Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.25808.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 10x^{2} - 6x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.707500\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-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 | ||||||||
\(5\) | 1.96666 | 0.879517 | 0.439758 | − | 0.898116i | \(-0.355064\pi\) | ||||
0.439758 | + | 0.898116i | \(0.355064\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.38166 | −1.01961 | −0.509804 | − | 0.860290i | \(-0.670282\pi\) | ||||
−0.509804 | + | 0.860290i | \(0.670282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.48057 | 1.79739 | 0.898693 | − | 0.438578i | \(-0.144518\pi\) | ||||
0.898693 | + | 0.438578i | \(0.144518\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.06557 | −1.22858 | −0.614291 | − | 0.789080i | \(-0.710558\pi\) | ||||
−0.614291 | + | 0.789080i | \(0.710558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.13225 | 0.948003 | 0.474002 | − | 0.880524i | \(-0.342809\pi\) | ||||
0.474002 | + | 0.880524i | \(0.342809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.09891 | −1.48023 | −0.740113 | − | 0.672483i | \(-0.765228\pi\) | ||||
−0.740113 | + | 0.672483i | \(0.765228\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.13225 | −0.226450 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.48057 | 1.20341 | 0.601706 | − | 0.798718i | \(-0.294488\pi\) | ||||
0.601706 | + | 0.798718i | \(0.294488\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.34832 | −1.14019 | −0.570096 | − | 0.821578i | \(-0.693094\pi\) | ||||
−0.570096 | + | 0.821578i | \(0.693094\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.96666 | −0.332426 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.65057 | −1.09335 | −0.546674 | − | 0.837346i | \(-0.684106\pi\) | ||||
−0.546674 | + | 0.837346i | \(0.684106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.44723 | −1.31924 | −0.659618 | − | 0.751601i | \(-0.729282\pi\) | ||||
−0.659618 | + | 0.751601i | \(0.729282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.65057 | −0.861704 | −0.430852 | − | 0.902423i | \(-0.641787\pi\) | ||||
−0.430852 | + | 0.902423i | \(0.641787\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.71725 | −0.542217 | −0.271108 | − | 0.962549i | \(-0.587390\pi\) | ||||
−0.271108 | + | 0.962549i | \(0.587390\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.17000 | 0.160712 | 0.0803560 | − | 0.996766i | \(-0.474394\pi\) | ||||
0.0803560 | + | 0.996766i | \(0.474394\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.65057 | −0.896763 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.5473 | −1.37314 | −0.686568 | − | 0.727066i | \(-0.740883\pi\) | ||||
−0.686568 | + | 0.727066i | \(0.740883\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1311 | 1.29716 | 0.648580 | − | 0.761147i | \(-0.275363\pi\) | ||||
0.648580 | + | 0.761147i | \(0.275363\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.7451 | 1.58083 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.216067 | −0.0263968 | −0.0131984 | − | 0.999913i | \(-0.504201\pi\) | ||||
−0.0131984 | + | 0.999913i | \(0.504201\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.16448 | 0.968946 | 0.484473 | − | 0.874806i | \(-0.339011\pi\) | ||||
0.484473 | + | 0.874806i | \(0.339011\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3472 | −1.44513 | −0.722566 | − | 0.691302i | \(-0.757037\pi\) | ||||
−0.722566 | + | 0.691302i | \(0.757037\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.38166 | 0.385376 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.3106 | 1.27254 | 0.636269 | − | 0.771467i | \(-0.280477\pi\) | ||||
0.636269 | + | 0.771467i | \(0.280477\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.48057 | 0.272278 | 0.136139 | − | 0.990690i | \(-0.456531\pi\) | ||||
0.136139 | + | 0.990690i | \(0.456531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.96225 | −1.08056 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.5139 | 1.32647 | 0.663236 | − | 0.748410i | \(-0.269183\pi\) | ||||
0.663236 | + | 0.748410i | \(0.269183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.48057 | −0.679348 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.12673 | 0.833785 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.86664 | 0.798736 | 0.399368 | − | 0.916791i | \(-0.369230\pi\) | ||||
0.399368 | + | 0.916791i | \(0.369230\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.19893 | −0.119298 | −0.0596491 | − | 0.998219i | \(-0.518998\pi\) | ||||
−0.0596491 | + | 0.998219i | \(0.518998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.3095 | −1.90262 | −0.951309 | − | 0.308240i | \(-0.900260\pi\) | ||||
−0.951309 | + | 0.308240i | \(0.900260\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.86775 | −0.663930 | −0.331965 | − | 0.943292i | \(-0.607712\pi\) | ||||
