Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 12x^{7} - 4x^{6} + 48x^{5} + 27x^{4} - 72x^{3} - 51x^{2} + 27x + 19 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.68361\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.68361 | −1.19049 | −0.595245 | − | 0.803544i | \(-0.702945\pi\) | ||||
−0.595245 | + | 0.803544i | \(0.702945\pi\) | |||||||
\(3\) | 3.25202 | 1.87755 | 0.938777 | − | 0.344526i | \(-0.111960\pi\) | ||||
0.938777 | + | 0.344526i | \(0.111960\pi\) | |||||||
\(4\) | 0.834534 | 0.417267 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −5.47512 | −2.23521 | ||||||||
\(7\) | −0.548389 | −0.207272 | −0.103636 | − | 0.994615i | \(-0.533048\pi\) | ||||
−0.103636 | + | 0.994615i | \(0.533048\pi\) | |||||||
\(8\) | 1.96219 | 0.693738 | ||||||||
\(9\) | 7.57562 | 2.52521 | ||||||||
\(10\) | 1.68361 | 0.532403 | ||||||||
\(11\) | 0.331202 | 0.0998611 | 0.0499306 | − | 0.998753i | \(-0.484100\pi\) | ||||
0.0499306 | + | 0.998753i | \(0.484100\pi\) | |||||||
\(12\) | 2.71392 | 0.783441 | ||||||||
\(13\) | −4.82155 | −1.33726 | −0.668629 | − | 0.743596i | \(-0.733118\pi\) | ||||
−0.668629 | + | 0.743596i | \(0.733118\pi\) | |||||||
\(14\) | 0.923272 | 0.246755 | ||||||||
\(15\) | −3.25202 | −0.839667 | ||||||||
\(16\) | −4.97262 | −1.24316 | ||||||||
\(17\) | 5.28074 | 1.28077 | 0.640384 | − | 0.768055i | \(-0.278775\pi\) | ||||
0.640384 | + | 0.768055i | \(0.278775\pi\) | |||||||
\(18\) | −12.7544 | −3.00623 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −0.834534 | −0.186607 | ||||||||
\(21\) | −1.78337 | −0.389163 | ||||||||
\(22\) | −0.557614 | −0.118884 | ||||||||
\(23\) | −1.11005 | −0.231462 | −0.115731 | − | 0.993281i | \(-0.536921\pi\) | ||||
−0.115731 | + | 0.993281i | \(0.536921\pi\) | |||||||
\(24\) | 6.38107 | 1.30253 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 8.11760 | 1.59199 | ||||||||
\(27\) | 14.8800 | 2.86366 | ||||||||
\(28\) | −0.457649 | −0.0864876 | ||||||||
\(29\) | 3.20529 | 0.595207 | 0.297604 | − | 0.954690i | \(-0.403813\pi\) | ||||
0.297604 | + | 0.954690i | \(0.403813\pi\) | |||||||
\(30\) | 5.47512 | 0.999616 | ||||||||
\(31\) | 6.02121 | 1.08144 | 0.540720 | − | 0.841202i | \(-0.318152\pi\) | ||||
0.540720 | + | 0.841202i | \(0.318152\pi\) | |||||||
\(32\) | 4.44757 | 0.786226 | ||||||||
\(33\) | 1.07707 | 0.187495 | ||||||||
\(34\) | −8.89069 | −1.52474 | ||||||||
\(35\) | 0.548389 | 0.0926947 | ||||||||
\(36\) | 6.32211 | 1.05369 | ||||||||
\(37\) | 6.67261 | 1.09697 | 0.548485 | − | 0.836161i | \(-0.315205\pi\) | ||||
0.548485 | + | 0.836161i | \(0.315205\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.6798 | −2.51077 | ||||||||
\(40\) | −1.96219 | −0.310249 | ||||||||
\(41\) | 7.91140 | 1.23555 | 0.617777 | − | 0.786354i | \(-0.288034\pi\) | ||||
0.617777 | + | 0.786354i | \(0.288034\pi\) | |||||||
\(42\) | 3.00250 | 0.463295 | ||||||||
\(43\) | 1.63905 | 0.249953 | 0.124977 | − | 0.992160i | \(-0.460114\pi\) | ||||
0.124977 | + | 0.992160i | \(0.460114\pi\) | |||||||
\(44\) | 0.276399 | 0.0416687 | ||||||||
\(45\) | −7.57562 | −1.12931 | ||||||||
\(46\) | 1.86889 | 0.275553 | ||||||||
\(47\) | −4.60129 | −0.671167 | −0.335584 | − | 0.942010i | \(-0.608933\pi\) | ||||
−0.335584 | + | 0.942010i | \(0.608933\pi\) | |||||||
\(48\) | −16.1711 | −2.33409 | ||||||||
\(49\) | −6.69927 | −0.957039 | ||||||||
\(50\) | −1.68361 | −0.238098 | ||||||||
\(51\) | 17.1731 | 2.40471 | ||||||||
\(52\) | −4.02375 | −0.557993 | ||||||||
\(53\) | −6.72620 | −0.923914 | −0.461957 | − | 0.886902i | \(-0.652853\pi\) | ||||
−0.461957 | + | 0.886902i | \(0.652853\pi\) | |||||||
\(54\) | −25.0521 | −3.40916 | ||||||||
\(55\) | −0.331202 | −0.0446592 | ||||||||
\(56\) | −1.07604 | −0.143792 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.39645 | −0.708588 | ||||||||
\(59\) | 6.80362 | 0.885756 | 0.442878 | − | 0.896582i | \(-0.353958\pi\) | ||||
0.442878 | + | 0.896582i | \(0.353958\pi\) | |||||||
\(60\) | −2.71392 | −0.350365 | ||||||||
\(61\) | 0.679648 | 0.0870200 | 0.0435100 | − | 0.999053i | \(-0.486146\pi\) | ||||
0.0435100 | + | 0.999053i | \(0.486146\pi\) | |||||||
\(62\) | −10.1374 | −1.28744 | ||||||||
\(63\) | −4.15439 | −0.523404 | ||||||||
\(64\) | 2.45729 | 0.307161 | ||||||||
\(65\) | 4.82155 | 0.598040 | ||||||||
\(66\) | −1.81337 | −0.223210 | ||||||||
\(67\) | 7.77194 | 0.949494 | 0.474747 | − | 0.880122i | \(-0.342540\pi\) | ||||
0.474747 | + | 0.880122i | \(0.342540\pi\) | |||||||
\(68\) | 4.40696 | 0.534422 | ||||||||
\(69\) | −3.60991 | −0.434583 | ||||||||
\(70\) | −0.923272 | −0.110352 | ||||||||
\(71\) | 1.08685 | 0.128985 | 0.0644926 | − | 0.997918i | \(-0.479457\pi\) | ||||
0.0644926 | + | 0.997918i | \(0.479457\pi\) | |||||||
\(72\) | 14.8648 | 1.75183 | ||||||||
\(73\) | 13.9512 | 1.63287 | 0.816435 | − | 0.577437i | \(-0.195947\pi\) | ||||
0.816435 | + | 0.577437i | \(0.195947\pi\) | |||||||
\(74\) | −11.2340 | −1.30593 | ||||||||
\(75\) | 3.25202 | 0.375511 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.181627 | −0.0206984 | ||||||||
\(78\) | 26.3986 | 2.98905 | ||||||||
\(79\) | 1.40438 | 0.158005 | 0.0790025 | − | 0.996874i | \(-0.474826\pi\) | ||||
0.0790025 | + | 0.996874i | \(0.474826\pi\) | |||||||
\(80\) | 4.97262 | 0.555956 | ||||||||
\(81\) | 25.6632 | 2.85146 | ||||||||
\(82\) | −13.3197 | −1.47091 | ||||||||
\(83\) | −0.854878 | −0.0938351 | −0.0469176 | − | 0.998899i | \(-0.514940\pi\) | ||||
−0.0469176 | + | 0.998899i | \(0.514940\pi\) | |||||||
\(84\) | −1.48828 | −0.162385 | ||||||||
\(85\) | −5.28074 | −0.572777 | ||||||||
\(86\) | −2.75952 | −0.297567 | ||||||||
\(87\) | 10.4237 | 1.11753 | ||||||||
\(88\) | 0.649880 | 0.0692775 | ||||||||
\(89\) | −14.5520 | −1.54251 | −0.771257 | − | 0.636524i | \(-0.780372\pi\) | ||||
−0.771257 | + | 0.636524i | \(0.780372\pi\) | |||||||
\(90\) | 12.7544 | 1.34443 | ||||||||
\(91\) | 2.64409 | 0.277175 | ||||||||
\(92\) | −0.926377 | −0.0965815 | ||||||||
\(93\) | 19.5811 | 2.03046 | ||||||||
\(94\) | 7.74677 | 0.799018 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 14.4636 | 1.47618 | ||||||||
\(97\) | 7.02143 | 0.712918 | 0.356459 | − | 0.934311i | \(-0.383984\pi\) | ||||
0.356459 | + | 0.934311i | \(0.383984\pi\) | |||||||
\(98\) | 11.2789 | 1.13934 | ||||||||
\(99\) | 2.50906 | 0.252170 | ||||||||
\(100\) | 0.834534 | 0.0834534 | ||||||||
\(101\) | −7.20677 | −0.717100 | −0.358550 | − | 0.933510i | \(-0.616729\pi\) | ||||
−0.358550 | + | 0.933510i | \(0.616729\pi\) | |||||||
\(102\) | −28.9127 | −2.86278 | ||||||||
\(103\) | −7.07518 | −0.697138 | −0.348569 | − | 0.937283i | \(-0.613332\pi\) | ||||
−0.348569 | + | 0.937283i | \(0.613332\pi\) | |||||||
\(104\) | −9.46079 | −0.927706 | ||||||||
\(105\) | 1.78337 | 0.174039 | ||||||||
\(106\) | 11.3243 | 1.09991 | ||||||||
\(107\) | 6.50106 | 0.628481 | 0.314241 | − | 0.949343i | \(-0.398250\pi\) | ||||
0.314241 | + | 0.949343i | \(0.398250\pi\) | |||||||
\(108\) | 12.4179 | 1.19491 | ||||||||
\(109\) | 17.6607 | 1.69159 | 0.845793 | − | 0.533512i | \(-0.179128\pi\) | ||||
0.845793 | + | 0.533512i | \(0.179128\pi\) | |||||||
\(110\) | 0.557614 | 0.0531664 | ||||||||
\(111\) | 21.6994 | 2.05962 | ||||||||
\(112\) | 2.72693 | 0.257671 | ||||||||
