Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4232,2,Mod(1,4232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4232, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4232.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4232 = 2^{3} \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4232.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: | \(33.7926901354\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - x^{14} - 30 x^{13} + 28 x^{12} + 354 x^{11} - 302 x^{10} - 2111 x^{9} + 1596 x^{8} + 6777 x^{7} + \cdots - 419 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 184) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.01779\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4232.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.01779 | −1.16497 | −0.582485 | − | 0.812841i | \(-0.697920\pi\) | ||||
−0.582485 | + | 0.812841i | \(0.697920\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.684021 | 0.305904 | 0.152952 | − | 0.988234i | \(-0.451122\pi\) | ||||
0.152952 | + | 0.988234i | \(0.451122\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.16510 | 0.818331 | 0.409166 | − | 0.912460i | \(-0.365820\pi\) | ||||
0.409166 | + | 0.912460i | \(0.365820\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.07147 | 0.357157 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.89186 | 0.570417 | 0.285208 | − | 0.958466i | \(-0.407937\pi\) | ||||
0.285208 | + | 0.958466i | \(0.407937\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.22346 | −0.616677 | −0.308339 | − | 0.951277i | \(-0.599773\pi\) | ||||
−0.308339 | + | 0.951277i | \(0.599773\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.38021 | −0.356369 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.80474 | 0.680250 | 0.340125 | − | 0.940380i | \(-0.389531\pi\) | ||||
0.340125 | + | 0.940380i | \(0.389531\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.23273 | −0.512222 | −0.256111 | − | 0.966647i | \(-0.582441\pi\) | ||||
−0.256111 | + | 0.966647i | \(0.582441\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.36872 | −0.953332 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.53211 | −0.906423 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.89136 | 0.748893 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.59972 | −1.59693 | −0.798464 | − | 0.602042i | \(-0.794354\pi\) | ||||
−0.798464 | + | 0.602042i | \(0.794354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.31109 | −0.415084 | −0.207542 | − | 0.978226i | \(-0.566546\pi\) | ||||
−0.207542 | + | 0.978226i | \(0.566546\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.81737 | −0.664519 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.48098 | 0.250331 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.55335 | 0.912966 | 0.456483 | − | 0.889732i | \(-0.349109\pi\) | ||||
0.456483 | + | 0.889732i | \(0.349109\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.48647 | 0.718411 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.44767 | 0.538436 | 0.269218 | − | 0.963079i | \(-0.413235\pi\) | ||||
0.269218 | + | 0.963079i | \(0.413235\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.37494 | −0.209676 | −0.104838 | − | 0.994489i | \(-0.533432\pi\) | ||||
−0.104838 | + | 0.994489i | \(0.533432\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.732910 | 0.109256 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.4999 | −1.67743 | −0.838717 | − | 0.544568i | \(-0.816694\pi\) | ||||
−0.838717 | + | 0.544568i | \(0.816694\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.31234 | −0.330334 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.65938 | −0.792472 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.37106 | 1.14985 | 0.574927 | − | 0.818205i | \(-0.305030\pi\) | ||||
0.574927 | + | 0.818205i | \(0.305030\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.29407 | 0.174493 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.50517 | 0.596724 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.40725 | −1.09453 | −0.547265 | − | 0.836959i | \(-0.684331\pi\) | ||||
−0.547265 | + | 0.836959i | \(0.684331\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.71825 | 0.732147 | 0.366073 | − | 0.930586i | \(-0.380702\pi\) | ||||
0.366073 | + | 0.930586i | \(0.380702\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.31985 | 0.292273 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.52089 | −0.188644 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.4601 | −1.88875 | −0.944376 | − | 0.328868i | \(-0.893333\pi\) | ||||
−0.944376 | + | 0.328868i | \(0.893333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.24569 | −0.147836 | −0.0739180 | − | 0.997264i | \(-0.523550\pi\) | ||||
−0.0739180 | + | 0.997264i | \(0.523550\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4084 | 1.56934 | 0.784668 | − | 0.619916i | \(-0.212833\pi\) | ||||
0.784668 | + | 0.619916i | \(0.212833\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.14485 | 1.05596 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.09607 | 0.466790 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.14191 | −0.916036 | −0.458018 | − | 0.888943i | \(-0.651440\pi\) | ||||
−0.458018 | + | 0.888943i | \(0.651440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0664 | −1.22960 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.82785 | −1.07875 | −0.539374 | − | 0.842067i | \(-0.681339\pi\) | ||||
−0.539374 | + | 0.842067i | \(0.681339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.91850 | 0.208091 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17.3524 | 1.86038 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.0489 | 1.17118 | 0.585590 | − | 0.810607i | \(-0.300863\pi\) | ||||
0.585590 | + | 0.810607i | \(0.300863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.81402 | −0.504646 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.66329 | 0.483560 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.52723 | −0.156691 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.8611 | 1.71199 | 0.855993 | − | 0.516988i | \(-0.172947\pi\) | ||||
0.855993 | + | 0.516988i | \(0.172947\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.02707 | 0.203729 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.43369 | 0.640176 | 0.320088 | − | 0.947388i | \(-0.396288\pi\) | ||||
