Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,2,Mod(1,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, 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("3584.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.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: | \(28.6183840844\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.18857984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 9x^{4} + 16x^{3} + 6x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.752719\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1 |
$q$-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 | ||||||||
\(3\) | −2.53584 | −1.46407 | −0.732034 | − | 0.681268i | \(-0.761429\pi\) | ||||
−0.732034 | + | 0.681268i | \(0.761429\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.47134 | −0.658002 | −0.329001 | − | 0.944330i | \(-0.606712\pi\) | ||||
−0.329001 | + | 0.944330i | \(0.606712\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.43049 | 1.14350 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.35014 | 1.61313 | 0.806564 | − | 0.591146i | \(-0.201324\pi\) | ||||
0.806564 | + | 0.591146i | \(0.201324\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.55212 | 0.985181 | 0.492590 | − | 0.870261i | \(-0.336050\pi\) | ||||
0.492590 | + | 0.870261i | \(0.336050\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.73108 | 0.963359 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.73782 | −0.664018 | −0.332009 | − | 0.943276i | \(-0.607727\pi\) | ||||
−0.332009 | + | 0.943276i | \(0.607727\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.61663 | 1.97679 | 0.988395 | − | 0.151908i | \(-0.0485417\pi\) | ||||
0.988395 | + | 0.151908i | \(0.0485417\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.53584 | 0.553366 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.17919 | −1.28845 | −0.644225 | − | 0.764836i | \(-0.722820\pi\) | ||||
−0.644225 | + | 0.764836i | \(0.722820\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.83517 | −0.567034 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.09166 | −0.210090 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.49543 | −1.57756 | −0.788781 | − | 0.614674i | \(-0.789287\pi\) | ||||
−0.788781 | + | 0.614674i | \(0.789287\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0009 | 1.79621 | 0.898105 | − | 0.439782i | \(-0.144944\pi\) | ||||
0.898105 | + | 0.439782i | \(0.144944\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −13.5671 | −2.36173 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.47134 | 0.248701 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.333865 | 0.0548871 | 0.0274435 | − | 0.999623i | \(-0.491263\pi\) | ||||
0.0274435 | + | 0.999623i | \(0.491263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.00761 | −1.44237 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.30058 | −0.203117 | −0.101559 | − | 0.994830i | \(-0.532383\pi\) | ||||
−0.101559 | + | 0.994830i | \(0.532383\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.82230 | 0.887892 | 0.443946 | − | 0.896053i | \(-0.353578\pi\) | ||||
0.443946 | + | 0.896053i | \(0.353578\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.04741 | −0.752423 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.00348 | −1.31329 | −0.656646 | − | 0.754199i | \(-0.728026\pi\) | ||||
−0.656646 | + | 0.754199i | \(0.728026\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.94267 | 0.972169 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.20997 | −0.166203 | −0.0831014 | − | 0.996541i | \(-0.526483\pi\) | ||||
−0.0831014 | + | 0.996541i | \(0.526483\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.87186 | −1.06144 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −21.8504 | −2.89416 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.71738 | −0.353773 | −0.176887 | − | 0.984231i | \(-0.556603\pi\) | ||||
−0.176887 | + | 0.984231i | \(0.556603\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.48221 | 0.573888 | 0.286944 | − | 0.957947i | \(-0.407361\pi\) | ||||
0.286944 | + | 0.957947i | \(0.407361\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.43049 | −0.432201 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.22636 | −0.648250 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.45438 | −1.03287 | −0.516434 | − | 0.856327i | \(-0.672741\pi\) | ||||
−0.516434 | + | 0.856327i | \(0.672741\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.6694 | 1.88638 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.46718 | −0.292801 | −0.146400 | − | 0.989225i | \(-0.546769\pi\) | ||||
−0.146400 | + | 0.989225i | \(0.546769\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.31997 | −0.739696 | −0.369848 | − | 0.929092i | \(-0.620590\pi\) | ||||
−0.369848 | + | 0.929092i | \(0.620590\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.18954 | 0.830177 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.35014 | −0.609705 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3091 | 1.27237 | 0.636186 | − | 0.771536i | \(-0.280511\pi\) | ||||
0.636186 | + | 0.771536i | \(0.280511\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.52320 | −0.835911 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.41031 | −0.593859 | −0.296929 | − | 0.954899i | \(-0.595963\pi\) | ||||
−0.296929 | + | 0.954899i | \(0.595963\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.02825 | 0.436925 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.5431 | 2.30966 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.44811 | 0.683498 | 0.341749 | − | 0.939791i | \(-0.388981\pi\) | ||||
0.341749 | + | 0.939791i | \(0.388981\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.55212 | −0.372363 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −25.3606 | −2.62977 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.6780 | −1.30073 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.95282 | 0.502883 | 0.251441 | − | 0.967872i | \(-0.419095\pi\) | ||||
0.251441 | + | 0.967872i | \(0.419095\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.3536 | 1.84461 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.20897 | 0.916327 | 0.458164 | − | 0.888868i | \(-0.348507\pi\) | ||||
0.458164 | + | 0.888868i | \(0.348507\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.26803 | −0.124942 | −0.0624712 | − | 0.998047i | \(-0.519898\pi\) | ||||
−0.0624712 | + | 0.998047i | \(0.519898\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.73108 | −0.364116 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.25678 | 0.121497 | 0.0607487 | − | 0.998153i | \(-0.480651\pi\) | ||||
