Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.26 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.66842 | 1.17975 | 0.589876 | − | 0.807494i | \(-0.299177\pi\) | ||||
0.589876 | + | 0.807494i | \(0.299177\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.783626 | 0.391813 | ||||||||
\(5\) | 3.76494 | 1.68373 | 0.841866 | − | 0.539687i | \(-0.181457\pi\) | ||||
0.841866 | + | 0.539687i | \(0.181457\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.02942 | −0.717509 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.28150 | 1.98638 | ||||||||
\(11\) | −3.16270 | −0.953591 | −0.476795 | − | 0.879014i | \(-0.658202\pi\) | ||||
−0.476795 | + | 0.879014i | \(0.658202\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.02168 | −0.838063 | −0.419031 | − | 0.907972i | \(-0.637630\pi\) | ||||
−0.419031 | + | 0.907972i | \(0.637630\pi\) | |||||||
\(14\) | −1.66842 | −0.445904 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.95318 | −1.23830 | ||||||||
\(17\) | 1.05689 | 0.256333 | 0.128167 | − | 0.991753i | \(-0.459091\pi\) | ||||
0.128167 | + | 0.991753i | \(0.459091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.14601 | 0.721744 | 0.360872 | − | 0.932615i | \(-0.382479\pi\) | ||||
0.360872 | + | 0.932615i | \(0.382479\pi\) | |||||||
\(20\) | 2.95030 | 0.659708 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.27672 | −1.12500 | ||||||||
\(23\) | −7.12860 | −1.48642 | −0.743208 | − | 0.669060i | \(-0.766697\pi\) | ||||
−0.743208 | + | 0.669060i | \(0.766697\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.17476 | 1.83495 | ||||||||
\(26\) | −5.04143 | −0.988705 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.783626 | −0.148091 | ||||||||
\(29\) | 2.67282 | 0.496329 | 0.248165 | − | 0.968718i | \(-0.420173\pi\) | ||||
0.248165 | + | 0.968718i | \(0.420173\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.88393 | −1.59560 | −0.797801 | − | 0.602921i | \(-0.794003\pi\) | ||||
−0.797801 | + | 0.602921i | \(0.794003\pi\) | |||||||
\(32\) | −4.20514 | −0.743372 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.76334 | 0.302410 | ||||||||
\(35\) | −3.76494 | −0.636391 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.943469 | 0.155105 | 0.0775527 | − | 0.996988i | \(-0.475289\pi\) | ||||
0.0775527 | + | 0.996988i | \(0.475289\pi\) | |||||||
\(38\) | 5.24887 | 0.851479 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.64065 | −1.20809 | ||||||||
\(41\) | 9.90868 | 1.54748 | 0.773738 | − | 0.633506i | \(-0.218385\pi\) | ||||
0.773738 | + | 0.633506i | \(0.218385\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8524 | −1.65498 | −0.827489 | − | 0.561482i | \(-0.810232\pi\) | ||||
−0.827489 | + | 0.561482i | \(0.810232\pi\) | |||||||
\(44\) | −2.47838 | −0.373629 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −11.8935 | −1.75360 | ||||||||
\(47\) | 4.25536 | 0.620709 | 0.310354 | − | 0.950621i | \(-0.399552\pi\) | ||||
0.310354 | + | 0.950621i | \(0.399552\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 15.3074 | 2.16479 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.36787 | −0.328364 | ||||||||
\(53\) | −5.14637 | −0.706908 | −0.353454 | − | 0.935452i | \(-0.614993\pi\) | ||||
−0.353454 | + | 0.935452i | \(0.614993\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.9074 | −1.60559 | ||||||||
\(56\) | 2.02942 | 0.271193 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.45938 | 0.585545 | ||||||||
\(59\) | −4.15250 | −0.540609 | −0.270305 | − | 0.962775i | \(-0.587124\pi\) | ||||
−0.270305 | + | 0.962775i | \(0.587124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.23055 | 0.157556 | 0.0787778 | − | 0.996892i | \(-0.474898\pi\) | ||||
0.0787778 | + | 0.996892i | \(0.474898\pi\) | |||||||
\(62\) | −14.8221 | −1.88241 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.89042 | 0.361302 | ||||||||
\(65\) | −11.3764 | −1.41107 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7930 | −1.31857 | −0.659285 | − | 0.751893i | \(-0.729141\pi\) | ||||
−0.659285 | + | 0.751893i | \(0.729141\pi\) | |||||||
\(68\) | 0.828207 | 0.100435 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.28150 | −0.750783 | ||||||||
\(71\) | −15.1564 | −1.79874 | −0.899369 | − | 0.437191i | \(-0.855973\pi\) | ||||
−0.899369 | + | 0.437191i | \(0.855973\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.29623 | 0.853959 | 0.426980 | − | 0.904261i | \(-0.359578\pi\) | ||||
0.426980 | + | 0.904261i | \(0.359578\pi\) | |||||||
\(74\) | 1.57410 | 0.182986 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.46530 | 0.282789 | ||||||||
\(77\) | 3.16270 | 0.360423 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.09038 | 0.572713 | 0.286357 | − | 0.958123i | \(-0.407556\pi\) | ||||
0.286357 | + | 0.958123i | \(0.407556\pi\) | |||||||
\(80\) | −18.6484 | −2.08496 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 16.5318 | 1.82564 | ||||||||
\(83\) | −8.93203 | −0.980417 | −0.490209 | − | 0.871605i | \(-0.663079\pi\) | ||||
−0.490209 | + | 0.871605i | \(0.663079\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.97913 | 0.431597 | ||||||||
\(86\) | −18.1064 | −1.95246 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.41846 | 0.684210 | ||||||||
\(89\) | 5.97445 | 0.633291 | 0.316645 | − | 0.948544i | \(-0.397443\pi\) | ||||
0.316645 | + | 0.948544i | \(0.397443\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.02168 | 0.316758 | ||||||||
\(92\) | −5.58616 | −0.582397 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.09974 | 0.732282 | ||||||||
\(95\) | 11.8445 | 1.21522 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.75834 | −0.990809 | −0.495405 | − | 0.868662i | \(-0.664980\pi\) | ||||
−0.495405 | + | 0.868662i | \(0.664980\pi\) | |||||||
\(98\) | 1.66842 | 0.168536 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.18958 | 0.718958 | ||||||||
\(101\) | −11.6815 | −1.16235 | −0.581174 | − | 0.813779i | \(-0.697407\pi\) | ||||
−0.581174 | + | 0.813779i | \(0.697407\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.9511 | 1.37465 | 0.687323 | − | 0.726352i | \(-0.258786\pi\) | ||||
0.687323 | + | 0.726352i | \(0.258786\pi\) | |||||||
\(104\) | 6.13226 | 0.601318 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.58631 | −0.833976 | ||||||||
\(107\) | −16.0629 | −1.55286 | −0.776432 | − | 0.630202i | \(-0.782972\pi\) | ||||
−0.776432 | + | 0.630202i | \(0.782972\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.53849 | −0.147360 | −0.0736802 | − | 0.997282i | \(-0.523474\pi\) | ||||
−0.0736802 | + | 0.997282i | \(0.523474\pi\) | |||||||
\(110\) | −19.8665 | −1.89420 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.95318 | 0.468032 | ||||||||
