Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3380,2,Mod(1,3380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3380, 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("3380.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3380.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: | \(26.9894358832\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.756.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - 6x - 2 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.26180\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3380.1 |
$q$-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 | ||||||||
\(3\) | −2.26180 | −1.30585 | −0.652926 | − | 0.757422i | \(-0.726459\pi\) | ||||
−0.652926 | + | 0.757422i | \(0.726459\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.11575 | 0.421714 | 0.210857 | − | 0.977517i | \(-0.432375\pi\) | ||||
0.210857 | + | 0.977517i | \(0.432375\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.11575 | 0.705250 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.37755 | 1.62139 | 0.810696 | − | 0.585467i | \(-0.199089\pi\) | ||||
0.810696 | + | 0.585467i | \(0.199089\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.26180 | −0.583995 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.90116 | −1.81265 | −0.906325 | − | 0.422582i | \(-0.861124\pi\) | ||||
−0.906325 | + | 0.422582i | \(0.861124\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.52360 | −0.550696 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.49330 | 1.35395 | 0.676973 | − | 0.736007i | \(-0.263291\pi\) | ||||
0.676973 | + | 0.736007i | \(0.263291\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.00000 | 0.384900 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.63935 | 0.675811 | 0.337906 | − | 0.941180i | \(-0.390282\pi\) | ||||
0.337906 | + | 0.941180i | \(0.390282\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.14605 | 0.565048 | 0.282524 | − | 0.959260i | \(-0.408828\pi\) | ||||
0.282524 | + | 0.959260i | \(0.408828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −12.1630 | −2.11730 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.11575 | 0.188596 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.40786 | 1.21784 | 0.608922 | − | 0.793230i | \(-0.291602\pi\) | ||||
0.608922 | + | 0.793230i | \(0.291602\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.75510 | 0.742622 | 0.371311 | − | 0.928508i | \(-0.378908\pi\) | ||||
0.371311 | + | 0.928508i | \(0.378908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.78541 | 0.729768 | 0.364884 | − | 0.931053i | \(-0.381109\pi\) | ||||
0.364884 | + | 0.931053i | \(0.381109\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.11575 | 0.315397 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.16296 | −0.898960 | −0.449480 | − | 0.893290i | \(-0.648391\pi\) | ||||
−0.449480 | + | 0.893290i | \(0.648391\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.75510 | −0.822158 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.292106 | 0.0401238 | 0.0200619 | − | 0.999799i | \(-0.493614\pi\) | ||||
0.0200619 | + | 0.999799i | \(0.493614\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.37755 | 0.725109 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.8709 | 2.36705 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.3776 | −1.48123 | −0.740616 | − | 0.671929i | \(-0.765466\pi\) | ||||
−0.740616 | + | 0.671929i | \(0.765466\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.34725 | −0.684645 | −0.342322 | − | 0.939583i | \(-0.611214\pi\) | ||||
−0.342322 | + | 0.939583i | \(0.611214\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.36065 | 0.297413 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8709 | −1.45026 | −0.725128 | − | 0.688614i | \(-0.758219\pi\) | ||||
−0.725128 | + | 0.688614i | \(0.758219\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.6866 | −1.76805 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.43816 | −0.408034 | −0.204017 | − | 0.978967i | \(-0.565400\pi\) | ||||
−0.204017 | + | 0.978967i | \(0.565400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.59214 | 0.537470 | 0.268735 | − | 0.963214i | \(-0.413394\pi\) | ||||
0.268735 | + | 0.963214i | \(0.413394\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.26180 | −0.261170 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8157 | −1.21686 | −0.608431 | − | 0.793607i | \(-0.708201\pi\) | ||||
−0.608431 | + | 0.793607i | \(0.708201\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.8709 | −1.20787 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.40786 | 0.813118 | 0.406559 | − | 0.913625i | \(-0.366729\pi\) | ||||
0.406559 | + | 0.913625i | \(0.366729\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.23150 | −0.882509 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.8157 | 1.57046 | 0.785231 | − | 0.619203i | \(-0.212544\pi\) | ||||
0.785231 | + | 0.619203i | \(0.212544\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.11575 | −0.737869 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.90116 | −0.810642 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.76850 | 0.382633 | 0.191317 | − | 0.981528i | \(-0.438724\pi\) | ||||
0.191317 | + | 0.981528i | \(0.438724\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11.3776 | 1.14349 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.292106 | 0.0290656 | 0.0145328 | − | 0.999894i | \(-0.495374\pi\) | ||||
0.0145328 | + | 0.999894i | \(0.495374\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.03030 | −0.397118 | −0.198559 | − | 0.980089i | \(-0.563626\pi\) | ||||
−0.198559 | + | 0.980089i | \(0.563626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.52360 | −0.246279 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.50670 | 0.532353 | 0.266176 | − | 0.963924i | \(-0.414240\pi\) | ||||
0.266176 | + | 0.963924i | \(0.414240\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.27871 | −0.122478 | −0.0612390 | − | 0.998123i | \(-0.519505\pi\) | ||||