0.0607487 | + | 0.998153i | \(0.480651\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.3048 | −1.08280 | −0.541401 | − | 0.840764i | \(-0.682106\pi\) | ||||
−0.541401 | + | 0.840764i | \(0.682106\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.846628 | −0.0803584 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.9407 | 1.40550 | 0.702751 | − | 0.711436i | \(-0.251955\pi\) | ||||
0.702751 | + | 0.711436i | \(0.251955\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.09166 | 0.847802 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.1855 | 1.12655 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.73782 | 0.250975 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.6240 | 1.60218 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.29807 | 0.297377 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.5282 | 1.03111 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.3442 | 1.36158 | 0.680790 | − | 0.732478i | \(-0.261637\pi\) | ||||
0.680790 | + | 0.732478i | \(0.261637\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.7644 | −1.29994 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.07758 | 0.531001 | 0.265500 | − | 0.964111i | \(-0.414463\pi\) | ||||
0.265500 | + | 0.964111i | \(0.414463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.61663 | −0.747156 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.60620 | 0.138239 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.27393 | 0.706889 | 0.353445 | − | 0.935455i | \(-0.385010\pi\) | ||||
0.353445 | + | 0.935455i | \(0.385010\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 22.5020 | 1.90859 | 0.954296 | − | 0.298863i | \(-0.0966073\pi\) | ||||
0.954296 | + | 0.298863i | \(0.0966073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.8314 | 1.92275 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 19.0043 | 1.58922 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.4996 | 1.03804 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.53584 | −0.209153 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.36212 | 0.357358 | 0.178679 | − | 0.983907i | \(-0.442818\pi\) | ||||
0.178679 | + | 0.983907i | \(0.442818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0941 | −1.30972 | −0.654858 | − | 0.755752i | \(-0.727272\pi\) | ||||
−0.654858 | + | 0.755752i | \(0.727272\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.39206 | −0.759303 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −14.7146 | −1.18191 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.677651 | −0.0540824 | −0.0270412 | − | 0.999634i | \(-0.508609\pi\) | ||||
−0.0270412 | + | 0.999634i | \(0.508609\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.06830 | 0.243332 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.17919 | 0.486988 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.49003 | −0.195034 | −0.0975171 | − | 0.995234i | \(-0.531090\pi\) | ||||
−0.0975171 | + | 0.995234i | \(0.531090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 19.9618 | 1.55402 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.0052 | 1.62543 | 0.812716 | − | 0.582660i | \(-0.197988\pi\) | ||||
0.812716 | + | 0.582660i | \(0.197988\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.382445 | −0.0294189 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 29.5593 | 2.26045 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.2107 | −1.61262 | −0.806310 | − | 0.591493i | \(-0.798539\pi\) | ||||
−0.806310 | + | 0.591493i | \(0.798539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.83517 | 0.214319 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.89086 | 0.517949 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.14067 | 0.384232 | 0.192116 | − | 0.981372i | \(-0.438465\pi\) | ||||
0.192116 | + | 0.981372i | \(0.438465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.81366 | −0.506455 | −0.253228 | − | 0.967407i | \(-0.581492\pi\) | ||||
−0.253228 | + | 0.967407i | \(0.581492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.3662 | −0.840212 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.491228 | −0.0361158 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.6477 | −1.07115 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.09166 | 0.0794065 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.1650 | −1.24202 | −0.621010 | − | 0.783803i | \(-0.713277\pi\) | ||||
−0.621010 | + | 0.783803i | \(0.713277\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.9566 | −1.36453 | −0.682263 | − | 0.731107i | \(-0.739004\pi\) | ||||
−0.682263 | + | 0.731107i | \(0.739004\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.2532 | 0.949083 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.08800 | 0.220011 | 0.110005 | − | 0.993931i | \(-0.464913\pi\) | ||||
0.110005 | + | 0.993931i | \(0.464913\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.49652 | 0.106085 | 0.0530426 | − | 0.998592i | \(-0.483108\pi\) | ||||
0.0530426 | + | 0.998592i | \(0.483108\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.4390 | 1.51219 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.49543 | 0.596262 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.91360 | 0.133651 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.1976 | −1.47334 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 46.1002 | 3.18882 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 20.0643 | 1.38129 | 0.690643 | − | 0.723196i | \(-0.257328\pi\) | ||||
0.690643 | + | 0.723196i | \(0.257328\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.25638 | 0.428680 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.56656 | −0.584235 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0009 | −0.678903 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.0264 | 1.08297 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.72506 | −0.654178 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1569 | 1.08194 | 0.540971 | − | 0.841041i | \(-0.318057\pi\) | ||||
0.540971 | + | 0.841041i | \(0.318057\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.72603 | −0.648402 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.81256 | 0.452165 | 0.226083 | − | 0.974108i | \(-0.427408\pi\) | ||||
0.226083 | + | 0.974108i | \(0.427408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.88613 | −0.455048 | −0.227524 | − | 0.973772i | \(-0.573063\pi\) | ||||
