Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 17 x^{10} + 79 x^{9} + 80 x^{8} - 536 x^{7} - 4 x^{6} + 1484 x^{5} - 682 x^{4} + \cdots - 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(1.75763\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.75763 | 1.01477 | 0.507384 | − | 0.861720i | \(-0.330613\pi\) | ||||
0.507384 | + | 0.861720i | \(0.330613\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.24204 | −1.44989 | −0.724943 | − | 0.688809i | \(-0.758134\pi\) | ||||
−0.724943 | + | 0.688809i | \(0.758134\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.0892594 | 0.0297531 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.69831 | −1.47130 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.0754893 | 0.0183088 | 0.00915442 | − | 0.999958i | \(-0.497086\pi\) | ||||
0.00915442 | + | 0.999958i | \(0.497086\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.53631 | −1.49953 | −0.749766 | − | 0.661703i | \(-0.769834\pi\) | ||||
−0.749766 | + | 0.661703i | \(0.769834\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.75763 | 0.383546 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.67581 | −1.80903 | −0.904516 | − | 0.426441i | \(-0.859767\pi\) | ||||
−0.904516 | + | 0.426441i | \(0.859767\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.51085 | 1.10217 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.11600 | −0.984575 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.22876 | 0.599566 | 0.299783 | − | 0.954007i | \(-0.403086\pi\) | ||||
0.299783 | + | 0.954007i | \(0.403086\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.81883 | 1.04509 | 0.522546 | − | 0.852611i | \(-0.324982\pi\) | ||||
0.522546 | + | 0.852611i | \(0.324982\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.75763 | 0.305964 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.24204 | −0.548006 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.83193 | 0.301168 | 0.150584 | − | 0.988597i | \(-0.451885\pi\) | ||||
0.150584 | + | 0.988597i | \(0.451885\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.75763 | 0.281446 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.76053 | 1.52434 | 0.762169 | − | 0.647378i | \(-0.224134\pi\) | ||||
0.762169 | + | 0.647378i | \(0.224134\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.89313 | −0.593697 | −0.296848 | − | 0.954925i | \(-0.595936\pi\) | ||||
−0.296848 | + | 0.954925i | \(0.595936\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.289383 | −0.0431387 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.46368 | −0.213500 | −0.106750 | − | 0.994286i | \(-0.534044\pi\) | ||||
−0.106750 | + | 0.994286i | \(0.534044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.132682 | 0.0185792 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.85251 | 1.21599 | 0.607993 | − | 0.793942i | \(-0.291975\pi\) | ||||
0.607993 | + | 0.793942i | \(0.291975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.24204 | −0.437157 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.4884 | −1.52168 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.8022 | 1.53651 | 0.768257 | − | 0.640141i | \(-0.221124\pi\) | ||||
0.768257 | + | 0.640141i | \(0.221124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.744116 | −0.0952742 | −0.0476371 | − | 0.998865i | \(-0.515169\pi\) | ||||
−0.0476371 | + | 0.998865i | \(0.515169\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.0892594 | 0.0112456 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.24204 | −0.402126 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.6894 | −1.30591 | −0.652957 | − | 0.757395i | \(-0.726472\pi\) | ||||
−0.652957 | + | 0.757395i | \(0.726472\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15.2489 | −1.83575 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.68968 | 0.912597 | 0.456298 | − | 0.889827i | \(-0.349175\pi\) | ||||
0.456298 | + | 0.889827i | \(0.349175\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.86228 | 1.15429 | 0.577146 | − | 0.816641i | \(-0.304166\pi\) | ||||
0.577146 | + | 0.816641i | \(0.304166\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.68604 | 1.11845 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.6204 | 1.19489 | 0.597447 | − | 0.801908i | \(-0.296182\pi\) | ||||
0.597447 | + | 0.801908i | \(0.296182\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.25981 | −1.02887 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.12381 | −0.342883 | −0.171441 | − | 0.985194i | \(-0.554842\pi\) | ||||
−0.171441 | + | 0.985194i | \(0.554842\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.244740 | −0.0265458 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.67496 | 0.608420 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.35214 | 0.249327 | 0.124663 | − | 0.992199i | \(-0.460215\pi\) | ||||
0.124663 | + | 0.992199i | \(0.460215\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.2273 | 1.06053 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.1910 | 2.17415 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.9322 | −1.71920 | −0.859601 | − | 0.510966i | \(-0.829288\pi\) | ||||
−0.859601 | + | 0.510966i | \(0.829288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.0892594 | 0.00897091 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.3213 | −1.72353 | −0.861764 | − | 0.507309i | \(-0.830640\pi\) | ||||
−0.861764 | + | 0.507309i | \(0.830640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.5088 | 1.33106 | 0.665530 | − | 0.746371i | \(-0.268206\pi\) | ||||
0.665530 | + | 0.746371i | \(0.268206\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.69831 | −0.556098 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.2803 | 1.47720 | 0.738599 | − | 0.674145i | \(-0.235488\pi\) | ||||
0.738599 | + | 0.674145i | \(0.235488\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.1537 | 1.64302 | 0.821511 | − | 0.570193i | \(-0.193132\pi\) | ||||
0.821511 | + | 0.570193i | \(0.193132\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.21986 | 0.305615 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.7809 | 1.86084 | 0.930418 | − | 0.366501i | \(-0.119445\pi\) | ||||
