Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, 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("1216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 608) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.32973\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.56155 | −0.901563 | −0.450781 | − | 0.892634i | \(-0.648855\pi\) | ||||
−0.450781 | + | 0.892634i | \(0.648855\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.844614 | 0.377723 | 0.188861 | − | 0.982004i | \(-0.439520\pi\) | ||||
0.188861 | + | 0.982004i | \(0.439520\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.06562 | 1.91462 | 0.957312 | − | 0.289056i | \(-0.0933412\pi\) | ||||
0.957312 | + | 0.289056i | \(0.0933412\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.561553 | −0.187184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.84461 | 0.857683 | 0.428842 | − | 0.903380i | \(-0.358922\pi\) | ||||
0.428842 | + | 0.903380i | \(0.358922\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.90210 | −0.804897 | −0.402449 | − | 0.915443i | \(-0.631841\pi\) | ||||
−0.402449 | + | 0.915443i | \(0.631841\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.31891 | −0.340541 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.72508 | 1.87361 | 0.936803 | − | 0.349857i | \(-0.113770\pi\) | ||||
0.936803 | + | 0.349857i | \(0.113770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.91023 | −1.72615 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.91023 | −0.815340 | −0.407670 | − | 0.913129i | \(-0.633659\pi\) | ||||
−0.407670 | + | 0.913129i | \(0.633659\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.28663 | −0.857326 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.56155 | 1.07032 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.90210 | −0.538906 | −0.269453 | − | 0.963014i | \(-0.586843\pi\) | ||||
−0.269453 | + | 0.963014i | \(0.586843\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00814 | 1.25870 | 0.629349 | − | 0.777123i | \(-0.283322\pi\) | ||||
0.629349 | + | 0.777123i | \(0.283322\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.44201 | −0.773255 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.27849 | 0.723197 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.00814 | −1.48093 | −0.740464 | − | 0.672096i | \(-0.765394\pi\) | ||||
−0.740464 | + | 0.672096i | \(0.765394\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.53178 | 0.725666 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.81233 | −1.06391 | −0.531954 | − | 0.846773i | \(-0.678542\pi\) | ||||
−0.531954 | + | 0.846773i | \(0.678542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.96772 | 0.910069 | 0.455034 | − | 0.890474i | \(-0.349627\pi\) | ||||
0.455034 | + | 0.890474i | \(0.349627\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.474295 | −0.0707037 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.04042 | 0.151760 | 0.0758802 | − | 0.997117i | \(-0.475823\pi\) | ||||
0.0758802 | + | 0.997117i | \(0.475823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.6605 | 2.66579 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.0631 | −1.68917 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.03334 | 1.24082 | 0.620412 | − | 0.784276i | \(-0.286965\pi\) | ||||
0.620412 | + | 0.784276i | \(0.286965\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.40260 | 0.323966 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.56155 | −0.206833 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.749220 | 0.0975401 | 0.0487701 | − | 0.998810i | \(-0.484470\pi\) | ||||
0.0487701 | + | 0.998810i | \(0.484470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.27849 | −0.291731 | −0.145866 | − | 0.989304i | \(-0.546597\pi\) | ||||
−0.145866 | + | 0.989304i | \(0.546597\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.84461 | −0.358388 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.45115 | −0.304028 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3739 | 1.26737 | 0.633686 | − | 0.773590i | \(-0.281541\pi\) | ||||
0.633686 | + | 0.773590i | \(0.281541\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.10604 | 0.735081 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.13124 | −0.252932 | −0.126466 | − | 0.991971i | \(-0.540363\pi\) | ||||
−0.126466 | + | 0.991971i | \(0.540363\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.60197 | 0.538620 | 0.269310 | − | 0.963054i | \(-0.413204\pi\) | ||||
0.269310 | + | 0.963054i | \(0.413204\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.69380 | 0.772933 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.4097 | 1.64214 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.88503 | −0.437100 | −0.218550 | − | 0.975826i | \(-0.570133\pi\) | ||||
−0.218550 | + | 0.975826i | \(0.570133\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.44201 | 0.926631 | 0.463316 | − | 0.886193i | \(-0.346660\pi\) | ||||
0.463316 | + | 0.886193i | \(0.346660\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.52470 | 0.707703 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.53178 | 0.485858 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 16.0667 | 1.70306 | 0.851532 | − | 0.524302i | \(-0.175674\pi\) | ||||
0.851532 | + | 0.524302i | \(0.175674\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.7009 | −1.54108 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.9436 | −1.13480 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.844614 | 0.0866555 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.68923 | −0.374584 | −0.187292 | − | 0.982304i | \(-0.559971\pi\) | ||||
−0.187292 | + | 0.982304i | \(0.559971\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.59740 | −0.160545 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.2462 | 1.61656 | 0.808279 | − | 0.588799i | \(-0.200399\pi\) | ||||
0.808279 | + | 0.588799i | \(0.200399\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.812333 | 0.0800415 | 0.0400208 | − | 0.999199i | \(-0.487258\pi\) | ||||
0.0400208 | + | 0.999199i | \(0.487258\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.68109 | −0.652008 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.88860 | 0.955967 | 0.477983 | − | 0.878369i | \(-0.341368\pi\) | ||||
0.477983 | + | 0.878369i | \(0.341368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.8375 | 1.03805 | 0.519024 | − | 0.854760i | \(-0.326296\pi\) | ||||
