Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7168,2,Mod(1,7168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7168, 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("7168.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7168 = 2^{10} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7168.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: | \(57.2367681689\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 24x^{10} + 221x^{8} - 968x^{6} + 2008x^{4} - 1640x^{2} + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 112) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(0.377920\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7168.1 |
$q$-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 | ||||||||
\(3\) | −0.589521 | −0.340360 | −0.170180 | − | 0.985413i | \(-0.554435\pi\) | ||||
−0.170180 | + | 0.985413i | \(0.554435\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.60045 | 0.715744 | 0.357872 | − | 0.933771i | \(-0.383502\pi\) | ||||
0.357872 | + | 0.933771i | \(0.383502\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.65247 | −0.884155 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.45487 | −1.64471 | −0.822353 | − | 0.568978i | \(-0.807339\pi\) | ||||
−0.822353 | + | 0.568978i | \(0.807339\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.59464 | −1.82902 | −0.914512 | − | 0.404559i | \(-0.867425\pi\) | ||||
−0.914512 | + | 0.404559i | \(0.867425\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.943500 | −0.243611 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.33230 | 1.29327 | 0.646637 | − | 0.762798i | \(-0.276175\pi\) | ||||
0.646637 | + | 0.762798i | \(0.276175\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.61925 | −0.830312 | −0.415156 | − | 0.909750i | \(-0.636273\pi\) | ||||
−0.415156 | + | 0.909750i | \(0.636273\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.589521 | 0.128644 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.60484 | 0.543147 | 0.271574 | − | 0.962418i | \(-0.412456\pi\) | ||||
0.271574 | + | 0.962418i | \(0.412456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.43855 | −0.487710 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.33225 | 0.641291 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.72929 | −0.321121 | −0.160560 | − | 0.987026i | \(-0.551330\pi\) | ||||
−0.160560 | + | 0.987026i | \(0.551330\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.833708 | 0.149738 | 0.0748692 | − | 0.997193i | \(-0.476146\pi\) | ||||
0.0748692 | + | 0.997193i | \(0.476146\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.21576 | 0.559792 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.60045 | −0.270526 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.26450 | 1.02988 | 0.514939 | − | 0.857227i | \(-0.327815\pi\) | ||||
0.514939 | + | 0.857227i | \(0.327815\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.88768 | 0.622526 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.263382 | −0.0411333 | −0.0205667 | − | 0.999788i | \(-0.506547\pi\) | ||||
−0.0205667 | + | 0.999788i | \(0.506547\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.77107 | −0.270085 | −0.135043 | − | 0.990840i | \(-0.543117\pi\) | ||||
−0.135043 | + | 0.990840i | \(0.543117\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.24514 | −0.632829 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.7559 | −1.56891 | −0.784455 | − | 0.620186i | \(-0.787057\pi\) | ||||
−0.784455 | + | 0.620186i | \(0.787057\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.14350 | −0.440178 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0673478 | 0.00925093 | 0.00462546 | − | 0.999989i | \(-0.498528\pi\) | ||||
0.00462546 | + | 0.999989i | \(0.498528\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.73026 | −1.17719 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.13362 | 0.282605 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.10081 | −0.664069 | −0.332034 | − | 0.943267i | \(-0.607735\pi\) | ||||
−0.332034 | + | 0.943267i | \(0.607735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.31304 | 0.808302 | 0.404151 | − | 0.914692i | \(-0.367567\pi\) | ||||
0.404151 | + | 0.914692i | \(0.367567\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.65247 | 0.334179 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.5544 | −1.30911 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.4487 | −1.64302 | −0.821508 | − | 0.570197i | \(-0.806867\pi\) | ||||
−0.821508 | + | 0.570197i | \(0.806867\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.53561 | −0.184866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.05301 | 0.243647 | 0.121824 | − | 0.992552i | \(-0.461126\pi\) | ||||
0.121824 | + | 0.992552i | \(0.461126\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.48268 | −0.641700 | −0.320850 | − | 0.947130i | \(-0.603968\pi\) | ||||
−0.320850 | + | 0.947130i | \(0.603968\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.43758 | 0.165997 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.45487 | 0.621640 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.21576 | 0.586819 | 0.293409 | − | 0.955987i | \(-0.405210\pi\) | ||||
0.293409 | + | 0.955987i | \(0.405210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.99297 | 0.665885 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.25965 | 0.906614 | 0.453307 | − | 0.891354i | \(-0.350244\pi\) | ||||
0.453307 | + | 0.891354i | \(0.350244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.53410 | 0.925653 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.01945 | 0.109297 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.32651 | 0.670609 | 0.335304 | − | 0.942110i | \(-0.391161\pi\) | ||||
0.335304 | + | 0.942110i | \(0.391161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.59464 | 0.691306 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.491488 | −0.0509650 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.79243 | −0.594291 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.8089 | 1.90976 | 0.954878 | − | 0.296999i | \(-0.0959858\pi\) | ||||
0.954878 | + | 0.296999i | \(0.0959858\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 14.4689 | 1.45417 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.08033 | 0.406008 | 0.203004 | − | 0.979178i | \(-0.434930\pi\) | ||||
0.203004 | + | 0.979178i | \(0.434930\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.74040 | −0.762684 | −0.381342 | − | 0.924434i | \(-0.624538\pi\) | ||||
−0.381342 | + | 0.924434i | \(0.624538\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.943500 | 0.0920762 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.30144 | 0.319162 | 0.159581 | − | 0.987185i | \(-0.448986\pi\) | ||||
