Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1734,2,Mod(1,1734)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1734, 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("1734.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1734 = 2 \cdot 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1734.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: | \(13.8460597105\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
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 | 1.1 | ||
Root | \(-1.53209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1734.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.53209 | −1.57960 | −0.789799 | − | 0.613366i | \(-0.789815\pi\) | ||||
−0.789799 | + | 0.613366i | \(0.789815\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.75877 | 1.04272 | 0.521359 | − | 0.853338i | \(-0.325425\pi\) | ||||
0.521359 | + | 0.853338i | \(0.325425\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.53209 | 1.11694 | ||||||||
\(11\) | 2.94356 | 0.887518 | 0.443759 | − | 0.896146i | \(-0.353645\pi\) | ||||
0.443759 | + | 0.896146i | \(0.353645\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 5.06418 | 1.40455 | 0.702275 | − | 0.711906i | \(-0.252168\pi\) | ||||
0.702275 | + | 0.711906i | \(0.252168\pi\) | |||||||
\(14\) | −2.75877 | −0.737312 | ||||||||
\(15\) | 3.53209 | 0.911981 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.36959 | −1.00245 | −0.501226 | − | 0.865317i | \(-0.667117\pi\) | ||||
−0.501226 | + | 0.865317i | \(0.667117\pi\) | |||||||
\(20\) | −3.53209 | −0.789799 | ||||||||
\(21\) | −2.75877 | −0.602013 | ||||||||
\(22\) | −2.94356 | −0.627570 | ||||||||
\(23\) | −6.00000 | −1.25109 | −0.625543 | − | 0.780189i | \(-0.715123\pi\) | ||||
−0.625543 | + | 0.780189i | \(0.715123\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 7.47565 | 1.49513 | ||||||||
\(26\) | −5.06418 | −0.993167 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.75877 | 0.521359 | ||||||||
\(29\) | 4.80066 | 0.891460 | 0.445730 | − | 0.895167i | \(-0.352944\pi\) | ||||
0.445730 | + | 0.895167i | \(0.352944\pi\) | |||||||
\(30\) | −3.53209 | −0.644868 | ||||||||
\(31\) | −0.716881 | −0.128756 | −0.0643779 | − | 0.997926i | \(-0.520506\pi\) | ||||
−0.0643779 | + | 0.997926i | \(0.520506\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.94356 | −0.512409 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.74422 | −1.64707 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.2121 | −1.67886 | −0.839432 | − | 0.543464i | \(-0.817112\pi\) | ||||
−0.839432 | + | 0.543464i | \(0.817112\pi\) | |||||||
\(38\) | 4.36959 | 0.708840 | ||||||||
\(39\) | −5.06418 | −0.810917 | ||||||||
\(40\) | 3.53209 | 0.558472 | ||||||||
\(41\) | −12.5817 | −1.96493 | −0.982467 | − | 0.186436i | \(-0.940306\pi\) | ||||
−0.982467 | + | 0.186436i | \(0.940306\pi\) | |||||||
\(42\) | 2.75877 | 0.425688 | ||||||||
\(43\) | 10.9067 | 1.66326 | 0.831630 | − | 0.555330i | \(-0.187408\pi\) | ||||
0.831630 | + | 0.555330i | \(0.187408\pi\) | |||||||
\(44\) | 2.94356 | 0.443759 | ||||||||
\(45\) | −3.53209 | −0.526533 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 5.14796 | 0.750907 | 0.375453 | − | 0.926841i | \(-0.377487\pi\) | ||||
0.375453 | + | 0.926841i | \(0.377487\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 0.610815 | 0.0872592 | ||||||||
\(50\) | −7.47565 | −1.05722 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.06418 | 0.702275 | ||||||||
\(53\) | 4.57398 | 0.628284 | 0.314142 | − | 0.949376i | \(-0.398283\pi\) | ||||
0.314142 | + | 0.949376i | \(0.398283\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −10.3969 | −1.40192 | ||||||||
\(56\) | −2.75877 | −0.368656 | ||||||||
\(57\) | 4.36959 | 0.578766 | ||||||||
\(58\) | −4.80066 | −0.630357 | ||||||||
\(59\) | 5.53209 | 0.720217 | 0.360108 | − | 0.932911i | \(-0.382740\pi\) | ||||
0.360108 | + | 0.932911i | \(0.382740\pi\) | |||||||
\(60\) | 3.53209 | 0.455991 | ||||||||
\(61\) | 6.24123 | 0.799108 | 0.399554 | − | 0.916710i | \(-0.369165\pi\) | ||||
0.399554 | + | 0.916710i | \(0.369165\pi\) | |||||||
\(62\) | 0.716881 | 0.0910440 | ||||||||
\(63\) | 2.75877 | 0.347572 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −17.8871 | −2.21862 | ||||||||
\(66\) | 2.94356 | 0.362328 | ||||||||
\(67\) | 5.67499 | 0.693311 | 0.346655 | − | 0.937993i | \(-0.387317\pi\) | ||||
0.346655 | + | 0.937993i | \(0.387317\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 9.74422 | 1.16466 | ||||||||
\(71\) | 9.80335 | 1.16344 | 0.581722 | − | 0.813388i | \(-0.302379\pi\) | ||||
0.581722 | + | 0.813388i | \(0.302379\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 9.04189 | 1.05827 | 0.529137 | − | 0.848537i | \(-0.322516\pi\) | ||||
0.529137 | + | 0.848537i | \(0.322516\pi\) | |||||||
\(74\) | 10.2121 | 1.18714 | ||||||||
\(75\) | −7.47565 | −0.863214 | ||||||||
\(76\) | −4.36959 | −0.501226 | ||||||||
\(77\) | 8.12061 | 0.925430 | ||||||||
\(78\) | 5.06418 | 0.573405 | ||||||||
\(79\) | 6.61856 | 0.744646 | 0.372323 | − | 0.928103i | \(-0.378561\pi\) | ||||
0.372323 | + | 0.928103i | \(0.378561\pi\) | |||||||
\(80\) | −3.53209 | −0.394900 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.5817 | 1.38942 | ||||||||
\(83\) | −3.32501 | −0.364967 | −0.182484 | − | 0.983209i | \(-0.558414\pi\) | ||||
−0.182484 | + | 0.983209i | \(0.558414\pi\) | |||||||
\(84\) | −2.75877 | −0.301007 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −10.9067 | −1.17610 | ||||||||
\(87\) | −4.80066 | −0.514685 | ||||||||
\(88\) | −2.94356 | −0.313785 | ||||||||
\(89\) | 13.8425 | 1.46731 | 0.733654 | − | 0.679524i | \(-0.237814\pi\) | ||||
0.733654 | + | 0.679524i | \(0.237814\pi\) | |||||||
\(90\) | 3.53209 | 0.372315 | ||||||||
\(91\) | 13.9709 | 1.46455 | ||||||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | 0.716881 | 0.0743371 | ||||||||
\(94\) | −5.14796 | −0.530971 | ||||||||
\(95\) | 15.4338 | 1.58347 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 11.0273 | 1.11966 | 0.559828 | − | 0.828609i | \(-0.310867\pi\) | ||||
0.559828 | + | 0.828609i | \(0.310867\pi\) | |||||||
\(98\) | −0.610815 | −0.0617016 | ||||||||
\(99\) | 2.94356 | 0.295839 | ||||||||
\(100\) | 7.47565 | 0.747565 | ||||||||
\(101\) | 0.921274 | 0.0916702 | 0.0458351 | − | 0.998949i | \(-0.485405\pi\) | ||||
0.0458351 | + | 0.998949i | \(0.485405\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9736 | −1.67246 | −0.836229 | − | 0.548381i | \(-0.815245\pi\) | ||||
−0.836229 | + | 0.548381i | \(0.815245\pi\) | |||||||
\(104\) | −5.06418 | −0.496583 | ||||||||
\(105\) | 9.74422 | 0.950939 | ||||||||
\(106\) | −4.57398 | −0.444264 | ||||||||
\(107\) | 3.08647 | 0.298380 | 0.149190 | − | 0.988809i | \(-0.452333\pi\) | ||||
0.149190 | + | 0.988809i | \(0.452333\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 2.24123 | 0.214671 | 0.107335 | − | 0.994223i | \(-0.465768\pi\) | ||||
0.107335 | + | 0.994223i | \(0.465768\pi\) | |||||||
\(110\) | 10.3969 | 0.991308 | ||||||||
\(111\) | 10.2121 | 0.969293 | ||||||||
\(112\) | 2.75877 | 0.260679 | ||||||||
\(113\) | −11.4338 | −1.07560 | −0.537799 | − | 0.843073i | \(-0.680744\pi\) | ||||