−0.331965 | + | 0.943292i | \(0.607712\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.34832 | −0.608059 | −0.304029 | − | 0.952663i | \(-0.598332\pi\) | ||||
−0.304029 | + | 0.952663i | \(0.598332\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.9333 | −1.49888 | −0.749440 | − | 0.662072i | \(-0.769677\pi\) | ||||
−0.749440 | + | 0.662072i | \(0.769677\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.9611 | −1.30188 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.06557 | 0.464360 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.435615 | 0.0396014 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0600 | −1.07868 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.65057 | 0.323936 | 0.161968 | − | 0.986796i | \(-0.448216\pi\) | ||||
0.161968 | + | 0.986796i | \(0.448216\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.41389 | 0.210902 | 0.105451 | − | 0.994424i | \(-0.466371\pi\) | ||||
0.105451 | + | 0.994424i | \(0.466371\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.13225 | −0.358312 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.9151 | −1.18884 | −0.594422 | − | 0.804153i | \(-0.702619\pi\) | ||||
−0.594422 | + | 0.804153i | \(0.702619\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.69664 | 0.568001 | 0.284001 | − | 0.958824i | \(-0.408338\pi\) | ||||
0.284001 | + | 0.958824i | \(0.408338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −21.9151 | −1.83263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12.7451 | 1.05842 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.8945 | 1.05636 | 0.528178 | − | 0.849134i | \(-0.322876\pi\) | ||||
0.528178 | + | 0.849134i | \(0.322876\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.1311 | 1.31273 | 0.656367 | − | 0.754442i | \(-0.272092\pi\) | ||||
0.656367 | + | 0.754442i | \(0.272092\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.4850 | −1.00282 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.5172 | −1.23841 | −0.619204 | − | 0.785230i | \(-0.712545\pi\) | ||||
−0.619204 | + | 0.785230i | \(0.712545\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.09891 | 0.559473 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.04607 | 0.551890 | 0.275945 | − | 0.961173i | \(-0.411009\pi\) | ||||
0.275945 | + | 0.961173i | \(0.411009\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.6300 | −1.75116 | −0.875579 | − | 0.483075i | \(-0.839520\pi\) | ||||
−0.875579 | + | 0.483075i | \(0.839520\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 28.9978 | 2.23060 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.09891 | −0.539720 | −0.269860 | − | 0.962900i | \(-0.586977\pi\) | ||||
−0.269860 | + | 0.962900i | \(0.586977\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.13225 | 0.0855901 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −19.2634 | −1.43981 | −0.719907 | − | 0.694071i | \(-0.755815\pi\) | ||||
−0.719907 | + | 0.694071i | \(0.755815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.5266 | −1.15409 | −0.577043 | − | 0.816714i | \(-0.695793\pi\) | ||||
−0.577043 | + | 0.816714i | \(0.695793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.0794 | −0.961617 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.1300 | 1.25267 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.99559 | −0.433826 | −0.216913 | − | 0.976191i | \(-0.569599\pi\) | ||||
−0.216913 | + | 0.976191i | \(0.569599\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.6966 | 1.20185 | 0.600925 | − | 0.799305i | \(-0.294799\pi\) | ||||
0.600925 | + | 0.799305i | \(0.294799\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.8945 | 1.20368 | 0.601840 | − | 0.798617i | \(-0.294434\pi\) | ||||
0.601840 | + | 0.798617i | \(0.294434\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.6117 | 0.823132 | 0.411566 | − | 0.911380i | \(-0.364982\pi\) | ||||
0.411566 | + | 0.911380i | \(0.364982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.48057 | −0.454847 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.6128 | −1.16029 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.9739 | −0.966592 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.8278 | 1.29616 | 0.648079 | − | 0.761573i | \(-0.275573\pi\) | ||||
0.648079 | + | 0.761573i | \(0.275573\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.1127 | −0.757883 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.34832 | 0.430952 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −32.8278 | −2.20824 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.65057 | 0.579285 | 0.289643 | − | 0.957135i | \(-0.406464\pi\) | ||||
0.289643 | + | 0.957135i | \(0.406464\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.8945 | 0.855835 | 0.427918 | − | 0.903818i | \(-0.359247\pi\) | ||||
0.427918 | + | 0.903818i | \(0.359247\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.1311 | −1.72679 | −0.863397 | − | 0.504525i | \(-0.831668\pi\) | ||||
