Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(113\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09226 | −1.47945 | −0.739725 | − | 0.672909i | \(-0.765045\pi\) | ||||
−0.739725 | + | 0.672909i | \(0.765045\pi\) | |||||||
\(3\) | 2.92082 | 1.68634 | 0.843169 | − | 0.537649i | \(-0.180687\pi\) | ||||
0.843169 | + | 0.537649i | \(0.180687\pi\) | |||||||
\(4\) | 2.37755 | 1.18877 | ||||||||
\(5\) | −1.12068 | −0.501182 | −0.250591 | − | 0.968093i | \(-0.580625\pi\) | ||||
−0.250591 | + | 0.968093i | \(0.580625\pi\) | |||||||
\(6\) | −6.11112 | −2.49485 | ||||||||
\(7\) | −1.50686 | −0.569540 | −0.284770 | − | 0.958596i | \(-0.591917\pi\) | ||||
−0.284770 | + | 0.958596i | \(0.591917\pi\) | |||||||
\(8\) | −0.789928 | −0.279282 | ||||||||
\(9\) | 5.53120 | 1.84373 | ||||||||
\(10\) | 2.34475 | 0.741474 | ||||||||
\(11\) | 2.91595 | 0.879192 | 0.439596 | − | 0.898196i | \(-0.355122\pi\) | ||||
0.439596 | + | 0.898196i | \(0.355122\pi\) | |||||||
\(12\) | 6.94439 | 2.00467 | ||||||||
\(13\) | 2.05981 | 0.571290 | 0.285645 | − | 0.958336i | \(-0.407792\pi\) | ||||
0.285645 | + | 0.958336i | \(0.407792\pi\) | |||||||
\(14\) | 3.15274 | 0.842606 | ||||||||
\(15\) | −3.27330 | −0.845162 | ||||||||
\(16\) | −3.10236 | −0.775591 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −11.5727 | −2.72771 | ||||||||
\(19\) | −4.71794 | −1.08237 | −0.541184 | − | 0.840904i | \(-0.682024\pi\) | ||||
−0.541184 | + | 0.840904i | \(0.682024\pi\) | |||||||
\(20\) | −2.66446 | −0.595792 | ||||||||
\(21\) | −4.40127 | −0.960436 | ||||||||
\(22\) | −6.10092 | −1.30072 | ||||||||
\(23\) | −3.53888 | −0.737907 | −0.368954 | − | 0.929448i | \(-0.620284\pi\) | ||||
−0.368954 | + | 0.929448i | \(0.620284\pi\) | |||||||
\(24\) | −2.30724 | −0.470963 | ||||||||
\(25\) | −3.74408 | −0.748816 | ||||||||
\(26\) | −4.30967 | −0.845195 | ||||||||
\(27\) | 7.39319 | 1.42282 | ||||||||
\(28\) | −3.58263 | −0.677054 | ||||||||
\(29\) | −7.98982 | −1.48367 | −0.741836 | − | 0.670581i | \(-0.766045\pi\) | ||||
−0.741836 | + | 0.670581i | \(0.766045\pi\) | |||||||
\(30\) | 6.84859 | 1.25038 | ||||||||
\(31\) | 1.63173 | 0.293068 | 0.146534 | − | 0.989206i | \(-0.453188\pi\) | ||||
0.146534 | + | 0.989206i | \(0.453188\pi\) | |||||||
\(32\) | 8.07080 | 1.42673 | ||||||||
\(33\) | 8.51697 | 1.48261 | ||||||||
\(34\) | 2.09226 | 0.358819 | ||||||||
\(35\) | 1.68870 | 0.285443 | ||||||||
\(36\) | 13.1507 | 2.19178 | ||||||||
\(37\) | 4.82817 | 0.793746 | 0.396873 | − | 0.917874i | \(-0.370095\pi\) | ||||
0.396873 | + | 0.917874i | \(0.370095\pi\) | |||||||
\(38\) | 9.87114 | 1.60131 | ||||||||
\(39\) | 6.01635 | 0.963387 | ||||||||
\(40\) | 0.885254 | 0.139971 | ||||||||
\(41\) | 6.18730 | 0.966294 | 0.483147 | − | 0.875539i | \(-0.339494\pi\) | ||||
0.483147 | + | 0.875539i | \(0.339494\pi\) | |||||||
\(42\) | 9.20860 | 1.42092 | ||||||||
\(43\) | 3.96664 | 0.604907 | 0.302453 | − | 0.953164i | \(-0.402194\pi\) | ||||
0.302453 | + | 0.953164i | \(0.402194\pi\) | |||||||
\(44\) | 6.93281 | 1.04516 | ||||||||
\(45\) | −6.19869 | −0.924047 | ||||||||
\(46\) | 7.40425 | 1.09170 | ||||||||
\(47\) | −6.74019 | −0.983158 | −0.491579 | − | 0.870833i | \(-0.663580\pi\) | ||||
−0.491579 | + | 0.870833i | \(0.663580\pi\) | |||||||
\(48\) | −9.06145 | −1.30791 | ||||||||
\(49\) | −4.72937 | −0.675625 | ||||||||
\(50\) | 7.83359 | 1.10784 | ||||||||
\(51\) | −2.92082 | −0.408997 | ||||||||
\(52\) | 4.89731 | 0.679134 | ||||||||
\(53\) | −7.29570 | −1.00214 | −0.501071 | − | 0.865406i | \(-0.667060\pi\) | ||||
−0.501071 | + | 0.865406i | \(0.667060\pi\) | |||||||
\(54\) | −15.4685 | −2.10499 | ||||||||
\(55\) | −3.26784 | −0.440635 | ||||||||
\(56\) | 1.19031 | 0.159062 | ||||||||
\(57\) | −13.7802 | −1.82524 | ||||||||
\(58\) | 16.7168 | 2.19502 | ||||||||
\(59\) | 13.3308 | 1.73552 | 0.867761 | − | 0.496982i | \(-0.165558\pi\) | ||||
0.867761 | + | 0.496982i | \(0.165558\pi\) | |||||||
\(60\) | −7.78243 | −1.00471 | ||||||||
\(61\) | −8.67070 | −1.11017 | −0.555084 | − | 0.831794i | \(-0.687314\pi\) | ||||
−0.555084 | + | 0.831794i | \(0.687314\pi\) | |||||||
\(62\) | −3.41400 | −0.433579 | ||||||||
\(63\) | −8.33475 | −1.05008 | ||||||||
\(64\) | −10.6815 | −1.33519 | ||||||||
\(65\) | −2.30839 | −0.286320 | ||||||||
\(66\) | −17.8197 | −2.19345 | ||||||||
\(67\) | 2.10029 | 0.256591 | 0.128295 | − | 0.991736i | \(-0.459049\pi\) | ||||
0.128295 | + | 0.991736i | \(0.459049\pi\) | |||||||
\(68\) | −2.37755 | −0.288320 | ||||||||
\(69\) | −10.3364 | −1.24436 | ||||||||
\(70\) | −3.53321 | −0.422299 | ||||||||
\(71\) | −10.5667 | −1.25404 | −0.627019 | − | 0.779004i | \(-0.715725\pi\) | ||||
−0.627019 | + | 0.779004i | \(0.715725\pi\) | |||||||
\(72\) | −4.36925 | −0.514921 | ||||||||
\(73\) | −4.60744 | −0.539261 | −0.269630 | − | 0.962964i | \(-0.586901\pi\) | ||||
−0.269630 | + | 0.962964i | \(0.586901\pi\) | |||||||
\(74\) | −10.1018 | −1.17431 | ||||||||
\(75\) | −10.9358 | −1.26276 | ||||||||
\(76\) | −11.2171 | −1.28669 | ||||||||
\(77\) | −4.39393 | −0.500735 | ||||||||
\(78\) | −12.5878 | −1.42528 | ||||||||
\(79\) | 3.40285 | 0.382850 | 0.191425 | − | 0.981507i | \(-0.438689\pi\) | ||||
0.191425 | + | 0.981507i | \(0.438689\pi\) | |||||||
\(80\) | 3.47675 | 0.388712 | ||||||||
\(81\) | 5.00058 | 0.555620 | ||||||||
\(82\) | −12.9454 | −1.42958 | ||||||||
\(83\) | −1.33273 | −0.146286 | −0.0731429 | − | 0.997321i | \(-0.523303\pi\) | ||||
−0.0731429 | + | 0.997321i | \(0.523303\pi\) | |||||||
\(84\) | −10.4642 | −1.14174 | ||||||||
\(85\) | 1.12068 | 0.121555 | ||||||||
\(86\) | −8.29923 | −0.894929 | ||||||||
\(87\) | −23.3368 | −2.50197 | ||||||||
\(88\) | −2.30339 | −0.245542 | ||||||||
\(89\) | −11.1870 | −1.18582 | −0.592911 | − | 0.805268i | \(-0.702021\pi\) | ||||
−0.592911 | + | 0.805268i | \(0.702021\pi\) | |||||||
\(90\) | 12.9693 | 1.36708 | ||||||||
\(91\) | −3.10385 | −0.325372 | ||||||||
\(92\) | −8.41385 | −0.877205 | ||||||||
\(93\) | 4.76600 | 0.494211 | ||||||||
\(94\) | 14.1022 | 1.45453 | ||||||||
\(95\) | 5.28728 | 0.542464 | ||||||||
\(96\) | 23.5734 | 2.40595 | ||||||||
\(97\) | −13.1324 | −1.33339 | −0.666696 | − | 0.745329i | \(-0.732292\pi\) | ||||
−0.666696 | + | 0.745329i | \(0.732292\pi\) | |||||||
\(98\) | 9.89507 | 0.999553 | ||||||||
\(99\) | 16.1287 | 1.62100 | ||||||||
\(100\) | −8.90173 | −0.890173 | ||||||||
\(101\) | −4.54060 | −0.451807 | −0.225903 | − | 0.974150i | \(-0.572533\pi\) | ||||
−0.225903 | + | 0.974150i | \(0.572533\pi\) | |||||||
\(102\) | 6.11112 | 0.605091 | ||||||||
\(103\) | 1.54723 | 0.152453 | 0.0762267 | − | 0.997091i | \(-0.475713\pi\) | ||||
0.0762267 | + | 0.997091i | \(0.475713\pi\) | |||||||
\(104\) | −1.62710 | −0.159551 | ||||||||
\(105\) | 4.93241 | 0.481353 | ||||||||
\(106\) | 15.2645 | 1.48262 | ||||||||
\(107\) | −16.6699 | −1.61154 | −0.805771 | − | 0.592227i | \(-0.798249\pi\) | ||||
−0.805771 | + | 0.592227i | \(0.798249\pi\) | |||||||
\(108\) | 17.5777 | 1.69141 | ||||||||
\(109\) | −10.4819 | −1.00398 | −0.501991 | − | 0.864873i | \(-0.667399\pi\) | ||||
−0.501991 | + | 0.864873i | \(0.667399\pi\) | |||||||