0.159581 | + | 0.987185i | \(0.448986\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.96962 | 0.667569 | 0.333784 | − | 0.942649i | \(-0.391674\pi\) | ||||
0.333784 | + | 0.942649i | \(0.391674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.69306 | −0.350529 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.24381 | −0.493296 | −0.246648 | − | 0.969105i | \(-0.579329\pi\) | ||||
−0.246648 | + | 0.969105i | \(0.579329\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.16893 | 0.388755 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.4921 | 1.61714 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.33230 | −0.488811 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.7556 | 1.70506 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.155269 | 0.0140001 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.9050 | −1.06482 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6789 | 1.56875 | 0.784373 | − | 0.620290i | \(-0.212985\pi\) | ||||
0.784373 | + | 0.620290i | \(0.212985\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.04408 | 0.0919262 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.08173 | 0.269252 | 0.134626 | − | 0.990896i | \(-0.457017\pi\) | ||||
0.134626 | + | 0.990896i | \(0.457017\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.61925 | 0.313828 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.33310 | 0.459000 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.54650 | 0.730177 | 0.365088 | − | 0.930973i | \(-0.381039\pi\) | ||||
0.365088 | + | 0.930973i | \(0.381039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.09706 | 0.686784 | 0.343392 | − | 0.939192i | \(-0.388424\pi\) | ||||
0.343392 | + | 0.939192i | \(0.388424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.34083 | 0.533994 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 35.9729 | 3.00821 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.76764 | −0.229840 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.589521 | −0.0486229 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.558836 | 0.0457816 | 0.0228908 | − | 0.999738i | \(-0.492713\pi\) | ||||
0.0228908 | + | 0.999738i | \(0.492713\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.71559 | 0.302371 | 0.151185 | − | 0.988505i | \(-0.451691\pi\) | ||||
0.151185 | + | 0.988505i | \(0.451691\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.1437 | −1.14345 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.33431 | 0.107174 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.65037 | 0.450949 | 0.225474 | − | 0.974249i | \(-0.427607\pi\) | ||||
0.225474 | + | 0.974249i | \(0.427607\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0397029 | −0.00314864 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.60484 | −0.205290 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.76827 | −0.373480 | −0.186740 | − | 0.982409i | \(-0.559792\pi\) | ||||
−0.186740 | + | 0.982409i | \(0.559792\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.14667 | 0.400668 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.4233 | −0.961345 | −0.480673 | − | 0.876900i | \(-0.659607\pi\) | ||||
−0.480673 | + | 0.876900i | \(0.659607\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 30.4893 | 2.34533 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.59993 | 0.734125 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0943 | −0.995542 | −0.497771 | − | 0.867308i | \(-0.665848\pi\) | ||||
−0.497771 | + | 0.867308i | \(0.665848\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.43855 | 0.184337 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.00703 | 0.226022 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.0788 | −1.05230 | −0.526150 | − | 0.850392i | \(-0.676365\pi\) | ||||
−0.526150 | + | 0.850392i | \(0.676365\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.18598 | −0.534130 | −0.267065 | − | 0.963679i | \(-0.586054\pi\) | ||||
−0.267065 | + | 0.963679i | \(0.586054\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.72167 | −0.275114 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.0260 | 0.737129 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −29.0870 | −2.12705 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.33225 | −0.242385 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.7927 | −1.50451 | −0.752254 | − | 0.658873i | \(-0.771033\pi\) | ||||
−0.752254 | + | 0.658873i | \(0.771033\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.3447 | 0.960574 | 0.480287 | − | 0.877111i | \(-0.340533\pi\) | ||||
0.480287 | + | 0.877111i | \(0.340533\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.22204 | 0.445570 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.275011 | −0.0195937 | −0.00979687 | − | 0.999952i | \(-0.503118\pi\) | ||||
−0.00979687 | + | 0.999952i | \(0.503118\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.4003 | −1.02081 | −0.510403 | − | 0.859935i | \(-0.670504\pi\) | ||||
−0.510403 | + | 0.859935i | \(0.670504\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.92827 | 0.559217 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.72929 | 0.121372 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.421530 | −0.0294409 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.90926 | −0.480227 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 19.7425 | 1.36562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.9228 | 0.751954 | 0.375977 | − | 0.926629i | \(-0.377307\pi\) | ||||
0.375977 | + | 0.926629i | \(0.377307\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.21029 | −0.0829278 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.83451 | −0.193312 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.833708 | −0.0565958 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.23216 | 0.218409 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −35.1646 | −2.36543 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.06285 | 0.472963 | 0.236482 | − | 0.971636i | \(-0.424006\pi\) | ||||
0.236482 | + | 0.971636i | \(0.424006\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.46817 | 0.431212 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.7200 | 1.10975 | 0.554874 | − | 0.831934i | \(-0.312766\pi\) | ||||
0.554874 | + | 0.831934i | \(0.312766\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.2627 | 0.876425 | 0.438212 | − | 0.898872i | \(-0.355612\pi\) | ||||
0.438212 | + | 0.898872i | \(0.355612\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.21576 | −0.211581 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 24.4385 | 1.60102 | 0.800511 | − | 0.599318i | \(-0.204561\pi\) | ||||
