Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 23 x^{10} + 142 x^{9} + 104 x^{8} - 1302 x^{7} + 607 x^{6} + 4323 x^{5} - 4461 x^{4} + \cdots - 553 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.09224\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-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 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.09224 | 0.488467 | 0.244233 | − | 0.969716i | \(-0.421464\pi\) | ||||
0.244233 | + | 0.969716i | \(0.421464\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.25253 | −0.473411 | −0.236705 | − | 0.971581i | \(-0.576068\pi\) | ||||
−0.236705 | + | 0.971581i | \(0.576068\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.09224 | −0.345398 | ||||||||
\(11\) | −0.173738 | −0.0523839 | −0.0261920 | − | 0.999657i | \(-0.508338\pi\) | ||||
−0.0261920 | + | 0.999657i | \(0.508338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.22835 | 1.17273 | 0.586367 | − | 0.810046i | \(-0.300558\pi\) | ||||
0.586367 | + | 0.810046i | \(0.300558\pi\) | |||||||
\(14\) | 1.25253 | 0.334752 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.61561 | −1.11945 | −0.559725 | − | 0.828678i | \(-0.689093\pi\) | ||||
−0.559725 | + | 0.828678i | \(0.689093\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.05127 | 0.700009 | 0.350005 | − | 0.936748i | \(-0.386180\pi\) | ||||
0.350005 | + | 0.936748i | \(0.386180\pi\) | |||||||
\(20\) | 1.09224 | 0.244233 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.173738 | 0.0370410 | ||||||||
\(23\) | −0.515996 | −0.107593 | −0.0537963 | − | 0.998552i | \(-0.517132\pi\) | ||||
−0.0537963 | + | 0.998552i | \(0.517132\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.80700 | −0.761400 | ||||||||
\(26\) | −4.22835 | −0.829248 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.25253 | −0.236705 | ||||||||
\(29\) | 5.77684 | 1.07273 | 0.536366 | − | 0.843985i | \(-0.319797\pi\) | ||||
0.536366 | + | 0.843985i | \(0.319797\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0135315 | 0.00243032 | 0.00121516 | − | 0.999999i | \(-0.499613\pi\) | ||||
0.00121516 | + | 0.999999i | \(0.499613\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.61561 | 0.791571 | ||||||||
\(35\) | −1.36807 | −0.231245 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.73328 | −1.27134 | −0.635671 | − | 0.771960i | \(-0.719277\pi\) | ||||
−0.635671 | + | 0.771960i | \(0.719277\pi\) | |||||||
\(38\) | −3.05127 | −0.494981 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.09224 | −0.172699 | ||||||||
\(41\) | −7.34603 | −1.14726 | −0.573629 | − | 0.819115i | \(-0.694465\pi\) | ||||
−0.573629 | + | 0.819115i | \(0.694465\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.19948 | 0.792913 | 0.396457 | − | 0.918053i | \(-0.370240\pi\) | ||||
0.396457 | + | 0.918053i | \(0.370240\pi\) | |||||||
\(44\) | −0.173738 | −0.0261920 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.515996 | 0.0760794 | ||||||||
\(47\) | −2.23044 | −0.325343 | −0.162671 | − | 0.986680i | \(-0.552011\pi\) | ||||
−0.162671 | + | 0.986680i | \(0.552011\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.43118 | −0.775882 | ||||||||
\(50\) | 3.80700 | 0.538391 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.22835 | 0.586367 | ||||||||
\(53\) | −1.74794 | −0.240099 | −0.120049 | − | 0.992768i | \(-0.538305\pi\) | ||||
−0.120049 | + | 0.992768i | \(0.538305\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.189764 | −0.0255878 | ||||||||
\(56\) | 1.25253 | 0.167376 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.77684 | −0.758537 | ||||||||
\(59\) | −8.36601 | −1.08916 | −0.544581 | − | 0.838708i | \(-0.683311\pi\) | ||||
−0.544581 | + | 0.838708i | \(0.683311\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.66842 | 0.853804 | 0.426902 | − | 0.904298i | \(-0.359605\pi\) | ||||
0.426902 | + | 0.904298i | \(0.359605\pi\) | |||||||
\(62\) | −0.0135315 | −0.00171850 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.61839 | 0.572841 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.2370 | −1.37281 | −0.686406 | − | 0.727218i | \(-0.740813\pi\) | ||||
−0.686406 | + | 0.727218i | \(0.740813\pi\) | |||||||
\(68\) | −4.61561 | −0.559725 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.36807 | 0.163515 | ||||||||
\(71\) | −5.70549 | −0.677117 | −0.338558 | − | 0.940945i | \(-0.609939\pi\) | ||||
−0.338558 | + | 0.940945i | \(0.609939\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.5008 | 1.69719 | 0.848597 | − | 0.529040i | \(-0.177448\pi\) | ||||
0.848597 | + | 0.529040i | \(0.177448\pi\) | |||||||
\(74\) | 7.73328 | 0.898975 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.05127 | 0.350005 | ||||||||
\(77\) | 0.217611 | 0.0247991 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.27461 | −0.143405 | −0.0717026 | − | 0.997426i | \(-0.522843\pi\) | ||||
−0.0717026 | + | 0.997426i | \(0.522843\pi\) | |||||||
\(80\) | 1.09224 | 0.122117 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.34603 | 0.811234 | ||||||||
\(83\) | 4.98613 | 0.547299 | 0.273650 | − | 0.961829i | \(-0.411769\pi\) | ||||
0.273650 | + | 0.961829i | \(0.411769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.04138 | −0.546814 | ||||||||
\(86\) | −5.19948 | −0.560674 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.173738 | 0.0185205 | ||||||||
\(89\) | −3.60101 | −0.381706 | −0.190853 | − | 0.981619i | \(-0.561125\pi\) | ||||
−0.190853 | + | 0.981619i | \(0.561125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.29613 | −0.555185 | ||||||||
\(92\) | −0.515996 | −0.0537963 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.23044 | 0.230052 | ||||||||
\(95\) | 3.33273 | 0.341931 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.13298 | −0.724244 | −0.362122 | − | 0.932131i | \(-0.617948\pi\) | ||||
−0.362122 | + | 0.932131i | \(0.617948\pi\) | |||||||
\(98\) | 5.43118 | 0.548632 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.80700 | −0.380700 | ||||||||
\(101\) | −12.5976 | −1.25350 | −0.626752 | − | 0.779219i | \(-0.715616\pi\) | ||||
−0.626752 | + | 0.779219i | \(0.715616\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.697965 | 0.0687725 | 0.0343862 | − | 0.999409i | \(-0.489052\pi\) | ||||
0.0343862 | + | 0.999409i | \(0.489052\pi\) | |||||||
\(104\) | −4.22835 | −0.414624 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.74794 | 0.169775 | ||||||||
\(107\) | 8.15974 | 0.788832 | 0.394416 | − | 0.918932i | \(-0.370947\pi\) | ||||
0.394416 | + | 0.918932i | \(0.370947\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8923 | 1.33064 | 0.665319 | − | 0.746559i | \(-0.268295\pi\) | ||||
0.665319 | + | 0.746559i | \(0.268295\pi\) | |||||||