0.930418 | + | 0.366501i | \(0.119445\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.1274 | 2.62289 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0892594 | 0.00825204 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0754893 | 0.00692009 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.1554 | 1.54685 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.65621 | −0.148136 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.10996 | −0.719643 | −0.359821 | − | 0.933021i | \(-0.617162\pi\) | ||||
−0.359821 | + | 0.933021i | \(0.617162\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.84268 | −0.602464 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.82740 | −0.421772 | −0.210886 | − | 0.977511i | \(-0.567635\pi\) | ||||
−0.210886 | + | 0.977511i | \(0.567635\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.53631 | −0.566770 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.5863 | 1.42752 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.73129 | 0.233350 | 0.116675 | − | 0.993170i | \(-0.462776\pi\) | ||||
0.116675 | + | 0.993170i | \(0.462776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.80299 | 0.322565 | 0.161283 | − | 0.986908i | \(-0.448437\pi\) | ||||
0.161283 | + | 0.986908i | \(0.448437\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.57261 | −0.216653 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.4678 | −0.869302 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.75763 | 0.144967 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −18.6555 | −1.52832 | −0.764160 | − | 0.645027i | \(-0.776846\pi\) | ||||
−0.764160 | + | 0.645027i | \(0.776846\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.5787 | −1.83742 | −0.918712 | − | 0.394927i | \(-0.870770\pi\) | ||||
−0.918712 | + | 0.394927i | \(0.870770\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.00673813 | 0.000544746 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.8649 | −1.51526 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.9589 | 1.51308 | 0.756542 | − | 0.653945i | \(-0.226887\pi\) | ||||
0.756542 | + | 0.653945i | \(0.226887\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 15.5594 | 1.23394 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.67581 | −0.683750 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.19359 | −0.641772 | −0.320886 | − | 0.947118i | \(-0.603981\pi\) | ||||
−0.320886 | + | 0.947118i | \(0.603981\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.69831 | −0.443613 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.673652 | 0.0521287 | 0.0260644 | − | 0.999660i | \(-0.491703\pi\) | ||||
0.0260644 | + | 0.999660i | \(0.491703\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.583427 | −0.0446158 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.6596 | 1.34263 | 0.671316 | − | 0.741171i | \(-0.265729\pi\) | ||||
0.671316 | + | 0.741171i | \(0.265729\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.51085 | 0.416581 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.7439 | 1.55921 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.783353 | −0.0585505 | −0.0292753 | − | 0.999571i | \(-0.509320\pi\) | ||||
−0.0292753 | + | 0.999571i | \(0.509320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.49721 | −0.482934 | −0.241467 | − | 0.970409i | \(-0.577629\pi\) | ||||
−0.241467 | + | 0.970409i | \(0.577629\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.30788 | −0.0966812 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.93921 | −0.436659 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0754893 | 0.00552033 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.11600 | −0.372134 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3294 | 1.39862 | 0.699311 | − | 0.714817i | \(-0.253490\pi\) | ||||
0.699311 | + | 0.714817i | \(0.253490\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.3860 | −0.963542 | −0.481771 | − | 0.876297i | \(-0.660006\pi\) | ||||
−0.481771 | + | 0.876297i | \(0.660006\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.69831 | −0.408065 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.509594 | 0.0363071 | 0.0181535 | − | 0.999835i | \(-0.494221\pi\) | ||||
0.0181535 | + | 0.999835i | \(0.494221\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.2846 | 1.15439 | 0.577193 | − | 0.816608i | \(-0.304148\pi\) | ||||
0.577193 | + | 0.816608i | \(0.304148\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.7879 | −1.32520 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.22876 | 0.226614 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −31.6441 | −2.21012 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.774398 | −0.0538244 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.53631 | −0.452126 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4003 | −0.784828 | −0.392414 | − | 0.919789i | \(-0.628360\pi\) | ||||
−0.392414 | + | 0.919789i | \(0.628360\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.5156 | 0.926074 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 12.6217 | 0.860793 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.81883 | 0.395008 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 17.3342 | 1.17134 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.0754893 | 0.00507796 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.1093 | −0.877867 | −0.438933 | − | 0.898520i | \(-0.644644\pi\) | ||||
−0.438933 | + | 0.898520i | \(0.644644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.491896 | 0.0327930 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.1084 | −0.670916 | −0.335458 | − | 0.942055i | \(-0.608891\pi\) | ||||
−0.335458 | + | 0.942055i | \(0.608891\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.22668 | 0.345388 | 0.172694 | − | 0.984975i | \(-0.444753\pi\) | ||||
0.172694 | + | 0.984975i | \(0.444753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.75763 | 0.115643 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.7762 | 0.705972 | 0.352986 | − | 0.935629i | \(-0.385166\pi\) | ||||
0.352986 | + | 0.935629i | \(0.385166\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.74532 | 0.309551 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.6668 | 1.21254 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.3801 | 1.77107 | 0.885535 | − | 0.464573i | \(-0.153792\pi\) | ||||
0.885535 | + | 0.464573i | \(0.153792\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.7988 | 0.695610 | 0.347805 | − | 0.937567i | \(-0.386927\pi\) | ||||
