Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(1,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | 1.2 | ||
Root | \(2.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.79129 | 1.05501 | 0.527504 | − | 0.849553i | \(-0.323128\pi\) | ||||
0.527504 | + | 0.849553i | \(0.323128\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −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 | \(-0.446392\pi\) | ||||
0.167618 | + | 0.985852i | \(0.446392\pi\) | |||||||
\(14\) | 2.79129 | 0.746003 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.79129 | 0.919522 | 0.459761 | − | 0.888043i | \(-0.347935\pi\) | ||||
0.459761 | + | 0.888043i | \(0.347935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.20871 | 0.277298 | 0.138649 | − | 0.990342i | \(-0.455724\pi\) | ||||
0.138649 | + | 0.990342i | \(0.455724\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.79129 | −0.808305 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.20871 | 0.237048 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.79129 | 0.527504 | ||||||||
\(29\) | 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 | \(0.118413\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.79129 | 0.650201 | ||||||||
\(35\) | 2.79129 | 0.471814 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 1.20871 | 0.196079 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.20871 | 0.344943 | 0.172471 | − | 0.985015i | \(-0.444825\pi\) | ||||
0.172471 | + | 0.985015i | \(0.444825\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.16515 | −1.09268 | −0.546338 | − | 0.837565i | \(-0.683978\pi\) | ||||
−0.546338 | + | 0.837565i | \(0.683978\pi\) | |||||||
\(44\) | −3.79129 | −0.571558 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 13.5826 | 1.98122 | 0.990611 | − | 0.136710i | \(-0.0436528\pi\) | ||||
0.990611 | + | 0.136710i | \(0.0436528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.791288 | 0.113041 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.20871 | 0.167618 | ||||||||
\(53\) | −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 | ||||||||
\(56\) | 2.79129 | 0.373002 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.58258 | 0.207802 | ||||||||
\(59\) | 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 | \(-0.569298\pi\) | ||||
−0.215989 | + | 0.976396i | \(0.569298\pi\) | |||||||
\(62\) | 10.3739 | 1.31748 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.20871 | 0.149922 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.16515 | −0.875363 | −0.437681 | − | 0.899130i | \(-0.644200\pi\) | ||||
−0.437681 | + | 0.899130i | \(0.644200\pi\) | |||||||
\(68\) | 3.79129 | 0.459761 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.79129 | 0.333623 | ||||||||
\(71\) | 5.37386 | 0.637760 | 0.318880 | − | 0.947795i | \(-0.396693\pi\) | ||||
0.318880 | + | 0.947795i | \(0.396693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.7477 | −1.72609 | −0.863045 | − | 0.505126i | \(-0.831446\pi\) | ||||
−0.863045 | + | 0.505126i | \(0.831446\pi\) | |||||||
\(74\) | −4.00000 | −0.464991 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.20871 | 0.138649 | ||||||||
\(77\) | −10.5826 | −1.20600 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.20871 | 0.243911 | ||||||||
\(83\) | 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 | ||||||||
\(86\) | −7.16515 | −0.772638 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.79129 | −0.404153 | ||||||||
\(89\) | 3.16515 | 0.335505 | 0.167753 | − | 0.985829i | \(-0.446349\pi\) | ||||
0.167753 | + | 0.985829i | \(0.446349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.37386 | 0.353677 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.5826 | 1.40094 | ||||||||
\(95\) | 1.20871 | 0.124011 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.9564 | 1.51860 | 0.759298 | − | 0.650743i | \(-0.225542\pi\) | ||||
0.759298 | + | 0.650743i | \(0.225542\pi\) | |||||||
\(98\) | 0.791288 | 0.0799321 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −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 | \(0.381655\pi\) | |||||||
\(104\) | 1.20871 | 0.118524 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −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 | \(-0.334502\pi\) | ||||
0.496818 | + | 0.867855i | \(0.334502\pi\) | |||||||
\(110\) | −3.79129 | −0.361485 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.79129 | 0.263752 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 1.58258 | 0.146938 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.41742 | 0.406657 | ||||||||
\(119\) | 10.5826 | 0.970103 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.37386 | 0.306715 | ||||||||
\(122\) | −3.37386 | −0.305455 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.3739 | 0.931600 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.7477 | −1.30865 | −0.654325 | − | 0.756214i | \(-0.727047\pi\) | ||||
−0.654325 | + | 0.756214i | \(0.727047\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.20871 | 0.106011 | ||||||||
\(131\) | −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 | ||||||||
\(134\) | −7.16515 | −0.618975 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.79129 | 0.325100 | ||||||||
\(137\) | 0.791288 | 0.0676043 | 0.0338021 | − | 0.999429i | \(-0.489238\pi\) | ||||
0.0338021 | + | 0.999429i | \(0.489238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.7477 | −1.25089 | −0.625443 | − | 0.780270i | \(-0.715082\pi\) | ||||
−0.625443 | + | 0.780270i | \(0.715082\pi\) | |||||||
\(140\) | 2.79129 | 0.235907 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.37386 | 0.450965 | ||||||||
