Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86289 | 1.31726 | 0.658630 | − | 0.752467i | \(-0.271136\pi\) | ||||
0.658630 | + | 0.752467i | \(0.271136\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.47035 | 0.735176 | ||||||||
\(5\) | 4.02931 | 1.80196 | 0.900982 | − | 0.433857i | \(-0.142848\pi\) | ||||
0.900982 | + | 0.433857i | \(0.142848\pi\) | |||||||
\(6\) | −1.86289 | −0.760521 | ||||||||
\(7\) | 3.22519 | 1.21901 | 0.609503 | − | 0.792784i | \(-0.291369\pi\) | ||||
0.609503 | + | 0.792784i | \(0.291369\pi\) | |||||||
\(8\) | −0.986675 | −0.348842 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.50616 | 2.37366 | ||||||||
\(11\) | −3.00398 | −0.905733 | −0.452867 | − | 0.891578i | \(-0.649599\pi\) | ||||
−0.452867 | + | 0.891578i | \(0.649599\pi\) | |||||||
\(12\) | −1.47035 | −0.424454 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 6.00816 | 1.60575 | ||||||||
\(15\) | −4.02931 | −1.04036 | ||||||||
\(16\) | −4.77877 | −1.19469 | ||||||||
\(17\) | 4.28605 | 1.03952 | 0.519760 | − | 0.854312i | \(-0.326021\pi\) | ||||
0.519760 | + | 0.854312i | \(0.326021\pi\) | |||||||
\(18\) | 1.86289 | 0.439087 | ||||||||
\(19\) | −6.27499 | −1.43958 | −0.719791 | − | 0.694191i | \(-0.755762\pi\) | ||||
−0.719791 | + | 0.694191i | \(0.755762\pi\) | |||||||
\(20\) | 5.92451 | 1.32476 | ||||||||
\(21\) | −3.22519 | −0.703794 | ||||||||
\(22\) | −5.59607 | −1.19309 | ||||||||
\(23\) | 7.70305 | 1.60620 | 0.803099 | − | 0.595846i | \(-0.203183\pi\) | ||||
0.803099 | + | 0.595846i | \(0.203183\pi\) | |||||||
\(24\) | 0.986675 | 0.201404 | ||||||||
\(25\) | 11.2354 | 2.24707 | ||||||||
\(26\) | −1.86289 | −0.365342 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.74216 | 0.896184 | ||||||||
\(29\) | −5.15412 | −0.957095 | −0.478548 | − | 0.878062i | \(-0.658837\pi\) | ||||
−0.478548 | + | 0.878062i | \(0.658837\pi\) | |||||||
\(30\) | −7.50616 | −1.37043 | ||||||||
\(31\) | 6.62744 | 1.19032 | 0.595162 | − | 0.803606i | \(-0.297088\pi\) | ||||
0.595162 | + | 0.803606i | \(0.297088\pi\) | |||||||
\(32\) | −6.92896 | −1.22488 | ||||||||
\(33\) | 3.00398 | 0.522925 | ||||||||
\(34\) | 7.98443 | 1.36932 | ||||||||
\(35\) | 12.9953 | 2.19660 | ||||||||
\(36\) | 1.47035 | 0.245059 | ||||||||
\(37\) | 7.68405 | 1.26325 | 0.631625 | − | 0.775274i | \(-0.282388\pi\) | ||||
0.631625 | + | 0.775274i | \(0.282388\pi\) | |||||||
\(38\) | −11.6896 | −1.89630 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −3.97562 | −0.628601 | ||||||||
\(41\) | 1.36900 | 0.213802 | 0.106901 | − | 0.994270i | \(-0.465907\pi\) | ||||
0.106901 | + | 0.994270i | \(0.465907\pi\) | |||||||
\(42\) | −6.00816 | −0.927080 | ||||||||
\(43\) | 10.8702 | 1.65768 | 0.828841 | − | 0.559484i | \(-0.189001\pi\) | ||||
0.828841 | + | 0.559484i | \(0.189001\pi\) | |||||||
\(44\) | −4.41690 | −0.665873 | ||||||||
\(45\) | 4.02931 | 0.600654 | ||||||||
\(46\) | 14.3499 | 2.11578 | ||||||||
\(47\) | 5.13698 | 0.749305 | 0.374653 | − | 0.927165i | \(-0.377762\pi\) | ||||
0.374653 | + | 0.927165i | \(0.377762\pi\) | |||||||
\(48\) | 4.77877 | 0.689756 | ||||||||
\(49\) | 3.40183 | 0.485976 | ||||||||
\(50\) | 20.9302 | 2.95998 | ||||||||
\(51\) | −4.28605 | −0.600167 | ||||||||
\(52\) | −1.47035 | −0.203901 | ||||||||
\(53\) | −0.715373 | −0.0982640 | −0.0491320 | − | 0.998792i | \(-0.515645\pi\) | ||||
−0.0491320 | + | 0.998792i | \(0.515645\pi\) | |||||||
\(54\) | −1.86289 | −0.253507 | ||||||||
\(55\) | −12.1040 | −1.63210 | ||||||||
\(56\) | −3.18221 | −0.425241 | ||||||||
\(57\) | 6.27499 | 0.831143 | ||||||||
\(58\) | −9.60154 | −1.26074 | ||||||||
\(59\) | 4.67528 | 0.608670 | 0.304335 | − | 0.952565i | \(-0.401566\pi\) | ||||
0.304335 | + | 0.952565i | \(0.401566\pi\) | |||||||
\(60\) | −5.92451 | −0.764851 | ||||||||
\(61\) | 1.19246 | 0.152679 | 0.0763395 | − | 0.997082i | \(-0.475677\pi\) | ||||
0.0763395 | + | 0.997082i | \(0.475677\pi\) | |||||||
\(62\) | 12.3462 | 1.56797 | ||||||||
\(63\) | 3.22519 | 0.406335 | ||||||||
\(64\) | −3.35034 | −0.418793 | ||||||||
\(65\) | −4.02931 | −0.499775 | ||||||||
\(66\) | 5.59607 | 0.688829 | ||||||||
\(67\) | −1.94836 | −0.238030 | −0.119015 | − | 0.992892i | \(-0.537974\pi\) | ||||
−0.119015 | + | 0.992892i | \(0.537974\pi\) | |||||||
\(68\) | 6.30200 | 0.764230 | ||||||||
\(69\) | −7.70305 | −0.927338 | ||||||||
\(70\) | 24.2088 | 2.89350 | ||||||||
\(71\) | 8.42340 | 0.999674 | 0.499837 | − | 0.866120i | \(-0.333393\pi\) | ||||
0.499837 | + | 0.866120i | \(0.333393\pi\) | |||||||
\(72\) | −0.986675 | −0.116281 | ||||||||
\(73\) | −12.1934 | −1.42712 | −0.713562 | − | 0.700592i | \(-0.752919\pi\) | ||||
−0.713562 | + | 0.700592i | \(0.752919\pi\) | |||||||
\(74\) | 14.3145 | 1.66403 | ||||||||
\(75\) | −11.2354 | −1.29735 | ||||||||
\(76\) | −9.22644 | −1.05835 | ||||||||
\(77\) | −9.68839 | −1.10409 | ||||||||
\(78\) | 1.86289 | 0.210931 | ||||||||
\(79\) | 4.74780 | 0.534170 | 0.267085 | − | 0.963673i | \(-0.413940\pi\) | ||||
0.267085 | + | 0.963673i | \(0.413940\pi\) | |||||||
\(80\) | −19.2552 | −2.15279 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 2.55030 | 0.281633 | ||||||||
\(83\) | −10.7359 | −1.17842 | −0.589209 | − | 0.807980i | \(-0.700561\pi\) | ||||
−0.589209 | + | 0.807980i | \(0.700561\pi\) | |||||||
\(84\) | −4.74216 | −0.517412 | ||||||||
\(85\) | 17.2698 | 1.87318 | ||||||||
\(86\) | 20.2499 | 2.18360 | ||||||||
\(87\) | 5.15412 | 0.552579 | ||||||||
\(88\) | 2.96395 | 0.315958 | ||||||||
\(89\) | −3.76088 | −0.398652 | −0.199326 | − | 0.979933i | \(-0.563875\pi\) | ||||
−0.199326 | + | 0.979933i | \(0.563875\pi\) | |||||||
\(90\) | 7.50616 | 0.791218 | ||||||||
\(91\) | −3.22519 | −0.338092 | ||||||||
\(92\) | 11.3262 | 1.18084 | ||||||||
\(93\) | −6.62744 | −0.687234 | ||||||||
\(94\) | 9.56962 | 0.987031 | ||||||||
\(95\) | −25.2839 | −2.59407 | ||||||||
\(96\) | 6.92896 | 0.707184 | ||||||||
\(97\) | −8.35697 | −0.848521 | −0.424261 | − | 0.905540i | \(-0.639466\pi\) | ||||
−0.424261 | + | 0.905540i | \(0.639466\pi\) | |||||||
\(98\) | 6.33724 | 0.640158 | ||||||||
\(99\) | −3.00398 | −0.301911 | ||||||||
\(100\) | 16.5199 | 1.65199 | ||||||||
\(101\) | −8.27275 | −0.823170 | −0.411585 | − | 0.911371i | \(-0.635025\pi\) | ||||
−0.411585 | + | 0.911371i | \(0.635025\pi\) | |||||||
\(102\) | −7.98443 | −0.790577 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | 0.986675 | 0.0967514 | ||||||||
\(105\) | −12.9953 | −1.26821 | ||||||||
\(106\) | −1.33266 | −0.129439 | ||||||||
\(107\) | 10.1157 | 0.977917 | 0.488959 | − | 0.872307i | \(-0.337377\pi\) | ||||
0.488959 | + | 0.872307i | \(0.337377\pi\) | |||||||
\(108\) | −1.47035 | −0.141485 | ||||||||
\(109\) | −14.5820 | −1.39670 | −0.698351 | − | 0.715756i | \(-0.746082\pi\) | ||||
−0.698351 | + | 0.715756i | \(0.746082\pi\) | |||||||
\(110\) | −22.5483 | −2.14990 | ||||||||
\(111\) | −7.68405 | −0.729338 | ||||||||
\(112\) | −15.4124 | −1.45634 | ||||||||
\(113\) | −7.92776 | −0.745780 | −0.372890 | − | 0.927875i | \(-0.621633\pi\) | ||||
−0.372890 | + | 0.927875i | \(0.621633\pi\) | |||||||
\(114\) | 11.6896 | 1.09483 | ||||||||