\(110\) | 6.83717 | 0.651898 | ||||||||
\(111\) | 14.1022 | 1.33852 | ||||||||
\(112\) | 4.67483 | 0.441730 | ||||||||
\(113\) | 2.20891 | 0.207797 | 0.103899 | − | 0.994588i | \(-0.466868\pi\) | ||||
0.103899 | + | 0.994588i | \(0.466868\pi\) | |||||||
\(114\) | 28.8318 | 2.70035 | ||||||||
\(115\) | 3.96594 | 0.369826 | ||||||||
\(116\) | −18.9962 | −1.76375 | ||||||||
\(117\) | 11.3932 | 1.05331 | ||||||||
\(118\) | −27.8915 | −2.56762 | ||||||||
\(119\) | 1.50686 | 0.138134 | ||||||||
\(120\) | 2.58567 | 0.236038 | ||||||||
\(121\) | −2.49724 | −0.227021 | ||||||||
\(122\) | 18.1413 | 1.64244 | ||||||||
\(123\) | 18.0720 | 1.62950 | ||||||||
\(124\) | 3.87952 | 0.348391 | ||||||||
\(125\) | 9.79930 | 0.876476 | ||||||||
\(126\) | 17.4385 | 1.55354 | ||||||||
\(127\) | −4.30706 | −0.382190 | −0.191095 | − | 0.981572i | \(-0.561204\pi\) | ||||
−0.191095 | + | 0.981572i | \(0.561204\pi\) | |||||||
\(128\) | 6.20682 | 0.548611 | ||||||||
\(129\) | 11.5858 | 1.02008 | ||||||||
\(130\) | 4.82975 | 0.423597 | ||||||||
\(131\) | 15.1256 | 1.32153 | 0.660764 | − | 0.750593i | \(-0.270232\pi\) | ||||
0.660764 | + | 0.750593i | \(0.270232\pi\) | |||||||
\(132\) | 20.2495 | 1.76249 | ||||||||
\(133\) | 7.10927 | 0.616452 | ||||||||
\(134\) | −4.39434 | −0.379613 | ||||||||
\(135\) | −8.28538 | −0.713092 | ||||||||
\(136\) | 0.789928 | 0.0677358 | ||||||||
\(137\) | 7.59385 | 0.648786 | 0.324393 | − | 0.945922i | \(-0.394840\pi\) | ||||
0.324393 | + | 0.945922i | \(0.394840\pi\) | |||||||
\(138\) | 21.6265 | 1.84097 | ||||||||
\(139\) | 18.4518 | 1.56506 | 0.782531 | − | 0.622611i | \(-0.213928\pi\) | ||||
0.782531 | + | 0.622611i | \(0.213928\pi\) | |||||||
\(140\) | 4.01498 | 0.339327 | ||||||||
\(141\) | −19.6869 | −1.65794 | ||||||||
\(142\) | 22.1083 | 1.85529 | ||||||||
\(143\) | 6.00632 | 0.502273 | ||||||||
\(144\) | −17.1598 | −1.42998 | ||||||||
\(145\) | 8.95401 | 0.743590 | ||||||||
\(146\) | 9.63997 | 0.797809 | ||||||||
\(147\) | −13.8137 | −1.13933 | ||||||||
\(148\) | 11.4792 | 0.943584 | ||||||||
\(149\) | −19.4594 | −1.59418 | −0.797089 | − | 0.603862i | \(-0.793628\pi\) | ||||
−0.797089 | + | 0.603862i | \(0.793628\pi\) | |||||||
\(150\) | 22.8805 | 1.86819 | ||||||||
\(151\) | 10.1222 | 0.823734 | 0.411867 | − | 0.911244i | \(-0.364877\pi\) | ||||
0.411867 | + | 0.911244i | \(0.364877\pi\) | |||||||
\(152\) | 3.72683 | 0.302286 | ||||||||
\(153\) | −5.53120 | −0.447171 | ||||||||
\(154\) | 9.19324 | 0.740812 | ||||||||
\(155\) | −1.82864 | −0.146880 | ||||||||
\(156\) | 14.3042 | 1.14525 | ||||||||
\(157\) | 7.17830 | 0.572891 | 0.286445 | − | 0.958097i | \(-0.407526\pi\) | ||||
0.286445 | + | 0.958097i | \(0.407526\pi\) | |||||||
\(158\) | −7.11964 | −0.566408 | ||||||||
\(159\) | −21.3094 | −1.68995 | ||||||||
\(160\) | −9.04476 | −0.715051 | ||||||||
\(161\) | 5.33260 | 0.420267 | ||||||||
\(162\) | −10.4625 | −0.822013 | ||||||||
\(163\) | −20.1790 | −1.58054 | −0.790269 | − | 0.612760i | \(-0.790059\pi\) | ||||
−0.790269 | + | 0.612760i | \(0.790059\pi\) | |||||||
\(164\) | 14.7106 | 1.14871 | ||||||||
\(165\) | −9.54478 | −0.743060 | ||||||||
\(166\) | 2.78841 | 0.216423 | ||||||||
\(167\) | 9.37290 | 0.725297 | 0.362648 | − | 0.931926i | \(-0.381873\pi\) | ||||
0.362648 | + | 0.931926i | \(0.381873\pi\) | |||||||
\(168\) | 3.47669 | 0.268232 | ||||||||
\(169\) | −8.75716 | −0.673628 | ||||||||
\(170\) | −2.34475 | −0.179834 | ||||||||
\(171\) | −26.0958 | −1.99560 | ||||||||
\(172\) | 9.43087 | 0.719097 | ||||||||
\(173\) | 5.30304 | 0.403182 | 0.201591 | − | 0.979470i | \(-0.435389\pi\) | ||||
0.201591 | + | 0.979470i | \(0.435389\pi\) | |||||||
\(174\) | 48.8267 | 3.70154 | ||||||||
\(175\) | 5.64181 | 0.426481 | ||||||||
\(176\) | −9.04633 | −0.681893 | ||||||||
\(177\) | 38.9369 | 2.92668 | ||||||||
\(178\) | 23.4061 | 1.75436 | ||||||||
\(179\) | −1.67012 | −0.124831 | −0.0624153 | − | 0.998050i | \(-0.519880\pi\) | ||||
−0.0624153 | + | 0.998050i | \(0.519880\pi\) | |||||||
\(180\) | −14.7377 | −1.09848 | ||||||||
\(181\) | 24.2813 | 1.80482 | 0.902408 | − | 0.430882i | \(-0.141797\pi\) | ||||
0.902408 | + | 0.430882i | \(0.141797\pi\) | |||||||
\(182\) | 6.49406 | 0.481372 | ||||||||
\(183\) | −25.3256 | −1.87212 | ||||||||
\(184\) | 2.79546 | 0.206084 | ||||||||
\(185\) | −5.41082 | −0.397811 | ||||||||
\(186\) | −9.97170 | −0.731160 | ||||||||
\(187\) | −2.91595 | −0.213235 | ||||||||
\(188\) | −16.0251 | −1.16875 | ||||||||
\(189\) | −11.1405 | −0.810352 | ||||||||
\(190\) | −11.0624 | −0.802548 | ||||||||
\(191\) | 3.63498 | 0.263018 | 0.131509 | − | 0.991315i | \(-0.458018\pi\) | ||||
0.131509 | + | 0.991315i | \(0.458018\pi\) | |||||||
\(192\) | −31.1987 | −2.25157 | ||||||||
\(193\) | −19.6443 | −1.41403 | −0.707014 | − | 0.707199i | \(-0.749958\pi\) | ||||
−0.707014 | + | 0.707199i | \(0.749958\pi\) | |||||||
\(194\) | 27.4764 | 1.97269 | ||||||||
\(195\) | −6.74239 | −0.482833 | ||||||||
\(196\) | −11.2443 | −0.803165 | ||||||||
\(197\) | −16.6592 | −1.18692 | −0.593459 | − | 0.804864i | \(-0.702238\pi\) | ||||
−0.593459 | + | 0.804864i | \(0.702238\pi\) | |||||||
\(198\) | −33.7454 | −2.39818 | ||||||||
\(199\) | −9.05940 | −0.642204 | −0.321102 | − | 0.947045i | \(-0.604053\pi\) | ||||
−0.321102 | + | 0.947045i | \(0.604053\pi\) | |||||||
\(200\) | 2.95755 | 0.209131 | ||||||||
\(201\) | 6.13456 | 0.432699 | ||||||||
\(202\) | 9.50011 | 0.668426 | ||||||||
\(203\) | 12.0395 | 0.845010 | ||||||||
\(204\) | −6.94439 | −0.486205 | ||||||||
\(205\) | −6.93397 | −0.484290 | ||||||||
\(206\) | −3.23721 | −0.225547 | ||||||||
\(207\) | −19.5742 | −1.36050 | ||||||||
\(208\) | −6.39029 | −0.443087 | ||||||||
\(209\) | −13.7573 | −0.951610 | ||||||||
\(210\) | −10.3199 | −0.712139 | ||||||||
\(211\) | 26.2273 | 1.80556 | 0.902782 | − | 0.430099i | \(-0.141522\pi\) | ||||
0.902782 | + | 0.430099i | \(0.141522\pi\) | |||||||
\(212\) | −17.3459 | −1.19132 | ||||||||
\(213\) | −30.8635 | −2.11473 | ||||||||
\(214\) | 34.8778 | 2.38420 | ||||||||
\(215\) | −4.44532 | −0.303168 | ||||||||
\(216\) | −5.84009 | −0.397367 | ||||||||
\(217\) | −2.45879 | −0.166914 | ||||||||
\(218\) | 21.9308 | 1.48534 | ||||||||
\(219\) | −13.4575 | −0.909375 | ||||||||
\(220\) | −7.76944 | −0.523816 | ||||||||
\(221\) | −2.05981 | −0.138558 | ||||||||
\(222\) | −29.5055 | −1.98028 | ||||||||
\(223\) | 22.5006 | 1.50675 | 0.753375 | − | 0.657591i | \(-0.228425\pi\) | ||||
0.753375 | + | 0.657591i | \(0.228425\pi\) | |||||||
\(224\) | −12.1616 | −0.812579 | ||||||||
\(225\) | −20.7093 | −1.38062 | ||||||||
\(226\) | −4.62162 | −0.307425 | ||||||||
\(227\) | −2.82082 | −0.187224 | −0.0936120 | − | 0.995609i | \(-0.529841\pi\) | ||||
−0.0936120 | + | 0.995609i | \(0.529841\pi\) | |||||||
\(228\) | −32.7632 | −2.16980 | ||||||||
\(229\) | 7.50404 | 0.495881 | 0.247940 | − | 0.968775i | \(-0.420246\pi\) | ||||
0.247940 | + | 0.968775i | \(0.420246\pi\) | |||||||
\(230\) | −8.29778 | −0.547139 | ||||||||
\(231\) | −12.8339 | −0.844408 | ||||||||
\(232\) | 6.31138 | 0.414362 | ||||||||
\(233\) | 25.0945 | 1.64399 | 0.821996 | − | 0.569493i | \(-0.192860\pi\) | ||||
