Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1859,2,Mod(1,1859)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1859, 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("1859.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1859 = 11 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1859.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: | \(14.8441897358\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 1859.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.53678 | −1.08667 | −0.543335 | − | 0.839516i | \(-0.682839\pi\) | ||||
−0.543335 | + | 0.839516i | \(0.682839\pi\) | |||||||
\(3\) | −3.28188 | −1.89479 | −0.947396 | − | 0.320064i | \(-0.896296\pi\) | ||||
−0.947396 | + | 0.320064i | \(0.896296\pi\) | |||||||
\(4\) | 0.361702 | 0.180851 | ||||||||
\(5\) | −1.21246 | −0.542227 | −0.271113 | − | 0.962547i | \(-0.587392\pi\) | ||||
−0.271113 | + | 0.962547i | \(0.587392\pi\) | |||||||
\(6\) | 5.04353 | 2.05901 | ||||||||
\(7\) | −1.98662 | −0.750871 | −0.375436 | − | 0.926848i | \(-0.622507\pi\) | ||||
−0.375436 | + | 0.926848i | \(0.622507\pi\) | |||||||
\(8\) | 2.51771 | 0.890144 | ||||||||
\(9\) | 7.77071 | 2.59024 | ||||||||
\(10\) | 1.86328 | 0.589222 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −1.18706 | −0.342675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 3.05300 | 0.815949 | ||||||||
\(15\) | 3.97913 | 1.02741 | ||||||||
\(16\) | −4.59258 | −1.14814 | ||||||||
\(17\) | 6.12307 | 1.48506 | 0.742531 | − | 0.669812i | \(-0.233625\pi\) | ||||
0.742531 | + | 0.669812i | \(0.233625\pi\) | |||||||
\(18\) | −11.9419 | −2.81473 | ||||||||
\(19\) | 3.70133 | 0.849143 | 0.424572 | − | 0.905394i | \(-0.360425\pi\) | ||||
0.424572 | + | 0.905394i | \(0.360425\pi\) | |||||||
\(20\) | −0.438548 | −0.0980624 | ||||||||
\(21\) | 6.51984 | 1.42275 | ||||||||
\(22\) | −1.53678 | −0.327643 | ||||||||
\(23\) | −5.04028 | −1.05097 | −0.525485 | − | 0.850803i | \(-0.676116\pi\) | ||||
−0.525485 | + | 0.850803i | \(0.676116\pi\) | |||||||
\(24\) | −8.26281 | −1.68664 | ||||||||
\(25\) | −3.52995 | −0.705990 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −15.6569 | −3.01317 | ||||||||
\(28\) | −0.718565 | −0.135796 | ||||||||
\(29\) | 8.47487 | 1.57374 | 0.786872 | − | 0.617117i | \(-0.211699\pi\) | ||||
0.786872 | + | 0.617117i | \(0.211699\pi\) | |||||||
\(30\) | −6.11506 | −1.11645 | ||||||||
\(31\) | 3.43530 | 0.616998 | 0.308499 | − | 0.951225i | \(-0.400173\pi\) | ||||
0.308499 | + | 0.951225i | \(0.400173\pi\) | |||||||
\(32\) | 2.02238 | 0.357509 | ||||||||
\(33\) | −3.28188 | −0.571301 | ||||||||
\(34\) | −9.40983 | −1.61377 | ||||||||
\(35\) | 2.40869 | 0.407143 | ||||||||
\(36\) | 2.81069 | 0.468448 | ||||||||
\(37\) | −8.15204 | −1.34019 | −0.670094 | − | 0.742276i | \(-0.733746\pi\) | ||||
−0.670094 | + | 0.742276i | \(0.733746\pi\) | |||||||
\(38\) | −5.68814 | −0.922738 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.05261 | −0.482660 | ||||||||
\(41\) | −3.80914 | −0.594887 | −0.297443 | − | 0.954739i | \(-0.596134\pi\) | ||||
−0.297443 | + | 0.954739i | \(0.596134\pi\) | |||||||
\(42\) | −10.0196 | −1.54605 | ||||||||
\(43\) | 1.79628 | 0.273929 | 0.136965 | − | 0.990576i | \(-0.456265\pi\) | ||||
0.136965 | + | 0.990576i | \(0.456265\pi\) | |||||||
\(44\) | 0.361702 | 0.0545287 | ||||||||
\(45\) | −9.42165 | −1.40450 | ||||||||
\(46\) | 7.74582 | 1.14206 | ||||||||
\(47\) | −5.02969 | −0.733656 | −0.366828 | − | 0.930289i | \(-0.619556\pi\) | ||||
−0.366828 | + | 0.930289i | \(0.619556\pi\) | |||||||
\(48\) | 15.0723 | 2.17549 | ||||||||
\(49\) | −3.05334 | −0.436192 | ||||||||
\(50\) | 5.42477 | 0.767178 | ||||||||
\(51\) | −20.0951 | −2.81388 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.97705 | 1.37045 | 0.685226 | − | 0.728330i | \(-0.259703\pi\) | ||||
0.685226 | + | 0.728330i | \(0.259703\pi\) | |||||||
\(54\) | 24.0612 | 3.27432 | ||||||||
\(55\) | −1.21246 | −0.163488 | ||||||||
\(56\) | −5.00173 | −0.668384 | ||||||||
\(57\) | −12.1473 | −1.60895 | ||||||||
\(58\) | −13.0240 | −1.71014 | ||||||||
\(59\) | −11.9103 | −1.55058 | −0.775291 | − | 0.631604i | \(-0.782397\pi\) | ||||
−0.775291 | + | 0.631604i | \(0.782397\pi\) | |||||||
\(60\) | 1.43926 | 0.185808 | ||||||||
\(61\) | 3.23779 | 0.414557 | 0.207278 | − | 0.978282i | \(-0.433539\pi\) | ||||
0.207278 | + | 0.978282i | \(0.433539\pi\) | |||||||
\(62\) | −5.27931 | −0.670473 | ||||||||
\(63\) | −15.4374 | −1.94493 | ||||||||
\(64\) | 6.07720 | 0.759650 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.04353 | 0.620816 | ||||||||
\(67\) | 0.832597 | 0.101718 | 0.0508590 | − | 0.998706i | \(-0.483804\pi\) | ||||
0.0508590 | + | 0.998706i | \(0.483804\pi\) | |||||||
\(68\) | 2.21473 | 0.268575 | ||||||||
\(69\) | 16.5416 | 1.99137 | ||||||||
\(70\) | −3.70163 | −0.442430 | ||||||||
\(71\) | −5.22675 | −0.620301 | −0.310150 | − | 0.950688i | \(-0.600379\pi\) | ||||
−0.310150 | + | 0.950688i | \(0.600379\pi\) | |||||||
\(72\) | 19.5644 | 2.30568 | ||||||||
\(73\) | 9.29337 | 1.08771 | 0.543853 | − | 0.839180i | \(-0.316965\pi\) | ||||
0.543853 | + | 0.839180i | \(0.316965\pi\) | |||||||
\(74\) | 12.5279 | 1.45634 | ||||||||
\(75\) | 11.5849 | 1.33770 | ||||||||
\(76\) | 1.33878 | 0.153569 | ||||||||
\(77\) | −1.98662 | −0.226396 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.72080 | 0.193605 | 0.0968026 | − | 0.995304i | \(-0.469138\pi\) | ||||
0.0968026 | + | 0.995304i | \(0.469138\pi\) | |||||||
\(80\) | 5.56830 | 0.622555 | ||||||||
\(81\) | 28.0718 | 3.11909 | ||||||||
\(82\) | 5.85381 | 0.646446 | ||||||||
\(83\) | −13.3621 | −1.46668 | −0.733342 | − | 0.679860i | \(-0.762041\pi\) | ||||
−0.733342 | + | 0.679860i | \(0.762041\pi\) | |||||||
\(84\) | 2.35824 | 0.257305 | ||||||||
\(85\) | −7.42395 | −0.805241 | ||||||||
\(86\) | −2.76049 | −0.297671 | ||||||||
\(87\) | −27.8135 | −2.98192 | ||||||||
\(88\) | 2.51771 | 0.268389 | ||||||||
\(89\) | 3.92753 | 0.416317 | 0.208159 | − | 0.978095i | \(-0.433253\pi\) | ||||
0.208159 | + | 0.978095i | \(0.433253\pi\) | |||||||
\(90\) | 14.4790 | 1.52622 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.82308 | −0.190069 | ||||||||
\(93\) | −11.2742 | −1.16908 | ||||||||
\(94\) | 7.72954 | 0.797241 | ||||||||
\(95\) | −4.48770 | −0.460428 | ||||||||
\(96\) | −6.63719 | −0.677406 | ||||||||
\(97\) | −13.3265 | −1.35311 | −0.676553 | − | 0.736394i | \(-0.736527\pi\) | ||||
−0.676553 | + | 0.736394i | \(0.736527\pi\) | |||||||
\(98\) | 4.69233 | 0.473997 | ||||||||
\(99\) | 7.77071 | 0.780986 | ||||||||
\(100\) | −1.27679 | −0.127679 | ||||||||
\(101\) | 4.16147 | 0.414081 | 0.207041 | − | 0.978332i | \(-0.433617\pi\) | ||||
0.207041 | + | 0.978332i | \(0.433617\pi\) | |||||||
\(102\) | 30.8819 | 3.05776 | ||||||||
\(103\) | 12.0087 | 1.18325 | 0.591624 | − | 0.806214i | \(-0.298487\pi\) | ||||
0.591624 | + | 0.806214i | \(0.298487\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.90502 | −0.771451 | ||||||||
\(106\) | −15.3326 | −1.48923 | ||||||||
\(107\) | 3.84674 | 0.371878 | 0.185939 | − | 0.982561i | \(-0.440467\pi\) | ||||
