194\pi\) | |||||||
\(200\) | −3.62993 | −0.256675 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.32214 | 0.304105 | ||||||||
\(203\) | −2.13714 | −0.149998 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.3470 | −0.862353 | ||||||||
\(206\) | 6.94103 | 0.483604 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.61369 | −0.250565 | ||||||||
\(209\) | −9.06900 | −0.627316 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.3550 | 0.919398 | 0.459699 | − | 0.888075i | \(-0.347957\pi\) | ||||
0.459699 | + | 0.888075i | \(0.347957\pi\) | |||||||
\(212\) | −12.8841 | −0.884880 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.3087 | 0.978122 | ||||||||
\(215\) | −8.00720 | −0.546087 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.66790 | −0.113224 | ||||||||
\(218\) | −7.75669 | −0.525350 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.54236 | 0.306246 | ||||||||
\(221\) | 25.1234 | 1.68998 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7279 | 1.25411 | 0.627057 | − | 0.778974i | \(-0.284259\pi\) | ||||
0.627057 | + | 0.778974i | \(0.284259\pi\) | |||||||
\(224\) | 0.506529 | 0.0338439 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.71654 | 0.114183 | ||||||||
\(227\) | −8.54460 | −0.567125 | −0.283562 | − | 0.958954i | \(-0.591516\pi\) | ||||
−0.283562 | + | 0.958954i | \(0.591516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.34208 | −0.353015 | −0.176507 | − | 0.984299i | \(-0.556480\pi\) | ||||
−0.176507 | + | 0.984299i | \(0.556480\pi\) | |||||||
\(230\) | 2.02085 | 0.133251 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.21919 | −0.277003 | ||||||||
\(233\) | −14.8123 | −0.970387 | −0.485194 | − | 0.874407i | \(-0.661251\pi\) | ||||
−0.485194 | + | 0.874407i | \(0.661251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.88898 | 0.318922 | ||||||||
\(236\) | 7.05273 | 0.459094 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.52153 | −0.228267 | ||||||||
\(239\) | −6.91374 | −0.447212 | −0.223606 | − | 0.974680i | \(-0.571783\pi\) | ||||
−0.223606 | + | 0.974680i | \(0.571783\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.56369 | 0.551636 | 0.275818 | − | 0.961210i | \(-0.411051\pi\) | ||||
0.275818 | + | 0.961210i | \(0.411051\pi\) | |||||||
\(242\) | 4.05985 | 0.260977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.2400 | 0.719566 | ||||||||
\(245\) | −7.89318 | −0.504277 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.44501 | 0.537343 | ||||||||
\(248\) | −3.29279 | −0.209093 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.1013 | −0.638864 | ||||||||
\(251\) | −16.1199 | −1.01748 | −0.508741 | − | 0.860920i | \(-0.669889\pi\) | ||||
−0.508741 | + | 0.860920i | \(0.669889\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.69998 | 0.421224 | ||||||||
\(254\) | 3.86129 | 0.242279 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.39190 | −0.149203 | −0.0746013 | − | 0.997213i | \(-0.523768\pi\) | ||||
−0.0746013 | + | 0.997213i | \(0.523768\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.56727 | −0.221660 | ||||||||
\(260\) | −4.22983 | −0.262323 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.45036 | 0.460285 | ||||||||
\(263\) | 28.7218 | 1.77106 | 0.885532 | − | 0.464579i | \(-0.153794\pi\) | ||||
0.885532 | + | 0.464579i | \(0.153794\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0808 | −0.926405 | ||||||||
\(266\) | −1.18373 | −0.0725792 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.00991 | −0.306029 | ||||||||
\(269\) | 10.6420 | 0.648853 | 0.324427 | − | 0.945911i | \(-0.394829\pi\) | ||||
0.324427 | + | 0.945911i | \(0.394829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.2311 | −0.985969 | −0.492984 | − | 0.870038i | \(-0.664094\pi\) | ||||
−0.492984 | + | 0.870038i | \(0.664094\pi\) | |||||||
\(272\) | −6.95227 | −0.421544 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.7309 | 0.708687 | ||||||||
\(275\) | −14.0867 | −0.849459 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.4271 | −1.04709 | −0.523545 | − | 0.851998i | \(-0.675391\pi\) | ||||
−0.523545 | + | 0.851998i | \(0.675391\pi\) | |||||||
\(278\) | −0.614537 | −0.0368575 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.592892 | 0.0354321 | ||||||||
\(281\) | −10.0480 | −0.599414 | −0.299707 | − | 0.954031i | \(-0.596889\pi\) | ||||
−0.299707 | + | 0.954031i | \(0.596889\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.11210 | −0.125551 | −0.0627756 | − | 0.998028i | \(-0.519995\pi\) | ||||
−0.0627756 | + | 0.998028i | \(0.519995\pi\) | |||||||
\(284\) | 0.923816 | 0.0548184 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −14.0237 | −0.829237 | ||||||||
\(287\) | −5.34312 | −0.315394 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.3341 | 1.84318 | ||||||||
\(290\) | −4.93855 | −0.290002 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.46929 | 0.144505 | ||||||||
\(293\) | 17.4877 | 1.02164 | 0.510820 | − | 0.859687i | \(-0.329342\pi\) | ||||
0.510820 | + | 0.859687i | \(0.329342\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.25522 | 0.480638 | ||||||||
\(296\) | −7.04259 | −0.409342 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | −6.23900 | −0.360810 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.46508 | −0.199724 | ||||||||