0.821996 | + | 0.569493i | \(0.192860\pi\) | |||||||
\(234\) | −23.8376 | −1.55831 | ||||||||
\(235\) | 7.55358 | 0.492741 | ||||||||
\(236\) | 31.6946 | 2.06314 | ||||||||
\(237\) | 9.93911 | 0.645615 | ||||||||
\(238\) | −3.15274 | −0.204362 | ||||||||
\(239\) | −22.1072 | −1.42999 | −0.714997 | − | 0.699127i | \(-0.753572\pi\) | ||||
−0.714997 | + | 0.699127i | \(0.753572\pi\) | |||||||
\(240\) | 10.1550 | 0.655500 | ||||||||
\(241\) | 0.581873 | 0.0374818 | 0.0187409 | − | 0.999824i | \(-0.494034\pi\) | ||||
0.0187409 | + | 0.999824i | \(0.494034\pi\) | |||||||
\(242\) | 5.22486 | 0.335867 | ||||||||
\(243\) | −7.57375 | −0.485856 | ||||||||
\(244\) | −20.6150 | −1.31974 | ||||||||
\(245\) | 5.30010 | 0.338611 | ||||||||
\(246\) | −37.8113 | −2.41076 | ||||||||
\(247\) | −9.71807 | −0.618346 | ||||||||
\(248\) | −1.28895 | −0.0818484 | ||||||||
\(249\) | −3.89266 | −0.246687 | ||||||||
\(250\) | −20.5027 | −1.29670 | ||||||||
\(251\) | −8.94918 | −0.564867 | −0.282434 | − | 0.959287i | \(-0.591142\pi\) | ||||
−0.282434 | + | 0.959287i | \(0.591142\pi\) | |||||||
\(252\) | −19.8163 | −1.24831 | ||||||||
\(253\) | −10.3192 | −0.648762 | ||||||||
\(254\) | 9.01148 | 0.565431 | ||||||||
\(255\) | 3.27330 | 0.204982 | ||||||||
\(256\) | 8.37668 | 0.523542 | ||||||||
\(257\) | 3.11937 | 0.194581 | 0.0972906 | − | 0.995256i | \(-0.468982\pi\) | ||||
0.0972906 | + | 0.995256i | \(0.468982\pi\) | |||||||
\(258\) | −24.2406 | −1.50915 | ||||||||
\(259\) | −7.27537 | −0.452070 | ||||||||
\(260\) | −5.48830 | −0.340370 | ||||||||
\(261\) | −44.1933 | −2.73550 | ||||||||
\(262\) | −31.6466 | −1.95514 | ||||||||
\(263\) | 2.45658 | 0.151479 | 0.0757397 | − | 0.997128i | \(-0.475868\pi\) | ||||
0.0757397 | + | 0.997128i | \(0.475868\pi\) | |||||||
\(264\) | −6.72779 | −0.414067 | ||||||||
\(265\) | 8.17613 | 0.502255 | ||||||||
\(266\) | −14.8744 | −0.912010 | ||||||||
\(267\) | −32.6753 | −1.99970 | ||||||||
\(268\) | 4.99353 | 0.305028 | ||||||||
\(269\) | −24.8873 | −1.51740 | −0.758701 | − | 0.651439i | \(-0.774166\pi\) | ||||
−0.758701 | + | 0.651439i | \(0.774166\pi\) | |||||||
\(270\) | 17.3352 | 1.05498 | ||||||||
\(271\) | 5.07021 | 0.307993 | 0.153997 | − | 0.988071i | \(-0.450785\pi\) | ||||
0.153997 | + | 0.988071i | \(0.450785\pi\) | |||||||
\(272\) | 3.10236 | 0.188108 | ||||||||
\(273\) | −9.06580 | −0.548687 | ||||||||
\(274\) | −15.8883 | −0.959847 | ||||||||
\(275\) | −10.9176 | −0.658353 | ||||||||
\(276\) | −24.5754 | −1.47926 | ||||||||
\(277\) | 4.25681 | 0.255767 | 0.127883 | − | 0.991789i | \(-0.459182\pi\) | ||||
0.127883 | + | 0.991789i | \(0.459182\pi\) | |||||||
\(278\) | −38.6060 | −2.31543 | ||||||||
\(279\) | 9.02543 | 0.540338 | ||||||||
\(280\) | −1.33395 | −0.0797190 | ||||||||
\(281\) | 20.3334 | 1.21299 | 0.606494 | − | 0.795088i | \(-0.292576\pi\) | ||||
0.606494 | + | 0.795088i | \(0.292576\pi\) | |||||||
\(282\) | 41.1901 | 2.45283 | ||||||||
\(283\) | 22.4162 | 1.33251 | 0.666253 | − | 0.745726i | \(-0.267897\pi\) | ||||
0.666253 | + | 0.745726i | \(0.267897\pi\) | |||||||
\(284\) | −25.1228 | −1.49077 | ||||||||
\(285\) | 15.4432 | 0.914777 | ||||||||
\(286\) | −12.5668 | −0.743089 | ||||||||
\(287\) | −9.32340 | −0.550343 | ||||||||
\(288\) | 44.6412 | 2.63051 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −18.7341 | −1.10010 | ||||||||
\(291\) | −38.3574 | −2.24855 | ||||||||
\(292\) | −10.9544 | −0.641059 | ||||||||
\(293\) | −29.6747 | −1.73361 | −0.866807 | − | 0.498644i | \(-0.833831\pi\) | ||||
−0.866807 | + | 0.498644i | \(0.833831\pi\) | |||||||
\(294\) | 28.9017 | 1.68558 | ||||||||
\(295\) | −14.9395 | −0.869813 | ||||||||
\(296\) | −3.81390 | −0.221679 | ||||||||
\(297\) | 21.5582 | 1.25093 | ||||||||
\(298\) | 40.7142 | 2.35851 | ||||||||
\(299\) | −7.28943 | −0.421559 | ||||||||
\(300\) | −26.0004 | −1.50113 | ||||||||
\(301\) | −5.97717 | −0.344518 | ||||||||
\(302\) | −21.1783 | −1.21867 | ||||||||
\(303\) | −13.2623 | −0.761899 | ||||||||
\(304\) | 14.6367 | 0.839475 | ||||||||
\(305\) | 9.71705 | 0.556397 | ||||||||
\(306\) | 11.5727 | 0.661568 | ||||||||
\(307\) | −29.6246 | −1.69076 | −0.845381 | − | 0.534163i | \(-0.820627\pi\) | ||||
−0.845381 | + | 0.534163i | \(0.820627\pi\) | |||||||
\(308\) | −10.4468 | −0.595260 | ||||||||
\(309\) | 4.51919 | 0.257088 | ||||||||
\(310\) | 3.82600 | 0.217302 | ||||||||
\(311\) | 0.336416 | 0.0190764 | 0.00953821 | − | 0.999955i | \(-0.496964\pi\) | ||||
0.00953821 | + | 0.999955i | \(0.496964\pi\) | |||||||
\(312\) | −4.75248 | −0.269056 | ||||||||
\(313\) | 23.5306 | 1.33003 | 0.665014 | − | 0.746831i | \(-0.268426\pi\) | ||||
0.665014 | + | 0.746831i | \(0.268426\pi\) | |||||||
\(314\) | −15.0189 | −0.847564 | ||||||||
\(315\) | 9.34056 | 0.526281 | ||||||||
\(316\) | 8.09043 | 0.455122 | ||||||||
\(317\) | −30.6356 | −1.72067 | −0.860335 | − | 0.509729i | \(-0.829745\pi\) | ||||
−0.860335 | + | 0.509729i | \(0.829745\pi\) | |||||||
\(318\) | 44.5849 | 2.50019 | ||||||||
\(319\) | −23.2979 | −1.30443 | ||||||||
\(320\) | 11.9705 | 0.669171 | ||||||||
\(321\) | −48.6899 | −2.71760 | ||||||||
\(322\) | −11.1572 | −0.621765 | ||||||||
\(323\) | 4.71794 | 0.262513 | ||||||||
\(324\) | 11.8891 | 0.660507 | ||||||||
\(325\) | −7.71211 | −0.427791 | ||||||||
\(326\) | 42.2196 | 2.33833 | ||||||||
\(327\) | −30.6157 | −1.69305 | ||||||||
\(328\) | −4.88752 | −0.269868 | ||||||||
\(329\) | 10.1565 | 0.559948 | ||||||||
\(330\) | 19.9701 | 1.09932 | ||||||||
\(331\) | 24.0344 | 1.32105 | 0.660524 | − | 0.750805i | \(-0.270334\pi\) | ||||
0.660524 | + | 0.750805i | \(0.270334\pi\) | |||||||
\(332\) | −3.16862 | −0.173901 | ||||||||
\(333\) | 26.7056 | 1.46346 | ||||||||
\(334\) | −19.6105 | −1.07304 | ||||||||
\(335\) | −2.35374 | −0.128599 | ||||||||
\(336\) | 13.6543 | 0.744905 | ||||||||
\(337\) | −21.5952 | −1.17636 | −0.588182 | − | 0.808729i | \(-0.700156\pi\) | ||||
−0.588182 | + | 0.808729i | \(0.700156\pi\) | |||||||
\(338\) | 18.3223 | 0.996599 | ||||||||
\(339\) | 6.45184 | 0.350416 | ||||||||
\(340\) | 2.66446 | 0.144501 | ||||||||
\(341\) | 4.75805 | 0.257663 | ||||||||
\(342\) | 54.5993 | 2.95239 | ||||||||
\(343\) | 17.6745 | 0.954335 | ||||||||
\(344\) | −3.13336 | −0.168939 | ||||||||
\(345\) | 11.5838 | 0.623651 | ||||||||
\(346\) | −11.0953 | −0.596489 | ||||||||
\(347\) | −4.64292 | −0.249245 | −0.124623 | − | 0.992204i | \(-0.539772\pi\) | ||||
−0.124623 | + | 0.992204i | \(0.539772\pi\) | |||||||
\(348\) | −55.4844 | −2.97428 | ||||||||
\(349\) | 0.514772 | 0.0275551 | 0.0137776 | − | 0.999905i | \(-0.495614\pi\) | ||||
0.0137776 | + | 0.999905i | \(0.495614\pi\) | |||||||
\(350\) | −11.8041 | −0.630957 | ||||||||
\(351\) | 15.2286 | 0.812842 | ||||||||
\(352\) | 23.5341 | 1.25437 | ||||||||
\(353\) | −1.00000 | −0.0532246 | ||||||||
\(354\) | −81.4661 | −4.32987 | ||||||||
\(355\) | 11.8419 | 0.628501 | ||||||||
\(356\) | −26.5977 | −1.40967 | ||||||||
\(357\) | 4.40127 | 0.232940 | ||||||||
\(358\) | 3.49433 | 0.184681 | ||||||||
\(359\) | 35.6011 | 1.87896 | 0.939478 | − | 0.342610i | \(-0.111311\pi\) | ||||
0.939478 | + | 0.342610i | \(0.111311\pi\) | |||||||