0.185939 | + | 0.982561i | \(0.440467\pi\) | |||||||
\(108\) | −5.66313 | −0.544935 | ||||||||
\(109\) | 5.72918 | 0.548756 | 0.274378 | − | 0.961622i | \(-0.411528\pi\) | ||||
0.274378 | + | 0.961622i | \(0.411528\pi\) | |||||||
\(110\) | 1.86328 | 0.177657 | ||||||||
\(111\) | 26.7540 | 2.53938 | ||||||||
\(112\) | 9.12370 | 0.862109 | ||||||||
\(113\) | −9.59740 | −0.902847 | −0.451424 | − | 0.892310i | \(-0.649084\pi\) | ||||
−0.451424 | + | 0.892310i | \(0.649084\pi\) | |||||||
\(114\) | 18.6678 | 1.74840 | ||||||||
\(115\) | 6.11112 | 0.569865 | ||||||||
\(116\) | 3.06538 | 0.284613 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.3035 | 1.68497 | ||||||||
\(119\) | −12.1642 | −1.11509 | ||||||||
\(120\) | 10.0183 | 0.914541 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −4.97578 | −0.450486 | ||||||||
\(123\) | 12.5011 | 1.12719 | ||||||||
\(124\) | 1.24256 | 0.111585 | ||||||||
\(125\) | 10.3422 | 0.925034 | ||||||||
\(126\) | 23.7240 | 2.11350 | ||||||||
\(127\) | −7.39494 | −0.656195 | −0.328097 | − | 0.944644i | \(-0.606407\pi\) | ||||
−0.328097 | + | 0.944644i | \(0.606407\pi\) | |||||||
\(128\) | −13.3841 | −1.18300 | ||||||||
\(129\) | −5.89515 | −0.519039 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.5630 | 1.27237 | 0.636187 | − | 0.771535i | \(-0.280511\pi\) | ||||
0.636187 | + | 0.771535i | \(0.280511\pi\) | |||||||
\(132\) | −1.18706 | −0.103321 | ||||||||
\(133\) | −7.35313 | −0.637597 | ||||||||
\(134\) | −1.27952 | −0.110534 | ||||||||
\(135\) | 18.9833 | 1.63382 | ||||||||
\(136\) | 15.4161 | 1.32192 | ||||||||
\(137\) | 1.85385 | 0.158385 | 0.0791924 | − | 0.996859i | \(-0.474766\pi\) | ||||
0.0791924 | + | 0.996859i | \(0.474766\pi\) | |||||||
\(138\) | −25.4208 | −2.16396 | ||||||||
\(139\) | 21.5418 | 1.82715 | 0.913576 | − | 0.406668i | \(-0.133309\pi\) | ||||
0.913576 | + | 0.406668i | \(0.133309\pi\) | |||||||
\(140\) | 0.871229 | 0.0736323 | ||||||||
\(141\) | 16.5068 | 1.39012 | ||||||||
\(142\) | 8.03237 | 0.674062 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −35.6876 | −2.97397 | ||||||||
\(145\) | −10.2754 | −0.853326 | ||||||||
\(146\) | −14.2819 | −1.18198 | ||||||||
\(147\) | 10.0207 | 0.826493 | ||||||||
\(148\) | −2.94861 | −0.242375 | ||||||||
\(149\) | −14.8011 | −1.21255 | −0.606275 | − | 0.795255i | \(-0.707337\pi\) | ||||
−0.606275 | + | 0.795255i | \(0.707337\pi\) | |||||||
\(150\) | −17.8034 | −1.45364 | ||||||||
\(151\) | 10.3080 | 0.838856 | 0.419428 | − | 0.907789i | \(-0.362231\pi\) | ||||
0.419428 | + | 0.907789i | \(0.362231\pi\) | |||||||
\(152\) | 9.31887 | 0.755860 | ||||||||
\(153\) | 47.5806 | 3.84666 | ||||||||
\(154\) | 3.05300 | 0.246018 | ||||||||
\(155\) | −4.16515 | −0.334553 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.44935 | 0.275288 | 0.137644 | − | 0.990482i | \(-0.456047\pi\) | ||||
0.137644 | + | 0.990482i | \(0.456047\pi\) | |||||||
\(158\) | −2.64450 | −0.210385 | ||||||||
\(159\) | −32.7434 | −2.59672 | ||||||||
\(160\) | −2.45204 | −0.193851 | ||||||||
\(161\) | 10.0131 | 0.789144 | ||||||||
\(162\) | −43.1403 | −3.38942 | ||||||||
\(163\) | −19.3269 | −1.51380 | −0.756899 | − | 0.653532i | \(-0.773287\pi\) | ||||
−0.756899 | + | 0.653532i | \(0.773287\pi\) | |||||||
\(164\) | −1.37777 | −0.107586 | ||||||||
\(165\) | 3.97913 | 0.309775 | ||||||||
\(166\) | 20.5347 | 1.59380 | ||||||||
\(167\) | 13.8906 | 1.07488 | 0.537442 | − | 0.843301i | \(-0.319391\pi\) | ||||
0.537442 | + | 0.843301i | \(0.319391\pi\) | |||||||
\(168\) | 16.4150 | 1.26645 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 11.4090 | 0.875031 | ||||||||
\(171\) | 28.7620 | 2.19948 | ||||||||
\(172\) | 0.649717 | 0.0495405 | ||||||||
\(173\) | −20.4360 | −1.55372 | −0.776859 | − | 0.629675i | \(-0.783188\pi\) | ||||
−0.776859 | + | 0.629675i | \(0.783188\pi\) | |||||||
\(174\) | 42.7433 | 3.24036 | ||||||||
\(175\) | 7.01267 | 0.530108 | ||||||||
\(176\) | −4.59258 | −0.346178 | ||||||||
\(177\) | 39.0880 | 2.93803 | ||||||||
\(178\) | −6.03576 | −0.452400 | ||||||||
\(179\) | −21.6947 | −1.62154 | −0.810771 | − | 0.585364i | \(-0.800952\pi\) | ||||
−0.810771 | + | 0.585364i | \(0.800952\pi\) | |||||||
\(180\) | −3.40783 | −0.254005 | ||||||||
\(181\) | 8.01583 | 0.595812 | 0.297906 | − | 0.954595i | \(-0.403712\pi\) | ||||
0.297906 | + | 0.954595i | \(0.403712\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.6260 | −0.785499 | ||||||||
\(184\) | −12.6900 | −0.935516 | ||||||||
\(185\) | 9.88400 | 0.726686 | ||||||||
\(186\) | 17.3260 | 1.27041 | ||||||||
\(187\) | 6.12307 | 0.447763 | ||||||||
\(188\) | −1.81925 | −0.132683 | ||||||||
\(189\) | 31.1043 | 2.26250 | ||||||||
\(190\) | 6.89662 | 0.500333 | ||||||||
\(191\) | −18.1275 | −1.31166 | −0.655828 | − | 0.754910i | \(-0.727680\pi\) | ||||
−0.655828 | + | 0.754910i | \(0.727680\pi\) | |||||||
\(192\) | −19.9446 | −1.43938 | ||||||||
\(193\) | 14.9366 | 1.07516 | 0.537582 | − | 0.843212i | \(-0.319338\pi\) | ||||
0.537582 | + | 0.843212i | \(0.319338\pi\) | |||||||
\(194\) | 20.4800 | 1.47038 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.10440 | −0.0788859 | ||||||||
\(197\) | 20.7866 | 1.48098 | 0.740491 | − | 0.672066i | \(-0.234593\pi\) | ||||
0.740491 | + | 0.672066i | \(0.234593\pi\) | |||||||
\(198\) | −11.9419 | −0.848674 | ||||||||
\(199\) | 3.75388 | 0.266105 | 0.133053 | − | 0.991109i | \(-0.457522\pi\) | ||||
0.133053 | + | 0.991109i | \(0.457522\pi\) | |||||||
\(200\) | −8.88738 | −0.628433 | ||||||||
\(201\) | −2.73248 | −0.192734 | ||||||||
\(202\) | −6.39527 | −0.449970 | ||||||||
\(203\) | −16.8363 | −1.18168 | ||||||||
\(204\) | −7.26846 | −0.508894 | ||||||||
\(205\) | 4.61841 | 0.322564 | ||||||||
\(206\) | −18.4547 | −1.28580 | ||||||||
\(207\) | −39.1666 | −2.72226 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.70133 | 0.256026 | ||||||||
\(210\) | 12.1483 | 0.838312 | ||||||||
\(211\) | 12.8237 | 0.882817 | 0.441408 | − | 0.897306i | \(-0.354479\pi\) | ||||
0.441408 | + | 0.897306i | \(0.354479\pi\) | |||||||
\(212\) | 3.60872 | 0.247848 | ||||||||
\(213\) | 17.1535 | 1.17534 | ||||||||
\(214\) | −5.91160 | −0.404109 | ||||||||
\(215\) | −2.17791 | −0.148532 | ||||||||
\(216\) | −39.4195 | −2.68215 | ||||||||
\(217\) | −6.82463 | −0.463286 | ||||||||
\(218\) | −8.80450 | −0.596316 | ||||||||
\(219\) | −30.4997 | −2.06098 | ||||||||
\(220\) | −0.438548 | −0.0295669 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −41.1151 | −2.75946 | ||||||||
\(223\) | −14.4246 | −0.965946 | −0.482973 | − | 0.875635i | \(-0.660443\pi\) | ||||
−0.482973 | + | 0.875635i | \(0.660443\pi\) | |||||||
\(224\) | −4.01769 | −0.268443 | ||||||||
\(225\) | −27.4302 | −1.82868 | ||||||||
\(226\) | 14.7491 | 0.981097 | ||||||||
\(227\) | 16.7827 | 1.11390 | 0.556952 | − | 0.830544i | \(-0.311971\pi\) | ||||
0.556952 | + | 0.830544i | \(0.311971\pi\) | |||||||
\(228\) | −4.39371 | −0.290980 | ||||||||
\(229\) | −4.78314 | −0.316079 | −0.158039 | − | 0.987433i | \(-0.550517\pi\) | ||||
−0.158039 | + | 0.987433i | \(0.550517\pi\) | |||||||
\(230\) | −9.39146 | −0.619255 | ||||||||