\(302\) | 17.5323 | 1.00887 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.33695 | −0.134033 | ||||||||
\(305\) | 13.1564 | 0.753333 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.4985 | 0.827474 | 0.413737 | − | 0.910396i | \(-0.364223\pi\) | ||||
0.413737 | + | 0.910396i | \(0.364223\pi\) | |||||||
\(308\) | 1.96569 | 0.112005 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.85422 | −0.218905 | ||||||||
\(311\) | 27.0815 | 1.53565 | 0.767826 | − | 0.640659i | \(-0.221339\pi\) | ||||
0.767826 | + | 0.640659i | \(0.221339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.4400 | 1.15534 | 0.577668 | − | 0.816272i | \(-0.303963\pi\) | ||||
0.577668 | + | 0.816272i | \(0.303963\pi\) | |||||||
\(314\) | 22.2770 | 1.25716 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.80783 | −0.439225 | ||||||||
\(317\) | 10.5261 | 0.591206 | 0.295603 | − | 0.955311i | \(-0.404479\pi\) | ||||
0.295603 | + | 0.955311i | \(0.404479\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.3734 | −0.916735 | ||||||||
\(320\) | 1.17050 | 0.0654329 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.874515 | 0.0487348 | ||||||||
\(323\) | 16.2471 | 0.904013 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.1175 | 0.727626 | ||||||||
\(326\) | 13.4831 | 0.746758 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.5485 | −0.582444 | ||||||||
\(329\) | 2.11568 | 0.116641 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.1909 | −0.560140 | −0.280070 | − | 0.959980i | \(-0.590358\pi\) | ||||
−0.280070 | + | 0.959980i | \(0.590358\pi\) | |||||||
\(332\) | 8.00835 | 0.439515 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.6208 | −0.690578 | ||||||||
\(335\) | −5.86410 | −0.320390 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.6134 | −0.796042 | −0.398021 | − | 0.917376i | \(-0.630303\pi\) | ||||
−0.398021 | + | 0.917376i | \(0.630303\pi\) | |||||||
\(338\) | 0.0587896 | 0.00319773 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.13763 | −0.441325 | ||||||||
\(341\) | −12.7784 | −0.691987 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.96144 | −0.375882 | ||||||||
\(344\) | −6.84084 | −0.368833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.5303 | −0.727395 | ||||||||
\(347\) | −18.1962 | −0.976822 | −0.488411 | − | 0.872614i | \(-0.662423\pi\) | ||||
−0.488411 | + | 0.872614i | \(0.662423\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.9456 | 1.01413 | 0.507067 | − | 0.861907i | \(-0.330730\pi\) | ||||
0.507067 | + | 0.861907i | \(0.330730\pi\) | |||||||
\(350\) | −1.83866 | −0.0982807 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.88070 | 0.206842 | ||||||||
\(353\) | −36.1335 | −1.92319 | −0.961596 | − | 0.274468i | \(-0.911498\pi\) | ||||
−0.961596 | + | 0.274468i | \(0.911498\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.08133 | 0.0573908 | ||||||||
\(356\) | −15.6581 | −0.829877 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.23353 | 0.382304 | ||||||||
\(359\) | −13.2222 | −0.697842 | −0.348921 | − | 0.937152i | \(-0.613452\pi\) | ||||
−0.348921 | + | 0.937152i | \(0.613452\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.5387 | −0.712562 | ||||||||
\(362\) | 3.30723 | 0.173824 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.83044 | −0.0959411 | ||||||||
\(365\) | 2.89031 | 0.151286 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.09001 | −0.109098 | −0.0545488 | − | 0.998511i | \(-0.517372\pi\) | ||||
−0.0545488 | + | 0.998511i | \(0.517372\pi\) | |||||||
\(368\) | 1.72649 | 0.0899993 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.24335 | −0.428551 | ||||||||
\(371\) | −6.52614 | −0.338820 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.6737 | −0.811552 | −0.405776 | − | 0.913973i | \(-0.632999\pi\) | ||||
−0.405776 | + | 0.913973i | \(0.632999\pi\) | |||||||
\(374\) | −26.9797 | −1.39509 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.17683 | 0.215404 | ||||||||
\(377\) | 15.2468 | 0.785253 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.1521 | 1.49744 | 0.748722 | − | 0.662884i | \(-0.230668\pi\) | ||||
0.748722 | + | 0.662884i | \(0.230668\pi\) | |||||||
\(380\) | −2.73540 | −0.140323 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.7158 | −0.650597 | ||||||||
\(383\) | 13.1248 | 0.670648 | 0.335324 | − | 0.942103i | \(-0.391154\pi\) | ||||
0.335324 | + | 0.942103i | \(0.391154\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.30084 | 0.117261 | ||||||||
\(386\) | −3.36901 | −0.171478 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.02168 | 0.0518681 | ||||||||
\(389\) | −32.1642 | −1.63079 | −0.815394 | − | 0.578907i | \(-0.803479\pi\) | ||||
−0.815394 | + | 0.578907i | \(0.803479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0030 | −0.607018 | ||||||||
\(392\) | −6.74343 | −0.340595 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.815685 | 0.0410936 | ||||||||
\(395\) | −9.13906 | −0.459836 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.8252 | 1.69764 | 0.848818 | − | 0.528685i | \(-0.177315\pi\) | ||||
0.848818 | + | 0.528685i | \(0.177315\pi\) | |||||||