−0.863397 | + | 0.504525i | \(0.831668\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.49881 | 0.556776 | 0.278388 | − | 0.960469i | \(-0.410200\pi\) | ||||
0.278388 | + | 0.960469i | \(0.410200\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.31057 | −0.476889 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.0934 | −1.68784 | −0.843921 | − | 0.536468i | \(-0.819758\pi\) | ||||
−0.843921 | + | 0.536468i | \(0.819758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.5172 | −0.870720 | −0.435360 | − | 0.900256i | \(-0.643379\pi\) | ||||
−0.435360 | + | 0.900256i | \(0.643379\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.96666 | 0.125645 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.7793 | 1.70393 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.39787 | −0.151352 | −0.0756760 | − | 0.997132i | \(-0.524111\pi\) | ||||
−0.0756760 | + | 0.997132i | \(0.524111\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 24.0061 | 1.50925 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.3428 | 1.01944 | 0.509718 | − | 0.860342i | \(-0.329750\pi\) | ||||
0.509718 | + | 0.860342i | \(0.329750\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.65057 | 0.413246 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.8900 | −1.90476 | −0.952381 | − | 0.304911i | \(-0.901373\pi\) | ||||
−0.952381 | + | 0.304911i | \(0.901373\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.30099 | 0.141349 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.1934 | 1.23121 | 0.615607 | − | 0.788053i | \(-0.288911\pi\) | ||||
0.615607 | + | 0.788053i | \(0.288911\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.2256 | −1.41086 | −0.705429 | − | 0.708781i | \(-0.749245\pi\) | ||||
−0.705429 | + | 0.708781i | \(0.749245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.82889 | 0.230891 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.08270 | 0.0650534 | 0.0325267 | − | 0.999471i | \(-0.489645\pi\) | ||||
0.0325267 | + | 0.999471i | \(0.489645\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.58611 | −0.0946195 | −0.0473098 | − | 0.998880i | \(-0.515065\pi\) | ||||
−0.0473098 | + | 0.998880i | \(0.515065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.96114 | −0.532684 | −0.266342 | − | 0.963879i | \(-0.585815\pi\) | ||||
−0.266342 | + | 0.963879i | \(0.585815\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.44723 | 0.498624 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.66000 | 0.509412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.49770 | 0.554862 | 0.277431 | − | 0.960746i | \(-0.410517\pi\) | ||||
0.277431 | + | 0.960746i | \(0.410517\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.7428 | −1.20770 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −46.0050 | −2.66054 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.65057 | 0.325693 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 19.9245 | 1.14087 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.86775 | 0.334890 | 0.167445 | − | 0.985881i | \(-0.446448\pi\) | ||||
0.167445 | + | 0.985881i | \(0.446448\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −22.2138 | −1.25963 | −0.629816 | − | 0.776745i | \(-0.716870\pi\) | ||||
−0.629816 | + | 0.776745i | \(0.716870\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.5194 | 0.764163 | 0.382082 | − | 0.924129i | \(-0.375207\pi\) | ||||
0.382082 | + | 0.924129i | \(0.375207\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.11052 | −0.511698 | −0.255849 | − | 0.966717i | \(-0.582355\pi\) | ||||
−0.255849 | + | 0.966717i | \(0.582355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.9151 | −1.22701 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −20.9322 | −1.16470 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.33763 | −0.407019 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.71725 | 0.204939 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.6966 | −1.46738 | −0.733690 | − | 0.679484i | \(-0.762204\pi\) | ||||
−0.733690 | + | 0.679484i | \(0.762204\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.424930 | −0.0232164 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9611 | 0.869459 | 0.434729 | − | 0.900561i | \(-0.356844\pi\) | ||||
0.434729 | + | 0.900561i | \(0.356844\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.4678 | 1.16255 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.2361 | 1.83789 | 0.918946 | − | 0.394383i | \(-0.129042\pi\) | ||||
0.918946 | + | 0.394383i | \(0.129042\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.9611 | 0.800851 | 0.400426 | − | 0.916329i | \(-0.368862\pi\) | ||||
0.400426 | + | 0.916329i | \(0.368862\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.6450 | −1.63107 | −0.815536 | − | 0.578707i | \(-0.803558\pi\) | ||||
−0.815536 | + | 0.578707i | \(0.803558\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.0568 | 0.852204 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.3023 | −0.543732 | −0.271866 | − | 0.962335i | \(-0.587641\pi\) | ||||