−0.227524 | + | 0.973772i | \(0.573063\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.5671 | 0.892651 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.00584477 | 0.000382903 0 | 0.000191452 | − | 1.00000i | \(-0.499939\pi\) | ||||
0.000191452 | 1.00000i | \(0.499939\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 13.2471 | 0.864148 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.6781 | −1.86284 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.7496 | −0.824703 | −0.412351 | − | 0.911025i | \(-0.635292\pi\) | ||||
−0.412351 | + | 0.911025i | \(0.635292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.1923 | 1.62278 | 0.811389 | − | 0.584507i | \(-0.198712\pi\) | ||||
0.811389 | + | 0.584507i | \(0.198712\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3526 | 1.43392 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.47134 | −0.0940002 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.6073 | 1.94749 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.7197 | 0.869450 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.7552 | 1.24694 | 0.623468 | − | 0.781849i | \(-0.285723\pi\) | ||||
0.623468 | + | 0.781849i | \(0.285723\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −33.0595 | −2.07843 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.2150 | −0.639688 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.70413 | 0.231057 | 0.115529 | − | 0.993304i | \(-0.463144\pi\) | ||||
0.115529 | + | 0.993304i | \(0.463144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.333865 | −0.0207454 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.1435 | −1.80394 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.22781 | −0.507348 | −0.253674 | − | 0.967290i | \(-0.581639\pi\) | ||||
−0.253674 | + | 0.967290i | \(0.581639\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.78028 | 0.109362 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.3514 | −1.00069 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.57387 | 0.0959606 | 0.0479803 | − | 0.998848i | \(-0.484722\pi\) | ||||
0.0479803 | + | 0.998848i | \(0.484722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.5357 | −1.42969 | −0.714845 | − | 0.699283i | \(-0.753503\pi\) | ||||
−0.714845 | + | 0.699283i | \(0.753503\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.00761 | 0.545166 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.1686 | −0.914699 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.62846 | −0.398265 | −0.199133 | − | 0.979973i | \(-0.563812\pi\) | ||||
−0.199133 | + | 0.979973i | \(0.563812\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 34.3079 | 2.05396 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.3905 | 1.15674 | 0.578370 | − | 0.815774i | \(-0.303689\pi\) | ||||
0.578370 | + | 0.815774i | \(0.303689\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.65625 | 0.276785 | 0.138393 | − | 0.990377i | \(-0.455806\pi\) | ||||
0.138393 | + | 0.990377i | \(0.455806\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 32.1493 | 1.90436 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.30058 | 0.0767710 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50435 | −0.559080 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.5596 | −0.736255 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.3806 | 1.59959 | 0.799796 | − | 0.600272i | \(-0.204941\pi\) | ||||
0.799796 | + | 0.600272i | \(0.204941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.99819 | 0.232783 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.84053 | −0.338902 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −21.9492 | −1.26936 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.82230 | −0.335592 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −23.3525 | −1.34157 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.59484 | −0.377619 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.34520 | 0.533359 | 0.266679 | − | 0.963785i | \(-0.414074\pi\) | ||||
0.266679 | + | 0.963785i | \(0.414074\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.21551 | 0.182924 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.237720 | 0.0134798 | 0.00673992 | − | 0.999977i | \(-0.497855\pi\) | ||||
0.00673992 | + | 0.999977i | \(0.497855\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.86308 | 0.274878 | 0.137439 | − | 0.990510i | \(-0.456113\pi\) | ||||
0.137439 | + | 0.990510i | \(0.456113\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.04741 | 0.284389 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.8299 | 1.33842 | 0.669210 | − | 0.743073i | \(-0.266633\pi\) | ||||
0.669210 | + | 0.743073i | \(0.266633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −45.4518 | −2.54481 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.18699 | −0.177881 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −23.5908 | −1.31262 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.0709 | −0.558631 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 28.6671 | 1.58530 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.00348 | 0.496378 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.23230 | −0.452488 | −0.226244 | − | 0.974071i | \(-0.572645\pi\) | ||||
−0.226244 | + | 0.974071i | \(0.572645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.14532 | 0.0627632 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.4392 | 0.679628 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.2587 | −1.10356 | −0.551780 | − | 0.833990i | \(-0.686051\pi\) | ||||
−0.551780 | + | 0.833990i | \(0.686051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −37.8872 | −2.05775 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 53.5061 | 2.89752 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.0550 | −1.24124 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.7190 | 1.16594 | 0.582968 | − | 0.812495i | \(-0.301891\pi\) | ||||
0.582968 | + | 0.812495i | \(0.301891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 15.6559 | 0.838043 | 0.419021 | − | 0.907976i | \(-0.362373\pi\) | ||||
0.419021 | + | 0.907976i | \(0.362373\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.87770 | −0.206977 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.1663 | 0.807219 | 0.403610 | − | 0.914931i | \(-0.367755\pi\) | ||||
0.403610 | + | 0.914931i | \(0.367755\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.63005 | 0.192663 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.94267 | −0.367445 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −35.1850 | −1.85699 | −0.928496 | − | 0.371342i | \(-0.878898\pi\) | ||||