\(398\) | 5.35685 | 0.268514 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.62993 | −0.181497 | ||||||||
\(401\) | 9.59093 | 0.478948 | 0.239474 | − | 0.970903i | \(-0.423025\pi\) | ||||
0.239474 | + | 0.970903i | \(0.423025\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8992 | 0.592739 | ||||||||
\(404\) | 4.32214 | 0.215035 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.13714 | −0.106064 | ||||||||
\(407\) | −27.3302 | −1.35471 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.89619 | −0.340995 | −0.170497 | − | 0.985358i | \(-0.554537\pi\) | ||||
−0.170497 | + | 0.985358i | \(0.554537\pi\) | |||||||
\(410\) | −12.3470 | −0.609776 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.94103 | 0.341960 | ||||||||
\(413\) | 3.57241 | 0.175787 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.37377 | 0.460140 | ||||||||
\(416\) | −3.61369 | −0.177176 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.06900 | −0.443579 | ||||||||
\(419\) | −3.01240 | −0.147165 | −0.0735827 | − | 0.997289i | \(-0.523443\pi\) | ||||
−0.0735827 | + | 0.997289i | \(0.523443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.9520 | −1.89840 | −0.949201 | − | 0.314670i | \(-0.898106\pi\) | ||||
−0.949201 | + | 0.314670i | \(0.898106\pi\) | |||||||
\(422\) | 13.3550 | 0.650113 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.8841 | −0.625705 | ||||||||
\(425\) | 25.2363 | 1.22414 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.69337 | 0.275522 | ||||||||
\(428\) | 14.3087 | 0.691636 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00720 | −0.386142 | ||||||||
\(431\) | 5.42792 | 0.261454 | 0.130727 | − | 0.991418i | \(-0.458269\pi\) | ||||
0.130727 | + | 0.991418i | \(0.458269\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.8723 | 1.09917 | 0.549587 | − | 0.835436i | \(-0.314785\pi\) | ||||
0.549587 | + | 0.835436i | \(0.314785\pi\) | |||||||
\(434\) | −1.66790 | −0.0800615 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.75669 | −0.371478 | ||||||||
\(437\) | −4.03471 | −0.193006 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.90666 | −0.377364 | −0.188682 | − | 0.982038i | \(-0.560422\pi\) | ||||
−0.188682 | + | 0.982038i | \(0.560422\pi\) | |||||||
\(440\) | 4.54236 | 0.216549 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25.1234 | 1.19500 | ||||||||
\(443\) | 10.0631 | 0.478110 | 0.239055 | − | 0.971006i | \(-0.423162\pi\) | ||||
0.239055 | + | 0.971006i | \(0.423162\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.3278 | −0.868821 | ||||||||
\(446\) | 18.7279 | 0.886792 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.506529 | 0.0239312 | ||||||||
\(449\) | −13.1764 | −0.621831 | −0.310915 | − | 0.950438i | \(-0.600636\pi\) | ||||
−0.310915 | + | 0.950438i | \(0.600636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40.9356 | −1.92758 | ||||||||
\(452\) | 1.71654 | 0.0807393 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.54460 | −0.401018 | ||||||||
\(455\) | −2.14253 | −0.100443 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0444 | 0.703749 | 0.351874 | − | 0.936047i | \(-0.385544\pi\) | ||||
0.351874 | + | 0.936047i | \(0.385544\pi\) | |||||||
\(458\) | −5.34208 | −0.249619 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.02085 | 0.0942227 | ||||||||
\(461\) | 0.361142 | 0.0168201 | 0.00841003 | − | 0.999965i | \(-0.497323\pi\) | ||||
0.00841003 | + | 0.999965i | \(0.497323\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.07957 | 0.143120 | 0.0715599 | − | 0.997436i | \(-0.477202\pi\) | ||||
0.0715599 | + | 0.997436i | \(0.477202\pi\) | |||||||
\(464\) | −4.21919 | −0.195871 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.8123 | −0.686167 | ||||||||
\(467\) | −25.3161 | −1.17149 | −0.585746 | − | 0.810495i | \(-0.699198\pi\) | ||||
−0.585746 | + | 0.810495i | \(0.699198\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.53766 | −0.117178 | ||||||||
\(470\) | 4.88898 | 0.225512 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.05273 | 0.324628 | ||||||||
\(473\) | −26.5473 | −1.22064 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.48296 | 0.389225 | ||||||||
\(476\) | −3.52153 | −0.161409 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.91374 | −0.316227 | ||||||||
\(479\) | −11.9963 | −0.548123 | −0.274062 | − | 0.961712i | \(-0.588367\pi\) | ||||
−0.274062 | + | 0.961712i | \(0.588367\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.4498 | 1.16041 | ||||||||
\(482\) | 8.56369 | 0.390065 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.05985 | 0.184539 | ||||||||
\(485\) | 1.19588 | 0.0543021 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.3061 | −0.693585 | −0.346792 | − | 0.937942i | \(-0.612729\pi\) | ||||
−0.346792 | + | 0.937942i | \(0.612729\pi\) | |||||||
\(488\) | 11.2400 | 0.508810 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.89318 | −0.356578 | ||||||||
\(491\) | −18.7839 | −0.847706 | −0.423853 | − | 0.905731i | \(-0.639323\pi\) | ||||
−0.423853 | + | 0.905731i | \(0.639323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.3329 | 1.32109 | ||||||||
\(494\) | 8.44501 | 0.379959 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.29279 | −0.147851 | ||||||||
