Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.745749504.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 18x^{4} - 4x^{3} + 81x^{2} + 36x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.40870\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | −3.40870 | −1.96801 | −0.984007 | − | 0.178129i | \(-0.942995\pi\) | ||||
−0.984007 | + | 0.178129i | \(0.942995\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −3.40870 | −1.39160 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 8.61924 | 2.87308 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.40870 | −0.984007 | ||||||||
\(13\) | −3.69350 | −1.02439 | −0.512197 | − | 0.858868i | \(-0.671168\pi\) | ||||
−0.512197 | + | 0.858868i | \(0.671168\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 3.40870 | 0.880123 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.63060 | −0.880551 | −0.440275 | − | 0.897863i | \(-0.645119\pi\) | ||||
−0.440275 | + | 0.897863i | \(0.645119\pi\) | |||||||
\(18\) | 8.61924 | 2.03157 | ||||||||
\(19\) | 2.01685 | 0.462698 | 0.231349 | − | 0.972871i | \(-0.425686\pi\) | ||||
0.231349 | + | 0.972871i | \(0.425686\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 3.40870 | 0.743839 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.90404 | −1.23108 | −0.615539 | − | 0.788106i | \(-0.711062\pi\) | ||||
−0.615539 | + | 0.788106i | \(0.711062\pi\) | |||||||
\(24\) | −3.40870 | −0.695798 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.69350 | −0.724356 | ||||||||
\(27\) | −19.1543 | −3.68625 | ||||||||
\(28\) | −1.00000 | −0.188982 | ||||||||
\(29\) | −2.77810 | −0.515880 | −0.257940 | − | 0.966161i | \(-0.583044\pi\) | ||||
−0.257940 | + | 0.966161i | \(0.583044\pi\) | |||||||
\(30\) | 3.40870 | 0.622341 | ||||||||
\(31\) | 2.98864 | 0.536775 | 0.268387 | − | 0.963311i | \(-0.413509\pi\) | ||||
0.268387 | + | 0.963311i | \(0.413509\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.63060 | −0.622643 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 8.61924 | 1.43654 | ||||||||
\(37\) | 3.22190 | 0.529678 | 0.264839 | − | 0.964293i | \(-0.414681\pi\) | ||||
0.264839 | + | 0.964293i | \(0.414681\pi\) | |||||||
\(38\) | 2.01685 | 0.327177 | ||||||||
\(39\) | 12.5900 | 2.01602 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −8.13344 | −1.27023 | −0.635115 | − | 0.772417i | \(-0.719047\pi\) | ||||
−0.635115 | + | 0.772417i | \(0.719047\pi\) | |||||||
\(42\) | 3.40870 | 0.525974 | ||||||||
\(43\) | −3.87280 | −0.590597 | −0.295298 | − | 0.955405i | \(-0.595419\pi\) | ||||
−0.295298 | + | 0.955405i | \(0.595419\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.61924 | −1.28488 | ||||||||
\(46\) | −5.90404 | −0.870504 | ||||||||
\(47\) | 9.67464 | 1.41119 | 0.705596 | − | 0.708615i | \(-0.250680\pi\) | ||||
0.705596 | + | 0.708615i | \(0.250680\pi\) | |||||||
\(48\) | −3.40870 | −0.492004 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 12.3756 | 1.73294 | ||||||||
\(52\) | −3.69350 | −0.512197 | ||||||||
\(53\) | 9.39390 | 1.29035 | 0.645175 | − | 0.764035i | \(-0.276784\pi\) | ||||
0.645175 | + | 0.764035i | \(0.276784\pi\) | |||||||
\(54\) | −19.1543 | −2.60657 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −6.87485 | −0.910596 | ||||||||
\(58\) | −2.77810 | −0.364782 | ||||||||
\(59\) | 12.8803 | 1.67687 | 0.838436 | − | 0.545000i | \(-0.183470\pi\) | ||||
0.838436 | + | 0.545000i | \(0.183470\pi\) | |||||||
\(60\) | 3.40870 | 0.440061 | ||||||||
\(61\) | −6.61375 | −0.846804 | −0.423402 | − | 0.905942i | \(-0.639164\pi\) | ||||
−0.423402 | + | 0.905942i | \(0.639164\pi\) | |||||||
\(62\) | 2.98864 | 0.379557 | ||||||||
\(63\) | −8.61924 | −1.08592 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.69350 | 0.458123 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.48599 | −0.425881 | −0.212941 | − | 0.977065i | \(-0.568304\pi\) | ||||
−0.212941 | + | 0.977065i | \(0.568304\pi\) | |||||||
\(68\) | −3.63060 | −0.440275 | ||||||||
\(69\) | 20.1251 | 2.42278 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −5.18885 | −0.615803 | −0.307901 | − | 0.951418i | \(-0.599627\pi\) | ||||
−0.307901 | + | 0.951418i | \(0.599627\pi\) | |||||||
\(72\) | 8.61924 | 1.01579 | ||||||||
\(73\) | −1.83909 | −0.215250 | −0.107625 | − | 0.994192i | \(-0.534325\pi\) | ||||
−0.107625 | + | 0.994192i | \(0.534325\pi\) | |||||||
\(74\) | 3.22190 | 0.374539 | ||||||||
\(75\) | −3.40870 | −0.393603 | ||||||||
\(76\) | 2.01685 | 0.231349 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.5900 | 1.42554 | ||||||||
\(79\) | 2.95191 | 0.332115 | 0.166058 | − | 0.986116i | \(-0.446896\pi\) | ||||
0.166058 | + | 0.986116i | \(0.446896\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 39.4336 | 4.38151 | ||||||||
\(82\) | −8.13344 | −0.898189 | ||||||||
\(83\) | −8.37746 | −0.919546 | −0.459773 | − | 0.888037i | \(-0.652069\pi\) | ||||
−0.459773 | + | 0.888037i | \(0.652069\pi\) | |||||||
\(84\) | 3.40870 | 0.371920 | ||||||||
\(85\) | 3.63060 | 0.393794 | ||||||||
\(86\) | −3.87280 | −0.417615 | ||||||||
\(87\) | 9.46970 | 1.01526 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.85724 | 0.514866 | 0.257433 | − | 0.966296i | \(-0.417123\pi\) | ||||
0.257433 | + | 0.966296i | \(0.417123\pi\) | |||||||
\(90\) | −8.61924 | −0.908548 | ||||||||
\(91\) | 3.69350 | 0.387184 | ||||||||
\(92\) | −5.90404 | −0.615539 | ||||||||
\(93\) | −10.1874 | −1.05638 | ||||||||
\(94\) | 9.67464 | 0.997863 | ||||||||
\(95\) | −2.01685 | −0.206925 | ||||||||
\(96\) | −3.40870 | −0.347899 | ||||||||
\(97\) | −16.0944 | −1.63414 | −0.817071 | − | 0.576537i | \(-0.804404\pi\) | ||||
−0.817071 | + | 0.576537i | \(0.804404\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −18.8577 | −1.87641 | −0.938207 | − | 0.346076i | \(-0.887514\pi\) | ||||
−0.938207 | + | 0.346076i | \(0.887514\pi\) | |||||||
\(102\) | 12.3756 | 1.22537 | ||||||||
\(103\) | −15.0231 | −1.48027 | −0.740135 | − | 0.672458i | \(-0.765238\pi\) | ||||
−0.740135 | + | 0.672458i | \(0.765238\pi\) | |||||||
\(104\) | −3.69350 | −0.362178 | ||||||||
\(105\) | −3.40870 | −0.332655 | ||||||||
\(106\) | 9.39390 | 0.912416 | ||||||||
\(107\) | −3.93323 | −0.380240 | −0.190120 | − | 0.981761i | \(-0.560888\pi\) | ||||
−0.190120 | + | 0.981761i | \(0.560888\pi\) | |||||||
\(108\) | −19.1543 | −1.84312 | ||||||||
\(109\) | −19.7477 | −1.89148 | −0.945741 | − | 0.324921i | \(-0.894662\pi\) | ||||
−0.945741 | + | 0.324921i | \(0.894662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.9825 | −1.04241 | ||||||||
\(112\) | −1.00000 | −0.0944911 | ||||||||
\(113\) | −11.8492 | −1.11468 | −0.557340 | − | 0.830284i | \(-0.688178\pi\) | ||||
−0.557340 | + | 0.830284i | \(0.688178\pi\) | |||||||
\(114\) | −6.87485 | −0.643889 | ||||||||
\(115\) | 5.90404 | 0.550555 | ||||||||
\(116\) | −2.77810 | −0.257940 | ||||||||
\(117\) | −31.8352 | −2.94316 | ||||||||
\(118\) | 12.8803 | 1.18573 | ||||||||