\(360\) | 4.89652 | 0.258069 | ||||||||
\(361\) | 3.25891 | 0.171522 | ||||||||
\(362\) | −50.8028 | −2.67014 | ||||||||
\(363\) | −7.29398 | −0.382835 | ||||||||
\(364\) | −7.37956 | −0.386794 | ||||||||
\(365\) | 5.16346 | 0.270268 | ||||||||
\(366\) | 52.9876 | 2.76971 | ||||||||
\(367\) | −3.37188 | −0.176011 | −0.0880054 | − | 0.996120i | \(-0.528049\pi\) | ||||
−0.0880054 | + | 0.996120i | \(0.528049\pi\) | |||||||
\(368\) | 10.9789 | 0.572314 | ||||||||
\(369\) | 34.2232 | 1.78159 | ||||||||
\(370\) | 11.3208 | 0.588542 | ||||||||
\(371\) | 10.9936 | 0.570759 | ||||||||
\(372\) | 11.3314 | 0.587505 | ||||||||
\(373\) | 27.8269 | 1.44082 | 0.720412 | − | 0.693546i | \(-0.243953\pi\) | ||||
0.720412 | + | 0.693546i | \(0.243953\pi\) | |||||||
\(374\) | 6.10092 | 0.315471 | ||||||||
\(375\) | 28.6220 | 1.47803 | ||||||||
\(376\) | 5.32427 | 0.274578 | ||||||||
\(377\) | −16.4575 | −0.847607 | ||||||||
\(378\) | 23.3088 | 1.19888 | ||||||||
\(379\) | −17.7981 | −0.914227 | −0.457114 | − | 0.889408i | \(-0.651117\pi\) | ||||
−0.457114 | + | 0.889408i | \(0.651117\pi\) | |||||||
\(380\) | 12.5708 | 0.644867 | ||||||||
\(381\) | −12.5801 | −0.644501 | ||||||||
\(382\) | −7.60532 | −0.389122 | ||||||||
\(383\) | −33.1229 | −1.69250 | −0.846251 | − | 0.532785i | \(-0.821146\pi\) | ||||
−0.846251 | + | 0.532785i | \(0.821146\pi\) | |||||||
\(384\) | 18.1290 | 0.925143 | ||||||||
\(385\) | 4.92418 | 0.250959 | ||||||||
\(386\) | 41.1010 | 2.09199 | ||||||||
\(387\) | 21.9403 | 1.11529 | ||||||||
\(388\) | −31.2229 | −1.58510 | ||||||||
\(389\) | −9.24216 | −0.468596 | −0.234298 | − | 0.972165i | \(-0.575279\pi\) | ||||
−0.234298 | + | 0.972165i | \(0.575279\pi\) | |||||||
\(390\) | 14.1068 | 0.714327 | ||||||||
\(391\) | 3.53888 | 0.178969 | ||||||||
\(392\) | 3.73586 | 0.188690 | ||||||||
\(393\) | 44.1792 | 2.22854 | ||||||||
\(394\) | 34.8553 | 1.75599 | ||||||||
\(395\) | −3.81349 | −0.191878 | ||||||||
\(396\) | 38.3468 | 1.92700 | ||||||||
\(397\) | 14.0389 | 0.704595 | 0.352297 | − | 0.935888i | \(-0.385401\pi\) | ||||
0.352297 | + | 0.935888i | \(0.385401\pi\) | |||||||
\(398\) | 18.9546 | 0.950109 | ||||||||
\(399\) | 20.7649 | 1.03955 | ||||||||
\(400\) | 11.6155 | 0.580775 | ||||||||
\(401\) | 6.15096 | 0.307164 | 0.153582 | − | 0.988136i | \(-0.450919\pi\) | ||||
0.153582 | + | 0.988136i | \(0.450919\pi\) | |||||||
\(402\) | −12.8351 | −0.640156 | ||||||||
\(403\) | 3.36106 | 0.167426 | ||||||||
\(404\) | −10.7955 | −0.537096 | ||||||||
\(405\) | −5.60404 | −0.278467 | ||||||||
\(406\) | −25.1898 | −1.25015 | ||||||||
\(407\) | 14.0787 | 0.697855 | ||||||||
\(408\) | 2.30724 | 0.114225 | ||||||||
\(409\) | 8.60550 | 0.425514 | 0.212757 | − | 0.977105i | \(-0.431756\pi\) | ||||
0.212757 | + | 0.977105i | \(0.431756\pi\) | |||||||
\(410\) | 14.5077 | 0.716482 | ||||||||
\(411\) | 22.1803 | 1.09407 | ||||||||
\(412\) | 3.67862 | 0.181233 | ||||||||
\(413\) | −20.0876 | −0.988449 | ||||||||
\(414\) | 40.9544 | 2.01280 | ||||||||
\(415\) | 1.49356 | 0.0733158 | ||||||||
\(416\) | 16.6244 | 0.815076 | ||||||||
\(417\) | 53.8945 | 2.63922 | ||||||||
\(418\) | 28.7838 | 1.40786 | ||||||||
\(419\) | −1.64627 | −0.0804257 | −0.0402129 | − | 0.999191i | \(-0.512804\pi\) | ||||
−0.0402129 | + | 0.999191i | \(0.512804\pi\) | |||||||
\(420\) | 11.7270 | 0.572220 | ||||||||
\(421\) | −13.5816 | −0.661926 | −0.330963 | − | 0.943644i | \(-0.607373\pi\) | ||||
−0.330963 | + | 0.943644i | \(0.607373\pi\) | |||||||
\(422\) | −54.8743 | −2.67124 | ||||||||
\(423\) | −37.2814 | −1.81268 | ||||||||
\(424\) | 5.76308 | 0.279880 | ||||||||
\(425\) | 3.74408 | 0.181615 | ||||||||
\(426\) | 64.5744 | 3.12864 | ||||||||
\(427\) | 13.0655 | 0.632285 | ||||||||
\(428\) | −39.6335 | −1.91576 | ||||||||
\(429\) | 17.5434 | 0.847002 | ||||||||
\(430\) | 9.30077 | 0.448523 | ||||||||
\(431\) | −1.75410 | −0.0844918 | −0.0422459 | − | 0.999107i | \(-0.513451\pi\) | ||||
−0.0422459 | + | 0.999107i | \(0.513451\pi\) | |||||||
\(432\) | −22.9363 | −1.10353 | ||||||||
\(433\) | 21.4367 | 1.03018 | 0.515092 | − | 0.857135i | \(-0.327758\pi\) | ||||
0.515092 | + | 0.857135i | \(0.327758\pi\) | |||||||
\(434\) | 5.14443 | 0.246940 | ||||||||
\(435\) | 26.1531 | 1.25394 | ||||||||
\(436\) | −24.9212 | −1.19351 | ||||||||
\(437\) | 16.6962 | 0.798687 | ||||||||
\(438\) | 28.1566 | 1.34538 | ||||||||
\(439\) | −32.2632 | −1.53984 | −0.769919 | − | 0.638141i | \(-0.779704\pi\) | ||||
−0.769919 | + | 0.638141i | \(0.779704\pi\) | |||||||
\(440\) | 2.58136 | 0.123061 | ||||||||
\(441\) | −26.1591 | −1.24567 | ||||||||
\(442\) | 4.30967 | 0.204990 | ||||||||
\(443\) | −33.4587 | −1.58967 | −0.794834 | − | 0.606826i | \(-0.792442\pi\) | ||||
−0.794834 | + | 0.606826i | \(0.792442\pi\) | |||||||
\(444\) | 33.5287 | 1.59120 | ||||||||
\(445\) | 12.5370 | 0.594313 | ||||||||
\(446\) | −47.0770 | −2.22916 | ||||||||
\(447\) | −56.8375 | −2.68832 | ||||||||
\(448\) | 16.0955 | 0.760441 | ||||||||
\(449\) | −22.1528 | −1.04545 | −0.522727 | − | 0.852500i | \(-0.675085\pi\) | ||||
−0.522727 | + | 0.852500i | \(0.675085\pi\) | |||||||
\(450\) | 43.3292 | 2.04256 | ||||||||
\(451\) | 18.0419 | 0.849558 | ||||||||
\(452\) | 5.25179 | 0.247024 | ||||||||
\(453\) | 29.5652 | 1.38909 | ||||||||
\(454\) | 5.90188 | 0.276989 | ||||||||
\(455\) | 3.47842 | 0.163071 | ||||||||
\(456\) | 10.8854 | 0.509756 | ||||||||
\(457\) | −3.69841 | −0.173004 | −0.0865021 | − | 0.996252i | \(-0.527569\pi\) | ||||
−0.0865021 | + | 0.996252i | \(0.527569\pi\) | |||||||
\(458\) | −15.7004 | −0.733631 | ||||||||
\(459\) | −7.39319 | −0.345084 | ||||||||
\(460\) | 9.42922 | 0.439639 | ||||||||
\(461\) | −0.428070 | −0.0199372 | −0.00996861 | − | 0.999950i | \(-0.503173\pi\) | ||||
−0.00996861 | + | 0.999950i | \(0.503173\pi\) | |||||||
\(462\) | 26.8518 | 1.24926 | ||||||||
\(463\) | −20.3406 | −0.945307 | −0.472654 | − | 0.881248i | \(-0.656704\pi\) | ||||
−0.472654 | + | 0.881248i | \(0.656704\pi\) | |||||||
\(464\) | 24.7873 | 1.15072 | ||||||||
\(465\) | −5.34114 | −0.247690 | ||||||||
\(466\) | −52.5041 | −2.43221 | ||||||||
\(467\) | −31.7998 | −1.47152 | −0.735760 | − | 0.677243i | \(-0.763175\pi\) | ||||
−0.735760 | + | 0.677243i | \(0.763175\pi\) | |||||||
\(468\) | 27.0880 | 1.25214 | ||||||||
\(469\) | −3.16484 | −0.146139 | ||||||||
\(470\) | −15.8041 | −0.728987 | ||||||||
\(471\) | 20.9665 | 0.966087 | ||||||||
\(472\) | −10.5304 | −0.484699 | ||||||||
\(473\) | 11.5665 | 0.531829 | ||||||||
\(474\) | −20.7952 | −0.955155 | ||||||||
\(475\) | 17.6643 | 0.810495 | ||||||||
\(476\) | 3.58263 | 0.164210 | ||||||||
\(477\) | −40.3540 | −1.84768 | ||||||||
\(478\) | 46.2539 | 2.11561 | ||||||||
\(479\) | −24.6985 | −1.12850 | −0.564251 | − | 0.825603i | \(-0.690835\pi\) | ||||
−0.564251 | + | 0.825603i | \(0.690835\pi\) | |||||||
\(480\) | −26.4181 | −1.20582 | ||||||||
\(481\) | 9.94513 | 0.453459 | ||||||||
\(482\) | −1.21743 | −0.0554524 | ||||||||
\(483\) | 15.5756 | 0.708713 | ||||||||
\(484\) | −5.93730 | −0.269877 | ||||||||
\(485\) | 14.7172 | 0.668273 | ||||||||
\(486\) | 15.8462 | 0.718800 | ||||||||
