Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 3 x^{10} + 41 x^{9} - 11 x^{8} - 123 x^{7} + 44 x^{6} + 159 x^{5} - 39 x^{4} - 71 x^{3} + 16 x^{2} + 7 x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 889) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(-1.77927\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.77927 | 1.96524 | 0.982621 | − | 0.185625i | \(-0.0594311\pi\) | ||||
0.982621 | + | 0.185625i | \(0.0594311\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.72435 | 2.86217 | ||||||||
\(5\) | 1.30046 | 0.581582 | 0.290791 | − | 0.956787i | \(-0.406082\pi\) | ||||
0.290791 | + | 0.956787i | \(0.406082\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 10.3510 | 3.65962 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.61432 | 1.14295 | ||||||||
\(11\) | −1.22388 | −0.369015 | −0.184507 | − | 0.982831i | \(-0.559069\pi\) | ||||
−0.184507 | + | 0.982831i | \(0.559069\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.99365 | 0.552939 | 0.276470 | − | 0.961023i | \(-0.410835\pi\) | ||||
0.276470 | + | 0.961023i | \(0.410835\pi\) | |||||||
\(14\) | 2.77927 | 0.742791 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 17.3194 | 4.32986 | ||||||||
\(17\) | −3.84365 | −0.932223 | −0.466112 | − | 0.884726i | \(-0.654345\pi\) | ||||
−0.466112 | + | 0.884726i | \(0.654345\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.61093 | −1.74607 | −0.873033 | − | 0.487661i | \(-0.837850\pi\) | ||||
−0.873033 | + | 0.487661i | \(0.837850\pi\) | |||||||
\(20\) | 7.44427 | 1.66459 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.40150 | −0.725203 | ||||||||
\(23\) | 5.59005 | 1.16561 | 0.582803 | − | 0.812613i | \(-0.301956\pi\) | ||||
0.582803 | + | 0.812613i | \(0.301956\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.30881 | −0.661762 | ||||||||
\(26\) | 5.54090 | 1.08666 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 5.72435 | 1.08180 | ||||||||
\(29\) | 1.90776 | 0.354263 | 0.177131 | − | 0.984187i | \(-0.443318\pi\) | ||||
0.177131 | + | 0.984187i | \(0.443318\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.73151 | 0.849805 | 0.424903 | − | 0.905239i | \(-0.360308\pi\) | ||||
0.424903 | + | 0.905239i | \(0.360308\pi\) | |||||||
\(32\) | 27.4335 | 4.84960 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.6826 | −1.83204 | ||||||||
\(35\) | 1.30046 | 0.219817 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.21595 | 1.18630 | 0.593148 | − | 0.805094i | \(-0.297885\pi\) | ||||
0.593148 | + | 0.805094i | \(0.297885\pi\) | |||||||
\(38\) | −21.1528 | −3.43144 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.4610 | 2.12837 | ||||||||
\(41\) | 6.26895 | 0.979046 | 0.489523 | − | 0.871990i | \(-0.337171\pi\) | ||||
0.489523 | + | 0.871990i | \(0.337171\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.73579 | 0.264705 | 0.132353 | − | 0.991203i | \(-0.457747\pi\) | ||||
0.132353 | + | 0.991203i | \(0.457747\pi\) | |||||||
\(44\) | −7.00593 | −1.05618 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.5363 | 2.29070 | ||||||||
\(47\) | 3.16118 | 0.461106 | 0.230553 | − | 0.973060i | \(-0.425946\pi\) | ||||
0.230553 | + | 0.973060i | \(0.425946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −9.19608 | −1.30052 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 11.4123 | 1.58261 | ||||||||
\(53\) | 0.926242 | 0.127229 | 0.0636146 | − | 0.997975i | \(-0.479737\pi\) | ||||
0.0636146 | + | 0.997975i | \(0.479737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.59161 | −0.214612 | ||||||||
\(56\) | 10.3510 | 1.38321 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.30219 | 0.696211 | ||||||||
\(59\) | 4.37513 | 0.569593 | 0.284796 | − | 0.958588i | \(-0.408074\pi\) | ||||
0.284796 | + | 0.958588i | \(0.408074\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.05486 | −1.03132 | −0.515660 | − | 0.856793i | \(-0.672453\pi\) | ||||
−0.515660 | + | 0.856793i | \(0.672453\pi\) | |||||||
\(62\) | 13.1502 | 1.67007 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 41.6062 | 5.20078 | ||||||||
\(65\) | 2.59266 | 0.321580 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.47559 | −0.180273 | −0.0901363 | − | 0.995929i | \(-0.528730\pi\) | ||||
−0.0901363 | + | 0.995929i | \(0.528730\pi\) | |||||||
\(68\) | −22.0024 | −2.66818 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.61432 | 0.431994 | ||||||||
\(71\) | 8.77195 | 1.04104 | 0.520520 | − | 0.853850i | \(-0.325738\pi\) | ||||
0.520520 | + | 0.853850i | \(0.325738\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.71314 | −0.200508 | −0.100254 | − | 0.994962i | \(-0.531966\pi\) | ||||
−0.100254 | + | 0.994962i | \(0.531966\pi\) | |||||||
\(74\) | 20.0551 | 2.33136 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −43.5676 | −4.99754 | ||||||||
\(77\) | −1.22388 | −0.139474 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.14825 | 0.579223 | 0.289612 | − | 0.957144i | \(-0.406474\pi\) | ||||
0.289612 | + | 0.957144i | \(0.406474\pi\) | |||||||
\(80\) | 22.5232 | 2.51817 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 17.4231 | 1.92406 | ||||||||
\(83\) | −6.39753 | −0.702220 | −0.351110 | − | 0.936334i | \(-0.614196\pi\) | ||||
−0.351110 | + | 0.936334i | \(0.614196\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.99851 | −0.542164 | ||||||||
\(86\) | 4.82423 | 0.520210 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.6684 | −1.35045 | ||||||||
\(89\) | 6.15316 | 0.652234 | 0.326117 | − | 0.945329i | \(-0.394260\pi\) | ||||
0.326117 | + | 0.945329i | \(0.394260\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.99365 | 0.208991 | ||||||||
\(92\) | 31.9994 | 3.33617 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.78579 | 0.906185 | ||||||||
\(95\) | −9.89768 | −1.01548 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.84875 | −0.999989 | −0.499995 | − | 0.866029i | \(-0.666665\pi\) | ||||
−0.499995 | + | 0.866029i | \(0.666665\pi\) | |||||||
\(98\) | 2.77927 | 0.280749 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −18.9408 | −1.89408 | ||||||||
\(101\) | 17.3913 | 1.73050 | 0.865250 | − | 0.501340i | \(-0.167159\pi\) | ||||
0.865250 | + | 0.501340i | \(0.167159\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.13951 | −0.604943 | −0.302472 | − | 0.953158i | \(-0.597812\pi\) | ||||
−0.302472 | + | 0.953158i | \(0.597812\pi\) | |||||||
\(104\) | 20.6362 | 2.02355 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.57428 | 0.250036 | ||||||||
\(107\) | 10.7901 | 1.04312 | 0.521559 | − | 0.853215i | \(-0.325350\pi\) | ||||
0.521559 | + | 0.853215i | \(0.325350\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.4321 | −1.38234 | −0.691170 | − | 0.722692i | \(-0.742905\pi\) | ||||
−0.691170 | + | 0.722692i | \(0.742905\pi\) | |||||||
\(110\) | −4.42351 | −0.421765 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 17.3194 | 1.63653 | ||||||||
\(113\) | −19.2485 | −1.81075 | −0.905375 | − | 0.424614i | \(-0.860410\pi\) | ||||
−0.905375 | + | 0.424614i | \(0.860410\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.26962 | 0.677896 | ||||||||
\(116\) | 10.9207 | 1.01396 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.1597 | 1.11939 | ||||||||
\(119\) | −3.84365 | −0.352347 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.50211 | −0.863828 | ||||||||
\(122\) | −22.3866 | −2.02679 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 27.0848 | 2.43229 | ||||||||
\(125\) | −10.8053 | −0.966451 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | 60.7679 | 5.37118 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.20570 | 0.631981 | ||||||||
\(131\) | −10.2834 | −0.898468 | −0.449234 | − | 0.893414i | \(-0.648303\pi\) | ||||
−0.449234 | + | 0.893414i | \(0.648303\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.61093 | −0.659951 | ||||||||
\(134\) | −4.10108 | −0.354279 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −39.7855 | −3.41158 | ||||||||
\(137\) | 14.7634 | 1.26132 | 0.630661 | − | 0.776058i | \(-0.282784\pi\) | ||||
0.630661 | + | 0.776058i | \(0.282784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.4741 | −1.65177 | −0.825885 | − | 0.563838i | \(-0.809324\pi\) | ||||
−0.825885 | + | 0.563838i | \(0.809324\pi\) | |||||||
\(140\) | 7.44427 | 0.629155 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 24.3796 | 2.04589 | ||||||||
\(143\) | −2.44000 | −0.204043 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.48096 | 0.206033 | ||||||||
\(146\) | −4.76128 | −0.394047 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 41.3066 | 3.39538 | ||||||||
\(149\) | 7.55089 | 0.618593 | 0.309296 | − | 0.950966i | \(-0.399906\pi\) | ||||
0.309296 | + | 0.950966i | \(0.399906\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.1272 | −1.88206 | −0.941032 | − | 0.338318i | \(-0.890142\pi\) | ||||
−0.941032 | + | 0.338318i | \(0.890142\pi\) | |||||||
\(152\) | −78.7804 | −6.38994 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.40150 | −0.274101 | ||||||||
\(155\) | 6.15313 | 0.494231 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3630 | 1.30591 | 0.652954 | − | 0.757398i | \(-0.273530\pi\) | ||||
0.652954 | + | 0.757398i | \(0.273530\pi\) | |||||||
\(158\) | 14.3084 | 1.13831 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 35.6761 | 2.82044 | ||||||||
\(161\) | 5.59005 | 0.440558 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.4504 | −1.52347 | −0.761737 | − | 0.647886i | \(-0.775653\pi\) | ||||
−0.761737 | + | 0.647886i | \(0.775653\pi\) | |||||||
\(164\) | 35.8857 | 2.80220 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.7805 | −1.38003 | ||||||||
\(167\) | −21.8043 | −1.68726 | −0.843632 | − | 0.536922i | \(-0.819587\pi\) | ||||
−0.843632 | + | 0.536922i | \(0.819587\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.02536 | −0.694258 | ||||||||
\(170\) | −13.8922 | −1.06548 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.93625 | 0.757632 | ||||||||
\(173\) | −10.1178 | −0.769239 | −0.384620 | − | 0.923075i | \(-0.625667\pi\) | ||||
−0.384620 | + | 0.923075i | \(0.625667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.30881 | −0.250123 | ||||||||
\(176\) | −21.1970 | −1.59778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.1013 | 1.28180 | ||||||||
\(179\) | 5.76419 | 0.430836 | 0.215418 | − | 0.976522i | \(-0.430889\pi\) | ||||
0.215418 | + | 0.976522i | \(0.430889\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4234 | 0.774763 | 0.387382 | − | 0.921919i | \(-0.373380\pi\) | ||||
0.387382 | + | 0.921919i | \(0.373380\pi\) | |||||||
\(182\) | 5.54090 | 0.410718 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 57.8624 | 4.26568 | ||||||||
\(185\) | 9.38404 | 0.689928 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.70418 | 0.344004 | ||||||||
\(188\) | 18.0957 | 1.31977 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −27.5083 | −1.99567 | ||||||||
\(191\) | −18.9663 | −1.37235 | −0.686176 | − | 0.727436i | \(-0.740712\pi\) | ||||
−0.686176 | + | 0.727436i | \(0.740712\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.5961 | −0.906688 | −0.453344 | − | 0.891336i | \(-0.649769\pi\) | ||||
−0.453344 | + | 0.891336i | \(0.649769\pi\) | |||||||
\(194\) | −27.3723 | −1.96522 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.72435 | 0.408882 | ||||||||
\(197\) | −4.25793 | −0.303365 | −0.151682 | − | 0.988429i | \(-0.548469\pi\) | ||||
−0.151682 | + | 0.988429i | \(0.548469\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0155 | 0.780867 | 0.390433 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390433 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(200\) | −34.2494 | −2.42180 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 48.3352 | 3.40085 | ||||||||
\(203\) | 1.90776 | 0.133899 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.15250 | 0.569396 | ||||||||
\(206\) | −17.0633 | −1.18886 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 34.5289 | 2.39415 | ||||||||
\(209\) | 9.31489 | 0.644324 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.1891 | 1.32103 | 0.660515 | − | 0.750813i | \(-0.270338\pi\) | ||||
0.660515 | + | 0.750813i | \(0.270338\pi\) | |||||||
\(212\) | 5.30213 | 0.364152 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 29.9886 | 2.04998 | ||||||||
\(215\) | 2.25732 | 0.153948 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.73151 | 0.321196 | ||||||||
\(218\) | −40.1106 | −2.71663 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.11091 | −0.614258 | ||||||||
\(221\) | −7.66290 | −0.515463 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.8093 | −0.991704 | −0.495852 | − | 0.868407i | \(-0.665144\pi\) | ||||
−0.495852 | + | 0.868407i | \(0.665144\pi\) | |||||||
\(224\) | 27.4335 | 1.83298 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −53.4969 | −3.55856 | ||||||||
\(227\) | 1.08703 | 0.0721487 | 0.0360743 | − | 0.999349i | \(-0.488515\pi\) | ||||
0.0360743 | + | 0.999349i | \(0.488515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −29.8776 | −1.97437 | −0.987185 | − | 0.159580i | \(-0.948986\pi\) | ||||
−0.987185 | + | 0.159580i | \(0.948986\pi\) | |||||||
\(230\) | 20.2043 | 1.33223 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.7472 | 1.29647 | ||||||||
\(233\) | −12.5209 | −0.820274 | −0.410137 | − | 0.912024i | \(-0.634519\pi\) | ||||
−0.410137 | + | 0.912024i | \(0.634519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.11098 | 0.268171 | ||||||||
\(236\) | 25.0447 | 1.63027 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.6826 | −0.692447 | ||||||||
\(239\) | 13.5100 | 0.873891 | 0.436946 | − | 0.899488i | \(-0.356060\pi\) | ||||
0.436946 | + | 0.899488i | \(0.356060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.97228 | 0.255877 | 0.127939 | − | 0.991782i | \(-0.459164\pi\) | ||||
0.127939 | + | 0.991782i | \(0.459164\pi\) | |||||||
\(242\) | −26.4089 | −1.69763 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −46.1088 | −2.95181 | ||||||||
\(245\) | 1.30046 | 0.0830832 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.1735 | −0.965469 | ||||||||
\(248\) | 48.9757 | 3.10996 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −30.0307 | −1.89931 | ||||||||
\(251\) | −16.6044 | −1.04806 | −0.524029 | − | 0.851701i | \(-0.675572\pi\) | ||||
−0.524029 | + | 0.851701i | \(0.675572\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.84157 | −0.430126 | ||||||||
\(254\) | 2.77927 | 0.174387 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 85.6781 | 5.35488 | ||||||||
\(257\) | −17.9690 | −1.12088 | −0.560438 | − | 0.828197i | \(-0.689367\pi\) | ||||
−0.560438 | + | 0.828197i | \(0.689367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.21595 | 0.448378 | ||||||||
\(260\) | 14.8413 | 0.920416 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −28.5805 | −1.76571 | ||||||||
\(263\) | 7.18373 | 0.442968 | 0.221484 | − | 0.975164i | \(-0.428910\pi\) | ||||
0.221484 | + | 0.975164i | \(0.428910\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.20454 | 0.0739942 | ||||||||
\(266\) | −21.1528 | −1.29696 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.44681 | −0.515971 | ||||||||
\(269\) | −15.3889 | −0.938280 | −0.469140 | − | 0.883124i | \(-0.655436\pi\) | ||||
−0.469140 | + | 0.883124i | \(0.655436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.1037 | −1.46419 | −0.732096 | − | 0.681201i | \(-0.761458\pi\) | ||||
−0.732096 | + | 0.681201i | \(0.761458\pi\) | |||||||
\(272\) | −66.5700 | −4.03640 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 41.0315 | 2.47880 | ||||||||
\(275\) | 4.04960 | 0.244200 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 27.5990 | 1.65826 | 0.829132 | − | 0.559053i | \(-0.188835\pi\) | ||||
0.829132 | + | 0.559053i | \(0.188835\pi\) | |||||||
\(278\) | −54.1238 | −3.24613 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 13.4610 | 0.804448 | ||||||||
\(281\) | −5.36018 | −0.319762 | −0.159881 | − | 0.987136i | \(-0.551111\pi\) | ||||
−0.159881 | + | 0.987136i | \(0.551111\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.46356 | −0.384219 | −0.192109 | − | 0.981374i | \(-0.561533\pi\) | ||||
−0.192109 | + | 0.981374i | \(0.561533\pi\) | |||||||
\(284\) | 50.2137 | 2.97963 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.78141 | −0.400993 | ||||||||
\(287\) | 6.26895 | 0.370045 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.22632 | −0.130960 | ||||||||
\(290\) | 6.89527 | 0.404904 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.80662 | −0.573889 | ||||||||
\(293\) | 7.99366 | 0.466995 | 0.233497 | − | 0.972357i | \(-0.424983\pi\) | ||||
0.233497 | + | 0.972357i | \(0.424983\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.68966 | 0.331265 | ||||||||
\(296\) | 74.6921 | 4.34139 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 20.9860 | 1.21568 | ||||||||
\(299\) | 11.1446 | 0.644510 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.73579 | 0.100049 | ||||||||
\(302\) | −64.2767 | −3.69871 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −131.817 | −7.56022 | ||||||||
\(305\) | −10.4750 | −0.599797 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.0044 | 0.628053 | 0.314026 | − | 0.949414i | \(-0.398322\pi\) | ||||
0.314026 | + | 0.949414i | \(0.398322\pi\) | |||||||
\(308\) | −7.00593 | −0.399200 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 17.1012 | 0.971284 | ||||||||
\(311\) | −7.25990 | −0.411671 | −0.205836 | − | 0.978587i | \(-0.565991\pi\) | ||||
−0.205836 | + | 0.978587i | \(0.565991\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.5487 | 1.21800 | 0.609001 | − | 0.793169i | \(-0.291571\pi\) | ||||
0.609001 | + | 0.793169i | \(0.291571\pi\) | |||||||
\(314\) | 45.4771 | 2.56642 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 29.4704 | 1.65784 | ||||||||
\(317\) | −19.3937 | −1.08926 | −0.544628 | − | 0.838677i | \(-0.683329\pi\) | ||||
−0.544628 | + | 0.838677i | \(0.683329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.33488 | −0.130728 | ||||||||
\(320\) | 54.1071 | 3.02468 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 15.5363 | 0.865803 | ||||||||
\(323\) | 29.2538 | 1.62772 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.59661 | −0.365914 | ||||||||
\(326\) | −54.0580 | −2.99399 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 64.8897 | 3.58293 | ||||||||
\(329\) | 3.16118 | 0.174282 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.1563 | 1.71250 | 0.856252 | − | 0.516559i | \(-0.172787\pi\) | ||||
0.856252 | + | 0.516559i | \(0.172787\pi\) | |||||||
\(332\) | −36.6216 | −2.00987 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −60.5999 | −3.31588 | ||||||||
\(335\) | −1.91895 | −0.104843 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.6388 | −1.61453 | −0.807264 | − | 0.590190i | \(-0.799053\pi\) | ||||
−0.807264 | + | 0.590190i | \(0.799053\pi\) | |||||||
\(338\) | −25.0839 | −1.36438 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −28.6132 | −1.55177 | ||||||||
\(341\) | −5.79082 | −0.313591 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 17.9671 | 0.968720 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −28.1200 | −1.51174 | ||||||||
\(347\) | 2.89297 | 0.155303 | 0.0776514 | − | 0.996981i | \(-0.475258\pi\) | ||||
0.0776514 | + | 0.996981i | \(0.475258\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.62684 | 0.461784 | 0.230892 | − | 0.972979i | \(-0.425836\pi\) | ||||
0.230892 | + | 0.972979i | \(0.425836\pi\) | |||||||
\(350\) | −9.19608 | −0.491551 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −33.5754 | −1.78957 | ||||||||
\(353\) | −29.3126 | −1.56015 | −0.780077 | − | 0.625684i | \(-0.784820\pi\) | ||||
−0.780077 | + | 0.625684i | \(0.784820\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.4075 | 0.605450 | ||||||||
\(356\) | 35.2228 | 1.86681 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.0203 | 0.846697 | ||||||||
\(359\) | 29.4378 | 1.55367 | 0.776833 | − | 0.629707i | \(-0.216825\pi\) | ||||
0.776833 | + | 0.629707i | \(0.216825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 38.9262 | 2.04875 | ||||||||
\(362\) | 28.9694 | 1.52260 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 11.4123 | 0.598169 | ||||||||
\(365\) | −2.22787 | −0.116612 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.0234964 | 0.00122650 | 0.000613251 | − | 1.00000i | \(-0.499805\pi\) | ||||
0.000613251 | 1.00000i | \(0.499805\pi\) | ||||||||
\(368\) | 96.8166 | 5.04691 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.0808 | 1.35588 | ||||||||
\(371\) | 0.926242 | 0.0480881 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.413267 | 0.0213982 | 0.0106991 | − | 0.999943i | \(-0.496594\pi\) | ||||
0.0106991 | + | 0.999943i | \(0.496594\pi\) | |||||||
\(374\) | 13.0742 | 0.676051 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 32.7213 | 1.68747 | ||||||||
\(377\) | 3.80341 | 0.195886 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.7696 | −0.655928 | −0.327964 | − | 0.944690i | \(-0.606362\pi\) | ||||
−0.327964 | + | 0.944690i | \(0.606362\pi\) | |||||||
\(380\) | −56.6578 | −2.90648 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −52.7124 | −2.69700 | ||||||||
\(383\) | 21.2538 | 1.08602 | 0.543009 | − | 0.839727i | \(-0.317285\pi\) | ||||
0.543009 | + | 0.839727i | \(0.317285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.59161 | −0.0811159 | ||||||||
\(386\) | −35.0080 | −1.78186 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −56.3777 | −2.86214 | ||||||||
\(389\) | 0.127498 | 0.00646441 | 0.00323220 | − | 0.999995i | \(-0.498971\pi\) | ||||
0.00323220 | + | 0.999995i | \(0.498971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.4862 | −1.08661 | ||||||||
\(392\) | 10.3510 | 0.522803 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −11.8339 | −0.596185 | ||||||||
\(395\) | 6.69508 | 0.336866 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.42114 | −0.322268 | −0.161134 | − | 0.986933i | \(-0.551515\pi\) | ||||
−0.161134 | + | 0.986933i | \(0.551515\pi\) | |||||||
\(398\) | 30.6150 | 1.53459 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −57.3068 | −2.86534 | ||||||||
\(401\) | −31.3010 | −1.56310 | −0.781549 | − | 0.623843i | \(-0.785570\pi\) | ||||
−0.781549 | + | 0.623843i | \(0.785570\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.43299 | 0.469891 | ||||||||
\(404\) | 99.5539 | 4.95299 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.30219 | 0.263143 | ||||||||
\(407\) | −8.83149 | −0.437760 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.1486 | 1.58965 | 0.794824 | − | 0.606841i | \(-0.207563\pi\) | ||||
0.794824 | + | 0.606841i | \(0.207563\pi\) | |||||||
\(410\) | 22.6580 | 1.11900 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −35.1447 | −1.73145 | ||||||||
\(413\) | 4.37513 | 0.215286 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.31971 | −0.408398 | ||||||||
\(416\) | 54.6928 | 2.68154 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.8886 | 1.26625 | ||||||||
\(419\) | −30.9045 | −1.50978 | −0.754892 | − | 0.655849i | \(-0.772311\pi\) | ||||
−0.754892 | + | 0.655849i | \(0.772311\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.57947 | −0.466875 | −0.233437 | − | 0.972372i | \(-0.574997\pi\) | ||||
−0.233437 | + | 0.972372i | \(0.574997\pi\) | |||||||
\(422\) | 53.3316 | 2.59614 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.58750 | 0.465610 | ||||||||
\(425\) | 12.7179 | 0.616910 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.05486 | −0.389802 | ||||||||
\(428\) | 61.7663 | 2.98559 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.27370 | 0.302545 | ||||||||
\(431\) | 31.9913 | 1.54097 | 0.770483 | − | 0.637461i | \(-0.220015\pi\) | ||||
0.770483 | + | 0.637461i | \(0.220015\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.2429 | 0.876697 | 0.438349 | − | 0.898805i | \(-0.355564\pi\) | ||||
0.438349 | + | 0.898805i | \(0.355564\pi\) | |||||||
\(434\) | 13.1502 | 0.631228 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −82.6141 | −3.95650 | ||||||||
\(437\) | −42.5455 | −2.03523 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.4213 | 1.73829 | 0.869146 | − | 0.494556i | \(-0.164669\pi\) | ||||
0.869146 | + | 0.494556i | \(0.164669\pi\) | |||||||
\(440\) | −16.4747 | −0.785399 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.2973 | −1.01301 | ||||||||
\(443\) | 20.3418 | 0.966468 | 0.483234 | − | 0.875491i | \(-0.339462\pi\) | ||||
0.483234 | + | 0.875491i | \(0.339462\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.00193 | 0.379328 | ||||||||
\(446\) | −41.1590 | −1.94894 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 41.6062 | 1.96571 | ||||||||
\(449\) | 8.60191 | 0.405949 | 0.202975 | − | 0.979184i | \(-0.434939\pi\) | ||||
0.202975 | + | 0.979184i | \(0.434939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.67247 | −0.361282 | ||||||||
\(452\) | −110.185 | −5.18268 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.02115 | 0.141790 | ||||||||
\(455\) | 2.59266 | 0.121546 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.0041 | 1.16964 | 0.584821 | − | 0.811163i | \(-0.301165\pi\) | ||||
0.584821 | + | 0.811163i | \(0.301165\pi\) | |||||||
\(458\) | −83.0381 | −3.88011 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 41.6138 | 1.94026 | ||||||||
\(461\) | −27.0304 | −1.25893 | −0.629465 | − | 0.777029i | \(-0.716726\pi\) | ||||
−0.629465 | + | 0.777029i | \(0.716726\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.2177 | 0.707228 | 0.353614 | − | 0.935391i | \(-0.384953\pi\) | ||||
0.353614 | + | 0.935391i | \(0.384953\pi\) | |||||||
\(464\) | 33.0414 | 1.53391 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −34.7991 | −1.61204 | ||||||||
\(467\) | 0.539310 | 0.0249563 | 0.0124781 | − | 0.999922i | \(-0.496028\pi\) | ||||
0.0124781 | + | 0.999922i | \(0.496028\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.47559 | −0.0681366 | ||||||||
\(470\) | 11.4255 | 0.527021 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 45.2868 | 2.08449 | ||||||||
\(473\) | −2.12440 | −0.0976801 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.1831 | 1.15548 | ||||||||
\(476\) | −22.0024 | −1.00848 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 37.5480 | 1.71741 | ||||||||
\(479\) | 22.5610 | 1.03084 | 0.515420 | − | 0.856938i | \(-0.327636\pi\) | ||||
0.515420 | + | 0.856938i | \(0.327636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.3861 | 0.655949 | ||||||||
\(482\) | 11.0400 | 0.502860 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −54.3934 | −2.47243 | ||||||||
\(485\) | −12.8079 | −0.581576 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.8681 | 1.39877 | 0.699383 | − | 0.714747i | \(-0.253458\pi\) | ||||
0.699383 | + | 0.714747i | \(0.253458\pi\) | |||||||
\(488\) | −83.3756 | −3.77424 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.61432 | 0.163278 | ||||||||
\(491\) | −7.14793 | −0.322582 | −0.161291 | − | 0.986907i | \(-0.551566\pi\) | ||||
−0.161291 | + | 0.986907i | \(0.551566\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.33278 | −0.330252 | ||||||||
\(494\) | −42.1713 | −1.89738 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 81.9472 | 3.67954 | ||||||||
\(497\) | 8.77195 | 0.393476 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.21761 | 0.278338 | 0.139169 | − | 0.990269i | \(-0.455557\pi\) | ||||
0.139169 | + | 0.990269i | \(0.455557\pi\) | |||||||
\(500\) | −61.8530 | −2.76615 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −46.1480 | −2.05969 | ||||||||
\(503\) | 33.1941 | 1.48005 | 0.740026 | − | 0.672579i | \(-0.234813\pi\) | ||||
0.740026 | + | 0.672579i | \(0.234813\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.6167 | 1.00643 | ||||||||
\(506\) | −19.0146 | −0.845301 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.72435 | 0.253977 | ||||||||
\(509\) | −39.3796 | −1.74547 | −0.872736 | − | 0.488193i | \(-0.837656\pi\) | ||||
−0.872736 | + | 0.488193i | \(0.837656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.71314 | −0.0757849 | ||||||||
\(512\) | 116.587 | 5.15246 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −49.9407 | −2.20279 | ||||||||
\(515\) | −7.98416 | −0.351824 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.86892 | −0.170155 | ||||||||
\(518\) | 20.0551 | 0.881170 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 26.8365 | 1.17686 | ||||||||
\(521\) | 13.6202 | 0.596714 | 0.298357 | − | 0.954454i | \(-0.403561\pi\) | ||||
0.298357 | + | 0.954454i | \(0.403561\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −38.5952 | −1.68765 | −0.843826 | − | 0.536617i | \(-0.819702\pi\) | ||||
−0.843826 | + | 0.536617i | \(0.819702\pi\) | |||||||
\(524\) | −58.8660 | −2.57157 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.9655 | 0.870539 | ||||||||
\(527\) | −18.1863 | −0.792208 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.24869 | 0.358639 | ||||||||
\(530\) | 3.34774 | 0.145416 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −43.5676 | −1.88889 | ||||||||
\(533\) | 12.4981 | 0.541353 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0321 | 0.606659 | ||||||||
\(536\) | −15.2738 | −0.659729 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −42.7700 | −1.84395 | ||||||||
\(539\) | −1.22388 | −0.0527164 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.36149 | 0.316495 | 0.158248 | − | 0.987399i | \(-0.449416\pi\) | ||||
0.158248 | + | 0.987399i | \(0.449416\pi\) | |||||||
\(542\) | −66.9906 | −2.87749 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −105.445 | −4.52091 | ||||||||
\(545\) | −18.7683 | −0.803945 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.7632 | −1.31534 | −0.657669 | − | 0.753307i | \(-0.728458\pi\) | ||||
−0.657669 | + | 0.753307i | \(0.728458\pi\) | |||||||
\(548\) | 84.5108 | 3.61012 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.2549 | 0.479912 | ||||||||
\(551\) | −14.5198 | −0.618566 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.14825 | 0.218926 | ||||||||
\(554\) | 76.7051 | 3.25889 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −111.476 | −4.72765 | ||||||||
\(557\) | −3.54294 | −0.150119 | −0.0750595 | − | 0.997179i | \(-0.523915\pi\) | ||||
−0.0750595 | + | 0.997179i | \(0.523915\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.46056 | 0.146366 | ||||||||
\(560\) | 22.5232 | 0.951779 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.8974 | −0.628409 | ||||||||
\(563\) | 4.73790 | 0.199679 | 0.0998394 | − | 0.995004i | \(-0.468167\pi\) | ||||
0.0998394 | + | 0.995004i | \(0.468167\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.0319 | −1.05310 | ||||||||
\(566\) | −17.9640 | −0.755083 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 90.7982 | 3.80981 | ||||||||
\(569\) | −0.229871 | −0.00963669 | −0.00481834 | − | 0.999988i | \(-0.501534\pi\) | ||||
−0.00481834 | + | 0.999988i | \(0.501534\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.08679 | −0.296573 | −0.148286 | − | 0.988944i | \(-0.547376\pi\) | ||||
−0.148286 | + | 0.988944i | \(0.547376\pi\) | |||||||
\(572\) | −13.9674 | −0.584006 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 17.4231 | 0.727227 | ||||||||
\(575\) | −18.4964 | −0.771354 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.3215 | 1.84513 | 0.922563 | − | 0.385846i | \(-0.126090\pi\) | ||||
0.922563 | + | 0.385846i | \(0.126090\pi\) | |||||||
\(578\) | −6.18755 | −0.257368 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.2019 | 0.589701 | ||||||||
\(581\) | −6.39753 | −0.265414 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.13361 | −0.0469494 | ||||||||
\(584\) | −17.7327 | −0.733783 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 22.2166 | 0.917758 | ||||||||
\(587\) | −41.7718 | −1.72411 | −0.862053 | − | 0.506817i | \(-0.830822\pi\) | ||||
−0.862053 | + | 0.506817i | \(0.830822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −36.0112 | −1.48382 | ||||||||
\(590\) | 15.8131 | 0.651016 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 124.976 | 5.13649 | ||||||||
\(593\) | 19.4400 | 0.798304 | 0.399152 | − | 0.916885i | \(-0.369305\pi\) | ||||
0.399152 | + | 0.916885i | \(0.369305\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.99851 | −0.204919 | ||||||||
\(596\) | 43.2239 | 1.77052 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 30.9739 | 1.26662 | ||||||||
\(599\) | −0.285281 | −0.0116563 | −0.00582813 | − | 0.999983i | \(-0.501855\pi\) | ||||
−0.00582813 | + | 0.999983i | \(0.501855\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.41769 | −0.302574 | −0.151287 | − | 0.988490i | \(-0.548342\pi\) | ||||
−0.151287 | + | 0.988490i | \(0.548342\pi\) | |||||||
\(602\) | 4.82423 | 0.196621 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −132.388 | −5.38679 | ||||||||
\(605\) | −12.3571 | −0.502387 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −27.5980 | −1.12017 | −0.560084 | − | 0.828436i | \(-0.689231\pi\) | ||||
−0.560084 | + | 0.828436i | \(0.689231\pi\) | |||||||
\(608\) | −208.794 | −8.46773 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −29.1129 | −1.17875 | ||||||||
\(611\) | 6.30230 | 0.254964 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.7794 | −1.36434 | −0.682169 | − | 0.731194i | \(-0.738963\pi\) | ||||
−0.682169 | + | 0.731194i | \(0.738963\pi\) | |||||||
\(614\) | 30.5841 | 1.23428 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.6684 | −0.510423 | ||||||||
\(617\) | 31.6964 | 1.27605 | 0.638024 | − | 0.770017i | \(-0.279752\pi\) | ||||
0.638024 | + | 0.770017i | \(0.279752\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.48718 | −0.0597747 | −0.0298874 | − | 0.999553i | \(-0.509515\pi\) | ||||
−0.0298874 | + | 0.999553i | \(0.509515\pi\) | |||||||
\(620\) | 35.2227 | 1.41458 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.1772 | −0.809033 | ||||||||
\(623\) | 6.15316 | 0.246521 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.49229 | 0.0996914 | ||||||||
\(626\) | 59.8895 | 2.39367 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 93.6673 | 3.73773 | ||||||||
\(629\) | −27.7356 | −1.10589 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.35865 | 0.253134 | 0.126567 | − | 0.991958i | \(-0.459604\pi\) | ||||
0.126567 | + | 0.991958i | \(0.459604\pi\) | |||||||
\(632\) | 53.2894 | 2.11974 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −53.9002 | −2.14065 | ||||||||
\(635\) | 1.30046 | 0.0516071 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.99365 | 0.0789913 | ||||||||
\(638\) | −6.48926 | −0.256912 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 79.0261 | 3.12378 | ||||||||
\(641\) | −17.6050 | −0.695357 | −0.347678 | − | 0.937614i | \(-0.613030\pi\) | ||||
−0.347678 | + | 0.937614i | \(0.613030\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.1486 | 1.38612 | 0.693062 | − | 0.720878i | \(-0.256261\pi\) | ||||
0.693062 | + | 0.720878i | \(0.256261\pi\) | |||||||
\(644\) | 31.9994 | 1.26095 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 81.3042 | 3.19887 | ||||||||
\(647\) | 21.8303 | 0.858239 | 0.429120 | − | 0.903248i | \(-0.358824\pi\) | ||||
0.429120 | + | 0.903248i | \(0.358824\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.35464 | −0.210188 | ||||||||
\(650\) | −18.3338 | −0.719110 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −111.341 | −4.36045 | ||||||||
\(653\) | 23.8766 | 0.934364 | 0.467182 | − | 0.884161i | \(-0.345269\pi\) | ||||
0.467182 | + | 0.884161i | \(0.345269\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.3732 | −0.522533 | ||||||||
\(656\) | 108.575 | 4.23913 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.78579 | 0.342506 | ||||||||
\(659\) | 12.8713 | 0.501393 | 0.250697 | − | 0.968066i | \(-0.419340\pi\) | ||||
0.250697 | + | 0.968066i | \(0.419340\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.331054 | 0.0128765 | 0.00643826 | − | 0.999979i | \(-0.497951\pi\) | ||||
0.00643826 | + | 0.999979i | \(0.497951\pi\) | |||||||
\(662\) | 86.5917 | 3.36548 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −66.2206 | −2.56986 | ||||||||
\(665\) | −9.89768 | −0.383816 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.6645 | 0.412931 | ||||||||
\(668\) | −124.815 | −4.82924 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.33327 | −0.206042 | ||||||||
\(671\) | 9.85821 | 0.380572 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 46.1771 | 1.78000 | 0.889998 | − | 0.455965i | \(-0.150706\pi\) | ||||
0.889998 | + | 0.455965i | \(0.150706\pi\) | |||||||
\(674\) | −82.3743 | −3.17294 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −51.6643 | −1.98709 | ||||||||
\(677\) | 15.5181 | 0.596408 | 0.298204 | − | 0.954502i | \(-0.403612\pi\) | ||||
0.298204 | + | 0.954502i | \(0.403612\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.84875 | −0.377960 | ||||||||
\(680\) | −51.7394 | −1.98411 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −16.0943 | −0.616281 | ||||||||
\(683\) | 30.6461 | 1.17264 | 0.586319 | − | 0.810080i | \(-0.300576\pi\) | ||||
0.586319 | + | 0.810080i | \(0.300576\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 19.1992 | 0.733563 | ||||||||
\(686\) | 2.77927 | 0.106113 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.0629 | 1.14614 | ||||||||
\(689\) | 1.84660 | 0.0703500 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.6963 | 1.51012 | 0.755060 | − | 0.655656i | \(-0.227608\pi\) | ||||
0.755060 | + | 0.655656i | \(0.227608\pi\) | |||||||
\(692\) | −57.9176 | −2.20170 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.04035 | 0.305208 | ||||||||
\(695\) | −25.3252 | −0.960640 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0957 | −0.912689 | ||||||||
\(698\) | 23.9763 | 0.907517 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −18.9408 | −0.715894 | ||||||||
\(701\) | 27.9108 | 1.05417 | 0.527087 | − | 0.849811i | \(-0.323284\pi\) | ||||
0.527087 | + | 0.849811i | \(0.323284\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −54.9201 | −2.07135 | ||||||||
\(704\) | −50.9211 | −1.91916 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −81.4677 | −3.06608 | ||||||||
\(707\) | 17.3913 | 0.654068 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29.9459 | −1.12464 | −0.562320 | − | 0.826920i | \(-0.690091\pi\) | ||||
−0.562320 | + | 0.826920i | \(0.690091\pi\) | |||||||
\(710\) | 31.7047 | 1.18985 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 63.6912 | 2.38693 | ||||||||
\(713\) | 26.4494 | 0.990538 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.17311 | −0.118668 | ||||||||
\(716\) | 32.9962 | 1.23313 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 81.8155 | 3.05333 | ||||||||
\(719\) | 10.8582 | 0.404944 | 0.202472 | − | 0.979288i | \(-0.435103\pi\) | ||||
0.202472 | + | 0.979288i | \(0.435103\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.13951 | −0.228647 | ||||||||
\(722\) | 108.186 | 4.02628 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 59.6670 | 2.21751 | ||||||||
\(725\) | −6.31242 | −0.234438 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.9620 | −1.11123 | −0.555614 | − | 0.831440i | \(-0.687517\pi\) | ||||
−0.555614 | + | 0.831440i | \(0.687517\pi\) | |||||||
\(728\) | 20.6362 | 0.764829 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.19185 | −0.229171 | ||||||||
\(731\) | −6.67177 | −0.246764 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.30193 | −0.232767 | −0.116384 | − | 0.993204i | \(-0.537130\pi\) | ||||
−0.116384 | + | 0.993204i | \(0.537130\pi\) | |||||||
\(734\) | 0.0653029 | 0.00241037 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 153.355 | 5.65273 | ||||||||
\(737\) | 1.80596 | 0.0665232 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.3572 | 0.748851 | 0.374425 | − | 0.927257i | \(-0.377840\pi\) | ||||
0.374425 | + | 0.927257i | \(0.377840\pi\) | |||||||
\(740\) | 53.7175 | 1.97469 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.57428 | 0.0945047 | ||||||||
\(743\) | −22.8445 | −0.838082 | −0.419041 | − | 0.907967i | \(-0.637634\pi\) | ||||
−0.419041 | + | 0.907967i | \(0.637634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.81961 | 0.359763 | ||||||||
\(746\) | 1.14858 | 0.0420526 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 26.9284 | 0.984599 | ||||||||
\(749\) | 10.7901 | 0.394262 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.4377 | −0.818763 | −0.409382 | − | 0.912363i | \(-0.634256\pi\) | ||||
−0.409382 | + | 0.912363i | \(0.634256\pi\) | |||||||
\(752\) | 54.7499 | 1.99653 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.5707 | 0.384963 | ||||||||
\(755\) | −30.0759 | −1.09457 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.2552 | −1.42675 | −0.713377 | − | 0.700781i | \(-0.752835\pi\) | ||||
−0.713377 | + | 0.700781i | \(0.752835\pi\) | |||||||
\(758\) | −35.4900 | −1.28906 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −102.451 | −3.71627 | ||||||||
\(761\) | 33.9943 | 1.23229 | 0.616147 | − | 0.787631i | \(-0.288693\pi\) | ||||
0.616147 | + | 0.787631i | \(0.288693\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.4321 | −0.522476 | ||||||||
\(764\) | −108.570 | −3.92791 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 59.0701 | 2.13429 | ||||||||
\(767\) | 8.72247 | 0.314950 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.2905 | −1.56109 | −0.780547 | − | 0.625097i | \(-0.785059\pi\) | ||||
−0.780547 | + | 0.625097i | \(0.785059\pi\) | |||||||
\(770\) | −4.42351 | −0.159412 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −72.1045 | −2.59510 | ||||||||
\(773\) | −49.0758 | −1.76513 | −0.882567 | − | 0.470186i | \(-0.844187\pi\) | ||||
−0.882567 | + | 0.470186i | \(0.844187\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.6557 | −0.562369 | ||||||||
\(776\) | −101.944 | −3.65958 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.354352 | 0.0127041 | ||||||||
\(779\) | −47.7125 | −1.70948 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.7358 | −0.384159 | ||||||||
\(782\) | −59.7161 | −2.13544 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17.3194 | 0.618552 | ||||||||
\(785\) | 21.2793 | 0.759492 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.0838 | 0.822847 | 0.411424 | − | 0.911444i | \(-0.365032\pi\) | ||||
0.411424 | + | 0.911444i | \(0.365032\pi\) | |||||||
\(788\) | −24.3738 | −0.868282 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 18.6074 | 0.662023 | ||||||||
\(791\) | −19.2485 | −0.684399 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.0586 | −0.570257 | ||||||||
\(794\) | −17.8461 | −0.633334 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 63.0564 | 2.23498 | ||||||||
\(797\) | 39.3361 | 1.39336 | 0.696679 | − | 0.717383i | \(-0.254660\pi\) | ||||
0.696679 | + | 0.717383i | \(0.254660\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.1505 | −0.429854 | ||||||||
\(800\) | −90.7722 | −3.20928 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −86.9940 | −3.07187 | ||||||||
\(803\) | 2.09669 | 0.0739904 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.26962 | 0.256221 | ||||||||
\(806\) | 26.2168 | 0.923448 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 180.017 | 6.33297 | ||||||||
\(809\) | 14.6267 | 0.514248 | 0.257124 | − | 0.966378i | \(-0.417225\pi\) | ||||
0.257124 | + | 0.966378i | \(0.417225\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −26.4080 | −0.927311 | −0.463656 | − | 0.886015i | \(-0.653463\pi\) | ||||
−0.463656 | + | 0.886015i | \(0.653463\pi\) | |||||||
\(812\) | 10.9207 | 0.383241 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −24.5451 | −0.860305 | ||||||||
\(815\) | −25.2944 | −0.886026 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.2110 | −0.462193 | ||||||||
\(818\) | 89.3497 | 3.12404 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 46.6678 | 1.62971 | ||||||||
\(821\) | 8.01626 | 0.279769 | 0.139885 | − | 0.990168i | \(-0.455327\pi\) | ||||
0.139885 | + | 0.990168i | \(0.455327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.1365 | −1.01564 | −0.507818 | − | 0.861465i | \(-0.669548\pi\) | ||||
−0.507818 | + | 0.861465i | \(0.669548\pi\) | |||||||
\(824\) | −63.5498 | −2.21386 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.1597 | 0.423089 | ||||||||
\(827\) | 11.0859 | 0.385495 | 0.192748 | − | 0.981248i | \(-0.438260\pi\) | ||||
0.192748 | + | 0.981248i | \(0.438260\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.10638 | 0.212083 | 0.106042 | − | 0.994362i | \(-0.466182\pi\) | ||||
0.106042 | + | 0.994362i | \(0.466182\pi\) | |||||||
\(830\) | −23.1227 | −0.802601 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 82.9483 | 2.87571 | ||||||||
\(833\) | −3.84365 | −0.133175 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −28.3555 | −0.981283 | ||||||||
\(836\) | 53.3216 | 1.84417 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −85.8920 | −2.96709 | ||||||||
\(839\) | 36.9264 | 1.27484 | 0.637421 | − | 0.770516i | \(-0.280001\pi\) | ||||
0.637421 | + | 0.770516i | \(0.280001\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.3604 | −0.874498 | ||||||||
\(842\) | −26.6239 | −0.917521 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 109.845 | 3.78101 | ||||||||
\(845\) | −11.7371 | −0.403768 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.50211 | −0.326496 | ||||||||
\(848\) | 16.0420 | 0.550885 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 35.3466 | 1.21238 | ||||||||
\(851\) | 40.3376 | 1.38275 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.10893 | 0.174926 | 0.0874632 | − | 0.996168i | \(-0.472124\pi\) | ||||
0.0874632 | + | 0.996168i | \(0.472124\pi\) | |||||||
\(854\) | −22.3866 | −0.766055 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 111.688 | 3.81742 | ||||||||
\(857\) | 0.0840423 | 0.00287083 | 0.00143541 | − | 0.999999i | \(-0.499543\pi\) | ||||
0.00143541 | + | 0.999999i | \(0.499543\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.9612 | 1.26110 | 0.630550 | − | 0.776149i | \(-0.282829\pi\) | ||||
0.630550 | + | 0.776149i | \(0.282829\pi\) | |||||||
\(860\) | 12.9217 | 0.440625 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 88.9124 | 3.02837 | ||||||||
\(863\) | 9.69124 | 0.329894 | 0.164947 | − | 0.986302i | \(-0.447255\pi\) | ||||
0.164947 | + | 0.986302i | \(0.447255\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.1577 | −0.447376 | ||||||||
\(866\) | 50.7019 | 1.72292 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 27.0848 | 0.919319 | ||||||||
\(869\) | −6.30086 | −0.213742 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.94182 | −0.0996797 | ||||||||
\(872\) | −149.386 | −5.05884 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −118.245 | −3.99971 | ||||||||
\(875\) | −10.8053 | −0.365284 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.7769 | 1.57954 | 0.789772 | − | 0.613400i | \(-0.210199\pi\) | ||||
0.789772 | + | 0.613400i | \(0.210199\pi\) | |||||||
\(878\) | 101.225 | 3.41616 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −27.5658 | −0.929242 | ||||||||
\(881\) | −41.5070 | −1.39841 | −0.699203 | − | 0.714924i | \(-0.746461\pi\) | ||||
−0.699203 | + | 0.714924i | \(0.746461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.0657 | −0.877181 | −0.438590 | − | 0.898687i | \(-0.644522\pi\) | ||||
−0.438590 | + | 0.898687i | \(0.644522\pi\) | |||||||
\(884\) | −43.8651 | −1.47534 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 56.5353 | 1.89934 | ||||||||
\(887\) | −1.81271 | −0.0608647 | −0.0304324 | − | 0.999537i | \(-0.509688\pi\) | ||||
−0.0304324 | + | 0.999537i | \(0.509688\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | 22.2395 | 0.745470 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −84.7735 | −2.83843 | ||||||||
\(893\) | −24.0595 | −0.805122 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.49609 | 0.250567 | ||||||||
\(896\) | 60.7679 | 2.03011 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 23.9070 | 0.797788 | ||||||||
\(899\) | 9.02660 | 0.301054 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.56016 | −0.118606 | ||||||||
\(902\) | −21.3239 | −0.710007 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −199.241 | −6.62665 | ||||||||
\(905\) | 13.5552 | 0.450588 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.56696 | 0.0852344 | 0.0426172 | − | 0.999091i | \(-0.486430\pi\) | ||||
0.0426172 | + | 0.999091i | \(0.486430\pi\) | |||||||
\(908\) | 6.22253 | 0.206502 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.20570 | 0.238867 | ||||||||
\(911\) | −39.1665 | −1.29764 | −0.648822 | − | 0.760940i | \(-0.724738\pi\) | ||||
−0.648822 | + | 0.760940i | \(0.724738\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.82982 | 0.259129 | ||||||||
\(914\) | 69.4931 | 2.29863 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −171.030 | −5.65099 | ||||||||
\(917\) | −10.2834 | −0.339589 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.749666 | 0.0247292 | 0.0123646 | − | 0.999924i | \(-0.496064\pi\) | ||||
0.0123646 | + | 0.999924i | \(0.496064\pi\) | |||||||
\(920\) | 75.2476 | 2.48084 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −75.1248 | −2.47410 | ||||||||
\(923\) | 17.4882 | 0.575631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.8762 | −0.785045 | ||||||||
\(926\) | 42.2942 | 1.38987 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 52.3366 | 1.71803 | ||||||||
\(929\) | −2.66217 | −0.0873428 | −0.0436714 | − | 0.999046i | \(-0.513905\pi\) | ||||
−0.0436714 | + | 0.999046i | \(0.513905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.61093 | −0.249438 | ||||||||
\(932\) | −71.6742 | −2.34777 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.49889 | 0.0490451 | ||||||||
\(935\) | 6.11759 | 0.200067 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.03927 | −0.131957 | −0.0659787 | − | 0.997821i | \(-0.521017\pi\) | ||||
−0.0659787 | + | 0.997821i | \(0.521017\pi\) | |||||||
\(938\) | −4.10108 | −0.133905 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 23.5327 | 0.767552 | ||||||||
\(941\) | −45.3228 | −1.47748 | −0.738740 | − | 0.673990i | \(-0.764579\pi\) | ||||
−0.738740 | + | 0.673990i | \(0.764579\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 35.0438 | 1.14118 | ||||||||
\(944\) | 75.7747 | 2.46626 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.90429 | −0.191965 | ||||||||
\(947\) | 42.7254 | 1.38839 | 0.694195 | − | 0.719787i | \(-0.255761\pi\) | ||||
0.694195 | + | 0.719787i | \(0.255761\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.41541 | −0.110869 | ||||||||
\(950\) | 69.9907 | 2.27080 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −39.7855 | −1.28946 | ||||||||
\(953\) | 16.1878 | 0.524375 | 0.262188 | − | 0.965017i | \(-0.415556\pi\) | ||||
0.262188 | + | 0.965017i | \(0.415556\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.6648 | −0.798135 | ||||||||
\(956\) | 77.3361 | 2.50123 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 62.7032 | 2.02585 | ||||||||
\(959\) | 14.7634 | 0.476735 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.61277 | −0.277831 | ||||||||
\(962\) | 39.9828 | 1.28910 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.7387 | 0.732365 | ||||||||
\(965\) | −16.3807 | −0.527314 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.4936 | −0.659030 | −0.329515 | − | 0.944150i | \(-0.606885\pi\) | ||||
−0.329515 | + | 0.944150i | \(0.606885\pi\) | |||||||
\(968\) | −98.3560 | −3.16128 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −35.5966 | −1.14294 | ||||||||
\(971\) | −18.7588 | −0.601997 | −0.300999 | − | 0.953625i | \(-0.597320\pi\) | ||||
−0.300999 | + | 0.953625i | \(0.597320\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.4741 | −0.624311 | ||||||||
\(974\) | 85.7907 | 2.74891 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −139.506 | −4.46547 | ||||||||
\(977\) | −27.9229 | −0.893331 | −0.446666 | − | 0.894701i | \(-0.647389\pi\) | ||||
−0.446666 | + | 0.894701i | \(0.647389\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.53075 | −0.240684 | ||||||||
\(980\) | 7.44427 | 0.237798 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.8660 | −0.633951 | ||||||||
\(983\) | −17.0824 | −0.544845 | −0.272423 | − | 0.962178i | \(-0.587825\pi\) | ||||
−0.272423 | + | 0.962178i | \(0.587825\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.53725 | −0.176431 | ||||||||
\(986\) | −20.3798 | −0.649024 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −86.8585 | −2.76334 | ||||||||
\(989\) | 9.70315 | 0.308542 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.7507 | −0.436804 | −0.218402 | − | 0.975859i | \(-0.570084\pi\) | ||||
−0.218402 | + | 0.975859i | \(0.570084\pi\) | |||||||
\(992\) | 129.802 | 4.12122 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.3796 | 0.773275 | ||||||||
\(995\) | 14.3252 | 0.454138 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.83250 | 0.311398 | 0.155699 | − | 0.987805i | \(-0.450237\pi\) | ||||
0.155699 | + | 0.987805i | \(0.450237\pi\) | |||||||
\(998\) | 17.2804 | 0.547002 | ||||||||
\(999\) | 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 | 8001.2.a.n.1.12 | 12 | ||
3.2 | odd | 2 | 889.2.a.a.1.1 | ✓ | 12 | ||
21.20 | even | 2 | 6223.2.a.i.1.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
889.2.a.a.1.1 | ✓ | 12 | 3.2 | odd | 2 | ||
6223.2.a.i.1.1 | 12 | 21.20 | even | 2 | |||
8001.2.a.n.1.12 | 12 | 1.1 | even | 1 | trivial |