Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7537.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + 4x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.04717\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19091 | 0.842100 | 0.421050 | − | 0.907037i | \(-0.361662\pi\) | ||||
0.421050 | + | 0.907037i | \(0.361662\pi\) | |||||||
\(3\) | −3.04717 | −1.75929 | −0.879643 | − | 0.475635i | \(-0.842218\pi\) | ||||
−0.879643 | + | 0.475635i | \(0.842218\pi\) | |||||||
\(4\) | −0.581734 | −0.290867 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −3.62891 | −1.48149 | ||||||||
\(7\) | −0.609175 | −0.230247 | −0.115123 | − | 0.993351i | \(-0.536726\pi\) | ||||
−0.115123 | + | 0.993351i | \(0.536726\pi\) | |||||||
\(8\) | −3.07461 | −1.08704 | ||||||||
\(9\) | 6.28525 | 2.09508 | ||||||||
\(10\) | 1.19091 | 0.376599 | ||||||||
\(11\) | 4.48517 | 1.35233 | 0.676164 | − | 0.736751i | \(-0.263641\pi\) | ||||
0.676164 | + | 0.736751i | \(0.263641\pi\) | |||||||
\(12\) | 1.77264 | 0.511718 | ||||||||
\(13\) | −4.43800 | −1.23088 | −0.615439 | − | 0.788184i | \(-0.711021\pi\) | ||||
−0.615439 | + | 0.788184i | \(0.711021\pi\) | |||||||
\(14\) | −0.725473 | −0.193891 | ||||||||
\(15\) | −3.04717 | −0.786776 | ||||||||
\(16\) | −2.49812 | −0.624529 | ||||||||
\(17\) | 2.90343 | 0.704186 | 0.352093 | − | 0.935965i | \(-0.385470\pi\) | ||||
0.352093 | + | 0.935965i | \(0.385470\pi\) | |||||||
\(18\) | 7.48517 | 1.76427 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.581734 | −0.130080 | ||||||||
\(21\) | 1.85626 | 0.405069 | ||||||||
\(22\) | 5.34143 | 1.13880 | ||||||||
\(23\) | −2.84726 | −0.593694 | −0.296847 | − | 0.954925i | \(-0.595935\pi\) | ||||
−0.296847 | + | 0.954925i | \(0.595935\pi\) | |||||||
\(24\) | 9.36887 | 1.91241 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.28525 | −1.03652 | ||||||||
\(27\) | −10.0107 | −1.92656 | ||||||||
\(28\) | 0.354378 | 0.0669712 | ||||||||
\(29\) | −1.11630 | −0.207291 | −0.103646 | − | 0.994614i | \(-0.533051\pi\) | ||||
−0.103646 | + | 0.994614i | \(0.533051\pi\) | |||||||
\(30\) | −3.62891 | −0.662544 | ||||||||
\(31\) | 6.22908 | 1.11877 | 0.559387 | − | 0.828906i | \(-0.311036\pi\) | ||||
0.559387 | + | 0.828906i | \(0.311036\pi\) | |||||||
\(32\) | 3.17419 | 0.561123 | ||||||||
\(33\) | −13.6671 | −2.37913 | ||||||||
\(34\) | 3.45773 | 0.592995 | ||||||||
\(35\) | −0.609175 | −0.102969 | ||||||||
\(36\) | −3.65635 | −0.609391 | ||||||||
\(37\) | 3.77264 | 0.620219 | 0.310109 | − | 0.950701i | \(-0.399634\pi\) | ||||
0.310109 | + | 0.950701i | \(0.399634\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 13.5233 | 2.16547 | ||||||||
\(40\) | −3.07461 | −0.486139 | ||||||||
\(41\) | 8.30369 | 1.29682 | 0.648409 | − | 0.761292i | \(-0.275435\pi\) | ||||
0.648409 | + | 0.761292i | \(0.275435\pi\) | |||||||
\(42\) | 2.21064 | 0.341109 | ||||||||
\(43\) | −9.98877 | −1.52327 | −0.761637 | − | 0.648004i | \(-0.775604\pi\) | ||||
−0.761637 | + | 0.648004i | \(0.775604\pi\) | |||||||
\(44\) | −2.60918 | −0.393348 | ||||||||
\(45\) | 6.28525 | 0.936950 | ||||||||
\(46\) | −3.39082 | −0.499950 | ||||||||
\(47\) | −5.88500 | −0.858415 | −0.429208 | − | 0.903206i | \(-0.641207\pi\) | ||||
−0.429208 | + | 0.903206i | \(0.641207\pi\) | |||||||
\(48\) | 7.61219 | 1.09872 | ||||||||
\(49\) | −6.62891 | −0.946986 | ||||||||
\(50\) | 1.19091 | 0.168420 | ||||||||
\(51\) | −8.84726 | −1.23886 | ||||||||
\(52\) | 2.58173 | 0.358022 | ||||||||
\(53\) | −8.44872 | −1.16052 | −0.580261 | − | 0.814431i | \(-0.697049\pi\) | ||||
−0.580261 | + | 0.814431i | \(0.697049\pi\) | |||||||
\(54\) | −11.9219 | −1.62236 | ||||||||
\(55\) | 4.48517 | 0.604780 | ||||||||
\(56\) | 1.87298 | 0.250287 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.32941 | −0.174560 | ||||||||
\(59\) | −10.2359 | −1.33259 | −0.666297 | − | 0.745686i | \(-0.732122\pi\) | ||||
−0.666297 | + | 0.745686i | \(0.732122\pi\) | |||||||
\(60\) | 1.77264 | 0.228847 | ||||||||
\(61\) | −4.98199 | −0.637878 | −0.318939 | − | 0.947775i | \(-0.603327\pi\) | ||||
−0.318939 | + | 0.947775i | \(0.603327\pi\) | |||||||
\(62\) | 7.41827 | 0.942121 | ||||||||
\(63\) | −3.82882 | −0.482386 | ||||||||
\(64\) | 8.77641 | 1.09705 | ||||||||
\(65\) | −4.43800 | −0.550466 | ||||||||
\(66\) | −16.2762 | −2.00347 | ||||||||
\(67\) | −8.47616 | −1.03553 | −0.517764 | − | 0.855524i | \(-0.673235\pi\) | ||||
−0.517764 | + | 0.855524i | \(0.673235\pi\) | |||||||
\(68\) | −1.68903 | −0.204825 | ||||||||
\(69\) | 8.67608 | 1.04448 | ||||||||
\(70\) | −0.725473 | −0.0867106 | ||||||||
\(71\) | −11.6199 | −1.37903 | −0.689514 | − | 0.724272i | \(-0.742176\pi\) | ||||
−0.689514 | + | 0.724272i | \(0.742176\pi\) | |||||||
\(72\) | −19.3247 | −2.27744 | ||||||||
\(73\) | 3.72325 | 0.435773 | 0.217887 | − | 0.975974i | \(-0.430084\pi\) | ||||
0.217887 | + | 0.975974i | \(0.430084\pi\) | |||||||
\(74\) | 4.49288 | 0.522286 | ||||||||
\(75\) | −3.04717 | −0.351857 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.73225 | −0.311369 | ||||||||
\(78\) | 16.1051 | 1.82354 | ||||||||
\(79\) | −9.03817 | −1.01687 | −0.508437 | − | 0.861099i | \(-0.669776\pi\) | ||||
−0.508437 | + | 0.861099i | \(0.669776\pi\) | |||||||
\(80\) | −2.49812 | −0.279298 | ||||||||
\(81\) | 11.6486 | 1.29429 | ||||||||
\(82\) | 9.88894 | 1.09205 | ||||||||
\(83\) | −2.12178 | −0.232896 | −0.116448 | − | 0.993197i | \(-0.537151\pi\) | ||||
−0.116448 | + | 0.993197i | \(0.537151\pi\) | |||||||
\(84\) | −1.07985 | −0.117821 | ||||||||
\(85\) | 2.90343 | 0.314921 | ||||||||
\(86\) | −11.8957 | −1.28275 | ||||||||
\(87\) | 3.40155 | 0.364684 | ||||||||
\(88\) | −13.7901 | −1.47003 | ||||||||
\(89\) | −7.93217 | −0.840808 | −0.420404 | − | 0.907337i | \(-0.638112\pi\) | ||||
−0.420404 | + | 0.907337i | \(0.638112\pi\) | |||||||
\(90\) | 7.48517 | 0.789006 | ||||||||
\(91\) | 2.70352 | 0.283406 | ||||||||
\(92\) | 1.65635 | 0.172686 | ||||||||
\(93\) | −18.9811 | −1.96824 | ||||||||
\(94\) | −7.00850 | −0.722872 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.67231 | −0.987176 | ||||||||
\(97\) | 9.67256 | 0.982099 | 0.491050 | − | 0.871132i | \(-0.336613\pi\) | ||||
0.491050 | + | 0.871132i | \(0.336613\pi\) | |||||||
\(98\) | −7.89443 | −0.797458 | ||||||||
\(99\) | 28.1904 | 2.83324 | ||||||||
\(100\) | −0.581734 | −0.0581734 | ||||||||
\(101\) | −0.971265 | −0.0966444 | −0.0483222 | − | 0.998832i | \(-0.515387\pi\) | ||||
−0.0483222 | + | 0.998832i | \(0.515387\pi\) | |||||||
\(102\) | −10.5363 | −1.04325 | ||||||||
\(103\) | 3.34143 | 0.329241 | 0.164620 | − | 0.986357i | \(-0.447360\pi\) | ||||
0.164620 | + | 0.986357i | \(0.447360\pi\) | |||||||
\(104\) | 13.6451 | 1.33801 | ||||||||
\(105\) | 1.85626 | 0.181153 | ||||||||
\(106\) | −10.0617 | −0.977275 | ||||||||
\(107\) | −9.51655 | −0.920000 | −0.460000 | − | 0.887919i | \(-0.652151\pi\) | ||||
−0.460000 | + | 0.887919i | \(0.652151\pi\) | |||||||
\(108\) | 5.82358 | 0.560374 | ||||||||
\(109\) | −5.54357 | −0.530978 | −0.265489 | − | 0.964114i | \(-0.585533\pi\) | ||||
−0.265489 | + | 0.964114i | \(0.585533\pi\) | |||||||
\(110\) | 5.34143 | 0.509285 | ||||||||
\(111\) | −11.4959 | −1.09114 | ||||||||
\(112\) | 1.52179 | 0.143796 | ||||||||
