Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4019,2,Mod(1,4019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4019 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4019.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: | \(32.0918765724\) |
Analytic rank: | \(0\) |
Dimension: | \(186\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 4019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.43453 | −1.72148 | −0.860738 | − | 0.509048i | \(-0.829997\pi\) | ||||
−0.860738 | + | 0.509048i | \(0.829997\pi\) | |||||||
\(3\) | 2.49356 | 1.43966 | 0.719828 | − | 0.694153i | \(-0.244221\pi\) | ||||
0.719828 | + | 0.694153i | \(0.244221\pi\) | |||||||
\(4\) | 3.92696 | 1.96348 | ||||||||
\(5\) | 3.69129 | 1.65080 | 0.825398 | − | 0.564551i | \(-0.190951\pi\) | ||||
0.825398 | + | 0.564551i | \(0.190951\pi\) | |||||||
\(6\) | −6.07065 | −2.47833 | ||||||||
\(7\) | 0.601351 | 0.227289 | 0.113645 | − | 0.993521i | \(-0.463747\pi\) | ||||
0.113645 | + | 0.993521i | \(0.463747\pi\) | |||||||
\(8\) | −4.69125 | −1.65861 | ||||||||
\(9\) | 3.21782 | 1.07261 | ||||||||
\(10\) | −8.98658 | −2.84181 | ||||||||
\(11\) | −5.31971 | −1.60395 | −0.801976 | − | 0.597356i | \(-0.796218\pi\) | ||||
−0.801976 | + | 0.597356i | \(0.796218\pi\) | |||||||
\(12\) | 9.79209 | 2.82673 | ||||||||
\(13\) | 3.09616 | 0.858721 | 0.429360 | − | 0.903133i | \(-0.358739\pi\) | ||||
0.429360 | + | 0.903133i | \(0.358739\pi\) | |||||||
\(14\) | −1.46401 | −0.391273 | ||||||||
\(15\) | 9.20444 | 2.37658 | ||||||||
\(16\) | 3.56709 | 0.891773 | ||||||||
\(17\) | 0.734755 | 0.178204 | 0.0891021 | − | 0.996022i | \(-0.471600\pi\) | ||||
0.0891021 | + | 0.996022i | \(0.471600\pi\) | |||||||
\(18\) | −7.83390 | −1.84647 | ||||||||
\(19\) | 2.83652 | 0.650742 | 0.325371 | − | 0.945587i | \(-0.394511\pi\) | ||||
0.325371 | + | 0.945587i | \(0.394511\pi\) | |||||||
\(20\) | 14.4956 | 3.24130 | ||||||||
\(21\) | 1.49950 | 0.327218 | ||||||||
\(22\) | 12.9510 | 2.76117 | ||||||||
\(23\) | −1.79373 | −0.374018 | −0.187009 | − | 0.982358i | \(-0.559879\pi\) | ||||
−0.187009 | + | 0.982358i | \(0.559879\pi\) | |||||||
\(24\) | −11.6979 | −2.38782 | ||||||||
\(25\) | 8.62564 | 1.72513 | ||||||||
\(26\) | −7.53771 | −1.47827 | ||||||||
\(27\) | 0.543152 | 0.104530 | ||||||||
\(28\) | 2.36148 | 0.446278 | ||||||||
\(29\) | 7.08600 | 1.31584 | 0.657919 | − | 0.753089i | \(-0.271437\pi\) | ||||
0.657919 | + | 0.753089i | \(0.271437\pi\) | |||||||
\(30\) | −22.4085 | −4.09122 | ||||||||
\(31\) | 2.28441 | 0.410292 | 0.205146 | − | 0.978731i | \(-0.434233\pi\) | ||||
0.205146 | + | 0.978731i | \(0.434233\pi\) | |||||||
\(32\) | 0.698289 | 0.123441 | ||||||||
\(33\) | −13.2650 | −2.30914 | ||||||||
\(34\) | −1.78879 | −0.306774 | ||||||||
\(35\) | 2.21976 | 0.375208 | ||||||||
\(36\) | 12.6363 | 2.10604 | ||||||||
\(37\) | 9.08400 | 1.49340 | 0.746700 | − | 0.665161i | \(-0.231637\pi\) | ||||
0.746700 | + | 0.665161i | \(0.231637\pi\) | |||||||
\(38\) | −6.90560 | −1.12024 | ||||||||
\(39\) | 7.72045 | 1.23626 | ||||||||
\(40\) | −17.3168 | −2.73802 | ||||||||
\(41\) | 1.45684 | 0.227521 | 0.113760 | − | 0.993508i | \(-0.463710\pi\) | ||||
0.113760 | + | 0.993508i | \(0.463710\pi\) | |||||||
\(42\) | −3.65059 | −0.563298 | ||||||||
\(43\) | 0.573711 | 0.0874901 | 0.0437450 | − | 0.999043i | \(-0.486071\pi\) | ||||
0.0437450 | + | 0.999043i | \(0.486071\pi\) | |||||||
\(44\) | −20.8903 | −3.14933 | ||||||||
\(45\) | 11.8779 | 1.77066 | ||||||||
\(46\) | 4.36689 | 0.643862 | ||||||||
\(47\) | −7.18313 | −1.04777 | −0.523884 | − | 0.851790i | \(-0.675517\pi\) | ||||
−0.523884 | + | 0.851790i | \(0.675517\pi\) | |||||||
\(48\) | 8.89475 | 1.28385 | ||||||||
\(49\) | −6.63838 | −0.948340 | ||||||||
\(50\) | −20.9994 | −2.96976 | ||||||||
\(51\) | 1.83215 | 0.256553 | ||||||||
\(52\) | 12.1585 | 1.68608 | ||||||||
\(53\) | 1.63729 | 0.224899 | 0.112449 | − | 0.993657i | \(-0.464130\pi\) | ||||
0.112449 | + | 0.993657i | \(0.464130\pi\) | |||||||
\(54\) | −1.32232 | −0.179945 | ||||||||
\(55\) | −19.6366 | −2.64780 | ||||||||
\(56\) | −2.82109 | −0.376984 | ||||||||
\(57\) | 7.07301 | 0.936844 | ||||||||
\(58\) | −17.2511 | −2.26518 | ||||||||
\(59\) | 0.375061 | 0.0488288 | 0.0244144 | − | 0.999702i | \(-0.492228\pi\) | ||||
0.0244144 | + | 0.999702i | \(0.492228\pi\) | |||||||
\(60\) | 36.1455 | 4.66636 | ||||||||
\(61\) | −3.59350 | −0.460101 | −0.230051 | − | 0.973179i | \(-0.573889\pi\) | ||||
−0.230051 | + | 0.973179i | \(0.573889\pi\) | |||||||
\(62\) | −5.56147 | −0.706308 | ||||||||
\(63\) | 1.93504 | 0.243792 | ||||||||
\(64\) | −8.83420 | −1.10427 | ||||||||
\(65\) | 11.4288 | 1.41757 | ||||||||
\(66\) | 32.2941 | 3.97513 | ||||||||
\(67\) | 9.13823 | 1.11641 | 0.558206 | − | 0.829702i | \(-0.311490\pi\) | ||||
0.558206 | + | 0.829702i | \(0.311490\pi\) | |||||||
\(68\) | 2.88535 | 0.349900 | ||||||||
\(69\) | −4.47276 | −0.538457 | ||||||||
\(70\) | −5.40409 | −0.645912 | ||||||||
\(71\) | −3.82383 | −0.453806 | −0.226903 | − | 0.973917i | \(-0.572860\pi\) | ||||
−0.226903 | + | 0.973917i | \(0.572860\pi\) | |||||||
\(72\) | −15.0956 | −1.77903 | ||||||||
\(73\) | 6.13553 | 0.718109 | 0.359055 | − | 0.933317i | \(-0.383099\pi\) | ||||
0.359055 | + | 0.933317i | \(0.383099\pi\) | |||||||
\(74\) | −22.1153 | −2.57085 | ||||||||
\(75\) | 21.5085 | 2.48359 | ||||||||
\(76\) | 11.1389 | 1.27772 | ||||||||
\(77\) | −3.19901 | −0.364561 | ||||||||
\(78\) | −18.7957 | −2.12820 | ||||||||
\(79\) | 5.08529 | 0.572140 | 0.286070 | − | 0.958209i | \(-0.407651\pi\) | ||||
0.286070 | + | 0.958209i | \(0.407651\pi\) | |||||||
\(80\) | 13.1672 | 1.47214 | ||||||||
\(81\) | −8.29909 | −0.922121 | ||||||||
\(82\) | −3.54673 | −0.391671 | ||||||||
\(83\) | −1.18851 | −0.130456 | −0.0652278 | − | 0.997870i | \(-0.520777\pi\) | ||||
−0.0652278 | + | 0.997870i | \(0.520777\pi\) | |||||||
\(84\) | 5.88849 | 0.642486 | ||||||||
\(85\) | 2.71219 | 0.294179 | ||||||||
\(86\) | −1.39672 | −0.150612 | ||||||||
\(87\) | 17.6693 | 1.89435 | ||||||||
\(88\) | 24.9561 | 2.66033 | ||||||||
\(89\) | −15.1270 | −1.60346 | −0.801731 | − | 0.597685i | \(-0.796087\pi\) | ||||
−0.801731 | + | 0.597685i | \(0.796087\pi\) | |||||||
\(90\) | −28.9172 | −3.04814 | ||||||||
\(91\) | 1.86188 | 0.195178 | ||||||||
\(92\) | −7.04389 | −0.734376 | ||||||||
\(93\) | 5.69630 | 0.590679 | ||||||||
\(94\) | 17.4876 | 1.80371 | ||||||||
\(95\) | 10.4704 | 1.07424 | ||||||||
\(96\) | 1.74122 | 0.177713 | ||||||||
\(97\) | 5.67676 | 0.576387 | 0.288194 | − | 0.957572i | \(-0.406945\pi\) | ||||
0.288194 | + | 0.957572i | \(0.406945\pi\) | |||||||
\(98\) | 16.1614 | 1.63254 | ||||||||
\(99\) | −17.1179 | −1.72041 | ||||||||
\(100\) | 33.8725 | 3.38725 | ||||||||
\(101\) | 4.69810 | 0.467478 | 0.233739 | − | 0.972299i | \(-0.424904\pi\) | ||||
0.233739 | + | 0.972299i | \(0.424904\pi\) | |||||||
\(102\) | −4.46044 | −0.441649 | ||||||||
\(103\) | 0.0154012 | 0.00151752 | 0.000758762 | − | 1.00000i | \(-0.499758\pi\) | ||||
0.000758762 | 1.00000i | \(0.499758\pi\) | ||||||||
\(104\) | −14.5249 | −1.42428 | ||||||||
\(105\) | 5.53510 | 0.540171 | ||||||||
\(106\) | −3.98604 | −0.387158 | ||||||||