\(119\) | 3.63060 | 0.332817 | ||||||||
\(120\) | 3.40870 | 0.311170 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −6.61375 | −0.598781 | ||||||||
\(123\) | 27.7245 | 2.49983 | ||||||||
\(124\) | 2.98864 | 0.268387 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −8.61924 | −0.767863 | ||||||||
\(127\) | 16.7243 | 1.48404 | 0.742020 | − | 0.670378i | \(-0.233868\pi\) | ||||
0.742020 | + | 0.670378i | \(0.233868\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 13.2012 | 1.16230 | ||||||||
\(130\) | 3.69350 | 0.323942 | ||||||||
\(131\) | −13.1921 | −1.15260 | −0.576299 | − | 0.817239i | \(-0.695504\pi\) | ||||
−0.576299 | + | 0.817239i | \(0.695504\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.01685 | −0.174883 | ||||||||
\(134\) | −3.48599 | −0.301143 | ||||||||
\(135\) | 19.1543 | 1.64854 | ||||||||
\(136\) | −3.63060 | −0.311322 | ||||||||
\(137\) | 0.0587014 | 0.00501520 | 0.00250760 | − | 0.999997i | \(-0.499202\pi\) | ||||
0.00250760 | + | 0.999997i | \(0.499202\pi\) | |||||||
\(138\) | 20.1251 | 1.71316 | ||||||||
\(139\) | 20.9129 | 1.77381 | 0.886903 | − | 0.461956i | \(-0.152852\pi\) | ||||
0.886903 | + | 0.461956i | \(0.152852\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −32.9780 | −2.77724 | ||||||||
\(142\) | −5.18885 | −0.435438 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.61924 | 0.718270 | ||||||||
\(145\) | 2.77810 | 0.230708 | ||||||||
\(146\) | −1.83909 | −0.152205 | ||||||||
\(147\) | −3.40870 | −0.281145 | ||||||||
\(148\) | 3.22190 | 0.264839 | ||||||||
\(149\) | 14.8904 | 1.21987 | 0.609935 | − | 0.792451i | \(-0.291195\pi\) | ||||
0.609935 | + | 0.792451i | \(0.291195\pi\) | |||||||
\(150\) | −3.40870 | −0.278319 | ||||||||
\(151\) | −12.3644 | −1.00620 | −0.503101 | − | 0.864227i | \(-0.667808\pi\) | ||||
−0.503101 | + | 0.864227i | \(0.667808\pi\) | |||||||
\(152\) | 2.01685 | 0.163588 | ||||||||
\(153\) | −31.2930 | −2.52989 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.98864 | −0.240053 | ||||||||
\(156\) | 12.5900 | 1.00801 | ||||||||
\(157\) | −22.0362 | −1.75868 | −0.879342 | − | 0.476192i | \(-0.842017\pi\) | ||||
−0.879342 | + | 0.476192i | \(0.842017\pi\) | |||||||
\(158\) | 2.95191 | 0.234841 | ||||||||
\(159\) | −32.0210 | −2.53943 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 5.90404 | 0.465304 | ||||||||
\(162\) | 39.4336 | 3.09819 | ||||||||
\(163\) | 15.4758 | 1.21216 | 0.606081 | − | 0.795403i | \(-0.292741\pi\) | ||||
0.606081 | + | 0.795403i | \(0.292741\pi\) | |||||||
\(164\) | −8.13344 | −0.635115 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.37746 | −0.650217 | ||||||||
\(167\) | 17.4387 | 1.34945 | 0.674723 | − | 0.738071i | \(-0.264263\pi\) | ||||
0.674723 | + | 0.738071i | \(0.264263\pi\) | |||||||
\(168\) | 3.40870 | 0.262987 | ||||||||
\(169\) | 0.641969 | 0.0493822 | ||||||||
\(170\) | 3.63060 | 0.278455 | ||||||||
\(171\) | 17.3837 | 1.32937 | ||||||||
\(172\) | −3.87280 | −0.295298 | ||||||||
\(173\) | −15.2949 | −1.16285 | −0.581425 | − | 0.813600i | \(-0.697505\pi\) | ||||
−0.581425 | + | 0.813600i | \(0.697505\pi\) | |||||||
\(174\) | 9.46970 | 0.717896 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −43.9051 | −3.30011 | ||||||||
\(178\) | 4.85724 | 0.364065 | ||||||||
\(179\) | 11.6746 | 0.872604 | 0.436302 | − | 0.899800i | \(-0.356288\pi\) | ||||
0.436302 | + | 0.899800i | \(0.356288\pi\) | |||||||
\(180\) | −8.61924 | −0.642440 | ||||||||
\(181\) | 9.93097 | 0.738163 | 0.369082 | − | 0.929397i | \(-0.379672\pi\) | ||||
0.369082 | + | 0.929397i | \(0.379672\pi\) | |||||||
\(182\) | 3.69350 | 0.273781 | ||||||||
\(183\) | 22.5443 | 1.66652 | ||||||||
\(184\) | −5.90404 | −0.435252 | ||||||||
\(185\) | −3.22190 | −0.236879 | ||||||||
\(186\) | −10.1874 | −0.746974 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.67464 | 0.705596 | ||||||||
\(189\) | 19.1543 | 1.39327 | ||||||||
\(190\) | −2.01685 | −0.146318 | ||||||||
\(191\) | 14.1868 | 1.02652 | 0.513260 | − | 0.858233i | \(-0.328438\pi\) | ||||
0.513260 | + | 0.858233i | \(0.328438\pi\) | |||||||
\(192\) | −3.40870 | −0.246002 | ||||||||
\(193\) | 20.1766 | 1.45235 | 0.726173 | − | 0.687512i | \(-0.241297\pi\) | ||||
0.726173 | + | 0.687512i | \(0.241297\pi\) | |||||||
\(194\) | −16.0944 | −1.15551 | ||||||||
\(195\) | −12.5900 | −0.901592 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 11.7016 | 0.833702 | 0.416851 | − | 0.908975i | \(-0.363134\pi\) | ||||
0.416851 | + | 0.908975i | \(0.363134\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.24220 | 0.584274 | 0.292137 | − | 0.956376i | \(-0.405634\pi\) | ||||
0.292137 | + | 0.956376i | \(0.405634\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 11.8827 | 0.838140 | ||||||||
\(202\) | −18.8577 | −1.32682 | ||||||||
\(203\) | 2.77810 | 0.194984 | ||||||||
\(204\) | 12.3756 | 0.866468 | ||||||||
\(205\) | 8.13344 | 0.568064 | ||||||||
\(206\) | −15.0231 | −1.04671 | ||||||||
\(207\) | −50.8884 | −3.53699 | ||||||||
\(208\) | −3.69350 | −0.256098 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.40870 | −0.235223 | ||||||||
\(211\) | 9.71032 | 0.668486 | 0.334243 | − | 0.942487i | \(-0.391519\pi\) | ||||
0.334243 | + | 0.942487i | \(0.391519\pi\) | |||||||
\(212\) | 9.39390 | 0.645175 | ||||||||
\(213\) | 17.6872 | 1.21191 | ||||||||
\(214\) | −3.93323 | −0.268870 | ||||||||
\(215\) | 3.87280 | 0.264123 | ||||||||
\(216\) | −19.1543 | −1.30329 | ||||||||
\(217\) | −2.98864 | −0.202882 | ||||||||
\(218\) | −19.7477 | −1.33748 | ||||||||
\(219\) | 6.26892 | 0.423615 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.4096 | 0.902031 | ||||||||
\(222\) | −10.9825 | −0.737097 | ||||||||
\(223\) | 2.64541 | 0.177150 | 0.0885749 | − | 0.996070i | \(-0.471769\pi\) | ||||
0.0885749 | + | 0.996070i | \(0.471769\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 8.61924 | 0.574616 | ||||||||
\(226\) | −11.8492 | −0.788198 | ||||||||
\(227\) | −2.30423 | −0.152937 | −0.0764686 | − | 0.997072i | \(-0.524365\pi\) | ||||
−0.0764686 | + | 0.997072i | \(0.524365\pi\) | |||||||
\(228\) | −6.87485 | −0.455298 | ||||||||
\(229\) | 3.72474 | 0.246138 | 0.123069 | − | 0.992398i | \(-0.460726\pi\) | ||||
0.123069 | + | 0.992398i | \(0.460726\pi\) | |||||||
\(230\) | 5.90404 | 0.389301 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.77810 | −0.182391 | ||||||||
\(233\) | 1.72846 | 0.113235 | 0.0566177 | − | 0.998396i | \(-0.481968\pi\) | ||||
0.0566177 | + | 0.998396i | \(0.481968\pi\) | |||||||
\(234\) | −31.8352 | −2.08113 | ||||||||
\(235\) | −9.67464 | −0.631104 | ||||||||
\(236\) | 12.8803 | 0.838436 | ||||||||
\(237\) | −10.0622 | −0.653608 | ||||||||
\(238\) | 3.63060 | 0.235337 | ||||||||
\(239\) | −10.6465 | −0.688664 | −0.344332 | − | 0.938848i | \(-0.611895\pi\) | ||||
−0.344332 | + | 0.938848i | \(0.611895\pi\) | |||||||
\(240\) | 3.40870 | 0.220031 | ||||||||
\(241\) | 22.2210 | 1.43138 | 0.715690 | − | 0.698418i | \(-0.246112\pi\) | ||||
