Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.424349 | 0.300060 | 0.150030 | − | 0.988681i | \(-0.452063\pi\) | ||||
0.150030 | + | 0.988681i | \(0.452063\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.81993 | −0.909964 | ||||||||
\(5\) | 2.43761 | 1.09013 | 0.545067 | − | 0.838392i | \(-0.316504\pi\) | ||||
0.545067 | + | 0.838392i | \(0.316504\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.41293 | 1.28997 | 0.644984 | − | 0.764196i | \(-0.276864\pi\) | ||||
0.644984 | + | 0.764196i | \(0.276864\pi\) | |||||||
\(8\) | −1.62098 | −0.573104 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.03440 | 0.327106 | ||||||||
\(11\) | −5.84264 | −1.76162 | −0.880811 | − | 0.473468i | \(-0.843002\pi\) | ||||
−0.880811 | + | 0.473468i | \(0.843002\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.73637 | −1.86833 | −0.934167 | − | 0.356837i | \(-0.883855\pi\) | ||||
−0.934167 | + | 0.356837i | \(0.883855\pi\) | |||||||
\(14\) | 1.44828 | 0.387068 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.95199 | 0.737998 | ||||||||
\(17\) | 4.57994 | 1.11080 | 0.555399 | − | 0.831584i | \(-0.312565\pi\) | ||||
0.555399 | + | 0.831584i | \(0.312565\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.36654 | 0.772337 | 0.386169 | − | 0.922428i | \(-0.373798\pi\) | ||||
0.386169 | + | 0.922428i | \(0.373798\pi\) | |||||||
\(20\) | −4.43628 | −0.991983 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.47932 | −0.528593 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.941962 | 0.188392 | ||||||||
\(26\) | −2.85857 | −0.560612 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.21129 | −1.17382 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.25875 | −0.405684 | −0.202842 | − | 0.979212i | \(-0.565018\pi\) | ||||
−0.202842 | + | 0.979212i | \(0.565018\pi\) | |||||||
\(32\) | 4.49464 | 0.794548 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.94349 | 0.333306 | ||||||||
\(35\) | 8.31942 | 1.40624 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.84124 | −0.795895 | −0.397948 | − | 0.917408i | \(-0.630277\pi\) | ||||
−0.397948 | + | 0.917408i | \(0.630277\pi\) | |||||||
\(38\) | 1.42859 | 0.231748 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.95133 | −0.624760 | ||||||||
\(41\) | 4.80077 | 0.749754 | 0.374877 | − | 0.927075i | \(-0.377685\pi\) | ||||
0.374877 | + | 0.927075i | \(0.377685\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.09307 | 1.08168 | 0.540841 | − | 0.841125i | \(-0.318106\pi\) | ||||
0.540841 | + | 0.841125i | \(0.318106\pi\) | |||||||
\(44\) | 10.6332 | 1.60301 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.424349 | −0.0625669 | ||||||||
\(47\) | 3.50228 | 0.510860 | 0.255430 | − | 0.966828i | \(-0.417783\pi\) | ||||
0.255430 | + | 0.966828i | \(0.417783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.64812 | 0.664017 | ||||||||
\(50\) | 0.399721 | 0.0565291 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.2597 | 1.70012 | ||||||||
\(53\) | −0.803109 | −0.110316 | −0.0551578 | − | 0.998478i | \(-0.517566\pi\) | ||||
−0.0551578 | + | 0.998478i | \(0.517566\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.2421 | −1.92040 | ||||||||
\(56\) | −5.53231 | −0.739286 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.424349 | −0.0557198 | ||||||||
\(59\) | −8.37512 | −1.09035 | −0.545174 | − | 0.838323i | \(-0.683536\pi\) | ||||
−0.545174 | + | 0.838323i | \(0.683536\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3218 | −1.57764 | −0.788821 | − | 0.614623i | \(-0.789308\pi\) | ||||
−0.788821 | + | 0.614623i | \(0.789308\pi\) | |||||||
\(62\) | −0.958499 | −0.121729 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.99669 | −0.499586 | ||||||||
\(65\) | −16.4207 | −2.03673 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.03184 | 0.859076 | 0.429538 | − | 0.903049i | \(-0.358677\pi\) | ||||
0.429538 | + | 0.903049i | \(0.358677\pi\) | |||||||
\(68\) | −8.33516 | −1.01079 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.53034 | 0.421956 | ||||||||
\(71\) | −6.87668 | −0.816112 | −0.408056 | − | 0.912957i | \(-0.633793\pi\) | ||||
−0.408056 | + | 0.912957i | \(0.633793\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.29707 | −0.385893 | −0.192946 | − | 0.981209i | \(-0.561804\pi\) | ||||
−0.192946 | + | 0.981209i | \(0.561804\pi\) | |||||||
\(74\) | −2.05438 | −0.238816 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.12686 | −0.702799 | ||||||||
\(77\) | −19.9406 | −2.27244 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.0450 | −1.35517 | −0.677584 | − | 0.735445i | \(-0.736973\pi\) | ||||
−0.677584 | + | 0.735445i | \(0.736973\pi\) | |||||||
\(80\) | 7.19582 | 0.804517 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.03720 | 0.224971 | ||||||||
\(83\) | −15.2301 | −1.67172 | −0.835858 | − | 0.548945i | \(-0.815030\pi\) | ||||
−0.835858 | + | 0.548945i | \(0.815030\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.1641 | 1.21092 | ||||||||
\(86\) | 3.00994 | 0.324570 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.47082 | 1.00959 | ||||||||
\(89\) | −7.50144 | −0.795151 | −0.397575 | − | 0.917570i | \(-0.630148\pi\) | ||||
−0.397575 | + | 0.917570i | \(0.630148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.9908 | −2.41009 | ||||||||
\(92\) | 1.81993 | 0.189741 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.48619 | 0.153289 | ||||||||
\(95\) | 8.20633 | 0.841951 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.65226 | −0.980038 | −0.490019 | − | 0.871712i | \(-0.663010\pi\) | ||||
−0.490019 | + | 0.871712i | \(0.663010\pi\) | |||||||
\(98\) | 1.97243 | 0.199245 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.71430 | −0.171430 | ||||||||
\(101\) | −6.89515 | −0.686094 | −0.343047 | − | 0.939318i | \(-0.611459\pi\) | ||||
−0.343047 | + | 0.939318i | \(0.611459\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.4211 | 1.51948 | 0.759742 | − | 0.650224i | \(-0.225325\pi\) | ||||
0.759742 | + | 0.650224i | \(0.225325\pi\) | |||||||
\(104\) | 10.9195 | 1.07075 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.340799 | −0.0331013 | ||||||||
\(107\) | −14.2228 | −1.37497 | −0.687486 | − | 0.726198i | \(-0.741286\pi\) | ||||
−0.687486 | + | 0.726198i | \(0.741286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.67649 | 0.639492 | 0.319746 | − | 0.947503i | \(-0.396403\pi\) | ||||
0.319746 | + | 0.947503i | \(0.396403\pi\) | |||||||
\(110\) | −6.04362 | −0.576237 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.0750 | 0.951994 | ||||||||
\(113\) | 11.2542 | 1.05870 | 0.529352 | − | 0.848402i | \(-0.322435\pi\) | ||||