\(115\) | 31.0380 | 2.89431 | ||||||||
\(116\) | −7.57836 | −0.703633 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 8.70953 | 0.801777 | ||||||||
\(119\) | 13.8233 | 1.26718 | ||||||||
\(120\) | 3.97562 | 0.362923 | ||||||||
\(121\) | −1.97612 | −0.179647 | ||||||||
\(122\) | 2.22142 | 0.201118 | ||||||||
\(123\) | −1.36900 | −0.123439 | ||||||||
\(124\) | 9.74467 | 0.875097 | ||||||||
\(125\) | 25.1242 | 2.24718 | ||||||||
\(126\) | 6.00816 | 0.535250 | ||||||||
\(127\) | 4.36807 | 0.387604 | 0.193802 | − | 0.981041i | \(-0.437918\pi\) | ||||
0.193802 | + | 0.981041i | \(0.437918\pi\) | |||||||
\(128\) | 7.61661 | 0.673220 | ||||||||
\(129\) | −10.8702 | −0.957063 | ||||||||
\(130\) | −7.50616 | −0.658334 | ||||||||
\(131\) | 12.5592 | 1.09730 | 0.548651 | − | 0.836052i | \(-0.315142\pi\) | ||||
0.548651 | + | 0.836052i | \(0.315142\pi\) | |||||||
\(132\) | 4.41690 | 0.384442 | ||||||||
\(133\) | −20.2380 | −1.75486 | ||||||||
\(134\) | −3.62957 | −0.313547 | ||||||||
\(135\) | −4.02931 | −0.346788 | ||||||||
\(136\) | −4.22894 | −0.362628 | ||||||||
\(137\) | −13.2503 | −1.13205 | −0.566024 | − | 0.824389i | \(-0.691519\pi\) | ||||
−0.566024 | + | 0.824389i | \(0.691519\pi\) | |||||||
\(138\) | −14.3499 | −1.22155 | ||||||||
\(139\) | 12.9235 | 1.09616 | 0.548080 | − | 0.836426i | \(-0.315359\pi\) | ||||
0.548080 | + | 0.836426i | \(0.315359\pi\) | |||||||
\(140\) | 19.1076 | 1.61489 | ||||||||
\(141\) | −5.13698 | −0.432612 | ||||||||
\(142\) | 15.6919 | 1.31683 | ||||||||
\(143\) | 3.00398 | 0.251205 | ||||||||
\(144\) | −4.77877 | −0.398231 | ||||||||
\(145\) | −20.7675 | −1.72465 | ||||||||
\(146\) | −22.7149 | −1.87990 | ||||||||
\(147\) | −3.40183 | −0.280579 | ||||||||
\(148\) | 11.2983 | 0.928711 | ||||||||
\(149\) | 1.14194 | 0.0935514 | 0.0467757 | − | 0.998905i | \(-0.485105\pi\) | ||||
0.0467757 | + | 0.998905i | \(0.485105\pi\) | |||||||
\(150\) | −20.9302 | −1.70894 | ||||||||
\(151\) | −10.3512 | −0.842366 | −0.421183 | − | 0.906976i | \(-0.638385\pi\) | ||||
−0.421183 | + | 0.906976i | \(0.638385\pi\) | |||||||
\(152\) | 6.19137 | 0.502187 | ||||||||
\(153\) | 4.28605 | 0.346507 | ||||||||
\(154\) | −18.0484 | −1.45438 | ||||||||
\(155\) | 26.7040 | 2.14492 | ||||||||
\(156\) | 1.47035 | 0.117722 | ||||||||
\(157\) | −11.7224 | −0.935552 | −0.467776 | − | 0.883847i | \(-0.654945\pi\) | ||||
−0.467776 | + | 0.883847i | \(0.654945\pi\) | |||||||
\(158\) | 8.84462 | 0.703641 | ||||||||
\(159\) | 0.715373 | 0.0567327 | ||||||||
\(160\) | −27.9189 | −2.20719 | ||||||||
\(161\) | 24.8438 | 1.95796 | ||||||||
\(162\) | 1.86289 | 0.146362 | ||||||||
\(163\) | 13.6038 | 1.06553 | 0.532766 | − | 0.846262i | \(-0.321152\pi\) | ||||
0.532766 | + | 0.846262i | \(0.321152\pi\) | |||||||
\(164\) | 2.01292 | 0.157182 | ||||||||
\(165\) | 12.1040 | 0.942292 | ||||||||
\(166\) | −19.9998 | −1.55229 | ||||||||
\(167\) | −7.81237 | −0.604540 | −0.302270 | − | 0.953222i | \(-0.597744\pi\) | ||||
−0.302270 | + | 0.953222i | \(0.597744\pi\) | |||||||
\(168\) | 3.18221 | 0.245513 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 32.1718 | 2.46746 | ||||||||
\(171\) | −6.27499 | −0.479860 | ||||||||
\(172\) | 15.9829 | 1.21869 | ||||||||
\(173\) | 11.6753 | 0.887653 | 0.443826 | − | 0.896113i | \(-0.353621\pi\) | ||||
0.443826 | + | 0.896113i | \(0.353621\pi\) | |||||||
\(174\) | 9.60154 | 0.727891 | ||||||||
\(175\) | 36.2361 | 2.73919 | ||||||||
\(176\) | 14.3553 | 1.08207 | ||||||||
\(177\) | −4.67528 | −0.351416 | ||||||||
\(178\) | −7.00609 | −0.525129 | ||||||||
\(179\) | −26.0265 | −1.94531 | −0.972654 | − | 0.232258i | \(-0.925389\pi\) | ||||
−0.972654 | + | 0.232258i | \(0.925389\pi\) | |||||||
\(180\) | 5.92451 | 0.441587 | ||||||||
\(181\) | −7.07137 | −0.525611 | −0.262805 | − | 0.964849i | \(-0.584648\pi\) | ||||
−0.262805 | + | 0.964849i | \(0.584648\pi\) | |||||||
\(182\) | −6.00816 | −0.445355 | ||||||||
\(183\) | −1.19246 | −0.0881492 | ||||||||
\(184\) | −7.60041 | −0.560309 | ||||||||
\(185\) | 30.9614 | 2.27633 | ||||||||
\(186\) | −12.3462 | −0.905266 | ||||||||
\(187\) | −12.8752 | −0.941528 | ||||||||
\(188\) | 7.55317 | 0.550871 | ||||||||
\(189\) | −3.22519 | −0.234598 | ||||||||
\(190\) | −47.1011 | −3.41707 | ||||||||
\(191\) | 10.1201 | 0.732264 | 0.366132 | − | 0.930563i | \(-0.380682\pi\) | ||||
0.366132 | + | 0.930563i | \(0.380682\pi\) | |||||||
\(192\) | 3.35034 | 0.241790 | ||||||||
\(193\) | −17.7397 | −1.27693 | −0.638465 | − | 0.769651i | \(-0.720430\pi\) | ||||
−0.638465 | + | 0.769651i | \(0.720430\pi\) | |||||||
\(194\) | −15.5681 | −1.11772 | ||||||||
\(195\) | 4.02931 | 0.288545 | ||||||||
\(196\) | 5.00189 | 0.357278 | ||||||||
\(197\) | −13.0312 | −0.928434 | −0.464217 | − | 0.885721i | \(-0.653664\pi\) | ||||
−0.464217 | + | 0.885721i | \(0.653664\pi\) | |||||||
\(198\) | −5.59607 | −0.397696 | ||||||||
\(199\) | 20.8216 | 1.47600 | 0.738002 | − | 0.674798i | \(-0.235769\pi\) | ||||
0.738002 | + | 0.674798i | \(0.235769\pi\) | |||||||
\(200\) | −11.0856 | −0.783873 | ||||||||
\(201\) | 1.94836 | 0.137426 | ||||||||
\(202\) | −15.4112 | −1.08433 | ||||||||
\(203\) | −16.6230 | −1.16671 | ||||||||
\(204\) | −6.30200 | −0.441228 | ||||||||
\(205\) | 5.51614 | 0.385264 | ||||||||
\(206\) | 1.86289 | 0.129794 | ||||||||
\(207\) | 7.70305 | 0.535399 | ||||||||
\(208\) | 4.77877 | 0.331348 | ||||||||
\(209\) | 18.8499 | 1.30388 | ||||||||
\(210\) | −24.2088 | −1.67056 | ||||||||
\(211\) | −5.21341 | −0.358906 | −0.179453 | − | 0.983767i | \(-0.557433\pi\) | ||||
−0.179453 | + | 0.983767i | \(0.557433\pi\) | |||||||
\(212\) | −1.05185 | −0.0722413 | ||||||||
\(213\) | −8.42340 | −0.577162 | ||||||||
\(214\) | 18.8443 | 1.28817 | ||||||||
\(215\) | 43.7992 | 2.98708 | ||||||||
\(216\) | 0.986675 | 0.0671347 | ||||||||
\(217\) | 21.3747 | 1.45101 | ||||||||
\(218\) | −27.1646 | −1.83982 | ||||||||
\(219\) | 12.1934 | 0.823951 | ||||||||
\(220\) | −17.7971 | −1.19988 | ||||||||
\(221\) | −4.28605 | −0.288311 | ||||||||
\(222\) | −14.3145 | −0.960728 | ||||||||
\(223\) | 0.912908 | 0.0611329 | 0.0305664 | − | 0.999533i | \(-0.490269\pi\) | ||||
0.0305664 | + | 0.999533i | \(0.490269\pi\) | |||||||
\(224\) | −22.3472 | −1.49314 | ||||||||
\(225\) | 11.2354 | 0.749024 | ||||||||
\(226\) | −14.7685 | −0.982387 | ||||||||
\(227\) | −16.4016 | −1.08861 | −0.544305 | − | 0.838887i | \(-0.683207\pi\) | ||||
−0.544305 | + | 0.838887i | \(0.683207\pi\) | |||||||
\(228\) | 9.22644 | 0.611036 | ||||||||
\(229\) | 25.9445 | 1.71446 | 0.857231 | − | 0.514932i | \(-0.172183\pi\) | ||||
0.857231 | + | 0.514932i | \(0.172183\pi\) | |||||||
\(230\) | 57.8203 | 3.81256 | ||||||||
\(231\) | 9.68839 | 0.637449 | ||||||||
\(232\) | 5.08544 | 0.333875 | ||||||||
\(233\) | −10.7098 | −0.701622 | −0.350811 | − | 0.936446i | \(-0.614094\pi\) | ||||
−0.350811 | + | 0.936446i | \(0.614094\pi\) | |||||||
\(234\) | −1.86289 | −0.121781 | ||||||||
\(235\) | 20.6985 | 1.35022 | ||||||||
\(236\) | 6.87431 | 0.447480 | ||||||||
\(237\) | −4.74780 | −0.308403 | ||||||||
\(238\) | 25.7513 | 1.66921 | ||||||||