\(497\) | 0.467939 | 0.0209899 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.22731 | −0.0997079 | −0.0498540 | − | 0.998757i | \(-0.515876\pi\) | ||||
−0.0498540 | + | 0.998757i | \(0.515876\pi\) | |||||||
\(500\) | −10.1013 | −0.451745 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.1199 | −0.719468 | ||||||||
\(503\) | −10.4225 | −0.464716 | −0.232358 | − | 0.972630i | \(-0.574644\pi\) | ||||
−0.232358 | + | 0.972630i | \(0.574644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.05907 | 0.225126 | ||||||||
\(506\) | 6.69998 | 0.297850 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.86129 | 0.171317 | ||||||||
\(509\) | −25.1510 | −1.11480 | −0.557400 | − | 0.830244i | \(-0.688201\pi\) | ||||
−0.557400 | + | 0.830244i | \(0.688201\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.25077 | 0.0553307 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.39190 | −0.105502 | ||||||||
\(515\) | 8.12447 | 0.358007 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.2090 | 0.712873 | ||||||||
\(518\) | −3.56727 | −0.156737 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.22983 | −0.185490 | ||||||||
\(521\) | −30.0875 | −1.31816 | −0.659078 | − | 0.752074i | \(-0.729053\pi\) | ||||
−0.659078 | + | 0.752074i | \(0.729053\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.8359 | −1.04227 | −0.521137 | − | 0.853473i | \(-0.674492\pi\) | ||||
−0.521137 | + | 0.853473i | \(0.674492\pi\) | |||||||
\(524\) | 7.45036 | 0.325470 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.7218 | 1.25233 | ||||||||
\(527\) | 22.8924 | 0.997209 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.0192 | −0.870402 | ||||||||
\(530\) | −15.0808 | −0.655067 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.18373 | −0.0513212 | ||||||||
\(533\) | 38.1191 | 1.65112 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.7483 | 0.724093 | ||||||||
\(536\) | −5.00991 | −0.216395 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.6420 | 0.458808 | ||||||||
\(539\) | −26.1692 | −1.12719 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.0897 | −0.691750 | −0.345875 | − | 0.938281i | \(-0.612418\pi\) | ||||
−0.345875 | + | 0.938281i | \(0.612418\pi\) | |||||||
\(542\) | −16.2311 | −0.697185 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.95227 | −0.298076 | ||||||||
\(545\) | −9.07921 | −0.388910 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.17274 | −0.0501429 | −0.0250715 | − | 0.999686i | \(-0.507981\pi\) | ||||
−0.0250715 | + | 0.999686i | \(0.507981\pi\) | |||||||
\(548\) | 11.7309 | 0.501117 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.0867 | −0.600658 | ||||||||
\(551\) | 9.86001 | 0.420051 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.95489 | −0.168179 | ||||||||
\(554\) | −17.4271 | −0.740404 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.614537 | −0.0260622 | ||||||||
\(557\) | 32.1956 | 1.36417 | 0.682086 | − | 0.731272i | \(-0.261073\pi\) | ||||
0.682086 | + | 0.731272i | \(0.261073\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.7207 | 1.04557 | ||||||||
\(560\) | 0.592892 | 0.0250542 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.0480 | −0.423850 | ||||||||
\(563\) | −39.9085 | −1.68194 | −0.840970 | − | 0.541081i | \(-0.818015\pi\) | ||||
−0.840970 | + | 0.541081i | \(0.818015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00921 | 0.0845282 | ||||||||
\(566\) | −2.11210 | −0.0887780 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.923816 | 0.0387624 | ||||||||
\(569\) | −45.1626 | −1.89331 | −0.946657 | − | 0.322244i | \(-0.895563\pi\) | ||||
−0.946657 | + | 0.322244i | \(0.895563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.79540 | 0.368076 | 0.184038 | − | 0.982919i | \(-0.441083\pi\) | ||||
0.184038 | + | 0.982919i | \(0.441083\pi\) | |||||||
\(572\) | −14.0237 | −0.586359 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.34312 | −0.223018 | ||||||||
\(575\) | −6.26703 | −0.261353 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.4382 | 0.850855 | 0.425427 | − | 0.904993i | \(-0.360124\pi\) | ||||
0.425427 | + | 0.904993i | \(0.360124\pi\) | |||||||
\(578\) | 31.3341 | 1.30333 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.93855 | −0.205062 | ||||||||
\(581\) | 4.05646 | 0.168290 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.9992 | −2.07075 | ||||||||
\(584\) | 2.46929 | 0.102180 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.4877 | 0.722409 | ||||||||
\(587\) | 40.4128 | 1.66801 | 0.834007 | − | 0.551753i | \(-0.186041\pi\) | ||||
0.834007 | + | 0.551753i | \(0.186041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.69509 | 0.317071 | ||||||||
\(590\) | 8.25522 | 0.339862 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.04259 | −0.289449 | ||||||||
\(593\) | −17.1642 | −0.704850 | −0.352425 | − | 0.935840i | \(-0.614643\pi\) | ||||
−0.352425 | + | 0.935840i | \(0.614643\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.12195 | −0.168983 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.23900 | −0.255131 | ||||||||
\(599\) | −11.0793 | −0.452689 | −0.226345 | − | 0.974047i | \(-0.572678\pi\) | ||||
