Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1000,2,Mod(1,1000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1000, 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("1000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1000.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(7.98504020213\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.10025.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 11x^{2} + 10x + 20 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.39867\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1000.1 |
$q$-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 | ||||||||
\(3\) | 2.39867 | 1.38487 | 0.692436 | − | 0.721479i | \(-0.256538\pi\) | ||||
0.692436 | + | 0.721479i | \(0.256538\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.13558 | 0.429207 | 0.214604 | − | 0.976701i | \(-0.431154\pi\) | ||||
0.214604 | + | 0.976701i | \(0.431154\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.75361 | 0.917870 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.01670 | −0.608059 | −0.304029 | − | 0.952663i | \(-0.598332\pi\) | ||||
−0.304029 | + | 0.952663i | \(0.598332\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.26309 | 0.627669 | 0.313835 | − | 0.949478i | \(-0.398386\pi\) | ||||
0.313835 | + | 0.949478i | \(0.398386\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.08379 | −0.262858 | −0.131429 | − | 0.991326i | \(-0.541956\pi\) | ||||
−0.131429 | + | 0.991326i | \(0.541956\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.58295 | 1.28082 | 0.640408 | − | 0.768035i | \(-0.278765\pi\) | ||||
0.640408 | + | 0.768035i | \(0.278765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.72387 | 0.594397 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.33656 | 1.73829 | 0.869147 | − | 0.494555i | \(-0.164669\pi\) | ||||
0.869147 | + | 0.494555i | \(0.164669\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.591009 | −0.113740 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.11719 | 1.69302 | 0.846510 | − | 0.532372i | \(-0.178699\pi\) | ||||
0.846510 | + | 0.532372i | \(0.178699\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.75193 | −1.57189 | −0.785947 | − | 0.618294i | \(-0.787824\pi\) | ||||
−0.785947 | + | 0.618294i | \(0.787824\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.83740 | −0.842083 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.54457 | −0.418324 | −0.209162 | − | 0.977881i | \(-0.567074\pi\) | ||||
−0.209162 | + | 0.977881i | \(0.567074\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.42841 | 0.869241 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.82934 | 1.53509 | 0.767543 | − | 0.640998i | \(-0.221479\pi\) | ||||
0.767543 | + | 0.640998i | \(0.221479\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.91621 | −0.444718 | −0.222359 | − | 0.974965i | \(-0.571376\pi\) | ||||
−0.222359 | + | 0.974965i | \(0.571376\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.09017 | −0.304883 | −0.152441 | − | 0.988313i | \(-0.548714\pi\) | ||||
−0.152441 | + | 0.988313i | \(0.548714\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.71047 | −0.815781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.59965 | −0.364024 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.5326 | −1.44676 | −0.723380 | − | 0.690451i | \(-0.757412\pi\) | ||||
−0.723380 | + | 0.690451i | \(0.757412\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.3916 | 1.77377 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.53424 | 0.720497 | 0.360249 | − | 0.932856i | \(-0.382692\pi\) | ||||
0.360249 | + | 0.932856i | \(0.382692\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.63474 | −0.209307 | −0.104653 | − | 0.994509i | \(-0.533373\pi\) | ||||
−0.104653 | + | 0.994509i | \(0.533373\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.12693 | 0.393956 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5844 | −1.29308 | −0.646542 | − | 0.762878i | \(-0.723786\pi\) | ||||
−0.646542 | + | 0.762878i | \(0.723786\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.9966 | 2.40731 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.9496 | 1.53684 | 0.768418 | − | 0.639948i | \(-0.221044\pi\) | ||||
0.768418 | + | 0.639948i | \(0.221044\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.2447 | −1.55018 | −0.775088 | − | 0.631853i | \(-0.782295\pi\) | ||||
−0.775088 | + | 0.631853i | \(0.782295\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.29012 | −0.260983 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.84604 | 0.770240 | 0.385120 | − | 0.922866i | \(-0.374160\pi\) | ||||
0.385120 | + | 0.922866i | \(0.374160\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.67846 | −1.07538 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.81798 | −0.309314 | −0.154657 | − | 0.987968i | \(-0.549427\pi\) | ||||
−0.154657 | + | 0.987968i | \(0.549427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 21.8691 | 2.34462 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15.1673 | −1.60773 | −0.803865 | − | 0.594811i | \(-0.797227\pi\) | ||||
−0.803865 | + | 0.594811i | \(0.797227\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.56991 | 0.269400 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.9930 | −2.17687 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.2591 | −1.85394 | −0.926968 | − | 0.375141i | \(-0.877594\pi\) | ||||
−0.926968 | + | 0.375141i | \(0.877594\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.55321 | −0.558119 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.04871 | −0.601869 | −0.300934 | − | 0.953645i | \(-0.597299\pi\) | ||||
−0.300934 | + | 0.953645i | \(0.597299\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.03735 | 0.594878 | 0.297439 | − | 0.954741i | \(-0.403868\pi\) | ||||