\(143\) | −4.58258 | −0.383214 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.58258 | 0.131426 | ||||||||
\(146\) | −14.7477 | −1.22053 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | −0.328798 | ||||||||
\(149\) | −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 | \(0.581295\pi\) | |||||||
\(152\) | 1.20871 | 0.0980395 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.5826 | −0.852768 | ||||||||
\(155\) | 10.3739 | 0.833249 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7477 | 1.01738 | 0.508690 | − | 0.860950i | \(-0.330130\pi\) | ||||
0.508690 | + | 0.860950i | \(0.330130\pi\) | |||||||
\(158\) | 8.00000 | 0.636446 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −2.79129 | −0.219984 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.3739 | 1.75246 | 0.876228 | − | 0.481897i | \(-0.160052\pi\) | ||||
0.876228 | + | 0.481897i | \(0.160052\pi\) | |||||||
\(164\) | 2.20871 | 0.172471 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | 18.3303 | 1.41844 | 0.709221 | − | 0.704987i | \(-0.249047\pi\) | ||||
0.709221 | + | 0.704987i | \(0.249047\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5390 | −0.887617 | ||||||||
\(170\) | 3.79129 | 0.290779 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.16515 | −0.546338 | ||||||||
\(173\) | 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 | ||||||||
\(176\) | −3.79129 | −0.285779 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.16515 | 0.237238 | ||||||||
\(179\) | 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 | \(-0.332166\pi\) | ||||
0.503174 | + | 0.864185i | \(0.332166\pi\) | |||||||
\(182\) | 3.37386 | 0.250087 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −4.00000 | −0.294086 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.3739 | −1.05112 | ||||||||
\(188\) | 13.5826 | 0.990611 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.20871 | 0.0876892 | ||||||||
\(191\) | −16.4174 | −1.18792 | −0.593962 | − | 0.804493i | \(-0.702437\pi\) | ||||
−0.593962 | + | 0.804493i | \(0.702437\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.74773 | 0.485712 | 0.242856 | − | 0.970062i | \(-0.421916\pi\) | ||||
0.242856 | + | 0.970062i | \(0.421916\pi\) | |||||||
\(194\) | 14.9564 | 1.07381 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.791288 | 0.0565206 | ||||||||
\(197\) | −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 | \(0.243872\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.5826 | −0.955667 | ||||||||
\(203\) | 4.41742 | 0.310042 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.20871 | 0.154263 | ||||||||
\(206\) | 7.37386 | 0.513761 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.20871 | 0.0838091 | ||||||||
\(209\) | −4.58258 | −0.316983 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.0000 | −0.688428 | −0.344214 | − | 0.938891i | \(-0.611855\pi\) | ||||
−0.344214 | + | 0.938891i | \(0.611855\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.5826 | −0.928486 | ||||||||
\(215\) | −7.16515 | −0.488659 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 28.9564 | 1.96569 | ||||||||
\(218\) | 10.3739 | 0.702607 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.79129 | −0.255609 | ||||||||
\(221\) | 4.58258 | 0.308257 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1652 | 0.747674 | 0.373837 | − | 0.927494i | \(-0.378042\pi\) | ||||
0.373837 | + | 0.927494i | \(0.378042\pi\) | |||||||
\(224\) | 2.79129 | 0.186501 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | −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 | \(-0.681413\pi\) | ||||
−0.539568 | + | 0.841942i | \(0.681413\pi\) | |||||||
\(230\) | −1.00000 | −0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.58258 | 0.103901 | ||||||||
\(233\) | −7.58258 | −0.496751 | −0.248376 | − | 0.968664i | \(-0.579897\pi\) | ||||
−0.248376 | + | 0.968664i | \(0.579897\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.5826 | 0.886030 | ||||||||
\(236\) | 4.41742 | 0.287550 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.5826 | 0.685966 | ||||||||
\(239\) | −3.16515 | −0.204737 | −0.102368 | − | 0.994747i | \(-0.532642\pi\) | ||||
−0.102368 | + | 0.994747i | \(0.532642\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.0000 | −1.80364 | −0.901819 | − | 0.432113i | \(-0.857768\pi\) | ||||
−0.901819 | + | 0.432113i | \(0.857768\pi\) | |||||||
\(242\) | 3.37386 | 0.216880 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.37386 | −0.215989 | ||||||||
\(245\) | 0.791288 | 0.0505535 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.46099 | 0.0929603 | ||||||||
\(248\) | 10.3739 | 0.658741 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −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 | ||||||||
\(254\) | −14.7477 | −0.925355 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −22.7477 | −1.41896 | −0.709482 | − | 0.704723i | \(-0.751071\pi\) | ||||
−0.709482 | + | 0.704723i | \(0.751071\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.1652 | −0.693769 | ||||||||
\(260\) | 1.20871 | 0.0749611 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.16515 | −0.566225 | ||||||||
\(263\) | −15.7913 | −0.973733 | −0.486866 | − | 0.873477i | \(-0.661860\pi\) | ||||
−0.486866 | + | 0.873477i | \(0.661860\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 3.37386 | 0.206865 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.16515 | −0.437681 | ||||||||
\(269\) | −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 | \(0.747829\pi\) | |||||||