0.519024 | + | 0.854760i | \(0.326296\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0667 | 1.33515 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.310773 | −0.0292351 | −0.0146175 | − | 0.999893i | \(-0.504653\pi\) | ||||
−0.0146175 | + | 0.999893i | \(0.504653\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.30264 | −0.307972 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.62968 | 0.150664 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 39.1323 | 3.58725 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.90817 | −0.264379 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.6378 | 0.959180 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.84361 | −0.701554 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.6882 | −1.65831 | −0.829156 | − | 0.559017i | \(-0.811178\pi\) | ||||
−0.829156 | + | 0.559017i | \(0.811178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.31891 | −0.820484 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.6055 | −1.45083 | −0.725416 | − | 0.688310i | \(-0.758353\pi\) | ||||
−0.725416 | + | 0.688310i | \(0.758353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.06562 | 0.439245 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.69736 | 0.404285 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.91274 | −0.248852 | −0.124426 | − | 0.992229i | \(-0.539709\pi\) | ||||
−0.124426 | + | 0.992229i | \(0.539709\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.278492 | −0.0236214 | −0.0118107 | − | 0.999930i | \(-0.503760\pi\) | ||||
−0.0118107 | + | 0.999930i | \(0.503760\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.62467 | −0.136822 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.25535 | −0.690347 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.45115 | −0.203557 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −29.1394 | −2.40338 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.08269 | 0.662160 | 0.331080 | − | 0.943603i | \(-0.392587\pi\) | ||||
0.331080 | + | 0.943603i | \(0.392587\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.0585 | −1.22545 | −0.612723 | − | 0.790297i | \(-0.709926\pi\) | ||||
−0.612723 | + | 0.790297i | \(0.709926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.33804 | −0.350710 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.91917 | 0.475439 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.9273 | −0.872094 | −0.436047 | − | 0.899924i | \(-0.643622\pi\) | ||||
−0.436047 | + | 0.899924i | \(0.643622\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.1060 | −1.11868 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.8078 | −1.56107 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.697363 | 0.0546217 | 0.0273108 | − | 0.999627i | \(-0.491306\pi\) | ||||
0.0273108 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.75179 | −0.292076 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.24621 | −0.483346 | −0.241673 | − | 0.970358i | \(-0.577696\pi\) | ||||
−0.241673 | + | 0.970358i | \(0.577696\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.57782 | −0.352140 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.561553 | −0.0429430 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.69736 | −0.509191 | −0.254596 | − | 0.967048i | \(-0.581942\pi\) | ||||
−0.254596 | + | 0.967048i | \(0.581942\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −21.7144 | −1.64146 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.16995 | −0.0879386 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.2462 | 1.36379 | 0.681893 | − | 0.731452i | \(-0.261157\pi\) | ||||
0.681893 | + | 0.731452i | \(0.261157\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.5651 | −1.30561 | −0.652803 | − | 0.757528i | \(-0.726407\pi\) | ||||
−0.652803 | + | 0.757528i | \(0.726407\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.55799 | 0.263014 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.60839 | −0.559380 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.9749 | 1.60696 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 28.1727 | 2.04926 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.19686 | −0.520747 | −0.260373 | − | 0.965508i | \(-0.583846\pi\) | ||||
−0.260373 | + | 0.965508i | \(0.583846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.92730 | −0.210712 | −0.105356 | − | 0.994435i | \(-0.533598\pi\) | ||||
−0.105356 | + | 0.994435i | \(0.533598\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.82760 | 0.274100 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1394 | 0.793648 | 0.396824 | − | 0.917895i | \(-0.370112\pi\) | ||||
0.396824 | + | 0.917895i | \(0.370112\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.57220 | −0.395003 | −0.197501 | − | 0.980303i | \(-0.563283\pi\) | ||||
−0.197501 | + | 0.980303i | \(0.563283\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.1994 | −1.14262 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.7009 | −1.03180 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.75379 | −0.401862 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.19580 | 0.152619 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.84461 | 0.196766 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.23451 | −0.0849871 | −0.0424935 | − | 0.999097i | \(-0.513530\pi\) | ||||
−0.0424935 | + | 0.999097i | \(0.513530\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.32805 | 0.228034 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.04042 | 0.343754 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 35.5006 | 2.40993 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.18622 | −0.485600 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.4189 | −1.50806 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.76092 | 0.385780 | 0.192890 | − | 0.981220i | \(-0.438214\pi\) | ||||
0.192890 | + | 0.981220i | \(0.438214\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.40717 | 0.160478 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.1862 | −0.742455 | −0.371228 | − | 0.928542i | \(-0.621063\pi\) | ||||
−0.371228 | + | 0.928542i | \(0.621063\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.3624 | −1.67600 | −0.837999 | − | 0.545672i | \(-0.816274\pi\) | ||||
−0.837999 | + | 0.545672i | \(0.816274\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −22.5016 | −1.48049 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.33804 | 0.546243 | 0.273122 | − | 0.961980i | \(-0.411944\pi\) | ||||