−0.928496 | + | 0.371342i | \(0.878898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 55.2462 | 2.90770 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −44.6918 | −2.34571 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.29880 | 0.486721 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.1677 | −0.530751 | −0.265376 | − | 0.964145i | \(-0.585496\pi\) | ||||
−0.265376 | + | 0.964145i | \(0.585496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.46164 | −0.232264 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.20997 | 0.0628187 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0935 | 0.574400 | 0.287200 | − | 0.957871i | \(-0.407276\pi\) | ||||
0.287200 | + | 0.957871i | \(0.407276\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −29.2336 | −1.50962 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −30.1768 | −1.55418 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.0994 | 1.85430 | 0.927152 | − | 0.374686i | \(-0.122249\pi\) | ||||
0.927152 | + | 0.374686i | \(0.122249\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −38.9105 | −1.99345 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.18325 | 0.367047 | 0.183523 | − | 0.983015i | \(-0.441250\pi\) | ||||
0.183523 | + | 0.983015i | \(0.441250\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.87186 | 0.401187 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 19.9734 | 1.01530 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.6497 | −1.30049 | −0.650245 | − | 0.759725i | \(-0.725334\pi\) | ||||
−0.650245 | + | 0.759725i | \(0.725334\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.9175 | 0.855554 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.4118 | −0.777422 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.6395 | −0.837223 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1738 | 1.41400 | 0.707002 | − | 0.707212i | \(-0.250047\pi\) | ||||
0.707002 | + | 0.707212i | \(0.250047\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.8504 | 1.09389 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.2803 | 0.513371 | 0.256686 | − | 0.966495i | \(-0.417369\pi\) | ||||
0.256686 | + | 0.966495i | \(0.417369\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.5243 | 1.76959 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.0692 | 0.550031 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.78623 | 0.0885399 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.0375 | −0.941343 | −0.470672 | − | 0.882309i | \(-0.655988\pi\) | ||||
−0.470672 | + | 0.882309i | \(0.655988\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.9814 | −1.03493 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.71738 | 0.133714 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.96039 | 0.390760 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −57.0614 | −2.79431 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.952050 | 0.0465107 | 0.0232553 | − | 0.999730i | \(-0.492597\pi\) | ||||
0.0232553 | + | 0.999730i | \(0.492597\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.1640 | 1.32389 | 0.661946 | − | 0.749552i | \(-0.269731\pi\) | ||||
0.661946 | + | 0.749552i | \(0.269731\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.8864 | −1.50175 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.76218 | 0.376521 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.48221 | −0.216909 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −48.1920 | −2.32673 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.4598 | 1.75621 | 0.878104 | − | 0.478470i | \(-0.158809\pi\) | ||||
0.878104 | + | 0.478470i | \(0.158809\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.9245 | −0.909456 | −0.454728 | − | 0.890630i | \(-0.650263\pi\) | ||||
−0.454728 | + | 0.890630i | \(0.650263\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.6971 | −1.51976 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −53.2437 | −2.54699 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.9378 | −0.999306 | −0.499653 | − | 0.866226i | \(-0.666539\pi\) | ||||
−0.499653 | + | 0.866226i | \(0.666539\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.43049 | 0.163357 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.7793 | 1.36734 | 0.683672 | − | 0.729790i | \(-0.260382\pi\) | ||||
0.683672 | + | 0.729790i | \(0.260382\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.48734 | −0.449743 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.0616 | −0.523197 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.1940 | −1.04740 | −0.523700 | − | 0.851903i | \(-0.675449\pi\) | ||||
−0.523700 | + | 0.851903i | \(0.675449\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.95831 | −0.327654 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 40.8120 | 1.91751 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.22636 | 0.245016 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.6211 | 1.15173 | 0.575863 | − | 0.817546i | \(-0.304666\pi\) | ||||
0.575863 | + | 0.817546i | \(0.304666\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.98876 | 0.139504 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.4057 | −0.857239 | −0.428619 | − | 0.903485i | \(-0.641000\pi\) | ||||
−0.428619 | + | 0.903485i | \(0.641000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.8454 | 1.89825 | 0.949123 | − | 0.314905i | \(-0.101973\pi\) | ||||
0.949123 | + | 0.314905i | \(0.101973\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 37.3140 | 1.73040 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.56396 | −0.350018 | −0.175009 | − | 0.984567i | \(-0.555996\pi\) | ||||
−0.175009 | + | 0.984567i | \(0.555996\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.45438 | 0.390387 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.71841 | 0.0791804 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.1501 | 1.43228 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.4296 | −1.12091 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.15081 | −0.190052 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.8779 | 1.73069 | 0.865343 | − | 0.501181i | \(-0.167101\pi\) | ||||
0.865343 | + | 0.501181i | \(0.167101\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.18593 | 0.0540737 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.6694 | −0.712984 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.28727 | −0.330898 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.7938 | −0.851630 | −0.425815 | − | 0.904810i | \(-0.640013\pi\) | ||||
