Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 28 x^{15} + 54 x^{14} + 317 x^{13} - 582 x^{12} - 1867 x^{11} + 3178 x^{10} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 251) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.27410\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.935470 | −0.540094 | −0.270047 | − | 0.962847i | \(-0.587039\pi\) | ||||
−0.270047 | + | 0.962847i | \(0.587039\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.41593 | 1.52765 | 0.763826 | − | 0.645423i | \(-0.223319\pi\) | ||||
0.763826 | + | 0.645423i | \(0.223319\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.69332 | −1.39594 | −0.697971 | − | 0.716126i | \(-0.745914\pi\) | ||||
−0.697971 | + | 0.716126i | \(0.745914\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.12490 | −0.708299 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.09538 | 0.330269 | 0.165135 | − | 0.986271i | \(-0.447194\pi\) | ||||
0.165135 | + | 0.986271i | \(0.447194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0975293 | 0.0270498 | 0.0135249 | − | 0.999909i | \(-0.495695\pi\) | ||||
0.0135249 | + | 0.999909i | \(0.495695\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.19550 | −0.825075 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.03572 | −0.978807 | −0.489403 | − | 0.872057i | \(-0.662785\pi\) | ||||
−0.489403 | + | 0.872057i | \(0.662785\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.04841 | −1.15819 | −0.579093 | − | 0.815262i | \(-0.696593\pi\) | ||||
−0.579093 | + | 0.815262i | \(0.696593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.45499 | 0.753940 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.592256 | 0.123494 | 0.0617469 | − | 0.998092i | \(-0.480333\pi\) | ||||
0.0617469 | + | 0.998092i | \(0.480333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.66859 | 1.33372 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.79419 | 0.922641 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.45917 | −0.642352 | −0.321176 | − | 0.947020i | \(-0.604078\pi\) | ||||
−0.321176 | + | 0.947020i | \(0.604078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.372983 | 0.0669897 | 0.0334948 | − | 0.999439i | \(-0.489336\pi\) | ||||
0.0334948 | + | 0.999439i | \(0.489336\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.02469 | −0.178376 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.6161 | −2.13251 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.18783 | 1.01727 | 0.508636 | − | 0.860981i | \(-0.330150\pi\) | ||||
0.508636 | + | 0.860981i | \(0.330150\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.0912357 | −0.0146094 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.3439 | 1.77161 | 0.885807 | − | 0.464054i | \(-0.153605\pi\) | ||||
0.885807 | + | 0.464054i | \(0.153605\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.37250 | 0.819298 | 0.409649 | − | 0.912243i | \(-0.365651\pi\) | ||||
0.409649 | + | 0.912243i | \(0.365651\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.25850 | −1.08203 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.3815 | 1.51430 | 0.757152 | − | 0.653239i | \(-0.226590\pi\) | ||||
0.757152 | + | 0.653239i | \(0.226590\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.64059 | 0.948655 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.77530 | 0.528647 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.2337 | −1.54306 | −0.771531 | − | 0.636192i | \(-0.780508\pi\) | ||||
−0.771531 | + | 0.636192i | \(0.780508\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.74174 | 0.504537 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.72264 | 0.625529 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.25509 | 0.944533 | 0.472266 | − | 0.881456i | \(-0.343436\pi\) | ||||
0.472266 | + | 0.881456i | \(0.343436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.601444 | 0.0770070 | 0.0385035 | − | 0.999258i | \(-0.487741\pi\) | ||||
0.0385035 | + | 0.999258i | \(0.487741\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.84791 | 0.988744 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.333153 | 0.0413226 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6371 | −1.42170 | −0.710848 | − | 0.703346i | \(-0.751689\pi\) | ||||
−0.710848 | + | 0.703346i | \(0.751689\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.554038 | −0.0666983 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.624713 | 0.0741397 | 0.0370699 | − | 0.999313i | \(-0.488198\pi\) | ||||
0.0370699 | + | 0.999313i | \(0.488198\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.71599 | 1.13717 | 0.568585 | − | 0.822624i | \(-0.307491\pi\) | ||||
0.568585 | + | 0.822624i | \(0.307491\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6.23827 | −0.720333 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.04558 | −0.461037 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.82487 | 0.767858 | 0.383929 | − | 0.923363i | \(-0.374571\pi\) | ||||
0.383929 | + | 0.923363i | \(0.374571\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.88987 | 0.209986 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.5486 | 1.70668 | 0.853341 | − | 0.521353i | \(-0.174572\pi\) | ||||
0.853341 | + | 0.521353i | \(0.174572\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.7858 | −1.49528 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.23595 | 0.346930 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.9119 | 1.68665 | 0.843327 | − | 0.537401i | \(-0.180594\pi\) | ||||
0.843327 | + | 0.537401i | \(0.180594\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.360206 | −0.0377599 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.348914 | −0.0361807 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −17.2450 | −1.76930 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.70534 | −0.782359 | −0.391179 | − | 0.920314i | \(-0.627933\pi\) | ||||
−0.391179 | + | 0.920314i | \(0.627933\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.32757 | −0.233929 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.0872 | 1.79975 | 0.899873 | − | 0.436153i | \(-0.143659\pi\) | ||||
0.899873 | + | 0.436153i | \(0.143659\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.78184 | 0.766767 | 0.383384 | − | 0.923589i | \(-0.374759\pi\) | ||||
0.383384 | + | 0.923589i | \(0.374759\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.8020 | 1.15176 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.56314 | 0.247788 | 0.123894 | − | 0.992295i | \(-0.460462\pi\) | ||||
