Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(23\) |
Twist minimal: | no (minimal twist has level 2008) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | 2.74485 | 1.58474 | 0.792370 | − | 0.610041i | \(-0.208847\pi\) | ||||
0.792370 | + | 0.610041i | \(0.208847\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.14962 | 0.961341 | 0.480671 | − | 0.876901i | \(-0.340393\pi\) | ||||
0.480671 | + | 0.876901i | \(0.340393\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.54966 | 1.34164 | 0.670822 | − | 0.741618i | \(-0.265941\pi\) | ||||
0.670822 | + | 0.741618i | \(0.265941\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.53421 | 1.51140 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.54587 | −1.97365 | −0.986827 | − | 0.161780i | \(-0.948276\pi\) | ||||
−0.986827 | + | 0.161780i | \(0.948276\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.92187 | 1.64243 | 0.821216 | − | 0.570617i | \(-0.193296\pi\) | ||||
0.821216 | + | 0.570617i | \(0.193296\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.90040 | 1.52348 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.02967 | 0.734803 | 0.367402 | − | 0.930062i | \(-0.380247\pi\) | ||||
0.367402 | + | 0.930062i | \(0.380247\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.44528 | 1.24923 | 0.624616 | − | 0.780932i | \(-0.285255\pi\) | ||||
0.624616 | + | 0.780932i | \(0.285255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.74328 | 2.12616 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.97810 | 0.620976 | 0.310488 | − | 0.950577i | \(-0.399508\pi\) | ||||
0.310488 | + | 0.950577i | \(0.399508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.379115 | −0.0758230 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.21117 | 0.810439 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.08516 | −1.31568 | −0.657841 | − | 0.753157i | \(-0.728530\pi\) | ||||
−0.657841 | + | 0.753157i | \(0.728530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.90565 | 0.521871 | 0.260935 | − | 0.965356i | \(-0.415969\pi\) | ||||
0.260935 | + | 0.965356i | \(0.415969\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.9674 | −3.12773 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.63043 | 1.28978 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.80826 | 0.954872 | 0.477436 | − | 0.878666i | \(-0.341566\pi\) | ||||
0.477436 | + | 0.878666i | \(0.341566\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.2547 | 2.60283 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.06047 | −1.25883 | −0.629417 | − | 0.777068i | \(-0.716706\pi\) | ||||
−0.629417 | + | 0.777068i | \(0.716706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.02892 | −1.22440 | −0.612200 | − | 0.790703i | \(-0.709715\pi\) | ||||
−0.612200 | + | 0.790703i | \(0.709715\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.74684 | 1.45297 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.1568 | −1.77325 | −0.886623 | − | 0.462494i | \(-0.846955\pi\) | ||||
−0.886623 | + | 0.462494i | \(0.846955\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.60008 | 0.800011 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.31599 | 1.16447 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.41139 | −0.605952 | −0.302976 | − | 0.952998i | \(-0.597980\pi\) | ||||
−0.302976 | + | 0.952998i | \(0.597980\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.0712 | −1.89735 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.9465 | 1.97971 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.8456 | −1.41198 | −0.705992 | − | 0.708220i | \(-0.749498\pi\) | ||||
−0.705992 | + | 0.708220i | \(0.749498\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.39774 | 0.435036 | 0.217518 | − | 0.976056i | \(-0.430204\pi\) | ||||
0.217518 | + | 0.976056i | \(0.430204\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.0949 | 2.02776 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.7298 | 1.57894 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.2601 | −1.49780 | −0.748902 | − | 0.662681i | \(-0.769419\pi\) | ||||
−0.748902 | + | 0.662681i | \(0.769419\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.17443 | 0.984086 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.79662 | 0.450576 | 0.225288 | − | 0.974292i | \(-0.427668\pi\) | ||||
0.225288 | + | 0.974292i | \(0.427668\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.43917 | −0.636606 | −0.318303 | − | 0.947989i | \(-0.603113\pi\) | ||||
−0.318303 | + | 0.947989i | \(0.603113\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.04061 | −0.120160 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −23.2356 | −2.64794 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.75747 | 0.647766 | 0.323883 | − | 0.946097i | \(-0.395012\pi\) | ||||
0.323883 | + | 0.946097i | \(0.395012\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.04360 | −0.227066 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.88983 | 0.317201 | 0.158600 | − | 0.987343i | \(-0.449302\pi\) | ||||
0.158600 | + | 0.987343i | \(0.449302\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.51265 | 0.706396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −19.4477 | −2.08501 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.2847 | 1.83218 | 0.916090 | − | 0.400973i | \(-0.131328\pi\) | ||||
0.916090 | + | 0.400973i | \(0.131328\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 21.0206 | 2.20356 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.97559 | 0.827030 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.7053 | 1.20094 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.2466 | 1.04039 | 0.520194 | − | 0.854048i | \(-0.325859\pi\) | ||||
0.520194 | + | 0.854048i | \(0.325859\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −29.6803 | −2.98298 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.2411 | −1.51654 | −0.758271 | − | 0.651939i | \(-0.773956\pi\) | ||||
−0.758271 | + | 0.651939i | \(0.773956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.10404 | −0.404383 | −0.202191 | − | 0.979346i | \(-0.564806\pi\) | ||||
−0.202191 | + | 0.979346i | \(0.564806\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 20.9444 | 2.04396 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.91806 | 0.475447 | 0.237723 | − | 0.971333i | \(-0.423599\pi\) | ||||
0.237723 | + | 0.971333i | \(0.423599\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.54452 | 0.914200 | 0.457100 | − | 0.889415i | \(-0.348888\pi\) | ||||