0.800511 | + | 0.599318i | \(0.204561\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.2143 | −1.12294 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.07480 | −0.199730 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.27660 | −0.406000 | −0.203000 | − | 0.979179i | \(-0.565069\pi\) | ||||
−0.203000 | + | 0.979179i | \(0.565069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0124 | 0.967034 | 0.483517 | − | 0.875335i | \(-0.339359\pi\) | ||||
0.483517 | + | 0.875335i | \(0.339359\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5297 | −0.867932 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.60045 | 0.102249 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.8676 | 1.51866 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.86923 | −0.308575 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.6772 | 1.05265 | 0.526327 | − | 0.850282i | \(-0.323569\pi\) | ||||
0.526327 | + | 0.850282i | \(0.323569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.2091 | −0.893317 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.03103 | −0.315055 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.3977 | 1.27237 | 0.636186 | − | 0.771536i | \(-0.280511\pi\) | ||||
0.636186 | + | 0.771536i | \(0.280511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.26450 | −0.389257 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.58688 | 0.283921 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.3452 | 1.43953 | 0.719764 | − | 0.694219i | \(-0.244250\pi\) | ||||
0.719764 | + | 0.694219i | \(0.244250\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.107787 | 0.00662130 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.72961 | −0.228248 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.2124 | −1.90306 | −0.951528 | − | 0.307563i | \(-0.900487\pi\) | ||||
−0.951528 | + | 0.307563i | \(0.900487\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.46392 | 0.0889266 | 0.0444633 | − | 0.999011i | \(-0.485842\pi\) | ||||
0.0444633 | + | 0.999011i | \(0.485842\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.88768 | −0.235293 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.3020 | 0.802140 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.96907 | −0.118310 | −0.0591550 | − | 0.998249i | \(-0.518841\pi\) | ||||
−0.0591550 | + | 0.998249i | \(0.518841\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.21138 | −0.132392 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.66742 | 0.338090 | 0.169045 | − | 0.985608i | \(-0.445932\pi\) | ||||
0.169045 | + | 0.985608i | \(0.445932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.5629 | −1.40067 | −0.700336 | − | 0.713814i | \(-0.746966\pi\) | ||||
−0.700336 | + | 0.713814i | \(0.746966\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.41476 | 0.202273 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.263382 | 0.0155469 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.4334 | 0.672555 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0882 | −0.650004 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.2001 | −1.41379 | −0.706893 | − | 0.707320i | \(-0.749904\pi\) | ||||
−0.706893 | + | 0.707320i | \(0.749904\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.16360 | −0.475303 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.1770 | −1.05473 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −17.1780 | −0.993429 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.77107 | 0.102083 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.40544 | −0.138189 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.1037 | 0.578537 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.5741 | −0.774717 | −0.387359 | − | 0.921929i | \(-0.626612\pi\) | ||||
−0.387359 | + | 0.921929i | \(0.626612\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.56312 | 0.259587 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.1866 | 1.08797 | 0.543987 | − | 0.839094i | \(-0.316914\pi\) | ||||
0.543987 | + | 0.839094i | \(0.316914\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.03963 | 0.284857 | 0.142428 | − | 0.989805i | \(-0.454509\pi\) | ||||
0.142428 | + | 0.989805i | \(0.454509\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.24514 | 0.239187 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.81489 | 0.438928 | 0.219464 | − | 0.975621i | \(-0.429569\pi\) | ||||
0.219464 | + | 0.975621i | \(0.429569\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.43305 | 0.528149 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.94627 | −0.108630 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.2989 | −1.07382 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 16.0814 | 0.892034 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.10874 | −0.227214 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.7559 | 0.592992 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.8617 | 1.14666 | 0.573331 | − | 0.819324i | \(-0.305651\pi\) | ||||
0.573331 | + | 0.819324i | \(0.305651\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.6164 | −0.910572 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.5239 | −1.17598 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.7111 | −0.910311 | −0.455156 | − | 0.890412i | \(-0.650416\pi\) | ||||
−0.455156 | + | 0.890412i | \(0.650416\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.09133 | 0.167898 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.54777 | −0.246276 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.45767 | −0.132316 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.89025 | 0.423571 | 0.211785 | − | 0.977316i | \(-0.432072\pi\) | ||||
0.211785 | + | 0.977316i | \(0.432072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.4260 | −1.36102 | −0.680511 | − | 0.732738i | \(-0.738242\pi\) | ||||
−0.680511 | + | 0.732738i | \(0.738242\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.9750 | −1.17294 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.0318 | −1.33231 | −0.666155 | − | 0.745814i | \(-0.732061\pi\) | ||||
−0.666155 | + | 0.745814i | \(0.732061\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.28574 | 0.174389 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.14350 | 0.166372 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.9910 | 0.949526 | 0.474763 | − | 0.880114i | \(-0.342534\pi\) | ||||
0.474763 | + | 0.880114i | \(0.342534\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.90105 | −0.310582 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −11.0568 | −0.580333 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.77477 | −0.459293 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.3077 | 0.538060 | 0.269030 | − | 0.963132i | \(-0.413297\pi\) | ||||
