Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7728,2,Mod(1,7728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7728, 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("7728.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7728 = 2^{4} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7728.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: | \(61.7083906820\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 483) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7728.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.697224 | −0.311808 | −0.155904 | − | 0.987772i | \(-0.549829\pi\) | ||||
−0.155904 | + | 0.987772i | \(0.549829\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.00000 | 1.50756 | 0.753778 | − | 0.657129i | \(-0.228229\pi\) | ||||
0.753778 | + | 0.657129i | \(0.228229\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.30278 | 0.638675 | 0.319338 | − | 0.947641i | \(-0.396540\pi\) | ||||
0.319338 | + | 0.947641i | \(0.396540\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.697224 | 0.180023 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.60555 | −1.35955 | −0.679773 | − | 0.733423i | \(-0.737922\pi\) | ||||
−0.679773 | + | 0.733423i | \(0.737922\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.60555 | 0.368339 | 0.184169 | − | 0.982895i | \(-0.441041\pi\) | ||||
0.184169 | + | 0.982895i | \(0.441041\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.51388 | −0.902776 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.21110 | 1.15337 | 0.576686 | − | 0.816966i | \(-0.304345\pi\) | ||||
0.576686 | + | 0.816966i | \(0.304345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | −0.538816 | −0.269408 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269408 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.00000 | −0.870388 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.697224 | −0.117852 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.00000 | −1.47959 | −0.739795 | − | 0.672832i | \(-0.765078\pi\) | ||||
−0.739795 | + | 0.672832i | \(0.765078\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.30278 | −0.368739 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.2111 | −1.90705 | −0.953527 | − | 0.301308i | \(-0.902577\pi\) | ||||
−0.953527 | + | 0.301308i | \(0.902577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.51388 | −0.840859 | −0.420429 | − | 0.907325i | \(-0.638121\pi\) | ||||
−0.420429 | + | 0.907325i | \(0.638121\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.697224 | −0.103936 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.60555 | 1.25525 | 0.627624 | − | 0.778516i | \(-0.284027\pi\) | ||||
0.627624 | + | 0.778516i | \(0.284027\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.60555 | 0.784934 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12.5139 | −1.71891 | −0.859457 | − | 0.511209i | \(-0.829198\pi\) | ||||
−0.859457 | + | 0.511209i | \(0.829198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.48612 | −0.470069 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.60555 | −0.212660 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.90833 | −0.508821 | −0.254410 | − | 0.967096i | \(-0.581881\pi\) | ||||
−0.254410 | + | 0.967096i | \(0.581881\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.09167 | −0.139774 | −0.0698872 | − | 0.997555i | \(-0.522264\pi\) | ||||
−0.0698872 | + | 0.997555i | \(0.522264\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.60555 | −0.199144 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.9083 | 1.45483 | 0.727417 | − | 0.686196i | \(-0.240721\pi\) | ||||
0.727417 | + | 0.686196i | \(0.240721\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.908327 | −0.107799 | −0.0538993 | − | 0.998546i | \(-0.517165\pi\) | ||||
−0.0538993 | + | 0.998546i | \(0.517165\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.21110 | −0.258790 | −0.129395 | − | 0.991593i | \(-0.541304\pi\) | ||||
−0.129395 | + | 0.991593i | \(0.541304\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.51388 | 0.521218 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.00000 | 0.569803 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.00000 | 0.112509 | 0.0562544 | − | 0.998416i | \(-0.482084\pi\) | ||||
0.0562544 | + | 0.998416i | \(0.482084\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.60555 | −0.615289 | −0.307645 | − | 0.951501i | \(-0.599541\pi\) | ||||
−0.307645 | + | 0.951501i | \(0.599541\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.90833 | 0.423918 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.21110 | −0.665900 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.9083 | 1.15628 | 0.578140 | − | 0.815937i | \(-0.303779\pi\) | ||||
0.578140 | + | 0.815937i | \(0.303779\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.30278 | 0.241396 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.00000 | 0.311086 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.11943 | −0.114851 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −17.6056 | −1.78757 | −0.893786 | − | 0.448493i | \(-0.851961\pi\) | ||||
−0.893786 | + | 0.448493i | \(0.851961\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.00000 | 0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.30278 | 0.925661 | 0.462830 | − | 0.886447i | \(-0.346834\pi\) | ||||
0.462830 | + | 0.886447i | \(0.346834\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.697224 | 0.0680421 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.51388 | −0.726394 | −0.363197 | − | 0.931712i | \(-0.618315\pi\) | ||||
−0.363197 | + | 0.931712i | \(0.618315\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.90833 | −0.374350 | −0.187175 | − | 0.982327i | \(-0.559933\pi\) | ||||
−0.187175 | + | 0.982327i | \(0.559933\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.00000 | 0.854242 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.30278 | 0.498843 | 0.249422 | − | 0.968395i | \(-0.419760\pi\) | ||||