0.297439 | + | 0.954741i | \(0.403868\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.36359 | −0.518517 | −0.259259 | − | 0.965808i | \(-0.583478\pi\) | ||||
−0.259259 | + | 0.965808i | \(0.583478\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.59965 | 0.632132 | 0.316066 | − | 0.948737i | \(-0.397638\pi\) | ||||
0.316066 | + | 0.948737i | \(0.397638\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.10357 | −0.579325 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.77756 | 0.919795 | 0.459898 | − | 0.887972i | \(-0.347886\pi\) | ||||
0.459898 | + | 0.887972i | \(0.347886\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.23167 | 0.576118 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.23073 | −0.112820 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.93291 | −0.630265 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 23.5773 | 2.12590 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.20266 | 0.639133 | 0.319567 | − | 0.947564i | \(-0.396463\pi\) | ||||
0.319567 | + | 0.947564i | \(0.396463\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.99502 | −0.615877 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.20904 | 0.542487 | 0.271243 | − | 0.962511i | \(-0.412565\pi\) | ||||
0.271243 | + | 0.962511i | \(0.412565\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.33986 | 0.549736 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.94550 | −0.593394 | −0.296697 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296697 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.38695 | −0.626553 | −0.313276 | − | 0.949662i | \(-0.601427\pi\) | ||||
−0.313276 | + | 0.949662i | \(0.601427\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.01362 | −0.422223 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.56398 | −0.381660 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.6975 | −1.12975 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.09655 | −0.581372 | −0.290686 | − | 0.956819i | \(-0.593884\pi\) | ||||
−0.290686 | + | 0.956819i | \(0.593884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.3132 | 1.00203 | 0.501017 | − | 0.865437i | \(-0.332959\pi\) | ||||
0.501017 | + | 0.865437i | \(0.332959\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.98434 | −0.241269 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.4114 | 0.990540 | 0.495270 | − | 0.868739i | \(-0.335069\pi\) | ||||
0.495270 | + | 0.868739i | \(0.335069\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25.2641 | −2.00358 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.46679 | 0.746088 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.2257 | 1.11425 | 0.557123 | − | 0.830430i | \(-0.311905\pi\) | ||||
0.557123 | + | 0.830430i | \(0.311905\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.7790 | −0.834101 | −0.417050 | − | 0.908883i | \(-0.636936\pi\) | ||||
−0.417050 | + | 0.908883i | \(0.636936\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.87841 | −0.606032 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.3733 | 1.17562 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.96632 | 0.757725 | 0.378863 | − | 0.925453i | \(-0.376315\pi\) | ||||
0.378863 | + | 0.925453i | \(0.376315\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.2748 | 0.997796 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.15622 | 0.0864200 | 0.0432100 | − | 0.999066i | \(-0.486242\pi\) | ||||
0.0432100 | + | 0.999066i | \(0.486242\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.58191 | −0.117583 | −0.0587914 | − | 0.998270i | \(-0.518725\pi\) | ||||
−0.0587914 | + | 0.998270i | \(0.518725\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.92119 | −0.289863 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.18568 | 0.159833 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.671136 | −0.0488179 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.12629 | 0.587998 | 0.293999 | − | 0.955806i | \(-0.405014\pi\) | ||||
0.293999 | + | 0.955806i | \(0.405014\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.279795 | 0.0201401 | 0.0100700 | − | 0.999949i | \(-0.496795\pi\) | ||||
0.0100700 | + | 0.999949i | \(0.496795\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14.4201 | −1.02739 | −0.513694 | − | 0.857974i | \(-0.671723\pi\) | ||||
−0.513694 | + | 0.857974i | \(0.671723\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.01276 | 0.426233 | 0.213117 | − | 0.977027i | \(-0.431639\pi\) | ||||
0.213117 | + | 0.977027i | \(0.431639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −25.3883 | −1.79076 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.3533 | 0.726657 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 22.9556 | 1.59553 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.2591 | −0.778812 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.5528 | −1.48376 | −0.741880 | − | 0.670533i | \(-0.766065\pi\) | ||||
−0.741880 | + | 0.670533i | \(0.766065\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 31.0618 | 2.12832 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.93848 | −0.674668 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −31.7697 | −2.14680 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.45272 | −0.164988 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.70409 | 0.649834 | 0.324917 | − | 0.945743i | \(-0.394664\pi\) | ||||
0.324917 | + | 0.945743i | \(0.394664\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.4969 | −0.696703 | −0.348352 | − | 0.937364i | \(-0.613259\pi\) | ||||
−0.348352 | + | 0.937364i | \(0.613259\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.1573 | −1.13378 | −0.566892 | − | 0.823792i | \(-0.691854\pi\) | ||||