\(272\) | 3.79129 | 0.229881 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.791288 | 0.0478034 | ||||||||
\(275\) | −3.79129 | −0.228623 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.16515 | −0.0700072 | −0.0350036 | − | 0.999387i | \(-0.511144\pi\) | ||||
−0.0350036 | + | 0.999387i | \(0.511144\pi\) | |||||||
\(278\) | −14.7477 | −0.884510 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.79129 | 0.166811 | ||||||||
\(281\) | 16.7477 | 0.999086 | 0.499543 | − | 0.866289i | \(-0.333501\pi\) | ||||
0.499543 | + | 0.866289i | \(0.333501\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.3303 | −1.68406 | −0.842031 | − | 0.539429i | \(-0.818640\pi\) | ||||
−0.842031 | + | 0.539429i | \(0.818640\pi\) | |||||||
\(284\) | 5.37386 | 0.318880 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.58258 | −0.270973 | ||||||||
\(287\) | 6.16515 | 0.363917 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.62614 | −0.154479 | ||||||||
\(290\) | 1.58258 | 0.0929320 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.7477 | −0.863045 | ||||||||
\(293\) | 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 | ||||||||
\(296\) | −4.00000 | −0.232495 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.7913 | −0.740979 | ||||||||
\(299\) | −1.20871 | −0.0699016 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.0000 | −1.15278 | ||||||||
\(302\) | −6.20871 | −0.357271 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.20871 | 0.0693244 | ||||||||
\(305\) | −3.37386 | −0.193187 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5390 | 0.943931 | 0.471966 | − | 0.881617i | \(-0.343545\pi\) | ||||
0.471966 | + | 0.881617i | \(0.343545\pi\) | |||||||
\(308\) | −10.5826 | −0.602998 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.3739 | 0.589196 | ||||||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.3739 | −1.03855 | −0.519276 | − | 0.854607i | \(-0.673798\pi\) | ||||
−0.519276 | + | 0.854607i | \(0.673798\pi\) | |||||||
\(314\) | 12.7477 | 0.719396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | −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 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.79129 | −0.155552 | ||||||||
\(323\) | 4.58258 | 0.254981 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.20871 | 0.0670473 | ||||||||
\(326\) | 22.3739 | 1.23917 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.20871 | 0.121956 | ||||||||
\(329\) | 37.9129 | 2.09020 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.74773 | 0.370889 | 0.185444 | − | 0.982655i | \(-0.440628\pi\) | ||||
0.185444 | + | 0.982655i | \(0.440628\pi\) | |||||||
\(332\) | 6.00000 | 0.329293 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.3303 | 1.00299 | ||||||||
\(335\) | −7.16515 | −0.391474 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.7913 | −0.914680 | −0.457340 | − | 0.889292i | \(-0.651198\pi\) | ||||
−0.457340 | + | 0.889292i | \(0.651198\pi\) | |||||||
\(338\) | −11.5390 | −0.627640 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.79129 | 0.205611 | ||||||||
\(341\) | −39.3303 | −2.12986 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.3303 | −0.935748 | ||||||||
\(344\) | −7.16515 | −0.386319 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.2087 | 0.763865 | ||||||||
\(347\) | −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 | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 2.79129 | 0.149201 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.79129 | −0.202076 | ||||||||
\(353\) | 15.1652 | 0.807160 | 0.403580 | − | 0.914944i | \(-0.367766\pi\) | ||||
0.403580 | + | 0.914944i | \(0.367766\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.37386 | 0.285215 | ||||||||
\(356\) | 3.16515 | 0.167753 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.7477 | 0.885145 | ||||||||
\(359\) | 9.16515 | 0.483718 | 0.241859 | − | 0.970311i | \(-0.422243\pi\) | ||||
0.241859 | + | 0.970311i | \(0.422243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5390 | −0.923106 | ||||||||
\(362\) | 13.5390 | 0.711595 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.37386 | 0.176838 | ||||||||
\(365\) | −14.7477 | −0.771931 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.834849 | −0.0435787 | −0.0217894 | − | 0.999763i | \(-0.506936\pi\) | ||||
−0.0217894 | + | 0.999763i | \(0.506936\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.00000 | −0.207950 | ||||||||
\(371\) | −16.7477 | −0.869499 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7477 | −0.763608 | −0.381804 | − | 0.924243i | \(-0.624697\pi\) | ||||
−0.381804 | + | 0.924243i | \(0.624697\pi\) | |||||||
\(374\) | −14.3739 | −0.743255 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.5826 | 0.700468 | ||||||||
\(377\) | 1.91288 | 0.0985183 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.37386 | 0.378770 | 0.189385 | − | 0.981903i | \(-0.439351\pi\) | ||||
0.189385 | + | 0.981903i | \(0.439351\pi\) | |||||||
\(380\) | 1.20871 | 0.0620056 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.4174 | −0.839989 | ||||||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.5826 | −0.539338 | ||||||||
\(386\) | 6.74773 | 0.343450 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.9564 | 0.759298 | ||||||||
\(389\) | −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 | ||||||||
\(392\) | 0.791288 | 0.0399661 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20.5390 | −1.03474 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.5390 | 0.830069 | 0.415035 | − | 0.909806i | \(-0.363769\pi\) | ||||
0.415035 | + | 0.909806i | \(0.363769\pi\) | |||||||
