Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | −0.00804327 | −0.00464379 | −0.00232189 | − | 0.999997i | \(-0.500739\pi\) | ||||
−0.00232189 | + | 0.999997i | \(0.500739\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.67628 | 1.64408 | 0.822041 | − | 0.569428i | \(-0.192835\pi\) | ||||
0.822041 | + | 0.569428i | \(0.192835\pi\) | |||||||
\(6\) | −0.00804327 | −0.00328365 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.99994 | −0.999978 | ||||||||
\(10\) | 3.67628 | 1.16254 | ||||||||
\(11\) | −3.60308 | −1.08637 | −0.543184 | − | 0.839613i | \(-0.682782\pi\) | ||||
−0.543184 | + | 0.839613i | \(0.682782\pi\) | |||||||
\(12\) | −0.00804327 | −0.00232189 | ||||||||
\(13\) | −5.05961 | −1.40328 | −0.701642 | − | 0.712530i | \(-0.747549\pi\) | ||||
−0.701642 | + | 0.712530i | \(0.747549\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −0.0295693 | −0.00763476 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.25537 | −1.03208 | −0.516039 | − | 0.856565i | \(-0.672594\pi\) | ||||
−0.516039 | + | 0.856565i | \(0.672594\pi\) | |||||||
\(18\) | −2.99994 | −0.707092 | ||||||||
\(19\) | −7.20088 | −1.65200 | −0.825998 | − | 0.563674i | \(-0.809388\pi\) | ||||
−0.825998 | + | 0.563674i | \(0.809388\pi\) | |||||||
\(20\) | 3.67628 | 0.822041 | ||||||||
\(21\) | −0.00804327 | −0.00175519 | ||||||||
\(22\) | −3.60308 | −0.768179 | ||||||||
\(23\) | −5.45457 | −1.13736 | −0.568678 | − | 0.822560i | \(-0.692545\pi\) | ||||
−0.568678 | + | 0.822560i | \(0.692545\pi\) | |||||||
\(24\) | −0.00804327 | −0.00164183 | ||||||||
\(25\) | 8.51503 | 1.70301 | ||||||||
\(26\) | −5.05961 | −0.992272 | ||||||||
\(27\) | 0.0482591 | 0.00928747 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 5.38015 | 0.999068 | 0.499534 | − | 0.866294i | \(-0.333505\pi\) | ||||
0.499534 | + | 0.866294i | \(0.333505\pi\) | |||||||
\(30\) | −0.0295693 | −0.00539859 | ||||||||
\(31\) | 8.43957 | 1.51579 | 0.757896 | − | 0.652376i | \(-0.226228\pi\) | ||||
0.757896 | + | 0.652376i | \(0.226228\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.0289805 | 0.00504486 | ||||||||
\(34\) | −4.25537 | −0.729790 | ||||||||
\(35\) | 3.67628 | 0.621405 | ||||||||
\(36\) | −2.99994 | −0.499989 | ||||||||
\(37\) | −6.72749 | −1.10599 | −0.552997 | − | 0.833183i | \(-0.686516\pi\) | ||||
−0.552997 | + | 0.833183i | \(0.686516\pi\) | |||||||
\(38\) | −7.20088 | −1.16814 | ||||||||
\(39\) | 0.0406958 | 0.00651655 | ||||||||
\(40\) | 3.67628 | 0.581271 | ||||||||
\(41\) | −2.42117 | −0.378123 | −0.189061 | − | 0.981965i | \(-0.560545\pi\) | ||||
−0.189061 | + | 0.981965i | \(0.560545\pi\) | |||||||
\(42\) | −0.00804327 | −0.00124110 | ||||||||
\(43\) | 1.62203 | 0.247358 | 0.123679 | − | 0.992322i | \(-0.460531\pi\) | ||||
0.123679 | + | 0.992322i | \(0.460531\pi\) | |||||||
\(44\) | −3.60308 | −0.543184 | ||||||||
\(45\) | −11.0286 | −1.64405 | ||||||||
\(46\) | −5.45457 | −0.804233 | ||||||||
\(47\) | 11.8922 | 1.73465 | 0.867326 | − | 0.497741i | \(-0.165837\pi\) | ||||
0.867326 | + | 0.497741i | \(0.165837\pi\) | |||||||
\(48\) | −0.00804327 | −0.00116095 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 8.51503 | 1.20421 | ||||||||
\(51\) | 0.0342271 | 0.00479275 | ||||||||
\(52\) | −5.05961 | −0.701642 | ||||||||
\(53\) | −6.86493 | −0.942971 | −0.471485 | − | 0.881874i | \(-0.656282\pi\) | ||||
−0.471485 | + | 0.881874i | \(0.656282\pi\) | |||||||
\(54\) | 0.0482591 | 0.00656723 | ||||||||
\(55\) | −13.2459 | −1.78608 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0.0579186 | 0.00767151 | ||||||||
\(58\) | 5.38015 | 0.706448 | ||||||||
\(59\) | −3.53286 | −0.459940 | −0.229970 | − | 0.973198i | \(-0.573863\pi\) | ||||
−0.229970 | + | 0.973198i | \(0.573863\pi\) | |||||||
\(60\) | −0.0295693 | −0.00381738 | ||||||||
\(61\) | −1.04894 | −0.134303 | −0.0671516 | − | 0.997743i | \(-0.521391\pi\) | ||||
−0.0671516 | + | 0.997743i | \(0.521391\pi\) | |||||||
\(62\) | 8.43957 | 1.07183 | ||||||||
\(63\) | −2.99994 | −0.377956 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −18.6006 | −2.30711 | ||||||||
\(66\) | 0.0289805 | 0.00356726 | ||||||||
\(67\) | −12.1661 | −1.48633 | −0.743165 | − | 0.669108i | \(-0.766676\pi\) | ||||
−0.743165 | + | 0.669108i | \(0.766676\pi\) | |||||||
\(68\) | −4.25537 | −0.516039 | ||||||||
\(69\) | 0.0438726 | 0.00528164 | ||||||||
\(70\) | 3.67628 | 0.439399 | ||||||||
\(71\) | −9.30064 | −1.10378 | −0.551892 | − | 0.833916i | \(-0.686094\pi\) | ||||
−0.551892 | + | 0.833916i | \(0.686094\pi\) | |||||||
\(72\) | −2.99994 | −0.353546 | ||||||||
\(73\) | −2.31874 | −0.271388 | −0.135694 | − | 0.990751i | \(-0.543326\pi\) | ||||
−0.135694 | + | 0.990751i | \(0.543326\pi\) | |||||||
\(74\) | −6.72749 | −0.782055 | ||||||||
\(75\) | −0.0684887 | −0.00790840 | ||||||||
\(76\) | −7.20088 | −0.825998 | ||||||||
\(77\) | −3.60308 | −0.410609 | ||||||||
\(78\) | 0.0406958 | 0.00460790 | ||||||||
\(79\) | 2.18286 | 0.245591 | 0.122796 | − | 0.992432i | \(-0.460814\pi\) | ||||
0.122796 | + | 0.992432i | \(0.460814\pi\) | |||||||
\(80\) | 3.67628 | 0.411021 | ||||||||
\(81\) | 8.99942 | 0.999935 | ||||||||
\(82\) | −2.42117 | −0.267373 | ||||||||
\(83\) | −11.3539 | −1.24625 | −0.623125 | − | 0.782122i | \(-0.714137\pi\) | ||||
−0.623125 | + | 0.782122i | \(0.714137\pi\) | |||||||
\(84\) | −0.00804327 | −0.000877593 0 | ||||||||
\(85\) | −15.6439 | −1.69682 | ||||||||
\(86\) | 1.62203 | 0.174908 | ||||||||
\(87\) | −0.0432740 | −0.00463946 | ||||||||
\(88\) | −3.60308 | −0.384089 | ||||||||
\(89\) | 3.87667 | 0.410926 | 0.205463 | − | 0.978665i | \(-0.434130\pi\) | ||||
0.205463 | + | 0.978665i | \(0.434130\pi\) | |||||||
\(90\) | −11.0286 | −1.16252 | ||||||||
\(91\) | −5.05961 | −0.530392 | ||||||||
\(92\) | −5.45457 | −0.568678 | ||||||||
\(93\) | −0.0678817 | −0.00703901 | ||||||||
\(94\) | 11.8922 | 1.22658 | ||||||||
\(95\) | −26.4724 | −2.71602 | ||||||||
\(96\) | −0.00804327 | −0.000820913 0 | ||||||||
\(97\) | −5.64654 | −0.573319 | −0.286660 | − | 0.958033i | \(-0.592545\pi\) | ||||
−0.286660 | + | 0.958033i | \(0.592545\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 10.8090 | 1.08635 | ||||||||
\(100\) | 8.51503 | 0.851503 | ||||||||
\(101\) | −6.63060 | −0.659769 | −0.329885 | − | 0.944021i | \(-0.607010\pi\) | ||||
−0.329885 | + | 0.944021i | \(0.607010\pi\) | |||||||
\(102\) | 0.0342271 | 0.00338899 | ||||||||
\(103\) | −3.07660 | −0.303146 | −0.151573 | − | 0.988446i | \(-0.548434\pi\) | ||||
−0.151573 | + | 0.988446i | \(0.548434\pi\) | |||||||
\(104\) | −5.05961 | −0.496136 | ||||||||
\(105\) | −0.0295693 | −0.00288567 | ||||||||
\(106\) | −6.86493 | −0.666781 | ||||||||
\(107\) | 18.6160 | 1.79968 | 0.899838 | − | 0.436224i | \(-0.143684\pi\) | ||||
0.899838 | + | 0.436224i | \(0.143684\pi\) | |||||||
\(108\) | 0.0482591 | 0.00464374 | ||||||||
\(109\) | 9.63832 | 0.923183 | 0.461592 | − | 0.887093i | \(-0.347279\pi\) | ||||
0.461592 | + | 0.887093i | \(0.347279\pi\) | |||||||
\(110\) | −13.2459 | −1.26295 | ||||||||
\(111\) | 0.0541111 | 0.00513600 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −13.1349 | −1.23563 | −0.617813 | − | 0.786325i | \(-0.711981\pi\) | ||||
−0.617813 | + | 0.786325i | \(0.711981\pi\) | |||||||
\(114\) | 0.0579186 | 0.00542458 | ||||||||
\(115\) | −20.0525 | −1.86991 | ||||||||
\(116\) | 5.38015 | 0.499534 | ||||||||
\(117\) | 15.1785 | 1.40325 | ||||||||
\(118\) | −3.53286 | −0.325226 | ||||||||
\(119\) | −4.25537 | −0.390089 | ||||||||
\(120\) | −0.0295693 | −0.00269930 | ||||||||
\(121\) | 1.98216 | 0.180197 | ||||||||
\(122\) | −1.04894 | −0.0949667 | ||||||||
\(123\) | 0.0194741 | 0.00175592 | ||||||||
\(124\) | 8.43957 | 0.757896 | ||||||||
\(125\) | 12.9222 | 1.15580 | ||||||||
\(126\) | −2.99994 | −0.267255 | ||||||||
\(127\) | 10.2959 | 0.913612 | 0.456806 | − | 0.889566i | \(-0.348993\pi\) | ||||
0.456806 | + | 0.889566i | \(0.348993\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.0130465 | −0.00114868 | ||||||||
\(130\) | −18.6006 | −1.63138 | ||||||||
\(131\) | −13.1782 | −1.15139 | −0.575694 | − | 0.817665i | \(-0.695268\pi\) | ||||
−0.575694 | + | 0.817665i | \(0.695268\pi\) | |||||||
\(132\) | 0.0289805 | 0.00252243 | ||||||||
\(133\) | −7.20088 | −0.624396 | ||||||||
\(134\) | −12.1661 | −1.05099 | ||||||||
\(135\) | 0.177414 | 0.0152694 | ||||||||
\(136\) | −4.25537 | −0.364895 | ||||||||
\(137\) | 6.71144 | 0.573397 | 0.286699 | − | 0.958021i | \(-0.407442\pi\) | ||||
0.286699 | + | 0.958021i | \(0.407442\pi\) | |||||||
\(138\) | 0.0438726 | 0.00373468 | ||||||||
\(139\) | −20.1114 | −1.70583 | −0.852914 | − | 0.522052i | \(-0.825167\pi\) | ||||
−0.852914 | + | 0.522052i | \(0.825167\pi\) | |||||||
\(140\) | 3.67628 | 0.310702 | ||||||||
\(141\) | −0.0956520 | −0.00805535 | ||||||||
\(142\) | −9.30064 | −0.780493 | ||||||||
\(143\) | 18.2302 | 1.52448 | ||||||||
\(144\) | −2.99994 | −0.249995 | ||||||||
\(145\) | 19.7789 | 1.64255 | ||||||||
\(146\) | −2.31874 | −0.191900 | ||||||||
\(147\) | −0.00804327 | −0.000663398 0 | ||||||||
\(148\) | −6.72749 | −0.552997 | ||||||||
\(149\) | −5.97613 | −0.489584 | −0.244792 | − | 0.969576i | \(-0.578720\pi\) | ||||
−0.244792 | + | 0.969576i | \(0.578720\pi\) | |||||||
\(150\) | −0.0684887 | −0.00559208 | ||||||||
\(151\) | 11.6553 | 0.948497 | 0.474248 | − | 0.880391i | \(-0.342720\pi\) | ||||
0.474248 | + | 0.880391i | \(0.342720\pi\) | |||||||
\(152\) | −7.20088 | −0.584069 | ||||||||
\(153\) | 12.7658 | 1.03206 | ||||||||
\(154\) | −3.60308 | −0.290344 | ||||||||
\(155\) | 31.0262 | 2.49208 | ||||||||
\(156\) | 0.0406958 | 0.00325828 | ||||||||
\(157\) | −23.2638 | −1.85665 | −0.928326 | − | 0.371768i | \(-0.878752\pi\) | ||||
−0.928326 | + | 0.371768i | \(0.878752\pi\) | |||||||
\(158\) | 2.18286 | 0.173659 | ||||||||
\(159\) | 0.0552165 | 0.00437895 | ||||||||
\(160\) | 3.67628 | 0.290635 | ||||||||
\(161\) | −5.45457 | −0.429880 | ||||||||
\(162\) | 8.99942 | 0.707061 | ||||||||
\(163\) | 13.7297 | 1.07539 | 0.537697 | − | 0.843138i | \(-0.319295\pi\) | ||||
0.537697 | + | 0.843138i | \(0.319295\pi\) | |||||||
\(164\) | −2.42117 | −0.189061 | ||||||||
\(165\) | 0.106541 | 0.00829417 | ||||||||
\(166\) | −11.3539 | −0.881233 | ||||||||
\(167\) | 17.2313 | 1.33340 | 0.666698 | − | 0.745328i | \(-0.267707\pi\) | ||||
0.666698 | + | 0.745328i | \(0.267707\pi\) | |||||||
\(168\) | −0.00804327 | −0.000620552 0 | ||||||||
\(169\) | 12.5997 | 0.969207 | ||||||||
\(170\) | −15.6439 | −1.19983 | ||||||||
\(171\) | 21.6022 | 1.65196 | ||||||||
\(172\) | 1.62203 | 0.123679 | ||||||||
\(173\) | 19.1073 | 1.45270 | 0.726349 | − | 0.687326i | \(-0.241216\pi\) | ||||
0.726349 | + | 0.687326i | \(0.241216\pi\) | |||||||
\(174\) | −0.0432740 | −0.00328059 | ||||||||
\(175\) | 8.51503 | 0.643676 | ||||||||
\(176\) | −3.60308 | −0.271592 | ||||||||
\(177\) | 0.0284158 | 0.00213586 | ||||||||
\(178\) | 3.87667 | 0.290569 | ||||||||
\(179\) | −17.4364 | −1.30325 | −0.651627 | − | 0.758539i | \(-0.725913\pi\) | ||||
−0.651627 | + | 0.758539i | \(0.725913\pi\) | |||||||
\(180\) | −11.0286 | −0.822023 | ||||||||
\(181\) | −14.6608 | −1.08973 | −0.544863 | − | 0.838525i | \(-0.683418\pi\) | ||||
−0.544863 | + | 0.838525i | \(0.683418\pi\) | |||||||
\(182\) | −5.05961 | −0.375043 | ||||||||
\(183\) | 0.00843692 | 0.000623675 0 | ||||||||
\(184\) | −5.45457 | −0.402116 | ||||||||
\(185\) | −24.7322 | −1.81834 | ||||||||
\(186\) | −0.0678817 | −0.00497733 | ||||||||
\(187\) | 15.3324 | 1.12122 | ||||||||
\(188\) | 11.8922 | 0.867326 | ||||||||
\(189\) | 0.0482591 | 0.00351033 | ||||||||
\(190\) | −26.4724 | −1.92051 | ||||||||
\(191\) | −17.4442 | −1.26221 | −0.631107 | − | 0.775696i | \(-0.717399\pi\) | ||||
−0.631107 | + | 0.775696i | \(0.717399\pi\) | |||||||
\(192\) | −0.00804327 | −0.000580473 0 | ||||||||
\(193\) | 17.1234 | 1.23257 | 0.616286 | − | 0.787522i | \(-0.288637\pi\) | ||||
0.616286 | + | 0.787522i | \(0.288637\pi\) | |||||||
\(194\) | −5.64654 | −0.405398 | ||||||||
\(195\) | 0.149609 | 0.0107137 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 1.01990 | 0.0726646 | 0.0363323 | − | 0.999340i | \(-0.488433\pi\) | ||||
0.0363323 | + | 0.999340i | \(0.488433\pi\) | |||||||
\(198\) | 10.8090 | 0.768162 | ||||||||
\(199\) | 17.4049 | 1.23380 | 0.616901 | − | 0.787041i | \(-0.288388\pi\) | ||||
0.616901 | + | 0.787041i | \(0.288388\pi\) | |||||||
\(200\) | 8.51503 | 0.602104 | ||||||||
\(201\) | 0.0978556 | 0.00690220 | ||||||||
\(202\) | −6.63060 | −0.466527 | ||||||||
\(203\) | 5.38015 | 0.377612 | ||||||||
\(204\) | 0.0342271 | 0.00239637 | ||||||||
\(205\) | −8.90089 | −0.621665 | ||||||||
\(206\) | −3.07660 | −0.214357 | ||||||||
\(207\) | 16.3634 | 1.13733 | ||||||||
\(208\) | −5.05961 | −0.350821 | ||||||||
\(209\) | 25.9453 | 1.79468 | ||||||||
\(210\) | −0.0295693 | −0.00204048 | ||||||||
\(211\) | −21.0824 | −1.45137 | −0.725687 | − | 0.688025i | \(-0.758478\pi\) | ||||
−0.725687 | + | 0.688025i | \(0.758478\pi\) | |||||||
\(212\) | −6.86493 | −0.471485 | ||||||||
\(213\) | 0.0748076 | 0.00512573 | ||||||||
\(214\) | 18.6160 | 1.27256 | ||||||||
\(215\) | 5.96305 | 0.406677 | ||||||||
\(216\) | 0.0482591 | 0.00328362 | ||||||||
\(217\) | 8.43957 | 0.572915 | ||||||||
\(218\) | 9.63832 | 0.652789 | ||||||||
\(219\) | 0.0186503 | 0.00126027 | ||||||||
\(220\) | −13.2459 | −0.893040 | ||||||||
\(221\) | 21.5305 | 1.44830 | ||||||||
\(222\) | 0.0541111 | 0.00363170 | ||||||||
\(223\) | 28.2233 | 1.88997 | 0.944985 | − | 0.327113i | \(-0.106076\pi\) | ||||
0.944985 | + | 0.327113i | \(0.106076\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −25.5445 | −1.70297 | ||||||||
\(226\) | −13.1349 | −0.873719 | ||||||||
\(227\) | 21.3480 | 1.41692 | 0.708458 | − | 0.705753i | \(-0.249391\pi\) | ||||
0.708458 | + | 0.705753i | \(0.249391\pi\) | |||||||
\(228\) | 0.0579186 | 0.00383576 | ||||||||
\(229\) | −7.49251 | −0.495119 | −0.247560 | − | 0.968873i | \(-0.579629\pi\) | ||||
−0.247560 | + | 0.968873i | \(0.579629\pi\) | |||||||
\(230\) | −20.0525 | −1.32222 | ||||||||
\(231\) | 0.0289805 | 0.00190678 | ||||||||
\(232\) | 5.38015 | 0.353224 | ||||||||
\(233\) | −11.3480 | −0.743434 | −0.371717 | − | 0.928346i | \(-0.621231\pi\) | ||||
−0.371717 | + | 0.928346i | \(0.621231\pi\) | |||||||
\(234\) | 15.1785 | 0.992250 | ||||||||
\(235\) | 43.7189 | 2.85191 | ||||||||
\(236\) | −3.53286 | −0.229970 | ||||||||
\(237\) | −0.0175574 | −0.00114047 | ||||||||
\(238\) | −4.25537 | −0.275835 | ||||||||
\(239\) | 18.9903 | 1.22838 | 0.614190 | − | 0.789159i | \(-0.289483\pi\) | ||||
0.614190 | + | 0.789159i | \(0.289483\pi\) | |||||||
\(240\) | −0.0295693 | −0.00190869 | ||||||||
\(241\) | −3.35203 | −0.215923 | −0.107962 | − | 0.994155i | \(-0.534432\pi\) | ||||
−0.107962 | + | 0.994155i | \(0.534432\pi\) | |||||||
\(242\) | 1.98216 | 0.127418 | ||||||||
\(243\) | −0.217162 | −0.0139310 | ||||||||
\(244\) | −1.04894 | −0.0671516 | ||||||||
\(245\) | 3.67628 | 0.234869 | ||||||||
\(246\) | 0.0194741 | 0.00124162 | ||||||||
\(247\) | 36.4337 | 2.31822 | ||||||||
\(248\) | 8.43957 | 0.535913 | ||||||||
\(249\) | 0.0913224 | 0.00578732 | ||||||||
\(250\) | 12.9222 | 0.817274 | ||||||||
\(251\) | −8.32729 | −0.525614 | −0.262807 | − | 0.964848i | \(-0.584648\pi\) | ||||
−0.262807 | + | 0.964848i | \(0.584648\pi\) | |||||||
\(252\) | −2.99994 | −0.188978 | ||||||||
\(253\) | 19.6532 | 1.23559 | ||||||||
\(254\) | 10.2959 | 0.646021 | ||||||||
\(255\) | 0.125828 | 0.00787967 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −24.0267 | −1.49875 | −0.749373 | − | 0.662148i | \(-0.769645\pi\) | ||||
−0.749373 | + | 0.662148i | \(0.769645\pi\) | |||||||
\(258\) | −0.0130465 | −0.000812237 0 | ||||||||
\(259\) | −6.72749 | −0.418026 | ||||||||
\(260\) | −18.6006 | −1.15356 | ||||||||
\(261\) | −16.1401 | −0.999046 | ||||||||
\(262\) | −13.1782 | −0.814155 | ||||||||
\(263\) | −7.01033 | −0.432275 | −0.216138 | − | 0.976363i | \(-0.569346\pi\) | ||||
−0.216138 | + | 0.976363i | \(0.569346\pi\) | |||||||
\(264\) | 0.0289805 | 0.00178363 | ||||||||
\(265\) | −25.2374 | −1.55032 | ||||||||
\(266\) | −7.20088 | −0.441514 | ||||||||
\(267\) | −0.0311811 | −0.00190825 | ||||||||
\(268\) | −12.1661 | −0.743165 | ||||||||
\(269\) | 10.4599 | 0.637754 | 0.318877 | − | 0.947796i | \(-0.396694\pi\) | ||||
0.318877 | + | 0.947796i | \(0.396694\pi\) | |||||||
\(270\) | 0.177414 | 0.0107971 | ||||||||
\(271\) | 3.54452 | 0.215314 | 0.107657 | − | 0.994188i | \(-0.465665\pi\) | ||||
0.107657 | + | 0.994188i | \(0.465665\pi\) | |||||||
\(272\) | −4.25537 | −0.258020 | ||||||||
\(273\) | 0.0406958 | 0.00246302 | ||||||||
\(274\) | 6.71144 | 0.405453 | ||||||||
\(275\) | −30.6803 | −1.85009 | ||||||||
\(276\) | 0.0438726 | 0.00264082 | ||||||||
\(277\) | −20.4046 | −1.22599 | −0.612996 | − | 0.790086i | \(-0.710036\pi\) | ||||
−0.612996 | + | 0.790086i | \(0.710036\pi\) | |||||||
\(278\) | −20.1114 | −1.20620 | ||||||||
\(279\) | −25.3182 | −1.51576 | ||||||||
\(280\) | 3.67628 | 0.219700 | ||||||||
\(281\) | 22.7551 | 1.35745 | 0.678726 | − | 0.734391i | \(-0.262532\pi\) | ||||
0.678726 | + | 0.734391i | \(0.262532\pi\) | |||||||
\(282\) | −0.0956520 | −0.00569599 | ||||||||
\(283\) | −23.5185 | −1.39803 | −0.699015 | − | 0.715107i | \(-0.746378\pi\) | ||||
−0.699015 | + | 0.715107i | \(0.746378\pi\) | |||||||
\(284\) | −9.30064 | −0.551892 | ||||||||
\(285\) | 0.212925 | 0.0126126 | ||||||||
\(286\) | 18.2302 | 1.07797 | ||||||||
\(287\) | −2.42117 | −0.142917 | ||||||||
\(288\) | −2.99994 | −0.176773 | ||||||||
\(289\) | 1.10815 | 0.0651854 | ||||||||
\(290\) | 19.7789 | 1.16146 | ||||||||
\(291\) | 0.0454166 | 0.00266237 | ||||||||
\(292\) | −2.31874 | −0.135694 | ||||||||
\(293\) | 11.1622 | 0.652104 | 0.326052 | − | 0.945352i | \(-0.394282\pi\) | ||||
0.326052 | + | 0.945352i | \(0.394282\pi\) | |||||||
\(294\) | −0.00804327 | −0.000469093 0 | ||||||||
\(295\) | −12.9878 | −0.756179 | ||||||||
\(296\) | −6.72749 | −0.391028 | ||||||||
\(297\) | −0.173881 | −0.0100896 | ||||||||
\(298\) | −5.97613 | −0.346188 | ||||||||
\(299\) | 27.5980 | 1.59603 | ||||||||
\(300\) | −0.0684887 | −0.00395420 | ||||||||
\(301\) | 1.62203 | 0.0934925 | ||||||||
\(302\) | 11.6553 | 0.670688 | ||||||||
\(303\) | 0.0533317 | 0.00306383 | ||||||||
\(304\) | −7.20088 | −0.412999 | ||||||||
\(305\) | −3.85620 | −0.220806 | ||||||||
\(306\) | 12.7658 | 0.729774 | ||||||||
\(307\) | 14.9617 | 0.853907 | 0.426953 | − | 0.904274i | \(-0.359587\pi\) | ||||
0.426953 | + | 0.904274i | \(0.359587\pi\) | |||||||
\(308\) | −3.60308 | −0.205304 | ||||||||
\(309\) | 0.0247459 | 0.00140774 | ||||||||
\(310\) | 31.0262 | 1.76217 | ||||||||
\(311\) | −7.03415 | −0.398870 | −0.199435 | − | 0.979911i | \(-0.563911\pi\) | ||||
−0.199435 | + | 0.979911i | \(0.563911\pi\) | |||||||
\(312\) | 0.0406958 | 0.00230395 | ||||||||
\(313\) | −7.86480 | −0.444545 | −0.222272 | − | 0.974985i | \(-0.571347\pi\) | ||||
−0.222272 | + | 0.974985i | \(0.571347\pi\) | |||||||
\(314\) | −23.2638 | −1.31285 | ||||||||
\(315\) | −11.0286 | −0.621391 | ||||||||
\(316\) | 2.18286 | 0.122796 | ||||||||
\(317\) | −17.7786 | −0.998545 | −0.499273 | − | 0.866445i | \(-0.666399\pi\) | ||||
−0.499273 | + | 0.866445i | \(0.666399\pi\) | |||||||
\(318\) | 0.0552165 | 0.00309639 | ||||||||
\(319\) | −19.3851 | −1.08536 | ||||||||
\(320\) | 3.67628 | 0.205510 | ||||||||
\(321\) | −0.149734 | −0.00835731 | ||||||||
\(322\) | −5.45457 | −0.303971 | ||||||||
\(323\) | 30.6424 | 1.70499 | ||||||||
\(324\) | 8.99942 | 0.499968 | ||||||||
\(325\) | −43.0828 | −2.38980 | ||||||||
\(326\) | 13.7297 | 0.760418 | ||||||||
\(327\) | −0.0775236 | −0.00428706 | ||||||||
\(328\) | −2.42117 | −0.133687 | ||||||||
\(329\) | 11.8922 | 0.655637 | ||||||||
\(330\) | 0.106541 | 0.00586486 | ||||||||
\(331\) | 6.22370 | 0.342085 | 0.171043 | − | 0.985264i | \(-0.445286\pi\) | ||||
0.171043 | + | 0.985264i | \(0.445286\pi\) | |||||||
\(332\) | −11.3539 | −0.623125 | ||||||||
\(333\) | 20.1820 | 1.10597 | ||||||||
\(334\) | 17.2313 | 0.942853 | ||||||||
\(335\) | −44.7261 | −2.44365 | ||||||||
\(336\) | −0.00804327 | −0.000438796 0 | ||||||||
\(337\) | 3.00215 | 0.163538 | 0.0817688 | − | 0.996651i | \(-0.473943\pi\) | ||||
0.0817688 | + | 0.996651i | \(0.473943\pi\) | |||||||
\(338\) | 12.5997 | 0.685333 | ||||||||
\(339\) | 0.105647 | 0.00573798 | ||||||||
\(340\) | −15.6439 | −0.848411 | ||||||||
\(341\) | −30.4084 | −1.64671 | ||||||||
\(342\) | 21.6022 | 1.16811 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.62203 | 0.0874542 | ||||||||
\(345\) | 0.161288 | 0.00868345 | ||||||||
\(346\) | 19.1073 | 1.02721 | ||||||||
\(347\) | 14.3532 | 0.770522 | 0.385261 | − | 0.922808i | \(-0.374111\pi\) | ||||
0.385261 | + | 0.922808i | \(0.374111\pi\) | |||||||
\(348\) | −0.0432740 | −0.00231973 | ||||||||
\(349\) | −11.5459 | −0.618038 | −0.309019 | − | 0.951056i | \(-0.600001\pi\) | ||||
−0.309019 | + | 0.951056i | \(0.600001\pi\) | |||||||
\(350\) | 8.51503 | 0.455148 | ||||||||
\(351\) | −0.244172 | −0.0130330 | ||||||||
\(352\) | −3.60308 | −0.192045 | ||||||||
\(353\) | 2.33498 | 0.124278 | 0.0621391 | − | 0.998067i | \(-0.480208\pi\) | ||||
0.0621391 | + | 0.998067i | \(0.480208\pi\) | |||||||
\(354\) | 0.0284158 | 0.00151028 | ||||||||
\(355\) | −34.1918 | −1.81471 | ||||||||
\(356\) | 3.87667 | 0.205463 | ||||||||
\(357\) | 0.0342271 | 0.00181149 | ||||||||
\(358\) | −17.4364 | −0.921540 | ||||||||
\(359\) | −33.1350 | −1.74880 | −0.874399 | − | 0.485208i | \(-0.838744\pi\) | ||||
−0.874399 | + | 0.485208i | \(0.838744\pi\) | |||||||
\(360\) | −11.0286 | −0.581258 | ||||||||
\(361\) | 32.8527 | 1.72909 | ||||||||
\(362\) | −14.6608 | −0.770553 | ||||||||
\(363\) | −0.0159431 | −0.000836795 0 | ||||||||
\(364\) | −5.05961 | −0.265196 | ||||||||
\(365\) | −8.52434 | −0.446185 | ||||||||
\(366\) | 0.00843692 | 0.000441005 0 | ||||||||
\(367\) | 26.5067 | 1.38364 | 0.691820 | − | 0.722070i | \(-0.256809\pi\) | ||||
0.691820 | + | 0.722070i | \(0.256809\pi\) | |||||||
\(368\) | −5.45457 | −0.284339 | ||||||||
\(369\) | 7.26334 | 0.378115 | ||||||||
\(370\) | −24.7322 | −1.28576 | ||||||||
\(371\) | −6.86493 | −0.356409 | ||||||||
\(372\) | −0.0678817 | −0.00351950 | ||||||||
\(373\) | 0.807279 | 0.0417993 | 0.0208997 | − | 0.999782i | \(-0.493347\pi\) | ||||
0.0208997 | + | 0.999782i | \(0.493347\pi\) | |||||||
\(374\) | 15.3324 | 0.792820 | ||||||||
\(375\) | −0.103937 | −0.00536729 | ||||||||
\(376\) | 11.8922 | 0.613292 | ||||||||
\(377\) | −27.2215 | −1.40198 | ||||||||
\(378\) | 0.0482591 | 0.00248218 | ||||||||
\(379\) | 35.8614 | 1.84208 | 0.921039 | − | 0.389469i | \(-0.127342\pi\) | ||||
0.921039 | + | 0.389469i | \(0.127342\pi\) | |||||||
\(380\) | −26.4724 | −1.35801 | ||||||||
\(381\) | −0.0828126 | −0.00424262 | ||||||||
\(382\) | −17.4442 | −0.892520 | ||||||||
\(383\) | −5.11537 | −0.261383 | −0.130692 | − | 0.991423i | \(-0.541720\pi\) | ||||
−0.130692 | + | 0.991423i | \(0.541720\pi\) | |||||||
\(384\) | −0.00804327 | −0.000410457 0 | ||||||||
\(385\) | −13.2459 | −0.675074 | ||||||||
\(386\) | 17.1234 | 0.871560 | ||||||||
\(387\) | −4.86600 | −0.247352 | ||||||||
\(388\) | −5.64654 | −0.286660 | ||||||||
\(389\) | −20.0433 | −1.01624 | −0.508118 | − | 0.861287i | \(-0.669659\pi\) | ||||
−0.508118 | + | 0.861287i | \(0.669659\pi\) | |||||||
\(390\) | 0.149609 | 0.00757576 | ||||||||
\(391\) | 23.2112 | 1.17384 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0.105996 | 0.00534680 | ||||||||
\(394\) | 1.01990 | 0.0513817 | ||||||||
\(395\) | 8.02481 | 0.403772 | ||||||||
\(396\) | 10.8090 | 0.543173 | ||||||||
\(397\) | −3.94502 | −0.197995 | −0.0989975 | − | 0.995088i | \(-0.531564\pi\) | ||||
−0.0989975 | + | 0.995088i | \(0.531564\pi\) | |||||||
\(398\) | 17.4049 | 0.872430 | ||||||||
\(399\) | 0.0579186 | 0.00289956 | ||||||||
\(400\) | 8.51503 | 0.425752 | ||||||||
\(401\) | 1.21403 | 0.0606256 | 0.0303128 | − | 0.999540i | \(-0.490350\pi\) | ||||
0.0303128 | + | 0.999540i | \(0.490350\pi\) | |||||||
\(402\) | 0.0978556 | 0.00488059 | ||||||||
\(403\) | −42.7009 | −2.12709 | ||||||||
\(404\) | −6.63060 | −0.329885 | ||||||||
\(405\) | 33.0844 | 1.64398 | ||||||||
\(406\) | 5.38015 | 0.267012 | ||||||||
\(407\) | 24.2397 | 1.20152 | ||||||||
\(408\) | 0.0342271 | 0.00169449 | ||||||||
\(409\) | 3.37254 | 0.166761 | 0.0833806 | − | 0.996518i | \(-0.473428\pi\) | ||||
0.0833806 | + | 0.996518i | \(0.473428\pi\) | |||||||
\(410\) | −8.90089 | −0.439583 | ||||||||
\(411\) | −0.0539819 | −0.00266273 | ||||||||
\(412\) | −3.07660 | −0.151573 | ||||||||
\(413\) | −3.53286 | −0.173841 | ||||||||
\(414\) | 16.3634 | 0.804215 | ||||||||
\(415\) | −41.7401 | −2.04894 | ||||||||
\(416\) | −5.05961 | −0.248068 | ||||||||
\(417\) | 0.161762 | 0.00792150 | ||||||||
\(418\) | 25.9453 | 1.26903 | ||||||||
\(419\) | 14.1407 | 0.690817 | 0.345409 | − | 0.938452i | \(-0.387740\pi\) | ||||
0.345409 | + | 0.938452i | \(0.387740\pi\) | |||||||
\(420\) | −0.0295693 | −0.00144283 | ||||||||
\(421\) | 24.9368 | 1.21535 | 0.607674 | − | 0.794187i | \(-0.292103\pi\) | ||||
0.607674 | + | 0.794187i | \(0.292103\pi\) | |||||||
\(422\) | −21.0824 | −1.02628 | ||||||||
\(423\) | −35.6757 | −1.73461 | ||||||||
\(424\) | −6.86493 | −0.333391 | ||||||||
\(425\) | −36.2346 | −1.75764 | ||||||||
\(426\) | 0.0748076 | 0.00362444 | ||||||||
\(427\) | −1.04894 | −0.0507618 | ||||||||
\(428\) | 18.6160 | 0.899838 | ||||||||
\(429\) | −0.146630 | −0.00707938 | ||||||||
\(430\) | 5.96305 | 0.287564 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | 0.0482591 | 0.00232187 | ||||||||
\(433\) | 23.8411 | 1.14573 | 0.572866 | − | 0.819649i | \(-0.305832\pi\) | ||||
0.572866 | + | 0.819649i | \(0.305832\pi\) | |||||||
\(434\) | 8.43957 | 0.405112 | ||||||||
\(435\) | −0.159087 | −0.00762765 | ||||||||
\(436\) | 9.63832 | 0.461592 | ||||||||
\(437\) | 39.2777 | 1.87891 | ||||||||
\(438\) | 0.0186503 | 0.000891144 0 | ||||||||
\(439\) | 1.62172 | 0.0774007 | 0.0387004 | − | 0.999251i | \(-0.487678\pi\) | ||||
0.0387004 | + | 0.999251i | \(0.487678\pi\) | |||||||
\(440\) | −13.2459 | −0.631474 | ||||||||
\(441\) | −2.99994 | −0.142854 | ||||||||
\(442\) | 21.5305 | 1.02410 | ||||||||
\(443\) | −7.44042 | −0.353505 | −0.176752 | − | 0.984255i | \(-0.556559\pi\) | ||||
−0.176752 | + | 0.984255i | \(0.556559\pi\) | |||||||
\(444\) | 0.0541111 | 0.00256800 | ||||||||
\(445\) | 14.2517 | 0.675596 | ||||||||
\(446\) | 28.2233 | 1.33641 | ||||||||
\(447\) | 0.0480677 | 0.00227352 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 41.3656 | 1.95216 | 0.976081 | − | 0.217406i | \(-0.0697595\pi\) | ||||
0.976081 | + | 0.217406i | \(0.0697595\pi\) | |||||||
\(450\) | −25.5445 | −1.20418 | ||||||||
\(451\) | 8.72365 | 0.410781 | ||||||||
\(452\) | −13.1349 | −0.617813 | ||||||||
\(453\) | −0.0937469 | −0.00440461 | ||||||||
\(454\) | 21.3480 | 1.00191 | ||||||||
\(455\) | −18.6006 | −0.872007 | ||||||||
\(456\) | 0.0579186 | 0.00271229 | ||||||||
\(457\) | −10.7143 | −0.501192 | −0.250596 | − | 0.968092i | \(-0.580627\pi\) | ||||
−0.250596 | + | 0.968092i | \(0.580627\pi\) | |||||||
\(458\) | −7.49251 | −0.350102 | ||||||||
\(459\) | −0.205360 | −0.00958540 | ||||||||
\(460\) | −20.0525 | −0.934954 | ||||||||
\(461\) | −19.1525 | −0.892019 | −0.446009 | − | 0.895028i | \(-0.647155\pi\) | ||||
−0.446009 | + | 0.895028i | \(0.647155\pi\) | |||||||
\(462\) | 0.0289805 | 0.00134830 | ||||||||
\(463\) | 1.76427 | 0.0819924 | 0.0409962 | − | 0.999159i | \(-0.486947\pi\) | ||||
0.0409962 | + | 0.999159i | \(0.486947\pi\) | |||||||
\(464\) | 5.38015 | 0.249767 | ||||||||
\(465\) | −0.249552 | −0.0115727 | ||||||||
\(466\) | −11.3480 | −0.525687 | ||||||||
\(467\) | 40.3408 | 1.86675 | 0.933375 | − | 0.358904i | \(-0.116849\pi\) | ||||
0.933375 | + | 0.358904i | \(0.116849\pi\) | |||||||
\(468\) | 15.1785 | 0.701627 | ||||||||
\(469\) | −12.1661 | −0.561780 | ||||||||
\(470\) | 43.7189 | 2.01660 | ||||||||
\(471\) | 0.187117 | 0.00862189 | ||||||||
\(472\) | −3.53286 | −0.162613 | ||||||||
\(473\) | −5.84431 | −0.268722 | ||||||||
\(474\) | −0.0175574 | −0.000806436 0 | ||||||||
\(475\) | −61.3157 | −2.81336 | ||||||||
\(476\) | −4.25537 | −0.195044 | ||||||||
\(477\) | 20.5944 | 0.942951 | ||||||||
\(478\) | 18.9903 | 0.868595 | ||||||||
\(479\) | 11.5365 | 0.527114 | 0.263557 | − | 0.964644i | \(-0.415104\pi\) | ||||
0.263557 | + | 0.964644i | \(0.415104\pi\) | |||||||
\(480\) | −0.0295693 | −0.00134965 | ||||||||
\(481\) | 34.0385 | 1.55202 | ||||||||
\(482\) | −3.35203 | −0.152681 | ||||||||
\(483\) | 0.0438726 | 0.00199627 | ||||||||
\(484\) | 1.98216 | 0.0900984 | ||||||||
\(485\) | −20.7583 | −0.942584 | ||||||||
\(486\) | −0.217162 | −0.00985067 | ||||||||
\(487\) | −14.8135 | −0.671262 | −0.335631 | − | 0.941994i | \(-0.608950\pi\) | ||||
−0.335631 | + | 0.941994i | \(0.608950\pi\) | |||||||
\(488\) | −1.04894 | −0.0474834 | ||||||||
\(489\) | −0.110432 | −0.00499390 | ||||||||
\(490\) | 3.67628 | 0.166077 | ||||||||
\(491\) | 1.74825 | 0.0788976 | 0.0394488 | − | 0.999222i | \(-0.487440\pi\) | ||||
0.0394488 | + | 0.999222i | \(0.487440\pi\) | |||||||
\(492\) | 0.0194741 | 0.000877960 0 | ||||||||
\(493\) | −22.8945 | −1.03112 | ||||||||
\(494\) | 36.4337 | 1.63923 | ||||||||
\(495\) | 39.7369 | 1.78604 | ||||||||
\(496\) | 8.43957 | 0.378948 | ||||||||
\(497\) | −9.30064 | −0.417191 | ||||||||
\(498\) | 0.0913224 | 0.00409225 | ||||||||
\(499\) | 7.34260 | 0.328700 | 0.164350 | − | 0.986402i | \(-0.447447\pi\) | ||||
0.164350 | + | 0.986402i | \(0.447447\pi\) | |||||||
\(500\) | 12.9222 | 0.577900 | ||||||||
\(501\) | −0.138596 | −0.00619200 | ||||||||
\(502\) | −8.32729 | −0.371665 | ||||||||
\(503\) | 41.2397 | 1.83879 | 0.919393 | − | 0.393341i | \(-0.128681\pi\) | ||||
0.919393 | + | 0.393341i | \(0.128681\pi\) | |||||||
\(504\) | −2.99994 | −0.133628 | ||||||||
\(505\) | −24.3759 | −1.08471 | ||||||||
\(506\) | 19.6532 | 0.873693 | ||||||||
\(507\) | −0.101343 | −0.00450079 | ||||||||
\(508\) | 10.2959 | 0.456806 | ||||||||
\(509\) | −7.15620 | −0.317193 | −0.158597 | − | 0.987343i | \(-0.550697\pi\) | ||||
−0.158597 | + | 0.987343i | \(0.550697\pi\) | |||||||
\(510\) | 0.125828 | 0.00557177 | ||||||||
\(511\) | −2.31874 | −0.102575 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.347508 | −0.0153429 | ||||||||
\(514\) | −24.0267 | −1.05977 | ||||||||
\(515\) | −11.3104 | −0.498397 | ||||||||
\(516\) | −0.0130465 | −0.000574338 0 | ||||||||
\(517\) | −42.8484 | −1.88447 | ||||||||
\(518\) | −6.72749 | −0.295589 | ||||||||
\(519\) | −0.153685 | −0.00674602 | ||||||||
\(520\) | −18.6006 | −0.815688 | ||||||||
\(521\) | 18.0507 | 0.790816 | 0.395408 | − | 0.918506i | \(-0.370603\pi\) | ||||
0.395408 | + | 0.918506i | \(0.370603\pi\) | |||||||
\(522\) | −16.1401 | −0.706432 | ||||||||
\(523\) | −27.4308 | −1.19947 | −0.599733 | − | 0.800200i | \(-0.704727\pi\) | ||||
−0.599733 | + | 0.800200i | \(0.704727\pi\) | |||||||
\(524\) | −13.1782 | −0.575694 | ||||||||
\(525\) | −0.0684887 | −0.00298909 | ||||||||
\(526\) | −7.01033 | −0.305665 | ||||||||
\(527\) | −35.9135 | −1.56441 | ||||||||
\(528\) | 0.0289805 | 0.00126122 | ||||||||
\(529\) | 6.75236 | 0.293581 | ||||||||
\(530\) | −25.2374 | −1.09624 | ||||||||
\(531\) | 10.5984 | 0.459930 | ||||||||
\(532\) | −7.20088 | −0.312198 | ||||||||
\(533\) | 12.2502 | 0.530614 | ||||||||
\(534\) | −0.0311811 | −0.00134934 | ||||||||
\(535\) | 68.4376 | 2.95882 | ||||||||
\(536\) | −12.1661 | −0.525497 | ||||||||
\(537\) | 0.140245 | 0.00605203 | ||||||||
\(538\) | 10.4599 | 0.450960 | ||||||||
\(539\) | −3.60308 | −0.155196 | ||||||||
\(540\) | 0.177414 | 0.00763468 | ||||||||
\(541\) | −30.5733 | −1.31445 | −0.657224 | − | 0.753696i | \(-0.728269\pi\) | ||||
−0.657224 | + | 0.753696i | \(0.728269\pi\) | |||||||
\(542\) | 3.54452 | 0.152250 | ||||||||
\(543\) | 0.117921 | 0.00506046 | ||||||||
\(544\) | −4.25537 | −0.182447 | ||||||||
\(545\) | 35.4331 | 1.51779 | ||||||||
\(546\) | 0.0406958 | 0.00174162 | ||||||||
\(547\) | −42.0481 | −1.79785 | −0.898924 | − | 0.438104i | \(-0.855650\pi\) | ||||
−0.898924 | + | 0.438104i | \(0.855650\pi\) | |||||||
\(548\) | 6.71144 | 0.286699 | ||||||||
\(549\) | 3.14676 | 0.134300 | ||||||||
\(550\) | −30.6803 | −1.30821 | ||||||||
\(551\) | −38.7418 | −1.65046 | ||||||||
\(552\) | 0.0438726 | 0.00186734 | ||||||||
\(553\) | 2.18286 | 0.0928248 | ||||||||
\(554\) | −20.4046 | −0.866907 | ||||||||
\(555\) | 0.198927 | 0.00844400 | ||||||||
\(556\) | −20.1114 | −0.852914 | ||||||||
\(557\) | −29.8321 | −1.26403 | −0.632013 | − | 0.774958i | \(-0.717771\pi\) | ||||
−0.632013 | + | 0.774958i | \(0.717771\pi\) | |||||||
\(558\) | −25.3182 | −1.07180 | ||||||||
\(559\) | −8.20686 | −0.347113 | ||||||||
\(560\) | 3.67628 | 0.155351 | ||||||||
\(561\) | −0.123323 | −0.00520669 | ||||||||
\(562\) | 22.7551 | 0.959864 | ||||||||
\(563\) | 16.6815 | 0.703042 | 0.351521 | − | 0.936180i | \(-0.385665\pi\) | ||||
0.351521 | + | 0.936180i | \(0.385665\pi\) | |||||||
\(564\) | −0.0956520 | −0.00402767 | ||||||||
\(565\) | −48.2875 | −2.03147 | ||||||||
\(566\) | −23.5185 | −0.988556 | ||||||||
\(567\) | 8.99942 | 0.377940 | ||||||||
\(568\) | −9.30064 | −0.390246 | ||||||||
\(569\) | 38.3267 | 1.60674 | 0.803370 | − | 0.595480i | \(-0.203038\pi\) | ||||
0.803370 | + | 0.595480i | \(0.203038\pi\) | |||||||
\(570\) | 0.212925 | 0.00891845 | ||||||||
\(571\) | 4.55935 | 0.190803 | 0.0954014 | − | 0.995439i | \(-0.469587\pi\) | ||||
0.0954014 | + | 0.995439i | \(0.469587\pi\) | |||||||
\(572\) | 18.2302 | 0.762242 | ||||||||
\(573\) | 0.140308 | 0.00586145 | ||||||||
\(574\) | −2.42117 | −0.101058 | ||||||||
\(575\) | −46.4458 | −1.93693 | ||||||||
\(576\) | −2.99994 | −0.124997 | ||||||||
\(577\) | 32.7745 | 1.36442 | 0.682210 | − | 0.731156i | \(-0.261019\pi\) | ||||
0.682210 | + | 0.731156i | \(0.261019\pi\) | |||||||
\(578\) | 1.10815 | 0.0460931 | ||||||||
\(579\) | −0.137728 | −0.00572380 | ||||||||
\(580\) | 19.7789 | 0.821275 | ||||||||
\(581\) | −11.3539 | −0.471039 | ||||||||
\(582\) | 0.0454166 | 0.00188258 | ||||||||
\(583\) | 24.7349 | 1.02441 | ||||||||
\(584\) | −2.31874 | −0.0959502 | ||||||||
\(585\) | 55.8005 | 2.30706 | ||||||||
\(586\) | 11.1622 | 0.461107 | ||||||||
\(587\) | 3.66236 | 0.151162 | 0.0755808 | − | 0.997140i | \(-0.475919\pi\) | ||||
0.0755808 | + | 0.997140i | \(0.475919\pi\) | |||||||
\(588\) | −0.00804327 | −0.000331699 0 | ||||||||
\(589\) | −60.7723 | −2.50408 | ||||||||
\(590\) | −12.9878 | −0.534699 | ||||||||
\(591\) | −0.00820331 | −0.000337439 0 | ||||||||
\(592\) | −6.72749 | −0.276498 | ||||||||
\(593\) | 19.4037 | 0.796816 | 0.398408 | − | 0.917208i | \(-0.369563\pi\) | ||||
0.398408 | + | 0.917208i | \(0.369563\pi\) | |||||||
\(594\) | −0.173881 | −0.00713444 | ||||||||
\(595\) | −15.6439 | −0.641338 | ||||||||
\(596\) | −5.97613 | −0.244792 | ||||||||
\(597\) | −0.139992 | −0.00572951 | ||||||||
\(598\) | 27.5980 | 1.12857 | ||||||||
\(599\) | 15.7059 | 0.641726 | 0.320863 | − | 0.947126i | \(-0.396027\pi\) | ||||
0.320863 | + | 0.947126i | \(0.396027\pi\) | |||||||
\(600\) | −0.0684887 | −0.00279604 | ||||||||
\(601\) | −42.6411 | −1.73937 | −0.869683 | − | 0.493612i | \(-0.835676\pi\) | ||||
−0.869683 | + | 0.493612i | \(0.835676\pi\) | |||||||
\(602\) | 1.62203 | 0.0661092 | ||||||||
\(603\) | 36.4976 | 1.48630 | ||||||||
\(604\) | 11.6553 | 0.474248 | ||||||||
\(605\) | 7.28699 | 0.296258 | ||||||||
\(606\) | 0.0533317 | 0.00216645 | ||||||||
\(607\) | −8.63014 | −0.350287 | −0.175143 | − | 0.984543i | \(-0.556039\pi\) | ||||
−0.175143 | + | 0.984543i | \(0.556039\pi\) | |||||||
\(608\) | −7.20088 | −0.292034 | ||||||||
\(609\) | −0.0432740 | −0.00175355 | ||||||||
\(610\) | −3.85620 | −0.156133 | ||||||||
\(611\) | −60.1698 | −2.43421 | ||||||||
\(612\) | 12.7658 | 0.516028 | ||||||||
\(613\) | −26.3179 | −1.06297 | −0.531484 | − | 0.847068i | \(-0.678365\pi\) | ||||
−0.531484 | + | 0.847068i | \(0.678365\pi\) | |||||||
\(614\) | 14.9617 | 0.603803 | ||||||||
\(615\) | 0.0715922 | 0.00288688 | ||||||||
\(616\) | −3.60308 | −0.145172 | ||||||||
\(617\) | 17.2089 | 0.692804 | 0.346402 | − | 0.938086i | \(-0.387403\pi\) | ||||
0.346402 | + | 0.938086i | \(0.387403\pi\) | |||||||
\(618\) | 0.0247459 | 0.000995426 0 | ||||||||
\(619\) | −6.01725 | −0.241854 | −0.120927 | − | 0.992661i | \(-0.538587\pi\) | ||||
−0.120927 | + | 0.992661i | \(0.538587\pi\) | |||||||
\(620\) | 31.0262 | 1.24604 | ||||||||
\(621\) | −0.263233 | −0.0105632 | ||||||||
\(622\) | −7.03415 | −0.282044 | ||||||||
\(623\) | 3.87667 | 0.155315 | ||||||||
\(624\) | 0.0406958 | 0.00162914 | ||||||||
\(625\) | 4.93060 | 0.197224 | ||||||||
\(626\) | −7.86480 | −0.314340 | ||||||||
\(627\) | −0.208685 | −0.00833409 | ||||||||
\(628\) | −23.2638 | −0.928326 | ||||||||
\(629\) | 28.6280 | 1.14147 | ||||||||
\(630\) | −11.0286 | −0.439390 | ||||||||
\(631\) | −14.9168 | −0.593828 | −0.296914 | − | 0.954904i | \(-0.595957\pi\) | ||||
−0.296914 | + | 0.954904i | \(0.595957\pi\) | |||||||
\(632\) | 2.18286 | 0.0868296 | ||||||||
\(633\) | 0.169572 | 0.00673987 | ||||||||
\(634\) | −17.7786 | −0.706078 | ||||||||
\(635\) | 37.8506 | 1.50205 | ||||||||
\(636\) | 0.0552165 | 0.00218948 | ||||||||
\(637\) | −5.05961 | −0.200469 | ||||||||
\(638\) | −19.3851 | −0.767463 | ||||||||
\(639\) | 27.9013 | 1.10376 | ||||||||
\(640\) | 3.67628 | 0.145318 | ||||||||
\(641\) | −35.8076 | −1.41432 | −0.707158 | − | 0.707055i | \(-0.750023\pi\) | ||||
−0.707158 | + | 0.707055i | \(0.750023\pi\) | |||||||
\(642\) | −0.149734 | −0.00590951 | ||||||||
\(643\) | 7.84327 | 0.309308 | 0.154654 | − | 0.987969i | \(-0.450574\pi\) | ||||
0.154654 | + | 0.987969i | \(0.450574\pi\) | |||||||
\(644\) | −5.45457 | −0.214940 | ||||||||
\(645\) | −0.0479624 | −0.00188852 | ||||||||
\(646\) | 30.6424 | 1.20561 | ||||||||
\(647\) | −13.4672 | −0.529449 | −0.264725 | − | 0.964324i | \(-0.585281\pi\) | ||||
−0.264725 | + | 0.964324i | \(0.585281\pi\) | |||||||
\(648\) | 8.99942 | 0.353531 | ||||||||
\(649\) | 12.7292 | 0.499664 | ||||||||
\(650\) | −43.0828 | −1.68984 | ||||||||
\(651\) | −0.0678817 | −0.00266050 | ||||||||
\(652\) | 13.7297 | 0.537697 | ||||||||
\(653\) | −25.7253 | −1.00671 | −0.503355 | − | 0.864080i | \(-0.667901\pi\) | ||||
−0.503355 | + | 0.864080i | \(0.667901\pi\) | |||||||
\(654\) | −0.0775236 | −0.00303141 | ||||||||
\(655\) | −48.4469 | −1.89298 | ||||||||
\(656\) | −2.42117 | −0.0945307 | ||||||||
\(657\) | 6.95608 | 0.271382 | ||||||||
\(658\) | 11.8922 | 0.463605 | ||||||||
\(659\) | −10.6933 | −0.416551 | −0.208276 | − | 0.978070i | \(-0.566785\pi\) | ||||
−0.208276 | + | 0.978070i | \(0.566785\pi\) | |||||||
\(660\) | 0.106541 | 0.00414708 | ||||||||
\(661\) | 20.5741 | 0.800240 | 0.400120 | − | 0.916463i | \(-0.368968\pi\) | ||||
0.400120 | + | 0.916463i | \(0.368968\pi\) | |||||||
\(662\) | 6.22370 | 0.241891 | ||||||||
\(663\) | −0.173176 | −0.00672559 | ||||||||
\(664\) | −11.3539 | −0.440616 | ||||||||
\(665\) | −26.4724 | −1.02656 | ||||||||
\(666\) | 20.1820 | 0.782039 | ||||||||
\(667\) | −29.3464 | −1.13630 | ||||||||
\(668\) | 17.2313 | 0.666698 | ||||||||
\(669\) | −0.227008 | −0.00877662 | ||||||||
\(670\) | −44.7261 | −1.72792 | ||||||||
\(671\) | 3.77942 | 0.145903 | ||||||||
\(672\) | −0.00804327 | −0.000310276 0 | ||||||||
\(673\) | −38.8725 | −1.49843 | −0.749213 | − | 0.662329i | \(-0.769568\pi\) | ||||
−0.749213 | + | 0.662329i | \(0.769568\pi\) | |||||||
\(674\) | 3.00215 | 0.115638 | ||||||||
\(675\) | 0.410928 | 0.0158166 | ||||||||
\(676\) | 12.5997 | 0.484603 | ||||||||
\(677\) | −32.1969 | −1.23743 | −0.618714 | − | 0.785616i | \(-0.712346\pi\) | ||||
−0.618714 | + | 0.785616i | \(0.712346\pi\) | |||||||
\(678\) | 0.105647 | 0.00405736 | ||||||||
\(679\) | −5.64654 | −0.216694 | ||||||||
\(680\) | −15.6439 | −0.599917 | ||||||||
\(681\) | −0.171708 | −0.00657986 | ||||||||
\(682\) | −30.4084 | −1.16440 | ||||||||
\(683\) | 8.55728 | 0.327435 | 0.163718 | − | 0.986507i | \(-0.447651\pi\) | ||||
0.163718 | + | 0.986507i | \(0.447651\pi\) | |||||||
\(684\) | 21.6022 | 0.825980 | ||||||||
\(685\) | 24.6731 | 0.942712 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0.0602643 | 0.00229923 | ||||||||
\(688\) | 1.62203 | 0.0618395 | ||||||||
\(689\) | 34.7339 | 1.32326 | ||||||||
\(690\) | 0.161288 | 0.00614013 | ||||||||
\(691\) | 17.1130 | 0.651009 | 0.325504 | − | 0.945541i | \(-0.394466\pi\) | ||||
0.325504 | + | 0.945541i | \(0.394466\pi\) | |||||||
\(692\) | 19.1073 | 0.726349 | ||||||||
\(693\) | 10.8090 | 0.410600 | ||||||||
\(694\) | 14.3532 | 0.544841 | ||||||||
\(695\) | −73.9352 | −2.80452 | ||||||||
\(696\) | −0.0432740 | −0.00164030 | ||||||||
\(697\) | 10.3030 | 0.390252 | ||||||||
\(698\) | −11.5459 | −0.437019 | ||||||||
\(699\) | 0.0912752 | 0.00345235 | ||||||||
\(700\) | 8.51503 | 0.321838 | ||||||||
\(701\) | 35.5121 | 1.34127 | 0.670637 | − | 0.741786i | \(-0.266021\pi\) | ||||
0.670637 | + | 0.741786i | \(0.266021\pi\) | |||||||
\(702\) | −0.244172 | −0.00921570 | ||||||||
\(703\) | 48.4439 | 1.82710 | ||||||||
\(704\) | −3.60308 | −0.135796 | ||||||||
\(705\) | −0.351643 | −0.0132437 | ||||||||
\(706\) | 2.33498 | 0.0878780 | ||||||||
\(707\) | −6.63060 | −0.249369 | ||||||||
\(708\) | 0.0284158 | 0.00106793 | ||||||||
\(709\) | 24.6240 | 0.924773 | 0.462387 | − | 0.886678i | \(-0.346993\pi\) | ||||
0.462387 | + | 0.886678i | \(0.346993\pi\) | |||||||
\(710\) | −34.1918 | −1.28319 | ||||||||
\(711\) | −6.54845 | −0.245586 | ||||||||
\(712\) | 3.87667 | 0.145284 | ||||||||
\(713\) | −46.0342 | −1.72400 | ||||||||
\(714\) | 0.0342271 | 0.00128092 | ||||||||
\(715\) | 67.0192 | 2.50638 | ||||||||
\(716\) | −17.4364 | −0.651627 | ||||||||
\(717\) | −0.152744 | −0.00570433 | ||||||||
\(718\) | −33.1350 | −1.23659 | ||||||||
\(719\) | 9.82335 | 0.366349 | 0.183175 | − | 0.983080i | \(-0.441363\pi\) | ||||
0.183175 | + | 0.983080i | \(0.441363\pi\) | |||||||
\(720\) | −11.0286 | −0.411012 | ||||||||
\(721\) | −3.07660 | −0.114578 | ||||||||
\(722\) | 32.8527 | 1.22265 | ||||||||
\(723\) | 0.0269613 | 0.00100270 | ||||||||
\(724\) | −14.6608 | −0.544863 | ||||||||
\(725\) | 45.8121 | 1.70142 | ||||||||
\(726\) | −0.0159431 | −0.000591703 0 | ||||||||
\(727\) | 35.1134 | 1.30228 | 0.651142 | − | 0.758956i | \(-0.274290\pi\) | ||||
0.651142 | + | 0.758956i | \(0.274290\pi\) | |||||||
\(728\) | −5.05961 | −0.187522 | ||||||||
\(729\) | −26.9965 | −0.999871 | ||||||||
\(730\) | −8.52434 | −0.315500 | ||||||||
\(731\) | −6.90235 | −0.255293 | ||||||||
\(732\) | 0.00843692 | 0.000311838 0 | ||||||||
\(733\) | 31.0350 | 1.14630 | 0.573152 | − | 0.819449i | \(-0.305721\pi\) | ||||
0.573152 | + | 0.819449i | \(0.305721\pi\) | |||||||
\(734\) | 26.5067 | 0.978382 | ||||||||
\(735\) | −0.0295693 | −0.00109068 | ||||||||
\(736\) | −5.45457 | −0.201058 | ||||||||
\(737\) | 43.8355 | 1.61470 | ||||||||
\(738\) | 7.26334 | 0.267367 | ||||||||
\(739\) | 41.7988 | 1.53760 | 0.768798 | − | 0.639492i | \(-0.220855\pi\) | ||||
0.768798 | + | 0.639492i | \(0.220855\pi\) | |||||||
\(740\) | −24.7322 | −0.909172 | ||||||||
\(741\) | −0.293046 | −0.0107653 | ||||||||
\(742\) | −6.86493 | −0.252020 | ||||||||
\(743\) | 18.3509 | 0.673231 | 0.336615 | − | 0.941642i | \(-0.390718\pi\) | ||||
0.336615 | + | 0.941642i | \(0.390718\pi\) | |||||||
\(744\) | −0.0678817 | −0.00248867 | ||||||||
\(745\) | −21.9699 | −0.804916 | ||||||||
\(746\) | 0.807279 | 0.0295566 | ||||||||
\(747\) | 34.0609 | 1.24622 | ||||||||
\(748\) | 15.3324 | 0.560609 | ||||||||
\(749\) | 18.6160 | 0.680214 | ||||||||
\(750\) | −0.103937 | −0.00379524 | ||||||||
\(751\) | −43.1154 | −1.57330 | −0.786651 | − | 0.617398i | \(-0.788187\pi\) | ||||
−0.786651 | + | 0.617398i | \(0.788187\pi\) | |||||||
\(752\) | 11.8922 | 0.433663 | ||||||||
\(753\) | 0.0669787 | 0.00244084 | ||||||||
\(754\) | −27.2215 | −0.991347 | ||||||||
\(755\) | 42.8482 | 1.55941 | ||||||||
\(756\) | 0.0482591 | 0.00175517 | ||||||||
\(757\) | 11.7488 | 0.427018 | 0.213509 | − | 0.976941i | \(-0.431511\pi\) | ||||
0.213509 | + | 0.976941i | \(0.431511\pi\) | |||||||
\(758\) | 35.8614 | 1.30255 | ||||||||
\(759\) | −0.158076 | −0.00573781 | ||||||||
\(760\) | −26.4724 | −0.960257 | ||||||||
\(761\) | −5.68188 | −0.205968 | −0.102984 | − | 0.994683i | \(-0.532839\pi\) | ||||
−0.102984 | + | 0.994683i | \(0.532839\pi\) | |||||||
\(762\) | −0.0828126 | −0.00299999 | ||||||||
\(763\) | 9.63832 | 0.348930 | ||||||||
\(764\) | −17.4442 | −0.631107 | ||||||||
\(765\) | 46.9307 | 1.69678 | ||||||||
\(766\) | −5.11537 | −0.184826 | ||||||||
\(767\) | 17.8749 | 0.645426 | ||||||||
\(768\) | −0.00804327 | −0.000290237 0 | ||||||||
\(769\) | −10.9305 | −0.394165 | −0.197082 | − | 0.980387i | \(-0.563147\pi\) | ||||
−0.197082 | + | 0.980387i | \(0.563147\pi\) | |||||||
\(770\) | −13.2459 | −0.477350 | ||||||||
\(771\) | 0.193254 | 0.00695986 | ||||||||
\(772\) | 17.1234 | 0.616286 | ||||||||
\(773\) | −42.3246 | −1.52231 | −0.761156 | − | 0.648569i | \(-0.775368\pi\) | ||||
−0.761156 | + | 0.648569i | \(0.775368\pi\) | |||||||
\(774\) | −4.86600 | −0.174905 | ||||||||
\(775\) | 71.8632 | 2.58140 | ||||||||
\(776\) | −5.64654 | −0.202699 | ||||||||
\(777\) | 0.0541111 | 0.00194122 | ||||||||
\(778\) | −20.0433 | −0.718588 | ||||||||
\(779\) | 17.4345 | 0.624657 | ||||||||
\(780\) | 0.149609 | 0.00535687 | ||||||||
\(781\) | 33.5109 | 1.19912 | ||||||||
\(782\) | 23.2112 | 0.830031 | ||||||||
\(783\) | 0.259641 | 0.00927881 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −85.5241 | −3.05249 | ||||||||
\(786\) | 0.105996 | 0.00378076 | ||||||||
\(787\) | −44.5269 | −1.58721 | −0.793607 | − | 0.608431i | \(-0.791799\pi\) | ||||
−0.793607 | + | 0.608431i | \(0.791799\pi\) | |||||||
\(788\) | 1.01990 | 0.0363323 | ||||||||
\(789\) | 0.0563860 | 0.00200739 | ||||||||
\(790\) | 8.02481 | 0.285510 | ||||||||
\(791\) | −13.1349 | −0.467023 | ||||||||
\(792\) | 10.8090 | 0.384081 | ||||||||
\(793\) | 5.30724 | 0.188466 | ||||||||
\(794\) | −3.94502 | −0.140004 | ||||||||
\(795\) | 0.202991 | 0.00719936 | ||||||||
\(796\) | 17.4049 | 0.616901 | ||||||||
\(797\) | −37.2080 | −1.31797 | −0.658987 | − | 0.752154i | \(-0.729015\pi\) | ||||
−0.658987 | + | 0.752154i | \(0.729015\pi\) | |||||||
\(798\) | 0.0579186 | 0.00205030 | ||||||||
\(799\) | −50.6056 | −1.79030 | ||||||||
\(800\) | 8.51503 | 0.301052 | ||||||||
\(801\) | −11.6298 | −0.410917 | ||||||||
\(802\) | 1.21403 | 0.0428688 | ||||||||
\(803\) | 8.35461 | 0.294828 | ||||||||
\(804\) | 0.0978556 | 0.00345110 | ||||||||
\(805\) | −20.0525 | −0.706759 | ||||||||
\(806\) | −42.7009 | −1.50408 | ||||||||
\(807\) | −0.0841321 | −0.00296159 | ||||||||
\(808\) | −6.63060 | −0.233264 | ||||||||
\(809\) | 10.8896 | 0.382859 | 0.191430 | − | 0.981506i | \(-0.438688\pi\) | ||||
0.191430 | + | 0.981506i | \(0.438688\pi\) | |||||||
\(810\) | 33.0844 | 1.16247 | ||||||||
\(811\) | 24.7326 | 0.868479 | 0.434240 | − | 0.900797i | \(-0.357017\pi\) | ||||
0.434240 | + | 0.900797i | \(0.357017\pi\) | |||||||
\(812\) | 5.38015 | 0.188806 | ||||||||
\(813\) | −0.0285096 | −0.000999874 0 | ||||||||
\(814\) | 24.2397 | 0.849600 | ||||||||
\(815\) | 50.4742 | 1.76804 | ||||||||
\(816\) | 0.0342271 | 0.00119819 | ||||||||
\(817\) | −11.6801 | −0.408634 | ||||||||
\(818\) | 3.37254 | 0.117918 | ||||||||
\(819\) | 15.1785 | 0.530380 | ||||||||
\(820\) | −8.90089 | −0.310832 | ||||||||
\(821\) | −13.9820 | −0.487976 | −0.243988 | − | 0.969778i | \(-0.578456\pi\) | ||||
−0.243988 | + | 0.969778i | \(0.578456\pi\) | |||||||
\(822\) | −0.0539819 | −0.00188284 | ||||||||
\(823\) | −46.6363 | −1.62564 | −0.812820 | − | 0.582515i | \(-0.802069\pi\) | ||||
−0.812820 | + | 0.582515i | \(0.802069\pi\) | |||||||
\(824\) | −3.07660 | −0.107178 | ||||||||
\(825\) | 0.246770 | 0.00859143 | ||||||||
\(826\) | −3.53286 | −0.122924 | ||||||||
\(827\) | 1.01238 | 0.0352040 | 0.0176020 | − | 0.999845i | \(-0.494397\pi\) | ||||
0.0176020 | + | 0.999845i | \(0.494397\pi\) | |||||||
\(828\) | 16.3634 | 0.568666 | ||||||||
\(829\) | −48.6340 | −1.68913 | −0.844565 | − | 0.535453i | \(-0.820141\pi\) | ||||
−0.844565 | + | 0.535453i | \(0.820141\pi\) | |||||||
\(830\) | −41.7401 | −1.44882 | ||||||||
\(831\) | 0.164120 | 0.00569325 | ||||||||
\(832\) | −5.05961 | −0.175411 | ||||||||
\(833\) | −4.25537 | −0.147440 | ||||||||
\(834\) | 0.161762 | 0.00560135 | ||||||||
\(835\) | 63.3470 | 2.19221 | ||||||||
\(836\) | 25.9453 | 0.897338 | ||||||||
\(837\) | 0.407286 | 0.0140779 | ||||||||
\(838\) | 14.1407 | 0.488482 | ||||||||
\(839\) | −21.3569 | −0.737321 | −0.368661 | − | 0.929564i | \(-0.620184\pi\) | ||||
−0.368661 | + | 0.929564i | \(0.620184\pi\) | |||||||
\(840\) | −0.0295693 | −0.00102024 | ||||||||
\(841\) | −0.0540379 | −0.00186338 | ||||||||
\(842\) | 24.9368 | 0.859380 | ||||||||
\(843\) | −0.183025 | −0.00630372 | ||||||||
\(844\) | −21.0824 | −0.725687 | ||||||||
\(845\) | 46.3200 | 1.59346 | ||||||||
\(846\) | −35.6757 | −1.22656 | ||||||||
\(847\) | 1.98216 | 0.0681080 | ||||||||
\(848\) | −6.86493 | −0.235743 | ||||||||
\(849\) | 0.189166 | 0.00649215 | ||||||||
\(850\) | −36.2346 | −1.24284 | ||||||||
\(851\) | 36.6956 | 1.25791 | ||||||||
\(852\) | 0.0748076 | 0.00256287 | ||||||||
\(853\) | 26.1396 | 0.895005 | 0.447502 | − | 0.894283i | \(-0.352314\pi\) | ||||
0.447502 | + | 0.894283i | \(0.352314\pi\) | |||||||
\(854\) | −1.04894 | −0.0358940 | ||||||||
\(855\) | 79.4156 | 2.71596 | ||||||||
\(856\) | 18.6160 | 0.636282 | ||||||||
\(857\) | 2.73904 | 0.0935638 | 0.0467819 | − | 0.998905i | \(-0.485103\pi\) | ||||
0.0467819 | + | 0.998905i | \(0.485103\pi\) | |||||||
\(858\) | −0.146630 | −0.00500587 | ||||||||
\(859\) | 8.65838 | 0.295420 | 0.147710 | − | 0.989031i | \(-0.452810\pi\) | ||||
0.147710 | + | 0.989031i | \(0.452810\pi\) | |||||||
\(860\) | 5.96305 | 0.203338 | ||||||||
\(861\) | 0.0194741 | 0.000663676 0 | ||||||||
\(862\) | −1.00000 | −0.0340601 | ||||||||
\(863\) | −41.0294 | −1.39666 | −0.698328 | − | 0.715778i | \(-0.746072\pi\) | ||||
−0.698328 | + | 0.715778i | \(0.746072\pi\) | |||||||
\(864\) | 0.0482591 | 0.00164181 | ||||||||
\(865\) | 70.2436 | 2.38835 | ||||||||
\(866\) | 23.8411 | 0.810155 | ||||||||
\(867\) | −0.00891317 | −0.000302707 0 | ||||||||
\(868\) | 8.43957 | 0.286458 | ||||||||
\(869\) | −7.86502 | −0.266803 | ||||||||
\(870\) | −0.159087 | −0.00539356 | ||||||||
\(871\) | 61.5560 | 2.08574 | ||||||||
\(872\) | 9.63832 | 0.326395 | ||||||||
\(873\) | 16.9393 | 0.573307 | ||||||||
\(874\) | 39.2777 | 1.32859 | ||||||||
\(875\) | 12.9222 | 0.436851 | ||||||||
\(876\) | 0.0186503 | 0.000630134 0 | ||||||||
\(877\) | 8.64418 | 0.291893 | 0.145947 | − | 0.989292i | \(-0.453377\pi\) | ||||
0.145947 | + | 0.989292i | \(0.453377\pi\) | |||||||
\(878\) | 1.62172 | 0.0547306 | ||||||||
\(879\) | −0.0897808 | −0.00302823 | ||||||||
\(880\) | −13.2459 | −0.446520 | ||||||||
\(881\) | 9.47119 | 0.319092 | 0.159546 | − | 0.987190i | \(-0.448997\pi\) | ||||
0.159546 | + | 0.987190i | \(0.448997\pi\) | |||||||
\(882\) | −2.99994 | −0.101013 | ||||||||
\(883\) | −25.4208 | −0.855478 | −0.427739 | − | 0.903902i | \(-0.640690\pi\) | ||||
−0.427739 | + | 0.903902i | \(0.640690\pi\) | |||||||
\(884\) | 21.5305 | 0.724150 | ||||||||
\(885\) | 0.104464 | 0.00351153 | ||||||||
\(886\) | −7.44042 | −0.249966 | ||||||||
\(887\) | 26.0472 | 0.874580 | 0.437290 | − | 0.899321i | \(-0.355938\pi\) | ||||
0.437290 | + | 0.899321i | \(0.355938\pi\) | |||||||
\(888\) | 0.0541111 | 0.00181585 | ||||||||
\(889\) | 10.2959 | 0.345313 | ||||||||
\(890\) | 14.2517 | 0.477719 | ||||||||
\(891\) | −32.4256 | −1.08630 | ||||||||
\(892\) | 28.2233 | 0.944985 | ||||||||
\(893\) | −85.6341 | −2.86564 | ||||||||
\(894\) | 0.0480677 | 0.00160762 | ||||||||
\(895\) | −64.1009 | −2.14266 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −0.221978 | −0.00741164 | ||||||||
\(898\) | 41.3656 | 1.38039 | ||||||||
\(899\) | 45.4061 | 1.51438 | ||||||||
\(900\) | −25.5445 | −0.851485 | ||||||||
\(901\) | 29.2128 | 0.973220 | ||||||||
\(902\) | 8.72365 | 0.290466 | ||||||||
\(903\) | −0.0130465 | −0.000434159 0 | ||||||||
\(904\) | −13.1349 | −0.436860 | ||||||||
\(905\) | −53.8971 | −1.79160 | ||||||||
\(906\) | −0.0937469 | −0.00311453 | ||||||||
\(907\) | 21.7891 | 0.723495 | 0.361747 | − | 0.932276i | \(-0.382180\pi\) | ||||
0.361747 | + | 0.932276i | \(0.382180\pi\) | |||||||
\(908\) | 21.3480 | 0.708458 | ||||||||
\(909\) | 19.8914 | 0.659755 | ||||||||
\(910\) | −18.6006 | −0.616602 | ||||||||
\(911\) | −22.0127 | −0.729314 | −0.364657 | − | 0.931142i | \(-0.618814\pi\) | ||||
−0.364657 | + | 0.931142i | \(0.618814\pi\) | |||||||
\(912\) | 0.0579186 | 0.00191788 | ||||||||
\(913\) | 40.9089 | 1.35389 | ||||||||
\(914\) | −10.7143 | −0.354397 | ||||||||
\(915\) | 0.0310165 | 0.00102537 | ||||||||
\(916\) | −7.49251 | −0.247560 | ||||||||
\(917\) | −13.1782 | −0.435184 | ||||||||
\(918\) | −0.205360 | −0.00677790 | ||||||||
\(919\) | −8.31675 | −0.274344 | −0.137172 | − | 0.990547i | \(-0.543801\pi\) | ||||
−0.137172 | + | 0.990547i | \(0.543801\pi\) | |||||||
\(920\) | −20.0525 | −0.661112 | ||||||||
\(921\) | −0.120341 | −0.00396536 | ||||||||
\(922\) | −19.1525 | −0.630752 | ||||||||
\(923\) | 47.0577 | 1.54892 | ||||||||
\(924\) | 0.0289805 | 0.000953389 0 | ||||||||
\(925\) | −57.2848 | −1.88351 | ||||||||
\(926\) | 1.76427 | 0.0579774 | ||||||||
\(927\) | 9.22959 | 0.303139 | ||||||||
\(928\) | 5.38015 | 0.176612 | ||||||||
\(929\) | −44.2451 | −1.45163 | −0.725817 | − | 0.687888i | \(-0.758538\pi\) | ||||
−0.725817 | + | 0.687888i | \(0.758538\pi\) | |||||||
\(930\) | −0.249552 | −0.00818314 | ||||||||
\(931\) | −7.20088 | −0.235999 | ||||||||
\(932\) | −11.3480 | −0.371717 | ||||||||
\(933\) | 0.0565776 | 0.00185227 | ||||||||
\(934\) | 40.3408 | 1.31999 | ||||||||
\(935\) | 56.3662 | 1.84337 | ||||||||
\(936\) | 15.1785 | 0.496125 | ||||||||
\(937\) | 21.1189 | 0.689924 | 0.344962 | − | 0.938617i | \(-0.387892\pi\) | ||||
0.344962 | + | 0.938617i | \(0.387892\pi\) | |||||||
\(938\) | −12.1661 | −0.397239 | ||||||||
\(939\) | 0.0632587 | 0.00206437 | ||||||||
\(940\) | 43.7189 | 1.42595 | ||||||||
\(941\) | −35.1986 | −1.14744 | −0.573721 | − | 0.819051i | \(-0.694501\pi\) | ||||
−0.573721 | + | 0.819051i | \(0.694501\pi\) | |||||||
\(942\) | 0.187117 | 0.00609660 | ||||||||
\(943\) | 13.2064 | 0.430060 | ||||||||
\(944\) | −3.53286 | −0.114985 | ||||||||
\(945\) | 0.177414 | 0.00577128 | ||||||||
\(946\) | −5.84431 | −0.190015 | ||||||||
\(947\) | 25.7086 | 0.835419 | 0.417709 | − | 0.908581i | \(-0.362833\pi\) | ||||
0.417709 | + | 0.908581i | \(0.362833\pi\) | |||||||
\(948\) | −0.0175574 | −0.000570236 0 | ||||||||
\(949\) | 11.7319 | 0.380835 | ||||||||
\(950\) | −61.3157 | −1.98934 | ||||||||
\(951\) | 0.142998 | 0.00463703 | ||||||||
\(952\) | −4.25537 | −0.137917 | ||||||||
\(953\) | −24.9156 | −0.807097 | −0.403548 | − | 0.914958i | \(-0.632223\pi\) | ||||
−0.403548 | + | 0.914958i | \(0.632223\pi\) | |||||||
\(954\) | 20.5944 | 0.666767 | ||||||||
\(955\) | −64.1296 | −2.07518 | ||||||||
\(956\) | 18.9903 | 0.614190 | ||||||||
\(957\) | 0.155919 | 0.00504016 | ||||||||
\(958\) | 11.5365 | 0.372726 | ||||||||
\(959\) | 6.71144 | 0.216724 | ||||||||
\(960\) | −0.0295693 | −0.000954346 0 | ||||||||
\(961\) | 40.2263 | 1.29762 | ||||||||
\(962\) | 34.0385 | 1.09745 | ||||||||
\(963\) | −55.8468 | −1.79964 | ||||||||
\(964\) | −3.35203 | −0.107962 | ||||||||
\(965\) | 62.9505 | 2.02645 | ||||||||
\(966\) | 0.0438726 | 0.00141158 | ||||||||
\(967\) | −16.6784 | −0.536341 | −0.268170 | − | 0.963371i | \(-0.586419\pi\) | ||||
−0.268170 | + | 0.963371i | \(0.586419\pi\) | |||||||
\(968\) | 1.98216 | 0.0637092 | ||||||||
\(969\) | −0.246465 | −0.00791760 | ||||||||
\(970\) | −20.7583 | −0.666507 | ||||||||
\(971\) | −45.0491 | −1.44570 | −0.722848 | − | 0.691007i | \(-0.757167\pi\) | ||||
−0.722848 | + | 0.691007i | \(0.757167\pi\) | |||||||
\(972\) | −0.217162 | −0.00696548 | ||||||||
\(973\) | −20.1114 | −0.644742 | ||||||||
\(974\) | −14.8135 | −0.474654 | ||||||||
\(975\) | 0.346526 | 0.0110977 | ||||||||
\(976\) | −1.04894 | −0.0335758 | ||||||||
\(977\) | −35.5982 | −1.13889 | −0.569444 | − | 0.822030i | \(-0.692841\pi\) | ||||
−0.569444 | + | 0.822030i | \(0.692841\pi\) | |||||||
\(978\) | −0.110432 | −0.00353122 | ||||||||
\(979\) | −13.9679 | −0.446417 | ||||||||
\(980\) | 3.67628 | 0.117434 | ||||||||
\(981\) | −28.9143 | −0.923163 | ||||||||
\(982\) | 1.74825 | 0.0557890 | ||||||||
\(983\) | 46.1059 | 1.47055 | 0.735274 | − | 0.677770i | \(-0.237053\pi\) | ||||
0.735274 | + | 0.677770i | \(0.237053\pi\) | |||||||
\(984\) | 0.0194741 | 0.000620812 0 | ||||||||
\(985\) | 3.74943 | 0.119467 | ||||||||
\(986\) | −22.8945 | −0.729109 | ||||||||
\(987\) | −0.0956520 | −0.00304464 | ||||||||
\(988\) | 36.4337 | 1.15911 | ||||||||
\(989\) | −8.84750 | −0.281334 | ||||||||
\(990\) | 39.7369 | 1.26292 | ||||||||
\(991\) | −37.6985 | −1.19753 | −0.598767 | − | 0.800923i | \(-0.704342\pi\) | ||||
−0.598767 | + | 0.800923i | \(0.704342\pi\) | |||||||
\(992\) | 8.43957 | 0.267957 | ||||||||
\(993\) | −0.0500589 | −0.00158857 | ||||||||
\(994\) | −9.30064 | −0.294998 | ||||||||
\(995\) | 63.9853 | 2.02847 | ||||||||
\(996\) | 0.0913224 | 0.00289366 | ||||||||
\(997\) | 24.0356 | 0.761216 | 0.380608 | − | 0.924737i | \(-0.375715\pi\) | ||||
0.380608 | + | 0.924737i | \(0.375715\pi\) | |||||||
\(998\) | 7.34260 | 0.232426 | ||||||||
\(999\) | −0.324663 | −0.0102719 |
(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 | 6034.2.a.m.1.12 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.m.1.12 | ✓ | 21 | 1.1 | even | 1 | trivial |