\(239\) | −3.15424 | −0.204031 | −0.102015 | − | 0.994783i | \(-0.532529\pi\) | ||||
−0.102015 | + | 0.994783i | \(0.532529\pi\) | |||||||
\(240\) | 19.2552 | 1.24291 | ||||||||
\(241\) | −0.587519 | −0.0378454 | −0.0189227 | − | 0.999821i | \(-0.506024\pi\) | ||||
−0.0189227 | + | 0.999821i | \(0.506024\pi\) | |||||||
\(242\) | −3.68129 | −0.236642 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.75334 | 0.112246 | ||||||||
\(245\) | 13.7071 | 0.875712 | ||||||||
\(246\) | −2.55030 | −0.162601 | ||||||||
\(247\) | 6.27499 | 0.399268 | ||||||||
\(248\) | −6.53913 | −0.415235 | ||||||||
\(249\) | 10.7359 | 0.680360 | ||||||||
\(250\) | 46.8036 | 2.96012 | ||||||||
\(251\) | −18.6666 | −1.17822 | −0.589112 | − | 0.808051i | \(-0.700522\pi\) | ||||
−0.589112 | + | 0.808051i | \(0.700522\pi\) | |||||||
\(252\) | 4.74216 | 0.298728 | ||||||||
\(253\) | −23.1398 | −1.45479 | ||||||||
\(254\) | 8.13723 | 0.510575 | ||||||||
\(255\) | −17.2698 | −1.08148 | ||||||||
\(256\) | 20.8896 | 1.30560 | ||||||||
\(257\) | 25.3211 | 1.57948 | 0.789742 | − | 0.613439i | \(-0.210214\pi\) | ||||
0.789742 | + | 0.613439i | \(0.210214\pi\) | |||||||
\(258\) | −20.2499 | −1.26070 | ||||||||
\(259\) | 24.7825 | 1.53991 | ||||||||
\(260\) | −5.92451 | −0.367422 | ||||||||
\(261\) | −5.15412 | −0.319032 | ||||||||
\(262\) | 23.3964 | 1.44543 | ||||||||
\(263\) | −9.86212 | −0.608124 | −0.304062 | − | 0.952652i | \(-0.598343\pi\) | ||||
−0.304062 | + | 0.952652i | \(0.598343\pi\) | |||||||
\(264\) | −2.96395 | −0.182418 | ||||||||
\(265\) | −2.88246 | −0.177068 | ||||||||
\(266\) | −37.7012 | −2.31161 | ||||||||
\(267\) | 3.76088 | 0.230162 | ||||||||
\(268\) | −2.86477 | −0.174994 | ||||||||
\(269\) | 23.6713 | 1.44326 | 0.721631 | − | 0.692278i | \(-0.243393\pi\) | ||||
0.721631 | + | 0.692278i | \(0.243393\pi\) | |||||||
\(270\) | −7.50616 | −0.456810 | ||||||||
\(271\) | −9.87442 | −0.599828 | −0.299914 | − | 0.953966i | \(-0.596958\pi\) | ||||
−0.299914 | + | 0.953966i | \(0.596958\pi\) | |||||||
\(272\) | −20.4820 | −1.24191 | ||||||||
\(273\) | 3.22519 | 0.195197 | ||||||||
\(274\) | −24.6838 | −1.49120 | ||||||||
\(275\) | −33.7508 | −2.03525 | ||||||||
\(276\) | −11.3262 | −0.681757 | ||||||||
\(277\) | 16.4259 | 0.986934 | 0.493467 | − | 0.869764i | \(-0.335729\pi\) | ||||
0.493467 | + | 0.869764i | \(0.335729\pi\) | |||||||
\(278\) | 24.0751 | 1.44393 | ||||||||
\(279\) | 6.62744 | 0.396775 | ||||||||
\(280\) | −12.8221 | −0.766269 | ||||||||
\(281\) | −22.0337 | −1.31442 | −0.657211 | − | 0.753706i | \(-0.728264\pi\) | ||||
−0.657211 | + | 0.753706i | \(0.728264\pi\) | |||||||
\(282\) | −9.56962 | −0.569862 | ||||||||
\(283\) | 5.97027 | 0.354896 | 0.177448 | − | 0.984130i | \(-0.443216\pi\) | ||||
0.177448 | + | 0.984130i | \(0.443216\pi\) | |||||||
\(284\) | 12.3854 | 0.734936 | ||||||||
\(285\) | 25.2839 | 1.49769 | ||||||||
\(286\) | 5.59607 | 0.330903 | ||||||||
\(287\) | 4.41529 | 0.260626 | ||||||||
\(288\) | −6.92896 | −0.408293 | ||||||||
\(289\) | 1.37022 | 0.0806014 | ||||||||
\(290\) | −38.6876 | −2.27181 | ||||||||
\(291\) | 8.35697 | 0.489894 | ||||||||
\(292\) | −17.9285 | −1.04919 | ||||||||
\(293\) | −14.3699 | −0.839500 | −0.419750 | − | 0.907640i | \(-0.637882\pi\) | ||||
−0.419750 | + | 0.907640i | \(0.637882\pi\) | |||||||
\(294\) | −6.33724 | −0.369595 | ||||||||
\(295\) | 18.8382 | 1.09680 | ||||||||
\(296\) | −7.58166 | −0.440675 | ||||||||
\(297\) | 3.00398 | 0.174308 | ||||||||
\(298\) | 2.12731 | 0.123232 | ||||||||
\(299\) | −7.70305 | −0.445479 | ||||||||
\(300\) | −16.5199 | −0.953778 | ||||||||
\(301\) | 35.0583 | 2.02073 | ||||||||
\(302\) | −19.2831 | −1.10962 | ||||||||
\(303\) | 8.27275 | 0.475257 | ||||||||
\(304\) | 29.9867 | 1.71986 | ||||||||
\(305\) | 4.80480 | 0.275122 | ||||||||
\(306\) | 7.98443 | 0.456440 | ||||||||
\(307\) | −13.9995 | −0.798994 | −0.399497 | − | 0.916734i | \(-0.630815\pi\) | ||||
−0.399497 | + | 0.916734i | \(0.630815\pi\) | |||||||
\(308\) | −14.2453 | −0.811704 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 49.7466 | 2.82542 | ||||||||
\(311\) | 11.4607 | 0.649879 | 0.324939 | − | 0.945735i | \(-0.394656\pi\) | ||||
0.324939 | + | 0.945735i | \(0.394656\pi\) | |||||||
\(312\) | −0.986675 | −0.0558595 | ||||||||
\(313\) | −23.7411 | −1.34193 | −0.670964 | − | 0.741490i | \(-0.734119\pi\) | ||||
−0.670964 | + | 0.741490i | \(0.734119\pi\) | |||||||
\(314\) | −21.8376 | −1.23237 | ||||||||
\(315\) | 12.9953 | 0.732201 | ||||||||
\(316\) | 6.98094 | 0.392709 | ||||||||
\(317\) | −23.4510 | −1.31714 | −0.658571 | − | 0.752519i | \(-0.728839\pi\) | ||||
−0.658571 | + | 0.752519i | \(0.728839\pi\) | |||||||
\(318\) | 1.33266 | 0.0747318 | ||||||||
\(319\) | 15.4828 | 0.866873 | ||||||||
\(320\) | −13.4996 | −0.754649 | ||||||||
\(321\) | −10.1157 | −0.564601 | ||||||||
\(322\) | 46.2812 | 2.57915 | ||||||||
\(323\) | −26.8949 | −1.49647 | ||||||||
\(324\) | 1.47035 | 0.0816862 | ||||||||
\(325\) | −11.2354 | −0.623225 | ||||||||
\(326\) | 25.3424 | 1.40358 | ||||||||
\(327\) | 14.5820 | 0.806386 | ||||||||
\(328\) | −1.35076 | −0.0745833 | ||||||||
\(329\) | 16.5677 | 0.913408 | ||||||||
\(330\) | 22.5483 | 1.24124 | ||||||||
\(331\) | −21.6288 | −1.18883 | −0.594413 | − | 0.804160i | \(-0.702616\pi\) | ||||
−0.594413 | + | 0.804160i | \(0.702616\pi\) | |||||||
\(332\) | −15.7856 | −0.866345 | ||||||||
\(333\) | 7.68405 | 0.421083 | ||||||||
\(334\) | −14.5536 | −0.796336 | ||||||||
\(335\) | −7.85054 | −0.428921 | ||||||||
\(336\) | 15.4124 | 0.840817 | ||||||||
\(337\) | 15.6903 | 0.854704 | 0.427352 | − | 0.904085i | \(-0.359446\pi\) | ||||
0.427352 | + | 0.904085i | \(0.359446\pi\) | |||||||
\(338\) | 1.86289 | 0.101328 | ||||||||
\(339\) | 7.92776 | 0.430577 | ||||||||
\(340\) | 25.3927 | 1.37711 | ||||||||
\(341\) | −19.9087 | −1.07812 | ||||||||
\(342\) | −11.6896 | −0.632101 | ||||||||
\(343\) | −11.6048 | −0.626598 | ||||||||
\(344\) | −10.7253 | −0.578270 | ||||||||
\(345\) | −31.0380 | −1.67103 | ||||||||
\(346\) | 21.7497 | 1.16927 | ||||||||
\(347\) | 4.44235 | 0.238478 | 0.119239 | − | 0.992866i | \(-0.461955\pi\) | ||||
0.119239 | + | 0.992866i | \(0.461955\pi\) | |||||||
\(348\) | 7.57836 | 0.406243 | ||||||||
\(349\) | −33.5600 | −1.79642 | −0.898212 | − | 0.439563i | \(-0.855133\pi\) | ||||
−0.898212 | + | 0.439563i | \(0.855133\pi\) | |||||||
\(350\) | 67.5039 | 3.60823 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 20.8144 | 1.10941 | ||||||||
\(353\) | −26.8168 | −1.42731 | −0.713657 | − | 0.700496i | \(-0.752962\pi\) | ||||
−0.713657 | + | 0.700496i | \(0.752962\pi\) | |||||||
\(354\) | −8.70953 | −0.462906 | ||||||||
\(355\) | 33.9405 | 1.80138 | ||||||||
\(356\) | −5.52981 | −0.293079 | ||||||||
\(357\) | −13.8233 | −0.731607 | ||||||||
\(358\) | −48.4844 | −2.56248 | ||||||||
\(359\) | 10.5956 | 0.559215 | 0.279608 | − | 0.960114i | \(-0.409796\pi\) | ||||
0.279608 | + | 0.960114i | \(0.409796\pi\) | |||||||
\(360\) | −3.97562 | −0.209534 | ||||||||
\(361\) | 20.3755 | 1.07239 | ||||||||
\(362\) | −13.1732 | −0.692367 | ||||||||
\(363\) | 1.97612 | 0.103719 | ||||||||