0.457100 | + | 0.889415i | \(0.348888\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 15.9428 | 1.51322 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.77713 | 0.731611 | 0.365805 | − | 0.930691i | \(-0.380794\pi\) | ||||
0.365805 | + | 0.930691i | \(0.380794\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.40179 | 0.596970 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.8510 | 2.48238 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.7543 | 0.985845 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.8484 | 2.89531 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −22.1248 | −1.99492 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.5631 | −1.03423 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.2833 | −1.26744 | −0.633720 | − | 0.773562i | \(-0.718473\pi\) | ||||
−0.633720 | + | 0.773562i | \(0.718473\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.0382 | −1.94036 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.04115 | −0.615188 | −0.307594 | − | 0.951518i | \(-0.599524\pi\) | ||||
−0.307594 | + | 0.951518i | \(0.599524\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.3289 | 1.67603 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.05242 | 0.779109 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.449893 | −0.0384370 | −0.0192185 | − | 0.999815i | \(-0.506118\pi\) | ||||
−0.0192185 | + | 0.999815i | \(0.506118\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.85143 | 0.326674 | 0.163337 | − | 0.986570i | \(-0.447774\pi\) | ||||
0.163337 | + | 0.986570i | \(0.447774\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −33.3685 | −2.81013 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −38.7638 | −3.24159 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.2304 | −1.26482 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.3714 | 1.26781 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.40916 | 0.688905 | 0.344453 | − | 0.938804i | \(-0.388065\pi\) | ||||
0.344453 | + | 0.938804i | \(0.388065\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.60603 | −0.293454 | −0.146727 | − | 0.989177i | \(-0.546874\pi\) | ||||
−0.146727 | + | 0.989177i | \(0.546874\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.7371 | 1.11058 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.24606 | 0.501696 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.2108 | 1.77261 | 0.886306 | − | 0.463100i | \(-0.153263\pi\) | ||||
0.886306 | + | 0.463100i | \(0.153263\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.1086 | −0.960276 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.5712 | 0.833129 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1388 | 0.950781 | 0.475390 | − | 0.879775i | \(-0.342307\pi\) | ||||
0.475390 | + | 0.879775i | \(0.342307\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −38.6232 | −3.00681 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.16030 | 0.0897865 | 0.0448932 | − | 0.998992i | \(-0.485705\pi\) | ||||
0.0448932 | + | 0.998992i | \(0.485705\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.0686 | 1.69758 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.6900 | 1.88809 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.8853 | −1.89199 | −0.945997 | − | 0.324175i | \(-0.894913\pi\) | ||||
−0.945997 | + | 0.324175i | \(0.894913\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.34573 | −0.101728 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −29.7697 | −2.23763 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.2481 | −1.36393 | −0.681964 | − | 0.731386i | \(-0.738874\pi\) | ||||
−0.681964 | + | 0.731386i | \(0.738874\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.0683 | −0.971361 | −0.485681 | − | 0.874136i | \(-0.661428\pi\) | ||||
−0.485681 | + | 0.874136i | \(0.661428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.32629 | 0.689419 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.4856 | 0.917958 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −19.8318 | −1.45025 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.9482 | 1.08732 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.53780 | 0.400701 | 0.200351 | − | 0.979724i | \(-0.435792\pi\) | ||||
0.200351 | + | 0.979724i | \(0.435792\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.2677 | −0.739086 | −0.369543 | − | 0.929214i | \(-0.620486\pi\) | ||||
−0.369543 | + | 0.929214i | \(0.620486\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 34.9414 | 2.50221 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.7190 | 1.83240 | 0.916202 | − | 0.400716i | \(-0.131239\pi\) | ||||
0.916202 | + | 0.400716i | \(0.131239\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.78676 | −0.268436 | −0.134218 | − | 0.990952i | \(-0.542852\pi\) | ||||
−0.134218 | + | 0.990952i | \(0.542852\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −33.6520 | −2.37363 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −25.1499 | −1.76518 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.3270 | −1.21017 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.5033 | 0.938544 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −35.6441 | −2.46555 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.33696 | 0.573940 | 0.286970 | − | 0.957940i | \(-0.407352\pi\) | ||||
0.286970 | + | 0.957940i | \(0.407352\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.4211 | 0.714045 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.2592 | −1.17707 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.3141 | 0.700165 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.9297 | −1.00886 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.9413 | 1.20686 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.94350 | −0.665866 | −0.332933 | − | 0.942950i | \(-0.608038\pi\) | ||||
−0.332933 | + | 0.942950i | \(0.608038\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.71899 | −0.114599 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.6972 | 1.57284 | 0.786418 | − | 0.617695i | \(-0.211933\pi\) | ||||
0.786418 | + | 0.617695i | \(0.211933\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.54781 | 0.300528 | 0.150264 | − | 0.988646i | \(-0.451988\pi\) | ||||
0.150264 | + | 0.988646i | \(0.451988\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −63.7783 | −4.19630 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.0120 | 0.655909 | 0.327955 | − | 0.944694i | \(-0.393641\pi\) | ||||
