Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2296428209\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.29572 | −1.32544 | −0.662718 | − | 0.748869i | \(-0.730597\pi\) | ||||
−0.662718 | + | 0.748869i | \(0.730597\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.99611 | 1.88835 | 0.944176 | − | 0.329442i | \(-0.106861\pi\) | ||||
0.944176 | + | 0.329442i | \(0.106861\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.27034 | 0.756780 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.0910559 | −0.0274544 | −0.0137272 | − | 0.999906i | \(-0.504370\pi\) | ||||
−0.0137272 | + | 0.999906i | \(0.504370\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.74101 | 1.31492 | 0.657459 | − | 0.753490i | \(-0.271631\pi\) | ||||
0.657459 | + | 0.753490i | \(0.271631\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.29572 | −0.592753 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.08447 | 0.748094 | 0.374047 | − | 0.927410i | \(-0.377970\pi\) | ||||
0.374047 | + | 0.927410i | \(0.377970\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.48388 | 0.799257 | 0.399628 | − | 0.916677i | \(-0.369139\pi\) | ||||
0.399628 | + | 0.916677i | \(0.369139\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.4697 | −2.50289 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.20981 | 1.08632 | 0.543161 | − | 0.839629i | \(-0.317227\pi\) | ||||
0.543161 | + | 0.839629i | \(0.317227\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.67510 | 0.322372 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.87156 | 0.904627 | 0.452313 | − | 0.891859i | \(-0.350599\pi\) | ||||
0.452313 | + | 0.891859i | \(0.350599\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.75626 | −0.854250 | −0.427125 | − | 0.904193i | \(-0.640474\pi\) | ||||
−0.427125 | + | 0.904193i | \(0.640474\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.209039 | 0.0363890 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.99611 | 0.844497 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.85526 | 0.469402 | 0.234701 | − | 0.972068i | \(-0.424589\pi\) | ||||
0.234701 | + | 0.972068i | \(0.424589\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.8840 | −1.74284 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.46870 | 1.16641 | 0.583207 | − | 0.812323i | \(-0.301798\pi\) | ||||
0.583207 | + | 0.812323i | \(0.301798\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.78036 | −0.424001 | −0.212000 | − | 0.977270i | \(-0.567998\pi\) | ||||
−0.212000 | + | 0.977270i | \(0.567998\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.27034 | 0.338442 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.24075 | 1.20204 | 0.601018 | − | 0.799235i | \(-0.294762\pi\) | ||||
0.601018 | + | 0.799235i | \(0.294762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.9611 | 2.56587 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.08109 | −0.991551 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.79674 | −0.384162 | −0.192081 | − | 0.981379i | \(-0.561524\pi\) | ||||
−0.192081 | + | 0.981379i | \(0.561524\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.0910559 | −0.0122780 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.99802 | −1.05936 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.93952 | 0.643071 | 0.321535 | − | 0.946898i | \(-0.395801\pi\) | ||||
0.321535 | + | 0.946898i | \(0.395801\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.5686 | −1.99336 | −0.996680 | − | 0.0814198i | \(-0.974055\pi\) | ||||
−0.996680 | + | 0.0814198i | \(0.974055\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 11.3429 | 1.42907 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.74101 | 0.588049 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.961539 | 0.117471 | 0.0587353 | − | 0.998274i | \(-0.481293\pi\) | ||||
0.0587353 | + | 0.998274i | \(0.481293\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −11.9603 | −1.43985 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.81571 | −0.334164 | −0.167082 | − | 0.985943i | \(-0.553434\pi\) | ||||
−0.167082 | + | 0.985943i | \(0.553434\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.7476 | 1.96016 | 0.980081 | − | 0.198597i | \(-0.0636386\pi\) | ||||
0.980081 | + | 0.198597i | \(0.0636386\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.29572 | −0.265087 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.454925 | −0.0518435 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.64257 | −0.634839 | −0.317419 | − | 0.948285i | \(-0.602816\pi\) | ||||
−0.317419 | + | 0.948285i | \(0.602816\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.6566 | −1.18406 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.20514 | −0.790867 | −0.395433 | − | 0.918495i | \(-0.629406\pi\) | ||||
−0.395433 | + | 0.918495i | \(0.629406\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.08447 | 0.334558 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.1838 | −1.19902 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.59491 | 0.275060 | 0.137530 | − | 0.990498i | \(-0.456084\pi\) | ||||
0.137530 | + | 0.990498i | \(0.456084\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23.6866 | 2.48303 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.9191 | 1.13225 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.48388 | 0.357438 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.3132 | 1.35175 | 0.675877 | − | 0.737015i | \(-0.263765\pi\) | ||||
0.675877 | + | 0.737015i | \(0.263765\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.206728 | −0.0207769 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.41251 | 0.339557 | 0.169779 | − | 0.985482i | \(-0.445695\pi\) | ||||
0.169779 | + | 0.985482i | \(0.445695\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.6336 | −1.34335 | −0.671677 | − | 0.740844i | \(-0.734426\pi\) | ||||
−0.671677 | + | 0.740844i | \(0.734426\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.4697 | −1.11933 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.22568 | −0.891880 | −0.445940 | − | 0.895063i | \(-0.647131\pi\) | ||||
−0.445940 | + | 0.895063i | \(0.647131\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.17922 | −0.208732 | −0.104366 | − | 0.994539i | \(-0.533281\pi\) | ||||