\(107\) | 5.38239 | 0.520335 | 0.260168 | − | 0.965563i | \(-0.416222\pi\) | ||||
0.260168 | + | 0.965563i | \(0.416222\pi\) | |||||||
\(108\) | 2.13294 | 0.205242 | ||||||||
\(109\) | 5.66536 | 0.542643 | 0.271322 | − | 0.962489i | \(-0.412539\pi\) | ||||
0.271322 | + | 0.962489i | \(0.412539\pi\) | |||||||
\(110\) | 47.8060 | 4.55812 | ||||||||
\(111\) | 22.6515 | 2.14998 | ||||||||
\(112\) | 2.14507 | 0.202691 | ||||||||
\(113\) | 17.1675 | 1.61498 | 0.807491 | − | 0.589880i | \(-0.200825\pi\) | ||||
0.807491 | + | 0.589880i | \(0.200825\pi\) | |||||||
\(114\) | −17.2195 | −1.61275 | ||||||||
\(115\) | −6.62117 | −0.617427 | ||||||||
\(116\) | 27.8264 | 2.58362 | ||||||||
\(117\) | 9.96290 | 0.921070 | ||||||||
\(118\) | −0.913100 | −0.0840577 | ||||||||
\(119\) | 0.441846 | 0.0405039 | ||||||||
\(120\) | −43.1803 | −3.94181 | ||||||||
\(121\) | 17.2993 | 1.57266 | ||||||||
\(122\) | 8.74851 | 0.792053 | ||||||||
\(123\) | 3.63272 | 0.327551 | ||||||||
\(124\) | 8.97078 | 0.805600 | ||||||||
\(125\) | 13.3833 | 1.19704 | ||||||||
\(126\) | −4.71092 | −0.419682 | ||||||||
\(127\) | −4.41377 | −0.391659 | −0.195829 | − | 0.980638i | \(-0.562740\pi\) | ||||
−0.195829 | + | 0.980638i | \(0.562740\pi\) | |||||||
\(128\) | 20.1106 | 1.77754 | ||||||||
\(129\) | 1.43058 | 0.125956 | ||||||||
\(130\) | −27.8239 | −2.44032 | ||||||||
\(131\) | 10.1268 | 0.884780 | 0.442390 | − | 0.896823i | \(-0.354131\pi\) | ||||
0.442390 | + | 0.896823i | \(0.354131\pi\) | |||||||
\(132\) | −52.0911 | −4.53395 | ||||||||
\(133\) | 1.70574 | 0.147907 | ||||||||
\(134\) | −22.2473 | −1.92188 | ||||||||
\(135\) | 2.00493 | 0.172557 | ||||||||
\(136\) | −3.44692 | −0.295571 | ||||||||
\(137\) | −4.27066 | −0.364867 | −0.182434 | − | 0.983218i | \(-0.558397\pi\) | ||||
−0.182434 | + | 0.983218i | \(0.558397\pi\) | |||||||
\(138\) | 10.8891 | 0.926940 | ||||||||
\(139\) | −14.2167 | −1.20585 | −0.602924 | − | 0.797799i | \(-0.705998\pi\) | ||||
−0.602924 | + | 0.797799i | \(0.705998\pi\) | |||||||
\(140\) | 8.71692 | 0.736714 | ||||||||
\(141\) | −17.9115 | −1.50842 | ||||||||
\(142\) | 9.30926 | 0.781216 | ||||||||
\(143\) | −16.4707 | −1.37735 | ||||||||
\(144\) | 11.4783 | 0.956523 | ||||||||
\(145\) | 26.1565 | 2.17218 | ||||||||
\(146\) | −14.9372 | −1.23621 | ||||||||
\(147\) | −16.5532 | −1.36528 | ||||||||
\(148\) | 35.6725 | 2.93226 | ||||||||
\(149\) | 14.8062 | 1.21297 | 0.606487 | − | 0.795093i | \(-0.292578\pi\) | ||||
0.606487 | + | 0.795093i | \(0.292578\pi\) | |||||||
\(150\) | −52.3632 | −4.27544 | ||||||||
\(151\) | 5.28959 | 0.430461 | 0.215230 | − | 0.976563i | \(-0.430950\pi\) | ||||
0.215230 | + | 0.976563i | \(0.430950\pi\) | |||||||
\(152\) | −13.3068 | −1.07932 | ||||||||
\(153\) | 2.36431 | 0.191143 | ||||||||
\(154\) | 7.78811 | 0.627584 | ||||||||
\(155\) | 8.43242 | 0.677308 | ||||||||
\(156\) | 30.3179 | 2.42738 | ||||||||
\(157\) | 19.5849 | 1.56304 | 0.781522 | − | 0.623878i | \(-0.214444\pi\) | ||||
0.781522 | + | 0.623878i | \(0.214444\pi\) | |||||||
\(158\) | −12.3803 | −0.984925 | ||||||||
\(159\) | 4.08267 | 0.323777 | ||||||||
\(160\) | 2.57759 | 0.203776 | ||||||||
\(161\) | −1.07866 | −0.0850102 | ||||||||
\(162\) | 20.2044 | 1.58741 | ||||||||
\(163\) | −10.1123 | −0.792057 | −0.396029 | − | 0.918238i | \(-0.629612\pi\) | ||||
−0.396029 | + | 0.918238i | \(0.629612\pi\) | |||||||
\(164\) | 5.72096 | 0.446732 | ||||||||
\(165\) | −48.9650 | −3.81192 | ||||||||
\(166\) | 2.89346 | 0.224576 | ||||||||
\(167\) | −21.2967 | −1.64799 | −0.823995 | − | 0.566597i | \(-0.808260\pi\) | ||||
−0.823995 | + | 0.566597i | \(0.808260\pi\) | |||||||
\(168\) | −7.03454 | −0.542727 | ||||||||
\(169\) | −3.41378 | −0.262599 | ||||||||
\(170\) | −6.60293 | −0.506422 | ||||||||
\(171\) | 9.12741 | 0.697990 | ||||||||
\(172\) | 2.25294 | 0.171785 | ||||||||
\(173\) | −7.48612 | −0.569159 | −0.284579 | − | 0.958652i | \(-0.591854\pi\) | ||||
−0.284579 | + | 0.958652i | \(0.591854\pi\) | |||||||
\(174\) | −43.0166 | −3.26108 | ||||||||
\(175\) | 5.18703 | 0.392103 | ||||||||
\(176\) | −18.9759 | −1.43036 | ||||||||
\(177\) | 0.935237 | 0.0702967 | ||||||||
\(178\) | 36.8273 | 2.76032 | ||||||||
\(179\) | 10.0049 | 0.747799 | 0.373900 | − | 0.927469i | \(-0.378020\pi\) | ||||
0.373900 | + | 0.927469i | \(0.378020\pi\) | |||||||
\(180\) | 46.6441 | 3.47665 | ||||||||
\(181\) | 4.19987 | 0.312174 | 0.156087 | − | 0.987743i | \(-0.450112\pi\) | ||||
0.156087 | + | 0.987743i | \(0.450112\pi\) | |||||||
\(182\) | −4.53281 | −0.335994 | ||||||||
\(183\) | −8.96060 | −0.662387 | ||||||||
\(184\) | 8.41482 | 0.620349 | ||||||||
\(185\) | 33.5317 | 2.46530 | ||||||||
\(186\) | −13.8678 | −1.01684 | ||||||||
\(187\) | −3.90868 | −0.285831 | ||||||||
\(188\) | −28.2079 | −2.05727 | ||||||||
\(189\) | 0.326625 | 0.0237585 | ||||||||
\(190\) | −25.4906 | −1.84928 | ||||||||
\(191\) | 5.03540 | 0.364349 | 0.182174 | − | 0.983266i | \(-0.441686\pi\) | ||||
0.182174 | + | 0.983266i | \(0.441686\pi\) | |||||||
\(192\) | −22.0286 | −1.58977 | ||||||||
\(193\) | 8.26807 | 0.595149 | 0.297575 | − | 0.954699i | \(-0.403822\pi\) | ||||
0.297575 | + | 0.954699i | \(0.403822\pi\) | |||||||
\(194\) | −13.8203 | −0.992237 | ||||||||
\(195\) | 28.4984 | 2.04082 | ||||||||
\(196\) | −26.0686 | −1.86205 | ||||||||
\(197\) | −10.7100 | −0.763059 | −0.381530 | − | 0.924357i | \(-0.624603\pi\) | ||||
−0.381530 | + | 0.924357i | \(0.624603\pi\) | |||||||
\(198\) | 41.6741 | 2.96165 | ||||||||
\(199\) | −26.4384 | −1.87417 | −0.937085 | − | 0.349101i | \(-0.886487\pi\) | ||||
−0.937085 | + | 0.349101i | \(0.886487\pi\) | |||||||
\(200\) | −40.4650 | −2.86131 | ||||||||
\(201\) | 22.7867 | 1.60725 | ||||||||
\(202\) | −11.4377 | −0.804753 | ||||||||
\(203\) | 4.26117 | 0.299076 | ||||||||
\(204\) | 7.19479 | 0.503736 | ||||||||
\(205\) | 5.37763 | 0.375590 | ||||||||
\(206\) | −0.0374947 | −0.00261238 | ||||||||
\(207\) | −5.77189 | −0.401174 | ||||||||
\(208\) | 11.0443 | 0.765784 | ||||||||
\(209\) | −15.0894 | −1.04376 | ||||||||
\(210\) | −13.4754 | −0.929891 | ||||||||
\(211\) | 14.3172 | 0.985639 | 0.492820 | − | 0.870131i | \(-0.335966\pi\) | ||||
0.492820 | + | 0.870131i | \(0.335966\pi\) | |||||||
\(212\) | 6.42956 | 0.441584 | ||||||||
\(213\) | −9.53495 | −0.653324 | ||||||||
\(214\) | −13.1036 | −0.895745 | ||||||||
\(215\) | 2.11773 | 0.144428 | ||||||||
\(216\) | −2.54806 | −0.173374 | ||||||||
\(217\) | 1.37373 | 0.0932550 | ||||||||
\(218\) | −13.7925 | −0.934148 | ||||||||
\(219\) | 15.2993 | 1.03383 | ||||||||
\(220\) | −77.1121 | −5.19890 | ||||||||
\(221\) | 2.27492 | 0.153028 | ||||||||
\(222\) | −55.1458 | −3.70114 | ||||||||
\(223\) | 3.16593 | 0.212006 | 0.106003 | − | 0.994366i | \(-0.466195\pi\) | ||||
0.106003 | + | 0.994366i | \(0.466195\pi\) | |||||||
\(224\) | 0.419917 | 0.0280569 | ||||||||
\(225\) | 27.7558 | 1.85038 | ||||||||
\(226\) | −41.7949 | −2.78015 | ||||||||
\(227\) | −8.05663 | −0.534738 | −0.267369 | − | 0.963594i | \(-0.586154\pi\) | ||||
−0.267369 | + | 0.963594i | \(0.586154\pi\) | |||||||
\(228\) | 27.7754 | 1.83947 | ||||||||
\(229\) | −19.4781 | −1.28715 | −0.643576 | − | 0.765382i | \(-0.722550\pi\) | ||||
