Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.83142 | −1.63472 | −0.817360 | − | 0.576127i | \(-0.804563\pi\) | ||||
−0.817360 | + | 0.576127i | \(0.804563\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.26484 | 1.90729 | 0.953647 | − | 0.300928i | \(-0.0972964\pi\) | ||||
0.953647 | + | 0.300928i | \(0.0972964\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.89972 | 1.47396 | 0.736978 | − | 0.675916i | \(-0.236252\pi\) | ||||
0.736978 | + | 0.675916i | \(0.236252\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.01693 | 1.67231 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.11918 | 0.638957 | 0.319478 | − | 0.947594i | \(-0.396492\pi\) | ||||
0.319478 | + | 0.947594i | \(0.396492\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.93611 | 0.814330 | 0.407165 | − | 0.913355i | \(-0.366517\pi\) | ||||
0.407165 | + | 0.913355i | \(0.366517\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −12.0755 | −3.11789 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.84435 | −0.689856 | −0.344928 | − | 0.938629i | \(-0.612097\pi\) | ||||
−0.344928 | + | 0.938629i | \(0.612097\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.25277 | −1.66390 | −0.831950 | − | 0.554850i | \(-0.812776\pi\) | ||||
−0.831950 | + | 0.554850i | \(0.812776\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.0417 | −2.40951 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.341822 | 0.0712748 | 0.0356374 | − | 0.999365i | \(-0.488654\pi\) | ||||
0.0356374 | + | 0.999365i | \(0.488654\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.1888 | 2.63777 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.71078 | −1.09904 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.780311 | 0.144900 | 0.0724501 | − | 0.997372i | \(-0.476918\pi\) | ||||
0.0724501 | + | 0.997372i | \(0.476918\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.53879 | 0.994796 | 0.497398 | − | 0.867522i | \(-0.334289\pi\) | ||||
0.497398 | + | 0.867522i | \(0.334289\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.00029 | −1.04452 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 16.6317 | 2.81127 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.82954 | 1.12277 | 0.561385 | − | 0.827555i | \(-0.310269\pi\) | ||||
0.561385 | + | 0.827555i | \(0.310269\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.31336 | −1.33120 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.86143 | −1.38392 | −0.691962 | − | 0.721934i | \(-0.743253\pi\) | ||||
−0.691962 | + | 0.721934i | \(0.743253\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.55369 | −0.694431 | −0.347215 | − | 0.937785i | \(-0.612873\pi\) | ||||
−0.347215 | + | 0.937785i | \(0.612873\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 21.3964 | 3.18959 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.00906 | −1.31411 | −0.657053 | − | 0.753844i | \(-0.728197\pi\) | ||||
−0.657053 | + | 0.753844i | \(0.728197\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.20784 | 1.17255 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.05354 | 1.12772 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.97585 | 0.683485 | 0.341742 | − | 0.939794i | \(-0.388983\pi\) | ||||
0.341742 | + | 0.939794i | \(0.388983\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.03796 | 1.21868 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 20.5356 | 2.72001 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.52810 | 0.198941 | 0.0994707 | − | 0.995040i | \(-0.468285\pi\) | ||||
0.0994707 | + | 0.995040i | \(0.468285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.97529 | 1.02113 | 0.510566 | − | 0.859839i | \(-0.329436\pi\) | ||||
0.510566 | + | 0.859839i | \(0.329436\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19.5646 | 2.46491 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.5220 | 1.55317 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5064 | 1.28356 | 0.641778 | − | 0.766891i | \(-0.278197\pi\) | ||||
0.641778 | + | 0.766891i | \(0.278197\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.967841 | −0.116514 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.1735 | 1.56341 | 0.781706 | − | 0.623648i | \(-0.214350\pi\) | ||||
0.781706 | + | 0.623648i | \(0.214350\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.40366 | 0.983574 | 0.491787 | − | 0.870716i | \(-0.336344\pi\) | ||||
0.491787 | + | 0.870716i | \(0.336344\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −37.3432 | −4.31202 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.26421 | 0.941795 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.38763 | −0.268630 | −0.134315 | − | 0.990939i | \(-0.542883\pi\) | ||||
−0.134315 | + | 0.990939i | \(0.542883\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.11882 | 0.124313 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.0730 | −1.10566 | −0.552830 | − | 0.833294i | \(-0.686452\pi\) | ||||
−0.552830 | + | 0.833294i | \(0.686452\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.1307 | −1.31576 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.20939 | −0.236871 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.91403 | 0.414886 | 0.207443 | − | 0.978247i | \(-0.433486\pi\) | ||||
0.207443 | + | 0.978247i | \(0.433486\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.4500 | 1.20029 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.6826 | −1.62621 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −30.9319 | −3.17355 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.05224 | 0.411442 | 0.205721 | − | 0.978611i | \(-0.434046\pi\) | ||||
0.205721 | + | 0.978611i | \(0.434046\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.6318 | 1.06853 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.3529 | 1.22916 | 0.614580 | − | 0.788854i | \(-0.289325\pi\) | ||||
0.614580 | + | 0.788854i | \(0.289325\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.1312 | 1.78652 | 0.893262 | − | 0.449536i | \(-0.148411\pi\) | ||||
0.893262 | + | 0.449536i | \(0.148411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −47.0913 | −4.59564 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.8437 | −1.72501 | −0.862506 | − | 0.506047i | \(-0.831106\pi\) | ||||
−0.862506 | + | 0.506047i | \(0.831106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0803 | 1.63600 | 0.817999 | − | 0.575220i | \(-0.195084\pi\) | ||||
0.817999 | + | 0.575220i | \(0.195084\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −19.3373 | −1.83541 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.34564 | −0.879164 | −0.439582 | − | 0.898203i | \(-0.644873\pi\) | ||||
−0.439582 | + | 0.898203i | \(0.644873\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.45782 | 0.135942 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.7303 | 1.36181 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −11.0922 | −1.01682 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.50908 | −0.591734 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.0904 | 2.26233 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 34.9241 | 3.12371 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.2726 | −1.44396 | −0.721982 | − | 0.691912i | \(-0.756769\pi\) | ||||
−0.721982 | + | 0.691912i | \(0.756769\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.8934 | 1.13520 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.0185339 | 0.00161931 | 0.000809655 | − | 1.00000i | \(-0.499742\pi\) | ||||
0.000809655 | 1.00000i | \(0.499742\pi\) | ||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −28.2838 | −2.45252 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −24.3556 | −2.09619 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.93835 | 0.165605 | 0.0828023 | − | 0.996566i | \(-0.473613\pi\) | ||||
0.0828023 | + | 0.996566i | \(0.473613\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6399 | −0.987284 | −0.493642 | − | 0.869665i | \(-0.664335\pi\) | ||||
−0.493642 | + | 0.869665i | \(0.664335\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 25.5084 | 2.14820 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.22215 | 0.520322 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.32790 | 0.276367 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −23.2398 | −1.91679 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.32221 | 0.190243 | 0.0951215 | − | 0.995466i | \(-0.469676\pi\) | ||||
0.0951215 | + | 0.995466i | \(0.469676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.9111 | −0.887933 | −0.443966 | − | 0.896043i | \(-0.646429\pi\) | ||||
−0.443966 | + | 0.896043i | \(0.646429\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.2699 | −1.15365 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.6221 | 1.89737 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.3549 | −0.826413 | −0.413207 | − | 0.910637i | \(-0.635591\pi\) | ||||
−0.413207 | + | 0.910637i | \(0.635591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.0887 | −1.11731 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.33301 | 0.105056 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.98006 | −0.311742 | −0.155871 | − | 0.987777i | \(-0.549818\pi\) | ||||
−0.155871 | + | 0.987777i | \(0.549818\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −25.5903 | −1.99220 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.3238 | 1.18579 | 0.592894 | − | 0.805280i | \(-0.297985\pi\) | ||||
0.592894 | + | 0.805280i | \(0.297985\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.37926 | −0.336866 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −36.3867 | −2.78256 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.23052 | 0.473697 | 0.236849 | − | 0.971547i | \(-0.423885\pi\) | ||||
0.236849 | + | 0.971547i | \(0.423885\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 51.4328 | 3.88796 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.32668 | −0.325214 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.69979 | 0.127049 | 0.0635243 | − | 0.997980i | \(-0.479766\pi\) | ||||
0.0635243 | + | 0.997980i | \(0.479766\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −13.5760 | −1.00910 | −0.504549 | − | 0.863383i | \(-0.668341\pi\) | ||||
−0.504549 | + | 0.863383i | \(0.668341\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.5814 | −1.66926 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 29.1269 | 2.14145 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.02769 | −0.440788 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −22.2705 | −1.61994 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.5539 | −1.05308 | −0.526542 | − | 0.850149i | \(-0.676512\pi\) | ||||
−0.526542 | + | 0.850149i | \(0.676512\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.9503 | −1.79596 | −0.897981 | − | 0.440034i | \(-0.854966\pi\) | ||||
−0.897981 | + | 0.440034i | \(0.854966\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −35.4551 | −2.53899 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.0165 | −1.35487 | −0.677436 | − | 0.735582i | \(-0.736909\pi\) | ||||
−0.677436 | + | 0.735582i | \(0.736909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9265 | 1.41255 | 0.706277 | − | 0.707935i | \(-0.250373\pi\) | ||||
0.706277 | + | 0.707935i | \(0.250373\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −29.7479 | −2.09825 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.04300 | 0.213576 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −37.7926 | −2.63955 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.71490 | 0.119194 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.3699 | −1.06316 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9950 | 1.65189 | 0.825943 | − | 0.563754i | \(-0.190643\pi\) | ||||
0.825943 | + | 0.563754i | \(0.190643\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −37.2998 | −2.55574 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.4207 | −1.32448 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 21.5998 | 1.46629 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.7943 | −1.60787 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.35132 | −0.561770 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.43959 | 0.565157 | 0.282579 | − | 0.959244i | \(-0.408810\pi\) | ||||
0.282579 | + | 0.959244i | \(0.408810\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 66.1676 | 4.41117 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.51956 | 0.366346 | 0.183173 | − | 0.983081i | \(-0.441363\pi\) | ||||
0.183173 | + | 0.983081i | \(0.441363\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.8298 | 1.11214 | 0.556072 | − | 0.831134i | \(-0.312308\pi\) | ||||
0.556072 | + | 0.831134i | \(0.312308\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.3995 | −1.53957 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.63332 | −0.369051 | −0.184526 | − | 0.982828i | \(-0.559075\pi\) | ||||
−0.184526 | + | 0.982828i | \(0.559075\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −38.4222 | −2.50639 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.76039 | 0.439135 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.2855 | −1.50621 | −0.753106 | − | 0.657900i | \(-0.771445\pi\) | ||||
−0.753106 | + | 0.657900i | \(0.771445\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −22.5636 | −1.45345 | −0.726724 | − | 0.686929i | \(-0.758958\pi\) | ||||
−0.726724 | + | 0.686929i | \(0.758958\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9645 | 0.895823 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 35.0051 | 2.23639 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.2949 | −1.35496 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 28.5210 | 1.80744 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.5747 | 0.919947 | 0.459974 | − | 0.887933i | \(-0.347859\pi\) | ||||
0.459974 | + | 0.887933i | \(0.347859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.724382 | 0.0455415 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 34.3471 | 2.15090 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.5815 | 0.784810 | 0.392405 | − | 0.919793i | \(-0.371643\pi\) | ||||
0.392405 | + | 0.919793i | \(0.371643\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 26.6333 | 1.65491 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.91477 | 0.242318 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.60784 | −0.284132 | −0.142066 | − | 0.989857i | \(-0.545374\pi\) | ||||
−0.142066 | + | 0.989857i | \(0.545374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.2212 | 1.30361 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.0823 | −0.678223 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.5415 | 0.703698 | 0.351849 | − | 0.936057i | \(-0.385553\pi\) | ||||
0.351849 | + | 0.936057i | \(0.385553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.6168 | 1.79909 | 0.899547 | − | 0.436823i | \(-0.143897\pi\) | ||||
0.899547 | + | 0.436823i | \(0.143897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −32.4198 | −1.96213 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 27.9495 | 1.68542 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 28.2029 | 1.69455 | 0.847273 | − | 0.531158i | \(-0.178243\pi\) | ||||
0.847273 | + | 0.531158i | \(0.178243\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 27.7877 | 1.66361 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.55832 | 0.0929616 | 0.0464808 | − | 0.998919i | \(-0.485199\pi\) | ||||
0.0464808 | + | 0.998919i | \(0.485199\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.61488 | −0.214883 | −0.107441 | − | 0.994211i | \(-0.534266\pi\) | ||||
−0.107441 | + | 0.994211i | \(0.534266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 87.5812 | 5.18786 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −34.5571 | −2.03984 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.90968 | −0.524099 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.4736 | −0.672593 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.6850 | 0.916327 | 0.458163 | − | 0.888868i | \(-0.348507\pi\) | ||||
0.458163 | + | 0.888868i | \(0.348507\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.51709 | 0.379440 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.1022 | −0.702239 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.00363 | 0.0580412 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.7581 | −1.02356 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −34.9763 | −2.00933 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 34.0133 | 1.94760 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.4816 | 1.45431 | 0.727155 | − | 0.686473i | \(-0.240842\pi\) | ||||
0.727155 | + | 0.686473i | \(0.240842\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −51.3371 | −2.92047 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.7911 | 1.51918 | 0.759592 | − | 0.650400i | \(-0.225399\pi\) | ||||
0.759592 | + | 0.650400i | \(0.225399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 32.6430 | 1.84509 | 0.922546 | − | 0.385886i | \(-0.126104\pi\) | ||||
0.922546 | + | 0.385886i | \(0.126104\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 83.4401 | 4.70131 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.25413 | 0.295101 | 0.147551 | − | 0.989054i | \(-0.452861\pi\) | ||||
0.147551 | + | 0.989054i | \(0.452861\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.65362 | 0.0925849 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 50.5229 | 2.81991 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.6294 | 1.14785 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.7239 | 2.14802 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −48.3615 | −2.67440 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −35.1328 | −1.93694 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.8852 | −1.14795 | −0.573976 | − | 0.818872i | \(-0.694600\pi\) | ||||
−0.573976 | + | 0.818872i | \(0.694600\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 34.2634 | 1.87762 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 44.8079 | 2.44812 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.38006 | 0.347544 | 0.173772 | − | 0.984786i | \(-0.444404\pi\) | ||||
0.173772 | + | 0.984786i | \(0.444404\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.4614 | 1.43719 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.7377 | 0.635632 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.71022 | 0.254328 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.12769 | −0.222227 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.57016 | −0.352705 | −0.176352 | − | 0.984327i | \(-0.556430\pi\) | ||||
−0.176352 | + | 0.984327i | \(0.556430\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.2031 | −0.813801 | −0.406901 | − | 0.913472i | \(-0.633390\pi\) | ||||
−0.406901 | + | 0.913472i | \(0.633390\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.7675 | −0.894982 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.7242 | −0.836916 | −0.418458 | − | 0.908236i | \(-0.637429\pi\) | ||||
−0.418458 | + | 0.908236i | \(0.637429\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 56.1830 | 2.98188 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 31.4066 | 1.66221 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.5096 | −1.34635 | −0.673174 | − | 0.739484i | \(-0.735069\pi\) | ||||
−0.673174 | + | 0.739484i | \(0.735069\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.6027 | 1.76857 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 18.4299 | 0.967320 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 35.8403 | 1.87596 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.13935 | −0.424871 | −0.212435 | − | 0.977175i | \(-0.568139\pi\) | ||||
−0.212435 | + | 0.977175i | \(0.568139\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −44.4572 | −2.31435 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.4044 | 1.00743 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.29033 | 0.429257 | 0.214628 | − | 0.976696i | \(-0.431146\pi\) | ||||
0.214628 | + | 0.976696i | \(0.431146\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −98.8848 | −5.10639 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.29108 | 0.117997 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5481 | 0.695921 | 0.347960 | − | 0.937509i | \(-0.386874\pi\) | ||||
0.347960 | + | 0.937509i | \(0.386874\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 46.0747 | 2.36048 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.0800 | −1.07714 | −0.538568 | − | 0.842582i | \(-0.681034\pi\) | ||||
−0.538568 | + | 0.842582i | \(0.681034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 35.2455 | 1.79628 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −22.8455 | −1.16130 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.07613 | −0.460178 | −0.230089 | − | 0.973170i | \(-0.573902\pi\) | ||||
−0.230089 | + | 0.973170i | \(0.573902\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.972261 | −0.0491693 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.0524771 | −0.00264712 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.1829 | −0.512356 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.3595 | −0.821060 | −0.410530 | − | 0.911847i | \(-0.634656\pi\) | ||||
−0.410530 | + | 0.911847i | \(0.634656\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 80.0833 | 4.00918 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.7143 | 1.08436 | 0.542180 | − | 0.840263i | \(-0.317599\pi\) | ||||
0.542180 | + | 0.840263i | \(0.317599\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.2625 | 0.810093 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.77157 | 0.237101 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.4730 | 0.717402 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.0374 | −1.63360 | −0.816798 | − | 0.576924i | \(-0.804253\pi\) | ||||
−0.816798 | + | 0.576924i | \(0.804253\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.48829 | −0.270717 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.95916 | 0.293231 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −42.9599 | −2.10882 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 32.9574 | 1.61393 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.2484 | −1.38003 | −0.690013 | − | 0.723797i | \(-0.742395\pi\) | ||||
−0.690013 | + | 0.723797i | \(0.742395\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.83979 | −0.382088 | −0.191044 | − | 0.981581i | \(-0.561187\pi\) | ||||
−0.191044 | + | 0.981581i | \(0.561187\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −45.1978 | −2.19759 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37.5137 | −1.81968 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.1014 | 1.50510 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −17.6175 | −0.850581 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0936 | −0.630697 | −0.315348 | − | 0.948976i | \(-0.602121\pi\) | ||||
−0.315348 | + | 0.948976i | \(0.602121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.22919 | 0.155185 | 0.0775926 | − | 0.996985i | \(-0.475277\pi\) | ||||
0.0775926 | + | 0.996985i | \(0.475277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.42268 | −0.451783 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.47916 | −0.118594 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.1627 | −0.485039 | −0.242520 | − | 0.970147i | \(-0.577974\pi\) | ||||
−0.242520 | + | 0.970147i | \(0.577974\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 41.1782 | 1.96086 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.09206 | −0.0518855 | −0.0259427 | − | 0.999663i | \(-0.508259\pi\) | ||||
−0.0259427 | + | 0.999663i | \(0.508259\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.6927 | 0.791310 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.57516 | −0.310994 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.18522 | 0.433477 | 0.216739 | − | 0.976230i | \(-0.430458\pi\) | ||||
0.216739 | + | 0.976230i | \(0.430458\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.7790 | −0.884267 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 30.8939 | 1.45152 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 48.8325 | 2.28930 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.62771 | −0.0761412 | −0.0380706 | − | 0.999275i | \(-0.512121\pi\) | ||||
−0.0380706 | + | 0.999275i | \(0.512121\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.2435 | 0.758179 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.6795 | −0.776842 | −0.388421 | − | 0.921482i | \(-0.626979\pi\) | ||||
−0.388421 | + | 0.921482i | \(0.626979\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.78496 | 0.222376 | 0.111188 | − | 0.993799i | \(-0.464534\pi\) | ||||
0.111188 | + | 0.993799i | \(0.464534\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −66.8839 | −3.10167 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.6881 | 1.74400 | 0.871999 | − | 0.489508i | \(-0.162824\pi\) | ||||
0.871999 | + | 0.489508i | \(0.162824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.9719 | 1.89190 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.3191 | 1.35095 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.65009 | −0.443711 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −95.6557 | −4.38899 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.9635 | 1.14300 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.57745 | −0.117767 | −0.0588834 | − | 0.998265i | \(-0.518754\pi\) | ||||
−0.0588834 | + | 0.998265i | \(0.518754\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.0523 | 0.914306 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.77431 | −0.171737 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.2821 | 0.784741 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.99998 | 0.226571 | 0.113285 | − | 0.993562i | \(-0.463863\pi\) | ||||
0.113285 | + | 0.993562i | \(0.463863\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.2692 | 0.509612 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9889 | 0.766699 | 0.383350 | − | 0.923603i | \(-0.374770\pi\) | ||||
0.383350 | + | 0.923603i | \(0.374770\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.21948 | −0.0999602 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 45.3428 | 2.03801 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 51.3731 | 2.30440 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.9474 | 0.624373 | 0.312187 | − | 0.950021i | \(-0.398939\pi\) | ||||
0.312187 | + | 0.950021i | \(0.398939\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −43.3880 | −1.93843 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.7036 | −0.967717 | −0.483858 | − | 0.875146i | \(-0.660765\pi\) | ||||
−0.483858 | + | 0.875146i | \(0.660765\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 52.6832 | 2.34437 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.3995 | 0.550682 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.7333 | −0.963311 | −0.481656 | − | 0.876361i | \(-0.659964\pi\) | ||||
−0.481656 | + | 0.876361i | \(0.659964\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 32.7719 | 1.44975 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 41.4190 | 1.82869 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 77.3268 | 3.40743 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.0918 | −0.839657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.6412 | −0.774363 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.0548 | 0.747186 | 0.373593 | − | 0.927593i | \(-0.378126\pi\) | ||||
0.373593 | + | 0.927593i | \(0.378126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.3195 | 1.80678 | 0.903388 | − | 0.428824i | \(-0.141072\pi\) | ||||
0.903388 | + | 0.428824i | \(0.141072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −145.628 | −6.35572 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.7543 | −0.686266 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8832 | −0.994920 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.66636 | 0.332692 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −26.0181 | −1.12697 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −76.1003 | −3.29010 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.81283 | −0.207689 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.3939 | 0.749208 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −38.4177 | −1.65170 | −0.825852 | − | 0.563887i | \(-0.809305\pi\) | ||||
−0.825852 | + | 0.563887i | \(0.809305\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 38.4394 | 1.64959 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 72.8448 | 3.12033 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.4323 | −1.47222 | −0.736109 | − | 0.676864i | \(-0.763339\pi\) | ||||
−0.736109 | + | 0.676864i | \(0.763339\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 40.0115 | 1.70765 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.65942 | −0.241099 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.31111 | −0.395949 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −82.4704 | −3.50068 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −31.8370 | −1.34898 | −0.674488 | − | 0.738286i | \(-0.735636\pi\) | ||||
−0.674488 | + | 0.738286i | \(0.735636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.3701 | −0.565496 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.0669 | 0.720565 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.4508 | −0.482592 | −0.241296 | − | 0.970452i | \(-0.577572\pi\) | ||||
−0.241296 | + | 0.970452i | \(0.577572\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −39.8576 | −1.67682 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.36308 | 0.183232 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.5735 | −1.07210 | −0.536049 | − | 0.844187i | \(-0.680084\pi\) | ||||
−0.536049 | + | 0.844187i | \(0.680084\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.15130 | 0.257424 | 0.128712 | − | 0.991682i | \(-0.458916\pi\) | ||||
0.128712 | + | 0.991682i | \(0.458916\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 41.2082 | 1.72150 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.50824 | 0.188007 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0654 | −0.710444 | −0.355222 | − | 0.934782i | \(-0.615595\pi\) | ||||
−0.355222 | + | 0.934782i | \(0.615595\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 70.6448 | 2.93590 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.2821 | −1.62969 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5447 | 0.436717 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 62.8222 | 2.59738 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.9333 | 1.11166 | 0.555828 | − | 0.831298i | \(-0.312401\pi\) | ||||
0.555828 | + | 0.831298i | \(0.312401\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −40.1716 | −1.65524 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 53.8437 | 2.21484 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.1893 | −0.993334 | −0.496667 | − | 0.867941i | \(-0.665443\pi\) | ||||
−0.496667 | + | 0.867941i | \(0.665443\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −47.3063 | −1.93937 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −56.4204 | −2.30913 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.86196 | −0.321231 | −0.160615 | − | 0.987017i | \(-0.551348\pi\) | ||||
−0.160615 | + | 0.987017i | \(0.551348\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.6031 | −0.473300 | −0.236650 | − | 0.971595i | \(-0.576049\pi\) | ||||
−0.236650 | + | 0.971595i | \(0.576049\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 52.7097 | 2.14650 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −27.7602 | −1.12861 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.6568 | −0.676080 | −0.338040 | − | 0.941132i | \(-0.609764\pi\) | ||||
−0.338040 | + | 0.941132i | \(0.609764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.61600 | −0.349138 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.4516 | −1.07012 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.70838 | 0.392118 | 0.196059 | − | 0.980592i | \(-0.437186\pi\) | ||||
0.196059 | + | 0.980592i | \(0.437186\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 107.007 | 4.31492 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.9271 | 1.00353 | 0.501764 | − | 0.865004i | \(-0.332684\pi\) | ||||
0.501764 | + | 0.865004i | \(0.332684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.2158 | −0.973316 | −0.486658 | − | 0.873593i | \(-0.661784\pi\) | ||||
−0.486658 | + | 0.873593i | \(0.661784\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.95207 | −0.0783339 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.2636 | 0.611524 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 83.0015 | 3.32006 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 43.5187 | 1.73797 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19.4256 | −0.774549 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.57832 | 0.381307 | 0.190653 | − | 0.981657i | \(-0.438939\pi\) | ||||
0.190653 | + | 0.981657i | \(0.438939\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −67.9400 | −2.70037 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −69.4002 | −2.75406 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0991 | 0.954841 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 66.0907 | 2.61451 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.2024 | −1.19292 | −0.596461 | − | 0.802642i | \(-0.703427\pi\) | ||||
−0.596461 | + | 0.802642i | \(0.703427\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.2715 | −1.15436 | −0.577178 | − | 0.816618i | \(-0.695846\pi\) | ||||
−0.577178 | + | 0.816618i | \(0.695846\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 54.9883 | 2.16516 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.8158 | 1.09355 | 0.546776 | − | 0.837279i | \(-0.315855\pi\) | ||||
0.546776 | + | 0.837279i | \(0.315855\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.23831 | 0.127115 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −61.1579 | −2.39697 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.73215 | −0.224316 | −0.112158 | − | 0.993690i | \(-0.535776\pi\) | ||||
−0.112158 | + | 0.993690i | \(0.535776\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.0790439 | 0.00308850 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 42.1606 | 1.64484 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.2628 | 1.25678 | 0.628390 | − | 0.777898i | \(-0.283714\pi\) | ||||
0.628390 | + | 0.777898i | \(0.283714\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.2122 | −0.474999 | −0.237500 | − | 0.971388i | \(-0.576328\pi\) | ||||
−0.237500 | + | 0.971388i | \(0.576328\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.6461 | 0.918338 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −120.626 | −4.67767 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.266728 | 0.0103277 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.8960 | −0.923874 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.9011 | 0.652459 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.21631 | 0.162527 | 0.0812635 | − | 0.996693i | \(-0.474104\pi\) | ||||
0.0812635 | + | 0.996693i | \(0.474104\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −75.3186 | −2.89902 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.3291 | 1.43467 | 0.717337 | − | 0.696726i | \(-0.245361\pi\) | ||||
0.717337 | + | 0.696726i | \(0.245361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.8026 | 0.606448 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.6282 | −0.598873 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.4120 | 1.08715 | 0.543577 | − | 0.839359i | \(-0.317069\pi\) | ||||
0.543577 | + | 0.839359i | \(0.317069\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.26676 | 0.315857 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −47.6522 | −1.81804 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 14.6096 | 0.556582 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.8252 | −1.24873 | −0.624364 | − | 0.781134i | \(-0.714642\pi\) | ||||
−0.624364 | + | 0.781134i | \(0.714642\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 41.4610 | 1.57497 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −49.6423 | −1.88304 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.2050 | 0.954707 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.9503 | 0.603295 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −31.2548 | −1.18048 | −0.590239 | − | 0.807229i | \(-0.700967\pi\) | ||||
−0.590239 | + | 0.807229i | \(0.700967\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49.5331 | −1.86818 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 108.789 | 4.09724 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 48.1729 | 1.81173 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.69132 | −0.101075 | −0.0505373 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505373 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.9786 | −0.449233 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.89328 | 0.0709039 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.5364 | 0.992407 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 65.9309 | 2.46223 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.33934 | −0.199124 | −0.0995620 | − | 0.995031i | \(-0.531744\pi\) | ||||
−0.0995620 | + | 0.995031i | \(0.531744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 70.7068 | 2.63326 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 63.8870 | 2.37598 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.2914 | 0.382213 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9052 | −0.515716 | −0.257858 | − | 0.966183i | \(-0.583017\pi\) | ||||
−0.257858 | + | 0.966183i | \(0.583017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −42.8958 | −1.58873 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.9523 | 0.479057 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.5028 | 0.387931 | 0.193965 | − | 0.981008i | \(-0.437865\pi\) | ||||
0.193965 | + | 0.981008i | \(0.437865\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −99.1141 | −3.65588 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.2649 | 0.820136 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.6931 | −1.16585 | −0.582925 | − | 0.812526i | \(-0.698092\pi\) | ||||
−0.582925 | + | 0.812526i | \(0.698092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 60.2949 | 2.21499 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.02988 | 0.331274 | 0.165637 | − | 0.986187i | \(-0.447032\pi\) | ||||
0.165637 | + | 0.986187i | \(0.447032\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.90386 | 0.362849 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −50.5358 | −1.84901 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −69.5853 | −2.54259 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −41.2671 | −1.50386 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46.5341 | −1.69355 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.5770 | −0.602503 | −0.301251 | − | 0.953545i | \(-0.597404\pi\) | ||||
−0.301251 | + | 0.953545i | \(0.597404\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.05103 | −0.0744477 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.0104 | 0.906627 | 0.453313 | − | 0.891351i | \(-0.350242\pi\) | ||||
0.453313 | + | 0.891351i | \(0.350242\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 66.6085 | 2.41139 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −60.8588 | −2.20036 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.48666 | 0.162004 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.5552 | 0.957606 | 0.478803 | − | 0.877922i | \(-0.341071\pi\) | ||||
0.478803 | + | 0.877922i | \(0.341071\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −35.6234 | −1.28294 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.05848 | −0.217908 | −0.108954 | − | 0.994047i | \(-0.534750\pi\) | ||||
−0.108954 | + | 0.994047i | \(0.534750\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 73.0503 | 2.62404 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −75.4101 | −2.70532 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 64.2700 | 2.30271 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.9171 | 0.998952 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.45619 | −0.159251 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.1621 | −1.57621 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.26096 | 0.187533 | 0.0937665 | − | 0.995594i | \(-0.470109\pi\) | ||||
0.0937665 | + | 0.995594i | \(0.470109\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 13.0467 | 0.464476 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.4454 | −1.29585 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.4163 | 0.831538 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −60.0860 | −2.13103 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.80092 | 0.170057 | 0.0850287 | − | 0.996378i | \(-0.472902\pi\) | ||||
0.0850287 | + | 0.996378i | \(0.472902\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25.6249 | 0.906544 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 19.6364 | 0.693819 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.8089 | 0.628461 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.68508 | 0.200373 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −32.6789 | −1.15035 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38.2087 | −1.34335 | −0.671674 | − | 0.740847i | \(-0.734424\pi\) | ||||
−0.671674 | + | 0.740847i | \(0.734424\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.7417 | 1.07949 | 0.539743 | − | 0.841830i | \(-0.318521\pi\) | ||||
0.539743 | + | 0.841830i | \(0.318521\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −83.8577 | −2.94102 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.9743 | −0.594584 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33.0269 | 1.15546 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 57.4439 | 2.00725 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.2126 | 0.600725 | 0.300363 | − | 0.953825i | \(-0.402892\pi\) | ||||
0.300363 | + | 0.953825i | \(0.402892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.02994 | −0.245048 | −0.122524 | − | 0.992466i | \(-0.539099\pi\) | ||||
−0.122524 | + | 0.992466i | \(0.539099\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −79.1369 | −2.75519 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.4072 | 1.61374 | 0.806869 | − | 0.590731i | \(-0.201161\pi\) | ||||
0.806869 | + | 0.590731i | \(0.201161\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.7914 | −1.59040 | −0.795201 | − | 0.606346i | \(-0.792635\pi\) | ||||
−0.795201 | + | 0.606346i | \(0.792635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −79.8541 | −2.77011 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23.3459 | −0.808889 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 65.3534 | 2.26165 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.6308 | −1.09332 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.11008 | −0.245467 | −0.122734 | − | 0.992440i | \(-0.539166\pi\) | ||||
−0.122734 | + | 0.992440i | \(0.539166\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3911 | −0.979004 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.41226 | −0.151966 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.6768 | −0.642503 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.3836 | −0.872190 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.2353 | 0.351273 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.33449 | 0.0800252 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.4543 | 0.666102 | 0.333051 | − | 0.942909i | \(-0.391922\pi\) | ||||
0.333051 | + | 0.942909i | \(0.391922\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −155.183 | −5.30716 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.4375 | −0.732290 | −0.366145 | − | 0.930558i | \(-0.619323\pi\) | ||||
−0.366145 | + | 0.930558i | \(0.619323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.0759 | −1.02618 | −0.513089 | − | 0.858335i | \(-0.671499\pi\) | ||||
−0.513089 | + | 0.858335i | \(0.671499\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 97.8457 | 3.33457 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.2949 | 0.827008 | 0.413504 | − | 0.910502i | \(-0.364305\pi\) | ||||
0.413504 | + | 0.910502i | \(0.364305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.5722 | 0.903480 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25.2270 | 0.856755 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.05983 | −0.171643 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.8478 | 1.04524 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 20.3298 | 0.688059 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 136.194 | 4.60421 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.2901 | 1.05659 | 0.528296 | − | 0.849060i | \(-0.322831\pi\) | ||||
0.528296 | + | 0.849060i | \(0.322831\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −44.4108 | −1.49794 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.89954 | 0.0639970 | 0.0319985 | − | 0.999488i | \(-0.489813\pi\) | ||||
0.0319985 | + | 0.999488i | \(0.489813\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.1920 | 1.85736 | 0.928679 | − | 0.370884i | \(-0.120945\pi\) | ||||
0.928679 | + | 0.370884i | \(0.120945\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.4526 | −0.620278 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.6398 | −0.995206 | −0.497603 | − | 0.867405i | \(-0.665786\pi\) | ||||
−0.497603 | + | 0.867405i | \(0.665786\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −63.4588 | −2.12834 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.37098 | 0.0794307 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 65.3407 | 2.18654 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.24935 | 0.242319 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.84169 | −0.0948812 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.32198 | 0.144146 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.1530 | −0.471506 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 50.2807 | 1.67324 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −57.8995 | −1.92465 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 48.0318 | 1.59487 | 0.797436 | − | 0.603404i | \(-0.206189\pi\) | ||||
0.797436 | + | 0.603404i | \(0.206189\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 61.9737 | 2.05554 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.2868 | −0.672133 | −0.336066 | − | 0.941838i | \(-0.609097\pi\) | ||||
−0.336066 | + | 0.941838i | \(0.609097\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.3466 | −0.706469 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −96.3060 | −3.18378 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.0722769 | 0.00238679 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20.4138 | 0.673389 | 0.336694 | − | 0.941614i | \(-0.390691\pi\) | ||||
0.336694 | + | 0.941614i | \(0.390691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −72.1490 | −2.37739 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 38.6789 | 1.27313 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 90.0738 | 2.96161 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 90.9632 | 2.98762 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 15.9611 | 0.523666 | 0.261833 | − | 0.965113i | \(-0.415673\pi\) | ||||
0.261833 | + | 0.965113i | \(0.415673\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −59.5296 | −1.95100 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −75.8568 | −2.48344 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.7071 | −0.840712 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.6107 | 0.705991 | 0.352996 | − | 0.935625i | \(-0.385163\pi\) | ||||
0.352996 | + | 0.935625i | \(0.385163\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −92.4261 | −3.01621 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.0829 | 0.882876 | 0.441438 | − | 0.897292i | \(-0.354469\pi\) | ||||
0.441438 | + | 0.897292i | \(0.354469\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.02903 | −0.0986389 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −94.9799 | −3.08970 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.6301 | 1.67775 | 0.838876 | − | 0.544323i | \(-0.183213\pi\) | ||||
0.838876 | + | 0.544323i | \(0.183213\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.6741 | 0.800954 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.8766 | −0.482408 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −58.6944 | −1.90130 | −0.950649 | − | 0.310270i | \(-0.899581\pi\) | ||||
−0.950649 | + | 0.310270i | \(0.899581\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −62.0701 | −2.00854 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.68209 | −0.151350 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.55903 | 0.244094 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.321783 | −0.0103801 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −89.5205 | −2.88476 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −106.409 | −3.42543 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 40.5109 | 1.30274 | 0.651371 | − | 0.758759i | \(-0.274194\pi\) | ||||
0.651371 | + | 0.758759i | \(0.274194\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −58.4105 | −1.87642 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.3299 | 0.395686 | 0.197843 | − | 0.980234i | \(-0.436606\pi\) | ||||
0.197843 | + | 0.980234i | \(0.436606\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.3924 | −1.45521 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −109.644 | −3.51141 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.6190 | 0.627666 | 0.313833 | − | 0.949478i | \(-0.398387\pi\) | ||||
0.313833 | + | 0.949478i | \(0.398387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.29453 | 0.265094 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 85.6908 | 2.73590 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.6017 | 0.529512 | 0.264756 | − | 0.964315i | \(-0.414709\pi\) | ||||
0.264756 | + | 0.964315i | \(0.414709\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −81.1024 | −2.58414 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 99.4757 | 3.16635 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.55655 | −0.0494954 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.4425 | 0.395249 | 0.197624 | − | 0.980278i | \(-0.436677\pi\) | ||||
0.197624 | + | 0.980278i | \(0.436677\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 59.1346 | 1.87658 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 84.9835 | 2.69416 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.4078 | −0.963023 | −0.481512 | − | 0.876440i | \(-0.659912\pi\) | ||||
−0.481512 | + | 0.876440i | \(0.659912\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −39.0020 | −1.23397 |
(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 | 6008.2.a.e.1.5 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.e.1.5 | ✓ | 50 | 1.1 | even | 1 | trivial |