−0.104366 | + | 0.994539i | \(0.533281\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.55488 | −0.622162 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.8473 | −1.30264 | −0.651322 | − | 0.758801i | \(-0.725785\pi\) | ||||
−0.651322 | + | 0.758801i | \(0.725785\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.20981 | 0.485818 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.7637 | 0.995104 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.4104 | 1.41267 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9917 | −0.999246 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.1461 | −1.54601 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.3742 | −0.920558 | −0.460279 | − | 0.887774i | \(-0.652251\pi\) | ||||
−0.460279 | + | 0.887774i | \(0.652251\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.38293 | 0.561986 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.0953 | −1.40625 | −0.703127 | − | 0.711064i | \(-0.748214\pi\) | ||||
−0.703127 | + | 0.711064i | \(0.748214\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.4058 | 1.50928 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.67510 | 0.144169 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.40018 | −0.546804 | −0.273402 | − | 0.961900i | \(-0.588149\pi\) | ||||
−0.273402 | + | 0.961900i | \(0.588149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.6231 | −1.32513 | −0.662567 | − | 0.749002i | \(-0.730533\pi\) | ||||
−0.662567 | + | 0.749002i | \(0.730533\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.9185 | −1.59322 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.431697 | −0.0361003 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.87156 | 0.404561 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −41.2337 | −3.40090 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.99341 | 0.327153 | 0.163576 | − | 0.986531i | \(-0.447697\pi\) | ||||
0.163576 | + | 0.986531i | \(0.447697\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.00280 | 0.566143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.75626 | −0.382032 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.26269 | −0.260391 | −0.130195 | − | 0.991488i | \(-0.541560\pi\) | ||||
−0.130195 | + | 0.991488i | \(0.541560\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.42054 | 0.509182 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.0288 | 2.05136 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.1793 | −1.03228 | −0.516141 | − | 0.856503i | \(-0.672632\pi\) | ||||
−0.516141 | + | 0.856503i | \(0.672632\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.209039 | 0.0162737 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.26874 | 0.330325 | 0.165163 | − | 0.986266i | \(-0.447185\pi\) | ||||
0.165163 | + | 0.986266i | \(0.447185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.47714 | 0.729011 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.90959 | 0.604862 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.56099 | 0.422794 | 0.211397 | − | 0.977400i | \(-0.432199\pi\) | ||||
0.211397 | + | 0.977400i | \(0.432199\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.99611 | 0.377670 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.3398 | −0.852349 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.12353 | −0.382951 | −0.191475 | − | 0.981497i | \(-0.561327\pi\) | ||||
−0.191475 | + | 0.981497i | \(0.561327\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.888073 | −0.0660100 | −0.0330050 | − | 0.999455i | \(-0.510508\pi\) | ||||
−0.0330050 | + | 0.999455i | \(0.510508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35.7413 | 2.64207 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.85526 | 0.209923 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.280859 | −0.0205385 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.36896 | 0.608752 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.5361 | −0.907082 | −0.453541 | − | 0.891236i | \(-0.649839\pi\) | ||||
−0.453541 | + | 0.891236i | \(0.649839\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.12120 | −0.152688 | −0.0763438 | − | 0.997082i | \(-0.524325\pi\) | ||||
−0.0763438 | + | 0.997082i | \(0.524325\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.8840 | −0.779422 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.92506 | 0.350896 | 0.175448 | − | 0.984489i | \(-0.443863\pi\) | ||||
0.175448 | + | 0.984489i | \(0.443863\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.7707 | −1.40151 | −0.700755 | − | 0.713402i | \(-0.747153\pi\) | ||||
−0.700755 | + | 0.713402i | \(0.747153\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.20743 | −0.155700 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 24.3389 | 1.70825 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.46870 | 0.521636 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.8281 | 0.822106 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.317228 | −0.0219431 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7409 | 1.22134 | 0.610668 | − | 0.791887i | \(-0.290901\pi\) | ||||
0.610668 | + | 0.791887i | \(0.290901\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.46410 | 0.442913 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.78036 | −0.189619 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.7628 | −1.61312 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −38.4479 | −2.59807 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.6235 | 0.983683 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.0406 | −1.54291 | −0.771456 | − | 0.636282i | \(-0.780471\pi\) | ||||
−0.771456 | + | 0.636282i | \(0.780471\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.27034 | 0.151356 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.6592 | −1.10571 | −0.552855 | − | 0.833278i | \(-0.686461\pi\) | ||||
−0.552855 | + | 0.833278i | \(0.686461\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.8292 | −1.44251 | −0.721256 | − | 0.692668i | \(-0.756435\pi\) | ||||
−0.721256 | + | 0.692668i | \(0.756435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.04438 | 0.0687153 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.42410 | −0.158808 | −0.0794040 | − | 0.996843i | \(-0.525302\pi\) | ||||
−0.0794040 | + | 0.996843i | \(0.525302\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.24075 | 0.537567 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 12.9538 | 0.841438 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.0709 | 0.651435 | 0.325717 | − | 0.945467i | \(-0.394394\pi\) | ||||