−0.643576 | + | 0.765382i | \(0.722550\pi\) | |||||||
\(230\) | 16.1195 | 1.06289 | ||||||||
\(231\) | −7.97692 | −0.524843 | ||||||||
\(232\) | −33.2422 | −2.18246 | ||||||||
\(233\) | 4.21749 | 0.276297 | 0.138149 | − | 0.990412i | \(-0.455885\pi\) | ||||
0.138149 | + | 0.990412i | \(0.455885\pi\) | |||||||
\(234\) | −24.2550 | −1.58560 | ||||||||
\(235\) | −26.5150 | −1.72965 | ||||||||
\(236\) | 1.47285 | 0.0958744 | ||||||||
\(237\) | 12.6805 | 0.823684 | ||||||||
\(238\) | −1.07569 | −0.0697265 | ||||||||
\(239\) | 22.3511 | 1.44577 | 0.722887 | − | 0.690966i | \(-0.242815\pi\) | ||||
0.722887 | + | 0.690966i | \(0.242815\pi\) | |||||||
\(240\) | 32.8331 | 2.11937 | ||||||||
\(241\) | −14.0275 | −0.903588 | −0.451794 | − | 0.892122i | \(-0.649216\pi\) | ||||
−0.451794 | + | 0.892122i | \(0.649216\pi\) | |||||||
\(242\) | −42.1158 | −2.70730 | ||||||||
\(243\) | −22.3237 | −1.43207 | ||||||||
\(244\) | −14.1115 | −0.903399 | ||||||||
\(245\) | −24.5042 | −1.56552 | ||||||||
\(246\) | −8.84398 | −0.563872 | ||||||||
\(247\) | 8.78231 | 0.558805 | ||||||||
\(248\) | −10.7167 | −0.680513 | ||||||||
\(249\) | −2.96361 | −0.187811 | ||||||||
\(250\) | −32.5821 | −2.06067 | ||||||||
\(251\) | −23.6110 | −1.49032 | −0.745158 | − | 0.666888i | \(-0.767626\pi\) | ||||
−0.745158 | + | 0.666888i | \(0.767626\pi\) | |||||||
\(252\) | 7.59883 | 0.478681 | ||||||||
\(253\) | 9.54210 | 0.599907 | ||||||||
\(254\) | 10.7455 | 0.674231 | ||||||||
\(255\) | 6.76301 | 0.423516 | ||||||||
\(256\) | −31.2915 | −1.95572 | ||||||||
\(257\) | 7.43931 | 0.464052 | 0.232026 | − | 0.972710i | \(-0.425465\pi\) | ||||
0.232026 | + | 0.972710i | \(0.425465\pi\) | |||||||
\(258\) | −3.48280 | −0.216829 | ||||||||
\(259\) | 5.46267 | 0.339434 | ||||||||
\(260\) | 44.8806 | 2.78338 | ||||||||
\(261\) | 22.8015 | 1.41138 | ||||||||
\(262\) | −24.6540 | −1.52313 | ||||||||
\(263\) | −10.4682 | −0.645498 | −0.322749 | − | 0.946485i | \(-0.604607\pi\) | ||||
−0.322749 | + | 0.946485i | \(0.604607\pi\) | |||||||
\(264\) | 62.2294 | 3.82996 | ||||||||
\(265\) | 6.04371 | 0.371262 | ||||||||
\(266\) | −4.15269 | −0.254618 | ||||||||
\(267\) | −37.7201 | −2.30843 | ||||||||
\(268\) | 35.8854 | 2.19205 | ||||||||
\(269\) | −14.3566 | −0.875338 | −0.437669 | − | 0.899136i | \(-0.644196\pi\) | ||||
−0.437669 | + | 0.899136i | \(0.644196\pi\) | |||||||
\(270\) | −4.88108 | −0.297053 | ||||||||
\(271\) | 22.1562 | 1.34589 | 0.672946 | − | 0.739692i | \(-0.265029\pi\) | ||||
0.672946 | + | 0.739692i | \(0.265029\pi\) | |||||||
\(272\) | 2.62094 | 0.158918 | ||||||||
\(273\) | 4.64270 | 0.280989 | ||||||||
\(274\) | 10.3971 | 0.628110 | ||||||||
\(275\) | −45.8859 | −2.76702 | ||||||||
\(276\) | −17.5643 | −1.05725 | ||||||||
\(277\) | −17.3505 | −1.04249 | −0.521245 | − | 0.853407i | \(-0.674532\pi\) | ||||
−0.521245 | + | 0.853407i | \(0.674532\pi\) | |||||||
\(278\) | 34.6111 | 2.07584 | ||||||||
\(279\) | 7.35082 | 0.440082 | ||||||||
\(280\) | −10.4135 | −0.622323 | ||||||||
\(281\) | 25.3707 | 1.51349 | 0.756746 | − | 0.653709i | \(-0.226788\pi\) | ||||
0.756746 | + | 0.653709i | \(0.226788\pi\) | |||||||
\(282\) | 43.6063 | 2.59672 | ||||||||
\(283\) | 20.4560 | 1.21598 | 0.607992 | − | 0.793943i | \(-0.291975\pi\) | ||||
0.607992 | + | 0.793943i | \(0.291975\pi\) | |||||||
\(284\) | −15.0160 | −0.891038 | ||||||||
\(285\) | 26.1086 | 1.54654 | ||||||||
\(286\) | 40.0984 | 2.37107 | ||||||||
\(287\) | 0.876074 | 0.0517130 | ||||||||
\(288\) | 2.24697 | 0.132404 | ||||||||
\(289\) | −16.4601 | −0.968243 | ||||||||
\(290\) | −63.6789 | −3.73935 | ||||||||
\(291\) | 14.1553 | 0.829799 | ||||||||
\(292\) | 24.0940 | 1.40999 | ||||||||
\(293\) | −28.3662 | −1.65717 | −0.828585 | − | 0.559863i | \(-0.810854\pi\) | ||||
−0.828585 | + | 0.559863i | \(0.810854\pi\) | |||||||
\(294\) | 40.2993 | 2.35030 | ||||||||
\(295\) | 1.38446 | 0.0806064 | ||||||||
\(296\) | −42.6153 | −2.47696 | ||||||||
\(297\) | −2.88941 | −0.167661 | ||||||||
\(298\) | −36.0463 | −2.08811 | ||||||||
\(299\) | −5.55367 | −0.321177 | ||||||||
\(300\) | 84.4630 | 4.87648 | ||||||||
\(301\) | 0.345001 | 0.0198856 | ||||||||
\(302\) | −12.8777 | −0.741028 | ||||||||
\(303\) | 11.7150 | 0.673008 | ||||||||
\(304\) | 10.1181 | 0.580314 | ||||||||
\(305\) | −13.2647 | −0.759533 | ||||||||
\(306\) | −5.75600 | −0.329048 | ||||||||
\(307\) | 32.1940 | 1.83741 | 0.918705 | − | 0.394944i | \(-0.129236\pi\) | ||||
0.918705 | + | 0.394944i | \(0.129236\pi\) | |||||||
\(308\) | −12.5624 | −0.715809 | ||||||||
\(309\) | 0.0384037 | 0.00218471 | ||||||||
\(310\) | −20.5290 | −1.16597 | ||||||||
\(311\) | 2.09951 | 0.119053 | 0.0595263 | − | 0.998227i | \(-0.481041\pi\) | ||||
0.0595263 | + | 0.998227i | \(0.481041\pi\) | |||||||
\(312\) | −36.2186 | −2.05047 | ||||||||
\(313\) | 14.2327 | 0.804478 | 0.402239 | − | 0.915535i | \(-0.368232\pi\) | ||||
0.402239 | + | 0.915535i | \(0.368232\pi\) | |||||||
\(314\) | −47.6801 | −2.69074 | ||||||||
\(315\) | 7.14280 | 0.402451 | ||||||||
\(316\) | 19.9697 | 1.12338 | ||||||||
\(317\) | −8.68030 | −0.487534 | −0.243767 | − | 0.969834i | \(-0.578383\pi\) | ||||
−0.243767 | + | 0.969834i | \(0.578383\pi\) | |||||||
\(318\) | −9.93940 | −0.557374 | ||||||||
\(319\) | −37.6955 | −2.11054 | ||||||||
\(320\) | −32.6096 | −1.82293 | ||||||||
\(321\) | 13.4213 | 0.749104 | ||||||||
\(322\) | 2.62603 | 0.146343 | ||||||||
\(323\) | 2.08414 | 0.115965 | ||||||||
\(324\) | −32.5902 | −1.81057 | ||||||||
\(325\) | 26.7064 | 1.48140 | ||||||||
\(326\) | 24.6188 | 1.36351 | ||||||||
\(327\) | 14.1269 | 0.781220 | ||||||||
\(328\) | −6.83441 | −0.377367 | ||||||||
\(329\) | −4.31958 | −0.238146 | ||||||||
\(330\) | 119.207 | 6.56212 | ||||||||
\(331\) | −19.6921 | −1.08238 | −0.541189 | − | 0.840901i | \(-0.682026\pi\) | ||||
−0.541189 | + | 0.840901i | \(0.682026\pi\) | |||||||
\(332\) | −4.66722 | −0.256147 | ||||||||
\(333\) | 29.2307 | 1.60183 | ||||||||
\(334\) | 51.8476 | 2.83697 | ||||||||
\(335\) | 33.7319 | 1.84297 | ||||||||
\(336\) | 5.34886 | 0.291804 | ||||||||
\(337\) | 15.5386 | 0.846440 | 0.423220 | − | 0.906027i | \(-0.360900\pi\) | ||||
0.423220 | + | 0.906027i | \(0.360900\pi\) | |||||||
\(338\) | 8.31097 | 0.452057 | ||||||||
\(339\) | 42.8081 | 2.32502 | ||||||||
\(340\) | 10.6507 | 0.577614 | ||||||||
\(341\) | −12.1524 | −0.658089 | ||||||||
\(342\) | −22.2210 | −1.20157 | ||||||||
\(343\) | −8.20145 | −0.442837 | ||||||||
\(344\) | −2.69142 | −0.145112 | ||||||||
\(345\) | −16.5102 | −0.888882 | ||||||||
\(346\) | 18.2252 | 0.979794 | ||||||||
\(347\) | −25.0547 | −1.34501 | −0.672504 | − | 0.740093i | \(-0.734781\pi\) | ||||
−0.672504 | + | 0.740093i | \(0.734781\pi\) | |||||||
\(348\) | 69.3868 | 3.71952 | ||||||||
\(349\) | −13.2362 | −0.708516 | −0.354258 | − | 0.935148i | \(-0.615267\pi\) | ||||
−0.354258 | + | 0.935148i | \(0.615267\pi\) | |||||||
\(350\) | −12.6280 | −0.674996 | ||||||||
\(351\) | 1.68169 | 0.0897618 | ||||||||
\(352\) | −3.71470 | −0.197994 | ||||||||
\(353\) | −7.63692 | −0.406472 | −0.203236 | − | 0.979130i | \(-0.565146\pi\) | ||||
−0.203236 | + | 0.979130i | \(0.565146\pi\) | |||||||
\(354\) | −2.27687 | −0.121014 | ||||||||
