Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6020,2,Mod(1,6020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6020, 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("6020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6020 = 2^{2} \cdot 5 \cdot 7 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6020.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: | \(48.0699420168\) |
Analytic rank: | \(0\) |
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: | \( x^{13} - 27 x^{11} - 2 x^{10} + 268 x^{9} + 37 x^{8} - 1201 x^{7} - 189 x^{6} + 2384 x^{5} + 231 x^{4} + \cdots - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.18036\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6020.1 |
$q$-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 | ||||||||
\(3\) | −3.18036 | −1.83618 | −0.918092 | − | 0.396368i | \(-0.870270\pi\) | ||||
−0.918092 | + | 0.396368i | \(0.870270\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.11471 | 2.37157 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30215 | 0.392614 | 0.196307 | − | 0.980542i | \(-0.437105\pi\) | ||||
0.196307 | + | 0.980542i | \(0.437105\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.75566 | 1.31898 | 0.659492 | − | 0.751712i | \(-0.270772\pi\) | ||||
0.659492 | + | 0.751712i | \(0.270772\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.18036 | −0.821166 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.06042 | 1.46987 | 0.734934 | − | 0.678139i | \(-0.237213\pi\) | ||||
0.734934 | + | 0.678139i | \(0.237213\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.98339 | −0.684437 | −0.342218 | − | 0.939620i | \(-0.611178\pi\) | ||||
−0.342218 | + | 0.939620i | \(0.611178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.18036 | 0.694012 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.20473 | 1.29378 | 0.646888 | − | 0.762585i | \(-0.276070\pi\) | ||||
0.646888 | + | 0.762585i | \(0.276070\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −13.0863 | −2.51845 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.60010 | 1.59700 | 0.798499 | − | 0.601996i | \(-0.205628\pi\) | ||||
0.798499 | + | 0.601996i | \(0.205628\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.990013 | −0.177812 | −0.0889058 | − | 0.996040i | \(-0.528337\pi\) | ||||
−0.0889058 | + | 0.996040i | \(0.528337\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.14132 | −0.720911 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.56221 | 1.07882 | 0.539410 | − | 0.842043i | \(-0.318647\pi\) | ||||
0.539410 | + | 0.842043i | \(0.318647\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.1247 | −2.42190 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.73149 | 1.36363 | 0.681815 | − | 0.731525i | \(-0.261191\pi\) | ||||
0.681815 | + | 0.731525i | \(0.261191\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.11471 | 1.06060 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.91529 | 0.716969 | 0.358485 | − | 0.933536i | \(-0.383294\pi\) | ||||
0.358485 | + | 0.933536i | \(0.383294\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19.2743 | −2.69895 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.76076 | 0.241859 | 0.120930 | − | 0.992661i | \(-0.461412\pi\) | ||||
0.120930 | + | 0.992661i | \(0.461412\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.30215 | 0.175582 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.48827 | 1.25675 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.52699 | 1.11012 | 0.555060 | − | 0.831810i | \(-0.312695\pi\) | ||||
0.555060 | + | 0.831810i | \(0.312695\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.3664 | −1.32728 | −0.663642 | − | 0.748050i | \(-0.730990\pi\) | ||||
−0.663642 | + | 0.748050i | \(0.730990\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.11471 | −0.896369 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.75566 | 0.589867 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.67928 | 1.18251 | 0.591256 | − | 0.806484i | \(-0.298632\pi\) | ||||
0.591256 | + | 0.806484i | \(0.298632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −19.7333 | −2.37561 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.38967 | −0.283602 | −0.141801 | − | 0.989895i | \(-0.545289\pi\) | ||||
−0.141801 | + | 0.989895i | \(0.545289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.14046 | −0.367563 | −0.183781 | − | 0.982967i | \(-0.558834\pi\) | ||||
−0.183781 | + | 0.982967i | \(0.558834\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.18036 | −0.367237 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.30215 | −0.148394 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.8089 | −1.21609 | −0.608047 | − | 0.793901i | \(-0.708047\pi\) | ||||
−0.608047 | + | 0.793901i | \(0.708047\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 20.2749 | 2.25277 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.53377 | 0.826939 | 0.413469 | − | 0.910518i | \(-0.364317\pi\) | ||||
0.413469 | + | 0.910518i | \(0.364317\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.06042 | 0.657345 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −27.3514 | −2.93238 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.7316 | −1.45555 | −0.727775 | − | 0.685816i | \(-0.759445\pi\) | ||||
−0.727775 | + | 0.685816i | \(0.759445\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.75566 | −0.498529 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.14860 | 0.326495 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.98339 | −0.306090 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.5775 | −1.48012 | −0.740059 | − | 0.672542i | \(-0.765203\pi\) | ||||
−0.740059 | + | 0.672542i | \(0.765203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 9.26443 | 0.931111 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.6672 | 1.35994 | 0.679969 | − | 0.733241i | \(-0.261993\pi\) | ||||
0.679969 | + | 0.733241i | \(0.261993\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −18.0390 | −1.77743 | −0.888715 | − | 0.458459i | \(-0.848401\pi\) | ||||
−0.888715 | + | 0.458459i | \(0.848401\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.18036 | 0.310372 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.51445 | 0.629775 | 0.314888 | − | 0.949129i | \(-0.398033\pi\) | ||||
0.314888 | + | 0.949129i | \(0.398033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.4327 | −1.09506 | −0.547529 | − | 0.836786i | \(-0.684432\pi\) | ||||
−0.547529 | + | 0.836786i | \(0.684432\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −20.8702 | −1.98091 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.84050 | 0.643500 | 0.321750 | − | 0.946825i | \(-0.395729\pi\) | ||||
0.321750 | + | 0.946825i | \(0.395729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.20473 | 0.578594 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 33.8351 | 3.12806 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.06042 | −0.555558 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.30440 | −0.845854 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −27.7693 | −2.50387 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.9056 | 0.967720 | 0.483860 | − | 0.875146i | \(-0.339234\pi\) | ||||
0.483860 | + | 0.875146i | \(0.339234\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.18036 | −0.280015 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.2841 | −0.898526 | −0.449263 | − | 0.893400i | \(-0.648313\pi\) | ||||
−0.449263 | + | 0.893400i | \(0.648313\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.98339 | 0.258693 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.0863 | −1.12629 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.1789 | −1.55312 | −0.776562 | − | 0.630041i | \(-0.783038\pi\) | ||||
−0.776562 | + | 0.630041i | \(0.783038\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.60807 | 0.221214 | 0.110607 | − | 0.993864i | \(-0.464721\pi\) | ||||
0.110607 | + | 0.993864i | \(0.464721\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.6324 | −1.31649 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.19260 | 0.517851 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.60010 | 0.714200 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.18036 | −0.262312 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.7943 | −1.62161 | −0.810806 | − | 0.585315i | \(-0.800971\pi\) | ||||
−0.810806 | + | 0.585315i | \(0.800971\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.4222 | 1.74332 | 0.871659 | − | 0.490114i | \(-0.163045\pi\) | ||||
0.871659 | + | 0.490114i | \(0.163045\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 43.1181 | 3.48589 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.990013 | −0.0795198 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.6287 | 1.64635 | 0.823174 | − | 0.567789i | \(-0.192201\pi\) | ||||
0.823174 | + | 0.567789i | \(0.192201\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.59986 | −0.444098 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.20473 | −0.489001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.69126 | −0.289122 | −0.144561 | − | 0.989496i | \(-0.546177\pi\) | ||||
−0.144561 | + | 0.989496i | \(0.546177\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.14132 | −0.322401 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.0386 | 1.39587 | 0.697934 | − | 0.716162i | \(-0.254103\pi\) | ||||
0.697934 | + | 0.716162i | \(0.254103\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.61633 | 0.739718 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.2260 | −1.62319 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.09465 | −0.0832246 | −0.0416123 | − | 0.999134i | \(-0.513249\pi\) | ||||
−0.0416123 | + | 0.999134i | \(0.513249\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −27.1189 | −2.03838 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.91926 | 0.666657 | 0.333328 | − | 0.942811i | \(-0.391828\pi\) | ||||
0.333328 | + | 0.942811i | \(0.391828\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.5488 | −1.60171 | −0.800856 | − | 0.598857i | \(-0.795622\pi\) | ||||
−0.800856 | + | 0.598857i | \(0.795622\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 32.9690 | 2.43714 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.56221 | 0.482463 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.89159 | 0.577090 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 13.0863 | 0.951885 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.387012 | 0.0280032 | 0.0140016 | − | 0.999902i | \(-0.495543\pi\) | ||||
0.0140016 | + | 0.999902i | \(0.495543\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.7950 | 0.849024 | 0.424512 | − | 0.905422i | \(-0.360446\pi\) | ||||
0.424512 | + | 0.905422i | \(0.360446\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.1247 | −1.08310 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.73114 | −0.337080 | −0.168540 | − | 0.985695i | \(-0.553905\pi\) | ||||
−0.168540 | + | 0.985695i | \(0.553905\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.64496 | 0.541937 | 0.270969 | − | 0.962588i | \(-0.412656\pi\) | ||||
0.270969 | + | 0.962588i | \(0.412656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −30.7836 | −2.17131 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.60010 | −0.603609 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.73149 | 0.609834 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 44.1448 | 3.06828 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.88483 | −0.268719 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.2478 | 0.912019 | 0.456010 | − | 0.889975i | \(-0.349278\pi\) | ||||
0.456010 | + | 0.889975i | \(0.349278\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.60002 | 0.520745 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.990013 | 0.0672065 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.98779 | 0.674912 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.8213 | 1.93873 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −15.0307 | −1.00653 | −0.503264 | − | 0.864133i | \(-0.667868\pi\) | ||||
−0.503264 | + | 0.864133i | \(0.667868\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.11471 | 0.474314 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.4323 | −1.09065 | −0.545326 | − | 0.838224i | \(-0.683594\pi\) | ||||
−0.545326 | + | 0.838224i | \(0.683594\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.68386 | 0.243436 | 0.121718 | − | 0.992565i | \(-0.461160\pi\) | ||||
0.121718 | + | 0.992565i | \(0.461160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.14132 | 0.272479 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.9547 | −0.848691 | −0.424345 | − | 0.905500i | \(-0.639496\pi\) | ||||
−0.424345 | + | 0.905500i | \(0.639496\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.91529 | 0.320638 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 34.3762 | 2.23297 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.62603 | 0.234548 | 0.117274 | − | 0.993100i | \(-0.462584\pi\) | ||||
0.117274 | + | 0.993100i | \(0.462584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.5229 | −1.70849 | −0.854246 | − | 0.519869i | \(-0.825981\pi\) | ||||
−0.854246 | + | 0.519869i | \(0.825981\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −25.2228 | −1.61805 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.1880 | −0.902761 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.9601 | −1.51841 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.79330 | −0.302550 | −0.151275 | − | 0.988492i | \(-0.548338\pi\) | ||||
−0.151275 | + | 0.988492i | \(0.548338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.07951 | 0.507954 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −19.2743 | −1.20701 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.2569 | 0.702187 | 0.351093 | − | 0.936340i | \(-0.385810\pi\) | ||||
0.351093 | + | 0.936340i | \(0.385810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.56221 | −0.407756 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 61.1872 | 3.78739 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.93595 | 0.612677 | 0.306339 | − | 0.951923i | \(-0.400896\pi\) | ||||
0.306339 | + | 0.951923i | \(0.400896\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.76076 | 0.108163 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 43.6716 | 2.67266 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.6092 | 1.19559 | 0.597796 | − | 0.801648i | \(-0.296043\pi\) | ||||
0.597796 | + | 0.801648i | \(0.296043\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.2430 | −1.22968 | −0.614838 | − | 0.788653i | \(-0.710779\pi\) | ||||
−0.614838 | + | 0.788653i | \(0.710779\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.1247 | 0.915391 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.30215 | 0.0785228 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.10580 | 0.126525 | 0.0632627 | − | 0.997997i | \(-0.479849\pi\) | ||||
0.0632627 | + | 0.997997i | \(0.479849\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.04365 | −0.421692 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.92585 | −0.234197 | −0.117098 | − | 0.993120i | \(-0.537359\pi\) | ||||
−0.117098 | + | 0.993120i | \(0.537359\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.26452 | −0.491275 | −0.245637 | − | 0.969362i | \(-0.578997\pi\) | ||||
−0.245637 | + | 0.969362i | \(0.578997\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.48827 | 0.562036 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.73149 | −0.515403 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.7287 | 1.16051 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 46.3617 | 2.71777 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.3739 | −0.898154 | −0.449077 | − | 0.893493i | \(-0.648247\pi\) | ||||
−0.449077 | + | 0.893493i | \(0.648247\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.52699 | 0.496461 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −17.0403 | −0.988779 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 29.5076 | 1.70647 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | −0.0576390 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −43.4666 | −2.49709 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.3664 | −0.593579 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.91929 | 0.166613 | 0.0833064 | − | 0.996524i | \(-0.473452\pi\) | ||||
0.0833064 | + | 0.996524i | \(0.473452\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 57.3704 | 3.26369 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.7761 | −1.40493 | −0.702463 | − | 0.711721i | \(-0.747916\pi\) | ||||
−0.702463 | + | 0.711721i | \(0.747916\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.3422 | 1.43242 | 0.716212 | − | 0.697883i | \(-0.245874\pi\) | ||||
0.716212 | + | 0.697883i | \(0.245874\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.11471 | −0.400868 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.7123 | 1.61264 | 0.806321 | − | 0.591479i | \(-0.201456\pi\) | ||||
0.806321 | + | 0.591479i | \(0.201456\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.1986 | 0.627004 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −20.7183 | −1.15638 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −18.0806 | −1.00603 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.75566 | 0.263797 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 36.3603 | 2.01073 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.91529 | −0.270989 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.8823 | −1.09283 | −0.546415 | − | 0.837515i | \(-0.684008\pi\) | ||||
−0.546415 | + | 0.837515i | \(0.684008\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 46.6882 | 2.55850 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.67928 | 0.528836 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.0424 | −1.14625 | −0.573126 | − | 0.819467i | \(-0.694270\pi\) | ||||
−0.573126 | + | 0.819467i | \(0.694270\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −21.7553 | −1.18158 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.28915 | −0.0698113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.7333 | −1.06240 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.9030 | 1.60528 | 0.802639 | − | 0.596466i | \(-0.203429\pi\) | ||||
0.802639 | + | 0.596466i | \(0.203429\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.69644 | −0.465510 | −0.232755 | − | 0.972535i | \(-0.574774\pi\) | ||||
−0.232755 | + | 0.972535i | \(0.574774\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −62.2338 | −3.32180 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.21842 | −0.384197 | −0.192099 | − | 0.981376i | \(-0.561529\pi\) | ||||
−0.192099 | + | 0.981376i | \(0.561529\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.38967 | −0.126831 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.2743 | 1.02011 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.78366 | 0.199694 | 0.0998470 | − | 0.995003i | \(-0.468165\pi\) | ||||
0.0998470 | + | 0.995003i | \(0.468165\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0994 | −0.531546 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 29.5914 | 1.55314 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.14046 | −0.164379 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1312 | 0.789845 | 0.394922 | − | 0.918715i | \(-0.370771\pi\) | ||||
0.394922 | + | 0.918715i | \(0.370771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 62.1220 | 3.23394 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.76076 | −0.0914142 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.8205 | 1.38871 | 0.694357 | − | 0.719631i | \(-0.255689\pi\) | ||||
0.694357 | + | 0.719631i | \(0.255689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.18036 | −0.164233 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.8992 | 2.10642 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.2435 | 0.628906 | 0.314453 | − | 0.949273i | \(-0.398179\pi\) | ||||
0.314453 | + | 0.949273i | \(0.398179\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.6839 | −1.77691 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.33256 | −0.374676 | −0.187338 | − | 0.982295i | \(-0.559986\pi\) | ||||
−0.187338 | + | 0.982295i | \(0.559986\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.30215 | −0.0663639 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.11471 | 0.361661 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.4250 | 1.69471 | 0.847356 | − | 0.531024i | \(-0.178193\pi\) | ||||
0.847356 | + | 0.531024i | \(0.178193\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.6033 | 1.90168 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 32.7072 | 1.64986 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.8089 | −0.543854 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.8661 | −1.44875 | −0.724375 | − | 0.689406i | \(-0.757871\pi\) | ||||
−0.724375 | + | 0.689406i | \(0.757871\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.48827 | −0.475007 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.752328 | 0.0375695 | 0.0187847 | − | 0.999824i | \(-0.494020\pi\) | ||||
0.0187847 | + | 0.999824i | \(0.494020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.70817 | −0.234531 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 20.2749 | 1.00747 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.54500 | 0.423560 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.31526 | 0.361716 | 0.180858 | − | 0.983509i | \(-0.442113\pi\) | ||||
0.180858 | + | 0.983509i | \(0.442113\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 57.8154 | 2.85182 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.52699 | −0.419586 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.53377 | 0.369818 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.29461 | −0.406189 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.2155 | 1.37842 | 0.689210 | − | 0.724562i | \(-0.257958\pi\) | ||||
0.689210 | + | 0.724562i | \(0.257958\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.6067 | −0.565677 | −0.282838 | − | 0.959168i | \(-0.591276\pi\) | ||||
−0.282838 | + | 0.959168i | \(0.591276\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 34.9709 | 1.70034 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.06042 | 0.293973 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.3664 | 0.501666 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −19.6947 | −0.950870 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.1222 | −1.40277 | −0.701385 | − | 0.712783i | \(-0.747434\pi\) | ||||
−0.701385 | + | 0.712783i | \(0.747434\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.4237 | 1.60624 | 0.803121 | − | 0.595816i | \(-0.203171\pi\) | ||||
0.803121 | + | 0.595816i | \(0.203171\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −27.3514 | −1.31140 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.5111 | −0.885508 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.4518 | −1.07156 | −0.535782 | − | 0.844356i | \(-0.679983\pi\) | ||||
−0.535782 | + | 0.844356i | \(0.679983\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.11471 | 0.338796 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.07257 | 0.0984707 | 0.0492353 | − | 0.998787i | \(-0.484322\pi\) | ||||
0.0492353 | + | 0.998787i | \(0.484322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.7316 | −0.650942 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 62.9531 | 2.97758 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.0929 | 1.18421 | 0.592104 | − | 0.805861i | \(-0.298297\pi\) | ||||
0.592104 | + | 0.805861i | \(0.298297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.3697 | 0.535380 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −68.1305 | −3.20105 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.75566 | −0.222949 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.8495 | 1.30274 | 0.651372 | − | 0.758759i | \(-0.274194\pi\) | ||||
0.651372 | + | 0.758759i | \(0.274194\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −79.3082 | −3.70179 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.6554 | −0.868867 | −0.434434 | − | 0.900704i | \(-0.643051\pi\) | ||||
−0.434434 | + | 0.900704i | \(0.643051\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.5816 | 1.70009 | 0.850046 | − | 0.526709i | \(-0.176574\pi\) | ||||
0.850046 | + | 0.526709i | \(0.176574\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.14860 | 0.146013 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.0547 | −0.511552 | −0.255776 | − | 0.966736i | \(-0.582331\pi\) | ||||
−0.255776 | + | 0.966736i | \(0.582331\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.67928 | −0.446948 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −65.6067 | −3.02300 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.30215 | 0.0598730 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.98339 | −0.136887 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.5273 | 0.573586 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.15721 | 0.0528741 | 0.0264370 | − | 0.999650i | \(-0.491584\pi\) | ||||
0.0264370 | + | 0.999650i | \(0.491584\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 31.2077 | 1.42295 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.7333 | 0.897896 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.5775 | −0.661929 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.10177 | 0.0499262 | 0.0249631 | − | 0.999688i | \(-0.492053\pi\) | ||||
0.0249631 | + | 0.999688i | \(0.492053\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.7396 | 0.530881 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.66499 | 0.255657 | 0.127829 | − | 0.991796i | \(-0.459199\pi\) | ||||
0.127829 | + | 0.991796i | \(0.459199\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.1202 | 2.34738 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.26443 | 0.416405 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.38967 | 0.107191 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.70290 | −0.255297 | −0.127648 | − | 0.991819i | \(-0.540743\pi\) | ||||
−0.127648 | + | 0.991819i | \(0.540743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −57.3693 | −2.56307 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 28.4643 | 1.26916 | 0.634581 | − | 0.772857i | \(-0.281173\pi\) | ||||
0.634581 | + | 0.772857i | \(0.281173\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.6672 | 0.608182 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −30.5834 | −1.35826 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.1059 | −0.447936 | −0.223968 | − | 0.974596i | \(-0.571901\pi\) | ||||
−0.223968 | + | 0.974596i | \(0.571901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.14046 | 0.138926 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 39.0414 | 1.72372 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.0390 | −0.794891 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.40046 | 0.281492 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.48138 | 0.152816 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −34.8621 | −1.52734 | −0.763669 | − | 0.645608i | \(-0.776604\pi\) | ||||
−0.763669 | + | 0.645608i | \(0.776604\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.319347 | 0.0139641 | 0.00698203 | − | 0.999976i | \(-0.497778\pi\) | ||||
0.00698203 | + | 0.999976i | \(0.497778\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.18036 | 0.138802 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.99990 | −0.261360 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.4987 | 0.673855 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 60.6670 | 2.63273 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 41.5240 | 1.79860 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.51445 | 0.281644 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.3665 | −1.22410 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.30215 | 0.0560877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.8470 | 1.88513 | 0.942564 | − | 0.334026i | \(-0.108407\pi\) | ||||
0.942564 | + | 0.334026i | \(0.108407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 68.5331 | 2.94104 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.4327 | −0.489725 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.7915 | −1.01725 | −0.508626 | − | 0.860988i | \(-0.669846\pi\) | ||||
−0.508626 | + | 0.860988i | \(0.669846\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −73.7540 | −3.14774 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.6575 | −1.09305 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.8089 | 0.459641 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −20.8702 | −0.885891 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.3802 | −1.03302 | −0.516510 | − | 0.856281i | \(-0.672769\pi\) | ||||
−0.516510 | + | 0.856281i | \(0.672769\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.75566 | 0.201143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.0981 | −1.05964 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.3588 | 1.53234 | 0.766170 | − | 0.642638i | \(-0.222160\pi\) | ||||
0.766170 | + | 0.642638i | \(0.222160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.84050 | 0.287782 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.2749 | −0.851467 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.7210 | −0.533291 | −0.266645 | − | 0.963795i | \(-0.585915\pi\) | ||||
−0.266645 | + | 0.963795i | \(0.585915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.5261 | −0.817140 | −0.408570 | − | 0.912727i | \(-0.633972\pi\) | ||||
−0.408570 | + | 0.912727i | \(0.633972\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.23084 | −0.0514190 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.20473 | 0.258755 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.51679 | 0.188036 | 0.0940182 | − | 0.995570i | \(-0.470029\pi\) | ||||
0.0940182 | + | 0.995570i | \(0.470029\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −37.5125 | −1.55896 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.53377 | −0.312553 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.29278 | 0.0949573 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 33.8351 | 1.39891 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0214 | −0.496174 | −0.248087 | − | 0.968738i | \(-0.579802\pi\) | ||||
−0.248087 | + | 0.968738i | \(0.579802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.95360 | 0.121701 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0467 | 0.618940 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −46.2485 | −1.89920 | −0.949599 | − | 0.313467i | \(-0.898509\pi\) | ||||
−0.949599 | + | 0.313467i | \(0.898509\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.06042 | −0.248453 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.3138 | −0.995096 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.36510 | 0.219212 | 0.109606 | − | 0.993975i | \(-0.465041\pi\) | ||||
0.109606 | + | 0.993975i | \(0.465041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.36825 | 0.0558120 | 0.0279060 | − | 0.999611i | \(-0.491116\pi\) | ||||
0.0279060 | + | 0.999611i | \(0.491116\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 68.8652 | 2.80441 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.30440 | −0.378278 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.72687 | −0.313624 | −0.156812 | − | 0.987628i | \(-0.550122\pi\) | ||||
−0.156812 | + | 0.987628i | \(0.550122\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.3514 | 1.10834 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3755 | 0.945671 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.6678 | 0.430868 | 0.215434 | − | 0.976518i | \(-0.430883\pi\) | ||||
0.215434 | + | 0.976518i | \(0.430883\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.7693 | −1.11977 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.5019 | −0.825374 | −0.412687 | − | 0.910873i | \(-0.635410\pi\) | ||||
−0.412687 | + | 0.910873i | \(0.635410\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.65376 | 0.0664702 | 0.0332351 | − | 0.999448i | \(-0.489419\pi\) | ||||
0.0332351 | + | 0.999448i | \(0.489419\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −81.1967 | −3.25831 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.7316 | 0.550146 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.3552 | 0.493418 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 39.7697 | 1.58572 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.8249 | −1.06788 | −0.533941 | − | 0.845522i | \(-0.679289\pi\) | ||||
−0.533941 | + | 0.845522i | \(0.679289\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −42.1330 | −1.67463 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.9056 | 0.432777 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.75566 | 0.188426 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.0018 | −0.672581 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.4475 | 1.00512 | 0.502558 | − | 0.864543i | \(-0.332392\pi\) | ||||
0.502558 | + | 0.864543i | \(0.332392\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.2150 | 0.915511 | 0.457755 | − | 0.889078i | \(-0.348654\pi\) | ||||
0.457755 | + | 0.889078i | \(0.348654\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.18036 | −0.125227 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.8103 | −1.91893 | −0.959466 | − | 0.281824i | \(-0.909061\pi\) | ||||
−0.959466 | + | 0.281824i | \(0.909061\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1034 | 0.435848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.14860 | −0.123403 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.5441 | −0.569154 | −0.284577 | − | 0.958653i | \(-0.591853\pi\) | ||||
−0.284577 | + | 0.958653i | \(0.591853\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.2841 | −0.401833 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.3434 | −0.871700 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.37716 | 0.0536464 | 0.0268232 | − | 0.999640i | \(-0.491461\pi\) | ||||
0.0268232 | + | 0.999640i | \(0.491461\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.6823 | −1.46567 | −0.732836 | − | 0.680406i | \(-0.761804\pi\) | ||||
−0.732836 | + | 0.680406i | \(0.761804\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −91.6622 | −3.55987 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.98339 | 0.115691 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 53.3613 | 2.06616 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.8029 | 1.84817 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.4987 | −0.521110 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.6957 | −0.990495 | −0.495247 | − | 0.868752i | \(-0.664923\pi\) | ||||
−0.495247 | + | 0.868752i | \(0.664923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −13.0863 | −0.503690 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.6465 | 0.678211 | 0.339105 | − | 0.940748i | \(-0.389876\pi\) | ||||
0.339105 | + | 0.940748i | \(0.389876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.5775 | 0.559432 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 52.2608 | 2.00264 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.4938 | −1.05202 | −0.526010 | − | 0.850478i | \(-0.676313\pi\) | ||||
−0.526010 | + | 0.850478i | \(0.676313\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.1789 | −0.694578 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.7160 | −0.446994 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.37360 | 0.319009 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.3522 | −1.61115 | −0.805577 | − | 0.592491i | \(-0.798145\pi\) | ||||
−0.805577 | + | 0.592491i | \(0.798145\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.26443 | −0.351927 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.60807 | 0.0989298 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 52.9165 | 2.00435 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 41.2006 | 1.55835 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.0520 | 1.21059 | 0.605293 | − | 0.796003i | \(-0.293056\pi\) | ||||
0.605293 | + | 0.796003i | \(0.293056\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19.5776 | −0.738385 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −15.6324 | −0.588751 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.6672 | −0.514008 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.4046 | 0.803865 | 0.401933 | − | 0.915669i | \(-0.368339\pi\) | ||||
0.401933 | + | 0.915669i | \(0.368339\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −76.9020 | −2.88405 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.14276 | −0.230048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.19260 | 0.231590 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.5321 | −0.430674 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.4118 | 0.761231 | 0.380615 | − | 0.924733i | \(-0.375712\pi\) | ||||
0.380615 | + | 0.924733i | \(0.375712\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0390 | 0.671806 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 84.3525 | 3.13710 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.60010 | 0.319400 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.3012 | −1.30925 | −0.654624 | − | 0.755955i | \(-0.727173\pi\) | ||||
−0.654624 | + | 0.755955i | \(0.727173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.3930 | 0.718259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.06042 | 0.224153 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15.3786 | −0.568021 | −0.284010 | − | 0.958821i | \(-0.591665\pi\) | ||||
−0.284010 | + | 0.958821i | \(0.591665\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.18036 | −0.117309 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.6039 | 0.464271 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.77309 | 0.175581 | 0.0877905 | − | 0.996139i | \(-0.472019\pi\) | ||||
0.0877905 | + | 0.996139i | \(0.472019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.1230 | 1.65763 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.1234 | 1.25187 | 0.625933 | − | 0.779877i | \(-0.284718\pi\) | ||||
0.625933 | + | 0.779877i | \(0.284718\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.7943 | −0.725207 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 53.6006 | 1.96114 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.51445 | −0.238033 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.42953 | −0.0886547 | −0.0443273 | − | 0.999017i | \(-0.514114\pi\) | ||||
−0.0443273 | + | 0.999017i | \(0.514114\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 15.2444 | 0.555538 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.4222 | 0.779635 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.32845 | 0.302703 | 0.151351 | − | 0.988480i | \(-0.451638\pi\) | ||||
0.151351 | + | 0.988480i | \(0.451638\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.6958 | −0.932697 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.95481 | −0.107112 | −0.0535558 | − | 0.998565i | \(-0.517056\pi\) | ||||
−0.0535558 | + | 0.998565i | \(0.517056\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.4327 | 0.413893 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 43.1181 | 1.55894 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.5515 | 1.46423 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.02104 | −0.0368196 | −0.0184098 | − | 0.999831i | \(-0.505860\pi\) | ||||
−0.0184098 | + | 0.999831i | \(0.505860\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.8011 | −1.28934 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.3176 | −1.59399 | −0.796997 | − | 0.603984i | \(-0.793579\pi\) | ||||
−0.796997 | + | 0.603984i | \(0.793579\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.990013 | −0.0355623 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.8702 | 0.748715 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −26.0494 | −0.933318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.11172 | −0.111346 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −112.543 | −4.02196 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.6287 | 0.736269 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −43.9282 | −1.56587 | −0.782936 | − | 0.622102i | \(-0.786279\pi\) | ||||
−0.782936 | + | 0.622102i | \(0.786279\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.5999 | −1.12499 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.84050 | −0.243220 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.2992 | −1.75067 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.59986 | −0.198607 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.4965 | 1.64699 | 0.823495 | − | 0.567323i | \(-0.192021\pi\) | ||||
0.823495 | + | 0.567323i | \(0.192021\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29.7887 | 1.05385 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −97.6965 | −3.45194 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.08935 | −0.144310 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.20473 | −0.218688 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −62.3642 | −2.19533 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 15.0874 | 0.530444 | 0.265222 | − | 0.964187i | \(-0.414555\pi\) | ||||
0.265222 | + | 0.964187i | \(0.414555\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.5258 | 1.03679 | 0.518395 | − | 0.855141i | \(-0.326530\pi\) | ||||
0.518395 | + | 0.855141i | \(0.326530\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 64.3802 | 2.25791 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.69126 | −0.129299 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.98339 | −0.104376 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −33.8351 | −1.18230 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.5622 | −1.03173 | −0.515865 | − | 0.856670i | \(-0.672529\pi\) | ||||
−0.515865 | + | 0.856670i | \(0.672529\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.9552 | −0.591020 | −0.295510 | − | 0.955340i | \(-0.595490\pi\) | ||||
−0.295510 | + | 0.955340i | \(0.595490\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.14132 | −0.144182 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.4016 | −0.570338 | −0.285169 | − | 0.958477i | \(-0.592050\pi\) | ||||
−0.285169 | + | 0.958477i | \(0.592050\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.2264 | 0.667759 | 0.333879 | − | 0.942616i | \(-0.391642\pi\) | ||||
0.333879 | + | 0.942616i | \(0.391642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.69722 | −0.232324 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.06042 | 0.209981 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.0386 | 0.624251 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 12.9556 | 0.447810 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.86135 | 0.236880 | 0.118440 | − | 0.992961i | \(-0.462211\pi\) | ||||
0.118440 | + | 0.992961i | \(0.462211\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.9617 | 1.55040 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.4856 | 0.430028 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.61633 | 0.330812 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.30440 | 0.319703 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.2842 | 0.902070 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 40.7167 | 1.39575 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.05755 | 0.104688 | 0.0523442 | − | 0.998629i | \(-0.483331\pi\) | ||||
0.0523442 | + | 0.998629i | \(0.483331\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −21.2260 | −0.725912 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.5506 | 0.599517 | 0.299759 | − | 0.954015i | \(-0.403094\pi\) | ||||
0.299759 | + | 0.954015i | \(0.403094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.9333 | 1.53310 | 0.766552 | − | 0.642182i | \(-0.221971\pi\) | ||||
0.766552 | + | 0.642182i | \(0.221971\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.7693 | 0.946375 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −46.0834 | −1.56870 | −0.784349 | − | 0.620320i | \(-0.787003\pi\) | ||||
−0.784349 | + | 0.620320i | \(0.787003\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.09465 | −0.0372192 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −62.7443 | −2.13091 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.0748 | −0.477456 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 46.0314 | 1.55971 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −103.714 | −3.51020 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.3879 | 0.958592 | 0.479296 | − | 0.877653i | \(-0.340892\pi\) | ||||
0.479296 | + | 0.877653i | \(0.340892\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 48.8946 | 1.64918 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −10.4272 | −0.351303 | −0.175651 | − | 0.984452i | \(-0.556203\pi\) | ||||
−0.175651 | + | 0.984452i | \(0.556203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.8573 | −0.365378 | −0.182689 | − | 0.983171i | \(-0.558480\pi\) | ||||
−0.182689 | + | 0.983171i | \(0.558480\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −27.1189 | −0.911593 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 35.6181 | 1.19594 | 0.597969 | − | 0.801519i | \(-0.295975\pi\) | ||||
0.597969 | + | 0.801519i | \(0.295975\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.9056 | −0.365764 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 26.4010 | 0.884468 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.6642 | −0.490720 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.91926 | 0.298138 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −93.8449 | −3.13339 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.51421 | −0.283965 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6710 | 0.355501 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.18036 | 0.105836 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.5488 | −0.716307 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −55.5349 | −1.84401 | −0.922003 | − | 0.387183i | \(-0.873448\pi\) | ||||
−0.922003 | + | 0.387183i | \(0.873448\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 97.2381 | 3.22518 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.15388 | −0.270150 | −0.135075 | − | 0.990835i | \(-0.543128\pi\) | ||||
−0.135075 | + | 0.990835i | \(0.543128\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.81012 | 0.324668 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.9690 | 1.08992 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.2841 | 0.339611 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0725 | −0.860053 | −0.430027 | − | 0.902816i | \(-0.641496\pi\) | ||||
−0.430027 | + | 0.902816i | \(0.641496\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.28441 | −0.305932 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.3645 | −0.374066 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.56221 | 0.215764 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −128.342 | −4.21530 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.60466 | 0.216692 | 0.108346 | − | 0.994113i | \(-0.465445\pi\) | ||||
0.108346 | + | 0.994113i | \(0.465445\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.98339 | −0.0977767 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 78.7971 | 2.57970 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.89159 | 0.258083 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55.1266 | −1.80091 | −0.900453 | − | 0.434953i | \(-0.856765\pi\) | ||||
−0.900453 | + | 0.434953i | \(0.856765\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −80.5973 | −2.63019 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.3574 | −0.794029 | −0.397015 | − | 0.917812i | \(-0.629954\pi\) | ||||
−0.397015 | + | 0.917812i | \(0.629954\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 54.1765 | 1.76423 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.0863 | 0.425696 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 58.8443 | 1.91218 | 0.956091 | − | 0.293068i | \(-0.0946764\pi\) | ||||
0.956091 | + | 0.293068i | \(0.0946764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.9350 | −0.484809 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −91.3154 | −2.96110 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.329481 | −0.0106729 | −0.00533646 | − | 0.999986i | \(-0.501699\pi\) | ||||
−0.00533646 | + | 0.999986i | \(0.501699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.387012 | 0.0125234 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −35.6158 | −1.15129 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.1789 | 0.587026 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0199 | −0.968383 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46.3484 | 1.49356 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.7950 | 0.379695 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.9899 | −1.28599 | −0.642995 | − | 0.765871i | \(-0.722308\pi\) | ||||
−0.642995 | + | 0.765871i | \(0.722308\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 57.5029 | 1.84726 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.8203 | −0.571882 | −0.285941 | − | 0.958247i | \(-0.592306\pi\) | ||||
−0.285941 | + | 0.958247i | \(0.592306\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.60807 | −0.0836109 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.1247 | −0.484379 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.2408 | 0.551582 | 0.275791 | − | 0.961218i | \(-0.411060\pi\) | ||||
0.275791 | + | 0.961218i | \(0.411060\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.8807 | −0.571469 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −81.3407 | −2.59701 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.8200 | −1.17437 | −0.587187 | − | 0.809451i | \(-0.699765\pi\) | ||||
−0.587187 | + | 0.809451i | \(0.699765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.73114 | −0.150747 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.6324 | 0.497585 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.20473 | 0.197299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.7611 | 1.07246 | 0.536229 | − | 0.844073i | \(-0.319849\pi\) | ||||
0.536229 | + | 0.844073i | \(0.319849\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 63.2329 | 2.00664 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.64496 | 0.242362 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.8761 | −1.26289 | −0.631444 | − | 0.775421i | \(-0.717537\pi\) | ||||
−0.631444 | + | 0.775421i | \(0.717537\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −85.8748 | −2.71696 |
(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 | 6020.2.a.k.1.1 | ✓ | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6020.2.a.k.1.1 | ✓ | 13 | 1.1 | even | 1 | trivial |