0.320088 | + | 0.947388i | \(0.396288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.5667 | 1.23824 | 0.619118 | − | 0.785298i | \(-0.287490\pi\) | ||||
0.619118 | + | 0.785298i | \(0.287490\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.98830 | −0.291628 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.32102 | −0.707750 | −0.353875 | − | 0.935293i | \(-0.615136\pi\) | ||||
−0.353875 | + | 0.935293i | \(0.615136\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.59291 | 0.823051 | 0.411526 | − | 0.911398i | \(-0.364996\pi\) | ||||
0.411526 | + | 0.911398i | \(0.364996\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.2055 | −1.06358 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.8763 | −1.11723 | −0.558615 | − | 0.829427i | \(-0.688667\pi\) | ||||
−0.558615 | + | 0.829427i | \(0.688667\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.38238 | −0.220251 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.07255 | 0.556670 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.42087 | −0.674625 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.95668 | −0.627263 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.52017 | −0.583182 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.96058 | 0.706387 | 0.353194 | − | 0.935550i | \(-0.385096\pi\) | ||||
0.353194 | + | 0.935550i | \(0.385096\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.77433 | 0.244267 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.26451 | −0.197851 | −0.0989256 | − | 0.995095i | \(-0.531541\pi\) | ||||
−0.0989256 | + | 0.995095i | \(0.531541\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.83408 | −0.419168 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.66177 | 0.229089 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.75279 | 0.406058 | 0.203029 | − | 0.979173i | \(-0.434921\pi\) | ||||
0.203029 | + | 0.979173i | \(0.434921\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.47555 | −0.718887 | −0.359444 | − | 0.933167i | \(-0.617033\pi\) | ||||
−0.359444 | + | 0.933167i | \(0.617033\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 23.2044 | 1.95416 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.20647 | −0.351763 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.88239 | −0.488506 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.66581 | 0.384829 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.6174 | −1.11558 | −0.557790 | − | 0.829982i | \(-0.688351\pi\) | ||||
−0.557790 | + | 0.829982i | \(0.688351\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.51335 | −0.123155 | −0.0615775 | − | 0.998102i | \(-0.519613\pi\) | ||||
−0.0615775 | + | 0.998102i | \(0.519613\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.00520 | 0.242956 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.58083 | −0.126976 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.3036 | −1.62041 | −0.810203 | − | 0.586149i | \(-0.800643\pi\) | ||||
−0.810203 | + | 0.586149i | \(0.800643\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.8910 | −1.33955 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.88736 | −0.304482 | −0.152241 | − | 0.988343i | \(-0.548649\pi\) | ||||
−0.152241 | + | 0.988343i | \(0.548649\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.61116 | −0.203279 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.52957 | 0.427891 | 0.213945 | − | 0.976846i | \(-0.431369\pi\) | ||||
0.213945 | + | 0.976846i | \(0.431369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.05622 | −0.619709 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.39230 | −0.182944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.1608 | −1.22868 | −0.614342 | − | 0.789040i | \(-0.710578\pi\) | ||||
−0.614342 | + | 0.789040i | \(0.710578\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.81249 | −0.741754 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.9640 | 1.27510 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.6453 | 0.945151 | 0.472576 | − | 0.881290i | \(-0.343324\pi\) | ||||
0.472576 | + | 0.881290i | \(0.343324\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4188 | −0.848749 | −0.424375 | − | 0.905487i | \(-0.639506\pi\) | ||||
−0.424375 | + | 0.905487i | \(0.639506\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.5382 | −0.852930 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.79861 | 0.279279 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.30618 | 0.388026 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.42519 | 0.612843 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.15177 | −0.228054 | −0.114027 | − | 0.993478i | \(-0.536375\pi\) | ||||
−0.114027 | + | 0.993478i | \(0.536375\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.5055 | 1.18809 | 0.594044 | − | 0.804432i | \(-0.297530\pi\) | ||||
0.594044 | + | 0.804432i | \(0.297530\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.06884 | 0.219764 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.5007 | −1.24688 | −0.623438 | − | 0.781873i | \(-0.714265\pi\) | ||||
−0.623438 | + | 0.781873i | \(0.714265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.94636 | 0.279750 | 0.139875 | − | 0.990169i | \(-0.455330\pi\) | ||||
0.139875 | + | 0.990169i | \(0.455330\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 31.1952 | 2.20034 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −18.6193 | −1.30682 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.35828 | 0.164710 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.22400 | −0.292180 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.9925 | −0.963284 | −0.481642 | − | 0.876368i | \(-0.659959\pi\) | ||||
−0.481642 | + | 0.876368i | \(0.659959\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.51353 | 0.172225 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.940487 | −0.0641407 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.00374 | −0.339676 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −27.0553 | −1.82823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.23624 | −0.419495 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.8055 | −1.79503 | −0.897515 | − | 0.440984i | \(-0.854630\pi\) | ||||
−0.897515 | + | 0.440984i | \(0.854630\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.85604 | −0.323736 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.1452 | −1.60257 | −0.801286 | − | 0.598281i | \(-0.795851\pi\) | ||||