0.347805 | + | 0.937567i | \(0.386927\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.927306 | −0.0594867 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.24204 | −0.207127 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.53631 | −0.415895 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.49050 | −0.347946 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.1726 | −1.02080 | −0.510402 | − | 0.859936i | \(-0.670503\pi\) | ||||
−0.510402 | + | 0.859936i | \(0.670503\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.67581 | −0.545443 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.430162 | −0.0269378 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.5195 | 0.718568 | 0.359284 | − | 0.933228i | \(-0.383021\pi\) | ||||
0.359284 | + | 0.933228i | \(0.383021\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.83193 | 0.113831 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.288197 | 0.0178390 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.7721 | 1.77416 | 0.887080 | − | 0.461615i | \(-0.152730\pi\) | ||||
0.887080 | + | 0.461615i | \(0.152730\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −28.7002 | −1.76304 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.13420 | 0.253009 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.4914 | 1.00550 | 0.502749 | − | 0.864433i | \(-0.332322\pi\) | ||||
0.502749 | + | 0.864433i | \(0.332322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.0468 | −0.914027 | −0.457014 | − | 0.889460i | \(-0.651081\pi\) | ||||
−0.457014 | + | 0.889460i | \(0.651081\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.75763 | 0.106377 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.51085 | 0.332317 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.7234 | −0.644304 | −0.322152 | − | 0.946688i | \(-0.604406\pi\) | ||||
−0.322152 | + | 0.946688i | \(0.604406\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.519385 | 0.0310948 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.8225 | −1.30182 | −0.650910 | − | 0.759155i | \(-0.725613\pi\) | ||||
−0.650910 | + | 0.759155i | \(0.725613\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.44645 | 0.442646 | 0.221323 | − | 0.975201i | \(-0.428963\pi\) | ||||
0.221323 | + | 0.975201i | \(0.428963\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 37.2459 | 2.20626 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.76053 | 0.576146 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9943 | −0.999665 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −29.7605 | −1.74459 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.0759 | 1.75705 | 0.878527 | − | 0.477693i | \(-0.158527\pi\) | ||||
0.878527 | + | 0.477693i | \(0.158527\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −38.2632 | −2.22777 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.11600 | −0.296861 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.67581 | −0.501735 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.89313 | −0.224396 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −30.4443 | −1.74898 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.41246 | 0.138137 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3098 | 1.27329 | 0.636644 | − | 0.771158i | \(-0.280322\pi\) | ||||
0.636644 | + | 0.771158i | \(0.280322\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.7434 | 1.35072 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.7857 | 0.611599 | 0.305800 | − | 0.952096i | \(-0.401076\pi\) | ||||
0.305800 | + | 0.952096i | \(0.401076\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.6570 | −1.05455 | −0.527277 | − | 0.849693i | \(-0.676787\pi\) | ||||
−0.527277 | + | 0.849693i | \(0.676787\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.289383 | −0.0163049 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 32.1366 | 1.80497 | 0.902485 | − | 0.430722i | \(-0.141741\pi\) | ||||
0.902485 | + | 0.430722i | \(0.141741\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.22876 | 0.180776 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.8570 | 1.49901 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.493422 | −0.0274547 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.51085 | 0.305687 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 30.1498 | 1.66729 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.46368 | −0.0806953 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.278064 | −0.0152838 | −0.00764188 | − | 0.999971i | \(-0.502433\pi\) | ||||
−0.00764188 | + | 0.999971i | \(0.502433\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.163517 | 0.00896069 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 34.6554 | 1.89343 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 30.3463 | 1.65307 | 0.826533 | − | 0.562888i | \(-0.190310\pi\) | ||||
0.826533 | + | 0.562888i | \(0.190310\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 34.7676 | 1.88831 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.81883 | 0.315107 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 49.4375 | 2.66162 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.5838 | 1.31973 | 0.659865 | − | 0.751384i | \(-0.270614\pi\) | ||||
0.659865 | + | 0.751384i | \(0.270614\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.1744 | 0.865798 | 0.432899 | − | 0.901443i | \(-0.357491\pi\) | ||||
0.432899 | + | 0.901443i | \(0.357491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.11600 | −0.273072 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.2617 | −0.865525 | −0.432763 | − | 0.901508i | \(-0.642461\pi\) | ||||
−0.432763 | + | 0.901508i | \(0.642461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.9303 | −1.32316 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.132682 | 0.00702229 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.4039 | −1.71021 | −0.855105 | − | 0.518454i | \(-0.826508\pi\) | ||||
−0.855105 | + | 0.518454i | \(0.826508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 23.7233 | 1.24860 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.75763 | 0.0922516 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.9740 | −1.67359 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.4781 | 1.79974 | 0.899871 | − | 0.436157i | \(-0.143661\pi\) | ||||