−0.425815 | + | 0.904810i | \(0.640013\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.31432 | 0.285543 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.9445 | −0.539045 | −0.269523 | − | 0.962994i | \(-0.586866\pi\) | ||||
−0.269523 | + | 0.962994i | \(0.586866\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.2589 | 1.04753 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −27.0043 | −1.21376 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.46718 | 0.110668 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.0387 | −0.717992 | −0.358996 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358996 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −53.2659 | −2.37975 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.25982 | 0.100760 | 0.0503801 | − | 0.998730i | \(-0.483957\pi\) | ||||
0.0503801 | + | 0.998730i | \(0.483957\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.5495 | −0.602945 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.969820 | 0.0430712 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.8827 | 0.881285 | 0.440642 | − | 0.897683i | \(-0.354751\pi\) | ||||
0.440642 | + | 0.897683i | \(0.354751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.31997 | 0.279579 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.40642 | −0.415303 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.86569 | 0.0822123 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −48.1699 | −2.11851 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 53.7870 | 2.36099 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.9222 | −0.653754 | −0.326877 | − | 0.945067i | \(-0.605996\pi\) | ||||
−0.326877 | + | 0.945067i | \(0.605996\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.2480 | −0.710474 | −0.355237 | − | 0.934776i | \(-0.615600\pi\) | ||||
−0.355237 | + | 0.934776i | \(0.615600\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.18954 | −0.313777 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.3806 | −1.19272 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.1823 | 0.660101 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.32197 | −0.404539 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.61983 | −0.200107 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.84914 | −0.0799455 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.0359 | −0.562542 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.35014 | 0.230447 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.7623 | 1.70952 | 0.854758 | − | 0.519027i | \(-0.173705\pi\) | ||||
0.854758 | + | 0.519027i | \(0.173705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 17.2784 | 0.741485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.6331 | 0.712486 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.7280 | 1.57038 | 0.785189 | − | 0.619256i | \(-0.212566\pi\) | ||||
0.785189 | + | 0.619256i | \(0.212566\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.3762 | 0.656240 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −73.2020 | −3.11851 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.3091 | −0.480912 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.24568 | 0.0528760 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.0967 | 1.06338 | 0.531691 | − | 0.846939i | \(-0.321557\pi\) | ||||
0.531691 | + | 0.846939i | \(0.321557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.6815 | 0.874734 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 37.1443 | 1.56823 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.5781 | 1.16228 | 0.581138 | − | 0.813805i | \(-0.302608\pi\) | ||||
0.581138 | + | 0.813805i | \(0.302608\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.9828 | −0.924822 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.52320 | 0.315945 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.4129 | −1.06536 | −0.532682 | − | 0.846315i | \(-0.678816\pi\) | ||||
−0.532682 | + | 0.846315i | \(0.678816\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.29583 | −0.263472 | −0.131736 | − | 0.991285i | \(-0.542055\pi\) | ||||
−0.131736 | + | 0.991285i | \(0.542055\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 43.5278 | 1.81840 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 17.5190 | 0.730594 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.39622 | 0.349539 | 0.174770 | − | 0.984609i | \(-0.444082\pi\) | ||||
0.174770 | + | 0.984609i | \(0.444082\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 48.0709 | 1.99776 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.41031 | 0.224458 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.47354 | −0.268106 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.9290 | −0.741273 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.7104 | −1.51520 | −0.757601 | − | 0.652718i | \(-0.773629\pi\) | ||||
−0.757601 | + | 0.652718i | \(0.773629\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 86.1737 | 3.55073 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.83068 | −0.322111 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.3627 | −1.53430 | −0.767152 | − | 0.641466i | \(-0.778327\pi\) | ||||
−0.767152 | + | 0.641466i | \(0.778327\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.02825 | −0.165142 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3.79493 | −0.155316 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.2380 | −0.745185 | −0.372592 | − | 0.927995i | \(-0.621531\pi\) | ||||
−0.372592 | + | 0.927995i | \(0.621531\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.2357 | 0.458314 | 0.229157 | − | 0.973389i | \(-0.426403\pi\) | ||||
0.229157 | + | 0.973389i | \(0.426403\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.0027 | −1.18108 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −25.9309 | −1.05424 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1984 | −0.657473 | −0.328737 | − | 0.944422i | \(-0.606623\pi\) | ||||
−0.328737 | + | 0.944422i | \(0.606623\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.5431 | −0.872969 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −31.9814 | −1.29383 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.5593 | −0.951550 | −0.475775 | − | 0.879567i | \(-0.657832\pi\) | ||||
−0.475775 | + | 0.879567i | \(0.657832\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.85257 | −0.195675 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.5014 | −0.704580 | −0.352290 | − | 0.935891i | \(-0.614597\pi\) | ||||
−0.352290 | + | 0.935891i | \(0.614597\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.7093 | 0.912764 | 0.456382 | − | 0.889784i | \(-0.349145\pi\) | ||||