0.529352 | + | 0.848402i | \(0.322435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.43761 | −0.227309 | ||||||||
\(116\) | 1.81993 | 0.168976 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.55397 | −0.327170 | ||||||||
\(119\) | 15.6310 | 1.43289 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.1365 | 2.10331 | ||||||||
\(122\) | −5.22874 | −0.473388 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.11076 | 0.369157 | ||||||||
\(125\) | −9.89193 | −0.884761 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.8522 | −1.58413 | −0.792063 | − | 0.610440i | \(-0.790993\pi\) | ||||
−0.792063 | + | 0.610440i | \(0.790993\pi\) | |||||||
\(128\) | −10.6853 | −0.944454 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.96810 | −0.611143 | ||||||||
\(131\) | 6.10711 | 0.533581 | 0.266790 | − | 0.963755i | \(-0.414037\pi\) | ||||
0.266790 | + | 0.963755i | \(0.414037\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.4898 | 0.996291 | ||||||||
\(134\) | 2.98395 | 0.257774 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.42401 | −0.636603 | ||||||||
\(137\) | 16.6372 | 1.42141 | 0.710707 | − | 0.703488i | \(-0.248375\pi\) | ||||
0.710707 | + | 0.703488i | \(0.248375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.3748 | −1.47371 | −0.736855 | − | 0.676051i | \(-0.763690\pi\) | ||||
−0.736855 | + | 0.676051i | \(0.763690\pi\) | |||||||
\(140\) | −15.1407 | −1.27963 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.91811 | −0.244883 | ||||||||
\(143\) | 39.3582 | 3.29130 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.43761 | −0.202433 | ||||||||
\(146\) | −1.39911 | −0.115791 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.81071 | 0.724236 | ||||||||
\(149\) | 15.5254 | 1.27189 | 0.635947 | − | 0.771733i | \(-0.280610\pi\) | ||||
0.635947 | + | 0.771733i | \(0.280610\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.45313 | −0.199633 | −0.0998165 | − | 0.995006i | \(-0.531826\pi\) | ||||
−0.0998165 | + | 0.995006i | \(0.531826\pi\) | |||||||
\(152\) | −5.45711 | −0.442630 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.46176 | −0.681868 | ||||||||
\(155\) | −5.50596 | −0.442250 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.35821 | −0.188205 | −0.0941027 | − | 0.995562i | \(-0.529998\pi\) | ||||
−0.0941027 | + | 0.995562i | \(0.529998\pi\) | |||||||
\(158\) | −5.11129 | −0.406632 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.9562 | 0.866164 | ||||||||
\(161\) | −3.41293 | −0.268977 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.3414 | −1.27996 | −0.639978 | − | 0.768393i | \(-0.721057\pi\) | ||||
−0.639978 | + | 0.768393i | \(0.721057\pi\) | |||||||
\(164\) | −8.73705 | −0.682249 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.46287 | −0.501616 | ||||||||
\(167\) | 5.89276 | 0.455995 | 0.227998 | − | 0.973662i | \(-0.426782\pi\) | ||||
0.227998 | + | 0.973662i | \(0.426782\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.3787 | 2.49067 | ||||||||
\(170\) | 4.73749 | 0.363349 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.9089 | −0.984292 | ||||||||
\(173\) | 1.20279 | 0.0914467 | 0.0457234 | − | 0.998954i | \(-0.485441\pi\) | ||||
0.0457234 | + | 0.998954i | \(0.485441\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.21485 | 0.243020 | ||||||||
\(176\) | −17.2474 | −1.30007 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.18323 | −0.238593 | ||||||||
\(179\) | 15.5040 | 1.15883 | 0.579413 | − | 0.815034i | \(-0.303282\pi\) | ||||
0.579413 | + | 0.815034i | \(0.303282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.2463 | −1.72789 | −0.863943 | − | 0.503590i | \(-0.832012\pi\) | ||||
−0.863943 | + | 0.503590i | \(0.832012\pi\) | |||||||
\(182\) | −9.75612 | −0.723172 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.62098 | 0.119500 | ||||||||
\(185\) | −11.8011 | −0.867633 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.7589 | −1.95681 | ||||||||
\(188\) | −6.37389 | −0.464864 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.48235 | 0.252636 | ||||||||
\(191\) | −18.0430 | −1.30555 | −0.652773 | − | 0.757553i | \(-0.726395\pi\) | ||||
−0.652773 | + | 0.757553i | \(0.726395\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.24298 | 0.449380 | 0.224690 | − | 0.974430i | \(-0.427863\pi\) | ||||
0.224690 | + | 0.974430i | \(0.427863\pi\) | |||||||
\(194\) | −4.09593 | −0.294070 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.45925 | −0.604232 | ||||||||
\(197\) | −14.9870 | −1.06778 | −0.533891 | − | 0.845553i | \(-0.679271\pi\) | ||||
−0.533891 | + | 0.845553i | \(0.679271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.83185 | −0.342521 | −0.171260 | − | 0.985226i | \(-0.554784\pi\) | ||||
−0.171260 | + | 0.985226i | \(0.554784\pi\) | |||||||
\(200\) | −1.52690 | −0.107968 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.92595 | −0.205869 | ||||||||
\(203\) | −3.41293 | −0.239541 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.7024 | 0.817332 | ||||||||
\(206\) | 6.54393 | 0.455937 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −19.8857 | −1.37883 | ||||||||
\(209\) | −19.6695 | −1.36057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.98291 | 0.687252 | 0.343626 | − | 0.939107i | \(-0.388345\pi\) | ||||
0.343626 | + | 0.939107i | \(0.388345\pi\) | |||||||
\(212\) | 1.46160 | 0.100383 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.03544 | −0.412574 | ||||||||
\(215\) | 17.2902 | 1.17918 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.70897 | −0.523319 | ||||||||
\(218\) | 2.83316 | 0.191886 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 25.9196 | 1.74750 | ||||||||
\(221\) | −30.8522 | −2.07534 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.51605 | −0.235452 | −0.117726 | − | 0.993046i | \(-0.537561\pi\) | ||||
−0.117726 | + | 0.993046i | \(0.537561\pi\) | |||||||
\(224\) | 15.3399 | 1.02494 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.77570 | 0.317675 | ||||||||
\(227\) | 9.22552 | 0.612319 | 0.306160 | − | 0.951980i | \(-0.400956\pi\) | ||||
0.306160 | + | 0.951980i | \(0.400956\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.97788 | −0.593275 | −0.296638 | − | 0.954990i | \(-0.595865\pi\) | ||||
−0.296638 | + | 0.954990i | \(0.595865\pi\) | |||||||
\(230\) | −1.03440 | −0.0682063 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.62098 | 0.106423 | ||||||||
\(233\) | 10.5134 | 0.688753 | 0.344376 | − | 0.938832i | \(-0.388090\pi\) | ||||
0.344376 | + | 0.938832i | \(0.388090\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.53720 | 0.556905 | ||||||||