\(355\) | −14.1149 | −0.749140 | ||||||||
\(356\) | −59.4032 | −3.14837 | ||||||||
\(357\) | 1.10177 | 0.0583117 | ||||||||
\(358\) | −24.3572 | −1.28732 | ||||||||
\(359\) | −24.6093 | −1.29883 | −0.649414 | − | 0.760435i | \(-0.724986\pi\) | ||||
−0.649414 | + | 0.760435i | \(0.724986\pi\) | |||||||
\(360\) | −55.7223 | −2.93682 | ||||||||
\(361\) | −10.9542 | −0.576535 | ||||||||
\(362\) | −10.2247 | −0.537400 | ||||||||
\(363\) | 43.1368 | 2.26409 | ||||||||
\(364\) | 7.31153 | 0.383228 | ||||||||
\(365\) | 22.6480 | 1.18545 | ||||||||
\(366\) | 21.8149 | 1.14028 | ||||||||
\(367\) | −0.284992 | −0.0148765 | −0.00743824 | − | 0.999972i | \(-0.502368\pi\) | ||||
−0.00743824 | + | 0.999972i | \(0.502368\pi\) | |||||||
\(368\) | −6.39839 | −0.333539 | ||||||||
\(369\) | 4.68786 | 0.244040 | ||||||||
\(370\) | −81.6341 | −4.24395 | ||||||||
\(371\) | 0.984585 | 0.0511171 | ||||||||
\(372\) | 22.3692 | 1.15979 | ||||||||
\(373\) | 23.9465 | 1.23990 | 0.619952 | − | 0.784639i | \(-0.287152\pi\) | ||||
0.619952 | + | 0.784639i | \(0.287152\pi\) | |||||||
\(374\) | 9.51582 | 0.492051 | ||||||||
\(375\) | 33.3720 | 1.72332 | ||||||||
\(376\) | 33.6979 | 1.73784 | ||||||||
\(377\) | 21.9394 | 1.12994 | ||||||||
\(378\) | −0.795180 | −0.0408997 | ||||||||
\(379\) | 3.26051 | 0.167481 | 0.0837405 | − | 0.996488i | \(-0.473313\pi\) | ||||
0.0837405 | + | 0.996488i | \(0.473313\pi\) | |||||||
\(380\) | 41.1169 | 2.10925 | ||||||||
\(381\) | −11.0060 | −0.563854 | ||||||||
\(382\) | −12.2589 | −0.627218 | ||||||||
\(383\) | 13.9046 | 0.710494 | 0.355247 | − | 0.934773i | \(-0.384397\pi\) | ||||
0.355247 | + | 0.934773i | \(0.384397\pi\) | |||||||
\(384\) | 50.1469 | 2.55905 | ||||||||
\(385\) | −11.8085 | −0.601816 | ||||||||
\(386\) | −20.1289 | −1.02453 | ||||||||
\(387\) | 1.84610 | 0.0938425 | ||||||||
\(388\) | 22.2924 | 1.13173 | ||||||||
\(389\) | −7.94227 | −0.402689 | −0.201344 | − | 0.979521i | \(-0.564531\pi\) | ||||
−0.201344 | + | 0.979521i | \(0.564531\pi\) | |||||||
\(390\) | −69.3805 | −3.51322 | ||||||||
\(391\) | −1.31795 | −0.0666515 | ||||||||
\(392\) | 31.1423 | 1.57292 | ||||||||
\(393\) | 25.2517 | 1.27378 | ||||||||
\(394\) | 26.0740 | 1.31359 | ||||||||
\(395\) | 18.7713 | 0.944486 | ||||||||
\(396\) | −67.2212 | −3.37799 | ||||||||
\(397\) | 11.3180 | 0.568032 | 0.284016 | − | 0.958820i | \(-0.408333\pi\) | ||||
0.284016 | + | 0.958820i | \(0.408333\pi\) | |||||||
\(398\) | 64.3653 | 3.22634 | ||||||||
\(399\) | 4.25336 | 0.212935 | ||||||||
\(400\) | 30.7684 | 1.53842 | ||||||||
\(401\) | 16.2927 | 0.813620 | 0.406810 | − | 0.913513i | \(-0.366641\pi\) | ||||
0.406810 | + | 0.913513i | \(0.366641\pi\) | |||||||
\(402\) | −55.4750 | −2.76684 | ||||||||
\(403\) | 7.07290 | 0.352326 | ||||||||
\(404\) | 18.4493 | 0.917885 | ||||||||
\(405\) | −30.6343 | −1.52223 | ||||||||
\(406\) | −10.3740 | −0.514852 | ||||||||
\(407\) | −48.3242 | −2.39534 | ||||||||
\(408\) | −8.59509 | −0.425520 | ||||||||
\(409\) | 25.7301 | 1.27227 | 0.636136 | − | 0.771577i | \(-0.280532\pi\) | ||||
0.636136 | + | 0.771577i | \(0.280532\pi\) | |||||||
\(410\) | −13.0920 | −0.646569 | ||||||||
\(411\) | −10.6491 | −0.525283 | ||||||||
\(412\) | 0.0604798 | 0.00297963 | ||||||||
\(413\) | 0.225544 | 0.0110983 | ||||||||
\(414\) | 14.0519 | 0.690612 | ||||||||
\(415\) | −4.38712 | −0.215355 | ||||||||
\(416\) | 2.16202 | 0.106002 | ||||||||
\(417\) | −35.4502 | −1.73600 | ||||||||
\(418\) | 36.7358 | 1.79681 | ||||||||
\(419\) | −12.2672 | −0.599294 | −0.299647 | − | 0.954050i | \(-0.596869\pi\) | ||||
−0.299647 | + | 0.954050i | \(0.596869\pi\) | |||||||
\(420\) | 21.7361 | 1.06061 | ||||||||
\(421\) | −24.3308 | −1.18581 | −0.592904 | − | 0.805273i | \(-0.702019\pi\) | ||||
−0.592904 | + | 0.805273i | \(0.702019\pi\) | |||||||
\(422\) | −34.8558 | −1.69675 | ||||||||
\(423\) | −23.1140 | −1.12384 | ||||||||
\(424\) | −7.68093 | −0.373019 | ||||||||
\(425\) | 6.33773 | 0.307425 | ||||||||
\(426\) | 23.2132 | 1.12468 | ||||||||
\(427\) | −2.16096 | −0.104576 | ||||||||
\(428\) | 21.1364 | 1.02167 | ||||||||
\(429\) | −41.0706 | −1.98291 | ||||||||
\(430\) | −5.15570 | −0.248630 | ||||||||
\(431\) | −16.4251 | −0.791167 | −0.395584 | − | 0.918430i | \(-0.629458\pi\) | ||||
−0.395584 | + | 0.918430i | \(0.629458\pi\) | |||||||
\(432\) | 1.93747 | 0.0932168 | ||||||||
\(433\) | −7.36783 | −0.354075 | −0.177038 | − | 0.984204i | \(-0.556651\pi\) | ||||
−0.177038 | + | 0.984204i | \(0.556651\pi\) | |||||||
\(434\) | −3.34440 | −0.160536 | ||||||||
\(435\) | 65.2227 | 3.12719 | ||||||||
\(436\) | 22.2477 | 1.06547 | ||||||||
\(437\) | −5.08793 | −0.243389 | ||||||||
\(438\) | −37.2466 | −1.77971 | ||||||||
\(439\) | −33.1716 | −1.58319 | −0.791596 | − | 0.611045i | \(-0.790749\pi\) | ||||
−0.791596 | + | 0.611045i | \(0.790749\pi\) | |||||||
\(440\) | 92.1202 | 4.39166 | ||||||||
\(441\) | −21.3611 | −1.01720 | ||||||||
\(442\) | −5.53837 | −0.263433 | ||||||||
\(443\) | −4.95690 | −0.235510 | −0.117755 | − | 0.993043i | \(-0.537570\pi\) | ||||
−0.117755 | + | 0.993043i | \(0.537570\pi\) | |||||||
\(444\) | 88.9514 | 4.22144 | ||||||||
\(445\) | −55.8383 | −2.64699 | ||||||||
\(446\) | −7.70756 | −0.364963 | ||||||||
\(447\) | 36.9202 | 1.74627 | ||||||||
\(448\) | −5.31245 | −0.250990 | ||||||||
\(449\) | 9.78207 | 0.461644 | 0.230822 | − | 0.972996i | \(-0.425858\pi\) | ||||
0.230822 | + | 0.972996i | \(0.425858\pi\) | |||||||
\(450\) | −67.5724 | −3.18539 | ||||||||
\(451\) | −7.74998 | −0.364932 | ||||||||
\(452\) | 67.4161 | 3.17099 | ||||||||
\(453\) | 13.1899 | 0.619715 | ||||||||
\(454\) | 19.6142 | 0.920538 | ||||||||
\(455\) | 6.87274 | 0.322199 | ||||||||
\(456\) | −33.1813 | −1.55386 | ||||||||
\(457\) | 27.9404 | 1.30700 | 0.653499 | − | 0.756928i | \(-0.273300\pi\) | ||||
0.653499 | + | 0.756928i | \(0.273300\pi\) | |||||||
\(458\) | 47.4202 | 2.21580 | ||||||||
\(459\) | 0.399084 | 0.0186276 | ||||||||
\(460\) | −26.0010 | −1.21231 | ||||||||
\(461\) | 9.97962 | 0.464797 | 0.232399 | − | 0.972621i | \(-0.425343\pi\) | ||||
0.232399 | + | 0.972621i | \(0.425343\pi\) | |||||||
\(462\) | 19.4201 | 0.903504 | ||||||||
\(463\) | −0.624714 | −0.0290329 | −0.0145165 | − | 0.999895i | \(-0.504621\pi\) | ||||
−0.0145165 | + | 0.999895i | \(0.504621\pi\) | |||||||
\(464\) | 25.2764 | 1.17343 | ||||||||
\(465\) | 21.0267 | 0.975091 | ||||||||
\(466\) | −10.2676 | −0.475639 | ||||||||
\(467\) | −32.4701 | −1.50254 | −0.751268 | − | 0.659998i | \(-0.770557\pi\) | ||||
−0.751268 | + | 0.659998i | \(0.770557\pi\) | |||||||
\(468\) | 39.1239 | 1.80850 | ||||||||
\(469\) | 5.49528 | 0.253749 | ||||||||
\(470\) | 64.5518 | 2.97755 | ||||||||
\(471\) | 48.8360 | 2.25024 | ||||||||
\(472\) | −1.75951 | −0.0809879 | ||||||||
\(473\) | −3.05197 | −0.140330 | ||||||||
\(474\) | −30.8710 | −1.41795 | ||||||||
\(475\) | 24.4668 | 1.12261 | ||||||||
\(476\) | 1.73511 | 0.0795286 | ||||||||
\(477\) | 5.26850 | 0.241228 | ||||||||
\(478\) | −54.4146 | −2.48886 | ||||||||
\(479\) | 4.41468 | 0.201712 | 0.100856 | − | 0.994901i | \(-0.467842\pi\) | ||||
0.100856 | + | 0.994901i | \(0.467842\pi\) | |||||||
\(480\) | 6.42737 | 0.293368 | ||||||||