0.123894 | + | 0.992295i | \(0.460462\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.411462 | 0.0394109 | 0.0197054 | − | 0.999806i | \(-0.493727\pi\) | ||||
0.0197054 | + | 0.999806i | \(0.493727\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.78853 | −0.549423 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.12662 | −0.388200 | −0.194100 | − | 0.980982i | \(-0.562179\pi\) | ||||
−0.194100 | + | 0.980982i | \(0.562179\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.02311 | 0.188656 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.207240 | −0.0191593 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.9052 | 1.36636 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.80014 | −0.890922 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.6118 | −0.956838 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.69980 | 0.509805 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8625 | 1.05263 | 0.526316 | − | 0.850289i | \(-0.323573\pi\) | ||||
0.526316 | + | 0.850289i | \(0.323573\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.02581 | −0.442498 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.4352 | −1.96017 | −0.980087 | − | 0.198570i | \(-0.936370\pi\) | ||||
−0.980087 | + | 0.198570i | \(0.936370\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.6454 | 1.61676 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.3766 | 1.40947 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.6248 | −0.907740 | −0.453870 | − | 0.891068i | \(-0.649957\pi\) | ||||
−0.453870 | + | 0.891068i | \(0.649957\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.7360 | 1.50435 | 0.752175 | − | 0.658964i | \(-0.229005\pi\) | ||||
0.752175 | + | 0.658964i | \(0.229005\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.71162 | −0.817866 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.106832 | 0.00893371 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.8163 | −0.981290 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.21207 | −0.512363 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.3371 | 0.846844 | 0.423422 | − | 0.905933i | \(-0.360829\pi\) | ||||
0.423422 | + | 0.905933i | \(0.360829\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.0755 | −0.901312 | −0.450656 | − | 0.892698i | \(-0.648810\pi\) | ||||
−0.450656 | + | 0.892698i | \(0.648810\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.57550 | 0.693288 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.27408 | 0.102337 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −24.3028 | −1.93957 | −0.969787 | − | 0.243955i | \(-0.921555\pi\) | ||||
−0.969787 | + | 0.243955i | \(0.921555\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.5087 | 0.833398 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18739 | −0.172390 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.6767 | 0.992913 | 0.496456 | − | 0.868062i | \(-0.334634\pi\) | ||||
0.496456 | + | 0.868062i | \(0.334634\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.50029 | −0.272497 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.35277 | −0.646357 | −0.323178 | − | 0.946338i | \(-0.604751\pi\) | ||||
−0.323178 | + | 0.946338i | \(0.604751\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9905 | −0.999268 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.7274 | 0.820342 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.8831 | 0.979487 | 0.489744 | − | 0.871866i | \(-0.337090\pi\) | ||||
0.489744 | + | 0.871866i | \(0.337090\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −24.6292 | −1.86179 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.78692 | −0.510136 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 26.3530 | 1.96971 | 0.984856 | − | 0.173373i | \(-0.0554666\pi\) | ||||
0.984856 | + | 0.173373i | \(0.0554666\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.9891 | −1.26279 | −0.631396 | − | 0.775461i | \(-0.717518\pi\) | ||||
−0.631396 | + | 0.775461i | \(0.717518\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.562633 | −0.0415910 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.1372 | 1.55404 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.42065 | −0.323270 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −17.7064 | −1.28795 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.24390 | −0.524151 | −0.262075 | − | 0.965047i | \(-0.584407\pi\) | ||||
−0.262075 | + | 0.965047i | \(0.584407\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.35410 | 0.169452 | 0.0847259 | − | 0.996404i | \(-0.472999\pi\) | ||||
0.0847259 | + | 0.996404i | \(0.472999\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.311655 | −0.0223181 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.2704 | −0.874233 | −0.437117 | − | 0.899405i | \(-0.644000\pi\) | ||||
−0.437117 | + | 0.899405i | \(0.644000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.62720 | −0.115349 | −0.0576745 | − | 0.998335i | \(-0.518369\pi\) | ||||
−0.0576745 | + | 0.998335i | \(0.518369\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.8861 | 0.767849 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.7758 | 0.896686 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 38.7499 | 2.70641 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.25848 | −0.0874706 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.52993 | −0.382513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7353 | −0.876736 | −0.438368 | − | 0.898796i | \(-0.644443\pi\) | ||||
−0.438368 | + | 0.898796i | \(0.644443\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.584400 | −0.0400424 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.3521 | 1.25160 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.37754 | −0.0935137 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.08901 | −0.614179 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.393601 | −0.0264765 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.4100 | −1.50069 | −0.750343 | − | 0.661048i | \(-0.770112\pi\) | ||||
−0.750343 | + | 0.661048i | \(0.770112\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.1701 | −0.944671 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.39073 | 0.623285 | 0.311642 | − | 0.950199i | \(-0.399121\pi\) | ||||
0.311642 | + | 0.950199i | \(0.399121\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8143 | 0.978957 | 0.489478 | − | 0.872015i | \(-0.337187\pi\) | ||||
