Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 36 x^{10} + 105 x^{9} + 465 x^{8} - 1287 x^{7} - 2668 x^{6} + 6443 x^{5} + 7140 x^{4} - 10858 x^{3} - 10086 x^{2} + 2072 x + 1496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(-1.13903\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.13903 | 0.509390 | 0.254695 | − | 0.967021i | \(-0.418025\pi\) | ||||
0.254695 | + | 0.967021i | \(0.418025\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 4.65781 | 1.76049 | 0.880244 | − | 0.474521i | \(-0.157379\pi\) | ||||
0.880244 | + | 0.474521i | \(0.157379\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.13903 | −0.360193 | ||||||||
\(11\) | −4.30320 | −1.29746 | −0.648732 | − | 0.761017i | \(-0.724700\pi\) | ||||
−0.648732 | + | 0.761017i | \(0.724700\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.92818 | −0.534780 | −0.267390 | − | 0.963588i | \(-0.586161\pi\) | ||||
−0.267390 | + | 0.963588i | \(0.586161\pi\) | |||||||
\(14\) | −4.65781 | −1.24485 | ||||||||
\(15\) | −1.13903 | −0.294097 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.94646 | −1.68476 | −0.842382 | − | 0.538881i | \(-0.818847\pi\) | ||||
−0.842382 | + | 0.538881i | \(0.818847\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.13903 | 0.254695 | ||||||||
\(21\) | −4.65781 | −1.01642 | ||||||||
\(22\) | 4.30320 | 0.917445 | ||||||||
\(23\) | 7.91164 | 1.64969 | 0.824846 | − | 0.565357i | \(-0.191262\pi\) | ||||
0.824846 | + | 0.565357i | \(0.191262\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.70261 | −0.740521 | ||||||||
\(26\) | 1.92818 | 0.378147 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.65781 | 0.880244 | ||||||||
\(29\) | 9.83797 | 1.82686 | 0.913432 | − | 0.406990i | \(-0.133422\pi\) | ||||
0.913432 | + | 0.406990i | \(0.133422\pi\) | |||||||
\(30\) | 1.13903 | 0.207958 | ||||||||
\(31\) | 1.28044 | 0.229975 | 0.114987 | − | 0.993367i | \(-0.463317\pi\) | ||||
0.114987 | + | 0.993367i | \(0.463317\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.30320 | 0.749091 | ||||||||
\(34\) | 6.94646 | 1.19131 | ||||||||
\(35\) | 5.30540 | 0.896776 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.818562 | 0.134571 | 0.0672854 | − | 0.997734i | \(-0.478566\pi\) | ||||
0.0672854 | + | 0.997734i | \(0.478566\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 1.92818 | 0.308756 | ||||||||
\(40\) | −1.13903 | −0.180097 | ||||||||
\(41\) | −8.18877 | −1.27887 | −0.639435 | − | 0.768845i | \(-0.720832\pi\) | ||||
−0.639435 | + | 0.768845i | \(0.720832\pi\) | |||||||
\(42\) | 4.65781 | 0.718716 | ||||||||
\(43\) | −10.6577 | −1.62528 | −0.812641 | − | 0.582764i | \(-0.801971\pi\) | ||||
−0.812641 | + | 0.582764i | \(0.801971\pi\) | |||||||
\(44\) | −4.30320 | −0.648732 | ||||||||
\(45\) | 1.13903 | 0.169797 | ||||||||
\(46\) | −7.91164 | −1.16651 | ||||||||
\(47\) | −6.78781 | −0.990104 | −0.495052 | − | 0.868863i | \(-0.664851\pi\) | ||||
−0.495052 | + | 0.868863i | \(0.664851\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 14.6952 | 2.09932 | ||||||||
\(50\) | 3.70261 | 0.523628 | ||||||||
\(51\) | 6.94646 | 0.972699 | ||||||||
\(52\) | −1.92818 | −0.267390 | ||||||||
\(53\) | −1.00000 | −0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −4.90148 | −0.660916 | ||||||||
\(56\) | −4.65781 | −0.622427 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −9.83797 | −1.29179 | ||||||||
\(59\) | −6.44178 | −0.838648 | −0.419324 | − | 0.907837i | \(-0.637733\pi\) | ||||
−0.419324 | + | 0.907837i | \(0.637733\pi\) | |||||||
\(60\) | −1.13903 | −0.147048 | ||||||||
\(61\) | 11.1555 | 1.42832 | 0.714158 | − | 0.699985i | \(-0.246810\pi\) | ||||
0.714158 | + | 0.699985i | \(0.246810\pi\) | |||||||
\(62\) | −1.28044 | −0.162617 | ||||||||
\(63\) | 4.65781 | 0.586829 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.19626 | −0.272412 | ||||||||
\(66\) | −4.30320 | −0.529687 | ||||||||
\(67\) | 13.1712 | 1.60912 | 0.804558 | − | 0.593874i | \(-0.202402\pi\) | ||||
0.804558 | + | 0.593874i | \(0.202402\pi\) | |||||||
\(68\) | −6.94646 | −0.842382 | ||||||||
\(69\) | −7.91164 | −0.952450 | ||||||||
\(70\) | −5.30540 | −0.634116 | ||||||||
\(71\) | −0.159757 | −0.0189597 | −0.00947986 | − | 0.999955i | \(-0.503018\pi\) | ||||
−0.00947986 | + | 0.999955i | \(0.503018\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −14.3502 | −1.67957 | −0.839783 | − | 0.542922i | \(-0.817318\pi\) | ||||
−0.839783 | + | 0.542922i | \(0.817318\pi\) | |||||||
\(74\) | −0.818562 | −0.0951559 | ||||||||
\(75\) | 3.70261 | 0.427540 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −20.0435 | −2.28417 | ||||||||
\(78\) | −1.92818 | −0.218323 | ||||||||
\(79\) | 8.88482 | 0.999620 | 0.499810 | − | 0.866135i | \(-0.333403\pi\) | ||||
0.499810 | + | 0.866135i | \(0.333403\pi\) | |||||||
\(80\) | 1.13903 | 0.127348 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 8.18877 | 0.904298 | ||||||||
\(83\) | −10.8297 | −1.18871 | −0.594355 | − | 0.804203i | \(-0.702592\pi\) | ||||
−0.594355 | + | 0.804203i | \(0.702592\pi\) | |||||||
\(84\) | −4.65781 | −0.508209 | ||||||||
\(85\) | −7.91224 | −0.858203 | ||||||||
\(86\) | 10.6577 | 1.14925 | ||||||||
\(87\) | −9.83797 | −1.05474 | ||||||||
\(88\) | 4.30320 | 0.458723 | ||||||||
\(89\) | −7.73787 | −0.820213 | −0.410107 | − | 0.912038i | \(-0.634508\pi\) | ||||
−0.410107 | + | 0.912038i | \(0.634508\pi\) | |||||||
\(90\) | −1.13903 | −0.120064 | ||||||||
\(91\) | −8.98109 | −0.941474 | ||||||||
\(92\) | 7.91164 | 0.824846 | ||||||||
\(93\) | −1.28044 | −0.132776 | ||||||||
\(94\) | 6.78781 | 0.700110 | ||||||||
\(95\) | −1.13903 | −0.116862 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −3.07525 | −0.312244 | −0.156122 | − | 0.987738i | \(-0.549899\pi\) | ||||
−0.156122 | + | 0.987738i | \(0.549899\pi\) | |||||||
\(98\) | −14.6952 | −1.48444 | ||||||||
\(99\) | −4.30320 | −0.432488 | ||||||||
\(100\) | −3.70261 | −0.370261 | ||||||||
\(101\) | −10.0253 | −0.997556 | −0.498778 | − | 0.866730i | \(-0.666218\pi\) | ||||
−0.498778 | + | 0.866730i | \(0.666218\pi\) | |||||||
\(102\) | −6.94646 | −0.687802 | ||||||||
\(103\) | 11.3695 | 1.12027 | 0.560137 | − | 0.828400i | \(-0.310748\pi\) | ||||
0.560137 | + | 0.828400i | \(0.310748\pi\) | |||||||
\(104\) | 1.92818 | 0.189073 | ||||||||
\(105\) | −5.30540 | −0.517754 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | −8.55575 | −0.827115 | −0.413558 | − | 0.910478i | \(-0.635714\pi\) | ||||
−0.413558 | + | 0.910478i | \(0.635714\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −14.9575 | −1.43267 | −0.716335 | − | 0.697756i | \(-0.754182\pi\) | ||||
−0.716335 | + | 0.697756i | \(0.754182\pi\) | |||||||
\(110\) | 4.90148 | 0.467338 | ||||||||
\(111\) | −0.818562 | −0.0776945 | ||||||||
\(112\) | 4.65781 | 0.440122 | ||||||||
\(113\) | −2.53394 | −0.238373 | −0.119186 | − | 0.992872i | \(-0.538029\pi\) | ||||
−0.119186 | + | 0.992872i | \(0.538029\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 9.01161 | 0.840337 | ||||||||
\(116\) | 9.83797 | 0.913432 | ||||||||
\(117\) | −1.92818 | −0.178260 | ||||||||