−0.271866 | + | 0.962335i | \(0.587641\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.92450 | −0.101289 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −24.2827 | −1.27102 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.38607 | 0.228951 | 0.114475 | − | 0.993426i | \(-0.463481\pi\) | ||||
0.114475 | + | 0.993426i | \(0.463481\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.17000 | −0.0607434 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.0838 | −0.625676 | −0.312838 | − | 0.949806i | \(-0.601280\pi\) | ||||
−0.312838 | + | 0.949806i | \(0.601280\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.9978 | 2.16300 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.6117 | 1.16149 | 0.580743 | − | 0.814087i | \(-0.302762\pi\) | ||||
0.580743 | + | 0.814087i | \(0.302762\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.02782 | 0.256910 | 0.128455 | − | 0.991715i | \(-0.458998\pi\) | ||||
0.128455 | + | 0.991715i | \(0.458998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.65057 | 0.338944 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.39550 | −0.374966 | −0.187483 | − | 0.982268i | \(-0.560033\pi\) | ||||
−0.187483 | + | 0.982268i | \(0.560033\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.9600 | 1.81858 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.2440 | 1.11922 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.5268 | −1.43172 | −0.715859 | − | 0.698245i | \(-0.753965\pi\) | ||||
−0.715859 | + | 0.698245i | \(0.753965\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.8762 | −1.14238 | −0.571192 | − | 0.820817i | \(-0.693519\pi\) | ||||
−0.571192 | + | 0.820817i | \(0.693519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −41.1407 | −2.04936 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.4900 | 1.11479 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.0096 | 1.83001 | 0.915003 | − | 0.403447i | \(-0.132188\pi\) | ||||
0.915003 | + | 0.403447i | \(0.132188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 10.5473 | 0.518996 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.87843 | 0.239473 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.99118 | −0.390395 | −0.195197 | − | 0.980764i | \(-0.562535\pi\) | ||||
−0.195197 | + | 0.980764i | \(0.562535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.6139 | −0.858451 | −0.429225 | − | 0.903197i | \(-0.641213\pi\) | ||||
−0.429225 | + | 0.903197i | \(0.641213\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.73550 | 0.278212 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.1311 | −0.490280 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.09891 | 0.341942 | 0.170971 | − | 0.985276i | \(-0.445309\pi\) | ||||
0.170971 | + | 0.985276i | \(0.445309\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.87606 | −0.282386 | −0.141193 | − | 0.989982i | \(-0.545094\pi\) | ||||
−0.141193 | + | 0.989982i | \(0.545094\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.3345 | −1.40326 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.34000 | 0.111682 | 0.0558411 | − | 0.998440i | \(-0.482216\pi\) | ||||
0.0558411 | + | 0.998440i | \(0.482216\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.3516 | −0.586843 | −0.293421 | − | 0.955983i | \(-0.594794\pi\) | ||||
−0.293421 | + | 0.955983i | \(0.594794\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.6106 | 1.16665 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −29.9890 | −1.41527 | −0.707633 | − | 0.706580i | \(-0.750237\pi\) | ||||
−0.707633 | + | 0.706580i | \(0.750237\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.5656 | 1.34510 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −12.7451 | −0.597498 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.73327 | −0.127857 | −0.0639286 | − | 0.997954i | \(-0.520363\pi\) | ||||
−0.0639286 | + | 0.997954i | \(0.520363\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.7867 | 1.38731 | 0.693653 | − | 0.720309i | \(-0.256000\pi\) | ||||
0.693653 | + | 0.720309i | \(0.256000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.9611 | 0.881199 | 0.440599 | − | 0.897704i | \(-0.354766\pi\) | ||||
0.440599 | + | 0.897704i | \(0.354766\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.3384 | 0.478404 | 0.239202 | − | 0.970970i | \(-0.423114\pi\) | ||||
0.239202 | + | 0.970970i | \(0.423114\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.216067 | 0.00997704 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.1083 | 0.878601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.67875 | −0.214676 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 28.3956 | 1.29743 | 0.648715 | − | 0.761031i | \(-0.275307\pi\) | ||||
0.648715 | + | 0.761031i | \(0.275307\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −43.0995 | −1.96517 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.4710 | 0.702502 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.44171 | 0.246587 | 0.123294 | − | 0.992370i | \(-0.460654\pi\) | ||||
