Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4004,2,Mod(1,4004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4004, 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("4004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4004.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: | \(31.9721009693\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 12x^{7} + 60x^{6} + 15x^{5} - 233x^{4} + 74x^{3} + 271x^{2} - 67x - 87 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.11788\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4004.1 |
$q$-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 | ||||||||
\(3\) | −3.11788 | −1.80011 | −0.900055 | − | 0.435777i | \(-0.856474\pi\) | ||||
−0.900055 | + | 0.435777i | \(0.856474\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.40203 | 1.96865 | 0.984324 | − | 0.176368i | \(-0.0564348\pi\) | ||||
0.984324 | + | 0.176368i | \(0.0564348\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.72118 | 2.24039 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −13.7250 | −3.54378 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.59028 | −0.385700 | −0.192850 | − | 0.981228i | \(-0.561773\pi\) | ||||
−0.192850 | + | 0.981228i | \(0.561773\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.13343 | 0.718858 | 0.359429 | − | 0.933172i | \(-0.382971\pi\) | ||||
0.359429 | + | 0.933172i | \(0.382971\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.11788 | −0.680378 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.76292 | −0.576108 | −0.288054 | − | 0.957614i | \(-0.593008\pi\) | ||||
−0.288054 | + | 0.957614i | \(0.593008\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.3779 | 2.87558 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.6022 | −2.23285 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.82484 | 0.338864 | 0.169432 | − | 0.985542i | \(-0.445807\pi\) | ||||
0.169432 | + | 0.985542i | \(0.445807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.86167 | 1.05279 | 0.526394 | − | 0.850241i | \(-0.323544\pi\) | ||||
0.526394 | + | 0.850241i | \(0.323544\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.11788 | 0.542753 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.40203 | 0.744079 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.94070 | 0.483448 | 0.241724 | − | 0.970345i | \(-0.422287\pi\) | ||||
0.241724 | + | 0.970345i | \(0.422287\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.11788 | −0.499261 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.96742 | −1.08813 | −0.544064 | − | 0.839044i | \(-0.683115\pi\) | ||||
−0.544064 | + | 0.839044i | \(0.683115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.12559 | 0.781645 | 0.390823 | − | 0.920466i | \(-0.372191\pi\) | ||||
0.390823 | + | 0.920466i | \(0.372191\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 29.5869 | 4.41055 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.67005 | 1.26466 | 0.632329 | − | 0.774700i | \(-0.282099\pi\) | ||||
0.632329 | + | 0.774700i | \(0.282099\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.95831 | 0.694302 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.705189 | −0.0968651 | −0.0484326 | − | 0.998826i | \(-0.515423\pi\) | ||||
−0.0484326 | + | 0.998826i | \(0.515423\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.40203 | −0.593570 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.76966 | −1.29402 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.2123 | −1.45972 | −0.729861 | − | 0.683595i | \(-0.760415\pi\) | ||||
−0.729861 | + | 0.683595i | \(0.760415\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.91210 | 0.885004 | 0.442502 | − | 0.896768i | \(-0.354091\pi\) | ||||
0.442502 | + | 0.896768i | \(0.354091\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.72118 | 0.846790 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.40203 | 0.546005 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.69117 | 0.328779 | 0.164389 | − | 0.986396i | \(-0.447435\pi\) | ||||
0.164389 | + | 0.986396i | \(0.447435\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.61444 | 1.03706 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.24458 | −1.09713 | −0.548565 | − | 0.836108i | \(-0.684826\pi\) | ||||
−0.548565 | + | 0.836108i | \(0.684826\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.2313 | 1.54861 | 0.774305 | − | 0.632813i | \(-0.218100\pi\) | ||||
0.774305 | + | 0.632813i | \(0.218100\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −44.8285 | −5.17635 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.32396 | 1.04903 | 0.524514 | − | 0.851402i | \(-0.324247\pi\) | ||||
0.524514 | + | 0.851402i | \(0.324247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 16.0108 | 1.77897 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.98352 | −0.766541 | −0.383270 | − | 0.923636i | \(-0.625202\pi\) | ||||
−0.383270 | + | 0.923636i | \(0.625202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.00047 | −0.759308 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.68963 | −0.609992 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.583301 | 0.0618298 | 0.0309149 | − | 0.999522i | \(-0.490158\pi\) | ||||
0.0309149 | + | 0.999522i | \(0.490158\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.2760 | −1.89513 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.7935 | 1.41518 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.299773 | 0.0304373 | 0.0152187 | − | 0.999884i | \(-0.495156\pi\) | ||||
0.0152187 | + | 0.999884i | \(0.495156\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.72118 | −0.675504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.94277 | −0.591327 | −0.295664 | − | 0.955292i | \(-0.595541\pi\) | ||||
−0.295664 | + | 0.955292i | \(0.595541\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.0401 | −1.67901 | −0.839505 | − | 0.543351i | \(-0.817155\pi\) | ||||
−0.839505 | + | 0.543351i | \(0.817155\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13.7250 | −1.33942 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.97928 | −0.868060 | −0.434030 | − | 0.900898i | \(-0.642909\pi\) | ||||
−0.434030 | + | 0.900898i | \(0.642909\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.6494 | 1.21159 | 0.605795 | − | 0.795620i | \(-0.292855\pi\) | ||||
0.605795 | + | 0.795620i | \(0.292855\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.16876 | −0.870260 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.30123 | −0.780914 | −0.390457 | − | 0.920621i | \(-0.627683\pi\) | ||||
−0.390457 | + | 0.920621i | \(0.627683\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.1624 | −1.13415 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.72118 | 0.621374 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.59028 | −0.145781 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.7236 | 1.95875 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 41.2818 | 3.69235 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −21.7835 | −1.93297 | −0.966486 | − | 0.256721i | \(-0.917358\pi\) | ||||
−0.966486 | + | 0.256721i | \(0.917358\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −15.9810 | −1.40705 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.17119 | 0.451809 | 0.225905 | − | 0.974149i | \(-0.427466\pi\) | ||||
0.225905 | + | 0.974149i | \(0.427466\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.13343 | 0.271703 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −51.0733 | −4.39569 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.1209 | 0.950121 | 0.475061 | − | 0.879953i | \(-0.342426\pi\) | ||||
0.475061 | + | 0.879953i | \(0.342426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.3566 | 1.72662 | 0.863312 | − | 0.504671i | \(-0.168386\pi\) | ||||
0.863312 | + | 0.504671i | \(0.168386\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −27.0322 | −2.27652 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.03300 | 0.667104 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.11788 | −0.257159 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.34391 | 0.273944 | 0.136972 | − | 0.990575i | \(-0.456263\pi\) | ||||
0.136972 | + | 0.990575i | \(0.456263\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.3852 | −1.33341 | −0.666704 | − | 0.745322i | \(-0.732296\pi\) | ||||
−0.666704 | + | 0.745322i | \(0.732296\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.6886 | −0.864120 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.8033 | 2.07257 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.4456 | −1.31250 | −0.656252 | − | 0.754541i | \(-0.727859\pi\) | ||||
−0.656252 | + | 0.754541i | \(0.727859\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.19870 | 0.174368 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.76292 | −0.217748 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.60889 | −0.752626 | −0.376313 | − | 0.926493i | \(-0.622808\pi\) | ||||
−0.376313 | + | 0.926493i | \(0.622808\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.7250 | 1.06849 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0173 | 0.929925 | 0.464962 | − | 0.885330i | \(-0.346068\pi\) | ||||
0.464962 | + | 0.885330i | \(0.346068\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.0604 | 1.61053 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.1081 | −1.52879 | −0.764396 | − | 0.644747i | \(-0.776963\pi\) | ||||
−0.764396 | + | 0.644747i | \(0.776963\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.3779 | 1.08687 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 34.9588 | 2.62766 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.3689 | 1.07398 | 0.536992 | − | 0.843588i | \(-0.319561\pi\) | ||||
0.536992 | + | 0.843588i | \(0.319561\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5788 | 0.786313 | 0.393157 | − | 0.919472i | \(-0.371383\pi\) | ||||
0.393157 | + | 0.919472i | \(0.371383\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −21.5511 | −1.59310 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.9451 | 0.951740 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.59028 | 0.116293 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.6022 | −0.843937 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.7043 | −1.20868 | −0.604339 | − | 0.796727i | \(-0.706563\pi\) | ||||
−0.604339 | + | 0.796727i | \(0.706563\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.33097 | −0.167787 | −0.0838936 | − | 0.996475i | \(-0.526736\pi\) | ||||
−0.0838936 | + | 0.996475i | \(0.526736\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.7250 | −0.982869 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.05196 | −0.644925 | −0.322463 | − | 0.946582i | \(-0.604511\pi\) | ||||
−0.322463 | + | 0.946582i | \(0.604511\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.9671 | 1.48632 | 0.743161 | − | 0.669113i | \(-0.233326\pi\) | ||||
0.743161 | + | 0.669113i | \(0.233326\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.39075 | −0.591838 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.82484 | 0.128079 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −30.6708 | −2.14214 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.5701 | −1.29071 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.13343 | −0.216744 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.6891 | 0.735869 | 0.367935 | − | 0.929852i | \(-0.380065\pi\) | ||||
0.367935 | + | 0.929852i | \(0.380065\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 28.8235 | 1.97495 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 22.5630 | 1.53879 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.86167 | 0.397916 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −41.2537 | −2.78767 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.59028 | −0.106974 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4147 | 1.16617 | 0.583086 | − | 0.812410i | \(-0.301845\pi\) | ||||
0.583086 | + | 0.812410i | \(0.301845\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 96.6364 | 6.44243 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.25306 | 0.149541 | 0.0747706 | − | 0.997201i | \(-0.476178\pi\) | ||||
0.0747706 | + | 0.997201i | \(0.476178\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.95142 | 0.657608 | 0.328804 | − | 0.944398i | \(-0.393354\pi\) | ||||
0.328804 | + | 0.944398i | \(0.393354\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.11788 | 0.205142 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 27.0633 | 1.77297 | 0.886486 | − | 0.462754i | \(-0.153139\pi\) | ||||
0.886486 | + | 0.462754i | \(0.153139\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 38.1659 | 2.48967 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −29.0710 | −1.88836 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.6316 | 1.07581 | 0.537906 | − | 0.843005i | \(-0.319216\pi\) | ||||
0.537906 | + | 0.843005i | \(0.319216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.1457 | 1.42653 | 0.713266 | − | 0.700893i | \(-0.247215\pi\) | ||||
0.713266 | + | 0.700893i | \(0.247215\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.1130 | −0.969502 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.40203 | 0.281236 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.13343 | 0.199375 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.7738 | 1.37986 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.6199 | 1.23839 | 0.619197 | − | 0.785236i | \(-0.287458\pi\) | ||||
0.619197 | + | 0.785236i | \(0.287458\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.76292 | 0.173703 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.8266 | 1.36684 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.91710 | −0.431477 | −0.215738 | − | 0.976451i | \(-0.569216\pi\) | ||||
−0.215738 | + | 0.976451i | \(0.569216\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.94070 | 0.182726 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.2651 | 0.759189 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.3498 | 1.50147 | 0.750737 | − | 0.660602i | \(-0.229699\pi\) | ||||
0.750737 | + | 0.660602i | \(0.229699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.10426 | −0.190693 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.81866 | −0.111300 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.53061 | 0.459149 | 0.229575 | − | 0.973291i | \(-0.426266\pi\) | ||||
0.229575 | + | 0.973291i | \(0.426266\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.1877 | 1.22632 | 0.613158 | − | 0.789960i | \(-0.289899\pi\) | ||||
0.613158 | + | 0.789960i | \(0.289899\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.11788 | −0.188703 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.3779 | −0.867019 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.11132 | 0.126857 | 0.0634286 | − | 0.997986i | \(-0.479796\pi\) | ||||
0.0634286 | + | 0.997986i | \(0.479796\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 39.3974 | 2.35866 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.7278 | −0.639969 | −0.319984 | − | 0.947423i | \(-0.603678\pi\) | ||||
−0.319984 | + | 0.947423i | \(0.603678\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 32.3124 | 1.92077 | 0.960385 | − | 0.278675i | \(-0.0898952\pi\) | ||||
0.960385 | + | 0.278675i | \(0.0898952\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −43.0064 | −2.54748 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.96742 | −0.411274 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.4710 | −0.851236 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.934656 | −0.0547905 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.0659 | 1.40594 | 0.702972 | − | 0.711217i | \(-0.251856\pi\) | ||||
0.702972 | + | 0.711217i | \(0.251856\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −49.3571 | −2.87368 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.6022 | 0.673229 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.76292 | −0.159784 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.12559 | 0.295434 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.5288 | 1.06445 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 30.4273 | 1.74226 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.0355 | −0.743978 | −0.371989 | − | 0.928237i | \(-0.621324\pi\) | ||||
−0.371989 | + | 0.928237i | \(0.621324\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 53.1290 | 3.02240 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.6464 | −1.56769 | −0.783843 | − | 0.620959i | \(-0.786743\pi\) | ||||
−0.783843 | + | 0.620959i | \(0.786743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.3230 | −1.37482 | −0.687409 | − | 0.726270i | \(-0.741252\pi\) | ||||
−0.687409 | + | 0.726270i | \(0.741252\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 29.5869 | 1.66703 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.18317 | 0.0664537 | 0.0332269 | − | 0.999448i | \(-0.489422\pi\) | ||||
0.0332269 | + | 0.999448i | \(0.489422\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.82484 | −0.102171 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 27.9963 | 1.56260 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.98304 | −0.277264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.3779 | 0.797542 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −39.4393 | −2.18100 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.67005 | 0.477995 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.0890 | 0.994264 | 0.497132 | − | 0.867675i | \(-0.334386\pi\) | ||||
0.497132 | + | 0.867675i | \(0.334386\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.7650 | 1.08312 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.8466 | 0.647250 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.59644 | −0.141437 | −0.0707185 | − | 0.997496i | \(-0.522529\pi\) | ||||
−0.0707185 | + | 0.997496i | \(0.522529\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.8822 | 1.40573 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.86167 | −0.317427 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 37.9211 | 2.04160 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.8501 | −1.38771 | −0.693854 | − | 0.720116i | \(-0.744089\pi\) | ||||
−0.693854 | + | 0.720116i | \(0.744089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.2982 | −1.51477 | −0.757384 | − | 0.652970i | \(-0.773523\pi\) | ||||
−0.757384 | + | 0.652970i | \(0.773523\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.6022 | −0.619280 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.2423 | −1.92898 | −0.964492 | − | 0.264113i | \(-0.914921\pi\) | ||||
−0.964492 | + | 0.264113i | \(0.914921\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −40.6949 | −2.15986 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.95831 | 0.262422 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.96447 | −0.473127 | −0.236563 | − | 0.971616i | \(-0.576021\pi\) | ||||
−0.236563 | + | 0.971616i | \(0.576021\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.18162 | −0.483243 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.11788 | −0.163646 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 58.2447 | 3.04867 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.558020 | 0.0291284 | 0.0145642 | − | 0.999894i | \(-0.495364\pi\) | ||||
0.0145642 | + | 0.999894i | \(0.495364\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −46.8293 | −2.43784 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.705189 | −0.0366116 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.9607 | −0.567525 | −0.283763 | − | 0.958895i | \(-0.591583\pi\) | ||||
−0.283763 | + | 0.958895i | \(0.591583\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −128.712 | −6.64664 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.82484 | 0.0939840 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.9617 | −1.17946 | −0.589731 | − | 0.807600i | \(-0.700766\pi\) | ||||
−0.589731 | + | 0.807600i | \(0.700766\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 67.9183 | 3.47956 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.8734 | 1.47536 | 0.737681 | − | 0.675149i | \(-0.235921\pi\) | ||||
0.737681 | + | 0.675149i | \(0.235921\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.40203 | −0.224348 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.4500 | 1.75119 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.5087 | −1.03983 | −0.519915 | − | 0.854218i | \(-0.674036\pi\) | ||||
−0.519915 | + | 0.854218i | \(0.674036\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.39381 | 0.222205 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.1232 | −0.813306 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 41.0444 | 2.06517 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.42381 | −0.322402 | −0.161201 | − | 0.986922i | \(-0.551537\pi\) | ||||
−0.161201 | + | 0.986922i | \(0.551537\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.76966 | −0.489095 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.5374 | 0.576148 | 0.288074 | − | 0.957608i | \(-0.406985\pi\) | ||||
0.288074 | + | 0.957608i | \(0.406985\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.86167 | 0.291991 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 70.4799 | 3.50218 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.94070 | −0.145765 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.08137 | 0.0534702 | 0.0267351 | − | 0.999643i | \(-0.491489\pi\) | ||||
0.0267351 | + | 0.999643i | \(0.491489\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −34.6736 | −1.71032 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.2123 | −0.551723 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.7417 | −1.50905 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −63.4694 | −3.10811 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.8080 | 0.576860 | 0.288430 | − | 0.957501i | \(-0.406867\pi\) | ||||
0.288430 | + | 0.957501i | \(0.406867\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.7001 | 0.765174 | 0.382587 | − | 0.923919i | \(-0.375033\pi\) | ||||
0.382587 | + | 0.923919i | \(0.375033\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 58.2730 | 2.83333 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.8649 | −1.10911 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.91210 | 0.334500 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.11788 | 0.150533 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.8166 | 1.86973 | 0.934865 | − | 0.355003i | \(-0.115520\pi\) | ||||
0.934865 | + | 0.355003i | \(0.115520\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.07206 | −0.387919 | −0.193959 | − | 0.981010i | \(-0.562133\pi\) | ||||
−0.193959 | + | 0.981010i | \(0.562133\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.0459 | −1.20086 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.65740 | −0.414140 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.6070 | 0.983518 | 0.491759 | − | 0.870731i | \(-0.336354\pi\) | ||||
0.491759 | + | 0.870731i | \(0.336354\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.72118 | 0.320056 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.64130 | −0.220515 | −0.110257 | − | 0.993903i | \(-0.535167\pi\) | ||||
−0.110257 | + | 0.993903i | \(0.535167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.56771 | 0.121721 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.4259 | −0.493129 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.3457 | −0.818594 | −0.409297 | − | 0.912401i | \(-0.634226\pi\) | ||||
−0.409297 | + | 0.912401i | \(0.634226\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.96742 | 0.328083 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 51.0871 | 2.40028 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.40203 | 0.206370 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.6146 | −1.10464 | −0.552321 | − | 0.833631i | \(-0.686258\pi\) | ||||
−0.552321 | + | 0.833631i | \(0.686258\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.4508 | 0.861209 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.5369 | 0.677052 | 0.338526 | − | 0.940957i | \(-0.390072\pi\) | ||||
0.338526 | + | 0.940957i | \(0.390072\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.0894 | −1.67722 | −0.838609 | − | 0.544734i | \(-0.816631\pi\) | ||||
−0.838609 | + | 0.544734i | \(0.816631\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −80.4515 | −3.73085 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 38.4901 | 1.78111 | 0.890555 | − | 0.454876i | \(-0.150316\pi\) | ||||
0.890555 | + | 0.454876i | \(0.150316\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.69117 | 0.124267 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 51.2755 | 2.36265 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.12559 | −0.235675 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 45.0521 | 2.06713 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.73970 | −0.217016 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.54964 | −0.207878 | −0.103939 | − | 0.994584i | \(-0.533145\pi\) | ||||
−0.103939 | + | 0.994584i | \(0.533145\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.94070 | 0.134084 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.61444 | 0.391971 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.31961 | 0.0599204 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.7711 | −1.34906 | −0.674528 | − | 0.738250i | \(-0.735653\pi\) | ||||
−0.674528 | + | 0.738250i | \(0.735653\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.9594 | 1.35481 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.8353 | −0.488990 | −0.244495 | − | 0.969651i | \(-0.578622\pi\) | ||||
−0.244495 | + | 0.969651i | \(0.578622\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.90201 | −0.130700 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −29.5869 | −1.32983 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.24458 | −0.414676 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4447 | 0.736167 | 0.368083 | − | 0.929793i | \(-0.380014\pi\) | ||||
0.368083 | + | 0.929793i | \(0.380014\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −37.4684 | −1.67397 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.7689 | 0.524751 | 0.262375 | − | 0.964966i | \(-0.415494\pi\) | ||||
0.262375 | + | 0.964966i | \(0.415494\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.1602 | −1.16412 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.11788 | −0.138470 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.65928 | 0.117870 | 0.0589352 | − | 0.998262i | \(-0.481229\pi\) | ||||
0.0589352 | + | 0.998262i | \(0.481229\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.2313 | 0.585320 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −36.3547 | −1.60510 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −75.0111 | −3.30538 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.67005 | −0.381308 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 62.6948 | 2.75199 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.6894 | 0.731176 | 0.365588 | − | 0.930777i | \(-0.380868\pi\) | ||||
0.365588 | + | 0.930777i | \(0.380868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 45.2942 | 1.98058 | 0.990289 | − | 0.139021i | \(-0.0443957\pi\) | ||||
0.990289 | + | 0.139021i | \(0.0443957\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −44.8285 | −1.95648 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.32171 | −0.406060 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.3663 | −0.668100 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −75.3602 | −3.27036 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.96742 | −0.301793 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39.5271 | −1.70891 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −44.8006 | −1.93329 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.93737 | 0.169281 | 0.0846405 | − | 0.996412i | \(-0.473026\pi\) | ||||
0.0846405 | + | 0.996412i | \(0.473026\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.9833 | −1.41545 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 55.6830 | 2.38520 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.1443 | −0.818550 | −0.409275 | − | 0.912411i | \(-0.634218\pi\) | ||||
−0.409275 | + | 0.912411i | \(0.634218\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 46.4575 | 1.98276 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.71800 | 0.243595 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.32396 | 0.396495 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −40.3612 | −1.71324 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.4472 | −0.696889 | −0.348445 | − | 0.937329i | \(-0.613290\pi\) | ||||
−0.348445 | + | 0.937329i | \(0.613290\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12559 | 0.216789 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.95831 | −0.209340 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.6079 | −0.489214 | −0.244607 | − | 0.969622i | \(-0.578659\pi\) | ||||
−0.244607 | + | 0.969622i | \(0.578659\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.5423 | −1.53735 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.0108 | 0.672389 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.9489 | 0.584768 | 0.292384 | − | 0.956301i | \(-0.405551\pi\) | ||||
0.292384 | + | 0.956301i | \(0.405551\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.24914 | 0.261518 | 0.130759 | − | 0.991414i | \(-0.458259\pi\) | ||||
0.130759 | + | 0.991414i | \(0.458259\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 52.0819 | 2.17575 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −39.7249 | −1.65664 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.3523 | 0.430970 | 0.215485 | − | 0.976507i | \(-0.430867\pi\) | ||||
0.215485 | + | 0.976507i | \(0.430867\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.26770 | 0.302035 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.98352 | −0.289725 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.705189 | 0.0292059 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 29.5869 | 1.22327 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.0542 | 1.81831 | 0.909155 | − | 0.416457i | \(-0.136728\pi\) | ||||
0.909155 | + | 0.416457i | \(0.136728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.3671 | 0.756805 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 28.2229 | 1.16094 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.7471 | −1.59115 | −0.795577 | − | 0.605853i | \(-0.792832\pi\) | ||||
−0.795577 | + | 0.605853i | \(0.792832\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.00047 | −0.286991 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −65.3731 | −2.67554 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.3148 | 0.870899 | 0.435450 | − | 0.900213i | \(-0.356589\pi\) | ||||
0.435450 | + | 0.900213i | \(0.356589\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.1302 | 1.59615 | 0.798076 | − | 0.602556i | \(-0.205851\pi\) | ||||
0.798076 | + | 0.602556i | \(0.205851\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.0879 | 0.736594 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.40203 | 0.178968 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.12471 | 0.329772 | 0.164886 | − | 0.986313i | \(-0.447274\pi\) | ||||
0.164886 | + | 0.986313i | \(0.447274\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.68963 | −0.230555 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.67005 | 0.350753 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.8590 | 0.680928 | 0.340464 | − | 0.940258i | \(-0.389416\pi\) | ||||
0.340464 | + | 0.940258i | \(0.389416\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 95.6280 | 3.85609 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3547 | −1.18177 | −0.590887 | − | 0.806754i | \(-0.701222\pi\) | ||||
−0.590887 | + | 0.806754i | \(0.701222\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.1330 | 0.487665 | 0.243832 | − | 0.969817i | \(-0.421595\pi\) | ||||
0.243832 | + | 0.969817i | \(0.421595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.0559 | 1.28636 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.583301 | 0.0233695 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 109.834 | 4.39337 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.76966 | 0.390163 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.67654 | −0.186466 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.12676 | 0.363331 | 0.181665 | − | 0.983360i | \(-0.441851\pi\) | ||||
0.181665 | + | 0.983360i | \(0.441851\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −33.3274 | −1.32465 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −95.8916 | −3.80534 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −62.1345 | −2.45800 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.5552 | −0.930373 | −0.465186 | − | 0.885213i | \(-0.654013\pi\) | ||||
−0.465186 | + | 0.885213i | \(0.654013\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.3696 | −1.11879 | −0.559394 | − | 0.828902i | \(-0.688966\pi\) | ||||
−0.559394 | + | 0.828902i | \(0.688966\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −70.3488 | −2.76998 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.8445 | −0.780169 | −0.390085 | − | 0.920779i | \(-0.627554\pi\) | ||||
−0.390085 | + | 0.920779i | \(0.627554\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.2123 | 0.440123 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.2760 | −0.716293 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 48.6537 | 1.90397 | 0.951984 | − | 0.306149i | \(-0.0990406\pi\) | ||||
0.951984 | + | 0.306149i | \(0.0990406\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.7638 | 0.889454 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 88.9302 | 3.46950 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.4053 | 1.26233 | 0.631166 | − | 0.775648i | \(-0.282577\pi\) | ||||
0.631166 | + | 0.775648i | \(0.282577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.89016 | 0.345787 | 0.172894 | − | 0.984941i | \(-0.444688\pi\) | ||||
0.172894 | + | 0.984941i | \(0.444688\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.95831 | 0.192565 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.7935 | 0.534887 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.04188 | −0.195222 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −54.2969 | −2.09924 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.91210 | −0.266839 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −48.8341 | −1.88242 | −0.941209 | − | 0.337825i | \(-0.890309\pi\) | ||||
−0.941209 | + | 0.337825i | \(0.890309\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −166.815 | −6.42072 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 50.9265 | 1.95726 | 0.978632 | − | 0.205620i | \(-0.0659211\pi\) | ||||
0.978632 | + | 0.205620i | \(0.0659211\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.299773 | 0.0115042 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.02479 | −0.269190 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.95801 | −0.113185 | −0.0565925 | − | 0.998397i | \(-0.518024\pi\) | ||||
−0.0565925 | + | 0.998397i | \(0.518024\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.9545 | 1.87046 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −31.0273 | −1.18377 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.705189 | −0.0268656 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.7041 | 1.32021 | 0.660103 | − | 0.751176i | \(-0.270513\pi\) | ||||
0.660103 | + | 0.751176i | \(0.270513\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.72118 | −0.255317 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 89.6103 | 3.39911 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.0802 | 0.419691 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −84.3800 | −3.19155 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.2432 | 0.537960 | 0.268980 | − | 0.963146i | \(-0.413313\pi\) | ||||
0.268980 | + | 0.963146i | \(0.413313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.21448 | 0.347531 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −118.997 | −4.48167 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.94277 | −0.223501 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.5130 | −1.33372 | −0.666860 | − | 0.745183i | \(-0.732362\pi\) | ||||
−0.666860 | + | 0.745183i | \(0.732362\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 62.6680 | 2.35024 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.1953 | −0.606519 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.40203 | −0.164627 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −51.8555 | −1.93658 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.8106 | −0.589635 | −0.294817 | − | 0.955554i | \(-0.595259\pi\) | ||||
−0.294817 | + | 0.955554i | \(0.595259\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.0401 | −0.634606 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −69.0478 | −2.56792 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.2373 | 0.974430 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.3117 | −0.864583 | −0.432292 | − | 0.901734i | \(-0.642295\pi\) | ||||
−0.432292 | + | 0.901734i | \(0.642295\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.911641 | −0.0337645 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.15113 | −0.301481 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.0355 | −0.850835 | −0.425418 | − | 0.904997i | \(-0.639873\pi\) | ||||
−0.425418 | + | 0.904997i | \(0.639873\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.7250 | −0.506255 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.69117 | −0.0991305 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.1229 | −0.629875 | −0.314938 | − | 0.949112i | \(-0.601984\pi\) | ||||
−0.314938 | + | 0.949112i | \(0.601984\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.76966 | −0.358898 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.4339 | −0.933080 | −0.466540 | − | 0.884500i | \(-0.654500\pi\) | ||||
−0.466540 | + | 0.884500i | \(0.654500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.7200 | 0.539299 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −46.9375 | −1.71735 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.97928 | −0.328096 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.27585 | −0.0830468 | −0.0415234 | − | 0.999138i | \(-0.513221\pi\) | ||||
−0.0415234 | + | 0.999138i | \(0.513221\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −61.1724 | −2.22925 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −72.1282 | −2.62501 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 45.0726 | 1.63819 | 0.819096 | − | 0.573656i | \(-0.194475\pi\) | ||||
0.819096 | + | 0.573656i | \(0.194475\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.61444 | −0.312685 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.8818 | −0.648216 | −0.324108 | − | 0.946020i | \(-0.605064\pi\) | ||||
−0.324108 | + | 0.946020i | \(0.605064\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.6494 | 0.457938 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −47.0515 | −1.70115 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.2123 | −0.404854 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.1844 | −1.12454 | −0.562269 | − | 0.826954i | \(-0.690072\pi\) | ||||
−0.562269 | + | 0.826954i | \(0.690072\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 21.5667 | 0.776705 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.87795 | 0.0675450 | 0.0337725 | − | 0.999430i | \(-0.489248\pi\) | ||||
0.0337725 | + | 0.999430i | \(0.489248\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 84.2785 | 3.02737 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.16876 | −0.328927 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.8319 | −0.782210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.24458 | 0.330797 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21.1722 | −0.756631 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −72.3942 | −2.58386 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.7663 | −0.633300 | −0.316650 | − | 0.948542i | \(-0.602558\pi\) | ||||
−0.316650 | + | 0.948542i | \(0.602558\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −75.9198 | −2.70282 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.30123 | −0.295158 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.91210 | 0.245456 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.67873 | 0.343269 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.28933 | 0.187358 | 0.0936789 | − | 0.995602i | \(-0.470137\pi\) | ||||
0.0936789 | + | 0.995602i | \(0.470137\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.7878 | −0.487778 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.92048 | 0.138523 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.2313 | −0.466923 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.1624 | −0.428670 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −23.4795 | −0.826519 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.7900 | 1.46926 | 0.734629 | − | 0.678470i | \(-0.237356\pi\) | ||||
0.734629 | + | 0.678470i | \(0.237356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.8870 | −0.452522 | −0.226261 | − | 0.974067i | \(-0.572650\pi\) | ||||
−0.226261 | + | 0.974067i | \(0.572650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −62.9429 | −2.20750 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −42.2986 | −1.48166 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0607 | 0.561892 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.72118 | 0.234857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.9826 | −0.697396 | −0.348698 | − | 0.937235i | \(-0.613376\pi\) | ||||
−0.348698 | + | 0.937235i | \(0.613376\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.6836 | 1.34843 | 0.674213 | − | 0.738537i | \(-0.264483\pi\) | ||||
0.674213 | + | 0.738537i | \(0.264483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 44.8285 | 1.56073 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.7188 | −1.52025 | −0.760126 | − | 0.649775i | \(-0.774863\pi\) | ||||
−0.760126 | + | 0.649775i | \(0.774863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.45743 | −0.328470 | −0.164235 | − | 0.986421i | \(-0.552516\pi\) | ||||
−0.164235 | + | 0.986421i | \(0.552516\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.58286 | −0.228357 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.59028 | −0.0551000 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 52.9004 | 1.83070 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −68.0084 | −2.35071 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.3236 | −0.598078 | −0.299039 | − | 0.954241i | \(-0.596666\pi\) | ||||
−0.299039 | + | 0.954241i | \(0.596666\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.6700 | −0.885171 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 33.4481 | 1.15201 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.40203 | 0.151435 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −100.746 | −3.45760 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.12491 | −0.278518 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.53061 | −0.0524069 | −0.0262035 | − | 0.999657i | \(-0.508342\pi\) | ||||
−0.0262035 | + | 0.999657i | \(0.508342\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 92.7084 | 3.17056 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.8561 | 0.507474 | 0.253737 | − | 0.967273i | \(-0.418340\pi\) | ||||
0.253737 | + | 0.967273i | \(0.418340\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.9383 | 1.70387 | 0.851936 | − | 0.523645i | \(-0.175428\pi\) | ||||
0.851936 | + | 0.523645i | \(0.175428\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 21.7236 | 0.740338 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.7598 | 0.910916 | 0.455458 | − | 0.890257i | \(-0.349476\pi\) | ||||
0.455458 | + | 0.890257i | \(0.349476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −88.5166 | −3.00966 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 45.1189 | 1.53232 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.32396 | −0.316294 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.69117 | 0.0911868 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.01483 | 0.0681916 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 41.2818 | 1.39558 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.5987 | 1.30339 | 0.651693 | − | 0.758483i | \(-0.274059\pi\) | ||||
0.651693 | + | 0.758483i | \(0.274059\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −75.0346 | −2.53085 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.1256 | 0.408523 | 0.204262 | − | 0.978916i | \(-0.434521\pi\) | ||||
0.204262 | + | 0.978916i | \(0.434521\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.8167 | 0.599581 | 0.299790 | − | 0.954005i | \(-0.403083\pi\) | ||||
0.299790 | + | 0.954005i | \(0.403083\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 153.890 | 5.17294 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.0049 | 0.570967 | 0.285484 | − | 0.958384i | \(-0.407846\pi\) | ||||
0.285484 | + | 0.958384i | \(0.407846\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.7835 | −0.730594 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.0108 | −0.536381 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 27.1670 | 0.909109 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 63.2524 | 2.11430 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.61444 | 0.287628 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10.6966 | 0.356752 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.12145 | 0.0373609 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.9810 | −0.531814 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 46.5680 | 1.54797 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.82387 | −0.292992 | −0.146496 | − | 0.989211i | \(-0.546800\pi\) | ||||
−0.146496 | + | 0.989211i | \(0.546800\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −39.9424 | −1.32481 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.6827 | −0.685248 | −0.342624 | − | 0.939473i | \(-0.611316\pi\) | ||||
−0.342624 | + | 0.939473i | \(0.611316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.98352 | 0.231121 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −94.8687 | −3.13626 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.17119 | 0.170768 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.7796 | 0.685457 | 0.342728 | − | 0.939435i | \(-0.388649\pi\) | ||||
0.342728 | + | 0.939435i | \(0.388649\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 40.6433 | 1.33924 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.24458 | −0.304289 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.2811 | 1.39019 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −114.530 | −3.76165 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.65036 | −0.119764 | −0.0598821 | − | 0.998205i | \(-0.519072\pi\) | ||||
−0.0598821 | + | 0.998205i | \(0.519072\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.13343 | 0.102694 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 86.1983 | 2.82201 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.00047 | 0.228940 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.2398 | −1.57593 | −0.787963 | − | 0.615722i | \(-0.788864\pi\) | ||||
−0.787963 | + | 0.615722i | \(0.788864\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 75.8363 | 2.47482 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.0198 | −0.717826 | −0.358913 | − | 0.933371i | \(-0.616853\pi\) | ||||
−0.358913 | + | 0.933371i | \(0.616853\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.2504 | 0.626879 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −51.0733 | −1.66141 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −61.3455 | −1.99346 | −0.996731 | − | 0.0807952i | \(-0.974254\pi\) | ||||
−0.996731 | + | 0.0807952i | \(0.974254\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.2313 | 0.429507 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.68900 | −0.119624 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.5852 | −0.375283 | −0.187641 | − | 0.982238i | \(-0.560084\pi\) | ||||
−0.187641 | + | 0.982238i | \(0.560084\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −73.5327 | −2.37946 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.68963 | 0.183920 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.1209 | 0.359112 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.35920 | 0.108361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −60.3514 | −1.94480 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.2610 | −0.330314 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.9422 | −0.416194 | −0.208097 | − | 0.978108i | \(-0.566727\pi\) | ||||
−0.208097 | + | 0.978108i | \(0.566727\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 15.5365 | 0.499105 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.2607 | −0.553924 | −0.276962 | − | 0.960881i | \(-0.589328\pi\) | ||||
−0.276962 | + | 0.960881i | \(0.589328\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.3566 | 0.652602 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −44.8285 | −1.43566 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.1370 | 0.452282 | 0.226141 | − | 0.974095i | \(-0.427389\pi\) | ||||
0.226141 | + | 0.974095i | \(0.427389\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.583301 | −0.0186424 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 85.0188 | 2.71444 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.9143 | −0.667063 | −0.333531 | − | 0.942739i | \(-0.608240\pi\) | ||||
−0.333531 | + | 0.942739i | \(0.608240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −39.8470 | −1.26963 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.0322 | −0.860444 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.1616 | −0.450312 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.4247 | −1.41120 | −0.705599 | − | 0.708611i | \(-0.749322\pi\) | ||||
−0.705599 | + | 0.708611i | \(0.749322\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −56.3995 | −1.78978 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 92.2981 | 2.92604 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.9041 | 1.26378 | 0.631888 | − | 0.775059i | \(-0.282280\pi\) | ||||
0.631888 | + | 0.775059i | \(0.282280\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34.1186 | −1.07947 |
(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 | 4004.2.a.i.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4004.2.a.i.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial |