Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7360,2,Mod(1,7360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7360 = 2^{6} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7360.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: | \(58.7698958877\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7360.1 |
$q$-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 | ||||||||
\(3\) | −1.79129 | −1.03420 | −0.517100 | − | 0.855925i | \(-0.672989\pi\) | ||||
−0.517100 | + | 0.855925i | \(0.672989\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.79129 | 1.05501 | 0.527504 | − | 0.849553i | \(-0.323128\pi\) | ||||
0.527504 | + | 0.849553i | \(0.323128\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.208712 | 0.0695707 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.79129 | −1.14312 | −0.571558 | − | 0.820562i | \(-0.693661\pi\) | ||||
−0.571558 | + | 0.820562i | \(0.693661\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.20871 | −0.335236 | −0.167618 | − | 0.985852i | \(-0.553608\pi\) | ||||
−0.167618 | + | 0.985852i | \(0.553608\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.79129 | −0.462509 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.79129 | −0.919522 | −0.459761 | − | 0.888043i | \(-0.652065\pi\) | ||||
−0.459761 | + | 0.888043i | \(0.652065\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.20871 | −0.277298 | −0.138649 | − | 0.990342i | \(-0.544276\pi\) | ||||
−0.138649 | + | 0.990342i | \(0.544276\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.00000 | −1.09109 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.58258 | 0.293877 | 0.146938 | − | 0.989146i | \(-0.453058\pi\) | ||||
0.146938 | + | 0.989146i | \(0.453058\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.3739 | 1.86320 | 0.931600 | − | 0.363484i | \(-0.118413\pi\) | ||||
0.931600 | + | 0.363484i | \(0.118413\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.79129 | 1.18221 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.79129 | 0.471814 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.16515 | 0.346702 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.20871 | −0.344943 | −0.172471 | − | 0.985015i | \(-0.555175\pi\) | ||||
−0.172471 | + | 0.985015i | \(0.555175\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.16515 | 1.09268 | 0.546338 | − | 0.837565i | \(-0.316022\pi\) | ||||
0.546338 | + | 0.837565i | \(0.316022\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.208712 | 0.0311130 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.5826 | −1.98122 | −0.990611 | − | 0.136710i | \(-0.956347\pi\) | ||||
−0.990611 | + | 0.136710i | \(0.956347\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.791288 | 0.113041 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.79129 | 0.950971 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.79129 | −0.511217 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.16515 | 0.286781 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.41742 | 0.575100 | 0.287550 | − | 0.957766i | \(-0.407159\pi\) | ||||
0.287550 | + | 0.957766i | \(0.407159\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.37386 | 0.431979 | 0.215989 | − | 0.976396i | \(-0.430702\pi\) | ||||
0.215989 | + | 0.976396i | \(0.430702\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.582576 | 0.0733976 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.20871 | −0.149922 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.16515 | 0.875363 | 0.437681 | − | 0.899130i | \(-0.355800\pi\) | ||||
0.437681 | + | 0.899130i | \(0.355800\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.79129 | −0.215646 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.37386 | −0.637760 | −0.318880 | − | 0.947795i | \(-0.603307\pi\) | ||||
−0.318880 | + | 0.947795i | \(0.603307\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.7477 | −1.72609 | −0.863045 | − | 0.505126i | \(-0.831446\pi\) | ||||
−0.863045 | + | 0.505126i | \(0.831446\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.79129 | −0.206840 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.5826 | −1.20600 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.58258 | −1.06473 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.79129 | −0.411223 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.83485 | −0.303928 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.16515 | −0.335505 | −0.167753 | − | 0.985829i | \(-0.553651\pi\) | ||||
−0.167753 | + | 0.985829i | \(0.553651\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.37386 | −0.353677 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.5826 | −1.92692 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.20871 | −0.124011 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9564 | 1.51860 | 0.759298 | − | 0.650743i | \(-0.225542\pi\) | ||||
0.759298 | + | 0.650743i | \(0.225542\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.791288 | −0.0795274 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.5826 | −1.35152 | −0.675758 | − | 0.737123i | \(-0.736184\pi\) | ||||
−0.675758 | + | 0.737123i | \(0.736184\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.37386 | 0.726568 | 0.363284 | − | 0.931678i | \(-0.381655\pi\) | ||||
0.363284 | + | 0.931678i | \(0.381655\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.00000 | −0.487950 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.5826 | −1.31308 | −0.656539 | − | 0.754292i | \(-0.727980\pi\) | ||||
−0.656539 | + | 0.754292i | \(0.727980\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.3739 | −0.993636 | −0.496818 | − | 0.867855i | \(-0.665498\pi\) | ||||
−0.496818 | + | 0.867855i | \(0.665498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.16515 | −0.680086 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.252273 | −0.0233226 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.5826 | −0.970103 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.37386 | 0.306715 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.95644 | 0.356740 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7477 | −1.30865 | −0.654325 | − | 0.756214i | \(-0.727047\pi\) | ||||