\(236\) | 15.2421 | 0.992177 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.63302 | 0.429955 | ||||||||
\(239\) | −14.4794 | −0.936596 | −0.468298 | − | 0.883571i | \(-0.655133\pi\) | ||||
−0.468298 | + | 0.883571i | \(0.655133\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.76018 | 0.113383 | 0.0566917 | − | 0.998392i | \(-0.481945\pi\) | ||||
0.0566917 | + | 0.998392i | \(0.481945\pi\) | |||||||
\(242\) | 9.81793 | 0.631121 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 22.4248 | 1.43560 | ||||||||
\(245\) | 11.3303 | 0.723868 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.6783 | −1.44298 | ||||||||
\(248\) | 3.66140 | 0.232499 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.19763 | −0.265482 | ||||||||
\(251\) | −11.6685 | −0.736506 | −0.368253 | − | 0.929726i | \(-0.620044\pi\) | ||||
−0.368253 | + | 0.929726i | \(0.620044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.84264 | 0.367324 | ||||||||
\(254\) | −7.57556 | −0.475333 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.45909 | 0.216193 | ||||||||
\(257\) | −9.01106 | −0.562094 | −0.281047 | − | 0.959694i | \(-0.590682\pi\) | ||||
−0.281047 | + | 0.959694i | \(0.590682\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.5228 | −1.02668 | ||||||||
\(260\) | 29.8844 | 1.85335 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.59155 | 0.160106 | ||||||||
\(263\) | 21.3050 | 1.31372 | 0.656861 | − | 0.754012i | \(-0.271884\pi\) | ||||
0.656861 | + | 0.754012i | \(0.271884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.95767 | −0.120259 | ||||||||
\(266\) | 4.87568 | 0.298947 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.7974 | −0.781728 | ||||||||
\(269\) | −6.35901 | −0.387716 | −0.193858 | − | 0.981030i | \(-0.562100\pi\) | ||||
−0.193858 | + | 0.981030i | \(0.562100\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.4931 | −1.67009 | −0.835044 | − | 0.550183i | \(-0.814558\pi\) | ||||
−0.835044 | + | 0.550183i | \(0.814558\pi\) | |||||||
\(272\) | 13.5200 | 0.819767 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.05999 | 0.426510 | ||||||||
\(275\) | −5.50355 | −0.331876 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.7357 | −1.78664 | −0.893322 | − | 0.449417i | \(-0.851632\pi\) | ||||
−0.893322 | + | 0.449417i | \(0.851632\pi\) | |||||||
\(278\) | −7.37298 | −0.442202 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −13.4856 | −0.805921 | ||||||||
\(281\) | 11.1902 | 0.667550 | 0.333775 | − | 0.942653i | \(-0.391677\pi\) | ||||
0.333775 | + | 0.942653i | \(0.391677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.7812 | 1.05698 | 0.528492 | − | 0.848938i | \(-0.322758\pi\) | ||||
0.528492 | + | 0.848938i | \(0.322758\pi\) | |||||||
\(284\) | 12.5151 | 0.742632 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 16.7016 | 0.987587 | ||||||||
\(287\) | 16.3847 | 0.967158 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.97586 | 0.233874 | ||||||||
\(290\) | −1.03440 | −0.0607420 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.00043 | 0.351148 | ||||||||
\(293\) | 15.5413 | 0.907931 | 0.453966 | − | 0.891019i | \(-0.350009\pi\) | ||||
0.453966 | + | 0.891019i | \(0.350009\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.4153 | −1.18863 | ||||||||
\(296\) | 7.84757 | 0.456131 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.58821 | 0.381645 | ||||||||
\(299\) | 6.73637 | 0.389574 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 24.2082 | 1.39534 | ||||||||
\(302\) | −1.04098 | −0.0599019 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.93800 | 0.569984 | ||||||||
\(305\) | −30.0357 | −1.71984 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1411 | 0.807075 | 0.403538 | − | 0.914963i | \(-0.367780\pi\) | ||||
0.403538 | + | 0.914963i | \(0.367780\pi\) | |||||||
\(308\) | 36.2904 | 2.06784 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.33645 | −0.132701 | ||||||||
\(311\) | −17.5960 | −0.997780 | −0.498890 | − | 0.866665i | \(-0.666259\pi\) | ||||
−0.498890 | + | 0.866665i | \(0.666259\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.544433 | 0.0307732 | 0.0153866 | − | 0.999882i | \(-0.495102\pi\) | ||||
0.0153866 | + | 0.999882i | \(0.495102\pi\) | |||||||
\(314\) | −1.00070 | −0.0564729 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.9210 | 1.23315 | ||||||||
\(317\) | −14.2193 | −0.798635 | −0.399318 | − | 0.916813i | \(-0.630753\pi\) | ||||
−0.399318 | + | 0.916813i | \(0.630753\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.84264 | 0.327125 | ||||||||
\(320\) | −9.74238 | −0.544616 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.44828 | −0.0807093 | ||||||||
\(323\) | 15.4186 | 0.857912 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.34540 | −0.351980 | ||||||||
\(326\) | −6.93445 | −0.384064 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.78196 | −0.429687 | ||||||||
\(329\) | 11.9530 | 0.658992 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3007 | 0.566176 | 0.283088 | − | 0.959094i | \(-0.408641\pi\) | ||||
0.283088 | + | 0.959094i | \(0.408641\pi\) | |||||||
\(332\) | 27.7176 | 1.52120 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.50059 | 0.136826 | ||||||||
\(335\) | 17.1409 | 0.936508 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.8924 | −1.41045 | −0.705224 | − | 0.708984i | \(-0.749154\pi\) | ||||
−0.705224 | + | 0.708984i | \(0.749154\pi\) | |||||||
\(338\) | 13.7399 | 0.747350 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −20.3179 | −1.10189 | ||||||||
\(341\) | 13.1971 | 0.714661 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.02681 | −0.433407 | ||||||||
\(344\) | −11.4977 | −0.619917 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.510404 | 0.0274395 | ||||||||
\(347\) | 13.4609 | 0.722621 | 0.361310 | − | 0.932446i | \(-0.382330\pi\) | ||||
0.361310 | + | 0.932446i | \(0.382330\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.3225 | −1.51607 | −0.758035 | − | 0.652213i | \(-0.773841\pi\) | ||||
−0.758035 | + | 0.652213i | \(0.773841\pi\) | |||||||
\(350\) | 1.36422 | 0.0729207 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −26.2606 | −1.39969 | ||||||||
\(353\) | 10.2989 | 0.548156 | 0.274078 | − | 0.961707i | \(-0.411627\pi\) | ||||
0.274078 | + | 0.961707i | \(0.411627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.7627 | −0.889671 | ||||||||
\(356\) | 13.6521 | 0.723559 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.57912 | 0.347717 | ||||||||
\(359\) | 23.4510 | 1.23770 | 0.618849 | − | 0.785510i | \(-0.287599\pi\) | ||||
0.618849 | + | 0.785510i | \(0.287599\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.66640 | −0.403495 | ||||||||