−0.226345 | + | 0.974047i | \(0.572678\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.3103 | −0.461358 | −0.230679 | − | 0.973030i | \(-0.574095\pi\) | ||||
−0.230679 | + | 0.973030i | \(0.574095\pi\) | |||||||
\(602\) | −3.46508 | −0.141226 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.5323 | 0.713378 | ||||||||
\(605\) | 4.75206 | 0.193199 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.9521 | −0.444533 | −0.222267 | − | 0.974986i | \(-0.571346\pi\) | ||||
−0.222267 | + | 0.974986i | \(0.571346\pi\) | |||||||
\(608\) | −2.33695 | −0.0947757 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 13.1564 | 0.532687 | ||||||||
\(611\) | −15.0938 | −0.610629 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.68464 | 0.269990 | 0.134995 | − | 0.990846i | \(-0.456898\pi\) | ||||
0.134995 | + | 0.990846i | \(0.456898\pi\) | |||||||
\(614\) | 14.4985 | 0.585112 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.96569 | 0.0791998 | ||||||||
\(617\) | −21.3178 | −0.858222 | −0.429111 | − | 0.903252i | \(-0.641173\pi\) | ||||
−0.429111 | + | 0.903252i | \(0.641173\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.6883 | −1.11289 | −0.556443 | − | 0.830885i | \(-0.687834\pi\) | ||||
−0.556443 | + | 0.830885i | \(0.687834\pi\) | |||||||
\(620\) | −3.85422 | −0.154789 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 27.0815 | 1.08587 | ||||||||
\(623\) | −7.93127 | −0.317760 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.32605 | 0.253042 | ||||||||
\(626\) | 20.4400 | 0.816946 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 22.2770 | 0.888950 | ||||||||
\(629\) | 48.9620 | 1.95224 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.1206 | 1.47775 | 0.738874 | − | 0.673843i | \(-0.235358\pi\) | ||||
0.738874 | + | 0.673843i | \(0.235358\pi\) | |||||||
\(632\) | −7.80783 | −0.310579 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.5261 | 0.418046 | ||||||||
\(635\) | 4.51964 | 0.179356 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.3687 | 0.965523 | ||||||||
\(638\) | −16.3734 | −0.648229 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.17050 | 0.0462681 | ||||||||
\(641\) | 8.02175 | 0.316840 | 0.158420 | − | 0.987372i | \(-0.449360\pi\) | ||||
0.158420 | + | 0.987372i | \(0.449360\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00334 | 0.0395677 | 0.0197839 | − | 0.999804i | \(-0.493702\pi\) | ||||
0.0197839 | + | 0.999804i | \(0.493702\pi\) | |||||||
\(644\) | 0.874515 | 0.0344607 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.2471 | 0.639234 | ||||||||
\(647\) | −27.4169 | −1.07787 | −0.538935 | − | 0.842347i | \(-0.681173\pi\) | ||||
−0.538935 | + | 0.842347i | \(0.681173\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.3696 | 1.07435 | ||||||||
\(650\) | 13.1175 | 0.514509 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.4831 | 0.528038 | ||||||||
\(653\) | −39.3088 | −1.53827 | −0.769137 | − | 0.639084i | \(-0.779314\pi\) | ||||
−0.769137 | + | 0.639084i | \(0.779314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.72064 | 0.340744 | ||||||||
\(656\) | −10.5485 | −0.411850 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.11568 | 0.0824780 | ||||||||
\(659\) | −36.5849 | −1.42515 | −0.712573 | − | 0.701598i | \(-0.752470\pi\) | ||||
−0.712573 | + | 0.701598i | \(0.752470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.5700 | −0.527810 | −0.263905 | − | 0.964549i | \(-0.585011\pi\) | ||||
−0.263905 | + | 0.964549i | \(0.585011\pi\) | |||||||
\(662\) | −10.1909 | −0.396079 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.00835 | 0.310784 | ||||||||
\(665\) | −1.38556 | −0.0537296 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.28437 | −0.282052 | ||||||||
\(668\) | −12.6208 | −0.488313 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.86410 | −0.226550 | ||||||||
\(671\) | 43.6190 | 1.68389 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.54169 | −0.0594279 | −0.0297139 | − | 0.999558i | \(-0.509460\pi\) | ||||
−0.0297139 | + | 0.999558i | \(0.509460\pi\) | |||||||
\(674\) | −14.6134 | −0.562886 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.0587896 | 0.00226114 | ||||||||
\(677\) | 2.97532 | 0.114351 | 0.0571755 | − | 0.998364i | \(-0.481791\pi\) | ||||
0.0571755 | + | 0.998364i | \(0.481791\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.517512 | 0.0198603 | ||||||||
\(680\) | −8.13763 | −0.312064 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.7784 | −0.489309 | ||||||||
\(683\) | −6.60805 | −0.252850 | −0.126425 | − | 0.991976i | \(-0.540350\pi\) | ||||
−0.126425 | + | 0.991976i | \(0.540350\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.7310 | 0.524633 | ||||||||
\(686\) | −6.96144 | −0.265789 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.84084 | −0.260805 | ||||||||
\(689\) | 46.5590 | 1.77376 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16.9869 | −0.646212 | −0.323106 | − | 0.946363i | \(-0.604727\pi\) | ||||
−0.323106 | + | 0.946363i | \(0.604727\pi\) | |||||||
\(692\) | −13.5303 | −0.514346 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.1962 | −0.690717 | ||||||||
\(695\) | −0.719316 | −0.0272852 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 73.3361 | 2.77780 | ||||||||