0.273122 | + | 0.961980i | \(0.411944\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.878750 | 0.0573233 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.06668 | 0.394073 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.4441 | 1.06368 | 0.531839 | − | 0.846845i | \(-0.321501\pi\) | ||||
0.531839 | + | 0.846845i | \(0.321501\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.8286 | −0.826363 | −0.413182 | − | 0.910649i | \(-0.635583\pi\) | ||||
−0.413182 | + | 0.910649i | \(0.635583\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.75379 | −0.369106 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.7609 | 1.00693 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.90210 | −0.184656 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.1827 | −0.835417 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.8527 | 1.12686 | 0.563428 | − | 0.826165i | \(-0.309482\pi\) | ||||
0.563428 | + | 0.826165i | \(0.309482\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.1231 | −0.699304 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.1887 | −0.638039 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.49342 | 0.0931572 | 0.0465786 | − | 0.998915i | \(-0.485168\pi\) | ||||
0.0465786 | + | 0.998915i | \(0.485168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −45.6318 | −2.83542 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.62968 | 0.100875 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.483433 | −0.0298097 | −0.0149049 | − | 0.999889i | \(-0.504745\pi\) | ||||
−0.0149049 | + | 0.999889i | \(0.504745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.62968 | 0.468688 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −25.0890 | −1.53542 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.45115 | −0.515276 | −0.257638 | − | 0.966242i | \(-0.582944\pi\) | ||||
−0.257638 | + | 0.966242i | \(0.582944\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.5822 | 1.00730 | 0.503648 | − | 0.863909i | \(-0.331991\pi\) | ||||
0.503648 | + | 0.863909i | \(0.331991\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.9563 | 1.38938 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −12.1938 | −0.735314 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.7124 | −0.944065 | −0.472032 | − | 0.881581i | \(-0.656479\pi\) | ||||
−0.472032 | + | 0.881581i | \(0.656479\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.93544 | −0.235609 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.13938 | 0.187280 | 0.0936398 | − | 0.995606i | \(-0.470150\pi\) | ||||
0.0936398 | + | 0.995606i | \(0.470150\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.3884 | −1.56863 | −0.784315 | − | 0.620363i | \(-0.786985\pi\) | ||||
−0.784315 | + | 0.620363i | \(0.786985\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.31891 | −0.0781254 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34.5087 | −2.03698 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 42.6768 | 2.51040 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.76092 | 0.337711 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.5903 | −0.793955 | −0.396978 | − | 0.917828i | \(-0.629941\pi\) | ||||
−0.396978 | + | 0.917828i | \(0.629941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.632801 | 0.0368431 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.8205 | 0.917997 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.3479 | 0.656265 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.2302 | 1.74244 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.3693 | −1.45743 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.92445 | −0.110193 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.44302 | −0.196503 | −0.0982516 | − | 0.995162i | \(-0.531325\pi\) | ||||
−0.0982516 | + | 0.995162i | \(0.531325\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.26850 | −0.0721625 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.4935 | 1.67242 | 0.836211 | − | 0.548408i | \(-0.184766\pi\) | ||||
0.836211 | + | 0.548408i | \(0.184766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0631 | −0.568801 | −0.284400 | − | 0.958706i | \(-0.591794\pi\) | ||||
−0.284400 | + | 0.958706i | \(0.591794\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.40260 | −0.135371 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.14931 | −0.233049 | −0.116524 | − | 0.993188i | \(-0.537175\pi\) | ||||
−0.116524 | + | 0.993188i | \(0.537175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.25535 | −0.462211 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.4416 | −0.861864 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7.72508 | 0.429835 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.4402 | 0.690059 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.9234 | −0.935865 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.27036 | 0.290564 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.8886 | 1.42297 | 0.711483 | − | 0.702703i | \(-0.248024\pi\) | ||||
0.711483 | + | 0.702703i | \(0.248024\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.05854 | 0.277207 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.76192 | 0.478715 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 31.5097 | 1.71644 | 0.858221 | − | 0.513280i | \(-0.171570\pi\) | ||||
0.858221 | + | 0.513280i | \(0.171570\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.485288 | 0.0263572 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.9354 | 1.07956 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 59.0677 | 3.18936 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.15724 | 0.277657 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.9173 | −0.747120 | −0.373560 | − | 0.927606i | \(-0.621863\pi\) | ||||
−0.373560 | + | 0.927606i | \(0.621863\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.34305 | −0.339536 | −0.169768 | − | 0.985484i | \(-0.554302\pi\) | ||||
−0.169768 | + | 0.985484i | \(0.554302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.1402 | −0.861499 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.0794 | −1.70741 | −0.853707 | − | 0.520754i | \(-0.825651\pi\) | ||||
−0.853707 | + | 0.520754i | \(0.825651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.80008 | −0.0955381 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −61.1072 | −3.23413 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.86670 | 0.0985205 | 0.0492603 | − | 0.998786i | \(-0.484314\pi\) | ||||