\(362\) | −9.86455 | −0.518469 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 41.8416 | 2.19309 | ||||||||
\(365\) | −8.03698 | −0.420675 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.1389 | −0.999040 | −0.499520 | − | 0.866302i | \(-0.666490\pi\) | ||||
−0.499520 | + | 0.866302i | \(0.666490\pi\) | |||||||
\(368\) | −2.95199 | −0.153883 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.00778 | −0.260342 | ||||||||
\(371\) | −2.74096 | −0.142304 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −36.6987 | −1.90019 | −0.950094 | − | 0.311964i | \(-0.899013\pi\) | ||||
−0.950094 | + | 0.311964i | \(0.899013\pi\) | |||||||
\(374\) | −11.3551 | −0.587160 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.67713 | −0.292776 | ||||||||
\(377\) | 6.73637 | 0.346941 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.5791 | −1.41664 | −0.708322 | − | 0.705889i | \(-0.750548\pi\) | ||||
−0.708322 | + | 0.705889i | \(0.750548\pi\) | |||||||
\(380\) | −14.9349 | −0.766145 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.65654 | −0.391743 | ||||||||
\(383\) | 22.2252 | 1.13566 | 0.567829 | − | 0.823147i | \(-0.307784\pi\) | ||||
0.567829 | + | 0.823147i | \(0.307784\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −48.6074 | −2.47726 | ||||||||
\(386\) | 2.64920 | 0.134841 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.5664 | 0.891800 | ||||||||
\(389\) | 8.46057 | 0.428968 | 0.214484 | − | 0.976728i | \(-0.431193\pi\) | ||||
0.214484 | + | 0.976728i | \(0.431193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.57994 | −0.231618 | ||||||||
\(392\) | −7.53453 | −0.380551 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.35973 | −0.320399 | ||||||||
\(395\) | −29.3611 | −1.47732 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.9140 | −1.40096 | −0.700481 | − | 0.713671i | \(-0.747031\pi\) | ||||
−0.700481 | + | 0.713671i | \(0.747031\pi\) | |||||||
\(398\) | −2.05039 | −0.102777 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.78066 | 0.139033 | ||||||||
\(401\) | −5.92439 | −0.295850 | −0.147925 | − | 0.988999i | \(-0.547259\pi\) | ||||
−0.147925 | + | 0.988999i | \(0.547259\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.2158 | 0.757952 | ||||||||
\(404\) | 12.5487 | 0.624320 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.44828 | −0.0718767 | ||||||||
\(407\) | 28.2856 | 1.40207 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.3485 | 0.709487 | 0.354744 | − | 0.934964i | \(-0.384568\pi\) | ||||
0.354744 | + | 0.934964i | \(0.384568\pi\) | |||||||
\(410\) | 4.96591 | 0.245249 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −28.0653 | −1.38268 | ||||||||
\(413\) | −28.5837 | −1.40651 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −37.1250 | −1.82240 | ||||||||
\(416\) | −30.2776 | −1.48448 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.34673 | −0.408252 | ||||||||
\(419\) | 36.2582 | 1.77133 | 0.885665 | − | 0.464325i | \(-0.153703\pi\) | ||||
0.885665 | + | 0.464325i | \(0.153703\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.7411 | 0.864650 | 0.432325 | − | 0.901718i | \(-0.357693\pi\) | ||||
0.432325 | + | 0.901718i | \(0.357693\pi\) | |||||||
\(422\) | 4.23624 | 0.206217 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.30183 | 0.0632223 | ||||||||
\(425\) | 4.31413 | 0.209266 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −42.0534 | −2.03511 | ||||||||
\(428\) | 25.8845 | 1.25118 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.33707 | 0.353825 | ||||||||
\(431\) | −18.7348 | −0.902422 | −0.451211 | − | 0.892417i | \(-0.649008\pi\) | ||||
−0.451211 | + | 0.892417i | \(0.649008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.71993 | 0.226825 | 0.113413 | − | 0.993548i | \(-0.463822\pi\) | ||||
0.113413 | + | 0.993548i | \(0.463822\pi\) | |||||||
\(434\) | −3.27129 | −0.157027 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.1507 | −0.581914 | ||||||||
\(437\) | −3.36654 | −0.161043 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.6405 | 1.17603 | 0.588014 | − | 0.808851i | \(-0.299910\pi\) | ||||
0.588014 | + | 0.808851i | \(0.299910\pi\) | |||||||
\(440\) | 23.0862 | 1.10059 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.0921 | −0.622727 | ||||||||
\(443\) | 11.2204 | 0.533097 | 0.266549 | − | 0.963821i | \(-0.414117\pi\) | ||||
0.266549 | + | 0.963821i | \(0.414117\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.2856 | −0.866821 | ||||||||
\(446\) | −1.49203 | −0.0706499 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −13.6404 | −0.644450 | ||||||||
\(449\) | 8.68202 | 0.409730 | 0.204865 | − | 0.978790i | \(-0.434324\pi\) | ||||
0.204865 | + | 0.978790i | \(0.434324\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −28.0492 | −1.32078 | ||||||||
\(452\) | −20.4818 | −0.963382 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.91484 | 0.183733 | ||||||||
\(455\) | −56.0427 | −2.62732 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.9401 | 1.77476 | 0.887382 | − | 0.461035i | \(-0.152522\pi\) | ||||
0.887382 | + | 0.461035i | \(0.152522\pi\) | |||||||
\(458\) | −3.80976 | −0.178018 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.43628 | 0.206843 | ||||||||
\(461\) | −40.1649 | −1.87066 | −0.935332 | − | 0.353770i | \(-0.884900\pi\) | ||||
−0.935332 | + | 0.353770i | \(0.884900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.2381 | −1.35881 | −0.679404 | − | 0.733764i | \(-0.737762\pi\) | ||||
−0.679404 | + | 0.733764i | \(0.737762\pi\) | |||||||
\(464\) | −2.95199 | −0.137043 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.46133 | 0.206667 | ||||||||
\(467\) | 32.6854 | 1.51250 | 0.756250 | − | 0.654283i | \(-0.227029\pi\) | ||||
0.756250 | + | 0.654283i | \(0.227029\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.9992 | 1.10818 | ||||||||
\(470\) | 3.62275 | 0.167105 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.5759 | 0.624883 | ||||||||
\(473\) | −41.4423 | −1.90552 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.17115 | 0.145503 | ||||||||
\(476\) | −28.4474 | −1.30388 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.14433 | −0.281035 | ||||||||
\(479\) | −2.99873 | −0.137016 | −0.0685078 | − | 0.997651i | \(-0.521824\pi\) | ||||
−0.0685078 | + | 0.997651i | \(0.521824\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.6124 | 1.48700 | ||||||||
\(482\) | 0.746932 | 0.0340218 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −42.1067 | −1.91394 | ||||||||
\(485\) | −23.5285 | −1.06837 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.57967 | 0.252839 | 0.126420 | − | 0.991977i | \(-0.459651\pi\) | ||||