0.249422 | + | 0.968395i | \(0.419760\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.697224 | 0.0650165 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.30278 | 0.212892 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.60555 | −0.513860 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.2111 | 1.10104 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.63331 | 0.593301 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.69722 | −0.150604 | −0.0753022 | − | 0.997161i | \(-0.523992\pi\) | ||||
−0.0753022 | + | 0.997161i | \(0.523992\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.51388 | 0.485470 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3944 | −0.908167 | −0.454084 | − | 0.890959i | \(-0.650033\pi\) | ||||
−0.454084 | + | 0.890959i | \(0.650033\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.60555 | 0.139219 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.697224 | 0.0600075 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.8167 | 1.43674 | 0.718372 | − | 0.695659i | \(-0.244888\pi\) | ||||
0.718372 | + | 0.695659i | \(0.244888\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.9083 | −1.34933 | −0.674663 | − | 0.738126i | \(-0.735711\pi\) | ||||
−0.674663 | + | 0.738126i | \(0.735711\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.60555 | −0.724718 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.5139 | 0.962839 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.33053 | −0.359631 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.60555 | 0.704994 | 0.352497 | − | 0.935813i | \(-0.385333\pi\) | ||||
0.352497 | + | 0.935813i | \(0.385333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.6056 | −1.35134 | −0.675670 | − | 0.737204i | \(-0.736146\pi\) | ||||
−0.675670 | + | 0.737204i | \(0.736146\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.60555 | −0.453182 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.09167 | 0.168007 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.81665 | −0.304602 | −0.152301 | − | 0.988334i | \(-0.548668\pi\) | ||||
−0.152301 | + | 0.988334i | \(0.548668\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.5139 | 0.992415 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.00000 | −0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7250 | 1.07502 | 0.537512 | − | 0.843256i | \(-0.319364\pi\) | ||||
0.537512 | + | 0.843256i | \(0.319364\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.48612 | 0.271394 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.81665 | −0.217959 | −0.108980 | − | 0.994044i | \(-0.534758\pi\) | ||||
−0.108980 | + | 0.994044i | \(0.534758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.69722 | −0.592094 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.60555 | 0.122780 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.2111 | −1.38456 | −0.692282 | − | 0.721627i | \(-0.743395\pi\) | ||||
−0.692282 | + | 0.721627i | \(0.743395\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.51388 | −0.341217 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.90833 | 0.293768 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.69722 | 0.201600 | 0.100800 | − | 0.994907i | \(-0.467860\pi\) | ||||
0.100800 | + | 0.994907i | \(0.467860\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.81665 | −0.506678 | −0.253339 | − | 0.967378i | \(-0.581529\pi\) | ||||
−0.253339 | + | 0.967378i | \(0.581529\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.09167 | 0.0806988 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.27502 | 0.461349 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.0278 | −2.04959 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.60555 | 0.333246 | 0.166623 | − | 0.986021i | \(-0.446714\pi\) | ||||
0.166623 | + | 0.986021i | \(0.446714\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.02776 | 0.649832 | 0.324916 | − | 0.945743i | \(-0.394664\pi\) | ||||
0.324916 | + | 0.945743i | \(0.394664\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.60555 | 0.114976 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.09167 | −0.505261 | −0.252630 | − | 0.967563i | \(-0.581296\pi\) | ||||
−0.252630 | + | 0.967563i | \(0.581296\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.5139 | −0.887085 | −0.443543 | − | 0.896253i | \(-0.646279\pi\) | ||||
−0.443543 | + | 0.896253i | \(0.646279\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.9083 | −0.839949 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.21110 | 0.435934 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.51388 | 0.594635 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.02776 | 0.555292 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.4222 | 1.88782 | 0.943911 | − | 0.330199i | \(-0.107116\pi\) | ||||
0.943911 | + | 0.330199i | \(0.107116\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.908327 | 0.0622375 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.84441 | 0.262187 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.21110 | 0.149412 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.9083 | −0.868308 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.9083 | −1.33316 | −0.666580 | − | 0.745433i | \(-0.732243\pi\) | ||||
−0.666580 | + | 0.745433i | \(0.732243\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.51388 | −0.300925 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.3305 | 1.34938 | 0.674692 | − | 0.738099i | \(-0.264276\pi\) | ||||
0.674692 | + | 0.738099i | \(0.264276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.51388 | 0.166122 | 0.0830609 | − | 0.996544i | \(-0.473530\pi\) | ||||
0.0830609 | + | 0.996544i | \(0.473530\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.00000 | −0.328976 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.3305 | −0.938824 | −0.469412 | − | 0.882979i | \(-0.655534\pi\) | ||||
−0.469412 | + | 0.882979i | \(0.655534\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0917 | 0.911515 | 0.455757 | − | 0.890104i | \(-0.349369\pi\) | ||||
0.455757 | + | 0.890104i | \(0.349369\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0278 | 0.774776 | 0.387388 | − | 0.921917i | \(-0.373377\pi\) | ||||
0.387388 | + | 0.921917i | \(0.373377\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.697224 | −0.0445440 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.69722 | 0.235249 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.60555 | 0.355237 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.8167 | −1.50329 | −0.751647 | − | 0.659566i | \(-0.770740\pi\) | ||||
