Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4500,2,Mod(1,4500)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4500, 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("4500.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4500 = 2^{2} \cdot 3^{2} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4500.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: | \(35.9326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.12400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 12x^{2} + 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 500) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.86986\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4500.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.64352 | −1.75509 | −0.877543 | − | 0.479497i | \(-0.840819\pi\) | ||||
−0.877543 | + | 0.479497i | \(0.840819\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.47214 | −1.34840 | −0.674200 | − | 0.738549i | \(-0.735511\pi\) | ||||
−0.674200 | + | 0.738549i | \(0.735511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.73971 | 1.59191 | 0.795955 | − | 0.605356i | \(-0.206969\pi\) | ||||
0.795955 | + | 0.605356i | \(0.206969\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.54734 | −0.860355 | −0.430178 | − | 0.902744i | \(-0.641549\pi\) | ||||
−0.430178 | + | 0.902744i | \(0.641549\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.23607 | −0.283573 | −0.141787 | − | 0.989897i | \(-0.545285\pi\) | ||||
−0.141787 | + | 0.989897i | \(0.545285\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.09619 | 0.228571 | 0.114285 | − | 0.993448i | \(-0.463542\pi\) | ||||
0.114285 | + | 0.993448i | \(0.463542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.61803 | −0.857547 | −0.428774 | − | 0.903412i | \(-0.641054\pi\) | ||||
−0.428774 | + | 0.903412i | \(0.641054\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.19237 | −0.360424 | −0.180212 | − | 0.983628i | \(-0.557678\pi\) | ||||
−0.180212 | + | 0.983628i | \(0.557678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.61803 | 0.408868 | 0.204434 | − | 0.978880i | \(-0.434465\pi\) | ||||
0.204434 | + | 0.978880i | \(0.434465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.96604 | −0.604816 | −0.302408 | − | 0.953179i | \(-0.597790\pi\) | ||||
−0.302408 | + | 0.953179i | \(0.597790\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.51338 | −1.09594 | −0.547969 | − | 0.836498i | \(-0.684599\pi\) | ||||
−0.547969 | + | 0.836498i | \(0.684599\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.5623 | 2.08033 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.4794 | −1.57682 | −0.788410 | − | 0.615150i | \(-0.789095\pi\) | ||||
−0.788410 | + | 0.615150i | \(0.789095\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.4721 | 1.62373 | 0.811867 | − | 0.583843i | \(-0.198451\pi\) | ||||
0.811867 | + | 0.583843i | \(0.198451\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.14590 | 0.146717 | 0.0733586 | − | 0.997306i | \(-0.476628\pi\) | ||||
0.0733586 | + | 0.997306i | \(0.476628\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.19237 | −0.267841 | −0.133921 | − | 0.990992i | \(-0.542757\pi\) | ||||
−0.133921 | + | 0.990992i | \(0.542757\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.23607 | −0.621407 | −0.310703 | − | 0.950507i | \(-0.600565\pi\) | ||||
−0.310703 | + | 0.950507i | \(0.600565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.73971 | 0.671782 | 0.335891 | − | 0.941901i | \(-0.390963\pi\) | ||||
0.335891 | + | 0.941901i | \(0.390963\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 20.7665 | 2.36656 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.70820 | 1.09226 | 0.546129 | − | 0.837701i | \(-0.316101\pi\) | ||||
0.546129 | + | 0.837701i | \(0.316101\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.83590 | −0.750337 | −0.375169 | − | 0.926957i | \(-0.622415\pi\) | ||||
−0.375169 | + | 0.926957i | \(0.622415\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3262 | 1.20058 | 0.600289 | − | 0.799783i | \(-0.295052\pi\) | ||||
0.600289 | + | 0.799783i | \(0.295052\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26.6525 | −2.79394 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.73971 | 0.582779 | 0.291390 | − | 0.956604i | \(-0.405882\pi\) | ||||
0.291390 | + | 0.956604i | \(0.405882\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 19.3262 | 1.92303 | 0.961516 | − | 0.274748i | \(-0.0885944\pi\) | ||||