−0.566892 | + | 0.823792i | \(0.691854\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.49323 | −0.361428 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.7586 | −0.835843 | −0.417922 | − | 0.908483i | \(-0.637241\pi\) | ||||
−0.417922 | + | 0.908483i | \(0.637241\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 16.4214 | 1.06668 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6150 | 0.815994 | 0.407997 | − | 0.912983i | \(-0.366227\pi\) | ||||
0.407997 | + | 0.912983i | \(0.366227\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.16532 | −0.203896 | −0.101948 | − | 0.994790i | \(-0.532508\pi\) | ||||
−0.101948 | + | 0.994790i | \(0.532508\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.4424 | −1.37553 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.6347 | 0.803929 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.75940 | −0.428360 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.0367 | 1.76966 | 0.884831 | − | 0.465913i | \(-0.154274\pi\) | ||||
0.884831 | + | 0.465913i | \(0.154274\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.8124 | −1.05698 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.0119 | 1.24831 | 0.624155 | − | 0.781300i | \(-0.285443\pi\) | ||||
0.624155 | + | 0.781300i | \(0.285443\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.88955 | −0.179548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.1052 | 1.55397 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.9507 | −0.675246 | −0.337623 | − | 0.941281i | \(-0.609623\pi\) | ||||
−0.337623 | + | 0.941281i | \(0.609623\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.3813 | −2.22650 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.61862 | −0.464515 | −0.232258 | − | 0.972654i | \(-0.574611\pi\) | ||||
−0.232258 | + | 0.972654i | \(0.574611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −28.7205 | −1.74465 | −0.872323 | − | 0.488929i | \(-0.837388\pi\) | ||||
−0.872323 | + | 0.488929i | \(0.837388\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.16437 | 0.373085 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −28.3774 | −1.70503 | −0.852516 | − | 0.522701i | \(-0.824924\pi\) | ||||
−0.852516 | + | 0.522701i | \(0.824924\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −24.0994 | −1.44279 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 31.6027 | 1.88526 | 0.942629 | − | 0.333843i | \(-0.108345\pi\) | ||||
0.942629 | + | 0.333843i | \(0.108345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.4226 | −1.33289 | −0.666443 | − | 0.745556i | \(-0.732184\pi\) | ||||
−0.666443 | + | 0.745556i | \(0.732184\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.1620 | 0.658870 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8254 | −0.930906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −43.7976 | −2.56746 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.6799 | −1.09129 | −0.545645 | − | 0.838017i | \(-0.683715\pi\) | ||||
−0.545645 | + | 0.838017i | \(0.683715\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.19189 | 0.0691604 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 18.8664 | 1.09107 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.31158 | −0.190876 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.5088 | −0.833511 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.72762 | 0.326893 | 0.163446 | − | 0.986552i | \(-0.447739\pi\) | ||||
0.163446 | + | 0.986552i | \(0.447739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.4816 | 0.823829 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.65452 | 0.490753 | 0.245376 | − | 0.969428i | \(-0.421088\pi\) | ||||
0.245376 | + | 0.969428i | \(0.421088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.34960 | 0.189331 | 0.0946653 | − | 0.995509i | \(-0.469822\pi\) | ||||
0.0946653 | + | 0.995509i | \(0.469822\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.04929 | 0.452093 | 0.226047 | − | 0.974116i | \(-0.427420\pi\) | ||||
0.226047 | + | 0.974116i | \(0.427420\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.3867 | −1.02946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.8655 | −0.718080 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.05075 | −0.336673 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.8304 | 0.875422 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.37355 | −0.130858 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.5509 | 1.01965 | 0.509826 | − | 0.860277i | \(-0.329710\pi\) | ||||
0.509826 | + | 0.860277i | \(0.329710\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.00674 | −0.383967 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.1300 | −1.36892 | −0.684458 | − | 0.729052i | \(-0.739961\pi\) | ||||
−0.684458 | + | 0.729052i | \(0.739961\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.4531 | 1.27380 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.6500 | 0.955803 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.4337 | −0.779346 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.2876 | −1.35751 | −0.678754 | − | 0.734366i | \(-0.737480\pi\) | ||||
−0.678754 | + | 0.734366i | \(0.737480\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.69911 | 0.144480 | 0.0722400 | − | 0.997387i | \(-0.476985\pi\) | ||||
0.0722400 | + | 0.997387i | \(0.476985\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.33751 | −0.0713909 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.1225 | 0.698442 | 0.349221 | − | 0.937040i | \(-0.386446\pi\) | ||||
0.349221 | + | 0.937040i | \(0.386446\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.95210 | −0.156242 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.72762 | −0.0911804 | −0.0455902 | − | 0.998960i | \(-0.514517\pi\) | ||||