0.899871 | + | 0.436157i | \(0.143661\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.871219 | 0.0453539 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.85251 | 0.459599 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.3982 | 0.952621 | 0.476310 | − | 0.879277i | \(-0.341974\pi\) | ||||
0.476310 | + | 0.879277i | \(0.341974\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.91101 | −0.150324 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.22876 | 0.166290 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6672 | −1.16433 | −0.582167 | − | 0.813069i | \(-0.697795\pi\) | ||||
−0.582167 | + | 0.813069i | \(0.697795\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.2543 | −0.730270 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.06237 | −0.463065 | −0.231533 | − | 0.972827i | \(-0.574374\pi\) | ||||
−0.231533 | + | 0.972827i | \(0.574374\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.24204 | −0.165230 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.347498 | −0.0176643 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.9903 | −1.16566 | −0.582828 | − | 0.812595i | \(-0.698054\pi\) | ||||
−0.582828 | + | 0.812595i | \(0.698054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.654931 | −0.0331213 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.48478 | −0.428001 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −34.4320 | −1.73246 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.3968 | −1.62595 | −0.812973 | − | 0.582301i | \(-0.802153\pi\) | ||||
−0.812973 | + | 0.582301i | \(0.802153\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.4884 | −0.575140 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.49899 | 0.424419 | 0.212210 | − | 0.977224i | \(-0.431934\pi\) | ||||
0.212210 | + | 0.977224i | \(0.431934\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.81883 | 0.289856 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 30.0207 | 1.49174 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.83193 | 0.0908056 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.26862 | −0.161623 | −0.0808113 | − | 0.996729i | \(-0.525751\pi\) | ||||
−0.0808113 | + | 0.996729i | \(0.525751\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.80060 | 0.236796 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.8022 | 0.580748 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.1275 | 0.497141 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.68425 | 0.327329 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0690 | 0.882727 | 0.441364 | − | 0.897328i | \(-0.354495\pi\) | ||||
0.441364 | + | 0.897328i | \(0.354495\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 37.1551 | 1.81083 | 0.905414 | − | 0.424531i | \(-0.139561\pi\) | ||||
0.905414 | + | 0.424531i | \(0.139561\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.130647 | −0.00635229 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.416011 | 0.0201795 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.744116 | −0.0360103 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.75763 | 0.0848591 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.8682 | −1.14969 | −0.574845 | − | 0.818262i | \(-0.694938\pi\) | ||||
−0.574845 | + | 0.818262i | \(0.694938\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.6722 | 0.945383 | 0.472692 | − | 0.881228i | \(-0.343282\pi\) | ||||
0.472692 | + | 0.881228i | \(0.343282\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −18.3985 | −0.882140 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 56.7078 | 2.71270 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.84411 | 0.469834 | 0.234917 | − | 0.972015i | \(-0.424518\pi\) | ||||
0.234917 | + | 0.972015i | \(0.424518\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0892594 | 0.00425045 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.77433 | 0.369370 | 0.184685 | − | 0.982798i | \(-0.440874\pi\) | ||||
0.184685 | + | 0.982798i | \(0.440874\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.62576 | −0.361496 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.7895 | −1.55089 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.8542 | 0.984169 | 0.492084 | − | 0.870548i | \(-0.336235\pi\) | ||||
0.492084 | + | 0.870548i | \(0.336235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.76053 | 0.459605 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −39.6849 | −1.86456 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.24204 | −0.151989 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3836 | 0.532505 | 0.266252 | − | 0.963903i | \(-0.414215\pi\) | ||||
0.266252 | + | 0.963903i | \(0.414215\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.386204 | −0.0180264 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.52353 | 0.0709581 | 0.0354790 | − | 0.999370i | \(-0.488704\pi\) | ||||
0.0354790 | + | 0.999370i | \(0.488704\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.76974 | 0.221668 | 0.110834 | − | 0.993839i | \(-0.464648\pi\) | ||||
0.110834 | + | 0.993839i | \(0.464648\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −33.1575 | −1.53764 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.5561 | 0.534753 | 0.267377 | − | 0.963592i | \(-0.413843\pi\) | ||||
0.267377 | + | 0.963592i | \(0.413843\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6894 | −0.493589 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 33.3227 | 1.53543 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.89313 | −0.179006 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.0206 | −1.65274 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.790170 | 0.0361794 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.2969 | 1.11016 | 0.555078 | − | 0.831798i | \(-0.312689\pi\) | ||||
0.555078 | + | 0.831798i | \(0.312689\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.83193 | 0.0835290 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.2489 | −0.693847 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 54.8949 | 2.49265 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.6886 | 0.937489 | 0.468744 | − | 0.883334i | \(-0.344707\pi\) | ||||
0.468744 | + | 0.883334i | \(0.344707\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −14.4013 | −0.651249 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −28.9083 | −1.30461 | −0.652307 | − | 0.757955i | \(-0.726199\pi\) | ||||