−0.801286 | + | 0.598281i | \(0.795851\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.7876 | −0.845030 | −0.422515 | − | 0.906356i | \(-0.638853\pi\) | ||||
−0.422515 | + | 0.906356i | \(0.638853\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.26500 | −0.543797 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.91413 | 0.518472 | 0.259236 | − | 0.965814i | \(-0.416529\pi\) | ||||
0.259236 | + | 0.965814i | \(0.416529\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.86618 | −0.513133 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.4286 | 1.06716 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0775 | 0.716546 | 0.358273 | − | 0.933617i | \(-0.383366\pi\) | ||||
0.358273 | + | 0.933617i | \(0.383366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.1980 | −1.68756 | −0.843780 | − | 0.536689i | \(-0.819675\pi\) | ||||
−0.843780 | + | 0.536689i | \(0.819675\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.6555 | 0.683551 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.58169 | −0.101050 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.96438 | 0.315876 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.8305 | 1.25671 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.4314 | 1.10026 | 0.550129 | − | 0.835080i | \(-0.314578\pi\) | ||||
0.550129 | + | 0.835080i | \(0.314578\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.87114 | −0.242420 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.3472 | 0.770195 | 0.385098 | − | 0.922876i | \(-0.374168\pi\) | ||||
0.385098 | + | 0.922876i | \(0.374168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.0236 | 0.747108 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.21436 | −0.570355 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.7587 | −0.910060 | −0.455030 | − | 0.890476i | \(-0.650371\pi\) | ||||
−0.455030 | + | 0.890476i | \(0.650371\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.72598 | 0.351744 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −22.2943 | −1.36439 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.59624 | 0.158295 | 0.0791476 | − | 0.996863i | \(-0.474780\pi\) | ||||
0.0791476 | + | 0.996863i | \(0.474780\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.5342 | 0.882888 | 0.441444 | − | 0.897289i | \(-0.354466\pi\) | ||||
0.441444 | + | 0.897289i | \(0.354466\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.71367 | 0.587898 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.57412 | −0.517039 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.2684 | 1.69848 | 0.849241 | − | 0.528006i | \(-0.177060\pi\) | ||||
0.849241 | + | 0.528006i | \(0.177060\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.47627 | −0.148250 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9980 | 0.656083 | 0.328042 | − | 0.944663i | \(-0.393611\pi\) | ||||
0.328042 | + | 0.944663i | \(0.393611\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.9745 | −1.78180 | −0.890898 | − | 0.454203i | \(-0.849924\pi\) | ||||
−0.890898 | + | 0.454203i | \(0.849924\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.08163 | 0.182540 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.46457 | 0.440619 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.13342 | −0.537260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −34.0221 | −1.99441 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.8721 | −0.927258 | −0.463629 | − | 0.886029i | \(-0.653453\pi\) | ||||
−0.463629 | + | 0.886029i | \(0.653453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.75073 | −0.334821 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.36191 | 0.427181 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.97688 | −0.171585 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.9818 | −0.745787 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.91140 | 0.223966 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.79066 | −0.330490 | −0.165245 | − | 0.986253i | \(-0.552842\pi\) | ||||
−0.165245 | + | 0.986253i | \(0.552842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.3570 | −1.44251 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.1064 | −1.14013 | −0.570065 | − | 0.821600i | \(-0.693082\pi\) | ||||
−0.570065 | + | 0.821600i | \(0.693082\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −34.0183 | −1.92283 | −0.961415 | − | 0.275101i | \(-0.911289\pi\) | ||||
−0.961415 | + | 0.275101i | \(0.911289\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.58682 | 0.0894074 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.2032 | −0.910061 | −0.455031 | − | 0.890476i | \(-0.650372\pi\) | ||||
−0.455031 | + | 0.890476i | \(0.650372\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.2695 | −0.910915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.7723 | 0.824508 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.26222 | −0.348439 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.0770 | 0.558970 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.3387 | −0.958831 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.8985 | −1.37270 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.7611 | 1.14113 | 0.570567 | − | 0.821251i | \(-0.306723\pi\) | ||||
0.570567 | + | 0.821251i | \(0.306723\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.95026 | 0.326072 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.5750 | −0.577776 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.76630 | 0.368584 | 0.184292 | − | 0.982872i | \(-0.441001\pi\) | ||||
0.184292 | + | 0.982872i | \(0.441001\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.9639 | 1.30154 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.37225 | −0.236771 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1622 | −1.08865 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.35663 | −0.126511 | −0.0632553 | − | 0.997997i | \(-0.520148\pi\) | ||||
−0.0632553 | + | 0.997997i | \(0.520148\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.910787 | −0.0487533 | −0.0243766 | − | 0.999703i | \(-0.507760\pi\) | ||||
−0.0243766 | + | 0.999703i | \(0.507760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.65229 | −0.461825 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.8083 | −1.16074 | −0.580370 | − | 0.814353i | \(-0.697092\pi\) | ||||