0.456382 | + | 0.889784i | \(0.349145\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.74556 | 0.270690 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.44811 | −0.258338 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.78596 | −0.111439 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −116.903 | −4.66865 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.914061 | −0.0364460 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.05047 | −0.0418185 | −0.0209092 | − | 0.999781i | \(-0.506656\pi\) | ||||
−0.0209092 | + | 0.999781i | \(0.506656\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −50.8799 | −2.02230 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.5765 | −0.895922 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.55212 | 0.140740 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.46365 | −0.334817 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.48096 | −0.216485 | −0.108242 | − | 0.994125i | \(-0.534522\pi\) | ||||
−0.108242 | + | 0.994125i | \(0.534522\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.22391 | −0.0482662 | −0.0241331 | − | 0.999709i | \(-0.507683\pi\) | ||||
−0.0241331 | + | 0.999709i | \(0.507683\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.7234 | 0.855360 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.7538 | −0.697975 | −0.348987 | − | 0.937127i | \(-0.613474\pi\) | ||||
−0.348987 | + | 0.937127i | \(0.613474\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.5384 | −0.570682 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 25.3606 | 0.993961 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −27.0233 | −1.05751 | −0.528753 | − | 0.848776i | \(-0.677340\pi\) | ||||
−0.528753 | + | 0.848776i | \(0.677340\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.94216 | −0.349399 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −21.6806 | −0.845841 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.2572 | 1.13970 | 0.569849 | − | 0.821750i | \(-0.307002\pi\) | ||||
0.569849 | + | 0.821750i | \(0.307002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.24828 | −0.0485523 | −0.0242762 | − | 0.999705i | \(-0.507728\pi\) | ||||
−0.0242762 | + | 0.999705i | \(0.507728\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 24.6612 | 0.957762 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.6780 | 0.491630 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 52.4949 | 2.03261 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −40.9712 | −1.58404 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.9805 | 0.925756 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0287 | 0.617861 | 0.308931 | − | 0.951085i | \(-0.400029\pi\) | ||||
0.308931 | + | 0.951085i | \(0.400029\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.09504 | 0.119128 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.28162 | −0.126123 | −0.0630614 | − | 0.998010i | \(-0.520086\pi\) | ||||
−0.0630614 | + | 0.998010i | \(0.520086\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.95282 | −0.190072 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.2756 | −0.662001 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.1046 | −0.692755 | −0.346377 | − | 0.938095i | \(-0.612588\pi\) | ||||
−0.346377 | + | 0.938095i | \(0.612588\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.1737 | −0.465134 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17.4621 | 0.666222 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.29797 | −0.163740 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.3412 | 0.621648 | 0.310824 | − | 0.950467i | \(-0.399395\pi\) | ||||
0.310824 | + | 0.950467i | \(0.399395\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.3536 | −0.697196 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −33.1080 | −1.25586 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.56076 | 0.134873 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −0.0148214 | −0.000560597 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.84196 | −0.220648 | −0.110324 | − | 0.993896i | \(-0.535189\pi\) | ||||
−0.110324 | + | 0.993896i | \(0.535189\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.87679 | 0.108500 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −33.5927 | −1.26517 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.20897 | −0.346339 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.7622 | −0.516851 | −0.258426 | − | 0.966031i | \(-0.583204\pi\) | ||||
−0.258426 | + | 0.966031i | \(0.583204\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 38.7958 | 1.45495 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −61.7972 | −2.31432 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.9618 | −1.04571 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 32.3309 | 1.20742 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.5551 | 0.953045 | 0.476522 | − | 0.879162i | \(-0.341897\pi\) | ||||
0.476522 | + | 0.879162i | \(0.341897\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.26803 | 0.0472238 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −63.8836 | −2.37586 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.0860 | 0.894531 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.7659 | −1.10395 | −0.551977 | − | 0.833859i | \(-0.686126\pi\) | ||||
−0.551977 | + | 0.833859i | \(0.686126\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.1131 | −1.26345 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.9404 | −0.589577 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32.2469 | 1.19107 | 0.595533 | − | 0.803331i | \(-0.296941\pi\) | ||||
0.595533 | + | 0.803331i | \(0.296941\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.73108 | 0.137623 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −45.2322 | −1.66615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.37793 | −0.308187 | −0.154094 | − | 0.988056i | \(-0.549246\pi\) | ||||
−0.154094 | + | 0.988056i | \(0.549246\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −77.6152 | −2.85127 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.4881 | 0.935068 | 0.467534 | − | 0.883975i | \(-0.345143\pi\) | ||||
0.467534 | + | 0.883975i | \(0.345143\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.41814 | −0.235142 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −18.5600 | −0.679076 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.25678 | −0.0459217 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.7490 | 1.01258 | 0.506288 | − | 0.862365i | \(-0.331017\pi\) | ||||