0.126420 | + | 0.991977i | \(0.459651\pi\) | |||||||
\(488\) | 19.9734 | 0.904153 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.80801 | 0.217204 | ||||||||
\(491\) | 15.3909 | 0.694583 | 0.347292 | − | 0.937757i | \(-0.387101\pi\) | ||||
0.347292 | + | 0.937757i | \(0.387101\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.57994 | −0.206270 | ||||||||
\(494\) | −9.62350 | −0.432982 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.66782 | −0.299394 | ||||||||
\(497\) | −23.4697 | −1.05276 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.711042 | −0.0318306 | −0.0159153 | − | 0.999873i | \(-0.505066\pi\) | ||||
−0.0159153 | + | 0.999873i | \(0.505066\pi\) | |||||||
\(500\) | 18.0026 | 0.805101 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.95150 | −0.220996 | ||||||||
\(503\) | −7.73183 | −0.344745 | −0.172373 | − | 0.985032i | \(-0.555143\pi\) | ||||
−0.172373 | + | 0.985032i | \(0.555143\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −16.8077 | −0.747934 | ||||||||
\(506\) | 2.47932 | 0.110219 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 32.4897 | 1.44150 | ||||||||
\(509\) | 29.1832 | 1.29352 | 0.646760 | − | 0.762693i | \(-0.276123\pi\) | ||||
0.646760 | + | 0.762693i | \(0.276123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.2527 | −0.497789 | ||||||||
\(512\) | 22.8384 | 1.00932 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.82383 | −0.168662 | ||||||||
\(515\) | 37.5907 | 1.65644 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −20.4625 | −0.899942 | ||||||||
\(518\) | −7.01145 | −0.308066 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 26.6176 | 1.16726 | ||||||||
\(521\) | −31.2501 | −1.36909 | −0.684547 | − | 0.728969i | \(-0.740000\pi\) | ||||
−0.684547 | + | 0.728969i | \(0.740000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.76052 | 0.383071 | 0.191535 | − | 0.981486i | \(-0.438653\pi\) | ||||
0.191535 | + | 0.981486i | \(0.438653\pi\) | |||||||
\(524\) | −11.1145 | −0.485539 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.04075 | 0.394196 | ||||||||
\(527\) | −10.3449 | −0.450633 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −0.830736 | −0.0360849 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −20.9106 | −0.906588 | ||||||||
\(533\) | −32.3397 | −1.40079 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −34.6698 | −1.49890 | ||||||||
\(536\) | −11.3985 | −0.492340 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.69844 | −0.116338 | ||||||||
\(539\) | −27.1573 | −1.16975 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.5448 | −1.18424 | −0.592121 | − | 0.805849i | \(-0.701709\pi\) | ||||
−0.592121 | + | 0.805849i | \(0.701709\pi\) | |||||||
\(542\) | −11.6667 | −0.501127 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.5852 | 0.882583 | ||||||||
\(545\) | 16.2747 | 0.697132 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6989 | 0.457451 | 0.228725 | − | 0.973491i | \(-0.426544\pi\) | ||||
0.228725 | + | 0.973491i | \(0.426544\pi\) | |||||||
\(548\) | −30.2785 | −1.29343 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.33542 | −0.0995829 | ||||||||
\(551\) | −3.36654 | −0.143419 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.1088 | −1.74812 | ||||||||
\(554\) | −12.6183 | −0.536101 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 31.6209 | 1.34102 | ||||||||
\(557\) | 14.8501 | 0.629217 | 0.314608 | − | 0.949222i | \(-0.398127\pi\) | ||||
0.314608 | + | 0.949222i | \(0.398127\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −47.7815 | −2.02094 | ||||||||
\(560\) | 24.5589 | 1.03780 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.74855 | 0.200305 | ||||||||
\(563\) | 32.9448 | 1.38846 | 0.694229 | − | 0.719754i | \(-0.255745\pi\) | ||||
0.694229 | + | 0.719754i | \(0.255745\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 27.4333 | 1.15413 | ||||||||
\(566\) | 7.54545 | 0.317159 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.1470 | 0.467717 | ||||||||
\(569\) | 0.826143 | 0.0346337 | 0.0173169 | − | 0.999850i | \(-0.494488\pi\) | ||||
0.0173169 | + | 0.999850i | \(0.494488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.0145 | 1.08867 | 0.544337 | − | 0.838867i | \(-0.316781\pi\) | ||||
0.544337 | + | 0.838867i | \(0.316781\pi\) | |||||||
\(572\) | −71.6291 | −2.99496 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.95283 | 0.290206 | ||||||||
\(575\) | −0.941962 | −0.0392825 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0333 | −0.709104 | −0.354552 | − | 0.935036i | \(-0.615367\pi\) | ||||
−0.354552 | + | 0.935036i | \(0.615367\pi\) | |||||||
\(578\) | 1.68715 | 0.0701762 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.43628 | 0.184207 | ||||||||
\(581\) | −51.9792 | −2.15646 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.69228 | 0.194334 | ||||||||
\(584\) | 5.34449 | 0.221157 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.59493 | 0.272434 | ||||||||
\(587\) | 4.52833 | 0.186904 | 0.0934522 | − | 0.995624i | \(-0.470210\pi\) | ||||
0.0934522 | + | 0.995624i | \(0.470210\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.60418 | −0.313325 | ||||||||
\(590\) | −8.66322 | −0.356659 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14.2913 | −0.587369 | ||||||||
\(593\) | −32.9549 | −1.35330 | −0.676648 | − | 0.736307i | \(-0.736568\pi\) | ||||
−0.676648 | + | 0.736307i | \(0.736568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 38.1024 | 1.56205 | ||||||||
\(596\) | −28.2552 | −1.15738 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.85857 | 0.116896 | ||||||||
\(599\) | −19.3328 | −0.789918 | −0.394959 | − | 0.918699i | \(-0.629241\pi\) | ||||
−0.394959 | + | 0.918699i | \(0.629241\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.3794 | 0.831294 | 0.415647 | − | 0.909526i | \(-0.363555\pi\) | ||||
0.415647 | + | 0.909526i | \(0.363555\pi\) | |||||||
\(602\) | 10.2727 | 0.418685 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.46452 | 0.181659 | ||||||||
\(605\) | 56.3977 | 2.29289 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5119 | 0.873143 | 0.436571 | − | 0.899670i | \(-0.356193\pi\) | ||||
0.436571 | + | 0.899670i | \(0.356193\pi\) | |||||||
\(608\) | 15.1314 | 0.613659 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.7456 | −0.516056 | ||||||||
\(611\) | −23.5926 | −0.954456 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.08436 | 0.326524 | 0.163262 | − | 0.986583i | \(-0.447798\pi\) | ||||
0.163262 | + | 0.986583i | \(0.447798\pi\) | |||||||