−0.580370 | + | 0.814353i | \(0.697092\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.852077 | −0.0452235 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −12.2531 | −0.648504 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.0442 | 1.16345 | 0.581725 | − | 0.813386i | \(-0.302378\pi\) | ||||
0.581725 | + | 0.813386i | \(0.302378\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.0149 | −0.737628 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.9737 | 0.785918 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.17164 | 0.480065 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.06460 | 0.473168 | 0.236584 | − | 0.971611i | \(-0.423972\pi\) | ||||
0.236584 | + | 0.971611i | \(0.423972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.69409 | 0.192307 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.1242 | 0.940961 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.6202 | −1.53367 | −0.766837 | − | 0.641842i | \(-0.778171\pi\) | ||||
−0.766837 | + | 0.641842i | \(0.778171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.1563 | 0.679390 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.1211 | 0.984789 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.7843 | −1.27308 | −0.636541 | − | 0.771243i | \(-0.719636\pi\) | ||||
−0.636541 | + | 0.771243i | \(0.719636\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.0628 | −0.822921 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.26313 | −0.473324 | −0.236662 | − | 0.971592i | \(-0.576053\pi\) | ||||
−0.236662 | + | 0.971592i | \(0.576053\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.80180 | 0.142793 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.47321 | −0.0748874 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.2531 | 0.621259 | 0.310629 | − | 0.950531i | \(-0.399460\pi\) | ||||
0.310629 | + | 0.950531i | \(0.399460\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.56930 | 0.230491 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.56924 | −0.280219 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.37752 | −0.269890 | −0.134945 | − | 0.990853i | \(-0.543086\pi\) | ||||
−0.134945 | + | 0.990853i | \(0.543086\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.75415 | 0.488318 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.9387 | 1.89457 | 0.947284 | − | 0.320396i | \(-0.103816\pi\) | ||||
0.947284 | + | 0.320396i | \(0.103816\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.13861 | 0.255973 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.56963 | −0.376138 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.5062 | 0.520771 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.0040 | −0.544111 | −0.272056 | − | 0.962282i | \(-0.587703\pi\) | ||||
−0.272056 | + | 0.962282i | \(0.587703\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.59013 | −0.473046 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.2025 | −0.895688 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.72246 | −0.329993 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.1019 | 0.837483 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.4458 | 0.510313 | 0.255156 | − | 0.966900i | \(-0.417873\pi\) | ||||
0.255156 | + | 0.966900i | \(0.417873\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.49732 | 0.462871 | 0.231436 | − | 0.972850i | \(-0.425658\pi\) | ||||
0.231436 | + | 0.972850i | \(0.425658\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −12.3218 | −0.599108 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.7114 | −0.616594 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.3806 | 0.599139 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.48778 | 0.409794 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.98527 | −0.480974 | −0.240487 | − | 0.970652i | \(-0.577307\pi\) | ||||
−0.240487 | + | 0.970652i | \(0.577307\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.7332 | 1.04443 | 0.522215 | − | 0.852814i | \(-0.325106\pi\) | ||||
0.522215 | + | 0.852814i | \(0.325106\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.8694 | 0.569096 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.5206 | −0.836215 | −0.418107 | − | 0.908398i | \(-0.637306\pi\) | ||||
−0.418107 | + | 0.908398i | \(0.637306\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.47760 | −0.117981 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.8304 | 0.942169 | 0.471085 | − | 0.882088i | \(-0.343863\pi\) | ||||
0.471085 | + | 0.882088i | \(0.343863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.55768 | 0.358268 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 27.4770 | 1.29962 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.6734 | −0.550904 | −0.275452 | − | 0.961315i | \(-0.588827\pi\) | ||||
−0.275452 | + | 0.961315i | \(0.588827\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.52251 | 0.307133 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.05363 | 0.143472 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.29289 | −0.154373 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.51241 | 0.444972 | 0.222486 | − | 0.974936i | \(-0.428583\pi\) | ||||
0.222486 | + | 0.974936i | \(0.428583\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.9143 | 0.509434 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.83581 | −0.178652 | −0.0893258 | − | 0.996002i | \(-0.528471\pi\) | ||||
−0.0893258 | + | 0.996002i | \(0.528471\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.6758 | −1.79741 | −0.898707 | − | 0.438549i | \(-0.855493\pi\) | ||||
−0.898707 | + | 0.438549i | \(0.855493\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.18979 | 0.147923 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.49328 | −0.207924 | −0.103962 | − | 0.994581i | \(-0.533152\pi\) | ||||
−0.103962 | + | 0.994581i | \(0.533152\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.4727 | −1.54562 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 40.9684 | 1.88773 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.60119 | −0.119603 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.1190 | 0.464290 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.96936 | 0.410679 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.7988 | −0.813247 | −0.406623 | − | 0.913596i | \(-0.633294\pi\) | ||||