\(113\) | −1.54134 | −0.144997 | −0.0724987 | − | 0.997369i | \(-0.523097\pi\) | ||||
−0.0724987 | + | 0.997369i | \(0.523097\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.84726 | −0.265508 | ||||||||
\(116\) | 0.649388 | 0.0602942 | ||||||||
\(117\) | −27.8939 | −2.57879 | ||||||||
\(118\) | −12.1900 | −1.12218 | ||||||||
\(119\) | −1.76870 | −0.162136 | ||||||||
\(120\) | 9.36887 | 0.855257 | ||||||||
\(121\) | 9.11672 | 0.828793 | ||||||||
\(122\) | −5.93310 | −0.537158 | ||||||||
\(123\) | −25.3028 | −2.28147 | ||||||||
\(124\) | −3.62367 | −0.325415 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −4.55978 | −0.406217 | ||||||||
\(127\) | −2.30549 | −0.204579 | −0.102289 | − | 0.994755i | \(-0.532617\pi\) | ||||
−0.102289 | + | 0.994755i | \(0.532617\pi\) | |||||||
\(128\) | 4.10353 | 0.362704 | ||||||||
\(129\) | 30.4375 | 2.67987 | ||||||||
\(130\) | −5.28525 | −0.463547 | ||||||||
\(131\) | −12.9181 | −1.12866 | −0.564330 | − | 0.825549i | \(-0.690865\pi\) | ||||
−0.564330 | + | 0.825549i | \(0.690865\pi\) | |||||||
\(132\) | 7.95060 | 0.692011 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.0943 | −0.872018 | ||||||||
\(135\) | −10.0107 | −0.861586 | ||||||||
\(136\) | −8.92693 | −0.765478 | ||||||||
\(137\) | −12.7335 | −1.08790 | −0.543950 | − | 0.839118i | \(-0.683072\pi\) | ||||
−0.543950 | + | 0.839118i | \(0.683072\pi\) | |||||||
\(138\) | 10.3324 | 0.879554 | ||||||||
\(139\) | 10.6087 | 0.899816 | 0.449908 | − | 0.893075i | \(-0.351457\pi\) | ||||
0.449908 | + | 0.893075i | \(0.351457\pi\) | |||||||
\(140\) | 0.354378 | 0.0299504 | ||||||||
\(141\) | 17.9326 | 1.51020 | ||||||||
\(142\) | −13.8383 | −1.16128 | ||||||||
\(143\) | −19.9052 | −1.66455 | ||||||||
\(144\) | −15.7013 | −1.30844 | ||||||||
\(145\) | −1.11630 | −0.0927035 | ||||||||
\(146\) | 4.43405 | 0.366965 | ||||||||
\(147\) | 20.1994 | 1.66602 | ||||||||
\(148\) | −2.19468 | −0.180401 | ||||||||
\(149\) | 3.77307 | 0.309102 | 0.154551 | − | 0.987985i | \(-0.450607\pi\) | ||||
0.154551 | + | 0.987985i | \(0.450607\pi\) | |||||||
\(150\) | −3.62891 | −0.296299 | ||||||||
\(151\) | 9.51562 | 0.774370 | 0.387185 | − | 0.922002i | \(-0.373447\pi\) | ||||
0.387185 | + | 0.922002i | \(0.373447\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.2488 | 1.47533 | ||||||||
\(154\) | −3.25387 | −0.262204 | ||||||||
\(155\) | 6.22908 | 0.500331 | ||||||||
\(156\) | −7.86699 | −0.629863 | ||||||||
\(157\) | −3.45643 | −0.275853 | −0.137927 | − | 0.990442i | \(-0.544044\pi\) | ||||
−0.137927 | + | 0.990442i | \(0.544044\pi\) | |||||||
\(158\) | −10.7636 | −0.856309 | ||||||||
\(159\) | 25.7447 | 2.04169 | ||||||||
\(160\) | 3.17419 | 0.250942 | ||||||||
\(161\) | 1.73448 | 0.136696 | ||||||||
\(162\) | 13.8725 | 1.08992 | ||||||||
\(163\) | 6.65283 | 0.521090 | 0.260545 | − | 0.965462i | \(-0.416098\pi\) | ||||
0.260545 | + | 0.965462i | \(0.416098\pi\) | |||||||
\(164\) | −4.83054 | −0.377202 | ||||||||
\(165\) | −13.6671 | −1.06398 | ||||||||
\(166\) | −2.52685 | −0.196122 | ||||||||
\(167\) | 16.4555 | 1.27336 | 0.636682 | − | 0.771126i | \(-0.280306\pi\) | ||||
0.636682 | + | 0.771126i | \(0.280306\pi\) | |||||||
\(168\) | −5.70728 | −0.440327 | ||||||||
\(169\) | 6.69581 | 0.515062 | ||||||||
\(170\) | 3.45773 | 0.265195 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.81081 | 0.443070 | ||||||||
\(173\) | 22.7824 | 1.73212 | 0.866058 | − | 0.499943i | \(-0.166646\pi\) | ||||
0.866058 | + | 0.499943i | \(0.166646\pi\) | |||||||
\(174\) | 4.05094 | 0.307101 | ||||||||
\(175\) | −0.609175 | −0.0460493 | ||||||||
\(176\) | −11.2045 | −0.844569 | ||||||||
\(177\) | 31.1904 | 2.34441 | ||||||||
\(178\) | −9.44650 | −0.708045 | ||||||||
\(179\) | 2.32916 | 0.174090 | 0.0870449 | − | 0.996204i | \(-0.472258\pi\) | ||||
0.0870449 | + | 0.996204i | \(0.472258\pi\) | |||||||
\(180\) | −3.65635 | −0.272528 | ||||||||
\(181\) | 22.3392 | 1.66046 | 0.830230 | − | 0.557421i | \(-0.188209\pi\) | ||||
0.830230 | + | 0.557421i | \(0.188209\pi\) | |||||||
\(182\) | 3.21965 | 0.238656 | ||||||||
\(183\) | 15.1810 | 1.12221 | ||||||||
\(184\) | 8.75421 | 0.645369 | ||||||||
\(185\) | 3.77264 | 0.277370 | ||||||||
\(186\) | −22.6047 | −1.65746 | ||||||||
\(187\) | 13.0224 | 0.952291 | ||||||||
\(188\) | 3.42350 | 0.249685 | ||||||||
\(189\) | 6.09829 | 0.443585 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.23766 | 0.161911 | 0.0809556 | − | 0.996718i | \(-0.474203\pi\) | ||||
0.0809556 | + | 0.996718i | \(0.474203\pi\) | |||||||
\(192\) | −26.7432 | −1.93003 | ||||||||
\(193\) | 4.54306 | 0.327017 | 0.163508 | − | 0.986542i | \(-0.447719\pi\) | ||||
0.163508 | + | 0.986542i | \(0.447719\pi\) | |||||||
\(194\) | 11.5191 | 0.827026 | ||||||||
\(195\) | 13.5233 | 0.968426 | ||||||||
\(196\) | 3.85626 | 0.275447 | ||||||||
\(197\) | −19.2236 | −1.36962 | −0.684812 | − | 0.728720i | \(-0.740116\pi\) | ||||
−0.684812 | + | 0.728720i | \(0.740116\pi\) | |||||||
\(198\) | 33.5722 | 2.38587 | ||||||||
\(199\) | −6.15094 | −0.436029 | −0.218014 | − | 0.975946i | \(-0.569958\pi\) | ||||
−0.218014 | + | 0.975946i | \(0.569958\pi\) | |||||||
\(200\) | −3.07461 | −0.217408 | ||||||||
\(201\) | 25.8283 | 1.82179 | ||||||||
\(202\) | −1.15669 | −0.0813843 | ||||||||
\(203\) | 0.680021 | 0.0477281 | ||||||||
\(204\) | 5.14675 | 0.360345 | ||||||||
\(205\) | 8.30369 | 0.579955 | ||||||||
\(206\) | 3.97934 | 0.277254 | ||||||||
\(207\) | −17.8957 | −1.24384 | ||||||||
\(208\) | 11.0866 | 0.768720 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.21064 | 0.152549 | ||||||||
\(211\) | −12.6932 | −0.873837 | −0.436919 | − | 0.899501i | \(-0.643930\pi\) | ||||
−0.436919 | + | 0.899501i | \(0.643930\pi\) | |||||||
\(212\) | 4.91491 | 0.337557 | ||||||||
\(213\) | 35.4078 | 2.42610 | ||||||||
\(214\) | −11.3334 | −0.774732 | ||||||||
\(215\) | −9.98877 | −0.681228 | ||||||||
\(216\) | 30.7791 | 2.09425 | ||||||||
\(217\) | −3.79460 | −0.257594 | ||||||||
\(218\) | −6.60189 | −0.447136 | ||||||||
\(219\) | −11.3454 | −0.766649 | ||||||||
\(220\) | −2.60918 | −0.175911 | ||||||||
\(221\) | −12.8854 | −0.866767 | ||||||||
\(222\) | −13.6906 | −0.918851 | ||||||||
\(223\) | −22.5376 | −1.50923 | −0.754614 | − | 0.656169i | \(-0.772176\pi\) | ||||
−0.754614 | + | 0.656169i | \(0.772176\pi\) | |||||||
\(224\) | −1.93364 | −0.129197 | ||||||||
\(225\) | 6.28525 | 0.419017 | ||||||||
\(226\) | −1.83560 | −0.122102 | ||||||||
\(227\) | −18.1124 | −1.20216 | −0.601080 | − | 0.799189i | \(-0.705263\pi\) | ||||
−0.601080 | + | 0.799189i | \(0.705263\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.41604 | −0.622229 | −0.311115 | − | 0.950372i | \(-0.600702\pi\) | ||||
−0.311115 | + | 0.950372i | \(0.600702\pi\) | |||||||
\(230\) | −3.39082 | −0.223584 | ||||||||
\(231\) | 8.32564 | 0.547787 | ||||||||
\(232\) | 3.43218 | 0.225334 | ||||||||
\(233\) | 15.7000 | 1.02854 | 0.514271 | − | 0.857628i | \(-0.328063\pi\) | ||||
0.514271 | + | 0.857628i | \(0.328063\pi\) | |||||||
\(234\) | −33.2191 | −2.17160 | ||||||||
\(235\) | −5.88500 | −0.383895 | ||||||||
\(236\) | 5.95455 | 0.387608 | ||||||||
\(237\) | 27.5408 | 1.78897 | ||||||||
\(238\) | −2.10636 | −0.136535 | ||||||||
\(239\) | −23.4610 | −1.51757 | −0.758783 | − | 0.651344i | \(-0.774205\pi\) | ||||
