Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [931,2,Mod(1,931)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(931, 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("931.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 931 = 7^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 931.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: | \(7.43407242818\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 13x^{8} + 24x^{7} + 57x^{6} - 98x^{5} - 93x^{4} + 152x^{3} + 39x^{2} - 58x - 7 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.20114\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 931.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.20114 | −1.55644 | −0.778220 | − | 0.627991i | \(-0.783877\pi\) | ||||
−0.778220 | + | 0.627991i | \(0.783877\pi\) | |||||||
\(3\) | −2.62563 | −1.51591 | −0.757955 | − | 0.652307i | \(-0.773801\pi\) | ||||
−0.757955 | + | 0.652307i | \(0.773801\pi\) | |||||||
\(4\) | 2.84501 | 1.42251 | ||||||||
\(5\) | −4.23731 | −1.89498 | −0.947490 | − | 0.319784i | \(-0.896390\pi\) | ||||
−0.947490 | + | 0.319784i | \(0.896390\pi\) | |||||||
\(6\) | 5.77938 | 2.35942 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.86000 | −0.657608 | ||||||||
\(9\) | 3.89394 | 1.29798 | ||||||||
\(10\) | 9.32690 | 2.94942 | ||||||||
\(11\) | −4.54922 | −1.37164 | −0.685821 | − | 0.727771i | \(-0.740556\pi\) | ||||
−0.685821 | + | 0.727771i | \(0.740556\pi\) | |||||||
\(12\) | −7.46996 | −2.15639 | ||||||||
\(13\) | −0.667049 | −0.185006 | −0.0925031 | − | 0.995712i | \(-0.529487\pi\) | ||||
−0.0925031 | + | 0.995712i | \(0.529487\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.1256 | 2.87262 | ||||||||
\(16\) | −1.59592 | −0.398980 | ||||||||
\(17\) | 1.86633 | 0.452652 | 0.226326 | − | 0.974052i | \(-0.427329\pi\) | ||||
0.226326 | + | 0.974052i | \(0.427329\pi\) | |||||||
\(18\) | −8.57111 | −2.02023 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −12.0552 | −2.69562 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 10.0135 | 2.13488 | ||||||||
\(23\) | 9.29601 | 1.93835 | 0.969176 | − | 0.246369i | \(-0.0792375\pi\) | ||||
0.969176 | + | 0.246369i | \(0.0792375\pi\) | |||||||
\(24\) | 4.88366 | 0.996873 | ||||||||
\(25\) | 12.9548 | 2.59095 | ||||||||
\(26\) | 1.46827 | 0.287951 | ||||||||
\(27\) | −2.34716 | −0.451711 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.31070 | −0.243390 | −0.121695 | − | 0.992568i | \(-0.538833\pi\) | ||||
−0.121695 | + | 0.992568i | \(0.538833\pi\) | |||||||
\(30\) | −24.4890 | −4.47106 | ||||||||
\(31\) | 3.90360 | 0.701108 | 0.350554 | − | 0.936542i | \(-0.385993\pi\) | ||||
0.350554 | + | 0.936542i | \(0.385993\pi\) | |||||||
\(32\) | 7.23283 | 1.27860 | ||||||||
\(33\) | 11.9446 | 2.07928 | ||||||||
\(34\) | −4.10806 | −0.704526 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 11.0783 | 1.84639 | ||||||||
\(37\) | 3.00492 | 0.494006 | 0.247003 | − | 0.969015i | \(-0.420554\pi\) | ||||
0.247003 | + | 0.969015i | \(0.420554\pi\) | |||||||
\(38\) | 2.20114 | 0.357072 | ||||||||
\(39\) | 1.75143 | 0.280453 | ||||||||
\(40\) | 7.88137 | 1.24615 | ||||||||
\(41\) | −5.48606 | −0.856779 | −0.428390 | − | 0.903594i | \(-0.640919\pi\) | ||||
−0.428390 | + | 0.903594i | \(0.640919\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.44567 | 0.677958 | 0.338979 | − | 0.940794i | \(-0.389918\pi\) | ||||
0.338979 | + | 0.940794i | \(0.389918\pi\) | |||||||
\(44\) | −12.9426 | −1.95117 | ||||||||
\(45\) | −16.4998 | −2.45965 | ||||||||
\(46\) | −20.4618 | −3.01693 | ||||||||
\(47\) | −5.81459 | −0.848146 | −0.424073 | − | 0.905628i | \(-0.639400\pi\) | ||||
−0.424073 | + | 0.905628i | \(0.639400\pi\) | |||||||
\(48\) | 4.19030 | 0.604818 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −28.5152 | −4.03266 | ||||||||
\(51\) | −4.90030 | −0.686179 | ||||||||
\(52\) | −1.89777 | −0.263173 | ||||||||
\(53\) | −9.95130 | −1.36692 | −0.683458 | − | 0.729990i | \(-0.739525\pi\) | ||||
−0.683458 | + | 0.729990i | \(0.739525\pi\) | |||||||
\(54\) | 5.16642 | 0.703061 | ||||||||
\(55\) | 19.2764 | 2.59923 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.62563 | 0.347773 | ||||||||
\(58\) | 2.88503 | 0.378823 | ||||||||
\(59\) | 2.07940 | 0.270714 | 0.135357 | − | 0.990797i | \(-0.456782\pi\) | ||||
0.135357 | + | 0.990797i | \(0.456782\pi\) | |||||||
\(60\) | 31.6525 | 4.08632 | ||||||||
\(61\) | 10.1390 | 1.29816 | 0.649080 | − | 0.760720i | \(-0.275154\pi\) | ||||
0.649080 | + | 0.760720i | \(0.275154\pi\) | |||||||
\(62\) | −8.59238 | −1.09123 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.7286 | −1.59108 | ||||||||
\(65\) | 2.82649 | 0.350583 | ||||||||
\(66\) | −26.2917 | −3.23628 | ||||||||
\(67\) | −0.523489 | −0.0639544 | −0.0319772 | − | 0.999489i | \(-0.510180\pi\) | ||||
−0.0319772 | + | 0.999489i | \(0.510180\pi\) | |||||||
\(68\) | 5.30974 | 0.643901 | ||||||||
\(69\) | −24.4079 | −2.93837 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.03304 | −0.478634 | −0.239317 | − | 0.970942i | \(-0.576923\pi\) | ||||
−0.239317 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(72\) | −7.24271 | −0.853562 | ||||||||
\(73\) | 5.38666 | 0.630461 | 0.315230 | − | 0.949015i | \(-0.397918\pi\) | ||||
0.315230 | + | 0.949015i | \(0.397918\pi\) | |||||||
\(74\) | −6.61425 | −0.768891 | ||||||||
\(75\) | −34.0144 | −3.92765 | ||||||||
\(76\) | −2.84501 | −0.326346 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.85513 | −0.436508 | ||||||||
\(79\) | −2.64530 | −0.297619 | −0.148810 | − | 0.988866i | \(-0.547544\pi\) | ||||
−0.148810 | + | 0.988866i | \(0.547544\pi\) | |||||||
\(80\) | 6.76240 | 0.756060 | ||||||||
\(81\) | −5.51905 | −0.613228 | ||||||||
\(82\) | 12.0756 | 1.33353 | ||||||||
\(83\) | 2.83415 | 0.311088 | 0.155544 | − | 0.987829i | \(-0.450287\pi\) | ||||
0.155544 | + | 0.987829i | \(0.450287\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.90822 | −0.857767 | ||||||||
\(86\) | −9.78554 | −1.05520 | ||||||||
\(87\) | 3.44141 | 0.368958 | ||||||||
\(88\) | 8.46152 | 0.902002 | ||||||||
\(89\) | −14.0986 | −1.49445 | −0.747225 | − | 0.664572i | \(-0.768614\pi\) | ||||
−0.747225 | + | 0.664572i | \(0.768614\pi\) | |||||||
\(90\) | 36.3184 | 3.82829 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 26.4473 | 2.75732 | ||||||||
\(93\) | −10.2494 | −1.06282 | ||||||||
\(94\) | 12.7987 | 1.32009 | ||||||||
\(95\) | 4.23731 | 0.434738 | ||||||||
\(96\) | −18.9908 | −1.93824 | ||||||||
\(97\) | −3.71220 | −0.376917 | −0.188459 | − | 0.982081i | \(-0.560349\pi\) | ||||
−0.188459 | + | 0.982081i | \(0.560349\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.7144 | −1.78036 | ||||||||
\(100\) | 36.8565 | 3.68565 | ||||||||
\(101\) | −3.14167 | −0.312608 | −0.156304 | − | 0.987709i | \(-0.549958\pi\) | ||||
−0.156304 | + | 0.987709i | \(0.549958\pi\) | |||||||
\(102\) | 10.7862 | 1.06800 | ||||||||
\(103\) | 11.4811 | 1.13127 | 0.565633 | − | 0.824657i | \(-0.308632\pi\) | ||||
0.565633 | + | 0.824657i | \(0.308632\pi\) | |||||||
\(104\) | 1.24071 | 0.121662 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 21.9042 | 2.12752 | ||||||||