\(110\) | 0.189764 | 0.0180933 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.25253 | −0.118353 | ||||||||
\(113\) | −4.70720 | −0.442816 | −0.221408 | − | 0.975181i | \(-0.571065\pi\) | ||||
−0.221408 | + | 0.975181i | \(0.571065\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.563594 | −0.0525554 | ||||||||
\(116\) | 5.77684 | 0.536366 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.36601 | 0.770154 | ||||||||
\(119\) | 5.78118 | 0.529960 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9698 | −0.997256 | ||||||||
\(122\) | −6.66842 | −0.603730 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.0135315 | 0.00121516 | ||||||||
\(125\) | −9.61940 | −0.860385 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.14529 | 0.722777 | 0.361389 | − | 0.932415i | \(-0.382303\pi\) | ||||
0.361389 | + | 0.932415i | \(0.382303\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.61839 | −0.405060 | ||||||||
\(131\) | −1.84870 | −0.161521 | −0.0807607 | − | 0.996734i | \(-0.525735\pi\) | ||||
−0.0807607 | + | 0.996734i | \(0.525735\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.82180 | −0.331392 | ||||||||
\(134\) | 11.2370 | 0.970725 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.61561 | 0.395785 | ||||||||
\(137\) | 12.4658 | 1.06502 | 0.532511 | − | 0.846423i | \(-0.321249\pi\) | ||||
0.532511 | + | 0.846423i | \(0.321249\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.51802 | 0.807308 | 0.403654 | − | 0.914912i | \(-0.367740\pi\) | ||||
0.403654 | + | 0.914912i | \(0.367740\pi\) | |||||||
\(140\) | −1.36807 | −0.115623 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.70549 | 0.478794 | ||||||||
\(143\) | −0.734624 | −0.0614324 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.30973 | 0.523994 | ||||||||
\(146\) | −14.5008 | −1.20010 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −7.73328 | −0.635671 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4423 | −0.849782 | −0.424891 | − | 0.905244i | \(-0.639688\pi\) | ||||
−0.424891 | + | 0.905244i | \(0.639688\pi\) | |||||||
\(152\) | −3.05127 | −0.247491 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.217611 | −0.0175356 | ||||||||
\(155\) | 0.0147797 | 0.00118713 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.12291 | −0.648278 | −0.324139 | − | 0.946009i | \(-0.605075\pi\) | ||||
−0.324139 | + | 0.946009i | \(0.605075\pi\) | |||||||
\(158\) | 1.27461 | 0.101403 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.09224 | −0.0863495 | ||||||||
\(161\) | 0.646299 | 0.0509355 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.0916217 | −0.00717637 | −0.00358818 | − | 0.999994i | \(-0.501142\pi\) | ||||
−0.00358818 | + | 0.999994i | \(0.501142\pi\) | |||||||
\(164\) | −7.34603 | −0.573629 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.98613 | −0.386999 | ||||||||
\(167\) | −13.1457 | −1.01725 | −0.508624 | − | 0.860989i | \(-0.669846\pi\) | ||||
−0.508624 | + | 0.860989i | \(0.669846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.87896 | 0.375305 | ||||||||
\(170\) | 5.04138 | 0.386656 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.19948 | 0.396457 | ||||||||
\(173\) | −6.71040 | −0.510182 | −0.255091 | − | 0.966917i | \(-0.582105\pi\) | ||||
−0.255091 | + | 0.966917i | \(0.582105\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.76837 | 0.360455 | ||||||||
\(176\) | −0.173738 | −0.0130960 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.60101 | 0.269907 | ||||||||
\(179\) | −18.5877 | −1.38931 | −0.694655 | − | 0.719343i | \(-0.744443\pi\) | ||||
−0.694655 | + | 0.719343i | \(0.744443\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.34620 | −0.471709 | −0.235855 | − | 0.971788i | \(-0.575789\pi\) | ||||
−0.235855 | + | 0.971788i | \(0.575789\pi\) | |||||||
\(182\) | 5.29613 | 0.392575 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.515996 | 0.0380397 | ||||||||
\(185\) | −8.44663 | −0.621009 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.801906 | 0.0586412 | ||||||||
\(188\) | −2.23044 | −0.162671 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.33273 | −0.241782 | ||||||||
\(191\) | −0.581014 | −0.0420407 | −0.0210203 | − | 0.999779i | \(-0.506691\pi\) | ||||
−0.0210203 | + | 0.999779i | \(0.506691\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.8034 | 1.49746 | 0.748729 | − | 0.662876i | \(-0.230664\pi\) | ||||
0.748729 | + | 0.662876i | \(0.230664\pi\) | |||||||
\(194\) | 7.13298 | 0.512118 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.43118 | −0.387941 | ||||||||
\(197\) | −10.3409 | −0.736756 | −0.368378 | − | 0.929676i | \(-0.620087\pi\) | ||||
−0.368378 | + | 0.929676i | \(0.620087\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.52240 | −0.675025 | −0.337513 | − | 0.941321i | \(-0.609586\pi\) | ||||
−0.337513 | + | 0.941321i | \(0.609586\pi\) | |||||||
\(200\) | 3.80700 | 0.269196 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.5976 | 0.886361 | ||||||||
\(203\) | −7.23565 | −0.507843 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.02367 | −0.560397 | ||||||||
\(206\) | −0.697965 | −0.0486295 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.22835 | 0.293183 | ||||||||
\(209\) | −0.530121 | −0.0366692 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.92251 | −0.407722 | −0.203861 | − | 0.979000i | \(-0.565349\pi\) | ||||
−0.203861 | + | 0.979000i | \(0.565349\pi\) | |||||||
\(212\) | −1.74794 | −0.120049 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.15974 | −0.557789 | ||||||||
\(215\) | 5.67911 | 0.387312 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0169485 | −0.00115054 | ||||||||
\(218\) | −13.8923 | −0.940904 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.189764 | −0.0127939 | ||||||||
\(221\) | −19.5164 | −1.31282 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7359 | 1.45554 | 0.727771 | − | 0.685820i | \(-0.240556\pi\) | ||||
0.727771 | + | 0.685820i | \(0.240556\pi\) | |||||||
\(224\) | 1.25253 | 0.0836880 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.70720 | 0.313118 | ||||||||
\(227\) | 0.0539413 | 0.00358021 | 0.00179010 | − | 0.999998i | \(-0.499430\pi\) | ||||
0.00179010 | + | 0.999998i | \(0.499430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.4074 | 1.01815 | 0.509073 | − | 0.860723i | \(-0.329988\pi\) | ||||
0.509073 | + | 0.860723i | \(0.329988\pi\) | |||||||
\(230\) | 0.563594 | 0.0371623 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.77684 | −0.379268 | ||||||||
\(233\) | 15.3630 | 1.00646 | 0.503232 | − | 0.864151i | \(-0.332144\pi\) | ||||
0.503232 | + | 0.864151i | \(0.332144\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.43618 | −0.158919 | ||||||||