\(113\) | 4.86487 | 0.457649 | 0.228824 | − | 0.973468i | \(-0.426512\pi\) | ||||
0.228824 | + | 0.973468i | \(0.426512\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.11005 | 0.103513 | ||||||||
\(116\) | 2.67492 | 0.248360 | ||||||||
\(117\) | −36.5262 | −3.37685 | ||||||||
\(118\) | −11.4546 | −1.05448 | ||||||||
\(119\) | −2.89590 | −0.265467 | ||||||||
\(120\) | −6.38107 | −0.582509 | ||||||||
\(121\) | −10.8903 | −0.990028 | ||||||||
\(122\) | −1.14426 | −0.103596 | ||||||||
\(123\) | 25.7280 | 2.31982 | ||||||||
\(124\) | 5.02490 | 0.451250 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 6.99436 | 0.623107 | ||||||||
\(127\) | 2.96929 | 0.263482 | 0.131741 | − | 0.991284i | \(-0.457943\pi\) | ||||
0.131741 | + | 0.991284i | \(0.457943\pi\) | |||||||
\(128\) | −13.0322 | −1.15190 | ||||||||
\(129\) | 5.33023 | 0.469300 | ||||||||
\(130\) | −8.11760 | −0.711961 | ||||||||
\(131\) | −7.99500 | −0.698527 | −0.349263 | − | 0.937025i | \(-0.613568\pi\) | ||||
−0.349263 | + | 0.937025i | \(0.613568\pi\) | |||||||
\(132\) | 0.898855 | 0.0782353 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −13.0849 | −1.13036 | ||||||||
\(135\) | −14.8800 | −1.28067 | ||||||||
\(136\) | 10.3618 | 0.888517 | ||||||||
\(137\) | 0.920774 | 0.0786671 | 0.0393335 | − | 0.999226i | \(-0.487477\pi\) | ||||
0.0393335 | + | 0.999226i | \(0.487477\pi\) | |||||||
\(138\) | 6.07768 | 0.517366 | ||||||||
\(139\) | −0.100054 | −0.00848647 | −0.00424323 | − | 0.999991i | \(-0.501351\pi\) | ||||
−0.00424323 | + | 0.999991i | \(0.501351\pi\) | |||||||
\(140\) | 0.457649 | 0.0386784 | ||||||||
\(141\) | −14.9635 | −1.26015 | ||||||||
\(142\) | −1.82983 | −0.153556 | ||||||||
\(143\) | −1.59691 | −0.133540 | ||||||||
\(144\) | −37.6707 | −3.13922 | ||||||||
\(145\) | −3.20529 | −0.266185 | ||||||||
\(146\) | −23.4884 | −1.94392 | ||||||||
\(147\) | −21.7861 | −1.79689 | ||||||||
\(148\) | 5.56851 | 0.457729 | ||||||||
\(149\) | −17.2975 | −1.41707 | −0.708533 | − | 0.705678i | \(-0.750643\pi\) | ||||
−0.708533 | + | 0.705678i | \(0.750643\pi\) | |||||||
\(150\) | −5.47512 | −0.447042 | ||||||||
\(151\) | 19.2178 | 1.56393 | 0.781963 | − | 0.623325i | \(-0.214219\pi\) | ||||
0.781963 | + | 0.623325i | \(0.214219\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 40.0049 | 3.23420 | ||||||||
\(154\) | 0.305789 | 0.0246412 | ||||||||
\(155\) | −6.02121 | −0.483635 | ||||||||
\(156\) | −13.0853 | −1.04766 | ||||||||
\(157\) | −6.58266 | −0.525353 | −0.262677 | − | 0.964884i | \(-0.584605\pi\) | ||||
−0.262677 | + | 0.964884i | \(0.584605\pi\) | |||||||
\(158\) | −2.36442 | −0.188103 | ||||||||
\(159\) | −21.8737 | −1.73470 | ||||||||
\(160\) | −4.44757 | −0.351611 | ||||||||
\(161\) | 0.608741 | 0.0479755 | ||||||||
\(162\) | −43.2067 | −3.39464 | ||||||||
\(163\) | −14.5927 | −1.14299 | −0.571496 | − | 0.820605i | \(-0.693637\pi\) | ||||
−0.571496 | + | 0.820605i | \(0.693637\pi\) | |||||||
\(164\) | 6.60233 | 0.515556 | ||||||||
\(165\) | −1.07707 | −0.0838501 | ||||||||
\(166\) | 1.43928 | 0.111710 | ||||||||
\(167\) | −3.50963 | −0.271584 | −0.135792 | − | 0.990737i | \(-0.543358\pi\) | ||||
−0.135792 | + | 0.990737i | \(0.543358\pi\) | |||||||
\(168\) | −3.49931 | −0.269977 | ||||||||
\(169\) | 10.2474 | 0.788258 | ||||||||
\(170\) | 8.89069 | 0.681885 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.36784 | 0.104297 | ||||||||
\(173\) | −2.50295 | −0.190296 | −0.0951478 | − | 0.995463i | \(-0.530332\pi\) | ||||
−0.0951478 | + | 0.995463i | \(0.530332\pi\) | |||||||
\(174\) | −17.5493 | −1.33041 | ||||||||
\(175\) | −0.548389 | −0.0414543 | ||||||||
\(176\) | −1.64694 | −0.124143 | ||||||||
\(177\) | 22.1255 | 1.66305 | ||||||||
\(178\) | 24.4999 | 1.83635 | ||||||||
\(179\) | 5.02058 | 0.375255 | 0.187628 | − | 0.982240i | \(-0.439920\pi\) | ||||
0.187628 | + | 0.982240i | \(0.439920\pi\) | |||||||
\(180\) | −6.32211 | −0.471222 | ||||||||
\(181\) | 5.42123 | 0.402957 | 0.201479 | − | 0.979493i | \(-0.435425\pi\) | ||||
0.201479 | + | 0.979493i | \(0.435425\pi\) | |||||||
\(182\) | −4.45160 | −0.329975 | ||||||||
\(183\) | 2.21023 | 0.163385 | ||||||||
\(184\) | −2.17813 | −0.160574 | ||||||||
\(185\) | −6.67261 | −0.490580 | ||||||||
\(186\) | −32.9668 | −2.41725 | ||||||||
\(187\) | 1.74899 | 0.127899 | ||||||||
\(188\) | −3.83993 | −0.280056 | ||||||||
\(189\) | −8.16003 | −0.593555 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.98517 | 0.433071 | 0.216536 | − | 0.976275i | \(-0.430524\pi\) | ||||
0.216536 | + | 0.976275i | \(0.430524\pi\) | |||||||
\(192\) | 7.99114 | 0.576711 | ||||||||
\(193\) | −2.16859 | −0.156099 | −0.0780494 | − | 0.996949i | \(-0.524869\pi\) | ||||
−0.0780494 | + | 0.996949i | \(0.524869\pi\) | |||||||
\(194\) | −11.8213 | −0.848722 | ||||||||
\(195\) | 15.6798 | 1.12285 | ||||||||
\(196\) | −5.59077 | −0.399341 | ||||||||
\(197\) | 16.5665 | 1.18032 | 0.590159 | − | 0.807287i | \(-0.299065\pi\) | ||||
0.590159 | + | 0.807287i | \(0.299065\pi\) | |||||||
\(198\) | −4.22427 | −0.300206 | ||||||||
\(199\) | 13.9801 | 0.991025 | 0.495513 | − | 0.868601i | \(-0.334980\pi\) | ||||
0.495513 | + | 0.868601i | \(0.334980\pi\) | |||||||
\(200\) | 1.96219 | 0.138748 | ||||||||
\(201\) | 25.2745 | 1.78273 | ||||||||
\(202\) | 12.1334 | 0.853701 | ||||||||
\(203\) | −1.75775 | −0.123370 | ||||||||
\(204\) | 14.3315 | 1.00341 | ||||||||
\(205\) | −7.91140 | −0.552556 | ||||||||
\(206\) | 11.9118 | 0.829936 | ||||||||
\(207\) | −8.40935 | −0.584490 | ||||||||
\(208\) | 23.9757 | 1.66242 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.00250 | −0.207192 | ||||||||
\(211\) | 18.0813 | 1.24476 | 0.622382 | − | 0.782713i | \(-0.286165\pi\) | ||||
0.622382 | + | 0.782713i | \(0.286165\pi\) | |||||||
\(212\) | −5.61324 | −0.385519 | ||||||||
\(213\) | 3.53445 | 0.242176 | ||||||||
\(214\) | −10.9452 | −0.748201 | ||||||||
\(215\) | −1.63905 | −0.111782 | ||||||||
\(216\) | 29.1974 | 1.98663 | ||||||||
\(217\) | −3.30196 | −0.224152 | ||||||||
\(218\) | −29.7336 | −2.01382 | ||||||||
\(219\) | 45.3697 | 3.06580 | ||||||||
\(220\) | −0.276399 | −0.0186348 | ||||||||
\(221\) | −25.4614 | −1.71272 | ||||||||
\(222\) | −36.5333 | −2.45196 | ||||||||
\(223\) | −26.2666 | −1.75894 | −0.879470 | − | 0.475954i | \(-0.842103\pi\) | ||||
−0.879470 | + | 0.475954i | \(0.842103\pi\) | |||||||
\(224\) | −2.43900 | −0.162962 | ||||||||
\(225\) | 7.57562 | 0.505041 | ||||||||
\(226\) | −8.19054 | −0.544826 | ||||||||
\(227\) | −6.97401 | −0.462881 | −0.231441 | − | 0.972849i | \(-0.574344\pi\) | ||||
−0.231441 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.62489 | 0.173458 | 0.0867288 | − | 0.996232i | \(-0.472359\pi\) | ||||
0.0867288 | + | 0.996232i | \(0.472359\pi\) | |||||||
\(230\) | −1.86889 | −0.123231 | ||||||||
\(231\) | −0.590656 | −0.0388623 | ||||||||
\(232\) | 6.28938 | 0.412918 | ||||||||
\(233\) | −26.6586 | −1.74646 | −0.873231 | − | 0.487306i | \(-0.837980\pi\) | ||||
−0.873231 | + | 0.487306i | \(0.837980\pi\) | |||||||
\(234\) | 61.4959 | 4.02011 | ||||||||
\(235\) | 4.60129 | 0.300155 | ||||||||
\(236\) | 5.67785 | 0.369596 | ||||||||
\(237\) | 4.56707 | 0.296663 | ||||||||
\(238\) | 4.87556 | 0.316036 | ||||||||
\(239\) | 13.1074 | 0.847846 | 0.423923 | − | 0.905698i | \(-0.360653\pi\) | ||||