\(107\) | 2.13866 | 0.206752 | 0.103376 | − | 0.994642i | \(-0.467035\pi\) | ||||
0.103376 | + | 0.994642i | \(0.467035\pi\) | |||||||
\(108\) | −6.67770 | −0.642562 | ||||||||
\(109\) | −7.02420 | −0.672796 | −0.336398 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336398 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(110\) | −42.4301 | −4.04555 | ||||||||
\(111\) | −7.88982 | −0.748868 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.54272 | 0.615487 | 0.307744 | − | 0.951469i | \(-0.400426\pi\) | ||||
0.307744 | + | 0.951469i | \(0.400426\pi\) | |||||||
\(114\) | −5.77938 | −0.541289 | ||||||||
\(115\) | −39.3900 | −3.67314 | ||||||||
\(116\) | −3.72895 | −0.346225 | ||||||||
\(117\) | −2.59745 | −0.240134 | ||||||||
\(118\) | −4.57704 | −0.421351 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −20.6936 | −1.88906 | ||||||||
\(121\) | 9.69539 | 0.881399 | ||||||||
\(122\) | −22.3173 | −2.02051 | ||||||||
\(123\) | 14.4044 | 1.29880 | ||||||||
\(124\) | 11.1058 | 0.997332 | ||||||||
\(125\) | −33.7067 | −3.01482 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.8356 | −1.76012 | −0.880061 | − | 0.474860i | \(-0.842499\pi\) | ||||
−0.880061 | + | 0.474860i | \(0.842499\pi\) | |||||||
\(128\) | 13.5518 | 1.19782 | ||||||||
\(129\) | −11.6727 | −1.02772 | ||||||||
\(130\) | −6.22150 | −0.545662 | ||||||||
\(131\) | 10.7068 | 0.935456 | 0.467728 | − | 0.883872i | \(-0.345073\pi\) | ||||
0.467728 | + | 0.883872i | \(0.345073\pi\) | |||||||
\(132\) | 33.9825 | 2.95780 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.15227 | 0.0995412 | ||||||||
\(135\) | 9.94563 | 0.855983 | ||||||||
\(136\) | −3.47137 | −0.297667 | ||||||||
\(137\) | 18.2869 | 1.56235 | 0.781177 | − | 0.624310i | \(-0.214620\pi\) | ||||
0.781177 | + | 0.624310i | \(0.214620\pi\) | |||||||
\(138\) | 53.7252 | 4.57339 | ||||||||
\(139\) | 6.71739 | 0.569762 | 0.284881 | − | 0.958563i | \(-0.408046\pi\) | ||||
0.284881 | + | 0.958563i | \(0.408046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.2670 | 1.28571 | ||||||||
\(142\) | 8.87728 | 0.744965 | ||||||||
\(143\) | 3.03455 | 0.253762 | ||||||||
\(144\) | −6.21442 | −0.517868 | ||||||||
\(145\) | 5.55383 | 0.461220 | ||||||||
\(146\) | −11.8568 | −0.981275 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.54905 | 0.702727 | ||||||||
\(149\) | 15.9572 | 1.30727 | 0.653633 | − | 0.756812i | \(-0.273244\pi\) | ||||
0.653633 | + | 0.756812i | \(0.273244\pi\) | |||||||
\(150\) | 74.8705 | 6.11315 | ||||||||
\(151\) | −19.1129 | −1.55539 | −0.777694 | − | 0.628643i | \(-0.783611\pi\) | ||||
−0.777694 | + | 0.628643i | \(0.783611\pi\) | |||||||
\(152\) | 1.86000 | 0.150866 | ||||||||
\(153\) | 7.26738 | 0.587533 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.5408 | −1.32859 | ||||||||
\(156\) | 4.98283 | 0.398946 | ||||||||
\(157\) | −3.10148 | −0.247525 | −0.123763 | − | 0.992312i | \(-0.539496\pi\) | ||||
−0.123763 | + | 0.992312i | \(0.539496\pi\) | |||||||
\(158\) | 5.82267 | 0.463226 | ||||||||
\(159\) | 26.1284 | 2.07212 | ||||||||
\(160\) | −30.6477 | −2.42292 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 12.1482 | 0.954452 | ||||||||
\(163\) | −4.45275 | −0.348766 | −0.174383 | − | 0.984678i | \(-0.555793\pi\) | ||||
−0.174383 | + | 0.984678i | \(0.555793\pi\) | |||||||
\(164\) | −15.6079 | −1.21877 | ||||||||
\(165\) | −50.6128 | −3.94020 | ||||||||
\(166\) | −6.23835 | −0.484190 | ||||||||
\(167\) | 18.9814 | 1.46883 | 0.734413 | − | 0.678703i | \(-0.237458\pi\) | ||||
0.734413 | + | 0.678703i | \(0.237458\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5550 | −0.965773 | ||||||||
\(170\) | 17.4071 | 1.33506 | ||||||||
\(171\) | −3.89394 | −0.297777 | ||||||||
\(172\) | 12.6480 | 0.964400 | ||||||||
\(173\) | 4.37027 | 0.332266 | 0.166133 | − | 0.986103i | \(-0.446872\pi\) | ||||
0.166133 | + | 0.986103i | \(0.446872\pi\) | |||||||
\(174\) | −7.57502 | −0.574261 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.26019 | 0.547258 | ||||||||
\(177\) | −5.45973 | −0.410379 | ||||||||
\(178\) | 31.0330 | 2.32602 | ||||||||
\(179\) | −5.77456 | −0.431611 | −0.215806 | − | 0.976436i | \(-0.569238\pi\) | ||||
−0.215806 | + | 0.976436i | \(0.569238\pi\) | |||||||
\(180\) | −46.9422 | −3.49887 | ||||||||
\(181\) | −8.85069 | −0.657867 | −0.328933 | − | 0.944353i | \(-0.606689\pi\) | ||||
−0.328933 | + | 0.944353i | \(0.606689\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −26.6212 | −1.96789 | ||||||||
\(184\) | −17.2905 | −1.27468 | ||||||||
\(185\) | −12.7328 | −0.936132 | ||||||||
\(186\) | 22.5604 | 1.65421 | ||||||||
\(187\) | −8.49035 | −0.620876 | ||||||||
\(188\) | −16.5426 | −1.20649 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.32690 | −0.676644 | ||||||||
\(191\) | 5.50278 | 0.398167 | 0.199084 | − | 0.979983i | \(-0.436203\pi\) | ||||
0.199084 | + | 0.979983i | \(0.436203\pi\) | |||||||
\(192\) | 33.4207 | 2.41193 | ||||||||
\(193\) | −18.5258 | −1.33352 | −0.666758 | − | 0.745274i | \(-0.732319\pi\) | ||||
−0.666758 | + | 0.745274i | \(0.732319\pi\) | |||||||
\(194\) | 8.17108 | 0.586649 | ||||||||
\(195\) | −7.42133 | −0.531452 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.47529 | 0.532593 | 0.266296 | − | 0.963891i | \(-0.414200\pi\) | ||||
0.266296 | + | 0.963891i | \(0.414200\pi\) | |||||||
\(198\) | 38.9918 | 2.77103 | ||||||||
\(199\) | 22.1007 | 1.56668 | 0.783338 | − | 0.621596i | \(-0.213515\pi\) | ||||
0.783338 | + | 0.621596i | \(0.213515\pi\) | |||||||
\(200\) | −24.0958 | −1.70383 | ||||||||
\(201\) | 1.37449 | 0.0969490 | ||||||||
\(202\) | 6.91525 | 0.486555 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −13.9414 | −0.976095 | ||||||||
\(205\) | 23.2461 | 1.62358 | ||||||||
\(206\) | −25.2715 | −1.76075 | ||||||||
\(207\) | 36.1981 | 2.51594 | ||||||||
\(208\) | 1.06456 | 0.0738138 | ||||||||
\(209\) | 4.54922 | 0.314676 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.3344 | 0.711449 | 0.355724 | − | 0.934591i | \(-0.384234\pi\) | ||||
0.355724 | + | 0.934591i | \(0.384234\pi\) | |||||||
\(212\) | −28.3116 | −1.94445 | ||||||||
\(213\) | 10.5893 | 0.725565 | ||||||||
\(214\) | −4.70749 | −0.321797 | ||||||||
\(215\) | −18.8377 | −1.28472 | ||||||||
\(216\) | 4.36570 | 0.297048 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 15.4612 | 1.04717 | ||||||||
\(219\) | −14.1434 | −0.955721 | ||||||||
\(220\) | 54.8417 | 3.69743 | ||||||||
\(221\) | −1.24494 | −0.0837434 | ||||||||
\(222\) | 17.3666 | 1.16557 | ||||||||
\(223\) | 17.9428 | 1.20154 | 0.600768 | − | 0.799423i | \(-0.294862\pi\) | ||||
0.600768 | + | 0.799423i | \(0.294862\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 50.4451 | 3.36300 | ||||||||
\(226\) | −14.4014 | −0.957970 | ||||||||
\(227\) | 14.5072 | 0.962875 | 0.481437 | − | 0.876481i | \(-0.340115\pi\) | ||||
0.481437 | + | 0.876481i | \(0.340115\pi\) | |||||||
\(228\) | 7.46996 | 0.494710 | ||||||||
\(229\) | −4.81034 | −0.317876 | −0.158938 | − | 0.987289i | \(-0.550807\pi\) | ||||