\(614\) | 6.00076 | 0.242171 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 32.3233 | 1.30234 | ||||||||
\(617\) | 5.79105 | 0.233139 | 0.116570 | − | 0.993183i | \(-0.462810\pi\) | ||||
0.116570 | + | 0.993183i | \(0.462810\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.5549 | −0.906559 | −0.453279 | − | 0.891368i | \(-0.649746\pi\) | ||||
−0.453279 | + | 0.891368i | \(0.649746\pi\) | |||||||
\(620\) | 10.0205 | 0.402431 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.46687 | −0.299394 | ||||||||
\(623\) | −25.6019 | −1.02572 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.8225 | −1.15290 | ||||||||
\(626\) | 0.231030 | 0.00923380 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.29177 | 0.171260 | ||||||||
\(629\) | −22.1726 | −0.884080 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.2346 | 1.80076 | 0.900381 | − | 0.435101i | \(-0.143287\pi\) | ||||
0.900381 | + | 0.435101i | \(0.143287\pi\) | |||||||
\(632\) | 19.5247 | 0.776653 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.03395 | −0.239639 | ||||||||
\(635\) | −43.5167 | −1.72691 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.3115 | −1.24061 | ||||||||
\(638\) | 2.47932 | 0.0981572 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −26.0466 | −1.02958 | ||||||||
\(641\) | 23.2117 | 0.916809 | 0.458404 | − | 0.888744i | \(-0.348421\pi\) | ||||
0.458404 | + | 0.888744i | \(0.348421\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.33923 | 0.289431 | 0.144715 | − | 0.989473i | \(-0.453773\pi\) | ||||
0.144715 | + | 0.989473i | \(0.453773\pi\) | |||||||
\(644\) | 6.21129 | 0.244759 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.54285 | 0.257425 | ||||||||
\(647\) | −22.3876 | −0.880148 | −0.440074 | − | 0.897962i | \(-0.645048\pi\) | ||||
−0.440074 | + | 0.897962i | \(0.645048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 48.9328 | 1.92078 | ||||||||
\(650\) | −2.69267 | −0.105615 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 29.7401 | 1.16471 | ||||||||
\(653\) | −19.8442 | −0.776564 | −0.388282 | − | 0.921541i | \(-0.626931\pi\) | ||||
−0.388282 | + | 0.921541i | \(0.626931\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.8868 | 0.581675 | ||||||||
\(656\) | 14.1718 | 0.553317 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.07226 | 0.197737 | ||||||||
\(659\) | 10.2160 | 0.397958 | 0.198979 | − | 0.980004i | \(-0.436237\pi\) | ||||
0.198979 | + | 0.980004i | \(0.436237\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.0111 | −0.467179 | −0.233589 | − | 0.972335i | \(-0.575047\pi\) | ||||
−0.233589 | + | 0.972335i | \(0.575047\pi\) | |||||||
\(662\) | 4.37108 | 0.169887 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.6877 | 0.958068 | ||||||||
\(665\) | 28.0077 | 1.08609 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −10.7244 | −0.414939 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7.27373 | 0.281009 | ||||||||
\(671\) | 71.9917 | 2.77921 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.1569 | 0.931179 | 0.465590 | − | 0.885001i | \(-0.345842\pi\) | ||||
0.465590 | + | 0.885001i | \(0.345842\pi\) | |||||||
\(674\) | −10.9874 | −0.423220 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −58.9269 | −2.26642 | ||||||||
\(677\) | 45.3916 | 1.74454 | 0.872271 | − | 0.489023i | \(-0.162647\pi\) | ||||
0.872271 | + | 0.489023i | \(0.162647\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −32.9425 | −1.26422 | ||||||||
\(680\) | −18.0969 | −0.693983 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.60016 | 0.214441 | ||||||||
\(683\) | −29.6148 | −1.13318 | −0.566589 | − | 0.824000i | \(-0.691737\pi\) | ||||
−0.566589 | + | 0.824000i | \(0.691737\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.5551 | 1.54953 | ||||||||
\(686\) | −3.40617 | −0.130048 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.9387 | 0.798280 | ||||||||
\(689\) | 5.41004 | 0.206106 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.0680 | 0.953633 | 0.476817 | − | 0.879003i | \(-0.341791\pi\) | ||||
0.476817 | + | 0.879003i | \(0.341791\pi\) | |||||||
\(692\) | −2.18900 | −0.0832132 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.71213 | 0.216830 | ||||||||
\(695\) | −42.3530 | −1.60654 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.9872 | 0.832826 | ||||||||
\(698\) | −12.0186 | −0.454912 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.85080 | −0.221140 | ||||||||
\(701\) | 6.49421 | 0.245283 | 0.122641 | − | 0.992451i | \(-0.460864\pi\) | ||||
0.122641 | + | 0.992451i | \(0.460864\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.2982 | −0.614700 | ||||||||
\(704\) | 23.3512 | 0.880082 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.37034 | 0.164480 | ||||||||
\(707\) | −23.5327 | −0.885039 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.52860 | 0.0949635 | 0.0474817 | − | 0.998872i | \(-0.484880\pi\) | ||||
0.0474817 | + | 0.998872i | \(0.484880\pi\) | |||||||
\(710\) | −7.11323 | −0.266955 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.1597 | 0.455704 | ||||||||
\(713\) | 2.25875 | 0.0845909 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 95.9401 | 3.58796 | ||||||||
\(716\) | −28.2162 | −1.05449 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.95142 | 0.371384 | ||||||||
\(719\) | 50.7768 | 1.89366 | 0.946828 | − | 0.321739i | \(-0.104267\pi\) | ||||
0.946828 | + | 0.321739i | \(0.104267\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 52.6312 | 1.96009 | ||||||||
\(722\) | −3.25323 | −0.121073 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 42.3066 | 1.57231 | ||||||||
\(725\) | −0.941962 | −0.0349836 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.8691 | −1.51575 | −0.757876 | − | 0.652399i | \(-0.773763\pi\) | ||||
−0.757876 | + | 0.652399i | \(0.773763\pi\) | |||||||
\(728\) | 37.2677 | 1.38123 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.41049 | −0.126228 | ||||||||
\(731\) | 32.4858 | 1.20153 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.3863 | −0.937665 | −0.468832 | − | 0.883287i | \(-0.655325\pi\) | ||||
−0.468832 | + | 0.883287i | \(0.655325\pi\) | |||||||
\(734\) | −8.12156 | −0.299772 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.49464 | −0.165675 | ||||||||
\(737\) | −41.0845 | −1.51337 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.1947 | −0.779658 | −0.389829 | − | 0.920887i | \(-0.627466\pi\) | ||||
−0.389829 | + | 0.920887i | \(0.627466\pi\) | |||||||
\(740\) | 21.4771 | 0.789514 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.16312 | −0.0426996 | ||||||||
\(743\) | 33.9818 | 1.24667 | 0.623336 | − | 0.781954i | \(-0.285777\pi\) | ||||
