Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6032,2,Mod(1,6032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6032.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6032 = 2^{4} \cdot 13 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6032.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: | \(48.1657624992\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5x^{10} - 9x^{9} + 65x^{8} + 19x^{7} - 298x^{6} + 17x^{5} + 541x^{4} - 60x^{3} - 287x^{2} + 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 3016) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Root | \(-2.12599\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6032.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.12599 | 1.80479 | 0.902395 | − | 0.430911i | \(-0.141808\pi\) | ||||
0.902395 | + | 0.430911i | \(0.141808\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.76339 | −1.68304 | −0.841520 | − | 0.540226i | \(-0.818339\pi\) | ||||
−0.841520 | + | 0.540226i | \(0.818339\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.42274 | 0.915711 | 0.457855 | − | 0.889027i | \(-0.348618\pi\) | ||||
0.457855 | + | 0.889027i | \(0.348618\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.77179 | 2.25726 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.57467 | 1.98234 | 0.991169 | − | 0.132606i | \(-0.0423345\pi\) | ||||
0.991169 | + | 0.132606i | \(0.0423345\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.7643 | −3.03753 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.11681 | −0.270866 | −0.135433 | − | 0.990786i | \(-0.543243\pi\) | ||||
−0.135433 | + | 0.990786i | \(0.543243\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.43474 | −0.787984 | −0.393992 | − | 0.919114i | \(-0.628906\pi\) | ||||
−0.393992 | + | 0.919114i | \(0.628906\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.57346 | 1.65266 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.69657 | −0.353760 | −0.176880 | − | 0.984232i | \(-0.556600\pi\) | ||||
−0.176880 | + | 0.984232i | \(0.556600\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.16312 | 1.83262 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 11.7906 | 2.26910 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.408632 | −0.0733924 | −0.0366962 | − | 0.999326i | \(-0.511683\pi\) | ||||
−0.0366962 | + | 0.999326i | \(0.511683\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 20.5523 | 3.57770 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.11773 | −1.54118 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.7164 | 1.92616 | 0.963080 | − | 0.269216i | \(-0.0867645\pi\) | ||||
0.963080 | + | 0.269216i | \(0.0867645\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.12599 | 0.500558 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.63876 | 0.568278 | 0.284139 | − | 0.958783i | \(-0.408292\pi\) | ||||
0.284139 | + | 0.958783i | \(0.408292\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.08949 | 1.23364 | 0.616818 | − | 0.787106i | \(-0.288421\pi\) | ||||
0.616818 | + | 0.787106i | \(0.288421\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −25.4849 | −3.79907 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.68287 | −0.828931 | −0.414466 | − | 0.910065i | \(-0.636031\pi\) | ||||
−0.414466 | + | 0.910065i | \(0.636031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.13032 | −0.161474 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.49113 | −0.488856 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.27099 | 0.174584 | 0.0872918 | − | 0.996183i | \(-0.472179\pi\) | ||||
0.0872918 | + | 0.996183i | \(0.472179\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24.7431 | −3.33635 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.7370 | −1.42215 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.03303 | −0.915623 | −0.457811 | − | 0.889049i | \(-0.651366\pi\) | ||||
−0.457811 | + | 0.889049i | \(0.651366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.02110 | −1.02700 | −0.513498 | − | 0.858091i | \(-0.671651\pi\) | ||||
−0.513498 | + | 0.858091i | \(0.671651\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.4063 | 2.06700 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.76339 | −0.466791 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.218288 | −0.0266681 | −0.0133340 | − | 0.999911i | \(-0.504244\pi\) | ||||
−0.0133340 | + | 0.999911i | \(0.504244\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.30347 | −0.638462 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.8425 | 1.76148 | 0.880738 | − | 0.473604i | \(-0.157047\pi\) | ||||
0.880738 | + | 0.473604i | \(0.157047\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.83100 | 0.799508 | 0.399754 | − | 0.916623i | \(-0.369096\pi\) | ||||
0.399754 | + | 0.916623i | \(0.369096\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 28.6438 | 3.30750 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.9287 | 1.81525 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2164 | −1.14944 | −0.574718 | − | 0.818352i | \(-0.694888\pi\) | ||||
−0.574718 | + | 0.818352i | \(0.694888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.5418 | 1.83798 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.23571 | −1.01375 | −0.506876 | − | 0.862019i | \(-0.669200\pi\) | ||||
−0.506876 | + | 0.862019i | \(0.669200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.20299 | 0.455879 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.12599 | −0.335141 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.26275 | 0.663850 | 0.331925 | − | 0.943306i | \(-0.392302\pi\) | ||||
0.331925 | + | 0.943306i | \(0.392302\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.42274 | 0.253972 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.27738 | −0.132458 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.9263 | 1.32621 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.3964 | 1.46173 | 0.730865 | − | 0.682522i | \(-0.239117\pi\) | ||||
0.730865 | + | 0.682522i | \(0.239117\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 44.5223 | 4.47466 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.0169 | −1.29523 | −0.647613 | − | 0.761970i | \(-0.724232\pi\) | ||||
−0.647613 | + | 0.761970i | \(0.724232\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4214 | −1.22392 | −0.611959 | − | 0.790890i | \(-0.709618\pi\) | ||||