−0.0612390 | + | 0.998123i | \(0.519505\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16.7551 | −1.59032 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 19.2787 | 1.81359 | 0.906794 | − | 0.421574i | \(-0.138522\pi\) | ||||
0.906794 | + | 0.421574i | \(0.138522\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.49330 | 0.605503 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.9181 | 1.62891 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.7551 | −0.969755 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.96970 | −0.707196 | −0.353598 | − | 0.935397i | \(-0.615042\pi\) | ||||
−0.353598 | + | 0.935397i | \(0.615042\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.8236 | −0.952969 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.27871 | 0.635944 | 0.317972 | − | 0.948100i | \(-0.396998\pi\) | ||||
0.317972 | + | 0.948100i | \(0.396998\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.81571 | −0.764419 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.00000 | 0.172133 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.75510 | 0.406256 | 0.203128 | − | 0.979152i | \(-0.434889\pi\) | ||||
0.203128 | + | 0.979152i | \(0.434889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.3259 | −1.38475 | −0.692373 | − | 0.721540i | \(-0.743435\pi\) | ||||
−0.692373 | + | 0.721540i | \(0.743435\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.9394 | 1.17391 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.63935 | 0.302232 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.0169 | 1.07362 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.81571 | 0.722211 | 0.361106 | − | 0.932525i | \(-0.382399\pi\) | ||||
0.361106 | + | 0.932525i | \(0.382399\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.9012 | 1.61953 | 0.809767 | − | 0.586752i | \(-0.199594\pi\) | ||||
0.809767 | + | 0.586752i | \(0.199594\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.14605 | 0.252697 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.7551 | 1.49682 | 0.748410 | − | 0.663236i | \(-0.230818\pi\) | ||||
0.748410 | + | 0.663236i | \(0.230818\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.660685 | −0.0523958 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.24490 | 0.570978 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4417 | 1.05283 | 0.526416 | − | 0.850227i | \(-0.323535\pi\) | ||||
0.526416 | + | 0.850227i | \(0.323535\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −12.1630 | −0.946885 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.91806 | −0.380571 | −0.190286 | − | 0.981729i | \(-0.560941\pi\) | ||||
−0.190286 | + | 0.981729i | \(0.560941\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.7169 | −1.27837 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.5708 | 1.48794 | 0.743971 | − | 0.668212i | \(-0.232940\pi\) | ||||
0.743971 | + | 0.668212i | \(0.232940\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.11575 | 0.0843427 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.7338 | 1.93427 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.9866 | 0.970664 | 0.485332 | − | 0.874330i | \(-0.338699\pi\) | ||||
0.485332 | + | 0.874330i | \(0.338699\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.40786 | −0.699280 | −0.349640 | − | 0.936884i | \(-0.613696\pi\) | ||||
−0.349640 | + | 0.936884i | \(0.613696\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.0944 | 0.894045 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.40786 | 0.544636 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.23150 | 0.162318 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.5574 | 1.92163 | 0.960814 | − | 0.277195i | \(-0.0894049\pi\) | ||||
0.960814 | + | 0.277195i | \(0.0894049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.8023 | 1.56936 | 0.784682 | − | 0.619898i | \(-0.212826\pi\) | ||||
0.784682 | + | 0.619898i | \(0.212826\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.57081 | 0.539398 | 0.269699 | − | 0.962945i | \(-0.413076\pi\) | ||||
0.269699 | + | 0.962945i | \(0.413076\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.5708 | −1.24556 | −0.622781 | − | 0.782396i | \(-0.713997\pi\) | ||||
−0.622781 | + | 0.782396i | \(0.713997\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.8495 | 1.89382 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.06061 | 0.284999 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.75510 | 0.332111 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.7382 | 0.954871 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −42.4889 | −2.93902 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0606069 | −0.00417235 | −0.00208618 | − | 0.999998i | \(-0.500664\pi\) | ||||
−0.00208618 | + | 0.999998i | \(0.500664\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.77643 | 0.532833 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.78541 | 0.326362 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.51021 | 0.238288 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.3865 | −0.701856 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.6260 | 1.51515 | 0.757573 | − | 0.652750i | \(-0.226385\pi\) | ||||
0.757573 | + | 0.652750i | \(0.226385\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.11575 | 0.141050 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.59214 | −0.304791 | −0.152396 | − | 0.988320i | \(-0.548699\pi\) | ||||
−0.152396 | + | 0.988320i | \(0.548699\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.986602 | −0.0651965 | −0.0325983 | − | 0.999469i | \(-0.510378\pi\) | ||||
−0.0325983 | + | 0.999469i | \(0.510378\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.5708 | −0.892894 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.2787 | −0.869917 | −0.434959 | − | 0.900450i | \(-0.643237\pi\) | ||||