\(364\) | −4.74216 | −0.248557 | ||||||||
\(365\) | −49.1309 | −2.57163 | ||||||||
\(366\) | −2.22142 | −0.116116 | ||||||||
\(367\) | −23.0186 | −1.20156 | −0.600781 | − | 0.799413i | \(-0.705144\pi\) | ||||
−0.600781 | + | 0.799413i | \(0.705144\pi\) | |||||||
\(368\) | −36.8111 | −1.91891 | ||||||||
\(369\) | 1.36900 | 0.0712674 | ||||||||
\(370\) | 57.6777 | 2.99852 | ||||||||
\(371\) | −2.30721 | −0.119784 | ||||||||
\(372\) | −9.74467 | −0.505238 | ||||||||
\(373\) | −16.6741 | −0.863352 | −0.431676 | − | 0.902029i | \(-0.642078\pi\) | ||||
−0.431676 | + | 0.902029i | \(0.642078\pi\) | |||||||
\(374\) | −23.9851 | −1.24024 | ||||||||
\(375\) | −25.1242 | −1.29741 | ||||||||
\(376\) | −5.06853 | −0.261389 | ||||||||
\(377\) | 5.15412 | 0.265450 | ||||||||
\(378\) | −6.00816 | −0.309027 | ||||||||
\(379\) | 16.4198 | 0.843427 | 0.421713 | − | 0.906729i | \(-0.361429\pi\) | ||||
0.421713 | + | 0.906729i | \(0.361429\pi\) | |||||||
\(380\) | −37.1762 | −1.90710 | ||||||||
\(381\) | −4.36807 | −0.223783 | ||||||||
\(382\) | 18.8526 | 0.964582 | ||||||||
\(383\) | 12.9842 | 0.663464 | 0.331732 | − | 0.943374i | \(-0.392367\pi\) | ||||
0.331732 | + | 0.943374i | \(0.392367\pi\) | |||||||
\(384\) | −7.61661 | −0.388684 | ||||||||
\(385\) | −39.0375 | −1.98954 | ||||||||
\(386\) | −33.0470 | −1.68205 | ||||||||
\(387\) | 10.8702 | 0.552561 | ||||||||
\(388\) | −12.2877 | −0.623812 | ||||||||
\(389\) | 29.9070 | 1.51634 | 0.758172 | − | 0.652054i | \(-0.226093\pi\) | ||||
0.758172 | + | 0.652054i | \(0.226093\pi\) | |||||||
\(390\) | 7.50616 | 0.380089 | ||||||||
\(391\) | 33.0157 | 1.66967 | ||||||||
\(392\) | −3.35651 | −0.169529 | ||||||||
\(393\) | −12.5592 | −0.633527 | ||||||||
\(394\) | −24.2757 | −1.22299 | ||||||||
\(395\) | 19.1304 | 0.962554 | ||||||||
\(396\) | −4.41690 | −0.221958 | ||||||||
\(397\) | 3.42665 | 0.171979 | 0.0859894 | − | 0.996296i | \(-0.472595\pi\) | ||||
0.0859894 | + | 0.996296i | \(0.472595\pi\) | |||||||
\(398\) | 38.7883 | 1.94428 | ||||||||
\(399\) | 20.2380 | 1.01317 | ||||||||
\(400\) | −53.6912 | −2.68456 | ||||||||
\(401\) | −31.5411 | −1.57509 | −0.787543 | − | 0.616260i | \(-0.788647\pi\) | ||||
−0.787543 | + | 0.616260i | \(0.788647\pi\) | |||||||
\(402\) | 3.62957 | 0.181026 | ||||||||
\(403\) | −6.62744 | −0.330136 | ||||||||
\(404\) | −12.1639 | −0.605175 | ||||||||
\(405\) | 4.02931 | 0.200218 | ||||||||
\(406\) | −30.9668 | −1.53685 | ||||||||
\(407\) | −23.0827 | −1.14417 | ||||||||
\(408\) | 4.22894 | 0.209364 | ||||||||
\(409\) | 31.5101 | 1.55808 | 0.779038 | − | 0.626977i | \(-0.215708\pi\) | ||||
0.779038 | + | 0.626977i | \(0.215708\pi\) | |||||||
\(410\) | 10.2759 | 0.507493 | ||||||||
\(411\) | 13.2503 | 0.653588 | ||||||||
\(412\) | 1.47035 | 0.0724390 | ||||||||
\(413\) | 15.0787 | 0.741973 | ||||||||
\(414\) | 14.3499 | 0.705260 | ||||||||
\(415\) | −43.2583 | −2.12347 | ||||||||
\(416\) | 6.92896 | 0.339720 | ||||||||
\(417\) | −12.9235 | −0.632868 | ||||||||
\(418\) | 35.1153 | 1.71755 | ||||||||
\(419\) | 20.3897 | 0.996104 | 0.498052 | − | 0.867147i | \(-0.334049\pi\) | ||||
0.498052 | + | 0.867147i | \(0.334049\pi\) | |||||||
\(420\) | −19.1076 | −0.932358 | ||||||||
\(421\) | −21.3544 | −1.04075 | −0.520376 | − | 0.853937i | \(-0.674208\pi\) | ||||
−0.520376 | + | 0.853937i | \(0.674208\pi\) | |||||||
\(422\) | −9.71199 | −0.472772 | ||||||||
\(423\) | 5.13698 | 0.249768 | ||||||||
\(424\) | 0.705840 | 0.0342786 | ||||||||
\(425\) | 48.1553 | 2.33588 | ||||||||
\(426\) | −15.6919 | −0.760273 | ||||||||
\(427\) | 3.84591 | 0.186117 | ||||||||
\(428\) | 14.8736 | 0.718941 | ||||||||
\(429\) | −3.00398 | −0.145033 | ||||||||
\(430\) | 81.5931 | 3.93477 | ||||||||
\(431\) | 3.08838 | 0.148762 | 0.0743810 | − | 0.997230i | \(-0.476302\pi\) | ||||
0.0743810 | + | 0.997230i | \(0.476302\pi\) | |||||||
\(432\) | 4.77877 | 0.229919 | ||||||||
\(433\) | −19.0477 | −0.915375 | −0.457688 | − | 0.889113i | \(-0.651322\pi\) | ||||
−0.457688 | + | 0.889113i | \(0.651322\pi\) | |||||||
\(434\) | 39.8188 | 1.91136 | ||||||||
\(435\) | 20.7675 | 0.995727 | ||||||||
\(436\) | −21.4407 | −1.02682 | ||||||||
\(437\) | −48.3366 | −2.31225 | ||||||||
\(438\) | 22.7149 | 1.08536 | ||||||||
\(439\) | 32.9555 | 1.57288 | 0.786441 | − | 0.617665i | \(-0.211921\pi\) | ||||
0.786441 | + | 0.617665i | \(0.211921\pi\) | |||||||
\(440\) | 11.9427 | 0.569345 | ||||||||
\(441\) | 3.40183 | 0.161992 | ||||||||
\(442\) | −7.98443 | −0.379781 | ||||||||
\(443\) | 17.7006 | 0.840980 | 0.420490 | − | 0.907297i | \(-0.361858\pi\) | ||||
0.420490 | + | 0.907297i | \(0.361858\pi\) | |||||||
\(444\) | −11.2983 | −0.536192 | ||||||||
\(445\) | −15.1537 | −0.718356 | ||||||||
\(446\) | 1.70065 | 0.0805279 | ||||||||
\(447\) | −1.14194 | −0.0540119 | ||||||||
\(448\) | −10.8055 | −0.510511 | ||||||||
\(449\) | 10.8535 | 0.512210 | 0.256105 | − | 0.966649i | \(-0.417561\pi\) | ||||
0.256105 | + | 0.966649i | \(0.417561\pi\) | |||||||
\(450\) | 20.9302 | 0.986660 | ||||||||
\(451\) | −4.11245 | −0.193648 | ||||||||
\(452\) | −11.6566 | −0.548280 | ||||||||
\(453\) | 10.3512 | 0.486340 | ||||||||
\(454\) | −30.5543 | −1.43398 | ||||||||
\(455\) | −12.9953 | −0.609228 | ||||||||
\(456\) | −6.19137 | −0.289938 | ||||||||
\(457\) | 10.0687 | 0.470994 | 0.235497 | − | 0.971875i | \(-0.424328\pi\) | ||||
0.235497 | + | 0.971875i | \(0.424328\pi\) | |||||||
\(458\) | 48.3317 | 2.25839 | ||||||||
\(459\) | −4.28605 | −0.200056 | ||||||||
\(460\) | 45.6368 | 2.12783 | ||||||||
\(461\) | −12.4728 | −0.580916 | −0.290458 | − | 0.956888i | \(-0.593808\pi\) | ||||
−0.290458 | + | 0.956888i | \(0.593808\pi\) | |||||||
\(462\) | 18.0484 | 0.839687 | ||||||||
\(463\) | 41.9870 | 1.95130 | 0.975650 | − | 0.219335i | \(-0.0703887\pi\) | ||||
0.975650 | + | 0.219335i | \(0.0703887\pi\) | |||||||
\(464\) | 24.6303 | 1.14343 | ||||||||
\(465\) | −26.7040 | −1.23837 | ||||||||
\(466\) | −19.9512 | −0.924220 | ||||||||
\(467\) | −18.8748 | −0.873421 | −0.436711 | − | 0.899602i | \(-0.643857\pi\) | ||||
−0.436711 | + | 0.899602i | \(0.643857\pi\) | |||||||
\(468\) | −1.47035 | −0.0679670 | ||||||||
\(469\) | −6.28381 | −0.290160 | ||||||||
\(470\) | 38.5590 | 1.77859 | ||||||||
\(471\) | 11.7224 | 0.540141 | ||||||||
\(472\) | −4.61298 | −0.212330 | ||||||||
\(473\) | −32.6537 | −1.50142 | ||||||||
\(474\) | −8.84462 | −0.406247 | ||||||||
\(475\) | −70.5017 | −3.23484 | ||||||||
\(476\) | 20.3251 | 0.931601 | ||||||||
\(477\) | −0.715373 | −0.0327547 | ||||||||
\(478\) | −5.87599 | −0.268762 | ||||||||
\(479\) | −11.5599 | −0.528187 | −0.264094 | − | 0.964497i | \(-0.585073\pi\) | ||||
−0.264094 | + | 0.964497i | \(0.585073\pi\) | |||||||
\(480\) | 27.9189 | 1.27432 | ||||||||
\(481\) | −7.68405 | −0.350363 | ||||||||
\(482\) | −1.09448 | −0.0498523 | ||||||||
\(483\) | −24.8438 | −1.13043 | ||||||||
\(484\) | −2.90559 | −0.132072 | ||||||||
\(485\) | −33.6728 | −1.52900 | ||||||||
\(486\) | −1.86289 | −0.0845023 | ||||||||
\(487\) | 6.09228 | 0.276068 | 0.138034 | − | 0.990428i | \(-0.455922\pi\) | ||||
0.138034 | + | 0.990428i | \(0.455922\pi\) | |||||||