0.325717 | + | 0.945467i | \(0.394394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.33315 | 0.214707 | 0.107354 | − | 0.994221i | \(-0.465762\pi\) | ||||
0.107354 | + | 0.994221i | \(0.465762\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.4393 | 1.24703 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.9611 | 1.14749 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.5171 | 1.05096 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.5410 | 1.04824 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.1622 | 0.893911 | 0.446955 | − | 0.894556i | \(-0.352508\pi\) | ||||
0.446955 | + | 0.894556i | \(0.352508\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.474384 | −0.0298243 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.08109 | −0.443435 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.38431 | 0.335864 | 0.167932 | − | 0.985799i | \(-0.446291\pi\) | ||||
0.167932 | + | 0.985799i | \(0.446291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.2652 | 0.886395 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.0601 | 0.684603 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.6732 | 0.966449 | 0.483225 | − | 0.875496i | \(-0.339465\pi\) | ||||
0.483225 | + | 0.875496i | \(0.339465\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.79674 | −0.171802 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.95718 | −0.364574 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.9301 | 1.33710 | 0.668551 | − | 0.743666i | \(-0.266915\pi\) | ||||
0.668551 | + | 0.743666i | \(0.266915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.45274 | −0.0882477 | −0.0441239 | − | 0.999026i | \(-0.514050\pi\) | ||||
−0.0441239 | + | 0.999026i | \(0.514050\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −54.3778 | −3.29110 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0910559 | −0.00549088 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.3443 | −1.28245 | −0.641227 | − | 0.767351i | \(-0.721574\pi\) | ||||
−0.641227 | + | 0.767351i | \(0.721574\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.7983 | −0.646479 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.7183 | 1.11664 | 0.558319 | − | 0.829626i | \(-0.311446\pi\) | ||||
0.558319 | + | 0.829626i | \(0.311446\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.39773 | 0.558637 | 0.279319 | − | 0.960199i | \(-0.409891\pi\) | ||||
0.279319 | + | 0.960199i | \(0.409891\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.99802 | −0.473762 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 37.3144 | 2.20260 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.48603 | −0.440355 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −30.5635 | −1.79166 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.71506 | −0.275456 | −0.137728 | − | 0.990470i | \(-0.543980\pi\) | ||||
−0.137728 | + | 0.990470i | \(0.543980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.93952 | 0.287590 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.152527 | −0.00885053 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 24.6998 | 1.42842 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.8910 | −0.800663 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −7.83417 | −0.450061 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −15.5686 | −0.891458 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.0915 | −1.83156 | −0.915781 | − | 0.401679i | \(-0.868427\pi\) | ||||
−0.915781 | + | 0.401679i | \(0.868427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.2989 | 1.78053 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.5615 | 1.67628 | 0.838140 | − | 0.545456i | \(-0.183643\pi\) | ||||
0.838140 | + | 0.545456i | \(0.183643\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.3182 | 1.20498 | 0.602489 | − | 0.798127i | \(-0.294176\pi\) | ||||
0.602489 | + | 0.798127i | \(0.294176\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 11.3429 | 0.639098 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.7507 | −1.10931 | −0.554655 | − | 0.832081i | \(-0.687150\pi\) | ||||
−0.554655 | + | 0.832081i | \(0.687150\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.443585 | −0.0248360 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.1796 | 1.18213 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.7459 | 0.597919 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.74101 | 0.262984 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.00289 | 0.276660 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 41.1717 | 2.26987 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.2818 | 1.27968 | 0.639842 | − | 0.768507i | \(-0.279000\pi\) | ||||
0.639842 | + | 0.768507i | \(0.279000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.48241 | 0.355234 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.961539 | 0.0525345 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.86711 | −0.156182 | −0.0780908 | − | 0.996946i | \(-0.524882\pi\) | ||||
−0.0780908 | + | 0.996946i | \(0.524882\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.7895 | 1.72657 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.433086 | 0.0234529 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 54.7629 | 2.95692 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.9603 | −0.643920 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −29.8394 | −1.60187 | −0.800933 | − | 0.598754i | \(-0.795663\pi\) | ||||
−0.800933 | + | 0.598754i | \(0.795663\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.7895 | 1.48754 | 0.743770 | − | 0.668436i | \(-0.233036\pi\) | ||||
0.743770 | + | 0.668436i | \(0.233036\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.94164 | 0.423893 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.38821 | 0.340010 | 0.170005 | − | 0.985443i | \(-0.445622\pi\) | ||||
0.170005 | + | 0.985443i | \(0.445622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.81571 | −0.149443 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −35.3779 | −1.87240 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.6112 | −0.612816 | −0.306408 | − | 0.951900i | \(-0.599127\pi\) | ||||
−0.306408 | + | 0.951900i | \(0.599127\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.86259 | −0.361189 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.2339 | 1.32444 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.7476 | 0.876611 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −35.9009 | −1.87401 | −0.937006 | − | 0.349314i | \(-0.886415\pi\) | ||||
−0.937006 | + | 0.349314i | \(0.886415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.9565 | 0.882719 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.9728 | −0.725433 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.29396 | −0.274111 | −0.137055 | − | 0.990563i | \(-0.543764\pi\) | ||||
−0.137055 | + | 0.990563i | \(0.543764\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.29572 | −0.118551 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.0961 | 1.18951 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.8767 | −1.22646 | −0.613232 | − | 0.789903i | \(-0.710131\pi\) | ||||
−0.613232 | + | 0.789903i | \(0.710131\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 23.8162 | 1.22014 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.33195 | −0.221352 | −0.110676 | − | 0.993857i | \(-0.535302\pi\) | ||||
−0.110676 | + | 0.993857i | \(0.535302\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.454925 | −0.0231851 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.31236 | −0.320876 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.6380 | 1.29990 | 0.649948 | − | 0.759979i | \(-0.274791\pi\) | ||||
0.649948 | + | 0.759979i | \(0.274791\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0695 | 0.812671 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.9504 | 1.86390 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.64257 | −0.283908 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.67229 | −0.485438 | −0.242719 | − | 0.970097i | \(-0.578039\pi\) | ||||
−0.242719 | + | 0.970097i | \(0.578039\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −39.9590 | −2.00045 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.0926 | 1.65256 | 0.826282 | − | 0.563257i | \(-0.190452\pi\) | ||||
0.826282 | + | 0.563257i | \(0.190452\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.5495 | −1.12327 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.6566 | −0.529529 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.259988 | −0.0128871 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.4378 | 1.10948 | 0.554739 | − | 0.832024i | \(-0.312818\pi\) | ||||
0.554739 | + | 0.832024i | \(0.312818\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.6930 | 0.724754 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 24.6784 | 1.21434 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.20514 | −0.353686 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 35.8663 | 1.75638 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.37539 | −0.262605 | −0.131302 | − | 0.991342i | \(-0.541916\pi\) | ||||
−0.131302 | + | 0.991342i | \(0.541916\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.0199154 | −0.000970619 0 | −0.000485309 | − | 1.00000i | \(-0.500154\pi\) | ||||
−0.000485309 | 1.00000i | \(0.500154\pi\) | ||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.7093 | 0.909678 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.08447 | 0.149619 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −77.7826 | −3.76416 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.991055 | 0.0478486 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.3684 | 0.643933 | 0.321966 | − | 0.946751i | \(-0.395656\pi\) | ||||
0.321966 | + | 0.946751i | \(0.395656\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.4711 | 1.27212 | 0.636059 | − | 0.771640i | \(-0.280563\pi\) | ||||
0.636059 | + | 0.771640i | \(0.280563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.1838 | −0.536220 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.1504 | 0.868250 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.1526 | 0.484556 | 0.242278 | − | 0.970207i | \(-0.422105\pi\) | ||||
0.242278 | + | 0.970207i | \(0.422105\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 40.7778 | 1.94180 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.671932 | 0.0319245 | 0.0159622 | − | 0.999873i | \(-0.494919\pi\) | ||||
0.0159622 | + | 0.999873i | \(0.494919\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.59491 | 0.123010 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.16776 | −0.433620 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1103 | −0.854680 | −0.427340 | − | 0.904091i | \(-0.640549\pi\) | ||||
−0.427340 | + | 0.904091i | \(0.640549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.680069 | −0.0320232 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.29572 | −0.107862 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 23.6866 | 1.11044 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.23106 | −0.385033 | −0.192516 | − | 0.981294i | \(-0.561665\pi\) | ||||
−0.192516 | + | 0.981294i | \(0.561665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.16679 | 0.241165 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.8788 | −0.879272 | −0.439636 | − | 0.898176i | \(-0.644892\pi\) | ||||
−0.439636 | + | 0.898176i | \(0.644892\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.68209 | 0.217595 | 0.108797 | − | 0.994064i | \(-0.465300\pi\) | ||||
0.108797 | + | 0.994064i | \(0.465300\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.9191 | 0.506359 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −42.1173 | −1.94896 | −0.974479 | − | 0.224478i | \(-0.927932\pi\) | ||||
−0.974479 | + | 0.224478i | \(0.927932\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.80395 | 0.221826 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.49023 | 0.345131 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.253168 | 0.0116407 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.48388 | 0.159851 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.34955 | −0.290726 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.5051 | 1.25674 | 0.628371 | − | 0.777914i | \(-0.283722\pi\) | ||||
0.628371 | + | 0.777914i | \(0.283722\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.5368 | 0.617225 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −59.7549 | −2.71894 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.3132 | 0.604522 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.3512 | 1.37535 | 0.687673 | − | 0.726020i | \(-0.258632\pi\) | ||||