−0.406623 | + | 0.913596i | \(0.633294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.3477 | −0.563005 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.5333 | 0.523702 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.4702 | 1.15416 | 0.577082 | − | 0.816686i | \(-0.304191\pi\) | ||||
0.577082 | + | 0.816686i | \(0.304191\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.84388 | 0.354712 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.9002 | 1.84580 | 0.922899 | − | 0.385042i | \(-0.125813\pi\) | ||||
0.922899 | + | 0.385042i | \(0.125813\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.1200 | −1.08631 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.38656 | 0.0623213 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.69704 | −0.120979 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.3557 | −0.776949 | −0.388474 | − | 0.921460i | \(-0.626998\pi\) | ||||
−0.388474 | + | 0.921460i | \(0.626998\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.1575 | −0.498480 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.32866 | −0.326769 | −0.163385 | − | 0.986562i | \(-0.552241\pi\) | ||||
−0.163385 | + | 0.986562i | \(0.552241\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.40078 | 0.195832 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 16.2558 | 0.721943 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.1177 | 0.670082 | 0.335041 | − | 0.942204i | \(-0.391250\pi\) | ||||
0.335041 | + | 0.942204i | \(0.391250\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.0306 | 1.28424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.68834 | −0.383600 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.59590 | 0.378781 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −21.7562 | −0.956836 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 32.6091 | 1.43138 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.7848 | 0.954411 | 0.477206 | − | 0.878792i | \(-0.341650\pi\) | ||||
0.477206 | + | 0.878792i | \(0.341650\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.8603 | −0.562343 | −0.281172 | − | 0.959657i | \(-0.590723\pi\) | ||||
−0.281172 | + | 0.959657i | \(0.590723\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.7995 | 0.864122 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.48201 | −0.282361 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.00813 | −0.390920 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.66577 | −0.332041 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.00774 | −0.216503 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.5155 | −1.10107 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.37461 | −0.188428 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 26.3283 | 1.13194 | 0.565971 | − | 0.824425i | \(-0.308502\pi\) | ||||
0.565971 | + | 0.824425i | \(0.308502\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.0406 | 0.988768 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.87773 | 0.251774 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −33.1023 | −1.41535 | −0.707676 | − | 0.706537i | \(-0.750257\pi\) | ||||
−0.707676 | + | 0.706537i | \(0.750257\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.12694 | 0.261492 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.2008 | 0.817983 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.6281 | −0.749621 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.66480 | −0.325352 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.0125 | 1.35641 | 0.678207 | − | 0.734871i | \(-0.262757\pi\) | ||||
0.678207 | + | 0.734871i | \(0.262757\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.05712 | 0.129302 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.7067 | −0.452039 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.9340 | 0.502959 | 0.251480 | − | 0.967863i | \(-0.419083\pi\) | ||||
0.251480 | + | 0.967863i | \(0.419083\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.12365 | −0.341765 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.9598 | −1.00622 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −28.2753 | −1.18536 | −0.592682 | − | 0.805436i | \(-0.701931\pi\) | ||||
−0.592682 | + | 0.805436i | \(0.701931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.2981 | −1.60272 | −0.801362 | − | 0.598179i | \(-0.795891\pi\) | ||||
−0.801362 | + | 0.598179i | \(0.795891\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.35961 | 0.265677 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.835083 | −0.0347650 | −0.0173825 | − | 0.999849i | \(-0.505533\pi\) | ||||
−0.0173825 | + | 0.999849i | \(0.505533\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −33.3045 | −1.38409 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −21.2783 | −0.882773 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.8369 | 0.655896 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.62960 | −0.0673755 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.2288 | 0.752382 | 0.376191 | − | 0.926542i | \(-0.377234\pi\) | ||||
0.376191 | + | 0.926542i | \(0.377234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.16003 | 0.212615 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 35.3128 | 1.45257 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 35.7660 | 1.46873 | 0.734366 | − | 0.678754i | \(-0.237480\pi\) | ||||
0.734366 | + | 0.678754i | \(0.237480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.15375 | 0.170287 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.96293 | −0.325901 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.11167 | −0.208857 | −0.104429 | − | 0.994532i | \(-0.533301\pi\) | ||||
−0.104429 | + | 0.994532i | \(0.533301\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.4661 | −1.69144 | −0.845720 | − | 0.533627i | \(-0.820829\pi\) | ||||
−0.845720 | + | 0.533627i | \(0.820829\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.5651 | −0.674582 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.07603 | −0.206370 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.78706 | −0.397245 | −0.198622 | − | 0.980076i | \(-0.563647\pi\) | ||||
−0.198622 | + | 0.980076i | \(0.563647\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 37.5698 | 1.52240 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.5696 | 1.03443 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.0624 | 0.850703 | 0.425351 | − | 0.905028i | \(-0.360150\pi\) | ||||
0.425351 | + | 0.905028i | \(0.360150\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.75852 | −0.191882 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.8273 | 1.36183 | 0.680917 | − | 0.732361i | \(-0.261581\pi\) | ||||
0.680917 | + | 0.732361i | \(0.261581\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.46841 | 0.0590204 | 0.0295102 | − | 0.999564i | \(-0.490605\pi\) | ||||
0.0295102 | + | 0.999564i | \(0.490605\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.9220 | 0.958414 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.2006 | 0.728026 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.52314 | 0.340382 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.5757 | 0.621045 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.13363 | 0.0451290 | 0.0225645 | − | 0.999745i | \(-0.492817\pi\) | ||||
0.0225645 | + | 0.999745i | \(0.492817\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.2339 | 1.12220 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.44521 | 0.216086 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.14139 | 0.203709 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.33472 | −0.0528007 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.9836 | 1.34227 | 0.671136 | − | 0.741335i | \(-0.265807\pi\) | ||||
0.671136 | + | 0.741335i | \(0.265807\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.17625 | 0.0463866 | 0.0231933 | − | 0.999731i | \(-0.492617\pi\) | ||||
0.0231933 | + | 0.999731i | \(0.492617\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.89770 | 0.0747220 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.2359 | −0.402416 | −0.201208 | − | 0.979549i | \(-0.564487\pi\) | ||||
−0.201208 | + | 0.979549i | \(0.564487\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.9053 | −0.624338 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.0965 | 0.395713 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −44.6392 | −1.74687 | −0.873433 | − | 0.486945i | \(-0.838111\pi\) | ||||
−0.873433 | + | 0.486945i | \(0.838111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.54897 | −0.0605234 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.3667 | 0.560500 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.7671 | 0.614199 | 0.307099 | − | 0.951677i | \(-0.400642\pi\) | ||||
0.307099 | + | 0.951677i | \(0.400642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.0071 | −0.661501 | −0.330751 | − | 0.943718i | \(-0.607302\pi\) | ||||
−0.330751 | + | 0.943718i | \(0.607302\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.5834 | 0.488699 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.30661 | −0.128225 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 54.0879 | 2.09116 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.8181 | 0.417629 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.81165 | 0.185476 | 0.0927378 | − | 0.995691i | \(-0.470438\pi\) | ||||
0.0927378 | + | 0.995691i | \(0.470438\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.6361 | −0.678814 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.4412 | 0.670322 | 0.335161 | − | 0.942161i | \(-0.391209\pi\) | ||||
0.335161 | + | 0.942161i | \(0.391209\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.5060 | 1.40097 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 48.7199 | 1.86695 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.4732 | −1.20429 | −0.602145 | − | 0.798387i | \(-0.705687\pi\) | ||||
−0.602145 | + | 0.798387i | \(0.705687\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.25101 | 0.124215 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.8027 | 0.984435 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.6127 | −0.709088 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.1989 | 0.920570 | 0.460285 | − | 0.887771i | \(-0.347747\pi\) | ||||
0.460285 | + | 0.887771i | \(0.347747\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.38882 | 0.166718 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.79746 | −0.219910 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.66984 | 0.366271 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.9691 | −0.604005 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.1778 | 0.573257 | 0.286629 | − | 0.958042i | \(-0.407465\pi\) | ||||
0.286629 | + | 0.958042i | \(0.407465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.3991 | −0.467641 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.8723 | 0.597785 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.9296 | 0.523876 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.2973 | 1.17540 | 0.587698 | − | 0.809080i | \(-0.300034\pi\) | ||||
0.587698 | + | 0.809080i | \(0.300034\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.72383 | −0.327169 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.87732 | −0.107606 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.3521 | −0.834755 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.8276 | −1.74638 | −0.873188 | − | 0.487383i | \(-0.837951\pi\) | ||||
−0.873188 | + | 0.487383i | \(0.837951\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 27.2082 | 1.01329 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 52.8620 | 1.96596 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 38.9749 | 1.44749 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.4833 | 1.50144 | 0.750721 | − | 0.660619i | \(-0.229706\pi\) | ||||
0.750721 | + | 0.660619i | \(0.229706\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.6985 | 0.433279 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.85635 | −0.142632 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.0451 | −0.925061 | −0.462530 | − | 0.886603i | \(-0.653058\pi\) | ||||
−0.462530 | + | 0.886603i | \(0.653058\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.19151 | 0.117721 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −29.2483 | −1.07738 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.01275 | 0.0372546 | 0.0186273 | − | 0.999826i | \(-0.494070\pi\) | ||||
0.0186273 | + | 0.999826i | \(0.494070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.0171 | −0.367986 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.1693 | 1.80385 | 0.901923 | − | 0.431896i | \(-0.142155\pi\) | ||||
0.901923 | + | 0.431896i | \(0.142155\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.31458 | −0.341260 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.5303 | −0.385283 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.8508 | −0.579174 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.2429 | 0.519731 | 0.259866 | − | 0.965645i | \(-0.416322\pi\) | ||||
0.259866 | + | 0.965645i | \(0.416322\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −35.1728 | −1.28177 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.03517 | −0.0376735 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.22786 | 0.117318 | 0.0586592 | − | 0.998278i | \(-0.481317\pi\) | ||||
0.0586592 | + | 0.998278i | \(0.481317\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.9756 | −0.651615 | −0.325808 | − | 0.945436i | \(-0.605636\pi\) | ||||
−0.325808 | + | 0.945436i | \(0.605636\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.6045 | 0.673529 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.05562 | 0.0743212 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 18.6932 | 0.674972 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.73961 | 0.0627320 | 0.0313660 | − | 0.999508i | \(-0.490014\pi\) | ||||
0.0313660 | + | 0.999508i | \(0.490014\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.9140 | −0.897255 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.05709 | −0.325761 | −0.162880 | − | 0.986646i | \(-0.552078\pi\) | ||||
−0.162880 | + | 0.986646i | \(0.552078\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.4741 | 0.376241 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.2610 | −0.870360 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.69771 | −0.275799 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.35667 | −0.0843281 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −33.4646 | −1.19593 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.8881 | −0.495688 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.9164 | −0.709943 | −0.354972 | − | 0.934877i | \(-0.615509\pi\) | ||||
−0.354972 | + | 0.934877i | \(0.615509\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.7799 | 1.06019 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.7134 | −0.914264 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.7143 | −0.451498 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.5538 | −0.409772 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.5349 | −1.36498 | −0.682488 | − | 0.730897i | \(-0.739102\pi\) | ||||
−0.682488 | + | 0.730897i | \(0.739102\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.2543 | −1.14107 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.8386 | 0.418296 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.3668 | 0.895176 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.23865 | −0.184409 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.6633 | 1.14838 | 0.574189 | − | 0.818722i | \(-0.305317\pi\) | ||||
0.574189 | + | 0.818722i | \(0.305317\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.0132 | −0.667645 | −0.333822 | − | 0.942636i | \(-0.608339\pi\) | ||||
−0.333822 | + | 0.942636i | \(0.608339\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.3269 | −1.02854 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.65904 | −0.0931420 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.06986 | 0.107401 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.15809 | −0.180238 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.5871 | −0.439291 | −0.219646 | − | 0.975580i | \(-0.570490\pi\) | ||||
−0.219646 | + | 0.975580i | \(0.570490\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.7562 | 0.793231 | 0.396616 | − | 0.917985i | \(-0.370185\pi\) | ||||
0.396616 | + | 0.917985i | \(0.370185\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.3008 | 0.602335 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 26.5016 | 0.921550 | 0.460775 | − | 0.887517i | \(-0.347572\pi\) | ||||
0.460775 | + | 0.887517i | \(0.347572\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.3904 | 1.26389 | 0.631946 | − | 0.775012i | \(-0.282256\pi\) | ||||
0.631946 | + | 0.775012i | \(0.282256\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.0396 | −1.97868 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.48551 | −0.224709 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.78234 | 0.130893 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.99328 | −0.310853 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.17356 | 0.0405158 | 0.0202579 | − | 0.999795i | \(-0.493551\pi\) | ||||
0.0202579 | + | 0.999795i | \(0.493551\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.9552 | 1.55018 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −22.1916 | −0.764318 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −5.51063 | −0.189571 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −16.0669 | −0.552066 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 60.4821 | 2.07574 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.163542 | 0.00559959 | 0.00279979 | − | 0.999996i | \(-0.499109\pi\) | ||||
0.00279979 | + | 0.999996i | \(0.499109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.63639 | −0.0559632 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.5196 | 0.359342 | 0.179671 | − | 0.983727i | \(-0.442497\pi\) | ||||
0.179671 | + | 0.983727i | \(0.442497\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.716641 | 0.0244515 | 0.0122257 | − | 0.999925i | \(-0.496108\pi\) | ||||
0.0122257 | + | 0.999925i | \(0.496108\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0619 | −0.513309 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 53.5759 | 1.82374 | 0.911872 | − | 0.410474i | \(-0.134637\pi\) | ||||
0.911872 | + | 0.410474i | \(0.134637\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.0543 | −0.375859 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.4293 | 0.625892 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15.4033 | −0.522522 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.3749 | 1.16475 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.0662 | 0.611448 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.1168 | −0.477236 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.6430 | −1.00097 | −0.500486 | − | 0.865745i | \(-0.666845\pi\) | ||||
−0.500486 | + | 0.865745i | \(0.666845\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.0266 | 1.08023 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.91347 | 0.165539 | 0.0827696 | − | 0.996569i | \(-0.473623\pi\) | ||||
0.0827696 | + | 0.996569i | \(0.473623\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11.4104 | −0.383989 | −0.191995 | − | 0.981396i | \(-0.561496\pi\) | ||||
−0.191995 | + | 0.981396i | \(0.561496\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.6038 | 0.390056 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.2006 | 0.913305 | 0.456653 | − | 0.889645i | \(-0.349048\pi\) | ||||
0.456653 | + | 0.889645i | \(0.349048\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.2355 | 0.578059 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.9360 | −0.701382 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.6761 | 0.859219 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.64963 | 0.289125 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.8747 | 0.662859 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.4787 | 0.782188 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.00672 | 0.199891 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.81067 | −0.259636 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.4093 | −0.611272 | −0.305636 | − | 0.952148i | \(-0.598869\pi\) | ||||
−0.305636 | + | 0.952148i | \(0.598869\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.89352 | 0.228644 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.7510 | 1.64833 | 0.824163 | − | 0.566353i | \(-0.191646\pi\) | ||||
0.824163 | + | 0.566353i | \(0.191646\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.5929 | −0.615336 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.89239 | −0.260914 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.90289 | −0.161908 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.6449 | 1.20880 | 0.604402 | − | 0.796680i | \(-0.293412\pi\) | ||||
0.604402 | + | 0.796680i | \(0.293412\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.6843 | 0.385012 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.76974 | 0.0911670 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −25.1684 | −0.827533 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.4649 | 0.442245 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.1338 | 0.988658 | 0.494329 | − | 0.869275i | \(-0.335414\pi\) | ||||
0.494329 | + | 0.869275i | \(0.335414\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.16281 | 0.169204 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 40.5705 | 1.32822 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.62954 | 0.118699 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.7552 | −0.808719 | −0.404359 | − | 0.914600i | \(-0.632505\pi\) | ||||
−0.404359 | + | 0.914600i | \(0.632505\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 68.6418 | 2.24004 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.15351 | 0.200599 | 0.100299 | − | 0.994957i | \(-0.468020\pi\) | ||||
0.100299 | + | 0.994957i | \(0.468020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.76301 | 0.187471 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −59.4254 | −1.93107 | −0.965533 | − | 0.260279i | \(-0.916185\pi\) | ||||
−0.965533 | + | 0.260279i | \(0.916185\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.8131 | −0.967773 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.6946 | 1.06019 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.8168 | 1.38697 | 0.693487 | − | 0.720469i | \(-0.256074\pi\) | ||||
0.693487 | + | 0.720469i | \(0.256074\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.15588 | −0.0697626 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.8283 | 1.06119 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.2903 | 0.332290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.6589 | −0.827706 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.84427 | −0.252778 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.2901 | 0.363441 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8748 | 0.414026 | 0.207013 | − | 0.978338i | \(-0.433626\pi\) | ||||
0.207013 | + | 0.978338i | \(0.433626\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.6358 | 0.405922 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 40.6407 | 1.30422 | 0.652111 | − | 0.758123i | \(-0.273884\pi\) | ||||
0.652111 | + | 0.758123i | \(0.273884\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3504 | −0.588288 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −20.3332 | −0.651184 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.9540 | −0.638384 | −0.319192 | − | 0.947690i | \(-0.603411\pi\) | ||||
−0.319192 | + | 0.947690i | \(0.603411\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.9030 | 0.668061 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.20706 | 0.293959 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.51066 | 0.175763 | 0.0878813 | − | 0.996131i | \(-0.471990\pi\) | ||||
0.0878813 | + | 0.996131i | \(0.471990\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.9709 | −0.381424 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 50.2398 | 1.59915 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.4831 | −0.841263 | −0.420632 | − | 0.907232i | \(-0.638191\pi\) | ||||
−0.420632 | + | 0.907232i | \(0.638191\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −41.8916 | −1.32939 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.69940 | 0.0855767 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.8330 | 1.35654 | 0.678268 | − | 0.734815i | \(-0.262731\pi\) | ||||
0.678268 | + | 0.734815i | \(0.262731\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.6101 | 0.683713 |
(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 | 4232.2.a.ba.1.4 | 15 | ||
4.3 | odd | 2 | 8464.2.a.ch.1.12 | 15 | |||
23.15 | odd | 22 | 184.2.i.b.41.3 | yes | 30 | ||
23.20 | odd | 22 | 184.2.i.b.9.3 | ✓ | 30 | ||
23.22 | odd | 2 | 4232.2.a.bb.1.4 | 15 | |||
92.15 | even | 22 | 368.2.m.e.225.1 | 30 | |||
92.43 | even | 22 | 368.2.m.e.193.1 | 30 | |||
92.91 | even | 2 | 8464.2.a.cg.1.12 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
184.2.i.b.9.3 | ✓ | 30 | 23.20 | odd | 22 | ||
184.2.i.b.41.3 | yes | 30 | 23.15 | odd | 22 | ||
368.2.m.e.193.1 | 30 | 92.43 | even | 22 | |||
368.2.m.e.225.1 | 30 | 92.15 | even | 22 | |||
4232.2.a.ba.1.4 | 15 | 1.1 | even | 1 | trivial | ||
4232.2.a.bb.1.4 | 15 | 23.22 | odd | 2 | |||
8464.2.a.cg.1.12 | 15 | 92.91 | even | 2 | |||
8464.2.a.ch.1.12 | 15 | 4.3 | odd | 2 |