−0.158938 | + | 0.987289i | \(0.550807\pi\) | |||||||
\(230\) | 86.7030 | 5.71702 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.43789 | 0.160055 | ||||||||
\(233\) | −19.2611 | −1.26184 | −0.630920 | − | 0.775848i | \(-0.717322\pi\) | ||||
−0.630920 | + | 0.775848i | \(0.717322\pi\) | |||||||
\(234\) | 5.71735 | 0.373755 | ||||||||
\(235\) | 24.6382 | 1.60722 | ||||||||
\(236\) | 5.91592 | 0.385093 | ||||||||
\(237\) | 6.94557 | 0.451163 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.84407 | 0.442706 | 0.221353 | − | 0.975194i | \(-0.428953\pi\) | ||||
0.221353 | + | 0.975194i | \(0.428953\pi\) | |||||||
\(240\) | −17.7556 | −1.14612 | ||||||||
\(241\) | 0.589968 | 0.0380032 | 0.0190016 | − | 0.999819i | \(-0.493951\pi\) | ||||
0.0190016 | + | 0.999819i | \(0.493951\pi\) | |||||||
\(242\) | −21.3409 | −1.37185 | ||||||||
\(243\) | 21.5325 | 1.38131 | ||||||||
\(244\) | 28.8455 | 1.84664 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −31.7060 | −2.02150 | ||||||||
\(247\) | 0.667049 | 0.0424433 | ||||||||
\(248\) | −7.26069 | −0.461054 | ||||||||
\(249\) | −7.44142 | −0.471581 | ||||||||
\(250\) | 74.1932 | 4.69239 | ||||||||
\(251\) | −7.77752 | −0.490913 | −0.245456 | − | 0.969408i | \(-0.578938\pi\) | ||||
−0.245456 | + | 0.969408i | \(0.578938\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −42.2896 | −2.65872 | ||||||||
\(254\) | 43.6609 | 2.73953 | ||||||||
\(255\) | 20.7641 | 1.30030 | ||||||||
\(256\) | −4.37220 | −0.273263 | ||||||||
\(257\) | 5.16184 | 0.321987 | 0.160993 | − | 0.986955i | \(-0.448530\pi\) | ||||
0.160993 | + | 0.986955i | \(0.448530\pi\) | |||||||
\(258\) | 25.6932 | 1.59959 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.04141 | 0.498707 | ||||||||
\(261\) | −5.10378 | −0.315916 | ||||||||
\(262\) | −23.5671 | −1.45598 | ||||||||
\(263\) | 21.2984 | 1.31331 | 0.656657 | − | 0.754190i | \(-0.271970\pi\) | ||||
0.656657 | + | 0.754190i | \(0.271970\pi\) | |||||||
\(264\) | −22.2168 | −1.36735 | ||||||||
\(265\) | 42.1667 | 2.59028 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 37.0177 | 2.26545 | ||||||||
\(268\) | −1.48933 | −0.0909756 | ||||||||
\(269\) | −10.2840 | −0.627025 | −0.313512 | − | 0.949584i | \(-0.601506\pi\) | ||||
−0.313512 | + | 0.949584i | \(0.601506\pi\) | |||||||
\(270\) | −21.8917 | −1.33229 | ||||||||
\(271\) | −25.2222 | −1.53214 | −0.766069 | − | 0.642758i | \(-0.777790\pi\) | ||||
−0.766069 | + | 0.642758i | \(0.777790\pi\) | |||||||
\(272\) | −2.97852 | −0.180599 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −40.2520 | −2.43171 | ||||||||
\(275\) | −58.9340 | −3.55386 | ||||||||
\(276\) | −69.4408 | −4.17985 | ||||||||
\(277\) | 11.2653 | 0.676864 | 0.338432 | − | 0.940991i | \(-0.390104\pi\) | ||||
0.338432 | + | 0.940991i | \(0.390104\pi\) | |||||||
\(278\) | −14.7859 | −0.886800 | ||||||||
\(279\) | 15.2004 | 0.910024 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.07464 | −0.422038 | −0.211019 | − | 0.977482i | \(-0.567678\pi\) | ||||
−0.211019 | + | 0.977482i | \(0.567678\pi\) | |||||||
\(282\) | −33.6047 | −2.00113 | ||||||||
\(283\) | −24.3703 | −1.44866 | −0.724331 | − | 0.689453i | \(-0.757851\pi\) | ||||
−0.724331 | + | 0.689453i | \(0.757851\pi\) | |||||||
\(284\) | −11.4741 | −0.680860 | ||||||||
\(285\) | −11.1256 | −0.659024 | ||||||||
\(286\) | −6.67948 | −0.394966 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 28.1642 | 1.65959 | ||||||||
\(289\) | −13.5168 | −0.795106 | ||||||||
\(290\) | −12.2247 | −0.717862 | ||||||||
\(291\) | 9.74688 | 0.571372 | ||||||||
\(292\) | 15.3251 | 0.896835 | ||||||||
\(293\) | −16.0761 | −0.939177 | −0.469588 | − | 0.882886i | \(-0.655598\pi\) | ||||
−0.469588 | + | 0.882886i | \(0.655598\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.81104 | −0.512999 | ||||||||
\(296\) | −5.58914 | −0.324862 | ||||||||
\(297\) | 10.6777 | 0.619585 | ||||||||
\(298\) | −35.1241 | −2.03468 | ||||||||
\(299\) | −6.20090 | −0.358607 | ||||||||
\(300\) | −96.7715 | −5.58711 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 42.0702 | 2.42087 | ||||||||
\(303\) | 8.24887 | 0.473885 | ||||||||
\(304\) | 1.59592 | 0.0915323 | ||||||||
\(305\) | −42.9619 | −2.45999 | ||||||||
\(306\) | −15.9965 | −0.914460 | ||||||||
\(307\) | 13.1085 | 0.748142 | 0.374071 | − | 0.927400i | \(-0.377962\pi\) | ||||
0.374071 | + | 0.927400i | \(0.377962\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −30.1451 | −1.71490 | ||||||||
\(310\) | 36.4085 | 2.06787 | ||||||||
\(311\) | 28.0359 | 1.58977 | 0.794885 | − | 0.606760i | \(-0.207531\pi\) | ||||
0.794885 | + | 0.606760i | \(0.207531\pi\) | |||||||
\(312\) | −3.25764 | −0.184428 | ||||||||
\(313\) | −9.53490 | −0.538945 | −0.269472 | − | 0.963008i | \(-0.586849\pi\) | ||||
−0.269472 | + | 0.963008i | \(0.586849\pi\) | |||||||
\(314\) | 6.82680 | 0.385258 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.52591 | −0.423365 | ||||||||
\(317\) | −11.1347 | −0.625389 | −0.312694 | − | 0.949854i | \(-0.601232\pi\) | ||||
−0.312694 | + | 0.949854i | \(0.601232\pi\) | |||||||
\(318\) | −57.5124 | −3.22513 | ||||||||
\(319\) | 5.96265 | 0.333844 | ||||||||
\(320\) | 53.9351 | 3.01506 | ||||||||
\(321\) | −5.61533 | −0.313417 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.86633 | −0.103845 | ||||||||
\(324\) | −15.7018 | −0.872321 | ||||||||
\(325\) | −8.64146 | −0.479342 | ||||||||
\(326\) | 9.80113 | 0.542834 | ||||||||
\(327\) | 18.4429 | 1.01990 | ||||||||
\(328\) | 10.2040 | 0.563424 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 111.406 | 6.13269 | ||||||||
\(331\) | −0.894117 | −0.0491451 | −0.0245726 | − | 0.999698i | \(-0.507822\pi\) | ||||
−0.0245726 | + | 0.999698i | \(0.507822\pi\) | |||||||
\(332\) | 8.06319 | 0.442525 | ||||||||
\(333\) | 11.7010 | 0.641210 | ||||||||
\(334\) | −41.7807 | −2.28614 | ||||||||
\(335\) | 2.21818 | 0.121192 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.4880 | −0.571315 | −0.285658 | − | 0.958332i | \(-0.592212\pi\) | ||||
−0.285658 | + | 0.958332i | \(0.592212\pi\) | |||||||
\(338\) | 27.6354 | 1.50317 | ||||||||
\(339\) | −17.1788 | −0.933023 | ||||||||
\(340\) | −22.4990 | −1.22018 | ||||||||
\(341\) | −17.7584 | −0.961669 | ||||||||
\(342\) | 8.57111 | 0.463472 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.26892 | −0.445830 | ||||||||
\(345\) | 103.424 | 5.56815 | ||||||||
\(346\) | −9.61958 | −0.517152 | ||||||||
\(347\) | 9.44400 | 0.506981 | 0.253490 | − | 0.967338i | \(-0.418421\pi\) | ||||
0.253490 | + | 0.967338i | \(0.418421\pi\) | |||||||
\(348\) | 9.79086 | 0.524845 | ||||||||
\(349\) | −21.5964 | −1.15603 | −0.578015 | − | 0.816026i | \(-0.696173\pi\) | ||||
−0.578015 | + | 0.816026i | \(0.696173\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.56567 | 0.0835693 | ||||||||
\(352\) | −32.9037 | −1.75378 | ||||||||
\(353\) | 0.973443 | 0.0518112 | 0.0259056 | − | 0.999664i | \(-0.491753\pi\) | ||||
0.0259056 | + | 0.999664i | \(0.491753\pi\) | |||||||
\(354\) | 12.0176 | 0.638730 | ||||||||
\(355\) | 17.0892 | 0.907002 | ||||||||