0.687673 | + | 0.726020i | \(0.258632\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30.2560 | 1.36822 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.73478 | −0.213677 | −0.106839 | − | 0.994276i | \(-0.534073\pi\) | ||||
−0.106839 | + | 0.994276i | \(0.534073\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0262 | 0.676746 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.206728 | −0.00929173 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.0676 | −0.631019 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.2043 | −1.79979 | −0.899896 | − | 0.436104i | \(-0.856358\pi\) | ||||
−0.899896 | + | 0.436104i | \(0.856358\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.79985 | −0.437825 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.3196 | 1.53024 | 0.765118 | − | 0.643890i | \(-0.222681\pi\) | ||||
0.765118 | + | 0.643890i | \(0.222681\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.41251 | 0.151855 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −21.7569 | −0.966257 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.4105 | 0.771707 | 0.385854 | − | 0.922560i | \(-0.373907\pi\) | ||||
0.385854 | + | 0.922560i | \(0.373907\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 83.6730 | 3.70148 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.83583 | 0.257658 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −13.6336 | −0.600767 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.750369 | −0.0330012 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.7665 | −0.560386 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.03291 | 0.0452526 | 0.0226263 | − | 0.999744i | \(-0.492797\pi\) | ||||
0.0226263 | + | 0.999744i | \(0.492797\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5864 | 0.594091 | 0.297046 | − | 0.954863i | \(-0.403999\pi\) | ||||
0.297046 | + | 0.954863i | \(0.403999\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.4697 | −0.500578 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.6706 | −0.639059 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.14216 | 0.180094 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.2144 | 0.486663 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.4091 | 1.53374 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.22568 | −0.398861 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 11.7622 | 0.507576 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.63546 | −0.0704445 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.07734 | −0.304279 | −0.152139 | − | 0.988359i | \(-0.548616\pi\) | ||||
−0.152139 | + | 0.988359i | \(0.548616\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.03877 | 0.0874920 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.17922 | −0.0933476 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.10611 | 0.346592 | 0.173296 | − | 0.984870i | \(-0.444558\pi\) | ||||
0.173296 | + | 0.984870i | \(0.444558\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −35.3461 | −1.50854 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.9719 | 0.723029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.1909 | −1.19880 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.55488 | −0.278239 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.4217 | 1.75509 | 0.877546 | − | 0.479492i | \(-0.159179\pi\) | ||||
0.877546 | + | 0.479492i | \(0.159179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.1817 | −0.557527 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.644775 | 0.0272224 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.2371 | −1.19005 | −0.595025 | − | 0.803707i | \(-0.702858\pi\) | ||||
−0.595025 | + | 0.803707i | \(0.702858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.8473 | −0.582560 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −53.2414 | −2.23593 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.7009 | 0.532450 | 0.266225 | − | 0.963911i | \(-0.414224\pi\) | ||||
0.266225 | + | 0.963911i | \(0.414224\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.73768 | −0.198266 | −0.0991330 | − | 0.995074i | \(-0.531607\pi\) | ||||
−0.0991330 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 28.7794 | 1.20228 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.20981 | 0.217264 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.4676 | −0.935339 | −0.467669 | − | 0.883903i | \(-0.654906\pi\) | ||||
−0.467669 | + | 0.883903i | \(0.654906\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.86969 | 0.202378 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −35.9977 | −1.49344 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.254660 | 0.0105469 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.7637 | 0.445024 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.93739 | 0.0799646 | 0.0399823 | − | 0.999200i | \(-0.487270\pi\) | ||||
0.0399823 | + | 0.999200i | \(0.487270\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.5702 | −0.682765 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.3066 | −0.465090 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −25.4894 | −1.04672 | −0.523361 | − | 0.852111i | \(-0.675322\pi\) | ||||
−0.523361 | + | 0.852111i | \(0.675322\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.4104 | 0.631763 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 45.3881 | 1.85761 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.44120 | 0.0588859 | 0.0294429 | − | 0.999566i | \(-0.490627\pi\) | ||||
0.0294429 | + | 0.999566i | \(0.490627\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.5905 | 0.676741 | 0.338370 | − | 0.941013i | \(-0.390124\pi\) | ||||
0.338370 | + | 0.941013i | \(0.390124\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.18302 | 0.0888995 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −10.9917 | −0.446877 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.8372 | 0.967521 | 0.483761 | − | 0.875200i | \(-0.339271\pi\) | ||||
0.483761 | + | 0.875200i | \(0.339271\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −55.8753 | −2.26418 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 39.0694 | 1.58058 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.9049 | −0.965510 | −0.482755 | − | 0.875756i | \(-0.660364\pi\) | ||||