−0.654325 | + | 0.756214i | \(0.727047\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.8348 | −1.13005 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.16515 | −0.800763 | −0.400381 | − | 0.916349i | \(-0.631122\pi\) | ||||
−0.400381 | + | 0.916349i | \(0.631122\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.37386 | −0.292551 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.00000 | 0.430331 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.791288 | −0.0676043 | −0.0338021 | − | 0.999429i | \(-0.510762\pi\) | ||||
−0.0338021 | + | 0.999429i | \(0.510762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7477 | 1.25089 | 0.625443 | − | 0.780270i | \(-0.284918\pi\) | ||||
0.625443 | + | 0.780270i | \(0.284918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.3303 | 2.04898 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.58258 | 0.383214 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.58258 | 0.131426 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.41742 | −0.116907 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.7913 | −1.04790 | −0.523952 | − | 0.851748i | \(-0.675543\pi\) | ||||
−0.523952 | + | 0.851748i | \(0.675543\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.20871 | −0.505258 | −0.252629 | − | 0.967563i | \(-0.581295\pi\) | ||||
−0.252629 | + | 0.967563i | \(0.581295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.791288 | −0.0639718 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3739 | 0.833249 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.7477 | −1.01738 | −0.508690 | − | 0.860950i | \(-0.669870\pi\) | ||||
−0.508690 | + | 0.860950i | \(0.669870\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.7477 | 0.852350 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.79129 | 0.219984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.3739 | −1.75246 | −0.876228 | − | 0.481897i | \(-0.839948\pi\) | ||||
−0.876228 | + | 0.481897i | \(0.839948\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.79129 | 0.528701 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −18.3303 | −1.41844 | −0.709221 | − | 0.704987i | \(-0.750953\pi\) | ||||
−0.709221 | + | 0.704987i | \(0.750953\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5390 | −0.887617 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.252273 | −0.0192918 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.2087 | 1.08027 | 0.540134 | − | 0.841579i | \(-0.318373\pi\) | ||||
0.540134 | + | 0.841579i | \(0.318373\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.79129 | 0.211002 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.91288 | −0.594768 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.7477 | 1.25178 | 0.625892 | − | 0.779910i | \(-0.284735\pi\) | ||||
0.625892 | + | 0.779910i | \(0.284735\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.5390 | −1.00635 | −0.503174 | − | 0.864185i | \(-0.667834\pi\) | ||||
−0.503174 | + | 0.864185i | \(0.667834\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.04356 | −0.446753 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | 0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.3739 | 1.05112 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.9564 | 1.01518 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.4174 | 1.18792 | 0.593962 | − | 0.804493i | \(-0.297563\pi\) | ||||
0.593962 | + | 0.804493i | \(0.297563\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.74773 | 0.485712 | 0.242856 | − | 0.970062i | \(-0.421916\pi\) | ||||
0.242856 | + | 0.970062i | \(0.421916\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.16515 | 0.155050 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.5390 | −1.46334 | −0.731672 | − | 0.681657i | \(-0.761260\pi\) | ||||
−0.731672 | + | 0.681657i | \(0.761260\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3303 | 1.44118 | 0.720588 | − | 0.693363i | \(-0.243872\pi\) | ||||
0.720588 | + | 0.693363i | \(0.243872\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.8348 | −0.905300 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.41742 | 0.310042 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.20871 | −0.154263 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.208712 | 0.0145065 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.58258 | 0.316983 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000 | 0.688428 | 0.344214 | − | 0.938891i | \(-0.388145\pi\) | ||||
0.344214 | + | 0.938891i | \(0.388145\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.62614 | 0.659572 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.16515 | 0.488659 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.9564 | 1.96569 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.4174 | 1.78512 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.58258 | 0.308257 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1652 | 0.747674 | 0.373837 | − | 0.927494i | \(-0.378042\pi\) | ||||
0.373837 | + | 0.927494i | \(0.378042\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.208712 | 0.0139141 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.74773 | −0.315118 | −0.157559 | − | 0.987510i | \(-0.550362\pi\) | ||||
−0.157559 | + | 0.987510i | \(0.550362\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.3303 | 1.07914 | 0.539568 | − | 0.841942i | \(-0.318587\pi\) | ||||
0.539568 | + | 0.841942i | \(0.318587\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.9564 | 1.24724 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.58258 | 0.496751 | 0.248376 | − | 0.968664i | \(-0.420103\pi\) | ||||
0.248376 | + | 0.968664i | \(0.420103\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.5826 | −0.886030 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.3303 | −0.930853 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.16515 | 0.204737 | 0.102368 | − | 0.994747i | \(-0.467358\pi\) | ||||
0.102368 | + | 0.994747i | \(0.467358\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.0000 | −1.80364 | −0.901819 | − | 0.432113i | \(-0.857768\pi\) | ||||