0.506288 | + | 0.862365i | \(0.331017\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −50.0960 | −1.82560 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 23.6798 | 0.861795 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.5446 | −0.455942 | −0.227971 | − | 0.973668i | \(-0.573209\pi\) | ||||
−0.227971 | + | 0.973668i | \(0.573209\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 83.8337 | 3.04297 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.9458 | 1.33929 | 0.669643 | − | 0.742683i | \(-0.266447\pi\) | ||||
0.669643 | + | 0.742683i | \(0.266447\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.3048 | 0.409261 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.8189 | 0.499623 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.65248 | −0.348531 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.5020 | −1.24417 | −0.622087 | − | 0.782948i | \(-0.713715\pi\) | ||||
−0.622087 | + | 0.782948i | \(0.713715\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.39308 | −0.338283 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.1677 | −0.437641 | −0.218820 | − | 0.975765i | \(-0.570221\pi\) | ||||
−0.218820 | + | 0.975765i | \(0.570221\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.3542 | −1.01851 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.846628 | 0.0303726 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.2066 | −0.401520 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.1998 | −0.472325 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.27412 | 0.331430 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.997052 | 0.0355863 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.2744 | −0.865289 | −0.432644 | − | 0.901565i | \(-0.642419\pi\) | ||||
−0.432644 | + | 0.901565i | \(0.642419\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.8644 | 0.742793 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.9407 | −0.531230 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.9214 | 0.565384 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.51451 | −0.160113 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.58429 | 0.162384 | 0.0811919 | − | 0.996698i | \(-0.474127\pi\) | ||||
0.0811919 | + | 0.996698i | \(0.474127\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.6499 | 0.872050 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.1202 | 0.781578 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −33.8127 | −1.19323 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.09166 | −0.320439 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.99109 | −0.140493 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.9465 | −1.12318 | −0.561589 | − | 0.827416i | \(-0.689810\pi\) | ||||
−0.561589 | + | 0.827416i | \(0.689810\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.10676 | −0.319781 | −0.159891 | − | 0.987135i | \(-0.551114\pi\) | ||||
−0.159891 | + | 0.987135i | \(0.551114\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 59.6827 | 2.09316 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.66367 | 0.128333 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 50.1686 | 1.75518 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −12.1855 | −0.425796 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.5354 | −0.995891 | −0.497946 | − | 0.867208i | \(-0.665912\pi\) | ||||
−0.497946 | + | 0.867208i | \(0.665912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.58038 | 0.264235 | 0.132118 | − | 0.991234i | \(-0.457822\pi\) | ||||
0.132118 | + | 0.991234i | \(0.457822\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 38.4651 | 1.33918 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.7460 | −0.617087 | −0.308544 | − | 0.951210i | \(-0.599842\pi\) | ||||
−0.308544 | + | 0.951210i | \(0.599842\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.6545 | −0.370046 | −0.185023 | − | 0.982734i | \(-0.559236\pi\) | ||||
−0.185023 | + | 0.982734i | \(0.559236\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.8087 | 0.583088 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.73782 | −0.0948598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.9057 | −1.06954 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.9175 | −0.377365 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 34.1821 | 1.18010 | 0.590048 | − | 0.807368i | \(-0.299109\pi\) | ||||
0.590048 | + | 0.807368i | \(0.299109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 43.1724 | 1.48870 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −49.1713 | −1.69355 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.562705 | 0.0193577 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.6240 | −0.605569 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.8075 | −0.405233 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.06301 | −0.0707192 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.6019 | 0.979312 | 0.489656 | − | 0.871916i | \(-0.337122\pi\) | ||||
0.489656 | + | 0.871916i | \(0.337122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −43.4916 | −1.48738 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.18332 | −0.142899 | −0.0714497 | − | 0.997444i | \(-0.522763\pi\) | ||||
−0.0714497 | + | 0.997444i | \(0.522763\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.9454 | 0.885245 | 0.442622 | − | 0.896708i | \(-0.354048\pi\) | ||||
0.442622 | + | 0.896708i | \(0.354048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.29807 | −0.112398 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.24075 | 0.0762759 | 0.0381379 | − | 0.999272i | \(-0.487857\pi\) | ||||
0.0381379 | + | 0.999272i | \(0.487857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.2081 | 1.06111 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.1015 | 0.818531 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 60.5053 | 2.05250 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.0310 | −1.01756 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 16.9906 | 0.575045 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.5282 | −0.389723 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.6413 | −1.03468 | −0.517341 | − | 0.855779i | \(-0.673078\pi\) | ||||
−0.517341 | + | 0.855779i | \(0.673078\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −69.4328 | −2.34191 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.8271 | 1.34181 | 0.670905 | − | 0.741543i | \(-0.265906\pi\) | ||||