−0.758783 | + | 0.651344i | \(0.774205\pi\) | |||||||
\(240\) | 7.61219 | 0.491365 | ||||||||
\(241\) | −13.1694 | −0.848314 | −0.424157 | − | 0.905589i | \(-0.639430\pi\) | ||||
−0.424157 | + | 0.905589i | \(0.639430\pi\) | |||||||
\(242\) | 10.8572 | 0.697927 | ||||||||
\(243\) | −5.46321 | −0.350465 | ||||||||
\(244\) | 2.89819 | 0.185538 | ||||||||
\(245\) | −6.62891 | −0.423505 | ||||||||
\(246\) | −30.1333 | −1.92123 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −19.1520 | −1.21615 | ||||||||
\(249\) | 6.46544 | 0.409730 | ||||||||
\(250\) | 1.19091 | 0.0753197 | ||||||||
\(251\) | −17.3251 | −1.09355 | −0.546776 | − | 0.837279i | \(-0.684145\pi\) | ||||
−0.546776 | + | 0.837279i | \(0.684145\pi\) | |||||||
\(252\) | 2.22736 | 0.140310 | ||||||||
\(253\) | −12.7704 | −0.802869 | ||||||||
\(254\) | −2.74563 | −0.172276 | ||||||||
\(255\) | −8.84726 | −0.554037 | ||||||||
\(256\) | −12.6659 | −0.791618 | ||||||||
\(257\) | 5.67960 | 0.354283 | 0.177142 | − | 0.984185i | \(-0.443315\pi\) | ||||
0.177142 | + | 0.984185i | \(0.443315\pi\) | |||||||
\(258\) | 36.2483 | 2.25672 | ||||||||
\(259\) | −2.29820 | −0.142803 | ||||||||
\(260\) | 2.58173 | 0.160112 | ||||||||
\(261\) | −7.01621 | −0.434293 | ||||||||
\(262\) | −15.3843 | −0.950445 | ||||||||
\(263\) | 5.65764 | 0.348865 | 0.174433 | − | 0.984669i | \(-0.444191\pi\) | ||||
0.174433 | + | 0.984669i | \(0.444191\pi\) | |||||||
\(264\) | 42.0209 | 2.58621 | ||||||||
\(265\) | −8.44872 | −0.519001 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.1707 | 1.47922 | ||||||||
\(268\) | 4.93087 | 0.301201 | ||||||||
\(269\) | 23.9918 | 1.46280 | 0.731402 | − | 0.681946i | \(-0.238866\pi\) | ||||
0.731402 | + | 0.681946i | \(0.238866\pi\) | |||||||
\(270\) | −11.9219 | −0.725542 | ||||||||
\(271\) | −21.2995 | −1.29385 | −0.646926 | − | 0.762553i | \(-0.723946\pi\) | ||||
−0.646926 | + | 0.762553i | \(0.723946\pi\) | |||||||
\(272\) | −7.25311 | −0.439785 | ||||||||
\(273\) | −8.23808 | −0.498591 | ||||||||
\(274\) | −15.1645 | −0.916121 | ||||||||
\(275\) | 4.48517 | 0.270466 | ||||||||
\(276\) | −5.04717 | −0.303804 | ||||||||
\(277\) | −0.821109 | −0.0493357 | −0.0246678 | − | 0.999696i | \(-0.507853\pi\) | ||||
−0.0246678 | + | 0.999696i | \(0.507853\pi\) | |||||||
\(278\) | 12.6340 | 0.757735 | ||||||||
\(279\) | 39.1513 | 2.34393 | ||||||||
\(280\) | 1.87298 | 0.111932 | ||||||||
\(281\) | 0.587479 | 0.0350461 | 0.0175230 | − | 0.999846i | \(-0.494422\pi\) | ||||
0.0175230 | + | 0.999846i | \(0.494422\pi\) | |||||||
\(282\) | 21.3561 | 1.27174 | ||||||||
\(283\) | 30.9424 | 1.83933 | 0.919667 | − | 0.392699i | \(-0.128459\pi\) | ||||
0.919667 | + | 0.392699i | \(0.128459\pi\) | |||||||
\(284\) | 6.75969 | 0.401114 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −23.7052 | −1.40172 | ||||||||
\(287\) | −5.05840 | −0.298588 | ||||||||
\(288\) | 19.9506 | 1.17560 | ||||||||
\(289\) | −8.57008 | −0.504122 | ||||||||
\(290\) | −1.32941 | −0.0780656 | ||||||||
\(291\) | −29.4739 | −1.72779 | ||||||||
\(292\) | −2.16594 | −0.126752 | ||||||||
\(293\) | −3.76271 | −0.219820 | −0.109910 | − | 0.993942i | \(-0.535056\pi\) | ||||
−0.109910 | + | 0.993942i | \(0.535056\pi\) | |||||||
\(294\) | 24.0557 | 1.40296 | ||||||||
\(295\) | −10.2359 | −0.595955 | ||||||||
\(296\) | −11.5994 | −0.674202 | ||||||||
\(297\) | −44.8998 | −2.60535 | ||||||||
\(298\) | 4.49338 | 0.260295 | ||||||||
\(299\) | 12.6361 | 0.730765 | ||||||||
\(300\) | 1.77264 | 0.102344 | ||||||||
\(301\) | 6.08491 | 0.350728 | ||||||||
\(302\) | 11.3322 | 0.652097 | ||||||||
\(303\) | 2.95961 | 0.170025 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.98199 | −0.285268 | ||||||||
\(306\) | 21.7327 | 1.24237 | ||||||||
\(307\) | −20.3419 | −1.16097 | −0.580485 | − | 0.814271i | \(-0.697137\pi\) | ||||
−0.580485 | + | 0.814271i | \(0.697137\pi\) | |||||||
\(308\) | 1.58945 | 0.0905670 | ||||||||
\(309\) | −10.1819 | −0.579228 | ||||||||
\(310\) | 7.41827 | 0.421329 | ||||||||
\(311\) | −7.67830 | −0.435397 | −0.217698 | − | 0.976016i | \(-0.569855\pi\) | ||||
−0.217698 | + | 0.976016i | \(0.569855\pi\) | |||||||
\(312\) | −41.5790 | −2.35395 | ||||||||
\(313\) | 23.9927 | 1.35615 | 0.678074 | − | 0.734993i | \(-0.262815\pi\) | ||||
0.678074 | + | 0.734993i | \(0.262815\pi\) | |||||||
\(314\) | −4.11630 | −0.232296 | ||||||||
\(315\) | −3.82882 | −0.215730 | ||||||||
\(316\) | 5.25781 | 0.295775 | ||||||||
\(317\) | −1.03904 | −0.0583580 | −0.0291790 | − | 0.999574i | \(-0.509289\pi\) | ||||
−0.0291790 | + | 0.999574i | \(0.509289\pi\) | |||||||
\(318\) | 30.6596 | 1.71931 | ||||||||
\(319\) | −5.00678 | −0.280326 | ||||||||
\(320\) | 8.77641 | 0.490616 | ||||||||
\(321\) | 28.9986 | 1.61854 | ||||||||
\(322\) | 2.06561 | 0.115112 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −6.77641 | −0.376467 | ||||||||
\(325\) | −4.43800 | −0.246176 | ||||||||
\(326\) | 7.92292 | 0.438810 | ||||||||
\(327\) | 16.8922 | 0.934141 | ||||||||
\(328\) | −25.5306 | −1.40969 | ||||||||
\(329\) | 3.58500 | 0.197647 | ||||||||
\(330\) | −16.2762 | −0.895978 | ||||||||
\(331\) | −30.8316 | −1.69466 | −0.847328 | − | 0.531069i | \(-0.821790\pi\) | ||||
−0.847328 | + | 0.531069i | \(0.821790\pi\) | |||||||
\(332\) | 1.23431 | 0.0677418 | ||||||||
\(333\) | 23.7120 | 1.29941 | ||||||||
\(334\) | 19.5970 | 1.07230 | ||||||||
\(335\) | −8.47616 | −0.463102 | ||||||||
\(336\) | −4.63716 | −0.252978 | ||||||||
\(337\) | −20.7153 | −1.12843 | −0.564217 | − | 0.825627i | \(-0.690822\pi\) | ||||
−0.564217 | + | 0.825627i | \(0.690822\pi\) | |||||||
\(338\) | 7.97410 | 0.433734 | ||||||||
\(339\) | 4.69674 | 0.255092 | ||||||||
\(340\) | −1.68903 | −0.0916003 | ||||||||
\(341\) | 27.9384 | 1.51295 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.30239 | 0.448287 | ||||||||
\(344\) | 30.7116 | 1.65586 | ||||||||
\(345\) | 8.67608 | 0.467104 | ||||||||
\(346\) | 27.1318 | 1.45862 | ||||||||
\(347\) | 8.22136 | 0.441346 | 0.220673 | − | 0.975348i | \(-0.429175\pi\) | ||||
0.220673 | + | 0.975348i | \(0.429175\pi\) | |||||||
\(348\) | −1.97880 | −0.106075 | ||||||||
\(349\) | 11.9216 | 0.638150 | 0.319075 | − | 0.947730i | \(-0.396628\pi\) | ||||
0.319075 | + | 0.947730i | \(0.396628\pi\) | |||||||
\(350\) | −0.725473 | −0.0387782 | ||||||||
\(351\) | 44.4276 | 2.37137 | ||||||||
\(352\) | 14.2368 | 0.758823 | ||||||||
\(353\) | −11.7983 | −0.627959 | −0.313980 | − | 0.949430i | \(-0.601662\pi\) | ||||
−0.313980 | + | 0.949430i | \(0.601662\pi\) | |||||||
\(354\) | 37.1450 | 1.97423 | ||||||||
\(355\) | −11.6199 | −0.616720 | ||||||||
\(356\) | 4.61441 | 0.244563 | ||||||||
\(357\) | 5.38953 | 0.285244 | ||||||||
\(358\) | 2.77382 | 0.146601 | ||||||||
\(359\) | 0.110812 | 0.00584841 | 0.00292420 | − | 0.999996i | \(-0.499069\pi\) | ||||
0.00292420 | + | 0.999996i | \(0.499069\pi\) | |||||||
\(360\) | −19.3247 | −1.01850 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 26.6040 | 1.39827 | ||||||||
\(363\) | −27.7802 | −1.45808 | ||||||||
\(364\) | −1.57273 | −0.0824334 | ||||||||
\(365\) | 3.72325 | 0.194884 | ||||||||
\(366\) | 18.0792 | 0.945013 | ||||||||
\(367\) | 11.7397 | 0.612808 | 0.306404 | − | 0.951902i | \(-0.400874\pi\) | ||||
0.306404 | + | 0.951902i | \(0.400874\pi\) | |||||||