\(488\) | −1.17657 | −0.0532609 | ||||||||
\(489\) | −13.6038 | −0.615185 | ||||||||
\(490\) | 25.5347 | 1.15354 | ||||||||
\(491\) | 12.5778 | 0.567627 | 0.283813 | − | 0.958880i | \(-0.408400\pi\) | ||||
0.283813 | + | 0.958880i | \(0.408400\pi\) | |||||||
\(492\) | −2.01292 | −0.0907492 | ||||||||
\(493\) | −22.0908 | −0.994919 | ||||||||
\(494\) | 11.6896 | 0.525940 | ||||||||
\(495\) | −12.1040 | −0.544033 | ||||||||
\(496\) | −31.6710 | −1.42207 | ||||||||
\(497\) | 27.1670 | 1.21861 | ||||||||
\(498\) | 19.9998 | 0.896212 | ||||||||
\(499\) | −31.4576 | −1.40823 | −0.704117 | − | 0.710084i | \(-0.748657\pi\) | ||||
−0.704117 | + | 0.710084i | \(0.748657\pi\) | |||||||
\(500\) | 36.9414 | 1.65207 | ||||||||
\(501\) | 7.81237 | 0.349031 | ||||||||
\(502\) | −34.7737 | −1.55203 | ||||||||
\(503\) | −35.1741 | −1.56833 | −0.784167 | − | 0.620549i | \(-0.786910\pi\) | ||||
−0.784167 | + | 0.620549i | \(0.786910\pi\) | |||||||
\(504\) | −3.18221 | −0.141747 | ||||||||
\(505\) | −33.3335 | −1.48332 | ||||||||
\(506\) | −43.1068 | −1.91633 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 6.42260 | 0.284957 | ||||||||
\(509\) | 18.2079 | 0.807052 | 0.403526 | − | 0.914968i | \(-0.367785\pi\) | ||||
0.403526 | + | 0.914968i | \(0.367785\pi\) | |||||||
\(510\) | −32.1718 | −1.42459 | ||||||||
\(511\) | −39.3259 | −1.73967 | ||||||||
\(512\) | 23.6817 | 1.04659 | ||||||||
\(513\) | 6.27499 | 0.277048 | ||||||||
\(514\) | 47.1703 | 2.08059 | ||||||||
\(515\) | 4.02931 | 0.177553 | ||||||||
\(516\) | −15.9829 | −0.703610 | ||||||||
\(517\) | −15.4314 | −0.678671 | ||||||||
\(518\) | 46.1670 | 2.02846 | ||||||||
\(519\) | −11.6753 | −0.512487 | ||||||||
\(520\) | 3.97562 | 0.174343 | ||||||||
\(521\) | −19.3930 | −0.849622 | −0.424811 | − | 0.905282i | \(-0.639659\pi\) | ||||
−0.424811 | + | 0.905282i | \(0.639659\pi\) | |||||||
\(522\) | −9.60154 | −0.420248 | ||||||||
\(523\) | −31.5819 | −1.38098 | −0.690490 | − | 0.723342i | \(-0.742605\pi\) | ||||
−0.690490 | + | 0.723342i | \(0.742605\pi\) | |||||||
\(524\) | 18.4664 | 0.806709 | ||||||||
\(525\) | −36.2361 | −1.58147 | ||||||||
\(526\) | −18.3720 | −0.801058 | ||||||||
\(527\) | 28.4055 | 1.23737 | ||||||||
\(528\) | −14.3553 | −0.624735 | ||||||||
\(529\) | 36.3370 | 1.57987 | ||||||||
\(530\) | −5.36970 | −0.233245 | ||||||||
\(531\) | 4.67528 | 0.202890 | ||||||||
\(532\) | −29.7570 | −1.29013 | ||||||||
\(533\) | −1.36900 | −0.0592981 | ||||||||
\(534\) | 7.00609 | 0.303183 | ||||||||
\(535\) | 40.7591 | 1.76217 | ||||||||
\(536\) | 1.92239 | 0.0830348 | ||||||||
\(537\) | 26.0265 | 1.12312 | ||||||||
\(538\) | 44.0969 | 1.90115 | ||||||||
\(539\) | −10.2190 | −0.440165 | ||||||||
\(540\) | −5.92451 | −0.254950 | ||||||||
\(541\) | 33.8590 | 1.45571 | 0.727855 | − | 0.685731i | \(-0.240517\pi\) | ||||
0.727855 | + | 0.685731i | \(0.240517\pi\) | |||||||
\(542\) | −18.3949 | −0.790130 | ||||||||
\(543\) | 7.07137 | 0.303462 | ||||||||
\(544\) | −29.6979 | −1.27329 | ||||||||
\(545\) | −58.7554 | −2.51680 | ||||||||
\(546\) | 6.00816 | 0.257126 | ||||||||
\(547\) | −45.2902 | −1.93647 | −0.968234 | − | 0.250047i | \(-0.919554\pi\) | ||||
−0.968234 | + | 0.250047i | \(0.919554\pi\) | |||||||
\(548\) | −19.4826 | −0.832254 | ||||||||
\(549\) | 1.19246 | 0.0508930 | ||||||||
\(550\) | −62.8739 | −2.68095 | ||||||||
\(551\) | 32.3420 | 1.37782 | ||||||||
\(552\) | 7.60041 | 0.323495 | ||||||||
\(553\) | 15.3126 | 0.651156 | ||||||||
\(554\) | 30.5995 | 1.30005 | ||||||||
\(555\) | −30.9614 | −1.31424 | ||||||||
\(556\) | 19.0021 | 0.805870 | ||||||||
\(557\) | −17.7246 | −0.751017 | −0.375509 | − | 0.926819i | \(-0.622532\pi\) | ||||
−0.375509 | + | 0.926819i | \(0.622532\pi\) | |||||||
\(558\) | 12.3462 | 0.522656 | ||||||||
\(559\) | −10.8702 | −0.459758 | ||||||||
\(560\) | −62.1015 | −2.62427 | ||||||||
\(561\) | 12.8752 | 0.543591 | ||||||||
\(562\) | −41.0464 | −1.73144 | ||||||||
\(563\) | 40.3638 | 1.70113 | 0.850566 | − | 0.525869i | \(-0.176260\pi\) | ||||
0.850566 | + | 0.525869i | \(0.176260\pi\) | |||||||
\(564\) | −7.55317 | −0.318046 | ||||||||
\(565\) | −31.9434 | −1.34387 | ||||||||
\(566\) | 11.1219 | 0.467490 | ||||||||
\(567\) | 3.22519 | 0.135445 | ||||||||
\(568\) | −8.31116 | −0.348728 | ||||||||
\(569\) | 30.9042 | 1.29557 | 0.647785 | − | 0.761823i | \(-0.275695\pi\) | ||||
0.647785 | + | 0.761823i | \(0.275695\pi\) | |||||||
\(570\) | 47.1011 | 1.97285 | ||||||||
\(571\) | −36.1512 | −1.51288 | −0.756441 | − | 0.654062i | \(-0.773064\pi\) | ||||
−0.756441 | + | 0.654062i | \(0.773064\pi\) | |||||||
\(572\) | 4.41690 | 0.184680 | ||||||||
\(573\) | −10.1201 | −0.422773 | ||||||||
\(574\) | 8.22519 | 0.343313 | ||||||||
\(575\) | 86.5465 | 3.60924 | ||||||||
\(576\) | −3.35034 | −0.139598 | ||||||||
\(577\) | 36.4780 | 1.51860 | 0.759299 | − | 0.650741i | \(-0.225542\pi\) | ||||
0.759299 | + | 0.650741i | \(0.225542\pi\) | |||||||
\(578\) | 2.55258 | 0.106173 | ||||||||
\(579\) | 17.7397 | 0.737235 | ||||||||
\(580\) | −30.5356 | −1.26792 | ||||||||
\(581\) | −34.6253 | −1.43650 | ||||||||
\(582\) | 15.5681 | 0.645318 | ||||||||
\(583\) | 2.14896 | 0.0890009 | ||||||||
\(584\) | 12.0309 | 0.497842 | ||||||||
\(585\) | −4.02931 | −0.166592 | ||||||||
\(586\) | −26.7696 | −1.10584 | ||||||||
\(587\) | −19.8035 | −0.817378 | −0.408689 | − | 0.912674i | \(-0.634014\pi\) | ||||
−0.408689 | + | 0.912674i | \(0.634014\pi\) | |||||||
\(588\) | −5.00189 | −0.206275 | ||||||||
\(589\) | −41.5871 | −1.71357 | ||||||||
\(590\) | 35.0934 | 1.44477 | ||||||||
\(591\) | 13.0312 | 0.536032 | ||||||||
\(592\) | −36.7203 | −1.50919 | ||||||||
\(593\) | 12.4830 | 0.512616 | 0.256308 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256308 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(594\) | 5.59607 | 0.229610 | ||||||||
\(595\) | 55.6985 | 2.28341 | ||||||||
\(596\) | 1.67905 | 0.0687767 | ||||||||
\(597\) | −20.8216 | −0.852172 | ||||||||
\(598\) | −14.3499 | −0.586812 | ||||||||
\(599\) | −27.9247 | −1.14097 | −0.570487 | − | 0.821307i | \(-0.693245\pi\) | ||||
−0.570487 | + | 0.821307i | \(0.693245\pi\) | |||||||
\(600\) | 11.0856 | 0.452570 | ||||||||
\(601\) | 30.9818 | 1.26378 | 0.631888 | − | 0.775060i | \(-0.282280\pi\) | ||||
0.631888 | + | 0.775060i | \(0.282280\pi\) | |||||||
\(602\) | 65.3096 | 2.66182 | ||||||||
\(603\) | −1.94836 | −0.0793432 | ||||||||
\(604\) | −15.2198 | −0.619287 | ||||||||
\(605\) | −7.96241 | −0.323718 | ||||||||
\(606\) | 15.4112 | 0.626038 | ||||||||
\(607\) | 19.9205 | 0.808550 | 0.404275 | − | 0.914638i | \(-0.367524\pi\) | ||||
0.404275 | + | 0.914638i | \(0.367524\pi\) | |||||||
\(608\) | 43.4792 | 1.76331 | ||||||||
\(609\) | 16.6230 | 0.673598 | ||||||||
\(610\) | 8.95080 | 0.362407 | ||||||||
\(611\) | −5.13698 | −0.207820 | ||||||||
\(612\) | 6.30200 | 0.254743 | ||||||||
\(613\) | −4.77158 | −0.192722 | −0.0963611 | − | 0.995346i | \(-0.530720\pi\) | ||||
−0.0963611 | + | 0.995346i | \(0.530720\pi\) | |||||||
\(614\) | −26.0795 | −1.05248 | ||||||||
\(615\) | −5.51614 | −0.222432 | ||||||||
\(616\) | 9.55929 | 0.385155 | ||||||||
\(617\) | 11.7537 | 0.473185 | 0.236593 | − | 0.971609i | \(-0.423969\pi\) | ||||
0.236593 | + | 0.971609i | \(0.423969\pi\) | |||||||
\(618\) | −1.86289 | −0.0749363 | ||||||||
\(619\) | 18.8643 | 0.758221 | 0.379110 | − | 0.925351i | \(-0.376230\pi\) | ||||
0.379110 | + | 0.925351i | \(0.376230\pi\) | |||||||
\(620\) | 39.2643 | 1.57689 | ||||||||
\(621\) | −7.70305 | −0.309113 | ||||||||
\(622\) | 21.3501 | 0.856060 | ||||||||
\(623\) | −12.1295 | −0.485959 | ||||||||
\(624\) | −4.77877 | −0.191304 | ||||||||
\(625\) | 45.0564 | 1.80226 | ||||||||
\(626\) | −44.2271 | −1.76767 | ||||||||
\(627\) | −18.8499 | −0.752793 | ||||||||
\(628\) | −17.2361 | −0.687796 | ||||||||
\(629\) | 32.9342 | 1.31317 | ||||||||
\(630\) | 24.2088 | 0.964500 | ||||||||
\(631\) | −44.0957 | −1.75542 | −0.877712 | − | 0.479188i | \(-0.840931\pi\) | ||||
−0.877712 | + | 0.479188i | \(0.840931\pi\) | |||||||
\(632\) | −4.68454 | −0.186341 | ||||||||
\(633\) | 5.21341 | 0.207214 | ||||||||
\(634\) | −43.6867 | −1.73502 | ||||||||
\(635\) | 17.6003 | 0.698448 | ||||||||
\(636\) | 1.05185 | 0.0417085 | ||||||||
\(637\) | −3.40183 | −0.134786 | ||||||||
\(638\) | 28.8428 | 1.14190 | ||||||||
\(639\) | 8.42340 | 0.333225 | ||||||||
\(640\) | 30.6897 | 1.21312 | ||||||||
\(641\) | 35.5445 | 1.40392 | 0.701962 | − | 0.712214i | \(-0.252307\pi\) | ||||
0.701962 | + | 0.712214i | \(0.252307\pi\) | |||||||
\(642\) | −18.8443 | −0.743726 | ||||||||
\(643\) | −3.11861 | −0.122986 | −0.0614931 | − | 0.998108i | \(-0.519586\pi\) | ||||
−0.0614931 | + | 0.998108i | \(0.519586\pi\) | |||||||
\(644\) | 36.5291 | 1.43945 | ||||||||
\(645\) | −43.7992 | −1.72459 | ||||||||
\(646\) | −50.1022 | −1.97125 | ||||||||
\(647\) | 30.4158 | 1.19577 | 0.597884 | − | 0.801583i | \(-0.296008\pi\) | ||||
0.597884 | + | 0.801583i | \(0.296008\pi\) | |||||||
\(648\) | −0.986675 | −0.0387603 | ||||||||
\(649\) | −14.0444 | −0.551293 | ||||||||
\(650\) | −20.9302 | −0.820950 | ||||||||
\(651\) | −21.3747 | −0.837742 | ||||||||
\(652\) | 20.0024 | 0.783354 | ||||||||
\(653\) | 12.5016 | 0.489225 | 0.244613 | − | 0.969621i | \(-0.421339\pi\) | ||||
0.244613 | + | 0.969621i | \(0.421339\pi\) | |||||||
\(654\) | 27.1646 | 1.06222 | ||||||||
\(655\) | 50.6049 | 1.97730 | ||||||||
\(656\) | −6.54215 | −0.255428 | ||||||||
\(657\) | −12.1934 | −0.475708 | ||||||||
\(658\) | 30.8638 | 1.20320 | ||||||||
\(659\) | 4.29862 | 0.167451 | 0.0837253 | − | 0.996489i | \(-0.473318\pi\) | ||||
0.0837253 | + | 0.996489i | \(0.473318\pi\) | |||||||
\(660\) | 17.7971 | 0.692751 | ||||||||
\(661\) | −46.2020 | −1.79705 | −0.898525 | − | 0.438923i | \(-0.855360\pi\) | ||||
−0.898525 | + | 0.438923i | \(0.855360\pi\) | |||||||
\(662\) | −40.2920 | −1.56599 | ||||||||
\(663\) | 4.28605 | 0.166456 | ||||||||
\(664\) | 10.5929 | 0.411082 | ||||||||
\(665\) | −81.5453 | −3.16219 | ||||||||
\(666\) | 14.3145 | 0.554677 | ||||||||
\(667\) | −39.7024 | −1.53728 | ||||||||
\(668\) | −11.4869 | −0.444443 | ||||||||
\(669\) | −0.912908 | −0.0352951 | ||||||||
\(670\) | −14.6247 | −0.565000 | ||||||||
\(671\) | −3.58213 | −0.138286 | ||||||||
\(672\) | 22.3472 | 0.862062 | ||||||||
\(673\) | −17.5086 | −0.674906 | −0.337453 | − | 0.941342i | \(-0.609565\pi\) | ||||
−0.337453 | + | 0.941342i | \(0.609565\pi\) | |||||||
\(674\) | 29.2292 | 1.12587 | ||||||||
\(675\) | −11.2354 | −0.432449 | ||||||||
\(676\) | 1.47035 | 0.0565520 | ||||||||
\(677\) | −29.3931 | −1.12967 | −0.564835 | − | 0.825204i | \(-0.691060\pi\) | ||||
−0.564835 | + | 0.825204i | \(0.691060\pi\) | |||||||
\(678\) | 14.7685 | 0.567182 | ||||||||
\(679\) | −26.9528 | −1.03435 | ||||||||
\(680\) | −17.0397 | −0.653443 | ||||||||
\(681\) | 16.4016 | 0.628510 | ||||||||
\(682\) | −37.0877 | −1.42016 | ||||||||
\(683\) | 9.36032 | 0.358163 | 0.179081 | − | 0.983834i | \(-0.442687\pi\) | ||||
0.179081 | + | 0.983834i | \(0.442687\pi\) | |||||||
\(684\) | −9.22644 | −0.352782 | ||||||||
\(685\) | −53.3895 | −2.03991 | ||||||||
\(686\) | −21.6184 | −0.825393 | ||||||||
\(687\) | −25.9445 | −0.989845 | ||||||||
\(688\) | −51.9459 | −1.98042 | ||||||||
\(689\) | 0.715373 | 0.0272535 | ||||||||
\(690\) | −57.8203 | −2.20118 | ||||||||
\(691\) | −41.4899 | −1.57835 | −0.789176 | − | 0.614167i | \(-0.789492\pi\) | ||||
−0.789176 | + | 0.614167i | \(0.789492\pi\) | |||||||
\(692\) | 17.1667 | 0.652581 | ||||||||
\(693\) | −9.68839 | −0.368032 | ||||||||
\(694\) | 8.27561 | 0.314138 | ||||||||
\(695\) | 52.0729 | 1.97524 | ||||||||
\(696\) | −5.08544 | −0.192763 | ||||||||
\(697\) | 5.86761 | 0.222252 | ||||||||
\(698\) | −62.5185 | −2.36636 | ||||||||
\(699\) | 10.7098 | 0.405082 | ||||||||
\(700\) | 53.2799 | 2.01379 | ||||||||
\(701\) | 12.3887 | 0.467914 | 0.233957 | − | 0.972247i | \(-0.424833\pi\) | ||||
0.233957 | + | 0.972247i | \(0.424833\pi\) | |||||||
\(702\) | 1.86289 | 0.0703102 | ||||||||
\(703\) | −48.2173 | −1.81855 | ||||||||
\(704\) | 10.0644 | 0.379315 | ||||||||
\(705\) | −20.6985 | −0.779550 | ||||||||
\(706\) | −49.9567 | −1.88014 | ||||||||
\(707\) | −26.6812 | −1.00345 | ||||||||
\(708\) | −6.87431 | −0.258352 | ||||||||
\(709\) | 10.5147 | 0.394886 | 0.197443 | − | 0.980314i | \(-0.436736\pi\) | ||||
0.197443 | + | 0.980314i | \(0.436736\pi\) | |||||||
\(710\) | 63.2274 | 2.37288 | ||||||||
\(711\) | 4.74780 | 0.178057 | ||||||||
\(712\) | 3.71076 | 0.139067 | ||||||||
\(713\) | 51.0515 | 1.91189 | ||||||||
\(714\) | −25.7513 | −0.963718 | ||||||||
\(715\) | 12.1040 | 0.452663 | ||||||||
\(716\) | −38.2680 | −1.43014 | ||||||||
\(717\) | 3.15424 | 0.117797 | ||||||||
\(718\) | 19.7385 | 0.736632 | ||||||||
\(719\) | −8.30235 | −0.309626 | −0.154813 | − | 0.987944i | \(-0.549477\pi\) | ||||
−0.154813 | + | 0.987944i | \(0.549477\pi\) | |||||||
\(720\) | −19.2552 | −0.717597 | ||||||||
\(721\) | 3.22519 | 0.120112 | ||||||||
\(722\) | 37.9572 | 1.41262 | ||||||||
\(723\) | 0.587519 | 0.0218501 | ||||||||
\(724\) | −10.3974 | −0.386417 | ||||||||
\(725\) | −57.9083 | −2.15066 | ||||||||
\(726\) | 3.68129 | 0.136626 | ||||||||
\(727\) | −22.7577 | −0.844038 | −0.422019 | − | 0.906587i | \(-0.638678\pi\) | ||||
−0.422019 | + | 0.906587i | \(0.638678\pi\) | |||||||
\(728\) | 3.18221 | 0.117941 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −91.5253 | −3.38750 | ||||||||
\(731\) | 46.5900 | 1.72319 | ||||||||
\(732\) | −1.75334 | −0.0648052 | ||||||||
\(733\) | 1.45793 | 0.0538500 | 0.0269250 | − | 0.999637i | \(-0.491428\pi\) | ||||
0.0269250 | + | 0.999637i | \(0.491428\pi\) | |||||||
\(734\) | −42.8811 | −1.58277 | ||||||||
\(735\) | −13.7071 | −0.505592 | ||||||||
\(736\) | −53.3741 | −1.96740 | ||||||||
\(737\) | 5.85282 | 0.215591 | ||||||||
\(738\) | 2.55030 | 0.0938778 | ||||||||
\(739\) | 4.24653 | 0.156211 | 0.0781055 | − | 0.996945i | \(-0.475113\pi\) | ||||
0.0781055 | + | 0.996945i | \(0.475113\pi\) | |||||||
\(740\) | 45.5242 | 1.67350 | ||||||||
\(741\) | −6.27499 | −0.230517 | ||||||||
\(742\) | −4.29807 | −0.157787 | ||||||||
\(743\) | 10.3154 | 0.378436 | 0.189218 | − | 0.981935i | \(-0.439405\pi\) | ||||
