Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(67.6332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.14896\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.14896 | 0.663353 | 0.331677 | − | 0.943393i | \(-0.392386\pi\) | ||||
0.331677 | + | 0.943393i | \(0.392386\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.14896 | 0.469061 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.67989 | −0.559963 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.14896 | 0.331677 | ||||||||
\(13\) | −3.79720 | −1.05315 | −0.526577 | − | 0.850127i | \(-0.676525\pi\) | ||||
−0.526577 | + | 0.850127i | \(0.676525\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.14896 | 0.296660 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.47709 | −1.57093 | −0.785463 | − | 0.618909i | \(-0.787575\pi\) | ||||
−0.785463 | + | 0.618909i | \(0.787575\pi\) | |||||||
\(18\) | −1.67989 | −0.395953 | ||||||||
\(19\) | −2.67989 | −0.614809 | −0.307404 | − | 0.951579i | \(-0.599460\pi\) | ||||
−0.307404 | + | 0.951579i | \(0.599460\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.14896 | 0.250724 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.65626 | 0.553869 | 0.276934 | − | 0.960889i | \(-0.410682\pi\) | ||||
0.276934 | + | 0.960889i | \(0.410682\pi\) | |||||||
\(24\) | 1.14896 | 0.234531 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −3.79720 | −0.744693 | ||||||||
\(27\) | −5.37701 | −1.03481 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −0.386922 | −0.0718497 | −0.0359248 | − | 0.999354i | \(-0.511438\pi\) | ||||
−0.0359248 | + | 0.999354i | \(0.511438\pi\) | |||||||
\(30\) | 1.14896 | 0.209771 | ||||||||
\(31\) | −6.01867 | −1.08099 | −0.540493 | − | 0.841349i | \(-0.681762\pi\) | ||||
−0.540493 | + | 0.841349i | \(0.681762\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.47709 | −1.11081 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −1.67989 | −0.279981 | ||||||||
\(37\) | 2.38692 | 0.392408 | 0.196204 | − | 0.980563i | \(-0.437139\pi\) | ||||
0.196204 | + | 0.980563i | \(0.437139\pi\) | |||||||
\(38\) | −2.67989 | −0.434735 | ||||||||
\(39\) | −4.36284 | −0.698613 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −9.47709 | −1.48007 | −0.740037 | − | 0.672567i | \(-0.765192\pi\) | ||||
−0.740037 | + | 0.672567i | \(0.765192\pi\) | |||||||
\(42\) | 1.14896 | 0.177289 | ||||||||
\(43\) | 4.66428 | 0.711296 | 0.355648 | − | 0.934620i | \(-0.384260\pi\) | ||||
0.355648 | + | 0.934620i | \(0.384260\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.67989 | −0.250423 | ||||||||
\(46\) | 2.65626 | 0.391644 | ||||||||
\(47\) | −4.48205 | −0.653774 | −0.326887 | − | 0.945063i | \(-0.606000\pi\) | ||||
−0.326887 | + | 0.945063i | \(0.606000\pi\) | |||||||
\(48\) | 1.14896 | 0.165838 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −7.44193 | −1.04208 | ||||||||
\(52\) | −3.79720 | −0.526577 | ||||||||
\(53\) | −5.09819 | −0.700290 | −0.350145 | − | 0.936695i | \(-0.613868\pi\) | ||||
−0.350145 | + | 0.936695i | \(0.613868\pi\) | |||||||
\(54\) | −5.37701 | −0.731718 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −3.07909 | −0.407835 | ||||||||
\(58\) | −0.386922 | −0.0508054 | ||||||||
\(59\) | 4.74643 | 0.617933 | 0.308966 | − | 0.951073i | \(-0.400017\pi\) | ||||
0.308966 | + | 0.951073i | \(0.400017\pi\) | |||||||
\(60\) | 1.14896 | 0.148330 | ||||||||
\(61\) | −11.6593 | −1.49282 | −0.746412 | − | 0.665484i | \(-0.768225\pi\) | ||||
−0.746412 | + | 0.665484i | \(0.768225\pi\) | |||||||
\(62\) | −6.01867 | −0.764372 | ||||||||
\(63\) | −1.67989 | −0.211646 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.79720 | −0.470985 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.71316 | 0.697974 | 0.348987 | − | 0.937128i | \(-0.386526\pi\) | ||||
0.348987 | + | 0.937128i | \(0.386526\pi\) | |||||||
\(68\) | −6.47709 | −0.785463 | ||||||||
\(69\) | 3.05194 | 0.367411 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 3.33119 | 0.395340 | 0.197670 | − | 0.980269i | \(-0.436663\pi\) | ||||
0.197670 | + | 0.980269i | \(0.436663\pi\) | |||||||
\(72\) | −1.67989 | −0.197977 | ||||||||
\(73\) | −15.0127 | −1.75710 | −0.878552 | − | 0.477646i | \(-0.841490\pi\) | ||||
−0.878552 | + | 0.477646i | \(0.841490\pi\) | |||||||
\(74\) | 2.38692 | 0.277474 | ||||||||
\(75\) | 1.14896 | 0.132671 | ||||||||
\(76\) | −2.67989 | −0.307404 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.36284 | −0.493994 | ||||||||
\(79\) | 6.03633 | 0.679141 | 0.339570 | − | 0.940581i | \(-0.389718\pi\) | ||||
0.339570 | + | 0.940581i | \(0.389718\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −1.13831 | −0.126479 | ||||||||
\(82\) | −9.47709 | −1.04657 | ||||||||
\(83\) | 11.1551 | 1.22443 | 0.612215 | − | 0.790691i | \(-0.290279\pi\) | ||||
0.612215 | + | 0.790691i | \(0.290279\pi\) | |||||||
\(84\) | 1.14896 | 0.125362 | ||||||||
\(85\) | −6.47709 | −0.702539 | ||||||||
\(86\) | 4.66428 | 0.502962 | ||||||||
\(87\) | −0.444559 | −0.0476617 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.87277 | −0.622513 | −0.311256 | − | 0.950326i | \(-0.600750\pi\) | ||||
−0.311256 | + | 0.950326i | \(0.600750\pi\) | |||||||
\(90\) | −1.67989 | −0.177076 | ||||||||
\(91\) | −3.79720 | −0.398055 | ||||||||
\(92\) | 2.65626 | 0.276934 | ||||||||
\(93\) | −6.91522 | −0.717075 | ||||||||
\(94\) | −4.48205 | −0.462288 | ||||||||
\(95\) | −2.67989 | −0.274951 | ||||||||
\(96\) | 1.14896 | 0.117265 | ||||||||
\(97\) | −3.30450 | −0.335522 | −0.167761 | − | 0.985828i | \(-0.553654\pi\) | ||||
−0.167761 | + | 0.985828i | \(0.553654\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.56420 | 0.553658 | 0.276829 | − | 0.960919i | \(-0.410716\pi\) | ||||
0.276829 | + | 0.960919i | \(0.410716\pi\) | |||||||
\(102\) | −7.44193 | −0.736861 | ||||||||
\(103\) | −7.95988 | −0.784310 | −0.392155 | − | 0.919899i | \(-0.628270\pi\) | ||||
−0.392155 | + | 0.919899i | \(0.628270\pi\) | |||||||
\(104\) | −3.79720 | −0.372346 | ||||||||
\(105\) | 1.14896 | 0.112127 | ||||||||
\(106\) | −5.09819 | −0.495180 | ||||||||
\(107\) | 17.4244 | 1.68448 | 0.842241 | − | 0.539100i | \(-0.181236\pi\) | ||||
0.842241 | + | 0.539100i | \(0.181236\pi\) | |||||||
\(108\) | −5.37701 | −0.517403 | ||||||||
\(109\) | −4.92398 | −0.471631 | −0.235816 | − | 0.971798i | \(-0.575776\pi\) | ||||
−0.235816 | + | 0.971798i | \(0.575776\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.74248 | 0.260305 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −11.3824 | −1.07077 | −0.535383 | − | 0.844609i | \(-0.679833\pi\) | ||||
−0.535383 | + | 0.844609i | \(0.679833\pi\) | |||||||
\(114\) | −3.07909 | −0.288383 | ||||||||
\(115\) | 2.65626 | 0.247698 | ||||||||
\(116\) | −0.386922 | −0.0359248 | ||||||||
\(117\) | 6.37888 | 0.589728 | ||||||||
\(118\) | 4.74643 | 0.436944 | ||||||||
\(119\) | −6.47709 | −0.593754 | ||||||||
\(120\) | 1.14896 | 0.104885 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −11.6593 | −1.05559 | ||||||||
\(123\) | −10.8888 | −0.981811 | ||||||||
\(124\) | −6.01867 | −0.540493 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.67989 | −0.149656 | ||||||||
\(127\) | 1.43724 | 0.127534 | 0.0637671 | − | 0.997965i | \(-0.479689\pi\) | ||||
0.0637671 | + | 0.997965i | \(0.479689\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 5.35908 | 0.471841 | ||||||||
\(130\) | −3.79720 | −0.333037 | ||||||||
\(131\) | −19.5165 | −1.70516 | −0.852582 | − | 0.522594i | \(-0.824964\pi\) | ||||
−0.852582 | + | 0.522594i | \(0.824964\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.67989 | −0.232376 | ||||||||
\(134\) | 5.71316 | 0.493542 | ||||||||
\(135\) | −5.37701 | −0.462779 | ||||||||
\(136\) | −6.47709 | −0.555406 | ||||||||
\(137\) | 18.9809 | 1.62165 | 0.810823 | − | 0.585292i | \(-0.199020\pi\) | ||||
0.810823 | + | 0.585292i | \(0.199020\pi\) | |||||||
\(138\) | 3.05194 | 0.259799 | ||||||||
\(139\) | −6.58593 | −0.558611 | −0.279306 | − | 0.960202i | \(-0.590104\pi\) | ||||
−0.279306 | + | 0.960202i | \(0.590104\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | −5.14970 | −0.433683 | ||||||||
\(142\) | 3.33119 | 0.279548 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.67989 | −0.139991 | ||||||||
\(145\) | −0.386922 | −0.0321321 | ||||||||
\(146\) | −15.0127 | −1.24246 | ||||||||
\(147\) | 1.14896 | 0.0947647 | ||||||||
\(148\) | 2.38692 | 0.196204 | ||||||||
\(149\) | −10.1138 | −0.828554 | −0.414277 | − | 0.910151i | \(-0.635966\pi\) | ||||
−0.414277 | + | 0.910151i | \(0.635966\pi\) | |||||||
\(150\) | 1.14896 | 0.0938123 | ||||||||
\(151\) | 11.8335 | 0.963000 | 0.481500 | − | 0.876446i | \(-0.340092\pi\) | ||||
0.481500 | + | 0.876446i | \(0.340092\pi\) | |||||||
\(152\) | −2.67989 | −0.217368 | ||||||||
\(153\) | 10.8808 | 0.879660 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.01867 | −0.483431 | ||||||||
\(156\) | −4.36284 | −0.349307 | ||||||||
\(157\) | 1.69054 | 0.134920 | 0.0674599 | − | 0.997722i | \(-0.478511\pi\) | ||||
0.0674599 | + | 0.997722i | \(0.478511\pi\) | |||||||
\(158\) | 6.03633 | 0.480225 | ||||||||
\(159\) | −5.85762 | −0.464540 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.65626 | 0.209343 | ||||||||
\(162\) | −1.13831 | −0.0894341 | ||||||||
\(163\) | −8.06159 | −0.631432 | −0.315716 | − | 0.948854i | \(-0.602245\pi\) | ||||
−0.315716 | + | 0.948854i | \(0.602245\pi\) | |||||||
\(164\) | −9.47709 | −0.740037 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.1551 | 0.865803 | ||||||||
\(167\) | −16.2178 | −1.25497 | −0.627487 | − | 0.778627i | \(-0.715916\pi\) | ||||
−0.627487 | + | 0.778627i | \(0.715916\pi\) | |||||||
\(168\) | 1.14896 | 0.0886443 | ||||||||
\(169\) | 1.41876 | 0.109135 | ||||||||
\(170\) | −6.47709 | −0.496770 | ||||||||
\(171\) | 4.50191 | 0.344270 | ||||||||
\(172\) | 4.66428 | 0.355648 | ||||||||
\(173\) | −12.1600 | −0.924511 | −0.462255 | − | 0.886747i | \(-0.652960\pi\) | ||||
−0.462255 | + | 0.886747i | \(0.652960\pi\) | |||||||
\(174\) | −0.444559 | −0.0337019 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.45347 | 0.409908 | ||||||||
\(178\) | −5.87277 | −0.440183 | ||||||||
\(179\) | −23.3033 | −1.74177 | −0.870886 | − | 0.491486i | \(-0.836454\pi\) | ||||
−0.870886 | + | 0.491486i | \(0.836454\pi\) | |||||||
\(180\) | −1.67989 | −0.125211 | ||||||||
\(181\) | 22.1288 | 1.64482 | 0.822411 | − | 0.568893i | \(-0.192628\pi\) | ||||
0.822411 | + | 0.568893i | \(0.192628\pi\) | |||||||
\(182\) | −3.79720 | −0.281467 | ||||||||
\(183\) | −13.3961 | −0.990269 | ||||||||
\(184\) | 2.65626 | 0.195822 | ||||||||
\(185\) | 2.38692 | 0.175490 | ||||||||
\(186\) | −6.91522 | −0.507048 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.48205 | −0.326887 | ||||||||
\(189\) | −5.37701 | −0.391120 | ||||||||
\(190\) | −2.67989 | −0.194420 | ||||||||
\(191\) | 20.2864 | 1.46787 | 0.733936 | − | 0.679219i | \(-0.237681\pi\) | ||||
0.733936 | + | 0.679219i | \(0.237681\pi\) | |||||||
\(192\) | 1.14896 | 0.0829191 | ||||||||
\(193\) | 3.84508 | 0.276775 | 0.138387 | − | 0.990378i | \(-0.455808\pi\) | ||||
0.138387 | + | 0.990378i | \(0.455808\pi\) | |||||||
\(194\) | −3.30450 | −0.237250 | ||||||||
\(195\) | −4.36284 | −0.312429 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −11.8159 | −0.841846 | −0.420923 | − | 0.907096i | \(-0.638294\pi\) | ||||
−0.420923 | + | 0.907096i | \(0.638294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5496 | 0.889617 | 0.444809 | − | 0.895626i | \(-0.353272\pi\) | ||||
0.444809 | + | 0.895626i | \(0.353272\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 6.56420 | 0.463003 | ||||||||
\(202\) | 5.56420 | 0.391496 | ||||||||
\(203\) | −0.386922 | −0.0271566 | ||||||||
\(204\) | −7.44193 | −0.521039 | ||||||||
\(205\) | −9.47709 | −0.661909 | ||||||||
\(206\) | −7.95988 | −0.554591 | ||||||||
\(207\) | −4.46222 | −0.310146 | ||||||||
\(208\) | −3.79720 | −0.263289 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.14896 | 0.0792859 | ||||||||
\(211\) | −3.99973 | −0.275353 | −0.137676 | − | 0.990477i | \(-0.543963\pi\) | ||||
−0.137676 | + | 0.990477i | \(0.543963\pi\) | |||||||
\(212\) | −5.09819 | −0.350145 | ||||||||
\(213\) | 3.82741 | 0.262250 | ||||||||
\(214\) | 17.4244 | 1.19111 | ||||||||
\(215\) | 4.66428 | 0.318101 | ||||||||
\(216\) | −5.37701 | −0.365859 | ||||||||
\(217\) | −6.01867 | −0.408574 | ||||||||
\(218\) | −4.92398 | −0.333494 | ||||||||
\(219\) | −17.2490 | −1.16558 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.5948 | 1.65443 | ||||||||
\(222\) | 2.74248 | 0.184063 | ||||||||
\(223\) | 17.8782 | 1.19721 | 0.598605 | − | 0.801044i | \(-0.295722\pi\) | ||||
0.598605 | + | 0.801044i | \(0.295722\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −1.67989 | −0.111993 | ||||||||
\(226\) | −11.3824 | −0.757146 | ||||||||
\(227\) | 5.76204 | 0.382440 | 0.191220 | − | 0.981547i | \(-0.438756\pi\) | ||||
0.191220 | + | 0.981547i | \(0.438756\pi\) | |||||||
\(228\) | −3.07909 | −0.203918 | ||||||||
\(229\) | −8.57617 | −0.566729 | −0.283365 | − | 0.959012i | \(-0.591451\pi\) | ||||
−0.283365 | + | 0.959012i | \(0.591451\pi\) | |||||||
\(230\) | 2.65626 | 0.175149 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.386922 | −0.0254027 | ||||||||
\(233\) | −14.4011 | −0.943445 | −0.471723 | − | 0.881747i | \(-0.656368\pi\) | ||||
−0.471723 | + | 0.881747i | \(0.656368\pi\) | |||||||
\(234\) | 6.37888 | 0.417000 | ||||||||
\(235\) | −4.48205 | −0.292377 | ||||||||
\(236\) | 4.74643 | 0.308966 | ||||||||
\(237\) | 6.93551 | 0.450510 | ||||||||
\(238\) | −6.47709 | −0.419848 | ||||||||
\(239\) | 24.0096 | 1.55305 | 0.776527 | − | 0.630084i | \(-0.216980\pi\) | ||||
0.776527 | + | 0.630084i | \(0.216980\pi\) | |||||||
\(240\) | 1.14896 | 0.0741651 | ||||||||
\(241\) | 16.7641 | 1.07987 | 0.539935 | − | 0.841707i | \(-0.318449\pi\) | ||||
0.539935 | + | 0.841707i | \(0.318449\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.8232 | 0.950906 | ||||||||
\(244\) | −11.6593 | −0.746412 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | −10.8888 | −0.694245 | ||||||||
\(247\) | 10.1761 | 0.647489 | ||||||||
\(248\) | −6.01867 | −0.382186 | ||||||||
\(249\) | 12.8168 | 0.812229 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −2.42488 | −0.153057 | −0.0765286 | − | 0.997067i | \(-0.524384\pi\) | ||||
−0.0765286 | + | 0.997067i | \(0.524384\pi\) | |||||||
\(252\) | −1.67989 | −0.105823 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.43724 | 0.0901803 | ||||||||
\(255\) | −7.44193 | −0.466032 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.18367 | 0.323348 | 0.161674 | − | 0.986844i | \(-0.448311\pi\) | ||||
0.161674 | + | 0.986844i | \(0.448311\pi\) | |||||||
\(258\) | 5.35908 | 0.333642 | ||||||||
\(259\) | 2.38692 | 0.148316 | ||||||||
\(260\) | −3.79720 | −0.235493 | ||||||||
\(261\) | 0.649986 | 0.0402331 | ||||||||
\(262\) | −19.5165 | −1.20573 | ||||||||
\(263\) | −20.3770 | −1.25650 | −0.628250 | − | 0.778011i | \(-0.716229\pi\) | ||||
−0.628250 | + | 0.778011i | \(0.716229\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.09819 | −0.313179 | ||||||||
\(266\) | −2.67989 | −0.164314 | ||||||||
\(267\) | −6.74759 | −0.412946 | ||||||||
\(268\) | 5.71316 | 0.348987 | ||||||||
\(269\) | −11.4504 | −0.698143 | −0.349072 | − | 0.937096i | \(-0.613503\pi\) | ||||
−0.349072 | + | 0.937096i | \(0.613503\pi\) | |||||||
\(270\) | −5.37701 | −0.327234 | ||||||||
\(271\) | −14.8199 | −0.900247 | −0.450124 | − | 0.892966i | \(-0.648620\pi\) | ||||
−0.450124 | + | 0.892966i | \(0.648620\pi\) | |||||||
\(272\) | −6.47709 | −0.392731 | ||||||||
\(273\) | −4.36284 | −0.264051 | ||||||||
\(274\) | 18.9809 | 1.14668 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.05194 | 0.183705 | ||||||||
\(277\) | −24.5158 | −1.47301 | −0.736504 | − | 0.676433i | \(-0.763525\pi\) | ||||
−0.736504 | + | 0.676433i | \(0.763525\pi\) | |||||||
\(278\) | −6.58593 | −0.394998 | ||||||||
\(279\) | 10.1107 | 0.605311 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 28.5929 | 1.70571 | 0.852856 | − | 0.522146i | \(-0.174868\pi\) | ||||
0.852856 | + | 0.522146i | \(0.174868\pi\) | |||||||
\(282\) | −5.14970 | −0.306660 | ||||||||
\(283\) | 5.19494 | 0.308807 | 0.154404 | − | 0.988008i | \(-0.450654\pi\) | ||||
0.154404 | + | 0.988008i | \(0.450654\pi\) | |||||||
\(284\) | 3.33119 | 0.197670 | ||||||||
\(285\) | −3.07909 | −0.182389 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.47709 | −0.559415 | ||||||||
\(288\) | −1.67989 | −0.0989884 | ||||||||
\(289\) | 24.9527 | 1.46781 | ||||||||
\(290\) | −0.386922 | −0.0227209 | ||||||||
\(291\) | −3.79675 | −0.222569 | ||||||||
\(292\) | −15.0127 | −0.878552 | ||||||||
\(293\) | −18.2205 | −1.06445 | −0.532225 | − | 0.846603i | \(-0.678644\pi\) | ||||
−0.532225 | + | 0.846603i | \(0.678644\pi\) | |||||||
\(294\) | 1.14896 | 0.0670088 | ||||||||
\(295\) | 4.74643 | 0.276348 | ||||||||
\(296\) | 2.38692 | 0.138737 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.1138 | −0.585876 | ||||||||
\(299\) | −10.0864 | −0.583310 | ||||||||
\(300\) | 1.14896 | 0.0663353 | ||||||||
\(301\) | 4.66428 | 0.268845 | ||||||||
\(302\) | 11.8335 | 0.680944 | ||||||||
\(303\) | 6.39305 | 0.367271 | ||||||||
\(304\) | −2.67989 | −0.153702 | ||||||||
\(305\) | −11.6593 | −0.667611 | ||||||||
\(306\) | 10.8808 | 0.622013 | ||||||||
\(307\) | 10.9710 | 0.626146 | 0.313073 | − | 0.949729i | \(-0.398642\pi\) | ||||
0.313073 | + | 0.949729i | \(0.398642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.14559 | −0.520275 | ||||||||
\(310\) | −6.01867 | −0.341837 | ||||||||
\(311\) | 20.8687 | 1.18335 | 0.591677 | − | 0.806175i | \(-0.298466\pi\) | ||||
0.591677 | + | 0.806175i | \(0.298466\pi\) | |||||||
\(312\) | −4.36284 | −0.246997 | ||||||||
\(313\) | 8.64805 | 0.488817 | 0.244408 | − | 0.969672i | \(-0.421406\pi\) | ||||
0.244408 | + | 0.969672i | \(0.421406\pi\) | |||||||
\(314\) | 1.69054 | 0.0954026 | ||||||||
\(315\) | −1.67989 | −0.0946510 | ||||||||
\(316\) | 6.03633 | 0.339570 | ||||||||
\(317\) | 3.53662 | 0.198636 | 0.0993182 | − | 0.995056i | \(-0.468334\pi\) | ||||
0.0993182 | + | 0.995056i | \(0.468334\pi\) | |||||||
\(318\) | −5.85762 | −0.328479 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 20.0200 | 1.11741 | ||||||||
\(322\) | 2.65626 | 0.148028 | ||||||||
\(323\) | 17.3579 | 0.965818 | ||||||||
\(324\) | −1.13831 | −0.0632395 | ||||||||
\(325\) | −3.79720 | −0.210631 | ||||||||
\(326\) | −8.06159 | −0.446490 | ||||||||
\(327\) | −5.65746 | −0.312858 | ||||||||
\(328\) | −9.47709 | −0.523285 | ||||||||
\(329\) | −4.48205 | −0.247103 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.1966 | 0.560458 | 0.280229 | − | 0.959933i | \(-0.409590\pi\) | ||||
0.280229 | + | 0.959933i | \(0.409590\pi\) | |||||||
\(332\) | 11.1551 | 0.612215 | ||||||||
\(333\) | −4.00976 | −0.219734 | ||||||||
\(334\) | −16.2178 | −0.887400 | ||||||||
\(335\) | 5.71316 | 0.312143 | ||||||||
\(336\) | 1.14896 | 0.0626810 | ||||||||
\(337\) | 14.1072 | 0.768469 | 0.384234 | − | 0.923236i | \(-0.374465\pi\) | ||||
0.384234 | + | 0.923236i | \(0.374465\pi\) | |||||||
\(338\) | 1.41876 | 0.0771702 | ||||||||
\(339\) | −13.0779 | −0.710296 | ||||||||
\(340\) | −6.47709 | −0.351270 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.50191 | 0.243436 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.66428 | 0.251481 | ||||||||
\(345\) | 3.05194 | 0.164311 | ||||||||
\(346\) | −12.1600 | −0.653728 | ||||||||
\(347\) | −4.16926 | −0.223817 | −0.111909 | − | 0.993718i | \(-0.535696\pi\) | ||||
−0.111909 | + | 0.993718i | \(0.535696\pi\) | |||||||
\(348\) | −0.444559 | −0.0238308 | ||||||||
\(349\) | −8.03734 | −0.430229 | −0.215114 | − | 0.976589i | \(-0.569012\pi\) | ||||
−0.215114 | + | 0.976589i | \(0.569012\pi\) | |||||||
\(350\) | 1.00000 | 0.0534522 | ||||||||
\(351\) | 20.4176 | 1.08981 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.7957 | 0.840723 | 0.420361 | − | 0.907357i | \(-0.361903\pi\) | ||||
0.420361 | + | 0.907357i | \(0.361903\pi\) | |||||||
\(354\) | 5.45347 | 0.289848 | ||||||||
\(355\) | 3.33119 | 0.176801 | ||||||||
\(356\) | −5.87277 | −0.311256 | ||||||||
\(357\) | −7.44193 | −0.393869 | ||||||||
\(358\) | −23.3033 | −1.23162 | ||||||||
\(359\) | −6.64022 | −0.350458 | −0.175229 | − | 0.984528i | \(-0.556067\pi\) | ||||
−0.175229 | + | 0.984528i | \(0.556067\pi\) | |||||||
\(360\) | −1.67989 | −0.0885379 | ||||||||
\(361\) | −11.8182 | −0.622010 | ||||||||
\(362\) | 22.1288 | 1.16307 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.79720 | −0.199028 | ||||||||
\(365\) | −15.0127 | −0.785801 | ||||||||
\(366\) | −13.3961 | −0.700226 | ||||||||
\(367\) | 16.6306 | 0.868108 | 0.434054 | − | 0.900887i | \(-0.357083\pi\) | ||||
0.434054 | + | 0.900887i | \(0.357083\pi\) | |||||||
\(368\) | 2.65626 | 0.138467 | ||||||||
\(369\) | 15.9205 | 0.828786 | ||||||||
\(370\) | 2.38692 | 0.124090 | ||||||||
\(371\) | −5.09819 | −0.264685 | ||||||||
\(372\) | −6.91522 | −0.358537 | ||||||||
\(373\) | 7.30477 | 0.378227 | 0.189113 | − | 0.981955i | \(-0.439439\pi\) | ||||
0.189113 | + | 0.981955i | \(0.439439\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.14896 | 0.0593321 | ||||||||
\(376\) | −4.48205 | −0.231144 | ||||||||
\(377\) | 1.46922 | 0.0756688 | ||||||||
\(378\) | −5.37701 | −0.276564 | ||||||||
\(379\) | −13.2798 | −0.682138 | −0.341069 | − | 0.940038i | \(-0.610789\pi\) | ||||
−0.341069 | + | 0.940038i | \(0.610789\pi\) | |||||||
\(380\) | −2.67989 | −0.137475 | ||||||||
\(381\) | 1.65133 | 0.0846002 | ||||||||
\(382\) | 20.2864 | 1.03794 | ||||||||
\(383\) | 17.1065 | 0.874100 | 0.437050 | − | 0.899437i | \(-0.356023\pi\) | ||||
0.437050 | + | 0.899437i | \(0.356023\pi\) | |||||||
\(384\) | 1.14896 | 0.0586327 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.84508 | 0.195709 | ||||||||
\(387\) | −7.83547 | −0.398299 | ||||||||
\(388\) | −3.30450 | −0.167761 | ||||||||
\(389\) | 8.54697 | 0.433348 | 0.216674 | − | 0.976244i | \(-0.430479\pi\) | ||||
0.216674 | + | 0.976244i | \(0.430479\pi\) | |||||||
\(390\) | −4.36284 | −0.220921 | ||||||||
\(391\) | −17.2049 | −0.870087 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | −22.4237 | −1.13113 | ||||||||
\(394\) | −11.8159 | −0.595275 | ||||||||
\(395\) | 6.03633 | 0.303721 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.0472 | 0.855572 | 0.427786 | − | 0.903880i | \(-0.359294\pi\) | ||||
0.427786 | + | 0.903880i | \(0.359294\pi\) | |||||||
\(398\) | 12.5496 | 0.629054 | ||||||||
\(399\) | −3.07909 | −0.154147 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −2.71053 | −0.135357 | −0.0676787 | − | 0.997707i | \(-0.521559\pi\) | ||||
−0.0676787 | + | 0.997707i | \(0.521559\pi\) | |||||||
\(402\) | 6.56420 | 0.327392 | ||||||||
\(403\) | 22.8541 | 1.13844 | ||||||||
\(404\) | 5.56420 | 0.276829 | ||||||||
\(405\) | −1.13831 | −0.0565631 | ||||||||
\(406\) | −0.386922 | −0.0192026 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.44193 | −0.368430 | ||||||||
\(409\) | −29.3149 | −1.44953 | −0.724763 | − | 0.688998i | \(-0.758051\pi\) | ||||
−0.724763 | + | 0.688998i | \(0.758051\pi\) | |||||||
\(410\) | −9.47709 | −0.468040 | ||||||||
\(411\) | 21.8083 | 1.07572 | ||||||||
\(412\) | −7.95988 | −0.392155 | ||||||||
\(413\) | 4.74643 | 0.233557 | ||||||||
\(414\) | −4.46222 | −0.219306 | ||||||||
\(415\) | 11.1551 | 0.547582 | ||||||||
\(416\) | −3.79720 | −0.186173 | ||||||||
\(417\) | −7.56698 | −0.370557 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.3776 | 1.87487 | 0.937434 | − | 0.348162i | \(-0.113194\pi\) | ||||
0.937434 | + | 0.348162i | \(0.113194\pi\) | |||||||
\(420\) | 1.14896 | 0.0560636 | ||||||||
\(421\) | −37.1605 | −1.81109 | −0.905545 | − | 0.424249i | \(-0.860538\pi\) | ||||
−0.905545 | + | 0.424249i | \(0.860538\pi\) | |||||||
\(422\) | −3.99973 | −0.194704 | ||||||||
\(423\) | 7.52934 | 0.366089 | ||||||||
\(424\) | −5.09819 | −0.247590 | ||||||||
\(425\) | −6.47709 | −0.314185 | ||||||||
\(426\) | 3.82741 | 0.185439 | ||||||||
\(427\) | −11.6593 | −0.564234 | ||||||||
\(428\) | 17.4244 | 0.842241 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.66428 | 0.224932 | ||||||||
\(431\) | 30.7450 | 1.48093 | 0.740467 | − | 0.672093i | \(-0.234605\pi\) | ||||
0.740467 | + | 0.672093i | \(0.234605\pi\) | |||||||
\(432\) | −5.37701 | −0.258702 | ||||||||
\(433\) | −8.55355 | −0.411057 | −0.205529 | − | 0.978651i | \(-0.565891\pi\) | ||||
−0.205529 | + | 0.978651i | \(0.565891\pi\) | |||||||
\(434\) | −6.01867 | −0.288905 | ||||||||
\(435\) | −0.444559 | −0.0213150 | ||||||||
\(436\) | −4.92398 | −0.235816 | ||||||||
\(437\) | −7.11849 | −0.340523 | ||||||||
\(438\) | −17.2490 | −0.824190 | ||||||||
\(439\) | 24.5405 | 1.17126 | 0.585628 | − | 0.810580i | \(-0.300848\pi\) | ||||
0.585628 | + | 0.810580i | \(0.300848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.67989 | −0.0799947 | ||||||||
\(442\) | 24.5948 | 1.16986 | ||||||||
\(443\) | 26.9683 | 1.28130 | 0.640652 | − | 0.767831i | \(-0.278664\pi\) | ||||
0.640652 | + | 0.767831i | \(0.278664\pi\) | |||||||
\(444\) | 2.74248 | 0.130152 | ||||||||
\(445\) | −5.87277 | −0.278396 | ||||||||
\(446\) | 17.8782 | 0.846555 | ||||||||
\(447\) | −11.6204 | −0.549624 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −35.1803 | −1.66026 | −0.830131 | − | 0.557569i | \(-0.811734\pi\) | ||||
−0.830131 | + | 0.557569i | \(0.811734\pi\) | |||||||
\(450\) | −1.67989 | −0.0791907 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −11.3824 | −0.535383 | ||||||||
\(453\) | 13.5963 | 0.638809 | ||||||||
\(454\) | 5.76204 | 0.270426 | ||||||||
\(455\) | −3.79720 | −0.178016 | ||||||||
\(456\) | −3.07909 | −0.144191 | ||||||||
\(457\) | −20.4364 | −0.955974 | −0.477987 | − | 0.878367i | \(-0.658633\pi\) | ||||
−0.477987 | + | 0.878367i | \(0.658633\pi\) | |||||||
\(458\) | −8.57617 | −0.400738 | ||||||||
\(459\) | 34.8274 | 1.62560 | ||||||||
\(460\) | 2.65626 | 0.123849 | ||||||||
\(461\) | −5.59541 | −0.260604 | −0.130302 | − | 0.991474i | \(-0.541595\pi\) | ||||
−0.130302 | + | 0.991474i | \(0.541595\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.5079 | −1.37135 | −0.685674 | − | 0.727909i | \(-0.740492\pi\) | ||||
−0.685674 | + | 0.727909i | \(0.740492\pi\) | |||||||
\(464\) | −0.386922 | −0.0179624 | ||||||||
\(465\) | −6.91522 | −0.320686 | ||||||||
\(466\) | −14.4011 | −0.667117 | ||||||||
\(467\) | 31.3408 | 1.45028 | 0.725140 | − | 0.688601i | \(-0.241775\pi\) | ||||
0.725140 | + | 0.688601i | \(0.241775\pi\) | |||||||
\(468\) | 6.37888 | 0.294864 | ||||||||
\(469\) | 5.71316 | 0.263809 | ||||||||
\(470\) | −4.48205 | −0.206741 | ||||||||
\(471\) | 1.94236 | 0.0894994 | ||||||||
\(472\) | 4.74643 | 0.218472 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 6.93551 | 0.318559 | ||||||||
\(475\) | −2.67989 | −0.122962 | ||||||||
\(476\) | −6.47709 | −0.296877 | ||||||||
\(477\) | 8.56439 | 0.392136 | ||||||||
\(478\) | 24.0096 | 1.09817 | ||||||||
\(479\) | −6.75139 | −0.308479 | −0.154239 | − | 0.988034i | \(-0.549293\pi\) | ||||
−0.154239 | + | 0.988034i | \(0.549293\pi\) | |||||||
\(480\) | 1.14896 | 0.0524427 | ||||||||
\(481\) | −9.06363 | −0.413266 | ||||||||
\(482\) | 16.7641 | 0.763584 | ||||||||
\(483\) | 3.05194 | 0.138868 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.30450 | −0.150050 | ||||||||
\(486\) | 14.8232 | 0.672392 | ||||||||
\(487\) | −25.3561 | −1.14900 | −0.574498 | − | 0.818506i | \(-0.694803\pi\) | ||||
−0.574498 | + | 0.818506i | \(0.694803\pi\) | |||||||
\(488\) | −11.6593 | −0.527793 | ||||||||
\(489\) | −9.26245 | −0.418863 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −19.7873 | −0.892987 | −0.446493 | − | 0.894787i | \(-0.647327\pi\) | ||||
−0.446493 | + | 0.894787i | \(0.647327\pi\) | |||||||
\(492\) | −10.8888 | −0.490905 | ||||||||
\(493\) | 2.50613 | 0.112870 | ||||||||
\(494\) | 10.1761 | 0.457844 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.01867 | −0.270246 | ||||||||
\(497\) | 3.33119 | 0.149424 | ||||||||
\(498\) | 12.8168 | 0.574333 | ||||||||
\(499\) | −26.7727 | −1.19851 | −0.599255 | − | 0.800559i | \(-0.704536\pi\) | ||||
−0.599255 | + | 0.800559i | \(0.704536\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −18.6337 | −0.832490 | ||||||||
\(502\) | −2.42488 | −0.108228 | ||||||||
\(503\) | 0.355087 | 0.0158326 | 0.00791628 | − | 0.999969i | \(-0.497480\pi\) | ||||
0.00791628 | + | 0.999969i | \(0.497480\pi\) | |||||||
\(504\) | −1.67989 | −0.0748282 | ||||||||
\(505\) | 5.56420 | 0.247604 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.63010 | 0.0723951 | ||||||||
\(508\) | 1.43724 | 0.0637671 | ||||||||
\(509\) | −23.9743 | −1.06264 | −0.531321 | − | 0.847171i | \(-0.678304\pi\) | ||||
−0.531321 | + | 0.847171i | \(0.678304\pi\) | |||||||
\(510\) | −7.44193 | −0.329534 | ||||||||
\(511\) | −15.0127 | −0.664123 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 14.4098 | 0.636208 | ||||||||
\(514\) | 5.18367 | 0.228642 | ||||||||
\(515\) | −7.95988 | −0.350754 | ||||||||
\(516\) | 5.35908 | 0.235920 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.38692 | 0.104875 | ||||||||
\(519\) | −13.9714 | −0.613277 | ||||||||
\(520\) | −3.79720 | −0.166518 | ||||||||
\(521\) | −7.25606 | −0.317894 | −0.158947 | − | 0.987287i | \(-0.550810\pi\) | ||||
−0.158947 | + | 0.987287i | \(0.550810\pi\) | |||||||
\(522\) | 0.649986 | 0.0284491 | ||||||||
\(523\) | 17.1723 | 0.750893 | 0.375447 | − | 0.926844i | \(-0.377489\pi\) | ||||
0.375447 | + | 0.926844i | \(0.377489\pi\) | |||||||
\(524\) | −19.5165 | −0.852582 | ||||||||
\(525\) | 1.14896 | 0.0501448 | ||||||||
\(526\) | −20.3770 | −0.888480 | ||||||||
\(527\) | 38.9835 | 1.69815 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.9443 | −0.693229 | ||||||||
\(530\) | −5.09819 | −0.221451 | ||||||||
\(531\) | −7.97348 | −0.346019 | ||||||||
\(532\) | −2.67989 | −0.116188 | ||||||||
\(533\) | 35.9865 | 1.55875 | ||||||||
\(534\) | −6.74759 | −0.291997 | ||||||||
\(535\) | 17.4244 | 0.753324 | ||||||||
\(536\) | 5.71316 | 0.246771 | ||||||||
\(537\) | −26.7746 | −1.15541 | ||||||||
\(538\) | −11.4504 | −0.493662 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.37701 | −0.231390 | ||||||||
\(541\) | 23.7882 | 1.02273 | 0.511366 | − | 0.859363i | \(-0.329140\pi\) | ||||
0.511366 | + | 0.859363i | \(0.329140\pi\) | |||||||
\(542\) | −14.8199 | −0.636571 | ||||||||
\(543\) | 25.4252 | 1.09110 | ||||||||
\(544\) | −6.47709 | −0.277703 | ||||||||
\(545\) | −4.92398 | −0.210920 | ||||||||
\(546\) | −4.36284 | −0.186712 | ||||||||
\(547\) | 39.2442 | 1.67796 | 0.838981 | − | 0.544161i | \(-0.183152\pi\) | ||||
0.838981 | + | 0.544161i | \(0.183152\pi\) | |||||||
\(548\) | 18.9809 | 0.810823 | ||||||||
\(549\) | 19.5864 | 0.835926 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.03691 | 0.0441738 | ||||||||
\(552\) | 3.05194 | 0.129899 | ||||||||
\(553\) | 6.03633 | 0.256691 | ||||||||
\(554\) | −24.5158 | −1.04157 | ||||||||
\(555\) | 2.74248 | 0.116412 | ||||||||
\(556\) | −6.58593 | −0.279306 | ||||||||
\(557\) | −43.0812 | −1.82541 | −0.912705 | − | 0.408618i | \(-0.866011\pi\) | ||||
−0.912705 | + | 0.408618i | \(0.866011\pi\) | |||||||
\(558\) | 10.1107 | 0.428020 | ||||||||
\(559\) | −17.7112 | −0.749105 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.5929 | 1.20612 | ||||||||
\(563\) | −40.8534 | −1.72176 | −0.860882 | − | 0.508804i | \(-0.830088\pi\) | ||||
−0.860882 | + | 0.508804i | \(0.830088\pi\) | |||||||
\(564\) | −5.14970 | −0.216841 | ||||||||
\(565\) | −11.3824 | −0.478861 | ||||||||
\(566\) | 5.19494 | 0.218360 | ||||||||
\(567\) | −1.13831 | −0.0478045 | ||||||||
\(568\) | 3.33119 | 0.139774 | ||||||||
\(569\) | 4.46455 | 0.187164 | 0.0935818 | − | 0.995612i | \(-0.470168\pi\) | ||||
0.0935818 | + | 0.995612i | \(0.470168\pi\) | |||||||
\(570\) | −3.07909 | −0.128969 | ||||||||
\(571\) | −31.4272 | −1.31519 | −0.657593 | − | 0.753373i | \(-0.728425\pi\) | ||||
−0.657593 | + | 0.753373i | \(0.728425\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 23.3083 | 0.973717 | ||||||||
\(574\) | −9.47709 | −0.395566 | ||||||||
\(575\) | 2.65626 | 0.110774 | ||||||||
\(576\) | −1.67989 | −0.0699953 | ||||||||
\(577\) | 8.24246 | 0.343138 | 0.171569 | − | 0.985172i | \(-0.445116\pi\) | ||||
0.171569 | + | 0.985172i | \(0.445116\pi\) | |||||||
\(578\) | 24.9527 | 1.03790 | ||||||||
\(579\) | 4.41784 | 0.183599 | ||||||||
\(580\) | −0.386922 | −0.0160661 | ||||||||
\(581\) | 11.1551 | 0.462791 | ||||||||
\(582\) | −3.79675 | −0.157380 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.0127 | −0.621230 | ||||||||
\(585\) | 6.37888 | 0.263734 | ||||||||
\(586\) | −18.2205 | −0.752680 | ||||||||
\(587\) | 1.10956 | 0.0457966 | 0.0228983 | − | 0.999738i | \(-0.492711\pi\) | ||||
0.0228983 | + | 0.999738i | \(0.492711\pi\) | |||||||
\(588\) | 1.14896 | 0.0473824 | ||||||||
\(589\) | 16.1294 | 0.664599 | ||||||||
\(590\) | 4.74643 | 0.195408 | ||||||||
\(591\) | −13.5760 | −0.558441 | ||||||||
\(592\) | 2.38692 | 0.0981019 | ||||||||
\(593\) | −46.0484 | −1.89098 | −0.945491 | − | 0.325648i | \(-0.894418\pi\) | ||||
−0.945491 | + | 0.325648i | \(0.894418\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.47709 | −0.265535 | ||||||||
\(596\) | −10.1138 | −0.414277 | ||||||||
\(597\) | 14.4190 | 0.590130 | ||||||||
\(598\) | −10.0864 | −0.412462 | ||||||||
\(599\) | −29.5604 | −1.20781 | −0.603903 | − | 0.797058i | \(-0.706389\pi\) | ||||
−0.603903 | + | 0.797058i | \(0.706389\pi\) | |||||||
\(600\) | 1.14896 | 0.0469061 | ||||||||
\(601\) | −5.68051 | −0.231713 | −0.115856 | − | 0.993266i | \(-0.536961\pi\) | ||||
−0.115856 | + | 0.993266i | \(0.536961\pi\) | |||||||
\(602\) | 4.66428 | 0.190102 | ||||||||
\(603\) | −9.59747 | −0.390839 | ||||||||
\(604\) | 11.8335 | 0.481500 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.39305 | 0.259700 | ||||||||
\(607\) | −24.3166 | −0.986980 | −0.493490 | − | 0.869751i | \(-0.664279\pi\) | ||||
−0.493490 | + | 0.869751i | \(0.664279\pi\) | |||||||
\(608\) | −2.67989 | −0.108684 | ||||||||
\(609\) | −0.444559 | −0.0180144 | ||||||||
\(610\) | −11.6593 | −0.472072 | ||||||||
\(611\) | 17.0193 | 0.688525 | ||||||||
\(612\) | 10.8808 | 0.439830 | ||||||||
\(613\) | −30.4381 | −1.22938 | −0.614692 | − | 0.788767i | \(-0.710720\pi\) | ||||
−0.614692 | + | 0.788767i | \(0.710720\pi\) | |||||||
\(614\) | 10.9710 | 0.442752 | ||||||||
\(615\) | −10.8888 | −0.439079 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4297 | 1.34583 | 0.672914 | − | 0.739721i | \(-0.265043\pi\) | ||||
0.672914 | + | 0.739721i | \(0.265043\pi\) | |||||||
\(618\) | −9.14559 | −0.367890 | ||||||||
\(619\) | −4.33525 | −0.174248 | −0.0871241 | − | 0.996197i | \(-0.527768\pi\) | ||||
−0.0871241 | + | 0.996197i | \(0.527768\pi\) | |||||||
\(620\) | −6.01867 | −0.241716 | ||||||||
\(621\) | −14.2827 | −0.573147 | ||||||||
\(622\) | 20.8687 | 0.836758 | ||||||||
\(623\) | −5.87277 | −0.235288 | ||||||||
\(624\) | −4.36284 | −0.174653 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.64805 | 0.345646 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.69054 | 0.0674599 | ||||||||
\(629\) | −15.4603 | −0.616443 | ||||||||
\(630\) | −1.67989 | −0.0669284 | ||||||||
\(631\) | −15.4234 | −0.613998 | −0.306999 | − | 0.951710i | \(-0.599325\pi\) | ||||
−0.306999 | + | 0.951710i | \(0.599325\pi\) | |||||||
\(632\) | 6.03633 | 0.240113 | ||||||||
\(633\) | −4.59554 | −0.182656 | ||||||||
\(634\) | 3.53662 | 0.140457 | ||||||||
\(635\) | 1.43724 | 0.0570350 | ||||||||
\(636\) | −5.85762 | −0.232270 | ||||||||
\(637\) | −3.79720 | −0.150451 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.59603 | −0.221376 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 35.5278 | 1.40327 | 0.701633 | − | 0.712539i | \(-0.252455\pi\) | ||||
0.701633 | + | 0.712539i | \(0.252455\pi\) | |||||||
\(642\) | 20.0200 | 0.790126 | ||||||||
\(643\) | 49.2065 | 1.94051 | 0.970257 | − | 0.242079i | \(-0.0778292\pi\) | ||||
0.970257 | + | 0.242079i | \(0.0778292\pi\) | |||||||
\(644\) | 2.65626 | 0.104671 | ||||||||
\(645\) | 5.35908 | 0.211013 | ||||||||
\(646\) | 17.3579 | 0.682937 | ||||||||
\(647\) | 11.9820 | 0.471063 | 0.235531 | − | 0.971867i | \(-0.424317\pi\) | ||||
0.235531 | + | 0.971867i | \(0.424317\pi\) | |||||||
\(648\) | −1.13831 | −0.0447171 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.79720 | −0.148939 | ||||||||
\(651\) | −6.91522 | −0.271029 | ||||||||
\(652\) | −8.06159 | −0.315716 | ||||||||
\(653\) | −50.4638 | −1.97480 | −0.987401 | − | 0.158241i | \(-0.949418\pi\) | ||||
−0.987401 | + | 0.158241i | \(0.949418\pi\) | |||||||
\(654\) | −5.65746 | −0.221224 | ||||||||
\(655\) | −19.5165 | −0.762572 | ||||||||
\(656\) | −9.47709 | −0.370018 | ||||||||
\(657\) | 25.2197 | 0.983913 | ||||||||
\(658\) | −4.48205 | −0.174728 | ||||||||
\(659\) | −29.2967 | −1.14124 | −0.570618 | − | 0.821216i | \(-0.693296\pi\) | ||||
−0.570618 | + | 0.821216i | \(0.693296\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.0445 | 1.36307 | 0.681537 | − | 0.731784i | \(-0.261312\pi\) | ||||
0.681537 | + | 0.731784i | \(0.261312\pi\) | |||||||
\(662\) | 10.1966 | 0.396304 | ||||||||
\(663\) | 28.2585 | 1.09747 | ||||||||
\(664\) | 11.1551 | 0.432901 | ||||||||
\(665\) | −2.67989 | −0.103922 | ||||||||
\(666\) | −4.00976 | −0.155375 | ||||||||
\(667\) | −1.02777 | −0.0397953 | ||||||||
\(668\) | −16.2178 | −0.627487 | ||||||||
\(669\) | 20.5413 | 0.794173 | ||||||||
\(670\) | 5.71316 | 0.220719 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.14896 | 0.0443221 | ||||||||
\(673\) | −37.4744 | −1.44453 | −0.722265 | − | 0.691616i | \(-0.756899\pi\) | ||||
−0.722265 | + | 0.691616i | \(0.756899\pi\) | |||||||
\(674\) | 14.1072 | 0.543390 | ||||||||
\(675\) | −5.37701 | −0.206961 | ||||||||
\(676\) | 1.41876 | 0.0545676 | ||||||||
\(677\) | −8.42279 | −0.323714 | −0.161857 | − | 0.986814i | \(-0.551748\pi\) | ||||
−0.161857 | + | 0.986814i | \(0.551748\pi\) | |||||||
\(678\) | −13.0779 | −0.502255 | ||||||||
\(679\) | −3.30450 | −0.126815 | ||||||||
\(680\) | −6.47709 | −0.248385 | ||||||||
\(681\) | 6.62036 | 0.253693 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.9986 | 0.573904 | 0.286952 | − | 0.957945i | \(-0.407358\pi\) | ||||
0.286952 | + | 0.957945i | \(0.407358\pi\) | |||||||
\(684\) | 4.50191 | 0.172135 | ||||||||
\(685\) | 18.9809 | 0.725222 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −9.85369 | −0.375942 | ||||||||
\(688\) | 4.66428 | 0.177824 | ||||||||
\(689\) | 19.3589 | 0.737514 | ||||||||
\(690\) | 3.05194 | 0.116185 | ||||||||
\(691\) | 43.8937 | 1.66980 | 0.834898 | − | 0.550404i | \(-0.185526\pi\) | ||||
0.834898 | + | 0.550404i | \(0.185526\pi\) | |||||||
\(692\) | −12.1600 | −0.462255 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.16926 | −0.158263 | ||||||||
\(695\) | −6.58593 | −0.249819 | ||||||||
\(696\) | −0.444559 | −0.0168510 | ||||||||
\(697\) | 61.3840 | 2.32508 | ||||||||
\(698\) | −8.03734 | −0.304218 | ||||||||
\(699\) | −16.5463 | −0.625837 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | 43.3836 | 1.63857 | 0.819287 | − | 0.573383i | \(-0.194369\pi\) | ||||
0.819287 | + | 0.573383i | \(0.194369\pi\) | |||||||
\(702\) | 20.4176 | 0.770613 | ||||||||
\(703\) | −6.39668 | −0.241256 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.14970 | −0.193949 | ||||||||
\(706\) | 15.7957 | 0.594481 | ||||||||
\(707\) | 5.56420 | 0.209263 | ||||||||
\(708\) | 5.45347 | 0.204954 | ||||||||
\(709\) | 6.61088 | 0.248277 | 0.124138 | − | 0.992265i | \(-0.460383\pi\) | ||||
0.124138 | + | 0.992265i | \(0.460383\pi\) | |||||||
\(710\) | 3.33119 | 0.125017 | ||||||||
\(711\) | −10.1404 | −0.380294 | ||||||||
\(712\) | −5.87277 | −0.220091 | ||||||||
\(713\) | −15.9872 | −0.598724 | ||||||||
\(714\) | −7.44193 | −0.278507 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −23.3033 | −0.870886 | ||||||||
\(717\) | 27.5861 | 1.03022 | ||||||||
\(718\) | −6.64022 | −0.247811 | ||||||||
\(719\) | −27.5111 | −1.02599 | −0.512995 | − | 0.858392i | \(-0.671464\pi\) | ||||
−0.512995 | + | 0.858392i | \(0.671464\pi\) | |||||||
\(720\) | −1.67989 | −0.0626057 | ||||||||
\(721\) | −7.95988 | −0.296441 | ||||||||
\(722\) | −11.8182 | −0.439828 | ||||||||
\(723\) | 19.2613 | 0.716335 | ||||||||
\(724\) | 22.1288 | 0.822411 | ||||||||
\(725\) | −0.386922 | −0.0143699 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.3895 | −0.496590 | −0.248295 | − | 0.968685i | \(-0.579870\pi\) | ||||
−0.248295 | + | 0.968685i | \(0.579870\pi\) | |||||||
\(728\) | −3.79720 | −0.140734 | ||||||||
\(729\) | 20.4462 | 0.757265 | ||||||||
\(730\) | −15.0127 | −0.555645 | ||||||||
\(731\) | −30.2110 | −1.11739 | ||||||||
\(732\) | −13.3961 | −0.495135 | ||||||||
\(733\) | 45.9046 | 1.69552 | 0.847762 | − | 0.530376i | \(-0.177949\pi\) | ||||
0.847762 | + | 0.530376i | \(0.177949\pi\) | |||||||
\(734\) | 16.6306 | 0.613845 | ||||||||
\(735\) | 1.14896 | 0.0423801 | ||||||||
\(736\) | 2.65626 | 0.0979111 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 15.9205 | 0.586040 | ||||||||
\(739\) | 15.5601 | 0.572388 | 0.286194 | − | 0.958172i | \(-0.407610\pi\) | ||||
0.286194 | + | 0.958172i | \(0.407610\pi\) | |||||||
\(740\) | 2.38692 | 0.0877450 | ||||||||
\(741\) | 11.6919 | 0.429514 | ||||||||
\(742\) | −5.09819 | −0.187160 | ||||||||
\(743\) | −31.9688 | −1.17282 | −0.586411 | − | 0.810014i | \(-0.699459\pi\) | ||||
−0.586411 | + | 0.810014i | \(0.699459\pi\) | |||||||
\(744\) | −6.91522 | −0.253524 | ||||||||
\(745\) | −10.1138 | −0.370541 | ||||||||
\(746\) | 7.30477 | 0.267447 | ||||||||
\(747\) | −18.7393 | −0.685635 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.4244 | 0.636675 | ||||||||
\(750\) | 1.14896 | 0.0419541 | ||||||||
\(751\) | 31.7056 | 1.15695 | 0.578476 | − | 0.815699i | \(-0.303647\pi\) | ||||
0.578476 | + | 0.815699i | \(0.303647\pi\) | |||||||
\(752\) | −4.48205 | −0.163443 | ||||||||
\(753\) | −2.78610 | −0.101531 | ||||||||
\(754\) | 1.46922 | 0.0535059 | ||||||||
\(755\) | 11.8335 | 0.430667 | ||||||||
\(756\) | −5.37701 | −0.195560 | ||||||||
\(757\) | −22.3306 | −0.811620 | −0.405810 | − | 0.913957i | \(-0.633011\pi\) | ||||
−0.405810 | + | 0.913957i | \(0.633011\pi\) | |||||||
\(758\) | −13.2798 | −0.482344 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.67989 | −0.0972098 | ||||||||
\(761\) | −17.3657 | −0.629508 | −0.314754 | − | 0.949173i | \(-0.601922\pi\) | ||||
−0.314754 | + | 0.949173i | \(0.601922\pi\) | |||||||
\(762\) | 1.65133 | 0.0598214 | ||||||||
\(763\) | −4.92398 | −0.178260 | ||||||||
\(764\) | 20.2864 | 0.733936 | ||||||||
\(765\) | 10.8808 | 0.393396 | ||||||||
\(766\) | 17.1065 | 0.618082 | ||||||||
\(767\) | −18.0232 | −0.650779 | ||||||||
\(768\) | 1.14896 | 0.0414596 | ||||||||
\(769\) | 36.3673 | 1.31144 | 0.655720 | − | 0.755004i | \(-0.272365\pi\) | ||||
0.655720 | + | 0.755004i | \(0.272365\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.95584 | 0.214494 | ||||||||
\(772\) | 3.84508 | 0.138387 | ||||||||
\(773\) | −53.0722 | −1.90887 | −0.954437 | − | 0.298413i | \(-0.903543\pi\) | ||||
−0.954437 | + | 0.298413i | \(0.903543\pi\) | |||||||
\(774\) | −7.83547 | −0.281640 | ||||||||
\(775\) | −6.01867 | −0.216197 | ||||||||
\(776\) | −3.30450 | −0.118625 | ||||||||
\(777\) | 2.74248 | 0.0983860 | ||||||||
\(778\) | 8.54697 | 0.306424 | ||||||||
\(779\) | 25.3975 | 0.909962 | ||||||||
\(780\) | −4.36284 | −0.156215 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −17.2049 | −0.615244 | ||||||||
\(783\) | 2.08048 | 0.0743505 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 1.69054 | 0.0603379 | ||||||||
\(786\) | −22.4237 | −0.799826 | ||||||||
\(787\) | 38.3366 | 1.36655 | 0.683276 | − | 0.730160i | \(-0.260555\pi\) | ||||
0.683276 | + | 0.730160i | \(0.260555\pi\) | |||||||
\(788\) | −11.8159 | −0.420923 | ||||||||
\(789\) | −23.4124 | −0.833503 | ||||||||
\(790\) | 6.03633 | 0.214763 | ||||||||
\(791\) | −11.3824 | −0.404711 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.2728 | 1.57217 | ||||||||
\(794\) | 17.0472 | 0.604981 | ||||||||
\(795\) | −5.85762 | −0.207748 | ||||||||
\(796\) | 12.5496 | 0.444809 | ||||||||
\(797\) | −30.5021 | −1.08044 | −0.540219 | − | 0.841524i | \(-0.681659\pi\) | ||||
−0.540219 | + | 0.841524i | \(0.681659\pi\) | |||||||
\(798\) | −3.07909 | −0.108999 | ||||||||
\(799\) | 29.0306 | 1.02703 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 9.86560 | 0.348584 | ||||||||
\(802\) | −2.71053 | −0.0957121 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 6.56420 | 0.231501 | ||||||||
\(805\) | 2.65626 | 0.0936209 | ||||||||
\(806\) | 22.8541 | 0.805002 | ||||||||
\(807\) | −13.1561 | −0.463116 | ||||||||
\(808\) | 5.56420 | 0.195748 | ||||||||
\(809\) | 33.8990 | 1.19183 | 0.595913 | − | 0.803049i | \(-0.296790\pi\) | ||||
0.595913 | + | 0.803049i | \(0.296790\pi\) | |||||||
\(810\) | −1.13831 | −0.0399962 | ||||||||
\(811\) | −42.9037 | −1.50655 | −0.753276 | − | 0.657705i | \(-0.771527\pi\) | ||||
−0.753276 | + | 0.657705i | \(0.771527\pi\) | |||||||
\(812\) | −0.386922 | −0.0135783 | ||||||||
\(813\) | −17.0275 | −0.597182 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.06159 | −0.282385 | ||||||||
\(816\) | −7.44193 | −0.260520 | ||||||||
\(817\) | −12.4998 | −0.437311 | ||||||||
\(818\) | −29.3149 | −1.02497 | ||||||||
\(819\) | 6.37888 | 0.222896 | ||||||||
\(820\) | −9.47709 | −0.330954 | ||||||||
\(821\) | −50.2053 | −1.75218 | −0.876088 | − | 0.482151i | \(-0.839856\pi\) | ||||
−0.876088 | + | 0.482151i | \(0.839856\pi\) | |||||||
\(822\) | 21.8083 | 0.760651 | ||||||||
\(823\) | −19.9384 | −0.695010 | −0.347505 | − | 0.937678i | \(-0.612971\pi\) | ||||
−0.347505 | + | 0.937678i | \(0.612971\pi\) | |||||||
\(824\) | −7.95988 | −0.277296 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.74643 | 0.165149 | ||||||||
\(827\) | 34.0394 | 1.18366 | 0.591832 | − | 0.806061i | \(-0.298405\pi\) | ||||
0.591832 | + | 0.806061i | \(0.298405\pi\) | |||||||
\(828\) | −4.46222 | −0.155073 | ||||||||
\(829\) | −12.9629 | −0.450222 | −0.225111 | − | 0.974333i | \(-0.572274\pi\) | ||||
−0.225111 | + | 0.974333i | \(0.572274\pi\) | |||||||
\(830\) | 11.1551 | 0.387199 | ||||||||
\(831\) | −28.1676 | −0.977125 | ||||||||
\(832\) | −3.79720 | −0.131644 | ||||||||
\(833\) | −6.47709 | −0.224418 | ||||||||
\(834\) | −7.56698 | −0.262023 | ||||||||
\(835\) | −16.2178 | −0.561241 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.3624 | 1.11861 | ||||||||
\(838\) | 38.3776 | 1.32573 | ||||||||
\(839\) | −14.4663 | −0.499430 | −0.249715 | − | 0.968319i | \(-0.580337\pi\) | ||||
−0.249715 | + | 0.968319i | \(0.580337\pi\) | |||||||
\(840\) | 1.14896 | 0.0396429 | ||||||||
\(841\) | −28.8503 | −0.994838 | ||||||||
\(842\) | −37.1605 | −1.28063 | ||||||||
\(843\) | 32.8522 | 1.13149 | ||||||||
\(844\) | −3.99973 | −0.137676 | ||||||||
\(845\) | 1.41876 | 0.0488067 | ||||||||
\(846\) | 7.52934 | 0.258864 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.09819 | −0.175073 | ||||||||
\(849\) | 5.96879 | 0.204848 | ||||||||
\(850\) | −6.47709 | −0.222162 | ||||||||
\(851\) | 6.34029 | 0.217342 | ||||||||
\(852\) | 3.82741 | 0.131125 | ||||||||
\(853\) | 51.1805 | 1.75239 | 0.876193 | − | 0.481960i | \(-0.160075\pi\) | ||||
0.876193 | + | 0.481960i | \(0.160075\pi\) | |||||||
\(854\) | −11.6593 | −0.398974 | ||||||||
\(855\) | 4.50191 | 0.153962 | ||||||||
\(856\) | 17.4244 | 0.595555 | ||||||||
\(857\) | 50.8960 | 1.73857 | 0.869287 | − | 0.494308i | \(-0.164578\pi\) | ||||
0.869287 | + | 0.494308i | \(0.164578\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.8508 | −0.711422 | −0.355711 | − | 0.934596i | \(-0.615761\pi\) | ||||
−0.355711 | + | 0.934596i | \(0.615761\pi\) | |||||||
\(860\) | 4.66428 | 0.159051 | ||||||||
\(861\) | −10.8888 | −0.371090 | ||||||||
\(862\) | 30.7450 | 1.04718 | ||||||||
\(863\) | 54.0762 | 1.84077 | 0.920387 | − | 0.391009i | \(-0.127874\pi\) | ||||
0.920387 | + | 0.391009i | \(0.127874\pi\) | |||||||
\(864\) | −5.37701 | −0.182930 | ||||||||
\(865\) | −12.1600 | −0.413454 | ||||||||
\(866\) | −8.55355 | −0.290661 | ||||||||
\(867\) | 28.6697 | 0.973674 | ||||||||
\(868\) | −6.01867 | −0.204287 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.444559 | −0.0150719 | ||||||||
\(871\) | −21.6940 | −0.735074 | ||||||||
\(872\) | −4.92398 | −0.166747 | ||||||||
\(873\) | 5.55120 | 0.187880 | ||||||||
\(874\) | −7.11849 | −0.240786 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | −17.2490 | −0.582790 | ||||||||
\(877\) | −2.58531 | −0.0872997 | −0.0436499 | − | 0.999047i | \(-0.513899\pi\) | ||||
−0.0436499 | + | 0.999047i | \(0.513899\pi\) | |||||||
\(878\) | 24.5405 | 0.828203 | ||||||||
\(879\) | −20.9346 | −0.706107 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.8631 | 1.44410 | 0.722048 | − | 0.691843i | \(-0.243201\pi\) | ||||
0.722048 | + | 0.691843i | \(0.243201\pi\) | |||||||
\(882\) | −1.67989 | −0.0565648 | ||||||||
\(883\) | −14.4297 | −0.485596 | −0.242798 | − | 0.970077i | \(-0.578065\pi\) | ||||
−0.242798 | + | 0.970077i | \(0.578065\pi\) | |||||||
\(884\) | 24.5948 | 0.827214 | ||||||||
\(885\) | 5.45347 | 0.183316 | ||||||||
\(886\) | 26.9683 | 0.906019 | ||||||||
\(887\) | 8.49359 | 0.285187 | 0.142593 | − | 0.989781i | \(-0.454456\pi\) | ||||
0.142593 | + | 0.989781i | \(0.454456\pi\) | |||||||
\(888\) | 2.74248 | 0.0920316 | ||||||||
\(889\) | 1.43724 | 0.0482034 | ||||||||
\(890\) | −5.87277 | −0.196856 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.8782 | 0.598605 | ||||||||
\(893\) | 12.0114 | 0.401946 | ||||||||
\(894\) | −11.6204 | −0.388643 | ||||||||
\(895\) | −23.3033 | −0.778944 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −11.5888 | −0.386940 | ||||||||
\(898\) | −35.1803 | −1.17398 | ||||||||
\(899\) | 2.32876 | 0.0776684 | ||||||||
\(900\) | −1.67989 | −0.0559963 | ||||||||
\(901\) | 33.0214 | 1.10010 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.35908 | 0.178339 | ||||||||
\(904\) | −11.3824 | −0.378573 | ||||||||
\(905\) | 22.1288 | 0.735587 | ||||||||
\(906\) | 13.5963 | 0.451706 | ||||||||
\(907\) | −47.4123 | −1.57430 | −0.787150 | − | 0.616762i | \(-0.788444\pi\) | ||||
−0.787150 | + | 0.616762i | \(0.788444\pi\) | |||||||
\(908\) | 5.76204 | 0.191220 | ||||||||
\(909\) | −9.34723 | −0.310028 | ||||||||
\(910\) | −3.79720 | −0.125876 | ||||||||
\(911\) | 14.7684 | 0.489300 | 0.244650 | − | 0.969611i | \(-0.421327\pi\) | ||||
0.244650 | + | 0.969611i | \(0.421327\pi\) | |||||||
\(912\) | −3.07909 | −0.101959 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −20.4364 | −0.675976 | ||||||||
\(915\) | −13.3961 | −0.442862 | ||||||||
\(916\) | −8.57617 | −0.283365 | ||||||||
\(917\) | −19.5165 | −0.644491 | ||||||||
\(918\) | 34.8274 | 1.14948 | ||||||||
\(919\) | −29.6648 | −0.978552 | −0.489276 | − | 0.872129i | \(-0.662739\pi\) | ||||
−0.489276 | + | 0.872129i | \(0.662739\pi\) | |||||||
\(920\) | 2.65626 | 0.0875744 | ||||||||
\(921\) | 12.6052 | 0.415356 | ||||||||
\(922\) | −5.59541 | −0.184275 | ||||||||
\(923\) | −12.6492 | −0.416354 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.38692 | 0.0784815 | ||||||||
\(926\) | −29.5079 | −0.969690 | ||||||||
\(927\) | 13.3717 | 0.439184 | ||||||||
\(928\) | −0.386922 | −0.0127013 | ||||||||
\(929\) | −14.6996 | −0.482277 | −0.241139 | − | 0.970491i | \(-0.577521\pi\) | ||||
−0.241139 | + | 0.970491i | \(0.577521\pi\) | |||||||
\(930\) | −6.91522 | −0.226759 | ||||||||
\(931\) | −2.67989 | −0.0878298 | ||||||||
\(932\) | −14.4011 | −0.471723 | ||||||||
\(933\) | 23.9773 | 0.784982 | ||||||||
\(934\) | 31.3408 | 1.02550 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.37888 | 0.208500 | ||||||||
\(937\) | −54.2518 | −1.77233 | −0.886164 | − | 0.463371i | \(-0.846640\pi\) | ||||
−0.886164 | + | 0.463371i | \(0.846640\pi\) | |||||||
\(938\) | 5.71316 | 0.186541 | ||||||||
\(939\) | 9.93628 | 0.324258 | ||||||||
\(940\) | −4.48205 | −0.146188 | ||||||||
\(941\) | −31.8477 | −1.03820 | −0.519102 | − | 0.854712i | \(-0.673734\pi\) | ||||
−0.519102 | + | 0.854712i | \(0.673734\pi\) | |||||||
\(942\) | 1.94236 | 0.0632856 | ||||||||
\(943\) | −25.1736 | −0.819767 | ||||||||
\(944\) | 4.74643 | 0.154483 | ||||||||
\(945\) | −5.37701 | −0.174914 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −44.7035 | −1.45267 | −0.726335 | − | 0.687341i | \(-0.758778\pi\) | ||||
−0.726335 | + | 0.687341i | \(0.758778\pi\) | |||||||
\(948\) | 6.93551 | 0.225255 | ||||||||
\(949\) | 57.0063 | 1.85050 | ||||||||
\(950\) | −2.67989 | −0.0869471 | ||||||||
\(951\) | 4.06344 | 0.131766 | ||||||||
\(952\) | −6.47709 | −0.209924 | ||||||||
\(953\) | 45.4259 | 1.47149 | 0.735745 | − | 0.677259i | \(-0.236832\pi\) | ||||
0.735745 | + | 0.677259i | \(0.236832\pi\) | |||||||
\(954\) | 8.56439 | 0.277282 | ||||||||
\(955\) | 20.2864 | 0.656452 | ||||||||
\(956\) | 24.0096 | 0.776527 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.75139 | −0.218127 | ||||||||
\(959\) | 18.9809 | 0.612924 | ||||||||
\(960\) | 1.14896 | 0.0370826 | ||||||||
\(961\) | 5.22439 | 0.168529 | ||||||||
\(962\) | −9.06363 | −0.292223 | ||||||||
\(963\) | −29.2711 | −0.943248 | ||||||||
\(964\) | 16.7641 | 0.539935 | ||||||||
\(965\) | 3.84508 | 0.123777 | ||||||||
\(966\) | 3.05194 | 0.0981946 | ||||||||
\(967\) | 34.6596 | 1.11458 | 0.557289 | − | 0.830319i | \(-0.311842\pi\) | ||||
0.557289 | + | 0.830319i | \(0.311842\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.9435 | 0.640679 | ||||||||
\(970\) | −3.30450 | −0.106101 | ||||||||
\(971\) | 4.29180 | 0.137730 | 0.0688651 | − | 0.997626i | \(-0.478062\pi\) | ||||
0.0688651 | + | 0.997626i | \(0.478062\pi\) | |||||||
\(972\) | 14.8232 | 0.475453 | ||||||||
\(973\) | −6.58593 | −0.211135 | ||||||||
\(974\) | −25.3561 | −0.812463 | ||||||||
\(975\) | −4.36284 | −0.139723 | ||||||||
\(976\) | −11.6593 | −0.373206 | ||||||||
\(977\) | −37.8036 | −1.20944 | −0.604722 | − | 0.796437i | \(-0.706716\pi\) | ||||
−0.604722 | + | 0.796437i | \(0.706716\pi\) | |||||||
\(978\) | −9.26245 | −0.296181 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 8.27173 | 0.264096 | ||||||||
\(982\) | −19.7873 | −0.631437 | ||||||||
\(983\) | −14.4139 | −0.459731 | −0.229866 | − | 0.973222i | \(-0.573829\pi\) | ||||
−0.229866 | + | 0.973222i | \(0.573829\pi\) | |||||||
\(984\) | −10.8888 | −0.347123 | ||||||||
\(985\) | −11.8159 | −0.376485 | ||||||||
\(986\) | 2.50613 | 0.0798115 | ||||||||
\(987\) | −5.14970 | −0.163917 | ||||||||
\(988\) | 10.1761 | 0.323744 | ||||||||
\(989\) | 12.3896 | 0.393965 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.3859 | −0.774644 | −0.387322 | − | 0.921944i | \(-0.626600\pi\) | ||||
−0.387322 | + | 0.921944i | \(0.626600\pi\) | |||||||
\(992\) | −6.01867 | −0.191093 | ||||||||
\(993\) | 11.7155 | 0.371782 | ||||||||
\(994\) | 3.33119 | 0.105659 | ||||||||
\(995\) | 12.5496 | 0.397849 | ||||||||
\(996\) | 12.8168 | 0.406115 | ||||||||
\(997\) | −15.5791 | −0.493395 | −0.246697 | − | 0.969093i | \(-0.579345\pi\) | ||||
−0.246697 | + | 0.969093i | \(0.579345\pi\) | |||||||
\(998\) | −26.7727 | −0.847474 | ||||||||
\(999\) | −12.8345 | −0.406066 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8470.2.a.cs.1.4 | 4 | ||
11.7 | odd | 10 | 770.2.n.f.71.1 | ✓ | 8 | ||
11.8 | odd | 10 | 770.2.n.f.141.1 | yes | 8 | ||
11.10 | odd | 2 | 8470.2.a.co.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.f.71.1 | ✓ | 8 | 11.7 | odd | 10 | ||
770.2.n.f.141.1 | yes | 8 | 11.8 | odd | 10 | ||
8470.2.a.co.1.4 | 4 | 11.10 | odd | 2 | |||
8470.2.a.cs.1.4 | 4 | 1.1 | even | 1 | trivial |