\(368\) | 7.11278 | 0.370779 | ||||||||
\(369\) | 52.1908 | 2.71694 | ||||||||
\(370\) | 4.49288 | 0.233574 | ||||||||
\(371\) | 5.14675 | 0.267206 | ||||||||
\(372\) | 11.0419 | 0.572498 | ||||||||
\(373\) | −14.5190 | −0.751763 | −0.375882 | − | 0.926668i | \(-0.622660\pi\) | ||||
−0.375882 | + | 0.926668i | \(0.622660\pi\) | |||||||
\(374\) | 15.5085 | 0.801924 | ||||||||
\(375\) | −3.04717 | −0.157355 | ||||||||
\(376\) | 18.0941 | 0.933131 | ||||||||
\(377\) | 4.95412 | 0.255150 | ||||||||
\(378\) | 7.26251 | 0.373543 | ||||||||
\(379\) | 6.59023 | 0.338518 | 0.169259 | − | 0.985572i | \(-0.445863\pi\) | ||||
0.169259 | + | 0.985572i | \(0.445863\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.02522 | 0.359913 | ||||||||
\(382\) | 2.66485 | 0.136345 | ||||||||
\(383\) | 2.86921 | 0.146610 | 0.0733049 | − | 0.997310i | \(-0.476645\pi\) | ||||
0.0733049 | + | 0.997310i | \(0.476645\pi\) | |||||||
\(384\) | −12.5041 | −0.638099 | ||||||||
\(385\) | −2.73225 | −0.139249 | ||||||||
\(386\) | 5.41038 | 0.275381 | ||||||||
\(387\) | −62.7819 | −3.19138 | ||||||||
\(388\) | −5.62686 | −0.285660 | ||||||||
\(389\) | −6.33149 | −0.321019 | −0.160510 | − | 0.987034i | \(-0.551314\pi\) | ||||
−0.160510 | + | 0.987034i | \(0.551314\pi\) | |||||||
\(390\) | 16.1051 | 0.815512 | ||||||||
\(391\) | −8.26682 | −0.418071 | ||||||||
\(392\) | 20.3813 | 1.02941 | ||||||||
\(393\) | 39.3637 | 1.98563 | ||||||||
\(394\) | −22.8936 | −1.15336 | ||||||||
\(395\) | −9.03817 | −0.454759 | ||||||||
\(396\) | −16.3993 | −0.824097 | ||||||||
\(397\) | −30.5498 | −1.53325 | −0.766626 | − | 0.642094i | \(-0.778066\pi\) | ||||
−0.766626 | + | 0.642094i | \(0.778066\pi\) | |||||||
\(398\) | −7.32522 | −0.367180 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.49812 | −0.124906 | ||||||||
\(401\) | −30.3422 | −1.51522 | −0.757609 | − | 0.652709i | \(-0.773633\pi\) | ||||
−0.757609 | + | 0.652709i | \(0.773633\pi\) | |||||||
\(402\) | 30.7592 | 1.53413 | ||||||||
\(403\) | −27.6446 | −1.37708 | ||||||||
\(404\) | 0.565018 | 0.0281107 | ||||||||
\(405\) | 11.6486 | 0.578825 | ||||||||
\(406\) | 0.809843 | 0.0401919 | ||||||||
\(407\) | 16.9209 | 0.838740 | ||||||||
\(408\) | 27.2019 | 1.34669 | ||||||||
\(409\) | 14.9726 | 0.740345 | 0.370173 | − | 0.928963i | \(-0.379299\pi\) | ||||
0.370173 | + | 0.928963i | \(0.379299\pi\) | |||||||
\(410\) | 9.88894 | 0.488380 | ||||||||
\(411\) | 38.8013 | 1.91393 | ||||||||
\(412\) | −1.94382 | −0.0957653 | ||||||||
\(413\) | 6.23543 | 0.306825 | ||||||||
\(414\) | −21.3122 | −1.04744 | ||||||||
\(415\) | −2.12178 | −0.104154 | ||||||||
\(416\) | −14.0871 | −0.690675 | ||||||||
\(417\) | −32.3264 | −1.58303 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.17419 | −0.301629 | −0.150815 | − | 0.988562i | \(-0.548190\pi\) | ||||
−0.150815 | + | 0.988562i | \(0.548190\pi\) | |||||||
\(420\) | −1.07985 | −0.0526913 | ||||||||
\(421\) | 27.5428 | 1.34235 | 0.671177 | − | 0.741297i | \(-0.265789\pi\) | ||||
0.671177 | + | 0.741297i | \(0.265789\pi\) | |||||||
\(422\) | −15.1165 | −0.735858 | ||||||||
\(423\) | −36.9887 | −1.79845 | ||||||||
\(424\) | 25.9765 | 1.26153 | ||||||||
\(425\) | 2.90343 | 0.140837 | ||||||||
\(426\) | 42.1675 | 2.04302 | ||||||||
\(427\) | 3.03490 | 0.146869 | ||||||||
\(428\) | 5.53610 | 0.267598 | ||||||||
\(429\) | 60.6544 | 2.92842 | ||||||||
\(430\) | −11.8957 | −0.573663 | ||||||||
\(431\) | 15.0588 | 0.725358 | 0.362679 | − | 0.931914i | \(-0.381862\pi\) | ||||
0.362679 | + | 0.931914i | \(0.381862\pi\) | |||||||
\(432\) | 25.0080 | 1.20320 | ||||||||
\(433\) | 0.970840 | 0.0466556 | 0.0233278 | − | 0.999728i | \(-0.492574\pi\) | ||||
0.0233278 | + | 0.999728i | \(0.492574\pi\) | |||||||
\(434\) | −4.51902 | −0.216920 | ||||||||
\(435\) | 3.40155 | 0.163092 | ||||||||
\(436\) | 3.22488 | 0.154444 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −13.5113 | −0.645596 | ||||||||
\(439\) | 27.4375 | 1.30952 | 0.654760 | − | 0.755837i | \(-0.272770\pi\) | ||||
0.654760 | + | 0.755837i | \(0.272770\pi\) | |||||||
\(440\) | −13.7901 | −0.657420 | ||||||||
\(441\) | −41.6643 | −1.98402 | ||||||||
\(442\) | −15.3454 | −0.729905 | ||||||||
\(443\) | −8.76544 | −0.416459 | −0.208229 | − | 0.978080i | \(-0.566770\pi\) | ||||
−0.208229 | + | 0.978080i | \(0.566770\pi\) | |||||||
\(444\) | 6.68755 | 0.317377 | ||||||||
\(445\) | −7.93217 | −0.376021 | ||||||||
\(446\) | −26.8402 | −1.27092 | ||||||||
\(447\) | −11.4972 | −0.543798 | ||||||||
\(448\) | −5.34637 | −0.252592 | ||||||||
\(449\) | 9.63397 | 0.454655 | 0.227327 | − | 0.973818i | \(-0.427001\pi\) | ||||
0.227327 | + | 0.973818i | \(0.427001\pi\) | |||||||
\(450\) | 7.48517 | 0.352854 | ||||||||
\(451\) | 37.2434 | 1.75372 | ||||||||
\(452\) | 0.896652 | 0.0421750 | ||||||||
\(453\) | −28.9957 | −1.36234 | ||||||||
\(454\) | −21.5702 | −1.01234 | ||||||||
\(455\) | 2.70352 | 0.126743 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.6708 | −0.499161 | −0.249580 | − | 0.968354i | \(-0.580293\pi\) | ||||
−0.249580 | + | 0.968354i | \(0.580293\pi\) | |||||||
\(458\) | −11.2137 | −0.523980 | ||||||||
\(459\) | −29.0655 | −1.35666 | ||||||||
\(460\) | 1.65635 | 0.0772276 | ||||||||
\(461\) | 5.68680 | 0.264861 | 0.132430 | − | 0.991192i | \(-0.457722\pi\) | ||||
0.132430 | + | 0.991192i | \(0.457722\pi\) | |||||||
\(462\) | 9.91509 | 0.461292 | ||||||||
\(463\) | 35.3550 | 1.64309 | 0.821543 | − | 0.570147i | \(-0.193114\pi\) | ||||
0.821543 | + | 0.570147i | \(0.193114\pi\) | |||||||
\(464\) | 2.78864 | 0.129459 | ||||||||
\(465\) | −18.9811 | −0.880226 | ||||||||
\(466\) | 18.6973 | 0.866135 | ||||||||
\(467\) | −32.9071 | −1.52276 | −0.761380 | − | 0.648306i | \(-0.775478\pi\) | ||||
−0.761380 | + | 0.648306i | \(0.775478\pi\) | |||||||
\(468\) | 16.2269 | 0.750086 | ||||||||
\(469\) | 5.16347 | 0.238427 | ||||||||
\(470\) | −7.00850 | −0.323278 | ||||||||
\(471\) | 10.5323 | 0.485305 | ||||||||
\(472\) | 31.4713 | 1.44858 | ||||||||
\(473\) | −44.8013 | −2.05997 | ||||||||
\(474\) | 32.7986 | 1.50649 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.02891 | 0.0471602 | ||||||||
\(477\) | −53.1023 | −2.43139 | ||||||||
\(478\) | −27.9399 | −1.27794 | ||||||||
\(479\) | −9.05721 | −0.413835 | −0.206917 | − | 0.978358i | \(-0.566343\pi\) | ||||
−0.206917 | + | 0.978358i | \(0.566343\pi\) | |||||||
\(480\) | −9.67231 | −0.441479 | ||||||||
\(481\) | −16.7430 | −0.763414 | ||||||||
\(482\) | −15.6835 | −0.714366 | ||||||||
\(483\) | −5.28525 | −0.240487 | ||||||||
\(484\) | −5.30351 | −0.241069 | ||||||||
\(485\) | 9.67256 | 0.439208 | ||||||||
\(486\) | −6.50619 | −0.295127 | ||||||||
\(487\) | 16.5206 | 0.748620 | 0.374310 | − | 0.927304i | \(-0.377880\pi\) | ||||
0.374310 | + | 0.927304i | \(0.377880\pi\) | |||||||
\(488\) | 15.3177 | 0.693399 | ||||||||
\(489\) | −20.2723 | −0.916745 | ||||||||
\(490\) | −7.89443 | −0.356634 | ||||||||
\(491\) | −1.39125 | −0.0627862 | −0.0313931 | − | 0.999507i | \(-0.509994\pi\) | ||||
−0.0313931 | + | 0.999507i | \(0.509994\pi\) | |||||||
\(492\) | 14.7195 | 0.663605 | ||||||||
\(493\) | −3.24109 | −0.145972 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 28.1904 | 1.26706 | ||||||||
\(496\) | −15.5610 | −0.698708 | ||||||||
\(497\) | 7.07856 | 0.317517 | ||||||||
\(498\) | 7.69975 | 0.345034 | ||||||||
\(499\) | −16.6651 | −0.746033 | −0.373016 | − | 0.927825i | \(-0.621676\pi\) | ||||
−0.373016 | + | 0.927825i | \(0.621676\pi\) | |||||||
\(500\) | −0.581734 | −0.0260159 | ||||||||
\(501\) | −50.1427 | −2.24021 | ||||||||
\(502\) | −20.6327 | −0.920881 | ||||||||
\(503\) | 15.6391 | 0.697314 | 0.348657 | − | 0.937250i | \(-0.386638\pi\) | ||||
0.348657 | + | 0.937250i | \(0.386638\pi\) | |||||||
\(504\) | 11.7721 | 0.524373 | ||||||||
\(505\) | −0.971265 | −0.0432207 | ||||||||
\(506\) | −15.2084 | −0.676096 | ||||||||
\(507\) | −20.4033 | −0.906141 | ||||||||
\(508\) | 1.34118 | 0.0595053 | ||||||||
\(509\) | 19.1540 | 0.848988 | 0.424494 | − | 0.905431i | \(-0.360452\pi\) | ||||
0.424494 | + | 0.905431i | \(0.360452\pi\) | |||||||
\(510\) | −10.5363 | −0.466554 | ||||||||
\(511\) | −2.26811 | −0.100335 | ||||||||
\(512\) | −23.2910 | −1.02933 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.76389 | 0.298342 | ||||||||
\(515\) | 3.34143 | 0.147241 | ||||||||
\(516\) | −17.7065 | −0.779487 | ||||||||
\(517\) | −26.3952 | −1.16086 | ||||||||
\(518\) | −2.73695 | −0.120255 | ||||||||
\(519\) | −69.4220 | −3.04729 | ||||||||
\(520\) | 13.6451 | 0.598378 | ||||||||
\(521\) | 19.2394 | 0.842892 | 0.421446 | − | 0.906853i | \(-0.361523\pi\) | ||||
0.421446 | + | 0.906853i | \(0.361523\pi\) | |||||||
\(522\) | −8.35567 | −0.365718 | ||||||||
\(523\) | −6.63945 | −0.290323 | −0.145161 | − | 0.989408i | \(-0.546370\pi\) | ||||
−0.145161 | + | 0.989408i | \(0.546370\pi\) | |||||||
\(524\) | 7.51490 | 0.328290 | ||||||||
\(525\) | 1.85626 | 0.0810139 | ||||||||
\(526\) | 6.73774 | 0.293779 | ||||||||
\(527\) | 18.0857 | 0.787825 | ||||||||
\(528\) | 34.1419 | 1.48584 | ||||||||
\(529\) | −14.8931 | −0.647528 | ||||||||
\(530\) | −10.0617 | −0.437051 | ||||||||
\(531\) | −64.3349 | −2.79190 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.8517 | −1.59623 | ||||||||
\(534\) | 28.7851 | 1.24565 | ||||||||
\(535\) | −9.51655 | −0.411436 | ||||||||
\(536\) | 26.0609 | 1.12566 | ||||||||
\(537\) | −7.09736 | −0.306274 | ||||||||
\(538\) | 28.5720 | 1.23183 | ||||||||
\(539\) | −29.7317 | −1.28064 | ||||||||
\(540\) | 5.82358 | 0.250607 | ||||||||
\(541\) | 41.7511 | 1.79502 | 0.897510 | − | 0.440994i | \(-0.145374\pi\) | ||||
0.897510 | + | 0.440994i | \(0.145374\pi\) | |||||||
\(542\) | −25.3658 | −1.08955 | ||||||||
\(543\) | −68.0714 | −2.92122 | ||||||||
\(544\) | 9.21606 | 0.395135 | ||||||||
\(545\) | −5.54357 | −0.237460 | ||||||||
\(546\) | −9.81081 | −0.419864 | ||||||||
\(547\) | −12.2052 | −0.521855 | −0.260927 | − | 0.965358i | \(-0.584028\pi\) | ||||
−0.260927 | + | 0.965358i | \(0.584028\pi\) | |||||||
\(548\) | 7.40754 | 0.316434 | ||||||||
\(549\) | −31.3131 | −1.33641 | ||||||||
\(550\) | 5.34143 | 0.227759 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −26.6756 | −1.13539 | ||||||||
\(553\) | 5.50583 | 0.234132 | ||||||||
\(554\) | −0.977867 | −0.0415456 | ||||||||
\(555\) | −11.4959 | −0.487973 | ||||||||
\(556\) | −6.17143 | −0.261727 | ||||||||
\(557\) | 35.1548 | 1.48956 | 0.744779 | − | 0.667311i | \(-0.232555\pi\) | ||||
0.744779 | + | 0.667311i | \(0.232555\pi\) | |||||||
\(558\) | 46.6257 | 1.97382 | ||||||||
\(559\) | 44.3301 | 1.87496 | ||||||||
\(560\) | 1.52179 | 0.0643074 | ||||||||
\(561\) | −39.6814 | −1.67535 | ||||||||
\(562\) | 0.699634 | 0.0295123 | ||||||||
\(563\) | −17.8406 | −0.751891 | −0.375945 | − | 0.926642i | \(-0.622682\pi\) | ||||
−0.375945 | + | 0.926642i | \(0.622682\pi\) | |||||||
\(564\) | −10.4320 | −0.439267 | ||||||||
\(565\) | −1.54134 | −0.0648448 | ||||||||
\(566\) | 36.8496 | 1.54890 | ||||||||
\(567\) | −7.09606 | −0.298007 | ||||||||
\(568\) | 35.7267 | 1.49906 | ||||||||
\(569\) | −31.6042 | −1.32492 | −0.662459 | − | 0.749098i | \(-0.730487\pi\) | ||||
−0.662459 | + | 0.749098i | \(0.730487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.73053 | −0.197967 | −0.0989833 | − | 0.995089i | \(-0.531559\pi\) | ||||
−0.0989833 | + | 0.995089i | \(0.531559\pi\) | |||||||
\(572\) | 11.5795 | 0.484164 | ||||||||
\(573\) | −6.81852 | −0.284848 | ||||||||
\(574\) | −6.02410 | −0.251441 | ||||||||
\(575\) | −2.84726 | −0.118739 | ||||||||
\(576\) | 55.1620 | 2.29841 | ||||||||
\(577\) | 24.4074 | 1.01609 | 0.508047 | − | 0.861330i | \(-0.330368\pi\) | ||||
0.508047 | + | 0.861330i | \(0.330368\pi\) | |||||||
\(578\) | −10.2062 | −0.424522 | ||||||||
\(579\) | −13.8435 | −0.575316 | ||||||||
\(580\) | 0.649388 | 0.0269644 | ||||||||
\(581\) | 1.29254 | 0.0536235 | ||||||||
\(582\) | −35.1008 | −1.45497 | ||||||||
\(583\) | −37.8939 | −1.56941 | ||||||||
\(584\) | −11.4475 | −0.473703 | ||||||||
\(585\) | −27.8939 | −1.15327 | ||||||||
\(586\) | −4.48104 | −0.185110 | ||||||||
\(587\) | −28.6154 | −1.18109 | −0.590543 | − | 0.807006i | \(-0.701086\pi\) | ||||
−0.590543 | + | 0.807006i | \(0.701086\pi\) | |||||||
\(588\) | −11.7507 | −0.484590 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −12.1900 | −0.501853 | ||||||||
\(591\) | 58.5776 | 2.40956 | ||||||||
\(592\) | −9.42450 | −0.387345 | ||||||||
\(593\) | 3.71511 | 0.152561 | 0.0762807 | − | 0.997086i | \(-0.475695\pi\) | ||||
0.0762807 | + | 0.997086i | \(0.475695\pi\) | |||||||
\(594\) | −53.4716 | −2.19397 | ||||||||
\(595\) | −1.76870 | −0.0725096 | ||||||||
\(596\) | −2.19492 | −0.0899076 | ||||||||
\(597\) | 18.7430 | 0.767099 | ||||||||
\(598\) | 15.0485 | 0.615378 | ||||||||
\(599\) | −7.09940 | −0.290074 | −0.145037 | − | 0.989426i | \(-0.546330\pi\) | ||||
−0.145037 | + | 0.989426i | \(0.546330\pi\) | |||||||
\(600\) | 9.36887 | 0.382482 | ||||||||
\(601\) | 11.0596 | 0.451131 | 0.225566 | − | 0.974228i | \(-0.427577\pi\) | ||||
0.225566 | + | 0.974228i | \(0.427577\pi\) | |||||||
\(602\) | 7.24658 | 0.295349 | ||||||||
\(603\) | −53.2748 | −2.16952 | ||||||||
\(604\) | −5.53556 | −0.225239 | ||||||||
\(605\) | 9.11672 | 0.370647 | ||||||||
\(606\) | 3.52463 | 0.143178 | ||||||||
\(607\) | −27.1193 | −1.10074 | −0.550369 | − | 0.834921i | \(-0.685513\pi\) | ||||
−0.550369 | + | 0.834921i | \(0.685513\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.07214 | −0.0839673 | ||||||||
\(610\) | −5.93310 | −0.240224 | ||||||||
\(611\) | 26.1176 | 1.05660 | ||||||||
\(612\) | −10.6160 | −0.429125 | ||||||||
\(613\) | 41.8312 | 1.68954 | 0.844772 | − | 0.535126i | \(-0.179736\pi\) | ||||
0.844772 | + | 0.535126i | \(0.179736\pi\) | |||||||
\(614\) | −24.2253 | −0.977654 | ||||||||
\(615\) | −25.3028 | −1.02031 | ||||||||
\(616\) | 8.40062 | 0.338471 | ||||||||
\(617\) | −17.7052 | −0.712786 | −0.356393 | − | 0.934336i | \(-0.615994\pi\) | ||||
−0.356393 | + | 0.934336i | \(0.615994\pi\) | |||||||
\(618\) | −12.1257 | −0.487768 | ||||||||
\(619\) | −39.8064 | −1.59995 | −0.799976 | − | 0.600032i | \(-0.795155\pi\) | ||||
−0.799976 | + | 0.600032i | \(0.795155\pi\) | |||||||
\(620\) | −3.62367 | −0.145530 | ||||||||
\(621\) | 28.5031 | 1.14379 | ||||||||
\(622\) | −9.14416 | −0.366648 | ||||||||
\(623\) | 4.83208 | 0.193593 | ||||||||
\(624\) | −33.7829 | −1.35240 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 28.5732 | 1.14201 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.01072 | 0.0802366 | ||||||||
