Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.71451 | −1.21396 | −0.606982 | − | 0.794716i | \(-0.707620\pi\) | ||||
−0.606982 | + | 0.794716i | \(0.707620\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.53717 | −0.580997 | −0.290498 | − | 0.956875i | \(-0.593821\pi\) | ||||
−0.290498 | + | 0.956875i | \(0.593821\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.37579 | 1.01784 | 0.508919 | − | 0.860815i | \(-0.330045\pi\) | ||||
0.508919 | + | 0.860815i | \(0.330045\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.94514 | 1.09418 | 0.547092 | − | 0.837072i | \(-0.315735\pi\) | ||||
0.547092 | + | 0.837072i | \(0.315735\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.71451 | −0.700882 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.09305 | 0.507640 | 0.253820 | − | 0.967251i | \(-0.418313\pi\) | ||||
0.253820 | + | 0.967251i | \(0.418313\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.92796 | −0.442305 | −0.221152 | − | 0.975239i | \(-0.570982\pi\) | ||||
−0.221152 | + | 0.975239i | \(0.570982\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.53717 | −0.335439 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.550188 | 0.114722 | 0.0573611 | − | 0.998353i | \(-0.481731\pi\) | ||||
0.0573611 | + | 0.998353i | \(0.481731\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.36854 | 0.473709 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.84336 | 1.08508 | 0.542542 | − | 0.840029i | \(-0.317462\pi\) | ||||
0.542542 | + | 0.840029i | \(0.317462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.35732 | −1.50102 | −0.750510 | − | 0.660859i | \(-0.770192\pi\) | ||||
−0.750510 | + | 0.660859i | \(0.770192\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.37579 | 0.587649 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.17267 | 0.705309 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.61307 | 1.58038 | 0.790189 | − | 0.612863i | \(-0.209982\pi\) | ||||
0.790189 | + | 0.612863i | \(0.209982\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.94514 | 0.631728 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4801 | −1.79289 | −0.896444 | − | 0.443158i | \(-0.853858\pi\) | ||||
−0.896444 | + | 0.443158i | \(0.853858\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.25876 | −0.344457 | −0.172229 | − | 0.985057i | \(-0.555097\pi\) | ||||
−0.172229 | + | 0.985057i | \(0.555097\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.71451 | −0.404655 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.28095 | −1.06204 | −0.531018 | − | 0.847361i | \(-0.678190\pi\) | ||||
−0.531018 | + | 0.847361i | \(0.678190\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.63710 | −0.662443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.09305 | 0.293086 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.23615 | 0.856601 | 0.428300 | − | 0.903636i | \(-0.359113\pi\) | ||||
0.428300 | + | 0.903636i | \(0.359113\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.16359 | −1.23562 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.92796 | −0.255365 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.619676 | 0.0806750 | 0.0403375 | − | 0.999186i | \(-0.487157\pi\) | ||||
0.0403375 | + | 0.999186i | \(0.487157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4658 | 1.85216 | 0.926078 | − | 0.377332i | \(-0.123158\pi\) | ||||
0.926078 | + | 0.377332i | \(0.123158\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.53717 | −0.193666 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.7091 | −1.32830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.35747 | −0.898858 | −0.449429 | − | 0.893316i | \(-0.648372\pi\) | ||||
−0.449429 | + | 0.893316i | \(0.648372\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.550188 | 0.0662349 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.63521 | 0.312742 | 0.156371 | − | 0.987698i | \(-0.450020\pi\) | ||||
0.156371 | + | 0.987698i | \(0.450020\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.8616 | 1.62238 | 0.811188 | − | 0.584785i | \(-0.198821\pi\) | ||||
0.811188 | + | 0.584785i | \(0.198821\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.36854 | 0.273496 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.18917 | −0.591360 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.77019 | 0.311671 | 0.155835 | − | 0.987783i | \(-0.450193\pi\) | ||||
0.155835 | + | 0.987783i | \(0.450193\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.13535 | 0.453914 | 0.226957 | − | 0.973905i | \(-0.427122\pi\) | ||||
0.226957 | + | 0.973905i | \(0.427122\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.68160 | −0.616257 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.84336 | 0.626474 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.3614 | −1.31030 | −0.655152 | − | 0.755497i | \(-0.727396\pi\) | ||||
−0.655152 | + | 0.755497i | \(0.727396\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.06436 | −0.635718 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.35732 | −0.866614 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.23346 | 0.536942 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.5240 | 1.06855 | 0.534275 | − | 0.845311i | \(-0.320585\pi\) | ||||
0.534275 | + | 0.845311i | \(0.320585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.37579 | 0.339279 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.1634 | 1.50882 | 0.754409 | − | 0.656405i | \(-0.227924\pi\) | ||||
0.754409 | + | 0.656405i | \(0.227924\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.09047 | 0.403046 | 0.201523 | − | 0.979484i | \(-0.435411\pi\) | ||||
0.201523 | + | 0.979484i | \(0.435411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.17267 | 0.407210 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.2461 | 1.08720 | 0.543600 | − | 0.839344i | \(-0.317061\pi\) | ||||
0.543600 | + | 0.839344i | \(0.317061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.9901 | −1.53158 | −0.765788 | − | 0.643094i | \(-0.777651\pi\) | ||||
−0.765788 | + | 0.643094i | \(0.777651\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.61307 | 0.912432 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.33778 | −0.596209 | −0.298104 | − | 0.954533i | \(-0.596354\pi\) | ||||