0.0492603 | + | 0.998786i | \(0.484314\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.54127 | 0.238355 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.88689 | 0.203449 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.8840 | −1.09014 | −0.545069 | − | 0.838391i | \(-0.683496\pi\) | ||||
−0.545069 | + | 0.838391i | \(0.683496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.82548 | 0.199147 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 45.7595 | 2.37571 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −25.9819 | −1.34529 | −0.672647 | − | 0.739964i | \(-0.734843\pi\) | ||||
−0.672647 | + | 0.739964i | \(0.734843\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.2482 | 0.632495 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.42218 | 0.433764 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.50301 | 0.128571 | 0.0642855 | − | 0.997932i | \(-0.479523\pi\) | ||||
0.0642855 | + | 0.997932i | \(0.479523\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 29.1827 | 1.49507 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.8155 | 1.11472 | 0.557359 | − | 0.830272i | \(-0.311815\pi\) | ||||
0.557359 | + | 0.830272i | \(0.311815\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.1707 | 0.620274 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.35119 | −0.170351 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.2383 | −1.78665 | −0.893327 | − | 0.449407i | \(-0.851635\pi\) | ||||
−0.893327 | + | 0.449407i | \(0.851635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.2069 | −1.52763 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.9304 | 1.30802 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.28135 | −0.165103 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.0263 | 1.35641 | 0.678205 | − | 0.734873i | \(-0.262758\pi\) | ||||
0.678205 | + | 0.734873i | \(0.262758\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.91023 | −0.396007 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.8932 | −1.24311 | −0.621553 | − | 0.783372i | \(-0.713498\pi\) | ||||
−0.621553 | + | 0.783372i | \(0.713498\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.3383 | −1.01312 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.91230 | −0.293784 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.6247 | −1.27017 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.8336 | −0.733475 | −0.366738 | − | 0.930324i | \(-0.619525\pi\) | ||||
−0.366738 | + | 0.930324i | \(0.619525\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.54840 | 0.224356 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.79526 | 0.186753 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.13024 | 0.350010 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.434880 | 0.0212962 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.05955 | −0.296028 | −0.148014 | − | 0.988985i | \(-0.547288\pi\) | ||||
−0.148014 | + | 0.988985i | \(0.547288\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.8670 | −0.675834 | −0.337917 | − | 0.941176i | \(-0.609722\pi\) | ||||
−0.337917 | + | 0.941176i | \(0.609722\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.584249 | −0.0284072 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −33.1145 | −1.60629 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.5420 | −0.558555 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.8912 | 0.622391 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.5580 | 0.556729 | 0.278364 | − | 0.960476i | \(-0.410208\pi\) | ||||
0.278364 | + | 0.960476i | \(0.410208\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.7468 | −1.52565 | −0.762826 | − | 0.646604i | \(-0.776189\pi\) | ||||
−0.762826 | + | 0.646604i | \(0.776189\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.82760 | 0.183520 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.91023 | −0.187052 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.8840 | 1.18765 | 0.593825 | − | 0.804594i | \(-0.297617\pi\) | ||||
0.593825 | + | 0.804594i | \(0.297617\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.4789 | −0.498994 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.9911 | −1.13985 | −0.569926 | − | 0.821696i | \(-0.693028\pi\) | ||||
−0.569926 | + | 0.821696i | \(0.693028\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5701 | 0.643286 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.6215 | −0.596979 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 32.1384 | 1.51670 | 0.758352 | − | 0.651845i | \(-0.226005\pi\) | ||||
0.758352 | + | 0.651845i | \(0.226005\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.3785 | −0.912496 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 23.5147 | 1.10482 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.4166 | −0.582099 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.1590 | 1.36400 | 0.681999 | − | 0.731353i | \(-0.261111\pi\) | ||||
0.681999 | + | 0.731353i | \(0.261111\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 42.9634 | 2.00536 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.6559 | −0.868894 | −0.434447 | − | 0.900697i | \(-0.643056\pi\) | ||||
−0.434447 | + | 0.900697i | \(0.643056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.6005 | −1.05034 | −0.525168 | − | 0.850999i | \(-0.675997\pi\) | ||||
−0.525168 | + | 0.850999i | \(0.675997\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.24309 | −0.428638 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.1666 | −0.794377 | −0.397189 | − | 0.917737i | \(-0.630014\pi\) | ||||
−0.397189 | + | 0.917737i | \(0.630014\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 52.5502 | 2.42654 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.0636 | 0.786247 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.9759 | 0.780551 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.28663 | −0.196684 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.07270 | −0.232263 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.2625 | 0.743052 | 0.371526 | − | 0.928423i | \(-0.378835\pi\) | ||||
0.371526 | + | 0.928423i | \(0.378835\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.1425 | 1.19200 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 30.9309 | 1.40740 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.11597 | −0.141489 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.2071 | −0.825041 | −0.412520 | − | 0.910948i | \(-0.635351\pi\) | ||||