\(398\) | 20.3303 | 1.01907 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −22.7477 | −1.13597 | −0.567984 | − | 0.823040i | \(-0.692276\pi\) | ||||
−0.567984 | + | 0.823040i | \(0.692276\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5390 | 0.624613 | ||||||||
\(404\) | −13.5826 | −0.675758 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.41742 | 0.219233 | ||||||||
\(407\) | 15.1652 | 0.751709 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.7913 | −1.12696 | −0.563478 | − | 0.826131i | \(-0.690537\pi\) | ||||
−0.563478 | + | 0.826131i | \(0.690537\pi\) | |||||||
\(410\) | 2.20871 | 0.109081 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.37386 | 0.363284 | ||||||||
\(413\) | 12.3303 | 0.606735 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 1.20871 | 0.0592620 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.58258 | −0.224141 | ||||||||
\(419\) | −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 | \(-0.690522\pi\) | ||||
−0.563439 | + | 0.826158i | \(0.690522\pi\) | |||||||
\(422\) | −10.0000 | −0.486792 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 3.79129 | 0.183904 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.41742 | −0.455741 | ||||||||
\(428\) | −13.5826 | −0.656539 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.16515 | −0.345534 | ||||||||
\(431\) | 19.9129 | 0.959170 | 0.479585 | − | 0.877496i | \(-0.340787\pi\) | ||||
0.479585 | + | 0.877496i | \(0.340787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.53901 | 0.0739603 | 0.0369802 | − | 0.999316i | \(-0.488226\pi\) | ||||
0.0369802 | + | 0.999316i | \(0.488226\pi\) | |||||||
\(434\) | 28.9564 | 1.38995 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.3739 | 0.496818 | ||||||||
\(437\) | −1.20871 | −0.0578205 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.5390 | 1.21891 | 0.609455 | − | 0.792820i | \(-0.291388\pi\) | ||||
0.609455 | + | 0.792820i | \(0.291388\pi\) | |||||||
\(440\) | −3.79129 | −0.180743 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.58258 | 0.217971 | ||||||||
\(443\) | 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 | ||||||||
\(446\) | 11.1652 | 0.528685 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.79129 | 0.131876 | ||||||||
\(449\) | −25.1216 | −1.18556 | −0.592781 | − | 0.805364i | \(-0.701970\pi\) | ||||
−0.592781 | + | 0.805364i | \(0.701970\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.37386 | −0.394310 | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.74773 | −0.222822 | ||||||||
\(455\) | 3.37386 | 0.158169 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | −16.3303 | −0.763065 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | 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 | \(0.574648\pi\) | |||||||
\(464\) | 1.58258 | 0.0734692 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.58258 | −0.351256 | ||||||||
\(467\) | −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 | ||||||||
\(470\) | 13.5826 | 0.626517 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.41742 | 0.203328 | ||||||||
\(473\) | 27.1652 | 1.24905 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.20871 | 0.0554595 | ||||||||
\(476\) | 10.5826 | 0.485052 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.16515 | −0.144771 | ||||||||
\(479\) | 39.4955 | 1.80459 | 0.902297 | − | 0.431116i | \(-0.141880\pi\) | ||||
0.902297 | + | 0.431116i | \(0.141880\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.83485 | −0.220450 | ||||||||
\(482\) | −28.0000 | −1.27537 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.37386 | 0.153357 | ||||||||
\(485\) | 14.9564 | 0.679137 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.5826 | 0.706114 | 0.353057 | − | 0.935602i | \(-0.385142\pi\) | ||||
0.353057 | + | 0.935602i | \(0.385142\pi\) | |||||||
\(488\) | −3.37386 | −0.152728 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.791288 | 0.0357467 | ||||||||
\(491\) | 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 | ||||||||
\(494\) | 1.46099 | 0.0657328 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.3739 | 0.465800 | ||||||||
\(497\) | 15.0000 | 0.672842 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.1652 | 1.03701 | 0.518507 | − | 0.855073i | \(-0.326488\pi\) | ||||
0.518507 | + | 0.855073i | \(0.326488\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.7913 | −1.37428 | ||||||||
\(503\) | −18.7913 | −0.837862 | −0.418931 | − | 0.908018i | \(-0.637595\pi\) | ||||
−0.418931 | + | 0.908018i | \(0.637595\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.5826 | −0.604417 | ||||||||
\(506\) | 3.79129 | 0.168543 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −14.7477 | −0.654325 | ||||||||
\(509\) | −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 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −22.7477 | −1.00336 | ||||||||
\(515\) | 7.37386 | 0.324931 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −51.4955 | −2.26477 | ||||||||
\(518\) | −11.1652 | −0.490569 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.20871 | 0.0530055 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.16515 | −0.0509485 | −0.0254743 | − | 0.999675i | \(-0.508110\pi\) | ||||
−0.0254743 | + | 0.999675i | \(0.508110\pi\) | |||||||
\(524\) | −9.16515 | −0.400381 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.7913 | −0.688533 | ||||||||
\(527\) | 39.3303 | 1.71325 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −6.00000 | −0.260623 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.37386 | 0.146276 | ||||||||