−0.751647 | + | 0.659566i | \(0.770740\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.00000 | −0.314347 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.90833 | −0.244749 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.0278 | 1.68595 | 0.842973 | − | 0.537957i | \(-0.180804\pi\) | ||||
0.842973 | + | 0.537957i | \(0.180804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.00000 | −0.559233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.21110 | 0.384458 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.3944 | −0.640949 | −0.320475 | − | 0.947257i | \(-0.603842\pi\) | ||||
−0.320475 | + | 0.947257i | \(0.603842\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.72498 | 0.535971 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9083 | −0.667579 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.908327 | 0.0553817 | 0.0276908 | − | 0.999617i | \(-0.491185\pi\) | ||||
0.0276908 | + | 0.999617i | \(0.491185\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.60555 | −0.219022 | −0.109511 | − | 0.993986i | \(-0.534928\pi\) | ||||
−0.109511 | + | 0.993986i | \(0.534928\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.30278 | −0.139370 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −22.5694 | −1.36099 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.3028 | −0.739202 | −0.369601 | − | 0.929191i | \(-0.620506\pi\) | ||||
−0.369601 | + | 0.929191i | \(0.620506\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.00000 | −0.179605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.8167 | 1.65940 | 0.829701 | − | 0.558208i | \(-0.188511\pi\) | ||||
0.829701 | + | 0.558208i | \(0.188511\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −17.3028 | −1.02854 | −0.514272 | − | 0.857627i | \(-0.671938\pi\) | ||||
−0.514272 | + | 0.857627i | \(0.671938\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.11943 | 0.0663093 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.2111 | −0.720799 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.4222 | 0.848365 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 17.6056 | 1.03206 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.8444 | −1.45143 | −0.725713 | − | 0.687998i | \(-0.758490\pi\) | ||||
−0.725713 | + | 0.687998i | \(0.758490\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.72498 | 0.158655 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.00000 | −0.290129 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.30278 | −0.133173 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.51388 | −0.317815 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.30278 | −0.534430 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.761141 | 0.0435828 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.2111 | −1.03936 | −0.519681 | − | 0.854360i | \(-0.673949\pi\) | ||||
−0.519681 | + | 0.854360i | \(0.673949\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.51388 | 0.539483 | 0.269741 | − | 0.962933i | \(-0.413062\pi\) | ||||
0.269741 | + | 0.962933i | \(0.413062\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.21110 | 0.0684556 | 0.0342278 | − | 0.999414i | \(-0.489103\pi\) | ||||
0.0342278 | + | 0.999414i | \(0.489103\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.697224 | −0.0392841 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −30.5139 | −1.71383 | −0.856915 | − | 0.515458i | \(-0.827622\pi\) | ||||
−0.856915 | + | 0.515458i | \(0.827622\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.0555 | 1.73877 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.51388 | 0.419384 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.00000 | −0.500773 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.3944 | −0.576580 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.90833 | 0.216131 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.60555 | 0.474439 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6333 | −0.969214 | −0.484607 | − | 0.874732i | \(-0.661037\pi\) | ||||
−0.484607 | + | 0.874732i | \(0.661037\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.00000 | −0.493197 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.30278 | −0.453629 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.6972 | −0.855082 | −0.427541 | − | 0.903996i | \(-0.640620\pi\) | ||||
−0.427541 | + | 0.903996i | \(0.640620\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.30278 | −0.288007 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.0000 | −0.812296 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.697224 | −0.0375373 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.6333 | −0.785557 | −0.392779 | − | 0.919633i | \(-0.628486\pi\) | ||||
−0.392779 | + | 0.919633i | \(0.628486\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0917 | −0.540195 | −0.270097 | − | 0.962833i | \(-0.587056\pi\) | ||||
−0.270097 | + | 0.962833i | \(0.587056\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.30278 | −0.122913 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.0000 | −0.585471 | −0.292735 | − | 0.956193i | \(-0.594566\pi\) | ||||
−0.292735 | + | 0.956193i | \(0.594566\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.633308 | 0.0336125 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.60555 | 0.296677 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 35.5416 | 1.87582 | 0.937908 | − | 0.346884i | \(-0.112760\pi\) | ||||
0.937908 | + | 0.346884i | \(0.112760\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.4222 | −0.864327 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.0000 | −0.734809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.54163 | 0.0806928 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.5139 | −1.12302 | −0.561508 | − | 0.827472i | \(-0.689778\pi\) | ||||
−0.561508 | + | 0.827472i | \(0.689778\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12.2111 | −0.635685 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.5139 | −0.649688 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.2111 | 0.839379 | 0.419690 | − | 0.907668i | \(-0.362139\pi\) | ||||