0.327955 | + | 0.944694i | \(0.393641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.1325 | −1.70469 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.8034 | 1.02654 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.3052 | −1.63685 | −0.818427 | − | 0.574610i | \(-0.805154\pi\) | ||||
−0.818427 | + | 0.574610i | \(0.805154\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.7184 | −1.07693 | −0.538464 | − | 0.842649i | \(-0.680995\pi\) | ||||
−0.538464 | + | 0.842649i | \(0.680995\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −18.2429 | −1.17028 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.0381 | 0.769084 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 32.2463 | 2.05178 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.93216 | 0.502680 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.4942 | −1.22559 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.8763 | 1.11945 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.7416 | 1.35620 | 0.678101 | − | 0.734969i | \(-0.262803\pi\) | ||||
0.678101 | + | 0.734969i | \(0.262803\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.6173 | 1.28110 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −32.1256 | −1.98852 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.27198 | 0.0784339 | 0.0392169 | − | 0.999231i | \(-0.487514\pi\) | ||||
0.0392169 | + | 0.999231i | \(0.487514\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.48284 | −0.582526 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 47.4441 | 2.90353 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.77658 | 0.413175 | 0.206588 | − | 0.978428i | \(-0.433764\pi\) | ||||
0.206588 | + | 0.978428i | \(0.433764\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.07518 | −0.126058 | −0.0630292 | − | 0.998012i | \(-0.520076\pi\) | ||||
−0.0630292 | + | 0.998012i | \(0.520076\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 57.6985 | 3.49207 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.48164 | 0.149648 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.9588 | 0.658451 | 0.329226 | − | 0.944251i | \(-0.393212\pi\) | ||||
0.329226 | + | 0.944251i | \(0.393212\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.1748 | 0.788757 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.68447 | 0.160142 | 0.0800711 | − | 0.996789i | \(-0.474485\pi\) | ||||
0.0800711 | + | 0.996789i | \(0.474485\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.10824 | −0.541428 | −0.270714 | − | 0.962660i | \(-0.587260\pi\) | ||||
−0.270714 | + | 0.962660i | \(0.587260\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 32.1293 | 1.90318 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.6119 | −1.68891 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.82110 | −0.460065 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.1255 | 1.64875 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.16669 | −0.360262 | −0.180131 | − | 0.983643i | \(-0.557652\pi\) | ||||
−0.180131 | + | 0.983643i | \(0.557652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −23.3141 | −1.35740 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −27.5657 | −1.59953 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.6359 | 1.01991 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.4999 | −1.64271 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −41.8344 | −2.40333 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.30387 | 0.418218 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.52823 | 0.0872205 | 0.0436102 | − | 0.999049i | \(-0.486114\pi\) | ||||
0.0436102 | + | 0.999049i | \(0.486114\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.2650 | −0.640842 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.12444 | −0.0637610 | −0.0318805 | − | 0.999492i | \(-0.510150\pi\) | ||||
−0.0318805 | + | 0.999492i | \(0.510150\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.9524 | 1.91910 | 0.959550 | − | 0.281537i | \(-0.0908441\pi\) | ||||
0.959550 | + | 0.281537i | \(0.0908441\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 34.5980 | 1.94937 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.9388 | 0.670551 | 0.335275 | − | 0.942120i | \(-0.391171\pi\) | ||||
0.335275 | + | 0.942120i | \(0.391171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 46.3785 | 2.59670 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 13.4993 | 0.753459 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.4974 | 0.917940 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.24507 | −0.124534 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 26.1983 | 1.44877 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −43.1523 | −2.37907 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.86021 | 0.541966 | 0.270983 | − | 0.962584i | \(-0.412651\pi\) | ||||
0.270983 | + | 0.962584i | \(0.412651\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 26.3358 | 1.44320 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −26.3545 | −1.43990 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.8956 | 0.647996 | 0.323998 | − | 0.946058i | \(-0.394973\pi\) | ||||
0.323998 | + | 0.946058i | \(0.394973\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.3471 | 1.15941 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.0200 | −1.02999 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.96924 | −0.268314 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.5720 | 0.946042 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.6786 | −0.626942 | −0.313471 | − | 0.949598i | \(-0.601492\pi\) | ||||
−0.313471 | + | 0.949598i | \(0.601492\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0249 | −1.28602 | −0.643012 | − | 0.765856i | \(-0.722315\pi\) | ||||
−0.643012 | + | 0.765856i | \(0.722315\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 24.9380 | 1.33109 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.37513 | 0.0731906 | 0.0365953 | − | 0.999330i | \(-0.488349\pi\) | ||||
0.0365953 | + | 0.999330i | \(0.488349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.16130 | 0.433157 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.5189 | 1.56231 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.1819 | 1.69850 | 0.849249 | − | 0.527993i | \(-0.177055\pi\) | ||||