0.269030 | + | 0.963132i | \(0.413297\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.698611 | 0.0363682 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0673478 | −0.00349652 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.7060 | 1.17567 | 0.587835 | − | 0.808981i | \(-0.299981\pi\) | ||||
0.587835 | + | 0.808981i | \(0.299981\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.01827 | 0.362422 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 11.4040 | 0.587338 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.3335 | 1.14720 | 0.573598 | − | 0.819137i | \(-0.305547\pi\) | ||||
0.573598 | + | 0.819137i | \(0.305547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.4221 | −0.533938 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.3633 | −0.938319 | −0.469160 | − | 0.883113i | \(-0.655443\pi\) | ||||
−0.469160 | + | 0.883113i | \(0.655443\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.73026 | 0.444935 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.69769 | 0.238797 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −19.7359 | −1.00065 | −0.500324 | − | 0.865838i | \(-0.666786\pi\) | ||||
−0.500324 | + | 0.865838i | \(0.666786\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.8898 | 0.702438 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.81674 | −0.0916426 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.34758 | 0.420012 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.59544 | 0.0800730 | 0.0400365 | − | 0.999198i | \(-0.487253\pi\) | ||||
0.0400365 | + | 0.999198i | \(0.487253\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.13362 | −0.106815 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.3470 | 0.716454 | 0.358227 | − | 0.933635i | \(-0.383381\pi\) | ||||
0.358227 | + | 0.933635i | \(0.383381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.49800 | −0.273875 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.59146 | 0.476604 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.1721 | −1.69385 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 39.2518 | 1.94088 | 0.970438 | − | 0.241350i | \(-0.0775901\pi\) | ||||
0.970438 | + | 0.241350i | \(0.0775901\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.03834 | −0.248523 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.10081 | 0.250994 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.2192 | 0.648904 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.77338 | −0.233754 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.24337 | 0.305008 | 0.152504 | − | 0.988303i | \(-0.451266\pi\) | ||||
0.152504 | + | 0.988303i | \(0.451266\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7126 | 0.522099 | 0.261050 | − | 0.965325i | \(-0.415931\pi\) | ||||
0.261050 | + | 0.965325i | \(0.415931\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 28.5297 | 1.38716 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.0031 | −0.630743 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.31304 | −0.305509 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.2068 | −1.02387 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.5396 | −0.893020 | −0.446510 | − | 0.894779i | \(-0.647333\pi\) | ||||
−0.446510 | + | 0.894779i | \(0.647333\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.21190 | −0.346582 | −0.173291 | − | 0.984871i | \(-0.555440\pi\) | ||||
−0.173291 | + | 0.984871i | \(0.555440\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.63158 | 0.0782285 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.42757 | −0.450982 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.1615 | −0.723617 | −0.361809 | − | 0.932252i | \(-0.617841\pi\) | ||||
−0.361809 | + | 0.932252i | \(0.617841\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.65247 | −0.126308 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.99454 | −0.142275 | −0.0711374 | − | 0.997467i | \(-0.522663\pi\) | ||||
−0.0711374 | + | 0.997467i | \(0.522663\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1253 | 0.479984 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.329445 | −0.0155822 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.29509 | 0.202698 | 0.101349 | − | 0.994851i | \(-0.467684\pi\) | ||||
0.101349 | + | 0.994851i | \(0.467684\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.43671 | 0.0676522 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.19042 | −0.102915 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.5544 | 0.494798 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.7833 | −1.29965 | −0.649823 | − | 0.760085i | \(-0.725157\pi\) | ||||
−0.649823 | + | 0.760085i | \(0.725157\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.7685 | 0.829364 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.20528 | 0.428733 | 0.214366 | − | 0.976753i | \(-0.431231\pi\) | ||||
0.214366 | + | 0.976753i | \(0.431231\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −39.1018 | −1.81722 | −0.908608 | − | 0.417650i | \(-0.862854\pi\) | ||||
−0.908608 | + | 0.417650i | \(0.862854\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.786604 | −0.0364779 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.2805 | 1.07729 | 0.538647 | − | 0.842531i | \(-0.318936\pi\) | ||||
0.538647 | + | 0.842531i | \(0.318936\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.4487 | 0.621002 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.33101 | −0.153485 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.66094 | 0.444210 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.82572 | 0.404952 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.178638 | −0.00817925 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.2565 | 1.70229 | 0.851145 | − | 0.524930i | \(-0.175908\pi\) | ||||
0.851145 | + | 0.524930i | \(0.175908\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −41.3121 | −1.88367 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.53561 | 0.0698726 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.1028 | 1.36690 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.4219 | −1.74106 | −0.870531 | − | 0.492113i | \(-0.836225\pi\) | ||||
−0.870531 | + | 0.492113i | \(0.836225\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.81100 | 0.127118 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.4680 | −0.607802 | −0.303901 | − | 0.952704i | \(-0.598289\pi\) | ||||
−0.303901 | + | 0.952704i | \(0.598289\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.22109 | −0.415297 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.1567 | 1.04082 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.05301 | −0.0920901 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.8337 | 0.619281 | 0.309641 | − | 0.950854i | \(-0.399791\pi\) | ||||