−0.652307 | + | 0.757955i | \(0.726199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.243737 | 0.0109774 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.289383 | −0.0130068 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.68968 | 0.344929 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.2643 | −0.862387 | −0.431194 | − | 0.902259i | \(-0.641907\pi\) | ||||
−0.431194 | + | 0.902259i | \(0.641907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.18403 | 0.0528986 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.73844 | 0.345040 | 0.172520 | − | 0.985006i | \(-0.444809\pi\) | ||||
0.172520 | + | 0.985006i | \(0.444809\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 56.1563 | 2.49892 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.75763 | 0.0780590 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.3765 | 0.947497 | 0.473748 | − | 0.880660i | \(-0.342901\pi\) | ||||
0.473748 | + | 0.880660i | \(0.342901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.86228 | 0.436282 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 33.4398 | 1.47640 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −43.7961 | −1.92989 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.46368 | −0.0643726 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.0390 | 1.36246 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.83720 | 0.124300 | 0.0621500 | − | 0.998067i | \(-0.480204\pi\) | ||||
0.0621500 | + | 0.998067i | \(0.480204\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.47295 | −0.108134 | −0.0540672 | − | 0.998537i | \(-0.517219\pi\) | ||||
−0.0540672 | + | 0.998537i | \(0.517219\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.68604 | 0.422733 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.439259 | 0.0191344 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 52.2697 | 2.27259 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.05346 | 0.0457161 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.76053 | 0.422776 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −49.5393 | −2.14177 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.37684 | −0.0594152 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5729 | 0.626540 | 0.313270 | − | 0.949664i | \(-0.398576\pi\) | ||||
0.313270 | + | 0.949664i | \(0.398576\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.4197 | −0.490065 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −55.6129 | −2.38220 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.4275 | −0.958931 | −0.479466 | − | 0.877561i | \(-0.659169\pi\) | ||||
−0.479466 | + | 0.877561i | \(0.659169\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.0664193 | −0.00283471 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.1042 | −0.899068 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.6204 | 0.451627 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.4389 | −0.443108 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.4660 | −0.485832 | −0.242916 | − | 0.970047i | \(-0.578104\pi\) | ||||
−0.242916 | + | 0.970047i | \(0.578104\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.89313 | −0.164662 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.132682 | 0.00560185 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 23.2863 | 0.981401 | 0.490700 | − | 0.871328i | \(-0.336741\pi\) | ||||
0.490700 | + | 0.871328i | \(0.336741\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −64.1307 | −2.69800 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.25981 | −0.388876 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.3211 | −0.600371 | −0.300186 | − | 0.953881i | \(-0.597049\pi\) | ||||
−0.300186 | + | 0.953881i | \(0.597049\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.7368 | −0.658564 | −0.329282 | − | 0.944232i | \(-0.606807\pi\) | ||||
−0.329282 | + | 0.944232i | \(0.606807\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 33.9738 | 1.41928 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −47.8111 | −1.99386 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.0408 | −0.542895 | −0.271448 | − | 0.962453i | \(-0.587502\pi\) | ||||
−0.271448 | + | 0.962453i | \(0.587502\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −23.5275 | −0.977771 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.12381 | −0.129597 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.85251 | 0.366634 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.289383 | −0.0119645 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.7549 | 0.774097 | 0.387048 | − | 0.922059i | \(-0.373495\pi\) | ||||
0.387048 | + | 0.922059i | \(0.373495\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −38.0336 | −1.56715 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.895678 | 0.0368433 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.4021 | −1.57698 | −0.788492 | − | 0.615045i | \(-0.789138\pi\) | ||||
−0.788492 | + | 0.615045i | \(0.789138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.244740 | −0.0100334 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 28.6223 | 1.17143 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.4888 | 1.36831 | 0.684157 | − | 0.729335i | \(-0.260170\pi\) | ||||
0.684157 | + | 0.729335i | \(0.260170\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 23.7671 | 0.969481 | 0.484741 | − | 0.874658i | \(-0.338914\pi\) | ||||
0.484741 | + | 0.874658i | \(0.338914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.954126 | −0.0388550 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.24204 | −0.131808 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.8829 | 1.45644 | 0.728221 | − | 0.685343i | \(-0.240348\pi\) | ||||
0.728221 | + | 0.685343i | \(0.240348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.67496 | 0.229961 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.46368 | −0.0592142 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29.5774 | −1.19462 | −0.597309 | − | 0.802011i | \(-0.703763\pi\) | ||||
−0.597309 | + | 0.802011i | \(0.703763\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −55.6186 | −2.24276 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −40.5472 | −1.63237 | −0.816185 | − | 0.577790i | \(-0.803915\pi\) | ||||