0.715690 | + | 0.698418i | \(0.246112\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −76.9543 | −4.93662 | ||||||||
\(244\) | −6.61375 | −0.423402 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 27.7245 | 1.76765 | ||||||||
\(247\) | −7.44926 | −0.473985 | ||||||||
\(248\) | 2.98864 | 0.189779 | ||||||||
\(249\) | 28.5563 | 1.80968 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 30.4213 | 1.92017 | 0.960087 | − | 0.279701i | \(-0.0902354\pi\) | ||||
0.960087 | + | 0.279701i | \(0.0902354\pi\) | |||||||
\(252\) | −8.61924 | −0.542961 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.7243 | 1.04937 | ||||||||
\(255\) | −12.3756 | −0.774993 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.8674 | 0.927403 | 0.463701 | − | 0.885992i | \(-0.346521\pi\) | ||||
0.463701 | + | 0.885992i | \(0.346521\pi\) | |||||||
\(258\) | 13.2012 | 0.821872 | ||||||||
\(259\) | −3.22190 | −0.200199 | ||||||||
\(260\) | 3.69350 | 0.229061 | ||||||||
\(261\) | −23.9451 | −1.48216 | ||||||||
\(262\) | −13.1921 | −0.815010 | ||||||||
\(263\) | 27.6050 | 1.70220 | 0.851098 | − | 0.525006i | \(-0.175937\pi\) | ||||
0.851098 | + | 0.525006i | \(0.175937\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.39390 | −0.577062 | ||||||||
\(266\) | −2.01685 | −0.123661 | ||||||||
\(267\) | −16.5569 | −1.01326 | ||||||||
\(268\) | −3.48599 | −0.212941 | ||||||||
\(269\) | −4.63204 | −0.282420 | −0.141210 | − | 0.989980i | \(-0.545099\pi\) | ||||
−0.141210 | + | 0.989980i | \(0.545099\pi\) | |||||||
\(270\) | 19.1543 | 1.16569 | ||||||||
\(271\) | −4.31521 | −0.262130 | −0.131065 | − | 0.991374i | \(-0.541840\pi\) | ||||
−0.131065 | + | 0.991374i | \(0.541840\pi\) | |||||||
\(272\) | −3.63060 | −0.220138 | ||||||||
\(273\) | −12.5900 | −0.761984 | ||||||||
\(274\) | 0.0587014 | 0.00354628 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 20.1251 | 1.21139 | ||||||||
\(277\) | 14.4149 | 0.866110 | 0.433055 | − | 0.901367i | \(-0.357436\pi\) | ||||
0.433055 | + | 0.901367i | \(0.357436\pi\) | |||||||
\(278\) | 20.9129 | 1.25427 | ||||||||
\(279\) | 25.7598 | 1.54220 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 29.1262 | 1.73753 | 0.868763 | − | 0.495229i | \(-0.164916\pi\) | ||||
0.868763 | + | 0.495229i | \(0.164916\pi\) | |||||||
\(282\) | −32.9780 | −1.96381 | ||||||||
\(283\) | −19.8862 | −1.18211 | −0.591057 | − | 0.806630i | \(-0.701289\pi\) | ||||
−0.591057 | + | 0.806630i | \(0.701289\pi\) | |||||||
\(284\) | −5.18885 | −0.307901 | ||||||||
\(285\) | 6.87485 | 0.407231 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.13344 | 0.480102 | ||||||||
\(288\) | 8.61924 | 0.507894 | ||||||||
\(289\) | −3.81871 | −0.224630 | ||||||||
\(290\) | 2.77810 | 0.163135 | ||||||||
\(291\) | 54.8611 | 3.21601 | ||||||||
\(292\) | −1.83909 | −0.107625 | ||||||||
\(293\) | 1.28362 | 0.0749899 | 0.0374949 | − | 0.999297i | \(-0.488062\pi\) | ||||
0.0374949 | + | 0.999297i | \(0.488062\pi\) | |||||||
\(294\) | −3.40870 | −0.198799 | ||||||||
\(295\) | −12.8803 | −0.749920 | ||||||||
\(296\) | 3.22190 | 0.187269 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.8904 | 0.862578 | ||||||||
\(299\) | 21.8066 | 1.26111 | ||||||||
\(300\) | −3.40870 | −0.196801 | ||||||||
\(301\) | 3.87280 | 0.223225 | ||||||||
\(302\) | −12.3644 | −0.711493 | ||||||||
\(303\) | 64.2803 | 3.69281 | ||||||||
\(304\) | 2.01685 | 0.115675 | ||||||||
\(305\) | 6.61375 | 0.378702 | ||||||||
\(306\) | −31.2930 | −1.78890 | ||||||||
\(307\) | −16.0559 | −0.916357 | −0.458179 | − | 0.888860i | \(-0.651498\pi\) | ||||
−0.458179 | + | 0.888860i | \(0.651498\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 51.2093 | 2.91319 | ||||||||
\(310\) | −2.98864 | −0.169743 | ||||||||
\(311\) | 5.84180 | 0.331258 | 0.165629 | − | 0.986188i | \(-0.447035\pi\) | ||||
0.165629 | + | 0.986188i | \(0.447035\pi\) | |||||||
\(312\) | 12.5900 | 0.712771 | ||||||||
\(313\) | 23.0324 | 1.30187 | 0.650934 | − | 0.759134i | \(-0.274377\pi\) | ||||
0.650934 | + | 0.759134i | \(0.274377\pi\) | |||||||
\(314\) | −22.0362 | −1.24358 | ||||||||
\(315\) | 8.61924 | 0.485639 | ||||||||
\(316\) | 2.95191 | 0.166058 | ||||||||
\(317\) | 25.6295 | 1.43950 | 0.719748 | − | 0.694236i | \(-0.244257\pi\) | ||||
0.719748 | + | 0.694236i | \(0.244257\pi\) | |||||||
\(318\) | −32.0210 | −1.79565 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 13.4072 | 0.748318 | ||||||||
\(322\) | 5.90404 | 0.329019 | ||||||||
\(323\) | −7.32240 | −0.407429 | ||||||||
\(324\) | 39.4336 | 2.19075 | ||||||||
\(325\) | −3.69350 | −0.204879 | ||||||||
\(326\) | 15.4758 | 0.857127 | ||||||||
\(327\) | 67.3138 | 3.72246 | ||||||||
\(328\) | −8.13344 | −0.449094 | ||||||||
\(329\) | −9.67464 | −0.533380 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.61474 | −0.0887542 | −0.0443771 | − | 0.999015i | \(-0.514130\pi\) | ||||
−0.0443771 | + | 0.999015i | \(0.514130\pi\) | |||||||
\(332\) | −8.37746 | −0.459773 | ||||||||
\(333\) | 27.7704 | 1.52181 | ||||||||
\(334\) | 17.4387 | 0.954203 | ||||||||
\(335\) | 3.48599 | 0.190460 | ||||||||
\(336\) | 3.40870 | 0.185960 | ||||||||
\(337\) | 11.2918 | 0.615105 | 0.307553 | − | 0.951531i | \(-0.400490\pi\) | ||||
0.307553 | + | 0.951531i | \(0.400490\pi\) | |||||||
\(338\) | 0.641969 | 0.0349185 | ||||||||
\(339\) | 40.3904 | 2.19371 | ||||||||
\(340\) | 3.63060 | 0.196897 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 17.3837 | 0.940005 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −3.87280 | −0.208807 | ||||||||
\(345\) | −20.1251 | −1.08350 | ||||||||
\(346\) | −15.2949 | −0.822260 | ||||||||
\(347\) | −3.57419 | −0.191873 | −0.0959363 | − | 0.995387i | \(-0.530585\pi\) | ||||
−0.0959363 | + | 0.995387i | \(0.530585\pi\) | |||||||
\(348\) | 9.46970 | 0.507629 | ||||||||
\(349\) | 2.69597 | 0.144312 | 0.0721560 | − | 0.997393i | \(-0.477012\pi\) | ||||
0.0721560 | + | 0.997393i | \(0.477012\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 70.7465 | 3.77617 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.3929 | 1.77732 | 0.888662 | − | 0.458563i | \(-0.151635\pi\) | ||||
0.888662 | + | 0.458563i | \(0.151635\pi\) | |||||||
\(354\) | −43.9051 | −2.33353 | ||||||||
\(355\) | 5.18885 | 0.275395 | ||||||||
\(356\) | 4.85724 | 0.257433 | ||||||||
\(357\) | −12.3756 | −0.654988 | ||||||||
\(358\) | 11.6746 | 0.617024 | ||||||||
\(359\) | 10.5951 | 0.559189 | 0.279594 | − | 0.960118i | \(-0.409800\pi\) | ||||
0.279594 | + | 0.960118i | \(0.409800\pi\) | |||||||
\(360\) | −8.61924 | −0.454274 | ||||||||
\(361\) | −14.9323 | −0.785911 | ||||||||
\(362\) | 9.93097 | 0.521960 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.69350 | 0.193592 | ||||||||
\(365\) | 1.83909 | 0.0962626 | ||||||||
\(366\) | 22.5443 | 1.17841 | ||||||||
\(367\) | 0.872611 | 0.0455499 | 0.0227750 | − | 0.999741i | \(-0.492750\pi\) | ||||
0.0227750 | + | 0.999741i | \(0.492750\pi\) | |||||||