−0.901819 | + | 0.432113i | \(0.857768\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.16515 | 0.138895 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.791288 | 0.0505535 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.46099 | 0.0929603 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.7477 | −0.681110 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.7913 | −1.94353 | −0.971764 | − | 0.235953i | \(-0.924179\pi\) | ||||
−0.971764 | + | 0.235953i | \(0.924179\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.79129 | −0.238356 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.79129 | 0.425287 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.7477 | 1.41896 | 0.709482 | − | 0.704723i | \(-0.248929\pi\) | ||||
0.709482 | + | 0.704723i | \(0.248929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1652 | 0.693769 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.330303 | 0.0204452 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.7913 | 0.973733 | 0.486866 | − | 0.873477i | \(-0.338140\pi\) | ||||
0.486866 | + | 0.873477i | \(0.338140\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.66970 | 0.346980 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.7477 | −1.02113 | −0.510563 | − | 0.859840i | \(-0.670563\pi\) | ||||
−0.510563 | + | 0.859840i | \(0.670563\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.1216 | −1.40454 | −0.702268 | − | 0.711912i | \(-0.747829\pi\) | ||||
−0.702268 | + | 0.711912i | \(0.747829\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.04356 | 0.365773 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.79129 | −0.228623 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.16515 | 0.0700072 | 0.0350036 | − | 0.999387i | \(-0.488856\pi\) | ||||
0.0350036 | + | 0.999387i | \(0.488856\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.16515 | 0.129624 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.7477 | −0.999086 | −0.499543 | − | 0.866289i | \(-0.666499\pi\) | ||||
−0.499543 | + | 0.866289i | \(0.666499\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.3303 | 1.68406 | 0.842031 | − | 0.539429i | \(-0.181360\pi\) | ||||
0.842031 | + | 0.539429i | \(0.181360\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.16515 | 0.128252 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.16515 | −0.363917 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.62614 | −0.154479 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −26.7913 | −1.57053 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.4955 | 1.60630 | 0.803151 | − | 0.595776i | \(-0.203155\pi\) | ||||
0.803151 | + | 0.595776i | \(0.203155\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.41742 | 0.257192 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.9564 | −1.09996 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.20871 | −0.0699016 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | 1.15278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.3303 | 1.39774 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.37386 | 0.193187 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.5390 | −0.943931 | −0.471966 | − | 0.881617i | \(-0.656455\pi\) | ||||
−0.471966 | + | 0.881617i | \(0.656455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.2087 | −0.751417 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.3739 | −1.03855 | −0.519276 | − | 0.854607i | \(-0.673798\pi\) | ||||
−0.519276 | + | 0.854607i | \(0.673798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.582576 | 0.0328244 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.20871 | −0.292550 | −0.146275 | − | 0.989244i | \(-0.546729\pi\) | ||||
−0.146275 | + | 0.989244i | \(0.546729\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.00000 | −0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 24.3303 | 1.35799 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.58258 | 0.254981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.20871 | −0.0670473 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.5826 | 1.02762 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −37.9129 | −2.09020 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.74773 | −0.370889 | −0.185444 | − | 0.982655i | \(-0.559372\pi\) | ||||
−0.185444 | + | 0.982655i | \(0.559372\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.834849 | 0.0457494 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.16515 | 0.391474 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.7913 | −0.914680 | −0.457340 | − | 0.889292i | \(-0.651198\pi\) | ||||
−0.457340 | + | 0.889292i | \(0.651198\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.7477 | −0.583736 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −39.3303 | −2.12986 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.3303 | −0.935748 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.79129 | −0.0964397 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.79129 | −0.525624 | −0.262812 | − | 0.964847i | \(-0.584650\pi\) | ||||
−0.262812 | + | 0.964847i | \(0.584650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.04356 | −0.322581 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.1652 | −0.807160 | −0.403580 | − | 0.914944i | \(-0.632234\pi\) | ||||
−0.403580 | + | 0.914944i | \(0.632234\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.37386 | −0.285215 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 18.9564 | 1.00328 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.16515 | −0.483718 | −0.241859 | − | 0.970311i | \(-0.577757\pi\) | ||||
−0.241859 | + | 0.970311i | \(0.577757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5390 | −0.923106 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.04356 | −0.317205 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.7477 | −0.771931 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.834849 | −0.0435787 | −0.0217894 | − | 0.999763i | \(-0.506936\pi\) | ||||
−0.0217894 | + | 0.999763i | \(0.506936\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.460985 | −0.0239979 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.7477 | −0.869499 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7477 | 0.763608 | 0.381804 | − | 0.924243i | \(-0.375303\pi\) | ||||