0.123294 | + | 0.992370i | \(0.460654\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.4750 | −0.788638 | −0.394319 | − | 0.918974i | \(-0.629019\pi\) | ||||
−0.394319 | + | 0.918974i | \(0.629019\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −32.8278 | −1.47849 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.16448 | −0.366227 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.7084 | −0.792738 | −0.396369 | − | 0.918091i | \(-0.629730\pi\) | ||||
−0.396369 | + | 0.918091i | \(0.629730\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.5172 | −0.513527 | −0.256763 | − | 0.966474i | \(-0.582656\pi\) | ||||
−0.256763 | + | 0.966474i | \(0.582656\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.35789 | −0.104925 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −19.6288 | −0.870033 | −0.435017 | − | 0.900422i | \(-0.643257\pi\) | ||||
−0.435017 | + | 0.900422i | \(0.643257\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.3472 | 0.546208 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −37.9751 | −1.67338 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.5705 | 0.552849 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.0506 | 1.31654 | 0.658271 | − | 0.752781i | \(-0.271288\pi\) | ||||
0.658271 | + | 0.752781i | \(0.271288\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.56564 | −0.287096 | −0.143548 | − | 0.989643i | \(-0.545851\pi\) | ||||
−0.143548 | + | 0.989643i | \(0.545851\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.1578 | 1.40082 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.3945 | 1.19107 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −54.7428 | −2.37118 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.5065 | −0.583938 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.38166 | −0.145658 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.91507 | 0.125329 | 0.0626644 | − | 0.998035i | \(-0.480040\pi\) | ||||
0.0626644 | + | 0.998035i | \(0.480040\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.4850 | −0.534798 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.4321 | −0.702587 | −0.351294 | − | 0.936265i | \(-0.614258\pi\) | ||||
−0.351294 | + | 0.936265i | \(0.614258\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.7793 | 1.14084 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.3106 | −0.480974 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.9333 | 0.505631 | 0.252815 | − | 0.967515i | \(-0.418643\pi\) | ||||
0.252815 | + | 0.967515i | \(0.418643\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.6189 | −1.54881 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.5751 | −0.656411 | −0.328205 | − | 0.944606i | \(-0.606444\pi\) | ||||
−0.328205 | + | 0.944606i | \(0.606444\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −31.3354 | −1.31829 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 42.8922 | 1.79814 | 0.899068 | − | 0.437809i | \(-0.144245\pi\) | ||||
0.899068 | + | 0.437809i | \(0.144245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.0945 | 0.966475 | 0.483237 | − | 0.875489i | \(-0.339461\pi\) | ||||
0.483237 | + | 0.875489i | \(0.339461\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.03775 | 0.335197 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.2256 | −0.717113 | −0.358556 | − | 0.933508i | \(-0.616731\pi\) | ||||
−0.358556 | + | 0.933508i | \(0.616731\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.48057 | −0.102911 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.95654 | −0.163863 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.200044 | −0.00825671 | −0.00412835 | − | 0.999991i | \(-0.501314\pi\) | ||||
−0.00412835 | + | 0.999991i | \(0.501314\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −26.2328 | −1.08091 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.4872 | 0.759178 | 0.379589 | − | 0.925155i | \(-0.376065\pi\) | ||||
0.379589 | + | 0.925155i | \(0.376065\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.96225 | 0.408412 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.37223 | −0.219503 | −0.109752 | − | 0.993959i | \(-0.535006\pi\) | ||||
−0.109752 | + | 0.993959i | \(0.535006\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.34943 | 0.340580 | 0.170290 | − | 0.985394i | \(-0.445529\pi\) | ||||
0.170290 | + | 0.985394i | \(0.445529\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.856707 | 0.0348301 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.0366 | −1.01621 | −0.508103 | − | 0.861296i | \(-0.669653\pi\) | ||||
−0.508103 | + | 0.861296i | \(0.669653\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −24.0899 | −0.974573 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6106 | 0.428558 | 0.214279 | − | 0.976772i | \(-0.431260\pi\) | ||||