−0.412520 | + | 0.910948i | \(0.635351\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.08897 | −0.0492449 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.2493 | 1.77130 | 0.885649 | − | 0.464356i | \(-0.153714\pi\) | ||||
0.885649 | + | 0.464356i | \(0.153714\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.4189 | −1.00970 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.34919 | −0.0606414 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10.7961 | −0.484270 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −35.7541 | −1.60057 | −0.800286 | − | 0.599619i | \(-0.795319\pi\) | ||||
−0.800286 | + | 0.599619i | \(0.795319\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.75379 | 0.435767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.5512 | −1.22845 | −0.614223 | − | 0.789132i | \(-0.710530\pi\) | ||||
−0.614223 | + | 0.789132i | \(0.710530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.7218 | 0.610611 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.14851 | 0.317477 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.6328 | 0.648588 | 0.324294 | − | 0.945956i | \(-0.394873\pi\) | ||||
0.324294 | + | 0.945956i | \(0.394873\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.3118 | 1.03125 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.56155 | 0.245549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.686107 | 0.0302335 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.95958 | 0.130162 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.4583 | 0.459068 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.59926 | −0.332929 | −0.166465 | − | 0.986047i | \(-0.553235\pi\) | ||||
−0.166465 | + | 0.986047i | \(0.553235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.8723 | 0.868956 | 0.434478 | − | 0.900682i | \(-0.356933\pi\) | ||||
0.434478 | + | 0.900682i | \(0.356933\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 33.9082 | 1.47988 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 54.1384 | 2.35830 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.71007 | −0.335220 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.420727 | −0.0182580 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.7701 | 0.856336 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.35204 | 0.361090 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.4924 | −1.22954 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 53.0820 | 2.28640 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.6982 | −1.19084 | −0.595420 | − | 0.803415i | \(-0.703014\pi\) | ||||
−0.595420 | + | 0.803415i | \(0.703014\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.4289 | 1.17709 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.15353 | 0.392094 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.8871 | 1.44891 | 0.724455 | − | 0.689322i | \(-0.242092\pi\) | ||||
0.724455 | + | 0.689322i | \(0.242092\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.27949 | 0.0546075 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.90210 | −0.123634 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.6801 | −0.836883 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 11.8809 | 0.504316 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.28763 | 0.351158 | 0.175579 | − | 0.984465i | \(-0.443820\pi\) | ||||
0.175579 | + | 0.984465i | \(0.443820\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.3189 | −0.732512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −34.3149 | −1.44878 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.11397 | −0.215528 | −0.107764 | − | 0.994177i | \(-0.534369\pi\) | ||||
−0.107764 | + | 0.994177i | \(0.534369\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.262483 | −0.0110427 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −35.4593 | −1.48915 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.92830 | 0.0808387 | 0.0404194 | − | 0.999183i | \(-0.487131\pi\) | ||||
0.0404194 | + | 0.999183i | \(0.487131\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.3785 | −0.978358 | −0.489179 | − | 0.872183i | \(-0.662703\pi\) | ||||
−0.489179 | + | 0.872183i | \(0.662703\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.2383 | 0.469486 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.7617 | 0.699012 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.8807 | −1.11906 | −0.559530 | − | 0.828810i | \(-0.689018\pi\) | ||||
−0.559530 | + | 0.828810i | \(0.689018\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.57114 | 0.189970 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 42.7640 | 1.77415 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.6964 | 1.06423 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.37645 | 0.0569093 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.7922 | −1.51858 | −0.759288 | − | 0.650754i | \(-0.774453\pi\) | ||||
−0.759288 | + | 0.650754i | \(0.774453\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.00814 | 0.288765 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.3947 | −0.715523 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −33.9034 | −1.39225 | −0.696123 | − | 0.717922i | \(-0.745093\pi\) | ||||
−0.696123 | + | 0.717922i | \(0.745093\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 33.0517 | 1.35499 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.70128 | 0.356120 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.06456 | 0.166073 | 0.0830367 | − | 0.996546i | \(-0.473538\pi\) | ||||
0.0830367 | + | 0.996546i | \(0.473538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.5560 | −1.12403 | −0.562016 | − | 0.827126i | \(-0.689974\pi\) | ||||
−0.562016 | + | 0.827126i | \(0.689974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.82548 | −0.237232 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.45628 | −0.0998621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.5743 | −1.03803 | −0.519014 | − | 0.854766i | \(-0.673701\pi\) | ||||
−0.519014 | + | 0.854766i | \(0.673701\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 22.9563 | 0.930235 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.01939 | −0.122152 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.2383 | 1.26170 | 0.630852 | − | 0.775903i | \(-0.282705\pi\) | ||||
0.630852 | + | 0.775903i | \(0.282705\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.98485 | 0.362304 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.86189 | −0.235991 | −0.117995 | − | 0.993014i | \(-0.537647\pi\) | ||||