−0.482755 | + | 0.875756i | \(0.660364\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.1461 | −0.691396 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.8968 | 0.962050 | 0.481025 | − | 0.876707i | \(-0.340265\pi\) | ||||
0.481025 | + | 0.876707i | \(0.340265\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.3190 | 1.25882 | 0.629409 | − | 0.777074i | \(-0.283297\pi\) | ||||
0.629409 | + | 0.777074i | \(0.283297\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.72694 | 0.350200 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.9644 | 0.519409 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.728267 | 0.0290842 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.80696 | 0.351157 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.3148 | 1.28643 | 0.643215 | − | 0.765685i | \(-0.277600\pi\) | ||||
0.643215 | + | 0.765685i | \(0.277600\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −40.7282 | −1.61880 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.3742 | −0.411686 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 85.1537 | 3.37391 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.39263 | −0.252889 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.8511 | −1.41603 | −0.708016 | − | 0.706197i | \(-0.750409\pi\) | ||||
−0.708016 | + | 0.706197i | \(0.750409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.3341 | 1.11739 | 0.558695 | − | 0.829373i | \(-0.311302\pi\) | ||||
0.558695 | + | 0.829373i | \(0.311302\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.38293 | 0.251328 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −41.4329 | −1.62890 | −0.814448 | − | 0.580236i | \(-0.802960\pi\) | ||||
−0.814448 | + | 0.580236i | \(0.802960\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.449772 | −0.0176551 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 54.5528 | 2.13809 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.7251 | 1.04583 | 0.522916 | − | 0.852384i | \(-0.324844\pi\) | ||||
0.522916 | + | 0.852384i | \(0.324844\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.0953 | −0.628896 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38.0228 | 1.48341 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.2412 | 1.48967 | 0.744833 | − | 0.667251i | \(-0.232529\pi\) | ||||
0.744833 | + | 0.667251i | \(0.232529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.4182 | −0.988653 | −0.494327 | − | 0.869276i | \(-0.664585\pi\) | ||||
−0.494327 | + | 0.869276i | \(0.664585\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.5715 | −1.30381 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 17.4058 | 0.674970 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.3799 | 0.982715 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 52.8948 | 2.04503 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.41762 | 0.0547265 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3957 | −0.632009 | −0.316004 | − | 0.948758i | \(-0.602341\pi\) | ||||
−0.316004 | + | 0.948758i | \(0.602341\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.67510 | 0.0644745 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.4707 | −0.863621 | −0.431810 | − | 0.901964i | \(-0.642125\pi\) | ||||
−0.431810 | + | 0.901964i | \(0.642125\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 66.5143 | 2.55259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 38.2449 | 1.46555 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.9550 | −0.610499 | −0.305250 | − | 0.952272i | \(-0.598740\pi\) | ||||
−0.305250 | + | 0.952272i | \(0.598740\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.40018 | −0.244538 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 50.1137 | 1.91196 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.2594 | −0.505141 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −39.6298 | −1.50759 | −0.753795 | − | 0.657110i | \(-0.771779\pi\) | ||||
−0.753795 | + | 0.657110i | \(0.771779\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.03284 | −0.0392342 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.6231 | −0.592618 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.0370 | 0.872588 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.56506 | 0.210490 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.6715 | 0.516367 | 0.258184 | − | 0.966096i | \(-0.416876\pi\) | ||||
0.258184 | + | 0.966096i | \(0.416876\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.94738 | 0.375172 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.9185 | −0.712511 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.0493 | 0.641203 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4047 | −0.616093 | −0.308046 | − | 0.951371i | \(-0.599675\pi\) | ||||
−0.308046 | + | 0.951371i | \(0.599675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −12.8106 | −0.480433 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.7792 | −0.927990 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.431697 | −0.0161445 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −23.1201 | −0.863435 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.6607 | −1.51639 | −0.758195 | − | 0.652028i | \(-0.773918\pi\) | ||||
−0.758195 | + | 0.652028i | \(0.773918\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −68.1148 | −2.53673 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.65199 | −0.284580 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.87156 | 0.180925 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.5670 | −0.503172 | −0.251586 | − | 0.967835i | \(-0.580952\pi\) | ||||
−0.251586 | + | 0.967835i | \(0.580952\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −12.6574 | −0.468792 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.57594 | −0.317193 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.19748 | 0.191973 | 0.0959866 | − | 0.995383i | \(-0.469399\pi\) | ||||
0.0959866 | + | 0.995383i | \(0.469399\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −41.2337 | −1.52093 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −0.0875538 | −0.00322508 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −48.8323 | −1.79633 | −0.898163 | − | 0.439663i | \(-0.855098\pi\) | ||||
−0.898163 | + | 0.439663i | \(0.855098\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −37.9187 | −1.39298 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.4597 | 1.26420 | 0.632101 | − | 0.774886i | \(-0.282193\pi\) | ||||