\(368\) | −5.90404 | −0.307769 | ||||||||
\(369\) | −70.1041 | −3.64947 | ||||||||
\(370\) | −3.22190 | −0.167499 | ||||||||
\(371\) | −9.39390 | −0.487707 | ||||||||
\(372\) | −10.1874 | −0.528190 | ||||||||
\(373\) | −17.9629 | −0.930085 | −0.465042 | − | 0.885288i | \(-0.653961\pi\) | ||||
−0.465042 | + | 0.885288i | \(0.653961\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.40870 | 0.176025 | ||||||||
\(376\) | 9.67464 | 0.498931 | ||||||||
\(377\) | 10.2609 | 0.528464 | ||||||||
\(378\) | 19.1543 | 0.985191 | ||||||||
\(379\) | −13.6701 | −0.702185 | −0.351093 | − | 0.936341i | \(-0.614190\pi\) | ||||
−0.351093 | + | 0.936341i | \(0.614190\pi\) | |||||||
\(380\) | −2.01685 | −0.103462 | ||||||||
\(381\) | −57.0080 | −2.92061 | ||||||||
\(382\) | 14.1868 | 0.725860 | ||||||||
\(383\) | 35.5188 | 1.81492 | 0.907462 | − | 0.420134i | \(-0.138017\pi\) | ||||
0.907462 | + | 0.420134i | \(0.138017\pi\) | |||||||
\(384\) | −3.40870 | −0.173950 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 20.1766 | 1.02696 | ||||||||
\(387\) | −33.3806 | −1.69683 | ||||||||
\(388\) | −16.0944 | −0.817071 | ||||||||
\(389\) | −25.8447 | −1.31038 | −0.655189 | − | 0.755465i | \(-0.727411\pi\) | ||||
−0.655189 | + | 0.755465i | \(0.727411\pi\) | |||||||
\(390\) | −12.5900 | −0.637522 | ||||||||
\(391\) | 21.4352 | 1.08403 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 44.9679 | 2.26833 | ||||||||
\(394\) | 11.7016 | 0.589516 | ||||||||
\(395\) | −2.95191 | −0.148526 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −38.5967 | −1.93711 | −0.968557 | − | 0.248793i | \(-0.919966\pi\) | ||||
−0.968557 | + | 0.248793i | \(0.919966\pi\) | |||||||
\(398\) | 8.24220 | 0.413144 | ||||||||
\(399\) | 6.87485 | 0.344173 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −20.0070 | −0.999100 | −0.499550 | − | 0.866285i | \(-0.666501\pi\) | ||||
−0.499550 | + | 0.866285i | \(0.666501\pi\) | |||||||
\(402\) | 11.8827 | 0.592654 | ||||||||
\(403\) | −11.0385 | −0.549869 | ||||||||
\(404\) | −18.8577 | −0.938207 | ||||||||
\(405\) | −39.4336 | −1.95947 | ||||||||
\(406\) | 2.77810 | 0.137875 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 12.3756 | 0.612686 | ||||||||
\(409\) | −2.18374 | −0.107979 | −0.0539894 | − | 0.998542i | \(-0.517194\pi\) | ||||
−0.0539894 | + | 0.998542i | \(0.517194\pi\) | |||||||
\(410\) | 8.13344 | 0.401682 | ||||||||
\(411\) | −0.200095 | −0.00986998 | ||||||||
\(412\) | −15.0231 | −0.740135 | ||||||||
\(413\) | −12.8803 | −0.633798 | ||||||||
\(414\) | −50.8884 | −2.50103 | ||||||||
\(415\) | 8.37746 | 0.411233 | ||||||||
\(416\) | −3.69350 | −0.181089 | ||||||||
\(417\) | −71.2857 | −3.49088 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.7452 | −0.866909 | −0.433455 | − | 0.901175i | \(-0.642706\pi\) | ||||
−0.433455 | + | 0.901175i | \(0.642706\pi\) | |||||||
\(420\) | −3.40870 | −0.166328 | ||||||||
\(421\) | 15.0491 | 0.733447 | 0.366723 | − | 0.930330i | \(-0.380480\pi\) | ||||
0.366723 | + | 0.930330i | \(0.380480\pi\) | |||||||
\(422\) | 9.71032 | 0.472691 | ||||||||
\(423\) | 83.3880 | 4.05447 | ||||||||
\(424\) | 9.39390 | 0.456208 | ||||||||
\(425\) | −3.63060 | −0.176110 | ||||||||
\(426\) | 17.6872 | 0.856949 | ||||||||
\(427\) | 6.61375 | 0.320062 | ||||||||
\(428\) | −3.93323 | −0.190120 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.87280 | 0.186763 | ||||||||
\(431\) | −9.60354 | −0.462586 | −0.231293 | − | 0.972884i | \(-0.574296\pi\) | ||||
−0.231293 | + | 0.972884i | \(0.574296\pi\) | |||||||
\(432\) | −19.1543 | −0.921562 | ||||||||
\(433\) | 24.2421 | 1.16500 | 0.582501 | − | 0.812830i | \(-0.302074\pi\) | ||||
0.582501 | + | 0.812830i | \(0.302074\pi\) | |||||||
\(434\) | −2.98864 | −0.143459 | ||||||||
\(435\) | −9.46970 | −0.454037 | ||||||||
\(436\) | −19.7477 | −0.945741 | ||||||||
\(437\) | −11.9076 | −0.569617 | ||||||||
\(438\) | 6.26892 | 0.299541 | ||||||||
\(439\) | 32.3368 | 1.54335 | 0.771677 | − | 0.636015i | \(-0.219418\pi\) | ||||
0.771677 | + | 0.636015i | \(0.219418\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.61924 | 0.410440 | ||||||||
\(442\) | 13.4096 | 0.637832 | ||||||||
\(443\) | −21.8977 | −1.04039 | −0.520195 | − | 0.854048i | \(-0.674141\pi\) | ||||
−0.520195 | + | 0.854048i | \(0.674141\pi\) | |||||||
\(444\) | −10.9825 | −0.521207 | ||||||||
\(445\) | −4.85724 | −0.230255 | ||||||||
\(446\) | 2.64541 | 0.125264 | ||||||||
\(447\) | −50.7570 | −2.40072 | ||||||||
\(448\) | −1.00000 | −0.0472456 | ||||||||
\(449\) | −12.5764 | −0.593518 | −0.296759 | − | 0.954952i | \(-0.595906\pi\) | ||||
−0.296759 | + | 0.954952i | \(0.595906\pi\) | |||||||
\(450\) | 8.61924 | 0.406315 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −11.8492 | −0.557340 | ||||||||
\(453\) | 42.1466 | 1.98022 | ||||||||
\(454\) | −2.30423 | −0.108143 | ||||||||
\(455\) | −3.69350 | −0.173154 | ||||||||
\(456\) | −6.87485 | −0.321944 | ||||||||
\(457\) | −30.6714 | −1.43475 | −0.717374 | − | 0.696688i | \(-0.754656\pi\) | ||||
−0.717374 | + | 0.696688i | \(0.754656\pi\) | |||||||
\(458\) | 3.72474 | 0.174046 | ||||||||
\(459\) | 69.5417 | 3.24593 | ||||||||
\(460\) | 5.90404 | 0.275277 | ||||||||
\(461\) | 19.5978 | 0.912762 | 0.456381 | − | 0.889784i | \(-0.349145\pi\) | ||||
0.456381 | + | 0.889784i | \(0.349145\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.29483 | −0.199598 | −0.0997989 | − | 0.995008i | \(-0.531820\pi\) | ||||
−0.0997989 | + | 0.995008i | \(0.531820\pi\) | |||||||
\(464\) | −2.77810 | −0.128970 | ||||||||
\(465\) | 10.1874 | 0.472428 | ||||||||
\(466\) | 1.72846 | 0.0800695 | ||||||||
\(467\) | −1.40460 | −0.0649973 | −0.0324986 | − | 0.999472i | \(-0.510346\pi\) | ||||
−0.0324986 | + | 0.999472i | \(0.510346\pi\) | |||||||
\(468\) | −31.8352 | −1.47158 | ||||||||
\(469\) | 3.48599 | 0.160968 | ||||||||
\(470\) | −9.67464 | −0.446258 | ||||||||
\(471\) | 75.1149 | 3.46111 | ||||||||
\(472\) | 12.8803 | 0.592864 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −10.0622 | −0.462170 | ||||||||
\(475\) | 2.01685 | 0.0925396 | ||||||||
\(476\) | 3.63060 | 0.166408 | ||||||||
\(477\) | 80.9682 | 3.70728 | ||||||||
\(478\) | −10.6465 | −0.486959 | ||||||||
\(479\) | 32.3519 | 1.47820 | 0.739098 | − | 0.673598i | \(-0.235252\pi\) | ||||
0.739098 | + | 0.673598i | \(0.235252\pi\) | |||||||
\(480\) | 3.40870 | 0.155585 | ||||||||
\(481\) | −11.9001 | −0.542598 | ||||||||
\(482\) | 22.2210 | 1.01214 | ||||||||
\(483\) | −20.1251 | −0.915724 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.0944 | 0.730810 | ||||||||
\(486\) | −76.9543 | −3.49072 | ||||||||
\(487\) | −3.75142 | −0.169993 | −0.0849965 | − | 0.996381i | \(-0.527088\pi\) | ||||
−0.0849965 | + | 0.996381i | \(0.527088\pi\) | |||||||
\(488\) | −6.61375 | −0.299390 | ||||||||
\(489\) | −52.7525 | −2.38555 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 11.1293 | 0.502257 | 0.251129 | − | 0.967954i | \(-0.419198\pi\) | ||||
0.251129 | + | 0.967954i | \(0.419198\pi\) | |||||||
\(492\) | 27.7245 | 1.24992 | ||||||||
\(493\) | 10.0862 | 0.454258 | ||||||||
\(494\) | −7.44926 | −0.335158 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.98864 | 0.134194 | ||||||||
\(497\) | 5.18885 | 0.232752 | ||||||||
\(498\) | 28.5563 | 1.27964 | ||||||||
\(499\) | −23.2827 | −1.04228 | −0.521139 | − | 0.853472i | \(-0.674493\pi\) | ||||
−0.521139 | + | 0.853472i | \(0.674493\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −59.4433 | −2.65573 | ||||||||
\(502\) | 30.4213 | 1.35777 | ||||||||
\(503\) | 35.8718 | 1.59945 | 0.799723 | − | 0.600370i | \(-0.204980\pi\) | ||||
0.799723 | + | 0.600370i | \(0.204980\pi\) | |||||||
\(504\) | −8.61924 | −0.383931 | ||||||||
\(505\) | 18.8577 | 0.839157 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.18828 | −0.0971849 | ||||||||
\(508\) | 16.7243 | 0.742020 | ||||||||
\(509\) | −23.2092 | −1.02873 | −0.514365 | − | 0.857571i | \(-0.671972\pi\) | ||||
−0.514365 | + | 0.857571i | \(0.671972\pi\) | |||||||
\(510\) | −12.3756 | −0.548003 | ||||||||
\(511\) | 1.83909 | 0.0813568 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −38.6314 | −1.70562 | ||||||||
\(514\) | 14.8674 | 0.655773 | ||||||||
\(515\) | 15.0231 | 0.661997 | ||||||||
\(516\) | 13.2012 | 0.581151 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −3.22190 | −0.141562 | ||||||||
\(519\) | 52.1358 | 2.28851 | ||||||||
\(520\) | 3.69350 | 0.161971 | ||||||||
\(521\) | −9.71728 | −0.425722 | −0.212861 | − | 0.977083i | \(-0.568278\pi\) | ||||
−0.212861 | + | 0.977083i | \(0.568278\pi\) | |||||||
\(522\) | −23.9451 | −1.04805 | ||||||||
\(523\) | −1.70495 | −0.0745523 | −0.0372762 | − | 0.999305i | \(-0.511868\pi\) | ||||
−0.0372762 | + | 0.999305i | \(0.511868\pi\) | |||||||
\(524\) | −13.1921 | −0.576299 | ||||||||
\(525\) | 3.40870 | 0.148768 | ||||||||
\(526\) | 27.6050 | 1.20363 | ||||||||
\(527\) | −10.8506 | −0.472657 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.8577 | 0.515553 | ||||||||
\(530\) | −9.39390 | −0.408045 | ||||||||
\(531\) | 111.018 | 4.81779 | ||||||||
\(532\) | −2.01685 | −0.0874417 | ||||||||
\(533\) | 30.0409 | 1.30122 | ||||||||
\(534\) | −16.5569 | −0.716486 | ||||||||
\(535\) | 3.93323 | 0.170049 | ||||||||
\(536\) | −3.48599 | −0.150572 | ||||||||
\(537\) | −39.7954 | −1.71730 | ||||||||
\(538\) | −4.63204 | −0.199701 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.1543 | 0.824270 | ||||||||
\(541\) | −31.0627 | −1.33549 | −0.667745 | − | 0.744390i | \(-0.732740\pi\) | ||||
−0.667745 | + | 0.744390i | \(0.732740\pi\) | |||||||
\(542\) | −4.31521 | −0.185354 | ||||||||
\(543\) | −33.8517 | −1.45272 | ||||||||
\(544\) | −3.63060 | −0.155661 | ||||||||
\(545\) | 19.7477 | 0.845897 | ||||||||
\(546\) | −12.5900 | −0.538804 | ||||||||
\(547\) | 11.5948 | 0.495760 | 0.247880 | − | 0.968791i | \(-0.420266\pi\) | ||||
0.247880 | + | 0.968791i | \(0.420266\pi\) | |||||||
\(548\) | 0.0587014 | 0.00250760 | ||||||||
\(549\) | −57.0055 | −2.43294 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.60301 | −0.238696 | ||||||||
\(552\) | 20.1251 | 0.856582 | ||||||||
\(553\) | −2.95191 | −0.125528 | ||||||||
\(554\) | 14.4149 | 0.612432 | ||||||||
\(555\) | 10.9825 | 0.466181 | ||||||||
\(556\) | 20.9129 | 0.886903 | ||||||||
\(557\) | −2.80080 | −0.118674 | −0.0593369 | − | 0.998238i | \(-0.518899\pi\) | ||||
−0.0593369 | + | 0.998238i | \(0.518899\pi\) | |||||||
\(558\) | 25.7598 | 1.09050 | ||||||||
\(559\) | 14.3042 | 0.605004 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 29.1262 | 1.22862 | ||||||||
\(563\) | −12.9733 | −0.546758 | −0.273379 | − | 0.961906i | \(-0.588141\pi\) | ||||
−0.273379 | + | 0.961906i | \(0.588141\pi\) | |||||||
\(564\) | −32.9780 | −1.38862 | ||||||||
\(565\) | 11.8492 | 0.498500 | ||||||||
\(566\) | −19.8862 | −0.835881 | ||||||||
\(567\) | −39.4336 | −1.65605 | ||||||||
\(568\) | −5.18885 | −0.217719 | ||||||||
\(569\) | 0.243705 | 0.0102166 | 0.00510832 | − | 0.999987i | \(-0.498374\pi\) | ||||
0.00510832 | + | 0.999987i | \(0.498374\pi\) | |||||||
\(570\) | 6.87485 | 0.287956 | ||||||||
\(571\) | 7.03817 | 0.294538 | 0.147269 | − | 0.989096i | \(-0.452952\pi\) | ||||
0.147269 | + | 0.989096i | \(0.452952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −48.3585 | −2.02021 | ||||||||
\(574\) | 8.13344 | 0.339483 | ||||||||
\(575\) | −5.90404 | −0.246216 | ||||||||
\(576\) | 8.61924 | 0.359135 | ||||||||
\(577\) | 33.3549 | 1.38858 | 0.694291 | − | 0.719694i | \(-0.255718\pi\) | ||||
0.694291 | + | 0.719694i | \(0.255718\pi\) | |||||||
\(578\) | −3.81871 | −0.158838 | ||||||||
\(579\) | −68.7762 | −2.85824 | ||||||||
\(580\) | 2.77810 | 0.115354 | ||||||||
\(581\) | 8.37746 | 0.347556 | ||||||||
\(582\) | 54.8611 | 2.27407 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.83909 | −0.0761023 | ||||||||
\(585\) | 31.8352 | 1.31622 | ||||||||
\(586\) | 1.28362 | 0.0530258 | ||||||||
\(587\) | −18.3333 | −0.756695 | −0.378347 | − | 0.925664i | \(-0.623508\pi\) | ||||
−0.378347 | + | 0.925664i | \(0.623508\pi\) | |||||||
\(588\) | −3.40870 | −0.140572 | ||||||||
\(589\) | 6.02764 | 0.248365 | ||||||||
\(590\) | −12.8803 | −0.530274 | ||||||||
\(591\) | −39.8871 | −1.64074 | ||||||||
\(592\) | 3.22190 | 0.132419 | ||||||||
\(593\) | 40.6951 | 1.67115 | 0.835573 | − | 0.549380i | \(-0.185136\pi\) | ||||
0.835573 | + | 0.549380i | \(0.185136\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.63060 | −0.148840 | ||||||||
\(596\) | 14.8904 | 0.609935 | ||||||||
\(597\) | −28.0952 | −1.14986 | ||||||||
\(598\) | 21.8066 | 0.891738 | ||||||||
\(599\) | 27.7826 | 1.13516 | 0.567582 | − | 0.823317i | \(-0.307879\pi\) | ||||
0.567582 | + | 0.823317i | \(0.307879\pi\) | |||||||
\(600\) | −3.40870 | −0.139160 | ||||||||
\(601\) | 28.0280 | 1.14329 | 0.571643 | − | 0.820502i | \(-0.306306\pi\) | ||||
0.571643 | + | 0.820502i | \(0.306306\pi\) | |||||||
\(602\) | 3.87280 | 0.157844 | ||||||||
\(603\) | −30.0466 | −1.22359 | ||||||||
\(604\) | −12.3644 | −0.503101 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 64.2803 | 2.61121 | ||||||||
\(607\) | −15.2484 | −0.618912 | −0.309456 | − | 0.950914i | \(-0.600147\pi\) | ||||
−0.309456 | + | 0.950914i | \(0.600147\pi\) | |||||||
\(608\) | 2.01685 | 0.0817942 | ||||||||
\(609\) | −9.46970 | −0.383732 | ||||||||
\(610\) | 6.61375 | 0.267783 | ||||||||
\(611\) | −35.7333 | −1.44562 | ||||||||
\(612\) | −31.2930 | −1.26495 | ||||||||
\(613\) | 5.19985 | 0.210020 | 0.105010 | − | 0.994471i | \(-0.466513\pi\) | ||||
0.105010 | + | 0.994471i | \(0.466513\pi\) | |||||||
\(614\) | −16.0559 | −0.647963 | ||||||||
\(615\) | −27.7245 | −1.11796 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.07263 | 0.204217 | 0.102108 | − | 0.994773i | \(-0.467441\pi\) | ||||
0.102108 | + | 0.994773i | \(0.467441\pi\) | |||||||
\(618\) | 51.2093 | 2.05994 | ||||||||
\(619\) | 18.1421 | 0.729194 | 0.364597 | − | 0.931165i | \(-0.381207\pi\) | ||||
0.364597 | + | 0.931165i | \(0.381207\pi\) | |||||||
\(620\) | −2.98864 | −0.120026 | ||||||||
\(621\) | 113.088 | 4.53806 | ||||||||
\(622\) | 5.84180 | 0.234235 | ||||||||
\(623\) | −4.85724 | −0.194601 | ||||||||
\(624\) | 12.5900 | 0.504005 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.0324 | 0.920560 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.0362 | −0.879342 | ||||||||
\(629\) | −11.6975 | −0.466408 | ||||||||
\(630\) | 8.61924 | 0.343399 | ||||||||
\(631\) | −23.7253 | −0.944490 | −0.472245 | − | 0.881467i | \(-0.656556\pi\) | ||||
−0.472245 | + | 0.881467i | \(0.656556\pi\) | |||||||
\(632\) | 2.95191 | 0.117421 | ||||||||
\(633\) | −33.0996 | −1.31559 | ||||||||
\(634\) | 25.6295 | 1.01788 | ||||||||
\(635\) | −16.7243 | −0.663683 | ||||||||
\(636\) | −32.0210 | −1.26971 | ||||||||
\(637\) | −3.69350 | −0.146342 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −44.7239 | −1.76925 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 25.0709 | 0.990240 | 0.495120 | − | 0.868825i | \(-0.335124\pi\) | ||||
0.495120 | + | 0.868825i | \(0.335124\pi\) | |||||||
\(642\) | 13.4072 | 0.529141 | ||||||||
\(643\) | 39.6473 | 1.56354 | 0.781768 | − | 0.623569i | \(-0.214318\pi\) | ||||
0.781768 | + | 0.623569i | \(0.214318\pi\) | |||||||
\(644\) | 5.90404 | 0.232652 | ||||||||
\(645\) | −13.2012 | −0.519798 | ||||||||
\(646\) | −7.32240 | −0.288096 | ||||||||
\(647\) | 33.8481 | 1.33070 | 0.665352 | − | 0.746530i | \(-0.268281\pi\) | ||||
0.665352 | + | 0.746530i | \(0.268281\pi\) | |||||||
\(648\) | 39.4336 | 1.54910 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.69350 | −0.144871 | ||||||||
\(651\) | 10.1874 | 0.399274 | ||||||||
\(652\) | 15.4758 | 0.606081 | ||||||||
\(653\) | 2.39913 | 0.0938852 | 0.0469426 | − | 0.998898i | \(-0.485052\pi\) | ||||
0.0469426 | + | 0.998898i | \(0.485052\pi\) | |||||||
\(654\) | 67.3138 | 2.63218 | ||||||||
\(655\) | 13.1921 | 0.515458 | ||||||||
\(656\) | −8.13344 | −0.317558 | ||||||||
\(657\) | −15.8516 | −0.618430 | ||||||||
\(658\) | −9.67464 | −0.377157 | ||||||||
\(659\) | −14.5152 | −0.565430 | −0.282715 | − | 0.959204i | \(-0.591235\pi\) | ||||
−0.282715 | + | 0.959204i | \(0.591235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.1729 | 0.395680 | 0.197840 | − | 0.980234i | \(-0.436607\pi\) | ||||
0.197840 | + | 0.980234i | \(0.436607\pi\) | |||||||
\(662\) | −1.61474 | −0.0627587 | ||||||||
\(663\) | −45.7095 | −1.77521 | ||||||||
\(664\) | −8.37746 | −0.325109 | ||||||||
\(665\) | 2.01685 | 0.0782102 | ||||||||
\(666\) | 27.7704 | 1.07608 | ||||||||
\(667\) | 16.4020 | 0.635088 | ||||||||
\(668\) | 17.4387 | 0.674723 | ||||||||
\(669\) | −9.01741 | −0.348633 | ||||||||
\(670\) | 3.48599 | 0.134675 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.40870 | 0.131493 | ||||||||
\(673\) | 9.89134 | 0.381283 | 0.190642 | − | 0.981660i | \(-0.438943\pi\) | ||||
0.190642 | + | 0.981660i | \(0.438943\pi\) | |||||||
\(674\) | 11.2918 | 0.434945 | ||||||||
\(675\) | −19.1543 | −0.737250 | ||||||||
\(676\) | 0.641969 | 0.0246911 | ||||||||
\(677\) | −19.2252 | −0.738886 | −0.369443 | − | 0.929253i | \(-0.620451\pi\) | ||||
−0.369443 | + | 0.929253i | \(0.620451\pi\) | |||||||
\(678\) | 40.3904 | 1.55118 | ||||||||
\(679\) | 16.0944 | 0.617647 | ||||||||
\(680\) | 3.63060 | 0.139227 | ||||||||
\(681\) | 7.85444 | 0.300983 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 37.5641 | 1.43735 | 0.718674 | − | 0.695347i | \(-0.244749\pi\) | ||||
0.718674 | + | 0.695347i | \(0.244749\pi\) | |||||||
\(684\) | 17.3837 | 0.664684 | ||||||||
\(685\) | −0.0587014 | −0.00224286 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −12.6965 | −0.484403 | ||||||||
\(688\) | −3.87280 | −0.147649 | ||||||||
\(689\) | −34.6964 | −1.32183 | ||||||||
\(690\) | −20.1251 | −0.766150 | ||||||||
\(691\) | 50.4772 | 1.92024 | 0.960121 | − | 0.279585i | \(-0.0901970\pi\) | ||||
0.960121 | + | 0.279585i | \(0.0901970\pi\) | |||||||
\(692\) | −15.2949 | −0.581425 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.57419 | −0.135674 | ||||||||
\(695\) | −20.9129 | −0.793270 | ||||||||
\(696\) | 9.46970 | 0.358948 | ||||||||
\(697\) | 29.5293 | 1.11850 | ||||||||
\(698\) | 2.69597 | 0.102044 | ||||||||
\(699\) | −5.89181 | −0.222849 | ||||||||
\(700\) | −1.00000 | −0.0377964 | ||||||||
\(701\) | −3.21370 | −0.121380 | −0.0606899 | − | 0.998157i | \(-0.519330\pi\) | ||||
−0.0606899 | + | 0.998157i | \(0.519330\pi\) | |||||||
\(702\) | 70.7465 | 2.67015 | ||||||||
\(703\) | 6.49811 | 0.245081 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32.9780 | 1.24202 | ||||||||
\(706\) | 33.3929 | 1.25676 | ||||||||
\(707\) | 18.8577 | 0.709217 | ||||||||
\(708\) | −43.9051 | −1.65005 | ||||||||
\(709\) | −23.5837 | −0.885706 | −0.442853 | − | 0.896594i | \(-0.646034\pi\) | ||||
−0.442853 | + | 0.896594i | \(0.646034\pi\) | |||||||
\(710\) | 5.18885 | 0.194734 | ||||||||
\(711\) | 25.4432 | 0.954194 | ||||||||
\(712\) | 4.85724 | 0.182033 | ||||||||
\(713\) | −17.6450 | −0.660812 | ||||||||
\(714\) | −12.3756 | −0.463147 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.6746 | 0.436302 | ||||||||
\(717\) | 36.2907 | 1.35530 | ||||||||
\(718\) | 10.5951 | 0.395406 | ||||||||
\(719\) | 31.6922 | 1.18192 | 0.590959 | − | 0.806702i | \(-0.298749\pi\) | ||||
0.590959 | + | 0.806702i | \(0.298749\pi\) | |||||||
\(720\) | −8.61924 | −0.321220 | ||||||||
\(721\) | 15.0231 | 0.559490 | ||||||||
\(722\) | −14.9323 | −0.555723 | ||||||||
\(723\) | −75.7447 | −2.81697 | ||||||||
\(724\) | 9.93097 | 0.369082 | ||||||||
\(725\) | −2.77810 | −0.103176 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.59020 | 0.318593 | 0.159296 | − | 0.987231i | \(-0.449077\pi\) | ||||
0.159296 | + | 0.987231i | \(0.449077\pi\) | |||||||
\(728\) | 3.69350 | 0.136890 | ||||||||
\(729\) | 144.014 | 5.33383 | ||||||||
\(730\) | 1.83909 | 0.0680679 | ||||||||
\(731\) | 14.0606 | 0.520051 | ||||||||
\(732\) | 22.5443 | 0.833261 | ||||||||
\(733\) | 17.1149 | 0.632155 | 0.316077 | − | 0.948733i | \(-0.397634\pi\) | ||||
0.316077 | + | 0.948733i | \(0.397634\pi\) | |||||||
\(734\) | 0.872611 | 0.0322086 | ||||||||
\(735\) | 3.40870 | 0.125732 | ||||||||
\(736\) | −5.90404 | −0.217626 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −70.1041 | −2.58057 | ||||||||
\(739\) | 16.6965 | 0.614189 | 0.307094 | − | 0.951679i | \(-0.400643\pi\) | ||||
0.307094 | + | 0.951679i | \(0.400643\pi\) | |||||||
\(740\) | −3.22190 | −0.118440 | ||||||||
\(741\) | 25.3923 | 0.932809 | ||||||||
\(742\) | −9.39390 | −0.344861 | ||||||||
\(743\) | −0.812545 | −0.0298094 | −0.0149047 | − | 0.999889i | \(-0.504744\pi\) | ||||
−0.0149047 | + | 0.999889i | \(0.504744\pi\) | |||||||
\(744\) | −10.1874 | −0.373487 | ||||||||
\(745\) | −14.8904 | −0.545543 | ||||||||
\(746\) | −17.9629 | −0.657669 | ||||||||
\(747\) | −72.2073 | −2.64193 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.93323 | 0.143717 | ||||||||
\(750\) | 3.40870 | 0.124468 | ||||||||
\(751\) | 3.97989 | 0.145228 | 0.0726140 | − | 0.997360i | \(-0.476866\pi\) | ||||
0.0726140 | + | 0.997360i | \(0.476866\pi\) | |||||||
\(752\) | 9.67464 | 0.352798 | ||||||||
\(753\) | −103.697 | −3.77893 | ||||||||
\(754\) | 10.2609 | 0.373680 | ||||||||
\(755\) | 12.3644 | 0.449988 | ||||||||
\(756\) | 19.1543 | 0.696635 | ||||||||
\(757\) | 49.2340 | 1.78944 | 0.894720 | − | 0.446627i | \(-0.147375\pi\) | ||||
0.894720 | + | 0.446627i | \(0.147375\pi\) | |||||||
\(758\) | −13.6701 | −0.496520 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.01685 | −0.0731590 | ||||||||
\(761\) | −35.5947 | −1.29031 | −0.645154 | − | 0.764052i | \(-0.723207\pi\) | ||||
−0.645154 | + | 0.764052i | \(0.723207\pi\) | |||||||
\(762\) | −57.0080 | −2.06518 | ||||||||
\(763\) | 19.7477 | 0.714913 | ||||||||
\(764\) | 14.1868 | 0.513260 | ||||||||
\(765\) | 31.2930 | 1.13140 | ||||||||
\(766\) | 35.5188 | 1.28335 | ||||||||
\(767\) | −47.5734 | −1.71778 | ||||||||
\(768\) | −3.40870 | −0.123001 | ||||||||
\(769\) | −6.16367 | −0.222268 | −0.111134 | − | 0.993805i | \(-0.535448\pi\) | ||||
−0.111134 | + | 0.993805i | \(0.535448\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −50.6785 | −1.82514 | ||||||||
\(772\) | 20.1766 | 0.726173 | ||||||||
\(773\) | −18.3589 | −0.660323 | −0.330162 | − | 0.943924i | \(-0.607103\pi\) | ||||
−0.330162 | + | 0.943924i | \(0.607103\pi\) | |||||||
\(774\) | −33.3806 | −1.19984 | ||||||||
\(775\) | 2.98864 | 0.107355 | ||||||||
\(776\) | −16.0944 | −0.577756 | ||||||||
\(777\) | 10.9825 | 0.393995 | ||||||||
\(778\) | −25.8447 | −0.926577 | ||||||||
\(779\) | −16.4040 | −0.587733 | ||||||||
\(780\) | −12.5900 | −0.450796 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 21.4352 | 0.766523 | ||||||||
\(783\) | 53.2125 | 1.90166 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 22.0362 | 0.786507 | ||||||||
\(786\) | 44.9679 | 1.60395 | ||||||||
\(787\) | 12.0202 | 0.428475 | 0.214237 | − | 0.976782i | \(-0.431273\pi\) | ||||
0.214237 | + | 0.976782i | \(0.431273\pi\) | |||||||
\(788\) | 11.7016 | 0.416851 | ||||||||
\(789\) | −94.0972 | −3.34995 | ||||||||
\(790\) | −2.95191 | −0.105024 | ||||||||
\(791\) | 11.8492 | 0.421309 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.4279 | 0.867461 | ||||||||
\(794\) | −38.5967 | −1.36975 | ||||||||
\(795\) | 32.0210 | 1.13567 | ||||||||
\(796\) | 8.24220 | 0.292137 | ||||||||
\(797\) | 15.7618 | 0.558313 | 0.279156 | − | 0.960246i | \(-0.409945\pi\) | ||||
0.279156 | + | 0.960246i | \(0.409945\pi\) | |||||||
\(798\) | 6.87485 | 0.243367 | ||||||||
\(799\) | −35.1248 | −1.24263 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 41.8657 | 1.47925 | ||||||||
\(802\) | −20.0070 | −0.706470 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 11.8827 | 0.419070 | ||||||||
\(805\) | −5.90404 | −0.208090 | ||||||||
\(806\) | −11.0385 | −0.388816 | ||||||||
\(807\) | 15.7892 | 0.555807 | ||||||||
\(808\) | −18.8577 | −0.663412 | ||||||||
\(809\) | −26.5335 | −0.932867 | −0.466434 | − | 0.884556i | \(-0.654461\pi\) | ||||
−0.466434 | + | 0.884556i | \(0.654461\pi\) | |||||||
\(810\) | −39.4336 | −1.38555 | ||||||||
\(811\) | 2.76840 | 0.0972117 | 0.0486059 | − | 0.998818i | \(-0.484522\pi\) | ||||
0.0486059 | + | 0.998818i | \(0.484522\pi\) | |||||||
\(812\) | 2.77810 | 0.0974921 | ||||||||
\(813\) | 14.7093 | 0.515876 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −15.4758 | −0.542095 | ||||||||
\(816\) | 12.3756 | 0.433234 | ||||||||
\(817\) | −7.81088 | −0.273268 | ||||||||
\(818\) | −2.18374 | −0.0763525 | ||||||||
\(819\) | 31.8352 | 1.11241 | ||||||||
\(820\) | 8.13344 | 0.284032 | ||||||||
\(821\) | −7.47931 | −0.261030 | −0.130515 | − | 0.991446i | \(-0.541663\pi\) | ||||
−0.130515 | + | 0.991446i | \(0.541663\pi\) | |||||||
\(822\) | −0.200095 | −0.00697913 | ||||||||
\(823\) | 28.1564 | 0.981472 | 0.490736 | − | 0.871308i | \(-0.336728\pi\) | ||||
0.490736 | + | 0.871308i | \(0.336728\pi\) | |||||||
\(824\) | −15.0231 | −0.523355 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.8803 | −0.448163 | ||||||||
\(827\) | 43.0851 | 1.49821 | 0.749107 | − | 0.662449i | \(-0.230483\pi\) | ||||
0.749107 | + | 0.662449i | \(0.230483\pi\) | |||||||
\(828\) | −50.8884 | −1.76849 | ||||||||
\(829\) | −6.22008 | −0.216032 | −0.108016 | − | 0.994149i | \(-0.534450\pi\) | ||||
−0.108016 | + | 0.994149i | \(0.534450\pi\) | |||||||
\(830\) | 8.37746 | 0.290786 | ||||||||
\(831\) | −49.1362 | −1.70452 | ||||||||
\(832\) | −3.69350 | −0.128049 | ||||||||
\(833\) | −3.63060 | −0.125793 | ||||||||
\(834\) | −71.2857 | −2.46842 | ||||||||
\(835\) | −17.4387 | −0.603491 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −57.2452 | −1.97868 | ||||||||
\(838\) | −17.7452 | −0.612997 | ||||||||
\(839\) | 14.5476 | 0.502240 | 0.251120 | − | 0.967956i | \(-0.419201\pi\) | ||||
0.251120 | + | 0.967956i | \(0.419201\pi\) | |||||||
\(840\) | −3.40870 | −0.117611 | ||||||||
\(841\) | −21.2822 | −0.733868 | ||||||||
\(842\) | 15.0491 | 0.518625 | ||||||||
\(843\) | −99.2826 | −3.41947 | ||||||||
\(844\) | 9.71032 | 0.334243 | ||||||||
\(845\) | −0.641969 | −0.0220844 | ||||||||
\(846\) | 83.3880 | 2.86694 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 9.39390 | 0.322588 | ||||||||
\(849\) | 67.7863 | 2.32642 | ||||||||
\(850\) | −3.63060 | −0.124529 | ||||||||
\(851\) | −19.0223 | −0.652075 | ||||||||
\(852\) | 17.6872 | 0.605954 | ||||||||
\(853\) | 46.3967 | 1.58859 | 0.794296 | − | 0.607531i | \(-0.207840\pi\) | ||||
0.794296 | + | 0.607531i | \(0.207840\pi\) | |||||||
\(854\) | 6.61375 | 0.226318 | ||||||||
\(855\) | −17.3837 | −0.594512 | ||||||||
\(856\) | −3.93323 | −0.134435 | ||||||||
\(857\) | −47.0412 | −1.60690 | −0.803448 | − | 0.595374i | \(-0.797004\pi\) | ||||
−0.803448 | + | 0.595374i | \(0.797004\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.80378 | −0.129783 | −0.0648917 | − | 0.997892i | \(-0.520670\pi\) | ||||
−0.0648917 | + | 0.997892i | \(0.520670\pi\) | |||||||
\(860\) | 3.87280 | 0.132061 | ||||||||
\(861\) | −27.7245 | −0.944848 | ||||||||
\(862\) | −9.60354 | −0.327098 | ||||||||
\(863\) | −30.7524 | −1.04682 | −0.523412 | − | 0.852080i | \(-0.675341\pi\) | ||||
−0.523412 | + | 0.852080i | \(0.675341\pi\) | |||||||
\(864\) | −19.1543 | −0.651643 | ||||||||
\(865\) | 15.2949 | 0.520043 | ||||||||
\(866\) | 24.2421 | 0.823780 | ||||||||
\(867\) | 13.0168 | 0.442075 | ||||||||
\(868\) | −2.98864 | −0.101441 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −9.46970 | −0.321053 | ||||||||
\(871\) | 12.8755 | 0.436270 | ||||||||
\(872\) | −19.7477 | −0.668740 | ||||||||
\(873\) | −138.722 | −4.69502 | ||||||||
\(874\) | −11.9076 | −0.402780 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 6.26892 | 0.211807 | ||||||||
\(877\) | −12.0703 | −0.407583 | −0.203792 | − | 0.979014i | \(-0.565327\pi\) | ||||
−0.203792 | + | 0.979014i | \(0.565327\pi\) | |||||||
\(878\) | 32.3368 | 1.09132 | ||||||||
\(879\) | −4.37548 | −0.147581 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.7309 | 1.54071 | 0.770357 | − | 0.637613i | \(-0.220078\pi\) | ||||
0.770357 | + | 0.637613i | \(0.220078\pi\) | |||||||
\(882\) | 8.61924 | 0.290225 | ||||||||
\(883\) | −12.6357 | −0.425225 | −0.212612 | − | 0.977137i | \(-0.568197\pi\) | ||||
−0.212612 | + | 0.977137i | \(0.568197\pi\) | |||||||
\(884\) | 13.4096 | 0.451015 | ||||||||
\(885\) | 43.9051 | 1.47585 | ||||||||
\(886\) | −21.8977 | −0.735667 | ||||||||
\(887\) | −2.54891 | −0.0855840 | −0.0427920 | − | 0.999084i | \(-0.513625\pi\) | ||||
−0.0427920 | + | 0.999084i | \(0.513625\pi\) | |||||||
\(888\) | −10.9825 | −0.368549 | ||||||||
\(889\) | −16.7243 | −0.560914 | ||||||||
\(890\) | −4.85724 | −0.162815 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.64541 | 0.0885749 | ||||||||
\(893\) | 19.5123 | 0.652955 | ||||||||
\(894\) | −50.7570 | −1.69757 | ||||||||
\(895\) | −11.6746 | −0.390240 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −74.3322 | −2.48188 | ||||||||
\(898\) | −12.5764 | −0.419681 | ||||||||
\(899\) | −8.30272 | −0.276911 | ||||||||
\(900\) | 8.61924 | 0.287308 | ||||||||
\(901\) | −34.1055 | −1.13622 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.2012 | −0.439309 | ||||||||
\(904\) | −11.8492 | −0.394099 | ||||||||
\(905\) | −9.93097 | −0.330117 | ||||||||
\(906\) | 42.1466 | 1.40023 | ||||||||
\(907\) | 16.6544 | 0.553001 | 0.276500 | − | 0.961014i | \(-0.410825\pi\) | ||||
0.276500 | + | 0.961014i | \(0.410825\pi\) | |||||||
\(908\) | −2.30423 | −0.0764686 | ||||||||
\(909\) | −162.539 | −5.39108 | ||||||||
\(910\) | −3.69350 | −0.122438 | ||||||||
\(911\) | −26.6728 | −0.883709 | −0.441855 | − | 0.897087i | \(-0.645679\pi\) | ||||
−0.441855 | + | 0.897087i | \(0.645679\pi\) | |||||||
\(912\) | −6.87485 | −0.227649 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −30.6714 | −1.01452 | ||||||||
\(915\) | −22.5443 | −0.745291 | ||||||||
\(916\) | 3.72474 | 0.123069 | ||||||||
\(917\) | 13.1921 | 0.435641 | ||||||||
\(918\) | 69.5417 | 2.29522 | ||||||||
\(919\) | 55.8882 | 1.84358 | 0.921791 | − | 0.387687i | \(-0.126726\pi\) | ||||
0.921791 | + | 0.387687i | \(0.126726\pi\) | |||||||
\(920\) | 5.90404 | 0.194651 | ||||||||
\(921\) | 54.7297 | 1.80340 | ||||||||
\(922\) | 19.5978 | 0.645420 | ||||||||
\(923\) | 19.1650 | 0.630824 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.22190 | 0.105936 | ||||||||
\(926\) | −4.29483 | −0.141137 | ||||||||
\(927\) | −129.488 | −4.25293 | ||||||||
\(928\) | −2.77810 | −0.0911955 | ||||||||
\(929\) | −45.2542 | −1.48474 | −0.742371 | − | 0.669989i | \(-0.766299\pi\) | ||||
−0.742371 | + | 0.669989i | \(0.766299\pi\) | |||||||
\(930\) | 10.1874 | 0.334057 | ||||||||
\(931\) | 2.01685 | 0.0660997 | ||||||||
\(932\) | 1.72846 | 0.0566177 | ||||||||
\(933\) | −19.9129 | −0.651921 | ||||||||
\(934\) | −1.40460 | −0.0459600 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −31.8352 | −1.04057 | ||||||||
\(937\) | 29.5196 | 0.964364 | 0.482182 | − | 0.876071i | \(-0.339844\pi\) | ||||
0.482182 | + | 0.876071i | \(0.339844\pi\) | |||||||
\(938\) | 3.48599 | 0.113821 | ||||||||
\(939\) | −78.5106 | −2.56210 | ||||||||
\(940\) | −9.67464 | −0.315552 | ||||||||
\(941\) | 5.88530 | 0.191855 | 0.0959277 | − | 0.995388i | \(-0.469418\pi\) | ||||
0.0959277 | + | 0.995388i | \(0.469418\pi\) | |||||||
\(942\) | 75.1149 | 2.44738 | ||||||||
\(943\) | 48.0202 | 1.56375 | ||||||||
\(944\) | 12.8803 | 0.419218 | ||||||||
\(945\) | −19.1543 | −0.623090 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.3432 | −0.336109 | −0.168055 | − | 0.985778i | \(-0.553749\pi\) | ||||
−0.168055 | + | 0.985778i | \(0.553749\pi\) | |||||||
\(948\) | −10.0622 | −0.326804 | ||||||||
\(949\) | 6.79270 | 0.220500 | ||||||||
\(950\) | 2.01685 | 0.0654354 | ||||||||
\(951\) | −87.3633 | −2.83295 | ||||||||
\(952\) | 3.63060 | 0.117669 | ||||||||
\(953\) | 21.6287 | 0.700623 | 0.350311 | − | 0.936633i | \(-0.386076\pi\) | ||||
0.350311 | + | 0.936633i | \(0.386076\pi\) | |||||||
\(954\) | 80.9682 | 2.62144 | ||||||||
\(955\) | −14.1868 | −0.459074 | ||||||||
\(956\) | −10.6465 | −0.344332 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32.3519 | 1.04524 | ||||||||
\(959\) | −0.0587014 | −0.00189557 | ||||||||
\(960\) | 3.40870 | 0.110015 | ||||||||
\(961\) | −22.0681 | −0.711873 | ||||||||
\(962\) | −11.9001 | −0.383675 | ||||||||
\(963\) | −33.9015 | −1.09246 | ||||||||
\(964\) | 22.2210 | 0.715690 | ||||||||
\(965\) | −20.1766 | −0.649509 | ||||||||
\(966\) | −20.1251 | −0.647515 | ||||||||
\(967\) | −38.1124 | −1.22561 | −0.612806 | − | 0.790233i | \(-0.709959\pi\) | ||||
−0.612806 | + | 0.790233i | \(0.709959\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 24.9599 | 0.801826 | ||||||||
\(970\) | 16.0944 | 0.516761 | ||||||||
\(971\) | −16.2741 | −0.522261 | −0.261130 | − | 0.965304i | \(-0.584095\pi\) | ||||
−0.261130 | + | 0.965304i | \(0.584095\pi\) | |||||||
\(972\) | −76.9543 | −2.46831 | ||||||||
\(973\) | −20.9129 | −0.670436 | ||||||||
\(974\) | −3.75142 | −0.120203 | ||||||||
\(975\) | 12.5900 | 0.403204 | ||||||||
\(976\) | −6.61375 | −0.211701 | ||||||||
\(977\) | 33.2995 | 1.06535 | 0.532673 | − | 0.846321i | \(-0.321187\pi\) | ||||
0.532673 | + | 0.846321i | \(0.321187\pi\) | |||||||
\(978\) | −52.7525 | −1.68684 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −170.210 | −5.43438 | ||||||||
\(982\) | 11.1293 | 0.355150 | ||||||||
\(983\) | −28.8235 | −0.919326 | −0.459663 | − | 0.888094i | \(-0.652030\pi\) | ||||
−0.459663 | + | 0.888094i | \(0.652030\pi\) | |||||||
\(984\) | 27.7245 | 0.883824 | ||||||||
\(985\) | −11.7016 | −0.372843 | ||||||||
\(986\) | 10.0862 | 0.321209 | ||||||||
\(987\) | 32.9780 | 1.04970 | ||||||||
\(988\) | −7.44926 | −0.236992 | ||||||||
\(989\) | 22.8652 | 0.727071 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.6269 | 0.623469 | 0.311734 | − | 0.950169i | \(-0.399090\pi\) | ||||
0.311734 | + | 0.950169i | \(0.399090\pi\) | |||||||
\(992\) | 2.98864 | 0.0948893 | ||||||||
\(993\) | 5.50417 | 0.174670 | ||||||||
\(994\) | 5.18885 | 0.164580 | ||||||||
\(995\) | −8.24220 | −0.261295 | ||||||||
\(996\) | 28.5563 | 0.904840 | ||||||||
\(997\) | −18.3518 | −0.581207 | −0.290603 | − | 0.956844i | \(-0.593856\pi\) | ||||
−0.290603 | + | 0.956844i | \(0.593856\pi\) | |||||||
\(998\) | −23.2827 | −0.737002 | ||||||||
\(999\) | −61.7133 | −1.95252 |
(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 | 8470.2.a.dd.1.1 | yes | 6 | |
11.10 | odd | 2 | 8470.2.a.cx.1.1 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cx.1.1 | ✓ | 6 | 11.10 | odd | 2 | ||
8470.2.a.dd.1.1 | yes | 6 | 1.1 | even | 1 | trivial |