0.309641 | + | 0.950854i | \(0.399791\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.32380 | 0.327203 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.0554 | 0.492938 | 0.246469 | − | 0.969151i | \(-0.420730\pi\) | ||||
0.246469 | + | 0.969151i | \(0.420730\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.53038 | 0.290598 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −17.9741 | −0.798256 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.244998 | −0.0108593 | −0.00542967 | − | 0.999985i | \(-0.501728\pi\) | ||||
−0.00542967 | + | 0.999985i | \(0.501728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.48268 | 0.242540 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.0602 | −0.532472 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.3881 | −0.545886 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 58.6721 | 2.58039 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.71937 | 0.338843 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.9861 | 1.31371 | 0.656857 | − | 0.754015i | \(-0.271885\pi\) | ||||
0.656857 | + | 0.754015i | \(0.271885\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.10620 | −0.0920976 | −0.0460488 | − | 0.998939i | \(-0.514663\pi\) | ||||
−0.0460488 | + | 0.998939i | \(0.514663\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.43758 | −0.0627410 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.44558 | 0.193653 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2148 | −0.704991 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.5297 | 0.587140 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.73691 | 0.0752338 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.28380 | 0.228439 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.29975 | 0.358161 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.45487 | −0.234958 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.0889 | 0.734711 | 0.367355 | − | 0.930081i | \(-0.380263\pi\) | ||||
0.367355 | + | 0.930081i | \(0.380263\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.23628 | 0.181796 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.1545 | 0.477808 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.3471 | −0.741710 | −0.370855 | − | 0.928691i | \(-0.620935\pi\) | ||||
−0.370855 | + | 0.928691i | \(0.620935\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.7451 | −0.714664 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.25872 | 0.266631 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.21576 | −0.221797 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.91056 | −0.250889 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.29115 | 0.139451 | 0.0697253 | − | 0.997566i | \(-0.477788\pi\) | ||||
0.0697253 | + | 0.997566i | \(0.477788\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.6795 | 0.493992 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.1474 | 0.723964 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.0513 | −0.718627 | −0.359314 | − | 0.933217i | \(-0.616989\pi\) | ||||
−0.359314 | + | 0.933217i | \(0.616989\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.39246 | −0.353074 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.99297 | −0.251681 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.99770 | 0.335281 | 0.167641 | − | 0.985848i | \(-0.446385\pi\) | ||||
0.167641 | + | 0.985848i | \(0.446385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.1857 | 1.30508 | 0.652541 | − | 0.757754i | \(-0.273703\pi\) | ||||
0.652541 | + | 0.757754i | \(0.273703\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.2577 | 0.512074 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.35204 | −0.264899 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.4199 | 1.80760 | 0.903798 | − | 0.427960i | \(-0.140768\pi\) | ||||
0.903798 | + | 0.427960i | \(0.140768\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.86699 | −0.326941 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.25965 | −0.342668 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.367373 | −0.0152150 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.9952 | 1.15746 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.7775 | 1.06395 | 0.531975 | − | 0.846760i | \(-0.321450\pi\) | ||||
0.531975 | + | 0.846760i | \(0.321450\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.01740 | −0.124330 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.162125 | 0.00666892 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 39.7514 | 1.63239 | 0.816197 | − | 0.577773i | \(-0.196078\pi\) | ||||
0.816197 | + | 0.577773i | \(0.196078\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.53410 | −0.349864 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.48925 | 0.347442 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.5296 | −1.53342 | −0.766708 | − | 0.641996i | \(-0.778107\pi\) | ||||
−0.766708 | + | 0.641996i | \(0.778107\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.99899 | −0.163122 | −0.0815611 | − | 0.996668i | \(-0.525991\pi\) | ||||
−0.0815611 | + | 0.996668i | \(0.525991\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35.6721 | 1.45268 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 30.0175 | 1.22038 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.3672 | 0.989035 | 0.494517 | − | 0.869168i | \(-0.335345\pi\) | ||||
0.494517 | + | 0.869168i | \(0.335345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.01945 | −0.0413103 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 70.9313 | 2.86957 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.6409 | 0.954848 | 0.477424 | − | 0.878673i | \(-0.341571\pi\) | ||||
0.477424 | + | 0.878673i | \(0.341571\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.248501 | 0.0100205 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.64202 | 0.106364 | 0.0531819 | − | 0.998585i | \(-0.483064\pi\) | ||||
0.0531819 | + | 0.998585i | \(0.483064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −38.1516 | −1.53344 | −0.766721 | − | 0.641981i | \(-0.778113\pi\) | ||||
−0.766721 | + | 0.641981i | \(0.778113\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.67998 | 0.348315 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.32651 | −0.253466 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.86071 | −0.274428 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.6386 | −0.464802 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.4042 | 1.33191 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.9710 | 0.755223 | 0.377611 | − | 0.925964i | \(-0.376746\pi\) | ||||