−0.434959 | + | 0.900450i | \(0.643237\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.16296 | −0.402027 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 24.4630 | 1.58904 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.6429 | 1.65870 | 0.829349 | − | 0.558730i | \(-0.188711\pi\) | ||||
0.829349 | + | 0.558730i | \(0.188711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5236 | 0.935548 | 0.467774 | − | 0.883848i | \(-0.345056\pi\) | ||||
0.467774 | + | 0.883848i | \(0.345056\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 18.5877 | 1.19240 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.75510 | −0.367680 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.7551 | −1.06181 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.2653 | −1.27914 | −0.639568 | − | 0.768735i | \(-0.720887\pi\) | ||||
−0.639568 | + | 0.768735i | \(0.720887\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.9181 | 2.19528 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.58421 | −0.410712 | −0.205356 | − | 0.978687i | \(-0.565835\pi\) | ||||
−0.205356 | + | 0.978687i | \(0.565835\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.26531 | 0.513581 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.69996 | 0.476616 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.7854 | −1.15836 | −0.579179 | − | 0.815200i | \(-0.696627\pi\) | ||||
−0.579179 | + | 0.815200i | \(0.696627\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.292106 | 0.0179439 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −33.5102 | −2.05079 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8495 | −0.905391 | −0.452696 | − | 0.891665i | \(-0.649538\pi\) | ||||
−0.452696 | + | 0.891665i | \(0.649538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.8878 | −1.26884 | −0.634420 | − | 0.772988i | \(-0.718761\pi\) | ||||
−0.634420 | + | 0.772988i | \(0.718761\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.37755 | 0.324279 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.2653 | −1.33779 | −0.668896 | − | 0.743356i | \(-0.733233\pi\) | ||||
−0.668896 | + | 0.743356i | \(0.733233\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.65626 | 0.398500 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.57081 | 0.451637 | 0.225818 | − | 0.974169i | \(-0.427494\pi\) | ||||
0.225818 | + | 0.974169i | \(0.427494\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.724800 | −0.0430849 | −0.0215424 | − | 0.999768i | \(-0.506858\pi\) | ||||
−0.0215424 | + | 0.999768i | \(0.506858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.8709 | 1.05858 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.30550 | 0.313174 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.52360 | −0.499663 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2236 | 0.597267 | 0.298634 | − | 0.954368i | \(-0.403469\pi\) | ||||
0.298634 | + | 0.954368i | \(0.403469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.3776 | −0.662427 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 10.7551 | 0.624074 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.33931 | 0.307753 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.660685 | −0.0379554 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.34725 | −0.306183 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6394 | 1.23502 | 0.617512 | − | 0.786562i | \(-0.288141\pi\) | ||||
0.617512 | + | 0.786562i | \(0.288141\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.11575 | 0.518577 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.986602 | −0.0559451 | −0.0279725 | − | 0.999609i | \(-0.508905\pi\) | ||||
−0.0279725 | + | 0.999609i | \(0.508905\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.8361 | 1.46034 | 0.730172 | − | 0.683263i | \(-0.239440\pi\) | ||||
0.730172 | + | 0.683263i | \(0.239440\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.36065 | 0.133007 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.4283 | −1.48436 | −0.742180 | − | 0.670201i | \(-0.766208\pi\) | ||||
−0.742180 | + | 0.670201i | \(0.766208\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.5708 | 1.09576 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.4551 | −0.695174 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.89218 | 0.159938 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.87632 | −0.379104 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.8878 | −0.818305 | −0.409153 | − | 0.912466i | \(-0.634176\pi\) | ||||
−0.409153 | + | 0.912466i | \(0.634176\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.6732 | 0.858884 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.8709 | −0.648574 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0000 | 1.08947 | 0.544735 | − | 0.838608i | \(-0.316630\pi\) | ||||
0.544735 | + | 0.838608i | \(0.316630\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −43.6046 | −2.36828 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9181 | 0.916164 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2315 | −0.768429 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −14.6866 | −0.790698 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.0641 | −1.39919 | −0.699597 | − | 0.714537i | \(-0.746637\pi\) | ||||
−0.699597 | + | 0.714537i | \(0.746637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.7551 | −0.575707 | −0.287854 | − | 0.957674i | \(-0.592942\pi\) | ||||
−0.287854 | + | 0.957674i | \(0.592942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −35.6126 | −1.89547 | −0.947733 | − | 0.319066i | \(-0.896631\pi\) | ||||
−0.947733 | + | 0.319066i | \(0.896631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.43816 | −0.182479 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.07205 | 0.320470 | 0.160235 | − | 0.987079i | \(-0.448775\pi\) | ||||
0.160235 | + | 0.987079i | \(0.448775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.4283 | 2.28570 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −40.5271 | −2.12712 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.59214 | 0.240364 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.7854 | 1.39819 | 0.699093 | − | 0.715030i | \(-0.253587\pi\) | ||||