\(698\) | 18.9456 | 0.717101 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.83866 | −0.0694950 | ||||||||
\(701\) | −16.5146 | −0.623747 | −0.311873 | − | 0.950124i | \(-0.600956\pi\) | ||||
−0.311873 | + | 0.950124i | \(0.600956\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.4582 | 0.620731 | ||||||||
\(704\) | 3.88070 | 0.146259 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −36.1335 | −1.35990 | ||||||||
\(707\) | 2.18929 | 0.0823367 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.25383 | −0.0470885 | −0.0235442 | − | 0.999723i | \(-0.507495\pi\) | ||||
−0.0235442 | + | 0.999723i | \(0.507495\pi\) | |||||||
\(710\) | 1.08133 | 0.0405814 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.6581 | −0.586812 | ||||||||
\(713\) | −5.68497 | −0.212904 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.4147 | −0.613875 | ||||||||
\(716\) | 7.23353 | 0.270330 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.2222 | −0.493449 | ||||||||
\(719\) | −50.6632 | −1.88942 | −0.944709 | − | 0.327909i | \(-0.893656\pi\) | ||||
−0.944709 | + | 0.327909i | \(0.893656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.51583 | 0.130936 | ||||||||
\(722\) | −13.5387 | −0.503857 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.30723 | 0.122912 | ||||||||
\(725\) | 15.3154 | 0.568798 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.3402 | 0.754378 | 0.377189 | − | 0.926136i | \(-0.376891\pi\) | ||||
0.377189 | + | 0.926136i | \(0.376891\pi\) | |||||||
\(728\) | −1.83044 | −0.0678406 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.89031 | 0.106975 | ||||||||
\(731\) | 47.5594 | 1.75905 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.1935 | 0.635058 | 0.317529 | − | 0.948249i | \(-0.397147\pi\) | ||||
0.317529 | + | 0.948249i | \(0.397147\pi\) | |||||||
\(734\) | −2.09001 | −0.0771437 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.72649 | 0.0636391 | ||||||||
\(737\) | −19.4420 | −0.716154 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.2873 | 1.48199 | 0.740996 | − | 0.671509i | \(-0.234354\pi\) | ||||
0.740996 | + | 0.671509i | \(0.234354\pi\) | |||||||
\(740\) | −8.24335 | −0.303032 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.52614 | −0.239582 | ||||||||
\(743\) | 13.2514 | 0.486145 | 0.243073 | − | 0.970008i | \(-0.421845\pi\) | ||||
0.243073 | + | 0.970008i | \(0.421845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.17050 | −0.0428838 | ||||||||
\(746\) | −15.6737 | −0.573854 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −26.9797 | −0.986476 | ||||||||
\(749\) | 7.24776 | 0.264827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.9147 | 1.42002 | 0.710010 | − | 0.704192i | \(-0.248691\pi\) | ||||
0.710010 | + | 0.704192i | \(0.248691\pi\) | |||||||
\(752\) | 4.17683 | 0.152313 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.2468 | 0.555257 | ||||||||
\(755\) | 20.5215 | 0.746855 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.51490 | 0.200442 | 0.100221 | − | 0.994965i | \(-0.468045\pi\) | ||||
0.100221 | + | 0.994965i | \(0.468045\pi\) | |||||||
\(758\) | 29.1521 | 1.05885 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.73540 | −0.0992232 | ||||||||
\(761\) | 40.3355 | 1.46216 | 0.731081 | − | 0.682291i | \(-0.239016\pi\) | ||||
0.731081 | + | 0.682291i | \(0.239016\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.92899 | −0.142239 | ||||||||
\(764\) | −12.7158 | −0.460042 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.1248 | 0.474219 | ||||||||
\(767\) | −25.4864 | −0.920262 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.9355 | 0.574648 | 0.287324 | − | 0.957833i | \(-0.407234\pi\) | ||||
0.287324 | + | 0.957833i | \(0.407234\pi\) | |||||||
\(770\) | 2.30084 | 0.0829164 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.36901 | −0.121253 | ||||||||
\(773\) | 26.9572 | 0.969584 | 0.484792 | − | 0.874629i | \(-0.338895\pi\) | ||||
0.484792 | + | 0.874629i | \(0.338895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.9526 | 0.429351 | ||||||||
\(776\) | 1.02168 | 0.0366763 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −32.1642 | −1.15314 | ||||||||
\(779\) | 24.6513 | 0.883225 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.58505 | 0.128283 | ||||||||
\(782\) | −12.0030 | −0.429227 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.74343 | −0.240837 | ||||||||
\(785\) | 26.0752 | 0.930665 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 51.2529 | 1.82697 | 0.913484 | − | 0.406875i | \(-0.133381\pi\) | ||||
0.913484 | + | 0.406875i | \(0.133381\pi\) | |||||||
\(788\) | 0.815685 | 0.0290576 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.13906 | −0.325153 | ||||||||
\(791\) | 0.869478 | 0.0309151 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.6179 | −1.44238 | ||||||||
\(794\) | 33.8252 | 1.20041 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.35685 | 0.189868 | ||||||||
\(797\) | 10.0808 | 0.357082 | 0.178541 | − | 0.983933i | \(-0.442862\pi\) | ||||
0.178541 | + | 0.983933i | \(0.442862\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −29.0385 | −1.02731 | ||||||||
\(800\) | −3.62993 | −0.128337 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.59093 | 0.338667 | ||||||||