−0.0455902 | + | 0.998960i | \(0.514517\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.1693 | 0.640492 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.6298 | −0.872836 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.4287 | 1.79716 | 0.898582 | − | 0.438805i | \(-0.144598\pi\) | ||||
0.898582 | + | 0.438805i | \(0.144598\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 27.0662 | 1.40901 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.9605 | −0.620959 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.5994 | 1.37726 | 0.688632 | − | 0.725111i | \(-0.258212\pi\) | ||||
0.688632 | + | 0.725111i | \(0.258212\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.6331 | 1.06266 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.0117 | 0.668367 | 0.334184 | − | 0.942508i | \(-0.391539\pi\) | ||||
0.334184 | + | 0.942508i | \(0.391539\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.2768 | 0.885117 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8421 | −0.911689 | −0.455844 | − | 0.890059i | \(-0.650663\pi\) | ||||
−0.455844 | + | 0.890059i | \(0.650663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.03010 | −0.408193 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.94794 | −0.0987643 | −0.0493821 | − | 0.998780i | \(-0.515725\pi\) | ||||
−0.0493821 | + | 0.998780i | \(0.515725\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.03508 | −0.456924 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.8934 | 0.751274 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5726 | −0.631002 | −0.315501 | − | 0.948925i | \(-0.602173\pi\) | ||||
−0.315501 | + | 0.948925i | \(0.602173\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.2072 | 0.761314 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.2160 | 1.20929 | 0.604645 | − | 0.796495i | \(-0.293315\pi\) | ||||
0.604645 | + | 0.796495i | \(0.293315\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.8064 | −0.986629 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.13163 | 0.254366 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.0728 | 1.33867 | 0.669333 | − | 0.742963i | \(-0.266580\pi\) | ||||
0.669333 | + | 0.742963i | \(0.266580\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.6599 | −0.821775 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.28455 | 0.309243 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17.7188 | −0.867695 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −33.1266 | −1.61834 | −0.809170 | − | 0.587574i | \(-0.800083\pi\) | ||||
−0.809170 | + | 0.587574i | \(0.800083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.8125 | −1.84287 | −0.921435 | − | 0.388532i | \(-0.872982\pi\) | ||||
−0.921435 | + | 0.388532i | \(0.872982\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.75551 | −0.279843 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.85637 | −0.0898359 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.9475 | −0.528550 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0656 | −0.773852 | −0.386926 | − | 0.922111i | \(-0.626463\pi\) | ||||
−0.386926 | + | 0.922111i | \(0.626463\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.0940 | 1.59040 | 0.795198 | − | 0.606350i | \(-0.207367\pi\) | ||||
0.795198 | + | 0.606350i | \(0.207367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 46.5426 | 2.22643 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.1634 | 1.58280 | 0.791400 | − | 0.611298i | \(-0.209352\pi\) | ||||
0.791400 | + | 0.611298i | \(0.209352\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.7244 | −0.748781 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.78036 | 0.274633 | 0.137316 | − | 0.990527i | \(-0.456152\pi\) | ||||
0.137316 | + | 0.990527i | \(0.456152\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −17.0223 | −0.805126 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.6234 | 0.973277 | 0.486639 | − | 0.873603i | \(-0.338223\pi\) | ||||
0.486639 | + | 0.873603i | \(0.338223\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.8229 | −0.933422 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 29.5353 | 1.38769 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.42094 | 0.440693 | 0.220346 | − | 0.975422i | \(-0.429281\pi\) | ||||
0.220346 | + | 0.975422i | \(0.429281\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.640530 | 0.0298974 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.9744 | 1.16317 | 0.581586 | − | 0.813485i | \(-0.302432\pi\) | ||||
0.581586 | + | 0.813485i | \(0.302432\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.8110 | 1.29248 | 0.646242 | − | 0.763132i | \(-0.276339\pi\) | ||||
0.646242 | + | 0.763132i | \(0.276339\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.80898 | −0.176258 | −0.0881292 | − | 0.996109i | \(-0.528089\pi\) | ||||
−0.0881292 | + | 0.996109i | \(0.528089\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0193 | −0.555001 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.7709 | 1.37177 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.88113 | 0.270414 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −29.0026 | −1.32794 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.45272 | 0.203450 | 0.101725 | − | 0.994813i | \(-0.467564\pi\) | ||||
0.101725 | + | 0.994813i | \(0.467564\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.75859 | −0.262569 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 22.7077 | 1.03324 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.42116 | 0.426914 | 0.213457 | − | 0.976952i | \(-0.431528\pi\) | ||||