\(356\) | −40.1107 | −2.12586 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 12.7106 | 0.671777 | ||||||||
\(359\) | −4.13501 | −0.218238 | −0.109119 | − | 0.994029i | \(-0.534803\pi\) | ||||
−0.109119 | + | 0.994029i | \(0.534803\pi\) | |||||||
\(360\) | 30.6896 | 1.61748 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 19.4816 | 1.02393 | ||||||||
\(363\) | −25.4565 | −1.33612 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −22.8249 | −1.19471 | ||||||||
\(366\) | 58.5969 | 3.06291 | ||||||||
\(367\) | −31.0923 | −1.62301 | −0.811503 | − | 0.584348i | \(-0.801350\pi\) | ||||
−0.811503 | + | 0.584348i | \(0.801350\pi\) | |||||||
\(368\) | −14.8357 | −0.773364 | ||||||||
\(369\) | −21.3624 | −1.11208 | ||||||||
\(370\) | 28.0266 | 1.45703 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −29.1598 | −1.51186 | ||||||||
\(373\) | −16.6976 | −0.864569 | −0.432285 | − | 0.901737i | \(-0.642292\pi\) | ||||
−0.432285 | + | 0.901737i | \(0.642292\pi\) | |||||||
\(374\) | 18.6884 | 0.966356 | ||||||||
\(375\) | 88.5015 | 4.57020 | ||||||||
\(376\) | 10.8151 | 0.557747 | ||||||||
\(377\) | 0.874300 | 0.0450287 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.93613 | −0.356285 | −0.178142 | − | 0.984005i | \(-0.557009\pi\) | ||||
−0.178142 | + | 0.984005i | \(0.557009\pi\) | |||||||
\(380\) | 12.0552 | 0.618419 | ||||||||
\(381\) | 52.0809 | 2.66819 | ||||||||
\(382\) | −12.1124 | −0.619723 | ||||||||
\(383\) | −26.4779 | −1.35296 | −0.676478 | − | 0.736463i | \(-0.736495\pi\) | ||||
−0.676478 | + | 0.736463i | \(0.736495\pi\) | |||||||
\(384\) | −35.5821 | −1.81579 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 40.7779 | 2.07554 | ||||||||
\(387\) | 17.3112 | 0.879976 | ||||||||
\(388\) | −10.5613 | −0.536168 | ||||||||
\(389\) | 19.4236 | 0.984813 | 0.492407 | − | 0.870365i | \(-0.336117\pi\) | ||||
0.492407 | + | 0.870365i | \(0.336117\pi\) | |||||||
\(390\) | 16.3354 | 0.827174 | ||||||||
\(391\) | 17.3494 | 0.877399 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.1121 | −1.41807 | ||||||||
\(394\) | −16.4542 | −0.828949 | ||||||||
\(395\) | 11.2089 | 0.563982 | ||||||||
\(396\) | −50.3977 | −2.53258 | ||||||||
\(397\) | −6.44353 | −0.323392 | −0.161696 | − | 0.986841i | \(-0.551696\pi\) | ||||
−0.161696 | + | 0.986841i | \(0.551696\pi\) | |||||||
\(398\) | −48.6467 | −2.43844 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20.6748 | −1.03374 | ||||||||
\(401\) | −19.1953 | −0.958570 | −0.479285 | − | 0.877659i | \(-0.659104\pi\) | ||||
−0.479285 | + | 0.877659i | \(0.659104\pi\) | |||||||
\(402\) | −3.02544 | −0.150895 | ||||||||
\(403\) | −2.60390 | −0.129709 | ||||||||
\(404\) | −8.93810 | −0.444687 | ||||||||
\(405\) | 23.3859 | 1.16205 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.6700 | −0.677599 | ||||||||
\(408\) | 9.11453 | 0.451237 | ||||||||
\(409\) | −21.7829 | −1.07709 | −0.538547 | − | 0.842595i | \(-0.681027\pi\) | ||||
−0.538547 | + | 0.842595i | \(0.681027\pi\) | |||||||
\(410\) | −51.1680 | −2.52701 | ||||||||
\(411\) | −48.0146 | −2.36839 | ||||||||
\(412\) | 32.6639 | 1.60924 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −79.6771 | −3.91592 | ||||||||
\(415\) | −12.0091 | −0.589506 | ||||||||
\(416\) | −4.82466 | −0.236548 | ||||||||
\(417\) | −17.6374 | −0.863707 | ||||||||
\(418\) | −10.0135 | −0.489775 | ||||||||
\(419\) | 12.7698 | 0.623844 | 0.311922 | − | 0.950108i | \(-0.399027\pi\) | ||||
0.311922 | + | 0.950108i | \(0.399027\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.1544 | 1.46963 | 0.734817 | − | 0.678266i | \(-0.237268\pi\) | ||||
0.734817 | + | 0.678266i | \(0.237268\pi\) | |||||||
\(422\) | −22.7474 | −1.10733 | ||||||||
\(423\) | −22.6417 | −1.10088 | ||||||||
\(424\) | 18.5094 | 0.898895 | ||||||||
\(425\) | 24.1779 | 1.17280 | ||||||||
\(426\) | −23.3085 | −1.12930 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.08452 | 0.294106 | ||||||||
\(429\) | −7.96762 | −0.384680 | ||||||||
\(430\) | 41.4643 | 1.99959 | ||||||||
\(431\) | 2.95699 | 0.142433 | 0.0712165 | − | 0.997461i | \(-0.477312\pi\) | ||||
0.0712165 | + | 0.997461i | \(0.477312\pi\) | |||||||
\(432\) | 3.74588 | 0.180224 | ||||||||
\(433\) | 1.44760 | 0.0695674 | 0.0347837 | − | 0.999395i | \(-0.488926\pi\) | ||||
0.0347837 | + | 0.999395i | \(0.488926\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −14.5823 | −0.699168 | ||||||||
\(436\) | −19.9839 | −0.957057 | ||||||||
\(437\) | −9.29601 | −0.444689 | ||||||||
\(438\) | 31.1316 | 1.48752 | ||||||||
\(439\) | −2.08826 | −0.0996671 | −0.0498336 | − | 0.998758i | \(-0.515869\pi\) | ||||
−0.0498336 | + | 0.998758i | \(0.515869\pi\) | |||||||
\(440\) | −35.8541 | −1.70928 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.74028 | 0.130342 | ||||||||
\(443\) | −27.9091 | −1.32600 | −0.663001 | − | 0.748618i | \(-0.730718\pi\) | ||||
−0.663001 | + | 0.748618i | \(0.730718\pi\) | |||||||
\(444\) | −22.4466 | −1.06527 | ||||||||
\(445\) | 59.7401 | 2.83195 | ||||||||
\(446\) | −39.4945 | −1.87012 | ||||||||
\(447\) | −41.8978 | −1.98170 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.9394 | 1.64889 | 0.824446 | − | 0.565941i | \(-0.191487\pi\) | ||||
0.824446 | + | 0.565941i | \(0.191487\pi\) | |||||||
\(450\) | −111.037 | −5.23432 | ||||||||
\(451\) | 24.9573 | 1.17519 | ||||||||
\(452\) | 18.6141 | 0.875535 | ||||||||
\(453\) | 50.1835 | 2.35783 | ||||||||
\(454\) | −31.9323 | −1.49866 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −4.88366 | −0.228698 | ||||||||
\(457\) | −19.1491 | −0.895759 | −0.447879 | − | 0.894094i | \(-0.647821\pi\) | ||||
−0.447879 | + | 0.894094i | \(0.647821\pi\) | |||||||
\(458\) | 10.5882 | 0.494755 | ||||||||
\(459\) | −4.38058 | −0.204468 | ||||||||
\(460\) | −112.065 | −5.22507 | ||||||||
\(461\) | −30.7840 | −1.43375 | −0.716877 | − | 0.697200i | \(-0.754429\pi\) | ||||
−0.716877 | + | 0.697200i | \(0.754429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.88109 | −0.459213 | −0.229607 | − | 0.973284i | \(-0.573744\pi\) | ||||
−0.229607 | + | 0.973284i | \(0.573744\pi\) | |||||||
\(464\) | 2.09177 | 0.0971079 | ||||||||
\(465\) | 43.4300 | 2.01402 | ||||||||
\(466\) | 42.3965 | 1.96398 | ||||||||
\(467\) | 10.5101 | 0.486349 | 0.243174 | − | 0.969983i | \(-0.421811\pi\) | ||||
0.243174 | + | 0.969983i | \(0.421811\pi\) | |||||||
\(468\) | −7.38979 | −0.341593 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −54.2321 | −2.50154 | ||||||||
\(471\) | 8.14335 | 0.375226 | ||||||||
\(472\) | −3.86767 | −0.178024 | ||||||||
\(473\) | −20.2243 | −0.929915 | ||||||||
\(474\) | −15.2882 | −0.702209 | ||||||||
\(475\) | −12.9548 | −0.594405 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −38.7498 | −1.77423 | ||||||||
\(478\) | −15.0648 | −0.689046 | ||||||||
\(479\) | 21.1885 | 0.968127 | 0.484063 | − | 0.875033i | \(-0.339160\pi\) | ||||
0.484063 | + | 0.875033i | \(0.339160\pi\) | |||||||
\(480\) | 80.4696 | 3.67292 | ||||||||
\(481\) | −2.00443 | −0.0913942 | ||||||||
\(482\) | −1.29860 | −0.0591497 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 27.5835 | 1.25380 | ||||||||
\(485\) | 15.7297 | 0.714251 | ||||||||
\(486\) | −47.3960 | −2.14992 | ||||||||
\(487\) | −2.06595 | −0.0936171 | −0.0468085 | − | 0.998904i | \(-0.514905\pi\) | ||||
−0.0468085 | + | 0.998904i | \(0.514905\pi\) | |||||||
\(488\) | −18.8584 | −0.853680 | ||||||||
\(489\) | 11.6913 | 0.528698 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.6735 | 0.797594 | 0.398797 | − | 0.917039i | \(-0.369428\pi\) | ||||
0.398797 | + | 0.917039i | \(0.369428\pi\) | |||||||
\(492\) | 40.9807 | 1.84755 | ||||||||
\(493\) | −2.44620 | −0.110171 | ||||||||
\(494\) | −1.46827 | −0.0660605 | ||||||||
\(495\) | 75.0613 | 3.37375 | ||||||||
\(496\) | −6.22984 | −0.279728 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 16.3796 | 0.733988 | ||||||||
\(499\) | 8.94463 | 0.400417 | 0.200208 | − | 0.979753i | \(-0.435838\pi\) | ||||
0.200208 | + | 0.979753i | \(0.435838\pi\) | |||||||
\(500\) | −95.8962 | −4.28861 | ||||||||
\(501\) | −49.8382 | −2.22661 | ||||||||
\(502\) | 17.1194 | 0.764077 | ||||||||
\(503\) | −18.8431 | −0.840171 | −0.420085 | − | 0.907485i | \(-0.638000\pi\) | ||||
−0.420085 | + | 0.907485i | \(0.638000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3122 | 0.592386 | ||||||||
\(506\) | 93.0853 | 4.13815 | ||||||||
\(507\) | 32.9649 | 1.46402 | ||||||||
\(508\) | −56.4325 | −2.50379 | ||||||||
\(509\) | 10.7558 | 0.476743 | 0.238371 | − | 0.971174i | \(-0.423386\pi\) | ||||
0.238371 | + | 0.971174i | \(0.423386\pi\) | |||||||
\(510\) | −45.7046 | −2.02383 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −17.4798 | −0.772507 | ||||||||
\(513\) | 2.34716 | 0.103630 | ||||||||
\(514\) | −11.3619 | −0.501153 | ||||||||
\(515\) | −48.6489 | −2.14373 | ||||||||
\(516\) | −33.2090 | −1.46194 | ||||||||
\(517\) | 26.4519 | 1.16335 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.4747 | −0.503684 | ||||||||
\(520\) | −5.25726 | −0.230546 | ||||||||
\(521\) | −3.90860 | −0.171239 | −0.0856194 | − | 0.996328i | \(-0.527287\pi\) | ||||
−0.0856194 | + | 0.996328i | \(0.527287\pi\) | |||||||
\(522\) | 11.2341 | 0.491704 | ||||||||
\(523\) | 34.5912 | 1.51257 | 0.756284 | − | 0.654243i | \(-0.227013\pi\) | ||||
0.756284 | + | 0.654243i | \(0.227013\pi\) | |||||||
\(524\) | 30.4610 | 1.33069 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −46.8807 | −2.04409 | ||||||||
\(527\) | 7.28542 | 0.317358 | ||||||||
\(528\) | −19.0626 | −0.829593 | ||||||||
\(529\) | 63.4158 | 2.75721 | ||||||||
\(530\) | −92.8148 | −4.03162 | ||||||||
\(531\) | 8.09705 | 0.351382 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.65947 | 0.158509 | ||||||||
\(534\) | −81.4812 | −3.52604 | ||||||||
\(535\) | −9.06216 | −0.391791 | ||||||||
\(536\) | 0.973687 | 0.0420569 | ||||||||
\(537\) | 15.1619 | 0.654283 | ||||||||
\(538\) | 22.6365 | 0.975927 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 28.2955 | 1.21764 | ||||||||
\(541\) | 0.256694 | 0.0110361 | 0.00551807 | − | 0.999985i | \(-0.498244\pi\) | ||||
0.00551807 | + | 0.999985i | \(0.498244\pi\) | |||||||
\(542\) | 55.5175 | 2.38468 | ||||||||
\(543\) | 23.2387 | 0.997266 | ||||||||
\(544\) | 13.4989 | 0.578759 | ||||||||
\(545\) | 29.7637 | 1.27494 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.24778 | −0.352650 | −0.176325 | − | 0.984332i | \(-0.556421\pi\) | ||||
−0.176325 | + | 0.984332i | \(0.556421\pi\) | |||||||
\(548\) | 52.0265 | 2.22246 | ||||||||
\(549\) | 39.4805 | 1.68499 | ||||||||
\(550\) | 129.722 | 5.53137 | ||||||||
\(551\) | 1.31070 | 0.0558376 | ||||||||
\(552\) | 45.3986 | 1.93229 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −24.7964 | −1.05350 | ||||||||
\(555\) | 33.4316 | 1.41909 | ||||||||
\(556\) | 19.1111 | 0.810490 | ||||||||
\(557\) | −3.18844 | −0.135098 | −0.0675492 | − | 0.997716i | \(-0.521518\pi\) | ||||
−0.0675492 | + | 0.997716i | \(0.521518\pi\) | |||||||
\(558\) | −33.4582 | −1.41640 | ||||||||
\(559\) | −2.96548 | −0.125426 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.2925 | 0.941191 | ||||||||
\(562\) | 15.5723 | 0.656876 | ||||||||
\(563\) | −32.5758 | −1.37291 | −0.686453 | − | 0.727175i | \(-0.740833\pi\) | ||||
−0.686453 | + | 0.727175i | \(0.740833\pi\) | |||||||
\(564\) | 43.4348 | 1.82893 | ||||||||
\(565\) | −27.7235 | −1.16634 | ||||||||
\(566\) | 53.6423 | 2.25476 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.50143 | 0.314753 | ||||||||
\(569\) | −39.5612 | −1.65849 | −0.829246 | − | 0.558884i | \(-0.811230\pi\) | ||||
−0.829246 | + | 0.558884i | \(0.811230\pi\) | |||||||
\(570\) | 24.4890 | 1.02573 | ||||||||
\(571\) | −6.55004 | −0.274111 | −0.137055 | − | 0.990563i | \(-0.543764\pi\) | ||||
−0.137055 | + | 0.990563i | \(0.543764\pi\) | |||||||
\(572\) | 8.63335 | 0.360978 | ||||||||
\(573\) | −14.4483 | −0.603585 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 120.428 | 5.02218 | ||||||||
\(576\) | −49.5645 | −2.06519 | ||||||||
\(577\) | 17.5603 | 0.731045 | 0.365522 | − | 0.930803i | \(-0.380890\pi\) | ||||
0.365522 | + | 0.930803i | \(0.380890\pi\) | |||||||
\(578\) | 29.7524 | 1.23754 | ||||||||
\(579\) | 48.6419 | 2.02149 | ||||||||
\(580\) | 15.8007 | 0.656089 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21.4542 | −0.889307 | ||||||||
\(583\) | 45.2706 | 1.87492 | ||||||||
\(584\) | −10.0192 | −0.414596 | ||||||||
\(585\) | 11.0062 | 0.455050 | ||||||||
\(586\) | 35.3858 | 1.46177 | ||||||||
\(587\) | 30.2766 | 1.24965 | 0.624825 | − | 0.780765i | \(-0.285170\pi\) | ||||
0.624825 | + | 0.780765i | \(0.285170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.90360 | −0.160845 | ||||||||
\(590\) | 19.3943 | 0.798452 | ||||||||
\(591\) | −19.6274 | −0.807362 | ||||||||
\(592\) | −4.79562 | −0.197099 | ||||||||
\(593\) | −24.8433 | −1.02019 | −0.510097 | − | 0.860117i | \(-0.670390\pi\) | ||||
−0.510097 | + | 0.860117i | \(0.670390\pi\) | |||||||
\(594\) | −23.5032 | −0.964347 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 45.3985 | 1.85960 | ||||||||
\(597\) | −58.0282 | −2.37494 | ||||||||
\(598\) | 13.6490 | 0.558151 | ||||||||
\(599\) | −29.8211 | −1.21846 | −0.609228 | − | 0.792995i | \(-0.708521\pi\) | ||||
−0.609228 | + | 0.792995i | \(0.708521\pi\) | |||||||
\(600\) | 63.2667 | 2.58285 | ||||||||
\(601\) | −43.8767 | −1.78977 | −0.894884 | − | 0.446298i | \(-0.852742\pi\) | ||||
−0.894884 | + | 0.446298i | \(0.852742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.03844 | −0.0830115 | ||||||||
\(604\) | −54.3765 | −2.21255 | ||||||||
\(605\) | −41.0823 | −1.67023 | ||||||||
\(606\) | −18.1569 | −0.737574 | ||||||||
\(607\) | −6.47053 | −0.262631 | −0.131315 | − | 0.991341i | \(-0.541920\pi\) | ||||
−0.131315 | + | 0.991341i | \(0.541920\pi\) | |||||||
\(608\) | −7.23283 | −0.293330 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 94.5651 | 3.82883 | ||||||||
\(611\) | 3.87862 | 0.156912 | ||||||||
\(612\) | 20.6758 | 0.835770 | ||||||||
\(613\) | −40.0247 | −1.61658 | −0.808291 | − | 0.588783i | \(-0.799607\pi\) | ||||
−0.808291 | + | 0.588783i | \(0.799607\pi\) | |||||||
\(614\) | −28.8536 | −1.16444 | ||||||||
\(615\) | −61.0358 | −2.46120 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.7730 | −0.715513 | −0.357757 | − | 0.933815i | \(-0.616458\pi\) | ||||
−0.357757 | + | 0.933815i | \(0.616458\pi\) | |||||||
\(618\) | 66.3537 | 2.66914 | ||||||||
\(619\) | −20.5165 | −0.824628 | −0.412314 | − | 0.911042i | \(-0.635279\pi\) | ||||
−0.412314 | + | 0.911042i | \(0.635279\pi\) | |||||||
\(620\) | −47.0587 | −1.88992 | ||||||||
\(621\) | −21.8192 | −0.875575 | ||||||||
\(622\) | −61.7109 | −2.47438 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −2.79514 | −0.111895 | ||||||||
\(625\) | 78.0520 | 3.12208 | ||||||||
\(626\) | 20.9877 | 0.838835 | ||||||||
\(627\) | −11.9446 | −0.477020 | ||||||||
\(628\) | −8.82376 | −0.352106 | ||||||||
\(629\) | 5.60818 | 0.223613 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.78970 | −0.111056 | −0.0555281 | − | 0.998457i | \(-0.517684\pi\) | ||||
−0.0555281 | + | 0.998457i | \(0.517684\pi\) | |||||||
\(632\) | 4.92024 | 0.195717 | ||||||||
\(633\) | −27.1343 | −1.07849 | ||||||||
\(634\) | 24.5091 | 0.973380 | ||||||||
\(635\) | 84.0494 | 3.33540 | ||||||||
\(636\) | 74.3358 | 2.94761 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.1246 | −0.519609 | ||||||||
\(639\) | −15.7044 | −0.621257 | ||||||||
\(640\) | −57.4233 | −2.26985 | ||||||||
\(641\) | −34.5824 | −1.36592 | −0.682961 | − | 0.730455i | \(-0.739308\pi\) | ||||
−0.682961 | + | 0.730455i | \(0.739308\pi\) | |||||||
\(642\) | 12.3601 | 0.487815 | ||||||||
\(643\) | 20.5081 | 0.808761 | 0.404381 | − | 0.914591i | \(-0.367487\pi\) | ||||
0.404381 | + | 0.914591i | \(0.367487\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 49.4607 | 1.94751 | ||||||||
\(646\) | 4.10806 | 0.161629 | ||||||||
\(647\) | 18.5977 | 0.731153 | 0.365576 | − | 0.930781i | \(-0.380872\pi\) | ||||
0.365576 | + | 0.930781i | \(0.380872\pi\) | |||||||
\(648\) | 10.2654 | 0.403263 | ||||||||
\(649\) | −9.45963 | −0.371323 | ||||||||
\(650\) | 19.0211 | 0.746068 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.6681 | −0.496123 | ||||||||
\(653\) | −42.3665 | −1.65793 | −0.828964 | − | 0.559302i | \(-0.811069\pi\) | ||||
−0.828964 | + | 0.559302i | \(0.811069\pi\) | |||||||
\(654\) | −40.5955 | −1.58741 | ||||||||
\(655\) | −45.3679 | −1.77267 | ||||||||
\(656\) | 8.75532 | 0.341838 | ||||||||
\(657\) | 20.9753 | 0.818326 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.3476 | 1.45486 | 0.727429 | − | 0.686183i | \(-0.240715\pi\) | ||||
0.727429 | + | 0.686183i | \(0.240715\pi\) | |||||||
\(660\) | −143.994 | −5.60496 | ||||||||
\(661\) | 41.0123 | 1.59519 | 0.797596 | − | 0.603192i | \(-0.206105\pi\) | ||||
0.797596 | + | 0.603192i | \(0.206105\pi\) | |||||||
\(662\) | 1.96808 | 0.0764915 | ||||||||
\(663\) | 3.26874 | 0.126947 | ||||||||
\(664\) | −5.27150 | −0.204574 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −25.7555 | −0.998005 | ||||||||
\(667\) | −12.1843 | −0.471776 | ||||||||
\(668\) | 54.0024 | 2.08942 | ||||||||
\(669\) | −47.1111 | −1.82142 | ||||||||
\(670\) | −4.88253 | −0.188629 | ||||||||
\(671\) | −46.1243 | −1.78061 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 42.3029 | 1.63066 | 0.815329 | − | 0.578998i | \(-0.196556\pi\) | ||||
0.815329 | + | 0.578998i | \(0.196556\pi\) | |||||||
\(674\) | 23.0855 | 0.889219 | ||||||||
\(675\) | −30.4069 | −1.17036 | ||||||||
\(676\) | −35.7193 | −1.37382 | ||||||||
\(677\) | 36.5041 | 1.40297 | 0.701483 | − | 0.712686i | \(-0.252522\pi\) | ||||
0.701483 | + | 0.712686i | \(0.252522\pi\) | |||||||
\(678\) | 37.8129 | 1.45219 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.7092 | 0.564074 | ||||||||
\(681\) | −38.0905 | −1.45963 | ||||||||
\(682\) | 39.0886 | 1.49678 | ||||||||
\(683\) | 27.0271 | 1.03416 | 0.517082 | − | 0.855936i | \(-0.327018\pi\) | ||||
0.517082 | + | 0.855936i | \(0.327018\pi\) | |||||||
\(684\) | −11.0783 | −0.423590 | ||||||||
\(685\) | −77.4871 | −2.96063 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.6302 | 0.481871 | ||||||||
\(688\) | −7.09493 | −0.270492 | ||||||||
\(689\) | 6.63801 | 0.252888 | ||||||||
\(690\) | −227.650 | −8.66649 | ||||||||
\(691\) | 5.49793 | 0.209151 | 0.104576 | − | 0.994517i | \(-0.466652\pi\) | ||||
0.104576 | + | 0.994517i | \(0.466652\pi\) | |||||||
\(692\) | 12.4335 | 0.472650 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.7876 | −0.789085 | ||||||||
\(695\) | −28.4636 | −1.07969 | ||||||||
\(696\) | −6.40100 | −0.242629 | ||||||||
\(697\) | −10.2388 | −0.387823 | ||||||||
\(698\) | 47.5368 | 1.79929 | ||||||||
\(699\) | 50.5727 | 1.91283 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.8214 | −1.23965 | −0.619824 | − | 0.784741i | \(-0.712796\pi\) | ||||
−0.619824 | + | 0.784741i | \(0.712796\pi\) | |||||||
\(702\) | −3.44626 | −0.130071 | ||||||||
\(703\) | −3.00492 | −0.113333 | ||||||||
\(704\) | 57.9053 | 2.18239 | ||||||||
\(705\) | −64.6908 | −2.43640 | ||||||||
\(706\) | −2.14268 | −0.0806410 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −15.5330 | −0.583766 | ||||||||
\(709\) | 4.93049 | 0.185168 | 0.0925842 | − | 0.995705i | \(-0.470487\pi\) | ||||
0.0925842 | + | 0.995705i | \(0.470487\pi\) | |||||||
\(710\) | −37.6158 | −1.41169 | ||||||||
\(711\) | −10.3006 | −0.386304 | ||||||||
\(712\) | 26.2233 | 0.982761 | ||||||||
\(713\) | 36.2880 | 1.35899 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.8583 | −0.480874 | ||||||||
\(716\) | −16.4287 | −0.613970 | ||||||||
\(717\) | −17.9700 | −0.671102 | ||||||||
\(718\) | 9.10174 | 0.339674 | ||||||||
\(719\) | −15.6062 | −0.582014 | −0.291007 | − | 0.956721i | \(-0.593990\pi\) | ||||
−0.291007 | + | 0.956721i | \(0.593990\pi\) | |||||||
\(720\) | 26.3324 | 0.981350 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.20114 | −0.0819179 | ||||||||
\(723\) | −1.54904 | −0.0576094 | ||||||||
\(724\) | −25.1803 | −0.935820 | ||||||||
\(725\) | −16.9798 | −0.630613 | ||||||||
\(726\) | 56.0333 | 2.07959 | ||||||||
\(727\) | −26.5642 | −0.985213 | −0.492606 | − | 0.870252i | \(-0.663956\pi\) | ||||
−0.492606 | + | 0.870252i | \(0.663956\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.9792 | −1.48071 | ||||||||
\(730\) | 50.2408 | 1.85950 | ||||||||
\(731\) | 8.29709 | 0.306879 | ||||||||
\(732\) | −75.7376 | −2.79934 | ||||||||
\(733\) | −37.8191 | −1.39688 | −0.698440 | − | 0.715668i | \(-0.746122\pi\) | ||||
−0.698440 | + | 0.715668i | \(0.746122\pi\) | |||||||
\(734\) | 68.4385 | 2.52611 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 67.2365 | 2.47837 | ||||||||
\(737\) | 2.38147 | 0.0877224 | ||||||||
\(738\) | 47.0216 | 1.73089 | ||||||||
\(739\) | 42.8341 | 1.57568 | 0.787839 | − | 0.615881i | \(-0.211200\pi\) | ||||
0.787839 | + | 0.615881i | \(0.211200\pi\) | |||||||
\(740\) | −36.2249 | −1.33165 | ||||||||
\(741\) | −1.75143 | −0.0643402 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −35.0205 | −1.28478 | −0.642389 | − | 0.766379i | \(-0.722057\pi\) | ||||
−0.642389 | + | 0.766379i | \(0.722057\pi\) | |||||||
\(744\) | 19.0639 | 0.698916 | ||||||||
\(745\) | −67.6156 | −2.47724 | ||||||||
\(746\) | 36.7538 | 1.34565 | ||||||||
\(747\) | 11.0360 | 0.403786 | ||||||||
\(748\) | −24.1552 | −0.883201 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −194.804 | −7.11324 | ||||||||
\(751\) | −11.6655 | −0.425679 | −0.212839 | − | 0.977087i | \(-0.568271\pi\) | ||||
−0.212839 | + | 0.977087i | \(0.568271\pi\) | |||||||
\(752\) | 9.27963 | 0.338393 | ||||||||
\(753\) | 20.4209 | 0.744179 | ||||||||
\(754\) | −1.92446 | −0.0700846 | ||||||||
\(755\) | 80.9873 | 2.94743 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.5376 | −0.492031 | −0.246016 | − | 0.969266i | \(-0.579121\pi\) | ||||
−0.246016 | + | 0.969266i | \(0.579121\pi\) | |||||||
\(758\) | 15.2674 | 0.554536 | ||||||||
\(759\) | 111.037 | 4.03038 | ||||||||
\(760\) | −7.88137 | −0.285887 | ||||||||
\(761\) | −46.4300 | −1.68309 | −0.841543 | − | 0.540190i | \(-0.818352\pi\) | ||||
−0.841543 | + | 0.540190i | \(0.818352\pi\) | |||||||
\(762\) | −114.637 | −4.15287 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 15.6555 | 0.566396 | ||||||||
\(765\) | −30.7941 | −1.11336 | ||||||||
\(766\) | 58.2815 | 2.10580 | ||||||||
\(767\) | −1.38706 | −0.0500839 | ||||||||
\(768\) | 11.4798 | 0.414241 | ||||||||
\(769\) | 12.0896 | 0.435963 | 0.217981 | − | 0.975953i | \(-0.430053\pi\) | ||||
0.217981 | + | 0.975953i | \(0.430053\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.5531 | −0.488103 | ||||||||
\(772\) | −52.7062 | −1.89694 | ||||||||
\(773\) | −41.3224 | −1.48627 | −0.743133 | − | 0.669144i | \(-0.766661\pi\) | ||||
−0.743133 | + | 0.669144i | \(0.766661\pi\) | |||||||
\(774\) | −38.1043 | −1.36963 | ||||||||
\(775\) | 50.5703 | 1.81654 | ||||||||
\(776\) | 6.90468 | 0.247864 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −42.7540 | −1.53280 | ||||||||
\(779\) | 5.48606 | 0.196559 | ||||||||
\(780\) | −21.1138 | −0.755995 | ||||||||
\(781\) | 18.3472 | 0.656514 | ||||||||
\(782\) | −38.1885 | −1.36562 | ||||||||
\(783\) | 3.07641 | 0.109942 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 13.1419 | 0.469056 | ||||||||
\(786\) | 61.8786 | 2.20714 | ||||||||
\(787\) | 12.6708 | 0.451664 | 0.225832 | − | 0.974166i | \(-0.427490\pi\) | ||||
0.225832 | + | 0.974166i | \(0.427490\pi\) | |||||||
\(788\) | 21.2673 | 0.757617 | ||||||||
\(789\) | −55.9217 | −1.99086 | ||||||||
\(790\) | −24.6724 | −0.877805 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 32.9487 | 1.17078 | ||||||||
\(793\) | −6.76319 | −0.240168 | ||||||||
\(794\) | 14.1831 | 0.503340 | ||||||||
\(795\) | −110.714 | −3.92663 | ||||||||
\(796\) | 62.8768 | 2.22861 | ||||||||
\(797\) | −8.94088 | −0.316702 | −0.158351 | − | 0.987383i | \(-0.550618\pi\) | ||||
−0.158351 | + | 0.987383i | \(0.550618\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.8520 | −0.383915 | ||||||||
\(800\) | 93.6996 | 3.31278 | ||||||||
\(801\) | −54.8991 | −1.93977 | ||||||||
\(802\) | 42.2516 | 1.49196 | ||||||||
\(803\) | −24.5051 | −0.864766 | ||||||||
\(804\) | 3.91044 | 0.137911 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.73154 | 0.201885 | ||||||||
\(807\) | 27.0019 | 0.950513 | ||||||||
\(808\) | 5.84349 | 0.205573 | ||||||||
\(809\) | 19.5233 | 0.686404 | 0.343202 | − | 0.939262i | \(-0.388488\pi\) | ||||
0.343202 | + | 0.939262i | \(0.388488\pi\) | |||||||
\(810\) | −51.4756 | −1.80867 | ||||||||
\(811\) | −22.4029 | −0.786671 | −0.393336 | − | 0.919395i | \(-0.628679\pi\) | ||||
−0.393336 | + | 0.919395i | \(0.628679\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 66.2241 | 2.32258 | ||||||||
\(814\) | 30.0897 | 1.05464 | ||||||||
\(815\) | 18.8677 | 0.660906 | ||||||||
\(816\) | 7.82049 | 0.273772 | ||||||||
\(817\) | −4.44567 | −0.155534 | ||||||||
\(818\) | 47.9472 | 1.67643 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 66.1356 | 2.30955 | ||||||||
\(821\) | 52.6094 | 1.83608 | 0.918040 | − | 0.396487i | \(-0.129771\pi\) | ||||
0.918040 | + | 0.396487i | \(0.129771\pi\) | |||||||
\(822\) | 105.687 | 3.68625 | ||||||||
\(823\) | 9.72070 | 0.338842 | 0.169421 | − | 0.985544i | \(-0.445810\pi\) | ||||
0.169421 | + | 0.985544i | \(0.445810\pi\) | |||||||
\(824\) | −21.3548 | −0.743930 | ||||||||
\(825\) | 154.739 | 5.38732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.0766 | 1.81088 | 0.905440 | − | 0.424473i | \(-0.139541\pi\) | ||||
0.905440 | + | 0.424473i | \(0.139541\pi\) | |||||||
\(828\) | 102.984 | 3.57895 | ||||||||
\(829\) | −6.02902 | −0.209396 | −0.104698 | − | 0.994504i | \(-0.533388\pi\) | ||||
−0.104698 | + | 0.994504i | \(0.533388\pi\) | |||||||
\(830\) | 26.4338 | 0.917531 | ||||||||
\(831\) | −29.5784 | −1.02606 | ||||||||
\(832\) | 8.49063 | 0.294360 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 38.8224 | 1.34431 | ||||||||
\(835\) | −80.4300 | −2.78340 | ||||||||
\(836\) | 12.9426 | 0.447629 | ||||||||
\(837\) | −9.16238 | −0.316698 | ||||||||
\(838\) | −28.1080 | −0.970976 | ||||||||
\(839\) | −52.1776 | −1.80137 | −0.900685 | − | 0.434473i | \(-0.856935\pi\) | ||||
−0.900685 | + | 0.434473i | \(0.856935\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2821 | −0.940761 | ||||||||
\(842\) | −66.3740 | −2.28740 | ||||||||
\(843\) | 18.5754 | 0.639770 | ||||||||
\(844\) | 29.4015 | 1.01204 | ||||||||
\(845\) | 53.1996 | 1.83012 | ||||||||
\(846\) | 49.8375 | 1.71345 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 15.8815 | 0.545372 | ||||||||
\(849\) | 63.9873 | 2.19604 | ||||||||
\(850\) | −53.2189 | −1.82539 | ||||||||
\(851\) | 27.9338 | 0.957558 | ||||||||
\(852\) | 30.1266 | 1.03212 | ||||||||
\(853\) | −32.7787 | −1.12232 | −0.561161 | − | 0.827707i | \(-0.689645\pi\) | ||||
−0.561161 | + | 0.827707i | \(0.689645\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.4998 | 0.564282 | ||||||||
\(856\) | −3.97790 | −0.135962 | ||||||||
\(857\) | 52.7222 | 1.80095 | 0.900477 | − | 0.434903i | \(-0.143217\pi\) | ||||
0.900477 | + | 0.434903i | \(0.143217\pi\) | |||||||
\(858\) | 17.5378 | 0.598732 | ||||||||
\(859\) | 38.9499 | 1.32895 | 0.664476 | − | 0.747309i | \(-0.268655\pi\) | ||||
0.664476 | + | 0.747309i | \(0.268655\pi\) | |||||||
\(860\) | −53.5934 | −1.82752 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.50874 | −0.221689 | ||||||||
\(863\) | −42.4625 | −1.44544 | −0.722721 | − | 0.691140i | \(-0.757109\pi\) | ||||
−0.722721 | + | 0.691140i | \(0.757109\pi\) | |||||||
\(864\) | −16.9766 | −0.577556 | ||||||||
\(865\) | −18.5182 | −0.629637 | ||||||||
\(866\) | −3.18638 | −0.108278 | ||||||||
\(867\) | 35.4902 | 1.20531 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0340 | 0.408227 | ||||||||
\(870\) | 32.0977 | 1.08821 | ||||||||
\(871\) | 0.349193 | 0.0118320 | ||||||||
\(872\) | 13.0650 | 0.442436 | ||||||||
\(873\) | −14.4551 | −0.489231 | ||||||||
\(874\) | 20.4618 | 0.692131 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −40.2381 | −1.35952 | ||||||||
\(877\) | 34.0068 | 1.14833 | 0.574163 | − | 0.818741i | \(-0.305327\pi\) | ||||
0.574163 | + | 0.818741i | \(0.305327\pi\) | |||||||
\(878\) | 4.59655 | 0.155126 | ||||||||
\(879\) | 42.2099 | 1.42371 | ||||||||
\(880\) | −30.7637 | −1.03704 | ||||||||