\(487\) | 0.972038 | 0.0440473 | 0.0220236 | − | 0.999757i | \(-0.492989\pi\) | ||||
0.0220236 | + | 0.999757i | \(0.492989\pi\) | |||||||
\(488\) | 6.84922 | 0.310050 | ||||||||
\(489\) | −58.9392 | −2.66532 | ||||||||
\(490\) | −11.0892 | −0.500958 | ||||||||
\(491\) | −28.5399 | −1.28799 | −0.643995 | − | 0.765030i | \(-0.722724\pi\) | ||||
−0.643995 | + | 0.765030i | \(0.722724\pi\) | |||||||
\(492\) | 42.9671 | 1.93711 | ||||||||
\(493\) | 7.98982 | 0.359843 | ||||||||
\(494\) | 20.3327 | 0.914812 | ||||||||
\(495\) | −18.0751 | −0.812414 | ||||||||
\(496\) | −5.06222 | −0.227300 | ||||||||
\(497\) | 15.9225 | 0.714224 | ||||||||
\(498\) | 8.14445 | 0.364962 | ||||||||
\(499\) | −33.3035 | −1.49087 | −0.745435 | − | 0.666578i | \(-0.767758\pi\) | ||||
−0.745435 | + | 0.666578i | \(0.767758\pi\) | |||||||
\(500\) | 23.2983 | 1.04193 | ||||||||
\(501\) | 27.3766 | 1.22310 | ||||||||
\(502\) | 18.7240 | 0.835693 | ||||||||
\(503\) | 4.22601 | 0.188429 | 0.0942143 | − | 0.995552i | \(-0.469966\pi\) | ||||
0.0942143 | + | 0.995552i | \(0.469966\pi\) | |||||||
\(504\) | 6.58385 | 0.293268 | ||||||||
\(505\) | 5.08855 | 0.226438 | ||||||||
\(506\) | 21.5904 | 0.959811 | ||||||||
\(507\) | −25.5781 | −1.13596 | ||||||||
\(508\) | −10.2402 | −0.454337 | ||||||||
\(509\) | −29.4232 | −1.30416 | −0.652080 | − | 0.758150i | \(-0.726104\pi\) | ||||
−0.652080 | + | 0.758150i | \(0.726104\pi\) | |||||||
\(510\) | −6.84859 | −0.303261 | ||||||||
\(511\) | 6.94277 | 0.307130 | ||||||||
\(512\) | −29.9398 | −1.32317 | ||||||||
\(513\) | −34.8806 | −1.54002 | ||||||||
\(514\) | −6.52653 | −0.287873 | ||||||||
\(515\) | −1.73395 | −0.0764069 | ||||||||
\(516\) | 27.5459 | 1.21264 | ||||||||
\(517\) | −19.6541 | −0.864385 | ||||||||
\(518\) | 15.2220 | 0.668815 | ||||||||
\(519\) | 15.4892 | 0.679902 | ||||||||
\(520\) | 1.82346 | 0.0799640 | ||||||||
\(521\) | −39.3172 | −1.72252 | −0.861260 | − | 0.508165i | \(-0.830324\pi\) | ||||
−0.861260 | + | 0.508165i | \(0.830324\pi\) | |||||||
\(522\) | 92.4638 | 4.04703 | ||||||||
\(523\) | 38.4232 | 1.68013 | 0.840064 | − | 0.542487i | \(-0.182517\pi\) | ||||
0.840064 | + | 0.542487i | \(0.182517\pi\) | |||||||
\(524\) | 35.9618 | 1.57100 | ||||||||
\(525\) | 16.4787 | 0.719190 | ||||||||
\(526\) | −5.13981 | −0.224106 | ||||||||
\(527\) | −1.63173 | −0.0710793 | ||||||||
\(528\) | −26.4227 | −1.14990 | ||||||||
\(529\) | −10.4763 | −0.455493 | ||||||||
\(530\) | −17.1066 | −0.743062 | ||||||||
\(531\) | 73.7353 | 3.19984 | ||||||||
\(532\) | 16.9026 | 0.732822 | ||||||||
\(533\) | 12.7447 | 0.552034 | ||||||||
\(534\) | 68.3652 | 2.95845 | ||||||||
\(535\) | 18.6816 | 0.807676 | ||||||||
\(536\) | −1.65907 | −0.0716611 | ||||||||
\(537\) | −4.87813 | −0.210507 | ||||||||
\(538\) | 52.0706 | 2.24492 | ||||||||
\(539\) | −13.7906 | −0.594004 | ||||||||
\(540\) | −19.6989 | −0.847705 | ||||||||
\(541\) | −15.5468 | −0.668408 | −0.334204 | − | 0.942501i | \(-0.608467\pi\) | ||||
−0.334204 | + | 0.942501i | \(0.608467\pi\) | |||||||
\(542\) | −10.6082 | −0.455661 | ||||||||
\(543\) | 70.9214 | 3.04353 | ||||||||
\(544\) | −8.07080 | −0.346033 | ||||||||
\(545\) | 11.7468 | 0.503178 | ||||||||
\(546\) | 18.9680 | 0.811756 | ||||||||
\(547\) | 32.1816 | 1.37599 | 0.687994 | − | 0.725717i | \(-0.258492\pi\) | ||||
0.687994 | + | 0.725717i | \(0.258492\pi\) | |||||||
\(548\) | 18.0547 | 0.771260 | ||||||||
\(549\) | −47.9594 | −2.04686 | ||||||||
\(550\) | 22.8424 | 0.974001 | ||||||||
\(551\) | 37.6954 | 1.60588 | ||||||||
\(552\) | 8.16504 | 0.347527 | ||||||||
\(553\) | −5.12762 | −0.218048 | ||||||||
\(554\) | −8.90635 | −0.378394 | ||||||||
\(555\) | −15.8040 | −0.670844 | ||||||||
\(556\) | 43.8701 | 1.86051 | ||||||||
\(557\) | −8.19439 | −0.347207 | −0.173604 | − | 0.984816i | \(-0.555541\pi\) | ||||
−0.173604 | + | 0.984816i | \(0.555541\pi\) | |||||||
\(558\) | −18.8835 | −0.799404 | ||||||||
\(559\) | 8.17054 | 0.345577 | ||||||||
\(560\) | −5.23897 | −0.221387 | ||||||||
\(561\) | −8.51697 | −0.359587 | ||||||||
\(562\) | −42.5427 | −1.79455 | ||||||||
\(563\) | 14.7296 | 0.620779 | 0.310390 | − | 0.950609i | \(-0.399540\pi\) | ||||
0.310390 | + | 0.950609i | \(0.399540\pi\) | |||||||
\(564\) | −46.8066 | −1.97091 | ||||||||
\(565\) | −2.47548 | −0.104144 | ||||||||
\(566\) | −46.9005 | −1.97138 | ||||||||
\(567\) | −7.53518 | −0.316448 | ||||||||
\(568\) | 8.34693 | 0.350230 | ||||||||
\(569\) | 17.0456 | 0.714588 | 0.357294 | − | 0.933992i | \(-0.383699\pi\) | ||||
0.357294 | + | 0.933992i | \(0.383699\pi\) | |||||||
\(570\) | −32.3112 | −1.35337 | ||||||||
\(571\) | 14.3775 | 0.601681 | 0.300840 | − | 0.953675i | \(-0.402733\pi\) | ||||
0.300840 | + | 0.953675i | \(0.402733\pi\) | |||||||
\(572\) | 14.2803 | 0.597090 | ||||||||
\(573\) | 10.6171 | 0.443537 | ||||||||
\(574\) | 19.5070 | 0.814205 | ||||||||
\(575\) | 13.2499 | 0.552557 | ||||||||
\(576\) | −59.0814 | −2.46173 | ||||||||
\(577\) | 28.8467 | 1.20090 | 0.600451 | − | 0.799661i | \(-0.294988\pi\) | ||||
0.600451 | + | 0.799661i | \(0.294988\pi\) | |||||||
\(578\) | −2.09226 | −0.0870265 | ||||||||
\(579\) | −57.3775 | −2.38453 | ||||||||
\(580\) | 21.2886 | 0.883960 | ||||||||
\(581\) | 2.00823 | 0.0833156 | ||||||||
\(582\) | 80.2536 | 3.32662 | ||||||||
\(583\) | −21.2739 | −0.881075 | ||||||||
\(584\) | 3.63955 | 0.150606 | ||||||||
\(585\) | −12.7682 | −0.527898 | ||||||||
\(586\) | 62.0871 | 2.56479 | ||||||||
\(587\) | −1.87269 | −0.0772942 | −0.0386471 | − | 0.999253i | \(-0.512305\pi\) | ||||
−0.0386471 | + | 0.999253i | \(0.512305\pi\) | |||||||
\(588\) | −32.8426 | −1.35441 | ||||||||
\(589\) | −7.69840 | −0.317207 | ||||||||
\(590\) | 31.2574 | 1.28684 | ||||||||
\(591\) | −48.6585 | −2.00154 | ||||||||
\(592\) | −14.9787 | −0.615622 | ||||||||
\(593\) | 35.0188 | 1.43805 | 0.719025 | − | 0.694984i | \(-0.244589\pi\) | ||||
0.719025 | + | 0.694984i | \(0.244589\pi\) | |||||||
\(594\) | −45.1053 | −1.85069 | ||||||||
\(595\) | −1.68870 | −0.0692301 | ||||||||
\(596\) | −46.2657 | −1.89512 | ||||||||
\(597\) | −26.4609 | −1.08297 | ||||||||
\(598\) | 15.2514 | 0.623675 | ||||||||
\(599\) | −42.0083 | −1.71641 | −0.858207 | − | 0.513304i | \(-0.828421\pi\) | ||||
−0.858207 | + | 0.513304i | \(0.828421\pi\) | |||||||
\(600\) | 8.63849 | 0.352665 | ||||||||
\(601\) | −20.8721 | −0.851392 | −0.425696 | − | 0.904866i | \(-0.639971\pi\) | ||||
−0.425696 | + | 0.904866i | \(0.639971\pi\) | |||||||
\(602\) | 12.5058 | 0.509698 | ||||||||
\(603\) | 11.6171 | 0.473085 | ||||||||
\(604\) | 24.0661 | 0.979234 | ||||||||
\(605\) | 2.79860 | 0.113779 | ||||||||
\(606\) | 27.7481 | 1.12719 | ||||||||
\(607\) | −20.8316 | −0.845529 | −0.422764 | − | 0.906240i | \(-0.638940\pi\) | ||||
−0.422764 | + | 0.906240i | \(0.638940\pi\) | |||||||
\(608\) | −38.0775 | −1.54425 | ||||||||
\(609\) | 35.1654 | 1.42497 | ||||||||
\(610\) | −20.3306 | −0.823162 | ||||||||
\(611\) | −13.8835 | −0.561668 | ||||||||
\(612\) | −13.1507 | −0.531585 | ||||||||
\(613\) | −7.37783 | −0.297988 | −0.148994 | − | 0.988838i | \(-0.547603\pi\) | ||||
−0.148994 | + | 0.988838i | \(0.547603\pi\) | |||||||
\(614\) | 61.9822 | 2.50140 | ||||||||