0.849249 | + | 0.527993i | \(0.177055\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.6511 | 0.560582 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 87.4191 | 4.58831 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.6922 | −0.611996 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.98147 | −0.468829 | −0.234414 | − | 0.972137i | \(-0.575317\pi\) | ||||
−0.234414 | + | 0.972137i | \(0.575317\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.5478 | −1.90260 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.6589 | −0.812972 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −26.9056 | −1.39312 | −0.696559 | − | 0.717499i | \(-0.745287\pi\) | ||||
−0.696559 | + | 0.717499i | \(0.745287\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.7389 | −1.63899 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −41.9574 | −2.16092 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.2662 | −0.527340 | −0.263670 | − | 0.964613i | \(-0.584933\pi\) | ||||
−0.263670 | + | 0.964613i | \(0.584933\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.2056 | −2.00856 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.9393 | 1.32544 | 0.662718 | − | 0.748869i | \(-0.269403\pi\) | ||||
0.662718 | + | 0.748869i | \(0.269403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −49.9478 | −2.54558 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −36.4048 | −1.85056 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.6478 | 0.844079 | 0.422039 | − | 0.906577i | \(-0.361314\pi\) | ||||
0.422039 | + | 0.906577i | \(0.361314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.02265 | 0.456295 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −19.3269 | −0.974914 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.3764 | 0.622724 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9366 | −1.15116 | −0.575578 | − | 0.817747i | \(-0.695223\pi\) | ||||
−0.575578 | + | 0.817747i | \(0.695223\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 53.0549 | 2.65607 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4812 | 0.723154 | 0.361577 | − | 0.932342i | \(-0.382238\pi\) | ||||
0.361577 | + | 0.932342i | \(0.382238\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.2069 | 0.857138 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.39296 | −0.218288 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −38.0201 | −1.88459 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.3102 | −0.806486 | −0.403243 | − | 0.915093i | \(-0.632117\pi\) | ||||
−0.403243 | + | 0.915093i | \(0.632117\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.23489 | −0.0609126 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −38.4984 | −1.89438 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.21206 | 0.304938 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.5716 | 0.517693 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.69777 | 0.131795 | 0.0658973 | − | 0.997826i | \(-0.479009\pi\) | ||||
0.0658973 | + | 0.997826i | \(0.479009\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.6445 | 0.664991 | 0.332495 | − | 0.943105i | \(-0.392109\pi\) | ||||
0.332495 | + | 0.943105i | \(0.392109\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −55.1212 | −2.68009 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.14859 | −0.0557150 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.0608 | 0.583664 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −106.401 | −5.13708 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.166970 | 0.00804268 | 0.00402134 | − | 0.999992i | \(-0.498720\pi\) | ||||
0.00402134 | + | 0.999992i | \(0.498720\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.0726 | 0.580171 | 0.290085 | − | 0.957001i | \(-0.406316\pi\) | ||||
0.290085 | + | 0.957001i | \(0.406316\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −41.8053 | −2.00441 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 16.2166 | 0.775744 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.96878 | −0.380329 | −0.190165 | − | 0.981752i | \(-0.560902\pi\) | ||||
−0.190165 | + | 0.981752i | \(0.560902\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25.3919 | 1.20914 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.3635 | −0.587407 | −0.293704 | − | 0.955897i | \(-0.594888\pi\) | ||||
−0.293704 | + | 0.955897i | \(0.594888\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37.1557 | 1.76135 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 23.0819 | 1.09174 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.54161 | 0.167139 | 0.0835694 | − | 0.996502i | \(-0.473368\pi\) | ||||
0.0835694 | + | 0.996502i | \(0.473368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 52.7628 | 2.48450 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.89800 | −0.465049 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 45.1865 | 2.11837 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.9259 | −0.885314 | −0.442657 | − | 0.896691i | \(-0.645964\pi\) | ||||
−0.442657 | + | 0.896691i | \(0.645964\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 12.7584 | 0.595513 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.2051 | 0.801320 | 0.400660 | − | 0.916227i | \(-0.368781\pi\) | ||||
0.400660 | + | 0.916227i | \(0.368781\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.2631 | −0.755809 | −0.377905 | − | 0.925844i | \(-0.623355\pi\) | ||||
−0.377905 | + | 0.925844i | \(0.623355\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.1445 | 0.795058 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.23047 | 0.288312 | 0.144156 | − | 0.989555i | \(-0.453953\pi\) | ||||
0.144156 | + | 0.989555i | \(0.453953\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −43.5190 | −2.00952 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 60.9652 | 2.80913 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 52.5563 | 2.41654 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.06439 | −0.0947206 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.0022 | −0.915837 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.2103 | −1.42603 | −0.713017 | − | 0.701147i | \(-0.752672\pi\) | ||||
−0.713017 | + | 0.701147i | \(0.752672\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.3958 | 1.56831 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 29.0164 | 1.32029 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.0264 | 1.00017 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.6600 | −0.664309 | −0.332155 | − | 0.943225i | \(-0.607776\pi\) | ||||
−0.332155 | + | 0.943225i | \(0.607776\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 33.3191 | 1.50674 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.8141 | −1.66140 | −0.830699 | − | 0.556722i | \(-0.812059\pi\) | ||||
−0.830699 | + | 0.556722i | \(0.812059\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −21.4657 | −0.966767 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −63.8015 | −2.86767 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 13.4767 | 0.604512 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.75326 | 0.391850 | 0.195925 | − | 0.980619i | \(-0.437229\pi\) | ||||
0.195925 | + | 0.980619i | \(0.437229\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.18484 | 0.142288 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.1327 | 1.25437 | 0.627187 | − | 0.778869i | \(-0.284206\pi\) | ||||
0.627187 | + | 0.778869i | \(0.284206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32.7626 | −1.45791 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 60.5750 | 2.69023 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.3215 | −0.989385 | −0.494692 | − | 0.869068i | \(-0.664719\pi\) | ||||
−0.494692 | + | 0.869068i | \(0.664719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.3072 | −0.854100 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 22.9310 | 1.01243 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.82214 | −0.388750 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 79.5765 | 3.49977 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −68.3064 | −2.99832 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.1435 | −1.27680 | −0.638399 | − | 0.769705i | \(-0.720403\pi\) | ||||
−0.638399 | + | 0.769705i | \(0.720403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.0289 | 1.00698 | 0.503491 | − | 0.864000i | \(-0.332049\pi\) | ||||
0.503491 | + | 0.864000i | \(0.332049\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.69383 | −0.161212 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.80317 | 0.383472 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14.1309 | −0.614389 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −49.1764 | −2.13407 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −47.7331 | −2.06755 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.5720 | 0.457066 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −50.0883 | −2.16147 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.6574 | −1.57894 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −31.0582 | −1.33530 | −0.667649 | − | 0.744476i | \(-0.732699\pi\) | ||||
−0.667649 | + | 0.744476i | \(0.732699\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −35.8706 | −1.53936 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.5171 | 0.878858 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.154505 | 0.00660614 | 0.00330307 | − | 0.999995i | \(-0.498949\pi\) | ||||
0.00330307 | + | 0.999995i | \(0.498949\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.4061 | 0.657515 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.5807 | −1.64359 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.4371 | 0.869072 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 34.2710 | 1.45472 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 39.0419 | 1.65426 | 0.827129 | − | 0.562012i | \(-0.189973\pi\) | ||||
0.827129 | + | 0.562012i | \(0.189973\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.5463 | −2.01099 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −54.4354 | −2.29826 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.9413 | 1.34616 | 0.673082 | − | 0.739567i | \(-0.264970\pi\) | ||||
0.673082 | + | 0.739567i | \(0.264970\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.7179 | 0.703327 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.25407 | −0.304642 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.966749 | 0.0405282 | 0.0202641 | − | 0.999795i | \(-0.493549\pi\) | ||||
0.0202641 | + | 0.999795i | \(0.493549\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.10421 | −0.129907 | −0.0649535 | − | 0.997888i | \(-0.520690\pi\) | ||||
−0.0649535 | + | 0.997888i | \(0.520690\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.2004 | 0.635007 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.12904 | −0.0470843 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.6469 | −1.81705 | −0.908523 | − | 0.417835i | \(-0.862789\pi\) | ||||
−0.908523 | + | 0.417835i | \(0.862789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.1833 | −1.17126 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.2579 | 0.425571 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.8764 | 1.19594 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 57.7196 | 2.38641 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 37.7925 | 1.55986 | 0.779931 | − | 0.625865i | \(-0.215254\pi\) | ||||
0.779931 | + | 0.625865i | \(0.215254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.8221 | 0.651938 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 70.5949 | 2.90389 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.4832 | −0.676882 | −0.338441 | − | 0.940988i | \(-0.609900\pi\) | ||||
−0.338441 | + | 0.940988i | \(0.609900\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.1177 | 0.947733 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.3941 | −0.425401 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.27806 | 0.338232 | 0.169116 | − | 0.985596i | \(-0.445909\pi\) | ||||
0.169116 | + | 0.985596i | \(0.445909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0477 | 0.980928 | 0.490464 | − | 0.871461i | \(-0.336827\pi\) | ||||
0.490464 | + | 0.871461i | \(0.336827\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −55.5896 | −2.26378 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 68.4621 | 2.78338 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1529 | 0.493271 | 0.246635 | − | 0.969108i | \(-0.420675\pi\) | ||||
0.246635 | + | 0.969108i | \(0.420675\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −69.0328 | −2.79735 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −71.9908 | −2.91244 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.4177 | −0.501547 | −0.250774 | − | 0.968046i | \(-0.580685\pi\) | ||||
