Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(1,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.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: | \(5.82109430735\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.7459857.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 3x^{5} - 6x^{4} + 13x^{3} + 12x^{2} - 12x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.578404\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45779 | 1.73792 | 0.868960 | − | 0.494883i | \(-0.164789\pi\) | ||||
0.868960 | + | 0.494883i | \(0.164789\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.04073 | 2.02036 | ||||||||
\(5\) | 3.08026 | 1.37754 | 0.688768 | − | 0.724982i | \(-0.258152\pi\) | ||||
0.688768 | + | 0.724982i | \(0.258152\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.65867 | −1.00488 | −0.502441 | − | 0.864612i | \(-0.667565\pi\) | ||||
−0.502441 | + | 0.864612i | \(0.667565\pi\) | |||||||
\(8\) | 5.01568 | 1.77331 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.57064 | 2.39405 | ||||||||
\(11\) | 3.43434 | 1.03549 | 0.517746 | − | 0.855534i | \(-0.326771\pi\) | ||||
0.517746 | + | 0.855534i | \(0.326771\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.34396 | −0.927447 | −0.463723 | − | 0.885980i | \(-0.653487\pi\) | ||||
−0.463723 | + | 0.885980i | \(0.653487\pi\) | |||||||
\(14\) | −6.53444 | −1.74640 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.24603 | 1.06151 | ||||||||
\(17\) | −2.57282 | −0.624000 | −0.312000 | − | 0.950082i | \(-0.600999\pi\) | ||||
−0.312000 | + | 0.950082i | \(0.600999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.09676 | −0.481030 | −0.240515 | − | 0.970645i | \(-0.577316\pi\) | ||||
−0.240515 | + | 0.970645i | \(0.577316\pi\) | |||||||
\(20\) | 12.4465 | 2.78312 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8.44089 | 1.79960 | ||||||||
\(23\) | −0.534444 | −0.111439 | −0.0557196 | − | 0.998446i | \(-0.517745\pi\) | ||||
−0.0557196 | + | 0.998446i | \(0.517745\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.48802 | 0.897604 | ||||||||
\(26\) | −8.21874 | −1.61183 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.7430 | −2.03023 | ||||||||
\(29\) | −2.53089 | −0.469975 | −0.234988 | − | 0.971998i | \(-0.575505\pi\) | ||||
−0.234988 | + | 0.971998i | \(0.575505\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.71470 | 1.38560 | 0.692801 | − | 0.721129i | \(-0.256377\pi\) | ||||
0.692801 | + | 0.721129i | \(0.256377\pi\) | |||||||
\(32\) | 0.404491 | 0.0715045 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.32344 | −1.08446 | ||||||||
\(35\) | −8.18939 | −1.38426 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2957 | −1.69260 | −0.846298 | − | 0.532709i | \(-0.821174\pi\) | ||||
−0.846298 | + | 0.532709i | \(0.821174\pi\) | |||||||
\(38\) | −5.15340 | −0.835992 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 15.4496 | 2.44280 | ||||||||
\(41\) | 4.88501 | 0.762910 | 0.381455 | − | 0.924387i | \(-0.375423\pi\) | ||||
0.381455 | + | 0.924387i | \(0.375423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.74149 | 0.418073 | 0.209037 | − | 0.977908i | \(-0.432967\pi\) | ||||
0.209037 | + | 0.977908i | \(0.432967\pi\) | |||||||
\(44\) | 13.8772 | 2.09207 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.31355 | −0.193673 | ||||||||
\(47\) | 5.65800 | 0.825304 | 0.412652 | − | 0.910889i | \(-0.364603\pi\) | ||||
0.412652 | + | 0.910889i | \(0.364603\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0685109 | 0.00978728 | ||||||||
\(50\) | 11.0306 | 1.55996 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.5120 | −1.87378 | ||||||||
\(53\) | −6.42657 | −0.882758 | −0.441379 | − | 0.897321i | \(-0.645511\pi\) | ||||
−0.441379 | + | 0.897321i | \(0.645511\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.5787 | 1.42643 | ||||||||
\(56\) | −13.3350 | −1.78197 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.22040 | −0.816779 | ||||||||
\(59\) | −1.65495 | −0.215456 | −0.107728 | − | 0.994180i | \(-0.534358\pi\) | ||||
−0.107728 | + | 0.994180i | \(0.534358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.3722 | 1.84017 | 0.920086 | − | 0.391716i | \(-0.128118\pi\) | ||||
0.920086 | + | 0.391716i | \(0.128118\pi\) | |||||||
\(62\) | 18.9611 | 2.40806 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.49791 | −0.937239 | ||||||||
\(65\) | −10.3003 | −1.27759 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.87898 | −0.718232 | −0.359116 | − | 0.933293i | \(-0.616922\pi\) | ||||
−0.359116 | + | 0.933293i | \(0.616922\pi\) | |||||||
\(68\) | −10.3961 | −1.26071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −20.1278 | −2.40573 | ||||||||
\(71\) | −14.8163 | −1.75837 | −0.879184 | − | 0.476483i | \(-0.841911\pi\) | ||||
−0.879184 | + | 0.476483i | \(0.841911\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.88140 | 0.220201 | 0.110101 | − | 0.993920i | \(-0.464883\pi\) | ||||
0.110101 | + | 0.993920i | \(0.464883\pi\) | |||||||
\(74\) | −25.3046 | −2.94160 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.47245 | −0.971857 | ||||||||
\(77\) | −9.13077 | −1.04055 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.1935 | 1.93442 | 0.967209 | − | 0.253981i | \(-0.0817400\pi\) | ||||
0.967209 | + | 0.253981i | \(0.0817400\pi\) | |||||||
\(80\) | 13.0789 | 1.46227 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.0063 | 1.32588 | ||||||||
\(83\) | −3.96878 | −0.435631 | −0.217815 | − | 0.975990i | \(-0.569893\pi\) | ||||
−0.217815 | + | 0.975990i | \(0.569893\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.92496 | −0.859582 | ||||||||
\(86\) | 6.73801 | 0.726578 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 17.2256 | 1.83625 | ||||||||
\(89\) | −5.09880 | −0.540471 | −0.270236 | − | 0.962794i | \(-0.587102\pi\) | ||||
−0.270236 | + | 0.962794i | \(0.587102\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.89047 | 0.931974 | ||||||||
\(92\) | −2.15954 | −0.225148 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.9062 | 1.43431 | ||||||||
\(95\) | −6.45858 | −0.662637 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6319 | −1.07950 | −0.539752 | − | 0.841824i | \(-0.681482\pi\) | ||||
−0.539752 | + | 0.841824i | \(0.681482\pi\) | |||||||
\(98\) | 0.168385 | 0.0170095 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 18.1349 | 1.81349 | ||||||||
\(101\) | −5.65809 | −0.563001 | −0.281500 | − | 0.959561i | \(-0.590832\pi\) | ||||
−0.281500 | + | 0.959561i | \(0.590832\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3705 | 1.02184 | 0.510920 | − | 0.859628i | \(-0.329305\pi\) | ||||
0.510920 | + | 0.859628i | \(0.329305\pi\) | |||||||
\(104\) | −16.7722 | −1.64465 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15.7952 | −1.53416 | ||||||||
\(107\) | 14.2457 | 1.37719 | 0.688594 | − | 0.725147i | \(-0.258228\pi\) | ||||
0.688594 | + | 0.725147i | \(0.258228\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.76064 | 0.551769 | 0.275884 | − | 0.961191i | \(-0.411029\pi\) | ||||
0.275884 | + | 0.961191i | \(0.411029\pi\) | |||||||
\(110\) | 26.0001 | 2.47902 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.2888 | −1.06669 | ||||||||
\(113\) | 11.4167 | 1.07399 | 0.536996 | − | 0.843585i | \(-0.319559\pi\) | ||||
0.536996 | + | 0.843585i | \(0.319559\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.64623 | −0.153512 | ||||||||
\(116\) | −10.2267 | −0.949521 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.06752 | −0.374445 | ||||||||
\(119\) | 6.84027 | 0.627046 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.794696 | 0.0722451 | ||||||||
\(122\) | 35.3239 | 3.19807 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 31.1730 | 2.79942 | ||||||||
\(125\) | −1.57703 | −0.141054 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.59019 | 0.229843 | 0.114921 | − | 0.993375i | \(-0.463338\pi\) | ||||
0.114921 | + | 0.993375i | \(0.463338\pi\) | |||||||
\(128\) | −19.2373 | −1.70035 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −25.3159 | −2.22035 | ||||||||
\(131\) | 4.41099 | 0.385390 | 0.192695 | − | 0.981259i | \(-0.438277\pi\) | ||||
0.192695 | + | 0.981259i | \(0.438277\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.57460 | 0.483379 | ||||||||
\(134\) | −14.4493 | −1.24823 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.9044 | −1.10655 | ||||||||
\(137\) | −18.1677 | −1.55217 | −0.776085 | − | 0.630628i | \(-0.782797\pi\) | ||||
−0.776085 | + | 0.630628i | \(0.782797\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.95794 | 0.166071 | 0.0830353 | − | 0.996547i | \(-0.473539\pi\) | ||||
0.0830353 | + | 0.996547i | \(0.473539\pi\) | |||||||
\(140\) | −33.0911 | −2.79671 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −36.4153 | −3.05590 | ||||||||
\(143\) | −11.4843 | −0.960364 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.79582 | −0.647407 | ||||||||
\(146\) | 4.62408 | 0.382692 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −41.6020 | −3.41966 | ||||||||
\(149\) | −7.31519 | −0.599284 | −0.299642 | − | 0.954052i | \(-0.596867\pi\) | ||||
−0.299642 | + | 0.954052i | \(0.596867\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.85099 | 0.394768 | 0.197384 | − | 0.980326i | \(-0.436755\pi\) | ||||
0.197384 | + | 0.980326i | \(0.436755\pi\) | |||||||
\(152\) | −10.5167 | −0.853017 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −22.4415 | −1.80839 | ||||||||
\(155\) | 23.7633 | 1.90871 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.47670 | 0.117854 | 0.0589269 | − | 0.998262i | \(-0.481232\pi\) | ||||
0.0589269 | + | 0.998262i | \(0.481232\pi\) | |||||||
\(158\) | 42.2580 | 3.36186 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.24594 | 0.0985000 | ||||||||
\(161\) | 1.42091 | 0.111983 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2536 | −1.35141 | −0.675703 | − | 0.737174i | \(-0.736160\pi\) | ||||
−0.675703 | + | 0.737174i | \(0.736160\pi\) | |||||||
\(164\) | 19.7390 | 1.54136 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.75444 | −0.757091 | ||||||||
\(167\) | −6.84036 | −0.529323 | −0.264662 | − | 0.964341i | \(-0.585260\pi\) | ||||
−0.264662 | + | 0.964341i | \(0.585260\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.81796 | −0.139843 | ||||||||
\(170\) | −19.4779 | −1.49388 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0776 | 0.844661 | ||||||||
\(173\) | 23.9674 | 1.82221 | 0.911103 | − | 0.412179i | \(-0.135232\pi\) | ||||
0.911103 | + | 0.412179i | \(0.135232\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.9322 | −0.901986 | ||||||||
\(176\) | 14.5823 | 1.09918 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.5318 | −0.939296 | ||||||||
\(179\) | 20.5722 | 1.53764 | 0.768820 | − | 0.639466i | \(-0.220844\pi\) | ||||
0.768820 | + | 0.639466i | \(0.220844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4701 | −1.14989 | −0.574943 | − | 0.818194i | \(-0.694976\pi\) | ||||
−0.574943 | + | 0.818194i | \(0.694976\pi\) | |||||||
\(182\) | 21.8509 | 1.61970 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.68060 | −0.197617 | ||||||||
\(185\) | −31.7133 | −2.33161 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.83593 | −0.646147 | ||||||||
\(188\) | 22.8624 | 1.66741 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.8738 | −1.15161 | ||||||||
\(191\) | 10.9508 | 0.792376 | 0.396188 | − | 0.918170i | \(-0.370333\pi\) | ||||
0.396188 | + | 0.918170i | \(0.370333\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.14485 | 0.0824082 | 0.0412041 | − | 0.999151i | \(-0.486881\pi\) | ||||
0.0412041 | + | 0.999151i | \(0.486881\pi\) | |||||||
\(194\) | −26.1309 | −1.87609 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.276834 | 0.0197739 | ||||||||
\(197\) | 5.04195 | 0.359224 | 0.179612 | − | 0.983738i | \(-0.442516\pi\) | ||||
0.179612 | + | 0.983738i | \(0.442516\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.7258 | 0.972997 | 0.486499 | − | 0.873681i | \(-0.338274\pi\) | ||||
0.486499 | + | 0.873681i | \(0.338274\pi\) | |||||||
\(200\) | 22.5105 | 1.59173 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −13.9064 | −0.978450 | ||||||||
\(203\) | 6.72880 | 0.472269 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.0471 | 1.05094 | ||||||||
\(206\) | 25.4886 | 1.77588 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.1985 | −0.984492 | ||||||||
\(209\) | −7.20100 | −0.498104 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.83513 | −0.401707 | −0.200854 | − | 0.979621i | \(-0.564372\pi\) | ||||
−0.200854 | + | 0.979621i | \(0.564372\pi\) | |||||||
\(212\) | −25.9680 | −1.78349 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 35.0130 | 2.39344 | ||||||||
\(215\) | 8.44451 | 0.575911 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.5108 | −1.39237 | ||||||||
\(218\) | 14.1584 | 0.958930 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 42.7455 | 2.88190 | ||||||||
\(221\) | 8.60339 | 0.578727 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.72868 | 0.584516 | 0.292258 | − | 0.956340i | \(-0.405593\pi\) | ||||
0.292258 | + | 0.956340i | \(0.405593\pi\) | |||||||
\(224\) | −1.07541 | −0.0718536 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 28.0598 | 1.86651 | ||||||||
\(227\) | −24.2825 | −1.61169 | −0.805844 | − | 0.592128i | \(-0.798288\pi\) | ||||
−0.805844 | + | 0.592128i | \(0.798288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.1514 | 1.19948 | 0.599740 | − | 0.800195i | \(-0.295271\pi\) | ||||
0.599740 | + | 0.800195i | \(0.295271\pi\) | |||||||
\(230\) | −4.04608 | −0.266791 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.6942 | −0.833412 | ||||||||
\(233\) | −10.5380 | −0.690367 | −0.345183 | − | 0.938535i | \(-0.612183\pi\) | ||||
−0.345183 | + | 0.938535i | \(0.612183\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.4281 | 1.13688 | ||||||||
\(236\) | −6.68720 | −0.435300 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.8119 | 1.08976 | ||||||||
\(239\) | 9.53660 | 0.616871 | 0.308436 | − | 0.951245i | \(-0.400195\pi\) | ||||
0.308436 | + | 0.951245i | \(0.400195\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.03728 | −0.453311 | −0.226656 | − | 0.973975i | \(-0.572779\pi\) | ||||
−0.226656 | + | 0.973975i | \(0.572779\pi\) | |||||||
\(242\) | 1.95320 | 0.125556 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 58.0742 | 3.71782 | ||||||||
\(245\) | 0.211032 | 0.0134823 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.01148 | 0.446130 | ||||||||
\(248\) | 38.6945 | 2.45710 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.87602 | −0.245141 | ||||||||
\(251\) | 15.5870 | 0.983843 | 0.491921 | − | 0.870640i | \(-0.336295\pi\) | ||||
0.491921 | + | 0.870640i | \(0.336295\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.83546 | −0.115395 | ||||||||
\(254\) | 6.36615 | 0.399448 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.2853 | −2.01783 | ||||||||
\(257\) | 12.1898 | 0.760377 | 0.380189 | − | 0.924909i | \(-0.375859\pi\) | ||||
0.380189 | + | 0.924909i | \(0.375859\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.3727 | 1.70086 | ||||||||
\(260\) | −41.6206 | −2.58120 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.8413 | 0.669776 | ||||||||
\(263\) | −6.88963 | −0.424833 | −0.212417 | − | 0.977179i | \(-0.568133\pi\) | ||||
−0.212417 | + | 0.977179i | \(0.568133\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.7955 | −1.21603 | ||||||||
\(266\) | 13.7012 | 0.840073 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −23.7554 | −1.45109 | ||||||||
\(269\) | 7.05875 | 0.430380 | 0.215190 | − | 0.976572i | \(-0.430963\pi\) | ||||
0.215190 | + | 0.976572i | \(0.430963\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.7575 | 1.44316 | 0.721581 | − | 0.692330i | \(-0.243416\pi\) | ||||
0.721581 | + | 0.692330i | \(0.243416\pi\) | |||||||
\(272\) | −10.9243 | −0.662381 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −44.6523 | −2.69755 | ||||||||
\(275\) | 15.4134 | 0.929462 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.104464 | −0.00627662 | −0.00313831 | − | 0.999995i | \(-0.500999\pi\) | ||||
−0.00313831 | + | 0.999995i | \(0.500999\pi\) | |||||||
\(278\) | 4.81221 | 0.288617 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −41.0754 | −2.45472 | ||||||||
\(281\) | 8.15220 | 0.486319 | 0.243160 | − | 0.969986i | \(-0.421816\pi\) | ||||
0.243160 | + | 0.969986i | \(0.421816\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.6160 | 1.40382 | 0.701912 | − | 0.712263i | \(-0.252330\pi\) | ||||
0.701912 | + | 0.712263i | \(0.252330\pi\) | |||||||
\(284\) | −59.8685 | −3.55254 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28.2260 | −1.66904 | ||||||||
\(287\) | −12.9876 | −0.766634 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.3806 | −0.610624 | ||||||||
\(290\) | −19.1605 | −1.12514 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.60222 | 0.444886 | ||||||||
\(293\) | 21.6258 | 1.26339 | 0.631695 | − | 0.775217i | \(-0.282360\pi\) | ||||
0.631695 | + | 0.775217i | \(0.282360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.09768 | −0.296798 | ||||||||
\(296\) | −51.6398 | −3.00150 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.9792 | −1.04151 | ||||||||
\(299\) | 1.78716 | 0.103354 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.28871 | −0.420114 | ||||||||
\(302\) | 11.9227 | 0.686074 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.90293 | −0.510618 | ||||||||
\(305\) | 44.2702 | 2.53490 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.3599 | 0.933711 | 0.466855 | − | 0.884334i | \(-0.345387\pi\) | ||||
0.466855 | + | 0.884334i | \(0.345387\pi\) | |||||||
\(308\) | −36.8950 | −2.10229 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 58.4052 | 3.31719 | ||||||||
\(311\) | 7.75486 | 0.439738 | 0.219869 | − | 0.975529i | \(-0.429437\pi\) | ||||
0.219869 | + | 0.975529i | \(0.429437\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.4181 | 0.871480 | 0.435740 | − | 0.900073i | \(-0.356487\pi\) | ||||
0.435740 | + | 0.900073i | \(0.356487\pi\) | |||||||
\(314\) | 3.62942 | 0.204820 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 69.4742 | 3.90823 | ||||||||
\(317\) | −8.63621 | −0.485058 | −0.242529 | − | 0.970144i | \(-0.577977\pi\) | ||||
−0.242529 | + | 0.970144i | \(0.577977\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.69195 | −0.486656 | ||||||||
\(320\) | −23.0955 | −1.29108 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.49229 | 0.194618 | ||||||||
\(323\) | 5.39459 | 0.300163 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0077 | −0.832480 | ||||||||
\(326\) | −42.4057 | −2.34864 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 24.5016 | 1.35288 | ||||||||
\(329\) | −15.0427 | −0.829332 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.5445 | 1.12923 | 0.564614 | − | 0.825355i | \(-0.309025\pi\) | ||||
0.564614 | + | 0.825355i | \(0.309025\pi\) | |||||||
\(332\) | −16.0368 | −0.880133 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −16.8122 | −0.919921 | ||||||||
\(335\) | −18.1088 | −0.989390 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9782 | 0.870388 | 0.435194 | − | 0.900337i | \(-0.356680\pi\) | ||||
0.435194 | + | 0.900337i | \(0.356680\pi\) | |||||||
\(338\) | −4.46816 | −0.243036 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −32.0226 | −1.73667 | ||||||||
\(341\) | 26.4949 | 1.43478 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4285 | 0.995047 | ||||||||
\(344\) | 13.7504 | 0.741374 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 58.9068 | 3.16685 | ||||||||
\(347\) | 9.80427 | 0.526321 | 0.263161 | − | 0.964752i | \(-0.415235\pi\) | ||||
0.263161 | + | 0.964752i | \(0.415235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.43497 | −0.505043 | −0.252521 | − | 0.967591i | \(-0.581260\pi\) | ||||
−0.252521 | + | 0.967591i | \(0.581260\pi\) | |||||||
\(350\) | −29.3267 | −1.56758 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.38916 | 0.0740424 | ||||||||
\(353\) | 3.38516 | 0.180174 | 0.0900870 | − | 0.995934i | \(-0.471285\pi\) | ||||
0.0900870 | + | 0.995934i | \(0.471285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −45.6380 | −2.42221 | ||||||||
\(356\) | −20.6029 | −1.09195 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 50.5622 | 2.67229 | ||||||||
\(359\) | −35.2273 | −1.85923 | −0.929614 | − | 0.368535i | \(-0.879859\pi\) | ||||
−0.929614 | + | 0.368535i | \(0.879859\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.6036 | −0.768610 | ||||||||
\(362\) | −38.0223 | −1.99841 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 35.9240 | 1.88293 | ||||||||
\(365\) | 5.79520 | 0.303335 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.5454 | −1.64666 | −0.823329 | − | 0.567564i | \(-0.807886\pi\) | ||||
−0.823329 | + | 0.567564i | \(0.807886\pi\) | |||||||
\(368\) | −2.26927 | −0.118294 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −77.9447 | −4.05215 | ||||||||
\(371\) | 17.0861 | 0.887067 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.4423 | 0.747795 | 0.373897 | − | 0.927470i | \(-0.378021\pi\) | ||||
0.373897 | + | 0.927470i | \(0.378021\pi\) | |||||||
\(374\) | −21.7169 | −1.12295 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 28.3787 | 1.46352 | ||||||||
\(377\) | 8.46320 | 0.435877 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00099 | 0.0514176 | 0.0257088 | − | 0.999669i | \(-0.491816\pi\) | ||||
0.0257088 | + | 0.999669i | \(0.491816\pi\) | |||||||
\(380\) | −26.0974 | −1.33877 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 26.9149 | 1.37709 | ||||||||
\(383\) | −4.11734 | −0.210386 | −0.105193 | − | 0.994452i | \(-0.533546\pi\) | ||||
−0.105193 | + | 0.994452i | \(0.533546\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −28.1252 | −1.43339 | ||||||||
\(386\) | 2.81380 | 0.143219 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −42.9605 | −2.18099 | ||||||||
\(389\) | 15.5199 | 0.786891 | 0.393445 | − | 0.919348i | \(-0.371283\pi\) | ||||
0.393445 | + | 0.919348i | \(0.371283\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.37503 | 0.0695381 | ||||||||
\(392\) | 0.343629 | 0.0173559 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.3920 | 0.624302 | ||||||||
\(395\) | 52.9605 | 2.66473 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.54893 | −0.0777384 | −0.0388692 | − | 0.999244i | \(-0.512376\pi\) | ||||
−0.0388692 | + | 0.999244i | \(0.512376\pi\) | |||||||
\(398\) | 33.7352 | 1.69099 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.0563 | 0.952814 | ||||||||
\(401\) | −7.94738 | −0.396873 | −0.198437 | − | 0.980114i | \(-0.563586\pi\) | ||||
−0.198437 | + | 0.980114i | \(0.563586\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −25.7976 | −1.28507 | ||||||||
\(404\) | −22.8628 | −1.13747 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.5380 | 0.820766 | ||||||||
\(407\) | −35.3588 | −1.75267 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.4554 | 1.30814 | 0.654068 | − | 0.756436i | \(-0.273061\pi\) | ||||
0.654068 | + | 0.756436i | \(0.273061\pi\) | |||||||
\(410\) | 36.9826 | 1.82644 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 41.9045 | 2.06449 | ||||||||
\(413\) | 4.39996 | 0.216508 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.2249 | −0.600097 | ||||||||
\(416\) | −1.35260 | −0.0663166 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.6985 | −0.865664 | ||||||||
\(419\) | −38.3400 | −1.87303 | −0.936516 | − | 0.350626i | \(-0.885969\pi\) | ||||
−0.936516 | + | 0.350626i | \(0.885969\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.34450 | 0.357949 | 0.178974 | − | 0.983854i | \(-0.442722\pi\) | ||||
0.178974 | + | 0.983854i | \(0.442722\pi\) | |||||||
\(422\) | −14.3415 | −0.698134 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −32.2337 | −1.56540 | ||||||||
\(425\) | −11.5469 | −0.560105 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −38.2109 | −1.84916 | ||||||||
\(428\) | 57.5632 | 2.78242 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20.7548 | 1.00089 | ||||||||
\(431\) | 15.8463 | 0.763289 | 0.381644 | − | 0.924309i | \(-0.375358\pi\) | ||||
0.381644 | + | 0.924309i | \(0.375358\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.8507 | −1.14619 | −0.573097 | − | 0.819488i | \(-0.694258\pi\) | ||||
−0.573097 | + | 0.819488i | \(0.694258\pi\) | |||||||
\(434\) | −50.4113 | −2.41982 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 23.2772 | 1.11477 | ||||||||
\(437\) | 1.12060 | 0.0536057 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.4699 | −1.02470 | −0.512352 | − | 0.858776i | \(-0.671226\pi\) | ||||
−0.512352 | + | 0.858776i | \(0.671226\pi\) | |||||||
\(440\) | 53.0593 | 2.52950 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 21.1453 | 1.00578 | ||||||||
\(443\) | −31.5479 | −1.49889 | −0.749443 | − | 0.662068i | \(-0.769679\pi\) | ||||
−0.749443 | + | 0.662068i | \(0.769679\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.7056 | −0.744518 | ||||||||
\(446\) | 21.4533 | 1.01584 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 19.9345 | 0.941815 | ||||||||
\(449\) | −20.7898 | −0.981130 | −0.490565 | − | 0.871405i | \(-0.663210\pi\) | ||||
−0.490565 | + | 0.871405i | \(0.663210\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.7768 | 0.789988 | ||||||||
\(452\) | 46.1318 | 2.16986 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −59.6813 | −2.80098 | ||||||||
\(455\) | 27.3850 | 1.28383 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.4277 | −0.815235 | −0.407618 | − | 0.913153i | \(-0.633640\pi\) | ||||
−0.407618 | + | 0.913153i | \(0.633640\pi\) | |||||||
\(458\) | 44.6124 | 2.08460 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.65196 | −0.310149 | ||||||||
\(461\) | 31.0045 | 1.44402 | 0.722011 | − | 0.691882i | \(-0.243218\pi\) | ||||
0.722011 | + | 0.691882i | \(0.243218\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.48795 | 0.301521 | 0.150760 | − | 0.988570i | \(-0.451828\pi\) | ||||
0.150760 | + | 0.988570i | \(0.451828\pi\) | |||||||
\(464\) | −10.7463 | −0.498883 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.9002 | −1.19980 | ||||||||
\(467\) | −1.94390 | −0.0899530 | −0.0449765 | − | 0.998988i | \(-0.514321\pi\) | ||||
−0.0449765 | + | 0.998988i | \(0.514321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.6303 | 0.721738 | ||||||||
\(470\) | 42.8346 | 1.97581 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.30070 | −0.382071 | ||||||||
\(473\) | 9.41521 | 0.432912 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.41031 | −0.431775 | ||||||||
\(476\) | 27.6397 | 1.26686 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 23.4390 | 1.07207 | ||||||||
\(479\) | −1.32939 | −0.0607414 | −0.0303707 | − | 0.999539i | \(-0.509669\pi\) | ||||
−0.0303707 | + | 0.999539i | \(0.509669\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.4282 | 1.56979 | ||||||||
\(482\) | −17.2962 | −0.787818 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.21115 | 0.145961 | ||||||||
\(485\) | −32.7490 | −1.48705 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.2040 | 0.960844 | 0.480422 | − | 0.877037i | \(-0.340484\pi\) | ||||
0.480422 | + | 0.877037i | \(0.340484\pi\) | |||||||
\(488\) | 72.0864 | 3.26320 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.518671 | 0.0234312 | ||||||||
\(491\) | −27.0101 | −1.21895 | −0.609475 | − | 0.792805i | \(-0.708620\pi\) | ||||
−0.609475 | + | 0.792805i | \(0.708620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.51153 | 0.293265 | ||||||||
\(494\) | 17.2328 | 0.775338 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.7569 | 1.47083 | ||||||||
\(497\) | 39.3915 | 1.76695 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.0389 | 0.673234 | 0.336617 | − | 0.941642i | \(-0.390717\pi\) | ||||
0.336617 | + | 0.941642i | \(0.390717\pi\) | |||||||
\(500\) | −6.37237 | −0.284981 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 38.3096 | 1.70984 | ||||||||
\(503\) | −4.60650 | −0.205394 | −0.102697 | − | 0.994713i | \(-0.532747\pi\) | ||||
−0.102697 | + | 0.994713i | \(0.532747\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.4284 | −0.775554 | ||||||||
\(506\) | −4.51118 | −0.200546 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.4663 | 0.464366 | ||||||||
\(509\) | −29.7967 | −1.32071 | −0.660357 | − | 0.750952i | \(-0.729595\pi\) | ||||
−0.660357 | + | 0.750952i | \(0.729595\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.00201 | −0.221276 | ||||||||
\(512\) | −40.8760 | −1.80648 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29.9599 | 1.32147 | ||||||||
\(515\) | 31.9440 | 1.40762 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19.4315 | 0.854596 | ||||||||
\(518\) | 67.2764 | 2.95596 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −51.6629 | −2.26557 | ||||||||
\(521\) | 11.7621 | 0.515306 | 0.257653 | − | 0.966237i | \(-0.417051\pi\) | ||||
0.257653 | + | 0.966237i | \(0.417051\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.3853 | 1.28493 | 0.642464 | − | 0.766316i | \(-0.277912\pi\) | ||||
0.642464 | + | 0.766316i | \(0.277912\pi\) | |||||||
\(524\) | 17.8236 | 0.778627 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.9333 | −0.738326 | ||||||||
\(527\) | −19.8485 | −0.864615 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7144 | −0.987581 | ||||||||
\(530\) | −48.6533 | −2.11336 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 22.5254 | 0.976601 | ||||||||
\(533\) | −16.3352 | −0.707558 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.8806 | 1.89712 | ||||||||
\(536\) | −29.4871 | −1.27365 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.3489 | 0.747965 | ||||||||
\(539\) | 0.235290 | 0.0101347 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9116 | −0.985046 | −0.492523 | − | 0.870300i | \(-0.663925\pi\) | ||||
−0.492523 | + | 0.870300i | \(0.663925\pi\) | |||||||
\(542\) | 58.3908 | 2.50810 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.04068 | −0.0446188 | ||||||||
\(545\) | 17.7443 | 0.760081 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.7577 | −0.588237 | −0.294118 | − | 0.955769i | \(-0.595026\pi\) | ||||
−0.294118 | + | 0.955769i | \(0.595026\pi\) | |||||||
\(548\) | −73.4107 | −3.13595 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 37.8829 | 1.61533 | ||||||||
\(551\) | 5.30668 | 0.226072 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.7118 | −1.94386 | ||||||||
\(554\) | −0.256750 | −0.0109083 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.91152 | 0.335523 | ||||||||
\(557\) | −21.9041 | −0.928105 | −0.464053 | − | 0.885808i | \(-0.653605\pi\) | ||||
−0.464053 | + | 0.885808i | \(0.653605\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.16742 | −0.387741 | ||||||||
\(560\) | −34.7724 | −1.46940 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.0364 | 0.845184 | ||||||||
\(563\) | −14.5684 | −0.613986 | −0.306993 | − | 0.951712i | \(-0.599323\pi\) | ||||
−0.306993 | + | 0.951712i | \(0.599323\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.1664 | 1.47946 | ||||||||
\(566\) | 58.0431 | 2.43973 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −74.3137 | −3.11813 | ||||||||
\(569\) | 22.3570 | 0.937255 | 0.468628 | − | 0.883396i | \(-0.344749\pi\) | ||||
0.468628 | + | 0.883396i | \(0.344749\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.4261 | −0.645564 | −0.322782 | − | 0.946473i | \(-0.604618\pi\) | ||||
−0.322782 | + | 0.946473i | \(0.604618\pi\) | |||||||
\(572\) | −46.4049 | −1.94029 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −31.9208 | −1.33235 | ||||||||
\(575\) | −2.39860 | −0.100028 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.8081 | 1.36582 | 0.682909 | − | 0.730503i | \(-0.260714\pi\) | ||||
0.682909 | + | 0.730503i | \(0.260714\pi\) | |||||||
\(578\) | −25.5133 | −1.06122 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −31.5008 | −1.30800 | ||||||||
\(581\) | 10.5517 | 0.437757 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.0710 | −0.914089 | ||||||||
\(584\) | 9.43650 | 0.390485 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 53.1515 | 2.19567 | ||||||||
\(587\) | −30.2343 | −1.24790 | −0.623951 | − | 0.781464i | \(-0.714473\pi\) | ||||
−0.623951 | + | 0.781464i | \(0.714473\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.1759 | −0.666516 | ||||||||
\(590\) | −12.5290 | −0.515812 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −43.7157 | −1.79671 | ||||||||
\(593\) | −41.1023 | −1.68787 | −0.843935 | − | 0.536446i | \(-0.819766\pi\) | ||||
−0.843935 | + | 0.536446i | \(0.819766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.0698 | 0.863778 | ||||||||
\(596\) | −29.5587 | −1.21077 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.39246 | 0.179621 | ||||||||
\(599\) | −36.5505 | −1.49341 | −0.746707 | − | 0.665153i | \(-0.768366\pi\) | ||||
−0.746707 | + | 0.665153i | \(0.768366\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.94580 | 0.160953 | 0.0804764 | − | 0.996757i | \(-0.474356\pi\) | ||||
0.0804764 | + | 0.996757i | \(0.474356\pi\) | |||||||
\(602\) | −17.9141 | −0.730125 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.6015 | 0.797575 | ||||||||
\(605\) | 2.44787 | 0.0995202 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.0115 | 0.406355 | 0.203178 | − | 0.979142i | \(-0.434873\pi\) | ||||
0.203178 | + | 0.979142i | \(0.434873\pi\) | |||||||
\(608\) | −0.848121 | −0.0343958 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 108.807 | 4.40546 | ||||||||
\(611\) | −18.9201 | −0.765425 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.7568 | −0.757578 | −0.378789 | − | 0.925483i | \(-0.623659\pi\) | ||||
−0.378789 | + | 0.925483i | \(0.623659\pi\) | |||||||
\(614\) | 40.2093 | 1.62271 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −45.7970 | −1.84522 | ||||||||
\(617\) | 23.0101 | 0.926350 | 0.463175 | − | 0.886267i | \(-0.346710\pi\) | ||||
0.463175 | + | 0.886267i | \(0.346710\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.41402 | 0.297995 | 0.148997 | − | 0.988838i | \(-0.452395\pi\) | ||||
0.148997 | + | 0.988838i | \(0.452395\pi\) | |||||||
\(620\) | 96.0211 | 3.85630 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.0598 | 0.764229 | ||||||||
\(623\) | 13.5560 | 0.543110 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.2978 | −1.09191 | ||||||||
\(626\) | 37.8943 | 1.51456 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.96696 | 0.238107 | ||||||||
\(629\) | 26.4889 | 1.05618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.9924 | −1.23379 | −0.616894 | − | 0.787046i | \(-0.711609\pi\) | ||||
−0.616894 | + | 0.787046i | \(0.711609\pi\) | |||||||
\(632\) | 86.2371 | 3.43033 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −21.2260 | −0.842991 | ||||||||
\(635\) | 7.97848 | 0.316616 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.229098 | −0.00907717 | ||||||||
\(638\) | −21.3630 | −0.845769 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −59.2559 | −2.34229 | ||||||||
\(641\) | 35.3461 | 1.39609 | 0.698044 | − | 0.716055i | \(-0.254054\pi\) | ||||
0.698044 | + | 0.716055i | \(0.254054\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.7009 | −0.776929 | −0.388465 | − | 0.921464i | \(-0.626994\pi\) | ||||
−0.388465 | + | 0.921464i | \(0.626994\pi\) | |||||||
\(644\) | 5.74151 | 0.226247 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.2588 | 0.521659 | ||||||||
\(647\) | −46.8317 | −1.84114 | −0.920572 | − | 0.390572i | \(-0.872277\pi\) | ||||
−0.920572 | + | 0.390572i | \(0.872277\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.68366 | −0.223103 | ||||||||
\(650\) | −36.8859 | −1.44678 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −69.7171 | −2.73033 | ||||||||
\(653\) | −17.3267 | −0.678047 | −0.339023 | − | 0.940778i | \(-0.610097\pi\) | ||||
−0.339023 | + | 0.940778i | \(0.610097\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.5870 | 0.530888 | ||||||||
\(656\) | 20.7419 | 0.809835 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −36.9719 | −1.44131 | ||||||||
\(659\) | −43.7342 | −1.70364 | −0.851821 | − | 0.523833i | \(-0.824502\pi\) | ||||
−0.851821 | + | 0.523833i | \(0.824502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.08686 | −0.353438 | −0.176719 | − | 0.984261i | \(-0.556548\pi\) | ||||
−0.176719 | + | 0.984261i | \(0.556548\pi\) | |||||||
\(662\) | 50.4941 | 1.96251 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −19.9062 | −0.772509 | ||||||||
\(665\) | 17.1712 | 0.665871 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.35262 | 0.0523737 | ||||||||
\(668\) | −27.6401 | −1.06943 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −44.5076 | −1.71948 | ||||||||
\(671\) | 49.3591 | 1.90549 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.49668 | 0.288976 | 0.144488 | − | 0.989507i | \(-0.453846\pi\) | ||||
0.144488 | + | 0.989507i | \(0.453846\pi\) | |||||||
\(674\) | 39.2711 | 1.51266 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.34587 | −0.282534 | ||||||||
\(677\) | −15.3626 | −0.590431 | −0.295215 | − | 0.955431i | \(-0.595391\pi\) | ||||
−0.295215 | + | 0.955431i | \(0.595391\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.2666 | 1.08477 | ||||||||
\(680\) | −39.7491 | −1.52431 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 65.1189 | 2.49353 | ||||||||
\(683\) | −6.62157 | −0.253367 | −0.126684 | − | 0.991943i | \(-0.540433\pi\) | ||||
−0.126684 | + | 0.991943i | \(0.540433\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −55.9612 | −2.13817 | ||||||||
\(686\) | 45.2934 | 1.72931 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.6405 | 0.443788 | ||||||||
\(689\) | 21.4902 | 0.818711 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.6569 | −0.709740 | −0.354870 | − | 0.934916i | \(-0.615475\pi\) | ||||
−0.354870 | + | 0.934916i | \(0.615475\pi\) | |||||||
\(692\) | 96.8457 | 3.68152 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 24.0968 | 0.914704 | ||||||||
\(695\) | 6.03098 | 0.228768 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.5682 | −0.476056 | ||||||||
\(698\) | −23.1892 | −0.877723 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −48.2146 | −1.82234 | ||||||||
\(701\) | −24.8903 | −0.940092 | −0.470046 | − | 0.882642i | \(-0.655763\pi\) | ||||
−0.470046 | + | 0.882642i | \(0.655763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.5876 | 0.814190 | ||||||||
\(704\) | −25.7504 | −0.970504 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.32002 | 0.313128 | ||||||||
\(707\) | 15.0430 | 0.565749 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.1787 | −0.983163 | −0.491582 | − | 0.870831i | \(-0.663581\pi\) | ||||
−0.491582 | + | 0.870831i | \(0.663581\pi\) | |||||||
\(710\) | −112.169 | −4.20961 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25.5739 | −0.958424 | ||||||||
\(713\) | −4.12308 | −0.154410 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −35.3746 | −1.32294 | ||||||||
\(716\) | 83.1267 | 3.10659 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −86.5814 | −3.23119 | ||||||||
\(719\) | −21.0290 | −0.784251 | −0.392125 | − | 0.919912i | \(-0.628260\pi\) | ||||
−0.392125 | + | 0.919912i | \(0.628260\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.5718 | −1.02683 | ||||||||
\(722\) | −35.8925 | −1.33578 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −62.5106 | −2.32319 | ||||||||
\(725\) | −11.3587 | −0.421852 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.3957 | 1.53528 | 0.767640 | − | 0.640881i | \(-0.221431\pi\) | ||||
0.767640 | + | 0.640881i | \(0.221431\pi\) | |||||||
\(728\) | 44.5918 | 1.65268 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.2434 | 0.527171 | ||||||||
\(731\) | −7.05336 | −0.260878 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.6267 | 1.24203 | 0.621016 | − | 0.783798i | \(-0.286720\pi\) | ||||
0.621016 | + | 0.783798i | \(0.286720\pi\) | |||||||
\(734\) | −77.5320 | −2.86176 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.216178 | −0.00796841 | ||||||||
\(737\) | −20.1904 | −0.743724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.9454 | −0.476202 | −0.238101 | − | 0.971240i | \(-0.576525\pi\) | ||||
−0.238101 | + | 0.971240i | \(0.576525\pi\) | |||||||
\(740\) | −128.145 | −4.71071 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 41.9941 | 1.54165 | ||||||||
\(743\) | 0.0879292 | 0.00322581 | 0.00161290 | − | 0.999999i | \(-0.499487\pi\) | ||||
0.00161290 | + | 0.999999i | \(0.499487\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.5327 | −0.825534 | ||||||||
\(746\) | 35.4962 | 1.29961 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −35.7036 | −1.30545 | ||||||||
\(749\) | −37.8747 | −1.38391 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.8960 | 1.82073 | 0.910366 | − | 0.413804i | \(-0.135800\pi\) | ||||
0.910366 | + | 0.413804i | \(0.135800\pi\) | |||||||
\(752\) | 24.0240 | 0.876067 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 20.8008 | 0.757519 | ||||||||
\(755\) | 14.9423 | 0.543806 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.8679 | −0.431348 | −0.215674 | − | 0.976465i | \(-0.569195\pi\) | ||||
−0.215674 | + | 0.976465i | \(0.569195\pi\) | |||||||
\(758\) | 2.46023 | 0.0893596 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −32.3942 | −1.17506 | ||||||||
\(761\) | −3.79030 | −0.137398 | −0.0686992 | − | 0.997637i | \(-0.521885\pi\) | ||||
−0.0686992 | + | 0.997637i | \(0.521885\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3156 | −0.554462 | ||||||||
\(764\) | 44.2494 | 1.60089 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.1196 | −0.365634 | ||||||||
\(767\) | 5.53408 | 0.199824 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.26950 | 0.226084 | 0.113042 | − | 0.993590i | \(-0.463941\pi\) | ||||
0.113042 | + | 0.993590i | \(0.463941\pi\) | |||||||
\(770\) | −69.1257 | −2.49112 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.62603 | 0.166495 | ||||||||
\(773\) | 1.29536 | 0.0465907 | 0.0232954 | − | 0.999729i | \(-0.492584\pi\) | ||||
0.0232954 | + | 0.999729i | \(0.492584\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.6237 | 1.24372 | ||||||||
\(776\) | −53.3261 | −1.91430 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.1447 | 1.36755 | ||||||||
\(779\) | −10.2427 | −0.366983 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −50.8841 | −1.82078 | ||||||||
\(782\) | 3.37953 | 0.120852 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.290900 | 0.0103893 | ||||||||
\(785\) | 4.54863 | 0.162348 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.3922 | −0.441735 | −0.220867 | − | 0.975304i | \(-0.570889\pi\) | ||||
−0.220867 | + | 0.975304i | \(0.570889\pi\) | |||||||
\(788\) | 20.3731 | 0.725763 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 130.166 | 4.63109 | ||||||||
\(791\) | −30.3532 | −1.07924 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.0600 | −1.70666 | ||||||||
\(794\) | −3.80693 | −0.135103 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 55.4623 | 1.96581 | ||||||||
\(797\) | −24.3827 | −0.863680 | −0.431840 | − | 0.901950i | \(-0.642135\pi\) | ||||
−0.431840 | + | 0.901950i | \(0.642135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.5570 | −0.514989 | ||||||||
\(800\) | 1.81536 | 0.0641827 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.5330 | −0.689734 | ||||||||
\(803\) | 6.46136 | 0.228017 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.37677 | 0.154261 | ||||||||
\(806\) | −63.4051 | −2.23335 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.3792 | −0.998376 | ||||||||
\(809\) | −24.1156 | −0.847861 | −0.423930 | − | 0.905695i | \(-0.639350\pi\) | ||||
−0.423930 | + | 0.905695i | \(0.639350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.1121 | 1.68944 | 0.844721 | − | 0.535206i | \(-0.179766\pi\) | ||||
0.844721 | + | 0.535206i | \(0.179766\pi\) | |||||||
\(812\) | 27.1893 | 0.954156 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −86.9045 | −3.04600 | ||||||||
\(815\) | −53.1456 | −1.86161 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.74826 | −0.201106 | ||||||||
\(818\) | 65.0218 | 2.27343 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 60.8013 | 2.12327 | ||||||||
\(821\) | 16.9388 | 0.591169 | 0.295585 | − | 0.955317i | \(-0.404486\pi\) | ||||
0.295585 | + | 0.955317i | \(0.404486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5559 | 0.402815 | 0.201407 | − | 0.979508i | \(-0.435449\pi\) | ||||
0.201407 | + | 0.979508i | \(0.435449\pi\) | |||||||
\(824\) | 52.0153 | 1.81204 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.8142 | 0.376273 | ||||||||
\(827\) | 10.2374 | 0.355988 | 0.177994 | − | 0.984032i | \(-0.443039\pi\) | ||||
0.177994 | + | 0.984032i | \(0.443039\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.35244 | 0.324824 | 0.162412 | − | 0.986723i | \(-0.448073\pi\) | ||||
0.162412 | + | 0.986723i | \(0.448073\pi\) | |||||||
\(830\) | −30.0462 | −1.04292 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 25.0727 | 0.869239 | ||||||||
\(833\) | −0.176266 | −0.00610726 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.0701 | −0.729161 | ||||||||
\(836\) | −29.0973 | −1.00635 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −94.2316 | −3.25518 | ||||||||
\(839\) | −11.8451 | −0.408939 | −0.204469 | − | 0.978873i | \(-0.565547\pi\) | ||||
−0.204469 | + | 0.978873i | \(0.565547\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.5946 | −0.779123 | ||||||||
\(842\) | 18.0512 | 0.622086 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23.5782 | −0.811595 | ||||||||
\(845\) | −5.59979 | −0.192639 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.11283 | −0.0725978 | ||||||||
\(848\) | −27.2874 | −0.937055 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −28.3797 | −0.973417 | ||||||||
\(851\) | 5.50246 | 0.188622 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −37.2713 | −1.27614 | −0.638072 | − | 0.769976i | \(-0.720268\pi\) | ||||
−0.638072 | + | 0.769976i | \(0.720268\pi\) | |||||||
\(854\) | −93.9144 | −3.21368 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 71.4521 | 2.44218 | ||||||||
\(857\) | −41.4318 | −1.41528 | −0.707642 | − | 0.706571i | \(-0.750241\pi\) | ||||
−0.707642 | + | 0.706571i | \(0.750241\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.25851 | −0.315896 | −0.157948 | − | 0.987447i | \(-0.550488\pi\) | ||||
−0.157948 | + | 0.987447i | \(0.550488\pi\) | |||||||
\(860\) | 34.1220 | 1.16355 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 38.9468 | 1.32653 | ||||||||
\(863\) | 51.4748 | 1.75222 | 0.876110 | − | 0.482110i | \(-0.160130\pi\) | ||||
0.876110 | + | 0.482110i | \(0.160130\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 73.8258 | 2.51015 | ||||||||
\(866\) | −58.6201 | −1.99199 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −82.8787 | −2.81309 | ||||||||
\(869\) | 59.0483 | 2.00308 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.6591 | 0.666122 | ||||||||
\(872\) | 28.8935 | 0.978458 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.75421 | 0.0931624 | ||||||||
\(875\) | 4.19281 | 0.141743 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.8990 | −0.840781 | −0.420390 | − | 0.907343i | \(-0.638107\pi\) | ||||
−0.420390 | + | 0.907343i | \(0.638107\pi\) | |||||||
\(878\) | −52.7686 | −1.78085 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 44.9174 | 1.51416 | ||||||||
\(881\) | −1.43361 | −0.0482997 | −0.0241498 | − | 0.999708i | \(-0.507688\pi\) | ||||
−0.0241498 | + | 0.999708i | \(0.507688\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.2046 | 0.881855 | 0.440928 | − | 0.897543i | \(-0.354650\pi\) | ||||
0.440928 | + | 0.897543i | \(0.354650\pi\) | |||||||
\(884\) | 34.7640 | 1.16924 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −77.5381 | −2.60494 | ||||||||
\(887\) | 43.3726 | 1.45631 | 0.728154 | − | 0.685414i | \(-0.240379\pi\) | ||||
0.728154 | + | 0.685414i | \(0.240379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.88646 | −0.230965 | ||||||||
\(890\) | −38.6011 | −1.29391 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 35.2702 | 1.18093 | ||||||||
\(893\) | −11.8635 | −0.396996 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 63.3678 | 2.11815 | ||||||||
\(896\) | 51.1455 | 1.70865 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −51.0969 | −1.70513 | ||||||||
\(899\) | −19.5251 | −0.651198 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.5344 | 0.550841 | ||||||||
\(902\) | 41.2338 | 1.37293 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 57.2625 | 1.90452 | ||||||||
\(905\) | −47.6521 | −1.58401 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 23.8718 | 0.792649 | 0.396325 | − | 0.918110i | \(-0.370286\pi\) | ||||
0.396325 | + | 0.918110i | \(0.370286\pi\) | |||||||
\(908\) | −98.1191 | −3.25620 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 67.3065 | 2.23119 | ||||||||
\(911\) | 4.32052 | 0.143145 | 0.0715726 | − | 0.997435i | \(-0.477198\pi\) | ||||
0.0715726 | + | 0.997435i | \(0.477198\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.6302 | −0.451092 | ||||||||
\(914\) | −42.8337 | −1.41681 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 73.3450 | 2.42339 | ||||||||
\(917\) | −11.7273 | −0.387271 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.56151 | 0.117483 | 0.0587417 | − | 0.998273i | \(-0.481291\pi\) | ||||
0.0587417 | + | 0.998273i | \(0.481291\pi\) | |||||||
\(920\) | −8.25696 | −0.272224 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 76.2025 | 2.50959 | ||||||||
\(923\) | 49.5449 | 1.63079 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −46.2071 | −1.51928 | ||||||||
\(926\) | 15.9460 | 0.524019 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.02372 | −0.0336053 | ||||||||
\(929\) | −33.3258 | −1.09338 | −0.546692 | − | 0.837334i | \(-0.684113\pi\) | ||||
−0.546692 | + | 0.837334i | \(0.684113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.143651 | −0.00470798 | ||||||||
\(932\) | −42.5812 | −1.39479 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.77770 | −0.156331 | ||||||||
\(935\) | −27.2170 | −0.890091 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0594 | 0.851322 | 0.425661 | − | 0.904883i | \(-0.360042\pi\) | ||||
0.425661 | + | 0.904883i | \(0.360042\pi\) | |||||||
\(938\) | 38.4159 | 1.25432 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 70.4223 | 2.29692 | ||||||||
\(941\) | −23.9936 | −0.782167 | −0.391084 | − | 0.920355i | \(-0.627900\pi\) | ||||
−0.391084 | + | 0.920355i | \(0.627900\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.61076 | −0.0850181 | ||||||||
\(944\) | −7.02697 | −0.228708 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.1406 | 0.752366 | ||||||||
\(947\) | 29.8847 | 0.971121 | 0.485561 | − | 0.874203i | \(-0.338615\pi\) | ||||
0.485561 | + | 0.874203i | \(0.338615\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.29131 | −0.204225 | ||||||||
\(950\) | −23.1286 | −0.750390 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 34.3086 | 1.11195 | ||||||||
\(953\) | −10.1934 | −0.330196 | −0.165098 | − | 0.986277i | \(-0.552794\pi\) | ||||
−0.165098 | + | 0.986277i | \(0.552794\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.7315 | 1.09153 | ||||||||
\(956\) | 38.5348 | 1.24631 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.26736 | −0.105564 | ||||||||
\(959\) | 48.3018 | 1.55975 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.5166 | 0.919891 | ||||||||
\(962\) | 84.6174 | 2.72817 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −28.4357 | −0.915854 | ||||||||
\(965\) | 3.52644 | 0.113520 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.7666 | −0.603493 | −0.301747 | − | 0.953388i | \(-0.597570\pi\) | ||||
−0.301747 | + | 0.953388i | \(0.597570\pi\) | |||||||
\(968\) | 3.98594 | 0.128113 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −80.4901 | −2.58438 | ||||||||
\(971\) | −51.9535 | −1.66727 | −0.833633 | − | 0.552319i | \(-0.813743\pi\) | ||||
−0.833633 | + | 0.552319i | \(0.813743\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.20552 | −0.166881 | ||||||||
\(974\) | 52.1149 | 1.66987 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 61.0249 | 1.95336 | ||||||||
\(977\) | 32.5841 | 1.04246 | 0.521229 | − | 0.853417i | \(-0.325474\pi\) | ||||
0.521229 | + | 0.853417i | \(0.325474\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.5110 | −0.559654 | ||||||||
\(980\) | 0.852722 | 0.0272392 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −66.3852 | −2.11844 | ||||||||
\(983\) | 35.0795 | 1.11886 | 0.559431 | − | 0.828877i | \(-0.311020\pi\) | ||||
0.559431 | + | 0.828877i | \(0.311020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.5305 | 0.494844 | ||||||||
\(986\) | 16.0040 | 0.509670 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.3315 | 0.901345 | ||||||||
\(989\) | −1.46517 | −0.0465898 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.7635 | −1.73962 | −0.869810 | − | 0.493386i | \(-0.835759\pi\) | ||||
−0.869810 | + | 0.493386i | \(0.835759\pi\) | |||||||
\(992\) | 3.12052 | 0.0990767 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 96.8161 | 3.07082 | ||||||||
\(995\) | 42.2791 | 1.34034 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.3301 | 1.59397 | 0.796984 | − | 0.604000i | \(-0.206427\pi\) | ||||
0.796984 | + | 0.604000i | \(0.206427\pi\) | |||||||
\(998\) | 36.9625 | 1.17003 | ||||||||
\(999\) | 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 | 729.2.a.b.1.6 | ✓ | 6 | |
3.2 | odd | 2 | 729.2.a.e.1.1 | yes | 6 | ||
9.2 | odd | 6 | 729.2.c.a.244.6 | 12 | |||
9.4 | even | 3 | 729.2.c.d.487.1 | 12 | |||
9.5 | odd | 6 | 729.2.c.a.487.6 | 12 | |||
9.7 | even | 3 | 729.2.c.d.244.1 | 12 | |||
27.2 | odd | 18 | 729.2.e.u.568.2 | 12 | |||
27.4 | even | 9 | 729.2.e.s.406.2 | 12 | |||
27.5 | odd | 18 | 729.2.e.k.649.1 | 12 | |||
27.7 | even | 9 | 729.2.e.s.325.2 | 12 | |||
27.11 | odd | 18 | 729.2.e.k.82.1 | 12 | |||
27.13 | even | 9 | 729.2.e.j.163.1 | 12 | |||
27.14 | odd | 18 | 729.2.e.u.163.2 | 12 | |||
27.16 | even | 9 | 729.2.e.t.82.2 | 12 | |||
27.20 | odd | 18 | 729.2.e.l.325.1 | 12 | |||
27.22 | even | 9 | 729.2.e.t.649.2 | 12 | |||
27.23 | odd | 18 | 729.2.e.l.406.1 | 12 | |||
27.25 | even | 9 | 729.2.e.j.568.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
729.2.a.b.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
729.2.a.e.1.1 | yes | 6 | 3.2 | odd | 2 | ||
729.2.c.a.244.6 | 12 | 9.2 | odd | 6 | |||
729.2.c.a.487.6 | 12 | 9.5 | odd | 6 | |||
729.2.c.d.244.1 | 12 | 9.7 | even | 3 | |||
729.2.c.d.487.1 | 12 | 9.4 | even | 3 | |||
729.2.e.j.163.1 | 12 | 27.13 | even | 9 | |||
729.2.e.j.568.1 | 12 | 27.25 | even | 9 | |||
729.2.e.k.82.1 | 12 | 27.11 | odd | 18 | |||
729.2.e.k.649.1 | 12 | 27.5 | odd | 18 | |||
729.2.e.l.325.1 | 12 | 27.20 | odd | 18 | |||
729.2.e.l.406.1 | 12 | 27.23 | odd | 18 | |||
729.2.e.s.325.2 | 12 | 27.7 | even | 9 | |||
729.2.e.s.406.2 | 12 | 27.4 | even | 9 | |||
729.2.e.t.82.2 | 12 | 27.16 | even | 9 | |||
729.2.e.t.649.2 | 12 | 27.22 | even | 9 | |||
729.2.e.u.163.2 | 12 | 27.14 | odd | 18 | |||
729.2.e.u.568.2 | 12 | 27.2 | odd | 18 |