\(481\) | 28.1255 | 1.28241 | ||||||||
\(482\) | 34.1503 | 1.55551 | ||||||||
\(483\) | −2.68970 | −0.122385 | ||||||||
\(484\) | 67.9337 | 3.08789 | ||||||||
\(485\) | 20.9546 | 0.951498 | ||||||||
\(486\) | 54.3478 | 2.46527 | ||||||||
\(487\) | 36.9204 | 1.67303 | 0.836513 | − | 0.547948i | \(-0.184591\pi\) | ||||
0.836513 | + | 0.547948i | \(0.184591\pi\) | |||||||
\(488\) | 16.8580 | 0.763127 | ||||||||
\(489\) | −25.2156 | −1.14029 | ||||||||
\(490\) | 59.6563 | 2.69500 | ||||||||
\(491\) | 13.5450 | 0.611276 | 0.305638 | − | 0.952148i | \(-0.401130\pi\) | ||||
0.305638 | + | 0.952148i | \(0.401130\pi\) | |||||||
\(492\) | 14.2655 | 0.643140 | ||||||||
\(493\) | 5.20647 | 0.234488 | ||||||||
\(494\) | −21.3809 | −0.961970 | ||||||||
\(495\) | −63.1871 | −2.84005 | ||||||||
\(496\) | 8.14870 | 0.365887 | ||||||||
\(497\) | −2.29947 | −0.103145 | ||||||||
\(498\) | 7.21501 | 0.323312 | ||||||||
\(499\) | −1.60533 | −0.0718645 | −0.0359322 | − | 0.999354i | \(-0.511440\pi\) | ||||
−0.0359322 | + | 0.999354i | \(0.511440\pi\) | |||||||
\(500\) | 52.5556 | 2.35036 | ||||||||
\(501\) | −53.1046 | −2.37254 | ||||||||
\(502\) | 57.4819 | 2.56554 | ||||||||
\(503\) | −34.7901 | −1.55121 | −0.775607 | − | 0.631217i | \(-0.782556\pi\) | ||||
−0.775607 | + | 0.631217i | \(0.782556\pi\) | |||||||
\(504\) | −9.07776 | −0.404356 | ||||||||
\(505\) | 17.3421 | 0.771712 | ||||||||
\(506\) | −23.2306 | −1.03273 | ||||||||
\(507\) | −8.51246 | −0.378051 | ||||||||
\(508\) | −17.3327 | −0.769014 | ||||||||
\(509\) | −5.63955 | −0.249969 | −0.124984 | − | 0.992159i | \(-0.539888\pi\) | ||||
−0.124984 | + | 0.992159i | \(0.539888\pi\) | |||||||
\(510\) | −16.4648 | −0.729073 | ||||||||
\(511\) | 3.68961 | 0.163219 | ||||||||
\(512\) | 35.9591 | 1.58918 | ||||||||
\(513\) | 1.54066 | 0.0680218 | ||||||||
\(514\) | −18.1113 | −0.798854 | ||||||||
\(515\) | 0.0568503 | 0.00250512 | ||||||||
\(516\) | 5.61783 | 0.247311 | ||||||||
\(517\) | 38.2122 | 1.68057 | ||||||||
\(518\) | −13.2991 | −0.584327 | ||||||||
\(519\) | −18.6671 | −0.819393 | ||||||||
\(520\) | −53.6155 | −2.35120 | ||||||||
\(521\) | 18.7120 | 0.819787 | 0.409893 | − | 0.912133i | \(-0.365566\pi\) | ||||
0.409893 | + | 0.912133i | \(0.365566\pi\) | |||||||
\(522\) | −55.5110 | −2.42965 | ||||||||
\(523\) | −36.5166 | −1.59676 | −0.798380 | − | 0.602153i | \(-0.794310\pi\) | ||||
−0.798380 | + | 0.602153i | \(0.794310\pi\) | |||||||
\(524\) | 39.7674 | 1.73725 | ||||||||
\(525\) | 12.9342 | 0.564493 | ||||||||
\(526\) | 25.4853 | 1.11121 | ||||||||
\(527\) | 1.67848 | 0.0731158 | ||||||||
\(528\) | −47.3175 | −2.05923 | ||||||||
\(529\) | −19.7825 | −0.860111 | ||||||||
\(530\) | −14.7136 | −0.639119 | ||||||||
\(531\) | 1.20688 | 0.0523742 | ||||||||
\(532\) | 6.69838 | 0.290412 | ||||||||
\(533\) | 4.51062 | 0.195377 | ||||||||
\(534\) | 91.8309 | 3.97391 | ||||||||
\(535\) | 19.8680 | 0.858968 | ||||||||
\(536\) | −42.8697 | −1.85169 | ||||||||
\(537\) | 24.9477 | 1.07657 | ||||||||
\(538\) | 34.9517 | 1.50687 | ||||||||
\(539\) | 35.3142 | 1.52109 | ||||||||
\(540\) | 7.87329 | 0.338813 | ||||||||
\(541\) | −15.4034 | −0.662246 | −0.331123 | − | 0.943588i | \(-0.607427\pi\) | ||||
−0.331123 | + | 0.943588i | \(0.607427\pi\) | |||||||
\(542\) | −53.9400 | −2.31692 | ||||||||
\(543\) | 10.4726 | 0.449423 | ||||||||
\(544\) | 0.513072 | 0.0219978 | ||||||||
\(545\) | 20.9125 | 0.895794 | ||||||||
\(546\) | −11.3028 | −0.483716 | ||||||||
\(547\) | 15.4116 | 0.658952 | 0.329476 | − | 0.944164i | \(-0.393128\pi\) | ||||
0.329476 | + | 0.944164i | \(0.393128\pi\) | |||||||
\(548\) | −16.7707 | −0.716409 | ||||||||
\(549\) | −11.5633 | −0.493508 | ||||||||
\(550\) | 111.711 | 4.76336 | ||||||||
\(551\) | 20.0996 | 0.856270 | ||||||||
\(552\) | 20.9828 | 0.893088 | ||||||||
\(553\) | 3.05804 | 0.130041 | ||||||||
\(554\) | 42.2404 | 1.79462 | ||||||||
\(555\) | 83.6131 | 3.54918 | ||||||||
\(556\) | −55.8285 | −2.36766 | ||||||||
\(557\) | −29.1179 | −1.23376 | −0.616882 | − | 0.787056i | \(-0.711604\pi\) | ||||
−0.616882 | + | 0.787056i | \(0.711604\pi\) | |||||||
\(558\) | −17.8958 | −0.757591 | ||||||||
\(559\) | 1.77630 | 0.0751295 | ||||||||
\(560\) | 7.91810 | 0.334601 | ||||||||
\(561\) | −9.74652 | −0.411498 | ||||||||
\(562\) | −61.7659 | −2.60544 | ||||||||
\(563\) | 12.8153 | 0.540098 | 0.270049 | − | 0.962847i | \(-0.412960\pi\) | ||||
0.270049 | + | 0.962847i | \(0.412960\pi\) | |||||||
\(564\) | −70.3379 | −2.96176 | ||||||||
\(565\) | 63.3702 | 2.66601 | ||||||||
\(566\) | −49.8009 | −2.09329 | ||||||||
\(567\) | −4.99066 | −0.209588 | ||||||||
\(568\) | 17.9386 | 0.752685 | ||||||||
\(569\) | −16.0969 | −0.674819 | −0.337409 | − | 0.941358i | \(-0.609551\pi\) | ||||
−0.337409 | + | 0.941358i | \(0.609551\pi\) | |||||||
\(570\) | −63.5622 | −2.66233 | ||||||||
\(571\) | −23.5591 | −0.985918 | −0.492959 | − | 0.870053i | \(-0.664085\pi\) | ||||
−0.492959 | + | 0.870053i | \(0.664085\pi\) | |||||||
\(572\) | −64.6797 | −2.70439 | ||||||||
\(573\) | 12.5561 | 0.524537 | ||||||||
\(574\) | −2.13283 | −0.0890227 | ||||||||
\(575\) | −15.4720 | −0.645228 | ||||||||
\(576\) | −28.4269 | −1.18445 | ||||||||
\(577\) | 8.56909 | 0.356736 | 0.178368 | − | 0.983964i | \(-0.442918\pi\) | ||||
0.178368 | + | 0.983964i | \(0.442918\pi\) | |||||||
\(578\) | 40.0728 | 1.66681 | ||||||||
\(579\) | 20.6169 | 0.856809 | ||||||||
\(580\) | 102.716 | 4.26503 | ||||||||
\(581\) | −0.714710 | −0.0296511 | ||||||||
\(582\) | −34.4616 | −1.42848 | ||||||||
\(583\) | −8.70990 | −0.360727 | ||||||||
\(584\) | −28.7833 | −1.19106 | ||||||||
\(585\) | 36.7760 | 1.52050 | ||||||||
\(586\) | 69.0585 | 2.85278 | ||||||||
\(587\) | −7.07398 | −0.291974 | −0.145987 | − | 0.989286i | \(-0.546636\pi\) | ||||
−0.145987 | + | 0.989286i | \(0.546636\pi\) | |||||||
\(588\) | −65.0036 | −2.68070 | ||||||||
\(589\) | 6.47977 | 0.266994 | ||||||||
\(590\) | −3.37052 | −0.138762 | ||||||||
\(591\) | −26.7061 | −1.09854 | ||||||||
\(592\) | 32.4035 | 1.33177 | ||||||||
\(593\) | 1.55758 | 0.0639621 | 0.0319810 | − | 0.999488i | \(-0.489818\pi\) | ||||
0.0319810 | + | 0.999488i | \(0.489818\pi\) | |||||||
\(594\) | 7.03437 | 0.288624 | ||||||||
\(595\) | 1.63098 | 0.0668637 | ||||||||
\(596\) | 58.1435 | 2.38165 | ||||||||
\(597\) | −65.9257 | −2.69816 | ||||||||
\(598\) | 13.5206 | 0.552898 | ||||||||
\(599\) | −6.57098 | −0.268483 | −0.134241 | − | 0.990949i | \(-0.542860\pi\) | ||||
−0.134241 | + | 0.990949i | \(0.542860\pi\) | |||||||
\(600\) | −100.902 | −4.11930 | ||||||||
\(601\) | 45.8307 | 1.86947 | 0.934736 | − | 0.355342i | \(-0.115636\pi\) | ||||
0.934736 | + | 0.355342i | \(0.115636\pi\) | |||||||
\(602\) | −0.839918 | −0.0342325 | ||||||||
\(603\) | 29.4052 | 1.19747 | ||||||||
\(604\) | 20.7720 | 0.845201 | ||||||||
\(605\) | 63.8568 | 2.59615 | ||||||||
\(606\) | −28.5205 | −1.15857 | ||||||||
\(607\) | 41.8400 | 1.69823 | 0.849116 | − | 0.528206i | \(-0.177135\pi\) | ||||
0.849116 | + | 0.528206i | \(0.177135\pi\) | |||||||
\(608\) | 1.98071 | 0.0803284 | ||||||||
\(609\) | 10.6255 | 0.430566 | ||||||||
\(610\) | 32.2933 | 1.30752 | ||||||||
\(611\) | −22.2401 | −0.899740 | ||||||||