\(629\) | 10.9536 | 0.436749 | ||||||||
\(630\) | −4.55978 | −0.181666 | ||||||||
\(631\) | 46.1980 | 1.83911 | 0.919557 | − | 0.392956i | \(-0.128547\pi\) | ||||
0.919557 | + | 0.392956i | \(0.128547\pi\) | |||||||
\(632\) | 27.7889 | 1.10538 | ||||||||
\(633\) | 38.6784 | 1.53733 | ||||||||
\(634\) | −1.23740 | −0.0491433 | ||||||||
\(635\) | −2.30549 | −0.0914905 | ||||||||
\(636\) | −14.9766 | −0.593860 | ||||||||
\(637\) | 29.4191 | 1.16563 | ||||||||
\(638\) | −5.96262 | −0.236062 | ||||||||
\(639\) | −73.0340 | −2.88918 | ||||||||
\(640\) | 4.10353 | 0.162206 | ||||||||
\(641\) | −6.61348 | −0.261217 | −0.130608 | − | 0.991434i | \(-0.541693\pi\) | ||||
−0.130608 | + | 0.991434i | \(0.541693\pi\) | |||||||
\(642\) | 34.5347 | 1.36297 | ||||||||
\(643\) | −30.6152 | −1.20735 | −0.603673 | − | 0.797232i | \(-0.706297\pi\) | ||||
−0.603673 | + | 0.797232i | \(0.706297\pi\) | |||||||
\(644\) | −1.00901 | −0.0397604 | ||||||||
\(645\) | 30.4375 | 1.19847 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.8979 | −0.467753 | −0.233877 | − | 0.972266i | \(-0.575141\pi\) | ||||
−0.233877 | + | 0.972266i | \(0.575141\pi\) | |||||||
\(648\) | −35.8150 | −1.40695 | ||||||||
\(649\) | −45.9095 | −1.80211 | ||||||||
\(650\) | −5.28525 | −0.207305 | ||||||||
\(651\) | 11.5628 | 0.453182 | ||||||||
\(652\) | −3.87018 | −0.151568 | ||||||||
\(653\) | −1.42899 | −0.0559207 | −0.0279604 | − | 0.999609i | \(-0.508901\pi\) | ||||
−0.0279604 | + | 0.999609i | \(0.508901\pi\) | |||||||
\(654\) | 20.1171 | 0.786640 | ||||||||
\(655\) | −12.9181 | −0.504752 | ||||||||
\(656\) | −20.7436 | −0.809901 | ||||||||
\(657\) | 23.4015 | 0.912981 | ||||||||
\(658\) | 4.26941 | 0.166439 | ||||||||
\(659\) | 24.4970 | 0.954268 | 0.477134 | − | 0.878831i | \(-0.341676\pi\) | ||||
0.477134 | + | 0.878831i | \(0.341676\pi\) | |||||||
\(660\) | 7.95060 | 0.309477 | ||||||||
\(661\) | 3.22606 | 0.125479 | 0.0627396 | − | 0.998030i | \(-0.480016\pi\) | ||||
0.0627396 | + | 0.998030i | \(0.480016\pi\) | |||||||
\(662\) | −36.7176 | −1.42707 | ||||||||
\(663\) | 39.2641 | 1.52489 | ||||||||
\(664\) | 6.52366 | 0.253167 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 28.2389 | 1.09423 | ||||||||
\(667\) | 3.17838 | 0.123068 | ||||||||
\(668\) | −9.57273 | −0.370380 | ||||||||
\(669\) | 68.6759 | 2.65516 | ||||||||
\(670\) | −10.0943 | −0.389978 | ||||||||
\(671\) | −22.3451 | −0.862621 | ||||||||
\(672\) | 5.89213 | 0.227294 | ||||||||
\(673\) | −37.1424 | −1.43173 | −0.715866 | − | 0.698237i | \(-0.753968\pi\) | ||||
−0.715866 | + | 0.698237i | \(0.753968\pi\) | |||||||
\(674\) | −24.6700 | −0.950254 | ||||||||
\(675\) | −10.0107 | −0.385313 | ||||||||
\(676\) | −3.89518 | −0.149815 | ||||||||
\(677\) | 24.7550 | 0.951412 | 0.475706 | − | 0.879604i | \(-0.342193\pi\) | ||||
0.475706 | + | 0.879604i | \(0.342193\pi\) | |||||||
\(678\) | 5.59339 | 0.214813 | ||||||||
\(679\) | −5.89228 | −0.226125 | ||||||||
\(680\) | −8.92693 | −0.342332 | ||||||||
\(681\) | 55.1914 | 2.11494 | ||||||||
\(682\) | 33.2722 | 1.27406 | ||||||||
\(683\) | −40.1153 | −1.53497 | −0.767484 | − | 0.641068i | \(-0.778492\pi\) | ||||
−0.767484 | + | 0.641068i | \(0.778492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.7335 | −0.486524 | ||||||||
\(686\) | 9.88740 | 0.377503 | ||||||||
\(687\) | 28.6923 | 1.09468 | ||||||||
\(688\) | 24.9531 | 0.951328 | ||||||||
\(689\) | 37.4954 | 1.42846 | ||||||||
\(690\) | 10.3324 | 0.393349 | ||||||||
\(691\) | 39.4963 | 1.50251 | 0.751254 | − | 0.660013i | \(-0.229449\pi\) | ||||
0.751254 | + | 0.660013i | \(0.229449\pi\) | |||||||
\(692\) | −13.2533 | −0.503816 | ||||||||
\(693\) | −17.1729 | −0.652344 | ||||||||
\(694\) | 9.79090 | 0.371658 | ||||||||
\(695\) | 10.6087 | 0.402410 | ||||||||
\(696\) | −10.4584 | −0.396426 | ||||||||
\(697\) | 24.1092 | 0.913201 | ||||||||
\(698\) | 14.1976 | 0.537386 | ||||||||
\(699\) | −47.8406 | −1.80950 | ||||||||
\(700\) | 0.354378 | 0.0133942 | ||||||||
\(701\) | 0.0219552 | 0.000829236 0 | 0.000414618 | − | 1.00000i | \(-0.499868\pi\) | ||||
0.000414618 | 1.00000i | \(0.499868\pi\) | ||||||||
\(702\) | 52.9092 | 1.99693 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 39.3637 | 1.48357 | ||||||||
\(705\) | 17.9326 | 0.675381 | ||||||||
\(706\) | −14.0507 | −0.528805 | ||||||||
\(707\) | 0.591670 | 0.0222521 | ||||||||
\(708\) | −18.1445 | −0.681913 | ||||||||
\(709\) | −17.8017 | −0.668558 | −0.334279 | − | 0.942474i | \(-0.608493\pi\) | ||||
−0.334279 | + | 0.942474i | \(0.608493\pi\) | |||||||
\(710\) | −13.8383 | −0.519340 | ||||||||
\(711\) | −56.8071 | −2.13043 | ||||||||
\(712\) | 24.3883 | 0.913992 | ||||||||
\(713\) | −17.7358 | −0.664210 | ||||||||
\(714\) | 6.41844 | 0.240204 | ||||||||
\(715\) | −19.9052 | −0.744410 | ||||||||
\(716\) | −1.35495 | −0.0506370 | ||||||||
\(717\) | 71.4896 | 2.66983 | ||||||||
\(718\) | 0.131967 | 0.00492495 | ||||||||
\(719\) | 18.8103 | 0.701506 | 0.350753 | − | 0.936468i | \(-0.385926\pi\) | ||||
0.350753 | + | 0.936468i | \(0.385926\pi\) | |||||||
\(720\) | −15.7013 | −0.585153 | ||||||||
\(721\) | −2.03552 | −0.0758066 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.1294 | 1.49243 | ||||||||
\(724\) | −12.9955 | −0.482973 | ||||||||
\(725\) | −1.11630 | −0.0414582 | ||||||||
\(726\) | −33.0837 | −1.22785 | ||||||||
\(727\) | 5.00301 | 0.185552 | 0.0927758 | − | 0.995687i | \(-0.470426\pi\) | ||||
0.0927758 | + | 0.995687i | \(0.470426\pi\) | |||||||
\(728\) | −8.31227 | −0.308073 | ||||||||
\(729\) | −18.2986 | −0.677725 | ||||||||
\(730\) | 4.43405 | 0.164112 | ||||||||
\(731\) | −29.0017 | −1.07267 | ||||||||
\(732\) | −8.83129 | −0.326414 | ||||||||
\(733\) | −23.5259 | −0.868950 | −0.434475 | − | 0.900684i | \(-0.643066\pi\) | ||||
−0.434475 | + | 0.900684i | \(0.643066\pi\) | |||||||
\(734\) | 13.9809 | 0.516046 | ||||||||
\(735\) | 20.1994 | 0.745066 | ||||||||
\(736\) | −9.03774 | −0.333136 | ||||||||
\(737\) | −38.0170 | −1.40037 | ||||||||
\(738\) | 62.1545 | 2.28794 | ||||||||
\(739\) | −37.3836 | −1.37518 | −0.687590 | − | 0.726099i | \(-0.741331\pi\) | ||||
−0.687590 | + | 0.726099i | \(0.741331\pi\) | |||||||
\(740\) | −2.19468 | −0.0806779 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.12932 | 0.225014 | ||||||||
\(743\) | −10.3886 | −0.381121 | −0.190560 | − | 0.981675i | \(-0.561030\pi\) | ||||
−0.190560 | + | 0.981675i | \(0.561030\pi\) | |||||||
\(744\) | 58.3594 | 2.13956 | ||||||||
\(745\) | 3.77307 | 0.138235 | ||||||||
\(746\) | −17.2908 | −0.633060 | ||||||||
\(747\) | −13.3359 | −0.487937 | ||||||||
\(748\) | −7.57556 | −0.276990 | ||||||||
\(749\) | 5.79725 | 0.211827 | ||||||||
\(750\) | −3.62891 | −0.132509 | ||||||||
\(751\) | 31.2825 | 1.14152 | 0.570758 | − | 0.821119i | \(-0.306650\pi\) | ||||
0.570758 | + | 0.821119i | \(0.306650\pi\) | |||||||
\(752\) | 14.7014 | 0.536105 | ||||||||
\(753\) | 52.7927 | 1.92387 | ||||||||
\(754\) | 5.89991 | 0.214862 | ||||||||
\(755\) | 9.51562 | 0.346309 | ||||||||
\(756\) | −3.54758 | −0.129024 | ||||||||
\(757\) | −12.6241 | −0.458830 | −0.229415 | − | 0.973329i | \(-0.573681\pi\) | ||||
−0.229415 | + | 0.973329i | \(0.573681\pi\) | |||||||
\(758\) | 7.84837 | 0.285066 | ||||||||