0.213457 | + | 0.976952i | \(0.431528\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.1228 | 1.54309 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.0769 | 1.49274 | 0.746369 | − | 0.665533i | \(-0.231796\pi\) | ||||
0.746369 | + | 0.665533i | \(0.231796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.88113 | −0.445024 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.7053 | 0.659621 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.2197 | 1.44235 | 0.721175 | − | 0.692753i | \(-0.243602\pi\) | ||||
0.721175 | + | 0.692753i | \(0.243602\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −25.8551 | −1.15512 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.6317 | 0.474042 | 0.237021 | − | 0.971505i | \(-0.423829\pi\) | ||||
0.237021 | + | 0.971505i | \(0.423829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.8977 | −0.839276 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.69824 | −0.341219 | −0.170609 | − | 0.985339i | \(-0.554574\pi\) | ||||
−0.170609 | + | 0.985339i | \(0.554574\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15.0404 | −0.665347 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.29958 | −0.145680 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.21525 | 0.185387 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.9059 | 1.04935 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2597 | −0.449487 | −0.224744 | − | 0.974418i | \(-0.572154\pi\) | ||||
−0.224744 | + | 0.974418i | \(0.572154\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −32.7292 | −1.43115 | −0.715575 | − | 0.698536i | \(-0.753835\pi\) | ||||
−0.715575 | + | 0.698536i | \(0.753835\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.48526 | 0.413184 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 46.4982 | 2.02166 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.2391 | 0.661323 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.2447 | 0.963525 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.77339 | 0.119681 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.5163 | 0.496043 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.94875 | −0.341743 | −0.170872 | − | 0.985293i | \(-0.554658\pi\) | ||||
−0.170872 | + | 0.985293i | \(0.554658\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.79449 | −0.162837 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.77593 | −0.118690 | −0.0593452 | − | 0.998238i | \(-0.518901\pi\) | ||||
−0.0593452 | + | 0.998238i | \(0.518901\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.50143 | −0.192116 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 50.9009 | 2.16845 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.77420 | 0.330593 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −28.2457 | −1.19681 | −0.598405 | − | 0.801193i | \(-0.704199\pi\) | ||||
−0.598405 | + | 0.801193i | \(0.704199\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.59965 | −0.279136 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.24273 | 0.221348 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.4749 | 0.441466 | 0.220733 | − | 0.975334i | \(-0.429155\pi\) | ||||
0.220733 | + | 0.975334i | \(0.429155\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.9906 | −0.461563 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.2564 | 1.26842 | 0.634208 | − | 0.773163i | \(-0.281326\pi\) | ||||
0.634208 | + | 0.773163i | \(0.281326\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.0909 | 1.38481 | 0.692406 | − | 0.721508i | \(-0.256551\pi\) | ||||
0.692406 | + | 0.721508i | \(0.256551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19.4923 | 0.814301 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.3160 | 1.55349 | 0.776744 | − | 0.629817i | \(-0.216870\pi\) | ||||
0.776744 | + | 0.629817i | \(0.216870\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.671136 | 0.0278914 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.20003 | −0.132760 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.2410 | 0.879714 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −30.9409 | −1.27707 | −0.638534 | − | 0.769594i | \(-0.720459\pi\) | ||||
−0.638534 | + | 0.769594i | \(0.720459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −48.8616 | −2.01331 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.5890 | −1.42280 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 44.1444 | 1.81279 | 0.906396 | − | 0.422428i | \(-0.138822\pi\) | ||||
0.906396 | + | 0.422428i | \(0.138822\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.4226 | 0.590278 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.25996 | 0.255775 | 0.127888 | − | 0.991789i | \(-0.459180\pi\) | ||||
0.127888 | + | 0.991789i | \(0.459180\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.31678 | −0.216876 | −0.108438 | − | 0.994103i | \(-0.534585\pi\) | ||||
−0.108438 | + | 0.994103i | \(0.534585\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.1452 | −1.18688 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.0584 | 1.46356 | 0.731782 | − | 0.681538i | \(-0.238689\pi\) | ||||
0.731782 | + | 0.681538i | \(0.238689\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 24.8340 | 1.00633 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.73025 | −0.191365 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.04390 | 0.365280 | 0.182640 | − | 0.983180i | \(-0.441536\pi\) | ||||
0.182640 | + | 0.983180i | \(0.441536\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −43.9318 | −1.76863 | −0.884314 | − | 0.466892i | \(-0.845374\pi\) | ||||
−0.884314 | + | 0.466892i | \(0.845374\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.08071 | −0.0836309 | −0.0418154 | − | 0.999125i | \(-0.513314\pi\) | ||||