\(612\) | 9.28455 | 0.375306 | ||||||||
\(613\) | 12.7214 | 0.513813 | 0.256906 | − | 0.966436i | \(-0.417297\pi\) | ||||
0.256906 | + | 0.966436i | \(0.417297\pi\) | |||||||
\(614\) | −78.3775 | −3.16306 | ||||||||
\(615\) | 13.4094 | 0.540720 | ||||||||
\(616\) | 15.0074 | 0.604664 | ||||||||
\(617\) | −46.8984 | −1.88806 | −0.944029 | − | 0.329862i | \(-0.892998\pi\) | ||||
−0.944029 | + | 0.329862i | \(0.892998\pi\) | |||||||
\(618\) | −0.0934952 | −0.00376093 | ||||||||
\(619\) | 11.5737 | 0.465187 | 0.232593 | − | 0.972574i | \(-0.425279\pi\) | ||||
0.232593 | + | 0.972574i | \(0.425279\pi\) | |||||||
\(620\) | 33.1138 | 1.32988 | ||||||||
\(621\) | −0.974266 | −0.0390960 | ||||||||
\(622\) | −5.11134 | −0.204946 | ||||||||
\(623\) | −9.09666 | −0.364450 | ||||||||
\(624\) | 27.5396 | 1.10247 | ||||||||
\(625\) | 6.27341 | 0.250936 | ||||||||
\(626\) | −34.6499 | −1.38489 | ||||||||
\(627\) | −37.6264 | −1.50265 | ||||||||
\(628\) | 76.9090 | 3.06900 | ||||||||
\(629\) | 6.67451 | 0.266130 | ||||||||
\(630\) | −17.3894 | −0.692810 | ||||||||
\(631\) | 10.0405 | 0.399705 | 0.199852 | − | 0.979826i | \(-0.435954\pi\) | ||||
0.199852 | + | 0.979826i | \(0.435954\pi\) | |||||||
\(632\) | −23.8564 | −0.948955 | ||||||||
\(633\) | 35.7008 | 1.41898 | ||||||||
\(634\) | 21.1325 | 0.839279 | ||||||||
\(635\) | −16.2925 | −0.646549 | ||||||||
\(636\) | 16.0325 | 0.635729 | ||||||||
\(637\) | −20.5535 | −0.814359 | ||||||||
\(638\) | 91.7709 | 3.63325 | ||||||||
\(639\) | −12.3044 | −0.486755 | ||||||||
\(640\) | 74.2340 | 2.93436 | ||||||||
\(641\) | −16.0539 | −0.634093 | −0.317046 | − | 0.948410i | \(-0.602691\pi\) | ||||
−0.317046 | + | 0.948410i | \(0.602691\pi\) | |||||||
\(642\) | −32.6746 | −1.28956 | ||||||||
\(643\) | 20.4249 | 0.805481 | 0.402741 | − | 0.915314i | \(-0.368058\pi\) | ||||
0.402741 | + | 0.915314i | \(0.368058\pi\) | |||||||
\(644\) | −4.23585 | −0.166916 | ||||||||
\(645\) | 5.28069 | 0.207927 | ||||||||
\(646\) | −5.07392 | −0.199631 | ||||||||
\(647\) | −22.2969 | −0.876581 | −0.438290 | − | 0.898833i | \(-0.644416\pi\) | ||||
−0.438290 | + | 0.898833i | \(0.644416\pi\) | |||||||
\(648\) | 38.9331 | 1.52944 | ||||||||
\(649\) | −1.99522 | −0.0783191 | ||||||||
\(650\) | −65.0176 | −2.55020 | ||||||||
\(651\) | 3.42548 | 0.134255 | ||||||||
\(652\) | −39.7106 | −1.55519 | ||||||||
\(653\) | −1.68848 | −0.0660753 | −0.0330377 | − | 0.999454i | \(-0.510518\pi\) | ||||
−0.0330377 | + | 0.999454i | \(0.510518\pi\) | |||||||
\(654\) | −34.3924 | −1.34485 | ||||||||
\(655\) | 37.3809 | 1.46059 | ||||||||
\(656\) | 5.19669 | 0.202897 | ||||||||
\(657\) | 19.7430 | 0.770249 | ||||||||
\(658\) | 10.5162 | 0.409963 | ||||||||
\(659\) | −33.4864 | −1.30445 | −0.652223 | − | 0.758027i | \(-0.726163\pi\) | ||||
−0.652223 | + | 0.758027i | \(0.726163\pi\) | |||||||
\(660\) | −192.283 | −7.48462 | ||||||||
\(661\) | 30.4639 | 1.18491 | 0.592454 | − | 0.805605i | \(-0.298159\pi\) | ||||
0.592454 | + | 0.805605i | \(0.298159\pi\) | |||||||
\(662\) | 47.9412 | 1.86329 | ||||||||
\(663\) | 5.67264 | 0.220307 | ||||||||
\(664\) | 5.57558 | 0.216374 | ||||||||
\(665\) | 6.29639 | 0.244164 | ||||||||
\(666\) | −71.1631 | −2.75752 | ||||||||
\(667\) | −12.7103 | −0.492146 | ||||||||
\(668\) | −83.6314 | −3.23579 | ||||||||
\(669\) | 7.89441 | 0.305216 | ||||||||
\(670\) | −82.1214 | −3.17263 | ||||||||
\(671\) | 19.1164 | 0.737980 | ||||||||
\(672\) | 1.04709 | 0.0403923 | ||||||||
\(673\) | 27.0782 | 1.04379 | 0.521895 | − | 0.853010i | \(-0.325225\pi\) | ||||
0.521895 | + | 0.853010i | \(0.325225\pi\) | |||||||
\(674\) | −37.8292 | −1.45713 | ||||||||
\(675\) | 4.68503 | 0.180327 | ||||||||
\(676\) | −13.4058 | −0.515607 | ||||||||
\(677\) | 39.1940 | 1.50635 | 0.753173 | − | 0.657822i | \(-0.228522\pi\) | ||||
0.753173 | + | 0.657822i | \(0.228522\pi\) | |||||||
\(678\) | −104.218 | −4.00246 | ||||||||
\(679\) | 3.41372 | 0.131007 | ||||||||
\(680\) | −12.7236 | −0.487927 | ||||||||
\(681\) | −20.0897 | −0.769838 | ||||||||
\(682\) | 29.5854 | 1.13288 | ||||||||
\(683\) | −36.9955 | −1.41559 | −0.707797 | − | 0.706416i | \(-0.750311\pi\) | ||||
−0.707797 | + | 0.706416i | \(0.750311\pi\) | |||||||
\(684\) | 35.8430 | 1.37049 | ||||||||
\(685\) | −15.7643 | −0.602321 | ||||||||
\(686\) | 19.9667 | 0.762333 | ||||||||
\(687\) | −48.5698 | −1.85306 | ||||||||
\(688\) | 2.04648 | 0.0780213 | ||||||||
\(689\) | 5.06931 | 0.193125 | ||||||||
\(690\) | 40.1948 | 1.53019 | ||||||||
\(691\) | −26.1845 | −0.996106 | −0.498053 | − | 0.867147i | \(-0.665952\pi\) | ||||
−0.498053 | + | 0.867147i | \(0.665952\pi\) | |||||||
\(692\) | −29.3977 | −1.11753 | ||||||||
\(693\) | −10.2939 | −0.391031 | ||||||||
\(694\) | 60.9966 | 2.31540 | ||||||||
\(695\) | −52.4781 | −1.99061 | ||||||||
\(696\) | −82.8913 | −3.14199 | ||||||||
\(697\) | 1.07042 | 0.0405451 | ||||||||
\(698\) | 32.2239 | 1.21969 | ||||||||
\(699\) | 10.5166 | 0.397773 | ||||||||
\(700\) | 20.3693 | 0.769886 | ||||||||
\(701\) | 0.832365 | 0.0314380 | 0.0157190 | − | 0.999876i | \(-0.494996\pi\) | ||||
0.0157190 | + | 0.999876i | \(0.494996\pi\) | |||||||
\(702\) | −4.09413 | −0.154523 | ||||||||
\(703\) | 25.7669 | 0.971817 | ||||||||
\(704\) | 46.9954 | 1.77120 | ||||||||
\(705\) | −66.1167 | −2.49010 | ||||||||
\(706\) | 18.5924 | 0.699733 | ||||||||
\(707\) | 2.82521 | 0.106253 | ||||||||
\(708\) | 3.67264 | 0.138026 | ||||||||
\(709\) | 42.3148 | 1.58916 | 0.794582 | − | 0.607157i | \(-0.207690\pi\) | ||||
0.794582 | + | 0.607157i | \(0.207690\pi\) | |||||||
\(710\) | 34.3632 | 1.28963 | ||||||||
\(711\) | 16.3636 | 0.613681 | ||||||||
\(712\) | 70.9647 | 2.65951 | ||||||||
\(713\) | −4.09760 | −0.153456 | ||||||||
\(714\) | −2.68229 | −0.100382 | ||||||||
\(715\) | −60.7981 | −2.27372 | ||||||||
\(716\) | 39.2887 | 1.46829 | ||||||||
\(717\) | 55.7338 | 2.08142 | ||||||||
\(718\) | 59.9121 | 2.23590 | ||||||||
\(719\) | −23.7287 | −0.884930 | −0.442465 | − | 0.896786i | \(-0.645896\pi\) | ||||
−0.442465 | + | 0.896786i | \(0.645896\pi\) | |||||||
\(720\) | 42.3696 | 1.57902 | ||||||||
\(721\) | 0.00926152 | 0.000344917 0 | ||||||||
\(722\) | 26.6683 | 0.992492 | ||||||||
\(723\) | −34.9783 | −1.30086 | ||||||||
\(724\) | 16.4927 | 0.612947 | ||||||||
\(725\) | 61.1213 | 2.26999 | ||||||||
\(726\) | −105.018 | −3.89758 | ||||||||
\(727\) | −39.8410 | −1.47762 | −0.738811 | − | 0.673913i | \(-0.764612\pi\) | ||||
−0.738811 | + | 0.673913i | \(0.764612\pi\) | |||||||
\(728\) | −8.73455 | −0.323724 | ||||||||
\(729\) | −30.7681 | −1.13956 | ||||||||
\(730\) | −55.1374 | −2.04073 | ||||||||
\(731\) | 0.421537 | 0.0155911 | ||||||||
\(732\) | −35.1879 | −1.30058 | ||||||||
\(733\) | −37.7531 | −1.39444 | −0.697222 | − | 0.716855i | \(-0.745581\pi\) | ||||
−0.697222 | + | 0.716855i | \(0.745581\pi\) | |||||||
\(734\) | 0.693824 | 0.0256095 | ||||||||
\(735\) | −61.1026 | −2.25380 | ||||||||
\(736\) | −1.25254 | −0.0461692 | ||||||||
\(737\) | −48.6127 | −1.79067 | ||||||||
\(738\) | −11.4128 | −0.420110 | ||||||||
\(739\) | −1.66619 | −0.0612918 | −0.0306459 | − | 0.999530i | \(-0.509756\pi\) | ||||
−0.0306459 | + | 0.999530i | \(0.509756\pi\) | |||||||
\(740\) | 131.678 | 4.84056 | ||||||||