0.961516 | + | 0.274748i | \(0.0885944\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.28705 | −0.915080 | −0.457540 | − | 0.889189i | \(-0.651269\pi\) | ||||
−0.457540 | + | 0.889189i | \(0.651269\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.418706 | 0.0404779 | 0.0202389 | − | 0.999795i | \(-0.493557\pi\) | ||||
0.0202389 | + | 0.999795i | \(0.493557\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.3820 | 1.28176 | 0.640880 | − | 0.767641i | \(-0.278570\pi\) | ||||
0.640880 | + | 0.767641i | \(0.278570\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2191 | 1.61984 | 0.809920 | − | 0.586541i | \(-0.199511\pi\) | ||||
0.809920 | + | 0.586541i | \(0.199511\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.4721 | 1.51000 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6080 | 1.29625 | 0.648127 | − | 0.761532i | \(-0.275552\pi\) | ||||
0.648127 | + | 0.761532i | \(0.275552\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.23607 | 0.632218 | 0.316109 | − | 0.948723i | \(-0.397623\pi\) | ||||
0.316109 | + | 0.948723i | \(0.397623\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.73971 | 0.497696 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.0268 | −1.28382 | −0.641911 | − | 0.766779i | \(-0.721858\pi\) | ||||
−0.641911 | + | 0.766779i | \(0.721858\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.29180 | −0.194388 | −0.0971938 | − | 0.995265i | \(-0.530987\pi\) | ||||
−0.0971938 | + | 0.995265i | \(0.530987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.6688 | −2.14653 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.32624 | −0.764035 | −0.382018 | − | 0.924155i | \(-0.624771\pi\) | ||||
−0.382018 | + | 0.924155i | \(0.624771\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.70820 | −0.139012 | −0.0695058 | − | 0.997582i | \(-0.522142\pi\) | ||||
−0.0695058 | + | 0.997582i | \(0.522142\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0268 | 1.19927 | 0.599633 | − | 0.800275i | \(-0.295313\pi\) | ||||
0.599633 | + | 0.800275i | \(0.295313\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.09017 | −0.401162 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.2855 | 1.19726 | 0.598628 | − | 0.801027i | \(-0.295713\pi\) | ||||
0.598628 | + | 0.801027i | \(0.295713\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.77367 | 0.137251 | 0.0686253 | − | 0.997643i | \(-0.478139\pi\) | ||||
0.0686253 | + | 0.997643i | \(0.478139\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.9443 | 1.53417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.1214 | 1.68186 | 0.840931 | − | 0.541143i | \(-0.182008\pi\) | ||||
0.840931 | + | 0.541143i | \(0.182008\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.52786 | −0.263685 | −0.131842 | − | 0.991271i | \(-0.542089\pi\) | ||||
−0.131842 | + | 0.991271i | \(0.542089\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.43769 | 0.181192 | 0.0905962 | − | 0.995888i | \(-0.471123\pi\) | ||||
0.0905962 | + | 0.995888i | \(0.471123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8642 | 1.16010 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.65248 | −0.626071 | −0.313036 | − | 0.949741i | \(-0.601346\pi\) | ||||
−0.313036 | + | 0.949741i | \(0.601346\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.28705 | 0.668496 | 0.334248 | − | 0.942485i | \(-0.391518\pi\) | ||||
0.334248 | + | 0.942485i | \(0.391518\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.6420 | 0.758212 | 0.379106 | − | 0.925353i | \(-0.376232\pi\) | ||||
0.379106 | + | 0.925353i | \(0.376232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.7082 | 1.39708 | 0.698539 | − | 0.715572i | \(-0.253834\pi\) | ||||
0.698539 | + | 0.715572i | \(0.253834\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.4439 | 1.50507 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.52786 | 0.382370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.29180 | 0.157774 | 0.0788869 | − | 0.996884i | \(-0.474863\pi\) | ||||
0.0788869 | + | 0.996884i | \(0.474863\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −27.8611 | −1.89134 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.3607 | −1.36961 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.8004 | −1.12504 | −0.562520 | − | 0.826784i | \(-0.690168\pi\) | ||||
−0.562520 | + | 0.826784i | \(0.690168\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.83590 | 0.453714 | 0.226857 | − | 0.973928i | \(-0.427155\pi\) | ||||