\(118\) | 6.44178 | 0.593014 | ||||||||
\(119\) | −32.3553 | −2.96601 | ||||||||
\(120\) | 1.13903 | 0.103979 | ||||||||
\(121\) | 7.51753 | 0.683412 | ||||||||
\(122\) | −11.1555 | −1.00997 | ||||||||
\(123\) | 8.18877 | 0.738356 | ||||||||
\(124\) | 1.28044 | 0.114987 | ||||||||
\(125\) | −9.91254 | −0.886605 | ||||||||
\(126\) | −4.65781 | −0.414951 | ||||||||
\(127\) | −12.5689 | −1.11531 | −0.557656 | − | 0.830072i | \(-0.688299\pi\) | ||||
−0.557656 | + | 0.830072i | \(0.688299\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.6577 | 0.938357 | ||||||||
\(130\) | 2.19626 | 0.192624 | ||||||||
\(131\) | −12.4130 | −1.08453 | −0.542265 | − | 0.840208i | \(-0.682433\pi\) | ||||
−0.542265 | + | 0.840208i | \(0.682433\pi\) | |||||||
\(132\) | 4.30320 | 0.374545 | ||||||||
\(133\) | −4.65781 | −0.403884 | ||||||||
\(134\) | −13.1712 | −1.13782 | ||||||||
\(135\) | −1.13903 | −0.0980322 | ||||||||
\(136\) | 6.94646 | 0.595654 | ||||||||
\(137\) | 2.04158 | 0.174424 | 0.0872119 | − | 0.996190i | \(-0.472204\pi\) | ||||
0.0872119 | + | 0.996190i | \(0.472204\pi\) | |||||||
\(138\) | 7.91164 | 0.673484 | ||||||||
\(139\) | −16.4948 | −1.39907 | −0.699536 | − | 0.714597i | \(-0.746610\pi\) | ||||
−0.699536 | + | 0.714597i | \(0.746610\pi\) | |||||||
\(140\) | 5.30540 | 0.448388 | ||||||||
\(141\) | 6.78781 | 0.571637 | ||||||||
\(142\) | 0.159757 | 0.0134065 | ||||||||
\(143\) | 8.29733 | 0.693858 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 11.2058 | 0.930587 | ||||||||
\(146\) | 14.3502 | 1.18763 | ||||||||
\(147\) | −14.6952 | −1.21204 | ||||||||
\(148\) | 0.818562 | 0.0672854 | ||||||||
\(149\) | 3.48835 | 0.285777 | 0.142888 | − | 0.989739i | \(-0.454361\pi\) | ||||
0.142888 | + | 0.989739i | \(0.454361\pi\) | |||||||
\(150\) | −3.70261 | −0.302317 | ||||||||
\(151\) | 12.2747 | 0.998904 | 0.499452 | − | 0.866342i | \(-0.333535\pi\) | ||||
0.499452 | + | 0.866342i | \(0.333535\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −6.94646 | −0.561588 | ||||||||
\(154\) | 20.0435 | 1.61515 | ||||||||
\(155\) | 1.45847 | 0.117147 | ||||||||
\(156\) | 1.92818 | 0.154378 | ||||||||
\(157\) | 15.5243 | 1.23898 | 0.619488 | − | 0.785006i | \(-0.287340\pi\) | ||||
0.619488 | + | 0.785006i | \(0.287340\pi\) | |||||||
\(158\) | −8.88482 | −0.706838 | ||||||||
\(159\) | 1.00000 | 0.0793052 | ||||||||
\(160\) | −1.13903 | −0.0900484 | ||||||||
\(161\) | 36.8510 | 2.90426 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 5.08704 | 0.398447 | 0.199224 | − | 0.979954i | \(-0.436158\pi\) | ||||
0.199224 | + | 0.979954i | \(0.436158\pi\) | |||||||
\(164\) | −8.18877 | −0.639435 | ||||||||
\(165\) | 4.90148 | 0.381580 | ||||||||
\(166\) | 10.8297 | 0.840545 | ||||||||
\(167\) | 12.5322 | 0.969772 | 0.484886 | − | 0.874577i | \(-0.338861\pi\) | ||||
0.484886 | + | 0.874577i | \(0.338861\pi\) | |||||||
\(168\) | 4.65781 | 0.359358 | ||||||||
\(169\) | −9.28213 | −0.714010 | ||||||||
\(170\) | 7.91224 | 0.606841 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | −10.6577 | −0.812641 | ||||||||
\(173\) | −21.4077 | −1.62760 | −0.813800 | − | 0.581146i | \(-0.802605\pi\) | ||||
−0.813800 | + | 0.581146i | \(0.802605\pi\) | |||||||
\(174\) | 9.83797 | 0.745814 | ||||||||
\(175\) | −17.2461 | −1.30368 | ||||||||
\(176\) | −4.30320 | −0.324366 | ||||||||
\(177\) | 6.44178 | 0.484194 | ||||||||
\(178\) | 7.73787 | 0.579978 | ||||||||
\(179\) | −0.147626 | −0.0110341 | −0.00551706 | − | 0.999985i | \(-0.501756\pi\) | ||||
−0.00551706 | + | 0.999985i | \(0.501756\pi\) | |||||||
\(180\) | 1.13903 | 0.0848984 | ||||||||
\(181\) | 19.8585 | 1.47607 | 0.738034 | − | 0.674764i | \(-0.235755\pi\) | ||||
0.738034 | + | 0.674764i | \(0.235755\pi\) | |||||||
\(182\) | 8.98109 | 0.665723 | ||||||||
\(183\) | −11.1555 | −0.824638 | ||||||||
\(184\) | −7.91164 | −0.583254 | ||||||||
\(185\) | 0.932368 | 0.0685491 | ||||||||
\(186\) | 1.28044 | 0.0938867 | ||||||||
\(187\) | 29.8920 | 2.18592 | ||||||||
\(188\) | −6.78781 | −0.495052 | ||||||||
\(189\) | −4.65781 | −0.338806 | ||||||||
\(190\) | 1.13903 | 0.0826340 | ||||||||
\(191\) | −1.38890 | −0.100497 | −0.0502485 | − | 0.998737i | \(-0.516001\pi\) | ||||
−0.0502485 | + | 0.998737i | \(0.516001\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 2.72902 | 0.196439 | 0.0982197 | − | 0.995165i | \(-0.468685\pi\) | ||||
0.0982197 | + | 0.995165i | \(0.468685\pi\) | |||||||
\(194\) | 3.07525 | 0.220790 | ||||||||
\(195\) | 2.19626 | 0.157277 | ||||||||
\(196\) | 14.6952 | 1.04966 | ||||||||
\(197\) | 2.54933 | 0.181632 | 0.0908162 | − | 0.995868i | \(-0.471052\pi\) | ||||
0.0908162 | + | 0.995868i | \(0.471052\pi\) | |||||||
\(198\) | 4.30320 | 0.305815 | ||||||||
\(199\) | −8.95183 | −0.634579 | −0.317289 | − | 0.948329i | \(-0.602773\pi\) | ||||
−0.317289 | + | 0.948329i | \(0.602773\pi\) | |||||||
\(200\) | 3.70261 | 0.261814 | ||||||||
\(201\) | −13.1712 | −0.929024 | ||||||||
\(202\) | 10.0253 | 0.705378 | ||||||||
\(203\) | 45.8234 | 3.21617 | ||||||||
\(204\) | 6.94646 | 0.486349 | ||||||||
\(205\) | −9.32727 | −0.651445 | ||||||||
\(206\) | −11.3695 | −0.792154 | ||||||||
\(207\) | 7.91164 | 0.549897 | ||||||||
\(208\) | −1.92818 | −0.133695 | ||||||||
\(209\) | 4.30320 | 0.297659 | ||||||||
\(210\) | 5.30540 | 0.366107 | ||||||||
\(211\) | 16.0300 | 1.10355 | 0.551775 | − | 0.833993i | \(-0.313951\pi\) | ||||
0.551775 | + | 0.833993i | \(0.313951\pi\) | |||||||
\(212\) | −1.00000 | −0.0686803 | ||||||||
\(213\) | 0.159757 | 0.0109464 | ||||||||
\(214\) | 8.55575 | 0.584859 | ||||||||
\(215\) | −12.1394 | −0.827903 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 5.96407 | 0.404868 | ||||||||
\(218\) | 14.9575 | 1.01305 | ||||||||
\(219\) | 14.3502 | 0.969698 | ||||||||
\(220\) | −4.90148 | −0.330458 | ||||||||
\(221\) | 13.3940 | 0.900978 | ||||||||
\(222\) | 0.818562 | 0.0549383 | ||||||||
\(223\) | 15.7753 | 1.05639 | 0.528195 | − | 0.849123i | \(-0.322869\pi\) | ||||
0.528195 | + | 0.849123i | \(0.322869\pi\) | |||||||
\(224\) | −4.65781 | −0.311213 | ||||||||
\(225\) | −3.70261 | −0.246840 | ||||||||
\(226\) | 2.53394 | 0.168555 | ||||||||
\(227\) | −4.98013 | −0.330543 | −0.165271 | − | 0.986248i | \(-0.552850\pi\) | ||||
−0.165271 | + | 0.986248i | \(0.552850\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 0.629002 | 0.0415656 | 0.0207828 | − | 0.999784i | \(-0.493384\pi\) | ||||
0.0207828 | + | 0.999784i | \(0.493384\pi\) | |||||||
\(230\) | −9.01161 | −0.594208 | ||||||||
\(231\) | 20.0435 | 1.31877 | ||||||||
\(232\) | −9.83797 | −0.645894 | ||||||||
\(233\) | 14.0856 | 0.922778 | 0.461389 | − | 0.887198i | \(-0.347351\pi\) | ||||
0.461389 | + | 0.887198i | \(0.347351\pi\) | |||||||
\(234\) | 1.92818 | 0.126049 | ||||||||
\(235\) | −7.73154 | −0.504350 | ||||||||
\(236\) | −6.44178 | −0.419324 | ||||||||
\(237\) | −8.88482 | −0.577131 | ||||||||
\(238\) | 32.3553 | 2.09728 | ||||||||
\(239\) | −22.0582 | −1.42682 | −0.713412 | − | 0.700745i | \(-0.752851\pi\) | ||||
−0.713412 | + | 0.700745i | \(0.752851\pi\) | |||||||
\(240\) | −1.13903 | −0.0735242 | ||||||||