\(803\) | 9.58260 | 0.338163 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.02362 | 0.0360778 | ||||||||
\(806\) | 11.8992 | 0.419130 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.32214 | 0.152052 | ||||||||
\(809\) | 8.55995 | 0.300952 | 0.150476 | − | 0.988614i | \(-0.451919\pi\) | ||||
0.150476 | + | 0.988614i | \(0.451919\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.01809 | −0.246439 | −0.123219 | − | 0.992379i | \(-0.539322\pi\) | ||||
−0.123219 | + | 0.992379i | \(0.539322\pi\) | |||||||
\(812\) | −2.13714 | −0.0749989 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −27.3302 | −0.957923 | ||||||||
\(815\) | 15.7819 | 0.552817 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.9867 | 0.559303 | ||||||||
\(818\) | −6.89619 | −0.241120 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.3470 | −0.431177 | ||||||||
\(821\) | 16.3421 | 0.570344 | 0.285172 | − | 0.958476i | \(-0.407949\pi\) | ||||
0.285172 | + | 0.958476i | \(0.407949\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.5614 | 1.06530 | 0.532652 | − | 0.846335i | \(-0.321196\pi\) | ||||
0.532652 | + | 0.846335i | \(0.321196\pi\) | |||||||
\(824\) | 6.94103 | 0.241802 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.57241 | 0.124300 | ||||||||
\(827\) | 3.44532 | 0.119805 | 0.0599027 | − | 0.998204i | \(-0.480921\pi\) | ||||
0.0599027 | + | 0.998204i | \(0.480921\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.4705 | −0.433120 | −0.216560 | − | 0.976269i | \(-0.569484\pi\) | ||||
−0.216560 | + | 0.976269i | \(0.569484\pi\) | |||||||
\(830\) | 9.37377 | 0.325368 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.61369 | −0.125282 | ||||||||
\(833\) | 46.8822 | 1.62437 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.7726 | −0.511228 | ||||||||
\(836\) | −9.06900 | −0.313658 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.01240 | −0.104062 | ||||||||
\(839\) | −30.3546 | −1.04796 | −0.523979 | − | 0.851731i | \(-0.675553\pi\) | ||||
−0.523979 | + | 0.851731i | \(0.675553\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.1985 | −0.386154 | ||||||||
\(842\) | −38.9520 | −1.34237 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.3550 | 0.459699 | ||||||||
\(845\) | 0.0688132 | 0.00236724 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.05643 | 0.0706598 | ||||||||
\(848\) | −12.8841 | −0.442440 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 25.2363 | 0.865597 | ||||||||
\(851\) | −12.1589 | −0.416803 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.6101 | −1.42470 | −0.712351 | − | 0.701824i | \(-0.752369\pi\) | ||||
−0.712351 | + | 0.701824i | \(0.752369\pi\) | |||||||
\(854\) | 5.69337 | 0.194823 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.3087 | 0.489061 | ||||||||
\(857\) | −39.6564 | −1.35464 | −0.677318 | − | 0.735690i | \(-0.736858\pi\) | ||||
−0.677318 | + | 0.735690i | \(0.736858\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.6299 | 1.59099 | 0.795497 | − | 0.605958i | \(-0.207210\pi\) | ||||
0.795497 | + | 0.605958i | \(0.207210\pi\) | |||||||
\(860\) | −8.00720 | −0.273043 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.42792 | 0.184876 | ||||||||
\(863\) | −32.8049 | −1.11669 | −0.558346 | − | 0.829608i | \(-0.688564\pi\) | ||||
−0.558346 | + | 0.829608i | \(0.688564\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.8372 | −0.538482 | ||||||||
\(866\) | 22.8723 | 0.777234 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.66790 | −0.0566121 | ||||||||
\(869\) | −30.2999 | −1.02785 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.1043 | 0.613440 | ||||||||
\(872\) | −7.75669 | −0.262675 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.03471 | −0.136476 | ||||||||
\(875\) | −5.11661 | −0.172973 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −39.7704 | −1.34295 | −0.671475 | − | 0.741027i | \(-0.734339\pi\) | ||||
−0.671475 | + | 0.741027i | \(0.734339\pi\) | |||||||
\(878\) | −7.90666 | −0.266837 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.54236 | 0.153123 | ||||||||
\(881\) | −27.5405 | −0.927861 | −0.463931 | − | 0.885871i | \(-0.653561\pi\) | ||||
−0.463931 | + | 0.885871i | \(0.653561\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.8260 | 1.60947 | 0.804737 | − | 0.593632i | \(-0.202306\pi\) | ||||
0.804737 | + | 0.593632i | \(0.202306\pi\) | |||||||
\(884\) | 25.1234 | 0.844991 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.0631 | 0.338075 | ||||||||
\(887\) | 45.4546 | 1.52622 | 0.763108 | − | 0.646271i | \(-0.223673\pi\) | ||||
0.763108 | + | 0.646271i | \(0.223673\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.95585 | 0.0655972 | ||||||||
\(890\) | −18.3278 | −0.614349 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.7279 | 0.627057 | ||||||||
\(893\) | −9.76103 | −0.326640 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.46684 | 0.283015 | ||||||||
\(896\) | 0.506529 | 0.0169219 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.1764 | −0.439701 | ||||||||
\(899\) | 13.8929 | 0.463355 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 89.5735 | 2.98412 | ||||||||
\(902\) | −40.9356 | −1.36301 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.71654 | 0.0570913 | ||||||||