0.699093 | + | 0.715030i | \(0.253587\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0606 | 0.523734 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.325917 | 0.0169208 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.8763 | 0.563154 | 0.281577 | − | 0.959539i | \(-0.409142\pi\) | ||||
0.281577 | + | 0.959539i | \(0.409142\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.26180 | −0.116799 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.96176 | 0.306235 | 0.153118 | − | 0.988208i | \(-0.451069\pi\) | ||||
0.153118 | + | 0.988208i | \(0.451069\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0259 | 0.923494 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −19.4079 | −0.991695 | −0.495848 | − | 0.868410i | \(-0.665143\pi\) | ||||
−0.495848 | + | 0.868410i | \(0.665143\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | 0.305788 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.1247 | 0.514669 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.55742 | 0.433878 | 0.216939 | − | 0.976185i | \(-0.430393\pi\) | ||||
0.216939 | + | 0.976185i | \(0.430393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.4630 | −0.830448 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.8157 | −0.544197 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.9449 | 0.750061 | 0.375030 | − | 0.927012i | \(-0.377632\pi\) | ||||
0.375030 | + | 0.927012i | \(0.377632\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.9394 | 0.998218 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.1416 | 1.35539 | 0.677694 | − | 0.735344i | \(-0.262979\pi\) | ||||
0.677694 | + | 0.735344i | \(0.262979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.8709 | −0.540177 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 39.8361 | 1.97460 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.2181 | 1.64253 | 0.821265 | − | 0.570547i | \(-0.193269\pi\) | ||||
0.821265 | + | 0.570547i | \(0.193269\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.7551 | −0.530510 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.6945 | −0.624655 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.40786 | 0.363637 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.9260 | 1.80827 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.7079 | −0.865087 | −0.432544 | − | 0.901613i | \(-0.642384\pi\) | ||||
−0.432544 | + | 0.901613i | \(0.642384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.2047 | 1.08219 | 0.541096 | − | 0.840961i | \(-0.318010\pi\) | ||||
0.541096 | + | 0.840961i | \(0.318010\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.0393 | −0.633991 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.96619 | −0.288724 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.6831 | 0.514585 | 0.257292 | − | 0.966334i | \(-0.417170\pi\) | ||||
0.257292 | + | 0.966334i | \(0.417170\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.23150 | −0.394670 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −51.3046 | −2.45423 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.24490 | 0.250325 | 0.125163 | − | 0.992136i | \(-0.460055\pi\) | ||||
0.125163 | + | 0.992136i | \(0.460055\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.1764 | −0.579826 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.4799 | 1.21059 | 0.605293 | − | 0.796002i | \(-0.293056\pi\) | ||||
0.605293 | + | 0.796002i | \(0.293056\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.8157 | 0.702332 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.9394 | −0.943101 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.9394 | 0.657841 | 0.328920 | − | 0.944358i | \(-0.393315\pi\) | ||||
0.328920 | + | 0.944358i | \(0.393315\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.5708 | 1.20408 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −45.0125 | −2.11487 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.6945 | 0.593823 | 0.296912 | − | 0.954905i | \(-0.404043\pi\) | ||||
0.296912 | + | 0.954905i | \(0.404043\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.0810 | −1.07499 | −0.537495 | − | 0.843267i | \(-0.680629\pi\) | ||||
−0.537495 | + | 0.843267i | \(0.680629\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.16296 | −0.286417 | −0.143208 | − | 0.989693i | \(-0.545742\pi\) | ||||
−0.143208 | + | 0.989693i | \(0.545742\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.11575 | −0.329985 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.5067 | 1.08776 | 0.543880 | − | 0.839163i | \(-0.316955\pi\) | ||||
0.543880 | + | 0.839163i | \(0.316955\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.2449 | −0.611593 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −42.4203 | −1.95463 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.7338 | 1.18324 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.90116 | −0.362530 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.618022 | 0.0282973 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 33.2137 | 1.51757 | 0.758786 | − | 0.651340i | \(-0.225793\pi\) | ||||
0.758786 | + | 0.651340i | \(0.225793\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.3865 | −0.745613 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.76850 | 0.171119 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.7472 | −0.849515 | −0.424758 | − | 0.905307i | \(-0.639641\pi\) | ||||
−0.424758 | + | 0.905307i | \(0.639641\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −30.4024 | −1.37484 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.5574 | −1.19852 | −0.599260 | − | 0.800555i | \(-0.704538\pi\) | ||||
−0.599260 | + | 0.800555i | \(0.704538\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.3776 | 0.511383 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.83612 | −0.172074 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.8539 | −1.20215 | −0.601074 | − | 0.799193i | \(-0.705260\pi\) | ||||
−0.601074 | + | 0.799193i | \(0.705260\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 11.1237 | 0.496970 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.4665 | −0.912556 | −0.456278 | − | 0.889837i | \(-0.650818\pi\) | ||||
−0.456278 | + | 0.889837i | \(0.650818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.292106 | 0.0129985 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.9598 | 1.19497 | 0.597486 | − | 0.801879i | \(-0.296166\pi\) | ||||
0.597486 | + | 0.801879i | \(0.296166\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.12368 | 0.226658 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.8023 | −0.697689 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.03030 | −0.177596 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.1416 | −1.45757 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −44.2653 | −1.94303 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.36065 | −0.366287 | −0.183143 | − | 0.983086i | \(-0.558627\pi\) | ||||
−0.183143 | + | 0.983086i | \(0.558627\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.7248 | −0.818778 | −0.409389 | − | 0.912360i | \(-0.634258\pi\) | ||||
−0.409389 | + | 0.912360i | \(0.634258\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.52360 | −0.110139 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.1630 | 0.833172 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.0720 | −1.04464 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.50670 | 0.238075 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −29.3731 | −1.26754 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.9484 | −1.33304 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.9439 | −1.84630 | −0.923152 | − | 0.384435i | \(-0.874396\pi\) | ||||
−0.923152 | + | 0.384435i | \(0.874396\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.2787 | 0.913157 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.27871 | −0.0547738 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0909 | 0.602484 | 0.301242 | − | 0.953548i | \(-0.402599\pi\) | ||||
0.301242 | + | 0.953548i | \(0.402599\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.3134 | −0.482846 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.7551 | −1.22501 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.0676 | −0.513167 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.7551 | −0.711215 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.713359 | −0.0302260 | −0.0151130 | − | 0.999886i | \(-0.504811\pi\) | ||||
−0.0151130 | + | 0.999886i | \(0.504811\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.2012 | 0.514219 | 0.257110 | − | 0.966382i | \(-0.417230\pi\) | ||||
0.257110 | + | 0.966382i | \(0.417230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 19.2787 | 0.811061 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.1291 | −0.509376 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −16.6260 | −0.696996 | −0.348498 | − | 0.937309i | \(-0.613308\pi\) | ||||
−0.348498 | + | 0.937309i | \(0.613308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.3259 | 0.850613 | 0.425307 | − | 0.905049i | \(-0.360166\pi\) | ||||
0.425307 | + | 0.905049i | \(0.360166\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −60.0676 | −2.50936 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.49330 | 0.270789 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.1496 | 0.797207 | 0.398603 | − | 0.917123i | \(-0.369495\pi\) | ||||
0.398603 | + | 0.917123i | \(0.369495\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −49.3125 | −2.04936 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.26531 | 0.342903 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.57081 | 0.0650564 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.4889 | 1.25841 | 0.629205 | − | 0.777239i | \(-0.283380\pi\) | ||||
0.629205 | + | 0.777239i | \(0.283380\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.8575 | −1.02423 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.1237 | −0.704374 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −42.3259 | −1.73812 | −0.869059 | − | 0.494709i | \(-0.835275\pi\) | ||||
−0.869059 | + | 0.494709i | \(0.835275\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 39.7417 | 1.62652 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.5440 | 0.635111 | 0.317556 | − | 0.948240i | \(-0.397138\pi\) | ||||
0.317556 | + | 0.948240i | \(0.397138\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.1416 | 1.02555 | 0.512774 | − | 0.858524i | \(-0.328618\pi\) | ||||
0.512774 | + | 0.858524i | \(0.328618\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25.1157 | −1.02279 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.9181 | 0.728473 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.0909 | −0.409577 | −0.204789 | − | 0.978806i | \(-0.565651\pi\) | ||||
−0.204789 | + | 0.978806i | \(0.565651\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.18429 | −0.372166 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.0204 | 1.49524 | 0.747620 | − | 0.664127i | \(-0.231196\pi\) | ||||
0.747620 | + | 0.664127i | \(0.231196\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.7551 | −0.433688 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.63389 | 0.347587 | 0.173794 | − | 0.984782i | \(-0.444397\pi\) | ||||
0.173794 | + | 0.984782i | \(0.444397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.47197 | −0.380711 | −0.190355 | − | 0.981715i | \(-0.560964\pi\) | ||||
−0.190355 | + | 0.981715i | \(0.560964\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.9866 | 0.521134 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.5306 | 0.662285 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 96.1014 | 3.83792 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0382 | 0.718091 | 0.359045 | − | 0.933320i | \(-0.383102\pi\) | ||||
0.359045 | + | 0.933320i | \(0.383102\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.137081 | 0.00544847 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.96970 | −0.316268 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.27428 | −0.287766 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.4158 | −0.687882 | −0.343941 | − | 0.938991i | \(-0.611762\pi\) | ||||
−0.343941 | + | 0.938991i | \(0.611762\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.3472 | 0.605236 | 0.302618 | − | 0.953112i | \(-0.402139\pi\) | ||||
0.302618 | + | 0.953112i | \(0.402139\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.8236 | −0.426181 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.05072 | 0.119936 | 0.0599680 | − | 0.998200i | \(-0.480900\pi\) | ||||
0.0599680 | + | 0.998200i | \(0.480900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −61.1834 | −2.40166 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.93939 | −0.311169 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.5708 | −1.00066 | −0.500332 | − | 0.865834i | \(-0.666789\pi\) | ||||
−0.500332 | + | 0.865834i | \(0.666789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.27871 | 0.284403 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.71583 | 0.379051 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.29211 | 0.245106 | 0.122553 | − | 0.992462i | \(-0.460892\pi\) | ||||
0.122553 | + | 0.992462i | \(0.460892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.5102 | −1.53677 | −0.768384 | − | 0.639989i | \(-0.778939\pi\) | ||||
−0.768384 | + | 0.639989i | \(0.778939\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.81571 | −0.341859 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.6314 | 0.915012 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −51.1754 | −1.97856 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.7551 | −1.11008 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.30550 | −0.0503235 | −0.0251617 | − | 0.999683i | \(-0.508010\pi\) | ||||
−0.0251617 | + | 0.999683i | \(0.508010\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.00000 | 0.0769800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.01340 | 0.192681 | 0.0963403 | − | 0.995348i | \(-0.469286\pi\) | ||||
0.0963403 | + | 0.995348i | \(0.469286\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.20470 | 0.161362 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.3865 | 0.398012 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.4079 | −0.742621 | −0.371310 | − | 0.928509i | \(-0.621091\pi\) | ||||
−0.371310 | + | 0.928509i | \(0.621091\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.75510 | 0.181683 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.23150 | 0.0851370 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.56184 | −0.0974570 | −0.0487285 | − | 0.998812i | \(-0.515517\pi\) | ||||
−0.0487285 | + | 0.998812i | \(0.515517\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 12.6945 | 0.482224 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.3259 | −0.619277 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.0338 | 1.13598 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.8495 | −1.46733 | −0.733663 | − | 0.679513i | \(-0.762191\pi\) | ||||
−0.733663 | + | 0.679513i | \(0.762191\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −58.5306 | −2.20752 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.9394 | 0.524988 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.325917 | 0.0122574 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.3393 | 1.32720 | 0.663598 | − | 0.748089i | \(-0.269029\pi\) | ||||
0.663598 | + | 0.748089i | \(0.269029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.8833 | −0.858192 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.4283 | 0.765045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −57.9991 | −2.16602 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.11028 | −0.227875 | −0.113938 | − | 0.993488i | \(-0.536346\pi\) | ||||
−0.113938 | + | 0.993488i | \(0.536346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.49681 | −0.167470 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −32.8495 | −1.22169 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.63935 | 0.135162 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.05072 | −0.0389689 | −0.0194845 | − | 0.999810i | \(-0.506202\pi\) | ||||
−0.0194845 | + | 0.999810i | \(0.506202\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.42919 | −0.349229 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.5708 | −1.16609 | −0.583047 | − | 0.812438i | \(-0.698140\pi\) | ||||
−0.583047 | + | 0.812438i | \(0.698140\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.0169 | 0.480136 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −63.8361 | −2.35143 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.8673 | −1.17226 | −0.586130 | − | 0.810217i | \(-0.699349\pi\) | ||||
−0.586130 | + | 0.810217i | \(0.699349\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 39.8550 | 1.46214 | 0.731069 | − | 0.682304i | \(-0.239022\pi\) | ||||
0.731069 | + | 0.682304i | \(0.239022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.81571 | 0.322983 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.6732 | 0.573451 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.14410 | 0.224500 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.24490 | −0.337351 | −0.168676 | − | 0.985672i | \(-0.553949\pi\) | ||||
−0.168676 | + | 0.985672i | \(0.553949\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 45.8361 | 1.67036 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 19.9012 | 0.724277 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.5912 | −0.821092 | −0.410546 | − | 0.911840i | \(-0.634662\pi\) | ||||
−0.410546 | + | 0.911840i | \(0.634662\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −78.9778 | −2.86671 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.2047 | −0.587420 | −0.293710 | − | 0.955895i | \(-0.594890\pi\) | ||||
−0.293710 | + | 0.955895i | \(0.594890\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.42672 | −0.0516506 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.7889 | −0.605424 | −0.302712 | − | 0.953082i | \(-0.597892\pi\) | ||||
−0.302712 | + | 0.953082i | \(0.597892\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.8922 | 0.536329 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.5921 | −0.596778 | −0.298389 | − | 0.954444i | \(-0.596449\pi\) | ||||
−0.298389 | + | 0.954444i | \(0.596449\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.14605 | 0.113010 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.6945 | −0.670661 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −37.5708 | −1.34611 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.4889 | −0.661584 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.27871 | 0.260120 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.7551 | 0.669398 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.1496 | 1.11036 | 0.555181 | − | 0.831730i | \(-0.312649\pi\) | ||||
0.555181 | + | 0.831730i | \(0.312649\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 42.4889 | 1.51264 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21.5102 | 0.764815 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.660685 | −0.0234321 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.402391 | 0.0142534 | 0.00712670 | − | 0.999975i | \(-0.497731\pi\) | ||||
0.00712670 | + | 0.999975i | \(0.497731\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 31.3463 | 1.10757 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.6945 | 0.871450 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.24490 | 0.255349 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 33.5867 | 1.18231 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −55.3652 | −1.94654 | −0.973268 | − | 0.229671i | \(-0.926235\pi\) | ||||
−0.973268 | + | 0.229671i | \(0.926235\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.1461 | −0.953227 | −0.476613 | − | 0.879113i | \(-0.658136\pi\) | ||||
−0.476613 | + | 0.879113i | \(0.658136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 47.2440 | 1.65692 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.4417 | 0.470841 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.8102 | −1.32281 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.8361 | −0.971487 | −0.485744 | − | 0.874101i | \(-0.661451\pi\) | ||||
−0.485744 | + | 0.874101i | \(0.661451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.2146 | −0.878925 | −0.439463 | − | 0.898261i | \(-0.644831\pi\) | ||||
−0.439463 | + | 0.898261i | \(0.644831\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.1630 | −0.423460 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.03928 | 0.0361391 | 0.0180696 | − | 0.999837i | \(-0.494248\pi\) | ||||
0.0180696 | + | 0.999837i | \(0.494248\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.97867 | −0.242379 | −0.121190 | − | 0.992629i | \(-0.538671\pi\) | ||||
−0.121190 | + | 0.992629i | \(0.538671\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 50.3597 | 1.74696 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.91806 | −0.170197 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.29211 | 0.217487 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −13.3169 | −0.459752 | −0.229876 | − | 0.973220i | \(-0.573832\pi\) | ||||
−0.229876 | + | 0.973220i | \(0.573832\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.7551 | −0.543279 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.1237 | −0.589771 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 19.9921 | 0.686936 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.63935 | 0.0562625 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 48.1014 | 1.64890 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.5653 | 1.04654 | 0.523269 | − | 0.852168i | \(-0.324712\pi\) | ||||
0.523269 | + | 0.852168i | \(0.324712\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.7169 | −0.571705 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 52.4203 | 1.79064 | 0.895322 | − | 0.445419i | \(-0.146945\pi\) | ||||
0.895322 | + | 0.445419i | \(0.146945\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.1416 | 0.653104 | 0.326552 | − | 0.945179i | \(-0.394113\pi\) | ||||
0.326552 | + | 0.945179i | \(0.394113\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | −0.408959 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.8575 | −1.25464 | −0.627321 | − | 0.778761i | \(-0.715849\pi\) | ||||
−0.627321 | + | 0.778761i | \(0.715849\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.5708 | 0.665428 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 38.4506 | 1.30585 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −58.1620 | −1.97301 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.97320 | 0.269852 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.11575 | 0.0377192 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.5370 | 1.26753 | 0.633767 | − | 0.773524i | \(-0.281508\pi\) | ||||
0.633767 | + | 0.773524i | \(0.281508\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.1237 | −0.779942 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.8212 | 0.533029 | 0.266514 | − | 0.963831i | \(-0.414128\pi\) | ||||
0.266514 | + | 0.963831i | \(0.414128\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −49.0507 | −1.65069 | −0.825344 | − | 0.564630i | \(-0.809019\pi\) | ||||
−0.825344 | + | 0.564630i | \(0.809019\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.7338 | 0.865031 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0909 | 0.405973 | 0.202987 | − | 0.979182i | \(-0.434935\pi\) | ||||
0.202987 | + | 0.979182i | \(0.434935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.89218 | −0.298234 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −58.4586 | −1.95844 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 48.6945 | 1.62950 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.9866 | 0.434094 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.4496 | 0.381866 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.0765 | −0.401880 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.40786 | −0.312728 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.54051 | −0.316787 | −0.158394 | − | 0.987376i | \(-0.550632\pi\) | ||||
−0.158394 | + | 0.987376i | \(0.550632\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.618022 | 0.0204985 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.7392 | −0.885910 | −0.442955 | − | 0.896544i | \(-0.646070\pi\) | ||||
−0.442955 | + | 0.896544i | \(0.646070\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.8361 | 1.31838 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 12.0944 | 0.399829 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.12121 | 0.268186 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.0810 | 1.68501 | 0.842504 | − | 0.538691i | \(-0.181081\pi\) | ||||
0.842504 | + | 0.538691i | \(0.181081\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −48.9439 | −1.61276 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.40786 | 0.243569 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.52711 | −0.280067 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.1237 | −0.364956 | −0.182478 | − | 0.983210i | \(-0.558412\pi\) | ||||
−0.182478 | + | 0.983210i | \(0.558412\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.4720 | 1.49028 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.23150 | 0.0730560 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.3055 | 0.500009 | 0.250005 | − | 0.968245i | \(-0.419568\pi\) | ||||
0.250005 | + | 0.968245i | \(0.419568\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −58.4362 | −1.90699 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.7124 | −0.935999 | −0.467999 | − | 0.883729i | \(-0.655025\pi\) | ||||
−0.467999 | + | 0.883729i | \(0.655025\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.8763 | 1.00547 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.23150 | 0.0725907 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.1024 | −0.458265 | −0.229132 | − | 0.973395i | \(-0.573589\pi\) | ||||
−0.229132 | + | 0.973395i | \(0.573589\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 59.7755 | 1.93835 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15.8361 | −0.512982 | −0.256491 | − | 0.966547i | \(-0.582566\pi\) | ||||
−0.256491 | + | 0.966547i | \(0.582566\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 26.5574 | 0.859378 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −44.2653 | −1.43089 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.30550 | 0.171324 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.1024 | −0.680721 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.6508 | 0.375442 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.8023 | 0.701841 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.713359 | −0.0229401 | −0.0114700 | − | 0.999934i | \(-0.503651\pi\) | ||||
−0.0114700 | + | 0.999934i | \(0.503651\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.8182 | −0.379263 | −0.189632 | − | 0.981855i | \(-0.560729\pi\) | ||||
−0.189632 | + | 0.981855i | \(0.560729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.2156 | −0.583966 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.9181 | −0.541257 | −0.270628 | − | 0.962684i | \(-0.587231\pi\) | ||||
−0.270628 | + | 0.962684i | \(0.587231\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 79.6722 | 2.54634 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.70543 | −0.0863776 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.5315 | −0.399694 | −0.199847 | − | 0.979827i | \(-0.564045\pi\) | ||||
−0.199847 | + | 0.979827i | \(0.564045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.57081 | 0.241226 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.5529 | 0.495053 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.0731 | 0.988067 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49.6543 | −1.57732 | −0.788660 | − | 0.614829i | \(-0.789225\pi\) | ||||
−0.788660 | + | 0.614829i | \(0.789225\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.6732 | 1.06859 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −17.5708 | −0.557032 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.5912 | −1.72892 | −0.864461 | − | 0.502700i | \(-0.832340\pi\) | ||||
−0.864461 | + | 0.502700i | \(0.832340\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.8157 | 0.468748 |
(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 | 3380.2.a.n.1.1 | 3 | ||
13.5 | odd | 4 | 260.2.f.a.181.1 | ✓ | 6 | ||
13.8 | odd | 4 | 260.2.f.a.181.2 | yes | 6 | ||
13.12 | even | 2 | 3380.2.a.m.1.1 | 3 | |||
39.5 | even | 4 | 2340.2.c.d.181.5 | 6 | |||
39.8 | even | 4 | 2340.2.c.d.181.2 | 6 | |||
52.31 | even | 4 | 1040.2.k.c.961.5 | 6 | |||
52.47 | even | 4 | 1040.2.k.c.961.6 | 6 | |||
65.8 | even | 4 | 1300.2.d.c.649.2 | 6 | |||
65.18 | even | 4 | 1300.2.d.d.649.2 | 6 | |||
65.34 | odd | 4 | 1300.2.f.e.701.6 | 6 | |||
65.44 | odd | 4 | 1300.2.f.e.701.5 | 6 | |||
65.47 | even | 4 | 1300.2.d.d.649.5 | 6 | |||
65.57 | even | 4 | 1300.2.d.c.649.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.f.a.181.1 | ✓ | 6 | 13.5 | odd | 4 | ||
260.2.f.a.181.2 | yes | 6 | 13.8 | odd | 4 | ||
1040.2.k.c.961.5 | 6 | 52.31 | even | 4 | |||
1040.2.k.c.961.6 | 6 | 52.47 | even | 4 | |||
1300.2.d.c.649.2 | 6 | 65.8 | even | 4 | |||
1300.2.d.c.649.5 | 6 | 65.57 | even | 4 | |||
1300.2.d.d.649.2 | 6 | 65.18 | even | 4 | |||
1300.2.d.d.649.5 | 6 | 65.47 | even | 4 | |||
1300.2.f.e.701.5 | 6 | 65.44 | odd | 4 | |||
1300.2.f.e.701.6 | 6 | 65.34 | odd | 4 | |||
2340.2.c.d.181.2 | 6 | 39.8 | even | 4 | |||
2340.2.c.d.181.5 | 6 | 39.5 | even | 4 | |||
3380.2.a.m.1.1 | 3 | 13.12 | even | 2 | |||
3380.2.a.n.1.1 | 3 | 1.1 | even | 1 | trivial |