\(113\) | −15.3117 | −1.44040 | −0.720202 | − | 0.693765i | \(-0.755951\pi\) | ||||
−0.720202 | + | 0.693765i | \(0.755951\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −26.8387 | −2.50273 | ||||||||
\(116\) | 2.09449 | 0.194468 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.92811 | −0.637784 | ||||||||
\(119\) | −1.05689 | −0.0968849 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.997312 | −0.0906647 | ||||||||
\(122\) | 2.05307 | 0.185876 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.96168 | −0.625178 | ||||||||
\(125\) | 15.7177 | 1.40583 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 13.2327 | 1.16962 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.9807 | −1.66471 | ||||||||
\(131\) | −3.78335 | −0.330553 | −0.165277 | − | 0.986247i | \(-0.552852\pi\) | ||||
−0.165277 | + | 0.986247i | \(0.552852\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.14601 | −0.272794 | ||||||||
\(134\) | −18.0072 | −1.55559 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.14488 | −0.183922 | ||||||||
\(137\) | −21.8842 | −1.86969 | −0.934847 | − | 0.355050i | \(-0.884464\pi\) | ||||
−0.934847 | + | 0.355050i | \(0.884464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.85829 | 0.836169 | 0.418085 | − | 0.908408i | \(-0.362702\pi\) | ||||
0.418085 | + | 0.908408i | \(0.362702\pi\) | |||||||
\(140\) | −2.95030 | −0.249346 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −25.2873 | −2.12206 | ||||||||
\(143\) | 9.55667 | 0.799169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0630 | 0.835685 | ||||||||
\(146\) | 12.1732 | 1.00746 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.739327 | 0.0607723 | ||||||||
\(149\) | 1.98780 | 0.162847 | 0.0814233 | − | 0.996680i | \(-0.474053\pi\) | ||||
0.0814233 | + | 0.996680i | \(0.474053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.05456 | −0.655471 | −0.327735 | − | 0.944770i | \(-0.606285\pi\) | ||||
−0.327735 | + | 0.944770i | \(0.606285\pi\) | |||||||
\(152\) | −6.38459 | −0.517858 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.27672 | 0.425210 | ||||||||
\(155\) | −33.4475 | −2.68656 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.72055 | −0.775784 | −0.387892 | − | 0.921705i | \(-0.626797\pi\) | ||||
−0.387892 | + | 0.921705i | \(0.626797\pi\) | |||||||
\(158\) | 8.49290 | 0.675659 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −15.8321 | −1.25164 | ||||||||
\(161\) | 7.12860 | 0.561812 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.77862 | 0.374290 | 0.187145 | − | 0.982332i | \(-0.440077\pi\) | ||||
0.187145 | + | 0.982332i | \(0.440077\pi\) | |||||||
\(164\) | 7.76470 | 0.606321 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −14.9024 | −1.15665 | ||||||||
\(167\) | 20.9276 | 1.61943 | 0.809713 | − | 0.586827i | \(-0.199623\pi\) | ||||
0.809713 | + | 0.586827i | \(0.199623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.86947 | −0.297651 | ||||||||
\(170\) | 6.63885 | 0.509177 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.50424 | −0.648442 | ||||||||
\(173\) | 13.7591 | 1.04609 | 0.523044 | − | 0.852306i | \(-0.324796\pi\) | ||||
0.523044 | + | 0.852306i | \(0.324796\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.17476 | −0.693547 | ||||||||
\(176\) | 15.6654 | 1.18083 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.96790 | 0.747126 | ||||||||
\(179\) | −9.24850 | −0.691265 | −0.345633 | − | 0.938370i | \(-0.612336\pi\) | ||||
−0.345633 | + | 0.938370i | \(0.612336\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.1657 | 1.05293 | 0.526465 | − | 0.850197i | \(-0.323517\pi\) | ||||
0.526465 | + | 0.850197i | \(0.323517\pi\) | |||||||
\(182\) | 5.04143 | 0.373696 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.4669 | 1.06652 | ||||||||
\(185\) | 3.55210 | 0.261156 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.34263 | −0.244437 | ||||||||
\(188\) | 3.33461 | 0.243202 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 19.7617 | 1.43366 | ||||||||
\(191\) | −3.34589 | −0.242100 | −0.121050 | − | 0.992646i | \(-0.538626\pi\) | ||||
−0.121050 | + | 0.992646i | \(0.538626\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.91295 | 0.497605 | 0.248802 | − | 0.968554i | \(-0.419963\pi\) | ||||
0.248802 | + | 0.968554i | \(0.419963\pi\) | |||||||
\(194\) | −16.2810 | −1.16891 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.783626 | 0.0559733 | ||||||||
\(197\) | 17.8080 | 1.26877 | 0.634385 | − | 0.773017i | \(-0.281253\pi\) | ||||
0.634385 | + | 0.773017i | \(0.281253\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.6199 | −1.17815 | −0.589077 | − | 0.808077i | \(-0.700509\pi\) | ||||
−0.589077 | + | 0.808077i | \(0.700509\pi\) | |||||||
\(200\) | −18.6195 | −1.31659 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −19.4896 | −1.37128 | ||||||||
\(203\) | −2.67282 | −0.187595 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 37.3056 | 2.60553 | ||||||||
\(206\) | 23.2764 | 1.62174 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.9669 | 1.03777 | ||||||||
\(209\) | −9.94990 | −0.688249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.6764 | −1.01037 | −0.505184 | − | 0.863012i | \(-0.668575\pi\) | ||||
−0.505184 | + | 0.863012i | \(0.668575\pi\) | |||||||
\(212\) | −4.03283 | −0.276976 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −26.7997 | −1.83199 | ||||||||
\(215\) | −40.8587 | −2.78654 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.88393 | 0.603081 | ||||||||
\(218\) | −2.56685 | −0.173849 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.33094 | −0.629092 | ||||||||
\(221\) | −3.19358 | −0.214823 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.2818 | 1.15728 | 0.578639 | − | 0.815584i | \(-0.303584\pi\) | ||||
0.578639 | + | 0.815584i | \(0.303584\pi\) | |||||||
\(224\) | 4.20514 | 0.280968 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −25.5464 | −1.69932 | ||||||||
\(227\) | 7.13775 | 0.473749 | 0.236875 | − | 0.971540i | \(-0.423877\pi\) | ||||
0.236875 | + | 0.971540i | \(0.423877\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.65153 | 0.571709 | 0.285855 | − | 0.958273i | \(-0.407723\pi\) | ||||
0.285855 | + | 0.958273i | \(0.407723\pi\) | |||||||
\(230\) | −44.7783 | −2.95259 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.42427 | −0.356121 | ||||||||
\(233\) | 2.76388 | 0.181068 | 0.0905340 | − | 0.995893i | \(-0.471143\pi\) | ||||
0.0905340 | + | 0.995893i | \(0.471143\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0212 | 1.04511 | ||||||||