0.381804 | + | 0.924243i | \(0.375303\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.79129 | −0.0925017 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.91288 | −0.0985183 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.37386 | −0.378770 | −0.189385 | − | 0.981903i | \(-0.560649\pi\) | ||||
−0.189385 | + | 0.981903i | \(0.560649\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 26.4174 | 1.35341 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5826 | −0.539338 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.49545 | 0.0760182 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −29.7042 | −1.50606 | −0.753031 | − | 0.657986i | \(-0.771409\pi\) | ||||
−0.753031 | + | 0.657986i | \(0.771409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.79129 | −0.191734 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.4174 | 0.828150 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5390 | −0.830069 | −0.415035 | − | 0.909806i | \(-0.636231\pi\) | ||||
−0.415035 | + | 0.909806i | \(0.636231\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.04356 | 0.302556 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.7477 | 1.13597 | 0.567984 | − | 0.823040i | \(-0.307724\pi\) | ||||
0.567984 | + | 0.823040i | \(0.307724\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.5390 | −0.624613 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −9.58258 | −0.476162 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.1652 | −0.751709 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.7913 | −1.12696 | −0.563478 | − | 0.826131i | \(-0.690537\pi\) | ||||
−0.563478 | + | 0.826131i | \(0.690537\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.41742 | 0.0699164 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.3303 | 0.606735 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.4174 | −1.29367 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.1652 | −1.91334 | −0.956671 | − | 0.291170i | \(-0.905956\pi\) | ||||
−0.956671 | + | 0.291170i | \(0.905956\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.1216 | 1.12688 | 0.563439 | − | 0.826158i | \(-0.309478\pi\) | ||||
0.563439 | + | 0.826158i | \(0.309478\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.83485 | −0.137835 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.79129 | −0.183904 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.41742 | 0.455741 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.20871 | −0.396320 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.9129 | −0.959170 | −0.479585 | − | 0.877496i | \(-0.659213\pi\) | ||||
−0.479585 | + | 0.877496i | \(0.659213\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.53901 | 0.0739603 | 0.0369802 | − | 0.999316i | \(-0.488226\pi\) | ||||
0.0369802 | + | 0.999316i | \(0.488226\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.83485 | −0.135921 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.20871 | −0.0578205 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.5390 | 1.21891 | 0.609455 | − | 0.792820i | \(-0.291388\pi\) | ||||
0.609455 | + | 0.792820i | \(0.291388\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.165151 | 0.00786435 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 35.2087 | 1.67282 | 0.836408 | − | 0.548107i | \(-0.184651\pi\) | ||||
0.836408 | + | 0.548107i | \(0.184651\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.16515 | −0.150043 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.9129 | 1.08374 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.1216 | 1.18556 | 0.592781 | − | 0.805364i | \(-0.298030\pi\) | ||||
0.592781 | + | 0.805364i | \(0.298030\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.37386 | 0.394310 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.1216 | 0.522538 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.37386 | −0.158169 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.9564 | −0.884811 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.25227 | 0.0583242 | 0.0291621 | − | 0.999575i | \(-0.490716\pi\) | ||||
0.0291621 | + | 0.999575i | \(0.490716\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.0000 | −0.464739 | −0.232370 | − | 0.972628i | \(-0.574648\pi\) | ||||
−0.232370 | + | 0.972628i | \(0.574648\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −18.5826 | −0.861746 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.9129 | −1.19911 | −0.599553 | − | 0.800335i | \(-0.704655\pi\) | ||||
−0.599553 | + | 0.800335i | \(0.704655\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0000 | 0.923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.8348 | 1.05217 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.1652 | −1.24905 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.20871 | −0.0554595 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.25227 | −0.0573376 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.4955 | −1.80459 | −0.902297 | − | 0.431116i | \(-0.858120\pi\) | ||||
−0.902297 | + | 0.431116i | \(0.858120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.83485 | −0.220450 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.00000 | −0.227508 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.9564 | 0.679137 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5826 | 0.706114 | 0.353057 | − | 0.935602i | \(-0.385142\pi\) | ||||
0.353057 | + | 0.935602i | \(0.385142\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.0780 | 1.81239 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.7477 | 0.755814 | 0.377907 | − | 0.925843i | \(-0.376644\pi\) | ||||
0.377907 | + | 0.925843i | \(0.376644\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | −0.270226 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.791288 | −0.0355657 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.0000 | −0.672842 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.1652 | −1.03701 | −0.518507 | − | 0.855073i | \(-0.673512\pi\) | ||||
−0.518507 | + | 0.855073i | \(0.673512\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.8348 | 1.46695 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.7913 | 0.837862 | 0.418931 | − | 0.908018i | \(-0.362405\pi\) | ||||
