Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4018,2,Mod(1,4018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4018, 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("4018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4018 = 2 \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4018.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: | \(32.0838915322\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.52046292.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 10x^{4} + 9x^{3} + 24x^{2} - 18x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 574) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(0.0605469\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.302513 | 0.174656 | 0.0873279 | − | 0.996180i | \(-0.472167\pi\) | ||||
0.0873279 | + | 0.996180i | \(0.472167\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.67551 | −1.19652 | −0.598261 | − | 0.801301i | \(-0.704141\pi\) | ||||
−0.598261 | + | 0.801301i | \(0.704141\pi\) | |||||||
\(6\) | −0.302513 | −0.123500 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.90849 | −0.969495 | ||||||||
\(10\) | 2.67551 | 0.846069 | ||||||||
\(11\) | −4.53183 | −1.36640 | −0.683199 | − | 0.730232i | \(-0.739412\pi\) | ||||
−0.683199 | + | 0.730232i | \(0.739412\pi\) | |||||||
\(12\) | 0.302513 | 0.0873279 | ||||||||
\(13\) | −5.61129 | −1.55629 | −0.778146 | − | 0.628083i | \(-0.783840\pi\) | ||||
−0.778146 | + | 0.628083i | \(0.783840\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.809374 | −0.208980 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.23298 | −0.299042 | −0.149521 | − | 0.988759i | \(-0.547773\pi\) | ||||
−0.149521 | + | 0.988759i | \(0.547773\pi\) | |||||||
\(18\) | 2.90849 | 0.685537 | ||||||||
\(19\) | −5.44398 | −1.24893 | −0.624467 | − | 0.781051i | \(-0.714684\pi\) | ||||
−0.624467 | + | 0.781051i | \(0.714684\pi\) | |||||||
\(20\) | −2.67551 | −0.598261 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.53183 | 0.966189 | ||||||||
\(23\) | 4.32083 | 0.900955 | 0.450478 | − | 0.892788i | \(-0.351254\pi\) | ||||
0.450478 | + | 0.892788i | \(0.351254\pi\) | |||||||
\(24\) | −0.302513 | −0.0617502 | ||||||||
\(25\) | 2.15833 | 0.431666 | ||||||||
\(26\) | 5.61129 | 1.10046 | ||||||||
\(27\) | −1.78739 | −0.343984 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.63327 | −0.488987 | −0.244493 | − | 0.969651i | \(-0.578622\pi\) | ||||
−0.244493 | + | 0.969651i | \(0.578622\pi\) | |||||||
\(30\) | 0.809374 | 0.147771 | ||||||||
\(31\) | −0.837499 | −0.150419 | −0.0752096 | − | 0.997168i | \(-0.523963\pi\) | ||||
−0.0752096 | + | 0.997168i | \(0.523963\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.37094 | −0.238649 | ||||||||
\(34\) | 1.23298 | 0.211454 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.90849 | −0.484748 | ||||||||
\(37\) | −10.6865 | −1.75685 | −0.878424 | − | 0.477882i | \(-0.841405\pi\) | ||||
−0.878424 | + | 0.477882i | \(0.841405\pi\) | |||||||
\(38\) | 5.44398 | 0.883130 | ||||||||
\(39\) | −1.69749 | −0.271816 | ||||||||
\(40\) | 2.67551 | 0.423035 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.192081 | −0.0292921 | −0.0146461 | − | 0.999893i | \(-0.504662\pi\) | ||||
−0.0146461 | + | 0.999893i | \(0.504662\pi\) | |||||||
\(44\) | −4.53183 | −0.683199 | ||||||||
\(45\) | 7.78167 | 1.16002 | ||||||||
\(46\) | −4.32083 | −0.637071 | ||||||||
\(47\) | −9.24823 | −1.34899 | −0.674497 | − | 0.738278i | \(-0.735639\pi\) | ||||
−0.674497 | + | 0.738278i | \(0.735639\pi\) | |||||||
\(48\) | 0.302513 | 0.0436639 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.15833 | −0.305234 | ||||||||
\(51\) | −0.372992 | −0.0522294 | ||||||||
\(52\) | −5.61129 | −0.778146 | ||||||||
\(53\) | 7.10771 | 0.976320 | 0.488160 | − | 0.872754i | \(-0.337668\pi\) | ||||
0.488160 | + | 0.872754i | \(0.337668\pi\) | |||||||
\(54\) | 1.78739 | 0.243233 | ||||||||
\(55\) | 12.1249 | 1.63492 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.64687 | −0.218134 | ||||||||
\(58\) | 2.63327 | 0.345766 | ||||||||
\(59\) | −5.34162 | −0.695420 | −0.347710 | − | 0.937602i | \(-0.613041\pi\) | ||||
−0.347710 | + | 0.937602i | \(0.613041\pi\) | |||||||
\(60\) | −0.809374 | −0.104490 | ||||||||
\(61\) | −1.85948 | −0.238082 | −0.119041 | − | 0.992889i | \(-0.537982\pi\) | ||||
−0.119041 | + | 0.992889i | \(0.537982\pi\) | |||||||
\(62\) | 0.837499 | 0.106362 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 15.0130 | 1.86214 | ||||||||
\(66\) | 1.37094 | 0.168750 | ||||||||
\(67\) | −15.8741 | −1.93932 | −0.969662 | − | 0.244450i | \(-0.921393\pi\) | ||||
−0.969662 | + | 0.244450i | \(0.921393\pi\) | |||||||
\(68\) | −1.23298 | −0.149521 | ||||||||
\(69\) | 1.30711 | 0.157357 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.9802 | 1.42179 | 0.710894 | − | 0.703299i | \(-0.248291\pi\) | ||||
0.710894 | + | 0.703299i | \(0.248291\pi\) | |||||||
\(72\) | 2.90849 | 0.342768 | ||||||||
\(73\) | 8.70958 | 1.01938 | 0.509690 | − | 0.860358i | \(-0.329760\pi\) | ||||
0.509690 | + | 0.860358i | \(0.329760\pi\) | |||||||
\(74\) | 10.6865 | 1.24228 | ||||||||
\(75\) | 0.652922 | 0.0753929 | ||||||||
\(76\) | −5.44398 | −0.624467 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.69749 | 0.192203 | ||||||||
\(79\) | 10.7417 | 1.20854 | 0.604269 | − | 0.796781i | \(-0.293465\pi\) | ||||
0.604269 | + | 0.796781i | \(0.293465\pi\) | |||||||
\(80\) | −2.67551 | −0.299131 | ||||||||
\(81\) | 8.18475 | 0.909417 | ||||||||
\(82\) | −1.00000 | −0.110432 | ||||||||
\(83\) | 8.34120 | 0.915566 | 0.457783 | − | 0.889064i | \(-0.348644\pi\) | ||||
0.457783 | + | 0.889064i | \(0.348644\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.29885 | 0.357810 | ||||||||
\(86\) | 0.192081 | 0.0207126 | ||||||||
\(87\) | −0.796599 | −0.0854044 | ||||||||
\(88\) | 4.53183 | 0.483094 | ||||||||
\(89\) | 2.04328 | 0.216587 | 0.108294 | − | 0.994119i | \(-0.465461\pi\) | ||||
0.108294 | + | 0.994119i | \(0.465461\pi\) | |||||||
\(90\) | −7.78167 | −0.820260 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.32083 | 0.450478 | ||||||||
\(93\) | −0.253354 | −0.0262716 | ||||||||
\(94\) | 9.24823 | 0.953882 | ||||||||
\(95\) | 14.5654 | 1.49438 | ||||||||
\(96\) | −0.302513 | −0.0308751 | ||||||||
\(97\) | −2.40675 | −0.244368 | −0.122184 | − | 0.992507i | \(-0.538990\pi\) | ||||
−0.122184 | + | 0.992507i | \(0.538990\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13.1808 | 1.32472 | ||||||||
\(100\) | 2.15833 | 0.215833 | ||||||||
\(101\) | −14.2320 | −1.41614 | −0.708070 | − | 0.706142i | \(-0.750434\pi\) | ||||
−0.708070 | + | 0.706142i | \(0.750434\pi\) | |||||||
\(102\) | 0.372992 | 0.0369318 | ||||||||
\(103\) | −12.4403 | −1.22578 | −0.612890 | − | 0.790168i | \(-0.709993\pi\) | ||||
−0.612890 | + | 0.790168i | \(0.709993\pi\) | |||||||
\(104\) | 5.61129 | 0.550232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.10771 | −0.690362 | ||||||||
\(107\) | 6.75937 | 0.653452 | 0.326726 | − | 0.945119i | \(-0.394054\pi\) | ||||
0.326726 | + | 0.945119i | \(0.394054\pi\) | |||||||
\(108\) | −1.78739 | −0.171992 | ||||||||
\(109\) | −8.19117 | −0.784572 | −0.392286 | − | 0.919843i | \(-0.628316\pi\) | ||||
−0.392286 | + | 0.919843i | \(0.628316\pi\) | |||||||
\(110\) | −12.1249 | −1.15607 | ||||||||
\(111\) | −3.23280 | −0.306844 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.2861 | 1.15578 | 0.577888 | − | 0.816116i | \(-0.303877\pi\) | ||||
0.577888 | + | 0.816116i | \(0.303877\pi\) | |||||||
\(114\) | 1.64687 | 0.154244 | ||||||||
\(115\) | −11.5604 | −1.07801 | ||||||||
\(116\) | −2.63327 | −0.244493 | ||||||||
\(117\) | 16.3204 | 1.50882 | ||||||||
\(118\) | 5.34162 | 0.491736 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.809374 | 0.0738854 | ||||||||
\(121\) | 9.53746 | 0.867042 | ||||||||
\(122\) | 1.85948 | 0.168349 | ||||||||
\(123\) | 0.302513 | 0.0272767 | ||||||||
\(124\) | −0.837499 | −0.0752096 | ||||||||
\(125\) | 7.60291 | 0.680025 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.23213 | 0.198069 | 0.0990346 | − | 0.995084i | \(-0.468425\pi\) | ||||
0.0990346 | + | 0.995084i | \(0.468425\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.0581070 | −0.00511604 | ||||||||
\(130\) | −15.0130 | −1.31673 | ||||||||
\(131\) | −21.0340 | −1.83775 | −0.918875 | − | 0.394548i | \(-0.870901\pi\) | ||||
−0.918875 | + | 0.394548i | \(0.870901\pi\) | |||||||
\(132\) | −1.37094 | −0.119325 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 15.8741 | 1.37131 | ||||||||
\(135\) | 4.78218 | 0.411584 | ||||||||
\(136\) | 1.23298 | 0.105727 | ||||||||
\(137\) | −3.54818 | −0.303142 | −0.151571 | − | 0.988446i | \(-0.548433\pi\) | ||||
−0.151571 | + | 0.988446i | \(0.548433\pi\) | |||||||
\(138\) | −1.30711 | −0.111268 | ||||||||
\(139\) | −2.80375 | −0.237811 | −0.118905 | − | 0.992906i | \(-0.537938\pi\) | ||||
−0.118905 | + | 0.992906i | \(0.537938\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.79771 | −0.235610 | ||||||||
\(142\) | −11.9802 | −1.00536 | ||||||||
\(143\) | 25.4294 | 2.12651 | ||||||||
\(144\) | −2.90849 | −0.242374 | ||||||||
\(145\) | 7.04534 | 0.585084 | ||||||||
\(146\) | −8.70958 | −0.720810 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.6865 | −0.878424 | ||||||||
\(149\) | −0.0302850 | −0.00248105 | −0.00124052 | − | 0.999999i | \(-0.500395\pi\) | ||||
−0.00124052 | + | 0.999999i | \(0.500395\pi\) | |||||||
\(150\) | −0.652922 | −0.0533108 | ||||||||
\(151\) | −17.2199 | −1.40134 | −0.700669 | − | 0.713487i | \(-0.747115\pi\) | ||||
−0.700669 | + | 0.713487i | \(0.747115\pi\) | |||||||
\(152\) | 5.44398 | 0.441565 | ||||||||
\(153\) | 3.58611 | 0.289920 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.24073 | 0.179980 | ||||||||
\(156\) | −1.69749 | −0.135908 | ||||||||
\(157\) | 18.3765 | 1.46661 | 0.733303 | − | 0.679902i | \(-0.237978\pi\) | ||||
0.733303 | + | 0.679902i | \(0.237978\pi\) | |||||||
\(158\) | −10.7417 | −0.854565 | ||||||||
\(159\) | 2.15017 | 0.170520 | ||||||||
\(160\) | 2.67551 | 0.211517 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −8.18475 | −0.643055 | ||||||||
\(163\) | −3.05903 | −0.239602 | −0.119801 | − | 0.992798i | \(-0.538226\pi\) | ||||
−0.119801 | + | 0.992798i | \(0.538226\pi\) | |||||||
\(164\) | 1.00000 | 0.0780869 | ||||||||
\(165\) | 3.66795 | 0.285549 | ||||||||
\(166\) | −8.34120 | −0.647403 | ||||||||
\(167\) | −9.88049 | −0.764575 | −0.382287 | − | 0.924043i | \(-0.624864\pi\) | ||||
−0.382287 | + | 0.924043i | \(0.624864\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 18.4866 | 1.42205 | ||||||||
\(170\) | −3.29885 | −0.253010 | ||||||||
\(171\) | 15.8337 | 1.21084 | ||||||||
\(172\) | −0.192081 | −0.0146461 | ||||||||
\(173\) | −11.6774 | −0.887815 | −0.443907 | − | 0.896073i | \(-0.646408\pi\) | ||||
−0.443907 | + | 0.896073i | \(0.646408\pi\) | |||||||
\(174\) | 0.796599 | 0.0603900 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.53183 | −0.341599 | ||||||||
\(177\) | −1.61591 | −0.121459 | ||||||||
\(178\) | −2.04328 | −0.153150 | ||||||||
\(179\) | 7.20884 | 0.538814 | 0.269407 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269407 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(180\) | 7.78167 | 0.580011 | ||||||||
\(181\) | −17.2003 | −1.27849 | −0.639246 | − | 0.769002i | \(-0.720753\pi\) | ||||
−0.639246 | + | 0.769002i | \(0.720753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.562517 | −0.0415824 | ||||||||
\(184\) | −4.32083 | −0.318536 | ||||||||
\(185\) | 28.5918 | 2.10211 | ||||||||
\(186\) | 0.253354 | 0.0185768 | ||||||||
\(187\) | 5.58766 | 0.408610 | ||||||||
\(188\) | −9.24823 | −0.674497 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −14.5654 | −1.05668 | ||||||||
\(191\) | 9.14524 | 0.661726 | 0.330863 | − | 0.943679i | \(-0.392660\pi\) | ||||
0.330863 | + | 0.943679i | \(0.392660\pi\) | |||||||
\(192\) | 0.302513 | 0.0218320 | ||||||||
\(193\) | −13.4178 | −0.965837 | −0.482918 | − | 0.875665i | \(-0.660423\pi\) | ||||
−0.482918 | + | 0.875665i | \(0.660423\pi\) | |||||||
\(194\) | 2.40675 | 0.172794 | ||||||||
\(195\) | 4.54164 | 0.325233 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.3793 | −1.16698 | −0.583489 | − | 0.812121i | \(-0.698313\pi\) | ||||
−0.583489 | + | 0.812121i | \(0.698313\pi\) | |||||||
\(198\) | −13.1808 | −0.936716 | ||||||||
\(199\) | −11.7741 | −0.834645 | −0.417322 | − | 0.908758i | \(-0.637031\pi\) | ||||
−0.417322 | + | 0.908758i | \(0.637031\pi\) | |||||||
\(200\) | −2.15833 | −0.152617 | ||||||||
\(201\) | −4.80210 | −0.338714 | ||||||||
\(202\) | 14.2320 | 1.00136 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.372992 | −0.0261147 | ||||||||
\(205\) | −2.67551 | −0.186865 | ||||||||
\(206\) | 12.4403 | 0.866758 | ||||||||
\(207\) | −12.5671 | −0.873472 | ||||||||
\(208\) | −5.61129 | −0.389073 | ||||||||
\(209\) | 24.6712 | 1.70654 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.3313 | 1.26198 | 0.630990 | − | 0.775791i | \(-0.282649\pi\) | ||||
0.630990 | + | 0.775791i | \(0.282649\pi\) | |||||||
\(212\) | 7.10771 | 0.488160 | ||||||||
\(213\) | 3.62416 | 0.248324 | ||||||||
\(214\) | −6.75937 | −0.462061 | ||||||||
\(215\) | 0.513914 | 0.0350487 | ||||||||
\(216\) | 1.78739 | 0.121617 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.19117 | 0.554776 | ||||||||
\(219\) | 2.63476 | 0.178041 | ||||||||
\(220\) | 12.1249 | 0.817462 | ||||||||
\(221\) | 6.91862 | 0.465396 | ||||||||
\(222\) | 3.23280 | 0.216971 | ||||||||
\(223\) | −19.6446 | −1.31550 | −0.657749 | − | 0.753237i | \(-0.728491\pi\) | ||||
−0.657749 | + | 0.753237i | \(0.728491\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.27747 | −0.418498 | ||||||||
\(226\) | −12.2861 | −0.817257 | ||||||||
\(227\) | −8.78493 | −0.583076 | −0.291538 | − | 0.956559i | \(-0.594167\pi\) | ||||
−0.291538 | + | 0.956559i | \(0.594167\pi\) | |||||||
\(228\) | −1.64687 | −0.109067 | ||||||||
\(229\) | 6.89649 | 0.455733 | 0.227867 | − | 0.973692i | \(-0.426825\pi\) | ||||
0.227867 | + | 0.973692i | \(0.426825\pi\) | |||||||
\(230\) | 11.5604 | 0.762270 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.63327 | 0.172883 | ||||||||
\(233\) | 30.4233 | 1.99309 | 0.996547 | − | 0.0830274i | \(-0.0264589\pi\) | ||||
0.996547 | + | 0.0830274i | \(0.0264589\pi\) | |||||||
\(234\) | −16.3204 | −1.06690 | ||||||||
\(235\) | 24.7437 | 1.61410 | ||||||||
\(236\) | −5.34162 | −0.347710 | ||||||||
\(237\) | 3.24951 | 0.211078 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.29887 | 0.407440 | 0.203720 | − | 0.979029i | \(-0.434697\pi\) | ||||
0.203720 | + | 0.979029i | \(0.434697\pi\) | |||||||
\(240\) | −0.809374 | −0.0522449 | ||||||||
\(241\) | 9.49953 | 0.611919 | 0.305959 | − | 0.952045i | \(-0.401023\pi\) | ||||
0.305959 | + | 0.952045i | \(0.401023\pi\) | |||||||
\(242\) | −9.53746 | −0.613091 | ||||||||
\(243\) | 7.83817 | 0.502819 | ||||||||
\(244\) | −1.85948 | −0.119041 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.302513 | −0.0192875 | ||||||||
\(247\) | 30.5478 | 1.94371 | ||||||||
\(248\) | 0.837499 | 0.0531812 | ||||||||
\(249\) | 2.52332 | 0.159909 | ||||||||
\(250\) | −7.60291 | −0.480850 | ||||||||
\(251\) | −11.1562 | −0.704173 | −0.352087 | − | 0.935967i | \(-0.614528\pi\) | ||||
−0.352087 | + | 0.935967i | \(0.614528\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.5813 | −1.23106 | ||||||||
\(254\) | −2.23213 | −0.140056 | ||||||||
\(255\) | 0.997943 | 0.0624936 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.6549 | 0.851769 | 0.425884 | − | 0.904778i | \(-0.359963\pi\) | ||||
0.425884 | + | 0.904778i | \(0.359963\pi\) | |||||||
\(258\) | 0.0581070 | 0.00361758 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 15.0130 | 0.931069 | ||||||||
\(261\) | 7.65884 | 0.474070 | ||||||||
\(262\) | 21.0340 | 1.29949 | ||||||||
\(263\) | 5.43132 | 0.334910 | 0.167455 | − | 0.985880i | \(-0.446445\pi\) | ||||
0.167455 | + | 0.985880i | \(0.446445\pi\) | |||||||
\(264\) | 1.37094 | 0.0843752 | ||||||||
\(265\) | −19.0167 | −1.16819 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.618119 | 0.0378283 | ||||||||
\(268\) | −15.8741 | −0.969662 | ||||||||
\(269\) | 19.3636 | 1.18062 | 0.590311 | − | 0.807176i | \(-0.299005\pi\) | ||||
0.590311 | + | 0.807176i | \(0.299005\pi\) | |||||||
\(270\) | −4.78218 | −0.291034 | ||||||||
\(271\) | 15.6578 | 0.951142 | 0.475571 | − | 0.879677i | \(-0.342242\pi\) | ||||
0.475571 | + | 0.879677i | \(0.342242\pi\) | |||||||
\(272\) | −1.23298 | −0.0747604 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.54818 | 0.214353 | ||||||||
\(275\) | −9.78117 | −0.589827 | ||||||||
\(276\) | 1.30711 | 0.0786785 | ||||||||
\(277\) | 1.44438 | 0.0867845 | 0.0433923 | − | 0.999058i | \(-0.486183\pi\) | ||||
0.0433923 | + | 0.999058i | \(0.486183\pi\) | |||||||
\(278\) | 2.80375 | 0.168157 | ||||||||
\(279\) | 2.43585 | 0.145831 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.76875 | −0.582755 | −0.291377 | − | 0.956608i | \(-0.594113\pi\) | ||||
−0.291377 | + | 0.956608i | \(0.594113\pi\) | |||||||
\(282\) | 2.79771 | 0.166601 | ||||||||
\(283\) | −18.8705 | −1.12174 | −0.560869 | − | 0.827905i | \(-0.689533\pi\) | ||||
−0.560869 | + | 0.827905i | \(0.689533\pi\) | |||||||
\(284\) | 11.9802 | 0.710894 | ||||||||
\(285\) | 4.40622 | 0.261002 | ||||||||
\(286\) | −25.4294 | −1.50367 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.90849 | 0.171384 | ||||||||
\(289\) | −15.4798 | −0.910574 | ||||||||
\(290\) | −7.04534 | −0.413717 | ||||||||
\(291\) | −0.728071 | −0.0426803 | ||||||||
\(292\) | 8.70958 | 0.509690 | ||||||||
\(293\) | 7.66092 | 0.447556 | 0.223778 | − | 0.974640i | \(-0.428161\pi\) | ||||
0.223778 | + | 0.974640i | \(0.428161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.2915 | 0.832085 | ||||||||
\(296\) | 10.6865 | 0.621140 | ||||||||
\(297\) | 8.10015 | 0.470019 | ||||||||
\(298\) | 0.0302850 | 0.00175436 | ||||||||
\(299\) | −24.2454 | −1.40215 | ||||||||
\(300\) | 0.652922 | 0.0376964 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.2199 | 0.990895 | ||||||||
\(303\) | −4.30537 | −0.247337 | ||||||||
\(304\) | −5.44398 | −0.312234 | ||||||||
\(305\) | 4.97505 | 0.284871 | ||||||||
\(306\) | −3.58611 | −0.205004 | ||||||||
\(307\) | −3.85361 | −0.219937 | −0.109969 | − | 0.993935i | \(-0.535075\pi\) | ||||
−0.109969 | + | 0.993935i | \(0.535075\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.76335 | −0.214090 | ||||||||
\(310\) | −2.24073 | −0.127265 | ||||||||
\(311\) | −0.951906 | −0.0539777 | −0.0269888 | − | 0.999636i | \(-0.508592\pi\) | ||||
−0.0269888 | + | 0.999636i | \(0.508592\pi\) | |||||||
\(312\) | 1.69749 | 0.0961013 | ||||||||
\(313\) | −23.7853 | −1.34443 | −0.672213 | − | 0.740358i | \(-0.734656\pi\) | ||||
−0.672213 | + | 0.740358i | \(0.734656\pi\) | |||||||
\(314\) | −18.3765 | −1.03705 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.7417 | 0.604269 | ||||||||
\(317\) | −7.44237 | −0.418005 | −0.209003 | − | 0.977915i | \(-0.567022\pi\) | ||||
−0.209003 | + | 0.977915i | \(0.567022\pi\) | |||||||
\(318\) | −2.15017 | −0.120576 | ||||||||
\(319\) | 11.9335 | 0.668150 | ||||||||
\(320\) | −2.67551 | −0.149565 | ||||||||
\(321\) | 2.04479 | 0.114129 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.71232 | 0.373484 | ||||||||
\(324\) | 8.18475 | 0.454708 | ||||||||
\(325\) | −12.1110 | −0.671798 | ||||||||
\(326\) | 3.05903 | 0.169424 | ||||||||
\(327\) | −2.47793 | −0.137030 | ||||||||
\(328\) | −1.00000 | −0.0552158 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.66795 | −0.201914 | ||||||||
\(331\) | 20.3269 | 1.11727 | 0.558634 | − | 0.829414i | \(-0.311326\pi\) | ||||
0.558634 | + | 0.829414i | \(0.311326\pi\) | |||||||
\(332\) | 8.34120 | 0.457783 | ||||||||
\(333\) | 31.0815 | 1.70326 | ||||||||
\(334\) | 9.88049 | 0.540636 | ||||||||
\(335\) | 42.4711 | 2.32044 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −32.6366 | −1.77783 | −0.888914 | − | 0.458075i | \(-0.848539\pi\) | ||||
−0.888914 | + | 0.458075i | \(0.848539\pi\) | |||||||
\(338\) | −18.4866 | −1.00554 | ||||||||
\(339\) | 3.71669 | 0.201863 | ||||||||
\(340\) | 3.29885 | 0.178905 | ||||||||
\(341\) | 3.79540 | 0.205532 | ||||||||
\(342\) | −15.8337 | −0.856191 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0.192081 | 0.0103563 | ||||||||
\(345\) | −3.49717 | −0.188281 | ||||||||
\(346\) | 11.6774 | 0.627780 | ||||||||
\(347\) | 34.9767 | 1.87765 | 0.938824 | − | 0.344398i | \(-0.111917\pi\) | ||||
0.938824 | + | 0.344398i | \(0.111917\pi\) | |||||||
\(348\) | −0.796599 | −0.0427022 | ||||||||
\(349\) | −2.25155 | −0.120523 | −0.0602614 | − | 0.998183i | \(-0.519193\pi\) | ||||
−0.0602614 | + | 0.998183i | \(0.519193\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.0296 | 0.535339 | ||||||||
\(352\) | 4.53183 | 0.241547 | ||||||||
\(353\) | −30.6220 | −1.62984 | −0.814921 | − | 0.579571i | \(-0.803220\pi\) | ||||
−0.814921 | + | 0.579571i | \(0.803220\pi\) | |||||||
\(354\) | 1.61591 | 0.0858846 | ||||||||
\(355\) | −32.0531 | −1.70120 | ||||||||
\(356\) | 2.04328 | 0.108294 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.20884 | −0.380999 | ||||||||
\(359\) | −19.1701 | −1.01176 | −0.505879 | − | 0.862604i | \(-0.668832\pi\) | ||||
−0.505879 | + | 0.862604i | \(0.668832\pi\) | |||||||
\(360\) | −7.78167 | −0.410130 | ||||||||
\(361\) | 10.6369 | 0.559838 | ||||||||
\(362\) | 17.2003 | 0.904030 | ||||||||
\(363\) | 2.88520 | 0.151434 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.3025 | −1.21971 | ||||||||
\(366\) | 0.562517 | 0.0294032 | ||||||||
\(367\) | −30.3024 | −1.58177 | −0.790887 | − | 0.611963i | \(-0.790380\pi\) | ||||
−0.790887 | + | 0.611963i | \(0.790380\pi\) | |||||||
\(368\) | 4.32083 | 0.225239 | ||||||||
\(369\) | −2.90849 | −0.151410 | ||||||||
\(370\) | −28.5918 | −1.48641 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.253354 | −0.0131358 | ||||||||
\(373\) | 28.5671 | 1.47915 | 0.739575 | − | 0.673074i | \(-0.235026\pi\) | ||||
0.739575 | + | 0.673074i | \(0.235026\pi\) | |||||||
\(374\) | −5.58766 | −0.288931 | ||||||||
\(375\) | 2.29998 | 0.118770 | ||||||||
\(376\) | 9.24823 | 0.476941 | ||||||||
\(377\) | 14.7761 | 0.761006 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.0736 | −1.69888 | −0.849439 | − | 0.527687i | \(-0.823060\pi\) | ||||
−0.849439 | + | 0.527687i | \(0.823060\pi\) | |||||||
\(380\) | 14.5654 | 0.747189 | ||||||||
\(381\) | 0.675247 | 0.0345939 | ||||||||
\(382\) | −9.14524 | −0.467911 | ||||||||
\(383\) | 17.0073 | 0.869032 | 0.434516 | − | 0.900664i | \(-0.356919\pi\) | ||||
0.434516 | + | 0.900664i | \(0.356919\pi\) | |||||||
\(384\) | −0.302513 | −0.0154375 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.4178 | 0.682950 | ||||||||
\(387\) | 0.558665 | 0.0283986 | ||||||||
\(388\) | −2.40675 | −0.122184 | ||||||||
\(389\) | 20.2684 | 1.02765 | 0.513824 | − | 0.857896i | \(-0.328228\pi\) | ||||
0.513824 | + | 0.857896i | \(0.328228\pi\) | |||||||
\(390\) | −4.54164 | −0.229975 | ||||||||
\(391\) | −5.32750 | −0.269423 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.36306 | −0.320974 | ||||||||
\(394\) | 16.3793 | 0.825177 | ||||||||
\(395\) | −28.7395 | −1.44604 | ||||||||
\(396\) | 13.1808 | 0.662358 | ||||||||
\(397\) | −10.9200 | −0.548060 | −0.274030 | − | 0.961721i | \(-0.588357\pi\) | ||||
−0.274030 | + | 0.961721i | \(0.588357\pi\) | |||||||
\(398\) | 11.7741 | 0.590183 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.15833 | 0.107916 | ||||||||
\(401\) | −13.3283 | −0.665586 | −0.332793 | − | 0.943000i | \(-0.607991\pi\) | ||||
−0.332793 | + | 0.943000i | \(0.607991\pi\) | |||||||
\(402\) | 4.80210 | 0.239507 | ||||||||
\(403\) | 4.69945 | 0.234096 | ||||||||
\(404\) | −14.2320 | −0.708070 | ||||||||
\(405\) | −21.8983 | −1.08814 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 48.4293 | 2.40055 | ||||||||
\(408\) | 0.372992 | 0.0184659 | ||||||||
\(409\) | −18.8109 | −0.930139 | −0.465070 | − | 0.885274i | \(-0.653971\pi\) | ||||
−0.465070 | + | 0.885274i | \(0.653971\pi\) | |||||||
\(410\) | 2.67551 | 0.132134 | ||||||||
\(411\) | −1.07337 | −0.0529454 | ||||||||
\(412\) | −12.4403 | −0.612890 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.5671 | 0.617638 | ||||||||
\(415\) | −22.3169 | −1.09549 | ||||||||
\(416\) | 5.61129 | 0.275116 | ||||||||
\(417\) | −0.848169 | −0.0415350 | ||||||||
\(418\) | −24.6712 | −1.20671 | ||||||||
\(419\) | 8.19107 | 0.400160 | 0.200080 | − | 0.979780i | \(-0.435880\pi\) | ||||
0.200080 | + | 0.979780i | \(0.435880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 40.6667 | 1.98198 | 0.990988 | − | 0.133951i | \(-0.0427665\pi\) | ||||
0.990988 | + | 0.133951i | \(0.0427665\pi\) | |||||||
\(422\) | −18.3313 | −0.892354 | ||||||||
\(423\) | 26.8984 | 1.30784 | ||||||||
\(424\) | −7.10771 | −0.345181 | ||||||||
\(425\) | −2.66118 | −0.129086 | ||||||||
\(426\) | −3.62416 | −0.175591 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.75937 | 0.326726 | ||||||||
\(429\) | 7.69272 | 0.371408 | ||||||||
\(430\) | −0.513914 | −0.0247831 | ||||||||
\(431\) | −10.8454 | −0.522402 | −0.261201 | − | 0.965284i | \(-0.584119\pi\) | ||||
−0.261201 | + | 0.965284i | \(0.584119\pi\) | |||||||
\(432\) | −1.78739 | −0.0859959 | ||||||||
\(433\) | −12.5834 | −0.604719 | −0.302360 | − | 0.953194i | \(-0.597774\pi\) | ||||
−0.302360 | + | 0.953194i | \(0.597774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.13130 | 0.102188 | ||||||||
\(436\) | −8.19117 | −0.392286 | ||||||||
\(437\) | −23.5225 | −1.12523 | ||||||||
\(438\) | −2.63476 | −0.125894 | ||||||||
\(439\) | 30.3023 | 1.44625 | 0.723126 | − | 0.690716i | \(-0.242705\pi\) | ||||
0.723126 | + | 0.690716i | \(0.242705\pi\) | |||||||
\(440\) | −12.1249 | −0.578033 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.91862 | −0.329085 | ||||||||
\(443\) | −20.0561 | −0.952893 | −0.476447 | − | 0.879203i | \(-0.658075\pi\) | ||||
−0.476447 | + | 0.879203i | \(0.658075\pi\) | |||||||
\(444\) | −3.23280 | −0.153422 | ||||||||
\(445\) | −5.46681 | −0.259152 | ||||||||
\(446\) | 19.6446 | 0.930198 | ||||||||
\(447\) | −0.00916161 | −0.000433329 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.2349 | 1.66284 | 0.831420 | − | 0.555645i | \(-0.187529\pi\) | ||||
0.831420 | + | 0.555645i | \(0.187529\pi\) | |||||||
\(450\) | 6.27747 | 0.295923 | ||||||||
\(451\) | −4.53183 | −0.213395 | ||||||||
\(452\) | 12.2861 | 0.577888 | ||||||||
\(453\) | −5.20925 | −0.244752 | ||||||||
\(454\) | 8.78493 | 0.412297 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.64687 | 0.0771219 | ||||||||
\(457\) | 33.9064 | 1.58607 | 0.793036 | − | 0.609174i | \(-0.208499\pi\) | ||||
0.793036 | + | 0.609174i | \(0.208499\pi\) | |||||||
\(458\) | −6.89649 | −0.322252 | ||||||||
\(459\) | 2.20382 | 0.102866 | ||||||||
\(460\) | −11.5604 | −0.539006 | ||||||||
\(461\) | 12.2136 | 0.568845 | 0.284423 | − | 0.958699i | \(-0.408198\pi\) | ||||
0.284423 | + | 0.958699i | \(0.408198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.17302 | −0.426306 | −0.213153 | − | 0.977019i | \(-0.568373\pi\) | ||||
−0.213153 | + | 0.977019i | \(0.568373\pi\) | |||||||
\(464\) | −2.63327 | −0.122247 | ||||||||
\(465\) | 0.677850 | 0.0314345 | ||||||||
\(466\) | −30.4233 | −1.40933 | ||||||||
\(467\) | 17.3031 | 0.800693 | 0.400346 | − | 0.916364i | \(-0.368890\pi\) | ||||
0.400346 | + | 0.916364i | \(0.368890\pi\) | |||||||
\(468\) | 16.3204 | 0.754409 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −24.7437 | −1.14134 | ||||||||
\(471\) | 5.55913 | 0.256151 | ||||||||
\(472\) | 5.34162 | 0.245868 | ||||||||
\(473\) | 0.870479 | 0.0400247 | ||||||||
\(474\) | −3.24951 | −0.149255 | ||||||||
\(475\) | −11.7499 | −0.539122 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −20.6727 | −0.946537 | ||||||||
\(478\) | −6.29887 | −0.288103 | ||||||||
\(479\) | 38.6426 | 1.76563 | 0.882813 | − | 0.469724i | \(-0.155647\pi\) | ||||
0.882813 | + | 0.469724i | \(0.155647\pi\) | |||||||
\(480\) | 0.809374 | 0.0369427 | ||||||||
\(481\) | 59.9650 | 2.73417 | ||||||||
\(482\) | −9.49953 | −0.432692 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.53746 | 0.433521 | ||||||||
