Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, 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("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.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: | \(48.5490444289\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3040) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-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 | ||||||||
\(3\) | 1.67513 | 0.967137 | 0.483569 | − | 0.875306i | \(-0.339340\pi\) | ||||
0.483569 | + | 0.875306i | \(0.339340\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.15633 | 1.57094 | 0.785472 | − | 0.618898i | \(-0.212420\pi\) | ||||
0.785472 | + | 0.618898i | \(0.212420\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.193937 | −0.0646455 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.806063 | 0.243037 | 0.121519 | − | 0.992589i | \(-0.461224\pi\) | ||||
0.121519 | + | 0.992589i | \(0.461224\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.481194 | −0.133459 | −0.0667296 | − | 0.997771i | \(-0.521257\pi\) | ||||
−0.0667296 | + | 0.997771i | \(0.521257\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.67513 | −0.432517 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.61213 | −0.876069 | −0.438035 | − | 0.898958i | \(-0.644325\pi\) | ||||
−0.438035 | + | 0.898958i | \(0.644325\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.96239 | 1.51932 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.76845 | −1.20281 | −0.601403 | − | 0.798946i | \(-0.705391\pi\) | ||||
−0.601403 | + | 0.798946i | \(0.705391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.35026 | −1.02966 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.57452 | 1.59225 | 0.796124 | − | 0.605134i | \(-0.206880\pi\) | ||||
0.796124 | + | 0.605134i | \(0.206880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.61213 | 0.648757 | 0.324379 | − | 0.945927i | \(-0.394845\pi\) | ||||
0.324379 | + | 0.945927i | \(0.394845\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.35026 | 0.235050 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.15633 | −0.702547 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.18172 | 1.50947 | 0.754733 | − | 0.656033i | \(-0.227767\pi\) | ||||
0.754733 | + | 0.656033i | \(0.227767\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.806063 | −0.129073 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.312650 | 0.0488278 | 0.0244139 | − | 0.999702i | \(-0.492228\pi\) | ||||
0.0244139 | + | 0.999702i | \(0.492228\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.19394 | 0.487071 | 0.243535 | − | 0.969892i | \(-0.421693\pi\) | ||||
0.243535 | + | 0.969892i | \(0.421693\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.193937 | 0.0289104 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.76845 | −0.841415 | −0.420708 | − | 0.907196i | \(-0.638218\pi\) | ||||
−0.420708 | + | 0.907196i | \(0.638218\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.2750 | 1.46786 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.05079 | −0.847279 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.21933 | 1.12901 | 0.564506 | − | 0.825429i | \(-0.309067\pi\) | ||||
0.564506 | + | 0.825429i | \(0.309067\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.806063 | −0.108690 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.67513 | 0.221877 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.88717 | 1.15701 | 0.578505 | − | 0.815679i | \(-0.303636\pi\) | ||||
0.578505 | + | 0.815679i | \(0.303636\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.58181 | 0.714677 | 0.357339 | − | 0.933975i | \(-0.383684\pi\) | ||||
0.357339 | + | 0.933975i | \(0.383684\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.806063 | −0.101554 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.481194 | 0.0596848 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.59991 | −1.17282 | −0.586408 | − | 0.810016i | \(-0.699458\pi\) | ||||
−0.586408 | + | 0.810016i | \(0.699458\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.66291 | −1.16328 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.2374 | 1.92703 | 0.963514 | − | 0.267658i | \(-0.0862496\pi\) | ||||
0.963514 | + | 0.267658i | \(0.0862496\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.12601 | −0.248830 | −0.124415 | − | 0.992230i | \(-0.539705\pi\) | ||||
−0.124415 | + | 0.992230i | \(0.539705\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.67513 | 0.193427 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.35026 | 0.381798 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.8872 | 1.89995 | 0.949977 | − | 0.312319i | \(-0.101106\pi\) | ||||
0.949977 | + | 0.312319i | \(0.101106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.38058 | −0.931175 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.89446 | 0.647001 | 0.323501 | − | 0.946228i | \(-0.395140\pi\) | ||||
0.323501 | + | 0.946228i | \(0.395140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.61213 | 0.391790 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 14.3634 | 1.53992 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.2750 | −1.19515 | −0.597576 | − | 0.801812i | \(-0.703869\pi\) | ||||
−0.597576 | + | 0.801812i | \(0.703869\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.05079 | 0.627437 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.4944 | 1.77628 | 0.888142 | − | 0.459569i | \(-0.151996\pi\) | ||||
0.888142 | + | 0.459569i | \(0.151996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.156325 | −0.0157113 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.69323 | −0.765505 | −0.382752 | − | 0.923851i | \(-0.625024\pi\) | ||||
−0.382752 | + | 0.923851i | \(0.625024\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.950170 | −0.0936230 | −0.0468115 | − | 0.998904i | \(-0.514906\pi\) | ||||
−0.0468115 | + | 0.998904i | \(0.514906\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.96239 | −0.679460 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.7259 | −1.32693 | −0.663467 | − | 0.748205i | \(-0.730916\pi\) | ||||
−0.663467 | + | 0.748205i | \(0.730916\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.9756 | 1.91331 | 0.956656 | − | 0.291221i | \(-0.0940614\pi\) | ||||
0.956656 | + | 0.291221i | \(0.0940614\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.3806 | 1.45986 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.53198 | 0.614477 | 0.307238 | − | 0.951633i | \(-0.400595\pi\) | ||||