\(231\) | 6.51984 | 0.428974 | ||||||||
\(232\) | 21.3372 | 1.40086 | ||||||||
\(233\) | −2.47540 | −0.162169 | −0.0810843 | − | 0.996707i | \(-0.525838\pi\) | ||||
−0.0810843 | + | 0.996707i | \(0.525838\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.09828 | 0.397808 | ||||||||
\(236\) | −4.30797 | −0.280425 | ||||||||
\(237\) | −5.64745 | −0.366842 | ||||||||
\(238\) | 18.6937 | 1.21174 | ||||||||
\(239\) | −17.6139 | −1.13935 | −0.569675 | − | 0.821870i | \(-0.692931\pi\) | ||||
−0.569675 | + | 0.821870i | \(0.692931\pi\) | |||||||
\(240\) | −18.2745 | −1.17961 | ||||||||
\(241\) | 3.16351 | 0.203779 | 0.101890 | − | 0.994796i | \(-0.467511\pi\) | ||||
0.101890 | + | 0.994796i | \(0.467511\pi\) | |||||||
\(242\) | −1.53678 | −0.0987882 | ||||||||
\(243\) | −45.1576 | −2.89686 | ||||||||
\(244\) | 1.17112 | 0.0749731 | ||||||||
\(245\) | 3.70205 | 0.236515 | ||||||||
\(246\) | −19.2115 | −1.22488 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.64908 | 0.549217 | ||||||||
\(249\) | 43.8529 | 2.77906 | ||||||||
\(250\) | −15.8937 | −1.00521 | ||||||||
\(251\) | 8.49701 | 0.536327 | 0.268163 | − | 0.963373i | \(-0.413583\pi\) | ||||
0.268163 | + | 0.963373i | \(0.413583\pi\) | |||||||
\(252\) | −5.58376 | −0.351744 | ||||||||
\(253\) | −5.04028 | −0.316880 | ||||||||
\(254\) | 11.3644 | 0.713067 | ||||||||
\(255\) | 24.3645 | 1.52576 | ||||||||
\(256\) | 8.41405 | 0.525878 | ||||||||
\(257\) | −3.24187 | −0.202222 | −0.101111 | − | 0.994875i | \(-0.532240\pi\) | ||||
−0.101111 | + | 0.994875i | \(0.532240\pi\) | |||||||
\(258\) | 9.05957 | 0.564024 | ||||||||
\(259\) | 16.1950 | 1.00631 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 65.8557 | 4.07637 | ||||||||
\(262\) | −22.3802 | −1.38265 | ||||||||
\(263\) | −2.08594 | −0.128624 | −0.0643122 | − | 0.997930i | \(-0.520485\pi\) | ||||
−0.0643122 | + | 0.997930i | \(0.520485\pi\) | |||||||
\(264\) | −8.26281 | −0.508541 | ||||||||
\(265\) | −12.0967 | −0.743096 | ||||||||
\(266\) | 11.3002 | 0.692858 | ||||||||
\(267\) | −12.8897 | −0.788835 | ||||||||
\(268\) | 0.301153 | 0.0183958 | ||||||||
\(269\) | 30.8543 | 1.88122 | 0.940610 | − | 0.339490i | \(-0.110254\pi\) | ||||
0.940610 | + | 0.339490i | \(0.110254\pi\) | |||||||
\(270\) | −29.1732 | −1.77542 | ||||||||
\(271\) | −7.66076 | −0.465358 | −0.232679 | − | 0.972554i | \(-0.574749\pi\) | ||||
−0.232679 | + | 0.972554i | \(0.574749\pi\) | |||||||
\(272\) | −28.1207 | −1.70507 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.84896 | −0.172112 | ||||||||
\(275\) | −3.52995 | −0.212864 | ||||||||
\(276\) | 5.98313 | 0.360142 | ||||||||
\(277\) | 14.0673 | 0.845225 | 0.422612 | − | 0.906310i | \(-0.361113\pi\) | ||||
0.422612 | + | 0.906310i | \(0.361113\pi\) | |||||||
\(278\) | −33.1051 | −1.98551 | ||||||||
\(279\) | 26.6947 | 1.59817 | ||||||||
\(280\) | 6.06437 | 0.362416 | ||||||||
\(281\) | 3.17033 | 0.189126 | 0.0945629 | − | 0.995519i | \(-0.469855\pi\) | ||||
0.0945629 | + | 0.995519i | \(0.469855\pi\) | |||||||
\(282\) | −25.3674 | −1.51061 | ||||||||
\(283\) | −2.04430 | −0.121521 | −0.0607604 | − | 0.998152i | \(-0.519353\pi\) | ||||
−0.0607604 | + | 0.998152i | \(0.519353\pi\) | |||||||
\(284\) | −1.89053 | −0.112182 | ||||||||
\(285\) | 14.7281 | 0.872416 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.56730 | 0.446684 | ||||||||
\(288\) | 15.7153 | 0.926034 | ||||||||
\(289\) | 20.4920 | 1.20541 | ||||||||
\(290\) | 15.7911 | 0.927284 | ||||||||
\(291\) | 43.7361 | 2.56385 | ||||||||
\(292\) | 3.36143 | 0.196713 | ||||||||
\(293\) | 9.77243 | 0.570911 | 0.285456 | − | 0.958392i | \(-0.407855\pi\) | ||||
0.285456 | + | 0.958392i | \(0.407855\pi\) | |||||||
\(294\) | −15.3996 | −0.898125 | ||||||||
\(295\) | 14.4407 | 0.840768 | ||||||||
\(296\) | −20.5245 | −1.19296 | ||||||||
\(297\) | −15.6569 | −0.908504 | ||||||||
\(298\) | 22.7460 | 1.31764 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.19027 | 0.241925 | ||||||||
\(301\) | −3.56851 | −0.205686 | ||||||||
\(302\) | −15.8412 | −0.911560 | ||||||||
\(303\) | −13.6574 | −0.784598 | ||||||||
\(304\) | −16.9986 | −0.974939 | ||||||||
\(305\) | −3.92568 | −0.224784 | ||||||||
\(306\) | −73.1210 | −4.18005 | ||||||||
\(307\) | −13.0036 | −0.742152 | −0.371076 | − | 0.928603i | \(-0.621011\pi\) | ||||
−0.371076 | + | 0.928603i | \(0.621011\pi\) | |||||||
\(308\) | −0.718565 | −0.0409440 | ||||||||
\(309\) | −39.4109 | −2.24201 | ||||||||
\(310\) | 6.40093 | 0.363548 | ||||||||
\(311\) | −20.9389 | −1.18734 | −0.593668 | − | 0.804710i | \(-0.702321\pi\) | ||||
−0.593668 | + | 0.804710i | \(0.702321\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.484921 | 0.0274094 | 0.0137047 | − | 0.999906i | \(-0.495638\pi\) | ||||
0.0137047 | + | 0.999906i | \(0.495638\pi\) | |||||||
\(314\) | −5.30091 | −0.299148 | ||||||||
\(315\) | 18.7172 | 1.05460 | ||||||||
\(316\) | 0.622418 | 0.0350137 | ||||||||
\(317\) | −24.9983 | −1.40404 | −0.702021 | − | 0.712156i | \(-0.747719\pi\) | ||||
−0.702021 | + | 0.712156i | \(0.747719\pi\) | |||||||
\(318\) | 50.3196 | 2.82178 | ||||||||
\(319\) | 8.47487 | 0.474501 | ||||||||
\(320\) | −7.36834 | −0.411902 | ||||||||
\(321\) | −12.6245 | −0.704632 | ||||||||
\(322\) | −15.3880 | −0.857539 | ||||||||
\(323\) | 22.6635 | 1.26103 | ||||||||
\(324\) | 10.1536 | 0.564091 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.7012 | 1.64500 | ||||||||
\(327\) | −18.8025 | −1.03978 | ||||||||
\(328\) | −9.59029 | −0.529535 | ||||||||
\(329\) | 9.99208 | 0.550881 | ||||||||
\(330\) | −6.11506 | −0.336623 | ||||||||
\(331\) | 14.6088 | 0.802972 | 0.401486 | − | 0.915865i | \(-0.368494\pi\) | ||||
0.401486 | + | 0.915865i | \(0.368494\pi\) | |||||||
\(332\) | −4.83312 | −0.265252 | ||||||||
\(333\) | −63.3472 | −3.47140 | ||||||||
\(334\) | −21.3468 | −1.16804 | ||||||||
\(335\) | −1.00949 | −0.0551542 | ||||||||
\(336\) | −29.9429 | −1.63352 | ||||||||
\(337\) | −12.3867 | −0.674748 | −0.337374 | − | 0.941371i | \(-0.609539\pi\) | ||||
−0.337374 | + | 0.941371i | \(0.609539\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 31.4975 | 1.71071 | ||||||||
\(340\) | −2.68526 | −0.145629 | ||||||||
\(341\) | 3.43530 | 0.186032 | ||||||||
\(342\) | −44.2009 | −2.39011 | ||||||||
\(343\) | 19.9722 | 1.07840 | ||||||||
\(344\) | 4.52250 | 0.243837 | ||||||||
\(345\) | −20.0559 | −1.07978 | ||||||||
\(346\) | 31.4057 | 1.68838 | ||||||||
\(347\) | −11.4789 | −0.616221 | −0.308111 | − | 0.951351i | \(-0.599697\pi\) | ||||
−0.308111 | + | 0.951351i | \(0.599697\pi\) | |||||||
\(348\) | −10.0602 | −0.539283 | ||||||||
\(349\) | 16.7829 | 0.898366 | 0.449183 | − | 0.893440i | \(-0.351715\pi\) | ||||
0.449183 | + | 0.893440i | \(0.351715\pi\) | |||||||
\(350\) | −10.7769 | −0.576052 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.02238 | 0.107793 | ||||||||
\(353\) | 17.8330 | 0.949156 | 0.474578 | − | 0.880213i | \(-0.342601\pi\) | ||||
0.474578 | + | 0.880213i | \(0.342601\pi\) | |||||||
\(354\) | −60.0697 | −3.19267 | ||||||||
\(355\) | 6.33720 | 0.336344 | ||||||||
\(356\) | 1.42060 | 0.0752915 | ||||||||