0.226857 | + | 0.973928i | \(0.427155\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.85410 | 0.320768 | 0.160384 | − | 0.987055i | \(-0.448727\pi\) | ||||
0.160384 | + | 0.987055i | \(0.448727\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −19.4115 | −1.27169 | −0.635845 | − | 0.771817i | \(-0.719348\pi\) | ||||
−0.635845 | + | 0.771817i | \(0.719348\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.2918 | −0.924459 | −0.462230 | − | 0.886760i | \(-0.652950\pi\) | ||||
−0.462230 | + | 0.886760i | \(0.652950\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.3820 | 1.31292 | 0.656459 | − | 0.754362i | \(-0.272054\pi\) | ||||
0.656459 | + | 0.754362i | \(0.272054\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.09467 | −0.451423 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.90230 | −0.308205 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.1893 | 0.885107 | 0.442553 | − | 0.896742i | \(-0.354073\pi\) | ||||
0.442553 | + | 0.896742i | \(0.354073\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.1803 | 0.632576 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.77367 | −0.109369 | −0.0546845 | − | 0.998504i | \(-0.517415\pi\) | ||||
−0.0546845 | + | 0.998504i | \(0.517415\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.9443 | 0.667284 | 0.333642 | − | 0.942700i | \(-0.391722\pi\) | ||||
0.333642 | + | 0.942700i | \(0.391722\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.52786 | 0.335794 | 0.167897 | − | 0.985805i | \(-0.446302\pi\) | ||||
0.167897 | + | 0.985805i | \(0.446302\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.4115 | −1.16632 | −0.583162 | − | 0.812356i | \(-0.698185\pi\) | ||||
−0.583162 | + | 0.812356i | \(0.698185\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.0344 | 0.658260 | 0.329130 | − | 0.944285i | \(-0.393245\pi\) | ||||
0.329130 | + | 0.944285i | \(0.393245\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.28705 | −0.552058 | −0.276029 | − | 0.961149i | \(-0.589019\pi\) | ||||
−0.276029 | + | 0.961149i | \(0.589019\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.1569 | −0.717599 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.41641 | −0.259789 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.8344 | 0.749793 | 0.374896 | − | 0.927067i | \(-0.377678\pi\) | ||||
0.374896 | + | 0.927067i | \(0.377678\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.29180 | 0.363864 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.4164 | 1.06150 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.28856 | 0.187688 | 0.0938441 | − | 0.995587i | \(-0.470084\pi\) | ||||
0.0938441 | + | 0.995587i | \(0.470084\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −25.4164 | −1.44123 | −0.720616 | − | 0.693334i | \(-0.756141\pi\) | ||||
−0.720616 | + | 0.693334i | \(0.756141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.5741 | −1.04987 | −0.524935 | − | 0.851142i | \(-0.675910\pi\) | ||||
−0.524935 | + | 0.851142i | \(0.675910\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.3817 | −0.920089 | −0.460044 | − | 0.887896i | \(-0.652167\pi\) | ||||
−0.460044 | + | 0.887896i | \(0.652167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.6525 | 1.15632 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.38475 | 0.243974 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 34.8885 | 1.92347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.2918 | −0.565688 | −0.282844 | − | 0.959166i | \(-0.591278\pi\) | ||||
−0.282844 | + | 0.959166i | \(0.591278\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −27.8611 | −1.51769 | −0.758846 | − | 0.651270i | \(-0.774237\pi\) | ||||
−0.758846 | + | 0.651270i | \(0.774237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.8328 | −1.45308 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −35.1157 | −1.89607 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.2474 | −1.40903 | −0.704517 | − | 0.709687i | \(-0.748836\pi\) | ||||
−0.704517 | + | 0.709687i | \(0.748836\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −25.9787 | −1.39061 | −0.695304 | − | 0.718715i | \(-0.744730\pi\) | ||||
−0.695304 | + | 0.718715i | \(0.744730\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.73971 | 0.305494 | 0.152747 | − | 0.988265i | \(-0.451188\pi\) | ||||
0.152747 | + | 0.988265i | \(0.451188\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.9443 | 0.788729 | 0.394364 | − | 0.918954i | \(-0.370965\pi\) | ||||