0.632101 | + | 0.774886i | \(0.282193\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.99341 | 0.146307 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.3581 | −0.598512 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.0925 | −1.68418 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.6104 | −1.00752 | −0.503758 | − | 0.863845i | \(-0.668050\pi\) | ||||
−0.503758 | + | 0.863845i | \(0.668050\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −32.5125 | −1.18482 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.67066 | −0.278795 | −0.139397 | − | 0.990237i | \(-0.544517\pi\) | ||||
−0.139397 | + | 0.990237i | \(0.544517\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.08905 | 0.0395302 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.0784 | −0.872840 | −0.436420 | − | 0.899743i | \(-0.643754\pi\) | ||||
−0.436420 | + | 0.899743i | \(0.643754\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8876 | −0.394159 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.00280 | 0.253187 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.4183 | 0.845585 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.3074 | −0.768363 | −0.384182 | − | 0.923258i | \(-0.625516\pi\) | ||||
−0.384182 | + | 0.923258i | \(0.625516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.3609 | −0.445166 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.3680 | −0.804522 | −0.402261 | − | 0.915525i | \(-0.631776\pi\) | ||||
−0.402261 | + | 0.915525i | \(0.631776\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.75626 | −0.170850 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −32.7489 | −1.17486 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.0200 | 0.932265 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.256387 | 0.00917426 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.16033 | 0.291627 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.26269 | −0.116450 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.8576 | −0.422678 | −0.211339 | − | 0.977413i | \(-0.567782\pi\) | ||||
−0.211339 | + | 0.977413i | \(0.567782\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −35.9812 | −1.28097 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −69.1826 | −2.45985 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −73.8110 | −2.62111 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.42054 | 0.227713 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.8401 | −0.454821 | −0.227410 | − | 0.973799i | \(-0.573026\pi\) | ||||
−0.227410 | + | 0.973799i | \(0.573026\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.4184 | 0.899237 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.89132 | 0.208160 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.52497 | −0.0538150 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.0288 | 0.917395 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −50.3455 | −1.77224 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 53.9336 | 1.89621 | 0.948103 | − | 0.317964i | \(-0.102999\pi\) | ||||
0.948103 | + | 0.317964i | \(0.102999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.9370 | 1.57795 | 0.788975 | − | 0.614425i | \(-0.210612\pi\) | ||||
0.788975 | + | 0.614425i | \(0.210612\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.33509 | 0.116967 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.1793 | −0.461651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.68644 | −0.338886 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 53.7766 | 1.87911 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.7495 | −1.70137 | −0.850685 | − | 0.525675i | \(-0.823813\pi\) | ||||
−0.850685 | + | 0.525675i | \(0.823813\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.3637 | −1.23270 | −0.616350 | − | 0.787472i | \(-0.711389\pi\) | ||||
−0.616350 | + | 0.787472i | \(0.711389\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.209039 | 0.00727781 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.7094 | −1.38083 | −0.690416 | − | 0.723412i | \(-0.742573\pi\) | ||||
−0.690416 | + | 0.723412i | \(0.742573\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.8533 | 0.620072 | 0.310036 | − | 0.950725i | \(-0.399659\pi\) | ||||
0.310036 | + | 0.950725i | \(0.399659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 49.0005 | 1.69981 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 55.4005 | 1.91951 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.26874 | 0.147726 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.96719 | −0.275386 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.2648 | 0.527000 | 0.263500 | − | 0.964659i | \(-0.415123\pi\) | ||||
0.263500 | + | 0.964659i | \(0.415123\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.26788 | −0.181651 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −42.9719 | −1.48003 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.47714 | 0.326024 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −54.9158 | −1.88693 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.5746 | −0.740438 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.8754 | 0.509921 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −52.3822 | −1.79353 | −0.896766 | − | 0.442506i | \(-0.854090\pi\) | ||||
−0.896766 | + | 0.442506i | \(0.854090\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.90959 | 0.270502 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.09873 | 0.174169 | 0.0870847 | − | 0.996201i | \(-0.472245\pi\) | ||||
0.0870847 | + | 0.996201i | \(0.472245\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23.9449 | 0.816988 | 0.408494 | − | 0.912761i | \(-0.366054\pi\) | ||||
0.408494 | + | 0.912761i | \(0.366054\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −85.6636 | −2.91941 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.6116 | −1.28031 | −0.640157 | − | 0.768244i | \(-0.721131\pi\) | ||||
−0.640157 | + | 0.768244i | \(0.721131\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.56099 | 0.189079 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 17.1859 | 0.583662 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.513789 | 0.0174291 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.55866 | 0.154464 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.2256 | 1.02298 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.99611 | 0.168899 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.6925 | −0.698737 | −0.349369 | − | 0.936985i | \(-0.613604\pi\) | ||||
−0.349369 | + | 0.936985i | \(0.613604\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.8245 | 0.365100 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.2843 | 0.582324 | 0.291162 | − | 0.956674i | \(-0.405958\pi\) | ||||
0.291162 | + | 0.956674i | \(0.405958\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.1431 | −0.711523 | −0.355761 | − | 0.934577i | \(-0.615778\pi\) | ||||
−0.355761 | + | 0.934577i | \(0.615778\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.3398 | −0.381182 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.0783 | 0.707739 | 0.353869 | − | 0.935295i | \(-0.384866\pi\) | ||||
0.353869 | + | 0.935295i | \(0.384866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −51.8304 | −1.73834 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.970344 | 0.0325077 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.7098 | 0.960736 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.12353 | −0.171261 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −56.7038 | −1.89328 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23.1704 | −0.772777 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.62647 | −0.287389 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.8898 | 1.06123 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.888073 | −0.0295206 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 19.3399 | 0.642172 | 0.321086 | − | 0.947050i | \(-0.395952\pi\) | ||||
0.321086 | + | 0.947050i | \(0.395952\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.74755 | 0.256970 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0223 | 1.12721 | 0.563604 | − | 0.826045i | \(-0.309414\pi\) | ||||
0.563604 | + | 0.826045i | \(0.309414\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.656071 | 0.0217128 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 35.7413 | 1.18157 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −80.4140 | −2.65550 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.2942 | 1.26321 | 0.631604 | − | 0.775291i | \(-0.282397\pi\) | ||||
0.631604 | + | 0.775291i | \(0.282397\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 73.6733 | 2.42762 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.3493 | −0.439398 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.85526 | 0.0938803 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.9528 | −1.01662 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.5559 | −1.00251 | −0.501253 | − | 0.865301i | \(-0.667127\pi\) | ||||
−0.501253 | + | 0.865301i | \(0.667127\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 62.5743 | 2.05079 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −67.8650 | −2.22180 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.280859 | −0.00918508 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.1420 | 0.984696 | 0.492348 | − | 0.870398i | \(-0.336139\pi\) | ||||
0.492348 | + | 0.870398i | \(0.336139\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.9407 | −1.59712 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.4882 | 0.602697 | 0.301348 | − | 0.953514i | \(-0.402563\pi\) | ||||
0.301348 | + | 0.953514i | \(0.402563\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 38.9105 | 1.26710 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.36896 | 0.272242 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 29.5051 | 0.958788 | 0.479394 | − | 0.877600i | \(-0.340856\pi\) | ||||
0.479394 | + | 0.877600i | \(0.340856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 79.4006 | 2.57745 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 45.3421 | 1.47032 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.9527 | −1.00266 | −0.501329 | − | 0.865257i | \(-0.667155\pi\) | ||||
−0.501329 | + | 0.865257i | \(0.667155\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.5361 | −0.405659 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.01835 | 0.0329185 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.9760 | −1.03256 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.37798 | −0.270257 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.9454 | −0.674957 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.12120 | −0.0682840 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.8683 | 1.70013 | 0.850065 | − | 0.526678i | \(-0.176563\pi\) | ||||
0.850065 | + | 0.526678i | \(0.176563\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.6697 | −0.792504 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.8004 | 1.40562 | 0.702811 | − | 0.711376i | \(-0.251928\pi\) | ||||
0.702811 | + | 0.711376i | \(0.251928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −78.0548 | −2.50232 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.8840 | −0.348568 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.0987 | 0.323085 | 0.161542 | − | 0.986866i | \(-0.448353\pi\) | ||||
0.161542 | + | 0.986866i | \(0.448353\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.236282 | −0.00755159 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.94757 | −0.157964 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0.469222 | 0.0149658 | 0.00748292 | − | 0.999972i | \(-0.497618\pi\) | ||||
0.00748292 | + | 0.999972i | \(0.497618\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.92506 | 0.156925 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −94.5188 | −3.00857 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.4852 | −0.460601 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.2793 | −1.21598 | −0.607992 | − | 0.793943i | \(-0.708025\pi\) | ||||
−0.607992 | + | 0.793943i | \(0.708025\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −53.4485 | −1.69614 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.7707 | −0.626774 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.4094 | −0.931405 | −0.465703 | − | 0.884941i | \(-0.654198\pi\) | ||||
−0.465703 | + | 0.884941i | \(0.654198\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4.78283 | 0.151322 |
(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 | 6040.2.a.s.1.6 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.s.1.6 | ✓ | 24 | 1.1 | even | 1 | trivial |