\(357\) | 39.9214 | 2.11286 | ||||||||
\(358\) | 33.3401 | 1.76208 | ||||||||
\(359\) | −10.5901 | −0.558922 | −0.279461 | − | 0.960157i | \(-0.590156\pi\) | ||||
−0.279461 | + | 0.960157i | \(0.590156\pi\) | |||||||
\(360\) | −23.7210 | −1.25020 | ||||||||
\(361\) | −5.30017 | −0.278956 | ||||||||
\(362\) | −12.3186 | −0.647451 | ||||||||
\(363\) | −3.28188 | −0.172254 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.2678 | −0.589784 | ||||||||
\(366\) | 16.3299 | 0.853578 | ||||||||
\(367\) | 12.3094 | 0.642545 | 0.321272 | − | 0.946987i | \(-0.395889\pi\) | ||||
0.321272 | + | 0.946987i | \(0.395889\pi\) | |||||||
\(368\) | 23.1479 | 1.20667 | ||||||||
\(369\) | −29.5997 | −1.54090 | ||||||||
\(370\) | −15.1896 | −0.789668 | ||||||||
\(371\) | −19.8206 | −1.02903 | ||||||||
\(372\) | −4.07791 | −0.211430 | ||||||||
\(373\) | 4.19426 | 0.217171 | 0.108585 | − | 0.994087i | \(-0.465368\pi\) | ||||
0.108585 | + | 0.994087i | \(0.465368\pi\) | |||||||
\(374\) | −9.40983 | −0.486571 | ||||||||
\(375\) | −33.9418 | −1.75275 | ||||||||
\(376\) | −12.6633 | −0.653059 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −47.8005 | −2.45859 | ||||||||
\(379\) | 16.7368 | 0.859710 | 0.429855 | − | 0.902898i | \(-0.358565\pi\) | ||||
0.429855 | + | 0.902898i | \(0.358565\pi\) | |||||||
\(380\) | −1.62321 | −0.0832690 | ||||||||
\(381\) | 24.2693 | 1.24335 | ||||||||
\(382\) | 27.8580 | 1.42534 | ||||||||
\(383\) | 4.41154 | 0.225419 | 0.112709 | − | 0.993628i | \(-0.464047\pi\) | ||||
0.112709 | + | 0.993628i | \(0.464047\pi\) | |||||||
\(384\) | 43.9249 | 2.24153 | ||||||||
\(385\) | 2.40869 | 0.122758 | ||||||||
\(386\) | −22.9544 | −1.16835 | ||||||||
\(387\) | 13.9583 | 0.709542 | ||||||||
\(388\) | −4.82024 | −0.244711 | ||||||||
\(389\) | 15.4167 | 0.781658 | 0.390829 | − | 0.920463i | \(-0.372188\pi\) | ||||
0.390829 | + | 0.920463i | \(0.372188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.8620 | −1.56076 | ||||||||
\(392\) | −7.68743 | −0.388274 | ||||||||
\(393\) | −47.7939 | −2.41089 | ||||||||
\(394\) | −31.9445 | −1.60934 | ||||||||
\(395\) | −2.08640 | −0.104978 | ||||||||
\(396\) | 2.81069 | 0.141242 | ||||||||
\(397\) | 25.8026 | 1.29500 | 0.647498 | − | 0.762067i | \(-0.275815\pi\) | ||||
0.647498 | + | 0.762067i | \(0.275815\pi\) | |||||||
\(398\) | −5.76890 | −0.289169 | ||||||||
\(399\) | 24.1321 | 1.20811 | ||||||||
\(400\) | 16.2116 | 0.810578 | ||||||||
\(401\) | −21.7169 | −1.08449 | −0.542246 | − | 0.840220i | \(-0.682426\pi\) | ||||
−0.542246 | + | 0.840220i | \(0.682426\pi\) | |||||||
\(402\) | 4.19923 | 0.209439 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.50521 | 0.0748871 | ||||||||
\(405\) | −34.0358 | −1.69125 | ||||||||
\(406\) | 25.8738 | 1.28409 | ||||||||
\(407\) | −8.15204 | −0.404082 | ||||||||
\(408\) | −50.5937 | −2.50476 | ||||||||
\(409\) | 11.1416 | 0.550917 | 0.275459 | − | 0.961313i | \(-0.411170\pi\) | ||||
0.275459 | + | 0.961313i | \(0.411170\pi\) | |||||||
\(410\) | −7.09749 | −0.350520 | ||||||||
\(411\) | −6.08409 | −0.300106 | ||||||||
\(412\) | 4.34356 | 0.213992 | ||||||||
\(413\) | 23.6611 | 1.16429 | ||||||||
\(414\) | 60.1905 | 2.95820 | ||||||||
\(415\) | 16.2010 | 0.795276 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −70.6975 | −3.46207 | ||||||||
\(418\) | −5.68814 | −0.278216 | ||||||||
\(419\) | 5.97393 | 0.291846 | 0.145923 | − | 0.989296i | \(-0.453385\pi\) | ||||
0.145923 | + | 0.989296i | \(0.453385\pi\) | |||||||
\(420\) | −2.85926 | −0.139518 | ||||||||
\(421\) | −5.46498 | −0.266347 | −0.133173 | − | 0.991093i | \(-0.542517\pi\) | ||||
−0.133173 | + | 0.991093i | \(0.542517\pi\) | |||||||
\(422\) | −19.7072 | −0.959330 | ||||||||
\(423\) | −39.0843 | −1.90034 | ||||||||
\(424\) | 25.1193 | 1.21990 | ||||||||
\(425\) | −21.6141 | −1.04844 | ||||||||
\(426\) | −26.3613 | −1.27721 | ||||||||
\(427\) | −6.43226 | −0.311279 | ||||||||
\(428\) | 1.39137 | 0.0672546 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.34697 | 0.161405 | ||||||||
\(431\) | 8.56335 | 0.412482 | 0.206241 | − | 0.978501i | \(-0.433877\pi\) | ||||
0.206241 | + | 0.978501i | \(0.433877\pi\) | |||||||
\(432\) | 71.9054 | 3.45955 | ||||||||
\(433\) | −0.526285 | −0.0252917 | −0.0126458 | − | 0.999920i | \(-0.504025\pi\) | ||||
−0.0126458 | + | 0.999920i | \(0.504025\pi\) | |||||||
\(434\) | 10.4880 | 0.503439 | ||||||||
\(435\) | 33.7226 | 1.61688 | ||||||||
\(436\) | 2.07226 | 0.0992432 | ||||||||
\(437\) | −18.6557 | −0.892425 | ||||||||
\(438\) | 46.8714 | 2.23960 | ||||||||
\(439\) | −2.41736 | −0.115374 | −0.0576871 | − | 0.998335i | \(-0.518373\pi\) | ||||
−0.0576871 | + | 0.998335i | \(0.518373\pi\) | |||||||
\(440\) | −3.05261 | −0.145528 | ||||||||
\(441\) | −23.7267 | −1.12984 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −24.0014 | −1.14034 | −0.570171 | − | 0.821526i | \(-0.693123\pi\) | ||||
−0.570171 | + | 0.821526i | \(0.693123\pi\) | |||||||
\(444\) | 9.67699 | 0.459249 | ||||||||
\(445\) | −4.76196 | −0.225738 | ||||||||
\(446\) | 22.1676 | 1.04966 | ||||||||
\(447\) | 48.5752 | 2.29753 | ||||||||
\(448\) | −12.0731 | −0.570399 | ||||||||
\(449\) | −7.41494 | −0.349933 | −0.174966 | − | 0.984574i | \(-0.555982\pi\) | ||||
−0.174966 | + | 0.984574i | \(0.555982\pi\) | |||||||
\(450\) | 42.1543 | 1.98717 | ||||||||
\(451\) | −3.80914 | −0.179365 | ||||||||
\(452\) | −3.47140 | −0.163281 | ||||||||
\(453\) | −33.8297 | −1.58946 | ||||||||
\(454\) | −25.7913 | −1.21045 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −30.5834 | −1.43220 | ||||||||
\(457\) | −2.53108 | −0.118399 | −0.0591995 | − | 0.998246i | \(-0.518855\pi\) | ||||
−0.0591995 | + | 0.998246i | \(0.518855\pi\) | |||||||
\(458\) | 7.35065 | 0.343473 | ||||||||
\(459\) | −95.8681 | −4.47474 | ||||||||
\(460\) | 2.21041 | 0.103061 | ||||||||
\(461\) | 4.75026 | 0.221242 | 0.110621 | − | 0.993863i | \(-0.464716\pi\) | ||||
0.110621 | + | 0.993863i | \(0.464716\pi\) | |||||||
\(462\) | −10.0196 | −0.466153 | ||||||||
\(463\) | −8.86195 | −0.411850 | −0.205925 | − | 0.978568i | \(-0.566020\pi\) | ||||
−0.205925 | + | 0.978568i | \(0.566020\pi\) | |||||||
\(464\) | −38.9215 | −1.80688 | ||||||||
\(465\) | 13.6695 | 0.633908 | ||||||||
\(466\) | 3.80415 | 0.176224 | ||||||||
\(467\) | 0.900979 | 0.0416923 | 0.0208462 | − | 0.999783i | \(-0.493364\pi\) | ||||
0.0208462 | + | 0.999783i | \(0.493364\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.65405 | −0.0763771 | ||||||||
\(470\) | −9.37173 | −0.432286 | ||||||||
\(471\) | −11.3203 | −0.521614 | ||||||||
\(472\) | −29.9865 | −1.38024 | ||||||||
\(473\) | 1.79628 | 0.0825928 | ||||||||
\(474\) | 8.67891 | 0.398636 | ||||||||
\(475\) | −13.0655 | −0.599486 | ||||||||
\(476\) | −4.39982 | −0.201666 | ||||||||
\(477\) | 77.5288 | 3.54980 | ||||||||
\(478\) | 27.0688 | 1.23810 | ||||||||
\(479\) | −4.61882 | −0.211039 | −0.105520 | − | 0.994417i | \(-0.533651\pi\) | ||||
−0.105520 | + | 0.994417i | \(0.533651\pi\) | |||||||
\(480\) | 8.04731 | 0.367308 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −4.86162 | −0.221441 | ||||||||