−0.117995 | + | 0.993014i | \(0.537647\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.6481 | −1.27204 | −0.636022 | − | 0.771671i | \(-0.719421\pi\) | ||||
−0.636022 | + | 0.771671i | \(0.719421\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.7470 | −0.872676 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 81.3877 | 3.26073 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8083 | 0.592333 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.44201 | −0.177397 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −69.5885 | −2.77468 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.86189 | 0.153739 | 0.0768696 | − | 0.997041i | \(-0.475507\pi\) | ||||
0.0768696 | + | 0.997041i | \(0.475507\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.92775 | 0.0766212 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.7843 | −0.626382 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −54.1546 | −2.14569 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.19680 | 0.0473449 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.9919 | −0.592143 | −0.296072 | − | 0.955166i | \(-0.595677\pi\) | ||||
−0.296072 | + | 0.955166i | \(0.595677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.4906 | −0.492580 | −0.246290 | − | 0.969196i | \(-0.579212\pi\) | ||||
−0.246290 | + | 0.969196i | \(0.579212\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −7.87088 | −0.309915 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.5743 | 0.926802 | 0.463401 | − | 0.886149i | \(-0.346629\pi\) | ||||
0.463401 | + | 0.886149i | \(0.346629\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.13124 | 0.0836585 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −55.4360 | −2.17271 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.4693 | −1.19236 | −0.596178 | − | 0.802853i | \(-0.703315\pi\) | ||||
−0.596178 | + | 0.802853i | \(0.703315\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.0253 | −0.548012 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.58425 | −0.100821 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 39.9049 | 1.55447 | 0.777237 | − | 0.629209i | \(-0.216621\pi\) | ||||
0.777237 | + | 0.629209i | \(0.216621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.8156 | 0.887422 | 0.443711 | − | 0.896170i | \(-0.353662\pi\) | ||||
0.443711 | + | 0.896170i | \(0.353662\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.0083 | 1.35961 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.27849 | 0.165913 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3479 | 0.439392 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.99599 | −0.347805 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.48143 | −0.250213 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.0265 | −1.42727 | −0.713634 | − | 0.700519i | \(-0.752952\pi\) | ||||
−0.713634 | + | 0.700519i | \(0.752952\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −23.8403 | −0.917614 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 45.6733 | 1.75537 | 0.877683 | − | 0.479241i | \(-0.159088\pi\) | ||||
0.877683 | + | 0.479241i | \(0.159088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.6882 | −0.717188 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.4679 | 0.669370 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.9837 | 0.535072 | 0.267536 | − | 0.963548i | \(-0.413790\pi\) | ||||
0.267536 | + | 0.963548i | \(0.413790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.46014 | −0.0939972 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.6048 | 1.51102 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.2156 | −0.998736 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.00185566 | −7.05926e−5 0 | −3.52963e−5 | − | 1.00000i | \(-0.500011\pi\) | ||||
−3.52963e−5 | 1.00000i | \(0.500011\pi\) | ||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.09183 | −0.307383 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.235218 | −0.00892233 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −52.6258 | −1.99334 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.0203 | −0.492472 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.0071 | 0.831198 | 0.415599 | − | 0.909548i | \(-0.363572\pi\) | ||||
0.415599 | + | 0.909548i | \(0.363572\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.00814 | −0.339748 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.37221 | −0.0516806 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 82.2971 | 3.09510 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.94045 | −0.147987 | −0.0739934 | − | 0.997259i | \(-0.523574\pi\) | ||||
−0.0739934 | + | 0.997259i | \(0.523574\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.18165 | 0.0818183 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −27.4035 | −1.02627 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.97258 | −0.260760 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −25.6783 | −0.958973 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 29.0656 | 1.08396 | 0.541982 | − | 0.840390i | \(-0.317674\pi\) | ||||
0.541982 | + | 0.840390i | \(0.317674\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.11497 | 0.153249 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.0325 | 0.745018 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.4402 | 0.462018 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.1617 | −0.376877 | −0.188439 | − | 0.982085i | \(-0.560343\pi\) | ||||
−0.188439 | + | 0.982085i | \(0.560343\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.9848 | 1.11055 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.1011 | 1.70511 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −51.4777 | −1.90137 | −0.950686 | − | 0.310156i | \(-0.899619\pi\) | ||||
−0.950686 | + | 0.310156i | \(0.899619\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −24.6115 | −0.907809 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.5097 | 1.08700 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.1412 | 1.21912 | 0.609560 | − | 0.792740i | \(-0.291346\pi\) | ||||
0.609560 | + | 0.792740i | \(0.291346\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.53178 | 0.166479 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.5006 | −1.30239 | −0.651195 | − | 0.758911i | \(-0.725732\pi\) | ||||
−0.651195 | + | 0.758911i | \(0.725732\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.82675 | 0.250113 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.74064 | −0.173451 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 50.0919 | 1.83032 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.2594 | −0.556822 | −0.278411 | − | 0.960462i | \(-0.589808\pi\) | ||||