−0.298104 | + | 0.954533i | \(0.596354\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.49349 | −0.139269 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.94514 | 0.364728 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.21738 | −0.294937 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.395928 | 0.0359935 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −11.4801 | −1.03512 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.14311 | 0.638899 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.52367 | −0.135204 | −0.0676020 | − | 0.997712i | \(-0.521535\pi\) | ||||
−0.0676020 | + | 0.997712i | \(0.521535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.25876 | −0.198872 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.7658 | 1.81431 | 0.907157 | − | 0.420793i | \(-0.138248\pi\) | ||||
0.907157 | + | 0.420793i | \(0.138248\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.96361 | 0.256978 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.71451 | −0.233627 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.4083 | 0.974681 | 0.487340 | − | 0.873212i | \(-0.337967\pi\) | ||||
0.487340 | + | 0.873212i | \(0.337967\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.71570 | 0.230342 | 0.115171 | − | 0.993346i | \(-0.463258\pi\) | ||||
0.115171 | + | 0.993346i | \(0.463258\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.28095 | −0.613166 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.3179 | 1.11370 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.8618 | −1.31725 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.63710 | −0.382461 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 10.6937 | 0.876064 | 0.438032 | − | 0.898959i | \(-0.355676\pi\) | ||||
0.438032 | + | 0.898959i | \(0.355676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5063 | −0.854987 | −0.427493 | − | 0.904018i | \(-0.640603\pi\) | ||||
−0.427493 | + | 0.904018i | \(0.640603\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.09305 | 0.169213 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.6860 | 1.82218 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3552 | −0.826436 | −0.413218 | − | 0.910632i | \(-0.635595\pi\) | ||||
−0.413218 | + | 0.910632i | \(0.635595\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.23615 | 0.494559 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.845735 | −0.0666532 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.33893 | −0.496504 | −0.248252 | − | 0.968696i | \(-0.579856\pi\) | ||||
−0.248252 | + | 0.968696i | \(0.579856\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.16359 | −0.713385 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.395120 | 0.0305753 | 0.0152877 | − | 0.999883i | \(-0.495134\pi\) | ||||
0.0152877 | + | 0.999883i | \(0.495134\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.56411 | 0.197239 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.92796 | −0.147435 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.3781 | 1.32123 | 0.660614 | − | 0.750725i | \(-0.270296\pi\) | ||||
0.660614 | + | 0.750725i | \(0.270296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.64086 | −0.275223 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.619676 | 0.0465777 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.15569 | −0.235867 | −0.117934 | − | 0.993021i | \(-0.537627\pi\) | ||||
−0.117934 | + | 0.993021i | \(0.537627\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.9671 | 1.03817 | 0.519085 | − | 0.854723i | \(-0.326273\pi\) | ||||
0.519085 | + | 0.854723i | \(0.326273\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 14.4658 | 1.06934 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −26.0947 | −1.91852 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.06570 | 0.516695 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.53717 | −0.111813 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.7722 | −1.28595 | −0.642974 | − | 0.765888i | \(-0.722300\pi\) | ||||
−0.642974 | + | 0.765888i | \(0.722300\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.00421 | 0.576155 | 0.288078 | − | 0.957607i | \(-0.406984\pi\) | ||||
0.288078 | + | 0.957607i | \(0.406984\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −10.7091 | −0.766895 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.1777 | 0.796376 | 0.398188 | − | 0.917304i | \(-0.369639\pi\) | ||||
0.398188 | + | 0.917304i | \(0.369639\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.15795 | 0.507414 | 0.253707 | − | 0.967281i | \(-0.418350\pi\) | ||||
0.253707 | + | 0.967281i | \(0.418350\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.35747 | −0.518956 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.98225 | −0.630430 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.1627 | 2.17650 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.550188 | 0.0382407 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.50838 | −0.450194 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2867 | 1.12122 | 0.560611 | − | 0.828079i | \(-0.310566\pi\) | ||||
0.560611 | + | 0.828079i | \(0.310566\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.63521 | 0.180562 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.13141 | 0.418158 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.8467 | 0.872088 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.8616 | 0.936679 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.25738 | 0.555452 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.74204 | −0.183621 | −0.0918104 | − | 0.995777i | \(-0.529265\pi\) | ||||
−0.0918104 | + | 0.995777i | \(0.529265\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.36854 | 0.157903 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.70484 | 0.577760 | 0.288880 | − | 0.957365i | \(-0.406717\pi\) | ||||
0.288880 | + | 0.957365i | \(0.406717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.0163 | −1.52096 | −0.760481 | − | 0.649360i | \(-0.775037\pi\) | ||||
−0.760481 | + | 0.649360i | \(0.775037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.18917 | −0.341422 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.5846 | −0.824447 | −0.412224 | − | 0.911083i | \(-0.635248\pi\) | ||||
−0.412224 | + | 0.911083i | \(0.635248\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.7642 | 1.28927 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.77019 | 0.179943 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.2452 | 1.30955 | 0.654777 | − | 0.755822i | \(-0.272763\pi\) | ||||
0.654777 | + | 0.755822i | \(0.272763\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.77341 | −0.500730 | −0.250365 | − | 0.968152i | \(-0.580551\pi\) | ||||
−0.250365 | + | 0.968152i | \(0.580551\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 12.5874 | 0.804182 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.60607 | −0.483963 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.13535 | 0.262067 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.3141 | 1.91341 | 0.956706 | − | 0.291058i | \(-0.0940071\pi\) | ||||
0.956706 | + | 0.291058i | \(0.0940071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.85732 | 0.116769 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.68160 | −0.355796 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 28.4899 | 1.77715 | 0.888576 | − | 0.458730i | \(-0.151696\pi\) | ||||
0.888576 | + | 0.458730i | \(0.151696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.7769 | −0.918195 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.84336 | 0.361695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.3946 | 1.25759 | 0.628793 | − | 0.777573i | \(-0.283549\pi\) | ||||
0.628793 | + | 0.777573i | \(0.283549\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.9281 | −1.03988 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.3614 | −0.756505 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.4449 | 1.12461 | 0.562304 | − | 0.826931i | \(-0.309915\pi\) | ||||
0.562304 | + | 0.826931i | \(0.309915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.8716 | 0.903386 | 0.451693 | − | 0.892173i | \(-0.350820\pi\) | ||||
0.451693 | + | 0.892173i | \(0.350820\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.06436 | −0.367032 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.99569 | 0.482158 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.8774 | 1.73508 | 0.867538 | − | 0.497371i | \(-0.165701\pi\) | ||||
0.867538 | + | 0.497371i | \(0.165701\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.35732 | −0.500340 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.1244 | 1.79707 | 0.898537 | − | 0.438898i | \(-0.144631\pi\) | ||||
0.898537 | + | 0.438898i | \(0.144631\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.93521 | −0.115037 | −0.0575183 | − | 0.998344i | \(-0.518319\pi\) | ||||
−0.0575183 | + | 0.998344i | \(0.518319\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.23346 | 0.310003 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.6469 | 1.04166 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.6191 | −0.742302 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.5240 | 0.616927 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.9502 | 0.698140 | 0.349070 | − | 0.937097i | \(-0.386497\pi\) | ||||
0.349070 | + | 0.937097i | \(0.386497\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.68211 | −0.0979365 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.37579 | 0.195883 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.17057 | 0.125527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.47210 | 0.200128 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.1634 | 0.871117 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −39.2675 | −2.24845 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.04353 | 0.116631 | 0.0583153 | − | 0.998298i | \(-0.481427\pi\) | ||||
0.0583153 | + | 0.998298i | \(0.481427\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.09047 | 0.232699 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5423 | 0.938026 | 0.469013 | − | 0.883191i | \(-0.344610\pi\) | ||||
0.469013 | + | 0.883191i | \(0.344610\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.304714 | −0.0172235 | −0.00861174 | − | 0.999963i | \(-0.502741\pi\) | ||||
−0.00861174 | + | 0.999963i | \(0.502741\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.17267 | 0.235103 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.5420 | −0.704428 | −0.352214 | − | 0.935919i | \(-0.614571\pi\) | ||||
−0.352214 | + | 0.935919i | \(0.614571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 19.7259 | 1.10444 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.2461 | 0.627695 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.03532 | −0.224531 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.34423 | 0.518325 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.9901 | −0.884255 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 11.1921 | 0.617039 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.32409 | −0.127744 | −0.0638718 | − | 0.997958i | \(-0.520345\pi\) | ||||
−0.0638718 | + | 0.997958i | \(0.520345\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.61307 | 0.526793 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.9719 | 1.09118 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.42488 | −0.349986 | −0.174993 | − | 0.984570i | \(-0.555990\pi\) | ||||
−0.174993 | + | 0.984570i | \(0.555990\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.33778 | −0.344221 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.2125 | −1.52779 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.8882 | 0.965874 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.49349 | −0.0804068 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.7362 | −1.22054 | −0.610271 | − | 0.792193i | \(-0.708940\pi\) | ||||
−0.610271 | + | 0.792193i | \(0.708940\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.9408 | 0.746236 | 0.373118 | − | 0.927784i | \(-0.378289\pi\) | ||||
0.373118 | + | 0.927784i | \(0.378289\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.94514 | 0.210576 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.21088 | 0.437021 | 0.218511 | − | 0.975835i | \(-0.429880\pi\) | ||||
0.218511 | + | 0.975835i | \(0.429880\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.15330 | −0.379658 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.21738 | −0.170282 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −33.3585 | −1.76059 | −0.880297 | − | 0.474423i | \(-0.842657\pi\) | ||||
−0.880297 | + | 0.474423i | \(0.842657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2830 | −0.804367 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.395928 | 0.0207808 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −37.6274 | −1.96951 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.9325 | 1.82346 | 0.911730 | − | 0.410789i | \(-0.134747\pi\) | ||||
0.911730 | + | 0.410789i | \(0.134747\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.4801 | −0.597629 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.58604 | −0.497682 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.8544 | −1.13158 | −0.565789 | − | 0.824550i | \(-0.691428\pi\) | ||||
−0.565789 | + | 0.824550i | \(0.691428\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7.14311 | 0.368868 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 23.0528 | 1.18728 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.7463 | −1.21976 | −0.609881 | − | 0.792493i | \(-0.708783\pi\) | ||||
−0.609881 | + | 0.792493i | \(0.708783\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.52367 | −0.0780601 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.03462 | −0.257257 | −0.128628 | − | 0.991693i | \(-0.541057\pi\) | ||||
−0.128628 | + | 0.991693i | \(0.541057\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.0860 | 0.717890 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.25876 | −0.114819 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.05244 | 0.104063 | 0.0520313 | − | 0.998645i | \(-0.483430\pi\) | ||||
0.0520313 | + | 0.998645i | \(0.483430\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.15157 | 0.0582376 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.7658 | 1.04749 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.51969 | −0.378357 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.59868 | −0.230801 | −0.115400 | − | 0.993319i | \(-0.536815\pi\) | ||||
−0.115400 | + | 0.993319i | \(0.536815\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.96361 | 0.148366 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.33823 | 0.366454 | 0.183227 | − | 0.983071i | \(-0.441346\pi\) | ||||
0.183227 | + | 0.983071i | \(0.441346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.9708 | −1.64239 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.71451 | −0.134885 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.4516 | 1.60857 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.6193 | −1.71181 | −0.855907 | − | 0.517130i | \(-0.827001\pi\) | ||||
−0.855907 | + | 0.517130i | \(0.827001\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.4083 | 0.562732 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.952549 | −0.0468719 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.2254 | −0.551035 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.71570 | 0.132988 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.0494 | 1.07719 | 0.538593 | − | 0.842566i | \(-0.318956\pi\) | ||||
0.538593 | + | 0.842566i | \(0.318956\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.7226 | −0.571323 | −0.285661 | − | 0.958331i | \(-0.592213\pi\) | ||||
−0.285661 | + | 0.958331i | \(0.592213\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.28095 | −0.354012 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.95749 | 0.240473 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.2364 | −1.07610 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.3179 | 0.642996 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.2016 | 1.35842 | 0.679212 | − | 0.733942i | \(-0.262321\pi\) | ||||
0.679212 | + | 0.733942i | \(0.262321\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.97163 | −0.0947503 | −0.0473751 | − | 0.998877i | \(-0.515086\pi\) | ||||
−0.0473751 | + | 0.998877i | \(0.515086\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −15.8618 | −0.760516 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.06074 | −0.0507422 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.84816 | −0.326845 | −0.163422 | − | 0.986556i | \(-0.552253\pi\) | ||||
−0.163422 | + | 0.986556i | \(0.552253\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.63710 | −0.220814 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.0831 | −1.38178 | −0.690890 | − | 0.722960i | \(-0.742781\pi\) | ||||
−0.690890 | + | 0.722960i | \(0.742781\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.5551 | 1.59066 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.6937 | 0.505796 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.5580 | −1.39493 | −0.697463 | − | 0.716621i | \(-0.745688\pi\) | ||||
−0.697463 | + | 0.716621i | \(0.745688\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −38.7543 | −1.82487 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.5063 | −0.493627 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 16.4617 | 0.771738 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.44120 | −0.348085 | −0.174042 | − | 0.984738i | \(-0.555683\pi\) | ||||
−0.174042 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.09305 | 0.0976953 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.0065 | −0.792071 | −0.396036 | − | 0.918235i | \(-0.629614\pi\) | ||||
−0.396036 | + | 0.918235i | \(0.629614\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.9204 | −1.01873 | −0.509363 | − | 0.860552i | \(-0.670119\pi\) | ||||
−0.509363 | + | 0.860552i | \(0.670119\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.6860 | 1.05204 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.0467 | −0.603729 | −0.301864 | − | 0.953351i | \(-0.597609\pi\) | ||||
−0.301864 | + | 0.953351i | \(0.597609\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3097 | 0.522233 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.3552 | −0.477143 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.62508 | −0.350601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.56646 | −0.209523 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.23615 | 0.285534 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.6455 | 0.943319 | 0.471660 | − | 0.881781i | \(-0.343655\pi\) | ||||
0.471660 | + | 0.881781i | \(0.343655\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 37.9249 | 1.72923 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.845735 | −0.0384823 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −28.5674 | −1.29718 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.6425 | 1.29792 | 0.648958 | − | 0.760824i | \(-0.275205\pi\) | ||||
0.648958 | + | 0.760824i | \(0.275205\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.33893 | −0.286657 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.3406 | 0.692313 | 0.346157 | − | 0.938177i | \(-0.387487\pi\) | ||||
0.346157 | + | 0.938177i | \(0.387487\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.2305 | 0.550832 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.16359 | −0.411873 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.05078 | −0.181702 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.5833 | −0.787137 | −0.393568 | − | 0.919295i | \(-0.628760\pi\) | ||||
−0.393568 | + | 0.919295i | \(0.628760\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.395120 | 0.0176527 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −41.1612 | −1.83165 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.56411 | 0.113876 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.3822 | 1.03640 | 0.518200 | − | 0.855260i | \(-0.326602\pi\) | ||||
0.518200 | + | 0.855260i | \(0.326602\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.3077 | −0.942595 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.92796 | −0.0851216 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.1036 | −0.489284 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −24.5789 | −1.08098 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.3781 | 0.762812 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.77654 | −0.209264 | −0.104632 | − | 0.994511i | \(-0.533366\pi\) | ||||
−0.104632 | + | 0.994511i | \(0.533366\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.6939 | 1.77942 | 0.889710 | − | 0.456526i | \(-0.150906\pi\) | ||||
0.889710 | + | 0.456526i | \(0.150906\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.64086 | −0.158900 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.4923 | −0.761977 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6973 | −0.986839 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.619676 | 0.0268917 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −45.2905 | −1.96175 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.5276 | −1.31982 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.15569 | −0.136178 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.6539 | −0.674259 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.8769 | 0.725596 | 0.362798 | − | 0.931868i | \(-0.381821\pi\) | ||||
0.362798 | + | 0.931868i | \(0.381821\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.9671 | 0.599387 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 43.4053 | 1.85928 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.0868 | −1.50020 | −0.750102 | − | 0.661323i | \(-0.769995\pi\) | ||||
−0.750102 | + | 0.661323i | \(0.769995\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.4658 | 0.617385 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.2658 | −0.479938 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.25826 | −0.181080 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −26.0947 | −1.10766 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.1312 | 0.556389 | 0.278194 | − | 0.960525i | \(-0.410264\pi\) | ||||
0.278194 | + | 0.960525i | \(0.410264\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.91110 | −0.376900 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.06570 | 0.298314 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.5270 | 0.570095 | 0.285047 | − | 0.958513i | \(-0.407991\pi\) | ||||
0.285047 | + | 0.958513i | \(0.407991\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.2040 | 0.723776 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.53717 | −0.0645552 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.5449 | −0.442064 | −0.221032 | − | 0.975267i | \(-0.570943\pi\) | ||||
−0.221032 | + | 0.975267i | \(0.570943\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.8265 | −1.45744 | −0.728721 | − | 0.684811i | \(-0.759885\pi\) | ||||
−0.728721 | + | 0.684811i | \(0.759885\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.7722 | −0.742442 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.30314 | 0.0543449 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.7659 | 0.822865 | 0.411432 | − | 0.911440i | \(-0.365029\pi\) | ||||
0.411432 | + | 0.911440i | \(0.365029\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.00421 | 0.332643 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.35675 | −0.263722 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.0519 | 0.871880 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.7091 | −0.442767 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −37.0343 | −1.52857 | −0.764285 | − | 0.644878i | \(-0.776908\pi\) | ||||
−0.764285 | + | 0.644878i | \(0.776908\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.1126 | 0.663908 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.1777 | 0.459788 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.72990 | 0.358494 | 0.179247 | − | 0.983804i | \(-0.442634\pi\) | ||||
0.179247 | + | 0.983804i | \(0.442634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.73361 | 0.358043 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.15795 | 0.292955 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27.3967 | −1.11940 | −0.559699 | − | 0.828696i | \(-0.689083\pi\) | ||||
−0.559699 | + | 0.828696i | \(0.689083\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.6974 | 1.33376 | 0.666878 | − | 0.745167i | \(-0.267630\pi\) | ||||
0.666878 | + | 0.745167i | \(0.267630\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.35747 | −0.299619 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.07475 | −0.0436948 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.1537 | −1.10213 | −0.551067 | − | 0.834461i | \(-0.685779\pi\) | ||||
−0.551067 | + | 0.834461i | \(0.685779\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.98225 | −0.363979 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −28.7243 | −1.16206 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.7922 | 1.64758 | 0.823791 | − | 0.566894i | \(-0.191855\pi\) | ||||
0.823791 | + | 0.566894i | \(0.191855\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 31.1627 | 1.25660 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.0594 | 0.928336 | 0.464168 | − | 0.885747i | \(-0.346353\pi\) | ||||
0.464168 | + | 0.885747i | \(0.346353\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.6326 | 0.748908 | 0.374454 | − | 0.927246i | \(-0.377830\pi\) | ||||
0.374454 | + | 0.927246i | \(0.377830\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.550188 | 0.0220783 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 19.0016 | 0.761283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2327 | −1.24931 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.50838 | −0.259920 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.1207 | 0.802263 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.2473 | −0.766222 | −0.383111 | − | 0.923702i | \(-0.625147\pi\) | ||||
−0.383111 | + | 0.923702i | \(0.625147\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 16.2867 | 0.647338 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.13602 | 0.164133 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.2940 | −0.724834 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.63521 | 0.104247 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.0701 | −1.70117 | −0.850584 | − | 0.525840i | \(-0.823751\pi\) | ||||
−0.850584 | + | 0.525840i | \(0.823751\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.1497 | −1.62279 | −0.811393 | − | 0.584502i | \(-0.801290\pi\) | ||||
−0.811393 | + | 0.584502i | \(0.801290\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.13141 | 0.241424 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.4482 | 0.410761 | 0.205380 | − | 0.978682i | \(-0.434157\pi\) | ||||
0.205380 | + | 0.978682i | \(0.434157\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.09189 | 0.0821140 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.8467 | 0.503500 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.1008 | 1.53013 | 0.765066 | − | 0.643952i | \(-0.222706\pi\) | ||||
0.765066 | + | 0.643952i | \(0.222706\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −56.3688 | −2.20251 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 13.8616 | 0.540792 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.40413 | 0.171561 | 0.0857803 | − | 0.996314i | \(-0.472662\pi\) | ||||
0.0857803 | + | 0.996314i | \(0.472662\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.4676 | −0.679411 | −0.339706 | − | 0.940532i | \(-0.610327\pi\) | ||||
−0.339706 | + | 0.940532i | \(0.610327\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 8.25738 | 0.320690 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.04474 | −0.311961 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.21495 | 0.124483 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.74204 | −0.106013 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.8335 | 1.88519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0200 | −0.424790 | −0.212395 | − | 0.977184i | \(-0.568126\pi\) | ||||
−0.212395 | + | 0.977184i | \(0.568126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.36854 | 0.0911653 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.5546 | −1.17431 | −0.587154 | − | 0.809476i | \(-0.699752\pi\) | ||||
−0.587154 | + | 0.809476i | \(0.699752\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.1772 | −0.620824 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.70484 | 0.333570 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.71406 | −0.0655867 | −0.0327934 | − | 0.999462i | \(-0.510440\pi\) | ||||
−0.0327934 | + | 0.999462i | \(0.510440\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −30.9680 | −1.18323 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −23.0163 | −0.878128 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.6025 | 0.937279 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.6363 | −1.27959 | −0.639793 | − | 0.768547i | \(-0.720980\pi\) | ||||
−0.639793 | + | 0.768547i | \(0.720980\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.18917 | −0.197120 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.37177 | −0.279627 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0284 | −0.910141 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12.5846 | −0.475995 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.76444 | 0.255489 | 0.127745 | − | 0.991807i | \(-0.459226\pi\) | ||||
0.127745 | + | 0.991807i | \(0.459226\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.5336 | −0.699008 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.7642 | 0.744362 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.3088 | −0.876618 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.0188 | −0.714265 | −0.357132 | − | 0.934054i | \(-0.616245\pi\) | ||||
−0.357132 | + | 0.934054i | \(0.616245\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.77019 | 0.103890 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.59810 | −0.172200 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.1516 | −1.35199 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.2452 | 0.756071 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 40.0401 | 1.49324 | 0.746622 | − | 0.665249i | \(-0.231674\pi\) | ||||
0.746622 | + | 0.665249i | \(0.231674\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.28776 | −0.234169 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.77341 | −0.289096 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13.8402 | 0.514014 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.68094 | 0.321958 | 0.160979 | − | 0.986958i | \(-0.448535\pi\) | ||||
0.160979 | + | 0.986958i | \(0.448535\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.72770 | −0.174860 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.8498 | 1.25027 | 0.625136 | − | 0.780516i | \(-0.285044\pi\) | ||||
0.625136 | + | 0.780516i | \(0.285044\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.5874 | 0.464294 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.8372 | −0.914891 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 26.5103 | 0.975197 | 0.487599 | − | 0.873068i | \(-0.337873\pi\) | ||||
0.487599 | + | 0.873068i | \(0.337873\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.60607 | −0.279416 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.7990 | −1.57014 | −0.785071 | − | 0.619405i | \(-0.787374\pi\) | ||||
−0.785071 | + | 0.619405i | \(0.787374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −29.0282 | −1.06351 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.13535 | 0.151305 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.2872 | −0.631660 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.7938 | 1.30613 | 0.653067 | − | 0.757300i | \(-0.273482\pi\) | ||||
0.653067 | + | 0.757300i | \(0.273482\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.3141 | 1.10471 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.5193 | 1.03792 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0664 | −0.547597 | −0.273799 | − | 0.961787i | \(-0.588280\pi\) | ||||
−0.273799 | + | 0.961787i | \(0.588280\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.85732 | 0.0674164 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.20573 | −0.0799578 | −0.0399789 | − | 0.999201i | \(-0.512729\pi\) | ||||
−0.0399789 | + | 0.999201i | \(0.512729\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.5796 | 0.889840 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.68160 | −0.205419 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.44471 | 0.0882733 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.1805 | 0.367119 | 0.183559 | − | 0.983009i | \(-0.441238\pi\) | ||||
0.183559 | + | 0.983009i | \(0.441238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.4899 | 1.02604 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.56876 | 0.164327 | 0.0821635 | − | 0.996619i | \(-0.473817\pi\) | ||||
0.0821635 | + | 0.996619i | \(0.473817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.7947 | −0.711046 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.7769 | −0.530120 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 22.1331 | 0.793002 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.89591 | 0.318321 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.84336 | 0.208825 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.1093 | 1.00326 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5764 | 0.377008 | 0.188504 | − | 0.982072i | \(-0.439636\pi\) | ||||
0.188504 | + | 0.982072i | \(0.439636\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 20.3946 | 0.726067 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.74227 | 0.346395 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 57.0696 | 2.02660 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −16.9281 | −0.600376 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.8051 | −0.489003 | −0.244501 | − | 0.969649i | \(-0.578624\pi\) | ||||
−0.244501 | + | 0.969649i | \(0.578624\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.2394 | −0.539132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.3614 | −0.436768 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 46.7937 | 1.65132 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.29575 | 0.0809146 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.4449 | 0.649293 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.857865 | −0.0301609 | −0.0150805 | − | 0.999886i | \(-0.504800\pi\) | ||||
−0.0150805 | + | 0.999886i | \(0.504800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.8986 | 0.944536 | 0.472268 | − | 0.881455i | \(-0.343435\pi\) | ||||
0.472268 | + | 0.881455i | \(0.343435\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.8716 | 0.521570 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.2071 | 0.602738 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.35479 | 0.152355 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.06436 | −0.211906 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −32.4200 | −1.13147 | −0.565733 | − | 0.824588i | \(-0.691407\pi\) | ||||
−0.565733 | + | 0.824588i | \(0.691407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.6923 | 1.06986 | 0.534932 | − | 0.844895i | \(-0.320337\pi\) | ||||
0.534932 | + | 0.844895i | \(0.320337\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.99569 | 0.278374 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.7231 | −0.442427 | −0.221214 | − | 0.975225i | \(-0.571002\pi\) | ||||
−0.221214 | + | 0.975225i | \(0.571002\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.2117 | 1.67446 | 0.837231 | − | 0.546849i | \(-0.184173\pi\) | ||||
0.837231 | + | 0.546849i | \(0.184173\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 28.8774 | 1.00175 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.70569 | −0.336282 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.07256 | −0.0371173 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.35732 | −0.288871 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.9341 | 1.68939 | 0.844696 | − | 0.535247i | \(-0.179781\pi\) | ||||
0.844696 | + | 0.535247i | \(0.179781\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.14481 | 0.177407 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 30.1244 | 1.03754 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.96030 | −0.239441 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.608610 | −0.0209121 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.93521 | −0.0664164 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.28900 | 0.181304 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.43338 | 0.117557 | 0.0587783 | − | 0.998271i | \(-0.481279\pi\) | ||||
0.0587783 | + | 0.998271i | \(0.481279\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.23346 | 0.178981 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.2818 | −0.487857 | −0.243929 | − | 0.969793i | \(-0.578436\pi\) | ||||
−0.243929 | + | 0.969793i | \(0.578436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.155049 | 0.00529020 | 0.00264510 | − | 0.999997i | \(-0.499158\pi\) | ||||
0.00264510 | + | 0.999997i | \(0.499158\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 17.6469 | 0.601404 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.3250 | −1.37268 | −0.686339 | − | 0.727282i | \(-0.740783\pi\) | ||||
−0.686339 | + | 0.727282i | \(0.740783\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47.1728 | −1.60392 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.6191 | −0.428568 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.35156 | 0.317230 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −29.0262 | −0.983516 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.5240 | 0.356183 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.9802 | −0.371198 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.0702 | −0.779025 | −0.389513 | − | 0.921021i | \(-0.627357\pi\) | ||||
−0.389513 | + | 0.921021i | \(0.627357\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.9502 | 0.403071 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.0445 | 1.41652 | 0.708258 | − | 0.705954i | \(-0.249481\pi\) | ||||
0.708258 | + | 0.705954i | \(0.249481\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.215055 | −0.00723719 | −0.00361860 | − | 0.999993i | \(-0.501152\pi\) | ||||
−0.00361860 | + | 0.999993i | \(0.501152\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.68211 | −0.0565437 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.4124 | −1.02115 | −0.510575 | − | 0.859833i | \(-0.670567\pi\) | ||||
−0.510575 | + | 0.859833i | \(0.670567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.34215 | 0.0785531 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.37579 | 0.113093 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.0374 | 0.469743 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.56614 | 0.286334 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.17057 | 0.0724732 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −48.8348 | −1.62873 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.0526 | 0.434845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.47210 | 0.115544 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −37.9139 | −1.26030 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −54.7078 | −1.81654 | −0.908271 | − | 0.418381i | \(-0.862598\pi\) | ||||
−0.908271 | + | 0.418381i | \(0.862598\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.1634 | 0.502939 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.8367 | −1.81682 | −0.908410 | − | 0.418080i | \(-0.862703\pi\) | ||||
−0.908410 | + | 0.418080i | \(0.862703\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.9601 | 0.462011 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −39.2675 | −1.29814 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −31.9206 | −1.05411 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10.2671 | 0.338680 | 0.169340 | − | 0.985558i | \(-0.445836\pi\) | ||||
0.169340 | + | 0.985558i | \(0.445836\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.04353 | 0.0673367 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.3963 | 0.342197 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22.7690 | 0.748639 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.09047 | 0.134349 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.5010 | 1.16475 | 0.582375 | − | 0.812920i | \(-0.302124\pi\) | ||||
0.582375 | + | 0.812920i | \(0.302124\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.94015 | 0.293001 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 16.5423 | 0.541570 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.1799 | −0.627249 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.1731 | −1.27973 | −0.639865 | − | 0.768488i | \(-0.721010\pi\) | ||||
−0.639865 | + | 0.768488i | \(0.721010\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.304714 | −0.00994398 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.8375 | 1.00527 | 0.502637 | − | 0.864498i | \(-0.332363\pi\) | ||||
0.502637 | + | 0.864498i | \(0.332363\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.31621 | −0.205684 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.17267 | 0.135737 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −43.3454 | −1.40854 | −0.704269 | − | 0.709934i | \(-0.748725\pi\) | ||||
−0.704269 | + | 0.709934i | \(0.748725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 54.6859 | 1.77518 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.5420 | −0.406702 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −34.2923 | −1.11084 | −0.555418 | − | 0.831571i | \(-0.687442\pi\) | ||||
−0.555418 | + | 0.831571i | \(0.687442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 48.2426 | 1.56109 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 19.7259 | 0.637648 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.5366 | −0.566287 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38.8449 | 1.25306 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.2461 | 0.362400 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.7275 | −0.699432 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.9359 | −0.512464 | −0.256232 | − | 0.966615i | \(-0.582481\pi\) | ||||
−0.256232 | + | 0.966615i | \(0.582481\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.03532 | −0.129633 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.60353 | −0.179826 | −0.0899130 | − | 0.995950i | \(-0.528659\pi\) | ||||
−0.0899130 | + | 0.995950i | \(0.528659\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.17449 | −0.133828 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.34423 | 0.299255 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.31006 | −0.137891 | −0.0689454 | − | 0.997620i | \(-0.521963\pi\) | ||||
−0.0689454 | + | 0.997620i | \(0.521963\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.7294 | −1.33368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15.9901 | −0.510525 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43.5685 | −1.38962 | −0.694809 | − | 0.719194i | \(-0.744511\pi\) | ||||
−0.694809 | + | 0.719194i | \(0.744511\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.3419 | −0.966772 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11.1921 | 0.356248 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.24274 | −0.0395169 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.3251 | −1.24920 | −0.624602 | − | 0.780944i | \(-0.714739\pi\) | ||||
−0.624602 | + | 0.780944i | \(0.714739\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.32409 | −0.0737527 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.4303 | −0.615982 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.5764 | −1.47509 | −0.737545 | − | 0.675298i | \(-0.764015\pi\) | ||||
−0.737545 | + | 0.675298i | \(0.764015\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.61307 | 0.304144 |
(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 | 6036.2.a.h.1.4 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.h.1.4 | ✓ | 24 | 1.1 | even | 1 | trivial |