\(236\) | −8.36601 | −0.544581 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.78118 | −0.374738 | ||||||||
\(239\) | −25.0515 | −1.62045 | −0.810225 | − | 0.586119i | \(-0.800655\pi\) | ||||
−0.810225 | + | 0.586119i | \(0.800655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.66193 | 0.107054 | 0.0535270 | − | 0.998566i | \(-0.482954\pi\) | ||||
0.0535270 | + | 0.998566i | \(0.482954\pi\) | |||||||
\(242\) | 10.9698 | 0.705166 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.66842 | 0.426902 | ||||||||
\(245\) | −5.93217 | −0.378993 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.9018 | 0.820924 | ||||||||
\(248\) | −0.0135315 | −0.000859248 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.61940 | 0.608384 | ||||||||
\(251\) | −14.0249 | −0.885244 | −0.442622 | − | 0.896708i | \(-0.645952\pi\) | ||||
−0.442622 | + | 0.896708i | \(0.645952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0896480 | 0.00563612 | ||||||||
\(254\) | −8.14529 | −0.511081 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.25186 | 0.577115 | 0.288557 | − | 0.957463i | \(-0.406824\pi\) | ||||
0.288557 | + | 0.957463i | \(0.406824\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.68614 | 0.601868 | ||||||||
\(260\) | 4.61839 | 0.286421 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.84870 | 0.114213 | ||||||||
\(263\) | −3.86172 | −0.238124 | −0.119062 | − | 0.992887i | \(-0.537989\pi\) | ||||
−0.119062 | + | 0.992887i | \(0.537989\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.90918 | −0.117280 | ||||||||
\(266\) | 3.82180 | 0.234329 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.2370 | −0.686406 | ||||||||
\(269\) | −5.13433 | −0.313046 | −0.156523 | − | 0.987674i | \(-0.550028\pi\) | ||||
−0.156523 | + | 0.987674i | \(0.550028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0580 | 0.610981 | 0.305490 | − | 0.952195i | \(-0.401180\pi\) | ||||
0.305490 | + | 0.952195i | \(0.401180\pi\) | |||||||
\(272\) | −4.61561 | −0.279863 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.4658 | −0.753084 | ||||||||
\(275\) | 0.661420 | 0.0398851 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.1060 | −1.14797 | −0.573986 | − | 0.818865i | \(-0.694603\pi\) | ||||
−0.573986 | + | 0.818865i | \(0.694603\pi\) | |||||||
\(278\) | −9.51802 | −0.570853 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.36807 | 0.0817576 | ||||||||
\(281\) | −14.8839 | −0.887900 | −0.443950 | − | 0.896052i | \(-0.646423\pi\) | ||||
−0.443950 | + | 0.896052i | \(0.646423\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.8463 | 1.53640 | 0.768201 | − | 0.640208i | \(-0.221152\pi\) | ||||
0.768201 | + | 0.640208i | \(0.221152\pi\) | |||||||
\(284\) | −5.70549 | −0.338558 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.734624 | 0.0434393 | ||||||||
\(287\) | 9.20111 | 0.543124 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.30388 | 0.253169 | ||||||||
\(290\) | −6.30973 | −0.370520 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.5008 | 0.848597 | ||||||||
\(293\) | −21.3302 | −1.24612 | −0.623061 | − | 0.782173i | \(-0.714111\pi\) | ||||
−0.623061 | + | 0.782173i | \(0.714111\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.13773 | −0.532019 | ||||||||
\(296\) | 7.73328 | 0.449488 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | −2.18181 | −0.126177 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.51249 | −0.375374 | ||||||||
\(302\) | 10.4423 | 0.600887 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.05127 | 0.175002 | ||||||||
\(305\) | 7.28355 | 0.417055 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.9755 | −0.968845 | −0.484423 | − | 0.874834i | \(-0.660970\pi\) | ||||
−0.484423 | + | 0.874834i | \(0.660970\pi\) | |||||||
\(308\) | 0.217611 | 0.0123996 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.0147797 | −0.000839428 0 | ||||||||
\(311\) | −33.1623 | −1.88046 | −0.940230 | − | 0.340540i | \(-0.889390\pi\) | ||||
−0.940230 | + | 0.340540i | \(0.889390\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.8522 | 0.613405 | 0.306702 | − | 0.951805i | \(-0.400774\pi\) | ||||
0.306702 | + | 0.951805i | \(0.400774\pi\) | |||||||
\(314\) | 8.12291 | 0.458402 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.27461 | −0.0717026 | ||||||||
\(317\) | −27.2821 | −1.53231 | −0.766157 | − | 0.642654i | \(-0.777833\pi\) | ||||
−0.766157 | + | 0.642654i | \(0.777833\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.00366 | −0.0561939 | ||||||||
\(320\) | 1.09224 | 0.0610583 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.646299 | −0.0360168 | ||||||||
\(323\) | −14.0835 | −0.783625 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.0973 | −0.892920 | ||||||||
\(326\) | 0.0916217 | 0.00507446 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.34603 | 0.405617 | ||||||||
\(329\) | 2.79369 | 0.154021 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.9144 | 0.874733 | 0.437366 | − | 0.899283i | \(-0.355911\pi\) | ||||
0.437366 | + | 0.899283i | \(0.355911\pi\) | |||||||
\(332\) | 4.98613 | 0.273650 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.1457 | 0.719303 | ||||||||
\(335\) | −12.2735 | −0.670573 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.182766 | 0.00995592 | 0.00497796 | − | 0.999988i | \(-0.498415\pi\) | ||||
0.00497796 | + | 0.999988i | \(0.498415\pi\) | |||||||
\(338\) | −4.87896 | −0.265380 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.04138 | −0.273407 | ||||||||
\(341\) | −0.00235092 | −0.000127310 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5704 | 0.840722 | ||||||||
\(344\) | −5.19948 | −0.280337 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.71040 | 0.360753 | ||||||||
\(347\) | −7.90087 | −0.424141 | −0.212071 | − | 0.977254i | \(-0.568021\pi\) | ||||
−0.212071 | + | 0.977254i | \(0.568021\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.57512 | −0.512544 | −0.256272 | − | 0.966605i | \(-0.582494\pi\) | ||||
−0.256272 | + | 0.966605i | \(0.582494\pi\) | |||||||
\(350\) | −4.76837 | −0.254880 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.173738 | 0.00926025 | ||||||||
\(353\) | −6.58919 | −0.350707 | −0.175354 | − | 0.984506i | \(-0.556107\pi\) | ||||
−0.175354 | + | 0.984506i | \(0.556107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.23179 | −0.330749 | ||||||||
\(356\) | −3.60101 | −0.190853 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 18.5877 | 0.982390 | ||||||||
\(359\) | 11.2505 | 0.593777 | 0.296889 | − | 0.954912i | \(-0.404051\pi\) | ||||