−0.278411 | + | 0.960462i | \(0.589808\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.8780 | −1.01593 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.7187 | −0.462879 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.28161 | −0.264655 | −0.132327 | − | 0.991206i | \(-0.542245\pi\) | ||||
−0.132327 | + | 0.991206i | \(0.542245\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 17.3693 | 0.630466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.47886 | 0.343609 | 0.171804 | − | 0.985131i | \(-0.445040\pi\) | ||||
0.171804 | + | 0.985131i | \(0.445040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 54.8989 | 1.98747 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.66397 | −0.132471 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.17431 | −0.0785098 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.2760 | 0.695112 | 0.347556 | − | 0.937659i | \(-0.387012\pi\) | ||||
0.347556 | + | 0.937659i | \(0.387012\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.33206 | −0.0839871 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.19501 | −0.330721 | −0.165361 | − | 0.986233i | \(-0.552879\pi\) | ||||
−0.165361 | + | 0.986233i | \(0.552879\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −30.0413 | −1.07911 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 71.2565 | 2.55631 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.81233 | −0.244077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.06256 | −0.216935 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.1402 | −0.576803 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.22935 | −0.329410 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.6847 | 0.452159 | 0.226080 | − | 0.974109i | \(-0.427409\pi\) | ||||
0.226080 | + | 0.974109i | \(0.427409\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.754905 | 0.0268753 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.57426 | −0.0559741 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.61241 | 0.234814 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.9142 | −0.422551 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.4591 | −0.972651 | −0.486325 | − | 0.873778i | \(-0.661663\pi\) | ||||
−0.486325 | + | 0.873778i | \(0.661663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.03730 | 0.284339 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.02229 | −0.318787 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.0908 | 0.461965 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −16.7299 | −0.589652 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.1969 | 0.464554 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.2912 | 0.643084 | 0.321542 | − | 0.946895i | \(-0.395799\pi\) | ||||
0.321542 | + | 0.946895i | \(0.395799\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.28391 | 0.220658 | 0.110329 | − | 0.993895i | \(-0.464810\pi\) | ||||
0.110329 | + | 0.993895i | \(0.464810\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.8940 | −0.908141 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.589002 | 0.0206318 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.96772 | 0.208784 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.25535 | 0.288465 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.9103 | 1.53248 | 0.766240 | − | 0.642555i | \(-0.222125\pi\) | ||||
0.766240 | + | 0.642555i | \(0.222125\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.2483 | 0.914957 | 0.457479 | − | 0.889221i | \(-0.348753\pi\) | ||||
0.457479 | + | 0.889221i | \(0.348753\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19.0413 | 0.662932 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.7726 | −1.20916 | −0.604581 | − | 0.796543i | \(-0.706660\pi\) | ||||
−0.604581 | + | 0.796543i | \(0.706660\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.9184 | 0.726525 | 0.363263 | − | 0.931687i | \(-0.381663\pi\) | ||||
0.363263 | + | 0.931687i | \(0.381663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 24.5357 | 0.851134 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 144.154 | 4.99464 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.27563 | −0.182571 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 38.9761 | 1.34721 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.0061 | −1.41569 | −0.707844 | − | 0.706368i | \(-0.750332\pi\) | ||||
−0.707844 | + | 0.706368i | \(0.750332\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.5778 | −0.709580 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.90230 | −0.168844 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.86649 | −0.133011 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.7317 | −0.506187 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 41.2070 | 1.41422 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 35.2239 | 1.20746 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5056 | −0.393943 | −0.196972 | − | 0.980409i | \(-0.563111\pi\) | ||||
−0.196972 | + | 0.980409i | \(0.563111\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −0.474295 | −0.0162206 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.7478 | 0.503774 | 0.251887 | − | 0.967757i | \(-0.418949\pi\) | ||||
0.251887 | + | 0.967757i | \(0.418949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.3402 | 1.23991 | 0.619955 | − | 0.784637i | \(-0.287151\pi\) | ||||
0.619955 | + | 0.784637i | \(0.287151\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 53.8871 | 1.83647 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −48.3454 | −1.64570 | −0.822849 | − | 0.568260i | \(-0.807617\pi\) | ||||
−0.822849 | + | 0.568260i | \(0.807617\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.65668 | −0.192333 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −66.6421 | −2.26328 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.0514 | −0.374893 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.1060 | −1.02010 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.07170 | 0.0701163 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −39.7328 | −1.34321 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.23226 | 0.142913 | 0.0714567 | − | 0.997444i | \(-0.477235\pi\) | ||||
0.0714567 | + | 0.997444i | \(0.477235\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.2220 | 0.715801 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.6651 | 1.10051 | 0.550257 | − | 0.834995i | \(-0.314530\pi\) | ||||