\(905\) | 3.87111 | 0.128680 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7377 | −0.422947 | −0.211473 | − | 0.977384i | \(-0.567826\pi\) | ||||
−0.211473 | + | 0.977384i | \(0.567826\pi\) | |||||||
\(908\) | −8.54460 | −0.283562 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.14253 | −0.0710242 | ||||||||
\(911\) | −39.3617 | −1.30411 | −0.652055 | − | 0.758171i | \(-0.726093\pi\) | ||||
−0.652055 | + | 0.758171i | \(0.726093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.0780 | 1.02853 | ||||||||
\(914\) | 15.0444 | 0.497626 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.34208 | −0.176507 | ||||||||
\(917\) | 3.77382 | 0.124623 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.2378 | −0.700570 | −0.350285 | − | 0.936643i | \(-0.613915\pi\) | ||||
−0.350285 | + | 0.936643i | \(0.613915\pi\) | |||||||
\(920\) | 2.02085 | 0.0666255 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.361142 | 0.0118936 | ||||||||
\(923\) | −3.33839 | −0.109884 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.5641 | 0.840543 | ||||||||
\(926\) | 3.07957 | 0.101201 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.21919 | −0.138502 | ||||||||
\(929\) | −28.3154 | −0.928997 | −0.464498 | − | 0.885574i | \(-0.653765\pi\) | ||||
−0.464498 | + | 0.885574i | \(0.653765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.7590 | 0.516482 | ||||||||
\(932\) | −14.8123 | −0.485194 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −25.3161 | −0.828369 | ||||||||
\(935\) | −31.5797 | −1.03277 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.8706 | 1.33519 | 0.667593 | − | 0.744527i | \(-0.267325\pi\) | ||||
0.667593 | + | 0.744527i | \(0.267325\pi\) | |||||||
\(938\) | −2.53766 | −0.0828576 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.88898 | 0.159461 | ||||||||
\(941\) | 16.4529 | 0.536349 | 0.268174 | − | 0.963370i | \(-0.413580\pi\) | ||||
0.268174 | + | 0.963370i | \(0.413580\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.2119 | −0.593060 | ||||||||
\(944\) | 7.05273 | 0.229547 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −26.5473 | −0.863126 | ||||||||
\(947\) | 17.3768 | 0.564671 | 0.282335 | − | 0.959316i | \(-0.408891\pi\) | ||||
0.282335 | + | 0.959316i | \(0.408891\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.92328 | −0.289662 | ||||||||
\(950\) | 8.48296 | 0.275223 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.52153 | −0.114133 | ||||||||
\(953\) | 47.2562 | 1.53078 | 0.765389 | − | 0.643568i | \(-0.222547\pi\) | ||||
0.765389 | + | 0.643568i | \(0.222547\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.8838 | −0.481630 | ||||||||
\(956\) | −6.91374 | −0.223606 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11.9963 | −0.387582 | ||||||||
\(959\) | 5.94202 | 0.191878 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.1575 | −0.650242 | ||||||||
\(962\) | 25.4498 | 0.820534 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.56369 | 0.275818 | ||||||||
\(965\) | −3.94342 | −0.126943 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −45.1307 | −1.45131 | −0.725653 | − | 0.688061i | \(-0.758462\pi\) | ||||
−0.725653 | + | 0.688061i | \(0.758462\pi\) | |||||||
\(968\) | 4.05985 | 0.130489 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.19588 | 0.0383974 | ||||||||
\(971\) | −7.05507 | −0.226408 | −0.113204 | − | 0.993572i | \(-0.536111\pi\) | ||||
−0.113204 | + | 0.993572i | \(0.536111\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.311281 | −0.00997921 | ||||||||
\(974\) | −15.3061 | −0.490438 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.2400 | 0.359783 | ||||||||
\(977\) | 5.88708 | 0.188344 | 0.0941721 | − | 0.995556i | \(-0.469980\pi\) | ||||
0.0941721 | + | 0.995556i | \(0.469980\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −60.7644 | −1.94204 | ||||||||
\(980\) | −7.89318 | −0.252138 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −18.7839 | −0.599419 | ||||||||
\(983\) | 21.2758 | 0.678593 | 0.339297 | − | 0.940679i | \(-0.389811\pi\) | ||||
0.339297 | + | 0.940679i | \(0.389811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.954758 | 0.0304211 | ||||||||
\(986\) | 29.3329 | 0.934151 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.44501 | 0.268672 | ||||||||
\(989\) | −11.8106 | −0.375556 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.3295 | −1.05875 | −0.529373 | − | 0.848389i | \(-0.677573\pi\) | ||||
−0.529373 | + | 0.848389i | \(0.677573\pi\) | |||||||
\(992\) | −3.29279 | −0.104546 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.467939 | 0.0148421 | ||||||||
\(995\) | 6.27019 | 0.198778 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.18494 | −0.0691979 | −0.0345989 | − | 0.999401i | \(-0.511015\pi\) | ||||
−0.0345989 | + | 0.999401i | \(0.511015\pi\) | |||||||
\(998\) | −2.22731 | −0.0705042 | ||||||||
\(999\) | 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 | 8046.2.a.m.1.9 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.l.1.4 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.l.1.4 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.m.1.9 | yes | 12 | 1.1 | even | 1 | trivial |