0.423923 | + | 0.905698i | \(0.360653\pi\) | |||||||
\(240\) | 16.1711 | 1.04384 | ||||||||
\(241\) | 15.1619 | 0.976666 | 0.488333 | − | 0.872657i | \(-0.337605\pi\) | ||||
0.488333 | + | 0.872657i | \(0.337605\pi\) | |||||||
\(242\) | 18.3350 | 1.17862 | ||||||||
\(243\) | 38.8171 | 2.49012 | ||||||||
\(244\) | 0.567189 | 0.0363106 | ||||||||
\(245\) | 6.69927 | 0.428001 | ||||||||
\(246\) | −43.3159 | −2.76172 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 11.8147 | 0.750237 | ||||||||
\(249\) | −2.78008 | −0.176180 | ||||||||
\(250\) | 1.68361 | 0.106481 | ||||||||
\(251\) | 19.0064 | 1.19967 | 0.599835 | − | 0.800124i | \(-0.295233\pi\) | ||||
0.599835 | + | 0.800124i | \(0.295233\pi\) | |||||||
\(252\) | −3.46698 | −0.218399 | ||||||||
\(253\) | −0.367652 | −0.0231141 | ||||||||
\(254\) | −4.99913 | −0.313673 | ||||||||
\(255\) | −17.1731 | −1.07542 | ||||||||
\(256\) | 17.0266 | 1.06416 | ||||||||
\(257\) | −21.8382 | −1.36223 | −0.681115 | − | 0.732176i | \(-0.738505\pi\) | ||||
−0.681115 | + | 0.732176i | \(0.738505\pi\) | |||||||
\(258\) | −8.97401 | −0.558697 | ||||||||
\(259\) | −3.65918 | −0.227371 | ||||||||
\(260\) | 4.02375 | 0.249542 | ||||||||
\(261\) | 24.2821 | 1.50302 | ||||||||
\(262\) | 13.4604 | 0.831589 | ||||||||
\(263\) | −19.6212 | −1.20990 | −0.604948 | − | 0.796265i | \(-0.706806\pi\) | ||||
−0.604948 | + | 0.796265i | \(0.706806\pi\) | |||||||
\(264\) | 2.11342 | 0.130072 | ||||||||
\(265\) | 6.72620 | 0.413187 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −47.3235 | −2.89615 | ||||||||
\(268\) | 6.48595 | 0.396192 | ||||||||
\(269\) | 1.69133 | 0.103122 | 0.0515611 | − | 0.998670i | \(-0.483580\pi\) | ||||
0.0515611 | + | 0.998670i | \(0.483580\pi\) | |||||||
\(270\) | 25.0521 | 1.52462 | ||||||||
\(271\) | −7.93969 | −0.482302 | −0.241151 | − | 0.970488i | \(-0.577525\pi\) | ||||
−0.241151 | + | 0.970488i | \(0.577525\pi\) | |||||||
\(272\) | −26.2591 | −1.59219 | ||||||||
\(273\) | 8.59861 | 0.520412 | ||||||||
\(274\) | −1.55022 | −0.0936524 | ||||||||
\(275\) | 0.331202 | 0.0199722 | ||||||||
\(276\) | −3.01260 | −0.181337 | ||||||||
\(277\) | −9.47395 | −0.569234 | −0.284617 | − | 0.958641i | \(-0.591867\pi\) | ||||
−0.284617 | + | 0.958641i | \(0.591867\pi\) | |||||||
\(278\) | 0.168452 | 0.0101031 | ||||||||
\(279\) | 45.6144 | 2.73086 | ||||||||
\(280\) | 1.07604 | 0.0643058 | ||||||||
\(281\) | 12.5701 | 0.749867 | 0.374933 | − | 0.927052i | \(-0.377666\pi\) | ||||
0.374933 | + | 0.927052i | \(0.377666\pi\) | |||||||
\(282\) | 25.1926 | 1.50020 | ||||||||
\(283\) | −18.5840 | −1.10470 | −0.552351 | − | 0.833612i | \(-0.686269\pi\) | ||||
−0.552351 | + | 0.833612i | \(0.686269\pi\) | |||||||
\(284\) | 0.907012 | 0.0538212 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.68856 | 0.158978 | ||||||||
\(287\) | −4.33853 | −0.256095 | ||||||||
\(288\) | 33.6931 | 1.98538 | ||||||||
\(289\) | 10.8862 | 0.640366 | ||||||||
\(290\) | 5.39645 | 0.316890 | ||||||||
\(291\) | 22.8338 | 1.33854 | ||||||||
\(292\) | 11.6428 | 0.681343 | ||||||||
\(293\) | 17.3651 | 1.01448 | 0.507239 | − | 0.861806i | \(-0.330666\pi\) | ||||
0.507239 | + | 0.861806i | \(0.330666\pi\) | |||||||
\(294\) | 36.6793 | 2.13918 | ||||||||
\(295\) | −6.80362 | −0.396122 | ||||||||
\(296\) | 13.0929 | 0.761009 | ||||||||
\(297\) | 4.92828 | 0.285968 | ||||||||
\(298\) | 29.1222 | 1.68700 | ||||||||
\(299\) | 5.35218 | 0.309525 | ||||||||
\(300\) | 2.71392 | 0.156688 | ||||||||
\(301\) | −0.898838 | −0.0518082 | ||||||||
\(302\) | −32.3553 | −1.86184 | ||||||||
\(303\) | −23.4365 | −1.34639 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.679648 | −0.0389165 | ||||||||
\(306\) | −67.3525 | −3.85029 | ||||||||
\(307\) | 25.0504 | 1.42970 | 0.714851 | − | 0.699277i | \(-0.246494\pi\) | ||||
0.714851 | + | 0.699277i | \(0.246494\pi\) | |||||||
\(308\) | −0.151574 | −0.00863675 | ||||||||
\(309\) | −23.0086 | −1.30891 | ||||||||
\(310\) | 10.1374 | 0.575763 | ||||||||
\(311\) | −5.58411 | −0.316646 | −0.158323 | − | 0.987387i | \(-0.550609\pi\) | ||||
−0.158323 | + | 0.987387i | \(0.550609\pi\) | |||||||
\(312\) | −30.7666 | −1.74182 | ||||||||
\(313\) | −0.821107 | −0.0464117 | −0.0232059 | − | 0.999731i | \(-0.507387\pi\) | ||||
−0.0232059 | + | 0.999731i | \(0.507387\pi\) | |||||||
\(314\) | 11.0826 | 0.625428 | ||||||||
\(315\) | 4.15439 | 0.234073 | ||||||||
\(316\) | 1.17200 | 0.0659302 | ||||||||
\(317\) | −33.5325 | −1.88337 | −0.941686 | − | 0.336494i | \(-0.890759\pi\) | ||||
−0.941686 | + | 0.336494i | \(0.890759\pi\) | |||||||
\(318\) | 36.8268 | 2.06514 | ||||||||
\(319\) | 1.06160 | 0.0594381 | ||||||||
\(320\) | −2.45729 | −0.137366 | ||||||||
\(321\) | 21.1416 | 1.18001 | ||||||||
\(322\) | −1.02488 | −0.0571144 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 21.4168 | 1.18982 | ||||||||
\(325\) | −4.82155 | −0.267452 | ||||||||
\(326\) | 24.5684 | 1.36072 | ||||||||
\(327\) | 57.4328 | 3.17604 | ||||||||
\(328\) | 15.5237 | 0.857150 | ||||||||
\(329\) | 2.52330 | 0.139114 | ||||||||
\(330\) | 1.81337 | 0.0998228 | ||||||||
\(331\) | −11.2673 | −0.619306 | −0.309653 | − | 0.950850i | \(-0.600213\pi\) | ||||
−0.309653 | + | 0.950850i | \(0.600213\pi\) | |||||||
\(332\) | −0.713425 | −0.0391543 | ||||||||
\(333\) | 50.5491 | 2.77008 | ||||||||
\(334\) | 5.90885 | 0.323318 | ||||||||
\(335\) | −7.77194 | −0.424626 | ||||||||
\(336\) | 8.86803 | 0.483791 | ||||||||
\(337\) | −6.29577 | −0.342952 | −0.171476 | − | 0.985188i | \(-0.554854\pi\) | ||||
−0.171476 | + | 0.985188i | \(0.554854\pi\) | |||||||
\(338\) | −17.2525 | −0.938413 | ||||||||
\(339\) | 15.8207 | 0.859260 | ||||||||
\(340\) | −4.40696 | −0.239001 | ||||||||
\(341\) | 1.99424 | 0.107994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.51253 | 0.405638 | ||||||||
\(344\) | 3.21613 | 0.173402 | ||||||||
\(345\) | 3.60991 | 0.194351 | ||||||||
\(346\) | 4.21398 | 0.226545 | ||||||||
\(347\) | −17.5564 | −0.942479 | −0.471239 | − | 0.882005i | \(-0.656193\pi\) | ||||
−0.471239 | + | 0.882005i | \(0.656193\pi\) | |||||||
\(348\) | 8.69890 | 0.466310 | ||||||||
\(349\) | 12.5169 | 0.670013 | 0.335007 | − | 0.942216i | \(-0.391261\pi\) | ||||
0.335007 | + | 0.942216i | \(0.391261\pi\) | |||||||
\(350\) | 0.923272 | 0.0493510 | ||||||||
\(351\) | −71.7447 | −3.82945 | ||||||||
\(352\) | 1.47304 | 0.0785134 | ||||||||
\(353\) | 5.82818 | 0.310203 | 0.155101 | − | 0.987899i | \(-0.450430\pi\) | ||||
0.155101 | + | 0.987899i | \(0.450430\pi\) | |||||||
\(354\) | −37.2506 | −1.97985 | ||||||||
\(355\) | −1.08685 | −0.0576839 | ||||||||
\(356\) | −12.1442 | −0.643640 | ||||||||
\(357\) | −9.41752 | −0.498428 | ||||||||
\(358\) | −8.45268 | −0.446738 | ||||||||
\(359\) | 0.579539 | 0.0305869 | 0.0152934 | − | 0.999883i | \(-0.495132\pi\) | ||||
0.0152934 | + | 0.999883i | \(0.495132\pi\) | |||||||
\(360\) | −14.8648 | −0.783443 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −9.12723 | −0.479717 | ||||||||
\(363\) | −35.4155 | −1.85883 | ||||||||
\(364\) | 2.20658 | 0.115656 | ||||||||
\(365\) | −13.9512 | −0.730242 | ||||||||
\(366\) | −3.72115 | −0.194508 | ||||||||
\(367\) | −7.90625 | −0.412703 | −0.206352 | − | 0.978478i | \(-0.566159\pi\) | ||||