\(533\) | 2.66970 | 0.115637 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.5826 | −0.587226 | ||||||||
\(536\) | −7.16515 | −0.309487 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −16.7477 | −0.722046 | ||||||||
\(539\) | −3.00000 | −0.129219 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.3303 | 1.64795 | 0.823974 | − | 0.566627i | \(-0.191752\pi\) | ||||
0.823974 | + | 0.566627i | \(0.191752\pi\) | |||||||
\(542\) | −23.1216 | −0.993157 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.79129 | 0.162550 | ||||||||
\(545\) | 10.3739 | 0.444367 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.1216 | 0.646553 | 0.323276 | − | 0.946305i | \(-0.395216\pi\) | ||||
0.323276 | + | 0.946305i | \(0.395216\pi\) | |||||||
\(548\) | 0.791288 | 0.0338021 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.79129 | −0.161661 | ||||||||
\(551\) | 1.91288 | 0.0814914 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.3303 | 0.949581 | ||||||||
\(554\) | −1.16515 | −0.0495025 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.7477 | −0.625443 | ||||||||
\(557\) | −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 | ||||||||
\(560\) | 2.79129 | 0.117953 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.7477 | 0.706460 | ||||||||
\(563\) | −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 | ||||||||
\(566\) | −28.3303 | −1.19081 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.37386 | 0.225482 | ||||||||
\(569\) | −15.4955 | −0.649603 | −0.324802 | − | 0.945782i | \(-0.605298\pi\) | ||||
−0.324802 | + | 0.945782i | \(0.605298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 30.1216 | 1.26055 | 0.630275 | − | 0.776372i | \(-0.282942\pi\) | ||||
0.630275 | + | 0.776372i | \(0.282942\pi\) | |||||||
\(572\) | −4.58258 | −0.191607 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.16515 | 0.257328 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.8348 | 0.950627 | 0.475314 | − | 0.879816i | \(-0.342335\pi\) | ||||
0.475314 | + | 0.879816i | \(0.342335\pi\) | |||||||
\(578\) | −2.62614 | −0.109233 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.58258 | 0.0657129 | ||||||||
\(581\) | 16.7477 | 0.694813 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.7477 | 0.942115 | ||||||||
\(584\) | −14.7477 | −0.610265 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.4955 | 1.13583 | ||||||||
\(587\) | 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 | ||||||||
\(590\) | 4.41742 | 0.181862 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | −0.164399 | ||||||||
\(593\) | −13.9129 | −0.571333 | −0.285667 | − | 0.958329i | \(-0.592215\pi\) | ||||
−0.285667 | + | 0.958329i | \(0.592215\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5826 | 0.433843 | ||||||||
\(596\) | −12.7913 | −0.523952 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.20871 | −0.0494279 | ||||||||
\(599\) | 40.1216 | 1.63932 | 0.819662 | − | 0.572848i | \(-0.194161\pi\) | ||||
0.819662 | + | 0.572848i | \(0.194161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.7913 | −0.929676 | −0.464838 | − | 0.885396i | \(-0.653887\pi\) | ||||
−0.464838 | + | 0.885396i | \(0.653887\pi\) | |||||||
\(602\) | −20.0000 | −0.815139 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.20871 | −0.252629 | ||||||||
\(605\) | 3.37386 | 0.137167 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.0000 | −1.13648 | −0.568242 | − | 0.822861i | \(-0.692376\pi\) | ||||
−0.568242 | + | 0.822861i | \(0.692376\pi\) | |||||||
\(608\) | 1.20871 | 0.0490198 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.37386 | −0.136604 | ||||||||
\(611\) | 16.4174 | 0.664178 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | 16.5390 | 0.667460 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.5826 | −0.426384 | ||||||||
\(617\) | −44.8693 | −1.80637 | −0.903185 | − | 0.429251i | \(-0.858778\pi\) | ||||
−0.903185 | + | 0.429251i | \(0.858778\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.79129 | 0.112191 | 0.0560957 | − | 0.998425i | \(-0.482135\pi\) | ||||
0.0560957 | + | 0.998425i | \(0.482135\pi\) | |||||||
\(620\) | 10.3739 | 0.416624 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.0000 | −0.481156 | ||||||||
\(623\) | 8.83485 | 0.353961 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −18.3739 | −0.734367 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.7477 | 0.508690 | ||||||||
\(629\) | −15.1652 | −0.604674 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.9129 | −0.713100 | −0.356550 | − | 0.934276i | \(-0.616047\pi\) | ||||
−0.356550 | + | 0.934276i | \(0.616047\pi\) | |||||||
\(632\) | 8.00000 | 0.318223 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.20871 | −0.206864 | ||||||||
\(635\) | −14.7477 | −0.585246 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.956439 | 0.0378955 | ||||||||
\(638\) | −6.00000 | −0.237542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 3.16515 | 0.125016 | 0.0625080 | − | 0.998044i | \(-0.480090\pi\) | ||||
0.0625080 | + | 0.998044i | \(0.480090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.7477 | −0.818210 | −0.409105 | − | 0.912487i | \(-0.634159\pi\) | ||||
−0.409105 | + | 0.912487i | \(0.634159\pi\) | |||||||
\(644\) | −2.79129 | −0.109992 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.58258 | 0.180299 | ||||||||
\(647\) | −2.83485 | −0.111449 | −0.0557247 | − | 0.998446i | \(-0.517747\pi\) | ||||
−0.0557247 | + | 0.998446i | \(0.517747\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.7477 | −0.657406 | ||||||||
\(650\) | 1.20871 | 0.0474096 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 22.3739 | 0.876228 | ||||||||
\(653\) | −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 | ||||||||
\(656\) | 2.20871 | 0.0862357 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 37.9129 | 1.47800 | ||||||||
\(659\) | 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 | \(-0.777624\pi\) | ||||
−0.765733 | + | 0.643159i | \(0.777624\pi\) | |||||||
\(662\) | 6.74773 | 0.262258 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 3.37386 | 0.130833 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.58258 | −0.0612776 | ||||||||
\(668\) | 18.3303 | 0.709221 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.16515 | −0.276814 | ||||||||
\(671\) | 12.7913 | 0.493802 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 38.0000 | 1.46479 | 0.732396 | − | 0.680879i | \(-0.238402\pi\) | ||||
0.732396 | + | 0.680879i | \(0.238402\pi\) | |||||||
\(674\) | −16.7913 | −0.646776 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5390 | −0.443808 | ||||||||
\(677\) | 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 | ||||||||
\(680\) | 3.79129 | 0.145389 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −39.3303 | −1.50604 | ||||||||
\(683\) | −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 | ||||||||
\(686\) | −17.3303 | −0.661674 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.16515 | −0.273169 | ||||||||
\(689\) | −7.25227 | −0.276290 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.2523 | 0.580224 | 0.290112 | − | 0.956993i | \(-0.406307\pi\) | ||||
0.290112 | + | 0.956993i | \(0.406307\pi\) | |||||||
\(692\) | 14.2087 | 0.540134 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.79129 | −0.371672 | ||||||||
\(695\) | −14.7477 | −0.559413 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.37386 | 0.317183 | ||||||||
\(698\) | 26.0000 | 0.984115 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.79129 | 0.105501 | ||||||||
\(701\) | −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 | ||||||||
\(704\) | −3.79129 | −0.142890 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.1652 | 0.570748 | ||||||||
\(707\) | −37.9129 | −1.42586 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.5390 | 1.29714 | 0.648570 | − | 0.761155i | \(-0.275367\pi\) | ||||
0.648570 | + | 0.761155i | \(0.275367\pi\) | |||||||
\(710\) | 5.37386 | 0.201678 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.16515 | 0.118619 | ||||||||
\(713\) | −10.3739 | −0.388504 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.58258 | −0.171379 | ||||||||
\(716\) | 16.7477 | 0.625892 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.16515 | 0.342040 | ||||||||
\(719\) | 29.5390 | 1.10162 | 0.550810 | − | 0.834631i | \(-0.314319\pi\) | ||||
0.550810 | + | 0.834631i | \(0.314319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.5826 | 0.766535 | ||||||||
\(722\) | −17.5390 | −0.652735 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.5390 | 0.503174 | ||||||||
\(725\) | 1.58258 | 0.0587754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.12159 | −0.0786854 | −0.0393427 | − | 0.999226i | \(-0.512526\pi\) | ||||
−0.0393427 | + | 0.999226i | \(0.512526\pi\) | |||||||
\(728\) | 3.37386 | 0.125044 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −14.7477 | −0.545838 | ||||||||
\(731\) | −27.1652 | −1.00474 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0000 | 0.960332 | 0.480166 | − | 0.877178i | \(-0.340576\pi\) | ||||
0.480166 | + | 0.877178i | \(0.340576\pi\) | |||||||
\(734\) | −0.834849 | −0.0308148 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 27.1652 | 1.00064 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.00000 | 0.294285 | 0.147142 | − | 0.989115i | \(-0.452992\pi\) | ||||
0.147142 | + | 0.989115i | \(0.452992\pi\) | |||||||
\(740\) | −4.00000 | −0.147043 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.7477 | −0.614828 | ||||||||
\(743\) | −9.95644 | −0.365266 | −0.182633 | − | 0.983181i | \(-0.558462\pi\) | ||||
−0.182633 | + | 0.983181i | \(0.558462\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.7913 | −0.468637 | ||||||||
\(746\) | −14.7477 | −0.539953 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −14.3739 | −0.525561 | ||||||||
\(749\) | −37.9129 | −1.38531 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.7477 | 0.684114 | 0.342057 | − | 0.939679i | \(-0.388876\pi\) | ||||
0.342057 | + | 0.939679i | \(0.388876\pi\) | |||||||
\(752\) | 13.5826 | 0.495306 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.91288 | 0.0696629 | ||||||||
\(755\) | −6.20871 | −0.225958 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.3303 | 0.956991 | 0.478496 | − | 0.878090i | \(-0.341182\pi\) | ||||
0.478496 | + | 0.878090i | \(0.341182\pi\) | |||||||
\(758\) | 7.37386 | 0.267831 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.20871 | 0.0438446 | ||||||||
\(761\) | 33.9564 | 1.23092 | 0.615460 | − | 0.788168i | \(-0.288970\pi\) | ||||
0.615460 | + | 0.788168i | \(0.288970\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.9564 | 1.04829 | ||||||||
\(764\) | −16.4174 | −0.593962 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | 5.33939 | 0.192794 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.66970 | −0.132333 | −0.0661663 | − | 0.997809i | \(-0.521077\pi\) | ||||
−0.0661663 | + | 0.997809i | \(0.521077\pi\) | |||||||
\(770\) | −10.5826 | −0.381370 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.74773 | 0.242856 | ||||||||
\(773\) | 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 | ||||||||
\(776\) | 14.9564 | 0.536905 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29.7042 | −1.06495 | ||||||||
\(779\) | 2.66970 | 0.0956518 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.3739 | −0.729034 | ||||||||
\(782\) | −3.79129 | −0.135576 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.791288 | 0.0282603 | ||||||||
\(785\) | 12.7477 | 0.454986 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.41742 | −0.300049 | −0.150024 | − | 0.988682i | \(-0.547935\pi\) | ||||
−0.150024 | + | 0.988682i | \(0.547935\pi\) | |||||||
\(788\) | −20.5390 | −0.731672 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.00000 | 0.284627 | ||||||||
\(791\) | −16.7477 | −0.595481 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.07803 | −0.144815 | ||||||||
\(794\) | 16.5390 | 0.586948 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.3303 | 0.720588 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −22.7477 | −0.803250 | ||||||||
\(803\) | 55.9129 | 1.97312 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.79129 | −0.0983800 | ||||||||
\(806\) | 12.5390 | 0.441668 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −13.5826 | −0.477833 | ||||||||
\(809\) | −11.0436 | −0.388271 | −0.194135 | − | 0.980975i | \(-0.562190\pi\) | ||||
−0.194135 | + | 0.980975i | \(0.562190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.9129 | −1.68245 | −0.841224 | − | 0.540686i | \(-0.818165\pi\) | ||||
−0.841224 | + | 0.540686i | \(0.818165\pi\) | |||||||
\(812\) | 4.41742 | 0.155021 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.1652 | 0.531538 | ||||||||
\(815\) | 22.3739 | 0.783722 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.66061 | −0.302996 | ||||||||
\(818\) | −22.7913 | −0.796879 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.20871 | 0.0771316 | ||||||||
\(821\) | −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 | \(0.245303\pi\) | |||||||
\(824\) | 7.37386 | 0.256881 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.3303 | 0.429026 | ||||||||
\(827\) | −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 | \(-0.684208\pi\) | ||||
−0.546941 | + | 0.837171i | \(0.684208\pi\) | |||||||
\(830\) | 6.00000 | 0.208263 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.20871 | 0.0419046 | ||||||||
\(833\) | 3.00000 | 0.103944 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.3303 | 0.634346 | ||||||||
\(836\) | −4.58258 | −0.158492 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −39.1652 | −1.35294 | ||||||||
\(839\) | 22.4174 | 0.773935 | 0.386968 | − | 0.922093i | \(-0.373522\pi\) | ||||
0.386968 | + | 0.922093i | \(0.373522\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.4955 | −0.913636 | ||||||||
\(842\) | −23.1216 | −0.796823 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.0000 | −0.344214 | ||||||||
\(845\) | −11.5390 | −0.396954 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.41742 | 0.323587 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.79129 | 0.130040 | ||||||||
\(851\) | 4.00000 | 0.137118 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.46099 | 0.289699 | 0.144849 | − | 0.989454i | \(-0.453730\pi\) | ||||
0.144849 | + | 0.989454i | \(0.453730\pi\) | |||||||
\(854\) | −9.41742 | −0.322258 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.5826 | −0.464243 | ||||||||
\(857\) | −9.16515 | −0.313076 | −0.156538 | − | 0.987672i | \(-0.550033\pi\) | ||||
−0.156538 | + | 0.987672i | \(0.550033\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.747727 | 0.0255121 | 0.0127561 | − | 0.999919i | \(-0.495940\pi\) | ||||
0.0127561 | + | 0.999919i | \(0.495940\pi\) | |||||||
\(860\) | −7.16515 | −0.244330 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.9129 | 0.678235 | ||||||||
\(863\) | 31.5826 | 1.07508 | 0.537542 | − | 0.843237i | \(-0.319353\pi\) | ||||
0.537542 | + | 0.843237i | \(0.319353\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.2087 | 0.483111 | ||||||||
\(866\) | 1.53901 | 0.0522979 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 28.9564 | 0.982846 | ||||||||
\(869\) | −30.3303 | −1.02889 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.66061 | −0.293453 | ||||||||
\(872\) | 10.3739 | 0.351303 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.20871 | −0.0408853 | ||||||||
\(875\) | 2.79129 | 0.0943628 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.70417 | 0.260151 | 0.130076 | − | 0.991504i | \(-0.458478\pi\) | ||||
0.130076 | + | 0.991504i | \(0.458478\pi\) | |||||||
\(878\) | 25.5390 | 0.861900 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.79129 | −0.127804 | ||||||||
\(881\) | 6.33030 | 0.213273 | 0.106637 | − | 0.994298i | \(-0.465992\pi\) | ||||
0.106637 | + | 0.994298i | \(0.465992\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.0436 | −0.405298 | −0.202649 | − | 0.979251i | \(-0.564955\pi\) | ||||
−0.202649 | + | 0.979251i | \(0.564955\pi\) | |||||||
\(884\) | 4.58258 | 0.154129 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 35.2087 | 1.18286 | ||||||||
\(887\) | 3.16515 | 0.106275 | 0.0531377 | − | 0.998587i | \(-0.483078\pi\) | ||||
0.0531377 | + | 0.998587i | \(0.483078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −41.1652 | −1.38063 | ||||||||
\(890\) | 3.16515 | 0.106096 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.1652 | 0.373837 | ||||||||
\(893\) | 16.4174 | 0.549388 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.7477 | 0.559815 | ||||||||
\(896\) | 2.79129 | 0.0932504 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.1216 | −0.838318 | ||||||||
\(899\) | 16.4174 | 0.547552 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.7477 | −0.757837 | ||||||||
\(902\) | −8.37386 | −0.278819 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 13.5390 | 0.450052 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.7477 | −0.688917 | −0.344458 | − | 0.938802i | \(-0.611937\pi\) | ||||
−0.344458 | + | 0.938802i | \(0.611937\pi\) | |||||||
\(908\) | −4.74773 | −0.157559 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.37386 | 0.111842 | ||||||||
\(911\) | −13.5826 | −0.450011 | −0.225005 | − | 0.974358i | \(-0.572240\pi\) | ||||
−0.225005 | + | 0.974358i | \(0.572240\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −22.7477 | −0.752840 | ||||||||
\(914\) | −10.0000 | −0.330771 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.3303 | −0.539568 | ||||||||
\(917\) | −25.5826 | −0.844811 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.8348 | −1.21507 | −0.607535 | − | 0.794293i | \(-0.707841\pi\) | ||||
−0.607535 | + | 0.794293i | \(0.707841\pi\) | |||||||
\(920\) | −1.00000 | −0.0329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.25227 | 0.0412414 | ||||||||
\(923\) | 6.49545 | 0.213800 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | −10.0000 | −0.328620 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.58258 | 0.0519506 | ||||||||
\(929\) | 39.4955 | 1.29580 | 0.647902 | − | 0.761724i | \(-0.275647\pi\) | ||||
0.647902 | + | 0.761724i | \(0.275647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.956439 | 0.0313460 | ||||||||
\(932\) | −7.58258 | −0.248376 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −25.9129 | −0.847895 | ||||||||
\(935\) | −14.3739 | −0.470076 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 58.3739 | 1.90699 | 0.953495 | − | 0.301407i | \(-0.0974564\pi\) | ||||
0.953495 | + | 0.301407i | \(0.0974564\pi\) | |||||||
\(938\) | −20.0000 | −0.653023 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 13.5826 | 0.443015 | ||||||||
\(941\) | −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 | ||||||||
\(944\) | 4.41742 | 0.143775 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.1652 | 0.883215 | ||||||||
\(947\) | 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 | ||||||||
\(950\) | 1.20871 | 0.0392158 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.5826 | 0.342983 | ||||||||
\(953\) | 26.5390 | 0.859683 | 0.429842 | − | 0.902904i | \(-0.358569\pi\) | ||||
0.429842 | + | 0.902904i | \(0.358569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.4174 | −0.531255 | ||||||||
\(956\) | −3.16515 | −0.102368 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39.4955 | 1.27604 | ||||||||
\(959\) | 2.20871 | 0.0713230 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 76.6170 | 2.47152 | ||||||||
\(962\) | −4.83485 | −0.155882 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −28.0000 | −0.901819 | ||||||||
\(965\) | 6.74773 | 0.217217 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.25227 | −0.168902 | −0.0844509 | − | 0.996428i | \(-0.526914\pi\) | ||||
−0.0844509 | + | 0.996428i | \(0.526914\pi\) | |||||||
\(968\) | 3.37386 | 0.108440 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.9564 | 0.480222 | ||||||||
\(971\) | 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 | ||||||||
\(974\) | 15.5826 | 0.499298 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.37386 | −0.107995 | ||||||||
\(977\) | −7.12159 | −0.227840 | −0.113920 | − | 0.993490i | \(-0.536341\pi\) | ||||
−0.113920 | + | 0.993490i | \(0.536341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.0000 | −0.383522 | ||||||||
\(980\) | 0.791288 | 0.0252768 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.7477 | 0.534441 | ||||||||
\(983\) | 0.626136 | 0.0199707 | 0.00998533 | − | 0.999950i | \(-0.496822\pi\) | ||||
0.00998533 | + | 0.999950i | \(0.496822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.5390 | −0.654427 | ||||||||
\(986\) | 6.00000 | 0.191079 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.46099 | 0.0464801 | ||||||||
\(989\) | 7.16515 | 0.227839 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7913 | −1.20048 | −0.600240 | − | 0.799820i | \(-0.704928\pi\) | ||||
−0.600240 | + | 0.799820i | \(0.704928\pi\) | |||||||
\(992\) | 10.3739 | 0.329370 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15.0000 | 0.475771 | ||||||||
\(995\) | 20.3303 | 0.644514 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.4955 | 0.364065 | 0.182032 | − | 0.983293i | \(-0.441732\pi\) | ||||
0.182032 | + | 0.983293i | \(0.441732\pi\) | |||||||
\(998\) | 23.1652 | 0.733280 | ||||||||
\(999\) | 0 | 0 |
(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 | 2070.2.a.x.1.2 | 2 | ||
3.2 | odd | 2 | 230.2.a.a.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 1840.2.a.n.1.1 | 2 | |||
15.2 | even | 4 | 1150.2.b.g.599.1 | 4 | |||
15.8 | even | 4 | 1150.2.b.g.599.4 | 4 | |||
15.14 | odd | 2 | 1150.2.a.o.1.1 | 2 | |||
24.5 | odd | 2 | 7360.2.a.bq.1.1 | 2 | |||
24.11 | even | 2 | 7360.2.a.bk.1.2 | 2 | |||
60.59 | even | 2 | 9200.2.a.bs.1.2 | 2 | |||
69.68 | even | 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 | 3.2 | odd | 2 | ||
1150.2.a.o.1.1 | 2 | 15.14 | odd | 2 | |||
1150.2.b.g.599.1 | 4 | 15.2 | even | 4 | |||
1150.2.b.g.599.4 | 4 | 15.8 | even | 4 | |||
1840.2.a.n.1.1 | 2 | 12.11 | even | 2 | |||
2070.2.a.x.1.2 | 2 | 1.1 | even | 1 | trivial | ||
5290.2.a.e.1.2 | 2 | 69.68 | even | 2 | |||
7360.2.a.bk.1.2 | 2 | 24.11 | even | 2 | |||
7360.2.a.bq.1.1 | 2 | 24.5 | odd | 2 | |||
9200.2.a.bs.1.2 | 2 | 60.59 | even | 2 |