−0.0418154 | + | 0.999125i | \(0.513314\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.92698 | −0.197713 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.2236 | −0.690050 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −27.0070 | −1.07855 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.75778 | 0.109960 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.90711 | 0.314777 | 0.157389 | − | 0.987537i | \(-0.449692\pi\) | ||||
0.157389 | + | 0.987537i | \(0.449692\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −51.6981 | −2.05482 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.9233 | −0.512041 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 35.6582 | 1.41062 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.1496 | 0.440381 | 0.220191 | − | 0.975457i | \(-0.429332\pi\) | ||||
0.220191 | + | 0.975457i | \(0.429332\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.47544 | −0.176494 | −0.0882470 | − | 0.996099i | \(-0.528126\pi\) | ||||
−0.0882470 | + | 0.996099i | \(0.528126\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 44.4289 | 1.74668 | 0.873341 | − | 0.487109i | \(-0.161949\pi\) | ||||
0.873341 | + | 0.487109i | \(0.161949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.1609 | −0.438105 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −23.8391 | −0.934328 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28.7385 | −1.12463 | −0.562313 | − | 0.826925i | \(-0.690088\pi\) | ||||
−0.562313 | + | 0.826925i | \(0.690088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.4708 | −1.42286 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.9254 | 0.737230 | 0.368615 | − | 0.929582i | \(-0.379832\pi\) | ||||
0.368615 | + | 0.929582i | \(0.379832\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.6615 | −1.38707 | −0.693535 | − | 0.720423i | \(-0.743948\pi\) | ||||
−0.693535 | + | 0.720423i | \(0.743948\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.88326 | −0.228487 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 76.0060 | 2.94297 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 23.2769 | 0.899937 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.29678 | 0.127271 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.9521 | −1.23166 | −0.615831 | − | 0.787879i | \(-0.711179\pi\) | ||||
−0.615831 | + | 0.787879i | \(0.711179\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.9709 | 0.921278 | 0.460639 | − | 0.887588i | \(-0.347620\pi\) | ||||
0.460639 | + | 0.887588i | \(0.347620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.7346 | −0.795723 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.1786 | −0.964845 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.07047 | −0.270544 | −0.135272 | − | 0.990808i | \(-0.543191\pi\) | ||||
−0.135272 | + | 0.990808i | \(0.543191\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −41.1546 | −1.57014 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −23.8362 | −0.908086 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.97935 | −0.0752982 | −0.0376491 | − | 0.999291i | \(-0.511987\pi\) | ||||
−0.0376491 | + | 0.999291i | \(0.511987\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.30609 | −0.239549 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.6529 | −0.403509 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.6036 | −1.15754 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.8745 | −0.750648 | −0.375324 | − | 0.926894i | \(-0.622469\pi\) | ||||
−0.375324 | + | 0.926894i | \(0.622469\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.2062 | −0.535797 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.86876 | −0.258326 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.79068 | −0.330141 | −0.165070 | − | 0.986282i | \(-0.552785\pi\) | ||||
−0.165070 | + | 0.986282i | \(0.552785\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.8513 | 0.706980 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −72.9610 | −2.73241 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30.2591 | 1.13005 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.2898 | 0.383743 | 0.191872 | − | 0.981420i | \(-0.438544\pi\) | ||||
0.191872 | + | 0.981420i | \(0.438544\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.85586 | 0.255326 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.59254 | −0.282370 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.73934 | −0.361212 | −0.180606 | − | 0.983556i | \(-0.557806\pi\) | ||||
−0.180606 | + | 0.983556i | \(0.557806\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.3978 | −0.829548 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.16056 | 0.116898 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.2767 | −0.933617 | −0.466808 | − | 0.884358i | \(-0.654596\pi\) | ||||
−0.466808 | + | 0.884358i | \(0.654596\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21.3455 | 0.786271 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −39.6691 | −1.45925 | −0.729626 | − | 0.683847i | \(-0.760306\pi\) | ||||
−0.729626 | + | 0.683847i | \(0.760306\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.3065 | 1.11334 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.7732 | −0.688721 | −0.344360 | − | 0.938838i | \(-0.611904\pi\) | ||||
−0.344360 | + | 0.938838i | \(0.611904\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.75962 | −0.283910 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.09076 | −0.222551 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.1761 | 1.28359 | 0.641797 | − | 0.766874i | \(-0.278189\pi\) | ||||
0.641797 | + | 0.766874i | \(0.278189\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 67.2508 | 2.45075 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.9332 | −0.942559 | −0.471279 | − | 0.881984i | \(-0.656208\pi\) | ||||
−0.471279 | + | 0.881984i | \(0.656208\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −40.3273 | −1.46379 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.6131 | −0.420973 | −0.210486 | − | 0.977597i | \(-0.567505\pi\) | ||||
−0.210486 | + | 0.977597i | \(0.567505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.49440 | 0.271316 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.5245 | 0.452234 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.6988 | 0.638236 | 0.319118 | − | 0.947715i | \(-0.396613\pi\) | ||||
0.319118 | + | 0.947715i | \(0.396613\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 48.0020 | 1.72875 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 45.3363 | 1.63063 | 0.815316 | − | 0.579016i | \(-0.196563\pi\) | ||||
0.815316 | + | 0.579016i | \(0.196563\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.93106 | −0.248651 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 54.8767 | 1.96616 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.1155 | −0.934487 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.38835 | −0.192564 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.40446 | −0.0500637 | −0.0250318 | − | 0.999687i | \(-0.507969\pi\) | ||||
−0.0250318 | + | 0.999687i | \(0.507969\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −26.2670 | −0.935129 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.1032 | 0.394783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.69956 | −0.131375 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 41.1825 | 1.45876 | 0.729379 | − | 0.684109i | \(-0.239809\pi\) | ||||
0.729379 | + | 0.684109i | \(0.239809\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.26531 | 0.0801408 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −41.7648 | −1.47569 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 26.7106 | 0.942598 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.2745 | −0.643294 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.98976 | 0.245747 | 0.122873 | − | 0.992422i | \(-0.460789\pi\) | ||||
0.122873 | + | 0.992422i | \(0.460789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.9870 | −0.385804 | −0.192902 | − | 0.981218i | \(-0.561790\pi\) | ||||
−0.192902 | + | 0.981218i | \(0.561790\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −68.8910 | −2.41611 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.2811 | −0.569602 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.07654 | 0.247274 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.2863 | 1.23150 | 0.615751 | − | 0.787941i | \(-0.288853\pi\) | ||||
0.615751 | + | 0.787941i | \(0.288853\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.8164 | −1.35306 | −0.676528 | − | 0.736417i | \(-0.736516\pi\) | ||||
−0.676528 | + | 0.736417i | \(0.736516\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.6781 | −0.545181 | −0.272590 | − | 0.962130i | \(-0.587880\pi\) | ||||
−0.272590 | + | 0.962130i | \(0.587880\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.8171 | 0.966126 | 0.483063 | − | 0.875585i | \(-0.339524\pi\) | ||||
0.483063 | + | 0.875585i | \(0.339524\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −68.0679 | −2.36125 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.18895 | 0.214434 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.17247 | 0.178787 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −38.1703 | −1.31779 | −0.658893 | − | 0.752237i | \(-0.728975\pi\) | ||||
−0.658893 | + | 0.752237i | \(0.728975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 54.1232 | 1.86632 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 75.8043 | 2.61084 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.87284 | −0.270514 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −53.7844 | −1.84588 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.2129 | −0.727170 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −23.4987 | −0.804580 | −0.402290 | − | 0.915512i | \(-0.631786\pi\) | ||||
−0.402290 | + | 0.915512i | \(0.631786\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 20.7940 | 0.710309 | 0.355154 | − | 0.934808i | \(-0.384428\pi\) | ||||
0.355154 | + | 0.934808i | \(0.384428\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.4860 | −0.596616 | −0.298308 | − | 0.954470i | \(-0.596422\pi\) | ||||
−0.298308 | + | 0.954470i | \(0.596422\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.7738 | 0.912450 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.93490 | 0.133945 | 0.0669727 | − | 0.997755i | \(-0.478666\pi\) | ||||
0.0669727 | + | 0.997755i | \(0.478666\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.9599 | −1.28919 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.8064 | −0.468351 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.9534 | −0.811629 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −50.2786 | −1.70167 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.3758 | −1.02572 | −0.512859 | − | 0.858473i | \(-0.671414\pi\) | ||||
−0.512859 | + | 0.858473i | \(0.671414\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −44.8068 | −1.51130 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.4095 | 0.451778 | 0.225889 | − | 0.974153i | \(-0.427471\pi\) | ||||
0.225889 | + | 0.974153i | \(0.427471\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47.5905 | 1.60155 | 0.800774 | − | 0.598967i | \(-0.204422\pi\) | ||||
0.800774 | + | 0.598967i | \(0.204422\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.6312 | −0.457692 | −0.228846 | − | 0.973463i | \(-0.573495\pi\) | ||||
−0.228846 | + | 0.973463i | \(0.573495\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.17917 | 0.274320 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.5186 | 0.653897 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.6693 | −0.390499 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 45.2543 | 1.51100 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −79.7931 | −2.66125 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.4151 | 0.380292 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.94337 | −0.264339 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.5356 | 0.416239 | 0.208120 | − | 0.978103i | \(-0.433266\pi\) | ||||
0.208120 | + | 0.978103i | \(0.433266\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16.6558 | −0.552437 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.1877 | −1.13269 | −0.566344 | − | 0.824169i | \(-0.691643\pi\) | ||||
−0.566344 | + | 0.824169i | \(0.691643\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.68303 | 0.188081 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.05084 | 0.232839 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.6793 | 0.781109 | 0.390554 | − | 0.920580i | \(-0.372283\pi\) | ||||
0.390554 | + | 0.920580i | \(0.372283\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.7387 | 0.452704 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.3062 | 0.964625 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.6245 | 0.546020 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.48509 | −0.311196 | −0.155598 | − | 0.987820i | \(-0.549730\pi\) | ||||
−0.155598 | + | 0.987820i | \(0.549730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.8813 | −1.04487 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.7593 | 0.679629 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.5790 | −1.32566 | −0.662829 | − | 0.748771i | \(-0.730644\pi\) | ||||
−0.662829 | + | 0.748771i | \(0.730644\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.03458 | 0.262198 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.37604 | −0.273051 | −0.136526 | − | 0.990637i | \(-0.543594\pi\) | ||||
−0.136526 | + | 0.990637i | \(0.543594\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 81.9429 | 2.66843 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.3750 | 1.21453 | 0.607263 | − | 0.794501i | \(-0.292268\pi\) | ||||
0.607263 | + | 0.794501i | \(0.292268\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.9740 | −0.972998 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.3076 | 0.626091 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.5258 | 0.502931 | 0.251465 | − | 0.967866i | \(-0.419088\pi\) | ||||
0.251465 | + | 0.967866i | \(0.419088\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −44.1035 | −1.42566 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.88714 | −0.254689 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.5963 | 1.47085 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.7692 | −0.475931 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.6865 | 1.56565 | 0.782826 | − | 0.622240i | \(-0.213777\pi\) | ||||
0.782826 | + | 0.622240i | \(0.213777\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −14.5137 | −0.466248 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.4960 | −0.465199 | −0.232599 | − | 0.972573i | \(-0.574723\pi\) | ||||
−0.232599 | + | 0.972573i | \(0.574723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.38843 | −0.268921 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.35164 | −0.235200 | −0.117600 | − | 0.993061i | \(-0.537520\pi\) | ||||
−0.117600 | + | 0.993061i | \(0.537520\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.5879 | 0.977595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.1729 | 0.580215 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.6724 | 1.04209 | 0.521044 | − | 0.853530i | \(-0.325543\pi\) | ||||
0.521044 | + | 0.853530i | \(0.325543\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.69335 | −0.181221 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.3112 | −0.773050 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.7552 | 0.595780 | 0.297890 | − | 0.954600i | \(-0.403717\pi\) | ||||
0.297890 | + | 0.954600i | \(0.403717\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 44.4976 | 1.41209 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.42813 | 0.108570 | 0.0542850 | − | 0.998525i | \(-0.482712\pi\) | ||||
0.0542850 | + | 0.998525i | \(0.482712\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.50386 | 0.0475801 |
(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 | 1000.2.a.g.1.3 | yes | 4 | |
3.2 | odd | 2 | 9000.2.a.bb.1.2 | 4 | |||
4.3 | odd | 2 | 2000.2.a.n.1.2 | 4 | |||
5.2 | odd | 4 | 1000.2.c.c.249.3 | 8 | |||
5.3 | odd | 4 | 1000.2.c.c.249.6 | 8 | |||
5.4 | even | 2 | 1000.2.a.f.1.2 | ✓ | 4 | ||
8.3 | odd | 2 | 8000.2.a.bo.1.3 | 4 | |||
8.5 | even | 2 | 8000.2.a.bd.1.2 | 4 | |||
15.14 | odd | 2 | 9000.2.a.q.1.3 | 4 | |||
20.3 | even | 4 | 2000.2.c.i.1249.3 | 8 | |||
20.7 | even | 4 | 2000.2.c.i.1249.6 | 8 | |||
20.19 | odd | 2 | 2000.2.a.q.1.3 | 4 | |||
40.19 | odd | 2 | 8000.2.a.be.1.2 | 4 | |||
40.29 | even | 2 | 8000.2.a.bn.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1000.2.a.f.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
1000.2.a.g.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
1000.2.c.c.249.3 | 8 | 5.2 | odd | 4 | |||
1000.2.c.c.249.6 | 8 | 5.3 | odd | 4 | |||
2000.2.a.n.1.2 | 4 | 4.3 | odd | 2 | |||
2000.2.a.q.1.3 | 4 | 20.19 | odd | 2 | |||
2000.2.c.i.1249.3 | 8 | 20.3 | even | 4 | |||
2000.2.c.i.1249.6 | 8 | 20.7 | even | 4 | |||
8000.2.a.bd.1.2 | 4 | 8.5 | even | 2 | |||
8000.2.a.be.1.2 | 4 | 40.19 | odd | 2 | |||
8000.2.a.bn.1.3 | 4 | 40.29 | even | 2 | |||
8000.2.a.bo.1.3 | 4 | 8.3 | odd | 2 | |||
9000.2.a.q.1.3 | 4 | 15.14 | odd | 2 | |||
9000.2.a.bb.1.2 | 4 | 3.2 | odd | 2 |