−0.206352 | + | 0.978478i | \(0.566159\pi\) | |||||||
\(368\) | 5.51988 | 0.287743 | ||||||||
\(369\) | 59.9338 | 3.12003 | ||||||||
\(370\) | 11.2340 | 0.584030 | ||||||||
\(371\) | 3.68857 | 0.191501 | ||||||||
\(372\) | 16.3411 | 0.847245 | ||||||||
\(373\) | 8.30620 | 0.430079 | 0.215039 | − | 0.976605i | \(-0.431012\pi\) | ||||
0.215039 | + | 0.976605i | \(0.431012\pi\) | |||||||
\(374\) | −2.94461 | −0.152262 | ||||||||
\(375\) | −3.25202 | −0.167933 | ||||||||
\(376\) | −9.02859 | −0.465614 | ||||||||
\(377\) | −15.4545 | −0.795945 | ||||||||
\(378\) | 13.7383 | 0.706621 | ||||||||
\(379\) | −10.2928 | −0.528707 | −0.264354 | − | 0.964426i | \(-0.585159\pi\) | ||||
−0.264354 | + | 0.964426i | \(0.585159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.65620 | 0.494702 | ||||||||
\(382\) | −10.0767 | −0.515567 | ||||||||
\(383\) | −32.0284 | −1.63658 | −0.818288 | − | 0.574808i | \(-0.805077\pi\) | ||||
−0.818288 | + | 0.574808i | \(0.805077\pi\) | |||||||
\(384\) | −42.3811 | −2.16275 | ||||||||
\(385\) | 0.181627 | 0.00925659 | ||||||||
\(386\) | 3.65106 | 0.185834 | ||||||||
\(387\) | 12.4168 | 0.631183 | ||||||||
\(388\) | 5.85962 | 0.297477 | ||||||||
\(389\) | −30.6083 | −1.55190 | −0.775950 | − | 0.630794i | \(-0.782729\pi\) | ||||
−0.775950 | + | 0.630794i | \(0.782729\pi\) | |||||||
\(390\) | −26.3986 | −1.33674 | ||||||||
\(391\) | −5.86191 | −0.296449 | ||||||||
\(392\) | −13.1452 | −0.663934 | ||||||||
\(393\) | −25.9999 | −1.31152 | ||||||||
\(394\) | −27.8916 | −1.40516 | ||||||||
\(395\) | −1.40438 | −0.0706620 | ||||||||
\(396\) | 2.09390 | 0.105222 | ||||||||
\(397\) | 10.6204 | 0.533025 | 0.266512 | − | 0.963831i | \(-0.414129\pi\) | ||||
0.266512 | + | 0.963831i | \(0.414129\pi\) | |||||||
\(398\) | −23.5371 | −1.17981 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.97262 | −0.248631 | ||||||||
\(401\) | 15.2347 | 0.760782 | 0.380391 | − | 0.924826i | \(-0.375789\pi\) | ||||
0.380391 | + | 0.924826i | \(0.375789\pi\) | |||||||
\(402\) | −42.5523 | −2.12232 | ||||||||
\(403\) | −29.0316 | −1.44617 | ||||||||
\(404\) | −6.01429 | −0.299222 | ||||||||
\(405\) | −25.6632 | −1.27521 | ||||||||
\(406\) | 2.95935 | 0.146870 | ||||||||
\(407\) | 2.20998 | 0.109545 | ||||||||
\(408\) | 33.6968 | 1.66824 | ||||||||
\(409\) | 11.6641 | 0.576753 | 0.288377 | − | 0.957517i | \(-0.406884\pi\) | ||||
0.288377 | + | 0.957517i | \(0.406884\pi\) | |||||||
\(410\) | 13.3197 | 0.657813 | ||||||||
\(411\) | 2.99437 | 0.147702 | ||||||||
\(412\) | −5.90448 | −0.290893 | ||||||||
\(413\) | −3.73103 | −0.183592 | ||||||||
\(414\) | 14.1580 | 0.695830 | ||||||||
\(415\) | 0.854878 | 0.0419643 | ||||||||
\(416\) | −21.4442 | −1.05139 | ||||||||
\(417\) | −0.325377 | −0.0159338 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.7028 | 0.864840 | 0.432420 | − | 0.901672i | \(-0.357660\pi\) | ||||
0.432420 | + | 0.901672i | \(0.357660\pi\) | |||||||
\(420\) | 1.48828 | 0.0726208 | ||||||||
\(421\) | −20.6023 | −1.00410 | −0.502048 | − | 0.864840i | \(-0.667420\pi\) | ||||
−0.502048 | + | 0.864840i | \(0.667420\pi\) | |||||||
\(422\) | −30.4417 | −1.48188 | ||||||||
\(423\) | −34.8576 | −1.69484 | ||||||||
\(424\) | −13.1981 | −0.640955 | ||||||||
\(425\) | 5.28074 | 0.256154 | ||||||||
\(426\) | −5.95063 | −0.288309 | ||||||||
\(427\) | −0.372711 | −0.0180368 | ||||||||
\(428\) | 5.42535 | 0.262244 | ||||||||
\(429\) | −5.19317 | −0.250729 | ||||||||
\(430\) | 2.75952 | 0.133076 | ||||||||
\(431\) | −8.33155 | −0.401317 | −0.200658 | − | 0.979661i | \(-0.564308\pi\) | ||||
−0.200658 | + | 0.979661i | \(0.564308\pi\) | |||||||
\(432\) | −73.9926 | −3.55997 | ||||||||
\(433\) | −28.1941 | −1.35492 | −0.677460 | − | 0.735559i | \(-0.736919\pi\) | ||||
−0.677460 | + | 0.735559i | \(0.736919\pi\) | |||||||
\(434\) | 5.55921 | 0.266851 | ||||||||
\(435\) | −10.4237 | −0.499776 | ||||||||
\(436\) | 14.7384 | 0.705843 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −76.3848 | −3.64981 | ||||||||
\(439\) | −30.3824 | −1.45007 | −0.725037 | − | 0.688710i | \(-0.758177\pi\) | ||||
−0.725037 | + | 0.688710i | \(0.758177\pi\) | |||||||
\(440\) | −0.649880 | −0.0309818 | ||||||||
\(441\) | −50.7511 | −2.41672 | ||||||||
\(442\) | 42.8669 | 2.03897 | ||||||||
\(443\) | 24.5208 | 1.16502 | 0.582508 | − | 0.812825i | \(-0.302071\pi\) | ||||
0.582508 | + | 0.812825i | \(0.302071\pi\) | |||||||
\(444\) | 18.1089 | 0.859411 | ||||||||
\(445\) | 14.5520 | 0.689833 | ||||||||
\(446\) | 44.2226 | 2.09400 | ||||||||
\(447\) | −56.2518 | −2.66062 | ||||||||
\(448\) | −1.34755 | −0.0636657 | ||||||||
\(449\) | −24.6889 | −1.16514 | −0.582570 | − | 0.812781i | \(-0.697953\pi\) | ||||
−0.582570 | + | 0.812781i | \(0.697953\pi\) | |||||||
\(450\) | −12.7544 | −0.601247 | ||||||||
\(451\) | 2.62027 | 0.123384 | ||||||||
\(452\) | 4.05990 | 0.190962 | ||||||||
\(453\) | 62.4968 | 2.93635 | ||||||||
\(454\) | 11.7415 | 0.551056 | ||||||||
\(455\) | −2.64409 | −0.123957 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.16480 | 0.335155 | 0.167578 | − | 0.985859i | \(-0.446406\pi\) | ||||
0.167578 | + | 0.985859i | \(0.446406\pi\) | |||||||
\(458\) | −4.41929 | −0.206500 | ||||||||
\(459\) | 78.5774 | 3.66768 | ||||||||
\(460\) | 0.926377 | 0.0431926 | ||||||||
\(461\) | 21.7204 | 1.01162 | 0.505811 | − | 0.862645i | \(-0.331193\pi\) | ||||
0.505811 | + | 0.862645i | \(0.331193\pi\) | |||||||
\(462\) | 0.994432 | 0.0462652 | ||||||||
\(463\) | −31.9283 | −1.48384 | −0.741918 | − | 0.670491i | \(-0.766084\pi\) | ||||
−0.741918 | + | 0.670491i | \(0.766084\pi\) | |||||||
\(464\) | −15.9387 | −0.739935 | ||||||||
\(465\) | −19.5811 | −0.908051 | ||||||||
\(466\) | 44.8826 | 2.07915 | ||||||||
\(467\) | −19.5382 | −0.904121 | −0.452061 | − | 0.891987i | \(-0.649311\pi\) | ||||
−0.452061 | + | 0.891987i | \(0.649311\pi\) | |||||||
\(468\) | −30.4824 | −1.40905 | ||||||||
\(469\) | −4.26205 | −0.196803 | ||||||||
\(470\) | −7.74677 | −0.357332 | ||||||||
\(471\) | −21.4069 | −0.986379 | ||||||||
\(472\) | 13.3500 | 0.614482 | ||||||||
\(473\) | 0.542857 | 0.0249606 | ||||||||
\(474\) | −7.68914 | −0.353174 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.41673 | −0.110770 | ||||||||
\(477\) | −50.9551 | −2.33308 | ||||||||
\(478\) | −22.0677 | −1.00935 | ||||||||
\(479\) | −12.2388 | −0.559203 | −0.279601 | − | 0.960116i | \(-0.590202\pi\) | ||||
−0.279601 | + | 0.960116i | \(0.590202\pi\) | |||||||
\(480\) | −14.4636 | −0.660168 | ||||||||
\(481\) | −32.1723 | −1.46693 | ||||||||
\(482\) | −25.5267 | −1.16271 | ||||||||
\(483\) | 1.97964 | 0.0900766 | ||||||||
\(484\) | −9.08833 | −0.413106 | ||||||||
\(485\) | −7.02143 | −0.318827 | ||||||||
\(486\) | −65.3527 | −2.96446 | ||||||||
\(487\) | 14.1017 | 0.639010 | 0.319505 | − | 0.947585i | \(-0.396483\pi\) | ||||
0.319505 | + | 0.947585i | \(0.396483\pi\) | |||||||
\(488\) | 1.33360 | 0.0603691 | ||||||||
\(489\) | −47.4559 | −2.14603 | ||||||||
\(490\) | −11.2789 | −0.509531 | ||||||||
\(491\) | −19.8867 | −0.897474 | −0.448737 | − | 0.893664i | \(-0.648126\pi\) | ||||
−0.448737 | + | 0.893664i | \(0.648126\pi\) | |||||||
\(492\) | 21.4709 | 0.967983 | ||||||||
\(493\) | 16.9263 | 0.762322 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.50906 | −0.112774 | ||||||||
\(496\) | −29.9412 | −1.34440 | ||||||||
\(497\) | −0.596016 | −0.0267350 | ||||||||
\(498\) | 4.68056 | 0.209741 | ||||||||
\(499\) | −7.43742 | −0.332945 | −0.166472 | − | 0.986046i | \(-0.553238\pi\) | ||||
−0.166472 | + | 0.986046i | \(0.553238\pi\) | |||||||
\(500\) | −0.834534 | −0.0373215 | ||||||||
\(501\) | −11.4134 | −0.509913 | ||||||||
\(502\) | −31.9992 | −1.42820 | ||||||||
\(503\) | −13.5121 | −0.602475 | −0.301237 | − | 0.953549i | \(-0.597400\pi\) | ||||
−0.301237 | + | 0.953549i | \(0.597400\pi\) | |||||||
\(504\) | −8.15169 | −0.363105 | ||||||||
\(505\) | 7.20677 | 0.320697 | ||||||||
\(506\) | 0.618981 | 0.0275171 | ||||||||
\(507\) | 33.3246 | 1.48000 | ||||||||
\(508\) | 2.47798 | 0.109942 | ||||||||
\(509\) | 35.1737 | 1.55905 | 0.779523 | − | 0.626373i | \(-0.215461\pi\) | ||||
0.779523 | + | 0.626373i | \(0.215461\pi\) | |||||||
\(510\) | 28.9127 | 1.28028 | ||||||||
\(511\) | −7.65071 | −0.338448 | ||||||||
\(512\) | −2.60163 | −0.114977 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 36.7670 | 1.62172 | ||||||||
\(515\) | 7.07518 | 0.311770 | ||||||||
\(516\) | 4.44826 | 0.195824 | ||||||||
\(517\) | −1.52396 | −0.0670235 | ||||||||
\(518\) | 6.16063 | 0.270682 | ||||||||
\(519\) | −8.13963 | −0.357290 | ||||||||
\(520\) | 9.46079 | 0.414883 | ||||||||
\(521\) | 5.85595 | 0.256554 | 0.128277 | − | 0.991738i | \(-0.459055\pi\) | ||||
0.128277 | + | 0.991738i | \(0.459055\pi\) | |||||||
\(522\) | −40.8815 | −1.78933 | ||||||||
\(523\) | −11.5494 | −0.505021 | −0.252511 | − | 0.967594i | \(-0.581256\pi\) | ||||
−0.252511 | + | 0.967594i | \(0.581256\pi\) | |||||||
\(524\) | −6.67210 | −0.291472 | ||||||||
\(525\) | −1.78337 | −0.0778327 | ||||||||
\(526\) | 33.0344 | 1.44037 | ||||||||
\(527\) | 31.7964 | 1.38507 | ||||||||
\(528\) | −5.35588 | −0.233085 | ||||||||
\(529\) | −21.7678 | −0.946425 | ||||||||
\(530\) | −11.3243 | −0.491895 | ||||||||
\(531\) | 51.5416 | 2.23672 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −38.1452 | −1.65225 | ||||||||
\(534\) | 79.6742 | 3.44784 | ||||||||
\(535\) | −6.50106 | −0.281065 | ||||||||
\(536\) | 15.2500 | 0.658700 | ||||||||
\(537\) | 16.3270 | 0.704562 | ||||||||
\(538\) | −2.84754 | −0.122766 | ||||||||
\(539\) | −2.21881 | −0.0955709 | ||||||||
\(540\) | −12.4179 | −0.534380 | ||||||||
\(541\) | 11.7510 | 0.505216 | 0.252608 | − | 0.967569i | \(-0.418712\pi\) | ||||
0.252608 | + | 0.967569i | \(0.418712\pi\) | |||||||
\(542\) | 13.3673 | 0.574176 | ||||||||
\(543\) | 17.6299 | 0.756574 | ||||||||
\(544\) | 23.4864 | 1.00697 | ||||||||
\(545\) | −17.6607 | −0.756500 | ||||||||
\(546\) | −14.4767 | −0.619545 | ||||||||
\(547\) | 28.9598 | 1.23823 | 0.619116 | − | 0.785300i | \(-0.287491\pi\) | ||||
0.619116 | + | 0.785300i | \(0.287491\pi\) | |||||||
\(548\) | 0.768417 | 0.0328252 | ||||||||
\(549\) | 5.14875 | 0.219743 | ||||||||
\(550\) | −0.557614 | −0.0237767 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −7.08333 | −0.301486 | ||||||||
\(553\) | −0.770146 | −0.0327499 | ||||||||
\(554\) | 15.9504 | 0.677668 | ||||||||
\(555\) | −21.6994 | −0.921090 | ||||||||
\(556\) | −0.0834984 | −0.00354112 | ||||||||
\(557\) | −24.2154 | −1.02604 | −0.513021 | − | 0.858376i | \(-0.671474\pi\) | ||||
−0.513021 | + | 0.858376i | \(0.671474\pi\) | |||||||
\(558\) | −76.7967 | −3.25106 | ||||||||
\(559\) | −7.90277 | −0.334252 | ||||||||
\(560\) | −2.72693 | −0.115234 | ||||||||
\(561\) | 5.68775 | 0.240137 | ||||||||
\(562\) | −21.1630 | −0.892709 | ||||||||
\(563\) | −45.4464 | −1.91534 | −0.957669 | − | 0.287871i | \(-0.907053\pi\) | ||||
−0.957669 | + | 0.287871i | \(0.907053\pi\) | |||||||
\(564\) | −12.4875 | −0.525820 | ||||||||
\(565\) | −4.86487 | −0.204667 | ||||||||
\(566\) | 31.2881 | 1.31514 | ||||||||
\(567\) | −14.0734 | −0.591027 | ||||||||
\(568\) | 2.13260 | 0.0894819 | ||||||||
\(569\) | −28.1695 | −1.18093 | −0.590463 | − | 0.807065i | \(-0.701055\pi\) | ||||
−0.590463 | + | 0.807065i | \(0.701055\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.2742 | 0.764752 | 0.382376 | − | 0.924007i | \(-0.375106\pi\) | ||||
0.382376 | + | 0.924007i | \(0.375106\pi\) | |||||||
\(572\) | −1.33267 | −0.0557218 | ||||||||
\(573\) | 19.4639 | 0.813115 | ||||||||
\(574\) | 7.30437 | 0.304879 | ||||||||
\(575\) | −1.11005 | −0.0462924 | ||||||||
\(576\) | 18.6155 | 0.775644 | ||||||||
\(577\) | −20.1838 | −0.840263 | −0.420132 | − | 0.907463i | \(-0.638016\pi\) | ||||
−0.420132 | + | 0.907463i | \(0.638016\pi\) | |||||||
\(578\) | −18.3281 | −0.762350 | ||||||||
\(579\) | −7.05231 | −0.293084 | ||||||||
\(580\) | −2.67492 | −0.111070 | ||||||||
\(581\) | 0.468806 | 0.0194493 | ||||||||
\(582\) | −38.4432 | −1.59352 | ||||||||
\(583\) | −2.22773 | −0.0922631 | ||||||||
\(584\) | 27.3750 | 1.13278 | ||||||||
\(585\) | 36.5262 | 1.51017 | ||||||||
\(586\) | −29.2359 | −1.20773 | ||||||||
\(587\) | −18.4923 | −0.763260 | −0.381630 | − | 0.924315i | \(-0.624637\pi\) | ||||
−0.381630 | + | 0.924315i | \(0.624637\pi\) | |||||||
\(588\) | −18.1813 | −0.749783 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 11.4546 | 0.471579 | ||||||||
\(591\) | 53.8747 | 2.21611 | ||||||||
\(592\) | −33.1803 | −1.36370 | ||||||||
\(593\) | −5.10430 | −0.209608 | −0.104804 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104804 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(594\) | −8.29730 | −0.340442 | ||||||||
\(595\) | 2.89590 | 0.118720 | ||||||||
\(596\) | −14.4353 | −0.591295 | ||||||||
\(597\) | 45.4636 | 1.86070 | ||||||||
\(598\) | −9.01097 | −0.368486 | ||||||||
\(599\) | −35.7699 | −1.46152 | −0.730760 | − | 0.682635i | \(-0.760834\pi\) | ||||
−0.730760 | + | 0.682635i | \(0.760834\pi\) | |||||||
\(600\) | 6.38107 | 0.260506 | ||||||||
\(601\) | −34.3352 | −1.40056 | −0.700281 | − | 0.713867i | \(-0.746942\pi\) | ||||
−0.700281 | + | 0.713867i | \(0.746942\pi\) | |||||||
\(602\) | 1.51329 | 0.0616771 | ||||||||
\(603\) | 58.8773 | 2.39767 | ||||||||
\(604\) | 16.0379 | 0.652575 | ||||||||
\(605\) | 10.8903 | 0.442754 | ||||||||
\(606\) | 39.4579 | 1.60287 | ||||||||
\(607\) | 3.43239 | 0.139316 | 0.0696582 | − | 0.997571i | \(-0.477809\pi\) | ||||
0.0696582 | + | 0.997571i | \(0.477809\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.71622 | −0.231633 | ||||||||
\(610\) | 1.14426 | 0.0463297 | ||||||||
\(611\) | 22.1854 | 0.897523 | ||||||||
\(612\) | 33.3854 | 1.34953 | ||||||||
\(613\) | 28.1010 | 1.13499 | 0.567494 | − | 0.823378i | \(-0.307913\pi\) | ||||
0.567494 | + | 0.823378i | \(0.307913\pi\) | |||||||
\(614\) | −42.1750 | −1.70205 | ||||||||
\(615\) | −25.7280 | −1.03745 | ||||||||
\(616\) | −0.356387 | −0.0143592 | ||||||||
\(617\) | −11.9234 | −0.480019 | −0.240009 | − | 0.970771i | \(-0.577151\pi\) | ||||
−0.240009 | + | 0.970771i | \(0.577151\pi\) | |||||||
\(618\) | 38.7375 | 1.55825 | ||||||||
\(619\) | −27.8914 | −1.12105 | −0.560525 | − | 0.828137i | \(-0.689401\pi\) | ||||
−0.560525 | + | 0.828137i | \(0.689401\pi\) | |||||||
\(620\) | −5.02490 | −0.201805 | ||||||||
\(621\) | −16.5176 | −0.662828 | ||||||||
\(622\) | 9.40145 | 0.376964 | ||||||||
\(623\) | 7.98018 | 0.319719 | ||||||||
\(624\) | 77.9696 | 3.12128 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.38242 | 0.0552527 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.49345 | −0.219212 | ||||||||
\(629\) | 35.2363 | 1.40496 | ||||||||
\(630\) | −6.99436 | −0.278662 | ||||||||
\(631\) | 18.7543 | 0.746598 | 0.373299 | − | 0.927711i | \(-0.378227\pi\) | ||||
0.373299 | + | 0.927711i | \(0.378227\pi\) | |||||||
\(632\) | 2.75565 | 0.109614 | ||||||||
\(633\) | 58.8006 | 2.33711 | ||||||||
\(634\) | 56.4555 | 2.24213 | ||||||||
\(635\) | −2.96929 | −0.117833 | ||||||||
\(636\) | −18.2544 | −0.723832 | ||||||||
\(637\) | 32.3009 | 1.27981 | ||||||||
\(638\) | −1.78731 | −0.0707604 | ||||||||
\(639\) | 8.23355 | 0.325714 | ||||||||
\(640\) | 13.0322 | 0.515144 | ||||||||
\(641\) | 21.8102 | 0.861450 | 0.430725 | − | 0.902483i | \(-0.358258\pi\) | ||||
0.430725 | + | 0.902483i | \(0.358258\pi\) | |||||||
\(642\) | −35.5941 | −1.40479 | ||||||||
\(643\) | −47.4901 | −1.87283 | −0.936413 | − | 0.350901i | \(-0.885875\pi\) | ||||
−0.936413 | + | 0.350901i | \(0.885875\pi\) | |||||||
\(644\) | 0.508015 | 0.0200186 | ||||||||
\(645\) | −5.33023 | −0.209877 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.0985 | 1.37986 | 0.689932 | − | 0.723874i | \(-0.257640\pi\) | ||||
0.689932 | + | 0.723874i | \(0.257640\pi\) | |||||||
\(648\) | 50.3560 | 1.97817 | ||||||||
\(649\) | 2.25337 | 0.0884525 | ||||||||
\(650\) | 8.11760 | 0.318398 | ||||||||
\(651\) | −10.7380 | −0.420857 | ||||||||
\(652\) | −12.1781 | −0.476933 | ||||||||
\(653\) | 46.5164 | 1.82033 | 0.910163 | − | 0.414250i | \(-0.135956\pi\) | ||||
0.910163 | + | 0.414250i | \(0.135956\pi\) | |||||||
\(654\) | −96.6943 | −3.78105 | ||||||||
\(655\) | 7.99500 | 0.312391 | ||||||||
\(656\) | −39.3404 | −1.53598 | ||||||||
\(657\) | 105.689 | 4.12333 | ||||||||
\(658\) | −4.24824 | −0.165614 | ||||||||
\(659\) | 43.2332 | 1.68413 | 0.842063 | − | 0.539379i | \(-0.181341\pi\) | ||||
0.842063 | + | 0.539379i | \(0.181341\pi\) | |||||||
\(660\) | −0.898855 | −0.0349879 | ||||||||
\(661\) | 46.9045 | 1.82437 | 0.912186 | − | 0.409776i | \(-0.134393\pi\) | ||||
0.912186 | + | 0.409776i | \(0.134393\pi\) | |||||||
\(662\) | 18.9697 | 0.737277 | ||||||||
\(663\) | −82.8008 | −3.21572 | ||||||||
\(664\) | −1.67743 | −0.0650970 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −85.1049 | −3.29775 | ||||||||
\(667\) | −3.55804 | −0.137768 | ||||||||
\(668\) | −2.92891 | −0.113323 | ||||||||
\(669\) | −85.4194 | −3.30250 | ||||||||
\(670\) | 13.0849 | 0.505514 | ||||||||
\(671\) | 0.225101 | 0.00868991 | ||||||||
\(672\) | −7.93166 | −0.305970 | ||||||||
\(673\) | −14.3118 | −0.551679 | −0.275839 | − | 0.961204i | \(-0.588956\pi\) | ||||
−0.275839 | + | 0.961204i | \(0.588956\pi\) | |||||||
\(674\) | 10.5996 | 0.408281 | ||||||||
\(675\) | 14.8800 | 0.572732 | ||||||||
\(676\) | 8.55176 | 0.328914 | ||||||||
\(677\) | 27.6860 | 1.06406 | 0.532029 | − | 0.846726i | \(-0.321430\pi\) | ||||
0.532029 | + | 0.846726i | \(0.321430\pi\) | |||||||
\(678\) | −26.6358 | −1.02294 | ||||||||
\(679\) | −3.85048 | −0.147768 | ||||||||
\(680\) | −10.3618 | −0.397357 | ||||||||
\(681\) | −22.6796 | −0.869084 | ||||||||
\(682\) | −3.35751 | −0.128566 | ||||||||
\(683\) | −20.0771 | −0.768228 | −0.384114 | − | 0.923286i | \(-0.625493\pi\) | ||||
−0.384114 | + | 0.923286i | \(0.625493\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.920774 | −0.0351810 | ||||||||
\(686\) | −12.6481 | −0.482909 | ||||||||
\(687\) | 8.53619 | 0.325676 | ||||||||
\(688\) | −8.15039 | −0.310731 | ||||||||
\(689\) | 32.4307 | 1.23551 | ||||||||
\(690\) | −6.07768 | −0.231373 | ||||||||
\(691\) | −28.7356 | −1.09315 | −0.546577 | − | 0.837409i | \(-0.684069\pi\) | ||||
−0.546577 | + | 0.837409i | \(0.684069\pi\) | |||||||
\(692\) | −2.08880 | −0.0794041 | ||||||||
\(693\) | −1.37594 | −0.0522677 | ||||||||
\(694\) | 29.5581 | 1.12201 | ||||||||
\(695\) | 0.100054 | 0.00379526 | ||||||||
\(696\) | 20.4532 | 0.775275 | ||||||||
\(697\) | 41.7781 | 1.58246 | ||||||||
\(698\) | −21.0735 | −0.797644 | ||||||||
\(699\) | −86.6942 | −3.27908 | ||||||||
\(700\) | −0.457649 | −0.0172975 | ||||||||
\(701\) | −26.9089 | −1.01633 | −0.508167 | − | 0.861259i | \(-0.669677\pi\) | ||||
−0.508167 | + | 0.861259i | \(0.669677\pi\) | |||||||
\(702\) | 120.790 | 4.55892 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.813858 | 0.0306734 | ||||||||
\(705\) | 14.9635 | 0.563557 | ||||||||
\(706\) | −9.81237 | −0.369293 | ||||||||
\(707\) | 3.95211 | 0.148634 | ||||||||
\(708\) | 18.4645 | 0.693937 | ||||||||
\(709\) | −10.0327 | −0.376786 | −0.188393 | − | 0.982094i | \(-0.560328\pi\) | ||||
−0.188393 | + | 0.982094i | \(0.560328\pi\) | |||||||
\(710\) | 1.82983 | 0.0686721 | ||||||||
\(711\) | 10.6390 | 0.398995 | ||||||||
\(712\) | −28.5538 | −1.07010 | ||||||||
\(713\) | −6.68386 | −0.250313 | ||||||||
\(714\) | 15.8554 | 0.593374 | ||||||||
\(715\) | 1.59691 | 0.0597209 | ||||||||
\(716\) | 4.18984 | 0.156582 | ||||||||
\(717\) | 42.6254 | 1.59188 | ||||||||
\(718\) | −0.975715 | −0.0364134 | ||||||||
\(719\) | 26.3737 | 0.983572 | 0.491786 | − | 0.870716i | \(-0.336344\pi\) | ||||
0.491786 | + | 0.870716i | \(0.336344\pi\) | |||||||
\(720\) | 37.6707 | 1.40390 | ||||||||
\(721\) | 3.87995 | 0.144497 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 49.3069 | 1.83374 | ||||||||
\(724\) | 4.52420 | 0.168141 | ||||||||
\(725\) | 3.20529 | 0.119041 | ||||||||
\(726\) | 59.6257 | 2.21292 | ||||||||
\(727\) | −48.4127 | −1.79553 | −0.897765 | − | 0.440476i | \(-0.854810\pi\) | ||||
−0.897765 | + | 0.440476i | \(0.854810\pi\) | |||||||
\(728\) | 5.18819 | 0.192287 | ||||||||
\(729\) | 49.2444 | 1.82386 | ||||||||
\(730\) | 23.4884 | 0.869346 | ||||||||
\(731\) | 8.65541 | 0.320132 | ||||||||
\(732\) | 1.84451 | 0.0681750 | ||||||||
\(733\) | −35.3375 | −1.30522 | −0.652610 | − | 0.757694i | \(-0.726326\pi\) | ||||
−0.652610 | + | 0.757694i | \(0.726326\pi\) | |||||||
\(734\) | 13.3110 | 0.491319 | ||||||||
\(735\) | 21.7861 | 0.803594 | ||||||||
\(736\) | −4.93704 | −0.181982 | ||||||||
\(737\) | 2.57408 | 0.0948175 | ||||||||
\(738\) | −100.905 | −3.71436 | ||||||||
\(739\) | 19.4663 | 0.716080 | 0.358040 | − | 0.933706i | \(-0.383445\pi\) | ||||
0.358040 | + | 0.933706i | \(0.383445\pi\) | |||||||
\(740\) | −5.56851 | −0.204703 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.21011 | −0.227980 | ||||||||
\(743\) | −28.6013 | −1.04928 | −0.524640 | − | 0.851324i | \(-0.675800\pi\) | ||||
−0.524640 | + | 0.851324i | \(0.675800\pi\) | |||||||
\(744\) | 38.4217 | 1.40861 | ||||||||
\(745\) | 17.2975 | 0.633731 | ||||||||
\(746\) | −13.9844 | −0.512005 | ||||||||
\(747\) | −6.47624 | −0.236953 | ||||||||
\(748\) | 1.45959 | 0.0533680 | ||||||||
\(749\) | −3.56511 | −0.130266 | ||||||||
\(750\) | 5.47512 | 0.199923 | ||||||||
\(751\) | −47.5763 | −1.73608 | −0.868042 | − | 0.496490i | \(-0.834622\pi\) | ||||
−0.868042 | + | 0.496490i | \(0.834622\pi\) | |||||||
\(752\) | 22.8805 | 0.834365 | ||||||||
\(753\) | 61.8090 | 2.25245 | ||||||||
\(754\) | 26.0193 | 0.947565 | ||||||||
\(755\) | −19.2178 | −0.699409 | ||||||||
\(756\) | −6.80982 | −0.247671 | ||||||||
\(757\) | 11.8767 | 0.431665 | 0.215832 | − | 0.976430i | \(-0.430754\pi\) | ||||
0.215832 | + | 0.976430i | \(0.430754\pi\) | |||||||
\(758\) | 17.3291 | 0.629421 | ||||||||
\(759\) | −1.19561 | −0.0433979 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.1049 | 1.01880 | 0.509401 | − | 0.860530i | \(-0.329867\pi\) | ||||
0.509401 | + | 0.860530i | \(0.329867\pi\) | |||||||
\(762\) | −16.2572 | −0.588938 | ||||||||
\(763\) | −9.68492 | −0.350618 | ||||||||
\(764\) | 4.99482 | 0.180706 | ||||||||
\(765\) | −40.0049 | −1.44638 | ||||||||
\(766\) | 53.9233 | 1.94833 | ||||||||
\(767\) | −32.8040 | −1.18448 | ||||||||
\(768\) | 55.3708 | 1.99802 | ||||||||
\(769\) | 55.3734 | 1.99682 | 0.998408 | − | 0.0563960i | \(-0.0179609\pi\) | ||||
0.998408 | + | 0.0563960i | \(0.0179609\pi\) | |||||||
\(770\) | −0.305789 | −0.0110199 | ||||||||
\(771\) | −71.0183 | −2.55766 | ||||||||
\(772\) | −1.80977 | −0.0651349 | ||||||||
\(773\) | −17.8883 | −0.643396 | −0.321698 | − | 0.946842i | \(-0.604254\pi\) | ||||
−0.321698 | + | 0.946842i | \(0.604254\pi\) | |||||||
\(774\) | −20.9051 | −0.751418 | ||||||||
\(775\) | 6.02121 | 0.216288 | ||||||||
\(776\) | 13.7774 | 0.494578 | ||||||||
\(777\) | −11.8997 | −0.426900 | ||||||||
\(778\) | 51.5323 | 1.84752 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 13.0853 | 0.468529 | ||||||||
\(781\) | 0.359966 | 0.0128806 | ||||||||
\(782\) | 9.86915 | 0.352920 | ||||||||
\(783\) | 47.6947 | 1.70447 | ||||||||
\(784\) | 33.3129 | 1.18975 | ||||||||
\(785\) | 6.58266 | 0.234945 | ||||||||
\(786\) | 43.7736 | 1.56135 | ||||||||
\(787\) | −7.40295 | −0.263887 | −0.131943 | − | 0.991257i | \(-0.542122\pi\) | ||||
−0.131943 | + | 0.991257i | \(0.542122\pi\) | |||||||
\(788\) | 13.8253 | 0.492508 | ||||||||
\(789\) | −63.8086 | −2.27165 | ||||||||
\(790\) | 2.36442 | 0.0841224 | ||||||||
\(791\) | −2.66784 | −0.0948576 | ||||||||
\(792\) | 4.92325 | 0.174940 | ||||||||
\(793\) | −3.27696 | −0.116368 | ||||||||
\(794\) | −17.8807 | −0.634561 | ||||||||
\(795\) | 21.8737 | 0.775781 | ||||||||
\(796\) | 11.6669 | 0.413522 | ||||||||
\(797\) | −45.6568 | −1.61725 | −0.808624 | − | 0.588326i | \(-0.799787\pi\) | ||||
−0.808624 | + | 0.588326i | \(0.799787\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.2982 | −0.859609 | ||||||||
\(800\) | 4.44757 | 0.157245 | ||||||||
\(801\) | −110.241 | −3.89517 | ||||||||
\(802\) | −25.6492 | −0.905704 | ||||||||
\(803\) | 4.62068 | 0.163060 | ||||||||
\(804\) | 21.0924 | 0.743872 | ||||||||
\(805\) | −0.608741 | −0.0214553 | ||||||||
\(806\) | 48.8778 | 1.72165 | ||||||||
\(807\) | 5.50024 | 0.193618 | ||||||||
\(808\) | −14.1410 | −0.497480 | ||||||||
\(809\) | −19.3525 | −0.680398 | −0.340199 | − | 0.940353i | \(-0.610494\pi\) | ||||
−0.340199 | + | 0.940353i | \(0.610494\pi\) | |||||||
\(810\) | 43.2067 | 1.51813 | ||||||||
\(811\) | −20.8363 | −0.731661 | −0.365831 | − | 0.930681i | \(-0.619215\pi\) | ||||
−0.365831 | + | 0.930681i | \(0.619215\pi\) | |||||||
\(812\) | −1.46690 | −0.0514780 | ||||||||
\(813\) | −25.8200 | −0.905547 | ||||||||
\(814\) | −3.72074 | −0.130412 | ||||||||
\(815\) | 14.5927 | 0.511161 | ||||||||
\(816\) | −85.3951 | −2.98943 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −19.6378 | −0.686619 | ||||||||
\(819\) | 20.0306 | 0.699925 | ||||||||
\(820\) | −6.60233 | −0.230563 | ||||||||
\(821\) | −30.6430 | −1.06945 | −0.534723 | − | 0.845027i | \(-0.679584\pi\) | ||||
−0.534723 | + | 0.845027i | \(0.679584\pi\) | |||||||
\(822\) | −5.04135 | −0.175837 | ||||||||
\(823\) | 8.07545 | 0.281493 | 0.140746 | − | 0.990046i | \(-0.455050\pi\) | ||||
0.140746 | + | 0.990046i | \(0.455050\pi\) | |||||||
\(824\) | −13.8828 | −0.483631 | ||||||||
\(825\) | 1.07707 | 0.0374989 | ||||||||
\(826\) | 6.28159 | 0.218564 | ||||||||
\(827\) | 36.5412 | 1.27066 | 0.635332 | − | 0.772239i | \(-0.280863\pi\) | ||||
0.635332 | + | 0.772239i | \(0.280863\pi\) | |||||||
\(828\) | −7.01788 | −0.243888 | ||||||||
\(829\) | 42.7028 | 1.48313 | 0.741564 | − | 0.670882i | \(-0.234084\pi\) | ||||
0.741564 | + | 0.670882i | \(0.234084\pi\) | |||||||
\(830\) | −1.43928 | −0.0499581 | ||||||||
\(831\) | −30.8095 | −1.06877 | ||||||||
\(832\) | −11.8479 | −0.410753 | ||||||||
\(833\) | −35.3771 | −1.22574 | ||||||||
\(834\) | 0.547808 | 0.0189690 | ||||||||
\(835\) | 3.50963 | 0.121456 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 89.5956 | 3.09688 | ||||||||
\(838\) | −29.8046 | −1.02958 | ||||||||
\(839\) | −48.1211 | −1.66132 | −0.830662 | − | 0.556776i | \(-0.812038\pi\) | ||||
−0.830662 | + | 0.556776i | \(0.812038\pi\) | |||||||
\(840\) | 3.49931 | 0.120738 | ||||||||
\(841\) | −18.7261 | −0.645728 | ||||||||
\(842\) | 34.6862 | 1.19537 | ||||||||
\(843\) | 40.8781 | 1.40792 | ||||||||
\(844\) | 15.0894 | 0.519399 | ||||||||
\(845\) | −10.2474 | −0.352520 | ||||||||
\(846\) | 58.6866 | 2.01769 | ||||||||
\(847\) | 5.97212 | 0.205205 | ||||||||
\(848\) | 33.4468 | 1.14857 | ||||||||
\(849\) | −60.4354 | −2.07414 | ||||||||
\(850\) | −8.89069 | −0.304948 | ||||||||
\(851\) | −7.40695 | −0.253907 | ||||||||
\(852\) | 2.94962 | 0.101052 | ||||||||
\(853\) | 32.4486 | 1.11102 | 0.555510 | − | 0.831510i | \(-0.312523\pi\) | ||||
0.555510 | + | 0.831510i | \(0.312523\pi\) | |||||||
\(854\) | 0.627500 | 0.0214726 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.7563 | 0.436001 | ||||||||
\(857\) | −30.1775 | −1.03084 | −0.515422 | − | 0.856936i | \(-0.672365\pi\) | ||||
−0.515422 | + | 0.856936i | \(0.672365\pi\) | |||||||
\(858\) | 8.74326 | 0.298490 | ||||||||
\(859\) | 26.5675 | 0.906470 | 0.453235 | − | 0.891391i | \(-0.350270\pi\) | ||||
0.453235 | + | 0.891391i | \(0.350270\pi\) | |||||||
\(860\) | −1.36784 | −0.0466431 | ||||||||
\(861\) | −14.1090 | −0.480832 | ||||||||
\(862\) | 14.0271 | 0.477764 | ||||||||
\(863\) | −11.5566 | −0.393391 | −0.196696 | − | 0.980465i | \(-0.563021\pi\) | ||||
−0.196696 | + | 0.980465i | \(0.563021\pi\) | |||||||
\(864\) | 66.1798 | 2.25148 | ||||||||
\(865\) | 2.50295 | 0.0851028 | ||||||||
\(866\) | 47.4677 | 1.61302 | ||||||||
\(867\) | 35.4022 | 1.20232 | ||||||||
\(868\) | −2.75560 | −0.0935312 | ||||||||
\(869\) | 0.465133 | 0.0157786 | ||||||||
\(870\) | 17.5493 | 0.594979 | ||||||||
\(871\) | −37.4728 | −1.26972 | ||||||||
\(872\) | 34.6535 | 1.17352 | ||||||||
\(873\) | 53.1917 | 1.80027 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.548389 | 0.0185389 | ||||||||
\(876\) | 37.8626 | 1.27926 | ||||||||
\(877\) | −18.1665 | −0.613438 | −0.306719 | − | 0.951800i | \(-0.599231\pi\) | ||||
−0.306719 | + | 0.951800i | \(0.599231\pi\) | |||||||
\(878\) | 51.1521 | 1.72630 | ||||||||
\(879\) | 56.4715 | 1.90474 | ||||||||
\(880\) | 1.64694 | 0.0555184 | ||||||||
\(881\) | −39.8613 | −1.34296 | −0.671480 | − | 0.741023i | \(-0.734341\pi\) | ||||
−0.671480 | + | 0.741023i | \(0.734341\pi\) | |||||||
\(882\) | 85.4450 | 2.87708 | ||||||||
\(883\) | −26.3518 | −0.886810 | −0.443405 | − | 0.896321i | \(-0.646230\pi\) | ||||
−0.443405 | + | 0.896321i | \(0.646230\pi\) | |||||||
\(884\) | −21.2484 | −0.714660 | ||||||||
\(885\) | −22.1255 | −0.743740 | ||||||||
\(886\) | −41.2833 | −1.38694 | ||||||||
\(887\) | −55.9581 | −1.87889 | −0.939445 | − | 0.342700i | \(-0.888659\pi\) | ||||
−0.939445 | + | 0.342700i | \(0.888659\pi\) | |||||||
\(888\) | 42.5784 | 1.42884 | ||||||||
\(889\) | −1.62833 | −0.0546124 | ||||||||
\(890\) | −24.4999 | −0.821240 | ||||||||
\(891\) | 8.49969 | 0.284750 | ||||||||
\(892\) | −21.9203 | −0.733947 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 94.7059 | 3.16744 | ||||||||
\(895\) | −5.02058 | −0.167819 | ||||||||
\(896\) | 7.14674 | 0.238756 | ||||||||
\(897\) | 17.4054 | 0.581149 | ||||||||
\(898\) | 41.5664 | 1.38709 | ||||||||
\(899\) | 19.2997 | 0.643681 | ||||||||
\(900\) | 6.32211 | 0.210737 | ||||||||
\(901\) | −35.5193 | −1.18332 | ||||||||
\(902\) | −4.41151 | −0.146887 | ||||||||
\(903\) | −2.92304 | −0.0972726 | ||||||||
\(904\) | 9.54580 | 0.317488 | ||||||||
\(905\) | −5.42123 | −0.180208 | ||||||||
\(906\) | −105.220 | −3.49570 | ||||||||
\(907\) | 46.1120 | 1.53113 | 0.765563 | − | 0.643361i | \(-0.222461\pi\) | ||||
0.765563 | + | 0.643361i | \(0.222461\pi\) | |||||||
\(908\) | −5.82005 | −0.193145 | ||||||||
\(909\) | −54.5957 | −1.81083 | ||||||||
\(910\) | 4.45160 | 0.147569 | ||||||||
\(911\) | −1.40625 | −0.0465912 | −0.0232956 | − | 0.999729i | \(-0.507416\pi\) | ||||
−0.0232956 | + | 0.999729i | \(0.507416\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.283137 | −0.00937048 | ||||||||
\(914\) | −12.0627 | −0.398999 | ||||||||
\(915\) | −2.21023 | −0.0730678 | ||||||||
\(916\) | 2.19056 | 0.0723781 | ||||||||
\(917\) | 4.38437 | 0.144785 | ||||||||
\(918\) | −132.294 | −4.36634 | ||||||||
\(919\) | 47.0354 | 1.55155 | 0.775777 | − | 0.631007i | \(-0.217358\pi\) | ||||
0.775777 | + | 0.631007i | \(0.217358\pi\) | |||||||
\(920\) | 2.17813 | 0.0718109 | ||||||||
\(921\) | 81.4644 | 2.68434 | ||||||||
\(922\) | −36.5687 | −1.20433 | ||||||||
\(923\) | −5.24029 | −0.172486 | ||||||||
\(924\) | −0.492922 | −0.0162160 | ||||||||
\(925\) | 6.67261 | 0.219394 | ||||||||
\(926\) | 53.7548 | 1.76649 | ||||||||
\(927\) | −53.5989 | −1.76042 | ||||||||
\(928\) | 14.2557 | 0.467968 | ||||||||
\(929\) | −0.987098 | −0.0323856 | −0.0161928 | − | 0.999869i | \(-0.505155\pi\) | ||||
−0.0161928 | + | 0.999869i | \(0.505155\pi\) | |||||||
\(930\) | 32.9668 | 1.08103 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −22.2475 | −0.728741 | ||||||||
\(933\) | −18.1596 | −0.594520 | ||||||||
\(934\) | 32.8947 | 1.07635 | ||||||||
\(935\) | −1.74899 | −0.0571981 | ||||||||
\(936\) | −71.6713 | −2.34265 | ||||||||
\(937\) | −10.6228 | −0.347032 | −0.173516 | − | 0.984831i | \(-0.555513\pi\) | ||||
−0.173516 | + | 0.984831i | \(0.555513\pi\) | |||||||
\(938\) | 7.17561 | 0.234292 | ||||||||
\(939\) | −2.67025 | −0.0871405 | ||||||||
\(940\) | 3.83993 | 0.125245 | ||||||||
\(941\) | 10.5236 | 0.343059 | 0.171529 | − | 0.985179i | \(-0.445129\pi\) | ||||
0.171529 | + | 0.985179i | \(0.445129\pi\) | |||||||
\(942\) | 36.0408 | 1.17427 | ||||||||
\(943\) | −8.78208 | −0.285984 | ||||||||
\(944\) | −33.8318 | −1.10113 | ||||||||
\(945\) | 8.16003 | 0.265446 | ||||||||
\(946\) | −0.913958 | −0.0297153 | ||||||||
\(947\) | 35.1113 | 1.14096 | 0.570482 | − | 0.821310i | \(-0.306756\pi\) | ||||
0.570482 | + | 0.821310i | \(0.306756\pi\) | |||||||
\(948\) | 3.81137 | 0.123788 | ||||||||
\(949\) | −67.2667 | −2.18357 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −109.048 | −3.53613 | ||||||||
\(952\) | −5.68230 | −0.184164 | ||||||||
\(953\) | −21.0777 | −0.682775 | −0.341387 | − | 0.939923i | \(-0.610897\pi\) | ||||
−0.341387 | + | 0.939923i | \(0.610897\pi\) | |||||||
\(954\) | 85.7884 | 2.77750 | ||||||||
\(955\) | −5.98517 | −0.193675 | ||||||||
\(956\) | 10.9386 | 0.353778 | ||||||||
\(957\) | 3.45234 | 0.111598 | ||||||||
\(958\) | 20.6053 | 0.665726 | ||||||||
\(959\) | −0.504943 | −0.0163054 | ||||||||
\(960\) | −7.99114 | −0.257913 | ||||||||
\(961\) | 5.25495 | 0.169514 | ||||||||
\(962\) | 54.1655 | 1.74637 | ||||||||
\(963\) | 49.2496 | 1.58705 | ||||||||
\(964\) | 12.6531 | 0.407530 | ||||||||
\(965\) | 2.16859 | 0.0698095 | ||||||||
\(966\) | −3.33293 | −0.107235 | ||||||||
\(967\) | 47.4060 | 1.52448 | 0.762238 | − | 0.647297i | \(-0.224101\pi\) | ||||
0.762238 | + | 0.647297i | \(0.224101\pi\) | |||||||
\(968\) | −21.3688 | −0.686820 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.8213 | 0.379560 | ||||||||
\(971\) | 32.6009 | 1.04621 | 0.523106 | − | 0.852268i | \(-0.324773\pi\) | ||||
0.523106 | + | 0.852268i | \(0.324773\pi\) | |||||||
\(972\) | 32.3942 | 1.03904 | ||||||||
\(973\) | 0.0548685 | 0.00175900 | ||||||||
\(974\) | −23.7418 | −0.760736 | ||||||||
\(975\) | −15.6798 | −0.502155 | ||||||||
\(976\) | −3.37963 | −0.108179 | ||||||||
\(977\) | 23.9914 | 0.767553 | 0.383777 | − | 0.923426i | \(-0.374623\pi\) | ||||
0.383777 | + | 0.923426i | \(0.374623\pi\) | |||||||
\(978\) | 79.8970 | 2.55483 | ||||||||
\(979\) | −4.81967 | −0.154037 | ||||||||
\(980\) | 5.59077 | 0.178591 | ||||||||
\(981\) | 133.791 | 4.27160 | ||||||||
\(982\) | 33.4814 | 1.06843 | ||||||||
\(983\) | −4.28746 | −0.136749 | −0.0683743 | − | 0.997660i | \(-0.521781\pi\) | ||||
−0.0683743 | + | 0.997660i | \(0.521781\pi\) | |||||||
\(984\) | 50.4832 | 1.60935 | ||||||||
\(985\) | −16.5665 | −0.527854 | ||||||||
\(986\) | −28.4972 | −0.907537 | ||||||||
\(987\) | 8.20581 | 0.261194 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.81944 | −0.0578547 | ||||||||
\(990\) | 4.22427 | 0.134256 | ||||||||
\(991\) | 45.7393 | 1.45296 | 0.726479 | − | 0.687189i | \(-0.241155\pi\) | ||||
0.726479 | + | 0.687189i | \(0.241155\pi\) | |||||||
\(992\) | 26.7797 | 0.850257 | ||||||||
\(993\) | −36.6414 | −1.16278 | ||||||||
\(994\) | 1.00346 | 0.0318277 | ||||||||
\(995\) | −13.9801 | −0.443200 | ||||||||
\(996\) | −2.32007 | −0.0735143 | ||||||||
\(997\) | 11.9723 | 0.379167 | 0.189584 | − | 0.981865i | \(-0.439286\pi\) | ||||
0.189584 | + | 0.981865i | \(0.439286\pi\) | |||||||
\(998\) | 12.5217 | 0.396367 | ||||||||
\(999\) | 99.2884 | 3.14135 |
(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 | 1805.2.a.u.1.3 | 9 | ||
5.4 | even | 2 | 9025.2.a.cd.1.7 | 9 | |||
19.2 | odd | 18 | 95.2.k.b.61.1 | ✓ | 18 | ||
19.10 | odd | 18 | 95.2.k.b.81.1 | yes | 18 | ||
19.18 | odd | 2 | 1805.2.a.t.1.7 | 9 | |||
57.2 | even | 18 | 855.2.bs.b.631.3 | 18 | |||
57.29 | even | 18 | 855.2.bs.b.271.3 | 18 | |||
95.2 | even | 36 | 475.2.u.c.99.5 | 36 | |||
95.29 | odd | 18 | 475.2.l.b.176.3 | 18 | |||
95.48 | even | 36 | 475.2.u.c.24.5 | 36 | |||
95.59 | odd | 18 | 475.2.l.b.251.3 | 18 | |||
95.67 | even | 36 | 475.2.u.c.24.2 | 36 | |||
95.78 | even | 36 | 475.2.u.c.99.2 | 36 | |||
95.94 | odd | 2 | 9025.2.a.ce.1.3 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.61.1 | ✓ | 18 | 19.2 | odd | 18 | ||
95.2.k.b.81.1 | yes | 18 | 19.10 | odd | 18 | ||
475.2.l.b.176.3 | 18 | 95.29 | odd | 18 | |||
475.2.l.b.251.3 | 18 | 95.59 | odd | 18 | |||
475.2.u.c.24.2 | 36 | 95.67 | even | 36 | |||
475.2.u.c.24.5 | 36 | 95.48 | even | 36 | |||
475.2.u.c.99.2 | 36 | 95.78 | even | 36 | |||
475.2.u.c.99.5 | 36 | 95.2 | even | 36 | |||
855.2.bs.b.271.3 | 18 | 57.29 | even | 18 | |||
855.2.bs.b.631.3 | 18 | 57.2 | even | 18 | |||
1805.2.a.t.1.7 | 9 | 19.18 | odd | 2 | |||
1805.2.a.u.1.3 | 9 | 1.1 | even | 1 | trivial | ||
9025.2.a.cd.1.7 | 9 | 5.4 | even | 2 | |||
9025.2.a.ce.1.3 | 9 | 95.94 | odd | 2 |