0.418931 | + | 0.908018i | \(0.362405\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.5826 | −0.604417 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.6697 | 0.917973 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.25227 | −0.321451 | −0.160726 | − | 0.986999i | \(-0.551383\pi\) | ||||
−0.160726 | + | 0.986999i | \(0.551383\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.1652 | −1.82104 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.04356 | −0.266830 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.37386 | 0.324931 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 51.4955 | 2.26477 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.4519 | −1.11721 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.16515 | 0.0509485 | 0.0254743 | − | 0.999675i | \(-0.491890\pi\) | ||||
0.0254743 | + | 0.999675i | \(0.491890\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.00000 | −0.218218 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −39.3303 | −1.71325 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.921970 | 0.0400101 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.66970 | 0.115637 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.5826 | −0.587226 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −30.0000 | −1.29460 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.3303 | −1.64795 | −0.823974 | − | 0.566627i | \(-0.808248\pi\) | ||||
−0.823974 | + | 0.566627i | \(0.808248\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.2523 | 1.04076 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.3739 | −0.444367 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.1216 | −0.646553 | −0.323276 | − | 0.946305i | \(-0.604784\pi\) | ||||
−0.323276 | + | 0.946305i | \(0.604784\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.704166 | 0.0300531 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.91288 | −0.0814914 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.3303 | 0.949581 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.16515 | −0.304144 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −30.3303 | −1.28514 | −0.642568 | − | 0.766229i | \(-0.722131\pi\) | ||||
−0.642568 | + | 0.766229i | \(0.722131\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.66061 | −0.366305 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.7477 | −1.08707 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.16515 | −0.133395 | −0.0666976 | − | 0.997773i | \(-0.521246\pi\) | ||||
−0.0666976 | + | 0.997773i | \(0.521246\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000 | 0.252422 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −26.7477 | −1.12330 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.4955 | 0.649603 | 0.324802 | − | 0.945782i | \(-0.394702\pi\) | ||||
0.324802 | + | 0.945782i | \(0.394702\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.1216 | −1.26055 | −0.630275 | − | 0.776372i | \(-0.717058\pi\) | ||||
−0.630275 | + | 0.776372i | \(0.717058\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −29.4083 | −1.22855 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.8348 | 0.950627 | 0.475314 | − | 0.879816i | \(-0.342335\pi\) | ||||
0.475314 | + | 0.879816i | \(0.342335\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.0871 | −0.502324 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.7477 | 0.694813 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.7477 | 0.942115 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.252273 | −0.0104302 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.2087 | 1.08175 | 0.540875 | − | 0.841103i | \(-0.318093\pi\) | ||||
0.540875 | + | 0.841103i | \(0.318093\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.5390 | −0.516661 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.7913 | 1.51339 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.9129 | 0.571333 | 0.285667 | − | 0.958329i | \(-0.407785\pi\) | ||||
0.285667 | + | 0.958329i | \(0.407785\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.5826 | −0.433843 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −36.4174 | −1.49047 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −40.1216 | −1.63932 | −0.819662 | − | 0.572848i | \(-0.805839\pi\) | ||||
−0.819662 | + | 0.572848i | \(0.805839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.7913 | −0.929676 | −0.464838 | − | 0.885396i | \(-0.653887\pi\) | ||||
−0.464838 | + | 0.885396i | \(0.653887\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.49545 | 0.0608996 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.37386 | 0.137167 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.0000 | −1.13648 | −0.568242 | − | 0.822861i | \(-0.692376\pi\) | ||||
−0.568242 | + | 0.822861i | \(0.692376\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.91288 | −0.320646 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.4174 | 0.664178 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.0000 | −0.565455 | −0.282727 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282727 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.95644 | 0.159539 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.8693 | 1.80637 | 0.903185 | − | 0.429251i | \(-0.141222\pi\) | ||||
0.903185 | + | 0.429251i | \(0.141222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.79129 | −0.112191 | −0.0560957 | − | 0.998425i | \(-0.517865\pi\) | ||||
−0.0560957 | + | 0.998425i | \(0.517865\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.00000 | 0.200643 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.83485 | −0.353961 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.20871 | −0.327824 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.1652 | −0.604674 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.9129 | −0.713100 | −0.356550 | − | 0.934276i | \(-0.616047\pi\) | ||||
−0.356550 | + | 0.934276i | \(0.616047\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −17.9129 | −0.711973 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.7477 | −0.585246 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.956439 | −0.0378955 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.12159 | −0.0443694 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.16515 | −0.125016 | −0.0625080 | − | 0.998044i | \(-0.519910\pi\) | ||||
