Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.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: | \(32.0120261703\) |
Analytic rank: | \(1\) |
Dimension: | \(71\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.82251 | −1.99582 | −0.997909 | − | 0.0646411i | \(-0.979410\pi\) | ||||
−0.997909 | + | 0.0646411i | \(0.979410\pi\) | |||||||
\(3\) | 2.93474 | 1.69437 | 0.847186 | − | 0.531296i | \(-0.178295\pi\) | ||||
0.847186 | + | 0.531296i | \(0.178295\pi\) | |||||||
\(4\) | 5.96657 | 2.98329 | ||||||||
\(5\) | 0.420997 | 0.188275 | 0.0941377 | − | 0.995559i | \(-0.469991\pi\) | ||||
0.0941377 | + | 0.995559i | \(0.469991\pi\) | |||||||
\(6\) | −8.28333 | −3.38166 | ||||||||
\(7\) | −3.44749 | −1.30303 | −0.651515 | − | 0.758636i | \(-0.725866\pi\) | ||||
−0.651515 | + | 0.758636i | \(0.725866\pi\) | |||||||
\(8\) | −11.1957 | −3.95828 | ||||||||
\(9\) | 5.61269 | 1.87090 | ||||||||
\(10\) | −1.18827 | −0.375763 | ||||||||
\(11\) | −0.690697 | −0.208253 | −0.104126 | − | 0.994564i | \(-0.533205\pi\) | ||||
−0.104126 | + | 0.994564i | \(0.533205\pi\) | |||||||
\(12\) | 17.5103 | 5.05480 | ||||||||
\(13\) | −6.41936 | −1.78041 | −0.890204 | − | 0.455561i | \(-0.849439\pi\) | ||||
−0.890204 | + | 0.455561i | \(0.849439\pi\) | |||||||
\(14\) | 9.73058 | 2.60061 | ||||||||
\(15\) | 1.23552 | 0.319009 | ||||||||
\(16\) | 19.6668 | 4.91671 | ||||||||
\(17\) | 6.09680 | 1.47869 | 0.739346 | − | 0.673326i | \(-0.235135\pi\) | ||||
0.739346 | + | 0.673326i | \(0.235135\pi\) | |||||||
\(18\) | −15.8419 | −3.73397 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 2.51191 | 0.561680 | ||||||||
\(21\) | −10.1175 | −2.20782 | ||||||||
\(22\) | 1.94950 | 0.415635 | ||||||||
\(23\) | 6.89386 | 1.43747 | 0.718735 | − | 0.695284i | \(-0.244721\pi\) | ||||
0.718735 | + | 0.695284i | \(0.244721\pi\) | |||||||
\(24\) | −32.8564 | −6.70679 | ||||||||
\(25\) | −4.82276 | −0.964552 | ||||||||
\(26\) | 18.1187 | 3.55337 | ||||||||
\(27\) | 7.66757 | 1.47562 | ||||||||
\(28\) | −20.5697 | −3.88731 | ||||||||
\(29\) | −6.37730 | −1.18423 | −0.592117 | − | 0.805852i | \(-0.701708\pi\) | ||||
−0.592117 | + | 0.805852i | \(0.701708\pi\) | |||||||
\(30\) | −3.48726 | −0.636683 | ||||||||
\(31\) | −0.869751 | −0.156212 | −0.0781060 | − | 0.996945i | \(-0.524887\pi\) | ||||
−0.0781060 | + | 0.996945i | \(0.524887\pi\) | |||||||
\(32\) | −33.1185 | −5.85458 | ||||||||
\(33\) | −2.02701 | −0.352858 | ||||||||
\(34\) | −17.2083 | −2.95120 | ||||||||
\(35\) | −1.45138 | −0.245328 | ||||||||
\(36\) | 33.4885 | 5.58142 | ||||||||
\(37\) | 6.88837 | 1.13244 | 0.566220 | − | 0.824254i | \(-0.308405\pi\) | ||||
0.566220 | + | 0.824254i | \(0.308405\pi\) | |||||||
\(38\) | −2.82251 | −0.457872 | ||||||||
\(39\) | −18.8391 | −3.01668 | ||||||||
\(40\) | −4.71335 | −0.745246 | ||||||||
\(41\) | −8.97979 | −1.40241 | −0.701204 | − | 0.712961i | \(-0.747354\pi\) | ||||
−0.701204 | + | 0.712961i | \(0.747354\pi\) | |||||||
\(42\) | 28.5567 | 4.40640 | ||||||||
\(43\) | 2.33166 | 0.355575 | 0.177787 | − | 0.984069i | \(-0.443106\pi\) | ||||
0.177787 | + | 0.984069i | \(0.443106\pi\) | |||||||
\(44\) | −4.12109 | −0.621278 | ||||||||
\(45\) | 2.36293 | 0.352244 | ||||||||
\(46\) | −19.4580 | −2.86893 | ||||||||
\(47\) | −12.1493 | −1.77216 | −0.886078 | − | 0.463536i | \(-0.846580\pi\) | ||||
−0.886078 | + | 0.463536i | \(0.846580\pi\) | |||||||
\(48\) | 57.7170 | 8.33074 | ||||||||
\(49\) | 4.88519 | 0.697885 | ||||||||
\(50\) | 13.6123 | 1.92507 | ||||||||
\(51\) | 17.8925 | 2.50545 | ||||||||
\(52\) | −38.3015 | −5.31147 | ||||||||
\(53\) | −0.247210 | −0.0339569 | −0.0169784 | − | 0.999856i | \(-0.505405\pi\) | ||||
−0.0169784 | + | 0.999856i | \(0.505405\pi\) | |||||||
\(54\) | −21.6418 | −2.94508 | ||||||||
\(55\) | −0.290781 | −0.0392089 | ||||||||
\(56\) | 38.5971 | 5.15775 | ||||||||
\(57\) | 2.93474 | 0.388716 | ||||||||
\(58\) | 18.0000 | 2.36352 | ||||||||
\(59\) | −5.51539 | −0.718043 | −0.359021 | − | 0.933329i | \(-0.616889\pi\) | ||||
−0.359021 | + | 0.933329i | \(0.616889\pi\) | |||||||
\(60\) | 7.37179 | 0.951694 | ||||||||
\(61\) | −2.13549 | −0.273421 | −0.136711 | − | 0.990611i | \(-0.543653\pi\) | ||||
−0.136711 | + | 0.990611i | \(0.543653\pi\) | |||||||
\(62\) | 2.45488 | 0.311770 | ||||||||
\(63\) | −19.3497 | −2.43783 | ||||||||
\(64\) | 54.1436 | 6.76796 | ||||||||
\(65\) | −2.70253 | −0.335207 | ||||||||
\(66\) | 5.72127 | 0.704240 | ||||||||
\(67\) | 0.584061 | 0.0713544 | 0.0356772 | − | 0.999363i | \(-0.488641\pi\) | ||||
0.0356772 | + | 0.999363i | \(0.488641\pi\) | |||||||
\(68\) | 36.3770 | 4.41136 | ||||||||
\(69\) | 20.2317 | 2.43561 | ||||||||
\(70\) | 4.09654 | 0.489631 | ||||||||
\(71\) | −11.6130 | −1.37821 | −0.689103 | − | 0.724663i | \(-0.741995\pi\) | ||||
−0.689103 | + | 0.724663i | \(0.741995\pi\) | |||||||
\(72\) | −62.8380 | −7.40553 | ||||||||
\(73\) | 14.6875 | 1.71905 | 0.859523 | − | 0.511096i | \(-0.170760\pi\) | ||||
0.859523 | + | 0.511096i | \(0.170760\pi\) | |||||||
\(74\) | −19.4425 | −2.26014 | ||||||||
\(75\) | −14.1535 | −1.63431 | ||||||||
\(76\) | 5.96657 | 0.684413 | ||||||||
\(77\) | 2.38117 | 0.271360 | ||||||||
\(78\) | 53.1737 | 6.02073 | ||||||||
\(79\) | −7.62708 | −0.858114 | −0.429057 | − | 0.903277i | \(-0.641154\pi\) | ||||
−0.429057 | + | 0.903277i | \(0.641154\pi\) | |||||||
\(80\) | 8.27968 | 0.925696 | ||||||||
\(81\) | 5.66423 | 0.629359 | ||||||||
\(82\) | 25.3456 | 2.79895 | ||||||||
\(83\) | 10.1726 | 1.11659 | 0.558295 | − | 0.829643i | \(-0.311456\pi\) | ||||
0.558295 | + | 0.829643i | \(0.311456\pi\) | |||||||
\(84\) | −60.3667 | −6.58655 | ||||||||
\(85\) | 2.56673 | 0.278401 | ||||||||
\(86\) | −6.58114 | −0.709662 | ||||||||
\(87\) | −18.7157 | −2.00653 | ||||||||
\(88\) | 7.73283 | 0.824323 | ||||||||
\(89\) | −12.3693 | −1.31115 | −0.655574 | − | 0.755131i | \(-0.727573\pi\) | ||||
−0.655574 | + | 0.755131i | \(0.727573\pi\) | |||||||
\(90\) | −6.66938 | −0.703015 | ||||||||
\(91\) | 22.1307 | 2.31992 | ||||||||
\(92\) | 41.1327 | 4.28838 | ||||||||
\(93\) | −2.55249 | −0.264681 | ||||||||
\(94\) | 34.2915 | 3.53690 | ||||||||
\(95\) | 0.420997 | 0.0431934 | ||||||||
\(96\) | −97.1941 | −9.91983 | ||||||||
\(97\) | −0.0438413 | −0.00445141 | −0.00222571 | − | 0.999998i | \(-0.500708\pi\) | ||||
−0.00222571 | + | 0.999998i | \(0.500708\pi\) | |||||||
\(98\) | −13.7885 | −1.39285 | ||||||||
\(99\) | −3.87667 | −0.389620 | ||||||||
\(100\) | −28.7754 | −2.87754 | ||||||||
\(101\) | 3.15007 | 0.313443 | 0.156722 | − | 0.987643i | \(-0.449907\pi\) | ||||
0.156722 | + | 0.987643i | \(0.449907\pi\) | |||||||
\(102\) | −50.5018 | −5.00043 | ||||||||
\(103\) | −1.54513 | −0.152247 | −0.0761233 | − | 0.997098i | \(-0.524254\pi\) | ||||
−0.0761233 | + | 0.997098i | \(0.524254\pi\) | |||||||
\(104\) | 71.8692 | 7.04735 | ||||||||
\(105\) | −4.25943 | −0.415678 | ||||||||
\(106\) | 0.697753 | 0.0677718 | ||||||||
\(107\) | −2.99572 | −0.289607 | −0.144803 | − | 0.989460i | \(-0.546255\pi\) | ||||
−0.144803 | + | 0.989460i | \(0.546255\pi\) | |||||||
\(108\) | 45.7491 | 4.40221 | ||||||||
\(109\) | −1.35462 | −0.129749 | −0.0648747 | − | 0.997893i | \(-0.520665\pi\) | ||||
−0.0648747 | + | 0.997893i | \(0.520665\pi\) | |||||||
\(110\) | 0.820733 | 0.0782538 | ||||||||
\(111\) | 20.2156 | 1.91878 | ||||||||
\(112\) | −67.8012 | −6.40662 | ||||||||
\(113\) | −8.53263 | −0.802683 | −0.401341 | − | 0.915929i | \(-0.631456\pi\) | ||||
−0.401341 | + | 0.915929i | \(0.631456\pi\) | |||||||
\(114\) | −8.28333 | −0.775805 | ||||||||
\(115\) | 2.90229 | 0.270640 | ||||||||
\(116\) | −38.0506 | −3.53291 | ||||||||
\(117\) | −36.0299 | −3.33096 | ||||||||
\(118\) | 15.5673 | 1.43308 | ||||||||
\(119\) | −21.0187 | −1.92678 | ||||||||
\(120\) | −13.8325 | −1.26272 | ||||||||
\(121\) | −10.5229 | −0.956631 | ||||||||
\(122\) | 6.02744 | 0.545699 | ||||||||
\(123\) | −26.3534 | −2.37620 | ||||||||
\(124\) | −5.18943 | −0.466025 | ||||||||
\(125\) | −4.13535 | −0.369877 | ||||||||
\(126\) | 54.6148 | 4.86547 | ||||||||
\(127\) | 19.6258 | 1.74151 | 0.870753 | − | 0.491720i | \(-0.163632\pi\) | ||||
0.870753 | + | 0.491720i | \(0.163632\pi\) | |||||||
\(128\) | −86.5841 | −7.65303 | ||||||||
\(129\) | 6.84281 | 0.602476 | ||||||||
\(130\) | 7.62792 | 0.669013 | ||||||||
\(131\) | −2.64588 | −0.231172 | −0.115586 | − | 0.993297i | \(-0.536875\pi\) | ||||
−0.115586 | + | 0.993297i | \(0.536875\pi\) | |||||||
\(132\) | −12.0943 | −1.05268 | ||||||||
\(133\) | −3.44749 | −0.298935 | ||||||||
\(134\) | −1.64852 | −0.142410 | ||||||||
\(135\) | 3.22802 | 0.277824 | ||||||||
\(136\) | −68.2579 | −5.85307 | ||||||||
\(137\) | −4.38546 | −0.374675 | −0.187338 | − | 0.982296i | \(-0.559986\pi\) | ||||
−0.187338 | + | 0.982296i | \(0.559986\pi\) | |||||||
\(138\) | −57.1042 | −4.86103 | ||||||||
\(139\) | −12.8484 | −1.08979 | −0.544894 | − | 0.838505i | \(-0.683430\pi\) | ||||
−0.544894 | + | 0.838505i | \(0.683430\pi\) | |||||||
\(140\) | −8.65978 | −0.731885 | ||||||||
\(141\) | −35.6550 | −3.00269 | ||||||||
\(142\) | 32.7778 | 2.75065 | ||||||||
\(143\) | 4.43383 | 0.370775 | ||||||||
\(144\) | 110.384 | 9.19866 | ||||||||
\(145\) | −2.68482 | −0.222962 | ||||||||
\(146\) | −41.4558 | −3.43090 | ||||||||
\(147\) | 14.3368 | 1.18248 | ||||||||
\(148\) | 41.1000 | 3.37840 | ||||||||
\(149\) | −3.29810 | −0.270191 | −0.135095 | − | 0.990833i | \(-0.543134\pi\) | ||||
−0.135095 | + | 0.990833i | \(0.543134\pi\) | |||||||
\(150\) | 39.9485 | 3.26179 | ||||||||
\(151\) | −2.85234 | −0.232120 | −0.116060 | − | 0.993242i | \(-0.537027\pi\) | ||||
−0.116060 | + | 0.993242i | \(0.537027\pi\) | |||||||
\(152\) | −11.1957 | −0.908091 | ||||||||
\(153\) | 34.2195 | 2.76648 | ||||||||
\(154\) | −6.72088 | −0.541584 | ||||||||
\(155\) | −0.366162 | −0.0294109 | ||||||||
\(156\) | −112.405 | −8.99961 | ||||||||
\(157\) | −21.8181 | −1.74127 | −0.870637 | − | 0.491927i | \(-0.836293\pi\) | ||||
−0.870637 | + | 0.491927i | \(0.836293\pi\) | |||||||
\(158\) | 21.5275 | 1.71264 | ||||||||
\(159\) | −0.725497 | −0.0575356 | ||||||||
\(160\) | −13.9428 | −1.10227 | ||||||||
\(161\) | −23.7665 | −1.87307 | ||||||||
\(162\) | −15.9874 | −1.25609 | ||||||||
\(163\) | 5.70997 | 0.447240 | 0.223620 | − | 0.974676i | \(-0.428213\pi\) | ||||
0.223620 | + | 0.974676i | \(0.428213\pi\) | |||||||
\(164\) | −53.5786 | −4.18379 | ||||||||
\(165\) | −0.853367 | −0.0664345 | ||||||||
\(166\) | −28.7123 | −2.22851 | ||||||||
\(167\) | −12.5772 | −0.973250 | −0.486625 | − | 0.873611i | \(-0.661772\pi\) | ||||
−0.486625 | + | 0.873611i | \(0.661772\pi\) | |||||||
\(168\) | 113.272 | 8.73915 | ||||||||
\(169\) | 28.2081 | 2.16986 | ||||||||
\(170\) | −7.24464 | −0.555638 | ||||||||
\(171\) | 5.61269 | 0.429213 | ||||||||
\(172\) | 13.9120 | 1.06078 | ||||||||
\(173\) | −4.90077 | −0.372599 | −0.186299 | − | 0.982493i | \(-0.559649\pi\) | ||||
−0.186299 | + | 0.982493i | \(0.559649\pi\) | |||||||
\(174\) | 52.8253 | 4.00468 | ||||||||
\(175\) | 16.6264 | 1.25684 | ||||||||
\(176\) | −13.5838 | −1.02392 | ||||||||
\(177\) | −16.1862 | −1.21663 | ||||||||
\(178\) | 34.9126 | 2.61681 | ||||||||
\(179\) | −9.62514 | −0.719417 | −0.359708 | − | 0.933065i | \(-0.617124\pi\) | ||||
−0.359708 | + | 0.933065i | \(0.617124\pi\) | |||||||
\(180\) | 14.0986 | 1.05084 | ||||||||
\(181\) | −9.16903 | −0.681529 | −0.340764 | − | 0.940149i | \(-0.610686\pi\) | ||||
−0.340764 | + | 0.940149i | \(0.610686\pi\) | |||||||
\(182\) | −62.4641 | −4.63015 | ||||||||
\(183\) | −6.26710 | −0.463277 | ||||||||
\(184\) | −77.1816 | −5.68990 | ||||||||
\(185\) | 2.89998 | 0.213211 | ||||||||
\(186\) | 7.20444 | 0.528255 | ||||||||
\(187\) | −4.21104 | −0.307942 | ||||||||
\(188\) | −72.4896 | −5.28685 | ||||||||
\(189\) | −26.4339 | −1.92278 | ||||||||
\(190\) | −1.18827 | −0.0862060 | ||||||||
\(191\) | 1.25971 | 0.0911495 | 0.0455747 | − | 0.998961i | \(-0.485488\pi\) | ||||
0.0455747 | + | 0.998961i | \(0.485488\pi\) | |||||||
\(192\) | 158.897 | 11.4674 | ||||||||
\(193\) | 11.5044 | 0.828103 | 0.414052 | − | 0.910253i | \(-0.364113\pi\) | ||||
0.414052 | + | 0.910253i | \(0.364113\pi\) | |||||||
\(194\) | 0.123743 | 0.00888421 | ||||||||
\(195\) | −7.93121 | −0.567966 | ||||||||
\(196\) | 29.1479 | 2.08199 | ||||||||
\(197\) | −12.1097 | −0.862783 | −0.431391 | − | 0.902165i | \(-0.641977\pi\) | ||||
−0.431391 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(198\) | 10.9419 | 0.777610 | ||||||||
\(199\) | 5.90465 | 0.418569 | 0.209285 | − | 0.977855i | \(-0.432886\pi\) | ||||
0.209285 | + | 0.977855i | \(0.432886\pi\) | |||||||
\(200\) | 53.9942 | 3.81796 | ||||||||
\(201\) | 1.71407 | 0.120901 | ||||||||
\(202\) | −8.89110 | −0.625576 | ||||||||
\(203\) | 21.9857 | 1.54309 | ||||||||
\(204\) | 106.757 | 7.47449 | ||||||||
\(205\) | −3.78046 | −0.264039 | ||||||||
\(206\) | 4.36116 | 0.303856 | ||||||||
\(207\) | 38.6931 | 2.68936 | ||||||||
\(208\) | −126.248 | −8.75375 | ||||||||
\(209\) | −0.690697 | −0.0477765 | ||||||||
\(210\) | 12.0223 | 0.829617 | ||||||||
\(211\) | 1.00000 | 0.0688428 | ||||||||
\(212\) | −1.47500 | −0.101303 | ||||||||
\(213\) | −34.0811 | −2.33520 | ||||||||
\(214\) | 8.45545 | 0.578002 | ||||||||
\(215\) | 0.981621 | 0.0669460 | ||||||||
\(216\) | −85.8438 | −5.84093 | ||||||||
\(217\) | 2.99846 | 0.203549 | ||||||||
\(218\) | 3.82344 | 0.258956 | ||||||||
\(219\) | 43.1041 | 2.91271 | ||||||||
\(220\) | −1.73497 | −0.116971 | ||||||||
\(221\) | −39.1375 | −2.63268 | ||||||||
\(222\) | −57.0587 | −3.82953 | ||||||||
\(223\) | 15.6057 | 1.04503 | 0.522517 | − | 0.852629i | \(-0.324993\pi\) | ||||
0.522517 | + | 0.852629i | \(0.324993\pi\) | |||||||
\(224\) | 114.176 | 7.62868 | ||||||||
\(225\) | −27.0687 | −1.80458 | ||||||||
\(226\) | 24.0835 | 1.60201 | ||||||||
\(227\) | 15.8817 | 1.05410 | 0.527051 | − | 0.849833i | \(-0.323298\pi\) | ||||
0.527051 | + | 0.849833i | \(0.323298\pi\) | |||||||
\(228\) | 17.5103 | 1.15965 | ||||||||
\(229\) | 5.37560 | 0.355229 | 0.177615 | − | 0.984100i | \(-0.443162\pi\) | ||||
0.177615 | + | 0.984100i | \(0.443162\pi\) | |||||||
\(230\) | −8.19176 | −0.540149 | ||||||||
\(231\) | 6.98811 | 0.459784 | ||||||||
\(232\) | 71.3983 | 4.68753 | ||||||||
\(233\) | 13.3813 | 0.876640 | 0.438320 | − | 0.898819i | \(-0.355574\pi\) | ||||
0.438320 | + | 0.898819i | \(0.355574\pi\) | |||||||
\(234\) | 101.695 | 6.64799 | ||||||||
\(235\) | −5.11481 | −0.333654 | ||||||||
\(236\) | −32.9080 | −2.14213 | ||||||||
\(237\) | −22.3835 | −1.45396 | ||||||||
\(238\) | 59.3254 | 3.84550 | ||||||||
\(239\) | 7.25161 | 0.469068 | 0.234534 | − | 0.972108i | \(-0.424644\pi\) | ||||
0.234534 | + | 0.972108i | \(0.424644\pi\) | |||||||
\(240\) | 24.2987 | 1.56847 | ||||||||
\(241\) | −0.0642279 | −0.00413728 | −0.00206864 | − | 0.999998i | \(-0.500658\pi\) | ||||
−0.00206864 | + | 0.999998i | \(0.500658\pi\) | |||||||
\(242\) | 29.7011 | 1.90926 | ||||||||
\(243\) | −6.37966 | −0.409255 | ||||||||
\(244\) | −12.7415 | −0.815694 | ||||||||
\(245\) | 2.05665 | 0.131395 | ||||||||
\(246\) | 74.3826 | 4.74246 | ||||||||
\(247\) | −6.41936 | −0.408454 | ||||||||
\(248\) | 9.73747 | 0.618330 | ||||||||
\(249\) | 29.8540 | 1.89192 | ||||||||
\(250\) | 11.6721 | 0.738207 | ||||||||
\(251\) | −11.5298 | −0.727751 | −0.363876 | − | 0.931447i | \(-0.618547\pi\) | ||||
−0.363876 | + | 0.931447i | \(0.618547\pi\) | |||||||
\(252\) | −115.451 | −7.27275 | ||||||||
\(253\) | −4.76157 | −0.299357 | ||||||||
\(254\) | −55.3940 | −3.47573 | ||||||||
\(255\) | 7.53269 | 0.471716 | ||||||||
\(256\) | 136.097 | 8.50608 | ||||||||
\(257\) | 12.2960 | 0.767002 | 0.383501 | − | 0.923540i | \(-0.374718\pi\) | ||||
0.383501 | + | 0.923540i | \(0.374718\pi\) | |||||||
\(258\) | −19.3139 | −1.20243 | ||||||||
\(259\) | −23.7476 | −1.47560 | ||||||||
\(260\) | −16.1248 | −1.00002 | ||||||||
\(261\) | −35.7938 | −2.21558 | ||||||||
\(262\) | 7.46803 | 0.461376 | ||||||||
\(263\) | −30.0825 | −1.85497 | −0.927483 | − | 0.373864i | \(-0.878033\pi\) | ||||
−0.927483 | + | 0.373864i | \(0.878033\pi\) | |||||||
\(264\) | 22.6938 | 1.39671 | ||||||||
\(265\) | −0.104075 | −0.00639325 | ||||||||
\(266\) | 9.73058 | 0.596620 | ||||||||
\(267\) | −36.3008 | −2.22157 | ||||||||
\(268\) | 3.48484 | 0.212871 | ||||||||
\(269\) | −25.8489 | −1.57603 | −0.788017 | − | 0.615654i | \(-0.788892\pi\) | ||||
−0.788017 | + | 0.615654i | \(0.788892\pi\) | |||||||
\(270\) | −9.11113 | −0.554486 | ||||||||
\(271\) | −15.7209 | −0.954976 | −0.477488 | − | 0.878638i | \(-0.658453\pi\) | ||||
−0.477488 | + | 0.878638i | \(0.658453\pi\) | |||||||
\(272\) | 119.905 | 7.27030 | ||||||||
\(273\) | 64.9477 | 3.93082 | ||||||||
\(274\) | 12.3780 | 0.747783 | ||||||||
\(275\) | 3.33107 | 0.200871 | ||||||||
\(276\) | 120.714 | 7.26612 | ||||||||
\(277\) | −12.2223 | −0.734367 | −0.367184 | − | 0.930148i | \(-0.619678\pi\) | ||||
−0.367184 | + | 0.930148i | \(0.619678\pi\) | |||||||
\(278\) | 36.2648 | 2.17502 | ||||||||
\(279\) | −4.88165 | −0.292256 | ||||||||
\(280\) | 16.2492 | 0.971078 | ||||||||
\(281\) | −17.3205 | −1.03326 | −0.516628 | − | 0.856210i | \(-0.672813\pi\) | ||||
−0.516628 | + | 0.856210i | \(0.672813\pi\) | |||||||
\(282\) | 100.637 | 5.99282 | ||||||||
\(283\) | −19.3883 | −1.15251 | −0.576256 | − | 0.817269i | \(-0.695487\pi\) | ||||
−0.576256 | + | 0.817269i | \(0.695487\pi\) | |||||||
\(284\) | −69.2897 | −4.11159 | ||||||||
\(285\) | 1.23552 | 0.0731856 | ||||||||
\(286\) | −12.5145 | −0.740000 | ||||||||
\(287\) | 30.9578 | 1.82738 | ||||||||
\(288\) | −185.884 | −10.9533 | ||||||||
\(289\) | 20.1710 | 1.18653 | ||||||||
\(290\) | 7.57794 | 0.444992 | ||||||||
\(291\) | −0.128663 | −0.00754235 | ||||||||
\(292\) | 87.6343 | 5.12841 | ||||||||
\(293\) | 21.4669 | 1.25411 | 0.627056 | − | 0.778974i | \(-0.284260\pi\) | ||||
0.627056 | + | 0.778974i | \(0.284260\pi\) | |||||||
\(294\) | −40.4657 | −2.36001 | ||||||||
\(295\) | −2.32196 | −0.135190 | ||||||||
\(296\) | −77.1201 | −4.48251 | ||||||||
\(297\) | −5.29596 | −0.307303 | ||||||||
\(298\) | 9.30892 | 0.539251 | ||||||||
\(299\) | −44.2542 | −2.55928 | ||||||||
\(300\) | −84.4482 | −4.87562 | ||||||||
\(301\) | −8.03837 | −0.463324 | ||||||||
\(302\) | 8.05077 | 0.463270 | ||||||||
\(303\) | 9.24462 | 0.531090 | ||||||||
\(304\) | 19.6668 | 1.12797 | ||||||||
\(305\) | −0.899033 | −0.0514785 | ||||||||
\(306\) | −96.5848 | −5.52139 | ||||||||
\(307\) | 7.15175 | 0.408172 | 0.204086 | − | 0.978953i | \(-0.434578\pi\) | ||||
0.204086 | + | 0.978953i | \(0.434578\pi\) | |||||||
\(308\) | 14.2074 | 0.809543 | ||||||||
\(309\) | −4.53456 | −0.257962 | ||||||||
\(310\) | 1.03350 | 0.0586987 | ||||||||
\(311\) | −5.72304 | −0.324524 | −0.162262 | − | 0.986748i | \(-0.551879\pi\) | ||||
−0.162262 | + | 0.986748i | \(0.551879\pi\) | |||||||
\(312\) | 210.917 | 11.9408 | ||||||||
\(313\) | −8.01417 | −0.452988 | −0.226494 | − | 0.974013i | \(-0.572726\pi\) | ||||
−0.226494 | + | 0.974013i | \(0.572726\pi\) | |||||||
\(314\) | 61.5818 | 3.47526 | ||||||||
\(315\) | −8.14616 | −0.458984 | ||||||||
\(316\) | −45.5076 | −2.56000 | ||||||||
\(317\) | 19.8789 | 1.11651 | 0.558254 | − | 0.829670i | \(-0.311471\pi\) | ||||
0.558254 | + | 0.829670i | \(0.311471\pi\) | |||||||
\(318\) | 2.04772 | 0.114831 | ||||||||
\(319\) | 4.40478 | 0.246620 | ||||||||
\(320\) | 22.7943 | 1.27424 | ||||||||
\(321\) | −8.79165 | −0.490702 | ||||||||
\(322\) | 67.0813 | 3.73830 | ||||||||
\(323\) | 6.09680 | 0.339235 | ||||||||
\(324\) | 33.7961 | 1.87756 | ||||||||
\(325\) | 30.9590 | 1.71730 | ||||||||
\(326\) | −16.1165 | −0.892608 | ||||||||
\(327\) | −3.97547 | −0.219844 | ||||||||
\(328\) | 100.535 | 5.55112 | ||||||||
\(329\) | 41.8846 | 2.30917 | ||||||||
\(330\) | 2.40864 | 0.132591 | ||||||||
\(331\) | 28.1032 | 1.54469 | 0.772347 | − | 0.635201i | \(-0.219083\pi\) | ||||
0.772347 | + | 0.635201i | \(0.219083\pi\) | |||||||
\(332\) | 60.6956 | 3.33111 | ||||||||
\(333\) | 38.6623 | 2.11868 | ||||||||
\(334\) | 35.4992 | 1.94243 | ||||||||
\(335\) | 0.245888 | 0.0134343 | ||||||||
\(336\) | −198.979 | −10.8552 | ||||||||
\(337\) | 0.651770 | 0.0355042 | 0.0177521 | − | 0.999842i | \(-0.494349\pi\) | ||||
0.0177521 | + | 0.999842i | \(0.494349\pi\) | |||||||
\(338\) | −79.6178 | −4.33064 | ||||||||
\(339\) | −25.0411 | −1.36004 | ||||||||
\(340\) | 15.3146 | 0.830551 | ||||||||
\(341\) | 0.600734 | 0.0325316 | ||||||||
\(342\) | −15.8419 | −0.856631 | ||||||||
\(343\) | 7.29078 | 0.393665 | ||||||||
\(344\) | −26.1045 | −1.40746 | ||||||||
\(345\) | 8.51748 | 0.458566 | ||||||||
\(346\) | 13.8325 | 0.743639 | ||||||||
\(347\) | 3.04605 | 0.163521 | 0.0817604 | − | 0.996652i | \(-0.473946\pi\) | ||||
0.0817604 | + | 0.996652i | \(0.473946\pi\) | |||||||
\(348\) | −111.669 | −5.98607 | ||||||||
\(349\) | 5.48867 | 0.293802 | 0.146901 | − | 0.989151i | \(-0.453070\pi\) | ||||
0.146901 | + | 0.989151i | \(0.453070\pi\) | |||||||
\(350\) | −46.9283 | −2.50842 | ||||||||
\(351\) | −49.2208 | −2.62721 | ||||||||
\(352\) | 22.8748 | 1.21923 | ||||||||
\(353\) | −16.3157 | −0.868398 | −0.434199 | − | 0.900817i | \(-0.642969\pi\) | ||||
−0.434199 | + | 0.900817i | \(0.642969\pi\) | |||||||
\(354\) | 45.6858 | 2.42817 | ||||||||
\(355\) | −4.88903 | −0.259483 | ||||||||
\(356\) | −73.8026 | −3.91153 | ||||||||
\(357\) | −61.6843 | −3.26468 | ||||||||
\(358\) | 27.1671 | 1.43582 | ||||||||
\(359\) | −22.9094 | −1.20911 | −0.604556 | − | 0.796562i | \(-0.706650\pi\) | ||||
−0.604556 | + | 0.796562i | \(0.706650\pi\) | |||||||
\(360\) | −26.4546 | −1.39428 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 25.8797 | 1.36021 | ||||||||
\(363\) | −30.8821 | −1.62089 | ||||||||
\(364\) | 132.044 | 6.92100 | ||||||||
\(365\) | 6.18341 | 0.323654 | ||||||||
\(366\) | 17.6890 | 0.924617 | ||||||||
\(367\) | −10.1724 | −0.530992 | −0.265496 | − | 0.964112i | \(-0.585536\pi\) | ||||
−0.265496 | + | 0.964112i | \(0.585536\pi\) | |||||||
\(368\) | 135.581 | 7.06762 | ||||||||
\(369\) | −50.4008 | −2.62376 | ||||||||
\(370\) | −8.18523 | −0.425530 | ||||||||
\(371\) | 0.852254 | 0.0442468 | ||||||||
\(372\) | −15.2296 | −0.789620 | ||||||||
\(373\) | −24.2751 | −1.25692 | −0.628458 | − | 0.777843i | \(-0.716314\pi\) | ||||
−0.628458 | + | 0.777843i | \(0.716314\pi\) | |||||||
\(374\) | 11.8857 | 0.614596 | ||||||||
\(375\) | −12.1362 | −0.626709 | ||||||||
\(376\) | 136.020 | 7.01468 | ||||||||
\(377\) | 40.9381 | 2.10842 | ||||||||
\(378\) | 74.6099 | 3.83752 | ||||||||
\(379\) | −21.7880 | −1.11918 | −0.559588 | − | 0.828771i | \(-0.689041\pi\) | ||||
−0.559588 | + | 0.828771i | \(0.689041\pi\) | |||||||
\(380\) | 2.51191 | 0.128858 | ||||||||
\(381\) | 57.5966 | 2.95076 | ||||||||
\(382\) | −3.55555 | −0.181918 | ||||||||
\(383\) | 12.9552 | 0.661982 | 0.330991 | − | 0.943634i | \(-0.392617\pi\) | ||||
0.330991 | + | 0.943634i | \(0.392617\pi\) | |||||||
\(384\) | −254.102 | −12.9671 | ||||||||
\(385\) | 1.00247 | 0.0510904 | ||||||||
\(386\) | −32.4712 | −1.65274 | ||||||||
\(387\) | 13.0869 | 0.665244 | ||||||||
\(388\) | −0.261582 | −0.0132798 | ||||||||
\(389\) | −23.2414 | −1.17838 | −0.589192 | − | 0.807993i | \(-0.700554\pi\) | ||||
−0.589192 | + | 0.807993i | \(0.700554\pi\) | |||||||
\(390\) | 22.3859 | 1.13356 | ||||||||
\(391\) | 42.0305 | 2.12558 | ||||||||
\(392\) | −54.6931 | −2.76242 | ||||||||
\(393\) | −7.76497 | −0.391691 | ||||||||
\(394\) | 34.1799 | 1.72196 | ||||||||
\(395\) | −3.21098 | −0.161562 | ||||||||
\(396\) | −23.1304 | −1.16235 | ||||||||
\(397\) | 18.7989 | 0.943489 | 0.471745 | − | 0.881735i | \(-0.343624\pi\) | ||||
0.471745 | + | 0.881735i | \(0.343624\pi\) | |||||||
\(398\) | −16.6659 | −0.835388 | ||||||||
\(399\) | −10.1175 | −0.506508 | ||||||||
\(400\) | −94.8485 | −4.74242 | ||||||||
\(401\) | −30.5259 | −1.52439 | −0.762196 | − | 0.647346i | \(-0.775879\pi\) | ||||
−0.762196 | + | 0.647346i | \(0.775879\pi\) | |||||||
\(402\) | −4.83797 | −0.241296 | ||||||||
\(403\) | 5.58324 | 0.278121 | ||||||||
\(404\) | 18.7951 | 0.935091 | ||||||||
\(405\) | 2.38462 | 0.118493 | ||||||||
\(406\) | −62.0548 | −3.07973 | ||||||||
\(407\) | −4.75777 | −0.235834 | ||||||||
\(408\) | −200.319 | −9.91728 | ||||||||
\(409\) | 21.6876 | 1.07238 | 0.536190 | − | 0.844097i | \(-0.319863\pi\) | ||||
0.536190 | + | 0.844097i | \(0.319863\pi\) | |||||||
\(410\) | 10.6704 | 0.526974 | ||||||||
\(411\) | −12.8702 | −0.634839 | ||||||||
\(412\) | −9.21915 | −0.454195 | ||||||||
\(413\) | 19.0143 | 0.935631 | ||||||||
\(414\) | −109.212 | −5.36747 | ||||||||
\(415\) | 4.28264 | 0.210226 | ||||||||
\(416\) | 212.599 | 10.4235 | ||||||||
\(417\) | −37.7067 | −1.84651 | ||||||||
\(418\) | 1.94950 | 0.0953531 | ||||||||
\(419\) | 10.6826 | 0.521882 | 0.260941 | − | 0.965355i | \(-0.415967\pi\) | ||||
0.260941 | + | 0.965355i | \(0.415967\pi\) | |||||||
\(420\) | −25.4142 | −1.24009 | ||||||||
\(421\) | −17.0064 | −0.828839 | −0.414419 | − | 0.910086i | \(-0.636015\pi\) | ||||
−0.414419 | + | 0.910086i | \(0.636015\pi\) | |||||||
\(422\) | −2.82251 | −0.137398 | ||||||||
\(423\) | −68.1902 | −3.31552 | ||||||||
\(424\) | 2.76769 | 0.134411 | ||||||||
\(425\) | −29.4034 | −1.42628 | ||||||||
\(426\) | 96.1942 | 4.66062 | ||||||||
\(427\) | 7.36207 | 0.356276 | ||||||||
\(428\) | −17.8742 | −0.863980 | ||||||||
\(429\) | 13.0121 | 0.628231 | ||||||||
\(430\) | −2.77064 | −0.133612 | ||||||||
\(431\) | 6.43080 | 0.309761 | 0.154880 | − | 0.987933i | \(-0.450501\pi\) | ||||
0.154880 | + | 0.987933i | \(0.450501\pi\) | |||||||
\(432\) | 150.797 | 7.25522 | ||||||||
\(433\) | −7.96214 | −0.382636 | −0.191318 | − | 0.981528i | \(-0.561276\pi\) | ||||
−0.191318 | + | 0.981528i | \(0.561276\pi\) | |||||||
\(434\) | −8.46319 | −0.406246 | ||||||||
\(435\) | −7.87925 | −0.377781 | ||||||||
\(436\) | −8.08246 | −0.387080 | ||||||||
\(437\) | 6.89386 | 0.329778 | ||||||||
\(438\) | −121.662 | −5.81323 | ||||||||
\(439\) | 1.52263 | 0.0726714 | 0.0363357 | − | 0.999340i | \(-0.488431\pi\) | ||||
0.0363357 | + | 0.999340i | \(0.488431\pi\) | |||||||
\(440\) | 3.25550 | 0.155200 | ||||||||
\(441\) | 27.4191 | 1.30567 | ||||||||
\(442\) | 110.466 | 5.25434 | ||||||||
\(443\) | 9.83358 | 0.467207 | 0.233604 | − | 0.972332i | \(-0.424948\pi\) | ||||
0.233604 | + | 0.972332i | \(0.424948\pi\) | |||||||
\(444\) | 120.618 | 5.72426 | ||||||||
\(445\) | −5.20745 | −0.246857 | ||||||||
\(446\) | −44.0472 | −2.08570 | ||||||||
\(447\) | −9.67905 | −0.457803 | ||||||||
\(448\) | −186.660 | −8.81884 | ||||||||
\(449\) | 34.4302 | 1.62486 | 0.812430 | − | 0.583058i | \(-0.198144\pi\) | ||||
0.812430 | + | 0.583058i | \(0.198144\pi\) | |||||||
\(450\) | 76.4017 | 3.60161 | ||||||||
\(451\) | 6.20231 | 0.292056 | ||||||||
\(452\) | −50.9106 | −2.39463 | ||||||||
\(453\) | −8.37089 | −0.393298 | ||||||||
\(454\) | −44.8262 | −2.10380 | ||||||||
\(455\) | 9.31694 | 0.436785 | ||||||||
\(456\) | −32.8564 | −1.53864 | ||||||||
\(457\) | −17.7814 | −0.831780 | −0.415890 | − | 0.909415i | \(-0.636530\pi\) | ||||
−0.415890 | + | 0.909415i | \(0.636530\pi\) | |||||||
\(458\) | −15.1727 | −0.708973 | ||||||||
\(459\) | 46.7476 | 2.18199 | ||||||||
\(460\) | 17.3168 | 0.807398 | ||||||||
\(461\) | 7.65333 | 0.356451 | 0.178226 | − | 0.983990i | \(-0.442964\pi\) | ||||
0.178226 | + | 0.983990i | \(0.442964\pi\) | |||||||
\(462\) | −19.7240 | −0.917645 | ||||||||
\(463\) | −14.4561 | −0.671833 | −0.335916 | − | 0.941892i | \(-0.609046\pi\) | ||||
−0.335916 | + | 0.941892i | \(0.609046\pi\) | |||||||
\(464\) | −125.421 | −5.82254 | ||||||||
\(465\) | −1.07459 | −0.0498330 | ||||||||
\(466\) | −37.7689 | −1.74961 | ||||||||
\(467\) | 15.9899 | 0.739926 | 0.369963 | − | 0.929047i | \(-0.379370\pi\) | ||||
0.369963 | + | 0.929047i | \(0.379370\pi\) | |||||||
\(468\) | −214.975 | −9.93721 | ||||||||
\(469\) | −2.01355 | −0.0929769 | ||||||||
\(470\) | 14.4366 | 0.665911 | ||||||||
\(471\) | −64.0304 | −2.95036 | ||||||||
\(472\) | 61.7486 | 2.84221 | ||||||||
\(473\) | −1.61047 | −0.0740495 | ||||||||
\(474\) | 63.1777 | 2.90185 | ||||||||
\(475\) | −4.82276 | −0.221283 | ||||||||
\(476\) | −125.409 | −5.74813 | ||||||||
\(477\) | −1.38751 | −0.0635299 | ||||||||
\(478\) | −20.4678 | −0.936174 | ||||||||
\(479\) | 4.20152 | 0.191973 | 0.0959863 | − | 0.995383i | \(-0.469400\pi\) | ||||
0.0959863 | + | 0.995383i | \(0.469400\pi\) | |||||||
\(480\) | −40.9184 | −1.86766 | ||||||||
\(481\) | −44.2189 | −2.01621 | ||||||||
\(482\) | 0.181284 | 0.00825725 | ||||||||
\(483\) | −69.7486 | −3.17367 | ||||||||
\(484\) | −62.7859 | −2.85390 | ||||||||
\(485\) | −0.0184571 | −0.000838092 0 | ||||||||
\(486\) | 18.0067 | 0.816799 | ||||||||
\(487\) | 14.9208 | 0.676125 | 0.338063 | − | 0.941124i | \(-0.390228\pi\) | ||||
0.338063 | + | 0.941124i | \(0.390228\pi\) | |||||||
\(488\) | 23.9083 | 1.08228 | ||||||||
\(489\) | 16.7573 | 0.757790 | ||||||||
\(490\) | −5.80492 | −0.262240 | ||||||||
\(491\) | −34.1756 | −1.54232 | −0.771162 | − | 0.636639i | \(-0.780324\pi\) | ||||
−0.771162 | + | 0.636639i | \(0.780324\pi\) | |||||||
\(492\) | −157.239 | −7.08889 | ||||||||
\(493\) | −38.8811 | −1.75112 | ||||||||
\(494\) | 18.1187 | 0.815199 | ||||||||
\(495\) | −1.63206 | −0.0733558 | ||||||||
\(496\) | −17.1053 | −0.768049 | ||||||||
\(497\) | 40.0356 | 1.79584 | ||||||||
\(498\) | −84.2632 | −3.77592 | ||||||||
\(499\) | −35.3665 | −1.58322 | −0.791612 | − | 0.611024i | \(-0.790758\pi\) | ||||
−0.791612 | + | 0.611024i | \(0.790758\pi\) | |||||||
\(500\) | −24.6739 | −1.10345 | ||||||||
\(501\) | −36.9107 | −1.64905 | ||||||||
\(502\) | 32.5429 | 1.45246 | ||||||||
\(503\) | −36.3428 | −1.62044 | −0.810222 | − | 0.586123i | \(-0.800654\pi\) | ||||
−0.810222 | + | 0.586123i | \(0.800654\pi\) | |||||||
\(504\) | 216.633 | 9.64962 | ||||||||
\(505\) | 1.32617 | 0.0590137 | ||||||||
\(506\) | 13.4396 | 0.597462 | ||||||||
\(507\) | 82.7835 | 3.67654 | ||||||||
\(508\) | 117.099 | 5.19541 | ||||||||
\(509\) | 14.9231 | 0.661454 | 0.330727 | − | 0.943726i | \(-0.392706\pi\) | ||||
0.330727 | + | 0.943726i | \(0.392706\pi\) | |||||||
\(510\) | −21.2611 | −0.941458 | ||||||||
\(511\) | −50.6352 | −2.23997 | ||||||||
\(512\) | −210.968 | −9.32356 | ||||||||
\(513\) | 7.66757 | 0.338531 | ||||||||
\(514\) | −34.7055 | −1.53080 | ||||||||
\(515\) | −0.650496 | −0.0286643 | ||||||||
\(516\) | 40.8281 | 1.79736 | ||||||||
\(517\) | 8.39147 | 0.369057 | ||||||||
\(518\) | 67.0278 | 2.94503 | ||||||||
\(519\) | −14.3825 | −0.631321 | ||||||||
\(520\) | 30.2567 | 1.32684 | ||||||||
\(521\) | 1.35926 | 0.0595504 | 0.0297752 | − | 0.999557i | \(-0.490521\pi\) | ||||
0.0297752 | + | 0.999557i | \(0.490521\pi\) | |||||||
\(522\) | 101.028 | 4.42190 | ||||||||
\(523\) | −21.6227 | −0.945493 | −0.472746 | − | 0.881198i | \(-0.656737\pi\) | ||||
−0.472746 | + | 0.881198i | \(0.656737\pi\) | |||||||
\(524\) | −15.7868 | −0.689651 | ||||||||
\(525\) | 48.7942 | 2.12955 | ||||||||
\(526\) | 84.9082 | 3.70217 | ||||||||
\(527\) | −5.30270 | −0.230989 | ||||||||
\(528\) | −39.8650 | −1.73490 | ||||||||
\(529\) | 24.5254 | 1.06632 | ||||||||
\(530\) | 0.293752 | 0.0127598 | ||||||||
\(531\) | −30.9562 | −1.34338 | ||||||||
\(532\) | −20.5697 | −0.891810 | ||||||||
\(533\) | 57.6445 | 2.49686 | ||||||||
\(534\) | 102.459 | 4.43385 | ||||||||
\(535\) | −1.26119 | −0.0545259 | ||||||||
\(536\) | −6.53897 | −0.282441 | ||||||||
\(537\) | −28.2473 | −1.21896 | ||||||||
\(538\) | 72.9587 | 3.14547 | ||||||||
\(539\) | −3.37419 | −0.145337 | ||||||||
\(540\) | 19.2602 | 0.828828 | ||||||||
\(541\) | −2.82574 | −0.121488 | −0.0607440 | − | 0.998153i | \(-0.519347\pi\) | ||||
−0.0607440 | + | 0.998153i | \(0.519347\pi\) | |||||||
\(542\) | 44.3724 | 1.90596 | ||||||||
\(543\) | −26.9087 | −1.15476 | ||||||||
\(544\) | −201.917 | −8.65711 | ||||||||
\(545\) | −0.570292 | −0.0244286 | ||||||||
\(546\) | −183.316 | −7.84519 | ||||||||
\(547\) | 5.27972 | 0.225745 | 0.112872 | − | 0.993609i | \(-0.463995\pi\) | ||||
0.112872 | + | 0.993609i | \(0.463995\pi\) | |||||||
\(548\) | −26.1662 | −1.11776 | ||||||||
\(549\) | −11.9858 | −0.511543 | ||||||||
\(550\) | −9.40197 | −0.400901 | ||||||||
\(551\) | −6.37730 | −0.271682 | ||||||||
\(552\) | −226.508 | −9.64082 | ||||||||
\(553\) | 26.2943 | 1.11815 | ||||||||
\(554\) | 34.4976 | 1.46566 | ||||||||
\(555\) | 8.51069 | 0.361259 | ||||||||
\(556\) | −76.6609 | −3.25115 | ||||||||
\(557\) | 19.0028 | 0.805175 | 0.402587 | − | 0.915382i | \(-0.368111\pi\) | ||||
0.402587 | + | 0.915382i | \(0.368111\pi\) | |||||||
\(558\) | 13.7785 | 0.583290 | ||||||||
\(559\) | −14.9677 | −0.633068 | ||||||||
\(560\) | −28.5441 | −1.20621 | ||||||||
\(561\) | −12.3583 | −0.521768 | ||||||||
\(562\) | 48.8874 | 2.06219 | ||||||||
\(563\) | 35.7761 | 1.50778 | 0.753891 | − | 0.657000i | \(-0.228175\pi\) | ||||
0.753891 | + | 0.657000i | \(0.228175\pi\) | |||||||
\(564\) | −212.738 | −8.95789 | ||||||||
\(565\) | −3.59221 | −0.151125 | ||||||||
\(566\) | 54.7236 | 2.30020 | ||||||||
\(567\) | −19.5274 | −0.820073 | ||||||||
\(568\) | 130.015 | 5.45532 | ||||||||
\(569\) | 39.3100 | 1.64796 | 0.823980 | − | 0.566618i | \(-0.191749\pi\) | ||||
0.823980 | + | 0.566618i | \(0.191749\pi\) | |||||||
\(570\) | −3.48726 | −0.146065 | ||||||||
\(571\) | 32.3918 | 1.35556 | 0.677778 | − | 0.735267i | \(-0.262943\pi\) | ||||
0.677778 | + | 0.735267i | \(0.262943\pi\) | |||||||
\(572\) | 26.4548 | 1.10613 | ||||||||
\(573\) | 3.69692 | 0.154441 | ||||||||
\(574\) | −87.3786 | −3.64711 | ||||||||
\(575\) | −33.2475 | −1.38652 | ||||||||
\(576\) | 303.892 | 12.6622 | ||||||||
\(577\) | −2.95608 | −0.123063 | −0.0615317 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615317 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(578\) | −56.9329 | −2.36809 | ||||||||
\(579\) | 33.7623 | 1.40311 | ||||||||
\(580\) | −16.0192 | −0.665160 | ||||||||
\(581\) | −35.0700 | −1.45495 | ||||||||
\(582\) | 0.363152 | 0.0150532 | ||||||||
\(583\) | 0.170747 | 0.00707162 | ||||||||
\(584\) | −164.437 | −6.80446 | ||||||||
\(585\) | −15.1685 | −0.627138 | ||||||||
\(586\) | −60.5907 | −2.50298 | ||||||||
\(587\) | 13.6580 | 0.563725 | 0.281863 | − | 0.959455i | \(-0.409048\pi\) | ||||
0.281863 | + | 0.959455i | \(0.409048\pi\) | |||||||
\(588\) | 85.5413 | 3.52767 | ||||||||
\(589\) | −0.869751 | −0.0358375 | ||||||||
\(590\) | 6.55376 | 0.269814 | ||||||||
\(591\) | −35.5389 | −1.46188 | ||||||||
\(592\) | 135.472 | 5.56788 | ||||||||
\(593\) | 11.2049 | 0.460130 | 0.230065 | − | 0.973175i | \(-0.426106\pi\) | ||||
0.230065 | + | 0.973175i | \(0.426106\pi\) | |||||||
\(594\) | 14.9479 | 0.613321 | ||||||||
\(595\) | −8.84879 | −0.362765 | ||||||||
\(596\) | −19.6783 | −0.806056 | ||||||||
\(597\) | 17.3286 | 0.709212 | ||||||||
\(598\) | 124.908 | 5.10786 | ||||||||
\(599\) | 9.16037 | 0.374282 | 0.187141 | − | 0.982333i | \(-0.440078\pi\) | ||||
0.187141 | + | 0.982333i | \(0.440078\pi\) | |||||||
\(600\) | 158.459 | 6.46905 | ||||||||
\(601\) | 38.7626 | 1.58116 | 0.790579 | − | 0.612360i | \(-0.209780\pi\) | ||||
0.790579 | + | 0.612360i | \(0.209780\pi\) | |||||||
\(602\) | 22.6884 | 0.924710 | ||||||||
\(603\) | 3.27816 | 0.133497 | ||||||||
\(604\) | −17.0187 | −0.692482 | ||||||||
\(605\) | −4.43012 | −0.180110 | ||||||||
\(606\) | −26.0931 | −1.05996 | ||||||||
\(607\) | −25.6614 | −1.04156 | −0.520782 | − | 0.853690i | \(-0.674360\pi\) | ||||
−0.520782 | + | 0.853690i | \(0.674360\pi\) | |||||||
\(608\) | −33.1185 | −1.34313 | ||||||||
\(609\) | 64.5222 | 2.61457 | ||||||||
\(610\) | 2.53753 | 0.102742 | ||||||||
\(611\) | 77.9906 | 3.15516 | ||||||||
\(612\) | 204.173 | 8.25320 | ||||||||
\(613\) | 23.4250 | 0.946127 | 0.473063 | − | 0.881028i | \(-0.343148\pi\) | ||||
0.473063 | + | 0.881028i | \(0.343148\pi\) | |||||||
\(614\) | −20.1859 | −0.814637 | ||||||||
\(615\) | −11.0947 | −0.447381 | ||||||||
\(616\) | −26.6589 | −1.07412 | ||||||||
\(617\) | −10.0293 | −0.403765 | −0.201883 | − | 0.979410i | \(-0.564706\pi\) | ||||
−0.201883 | + | 0.979410i | \(0.564706\pi\) | |||||||
\(618\) | 12.7989 | 0.514846 | ||||||||
\(619\) | 11.4897 | 0.461811 | 0.230906 | − | 0.972976i | \(-0.425831\pi\) | ||||
0.230906 | + | 0.972976i | \(0.425831\pi\) | |||||||
\(620\) | −2.18473 | −0.0877411 | ||||||||
\(621\) | 52.8592 | 2.12117 | ||||||||
\(622\) | 16.1533 | 0.647690 | ||||||||
\(623\) | 42.6432 | 1.70846 | ||||||||
\(624\) | −370.506 | −14.8321 | ||||||||
\(625\) | 22.3728 | 0.894914 | ||||||||
\(626\) | 22.6201 | 0.904081 | ||||||||
\(627\) | −2.02701 | −0.0809512 | ||||||||
\(628\) | −130.179 | −5.19472 | ||||||||
\(629\) | 41.9970 | 1.67453 | ||||||||
\(630\) | 22.9926 | 0.916049 | ||||||||
\(631\) | 21.1201 | 0.840779 | 0.420390 | − | 0.907344i | \(-0.361893\pi\) | ||||
0.420390 | + | 0.907344i | \(0.361893\pi\) | |||||||
\(632\) | 85.3905 | 3.39665 | ||||||||
\(633\) | 2.93474 | 0.116645 | ||||||||
\(634\) | −56.1083 | −2.22835 | ||||||||
\(635\) | 8.26239 | 0.327883 | ||||||||
\(636\) | −4.32873 | −0.171645 | ||||||||
\(637\) | −31.3598 | −1.24252 | ||||||||
\(638\) | −12.4325 | −0.492209 | ||||||||
\(639\) | −65.1801 | −2.57848 | ||||||||
\(640\) | −36.4516 | −1.44088 | ||||||||
\(641\) | −13.8403 | −0.546658 | −0.273329 | − | 0.961921i | \(-0.588125\pi\) | ||||
−0.273329 | + | 0.961921i | \(0.588125\pi\) | |||||||
\(642\) | 24.8145 | 0.979351 | ||||||||
\(643\) | −18.1373 | −0.715265 | −0.357633 | − | 0.933862i | \(-0.616416\pi\) | ||||
−0.357633 | + | 0.933862i | \(0.616416\pi\) | |||||||
\(644\) | −141.805 | −5.58789 | ||||||||
\(645\) | 2.88080 | 0.113431 | ||||||||
\(646\) | −17.2083 | −0.677051 | ||||||||
\(647\) | −18.3540 | −0.721569 | −0.360785 | − | 0.932649i | \(-0.617491\pi\) | ||||
−0.360785 | + | 0.932649i | \(0.617491\pi\) | |||||||
\(648\) | −63.4150 | −2.49118 | ||||||||
\(649\) | 3.80946 | 0.149534 | ||||||||
\(650\) | −87.3822 | −3.42741 | ||||||||
\(651\) | 8.79970 | 0.344887 | ||||||||
\(652\) | 34.0690 | 1.33424 | ||||||||
\(653\) | 3.48619 | 0.136425 | 0.0682126 | − | 0.997671i | \(-0.478270\pi\) | ||||
0.0682126 | + | 0.997671i | \(0.478270\pi\) | |||||||
\(654\) | 11.2208 | 0.438768 | ||||||||
\(655\) | −1.11391 | −0.0435239 | ||||||||
\(656\) | −176.604 | −6.89523 | ||||||||
\(657\) | 82.4366 | 3.21616 | ||||||||
\(658\) | −118.220 | −4.60868 | ||||||||
\(659\) | 27.5969 | 1.07502 | 0.537512 | − | 0.843256i | \(-0.319364\pi\) | ||||
0.537512 | + | 0.843256i | \(0.319364\pi\) | |||||||
\(660\) | −5.09167 | −0.198193 | ||||||||
\(661\) | 10.4583 | 0.406782 | 0.203391 | − | 0.979098i | \(-0.434804\pi\) | ||||
0.203391 | + | 0.979098i | \(0.434804\pi\) | |||||||
\(662\) | −79.3217 | −3.08293 | ||||||||
\(663\) | −114.858 | −4.46073 | ||||||||
\(664\) | −113.889 | −4.41977 | ||||||||
\(665\) | −1.45138 | −0.0562822 | ||||||||
\(666\) | −109.125 | −4.22850 | ||||||||
\(667\) | −43.9642 | −1.70230 | ||||||||
\(668\) | −75.0425 | −2.90348 | ||||||||
\(669\) | 45.7986 | 1.77068 | ||||||||
\(670\) | −0.694021 | −0.0268124 | ||||||||
\(671\) | 1.47497 | 0.0569408 | ||||||||
\(672\) | 335.076 | 12.9258 | ||||||||
\(673\) | 15.2269 | 0.586953 | 0.293476 | − | 0.955966i | \(-0.405188\pi\) | ||||
0.293476 | + | 0.955966i | \(0.405188\pi\) | |||||||
\(674\) | −1.83963 | −0.0708599 | ||||||||
\(675\) | −36.9789 | −1.42332 | ||||||||
\(676\) | 168.306 | 6.47330 | ||||||||
\(677\) | −15.5958 | −0.599395 | −0.299697 | − | 0.954034i | \(-0.596886\pi\) | ||||
−0.299697 | + | 0.954034i | \(0.596886\pi\) | |||||||
\(678\) | 70.6787 | 2.71440 | ||||||||
\(679\) | 0.151143 | 0.00580032 | ||||||||
\(680\) | −28.7364 | −1.10199 | ||||||||
\(681\) | 46.6085 | 1.78604 | ||||||||
\(682\) | −1.69558 | −0.0649271 | ||||||||
\(683\) | 39.7788 | 1.52209 | 0.761047 | − | 0.648697i | \(-0.224686\pi\) | ||||
0.761047 | + | 0.648697i | \(0.224686\pi\) | |||||||
\(684\) | 33.4885 | 1.28047 | ||||||||
\(685\) | −1.84626 | −0.0705421 | ||||||||
\(686\) | −20.5783 | −0.785683 | ||||||||
\(687\) | 15.7760 | 0.601891 | ||||||||
\(688\) | 45.8564 | 1.74826 | ||||||||
\(689\) | 1.58693 | 0.0604572 | ||||||||
\(690\) | −24.0407 | −0.915213 | ||||||||
\(691\) | 6.35208 | 0.241644 | 0.120822 | − | 0.992674i | \(-0.461447\pi\) | ||||
0.120822 | + | 0.992674i | \(0.461447\pi\) | |||||||
\(692\) | −29.2408 | −1.11157 | ||||||||
\(693\) | 13.3648 | 0.507686 | ||||||||
\(694\) | −8.59752 | −0.326357 | ||||||||
\(695\) | −5.40914 | −0.205180 | ||||||||
\(696\) | 209.535 | 7.94242 | ||||||||
\(697\) | −54.7480 | −2.07373 | ||||||||
\(698\) | −15.4918 | −0.586375 | ||||||||
\(699\) | 39.2707 | 1.48535 | ||||||||
\(700\) | 99.2028 | 3.74951 | ||||||||
\(701\) | −30.1226 | −1.13772 | −0.568858 | − | 0.822436i | \(-0.692615\pi\) | ||||
−0.568858 | + | 0.822436i | \(0.692615\pi\) | |||||||
\(702\) | 138.926 | 5.24344 | ||||||||
\(703\) | 6.88837 | 0.259800 | ||||||||
\(704\) | −37.3968 | −1.40945 | ||||||||
\(705\) | −15.0106 | −0.565333 | ||||||||
\(706\) | 46.0513 | 1.73316 | ||||||||
\(707\) | −10.8598 | −0.408426 | ||||||||
\(708\) | −96.5763 | −3.62956 | ||||||||
\(709\) | 20.1582 | 0.757056 | 0.378528 | − | 0.925590i | \(-0.376430\pi\) | ||||
0.378528 | + | 0.925590i | \(0.376430\pi\) | |||||||
\(710\) | 13.7993 | 0.517880 | ||||||||
\(711\) | −42.8085 | −1.60544 | ||||||||
\(712\) | 138.483 | 5.18988 | ||||||||
\(713\) | −5.99595 | −0.224550 | ||||||||
\(714\) | 174.105 | 6.51570 | ||||||||
\(715\) | 1.86663 | 0.0698079 | ||||||||
\(716\) | −57.4291 | −2.14623 | ||||||||
\(717\) | 21.2816 | 0.794776 | ||||||||
\(718\) | 64.6621 | 2.41317 | ||||||||
\(719\) | 48.5936 | 1.81223 | 0.906117 | − | 0.423027i | \(-0.139033\pi\) | ||||
0.906117 | + | 0.423027i | \(0.139033\pi\) | |||||||
\(720\) | 46.4713 | 1.73188 | ||||||||
\(721\) | 5.32683 | 0.198382 | ||||||||
\(722\) | −2.82251 | −0.105043 | ||||||||
\(723\) | −0.188492 | −0.00701009 | ||||||||
\(724\) | −54.7077 | −2.03319 | ||||||||
\(725\) | 30.7562 | 1.14226 | ||||||||
\(726\) | 87.1650 | 3.23500 | ||||||||
\(727\) | −12.4327 | −0.461102 | −0.230551 | − | 0.973060i | \(-0.574053\pi\) | ||||
−0.230551 | + | 0.973060i | \(0.574053\pi\) | |||||||
\(728\) | −247.768 | −9.18290 | ||||||||
\(729\) | −35.7153 | −1.32279 | ||||||||
\(730\) | −17.4527 | −0.645955 | ||||||||
\(731\) | 14.2157 | 0.525785 | ||||||||
\(732\) | −37.3931 | −1.38209 | ||||||||
\(733\) | 9.65456 | 0.356599 | 0.178300 | − | 0.983976i | \(-0.442940\pi\) | ||||
0.178300 | + | 0.983976i | \(0.442940\pi\) | |||||||
\(734\) | 28.7116 | 1.05976 | ||||||||
\(735\) | 6.03573 | 0.222631 | ||||||||
\(736\) | −228.314 | −8.41578 | ||||||||
\(737\) | −0.403409 | −0.0148598 | ||||||||
\(738\) | 142.257 | 5.23655 | ||||||||
\(739\) | 16.9923 | 0.625072 | 0.312536 | − | 0.949906i | \(-0.398822\pi\) | ||||
0.312536 | + | 0.949906i | \(0.398822\pi\) | |||||||
\(740\) | 17.3029 | 0.636069 | ||||||||
\(741\) | −18.8391 | −0.692073 | ||||||||
\(742\) | −2.40550 | −0.0883086 | ||||||||
\(743\) | −12.0555 | −0.442273 | −0.221137 | − | 0.975243i | \(-0.570977\pi\) | ||||
−0.221137 | + | 0.975243i | \(0.570977\pi\) | |||||||
\(744\) | 28.5769 | 1.04768 | ||||||||
\(745\) | −1.38849 | −0.0508703 | ||||||||
\(746\) | 68.5167 | 2.50858 | ||||||||
\(747\) | 57.0957 | 2.08902 | ||||||||
\(748\) | −25.1255 | −0.918679 | ||||||||
\(749\) | 10.3277 | 0.377366 | ||||||||
\(750\) | 34.2545 | 1.25080 | ||||||||
\(751\) | −16.2218 | −0.591943 | −0.295971 | − | 0.955197i | \(-0.595643\pi\) | ||||
−0.295971 | + | 0.955197i | \(0.595643\pi\) | |||||||
\(752\) | −238.938 | −8.71318 | ||||||||
\(753\) | −33.8368 | −1.23308 | ||||||||
\(754\) | −115.548 | −4.20802 | ||||||||
\(755\) | −1.20083 | −0.0437026 | ||||||||
\(756\) | −157.720 | −5.73621 | ||||||||
\(757\) | 51.8528 | 1.88462 | 0.942311 | − | 0.334740i | \(-0.108648\pi\) | ||||
0.942311 | + | 0.334740i | \(0.108648\pi\) | |||||||
\(758\) | 61.4970 | 2.23367 | ||||||||
\(759\) | −13.9740 | −0.507223 | ||||||||
\(760\) | −4.71335 | −0.170971 | ||||||||
\(761\) | 12.6680 | 0.459214 | 0.229607 | − | 0.973283i | \(-0.426256\pi\) | ||||
0.229607 | + | 0.973283i | \(0.426256\pi\) | |||||||
\(762\) | −162.567 | −5.88918 | ||||||||
\(763\) | 4.67005 | 0.169067 | ||||||||
\(764\) | 7.51616 | 0.271925 | ||||||||
\(765\) | 14.4063 | 0.520860 | ||||||||
\(766\) | −36.5663 | −1.32119 | ||||||||
\(767\) | 35.4053 | 1.27841 | ||||||||
\(768\) | 399.410 | 14.4125 | ||||||||
\(769\) | 11.8069 | 0.425768 | 0.212884 | − | 0.977077i | \(-0.431714\pi\) | ||||
0.212884 | + | 0.977077i | \(0.431714\pi\) | |||||||
\(770\) | −2.82947 | −0.101967 | ||||||||
\(771\) | 36.0855 | 1.29959 | ||||||||
\(772\) | 68.6417 | 2.47047 | ||||||||
\(773\) | 0.366113 | 0.0131682 | 0.00658409 | − | 0.999978i | \(-0.497904\pi\) | ||||
0.00658409 | + | 0.999978i | \(0.497904\pi\) | |||||||
\(774\) | −36.9379 | −1.32770 | ||||||||
\(775\) | 4.19460 | 0.150675 | ||||||||
\(776\) | 0.490834 | 0.0176199 | ||||||||
\(777\) | −69.6930 | −2.50022 | ||||||||
\(778\) | 65.5991 | 2.35184 | ||||||||
\(779\) | −8.97979 | −0.321735 | ||||||||
\(780\) | −47.3222 | −1.69441 | ||||||||
\(781\) | 8.02105 | 0.287016 | ||||||||
\(782\) | −118.632 | −4.24226 | ||||||||
\(783\) | −48.8984 | −1.74749 | ||||||||
\(784\) | 96.0763 | 3.43130 | ||||||||
\(785\) | −9.18535 | −0.327839 | ||||||||
\(786\) | 21.9167 | 0.781743 | ||||||||
\(787\) | 17.3834 | 0.619650 | 0.309825 | − | 0.950794i | \(-0.399729\pi\) | ||||
0.309825 | + | 0.950794i | \(0.399729\pi\) | |||||||
\(788\) | −72.2536 | −2.57393 | ||||||||
\(789\) | −88.2843 | −3.14300 | ||||||||
\(790\) | 9.06302 | 0.322448 | ||||||||
\(791\) | 29.4162 | 1.04592 | ||||||||
\(792\) | 43.4020 | 1.54222 | ||||||||
\(793\) | 13.7085 | 0.486802 | ||||||||
\(794\) | −53.0601 | −1.88303 | ||||||||
\(795\) | −0.305432 | −0.0108325 | ||||||||
\(796\) | 35.2305 | 1.24871 | ||||||||
\(797\) | 2.59713 | 0.0919952 | 0.0459976 | − | 0.998942i | \(-0.485353\pi\) | ||||
0.0459976 | + | 0.998942i | \(0.485353\pi\) | |||||||
\(798\) | 28.5567 | 1.01090 | ||||||||
\(799\) | −74.0718 | −2.62047 | ||||||||
\(800\) | 159.723 | 5.64705 | ||||||||
\(801\) | −69.4253 | −2.45302 | ||||||||
\(802\) | 86.1598 | 3.04241 | ||||||||
\(803\) | −10.1446 | −0.357996 | ||||||||
\(804\) | 10.2271 | 0.360682 | ||||||||
\(805\) | −10.0056 | −0.352652 | ||||||||
\(806\) | −15.7588 | −0.555079 | ||||||||
\(807\) | −75.8597 | −2.67039 | ||||||||
\(808\) | −35.2672 | −1.24070 | ||||||||
\(809\) | −10.9044 | −0.383379 | −0.191690 | − | 0.981456i | \(-0.561397\pi\) | ||||
−0.191690 | + | 0.981456i | \(0.561397\pi\) | |||||||
\(810\) | −6.73063 | −0.236490 | ||||||||
\(811\) | 30.7678 | 1.08040 | 0.540202 | − | 0.841535i | \(-0.318348\pi\) | ||||
0.540202 | + | 0.841535i | \(0.318348\pi\) | |||||||
\(812\) | 131.179 | 4.60349 | ||||||||
\(813\) | −46.1367 | −1.61808 | ||||||||
\(814\) | 13.4289 | 0.470682 | ||||||||
\(815\) | 2.40388 | 0.0842042 | ||||||||
\(816\) | 351.889 | 12.3186 | ||||||||
\(817\) | 2.33166 | 0.0815744 | ||||||||
\(818\) | −61.2134 | −2.14028 | ||||||||
\(819\) | 124.213 | 4.34034 | ||||||||
\(820\) | −22.5564 | −0.787704 | ||||||||
\(821\) | −39.7355 | −1.38678 | −0.693390 | − | 0.720563i | \(-0.743884\pi\) | ||||
−0.693390 | + | 0.720563i | \(0.743884\pi\) | |||||||
\(822\) | 36.3262 | 1.26702 | ||||||||
\(823\) | 32.0151 | 1.11598 | 0.557989 | − | 0.829848i | \(-0.311573\pi\) | ||||
0.557989 | + | 0.829848i | \(0.311573\pi\) | |||||||
\(824\) | 17.2988 | 0.602634 | ||||||||
\(825\) | 9.77581 | 0.340350 | ||||||||
\(826\) | −53.6680 | −1.86735 | ||||||||
\(827\) | 13.8659 | 0.482166 | 0.241083 | − | 0.970504i | \(-0.422497\pi\) | ||||
0.241083 | + | 0.970504i | \(0.422497\pi\) | |||||||
\(828\) | 230.865 | 8.02313 | ||||||||
\(829\) | 2.23297 | 0.0775542 | 0.0387771 | − | 0.999248i | \(-0.487654\pi\) | ||||
0.0387771 | + | 0.999248i | \(0.487654\pi\) | |||||||
\(830\) | −12.0878 | −0.419573 | ||||||||
\(831\) | −35.8693 | −1.24429 | ||||||||
\(832\) | −347.567 | −12.0497 | ||||||||
\(833\) | 29.7841 | 1.03196 | ||||||||
\(834\) | 106.428 | 3.68529 | ||||||||
\(835\) | −5.29494 | −0.183239 | ||||||||
\(836\) | −4.12109 | −0.142531 | ||||||||
\(837\) | −6.66888 | −0.230510 | ||||||||
\(838\) | −30.1519 | −1.04158 | ||||||||
\(839\) | 33.5557 | 1.15847 | 0.579236 | − | 0.815160i | \(-0.303351\pi\) | ||||
0.579236 | + | 0.815160i | \(0.303351\pi\) | |||||||
\(840\) | 47.6873 | 1.64537 | ||||||||
\(841\) | 11.6699 | 0.402412 | ||||||||
\(842\) | 48.0006 | 1.65421 | ||||||||
\(843\) | −50.8313 | −1.75072 | ||||||||
\(844\) | 5.96657 | 0.205378 | ||||||||
\(845\) | 11.8755 | 0.408531 | ||||||||
\(846\) | 192.468 | 6.61717 | ||||||||
\(847\) | 36.2777 | 1.24652 | ||||||||
\(848\) | −4.86184 | −0.166956 | ||||||||
\(849\) | −56.8995 | −1.95278 | ||||||||
\(850\) | 82.9915 | 2.84659 | ||||||||
\(851\) | 47.4875 | 1.62785 | ||||||||
\(852\) | −203.347 | −6.96656 | ||||||||
\(853\) | −40.9089 | −1.40069 | −0.700347 | − | 0.713802i | \(-0.746972\pi\) | ||||
−0.700347 | + | 0.713802i | \(0.746972\pi\) | |||||||
\(854\) | −20.7795 | −0.711061 | ||||||||
\(855\) | 2.36293 | 0.0808103 | ||||||||
\(856\) | 33.5391 | 1.14634 | ||||||||
\(857\) | −57.8252 | −1.97527 | −0.987636 | − | 0.156763i | \(-0.949894\pi\) | ||||
−0.987636 | + | 0.156763i | \(0.949894\pi\) | |||||||
\(858\) | −36.7269 | −1.25383 | ||||||||
\(859\) | −5.77724 | −0.197117 | −0.0985585 | − | 0.995131i | \(-0.531423\pi\) | ||||
−0.0985585 | + | 0.995131i | \(0.531423\pi\) | |||||||
\(860\) | 5.85691 | 0.199719 | ||||||||
\(861\) | 90.8529 | 3.09626 | ||||||||
\(862\) | −18.1510 | −0.618226 | ||||||||
\(863\) | 10.4135 | 0.354481 | 0.177241 | − | 0.984168i | \(-0.443283\pi\) | ||||
0.177241 | + | 0.984168i | \(0.443283\pi\) | |||||||
\(864\) | −253.938 | −8.63916 | ||||||||
\(865\) | −2.06321 | −0.0701512 | ||||||||
\(866\) | 22.4732 | 0.763672 | ||||||||
\(867\) | 59.1966 | 2.01042 | ||||||||
\(868\) | 17.8905 | 0.607244 | ||||||||
\(869\) | 5.26800 | 0.178705 | ||||||||
\(870\) | 22.2393 | 0.753982 | ||||||||
\(871\) | −3.74930 | −0.127040 | ||||||||
\(872\) | 15.1660 | 0.513584 | ||||||||
\(873\) | −0.246068 | −0.00832814 | ||||||||
\(874\) | −19.4580 | −0.658177 | ||||||||
\(875\) | 14.2566 | 0.481961 | ||||||||
\(876\) | 257.184 | 8.68943 | ||||||||
\(877\) | −11.4111 | −0.385325 | −0.192663 | − | 0.981265i | \(-0.561712\pi\) | ||||
−0.192663 | + | 0.981265i | \(0.561712\pi\) | |||||||
\(878\) | −4.29765 | −0.145039 | ||||||||
\(879\) | 62.9998 | 2.12493 | ||||||||
\(880\) | −5.71874 | −0.192779 | ||||||||
\(881\) | 45.0574 | 1.51802 | 0.759012 | − | 0.651077i | \(-0.225682\pi\) | ||||
0.759012 | + | 0.651077i | \(0.225682\pi\) | |||||||
\(882\) | −77.3907 | −2.60588 | ||||||||
\(883\) | −51.0951 | −1.71949 | −0.859744 | − | 0.510726i | \(-0.829377\pi\) | ||||
−0.859744 | + | 0.510726i | \(0.829377\pi\) | |||||||
\(884\) | −233.517 | −7.85402 | ||||||||
\(885\) | −6.81435 | −0.229062 | ||||||||
\(886\) | −27.7554 | −0.932460 | ||||||||
\(887\) | 4.89146 | 0.164239 | 0.0821195 | − | 0.996622i | \(-0.473831\pi\) | ||||
0.0821195 | + | 0.996622i | \(0.473831\pi\) | |||||||
\(888\) | −226.327 | −7.59505 | ||||||||
\(889\) | −67.6597 | −2.26923 | ||||||||
\(890\) | 14.6981 | 0.492681 | ||||||||
\(891\) | −3.91227 | −0.131066 | ||||||||
\(892\) | 93.1125 | 3.11764 | ||||||||
\(893\) | −12.1493 | −0.406560 | ||||||||
\(894\) | 27.3192 | 0.913692 | ||||||||
\(895\) | −4.05215 | −0.135449 | ||||||||
\(896\) | 298.498 | 9.97211 | ||||||||
\(897\) | −129.874 | −4.33638 | ||||||||
\(898\) | −97.1796 | −3.24292 | ||||||||
\(899\) | 5.54666 | 0.184992 | ||||||||
\(900\) | −161.507 | −5.38357 | ||||||||
\(901\) | −1.50719 | −0.0502118 | ||||||||
\(902\) | −17.5061 | −0.582890 | ||||||||
\(903\) | −23.5905 | −0.785044 | ||||||||
\(904\) | 95.5288 | 3.17724 | ||||||||
\(905\) | −3.86013 | −0.128315 | ||||||||
\(906\) | 23.6269 | 0.784952 | ||||||||
\(907\) | −45.7022 | −1.51752 | −0.758758 | − | 0.651373i | \(-0.774193\pi\) | ||||
−0.758758 | + | 0.651373i | \(0.774193\pi\) | |||||||
\(908\) | 94.7591 | 3.14469 | ||||||||
\(909\) | 17.6804 | 0.586420 | ||||||||
\(910\) | −26.2972 | −0.871743 | ||||||||
\(911\) | 28.2317 | 0.935358 | 0.467679 | − | 0.883898i | \(-0.345090\pi\) | ||||
0.467679 | + | 0.883898i | \(0.345090\pi\) | |||||||
\(912\) | 57.7170 | 1.91120 | ||||||||
\(913\) | −7.02619 | −0.232533 | ||||||||
\(914\) | 50.1883 | 1.66008 | ||||||||
\(915\) | −2.63843 | −0.0872238 | ||||||||
\(916\) | 32.0739 | 1.05975 | ||||||||
\(917\) | 9.12165 | 0.301223 | ||||||||
\(918\) | −131.946 | −4.35486 | ||||||||
\(919\) | 15.0963 | 0.497982 | 0.248991 | − | 0.968506i | \(-0.419901\pi\) | ||||
0.248991 | + | 0.968506i | \(0.419901\pi\) | |||||||
\(920\) | −32.4932 | −1.07127 | ||||||||
\(921\) | 20.9885 | 0.691595 | ||||||||
\(922\) | −21.6016 | −0.711412 | ||||||||
\(923\) | 74.5478 | 2.45377 | ||||||||
\(924\) | 41.6951 | 1.37167 | ||||||||
\(925\) | −33.2210 | −1.09230 | ||||||||
\(926\) | 40.8026 | 1.34086 | ||||||||
\(927\) | −8.67236 | −0.284838 | ||||||||
\(928\) | 211.207 | 6.93319 | ||||||||
\(929\) | 20.6539 | 0.677631 | 0.338816 | − | 0.940853i | \(-0.389974\pi\) | ||||
0.338816 | + | 0.940853i | \(0.389974\pi\) | |||||||
\(930\) | 3.03305 | 0.0994575 | ||||||||
\(931\) | 4.88519 | 0.160106 | ||||||||
\(932\) | 79.8406 | 2.61527 | ||||||||
\(933\) | −16.7956 | −0.549864 | ||||||||
\(934\) | −45.1318 | −1.47676 | ||||||||
\(935\) | −1.77283 | −0.0579779 | ||||||||
\(936\) | 403.379 | 13.1849 | ||||||||
\(937\) | 32.1069 | 1.04889 | 0.524443 | − | 0.851446i | \(-0.324274\pi\) | ||||
0.524443 | + | 0.851446i | \(0.324274\pi\) | |||||||
\(938\) | 5.68326 | 0.185565 | ||||||||
\(939\) | −23.5195 | −0.767530 | ||||||||
\(940\) | −30.5179 | −0.995384 | ||||||||
\(941\) | 45.7400 | 1.49108 | 0.745541 | − | 0.666459i | \(-0.232191\pi\) | ||||
0.745541 | + | 0.666459i | \(0.232191\pi\) | |||||||
\(942\) | 180.727 | 5.88839 | ||||||||
\(943\) | −61.9055 | −2.01592 | ||||||||
\(944\) | −108.470 | −3.53041 | ||||||||
\(945\) | −11.1286 | −0.362013 | ||||||||
\(946\) | 4.54557 | 0.147789 | ||||||||
\(947\) | −38.0423 | −1.23621 | −0.618104 | − | 0.786096i | \(-0.712099\pi\) | ||||
−0.618104 | + | 0.786096i | \(0.712099\pi\) | |||||||
\(948\) | −133.553 | −4.33759 | ||||||||
\(949\) | −94.2846 | −3.06061 | ||||||||
\(950\) | 13.6123 | 0.441641 | ||||||||
\(951\) | 58.3393 | 1.89178 | ||||||||
\(952\) | 235.319 | 7.62672 | ||||||||
\(953\) | 55.0605 | 1.78359 | 0.891793 | − | 0.452444i | \(-0.149448\pi\) | ||||
0.891793 | + | 0.452444i | \(0.149448\pi\) | |||||||
\(954\) | 3.91627 | 0.126794 | ||||||||
\(955\) | 0.530334 | 0.0171612 | ||||||||
\(956\) | 43.2673 | 1.39936 | ||||||||
\(957\) | 12.9269 | 0.417867 | ||||||||
\(958\) | −11.8589 | −0.383142 | ||||||||
\(959\) | 15.1188 | 0.488212 | ||||||||
\(960\) | 66.8953 | 2.15904 | ||||||||
\(961\) | −30.2435 | −0.975598 | ||||||||
\(962\) | 124.808 | 4.02398 | ||||||||
\(963\) | −16.8140 | −0.541825 | ||||||||
\(964\) | −0.383220 | −0.0123427 | ||||||||
\(965\) | 4.84330 | 0.155911 | ||||||||
\(966\) | 196.866 | 6.33407 | ||||||||
\(967\) | −22.8863 | −0.735975 | −0.367987 | − | 0.929831i | \(-0.619953\pi\) | ||||
−0.367987 | + | 0.929831i | \(0.619953\pi\) | |||||||
\(968\) | 117.812 | 3.78661 | ||||||||
\(969\) | 17.8925 | 0.574791 | ||||||||
\(970\) | 0.0520953 | 0.00167268 | ||||||||
\(971\) | −56.2640 | −1.80560 | −0.902799 | − | 0.430064i | \(-0.858491\pi\) | ||||
−0.902799 | + | 0.430064i | \(0.858491\pi\) | |||||||
\(972\) | −38.0647 | −1.22093 | ||||||||
\(973\) | 44.2948 | 1.42002 | ||||||||
\(974\) | −42.1141 | −1.34942 | ||||||||
\(975\) | 90.8566 | 2.90974 | ||||||||
\(976\) | −41.9983 | −1.34433 | ||||||||
\(977\) | 28.5026 | 0.911878 | 0.455939 | − | 0.890011i | \(-0.349303\pi\) | ||||
0.455939 | + | 0.890011i | \(0.349303\pi\) | |||||||
\(978\) | −47.2976 | −1.51241 | ||||||||
\(979\) | 8.54346 | 0.273050 | ||||||||
\(980\) | 12.2712 | 0.391988 | ||||||||
\(981\) | −7.60308 | −0.242748 | ||||||||
\(982\) | 96.4610 | 3.07820 | ||||||||
\(983\) | −41.3832 | −1.31992 | −0.659959 | − | 0.751302i | \(-0.729426\pi\) | ||||
−0.659959 | + | 0.751302i | \(0.729426\pi\) | |||||||
\(984\) | 295.044 | 9.40566 | ||||||||
\(985\) | −5.09816 | −0.162441 | ||||||||
\(986\) | 109.742 | 3.49491 | ||||||||
\(987\) | 122.920 | 3.91259 | ||||||||
\(988\) | −38.3015 | −1.21853 | ||||||||
\(989\) | 16.0741 | 0.511128 | ||||||||
\(990\) | 4.60652 | 0.146405 | ||||||||
\(991\) | 49.9187 | 1.58572 | 0.792860 | − | 0.609404i | \(-0.208591\pi\) | ||||
0.792860 | + | 0.609404i | \(0.208591\pi\) | |||||||
\(992\) | 28.8048 | 0.914555 | ||||||||
\(993\) | 82.4757 | 2.61729 | ||||||||
\(994\) | −113.001 | −3.58418 | ||||||||
\(995\) | 2.48584 | 0.0788063 | ||||||||
\(996\) | 178.126 | 5.64413 | ||||||||
\(997\) | 19.2470 | 0.609559 | 0.304780 | − | 0.952423i | \(-0.401417\pi\) | ||||
0.304780 | + | 0.952423i | \(0.401417\pi\) | |||||||
\(998\) | 99.8225 | 3.15983 | ||||||||
\(999\) | 52.8170 | 1.67106 |
(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 | 4009.2.a.c.1.1 | ✓ | 71 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.c.1.1 | ✓ | 71 | 1.1 | even | 1 | trivial |