\(241\) | −9.89881 | −0.637638 | −0.318819 | − | 0.947816i | \(-0.603286\pi\) | ||||
−0.318819 | + | 0.947816i | \(0.603286\pi\) | |||||||
\(242\) | −7.51753 | −0.483245 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 11.1555 | 0.714158 | ||||||||
\(245\) | 16.7383 | 1.06937 | ||||||||
\(246\) | −8.18877 | −0.522097 | ||||||||
\(247\) | 1.92818 | 0.122687 | ||||||||
\(248\) | −1.28044 | −0.0813083 | ||||||||
\(249\) | 10.8297 | 0.686302 | ||||||||
\(250\) | 9.91254 | 0.626924 | ||||||||
\(251\) | −11.2298 | −0.708818 | −0.354409 | − | 0.935090i | \(-0.615318\pi\) | ||||
−0.354409 | + | 0.935090i | \(0.615318\pi\) | |||||||
\(252\) | 4.65781 | 0.293415 | ||||||||
\(253\) | −34.0454 | −2.14042 | ||||||||
\(254\) | 12.5689 | 0.788645 | ||||||||
\(255\) | 7.91224 | 0.495484 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.75460 | 0.358962 | 0.179481 | − | 0.983761i | \(-0.442558\pi\) | ||||
0.179481 | + | 0.983761i | \(0.442558\pi\) | |||||||
\(258\) | −10.6577 | −0.663519 | ||||||||
\(259\) | 3.81271 | 0.236910 | ||||||||
\(260\) | −2.19626 | −0.136206 | ||||||||
\(261\) | 9.83797 | 0.608955 | ||||||||
\(262\) | 12.4130 | 0.766878 | ||||||||
\(263\) | 14.0528 | 0.866531 | 0.433265 | − | 0.901266i | \(-0.357361\pi\) | ||||
0.433265 | + | 0.901266i | \(0.357361\pi\) | |||||||
\(264\) | −4.30320 | −0.264844 | ||||||||
\(265\) | −1.13903 | −0.0699702 | ||||||||
\(266\) | 4.65781 | 0.285589 | ||||||||
\(267\) | 7.73787 | 0.473550 | ||||||||
\(268\) | 13.1712 | 0.804558 | ||||||||
\(269\) | −11.9464 | −0.728382 | −0.364191 | − | 0.931324i | \(-0.618654\pi\) | ||||
−0.364191 | + | 0.931324i | \(0.618654\pi\) | |||||||
\(270\) | 1.13903 | 0.0693193 | ||||||||
\(271\) | −17.8176 | −1.08234 | −0.541171 | − | 0.840912i | \(-0.682019\pi\) | ||||
−0.541171 | + | 0.840912i | \(0.682019\pi\) | |||||||
\(272\) | −6.94646 | −0.421191 | ||||||||
\(273\) | 8.98109 | 0.543560 | ||||||||
\(274\) | −2.04158 | −0.123336 | ||||||||
\(275\) | 15.9331 | 0.960800 | ||||||||
\(276\) | −7.91164 | −0.476225 | ||||||||
\(277\) | −25.1299 | −1.50991 | −0.754954 | − | 0.655778i | \(-0.772341\pi\) | ||||
−0.754954 | + | 0.655778i | \(0.772341\pi\) | |||||||
\(278\) | 16.4948 | 0.989293 | ||||||||
\(279\) | 1.28044 | 0.0766582 | ||||||||
\(280\) | −5.30540 | −0.317058 | ||||||||
\(281\) | 1.06382 | 0.0634623 | 0.0317312 | − | 0.999496i | \(-0.489898\pi\) | ||||
0.0317312 | + | 0.999496i | \(0.489898\pi\) | |||||||
\(282\) | −6.78781 | −0.404208 | ||||||||
\(283\) | −7.83023 | −0.465459 | −0.232730 | − | 0.972541i | \(-0.574766\pi\) | ||||
−0.232730 | + | 0.972541i | \(0.574766\pi\) | |||||||
\(284\) | −0.159757 | −0.00947986 | ||||||||
\(285\) | 1.13903 | 0.0674704 | ||||||||
\(286\) | −8.29733 | −0.490632 | ||||||||
\(287\) | −38.1418 | −2.25144 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 31.2533 | 1.83843 | ||||||||
\(290\) | −11.2058 | −0.658025 | ||||||||
\(291\) | 3.07525 | 0.180274 | ||||||||
\(292\) | −14.3502 | −0.839783 | ||||||||
\(293\) | −11.6142 | −0.678506 | −0.339253 | − | 0.940695i | \(-0.610174\pi\) | ||||
−0.339253 | + | 0.940695i | \(0.610174\pi\) | |||||||
\(294\) | 14.6952 | 0.857043 | ||||||||
\(295\) | −7.33739 | −0.427199 | ||||||||
\(296\) | −0.818562 | −0.0475780 | ||||||||
\(297\) | 4.30320 | 0.249697 | ||||||||
\(298\) | −3.48835 | −0.202075 | ||||||||
\(299\) | −15.2551 | −0.882223 | ||||||||
\(300\) | 3.70261 | 0.213770 | ||||||||
\(301\) | −49.6415 | −2.86129 | ||||||||
\(302\) | −12.2747 | −0.706332 | ||||||||
\(303\) | 10.0253 | 0.575939 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 12.7065 | 0.727570 | ||||||||
\(306\) | 6.94646 | 0.397103 | ||||||||
\(307\) | −28.7680 | −1.64187 | −0.820937 | − | 0.571018i | \(-0.806549\pi\) | ||||
−0.820937 | + | 0.571018i | \(0.806549\pi\) | |||||||
\(308\) | −20.0435 | −1.14208 | ||||||||
\(309\) | −11.3695 | −0.646791 | ||||||||
\(310\) | −1.45847 | −0.0828353 | ||||||||
\(311\) | 24.8634 | 1.40987 | 0.704937 | − | 0.709270i | \(-0.250975\pi\) | ||||
0.704937 | + | 0.709270i | \(0.250975\pi\) | |||||||
\(312\) | −1.92818 | −0.109162 | ||||||||
\(313\) | −26.8861 | −1.51969 | −0.759846 | − | 0.650104i | \(-0.774726\pi\) | ||||
−0.759846 | + | 0.650104i | \(0.774726\pi\) | |||||||
\(314\) | −15.5243 | −0.876088 | ||||||||
\(315\) | 5.30540 | 0.298925 | ||||||||
\(316\) | 8.88482 | 0.499810 | ||||||||
\(317\) | −9.22070 | −0.517886 | −0.258943 | − | 0.965893i | \(-0.583374\pi\) | ||||
−0.258943 | + | 0.965893i | \(0.583374\pi\) | |||||||
\(318\) | −1.00000 | −0.0560772 | ||||||||
\(319\) | −42.3347 | −2.37029 | ||||||||
\(320\) | 1.13903 | 0.0636738 | ||||||||
\(321\) | 8.55575 | 0.477535 | ||||||||
\(322\) | −36.8510 | −2.05362 | ||||||||
\(323\) | 6.94646 | 0.386511 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 7.13928 | 0.396016 | ||||||||
\(326\) | −5.08704 | −0.281745 | ||||||||
\(327\) | 14.9575 | 0.827153 | ||||||||
\(328\) | 8.18877 | 0.452149 | ||||||||
\(329\) | −31.6164 | −1.74307 | ||||||||
\(330\) | −4.90148 | −0.269818 | ||||||||
\(331\) | 8.63527 | 0.474638 | 0.237319 | − | 0.971432i | \(-0.423731\pi\) | ||||
0.237319 | + | 0.971432i | \(0.423731\pi\) | |||||||
\(332\) | −10.8297 | −0.594355 | ||||||||
\(333\) | 0.818562 | 0.0448569 | ||||||||
\(334\) | −12.5322 | −0.685733 | ||||||||
\(335\) | 15.0024 | 0.819669 | ||||||||
\(336\) | −4.65781 | −0.254105 | ||||||||
\(337\) | 7.80648 | 0.425246 | 0.212623 | − | 0.977134i | \(-0.431799\pi\) | ||||
0.212623 | + | 0.977134i | \(0.431799\pi\) | |||||||
\(338\) | 9.28213 | 0.504881 | ||||||||
\(339\) | 2.53394 | 0.137625 | ||||||||
\(340\) | −7.91224 | −0.429101 | ||||||||
\(341\) | −5.51001 | −0.298384 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 35.8430 | 1.93534 | ||||||||
\(344\) | 10.6577 | 0.574624 | ||||||||
\(345\) | −9.01161 | −0.485169 | ||||||||
\(346\) | 21.4077 | 1.15089 | ||||||||
\(347\) | 21.0070 | 1.12771 | 0.563856 | − | 0.825873i | \(-0.309317\pi\) | ||||
0.563856 | + | 0.825873i | \(0.309317\pi\) | |||||||
\(348\) | −9.83797 | −0.527370 | ||||||||
\(349\) | −4.89268 | −0.261899 | −0.130950 | − | 0.991389i | \(-0.541803\pi\) | ||||
−0.130950 | + | 0.991389i | \(0.541803\pi\) | |||||||
\(350\) | 17.2461 | 0.921840 | ||||||||
\(351\) | 1.92818 | 0.102919 | ||||||||
\(352\) | 4.30320 | 0.229361 | ||||||||
\(353\) | −7.99387 | −0.425471 | −0.212736 | − | 0.977110i | \(-0.568237\pi\) | ||||
−0.212736 | + | 0.977110i | \(0.568237\pi\) | |||||||
\(354\) | −6.44178 | −0.342377 | ||||||||
\(355\) | −0.181969 | −0.00965790 | ||||||||
\(356\) | −7.73787 | −0.410107 | ||||||||
\(357\) | 32.3553 | 1.71242 | ||||||||
\(358\) | 0.147626 | 0.00780230 | ||||||||
\(359\) | −8.97136 | −0.473490 | −0.236745 | − | 0.971572i | \(-0.576081\pi\) | ||||
−0.236745 | + | 0.971572i | \(0.576081\pi\) | |||||||
\(360\) | −1.13903 | −0.0600322 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −19.8585 | −1.04374 | ||||||||
\(363\) | −7.51753 | −0.394568 | ||||||||
\(364\) | −8.98109 | −0.470737 | ||||||||
\(365\) | −16.3454 | −0.855555 | ||||||||
\(366\) | 11.1555 | 0.583107 | ||||||||
\(367\) | −18.0361 | −0.941476 | −0.470738 | − | 0.882273i | \(-0.656012\pi\) | ||||
−0.470738 | + | 0.882273i | \(0.656012\pi\) | |||||||
\(368\) | 7.91164 | 0.412423 | ||||||||
\(369\) | −8.18877 | −0.426290 | ||||||||
\(370\) | −0.932368 | −0.0484715 | ||||||||
\(371\) | −4.65781 | −0.241822 | ||||||||
\(372\) | −1.28044 | −0.0663879 | ||||||||
\(373\) | 8.01853 | 0.415184 | 0.207592 | − | 0.978216i | \(-0.433437\pi\) | ||||
0.207592 | + | 0.978216i | \(0.433437\pi\) | |||||||
\(374\) | −29.8920 | −1.54568 | ||||||||
\(375\) | 9.91254 | 0.511882 | ||||||||
\(376\) | 6.78781 | 0.350055 | ||||||||
\(377\) | −18.9694 | −0.976971 | ||||||||
\(378\) | 4.65781 | 0.239572 | ||||||||
\(379\) | −24.9640 | −1.28232 | −0.641158 | − | 0.767409i | \(-0.721546\pi\) | ||||
−0.641158 | + | 0.767409i | \(0.721546\pi\) | |||||||
\(380\) | −1.13903 | −0.0584311 | ||||||||
\(381\) | 12.5689 | 0.643926 | ||||||||
\(382\) | 1.38890 | 0.0710621 | ||||||||
\(383\) | 20.3392 | 1.03928 | 0.519642 | − | 0.854384i | \(-0.326065\pi\) | ||||
0.519642 | + | 0.854384i | \(0.326065\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −22.8302 | −1.16353 | ||||||||
\(386\) | −2.72902 | −0.138904 | ||||||||
\(387\) | −10.6577 | −0.541761 | ||||||||
\(388\) | −3.07525 | −0.156122 | ||||||||
\(389\) | 0.516054 | 0.0261650 | 0.0130825 | − | 0.999914i | \(-0.495836\pi\) | ||||
0.0130825 | + | 0.999914i | \(0.495836\pi\) | |||||||
\(390\) | −2.19626 | −0.111212 | ||||||||
\(391\) | −54.9579 | −2.77934 | ||||||||
\(392\) | −14.6952 | −0.742221 | ||||||||
\(393\) | 12.4130 | 0.626153 | ||||||||
\(394\) | −2.54933 | −0.128434 | ||||||||
\(395\) | 10.1201 | 0.509197 | ||||||||
\(396\) | −4.30320 | −0.216244 | ||||||||
\(397\) | 9.51624 | 0.477606 | 0.238803 | − | 0.971068i | \(-0.423245\pi\) | ||||
0.238803 | + | 0.971068i | \(0.423245\pi\) | |||||||
\(398\) | 8.95183 | 0.448715 | ||||||||
\(399\) | 4.65781 | 0.233182 | ||||||||
\(400\) | −3.70261 | −0.185130 | ||||||||
\(401\) | −12.6804 | −0.633228 | −0.316614 | − | 0.948554i | \(-0.602546\pi\) | ||||
−0.316614 | + | 0.948554i | \(0.602546\pi\) | |||||||
\(402\) | 13.1712 | 0.656919 | ||||||||
\(403\) | −2.46892 | −0.122986 | ||||||||
\(404\) | −10.0253 | −0.498778 | ||||||||
\(405\) | 1.13903 | 0.0565989 | ||||||||
\(406\) | −45.8234 | −2.27418 | ||||||||
\(407\) | −3.52244 | −0.174601 | ||||||||
\(408\) | −6.94646 | −0.343901 | ||||||||
\(409\) | 33.2874 | 1.64596 | 0.822978 | − | 0.568073i | \(-0.192311\pi\) | ||||
0.822978 | + | 0.568073i | \(0.192311\pi\) | |||||||
\(410\) | 9.32727 | 0.460641 | ||||||||
\(411\) | −2.04158 | −0.100704 | ||||||||
\(412\) | 11.3695 | 0.560137 | ||||||||
\(413\) | −30.0046 | −1.47643 | ||||||||
\(414\) | −7.91164 | −0.388836 | ||||||||
\(415\) | −12.3353 | −0.605517 | ||||||||
\(416\) | 1.92818 | 0.0945367 | ||||||||
\(417\) | 16.4948 | 0.807755 | ||||||||
\(418\) | −4.30320 | −0.210476 | ||||||||
\(419\) | −24.4159 | −1.19280 | −0.596398 | − | 0.802689i | \(-0.703402\pi\) | ||||
−0.596398 | + | 0.802689i | \(0.703402\pi\) | |||||||
\(420\) | −5.30540 | −0.258877 | ||||||||
\(421\) | 37.3518 | 1.82042 | 0.910208 | − | 0.414152i | \(-0.135922\pi\) | ||||
0.910208 | + | 0.414152i | \(0.135922\pi\) | |||||||
\(422\) | −16.0300 | −0.780328 | ||||||||
\(423\) | −6.78781 | −0.330035 | ||||||||
\(424\) | 1.00000 | 0.0485643 | ||||||||
\(425\) | 25.7200 | 1.24760 | ||||||||
\(426\) | −0.159757 | −0.00774027 | ||||||||
\(427\) | 51.9602 | 2.51453 | ||||||||
\(428\) | −8.55575 | −0.413558 | ||||||||
\(429\) | −8.29733 | −0.400599 | ||||||||
\(430\) | 12.1394 | 0.585416 | ||||||||
\(431\) | 12.2602 | 0.590551 | 0.295276 | − | 0.955412i | \(-0.404589\pi\) | ||||
0.295276 | + | 0.955412i | \(0.404589\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −31.3015 | −1.50425 | −0.752127 | − | 0.659019i | \(-0.770972\pi\) | ||||
−0.752127 | + | 0.659019i | \(0.770972\pi\) | |||||||
\(434\) | −5.96407 | −0.286285 | ||||||||
\(435\) | −11.2058 | −0.537275 | ||||||||
\(436\) | −14.9575 | −0.716335 | ||||||||
\(437\) | −7.91164 | −0.378465 | ||||||||
\(438\) | −14.3502 | −0.685680 | ||||||||
\(439\) | −25.5266 | −1.21832 | −0.609159 | − | 0.793048i | \(-0.708493\pi\) | ||||
−0.609159 | + | 0.793048i | \(0.708493\pi\) | |||||||
\(440\) | 4.90148 | 0.233669 | ||||||||
\(441\) | 14.6952 | 0.699773 | ||||||||
\(442\) | −13.3940 | −0.637088 | ||||||||
\(443\) | 0.0728399 | 0.00346073 | 0.00173036 | − | 0.999999i | \(-0.499449\pi\) | ||||
0.00173036 | + | 0.999999i | \(0.499449\pi\) | |||||||
\(444\) | −0.818562 | −0.0388473 | ||||||||
\(445\) | −8.81368 | −0.417809 | ||||||||
\(446\) | −15.7753 | −0.746981 | ||||||||
\(447\) | −3.48835 | −0.164993 | ||||||||
\(448\) | 4.65781 | 0.220061 | ||||||||
\(449\) | 14.6323 | 0.690539 | 0.345270 | − | 0.938504i | \(-0.387787\pi\) | ||||
0.345270 | + | 0.938504i | \(0.387787\pi\) | |||||||
\(450\) | 3.70261 | 0.174543 | ||||||||
\(451\) | 35.2379 | 1.65929 | ||||||||
\(452\) | −2.53394 | −0.119186 | ||||||||
\(453\) | −12.2747 | −0.576717 | ||||||||
\(454\) | 4.98013 | 0.233729 | ||||||||
\(455\) | −10.2297 | −0.479578 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 20.0024 | 0.935675 | 0.467838 | − | 0.883814i | \(-0.345033\pi\) | ||||
0.467838 | + | 0.883814i | \(0.345033\pi\) | |||||||
\(458\) | −0.629002 | −0.0293913 | ||||||||
\(459\) | 6.94646 | 0.324233 | ||||||||
\(460\) | 9.01161 | 0.420169 | ||||||||
\(461\) | 17.7467 | 0.826547 | 0.413273 | − | 0.910607i | \(-0.364385\pi\) | ||||
0.413273 | + | 0.910607i | \(0.364385\pi\) | |||||||
\(462\) | −20.0435 | −0.932508 | ||||||||
\(463\) | −4.84490 | −0.225162 | −0.112581 | − | 0.993643i | \(-0.535912\pi\) | ||||
−0.112581 | + | 0.993643i | \(0.535912\pi\) | |||||||
\(464\) | 9.83797 | 0.456716 | ||||||||
\(465\) | −1.45847 | −0.0676348 | ||||||||
\(466\) | −14.0856 | −0.652503 | ||||||||
\(467\) | −27.1798 | −1.25773 | −0.628866 | − | 0.777513i | \(-0.716481\pi\) | ||||
−0.628866 | + | 0.777513i | \(0.716481\pi\) | |||||||
\(468\) | −1.92818 | −0.0891300 | ||||||||
\(469\) | 61.3489 | 2.83283 | ||||||||
\(470\) | 7.73154 | 0.356629 | ||||||||
\(471\) | −15.5243 | −0.715323 | ||||||||
\(472\) | 6.44178 | 0.296507 | ||||||||
\(473\) | 45.8622 | 2.10874 | ||||||||
\(474\) | 8.88482 | 0.408093 | ||||||||
\(475\) | 3.70261 | 0.169887 | ||||||||
\(476\) | −32.3553 | −1.48300 | ||||||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | 22.0582 | 1.00892 | ||||||||
\(479\) | −32.4135 | −1.48101 | −0.740506 | − | 0.672049i | \(-0.765414\pi\) | ||||
−0.740506 | + | 0.672049i | \(0.765414\pi\) | |||||||
\(480\) | 1.13903 | 0.0519894 | ||||||||
\(481\) | −1.57833 | −0.0719658 | ||||||||
\(482\) | 9.89881 | 0.450878 | ||||||||
\(483\) | −36.8510 | −1.67678 | ||||||||
\(484\) | 7.51753 | 0.341706 | ||||||||
\(485\) | −3.50281 | −0.159054 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 10.7839 | 0.488665 | 0.244332 | − | 0.969692i | \(-0.421431\pi\) | ||||
0.244332 | + | 0.969692i | \(0.421431\pi\) | |||||||
\(488\) | −11.1555 | −0.504986 | ||||||||
\(489\) | −5.08704 | −0.230044 | ||||||||
\(490\) | −16.7383 | −0.756161 | ||||||||
\(491\) | −9.33661 | −0.421355 | −0.210678 | − | 0.977556i | \(-0.567567\pi\) | ||||
−0.210678 | + | 0.977556i | \(0.567567\pi\) | |||||||
\(492\) | 8.18877 | 0.369178 | ||||||||
\(493\) | −68.3390 | −3.07784 | ||||||||
\(494\) | −1.92818 | −0.0867528 | ||||||||
\(495\) | −4.90148 | −0.220305 | ||||||||
\(496\) | 1.28044 | 0.0574936 | ||||||||
\(497\) | −0.744120 | −0.0333784 | ||||||||
\(498\) | −10.8297 | −0.485289 | ||||||||
\(499\) | −28.6119 | −1.28085 | −0.640423 | − | 0.768022i | \(-0.721241\pi\) | ||||
−0.640423 | + | 0.768022i | \(0.721241\pi\) | |||||||
\(500\) | −9.91254 | −0.443302 | ||||||||
\(501\) | −12.5322 | −0.559898 | ||||||||
\(502\) | 11.2298 | 0.501210 | ||||||||
\(503\) | −30.7278 | −1.37008 | −0.685042 | − | 0.728504i | \(-0.740216\pi\) | ||||
−0.685042 | + | 0.728504i | \(0.740216\pi\) | |||||||
\(504\) | −4.65781 | −0.207476 | ||||||||
\(505\) | −11.4191 | −0.508145 | ||||||||
\(506\) | 34.0454 | 1.51350 | ||||||||
\(507\) | 9.28213 | 0.412234 | ||||||||
\(508\) | −12.5689 | −0.557656 | ||||||||
\(509\) | −3.37076 | −0.149406 | −0.0747031 | − | 0.997206i | \(-0.523801\pi\) | ||||
−0.0747031 | + | 0.997206i | \(0.523801\pi\) | |||||||
\(510\) | −7.91224 | −0.350360 | ||||||||
\(511\) | −66.8406 | −2.95686 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −5.75460 | −0.253825 | ||||||||
\(515\) | 12.9503 | 0.570657 | ||||||||
\(516\) | 10.6577 | 0.469179 | ||||||||
\(517\) | 29.2093 | 1.28462 | ||||||||
\(518\) | −3.81271 | −0.167521 | ||||||||
\(519\) | 21.4077 | 0.939695 | ||||||||
\(520\) | 2.19626 | 0.0963122 | ||||||||
\(521\) | 11.1178 | 0.487079 | 0.243540 | − | 0.969891i | \(-0.421691\pi\) | ||||
0.243540 | + | 0.969891i | \(0.421691\pi\) | |||||||
\(522\) | −9.83797 | −0.430596 | ||||||||
\(523\) | −35.8578 | −1.56795 | −0.783977 | − | 0.620790i | \(-0.786812\pi\) | ||||
−0.783977 | + | 0.620790i | \(0.786812\pi\) | |||||||
\(524\) | −12.4130 | −0.542265 | ||||||||
\(525\) | 17.2461 | 0.752680 | ||||||||
\(526\) | −14.0528 | −0.612730 | ||||||||
\(527\) | −8.89455 | −0.387453 | ||||||||
\(528\) | 4.30320 | 0.187273 | ||||||||
\(529\) | 39.5941 | 1.72148 | ||||||||
\(530\) | 1.13903 | 0.0494764 | ||||||||
\(531\) | −6.44178 | −0.279549 | ||||||||
\(532\) | −4.65781 | −0.201942 | ||||||||
\(533\) | 15.7894 | 0.683915 | ||||||||
\(534\) | −7.73787 | −0.334851 | ||||||||
\(535\) | −9.74527 | −0.421325 | ||||||||
\(536\) | −13.1712 | −0.568909 | ||||||||
\(537\) | 0.147626 | 0.00637055 | ||||||||
\(538\) | 11.9464 | 0.515044 | ||||||||
\(539\) | −63.2365 | −2.72379 | ||||||||
\(540\) | −1.13903 | −0.0490161 | ||||||||
\(541\) | 23.8571 | 1.02570 | 0.512849 | − | 0.858479i | \(-0.328590\pi\) | ||||
0.512849 | + | 0.858479i | \(0.328590\pi\) | |||||||
\(542\) | 17.8176 | 0.765332 | ||||||||
\(543\) | −19.8585 | −0.852208 | ||||||||
\(544\) | 6.94646 | 0.297827 | ||||||||
\(545\) | −17.0371 | −0.729788 | ||||||||
\(546\) | −8.98109 | −0.384355 | ||||||||
\(547\) | −28.7101 | −1.22756 | −0.613779 | − | 0.789478i | \(-0.710351\pi\) | ||||
−0.613779 | + | 0.789478i | \(0.710351\pi\) | |||||||
\(548\) | 2.04158 | 0.0872119 | ||||||||
\(549\) | 11.1555 | 0.476105 | ||||||||
\(550\) | −15.9331 | −0.679388 | ||||||||
\(551\) | −9.83797 | −0.419112 | ||||||||
\(552\) | 7.91164 | 0.336742 | ||||||||
\(553\) | 41.3838 | 1.75982 | ||||||||
\(554\) | 25.1299 | 1.06767 | ||||||||
\(555\) | −0.932368 | −0.0395768 | ||||||||
\(556\) | −16.4948 | −0.699536 | ||||||||
\(557\) | −35.8573 | −1.51932 | −0.759662 | − | 0.650318i | \(-0.774635\pi\) | ||||
−0.759662 | + | 0.650318i | \(0.774635\pi\) | |||||||
\(558\) | −1.28044 | −0.0542055 | ||||||||
\(559\) | 20.5499 | 0.869169 | ||||||||
\(560\) | 5.30540 | 0.224194 | ||||||||
\(561\) | −29.8920 | −1.26204 | ||||||||
\(562\) | −1.06382 | −0.0448746 | ||||||||
\(563\) | −34.1720 | −1.44018 | −0.720090 | − | 0.693881i | \(-0.755899\pi\) | ||||
−0.720090 | + | 0.693881i | \(0.755899\pi\) | |||||||
\(564\) | 6.78781 | 0.285819 | ||||||||
\(565\) | −2.88624 | −0.121425 | ||||||||
\(566\) | 7.83023 | 0.329129 | ||||||||
\(567\) | 4.65781 | 0.195610 | ||||||||
\(568\) | 0.159757 | 0.00670327 | ||||||||
\(569\) | −19.2906 | −0.808704 | −0.404352 | − | 0.914603i | \(-0.632503\pi\) | ||||
−0.404352 | + | 0.914603i | \(0.632503\pi\) | |||||||
\(570\) | −1.13903 | −0.0477088 | ||||||||
\(571\) | −23.1667 | −0.969496 | −0.484748 | − | 0.874654i | \(-0.661089\pi\) | ||||
−0.484748 | + | 0.874654i | \(0.661089\pi\) | |||||||
\(572\) | 8.29733 | 0.346929 | ||||||||
\(573\) | 1.38890 | 0.0580220 | ||||||||
\(574\) | 38.1418 | 1.59201 | ||||||||
\(575\) | −29.2937 | −1.22163 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 6.17964 | 0.257262 | 0.128631 | − | 0.991693i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991693i | \(0.458942\pi\) | |||||||
\(578\) | −31.2533 | −1.29997 | ||||||||
\(579\) | −2.72902 | −0.113414 | ||||||||
\(580\) | 11.2058 | 0.465294 | ||||||||
\(581\) | −50.4425 | −2.09271 | ||||||||
\(582\) | −3.07525 | −0.127473 | ||||||||
\(583\) | 4.30320 | 0.178220 | ||||||||
\(584\) | 14.3502 | 0.593816 | ||||||||
\(585\) | −2.19626 | −0.0908040 | ||||||||
\(586\) | 11.6142 | 0.479776 | ||||||||
\(587\) | −34.0495 | −1.40538 | −0.702688 | − | 0.711499i | \(-0.748017\pi\) | ||||
−0.702688 | + | 0.711499i | \(0.748017\pi\) | |||||||
\(588\) | −14.6952 | −0.606021 | ||||||||
\(589\) | −1.28044 | −0.0527598 | ||||||||
\(590\) | 7.33739 | 0.302075 | ||||||||
\(591\) | −2.54933 | −0.104866 | ||||||||
\(592\) | 0.818562 | 0.0336427 | ||||||||
\(593\) | 41.7749 | 1.71549 | 0.857745 | − | 0.514076i | \(-0.171865\pi\) | ||||
0.857745 | + | 0.514076i | \(0.171865\pi\) | |||||||
\(594\) | −4.30320 | −0.176562 | ||||||||
\(595\) | −36.8537 | −1.51086 | ||||||||
\(596\) | 3.48835 | 0.142888 | ||||||||
\(597\) | 8.95183 | 0.366374 | ||||||||
\(598\) | 15.2551 | 0.623826 | ||||||||
\(599\) | −4.22921 | −0.172801 | −0.0864005 | − | 0.996260i | \(-0.527536\pi\) | ||||
−0.0864005 | + | 0.996260i | \(0.527536\pi\) | |||||||
\(600\) | −3.70261 | −0.151158 | ||||||||
\(601\) | −31.3288 | −1.27793 | −0.638965 | − | 0.769236i | \(-0.720637\pi\) | ||||
−0.638965 | + | 0.769236i | \(0.720637\pi\) | |||||||
\(602\) | 49.6415 | 2.02324 | ||||||||
\(603\) | 13.1712 | 0.536372 | ||||||||
\(604\) | 12.2747 | 0.499452 | ||||||||
\(605\) | 8.56270 | 0.348123 | ||||||||
\(606\) | −10.0253 | −0.407250 | ||||||||
\(607\) | 32.6789 | 1.32639 | 0.663197 | − | 0.748445i | \(-0.269199\pi\) | ||||
0.663197 | + | 0.748445i | \(0.269199\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −45.8234 | −1.85686 | ||||||||
\(610\) | −12.7065 | −0.514470 | ||||||||
\(611\) | 13.0881 | 0.529488 | ||||||||
\(612\) | −6.94646 | −0.280794 | ||||||||
\(613\) | 21.6424 | 0.874128 | 0.437064 | − | 0.899430i | \(-0.356018\pi\) | ||||
0.437064 | + | 0.899430i | \(0.356018\pi\) | |||||||
\(614\) | 28.7680 | 1.16098 | ||||||||
\(615\) | 9.32727 | 0.376112 | ||||||||
\(616\) | 20.0435 | 0.807576 | ||||||||
\(617\) | 39.0830 | 1.57342 | 0.786710 | − | 0.617322i | \(-0.211783\pi\) | ||||
0.786710 | + | 0.617322i | \(0.211783\pi\) | |||||||
\(618\) | 11.3695 | 0.457350 | ||||||||
\(619\) | 29.5880 | 1.18924 | 0.594620 | − | 0.804007i | \(-0.297302\pi\) | ||||
0.594620 | + | 0.804007i | \(0.297302\pi\) | |||||||
\(620\) | 1.45847 | 0.0585734 | ||||||||
\(621\) | −7.91164 | −0.317483 | ||||||||
\(622\) | −24.8634 | −0.996931 | ||||||||
\(623\) | −36.0416 | −1.44398 | ||||||||
\(624\) | 1.92818 | 0.0771889 | ||||||||
\(625\) | 7.22233 | 0.288893 | ||||||||
\(626\) | 26.8861 | 1.07458 | ||||||||
\(627\) | −4.30320 | −0.171853 | ||||||||
\(628\) | 15.5243 | 0.619488 | ||||||||
\(629\) | −5.68611 | −0.226720 | ||||||||
\(630\) | −5.30540 | −0.211372 | ||||||||
\(631\) | −20.1558 | −0.802390 | −0.401195 | − | 0.915993i | \(-0.631405\pi\) | ||||
−0.401195 | + | 0.915993i | \(0.631405\pi\) | |||||||
\(632\) | −8.88482 | −0.353419 | ||||||||
\(633\) | −16.0300 | −0.637135 | ||||||||
\(634\) | 9.22070 | 0.366201 | ||||||||
\(635\) | −14.3164 | −0.568130 | ||||||||
\(636\) | 1.00000 | 0.0396526 | ||||||||
\(637\) | −28.3350 | −1.12267 | ||||||||
\(638\) | 42.3347 | 1.67605 | ||||||||
\(639\) | −0.159757 | −0.00631990 | ||||||||
\(640\) | −1.13903 | −0.0450242 | ||||||||
\(641\) | 13.9222 | 0.549893 | 0.274947 | − | 0.961460i | \(-0.411340\pi\) | ||||
0.274947 | + | 0.961460i | \(0.411340\pi\) | |||||||
\(642\) | −8.55575 | −0.337668 | ||||||||
\(643\) | −32.4486 | −1.27965 | −0.639823 | − | 0.768522i | \(-0.720992\pi\) | ||||
−0.639823 | + | 0.768522i | \(0.720992\pi\) | |||||||
\(644\) | 36.8510 | 1.45213 | ||||||||
\(645\) | 12.1394 | 0.477990 | ||||||||
\(646\) | −6.94646 | −0.273305 | ||||||||
\(647\) | 23.4019 | 0.920025 | 0.460012 | − | 0.887913i | \(-0.347845\pi\) | ||||
0.460012 | + | 0.887913i | \(0.347845\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 27.7203 | 1.08812 | ||||||||
\(650\) | −7.13928 | −0.280026 | ||||||||
\(651\) | −5.96407 | −0.233750 | ||||||||
\(652\) | 5.08704 | 0.199224 | ||||||||
\(653\) | 8.44705 | 0.330559 | 0.165279 | − | 0.986247i | \(-0.447147\pi\) | ||||
0.165279 | + | 0.986247i | \(0.447147\pi\) | |||||||
\(654\) | −14.9575 | −0.584885 | ||||||||
\(655\) | −14.1388 | −0.552449 | ||||||||
\(656\) | −8.18877 | −0.319718 | ||||||||
\(657\) | −14.3502 | −0.559855 | ||||||||
\(658\) | 31.6164 | 1.23253 | ||||||||
\(659\) | 36.8682 | 1.43618 | 0.718090 | − | 0.695950i | \(-0.245017\pi\) | ||||
0.718090 | + | 0.695950i | \(0.245017\pi\) | |||||||
\(660\) | 4.90148 | 0.190790 | ||||||||
\(661\) | −5.28919 | −0.205725 | −0.102863 | − | 0.994696i | \(-0.532800\pi\) | ||||
−0.102863 | + | 0.994696i | \(0.532800\pi\) | |||||||
\(662\) | −8.63527 | −0.335619 | ||||||||
\(663\) | −13.3940 | −0.520180 | ||||||||
\(664\) | 10.8297 | 0.420272 | ||||||||
\(665\) | −5.30540 | −0.205734 | ||||||||
\(666\) | −0.818562 | −0.0317186 | ||||||||
\(667\) | 77.8345 | 3.01376 | ||||||||
\(668\) | 12.5322 | 0.484886 | ||||||||
\(669\) | −15.7753 | −0.609907 | ||||||||
\(670\) | −15.0024 | −0.579593 | ||||||||
\(671\) | −48.0043 | −1.85319 | ||||||||
\(672\) | 4.65781 | 0.179679 | ||||||||
\(673\) | 7.62613 | 0.293966 | 0.146983 | − | 0.989139i | \(-0.453044\pi\) | ||||
0.146983 | + | 0.989139i | \(0.453044\pi\) | |||||||
\(674\) | −7.80648 | −0.300695 | ||||||||
\(675\) | 3.70261 | 0.142513 | ||||||||
\(676\) | −9.28213 | −0.357005 | ||||||||
\(677\) | −23.6354 | −0.908383 | −0.454191 | − | 0.890904i | \(-0.650072\pi\) | ||||
−0.454191 | + | 0.890904i | \(0.650072\pi\) | |||||||
\(678\) | −2.53394 | −0.0973153 | ||||||||
\(679\) | −14.3239 | −0.549703 | ||||||||
\(680\) | 7.91224 | 0.303420 | ||||||||
\(681\) | 4.98013 | 0.190839 | ||||||||
\(682\) | 5.51001 | 0.210989 | ||||||||
\(683\) | 45.0734 | 1.72468 | 0.862342 | − | 0.506326i | \(-0.168997\pi\) | ||||
0.862342 | + | 0.506326i | \(0.168997\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 2.32542 | 0.0888498 | ||||||||
\(686\) | −35.8430 | −1.36849 | ||||||||
\(687\) | −0.629002 | −0.0239979 | ||||||||
\(688\) | −10.6577 | −0.406321 | ||||||||
\(689\) | 1.92818 | 0.0734577 | ||||||||
\(690\) | 9.01161 | 0.343066 | ||||||||
\(691\) | 0.553888 | 0.0210709 | 0.0105355 | − | 0.999945i | \(-0.496646\pi\) | ||||
0.0105355 | + | 0.999945i | \(0.496646\pi\) | |||||||
\(692\) | −21.4077 | −0.813800 | ||||||||
\(693\) | −20.0435 | −0.761390 | ||||||||
\(694\) | −21.0070 | −0.797413 | ||||||||
\(695\) | −18.7881 | −0.712674 | ||||||||
\(696\) | 9.83797 | 0.372907 | ||||||||
\(697\) | 56.8829 | 2.15460 | ||||||||
\(698\) | 4.89268 | 0.185191 | ||||||||
\(699\) | −14.0856 | −0.532766 | ||||||||
\(700\) | −17.2461 | −0.651840 | ||||||||
\(701\) | −46.2402 | −1.74647 | −0.873233 | − | 0.487302i | \(-0.837981\pi\) | ||||
−0.873233 | + | 0.487302i | \(0.837981\pi\) | |||||||
\(702\) | −1.92818 | −0.0727744 | ||||||||
\(703\) | −0.818562 | −0.0308727 | ||||||||
\(704\) | −4.30320 | −0.162183 | ||||||||
\(705\) | 7.73154 | 0.291186 | ||||||||
\(706\) | 7.99387 | 0.300853 | ||||||||
\(707\) | −46.6960 | −1.75619 | ||||||||
\(708\) | 6.44178 | 0.242097 | ||||||||
\(709\) | 50.6279 | 1.90137 | 0.950685 | − | 0.310159i | \(-0.100382\pi\) | ||||
0.950685 | + | 0.310159i | \(0.100382\pi\) | |||||||
\(710\) | 0.181969 | 0.00682916 | ||||||||
\(711\) | 8.88482 | 0.333207 | ||||||||
\(712\) | 7.73787 | 0.289989 | ||||||||
\(713\) | 10.1304 | 0.379387 | ||||||||
\(714\) | −32.3553 | −1.21087 | ||||||||
\(715\) | 9.45093 | 0.353445 | ||||||||
\(716\) | −0.147626 | −0.00551706 | ||||||||
\(717\) | 22.0582 | 0.823778 | ||||||||
\(718\) | 8.97136 | 0.334808 | ||||||||
\(719\) | −8.33996 | −0.311028 | −0.155514 | − | 0.987834i | \(-0.549703\pi\) | ||||
−0.155514 | + | 0.987834i | \(0.549703\pi\) | |||||||
\(720\) | 1.13903 | 0.0424492 | ||||||||
\(721\) | 52.9572 | 1.97223 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 9.89881 | 0.368141 | ||||||||
\(724\) | 19.8585 | 0.738034 | ||||||||
\(725\) | −36.4261 | −1.35283 | ||||||||
\(726\) | 7.51753 | 0.279002 | ||||||||
\(727\) | 19.3224 | 0.716627 | 0.358314 | − | 0.933601i | \(-0.383352\pi\) | ||||
0.358314 | + | 0.933601i | \(0.383352\pi\) | |||||||
\(728\) | 8.98109 | 0.332861 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 16.3454 | 0.604969 | ||||||||
\(731\) | 74.0332 | 2.73822 | ||||||||
\(732\) | −11.1555 | −0.412319 | ||||||||
\(733\) | 49.0113 | 1.81027 | 0.905137 | − | 0.425120i | \(-0.139768\pi\) | ||||
0.905137 | + | 0.425120i | \(0.139768\pi\) | |||||||
\(734\) | 18.0361 | 0.665724 | ||||||||
\(735\) | −16.7383 | −0.617403 | ||||||||
\(736\) | −7.91164 | −0.291627 | ||||||||
\(737\) | −56.6782 | −2.08777 | ||||||||
\(738\) | 8.18877 | 0.301433 | ||||||||
\(739\) | 26.8178 | 0.986509 | 0.493255 | − | 0.869885i | \(-0.335807\pi\) | ||||
0.493255 | + | 0.869885i | \(0.335807\pi\) | |||||||
\(740\) | 0.932368 | 0.0342745 | ||||||||
\(741\) | −1.92818 | −0.0708334 | ||||||||
\(742\) | 4.65781 | 0.170994 | ||||||||
\(743\) | −9.16505 | −0.336233 | −0.168117 | − | 0.985767i | \(-0.553769\pi\) | ||||
−0.168117 | + | 0.985767i | \(0.553769\pi\) | |||||||
\(744\) | 1.28044 | 0.0469434 | ||||||||
\(745\) | 3.97334 | 0.145572 | ||||||||
\(746\) | −8.01853 | −0.293579 | ||||||||
\(747\) | −10.8297 | −0.396236 | ||||||||
\(748\) | 29.8920 | 1.09296 | ||||||||
\(749\) | −39.8511 | −1.45613 | ||||||||
\(750\) | −9.91254 | −0.361955 | ||||||||
\(751\) | 1.03554 | 0.0377872 | 0.0188936 | − | 0.999821i | \(-0.493986\pi\) | ||||
0.0188936 | + | 0.999821i | \(0.493986\pi\) | |||||||
\(752\) | −6.78781 | −0.247526 | ||||||||
\(753\) | 11.2298 | 0.409236 | ||||||||
\(754\) | 18.9694 | 0.690823 | ||||||||
\(755\) | 13.9813 | 0.508832 | ||||||||
\(756\) | −4.65781 | −0.169403 | ||||||||
\(757\) | −52.8901 | −1.92232 | −0.961161 | − | 0.275989i | \(-0.910995\pi\) | ||||
−0.961161 | + | 0.275989i | \(0.910995\pi\) | |||||||
\(758\) | 24.9640 | 0.906734 | ||||||||
\(759\) | 34.0454 | 1.23577 | ||||||||
\(760\) | 1.13903 | 0.0413170 | ||||||||
\(761\) | −3.57290 | −0.129517 | −0.0647587 | − | 0.997901i | \(-0.520628\pi\) | ||||
−0.0647587 | + | 0.997901i | \(0.520628\pi\) | |||||||
\(762\) | −12.5689 | −0.455324 | ||||||||
\(763\) | −69.6693 | −2.52220 | ||||||||
\(764\) | −1.38890 | −0.0502485 | ||||||||
\(765\) | −7.91224 | −0.286068 | ||||||||
\(766\) | −20.3392 | −0.734885 | ||||||||
\(767\) | 12.4209 | 0.448492 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −8.02930 | −0.289544 | −0.144772 | − | 0.989465i | \(-0.546245\pi\) | ||||
−0.144772 | + | 0.989465i | \(0.546245\pi\) | |||||||
\(770\) | 22.8302 | 0.822743 | ||||||||
\(771\) | −5.75460 | −0.207247 | ||||||||
\(772\) | 2.72902 | 0.0982197 | ||||||||
\(773\) | −29.3074 | −1.05411 | −0.527057 | − | 0.849830i | \(-0.676705\pi\) | ||||
−0.527057 | + | 0.849830i | \(0.676705\pi\) | |||||||
\(774\) | 10.6577 | 0.383083 | ||||||||
\(775\) | −4.74098 | −0.170301 | ||||||||
\(776\) | 3.07525 | 0.110395 | ||||||||
\(777\) | −3.81271 | −0.136780 | ||||||||
\(778\) | −0.516054 | −0.0185014 | ||||||||
\(779\) | 8.18877 | 0.293393 | ||||||||
\(780\) | 2.19626 | 0.0786386 | ||||||||
\(781\) | 0.687468 | 0.0245995 | ||||||||
\(782\) | 54.9579 | 1.96529 | ||||||||
\(783\) | −9.83797 | −0.351580 | ||||||||
\(784\) | 14.6952 | 0.524830 | ||||||||
\(785\) | 17.6827 | 0.631122 | ||||||||
\(786\) | −12.4130 | −0.442757 | ||||||||
\(787\) | −39.8830 | −1.42168 | −0.710838 | − | 0.703355i | \(-0.751684\pi\) | ||||
−0.710838 | + | 0.703355i | \(0.751684\pi\) | |||||||
\(788\) | 2.54933 | 0.0908162 | ||||||||
\(789\) | −14.0528 | −0.500292 | ||||||||
\(790\) | −10.1201 | −0.360057 | ||||||||
\(791\) | −11.8026 | −0.419653 | ||||||||
\(792\) | 4.30320 | 0.152908 | ||||||||
\(793\) | −21.5098 | −0.763835 | ||||||||
\(794\) | −9.51624 | −0.337719 | ||||||||
\(795\) | 1.13903 | 0.0403973 | ||||||||
\(796\) | −8.95183 | −0.317289 | ||||||||
\(797\) | −7.64697 | −0.270870 | −0.135435 | − | 0.990786i | \(-0.543243\pi\) | ||||
−0.135435 | + | 0.990786i | \(0.543243\pi\) | |||||||
\(798\) | −4.65781 | −0.164885 | ||||||||
\(799\) | 47.1513 | 1.66809 | ||||||||
\(800\) | 3.70261 | 0.130907 | ||||||||
\(801\) | −7.73787 | −0.273404 | ||||||||
\(802\) | 12.6804 | 0.447760 | ||||||||
\(803\) | 61.7518 | 2.17918 | ||||||||
\(804\) | −13.1712 | −0.464512 | ||||||||
\(805\) | 41.9744 | 1.47940 | ||||||||
\(806\) | 2.46892 | 0.0869641 | ||||||||
\(807\) | 11.9464 | 0.420532 | ||||||||
\(808\) | 10.0253 | 0.352689 | ||||||||
\(809\) | 28.1399 | 0.989347 | 0.494673 | − | 0.869079i | \(-0.335288\pi\) | ||||
0.494673 | + | 0.869079i | \(0.335288\pi\) | |||||||
\(810\) | −1.13903 | −0.0400215 | ||||||||
\(811\) | −20.5745 | −0.722470 | −0.361235 | − | 0.932475i | \(-0.617645\pi\) | ||||
−0.361235 | + | 0.932475i | \(0.617645\pi\) | |||||||
\(812\) | 45.8234 | 1.60809 | ||||||||
\(813\) | 17.8176 | 0.624891 | ||||||||
\(814\) | 3.52244 | 0.123461 | ||||||||
\(815\) | 5.79429 | 0.202965 | ||||||||
\(816\) | 6.94646 | 0.243175 | ||||||||
\(817\) | 10.6577 | 0.372865 | ||||||||
\(818\) | −33.2874 | −1.16387 | ||||||||
\(819\) | −8.98109 | −0.313825 | ||||||||
\(820\) | −9.32727 | −0.325722 | ||||||||
\(821\) | −17.2291 | −0.601298 | −0.300649 | − | 0.953735i | \(-0.597203\pi\) | ||||
−0.300649 | + | 0.953735i | \(0.597203\pi\) | |||||||
\(822\) | 2.04158 | 0.0712082 | ||||||||
\(823\) | 10.4954 | 0.365848 | 0.182924 | − | 0.983127i | \(-0.441444\pi\) | ||||
0.182924 | + | 0.983127i | \(0.441444\pi\) | |||||||
\(824\) | −11.3695 | −0.396077 | ||||||||
\(825\) | −15.9331 | −0.554718 | ||||||||
\(826\) | 30.0046 | 1.04399 | ||||||||
\(827\) | 17.9759 | 0.625082 | 0.312541 | − | 0.949904i | \(-0.398820\pi\) | ||||
0.312541 | + | 0.949904i | \(0.398820\pi\) | |||||||
\(828\) | 7.91164 | 0.274949 | ||||||||
\(829\) | 19.3940 | 0.673582 | 0.336791 | − | 0.941579i | \(-0.390658\pi\) | ||||
0.336791 | + | 0.941579i | \(0.390658\pi\) | |||||||
\(830\) | 12.3353 | 0.428165 | ||||||||
\(831\) | 25.1299 | 0.871746 | ||||||||
\(832\) | −1.92818 | −0.0668475 | ||||||||
\(833\) | −102.080 | −3.53686 | ||||||||
\(834\) | −16.4948 | −0.571169 | ||||||||
\(835\) | 14.2746 | 0.493993 | ||||||||
\(836\) | 4.30320 | 0.148829 | ||||||||
\(837\) | −1.28044 | −0.0442586 | ||||||||
\(838\) | 24.4159 | 0.843434 | ||||||||
\(839\) | 22.8320 | 0.788249 | 0.394125 | − | 0.919057i | \(-0.371048\pi\) | ||||
0.394125 | + | 0.919057i | \(0.371048\pi\) | |||||||
\(840\) | 5.30540 | 0.183054 | ||||||||
\(841\) | 67.7856 | 2.33744 | ||||||||
\(842\) | −37.3518 | −1.28723 | ||||||||
\(843\) | −1.06382 | −0.0366400 | ||||||||
\(844\) | 16.0300 | 0.551775 | ||||||||
\(845\) | −10.5726 | −0.363710 | ||||||||
\(846\) | 6.78781 | 0.233370 | ||||||||
\(847\) | 35.0153 | 1.20314 | ||||||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | 7.83023 | 0.268733 | ||||||||
\(850\) | −25.7200 | −0.882189 | ||||||||
\(851\) | 6.47617 | 0.222000 | ||||||||
\(852\) | 0.159757 | 0.00547320 | ||||||||
\(853\) | 6.14514 | 0.210405 | 0.105203 | − | 0.994451i | \(-0.466451\pi\) | ||||
0.105203 | + | 0.994451i | \(0.466451\pi\) | |||||||
\(854\) | −51.9602 | −1.77804 | ||||||||
\(855\) | −1.13903 | −0.0389541 | ||||||||
\(856\) | 8.55575 | 0.292429 | ||||||||
\(857\) | 34.8887 | 1.19178 | 0.595888 | − | 0.803068i | \(-0.296800\pi\) | ||||
0.595888 | + | 0.803068i | \(0.296800\pi\) | |||||||
\(858\) | 8.29733 | 0.283266 | ||||||||
\(859\) | −21.8355 | −0.745019 | −0.372509 | − | 0.928028i | \(-0.621503\pi\) | ||||
−0.372509 | + | 0.928028i | \(0.621503\pi\) | |||||||
\(860\) | −12.1394 | −0.413952 | ||||||||
\(861\) | 38.1418 | 1.29987 | ||||||||
\(862\) | −12.2602 | −0.417583 | ||||||||
\(863\) | −42.0704 | −1.43209 | −0.716046 | − | 0.698053i | \(-0.754050\pi\) | ||||
−0.716046 | + | 0.698053i | \(0.754050\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −24.3841 | −0.829083 | ||||||||
\(866\) | 31.3015 | 1.06367 | ||||||||
\(867\) | −31.2533 | −1.06142 | ||||||||
\(868\) | 5.96407 | 0.202434 | ||||||||
\(869\) | −38.2332 | −1.29697 | ||||||||
\(870\) | 11.2058 | 0.379911 | ||||||||
\(871\) | −25.3964 | −0.860524 | ||||||||
\(872\) | 14.9575 | 0.506525 | ||||||||
\(873\) | −3.07525 | −0.104081 | ||||||||
\(874\) | 7.91164 | 0.267615 | ||||||||
\(875\) | −46.1708 | −1.56086 | ||||||||
\(876\) | 14.3502 | 0.484849 | ||||||||
\(877\) | −38.0029 | −1.28327 | −0.641634 | − | 0.767011i | \(-0.721743\pi\) | ||||
−0.641634 | + | 0.767011i | \(0.721743\pi\) | |||||||
\(878\) | 25.5266 | 0.861482 | ||||||||
\(879\) | 11.6142 | 0.391736 | ||||||||
\(880\) | −4.90148 | −0.165229 | ||||||||
\(881\) | 19.0070 | 0.640362 | 0.320181 | − | 0.947356i | \(-0.396256\pi\) | ||||
0.320181 | + | 0.947356i | \(0.396256\pi\) | |||||||
\(882\) | −14.6952 | −0.494814 | ||||||||
\(883\) | −58.6118 | −1.97244 | −0.986222 | − | 0.165426i | \(-0.947100\pi\) | ||||
−0.986222 | + | 0.165426i | \(0.947100\pi\) | |||||||
\(884\) | 13.3940 | 0.450489 | ||||||||
\(885\) | 7.33739 | 0.246644 | ||||||||
\(886\) | −0.0728399 | −0.00244710 | ||||||||
\(887\) | 51.3140 | 1.72296 | 0.861478 | − | 0.507796i | \(-0.169539\pi\) | ||||
0.861478 | + | 0.507796i | \(0.169539\pi\) | |||||||
\(888\) | 0.818562 | 0.0274692 | ||||||||
\(889\) | −58.5438 | −1.96349 | ||||||||
\(890\) | 8.81368 | 0.295435 | ||||||||
\(891\) | −4.30320 | −0.144163 | ||||||||
\(892\) | 15.7753 | 0.528195 | ||||||||
\(893\) | 6.78781 | 0.227146 | ||||||||
\(894\) | 3.48835 | 0.116668 | ||||||||
\(895\) | −0.168151 | −0.00562067 | ||||||||
\(896\) | −4.65781 | −0.155607 | ||||||||
\(897\) | 15.2551 | 0.509352 | ||||||||
\(898\) | −14.6323 | −0.488285 | ||||||||
\(899\) | 12.5970 | 0.420133 | ||||||||
\(900\) | −3.70261 | −0.123420 | ||||||||
\(901\) | 6.94646 | 0.231420 | ||||||||
\(902\) | −35.2379 | −1.17329 | ||||||||
\(903\) | 49.6415 | 1.65197 | ||||||||
\(904\) | 2.53394 | 0.0842775 | ||||||||
\(905\) | 22.6194 | 0.751895 | ||||||||
\(906\) | 12.2747 | 0.407801 | ||||||||
\(907\) | −17.5093 | −0.581387 | −0.290694 | − | 0.956816i | \(-0.593886\pi\) | ||||
−0.290694 | + | 0.956816i | \(0.593886\pi\) | |||||||
\(908\) | −4.98013 | −0.165271 | ||||||||
\(909\) | −10.0253 | −0.332519 | ||||||||
\(910\) | 10.2297 | 0.339113 | ||||||||
\(911\) | −3.07644 | −0.101927 | −0.0509635 | − | 0.998701i | \(-0.516229\pi\) | ||||
−0.0509635 | + | 0.998701i | \(0.516229\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 46.6022 | 1.54231 | ||||||||
\(914\) | −20.0024 | −0.661622 | ||||||||
\(915\) | −12.7065 | −0.420063 | ||||||||
\(916\) | 0.629002 | 0.0207828 | ||||||||
\(917\) | −57.8175 | −1.90930 | ||||||||
\(918\) | −6.94646 | −0.229267 | ||||||||
\(919\) | −25.4540 | −0.839651 | −0.419826 | − | 0.907605i | \(-0.637909\pi\) | ||||
−0.419826 | + | 0.907605i | \(0.637909\pi\) | |||||||
\(920\) | −9.01161 | −0.297104 | ||||||||
\(921\) | 28.7680 | 0.947937 | ||||||||
\(922\) | −17.7467 | −0.584457 | ||||||||
\(923\) | 0.308041 | 0.0101393 | ||||||||
\(924\) | 20.0435 | 0.659383 | ||||||||
\(925\) | −3.03081 | −0.0996526 | ||||||||
\(926\) | 4.84490 | 0.159213 | ||||||||
\(927\) | 11.3695 | 0.373425 | ||||||||
\(928\) | −9.83797 | −0.322947 | ||||||||
\(929\) | 28.6295 | 0.939304 | 0.469652 | − | 0.882852i | \(-0.344379\pi\) | ||||
0.469652 | + | 0.882852i | \(0.344379\pi\) | |||||||
\(930\) | 1.45847 | 0.0478250 | ||||||||
\(931\) | −14.6952 | −0.481617 | ||||||||
\(932\) | 14.0856 | 0.461389 | ||||||||
\(933\) | −24.8634 | −0.813991 | ||||||||
\(934\) | 27.1798 | 0.889351 | ||||||||
\(935\) | 34.0479 | 1.11349 | ||||||||
\(936\) | 1.92818 | 0.0630245 | ||||||||
\(937\) | 26.4693 | 0.864716 | 0.432358 | − | 0.901702i | \(-0.357682\pi\) | ||||
0.432358 | + | 0.901702i | \(0.357682\pi\) | |||||||
\(938\) | −61.3489 | −2.00311 | ||||||||
\(939\) | 26.8861 | 0.877394 | ||||||||
\(940\) | −7.73154 | −0.252175 | ||||||||
\(941\) | 47.0663 | 1.53432 | 0.767159 | − | 0.641457i | \(-0.221670\pi\) | ||||
0.767159 | + | 0.641457i | \(0.221670\pi\) | |||||||
\(942\) | 15.5243 | 0.505810 | ||||||||
\(943\) | −64.7866 | −2.10974 | ||||||||
\(944\) | −6.44178 | −0.209662 | ||||||||
\(945\) | −5.30540 | −0.172585 | ||||||||
\(946\) | −45.8622 | −1.49111 | ||||||||
\(947\) | 6.08820 | 0.197840 | 0.0989199 | − | 0.995095i | \(-0.468461\pi\) | ||||
0.0989199 | + | 0.995095i | \(0.468461\pi\) | |||||||
\(948\) | −8.88482 | −0.288566 | ||||||||
\(949\) | 27.6698 | 0.898199 | ||||||||
\(950\) | −3.70261 | −0.120128 | ||||||||
\(951\) | 9.22070 | 0.299002 | ||||||||
\(952\) | 32.3553 | 1.04864 | ||||||||
\(953\) | 16.9019 | 0.547506 | 0.273753 | − | 0.961800i | \(-0.411735\pi\) | ||||
0.273753 | + | 0.961800i | \(0.411735\pi\) | |||||||
\(954\) | 1.00000 | 0.0323762 | ||||||||
\(955\) | −1.58200 | −0.0511922 | ||||||||
\(956\) | −22.0582 | −0.713412 | ||||||||
\(957\) | 42.3347 | 1.36849 | ||||||||
\(958\) | 32.4135 | 1.04723 | ||||||||
\(959\) | 9.50929 | 0.307071 | ||||||||
\(960\) | −1.13903 | −0.0367621 | ||||||||
\(961\) | −29.3605 | −0.947112 | ||||||||
\(962\) | 1.57833 | 0.0508875 | ||||||||
\(963\) | −8.55575 | −0.275705 | ||||||||
\(964\) | −9.89881 | −0.318819 | ||||||||
\(965\) | 3.10844 | 0.100064 | ||||||||
\(966\) | 36.8510 | 1.18566 | ||||||||
\(967\) | −25.6436 | −0.824641 | −0.412321 | − | 0.911039i | \(-0.635282\pi\) | ||||
−0.412321 | + | 0.911039i | \(0.635282\pi\) | |||||||
\(968\) | −7.51753 | −0.241623 | ||||||||
\(969\) | −6.94646 | −0.223152 | ||||||||
\(970\) | 3.50281 | 0.112468 | ||||||||
\(971\) | −56.2777 | −1.80604 | −0.903018 | − | 0.429602i | \(-0.858654\pi\) | ||||
−0.903018 | + | 0.429602i | \(0.858654\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −76.8298 | −2.46305 | ||||||||
\(974\) | −10.7839 | −0.345538 | ||||||||
\(975\) | −7.13928 | −0.228640 | ||||||||
\(976\) | 11.1555 | 0.357079 | ||||||||
\(977\) | 43.3750 | 1.38769 | 0.693845 | − | 0.720125i | \(-0.255915\pi\) | ||||
0.693845 | + | 0.720125i | \(0.255915\pi\) | |||||||
\(978\) | 5.08704 | 0.162665 | ||||||||
\(979\) | 33.2976 | 1.06420 | ||||||||
\(980\) | 16.7383 | 0.534686 | ||||||||
\(981\) | −14.9575 | −0.477557 | ||||||||
\(982\) | 9.33661 | 0.297943 | ||||||||
\(983\) | 12.3347 | 0.393415 | 0.196707 | − | 0.980462i | \(-0.436975\pi\) | ||||
0.196707 | + | 0.980462i | \(0.436975\pi\) | |||||||
\(984\) | −8.18877 | −0.261048 | ||||||||
\(985\) | 2.90377 | 0.0925219 | ||||||||
\(986\) | 68.3390 | 2.17636 | ||||||||
\(987\) | 31.6164 | 1.00636 | ||||||||
\(988\) | 1.92818 | 0.0613435 | ||||||||
\(989\) | −84.3199 | −2.68122 | ||||||||
\(990\) | 4.90148 | 0.155779 | ||||||||
\(991\) | −28.2911 | −0.898697 | −0.449349 | − | 0.893357i | \(-0.648344\pi\) | ||||
−0.449349 | + | 0.893357i | \(0.648344\pi\) | |||||||
\(992\) | −1.28044 | −0.0406541 | ||||||||
\(993\) | −8.63527 | −0.274032 | ||||||||
\(994\) | 0.744120 | 0.0236021 | ||||||||
\(995\) | −10.1964 | −0.323248 | ||||||||
\(996\) | 10.8297 | 0.343151 | ||||||||
\(997\) | 9.80170 | 0.310423 | 0.155211 | − | 0.987881i | \(-0.450394\pi\) | ||||
0.155211 | + | 0.987881i | \(0.450394\pi\) | |||||||
\(998\) | 28.6119 | 0.905695 | ||||||||
\(999\) | −0.818562 | −0.0258982 |
(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 | 6042.2.a.be.1.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.be.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial |