Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, 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("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 11x^{6} + 10x^{5} + 35x^{4} - 30x^{3} - 30x^{2} + 30x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.226211\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.226211 | −0.159956 | −0.0799778 | − | 0.996797i | \(-0.525485\pi\) | ||||
−0.0799778 | + | 0.996797i | \(0.525485\pi\) | |||||||
\(3\) | −0.219130 | −0.126514 | −0.0632572 | − | 0.997997i | \(-0.520149\pi\) | ||||
−0.0632572 | + | 0.997997i | \(0.520149\pi\) | |||||||
\(4\) | −1.94883 | −0.974414 | ||||||||
\(5\) | −2.49552 | −1.11603 | −0.558016 | − | 0.829830i | \(-0.688437\pi\) | ||||
−0.558016 | + | 0.829830i | \(0.688437\pi\) | |||||||
\(6\) | 0.0495696 | 0.0202367 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.893270 | 0.315819 | ||||||||
\(9\) | −2.95198 | −0.983994 | ||||||||
\(10\) | 0.564516 | 0.178516 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.427046 | 0.123278 | ||||||||
\(13\) | −5.13499 | −1.42419 | −0.712094 | − | 0.702084i | \(-0.752253\pi\) | ||||
−0.712094 | + | 0.702084i | \(0.752253\pi\) | |||||||
\(14\) | 0.226211 | 0.0604575 | ||||||||
\(15\) | 0.546843 | 0.141194 | ||||||||
\(16\) | 3.69559 | 0.923897 | ||||||||
\(17\) | 1.43752 | 0.348651 | 0.174325 | − | 0.984688i | \(-0.444226\pi\) | ||||
0.174325 | + | 0.984688i | \(0.444226\pi\) | |||||||
\(18\) | 0.667772 | 0.157395 | ||||||||
\(19\) | 6.06848 | 1.39220 | 0.696102 | − | 0.717943i | \(-0.254916\pi\) | ||||
0.696102 | + | 0.717943i | \(0.254916\pi\) | |||||||
\(20\) | 4.86335 | 1.08748 | ||||||||
\(21\) | 0.219130 | 0.0478180 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.08292 | 1.47689 | 0.738446 | − | 0.674313i | \(-0.235560\pi\) | ||||
0.738446 | + | 0.674313i | \(0.235560\pi\) | |||||||
\(24\) | −0.195742 | −0.0399556 | ||||||||
\(25\) | 1.22764 | 0.245528 | ||||||||
\(26\) | 1.16159 | 0.227807 | ||||||||
\(27\) | 1.30426 | 0.251004 | ||||||||
\(28\) | 1.94883 | 0.368294 | ||||||||
\(29\) | −6.51769 | −1.21030 | −0.605152 | − | 0.796110i | \(-0.706888\pi\) | ||||
−0.605152 | + | 0.796110i | \(0.706888\pi\) | |||||||
\(30\) | −0.123702 | −0.0225848 | ||||||||
\(31\) | 7.68895 | 1.38098 | 0.690488 | − | 0.723344i | \(-0.257396\pi\) | ||||
0.690488 | + | 0.723344i | \(0.257396\pi\) | |||||||
\(32\) | −2.62252 | −0.463601 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.325184 | −0.0557687 | ||||||||
\(35\) | 2.49552 | 0.421820 | ||||||||
\(36\) | 5.75291 | 0.958818 | ||||||||
\(37\) | −3.98432 | −0.655019 | −0.327509 | − | 0.944848i | \(-0.606209\pi\) | ||||
−0.327509 | + | 0.944848i | \(0.606209\pi\) | |||||||
\(38\) | −1.37276 | −0.222691 | ||||||||
\(39\) | 1.12523 | 0.180181 | ||||||||
\(40\) | −2.22918 | −0.352464 | ||||||||
\(41\) | −6.74900 | −1.05402 | −0.527008 | − | 0.849860i | \(-0.676686\pi\) | ||||
−0.527008 | + | 0.849860i | \(0.676686\pi\) | |||||||
\(42\) | −0.0495696 | −0.00764875 | ||||||||
\(43\) | 0.802299 | 0.122349 | 0.0611747 | − | 0.998127i | \(-0.480515\pi\) | ||||
0.0611747 | + | 0.998127i | \(0.480515\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.36674 | 1.09817 | ||||||||
\(46\) | −1.60224 | −0.236237 | ||||||||
\(47\) | 6.75222 | 0.984912 | 0.492456 | − | 0.870337i | \(-0.336099\pi\) | ||||
0.492456 | + | 0.870337i | \(0.336099\pi\) | |||||||
\(48\) | −0.809813 | −0.116886 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.277706 | −0.0392735 | ||||||||
\(51\) | −0.315004 | −0.0441094 | ||||||||
\(52\) | 10.0072 | 1.38775 | ||||||||
\(53\) | 6.58167 | 0.904062 | 0.452031 | − | 0.892002i | \(-0.350700\pi\) | ||||
0.452031 | + | 0.892002i | \(0.350700\pi\) | |||||||
\(54\) | −0.295037 | −0.0401495 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.893270 | −0.119368 | ||||||||
\(57\) | −1.32978 | −0.176134 | ||||||||
\(58\) | 1.47437 | 0.193595 | ||||||||
\(59\) | 2.87625 | 0.374456 | 0.187228 | − | 0.982316i | \(-0.440050\pi\) | ||||
0.187228 | + | 0.982316i | \(0.440050\pi\) | |||||||
\(60\) | −1.06570 | −0.137582 | ||||||||
\(61\) | 0.855342 | 0.109515 | 0.0547576 | − | 0.998500i | \(-0.482561\pi\) | ||||
0.0547576 | + | 0.998500i | \(0.482561\pi\) | |||||||
\(62\) | −1.73933 | −0.220895 | ||||||||
\(63\) | 2.95198 | 0.371915 | ||||||||
\(64\) | −6.79793 | −0.849742 | ||||||||
\(65\) | 12.8145 | 1.58944 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.64668 | −0.201174 | −0.100587 | − | 0.994928i | \(-0.532072\pi\) | ||||
−0.100587 | + | 0.994928i | \(0.532072\pi\) | |||||||
\(68\) | −2.80149 | −0.339730 | ||||||||
\(69\) | −1.55208 | −0.186848 | ||||||||
\(70\) | −0.564516 | −0.0674725 | ||||||||
\(71\) | 4.52077 | 0.536517 | 0.268258 | − | 0.963347i | \(-0.413552\pi\) | ||||
0.268258 | + | 0.963347i | \(0.413552\pi\) | |||||||
\(72\) | −2.63692 | −0.310764 | ||||||||
\(73\) | 14.8479 | 1.73782 | 0.868910 | − | 0.494970i | \(-0.164821\pi\) | ||||
0.868910 | + | 0.494970i | \(0.164821\pi\) | |||||||
\(74\) | 0.901299 | 0.104774 | ||||||||
\(75\) | −0.269012 | −0.0310628 | ||||||||
\(76\) | −11.8264 | −1.35658 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.254539 | −0.0288209 | ||||||||
\(79\) | −2.45291 | −0.275973 | −0.137987 | − | 0.990434i | \(-0.544063\pi\) | ||||
−0.137987 | + | 0.990434i | \(0.544063\pi\) | |||||||
\(80\) | −9.22243 | −1.03110 | ||||||||
\(81\) | 8.57015 | 0.952238 | ||||||||
\(82\) | 1.52670 | 0.168596 | ||||||||
\(83\) | −2.24780 | −0.246728 | −0.123364 | − | 0.992361i | \(-0.539368\pi\) | ||||
−0.123364 | + | 0.992361i | \(0.539368\pi\) | |||||||
\(84\) | −0.427046 | −0.0465945 | ||||||||
\(85\) | −3.58738 | −0.389106 | ||||||||
\(86\) | −0.181489 | −0.0195705 | ||||||||
\(87\) | 1.42822 | 0.153121 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.73566 | 0.183980 | 0.0919898 | − | 0.995760i | \(-0.470677\pi\) | ||||
0.0919898 | + | 0.995760i | \(0.470677\pi\) | |||||||
\(90\) | −1.66644 | −0.175658 | ||||||||
\(91\) | 5.13499 | 0.538293 | ||||||||
\(92\) | −13.8034 | −1.43910 | ||||||||
\(93\) | −1.68488 | −0.174714 | ||||||||
\(94\) | −1.52743 | −0.157542 | ||||||||
\(95\) | −15.1440 | −1.55374 | ||||||||
\(96\) | 0.574672 | 0.0586523 | ||||||||
\(97\) | −12.0776 | −1.22629 | −0.613145 | − | 0.789970i | \(-0.710096\pi\) | ||||
−0.613145 | + | 0.789970i | \(0.710096\pi\) | |||||||
\(98\) | −0.226211 | −0.0228508 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.39246 | −0.239246 | ||||||||
\(101\) | 3.69338 | 0.367505 | 0.183753 | − | 0.982973i | \(-0.441175\pi\) | ||||
0.183753 | + | 0.982973i | \(0.441175\pi\) | |||||||
\(102\) | 0.0712575 | 0.00705554 | ||||||||
\(103\) | −1.15156 | −0.113467 | −0.0567334 | − | 0.998389i | \(-0.518069\pi\) | ||||
−0.0567334 | + | 0.998389i | \(0.518069\pi\) | |||||||
\(104\) | −4.58693 | −0.449785 | ||||||||
\(105\) | −0.546843 | −0.0533664 | ||||||||
\(106\) | −1.48885 | −0.144610 | ||||||||
\(107\) | −1.16714 | −0.112831 | −0.0564157 | − | 0.998407i | \(-0.517967\pi\) | ||||
−0.0564157 | + | 0.998407i | \(0.517967\pi\) | |||||||
\(108\) | −2.54177 | −0.244582 | ||||||||
\(109\) | −9.30234 | −0.891003 | −0.445501 | − | 0.895281i | \(-0.646975\pi\) | ||||
−0.445501 | + | 0.895281i | \(0.646975\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.873083 | 0.0828694 | ||||||||
\(112\) | −3.69559 | −0.349200 | ||||||||
\(113\) | 3.29733 | 0.310187 | 0.155093 | − | 0.987900i | \(-0.450432\pi\) | ||||
0.155093 | + | 0.987900i | \(0.450432\pi\) | |||||||
\(114\) | 0.300812 | 0.0281736 | ||||||||
\(115\) | −17.6756 | −1.64826 | ||||||||
\(116\) | 12.7019 | 1.17934 | ||||||||
\(117\) | 15.1584 | 1.40139 | ||||||||
\(118\) | −0.650640 | −0.0598963 | ||||||||
\(119\) | −1.43752 | −0.131778 | ||||||||
\(120\) | 0.488478 | 0.0445918 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −0.193488 | −0.0175176 | ||||||||
\(123\) | 1.47891 | 0.133348 | ||||||||
\(124\) | −14.9844 | −1.34564 | ||||||||
\(125\) | 9.41402 | 0.842015 | ||||||||
\(126\) | −0.667772 | −0.0594898 | ||||||||
\(127\) | 0.289205 | 0.0256628 | 0.0128314 | − | 0.999918i | \(-0.495916\pi\) | ||||
0.0128314 | + | 0.999918i | \(0.495916\pi\) | |||||||
\(128\) | 6.78282 | 0.599522 | ||||||||
\(129\) | −0.175807 | −0.0154790 | ||||||||
\(130\) | −2.89878 | −0.254240 | ||||||||
\(131\) | 16.5059 | 1.44212 | 0.721062 | − | 0.692871i | \(-0.243654\pi\) | ||||
0.721062 | + | 0.692871i | \(0.243654\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.06848 | −0.526204 | ||||||||
\(134\) | 0.372498 | 0.0321789 | ||||||||
\(135\) | −3.25480 | −0.280129 | ||||||||
\(136\) | 1.28410 | 0.110110 | ||||||||
\(137\) | 9.32588 | 0.796763 | 0.398382 | − | 0.917220i | \(-0.369572\pi\) | ||||
0.398382 | + | 0.917220i | \(0.369572\pi\) | |||||||
\(138\) | 0.351097 | 0.0298874 | ||||||||
\(139\) | −4.82649 | −0.409377 | −0.204689 | − | 0.978827i | \(-0.565618\pi\) | ||||
−0.204689 | + | 0.978827i | \(0.565618\pi\) | |||||||
\(140\) | −4.86335 | −0.411028 | ||||||||
\(141\) | −1.47961 | −0.124606 | ||||||||
\(142\) | −1.02265 | −0.0858189 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −10.9093 | −0.909109 | ||||||||
\(145\) | 16.2650 | 1.35074 | ||||||||
\(146\) | −3.35877 | −0.277974 | ||||||||
\(147\) | −0.219130 | −0.0180735 | ||||||||
\(148\) | 7.76476 | 0.638260 | ||||||||
\(149\) | −0.921915 | −0.0755262 | −0.0377631 | − | 0.999287i | \(-0.512023\pi\) | ||||
−0.0377631 | + | 0.999287i | \(0.512023\pi\) | |||||||
\(150\) | 0.0608535 | 0.00496867 | ||||||||
\(151\) | −18.0964 | −1.47267 | −0.736333 | − | 0.676620i | \(-0.763444\pi\) | ||||
−0.736333 | + | 0.676620i | \(0.763444\pi\) | |||||||
\(152\) | 5.42079 | 0.439684 | ||||||||
\(153\) | −4.24355 | −0.343070 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.1880 | −1.54121 | ||||||||
\(156\) | −2.19287 | −0.175570 | ||||||||
\(157\) | −12.2733 | −0.979518 | −0.489759 | − | 0.871858i | \(-0.662915\pi\) | ||||
−0.489759 | + | 0.871858i | \(0.662915\pi\) | |||||||
\(158\) | 0.554875 | 0.0441435 | ||||||||
\(159\) | −1.44224 | −0.114377 | ||||||||
\(160\) | 6.54457 | 0.517394 | ||||||||
\(161\) | −7.08292 | −0.558212 | ||||||||
\(162\) | −1.93866 | −0.152316 | ||||||||
\(163\) | 8.09913 | 0.634373 | 0.317186 | − | 0.948363i | \(-0.397262\pi\) | ||||
0.317186 | + | 0.948363i | \(0.397262\pi\) | |||||||
\(164\) | 13.1526 | 1.02705 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.508478 | 0.0394655 | ||||||||
\(167\) | 13.0516 | 1.00996 | 0.504982 | − | 0.863130i | \(-0.331499\pi\) | ||||
0.504982 | + | 0.863130i | \(0.331499\pi\) | |||||||
\(168\) | 0.195742 | 0.0151018 | ||||||||
\(169\) | 13.3681 | 1.02831 | ||||||||
\(170\) | 0.811505 | 0.0622396 | ||||||||
\(171\) | −17.9140 | −1.36992 | ||||||||
\(172\) | −1.56354 | −0.119219 | ||||||||
\(173\) | −5.91219 | −0.449495 | −0.224748 | − | 0.974417i | \(-0.572156\pi\) | ||||
−0.224748 | + | 0.974417i | \(0.572156\pi\) | |||||||
\(174\) | −0.323079 | −0.0244926 | ||||||||
\(175\) | −1.22764 | −0.0928007 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.630271 | −0.0473741 | ||||||||
\(178\) | −0.392626 | −0.0294286 | ||||||||
\(179\) | 4.33508 | 0.324019 | 0.162009 | − | 0.986789i | \(-0.448202\pi\) | ||||
0.162009 | + | 0.986789i | \(0.448202\pi\) | |||||||
\(180\) | −14.3565 | −1.07007 | ||||||||
\(181\) | 10.8307 | 0.805040 | 0.402520 | − | 0.915411i | \(-0.368134\pi\) | ||||
0.402520 | + | 0.915411i | \(0.368134\pi\) | |||||||
\(182\) | −1.16159 | −0.0861029 | ||||||||
\(183\) | −0.187431 | −0.0138553 | ||||||||
\(184\) | 6.32696 | 0.466430 | ||||||||
\(185\) | 9.94297 | 0.731022 | ||||||||
\(186\) | 0.381138 | 0.0279464 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −13.1589 | −0.959713 | ||||||||
\(189\) | −1.30426 | −0.0948706 | ||||||||
\(190\) | 3.42575 | 0.248530 | ||||||||
\(191\) | 11.6556 | 0.843370 | 0.421685 | − | 0.906742i | \(-0.361439\pi\) | ||||
0.421685 | + | 0.906742i | \(0.361439\pi\) | |||||||
\(192\) | 1.48963 | 0.107505 | ||||||||
\(193\) | −22.4454 | −1.61566 | −0.807829 | − | 0.589418i | \(-0.799357\pi\) | ||||
−0.807829 | + | 0.589418i | \(0.799357\pi\) | |||||||
\(194\) | 2.73208 | 0.196152 | ||||||||
\(195\) | −2.80803 | −0.201087 | ||||||||
\(196\) | −1.94883 | −0.139202 | ||||||||
\(197\) | −24.1022 | −1.71721 | −0.858604 | − | 0.512639i | \(-0.828668\pi\) | ||||
−0.858604 | + | 0.512639i | \(0.828668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7205 | 1.32706 | 0.663531 | − | 0.748148i | \(-0.269057\pi\) | ||||
0.663531 | + | 0.748148i | \(0.269057\pi\) | |||||||
\(200\) | 1.09661 | 0.0775422 | ||||||||
\(201\) | 0.360836 | 0.0254514 | ||||||||
\(202\) | −0.835485 | −0.0587845 | ||||||||
\(203\) | 6.51769 | 0.457452 | ||||||||
\(204\) | 0.613889 | 0.0429808 | ||||||||
\(205\) | 16.8423 | 1.17632 | ||||||||
\(206\) | 0.260497 | 0.0181497 | ||||||||
\(207\) | −20.9087 | −1.45325 | ||||||||
\(208\) | −18.9768 | −1.31580 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.123702 | 0.00853625 | ||||||||
\(211\) | 7.56636 | 0.520890 | 0.260445 | − | 0.965489i | \(-0.416131\pi\) | ||||
0.260445 | + | 0.965489i | \(0.416131\pi\) | |||||||
\(212\) | −12.8266 | −0.880931 | ||||||||
\(213\) | −0.990634 | −0.0678771 | ||||||||
\(214\) | 0.264019 | 0.0180480 | ||||||||
\(215\) | −2.00216 | −0.136546 | ||||||||
\(216\) | 1.16505 | 0.0792717 | ||||||||
\(217\) | −7.68895 | −0.521960 | ||||||||
\(218\) | 2.10430 | 0.142521 | ||||||||
\(219\) | −3.25362 | −0.219859 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.38167 | −0.496545 | ||||||||
\(222\) | −0.197501 | −0.0132554 | ||||||||
\(223\) | 17.5244 | 1.17352 | 0.586760 | − | 0.809761i | \(-0.300403\pi\) | ||||
0.586760 | + | 0.809761i | \(0.300403\pi\) | |||||||
\(224\) | 2.62252 | 0.175225 | ||||||||
\(225\) | −3.62397 | −0.241598 | ||||||||
\(226\) | −0.745893 | −0.0496161 | ||||||||
\(227\) | 25.6773 | 1.70426 | 0.852130 | − | 0.523330i | \(-0.175311\pi\) | ||||
0.852130 | + | 0.523330i | \(0.175311\pi\) | |||||||
\(228\) | 2.59152 | 0.171627 | ||||||||
\(229\) | −19.8369 | −1.31086 | −0.655429 | − | 0.755257i | \(-0.727512\pi\) | ||||
−0.655429 | + | 0.755257i | \(0.727512\pi\) | |||||||
\(230\) | 3.99842 | 0.263648 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.82205 | −0.382236 | ||||||||
\(233\) | 20.2146 | 1.32430 | 0.662151 | − | 0.749371i | \(-0.269644\pi\) | ||||
0.662151 | + | 0.749371i | \(0.269644\pi\) | |||||||
\(234\) | −3.42900 | −0.224161 | ||||||||
\(235\) | −16.8503 | −1.09919 | ||||||||
\(236\) | −5.60532 | −0.364875 | ||||||||
\(237\) | 0.537504 | 0.0349146 | ||||||||
\(238\) | 0.325184 | 0.0210786 | ||||||||
\(239\) | −17.1004 | −1.10613 | −0.553066 | − | 0.833137i | \(-0.686542\pi\) | ||||
−0.553066 | + | 0.833137i | \(0.686542\pi\) | |||||||
\(240\) | 2.02091 | 0.130449 | ||||||||
\(241\) | 24.1529 | 1.55582 | 0.777912 | − | 0.628373i | \(-0.216279\pi\) | ||||
0.777912 | + | 0.628373i | \(0.216279\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.79074 | −0.371476 | ||||||||
\(244\) | −1.66691 | −0.106713 | ||||||||
\(245\) | −2.49552 | −0.159433 | ||||||||
\(246\) | −0.334545 | −0.0213298 | ||||||||
\(247\) | −31.1615 | −1.98276 | ||||||||
\(248\) | 6.86831 | 0.436138 | ||||||||
\(249\) | 0.492559 | 0.0312147 | ||||||||
\(250\) | −2.12956 | −0.134685 | ||||||||
\(251\) | 11.8947 | 0.750790 | 0.375395 | − | 0.926865i | \(-0.377507\pi\) | ||||
0.375395 | + | 0.926865i | \(0.377507\pi\) | |||||||
\(252\) | −5.75291 | −0.362399 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.0654215 | −0.00410491 | ||||||||
\(255\) | 0.786100 | 0.0492275 | ||||||||
\(256\) | 12.0615 | 0.753845 | ||||||||
\(257\) | 22.9609 | 1.43226 | 0.716131 | − | 0.697966i | \(-0.245911\pi\) | ||||
0.716131 | + | 0.697966i | \(0.245911\pi\) | |||||||
\(258\) | 0.0397696 | 0.00247595 | ||||||||
\(259\) | 3.98432 | 0.247574 | ||||||||
\(260\) | −24.9732 | −1.54877 | ||||||||
\(261\) | 19.2401 | 1.19093 | ||||||||
\(262\) | −3.73381 | −0.230676 | ||||||||
\(263\) | −1.93774 | −0.119486 | −0.0597432 | − | 0.998214i | \(-0.519028\pi\) | ||||
−0.0597432 | + | 0.998214i | \(0.519028\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.4247 | −1.00896 | ||||||||
\(266\) | 1.37276 | 0.0841692 | ||||||||
\(267\) | −0.380335 | −0.0232761 | ||||||||
\(268\) | 3.20910 | 0.196027 | ||||||||
\(269\) | 7.18676 | 0.438184 | 0.219092 | − | 0.975704i | \(-0.429690\pi\) | ||||
0.219092 | + | 0.975704i | \(0.429690\pi\) | |||||||
\(270\) | 0.736273 | 0.0448081 | ||||||||
\(271\) | −1.19110 | −0.0723543 | −0.0361772 | − | 0.999345i | \(-0.511518\pi\) | ||||
−0.0361772 | + | 0.999345i | \(0.511518\pi\) | |||||||
\(272\) | 5.31250 | 0.322118 | ||||||||
\(273\) | −1.12523 | −0.0681018 | ||||||||
\(274\) | −2.10962 | −0.127447 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.02473 | 0.182067 | ||||||||
\(277\) | −10.3402 | −0.621285 | −0.310642 | − | 0.950527i | \(-0.600544\pi\) | ||||
−0.310642 | + | 0.950527i | \(0.600544\pi\) | |||||||
\(278\) | 1.09181 | 0.0654822 | ||||||||
\(279\) | −22.6977 | −1.35887 | ||||||||
\(280\) | 2.22918 | 0.133219 | ||||||||
\(281\) | 13.1513 | 0.784541 | 0.392271 | − | 0.919850i | \(-0.371690\pi\) | ||||
0.392271 | + | 0.919850i | \(0.371690\pi\) | |||||||
\(282\) | 0.334705 | 0.0199314 | ||||||||
\(283\) | −0.300031 | −0.0178350 | −0.00891748 | − | 0.999960i | \(-0.502839\pi\) | ||||
−0.00891748 | + | 0.999960i | \(0.502839\pi\) | |||||||
\(284\) | −8.81021 | −0.522790 | ||||||||
\(285\) | 3.31850 | 0.196571 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.74900 | 0.398381 | ||||||||
\(288\) | 7.74164 | 0.456181 | ||||||||
\(289\) | −14.9335 | −0.878443 | ||||||||
\(290\) | −3.67934 | −0.216058 | ||||||||
\(291\) | 2.64655 | 0.155143 | ||||||||
\(292\) | −28.9361 | −1.69336 | ||||||||
\(293\) | −16.1441 | −0.943148 | −0.471574 | − | 0.881826i | \(-0.656314\pi\) | ||||
−0.471574 | + | 0.881826i | \(0.656314\pi\) | |||||||
\(294\) | 0.0495696 | 0.00289096 | ||||||||
\(295\) | −7.17775 | −0.417905 | ||||||||
\(296\) | −3.55908 | −0.206867 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.208548 | 0.0120808 | ||||||||
\(299\) | −36.3707 | −2.10337 | ||||||||
\(300\) | 0.524258 | 0.0302680 | ||||||||
\(301\) | −0.802299 | −0.0462437 | ||||||||
\(302\) | 4.09361 | 0.235561 | ||||||||
\(303\) | −0.809329 | −0.0464947 | ||||||||
\(304\) | 22.4266 | 1.28625 | ||||||||
\(305\) | −2.13453 | −0.122223 | ||||||||
\(306\) | 0.959939 | 0.0548760 | ||||||||
\(307\) | 28.6376 | 1.63443 | 0.817217 | − | 0.576330i | \(-0.195516\pi\) | ||||
0.817217 | + | 0.576330i | \(0.195516\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.252341 | 0.0143552 | ||||||||
\(310\) | 4.34053 | 0.246526 | ||||||||
\(311\) | −31.8228 | −1.80450 | −0.902252 | − | 0.431210i | \(-0.858087\pi\) | ||||
−0.902252 | + | 0.431210i | \(0.858087\pi\) | |||||||
\(312\) | 1.00513 | 0.0569044 | ||||||||
\(313\) | 0.0342232 | 0.00193441 | 0.000967206 | − | 1.00000i | \(-0.499692\pi\) | ||||
0.000967206 | 1.00000i | \(0.499692\pi\) | ||||||||
\(314\) | 2.77636 | 0.156679 | ||||||||
\(315\) | −7.36674 | −0.415069 | ||||||||
\(316\) | 4.78029 | 0.268912 | ||||||||
\(317\) | 22.3894 | 1.25752 | 0.628758 | − | 0.777601i | \(-0.283564\pi\) | ||||
0.628758 | + | 0.777601i | \(0.283564\pi\) | |||||||
\(318\) | 0.326251 | 0.0182952 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 16.9644 | 0.948339 | ||||||||
\(321\) | 0.255754 | 0.0142748 | ||||||||
\(322\) | 1.60224 | 0.0892892 | ||||||||
\(323\) | 8.72359 | 0.485393 | ||||||||
\(324\) | −16.7017 | −0.927875 | ||||||||
\(325\) | −6.30391 | −0.349678 | ||||||||
\(326\) | −1.83211 | −0.101471 | ||||||||
\(327\) | 2.03842 | 0.112725 | ||||||||
\(328\) | −6.02868 | −0.332878 | ||||||||
\(329\) | −6.75222 | −0.372262 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.7577 | 0.591297 | 0.295648 | − | 0.955297i | \(-0.404464\pi\) | ||||
0.295648 | + | 0.955297i | \(0.404464\pi\) | |||||||
\(332\) | 4.38057 | 0.240415 | ||||||||
\(333\) | 11.7617 | 0.644535 | ||||||||
\(334\) | −2.95242 | −0.161549 | ||||||||
\(335\) | 4.10933 | 0.224517 | ||||||||
\(336\) | 0.809813 | 0.0441789 | ||||||||
\(337\) | −7.50492 | −0.408819 | −0.204410 | − | 0.978885i | \(-0.565527\pi\) | ||||
−0.204410 | + | 0.978885i | \(0.565527\pi\) | |||||||
\(338\) | −3.02401 | −0.164485 | ||||||||
\(339\) | −0.722542 | −0.0392431 | ||||||||
\(340\) | 6.99118 | 0.379150 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.05236 | 0.219126 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.716669 | 0.0386402 | ||||||||
\(345\) | 3.87325 | 0.208529 | ||||||||
\(346\) | 1.33740 | 0.0718993 | ||||||||
\(347\) | 27.6818 | 1.48604 | 0.743019 | − | 0.669271i | \(-0.233393\pi\) | ||||
0.743019 | + | 0.669271i | \(0.233393\pi\) | |||||||
\(348\) | −2.78335 | −0.149203 | ||||||||
\(349\) | 11.0605 | 0.592055 | 0.296028 | − | 0.955179i | \(-0.404338\pi\) | ||||
0.296028 | + | 0.955179i | \(0.404338\pi\) | |||||||
\(350\) | 0.277706 | 0.0148440 | ||||||||
\(351\) | −6.69733 | −0.357477 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.9202 | 1.69894 | 0.849469 | − | 0.527638i | \(-0.176922\pi\) | ||||
0.849469 | + | 0.527638i | \(0.176922\pi\) | |||||||
\(354\) | 0.142575 | 0.00757775 | ||||||||
\(355\) | −11.2817 | −0.598770 | ||||||||
\(356\) | −3.38251 | −0.179272 | ||||||||
\(357\) | 0.315004 | 0.0166718 | ||||||||
\(358\) | −0.980644 | −0.0518286 | ||||||||
\(359\) | −3.57826 | −0.188854 | −0.0944268 | − | 0.995532i | \(-0.530102\pi\) | ||||
−0.0944268 | + | 0.995532i | \(0.530102\pi\) | |||||||
\(360\) | 6.58049 | 0.346822 | ||||||||
\(361\) | 17.8264 | 0.938233 | ||||||||
\(362\) | −2.45003 | −0.128771 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.0072 | −0.524520 | ||||||||
\(365\) | −37.0534 | −1.93946 | ||||||||
\(366\) | 0.0423989 | 0.00221623 | ||||||||
\(367\) | 2.29397 | 0.119744 | 0.0598720 | − | 0.998206i | \(-0.480931\pi\) | ||||
0.0598720 | + | 0.998206i | \(0.480931\pi\) | |||||||
\(368\) | 26.1756 | 1.36450 | ||||||||
\(369\) | 19.9229 | 1.03715 | ||||||||
\(370\) | −2.24921 | −0.116931 | ||||||||
\(371\) | −6.58167 | −0.341703 | ||||||||
\(372\) | 3.28354 | 0.170243 | ||||||||
\(373\) | −7.96856 | −0.412596 | −0.206298 | − | 0.978489i | \(-0.566142\pi\) | ||||
−0.206298 | + | 0.978489i | \(0.566142\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.06289 | −0.106527 | ||||||||
\(376\) | 6.03155 | 0.311054 | ||||||||
\(377\) | 33.4682 | 1.72370 | ||||||||
\(378\) | 0.295037 | 0.0151751 | ||||||||
\(379\) | −11.6212 | −0.596941 | −0.298470 | − | 0.954419i | \(-0.596476\pi\) | ||||
−0.298470 | + | 0.954419i | \(0.596476\pi\) | |||||||
\(380\) | 29.5131 | 1.51399 | ||||||||
\(381\) | −0.0633734 | −0.00324672 | ||||||||
\(382\) | −2.63663 | −0.134902 | ||||||||
\(383\) | 12.5785 | 0.642729 | 0.321364 | − | 0.946956i | \(-0.395859\pi\) | ||||
0.321364 | + | 0.946956i | \(0.395859\pi\) | |||||||
\(384\) | −1.48632 | −0.0758482 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.07741 | 0.258433 | ||||||||
\(387\) | −2.36837 | −0.120391 | ||||||||
\(388\) | 23.5371 | 1.19491 | ||||||||
\(389\) | −0.438294 | −0.0222224 | −0.0111112 | − | 0.999938i | \(-0.503537\pi\) | ||||
−0.0111112 | + | 0.999938i | \(0.503537\pi\) | |||||||
\(390\) | 0.635208 | 0.0321650 | ||||||||
\(391\) | 10.1819 | 0.514920 | ||||||||
\(392\) | 0.893270 | 0.0451169 | ||||||||
\(393\) | −3.61692 | −0.182450 | ||||||||
\(394\) | 5.45218 | 0.274677 | ||||||||
\(395\) | 6.12128 | 0.307995 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.8147 | 0.843905 | 0.421952 | − | 0.906618i | \(-0.361345\pi\) | ||||
0.421952 | + | 0.906618i | \(0.361345\pi\) | |||||||
\(398\) | −4.23480 | −0.212271 | ||||||||
\(399\) | 1.32978 | 0.0665724 | ||||||||
\(400\) | 4.53685 | 0.226842 | ||||||||
\(401\) | 36.8609 | 1.84074 | 0.920372 | − | 0.391043i | \(-0.127886\pi\) | ||||
0.920372 | + | 0.391043i | \(0.127886\pi\) | |||||||
\(402\) | −0.0816253 | −0.00407110 | ||||||||
\(403\) | −39.4827 | −1.96677 | ||||||||
\(404\) | −7.19776 | −0.358102 | ||||||||
\(405\) | −21.3870 | −1.06273 | ||||||||
\(406\) | −1.47437 | −0.0731720 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.281384 | −0.0139306 | ||||||||
\(409\) | −16.2739 | −0.804692 | −0.402346 | − | 0.915488i | \(-0.631805\pi\) | ||||
−0.402346 | + | 0.915488i | \(0.631805\pi\) | |||||||
\(410\) | −3.80992 | −0.188158 | ||||||||
\(411\) | −2.04357 | −0.100802 | ||||||||
\(412\) | 2.24420 | 0.110564 | ||||||||
\(413\) | −2.87625 | −0.141531 | ||||||||
\(414\) | 4.72978 | 0.232456 | ||||||||
\(415\) | 5.60944 | 0.275356 | ||||||||
\(416\) | 13.4666 | 0.660255 | ||||||||
\(417\) | 1.05763 | 0.0517922 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.56352 | 0.271796 | 0.135898 | − | 0.990723i | \(-0.456608\pi\) | ||||
0.135898 | + | 0.990723i | \(0.456608\pi\) | |||||||
\(420\) | 1.06570 | 0.0520010 | ||||||||
\(421\) | 21.4914 | 1.04743 | 0.523713 | − | 0.851895i | \(-0.324546\pi\) | ||||
0.523713 | + | 0.851895i | \(0.324546\pi\) | |||||||
\(422\) | −1.71160 | −0.0833192 | ||||||||
\(423\) | −19.9324 | −0.969148 | ||||||||
\(424\) | 5.87921 | 0.285520 | ||||||||
\(425\) | 1.76476 | 0.0856035 | ||||||||
\(426\) | 0.224093 | 0.0108573 | ||||||||
\(427\) | −0.855342 | −0.0413929 | ||||||||
\(428\) | 2.27455 | 0.109944 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.452910 | 0.0218413 | ||||||||
\(431\) | 27.7188 | 1.33517 | 0.667583 | − | 0.744536i | \(-0.267329\pi\) | ||||
0.667583 | + | 0.744536i | \(0.267329\pi\) | |||||||
\(432\) | 4.81999 | 0.231902 | ||||||||
\(433\) | 9.28812 | 0.446358 | 0.223179 | − | 0.974777i | \(-0.428356\pi\) | ||||
0.223179 | + | 0.974777i | \(0.428356\pi\) | |||||||
\(434\) | 1.73933 | 0.0834904 | ||||||||
\(435\) | −3.56415 | −0.170888 | ||||||||
\(436\) | 18.1287 | 0.868206 | ||||||||
\(437\) | 42.9826 | 2.05613 | ||||||||
\(438\) | 0.736006 | 0.0351678 | ||||||||
\(439\) | 14.7118 | 0.702156 | 0.351078 | − | 0.936346i | \(-0.385815\pi\) | ||||
0.351078 | + | 0.936346i | \(0.385815\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.95198 | −0.140571 | ||||||||
\(442\) | 1.66982 | 0.0794251 | ||||||||
\(443\) | 2.44345 | 0.116092 | 0.0580459 | − | 0.998314i | \(-0.481513\pi\) | ||||
0.0580459 | + | 0.998314i | \(0.481513\pi\) | |||||||
\(444\) | −1.70149 | −0.0807491 | ||||||||
\(445\) | −4.33138 | −0.205327 | ||||||||
\(446\) | −3.96421 | −0.187711 | ||||||||
\(447\) | 0.202019 | 0.00955516 | ||||||||
\(448\) | 6.79793 | 0.321172 | ||||||||
\(449\) | 4.76935 | 0.225080 | 0.112540 | − | 0.993647i | \(-0.464101\pi\) | ||||
0.112540 | + | 0.993647i | \(0.464101\pi\) | |||||||
\(450\) | 0.819782 | 0.0386449 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.42593 | −0.302250 | ||||||||
\(453\) | 3.96546 | 0.186313 | ||||||||
\(454\) | −5.80849 | −0.272606 | ||||||||
\(455\) | −12.8145 | −0.600752 | ||||||||
\(456\) | −1.18785 | −0.0556264 | ||||||||
\(457\) | −31.0875 | −1.45421 | −0.727106 | − | 0.686525i | \(-0.759135\pi\) | ||||
−0.727106 | + | 0.686525i | \(0.759135\pi\) | |||||||
\(458\) | 4.48733 | 0.209679 | ||||||||
\(459\) | 1.87490 | 0.0875128 | ||||||||
\(460\) | 34.4467 | 1.60609 | ||||||||
\(461\) | −29.7215 | −1.38427 | −0.692134 | − | 0.721769i | \(-0.743329\pi\) | ||||
−0.692134 | + | 0.721769i | \(0.743329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.4553 | −1.18301 | −0.591505 | − | 0.806302i | \(-0.701466\pi\) | ||||
−0.591505 | + | 0.806302i | \(0.701466\pi\) | |||||||
\(464\) | −24.0867 | −1.11820 | ||||||||
\(465\) | 4.20465 | 0.194986 | ||||||||
\(466\) | −4.57277 | −0.211829 | ||||||||
\(467\) | −3.18491 | −0.147380 | −0.0736901 | − | 0.997281i | \(-0.523478\pi\) | ||||
−0.0736901 | + | 0.997281i | \(0.523478\pi\) | |||||||
\(468\) | −29.5411 | −1.36554 | ||||||||
\(469\) | 1.64668 | 0.0760366 | ||||||||
\(470\) | 3.81173 | 0.175822 | ||||||||
\(471\) | 2.68945 | 0.123923 | ||||||||
\(472\) | 2.56927 | 0.118260 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −0.121590 | −0.00558479 | ||||||||
\(475\) | 7.44990 | 0.341825 | ||||||||
\(476\) | 2.80149 | 0.128406 | ||||||||
\(477\) | −19.4290 | −0.889592 | ||||||||
\(478\) | 3.86830 | 0.176932 | ||||||||
\(479\) | −3.23354 | −0.147744 | −0.0738720 | − | 0.997268i | \(-0.523536\pi\) | ||||
−0.0738720 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(480\) | −1.43411 | −0.0654578 | ||||||||
\(481\) | 20.4594 | 0.932870 | ||||||||
\(482\) | −5.46366 | −0.248863 | ||||||||
\(483\) | 1.55208 | 0.0706220 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 30.1398 | 1.36858 | ||||||||
\(486\) | 1.30993 | 0.0594197 | ||||||||
\(487\) | 9.87096 | 0.447296 | 0.223648 | − | 0.974670i | \(-0.428203\pi\) | ||||
0.223648 | + | 0.974670i | \(0.428203\pi\) | |||||||
\(488\) | 0.764051 | 0.0345870 | ||||||||
\(489\) | −1.77476 | −0.0802573 | ||||||||
\(490\) | 0.564516 | 0.0255022 | ||||||||
\(491\) | −4.22600 | −0.190717 | −0.0953584 | − | 0.995443i | \(-0.530400\pi\) | ||||
−0.0953584 | + | 0.995443i | \(0.530400\pi\) | |||||||
\(492\) | −2.88213 | −0.129937 | ||||||||
\(493\) | −9.36933 | −0.421974 | ||||||||
\(494\) | 7.04910 | 0.317154 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.4152 | 1.27588 | ||||||||
\(497\) | −4.52077 | −0.202784 | ||||||||
\(498\) | −0.111422 | −0.00499296 | ||||||||
\(499\) | −20.3953 | −0.913018 | −0.456509 | − | 0.889719i | \(-0.650900\pi\) | ||||
−0.456509 | + | 0.889719i | \(0.650900\pi\) | |||||||
\(500\) | −18.3463 | −0.820472 | ||||||||
\(501\) | −2.85999 | −0.127775 | ||||||||
\(502\) | −2.69073 | −0.120093 | ||||||||
\(503\) | 23.9593 | 1.06829 | 0.534145 | − | 0.845393i | \(-0.320634\pi\) | ||||
0.534145 | + | 0.845393i | \(0.320634\pi\) | |||||||
\(504\) | 2.63692 | 0.117458 | ||||||||
\(505\) | −9.21692 | −0.410147 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.92934 | −0.130097 | ||||||||
\(508\) | −0.563611 | −0.0250062 | ||||||||
\(509\) | 3.69341 | 0.163708 | 0.0818538 | − | 0.996644i | \(-0.473916\pi\) | ||||
0.0818538 | + | 0.996644i | \(0.473916\pi\) | |||||||
\(510\) | −0.177825 | −0.00787421 | ||||||||
\(511\) | −14.8479 | −0.656834 | ||||||||
\(512\) | −16.2941 | −0.720104 | ||||||||
\(513\) | 7.91484 | 0.349449 | ||||||||
\(514\) | −5.19402 | −0.229098 | ||||||||
\(515\) | 2.87375 | 0.126633 | ||||||||
\(516\) | 0.342618 | 0.0150829 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.901299 | −0.0396008 | ||||||||
\(519\) | 1.29554 | 0.0568677 | ||||||||
\(520\) | 11.4468 | 0.501975 | ||||||||
\(521\) | −0.238270 | −0.0104388 | −0.00521939 | − | 0.999986i | \(-0.501661\pi\) | ||||
−0.00521939 | + | 0.999986i | \(0.501661\pi\) | |||||||
\(522\) | −4.35233 | −0.190496 | ||||||||
\(523\) | 21.9914 | 0.961618 | 0.480809 | − | 0.876825i | \(-0.340343\pi\) | ||||
0.480809 | + | 0.876825i | \(0.340343\pi\) | |||||||
\(524\) | −32.1671 | −1.40523 | ||||||||
\(525\) | 0.269012 | 0.0117406 | ||||||||
\(526\) | 0.438339 | 0.0191125 | ||||||||
\(527\) | 11.0531 | 0.481479 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.1678 | 1.18121 | ||||||||
\(530\) | 3.71546 | 0.161389 | ||||||||
\(531\) | −8.49064 | −0.368462 | ||||||||
\(532\) | 11.8264 | 0.512740 | ||||||||
\(533\) | 34.6560 | 1.50112 | ||||||||
\(534\) | 0.0860360 | 0.00372314 | ||||||||
\(535\) | 2.91262 | 0.125923 | ||||||||
\(536\) | −1.47093 | −0.0635345 | ||||||||
\(537\) | −0.949944 | −0.0409931 | ||||||||
\(538\) | −1.62573 | −0.0700900 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.34305 | 0.272961 | ||||||||
\(541\) | −28.6309 | −1.23094 | −0.615470 | − | 0.788161i | \(-0.711034\pi\) | ||||
−0.615470 | + | 0.788161i | \(0.711034\pi\) | |||||||
\(542\) | 0.269441 | 0.0115735 | ||||||||
\(543\) | −2.37333 | −0.101849 | ||||||||
\(544\) | −3.76994 | −0.161635 | ||||||||
\(545\) | 23.2142 | 0.994388 | ||||||||
\(546\) | 0.254539 | 0.0108933 | ||||||||
\(547\) | −6.40847 | −0.274007 | −0.137003 | − | 0.990571i | \(-0.543747\pi\) | ||||
−0.137003 | + | 0.990571i | \(0.543747\pi\) | |||||||
\(548\) | −18.1745 | −0.776378 | ||||||||
\(549\) | −2.52495 | −0.107762 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.5524 | −1.68499 | ||||||||
\(552\) | −1.38642 | −0.0590101 | ||||||||
\(553\) | 2.45291 | 0.104308 | ||||||||
\(554\) | 2.33908 | 0.0993780 | ||||||||
\(555\) | −2.17880 | −0.0924849 | ||||||||
\(556\) | 9.40600 | 0.398903 | ||||||||
\(557\) | 22.5193 | 0.954172 | 0.477086 | − | 0.878857i | \(-0.341693\pi\) | ||||
0.477086 | + | 0.878857i | \(0.341693\pi\) | |||||||
\(558\) | 5.13447 | 0.217359 | ||||||||
\(559\) | −4.11979 | −0.174249 | ||||||||
\(560\) | 9.22243 | 0.389719 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.97498 | −0.125492 | ||||||||
\(563\) | 29.8267 | 1.25705 | 0.628523 | − | 0.777791i | \(-0.283660\pi\) | ||||
0.628523 | + | 0.777791i | \(0.283660\pi\) | |||||||
\(564\) | 2.88351 | 0.121418 | ||||||||
\(565\) | −8.22856 | −0.346178 | ||||||||
\(566\) | 0.0678703 | 0.00285280 | ||||||||
\(567\) | −8.57015 | −0.359912 | ||||||||
\(568\) | 4.03827 | 0.169442 | ||||||||
\(569\) | −29.2764 | −1.22733 | −0.613665 | − | 0.789567i | \(-0.710305\pi\) | ||||
−0.613665 | + | 0.789567i | \(0.710305\pi\) | |||||||
\(570\) | −0.750683 | −0.0314427 | ||||||||
\(571\) | −37.9252 | −1.58712 | −0.793559 | − | 0.608493i | \(-0.791774\pi\) | ||||
−0.793559 | + | 0.608493i | \(0.791774\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.55409 | −0.106699 | ||||||||
\(574\) | −1.52670 | −0.0637232 | ||||||||
\(575\) | 8.69527 | 0.362618 | ||||||||
\(576\) | 20.0674 | 0.836141 | ||||||||
\(577\) | 8.77263 | 0.365209 | 0.182605 | − | 0.983186i | \(-0.441547\pi\) | ||||
0.182605 | + | 0.983186i | \(0.441547\pi\) | |||||||
\(578\) | 3.37813 | 0.140512 | ||||||||
\(579\) | 4.91846 | 0.204404 | ||||||||
\(580\) | −31.6978 | −1.31618 | ||||||||
\(581\) | 2.24780 | 0.0932544 | ||||||||
\(582\) | −0.598679 | −0.0248161 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 13.2632 | 0.548836 | ||||||||
\(585\) | −37.8281 | −1.56400 | ||||||||
\(586\) | 3.65198 | 0.150862 | ||||||||
\(587\) | 9.17011 | 0.378491 | 0.189246 | − | 0.981930i | \(-0.439396\pi\) | ||||
0.189246 | + | 0.981930i | \(0.439396\pi\) | |||||||
\(588\) | 0.427046 | 0.0176111 | ||||||||
\(589\) | 46.6602 | 1.92260 | ||||||||
\(590\) | 1.62369 | 0.0668462 | ||||||||
\(591\) | 5.28150 | 0.217252 | ||||||||
\(592\) | −14.7244 | −0.605170 | ||||||||
\(593\) | −7.25596 | −0.297967 | −0.148983 | − | 0.988840i | \(-0.547600\pi\) | ||||
−0.148983 | + | 0.988840i | \(0.547600\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.58738 | 0.147068 | ||||||||
\(596\) | 1.79665 | 0.0735938 | ||||||||
\(597\) | −4.10222 | −0.167893 | ||||||||
\(598\) | 8.22747 | 0.336446 | ||||||||
\(599\) | −20.0181 | −0.817916 | −0.408958 | − | 0.912553i | \(-0.634108\pi\) | ||||
−0.408958 | + | 0.912553i | \(0.634108\pi\) | |||||||
\(600\) | −0.240300 | −0.00981021 | ||||||||
\(601\) | 11.2706 | 0.459736 | 0.229868 | − | 0.973222i | \(-0.426171\pi\) | ||||
0.229868 | + | 0.973222i | \(0.426171\pi\) | |||||||
\(602\) | 0.181489 | 0.00739694 | ||||||||
\(603\) | 4.86097 | 0.197954 | ||||||||
\(604\) | 35.2668 | 1.43499 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.183079 | 0.00743709 | ||||||||
\(607\) | 13.5260 | 0.549005 | 0.274502 | − | 0.961586i | \(-0.411487\pi\) | ||||
0.274502 | + | 0.961586i | \(0.411487\pi\) | |||||||
\(608\) | −15.9147 | −0.645427 | ||||||||
\(609\) | −1.42822 | −0.0578743 | ||||||||
\(610\) | 0.482854 | 0.0195502 | ||||||||
\(611\) | −34.6725 | −1.40270 | ||||||||
\(612\) | 8.26995 | 0.334293 | ||||||||
\(613\) | 30.7968 | 1.24387 | 0.621935 | − | 0.783069i | \(-0.286347\pi\) | ||||
0.621935 | + | 0.783069i | \(0.286347\pi\) | |||||||
\(614\) | −6.47815 | −0.261437 | ||||||||
\(615\) | −3.69064 | −0.148821 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.6896 | 0.953707 | 0.476853 | − | 0.878983i | \(-0.341777\pi\) | ||||
0.476853 | + | 0.878983i | \(0.341777\pi\) | |||||||
\(618\) | −0.0570825 | −0.00229619 | ||||||||
\(619\) | −32.4878 | −1.30579 | −0.652897 | − | 0.757446i | \(-0.726447\pi\) | ||||
−0.652897 | + | 0.757446i | \(0.726447\pi\) | |||||||
\(620\) | 37.3940 | 1.50178 | ||||||||
\(621\) | 9.23794 | 0.370706 | ||||||||
\(622\) | 7.19867 | 0.288640 | ||||||||
\(623\) | −1.73566 | −0.0695378 | ||||||||
\(624\) | 4.15838 | 0.166468 | ||||||||
\(625\) | −29.6311 | −1.18524 | ||||||||
\(626\) | −0.00774169 | −0.000309420 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 23.9186 | 0.954456 | ||||||||
\(629\) | −5.72756 | −0.228373 | ||||||||
\(630\) | 1.66644 | 0.0663926 | ||||||||
\(631\) | −15.1333 | −0.602448 | −0.301224 | − | 0.953553i | \(-0.597395\pi\) | ||||
−0.301224 | + | 0.953553i | \(0.597395\pi\) | |||||||
\(632\) | −2.19111 | −0.0871575 | ||||||||
\(633\) | −1.65801 | −0.0659001 | ||||||||
\(634\) | −5.06474 | −0.201147 | ||||||||
\(635\) | −0.721718 | −0.0286405 | ||||||||
\(636\) | 2.81068 | 0.111451 | ||||||||
\(637\) | −5.13499 | −0.203456 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.3452 | −0.527929 | ||||||||
\(640\) | −16.9267 | −0.669086 | ||||||||
\(641\) | −16.5502 | −0.653695 | −0.326848 | − | 0.945077i | \(-0.605986\pi\) | ||||
−0.326848 | + | 0.945077i | \(0.605986\pi\) | |||||||
\(642\) | −0.0578545 | −0.00228333 | ||||||||
\(643\) | 1.99506 | 0.0786773 | 0.0393387 | − | 0.999226i | \(-0.487475\pi\) | ||||
0.0393387 | + | 0.999226i | \(0.487475\pi\) | |||||||
\(644\) | 13.8034 | 0.543930 | ||||||||
\(645\) | 0.438731 | 0.0172750 | ||||||||
\(646\) | −1.97337 | −0.0776414 | ||||||||
\(647\) | 40.4517 | 1.59032 | 0.795160 | − | 0.606399i | \(-0.207387\pi\) | ||||
0.795160 | + | 0.606399i | \(0.207387\pi\) | |||||||
\(648\) | 7.65545 | 0.300735 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.42602 | 0.0559329 | ||||||||
\(651\) | 1.68488 | 0.0660355 | ||||||||
\(652\) | −15.7838 | −0.618142 | ||||||||
\(653\) | −41.4856 | −1.62346 | −0.811729 | − | 0.584034i | \(-0.801473\pi\) | ||||
−0.811729 | + | 0.584034i | \(0.801473\pi\) | |||||||
\(654\) | −0.461113 | −0.0180310 | ||||||||
\(655\) | −41.1908 | −1.60946 | ||||||||
\(656\) | −24.9415 | −0.973803 | ||||||||
\(657\) | −43.8309 | −1.71001 | ||||||||
\(658\) | 1.52743 | 0.0595454 | ||||||||
\(659\) | 51.1359 | 1.99197 | 0.995985 | − | 0.0895158i | \(-0.0285320\pi\) | ||||
0.995985 | + | 0.0895158i | \(0.0285320\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.8840 | −1.66800 | −0.833998 | − | 0.551768i | \(-0.813954\pi\) | ||||
−0.833998 | + | 0.551768i | \(0.813954\pi\) | |||||||
\(662\) | −2.43351 | −0.0945812 | ||||||||
\(663\) | 1.61754 | 0.0628201 | ||||||||
\(664\) | −2.00789 | −0.0779213 | ||||||||
\(665\) | 15.1440 | 0.587260 | ||||||||
\(666\) | −2.66062 | −0.103097 | ||||||||
\(667\) | −46.1643 | −1.78749 | ||||||||
\(668\) | −25.4353 | −0.984122 | ||||||||
\(669\) | −3.84011 | −0.148467 | ||||||||
\(670\) | −0.929577 | −0.0359127 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −0.574672 | −0.0221685 | ||||||||
\(673\) | 25.0072 | 0.963958 | 0.481979 | − | 0.876183i | \(-0.339918\pi\) | ||||
0.481979 | + | 0.876183i | \(0.339918\pi\) | |||||||
\(674\) | 1.69770 | 0.0653929 | ||||||||
\(675\) | 1.60115 | 0.0616284 | ||||||||
\(676\) | −26.0521 | −1.00200 | ||||||||
\(677\) | 9.91890 | 0.381214 | 0.190607 | − | 0.981666i | \(-0.438954\pi\) | ||||
0.190607 | + | 0.981666i | \(0.438954\pi\) | |||||||
\(678\) | 0.163447 | 0.00627715 | ||||||||
\(679\) | 12.0776 | 0.463494 | ||||||||
\(680\) | −3.20450 | −0.122887 | ||||||||
\(681\) | −5.62665 | −0.215614 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −39.8980 | −1.52666 | −0.763328 | − | 0.646011i | \(-0.776436\pi\) | ||||
−0.763328 | + | 0.646011i | \(0.776436\pi\) | |||||||
\(684\) | 34.9114 | 1.33487 | ||||||||
\(685\) | −23.2729 | −0.889214 | ||||||||
\(686\) | 0.226211 | 0.00863679 | ||||||||
\(687\) | 4.34685 | 0.165843 | ||||||||
\(688\) | 2.96497 | 0.113038 | ||||||||
\(689\) | −33.7968 | −1.28756 | ||||||||
\(690\) | −0.876172 | −0.0333553 | ||||||||
\(691\) | −6.61401 | −0.251609 | −0.125804 | − | 0.992055i | \(-0.540151\pi\) | ||||
−0.125804 | + | 0.992055i | \(0.540151\pi\) | |||||||
\(692\) | 11.5218 | 0.437995 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.26194 | −0.237700 | ||||||||
\(695\) | 12.0446 | 0.456878 | ||||||||
\(696\) | 1.27578 | 0.0483585 | ||||||||
\(697\) | −9.70185 | −0.367484 | ||||||||
\(698\) | −2.50201 | −0.0947025 | ||||||||
\(699\) | −4.42961 | −0.167543 | ||||||||
\(700\) | 2.39246 | 0.0904264 | ||||||||
\(701\) | −14.6016 | −0.551495 | −0.275748 | − | 0.961230i | \(-0.588925\pi\) | ||||
−0.275748 | + | 0.961230i | \(0.588925\pi\) | |||||||
\(702\) | 1.51501 | 0.0571805 | ||||||||
\(703\) | −24.1788 | −0.911920 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.69240 | 0.139064 | ||||||||
\(706\) | −7.22070 | −0.271755 | ||||||||
\(707\) | −3.69338 | −0.138904 | ||||||||
\(708\) | 1.22829 | 0.0461620 | ||||||||
\(709\) | −4.14406 | −0.155633 | −0.0778167 | − | 0.996968i | \(-0.524795\pi\) | ||||
−0.0778167 | + | 0.996968i | \(0.524795\pi\) | |||||||
\(710\) | 2.55205 | 0.0957766 | ||||||||
\(711\) | 7.24093 | 0.271556 | ||||||||
\(712\) | 1.55041 | 0.0581042 | ||||||||
\(713\) | 54.4602 | 2.03955 | ||||||||
\(714\) | −0.0712575 | −0.00266674 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.44832 | −0.315729 | ||||||||
\(717\) | 3.74720 | 0.139942 | ||||||||
\(718\) | 0.809444 | 0.0302082 | ||||||||
\(719\) | 17.0223 | 0.634823 | 0.317412 | − | 0.948288i | \(-0.397186\pi\) | ||||
0.317412 | + | 0.948288i | \(0.397186\pi\) | |||||||
\(720\) | 27.2245 | 1.01460 | ||||||||
\(721\) | 1.15156 | 0.0428864 | ||||||||
\(722\) | −4.03254 | −0.150076 | ||||||||
\(723\) | −5.29261 | −0.196834 | ||||||||
\(724\) | −21.1072 | −0.784442 | ||||||||
\(725\) | −8.00136 | −0.297163 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.6199 | −0.801837 | −0.400918 | − | 0.916114i | \(-0.631309\pi\) | ||||
−0.400918 | + | 0.916114i | \(0.631309\pi\) | |||||||
\(728\) | 4.58693 | 0.170003 | ||||||||
\(729\) | −24.4415 | −0.905241 | ||||||||
\(730\) | 8.38190 | 0.310228 | ||||||||
\(731\) | 1.15332 | 0.0426572 | ||||||||
\(732\) | 0.365270 | 0.0135008 | ||||||||
\(733\) | 48.2326 | 1.78151 | 0.890755 | − | 0.454484i | \(-0.150176\pi\) | ||||
0.890755 | + | 0.454484i | \(0.150176\pi\) | |||||||
\(734\) | −0.518921 | −0.0191537 | ||||||||
\(735\) | 0.546843 | 0.0201706 | ||||||||
\(736\) | −18.5751 | −0.684688 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −4.50679 | −0.165897 | ||||||||
\(739\) | 8.16347 | 0.300298 | 0.150149 | − | 0.988663i | \(-0.452025\pi\) | ||||
0.150149 | + | 0.988663i | \(0.452025\pi\) | |||||||
\(740\) | −19.3772 | −0.712318 | ||||||||
\(741\) | 6.82842 | 0.250848 | ||||||||
\(742\) | 1.48885 | 0.0546574 | ||||||||
\(743\) | −19.5612 | −0.717633 | −0.358816 | − | 0.933408i | \(-0.616820\pi\) | ||||
−0.358816 | + | 0.933408i | \(0.616820\pi\) | |||||||
\(744\) | −1.50505 | −0.0551778 | ||||||||
\(745\) | 2.30066 | 0.0842897 | ||||||||
\(746\) | 1.80258 | 0.0659971 | ||||||||
\(747\) | 6.63546 | 0.242779 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.16714 | 0.0426462 | ||||||||
\(750\) | 0.466649 | 0.0170396 | ||||||||
\(751\) | 1.11630 | 0.0407343 | 0.0203671 | − | 0.999793i | \(-0.493516\pi\) | ||||
0.0203671 | + | 0.999793i | \(0.493516\pi\) | |||||||
\(752\) | 24.9534 | 0.909958 | ||||||||
\(753\) | −2.60649 | −0.0949858 | ||||||||
\(754\) | −7.57089 | −0.275716 | ||||||||
\(755\) | 45.1600 | 1.64354 | ||||||||
\(756\) | 2.54177 | 0.0924433 | ||||||||
\(757\) | −26.5773 | −0.965969 | −0.482984 | − | 0.875629i | \(-0.660447\pi\) | ||||
−0.482984 | + | 0.875629i | \(0.660447\pi\) | |||||||
\(758\) | 2.62885 | 0.0954840 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.5277 | −0.490701 | ||||||||
\(761\) | −6.30003 | −0.228376 | −0.114188 | − | 0.993459i | \(-0.536427\pi\) | ||||
−0.114188 | + | 0.993459i | \(0.536427\pi\) | |||||||
\(762\) | 0.0143358 | 0.000519330 0 | ||||||||
\(763\) | 9.30234 | 0.336767 | ||||||||
\(764\) | −22.7148 | −0.821792 | ||||||||
\(765\) | 10.5899 | 0.382878 | ||||||||
\(766\) | −2.84539 | −0.102808 | ||||||||
\(767\) | −14.7695 | −0.533296 | ||||||||
\(768\) | −2.64303 | −0.0953723 | ||||||||
\(769\) | −13.1916 | −0.475700 | −0.237850 | − | 0.971302i | \(-0.576443\pi\) | ||||
−0.237850 | + | 0.971302i | \(0.576443\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.03141 | −0.181202 | ||||||||
\(772\) | 43.7423 | 1.57432 | ||||||||
\(773\) | 45.8178 | 1.64795 | 0.823976 | − | 0.566625i | \(-0.191751\pi\) | ||||
0.823976 | + | 0.566625i | \(0.191751\pi\) | |||||||
\(774\) | 0.535752 | 0.0192572 | ||||||||
\(775\) | 9.43925 | 0.339068 | ||||||||
\(776\) | −10.7885 | −0.387285 | ||||||||
\(777\) | −0.873083 | −0.0313217 | ||||||||
\(778\) | 0.0991470 | 0.00355459 | ||||||||
\(779\) | −40.9562 | −1.46741 | ||||||||
\(780\) | 5.47237 | 0.195942 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −2.30326 | −0.0823643 | ||||||||
\(783\) | −8.50073 | −0.303791 | ||||||||
\(784\) | 3.69559 | 0.131985 | ||||||||
\(785\) | 30.6284 | 1.09317 | ||||||||
\(786\) | 0.818189 | 0.0291838 | ||||||||
\(787\) | 18.8479 | 0.671856 | 0.335928 | − | 0.941888i | \(-0.390950\pi\) | ||||
0.335928 | + | 0.941888i | \(0.390950\pi\) | |||||||
\(788\) | 46.9710 | 1.67327 | ||||||||
\(789\) | 0.424617 | 0.0151168 | ||||||||
\(790\) | −1.38470 | −0.0492656 | ||||||||
\(791\) | −3.29733 | −0.117240 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.39217 | −0.155970 | ||||||||
\(794\) | −3.80367 | −0.134987 | ||||||||
\(795\) | 3.59914 | 0.127648 | ||||||||
\(796\) | −36.4831 | −1.29311 | ||||||||
\(797\) | −28.1613 | −0.997526 | −0.498763 | − | 0.866738i | \(-0.666212\pi\) | ||||
−0.498763 | + | 0.866738i | \(0.666212\pi\) | |||||||
\(798\) | −0.300812 | −0.0106486 | ||||||||
\(799\) | 9.70648 | 0.343391 | ||||||||
\(800\) | −3.21951 | −0.113827 | ||||||||
\(801\) | −5.12364 | −0.181035 | ||||||||
\(802\) | −8.33835 | −0.294437 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.703208 | −0.0248002 | ||||||||
\(805\) | 17.6756 | 0.622983 | ||||||||
\(806\) | 8.93143 | 0.314596 | ||||||||
\(807\) | −1.57483 | −0.0554367 | ||||||||
\(808\) | 3.29919 | 0.116065 | ||||||||
\(809\) | 6.54552 | 0.230128 | 0.115064 | − | 0.993358i | \(-0.463293\pi\) | ||||
0.115064 | + | 0.993358i | \(0.463293\pi\) | |||||||
\(810\) | 4.83798 | 0.169989 | ||||||||
\(811\) | −18.8046 | −0.660320 | −0.330160 | − | 0.943925i | \(-0.607103\pi\) | ||||
−0.330160 | + | 0.943925i | \(0.607103\pi\) | |||||||
\(812\) | −12.7019 | −0.445748 | ||||||||
\(813\) | 0.261006 | 0.00915387 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.2116 | −0.707980 | ||||||||
\(816\) | −1.16413 | −0.0407526 | ||||||||
\(817\) | 4.86873 | 0.170335 | ||||||||
\(818\) | 3.68134 | 0.128715 | ||||||||
\(819\) | −15.1584 | −0.529677 | ||||||||
\(820\) | −32.8227 | −1.14622 | ||||||||
\(821\) | 11.5880 | 0.404424 | 0.202212 | − | 0.979342i | \(-0.435187\pi\) | ||||
0.202212 | + | 0.979342i | \(0.435187\pi\) | |||||||
\(822\) | 0.462280 | 0.0161239 | ||||||||
\(823\) | 12.3464 | 0.430368 | 0.215184 | − | 0.976574i | \(-0.430965\pi\) | ||||
0.215184 | + | 0.976574i | \(0.430965\pi\) | |||||||
\(824\) | −1.02866 | −0.0358349 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.650640 | 0.0226387 | ||||||||
\(827\) | 4.49579 | 0.156334 | 0.0781669 | − | 0.996940i | \(-0.475093\pi\) | ||||
0.0781669 | + | 0.996940i | \(0.475093\pi\) | |||||||
\(828\) | 40.7474 | 1.41607 | ||||||||
\(829\) | −19.8629 | −0.689866 | −0.344933 | − | 0.938627i | \(-0.612098\pi\) | ||||
−0.344933 | + | 0.938627i | \(0.612098\pi\) | |||||||
\(830\) | −1.26892 | −0.0440448 | ||||||||
\(831\) | 2.26585 | 0.0786015 | ||||||||
\(832\) | 34.9073 | 1.21019 | ||||||||
\(833\) | 1.43752 | 0.0498073 | ||||||||
\(834\) | −0.239247 | −0.00828444 | ||||||||
\(835\) | −32.5706 | −1.12715 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.0284 | 0.346631 | ||||||||
\(838\) | −1.25853 | −0.0434753 | ||||||||
\(839\) | −43.8528 | −1.51397 | −0.756984 | − | 0.653434i | \(-0.773328\pi\) | ||||
−0.756984 | + | 0.653434i | \(0.773328\pi\) | |||||||
\(840\) | −0.488478 | −0.0168541 | ||||||||
\(841\) | 13.4802 | 0.464836 | ||||||||
\(842\) | −4.86160 | −0.167542 | ||||||||
\(843\) | −2.88184 | −0.0992558 | ||||||||
\(844\) | −14.7455 | −0.507562 | ||||||||
\(845\) | −33.3604 | −1.14763 | ||||||||
\(846\) | 4.50894 | 0.155021 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 24.3232 | 0.835261 | ||||||||
\(849\) | 0.0657456 | 0.00225638 | ||||||||
\(850\) | −0.399209 | −0.0136928 | ||||||||
\(851\) | −28.2207 | −0.967392 | ||||||||
\(852\) | 1.93058 | 0.0661405 | ||||||||
\(853\) | −39.1407 | −1.34015 | −0.670076 | − | 0.742293i | \(-0.733738\pi\) | ||||
−0.670076 | + | 0.742293i | \(0.733738\pi\) | |||||||
\(854\) | 0.193488 | 0.00662102 | ||||||||
\(855\) | 44.7049 | 1.52888 | ||||||||
\(856\) | −1.04257 | −0.0356342 | ||||||||
\(857\) | −35.0524 | −1.19737 | −0.598684 | − | 0.800986i | \(-0.704309\pi\) | ||||
−0.598684 | + | 0.800986i | \(0.704309\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.5206 | −1.10959 | −0.554794 | − | 0.831988i | \(-0.687203\pi\) | ||||
−0.554794 | + | 0.831988i | \(0.687203\pi\) | |||||||
\(860\) | 3.90186 | 0.133052 | ||||||||
\(861\) | −1.47891 | −0.0504010 | ||||||||
\(862\) | −6.27030 | −0.213567 | ||||||||
\(863\) | 12.6940 | 0.432107 | 0.216054 | − | 0.976381i | \(-0.430681\pi\) | ||||
0.216054 | + | 0.976381i | \(0.430681\pi\) | |||||||
\(864\) | −3.42044 | −0.116366 | ||||||||
\(865\) | 14.7540 | 0.501651 | ||||||||
\(866\) | −2.10108 | −0.0713975 | ||||||||
\(867\) | 3.27238 | 0.111136 | ||||||||
\(868\) | 14.9844 | 0.508605 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.806251 | 0.0273345 | ||||||||
\(871\) | 8.45568 | 0.286510 | ||||||||
\(872\) | −8.30950 | −0.281395 | ||||||||
\(873\) | 35.6527 | 1.20666 | ||||||||
\(874\) | −9.72314 | −0.328890 | ||||||||
\(875\) | −9.41402 | −0.318252 | ||||||||
\(876\) | 6.34075 | 0.214234 | ||||||||
\(877\) | 28.1340 | 0.950017 | 0.475008 | − | 0.879981i | \(-0.342445\pi\) | ||||
0.475008 | + | 0.879981i | \(0.342445\pi\) | |||||||
\(878\) | −3.32798 | −0.112314 | ||||||||
\(879\) | 3.53765 | 0.119322 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.7964 | −1.23970 | −0.619850 | − | 0.784720i | \(-0.712807\pi\) | ||||
−0.619850 | + | 0.784720i | \(0.712807\pi\) | |||||||
\(882\) | 0.667772 | 0.0224850 | ||||||||
\(883\) | −2.28419 | −0.0768692 | −0.0384346 | − | 0.999261i | \(-0.512237\pi\) | ||||
−0.0384346 | + | 0.999261i | \(0.512237\pi\) | |||||||
\(884\) | 14.3856 | 0.483840 | ||||||||
\(885\) | 1.57286 | 0.0528710 | ||||||||
\(886\) | −0.552736 | −0.0185695 | ||||||||
\(887\) | −42.2676 | −1.41921 | −0.709604 | − | 0.704600i | \(-0.751126\pi\) | ||||
−0.709604 | + | 0.704600i | \(0.751126\pi\) | |||||||
\(888\) | 0.779899 | 0.0261717 | ||||||||
\(889\) | −0.289205 | −0.00969963 | ||||||||
\(890\) | 0.979808 | 0.0328432 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −34.1520 | −1.14349 | ||||||||
\(893\) | 40.9757 | 1.37120 | ||||||||
\(894\) | −0.0456989 | −0.00152840 | ||||||||
\(895\) | −10.8183 | −0.361616 | ||||||||
\(896\) | −6.78282 | −0.226598 | ||||||||
\(897\) | 7.96990 | 0.266107 | ||||||||
\(898\) | −1.07888 | −0.0360027 | ||||||||
\(899\) | −50.1142 | −1.67140 | ||||||||
\(900\) | 7.06249 | 0.235416 | ||||||||
\(901\) | 9.46132 | 0.315202 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.175807 | 0.00585050 | ||||||||
\(904\) | 2.94540 | 0.0979627 | ||||||||
\(905\) | −27.0283 | −0.898451 | ||||||||
\(906\) | −0.897032 | −0.0298019 | ||||||||
\(907\) | 39.5286 | 1.31252 | 0.656262 | − | 0.754533i | \(-0.272136\pi\) | ||||
0.656262 | + | 0.754533i | \(0.272136\pi\) | |||||||
\(908\) | −50.0406 | −1.66065 | ||||||||
\(909\) | −10.9028 | −0.361623 | ||||||||
\(910\) | 2.89878 | 0.0960936 | ||||||||
\(911\) | −35.2296 | −1.16721 | −0.583604 | − | 0.812039i | \(-0.698358\pi\) | ||||
−0.583604 | + | 0.812039i | \(0.698358\pi\) | |||||||
\(912\) | −4.91433 | −0.162730 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 7.03234 | 0.232609 | ||||||||
\(915\) | 0.467737 | 0.0154629 | ||||||||
\(916\) | 38.6587 | 1.27732 | ||||||||
\(917\) | −16.5059 | −0.545072 | ||||||||
\(918\) | −0.424123 | −0.0139982 | ||||||||
\(919\) | 39.6105 | 1.30663 | 0.653314 | − | 0.757087i | \(-0.273378\pi\) | ||||
0.653314 | + | 0.757087i | \(0.273378\pi\) | |||||||
\(920\) | −15.7891 | −0.520551 | ||||||||
\(921\) | −6.27534 | −0.206780 | ||||||||
\(922\) | 6.72334 | 0.221421 | ||||||||
\(923\) | −23.2141 | −0.764101 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.89131 | −0.160825 | ||||||||
\(926\) | 5.75828 | 0.189229 | ||||||||
\(927\) | 3.39939 | 0.111651 | ||||||||
\(928\) | 17.0928 | 0.561098 | ||||||||
\(929\) | 2.61657 | 0.0858469 | 0.0429234 | − | 0.999078i | \(-0.486333\pi\) | ||||
0.0429234 | + | 0.999078i | \(0.486333\pi\) | |||||||
\(930\) | −0.951139 | −0.0311891 | ||||||||
\(931\) | 6.06848 | 0.198886 | ||||||||
\(932\) | −39.3947 | −1.29042 | ||||||||
\(933\) | 6.97331 | 0.228296 | ||||||||
\(934\) | 0.720463 | 0.0235743 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 13.5405 | 0.442586 | ||||||||
\(937\) | −53.8401 | −1.75888 | −0.879439 | − | 0.476011i | \(-0.842082\pi\) | ||||
−0.879439 | + | 0.476011i | \(0.842082\pi\) | |||||||
\(938\) | −0.372498 | −0.0121625 | ||||||||
\(939\) | −0.00749932 | −0.000244731 0 | ||||||||
\(940\) | 32.8384 | 1.07107 | ||||||||
\(941\) | −29.6476 | −0.966484 | −0.483242 | − | 0.875487i | \(-0.660541\pi\) | ||||
−0.483242 | + | 0.875487i | \(0.660541\pi\) | |||||||
\(942\) | −0.608384 | −0.0198222 | ||||||||
\(943\) | −47.8026 | −1.55667 | ||||||||
\(944\) | 10.6294 | 0.345959 | ||||||||
\(945\) | 3.25480 | 0.105879 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −15.7861 | −0.512980 | −0.256490 | − | 0.966547i | \(-0.582566\pi\) | ||||
−0.256490 | + | 0.966547i | \(0.582566\pi\) | |||||||
\(948\) | −1.04750 | −0.0340213 | ||||||||
\(949\) | −76.2440 | −2.47498 | ||||||||
\(950\) | −1.68525 | −0.0546768 | ||||||||
\(951\) | −4.90618 | −0.159094 | ||||||||
\(952\) | −1.28410 | −0.0416178 | ||||||||
\(953\) | 35.1119 | 1.13739 | 0.568693 | − | 0.822550i | \(-0.307449\pi\) | ||||
0.568693 | + | 0.822550i | \(0.307449\pi\) | |||||||
\(954\) | 4.39506 | 0.142295 | ||||||||
\(955\) | −29.0869 | −0.941229 | ||||||||
\(956\) | 33.3257 | 1.07783 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.731463 | 0.0236325 | ||||||||
\(959\) | −9.32588 | −0.301148 | ||||||||
\(960\) | −3.71740 | −0.119979 | ||||||||
\(961\) | 28.1200 | 0.907096 | ||||||||
\(962\) | −4.62816 | −0.149218 | ||||||||
\(963\) | 3.44537 | 0.111025 | ||||||||
\(964\) | −47.0698 | −1.51602 | ||||||||
\(965\) | 56.0131 | 1.80313 | ||||||||
\(966\) | −0.351097 | −0.0112964 | ||||||||
\(967\) | 49.2820 | 1.58480 | 0.792401 | − | 0.610001i | \(-0.208831\pi\) | ||||
0.792401 | + | 0.610001i | \(0.208831\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.91160 | −0.0614093 | ||||||||
\(970\) | −6.81797 | −0.218912 | ||||||||
\(971\) | 37.3424 | 1.19838 | 0.599188 | − | 0.800608i | \(-0.295490\pi\) | ||||
0.599188 | + | 0.800608i | \(0.295490\pi\) | |||||||
\(972\) | 11.2852 | 0.361971 | ||||||||
\(973\) | 4.82649 | 0.154730 | ||||||||
\(974\) | −2.23292 | −0.0715475 | ||||||||
\(975\) | 1.38137 | 0.0442393 | ||||||||
\(976\) | 3.16099 | 0.101181 | ||||||||
\(977\) | 40.0485 | 1.28126 | 0.640632 | − | 0.767848i | \(-0.278672\pi\) | ||||
0.640632 | + | 0.767848i | \(0.278672\pi\) | |||||||
\(978\) | 0.401470 | 0.0128376 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.86335 | 0.155354 | ||||||||
\(981\) | 27.4603 | 0.876741 | ||||||||
\(982\) | 0.955970 | 0.0305062 | ||||||||
\(983\) | −52.0414 | −1.65986 | −0.829932 | − | 0.557864i | \(-0.811621\pi\) | ||||
−0.829932 | + | 0.557864i | \(0.811621\pi\) | |||||||
\(984\) | 1.32106 | 0.0421139 | ||||||||
\(985\) | 60.1475 | 1.91646 | ||||||||
\(986\) | 2.11945 | 0.0674970 | ||||||||
\(987\) | 1.47961 | 0.0470965 | ||||||||
\(988\) | 60.7285 | 1.93203 | ||||||||
\(989\) | 5.68262 | 0.180697 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.4828 | 1.44481 | 0.722404 | − | 0.691471i | \(-0.243037\pi\) | ||||
0.722404 | + | 0.691471i | \(0.243037\pi\) | |||||||
\(992\) | −20.1645 | −0.640222 | ||||||||
\(993\) | −2.35733 | −0.0748076 | ||||||||
\(994\) | 1.02265 | 0.0324365 | ||||||||
\(995\) | −46.7175 | −1.48104 | ||||||||
\(996\) | −0.959913 | −0.0304160 | ||||||||
\(997\) | −27.9594 | −0.885482 | −0.442741 | − | 0.896650i | \(-0.645994\pi\) | ||||
−0.442741 | + | 0.896650i | \(0.645994\pi\) | |||||||
\(998\) | 4.61364 | 0.146042 | ||||||||
\(999\) | −5.19657 | −0.164412 |
(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 | 847.2.a.o.1.5 | 8 | ||
3.2 | odd | 2 | 7623.2.a.cw.1.4 | 8 | |||
7.6 | odd | 2 | 5929.2.a.bs.1.5 | 8 | |||
11.2 | odd | 10 | 77.2.f.b.15.3 | ✓ | 16 | ||
11.3 | even | 5 | 847.2.f.v.372.3 | 16 | |||
11.4 | even | 5 | 847.2.f.v.148.3 | 16 | |||
11.5 | even | 5 | 847.2.f.x.729.2 | 16 | |||
11.6 | odd | 10 | 77.2.f.b.36.3 | yes | 16 | ||
11.7 | odd | 10 | 847.2.f.w.148.2 | 16 | |||
11.8 | odd | 10 | 847.2.f.w.372.2 | 16 | |||
11.9 | even | 5 | 847.2.f.x.323.2 | 16 | |||
11.10 | odd | 2 | 847.2.a.p.1.4 | 8 | |||
33.2 | even | 10 | 693.2.m.i.631.2 | 16 | |||
33.17 | even | 10 | 693.2.m.i.190.2 | 16 | |||
33.32 | even | 2 | 7623.2.a.ct.1.5 | 8 | |||
77.2 | odd | 30 | 539.2.q.g.312.3 | 32 | |||
77.6 | even | 10 | 539.2.f.e.344.3 | 16 | |||
77.13 | even | 10 | 539.2.f.e.246.3 | 16 | |||
77.17 | even | 30 | 539.2.q.f.520.3 | 32 | |||
77.24 | even | 30 | 539.2.q.f.422.2 | 32 | |||
77.39 | odd | 30 | 539.2.q.g.520.3 | 32 | |||
77.46 | odd | 30 | 539.2.q.g.422.2 | 32 | |||
77.61 | even | 30 | 539.2.q.f.410.2 | 32 | |||
77.68 | even | 30 | 539.2.q.f.312.3 | 32 | |||
77.72 | odd | 30 | 539.2.q.g.410.2 | 32 | |||
77.76 | even | 2 | 5929.2.a.bt.1.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.b.15.3 | ✓ | 16 | 11.2 | odd | 10 | ||
77.2.f.b.36.3 | yes | 16 | 11.6 | odd | 10 | ||
539.2.f.e.246.3 | 16 | 77.13 | even | 10 | |||
539.2.f.e.344.3 | 16 | 77.6 | even | 10 | |||
539.2.q.f.312.3 | 32 | 77.68 | even | 30 | |||
539.2.q.f.410.2 | 32 | 77.61 | even | 30 | |||
539.2.q.f.422.2 | 32 | 77.24 | even | 30 | |||
539.2.q.f.520.3 | 32 | 77.17 | even | 30 | |||
539.2.q.g.312.3 | 32 | 77.2 | odd | 30 | |||
539.2.q.g.410.2 | 32 | 77.72 | odd | 30 | |||
539.2.q.g.422.2 | 32 | 77.46 | odd | 30 | |||
539.2.q.g.520.3 | 32 | 77.39 | odd | 30 | |||
693.2.m.i.190.2 | 16 | 33.17 | even | 10 | |||
693.2.m.i.631.2 | 16 | 33.2 | even | 10 | |||
847.2.a.o.1.5 | 8 | 1.1 | even | 1 | trivial | ||
847.2.a.p.1.4 | 8 | 11.10 | odd | 2 | |||
847.2.f.v.148.3 | 16 | 11.4 | even | 5 | |||
847.2.f.v.372.3 | 16 | 11.3 | even | 5 | |||
847.2.f.w.148.2 | 16 | 11.7 | odd | 10 | |||
847.2.f.w.372.2 | 16 | 11.8 | odd | 10 | |||
847.2.f.x.323.2 | 16 | 11.9 | even | 5 | |||
847.2.f.x.729.2 | 16 | 11.5 | even | 5 | |||
5929.2.a.bs.1.5 | 8 | 7.6 | odd | 2 | |||
5929.2.a.bt.1.4 | 8 | 77.76 | even | 2 | |||
7623.2.a.ct.1.5 | 8 | 33.32 | even | 2 | |||
7623.2.a.cw.1.4 | 8 | 3.2 | odd | 2 |