0.670905 | + | 0.741543i | \(0.265906\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.90916 | 0.0979010 | 0.0489505 | − | 0.998801i | \(-0.484412\pi\) | ||||
0.0489505 | + | 0.998801i | \(0.484412\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.1388 | −0.340811 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.3473 | 0.414580 | 0.207290 | − | 0.978279i | \(-0.433536\pi\) | ||||
0.207290 | + | 0.978279i | \(0.433536\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.3442 | −0.514629 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −40.2502 | −1.34843 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −77.5796 | −2.59610 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.56366 | −0.252825 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 55.6597 | 1.85842 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −84.9617 | −2.83363 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.31269 | 0.110362 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.7644 | 0.491329 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0252 | 0.333248 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.0705 | 0.932067 | 0.466034 | − | 0.884767i | \(-0.345683\pi\) | ||||
0.466034 | + | 0.884767i | \(0.345683\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.5913 | 1.04782 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.04576 | −0.0346474 | −0.0173237 | − | 0.999850i | \(-0.505515\pi\) | ||||
−0.0173237 | + | 0.999850i | \(0.505515\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −28.9459 | −0.957971 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.7235 | 0.552861 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.07758 | −0.200699 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.28887 | 0.0425159 | 0.0212579 | − | 0.999774i | \(-0.493233\pi\) | ||||
0.0212579 | + | 0.999774i | \(0.493233\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −23.6979 | −0.780874 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −8.76372 | −0.288461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.946564 | −0.0311228 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.34996 | −0.142871 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.26769 | −0.172827 | −0.0864137 | − | 0.996259i | \(-0.527541\pi\) | ||||
−0.0864137 | + | 0.996259i | \(0.527541\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.61663 | 0.282398 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.602819 | −0.0197354 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 21.5517 | 0.704817 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.7934 | 1.23466 | 0.617329 | − | 0.786705i | \(-0.288215\pi\) | ||||
0.617329 | + | 0.786705i | \(0.288215\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.3320 | −0.402440 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.6472 | 0.640481 | 0.320241 | − | 0.947336i | \(-0.396236\pi\) | ||||
0.320241 | + | 0.947336i | \(0.396236\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.03655 | 0.261706 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.60620 | −0.0522496 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.77421 | 0.317619 | 0.158810 | − | 0.987309i | \(-0.449234\pi\) | ||||
0.158810 | + | 0.987309i | \(0.449234\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.4493 | −0.728735 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −60.4289 | −1.95954 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.8098 | 1.90504 | 0.952519 | − | 0.304480i | \(-0.0984825\pi\) | ||||
0.952519 | + | 0.304480i | \(0.0984825\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 25.2556 | 0.817251 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 115.259 | 3.72578 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.27393 | −0.267179 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.0174 | 2.22637 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.31137 | 0.138932 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.8915 | 0.897860 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.9820 | 1.47868 | 0.739340 | − | 0.673332i | \(-0.235138\pi\) | ||||
0.739340 | + | 0.673332i | \(0.235138\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 59.8224 | 1.92177 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.1060 | −0.581048 | −0.290524 | − | 0.956868i | \(-0.593830\pi\) | ||||
−0.290524 | + | 0.956868i | \(0.593830\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.5020 | −0.721380 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.5381 | 0.817874 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.6440 | 0.660461 | 0.330231 | − | 0.943900i | \(-0.392873\pi\) | ||||
0.330231 | + | 0.943900i | \(0.392873\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.4983 | 1.10257 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.7810 | −1.23818 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.7075 | 1.84058 | 0.920291 | − | 0.391234i | \(-0.127952\pi\) | ||||
0.920291 | + | 0.391234i | \(0.127952\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.54349 | −0.144767 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.8314 | −0.726731 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.9771 | −1.14400 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.8234 | 0.502647 | 0.251323 | − | 0.967903i | \(-0.419134\pi\) | ||||
0.251323 | + | 0.967903i | \(0.419134\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20.8758 | 0.662474 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.20188 | −0.0698043 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.9024 | −1.32706 | −0.663530 | − | 0.748149i | \(-0.730943\pi\) | ||||
−0.663530 | + | 0.748149i | \(0.730943\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.364467 | −0.0115312 |
(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 | 3584.2.a.k.1.1 | yes | 6 | |
4.3 | odd | 2 | 3584.2.a.f.1.6 | yes | 6 | ||
8.3 | odd | 2 | 3584.2.a.l.1.1 | yes | 6 | ||
8.5 | even | 2 | 3584.2.a.e.1.6 | ✓ | 6 | ||
16.3 | odd | 4 | 3584.2.b.i.1793.10 | 12 | |||
16.5 | even | 4 | 3584.2.b.k.1793.10 | 12 | |||
16.11 | odd | 4 | 3584.2.b.i.1793.3 | 12 | |||
16.13 | even | 4 | 3584.2.b.k.1793.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.2.a.e.1.6 | ✓ | 6 | 8.5 | even | 2 | ||
3584.2.a.f.1.6 | yes | 6 | 4.3 | odd | 2 | ||
3584.2.a.k.1.1 | yes | 6 | 1.1 | even | 1 | trivial | |
3584.2.a.l.1.1 | yes | 6 | 8.3 | odd | 2 | ||
3584.2.b.i.1793.3 | 12 | 16.11 | odd | 4 | |||
3584.2.b.i.1793.10 | 12 | 16.3 | odd | 4 | |||
3584.2.b.k.1793.3 | 12 | 16.13 | even | 4 | |||
3584.2.b.k.1793.10 | 12 | 16.5 | even | 4 |