0.377611 | + | 0.925964i | \(0.376746\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.43919 | −0.255935 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.2942 | 1.12282 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.59464 | −0.261289 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.44554 | −0.215422 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.3762 | 1.23929 | 0.619643 | − | 0.784884i | \(-0.287277\pi\) | ||||
0.619643 | + | 0.784884i | \(0.287277\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.1895 | −0.756760 | −0.378380 | − | 0.925650i | \(-0.623519\pi\) | ||||
−0.378380 | + | 0.925650i | \(0.623519\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.67100 | 0.0657956 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.6587 | −1.55915 | −0.779573 | − | 0.626312i | \(-0.784564\pi\) | ||||
−0.779573 | + | 0.626312i | \(0.784564\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.8242 | 1.09220 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.491488 | 0.0192629 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.19547 | −0.164181 | −0.0820907 | − | 0.996625i | \(-0.526160\pi\) | ||||
−0.0820907 | + | 0.996625i | \(0.526160\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.93216 | 0.192715 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.5426 | 0.567362 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.5882 | −1.07468 | −0.537341 | − | 0.843365i | \(-0.680571\pi\) | ||||
−0.537341 | + | 0.843365i | \(0.680571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.9340 | 0.658655 | 0.329327 | − | 0.944216i | \(-0.393178\pi\) | ||||
0.329327 | + | 0.944216i | \(0.393178\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.7303 | 0.805097 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.79243 | 0.224621 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.50453 | −0.174416 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.16369 | −0.160978 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.4368 | −1.32942 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.9400 | −1.19265 | −0.596324 | − | 0.802744i | \(-0.703373\pi\) | ||||
−0.596324 | + | 0.802744i | \(0.703373\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.12585 | −0.312764 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.0174449 | 0.000670463 0 | 0.000335231 | − | 1.00000i | \(-0.499893\pi\) | ||||
0.000335231 | 1.00000i | \(0.499893\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.8089 | −0.721820 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.85681 | −0.377714 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.9899 | 0.764892 | 0.382446 | − | 0.923978i | \(-0.375082\pi\) | ||||
0.382446 | + | 0.923978i | \(0.375082\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.6783 | 0.522620 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.81864 | −0.298300 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.444134 | −0.0169202 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 44.5980 | 1.69659 | 0.848293 | − | 0.529527i | \(-0.177631\pi\) | ||||
0.848293 | + | 0.529527i | \(0.177631\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.4689 | −0.549626 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 12.9590 | 0.491561 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.40443 | −0.0531966 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.4070 | −0.544924 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.8513 | −0.900851 | −0.450425 | − | 0.892814i | \(-0.648728\pi\) | ||||
−0.450425 | + | 0.892814i | \(0.648728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22.6728 | −0.855120 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.1482 | 0.382203 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.08033 | −0.153457 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.5955 | −1.14904 | −0.574519 | − | 0.818491i | \(-0.694811\pi\) | ||||
−0.574519 | + | 0.818491i | \(0.694811\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.8346 | −0.518839 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.17168 | 0.0813300 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 57.5729 | 2.15311 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.70019 | 0.138186 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.3698 | 1.50554 | 0.752769 | − | 0.658284i | \(-0.228717\pi\) | ||||
0.752769 | + | 0.658284i | \(0.228717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.74040 | 0.288267 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.85013 | −0.329140 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.21696 | 0.156614 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.43634 | 0.127447 | 0.0637234 | − | 0.997968i | \(-0.479702\pi\) | ||||
0.0637234 | + | 0.997968i | \(0.479702\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.0029 | −0.370476 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.44386 | −0.349294 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38.6636 | −1.42807 | −0.714037 | − | 0.700108i | \(-0.753135\pi\) | ||||
−0.714037 | + | 0.700108i | \(0.753135\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.943500 | −0.0348015 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 73.3607 | 2.70228 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.1059 | 1.47532 | 0.737659 | − | 0.675173i | \(-0.235931\pi\) | ||||
0.737659 | + | 0.675173i | \(0.235931\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.0705 | −0.516891 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.1733 | −1.25370 | −0.626848 | − | 0.779141i | \(-0.715656\pi\) | ||||
−0.626848 | + | 0.779141i | \(0.715656\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.894391 | 0.0327679 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.9084 | −0.801588 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.30144 | −0.120632 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.55791 | 0.312282 | 0.156141 | − | 0.987735i | \(-0.450095\pi\) | ||||
0.156141 | + | 0.987735i | \(0.450095\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.83155 | −0.358281 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.94663 | 0.216420 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.4249 | −1.28754 | −0.643770 | − | 0.765219i | \(-0.722631\pi\) | ||||
−0.643770 | + | 0.765219i | \(0.722631\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.37655 | 0.304050 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.4224 | −1.03031 | −0.515155 | − | 0.857097i | \(-0.672266\pi\) | ||||
−0.515155 | + | 0.857097i | \(0.672266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.96962 | −0.252317 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.6364 | −0.818420 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.6380 | 1.21460 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.0189 | −0.433413 | −0.216707 | − | 0.976237i | \(-0.569531\pi\) | ||||