\(483\) | −32.8618 | −1.49526 | ||||||||
\(484\) | 0.361702 | 0.0164410 | ||||||||
\(485\) | 16.1578 | 0.733690 | ||||||||
\(486\) | 69.3974 | 3.14793 | ||||||||
\(487\) | 22.0991 | 1.00141 | 0.500703 | − | 0.865619i | \(-0.333075\pi\) | ||||
0.500703 | + | 0.865619i | \(0.333075\pi\) | |||||||
\(488\) | 8.15181 | 0.369015 | ||||||||
\(489\) | 63.4284 | 2.86833 | ||||||||
\(490\) | −5.68924 | −0.257014 | ||||||||
\(491\) | −6.73294 | −0.303853 | −0.151927 | − | 0.988392i | \(-0.548548\pi\) | ||||
−0.151927 | + | 0.988392i | \(0.548548\pi\) | |||||||
\(492\) | 4.52168 | 0.203853 | ||||||||
\(493\) | 51.8922 | 2.33711 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.42165 | −0.423472 | ||||||||
\(496\) | −15.7769 | −0.708402 | ||||||||
\(497\) | 10.3836 | 0.465766 | ||||||||
\(498\) | −67.3923 | −3.01992 | ||||||||
\(499\) | 38.3071 | 1.71486 | 0.857430 | − | 0.514600i | \(-0.172060\pi\) | ||||
0.857430 | + | 0.514600i | \(0.172060\pi\) | |||||||
\(500\) | 3.74080 | 0.167293 | ||||||||
\(501\) | −45.5871 | −2.03668 | ||||||||
\(502\) | −13.0581 | −0.582810 | ||||||||
\(503\) | −10.1501 | −0.452571 | −0.226285 | − | 0.974061i | \(-0.572658\pi\) | ||||
−0.226285 | + | 0.974061i | \(0.572658\pi\) | |||||||
\(504\) | −38.8670 | −1.73127 | ||||||||
\(505\) | −5.04560 | −0.224526 | ||||||||
\(506\) | 7.74582 | 0.344344 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.67477 | −0.118674 | ||||||||
\(509\) | −16.0023 | −0.709289 | −0.354644 | − | 0.935001i | \(-0.615398\pi\) | ||||
−0.354644 | + | 0.935001i | \(0.615398\pi\) | |||||||
\(510\) | −37.4429 | −1.65800 | ||||||||
\(511\) | −18.4624 | −0.816728 | ||||||||
\(512\) | 13.8376 | 0.611542 | ||||||||
\(513\) | −57.9513 | −2.55861 | ||||||||
\(514\) | 4.98204 | 0.219749 | ||||||||
\(515\) | −14.5600 | −0.641589 | ||||||||
\(516\) | −2.13229 | −0.0938689 | ||||||||
\(517\) | −5.02969 | −0.221205 | ||||||||
\(518\) | −24.8882 | −1.09353 | ||||||||
\(519\) | 67.0683 | 2.94397 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.9248 | 1.70533 | 0.852663 | − | 0.522461i | \(-0.174986\pi\) | ||||
0.852663 | + | 0.522461i | \(0.174986\pi\) | |||||||
\(522\) | −101.206 | −4.42967 | ||||||||
\(523\) | 40.0699 | 1.75214 | 0.876068 | − | 0.482188i | \(-0.160158\pi\) | ||||
0.876068 | + | 0.482188i | \(0.160158\pi\) | |||||||
\(524\) | 5.26747 | 0.230110 | ||||||||
\(525\) | −23.0147 | −1.00444 | ||||||||
\(526\) | 3.20563 | 0.139772 | ||||||||
\(527\) | 21.0346 | 0.916280 | ||||||||
\(528\) | 15.0723 | 0.655936 | ||||||||
\(529\) | 2.40442 | 0.104540 | ||||||||
\(530\) | 18.5901 | 0.807500 | ||||||||
\(531\) | −92.5511 | −4.01638 | ||||||||
\(532\) | −2.65965 | −0.115310 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 19.8086 | 0.857203 | ||||||||
\(535\) | −4.66400 | −0.201642 | ||||||||
\(536\) | 2.09624 | 0.0905437 | ||||||||
\(537\) | 71.1995 | 3.07248 | ||||||||
\(538\) | −47.4164 | −2.04426 | ||||||||
\(539\) | −3.05334 | −0.131517 | ||||||||
\(540\) | 6.86630 | 0.295479 | ||||||||
\(541\) | 34.1644 | 1.46884 | 0.734420 | − | 0.678695i | \(-0.237454\pi\) | ||||
0.734420 | + | 0.678695i | \(0.237454\pi\) | |||||||
\(542\) | 11.7729 | 0.505691 | ||||||||
\(543\) | −26.3070 | −1.12894 | ||||||||
\(544\) | 12.3832 | 0.530923 | ||||||||
\(545\) | −6.94638 | −0.297550 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.9397 | 0.681531 | 0.340766 | − | 0.940148i | \(-0.389314\pi\) | ||||
0.340766 | + | 0.940148i | \(0.389314\pi\) | |||||||
\(548\) | 0.670541 | 0.0286441 | ||||||||
\(549\) | 25.1599 | 1.07380 | ||||||||
\(550\) | 5.42477 | 0.231313 | ||||||||
\(551\) | 31.3683 | 1.33633 | ||||||||
\(552\) | 41.6469 | 1.77261 | ||||||||
\(553\) | −3.41857 | −0.145373 | ||||||||
\(554\) | −21.6185 | −0.918480 | ||||||||
\(555\) | −32.4381 | −1.37692 | ||||||||
\(556\) | 7.79172 | 0.330443 | ||||||||
\(557\) | 34.0051 | 1.44084 | 0.720421 | − | 0.693537i | \(-0.243949\pi\) | ||||
0.720421 | + | 0.693537i | \(0.243949\pi\) | |||||||
\(558\) | −41.0240 | −1.73668 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −11.0621 | −0.467458 | ||||||||
\(561\) | −20.0951 | −0.848418 | ||||||||
\(562\) | −4.87210 | −0.205517 | ||||||||
\(563\) | −9.89124 | −0.416866 | −0.208433 | − | 0.978037i | \(-0.566836\pi\) | ||||
−0.208433 | + | 0.978037i | \(0.566836\pi\) | |||||||
\(564\) | 5.97056 | 0.251406 | ||||||||
\(565\) | 11.6364 | 0.489548 | ||||||||
\(566\) | 3.14164 | 0.132053 | ||||||||
\(567\) | −55.7680 | −2.34204 | ||||||||
\(568\) | −13.1594 | −0.552157 | ||||||||
\(569\) | −8.41679 | −0.352850 | −0.176425 | − | 0.984314i | \(-0.556453\pi\) | ||||
−0.176425 | + | 0.984314i | \(0.556453\pi\) | |||||||
\(570\) | −22.6339 | −0.948028 | ||||||||
\(571\) | 34.0299 | 1.42411 | 0.712054 | − | 0.702125i | \(-0.247765\pi\) | ||||
0.712054 | + | 0.702125i | \(0.247765\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 59.4920 | 2.48532 | ||||||||
\(574\) | −11.6293 | −0.485398 | ||||||||
\(575\) | 17.7919 | 0.741975 | ||||||||
\(576\) | 47.2241 | 1.96767 | ||||||||
\(577\) | −12.1007 | −0.503760 | −0.251880 | − | 0.967759i | \(-0.581049\pi\) | ||||
−0.251880 | + | 0.967759i | \(0.581049\pi\) | |||||||
\(578\) | −31.4917 | −1.30988 | ||||||||
\(579\) | −49.0202 | −2.03721 | ||||||||
\(580\) | −3.71664 | −0.154325 | ||||||||
\(581\) | 26.5455 | 1.10129 | ||||||||
\(582\) | −67.2128 | −2.78606 | ||||||||
\(583\) | 9.97705 | 0.413207 | ||||||||
\(584\) | 23.3980 | 0.968216 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15.0181 | −0.620392 | ||||||||
\(587\) | 38.9939 | 1.60945 | 0.804726 | − | 0.593647i | \(-0.202312\pi\) | ||||
0.804726 | + | 0.593647i | \(0.202312\pi\) | |||||||
\(588\) | 3.62451 | 0.149472 | ||||||||
\(589\) | 12.7152 | 0.523919 | ||||||||
\(590\) | −22.1922 | −0.913637 | ||||||||
\(591\) | −68.2190 | −2.80615 | ||||||||
\(592\) | 37.4389 | 1.53873 | ||||||||
\(593\) | −24.7393 | −1.01592 | −0.507960 | − | 0.861381i | \(-0.669600\pi\) | ||||
−0.507960 | + | 0.861381i | \(0.669600\pi\) | |||||||
\(594\) | 24.0612 | 0.987244 | ||||||||
\(595\) | 14.7486 | 0.604632 | ||||||||
\(596\) | −5.35358 | −0.219291 | ||||||||
\(597\) | −12.3198 | −0.504215 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.54030 | 0.144653 | 0.0723264 | − | 0.997381i | \(-0.476958\pi\) | ||||
0.0723264 | + | 0.997381i | \(0.476958\pi\) | |||||||
\(600\) | 29.1673 | 1.19075 | ||||||||
\(601\) | 20.2708 | 0.826862 | 0.413431 | − | 0.910535i | \(-0.364330\pi\) | ||||
0.413431 | + | 0.910535i | \(0.364330\pi\) | |||||||
\(602\) | 5.48403 | 0.223513 | ||||||||
\(603\) | 6.46987 | 0.263474 | ||||||||
\(604\) | 3.72844 | 0.151708 | ||||||||
\(605\) | −1.21246 | −0.0492934 | ||||||||
\(606\) | 20.9885 | 0.852599 | ||||||||
\(607\) | 15.7189 | 0.638012 | 0.319006 | − | 0.947753i | \(-0.396651\pi\) | ||||
0.319006 | + | 0.947753i | \(0.396651\pi\) | |||||||
\(608\) | 7.48548 | 0.303576 | ||||||||
\(609\) | 55.2548 | 2.23904 | ||||||||
\(610\) | 6.03292 | 0.244266 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 17.2100 | 0.695674 | ||||||||
\(613\) | 43.5374 | 1.75846 | 0.879230 | − | 0.476397i | \(-0.158057\pi\) | ||||