0.214279 | + | 0.976772i | \(0.431260\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.5473 | −1.22979 | −0.614893 | − | 0.788611i | \(-0.710801\pi\) | ||||
−0.614893 | + | 0.788611i | \(0.710801\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.6189 | 1.67281 | 0.836403 | − | 0.548115i | \(-0.184655\pi\) | ||||
0.836403 | + | 0.548115i | \(0.184655\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.5139 | −0.501359 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.0568 | −0.722270 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.6889 | 1.34327 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −24.4806 | −0.974556 | −0.487278 | − | 0.873247i | \(-0.662010\pi\) | ||||
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.17943 | 0.284907 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.48057 | 0.256769 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 31.0256 | 1.22544 | 0.612719 | − | 0.790301i | \(-0.290076\pi\) | ||||
0.612719 | + | 0.790301i | \(0.290076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.7145 | −1.64506 | −0.822530 | − | 0.568722i | \(-0.807438\pi\) | ||||
−0.822530 | + | 0.568722i | \(0.807438\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −21.3194 | −0.838152 | −0.419076 | − | 0.907951i | \(-0.637646\pi\) | ||||
−0.419076 | + | 0.907951i | \(0.637646\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.6672 | 1.40006 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −32.5060 | −1.27206 | −0.636029 | − | 0.771665i | \(-0.719424\pi\) | ||||
−0.636029 | + | 0.771665i | \(0.719424\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.74729 | 0.185492 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.9083 | −0.970289 | −0.485145 | − | 0.874434i | \(-0.661233\pi\) | ||||
−0.485145 | + | 0.874434i | \(0.661233\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.3472 | −1.33595 | −0.667976 | − | 0.744183i | \(-0.732839\pi\) | ||||
−0.667976 | + | 0.744183i | \(0.732839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.12673 | −0.315141 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −46.0050 | −1.78132 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.2601 | −1.32259 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.9589 | −1.11628 | −0.558142 | − | 0.829745i | \(-0.688486\pi\) | ||||
−0.558142 | + | 0.829745i | \(0.688486\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.5045 | 0.711185 | 0.355593 | − | 0.934641i | \(-0.384279\pi\) | ||||
0.355593 | + | 0.934641i | \(0.384279\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.86664 | −0.301894 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.92830 | 0.303368 | 0.151684 | − | 0.988429i | \(-0.451530\pi\) | ||||
0.151684 | + | 0.988429i | \(0.451530\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.3662 | −1.04561 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.58227 | 0.288862 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.12877 | 0.271191 | 0.135596 | − | 0.990764i | \(-0.456705\pi\) | ||||
0.135596 | + | 0.990764i | \(0.456705\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.1700 | 0.499567 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.7900 | 1.62079 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.7795 | −1.65353 | −0.826764 | − | 0.562549i | \(-0.809821\pi\) | ||||
−0.826764 | + | 0.562549i | \(0.809821\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.4818 | −1.03650 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.19893 | 0.0450905 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.877323 | 0.0329486 | 0.0164743 | − | 0.999864i | \(-0.494756\pi\) | ||||
0.0164743 | + | 0.999864i | \(0.494756\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.0661 | 1.68774 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43.0995 | −1.61183 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.9040 | −1.18982 | −0.594910 | − | 0.803792i | \(-0.702812\pi\) | ||||
−0.594910 | + | 0.803792i | \(0.702812\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19.3095 | 0.719122 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.33763 | −0.272513 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.69886 | 0.322623 | 0.161311 | − | 0.986904i | \(-0.448428\pi\) | ||||
0.161311 | + | 0.986904i | \(0.448428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.6234 | 1.05867 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.5728 | 1.60940 | 0.804700 | − | 0.593682i | \(-0.202326\pi\) | ||||
0.804700 | + | 0.593682i | \(0.202326\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.730664 | 0.0269144 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.8300 | 1.06053 | 0.530264 | − | 0.847832i | \(-0.322093\pi\) | ||||
0.530264 | + | 0.847832i | \(0.322093\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.8611 | 1.27893 | 0.639465 | − | 0.768820i | \(-0.279156\pi\) | ||||