0.189218 | + | 0.981935i | \(0.439405\pi\) | |||||||
\(744\) | 6.53913 | 0.239736 | ||||||||
\(745\) | 4.60123 | 0.168576 | ||||||||
\(746\) | −31.0620 | −1.13726 | ||||||||
\(747\) | −10.7359 | −0.392806 | ||||||||
\(748\) | −18.9311 | −0.692189 | ||||||||
\(749\) | 32.6249 | 1.19209 | ||||||||
\(750\) | −46.8036 | −1.70902 | ||||||||
\(751\) | −21.3927 | −0.780629 | −0.390315 | − | 0.920681i | \(-0.627634\pi\) | ||||
−0.390315 | + | 0.920681i | \(0.627634\pi\) | |||||||
\(752\) | −24.5484 | −0.895189 | ||||||||
\(753\) | 18.6666 | 0.680248 | ||||||||
\(754\) | 9.60154 | 0.349667 | ||||||||
\(755\) | −41.7081 | −1.51791 | ||||||||
\(756\) | −4.74216 | −0.172471 | ||||||||
\(757\) | 49.9373 | 1.81500 | 0.907502 | − | 0.420049i | \(-0.137987\pi\) | ||||
0.907502 | + | 0.420049i | \(0.137987\pi\) | |||||||
\(758\) | 30.5882 | 1.11101 | ||||||||
\(759\) | 23.1398 | 0.839921 | ||||||||
\(760\) | 24.9470 | 0.904922 | ||||||||
\(761\) | 47.7800 | 1.73202 | 0.866011 | − | 0.500024i | \(-0.166676\pi\) | ||||
0.866011 | + | 0.500024i | \(0.166676\pi\) | |||||||
\(762\) | −8.13723 | −0.294781 | ||||||||
\(763\) | −47.0296 | −1.70259 | ||||||||
\(764\) | 14.8801 | 0.538343 | ||||||||
\(765\) | 17.2698 | 0.624392 | ||||||||
\(766\) | 24.1882 | 0.873955 | ||||||||
\(767\) | −4.67528 | −0.168815 | ||||||||
\(768\) | −20.8896 | −0.753788 | ||||||||
\(769\) | 12.1833 | 0.439342 | 0.219671 | − | 0.975574i | \(-0.429502\pi\) | ||||
0.219671 | + | 0.975574i | \(0.429502\pi\) | |||||||
\(770\) | −72.7226 | −2.62074 | ||||||||
\(771\) | −25.3211 | −0.911915 | ||||||||
\(772\) | −26.0836 | −0.938768 | ||||||||
\(773\) | 25.6557 | 0.922770 | 0.461385 | − | 0.887200i | \(-0.347353\pi\) | ||||
0.461385 | + | 0.887200i | \(0.347353\pi\) | |||||||
\(774\) | 20.2499 | 0.727867 | ||||||||
\(775\) | 74.4617 | 2.67474 | ||||||||
\(776\) | 8.24561 | 0.296000 | ||||||||
\(777\) | −24.7825 | −0.889067 | ||||||||
\(778\) | 55.7134 | 1.99742 | ||||||||
\(779\) | −8.59047 | −0.307786 | ||||||||
\(780\) | 5.92451 | 0.212131 | ||||||||
\(781\) | −25.3037 | −0.905438 | ||||||||
\(782\) | 61.5045 | 2.19940 | ||||||||
\(783\) | 5.15412 | 0.184193 | ||||||||
\(784\) | −16.2566 | −0.580592 | ||||||||
\(785\) | −47.2334 | −1.68583 | ||||||||
\(786\) | −23.3964 | −0.834520 | ||||||||
\(787\) | −46.9197 | −1.67251 | −0.836253 | − | 0.548344i | \(-0.815259\pi\) | ||||
−0.836253 | + | 0.548344i | \(0.815259\pi\) | |||||||
\(788\) | −19.1604 | −0.682563 | ||||||||
\(789\) | 9.86212 | 0.351101 | ||||||||
\(790\) | 35.6378 | 1.26793 | ||||||||
\(791\) | −25.5685 | −0.909111 | ||||||||
\(792\) | 2.96395 | 0.105319 | ||||||||
\(793\) | −1.19246 | −0.0423455 | ||||||||
\(794\) | 6.38347 | 0.226541 | ||||||||
\(795\) | 2.88246 | 0.102230 | ||||||||
\(796\) | 30.6151 | 1.08512 | ||||||||
\(797\) | 10.5564 | 0.373927 | 0.186963 | − | 0.982367i | \(-0.440135\pi\) | ||||
0.186963 | + | 0.982367i | \(0.440135\pi\) | |||||||
\(798\) | 37.7012 | 1.33461 | ||||||||
\(799\) | 22.0173 | 0.778918 | ||||||||
\(800\) | −77.8494 | −2.75239 | ||||||||
\(801\) | −3.76088 | −0.132884 | ||||||||
\(802\) | −58.7575 | −2.07480 | ||||||||
\(803\) | 36.6286 | 1.29259 | ||||||||
\(804\) | 2.86477 | 0.101033 | ||||||||
\(805\) | 100.103 | 3.52818 | ||||||||
\(806\) | −12.3462 | −0.434876 | ||||||||
\(807\) | −23.6713 | −0.833268 | ||||||||
\(808\) | 8.16252 | 0.287156 | ||||||||
\(809\) | −3.61205 | −0.126993 | −0.0634964 | − | 0.997982i | \(-0.520225\pi\) | ||||
−0.0634964 | + | 0.997982i | \(0.520225\pi\) | |||||||
\(810\) | 7.50616 | 0.263739 | ||||||||
\(811\) | −20.6541 | −0.725264 | −0.362632 | − | 0.931932i | \(-0.618122\pi\) | ||||
−0.362632 | + | 0.931932i | \(0.618122\pi\) | |||||||
\(812\) | −24.4416 | −0.857734 | ||||||||
\(813\) | 9.87442 | 0.346311 | ||||||||
\(814\) | −43.0005 | −1.50717 | ||||||||
\(815\) | 54.8140 | 1.92005 | ||||||||
\(816\) | 20.4820 | 0.717015 | ||||||||
\(817\) | −68.2101 | −2.38637 | ||||||||
\(818\) | 58.6998 | 2.05239 | ||||||||
\(819\) | −3.22519 | −0.112697 | ||||||||
\(820\) | 8.11066 | 0.283237 | ||||||||
\(821\) | 20.3161 | 0.709036 | 0.354518 | − | 0.935049i | \(-0.384645\pi\) | ||||
0.354518 | + | 0.935049i | \(0.384645\pi\) | |||||||
\(822\) | 24.6838 | 0.860945 | ||||||||
\(823\) | −11.3908 | −0.397057 | −0.198529 | − | 0.980095i | \(-0.563616\pi\) | ||||
−0.198529 | + | 0.980095i | \(0.563616\pi\) | |||||||
\(824\) | −0.986675 | −0.0343725 | ||||||||
\(825\) | 33.7508 | 1.17505 | ||||||||
\(826\) | 28.0899 | 0.977371 | ||||||||
\(827\) | −1.33613 | −0.0464616 | −0.0232308 | − | 0.999730i | \(-0.507395\pi\) | ||||
−0.0232308 | + | 0.999730i | \(0.507395\pi\) | |||||||
\(828\) | 11.3262 | 0.393612 | ||||||||
\(829\) | −34.1245 | −1.18519 | −0.592596 | − | 0.805500i | \(-0.701897\pi\) | ||||
−0.592596 | + | 0.805500i | \(0.701897\pi\) | |||||||
\(830\) | −80.5854 | −2.79716 | ||||||||
\(831\) | −16.4259 | −0.569807 | ||||||||
\(832\) | 3.35034 | 0.116152 | ||||||||
\(833\) | 14.5804 | 0.505182 | ||||||||
\(834\) | −24.0751 | −0.833652 | ||||||||
\(835\) | −31.4785 | −1.08936 | ||||||||
\(836\) | 27.7160 | 0.958579 | ||||||||
\(837\) | −6.62744 | −0.229078 | ||||||||
\(838\) | 37.9838 | 1.31213 | ||||||||
\(839\) | −40.3995 | −1.39474 | −0.697372 | − | 0.716709i | \(-0.745648\pi\) | ||||
−0.697372 | + | 0.716709i | \(0.745648\pi\) | |||||||
\(840\) | 12.8221 | 0.442405 | ||||||||
\(841\) | −2.43509 | −0.0839687 | ||||||||
\(842\) | −39.7809 | −1.37094 | ||||||||
\(843\) | 22.0337 | 0.758882 | ||||||||
\(844\) | −7.66554 | −0.263859 | ||||||||
\(845\) | 4.02931 | 0.138613 | ||||||||
\(846\) | 9.56962 | 0.329010 | ||||||||
\(847\) | −6.37336 | −0.218991 | ||||||||
\(848\) | 3.41860 | 0.117395 | ||||||||
\(849\) | −5.97027 | −0.204899 | ||||||||
\(850\) | 89.7079 | 3.07696 | ||||||||
\(851\) | 59.1906 | 2.02903 | ||||||||
\(852\) | −12.3854 | −0.424316 | ||||||||
\(853\) | −34.2554 | −1.17288 | −0.586441 | − | 0.809992i | \(-0.699471\pi\) | ||||
−0.586441 | + | 0.809992i | \(0.699471\pi\) | |||||||
\(854\) | 7.16450 | 0.245164 | ||||||||
\(855\) | −25.2839 | −0.864691 | ||||||||
\(856\) | −9.98086 | −0.341139 | ||||||||
\(857\) | −24.1172 | −0.823830 | −0.411915 | − | 0.911222i | \(-0.635140\pi\) | ||||
−0.411915 | + | 0.911222i | \(0.635140\pi\) | |||||||
\(858\) | −5.59607 | −0.191047 | ||||||||
\(859\) | −15.4801 | −0.528174 | −0.264087 | − | 0.964499i | \(-0.585071\pi\) | ||||
−0.264087 | + | 0.964499i | \(0.585071\pi\) | |||||||
\(860\) | 64.4003 | 2.19603 | ||||||||
\(861\) | −4.41529 | −0.150473 | ||||||||
\(862\) | 5.75330 | 0.195958 | ||||||||
\(863\) | 12.6939 | 0.432105 | 0.216053 | − | 0.976382i | \(-0.430682\pi\) | ||||
0.216053 | + | 0.976382i | \(0.430682\pi\) | |||||||
\(864\) | 6.92896 | 0.235728 | ||||||||
\(865\) | 47.0432 | 1.59952 | ||||||||
\(866\) | −35.4838 | −1.20579 | ||||||||
\(867\) | −1.37022 | −0.0465353 | ||||||||
\(868\) | 31.4284 | 1.06675 | ||||||||
\(869\) | −14.2623 | −0.483815 | ||||||||
\(870\) | 38.6876 | 1.31163 | ||||||||
\(871\) | 1.94836 | 0.0660175 | ||||||||
\(872\) | 14.3877 | 0.487228 | ||||||||