−0.816185 | + | 0.577790i | \(0.803915\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.13866 | 0.166347 | 0.0831735 | − | 0.996535i | \(-0.473494\pi\) | ||||
0.0831735 | + | 0.996535i | \(0.473494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.3855 | 1.78113 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.35214 | 0.0942367 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.1848 | −0.887390 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.4884 | −0.458803 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.138291 | 0.00551404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.1415 | −0.722203 | −0.361102 | − | 0.932526i | \(-0.617599\pi\) | ||||
−0.361102 | + | 0.932526i | \(0.617599\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.0375 | −0.796418 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26.2929 | 1.04340 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.686376 | 0.0271526 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.31231 | −0.328317 | −0.164158 | − | 0.986434i | \(-0.552491\pi\) | ||||
−0.164158 | + | 0.986434i | \(0.552491\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.2533 | −1.39025 | −0.695127 | − | 0.718887i | \(-0.744652\pi\) | ||||
−0.695127 | + | 0.718887i | \(0.744652\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.1843 | 0.873505 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.1678 | 0.753563 | 0.376781 | − | 0.926302i | \(-0.377031\pi\) | ||||
0.376781 | + | 0.926302i | \(0.377031\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.8022 | 0.463277 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.2273 | 0.400841 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.6834 | 0.535471 | 0.267736 | − | 0.963492i | \(-0.413725\pi\) | ||||
0.267736 | + | 0.963492i | \(0.413725\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.6507 | 0.611522 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.880301 | 0.0343438 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.23166 | 0.242751 | 0.121375 | − | 0.992607i | \(-0.461270\pi\) | ||||
0.121375 | + | 0.992607i | \(0.461270\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.98032 | 0.193712 | 0.0968559 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968559 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.132682 | 0.00515295 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.1910 | 0.821752 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.0121 | −1.08463 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.0414 | −0.890831 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.744116 | −0.0287263 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.47082 | −0.133790 | −0.0668951 | − | 0.997760i | \(-0.521309\pi\) | ||||
−0.0668951 | + | 0.997760i | \(0.521309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −28.1935 | −1.08517 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.0278 | 1.03876 | 0.519382 | − | 0.854542i | \(-0.326162\pi\) | ||||
0.519382 | + | 0.854542i | \(0.326162\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.9322 | −0.649797 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.7668 | −0.680824 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −26.2660 | −1.00504 | −0.502521 | − | 0.864565i | \(-0.667594\pi\) | ||||
−0.502521 | + | 0.864565i | \(0.667594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.85497 | −0.338331 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.18656 | 0.350489 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.85251 | 0.337254 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.8341 | −1.62949 | −0.814743 | − | 0.579822i | \(-0.803122\pi\) | ||||
−0.814743 | + | 0.579822i | \(0.803122\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.0892594 | 0.00339068 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.3295 | −0.467683 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.736816 | 0.0279089 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.9405 | 0.716397 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.4378 | −1.22516 | −0.612579 | − | 0.790409i | \(-0.709868\pi\) | ||||
−0.612579 | + | 0.790409i | \(0.709868\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.9741 | −0.451611 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.34051 | 0.314122 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.3213 | −0.651433 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5956 | 0.510593 | 0.255296 | − | 0.966863i | \(-0.417827\pi\) | ||||
0.255296 | + | 0.966863i | \(0.417827\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.947975 | 0.0355518 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −50.4830 | −1.89060 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.24204 | −0.121246 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 48.1240 | 1.79722 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.14514 | 0.117294 | 0.0586469 | − | 0.998279i | \(-0.481321\pi\) | ||||
0.0586469 | + | 0.998279i | \(0.481321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.5088 | 0.503093 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.9802 | 0.705883 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.7932 | 0.660824 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2267 | −0.675991 | −0.337996 | − | 0.941148i | \(-0.609749\pi\) | ||||
−0.337996 | + | 0.941148i | \(0.609749\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.1496 | 0.968503 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.293890 | −0.0108699 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.06580 | 0.0763022 | 0.0381511 | − | 0.999272i | \(-0.487853\pi\) | ||||
0.0381511 | + | 0.999272i | \(0.487853\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.69831 | −0.210185 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.6894 | −0.393748 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.79633 | 0.0660791 | 0.0330395 | − | 0.999454i | \(-0.489481\pi\) | ||||
0.0330395 | + | 0.999454i | \(0.489481\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.4884 | −0.422037 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.3480 | −1.11336 | −0.556679 | − | 0.830728i | \(-0.687925\pi\) | ||||
−0.556679 | + | 0.830728i | \(0.687925\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 60.4820 | 2.21589 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.278829 | −0.0102018 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.2803 | 0.558328 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.40115 | −0.270072 | −0.135036 | − | 0.990841i | \(-0.543115\pi\) | ||||
−0.135036 | + | 0.990841i | \(0.543115\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.4254 | −1.03588 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 73.2010 | 2.66406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.6920 | −1.69705 | −0.848525 | − | 0.529155i | \(-0.822509\pi\) | ||||
−0.848525 | + | 0.529155i | \(0.822509\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.2489 | −0.553498 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.34331 | −0.121195 | −0.0605975 | − | 0.998162i | \(-0.519301\pi\) | ||||
−0.0605975 | + | 0.998162i | \(0.519301\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.1537 | 0.621004 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.0218453 | −0.000789820 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.8022 | 0.426153 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.1711 | −0.619205 | −0.309603 | − | 0.950866i | \(-0.600196\pi\) | ||||
−0.309603 | + | 0.950866i | \(0.600196\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.2470 | 0.729179 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.0093 | −0.575816 | −0.287908 | − | 0.957658i | \(-0.592960\pi\) | ||||
−0.287908 | + | 0.957658i | \(0.592960\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.0667 | 1.15187 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.21986 | 0.115512 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −63.7978 | −2.28580 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.68968 | 0.275158 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.5183 | −0.590317 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −61.4656 | −2.19380 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.08461 | 0.216893 | 0.108446 | − | 0.994102i | \(-0.465412\pi\) | ||||
0.108446 | + | 0.994102i | \(0.465412\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 50.5706 | 1.80036 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19.7809 | 0.703330 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.744116 | −0.0264243 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −50.4444 | −1.78908 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.91516 | 0.174104 | 0.0870520 | − | 0.996204i | \(-0.472255\pi\) | ||||
0.0870520 | + | 0.996204i | \(0.472255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.110492 | −0.00390894 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.209951 | 0.00741825 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.86228 | 0.348032 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.1274 | 0.991359 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 28.9857 | 1.02035 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29.3258 | −1.03104 | −0.515520 | − | 0.856877i | \(-0.672401\pi\) | ||||
−0.515520 | + | 0.856877i | \(0.672401\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.3747 | 1.06660 | 0.533300 | − | 0.845926i | \(-0.320952\pi\) | ||||
0.533300 | + | 0.845926i | \(0.320952\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −26.4467 | −0.927525 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.5640 | 0.930496 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.4467 | 0.890267 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0892594 | 0.00311898 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.15582 | −0.0403383 | −0.0201692 | − | 0.999797i | \(-0.506420\pi\) | ||||
−0.0201692 | + | 0.999797i | \(0.506420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.3407 | 1.58048 | 0.790239 | − | 0.612799i | \(-0.209956\pi\) | ||||
0.790239 | + | 0.612799i | \(0.209956\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.68604 | 0.337225 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.2442 | −1.64284 | −0.821420 | − | 0.570323i | \(-0.806818\pi\) | ||||
−0.821420 | + | 0.570323i | \(0.806818\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0719 | 0.349812 | 0.174906 | − | 0.984585i | \(-0.444038\pi\) | ||||
0.174906 | + | 0.984585i | \(0.444038\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.8477 | −0.653819 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.0754893 | 0.00261555 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.18401 | −0.0755808 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −29.7691 | −1.02897 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 46.2194 | 1.59567 | 0.797835 | − | 0.602875i | \(-0.205978\pi\) | ||||
0.797835 | + | 0.602875i | \(0.205978\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.5751 | −0.640521 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −38.3558 | −1.32105 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.24204 | −0.111530 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.0881 | 0.449183 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −15.8935 | −0.544822 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.2108 | −0.589285 | −0.294642 | − | 0.955608i | \(-0.595201\pi\) | ||||
−0.294642 | + | 0.955608i | \(0.595201\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.89150 | 0.0646878 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.7450 | −1.22103 | −0.610514 | − | 0.792006i | \(-0.709037\pi\) | ||||
−0.610514 | + | 0.792006i | \(0.709037\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.9760 | −1.09101 | −0.545504 | − | 0.838108i | \(-0.683662\pi\) | ||||
−0.545504 | + | 0.838108i | \(0.683662\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.1554 | 0.584654 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.3699 | −1.10188 | −0.550942 | − | 0.834543i | \(-0.685731\pi\) | ||||
−0.550942 | + | 0.834543i | \(0.685731\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.2531 | −1.94667 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.8697 | −1.01443 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.6204 | 0.360274 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.6894 | −0.362195 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.51136 | −0.0511517 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.65621 | −0.0559902 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.7473 | −0.497980 | −0.248990 | − | 0.968506i | \(-0.580099\pi\) | ||||