0.419690 | + | 0.907668i | \(0.362139\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6.63331 | −0.342543 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.3028 | 0.736630 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.4222 | 1.15175 | 0.575876 | − | 0.817537i | \(-0.304661\pi\) | ||||
0.575876 | + | 0.817537i | \(0.304661\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.69722 | 0.0869514 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.81665 | −0.246120 | −0.123060 | − | 0.992399i | \(-0.539271\pi\) | ||||
−0.123060 | + | 0.992399i | \(0.539271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.48612 | −0.177669 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.51388 | −0.280286 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.6333 | −1.85738 | −0.928691 | − | 0.370854i | \(-0.879065\pi\) | ||||
−0.928691 | + | 0.370854i | \(0.879065\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.60555 | 0.283485 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.3944 | 0.524331 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.697224 | −0.0350812 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.3944 | −1.37489 | −0.687444 | − | 0.726237i | \(-0.741267\pi\) | ||||
−0.687444 | + | 0.726237i | \(0.741267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.60555 | −0.0803781 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.4222 | −0.670273 | −0.335136 | − | 0.942170i | \(-0.608782\pi\) | ||||
−0.335136 | + | 0.942170i | \(0.608782\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.90833 | −0.344128 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.697224 | −0.0346454 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −45.0000 | −2.23057 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.0278 | 1.18810 | 0.594048 | − | 0.804430i | \(-0.297529\pi\) | ||||
0.594048 | + | 0.804430i | \(0.297529\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.8167 | −0.829504 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.90833 | −0.192316 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.90833 | 0.191852 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.9083 | 0.779034 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.1194 | −0.738632 | −0.369316 | − | 0.929304i | \(-0.620408\pi\) | ||||
−0.369316 | + | 0.929304i | \(0.620408\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.69722 | 0.472614 | 0.236307 | − | 0.971678i | \(-0.424063\pi\) | ||||
0.236307 | + | 0.971678i | \(0.424063\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.60555 | 0.418416 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.3028 | 1.22736 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.09167 | −0.0528298 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.5139 | −0.555895 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.72498 | 0.420268 | 0.210134 | − | 0.977673i | \(-0.432610\pi\) | ||||
0.210134 | + | 0.977673i | \(0.432610\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.0278 | −1.01053 | −0.505265 | − | 0.862964i | \(-0.668605\pi\) | ||||
−0.505265 | + | 0.862964i | \(0.668605\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.33053 | 0.207633 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.60555 | −0.0768039 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.2111 | −0.964623 | −0.482312 | − | 0.876000i | \(-0.660203\pi\) | ||||
−0.482312 | + | 0.876000i | \(0.660203\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.8444 | 1.56049 | 0.780243 | − | 0.625477i | \(-0.215096\pi\) | ||||
0.780243 | + | 0.625477i | \(0.215096\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.60555 | −0.360538 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.60555 | −0.407029 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −35.7250 | −1.68597 | −0.842983 | − | 0.537940i | \(-0.819203\pi\) | ||||
−0.842983 | + | 0.537940i | \(0.819203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −61.0555 | −2.87499 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.6056 | 0.780197 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.60555 | −0.0752694 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.8806 | −0.508972 | −0.254486 | − | 0.967077i | \(-0.581906\pi\) | ||||
−0.254486 | + | 0.967077i | \(0.581906\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.60555 | 0.261645 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.72498 | 0.359788 | 0.179894 | − | 0.983686i | \(-0.442424\pi\) | ||||
0.179894 | + | 0.983686i | \(0.442424\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.8167 | 0.874484 | 0.437242 | − | 0.899344i | \(-0.355955\pi\) | ||||
0.437242 | + | 0.899344i | \(0.355955\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.09167 | −0.0969990 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.6056 | −1.09233 | −0.546167 | − | 0.837676i | \(-0.683914\pi\) | ||||
−0.546167 | + | 0.837676i | \(0.683914\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.9083 | 0.549875 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.81665 | 0.175862 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.5694 | −1.26764 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.24726 | −0.332527 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.5139 | −0.572971 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 18.2111 | 0.832087 | 0.416043 | − | 0.909345i | \(-0.363416\pi\) | ||||
0.416043 | + | 0.909345i | \(0.363416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.7250 | −0.944978 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12.2750 | 0.557380 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.816654 | 0.0370061 | 0.0185031 | − | 0.999829i | \(-0.494110\pi\) | ||||
0.0185031 | + | 0.999829i | \(0.494110\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.7250 | −0.620665 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.9361 | 0.809444 | 0.404722 | − | 0.914440i | \(-0.367368\pi\) | ||||
0.404722 | + | 0.914440i | \(0.367368\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.8167 | −1.56806 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.48612 | −0.156690 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.908327 | −0.0407440 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.9083 | −1.42841 | −0.714206 | − | 0.699935i | \(-0.753212\pi\) | ||||