0.879230 | + | 0.476397i | \(0.158057\pi\) | |||||||
\(614\) | 19.9836 | 0.806474 | ||||||||
\(615\) | −15.1570 | −0.611191 | ||||||||
\(616\) | −5.00173 | −0.201525 | ||||||||
\(617\) | 10.8608 | 0.437238 | 0.218619 | − | 0.975810i | \(-0.429845\pi\) | ||||
0.218619 | + | 0.975810i | \(0.429845\pi\) | |||||||
\(618\) | 60.5660 | 2.43632 | ||||||||
\(619\) | 21.8912 | 0.879883 | 0.439941 | − | 0.898027i | \(-0.354999\pi\) | ||||
0.439941 | + | 0.898027i | \(0.354999\pi\) | |||||||
\(620\) | −1.50654 | −0.0605043 | ||||||||
\(621\) | 78.9151 | 3.16675 | ||||||||
\(622\) | 32.1785 | 1.29024 | ||||||||
\(623\) | −7.80251 | −0.312601 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.11029 | 0.204412 | ||||||||
\(626\) | −0.745219 | −0.0297849 | ||||||||
\(627\) | −12.1473 | −0.485117 | ||||||||
\(628\) | 1.24764 | 0.0497862 | ||||||||
\(629\) | −49.9155 | −1.99026 | ||||||||
\(630\) | −28.7643 | −1.14600 | ||||||||
\(631\) | 29.9694 | 1.19306 | 0.596531 | − | 0.802590i | \(-0.296545\pi\) | ||||
0.596531 | + | 0.802590i | \(0.296545\pi\) | |||||||
\(632\) | 4.33247 | 0.172337 | ||||||||
\(633\) | −42.0856 | −1.67275 | ||||||||
\(634\) | 38.4169 | 1.52573 | ||||||||
\(635\) | 8.96604 | 0.355806 | ||||||||
\(636\) | −11.8434 | −0.469621 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.0240 | −0.515626 | ||||||||
\(639\) | −40.6155 | −1.60673 | ||||||||
\(640\) | 16.2276 | 0.641453 | ||||||||
\(641\) | 12.2732 | 0.484764 | 0.242382 | − | 0.970181i | \(-0.422071\pi\) | ||||
0.242382 | + | 0.970181i | \(0.422071\pi\) | |||||||
\(642\) | 19.4011 | 0.765702 | ||||||||
\(643\) | −12.2900 | −0.484671 | −0.242335 | − | 0.970193i | \(-0.577913\pi\) | ||||
−0.242335 | + | 0.970193i | \(0.577913\pi\) | |||||||
\(644\) | 3.62177 | 0.142718 | ||||||||
\(645\) | 7.14762 | 0.281437 | ||||||||
\(646\) | −34.8289 | −1.37032 | ||||||||
\(647\) | 0.936707 | 0.0368258 | 0.0184129 | − | 0.999830i | \(-0.494139\pi\) | ||||
0.0184129 | + | 0.999830i | \(0.494139\pi\) | |||||||
\(648\) | 70.6766 | 2.77644 | ||||||||
\(649\) | −11.9103 | −0.467518 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.3976 | 0.877830 | ||||||||
\(652\) | −6.99058 | −0.273772 | ||||||||
\(653\) | −7.80246 | −0.305334 | −0.152667 | − | 0.988278i | \(-0.548786\pi\) | ||||
−0.152667 | + | 0.988278i | \(0.548786\pi\) | |||||||
\(654\) | 28.8953 | 1.12990 | ||||||||
\(655\) | −17.6570 | −0.689916 | ||||||||
\(656\) | 17.4937 | 0.683016 | ||||||||
\(657\) | 72.2161 | 2.81742 | ||||||||
\(658\) | −15.3557 | −0.598626 | ||||||||
\(659\) | 5.75064 | 0.224013 | 0.112007 | − | 0.993707i | \(-0.464272\pi\) | ||||
0.112007 | + | 0.993707i | \(0.464272\pi\) | |||||||
\(660\) | 1.43926 | 0.0560232 | ||||||||
\(661\) | −28.9866 | −1.12745 | −0.563723 | − | 0.825964i | \(-0.690632\pi\) | ||||
−0.563723 | + | 0.825964i | \(0.690632\pi\) | |||||||
\(662\) | −22.4506 | −0.872566 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −33.6419 | −1.30556 | ||||||||
\(665\) | 8.91535 | 0.345722 | ||||||||
\(666\) | 97.3509 | 3.77227 | ||||||||
\(667\) | −42.7157 | −1.65396 | ||||||||
\(668\) | 5.02425 | 0.194394 | ||||||||
\(669\) | 47.3399 | 1.83027 | ||||||||
\(670\) | 1.55136 | 0.0599344 | ||||||||
\(671\) | 3.23779 | 0.124994 | ||||||||
\(672\) | 13.1856 | 0.508645 | ||||||||
\(673\) | −25.7021 | −0.990743 | −0.495371 | − | 0.868681i | \(-0.664968\pi\) | ||||
−0.495371 | + | 0.868681i | \(0.664968\pi\) | |||||||
\(674\) | 19.0357 | 0.733229 | ||||||||
\(675\) | 55.2680 | 2.12727 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 38.2945 | 1.47178 | 0.735889 | − | 0.677102i | \(-0.236764\pi\) | ||||
0.735889 | + | 0.677102i | \(0.236764\pi\) | |||||||
\(678\) | −48.4048 | −1.85897 | ||||||||
\(679\) | 26.4748 | 1.01601 | ||||||||
\(680\) | −18.6913 | −0.716780 | ||||||||
\(681\) | −55.0786 | −2.11062 | ||||||||
\(682\) | −5.27931 | −0.202155 | ||||||||
\(683\) | 16.1752 | 0.618928 | 0.309464 | − | 0.950911i | \(-0.399850\pi\) | ||||
0.309464 | + | 0.950911i | \(0.399850\pi\) | |||||||
\(684\) | 10.4033 | 0.397779 | ||||||||
\(685\) | −2.24771 | −0.0858805 | ||||||||
\(686\) | −30.6929 | −1.17186 | ||||||||
\(687\) | 15.6977 | 0.598904 | ||||||||
\(688\) | −8.24953 | −0.314510 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 30.8216 | 1.17336 | ||||||||
\(691\) | −32.0215 | −1.21816 | −0.609078 | − | 0.793111i | \(-0.708460\pi\) | ||||
−0.609078 | + | 0.793111i | \(0.708460\pi\) | |||||||
\(692\) | −7.39174 | −0.280992 | ||||||||
\(693\) | −15.4374 | −0.586420 | ||||||||
\(694\) | 17.6406 | 0.669629 | ||||||||
\(695\) | −26.1185 | −0.990731 | ||||||||
\(696\) | −70.0262 | −2.65434 | ||||||||
\(697\) | −23.3236 | −0.883444 | ||||||||
\(698\) | −25.7916 | −0.976228 | ||||||||
\(699\) | 8.12395 | 0.307276 | ||||||||
\(700\) | 2.53650 | 0.0958706 | ||||||||
\(701\) | 15.9319 | 0.601739 | 0.300870 | − | 0.953665i | \(-0.402723\pi\) | ||||
0.300870 | + | 0.953665i | \(0.402723\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.1734 | −1.13801 | ||||||||
\(704\) | 6.07720 | 0.229043 | ||||||||
\(705\) | −20.0138 | −0.753763 | ||||||||
\(706\) | −27.4055 | −1.03142 | ||||||||
\(707\) | −8.26725 | −0.310922 | ||||||||
\(708\) | 14.1382 | 0.531347 | ||||||||
\(709\) | −21.8336 | −0.819976 | −0.409988 | − | 0.912091i | \(-0.634467\pi\) | ||||
−0.409988 | + | 0.912091i | \(0.634467\pi\) | |||||||
\(710\) | −9.73890 | −0.365494 | ||||||||
\(711\) | 13.3718 | 0.501483 | ||||||||
\(712\) | 9.88837 | 0.370583 | ||||||||
\(713\) | −17.3149 | −0.648447 | ||||||||
\(714\) | −61.3505 | −2.29599 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.84704 | −0.293258 | ||||||||
\(717\) | 57.8068 | 2.15883 | ||||||||
\(718\) | 16.2746 | 0.607364 | ||||||||
\(719\) | 12.0186 | 0.448217 | 0.224108 | − | 0.974564i | \(-0.428053\pi\) | ||||
0.224108 | + | 0.974564i | \(0.428053\pi\) | |||||||
\(720\) | 43.2696 | 1.61256 | ||||||||
\(721\) | −23.8566 | −0.888467 | ||||||||
\(722\) | 8.14520 | 0.303133 | ||||||||
\(723\) | −10.3822 | −0.386119 | ||||||||
\(724\) | 2.89935 | 0.107753 | ||||||||
\(725\) | −29.9159 | −1.11105 | ||||||||
\(726\) | 5.04353 | 0.187183 | ||||||||
\(727\) | 46.1626 | 1.71208 | 0.856038 | − | 0.516913i | \(-0.172919\pi\) | ||||
0.856038 | + | 0.516913i | \(0.172919\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 63.9861 | 2.36986 | ||||||||
\(730\) | 17.3162 | 0.640900 | ||||||||
\(731\) | 10.9987 | 0.406802 | ||||||||
\(732\) | −3.84346 | −0.142058 | ||||||||
\(733\) | 35.0574 | 1.29487 | 0.647437 | − | 0.762119i | \(-0.275841\pi\) | ||||
0.647437 | + | 0.762119i | \(0.275841\pi\) | |||||||
\(734\) | −18.9169 | −0.698234 | ||||||||
\(735\) | −12.1497 | −0.448147 | ||||||||
\(736\) | −10.1933 | −0.375732 | ||||||||
\(737\) | 0.832597 | 0.0306691 | ||||||||
\(738\) | 45.4883 | 1.67445 | ||||||||
\(739\) | −14.7567 | −0.542833 | −0.271417 | − | 0.962462i | \(-0.587492\pi\) | ||||
−0.271417 | + | 0.962462i | \(0.587492\pi\) | |||||||
\(740\) | 3.57507 | 0.131422 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30.4600 | 1.11822 | ||||||||
\(743\) | 9.96561 | 0.365603 | 0.182801 | − | 0.983150i | \(-0.441483\pi\) | ||||
0.182801 | + | 0.983150i | \(0.441483\pi\) | |||||||
\(744\) | −28.3852 | −1.04065 | ||||||||
\(745\) | 17.9456 | 0.657477 | ||||||||
\(746\) | −6.44567 | −0.235993 | ||||||||
\(747\) | −103.833 | −3.79906 | ||||||||
\(748\) | 2.21473 | 0.0809785 | ||||||||
\(749\) | −7.64200 | −0.279233 | ||||||||
\(750\) | 52.1612 | 1.90466 | ||||||||
\(751\) | 45.5216 | 1.66111 | 0.830553 | − | 0.556939i | \(-0.188024\pi\) | ||||
0.830553 | + | 0.556939i | \(0.188024\pi\) | |||||||
\(752\) | 23.0992 | 0.842342 | ||||||||
\(753\) | −27.8861 | −1.01623 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.4980 | −0.454850 | ||||||||
\(756\) | 11.2505 | 0.409176 | ||||||||
\(757\) | −38.3244 | −1.39292 | −0.696462 | − | 0.717594i | \(-0.745243\pi\) | ||||
−0.696462 | + | 0.717594i | \(0.745243\pi\) | |||||||
\(758\) | −25.7208 | −0.934221 | ||||||||
\(759\) | 16.5416 | 0.600421 | ||||||||
\(760\) | −11.2987 | −0.409848 | ||||||||
\(761\) | −15.9628 | −0.578652 | −0.289326 | − | 0.957231i | \(-0.593431\pi\) | ||||
−0.289326 | + | 0.957231i | \(0.593431\pi\) | |||||||
\(762\) | −37.2966 | −1.35111 | ||||||||
\(763\) | −11.3817 | −0.412045 | ||||||||
\(764\) | −6.55674 | −0.237215 | ||||||||
\(765\) | −57.6894 | −2.08576 | ||||||||
\(766\) | −6.77957 | −0.244956 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −27.6139 | −0.996430 | ||||||||
\(769\) | −35.2975 | −1.27286 | −0.636431 | − | 0.771334i | \(-0.719590\pi\) | ||||
−0.636431 | + | 0.771334i | \(0.719590\pi\) | |||||||
\(770\) | −3.70163 | −0.133398 | ||||||||
\(771\) | 10.6394 | 0.383169 | ||||||||
\(772\) | 5.40262 | 0.194445 | ||||||||
\(773\) | 10.8588 | 0.390565 | 0.195283 | − | 0.980747i | \(-0.437438\pi\) | ||||
0.195283 | + | 0.980747i | \(0.437438\pi\) | |||||||
\(774\) | −21.4509 | −0.771038 | ||||||||
\(775\) | −12.1264 | −0.435594 | ||||||||
\(776\) | −33.5523 | −1.20446 | ||||||||
\(777\) | −53.1500 | −1.90675 | ||||||||
\(778\) | −23.6921 | −0.849404 | ||||||||
\(779\) | −14.0989 | −0.505144 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.22675 | −0.187028 | ||||||||
\(782\) | 47.4282 | 1.69603 | ||||||||
\(783\) | −132.690 | −4.74195 | ||||||||
\(784\) | 14.0227 | 0.500811 | ||||||||
\(785\) | −4.18219 | −0.149269 | ||||||||
\(786\) | 73.4489 | 2.61984 | ||||||||
\(787\) | 4.54676 | 0.162074 | 0.0810372 | − | 0.996711i | \(-0.474177\pi\) | ||||
0.0810372 | + | 0.996711i | \(0.474177\pi\) | |||||||
\(788\) | 7.51856 | 0.267838 | ||||||||
\(789\) | 6.84579 | 0.243716 | ||||||||
\(790\) | 3.20634 | 0.114076 | ||||||||
\(791\) | 19.0664 | 0.677922 | ||||||||
\(792\) | 19.5644 | 0.695190 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −39.6530 | −1.40723 | ||||||||
\(795\) | 39.7000 | 1.40801 | ||||||||
\(796\) | 1.35779 | 0.0481255 | ||||||||
\(797\) | 12.9330 | 0.458110 | 0.229055 | − | 0.973414i | \(-0.426436\pi\) | ||||
0.229055 | + | 0.973414i | \(0.426436\pi\) | |||||||
\(798\) | −37.0857 | −1.31282 | ||||||||
\(799\) | −30.7971 | −1.08952 | ||||||||
\(800\) | −7.13889 | −0.252398 | ||||||||
\(801\) | 30.5197 | 1.07836 | ||||||||
\(802\) | 33.3742 | 1.17848 | ||||||||
\(803\) | 9.29337 | 0.327956 | ||||||||
\(804\) | −0.988345 | −0.0348563 | ||||||||
\(805\) | −12.1405 | −0.427895 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −101.260 | −3.56452 | ||||||||
\(808\) | 10.4774 | 0.368592 | ||||||||
\(809\) | −37.0363 | −1.30213 | −0.651064 | − | 0.759023i | \(-0.725677\pi\) | ||||
−0.651064 | + | 0.759023i | \(0.725677\pi\) | |||||||
\(810\) | 52.3057 | 1.83784 | ||||||||
\(811\) | −30.7510 | −1.07981 | −0.539907 | − | 0.841725i | \(-0.681541\pi\) | ||||
−0.539907 | + | 0.841725i | \(0.681541\pi\) | |||||||
\(812\) | −6.08974 | −0.213708 | ||||||||
\(813\) | 25.1417 | 0.881757 | ||||||||
\(814\) | 12.5279 | 0.439104 | ||||||||
\(815\) | 23.4330 | 0.820822 | ||||||||
\(816\) | 92.2885 | 3.23074 | ||||||||
\(817\) | 6.64861 | 0.232605 | ||||||||
\(818\) | −17.1222 | −0.598665 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.67049 | 0.0583360 | ||||||||
\(821\) | 52.6472 | 1.83740 | 0.918699 | − | 0.394958i | \(-0.129241\pi\) | ||||
0.918699 | + | 0.394958i | \(0.129241\pi\) | |||||||
\(822\) | 9.34993 | 0.326116 | ||||||||
\(823\) | −36.0179 | −1.25551 | −0.627753 | − | 0.778413i | \(-0.716025\pi\) | ||||
−0.627753 | + | 0.778413i | \(0.716025\pi\) | |||||||
\(824\) | 30.2343 | 1.05326 | ||||||||
\(825\) | 11.5849 | 0.403333 | ||||||||
\(826\) | −36.3620 | −1.26520 | ||||||||
\(827\) | 46.4535 | 1.61535 | 0.807673 | − | 0.589631i | \(-0.200727\pi\) | ||||
0.807673 | + | 0.589631i | \(0.200727\pi\) | |||||||
\(828\) | −14.1666 | −0.492325 | ||||||||
\(829\) | −4.65695 | −0.161743 | −0.0808713 | − | 0.996725i | \(-0.525770\pi\) | ||||
−0.0808713 | + | 0.996725i | \(0.525770\pi\) | |||||||
\(830\) | −24.8974 | −0.864202 | ||||||||
\(831\) | −46.1673 | −1.60153 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.6958 | −0.647772 | ||||||||
\(834\) | 108.647 | 3.76213 | ||||||||
\(835\) | −16.8417 | −0.582831 | ||||||||
\(836\) | 1.33878 | 0.0463027 | ||||||||
\(837\) | −53.7860 | −1.85912 | ||||||||
\(838\) | −9.18064 | −0.317140 | ||||||||
\(839\) | 26.2967 | 0.907862 | 0.453931 | − | 0.891037i | \(-0.350021\pi\) | ||||
0.453931 | + | 0.891037i | \(0.350021\pi\) | |||||||
\(840\) | −19.9025 | −0.686702 | ||||||||
\(841\) | 42.8234 | 1.47667 | ||||||||
\(842\) | 8.39849 | 0.289431 | ||||||||
\(843\) | −10.4046 | −0.358354 | ||||||||
\(844\) | 4.63835 | 0.159658 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 60.0640 | 2.06504 | ||||||||
\(847\) | −1.98662 | −0.0682610 | ||||||||
\(848\) | −45.8204 | −1.57348 | ||||||||
\(849\) | 6.70913 | 0.230257 | ||||||||
\(850\) | 33.2162 | 1.13931 | ||||||||
\(851\) | 41.0886 | 1.40850 | ||||||||
\(852\) | 6.20447 | 0.212562 | ||||||||
\(853\) | −4.97399 | −0.170306 | −0.0851530 | − | 0.996368i | \(-0.527138\pi\) | ||||
−0.0851530 | + | 0.996368i | \(0.527138\pi\) | |||||||
\(854\) | 9.88499 | 0.338257 | ||||||||
\(855\) | −34.8726 | −1.19262 | ||||||||
\(856\) | 9.68496 | 0.331025 | ||||||||
\(857\) | 16.7189 | 0.571106 | 0.285553 | − | 0.958363i | \(-0.407823\pi\) | ||||
0.285553 | + | 0.958363i | \(0.407823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.68953 | 0.330603 | 0.165301 | − | 0.986243i | \(-0.447140\pi\) | ||||
0.165301 | + | 0.986243i | \(0.447140\pi\) | |||||||
\(860\) | −0.787754 | −0.0268622 | ||||||||
\(861\) | −24.8349 | −0.846373 | ||||||||
\(862\) | −13.1600 | −0.448232 | ||||||||
\(863\) | −2.96369 | −0.100885 | −0.0504426 | − | 0.998727i | \(-0.516063\pi\) | ||||
−0.0504426 | + | 0.998727i | \(0.516063\pi\) | |||||||
\(864\) | −31.6641 | −1.07724 | ||||||||
\(865\) | 24.7777 | 0.842468 | ||||||||
\(866\) | 0.808786 | 0.0274837 | ||||||||
\(867\) | −67.2521 | −2.28400 | ||||||||
\(868\) | −2.46848 | −0.0837858 | ||||||||
\(869\) | 1.72080 | 0.0583741 | ||||||||
\(870\) | −51.8243 | −1.75701 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 14.4244 | 0.488472 | ||||||||
\(873\) | −103.557 | −3.50486 | ||||||||
\(874\) | 28.6698 | 0.969771 | ||||||||
\(875\) | −20.5460 | −0.694581 | ||||||||
\(876\) | −11.0318 | −0.372730 | ||||||||
\(877\) | −3.63010 | −0.122580 | −0.0612898 | − | 0.998120i | \(-0.519521\pi\) | ||||
−0.0612898 | + | 0.998120i | \(0.519521\pi\) | |||||||
\(878\) | 3.71495 | 0.125374 | ||||||||
\(879\) | −32.0719 | −1.08176 | ||||||||
\(880\) | 5.56830 | 0.187707 | ||||||||
\(881\) | 38.8671 | 1.30947 | 0.654733 | − | 0.755860i | \(-0.272781\pi\) | ||||
0.654733 | + | 0.755860i | \(0.272781\pi\) | |||||||
\(882\) | 36.4627 | 1.22776 | ||||||||
\(883\) | −7.72302 | −0.259900 | −0.129950 | − | 0.991521i | \(-0.541482\pi\) | ||||
−0.129950 | + | 0.991521i | \(0.541482\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −47.3924 | −1.59308 | ||||||||
\(886\) | 36.8850 | 1.23918 | ||||||||
\(887\) | 13.5579 | 0.455231 | 0.227616 | − | 0.973751i | \(-0.426907\pi\) | ||||
0.227616 | + | 0.973751i | \(0.426907\pi\) | |||||||
\(888\) | 67.3588 | 2.26041 | ||||||||
\(889\) | 14.6909 | 0.492718 | ||||||||
\(890\) | 7.31810 | 0.245303 | ||||||||
\(891\) | 28.0718 | 0.940441 | ||||||||
\(892\) | −5.21743 | −0.174692 | ||||||||
\(893\) | −18.6165 | −0.622979 | ||||||||
\(894\) | −74.6496 | −2.49666 | ||||||||
\(895\) | 26.3039 | 0.879243 | ||||||||
\(896\) | 26.5891 | 0.888279 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.3952 | 0.380261 | ||||||||
\(899\) | 29.1137 | 0.970996 | ||||||||
\(900\) | −9.92158 | −0.330719 | ||||||||
\(901\) | 61.0901 | 2.03521 | ||||||||
\(902\) | 5.85381 | 0.194911 | ||||||||
\(903\) | 11.7114 | 0.389732 | ||||||||
\(904\) | −24.1634 | −0.803664 | ||||||||
\(905\) | −9.71885 | −0.323065 | ||||||||
\(906\) | 51.9889 | 1.72722 | ||||||||
\(907\) | 54.1005 | 1.79638 | 0.898189 | − | 0.439609i | \(-0.144883\pi\) | ||||
0.898189 | + | 0.439609i | \(0.144883\pi\) | |||||||
\(908\) | 6.07033 | 0.201451 | ||||||||
\(909\) | 32.3376 | 1.07257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.17721 | −0.237792 | −0.118896 | − | 0.992907i | \(-0.537935\pi\) | ||||
−0.118896 | + | 0.992907i | \(0.537935\pi\) | |||||||
\(912\) | 55.7874 | 1.84731 | ||||||||
\(913\) | −13.3621 | −0.442222 | ||||||||
\(914\) | 3.88973 | 0.128661 | ||||||||
\(915\) | 12.8836 | 0.425919 | ||||||||
\(916\) | −1.73007 | −0.0571632 | ||||||||
\(917\) | −28.9311 | −0.955390 | ||||||||
\(918\) | 147.329 | 4.86257 | ||||||||
\(919\) | −32.1437 | −1.06032 | −0.530162 | − | 0.847896i | \(-0.677869\pi\) | ||||
−0.530162 | + | 0.847896i | \(0.677869\pi\) | |||||||
\(920\) | 15.3860 | 0.507262 | ||||||||
\(921\) | 42.6760 | 1.40622 | ||||||||
\(922\) | −7.30012 | −0.240417 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 2.35824 | 0.0775804 | ||||||||
\(925\) | 28.7763 | 0.946159 | ||||||||
\(926\) | 13.6189 | 0.447545 | ||||||||
\(927\) | 93.3158 | 3.06489 | ||||||||
\(928\) | 17.1394 | 0.562628 | ||||||||
\(929\) | 37.2034 | 1.22061 | 0.610303 | − | 0.792168i | \(-0.291048\pi\) | ||||
0.610303 | + | 0.792168i | \(0.291048\pi\) | |||||||
\(930\) | −21.0071 | −0.688848 | ||||||||
\(931\) | −11.3014 | −0.370390 | ||||||||
\(932\) | −0.895357 | −0.0293284 | ||||||||
\(933\) | 68.7188 | 2.24975 | ||||||||
\(934\) | −1.38461 | −0.0453058 | ||||||||
\(935\) | −7.42395 | −0.242789 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.5166 | −1.12761 | −0.563804 | − | 0.825909i | \(-0.690662\pi\) | ||||
−0.563804 | + | 0.825909i | \(0.690662\pi\) | |||||||
\(938\) | 2.54192 | 0.0829967 | ||||||||
\(939\) | −1.59145 | −0.0519351 | ||||||||
\(940\) | 2.20576 | 0.0719440 | ||||||||
\(941\) | 55.3190 | 1.80335 | 0.901674 | − | 0.432417i | \(-0.142339\pi\) | ||||
0.901674 | + | 0.432417i | \(0.142339\pi\) | |||||||
\(942\) | 17.3969 | 0.566822 | ||||||||
\(943\) | 19.1991 | 0.625209 | ||||||||
\(944\) | 54.6987 | 1.78029 | ||||||||
\(945\) | −37.7126 | −1.22679 | ||||||||
\(946\) | −2.76049 | −0.0897511 | ||||||||
\(947\) | −2.49089 | −0.0809430 | −0.0404715 | − | 0.999181i | \(-0.512886\pi\) | ||||
−0.0404715 | + | 0.999181i | \(0.512886\pi\) | |||||||
\(948\) | −2.04270 | −0.0663437 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 20.0788 | 0.651444 | ||||||||
\(951\) | 82.0412 | 2.66037 | ||||||||
\(952\) | −30.6259 | −0.992591 | ||||||||
\(953\) | −27.7692 | −0.899533 | −0.449766 | − | 0.893146i | \(-0.648493\pi\) | ||||
−0.449766 | + | 0.893146i | \(0.648493\pi\) | |||||||
\(954\) | −119.145 | −3.85746 | ||||||||
\(955\) | 21.9787 | 0.711215 | ||||||||
\(956\) | −6.37100 | −0.206053 | ||||||||
\(957\) | −27.8135 | −0.899082 | ||||||||
\(958\) | 7.09813 | 0.229330 | ||||||||
\(959\) | −3.68289 | −0.118927 | ||||||||
\(960\) | 24.1820 | 0.780469 | ||||||||
\(961\) | −19.1987 | −0.619314 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 29.8919 | 0.963252 | ||||||||
\(964\) | 1.14425 | 0.0368537 | ||||||||
\(965\) | −18.1100 | −0.582982 | ||||||||
\(966\) | 50.5015 | 1.62486 | ||||||||
\(967\) | 47.5638 | 1.52955 | 0.764775 | − | 0.644298i | \(-0.222850\pi\) | ||||
0.764775 | + | 0.644298i | \(0.222850\pi\) | |||||||
\(968\) | 2.51771 | 0.0809222 | ||||||||
\(969\) | −74.3788 | −2.38939 | ||||||||
\(970\) | −24.8311 | −0.797279 | ||||||||
\(971\) | −32.9713 | −1.05810 | −0.529050 | − | 0.848591i | \(-0.677452\pi\) | ||||
−0.529050 | + | 0.848591i | \(0.677452\pi\) | |||||||
\(972\) | −16.3336 | −0.523901 | ||||||||
\(973\) | −42.7954 | −1.37196 | ||||||||
\(974\) | −33.9615 | −1.08820 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.8698 | −0.475971 | ||||||||
\(977\) | 0.741037 | 0.0237079 | 0.0118539 | − | 0.999930i | \(-0.496227\pi\) | ||||
0.0118539 | + | 0.999930i | \(0.496227\pi\) | |||||||
\(978\) | −97.4758 | −3.11693 | ||||||||
\(979\) | 3.92753 | 0.125524 | ||||||||
\(980\) | 1.33904 | 0.0427740 | ||||||||
\(981\) | 44.5198 | 1.42141 | ||||||||
\(982\) | 10.3471 | 0.330188 | ||||||||
\(983\) | 29.6646 | 0.946154 | 0.473077 | − | 0.881021i | \(-0.343143\pi\) | ||||
0.473077 | + | 0.881021i | \(0.343143\pi\) | |||||||
\(984\) | 31.4741 | 1.00336 | ||||||||
\(985\) | −25.2028 | −0.803029 | ||||||||
\(986\) | −79.7470 | −2.53966 | ||||||||
\(987\) | −32.7928 | −1.04380 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.05373 | −0.287892 | ||||||||
\(990\) | 14.4790 | 0.460174 | ||||||||
\(991\) | 18.6412 | 0.592158 | 0.296079 | − | 0.955163i | \(-0.404321\pi\) | ||||
0.296079 | + | 0.955163i | \(0.404321\pi\) | |||||||
\(992\) | 6.94747 | 0.220582 | ||||||||
\(993\) | −47.9443 | −1.52147 | ||||||||
\(994\) | −15.9573 | −0.506134 | ||||||||
\(995\) | −4.55141 | −0.144290 | ||||||||
\(996\) | 15.8617 | 0.502597 | ||||||||
\(997\) | 53.2981 | 1.68797 | 0.843984 | − | 0.536369i | \(-0.180204\pi\) | ||||
0.843984 | + | 0.536369i | \(0.180204\pi\) | |||||||
\(998\) | −58.8697 | −1.86349 | ||||||||
\(999\) | 127.636 | 4.03821 |
(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 | 1859.2.a.t.1.6 | yes | 21 | |
13.12 | even | 2 | 1859.2.a.s.1.16 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1859.2.a.s.1.16 | ✓ | 21 | 13.12 | even | 2 | ||
1859.2.a.t.1.6 | yes | 21 | 1.1 | even | 1 | trivial |