−0.0625080 | + | 0.998044i | \(0.519910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.7477 | 0.818210 | 0.409105 | − | 0.912487i | \(-0.365841\pi\) | ||||
0.409105 | + | 0.912487i | \(0.365841\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.8348 | −0.505372 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.83485 | 0.111449 | 0.0557247 | − | 0.998446i | \(-0.482253\pi\) | ||||
0.0557247 | + | 0.998446i | \(0.482253\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.7477 | −0.657406 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −51.8693 | −2.03292 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.5390 | −1.39075 | −0.695375 | − | 0.718647i | \(-0.744762\pi\) | ||||
−0.695375 | + | 0.718647i | \(0.744762\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.16515 | −0.358112 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.07803 | −0.120085 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 27.1652 | 1.05820 | 0.529102 | − | 0.848558i | \(-0.322529\pi\) | ||||
0.529102 | + | 0.848558i | \(0.322529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.3739 | 1.53147 | 0.765733 | − | 0.643159i | \(-0.222376\pi\) | ||||
0.765733 | + | 0.643159i | \(0.222376\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.20871 | −0.318800 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.37386 | −0.130833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.58258 | 0.0612776 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −20.0000 | −0.773245 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.7913 | −0.493802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.0000 | 1.46479 | 0.732396 | − | 0.680879i | \(-0.238402\pi\) | ||||
0.732396 | + | 0.680879i | \(0.238402\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000 | 0.192450 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.6606 | 1.17838 | 0.589191 | − | 0.807993i | \(-0.299446\pi\) | ||||
0.589191 | + | 0.807993i | \(0.299446\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41.7477 | 1.60213 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.50455 | 0.325895 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.37386 | −0.0908334 | −0.0454167 | − | 0.998968i | \(-0.514462\pi\) | ||||
−0.0454167 | + | 0.998968i | \(0.514462\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.791288 | −0.0302336 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.2523 | −1.11604 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.25227 | 0.276290 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.2523 | −0.580224 | −0.290112 | − | 0.956993i | \(-0.593693\pi\) | ||||
−0.290112 | + | 0.956993i | \(0.593693\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.20871 | −0.0839020 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.7477 | 0.559413 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.37386 | 0.317183 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.5826 | −0.513740 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.62614 | −0.363574 | −0.181787 | − | 0.983338i | \(-0.558188\pi\) | ||||
−0.181787 | + | 0.983338i | \(0.558188\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.83485 | −0.182350 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.3303 | 0.916332 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37.9129 | −1.42586 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.5390 | −1.29714 | −0.648570 | − | 0.761155i | \(-0.724633\pi\) | ||||
−0.648570 | + | 0.761155i | \(0.724633\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.66970 | 0.0626185 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.3739 | 0.388504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.58258 | 0.171379 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.66970 | −0.211739 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.5390 | −1.10162 | −0.550810 | − | 0.834631i | \(-0.685681\pi\) | ||||
−0.550810 | + | 0.834631i | \(0.685681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.5826 | 0.766535 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 50.1561 | 1.86532 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.58258 | 0.0587754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.12159 | −0.0786854 | −0.0393427 | − | 0.999226i | \(-0.512526\pi\) | ||||
−0.0393427 | + | 0.999226i | \(0.512526\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.8693 | 0.921086 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −27.1652 | −1.00474 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.0000 | −0.960332 | −0.480166 | − | 0.877178i | \(-0.659424\pi\) | ||||
−0.480166 | + | 0.877178i | \(0.659424\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.41742 | −0.0522825 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −27.1652 | −1.00064 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.00000 | −0.294285 | −0.147142 | − | 0.989115i | \(-0.547008\pi\) | ||||
−0.147142 | + | 0.989115i | \(0.547008\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.61704 | −0.0961395 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.95644 | 0.365266 | 0.182633 | − | 0.983181i | \(-0.441538\pi\) | ||||
0.182633 | + | 0.983181i | \(0.441538\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.7913 | −0.468637 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.25227 | 0.0458183 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.9129 | −1.38531 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.7477 | 0.684114 | 0.342057 | − | 0.939679i | \(-0.388876\pi\) | ||||
0.342057 | + | 0.939679i | \(0.388876\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 55.1561 | 2.01000 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −6.20871 | −0.225958 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.3303 | −0.956991 | −0.478496 | − | 0.878090i | \(-0.658818\pi\) | ||||
−0.478496 | + | 0.878090i | \(0.658818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.79129 | 0.246508 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.9564 | −1.23092 | −0.615460 | − | 0.788168i | \(-0.711030\pi\) | ||||