−0.611959 | + | 0.790890i | \(0.709618\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −28.5019 | −2.78150 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.23328 | 0.602594 | 0.301297 | − | 0.953530i | \(-0.402580\pi\) | ||||
0.301297 | + | 0.953530i | \(0.402580\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.49199 | −0.430255 | −0.215127 | − | 0.976586i | \(-0.569017\pi\) | ||||
−0.215127 | + | 0.976586i | \(0.569017\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 36.6252 | 3.47631 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.13873 | −0.859699 | −0.429850 | − | 0.902901i | \(-0.641433\pi\) | ||||
−0.429850 | + | 0.902901i | \(0.641433\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.38487 | 0.595392 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.77179 | 0.626052 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.70574 | −0.248035 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 32.2263 | 2.92966 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.3747 | 1.02562 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15.6674 | −1.40134 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.4929 | 1.81845 | 0.909226 | − | 0.416303i | \(-0.136674\pi\) | ||||
0.909226 | + | 0.416303i | \(0.136674\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 25.2876 | 2.22645 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.7999 | 1.03096 | 0.515479 | − | 0.856902i | \(-0.327614\pi\) | ||||
0.515479 | + | 0.856902i | \(0.327614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.32150 | −0.721566 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −44.3725 | −3.81898 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −17.5849 | −1.50238 | −0.751191 | − | 0.660085i | \(-0.770520\pi\) | ||||
−0.751191 | + | 0.660085i | \(0.770520\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.28759 | −0.533307 | −0.266653 | − | 0.963792i | \(-0.585918\pi\) | ||||
−0.266653 | + | 0.963792i | \(0.585918\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −17.7646 | −1.49605 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.57467 | 0.549802 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.76339 | 0.312533 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.53336 | −0.291426 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.69125 | 0.302399 | 0.151199 | − | 0.988503i | \(-0.451686\pi\) | ||||
0.151199 | + | 0.988503i | \(0.451686\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.22570 | 0.750777 | 0.375388 | − | 0.926868i | \(-0.377509\pi\) | ||||
0.375388 | + | 0.926868i | \(0.377509\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.56280 | −0.611416 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.53784 | 0.123522 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.45242 | 0.754385 | 0.377192 | − | 0.926135i | \(-0.376890\pi\) | ||||
0.377192 | + | 0.926135i | \(0.376890\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.97309 | 0.315087 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.11036 | −0.323942 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.77314 | 0.608840 | 0.304420 | − | 0.952538i | \(-0.401537\pi\) | ||||
0.304420 | + | 0.952538i | \(0.401537\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −77.3465 | −6.02141 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.3061 | −1.18442 | −0.592209 | − | 0.805784i | \(-0.701744\pi\) | ||||
−0.592209 | + | 0.805784i | \(0.701744\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −23.2594 | −1.77869 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.65999 | −0.658407 | −0.329203 | − | 0.944259i | \(-0.606780\pi\) | ||||
−0.329203 | + | 0.944259i | \(0.606780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 22.1999 | 1.67815 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.9852 | −1.65251 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18.2826 | −1.36650 | −0.683251 | − | 0.730183i | \(-0.739435\pi\) | ||||
−0.683251 | + | 0.730183i | \(0.739435\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.84457 | −0.285765 | −0.142882 | − | 0.989740i | \(-0.545637\pi\) | ||||
−0.142882 | + | 0.989740i | \(0.545637\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −25.0738 | −1.85351 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −44.0933 | −3.24180 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.34266 | −0.536948 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 28.5655 | 2.07784 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.9257 | 1.51413 | 0.757067 | − | 0.653338i | \(-0.226632\pi\) | ||||
0.757067 | + | 0.653338i | \(0.226632\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.82112 | 0.490995 | 0.245497 | − | 0.969397i | \(-0.421049\pi\) | ||||
0.245497 | + | 0.969397i | \(0.421049\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −11.7643 | −0.842460 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.7650 | 1.40820 | 0.704100 | − | 0.710101i | \(-0.251351\pi\) | ||||
0.704100 | + | 0.710101i | \(0.251351\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.66470 | −0.401560 | −0.200780 | − | 0.979636i | \(-0.564348\pi\) | ||||
−0.200780 | + | 0.979636i | \(0.564348\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.682364 | −0.0481303 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.42274 | −0.170043 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −13.6941 | −0.956435 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −11.4888 | −0.798530 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.5823 | −1.56205 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.2355 | 1.18654 | 0.593271 | − | 0.805002i | \(-0.297836\pi\) | ||||
0.593271 | + | 0.805002i | \(0.297836\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 46.3973 | 3.17909 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −30.4439 | −2.07626 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.990010 | −0.0672062 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.3536 | 1.44294 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.11681 | −0.0751248 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.0933 | −1.41251 | −0.706255 | − | 0.707957i | \(-0.749617\pi\) | ||||
−0.706255 | + | 0.707957i | \(0.749617\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 62.0507 | 4.13672 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.6870 | 1.50579 | 0.752895 | − | 0.658141i | \(-0.228657\pi\) | ||||
0.752895 | + | 0.658141i | \(0.228657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2248 | 1.40257 | 0.701286 | − | 0.712880i | \(-0.252610\pi\) | ||||
0.701286 | + | 0.712880i | \(0.252610\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 49.7930 | 3.27614 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.05642 | 0.331257 | 0.165628 | − | 0.986188i | \(-0.447035\pi\) | ||||
0.165628 | + | 0.986188i | \(0.447035\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.3869 | 1.39512 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −31.9363 | −2.07449 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.04827 | 0.391230 | 0.195615 | − | 0.980681i | \(-0.437330\pi\) | ||||
0.195615 | + | 0.980681i | \(0.437330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2437 | −1.23959 | −0.619797 | − | 0.784762i | \(-0.712785\pi\) | ||||
−0.619797 | + | 0.784762i | \(0.712785\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.3377 | 1.04806 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.25383 | 0.271767 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.43474 | −0.218547 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −28.8707 | −1.82961 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.1177 | 1.83789 | 0.918946 | − | 0.394383i | \(-0.129042\pi\) | ||||
0.918946 | + | 0.394383i | \(0.129042\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.1544 | −0.701272 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.1385 | 0.822765 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1233 | −0.693851 | −0.346925 | − | 0.937893i | \(-0.612774\pi\) | ||||
−0.346925 | + | 0.937893i | \(0.612774\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 28.3858 | 1.76381 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.77179 | −0.419163 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −27.2917 | −1.68288 | −0.841439 | − | 0.540351i | \(-0.818291\pi\) | ||||
−0.841439 | + | 0.540351i | \(0.818291\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.78323 | −0.293831 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.5773 | 1.19811 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.42461 | 0.269773 | 0.134887 | − | 0.990861i | \(-0.456933\pi\) | ||||
0.134887 | + | 0.990861i | \(0.456933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.76700 | 0.593303 | 0.296651 | − | 0.954986i | \(-0.404130\pi\) | ||||
0.296651 | + | 0.954986i | \(0.404130\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.57346 | 0.458367 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 60.2445 | 3.63288 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.4342 | −0.807182 | −0.403591 | − | 0.914939i | \(-0.632238\pi\) | ||||
−0.403591 | + | 0.914939i | \(0.632238\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.76717 | −0.165666 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.8153 | 1.36105 | 0.680523 | − | 0.732727i | \(-0.261753\pi\) | ||||
0.680523 | + | 0.732727i | \(0.261753\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.18390 | 0.129819 | 0.0649097 | − | 0.997891i | \(-0.479324\pi\) | ||||
0.0649097 | + | 0.997891i | \(0.479324\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 40.4074 | 2.39353 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.81577 | 0.520378 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7527 | −0.926632 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 45.0029 | 2.63812 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.55576 | −0.266151 | −0.133075 | − | 0.991106i | \(-0.542485\pi\) | ||||
−0.133075 | + | 0.991106i | \(0.542485\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.4680 | 1.54103 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 77.5191 | 4.49811 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.69657 | −0.0981154 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.5988 | 1.12965 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −40.6905 | −2.33761 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 30.1865 | 1.72848 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.9372 | −1.42324 | −0.711620 | − | 0.702565i | \(-0.752038\pi\) | ||||
−0.711620 | + | 0.702565i | \(0.752038\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −38.8291 | −2.20891 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.9496 | −1.52817 | −0.764087 | − | 0.645113i | \(-0.776810\pi\) | ||||
−0.764087 | + | 0.645113i | \(0.776810\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.3533 | −1.15044 | −0.575218 | − | 0.818000i | \(-0.695083\pi\) | ||||
−0.575218 | + | 0.818000i | \(0.695083\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −61.7434 | −3.47884 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.40162 | 0.471882 | 0.235941 | − | 0.971767i | \(-0.424183\pi\) | ||||
0.235941 | + | 0.971767i | \(0.424183\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.57467 | −0.368111 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.4851 | 1.08755 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.83596 | 0.213438 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.16312 | 0.508278 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.0419 | −0.776519 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.7681 | −0.759061 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.6995 | −0.588100 | −0.294050 | − | 0.955790i | \(-0.595003\pi\) | ||||
−0.294050 | + | 0.955790i | \(0.595003\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 79.3408 | 4.34785 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.821502 | 0.0448835 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.1513 | 0.879816 | 0.439908 | − | 0.898043i | \(-0.355011\pi\) | ||||
0.439908 | + | 0.898043i | \(0.355011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.5675 | −1.55158 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.68662 | −0.145489 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.6977 | −1.06357 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 19.9590 | 1.07456 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.4653 | −0.991267 | −0.495633 | − | 0.868532i | \(-0.665064\pi\) | ||||
−0.495633 | + | 0.868532i | \(0.665064\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.2890 | 1.08605 | 0.543024 | − | 0.839717i | \(-0.317279\pi\) | ||||
0.543024 | + | 0.839717i | \(0.317279\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.7906 | 0.629334 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.4547 | 0.822568 | 0.411284 | − | 0.911507i | \(-0.365080\pi\) | ||||
0.411284 | + | 0.911507i | \(0.365080\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −55.8580 | −2.96463 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.45812 | −0.447651 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.0776 | 1.69299 | 0.846497 | − | 0.532394i | \(-0.178708\pi\) | ||||
0.846497 | + | 0.532394i | \(0.178708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.20254 | −0.379081 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 100.739 | 5.28742 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −25.7077 | −1.34560 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7189 | 0.716119 | 0.358059 | − | 0.933699i | \(-0.383439\pi\) | ||||
0.358059 | + | 0.933699i | \(0.383439\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 24.6409 | 1.28275 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.07928 | 0.159868 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.802214 | 0.0415371 | 0.0207685 | − | 0.999784i | \(-0.493389\pi\) | ||||
0.0207685 | + | 0.999784i | \(0.493389\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −48.9762 | −2.52912 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.00000 | −0.0515026 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0194 | 1.07969 | 0.539846 | − | 0.841764i | \(-0.318483\pi\) | ||||
0.539846 | + | 0.841764i | \(0.318483\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 64.0606 | 3.28192 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −34.1486 | −1.74491 | −0.872455 | − | 0.488694i | \(-0.837473\pi\) | ||||
−0.872455 | + | 0.488694i | \(0.837473\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −59.9461 | −3.05513 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 54.7803 | 2.78464 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 31.7963 | 1.61213 | 0.806067 | − | 0.591824i | \(-0.201592\pi\) | ||||
0.806067 | + | 0.591824i | \(0.201592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.89475 | 0.0958217 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.8862 | 1.86066 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 38.4483 | 1.93455 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.8909 | 1.60056 | 0.800280 | − | 0.599627i | \(-0.204684\pi\) | ||||
0.800280 | + | 0.599627i | \(0.204684\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −26.0129 | −1.30227 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.38173 | −0.0690002 | −0.0345001 | − | 0.999405i | \(-0.510984\pi\) | ||||
−0.0345001 | + | 0.999405i | \(0.510984\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.408632 | −0.0203554 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −62.2532 | −3.09339 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 77.0313 | 3.81830 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.8107 | 0.633450 | 0.316725 | − | 0.948517i | \(-0.397417\pi\) | ||||
0.316725 | + | 0.948517i | \(0.397417\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −54.9703 | −2.71148 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.0392 | −0.838445 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 34.7576 | 1.70618 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −19.6549 | −0.962506 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.30321 | 0.454492 | 0.227246 | − | 0.973837i | \(-0.427028\pi\) | ||||
0.227246 | + | 0.973837i | \(0.427028\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.60630 | 0.273234 | 0.136617 | − | 0.990624i | \(-0.456377\pi\) | ||||
0.136617 | + | 0.990624i | \(0.456377\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −38.4832 | −1.87112 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.2335 | −0.496396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.4331 | −0.940431 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 20.5523 | 0.992276 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.2724 | −1.41000 | −0.705000 | − | 0.709207i | \(-0.749053\pi\) | ||||
−0.705000 | + | 0.709207i | \(0.749053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −31.3039 | −1.50437 | −0.752184 | − | 0.658954i | \(-0.770999\pi\) | ||||
−0.752184 | + | 0.658954i | \(0.770999\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.7643 | 0.564056 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.82730 | 0.278757 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.1088 | 0.577922 | 0.288961 | − | 0.957341i | \(-0.406690\pi\) | ||||
0.288961 | + | 0.957341i | \(0.406690\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.65428 | −0.364489 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5007 | −0.926506 | −0.463253 | − | 0.886226i | \(-0.653318\pi\) | ||||
−0.463253 | + | 0.886226i | \(0.653318\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −23.5692 | −1.11729 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.5388 | 0.545766 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.9909 | −1.22659 | −0.613293 | − | 0.789856i | \(-0.710155\pi\) | ||||
−0.613293 | + | 0.789856i | \(0.710155\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 23.9236 | 1.12652 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.8394 | 1.35499 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.11773 | −0.427446 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.863395 | 0.0403879 | 0.0201940 | − | 0.999796i | \(-0.493572\pi\) | ||||
0.0201940 | + | 0.999796i | \(0.493572\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.1678 | −0.614621 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −25.9598 | −1.20907 | −0.604533 | − | 0.796580i | \(-0.706640\pi\) | ||||
−0.604533 | + | 0.796580i | \(0.706640\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.0249 | 1.25595 | 0.627977 | − | 0.778232i | \(-0.283883\pi\) | ||||
0.627977 | + | 0.778232i | \(0.283883\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.80727 | 0.222932 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.2094 | −0.981456 | −0.490728 | − | 0.871313i | \(-0.663269\pi\) | ||||
−0.490728 | + | 0.871313i | \(0.663269\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.528855 | −0.0244202 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.5481 | 1.36151 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 53.1857 | 2.44548 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −31.4730 | −1.44408 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.60687 | 0.394081 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.17046 | 0.419009 | 0.209504 | − | 0.977808i | \(-0.432815\pi\) | ||||
0.209504 | + | 0.977808i | \(0.432815\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.7164 | 0.534221 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.8489 | −0.584647 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −54.1792 | −2.46015 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −28.0228 | −1.26983 | −0.634916 | − | 0.772581i | \(-0.718965\pi\) | ||||
−0.634916 | + | 0.772581i | \(0.718965\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 24.2987 | 1.09883 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −36.5743 | −1.65058 | −0.825288 | − | 0.564712i | \(-0.808987\pi\) | ||||
−0.825288 | + | 0.564712i | \(0.808987\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.11681 | 0.0502986 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −167.555 | −7.53103 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 35.9595 | 1.61300 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.84413 | −0.216853 | −0.108427 | − | 0.994104i | \(-0.534581\pi\) | ||||
−0.108427 | + | 0.994104i | \(0.534581\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −47.8465 | −2.13762 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.90875 | −0.308046 | −0.154023 | − | 0.988067i | \(-0.549223\pi\) | ||||
−0.154023 | + | 0.988067i | \(0.549223\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 48.9875 | 2.17992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.12599 | 0.138830 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.83407 | −0.214266 | −0.107133 | − | 0.994245i | \(-0.534167\pi\) | ||||
−0.107133 | + | 0.994245i | \(0.534167\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.5497 | 0.732118 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −40.4976 | −1.78801 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 46.7466 | 2.05990 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −37.3630 | −1.64322 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −27.0710 | −1.18829 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.8930 | −1.39726 | −0.698629 | − | 0.715484i | \(-0.746206\pi\) | ||||
−0.698629 | + | 0.715484i | \(0.746206\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.0320 | 0.744759 | 0.372379 | − | 0.928081i | \(-0.378542\pi\) | ||||
0.372379 | + | 0.928081i | \(0.378542\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 69.3965 | 3.02871 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.456364 | 0.0198795 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.1216 | −0.874854 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −47.6262 | −2.06680 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.63876 | 0.157612 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.4583 | −1.01419 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −57.1510 | −2.46625 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.43147 | −0.320096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.71304 | 0.202630 | 0.101315 | − | 0.994854i | \(-0.467695\pi\) | ||||
0.101315 | + | 0.994854i | \(0.467695\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12.0181 | −0.515745 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.9051 | 0.724136 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.4078 | 1.12911 | 0.564557 | − | 0.825394i | \(-0.309047\pi\) | ||||
0.564557 | + | 0.825394i | \(0.309047\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −54.3172 | −2.31820 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.43474 | 0.146325 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −24.7517 | −1.05255 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −137.835 | −5.85077 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.111362 | 0.00471856 | 0.00235928 | − | 0.999997i | \(-0.499249\pi\) | ||||
0.00235928 | + | 0.999997i | \(0.499249\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.08949 | 0.342149 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.9530 | −0.969078 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.6688 | −0.997519 | −0.498760 | − | 0.866740i | \(-0.666211\pi\) | ||||
−0.498760 | + | 0.866740i | \(0.666211\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.3926 | 1.44691 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 40.0765 | 1.68305 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.1601 | −0.803233 | −0.401617 | − | 0.915808i | \(-0.631552\pi\) | ||||
−0.401617 | + | 0.915808i | \(0.631552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.9804 | −1.17095 | −0.585473 | − | 0.810692i | \(-0.699091\pi\) | ||||
−0.585473 | + | 0.810692i | \(0.699091\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 65.4136 | 2.73269 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.5459 | −0.648309 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.7366 | −0.904906 | −0.452453 | − | 0.891788i | \(-0.649451\pi\) | ||||
−0.452453 | + | 0.891788i | \(0.649451\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.3227 | 0.886142 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −22.3758 | −0.928303 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.35633 | 0.346084 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −25.4849 | −1.05367 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.6844 | 0.482266 | 0.241133 | − | 0.970492i | \(-0.422481\pi\) | ||||
0.241133 | + | 0.970492i | \(0.422481\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.40355 | 0.0578321 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 61.7852 | 2.54150 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.32509 | −0.218675 | −0.109338 | − | 0.994005i | \(-0.534873\pi\) | ||||
−0.109338 | + | 0.994005i | \(0.534873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.1828 | 0.417453 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.7078 | −0.724731 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 26.4499 | 1.08071 | 0.540356 | − | 0.841437i | \(-0.318290\pi\) | ||||
0.540356 | + | 0.841437i | \(0.318290\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.3389 | 0.748058 | 0.374029 | − | 0.927417i | \(-0.377976\pi\) | ||||
0.374029 | + | 0.927417i | \(0.377976\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.47820 | −0.0601969 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −121.280 | −4.93074 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.9881 | −0.567761 | −0.283881 | − | 0.958860i | \(-0.591622\pi\) | ||||
−0.283881 | + | 0.958860i | \(0.591622\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.57346 | −0.306892 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.68287 | −0.229904 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.7353 | −0.433594 | −0.216797 | − | 0.976217i | \(-0.569561\pi\) | ||||
−0.216797 | + | 0.976217i | \(0.569561\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −42.8075 | −1.72616 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.5898 | −1.11072 | −0.555361 | − | 0.831609i | \(-0.687420\pi\) | ||||
−0.555361 | + | 0.831609i | \(0.687420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.3912 | −0.699012 | −0.349506 | − | 0.936934i | \(-0.613651\pi\) | ||||
−0.349506 | + | 0.936934i | \(0.613651\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.0036 | −0.802716 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.1730 | 0.607895 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.1471 | 0.525886 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −70.5920 | −2.81917 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −13.0850 | −0.521732 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.93788 | −0.0771458 | −0.0385729 | − | 0.999256i | \(-0.512281\pi\) | ||||
−0.0385729 | + | 0.999256i | \(0.512281\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 53.8780 | 2.14146 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −77.1229 | −3.06053 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.13032 | −0.0447848 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 100.510 | 3.97612 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −47.7710 | −1.88684 | −0.943421 | − | 0.331597i | \(-0.892413\pi\) | ||||
−0.943421 | + | 0.331597i | \(0.892413\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.20337 | −0.205201 | −0.102600 | − | 0.994723i | \(-0.532716\pi\) | ||||
−0.102600 | + | 0.994723i | \(0.532716\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −95.1673 | −3.74721 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.6049 | −0.652806 | −0.326403 | − | 0.945231i | \(-0.605837\pi\) | ||||
−0.326403 | + | 0.945231i | \(0.605837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.2399 | −1.81507 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.09476 | −0.121293 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.4293 | −0.603795 | −0.301898 | − | 0.953340i | \(-0.597620\pi\) | ||||
−0.301898 | + | 0.953340i | \(0.597620\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −44.4075 | −1.73514 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 46.2581 | 1.80470 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.7062 | −1.00137 | −0.500687 | − | 0.865629i | \(-0.666919\pi\) | ||||
−0.500687 | + | 0.865629i | \(0.666919\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.4703 | 1.14626 | 0.573130 | − | 0.819464i | \(-0.305729\pi\) | ||||
0.573130 | + | 0.819464i | \(0.305729\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.49113 | −0.135584 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 31.3171 | 1.21442 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.69657 | 0.0656916 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −65.9373 | −2.54928 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.7361 | −2.03585 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.76278 | 0.337780 | 0.168890 | − | 0.985635i | \(-0.445982\pi\) | ||||
0.168890 | + | 0.985635i | \(0.445982\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 108.038 | 4.15840 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.174750 | −0.00671620 | −0.00335810 | − | 0.999994i | \(-0.501069\pi\) | ||||
−0.00335810 | + | 0.999994i | \(0.501069\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.8787 | 1.33852 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 70.9193 | 2.71763 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 23.9721 | 0.917268 | 0.458634 | − | 0.888625i | \(-0.348339\pi\) | ||||
0.458634 | + | 0.888625i | \(0.348339\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 66.1790 | 2.52857 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 66.3483 | 2.53135 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.27099 | 0.0484208 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.9400 | 1.13897 | 0.569485 | − | 0.822002i | \(-0.307143\pi\) | ||||
0.569485 | + | 0.822002i | \(0.307143\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 107.866 | 4.09749 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.6627 | 0.897577 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.06380 | −0.153927 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.8063 | 0.597849 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −34.7099 | −1.31098 | −0.655488 | − | 0.755206i | \(-0.727537\pi\) | ||||
−0.655488 | + | 0.755206i | \(0.727537\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −40.2427 | −1.51778 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 66.8550 | 2.51791 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.5365 | −1.18605 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.3569 | 1.10252 | 0.551261 | − | 0.834333i | \(-0.314147\pi\) | ||||
0.551261 | + | 0.834333i | \(0.314147\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −69.1834 | −2.59458 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.693274 | 0.0259633 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.7431 | −0.925338 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 18.9068 | 0.706088 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −26.6369 | −0.993390 | −0.496695 | − | 0.867925i | \(-0.665453\pi\) | ||||
−0.496695 | + | 0.867925i | \(0.665453\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.0939 | −1.12075 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −60.1555 | −2.23721 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.16312 | −0.340310 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.0278 | 0.816964 | 0.408482 | − | 0.912766i | \(-0.366058\pi\) | ||||
0.408482 | + | 0.912766i | \(0.366058\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.44605 | 0.0535573 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.03442 | −0.334150 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.27136 | −0.0469586 | −0.0234793 | − | 0.999724i | \(-0.507474\pi\) | ||||
−0.0234793 | + | 0.999724i | \(0.507474\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.2974 | 0.490482 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.43517 | −0.0528651 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.1865 | −0.448287 | −0.224144 | − | 0.974556i | \(-0.571958\pi\) | ||||
−0.224144 | + | 0.974556i | \(0.571958\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.7370 | −0.394432 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.7183 | 1.12695 | 0.563473 | − | 0.826134i | \(-0.309465\pi\) | ||||
0.563473 | + | 0.826134i | \(0.309465\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −13.8916 | −0.508949 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −62.5423 | −2.28830 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.1016 | 0.551802 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.23116 | −0.300359 | −0.150180 | − | 0.988659i | \(-0.547985\pi\) | ||||
−0.150180 | + | 0.988659i | \(0.547985\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 91.0215 | 3.31701 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.7199 | −1.26359 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.6350 | −0.531917 | −0.265958 | − | 0.963985i | \(-0.585688\pi\) | ||||
−0.265958 | + | 0.963985i | \(0.585688\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.8685 | −1.26565 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.6624 | −1.51026 | −0.755131 | − | 0.655574i | \(-0.772427\pi\) | ||||
−0.755131 | + | 0.655574i | \(0.772427\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8829 | −0.393989 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 28.4618 | 1.02904 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7.03303 | −0.253948 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.3784 | −1.05941 | −0.529706 | − | 0.848181i | \(-0.677698\pi\) | ||||
−0.529706 | + | 0.848181i | \(0.677698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −34.7712 | −1.25225 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.7495 | −0.530504 | −0.265252 | − | 0.964179i | \(-0.585455\pi\) | ||||
−0.265252 | + | 0.964179i | \(0.585455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.74434 | −0.134501 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 88.7335 | 3.18330 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.4982 | −0.447794 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 97.5843 | 3.49184 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −11.7906 | −0.421361 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −35.5731 | −1.26966 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.6447 | −0.486383 | −0.243191 | − | 0.969978i | \(-0.578194\pi\) | ||||
−0.243191 | + | 0.969978i | \(0.578194\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −85.3135 | −3.03724 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.1408 | −0.787236 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.02110 | −0.284837 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.9523 | −0.530304 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.5309 | −0.868929 | −0.434465 | − | 0.900689i | \(-0.643062\pi\) | ||||
−0.434465 | + | 0.900689i | \(0.643062\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.34668 | 0.224529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 42.4100 | 1.49849 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44.9116 | 1.58489 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.4689 | 0.545207 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.8313 | 0.486884 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.8032 | −0.625926 | −0.312963 | − | 0.949765i | \(-0.601322\pi\) | ||||
−0.312963 | + | 0.949765i | \(0.601322\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.7178 | 0.867958 | 0.433979 | − | 0.900923i | \(-0.357109\pi\) | ||||
0.433979 | + | 0.900923i | \(0.357109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.5315 | 1.07079 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −29.2534 | −1.02470 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −27.7853 | −0.972086 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 16.4063 | 0.573283 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46.4017 | −1.61943 | −0.809715 | − | 0.586824i | \(-0.800378\pi\) | ||||
−0.809715 | + | 0.586824i | \(0.800378\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.7389 | −0.897202 | −0.448601 | − | 0.893732i | \(-0.648078\pi\) | ||||
−0.448601 | + | 0.893732i | \(0.648078\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 188.323 | 6.55658 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.2509 | 1.29534 | 0.647671 | − | 0.761920i | \(-0.275743\pi\) | ||||
0.647671 | + | 0.761920i | \(0.275743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.74066 | −0.0604557 | −0.0302278 | − | 0.999543i | \(-0.509623\pi\) | ||||
−0.0302278 | + | 0.999543i | \(0.509623\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −41.9951 | −1.45679 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.26235 | 0.0437378 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 57.6027 | 1.99342 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.81800 | −0.166534 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.77361 | 0.130279 | 0.0651397 | − | 0.997876i | \(-0.479251\pi\) | ||||
0.0651397 | + | 0.997876i | \(0.479251\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 71.3202 | 2.45640 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.76339 | −0.129465 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 78.0760 | 2.68272 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.82684 | 0.234297 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −19.8777 | −0.681399 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.5330 | 0.566077 | 0.283039 | − | 0.959108i | \(-0.408658\pi\) | ||||
0.283039 | + | 0.959108i | \(0.408658\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 87.5341 | 2.99360 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 43.0155 | 1.46938 | 0.734690 | − | 0.678403i | \(-0.237327\pi\) | ||||
0.734690 | + | 0.678403i | \(0.237327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.3081 | 0.658784 | 0.329392 | − | 0.944193i | \(-0.393156\pi\) | ||||
0.329392 | + | 0.944193i | \(0.393156\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.5580 | 0.939173 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −24.4677 | −0.832889 | −0.416444 | − | 0.909161i | \(-0.636724\pi\) | ||||
−0.416444 | + | 0.909161i | \(0.636724\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.5909 | 1.10813 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −49.2428 | −1.67237 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −67.1695 | −2.27857 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.218288 | −0.00739640 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 97.4892 | 3.29951 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −37.9582 | −1.28322 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.0083 | −0.574328 | −0.287164 | − | 0.957881i | \(-0.592712\pi\) | ||||
−0.287164 | + | 0.957881i | \(0.592712\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.2413 | −0.480346 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.4085 | 0.721269 | 0.360635 | − | 0.932707i | \(-0.382560\pi\) | ||||
0.360635 | + | 0.932707i | \(0.382560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.8993 | −0.535053 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 82.7388 | 2.78123 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.7696 | −1.43606 | −0.718031 | − | 0.696011i | \(-0.754956\pi\) | ||||
−0.718031 | + | 0.696011i | \(0.754956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 49.6491 | 1.66518 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 108.757 | 3.64349 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.5192 | 0.653185 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 68.8044 | 2.29988 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5.30347 | −0.177078 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.408632 | 0.0136286 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.41945 | −0.0472888 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 61.2654 | 2.03879 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.4686 | 0.480953 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37.1644 | 1.23402 | 0.617012 | − | 0.786954i | \(-0.288343\pi\) | ||||
0.617012 | + | 0.786954i | \(0.288343\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −88.1474 | −2.92367 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.1149 | 1.22967 | 0.614836 | − | 0.788655i | \(-0.289222\pi\) | ||||
0.614836 | + | 0.788655i | \(0.289222\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −60.7218 | −2.00960 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 94.3627 | 3.11953 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 28.5880 | 0.944060 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.63662 | −0.119961 | −0.0599806 | − | 0.998200i | \(-0.519104\pi\) | ||||
−0.0599806 | + | 0.998200i | \(0.519104\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −77.9533 | −2.56865 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.8425 | 0.488546 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 107.359 | 3.52993 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −84.1151 | −2.76270 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.75340 | 0.155954 | 0.0779770 | − | 0.996955i | \(-0.475154\pi\) | ||||
0.0779770 | + | 0.996955i | \(0.475154\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.88235 | 0.127239 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −84.2442 | −2.75803 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27.6333 | 0.903705 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.3383 | 1.35046 | 0.675232 | − | 0.737605i | \(-0.264043\pi\) | ||||
0.675232 | + | 0.737605i | \(0.264043\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −63.6241 | −2.07629 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.7623 | 0.383439 | 0.191719 | − | 0.981450i | \(-0.438594\pi\) | ||||
0.191719 | + | 0.981450i | \(0.438594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.17342 | −0.201034 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −107.503 | −3.49708 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.7489 | −0.966709 | −0.483354 | − | 0.875425i | \(-0.660582\pi\) | ||||
−0.483354 | + | 0.875425i | \(0.660582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.83100 | 0.221744 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.2633 | 0.851647 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.7480 | −0.963632 | −0.481816 | − | 0.876272i | \(-0.660023\pi\) | ||||
−0.481816 | + | 0.876272i | \(0.660023\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −78.7518 | −2.54835 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.5523 | −0.664362 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −42.6038 | −1.37575 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8330 | −0.994614 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 42.2105 | 1.36021 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.6705 | −0.826364 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.1335 | 1.38708 | 0.693541 | − | 0.720417i | \(-0.256050\pi\) | ||||
0.693541 | + | 0.720417i | \(0.256050\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.9911 | 0.385211 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.8830 | 0.477618 | 0.238809 | − | 0.971067i | \(-0.423243\pi\) | ||||
0.238809 | + | 0.971067i | \(0.423243\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.2332 | −0.488355 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 28.6438 | 0.917335 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35.4616 | −1.13452 | −0.567259 | − | 0.823540i | \(-0.691996\pi\) | ||||
−0.567259 | + | 0.823540i | \(0.691996\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41.1755 | 1.31598 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −30.4188 | −0.971198 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.6307 | 1.20023 | 0.600116 | − | 0.799913i | \(-0.295121\pi\) | ||||
0.600116 | + | 0.799913i | \(0.295121\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −74.3836 | −2.37006 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −43.0390 | −1.36995 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.7244 | −0.436411 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.1447 | −1.87879 | −0.939396 | − | 0.342833i | \(-0.888614\pi\) | ||||
−0.939396 | + | 0.342833i | \(0.888614\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.4466 | −1.06140 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.3185 | 0.675841 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.2679 | 0.610220 | 0.305110 | − | 0.952317i | \(-0.401307\pi\) | ||||
0.305110 | + | 0.952317i | \(0.401307\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 138.143 | 4.37064 |
(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 | 6032.2.a.bc.1.11 | 11 | ||
4.3 | odd | 2 | 3016.2.a.i.1.1 | ✓ | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3016.2.a.i.1.1 | ✓ | 11 | 4.3 | odd | 2 | ||
6032.2.a.bc.1.11 | 11 | 1.1 | even | 1 | trivial |