\(759\) | 38.9137 | 1.41248 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.5495 | 0.418668 | 0.209334 | − | 0.977844i | \(-0.432870\pi\) | ||||
0.209334 | + | 0.977844i | \(0.432870\pi\) | |||||||
\(762\) | 8.36640 | 0.303083 | ||||||||
\(763\) | 3.37701 | 0.122256 | ||||||||
\(764\) | −1.30172 | −0.0470946 | ||||||||
\(765\) | 18.2488 | 0.659787 | ||||||||
\(766\) | 3.41697 | 0.123460 | ||||||||
\(767\) | 45.4267 | 1.64026 | ||||||||
\(768\) | 38.5951 | 1.39268 | ||||||||
\(769\) | −26.9207 | −0.970784 | −0.485392 | − | 0.874297i | \(-0.661323\pi\) | ||||
−0.485392 | + | 0.874297i | \(0.661323\pi\) | |||||||
\(770\) | −3.25387 | −0.117261 | ||||||||
\(771\) | −17.3067 | −0.623286 | ||||||||
\(772\) | −2.64286 | −0.0951184 | ||||||||
\(773\) | −21.3331 | −0.767299 | −0.383649 | − | 0.923479i | \(-0.625333\pi\) | ||||
−0.383649 | + | 0.923479i | \(0.625333\pi\) | |||||||
\(774\) | −74.7676 | −2.68747 | ||||||||
\(775\) | 6.22908 | 0.223755 | ||||||||
\(776\) | −29.7394 | −1.06758 | ||||||||
\(777\) | 7.00301 | 0.251232 | ||||||||
\(778\) | −7.54024 | −0.270331 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −7.86699 | −0.281683 | ||||||||
\(781\) | −52.1172 | −1.86490 | ||||||||
\(782\) | −9.84503 | −0.352058 | ||||||||
\(783\) | 11.1749 | 0.399360 | ||||||||
\(784\) | 16.5598 | 0.591421 | ||||||||
\(785\) | −3.45643 | −0.123365 | ||||||||
\(786\) | 46.8786 | 1.67210 | ||||||||
\(787\) | −3.52489 | −0.125649 | −0.0628243 | − | 0.998025i | \(-0.520011\pi\) | ||||
−0.0628243 | + | 0.998025i | \(0.520011\pi\) | |||||||
\(788\) | 11.1830 | 0.398379 | ||||||||
\(789\) | −17.2398 | −0.613753 | ||||||||
\(790\) | −10.7636 | −0.382953 | ||||||||
\(791\) | 0.938948 | 0.0333852 | ||||||||
\(792\) | −86.6746 | −3.07985 | ||||||||
\(793\) | 22.1100 | 0.785151 | ||||||||
\(794\) | −36.3821 | −1.29115 | ||||||||
\(795\) | 25.7447 | 0.913070 | ||||||||
\(796\) | 3.57821 | 0.126826 | ||||||||
\(797\) | 39.0084 | 1.38175 | 0.690875 | − | 0.722974i | \(-0.257226\pi\) | ||||
0.690875 | + | 0.722974i | \(0.257226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.0867 | −0.604484 | ||||||||
\(800\) | 3.17419 | 0.112225 | ||||||||
\(801\) | −49.8557 | −1.76156 | ||||||||
\(802\) | −36.1348 | −1.27597 | ||||||||
\(803\) | 16.6994 | 0.589309 | ||||||||
\(804\) | −15.0252 | −0.529899 | ||||||||
\(805\) | 1.73448 | 0.0611323 | ||||||||
\(806\) | −32.9222 | −1.15964 | ||||||||
\(807\) | −73.1071 | −2.57349 | ||||||||
\(808\) | 2.98626 | 0.105056 | ||||||||
\(809\) | 50.7196 | 1.78321 | 0.891604 | − | 0.452816i | \(-0.149581\pi\) | ||||
0.891604 | + | 0.452816i | \(0.149581\pi\) | |||||||
\(810\) | 13.8725 | 0.487429 | ||||||||
\(811\) | −29.0376 | −1.01965 | −0.509824 | − | 0.860279i | \(-0.670289\pi\) | ||||
−0.509824 | + | 0.860279i | \(0.670289\pi\) | |||||||
\(812\) | −0.395591 | −0.0138825 | ||||||||
\(813\) | 64.9032 | 2.27625 | ||||||||
\(814\) | 20.1513 | 0.706303 | ||||||||
\(815\) | 6.65283 | 0.233038 | ||||||||
\(816\) | 22.1015 | 0.773706 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 17.8310 | 0.623445 | ||||||||
\(819\) | 16.9923 | 0.593759 | ||||||||
\(820\) | −4.83054 | −0.168690 | ||||||||
\(821\) | 32.9878 | 1.15128 | 0.575640 | − | 0.817703i | \(-0.304753\pi\) | ||||
0.575640 | + | 0.817703i | \(0.304753\pi\) | |||||||
\(822\) | 46.2088 | 1.61172 | ||||||||
\(823\) | −26.5533 | −0.925591 | −0.462796 | − | 0.886465i | \(-0.653154\pi\) | ||||
−0.462796 | + | 0.886465i | \(0.653154\pi\) | |||||||
\(824\) | −10.2736 | −0.357898 | ||||||||
\(825\) | −13.6671 | −0.475826 | ||||||||
\(826\) | 7.42583 | 0.258378 | ||||||||
\(827\) | 32.7666 | 1.13941 | 0.569703 | − | 0.821851i | \(-0.307058\pi\) | ||||
0.569703 | + | 0.821851i | \(0.307058\pi\) | |||||||
\(828\) | 10.4106 | 0.361792 | ||||||||
\(829\) | −32.4548 | −1.12720 | −0.563601 | − | 0.826047i | \(-0.690584\pi\) | ||||
−0.563601 | + | 0.826047i | \(0.690584\pi\) | |||||||
\(830\) | −2.52685 | −0.0877083 | ||||||||
\(831\) | 2.50206 | 0.0867955 | ||||||||
\(832\) | −38.9497 | −1.35034 | ||||||||
\(833\) | −19.2466 | −0.666854 | ||||||||
\(834\) | −38.4979 | −1.33307 | ||||||||
\(835\) | 16.4555 | 0.569466 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −62.3576 | −2.15539 | ||||||||
\(838\) | −7.35291 | −0.254002 | ||||||||
\(839\) | 35.2098 | 1.21558 | 0.607788 | − | 0.794099i | \(-0.292057\pi\) | ||||
0.607788 | + | 0.794099i | \(0.292057\pi\) | |||||||
\(840\) | −5.70728 | −0.196920 | ||||||||
\(841\) | −27.7539 | −0.957030 | ||||||||
\(842\) | 32.8010 | 1.13040 | ||||||||
\(843\) | −1.79015 | −0.0616560 | ||||||||
\(844\) | 7.38408 | 0.254171 | ||||||||
\(845\) | 6.69581 | 0.230343 | ||||||||
\(846\) | −44.0502 | −1.51448 | ||||||||
\(847\) | −5.55368 | −0.190827 | ||||||||
\(848\) | 21.1059 | 0.724779 | ||||||||
\(849\) | −94.2867 | −3.23591 | ||||||||
\(850\) | 3.45773 | 0.118599 | ||||||||
\(851\) | −10.7417 | −0.368220 | ||||||||
\(852\) | −20.5979 | −0.705674 | ||||||||
\(853\) | −1.78825 | −0.0612286 | −0.0306143 | − | 0.999531i | \(-0.509746\pi\) | ||||
−0.0306143 | + | 0.999531i | \(0.509746\pi\) | |||||||
\(854\) | 3.61430 | 0.123679 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 29.2597 | 1.00008 | ||||||||
\(857\) | −3.61379 | −0.123445 | −0.0617224 | − | 0.998093i | \(-0.519659\pi\) | ||||
−0.0617224 | + | 0.998093i | \(0.519659\pi\) | |||||||
\(858\) | 72.2339 | 2.46603 | ||||||||
\(859\) | −25.3648 | −0.865437 | −0.432719 | − | 0.901529i | \(-0.642446\pi\) | ||||
−0.432719 | + | 0.901529i | \(0.642446\pi\) | |||||||
\(860\) | 5.81081 | 0.198147 | ||||||||
\(861\) | 15.4138 | 0.525301 | ||||||||
\(862\) | 17.9337 | 0.610824 | ||||||||
\(863\) | 29.9878 | 1.02080 | 0.510398 | − | 0.859939i | \(-0.329498\pi\) | ||||
0.510398 | + | 0.859939i | \(0.329498\pi\) | |||||||
\(864\) | −31.7760 | −1.08104 | ||||||||
\(865\) | 22.7824 | 0.774626 | ||||||||
\(866\) | 1.15618 | 0.0392887 | ||||||||
\(867\) | 26.1145 | 0.886895 | ||||||||
\(868\) | 2.20745 | 0.0749257 | ||||||||
\(869\) | −40.5377 | −1.37515 | ||||||||
\(870\) | 4.05094 | 0.137340 | ||||||||
\(871\) | 37.6172 | 1.27461 | ||||||||
\(872\) | 17.0443 | 0.577194 | ||||||||
\(873\) | 60.7945 | 2.05758 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.609175 | −0.0205939 | ||||||||
\(876\) | 6.59999 | 0.222993 | ||||||||
\(877\) | −10.6478 | −0.359550 | −0.179775 | − | 0.983708i | \(-0.557537\pi\) | ||||
−0.179775 | + | 0.983708i | \(0.557537\pi\) | |||||||
\(878\) | 32.6756 | 1.10275 | ||||||||
\(879\) | 11.4656 | 0.386726 | ||||||||
\(880\) | −11.2045 | −0.377703 | ||||||||
\(881\) | −31.5797 | −1.06395 | −0.531973 | − | 0.846761i | \(-0.678549\pi\) | ||||
−0.531973 | + | 0.846761i | \(0.678549\pi\) | |||||||
\(882\) | −49.6185 | −1.67074 | ||||||||
\(883\) | 17.0174 | 0.572682 | 0.286341 | − | 0.958128i | \(-0.407561\pi\) | ||||
0.286341 | + | 0.958128i | \(0.407561\pi\) | |||||||
\(884\) | 7.49589 | 0.252114 | ||||||||
\(885\) | 31.1904 | 1.04845 | ||||||||
\(886\) | −10.4388 | −0.350700 | ||||||||
\(887\) | 13.2290 | 0.444187 | 0.222093 | − | 0.975025i | \(-0.428711\pi\) | ||||
0.222093 | + | 0.975025i | \(0.428711\pi\) | |||||||
\(888\) | 35.3454 | 1.18611 | ||||||||
\(889\) | 1.40445 | 0.0471036 | ||||||||
\(890\) | −9.44650 | −0.316647 | ||||||||