\(485\) | 6.43926 | 0.292392 | ||||||||
\(486\) | −7.83817 | −0.355546 | ||||||||
\(487\) | −15.0759 | −0.683156 | −0.341578 | − | 0.939853i | \(-0.610961\pi\) | ||||
−0.341578 | + | 0.939853i | \(0.610961\pi\) | |||||||
\(488\) | 1.85948 | 0.0841747 | ||||||||
\(489\) | −0.925397 | −0.0418479 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.05333 | −0.0926653 | −0.0463327 | − | 0.998926i | \(-0.514753\pi\) | ||||
−0.0463327 | + | 0.998926i | \(0.514753\pi\) | |||||||
\(492\) | 0.302513 | 0.0136383 | ||||||||
\(493\) | 3.24678 | 0.146227 | ||||||||
\(494\) | −30.5478 | −1.37441 | ||||||||
\(495\) | −35.2652 | −1.58505 | ||||||||
\(496\) | −0.837499 | −0.0376048 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.52332 | −0.113073 | ||||||||
\(499\) | −6.89466 | −0.308647 | −0.154324 | − | 0.988020i | \(-0.549320\pi\) | ||||
−0.154324 | + | 0.988020i | \(0.549320\pi\) | |||||||
\(500\) | 7.60291 | 0.340012 | ||||||||
\(501\) | −2.98897 | −0.133537 | ||||||||
\(502\) | 11.1562 | 0.497926 | ||||||||
\(503\) | −29.2548 | −1.30441 | −0.652204 | − | 0.758043i | \(-0.726156\pi\) | ||||
−0.652204 | + | 0.758043i | \(0.726156\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.0779 | 1.69444 | ||||||||
\(506\) | 19.5813 | 0.870493 | ||||||||
\(507\) | 5.59243 | 0.248369 | ||||||||
\(508\) | 2.23213 | 0.0990346 | ||||||||
\(509\) | −16.1722 | −0.716819 | −0.358409 | − | 0.933565i | \(-0.616681\pi\) | ||||
−0.358409 | + | 0.933565i | \(0.616681\pi\) | |||||||
\(510\) | −0.997943 | −0.0441897 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 9.73053 | 0.429613 | ||||||||
\(514\) | −13.6549 | −0.602291 | ||||||||
\(515\) | 33.2841 | 1.46667 | ||||||||
\(516\) | −0.0581070 | −0.00255802 | ||||||||
\(517\) | 41.9114 | 1.84326 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.53256 | −0.155062 | ||||||||
\(520\) | −15.0130 | −0.658365 | ||||||||
\(521\) | −12.1289 | −0.531379 | −0.265689 | − | 0.964059i | \(-0.585600\pi\) | ||||
−0.265689 | + | 0.964059i | \(0.585600\pi\) | |||||||
\(522\) | −7.65884 | −0.335218 | ||||||||
\(523\) | 2.15169 | 0.0940868 | 0.0470434 | − | 0.998893i | \(-0.485020\pi\) | ||||
0.0470434 | + | 0.998893i | \(0.485020\pi\) | |||||||
\(524\) | −21.0340 | −0.918875 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.43132 | −0.236817 | ||||||||
\(527\) | 1.03262 | 0.0449816 | ||||||||
\(528\) | −1.37094 | −0.0596623 | ||||||||
\(529\) | −4.33044 | −0.188280 | ||||||||
\(530\) | 19.0167 | 0.826034 | ||||||||
\(531\) | 15.5360 | 0.674206 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.61129 | −0.243052 | ||||||||
\(534\) | −0.618119 | −0.0267486 | ||||||||
\(535\) | −18.0847 | −0.781870 | ||||||||
\(536\) | 15.8741 | 0.685655 | ||||||||
\(537\) | 2.18077 | 0.0941070 | ||||||||
\(538\) | −19.3636 | −0.834826 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.78218 | 0.205792 | ||||||||
\(541\) | −14.8636 | −0.639035 | −0.319517 | − | 0.947580i | \(-0.603521\pi\) | ||||
−0.319517 | + | 0.947580i | \(0.603521\pi\) | |||||||
\(542\) | −15.6578 | −0.672559 | ||||||||
\(543\) | −5.20332 | −0.223296 | ||||||||
\(544\) | 1.23298 | 0.0528636 | ||||||||
\(545\) | 21.9155 | 0.938758 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.71360 | −0.287053 | −0.143526 | − | 0.989646i | \(-0.545844\pi\) | ||||
−0.143526 | + | 0.989646i | \(0.545844\pi\) | |||||||
\(548\) | −3.54818 | −0.151571 | ||||||||
\(549\) | 5.40827 | 0.230820 | ||||||||
\(550\) | 9.78117 | 0.417070 | ||||||||
\(551\) | 14.3355 | 0.610713 | ||||||||
\(552\) | −1.30711 | −0.0556341 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.44438 | −0.0613659 | ||||||||
\(555\) | 8.64937 | 0.367145 | ||||||||
\(556\) | −2.80375 | −0.118905 | ||||||||
\(557\) | 25.8666 | 1.09600 | 0.548002 | − | 0.836477i | \(-0.315389\pi\) | ||||
0.548002 | + | 0.836477i | \(0.315389\pi\) | |||||||
\(558\) | −2.43585 | −0.103118 | ||||||||
\(559\) | 1.07782 | 0.0455871 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.69034 | 0.0713661 | ||||||||
\(562\) | 9.76875 | 0.412070 | ||||||||
\(563\) | −9.18039 | −0.386907 | −0.193454 | − | 0.981109i | \(-0.561969\pi\) | ||||
−0.193454 | + | 0.981109i | \(0.561969\pi\) | |||||||
\(564\) | −2.79771 | −0.117805 | ||||||||
\(565\) | −32.8714 | −1.38291 | ||||||||
\(566\) | 18.8705 | 0.793188 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.9802 | −0.502678 | ||||||||
\(569\) | 4.68175 | 0.196269 | 0.0981346 | − | 0.995173i | \(-0.468712\pi\) | ||||
0.0981346 | + | 0.995173i | \(0.468712\pi\) | |||||||
\(570\) | −4.40622 | −0.184556 | ||||||||
\(571\) | −35.7090 | −1.49438 | −0.747188 | − | 0.664613i | \(-0.768597\pi\) | ||||
−0.747188 | + | 0.664613i | \(0.768597\pi\) | |||||||
\(572\) | 25.4294 | 1.06326 | ||||||||
\(573\) | 2.76655 | 0.115574 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.32576 | 0.388911 | ||||||||
\(576\) | −2.90849 | −0.121187 | ||||||||
\(577\) | 20.7675 | 0.864562 | 0.432281 | − | 0.901739i | \(-0.357709\pi\) | ||||
0.432281 | + | 0.901739i | \(0.357709\pi\) | |||||||
\(578\) | 15.4798 | 0.643873 | ||||||||
\(579\) | −4.05906 | −0.168689 | ||||||||
\(580\) | 7.04534 | 0.292542 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0.728071 | 0.0301795 | ||||||||
\(583\) | −32.2109 | −1.33404 | ||||||||
\(584\) | −8.70958 | −0.360405 | ||||||||
\(585\) | −43.6652 | −1.80533 | ||||||||
\(586\) | −7.66092 | −0.316470 | ||||||||
\(587\) | −3.24039 | −0.133745 | −0.0668727 | − | 0.997762i | \(-0.521302\pi\) | ||||
−0.0668727 | + | 0.997762i | \(0.521302\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.55933 | 0.187864 | ||||||||
\(590\) | −14.2915 | −0.588373 | ||||||||
\(591\) | −4.95495 | −0.203819 | ||||||||
\(592\) | −10.6865 | −0.439212 | ||||||||
\(593\) | −6.41962 | −0.263622 | −0.131811 | − | 0.991275i | \(-0.542079\pi\) | ||||
−0.131811 | + | 0.991275i | \(0.542079\pi\) | |||||||
\(594\) | −8.10015 | −0.332353 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.0302850 | −0.00124052 | ||||||||
\(597\) | −3.56182 | −0.145776 | ||||||||
\(598\) | 24.2454 | 0.991470 | ||||||||
\(599\) | −18.8108 | −0.768590 | −0.384295 | − | 0.923210i | \(-0.625555\pi\) | ||||
−0.384295 | + | 0.923210i | \(0.625555\pi\) | |||||||
\(600\) | −0.652922 | −0.0266554 | ||||||||
\(601\) | 25.4939 | 1.03992 | 0.519959 | − | 0.854191i | \(-0.325947\pi\) | ||||
0.519959 | + | 0.854191i | \(0.325947\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 46.1695 | 1.88017 | ||||||||
\(604\) | −17.2199 | −0.700669 | ||||||||
\(605\) | −25.5175 | −1.03744 | ||||||||
\(606\) | 4.30537 | 0.174894 | ||||||||
\(607\) | 35.3309 | 1.43404 | 0.717018 | − | 0.697054i | \(-0.245506\pi\) | ||||
0.717018 | + | 0.697054i | \(0.245506\pi\) | |||||||
\(608\) | 5.44398 | 0.220783 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.97505 | −0.201434 | ||||||||
\(611\) | 51.8945 | 2.09943 | ||||||||
\(612\) | 3.58611 | 0.144960 | ||||||||
\(613\) | −8.34101 | −0.336890 | −0.168445 | − | 0.985711i | \(-0.553875\pi\) | ||||
−0.168445 | + | 0.985711i | \(0.553875\pi\) | |||||||
\(614\) | 3.85361 | 0.155519 | ||||||||
\(615\) | −0.809374 | −0.0326371 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.8143 | 0.757435 | 0.378717 | − | 0.925512i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925512i | \(0.376365\pi\) | |||||||
\(618\) | 3.76335 | 0.151384 | ||||||||
\(619\) | −30.9426 | −1.24369 | −0.621844 | − | 0.783141i | \(-0.713616\pi\) | ||||
−0.621844 | + | 0.783141i | \(0.713616\pi\) | |||||||
\(620\) | 2.24073 | 0.0899900 | ||||||||
\(621\) | −7.72302 | −0.309914 | ||||||||
\(622\) | 0.951906 | 0.0381680 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.69749 | −0.0679539 | ||||||||
\(625\) | −31.1333 | −1.24533 | ||||||||
\(626\) | 23.7853 | 0.950653 | ||||||||
\(627\) | 7.46335 | 0.298057 | ||||||||
\(628\) | 18.3765 | 0.733303 | ||||||||
\(629\) | 13.1762 | 0.525371 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.4094 | −0.573629 | −0.286815 | − | 0.957986i | \(-0.592596\pi\) | ||||
−0.286815 | + | 0.957986i | \(0.592596\pi\) | |||||||
\(632\) | −10.7417 | −0.427283 | ||||||||
\(633\) | 5.54546 | 0.220412 | ||||||||
\(634\) | 7.44237 | 0.295574 | ||||||||
\(635\) | −5.97207 | −0.236994 | ||||||||
\(636\) | 2.15017 | 0.0852599 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.9335 | −0.472454 | ||||||||
\(639\) | −34.8442 | −1.37842 | ||||||||
\(640\) | 2.67551 | 0.105759 | ||||||||
\(641\) | −49.4030 | −1.95130 | −0.975650 | − | 0.219335i | \(-0.929611\pi\) | ||||
−0.975650 | + | 0.219335i | \(0.929611\pi\) | |||||||
\(642\) | −2.04479 | −0.0807016 | ||||||||
\(643\) | −0.960171 | −0.0378655 | −0.0189327 | − | 0.999821i | \(-0.506027\pi\) | ||||
−0.0189327 | + | 0.999821i | \(0.506027\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.155466 | 0.00612145 | ||||||||
\(646\) | −6.71232 | −0.264093 | ||||||||
\(647\) | −28.4291 | −1.11767 | −0.558833 | − | 0.829280i | \(-0.688751\pi\) | ||||
−0.558833 | + | 0.829280i | \(0.688751\pi\) | |||||||
\(648\) | −8.18475 | −0.321527 | ||||||||
\(649\) | 24.2073 | 0.950220 | ||||||||
\(650\) | 12.1110 | 0.475033 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.05903 | −0.119801 | ||||||||
\(653\) | −45.5729 | −1.78341 | −0.891703 | − | 0.452621i | \(-0.850489\pi\) | ||||
−0.891703 | + | 0.452621i | \(0.850489\pi\) | |||||||
\(654\) | 2.47793 | 0.0968948 | ||||||||
\(655\) | 56.2766 | 2.19891 | ||||||||
\(656\) | 1.00000 | 0.0390434 | ||||||||
\(657\) | −25.3317 | −0.988284 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −27.5301 | −1.07242 | −0.536211 | − | 0.844084i | \(-0.680145\pi\) | ||||
−0.536211 | + | 0.844084i | \(0.680145\pi\) | |||||||
\(660\) | 3.66795 | 0.142775 | ||||||||
\(661\) | −36.5640 | −1.42217 | −0.711087 | − | 0.703104i | \(-0.751797\pi\) | ||||
−0.711087 | + | 0.703104i | \(0.751797\pi\) | |||||||
\(662\) | −20.3269 | −0.790028 | ||||||||
\(663\) | 2.09297 | 0.0812842 | ||||||||
\(664\) | −8.34120 | −0.323701 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −31.0815 | −1.20438 | ||||||||
\(667\) | −11.3779 | −0.440555 | ||||||||
\(668\) | −9.88049 | −0.382287 | ||||||||
\(669\) | −5.94274 | −0.229759 | ||||||||
\(670\) | −42.4711 | −1.64080 | ||||||||
\(671\) | 8.42685 | 0.325315 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.2388 | 0.703053 | 0.351526 | − | 0.936178i | \(-0.385663\pi\) | ||||
0.351526 | + | 0.936178i | \(0.385663\pi\) | |||||||
\(674\) | 32.6366 | 1.25711 | ||||||||
\(675\) | −3.85778 | −0.148486 | ||||||||
\(676\) | 18.4866 | 0.711023 | ||||||||
\(677\) | 6.40683 | 0.246234 | 0.123117 | − | 0.992392i | \(-0.460711\pi\) | ||||
0.123117 | + | 0.992392i | \(0.460711\pi\) | |||||||
\(678\) | −3.71669 | −0.142739 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.29885 | −0.126505 | ||||||||
\(681\) | −2.65755 | −0.101838 | ||||||||
\(682\) | −3.79540 | −0.145333 | ||||||||
\(683\) | 21.4613 | 0.821195 | 0.410598 | − | 0.911817i | \(-0.365320\pi\) | ||||
0.410598 | + | 0.911817i | \(0.365320\pi\) | |||||||
\(684\) | 15.8337 | 0.605418 | ||||||||
\(685\) | 9.49318 | 0.362716 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.08628 | 0.0795964 | ||||||||
\(688\) | −0.192081 | −0.00732303 | ||||||||
\(689\) | −39.8835 | −1.51944 | ||||||||
\(690\) | 3.49717 | 0.133135 | ||||||||
\(691\) | 23.4540 | 0.892231 | 0.446115 | − | 0.894975i | \(-0.352807\pi\) | ||||
0.446115 | + | 0.894975i | \(0.352807\pi\) | |||||||
\(692\) | −11.6774 | −0.443907 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.9767 | −1.32770 | ||||||||
\(695\) | 7.50143 | 0.284546 | ||||||||
\(696\) | 0.796599 | 0.0301950 | ||||||||
\(697\) | −1.23298 | −0.0467025 | ||||||||
\(698\) | 2.25155 | 0.0852225 | ||||||||
\(699\) | 9.20343 | 0.348106 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.1862 | −1.06458 | −0.532290 | − | 0.846562i | \(-0.678668\pi\) | ||||
−0.532290 | + | 0.846562i | \(0.678668\pi\) | |||||||
\(702\) | −10.0296 | −0.378542 | ||||||||
\(703\) | 58.1770 | 2.19419 | ||||||||
\(704\) | −4.53183 | −0.170800 | ||||||||
\(705\) | 7.48528 | 0.281912 | ||||||||
\(706\) | 30.6220 | 1.15247 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.61591 | −0.0607296 | ||||||||
\(709\) | −5.90510 | −0.221771 | −0.110885 | − | 0.993833i | \(-0.535369\pi\) | ||||
−0.110885 | + | 0.993833i | \(0.535369\pi\) | |||||||
\(710\) | 32.0531 | 1.20293 | ||||||||
\(711\) | −31.2421 | −1.17167 | ||||||||
\(712\) | −2.04328 | −0.0765752 | ||||||||
\(713\) | −3.61869 | −0.135521 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −68.0365 | −2.54442 | ||||||||
\(716\) | 7.20884 | 0.269407 | ||||||||
\(717\) | 1.90549 | 0.0711617 | ||||||||
\(718\) | 19.1701 | 0.715421 | ||||||||
\(719\) | 34.0146 | 1.26853 | 0.634265 | − | 0.773115i | \(-0.281303\pi\) | ||||
0.634265 | + | 0.773115i | \(0.281303\pi\) | |||||||
\(720\) | 7.78167 | 0.290006 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −10.6369 | −0.395865 | ||||||||
\(723\) | 2.87373 | 0.106875 | ||||||||
\(724\) | −17.2003 | −0.639246 | ||||||||
\(725\) | −5.68347 | −0.211079 | ||||||||
\(726\) | −2.88520 | −0.107080 | ||||||||
\(727\) | 24.5472 | 0.910405 | 0.455202 | − | 0.890388i | \(-0.349567\pi\) | ||||
0.455202 | + | 0.890388i | \(0.349567\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.1831 | −0.821596 | ||||||||
\(730\) | 23.3025 | 0.862465 | ||||||||
\(731\) | 0.236832 | 0.00875956 | ||||||||
\(732\) | −0.562517 | −0.0207912 | ||||||||
\(733\) | 38.3455 | 1.41632 | 0.708162 | − | 0.706050i | \(-0.249525\pi\) | ||||
0.708162 | + | 0.706050i | \(0.249525\pi\) | |||||||
\(734\) | 30.3024 | 1.11848 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.32083 | −0.159268 | ||||||||
\(737\) | 71.9385 | 2.64989 | ||||||||
\(738\) | 2.90849 | 0.107063 | ||||||||
\(739\) | 22.2910 | 0.819986 | 0.409993 | − | 0.912089i | \(-0.365531\pi\) | ||||
0.409993 | + | 0.912089i | \(0.365531\pi\) | |||||||
\(740\) | 28.5918 | 1.05105 | ||||||||
\(741\) | 9.24109 | 0.339480 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.7524 | 0.871392 | 0.435696 | − | 0.900094i | \(-0.356502\pi\) | ||||
0.435696 | + | 0.900094i | \(0.356502\pi\) | |||||||
\(744\) | 0.253354 | 0.00928841 | ||||||||
\(745\) | 0.0810277 | 0.00296863 | ||||||||
\(746\) | −28.5671 | −1.04592 | ||||||||
\(747\) | −24.2603 | −0.887637 | ||||||||
\(748\) | 5.58766 | 0.204305 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −2.29998 | −0.0839833 | ||||||||
\(751\) | 32.5879 | 1.18915 | 0.594574 | − | 0.804041i | \(-0.297321\pi\) | ||||
0.594574 | + | 0.804041i | \(0.297321\pi\) | |||||||
\(752\) | −9.24823 | −0.337248 | ||||||||
\(753\) | −3.37489 | −0.122988 | ||||||||
\(754\) | −14.7761 | −0.538113 | ||||||||
\(755\) | 46.0720 | 1.67673 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.8281 | −0.829702 | −0.414851 | − | 0.909889i | \(-0.636166\pi\) | ||||
−0.414851 | + | 0.909889i | \(0.636166\pi\) | |||||||
\(758\) | 33.0736 | 1.20129 | ||||||||
\(759\) | −5.92358 | −0.215012 | ||||||||
\(760\) | −14.5654 | −0.528342 | ||||||||
\(761\) | −48.7280 | −1.76639 | −0.883195 | − | 0.469007i | \(-0.844612\pi\) | ||||
−0.883195 | + | 0.469007i | \(0.844612\pi\) | |||||||
\(762\) | −0.675247 | −0.0244616 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 9.14524 | 0.330863 | ||||||||
\(765\) | −9.59465 | −0.346895 | ||||||||
\(766\) | −17.0073 | −0.614498 | ||||||||
\(767\) | 29.9734 | 1.08228 | ||||||||
\(768\) | 0.302513 | 0.0109160 | ||||||||
\(769\) | 21.9943 | 0.793135 | 0.396568 | − | 0.918006i | \(-0.370201\pi\) | ||||
0.396568 | + | 0.918006i | \(0.370201\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.13078 | 0.148766 | ||||||||
\(772\) | −13.4178 | −0.482918 | ||||||||
\(773\) | 51.8024 | 1.86320 | 0.931602 | − | 0.363481i | \(-0.118412\pi\) | ||||
0.931602 | + | 0.363481i | \(0.118412\pi\) | |||||||
\(774\) | −0.558665 | −0.0200808 | ||||||||
\(775\) | −1.80760 | −0.0649308 | ||||||||
\(776\) | 2.40675 | 0.0863971 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −20.2684 | −0.726657 | ||||||||
\(779\) | −5.44398 | −0.195051 | ||||||||
\(780\) | 4.54164 | 0.162617 | ||||||||
\(781\) | −54.2922 | −1.94273 | ||||||||
\(782\) | 5.32750 | 0.190511 | ||||||||
\(783\) | 4.70669 | 0.168204 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −49.1665 | −1.75483 | ||||||||
\(786\) | 6.36306 | 0.226963 | ||||||||
\(787\) | 37.1629 | 1.32471 | 0.662357 | − | 0.749188i | \(-0.269556\pi\) | ||||
0.662357 | + | 0.749188i | \(0.269556\pi\) | |||||||
\(788\) | −16.3793 | −0.583489 | ||||||||
\(789\) | 1.64304 | 0.0584939 | ||||||||
\(790\) | 28.7395 | 1.02251 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −13.1808 | −0.468358 | ||||||||
\(793\) | 10.4341 | 0.370525 | ||||||||
\(794\) | 10.9200 | 0.387537 | ||||||||
\(795\) | −5.75280 | −0.204031 | ||||||||
\(796\) | −11.7741 | −0.417322 | ||||||||
\(797\) | 18.7534 | 0.664279 | 0.332139 | − | 0.943230i | \(-0.392230\pi\) | ||||
0.332139 | + | 0.943230i | \(0.392230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.4029 | 0.403405 | ||||||||
\(800\) | −2.15833 | −0.0763084 | ||||||||
\(801\) | −5.94286 | −0.209981 | ||||||||
\(802\) | 13.3283 | 0.470640 | ||||||||
\(803\) | −39.4703 | −1.39288 | ||||||||
\(804\) | −4.80210 | −0.169357 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.69945 | −0.165531 | ||||||||
\(807\) | 5.85775 | 0.206202 | ||||||||
\(808\) | 14.2320 | 0.500681 | ||||||||
\(809\) | 13.0276 | 0.458028 | 0.229014 | − | 0.973423i | \(-0.426450\pi\) | ||||
0.229014 | + | 0.973423i | \(0.426450\pi\) | |||||||
\(810\) | 21.8983 | 0.769429 | ||||||||
\(811\) | −35.4164 | −1.24364 | −0.621819 | − | 0.783161i | \(-0.713606\pi\) | ||||
−0.621819 | + | 0.783161i | \(0.713606\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.73667 | 0.166122 | ||||||||
\(814\) | −48.4293 | −1.69745 | ||||||||
\(815\) | 8.18446 | 0.286689 | ||||||||
\(816\) | −0.372992 | −0.0130573 | ||||||||
\(817\) | 1.04569 | 0.0365839 | ||||||||
\(818\) | 18.8109 | 0.657708 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.67551 | −0.0934327 | ||||||||
\(821\) | −43.7803 | −1.52794 | −0.763972 | − | 0.645250i | \(-0.776753\pi\) | ||||
−0.763972 | + | 0.645250i | \(0.776753\pi\) | |||||||
\(822\) | 1.07337 | 0.0374381 | ||||||||
\(823\) | 32.2317 | 1.12353 | 0.561764 | − | 0.827298i | \(-0.310123\pi\) | ||||
0.561764 | + | 0.827298i | \(0.310123\pi\) | |||||||
\(824\) | 12.4403 | 0.433379 | ||||||||
\(825\) | −2.95893 | −0.103017 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.4846 | 0.434132 | 0.217066 | − | 0.976157i | \(-0.430351\pi\) | ||||
0.217066 | + | 0.976157i | \(0.430351\pi\) | |||||||
\(828\) | −12.5671 | −0.436736 | ||||||||
\(829\) | −21.3862 | −0.742774 | −0.371387 | − | 0.928478i | \(-0.621118\pi\) | ||||
−0.371387 | + | 0.928478i | \(0.621118\pi\) | |||||||
\(830\) | 22.3169 | 0.774632 | ||||||||
\(831\) | 0.436944 | 0.0151574 | ||||||||
\(832\) | −5.61129 | −0.194537 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0.848169 | 0.0293697 | ||||||||
\(835\) | 26.4353 | 0.914831 | ||||||||
\(836\) | 24.6712 | 0.853271 | ||||||||
\(837\) | 1.49694 | 0.0517418 | ||||||||
\(838\) | −8.19107 | −0.282956 | ||||||||
\(839\) | −48.9609 | −1.69032 | −0.845159 | − | 0.534515i | \(-0.820494\pi\) | ||||
−0.845159 | + | 0.534515i | \(0.820494\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.0659 | −0.760892 | ||||||||
\(842\) | −40.6667 | −1.40147 | ||||||||
\(843\) | −2.95517 | −0.101781 | ||||||||
\(844\) | 18.3313 | 0.630990 | ||||||||
\(845\) | −49.4610 | −1.70151 | ||||||||
\(846\) | −26.8984 | −0.924785 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.10771 | 0.244080 | ||||||||
\(849\) | −5.70858 | −0.195918 | ||||||||
\(850\) | 2.66118 | 0.0912776 | ||||||||
\(851\) | −46.1745 | −1.58284 | ||||||||
\(852\) | 3.62416 | 0.124162 | ||||||||
\(853\) | −24.1910 | −0.828284 | −0.414142 | − | 0.910212i | \(-0.635918\pi\) | ||||
−0.414142 | + | 0.910212i | \(0.635918\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −42.3633 | −1.44879 | ||||||||
\(856\) | −6.75937 | −0.231030 | ||||||||
\(857\) | −47.5547 | −1.62444 | −0.812218 | − | 0.583353i | \(-0.801740\pi\) | ||||
−0.812218 | + | 0.583353i | \(0.801740\pi\) | |||||||
\(858\) | −7.69272 | −0.262625 | ||||||||
\(859\) | −27.7055 | −0.945299 | −0.472649 | − | 0.881251i | \(-0.656702\pi\) | ||||
−0.472649 | + | 0.881251i | \(0.656702\pi\) | |||||||
\(860\) | 0.513914 | 0.0175243 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.8454 | 0.369394 | ||||||||
\(863\) | −4.05610 | −0.138071 | −0.0690355 | − | 0.997614i | \(-0.521992\pi\) | ||||
−0.0690355 | + | 0.997614i | \(0.521992\pi\) | |||||||
\(864\) | 1.78739 | 0.0608083 | ||||||||
\(865\) | 31.2429 | 1.06229 | ||||||||
\(866\) | 12.5834 | 0.427601 | ||||||||
\(867\) | −4.68282 | −0.159037 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −48.6796 | −1.65134 | ||||||||
\(870\) | −2.13130 | −0.0722580 | ||||||||
\(871\) | 89.0739 | 3.01816 | ||||||||
\(872\) | 8.19117 | 0.277388 | ||||||||
\(873\) | 6.99999 | 0.236914 | ||||||||
\(874\) | 23.5225 | 0.795661 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.63476 | 0.0890203 | ||||||||
\(877\) | −35.6867 | −1.20505 | −0.602527 | − | 0.798098i | \(-0.705840\pi\) | ||||
−0.602527 | + | 0.798098i | \(0.705840\pi\) | |||||||
\(878\) | −30.3023 | −1.02265 | ||||||||
\(879\) | 2.31753 | 0.0781682 | ||||||||
\(880\) | 12.1249 | 0.408731 | ||||||||
\(881\) | −53.2845 | −1.79520 | −0.897601 | − | 0.440809i | \(-0.854692\pi\) | ||||
−0.897601 | + | 0.440809i | \(0.854692\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.6827 | 0.998902 | 0.499451 | − | 0.866342i | \(-0.333535\pi\) | ||||
0.499451 | + | 0.866342i | \(0.333535\pi\) | |||||||
\(884\) | 6.91862 | 0.232698 | ||||||||
\(885\) | 4.32337 | 0.145329 | ||||||||
\(886\) | 20.0561 | 0.673797 | ||||||||
\(887\) | 14.9807 | 0.503001 | 0.251501 | − | 0.967857i | \(-0.419076\pi\) | ||||
0.251501 | + | 0.967857i | \(0.419076\pi\) | |||||||
\(888\) | 3.23280 | 0.108486 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.46681 | 0.183248 | ||||||||
\(891\) | −37.0919 | −1.24262 | ||||||||
\(892\) | −19.6446 | −0.657749 | ||||||||
\(893\) | 50.3472 | 1.68480 | ||||||||
\(894\) | 0.00916161 | 0.000306410 0 | ||||||||
\(895\) | −19.2873 | −0.644703 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.33455 | −0.244894 | ||||||||
\(898\) | −35.2349 | −1.17581 | ||||||||
\(899\) | 2.20536 | 0.0735530 | ||||||||
\(900\) | −6.27747 | −0.209249 | ||||||||
\(901\) | −8.76368 | −0.291960 | ||||||||
\(902\) | 4.53183 | 0.150893 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.2861 | −0.408629 | ||||||||
\(905\) | 46.0196 | 1.52974 | ||||||||
\(906\) | 5.20925 | 0.173066 | ||||||||
\(907\) | 26.2259 | 0.870818 | 0.435409 | − | 0.900233i | \(-0.356604\pi\) | ||||
0.435409 | + | 0.900233i | \(0.356604\pi\) | |||||||
\(908\) | −8.78493 | −0.291538 | ||||||||
\(909\) | 41.3937 | 1.37294 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.6221 | −0.351926 | −0.175963 | − | 0.984397i | \(-0.556304\pi\) | ||||
−0.175963 | + | 0.984397i | \(0.556304\pi\) | |||||||
\(912\) | −1.64687 | −0.0545334 | ||||||||
\(913\) | −37.8009 | −1.25103 | ||||||||
\(914\) | −33.9064 | −1.12152 | ||||||||
\(915\) | 1.50502 | 0.0497543 | ||||||||
\(916\) | 6.89649 | 0.227867 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.20382 | −0.0727369 | ||||||||
\(919\) | 18.8892 | 0.623099 | 0.311549 | − | 0.950230i | \(-0.399152\pi\) | ||||
0.311549 | + | 0.950230i | \(0.399152\pi\) | |||||||
\(920\) | 11.5604 | 0.381135 | ||||||||
\(921\) | −1.16577 | −0.0384133 | ||||||||
\(922\) | −12.2136 | −0.402234 | ||||||||
\(923\) | −67.2244 | −2.21272 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.0649 | −0.758371 | ||||||||
\(926\) | 9.17302 | 0.301444 | ||||||||
\(927\) | 36.1825 | 1.18839 | ||||||||
\(928\) | 2.63327 | 0.0864415 | ||||||||
\(929\) | 9.37707 | 0.307652 | 0.153826 | − | 0.988098i | \(-0.450841\pi\) | ||||
0.153826 | + | 0.988098i | \(0.450841\pi\) | |||||||
\(930\) | −0.677850 | −0.0222276 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 30.4233 | 0.996547 | ||||||||
\(933\) | −0.287964 | −0.00942751 | ||||||||
\(934\) | −17.3031 | −0.566175 | ||||||||
\(935\) | −14.9498 | −0.488911 | ||||||||
\(936\) | −16.3204 | −0.533448 | ||||||||
\(937\) | −48.0417 | −1.56945 | −0.784727 | − | 0.619841i | \(-0.787197\pi\) | ||||
−0.784727 | + | 0.619841i | \(0.787197\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.19536 | −0.234812 | ||||||||
\(940\) | 24.7437 | 0.807050 | ||||||||
\(941\) | 6.62455 | 0.215954 | 0.107977 | − | 0.994153i | \(-0.465563\pi\) | ||||
0.107977 | + | 0.994153i | \(0.465563\pi\) | |||||||
\(942\) | −5.55913 | −0.181126 | ||||||||
\(943\) | 4.32083 | 0.140706 | ||||||||
\(944\) | −5.34162 | −0.173855 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.870479 | −0.0283017 | ||||||||
\(947\) | 38.1609 | 1.24006 | 0.620032 | − | 0.784577i | \(-0.287120\pi\) | ||||
0.620032 | + | 0.784577i | \(0.287120\pi\) | |||||||
\(948\) | 3.24951 | 0.105539 | ||||||||
\(949\) | −48.8720 | −1.58645 | ||||||||
\(950\) | 11.7499 | 0.381217 | ||||||||
\(951\) | −2.25141 | −0.0730070 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.36423 | −0.173765 | −0.0868823 | − | 0.996219i | \(-0.527690\pi\) | ||||
−0.0868823 | + | 0.996219i | \(0.527690\pi\) | |||||||
\(954\) | 20.6727 | 0.669303 | ||||||||
\(955\) | −24.4681 | −0.791770 | ||||||||
\(956\) | 6.29887 | 0.203720 | ||||||||
\(957\) | 3.61005 | 0.116696 | ||||||||
\(958\) | −38.6426 | −1.24849 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.809374 | −0.0261224 | ||||||||
\(961\) | −30.2986 | −0.977374 | ||||||||
\(962\) | −59.9650 | −1.93335 | ||||||||
\(963\) | −19.6595 | −0.633519 | ||||||||
\(964\) | 9.49953 | 0.305959 | ||||||||
\(965\) | 35.8995 | 1.15565 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.2209 | −0.553786 | −0.276893 | − | 0.960901i | \(-0.589305\pi\) | ||||
−0.276893 | + | 0.960901i | \(0.589305\pi\) | |||||||
\(968\) | −9.53746 | −0.306546 | ||||||||
\(969\) | 2.03056 | 0.0652311 | ||||||||
\(970\) | −6.43926 | −0.206752 | ||||||||
\(971\) | −45.3102 | −1.45407 | −0.727037 | − | 0.686598i | \(-0.759103\pi\) | ||||
−0.727037 | + | 0.686598i | \(0.759103\pi\) | |||||||
\(972\) | 7.83817 | 0.251409 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 15.0759 | 0.483064 | ||||||||
\(975\) | −3.66373 | −0.117333 | ||||||||
\(976\) | −1.85948 | −0.0595205 | ||||||||
\(977\) | −38.2813 | −1.22473 | −0.612364 | − | 0.790576i | \(-0.709781\pi\) | ||||
−0.612364 | + | 0.790576i | \(0.709781\pi\) | |||||||
\(978\) | 0.925397 | 0.0295909 | ||||||||
\(979\) | −9.25980 | −0.295945 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.8239 | 0.760639 | ||||||||
\(982\) | 2.05333 | 0.0655243 | ||||||||
\(983\) | 12.4157 | 0.395998 | 0.197999 | − | 0.980202i | \(-0.436556\pi\) | ||||
0.197999 | + | 0.980202i | \(0.436556\pi\) | |||||||
\(984\) | −0.302513 | −0.00964375 | ||||||||
\(985\) | 43.8229 | 1.39631 | ||||||||
\(986\) | −3.24678 | −0.103398 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 30.5478 | 0.971854 | ||||||||
\(989\) | −0.829950 | −0.0263909 | ||||||||
\(990\) | 35.2652 | 1.12080 | ||||||||
\(991\) | −23.3035 | −0.740260 | −0.370130 | − | 0.928980i | \(-0.620687\pi\) | ||||
−0.370130 | + | 0.928980i | \(0.620687\pi\) | |||||||
\(992\) | 0.837499 | 0.0265906 | ||||||||
\(993\) | 6.14915 | 0.195137 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.5017 | 0.998671 | ||||||||
\(996\) | 2.52332 | 0.0799544 | ||||||||
\(997\) | −32.5685 | −1.03145 | −0.515727 | − | 0.856753i | \(-0.672478\pi\) | ||||
−0.515727 | + | 0.856753i | \(0.672478\pi\) | |||||||
\(998\) | 6.89466 | 0.218247 | ||||||||
\(999\) | 19.1009 | 0.604327 |
(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 | 4018.2.a.bo.1.4 | 6 | ||
7.2 | even | 3 | 574.2.e.g.165.3 | ✓ | 12 | ||
7.4 | even | 3 | 574.2.e.g.247.3 | yes | 12 | ||
7.6 | odd | 2 | 4018.2.a.bn.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
574.2.e.g.165.3 | ✓ | 12 | 7.2 | even | 3 | ||
574.2.e.g.247.3 | yes | 12 | 7.4 | even | 3 | ||
4018.2.a.bn.1.3 | 6 | 7.6 | odd | 2 | |||
4018.2.a.bo.1.4 | 6 | 1.1 | even | 1 | trivial |