\(873\) | −8.35697 | −0.282840 | ||||||||
\(874\) | −90.0456 | −3.04584 | ||||||||
\(875\) | 81.0302 | 2.73932 | ||||||||
\(876\) | 17.9285 | 0.605749 | ||||||||
\(877\) | 14.1833 | 0.478936 | 0.239468 | − | 0.970904i | \(-0.423027\pi\) | ||||
0.239468 | + | 0.970904i | \(0.423027\pi\) | |||||||
\(878\) | 61.3925 | 2.07190 | ||||||||
\(879\) | 14.3699 | 0.484686 | ||||||||
\(880\) | 57.8420 | 1.94985 | ||||||||
\(881\) | 17.5865 | 0.592503 | 0.296251 | − | 0.955110i | \(-0.404263\pi\) | ||||
0.296251 | + | 0.955110i | \(0.404263\pi\) | |||||||
\(882\) | 6.33724 | 0.213386 | ||||||||
\(883\) | −12.3300 | −0.414939 | −0.207470 | − | 0.978241i | \(-0.566523\pi\) | ||||
−0.207470 | + | 0.978241i | \(0.566523\pi\) | |||||||
\(884\) | −6.30200 | −0.211959 | ||||||||
\(885\) | −18.8382 | −0.633238 | ||||||||
\(886\) | 32.9742 | 1.10779 | ||||||||
\(887\) | 47.5421 | 1.59631 | 0.798154 | − | 0.602454i | \(-0.205810\pi\) | ||||
0.798154 | + | 0.602454i | \(0.205810\pi\) | |||||||
\(888\) | 7.58166 | 0.254424 | ||||||||
\(889\) | 14.0879 | 0.472491 | ||||||||
\(890\) | −28.2297 | −0.946262 | ||||||||
\(891\) | −3.00398 | −0.100637 | ||||||||
\(892\) | 1.34230 | 0.0449434 | ||||||||
\(893\) | −32.2345 | −1.07869 | ||||||||
\(894\) | −2.12731 | −0.0711478 | ||||||||
\(895\) | −104.869 | −3.50537 | ||||||||
\(896\) | 24.5650 | 0.820659 | ||||||||
\(897\) | 7.70305 | 0.257197 | ||||||||
\(898\) | 20.2189 | 0.674715 | ||||||||
\(899\) | −34.1586 | −1.13925 | ||||||||
\(900\) | 16.5199 | 0.550664 | ||||||||
\(901\) | −3.06612 | −0.102147 | ||||||||
\(902\) | −7.66104 | −0.255085 | ||||||||
\(903\) | −35.0583 | −1.16667 | ||||||||
\(904\) | 7.82212 | 0.260160 | ||||||||
\(905\) | −28.4928 | −0.947132 | ||||||||
\(906\) | 19.2831 | 0.640637 | ||||||||
\(907\) | −35.1217 | −1.16620 | −0.583098 | − | 0.812402i | \(-0.698160\pi\) | ||||
−0.583098 | + | 0.812402i | \(0.698160\pi\) | |||||||
\(908\) | −24.1161 | −0.800320 | ||||||||
\(909\) | −8.27275 | −0.274390 | ||||||||
\(910\) | −24.2088 | −0.802513 | ||||||||
\(911\) | 18.7016 | 0.619611 | 0.309806 | − | 0.950800i | \(-0.399736\pi\) | ||||
0.309806 | + | 0.950800i | \(0.399736\pi\) | |||||||
\(912\) | −29.9867 | −0.992960 | ||||||||
\(913\) | 32.2504 | 1.06733 | ||||||||
\(914\) | 18.7569 | 0.620422 | ||||||||
\(915\) | −4.80480 | −0.158842 | ||||||||
\(916\) | 38.1476 | 1.26043 | ||||||||
\(917\) | 40.5057 | 1.33762 | ||||||||
\(918\) | −7.98443 | −0.263526 | ||||||||
\(919\) | −2.01636 | −0.0665136 | −0.0332568 | − | 0.999447i | \(-0.510588\pi\) | ||||
−0.0332568 | + | 0.999447i | \(0.510588\pi\) | |||||||
\(920\) | −30.6244 | −1.00966 | ||||||||
\(921\) | 13.9995 | 0.461300 | ||||||||
\(922\) | −23.2354 | −0.765218 | ||||||||
\(923\) | −8.42340 | −0.277260 | ||||||||
\(924\) | 14.2453 | 0.468637 | ||||||||
\(925\) | 86.3330 | 2.83861 | ||||||||
\(926\) | 78.2170 | 2.57037 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 35.7127 | 1.17233 | ||||||||
\(929\) | −33.0752 | −1.08516 | −0.542580 | − | 0.840004i | \(-0.682553\pi\) | ||||
−0.542580 | + | 0.840004i | \(0.682553\pi\) | |||||||
\(930\) | −49.7466 | −1.63126 | ||||||||
\(931\) | −21.3465 | −0.699602 | ||||||||
\(932\) | −15.7472 | −0.515816 | ||||||||
\(933\) | −11.4607 | −0.375208 | ||||||||
\(934\) | −35.1616 | −1.15052 | ||||||||
\(935\) | −51.8782 | −1.69660 | ||||||||
\(936\) | 0.986675 | 0.0322505 | ||||||||
\(937\) | −18.5285 | −0.605301 | −0.302651 | − | 0.953102i | \(-0.597872\pi\) | ||||
−0.302651 | + | 0.953102i | \(0.597872\pi\) | |||||||
\(938\) | −11.7060 | −0.382216 | ||||||||
\(939\) | 23.7411 | 0.774762 | ||||||||
\(940\) | 30.4341 | 0.992650 | ||||||||
\(941\) | −56.5431 | −1.84325 | −0.921627 | − | 0.388077i | \(-0.873139\pi\) | ||||
−0.921627 | + | 0.388077i | \(0.873139\pi\) | |||||||
\(942\) | 21.8376 | 0.711507 | ||||||||
\(943\) | 10.5455 | 0.343409 | ||||||||
\(944\) | −22.3421 | −0.727173 | ||||||||
\(945\) | −12.9953 | −0.422737 | ||||||||
\(946\) | −60.8302 | −1.97776 | ||||||||
\(947\) | −34.6953 | −1.12744 | −0.563722 | − | 0.825964i | \(-0.690631\pi\) | ||||
−0.563722 | + | 0.825964i | \(0.690631\pi\) | |||||||
\(948\) | −6.98094 | −0.226730 | ||||||||
\(949\) | 12.1934 | 0.395813 | ||||||||
\(950\) | −131.337 | −4.26113 | ||||||||
\(951\) | 23.4510 | 0.760452 | ||||||||
\(952\) | −13.6391 | −0.442046 | ||||||||
\(953\) | −16.7212 | −0.541653 | −0.270826 | − | 0.962628i | \(-0.587297\pi\) | ||||
−0.270826 | + | 0.962628i | \(0.587297\pi\) | |||||||
\(954\) | −1.33266 | −0.0431464 | ||||||||
\(955\) | 40.7770 | 1.31951 | ||||||||
\(956\) | −4.63784 | −0.149998 | ||||||||
\(957\) | −15.4828 | −0.500489 | ||||||||
\(958\) | −21.5349 | −0.695761 | ||||||||
\(959\) | −42.7346 | −1.37997 | ||||||||
\(960\) | 13.4996 | 0.435697 | ||||||||
\(961\) | 12.9230 | 0.416871 | ||||||||
\(962\) | −14.3145 | −0.461519 | ||||||||
\(963\) | 10.1157 | 0.325972 | ||||||||
\(964\) | −0.863859 | −0.0278230 | ||||||||
\(965\) | −71.4787 | −2.30098 | ||||||||
\(966\) | −46.2812 | −1.48907 | ||||||||
\(967\) | 50.9499 | 1.63844 | 0.819220 | − | 0.573480i | \(-0.194407\pi\) | ||||
0.819220 | + | 0.573480i | \(0.194407\pi\) | |||||||
\(968\) | 1.94979 | 0.0626686 | ||||||||
\(969\) | 26.8949 | 0.863989 | ||||||||
\(970\) | −62.7287 | −2.01410 | ||||||||
\(971\) | 5.49879 | 0.176465 | 0.0882323 | − | 0.996100i | \(-0.471878\pi\) | ||||
0.0882323 | + | 0.996100i | \(0.471878\pi\) | |||||||
\(972\) | −1.47035 | −0.0471616 | ||||||||
\(973\) | 41.6808 | 1.33623 | ||||||||
\(974\) | 11.3492 | 0.363653 | ||||||||
\(975\) | 11.2354 | 0.359819 | ||||||||
\(976\) | −5.69849 | −0.182404 | ||||||||
\(977\) | −38.9037 | −1.24464 | −0.622320 | − | 0.782763i | \(-0.713810\pi\) | ||||
−0.622320 | + | 0.782763i | \(0.713810\pi\) | |||||||
\(978\) | −25.3424 | −0.810360 | ||||||||
\(979\) | 11.2976 | 0.361072 | ||||||||
\(980\) | 20.1542 | 0.643802 | ||||||||
\(981\) | −14.5820 | −0.465567 | ||||||||
\(982\) | 23.4310 | 0.747712 | ||||||||
\(983\) | −9.84743 | −0.314084 | −0.157042 | − | 0.987592i | \(-0.550196\pi\) | ||||
−0.157042 | + | 0.987592i | \(0.550196\pi\) | |||||||
\(984\) | 1.35076 | 0.0430607 | ||||||||
\(985\) | −52.5068 | −1.67300 | ||||||||
\(986\) | −41.1527 | −1.31057 | ||||||||
\(987\) | −16.5677 | −0.527356 | ||||||||
\(988\) | 9.22644 | 0.293532 | ||||||||
\(989\) | 83.7333 | 2.66256 | ||||||||
\(990\) | −22.5483 | −0.716633 | ||||||||
\(991\) | −5.08594 | −0.161560 | −0.0807801 | − | 0.996732i | \(-0.525741\pi\) | ||||
−0.0807801 | + | 0.996732i | \(0.525741\pi\) | |||||||
\(992\) | −45.9213 | −1.45800 | ||||||||
\(993\) | 21.6288 | 0.686369 | ||||||||
\(994\) | 50.6092 | 1.60523 | ||||||||
\(995\) | 83.8968 | 2.65971 | ||||||||
\(996\) | 15.7856 | 0.500185 | ||||||||
\(997\) | −31.2027 | −0.988199 | −0.494099 | − | 0.869405i | \(-0.664502\pi\) | ||||
−0.494099 | + | 0.869405i | \(0.664502\pi\) | |||||||
\(998\) | −58.6020 | −1.85501 | ||||||||
\(999\) | −7.68405 | −0.243113 |
(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 | 4017.2.a.g.1.20 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.g.1.20 | ✓ | 24 | 1.1 | even | 1 | trivial |