\(615\) | −20.2529 | −0.816676 | ||||||||
\(616\) | 3.47089 | 0.139846 | ||||||||
\(617\) | −12.2365 | −0.492622 | −0.246311 | − | 0.969191i | \(-0.579218\pi\) | ||||
−0.246311 | + | 0.969191i | \(0.579218\pi\) | |||||||
\(618\) | −9.45532 | −0.380349 | ||||||||
\(619\) | 39.0435 | 1.56929 | 0.784645 | − | 0.619946i | \(-0.212845\pi\) | ||||
0.784645 | + | 0.619946i | \(0.212845\pi\) | |||||||
\(620\) | −4.34769 | −0.174607 | ||||||||
\(621\) | −26.1636 | −1.04991 | ||||||||
\(622\) | −0.703870 | −0.0282226 | ||||||||
\(623\) | 16.8573 | 0.675372 | ||||||||
\(624\) | −18.6649 | −0.747194 | ||||||||
\(625\) | 7.73856 | 0.309542 | ||||||||
\(626\) | −49.2321 | −1.96771 | ||||||||
\(627\) | −40.1825 | −1.60474 | ||||||||
\(628\) | 17.0668 | 0.681038 | ||||||||
\(629\) | −4.82817 | −0.192512 | ||||||||
\(630\) | −19.5429 | −0.778607 | ||||||||
\(631\) | −7.60087 | −0.302586 | −0.151293 | − | 0.988489i | \(-0.548344\pi\) | ||||
−0.151293 | + | 0.988489i | \(0.548344\pi\) | |||||||
\(632\) | −2.68800 | −0.106923 | ||||||||
\(633\) | 76.6053 | 3.04479 | ||||||||
\(634\) | 64.0977 | 2.54565 | ||||||||
\(635\) | 4.82682 | 0.191547 | ||||||||
\(636\) | −50.6642 | −2.00897 | ||||||||
\(637\) | −9.74163 | −0.385977 | ||||||||
\(638\) | 48.7453 | 1.92984 | ||||||||
\(639\) | −58.4466 | −2.31211 | ||||||||
\(640\) | −6.95585 | −0.274954 | ||||||||
\(641\) | 6.77343 | 0.267534 | 0.133767 | − | 0.991013i | \(-0.457293\pi\) | ||||
0.133767 | + | 0.991013i | \(0.457293\pi\) | |||||||
\(642\) | 101.872 | 4.02056 | ||||||||
\(643\) | −40.0262 | −1.57848 | −0.789239 | − | 0.614086i | \(-0.789525\pi\) | ||||
−0.789239 | + | 0.614086i | \(0.789525\pi\) | |||||||
\(644\) | 12.6785 | 0.499603 | ||||||||
\(645\) | −12.9840 | −0.511244 | ||||||||
\(646\) | −9.87114 | −0.388375 | ||||||||
\(647\) | 36.5553 | 1.43714 | 0.718568 | − | 0.695456i | \(-0.244798\pi\) | ||||
0.718568 | + | 0.695456i | \(0.244798\pi\) | |||||||
\(648\) | −3.95010 | −0.155175 | ||||||||
\(649\) | 38.8719 | 1.52586 | ||||||||
\(650\) | 16.1357 | 0.632896 | ||||||||
\(651\) | −7.18169 | −0.281473 | ||||||||
\(652\) | −47.9765 | −1.87890 | ||||||||
\(653\) | −32.7511 | −1.28165 | −0.640824 | − | 0.767688i | \(-0.721407\pi\) | ||||
−0.640824 | + | 0.767688i | \(0.721407\pi\) | |||||||
\(654\) | 64.0560 | 2.50479 | ||||||||
\(655\) | −16.9509 | −0.662327 | ||||||||
\(656\) | −19.1953 | −0.749449 | ||||||||
\(657\) | −25.4847 | −0.994253 | ||||||||
\(658\) | −21.2501 | −0.828415 | ||||||||
\(659\) | −18.2769 | −0.711968 | −0.355984 | − | 0.934492i | \(-0.615854\pi\) | ||||
−0.355984 | + | 0.934492i | \(0.615854\pi\) | |||||||
\(660\) | −22.6932 | −0.883330 | ||||||||
\(661\) | 38.4989 | 1.49743 | 0.748717 | − | 0.662890i | \(-0.230670\pi\) | ||||
0.748717 | + | 0.662890i | \(0.230670\pi\) | |||||||
\(662\) | −50.2861 | −1.95443 | ||||||||
\(663\) | −6.01635 | −0.233656 | ||||||||
\(664\) | 1.05276 | 0.0408549 | ||||||||
\(665\) | −7.96720 | −0.308955 | ||||||||
\(666\) | −55.8750 | −2.16511 | ||||||||
\(667\) | 28.2750 | 1.09481 | ||||||||
\(668\) | 22.2845 | 0.862214 | ||||||||
\(669\) | 65.7202 | 2.54089 | ||||||||
\(670\) | 4.92464 | 0.190255 | ||||||||
\(671\) | −25.2833 | −0.976052 | ||||||||
\(672\) | −35.5218 | −1.37028 | ||||||||
\(673\) | 25.6733 | 0.989631 | 0.494816 | − | 0.868998i | \(-0.335236\pi\) | ||||
0.494816 | + | 0.868998i | \(0.335236\pi\) | |||||||
\(674\) | 45.1827 | 1.74037 | ||||||||
\(675\) | −27.6807 | −1.06543 | ||||||||
\(676\) | −20.8206 | −0.800791 | ||||||||
\(677\) | −27.7345 | −1.06592 | −0.532962 | − | 0.846139i | \(-0.678921\pi\) | ||||
−0.532962 | + | 0.846139i | \(0.678921\pi\) | |||||||
\(678\) | −13.4989 | −0.518423 | ||||||||
\(679\) | 19.7887 | 0.759420 | ||||||||
\(680\) | −0.885254 | −0.0339480 | ||||||||
\(681\) | −8.23910 | −0.315723 | ||||||||
\(682\) | −9.95506 | −0.381199 | ||||||||
\(683\) | 1.38165 | 0.0528672 | 0.0264336 | − | 0.999651i | \(-0.491585\pi\) | ||||
0.0264336 | + | 0.999651i | \(0.491585\pi\) | |||||||
\(684\) | −62.0441 | −2.37232 | ||||||||
\(685\) | −8.51025 | −0.325160 | ||||||||
\(686\) | −36.9797 | −1.41189 | ||||||||
\(687\) | 21.9180 | 0.836222 | ||||||||
\(688\) | −12.3059 | −0.469160 | ||||||||
\(689\) | −15.0278 | −0.572513 | ||||||||
\(690\) | −24.2363 | −0.922661 | ||||||||
\(691\) | 6.55838 | 0.249492 | 0.124746 | − | 0.992189i | \(-0.460188\pi\) | ||||
0.124746 | + | 0.992189i | \(0.460188\pi\) | |||||||
\(692\) | 12.6082 | 0.479293 | ||||||||
\(693\) | −24.3037 | −0.923222 | ||||||||
\(694\) | 9.71420 | 0.368746 | ||||||||
\(695\) | −20.6785 | −0.784381 | ||||||||
\(696\) | 18.4344 | 0.698755 | ||||||||
\(697\) | −6.18730 | −0.234361 | ||||||||
\(698\) | −1.07704 | −0.0407664 | ||||||||
\(699\) | 73.2964 | 2.77233 | ||||||||
\(700\) | 13.4137 | 0.506989 | ||||||||
\(701\) | −7.67620 | −0.289926 | −0.144963 | − | 0.989437i | \(-0.546306\pi\) | ||||
−0.144963 | + | 0.989437i | \(0.546306\pi\) | |||||||
\(702\) | −31.8622 | −1.20256 | ||||||||
\(703\) | −22.7790 | −0.859125 | ||||||||
\(704\) | −31.1467 | −1.17388 | ||||||||
\(705\) | 22.0627 | 0.830928 | ||||||||
\(706\) | 2.09226 | 0.0787432 | ||||||||
\(707\) | 6.84205 | 0.257322 | ||||||||
\(708\) | 92.5743 | 3.47916 | ||||||||
\(709\) | −7.36959 | −0.276771 | −0.138385 | − | 0.990378i | \(-0.544191\pi\) | ||||
−0.138385 | + | 0.990378i | \(0.544191\pi\) | |||||||
\(710\) | −24.7763 | −0.929836 | ||||||||
\(711\) | 18.8218 | 0.705874 | ||||||||
\(712\) | 8.83694 | 0.331178 | ||||||||
\(713\) | −5.77450 | −0.216257 | ||||||||
\(714\) | −9.20860 | −0.344623 | ||||||||
\(715\) | −6.73114 | −0.251731 | ||||||||
\(716\) | −3.97079 | −0.148395 | ||||||||
\(717\) | −64.5711 | −2.41145 | ||||||||
\(718\) | −74.4868 | −2.77982 | ||||||||
\(719\) | 18.2251 | 0.679681 | 0.339841 | − | 0.940483i | \(-0.389627\pi\) | ||||
0.339841 | + | 0.940483i | \(0.389627\pi\) | |||||||
\(720\) | 19.2306 | 0.716682 | ||||||||
\(721\) | −2.33146 | −0.0868283 | ||||||||
\(722\) | −6.81849 | −0.253758 | ||||||||
\(723\) | 1.69955 | 0.0632069 | ||||||||
\(724\) | 57.7300 | 2.14552 | ||||||||
\(725\) | 29.9145 | 1.11100 | ||||||||
\(726\) | 15.2609 | 0.566385 | ||||||||
\(727\) | −17.0251 | −0.631427 | −0.315714 | − | 0.948855i | \(-0.602244\pi\) | ||||
−0.315714 | + | 0.948855i | \(0.602244\pi\) | |||||||
\(728\) | 2.45182 | 0.0908705 | ||||||||
\(729\) | −37.1233 | −1.37494 | ||||||||
\(730\) | −10.8033 | −0.399848 | ||||||||
\(731\) | −3.96664 | −0.146711 | ||||||||
\(732\) | −60.2127 | −2.22553 | ||||||||
\(733\) | −3.67794 | −0.135848 | −0.0679239 | − | 0.997691i | \(-0.521638\pi\) | ||||
−0.0679239 | + | 0.997691i | \(0.521638\pi\) | |||||||
\(734\) | 7.05485 | 0.260399 | ||||||||
\(735\) | 15.4807 | 0.571012 | ||||||||
\(736\) | −28.5616 | −1.05279 | ||||||||
\(737\) | 6.12433 | 0.225593 | ||||||||
\(738\) | −71.6038 | −2.63577 | ||||||||
\(739\) | −16.2366 | −0.597271 | −0.298636 | − | 0.954367i | \(-0.596532\pi\) | ||||
−0.298636 | + | 0.954367i | \(0.596532\pi\) | |||||||
\(740\) | −12.8645 | −0.472908 | ||||||||
\(741\) | −28.3848 | −1.04274 | ||||||||
\(742\) | −23.0015 | −0.844410 | ||||||||