0.550257 | + | 0.834995i | \(0.314530\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.3320 | −1.52554 | −0.762772 | − | 0.646668i | \(-0.776162\pi\) | ||||
−0.762772 | + | 0.646668i | \(0.776162\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.988153 | −0.0332164 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 50.5271 | 1.69653 | 0.848267 | − | 0.529569i | \(-0.177646\pi\) | ||||
0.848267 | + | 0.529569i | \(0.177646\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −94.6675 | −3.17504 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19.9123 | −0.667087 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.04042 | 0.0348162 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4110 | 0.515133 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.7203 | −0.591664 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.3383 | −0.678320 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 69.7832 | 2.32482 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −47.2061 | −1.57092 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −14.8357 | −0.493157 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.9823 | −0.729910 | −0.364955 | − | 0.931025i | \(-0.618916\pi\) | ||||
−0.364955 | + | 0.931025i | \(0.618916\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.12311 | −0.302594 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.9950 | 0.993778 | 0.496889 | − | 0.867814i | \(-0.334476\pi\) | ||||
0.496889 | + | 0.867814i | \(0.334476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.0143 | 0.794756 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.00512 | 0.0993463 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −84.1174 | −2.77780 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.5481 | 1.00769 | 0.503844 | − | 0.863795i | \(-0.331919\pi\) | ||||
0.503844 | + | 0.863795i | \(0.331919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.37645 | 0.177160 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.18507 | 0.203584 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.6145 | 1.26964 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.456168 | −0.0149825 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.67151 | −0.186076 | −0.0930380 | − | 0.995663i | \(-0.529658\pi\) | ||||
−0.0930380 | + | 0.995663i | \(0.529658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.6605 | 0.611574 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −46.0556 | −1.50779 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 18.5603 | 0.606985 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.6051 | 1.09783 | 0.548915 | − | 0.835878i | \(-0.315041\pi\) | ||||
0.548915 | + | 0.835878i | \(0.315041\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.7141 | 0.512810 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.0543 | −0.979743 | −0.489871 | − | 0.871795i | \(-0.662956\pi\) | ||||
−0.489871 | + | 0.871795i | \(0.662956\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.6378 | 0.867447 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 23.7951 | 0.774053 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.3058 | −0.399883 | −0.199942 | − | 0.979808i | \(-0.564075\pi\) | ||||
−0.199942 | + | 0.979808i | \(0.564075\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.3554 | −0.433534 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.47937 | 0.210108 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.4674 | 0.986937 | 0.493468 | − | 0.869764i | \(-0.335729\pi\) | ||||
0.493468 | + | 0.869764i | \(0.335729\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.07857 | −0.196698 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.8912 | 0.416712 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.7548 | −0.476459 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.1140 | 0.584322 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.55297 | −0.178942 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.47244 | −0.0795906 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.26560 | 0.169330 | 0.0846652 | − | 0.996409i | \(-0.473018\pi\) | ||||
0.0846652 | + | 0.996409i | \(0.473018\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.0631 | −0.387523 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54.7895 | −1.75828 | −0.879139 | − | 0.476566i | \(-0.841881\pi\) | ||||
−0.879139 | + | 0.476566i | \(0.841881\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.41074 | −0.0452261 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.4261 | −0.622132 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.9690 | 0.926800 | 0.463400 | − | 0.886149i | \(-0.346629\pi\) | ||||
0.463400 | + | 0.886149i | \(0.346629\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.7035 | 1.46069 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.08585 | −0.194306 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.2997 | −1.12589 | −0.562943 | − | 0.826495i | \(-0.690331\pi\) | ||||
−0.562943 | + | 0.826495i | \(0.690331\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.40847 | 0.299779 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.22994 | −0.261962 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.3352 | −0.742016 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.34833 | 0.265194 | 0.132597 | − | 0.991170i | \(-0.457668\pi\) | ||||
0.132597 | + | 0.991170i | \(0.457668\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40.4264 | −1.28289 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.70635 | −0.149201 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.81519 | −0.184169 | −0.0920845 | − | 0.995751i | \(-0.529353\pi\) | ||||
−0.0920845 | + | 0.995751i | \(0.529353\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −50.0992 | −1.58507 |
(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 | 1216.2.a.x.1.2 | 4 | ||
4.3 | odd | 2 | 1216.2.a.w.1.4 | 4 | |||
8.3 | odd | 2 | 608.2.a.j.1.1 | yes | 4 | ||
8.5 | even | 2 | 608.2.a.i.1.3 | ✓ | 4 | ||
24.5 | odd | 2 | 5472.2.a.bt.1.3 | 4 | |||
24.11 | even | 2 | 5472.2.a.bs.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.2.a.i.1.3 | ✓ | 4 | 8.5 | even | 2 | ||
608.2.a.j.1.1 | yes | 4 | 8.3 | odd | 2 | ||
1216.2.a.w.1.4 | 4 | 4.3 | odd | 2 | |||
1216.2.a.x.1.2 | 4 | 1.1 | even | 1 | trivial | ||
5472.2.a.bs.1.3 | 4 | 24.11 | even | 2 | |||
5472.2.a.bt.1.3 | 4 | 24.5 | odd | 2 |