0.394364 | + | 0.918954i | \(0.370965\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4721 | −0.919586 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.28856 | −0.171662 | −0.0858308 | − | 0.996310i | \(-0.527354\pi\) | ||||
−0.0858308 | + | 0.996310i | \(0.527354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 53.3050 | 2.76746 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.57712 | −0.340550 | −0.170275 | − | 0.985397i | \(-0.554466\pi\) | ||||
−0.170275 | + | 0.985397i | \(0.554466\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −26.5062 | −1.36514 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.3607 | 1.25132 | 0.625662 | − | 0.780094i | \(-0.284829\pi\) | ||||
0.625662 | + | 0.780094i | \(0.284829\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.3775 | 1.19454 | 0.597268 | − | 0.802041i | \(-0.296253\pi\) | ||||
0.597268 | + | 0.802041i | \(0.296253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.2148 | −0.619314 | −0.309657 | − | 0.950848i | \(-0.600214\pi\) | ||||
−0.309657 | + | 0.950848i | \(0.600214\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.88854 | −0.196652 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.6039 | 1.08427 | 0.542134 | − | 0.840292i | \(-0.317617\pi\) | ||||
0.542134 | + | 0.840292i | \(0.317617\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.4508 | 1.02127 | 0.510633 | − | 0.859799i | \(-0.329411\pi\) | ||||
0.510633 | + | 0.859799i | \(0.329411\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 34.4383 | 1.71549 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.80460 | 0.485996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.6180 | 0.970049 | 0.485025 | − | 0.874500i | \(-0.338811\pi\) | ||||
0.485025 | + | 0.874500i | \(0.338811\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −57.9147 | −2.84979 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.3607 | 0.799272 | 0.399636 | − | 0.916674i | \(-0.369137\pi\) | ||||
0.399636 | + | 0.916674i | \(0.369137\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.79837 | −0.428807 | −0.214403 | − | 0.976745i | \(-0.568781\pi\) | ||||
−0.214403 | + | 0.976745i | \(0.568781\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.32100 | −0.257501 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −23.2361 | −1.11924 | −0.559621 | − | 0.828749i | \(-0.689053\pi\) | ||||
−0.559621 | + | 0.828749i | \(0.689053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.9970 | −0.576538 | −0.288269 | − | 0.957550i | \(-0.593080\pi\) | ||||
−0.288269 | + | 0.957550i | \(0.593080\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.35496 | −0.0648166 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.1246 | 1.10368 | 0.551839 | − | 0.833951i | \(-0.313926\pi\) | ||||
0.551839 | + | 0.833951i | \(0.313926\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.02827 | 0.428946 | 0.214473 | − | 0.976730i | \(-0.431197\pi\) | ||||
0.214473 | + | 0.976730i | \(0.431197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7082 | −0.551318 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.1482 | −1.73772 | −0.868859 | − | 0.495059i | \(-0.835146\pi\) | ||||
−0.868859 | + | 0.495059i | \(0.835146\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.7984 | 1.38785 | 0.693924 | − | 0.720048i | \(-0.255880\pi\) | ||||
0.693924 | + | 0.720048i | \(0.255880\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.8627 | 1.01604 | 0.508022 | − | 0.861344i | \(-0.330377\pi\) | ||||
0.508022 | + | 0.861344i | \(0.330377\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.1497 | 1.44144 | 0.720718 | − | 0.693228i | \(-0.243812\pi\) | ||||
0.720718 | + | 0.693228i | \(0.243812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.1803 | 0.470084 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 17.7367 | 0.815533 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.2918 | −0.653009 | −0.326504 | − | 0.945196i | \(-0.605871\pi\) | ||||
−0.326504 | + | 0.945196i | \(0.605871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.5836 | −0.573762 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.32100 | 0.241118 | 0.120559 | − | 0.992706i | \(-0.461531\pi\) | ||||
0.120559 | + | 0.992706i | \(0.461531\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.18034 | −0.278915 | −0.139457 | − | 0.990228i | \(-0.544536\pi\) | ||||
−0.139457 | + | 0.990228i | \(0.544536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.3817 | 0.737795 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.3138 | 1.09062 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −39.1246 | −1.75146 | −0.875729 | − | 0.482803i | \(-0.839619\pi\) | ||||
−0.875729 | + | 0.482803i | \(0.839619\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 35.2146 | 1.57014 | 0.785070 | − | 0.619407i | \(-0.212627\pi\) | ||||
0.785070 | + | 0.619407i | \(0.212627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.5836 | 0.469109 | 0.234555 | − | 0.972103i | \(-0.424637\pi\) | ||||
0.234555 | + | 0.972103i | \(0.424637\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −26.6525 | −1.17904 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.6008 | 1.47776 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.9098 | 0.565590 | 0.282795 | − | 0.959180i | \(-0.408738\pi\) | ||||
0.282795 | + | 0.959180i | \(0.408738\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.51338 | 0.328537 | 0.164269 | − | 0.986416i | \(-0.447474\pi\) | ||||
0.164269 | + | 0.986416i | \(0.447474\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.2840 | −0.927146 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.7984 | −0.947755 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.0268 | 0.650881 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −65.1246 | −2.80512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.2705 | 1.43041 | 0.715205 | − | 0.698914i | \(-0.246333\pi\) | ||||
0.715205 | + | 0.698914i | \(0.246333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.5726 | 1.05065 | 0.525324 | − | 0.850902i | \(-0.323944\pi\) | ||||
0.525324 | + | 0.850902i | \(0.323944\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.70820 | 0.243178 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.0803 | −1.91701 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.7963 | 1.00828 | 0.504140 | − | 0.863622i | \(-0.331810\pi\) | ||||
0.504140 | + | 0.863622i | \(0.331810\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.7639 | −0.962812 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.6718 | −0.576197 | −0.288099 | − | 0.957601i | \(-0.593023\pi\) | ||||
−0.288099 | + | 0.957601i | \(0.593023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.9098 | 1.12812 | 0.564059 | − | 0.825734i | \(-0.309239\pi\) | ||||
0.564059 | + | 0.825734i | \(0.309239\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.3607 | −1.85644 | −0.928218 | − | 0.372036i | \(-0.878660\pi\) | ||||
−0.928218 | + | 0.372036i | \(0.878660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.70992 | −0.112816 | −0.0564078 | − | 0.998408i | \(-0.517965\pi\) | ||||
−0.0564078 | + | 0.998408i | \(0.517965\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 31.7426 | 1.31691 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 51.3375 | 2.12618 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.9558 | 1.44278 | 0.721390 | − | 0.692529i | \(-0.243503\pi\) | ||||
0.721390 | + | 0.692529i | \(0.243503\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.41641 | −0.305588 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.6718 | 0.561433 | 0.280717 | − | 0.959791i | \(-0.409428\pi\) | ||||
0.280717 | + | 0.959791i | \(0.409428\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.5967 | −0.800701 | −0.400351 | − | 0.916362i | \(-0.631112\pi\) | ||||
−0.400351 | + | 0.916362i | \(0.631112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.6869 | 1.74124 | 0.870618 | − | 0.491960i | \(-0.163719\pi\) | ||||
0.870618 | + | 0.491960i | \(0.163719\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.8611 | 1.13085 | 0.565424 | − | 0.824800i | \(-0.308712\pi\) | ||||
0.565424 | + | 0.824800i | \(0.308712\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −43.1246 | −1.74464 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.70992 | 0.109453 | 0.0547264 | − | 0.998501i | \(-0.482571\pi\) | ||||
0.0547264 | + | 0.998501i | \(0.482571\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22.1214 | 0.890575 | 0.445288 | − | 0.895388i | \(-0.353101\pi\) | ||||
0.445288 | + | 0.895388i | \(0.353101\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.76393 | −0.111092 | −0.0555459 | − | 0.998456i | \(-0.517690\pi\) | ||||
−0.0555459 | + | 0.998456i | \(0.517690\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −52.5936 | −2.10712 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.77709 | 0.310093 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.8328 | 1.14782 | 0.573908 | − | 0.818920i | \(-0.305427\pi\) | ||||
0.573908 | + | 0.818920i | \(0.305427\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 83.5834 | 3.31170 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.7426 | −1.01677 | −0.508387 | − | 0.861129i | \(-0.669758\pi\) | ||||
−0.508387 | + | 0.861129i | \(0.669758\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.5993 | 1.56165 | 0.780823 | − | 0.624753i | \(-0.214800\pi\) | ||||
0.780823 | + | 0.624753i | \(0.214800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −23.4764 | −0.922952 | −0.461476 | − | 0.887153i | \(-0.652680\pi\) | ||||
−0.461476 | + | 0.887153i | \(0.652680\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −55.7771 | −2.18944 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.3406 | −1.53952 | −0.769758 | − | 0.638336i | \(-0.779623\pi\) | ||||
−0.769758 | + | 0.638336i | \(0.779623\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.0689 | −0.781773 | −0.390886 | − | 0.920439i | \(-0.627831\pi\) | ||||
−0.390886 | + | 0.920439i | \(0.627831\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.61803 | 0.257412 | 0.128706 | − | 0.991683i | \(-0.458918\pi\) | ||||
0.128706 | + | 0.991683i | \(0.458918\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.06223 | −0.196010 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.12461 | −0.197833 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.0237 | −1.04169 | −0.520844 | − | 0.853652i | \(-0.674383\pi\) | ||||
−0.520844 | + | 0.853652i | \(0.674383\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.09467 | −0.272670 | −0.136335 | − | 0.990663i | \(-0.543532\pi\) | ||||
−0.136335 | + | 0.990663i | \(0.543532\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.6525 | −1.02283 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.77367 | 0.0678675 | 0.0339338 | − | 0.999424i | \(-0.489196\pi\) | ||||
0.0339338 | + | 0.999424i | \(0.489196\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −65.8885 | −2.51015 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.7082 | −1.28232 | −0.641160 | − | 0.767407i | \(-0.721547\pi\) | ||||
−0.641160 | + | 0.767407i | \(0.721547\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.28705 | −0.351772 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.88854 | 0.297946 | 0.148973 | − | 0.988841i | \(-0.452403\pi\) | ||||
0.148973 | + | 0.988841i | \(0.452403\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.70992 | 0.102207 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −89.7418 | −3.37509 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.49342 | 0.168754 | 0.0843770 | − | 0.996434i | \(-0.473110\pi\) | ||||
0.0843770 | + | 0.996434i | \(0.473110\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.57712 | 0.246315 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.0132 | 1.75329 | 0.876647 | − | 0.481133i | \(-0.159775\pi\) | ||||
0.876647 | + | 0.481133i | \(0.159775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.1246 | 1.60604 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1173 | −1.07990 | −0.539950 | − | 0.841697i | \(-0.681557\pi\) | ||||
−0.539950 | + | 0.841697i | \(0.681557\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.0689 | 0.520356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.5443 | −0.574142 | −0.287071 | − | 0.957909i | \(-0.592682\pi\) | ||||
−0.287071 | + | 0.957909i | \(0.592682\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.80460 | 0.361157 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.2918 | −0.672875 | −0.336437 | − | 0.941706i | \(-0.609222\pi\) | ||||
−0.336437 | + | 0.941706i | \(0.609222\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.3817 | 0.600987 | 0.300493 | − | 0.953784i | \(-0.402849\pi\) | ||||
0.300493 | + | 0.953784i | \(0.402849\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.94427 | −0.0710421 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.29180 | −0.0836288 | −0.0418144 | − | 0.999125i | \(-0.513314\pi\) | ||||
−0.0418144 | + | 0.999125i | \(0.513314\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.06489 | 0.147741 | 0.0738704 | − | 0.997268i | \(-0.476465\pi\) | ||||
0.0738704 | + | 0.997268i | \(0.476465\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.2705 | −1.31480 | −0.657402 | − | 0.753540i | \(-0.728345\pi\) | ||||
−0.657402 | + | 0.753540i | \(0.728345\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −62.1395 | −2.24960 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 71.5864 | 2.58484 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.4377 | 0.520637 | 0.260318 | − | 0.965523i | \(-0.416173\pi\) | ||||
0.260318 | + | 0.965523i | \(0.416173\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.80460 | −0.352647 | −0.176323 | − | 0.984332i | \(-0.556420\pi\) | ||||
−0.176323 | + | 0.984332i | \(0.556420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.23607 | −0.115944 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.4164 | 0.837905 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −44.1440 | −1.57356 | −0.786782 | − | 0.617231i | \(-0.788254\pi\) | ||||
−0.786782 | + | 0.617231i | \(0.788254\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −79.9574 | −2.84296 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.57712 | 0.233560 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 10.1245 | 0.358627 | 0.179313 | − | 0.983792i | \(-0.442612\pi\) | ||||
0.179313 | + | 0.983792i | \(0.442612\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.6525 | 0.942897 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.6688 | −0.905831 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.90983 | 0.278095 | 0.139047 | − | 0.990286i | \(-0.455596\pi\) | ||||
0.139047 | + | 0.990286i | \(0.455596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.832816 | 0.0292441 | 0.0146221 | − | 0.999893i | \(-0.495345\pi\) | ||||
0.0146221 | + | 0.999893i | \(0.495345\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.90230 | 0.171510 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.2148 | 0.949802 | 0.474901 | − | 0.880039i | \(-0.342484\pi\) | ||||
0.474901 | + | 0.880039i | \(0.342484\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.0565 | 0.629412 | 0.314706 | − | 0.949189i | \(-0.398094\pi\) | ||||
0.314706 | + | 0.949189i | \(0.398094\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.7665 | 0.722121 | 0.361060 | − | 0.932542i | \(-0.382415\pi\) | ||||
0.361060 | + | 0.932542i | \(0.382415\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.2016 | −0.805826 | −0.402913 | − | 0.915238i | \(-0.632002\pi\) | ||||
−0.402913 | + | 0.915238i | \(0.632002\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −51.6574 | −1.78982 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.2361 | 0.526007 | 0.263004 | − | 0.964795i | \(-0.415287\pi\) | ||||
0.263004 | + | 0.964795i | \(0.415287\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.67376 | −0.264612 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −41.7917 | −1.43598 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.40325 | −0.0823824 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.6688 | 0.878882 | 0.439441 | − | 0.898272i | \(-0.355177\pi\) | ||||
0.439441 | + | 0.898272i | \(0.355177\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −45.5978 | −1.55759 | −0.778796 | − | 0.627277i | \(-0.784169\pi\) | ||||
−0.778796 | + | 0.627277i | \(0.784169\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.8328 | −1.05200 | −0.526001 | − | 0.850484i | \(-0.676309\pi\) | ||||
−0.526001 | + | 0.850484i | \(0.676309\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.7650 | 0.911090 | 0.455545 | − | 0.890213i | \(-0.349444\pi\) | ||||
0.455545 | + | 0.890213i | \(0.349444\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −43.4164 | −1.47280 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.5836 | −0.426379 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.57712 | −0.222094 | −0.111047 | − | 0.993815i | \(-0.535420\pi\) | ||||
−0.111047 | + | 0.993815i | \(0.535420\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.97871 | 0.134046 | 0.0670231 | − | 0.997751i | \(-0.478650\pi\) | ||||
0.0670231 | + | 0.997751i | \(0.478650\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.9306 | 0.468801 | 0.234400 | − | 0.972140i | \(-0.424687\pi\) | ||||
0.234400 | + | 0.972140i | \(0.424687\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.28856 | 0.110419 | 0.0552095 | − | 0.998475i | \(-0.482417\pi\) | ||||
0.0552095 | + | 0.998475i | \(0.482417\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −67.8328 | −2.27504 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.28705 | 0.310779 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.7082 | −0.924120 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.7214 | 1.35663 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −58.1734 | −1.93162 | −0.965808 | − | 0.259257i | \(-0.916522\pi\) | ||||
−0.965808 | + | 0.259257i | \(0.916522\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.8328 | 1.48538 | 0.742689 | − | 0.669637i | \(-0.233550\pi\) | ||||
0.742689 | + | 0.669637i | \(0.233550\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.5711 | 1.01175 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.6008 | −1.10960 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.2361 | −0.436618 | −0.218309 | − | 0.975880i | \(-0.570054\pi\) | ||||
−0.218309 | + | 0.975880i | \(0.570054\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.0535 | −0.989223 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −29.5066 | −0.968079 | −0.484040 | − | 0.875046i | \(-0.660831\pi\) | ||||
−0.484040 | + | 0.875046i | \(0.660831\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.0000 | −0.589926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.5741 | −0.606789 | −0.303395 | − | 0.952865i | \(-0.598120\pi\) | ||||
−0.303395 | + | 0.952865i | \(0.598120\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.41641 | 0.0461736 | 0.0230868 | − | 0.999733i | \(-0.492651\pi\) | ||||
0.0230868 | + | 0.999733i | \(0.492651\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.86986 | 0.0934553 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.9630 | −0.518728 | −0.259364 | − | 0.965780i | \(-0.583513\pi\) | ||||
−0.259364 | + | 0.965780i | \(0.583513\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.9443 | 1.06942 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0535 | 0.973529 | 0.486764 | − | 0.873533i | \(-0.338177\pi\) | ||||
0.486764 | + | 0.873533i | \(0.338177\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 69.7771 | 2.25322 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.9547 | 0.963277 | 0.481639 | − | 0.876370i | \(-0.340042\pi\) | ||||
0.481639 | + | 0.876370i | \(0.340042\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.2361 | −1.38751 | −0.693756 | − | 0.720210i | \(-0.744045\pi\) | ||||
−0.693756 | + | 0.720210i | \(0.744045\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.6420 | 0.341167 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.8909 | −0.988288 | −0.494144 | − | 0.869380i | \(-0.664518\pi\) | ||||
−0.494144 | + | 0.869380i | \(0.664518\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −50.6525 | −1.61886 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.8611 | 0.888632 | 0.444316 | − | 0.895870i | \(-0.353447\pi\) | ||||
0.444316 | + | 0.895870i | \(0.353447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.34752 | −0.138243 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.7771 | −1.26356 | −0.631780 | − | 0.775147i | \(-0.717676\pi\) | ||||
−0.631780 | + | 0.775147i | \(0.717676\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.2161 | −0.925283 | −0.462642 | − | 0.886545i | \(-0.653098\pi\) | ||||
−0.462642 | + | 0.886545i | \(0.653098\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4500.2.a.q.1.1 | 4 | ||
3.2 | odd | 2 | 500.2.a.c.1.2 | ✓ | 4 | ||
5.2 | odd | 4 | 4500.2.d.e.4249.1 | 4 | |||
5.3 | odd | 4 | 4500.2.d.e.4249.4 | 4 | |||
5.4 | even | 2 | inner | 4500.2.a.q.1.4 | 4 | ||
12.11 | even | 2 | 2000.2.a.p.1.3 | 4 | |||
15.2 | even | 4 | 500.2.c.a.249.3 | 4 | |||
15.8 | even | 4 | 500.2.c.a.249.2 | 4 | |||
15.14 | odd | 2 | 500.2.a.c.1.3 | yes | 4 | ||
24.5 | odd | 2 | 8000.2.a.bl.1.3 | 4 | |||
24.11 | even | 2 | 8000.2.a.bm.1.2 | 4 | |||
60.23 | odd | 4 | 2000.2.c.a.1249.3 | 4 | |||
60.47 | odd | 4 | 2000.2.c.a.1249.2 | 4 | |||
60.59 | even | 2 | 2000.2.a.p.1.2 | 4 | |||
120.29 | odd | 2 | 8000.2.a.bl.1.2 | 4 | |||
120.59 | even | 2 | 8000.2.a.bm.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
500.2.a.c.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
500.2.a.c.1.3 | yes | 4 | 15.14 | odd | 2 | ||
500.2.c.a.249.2 | 4 | 15.8 | even | 4 | |||
500.2.c.a.249.3 | 4 | 15.2 | even | 4 | |||
2000.2.a.p.1.2 | 4 | 60.59 | even | 2 | |||
2000.2.a.p.1.3 | 4 | 12.11 | even | 2 | |||
2000.2.c.a.1249.2 | 4 | 60.47 | odd | 4 | |||
2000.2.c.a.1249.3 | 4 | 60.23 | odd | 4 | |||
4500.2.a.q.1.1 | 4 | 1.1 | even | 1 | trivial | ||
4500.2.a.q.1.4 | 4 | 5.4 | even | 2 | inner | ||
4500.2.d.e.4249.1 | 4 | 5.2 | odd | 4 | |||
4500.2.d.e.4249.4 | 4 | 5.3 | odd | 4 | |||
8000.2.a.bl.1.2 | 4 | 120.29 | odd | 2 | |||
8000.2.a.bl.1.3 | 4 | 24.5 | odd | 2 | |||
8000.2.a.bm.1.2 | 4 | 24.11 | even | 2 | |||
8000.2.a.bm.1.3 | 4 | 120.59 | even | 2 |