−0.250774 | + | 0.968046i | \(0.580685\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −47.5600 | −1.91780 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 44.3680 | 1.78619 | 0.893093 | − | 0.449871i | \(-0.148530\pi\) | ||||
0.893093 | + | 0.449871i | \(0.148530\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.4107 | −1.58405 | −0.792025 | − | 0.610489i | \(-0.790973\pi\) | ||||
−0.792025 | + | 0.610489i | \(0.790973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.5413 | 0.503263 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 61.3550 | 2.45813 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.9607 | −0.918428 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −97.8377 | −3.90726 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.5971 | 0.701643 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.28040 | 0.0907815 | 0.0453907 | − | 0.998969i | \(-0.485547\pi\) | ||||
0.0453907 | + | 0.998969i | \(0.485547\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 22.8837 | 0.909546 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −30.7038 | −1.21844 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.1630 | 1.31396 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.2146 | 0.681001 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.2719 | −0.682201 | −0.341100 | − | 0.940027i | \(-0.610800\pi\) | ||||
−0.341100 | + | 0.940027i | \(0.610800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.1244 | −1.03025 | −0.515123 | − | 0.857116i | \(-0.672254\pi\) | ||||
−0.515123 | + | 0.857116i | \(0.672254\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −47.3738 | −1.86534 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.5710 | −0.494216 | −0.247108 | − | 0.968988i | \(-0.579480\pi\) | ||||
−0.247108 | + | 0.968988i | \(0.579480\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 70.9942 | 2.78677 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.3106 | 1.10958 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.5660 | 1.11787 | 0.558936 | − | 0.829211i | \(-0.311210\pi\) | ||||
0.558936 | + | 0.829211i | \(0.311210\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.1358 | −0.591406 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.6623 | −0.962168 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.868932 | 0.0338488 | 0.0169244 | − | 0.999857i | \(-0.494613\pi\) | ||||
0.0169244 | + | 0.999857i | \(0.494613\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.5283 | −0.954041 | −0.477021 | − | 0.878892i | \(-0.658283\pi\) | ||||
−0.477021 | + | 0.878892i | \(0.658283\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 49.2463 | 1.91257 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 41.5498 | 1.61123 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.1003 | −0.817007 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −27.2934 | −1.05522 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.2412 | −0.858611 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0673 | 1.15901 | 0.579504 | − | 0.814969i | \(-0.303246\pi\) | ||||
0.579504 | + | 0.814969i | \(0.303246\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.59652 | −0.0614500 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34.7007 | 1.33366 | 0.666828 | − | 0.745212i | \(-0.267652\pi\) | ||||
0.666828 | + | 0.745212i | \(0.267652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.3721 | 1.39583 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 65.0452 | 2.49254 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.97088 | 0.190205 | 0.0951026 | − | 0.995467i | \(-0.469682\pi\) | ||||
0.0951026 | + | 0.995467i | \(0.469682\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.967101 | −0.0369510 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.4831 | 0.476258 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −26.1237 | −0.995235 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.9682 | 0.607460 | 0.303730 | − | 0.952758i | \(-0.401768\pi\) | ||||
0.303730 | + | 0.952758i | \(0.401768\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −105.355 | −4.00211 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.27912 | 0.314045 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.4206 | −0.924995 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 27.4815 | 1.03945 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.29023 | −0.0487311 | −0.0243656 | − | 0.999703i | \(-0.507757\pi\) | ||||
−0.0243656 | + | 0.999703i | \(0.507757\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.6276 | 1.19286 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −71.7297 | −2.70150 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −54.1006 | −2.03466 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.7870 | −1.34401 | −0.672004 | − | 0.740547i | \(-0.734566\pi\) | ||||
−0.672004 | + | 0.740547i | \(0.734566\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.1056 | 0.979035 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.65332 | 0.324069 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −83.3276 | −3.11628 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −69.4589 | −2.59399 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.0809 | 0.562424 | 0.281212 | − | 0.959646i | \(-0.409264\pi\) | ||||
0.281212 | + | 0.959646i | \(0.409264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.5679 | −0.542538 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −45.8895 | −1.70665 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.68609 | 0.0997590 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.95659 | 0.183830 | 0.0919150 | − | 0.995767i | \(-0.470701\pi\) | ||||
0.0919150 | + | 0.995767i | \(0.470701\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.9431 | −1.62752 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.3250 | −0.899692 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.73805 | 0.359683 | 0.179842 | − | 0.983696i | \(-0.442441\pi\) | ||||
0.179842 | + | 0.983696i | \(0.442441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 33.0427 | 1.21880 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 80.2527 | 2.95615 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.94296 | −0.181830 | −0.0909149 | − | 0.995859i | \(-0.528979\pi\) | ||||
−0.0909149 | + | 0.995859i | \(0.528979\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 88.5112 | 3.25154 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.6999 | 1.08958 | 0.544792 | − | 0.838571i | \(-0.316609\pi\) | ||||
0.544792 | + | 0.838571i | \(0.316609\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0765 | 0.662273 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.1031 | 0.479418 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.4574 | 0.637880 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.2689 | 0.849095 | 0.424548 | − | 0.905406i | \(-0.360433\pi\) | ||||
0.424548 | + | 0.905406i | \(0.360433\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.74485 | 0.100028 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.75160 | −0.282110 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.0623 | −0.402065 | −0.201032 | − | 0.979585i | \(-0.564430\pi\) | ||||
−0.201032 | + | 0.979585i | \(0.564430\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −53.5087 | −1.94224 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 51.7916 | 1.87744 | 0.938721 | − | 0.344678i | \(-0.112012\pi\) | ||||
0.938721 | + | 0.344678i | \(0.112012\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 33.8798 | 1.22653 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 29.5297 | 1.06765 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −64.2266 | −2.31909 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.44430 | 0.0520828 | 0.0260414 | − | 0.999661i | \(-0.491710\pi\) | ||||
0.0260414 | + | 0.999661i | \(0.491710\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 59.6773 | 2.14923 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.47720 | −0.340871 | −0.170436 | − | 0.985369i | \(-0.554517\pi\) | ||||
−0.170436 | + | 0.985369i | \(0.554517\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.10158 | −0.0395698 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 56.5915 | 2.03021 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.8915 | −1.57258 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.8522 | −0.889280 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −29.8368 | −1.06628 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.7448 | 1.70408 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.7921 | 1.20456 | 0.602280 | − | 0.798285i | \(-0.294259\pi\) | ||||
0.602280 | + | 0.798285i | \(0.294259\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.49141 | 0.124297 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27.6062 | 0.981562 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.1210 | 0.714518 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −26.0290 | −0.923153 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.8090 | −1.05589 | −0.527944 | − | 0.849279i | \(-0.677037\pi\) | ||||
−0.527944 | + | 0.849279i | \(0.677037\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.8310 | −1.30299 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 78.3726 | 2.76916 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 35.6041 | 1.25644 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.7242 | 0.800922 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.6007 | 0.654776 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.7449 | −0.518404 | −0.259202 | − | 0.965823i | \(-0.583460\pi\) | ||||
−0.259202 | + | 0.965823i | \(0.583460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.1003 | 0.565359 | 0.282679 | − | 0.959214i | \(-0.408777\pi\) | ||||
0.282679 | + | 0.959214i | \(0.408777\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.69606 | −0.199770 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.0938 | 0.914025 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43.7197 | −1.52956 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 95.3119 | 3.33047 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.80936 | −0.272549 | −0.136274 | − | 0.990671i | \(-0.543513\pi\) | ||||
−0.136274 | + | 0.990671i | \(0.543513\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.5503 | 0.507193 | 0.253597 | − | 0.967310i | \(-0.418386\pi\) | ||||
0.253597 | + | 0.967310i | \(0.418386\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.81173 | 0.237154 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.9267 | −1.07543 | −0.537714 | − | 0.843127i | \(-0.680712\pi\) | ||||
−0.537714 | + | 0.843127i | \(0.680712\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.6097 | −0.785268 | −0.392634 | − | 0.919695i | \(-0.628436\pi\) | ||||
−0.392634 | + | 0.919695i | \(0.628436\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.0803 | 1.04347 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.9664 | 0.587851 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.49420 | 0.0863154 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.2362 | 0.422945 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.27665 | 0.0440747 | 0.0220374 | − | 0.999757i | \(-0.492985\pi\) | ||||
0.0220374 | + | 0.999757i | \(0.492985\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1995 | 0.731018 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.36847 | 0.253784 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47.4392 | 1.63196 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 113.051 | 3.88448 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.0008 | −0.858024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.2976 | 0.592953 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.86031 | −0.0636959 | −0.0318480 | − | 0.999493i | \(-0.510139\pi\) | ||||
−0.0318480 | + | 0.999493i | \(0.510139\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 53.0743 | 1.81510 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.76520 | −0.231095 | −0.115547 | − | 0.993302i | \(-0.536862\pi\) | ||||
−0.115547 | + | 0.993302i | \(0.536862\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.5523 | 1.00831 | 0.504155 | − | 0.863613i | \(-0.331804\pi\) | ||||
0.504155 | + | 0.863613i | \(0.331804\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −78.5354 | −2.67648 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 56.5475 | 1.92490 | 0.962450 | − | 0.271458i | \(-0.0875059\pi\) | ||||
0.962450 | + | 0.271458i | \(0.0875059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −53.4940 | −1.81885 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.4677 | −0.729083 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −37.6877 | −1.27847 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −72.6025 | −2.46004 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.4604 | 1.57245 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.0450 | −1.38757 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.54396 | 0.119671 | 0.0598355 | − | 0.998208i | \(-0.480942\pi\) | ||||
0.0598355 | + | 0.998208i | \(0.480942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −16.9266 | −0.570922 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.30576 | −0.0776830 | −0.0388415 | − | 0.999245i | \(-0.512367\pi\) | ||||
−0.0388415 | + | 0.999245i | \(0.512367\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.0916 | −1.24823 | −0.624116 | − | 0.781332i | \(-0.714541\pi\) | ||||
−0.624116 | + | 0.781332i | \(0.714541\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −63.9937 | −2.15112 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.5188 | 0.957567 | 0.478784 | − | 0.877933i | \(-0.341078\pi\) | ||||
0.478784 | + | 0.877933i | \(0.341078\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −50.7009 | −1.70046 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.3771 | 0.448150 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −66.1969 | −2.21520 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −39.2266 | −1.31120 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 48.4079 | 1.61629 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.5870 | −0.686616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.3651 | −0.445255 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −78.2281 | −2.60327 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.0920 | −0.933810 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.7450 | −1.31971 | −0.659855 | − | 0.751393i | \(-0.729382\pi\) | ||||
−0.659855 | + | 0.751393i | \(0.729382\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −69.1061 | −2.29210 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.7963 | −1.21912 | −0.609558 | − | 0.792742i | \(-0.708653\pi\) | ||||
−0.609558 | + | 0.792742i | \(0.708653\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.9165 | −0.626044 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 20.0480 | 0.662767 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −24.9937 | −0.825365 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.53441 | 0.248537 | 0.124269 | − | 0.992249i | \(-0.460342\pi\) | ||||
0.124269 | + | 0.992249i | \(0.460342\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.19475 | 0.138222 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.4831 | 0.740040 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.20200 | −0.0724013 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −18.6086 | −0.611185 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12.5221 | 0.410838 | 0.205419 | − | 0.978674i | \(-0.434144\pi\) | ||||
0.205419 | + | 0.978674i | \(0.434144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.4940 | 0.999400 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.08641 | −0.101045 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −42.6310 | −1.39418 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.8994 | 1.33613 | 0.668063 | − | 0.744105i | \(-0.267124\pi\) | ||||
0.668063 | + | 0.744105i | \(0.267124\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 93.1942 | 3.04128 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.09750 | 0.296570 | 0.148285 | − | 0.988945i | \(-0.452625\pi\) | ||||
0.148285 | + | 0.988945i | \(0.452625\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −24.0048 | −0.781705 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 32.1330 | 1.04529 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.4429 | −0.729295 | −0.364648 | − | 0.931146i | \(-0.618811\pi\) | ||||
−0.364648 | + | 0.931146i | \(0.618811\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −32.2101 | −1.04558 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.7703 | 1.06265 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.8722 | 0.935263 | 0.467631 | − | 0.883924i | \(-0.345107\pi\) | ||||
0.467631 | + | 0.883924i | \(0.345107\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.9042 | 0.385210 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 127.302 | 4.11510 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.59697 | −0.0515688 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.5572 | −0.727651 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.2995 | 0.718591 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.0717 | −0.710513 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.8350 | −0.348430 | −0.174215 | − | 0.984708i | \(-0.555739\pi\) | ||||
−0.174215 | + | 0.984708i | \(0.555739\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 45.2829 | 1.45470 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.1539 | 0.967686 | 0.483843 | − | 0.875155i | \(-0.339241\pi\) | ||||
0.483843 | + | 0.875155i | \(0.339241\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.6712 | 0.438280 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.16239 | −0.197354 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.4510 | −0.590301 | −0.295150 | − | 0.955451i | \(-0.595370\pi\) | ||||
−0.295150 | + | 0.955451i | \(0.595370\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −113.144 | −3.61609 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.2768 | 1.38172 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.1888 | 0.388763 | 0.194382 | − | 0.980926i | \(-0.437730\pi\) | ||||
0.194382 | + | 0.980926i | \(0.437730\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 55.2862 | 1.76157 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −118.447 | −3.77020 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −23.9109 | −0.760323 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.65661 | 0.147922 | 0.0739610 | − | 0.997261i | \(-0.476436\pi\) | ||||
0.0739610 | + | 0.997261i | \(0.476436\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.0648 | 0.858876 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.14010 | −0.258059 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −57.5641 | −1.82307 | −0.911536 | − | 0.411220i | \(-0.865103\pi\) | ||||
−0.911536 | + | 0.411220i | \(0.865103\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.4595 | 0.773866 |
(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 | 4016.2.a.m.1.20 | 23 | ||
4.3 | odd | 2 | 2008.2.a.d.1.4 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2008.2.a.d.1.4 | ✓ | 23 | 4.3 | odd | 2 | ||
4016.2.a.m.1.20 | 23 | 1.1 | even | 1 | trivial |