−0.615460 | + | 0.788168i | \(0.711030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −28.9564 | −1.04829 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.791288 | −0.0286091 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.33939 | −0.192794 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.66970 | −0.132333 | −0.0661663 | − | 0.997809i | \(-0.521077\pi\) | ||||
−0.0661663 | + | 0.997809i | \(0.521077\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −40.7477 | −1.46749 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.4955 | 0.773138 | 0.386569 | − | 0.922261i | \(-0.373660\pi\) | ||||
0.386569 | + | 0.922261i | \(0.373660\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3739 | 0.372640 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.0000 | −0.717496 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.66970 | 0.0956518 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.3739 | 0.729034 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.91288 | 0.282783 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.7477 | −0.454986 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.41742 | 0.300049 | 0.150024 | − | 0.988682i | \(-0.452065\pi\) | ||||
0.150024 | + | 0.988682i | \(0.452065\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28.2867 | −1.00703 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.7477 | 0.595481 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.07803 | −0.144815 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 10.7477 | 0.381183 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 49.9129 | 1.76800 | 0.884002 | − | 0.467482i | \(-0.154839\pi\) | ||||
0.884002 | + | 0.467482i | \(0.154839\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51.4955 | 1.82178 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.660606 | −0.0233413 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 55.9129 | 1.97312 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.79129 | 0.0983800 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.0000 | 1.05605 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.0436 | 0.388271 | 0.194135 | − | 0.980975i | \(-0.437810\pi\) | ||||
0.194135 | + | 0.980975i | \(0.437810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.9129 | 1.68245 | 0.841224 | − | 0.540686i | \(-0.181835\pi\) | ||||
0.841224 | + | 0.540686i | \(0.181835\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 41.4174 | 1.45257 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.3739 | −0.783722 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.66061 | −0.302996 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.704166 | −0.0246056 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.83485 | −0.0989369 | −0.0494684 | − | 0.998776i | \(-0.515753\pi\) | ||||
−0.0494684 | + | 0.998776i | \(0.515753\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 41.1652 | 1.43493 | 0.717463 | − | 0.696596i | \(-0.245303\pi\) | ||||
0.717463 | + | 0.696596i | \(0.245303\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.79129 | 0.236442 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −41.0780 | −1.42842 | −0.714212 | − | 0.699930i | \(-0.753215\pi\) | ||||
−0.714212 | + | 0.699930i | \(0.753215\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.4955 | 1.09388 | 0.546941 | − | 0.837171i | \(-0.315792\pi\) | ||||
0.546941 | + | 0.837171i | \(0.315792\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.08712 | −0.0724014 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.00000 | −0.103944 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.3303 | −0.634346 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 51.8693 | 1.79287 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.4174 | −0.773935 | −0.386968 | − | 0.922093i | \(-0.626478\pi\) | ||||
−0.386968 | + | 0.922093i | \(0.626478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4955 | −0.913636 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.0000 | 1.03325 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.5390 | −0.396954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.41742 | 0.323587 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −50.7477 | −1.74166 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.00000 | 0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.46099 | −0.289699 | −0.144849 | − | 0.989454i | \(-0.546270\pi\) | ||||
−0.144849 | + | 0.989454i | \(0.546270\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.252273 | −0.00862755 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.16515 | 0.313076 | 0.156538 | − | 0.987672i | \(-0.449967\pi\) | ||||
0.156538 | + | 0.987672i | \(0.449967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.747727 | −0.0255121 | −0.0127561 | − | 0.999919i | \(-0.504060\pi\) | ||||
−0.0127561 | + | 0.999919i | \(0.504060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.0436 | 0.376364 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.5826 | −1.07508 | −0.537542 | − | 0.843237i | \(-0.680647\pi\) | ||||
−0.537542 | + | 0.843237i | \(0.680647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.2087 | 0.483111 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.70417 | 0.159762 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.3303 | −1.02889 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.66061 | −0.293453 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.12159 | 0.105650 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.79129 | 0.0943628 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.70417 | −0.260151 | −0.130076 | − | 0.991504i | \(-0.541522\pi\) | ||||
−0.130076 | + | 0.991504i | \(0.541522\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −49.2523 | −1.66124 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.33030 | −0.213273 | −0.106637 | − | 0.994298i | \(-0.534008\pi\) | ||||
−0.106637 | + | 0.994298i | \(0.534008\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0436 | 0.405298 | 0.202649 | − | 0.979251i | \(-0.435045\pi\) | ||||
0.202649 | + | 0.979251i | \(0.435045\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.91288 | −0.265989 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.16515 | −0.106275 | −0.0531377 | − | 0.998587i | \(-0.516922\pi\) | ||||
−0.0531377 | + | 0.998587i | \(0.516922\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.1652 | −1.38063 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.3303 | 1.21711 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.4174 | 0.549388 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.7477 | 0.559815 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.16515 | 0.0722923 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16.4174 | 0.547552 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22.7477 | 0.757837 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −35.8258 | −1.19221 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.5390 | −0.450052 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.7477 | 0.688917 | 0.344458 | − | 0.938802i | \(-0.388063\pi\) | ||||
0.344458 | + | 0.938802i | \(0.388063\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.83485 | −0.0940260 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.5826 | 0.450011 | 0.225005 | − | 0.974358i | \(-0.427760\pi\) | ||||
0.225005 | + | 0.974358i | \(0.427760\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.7477 | −0.752840 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.04356 | −0.199794 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −25.5826 | −0.844811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.8348 | −1.21507 | −0.607535 | − | 0.794293i | \(-0.707841\pi\) | ||||
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.6261 | 0.976214 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.49545 | 0.213800 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.53901 | 0.0505479 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.4955 | −1.29580 | −0.647902 | − | 0.761724i | \(-0.724353\pi\) | ||||
−0.647902 | + | 0.761724i | \(0.724353\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.956439 | −0.0313460 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.4955 | −0.703730 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.3739 | 0.470076 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.3739 | 1.90699 | 0.953495 | − | 0.301407i | \(-0.0974564\pi\) | ||||
0.953495 | + | 0.301407i | \(0.0974564\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32.9129 | 1.07407 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −54.9564 | −1.79153 | −0.895764 | − | 0.444529i | \(-0.853371\pi\) | ||||
−0.895764 | + | 0.444529i | \(0.853371\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.20871 | −0.0719256 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.9564 | 0.454003 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.5390 | 0.959889 | 0.479945 | − | 0.877299i | \(-0.340657\pi\) | ||||
0.479945 | + | 0.877299i | \(0.340657\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.8258 | 0.578649 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.33030 | 0.302556 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.5390 | −0.859683 | −0.429842 | − | 0.902904i | \(-0.641431\pi\) | ||||
−0.429842 | + | 0.902904i | \(0.641431\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.4174 | 0.531255 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 10.7477 | 0.347425 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.20871 | −0.0713230 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 76.6170 | 2.47152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.83485 | −0.0913517 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.74773 | 0.217217 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.25227 | −0.168902 | −0.0844509 | − | 0.996428i | \(-0.526914\pi\) | ||||
−0.0844509 | + | 0.996428i | \(0.526914\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.20871 | −0.263702 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.95644 | 0.223243 | 0.111621 | − | 0.993751i | \(-0.464396\pi\) | ||||
0.111621 | + | 0.993751i | \(0.464396\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.1652 | 1.31969 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.16515 | 0.0693403 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 7.12159 | 0.227840 | 0.113920 | − | 0.993490i | \(-0.463659\pi\) | ||||
0.113920 | + | 0.993490i | \(0.463659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.16515 | −0.0691280 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.626136 | −0.0199707 | −0.00998533 | − | 0.999950i | \(-0.503178\pi\) | ||||
−0.00998533 | + | 0.999950i | \(0.503178\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.5390 | −0.654427 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 67.9129 | 2.16169 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.16515 | 0.227839 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7913 | −1.20048 | −0.600240 | − | 0.799820i | \(-0.704928\pi\) | ||||
−0.600240 | + | 0.799820i | \(0.704928\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.0871 | 0.383573 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.3303 | 0.644514 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.4955 | −0.364065 | −0.182032 | − | 0.983293i | \(-0.558268\pi\) | ||||
−0.182032 | + | 0.983293i | \(0.558268\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.0000 | 0.632772 |
(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 | 7360.2.a.bq.1.1 | 2 | ||
4.3 | odd | 2 | 7360.2.a.bk.1.2 | 2 | |||
8.3 | odd | 2 | 1840.2.a.n.1.1 | 2 | |||
8.5 | even | 2 | 230.2.a.a.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 2070.2.a.x.1.2 | 2 | |||
40.13 | odd | 4 | 1150.2.b.g.599.4 | 4 | |||
40.19 | odd | 2 | 9200.2.a.bs.1.2 | 2 | |||
40.29 | even | 2 | 1150.2.a.o.1.1 | 2 | |||
40.37 | odd | 4 | 1150.2.b.g.599.1 | 4 | |||
184.45 | odd | 2 | 5290.2.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.a.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
1150.2.a.o.1.1 | 2 | 40.29 | even | 2 | |||
1150.2.b.g.599.1 | 4 | 40.37 | odd | 4 | |||
1150.2.b.g.599.4 | 4 | 40.13 | odd | 4 | |||
1840.2.a.n.1.1 | 2 | 8.3 | odd | 2 | |||
2070.2.a.x.1.2 | 2 | 24.5 | odd | 2 | |||
5290.2.a.e.1.2 | 2 | 184.45 | odd | 2 | |||
7360.2.a.bk.1.2 | 2 | 4.3 | odd | 2 | |||
7360.2.a.bq.1.1 | 2 | 1.1 | even | 1 | trivial | ||
9200.2.a.bs.1.2 | 2 | 40.19 | odd | 2 |