Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6027,2,Mod(1,6027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6027, 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("6027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6027 = 3 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6027.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: | \(48.1258372982\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 4 x^{12} - 11 x^{11} + 56 x^{10} + 26 x^{9} - 263 x^{8} + 50 x^{7} + 478 x^{6} - 174 x^{5} - 311 x^{4} + 84 x^{3} + 69 x^{2} - 12 x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 861) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-0.646272\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.646272 | 0.456983 | 0.228492 | − | 0.973546i | \(-0.426621\pi\) | ||||
0.228492 | + | 0.973546i | \(0.426621\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.58233 | −0.791166 | ||||||||
\(5\) | 2.20733 | 0.987147 | 0.493573 | − | 0.869704i | \(-0.335690\pi\) | ||||
0.493573 | + | 0.869704i | \(0.335690\pi\) | |||||||
\(6\) | 0.646272 | 0.263840 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.31516 | −0.818533 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.42653 | 0.451110 | ||||||||
\(11\) | −4.98739 | −1.50376 | −0.751878 | − | 0.659302i | \(-0.770852\pi\) | ||||
−0.751878 | + | 0.659302i | \(0.770852\pi\) | |||||||
\(12\) | −1.58233 | −0.456780 | ||||||||
\(13\) | −0.0981362 | −0.0272181 | −0.0136090 | − | 0.999907i | \(-0.504332\pi\) | ||||
−0.0136090 | + | 0.999907i | \(0.504332\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.20733 | 0.569929 | ||||||||
\(16\) | 1.66844 | 0.417110 | ||||||||
\(17\) | 6.26794 | 1.52020 | 0.760099 | − | 0.649807i | \(-0.225150\pi\) | ||||
0.760099 | + | 0.649807i | \(0.225150\pi\) | |||||||
\(18\) | 0.646272 | 0.152328 | ||||||||
\(19\) | −4.27090 | −0.979811 | −0.489905 | − | 0.871776i | \(-0.662969\pi\) | ||||
−0.489905 | + | 0.871776i | \(0.662969\pi\) | |||||||
\(20\) | −3.49272 | −0.780997 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.22321 | −0.687192 | ||||||||
\(23\) | 0.961432 | 0.200472 | 0.100236 | − | 0.994964i | \(-0.468040\pi\) | ||||
0.100236 | + | 0.994964i | \(0.468040\pi\) | |||||||
\(24\) | −2.31516 | −0.472580 | ||||||||
\(25\) | −0.127708 | −0.0255415 | ||||||||
\(26\) | −0.0634227 | −0.0124382 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.78221 | −1.63082 | −0.815408 | − | 0.578887i | \(-0.803487\pi\) | ||||
−0.815408 | + | 0.578887i | \(0.803487\pi\) | |||||||
\(30\) | 1.42653 | 0.260448 | ||||||||
\(31\) | 5.62989 | 1.01116 | 0.505579 | − | 0.862780i | \(-0.331279\pi\) | ||||
0.505579 | + | 0.862780i | \(0.331279\pi\) | |||||||
\(32\) | 5.70859 | 1.00915 | ||||||||
\(33\) | −4.98739 | −0.868194 | ||||||||
\(34\) | 4.05080 | 0.694706 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.58233 | −0.263722 | ||||||||
\(37\) | −8.43213 | −1.38623 | −0.693117 | − | 0.720825i | \(-0.743763\pi\) | ||||
−0.693117 | + | 0.720825i | \(0.743763\pi\) | |||||||
\(38\) | −2.76016 | −0.447757 | ||||||||
\(39\) | −0.0981362 | −0.0157144 | ||||||||
\(40\) | −5.11032 | −0.808012 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.42371 | −1.43710 | −0.718551 | − | 0.695474i | \(-0.755194\pi\) | ||||
−0.718551 | + | 0.695474i | \(0.755194\pi\) | |||||||
\(44\) | 7.89171 | 1.18972 | ||||||||
\(45\) | 2.20733 | 0.329049 | ||||||||
\(46\) | 0.621347 | 0.0916126 | ||||||||
\(47\) | 8.39723 | 1.22486 | 0.612431 | − | 0.790524i | \(-0.290192\pi\) | ||||
0.612431 | + | 0.790524i | \(0.290192\pi\) | |||||||
\(48\) | 1.66844 | 0.240818 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.0825339 | −0.0116721 | ||||||||
\(51\) | 6.26794 | 0.877687 | ||||||||
\(52\) | 0.155284 | 0.0215340 | ||||||||
\(53\) | −12.5970 | −1.73033 | −0.865167 | − | 0.501484i | \(-0.832788\pi\) | ||||
−0.865167 | + | 0.501484i | \(0.832788\pi\) | |||||||
\(54\) | 0.646272 | 0.0879465 | ||||||||
\(55\) | −11.0088 | −1.48443 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.27090 | −0.565694 | ||||||||
\(58\) | −5.67570 | −0.745256 | ||||||||
\(59\) | −1.30381 | −0.169741 | −0.0848707 | − | 0.996392i | \(-0.527048\pi\) | ||||
−0.0848707 | + | 0.996392i | \(0.527048\pi\) | |||||||
\(60\) | −3.49272 | −0.450909 | ||||||||
\(61\) | 1.74328 | 0.223204 | 0.111602 | − | 0.993753i | \(-0.464402\pi\) | ||||
0.111602 | + | 0.993753i | \(0.464402\pi\) | |||||||
\(62\) | 3.63844 | 0.462082 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.352424 | 0.0440531 | ||||||||
\(65\) | −0.216619 | −0.0268682 | ||||||||
\(66\) | −3.22321 | −0.396750 | ||||||||
\(67\) | 9.82028 | 1.19974 | 0.599869 | − | 0.800098i | \(-0.295219\pi\) | ||||
0.599869 | + | 0.800098i | \(0.295219\pi\) | |||||||
\(68\) | −9.91796 | −1.20273 | ||||||||
\(69\) | 0.961432 | 0.115743 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.18882 | −0.853156 | −0.426578 | − | 0.904451i | \(-0.640281\pi\) | ||||
−0.426578 | + | 0.904451i | \(0.640281\pi\) | |||||||
\(72\) | −2.31516 | −0.272844 | ||||||||
\(73\) | 0.547746 | 0.0641089 | 0.0320544 | − | 0.999486i | \(-0.489795\pi\) | ||||
0.0320544 | + | 0.999486i | \(0.489795\pi\) | |||||||
\(74\) | −5.44945 | −0.633486 | ||||||||
\(75\) | −0.127708 | −0.0147464 | ||||||||
\(76\) | 6.75797 | 0.775193 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.0634227 | −0.00718121 | ||||||||
\(79\) | −2.59244 | −0.291672 | −0.145836 | − | 0.989309i | \(-0.546587\pi\) | ||||
−0.145836 | + | 0.989309i | \(0.546587\pi\) | |||||||
\(80\) | 3.68279 | 0.411749 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.646272 | 0.0713688 | ||||||||
\(83\) | −1.01281 | −0.111170 | −0.0555851 | − | 0.998454i | \(-0.517702\pi\) | ||||
−0.0555851 | + | 0.998454i | \(0.517702\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8354 | 1.50066 | ||||||||
\(86\) | −6.09028 | −0.656732 | ||||||||
\(87\) | −8.78221 | −0.941552 | ||||||||
\(88\) | 11.5466 | 1.23087 | ||||||||
\(89\) | 14.7801 | 1.56668 | 0.783341 | − | 0.621592i | \(-0.213514\pi\) | ||||
0.783341 | + | 0.621592i | \(0.213514\pi\) | |||||||
\(90\) | 1.42653 | 0.150370 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.52130 | −0.158607 | ||||||||
\(93\) | 5.62989 | 0.583792 | ||||||||
\(94\) | 5.42690 | 0.559742 | ||||||||
\(95\) | −9.42726 | −0.967217 | ||||||||
\(96\) | 5.70859 | 0.582631 | ||||||||
\(97\) | −17.6877 | −1.79591 | −0.897956 | − | 0.440085i | \(-0.854948\pi\) | ||||
−0.897956 | + | 0.440085i | \(0.854948\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.98739 | −0.501252 | ||||||||
\(100\) | 0.202076 | 0.0202076 | ||||||||
\(101\) | −9.33195 | −0.928564 | −0.464282 | − | 0.885688i | \(-0.653688\pi\) | ||||
−0.464282 | + | 0.885688i | \(0.653688\pi\) | |||||||
\(102\) | 4.05080 | 0.401089 | ||||||||
\(103\) | −8.42596 | −0.830234 | −0.415117 | − | 0.909768i | \(-0.636259\pi\) | ||||
−0.415117 | + | 0.909768i | \(0.636259\pi\) | |||||||
\(104\) | 0.227201 | 0.0222789 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.14110 | −0.790734 | ||||||||
\(107\) | −10.8948 | −1.05324 | −0.526618 | − | 0.850102i | \(-0.676540\pi\) | ||||
−0.526618 | + | 0.850102i | \(0.676540\pi\) | |||||||
\(108\) | −1.58233 | −0.152260 | ||||||||
\(109\) | −6.99706 | −0.670197 | −0.335099 | − | 0.942183i | \(-0.608770\pi\) | ||||
−0.335099 | + | 0.942183i | \(0.608770\pi\) | |||||||
\(110\) | −7.11469 | −0.678359 | ||||||||
\(111\) | −8.43213 | −0.800342 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −20.1381 | −1.89443 | −0.947215 | − | 0.320600i | \(-0.896115\pi\) | ||||
−0.947215 | + | 0.320600i | \(0.896115\pi\) | |||||||
\(114\) | −2.76016 | −0.258513 | ||||||||
\(115\) | 2.12219 | 0.197896 | ||||||||
\(116\) | 13.8964 | 1.29025 | ||||||||
\(117\) | −0.0981362 | −0.00907269 | ||||||||
\(118\) | −0.842615 | −0.0775690 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.11032 | −0.466506 | ||||||||
\(121\) | 13.8741 | 1.26128 | ||||||||
\(122\) | 1.12663 | 0.102000 | ||||||||
\(123\) | 1.00000 | 0.0901670 | ||||||||
\(124\) | −8.90835 | −0.799994 | ||||||||
\(125\) | −11.3185 | −1.01236 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3189 | 1.18186 | 0.590929 | − | 0.806723i | \(-0.298761\pi\) | ||||
0.590929 | + | 0.806723i | \(0.298761\pi\) | |||||||
\(128\) | −11.1894 | −0.989014 | ||||||||
\(129\) | −9.42371 | −0.829712 | ||||||||
\(130\) | −0.139995 | −0.0122783 | ||||||||
\(131\) | −10.8574 | −0.948616 | −0.474308 | − | 0.880359i | \(-0.657302\pi\) | ||||
−0.474308 | + | 0.880359i | \(0.657302\pi\) | |||||||
\(132\) | 7.89171 | 0.686885 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.34657 | 0.548260 | ||||||||
\(135\) | 2.20733 | 0.189976 | ||||||||
\(136\) | −14.5113 | −1.24433 | ||||||||
\(137\) | 1.94714 | 0.166356 | 0.0831779 | − | 0.996535i | \(-0.473493\pi\) | ||||
0.0831779 | + | 0.996535i | \(0.473493\pi\) | |||||||
\(138\) | 0.621347 | 0.0528925 | ||||||||
\(139\) | 10.0192 | 0.849815 | 0.424907 | − | 0.905237i | \(-0.360307\pi\) | ||||
0.424907 | + | 0.905237i | \(0.360307\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.39723 | 0.707174 | ||||||||
\(142\) | −4.64594 | −0.389878 | ||||||||
\(143\) | 0.489444 | 0.0409293 | ||||||||
\(144\) | 1.66844 | 0.139037 | ||||||||
\(145\) | −19.3852 | −1.60985 | ||||||||
\(146\) | 0.353993 | 0.0292967 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.3424 | 1.09674 | ||||||||
\(149\) | 19.0408 | 1.55988 | 0.779940 | − | 0.625854i | \(-0.215249\pi\) | ||||
0.779940 | + | 0.625854i | \(0.215249\pi\) | |||||||
\(150\) | −0.0825339 | −0.00673886 | ||||||||
\(151\) | −14.8270 | −1.20661 | −0.603303 | − | 0.797512i | \(-0.706149\pi\) | ||||
−0.603303 | + | 0.797512i | \(0.706149\pi\) | |||||||
\(152\) | 9.88781 | 0.802008 | ||||||||
\(153\) | 6.26794 | 0.506733 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.4270 | 0.998161 | ||||||||
\(156\) | 0.155284 | 0.0124327 | ||||||||
\(157\) | −6.00342 | −0.479125 | −0.239563 | − | 0.970881i | \(-0.577004\pi\) | ||||
−0.239563 | + | 0.970881i | \(0.577004\pi\) | |||||||
\(158\) | −1.67542 | −0.133289 | ||||||||
\(159\) | −12.5970 | −0.999009 | ||||||||
\(160\) | 12.6007 | 0.996175 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.646272 | 0.0507759 | ||||||||
\(163\) | 12.5669 | 0.984313 | 0.492156 | − | 0.870507i | \(-0.336209\pi\) | ||||
0.492156 | + | 0.870507i | \(0.336209\pi\) | |||||||
\(164\) | −1.58233 | −0.123559 | ||||||||
\(165\) | −11.0088 | −0.857035 | ||||||||
\(166\) | −0.654550 | −0.0508029 | ||||||||
\(167\) | 17.9928 | 1.39233 | 0.696163 | − | 0.717884i | \(-0.254889\pi\) | ||||
0.696163 | + | 0.717884i | \(0.254889\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9904 | −0.999259 | ||||||||
\(170\) | 8.94143 | 0.685776 | ||||||||
\(171\) | −4.27090 | −0.326604 | ||||||||
\(172\) | 14.9114 | 1.13699 | ||||||||
\(173\) | −6.45076 | −0.490442 | −0.245221 | − | 0.969467i | \(-0.578861\pi\) | ||||
−0.245221 | + | 0.969467i | \(0.578861\pi\) | |||||||
\(174\) | −5.67570 | −0.430274 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.32116 | −0.627231 | ||||||||
\(177\) | −1.30381 | −0.0980003 | ||||||||
\(178\) | 9.55194 | 0.715948 | ||||||||
\(179\) | 3.46574 | 0.259042 | 0.129521 | − | 0.991577i | \(-0.458656\pi\) | ||||
0.129521 | + | 0.991577i | \(0.458656\pi\) | |||||||
\(180\) | −3.49272 | −0.260332 | ||||||||
\(181\) | 1.73409 | 0.128894 | 0.0644469 | − | 0.997921i | \(-0.479472\pi\) | ||||
0.0644469 | + | 0.997921i | \(0.479472\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.74328 | 0.128867 | ||||||||
\(184\) | −2.22587 | −0.164093 | ||||||||
\(185\) | −18.6125 | −1.36842 | ||||||||
\(186\) | 3.63844 | 0.266783 | ||||||||
\(187\) | −31.2607 | −2.28601 | ||||||||
\(188\) | −13.2872 | −0.969069 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.09258 | −0.442002 | ||||||||
\(191\) | 9.71393 | 0.702875 | 0.351438 | − | 0.936211i | \(-0.385693\pi\) | ||||
0.351438 | + | 0.936211i | \(0.385693\pi\) | |||||||
\(192\) | 0.352424 | 0.0254340 | ||||||||
\(193\) | −26.6411 | −1.91767 | −0.958833 | − | 0.283970i | \(-0.908348\pi\) | ||||
−0.958833 | + | 0.283970i | \(0.908348\pi\) | |||||||
\(194\) | −11.4311 | −0.820702 | ||||||||
\(195\) | −0.216619 | −0.0155124 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.169300 | −0.0120621 | −0.00603106 | − | 0.999982i | \(-0.501920\pi\) | ||||
−0.00603106 | + | 0.999982i | \(0.501920\pi\) | |||||||
\(198\) | −3.22321 | −0.229064 | ||||||||
\(199\) | −24.2237 | −1.71717 | −0.858587 | − | 0.512668i | \(-0.828657\pi\) | ||||
−0.858587 | + | 0.512668i | \(0.828657\pi\) | |||||||
\(200\) | 0.295664 | 0.0209066 | ||||||||
\(201\) | 9.82028 | 0.692669 | ||||||||
\(202\) | −6.03098 | −0.424338 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −9.91796 | −0.694396 | ||||||||
\(205\) | 2.20733 | 0.154166 | ||||||||
\(206\) | −5.44546 | −0.379403 | ||||||||
\(207\) | 0.961432 | 0.0668241 | ||||||||
\(208\) | −0.163734 | −0.0113529 | ||||||||
\(209\) | 21.3006 | 1.47340 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.40691 | −0.509912 | −0.254956 | − | 0.966953i | \(-0.582061\pi\) | ||||
−0.254956 | + | 0.966953i | \(0.582061\pi\) | |||||||
\(212\) | 19.9327 | 1.36898 | ||||||||
\(213\) | −7.18882 | −0.492570 | ||||||||
\(214\) | −7.04098 | −0.481312 | ||||||||
\(215\) | −20.8012 | −1.41863 | ||||||||
\(216\) | −2.31516 | −0.157527 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −4.52201 | −0.306269 | ||||||||
\(219\) | 0.547746 | 0.0370133 | ||||||||
\(220\) | 17.4196 | 1.17443 | ||||||||
\(221\) | −0.615112 | −0.0413769 | ||||||||
\(222\) | −5.44945 | −0.365743 | ||||||||
\(223\) | −28.5175 | −1.90967 | −0.954837 | − | 0.297129i | \(-0.903971\pi\) | ||||
−0.954837 | + | 0.297129i | \(0.903971\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.127708 | −0.00851384 | ||||||||
\(226\) | −13.0147 | −0.865723 | ||||||||
\(227\) | −15.4763 | −1.02720 | −0.513601 | − | 0.858029i | \(-0.671689\pi\) | ||||
−0.513601 | + | 0.858029i | \(0.671689\pi\) | |||||||
\(228\) | 6.75797 | 0.447558 | ||||||||
\(229\) | 2.59305 | 0.171353 | 0.0856766 | − | 0.996323i | \(-0.472695\pi\) | ||||
0.0856766 | + | 0.996323i | \(0.472695\pi\) | |||||||