−0.714206 | + | 0.699935i | \(0.753212\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.81665 | 0.125839 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.7250 | −0.790318 | −0.395159 | − | 0.918613i | \(-0.629310\pi\) | ||||
−0.395159 | + | 0.918613i | \(0.629310\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.48612 | −0.288629 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.69722 | 0.341846 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −33.4500 | −1.48264 | −0.741322 | − | 0.671150i | \(-0.765801\pi\) | ||||
−0.741322 | + | 0.671150i | \(0.765801\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.21110 | −0.0978134 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.60555 | −0.0708868 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.78890 | −0.122894 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.0278 | 1.89236 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.2111 | 0.799379 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.6333 | 0.947772 | 0.473886 | − | 0.880586i | \(-0.342851\pi\) | ||||
0.473886 | + | 0.880586i | \(0.342851\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.422205 | 0.0184617 | 0.00923087 | − | 0.999957i | \(-0.497062\pi\) | ||||
0.00923087 | + | 0.999957i | \(0.497062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.51388 | 0.197002 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.8167 | 0.732545 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.90833 | −0.169607 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.1194 | −1.21799 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.23886 | 0.226496 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.69722 | −0.116394 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.00000 | 0.215365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.81665 | −0.250077 | −0.125039 | − | 0.992152i | \(-0.539906\pi\) | ||||
−0.125039 | + | 0.992152i | \(0.539906\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.81665 | 0.292531 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.72498 | 0.116725 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.72498 | 0.330296 | 0.165148 | − | 0.986269i | \(-0.447190\pi\) | ||||
0.165148 | + | 0.986269i | \(0.447190\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.09167 | −0.0465915 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.97224 | 0.424832 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.00000 | 0.0425243 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.27502 | −0.266360 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.02776 | 0.213033 | 0.106516 | − | 0.994311i | \(-0.466030\pi\) | ||||
0.106516 | + | 0.994311i | \(0.466030\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.6972 | −0.537035 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.0278 | 1.18333 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 43.3305 | 1.82616 | 0.913082 | − | 0.407776i | \(-0.133695\pi\) | ||||
0.913082 | + | 0.407776i | \(0.133695\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.69722 | −0.155543 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.7889 | 0.452294 | 0.226147 | − | 0.974093i | \(-0.427387\pi\) | ||||
0.226147 | + | 0.974093i | \(0.427387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.2111 | −0.427321 | −0.213661 | − | 0.976908i | \(-0.568539\pi\) | ||||
−0.213661 | + | 0.976908i | \(0.568539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.60555 | −0.192400 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.51388 | 0.188242 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.4222 | −1.51628 | −0.758138 | − | 0.652094i | \(-0.773891\pi\) | ||||
−0.758138 | + | 0.652094i | \(0.773891\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.02776 | −0.375181 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.60555 | −0.232557 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −62.5694 | −2.59136 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.60555 | −0.0663814 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.1472 | 1.61578 | 0.807889 | − | 0.589335i | \(-0.200610\pi\) | ||||
0.807889 | + | 0.589335i | \(0.200610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.81665 | −0.198467 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.09167 | 0.291712 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 37.0278 | 1.52055 | 0.760274 | − | 0.649603i | \(-0.225065\pi\) | ||||
0.760274 | + | 0.649603i | \(0.225065\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.90833 | 0.160226 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.5139 | 0.512159 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.5139 | 1.61449 | 0.807247 | − | 0.590214i | \(-0.200957\pi\) | ||||
0.807247 | + | 0.590214i | \(0.200957\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.9361 | 1.66982 | 0.834909 | − | 0.550388i | \(-0.185520\pi\) | ||||
0.834909 | + | 0.550388i | \(0.185520\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.9083 | 0.484945 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.76114 | −0.396847 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4861 | 0.993861 | 0.496931 | − | 0.867790i | \(-0.334460\pi\) | ||||
0.496931 | + | 0.867790i | \(0.334460\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.21110 | −0.251687 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.8167 | 0.801696 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.81665 | 0.113764 | 0.0568818 | − | 0.998381i | \(-0.481884\pi\) | ||||
0.0568818 | + | 0.998381i | \(0.481884\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.51388 | −0.343313 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.7250 | 0.592805 | 0.296403 | − | 0.955063i | \(-0.404213\pi\) | ||||
0.296403 | + | 0.955063i | \(0.404213\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.88057 | −0.397134 | −0.198567 | − | 0.980087i | \(-0.563629\pi\) | ||||