\(891\) | 52.2461 | 1.75031 | ||||||||
\(892\) | 13.1109 | 0.438985 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −13.6921 | −0.457933 | ||||||||
\(895\) | 2.32916 | 0.0778553 | ||||||||
\(896\) | −2.49977 | −0.0835113 | ||||||||
\(897\) | −38.5044 | −1.28562 | ||||||||
\(898\) | 11.4732 | 0.382865 | ||||||||
\(899\) | −6.95350 | −0.231912 | ||||||||
\(900\) | −3.65635 | −0.121878 | ||||||||
\(901\) | −24.5303 | −0.817222 | ||||||||
\(902\) | 44.3536 | 1.47681 | ||||||||
\(903\) | −18.5418 | −0.617031 | ||||||||
\(904\) | 4.73903 | 0.157618 | ||||||||
\(905\) | 22.3392 | 0.742580 | ||||||||
\(906\) | −34.5313 | −1.14723 | ||||||||
\(907\) | 14.8904 | 0.494428 | 0.247214 | − | 0.968961i | \(-0.420485\pi\) | ||||
0.247214 | + | 0.968961i | \(0.420485\pi\) | |||||||
\(908\) | 10.5366 | 0.349669 | ||||||||
\(909\) | −6.10464 | −0.202478 | ||||||||
\(910\) | 3.21965 | 0.106730 | ||||||||
\(911\) | 49.5480 | 1.64160 | 0.820800 | − | 0.571216i | \(-0.193528\pi\) | ||||
0.820800 | + | 0.571216i | \(0.193528\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.51655 | −0.314952 | ||||||||
\(914\) | −12.7080 | −0.420343 | ||||||||
\(915\) | 15.1810 | 0.501868 | ||||||||
\(916\) | 5.47763 | 0.180986 | ||||||||
\(917\) | 7.86939 | 0.259870 | ||||||||
\(918\) | −34.6143 | −1.14244 | ||||||||
\(919\) | 27.3835 | 0.903300 | 0.451650 | − | 0.892195i | \(-0.350836\pi\) | ||||
0.451650 | + | 0.892195i | \(0.350836\pi\) | |||||||
\(920\) | 8.75421 | 0.288618 | ||||||||
\(921\) | 61.9851 | 2.04248 | ||||||||
\(922\) | 6.77247 | 0.223039 | ||||||||
\(923\) | 51.5691 | 1.69742 | ||||||||
\(924\) | −4.84331 | −0.159333 | ||||||||
\(925\) | 3.77264 | 0.124044 | ||||||||
\(926\) | 42.1046 | 1.38364 | ||||||||
\(927\) | 21.0017 | 0.689787 | ||||||||
\(928\) | −3.54334 | −0.116316 | ||||||||
\(929\) | 52.1894 | 1.71228 | 0.856139 | − | 0.516745i | \(-0.172857\pi\) | ||||
0.856139 | + | 0.516745i | \(0.172857\pi\) | |||||||
\(930\) | −22.6047 | −0.741238 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.13323 | −0.299169 | ||||||||
\(933\) | 23.3971 | 0.765987 | ||||||||
\(934\) | −39.1894 | −1.28232 | ||||||||
\(935\) | 13.0224 | 0.425877 | ||||||||
\(936\) | 85.7630 | 2.80325 | ||||||||
\(937\) | 15.5798 | 0.508968 | 0.254484 | − | 0.967077i | \(-0.418094\pi\) | ||||
0.254484 | + | 0.967077i | \(0.418094\pi\) | |||||||
\(938\) | 6.14922 | 0.200779 | ||||||||
\(939\) | −73.1099 | −2.38585 | ||||||||
\(940\) | 3.42350 | 0.111662 | ||||||||
\(941\) | 58.6553 | 1.91211 | 0.956055 | − | 0.293189i | \(-0.0947164\pi\) | ||||
0.956055 | + | 0.293189i | \(0.0947164\pi\) | |||||||
\(942\) | 12.5431 | 0.408675 | ||||||||
\(943\) | −23.6427 | −0.769913 | ||||||||
\(944\) | 25.5704 | 0.832244 | ||||||||
\(945\) | 6.09829 | 0.198377 | ||||||||
\(946\) | −53.3543 | −1.73470 | ||||||||
\(947\) | 12.3065 | 0.399908 | 0.199954 | − | 0.979805i | \(-0.435921\pi\) | ||||
0.199954 | + | 0.979805i | \(0.435921\pi\) | |||||||
\(948\) | −16.0214 | −0.520352 | ||||||||
\(949\) | −16.5238 | −0.536384 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.16612 | 0.102668 | ||||||||
\(952\) | 5.43807 | 0.176249 | ||||||||
\(953\) | −8.26997 | −0.267891 | −0.133945 | − | 0.990989i | \(-0.542765\pi\) | ||||
−0.133945 | + | 0.990989i | \(0.542765\pi\) | |||||||
\(954\) | −63.2401 | −2.04747 | ||||||||
\(955\) | 2.23766 | 0.0724088 | ||||||||
\(956\) | 13.6481 | 0.441410 | ||||||||
\(957\) | 15.2565 | 0.493173 | ||||||||
\(958\) | −10.7863 | −0.348490 | ||||||||
\(959\) | 7.75696 | 0.250485 | ||||||||
\(960\) | −26.7432 | −0.863134 | ||||||||
\(961\) | 7.80138 | 0.251657 | ||||||||
\(962\) | −19.9394 | −0.642871 | ||||||||
\(963\) | −59.8139 | −1.92748 | ||||||||
\(964\) | 7.66108 | 0.246747 | ||||||||
\(965\) | 4.54306 | 0.146246 | ||||||||
\(966\) | −6.29426 | −0.202514 | ||||||||
\(967\) | 14.2247 | 0.457436 | 0.228718 | − | 0.973493i | \(-0.426547\pi\) | ||||
0.228718 | + | 0.973493i | \(0.426547\pi\) | |||||||
\(968\) | −28.0304 | −0.900931 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.5191 | 0.369857 | ||||||||
\(971\) | −9.73861 | −0.312527 | −0.156263 | − | 0.987715i | \(-0.549945\pi\) | ||||
−0.156263 | + | 0.987715i | \(0.549945\pi\) | |||||||
\(972\) | 3.17814 | 0.101939 | ||||||||
\(973\) | −6.46254 | −0.207180 | ||||||||
\(974\) | 19.6745 | 0.630413 | ||||||||
\(975\) | 13.5233 | 0.433093 | ||||||||
\(976\) | 12.4456 | 0.398374 | ||||||||
\(977\) | 6.35308 | 0.203253 | 0.101627 | − | 0.994823i | \(-0.467595\pi\) | ||||
0.101627 | + | 0.994823i | \(0.467595\pi\) | |||||||
\(978\) | −24.1425 | −0.771991 | ||||||||
\(979\) | −35.5771 | −1.13705 | ||||||||
\(980\) | 3.85626 | 0.123184 | ||||||||
\(981\) | −34.8427 | −1.11244 | ||||||||
\(982\) | −1.65685 | −0.0528723 | ||||||||
\(983\) | −9.88087 | −0.315151 | −0.157575 | − | 0.987507i | \(-0.550368\pi\) | ||||
−0.157575 | + | 0.987507i | \(0.550368\pi\) | |||||||
\(984\) | 77.7962 | 2.48005 | ||||||||
\(985\) | −19.2236 | −0.612514 | ||||||||
\(986\) | −3.85985 | −0.122923 | ||||||||
\(987\) | −10.9241 | −0.347718 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 28.4406 | 0.904358 | ||||||||
\(990\) | 33.5722 | 1.06700 | ||||||||
\(991\) | −37.3350 | −1.18599 | −0.592993 | − | 0.805208i | \(-0.702054\pi\) | ||||
−0.592993 | + | 0.805208i | \(0.702054\pi\) | |||||||
\(992\) | 19.7723 | 0.627771 | ||||||||
\(993\) | 93.9491 | 2.98138 | ||||||||
\(994\) | 8.42992 | 0.267381 | ||||||||
\(995\) | −6.15094 | −0.194998 | ||||||||
\(996\) | −3.76117 | −0.119177 | ||||||||
\(997\) | −43.6948 | −1.38383 | −0.691914 | − | 0.721980i | \(-0.743232\pi\) | ||||
−0.691914 | + | 0.721980i | \(0.743232\pi\) | |||||||
\(998\) | −19.8466 | −0.628234 | ||||||||
\(999\) | −37.7669 | −1.19489 |
(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 | 1805.2.a.i.1.3 | 4 | ||
5.4 | even | 2 | 9025.2.a.bp.1.2 | 4 | |||
19.8 | odd | 6 | 95.2.e.c.26.3 | yes | 8 | ||
19.12 | odd | 6 | 95.2.e.c.11.3 | ✓ | 8 | ||
19.18 | odd | 2 | 1805.2.a.o.1.2 | 4 | |||
57.8 | even | 6 | 855.2.k.h.406.2 | 8 | |||
57.50 | even | 6 | 855.2.k.h.676.2 | 8 | |||
76.27 | even | 6 | 1520.2.q.o.881.4 | 8 | |||
76.31 | even | 6 | 1520.2.q.o.961.4 | 8 | |||
95.8 | even | 12 | 475.2.j.c.349.6 | 16 | |||
95.12 | even | 12 | 475.2.j.c.49.6 | 16 | |||
95.27 | even | 12 | 475.2.j.c.349.3 | 16 | |||
95.69 | odd | 6 | 475.2.e.e.201.2 | 8 | |||
95.84 | odd | 6 | 475.2.e.e.26.2 | 8 | |||
95.88 | even | 12 | 475.2.j.c.49.3 | 16 | |||
95.94 | odd | 2 | 9025.2.a.bg.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.e.c.11.3 | ✓ | 8 | 19.12 | odd | 6 | ||
95.2.e.c.26.3 | yes | 8 | 19.8 | odd | 6 | ||
475.2.e.e.26.2 | 8 | 95.84 | odd | 6 | |||
475.2.e.e.201.2 | 8 | 95.69 | odd | 6 | |||
475.2.j.c.49.3 | 16 | 95.88 | even | 12 | |||
475.2.j.c.49.6 | 16 | 95.12 | even | 12 | |||
475.2.j.c.349.3 | 16 | 95.27 | even | 12 | |||
475.2.j.c.349.6 | 16 | 95.8 | even | 12 | |||
855.2.k.h.406.2 | 8 | 57.8 | even | 6 | |||
855.2.k.h.676.2 | 8 | 57.50 | even | 6 | |||
1520.2.q.o.881.4 | 8 | 76.27 | even | 6 | |||
1520.2.q.o.961.4 | 8 | 76.31 | even | 6 | |||
1805.2.a.i.1.3 | 4 | 1.1 | even | 1 | trivial | ||
1805.2.a.o.1.2 | 4 | 19.18 | odd | 2 | |||
9025.2.a.bg.1.3 | 4 | 95.94 | odd | 2 | |||
9025.2.a.bp.1.2 | 4 | 5.4 | even | 2 |