0.296889 | + | 0.954912i | \(0.404051\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.68976 | −0.509987 | ||||||||
\(362\) | 6.34620 | 0.333549 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.29613 | −0.277592 | ||||||||
\(365\) | 15.8384 | 0.829022 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.21281 | 0.480905 | 0.240452 | − | 0.970661i | \(-0.422704\pi\) | ||||
0.240452 | + | 0.970661i | \(0.422704\pi\) | |||||||
\(368\) | −0.515996 | −0.0268981 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.44663 | 0.439119 | ||||||||
\(371\) | 2.18935 | 0.113665 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.9485 | −1.80956 | −0.904782 | − | 0.425874i | \(-0.859967\pi\) | ||||
−0.904782 | + | 0.425874i | \(0.859967\pi\) | |||||||
\(374\) | −0.801906 | −0.0414656 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.23044 | 0.115026 | ||||||||
\(377\) | 24.4265 | 1.25803 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.91395 | 0.149680 | 0.0748398 | − | 0.997196i | \(-0.476155\pi\) | ||||
0.0748398 | + | 0.997196i | \(0.476155\pi\) | |||||||
\(380\) | 3.33273 | 0.170966 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.581014 | 0.0297272 | ||||||||
\(383\) | −16.4250 | −0.839280 | −0.419640 | − | 0.907691i | \(-0.637844\pi\) | ||||
−0.419640 | + | 0.907691i | \(0.637844\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.237685 | 0.0121135 | ||||||||
\(386\) | −20.8034 | −1.05886 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.13298 | −0.362122 | ||||||||
\(389\) | 5.41838 | 0.274723 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.38164 | 0.120445 | ||||||||
\(392\) | 5.43118 | 0.274316 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.3409 | 0.520965 | ||||||||
\(395\) | −1.39219 | −0.0700486 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.7221 | 1.19058 | 0.595288 | − | 0.803513i | \(-0.297038\pi\) | ||||
0.595288 | + | 0.803513i | \(0.297038\pi\) | |||||||
\(398\) | 9.52240 | 0.477315 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.80700 | −0.190350 | ||||||||
\(401\) | 13.7355 | 0.685919 | 0.342959 | − | 0.939350i | \(-0.388571\pi\) | ||||
0.342959 | + | 0.939350i | \(0.388571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0572158 | 0.00285012 | ||||||||
\(404\) | −12.5976 | −0.626752 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.23565 | 0.359099 | ||||||||
\(407\) | 1.34356 | 0.0665979 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.3492 | −0.857863 | −0.428932 | − | 0.903337i | \(-0.641110\pi\) | ||||
−0.428932 | + | 0.903337i | \(0.641110\pi\) | |||||||
\(410\) | 8.02367 | 0.396261 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.697965 | 0.0343862 | ||||||||
\(413\) | 10.4787 | 0.515621 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.44608 | 0.267337 | ||||||||
\(416\) | −4.22835 | −0.207312 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.530121 | 0.0259290 | ||||||||
\(419\) | −0.488645 | −0.0238719 | −0.0119359 | − | 0.999929i | \(-0.503799\pi\) | ||||
−0.0119359 | + | 0.999929i | \(0.503799\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.8098 | −1.50158 | −0.750789 | − | 0.660542i | \(-0.770326\pi\) | ||||
−0.750789 | + | 0.660542i | \(0.770326\pi\) | |||||||
\(422\) | 5.92251 | 0.288303 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.74794 | 0.0848877 | ||||||||
\(425\) | 17.5716 | 0.852350 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.35238 | −0.404200 | ||||||||
\(428\) | 8.15974 | 0.394416 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.67911 | −0.273871 | ||||||||
\(431\) | 23.2831 | 1.12151 | 0.560755 | − | 0.827982i | \(-0.310511\pi\) | ||||
0.560755 | + | 0.827982i | \(0.310511\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −34.3793 | −1.65216 | −0.826082 | − | 0.563551i | \(-0.809435\pi\) | ||||
−0.826082 | + | 0.563551i | \(0.809435\pi\) | |||||||
\(434\) | 0.0169485 | 0.000813555 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 13.8923 | 0.665319 | ||||||||
\(437\) | −1.57444 | −0.0753158 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.22947 | −0.201862 | −0.100931 | − | 0.994893i | \(-0.532182\pi\) | ||||
−0.100931 | + | 0.994893i | \(0.532182\pi\) | |||||||
\(440\) | 0.189764 | 0.00904665 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.5164 | 0.928302 | ||||||||
\(443\) | 24.0179 | 1.14113 | 0.570563 | − | 0.821254i | \(-0.306725\pi\) | ||||
0.570563 | + | 0.821254i | \(0.306725\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.93318 | −0.186451 | ||||||||
\(446\) | −21.7359 | −1.02922 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.25253 | −0.0591764 | ||||||||
\(449\) | −13.7355 | −0.648218 | −0.324109 | − | 0.946020i | \(-0.605064\pi\) | ||||
−0.324109 | + | 0.946020i | \(0.605064\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.27628 | 0.0600978 | ||||||||
\(452\) | −4.70720 | −0.221408 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.0539413 | −0.00253159 | ||||||||
\(455\) | −5.78467 | −0.271189 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.2382 | −0.993483 | −0.496741 | − | 0.867899i | \(-0.665470\pi\) | ||||
−0.496741 | + | 0.867899i | \(0.665470\pi\) | |||||||
\(458\) | −15.4074 | −0.719939 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.563594 | −0.0262777 | ||||||||
\(461\) | −25.1134 | −1.16965 | −0.584825 | − | 0.811160i | \(-0.698837\pi\) | ||||
−0.584825 | + | 0.811160i | \(0.698837\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 36.1754 | 1.68122 | 0.840608 | − | 0.541644i | \(-0.182198\pi\) | ||||
0.840608 | + | 0.541644i | \(0.182198\pi\) | |||||||
\(464\) | 5.77684 | 0.268183 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.3630 | −0.711677 | ||||||||
\(467\) | −6.71738 | −0.310843 | −0.155422 | − | 0.987848i | \(-0.549674\pi\) | ||||
−0.155422 | + | 0.987848i | \(0.549674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.0746 | 0.649904 | ||||||||
\(470\) | 2.43618 | 0.112373 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.36601 | 0.385077 | ||||||||
\(473\) | −0.903346 | −0.0415359 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.6162 | −0.532987 | ||||||||
\(476\) | 5.78118 | 0.264980 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 25.0515 | 1.14583 | ||||||||
\(479\) | 34.5320 | 1.57781 | 0.788903 | − | 0.614518i | \(-0.210649\pi\) | ||||
0.788903 | + | 0.614518i | \(0.210649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −32.6990 | −1.49095 | ||||||||
\(482\) | −1.66193 | −0.0756987 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9698 | −0.498628 | ||||||||
\(485\) | −7.79096 | −0.353769 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7774 | 0.669628 | 0.334814 | − | 0.942284i | \(-0.391327\pi\) | ||||