−0.198567 | + | 0.980087i | \(0.563629\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 10.9083 | 0.437033 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.9445 | 0.717779 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.02776 | −0.320598 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 50.4500 | 2.01157 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.9722 | 0.476607 | 0.238304 | − | 0.971191i | \(-0.423409\pi\) | ||||
0.238304 | + | 0.971191i | \(0.423409\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −27.4222 | −1.08993 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.18335 | 0.0469597 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.30278 | 0.0912393 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.908327 | −0.0359329 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5416 | −0.416370 | −0.208185 | − | 0.978090i | \(-0.566756\pi\) | ||||
−0.208185 | + | 0.978090i | \(0.566756\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.5694 | −1.71821 | −0.859105 | − | 0.511800i | \(-0.828979\pi\) | ||||
−0.859105 | + | 0.511800i | \(0.828979\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.84441 | −0.151374 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.3305 | −0.642019 | −0.321010 | − | 0.947076i | \(-0.604022\pi\) | ||||
−0.321010 | + | 0.947076i | \(0.604022\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.5416 | −0.767076 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.00000 | 0.117579 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.5139 | 1.19410 | 0.597050 | − | 0.802204i | \(-0.296339\pi\) | ||||
0.597050 | + | 0.802204i | \(0.296339\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.24726 | 0.283174 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.21110 | −0.0862633 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −42.6333 | −1.66076 | −0.830379 | − | 0.557199i | \(-0.811876\pi\) | ||||
−0.830379 | + | 0.557199i | \(0.811876\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.8167 | 0.809674 | 0.404837 | − | 0.914389i | \(-0.367328\pi\) | ||||
0.404837 | + | 0.914389i | \(0.367328\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.9083 | 0.501318 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.11943 | −0.0434096 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.21110 | −0.240495 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.9083 | 0.769700 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.45837 | −0.210718 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.6333 | −1.02664 | −0.513319 | − | 0.858198i | \(-0.671584\pi\) | ||||
−0.513319 | + | 0.858198i | \(0.671584\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.51388 | 0.173739 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.1472 | 1.42768 | 0.713841 | − | 0.700308i | \(-0.246954\pi\) | ||||
0.713841 | + | 0.700308i | \(0.246954\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.6056 | −0.675639 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.3305 | −0.779068 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.42221 | 0.0544192 | 0.0272096 | − | 0.999630i | \(-0.491338\pi\) | ||||
0.0272096 | + | 0.999630i | \(0.491338\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.7250 | −0.447988 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.51388 | −0.0959104 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −28.8167 | −1.09783 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.5139 | 1.19884 | 0.599422 | − | 0.800433i | \(-0.295397\pi\) | ||||
0.599422 | + | 0.800433i | \(0.295397\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.00000 | 0.189934 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.0917 | 0.420731 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 68.4500 | 2.59273 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.3305 | 0.542031 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.5416 | −0.964694 | −0.482347 | − | 0.875980i | \(-0.660216\pi\) | ||||
−0.482347 | + | 0.875980i | \(0.660216\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.4500 | −0.544991 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.00000 | 0.225973 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.30278 | 0.349867 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.3305 | −1.77754 | −0.888768 | − | 0.458358i | \(-0.848438\pi\) | ||||
−0.888768 | + | 0.458358i | \(0.848438\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.00000 | 0.112351 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.02776 | −0.300221 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −14.0917 | −0.526263 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −14.2111 | −0.529985 | −0.264992 | − | 0.964251i | \(-0.585369\pi\) | ||||
−0.264992 | + | 0.964251i | \(0.585369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.0278 | −0.447317 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −28.0362 | −1.04124 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.8722 | 1.73839 | 0.869196 | − | 0.494467i | \(-0.164637\pi\) | ||||
0.869196 | + | 0.494467i | \(0.164637\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.9083 | 1.14319 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.6056 | −0.982698 | −0.491349 | − | 0.870963i | \(-0.663496\pi\) | ||||
−0.491349 | + | 0.870963i | \(0.663496\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.697224 | 0.0257175 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 59.5416 | 2.19324 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.4222 | 1.59731 | 0.798656 | − | 0.601788i | \(-0.205545\pi\) | ||||
0.798656 | + | 0.601788i | \(0.205545\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.69722 | −0.135821 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.5139 | −1.11945 | −0.559723 | − | 0.828680i | \(-0.689092\pi\) | ||||
−0.559723 | + | 0.828680i | \(0.689092\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | −0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.60555 | −0.205096 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.51388 | −0.274551 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.69722 | −0.317366 | −0.158683 | − | 0.987330i | \(-0.550725\pi\) | ||||
−0.158683 | + | 0.987330i | \(0.550725\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 23.8167 | 0.867927 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.5778 | 0.421359 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.36669 | −0.122365 | −0.0611823 | − | 0.998127i | \(-0.519487\pi\) | ||||