\(230\) | 1.37152 | 0.0904350 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 20.3322 | 1.33488 | ||||||||
\(233\) | 7.83806 | 0.513488 | 0.256744 | − | 0.966479i | \(-0.417350\pi\) | ||||
0.256744 | + | 0.966479i | \(0.417350\pi\) | |||||||
\(234\) | −0.0634227 | −0.00414607 | ||||||||
\(235\) | 18.5354 | 1.20912 | ||||||||
\(236\) | 2.06306 | 0.134294 | ||||||||
\(237\) | −2.59244 | −0.168397 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.90515 | −0.381972 | −0.190986 | − | 0.981593i | \(-0.561169\pi\) | ||||
−0.190986 | + | 0.981593i | \(0.561169\pi\) | |||||||
\(240\) | 3.68279 | 0.237723 | ||||||||
\(241\) | 29.9744 | 1.93082 | 0.965410 | − | 0.260738i | \(-0.0839660\pi\) | ||||
0.965410 | + | 0.260738i | \(0.0839660\pi\) | |||||||
\(242\) | 8.96644 | 0.576385 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.75844 | −0.176591 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.646272 | 0.0412048 | ||||||||
\(247\) | 0.419129 | 0.0266686 | ||||||||
\(248\) | −13.0341 | −0.827666 | ||||||||
\(249\) | −1.01281 | −0.0641841 | ||||||||
\(250\) | −7.31485 | −0.462632 | ||||||||
\(251\) | 1.69710 | 0.107120 | 0.0535600 | − | 0.998565i | \(-0.482943\pi\) | ||||
0.0535600 | + | 0.998565i | \(0.482943\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.79504 | −0.301461 | ||||||||
\(254\) | 8.60761 | 0.540090 | ||||||||
\(255\) | 13.8354 | 0.866406 | ||||||||
\(256\) | −7.93626 | −0.496016 | ||||||||
\(257\) | −2.03614 | −0.127011 | −0.0635054 | − | 0.997981i | \(-0.520228\pi\) | ||||
−0.0635054 | + | 0.997981i | \(0.520228\pi\) | |||||||
\(258\) | −6.09028 | −0.379164 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.342763 | 0.0212572 | ||||||||
\(261\) | −8.78221 | −0.543605 | ||||||||
\(262\) | −7.01684 | −0.433502 | ||||||||
\(263\) | 8.79054 | 0.542048 | 0.271024 | − | 0.962573i | \(-0.412638\pi\) | ||||
0.271024 | + | 0.962573i | \(0.412638\pi\) | |||||||
\(264\) | 11.5466 | 0.710646 | ||||||||
\(265\) | −27.8057 | −1.70809 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.7801 | 0.904525 | ||||||||
\(268\) | −15.5389 | −0.949192 | ||||||||
\(269\) | 4.68163 | 0.285444 | 0.142722 | − | 0.989763i | \(-0.454415\pi\) | ||||
0.142722 | + | 0.989763i | \(0.454415\pi\) | |||||||
\(270\) | 1.42653 | 0.0868161 | ||||||||
\(271\) | 15.2141 | 0.924189 | 0.462095 | − | 0.886831i | \(-0.347098\pi\) | ||||
0.462095 | + | 0.886831i | \(0.347098\pi\) | |||||||
\(272\) | 10.4577 | 0.634090 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.25838 | 0.0760218 | ||||||||
\(275\) | 0.636928 | 0.0384082 | ||||||||
\(276\) | −1.52130 | −0.0915718 | ||||||||
\(277\) | −29.2313 | −1.75634 | −0.878170 | − | 0.478349i | \(-0.841235\pi\) | ||||
−0.878170 | + | 0.478349i | \(0.841235\pi\) | |||||||
\(278\) | 6.47511 | 0.388351 | ||||||||
\(279\) | 5.62989 | 0.337053 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.86638 | 0.349959 | 0.174980 | − | 0.984572i | \(-0.444014\pi\) | ||||
0.174980 | + | 0.984572i | \(0.444014\pi\) | |||||||
\(282\) | 5.42690 | 0.323167 | ||||||||
\(283\) | 16.0598 | 0.954653 | 0.477327 | − | 0.878726i | \(-0.341606\pi\) | ||||
0.477327 | + | 0.878726i | \(0.341606\pi\) | |||||||
\(284\) | 11.3751 | 0.674988 | ||||||||
\(285\) | −9.42726 | −0.558423 | ||||||||
\(286\) | 0.316314 | 0.0187040 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 5.70859 | 0.336382 | ||||||||
\(289\) | 22.2871 | 1.31100 | ||||||||
\(290\) | −12.5281 | −0.735677 | ||||||||
\(291\) | −17.6877 | −1.03687 | ||||||||
\(292\) | −0.866717 | −0.0507208 | ||||||||
\(293\) | −12.9726 | −0.757870 | −0.378935 | − | 0.925423i | \(-0.623710\pi\) | ||||
−0.378935 | + | 0.925423i | \(0.623710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.87793 | −0.167560 | ||||||||
\(296\) | 19.5217 | 1.13468 | ||||||||
\(297\) | −4.98739 | −0.289398 | ||||||||
\(298\) | 12.3055 | 0.712840 | ||||||||
\(299\) | −0.0943512 | −0.00545647 | ||||||||
\(300\) | 0.202076 | 0.0116669 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −9.58229 | −0.551399 | ||||||||
\(303\) | −9.33195 | −0.536106 | ||||||||
\(304\) | −7.12573 | −0.408689 | ||||||||
\(305\) | 3.84798 | 0.220335 | ||||||||
\(306\) | 4.05080 | 0.231569 | ||||||||
\(307\) | 24.4190 | 1.39367 | 0.696834 | − | 0.717233i | \(-0.254592\pi\) | ||||
0.696834 | + | 0.717233i | \(0.254592\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.42596 | −0.479336 | ||||||||
\(310\) | 8.03123 | 0.456143 | ||||||||
\(311\) | 18.2933 | 1.03732 | 0.518660 | − | 0.854981i | \(-0.326431\pi\) | ||||
0.518660 | + | 0.854981i | \(0.326431\pi\) | |||||||
\(312\) | 0.227201 | 0.0128627 | ||||||||
\(313\) | 9.76655 | 0.552038 | 0.276019 | − | 0.961152i | \(-0.410985\pi\) | ||||
0.276019 | + | 0.961152i | \(0.410985\pi\) | |||||||
\(314\) | −3.87984 | −0.218952 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.10209 | 0.230761 | ||||||||
\(317\) | 11.2980 | 0.634560 | 0.317280 | − | 0.948332i | \(-0.397230\pi\) | ||||
0.317280 | + | 0.948332i | \(0.397230\pi\) | |||||||
\(318\) | −8.14110 | −0.456530 | ||||||||
\(319\) | 43.8004 | 2.45235 | ||||||||
\(320\) | 0.777916 | 0.0434868 | ||||||||
\(321\) | −10.8948 | −0.608086 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.7697 | −1.48951 | ||||||||
\(324\) | −1.58233 | −0.0879073 | ||||||||
\(325\) | 0.0125327 | 0.000695191 0 | ||||||||
\(326\) | 8.12162 | 0.449815 | ||||||||
\(327\) | −6.99706 | −0.386938 | ||||||||
\(328\) | −2.31516 | −0.127833 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.11469 | −0.391651 | ||||||||
\(331\) | −2.09392 | −0.115092 | −0.0575460 | − | 0.998343i | \(-0.518328\pi\) | ||||
−0.0575460 | + | 0.998343i | \(0.518328\pi\) | |||||||
\(332\) | 1.60260 | 0.0879540 | ||||||||
\(333\) | −8.43213 | −0.462078 | ||||||||
\(334\) | 11.6283 | 0.636270 | ||||||||
\(335\) | 21.6766 | 1.18432 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.67269 | 0.200064 | 0.100032 | − | 0.994984i | \(-0.468105\pi\) | ||||
0.100032 | + | 0.994984i | \(0.468105\pi\) | |||||||
\(338\) | −8.39532 | −0.456645 | ||||||||
\(339\) | −20.1381 | −1.09375 | ||||||||
\(340\) | −21.8922 | −1.18727 | ||||||||
\(341\) | −28.0785 | −1.52053 | ||||||||
\(342\) | −2.76016 | −0.149252 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 21.8174 | 1.17632 | ||||||||
\(345\) | 2.12219 | 0.114255 | ||||||||
\(346\) | −4.16895 | −0.224124 | ||||||||
\(347\) | 27.4690 | 1.47461 | 0.737307 | − | 0.675558i | \(-0.236097\pi\) | ||||
0.737307 | + | 0.675558i | \(0.236097\pi\) | |||||||
\(348\) | 13.8964 | 0.744924 | ||||||||
\(349\) | −12.9032 | −0.690690 | −0.345345 | − | 0.938476i | \(-0.612238\pi\) | ||||
−0.345345 | + | 0.938476i | \(0.612238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0981362 | −0.00523812 | ||||||||
\(352\) | −28.4710 | −1.51751 | ||||||||
\(353\) | −0.376084 | −0.0200169 | −0.0100085 | − | 0.999950i | \(-0.503186\pi\) | ||||
−0.0100085 | + | 0.999950i | \(0.503186\pi\) | |||||||
\(354\) | −0.842615 | −0.0447845 | ||||||||
\(355\) | −15.8681 | −0.842190 | ||||||||
\(356\) | −23.3870 | −1.23951 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.23981 | 0.118378 | ||||||||
\(359\) | −18.0589 | −0.953115 | −0.476557 | − | 0.879143i | \(-0.658116\pi\) | ||||
−0.476557 | + | 0.879143i | \(0.658116\pi\) | |||||||
\(360\) | −5.11032 | −0.269337 | ||||||||
\(361\) | −0.759455 | −0.0399713 | ||||||||
\(362\) | 1.12069 | 0.0589024 | ||||||||
\(363\) | 13.8741 | 0.728201 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.20906 | 0.0632849 | ||||||||
\(366\) | 1.12663 | 0.0588900 | ||||||||
\(367\) | 15.7573 | 0.822523 | 0.411262 | − | 0.911517i | \(-0.365088\pi\) | ||||
0.411262 | + | 0.911517i | \(0.365088\pi\) | |||||||
\(368\) | 1.60409 | 0.0836190 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | −12.0287 | −0.625343 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.90835 | −0.461877 | ||||||||
\(373\) | 26.1027 | 1.35155 | 0.675773 | − | 0.737110i | \(-0.263810\pi\) | ||||
0.675773 | + | 0.737110i | \(0.263810\pi\) | |||||||
\(374\) | −20.2029 | −1.04467 | ||||||||
\(375\) | −11.3185 | −0.584486 | ||||||||
\(376\) | −19.4409 | −1.00259 | ||||||||
\(377\) | 0.861853 | 0.0443877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.93660 | 0.356309 | 0.178155 | − | 0.984003i | \(-0.442987\pi\) | ||||
0.178155 | + | 0.984003i | \(0.442987\pi\) | |||||||
\(380\) | 14.9171 | 0.765229 | ||||||||
\(381\) | 13.3189 | 0.682346 | ||||||||
\(382\) | 6.27784 | 0.321202 | ||||||||
\(383\) | 24.0548 | 1.22914 | 0.614572 | − | 0.788861i | \(-0.289329\pi\) | ||||
0.614572 | + | 0.788861i | \(0.289329\pi\) | |||||||
\(384\) | −11.1894 | −0.571008 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.2174 | −0.876342 | ||||||||
\(387\) | −9.42371 | −0.479034 | ||||||||
\(388\) | 27.9878 | 1.42086 | ||||||||
\(389\) | 4.08597 | 0.207167 | 0.103584 | − | 0.994621i | \(-0.466969\pi\) | ||||
0.103584 | + | 0.994621i | \(0.466969\pi\) | |||||||
\(390\) | −0.139995 | −0.00708890 | ||||||||
\(391\) | 6.02620 | 0.304758 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.8574 | −0.547684 | ||||||||
\(394\) | −0.109414 | −0.00551219 | ||||||||
\(395\) | −5.72235 | −0.287923 | ||||||||
\(396\) | 7.89171 | 0.396574 | ||||||||
\(397\) | 0.556877 | 0.0279489 | 0.0139744 | − | 0.999902i | \(-0.495552\pi\) | ||||
0.0139744 | + | 0.999902i | \(0.495552\pi\) | |||||||
\(398\) | −15.6551 | −0.784720 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.213072 | −0.0106536 | ||||||||
\(401\) | −30.2668 | −1.51145 | −0.755726 | − | 0.654888i | \(-0.772716\pi\) | ||||
−0.755726 | + | 0.654888i | \(0.772716\pi\) | |||||||
\(402\) | 6.34657 | 0.316538 | ||||||||
\(403\) | −0.552496 | −0.0275218 | ||||||||
\(404\) | 14.7662 | 0.734648 | ||||||||
\(405\) | 2.20733 | 0.109683 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 42.0543 | 2.08456 | ||||||||
\(408\) | −14.5113 | −0.718416 | ||||||||
\(409\) | 7.57506 | 0.374562 | 0.187281 | − | 0.982306i | \(-0.440032\pi\) | ||||
0.187281 | + | 0.982306i | \(0.440032\pi\) | |||||||
\(410\) | 1.42653 | 0.0704515 | ||||||||
\(411\) | 1.94714 | 0.0960455 | ||||||||
\(412\) | 13.3327 | 0.656853 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.621347 | 0.0305375 | ||||||||
\(415\) | −2.23560 | −0.109741 | ||||||||
\(416\) | −0.560219 | −0.0274670 | ||||||||
\(417\) | 10.0192 | 0.490641 | ||||||||
\(418\) | 13.7660 | 0.673318 | ||||||||
\(419\) | −4.76050 | −0.232565 | −0.116283 | − | 0.993216i | \(-0.537098\pi\) | ||||
−0.116283 | + | 0.993216i | \(0.537098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.72997 | 0.279262 | 0.139631 | − | 0.990204i | \(-0.455408\pi\) | ||||
0.139631 | + | 0.990204i | \(0.455408\pi\) | |||||||
\(422\) | −4.78688 | −0.233022 | ||||||||
\(423\) | 8.39723 | 0.408287 | ||||||||
\(424\) | 29.1641 | 1.41634 | ||||||||
\(425\) | −0.800463 | −0.0388282 | ||||||||
\(426\) | −4.64594 | −0.225096 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 17.2391 | 0.833285 | ||||||||
\(429\) | 0.489444 | 0.0236306 | ||||||||
\(430\) | −13.4432 | −0.648291 | ||||||||
\(431\) | −36.1635 | −1.74193 | −0.870967 | − | 0.491341i | \(-0.836507\pi\) | ||||
−0.870967 | + | 0.491341i | \(0.836507\pi\) | |||||||
\(432\) | 1.66844 | 0.0802728 | ||||||||
\(433\) | −40.4381 | −1.94333 | −0.971666 | − | 0.236358i | \(-0.924046\pi\) | ||||
−0.971666 | + | 0.236358i | \(0.924046\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −19.3852 | −0.929450 | ||||||||
\(436\) | 11.0717 | 0.530237 | ||||||||
\(437\) | −4.10617 | −0.196425 | ||||||||
\(438\) | 0.353993 | 0.0169145 | ||||||||
\(439\) | −4.51440 | −0.215461 | −0.107730 | − | 0.994180i | \(-0.534358\pi\) | ||||
−0.107730 | + | 0.994180i | \(0.534358\pi\) | |||||||
\(440\) | 25.4872 | 1.21505 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.397530 | −0.0189086 | ||||||||
\(443\) | 2.29267 | 0.108928 | 0.0544641 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544641 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(444\) | 13.3424 | 0.633204 | ||||||||
\(445\) | 32.6244 | 1.54655 | ||||||||
\(446\) | −18.4301 | −0.872690 | ||||||||
\(447\) | 19.0408 | 0.900597 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.770455 | −0.0363600 | −0.0181800 | − | 0.999835i | \(-0.505787\pi\) | ||||
−0.0181800 | + | 0.999835i | \(0.505787\pi\) | |||||||
\(450\) | −0.0825339 | −0.00389068 | ||||||||
\(451\) | −4.98739 | −0.234847 | ||||||||
\(452\) | 31.8651 | 1.49881 | ||||||||
\(453\) | −14.8270 | −0.696634 | ||||||||
\(454\) | −10.0019 | −0.469414 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 9.88781 | 0.463039 | ||||||||
\(457\) | 9.33921 | 0.436870 | 0.218435 | − | 0.975851i | \(-0.429905\pi\) | ||||
0.218435 | + | 0.975851i | \(0.429905\pi\) | |||||||
\(458\) | 1.67581 | 0.0783056 | ||||||||
\(459\) | 6.26794 | 0.292562 | ||||||||
\(460\) | −3.35802 | −0.156568 | ||||||||
\(461\) | −38.2020 | −1.77925 | −0.889623 | − | 0.456695i | \(-0.849033\pi\) | ||||
−0.889623 | + | 0.456695i | \(0.849033\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.6784 | 0.589217 | 0.294609 | − | 0.955618i | \(-0.404811\pi\) | ||||
0.294609 | + | 0.955618i | \(0.404811\pi\) | |||||||
\(464\) | −14.6526 | −0.680229 | ||||||||
\(465\) | 12.4270 | 0.576288 | ||||||||
\(466\) | 5.06552 | 0.234656 | ||||||||
\(467\) | 2.95874 | 0.136914 | 0.0684571 | − | 0.997654i | \(-0.478192\pi\) | ||||
0.0684571 | + | 0.997654i | \(0.478192\pi\) | |||||||
\(468\) | 0.155284 | 0.00717801 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 11.9789 | 0.552547 | ||||||||
\(471\) | −6.00342 | −0.276623 | ||||||||
\(472\) | 3.01853 | 0.138939 | ||||||||
\(473\) | 46.9998 | 2.16105 | ||||||||
\(474\) | −1.67542 | −0.0769546 | ||||||||
\(475\) | 0.545426 | 0.0250258 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.5970 | −0.576778 | ||||||||
\(478\) | −3.81633 | −0.174555 | ||||||||
\(479\) | −13.9672 | −0.638179 | −0.319090 | − | 0.947725i | \(-0.603377\pi\) | ||||
−0.319090 | + | 0.947725i | \(0.603377\pi\) | |||||||
\(480\) | 12.6007 | 0.575142 | ||||||||
\(481\) | 0.827497 | 0.0377306 | ||||||||
\(482\) | 19.3716 | 0.882352 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.9534 | −0.997883 | ||||||||
\(485\) | −39.0425 | −1.77283 | ||||||||
\(486\) | 0.646272 | 0.0293155 | ||||||||
\(487\) | −1.83687 | −0.0832364 | −0.0416182 | − | 0.999134i | \(-0.513251\pi\) | ||||
−0.0416182 | + | 0.999134i | \(0.513251\pi\) | |||||||
\(488\) | −4.03597 | −0.182700 | ||||||||
\(489\) | 12.5669 | 0.568293 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.5775 | −0.703003 | −0.351502 | − | 0.936187i | \(-0.614329\pi\) | ||||
−0.351502 | + | 0.936187i | \(0.614329\pi\) | |||||||
\(492\) | −1.58233 | −0.0713370 | ||||||||
\(493\) | −55.0464 | −2.47916 | ||||||||
\(494\) | 0.270872 | 0.0121871 | ||||||||
\(495\) | −11.0088 | −0.494809 | ||||||||
\(496\) | 9.39313 | 0.421764 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.654550 | −0.0293311 | ||||||||
\(499\) | −19.1022 | −0.855133 | −0.427566 | − | 0.903984i | \(-0.640629\pi\) | ||||
−0.427566 | + | 0.903984i | \(0.640629\pi\) | |||||||
\(500\) | 17.9097 | 0.800945 | ||||||||
\(501\) | 17.9928 | 0.803860 | ||||||||
\(502\) | 1.09679 | 0.0489520 | ||||||||
\(503\) | 24.8976 | 1.11013 | 0.555066 | − | 0.831807i | \(-0.312693\pi\) | ||||
0.555066 | + | 0.831807i | \(0.312693\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −20.5987 | −0.916628 | ||||||||
\(506\) | −3.09890 | −0.137763 | ||||||||
\(507\) | −12.9904 | −0.576923 | ||||||||
\(508\) | −21.0749 | −0.935046 | ||||||||
\(509\) | −18.5591 | −0.822617 | −0.411309 | − | 0.911496i | \(-0.634928\pi\) | ||||
−0.411309 | + | 0.911496i | \(0.634928\pi\) | |||||||
\(510\) | 8.94143 | 0.395933 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 17.2499 | 0.762343 | ||||||||
\(513\) | −4.27090 | −0.188565 | ||||||||
\(514\) | −1.31590 | −0.0580419 | ||||||||
\(515\) | −18.5988 | −0.819563 | ||||||||
\(516\) | 14.9114 | 0.656440 | ||||||||
\(517\) | −41.8803 | −1.84189 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.45076 | −0.283157 | ||||||||
\(520\) | 0.501507 | 0.0219925 | ||||||||
\(521\) | −11.3049 | −0.495275 | −0.247638 | − | 0.968853i | \(-0.579654\pi\) | ||||
−0.247638 | + | 0.968853i | \(0.579654\pi\) | |||||||
\(522\) | −5.67570 | −0.248419 | ||||||||
\(523\) | 0.881218 | 0.0385330 | 0.0192665 | − | 0.999814i | \(-0.493867\pi\) | ||||
0.0192665 | + | 0.999814i | \(0.493867\pi\) | |||||||
\(524\) | 17.1800 | 0.750513 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.68108 | 0.247707 | ||||||||
\(527\) | 35.2878 | 1.53716 | ||||||||
\(528\) | −8.32116 | −0.362132 | ||||||||
\(529\) | −22.0756 | −0.959811 | ||||||||
\(530\) | −17.9701 | −0.780570 | ||||||||
\(531\) | −1.30381 | −0.0565805 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0981362 | −0.00425075 | ||||||||
\(534\) | 9.55194 | 0.413353 | ||||||||
\(535\) | −24.0483 | −1.03970 | ||||||||
\(536\) | −22.7355 | −0.982025 | ||||||||
\(537\) | 3.46574 | 0.149558 | ||||||||
\(538\) | 3.02561 | 0.130443 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.49272 | −0.150303 | ||||||||
\(541\) | 18.6630 | 0.802387 | 0.401194 | − | 0.915993i | \(-0.368595\pi\) | ||||
0.401194 | + | 0.915993i | \(0.368595\pi\) | |||||||
\(542\) | 9.83244 | 0.422339 | ||||||||
\(543\) | 1.73409 | 0.0744169 | ||||||||
\(544\) | 35.7811 | 1.53410 | ||||||||
\(545\) | −15.4448 | −0.661583 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.5439 | −1.00667 | −0.503333 | − | 0.864093i | \(-0.667893\pi\) | ||||
−0.503333 | + | 0.864093i | \(0.667893\pi\) | |||||||
\(548\) | −3.08103 | −0.131615 | ||||||||
\(549\) | 1.74328 | 0.0744012 | ||||||||
\(550\) | 0.411629 | 0.0175519 | ||||||||
\(551\) | 37.5079 | 1.59789 | ||||||||
\(552\) | −2.22587 | −0.0947393 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −18.8914 | −0.802618 | ||||||||
\(555\) | −18.6125 | −0.790055 | ||||||||
\(556\) | −15.8537 | −0.672345 | ||||||||
\(557\) | 9.73807 | 0.412615 | 0.206308 | − | 0.978487i | \(-0.433855\pi\) | ||||
0.206308 | + | 0.978487i | \(0.433855\pi\) | |||||||
\(558\) | 3.63844 | 0.154027 | ||||||||
\(559\) | 0.924807 | 0.0391152 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.2607 | −1.31983 | ||||||||
\(562\) | 3.79128 | 0.159926 | ||||||||
\(563\) | 28.0681 | 1.18293 | 0.591466 | − | 0.806330i | \(-0.298550\pi\) | ||||
0.591466 | + | 0.806330i | \(0.298550\pi\) | |||||||
\(564\) | −13.2872 | −0.559492 | ||||||||
\(565\) | −44.4513 | −1.87008 | ||||||||
\(566\) | 10.3790 | 0.436261 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.6433 | 0.698337 | ||||||||
\(569\) | −34.0959 | −1.42938 | −0.714688 | − | 0.699444i | \(-0.753431\pi\) | ||||
−0.714688 | + | 0.699444i | \(0.753431\pi\) | |||||||
\(570\) | −6.09258 | −0.255190 | ||||||||
\(571\) | 24.5038 | 1.02545 | 0.512727 | − | 0.858552i | \(-0.328635\pi\) | ||||
0.512727 | + | 0.858552i | \(0.328635\pi\) | |||||||
\(572\) | −0.774463 | −0.0323819 | ||||||||
\(573\) | 9.71393 | 0.405805 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.122782 | −0.00512037 | ||||||||
\(576\) | 0.352424 | 0.0146844 | ||||||||
\(577\) | −3.13999 | −0.130719 | −0.0653597 | − | 0.997862i | \(-0.520819\pi\) | ||||
−0.0653597 | + | 0.997862i | \(0.520819\pi\) | |||||||
\(578\) | 14.4035 | 0.599107 | ||||||||
\(579\) | −26.6411 | −1.10717 | ||||||||
\(580\) | 30.6739 | 1.27366 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −11.4311 | −0.473833 | ||||||||
\(583\) | 62.8263 | 2.60200 | ||||||||
\(584\) | −1.26812 | −0.0524753 | ||||||||
\(585\) | −0.216619 | −0.00895608 | ||||||||
\(586\) | −8.38386 | −0.346334 | ||||||||
\(587\) | −12.3401 | −0.509329 | −0.254665 | − | 0.967029i | \(-0.581965\pi\) | ||||
−0.254665 | + | 0.967029i | \(0.581965\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.0447 | −0.990743 | ||||||||
\(590\) | −1.85993 | −0.0765720 | ||||||||
\(591\) | −0.169300 | −0.00696407 | ||||||||
\(592\) | −14.0685 | −0.578212 | ||||||||
\(593\) | 28.6742 | 1.17751 | 0.588754 | − | 0.808312i | \(-0.299619\pi\) | ||||
0.588754 | + | 0.808312i | \(0.299619\pi\) | |||||||
\(594\) | −3.22321 | −0.132250 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −30.1288 | −1.23412 | ||||||||
\(597\) | −24.2237 | −0.991411 | ||||||||
\(598\) | −0.0609766 | −0.00249352 | ||||||||
\(599\) | 6.80349 | 0.277983 | 0.138991 | − | 0.990294i | \(-0.455614\pi\) | ||||
0.138991 | + | 0.990294i | \(0.455614\pi\) | |||||||
\(600\) | 0.295664 | 0.0120704 | ||||||||
\(601\) | −20.4130 | −0.832665 | −0.416333 | − | 0.909212i | \(-0.636685\pi\) | ||||
−0.416333 | + | 0.909212i | \(0.636685\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.82028 | 0.399913 | ||||||||
\(604\) | 23.4613 | 0.954625 | ||||||||
\(605\) | 30.6247 | 1.24507 | ||||||||
\(606\) | −6.03098 | −0.244992 | ||||||||
\(607\) | 9.15724 | 0.371681 | 0.185840 | − | 0.982580i | \(-0.440499\pi\) | ||||
0.185840 | + | 0.982580i | \(0.440499\pi\) | |||||||
\(608\) | −24.3808 | −0.988772 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.48684 | 0.100689 | ||||||||
\(611\) | −0.824072 | −0.0333384 | ||||||||
\(612\) | −9.91796 | −0.400910 | ||||||||
\(613\) | −36.1686 | −1.46083 | −0.730417 | − | 0.683001i | \(-0.760674\pi\) | ||||