\(236\) | −3.25401 | −0.211818 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.76334 | −0.114300 | ||||||||
\(239\) | −23.8172 | −1.54061 | −0.770304 | − | 0.637677i | \(-0.779896\pi\) | ||||
−0.770304 | + | 0.637677i | \(0.779896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6840 | −1.20354 | −0.601770 | − | 0.798670i | \(-0.705537\pi\) | ||||
−0.601770 | + | 0.798670i | \(0.705537\pi\) | |||||||
\(242\) | −1.66394 | −0.106962 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.964290 | 0.0617324 | ||||||||
\(245\) | 3.76494 | 0.240533 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.50623 | −0.604867 | ||||||||
\(248\) | 18.0293 | 1.14486 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 26.2237 | 1.65854 | ||||||||
\(251\) | −19.4770 | −1.22938 | −0.614690 | − | 0.788769i | \(-0.710719\pi\) | ||||
−0.614690 | + | 0.788769i | \(0.710719\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.5456 | 1.41743 | ||||||||
\(254\) | −1.66842 | −0.104686 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.2969 | 1.01856 | ||||||||
\(257\) | 9.85146 | 0.614517 | 0.307259 | − | 0.951626i | \(-0.400588\pi\) | ||||
0.307259 | + | 0.951626i | \(0.400588\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.943469 | −0.0586243 | ||||||||
\(260\) | −8.91487 | −0.552877 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.31222 | −0.389971 | ||||||||
\(263\) | 13.8741 | 0.855514 | 0.427757 | − | 0.903894i | \(-0.359304\pi\) | ||||
0.427757 | + | 0.903894i | \(0.359304\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.3758 | −1.19024 | ||||||||
\(266\) | −5.24887 | −0.321829 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.45765 | −0.516633 | ||||||||
\(269\) | 26.2278 | 1.59914 | 0.799568 | − | 0.600575i | \(-0.205062\pi\) | ||||
0.799568 | + | 0.600575i | \(0.205062\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.6970 | 1.19651 | 0.598255 | − | 0.801306i | \(-0.295861\pi\) | ||||
0.598255 | + | 0.801306i | \(0.295861\pi\) | |||||||
\(272\) | −5.23497 | −0.317417 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −36.5121 | −2.20577 | ||||||||
\(275\) | −29.0170 | −1.74979 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.14232 | −0.0686351 | −0.0343176 | − | 0.999411i | \(-0.510926\pi\) | ||||
−0.0343176 | + | 0.999411i | \(0.510926\pi\) | |||||||
\(278\) | 16.4478 | 0.986472 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.64065 | 0.456616 | ||||||||
\(281\) | −16.7929 | −1.00178 | −0.500891 | − | 0.865511i | \(-0.666994\pi\) | ||||
−0.500891 | + | 0.865511i | \(0.666994\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.1223 | 0.780042 | 0.390021 | − | 0.920806i | \(-0.372468\pi\) | ||||
0.390021 | + | 0.920806i | \(0.372468\pi\) | |||||||
\(284\) | −11.8770 | −0.704769 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.9445 | 0.942820 | ||||||||
\(287\) | −9.90868 | −0.584891 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8830 | −0.934293 | ||||||||
\(290\) | 16.7893 | 0.985901 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.71752 | 0.334593 | ||||||||
\(293\) | 8.84515 | 0.516739 | 0.258370 | − | 0.966046i | \(-0.416815\pi\) | ||||
0.258370 | + | 0.966046i | \(0.416815\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.6339 | −0.910241 | ||||||||
\(296\) | −1.91470 | −0.111290 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.31648 | 0.192118 | ||||||||
\(299\) | 21.5403 | 1.24571 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.8524 | 0.625523 | ||||||||
\(302\) | −13.4384 | −0.773292 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −15.5828 | −0.893733 | ||||||||
\(305\) | 4.63294 | 0.265281 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.38864 | 0.478765 | 0.239382 | − | 0.970925i | \(-0.423055\pi\) | ||||
0.239382 | + | 0.970925i | \(0.423055\pi\) | |||||||
\(308\) | 2.47838 | 0.141219 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −55.8044 | −3.16948 | ||||||||
\(311\) | 3.66921 | 0.208062 | 0.104031 | − | 0.994574i | \(-0.466826\pi\) | ||||
0.104031 | + | 0.994574i | \(0.466826\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.7568 | 1.56891 | 0.784453 | − | 0.620188i | \(-0.212944\pi\) | ||||
0.784453 | + | 0.620188i | \(0.212944\pi\) | |||||||
\(314\) | −16.2180 | −0.915232 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.98896 | 0.224397 | ||||||||
\(317\) | 8.76792 | 0.492455 | 0.246228 | − | 0.969212i | \(-0.420809\pi\) | ||||
0.246228 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.45332 | −0.473295 | ||||||||
\(320\) | 10.8822 | 0.608335 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 11.8935 | 0.662799 | ||||||||
\(323\) | 3.32499 | 0.185007 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −27.7232 | −1.53780 | ||||||||
\(326\) | 7.97274 | 0.441569 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −20.1089 | −1.11033 | ||||||||
\(329\) | −4.25536 | −0.234606 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.3095 | 1.44610 | 0.723051 | − | 0.690795i | \(-0.242739\pi\) | ||||
0.723051 | + | 0.690795i | \(0.242739\pi\) | |||||||
\(332\) | −6.99937 | −0.384140 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 34.9160 | 1.91052 | ||||||||
\(335\) | −40.6348 | −2.22012 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.194439 | 0.0105917 | 0.00529587 | − | 0.999986i | \(-0.498314\pi\) | ||||
0.00529587 | + | 0.999986i | \(0.498314\pi\) | |||||||
\(338\) | −6.45589 | −0.351154 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.11815 | 0.169105 | ||||||||
\(341\) | 28.0972 | 1.52155 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 22.0241 | 1.18746 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.9560 | 1.23412 | ||||||||
\(347\) | 20.8704 | 1.12038 | 0.560191 | − | 0.828363i | \(-0.310728\pi\) | ||||
0.560191 | + | 0.828363i | \(0.310728\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.06183 | −0.324483 | −0.162241 | − | 0.986751i | \(-0.551872\pi\) | ||||
−0.162241 | + | 0.986751i | \(0.551872\pi\) | |||||||
\(350\) | −15.3074 | −0.818212 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.2996 | 0.708872 | ||||||||
\(353\) | 18.0447 | 0.960424 | 0.480212 | − | 0.877152i | \(-0.340560\pi\) | ||||
0.480212 | + | 0.877152i | \(0.340560\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −57.0630 | −3.02859 | ||||||||
\(356\) | 4.68174 | 0.248132 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.4304 | −0.815521 | ||||||||
\(359\) | 34.6535 | 1.82894 | 0.914472 | − | 0.404650i | \(-0.132606\pi\) | ||||
0.914472 | + | 0.404650i | \(0.132606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.10261 | −0.479085 | ||||||||