−0.248990 | + | 0.968506i | \(0.580099\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 52.8623 | 1.78300 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.7221 | 1.10244 | 0.551218 | − | 0.834361i | \(-0.314163\pi\) | ||||
0.551218 | + | 0.834361i | \(0.314163\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.9772 | −1.91743 | −0.958717 | − | 0.284361i | \(-0.908218\pi\) | ||||
−0.958717 | + | 0.284361i | \(0.908218\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −67.2526 | −2.26067 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.6141 | −0.389962 | −0.194981 | − | 0.980807i | \(-0.562465\pi\) | ||||
−0.194981 | + | 0.980807i | \(0.562465\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.10996 | −0.271999 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.25981 | −0.310215 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.56707 | 0.320150 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.53967 | 0.0848917 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.2489 | −0.509144 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.7876 | 0.626601 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.668270 | 0.0222633 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.84268 | −0.227710 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 21.0642 | 0.700199 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.3541 | −1.37314 | −0.686570 | − | 0.727064i | \(-0.740884\pi\) | ||||
−0.686570 | + | 0.727064i | \(0.740884\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.54608 | −0.0512804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.2146 | 1.33237 | 0.666184 | − | 0.745787i | \(-0.267927\pi\) | ||||
0.666184 | + | 0.745787i | \(0.267927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.12381 | −0.103383 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.24020 | 0.140177 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.82740 | −0.159415 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.68843 | −0.121670 | −0.0608350 | − | 0.998148i | \(-0.519376\pi\) | ||||
−0.0608350 | + | 0.998148i | \(0.519376\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.2124 | 1.29209 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.68968 | 0.253109 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.0955 | 0.331939 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.20579 | 0.0396032 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.8268 | 0.453644 | 0.226822 | − | 0.973936i | \(-0.427166\pi\) | ||||
0.226822 | + | 0.973936i | \(0.427166\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.53631 | −0.214219 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.9572 | 0.620631 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.244740 | −0.00800385 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.63089 | 0.151285 | 0.0756423 | − | 0.997135i | \(-0.475899\pi\) | ||||
0.0756423 | + | 0.997135i | \(0.475899\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.7920 | −1.07013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.8959 | −1.75695 | −0.878477 | − | 0.477784i | \(-0.841440\pi\) | ||||
−0.878477 | + | 0.477784i | \(0.841440\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −84.6805 | −2.75758 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.5863 | 0.539553 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.2368 | 1.40501 | 0.702503 | − | 0.711681i | \(-0.252066\pi\) | ||||
0.702503 | + | 0.711681i | \(0.252066\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.86228 | 0.320143 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 56.4841 | 1.83162 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.4043 | 1.95669 | 0.978344 | − | 0.206984i | \(-0.0663647\pi\) | ||||
0.978344 | + | 0.206984i | \(0.0663647\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −62.6666 | −2.02784 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.67496 | 0.183445 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.73129 | 0.0881980 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.85873 | 0.0922170 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.36391 | 0.0439513 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 43.3979 | 1.39703 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.1489 | −1.41973 | −0.709866 | − | 0.704337i | \(-0.751245\pi\) | ||||
−0.709866 | + | 0.704337i | \(0.751245\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.867252 | −0.0278601 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.39621 | 0.269447 | 0.134724 | − | 0.990883i | \(-0.456985\pi\) | ||||
0.134724 | + | 0.990883i | \(0.456985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.80299 | 0.121918 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.68604 | 0.310201 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.7280 | 1.55895 | 0.779473 | − | 0.626436i | \(-0.215487\pi\) | ||||
0.779473 | + | 0.626436i | \(0.215487\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.35214 | 0.0751748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.53112 | 0.0488851 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.416637 | −0.0132887 | −0.00664433 | − | 0.999978i | \(-0.502115\pi\) | ||||
−0.00664433 | + | 0.999978i | \(0.502115\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.65213 | −0.0526412 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.57261 | −0.0818870 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.7760 | 1.07402 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.6837 | −1.61002 | −0.805010 | − | 0.593261i | \(-0.797840\pi\) | ||||
−0.805010 | + | 0.593261i | \(0.797840\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.488733 | −0.0155095 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −52.7955 | −1.67373 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.03497 | 0.254470 | 0.127235 | − | 0.991873i | \(-0.459390\pi\) | ||||
0.127235 | + | 0.991873i | \(0.459390\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −9.37217 | −0.296522 |
(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 | 8008.2.a.x.1.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.x.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial |