Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2151.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(17.1758214748\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 21 x^{18} + 96 x^{17} + 164 x^{16} - 936 x^{15} - 540 x^{14} + 4804 x^{13} + 229 x^{12} - 14020 x^{11} + 3356 x^{10} + 23404 x^{9} - 9429 x^{8} - 21252 x^{7} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(0.946263\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.946263 | 0.669109 | 0.334555 | − | 0.942376i | \(-0.391414\pi\) | ||||
0.334555 | + | 0.942376i | \(0.391414\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.10459 | −0.552293 | ||||||||
\(5\) | 4.23503 | 1.89396 | 0.946982 | − | 0.321286i | \(-0.104115\pi\) | ||||
0.946982 | + | 0.321286i | \(0.104115\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.19590 | 0.829973 | 0.414986 | − | 0.909828i | \(-0.363786\pi\) | ||||
0.414986 | + | 0.909828i | \(0.363786\pi\) | |||||||
\(8\) | −2.93776 | −1.03865 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.00746 | 1.26727 | ||||||||
\(11\) | −2.38110 | −0.717930 | −0.358965 | − | 0.933351i | \(-0.616870\pi\) | ||||
−0.358965 | + | 0.933351i | \(0.616870\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.96438 | −1.65422 | −0.827111 | − | 0.562038i | \(-0.810017\pi\) | ||||
−0.827111 | + | 0.562038i | \(0.810017\pi\) | |||||||
\(14\) | 2.07790 | 0.555342 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.570718 | −0.142680 | ||||||||
\(17\) | 4.21712 | 1.02280 | 0.511401 | − | 0.859342i | \(-0.329127\pi\) | ||||
0.511401 | + | 0.859342i | \(0.329127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.07539 | 1.16438 | 0.582188 | − | 0.813054i | \(-0.302197\pi\) | ||||
0.582188 | + | 0.813054i | \(0.302197\pi\) | |||||||
\(20\) | −4.67796 | −1.04602 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.25315 | −0.480373 | ||||||||
\(23\) | 0.949546 | 0.197994 | 0.0989970 | − | 0.995088i | \(-0.468437\pi\) | ||||
0.0989970 | + | 0.995088i | \(0.468437\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.9355 | 2.58710 | ||||||||
\(26\) | −5.64388 | −1.10686 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.42556 | −0.458388 | ||||||||
\(29\) | 0.816897 | 0.151694 | 0.0758470 | − | 0.997119i | \(-0.475834\pi\) | ||||
0.0758470 | + | 0.997119i | \(0.475834\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.04308 | 1.62419 | 0.812093 | − | 0.583528i | \(-0.198328\pi\) | ||||
0.812093 | + | 0.583528i | \(0.198328\pi\) | |||||||
\(32\) | 5.33546 | 0.943185 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.99051 | 0.684366 | ||||||||
\(35\) | 9.29972 | 1.57194 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.83456 | 1.61679 | 0.808396 | − | 0.588639i | \(-0.200336\pi\) | ||||
0.808396 | + | 0.588639i | \(0.200336\pi\) | |||||||
\(38\) | 4.80266 | 0.779094 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.4415 | −1.96717 | ||||||||
\(41\) | 4.51363 | 0.704911 | 0.352455 | − | 0.935829i | \(-0.385347\pi\) | ||||
0.352455 | + | 0.935829i | \(0.385347\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.33172 | −0.660581 | −0.330290 | − | 0.943879i | \(-0.607147\pi\) | ||||
−0.330290 | + | 0.943879i | \(0.607147\pi\) | |||||||
\(44\) | 2.63013 | 0.396507 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.898520 | 0.132480 | ||||||||
\(47\) | −6.16222 | −0.898852 | −0.449426 | − | 0.893317i | \(-0.648372\pi\) | ||||
−0.449426 | + | 0.893317i | \(0.648372\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.17802 | −0.311145 | ||||||||
\(50\) | 12.2404 | 1.73105 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.58817 | 0.913615 | ||||||||
\(53\) | −8.87566 | −1.21917 | −0.609583 | − | 0.792722i | \(-0.708663\pi\) | ||||
−0.609583 | + | 0.792722i | \(0.708663\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0840 | −1.35973 | ||||||||
\(56\) | −6.45102 | −0.862054 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.773000 | 0.101500 | ||||||||
\(59\) | 11.5005 | 1.49723 | 0.748616 | − | 0.663004i | \(-0.230719\pi\) | ||||
0.748616 | + | 0.663004i | \(0.230719\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.93819 | −0.376197 | −0.188098 | − | 0.982150i | \(-0.560232\pi\) | ||||
−0.188098 | + | 0.982150i | \(0.560232\pi\) | |||||||
\(62\) | 8.55714 | 1.08676 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.19019 | 0.773773 | ||||||||
\(65\) | −25.2594 | −3.13304 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.58957 | 1.17155 | 0.585776 | − | 0.810473i | \(-0.300790\pi\) | ||||
0.585776 | + | 0.810473i | \(0.300790\pi\) | |||||||
\(68\) | −4.65817 | −0.564886 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 8.79998 | 1.05180 | ||||||||
\(71\) | −3.41462 | −0.405241 | −0.202620 | − | 0.979257i | \(-0.564946\pi\) | ||||
−0.202620 | + | 0.979257i | \(0.564946\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.39326 | −0.865315 | −0.432658 | − | 0.901558i | \(-0.642424\pi\) | ||||
−0.432658 | + | 0.901558i | \(0.642424\pi\) | |||||||
\(74\) | 9.30609 | 1.08181 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.60621 | −0.643076 | ||||||||
\(77\) | −5.22867 | −0.595862 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.43221 | −0.948697 | −0.474349 | − | 0.880337i | \(-0.657316\pi\) | ||||
−0.474349 | + | 0.880337i | \(0.657316\pi\) | |||||||
\(80\) | −2.41701 | −0.270230 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.27108 | 0.471662 | ||||||||
\(83\) | −1.97759 | −0.217069 | −0.108535 | − | 0.994093i | \(-0.534616\pi\) | ||||
−0.108535 | + | 0.994093i | \(0.534616\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.8596 | 1.93715 | ||||||||
\(86\) | −4.09895 | −0.442001 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.99510 | 0.745680 | ||||||||
\(89\) | 15.1171 | 1.60241 | 0.801206 | − | 0.598388i | \(-0.204192\pi\) | ||||
0.801206 | + | 0.598388i | \(0.204192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.0972 | −1.37296 | ||||||||
\(92\) | −1.04885 | −0.109351 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.83108 | −0.601430 | ||||||||
\(95\) | 21.4945 | 2.20529 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.33650 | 0.338770 | 0.169385 | − | 0.985550i | \(-0.445822\pi\) | ||||
0.169385 | + | 0.985550i | \(0.445822\pi\) | |||||||
\(98\) | −2.06098 | −0.208190 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −14.2884 | −1.42884 | ||||||||
\(101\) | 13.4637 | 1.33968 | 0.669842 | − | 0.742503i | \(-0.266362\pi\) | ||||
0.669842 | + | 0.742503i | \(0.266362\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.6498 | −1.93615 | −0.968075 | − | 0.250659i | \(-0.919353\pi\) | ||||
−0.968075 | + | 0.250659i | \(0.919353\pi\) | |||||||
\(104\) | 17.5219 | 1.71816 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.39871 | −0.815755 | ||||||||
\(107\) | −6.99976 | −0.676693 | −0.338346 | − | 0.941022i | \(-0.609868\pi\) | ||||
−0.338346 | + | 0.941022i | \(0.609868\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.41477 | 0.614423 | 0.307212 | − | 0.951641i | \(-0.400604\pi\) | ||||
0.307212 | + | 0.951641i | \(0.400604\pi\) | |||||||
\(110\) | −9.54217 | −0.909810 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.25324 | −0.118420 | ||||||||
\(113\) | −1.55854 | −0.146615 | −0.0733077 | − | 0.997309i | \(-0.523356\pi\) | ||||
−0.0733077 | + | 0.997309i | \(0.523356\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.02136 | 0.374994 | ||||||||
\(116\) | −0.902333 | −0.0837795 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.8825 | 1.00181 | ||||||||
\(119\) | 9.26038 | 0.848898 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.33035 | −0.484577 | ||||||||
\(122\) | −2.78030 | −0.251717 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.98886 | −0.897026 | ||||||||
\(125\) | 33.6071 | 3.00591 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.3630 | −1.00830 | −0.504150 | − | 0.863616i | \(-0.668194\pi\) | ||||
−0.504150 | + | 0.863616i | \(0.668194\pi\) | |||||||
\(128\) | −4.81338 | −0.425446 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −23.9020 | −2.09634 | ||||||||
\(131\) | 16.0798 | 1.40490 | 0.702451 | − | 0.711732i | \(-0.252089\pi\) | ||||
0.702451 | + | 0.711732i | \(0.252089\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.1451 | 0.966400 | ||||||||
\(134\) | 9.07426 | 0.783896 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.3889 | −1.06234 | ||||||||
\(137\) | 15.6125 | 1.33386 | 0.666932 | − | 0.745119i | \(-0.267607\pi\) | ||||
0.666932 | + | 0.745119i | \(0.267607\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7408 | −1.33512 | −0.667558 | − | 0.744557i | \(-0.732661\pi\) | ||||
−0.667558 | + | 0.744557i | \(0.732661\pi\) | |||||||
\(140\) | −10.2723 | −0.868171 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.23113 | −0.271150 | ||||||||
\(143\) | 14.2018 | 1.18762 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.45959 | 0.287303 | ||||||||
\(146\) | −6.99597 | −0.578990 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.8631 | −0.892943 | ||||||||
\(149\) | −22.7671 | −1.86515 | −0.932576 | − | 0.360973i | \(-0.882445\pi\) | ||||
−0.932576 | + | 0.360973i | \(0.882445\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1715 | −0.909123 | −0.454561 | − | 0.890715i | \(-0.650204\pi\) | ||||
−0.454561 | + | 0.890715i | \(0.650204\pi\) | |||||||
\(152\) | −14.9103 | −1.20938 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.94770 | −0.398697 | ||||||||
\(155\) | 38.2978 | 3.07615 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.305290 | −0.0243648 | −0.0121824 | − | 0.999926i | \(-0.503878\pi\) | ||||
−0.0121824 | + | 0.999926i | \(0.503878\pi\) | |||||||
\(158\) | −7.97909 | −0.634782 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 22.5959 | 1.78636 | ||||||||
\(161\) | 2.08511 | 0.164330 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.47753 | 0.507360 | 0.253680 | − | 0.967288i | \(-0.418359\pi\) | ||||
0.253680 | + | 0.967288i | \(0.418359\pi\) | |||||||
\(164\) | −4.98569 | −0.389317 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.87132 | −0.145243 | ||||||||
\(167\) | 0.771956 | 0.0597358 | 0.0298679 | − | 0.999554i | \(-0.490491\pi\) | ||||
0.0298679 | + | 0.999554i | \(0.490491\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.5739 | 1.73645 | ||||||||
\(170\) | 16.8999 | 1.29617 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.78475 | 0.364834 | ||||||||
\(173\) | −11.2432 | −0.854803 | −0.427401 | − | 0.904062i | \(-0.640571\pi\) | ||||
−0.427401 | + | 0.904062i | \(0.640571\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 28.4051 | 2.14722 | ||||||||
\(176\) | 1.35894 | 0.102434 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 14.3048 | 1.07219 | ||||||||
\(179\) | −5.71268 | −0.426986 | −0.213493 | − | 0.976945i | \(-0.568484\pi\) | ||||
−0.213493 | + | 0.976945i | \(0.568484\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.76105 | −0.576875 | −0.288437 | − | 0.957499i | \(-0.593136\pi\) | ||||
−0.288437 | + | 0.957499i | \(0.593136\pi\) | |||||||
\(182\) | −12.3934 | −0.918660 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.78953 | −0.205647 | ||||||||
\(185\) | 41.6497 | 3.06215 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0414 | −0.734300 | ||||||||
\(188\) | 6.80670 | 0.496430 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 20.3394 | 1.47558 | ||||||||
\(191\) | 19.9452 | 1.44318 | 0.721592 | − | 0.692319i | \(-0.243411\pi\) | ||||
0.721592 | + | 0.692319i | \(0.243411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.59376 | −0.618592 | −0.309296 | − | 0.950966i | \(-0.600093\pi\) | ||||
−0.309296 | + | 0.950966i | \(0.600093\pi\) | |||||||
\(194\) | 3.15721 | 0.226674 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.40581 | 0.171843 | ||||||||
\(197\) | −7.93505 | −0.565349 | −0.282674 | − | 0.959216i | \(-0.591222\pi\) | ||||
−0.282674 | + | 0.959216i | \(0.591222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.9031 | −1.34001 | −0.670004 | − | 0.742357i | \(-0.733708\pi\) | ||||
−0.670004 | + | 0.742357i | \(0.733708\pi\) | |||||||
\(200\) | −38.0014 | −2.68710 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.7402 | 0.896395 | ||||||||
\(203\) | 1.79383 | 0.125902 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.1154 | 1.33508 | ||||||||
\(206\) | −18.5939 | −1.29550 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.40398 | 0.236024 | ||||||||
\(209\) | −12.0850 | −0.835939 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.18073 | 0.494342 | 0.247171 | − | 0.968972i | \(-0.420499\pi\) | ||||
0.247171 | + | 0.968972i | \(0.420499\pi\) | |||||||
\(212\) | 9.80393 | 0.673337 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.62362 | −0.452781 | ||||||||
\(215\) | −18.3450 | −1.25112 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.8577 | 1.34803 | ||||||||
\(218\) | 6.07006 | 0.411116 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.1387 | 0.750971 | ||||||||
\(221\) | −25.1525 | −1.69194 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.8849 | −1.13070 | −0.565348 | − | 0.824852i | \(-0.691258\pi\) | ||||
−0.565348 | + | 0.824852i | \(0.691258\pi\) | |||||||
\(224\) | 11.7161 | 0.782818 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.47479 | −0.0981018 | ||||||||
\(227\) | −18.1109 | −1.20207 | −0.601033 | − | 0.799224i | \(-0.705244\pi\) | ||||
−0.601033 | + | 0.799224i | \(0.705244\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.4187 | 1.87796 | 0.938980 | − | 0.343973i | \(-0.111773\pi\) | ||||
0.938980 | + | 0.343973i | \(0.111773\pi\) | |||||||
\(230\) | 3.80526 | 0.250912 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.39984 | −0.157558 | ||||||||
\(233\) | 17.1517 | 1.12364 | 0.561821 | − | 0.827259i | \(-0.310101\pi\) | ||||
0.561821 | + | 0.827259i | \(0.310101\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −26.0972 | −1.70239 | ||||||||
\(236\) | −12.7032 | −0.826910 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 8.76276 | 0.568005 | ||||||||
\(239\) | 1.00000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.97567 | 0.191680 | 0.0958399 | − | 0.995397i | \(-0.469446\pi\) | ||||
0.0958399 | + | 0.995397i | \(0.469446\pi\) | |||||||
\(242\) | −5.04391 | −0.324235 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.24548 | 0.207771 | ||||||||
\(245\) | −9.22397 | −0.589298 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −30.2716 | −1.92614 | ||||||||
\(248\) | −26.5664 | −1.68697 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 31.8012 | 2.01128 | ||||||||
\(251\) | −15.0788 | −0.951767 | −0.475883 | − | 0.879508i | \(-0.657872\pi\) | ||||
−0.475883 | + | 0.879508i | \(0.657872\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.26097 | −0.142146 | ||||||||
\(254\) | −10.7524 | −0.674663 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.9351 | −1.05844 | ||||||||
\(257\) | 2.15365 | 0.134341 | 0.0671704 | − | 0.997742i | \(-0.478603\pi\) | ||||
0.0671704 | + | 0.997742i | \(0.478603\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.5957 | 1.34189 | ||||||||
\(260\) | 27.9011 | 1.73036 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.2158 | 0.940033 | ||||||||
\(263\) | −5.70756 | −0.351943 | −0.175972 | − | 0.984395i | \(-0.556307\pi\) | ||||
−0.175972 | + | 0.984395i | \(0.556307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.5887 | −2.30906 | ||||||||
\(266\) | 10.5462 | 0.646627 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.5925 | −0.647040 | ||||||||
\(269\) | −5.16679 | −0.315025 | −0.157513 | − | 0.987517i | \(-0.550347\pi\) | ||||
−0.157513 | + | 0.987517i | \(0.550347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.13749 | 0.190589 | 0.0952943 | − | 0.995449i | \(-0.469621\pi\) | ||||
0.0952943 | + | 0.995449i | \(0.469621\pi\) | |||||||
\(272\) | −2.40679 | −0.145933 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.7735 | 0.892500 | ||||||||
\(275\) | −30.8008 | −1.85736 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.9634 | −1.13940 | −0.569701 | − | 0.821852i | \(-0.692941\pi\) | ||||
−0.569701 | + | 0.821852i | \(0.692941\pi\) | |||||||
\(278\) | −14.8949 | −0.893339 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −27.3203 | −1.63270 | ||||||||
\(281\) | 16.1906 | 0.965853 | 0.482927 | − | 0.875661i | \(-0.339574\pi\) | ||||
0.482927 | + | 0.875661i | \(0.339574\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.53384 | −0.328953 | −0.164476 | − | 0.986381i | \(-0.552593\pi\) | ||||
−0.164476 | + | 0.986381i | \(0.552593\pi\) | |||||||
\(284\) | 3.77174 | 0.223812 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.4387 | 0.794644 | ||||||||
\(287\) | 9.91149 | 0.585057 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.784104 | 0.0461238 | ||||||||
\(290\) | 3.27368 | 0.192237 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.16649 | 0.477907 | ||||||||
\(293\) | −30.0543 | −1.75579 | −0.877896 | − | 0.478851i | \(-0.841053\pi\) | ||||
−0.877896 | + | 0.478851i | \(0.841053\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 48.7048 | 2.83570 | ||||||||
\(296\) | −28.8915 | −1.67929 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −21.5437 | −1.24799 | ||||||||
\(299\) | −5.66346 | −0.327526 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.51203 | −0.548264 | ||||||||
\(302\) | −10.5712 | −0.608302 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.89662 | −0.166133 | ||||||||
\(305\) | −12.4433 | −0.712504 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.9061 | 0.736591 | 0.368296 | − | 0.929709i | \(-0.379941\pi\) | ||||
0.368296 | + | 0.929709i | \(0.379941\pi\) | |||||||
\(308\) | 5.77551 | 0.329090 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 36.2398 | 2.05828 | ||||||||
\(311\) | 19.6943 | 1.11676 | 0.558381 | − | 0.829585i | \(-0.311423\pi\) | ||||
0.558381 | + | 0.829585i | \(0.311423\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4786 | −0.818380 | −0.409190 | − | 0.912449i | \(-0.634189\pi\) | ||||
−0.409190 | + | 0.912449i | \(0.634189\pi\) | |||||||
\(314\) | −0.288885 | −0.0163027 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.31410 | 0.523959 | ||||||||
\(317\) | 0.816418 | 0.0458546 | 0.0229273 | − | 0.999737i | \(-0.492701\pi\) | ||||
0.0229273 | + | 0.999737i | \(0.492701\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.94512 | −0.108906 | ||||||||
\(320\) | 26.2157 | 1.46550 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.97306 | 0.109954 | ||||||||
\(323\) | 21.4036 | 1.19093 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −77.1523 | −4.27964 | ||||||||
\(326\) | 6.12945 | 0.339479 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.2599 | −0.732158 | ||||||||
\(329\) | −13.5316 | −0.746023 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.6673 | −0.586326 | −0.293163 | − | 0.956063i | \(-0.594708\pi\) | ||||
−0.293163 | + | 0.956063i | \(0.594708\pi\) | |||||||
\(332\) | 2.18442 | 0.119886 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.730474 | 0.0399698 | ||||||||
\(335\) | 40.6121 | 2.21888 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.6962 | 1.50871 | 0.754355 | − | 0.656466i | \(-0.227950\pi\) | ||||
0.754355 | + | 0.656466i | \(0.227950\pi\) | |||||||
\(338\) | 21.3608 | 1.16188 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −19.7275 | −1.06987 | ||||||||
\(341\) | −21.5325 | −1.16605 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1540 | −1.08821 | ||||||||
\(344\) | 12.7255 | 0.686114 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.6390 | −0.571956 | ||||||||
\(347\) | 18.4956 | 0.992898 | 0.496449 | − | 0.868066i | \(-0.334637\pi\) | ||||
0.496449 | + | 0.868066i | \(0.334637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.7763 | −1.32625 | −0.663123 | − | 0.748511i | \(-0.730769\pi\) | ||||
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(350\) | 26.8787 | 1.43673 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.7043 | −0.677140 | ||||||||
\(353\) | −0.00689704 | −0.000367092 0 | −0.000183546 | − | 1.00000i | \(-0.500058\pi\) | ||||
−0.000183546 | 1.00000i | \(0.500058\pi\) | ||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.4610 | −0.767512 | ||||||||