0.623336 | + | 0.781954i | \(0.285777\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.8450 | 1.38653 | ||||||||
\(746\) | −15.5731 | −0.570171 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 48.6994 | 1.78062 | ||||||||
\(749\) | −48.5416 | −1.77367 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.40956 | 0.306869 | 0.153435 | − | 0.988159i | \(-0.450967\pi\) | ||||
0.153435 | + | 0.988159i | \(0.450967\pi\) | |||||||
\(752\) | 10.3387 | 0.377013 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.85857 | 0.104103 | ||||||||
\(755\) | −5.97979 | −0.217627 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.3310 | 0.920670 | 0.460335 | − | 0.887745i | \(-0.347729\pi\) | ||||
0.460335 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(758\) | −11.7032 | −0.425079 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.3023 | −0.482526 | ||||||||
\(761\) | −20.1122 | −0.729067 | −0.364534 | − | 0.931190i | \(-0.618772\pi\) | ||||
−0.364534 | + | 0.931190i | \(0.618772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.7864 | 0.824924 | ||||||||
\(764\) | 32.8370 | 1.18800 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.43126 | 0.340765 | ||||||||
\(767\) | 56.4179 | 2.03713 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.2509 | −1.01875 | −0.509377 | − | 0.860543i | \(-0.670124\pi\) | ||||
−0.509377 | + | 0.860543i | \(0.670124\pi\) | |||||||
\(770\) | −20.6265 | −0.743327 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11.3618 | −0.408919 | ||||||||
\(773\) | 21.5840 | 0.776323 | 0.388161 | − | 0.921591i | \(-0.373110\pi\) | ||||
0.388161 | + | 0.921591i | \(0.373110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.12766 | −0.0764277 | ||||||||
\(776\) | 15.6461 | 0.561664 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.59024 | 0.128716 | ||||||||
\(779\) | 16.1620 | 0.579063 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.1780 | 1.43768 | ||||||||
\(782\) | −1.94349 | −0.0694992 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.7212 | 0.490044 | ||||||||
\(785\) | −5.74840 | −0.205169 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.3258 | −1.25923 | −0.629614 | − | 0.776908i | \(-0.716787\pi\) | ||||
−0.629614 | + | 0.776908i | \(0.716787\pi\) | |||||||
\(788\) | 27.2753 | 0.971643 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.4593 | −0.443283 | ||||||||
\(791\) | 38.4098 | 1.36569 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 83.0041 | 2.94756 | ||||||||
\(794\) | −11.8453 | −0.420373 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.79362 | 0.311682 | ||||||||
\(797\) | −16.5841 | −0.587439 | −0.293719 | − | 0.955892i | \(-0.594893\pi\) | ||||
−0.293719 | + | 0.955892i | \(0.594893\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.0402 | 0.567462 | ||||||||
\(800\) | 4.23378 | 0.149687 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.51401 | −0.0887728 | ||||||||
\(803\) | 19.2636 | 0.679797 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.31942 | −0.293221 | ||||||||
\(806\) | 6.45680 | 0.227431 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.1769 | 0.393203 | ||||||||
\(809\) | −46.3267 | −1.62876 | −0.814379 | − | 0.580333i | \(-0.802922\pi\) | ||||
−0.814379 | + | 0.580333i | \(0.802922\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.92923 | −0.243318 | −0.121659 | − | 0.992572i | \(-0.538821\pi\) | ||||
−0.121659 | + | 0.992572i | \(0.538821\pi\) | |||||||
\(812\) | 6.21129 | 0.217974 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.0030 | 0.420704 | ||||||||
\(815\) | −39.8340 | −1.39532 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.8791 | 0.835424 | ||||||||
\(818\) | 6.08877 | 0.212889 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21.2976 | −0.743743 | ||||||||
\(821\) | 12.4948 | 0.436070 | 0.218035 | − | 0.975941i | \(-0.430035\pi\) | ||||
0.218035 | + | 0.975941i | \(0.430035\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.6832 | 0.720971 | 0.360485 | − | 0.932765i | \(-0.382611\pi\) | ||||
0.360485 | + | 0.932765i | \(0.382611\pi\) | |||||||
\(824\) | −24.9973 | −0.870823 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.1295 | −0.422039 | ||||||||
\(827\) | 37.9507 | 1.31968 | 0.659838 | − | 0.751408i | \(-0.270625\pi\) | ||||
0.659838 | + | 0.751408i | \(0.270625\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.1196 | −0.802977 | −0.401489 | − | 0.915864i | \(-0.631507\pi\) | ||||
−0.401489 | + | 0.915864i | \(0.631507\pi\) | |||||||
\(830\) | −15.7540 | −0.546828 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 26.9232 | 0.933393 | ||||||||
\(833\) | 21.2881 | 0.737590 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.3643 | 0.497096 | ||||||||
\(836\) | 35.7970 | 1.23807 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 15.3861 | 0.531505 | ||||||||
\(839\) | 35.3974 | 1.22205 | 0.611027 | − | 0.791609i | \(-0.290757\pi\) | ||||
0.611027 | + | 0.791609i | \(0.290757\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 7.52844 | 0.259447 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.1682 | −0.625374 | ||||||||
\(845\) | 78.9267 | 2.71516 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 78.9632 | 2.71321 | ||||||||
\(848\) | −2.37077 | −0.0814127 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.83070 | 0.0627924 | ||||||||
\(851\) | 4.84124 | 0.165956 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.4871 | 0.872661 | 0.436331 | − | 0.899786i | \(-0.356278\pi\) | ||||
0.436331 | + | 0.899786i | \(0.356278\pi\) | |||||||
\(854\) | −17.8453 | −0.610655 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23.0550 | 0.788002 | ||||||||
\(857\) | 26.7263 | 0.912954 | 0.456477 | − | 0.889735i | \(-0.349111\pi\) | ||||
0.456477 | + | 0.889735i | \(0.349111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.6325 | −1.52284 | −0.761421 | − | 0.648257i | \(-0.775498\pi\) | ||||
−0.761421 | + | 0.648257i | \(0.775498\pi\) | |||||||
\(860\) | −31.4669 | −1.07301 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.95009 | −0.270781 | ||||||||
\(863\) | −38.5205 | −1.31125 | −0.655626 | − | 0.755085i | \(-0.727595\pi\) | ||||
−0.655626 | + | 0.755085i | \(0.727595\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.93195 | 0.0996892 | ||||||||
\(866\) | 2.00290 | 0.0680612 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.0298 | 0.476201 | ||||||||
\(869\) | 70.3746 | 2.38730 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.3691 | −1.60504 | ||||||||
\(872\) | −10.8225 | −0.366495 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.42859 | −0.0483227 | ||||||||
\(875\) | −33.7605 | −1.14131 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.2033 | −1.52641 | −0.763203 | − | 0.646158i | \(-0.776375\pi\) | ||||
−0.763203 | + | 0.646158i | \(0.776375\pi\) | |||||||
\(878\) | 10.4562 | 0.352879 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −42.0426 | −1.41726 | ||||||||
\(881\) | 34.1314 | 1.14992 | 0.574959 | − | 0.818182i | \(-0.305018\pi\) | ||||
0.574959 | + | 0.818182i | \(0.305018\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.9724 | 0.840387 | 0.420193 | − | 0.907435i | \(-0.361962\pi\) | ||||
0.420193 | + | 0.907435i | \(0.361962\pi\) | |||||||
\(884\) | 56.1487 | 1.88849 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.76137 | 0.159961 | ||||||||
\(887\) | 1.69868 | 0.0570362 | 0.0285181 | − | 0.999593i | \(-0.490921\pi\) | ||||
0.0285181 | + | 0.999593i | \(0.490921\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −60.9283 | −2.04347 | ||||||||
\(890\) | −7.75948 | −0.260098 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.39896 | 0.214253 | ||||||||
\(893\) | 11.7906 | 0.394556 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.7928 | 1.26328 | ||||||||
\(896\) | −36.4681 | −1.21832 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.68421 | 0.122944 | ||||||||
\(899\) | 2.25875 | 0.0753335 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.67819 | −0.122538 | ||||||||
\(902\) | −11.9026 | −0.396314 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −18.2428 | −0.606748 | ||||||||
\(905\) | −56.6655 | −1.88363 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.6791 | 0.686639 | 0.343320 | − | 0.939219i | \(-0.388449\pi\) | ||||
0.343320 | + | 0.939219i | \(0.388449\pi\) | |||||||
\(908\) | −16.7898 | −0.557188 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −23.7817 | −0.788354 | ||||||||
\(911\) | −56.7976 | −1.88179 | −0.940894 | − | 0.338700i | \(-0.890013\pi\) | ||||
−0.940894 | + | 0.338700i | \(0.890013\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 88.9838 | 2.94493 | ||||||||
\(914\) | 16.0999 | 0.532536 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.3391 | 0.539859 | ||||||||
\(917\) | 20.8432 | 0.688302 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −38.6718 | −1.27567 | −0.637833 | − | 0.770175i | \(-0.720169\pi\) | ||||
−0.637833 | + | 0.770175i | \(0.720169\pi\) | |||||||
\(920\) | 3.95133 | 0.130272 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.0439 | −0.561312 | ||||||||
\(923\) | 46.3239 | 1.52477 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.56027 | −0.149941 | ||||||||
\(926\) | −12.4072 | −0.407724 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.49464 | −0.147544 | ||||||||
\(929\) | −39.0509 | −1.28122 | −0.640609 | − | 0.767867i | \(-0.721318\pi\) | ||||
−0.640609 | + | 0.767867i | \(0.721318\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.6481 | 0.512846 | ||||||||
\(932\) | −19.1335 | −0.626740 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 13.8700 | 0.453841 | ||||||||
\(935\) | −65.2280 | −2.13318 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.2425 | −1.24933 | −0.624664 | − | 0.780894i | \(-0.714764\pi\) | ||||
−0.624664 | + | 0.780894i | \(0.714764\pi\) | |||||||
\(938\) | 10.1840 | 0.332521 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.5371 | −0.506764 | ||||||||
\(941\) | −26.9386 | −0.878172 | −0.439086 | − | 0.898445i | \(-0.644698\pi\) | ||||
−0.439086 | + | 0.898445i | \(0.644698\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.80077 | −0.156334 | ||||||||
\(944\) | −24.7233 | −0.804675 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.5860 | −0.571770 | ||||||||
\(947\) | 16.4580 | 0.534814 | 0.267407 | − | 0.963584i | \(-0.413833\pi\) | ||||
0.267407 | + | 0.963584i | \(0.413833\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22.2103 | 0.720976 | ||||||||
\(950\) | 1.34568 | 0.0436595 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −25.3376 | −0.821198 | ||||||||
\(953\) | 17.2466 | 0.558672 | 0.279336 | − | 0.960193i | \(-0.409886\pi\) | ||||
0.279336 | + | 0.960193i | \(0.409886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −43.9819 | −1.42322 | ||||||||
\(956\) | 26.3515 | 0.852268 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.27251 | −0.0411129 | ||||||||
\(959\) | 56.7817 | 1.83358 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25.8980 | −0.835421 | ||||||||
\(962\) | 13.8390 | 0.446189 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.20341 | −0.103175 | ||||||||
\(965\) | 15.2180 | 0.489884 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 47.6981 | 1.53387 | 0.766934 | − | 0.641726i | \(-0.221781\pi\) | ||||
0.766934 | + | 0.641726i | \(0.221781\pi\) | |||||||
\(968\) | −37.5038 | −1.20542 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.98429 | −0.320576 | ||||||||
\(971\) | −26.3554 | −0.845784 | −0.422892 | − | 0.906180i | \(-0.638985\pi\) | ||||
−0.422892 | + | 0.906180i | \(0.638985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −59.2990 | −1.90104 | ||||||||
\(974\) | 2.36773 | 0.0758670 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −36.3738 | −1.16430 | ||||||||
\(977\) | 28.7208 | 0.918858 | 0.459429 | − | 0.888214i | \(-0.348054\pi\) | ||||
0.459429 | + | 0.888214i | \(0.348054\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 43.8282 | 1.40076 | ||||||||
\(980\) | −20.6204 | −0.658694 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.53113 | 0.208417 | ||||||||
\(983\) | 0.767884 | 0.0244917 | 0.0122458 | − | 0.999925i | \(-0.496102\pi\) | ||||
0.0122458 | + | 0.999925i | \(0.496102\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.5326 | −1.16403 | ||||||||
\(986\) | −1.94349 | −0.0618935 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 41.2728 | 1.31306 | ||||||||
\(989\) | −7.09307 | −0.225546 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −29.3337 | −0.931815 | −0.465908 | − | 0.884833i | \(-0.654272\pi\) | ||||
−0.465908 | + | 0.884833i | \(0.654272\pi\) | |||||||
\(992\) | −10.1523 | −0.322335 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.95933 | −0.315891 | ||||||||
\(995\) | −11.7782 | −0.373394 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.7965 | −0.436940 | −0.218470 | − | 0.975844i | \(-0.570107\pi\) | ||||
−0.218470 | + | 0.975844i | \(0.570107\pi\) | |||||||
\(998\) | −0.301730 | −0.00955110 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.u.1.13 | yes | 22 | |
3.2 | odd | 2 | 6003.2.a.t.1.10 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.10 | ✓ | 22 | 3.2 | odd | 2 | ||
6003.2.a.u.1.13 | yes | 22 | 1.1 | even | 1 | trivial |