\(741\) | 21.8992 | 0.804487 | ||||||||
\(742\) | −2.39701 | −0.0879969 | ||||||||
\(743\) | −10.7136 | −0.393043 | −0.196521 | − | 0.980500i | \(-0.562965\pi\) | ||||
−0.196521 | + | 0.980500i | \(0.562965\pi\) | |||||||
\(744\) | −26.7228 | −0.979705 | ||||||||
\(745\) | 54.6542 | 2.00237 | ||||||||
\(746\) | −58.2987 | −2.13447 | ||||||||
\(747\) | −3.82440 | −0.139928 | ||||||||
\(748\) | −15.3492 | −0.561224 | ||||||||
\(749\) | 3.23671 | 0.118267 | ||||||||
\(750\) | −81.2452 | −2.96665 | ||||||||
\(751\) | −20.1714 | −0.736064 | −0.368032 | − | 0.929813i | \(-0.619968\pi\) | ||||
−0.368032 | + | 0.929813i | \(0.619968\pi\) | |||||||
\(752\) | −25.6229 | −0.934371 | ||||||||
\(753\) | −58.8754 | −2.14554 | ||||||||
\(754\) | −53.4123 | −1.94516 | ||||||||
\(755\) | 19.5254 | 0.710603 | ||||||||
\(756\) | 1.28264 | 0.0466493 | ||||||||
\(757\) | −34.6586 | −1.25969 | −0.629844 | − | 0.776722i | \(-0.716881\pi\) | ||||
−0.629844 | + | 0.776722i | \(0.716881\pi\) | |||||||
\(758\) | −7.93782 | −0.288315 | ||||||||
\(759\) | 23.7938 | 0.863659 | ||||||||
\(760\) | −49.1193 | −1.78174 | ||||||||
\(761\) | −45.1246 | −1.63577 | −0.817883 | − | 0.575385i | \(-0.804852\pi\) | ||||
−0.817883 | + | 0.575385i | \(0.804852\pi\) | |||||||
\(762\) | 26.7944 | 0.970661 | ||||||||
\(763\) | 3.40687 | 0.123337 | ||||||||
\(764\) | 19.7738 | 0.715392 | ||||||||
\(765\) | 8.72736 | 0.315538 | ||||||||
\(766\) | −33.8513 | −1.22310 | ||||||||
\(767\) | 1.16125 | 0.0419303 | ||||||||
\(768\) | −78.0271 | −2.81556 | ||||||||
\(769\) | −4.51050 | −0.162653 | −0.0813263 | − | 0.996688i | \(-0.525916\pi\) | ||||
−0.0813263 | + | 0.996688i | \(0.525916\pi\) | |||||||
\(770\) | 28.7482 | 1.03601 | ||||||||
\(771\) | 18.5503 | 0.668074 | ||||||||
\(772\) | 32.4684 | 1.16856 | ||||||||
\(773\) | 41.5940 | 1.49603 | 0.748016 | − | 0.663681i | \(-0.231007\pi\) | ||||
0.748016 | + | 0.663681i | \(0.231007\pi\) | |||||||
\(774\) | −4.49439 | −0.161548 | ||||||||
\(775\) | 19.7045 | 0.707806 | ||||||||
\(776\) | −26.6311 | −0.956001 | ||||||||
\(777\) | 13.6215 | 0.488668 | ||||||||
\(778\) | 19.3357 | 0.693219 | ||||||||
\(779\) | 4.13236 | 0.148057 | ||||||||
\(780\) | 111.912 | 4.00710 | ||||||||
\(781\) | 20.3417 | 0.727883 | ||||||||
\(782\) | 3.20859 | 0.114739 | ||||||||
\(783\) | 3.84878 | 0.137544 | ||||||||
\(784\) | −23.6797 | −0.845704 | ||||||||
\(785\) | 72.2935 | 2.58027 | ||||||||
\(786\) | −61.4761 | −2.19278 | ||||||||
\(787\) | 24.7458 | 0.882094 | 0.441047 | − | 0.897484i | \(-0.354607\pi\) | ||||
0.441047 | + | 0.897484i | \(0.354607\pi\) | |||||||
\(788\) | −42.0579 | −1.49825 | ||||||||
\(789\) | −26.1031 | −0.929295 | ||||||||
\(790\) | −45.6993 | −1.62591 | ||||||||
\(791\) | 10.3237 | 0.367068 | ||||||||
\(792\) | 80.3043 | 2.85349 | ||||||||
\(793\) | −11.1261 | −0.395098 | ||||||||
\(794\) | −27.5540 | −0.977853 | ||||||||
\(795\) | 15.0703 | 0.534489 | ||||||||
\(796\) | −103.823 | −3.67990 | ||||||||
\(797\) | −51.9929 | −1.84168 | −0.920842 | − | 0.389937i | \(-0.872497\pi\) | ||||
−0.920842 | + | 0.389937i | \(0.872497\pi\) | |||||||
\(798\) | −10.3550 | −0.366562 | ||||||||
\(799\) | −5.27784 | −0.186717 | ||||||||
\(800\) | 6.02319 | 0.212952 | ||||||||
\(801\) | −48.6761 | −1.71989 | ||||||||
\(802\) | −39.6652 | −1.40063 | ||||||||
\(803\) | −32.6392 | −1.15181 | ||||||||
\(804\) | 89.4824 | 3.15580 | ||||||||
\(805\) | −3.98164 | −0.140335 | ||||||||
\(806\) | −17.2192 | −0.606521 | ||||||||
\(807\) | −35.7990 | −1.26019 | ||||||||
\(808\) | −22.0400 | −0.775363 | ||||||||
\(809\) | 20.2651 | 0.712484 | 0.356242 | − | 0.934394i | \(-0.384058\pi\) | ||||
0.356242 | + | 0.934394i | \(0.384058\pi\) | |||||||
\(810\) | 74.5804 | 2.62049 | ||||||||
\(811\) | 10.0684 | 0.353550 | 0.176775 | − | 0.984251i | \(-0.443433\pi\) | ||||
0.176775 | + | 0.984251i | \(0.443433\pi\) | |||||||
\(812\) | 16.7335 | 0.587229 | ||||||||
\(813\) | 55.2477 | 1.93762 | ||||||||
\(814\) | 117.647 | 4.12353 | ||||||||
\(815\) | −37.3275 | −1.30753 | ||||||||
\(816\) | 6.53546 | 0.228787 | ||||||||
\(817\) | 1.62734 | 0.0569334 | ||||||||
\(818\) | −62.6408 | −2.19019 | ||||||||
\(819\) | 5.99120 | 0.209349 | ||||||||
\(820\) | 21.1177 | 0.737464 | ||||||||
\(821\) | 44.1178 | 1.53972 | 0.769861 | − | 0.638212i | \(-0.220326\pi\) | ||||
0.769861 | + | 0.638212i | \(0.220326\pi\) | |||||||
\(822\) | 25.9257 | 0.904262 | ||||||||
\(823\) | −32.2660 | −1.12472 | −0.562361 | − | 0.826892i | \(-0.690107\pi\) | ||||
−0.562361 | + | 0.826892i | \(0.690107\pi\) | |||||||
\(824\) | −0.0722508 | −0.00251698 | ||||||||
\(825\) | −114.419 | −3.98356 | ||||||||
\(826\) | −0.549094 | −0.0191054 | ||||||||
\(827\) | 6.98761 | 0.242983 | 0.121491 | − | 0.992592i | \(-0.461232\pi\) | ||||
0.121491 | + | 0.992592i | \(0.461232\pi\) | |||||||
\(828\) | −22.6660 | −0.787697 | ||||||||
\(829\) | 6.75511 | 0.234615 | 0.117307 | − | 0.993096i | \(-0.462574\pi\) | ||||
0.117307 | + | 0.993096i | \(0.462574\pi\) | |||||||
\(830\) | 10.6806 | 0.370729 | ||||||||
\(831\) | −43.2644 | −1.50083 | ||||||||
\(832\) | −27.3521 | −0.948263 | ||||||||
\(833\) | −4.87758 | −0.168998 | ||||||||
\(834\) | 86.3048 | 2.98849 | ||||||||
\(835\) | −78.6124 | −2.72049 | ||||||||
\(836\) | −59.2556 | −2.04940 | ||||||||
\(837\) | 1.24078 | 0.0428877 | ||||||||
\(838\) | 29.8650 | 1.03167 | ||||||||
\(839\) | −24.1545 | −0.833905 | −0.416952 | − | 0.908928i | \(-0.636902\pi\) | ||||
−0.416952 | + | 0.908928i | \(0.636902\pi\) | |||||||
\(840\) | −25.9665 | −0.895931 | ||||||||
\(841\) | 21.2114 | 0.731428 | ||||||||
\(842\) | 59.2341 | 2.04134 | ||||||||
\(843\) | 63.2634 | 2.17891 | ||||||||
\(844\) | 56.2232 | 1.93528 | ||||||||
\(845\) | −12.6013 | −0.433497 | ||||||||
\(846\) | 56.2719 | 1.93467 | ||||||||
\(847\) | 10.4030 | 0.357450 | ||||||||
\(848\) | 5.84036 | 0.200559 | ||||||||
\(849\) | 51.0083 | 1.75060 | ||||||||
\(850\) | −15.4294 | −0.529225 | ||||||||
\(851\) | −16.2942 | −0.558558 | ||||||||
\(852\) | −37.4433 | −1.28279 | ||||||||
\(853\) | −33.5108 | −1.14739 | −0.573694 | − | 0.819070i | \(-0.694490\pi\) | ||||
−0.573694 | + | 0.819070i | \(0.694490\pi\) | |||||||
\(854\) | 5.26093 | 0.180025 | ||||||||
\(855\) | 33.6919 | 1.15224 | ||||||||
\(856\) | −25.2501 | −0.863032 | ||||||||
\(857\) | −32.8649 | −1.12264 | −0.561322 | − | 0.827598i | \(-0.689707\pi\) | ||||
−0.561322 | + | 0.827598i | \(0.689707\pi\) | |||||||
\(858\) | 99.9877 | 3.41352 | ||||||||
\(859\) | 26.6143 | 0.908069 | 0.454035 | − | 0.890984i | \(-0.349984\pi\) | ||||
0.454035 | + | 0.890984i | \(0.349984\pi\) | |||||||
\(860\) | 8.31625 | 0.283582 | ||||||||
\(861\) | 2.18454 | 0.0744489 | ||||||||
\(862\) | 39.9874 | 1.36198 | ||||||||
\(863\) | 33.0835 | 1.12618 | 0.563088 | − | 0.826397i | \(-0.309613\pi\) | ||||
0.563088 | + | 0.826397i | \(0.309613\pi\) | |||||||
\(864\) | 0.379278 | 0.0129033 | ||||||||
\(865\) | −27.6334 | −0.939565 | ||||||||
\(866\) | 17.9372 | 0.609532 | ||||||||
\(867\) | −41.0443 | −1.39394 | ||||||||
\(868\) | 5.39459 | 0.183104 | ||||||||
\(869\) | −27.0523 | −0.917685 | ||||||||
\(870\) | −158.787 | −5.38338 | ||||||||
\(871\) | 28.2934 | 0.958686 | ||||||||
\(872\) | −26.5776 | −0.900032 | ||||||||
\(873\) | 18.2668 | 0.618237 | ||||||||
\(874\) | 12.3867 | 0.418988 | ||||||||
\(875\) | 8.04805 | 0.272074 | ||||||||
\(876\) | 60.0797 | 2.02990 | ||||||||
\(877\) | −36.8752 | −1.24519 | −0.622594 | − | 0.782545i | \(-0.713921\pi\) | ||||
−0.622594 | + | 0.782545i | \(0.713921\pi\) | |||||||
\(878\) | 80.7573 | 2.72543 | ||||||||
\(879\) | −70.7327 | −2.38575 | ||||||||
\(880\) | −70.0456 | −2.36124 | ||||||||
\(881\) | 35.5834 | 1.19884 | 0.599418 | − | 0.800436i | \(-0.295399\pi\) | ||||
0.599418 | + | 0.800436i | \(0.295399\pi\) | |||||||
\(882\) | 52.0044 | 1.75108 | ||||||||
\(883\) | −22.4567 | −0.755728 | −0.377864 | − | 0.925861i | \(-0.623341\pi\) | ||||
−0.377864 | + | 0.925861i | \(0.623341\pi\) | |||||||
\(884\) | 8.93352 | 0.300467 | ||||||||
\(885\) | 3.45223 | 0.116045 | ||||||||
\(886\) | 12.0678 | 0.405424 | ||||||||
\(887\) | 18.5758 | 0.623713 | 0.311856 | − | 0.950129i | \(-0.399049\pi\) | ||||
0.311856 | + | 0.950129i | \(0.399049\pi\) | |||||||
\(888\) | −106.264 | −3.56597 | ||||||||
\(889\) | −2.65423 | −0.0890199 | ||||||||
\(890\) | 135.940 | 4.55673 | ||||||||
\(891\) | 44.1487 | 1.47904 | ||||||||
\(892\) | 12.4325 | 0.416270 | ||||||||
\(893\) | −20.3751 | −0.681826 | ||||||||
\(894\) | −89.8835 | −3.00615 | ||||||||
\(895\) | 36.9309 | 1.23446 | ||||||||
\(896\) | 12.0935 | 0.404016 | ||||||||
\(897\) | −13.8484 | −0.462384 | ||||||||
\(898\) | −23.8148 | −0.794710 | ||||||||
\(899\) | 16.1873 | 0.539878 | ||||||||
\(900\) | 108.996 | 3.63319 | ||||||||
\(901\) | 1.20301 | 0.0400779 | ||||||||
\(902\) | 18.8676 | 0.628222 | ||||||||
\(903\) | 0.860281 | 0.0286283 | ||||||||
\(904\) | −80.5370 | −2.67862 | ||||||||
\(905\) | 15.5029 | 0.515335 | ||||||||
\(906\) | −32.1113 | −1.06683 | ||||||||
\(907\) | 37.8416 | 1.25651 | 0.628255 | − | 0.778008i | \(-0.283770\pi\) | ||||
0.628255 | + | 0.778008i | \(0.283770\pi\) | |||||||
\(908\) | −31.6381 | −1.04995 | ||||||||
\(909\) | 15.1177 | 0.501421 | ||||||||
\(910\) | −16.7319 | −0.554658 | ||||||||
\(911\) | −17.0920 | −0.566282 | −0.283141 | − | 0.959078i | \(-0.591376\pi\) | ||||
−0.283141 | + | 0.959078i | \(0.591376\pi\) | |||||||
\(912\) | 25.2301 | 0.835452 | ||||||||
\(913\) | 6.32251 | 0.209244 | ||||||||
\(914\) | −68.0219 | −2.24997 | ||||||||
\(915\) | −33.0762 | −1.09347 | ||||||||
\(916\) | −76.4899 | −2.52730 | ||||||||
\(917\) | 6.08975 | 0.201101 | ||||||||
\(918\) | −0.971583 | −0.0320670 | ||||||||
\(919\) | 30.6834 | 1.01215 | 0.506076 | − | 0.862489i | \(-0.331096\pi\) | ||||
0.506076 | + | 0.862489i | \(0.331096\pi\) | |||||||
\(920\) | 31.0615 | 1.02407 | ||||||||
\(921\) | 80.2776 | 2.64524 | ||||||||
\(922\) | −24.2957 | −0.800138 | ||||||||
\(923\) | −11.8392 | −0.389692 | ||||||||
\(924\) | −31.3250 | −1.03052 | ||||||||
\(925\) | 78.3553 | 2.57630 | ||||||||
\(926\) | 1.52089 | 0.0499795 | ||||||||
\(927\) | 0.0495583 | 0.00162771 | ||||||||
\(928\) | 4.94808 | 0.162429 | ||||||||
\(929\) | 57.6983 | 1.89302 | 0.946510 | − | 0.322674i | \(-0.104582\pi\) | ||||
0.946510 | + | 0.322674i | \(0.104582\pi\) | |||||||
\(930\) | −51.1903 | −1.67860 | ||||||||
\(931\) | −18.8299 | −0.617124 | ||||||||
\(932\) | 16.5619 | 0.542504 | ||||||||
\(933\) | 5.23526 | 0.171395 | ||||||||
\(934\) | 79.0495 | 2.58658 | ||||||||
\(935\) | −14.4281 | −0.471849 | ||||||||
\(936\) | −46.7385 | −1.52769 | ||||||||
\(937\) | −7.60650 | −0.248494 | −0.124247 | − | 0.992251i | \(-0.539651\pi\) | ||||
−0.124247 | + | 0.992251i | \(0.539651\pi\) | |||||||
\(938\) | −13.3785 | −0.436822 | ||||||||
\(939\) | 35.4899 | 1.15817 | ||||||||
\(940\) | −104.123 | −3.39613 | ||||||||
\(941\) | −23.5063 | −0.766284 | −0.383142 | − | 0.923689i | \(-0.625158\pi\) | ||||
−0.383142 | + | 0.923689i | \(0.625158\pi\) | |||||||
\(942\) | −118.893 | −3.87374 | ||||||||
\(943\) | −2.61318 | −0.0850967 | ||||||||
\(944\) | 1.33788 | 0.0435442 | ||||||||
\(945\) | 1.20567 | 0.0392204 | ||||||||
\(946\) | 7.43014 | 0.241575 | ||||||||
\(947\) | −32.2998 | −1.04960 | −0.524802 | − | 0.851224i | \(-0.675861\pi\) | ||||
−0.524802 | + | 0.851224i | \(0.675861\pi\) | |||||||
\(948\) | 49.7956 | 1.61729 | ||||||||
\(949\) | 18.9966 | 0.616655 | ||||||||
\(950\) | −59.5652 | −1.93255 | ||||||||
\(951\) | −21.6448 | −0.701881 | ||||||||
\(952\) | −2.07281 | −0.0671801 | ||||||||
\(953\) | −34.2499 | −1.10946 | −0.554731 | − | 0.832030i | \(-0.687179\pi\) | ||||
−0.554731 | + | 0.832030i | \(0.687179\pi\) | |||||||
\(954\) | −12.8264 | −0.415269 | ||||||||
\(955\) | 18.5871 | 0.601466 | ||||||||
\(956\) | 87.7719 | 2.83875 | ||||||||
\(957\) | −93.9958 | −3.03845 | ||||||||
\(958\) | −10.7477 | −0.347242 | ||||||||
\(959\) | −2.56817 | −0.0829304 | ||||||||
\(960\) | −81.3139 | −2.62439 | ||||||||
\(961\) | −25.7815 | −0.831660 | ||||||||
\(962\) | −68.4726 | −2.20764 | ||||||||
\(963\) | 17.3196 | 0.558116 | ||||||||
\(964\) | −55.0853 | −1.77418 | ||||||||
\(965\) | 30.5199 | 0.982470 | ||||||||
\(966\) | 6.54816 | 0.210684 | ||||||||
\(967\) | −9.48334 | −0.304964 | −0.152482 | − | 0.988306i | \(-0.548727\pi\) | ||||
−0.152482 | + | 0.988306i | \(0.548727\pi\) | |||||||
\(968\) | −81.1554 | −2.60843 | ||||||||
\(969\) | 5.19693 | 0.166949 | ||||||||
\(970\) | −51.0146 | −1.63798 | ||||||||
\(971\) | 0.642932 | 0.0206327 | 0.0103163 | − | 0.999947i | \(-0.496716\pi\) | ||||
0.0103163 | + | 0.999947i | \(0.496716\pi\) | |||||||
\(972\) | −87.6642 | −2.81183 | ||||||||
\(973\) | −8.54925 | −0.274076 | ||||||||
\(974\) | −89.8841 | −2.88007 | ||||||||
\(975\) | 66.5938 | 2.13271 | ||||||||
\(976\) | −12.8184 | −0.410306 | ||||||||
\(977\) | −23.2839 | −0.744919 | −0.372460 | − | 0.928048i | \(-0.621485\pi\) | ||||
−0.372460 | + | 0.928048i | \(0.621485\pi\) | |||||||
\(978\) | 61.3883 | 1.96298 | ||||||||
\(979\) | 80.4714 | 2.57188 | ||||||||
\(980\) | −96.2270 | −3.07386 | ||||||||
\(981\) | 18.2301 | 0.582043 | ||||||||
\(982\) | −32.9757 | −1.05230 | ||||||||
\(983\) | −20.0409 | −0.639204 | −0.319602 | − | 0.947552i | \(-0.603549\pi\) | ||||
−0.319602 | + | 0.947552i | \(0.603549\pi\) | |||||||
\(984\) | −17.0420 | −0.543279 | ||||||||
\(985\) | −39.5339 | −1.25965 | ||||||||
\(986\) | −12.6753 | −0.403665 | ||||||||
\(987\) | −10.7711 | −0.342849 | ||||||||
\(988\) | 34.4878 | 1.09720 | ||||||||
\(989\) | −1.02908 | −0.0327228 | ||||||||
\(990\) | 153.831 | 4.88908 | ||||||||
\(991\) | 19.1982 | 0.609852 | 0.304926 | − | 0.952376i | \(-0.401368\pi\) | ||||
0.304926 | + | 0.952376i | \(0.401368\pi\) | |||||||
\(992\) | 1.59518 | 0.0506470 | ||||||||
\(993\) | −49.1035 | −1.55825 | ||||||||
\(994\) | 5.59813 | 0.177562 | ||||||||
\(995\) | −97.5919 | −3.09387 | ||||||||
\(996\) | −11.6380 | −0.368763 | ||||||||
\(997\) | −47.9412 | −1.51831 | −0.759157 | − | 0.650908i | \(-0.774388\pi\) | ||||
−0.759157 | + | 0.650908i | \(0.774388\pi\) | |||||||
\(998\) | 3.90823 | 0.123713 | ||||||||
\(999\) | 4.93399 | 0.156105 |
(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 | 4019.2.a.b.1.17 | ✓ | 186 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4019.2.a.b.1.17 | ✓ | 186 | 1.1 | even | 1 | trivial |