0.639465 | + | 0.768820i | \(0.279156\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25.3590 | 0.929082 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.86775 | 0.250942 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.9495 | 1.42129 | 0.710644 | − | 0.703552i | \(-0.248404\pi\) | ||||
0.710644 | + | 0.703552i | \(0.248404\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 31.7245 | 1.15457 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.3544 | 0.739794 | 0.369897 | − | 0.929073i | \(-0.379393\pi\) | ||||
0.369897 | + | 0.929073i | \(0.379393\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.9534 | −0.578311 | −0.289156 | − | 0.957282i | \(-0.593375\pi\) | ||||
−0.289156 | + | 0.957282i | \(0.593375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.34832 | 0.229825 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −68.3522 | −2.46805 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 48.5362 | 1.75026 | 0.875130 | − | 0.483887i | \(-0.160776\pi\) | ||||
0.875130 | + | 0.483887i | \(0.160776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.0223 | −1.00789 | −0.503946 | − | 0.863735i | \(-0.668119\pi\) | ||||
−0.503946 | + | 0.863735i | \(0.668119\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.18789 | 0.258197 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −34.9061 | −1.25064 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27.6095 | −0.987945 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.5171 | −1.08920 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.3378 | −0.439794 | −0.219897 | − | 0.975523i | \(-0.570572\pi\) | ||||
−0.219897 | + | 0.975523i | \(0.570572\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.9333 | 0.566524 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 65.6556 | 2.33150 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.1258 | 1.35048 | 0.675242 | − | 0.737596i | \(-0.264039\pi\) | ||||
0.675242 | + | 0.737596i | \(0.264039\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.8300 | 0.666157 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 41.7540 | 1.47347 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.9611 | 0.492065 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −37.4395 | −1.31630 | −0.658151 | − | 0.752886i | \(-0.728661\pi\) | ||||
−0.658151 | + | 0.752886i | \(0.728661\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.4901 | 0.649277 | 0.324638 | − | 0.945838i | \(-0.394757\pi\) | ||||
0.324638 | + | 0.945838i | \(0.394757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.8572 | 0.485397 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.3496 | −0.816898 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.8850 | −0.519491 | −0.259746 | − | 0.965677i | \(-0.583639\pi\) | ||||
−0.259746 | + | 0.965677i | \(0.583639\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.47100 | −0.0512757 | −0.0256378 | − | 0.999671i | \(-0.508162\pi\) | ||||
−0.0256378 | + | 0.999671i | \(0.508162\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.3027 | 1.29714 | 0.648571 | − | 0.761155i | \(-0.275367\pi\) | ||||
0.648571 | + | 0.761155i | \(0.275367\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.04844 | −0.279534 | −0.139767 | − | 0.990184i | \(-0.544635\pi\) | ||||
−0.139767 | + | 0.990184i | \(0.544635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.06557 | −0.175512 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44.5054 | −1.54017 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.4806 | 0.361829 | 0.180915 | − | 0.983499i | \(-0.442094\pi\) | ||||
0.180915 | + | 0.983499i | \(0.442094\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.9978 | 0.448199 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 57.0287 | 1.96185 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.435615 | −0.0149679 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 47.2118 | 1.61840 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28.3956 | −0.972248 | −0.486124 | − | 0.873890i | \(-0.661590\pi\) | ||||
−0.486124 | + | 0.873890i | \(0.661590\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26.5784 | −0.907900 | −0.453950 | − | 0.891027i | \(-0.649985\pi\) | ||||
−0.453950 | + | 0.891027i | \(0.649985\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.47448 | 0.152667 | 0.0763336 | − | 0.997082i | \(-0.475679\pi\) | ||||
0.0763336 | + | 0.997082i | \(0.475679\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.2954 | 1.06531 | 0.532655 | − | 0.846333i | \(-0.321195\pi\) | ||||
0.532655 | + | 0.846333i | \(0.321195\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.9611 | −0.474693 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −38.2485 | −1.29749 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.40024 | −0.0474452 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0600 | 0.407704 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.99778 | −0.134995 | −0.0674977 | − | 0.997719i | \(-0.521502\pi\) | ||||
−0.0674977 | + | 0.997719i | \(0.521502\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 35.1439 | 1.18403 | 0.592013 | − | 0.805928i | \(-0.298333\pi\) | ||||
0.592013 | + | 0.805928i | \(0.298333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.7911 | 0.666025 | 0.333012 | − | 0.942922i | \(-0.391935\pi\) | ||||
0.333012 | + | 0.942922i | \(0.391935\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.9128 | 0.937222 | 0.468611 | − | 0.883405i | \(-0.344755\pi\) | ||||
0.468611 | + | 0.883405i | \(0.344755\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.65057 | −0.122436 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.3606 | −0.514023 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37.8845 | −1.26634 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −41.1407 | −1.37212 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.92672 | −0.197448 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −30.5356 | −1.01504 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.6922 | 1.61680 | 0.808399 | − | 0.588635i | \(-0.200335\pi\) | ||||
0.808399 | + | 0.588635i | \(0.200335\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.1667 | −0.668151 | −0.334076 | − | 0.942546i | \(-0.608424\pi\) | ||||
−0.334076 | + | 0.942546i | \(0.608424\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.38844 | −0.277617 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.41389 | −0.0797136 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −51.9779 | −1.71459 | −0.857297 | − | 0.514823i | \(-0.827858\pi\) | ||||
−0.857297 | + | 0.514823i | \(0.827858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 52.9105 | 1.74157 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.53012 | 0.247589 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.15992 | 0.300527 | 0.150264 | − | 0.988646i | \(-0.451988\pi\) | ||||
0.150264 | + | 0.988646i | \(0.451988\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.13225 | 0.135429 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.6889 | 1.10175 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.9224 | 1.66356 | 0.831782 | − | 0.555103i | \(-0.187321\pi\) | ||||
0.831782 | + | 0.555103i | \(0.187321\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.6568 | −1.03198 | −0.515992 | − | 0.856593i | \(-0.672577\pi\) | ||||
−0.515992 | + | 0.856593i | \(0.672577\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 59.9661 | 1.95277 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.3804 | 0.369813 | 0.184907 | − | 0.982756i | \(-0.440802\pi\) | ||||
0.184907 | + | 0.982756i | \(0.440802\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −80.0169 | −2.59746 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.7428 | 0.736713 | 0.368357 | − | 0.929685i | \(-0.379921\pi\) | ||||
0.368357 | + | 0.929685i | \(0.379921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −11.7913 | −0.381557 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 13.9151 | 0.449341 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.30114 | 0.300037 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32.8366 | 1.05705 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.5845 | −0.501164 | −0.250582 | − | 0.968095i | \(-0.580622\pi\) | ||||
−0.250582 | + | 0.968095i | \(0.580622\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.6507 | −0.405981 | −0.202990 | − | 0.979181i | \(-0.565066\pi\) | ||||
−0.202990 | + | 0.979181i | \(0.565066\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.69664 | −0.214684 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −15.5679 | −0.498060 | −0.249030 | − | 0.968496i | \(-0.580112\pi\) | ||||
−0.249030 | + | 0.968496i | \(0.580112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −42.3178 | −1.35248 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.45497 | 0.110197 | 0.0550983 | − | 0.998481i | \(-0.482453\pi\) | ||||
0.0550983 | + | 0.998481i | \(0.482453\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 33.2256 | 1.05866 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 40.1129 | 1.27552 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.44393 | −0.299996 | −0.149998 | − | 0.988686i | \(-0.547927\pi\) | ||||
−0.149998 | + | 0.988686i | \(0.547927\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.8363 | 0.723959 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.5290 | 0.586819 | 0.293410 | − | 0.955987i | \(-0.405210\pi\) | ||||
0.293410 | + | 0.955987i | \(0.405210\pi\) | |||||||
\(998\) | 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 | 6048.2.a.bq.1.3 | yes | 4 | |
3.2 | odd | 2 | 6048.2.a.bl.1.2 | ✓ | 4 | ||
4.3 | odd | 2 | 6048.2.a.bu.1.3 | yes | 4 | ||
12.11 | even | 2 | 6048.2.a.bn.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bl.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
6048.2.a.bn.1.2 | yes | 4 | 12.11 | even | 2 | ||
6048.2.a.bq.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
6048.2.a.bu.1.3 | yes | 4 | 4.3 | odd | 2 |