0.334814 | + | 0.942284i | \(0.391327\pi\) | |||||||
\(488\) | −6.66842 | −0.301865 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 5.93217 | 0.267988 | ||||||||
\(491\) | 25.0893 | 1.13227 | 0.566133 | − | 0.824314i | \(-0.308439\pi\) | ||||
0.566133 | + | 0.824314i | \(0.308439\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.6637 | −1.20087 | ||||||||
\(494\) | −12.9018 | −0.580481 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.0135315 | 0.000607580 0 | ||||||||
\(497\) | 7.14628 | 0.320554 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.2941 | 0.505592 | 0.252796 | − | 0.967520i | \(-0.418650\pi\) | ||||
0.252796 | + | 0.967520i | \(0.418650\pi\) | |||||||
\(500\) | −9.61940 | −0.430193 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.0249 | 0.625962 | ||||||||
\(503\) | 26.2467 | 1.17028 | 0.585141 | − | 0.810932i | \(-0.301039\pi\) | ||||
0.585141 | + | 0.810932i | \(0.301039\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.7596 | −0.612295 | ||||||||
\(506\) | −0.0896480 | −0.00398534 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.14529 | 0.361389 | ||||||||
\(509\) | 2.41347 | 0.106975 | 0.0534875 | − | 0.998569i | \(-0.482966\pi\) | ||||
0.0534875 | + | 0.998569i | \(0.482966\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.1627 | −0.803470 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.25186 | −0.408082 | ||||||||
\(515\) | 0.762348 | 0.0335931 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.387511 | 0.0170427 | ||||||||
\(518\) | −9.68614 | −0.425585 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.61839 | −0.202530 | ||||||||
\(521\) | −14.3007 | −0.626527 | −0.313263 | − | 0.949666i | \(-0.601422\pi\) | ||||
−0.313263 | + | 0.949666i | \(0.601422\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.7551 | 1.12619 | 0.563096 | − | 0.826392i | \(-0.309610\pi\) | ||||
0.563096 | + | 0.826392i | \(0.309610\pi\) | |||||||
\(524\) | −1.84870 | −0.0807607 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.86172 | 0.168379 | ||||||||
\(527\) | −0.0624560 | −0.00272062 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7337 | −0.988424 | ||||||||
\(530\) | 1.90918 | 0.0829296 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.82180 | −0.165696 | ||||||||
\(533\) | −31.0616 | −1.34543 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.91244 | 0.385318 | ||||||||
\(536\) | 11.2370 | 0.485363 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.13433 | 0.221357 | ||||||||
\(539\) | 0.943600 | 0.0406437 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.64575 | 0.328716 | 0.164358 | − | 0.986401i | \(-0.447445\pi\) | ||||
0.164358 | + | 0.986401i | \(0.447445\pi\) | |||||||
\(542\) | −10.0580 | −0.432029 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.61561 | 0.197893 | ||||||||
\(545\) | 15.1738 | 0.649973 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.0339 | −0.642803 | −0.321402 | − | 0.946943i | \(-0.604154\pi\) | ||||
−0.321402 | + | 0.946943i | \(0.604154\pi\) | |||||||
\(548\) | 12.4658 | 0.532511 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.661420 | −0.0282030 | ||||||||
\(551\) | 17.6267 | 0.750923 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.59649 | 0.0678895 | ||||||||
\(554\) | 19.1060 | 0.811738 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.51802 | 0.403654 | ||||||||
\(557\) | −21.8515 | −0.925878 | −0.462939 | − | 0.886390i | \(-0.653205\pi\) | ||||
−0.462939 | + | 0.886390i | \(0.653205\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.9852 | 0.929876 | ||||||||
\(560\) | −1.36807 | −0.0578114 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.8839 | 0.627840 | ||||||||
\(563\) | 15.5931 | 0.657173 | 0.328586 | − | 0.944474i | \(-0.393428\pi\) | ||||
0.328586 | + | 0.944474i | \(0.393428\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.14142 | −0.216301 | ||||||||
\(566\) | −25.8463 | −1.08640 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.70549 | 0.239397 | ||||||||
\(569\) | 0.929346 | 0.0389602 | 0.0194801 | − | 0.999810i | \(-0.493799\pi\) | ||||
0.0194801 | + | 0.999810i | \(0.493799\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.7144 | −1.03426 | −0.517132 | − | 0.855906i | \(-0.673000\pi\) | ||||
−0.517132 | + | 0.855906i | \(0.673000\pi\) | |||||||
\(572\) | −0.734624 | −0.0307162 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.20111 | −0.384047 | ||||||||
\(575\) | 1.96440 | 0.0819210 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.56144 | −0.231526 | −0.115763 | − | 0.993277i | \(-0.536931\pi\) | ||||
−0.115763 | + | 0.993277i | \(0.536931\pi\) | |||||||
\(578\) | −4.30388 | −0.179018 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.30973 | 0.261997 | ||||||||
\(581\) | −6.24527 | −0.259097 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.303684 | 0.0125773 | ||||||||
\(584\) | −14.5008 | −0.600048 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.3302 | 0.881141 | ||||||||
\(587\) | 1.85575 | 0.0765952 | 0.0382976 | − | 0.999266i | \(-0.487807\pi\) | ||||
0.0382976 | + | 0.999266i | \(0.487807\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0412881 | 0.00170125 | ||||||||
\(590\) | 9.13773 | 0.376194 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.73328 | −0.317836 | ||||||||
\(593\) | 24.9148 | 1.02313 | 0.511564 | − | 0.859245i | \(-0.329066\pi\) | ||||
0.511564 | + | 0.859245i | \(0.329066\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.31446 | 0.258868 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.18181 | 0.0892209 | ||||||||
\(599\) | −18.6921 | −0.763740 | −0.381870 | − | 0.924216i | \(-0.624720\pi\) | ||||
−0.381870 | + | 0.924216i | \(0.624720\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.2749 | −1.23494 | −0.617470 | − | 0.786595i | \(-0.711842\pi\) | ||||
−0.617470 | + | 0.786595i | \(0.711842\pi\) | |||||||
\(602\) | 6.51249 | 0.265429 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.4423 | −0.424891 | ||||||||
\(605\) | −11.9817 | −0.487126 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.04930 | 0.123767 | 0.0618837 | − | 0.998083i | \(-0.480289\pi\) | ||||
0.0618837 | + | 0.998083i | \(0.480289\pi\) | |||||||
\(608\) | −3.05127 | −0.123745 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.28355 | −0.294902 | ||||||||
\(611\) | −9.43108 | −0.381541 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9276 | 0.926037 | 0.463019 | − | 0.886349i | \(-0.346766\pi\) | ||||
0.463019 | + | 0.886349i | \(0.346766\pi\) | |||||||
\(614\) | 16.9755 | 0.685077 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.217611 | −0.00876781 | ||||||||
\(617\) | −17.9432 | −0.722366 | −0.361183 | − | 0.932495i | \(-0.617627\pi\) | ||||
−0.361183 | + | 0.932495i | \(0.617627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.5288 | 1.22706 | 0.613528 | − | 0.789673i | \(-0.289750\pi\) | ||||
0.613528 | + | 0.789673i | \(0.289750\pi\) | |||||||
\(620\) | 0.0147797 | 0.000593565 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 33.1623 | 1.32969 | ||||||||
\(623\) | 4.51036 | 0.180704 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.52827 | 0.341131 | ||||||||
\(626\) | −10.8522 | −0.433743 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.12291 | −0.324139 | ||||||||
\(629\) | 35.6938 | 1.42321 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.6736 | −1.10167 | −0.550834 | − | 0.834615i | \(-0.685690\pi\) | ||||
−0.550834 | + | 0.834615i | \(0.685690\pi\) | |||||||
\(632\) | 1.27461 | 0.0507014 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.2821 | 1.08351 | ||||||||
\(635\) | 8.89664 | 0.353053 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.9649 | −0.909903 | ||||||||
\(638\) | 1.00366 | 0.0397351 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.09224 | −0.0431748 | ||||||||
\(641\) | 18.5127 | 0.731208 | 0.365604 | − | 0.930771i | \(-0.380863\pi\) | ||||
0.365604 | + | 0.930771i | \(0.380863\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.8776 | −1.21769 | −0.608847 | − | 0.793287i | \(-0.708368\pi\) | ||||
−0.608847 | + | 0.793287i | \(0.708368\pi\) | |||||||
\(644\) | 0.646299 | 0.0254677 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.0835 | 0.554107 | ||||||||
\(647\) | −16.5474 | −0.650544 | −0.325272 | − | 0.945621i | \(-0.605456\pi\) | ||||
−0.325272 | + | 0.945621i | \(0.605456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.45349 | 0.0570546 | ||||||||
\(650\) | 16.0973 | 0.631390 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.0916217 | −0.00358818 | ||||||||
\(653\) | −9.00280 | −0.352307 | −0.176153 | − | 0.984363i | \(-0.556365\pi\) | ||||
−0.176153 | + | 0.984363i | \(0.556365\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.01923 | −0.0788978 | ||||||||
\(656\) | −7.34603 | −0.286814 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.79369 | −0.108909 | ||||||||
\(659\) | 10.7181 | 0.417516 | 0.208758 | − | 0.977967i | \(-0.433058\pi\) | ||||
0.208758 | + | 0.977967i | \(0.433058\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.29076 | −0.166891 | −0.0834456 | − | 0.996512i | \(-0.526592\pi\) | ||||
−0.0834456 | + | 0.996512i | \(0.526592\pi\) | |||||||
\(662\) | −15.9144 | −0.618529 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.98613 | −0.193500 | ||||||||
\(665\) | −4.17434 | −0.161874 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.98083 | −0.115418 | ||||||||
\(668\) | −13.1457 | −0.508624 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 12.2735 | 0.474167 | ||||||||
\(671\) | −1.15856 | −0.0447256 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.41744 | 0.324469 | 0.162234 | − | 0.986752i | \(-0.448130\pi\) | ||||
0.162234 | + | 0.986752i | \(0.448130\pi\) | |||||||
\(674\) | −0.182766 | −0.00703990 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.87896 | 0.187652 | ||||||||
\(677\) | −17.4120 | −0.669197 | −0.334599 | − | 0.942361i | \(-0.608601\pi\) | ||||
−0.334599 | + | 0.942361i | \(0.608601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.93425 | 0.342865 | ||||||||
\(680\) | 5.04138 | 0.193328 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.00235092 | 9.00216e−5 0 | ||||||||
\(683\) | 22.7209 | 0.869392 | 0.434696 | − | 0.900577i | \(-0.356856\pi\) | ||||
0.434696 | + | 0.900577i | \(0.356856\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.6157 | 0.520228 | ||||||||
\(686\) | −15.5704 | −0.594480 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.19948 | 0.198228 | ||||||||
\(689\) | −7.39092 | −0.281572 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.1774 | −0.805625 | −0.402812 | − | 0.915283i | \(-0.631967\pi\) | ||||
−0.402812 | + | 0.915283i | \(0.631967\pi\) | |||||||
\(692\) | −6.71040 | −0.255091 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.90087 | 0.299913 | ||||||||
\(695\) | 10.3960 | 0.394343 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.9064 | 1.28430 | ||||||||
\(698\) | 9.57512 | 0.362424 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.76837 | 0.180228 | ||||||||
\(701\) | 29.7208 | 1.12254 | 0.561269 | − | 0.827633i | \(-0.310313\pi\) | ||||
0.561269 | + | 0.827633i | \(0.310313\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.5963 | −0.889952 | ||||||||
\(704\) | −0.173738 | −0.00654799 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.58919 | 0.247987 | ||||||||
\(707\) | 15.7788 | 0.593422 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.9661 | −1.61363 | −0.806814 | − | 0.590806i | \(-0.798810\pi\) | ||||
−0.806814 | + | 0.590806i | \(0.798810\pi\) | |||||||
\(710\) | 6.23179 | 0.233875 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.60101 | 0.134953 | ||||||||
\(713\) | −0.00698217 | −0.000261484 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.802390 | −0.0300077 | ||||||||
\(716\) | −18.5877 | −0.694655 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −11.2505 | −0.419864 | ||||||||
\(719\) | 5.77459 | 0.215356 | 0.107678 | − | 0.994186i | \(-0.465658\pi\) | ||||
0.107678 | + | 0.994186i | \(0.465658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.874220 | −0.0325576 | ||||||||
\(722\) | 9.68976 | 0.360616 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.34620 | −0.235855 | ||||||||
\(725\) | −21.9924 | −0.816779 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.49085 | −0.0552924 | −0.0276462 | − | 0.999618i | \(-0.508801\pi\) | ||||
−0.0276462 | + | 0.999618i | \(0.508801\pi\) | |||||||
\(728\) | 5.29613 | 0.196288 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.8384 | −0.586207 | ||||||||
\(731\) | −23.9988 | −0.887627 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −39.7439 | −1.46797 | −0.733987 | − | 0.679164i | \(-0.762343\pi\) | ||||
−0.733987 | + | 0.679164i | \(0.762343\pi\) | |||||||
\(734\) | −9.21281 | −0.340051 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.515996 | 0.0190199 | ||||||||
\(737\) | 1.95228 | 0.0719133 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.2872 | −1.59235 | −0.796173 | − | 0.605069i | \(-0.793145\pi\) | ||||
−0.796173 | + | 0.605069i | \(0.793145\pi\) | |||||||
\(740\) | −8.44663 | −0.310504 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.18935 | −0.0803735 | ||||||||
\(743\) | −10.2674 | −0.376676 | −0.188338 | − | 0.982104i | \(-0.560310\pi\) | ||||
−0.188338 | + | 0.982104i | \(0.560310\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.09224 | 0.0400167 | ||||||||
\(746\) | 34.9485 | 1.27956 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.801906 | 0.0293206 | ||||||||
\(749\) | −10.2203 | −0.373442 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.1914 | −0.444870 | −0.222435 | − | 0.974948i | \(-0.571401\pi\) | ||||
−0.222435 | + | 0.974948i | \(0.571401\pi\) | |||||||
\(752\) | −2.23044 | −0.0813357 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −24.4265 | −0.889562 | ||||||||
\(755\) | −11.4055 | −0.415090 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.51744 | −0.127843 | −0.0639217 | − | 0.997955i | \(-0.520361\pi\) | ||||
−0.0639217 | + | 0.997955i | \(0.520361\pi\) | |||||||
\(758\) | −2.91395 | −0.105839 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.33273 | −0.120891 | ||||||||
\(761\) | −44.1493 | −1.60041 | −0.800206 | − | 0.599726i | \(-0.795276\pi\) | ||||
−0.800206 | + | 0.599726i | \(0.795276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.4005 | −0.629939 | ||||||||
\(764\) | −0.581014 | −0.0210203 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.4250 | 0.593461 | ||||||||
\(767\) | −35.3744 | −1.27730 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0500 | 0.542716 | 0.271358 | − | 0.962478i | \(-0.412527\pi\) | ||||
0.271358 | + | 0.962478i | \(0.412527\pi\) | |||||||
\(770\) | −0.237685 | −0.00856556 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.8034 | 0.748729 | ||||||||
\(773\) | −14.8464 | −0.533989 | −0.266995 | − | 0.963698i | \(-0.586031\pi\) | ||||
−0.266995 | + | 0.963698i | \(0.586031\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0515143 | −0.00185045 | ||||||||
\(776\) | 7.13298 | 0.256059 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.41838 | −0.194258 | ||||||||
\(779\) | −22.4147 | −0.803091 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.991259 | 0.0354700 | ||||||||
\(782\) | −2.38164 | −0.0851671 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.43118 | −0.193971 | ||||||||
\(785\) | −8.87220 | −0.316662 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −50.1456 | −1.78750 | −0.893749 | − | 0.448566i | \(-0.851935\pi\) | ||||
−0.893749 | + | 0.448566i | \(0.851935\pi\) | |||||||
\(788\) | −10.3409 | −0.368378 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.39219 | 0.0495318 | ||||||||
\(791\) | 5.89590 | 0.209634 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.1964 | 1.00128 | ||||||||
\(794\) | −23.7221 | −0.841864 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.52240 | −0.337513 | ||||||||
\(797\) | −41.8347 | −1.48186 | −0.740931 | − | 0.671582i | \(-0.765615\pi\) | ||||
−0.740931 | + | 0.671582i | \(0.765615\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2948 | 0.364205 | ||||||||
\(800\) | 3.80700 | 0.134598 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −13.7355 | −0.485018 | ||||||||
\(803\) | −2.51934 | −0.0889056 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.705916 | 0.0248803 | ||||||||
\(806\) | −0.0572158 | −0.00201534 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.5976 | 0.443181 | ||||||||
\(809\) | −12.5882 | −0.442578 | −0.221289 | − | 0.975208i | \(-0.571026\pi\) | ||||
−0.221289 | + | 0.975208i | \(0.571026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30.3817 | −1.06684 | −0.533422 | − | 0.845849i | \(-0.679094\pi\) | ||||
−0.533422 | + | 0.845849i | \(0.679094\pi\) | |||||||
\(812\) | −7.23565 | −0.253922 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.34356 | −0.0470918 | ||||||||
\(815\) | −0.100073 | −0.00350542 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.8650 | 0.555047 | ||||||||
\(818\) | 17.3492 | 0.606601 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.02367 | −0.280199 | ||||||||
\(821\) | 13.9419 | 0.486577 | 0.243289 | − | 0.969954i | \(-0.421774\pi\) | ||||
0.243289 | + | 0.969954i | \(0.421774\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.9495 | 0.660538 | 0.330269 | − | 0.943887i | \(-0.392860\pi\) | ||||
0.330269 | + | 0.943887i | \(0.392860\pi\) | |||||||
\(824\) | −0.697965 | −0.0243148 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.4787 | −0.364599 | ||||||||
\(827\) | 9.25287 | 0.321754 | 0.160877 | − | 0.986974i | \(-0.448568\pi\) | ||||
0.160877 | + | 0.986974i | \(0.448568\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −48.9325 | −1.69950 | −0.849748 | − | 0.527190i | \(-0.823246\pi\) | ||||
−0.849748 | + | 0.527190i | \(0.823246\pi\) | |||||||
\(830\) | −5.44608 | −0.189036 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.22835 | 0.146592 | ||||||||
\(833\) | 25.0682 | 0.868562 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.3584 | −0.496892 | ||||||||
\(836\) | −0.530121 | −0.0183346 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.488645 | 0.0168800 | ||||||||
\(839\) | −53.3647 | −1.84236 | −0.921178 | − | 0.389142i | \(-0.872771\pi\) | ||||
−0.921178 | + | 0.389142i | \(0.872771\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.37191 | 0.150756 | ||||||||
\(842\) | 30.8098 | 1.06178 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.92251 | −0.203861 | ||||||||
\(845\) | 5.32902 | 0.183324 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.7400 | 0.472112 | ||||||||
\(848\) | −1.74794 | −0.0600247 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −17.5716 | −0.602702 | ||||||||
\(851\) | 3.99034 | 0.136787 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.04264 | −0.309614 | −0.154807 | − | 0.987945i | \(-0.549476\pi\) | ||||
−0.154807 | + | 0.987945i | \(0.549476\pi\) | |||||||
\(854\) | 8.35238 | 0.285813 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.15974 | −0.278894 | ||||||||
\(857\) | 31.8134 | 1.08673 | 0.543363 | − | 0.839498i | \(-0.317151\pi\) | ||||
0.543363 | + | 0.839498i | \(0.317151\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.01136 | 0.170986 | 0.0854928 | − | 0.996339i | \(-0.472754\pi\) | ||||
0.0854928 | + | 0.996339i | \(0.472754\pi\) | |||||||
\(860\) | 5.67911 | 0.193656 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23.2831 | −0.793027 | ||||||||
\(863\) | 29.2328 | 0.995096 | 0.497548 | − | 0.867437i | \(-0.334234\pi\) | ||||
0.497548 | + | 0.867437i | \(0.334234\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.32939 | −0.249207 | ||||||||
\(866\) | 34.3793 | 1.16826 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.0169485 | −0.000575270 0 | ||||||||
\(869\) | 0.221448 | 0.00751212 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −47.5138 | −1.60994 | ||||||||
\(872\) | −13.8923 | −0.470452 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.57444 | 0.0532563 | ||||||||
\(875\) | 12.0486 | 0.407316 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.2618 | −0.515354 | −0.257677 | − | 0.966231i | \(-0.582957\pi\) | ||||
−0.257677 | + | 0.966231i | \(0.582957\pi\) | |||||||
\(878\) | 4.22947 | 0.142738 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.189764 | −0.00639695 | ||||||||
\(881\) | −58.0930 | −1.95720 | −0.978601 | − | 0.205766i | \(-0.934031\pi\) | ||||
−0.978601 | + | 0.205766i | \(0.934031\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.3203 | 1.22227 | 0.611137 | − | 0.791525i | \(-0.290712\pi\) | ||||
0.611137 | + | 0.791525i | \(0.290712\pi\) | |||||||
\(884\) | −19.5164 | −0.656409 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.0179 | −0.806898 | ||||||||
\(887\) | −9.97904 | −0.335063 | −0.167532 | − | 0.985867i | \(-0.553580\pi\) | ||||
−0.167532 | + | 0.985867i | \(0.553580\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.2022 | −0.342171 | ||||||||
\(890\) | 3.93318 | 0.131841 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21.7359 | 0.727771 | ||||||||
\(893\) | −6.80567 | −0.227743 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.3023 | −0.678631 | ||||||||
\(896\) | 1.25253 | 0.0418440 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.7355 | 0.458359 | ||||||||
\(899\) | 0.0781691 | 0.00260708 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.06783 | 0.268778 | ||||||||
\(902\) | −1.27628 | −0.0424956 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.70720 | 0.156559 | ||||||||
\(905\) | −6.93160 | −0.230414 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0426 | −0.466276 | −0.233138 | − | 0.972444i | \(-0.574899\pi\) | ||||
−0.233138 | + | 0.972444i | \(0.574899\pi\) | |||||||
\(908\) | 0.0539413 | 0.00179010 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.78467 | 0.191760 | ||||||||
\(911\) | 26.0282 | 0.862354 | 0.431177 | − | 0.902267i | \(-0.358098\pi\) | ||||
0.431177 | + | 0.902267i | \(0.358098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.866280 | −0.0286697 | ||||||||
\(914\) | 21.2382 | 0.702498 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.4074 | 0.509073 | ||||||||
\(917\) | 2.31554 | 0.0764660 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.3909 | 0.771593 | 0.385797 | − | 0.922584i | \(-0.373927\pi\) | ||||
0.385797 | + | 0.922584i | \(0.373927\pi\) | |||||||
\(920\) | 0.563594 | 0.0185811 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.1134 | 0.827067 | ||||||||
\(923\) | −24.1248 | −0.794078 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.4406 | 0.968001 | ||||||||
\(926\) | −36.1754 | −1.18880 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.77684 | −0.189634 | ||||||||
\(929\) | 55.6486 | 1.82577 | 0.912886 | − | 0.408215i | \(-0.133848\pi\) | ||||
0.912886 | + | 0.408215i | \(0.133848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −16.5720 | −0.543125 | ||||||||
\(932\) | 15.3630 | 0.503232 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 6.71738 | 0.219799 | ||||||||
\(935\) | 0.875878 | 0.0286443 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.22699 | −0.138090 | −0.0690449 | − | 0.997614i | \(-0.521995\pi\) | ||||
−0.0690449 | + | 0.997614i | \(0.521995\pi\) | |||||||
\(938\) | −14.0746 | −0.459552 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.43618 | −0.0794596 | ||||||||
\(941\) | 19.0791 | 0.621960 | 0.310980 | − | 0.950416i | \(-0.399343\pi\) | ||||
0.310980 | + | 0.950416i | \(0.399343\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.79052 | 0.123436 | ||||||||
\(944\) | −8.36601 | −0.272291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.903346 | 0.0293703 | ||||||||
\(947\) | 19.0693 | 0.619669 | 0.309835 | − | 0.950790i | \(-0.399726\pi\) | ||||
0.309835 | + | 0.950790i | \(0.399726\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 61.3146 | 1.99036 | ||||||||
\(950\) | 11.6162 | 0.376879 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.78118 | −0.187369 | ||||||||
\(953\) | 38.7971 | 1.25676 | 0.628380 | − | 0.777906i | \(-0.283718\pi\) | ||||
0.628380 | + | 0.777906i | \(0.283718\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.634609 | −0.0205355 | ||||||||
\(956\) | −25.0515 | −0.810225 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −34.5320 | −1.11568 | ||||||||
\(959\) | −15.6137 | −0.504193 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9998 | −0.999994 | ||||||||
\(962\) | 32.6990 | 1.05426 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.66193 | 0.0535270 | ||||||||
\(965\) | 22.7224 | 0.731459 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.0907 | −1.06413 | −0.532063 | − | 0.846705i | \(-0.678583\pi\) | ||||
−0.532063 | + | 0.846705i | \(0.678583\pi\) | |||||||
\(968\) | 10.9698 | 0.352583 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.79096 | 0.250153 | ||||||||
\(971\) | −36.7261 | −1.17860 | −0.589299 | − | 0.807915i | \(-0.700596\pi\) | ||||
−0.589299 | + | 0.807915i | \(0.700596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.9216 | −0.382188 | ||||||||
\(974\) | −14.7774 | −0.473498 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.66842 | 0.213451 | ||||||||
\(977\) | −8.47740 | −0.271216 | −0.135608 | − | 0.990763i | \(-0.543299\pi\) | ||||
−0.135608 | + | 0.990763i | \(0.543299\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.625631 | 0.0199953 | ||||||||
\(980\) | −5.93217 | −0.189496 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.0893 | −0.800633 | ||||||||
\(983\) | −12.1207 | −0.386590 | −0.193295 | − | 0.981141i | \(-0.561917\pi\) | ||||
−0.193295 | + | 0.981141i | \(0.561917\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2948 | −0.359881 | ||||||||
\(986\) | 26.6637 | 0.849144 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.9018 | 0.410462 | ||||||||
\(989\) | −2.68291 | −0.0853116 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.69712 | −0.244507 | −0.122254 | − | 0.992499i | \(-0.539012\pi\) | ||||
−0.122254 | + | 0.992499i | \(0.539012\pi\) | |||||||
\(992\) | −0.0135315 | −0.000429624 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.14628 | −0.226666 | ||||||||
\(995\) | −10.4008 | −0.329727 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.3270 | −0.738774 | −0.369387 | − | 0.929276i | \(-0.620432\pi\) | ||||
−0.369387 | + | 0.929276i | \(0.620432\pi\) | |||||||
\(998\) | −11.2941 | −0.357507 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8046.2.a.i.1.9 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.p.1.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.i.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.p.1.4 | yes | 12 | 3.2 | odd | 2 |