−0.537799 | + | 0.843073i | \(0.680744\pi\) | |||||||
\(114\) | −4.36959 | −0.409249 | ||||||||
\(115\) | 21.1925 | 1.97621 | ||||||||
\(116\) | 4.80066 | 0.445730 | ||||||||
\(117\) | 5.06418 | 0.468183 | ||||||||
\(118\) | −5.53209 | −0.509270 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.53209 | −0.322434 | ||||||||
\(121\) | −2.33544 | −0.212312 | ||||||||
\(122\) | −6.24123 | −0.565054 | ||||||||
\(123\) | 12.5817 | 1.13446 | ||||||||
\(124\) | −0.716881 | −0.0643779 | ||||||||
\(125\) | −8.74422 | −0.782107 | ||||||||
\(126\) | −2.75877 | −0.245771 | ||||||||
\(127\) | −8.75877 | −0.777215 | −0.388608 | − | 0.921403i | \(-0.627044\pi\) | ||||
−0.388608 | + | 0.921403i | \(0.627044\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.9067 | −0.960284 | ||||||||
\(130\) | 17.8871 | 1.56880 | ||||||||
\(131\) | −1.28581 | −0.112341 | −0.0561707 | − | 0.998421i | \(-0.517889\pi\) | ||||
−0.0561707 | + | 0.998421i | \(0.517889\pi\) | |||||||
\(132\) | −2.94356 | −0.256204 | ||||||||
\(133\) | −12.0547 | −1.04527 | ||||||||
\(134\) | −5.67499 | −0.490245 | ||||||||
\(135\) | 3.53209 | 0.303994 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.36959 | 0.202447 | 0.101224 | − | 0.994864i | \(-0.467724\pi\) | ||||
0.101224 | + | 0.994864i | \(0.467724\pi\) | |||||||
\(138\) | −6.00000 | −0.510754 | ||||||||
\(139\) | −5.64590 | −0.478879 | −0.239439 | − | 0.970911i | \(-0.576964\pi\) | ||||
−0.239439 | + | 0.970911i | \(0.576964\pi\) | |||||||
\(140\) | −9.74422 | −0.823537 | ||||||||
\(141\) | −5.14796 | −0.433536 | ||||||||
\(142\) | −9.80335 | −0.822679 | ||||||||
\(143\) | 14.9067 | 1.24656 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −16.9564 | −1.40815 | ||||||||
\(146\) | −9.04189 | −0.748312 | ||||||||
\(147\) | −0.610815 | −0.0503791 | ||||||||
\(148\) | −10.2121 | −0.839432 | ||||||||
\(149\) | 11.4260 | 0.936056 | 0.468028 | − | 0.883714i | \(-0.344965\pi\) | ||||
0.468028 | + | 0.883714i | \(0.344965\pi\) | |||||||
\(150\) | 7.47565 | 0.610384 | ||||||||
\(151\) | 11.7510 | 0.956285 | 0.478143 | − | 0.878282i | \(-0.341310\pi\) | ||||
0.478143 | + | 0.878282i | \(0.341310\pi\) | |||||||
\(152\) | 4.36959 | 0.354420 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.12061 | −0.654378 | ||||||||
\(155\) | 2.53209 | 0.203382 | ||||||||
\(156\) | −5.06418 | −0.405459 | ||||||||
\(157\) | −3.51754 | −0.280730 | −0.140365 | − | 0.990100i | \(-0.544828\pi\) | ||||
−0.140365 | + | 0.990100i | \(0.544828\pi\) | |||||||
\(158\) | −6.61856 | −0.526544 | ||||||||
\(159\) | −4.57398 | −0.362740 | ||||||||
\(160\) | 3.53209 | 0.279236 | ||||||||
\(161\) | −16.5526 | −1.30453 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 6.32501 | 0.495413 | 0.247706 | − | 0.968835i | \(-0.420323\pi\) | ||||
0.247706 | + | 0.968835i | \(0.420323\pi\) | |||||||
\(164\) | −12.5817 | −0.982467 | ||||||||
\(165\) | 10.3969 | 0.809400 | ||||||||
\(166\) | 3.32501 | 0.258071 | ||||||||
\(167\) | 14.3405 | 1.10970 | 0.554850 | − | 0.831950i | \(-0.312776\pi\) | ||||
0.554850 | + | 0.831950i | \(0.312776\pi\) | |||||||
\(168\) | 2.75877 | 0.212844 | ||||||||
\(169\) | 12.6459 | 0.972761 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.36959 | −0.334151 | ||||||||
\(172\) | 10.9067 | 0.831630 | ||||||||
\(173\) | 0.815207 | 0.0619791 | 0.0309895 | − | 0.999520i | \(-0.490134\pi\) | ||||
0.0309895 | + | 0.999520i | \(0.490134\pi\) | |||||||
\(174\) | 4.80066 | 0.363937 | ||||||||
\(175\) | 20.6236 | 1.55900 | ||||||||
\(176\) | 2.94356 | 0.221879 | ||||||||
\(177\) | −5.53209 | −0.415817 | ||||||||
\(178\) | −13.8425 | −1.03754 | ||||||||
\(179\) | 14.0642 | 1.05121 | 0.525603 | − | 0.850730i | \(-0.323840\pi\) | ||||
0.525603 | + | 0.850730i | \(0.323840\pi\) | |||||||
\(180\) | −3.53209 | −0.263266 | ||||||||
\(181\) | 20.3405 | 1.51190 | 0.755948 | − | 0.654631i | \(-0.227176\pi\) | ||||
0.755948 | + | 0.654631i | \(0.227176\pi\) | |||||||
\(182\) | −13.9709 | −1.03559 | ||||||||
\(183\) | −6.24123 | −0.461365 | ||||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | 36.0702 | 2.65193 | ||||||||
\(186\) | −0.716881 | −0.0525643 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.14796 | 0.375453 | ||||||||
\(189\) | −2.75877 | −0.200671 | ||||||||
\(190\) | −15.4338 | −1.11968 | ||||||||
\(191\) | 15.6459 | 1.13210 | 0.566049 | − | 0.824372i | \(-0.308471\pi\) | ||||
0.566049 | + | 0.824372i | \(0.308471\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −10.2713 | −0.739341 | −0.369671 | − | 0.929163i | \(-0.620529\pi\) | ||||
−0.369671 | + | 0.929163i | \(0.620529\pi\) | |||||||
\(194\) | −11.0273 | −0.791717 | ||||||||
\(195\) | 17.8871 | 1.28092 | ||||||||
\(196\) | 0.610815 | 0.0436296 | ||||||||
\(197\) | 8.72967 | 0.621964 | 0.310982 | − | 0.950416i | \(-0.399342\pi\) | ||||
0.310982 | + | 0.950416i | \(0.399342\pi\) | |||||||
\(198\) | −2.94356 | −0.209190 | ||||||||
\(199\) | −16.8922 | −1.19745 | −0.598727 | − | 0.800953i | \(-0.704327\pi\) | ||||
−0.598727 | + | 0.800953i | \(0.704327\pi\) | |||||||
\(200\) | −7.47565 | −0.528608 | ||||||||
\(201\) | −5.67499 | −0.400283 | ||||||||
\(202\) | −0.921274 | −0.0648206 | ||||||||
\(203\) | 13.2439 | 0.929541 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 44.4397 | 3.10381 | ||||||||
\(206\) | 16.9736 | 1.18261 | ||||||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | 5.06418 | 0.351138 | ||||||||
\(209\) | −12.8621 | −0.889693 | ||||||||
\(210\) | −9.74422 | −0.672415 | ||||||||
\(211\) | 14.0993 | 0.970633 | 0.485317 | − | 0.874339i | \(-0.338704\pi\) | ||||
0.485317 | + | 0.874339i | \(0.338704\pi\) | |||||||
\(212\) | 4.57398 | 0.314142 | ||||||||
\(213\) | −9.80335 | −0.671714 | ||||||||
\(214\) | −3.08647 | −0.210987 | ||||||||
\(215\) | −38.5235 | −2.62728 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −1.97771 | −0.134256 | ||||||||
\(218\) | −2.24123 | −0.151795 | ||||||||
\(219\) | −9.04189 | −0.610994 | ||||||||
\(220\) | −10.3969 | −0.700961 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.2121 | −0.685394 | ||||||||
\(223\) | −26.3037 | −1.76142 | −0.880711 | − | 0.473653i | \(-0.842935\pi\) | ||||
−0.880711 | + | 0.473653i | \(0.842935\pi\) | |||||||
\(224\) | −2.75877 | −0.184328 | ||||||||
\(225\) | 7.47565 | 0.498377 | ||||||||
\(226\) | 11.4338 | 0.760563 | ||||||||
\(227\) | 6.06418 | 0.402494 | 0.201247 | − | 0.979541i | \(-0.435501\pi\) | ||||
0.201247 | + | 0.979541i | \(0.435501\pi\) | |||||||
\(228\) | 4.36959 | 0.289383 | ||||||||
\(229\) | 8.56624 | 0.566073 | 0.283036 | − | 0.959109i | \(-0.408658\pi\) | ||||
0.283036 | + | 0.959109i | \(0.408658\pi\) | |||||||
\(230\) | −21.1925 | −1.39739 | ||||||||
\(231\) | −8.12061 | −0.534297 | ||||||||
\(232\) | −4.80066 | −0.315179 | ||||||||
\(233\) | −12.2121 | −0.800043 | −0.400022 | − | 0.916506i | \(-0.630997\pi\) | ||||
−0.400022 | + | 0.916506i | \(0.630997\pi\) | |||||||
\(234\) | −5.06418 | −0.331056 | ||||||||
\(235\) | −18.1830 | −1.18613 | ||||||||
\(236\) | 5.53209 | 0.360108 | ||||||||
\(237\) | −6.61856 | −0.429921 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.8716 | 0.767913 | 0.383956 | − | 0.923351i | \(-0.374561\pi\) | ||||
0.383956 | + | 0.923351i | \(0.374561\pi\) | |||||||
\(240\) | 3.53209 | 0.227995 | ||||||||
\(241\) | 23.9172 | 1.54064 | 0.770320 | − | 0.637658i | \(-0.220097\pi\) | ||||
0.770320 | + | 0.637658i | \(0.220097\pi\) | |||||||
\(242\) | 2.33544 | 0.150128 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.24123 | 0.399554 | ||||||||
\(245\) | −2.15745 | −0.137835 | ||||||||
\(246\) | −12.5817 | −0.802181 | ||||||||
\(247\) | −22.1284 | −1.40799 | ||||||||
\(248\) | 0.716881 | 0.0455220 | ||||||||
\(249\) | 3.32501 | 0.210714 | ||||||||
\(250\) | 8.74422 | 0.553033 | ||||||||
\(251\) | −18.6040 | −1.17427 | −0.587137 | − | 0.809487i | \(-0.699745\pi\) | ||||
−0.587137 | + | 0.809487i | \(0.699745\pi\) | |||||||
\(252\) | 2.75877 | 0.173786 | ||||||||
\(253\) | −17.6614 | −1.11036 | ||||||||
\(254\) | 8.75877 | 0.549574 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.16756 | −0.259965 | −0.129983 | − | 0.991516i | \(-0.541492\pi\) | ||||
−0.129983 | + | 0.991516i | \(0.541492\pi\) | |||||||
\(258\) | 10.9067 | 0.679023 | ||||||||
\(259\) | −28.1729 | −1.75058 | ||||||||
\(260\) | −17.8871 | −1.10931 | ||||||||
\(261\) | 4.80066 | 0.297153 | ||||||||
\(262\) | 1.28581 | 0.0794374 | ||||||||
\(263\) | 7.97090 | 0.491507 | 0.245754 | − | 0.969332i | \(-0.420965\pi\) | ||||
0.245754 | + | 0.969332i | \(0.420965\pi\) | |||||||
\(264\) | 2.94356 | 0.181164 | ||||||||
\(265\) | −16.1557 | −0.992437 | ||||||||
\(266\) | 12.0547 | 0.739120 | ||||||||
\(267\) | −13.8425 | −0.847150 | ||||||||
\(268\) | 5.67499 | 0.346655 | ||||||||
\(269\) | 5.96316 | 0.363580 | 0.181790 | − | 0.983337i | \(-0.441811\pi\) | ||||
0.181790 | + | 0.983337i | \(0.441811\pi\) | |||||||
\(270\) | −3.53209 | −0.214956 | ||||||||
\(271\) | −3.07098 | −0.186549 | −0.0932745 | − | 0.995640i | \(-0.529733\pi\) | ||||
−0.0932745 | + | 0.995640i | \(0.529733\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.9709 | −0.845558 | ||||||||
\(274\) | −2.36959 | −0.143152 | ||||||||
\(275\) | 22.0051 | 1.32695 | ||||||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | 23.2472 | 1.39679 | 0.698395 | − | 0.715713i | \(-0.253898\pi\) | ||||
0.698395 | + | 0.715713i | \(0.253898\pi\) | |||||||
\(278\) | 5.64590 | 0.338618 | ||||||||
\(279\) | −0.716881 | −0.0429186 | ||||||||
\(280\) | 9.74422 | 0.582329 | ||||||||
\(281\) | 21.7297 | 1.29628 | 0.648142 | − | 0.761520i | \(-0.275546\pi\) | ||||
0.648142 | + | 0.761520i | \(0.275546\pi\) | |||||||
\(282\) | 5.14796 | 0.306556 | ||||||||
\(283\) | 17.1925 | 1.02199 | 0.510995 | − | 0.859584i | \(-0.329277\pi\) | ||||
0.510995 | + | 0.859584i | \(0.329277\pi\) | |||||||
\(284\) | 9.80335 | 0.581722 | ||||||||
\(285\) | −15.4338 | −0.914217 | ||||||||
\(286\) | −14.9067 | −0.881453 | ||||||||
\(287\) | −34.7101 | −2.04887 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 16.9564 | 0.995712 | ||||||||
\(291\) | −11.0273 | −0.646434 | ||||||||
\(292\) | 9.04189 | 0.529137 | ||||||||
\(293\) | −9.20708 | −0.537883 | −0.268942 | − | 0.963156i | \(-0.586674\pi\) | ||||
−0.268942 | + | 0.963156i | \(0.586674\pi\) | |||||||
\(294\) | 0.610815 | 0.0356234 | ||||||||
\(295\) | −19.5398 | −1.13765 | ||||||||
\(296\) | 10.2121 | 0.593568 | ||||||||
\(297\) | −2.94356 | −0.170803 | ||||||||
\(298\) | −11.4260 | −0.661892 | ||||||||
\(299\) | −30.3851 | −1.75721 | ||||||||
\(300\) | −7.47565 | −0.431607 | ||||||||
\(301\) | 30.0892 | 1.73431 | ||||||||
\(302\) | −11.7510 | −0.676196 | ||||||||
\(303\) | −0.921274 | −0.0529258 | ||||||||
\(304\) | −4.36959 | −0.250613 | ||||||||
\(305\) | −22.0446 | −1.26227 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.90673 | 0.165896 | 0.0829478 | − | 0.996554i | \(-0.473567\pi\) | ||||
0.0829478 | + | 0.996554i | \(0.473567\pi\) | |||||||
\(308\) | 8.12061 | 0.462715 | ||||||||
\(309\) | 16.9736 | 0.965594 | ||||||||
\(310\) | −2.53209 | −0.143813 | ||||||||
\(311\) | 13.0351 | 0.739152 | 0.369576 | − | 0.929201i | \(-0.379503\pi\) | ||||
0.369576 | + | 0.929201i | \(0.379503\pi\) | |||||||
\(312\) | 5.06418 | 0.286703 | ||||||||
\(313\) | −3.22163 | −0.182097 | −0.0910486 | − | 0.995846i | \(-0.529022\pi\) | ||||
−0.0910486 | + | 0.995846i | \(0.529022\pi\) | |||||||
\(314\) | 3.51754 | 0.198506 | ||||||||
\(315\) | −9.74422 | −0.549025 | ||||||||
\(316\) | 6.61856 | 0.372323 | ||||||||
\(317\) | 19.0838 | 1.07185 | 0.535926 | − | 0.844265i | \(-0.319963\pi\) | ||||
0.535926 | + | 0.844265i | \(0.319963\pi\) | |||||||
\(318\) | 4.57398 | 0.256496 | ||||||||
\(319\) | 14.1310 | 0.791187 | ||||||||
\(320\) | −3.53209 | −0.197450 | ||||||||
\(321\) | −3.08647 | −0.172270 | ||||||||
\(322\) | 16.5526 | 0.922442 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 37.8580 | 2.09999 | ||||||||
\(326\) | −6.32501 | −0.350310 | ||||||||
\(327\) | −2.24123 | −0.123940 | ||||||||
\(328\) | 12.5817 | 0.694709 | ||||||||
\(329\) | 14.2020 | 0.782983 | ||||||||
\(330\) | −10.3969 | −0.572332 | ||||||||
\(331\) | 3.43376 | 0.188737 | 0.0943683 | − | 0.995537i | \(-0.469917\pi\) | ||||
0.0943683 | + | 0.995537i | \(0.469917\pi\) | |||||||
\(332\) | −3.32501 | −0.182484 | ||||||||
\(333\) | −10.2121 | −0.559621 | ||||||||
\(334\) | −14.3405 | −0.784677 | ||||||||
\(335\) | −20.0446 | −1.09515 | ||||||||
\(336\) | −2.75877 | −0.150503 | ||||||||
\(337\) | 35.7202 | 1.94580 | 0.972901 | − | 0.231222i | \(-0.0742723\pi\) | ||||
0.972901 | + | 0.231222i | \(0.0742723\pi\) | |||||||
\(338\) | −12.6459 | −0.687846 | ||||||||
\(339\) | 11.4338 | 0.620997 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.11019 | −0.114273 | ||||||||
\(342\) | 4.36959 | 0.236280 | ||||||||
\(343\) | −17.6263 | −0.951731 | ||||||||
\(344\) | −10.9067 | −0.588051 | ||||||||
\(345\) | −21.1925 | −1.14097 | ||||||||
\(346\) | −0.815207 | −0.0438258 | ||||||||
\(347\) | 1.10782 | 0.0594710 | 0.0297355 | − | 0.999558i | \(-0.490534\pi\) | ||||
0.0297355 | + | 0.999558i | \(0.490534\pi\) | |||||||
\(348\) | −4.80066 | −0.257342 | ||||||||
\(349\) | 11.2371 | 0.601509 | 0.300754 | − | 0.953702i | \(-0.402762\pi\) | ||||
0.300754 | + | 0.953702i | \(0.402762\pi\) | |||||||
\(350\) | −20.6236 | −1.10238 | ||||||||
\(351\) | −5.06418 | −0.270306 | ||||||||
\(352\) | −2.94356 | −0.156892 | ||||||||
\(353\) | −11.2608 | −0.599353 | −0.299677 | − | 0.954041i | \(-0.596879\pi\) | ||||
−0.299677 | + | 0.954041i | \(0.596879\pi\) | |||||||
\(354\) | 5.53209 | 0.294027 | ||||||||
\(355\) | −34.6263 | −1.83777 | ||||||||
\(356\) | 13.8425 | 0.733654 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.0642 | −0.743315 | ||||||||
\(359\) | 2.04458 | 0.107909 | 0.0539543 | − | 0.998543i | \(-0.482817\pi\) | ||||
0.0539543 | + | 0.998543i | \(0.482817\pi\) | |||||||
\(360\) | 3.53209 | 0.186157 | ||||||||
\(361\) | 0.0932736 | 0.00490914 | ||||||||
\(362\) | −20.3405 | −1.06907 | ||||||||
\(363\) | 2.33544 | 0.122579 | ||||||||
\(364\) | 13.9709 | 0.732274 | ||||||||
\(365\) | −31.9368 | −1.67165 | ||||||||
\(366\) | 6.24123 | 0.326234 | ||||||||
\(367\) | −24.4097 | −1.27418 | −0.637088 | − | 0.770791i | \(-0.719861\pi\) | ||||
−0.637088 | + | 0.770791i | \(0.719861\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | −12.5817 | −0.654978 | ||||||||
\(370\) | −36.0702 | −1.87520 | ||||||||
\(371\) | 12.6186 | 0.655123 | ||||||||
\(372\) | 0.716881 | 0.0371686 | ||||||||
\(373\) | 27.3756 | 1.41745 | 0.708727 | − | 0.705483i | \(-0.249270\pi\) | ||||
0.708727 | + | 0.705483i | \(0.249270\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.74422 | 0.451550 | ||||||||
\(376\) | −5.14796 | −0.265486 | ||||||||
\(377\) | 24.3114 | 1.25210 | ||||||||
\(378\) | 2.75877 | 0.141896 | ||||||||
\(379\) | −22.4979 | −1.15564 | −0.577821 | − | 0.816164i | \(-0.696097\pi\) | ||||
−0.577821 | + | 0.816164i | \(0.696097\pi\) | |||||||
\(380\) | 15.4338 | 0.791735 | ||||||||
\(381\) | 8.75877 | 0.448725 | ||||||||
\(382\) | −15.6459 | −0.800514 | ||||||||
\(383\) | 16.5972 | 0.848077 | 0.424039 | − | 0.905644i | \(-0.360612\pi\) | ||||
0.424039 | + | 0.905644i | \(0.360612\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −28.6827 | −1.46181 | ||||||||
\(386\) | 10.2713 | 0.522793 | ||||||||
\(387\) | 10.9067 | 0.554420 | ||||||||
\(388\) | 11.0273 | 0.559828 | ||||||||
\(389\) | −17.2249 | −0.873338 | −0.436669 | − | 0.899622i | \(-0.643842\pi\) | ||||
−0.436669 | + | 0.899622i | \(0.643842\pi\) | |||||||
\(390\) | −17.8871 | −0.905750 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.610815 | −0.0308508 | ||||||||
\(393\) | 1.28581 | 0.0648604 | ||||||||
\(394\) | −8.72967 | −0.439795 | ||||||||
\(395\) | −23.3773 | −1.17624 | ||||||||
\(396\) | 2.94356 | 0.147920 | ||||||||
\(397\) | −4.49794 | −0.225745 | −0.112873 | − | 0.993609i | \(-0.536005\pi\) | ||||
−0.112873 | + | 0.993609i | \(0.536005\pi\) | |||||||
\(398\) | 16.8922 | 0.846728 | ||||||||
\(399\) | 12.0547 | 0.603489 | ||||||||
\(400\) | 7.47565 | 0.373783 | ||||||||
\(401\) | −2.04458 | −0.102101 | −0.0510507 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510507 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(402\) | 5.67499 | 0.283043 | ||||||||
\(403\) | −3.63041 | −0.180844 | ||||||||
\(404\) | 0.921274 | 0.0458351 | ||||||||
\(405\) | −3.53209 | −0.175511 | ||||||||
\(406\) | −13.2439 | −0.657285 | ||||||||
\(407\) | −30.0601 | −1.49002 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2841 | 1.15132 | 0.575661 | − | 0.817688i | \(-0.304745\pi\) | ||||
0.575661 | + | 0.817688i | \(0.304745\pi\) | |||||||
\(410\) | −44.4397 | −2.19472 | ||||||||
\(411\) | −2.36959 | −0.116883 | ||||||||
\(412\) | −16.9736 | −0.836229 | ||||||||
\(413\) | 15.2618 | 0.750982 | ||||||||
\(414\) | 6.00000 | 0.294884 | ||||||||
\(415\) | 11.7442 | 0.576501 | ||||||||
\(416\) | −5.06418 | −0.248292 | ||||||||
\(417\) | 5.64590 | 0.276481 | ||||||||
\(418\) | 12.8621 | 0.629108 | ||||||||
\(419\) | −1.50299 | −0.0734260 | −0.0367130 | − | 0.999326i | \(-0.511689\pi\) | ||||
−0.0367130 | + | 0.999326i | \(0.511689\pi\) | |||||||
\(420\) | 9.74422 | 0.475469 | ||||||||
\(421\) | 18.1438 | 0.884277 | 0.442138 | − | 0.896947i | \(-0.354220\pi\) | ||||
0.442138 | + | 0.896947i | \(0.354220\pi\) | |||||||
\(422\) | −14.0993 | −0.686341 | ||||||||
\(423\) | 5.14796 | 0.250302 | ||||||||
\(424\) | −4.57398 | −0.222132 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.80335 | 0.474974 | ||||||||
\(427\) | 17.2181 | 0.833243 | ||||||||
\(428\) | 3.08647 | 0.149190 | ||||||||
\(429\) | −14.9067 | −0.719704 | ||||||||
\(430\) | 38.5235 | 1.85777 | ||||||||
\(431\) | −26.2276 | −1.26334 | −0.631670 | − | 0.775237i | \(-0.717630\pi\) | ||||
−0.631670 | + | 0.775237i | \(0.717630\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −27.6604 | −1.32928 | −0.664638 | − | 0.747165i | \(-0.731414\pi\) | ||||
−0.664638 | + | 0.747165i | \(0.731414\pi\) | |||||||
\(434\) | 1.97771 | 0.0949332 | ||||||||
\(435\) | 16.9564 | 0.812995 | ||||||||
\(436\) | 2.24123 | 0.107335 | ||||||||
\(437\) | 26.2175 | 1.25415 | ||||||||
\(438\) | 9.04189 | 0.432038 | ||||||||
\(439\) | −29.6459 | −1.41492 | −0.707461 | − | 0.706753i | \(-0.750159\pi\) | ||||
−0.707461 | + | 0.706753i | \(0.750159\pi\) | |||||||
\(440\) | 10.3969 | 0.495654 | ||||||||
\(441\) | 0.610815 | 0.0290864 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.3209 | −1.63063 | −0.815317 | − | 0.579014i | \(-0.803437\pi\) | ||||
−0.815317 | + | 0.579014i | \(0.803437\pi\) | |||||||
\(444\) | 10.2121 | 0.484646 | ||||||||
\(445\) | −48.8931 | −2.31776 | ||||||||
\(446\) | 26.3037 | 1.24551 | ||||||||
\(447\) | −11.4260 | −0.540432 | ||||||||
\(448\) | 2.75877 | 0.130340 | ||||||||
\(449\) | 23.8188 | 1.12408 | 0.562040 | − | 0.827110i | \(-0.310017\pi\) | ||||
0.562040 | + | 0.827110i | \(0.310017\pi\) | |||||||
\(450\) | −7.47565 | −0.352406 | ||||||||
\(451\) | −37.0351 | −1.74391 | ||||||||
\(452\) | −11.4338 | −0.537799 | ||||||||
\(453\) | −11.7510 | −0.552112 | ||||||||
\(454\) | −6.06418 | −0.284606 | ||||||||
\(455\) | −49.3465 | −2.31340 | ||||||||
\(456\) | −4.36959 | −0.204625 | ||||||||
\(457\) | −21.4662 | −1.00414 | −0.502072 | − | 0.864826i | \(-0.667429\pi\) | ||||
−0.502072 | + | 0.864826i | \(0.667429\pi\) | |||||||
\(458\) | −8.56624 | −0.400274 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 21.1925 | 0.988107 | ||||||||
\(461\) | −16.8898 | −0.786637 | −0.393319 | − | 0.919402i | \(-0.628673\pi\) | ||||
−0.393319 | + | 0.919402i | \(0.628673\pi\) | |||||||
\(462\) | 8.12061 | 0.377805 | ||||||||
\(463\) | −3.75784 | −0.174641 | −0.0873207 | − | 0.996180i | \(-0.527831\pi\) | ||||
−0.0873207 | + | 0.996180i | \(0.527831\pi\) | |||||||
\(464\) | 4.80066 | 0.222865 | ||||||||
\(465\) | −2.53209 | −0.117423 | ||||||||
\(466\) | 12.2121 | 0.565716 | ||||||||
\(467\) | 12.4311 | 0.575242 | 0.287621 | − | 0.957744i | \(-0.407136\pi\) | ||||
0.287621 | + | 0.957744i | \(0.407136\pi\) | |||||||
\(468\) | 5.06418 | 0.234092 | ||||||||
\(469\) | 15.6560 | 0.722927 | ||||||||
\(470\) | 18.1830 | 0.838721 | ||||||||
\(471\) | 3.51754 | 0.162080 | ||||||||
\(472\) | −5.53209 | −0.254635 | ||||||||
\(473\) | 32.1046 | 1.47617 | ||||||||
\(474\) | 6.61856 | 0.304000 | ||||||||
\(475\) | −32.6655 | −1.49880 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.57398 | 0.209428 | ||||||||
\(478\) | −11.8716 | −0.542996 | ||||||||
\(479\) | −11.6905 | −0.534151 | −0.267076 | − | 0.963676i | \(-0.586057\pi\) | ||||
−0.267076 | + | 0.963676i | \(0.586057\pi\) | |||||||
\(480\) | −3.53209 | −0.161217 | ||||||||
\(481\) | −51.7161 | −2.35805 | ||||||||
\(482\) | −23.9172 | −1.08940 | ||||||||
\(483\) | 16.5526 | 0.753170 | ||||||||
\(484\) | −2.33544 | −0.106156 | ||||||||
\(485\) | −38.9495 | −1.76861 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 7.33544 | 0.332400 | 0.166200 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166200 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(488\) | −6.24123 | −0.282527 | ||||||||
\(489\) | −6.32501 | −0.286027 | ||||||||
\(490\) | 2.15745 | 0.0974637 | ||||||||
\(491\) | 2.27126 | 0.102500 | 0.0512502 | − | 0.998686i | \(-0.483679\pi\) | ||||
0.0512502 | + | 0.998686i | \(0.483679\pi\) | |||||||
\(492\) | 12.5817 | 0.567228 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 22.1284 | 0.995602 | ||||||||
\(495\) | −10.3969 | −0.467307 | ||||||||
\(496\) | −0.716881 | −0.0321889 | ||||||||
\(497\) | 27.0452 | 1.21314 | ||||||||
\(498\) | −3.32501 | −0.148997 | ||||||||
\(499\) | 9.71957 | 0.435108 | 0.217554 | − | 0.976048i | \(-0.430192\pi\) | ||||
0.217554 | + | 0.976048i | \(0.430192\pi\) | |||||||
\(500\) | −8.74422 | −0.391054 | ||||||||
\(501\) | −14.3405 | −0.640686 | ||||||||
\(502\) | 18.6040 | 0.830337 | ||||||||
\(503\) | 17.7588 | 0.791824 | 0.395912 | − | 0.918288i | \(-0.370428\pi\) | ||||
0.395912 | + | 0.918288i | \(0.370428\pi\) | |||||||
\(504\) | −2.75877 | −0.122885 | ||||||||
\(505\) | −3.25402 | −0.144802 | ||||||||
\(506\) | 17.6614 | 0.785144 | ||||||||
\(507\) | −12.6459 | −0.561624 | ||||||||
\(508\) | −8.75877 | −0.388608 | ||||||||
\(509\) | −7.39786 | −0.327904 | −0.163952 | − | 0.986468i | \(-0.552424\pi\) | ||||
−0.163952 | + | 0.986468i | \(0.552424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.9445 | 1.10348 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.36959 | 0.192922 | ||||||||
\(514\) | 4.16756 | 0.183823 | ||||||||
\(515\) | 59.9522 | 2.64181 | ||||||||
\(516\) | −10.9067 | −0.480142 | ||||||||
\(517\) | 15.1533 | 0.666443 | ||||||||
\(518\) | 28.1729 | 1.23785 | ||||||||
\(519\) | −0.815207 | −0.0357836 | ||||||||
\(520\) | 17.8871 | 0.784402 | ||||||||
\(521\) | 4.12298 | 0.180631 | 0.0903155 | − | 0.995913i | \(-0.471212\pi\) | ||||
0.0903155 | + | 0.995913i | \(0.471212\pi\) | |||||||
\(522\) | −4.80066 | −0.210119 | ||||||||
\(523\) | −36.5134 | −1.59662 | −0.798310 | − | 0.602246i | \(-0.794272\pi\) | ||||
−0.798310 | + | 0.602246i | \(0.794272\pi\) | |||||||
\(524\) | −1.28581 | −0.0561707 | ||||||||
\(525\) | −20.6236 | −0.900088 | ||||||||
\(526\) | −7.97090 | −0.347548 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.94356 | −0.128102 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 16.1557 | 0.701759 | ||||||||
\(531\) | 5.53209 | 0.240072 | ||||||||
\(532\) | −12.0547 | −0.522637 | ||||||||
\(533\) | −63.7161 | −2.75985 | ||||||||
\(534\) | 13.8425 | 0.599026 | ||||||||
\(535\) | −10.9017 | −0.471320 | ||||||||
\(536\) | −5.67499 | −0.245122 | ||||||||
\(537\) | −14.0642 | −0.606914 | ||||||||
\(538\) | −5.96316 | −0.257090 | ||||||||
\(539\) | 1.79797 | 0.0774441 | ||||||||
\(540\) | 3.53209 | 0.151997 | ||||||||
\(541\) | 44.7939 | 1.92584 | 0.962919 | − | 0.269790i | \(-0.0869544\pi\) | ||||
0.962919 | + | 0.269790i | \(0.0869544\pi\) | |||||||
\(542\) | 3.07098 | 0.131910 | ||||||||
\(543\) | −20.3405 | −0.872894 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.91622 | −0.339094 | ||||||||
\(546\) | 13.9709 | 0.597900 | ||||||||
\(547\) | 22.0993 | 0.944896 | 0.472448 | − | 0.881359i | \(-0.343370\pi\) | ||||
0.472448 | + | 0.881359i | \(0.343370\pi\) | |||||||
\(548\) | 2.36959 | 0.101224 | ||||||||
\(549\) | 6.24123 | 0.266369 | ||||||||
\(550\) | −22.0051 | −0.938299 | ||||||||
\(551\) | −20.9769 | −0.893646 | ||||||||
\(552\) | −6.00000 | −0.255377 | ||||||||
\(553\) | 18.2591 | 0.776455 | ||||||||
\(554\) | −23.2472 | −0.987680 | ||||||||
\(555\) | −36.0702 | −1.53109 | ||||||||
\(556\) | −5.64590 | −0.239439 | ||||||||
\(557\) | 21.9905 | 0.931768 | 0.465884 | − | 0.884846i | \(-0.345736\pi\) | ||||
0.465884 | + | 0.884846i | \(0.345736\pi\) | |||||||
\(558\) | 0.716881 | 0.0303480 | ||||||||
\(559\) | 55.2336 | 2.33613 | ||||||||
\(560\) | −9.74422 | −0.411769 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −21.7297 | −0.916611 | ||||||||
\(563\) | −31.9486 | −1.34647 | −0.673237 | − | 0.739427i | \(-0.735097\pi\) | ||||
−0.673237 | + | 0.739427i | \(0.735097\pi\) | |||||||
\(564\) | −5.14796 | −0.216768 | ||||||||
\(565\) | 40.3851 | 1.69901 | ||||||||
\(566\) | −17.1925 | −0.722656 | ||||||||
\(567\) | 2.75877 | 0.115857 | ||||||||
\(568\) | −9.80335 | −0.411339 | ||||||||
\(569\) | −30.9614 | −1.29797 | −0.648985 | − | 0.760801i | \(-0.724806\pi\) | ||||
−0.648985 | + | 0.760801i | \(0.724806\pi\) | |||||||
\(570\) | 15.4338 | 0.646449 | ||||||||
\(571\) | 16.5080 | 0.690840 | 0.345420 | − | 0.938448i | \(-0.387736\pi\) | ||||
0.345420 | + | 0.938448i | \(0.387736\pi\) | |||||||
\(572\) | 14.9067 | 0.623282 | ||||||||
\(573\) | −15.6459 | −0.653617 | ||||||||
\(574\) | 34.7101 | 1.44877 | ||||||||
\(575\) | −44.8539 | −1.87054 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −18.9026 | −0.786926 | −0.393463 | − | 0.919340i | \(-0.628723\pi\) | ||||
−0.393463 | + | 0.919340i | \(0.628723\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.2713 | 0.426859 | ||||||||
\(580\) | −16.9564 | −0.704074 | ||||||||
\(581\) | −9.17293 | −0.380557 | ||||||||
\(582\) | 11.0273 | 0.457098 | ||||||||
\(583\) | 13.4638 | 0.557613 | ||||||||
\(584\) | −9.04189 | −0.374156 | ||||||||
\(585\) | −17.8871 | −0.739542 | ||||||||
\(586\) | 9.20708 | 0.380341 | ||||||||
\(587\) | 7.17799 | 0.296267 | 0.148134 | − | 0.988967i | \(-0.452673\pi\) | ||||
0.148134 | + | 0.988967i | \(0.452673\pi\) | |||||||
\(588\) | −0.610815 | −0.0251896 | ||||||||
\(589\) | 3.13247 | 0.129071 | ||||||||
\(590\) | 19.5398 | 0.804442 | ||||||||
\(591\) | −8.72967 | −0.359091 | ||||||||
\(592\) | −10.2121 | −0.419716 | ||||||||
\(593\) | 26.2823 | 1.07928 | 0.539642 | − | 0.841894i | \(-0.318559\pi\) | ||||
0.539642 | + | 0.841894i | \(0.318559\pi\) | |||||||
\(594\) | 2.94356 | 0.120776 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.4260 | 0.468028 | ||||||||
\(597\) | 16.8922 | 0.691351 | ||||||||
\(598\) | 30.3851 | 1.24254 | ||||||||
\(599\) | −28.3114 | −1.15677 | −0.578386 | − | 0.815763i | \(-0.696317\pi\) | ||||
−0.578386 | + | 0.815763i | \(0.696317\pi\) | |||||||
\(600\) | 7.47565 | 0.305192 | ||||||||
\(601\) | 11.4406 | 0.466671 | 0.233335 | − | 0.972396i | \(-0.425036\pi\) | ||||
0.233335 | + | 0.972396i | \(0.425036\pi\) | |||||||
\(602\) | −30.0892 | −1.22634 | ||||||||
\(603\) | 5.67499 | 0.231104 | ||||||||
\(604\) | 11.7510 | 0.478143 | ||||||||
\(605\) | 8.24897 | 0.335368 | ||||||||
\(606\) | 0.921274 | 0.0374242 | ||||||||
\(607\) | −32.4911 | −1.31877 | −0.659387 | − | 0.751804i | \(-0.729184\pi\) | ||||
−0.659387 | + | 0.751804i | \(0.729184\pi\) | |||||||
\(608\) | 4.36959 | 0.177210 | ||||||||
\(609\) | −13.2439 | −0.536671 | ||||||||
\(610\) | 22.0446 | 0.892559 | ||||||||
\(611\) | 26.0702 | 1.05469 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.2959 | −0.577406 | −0.288703 | − | 0.957419i | \(-0.593224\pi\) | ||||
−0.288703 | + | 0.957419i | \(0.593224\pi\) | |||||||
\(614\) | −2.90673 | −0.117306 | ||||||||
\(615\) | −44.4397 | −1.79198 | ||||||||
\(616\) | −8.12061 | −0.327189 | ||||||||
\(617\) | −41.4356 | −1.66814 | −0.834068 | − | 0.551662i | \(-0.813994\pi\) | ||||
−0.834068 | + | 0.551662i | \(0.813994\pi\) | |||||||
\(618\) | −16.9736 | −0.682778 | ||||||||
\(619\) | 8.05468 | 0.323745 | 0.161873 | − | 0.986812i | \(-0.448247\pi\) | ||||
0.161873 | + | 0.986812i | \(0.448247\pi\) | |||||||
\(620\) | 2.53209 | 0.101691 | ||||||||
\(621\) | 6.00000 | 0.240772 | ||||||||
\(622\) | −13.0351 | −0.522659 | ||||||||
\(623\) | 38.1884 | 1.52999 | ||||||||
\(624\) | −5.06418 | −0.202729 | ||||||||
\(625\) | −6.49289 | −0.259716 | ||||||||
\(626\) | 3.22163 | 0.128762 | ||||||||
\(627\) | 12.8621 | 0.513665 | ||||||||
\(628\) | −3.51754 | −0.140365 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 9.74422 | 0.388219 | ||||||||
\(631\) | 10.5885 | 0.421523 | 0.210761 | − | 0.977538i | \(-0.432406\pi\) | ||||
0.210761 | + | 0.977538i | \(0.432406\pi\) | |||||||
\(632\) | −6.61856 | −0.263272 | ||||||||
\(633\) | −14.0993 | −0.560395 | ||||||||
\(634\) | −19.0838 | −0.757914 | ||||||||
\(635\) | 30.9368 | 1.22769 | ||||||||
\(636\) | −4.57398 | −0.181370 | ||||||||
\(637\) | 3.09327 | 0.122560 | ||||||||
\(638\) | −14.1310 | −0.559453 | ||||||||
\(639\) | 9.80335 | 0.387814 | ||||||||
\(640\) | 3.53209 | 0.139618 | ||||||||
\(641\) | 32.5526 | 1.28575 | 0.642876 | − | 0.765971i | \(-0.277741\pi\) | ||||
0.642876 | + | 0.765971i | \(0.277741\pi\) | |||||||
\(642\) | 3.08647 | 0.121813 | ||||||||
\(643\) | −10.5817 | −0.417302 | −0.208651 | − | 0.977990i | \(-0.566907\pi\) | ||||
−0.208651 | + | 0.977990i | \(0.566907\pi\) | |||||||
\(644\) | −16.5526 | −0.652265 | ||||||||
\(645\) | 38.5235 | 1.51686 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −25.4884 | −1.00205 | −0.501027 | − | 0.865432i | \(-0.667044\pi\) | ||||
−0.501027 | + | 0.865432i | \(0.667044\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 16.2841 | 0.639205 | ||||||||
\(650\) | −37.8580 | −1.48491 | ||||||||
\(651\) | 1.97771 | 0.0775126 | ||||||||
\(652\) | 6.32501 | 0.247706 | ||||||||
\(653\) | 20.6108 | 0.806564 | 0.403282 | − | 0.915076i | \(-0.367869\pi\) | ||||
0.403282 | + | 0.915076i | \(0.367869\pi\) | |||||||
\(654\) | 2.24123 | 0.0876390 | ||||||||
\(655\) | 4.54158 | 0.177454 | ||||||||
\(656\) | −12.5817 | −0.491234 | ||||||||
\(657\) | 9.04189 | 0.352758 | ||||||||
\(658\) | −14.2020 | −0.553653 | ||||||||
\(659\) | −41.5117 | −1.61706 | −0.808532 | − | 0.588452i | \(-0.799738\pi\) | ||||
−0.808532 | + | 0.588452i | \(0.799738\pi\) | |||||||
\(660\) | 10.3969 | 0.404700 | ||||||||
\(661\) | −17.0060 | −0.661456 | −0.330728 | − | 0.943726i | \(-0.607294\pi\) | ||||
−0.330728 | + | 0.943726i | \(0.607294\pi\) | |||||||
\(662\) | −3.43376 | −0.133457 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.32501 | 0.129035 | ||||||||
\(665\) | 42.5782 | 1.65111 | ||||||||
\(666\) | 10.2121 | 0.395712 | ||||||||
\(667\) | −28.8040 | −1.11529 | ||||||||
\(668\) | 14.3405 | 0.554850 | ||||||||
\(669\) | 26.3037 | 1.01696 | ||||||||
\(670\) | 20.0446 | 0.774390 | ||||||||
\(671\) | 18.3715 | 0.709222 | ||||||||
\(672\) | 2.75877 | 0.106422 | ||||||||
\(673\) | −20.0392 | −0.772454 | −0.386227 | − | 0.922404i | \(-0.626222\pi\) | ||||
−0.386227 | + | 0.922404i | \(0.626222\pi\) | |||||||
\(674\) | −35.7202 | −1.37589 | ||||||||
\(675\) | −7.47565 | −0.287738 | ||||||||
\(676\) | 12.6459 | 0.486381 | ||||||||
\(677\) | 47.9823 | 1.84411 | 0.922054 | − | 0.387061i | \(-0.126510\pi\) | ||||
0.922054 | + | 0.387061i | \(0.126510\pi\) | |||||||
\(678\) | −11.4338 | −0.439111 | ||||||||
\(679\) | 30.4219 | 1.16749 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.06418 | −0.232380 | ||||||||
\(682\) | 2.11019 | 0.0808032 | ||||||||
\(683\) | −33.4739 | −1.28084 | −0.640422 | − | 0.768024i | \(-0.721240\pi\) | ||||
−0.640422 | + | 0.768024i | \(0.721240\pi\) | |||||||
\(684\) | −4.36959 | −0.167075 | ||||||||
\(685\) | −8.36959 | −0.319785 | ||||||||
\(686\) | 17.6263 | 0.672975 | ||||||||
\(687\) | −8.56624 | −0.326822 | ||||||||
\(688\) | 10.9067 | 0.415815 | ||||||||
\(689\) | 23.1634 | 0.882457 | ||||||||
\(690\) | 21.1925 | 0.806786 | ||||||||
\(691\) | −20.4979 | −0.779778 | −0.389889 | − | 0.920862i | \(-0.627487\pi\) | ||||
−0.389889 | + | 0.920862i | \(0.627487\pi\) | |||||||
\(692\) | 0.815207 | 0.0309895 | ||||||||
\(693\) | 8.12061 | 0.308477 | ||||||||
\(694\) | −1.10782 | −0.0420523 | ||||||||
\(695\) | 19.9418 | 0.756436 | ||||||||
\(696\) | 4.80066 | 0.181969 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −11.2371 | −0.425331 | ||||||||
\(699\) | 12.2121 | 0.461905 | ||||||||
\(700\) | 20.6236 | 0.779499 | ||||||||
\(701\) | 51.4415 | 1.94292 | 0.971459 | − | 0.237206i | \(-0.0762316\pi\) | ||||
0.971459 | + | 0.237206i | \(0.0762316\pi\) | |||||||
\(702\) | 5.06418 | 0.191135 | ||||||||
\(703\) | 44.6228 | 1.68298 | ||||||||
\(704\) | 2.94356 | 0.110940 | ||||||||
\(705\) | 18.1830 | 0.684813 | ||||||||
\(706\) | 11.2608 | 0.423807 | ||||||||
\(707\) | 2.54158 | 0.0955861 | ||||||||
\(708\) | −5.53209 | −0.207909 | ||||||||
\(709\) | 10.1438 | 0.380960 | 0.190480 | − | 0.981691i | \(-0.438996\pi\) | ||||
0.190480 | + | 0.981691i | \(0.438996\pi\) | |||||||
\(710\) | 34.6263 | 1.29950 | ||||||||
\(711\) | 6.61856 | 0.248215 | ||||||||
\(712\) | −13.8425 | −0.518771 | ||||||||
\(713\) | 4.30129 | 0.161085 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −52.6519 | −1.96907 | ||||||||
\(716\) | 14.0642 | 0.525603 | ||||||||
\(717\) | −11.8716 | −0.443355 | ||||||||
\(718\) | −2.04458 | −0.0763030 | ||||||||
\(719\) | 15.4047 | 0.574497 | 0.287249 | − | 0.957856i | \(-0.407259\pi\) | ||||
0.287249 | + | 0.957856i | \(0.407259\pi\) | |||||||
\(720\) | −3.53209 | −0.131633 | ||||||||
\(721\) | −46.8262 | −1.74390 | ||||||||
\(722\) | −0.0932736 | −0.00347128 | ||||||||
\(723\) | −23.9172 | −0.889489 | ||||||||
\(724\) | 20.3405 | 0.755948 | ||||||||
\(725\) | 35.8881 | 1.33285 | ||||||||
\(726\) | −2.33544 | −0.0866762 | ||||||||
\(727\) | −23.1097 | −0.857091 | −0.428545 | − | 0.903520i | \(-0.640974\pi\) | ||||
−0.428545 | + | 0.903520i | \(0.640974\pi\) | |||||||
\(728\) | −13.9709 | −0.517796 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 31.9368 | 1.18203 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −6.24123 | −0.230682 | ||||||||
\(733\) | −4.20676 | −0.155380 | −0.0776901 | − | 0.996978i | \(-0.524754\pi\) | ||||
−0.0776901 | + | 0.996978i | \(0.524754\pi\) | |||||||
\(734\) | 24.4097 | 0.900979 | ||||||||
\(735\) | 2.15745 | 0.0795788 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 16.7047 | 0.615325 | ||||||||
\(738\) | 12.5817 | 0.463139 | ||||||||
\(739\) | 7.79797 | 0.286853 | 0.143427 | − | 0.989661i | \(-0.454188\pi\) | ||||
0.143427 | + | 0.989661i | \(0.454188\pi\) | |||||||
\(740\) | 36.0702 | 1.32597 | ||||||||
\(741\) | 22.1284 | 0.812905 | ||||||||
\(742\) | −12.6186 | −0.463242 | ||||||||
\(743\) | 11.5567 | 0.423976 | 0.211988 | − | 0.977272i | \(-0.432006\pi\) | ||||
0.211988 | + | 0.977272i | \(0.432006\pi\) | |||||||
\(744\) | −0.716881 | −0.0262821 | ||||||||
\(745\) | −40.3577 | −1.47859 | ||||||||
\(746\) | −27.3756 | −1.00229 | ||||||||
\(747\) | −3.32501 | −0.121656 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.51485 | 0.311126 | ||||||||
\(750\) | −8.74422 | −0.319294 | ||||||||
\(751\) | 13.9172 | 0.507844 | 0.253922 | − | 0.967225i | \(-0.418279\pi\) | ||||
0.253922 | + | 0.967225i | \(0.418279\pi\) | |||||||
\(752\) | 5.14796 | 0.187727 | ||||||||
\(753\) | 18.6040 | 0.677968 | ||||||||
\(754\) | −24.3114 | −0.885369 | ||||||||
\(755\) | −41.5057 | −1.51055 | ||||||||
\(756\) | −2.75877 | −0.100336 | ||||||||
\(757\) | −18.0702 | −0.656771 | −0.328386 | − | 0.944544i | \(-0.606505\pi\) | ||||
−0.328386 | + | 0.944544i | \(0.606505\pi\) | |||||||
\(758\) | 22.4979 | 0.817162 | ||||||||
\(759\) | 17.6614 | 0.641067 | ||||||||
\(760\) | −15.4338 | −0.559841 | ||||||||
\(761\) | −0.241230 | −0.00874456 | −0.00437228 | − | 0.999990i | \(-0.501392\pi\) | ||||
−0.00437228 | + | 0.999990i | \(0.501392\pi\) | |||||||
\(762\) | −8.75877 | −0.317297 | ||||||||
\(763\) | 6.18304 | 0.223841 | ||||||||
\(764\) | 15.6459 | 0.566049 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.5972 | −0.599681 | ||||||||
\(767\) | 28.0155 | 1.01158 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 12.5963 | 0.454233 | 0.227116 | − | 0.973868i | \(-0.427070\pi\) | ||||
0.227116 | + | 0.973868i | \(0.427070\pi\) | |||||||
\(770\) | 28.6827 | 1.03365 | ||||||||
\(771\) | 4.16756 | 0.150091 | ||||||||
\(772\) | −10.2713 | −0.369671 | ||||||||
\(773\) | 33.4807 | 1.20422 | 0.602109 | − | 0.798414i | \(-0.294327\pi\) | ||||
0.602109 | + | 0.798414i | \(0.294327\pi\) | |||||||
\(774\) | −10.9067 | −0.392034 | ||||||||
\(775\) | −5.35916 | −0.192507 | ||||||||
\(776\) | −11.0273 | −0.395858 | ||||||||
\(777\) | 28.1729 | 1.01070 | ||||||||
\(778\) | 17.2249 | 0.617544 | ||||||||
\(779\) | 54.9769 | 1.96975 | ||||||||
\(780\) | 17.8871 | 0.640462 | ||||||||
\(781\) | 28.8568 | 1.03258 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.80066 | −0.171562 | ||||||||
\(784\) | 0.610815 | 0.0218148 | ||||||||
\(785\) | 12.4243 | 0.443441 | ||||||||
\(786\) | −1.28581 | −0.0458632 | ||||||||
\(787\) | −25.9181 | −0.923880 | −0.461940 | − | 0.886911i | \(-0.652846\pi\) | ||||
−0.461940 | + | 0.886911i | \(0.652846\pi\) | |||||||
\(788\) | 8.72967 | 0.310982 | ||||||||
\(789\) | −7.97090 | −0.283772 | ||||||||
\(790\) | 23.3773 | 0.831728 | ||||||||
\(791\) | −31.5431 | −1.12154 | ||||||||
\(792\) | −2.94356 | −0.104595 | ||||||||
\(793\) | 31.6067 | 1.12239 | ||||||||
\(794\) | 4.49794 | 0.159626 | ||||||||
\(795\) | 16.1557 | 0.572984 | ||||||||
\(796\) | −16.8922 | −0.598727 | ||||||||
\(797\) | 55.5580 | 1.96797 | 0.983983 | − | 0.178264i | \(-0.0570482\pi\) | ||||
0.983983 | + | 0.178264i | \(0.0570482\pi\) | |||||||
\(798\) | −12.0547 | −0.426731 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −7.47565 | −0.264304 | ||||||||
\(801\) | 13.8425 | 0.489102 | ||||||||
\(802\) | 2.04458 | 0.0721965 | ||||||||
\(803\) | 26.6154 | 0.939236 | ||||||||
\(804\) | −5.67499 | −0.200142 | ||||||||
\(805\) | 58.4653 | 2.06063 | ||||||||
\(806\) | 3.63041 | 0.127876 | ||||||||
\(807\) | −5.96316 | −0.209913 | ||||||||
\(808\) | −0.921274 | −0.0324103 | ||||||||
\(809\) | 17.9317 | 0.630445 | 0.315223 | − | 0.949018i | \(-0.397921\pi\) | ||||
0.315223 | + | 0.949018i | \(0.397921\pi\) | |||||||
\(810\) | 3.53209 | 0.124105 | ||||||||
\(811\) | 25.2472 | 0.886550 | 0.443275 | − | 0.896386i | \(-0.353817\pi\) | ||||
0.443275 | + | 0.896386i | \(0.353817\pi\) | |||||||
\(812\) | 13.2439 | 0.464770 | ||||||||
\(813\) | 3.07098 | 0.107704 | ||||||||
\(814\) | 30.0601 | 1.05360 | ||||||||
\(815\) | −22.3405 | −0.782553 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −47.6579 | −1.66734 | ||||||||
\(818\) | −23.2841 | −0.814108 | ||||||||
\(819\) | 13.9709 | 0.488183 | ||||||||
\(820\) | 44.4397 | 1.55190 | ||||||||
\(821\) | −2.68098 | −0.0935668 | −0.0467834 | − | 0.998905i | \(-0.514897\pi\) | ||||
−0.0467834 | + | 0.998905i | \(0.514897\pi\) | |||||||
\(822\) | 2.36959 | 0.0826488 | ||||||||
\(823\) | −25.1712 | −0.877412 | −0.438706 | − | 0.898631i | \(-0.644563\pi\) | ||||
−0.438706 | + | 0.898631i | \(0.644563\pi\) | |||||||
\(824\) | 16.9736 | 0.591303 | ||||||||
\(825\) | −22.0051 | −0.766118 | ||||||||
\(826\) | −15.2618 | −0.531025 | ||||||||
\(827\) | 11.4638 | 0.398635 | 0.199318 | − | 0.979935i | \(-0.436127\pi\) | ||||
0.199318 | + | 0.979935i | \(0.436127\pi\) | |||||||
\(828\) | −6.00000 | −0.208514 | ||||||||
\(829\) | 49.4593 | 1.71779 | 0.858897 | − | 0.512148i | \(-0.171150\pi\) | ||||
0.858897 | + | 0.512148i | \(0.171150\pi\) | |||||||
\(830\) | −11.7442 | −0.407648 | ||||||||
\(831\) | −23.2472 | −0.806437 | ||||||||
\(832\) | 5.06418 | 0.175569 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5.64590 | −0.195501 | ||||||||
\(835\) | −50.6519 | −1.75288 | ||||||||
\(836\) | −12.8621 | −0.444847 | ||||||||
\(837\) | 0.716881 | 0.0247790 | ||||||||
\(838\) | 1.50299 | 0.0519200 | ||||||||
\(839\) | 33.6560 | 1.16193 | 0.580967 | − | 0.813927i | \(-0.302674\pi\) | ||||
0.580967 | + | 0.813927i | \(0.302674\pi\) | |||||||
\(840\) | −9.74422 | −0.336208 | ||||||||
\(841\) | −5.95367 | −0.205299 | ||||||||
\(842\) | −18.1438 | −0.625278 | ||||||||
\(843\) | −21.7297 | −0.748410 | ||||||||
\(844\) | 14.0993 | 0.485317 | ||||||||
\(845\) | −44.6664 | −1.53657 | ||||||||
\(846\) | −5.14796 | −0.176990 | ||||||||
\(847\) | −6.44293 | −0.221382 | ||||||||
\(848\) | 4.57398 | 0.157071 | ||||||||
\(849\) | −17.1925 | −0.590046 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 61.2728 | 2.10040 | ||||||||
\(852\) | −9.80335 | −0.335857 | ||||||||
\(853\) | 2.42427 | 0.0830053 | 0.0415027 | − | 0.999138i | \(-0.486785\pi\) | ||||
0.0415027 | + | 0.999138i | \(0.486785\pi\) | |||||||
\(854\) | −17.2181 | −0.589192 | ||||||||
\(855\) | 15.4338 | 0.527824 | ||||||||
\(856\) | −3.08647 | −0.105493 | ||||||||
\(857\) | −3.21625 | −0.109865 | −0.0549325 | − | 0.998490i | \(-0.517494\pi\) | ||||
−0.0549325 | + | 0.998490i | \(0.517494\pi\) | |||||||
\(858\) | 14.9067 | 0.508907 | ||||||||
\(859\) | 23.4831 | 0.801232 | 0.400616 | − | 0.916246i | \(-0.368796\pi\) | ||||
0.400616 | + | 0.916246i | \(0.368796\pi\) | |||||||
\(860\) | −38.5235 | −1.31364 | ||||||||
\(861\) | 34.7101 | 1.18292 | ||||||||
\(862\) | 26.2276 | 0.893316 | ||||||||
\(863\) | 44.4344 | 1.51256 | 0.756282 | − | 0.654246i | \(-0.227014\pi\) | ||||
0.756282 | + | 0.654246i | \(0.227014\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −2.87939 | −0.0979020 | ||||||||
\(866\) | 27.6604 | 0.939940 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.97771 | −0.0671279 | ||||||||
\(869\) | 19.4821 | 0.660886 | ||||||||
\(870\) | −16.9564 | −0.574874 | ||||||||
\(871\) | 28.7392 | 0.973790 | ||||||||
\(872\) | −2.24123 | −0.0758976 | ||||||||
\(873\) | 11.0273 | 0.373219 | ||||||||
\(874\) | −26.2175 | −0.886821 | ||||||||
\(875\) | −24.1233 | −0.815516 | ||||||||
\(876\) | −9.04189 | −0.305497 | ||||||||
\(877\) | −9.07966 | −0.306598 | −0.153299 | − | 0.988180i | \(-0.548990\pi\) | ||||
−0.153299 | + | 0.988180i | \(0.548990\pi\) | |||||||
\(878\) | 29.6459 | 1.00050 | ||||||||
\(879\) | 9.20708 | 0.310547 | ||||||||
\(880\) | −10.3969 | −0.350480 | ||||||||
\(881\) | −25.5912 | −0.862190 | −0.431095 | − | 0.902307i | \(-0.641873\pi\) | ||||
−0.431095 | + | 0.902307i | \(0.641873\pi\) | |||||||
\(882\) | −0.610815 | −0.0205672 | ||||||||
\(883\) | −22.3506 | −0.752157 | −0.376079 | − | 0.926588i | \(-0.622728\pi\) | ||||
−0.376079 | + | 0.926588i | \(0.622728\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.5398 | 0.656824 | ||||||||
\(886\) | 34.3209 | 1.15303 | ||||||||
\(887\) | −26.4688 | −0.888737 | −0.444368 | − | 0.895844i | \(-0.646572\pi\) | ||||
−0.444368 | + | 0.895844i | \(0.646572\pi\) | |||||||
\(888\) | −10.2121 | −0.342697 | ||||||||
\(889\) | −24.1634 | −0.810416 | ||||||||
\(890\) | 48.8931 | 1.63890 | ||||||||
\(891\) | 2.94356 | 0.0986131 | ||||||||
\(892\) | −26.3037 | −0.880711 | ||||||||
\(893\) | −22.4944 | −0.752747 | ||||||||
\(894\) | 11.4260 | 0.382143 | ||||||||
\(895\) | −49.6759 | −1.66048 | ||||||||
\(896\) | −2.75877 | −0.0921641 | ||||||||
\(897\) | 30.3851 | 1.01453 | ||||||||
\(898\) | −23.8188 | −0.794845 | ||||||||
\(899\) | −3.44150 | −0.114781 | ||||||||
\(900\) | 7.47565 | 0.249188 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 37.0351 | 1.23313 | ||||||||
\(903\) | −30.0892 | −1.00130 | ||||||||
\(904\) | 11.4338 | 0.380281 | ||||||||
\(905\) | −71.8444 | −2.38819 | ||||||||
\(906\) | 11.7510 | 0.390402 | ||||||||
\(907\) | −55.5722 | −1.84525 | −0.922623 | − | 0.385704i | \(-0.873959\pi\) | ||||
−0.922623 | + | 0.385704i | \(0.873959\pi\) | |||||||
\(908\) | 6.06418 | 0.201247 | ||||||||
\(909\) | 0.921274 | 0.0305567 | ||||||||
\(910\) | 49.3465 | 1.63582 | ||||||||
\(911\) | 49.0506 | 1.62512 | 0.812559 | − | 0.582879i | \(-0.198074\pi\) | ||||
0.812559 | + | 0.582879i | \(0.198074\pi\) | |||||||
\(912\) | 4.36959 | 0.144691 | ||||||||
\(913\) | −9.78737 | −0.323915 | ||||||||
\(914\) | 21.4662 | 0.710037 | ||||||||
\(915\) | 22.0446 | 0.728771 | ||||||||
\(916\) | 8.56624 | 0.283036 | ||||||||
\(917\) | −3.54725 | −0.117140 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2020 | −0.501469 | −0.250734 | − | 0.968056i | \(-0.580672\pi\) | ||||
−0.250734 | + | 0.968056i | \(0.580672\pi\) | |||||||
\(920\) | −21.1925 | −0.698697 | ||||||||
\(921\) | −2.90673 | −0.0957799 | ||||||||
\(922\) | 16.8898 | 0.556236 | ||||||||
\(923\) | 49.6459 | 1.63411 | ||||||||
\(924\) | −8.12061 | −0.267149 | ||||||||
\(925\) | −76.3424 | −2.51012 | ||||||||
\(926\) | 3.75784 | 0.123490 | ||||||||
\(927\) | −16.9736 | −0.557486 | ||||||||
\(928\) | −4.80066 | −0.157589 | ||||||||
\(929\) | −22.8966 | −0.751214 | −0.375607 | − | 0.926779i | \(-0.622566\pi\) | ||||
−0.375607 | + | 0.926779i | \(0.622566\pi\) | |||||||
\(930\) | 2.53209 | 0.0830305 | ||||||||
\(931\) | −2.66901 | −0.0874731 | ||||||||
\(932\) | −12.2121 | −0.400022 | ||||||||
\(933\) | −13.0351 | −0.426749 | ||||||||
\(934\) | −12.4311 | −0.406757 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.06418 | −0.165528 | ||||||||
\(937\) | 3.34554 | 0.109294 | 0.0546470 | − | 0.998506i | \(-0.482597\pi\) | ||||
0.0546470 | + | 0.998506i | \(0.482597\pi\) | |||||||
\(938\) | −15.6560 | −0.511187 | ||||||||
\(939\) | 3.22163 | 0.105134 | ||||||||
\(940\) | −18.1830 | −0.593065 | ||||||||
\(941\) | −11.5877 | −0.377748 | −0.188874 | − | 0.982001i | \(-0.560484\pi\) | ||||
−0.188874 | + | 0.982001i | \(0.560484\pi\) | |||||||
\(942\) | −3.51754 | −0.114608 | ||||||||
\(943\) | 75.4903 | 2.45830 | ||||||||
\(944\) | 5.53209 | 0.180054 | ||||||||
\(945\) | 9.74422 | 0.316980 | ||||||||
\(946\) | −32.1046 | −1.04381 | ||||||||
\(947\) | −33.6792 | −1.09443 | −0.547214 | − | 0.836993i | \(-0.684312\pi\) | ||||
−0.547214 | + | 0.836993i | \(0.684312\pi\) | |||||||
\(948\) | −6.61856 | −0.214961 | ||||||||
\(949\) | 45.7897 | 1.48640 | ||||||||
\(950\) | 32.6655 | 1.05981 | ||||||||
\(951\) | −19.0838 | −0.618834 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.9655 | −0.452388 | −0.226194 | − | 0.974082i | \(-0.572628\pi\) | ||||
−0.226194 | + | 0.974082i | \(0.572628\pi\) | |||||||
\(954\) | −4.57398 | −0.148088 | ||||||||
\(955\) | −55.2627 | −1.78826 | ||||||||
\(956\) | 11.8716 | 0.383956 | ||||||||
\(957\) | −14.1310 | −0.456792 | ||||||||
\(958\) | 11.6905 | 0.377702 | ||||||||
\(959\) | 6.53714 | 0.211095 | ||||||||
\(960\) | 3.53209 | 0.113998 | ||||||||
\(961\) | −30.4861 | −0.983422 | ||||||||
\(962\) | 51.7161 | 1.66739 | ||||||||
\(963\) | 3.08647 | 0.0994600 | ||||||||
\(964\) | 23.9172 | 0.770320 | ||||||||
\(965\) | 36.2790 | 1.16786 | ||||||||
\(966\) | −16.5526 | −0.532572 | ||||||||
\(967\) | 47.0515 | 1.51307 | 0.756537 | − | 0.653951i | \(-0.226890\pi\) | ||||
0.756537 | + | 0.653951i | \(0.226890\pi\) | |||||||
\(968\) | 2.33544 | 0.0750638 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 38.9495 | 1.25059 | ||||||||
\(971\) | 30.2044 | 0.969305 | 0.484653 | − | 0.874707i | \(-0.338946\pi\) | ||||
0.484653 | + | 0.874707i | \(0.338946\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −15.5757 | −0.499335 | ||||||||
\(974\) | −7.33544 | −0.235043 | ||||||||
\(975\) | −37.8580 | −1.21243 | ||||||||
\(976\) | 6.24123 | 0.199777 | ||||||||
\(977\) | 12.4534 | 0.398418 | 0.199209 | − | 0.979957i | \(-0.436163\pi\) | ||||
0.199209 | + | 0.979957i | \(0.436163\pi\) | |||||||
\(978\) | 6.32501 | 0.202251 | ||||||||
\(979\) | 40.7464 | 1.30226 | ||||||||
\(980\) | −2.15745 | −0.0689173 | ||||||||
\(981\) | 2.24123 | 0.0715570 | ||||||||
\(982\) | −2.27126 | −0.0724788 | ||||||||
\(983\) | −42.9769 | −1.37075 | −0.685375 | − | 0.728190i | \(-0.740362\pi\) | ||||
−0.685375 | + | 0.728190i | \(0.740362\pi\) | |||||||
\(984\) | −12.5817 | −0.401091 | ||||||||
\(985\) | −30.8340 | −0.982453 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.2020 | −0.452056 | ||||||||
\(988\) | −22.1284 | −0.703997 | ||||||||
\(989\) | −65.4404 | −2.08088 | ||||||||
\(990\) | 10.3969 | 0.330436 | ||||||||
\(991\) | 9.24123 | 0.293557 | 0.146779 | − | 0.989169i | \(-0.453109\pi\) | ||||
0.146779 | + | 0.989169i | \(0.453109\pi\) | |||||||
\(992\) | 0.716881 | 0.0227610 | ||||||||
\(993\) | −3.43376 | −0.108967 | ||||||||
\(994\) | −27.0452 | −0.857821 | ||||||||
\(995\) | 59.6647 | 1.89150 | ||||||||
\(996\) | 3.32501 | 0.105357 | ||||||||
\(997\) | −28.2567 | −0.894899 | −0.447450 | − | 0.894309i | \(-0.647668\pi\) | ||||
−0.447450 | + | 0.894309i | \(0.647668\pi\) | |||||||
\(998\) | −9.71957 | −0.307668 | ||||||||
\(999\) | 10.2121 | 0.323098 |
(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 | 1734.2.a.p.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 5202.2.a.bp.1.3 | 3 | |||
17.2 | even | 8 | 1734.2.f.n.1483.3 | 12 | |||
17.4 | even | 4 | 1734.2.b.j.577.6 | 6 | |||
17.8 | even | 8 | 1734.2.f.n.829.4 | 12 | |||
17.9 | even | 8 | 1734.2.f.n.829.3 | 12 | |||
17.13 | even | 4 | 1734.2.b.j.577.1 | 6 | |||
17.15 | even | 8 | 1734.2.f.n.1483.4 | 12 | |||
17.16 | even | 2 | 1734.2.a.q.1.3 | yes | 3 | ||
51.50 | odd | 2 | 5202.2.a.bm.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1734.2.a.p.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1734.2.a.q.1.3 | yes | 3 | 17.16 | even | 2 | ||
1734.2.b.j.577.1 | 6 | 17.13 | even | 4 | |||
1734.2.b.j.577.6 | 6 | 17.4 | even | 4 | |||
1734.2.f.n.829.3 | 12 | 17.9 | even | 8 | |||
1734.2.f.n.829.4 | 12 | 17.8 | even | 8 | |||
1734.2.f.n.1483.3 | 12 | 17.2 | even | 8 | |||
1734.2.f.n.1483.4 | 12 | 17.15 | even | 8 | |||
5202.2.a.bm.1.1 | 3 | 51.50 | odd | 2 | |||
5202.2.a.bp.1.3 | 3 | 3.2 | odd | 2 |