−0.216707 | + | 0.976237i | \(0.569531\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0249 | −0.433065 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.16883 | −0.257845 | −0.128922 | − | 0.991655i | \(-0.541152\pi\) | ||||
−0.128922 | + | 0.991655i | \(0.541152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.03304 | −0.0730290 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.69306 | 0.132488 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.953244 | 0.0341535 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1989 | −0.400728 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.76241 | −0.205932 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.04315 | 0.322764 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.9900 | 0.855152 | 0.427576 | − | 0.903979i | \(-0.359368\pi\) | ||||
0.427576 | + | 0.903979i | \(0.359368\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.7625 | −0.489958 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.24381 | 0.186448 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.6322 | −1.47840 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.0635426 | −0.00225362 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 50.2908 | 1.78139 | 0.890695 | − | 0.454601i | \(-0.150218\pi\) | ||||
0.890695 | + | 0.454601i | \(0.150218\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −57.3537 | −2.02903 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.7808 | −0.592922 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.9073 | 1.05541 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.16893 | −0.146935 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.4004 | 0.647724 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11.8621 | 0.417050 | 0.208525 | − | 0.978017i | \(-0.433134\pi\) | ||||
0.208525 | + | 0.978017i | \(0.433134\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.9714 | −1.01732 | −0.508662 | − | 0.860966i | \(-0.669860\pi\) | ||||
−0.508662 | + | 0.860966i | \(0.669860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.863010 | −0.0302671 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.63140 | −0.267316 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.40993 | 0.224255 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.4921 | −0.611222 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.1122 | −1.43483 | −0.717413 | − | 0.696648i | \(-0.754674\pi\) | ||||
−0.717413 | + | 0.696648i | \(0.754674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −51.3595 | −1.79028 | −0.895140 | − | 0.445785i | \(-0.852925\pi\) | ||||
−0.895140 | + | 0.445785i | \(0.852925\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.84180 | −0.273016 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.5654 | −1.20196 | −0.600979 | − | 0.799265i | \(-0.705222\pi\) | ||||
−0.600979 | + | 0.799265i | \(0.705222\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.1023 | −0.559257 | −0.279629 | − | 0.960108i | \(-0.590211\pi\) | ||||
−0.279629 | + | 0.960108i | \(0.590211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.16081 | 0.0402680 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.33230 | 0.184753 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.8829 | −0.688077 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.77812 | 0.0960259 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 35.2906 | 1.21837 | 0.609184 | − | 0.793029i | \(-0.291497\pi\) | ||||
0.609184 | + | 0.793029i | \(0.291497\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0096 | −0.896881 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.34106 | −0.115072 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 48.7966 | 1.67865 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.7556 | −0.644451 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.8908 | 0.476732 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.3181 | 0.559376 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.80684 | −0.335780 | −0.167890 | − | 0.985806i | \(-0.553695\pi\) | ||||
−0.167890 | + | 0.985806i | \(0.553695\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.3642 | 0.525445 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.1791 | −0.996737 | −0.498369 | − | 0.866965i | \(-0.666067\pi\) | ||||
−0.498369 | + | 0.866965i | \(0.666067\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.29972 | −0.0784653 | −0.0392326 | − | 0.999230i | \(-0.512491\pi\) | ||||
−0.0392326 | + | 0.999230i | \(0.512491\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.155269 | −0.00529155 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.7059 | 1.14736 | 0.573681 | − | 0.819079i | \(-0.305515\pi\) | ||||
0.573681 | + | 0.819079i | \(0.305515\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.9568 | −0.712554 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.74025 | −0.228911 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.4513 | −0.965144 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 88.6891 | 3.00512 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −49.8900 | −1.68852 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.9050 | 0.402464 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.8993 | 1.21223 | 0.606116 | − | 0.795376i | \(-0.292727\pi\) | ||||
0.606116 | + | 0.795376i | \(0.292727\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.2665 | 0.481196 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.0482 | −0.439606 | −0.219803 | − | 0.975544i | \(-0.570541\pi\) | ||||
−0.219803 | + | 0.975544i | \(0.570541\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.3505 | −1.15599 | −0.577994 | − | 0.816041i | \(-0.696164\pi\) | ||||
−0.577994 | + | 0.816041i | \(0.696164\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.81261 | 0.161774 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.8489 | 0.666461 | 0.333230 | − | 0.942845i | \(-0.391861\pi\) | ||||
0.333230 | + | 0.942845i | \(0.391861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.6789 | −0.592930 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −32.6909 | −1.09519 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.9283 | 1.30268 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22.5325 | −0.753178 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.1268 | 0.338124 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.44172 | −0.0480841 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.359119 | 0.0119640 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.04408 | −0.0347448 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.5008 | −0.382300 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 56.0335 | 1.86056 | 0.930281 | − | 0.366848i | \(-0.119563\pi\) | ||||
0.930281 | + | 0.366848i | \(0.119563\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.8229 | −0.358974 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.6260 | 0.385188 | 0.192594 | − | 0.981279i | \(-0.438310\pi\) | ||||
0.192594 | + | 0.981279i | \(0.438310\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.0553 | −1.49111 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.95635 | −0.196911 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.08173 | −0.101768 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 42.1056 | 1.38894 | 0.694468 | − | 0.719523i | \(-0.255640\pi\) | ||||
0.694468 | + | 0.719523i | \(0.255640\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.00224 | 0.263683 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.5389 | −0.445637 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.2763 | −0.502282 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.5311 | 0.674331 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.3239 | 0.994894 | 0.497447 | − | 0.867494i | \(-0.334271\pi\) | ||||
0.497447 | + | 0.867494i | \(0.334271\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.61925 | −0.118616 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.3109 | −0.370303 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −46.5524 | −1.52243 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7772 | 0.580757 | 0.290378 | − | 0.956912i | \(-0.406219\pi\) | ||||
0.290378 | + | 0.956912i | \(0.406219\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.97097 | −0.0969538 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.9242 | 0.975500 | 0.487750 | − | 0.872983i | \(-0.337818\pi\) | ||||
0.487750 | + | 0.872983i | \(0.337818\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.686068 | −0.0223415 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.33310 | −0.173486 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.7581 | 0.544565 | 0.272283 | − | 0.962217i | \(-0.412221\pi\) | ||||
0.272283 | + | 0.962217i | \(0.412221\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.1563 | 1.17368 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.60704 | −0.149394 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.1855 | 0.459513 | 0.229757 | − | 0.973248i | \(-0.426207\pi\) | ||||
0.229757 | + | 0.973248i | \(0.426207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.2778 | −1.07684 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.56098 | −0.179761 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.54650 | −0.275981 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.3049 | −0.977578 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.75696 | −0.282189 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 21.3576 | 0.687525 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.54873 | 0.274909 | 0.137454 | − | 0.990508i | \(-0.456108\pi\) | ||||
0.137454 | + | 0.990508i | \(0.456108\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.3771 | 0.365485 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.0750 | 1.15770 | 0.578851 | − | 0.815433i | \(-0.303501\pi\) | ||||
0.578851 | + | 0.815433i | \(0.303501\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.09706 | −0.259580 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −9.48030 | −0.303613 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −13.2375 | −0.423506 | −0.211753 | − | 0.977323i | \(-0.567917\pi\) | ||||
−0.211753 | + | 0.977323i | \(0.567917\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −34.5103 | −1.10295 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.4867 | −0.590234 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 19.9233 | 0.635455 | 0.317727 | − | 0.948182i | \(-0.397080\pi\) | ||||
0.317727 | + | 0.948182i | \(0.397080\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.440142 | −0.0140241 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.34083 | −0.201831 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.61335 | −0.146696 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.3594 | −1.72678 | −0.863392 | − | 0.504533i | \(-0.831665\pi\) | ||||
−0.863392 | + | 0.504533i | \(0.831665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −12.2984 | −0.390278 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.0469 | −0.730637 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −20.3692 | −0.645098 | −0.322549 | − | 0.946553i | \(-0.604540\pi\) | ||||
−0.322549 | + | 0.946553i | \(0.604540\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.8749 | 0.660452 |
(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 | 7168.2.a.bi.1.6 | 12 | ||
4.3 | odd | 2 | 7168.2.a.bj.1.7 | 12 | |||
8.3 | odd | 2 | 7168.2.a.bj.1.6 | 12 | |||
8.5 | even | 2 | inner | 7168.2.a.bi.1.7 | 12 | ||
32.3 | odd | 8 | 112.2.m.d.29.5 | ✓ | 12 | ||
32.5 | even | 8 | 896.2.m.h.225.3 | 12 | |||
32.11 | odd | 8 | 112.2.m.d.85.5 | yes | 12 | ||
32.13 | even | 8 | 896.2.m.h.673.3 | 12 | |||
32.19 | odd | 8 | 896.2.m.g.673.4 | 12 | |||
32.21 | even | 8 | 448.2.m.d.113.4 | 12 | |||
32.27 | odd | 8 | 896.2.m.g.225.4 | 12 | |||
32.29 | even | 8 | 448.2.m.d.337.4 | 12 | |||
224.3 | even | 24 | 784.2.x.m.765.1 | 24 | |||
224.11 | odd | 24 | 784.2.x.l.373.4 | 24 | |||
224.67 | odd | 24 | 784.2.x.l.765.1 | 24 | |||
224.75 | even | 24 | 784.2.x.m.165.1 | 24 | |||
224.107 | odd | 24 | 784.2.x.l.165.1 | 24 | |||
224.131 | even | 24 | 784.2.x.m.557.4 | 24 | |||
224.139 | even | 8 | 784.2.m.h.197.5 | 12 | |||
224.163 | odd | 24 | 784.2.x.l.557.4 | 24 | |||
224.171 | even | 24 | 784.2.x.m.373.4 | 24 | |||
224.195 | even | 8 | 784.2.m.h.589.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.d.29.5 | ✓ | 12 | 32.3 | odd | 8 | ||
112.2.m.d.85.5 | yes | 12 | 32.11 | odd | 8 | ||
448.2.m.d.113.4 | 12 | 32.21 | even | 8 | |||
448.2.m.d.337.4 | 12 | 32.29 | even | 8 | |||
784.2.m.h.197.5 | 12 | 224.139 | even | 8 | |||
784.2.m.h.589.5 | 12 | 224.195 | even | 8 | |||
784.2.x.l.165.1 | 24 | 224.107 | odd | 24 | |||
784.2.x.l.373.4 | 24 | 224.11 | odd | 24 | |||
784.2.x.l.557.4 | 24 | 224.163 | odd | 24 | |||
784.2.x.l.765.1 | 24 | 224.67 | odd | 24 | |||
784.2.x.m.165.1 | 24 | 224.75 | even | 24 | |||
784.2.x.m.373.4 | 24 | 224.171 | even | 24 | |||
784.2.x.m.557.4 | 24 | 224.131 | even | 24 | |||
784.2.x.m.765.1 | 24 | 224.3 | even | 24 | |||
896.2.m.g.225.4 | 12 | 32.27 | odd | 8 | |||
896.2.m.g.673.4 | 12 | 32.19 | odd | 8 | |||
896.2.m.h.225.3 | 12 | 32.5 | even | 8 | |||
896.2.m.h.673.3 | 12 | 32.13 | even | 8 | |||
7168.2.a.bi.1.6 | 12 | 1.1 | even | 1 | trivial | ||
7168.2.a.bi.1.7 | 12 | 8.5 | even | 2 | inner | ||
7168.2.a.bj.1.6 | 12 | 8.3 | odd | 2 | |||
7168.2.a.bj.1.7 | 12 | 4.3 | odd | 2 |