−0.0611823 | + | 0.998127i | \(0.519487\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.00000 | 0.181489 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.0000 | 0.435000 | 0.217500 | − | 0.976060i | \(-0.430210\pi\) | ||||
0.217500 | + | 0.976060i | \(0.430210\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.90833 | −0.141491 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.90833 | 0.141306 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.00000 | −0.324971 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.4500 | −0.989871 | −0.494935 | − | 0.868930i | \(-0.664808\pi\) | ||||
−0.494935 | + | 0.868930i | \(0.664808\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.0278 | −0.973381 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.8444 | 1.14536 | 0.572682 | − | 0.819778i | \(-0.305903\pi\) | ||||
0.572682 | + | 0.819778i | \(0.305903\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.5416 | 0.486430 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.00000 | 0.322873 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −19.6056 | −0.702442 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.54163 | −0.162512 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.21110 | −0.221967 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.66106 | 0.0949774 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −32.1472 | −1.14592 | −0.572962 | − | 0.819582i | \(-0.694206\pi\) | ||||
−0.572962 | + | 0.819582i | \(0.694206\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.3944 | 0.370052 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.30278 | 0.188545 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.51388 | −0.0892704 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.72498 | −0.309443 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −39.0278 | −1.38243 | −0.691217 | − | 0.722647i | \(-0.742925\pi\) | ||||
−0.691217 | + | 0.722647i | \(0.742925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.2389 | −1.70657 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.9083 | 0.385427 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.0555 | −0.390141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.697224 | 0.0245739 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.908327 | −0.0319746 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.9361 | 0.911864 | 0.455932 | − | 0.890015i | \(-0.349306\pi\) | ||||
0.455932 | + | 0.890015i | \(0.349306\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3944 | 0.364998 | 0.182499 | − | 0.983206i | \(-0.441581\pi\) | ||||
0.182499 | + | 0.983206i | \(0.441581\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.60555 | 0.126452 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.56939 | −0.335201 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.85281 | −0.309721 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.30278 | 0.0804655 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.3944 | −0.676871 | −0.338435 | − | 0.940990i | \(-0.609898\pi\) | ||||
−0.338435 | + | 0.940990i | \(0.609898\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.51388 | −0.227060 | −0.113530 | − | 0.993535i | \(-0.536216\pi\) | ||||
−0.113530 | + | 0.993535i | \(0.536216\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 22.5694 | 0.785765 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.90833 | 0.344546 | 0.172273 | − | 0.985049i | \(-0.444889\pi\) | ||||
0.172273 | + | 0.985049i | \(0.444889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.4500 | −1.05757 | −0.528785 | − | 0.848756i | \(-0.677352\pi\) | ||||
−0.528785 | + | 0.848756i | \(0.677352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.3028 | 0.426779 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.60555 | −0.194221 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.96384 | 0.0679615 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.00000 | 0.103695 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.3028 | −1.32236 | −0.661179 | − | 0.750228i | \(-0.729944\pi\) | ||||
−0.661179 | + | 0.750228i | \(0.729944\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.57779 | 0.330269 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27.8167 | −0.958056 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.36669 | 0.184620 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0000 | 0.481046 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.3028 | 0.593830 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.00000 | 0.308516 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −58.2389 | −1.99406 | −0.997030 | − | 0.0770106i | \(-0.975462\pi\) | ||||
−0.997030 | + | 0.0770106i | \(0.975462\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.11943 | −0.0382837 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −50.2389 | −1.71613 | −0.858063 | − | 0.513544i | \(-0.828332\pi\) | ||||
−0.858063 | + | 0.513544i | \(0.828332\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.2111 | −1.47434 | −0.737172 | − | 0.675705i | \(-0.763839\pi\) | ||||
−0.737172 | + | 0.675705i | \(0.763839\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.2111 | 0.416153 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.76114 | 0.196112 | 0.0980558 | − | 0.995181i | \(-0.468738\pi\) | ||||
0.0980558 | + | 0.995181i | \(0.468738\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.6972 | 0.431719 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −14.4222 | −0.489804 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.00000 | 0.169613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.4222 | 0.929166 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −17.6056 | −0.595858 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6.63331 | 0.224247 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.7889 | −0.499386 | −0.249693 | − | 0.968325i | \(-0.580330\pi\) | ||||
−0.249693 | + | 0.968325i | \(0.580330\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.8444 | 0.837981 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.8167 | −1.47622 | −0.738110 | − | 0.674680i | \(-0.764282\pi\) | ||||
−0.738110 | + | 0.674680i | \(0.764282\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.4861 | 0.622108 | 0.311054 | − | 0.950392i | \(-0.399318\pi\) | ||||
0.311054 | + | 0.950392i | \(0.399318\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.72498 | −0.0915992 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.9361 | 0.400774 | 0.200387 | − | 0.979717i | \(-0.435780\pi\) | ||||
0.200387 | + | 0.979717i | \(0.435780\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.69722 | −0.0569231 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5.00000 | 0.167506 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.8167 | 0.462357 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.88057 | −0.0628605 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.30278 | 0.0768874 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.6333 | −0.621456 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 70.1472 | 2.33694 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.51388 | 0.183490 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.75274 | 0.157986 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.14719 | 0.270523 | 0.135261 | − | 0.990810i | \(-0.456813\pi\) | ||||
0.135261 | + | 0.990810i | \(0.456813\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.30278 | 0.308554 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.2389 | 0.803069 | 0.401535 | − | 0.915844i | \(-0.368477\pi\) | ||||
0.401535 | + | 0.915844i | \(0.368477\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.0278 | −0.927583 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.761141 | −0.0251625 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.3944 | −0.343255 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.3944 | 0.342881 | 0.171441 | − | 0.985194i | \(-0.445158\pi\) | ||||
0.171441 | + | 0.985194i | \(0.445158\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18.2111 | 0.600076 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.09167 | −0.0688483 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.6249 | 1.33574 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.00000 | 0.131377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 40.3305 | 1.32320 | 0.661601 | − | 0.749856i | \(-0.269877\pi\) | ||||
0.661601 | + | 0.749856i | \(0.269877\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.60555 | 0.0526198 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.51388 | −0.311470 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 19.5416 | 0.639080 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.57779 | −0.149550 | −0.0747750 | − | 0.997200i | \(-0.523824\pi\) | ||||
−0.0747750 | + | 0.997200i | \(0.523824\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.21110 | −0.0395228 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.844410 | −0.0275270 | −0.0137635 | − | 0.999905i | \(-0.504381\pi\) | ||||
−0.0137635 | + | 0.999905i | \(0.504381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.2111 | 0.397648 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.697224 | 0.0226807 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.6333 | 0.443023 | 0.221511 | − | 0.975158i | \(-0.428901\pi\) | ||||
0.221511 | + | 0.975158i | \(0.428901\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.09167 | −0.165283 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.5139 | 0.989480 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −51.3305 | −1.66276 | −0.831380 | − | 0.555705i | \(-0.812448\pi\) | ||||
−0.831380 | + | 0.555705i | \(0.812448\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.21110 | −0.103909 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −31.0555 | −1.00388 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.8167 | 0.543038 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.51388 | −0.242131 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.29437 | −0.202623 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.2666 | −1.32704 | −0.663522 | − | 0.748156i | \(-0.730939\pi\) | ||||
−0.663522 | + | 0.748156i | \(0.730939\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.00000 | 0.289122 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.0917 | 1.12615 | 0.563073 | − | 0.826407i | \(-0.309619\pi\) | ||||
0.563073 | + | 0.826407i | \(0.309619\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.9083 | −0.509998 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.3944 | 0.332889 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.1472 | 0.996487 | 0.498243 | − | 0.867037i | \(-0.333979\pi\) | ||||
0.498243 | + | 0.867037i | \(0.333979\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.5416 | 1.74316 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.90833 | −0.124783 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.8167 | 0.727738 | 0.363869 | − | 0.931450i | \(-0.381456\pi\) | ||||
0.363869 | + | 0.931450i | \(0.381456\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.94449 | 0.157544 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.60555 | −0.273918 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.51388 | 0.175331 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.5139 | −1.12814 | −0.564068 | − | 0.825729i | \(-0.690764\pi\) | ||||
−0.564068 | + | 0.825729i | \(0.690764\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.6333 | 0.559576 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.72498 | 0.276600 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.0277564 | −0.000879053 0 | −0.000439527 | − | 1.00000i | \(-0.500140\pi\) | ||||
−0.000439527 | 1.00000i | \(0.500140\pi\) | ||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.00000 | 0.284747 |
(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 | 7728.2.a.x.1.2 | 2 | ||
4.3 | odd | 2 | 483.2.a.f.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 1449.2.a.j.1.2 | 2 | |||
28.27 | even | 2 | 3381.2.a.p.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.a.f.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
1449.2.a.j.1.2 | 2 | 12.11 | even | 2 | |||
3381.2.a.p.1.1 | 2 | 28.27 | even | 2 | |||
7728.2.a.x.1.2 | 2 | 1.1 | even | 1 | trivial |