0.489478 | + | 0.872015i | \(0.337187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.78452 | 0.249003 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.7123 | 0.767297 | 0.383648 | − | 0.923479i | \(-0.374667\pi\) | ||||
0.383648 | + | 0.923479i | \(0.374667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 35.4627 | 2.31333 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.38446 | −0.414715 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.8228 | 1.67034 | 0.835168 | − | 0.549995i | \(-0.185371\pi\) | ||||
0.835168 | + | 0.549995i | \(0.185371\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.23762 | 0.337385 | 0.168692 | − | 0.985669i | \(-0.446046\pi\) | ||||
0.168692 | + | 0.985669i | \(0.446046\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1505 | −1.03605 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 22.6838 | 1.44921 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.492368 | −0.0313286 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −14.5453 | −0.921768 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.648745 | 0.0407863 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.8962 | 0.807589 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.3189 | 1.57935 | 0.789675 | − | 0.613525i | \(-0.210249\pi\) | ||||
0.789675 | + | 0.613525i | \(0.210249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −22.8536 | −1.42005 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.35038 | 0.454977 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.9977 | 0.678147 | 0.339074 | − | 0.940760i | \(-0.389886\pi\) | ||||
0.339074 | + | 0.940760i | \(0.389886\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −38.3734 | −2.35726 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.8851 | −0.910951 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.8062 | 1.51246 | 0.756230 | − | 0.654305i | \(-0.227039\pi\) | ||||
0.756230 | + | 0.654305i | \(0.227039\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.48722 | 0.333325 | 0.166662 | − | 0.986014i | \(-0.446701\pi\) | ||||
0.166662 | + | 0.986014i | \(0.446701\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.336962 | 0.0203939 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.30464 | 0.440486 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.78730 | 0.347725 | 0.173862 | − | 0.984770i | \(-0.444375\pi\) | ||||
0.173862 | + | 0.984770i | \(0.444375\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.792550 | −0.0474487 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7109 | 0.758266 | 0.379133 | − | 0.925342i | \(-0.376222\pi\) | ||||
0.379133 | + | 0.925342i | \(0.376222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.50578 | −0.505616 | −0.252808 | − | 0.967516i | \(-0.581354\pi\) | ||||
−0.252808 | + | 0.967516i | \(0.581354\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.1322 | 0.955590 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −41.8965 | −2.47307 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.712929 | −0.0419370 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.20811 | 0.422547 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.2686 | 1.12569 | 0.562843 | − | 0.826564i | \(-0.309708\pi\) | ||||
0.562843 | + | 0.826564i | \(0.309708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.7829 | 1.44292 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.25145 | 0.304720 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.0577623 | 0.00334048 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.8423 | −1.14369 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −16.9200 | −0.972031 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.05449 | 0.117640 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.292654 | 0.0167026 | 0.00835132 | − | 0.999965i | \(-0.497342\pi\) | ||||
0.00835132 | + | 0.999965i | \(0.497342\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.27967 | −0.414126 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.10705 | −0.289594 | −0.144797 | − | 0.989461i | \(-0.546253\pi\) | ||||
−0.144797 | + | 0.989461i | \(0.546253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.20479 | −0.407239 | −0.203619 | − | 0.979050i | \(-0.565271\pi\) | ||||
−0.203619 | + | 0.979050i | \(0.565271\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 26.8079 | 1.51046 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.6486 | −0.598086 | −0.299043 | − | 0.954240i | \(-0.596667\pi\) | ||||
−0.299043 | + | 0.954240i | \(0.596667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.78911 | −0.212149 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.39774 | −0.133829 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.3740 | 1.13364 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.650383 | 0.0360768 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.384910 | −0.0212856 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −38.3423 | −2.11388 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4433 | −0.903804 | −0.451902 | − | 0.892068i | \(-0.649254\pi\) | ||||
−0.451902 | + | 0.892068i | \(0.649254\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −13.1485 | −0.720533 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −39.7515 | −2.17186 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0936 | 0.767728 | 0.383864 | − | 0.923390i | \(-0.374593\pi\) | ||||
0.383864 | + | 0.923390i | \(0.374593\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.86033 | 0.209664 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.408558 | 0.0221246 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.32743 | 0.0716743 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.89255 | −0.101892 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.7871 | −0.579084 | −0.289542 | − | 0.957165i | \(-0.593503\pi\) | ||||
−0.289542 | + | 0.957165i | \(0.593503\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.97572 | 0.426930 | 0.213465 | − | 0.976951i | \(-0.431525\pi\) | ||||
0.213465 | + | 0.976951i | \(0.431525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.467573 | 0.0249572 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.2749 | 0.600104 | 0.300052 | − | 0.953923i | \(-0.402996\pi\) | ||||
0.300052 | + | 0.953923i | \(0.402996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.13398 | 0.113260 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.9434 | −0.737961 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1558 | −0.694339 | −0.347169 | − | 0.937802i | \(-0.612857\pi\) | ||||
−0.347169 | + | 0.937802i | \(0.612857\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.48649 | 0.341394 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.16774 | 0.481181 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 33.1892 | 1.73720 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.6315 | −0.554961 | −0.277481 | − | 0.960731i | \(-0.589499\pi\) | ||||
−0.277481 | + | 0.960731i | \(0.589499\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.1045 | −1.25483 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 41.4894 | 2.15402 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.1705 | −0.630163 | −0.315082 | − | 0.949065i | \(-0.602032\pi\) | ||||
−0.315082 | + | 0.949065i | \(0.602032\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.33199 | −0.275343 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.337370 | −0.0173755 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.32877 | 0.119621 | 0.0598103 | − | 0.998210i | \(-0.480950\pi\) | ||||
0.0598103 | + | 0.998210i | \(0.480950\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.0971 | −0.568519 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.235563 | −0.0120367 | −0.00601835 | − | 0.999982i | \(-0.501916\pi\) | ||||
−0.00601835 | + | 0.999982i | \(0.501916\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.8194 | −0.704304 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.4160 | −0.580308 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.8102 | −1.15652 | −0.578261 | − | 0.815852i | \(-0.696268\pi\) | ||||
−0.578261 | + | 0.815852i | \(0.696268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.39018 | −0.120877 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.9875 | 1.05868 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 23.3133 | 1.17302 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.5310 | 1.18099 | 0.590493 | − | 0.807043i | \(-0.298933\pi\) | ||||
0.590493 | + | 0.807043i | \(0.298933\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.4422 | −0.873202 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.765035 | −0.0382040 | −0.0191020 | − | 0.999818i | \(-0.506081\pi\) | ||||
−0.0191020 | + | 0.999818i | \(0.506081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0363767 | 0.00181205 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.45568 | 0.320785 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.77802 | 0.335974 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.60286 | −0.277044 | −0.138522 | − | 0.990359i | \(-0.544235\pi\) | ||||
−0.138522 | + | 0.990359i | \(0.544235\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 9.93920 | 0.490265 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.7954 | −1.31851 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 53.1130 | 2.60722 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.5915 | −0.812490 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.8299 | 1.21302 | 0.606509 | − | 0.795077i | \(-0.292569\pi\) | ||||
0.606509 | + | 0.795077i | \(0.292569\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.2521 | 0.597133 | 0.298566 | − | 0.954389i | \(-0.403492\pi\) | ||||
0.298566 | + | 0.954389i | \(0.403492\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.0597 | −1.07258 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −26.9126 | −1.30545 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.22132 | −0.107497 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.0999377 | −0.00482504 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.3396 | 1.17240 | 0.586199 | − | 0.810167i | \(-0.300624\pi\) | ||||
0.586199 | + | 0.810167i | \(0.300624\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.35633 | 0.401580 | 0.200790 | − | 0.979634i | \(-0.435649\pi\) | ||||
0.200790 | + | 0.979634i | \(0.435649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.0538 | 0.529988 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.98995 | −0.143029 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.67395 | 0.270803 | 0.135402 | − | 0.990791i | \(-0.456768\pi\) | ||||
0.135402 | + | 0.990791i | \(0.456768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.1106 | −0.671931 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.55735 | −0.169015 | −0.0845073 | − | 0.996423i | \(-0.526932\pi\) | ||||
−0.0845073 | + | 0.996423i | \(0.526932\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 54.3538 | 2.57662 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.67000 | −0.457375 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.9540 | 1.31923 | 0.659616 | − | 0.751603i | \(-0.270719\pi\) | ||||
0.659616 | + | 0.751603i | \(0.270719\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.4258 | 0.585110 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.3608 | 0.486793 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.23044 | −0.0576840 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2752 | 0.527430 | 0.263715 | − | 0.964601i | \(-0.415052\pi\) | ||||
0.263715 | + | 0.964601i | \(0.415052\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.3480 | −0.903088 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.2942 | 0.945193 | 0.472597 | − | 0.881279i | \(-0.343317\pi\) | ||||
0.472597 | + | 0.881279i | \(0.343317\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.6264 | 1.19096 | 0.595481 | − | 0.803370i | \(-0.296962\pi\) | ||||
0.595481 | + | 0.803370i | \(0.296962\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.19187 | −0.0552715 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.0460 | −0.881345 | −0.440673 | − | 0.897668i | \(-0.645260\pi\) | ||||
−0.440673 | + | 0.897668i | \(0.645260\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.9794 | 1.98461 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.7345 | 1.04755 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.88492 | 0.270589 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.6658 | −1.54469 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 23.8704 | 1.09295 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.620088 | −0.0283326 | −0.0141663 | − | 0.999900i | \(-0.504509\pi\) | ||||
−0.0141663 | + | 0.999900i | \(0.504509\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.603495 | 0.0275170 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.04624 | 0.0931070 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −26.3209 | −1.19517 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.10719 | −0.140800 | −0.0704000 | − | 0.997519i | \(-0.522428\pi\) | ||||
−0.0704000 | + | 0.997519i | \(0.522428\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −11.8586 | −0.536266 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.67757 | 0.0757079 | 0.0378539 | − | 0.999283i | \(-0.487948\pi\) | ||||
0.0378539 | + | 0.999283i | \(0.487948\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13.9603 | 0.628739 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.95082 | −0.357363 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.30726 | −0.103495 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.6142 | 0.833284 | 0.416642 | − | 0.909071i | \(-0.363207\pi\) | ||||
0.416642 | + | 0.909071i | \(0.363207\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.81376 | 0.349093 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 29.5856 | 1.31915 | 0.659577 | − | 0.751637i | \(-0.270735\pi\) | ||||
0.659577 | + | 0.751637i | \(0.270735\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 61.7847 | 2.74938 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.1522 | 0.539699 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.2807 | 1.12055 | 0.560274 | − | 0.828307i | \(-0.310696\pi\) | ||||
0.560274 | + | 0.828307i | \(0.310696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −35.8842 | −1.58742 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.2030 | −1.06859 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.5822 | 1.17135 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3717 | 0.500128 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0518 | −0.529015 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.4315 | 1.37704 | 0.688520 | − | 0.725217i | \(-0.258261\pi\) | ||||
0.688520 | + | 0.725217i | \(0.258261\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.72046 | −0.118957 | −0.0594786 | − | 0.998230i | \(-0.518944\pi\) | ||||
−0.0594786 | + | 0.998230i | \(0.518944\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 23.0399 | 1.00554 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.50526 | −0.0655699 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6492 | −0.984749 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −15.4163 | −0.669011 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.10636 | 0.0479217 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.75551 | 0.378534 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −24.6524 | −1.06383 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.27396 | 0.313312 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.7433 | 1.45074 | 0.725369 | − | 0.688360i | \(-0.241669\pi\) | ||||
0.725369 | + | 0.688360i | \(0.241669\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.8928 | 0.682026 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.40553 | 0.0602061 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.51530 | −0.0647894 | −0.0323947 | − | 0.999475i | \(-0.510313\pi\) | ||||
−0.0323947 | + | 0.999475i | \(0.510313\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.27801 | −0.0545440 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.4633 | 0.743963 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.2064 | −1.07189 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.7732 | −0.839326 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.08594 | −0.173127 | −0.0865633 | − | 0.996246i | \(-0.527588\pi\) | ||||
−0.0865633 | + | 0.996246i | \(0.527588\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.523976 | 0.0221618 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.13539 | 0.174596 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.30244 | −0.181326 | −0.0906631 | − | 0.995882i | \(-0.528899\pi\) | ||||
−0.0906631 | + | 0.995882i | \(0.528899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.0962 | −0.593034 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.97990 | −0.293128 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.8210 | −1.08247 | −0.541236 | − | 0.840871i | \(-0.682043\pi\) | ||||
−0.541236 | + | 0.840871i | \(0.682043\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.3752 | −1.10377 | −0.551884 | − | 0.833921i | \(-0.686091\pi\) | ||||
−0.551884 | + | 0.833921i | \(0.686091\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.77645 | 0.283090 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.94951 | 0.164706 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.3402 | −1.17982 | −0.589909 | − | 0.807470i | \(-0.700836\pi\) | ||||
−0.589909 | + | 0.807470i | \(0.700836\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.20219 | −0.0915199 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −57.4260 | −2.38243 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.3051 | −0.509626 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.707916 | −0.0292687 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21.1726 | −0.873885 | −0.436942 | − | 0.899489i | \(-0.643939\pi\) | ||||
−0.436942 | + | 0.899489i | \(0.643939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.88297 | −0.0775865 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.4786 | 0.472168 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.9627 | −1.43575 | −0.717873 | − | 0.696174i | \(-0.754884\pi\) | ||||
−0.717873 | + | 0.696174i | \(0.754884\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 50.9152 | 2.08732 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.52219 | 0.0622993 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.2409 | −1.48076 | −0.740381 | − | 0.672188i | \(-0.765355\pi\) | ||||
−0.740381 | + | 0.672188i | \(0.765355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.6251 | −1.08606 | −0.543030 | − | 0.839713i | \(-0.682723\pi\) | ||||
−0.543030 | + | 0.839713i | \(0.682723\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.7276 | 1.00699 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −33.4766 | −1.36102 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.0123 | −1.50228 | −0.751142 | − | 0.660140i | \(-0.770497\pi\) | ||||
−0.751142 | + | 0.660140i | \(0.770497\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −11.9514 | −0.484295 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.01250 | 0.0409616 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4713 | 0.544100 | 0.272050 | − | 0.962283i | \(-0.412298\pi\) | ||||
0.272050 | + | 0.962283i | \(0.412298\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.2493 | −1.46171 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.0747 | −1.37180 | −0.685899 | − | 0.727697i | \(-0.740591\pi\) | ||||
−0.685899 | + | 0.727697i | \(0.740591\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.1852 | −0.570150 | −0.285075 | − | 0.958505i | \(-0.592019\pi\) | ||||
−0.285075 | + | 0.958505i | \(0.592019\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.83938 | 0.113941 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −58.7675 | −2.35447 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.8728 | −0.554914 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.17308 | 0.206593 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.9724 | −0.995714 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.9613 | 1.11312 | 0.556560 | − | 0.830807i | \(-0.312121\pi\) | ||||
0.556560 | + | 0.830807i | \(0.312121\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.9135 | 0.473520 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 40.5217 | 1.60805 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.647652 | 0.0256609 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.32745 | −0.0525131 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.4718 | 1.28256 | 0.641279 | − | 0.767308i | \(-0.278404\pi\) | ||||
0.641279 | + | 0.767308i | \(0.278404\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.4307 | −1.12120 | −0.560599 | − | 0.828087i | \(-0.689429\pi\) | ||||
−0.560599 | + | 0.828087i | \(0.689429\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.1678 | −0.675982 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0028 | 0.471877 | 0.235938 | − | 0.971768i | \(-0.424184\pi\) | ||||
0.235938 | + | 0.971768i | \(0.424184\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.94708 | 0.311950 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.28865 | 0.0505062 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10.9544 | −0.428677 | −0.214338 | − | 0.976759i | \(-0.568760\pi\) | ||||
−0.214338 | + | 0.976759i | \(0.568760\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −76.6372 | −2.99446 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.6455 | −0.805456 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.12266 | −0.277460 | −0.138730 | − | 0.990330i | \(-0.544302\pi\) | ||||
−0.138730 | + | 0.990330i | \(0.544302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.5505 | 1.18828 | 0.594138 | − | 0.804363i | \(-0.297493\pi\) | ||||
0.594138 | + | 0.804363i | \(0.297493\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.368202 | 0.0142998 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 63.6914 | 2.46985 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.04871 | −0.0793266 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.9639 | 0.810511 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.658810 | 0.0254331 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.8945 | −0.689782 | −0.344891 | − | 0.938643i | \(-0.612084\pi\) | ||||
−0.344891 | + | 0.938643i | \(0.612084\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 31.9705 | 1.23054 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.2603 | 0.701802 | 0.350901 | − | 0.936413i | \(-0.385875\pi\) | ||||
0.350901 | + | 0.936413i | \(0.385875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.4583 | 1.09213 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.78474 | −0.336632 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.9531 | −1.41397 | −0.706985 | − | 0.707229i | \(-0.749945\pi\) | ||||
−0.706985 | + | 0.707229i | \(0.749945\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.2937 | −1.38671 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.8583 | −0.528728 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.09561 | −0.0417394 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.4630 | −1.15887 | −0.579434 | − | 0.815019i | \(-0.696726\pi\) | ||||
−0.579434 | + | 0.815019i | \(0.696726\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.59645 | 0.326552 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 60.5850 | 2.29812 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −45.7807 | −1.73407 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −10.9565 | −0.414412 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1239 | 0.873376 | 0.436688 | − | 0.899613i | \(-0.356151\pi\) | ||||
0.436688 | + | 0.899613i | \(0.356151\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.2387 | −1.17819 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.1742 | −1.24941 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −66.8018 | −2.51234 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 33.4421 | 1.25595 | 0.627973 | − | 0.778235i | \(-0.283885\pi\) | ||||
0.627973 | + | 0.778235i | \(0.283885\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.5021 | −0.543873 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.220901 | 0.00827281 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.364929 | 0.0136476 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.1564 | −0.902138 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.2243 | −1.20176 | −0.600882 | − | 0.799338i | \(-0.705184\pi\) | ||||
−0.600882 | + | 0.799338i | \(0.705184\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.7408 | −1.07036 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.89964 | −0.182219 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.0678 | −0.856717 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.5274 | 0.575881 | 0.287940 | − | 0.957648i | \(-0.407030\pi\) | ||||
0.287940 | + | 0.957648i | \(0.407030\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9.43866 | 0.349580 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −21.6819 | −0.801935 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.3519 | 0.419293 | 0.209646 | − | 0.977777i | \(-0.432769\pi\) | ||||
0.209646 | + | 0.977777i | \(0.432769\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −21.2200 | −0.782712 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.7470 | −0.469543 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.6988 | 1.27641 | 0.638207 | − | 0.769864i | \(-0.279676\pi\) | ||||
0.638207 | + | 0.769864i | \(0.279676\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.460596 | 0.0169204 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.1702 | 0.629912 | 0.314956 | − | 0.949106i | \(-0.398010\pi\) | ||||
0.314956 | + | 0.949106i | \(0.398010\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.3107 | 1.29368 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −33.0392 | −1.20884 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.46649 | −0.345898 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.5379 | −0.676457 | −0.338229 | − | 0.941064i | \(-0.609828\pi\) | ||||
−0.338229 | + | 0.941064i | \(0.609828\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.935470 | 0.0340904 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.8332 | −1.37689 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19.1921 | 0.697550 | 0.348775 | − | 0.937207i | \(-0.386598\pi\) | ||||
0.348775 | + | 0.937207i | \(0.386598\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.606881 | −0.0220284 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.6608 | 1.61895 | 0.809477 | − | 0.587152i | \(-0.199751\pi\) | ||||
0.809477 | + | 0.587152i | \(0.199751\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.51966 | −0.0550153 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 29.2933 | 1.05910 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.707584 | 0.0255494 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.1082 | 0.400572 | 0.200286 | − | 0.979737i | \(-0.435813\pi\) | ||||
0.200286 | + | 0.979737i | \(0.435813\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.6851 | −0.852997 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −54.3686 | −1.95550 | −0.977751 | − | 0.209769i | \(-0.932729\pi\) | ||||
−0.977751 | + | 0.209769i | \(0.932729\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.48727 | 0.0893454 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.3789 | 0.766963 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −57.2685 | −2.05186 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.684298 | 0.0244861 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.5839 | −0.592661 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −83.0167 | −2.96299 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.0428803 | −0.00152852 | −0.000764259 | − | 1.00000i | \(-0.500243\pi\) | ||||
−0.000764259 | 1.00000i | \(0.500243\pi\) | ||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −10.2880 | −0.366263 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.2409 | 0.541904 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0586584 | 0.00208302 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.8972 | 1.27314 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −42.0336 | −1.48891 | −0.744454 | − | 0.667674i | \(-0.767290\pi\) | ||||
−0.744454 | + | 0.667674i | \(0.767290\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −41.8971 | −1.48221 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.8110 | −1.19465 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.6427 | 0.375573 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.47197 | −0.263352 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.2055 | −0.816871 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.3621 | −1.24327 | −0.621633 | − | 0.783309i | \(-0.713530\pi\) | ||||
−0.621633 | + | 0.783309i | \(0.713530\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.0189 | 1.54571 | 0.772856 | − | 0.634582i | \(-0.218828\pi\) | ||||
0.772856 | + | 0.634582i | \(0.218828\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.13313 | −0.180027 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.3026 | 1.51682 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.1226 | −0.948899 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.765401 | 0.0267453 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.78216 | 0.131998 | 0.0659991 | − | 0.997820i | \(-0.478977\pi\) | ||||
0.0659991 | + | 0.997820i | \(0.478977\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.0108 | 1.42955 | 0.714774 | − | 0.699356i | \(-0.246530\pi\) | ||||
0.714774 | + | 0.699356i | \(0.246530\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.83327 | −0.237904 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.0262 | −1.49617 | −0.748083 | − | 0.663605i | \(-0.769026\pi\) | ||||
−0.748083 | + | 0.663605i | \(0.769026\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.6915 | 0.788108 | 0.394054 | − | 0.919087i | \(-0.371072\pi\) | ||||
0.394054 | + | 0.919087i | \(0.371072\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.41384 | −0.187804 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.7996 | −0.928550 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.5325 | −0.987407 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.78815 | 0.0618074 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −49.4834 | −1.70835 | −0.854177 | − | 0.519982i | \(-0.825939\pi\) | ||||
−0.854177 | + | 0.519982i | \(0.825939\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.0341 | −0.587384 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.8906 | −0.409535 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −44.3746 | −1.52653 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.1950 | 1.24368 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.95690 | 0.273080 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.66478 | 0.125627 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.5427 | 0.806087 | 0.403043 | − | 0.915181i | \(-0.367952\pi\) | ||||
0.403043 | + | 0.915181i | \(0.367952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36.6439 | 1.25320 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.5719 | −0.975996 | −0.487998 | − | 0.872845i | \(-0.662273\pi\) | ||||
−0.487998 | + | 0.872845i | \(0.662273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.5642 | 1.04284 | 0.521418 | − | 0.853301i | \(-0.325403\pi\) | ||||
0.521418 | + | 0.853301i | \(0.325403\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 39.1929 | 1.33569 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.3242 | 0.691845 | 0.345922 | − | 0.938263i | \(-0.387566\pi\) | ||||
0.345922 | + | 0.938263i | \(0.387566\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44.0079 | 1.49632 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.666923 | 0.0226499 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.47583 | 0.253600 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.13496 | −0.0384565 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.3730 | 0.554144 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.0512 | −0.711659 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.6408 | 0.528152 | 0.264076 | − | 0.964502i | \(-0.414933\pi\) | ||||
0.264076 | + | 0.964502i | \(0.414933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.0252 | −0.607975 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −46.2975 | −1.55980 | −0.779901 | − | 0.625902i | \(-0.784731\pi\) | ||||
−0.779901 | + | 0.625902i | \(0.784731\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.7796 | −0.800246 | −0.400123 | − | 0.916461i | \(-0.631033\pi\) | ||||
−0.400123 | + | 0.916461i | \(0.631033\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.1837 | −0.779310 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.44067 | −0.149103 | −0.0745515 | − | 0.997217i | \(-0.523753\pi\) | ||||
−0.0745515 | + | 0.997217i | \(0.523753\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −43.8121 | −1.46941 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.07013 | 0.0693519 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −52.4104 | −1.75385 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 90.0199 | 3.00903 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0540349 | −0.00180417 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.29021 | −0.0430309 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.3359 | 1.51036 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18.5619 | 0.617701 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −58.0337 | −1.92911 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.8394 | −0.492735 | −0.246368 | − | 0.969176i | \(-0.579237\pi\) | ||||
−0.246368 | + | 0.969176i | \(0.579237\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −38.4335 | −1.27476 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.2128 | −1.19978 | −0.599892 | − | 0.800081i | \(-0.704790\pi\) | ||||
−0.599892 | + | 0.800081i | \(0.704790\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.0316 | 0.563665 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.92192 | −0.0635366 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 82.8603 | 2.73629 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.1422 | −1.48910 | −0.744551 | − | 0.667565i | \(-0.767337\pi\) | ||||
−0.744551 | + | 0.667565i | \(0.767337\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.273769 | −0.00902099 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.0609278 | 0.00200546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 41.2641 | 1.35676 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.5356 | −0.543100 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.1799 | 1.54792 | 0.773961 | − | 0.633233i | \(-0.218273\pi\) | ||||
0.773961 | + | 0.633233i | \(0.218273\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.5244 | −1.09872 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.77749 | 0.156408 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −15.1006 | −0.493844 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.0230 | −1.43817 | −0.719084 | − | 0.694923i | \(-0.755439\pi\) | ||||
−0.719084 | + | 0.694923i | \(0.755439\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.73987 | 0.219947 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.1353 | 1.14538 | 0.572688 | − | 0.819773i | \(-0.305900\pi\) | ||||
0.572688 | + | 0.819773i | \(0.305900\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.71847 | 0.218784 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −60.4840 | −1.96755 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.6892 | −0.607316 | −0.303658 | − | 0.952781i | \(-0.598208\pi\) | ||||
−0.303658 | + | 0.952781i | \(0.598208\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.947593 | 0.0307602 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.96146 | 0.323022 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.80725 | −0.317688 | −0.158844 | − | 0.987304i | \(-0.550777\pi\) | ||||
−0.158844 | + | 0.987304i | \(0.550777\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.7447 | −0.800719 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.54459 | 0.114580 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 39.2408 | 1.26715 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8609 | −0.995512 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.44641 | −0.175508 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.04145 | 0.258863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.4028 | 0.334533 | 0.167266 | − | 0.985912i | \(-0.446506\pi\) | ||||
0.167266 | + | 0.985912i | \(0.446506\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.0593 | −0.612272 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.5079 | 1.17159 | 0.585797 | − | 0.810458i | \(-0.300782\pi\) | ||||
0.585797 | + | 0.810458i | \(0.300782\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −65.5047 | −2.09999 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.608414 | −0.0194848 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.60773 | −0.0834288 | −0.0417144 | − | 0.999130i | \(-0.513282\pi\) | ||||
−0.0417144 | + | 0.999130i | \(0.513282\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.4295 | 0.557050 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.874314 | −0.0279147 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 14.7408 | 0.470160 | 0.235080 | − | 0.971976i | \(-0.424465\pi\) | ||||
0.235080 | + | 0.971976i | \(0.424465\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.9150 | −1.33552 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 35.8681 | 1.14169 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.18189 | 0.101178 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.1779 | 0.704505 | 0.352252 | − | 0.935905i | \(-0.385416\pi\) | ||||
0.352252 | + | 0.935905i | \(0.385416\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 15.3822 | 0.488139 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.55840 | −0.176213 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.6820 | −1.09839 | −0.549194 | − | 0.835695i | \(-0.685065\pi\) | ||||
−0.549194 | + | 0.835695i | \(0.685065\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.6656 | 0.938578 |
(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 | 4016.2.a.k.1.7 | 17 | ||
4.3 | odd | 2 | 251.2.a.b.1.4 | ✓ | 17 | ||
12.11 | even | 2 | 2259.2.a.k.1.14 | 17 | |||
20.19 | odd | 2 | 6275.2.a.e.1.14 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
251.2.a.b.1.4 | ✓ | 17 | 4.3 | odd | 2 | ||
2259.2.a.k.1.14 | 17 | 12.11 | even | 2 | |||
4016.2.a.k.1.7 | 17 | 1.1 | even | 1 | trivial | ||
6275.2.a.e.1.14 | 17 | 20.19 | odd | 2 |