−0.730417 | + | 0.683001i | \(0.760674\pi\) | |||||||
\(614\) | 15.7813 | 0.636883 | ||||||||
\(615\) | 2.20733 | 0.0890080 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.38805 | 0.377949 | 0.188974 | − | 0.981982i | \(-0.439484\pi\) | ||||
0.188974 | + | 0.981982i | \(0.439484\pi\) | |||||||
\(618\) | −5.44546 | −0.219049 | ||||||||
\(619\) | −1.65438 | −0.0664951 | −0.0332476 | − | 0.999447i | \(-0.510585\pi\) | ||||
−0.0332476 | + | 0.999447i | \(0.510585\pi\) | |||||||
\(620\) | −19.6636 | −0.789711 | ||||||||
\(621\) | 0.961432 | 0.0385809 | ||||||||
\(622\) | 11.8225 | 0.474038 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.163734 | −0.00655462 | ||||||||
\(625\) | −24.3452 | −0.973806 | ||||||||
\(626\) | 6.31185 | 0.252272 | ||||||||
\(627\) | 21.3006 | 0.850665 | ||||||||
\(628\) | 9.49940 | 0.379068 | ||||||||
\(629\) | −52.8521 | −2.10735 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.71318 | −0.147819 | −0.0739097 | − | 0.997265i | \(-0.523548\pi\) | ||||
−0.0739097 | + | 0.997265i | \(0.523548\pi\) | |||||||
\(632\) | 6.00191 | 0.238743 | ||||||||
\(633\) | −7.40691 | −0.294398 | ||||||||
\(634\) | 7.30160 | 0.289984 | ||||||||
\(635\) | 29.3991 | 1.16667 | ||||||||
\(636\) | 19.9327 | 0.790382 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 28.3070 | 1.12068 | ||||||||
\(639\) | −7.18882 | −0.284385 | ||||||||
\(640\) | −24.6987 | −0.976302 | ||||||||
\(641\) | −12.6040 | −0.497829 | −0.248914 | − | 0.968526i | \(-0.580074\pi\) | ||||
−0.248914 | + | 0.968526i | \(0.580074\pi\) | |||||||
\(642\) | −7.04098 | −0.277885 | ||||||||
\(643\) | 26.4140 | 1.04167 | 0.520833 | − | 0.853658i | \(-0.325621\pi\) | ||||
0.520833 | + | 0.853658i | \(0.325621\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −20.8012 | −0.819047 | ||||||||
\(646\) | −17.3005 | −0.680680 | ||||||||
\(647\) | 27.0862 | 1.06487 | 0.532434 | − | 0.846471i | \(-0.321277\pi\) | ||||
0.532434 | + | 0.846471i | \(0.321277\pi\) | |||||||
\(648\) | −2.31516 | −0.0909481 | ||||||||
\(649\) | 6.50261 | 0.255250 | ||||||||
\(650\) | 0.00809956 | 0.000317691 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.8850 | −0.778755 | ||||||||
\(653\) | −8.49488 | −0.332431 | −0.166215 | − | 0.986089i | \(-0.553155\pi\) | ||||
−0.166215 | + | 0.986089i | \(0.553155\pi\) | |||||||
\(654\) | −4.52201 | −0.176825 | ||||||||
\(655\) | −23.9658 | −0.936423 | ||||||||
\(656\) | 1.66844 | 0.0651416 | ||||||||
\(657\) | 0.547746 | 0.0213696 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.15227 | −0.0838405 | −0.0419202 | − | 0.999121i | \(-0.513348\pi\) | ||||
−0.0419202 | + | 0.999121i | \(0.513348\pi\) | |||||||
\(660\) | 17.4196 | 0.678057 | ||||||||
\(661\) | −14.3926 | −0.559808 | −0.279904 | − | 0.960028i | \(-0.590303\pi\) | ||||
−0.279904 | + | 0.960028i | \(0.590303\pi\) | |||||||
\(662\) | −1.35324 | −0.0525952 | ||||||||
\(663\) | −0.615112 | −0.0238890 | ||||||||
\(664\) | 2.34481 | 0.0909964 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.44945 | −0.211162 | ||||||||
\(667\) | −8.44350 | −0.326934 | ||||||||
\(668\) | −28.4706 | −1.10156 | ||||||||
\(669\) | −28.5175 | −1.10255 | ||||||||
\(670\) | 14.0090 | 0.541213 | ||||||||
\(671\) | −8.69441 | −0.335644 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.6210 | 1.72001 | 0.860007 | − | 0.510282i | \(-0.170459\pi\) | ||||
0.860007 | + | 0.510282i | \(0.170459\pi\) | |||||||
\(674\) | 2.37356 | 0.0914260 | ||||||||
\(675\) | −0.127708 | −0.00491547 | ||||||||
\(676\) | 20.5551 | 0.790580 | ||||||||
\(677\) | −34.6693 | −1.33245 | −0.666226 | − | 0.745750i | \(-0.732091\pi\) | ||||
−0.666226 | + | 0.745750i | \(0.732091\pi\) | |||||||
\(678\) | −13.0147 | −0.499825 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −32.0312 | −1.22834 | ||||||||
\(681\) | −15.4763 | −0.593055 | ||||||||
\(682\) | −18.1463 | −0.694859 | ||||||||
\(683\) | 25.2748 | 0.967113 | 0.483556 | − | 0.875313i | \(-0.339345\pi\) | ||||
0.483556 | + | 0.875313i | \(0.339345\pi\) | |||||||
\(684\) | 6.75797 | 0.258398 | ||||||||
\(685\) | 4.29798 | 0.164217 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.59305 | 0.0989309 | ||||||||
\(688\) | −15.7229 | −0.599430 | ||||||||
\(689\) | 1.23622 | 0.0470964 | ||||||||
\(690\) | 1.37152 | 0.0522127 | ||||||||
\(691\) | −8.65506 | −0.329254 | −0.164627 | − | 0.986356i | \(-0.552642\pi\) | ||||
−0.164627 | + | 0.986356i | \(0.552642\pi\) | |||||||
\(692\) | 10.2072 | 0.388021 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.7525 | 0.673874 | ||||||||
\(695\) | 22.1156 | 0.838892 | ||||||||
\(696\) | 20.3322 | 0.770692 | ||||||||
\(697\) | 6.26794 | 0.237415 | ||||||||
\(698\) | −8.33896 | −0.315634 | ||||||||
\(699\) | 7.83806 | 0.296463 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −35.7541 | −1.35041 | −0.675207 | − | 0.737628i | \(-0.735946\pi\) | ||||
−0.675207 | + | 0.737628i | \(0.735946\pi\) | |||||||
\(702\) | −0.0634227 | −0.00239374 | ||||||||
\(703\) | 36.0127 | 1.35825 | ||||||||
\(704\) | −1.75768 | −0.0662450 | ||||||||
\(705\) | 18.5354 | 0.698085 | ||||||||
\(706\) | −0.243053 | −0.00914740 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.06306 | 0.0775345 | ||||||||
\(709\) | 18.7083 | 0.702606 | 0.351303 | − | 0.936262i | \(-0.385739\pi\) | ||||
0.351303 | + | 0.936262i | \(0.385739\pi\) | |||||||
\(710\) | −10.2551 | −0.384867 | ||||||||
\(711\) | −2.59244 | −0.0972239 | ||||||||
\(712\) | −34.2182 | −1.28238 | ||||||||
\(713\) | 5.41275 | 0.202709 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.08036 | 0.0404033 | ||||||||
\(716\) | −5.48395 | −0.204945 | ||||||||
\(717\) | −5.90515 | −0.220532 | ||||||||
\(718\) | −11.6710 | −0.435558 | ||||||||
\(719\) | 19.2531 | 0.718021 | 0.359011 | − | 0.933334i | \(-0.383114\pi\) | ||||
0.359011 | + | 0.933334i | \(0.383114\pi\) | |||||||
\(720\) | 3.68279 | 0.137250 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −0.490815 | −0.0182662 | ||||||||
\(723\) | 29.9744 | 1.11476 | ||||||||
\(724\) | −2.74391 | −0.101976 | ||||||||
\(725\) | 1.12156 | 0.0416535 | ||||||||
\(726\) | 8.96644 | 0.332776 | ||||||||
\(727\) | 23.3415 | 0.865689 | 0.432845 | − | 0.901469i | \(-0.357510\pi\) | ||||
0.432845 | + | 0.901469i | \(0.357510\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0.781379 | 0.0289201 | ||||||||
\(731\) | −59.0673 | −2.18468 | ||||||||
\(732\) | −2.75844 | −0.101955 | ||||||||
\(733\) | 41.3374 | 1.52683 | 0.763416 | − | 0.645907i | \(-0.223521\pi\) | ||||
0.763416 | + | 0.645907i | \(0.223521\pi\) | |||||||
\(734\) | 10.1835 | 0.375880 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.48842 | 0.202306 | ||||||||
\(737\) | −48.9776 | −1.80411 | ||||||||
\(738\) | 0.646272 | 0.0237896 | ||||||||
\(739\) | 18.3470 | 0.674904 | 0.337452 | − | 0.941343i | \(-0.390435\pi\) | ||||
0.337452 | + | 0.941343i | \(0.390435\pi\) | |||||||
\(740\) | 29.4511 | 1.08264 | ||||||||
\(741\) | 0.419129 | 0.0153971 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.1507 | 1.25287 | 0.626433 | − | 0.779475i | \(-0.284514\pi\) | ||||
0.626433 | + | 0.779475i | \(0.284514\pi\) | |||||||
\(744\) | −13.0341 | −0.477853 | ||||||||
\(745\) | 42.0292 | 1.53983 | ||||||||
\(746\) | 16.8694 | 0.617634 | ||||||||
\(747\) | −1.01281 | −0.0370567 | ||||||||
\(748\) | 49.4648 | 1.80861 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.31485 | −0.267101 | ||||||||
\(751\) | 25.7182 | 0.938471 | 0.469236 | − | 0.883073i | \(-0.344529\pi\) | ||||
0.469236 | + | 0.883073i | \(0.344529\pi\) | |||||||
\(752\) | 14.0103 | 0.510902 | ||||||||
\(753\) | 1.69710 | 0.0618457 | ||||||||
\(754\) | 0.556992 | 0.0202844 | ||||||||
\(755\) | −32.7281 | −1.19110 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.4055 | −0.632614 | −0.316307 | − | 0.948657i | \(-0.602443\pi\) | ||||
−0.316307 | + | 0.948657i | \(0.602443\pi\) | |||||||
\(758\) | 4.48293 | 0.162827 | ||||||||
\(759\) | −4.79504 | −0.174049 | ||||||||
\(760\) | 21.8256 | 0.791699 | ||||||||
\(761\) | 17.9597 | 0.651040 | 0.325520 | − | 0.945535i | \(-0.394461\pi\) | ||||
0.325520 | + | 0.945535i | \(0.394461\pi\) | |||||||
\(762\) | 8.60761 | 0.311821 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −15.3707 | −0.556091 | ||||||||
\(765\) | 13.8354 | 0.500220 | ||||||||
\(766\) | 15.5460 | 0.561698 | ||||||||
\(767\) | 0.127951 | 0.00462004 | ||||||||
\(768\) | −7.93626 | −0.286375 | ||||||||
\(769\) | 42.5558 | 1.53460 | 0.767301 | − | 0.641287i | \(-0.221599\pi\) | ||||
0.767301 | + | 0.641287i | \(0.221599\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.03614 | −0.0733297 | ||||||||
\(772\) | 42.1550 | 1.51719 | ||||||||
\(773\) | −30.2158 | −1.08679 | −0.543393 | − | 0.839478i | \(-0.682861\pi\) | ||||
−0.543393 | + | 0.839478i | \(0.682861\pi\) | |||||||
\(774\) | −6.09028 | −0.218911 | ||||||||
\(775\) | −0.718979 | −0.0258265 | ||||||||
\(776\) | 40.9498 | 1.47001 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.64065 | 0.0946719 | ||||||||
\(779\) | −4.27090 | −0.153021 | ||||||||
\(780\) | 0.342763 | 0.0122729 | ||||||||
\(781\) | 35.8535 | 1.28294 | ||||||||
\(782\) | 3.89456 | 0.139269 | ||||||||
\(783\) | −8.78221 | −0.313851 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.2515 | −0.472967 | ||||||||
\(786\) | −7.01684 | −0.250282 | ||||||||
\(787\) | 49.5326 | 1.76565 | 0.882824 | − | 0.469705i | \(-0.155640\pi\) | ||||
0.882824 | + | 0.469705i | \(0.155640\pi\) | |||||||
\(788\) | 0.267889 | 0.00954315 | ||||||||
\(789\) | 8.79054 | 0.312952 | ||||||||
\(790\) | −3.69820 | −0.131576 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 11.5466 | 0.410291 | ||||||||
\(793\) | −0.171078 | −0.00607518 | ||||||||
\(794\) | 0.359894 | 0.0127722 | ||||||||
\(795\) | −27.8057 | −0.986168 | ||||||||
\(796\) | 38.3300 | 1.35857 | ||||||||
\(797\) | −4.84228 | −0.171522 | −0.0857611 | − | 0.996316i | \(-0.527332\pi\) | ||||
−0.0857611 | + | 0.996316i | \(0.527332\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 52.6333 | 1.86203 | ||||||||
\(800\) | −0.729030 | −0.0257751 | ||||||||
\(801\) | 14.7801 | 0.522228 | ||||||||
\(802\) | −19.5606 | −0.690708 | ||||||||
\(803\) | −2.73183 | −0.0964041 | ||||||||
\(804\) | −15.5389 | −0.548016 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.357063 | −0.0125770 | ||||||||
\(807\) | 4.68163 | 0.164801 | ||||||||
\(808\) | 21.6050 | 0.760060 | ||||||||
\(809\) | 0.0759852 | 0.00267150 | 0.00133575 | − | 0.999999i | \(-0.499575\pi\) | ||||
0.00133575 | + | 0.999999i | \(0.499575\pi\) | |||||||
\(810\) | 1.42653 | 0.0501233 | ||||||||
\(811\) | 39.6990 | 1.39402 | 0.697010 | − | 0.717062i | \(-0.254513\pi\) | ||||
0.697010 | + | 0.717062i | \(0.254513\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.2141 | 0.533581 | ||||||||
\(814\) | 27.1786 | 0.952608 | ||||||||
\(815\) | 27.7392 | 0.971661 | ||||||||
\(816\) | 10.4577 | 0.366092 | ||||||||
\(817\) | 40.2477 | 1.40809 | ||||||||
\(818\) | 4.89555 | 0.171169 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.49272 | −0.121971 | ||||||||
\(821\) | −8.42503 | −0.294036 | −0.147018 | − | 0.989134i | \(-0.546967\pi\) | ||||
−0.147018 | + | 0.989134i | \(0.546967\pi\) | |||||||
\(822\) | 1.25838 | 0.0438912 | ||||||||
\(823\) | −32.0659 | −1.11775 | −0.558874 | − | 0.829253i | \(-0.688766\pi\) | ||||
−0.558874 | + | 0.829253i | \(0.688766\pi\) | |||||||
\(824\) | 19.5075 | 0.679574 | ||||||||
\(825\) | 0.636928 | 0.0221750 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.3100 | −1.19308 | −0.596539 | − | 0.802584i | \(-0.703458\pi\) | ||||
−0.596539 | + | 0.802584i | \(0.703458\pi\) | |||||||
\(828\) | −1.52130 | −0.0528690 | ||||||||
\(829\) | 43.6558 | 1.51623 | 0.758114 | − | 0.652122i | \(-0.226121\pi\) | ||||
0.758114 | + | 0.652122i | \(0.226121\pi\) | |||||||
\(830\) | −1.44481 | −0.0501499 | ||||||||
\(831\) | −29.2313 | −1.01402 | ||||||||
\(832\) | −0.0345856 | −0.00119904 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.47511 | 0.224215 | ||||||||
\(835\) | 39.7160 | 1.37443 | ||||||||
\(836\) | −33.7047 | −1.16570 | ||||||||
\(837\) | 5.62989 | 0.194597 | ||||||||
\(838\) | −3.07658 | −0.106279 | ||||||||
\(839\) | 39.1592 | 1.35192 | 0.675962 | − | 0.736936i | \(-0.263728\pi\) | ||||
0.675962 | + | 0.736936i | \(0.263728\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.1273 | 1.65956 | ||||||||
\(842\) | 3.70312 | 0.127618 | ||||||||
\(843\) | 5.86638 | 0.202049 | ||||||||
\(844\) | 11.7202 | 0.403425 | ||||||||
\(845\) | −28.6740 | −0.986415 | ||||||||
\(846\) | 5.42690 | 0.186581 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −21.0174 | −0.721739 | ||||||||
\(849\) | 16.0598 | 0.551169 | ||||||||
\(850\) | −0.517317 | −0.0177438 | ||||||||
\(851\) | −8.10692 | −0.277901 | ||||||||
\(852\) | 11.3751 | 0.389705 | ||||||||
\(853\) | 9.54494 | 0.326812 | 0.163406 | − | 0.986559i | \(-0.447752\pi\) | ||||
0.163406 | + | 0.986559i | \(0.447752\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.42726 | −0.322406 | ||||||||
\(856\) | 25.2231 | 0.862109 | ||||||||
\(857\) | −17.3645 | −0.593160 | −0.296580 | − | 0.955008i | \(-0.595846\pi\) | ||||
−0.296580 | + | 0.955008i | \(0.595846\pi\) | |||||||
\(858\) | 0.316314 | 0.0107988 | ||||||||
\(859\) | 1.22800 | 0.0418987 | 0.0209493 | − | 0.999781i | \(-0.493331\pi\) | ||||
0.0209493 | + | 0.999781i | \(0.493331\pi\) | |||||||
\(860\) | 32.9144 | 1.12237 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.3715 | −0.796035 | ||||||||
\(863\) | −18.2094 | −0.619854 | −0.309927 | − | 0.950760i | \(-0.600305\pi\) | ||||
−0.309927 | + | 0.950760i | \(0.600305\pi\) | |||||||
\(864\) | 5.70859 | 0.194210 | ||||||||
\(865\) | −14.2389 | −0.484139 | ||||||||
\(866\) | −26.1340 | −0.888071 | ||||||||
\(867\) | 22.2871 | 0.756909 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.9295 | 0.438603 | ||||||||
\(870\) | −12.5281 | −0.424743 | ||||||||
\(871\) | −0.963725 | −0.0326546 | ||||||||
\(872\) | 16.1993 | 0.548579 | ||||||||
\(873\) | −17.6877 | −0.598637 | ||||||||
\(874\) | −2.65371 | −0.0897629 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.866717 | −0.0292836 | ||||||||
\(877\) | 33.3435 | 1.12593 | 0.562964 | − | 0.826481i | \(-0.309661\pi\) | ||||
0.562964 | + | 0.826481i | \(0.309661\pi\) | |||||||
\(878\) | −2.91753 | −0.0984619 | ||||||||
\(879\) | −12.9726 | −0.437556 | ||||||||
\(880\) | −18.3675 | −0.619169 | ||||||||
\(881\) | 26.1078 | 0.879594 | 0.439797 | − | 0.898097i | \(-0.355050\pi\) | ||||
0.439797 | + | 0.898097i | \(0.355050\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.8036 | 1.03662 | 0.518311 | − | 0.855192i | \(-0.326561\pi\) | ||||
0.518311 | + | 0.855192i | \(0.326561\pi\) | |||||||
\(884\) | 0.973311 | 0.0327360 | ||||||||
\(885\) | −2.87793 | −0.0967406 | ||||||||
\(886\) | 1.48169 | 0.0497784 | ||||||||
\(887\) | −9.34789 | −0.313871 | −0.156936 | − | 0.987609i | \(-0.550162\pi\) | ||||
−0.156936 | + | 0.987609i | \(0.550162\pi\) | |||||||
\(888\) | 19.5217 | 0.655107 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 21.0843 | 0.706746 | ||||||||
\(891\) | −4.98739 | −0.167084 | ||||||||
\(892\) | 45.1242 | 1.51087 | ||||||||
\(893\) | −35.8637 | −1.20013 | ||||||||
\(894\) | 12.3055 | 0.411558 | ||||||||
\(895\) | 7.65002 | 0.255712 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.0943512 | −0.00315030 | ||||||||
\(898\) | −0.497924 | −0.0166159 | ||||||||
\(899\) | −49.4429 | −1.64901 | ||||||||
\(900\) | 0.202076 | 0.00673586 | ||||||||
\(901\) | −78.9574 | −2.63045 | ||||||||
\(902\) | −3.22321 | −0.107321 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 46.6229 | 1.55065 | ||||||||
\(905\) | 3.82770 | 0.127237 | ||||||||
\(906\) | −9.58229 | −0.318350 | ||||||||
\(907\) | −59.6860 | −1.98184 | −0.990920 | − | 0.134453i | \(-0.957072\pi\) | ||||
−0.990920 | + | 0.134453i | \(0.957072\pi\) | |||||||
\(908\) | 24.4887 | 0.812687 | ||||||||
\(909\) | −9.33195 | −0.309521 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.3828 | 0.774705 | 0.387353 | − | 0.921932i | \(-0.373390\pi\) | ||||
0.387353 | + | 0.921932i | \(0.373390\pi\) | |||||||
\(912\) | −7.12573 | −0.235956 | ||||||||
\(913\) | 5.05127 | 0.167173 | ||||||||
\(914\) | 6.03568 | 0.199642 | ||||||||
\(915\) | 3.84798 | 0.127210 | ||||||||
\(916\) | −4.10306 | −0.135569 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 4.05080 | 0.133696 | ||||||||
\(919\) | −29.2948 | −0.966347 | −0.483174 | − | 0.875525i | \(-0.660516\pi\) | ||||
−0.483174 | + | 0.875525i | \(0.660516\pi\) | |||||||
\(920\) | −4.91322 | −0.161984 | ||||||||
\(921\) | 24.4190 | 0.804634 | ||||||||
\(922\) | −24.6889 | −0.813086 | ||||||||
\(923\) | 0.705484 | 0.0232213 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.07685 | 0.0354065 | ||||||||
\(926\) | 8.19372 | 0.269262 | ||||||||
\(927\) | −8.42596 | −0.276745 | ||||||||
\(928\) | −50.1341 | −1.64573 | ||||||||
\(929\) | 30.3704 | 0.996422 | 0.498211 | − | 0.867056i | \(-0.333991\pi\) | ||||
0.498211 | + | 0.867056i | \(0.333991\pi\) | |||||||
\(930\) | 8.03123 | 0.263354 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −12.4024 | −0.406255 | ||||||||
\(933\) | 18.2933 | 0.598897 | ||||||||
\(934\) | 1.91215 | 0.0625675 | ||||||||
\(935\) | −69.0025 | −2.25662 | ||||||||
\(936\) | 0.227201 | 0.00742630 | ||||||||
\(937\) | 0.491253 | 0.0160485 | 0.00802426 | − | 0.999968i | \(-0.497446\pi\) | ||||
0.00802426 | + | 0.999968i | \(0.497446\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.76655 | 0.318719 | ||||||||
\(940\) | −29.3292 | −0.956613 | ||||||||
\(941\) | 30.8534 | 1.00579 | 0.502895 | − | 0.864347i | \(-0.332268\pi\) | ||||
0.502895 | + | 0.864347i | \(0.332268\pi\) | |||||||
\(942\) | −3.87984 | −0.126412 | ||||||||
\(943\) | 0.961432 | 0.0313085 | ||||||||
\(944\) | −2.17533 | −0.0708008 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.3746 | 0.987565 | ||||||||
\(947\) | −48.8549 | −1.58757 | −0.793786 | − | 0.608197i | \(-0.791893\pi\) | ||||
−0.793786 | + | 0.608197i | \(0.791893\pi\) | |||||||
\(948\) | 4.10209 | 0.133230 | ||||||||
\(949\) | −0.0537537 | −0.00174492 | ||||||||
\(950\) | 0.352493 | 0.0114364 | ||||||||
\(951\) | 11.2980 | 0.366364 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.3510 | 0.788806 | 0.394403 | − | 0.918938i | \(-0.370951\pi\) | ||||
0.394403 | + | 0.918938i | \(0.370951\pi\) | |||||||
\(954\) | −8.14110 | −0.263578 | ||||||||
\(955\) | 21.4418 | 0.693841 | ||||||||
\(956\) | 9.34390 | 0.302203 | ||||||||
\(957\) | 43.8004 | 1.41586 | ||||||||
\(958\) | −9.02663 | −0.291637 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.777916 | 0.0251071 | ||||||||
\(961\) | 0.695634 | 0.0224398 | ||||||||
\(962\) | 0.534788 | 0.0172423 | ||||||||
\(963\) | −10.8948 | −0.351079 | ||||||||
\(964\) | −47.4294 | −1.52760 | ||||||||
\(965\) | −58.8056 | −1.89302 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.6517 | −0.696273 | −0.348136 | − | 0.937444i | \(-0.613185\pi\) | ||||
−0.348136 | + | 0.937444i | \(0.613185\pi\) | |||||||
\(968\) | −32.1208 | −1.03240 | ||||||||
\(969\) | −26.7697 | −0.859967 | ||||||||
\(970\) | −25.2321 | −0.810153 | ||||||||
\(971\) | −15.0904 | −0.484274 | −0.242137 | − | 0.970242i | \(-0.577848\pi\) | ||||
−0.242137 | + | 0.970242i | \(0.577848\pi\) | |||||||
\(972\) | −1.58233 | −0.0507533 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.18712 | −0.0380377 | ||||||||
\(975\) | 0.0125327 | 0.000401369 0 | ||||||||
\(976\) | 2.90855 | 0.0931004 | ||||||||
\(977\) | −51.7542 | −1.65576 | −0.827882 | − | 0.560903i | \(-0.810454\pi\) | ||||
−0.827882 | + | 0.560903i | \(0.810454\pi\) | |||||||
\(978\) | 8.12162 | 0.259701 | ||||||||
\(979\) | −73.7139 | −2.35591 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.99706 | −0.223399 | ||||||||
\(982\) | −10.0673 | −0.321261 | ||||||||
\(983\) | −5.13872 | −0.163900 | −0.0819499 | − | 0.996636i | \(-0.526115\pi\) | ||||
−0.0819499 | + | 0.996636i | \(0.526115\pi\) | |||||||
\(984\) | −2.31516 | −0.0738047 | ||||||||
\(985\) | −0.373701 | −0.0119071 | ||||||||
\(986\) | −35.5750 | −1.13294 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.663202 | −0.0210993 | ||||||||
\(989\) | −9.06025 | −0.288099 | ||||||||
\(990\) | −7.11469 | −0.226120 | ||||||||
\(991\) | 57.3168 | 1.82073 | 0.910364 | − | 0.413808i | \(-0.135801\pi\) | ||||
0.910364 | + | 0.413808i | \(0.135801\pi\) | |||||||
\(992\) | 32.1387 | 1.02041 | ||||||||
\(993\) | −2.09392 | −0.0664485 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.4697 | −1.69510 | ||||||||
\(996\) | 1.60260 | 0.0507803 | ||||||||
\(997\) | 55.0860 | 1.74459 | 0.872296 | − | 0.488978i | \(-0.162630\pi\) | ||||
0.872296 | + | 0.488978i | \(0.162630\pi\) | |||||||
\(998\) | −12.3452 | −0.390782 | ||||||||
\(999\) | −8.43213 | −0.266781 |
(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 | 6027.2.a.bi.1.10 | 13 | ||
7.2 | even | 3 | 861.2.i.f.739.4 | yes | 26 | ||
7.4 | even | 3 | 861.2.i.f.247.4 | ✓ | 26 | ||
7.6 | odd | 2 | 6027.2.a.bh.1.10 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
861.2.i.f.247.4 | ✓ | 26 | 7.4 | even | 3 | ||
861.2.i.f.739.4 | yes | 26 | 7.2 | even | 3 | ||
6027.2.a.bh.1.10 | 13 | 7.6 | odd | 2 | |||
6027.2.a.bi.1.10 | 13 | 1.1 | even | 1 | trivial |