\(881\) | 19.0580 | 0.642079 | 0.321040 | − | 0.947066i | \(-0.395968\pi\) | ||||
0.321040 | + | 0.947066i | \(0.395968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.7499 | −1.37134 | −0.685671 | − | 0.727911i | \(-0.740491\pi\) | ||||
−0.685671 | + | 0.727911i | \(0.740491\pi\) | |||||||
\(884\) | −3.54186 | −0.119126 | ||||||||
\(885\) | 23.1346 | 0.777659 | ||||||||
\(886\) | 61.4319 | 2.06384 | ||||||||
\(887\) | −6.28833 | −0.211141 | −0.105571 | − | 0.994412i | \(-0.533667\pi\) | ||||
−0.105571 | + | 0.994412i | \(0.533667\pi\) | |||||||
\(888\) | 14.6750 | 0.492461 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −131.496 | −4.40777 | ||||||||
\(891\) | 25.1074 | 0.841128 | ||||||||
\(892\) | 51.0474 | 1.70919 | ||||||||
\(893\) | 5.81459 | 0.194578 | ||||||||
\(894\) | 92.2228 | 3.08439 | ||||||||
\(895\) | 24.4686 | 0.817895 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.2813 | 0.543616 | ||||||||
\(898\) | −76.9064 | −2.56640 | ||||||||
\(899\) | −5.11644 | −0.170643 | ||||||||
\(900\) | 143.517 | 4.78390 | ||||||||
\(901\) | −18.5724 | −0.618737 | ||||||||
\(902\) | −54.9345 | −1.82912 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.1694 | −0.404749 | ||||||||
\(905\) | 37.5031 | 1.24664 | ||||||||
\(906\) | −110.461 | −3.66982 | ||||||||
\(907\) | −25.7603 | −0.855355 | −0.427678 | − | 0.903931i | \(-0.640668\pi\) | ||||
−0.427678 | + | 0.903931i | \(0.640668\pi\) | |||||||
\(908\) | 41.2731 | 1.36970 | ||||||||
\(909\) | −12.2335 | −0.405759 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.3836 | −1.00665 | −0.503327 | − | 0.864096i | \(-0.667891\pi\) | ||||
−0.503327 | + | 0.864096i | \(0.667891\pi\) | |||||||
\(912\) | −4.19030 | −0.138755 | ||||||||
\(913\) | −12.8932 | −0.426701 | ||||||||
\(914\) | 42.1499 | 1.39420 | ||||||||
\(915\) | 112.802 | 3.72912 | ||||||||
\(916\) | −13.6855 | −0.452181 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 9.64226 | 0.318242 | ||||||||
\(919\) | 16.3148 | 0.538174 | 0.269087 | − | 0.963116i | \(-0.413278\pi\) | ||||
0.269087 | + | 0.963116i | \(0.413278\pi\) | |||||||
\(920\) | 73.2653 | 2.41548 | ||||||||
\(921\) | −34.4181 | −1.13411 | ||||||||
\(922\) | 67.7599 | 2.23155 | ||||||||
\(923\) | 2.69024 | 0.0885502 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.9280 | 1.27995 | ||||||||
\(926\) | 21.7497 | 0.714738 | ||||||||
\(927\) | 44.7067 | 1.46836 | ||||||||
\(928\) | −9.48006 | −0.311198 | ||||||||
\(929\) | −35.3308 | −1.15917 | −0.579583 | − | 0.814913i | \(-0.696784\pi\) | ||||
−0.579583 | + | 0.814913i | \(0.696784\pi\) | |||||||
\(930\) | −95.5954 | −3.13470 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −54.7982 | −1.79498 | ||||||||
\(933\) | −73.6119 | −2.40995 | ||||||||
\(934\) | −23.1342 | −0.756973 | ||||||||
\(935\) | 35.9762 | 1.17655 | ||||||||
\(936\) | 4.83125 | 0.157914 | ||||||||
\(937\) | −28.5431 | −0.932461 | −0.466231 | − | 0.884663i | \(-0.654388\pi\) | ||||
−0.466231 | + | 0.884663i | \(0.654388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.0351 | 0.816991 | ||||||||
\(940\) | 70.0961 | 2.28628 | ||||||||
\(941\) | −51.9012 | −1.69193 | −0.845966 | − | 0.533237i | \(-0.820975\pi\) | ||||
−0.845966 | + | 0.533237i | \(0.820975\pi\) | |||||||
\(942\) | −17.9246 | −0.584017 | ||||||||
\(943\) | −50.9985 | −1.66074 | ||||||||
\(944\) | −3.31855 | −0.108010 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 44.5165 | 1.44736 | ||||||||
\(947\) | 29.9686 | 0.973848 | 0.486924 | − | 0.873444i | \(-0.338119\pi\) | ||||
0.486924 | + | 0.873444i | \(0.338119\pi\) | |||||||
\(948\) | 19.7603 | 0.641783 | ||||||||
\(949\) | −3.59317 | −0.116639 | ||||||||
\(950\) | 28.5152 | 0.925156 | ||||||||
\(951\) | 29.2357 | 0.948032 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.6441 | 0.344796 | 0.172398 | − | 0.985027i | \(-0.444848\pi\) | ||||
0.172398 | + | 0.985027i | \(0.444848\pi\) | |||||||
\(954\) | 85.2937 | 2.76148 | ||||||||
\(955\) | −23.3170 | −0.754519 | ||||||||
\(956\) | 19.4715 | 0.629753 | ||||||||
\(957\) | −15.6557 | −0.506077 | ||||||||
\(958\) | −46.6388 | −1.50683 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −141.614 | −4.57056 | ||||||||
\(961\) | −15.7619 | −0.508447 | ||||||||
\(962\) | 4.41203 | 0.142250 | ||||||||
\(963\) | 8.32782 | 0.268360 | ||||||||
\(964\) | 1.67847 | 0.0540598 | ||||||||
\(965\) | 78.4995 | 2.52699 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.3775 | 1.45924 | 0.729620 | − | 0.683852i | \(-0.239697\pi\) | ||||
0.729620 | + | 0.683852i | \(0.239697\pi\) | |||||||
\(968\) | −18.0334 | −0.579615 | ||||||||
\(969\) | 4.90030 | 0.157420 | ||||||||
\(970\) | −34.6234 | −1.11169 | ||||||||
\(971\) | 10.6259 | 0.341000 | 0.170500 | − | 0.985358i | \(-0.445462\pi\) | ||||
0.170500 | + | 0.985358i | \(0.445462\pi\) | |||||||
\(972\) | 61.2602 | 1.96492 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.54744 | 0.145709 | ||||||||
\(975\) | 22.6893 | 0.726639 | ||||||||
\(976\) | −16.1810 | −0.517940 | ||||||||
\(977\) | 34.7509 | 1.11178 | 0.555890 | − | 0.831256i | \(-0.312378\pi\) | ||||
0.555890 | + | 0.831256i | \(0.312378\pi\) | |||||||
\(978\) | −25.7341 | −0.822887 | ||||||||
\(979\) | 64.1376 | 2.04985 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.3518 | −0.873276 | ||||||||
\(982\) | −38.9019 | −1.24141 | ||||||||
\(983\) | 31.8461 | 1.01573 | 0.507867 | − | 0.861436i | \(-0.330434\pi\) | ||||
0.507867 | + | 0.861436i | \(0.330434\pi\) | |||||||
\(984\) | −26.7921 | −0.854100 | ||||||||
\(985\) | −31.6751 | −1.00925 | ||||||||
\(986\) | 5.38442 | 0.171475 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.89777 | 0.0603760 | ||||||||
\(989\) | 41.3270 | 1.31412 | ||||||||
\(990\) | −165.220 | −5.25105 | ||||||||
\(991\) | −20.2572 | −0.643490 | −0.321745 | − | 0.946826i | \(-0.604269\pi\) | ||||
−0.321745 | + | 0.946826i | \(0.604269\pi\) | |||||||
\(992\) | 28.2341 | 0.896434 | ||||||||
\(993\) | 2.34762 | 0.0744995 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −93.6473 | −2.96882 | ||||||||
\(996\) | −21.1710 | −0.670828 | ||||||||
\(997\) | 28.8629 | 0.914096 | 0.457048 | − | 0.889442i | \(-0.348907\pi\) | ||||
0.457048 | + | 0.889442i | \(0.348907\pi\) | |||||||
\(998\) | −19.6884 | −0.623225 | ||||||||
\(999\) | −7.05303 | −0.223148 |
(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 | 931.2.a.p.1.2 | ✓ | 10 | |
3.2 | odd | 2 | 8379.2.a.ct.1.9 | 10 | |||
7.2 | even | 3 | 931.2.f.r.704.9 | 20 | |||
7.3 | odd | 6 | 931.2.f.q.324.9 | 20 | |||
7.4 | even | 3 | 931.2.f.r.324.9 | 20 | |||
7.5 | odd | 6 | 931.2.f.q.704.9 | 20 | |||
7.6 | odd | 2 | 931.2.a.q.1.2 | yes | 10 | ||
21.20 | even | 2 | 8379.2.a.cs.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
931.2.a.p.1.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
931.2.a.q.1.2 | yes | 10 | 7.6 | odd | 2 | ||
931.2.f.q.324.9 | 20 | 7.3 | odd | 6 | |||
931.2.f.q.704.9 | 20 | 7.5 | odd | 6 | |||
931.2.f.r.324.9 | 20 | 7.4 | even | 3 | |||
931.2.f.r.704.9 | 20 | 7.2 | even | 3 | |||
8379.2.a.cs.1.9 | 10 | 21.20 | even | 2 | |||
8379.2.a.ct.1.9 | 10 | 3.2 | odd | 2 |