\(362\) | 23.6344 | 1.24220 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.36787 | 0.124110 | ||||||||
\(365\) | 27.4699 | 1.43784 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.3162 | −0.590699 | −0.295349 | − | 0.955389i | \(-0.595436\pi\) | ||||
−0.295349 | + | 0.955389i | \(0.595436\pi\) | |||||||
\(368\) | 35.3093 | 1.84062 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.92640 | 0.308099 | ||||||||
\(371\) | 5.14637 | 0.267186 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.90440 | −0.202162 | −0.101081 | − | 0.994878i | \(-0.532230\pi\) | ||||
−0.101081 | + | 0.994878i | \(0.532230\pi\) | |||||||
\(374\) | −5.57691 | −0.288375 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.63593 | −0.445364 | ||||||||
\(377\) | −8.07639 | −0.415955 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 23.6160 | 1.21307 | 0.606537 | − | 0.795055i | \(-0.292558\pi\) | ||||
0.606537 | + | 0.795055i | \(0.292558\pi\) | |||||||
\(380\) | 9.28169 | 0.476141 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5.58235 | −0.285618 | ||||||||
\(383\) | −25.6133 | −1.30878 | −0.654388 | − | 0.756159i | \(-0.727074\pi\) | ||||
−0.654388 | + | 0.756159i | \(0.727074\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.9074 | 0.606856 | ||||||||
\(386\) | 11.5337 | 0.587050 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.64689 | −0.388212 | ||||||||
\(389\) | 15.4262 | 0.782140 | 0.391070 | − | 0.920361i | \(-0.372105\pi\) | ||||
0.391070 | + | 0.920361i | \(0.372105\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.53415 | −0.381018 | ||||||||
\(392\) | −2.02942 | −0.102501 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 29.7113 | 1.49683 | ||||||||
\(395\) | 19.1650 | 0.964295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.68868 | −0.285507 | −0.142753 | − | 0.989758i | \(-0.545596\pi\) | ||||
−0.142753 | + | 0.989758i | \(0.545596\pi\) | |||||||
\(398\) | −27.7290 | −1.38993 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −45.4443 | −2.27221 | ||||||||
\(401\) | 22.9927 | 1.14820 | 0.574101 | − | 0.818785i | \(-0.305352\pi\) | ||||
0.574101 | + | 0.818785i | \(0.305352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 26.8444 | 1.33721 | ||||||||
\(404\) | −9.15390 | −0.455423 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.45938 | −0.221315 | ||||||||
\(407\) | −2.98391 | −0.147907 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.0347 | −0.891761 | −0.445880 | − | 0.895093i | \(-0.647109\pi\) | ||||
−0.445880 | + | 0.895093i | \(0.647109\pi\) | |||||||
\(410\) | 62.2414 | 3.07388 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.9325 | 0.538604 | ||||||||
\(413\) | 4.15250 | 0.204331 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −33.6285 | −1.65076 | ||||||||
\(416\) | 12.7066 | 0.622992 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −16.6006 | −0.811962 | ||||||||
\(419\) | 13.0874 | 0.639360 | 0.319680 | − | 0.947525i | \(-0.396425\pi\) | ||||
0.319680 | + | 0.947525i | \(0.396425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.1201 | −1.95533 | −0.977667 | − | 0.210160i | \(-0.932602\pi\) | ||||
−0.977667 | + | 0.210160i | \(0.932602\pi\) | |||||||
\(422\) | −24.4865 | −1.19198 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.4442 | 0.507213 | ||||||||
\(425\) | 9.69671 | 0.470360 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.23055 | −0.0595504 | ||||||||
\(428\) | −12.5873 | −0.608432 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −68.1695 | −3.28742 | ||||||||
\(431\) | 16.9188 | 0.814951 | 0.407476 | − | 0.913216i | \(-0.366409\pi\) | ||||
0.407476 | + | 0.913216i | \(0.366409\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.66554 | −0.416439 | −0.208220 | − | 0.978082i | \(-0.566767\pi\) | ||||
−0.208220 | + | 0.978082i | \(0.566767\pi\) | |||||||
\(434\) | 14.8221 | 0.711485 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.20560 | −0.0577378 | ||||||||
\(437\) | −22.4267 | −1.07281 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.4905 | −1.21660 | −0.608298 | − | 0.793709i | \(-0.708147\pi\) | ||||
−0.608298 | + | 0.793709i | \(0.708147\pi\) | |||||||
\(440\) | 24.1651 | 1.15203 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.32823 | −0.253438 | ||||||||
\(443\) | −34.9265 | −1.65941 | −0.829703 | − | 0.558205i | \(-0.811490\pi\) | ||||
−0.829703 | + | 0.558205i | \(0.811490\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.4934 | 1.06629 | ||||||||
\(446\) | 28.8334 | 1.36530 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.89042 | −0.136559 | ||||||||
\(449\) | −29.0615 | −1.37150 | −0.685749 | − | 0.727838i | \(-0.740525\pi\) | ||||
−0.685749 | + | 0.727838i | \(0.740525\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.3382 | −1.47566 | ||||||||
\(452\) | −11.9987 | −0.564369 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.9088 | 0.558906 | ||||||||
\(455\) | 11.3764 | 0.533335 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.6346 | 0.778133 | 0.389066 | − | 0.921210i | \(-0.372798\pi\) | ||||
0.389066 | + | 0.921210i | \(0.372798\pi\) | |||||||
\(458\) | 14.4344 | 0.674475 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −21.0315 | −0.980601 | ||||||||
\(461\) | 1.69635 | 0.0790067 | 0.0395034 | − | 0.999219i | \(-0.487422\pi\) | ||||
0.0395034 | + | 0.999219i | \(0.487422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −33.3579 | −1.55027 | −0.775136 | − | 0.631795i | \(-0.782318\pi\) | ||||
−0.775136 | + | 0.631795i | \(0.782318\pi\) | |||||||
\(464\) | −13.2389 | −0.614602 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.61132 | 0.213615 | ||||||||
\(467\) | −22.2821 | −1.03109 | −0.515546 | − | 0.856862i | \(-0.672411\pi\) | ||||
−0.515546 | + | 0.856862i | \(0.672411\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.7930 | 0.498373 | ||||||||
\(470\) | 26.7301 | 1.23297 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.42717 | 0.387892 | ||||||||
\(473\) | 34.3230 | 1.57817 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 28.8639 | 1.32437 | ||||||||
\(476\) | −0.828207 | −0.0379608 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −39.7371 | −1.81753 | ||||||||
\(479\) | 10.4324 | 0.476667 | 0.238333 | − | 0.971183i | \(-0.423399\pi\) | ||||
0.238333 | + | 0.971183i | \(0.423399\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.85086 | −0.129988 | ||||||||
\(482\) | −31.1727 | −1.41988 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.781520 | −0.0355236 | ||||||||
\(485\) | −36.7395 | −1.66826 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.27431 | 0.193687 | 0.0968437 | − | 0.995300i | \(-0.469125\pi\) | ||||
0.0968437 | + | 0.995300i | \(0.469125\pi\) | |||||||
\(488\) | −2.49730 | −0.113048 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.28150 | 0.283769 | ||||||||
\(491\) | −12.2377 | −0.552281 | −0.276141 | − | 0.961117i | \(-0.589056\pi\) | ||||
−0.276141 | + | 0.961117i | \(0.589056\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.82487 | 0.127226 | ||||||||
\(494\) | −15.8604 | −0.713593 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 44.0037 | 1.97583 | ||||||||
\(497\) | 15.1564 | 0.679859 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0798 | 0.809361 | 0.404681 | − | 0.914458i | \(-0.367383\pi\) | ||||
0.404681 | + | 0.914458i | \(0.367383\pi\) | |||||||
\(500\) | 12.3168 | 0.550824 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −32.4959 | −1.45036 | ||||||||
\(503\) | −15.4918 | −0.690747 | −0.345373 | − | 0.938465i | \(-0.612248\pi\) | ||||
−0.345373 | + | 0.938465i | \(0.612248\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −43.9800 | −1.95708 | ||||||||
\(506\) | 37.6156 | 1.67222 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.783626 | −0.0347678 | ||||||||
\(509\) | −28.3379 | −1.25606 | −0.628029 | − | 0.778190i | \(-0.716138\pi\) | ||||
−0.628029 | + | 0.778190i | \(0.716138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.29623 | −0.322766 | ||||||||
\(512\) | 0.724649 | 0.0320253 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 16.4364 | 0.724978 | ||||||||
\(515\) | 52.5251 | 2.31453 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.4584 | −0.591902 | ||||||||
\(518\) | −1.57410 | −0.0691621 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 23.0876 | 1.01246 | ||||||||
\(521\) | 24.5238 | 1.07441 | 0.537205 | − | 0.843452i | \(-0.319480\pi\) | ||||
0.537205 | + | 0.843452i | \(0.319480\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 36.5848 | 1.59974 | 0.799870 | − | 0.600173i | \(-0.204902\pi\) | ||||
0.799870 | + | 0.600173i | \(0.204902\pi\) | |||||||
\(524\) | −2.96474 | −0.129515 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.1478 | 1.00929 | ||||||||
\(527\) | −9.38934 | −0.409006 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.8169 | 1.20943 | ||||||||
\(530\) | −32.3269 | −1.40419 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.46530 | −0.106884 | ||||||||
\(533\) | −29.9408 | −1.29688 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −60.4760 | −2.61460 | ||||||||
\(536\) | 21.9035 | 0.946087 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 43.7590 | 1.88658 | ||||||||
\(539\) | −3.16270 | −0.136227 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.7095 | −1.14833 | −0.574166 | − | 0.818739i | \(-0.694674\pi\) | ||||
−0.574166 | + | 0.818739i | \(0.694674\pi\) | |||||||
\(542\) | 32.8629 | 1.41158 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.44438 | −0.190551 | ||||||||
\(545\) | −5.79231 | −0.248115 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.3462 | 1.89611 | 0.948054 | − | 0.318109i | \(-0.103048\pi\) | ||||
0.948054 | + | 0.318109i | \(0.103048\pi\) | |||||||
\(548\) | −17.1490 | −0.732571 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −48.4126 | −2.06432 | ||||||||
\(551\) | 8.40871 | 0.358223 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.09038 | −0.216465 | ||||||||
\(554\) | −1.90586 | −0.0809724 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.72521 | 0.327622 | ||||||||
\(557\) | 25.7466 | 1.09092 | 0.545460 | − | 0.838137i | \(-0.316355\pi\) | ||||
0.545460 | + | 0.838137i | \(0.316355\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.7925 | 1.38698 | ||||||||
\(560\) | 18.6484 | 0.788040 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.0176 | −1.18185 | ||||||||
\(563\) | 28.0882 | 1.18378 | 0.591888 | − | 0.806021i | \(-0.298383\pi\) | ||||
0.591888 | + | 0.806021i | \(0.298383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −57.6476 | −2.42525 | ||||||||
\(566\) | 21.8936 | 0.920256 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 30.7588 | 1.29061 | ||||||||
\(569\) | 19.8532 | 0.832289 | 0.416144 | − | 0.909299i | \(-0.363381\pi\) | ||||
0.416144 | + | 0.909299i | \(0.363381\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5202 | −0.858745 | −0.429372 | − | 0.903128i | \(-0.641265\pi\) | ||||
−0.429372 | + | 0.903128i | \(0.641265\pi\) | |||||||
\(572\) | 7.48886 | 0.313125 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −16.5318 | −0.690026 | ||||||||
\(575\) | −65.4032 | −2.72750 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.0348 | −0.625908 | −0.312954 | − | 0.949768i | \(-0.601319\pi\) | ||||
−0.312954 | + | 0.949768i | \(0.601319\pi\) | |||||||
\(578\) | −26.4995 | −1.10223 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.88562 | 0.327432 | ||||||||
\(581\) | 8.93203 | 0.370563 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.2764 | 0.674101 | ||||||||
\(584\) | −14.8071 | −0.612724 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.7574 | 0.609624 | ||||||||
\(587\) | 39.4649 | 1.62889 | 0.814444 | − | 0.580242i | \(-0.197042\pi\) | ||||
0.814444 | + | 0.580242i | \(0.197042\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.9489 | −1.15162 | ||||||||
\(590\) | −26.0839 | −1.07386 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.67317 | −0.192066 | ||||||||
\(593\) | 7.71037 | 0.316627 | 0.158314 | − | 0.987389i | \(-0.449394\pi\) | ||||
0.158314 | + | 0.987389i | \(0.449394\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.97913 | −0.163128 | ||||||||
\(596\) | 1.55769 | 0.0638054 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 35.9383 | 1.46963 | ||||||||
\(599\) | −45.7827 | −1.87063 | −0.935315 | − | 0.353817i | \(-0.884884\pi\) | ||||
−0.935315 | + | 0.353817i | \(0.884884\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.7608 | −1.90741 | −0.953706 | − | 0.300739i | \(-0.902767\pi\) | ||||
−0.953706 | + | 0.300739i | \(0.902767\pi\) | |||||||
\(602\) | 18.1064 | 0.737962 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.31176 | −0.256822 | ||||||||
\(605\) | −3.75482 | −0.152655 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.1360 | 1.75084 | 0.875419 | − | 0.483366i | \(-0.160586\pi\) | ||||
0.875419 | + | 0.483366i | \(0.160586\pi\) | |||||||
\(608\) | −13.2294 | −0.536524 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.72969 | 0.312966 | ||||||||
\(611\) | −12.8583 | −0.520193 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.6862 | 0.795120 | 0.397560 | − | 0.917576i | \(-0.369857\pi\) | ||||
0.397560 | + | 0.917576i | \(0.369857\pi\) | |||||||
\(614\) | 13.9958 | 0.564824 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.41846 | −0.258607 | ||||||||
\(617\) | −5.42454 | −0.218384 | −0.109192 | − | 0.994021i | \(-0.534826\pi\) | ||||
−0.109192 | + | 0.994021i | \(0.534826\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −23.7411 | −0.954235 | −0.477118 | − | 0.878839i | \(-0.658318\pi\) | ||||
−0.477118 | + | 0.878839i | \(0.658318\pi\) | |||||||
\(620\) | −26.2103 | −1.05263 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.12178 | 0.245461 | ||||||||
\(623\) | −5.97445 | −0.239361 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.3024 | 0.532096 | ||||||||
\(626\) | 46.3100 | 1.85092 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.61728 | −0.303962 | ||||||||
\(629\) | 0.997143 | 0.0397587 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.7531 | 1.18445 | 0.592226 | − | 0.805772i | \(-0.298249\pi\) | ||||
0.592226 | + | 0.805772i | \(0.298249\pi\) | |||||||
\(632\) | −10.3305 | −0.410927 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 14.6286 | 0.580975 | ||||||||
\(635\) | −3.76494 | −0.149407 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.02168 | −0.119723 | ||||||||
\(638\) | −14.1037 | −0.558370 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 49.8204 | 1.96932 | ||||||||
\(641\) | −6.06350 | −0.239494 | −0.119747 | − | 0.992804i | \(-0.538208\pi\) | ||||
−0.119747 | + | 0.992804i | \(0.538208\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.0189 | 0.592287 | 0.296144 | − | 0.955143i | \(-0.404299\pi\) | ||||
0.296144 | + | 0.955143i | \(0.404299\pi\) | |||||||
\(644\) | 5.58616 | 0.220125 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.54748 | 0.218263 | ||||||||
\(647\) | 8.33725 | 0.327771 | 0.163886 | − | 0.986479i | \(-0.447597\pi\) | ||||
0.163886 | + | 0.986479i | \(0.447597\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.1331 | 0.515520 | ||||||||
\(650\) | −46.2539 | −1.81423 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.74465 | 0.146652 | ||||||||
\(653\) | −2.97846 | −0.116556 | −0.0582781 | − | 0.998300i | \(-0.518561\pi\) | ||||
−0.0582781 | + | 0.998300i | \(0.518561\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.2441 | −0.556563 | ||||||||
\(656\) | −49.0795 | −1.91623 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.09974 | −0.276776 | ||||||||
\(659\) | 0.632856 | 0.0246526 | 0.0123263 | − | 0.999924i | \(-0.496076\pi\) | ||||
0.0123263 | + | 0.999924i | \(0.496076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.4745 | −1.26311 | −0.631557 | − | 0.775330i | \(-0.717584\pi\) | ||||
−0.631557 | + | 0.775330i | \(0.717584\pi\) | |||||||
\(662\) | 43.8953 | 1.70604 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.1269 | 0.703459 | ||||||||
\(665\) | −11.8445 | −0.459311 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.0534 | −0.737752 | ||||||||
\(668\) | 16.3994 | 0.634512 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −67.7960 | −2.61919 | ||||||||
\(671\) | −3.89186 | −0.150244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.45807 | −0.364582 | −0.182291 | − | 0.983245i | \(-0.558351\pi\) | ||||
−0.182291 | + | 0.983245i | \(0.558351\pi\) | |||||||
\(674\) | 0.324405 | 0.0124956 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.03221 | −0.116624 | ||||||||
\(677\) | −10.2613 | −0.394372 | −0.197186 | − | 0.980366i | \(-0.563180\pi\) | ||||
−0.197186 | + | 0.980366i | \(0.563180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.75834 | 0.374491 | ||||||||
\(680\) | −8.07533 | −0.309675 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 46.8780 | 1.79505 | ||||||||
\(683\) | 1.93744 | 0.0741339 | 0.0370670 | − | 0.999313i | \(-0.488199\pi\) | ||||
0.0370670 | + | 0.999313i | \(0.488199\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −82.3927 | −3.14806 | ||||||||
\(686\) | −1.66842 | −0.0637006 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 53.7540 | 2.04935 | ||||||||
\(689\) | 15.5507 | 0.592433 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.6381 | 1.05140 | 0.525702 | − | 0.850669i | \(-0.323803\pi\) | ||||
0.525702 | + | 0.850669i | \(0.323803\pi\) | |||||||
\(692\) | 10.7820 | 0.409871 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 34.8206 | 1.32177 | ||||||||
\(695\) | 37.1158 | 1.40788 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.4724 | 0.396670 | ||||||||
\(698\) | −10.1137 | −0.382809 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.18958 | −0.271741 | ||||||||
\(701\) | −18.7994 | −0.710043 | −0.355022 | − | 0.934858i | \(-0.615526\pi\) | ||||
−0.355022 | + | 0.934858i | \(0.615526\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.96816 | 0.111946 | ||||||||
\(704\) | −9.14153 | −0.344534 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.1062 | 1.13306 | ||||||||
\(707\) | 11.6815 | 0.439327 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.4454 | −1.36874 | −0.684369 | − | 0.729136i | \(-0.739922\pi\) | ||||
−0.684369 | + | 0.729136i | \(0.739922\pi\) | |||||||
\(710\) | −95.2051 | −3.57298 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.1247 | −0.454392 | ||||||||
\(713\) | 63.3300 | 2.37173 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.9803 | 1.34559 | ||||||||
\(716\) | −7.24737 | −0.270847 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 57.8167 | 2.15770 | ||||||||
\(719\) | −25.7559 | −0.960533 | −0.480267 | − | 0.877123i | \(-0.659460\pi\) | ||||
−0.480267 | + | 0.877123i | \(0.659460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.9511 | −0.519567 | ||||||||
\(722\) | −15.1870 | −0.565201 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.1006 | 0.412552 | ||||||||
\(725\) | 24.5224 | 0.910740 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.347207 | 0.0128772 | 0.00643859 | − | 0.999979i | \(-0.497951\pi\) | ||||
0.00643859 | + | 0.999979i | \(0.497951\pi\) | |||||||
\(728\) | −6.13226 | −0.227277 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 45.8313 | 1.69629 | ||||||||
\(731\) | −11.4698 | −0.424226 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.7358 | −1.31993 | −0.659966 | − | 0.751295i | \(-0.729429\pi\) | ||||
−0.659966 | + | 0.751295i | \(0.729429\pi\) | |||||||
\(734\) | −18.8801 | −0.696878 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 29.9768 | 1.10496 | ||||||||
\(737\) | 34.1349 | 1.25738 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.6054 | −1.67762 | −0.838811 | − | 0.544422i | \(-0.816749\pi\) | ||||
−0.838811 | + | 0.544422i | \(0.816749\pi\) | |||||||
\(740\) | 2.78352 | 0.102324 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.58631 | 0.315213 | ||||||||
\(743\) | 32.1925 | 1.18103 | 0.590513 | − | 0.807028i | \(-0.298925\pi\) | ||||
0.590513 | + | 0.807028i | \(0.298925\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.48393 | 0.274190 | ||||||||
\(746\) | −6.51418 | −0.238501 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.61937 | −0.0957737 | ||||||||
\(749\) | 16.0629 | 0.586927 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.9426 | −1.42104 | −0.710518 | − | 0.703679i | \(-0.751540\pi\) | ||||
−0.710518 | + | 0.703679i | \(0.751540\pi\) | |||||||
\(752\) | −21.0776 | −0.768621 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.4748 | −0.490723 | ||||||||
\(755\) | −30.3249 | −1.10364 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.7030 | 0.643427 | 0.321714 | − | 0.946837i | \(-0.395741\pi\) | ||||
0.321714 | + | 0.946837i | \(0.395741\pi\) | |||||||
\(758\) | 39.4015 | 1.43113 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −24.0376 | −0.871934 | ||||||||
\(761\) | −13.0843 | −0.474305 | −0.237153 | − | 0.971472i | \(-0.576214\pi\) | ||||
−0.237153 | + | 0.971472i | \(0.576214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.53849 | 0.0556970 | ||||||||
\(764\) | −2.62193 | −0.0948580 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −42.7337 | −1.54403 | ||||||||
\(767\) | 12.5475 | 0.453064 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.4773 | 0.702371 | 0.351185 | − | 0.936306i | \(-0.385779\pi\) | ||||
0.351185 | + | 0.936306i | \(0.385779\pi\) | |||||||
\(770\) | 19.8665 | 0.715939 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.41717 | 0.194968 | ||||||||
\(773\) | 13.8332 | 0.497546 | 0.248773 | − | 0.968562i | \(-0.419973\pi\) | ||||
0.248773 | + | 0.968562i | \(0.419973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −81.5079 | −2.92785 | ||||||||
\(776\) | 19.8038 | 0.710915 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.7374 | 0.922731 | ||||||||
\(779\) | 31.1728 | 1.11688 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.9353 | 1.71526 | ||||||||
\(782\) | −12.5701 | −0.449507 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.95318 | −0.176899 | ||||||||
\(785\) | −36.5973 | −1.30621 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.07202 | −0.252090 | −0.126045 | − | 0.992025i | \(-0.540228\pi\) | ||||
−0.126045 | + | 0.992025i | \(0.540228\pi\) | |||||||
\(788\) | 13.9548 | 0.497121 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 31.9752 | 1.13763 | ||||||||
\(791\) | 15.3117 | 0.544421 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.71832 | −0.132041 | ||||||||
\(794\) | −9.49112 | −0.336827 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.0238 | −0.461617 | ||||||||
\(797\) | −14.5337 | −0.514809 | −0.257405 | − | 0.966304i | \(-0.582867\pi\) | ||||
−0.257405 | + | 0.966304i | \(0.582867\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.49745 | 0.159108 | ||||||||
\(800\) | −38.5812 | −1.36405 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 38.3615 | 1.35459 | ||||||||
\(803\) | −23.0758 | −0.814328 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.8387 | 0.945941 | ||||||||
\(806\) | 44.7877 | 1.57758 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 23.7066 | 0.833996 | ||||||||
\(809\) | 31.3659 | 1.10277 | 0.551383 | − | 0.834252i | \(-0.314100\pi\) | ||||
0.551383 | + | 0.834252i | \(0.314100\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.3232 | −0.643413 | −0.321707 | − | 0.946839i | \(-0.604257\pi\) | ||||
−0.321707 | + | 0.946839i | \(0.604257\pi\) | |||||||
\(812\) | −2.09449 | −0.0735021 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.97842 | −0.174494 | ||||||||
\(815\) | 17.9912 | 0.630204 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −34.1418 | −1.19447 | ||||||||
\(818\) | −30.0895 | −1.05206 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 29.2336 | 1.02088 | ||||||||
\(821\) | 9.46589 | 0.330362 | 0.165181 | − | 0.986263i | \(-0.447179\pi\) | ||||
0.165181 | + | 0.986263i | \(0.447179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5049 | 0.401036 | 0.200518 | − | 0.979690i | \(-0.435738\pi\) | ||||
0.200518 | + | 0.979690i | \(0.435738\pi\) | |||||||
\(824\) | −28.3127 | −0.986321 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.92811 | 0.241060 | ||||||||
\(827\) | 15.4743 | 0.538094 | 0.269047 | − | 0.963127i | \(-0.413291\pi\) | ||||
0.269047 | + | 0.963127i | \(0.413291\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.4745 | 0.502720 | 0.251360 | − | 0.967894i | \(-0.419122\pi\) | ||||
0.251360 | + | 0.967894i | \(0.419122\pi\) | |||||||
\(830\) | −56.1065 | −1.94749 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.73390 | −0.302794 | ||||||||
\(833\) | 1.05689 | 0.0366191 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 78.7911 | 2.72668 | ||||||||
\(836\) | −7.79700 | −0.269665 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.8353 | 0.754286 | ||||||||
\(839\) | 24.9719 | 0.862127 | 0.431063 | − | 0.902322i | \(-0.358139\pi\) | ||||
0.431063 | + | 0.902322i | \(0.358139\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.8561 | −0.753657 | ||||||||
\(842\) | −66.9372 | −2.30681 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.5008 | −0.395875 | ||||||||
\(845\) | −14.5683 | −0.501165 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.997312 | 0.0342680 | ||||||||
\(848\) | 25.4909 | 0.875361 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.1782 | 0.554907 | ||||||||
\(851\) | −6.72561 | −0.230551 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.627948 | 0.0215005 | 0.0107503 | − | 0.999942i | \(-0.496578\pi\) | ||||
0.0107503 | + | 0.999942i | \(0.496578\pi\) | |||||||
\(854\) | −2.05307 | −0.0702547 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 32.5985 | 1.11419 | ||||||||
\(857\) | −37.4706 | −1.27997 | −0.639986 | − | 0.768387i | \(-0.721060\pi\) | ||||
−0.639986 | + | 0.768387i | \(0.721060\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.464206 | 0.0158385 | 0.00791926 | − | 0.999969i | \(-0.497479\pi\) | ||||
0.00791926 | + | 0.999969i | \(0.497479\pi\) | |||||||
\(860\) | −32.0179 | −1.09180 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 28.2277 | 0.961440 | ||||||||
\(863\) | −13.3762 | −0.455333 | −0.227666 | − | 0.973739i | \(-0.573110\pi\) | ||||
−0.227666 | + | 0.973739i | \(0.573110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51.8023 | 1.76133 | ||||||||
\(866\) | −14.4578 | −0.491295 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.96168 | 0.236295 | ||||||||
\(869\) | −16.0994 | −0.546134 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.6129 | 1.10504 | ||||||||
\(872\) | 3.12224 | 0.105733 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −37.4171 | −1.26565 | ||||||||
\(875\) | −15.7177 | −0.531356 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.07242 | −0.137516 | −0.0687580 | − | 0.997633i | \(-0.521904\pi\) | ||||
−0.0687580 | + | 0.997633i | \(0.521904\pi\) | |||||||
\(878\) | −42.5289 | −1.43528 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 58.9794 | 1.98820 | ||||||||
\(881\) | 4.54811 | 0.153230 | 0.0766149 | − | 0.997061i | \(-0.475589\pi\) | ||||
0.0766149 | + | 0.997061i | \(0.475589\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.3985 | −0.753771 | −0.376885 | − | 0.926260i | \(-0.623005\pi\) | ||||
−0.376885 | + | 0.926260i | \(0.623005\pi\) | |||||||
\(884\) | −2.50257 | −0.0841707 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −58.2720 | −1.95769 | ||||||||
\(887\) | −4.37232 | −0.146808 | −0.0734040 | − | 0.997302i | \(-0.523386\pi\) | ||||
−0.0734040 | + | 0.997302i | \(0.523386\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 37.5285 | 1.25796 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.5425 | 0.453436 | ||||||||
\(893\) | 13.3874 | 0.447993 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.8200 | −1.16391 | ||||||||
\(896\) | −13.2327 | −0.442074 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −48.4868 | −1.61803 | ||||||||
\(899\) | −23.7451 | −0.791944 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.43915 | −0.181204 | ||||||||
\(902\) | −52.2853 | −1.74091 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 31.0739 | 1.03350 | ||||||||
\(905\) | 53.3331 | 1.77285 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.6987 | 0.753697 | 0.376849 | − | 0.926275i | \(-0.377008\pi\) | ||||
0.376849 | + | 0.926275i | \(0.377008\pi\) | |||||||
\(908\) | 5.59333 | 0.185621 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 18.9807 | 0.629203 | ||||||||
\(911\) | 26.5960 | 0.881165 | 0.440582 | − | 0.897712i | \(-0.354772\pi\) | ||||
0.440582 | + | 0.897712i | \(0.354772\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28.2493 | 0.934917 | ||||||||
\(914\) | 27.7535 | 0.918003 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.77957 | 0.224003 | ||||||||
\(917\) | 3.78335 | 0.124937 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −12.3633 | −0.407828 | −0.203914 | − | 0.978989i | \(-0.565366\pi\) | ||||
−0.203914 | + | 0.978989i | \(0.565366\pi\) | |||||||
\(920\) | 54.4671 | 1.79573 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.83022 | 0.0932083 | ||||||||
\(923\) | 45.7979 | 1.50745 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.65610 | 0.284611 | ||||||||
\(926\) | −55.6549 | −1.82893 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −11.2396 | −0.368957 | ||||||||
\(929\) | 40.0029 | 1.31245 | 0.656227 | − | 0.754563i | \(-0.272151\pi\) | ||||
0.656227 | + | 0.754563i | \(0.272151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.14601 | 0.103106 | ||||||||
\(932\) | 2.16585 | 0.0709448 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −37.1759 | −1.21643 | ||||||||
\(935\) | −12.5848 | −0.411567 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −51.5727 | −1.68481 | −0.842403 | − | 0.538848i | \(-0.818860\pi\) | ||||
−0.842403 | + | 0.538848i | \(0.818860\pi\) | |||||||
\(938\) | 18.0072 | 0.587956 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.5546 | 0.409487 | ||||||||
\(941\) | 43.1695 | 1.40729 | 0.703644 | − | 0.710553i | \(-0.251555\pi\) | ||||
0.703644 | + | 0.710553i | \(0.251555\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −70.6350 | −2.30019 | ||||||||
\(944\) | 20.5681 | 0.669434 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 57.2652 | 1.86185 | ||||||||
\(947\) | −32.9398 | −1.07040 | −0.535200 | − | 0.844726i | \(-0.679764\pi\) | ||||
−0.535200 | + | 0.844726i | \(0.679764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.0469 | −0.715671 | ||||||||
\(950\) | 48.1571 | 1.56242 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.14488 | 0.0695158 | ||||||||
\(953\) | 23.7506 | 0.769357 | 0.384679 | − | 0.923051i | \(-0.374312\pi\) | ||||
0.384679 | + | 0.923051i | \(0.374312\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.5971 | −0.407632 | ||||||||
\(956\) | −18.6638 | −0.603631 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.4056 | 0.562348 | ||||||||
\(959\) | 21.8842 | 0.706678 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 47.9242 | 1.54594 | ||||||||
\(962\) | −4.75643 | −0.153353 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.6412 | −0.471563 | ||||||||
\(965\) | 26.0268 | 0.837833 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.31829 | 0.0423934 | 0.0211967 | − | 0.999775i | \(-0.493252\pi\) | ||||
0.0211967 | + | 0.999775i | \(0.493252\pi\) | |||||||
\(968\) | 2.02397 | 0.0650528 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −61.2970 | −1.96813 | ||||||||
\(971\) | 46.5792 | 1.49480 | 0.747398 | − | 0.664376i | \(-0.231303\pi\) | ||||
0.747398 | + | 0.664376i | \(0.231303\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.85829 | −0.316042 | ||||||||
\(974\) | 7.13134 | 0.228503 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.09513 | −0.195100 | ||||||||
\(977\) | −46.4171 | −1.48501 | −0.742507 | − | 0.669839i | \(-0.766363\pi\) | ||||
−0.742507 | + | 0.669839i | \(0.766363\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.8954 | −0.603900 | ||||||||
\(980\) | 2.95030 | 0.0942440 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20.4177 | −0.651554 | ||||||||
\(983\) | 56.9936 | 1.81781 | 0.908907 | − | 0.416998i | \(-0.136918\pi\) | ||||
0.908907 | + | 0.416998i | \(0.136918\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 67.0462 | 2.13627 | ||||||||
\(986\) | 4.71307 | 0.150095 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.44933 | −0.236995 | ||||||||
\(989\) | 77.3626 | 2.45999 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.27979 | 0.199484 | 0.0997421 | − | 0.995013i | \(-0.468198\pi\) | ||||
0.0997421 | + | 0.995013i | \(0.468198\pi\) | |||||||
\(992\) | 37.3582 | 1.18612 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.2873 | 0.802064 | ||||||||
\(995\) | −62.5730 | −1.98370 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.8353 | 0.533179 | 0.266589 | − | 0.963810i | \(-0.414103\pi\) | ||||
0.266589 | + | 0.963810i | \(0.414103\pi\) | |||||||
\(998\) | 30.1646 | 0.954845 | ||||||||
\(999\) | 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 | 8001.2.a.z.1.26 | yes | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.7 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.7 | ✓ | 32 | 3.2 | odd | 2 | inner | |
8001.2.a.z.1.26 | yes | 32 | 1.1 | even | 1 | trivial |