0.307238 | + | 0.951633i | \(0.400595\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.76845 | 0.537911 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0933212 | 0.00862755 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −15.0132 | −1.37626 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3503 | −0.940933 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.523730 | 0.0472232 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.51151 | −0.577803 | −0.288902 | − | 0.957359i | \(-0.593290\pi\) | ||||
−0.288902 | + | 0.957359i | \(0.593290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.35026 | 0.471064 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.4387 | 1.43625 | 0.718126 | − | 0.695913i | \(-0.245000\pi\) | ||||
0.718126 | + | 0.695913i | \(0.245000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.15633 | 0.360399 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.35026 | 0.460477 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.6253 | −0.907781 | −0.453890 | − | 0.891058i | \(-0.649964\pi\) | ||||
−0.453890 | + | 0.891058i | \(0.649964\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.26916 | 0.446924 | 0.223462 | − | 0.974713i | \(-0.428264\pi\) | ||||
0.223462 | + | 0.974713i | \(0.428264\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.66291 | −0.813764 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.387873 | −0.0324356 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.57452 | −0.712075 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 17.2120 | 1.41962 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.7308 | 0.879105 | 0.439552 | − | 0.898217i | \(-0.355137\pi\) | ||||
0.439552 | + | 0.898217i | \(0.355137\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.66291 | −0.623599 | −0.311799 | − | 0.950148i | \(-0.600932\pi\) | ||||
−0.311799 | + | 0.950148i | \(0.600932\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.700523 | 0.0566340 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.61213 | −0.290133 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.8496 | −1.10531 | −0.552657 | − | 0.833409i | \(-0.686386\pi\) | ||||
−0.552657 | + | 0.833409i | \(0.686386\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.7685 | 1.09191 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −23.9756 | −1.88954 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.05808 | 0.709484 | 0.354742 | − | 0.934964i | \(-0.384569\pi\) | ||||
0.354742 | + | 0.934964i | \(0.384569\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.35026 | −0.105118 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.586734 | 0.0454029 | 0.0227014 | − | 0.999742i | \(-0.492773\pi\) | ||||
0.0227014 | + | 0.999742i | \(0.492773\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.7685 | −0.982189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.193937 | −0.0148307 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.4568 | −0.947070 | −0.473535 | − | 0.880775i | \(-0.657022\pi\) | ||||
−0.473535 | + | 0.880775i | \(0.657022\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.15633 | 0.314189 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.8872 | 1.11899 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.2144 | 1.13718 | 0.568589 | − | 0.822622i | \(-0.307489\pi\) | ||||
0.568589 | + | 0.822622i | \(0.307489\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.8496 | 1.92138 | 0.960691 | − | 0.277619i | \(-0.0895454\pi\) | ||||
0.960691 | + | 0.277619i | \(0.0895454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.35026 | 0.691191 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.18172 | −0.675053 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.91160 | −0.212918 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.2374 | −1.61753 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −27.3865 | −1.98161 | −0.990807 | − | 0.135281i | \(-0.956806\pi\) | ||||
−0.990807 | + | 0.135281i | \(0.956806\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.64481 | 0.118396 | 0.0591981 | − | 0.998246i | \(-0.481146\pi\) | ||||
0.0591981 | + | 0.998246i | \(0.481146\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.806063 | 0.0577234 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.261865 | −0.0186571 | −0.00932856 | − | 0.999956i | \(-0.502969\pi\) | ||||
−0.00932856 | + | 0.999956i | \(0.502969\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.92478 | −0.136444 | −0.0682219 | − | 0.997670i | \(-0.521733\pi\) | ||||
−0.0682219 | + | 0.997670i | \(0.521733\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.0811 | −1.13427 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 35.6385 | 2.50133 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.312650 | −0.0218364 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.11871 | 0.0777560 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.806063 | 0.0557566 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.58769 | −0.660044 | −0.330022 | − | 0.943973i | \(-0.607056\pi\) | ||||
−0.330022 | + | 0.943973i | \(0.607056\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 27.1998 | 1.86370 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.19394 | −0.217825 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.0132 | 1.01916 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.56134 | −0.240653 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.73813 | 0.116920 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.274084 | 0.0183540 | 0.00917701 | − | 0.999958i | \(-0.497079\pi\) | ||||
0.00917701 | + | 0.999958i | \(0.497079\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.193937 | −0.0129291 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.1138 | −0.804020 | −0.402010 | − | 0.915635i | \(-0.631688\pi\) | ||||
−0.402010 | + | 0.915635i | \(0.631688\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5574 | −1.16022 | −0.580112 | − | 0.814537i | \(-0.696991\pi\) | ||||
−0.580112 | + | 0.814537i | \(0.696991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.61213 | 0.369251 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −10.1866 | −0.667349 | −0.333675 | − | 0.942688i | \(-0.608289\pi\) | ||||
−0.333675 | + | 0.942688i | \(0.608289\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.76845 | 0.376292 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 28.2882 | 1.83752 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.9003 | −1.67535 | −0.837677 | − | 0.546166i | \(-0.816087\pi\) | ||||
−0.837677 | + | 0.546166i | \(0.816087\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.84955 | 0.247972 | 0.123986 | − | 0.992284i | \(-0.460432\pi\) | ||||
0.123986 | + | 0.992284i | \(0.460432\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.01222 | 0.129084 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.2750 | −0.656448 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.481194 | −0.0306177 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.87399 | 0.625739 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.312650 | 0.0197343 | 0.00986716 | − | 0.999951i | \(-0.496859\pi\) | ||||
0.00986716 | + | 0.999951i | \(0.496859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.64974 | −0.292327 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.05079 | 0.378915 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.6678 | 0.914955 | 0.457477 | − | 0.889221i | \(-0.348753\pi\) | ||||
0.457477 | + | 0.889221i | \(0.348753\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.1622 | 2.37128 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.66291 | −0.102932 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.06793 | 0.435827 | 0.217914 | − | 0.975968i | \(-0.430075\pi\) | ||||
0.217914 | + | 0.975968i | \(0.430075\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.21933 | −0.504909 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.8872 | −1.15588 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −24.2882 | −1.48088 | −0.740439 | − | 0.672123i | \(-0.765382\pi\) | ||||
−0.740439 | + | 0.672123i | \(0.765382\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.81924 | 0.232002 | 0.116001 | − | 0.993249i | \(-0.462992\pi\) | ||||
0.116001 | + | 0.993249i | \(0.462992\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.35026 | −0.202767 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.806063 | 0.0486075 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.70052 | −0.522764 | −0.261382 | − | 0.965235i | \(-0.584178\pi\) | ||||
−0.261382 | + | 0.965235i | \(0.584178\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.700523 | −0.0419392 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.93937 | −0.235003 | −0.117501 | − | 0.993073i | \(-0.537488\pi\) | ||||
−0.117501 | + | 0.993073i | \(0.537488\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1055 | 0.600712 | 0.300356 | − | 0.953827i | \(-0.402895\pi\) | ||||
0.300356 | + | 0.953827i | \(0.402895\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.67513 | −0.0992262 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.29948 | 0.0767057 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.95254 | −0.232502 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.3054 | 1.71791 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.57944 | 0.559637 | 0.279818 | − | 0.960053i | \(-0.409726\pi\) | ||||
0.279818 | + | 0.960053i | \(0.409726\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.88717 | −0.517431 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.31265 | −0.250245 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.77575 | 0.160526 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.2750 | 0.765161 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.8872 | −0.740348 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.58181 | −0.319613 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.8242 | 1.64508 | 0.822541 | − | 0.568706i | \(-0.192556\pi\) | ||||
0.822541 | + | 0.568706i | \(0.192556\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.59166 | −0.0905463 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.74543 | 0.269089 | 0.134544 | − | 0.990908i | \(-0.457043\pi\) | ||||
0.134544 | + | 0.990908i | \(0.457043\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.18664 | −0.123596 | −0.0617982 | − | 0.998089i | \(-0.519684\pi\) | ||||
−0.0617982 | + | 0.998089i | \(0.519684\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.806063 | 0.0454165 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.9805 | 0.953719 | 0.476860 | − | 0.878979i | \(-0.341775\pi\) | ||||
0.476860 | + | 0.878979i | \(0.341775\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.91160 | 0.386975 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −22.9927 | −1.28333 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.61213 | −0.200984 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.481194 | −0.0266919 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 33.4617 | 1.85044 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.9756 | −1.32182 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.64974 | −0.255573 | −0.127786 | − | 0.991802i | \(-0.540787\pi\) | ||||
−0.127786 | + | 0.991802i | \(0.540787\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.78067 | −0.0975802 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.59991 | 0.524499 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.63023 | −0.306698 | −0.153349 | − | 0.988172i | \(-0.549006\pi\) | ||||
−0.153349 | + | 0.988172i | \(0.549006\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.9419 | 0.594284 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.91160 | 0.157672 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.6121 | 0.734986 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.66291 | 0.520234 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.2301 | −0.817596 | −0.408798 | − | 0.912625i | \(-0.634052\pi\) | ||||
−0.408798 | + | 0.912625i | \(0.634052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.1998 | 1.13480 | 0.567400 | − | 0.823442i | \(-0.307949\pi\) | ||||
0.567400 | + | 0.823442i | \(0.307949\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.57452 | 0.137417 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.6859 | 1.20745 | 0.603725 | − | 0.797192i | \(-0.293682\pi\) | ||||
0.603725 | + | 0.797192i | \(0.293682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.2374 | −0.861793 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −25.1490 | −1.33103 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.6556 | 0.879050 | 0.439525 | − | 0.898230i | \(-0.355147\pi\) | ||||
0.439525 | + | 0.898230i | \(0.355147\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.3380 | −0.910011 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.12601 | 0.111280 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.4920 | 0.913075 | 0.456537 | − | 0.889704i | \(-0.349089\pi\) | ||||
0.456537 | + | 0.889704i | \(0.349089\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0606343 | −0.00315650 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.1622 | 1.77361 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.83146 | 0.301941 | 0.150971 | − | 0.988538i | \(-0.451760\pi\) | ||||
0.150971 | + | 0.988538i | \(0.451760\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.67513 | −0.0865034 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.12601 | −0.212500 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1768 | −0.522747 | −0.261373 | − | 0.965238i | \(-0.584175\pi\) | ||||
−0.261373 | + | 0.965238i | \(0.584175\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9076 | −0.558815 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.65069 | 0.390932 | 0.195466 | − | 0.980710i | \(-0.437378\pi\) | ||||
0.195466 | + | 0.980710i | \(0.437378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.35026 | −0.170745 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.619421 | −0.0314869 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.6761 | −1.45394 | −0.726968 | − | 0.686672i | \(-0.759071\pi\) | ||||
−0.726968 | + | 0.686672i | \(0.759071\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 20.8364 | 1.05374 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 27.5369 | 1.38905 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.8872 | −0.849686 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.5139 | −1.02956 | −0.514781 | − | 0.857322i | \(-0.672127\pi\) | ||||
−0.514781 | + | 0.857322i | \(0.672127\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.96239 | 0.348555 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.4894 | 0.823444 | 0.411722 | − | 0.911310i | \(-0.364928\pi\) | ||||
0.411722 | + | 0.911310i | \(0.364928\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.73813 | −0.0865827 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.38058 | 0.416434 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.40105 | 0.366856 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.3634 | −0.908013 | −0.454007 | − | 0.890998i | \(-0.650006\pi\) | ||||
−0.454007 | + | 0.890998i | \(0.650006\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.7988 | −0.877949 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.9380 | 1.81760 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.89446 | −0.289348 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.82653 | 0.432237 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.1246 | −1.42283 | −0.711415 | − | 0.702772i | \(-0.751945\pi\) | ||||
−0.711415 | + | 0.702772i | \(0.751945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.3258 | −1.13683 | −0.568416 | − | 0.822742i | \(-0.692443\pi\) | ||||
−0.568416 | + | 0.822742i | \(0.692443\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.11871 | 0.0543937 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.61213 | −0.175214 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.1998 | 1.12272 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.649738 | −0.0313697 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.2750 | −1.21746 | −0.608728 | − | 0.793379i | \(-0.708320\pi\) | ||||
−0.608728 | + | 0.793379i | \(0.708320\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.98190 | 0.383586 | 0.191793 | − | 0.981435i | \(-0.438570\pi\) | ||||
0.191793 | + | 0.981435i | \(0.438570\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.3634 | −0.688674 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.76845 | −0.275942 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3503 | 1.01899 | 0.509496 | − | 0.860473i | \(-0.329832\pi\) | ||||
0.509496 | + | 0.860473i | \(0.329832\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.99271 | −0.0948908 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.76845 | 0.0840217 | 0.0420108 | − | 0.999117i | \(-0.486624\pi\) | ||||
0.0420108 | + | 0.999117i | \(0.486624\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.2750 | 0.534488 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.9756 | 0.850215 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.64974 | −0.219435 | −0.109717 | − | 0.993963i | \(-0.534995\pi\) | ||||
−0.109717 | + | 0.993963i | \(0.534995\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.252016 | 0.0118670 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.8364 | −0.603106 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.00000 | 0.0937614 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0752228 | 0.00351877 | 0.00175939 | − | 0.999998i | \(-0.499440\pi\) | ||||
0.00175939 | + | 0.999998i | \(0.499440\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.3258 | 0.902052 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 32.1768 | 1.49862 | 0.749311 | − | 0.662218i | \(-0.230385\pi\) | ||||
0.749311 | + | 0.662218i | \(0.230385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.3331 | 1.03791 | 0.518954 | − | 0.854802i | \(-0.326322\pi\) | ||||
0.518954 | + | 0.854802i | \(0.326322\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.05079 | −0.280598 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.9175 | 0.505201 | 0.252600 | − | 0.967571i | \(-0.418714\pi\) | ||||
0.252600 | + | 0.967571i | \(0.418714\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.9003 | −1.84243 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.1998 | −1.06899 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.57452 | 0.118376 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.59403 | −0.0729856 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.8061 | 0.585124 | 0.292562 | − | 0.956247i | \(-0.405492\pi\) | ||||
0.292562 | + | 0.956247i | \(0.405492\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.41819 | −0.201452 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −40.1622 | −1.82744 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.4944 | −0.794378 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.2351 | −1.09820 | −0.549098 | − | 0.835758i | \(-0.685029\pi\) | ||||
−0.549098 | + | 0.835758i | \(0.685029\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 15.1735 | 0.686168 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5647 | −0.567035 | −0.283518 | − | 0.958967i | \(-0.591501\pi\) | ||||
−0.283518 | + | 0.958967i | \(0.591501\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.9722 | −1.39492 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.156325 | 0.00702629 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 67.4880 | 3.02725 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 41.4314 | 1.85472 | 0.927361 | − | 0.374167i | \(-0.122071\pi\) | ||||
0.927361 | + | 0.374167i | \(0.122071\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.982857 | 0.0439108 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.2301 | 1.03578 | 0.517890 | − | 0.855447i | \(-0.326718\pi\) | ||||
0.517890 | + | 0.855447i | \(0.326718\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.69323 | 0.342344 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.3888 | −0.949911 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.0362 | 0.976737 | 0.488369 | − | 0.872637i | \(-0.337592\pi\) | ||||
0.488369 | + | 0.872637i | \(0.337592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.83638 | −0.390898 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.35026 | −0.236220 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.950170 | 0.0418695 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.64974 | −0.204495 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.8667 | −0.915946 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.6121 | −0.508737 | −0.254368 | − | 0.967107i | \(-0.581868\pi\) | ||||
−0.254368 | + | 0.967107i | \(0.581868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.7489 | −0.557472 | −0.278736 | − | 0.960368i | \(-0.589915\pi\) | ||||
−0.278736 | + | 0.960368i | \(0.589915\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.96239 | 0.303864 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −13.0475 | −0.568356 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.2750 | 0.446741 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.72355 | −0.0747955 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.150446 | −0.00651652 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.7259 | 0.593423 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.4861 | 1.09981 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.28233 | 0.356745 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.2447 | 0.913382 | 0.456691 | − | 0.889625i | \(-0.349035\pi\) | ||||
0.456691 | + | 0.889625i | \(0.349035\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 43.3014 | 1.85824 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.9756 | −0.855659 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.3249 | −0.612487 | −0.306244 | − | 0.951953i | \(-0.599072\pi\) | ||||
−0.306244 | + | 0.951953i | \(0.599072\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.08252 | −0.0462007 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.57452 | 0.365287 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 70.1886 | 2.98472 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.3806 | −0.652869 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −38.3536 | −1.62509 | −0.812547 | − | 0.582896i | \(-0.801920\pi\) | ||||
−0.812547 | + | 0.582896i | \(0.801920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.53690 | −0.0650041 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.87732 | −0.205920 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.773377 | 0.0325939 | 0.0162970 | − | 0.999867i | \(-0.494812\pi\) | ||||
0.0162970 | + | 0.999867i | \(0.494812\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.53198 | −0.274802 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −34.8324 | −1.46282 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.0640 | −1.05074 | −0.525368 | − | 0.850875i | \(-0.676072\pi\) | ||||
−0.525368 | + | 0.850875i | \(0.676072\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.95509 | 0.0818182 | 0.0409091 | − | 0.999163i | \(-0.486975\pi\) | ||||
0.0409091 | + | 0.999163i | \(0.486975\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −45.8759 | −1.91649 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.76845 | −0.240561 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.0625 | −1.66783 | −0.833913 | − | 0.551896i | \(-0.813904\pi\) | ||||
−0.833913 | + | 0.551896i | \(0.813904\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.75528 | 0.114505 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.4993 | 1.01640 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.62530 | 0.274392 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0933212 | −0.00385836 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.8324 | 0.942394 | 0.471197 | − | 0.882028i | \(-0.343822\pi\) | ||||
0.471197 | + | 0.882028i | \(0.343822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.61213 | 0.148835 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.438658 | −0.0180440 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.22425 | −0.378795 | −0.189397 | − | 0.981901i | \(-0.560653\pi\) | ||||
−0.189397 | + | 0.981901i | \(0.560653\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.0132 | 0.615480 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.22425 | −0.131960 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6497 | 0.925443 | 0.462722 | − | 0.886504i | \(-0.346873\pi\) | ||||
0.462722 | + | 0.886504i | \(0.346873\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.1754 | 1.43483 | 0.717417 | − | 0.696644i | \(-0.245324\pi\) | ||||
0.717417 | + | 0.696644i | \(0.245324\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.86177 | 0.0758173 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3503 | 0.420798 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.0517 | −1.66624 | −0.833119 | − | 0.553093i | \(-0.813447\pi\) | ||||
−0.833119 | + | 0.553093i | \(0.813447\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 59.6991 | 2.41913 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.77575 | 0.112295 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.7513 | −1.08048 | −0.540238 | − | 0.841513i | \(-0.681666\pi\) | ||||
−0.540238 | + | 0.841513i | \(0.681666\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.523730 | −0.0211188 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.6761 | −0.832388 | −0.416194 | − | 0.909276i | \(-0.636636\pi\) | ||||
−0.416194 | + | 0.909276i | \(0.636636\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.35614 | −0.295668 | −0.147834 | − | 0.989012i | \(-0.547230\pi\) | ||||
−0.147834 | + | 0.989012i | \(0.547230\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.8627 | 1.23848 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −46.8627 | −1.87752 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.35026 | 0.0539243 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −33.1655 | −1.32240 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7308 | −0.427188 | −0.213594 | − | 0.976923i | \(-0.568517\pi\) | ||||
−0.213594 | + | 0.976923i | \(0.568517\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.0606 | −0.638353 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.51151 | 0.258401 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.94429 | −0.195900 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.14903 | −0.124574 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.2506 | −1.47131 | −0.735655 | − | 0.677356i | \(-0.763126\pi\) | ||||
−0.735655 | + | 0.677356i | \(0.763126\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.38058 | 0.291062 | 0.145531 | − | 0.989354i | \(-0.453511\pi\) | ||||
0.145531 | + | 0.989354i | \(0.453511\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.35026 | −0.210666 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.32979 | 0.209536 | 0.104768 | − | 0.994497i | \(-0.466590\pi\) | ||||
0.104768 | + | 0.994497i | \(0.466590\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.16362 | 0.281197 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.1490 | 0.985668 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.0230 | −0.431364 | −0.215682 | − | 0.976464i | \(-0.569197\pi\) | ||||
−0.215682 | + | 0.976464i | \(0.569197\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.4387 | −0.642312 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.412311 | 0.0160858 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.1114 | −0.471794 | −0.235897 | − | 0.971778i | \(-0.575803\pi\) | ||||
−0.235897 | + | 0.971778i | \(0.575803\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.22425 | −0.280991 | −0.140495 | − | 0.990081i | \(-0.544870\pi\) | ||||
−0.140495 | + | 0.990081i | \(0.544870\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.91160 | 0.113077 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.15633 | −0.161175 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −49.4617 | −1.91516 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.459126 | 0.0177509 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.49929 | 0.173693 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.06888 | −0.233938 | −0.116969 | − | 0.993136i | \(-0.537318\pi\) | ||||
−0.116969 | + | 0.993136i | \(0.537318\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.35026 | −0.205932 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −28.0933 | −1.07971 | −0.539857 | − | 0.841757i | \(-0.681522\pi\) | ||||
−0.539857 | + | 0.841757i | \(0.681522\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 72.7123 | 2.79044 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.2922 | −0.777598 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.5247 | −1.12973 | −0.564865 | − | 0.825183i | \(-0.691072\pi\) | ||||
−0.564865 | + | 0.825183i | \(0.691072\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.6253 | 0.405972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.4109 | −1.12210 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.95509 | −0.150677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.03032 | 0.305488 | 0.152744 | − | 0.988266i | \(-0.451189\pi\) | ||||
0.152744 | + | 0.988266i | \(0.451189\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.649738 | −0.0246815 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.26916 | −0.199871 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.12933 | −0.0427765 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.0640 | −0.645418 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.5672 | 0.739044 | 0.369522 | − | 0.929222i | \(-0.379521\pi\) | ||||
0.369522 | + | 0.929222i | \(0.379521\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.18172 | 0.346295 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.66291 | 0.363926 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.9756 | −1.20256 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.8251 | −1.42055 | −0.710276 | − | 0.703923i | \(-0.751430\pi\) | ||||
−0.710276 | + | 0.703923i | \(0.751430\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.27504 | −0.122824 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.8364 | −0.780329 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.387873 | 0.0145056 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −43.3865 | −1.62030 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −39.8799 | −1.48727 | −0.743634 | − | 0.668587i | \(-0.766900\pi\) | ||||
−0.743634 | + | 0.668587i | \(0.766900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.94921 | −0.147076 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.44851 | 0.239823 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.57452 | 0.318450 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −52.1319 | −1.93346 | −0.966732 | − | 0.255790i | \(-0.917664\pi\) | ||||
−0.966732 | + | 0.255790i | \(0.917664\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.5125 | 1.05602 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.5369 | −0.426708 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 46.1984 | 1.70638 | 0.853188 | − | 0.521603i | \(-0.174666\pi\) | ||||
0.853188 | + | 0.521603i | \(0.174666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.2120 | −0.634875 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.73813 | −0.285038 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.4010 | 0.640108 | 0.320054 | − | 0.947399i | \(-0.396299\pi\) | ||||
0.320054 | + | 0.947399i | \(0.396299\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.806063 | −0.0296115 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.7880 | 0.982755 | 0.491378 | − | 0.870947i | \(-0.336494\pi\) | ||||
0.491378 | + | 0.870947i | \(0.336494\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.7308 | −0.393148 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.14315 | −0.0418257 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −57.0494 | −2.08454 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.8529 | 1.78267 | 0.891333 | − | 0.453348i | \(-0.149771\pi\) | ||||
0.891333 | + | 0.453348i | \(0.149771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0.523730 | 0.0190858 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.66291 | 0.278882 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −37.0376 | −1.34615 | −0.673077 | − | 0.739572i | \(-0.735028\pi\) | ||||
−0.673077 | + | 0.739572i | \(0.735028\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.78892 | −0.282720 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.5705 | 1.03568 | 0.517841 | − | 0.855477i | \(-0.326736\pi\) | ||||
0.517841 | + | 0.855477i | \(0.326736\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 83.0249 | 3.00570 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.700523 | −0.0253275 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.27645 | −0.154414 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0679 | 0.976094 | 0.488047 | − | 0.872817i | \(-0.337709\pi\) | ||||
0.488047 | + | 0.872817i | \(0.337709\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.5705 | 0.884887 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.6350 | 0.490416 | 0.245208 | − | 0.969471i | \(-0.421144\pi\) | ||||
0.245208 | + | 0.969471i | \(0.421144\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.61213 | 0.129751 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 63.9267 | 2.29336 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.312650 | 0.0112019 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.0884 | 0.468340 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.8759 | −1.63947 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.8496 | 0.494312 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.77338 | −0.170152 | −0.0850762 | − | 0.996374i | \(-0.527113\pi\) | ||||
−0.0850762 | + | 0.996374i | \(0.527113\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.8397 | 0.421505 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.1490 | 0.965308 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.68594 | −0.0953803 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.7685 | −0.488317 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −35.4798 | −1.25676 | −0.628379 | − | 0.777907i | \(-0.716281\pi\) | ||||
−0.628379 | + | 0.777907i | \(0.716281\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.8364 | 0.737138 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.18664 | 0.0772612 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.71370 | −0.0604751 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.9756 | 0.845028 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.6859 | −1.43221 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −46.7024 | −1.64197 | −0.820985 | − | 0.570950i | \(-0.806575\pi\) | ||||
−0.820985 | + | 0.570950i | \(0.806575\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.3404 | 0.960052 | 0.480026 | − | 0.877254i | \(-0.340627\pi\) | ||||
0.480026 | + | 0.877254i | \(0.340627\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.39772 | 0.224378 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.05808 | −0.317291 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.19394 | 0.111742 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.387873 | 0.0135534 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.6761 | 1.83841 | 0.919204 | − | 0.393782i | \(-0.128833\pi\) | ||||
0.919204 | + | 0.393782i | \(0.128833\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.4788 | 0.365269 | 0.182634 | − | 0.983181i | \(-0.441538\pi\) | ||||
0.182634 | + | 0.983181i | \(0.441538\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.35026 | 0.0470101 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.874947 | 0.0304249 | 0.0152124 | − | 0.999884i | \(-0.495158\pi\) | ||||
0.0152124 | + | 0.999884i | \(0.495158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.6023 | −0.958667 | −0.479333 | − | 0.877633i | \(-0.659122\pi\) | ||||
−0.479333 | + | 0.877633i | \(0.659122\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.5745 | −0.505584 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37.1147 | −1.28595 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.586734 | −0.0203048 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.3258 | −0.667998 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.2750 | 1.07973 | 0.539867 | − | 0.841750i | \(-0.318474\pi\) | ||||
0.539867 | + | 0.841750i | \(0.318474\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.5223 | 1.53525 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.59895 | −0.227280 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.7685 | 0.439248 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.0191 | −1.47815 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 16.9281 | 0.580971 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −52.9643 | −1.81559 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39.3112 | −1.34599 | −0.672996 | − | 0.739647i | \(-0.734993\pi\) | ||||
−0.672996 | + | 0.739647i | \(0.734993\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.193937 | 0.00663249 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −39.3293 | −1.34346 | −0.671732 | − | 0.740794i | \(-0.734449\pi\) | ||||
−0.671732 | + | 0.740794i | \(0.734449\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.1721 | 0.620022 | 0.310011 | − | 0.950733i | \(-0.399667\pi\) | ||||
0.310011 | + | 0.950733i | \(0.399667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.17679 | 0.0741849 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.6751 | −0.737830 | −0.368915 | − | 0.929463i | \(-0.620271\pi\) | ||||
−0.368915 | + | 0.929463i | \(0.620271\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.4568 | 0.423542 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.62102 | −0.224862 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.6121 | 0.461760 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.61942 | 0.156523 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.39280 | −0.114829 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.15633 | −0.140509 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.2701 | −0.346797 | −0.173399 | − | 0.984852i | \(-0.555475\pi\) | ||||
−0.173399 | + | 0.984852i | \(0.555475\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.0468 | 0.541246 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −37.1187 | −1.25056 | −0.625281 | − | 0.780400i | \(-0.715015\pi\) | ||||
−0.625281 | + | 0.780400i | \(0.715015\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.63401 | 0.0886415 | 0.0443207 | − | 0.999017i | \(-0.485888\pi\) | ||||
0.0443207 | + | 0.999017i | \(0.485888\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.8872 | −0.500427 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.1876 | 0.375643 | 0.187821 | − | 0.982203i | \(-0.439857\pi\) | ||||
0.187821 | + | 0.982203i | \(0.439857\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27.0640 | −0.907696 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.75528 | −0.226310 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.76845 | −0.193034 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.2144 | −0.508561 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.64974 | 0.155250 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.9722 | 1.03298 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.6893 | −0.989093 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 22.2374 | 0.740015 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.8496 | −0.859268 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.824162 | 0.0273658 | 0.0136829 | − | 0.999906i | \(-0.495644\pi\) | ||||
0.0136829 | + | 0.999906i | \(0.495644\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.49200 | 0.0494865 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.3211 | 0.905188 | 0.452594 | − | 0.891717i | \(-0.350499\pi\) | ||||
0.452594 | + | 0.891717i | \(0.350499\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.75131 | 0.157245 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.35026 | −0.309110 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 68.3244 | 2.25627 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.3488 | 1.19904 | 0.599519 | − | 0.800361i | \(-0.295359\pi\) | ||||
0.599519 | + | 0.800361i | \(0.295359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 48.2842 | 1.59102 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.81336 | −0.257180 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.18172 | 0.301893 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.184273 | 0.00605231 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.0263 | −1.18199 | −0.590993 | − | 0.806677i | \(-0.701264\pi\) | ||||
−0.590993 | + | 0.806677i | \(0.701264\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.2750 | 0.336751 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.94921 | 0.260246 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.91160 | 0.0952196 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44.4241 | 1.45127 | 0.725636 | − | 0.688079i | \(-0.241546\pi\) | ||||
0.725636 | + | 0.688079i | \(0.241546\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.66291 | −0.119535 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.31406 | 0.303630 | 0.151815 | − | 0.988409i | \(-0.451488\pi\) | ||||
0.151815 | + | 0.988409i | \(0.451488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.80351 | −0.0587303 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22.2374 | 0.723384 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.4676 | −1.34751 | −0.673757 | − | 0.738953i | \(-0.735321\pi\) | ||||
−0.673757 | + | 0.738953i | \(0.735321\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.02302 | 0.0332087 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.4445 | 0.922377 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.2424 | −0.558535 | −0.279267 | − | 0.960213i | \(-0.590092\pi\) | ||||
−0.279267 | + | 0.960213i | \(0.590092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.3865 | 0.886205 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.5778 | 0.374258 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −44.1622 | −1.42607 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.9525 | −0.579114 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.66196 | 0.0857804 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.64481 | −0.0529484 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.84700 | 0.284500 | 0.142250 | − | 0.989831i | \(-0.454566\pi\) | ||||
0.142250 | + | 0.989831i | \(0.454566\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.05079 | −0.194379 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.9262 | −0.607370 | −0.303685 | − | 0.952772i | \(-0.598217\pi\) | ||||
−0.303685 | + | 0.952772i | \(0.598217\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.9003 | 0.702093 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.806063 | −0.0258147 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 49.2081 | 1.57431 | 0.787153 | − | 0.616758i | \(-0.211554\pi\) | ||||
0.787153 | + | 0.616758i | \(0.211554\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.08840 | −0.290466 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.87399 | −0.123687 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.162664 | 0.00518819 | 0.00259409 | − | 0.999997i | \(-0.499174\pi\) | ||||
0.00259409 | + | 0.999997i | \(0.499174\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.261865 | 0.00834372 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −40.1622 | −1.27838 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.4241 | −0.585851 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.5599 | −0.780172 | −0.390086 | − | 0.920778i | \(-0.627555\pi\) | ||||
−0.390086 | + | 0.920778i | \(0.627555\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.78892 | −0.247174 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.92478 | 0.0610195 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 43.3112 | 1.37168 | 0.685840 | − | 0.727752i | \(-0.259435\pi\) | ||||
0.685840 | + | 0.727752i | \(0.259435\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.1246 | −1.55423 |
(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 | 6080.2.a.bu.1.3 | 3 | ||
4.3 | odd | 2 | 6080.2.a.bt.1.1 | 3 | |||
8.3 | odd | 2 | 3040.2.a.l.1.3 | ✓ | 3 | ||
8.5 | even | 2 | 3040.2.a.m.1.1 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3040.2.a.l.1.3 | ✓ | 3 | 8.3 | odd | 2 | ||
3040.2.a.m.1.1 | yes | 3 | 8.5 | even | 2 | ||
6080.2.a.bt.1.1 | 3 | 4.3 | odd | 2 | |||
6080.2.a.bu.1.3 | 3 | 1.1 | even | 1 | trivial |