\(743\) | −8.90710 | −0.326770 | −0.163385 | − | 0.986562i | \(-0.552241\pi\) | ||||
−0.163385 | + | 0.986562i | \(0.552241\pi\) | |||||||
\(744\) | −3.76479 | −0.138024 | ||||||||
\(745\) | 21.8077 | 0.798974 | ||||||||
\(746\) | −58.2212 | −2.13163 | ||||||||
\(747\) | −7.37158 | −0.269712 | ||||||||
\(748\) | −6.93281 | −0.253489 | ||||||||
\(749\) | 25.1192 | 0.917837 | ||||||||
\(750\) | −59.8846 | −2.18668 | ||||||||
\(751\) | −38.4571 | −1.40332 | −0.701660 | − | 0.712512i | \(-0.747557\pi\) | ||||
−0.701660 | + | 0.712512i | \(0.747557\pi\) | |||||||
\(752\) | 20.9105 | 0.762528 | ||||||||
\(753\) | −26.1390 | −0.952557 | ||||||||
\(754\) | 34.4334 | 1.25399 | ||||||||
\(755\) | −11.3437 | −0.412841 | ||||||||
\(756\) | −26.4871 | −0.963326 | ||||||||
\(757\) | −12.7584 | −0.463713 | −0.231857 | − | 0.972750i | \(-0.574480\pi\) | ||||
−0.231857 | + | 0.972750i | \(0.574480\pi\) | |||||||
\(758\) | 37.2382 | 1.35255 | ||||||||
\(759\) | −30.1405 | −1.09403 | ||||||||
\(760\) | −4.17657 | −0.151500 | ||||||||
\(761\) | −28.0723 | −1.01762 | −0.508810 | − | 0.860879i | \(-0.669914\pi\) | ||||
−0.508810 | + | 0.860879i | \(0.669914\pi\) | |||||||
\(762\) | 26.3209 | 0.953507 | ||||||||
\(763\) | 15.7947 | 0.571808 | ||||||||
\(764\) | 8.64234 | 0.312669 | ||||||||
\(765\) | 6.19869 | 0.224114 | ||||||||
\(766\) | 69.3017 | 2.50397 | ||||||||
\(767\) | 27.4590 | 0.991486 | ||||||||
\(768\) | 24.4668 | 0.882869 | ||||||||
\(769\) | 0.902768 | 0.0325546 | 0.0162773 | − | 0.999868i | \(-0.494819\pi\) | ||||
0.0162773 | + | 0.999868i | \(0.494819\pi\) | |||||||
\(770\) | −10.3027 | −0.371282 | ||||||||
\(771\) | 9.11113 | 0.328129 | ||||||||
\(772\) | −46.7053 | −1.68096 | ||||||||
\(773\) | 41.0431 | 1.47622 | 0.738109 | − | 0.674682i | \(-0.235719\pi\) | ||||
0.738109 | + | 0.674682i | \(0.235719\pi\) | |||||||
\(774\) | −45.9047 | −1.65001 | ||||||||
\(775\) | −6.10933 | −0.219454 | ||||||||
\(776\) | 10.3736 | 0.372392 | ||||||||
\(777\) | −21.2501 | −0.762342 | ||||||||
\(778\) | 19.3370 | 0.693265 | ||||||||
\(779\) | −29.1913 | −1.04589 | ||||||||
\(780\) | −16.0304 | −0.573979 | ||||||||
\(781\) | −30.8120 | −1.10254 | ||||||||
\(782\) | −7.40425 | −0.264775 | ||||||||
\(783\) | −59.0702 | −2.11100 | ||||||||
\(784\) | 14.6722 | 0.524008 | ||||||||
\(785\) | −8.04456 | −0.287123 | ||||||||
\(786\) | −92.4342 | −3.29702 | ||||||||
\(787\) | 53.8797 | 1.92060 | 0.960302 | − | 0.278962i | \(-0.0899903\pi\) | ||||
0.960302 | + | 0.278962i | \(0.0899903\pi\) | |||||||
\(788\) | −39.6080 | −1.41098 | ||||||||
\(789\) | 7.17525 | 0.255446 | ||||||||
\(790\) | 7.97882 | 0.283874 | ||||||||
\(791\) | −3.32852 | −0.118349 | ||||||||
\(792\) | −12.7405 | −0.452714 | ||||||||
\(793\) | −17.8600 | −0.634228 | ||||||||
\(794\) | −29.3731 | −1.04241 | ||||||||
\(795\) | 23.8810 | 0.846972 | ||||||||
\(796\) | −21.5392 | −0.763435 | ||||||||
\(797\) | 17.6188 | 0.624091 | 0.312046 | − | 0.950067i | \(-0.398986\pi\) | ||||
0.312046 | + | 0.950067i | \(0.398986\pi\) | |||||||
\(798\) | −43.4456 | −1.53796 | ||||||||
\(799\) | 6.74019 | 0.238451 | ||||||||
\(800\) | −30.2177 | −1.06836 | ||||||||
\(801\) | −61.8776 | −2.18634 | ||||||||
\(802\) | −12.8694 | −0.454435 | ||||||||
\(803\) | −13.4351 | −0.474114 | ||||||||
\(804\) | 14.5852 | 0.514381 | ||||||||
\(805\) | −5.97612 | −0.210631 | ||||||||
\(806\) | −7.03221 | −0.247699 | ||||||||
\(807\) | −72.6912 | −2.55885 | ||||||||
\(808\) | 3.58675 | 0.126181 | ||||||||
\(809\) | 51.8905 | 1.82437 | 0.912186 | − | 0.409775i | \(-0.134393\pi\) | ||||
0.912186 | + | 0.409775i | \(0.134393\pi\) | |||||||
\(810\) | 11.7251 | 0.411978 | ||||||||
\(811\) | 15.5937 | 0.547568 | 0.273784 | − | 0.961791i | \(-0.411725\pi\) | ||||
0.273784 | + | 0.961791i | \(0.411725\pi\) | |||||||
\(812\) | 28.6246 | 1.00453 | ||||||||
\(813\) | 14.8092 | 0.519381 | ||||||||
\(814\) | −29.4563 | −1.03244 | ||||||||
\(815\) | 22.6141 | 0.792138 | ||||||||
\(816\) | 9.06145 | 0.317214 | ||||||||
\(817\) | −18.7143 | −0.654732 | ||||||||
\(818\) | −18.0049 | −0.629528 | ||||||||
\(819\) | −17.1680 | −0.599900 | ||||||||
\(820\) | −16.4858 | −0.575711 | ||||||||
\(821\) | −23.9770 | −0.836803 | −0.418401 | − | 0.908262i | \(-0.637409\pi\) | ||||
−0.418401 | + | 0.908262i | \(0.637409\pi\) | |||||||
\(822\) | −46.4069 | −1.61863 | ||||||||
\(823\) | −27.2545 | −0.950033 | −0.475017 | − | 0.879977i | \(-0.657558\pi\) | ||||
−0.475017 | + | 0.879977i | \(0.657558\pi\) | |||||||
\(824\) | −1.22220 | −0.0425774 | ||||||||
\(825\) | −31.8882 | −1.11021 | ||||||||
\(826\) | 42.0286 | 1.46236 | ||||||||
\(827\) | −46.3252 | −1.61089 | −0.805443 | − | 0.592674i | \(-0.798072\pi\) | ||||
−0.805443 | + | 0.592674i | \(0.798072\pi\) | |||||||
\(828\) | −46.5387 | −1.61733 | ||||||||
\(829\) | 28.6879 | 0.996374 | 0.498187 | − | 0.867070i | \(-0.333999\pi\) | ||||
0.498187 | + | 0.867070i | \(0.333999\pi\) | |||||||
\(830\) | −3.12491 | −0.108467 | ||||||||
\(831\) | 12.4334 | 0.431309 | ||||||||
\(832\) | −22.0019 | −0.762778 | ||||||||
\(833\) | 4.72937 | 0.163863 | ||||||||
\(834\) | −112.761 | −3.90460 | ||||||||
\(835\) | −10.5040 | −0.363506 | ||||||||
\(836\) | −32.7086 | −1.13125 | ||||||||
\(837\) | 12.0637 | 0.416982 | ||||||||
\(838\) | 3.44443 | 0.118986 | ||||||||
\(839\) | 1.94919 | 0.0672934 | 0.0336467 | − | 0.999434i | \(-0.489288\pi\) | ||||
0.0336467 | + | 0.999434i | \(0.489288\pi\) | |||||||
\(840\) | −3.89624 | −0.134433 | ||||||||
\(841\) | 34.8372 | 1.20128 | ||||||||
\(842\) | 28.4162 | 0.979286 | ||||||||
\(843\) | 59.3902 | 2.04551 | ||||||||
\(844\) | 62.3567 | 2.14641 | ||||||||
\(845\) | 9.81396 | 0.337610 | ||||||||
\(846\) | 78.0023 | 2.68177 | ||||||||
\(847\) | 3.76299 | 0.129298 | ||||||||
\(848\) | 22.6339 | 0.777251 | ||||||||
\(849\) | 65.4738 | 2.24705 | ||||||||
\(850\) | −7.83359 | −0.268690 | ||||||||
\(851\) | −17.0863 | −0.585711 | ||||||||
\(852\) | −73.3794 | −2.51394 | ||||||||
\(853\) | −7.34974 | −0.251650 | −0.125825 | − | 0.992052i | \(-0.540158\pi\) | ||||
−0.125825 | + | 0.992052i | \(0.540158\pi\) | |||||||
\(854\) | −27.3365 | −0.935435 | ||||||||
\(855\) | 29.2450 | 1.00016 | ||||||||
\(856\) | 13.1680 | 0.450074 | ||||||||
\(857\) | 27.9071 | 0.953287 | 0.476644 | − | 0.879097i | \(-0.341853\pi\) | ||||
0.476644 | + | 0.879097i | \(0.341853\pi\) | |||||||
\(858\) | −36.7053 | −1.25310 | ||||||||
\(859\) | 14.5279 | 0.495686 | 0.247843 | − | 0.968800i | \(-0.420278\pi\) | ||||
0.247843 | + | 0.968800i | \(0.420278\pi\) | |||||||
\(860\) | −10.5690 | −0.360399 | ||||||||
\(861\) | −27.2320 | −0.928064 | ||||||||
\(862\) | 3.67002 | 0.125001 | ||||||||
\(863\) | −22.4172 | −0.763089 | −0.381544 | − | 0.924350i | \(-0.624608\pi\) | ||||
−0.381544 | + | 0.924350i | \(0.624608\pi\) | |||||||
\(864\) | 59.6690 | 2.02998 | ||||||||
\(865\) | −5.94300 | −0.202068 | ||||||||
\(866\) | −44.8512 | −1.52411 | ||||||||
\(867\) | 2.92082 | 0.0991963 | ||||||||
\(868\) | −5.84589 | −0.198423 | ||||||||
\(869\) | 9.92253 | 0.336599 | ||||||||
\(870\) | −54.7190 | −1.85515 | ||||||||
\(871\) | 4.32620 | 0.146588 | ||||||||
\(872\) | 8.27993 | 0.280394 | ||||||||
\(873\) | −72.6379 | −2.45842 | ||||||||
\(874\) | −34.9328 | −1.18162 | ||||||||
\(875\) | −14.7662 | −0.499188 | ||||||||
\(876\) | −31.9959 | −1.08104 | ||||||||
\(877\) | 34.9189 | 1.17913 | 0.589564 | − | 0.807722i | \(-0.299300\pi\) | ||||
0.589564 | + | 0.807722i | \(0.299300\pi\) | |||||||
\(878\) | 67.5030 | 2.27812 | ||||||||
\(879\) | −86.6745 | −2.92346 | ||||||||
\(880\) | 10.1380 | 0.341753 | ||||||||
\(881\) | −48.8077 | −1.64437 | −0.822187 | − | 0.569217i | \(-0.807246\pi\) | ||||
−0.822187 | + | 0.569217i | \(0.807246\pi\) | |||||||
\(882\) | 54.7316 | 1.84291 | ||||||||
\(883\) | 18.5946 | 0.625757 | 0.312879 | − | 0.949793i | \(-0.398707\pi\) | ||||
0.312879 | + | 0.949793i | \(0.398707\pi\) | |||||||
\(884\) | −4.89731 | −0.164714 | ||||||||
\(885\) | −43.6357 | −1.46680 | ||||||||
\(886\) | 70.0042 | 2.35184 | ||||||||
\(887\) | 4.39004 | 0.147403 | 0.0737016 | − | 0.997280i | \(-0.476519\pi\) | ||||
0.0737016 | + | 0.997280i | \(0.476519\pi\) | |||||||
\(888\) | −11.1397 | −0.373825 | ||||||||
\(889\) | 6.49013 | 0.217672 | ||||||||
\(890\) | −26.2307 | −0.879256 | ||||||||
\(891\) | 14.5815 | 0.488497 | ||||||||
\(892\) | 53.4962 | 1.79118 | ||||||||
\(893\) | 31.7998 | 1.06414 | ||||||||
\(894\) | 118.919 | 3.97724 | ||||||||
\(895\) | 1.87167 | 0.0625629 | ||||||||
\(896\) | −9.35282 | −0.312456 | ||||||||
\(897\) | −21.2911 | −0.710890 | ||||||||
\(898\) | 46.3493 | 1.54670 | ||||||||
\(899\) | −13.0372 | −0.434816 | ||||||||
\(900\) | −49.2373 | −1.64124 | ||||||||
\(901\) | 7.29570 | 0.243055 | ||||||||
\(902\) | −37.7483 | −1.25688 | ||||||||
\(903\) | −17.4582 | −0.580974 | ||||||||
\(904\) | −1.74488 | −0.0580339 | ||||||||
\(905\) | −27.2115 | −0.904542 | ||||||||
\(906\) | −61.8580 | −2.05510 | ||||||||
\(907\) | 49.8365 | 1.65480 | 0.827398 | − | 0.561616i | \(-0.189820\pi\) | ||||
0.827398 | + | 0.561616i | \(0.189820\pi\) | |||||||
\(908\) | −6.70662 | −0.222567 | ||||||||
\(909\) | −25.1150 | −0.833011 | ||||||||
\(910\) | −7.27775 | −0.241255 | ||||||||
\(911\) | 40.5300 | 1.34282 | 0.671409 | − | 0.741087i | \(-0.265690\pi\) | ||||
0.671409 | + | 0.741087i | \(0.265690\pi\) | |||||||
\(912\) | 42.7513 | 1.41564 | ||||||||
\(913\) | −3.88617 | −0.128613 | ||||||||
\(914\) | 7.73802 | 0.255951 | ||||||||
\(915\) | 28.3818 | 0.938273 | ||||||||
\(916\) | 17.8412 | 0.589490 | ||||||||
\(917\) | −22.7922 | −0.752663 | ||||||||
\(918\) | 15.4685 | 0.510535 | ||||||||
\(919\) | −9.71693 | −0.320532 | −0.160266 | − | 0.987074i | \(-0.551235\pi\) | ||||
−0.160266 | + | 0.987074i | \(0.551235\pi\) | |||||||
\(920\) | −3.13281 | −0.103286 | ||||||||
\(921\) | −86.5280 | −2.85120 | ||||||||
\(922\) | 0.895634 | 0.0294961 | ||||||||
\(923\) | −21.7655 | −0.716419 | ||||||||
\(924\) | −30.5132 | −1.00381 | ||||||||
\(925\) | −18.0771 | −0.594370 | ||||||||
\(926\) | 42.5578 | 1.39854 | ||||||||
\(927\) | 8.55806 | 0.281083 | ||||||||
\(928\) | −64.4842 | −2.11680 | ||||||||
\(929\) | −50.6367 | −1.66134 | −0.830669 | − | 0.556767i | \(-0.812042\pi\) | ||||
−0.830669 | + | 0.556767i | \(0.812042\pi\) | |||||||
\(930\) | 11.1751 | 0.366445 | ||||||||
\(931\) | 22.3129 | 0.731275 | ||||||||
\(932\) | 59.6633 | 1.95434 | ||||||||
\(933\) | 0.982612 | 0.0321693 | ||||||||
\(934\) | 66.5334 | 2.17704 | ||||||||
\(935\) | 3.26784 | 0.106870 | ||||||||
\(936\) | −8.99984 | −0.294169 | ||||||||
\(937\) | 40.4166 | 1.32035 | 0.660177 | − | 0.751110i | \(-0.270481\pi\) | ||||
0.660177 | + | 0.751110i | \(0.270481\pi\) | |||||||
\(938\) | 6.62166 | 0.216205 | ||||||||
\(939\) | 68.7287 | 2.24288 | ||||||||
\(940\) | 17.9590 | 0.585758 | ||||||||
\(941\) | −21.1536 | −0.689589 | −0.344795 | − | 0.938678i | \(-0.612051\pi\) | ||||
−0.344795 | + | 0.938678i | \(0.612051\pi\) | |||||||
\(942\) | −43.8674 | −1.42928 | ||||||||
\(943\) | −21.8961 | −0.713036 | ||||||||
\(944\) | −41.3570 | −1.34605 | ||||||||
\(945\) | 12.4849 | 0.406134 | ||||||||
\(946\) | −24.2002 | −0.786815 | ||||||||
\(947\) | 21.2570 | 0.690761 | 0.345380 | − | 0.938463i | \(-0.387750\pi\) | ||||
0.345380 | + | 0.938463i | \(0.387750\pi\) | |||||||
\(948\) | 23.6307 | 0.767490 | ||||||||
\(949\) | −9.49048 | −0.308074 | ||||||||
\(950\) | −36.9584 | −1.19909 | ||||||||
\(951\) | −89.4813 | −2.90163 | ||||||||
\(952\) | −1.19031 | −0.0385782 | ||||||||
\(953\) | 3.38315 | 0.109591 | 0.0547955 | − | 0.998498i | \(-0.482549\pi\) | ||||
0.0547955 | + | 0.998498i | \(0.482549\pi\) | |||||||
\(954\) | 84.4310 | 2.73355 | ||||||||
\(955\) | −4.07364 | −0.131820 | ||||||||
\(956\) | −52.5609 | −1.69994 | ||||||||
\(957\) | −68.0491 | −2.19971 | ||||||||
\(958\) | 51.6756 | 1.66956 | ||||||||
\(959\) | −11.4429 | −0.369509 | ||||||||
\(960\) | 34.9637 | 1.12845 | ||||||||
\(961\) | −28.3375 | −0.914111 | ||||||||
\(962\) | −20.8078 | −0.670870 | ||||||||
\(963\) | −92.2047 | −2.97125 | ||||||||
\(964\) | 1.38343 | 0.0445573 | ||||||||
\(965\) | 22.0149 | 0.708686 | ||||||||
\(966\) | −32.5881 | −1.04851 | ||||||||
\(967\) | −31.4204 | −1.01041 | −0.505206 | − | 0.862999i | \(-0.668583\pi\) | ||||
−0.505206 | + | 0.862999i | \(0.668583\pi\) | |||||||
\(968\) | 1.97264 | 0.0634029 | ||||||||
\(969\) | 13.7802 | 0.442685 | ||||||||
\(970\) | −30.7922 | −0.988677 | ||||||||
\(971\) | 23.2615 | 0.746496 | 0.373248 | − | 0.927732i | \(-0.378244\pi\) | ||||
0.373248 | + | 0.927732i | \(0.378244\pi\) | |||||||
\(972\) | −18.0070 | −0.577573 | ||||||||
\(973\) | −27.8043 | −0.891365 | ||||||||
\(974\) | −2.03376 | −0.0651657 | ||||||||
\(975\) | −22.5257 | −0.721400 | ||||||||
\(976\) | 26.8996 | 0.861036 | ||||||||
\(977\) | 29.5856 | 0.946526 | 0.473263 | − | 0.880921i | \(-0.343076\pi\) | ||||
0.473263 | + | 0.880921i | \(0.343076\pi\) | |||||||
\(978\) | 123.316 | 3.94321 | ||||||||
\(979\) | −32.6208 | −1.04256 | ||||||||
\(980\) | 12.6012 | 0.402532 | ||||||||
\(981\) | −57.9774 | −1.85108 | ||||||||
\(982\) | 59.7129 | 1.90552 | ||||||||
\(983\) | −24.6121 | −0.785005 | −0.392503 | − | 0.919751i | \(-0.628391\pi\) | ||||
−0.392503 | + | 0.919751i | \(0.628391\pi\) | |||||||
\(984\) | −14.2756 | −0.455089 | ||||||||
\(985\) | 18.6696 | 0.594862 | ||||||||
\(986\) | −16.7168 | −0.532370 | ||||||||
\(987\) | 29.6654 | 0.944261 | ||||||||
\(988\) | −23.1052 | −0.735074 | ||||||||
\(989\) | −14.0374 | −0.446365 | ||||||||
\(990\) | 37.8177 | 1.20193 | ||||||||
\(991\) | 53.8035 | 1.70913 | 0.854563 | − | 0.519348i | \(-0.173825\pi\) | ||||
0.854563 | + | 0.519348i | \(0.173825\pi\) | |||||||
\(992\) | 13.1694 | 0.418128 | ||||||||
\(993\) | 70.2001 | 2.22773 | ||||||||
\(994\) | −33.3141 | −1.05666 | ||||||||
\(995\) | 10.1527 | 0.321861 | ||||||||
\(996\) | −9.25498 | −0.293255 | ||||||||
\(997\) | −15.2141 | −0.481834 | −0.240917 | − | 0.970546i | \(-0.577448\pi\) | ||||
−0.240917 | + | 0.970546i | \(0.577448\pi\) | |||||||
\(998\) | 69.6796 | 2.20567 | ||||||||
\(999\) | 35.6956 | 1.12936 |
(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 | 6001.2.a.a.1.20 | ✓ | 113 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.a.1.20 | ✓ | 113 | 1.1 | even | 1 | trivial |