\(356\) | −16.6982 | −0.885001 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.40570 | −0.285700 | ||||||||
\(359\) | −14.7259 | −0.777202 | −0.388601 | − | 0.921406i | \(-0.627041\pi\) | ||||
−0.388601 | + | 0.921406i | \(0.627041\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.75963 | 0.355770 | ||||||||
\(362\) | −7.34400 | −0.385992 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.4670 | 0.758276 | ||||||||
\(365\) | −31.3107 | −1.63888 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2522 | −0.535158 | −0.267579 | − | 0.963536i | \(-0.586224\pi\) | ||||
−0.267579 | + | 0.963536i | \(0.586224\pi\) | |||||||
\(368\) | −0.541923 | −0.0282497 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 39.4116 | 2.04891 | ||||||||
\(371\) | −19.4901 | −1.01187 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.7071 | 1.17573 | 0.587866 | − | 0.808959i | \(-0.299968\pi\) | ||||
0.587866 | + | 0.808959i | \(0.299968\pi\) | |||||||
\(374\) | −9.50181 | −0.491327 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.1031 | 0.933596 | ||||||||
\(377\) | −4.87229 | −0.250936 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6893 | −1.16547 | −0.582736 | − | 0.812661i | \(-0.698018\pi\) | ||||
−0.582736 | + | 0.812661i | \(0.698018\pi\) | |||||||
\(380\) | −23.7425 | −1.21796 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.8734 | 0.965647 | ||||||||
\(383\) | −28.2456 | −1.44328 | −0.721640 | − | 0.692268i | \(-0.756611\pi\) | ||||
−0.721640 | + | 0.692268i | \(0.756611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.1436 | −1.12854 | ||||||||
\(386\) | −8.13196 | −0.413906 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.68545 | −0.187100 | ||||||||
\(389\) | 30.2010 | 1.53125 | 0.765627 | − | 0.643285i | \(-0.222429\pi\) | ||||
0.765627 | + | 0.643285i | \(0.222429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00435 | 0.202509 | ||||||||
\(392\) | 6.39848 | 0.323172 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.50864 | −0.378280 | ||||||||
\(395\) | −35.7107 | −1.79680 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0056 | −0.552354 | −0.276177 | − | 0.961107i | \(-0.589068\pi\) | ||||
−0.276177 | + | 0.961107i | \(0.589068\pi\) | |||||||
\(398\) | −17.8873 | −0.896612 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.38253 | −0.369127 | ||||||||
\(401\) | 20.8723 | 1.04232 | 0.521158 | − | 0.853460i | \(-0.325500\pi\) | ||||
0.521158 | + | 0.853460i | \(0.325500\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −53.9364 | −2.68676 | ||||||||
\(404\) | −14.8718 | −0.739898 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.69743 | 0.0842421 | ||||||||
\(407\) | −23.4171 | −1.16074 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.2317 | 1.39597 | 0.697984 | − | 0.716113i | \(-0.254081\pi\) | ||||
0.697984 | + | 0.716113i | \(0.254081\pi\) | |||||||
\(410\) | 18.0882 | 0.893311 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 21.7049 | 1.06932 | ||||||||
\(413\) | 25.2539 | 1.24266 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.37517 | −0.411121 | ||||||||
\(416\) | −31.8227 | −1.56024 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.4356 | −0.559335 | ||||||||
\(419\) | −17.3156 | −0.845922 | −0.422961 | − | 0.906148i | \(-0.639009\pi\) | ||||
−0.422961 | + | 0.906148i | \(0.639009\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0043 | −0.682530 | −0.341265 | − | 0.939967i | \(-0.610855\pi\) | ||||
−0.341265 | + | 0.939967i | \(0.610855\pi\) | |||||||
\(422\) | 6.79486 | 0.330769 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 26.0745 | 1.26629 | ||||||||
\(425\) | 54.5506 | 2.64609 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.45198 | −0.312233 | ||||||||
\(428\) | 7.73184 | 0.373733 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −17.3592 | −0.837133 | ||||||||
\(431\) | −24.8909 | −1.19895 | −0.599476 | − | 0.800393i | \(-0.704624\pi\) | ||||
−0.599476 | + | 0.800393i | \(0.704624\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.6159 | 0.894624 | 0.447312 | − | 0.894378i | \(-0.352381\pi\) | ||||
0.447312 | + | 0.894378i | \(0.352381\pi\) | |||||||
\(434\) | 18.7906 | 0.901979 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.08566 | −0.339342 | ||||||||
\(437\) | 4.81932 | 0.230539 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −32.6083 | −1.55631 | −0.778155 | − | 0.628072i | \(-0.783844\pi\) | ||||
−0.778155 | + | 0.628072i | \(0.783844\pi\) | |||||||
\(440\) | 29.6245 | 1.41229 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23.8009 | −1.13209 | ||||||||
\(443\) | 18.3996 | 0.874191 | 0.437096 | − | 0.899415i | \(-0.356007\pi\) | ||||
0.437096 | + | 0.899415i | \(0.356007\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 64.0216 | 3.03491 | ||||||||
\(446\) | −15.9776 | −0.756559 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 13.5930 | 0.642211 | ||||||||
\(449\) | 20.7087 | 0.977304 | 0.488652 | − | 0.872479i | \(-0.337489\pi\) | ||||
0.488652 | + | 0.872479i | \(0.337489\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.7474 | −0.506076 | ||||||||
\(452\) | 1.72155 | 0.0809747 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −17.1377 | −0.804313 | ||||||||
\(455\) | −55.4671 | −2.60034 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5865 | −0.588770 | −0.294385 | − | 0.955687i | \(-0.595115\pi\) | ||||
−0.294385 | + | 0.955687i | \(0.595115\pi\) | |||||||
\(458\) | 26.8916 | 1.25656 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.44193 | −0.207106 | ||||||||
\(461\) | −32.5030 | −1.51382 | −0.756909 | − | 0.653521i | \(-0.773291\pi\) | ||||
−0.756909 | + | 0.653521i | \(0.773291\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.40154 | −0.111609 | −0.0558045 | − | 0.998442i | \(-0.517772\pi\) | ||||
−0.0558045 | + | 0.998442i | \(0.517772\pi\) | |||||||
\(464\) | −0.466218 | −0.0216436 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.2300 | 0.751840 | ||||||||
\(467\) | −26.0409 | −1.20503 | −0.602514 | − | 0.798109i | \(-0.705834\pi\) | ||||
−0.602514 | + | 0.798109i | \(0.705834\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.0578 | 0.972357 | ||||||||
\(470\) | −24.6948 | −1.13909 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −33.7855 | −1.55510 | ||||||||
\(473\) | 10.3143 | 0.474250 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 65.6528 | 3.01236 | ||||||||
\(476\) | −10.2289 | −0.468840 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.946263 | 0.0432811 | ||||||||
\(479\) | 18.4214 | 0.841695 | 0.420847 | − | 0.907131i | \(-0.361733\pi\) | ||||
0.420847 | + | 0.907131i | \(0.361733\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −58.6571 | −2.67453 | ||||||||
\(482\) | 2.81577 | 0.128255 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.88783 | 0.267629 | ||||||||
\(485\) | 14.1302 | 0.641619 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.5135 | 1.11081 | 0.555406 | − | 0.831579i | \(-0.312563\pi\) | ||||
0.555406 | + | 0.831579i | \(0.312563\pi\) | |||||||
\(488\) | 8.63169 | 0.390738 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.72830 | −0.394305 | ||||||||
\(491\) | 0.364931 | 0.0164691 | 0.00823454 | − | 0.999966i | \(-0.497379\pi\) | ||||
0.00823454 | + | 0.999966i | \(0.497379\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.44495 | 0.155153 | ||||||||
\(494\) | −28.6449 | −1.28880 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.16105 | −0.231738 | ||||||||
\(497\) | −7.49817 | −0.336339 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.24220 | 0.100375 | 0.0501874 | − | 0.998740i | \(-0.484018\pi\) | ||||
0.0501874 | + | 0.998740i | \(0.484018\pi\) | |||||||
\(500\) | −37.1220 | −1.66014 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.2685 | −0.636836 | ||||||||
\(503\) | −17.8943 | −0.797868 | −0.398934 | − | 0.916980i | \(-0.630620\pi\) | ||||
−0.398934 | + | 0.916980i | \(0.630620\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 57.0191 | 2.53732 | ||||||||
\(506\) | −2.13947 | −0.0951110 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.5514 | 0.556877 | ||||||||
\(509\) | −6.29346 | −0.278953 | −0.139476 | − | 0.990225i | \(-0.544542\pi\) | ||||
−0.139476 | + | 0.990225i | \(0.544542\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.2349 | −0.718188 | ||||||||
\(512\) | −6.39831 | −0.282768 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.03792 | 0.0898887 | ||||||||
\(515\) | −83.2175 | −3.66700 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.6729 | 0.645313 | ||||||||
\(518\) | 20.4352 | 0.897873 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 74.2058 | 3.25414 | ||||||||
\(521\) | 39.0853 | 1.71236 | 0.856178 | − | 0.516681i | \(-0.172833\pi\) | ||||
0.856178 | + | 0.516681i | \(0.172833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.0192 | 0.656745 | 0.328372 | − | 0.944548i | \(-0.393500\pi\) | ||||
0.328372 | + | 0.944548i | \(0.393500\pi\) | |||||||
\(524\) | −17.7616 | −0.775917 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.40085 | −0.235488 | ||||||||
\(527\) | 38.1358 | 1.66122 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0984 | −0.960798 | ||||||||
\(530\) | −35.5688 | −1.54501 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.3107 | −0.533736 | ||||||||
\(533\) | −26.9210 | −1.16608 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −29.6442 | −1.28163 | ||||||||
\(536\) | −28.1718 | −1.21684 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.88915 | −0.210786 | ||||||||
\(539\) | 5.18608 | 0.223380 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.27190 | 0.140670 | 0.0703349 | − | 0.997523i | \(-0.477593\pi\) | ||||
0.0703349 | + | 0.997523i | \(0.477593\pi\) | |||||||
\(542\) | 2.96889 | 0.127525 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 22.5003 | 0.964692 | ||||||||
\(545\) | 27.1668 | 1.16370 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.6602 | −1.48196 | −0.740981 | − | 0.671526i | \(-0.765639\pi\) | ||||
−0.740981 | + | 0.671526i | \(0.765639\pi\) | |||||||
\(548\) | −17.2453 | −0.736684 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −29.1456 | −1.24277 | ||||||||
\(551\) | 4.14608 | 0.176629 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.5163 | −0.787393 | ||||||||
\(554\) | −17.9444 | −0.762385 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.3871 | 0.737376 | ||||||||
\(557\) | 19.1211 | 0.810186 | 0.405093 | − | 0.914276i | \(-0.367239\pi\) | ||||
0.405093 | + | 0.914276i | \(0.367239\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.8360 | 1.09275 | ||||||||
\(560\) | −5.30752 | −0.224284 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.3206 | 0.646261 | ||||||||
\(563\) | 37.7459 | 1.59080 | 0.795399 | − | 0.606086i | \(-0.207261\pi\) | ||||
0.795399 | + | 0.606086i | \(0.207261\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.60049 | −0.277685 | ||||||||
\(566\) | −5.23647 | −0.220105 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.0313 | 0.420905 | ||||||||
\(569\) | −3.37306 | −0.141406 | −0.0707031 | − | 0.997497i | \(-0.522524\pi\) | ||||
−0.0707031 | + | 0.997497i | \(0.522524\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.5252 | −0.649709 | −0.324855 | − | 0.945764i | \(-0.605315\pi\) | ||||
−0.324855 | + | 0.945764i | \(0.605315\pi\) | |||||||
\(572\) | −15.6871 | −0.655911 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.37888 | 0.391467 | ||||||||
\(575\) | 12.2829 | 0.512230 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −30.3253 | −1.26246 | −0.631229 | − | 0.775596i | \(-0.717449\pi\) | ||||
−0.631229 | + | 0.775596i | \(0.717449\pi\) | |||||||
\(578\) | 0.741969 | 0.0308618 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.82141 | −0.158675 | ||||||||
\(581\) | −4.34260 | −0.180161 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.1339 | 0.875275 | ||||||||
\(584\) | 21.7196 | 0.898763 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.4393 | −1.17482 | ||||||||
\(587\) | −32.7853 | −1.35319 | −0.676597 | − | 0.736354i | \(-0.736546\pi\) | ||||
−0.676597 | + | 0.736354i | \(0.736546\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.8972 | 1.89116 | ||||||||
\(590\) | 46.0876 | 1.89739 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.61277 | −0.230683 | ||||||||
\(593\) | 35.8084 | 1.47047 | 0.735237 | − | 0.677810i | \(-0.237071\pi\) | ||||
0.735237 | + | 0.677810i | \(0.237071\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.2180 | 1.60778 | ||||||||
\(596\) | 25.1482 | 1.03011 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.35912 | −0.219151 | ||||||||
\(599\) | −0.743135 | −0.0303637 | −0.0151818 | − | 0.999885i | \(-0.504833\pi\) | ||||
−0.0151818 | + | 0.999885i | \(0.504833\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.26360 | −0.0923341 | −0.0461671 | − | 0.998934i | \(-0.514701\pi\) | ||||
−0.0461671 | + | 0.998934i | \(0.514701\pi\) | |||||||
\(602\) | −9.00088 | −0.366848 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.3399 | 0.502102 | ||||||||
\(605\) | −22.5742 | −0.917772 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.9036 | 1.41670 | 0.708348 | − | 0.705864i | \(-0.249441\pi\) | ||||
0.708348 | + | 0.705864i | \(0.249441\pi\) | |||||||
\(608\) | 27.0796 | 1.09822 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.7747 | −0.476743 | ||||||||
\(611\) | 36.7539 | 1.48690 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.0779 | 0.568603 | 0.284301 | − | 0.958735i | \(-0.408238\pi\) | ||||
0.284301 | + | 0.958735i | \(0.408238\pi\) | |||||||
\(614\) | 12.2126 | 0.492860 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.3605 | 0.618894 | ||||||||
\(617\) | −8.38378 | −0.337518 | −0.168759 | − | 0.985657i | \(-0.553976\pi\) | ||||
−0.168759 | + | 0.985657i | \(0.553976\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −43.7765 | −1.75952 | −0.879762 | − | 0.475414i | \(-0.842298\pi\) | ||||
−0.879762 | + | 0.475414i | \(0.842298\pi\) | |||||||
\(620\) | −42.3032 | −1.69894 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.6360 | 0.747235 | ||||||||
\(623\) | 33.1957 | 1.32996 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 77.6498 | 3.10599 | ||||||||
\(626\) | −13.7006 | −0.547585 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.337219 | 0.0134565 | ||||||||
\(629\) | 41.4735 | 1.65366 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 43.4013 | 1.72778 | 0.863890 | − | 0.503681i | \(-0.168021\pi\) | ||||
0.863890 | + | 0.503681i | \(0.168021\pi\) | |||||||
\(632\) | 24.7718 | 0.985368 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.772546 | 0.0306817 | ||||||||
\(635\) | −48.1225 | −1.90969 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.9905 | 0.514703 | ||||||||
\(638\) | −1.84059 | −0.0728698 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −20.3848 | −0.805780 | ||||||||
\(641\) | 25.0623 | 0.989903 | 0.494951 | − | 0.868921i | \(-0.335186\pi\) | ||||
0.494951 | + | 0.868921i | \(0.335186\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.5472 | −0.415941 | −0.207970 | − | 0.978135i | \(-0.566686\pi\) | ||||
−0.207970 | + | 0.978135i | \(0.566686\pi\) | |||||||
\(644\) | −2.30318 | −0.0907581 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.2534 | 0.796859 | ||||||||
\(647\) | 9.65606 | 0.379619 | 0.189809 | − | 0.981821i | \(-0.439213\pi\) | ||||
0.189809 | + | 0.981821i | \(0.439213\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.3838 | −1.07491 | ||||||||
\(650\) | −73.0064 | −2.86355 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.15499 | −0.280211 | ||||||||
\(653\) | 24.7538 | 0.968692 | 0.484346 | − | 0.874876i | \(-0.339058\pi\) | ||||
0.484346 | + | 0.874876i | \(0.339058\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 68.0986 | 2.66083 | ||||||||
\(656\) | −2.57601 | −0.100576 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.8045 | −0.499171 | ||||||||
\(659\) | 14.0114 | 0.545807 | 0.272904 | − | 0.962041i | \(-0.412016\pi\) | ||||
0.272904 | + | 0.962041i | \(0.412016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.6444 | 1.23082 | 0.615411 | − | 0.788206i | \(-0.288990\pi\) | ||||
0.615411 | + | 0.788206i | \(0.288990\pi\) | |||||||
\(662\) | −10.0940 | −0.392316 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.80969 | 0.225460 | ||||||||
\(665\) | 47.1997 | 1.83033 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.775681 | 0.0300345 | ||||||||
\(668\) | −0.852692 | −0.0329916 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 38.4298 | 1.48467 | ||||||||
\(671\) | 6.99614 | 0.270083 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.6489 | −0.641769 | −0.320885 | − | 0.947118i | \(-0.603980\pi\) | ||||
−0.320885 | + | 0.947118i | \(0.603980\pi\) | |||||||
\(674\) | 26.2079 | 1.00949 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.9348 | −0.959030 | ||||||||
\(677\) | −30.6653 | −1.17856 | −0.589281 | − | 0.807928i | \(-0.700589\pi\) | ||||
−0.589281 | + | 0.807928i | \(0.700589\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.32662 | 0.281170 | ||||||||
\(680\) | −52.4673 | −2.01203 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20.3754 | −0.780215 | ||||||||
\(683\) | 16.6909 | 0.638660 | 0.319330 | − | 0.947644i | \(-0.396542\pi\) | ||||
0.319330 | + | 0.947644i | \(0.396542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 66.1194 | 2.52629 | ||||||||
\(686\) | −19.0710 | −0.728135 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.47219 | 0.0942514 | ||||||||
\(689\) | 52.9378 | 2.01677 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.8963 | −0.680807 | −0.340404 | − | 0.940279i | \(-0.610564\pi\) | ||||
−0.340404 | + | 0.940279i | \(0.610564\pi\) | |||||||
\(692\) | 12.4191 | 0.472102 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 17.5017 | 0.664357 | ||||||||
\(695\) | −66.6628 | −2.52866 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.0345 | 0.720984 | ||||||||
\(698\) | −23.4449 | −0.887403 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −31.3759 | −1.18590 | ||||||||
\(701\) | 20.7781 | 0.784780 | 0.392390 | − | 0.919799i | \(-0.371648\pi\) | ||||
0.392390 | + | 0.919799i | \(0.371648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.9143 | 1.88255 | ||||||||
\(704\) | −14.7395 | −0.555515 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.00652641 | −0.000245625 0 | ||||||||
\(707\) | 29.5649 | 1.11190 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.7680 | −1.08041 | −0.540203 | − | 0.841535i | \(-0.681652\pi\) | ||||
−0.540203 | + | 0.841535i | \(0.681652\pi\) | |||||||
\(710\) | −13.6839 | −0.513549 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −44.4104 | −1.66435 | ||||||||
\(713\) | 8.58682 | 0.321579 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 60.1451 | 2.24930 | ||||||||
\(716\) | 6.31014 | 0.235821 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −13.9345 | −0.520033 | ||||||||
\(719\) | −11.7648 | −0.438754 | −0.219377 | − | 0.975640i | \(-0.570402\pi\) | ||||
−0.219377 | + | 0.975640i | \(0.570402\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.1490 | −1.60695 | ||||||||
\(722\) | 6.39639 | 0.238049 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.57275 | 0.318604 | ||||||||
\(725\) | 10.5670 | 0.392448 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.53649 | 0.205337 | 0.102668 | − | 0.994716i | \(-0.467262\pi\) | ||||
0.102668 | + | 0.994716i | \(0.467262\pi\) | |||||||
\(728\) | 38.4764 | 1.42603 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29.6282 | −1.09659 | ||||||||
\(731\) | −18.2674 | −0.675643 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.44675 | −0.238116 | −0.119058 | − | 0.992887i | \(-0.537987\pi\) | ||||
−0.119058 | + | 0.992887i | \(0.537987\pi\) | |||||||
\(734\) | −9.70124 | −0.358079 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.06626 | 0.186745 | ||||||||
\(737\) | −22.8337 | −0.841092 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.2860 | −0.930161 | −0.465081 | − | 0.885268i | \(-0.653975\pi\) | ||||
−0.465081 | + | 0.885268i | \(0.653975\pi\) | |||||||
\(740\) | −46.0057 | −1.69120 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −18.4427 | −0.677054 | ||||||||
\(743\) | −13.3483 | −0.489700 | −0.244850 | − | 0.969561i | \(-0.578739\pi\) | ||||
−0.244850 | + | 0.969561i | \(0.578739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −96.4194 | −3.53253 | ||||||||
\(746\) | 21.4869 | 0.786692 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.0916 | 0.405549 | ||||||||
\(749\) | −15.3708 | −0.561637 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.7601 | 1.08596 | 0.542981 | − | 0.839745i | \(-0.317296\pi\) | ||||
0.542981 | + | 0.839745i | \(0.317296\pi\) | |||||||
\(752\) | 3.51689 | 0.128248 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.61047 | −0.167903 | ||||||||
\(755\) | −47.3116 | −1.72185 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.87390 | 0.358873 | 0.179436 | − | 0.983770i | \(-0.442573\pi\) | ||||
0.179436 | + | 0.983770i | \(0.442573\pi\) | |||||||
\(758\) | −21.4701 | −0.779828 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −63.1455 | −2.29053 | ||||||||
\(761\) | −45.0481 | −1.63299 | −0.816495 | − | 0.577352i | \(-0.804086\pi\) | ||||
−0.816495 | + | 0.577352i | \(0.804086\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0862 | 0.509955 | ||||||||
\(764\) | −22.0312 | −0.797060 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −26.7277 | −0.965712 | ||||||||
\(767\) | −68.5931 | −2.47675 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.2285 | 1.27037 | 0.635186 | − | 0.772359i | \(-0.280923\pi\) | ||||
0.635186 | + | 0.772359i | \(0.280923\pi\) | |||||||
\(770\) | −20.9537 | −0.755117 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.49254 | 0.341644 | ||||||||
\(773\) | 47.4525 | 1.70675 | 0.853374 | − | 0.521300i | \(-0.174553\pi\) | ||||
0.853374 | + | 0.521300i | \(0.174553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 116.977 | 4.20193 | ||||||||
\(776\) | −9.80182 | −0.351865 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.5781 | 1.02458 | ||||||||
\(779\) | 22.9085 | 0.820781 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.13056 | 0.290934 | ||||||||
\(782\) | 3.78917 | 0.135500 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.24303 | 0.0443941 | ||||||||
\(785\) | −1.29291 | −0.0461461 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.48849 | −0.195643 | −0.0978217 | − | 0.995204i | \(-0.531188\pi\) | ||||
−0.0978217 | + | 0.995204i | \(0.531188\pi\) | |||||||
\(788\) | 8.76494 | 0.312238 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −33.7917 | −1.20225 | ||||||||
\(791\) | −3.42241 | −0.121687 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.5245 | 0.622313 | ||||||||
\(794\) | −10.4142 | −0.369585 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.8801 | 0.740077 | ||||||||
\(797\) | −25.3956 | −0.899558 | −0.449779 | − | 0.893140i | \(-0.648497\pi\) | ||||
−0.449779 | + | 0.893140i | \(0.648497\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −25.9868 | −0.919348 | ||||||||
\(800\) | 69.0169 | 2.44012 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.7507 | 0.697423 | ||||||||
\(803\) | 17.6041 | 0.621235 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.83051 | 0.311234 | ||||||||
\(806\) | −51.0381 | −1.79774 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −39.5530 | −1.39147 | ||||||||
\(809\) | −44.6599 | −1.57016 | −0.785079 | − | 0.619396i | \(-0.787378\pi\) | ||||
−0.785079 | + | 0.619396i | \(0.787378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29.4164 | −1.03295 | −0.516476 | − | 0.856302i | \(-0.672756\pi\) | ||||
−0.516476 | + | 0.856302i | \(0.672756\pi\) | |||||||
\(812\) | −1.98144 | −0.0695347 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −22.1587 | −0.776664 | ||||||||
\(815\) | 27.4326 | 0.960921 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.9852 | −0.769164 | ||||||||
\(818\) | 26.7146 | 0.934055 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21.1146 | −0.737353 | ||||||||
\(821\) | −30.4469 | −1.06260 | −0.531302 | − | 0.847182i | \(-0.678297\pi\) | ||||
−0.531302 | + | 0.847182i | \(0.678297\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.6616 | −0.545928 | −0.272964 | − | 0.962024i | \(-0.588004\pi\) | ||||
−0.272964 | + | 0.962024i | \(0.588004\pi\) | |||||||
\(824\) | 57.7263 | 2.01099 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23.8968 | 0.831476 | ||||||||
\(827\) | −14.6578 | −0.509701 | −0.254850 | − | 0.966980i | \(-0.582026\pi\) | ||||
−0.254850 | + | 0.966980i | \(0.582026\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.4386 | −1.40449 | −0.702246 | − | 0.711934i | \(-0.747819\pi\) | ||||
−0.702246 | + | 0.711934i | \(0.747819\pi\) | |||||||
\(830\) | −7.92512 | −0.275085 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −36.9207 | −1.27999 | ||||||||
\(833\) | −9.18496 | −0.318240 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.26926 | 0.113137 | ||||||||
\(836\) | 13.3490 | 0.461683 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.3851 | −0.566014 | ||||||||
\(839\) | −2.18300 | −0.0753655 | −0.0376828 | − | 0.999290i | \(-0.511998\pi\) | ||||
−0.0376828 | + | 0.999290i | \(0.511998\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3327 | −0.976989 | ||||||||
\(842\) | −13.2518 | −0.456687 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.93173 | −0.273021 | ||||||||
\(845\) | 95.6011 | 3.28878 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.7049 | −0.402186 | ||||||||
\(848\) | 5.06550 | 0.173950 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 51.6192 | 1.77052 | ||||||||
\(851\) | 9.33837 | 0.320115 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.6098 | 0.671428 | 0.335714 | − | 0.941964i | \(-0.391023\pi\) | ||||
0.335714 | + | 0.941964i | \(0.391023\pi\) | |||||||
\(854\) | −6.10527 | −0.208918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.5636 | 0.702849 | ||||||||
\(857\) | 21.1183 | 0.721387 | 0.360693 | − | 0.932684i | \(-0.382540\pi\) | ||||
0.360693 | + | 0.932684i | \(0.382540\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.6952 | −0.740231 | −0.370116 | − | 0.928986i | \(-0.620682\pi\) | ||||
−0.370116 | + | 0.928986i | \(0.620682\pi\) | |||||||
\(860\) | 20.2636 | 0.690983 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.5533 | −0.802230 | ||||||||
\(863\) | −17.3555 | −0.590788 | −0.295394 | − | 0.955375i | \(-0.595451\pi\) | ||||
−0.295394 | + | 0.955375i | \(0.595451\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −47.6152 | −1.61897 | ||||||||
\(866\) | 17.6156 | 0.598601 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −21.9346 | −0.744508 | ||||||||
\(869\) | 20.0780 | 0.681098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −57.1959 | −1.93801 | ||||||||
\(872\) | −18.8450 | −0.638173 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.56034 | 0.154256 | ||||||||
\(875\) | 73.7980 | 2.49483 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.1907 | −0.951932 | −0.475966 | − | 0.879464i | \(-0.657902\pi\) | ||||
−0.475966 | + | 0.879464i | \(0.657902\pi\) | |||||||
\(878\) | −30.8561 | −1.04134 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.75515 | 0.194006 | ||||||||
\(881\) | −24.1851 | −0.814818 | −0.407409 | − | 0.913246i | \(-0.633568\pi\) | ||||
−0.407409 | + | 0.913246i | \(0.633568\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.3377 | −1.79496 | −0.897479 | − | 0.441058i | \(-0.854603\pi\) | ||||
−0.897479 | + | 0.441058i | \(0.854603\pi\) | |||||||
\(884\) | 27.7831 | 0.934448 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.4109 | 0.584929 | ||||||||
\(887\) | −17.7250 | −0.595147 | −0.297574 | − | 0.954699i | \(-0.596177\pi\) | ||||
−0.297574 | + | 0.954699i | \(0.596177\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.9520 | −0.836862 | ||||||||
\(890\) | 60.5812 | 2.03069 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.6508 | 0.624476 | ||||||||
\(893\) | −31.2757 | −1.04660 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.1934 | −0.808695 | ||||||||
\(896\) | −10.5697 | −0.353109 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19.5959 | 0.653923 | ||||||||
\(899\) | 7.38727 | 0.246379 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.4297 | −1.24696 | ||||||||
\(902\) | −10.1699 | −0.338620 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.57862 | 0.152283 | ||||||||
\(905\) | −32.8683 | −1.09258 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.4045 | −1.17559 | −0.587793 | − | 0.809011i | \(-0.700003\pi\) | ||||
−0.587793 | + | 0.809011i | \(0.700003\pi\) | |||||||
\(908\) | 20.0051 | 0.663892 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −52.4865 | −1.73991 | ||||||||
\(911\) | 15.1901 | 0.503270 | 0.251635 | − | 0.967822i | \(-0.419032\pi\) | ||||
0.251635 | + | 0.967822i | \(0.419032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.70885 | 0.155840 | ||||||||
\(914\) | −11.9101 | −0.393952 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −31.3909 | −1.03718 | ||||||||
\(917\) | 35.3097 | 1.16603 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.7199 | −0.518550 | −0.259275 | − | 0.965804i | \(-0.583484\pi\) | ||||
−0.259275 | + | 0.965804i | \(0.583484\pi\) | |||||||
\(920\) | −11.8138 | −0.389488 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.7564 | −1.01291 | ||||||||
\(923\) | 20.3661 | 0.670358 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 127.215 | 4.18280 | ||||||||
\(926\) | −2.27249 | −0.0746786 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.35852 | 0.143076 | ||||||||
\(929\) | −22.1517 | −0.726773 | −0.363386 | − | 0.931638i | \(-0.618380\pi\) | ||||
−0.363386 | + | 0.931638i | \(0.618380\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.0543 | −0.362290 | ||||||||
\(932\) | −18.9455 | −0.620580 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.6415 | −0.806295 | ||||||||
\(935\) | −42.5257 | −1.39074 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.2669 | 0.564086 | 0.282043 | − | 0.959402i | \(-0.408988\pi\) | ||||
0.282043 | + | 0.959402i | \(0.408988\pi\) | |||||||
\(938\) | 19.9262 | 0.650613 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 28.8266 | 0.940220 | ||||||||
\(941\) | 45.5870 | 1.48609 | 0.743047 | − | 0.669239i | \(-0.233380\pi\) | ||||
0.743047 | + | 0.669239i | \(0.233380\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.28590 | 0.139568 | ||||||||
\(944\) | −6.56352 | −0.213624 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.76001 | 0.317325 | ||||||||
\(947\) | 36.0414 | 1.17119 | 0.585595 | − | 0.810604i | \(-0.300861\pi\) | ||||
0.585595 | + | 0.810604i | \(0.300861\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 44.0962 | 1.43142 | ||||||||
\(950\) | 62.1248 | 2.01560 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −27.2047 | −0.881711 | ||||||||
\(953\) | 23.8618 | 0.772960 | 0.386480 | − | 0.922298i | \(-0.373691\pi\) | ||||
0.386480 | + | 0.922298i | \(0.373691\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 84.4685 | 2.73334 | ||||||||
\(956\) | −1.10459 | −0.0357249 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.4315 | 0.563186 | ||||||||
\(959\) | 34.2835 | 1.10707 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 50.7774 | 1.63798 | ||||||||
\(962\) | −55.5051 | −1.78956 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.28688 | −0.105863 | ||||||||
\(965\) | −36.3949 | −1.17159 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.1614 | 1.32366 | 0.661830 | − | 0.749654i | \(-0.269780\pi\) | ||||
0.661830 | + | 0.749654i | \(0.269780\pi\) | |||||||
\(968\) | 15.6593 | 0.503308 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.3709 | 0.429313 | ||||||||
\(971\) | 37.7773 | 1.21233 | 0.606165 | − | 0.795339i | \(-0.292707\pi\) | ||||
0.606165 | + | 0.795339i | \(0.292707\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34.5652 | −1.10811 | ||||||||
\(974\) | 23.1962 | 0.743255 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.67688 | 0.0536756 | ||||||||
\(977\) | −2.87111 | −0.0918549 | −0.0459274 | − | 0.998945i | \(-0.514624\pi\) | ||||
−0.0459274 | + | 0.998945i | \(0.514624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.9954 | −1.15042 | ||||||||
\(980\) | 10.1887 | 0.325465 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.345320 | 0.0110196 | ||||||||
\(983\) | 8.67353 | 0.276643 | 0.138321 | − | 0.990387i | \(-0.455829\pi\) | ||||
0.138321 | + | 0.990387i | \(0.455829\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33.6052 | −1.07075 | ||||||||
\(986\) | 3.25983 | 0.103814 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 33.4376 | 1.06379 | ||||||||
\(989\) | −4.11316 | −0.130791 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7021 | −1.19765 | −0.598823 | − | 0.800881i | \(-0.704365\pi\) | ||||
−0.598823 | + | 0.800881i | \(0.704365\pi\) | |||||||
\(992\) | 48.2490 | 1.53191 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.09524 | −0.225047 | ||||||||
\(995\) | −80.0554 | −2.53793 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.1876 | −0.987720 | −0.493860 | − | 0.869541i | \(-0.664415\pi\) | ||||
−0.493860 | + | 0.869541i | \(0.664415\pi\) | |||||||
\(998\) | 2.12172 | 0.0671618 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2151.2.a.k.1.13 | yes | 20 | |
3.2 | odd | 2 | 2151.2.a.j.1.8 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.a.j.1.8 | ✓ | 20 | 3.2 | odd | 2 | ||
2151.2.a.k.1.13 | yes | 20 | 1.1 | even | 1 | trivial |