Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, 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("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.45 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.35796 | 1.66733 | 0.833663 | − | 0.552273i | \(-0.186239\pi\) | ||||
0.833663 | + | 0.552273i | \(0.186239\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.55996 | 1.77998 | ||||||||
\(5\) | 1.43169 | 0.640272 | 0.320136 | − | 0.947372i | \(-0.396271\pi\) | ||||
0.320136 | + | 0.947372i | \(0.396271\pi\) | |||||||
\(6\) | −2.35796 | −0.962631 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.67830 | 1.30048 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.37587 | 1.06754 | ||||||||
\(11\) | −4.36512 | −1.31613 | −0.658066 | − | 0.752960i | \(-0.728625\pi\) | ||||
−0.658066 | + | 0.752960i | \(0.728625\pi\) | |||||||
\(12\) | −3.55996 | −1.02767 | ||||||||
\(13\) | 6.27913 | 1.74152 | 0.870759 | − | 0.491710i | \(-0.163628\pi\) | ||||
0.870759 | + | 0.491710i | \(0.163628\pi\) | |||||||
\(14\) | 2.35796 | 0.630190 | ||||||||
\(15\) | −1.43169 | −0.369661 | ||||||||
\(16\) | 1.55337 | 0.388342 | ||||||||
\(17\) | 3.16581 | 0.767823 | 0.383911 | − | 0.923370i | \(-0.374577\pi\) | ||||
0.383911 | + | 0.923370i | \(0.374577\pi\) | |||||||
\(18\) | 2.35796 | 0.555775 | ||||||||
\(19\) | 2.39131 | 0.548604 | 0.274302 | − | 0.961644i | \(-0.411553\pi\) | ||||
0.274302 | + | 0.961644i | \(0.411553\pi\) | |||||||
\(20\) | 5.09676 | 1.13967 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −10.2927 | −2.19442 | ||||||||
\(23\) | −8.72942 | −1.82021 | −0.910105 | − | 0.414377i | \(-0.863999\pi\) | ||||
−0.910105 | + | 0.414377i | \(0.863999\pi\) | |||||||
\(24\) | −3.67830 | −0.750831 | ||||||||
\(25\) | −2.95026 | −0.590052 | ||||||||
\(26\) | 14.8059 | 2.90368 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 3.55996 | 0.672768 | ||||||||
\(29\) | 8.42255 | 1.56403 | 0.782014 | − | 0.623260i | \(-0.214192\pi\) | ||||
0.782014 | + | 0.623260i | \(0.214192\pi\) | |||||||
\(30\) | −3.37587 | −0.616346 | ||||||||
\(31\) | −3.52801 | −0.633650 | −0.316825 | − | 0.948484i | \(-0.602617\pi\) | ||||
−0.316825 | + | 0.948484i | \(0.602617\pi\) | |||||||
\(32\) | −3.69383 | −0.652984 | ||||||||
\(33\) | 4.36512 | 0.759869 | ||||||||
\(34\) | 7.46485 | 1.28021 | ||||||||
\(35\) | 1.43169 | 0.242000 | ||||||||
\(36\) | 3.55996 | 0.593326 | ||||||||
\(37\) | 9.12536 | 1.50020 | 0.750100 | − | 0.661325i | \(-0.230005\pi\) | ||||
0.750100 | + | 0.661325i | \(0.230005\pi\) | |||||||
\(38\) | 5.63860 | 0.914701 | ||||||||
\(39\) | −6.27913 | −1.00547 | ||||||||
\(40\) | 5.26620 | 0.832659 | ||||||||
\(41\) | 0.844792 | 0.131934 | 0.0659672 | − | 0.997822i | \(-0.478987\pi\) | ||||
0.0659672 | + | 0.997822i | \(0.478987\pi\) | |||||||
\(42\) | −2.35796 | −0.363840 | ||||||||
\(43\) | 10.7642 | 1.64153 | 0.820766 | − | 0.571264i | \(-0.193547\pi\) | ||||
0.820766 | + | 0.571264i | \(0.193547\pi\) | |||||||
\(44\) | −15.5396 | −2.34268 | ||||||||
\(45\) | 1.43169 | 0.213424 | ||||||||
\(46\) | −20.5836 | −3.03489 | ||||||||
\(47\) | 10.3940 | 1.51612 | 0.758059 | − | 0.652186i | \(-0.226148\pi\) | ||||
0.758059 | + | 0.652186i | \(0.226148\pi\) | |||||||
\(48\) | −1.55337 | −0.224210 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −6.95658 | −0.983809 | ||||||||
\(51\) | −3.16581 | −0.443303 | ||||||||
\(52\) | 22.3534 | 3.09986 | ||||||||
\(53\) | −6.07467 | −0.834421 | −0.417210 | − | 0.908810i | \(-0.636992\pi\) | ||||
−0.417210 | + | 0.908810i | \(0.636992\pi\) | |||||||
\(54\) | −2.35796 | −0.320877 | ||||||||
\(55\) | −6.24950 | −0.842682 | ||||||||
\(56\) | 3.67830 | 0.491534 | ||||||||
\(57\) | −2.39131 | −0.316736 | ||||||||
\(58\) | 19.8600 | 2.60775 | ||||||||
\(59\) | 11.3611 | 1.47909 | 0.739547 | − | 0.673105i | \(-0.235040\pi\) | ||||
0.739547 | + | 0.673105i | \(0.235040\pi\) | |||||||
\(60\) | −5.09676 | −0.657989 | ||||||||
\(61\) | −3.22662 | −0.413126 | −0.206563 | − | 0.978433i | \(-0.566228\pi\) | ||||
−0.206563 | + | 0.978433i | \(0.566228\pi\) | |||||||
\(62\) | −8.31889 | −1.05650 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | −11.8166 | −1.47708 | ||||||||
\(65\) | 8.98978 | 1.11505 | ||||||||
\(66\) | 10.2927 | 1.26695 | ||||||||
\(67\) | 0.00565557 | 0.000690938 0 | 0.000345469 | − | 1.00000i | \(-0.499890\pi\) | ||||
0.000345469 | 1.00000i | \(0.499890\pi\) | ||||||||
\(68\) | 11.2702 | 1.36671 | ||||||||
\(69\) | 8.72942 | 1.05090 | ||||||||
\(70\) | 3.37587 | 0.403493 | ||||||||
\(71\) | 7.39583 | 0.877723 | 0.438862 | − | 0.898555i | \(-0.355382\pi\) | ||||
0.438862 | + | 0.898555i | \(0.355382\pi\) | |||||||
\(72\) | 3.67830 | 0.433492 | ||||||||
\(73\) | 12.9942 | 1.52086 | 0.760431 | − | 0.649419i | \(-0.224988\pi\) | ||||
0.760431 | + | 0.649419i | \(0.224988\pi\) | |||||||
\(74\) | 21.5172 | 2.50132 | ||||||||
\(75\) | 2.95026 | 0.340666 | ||||||||
\(76\) | 8.51295 | 0.976502 | ||||||||
\(77\) | −4.36512 | −0.497451 | ||||||||
\(78\) | −14.8059 | −1.67644 | ||||||||
\(79\) | 12.5561 | 1.41267 | 0.706333 | − | 0.707879i | \(-0.250348\pi\) | ||||
0.706333 | + | 0.707879i | \(0.250348\pi\) | |||||||
\(80\) | 2.22395 | 0.248645 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.99198 | 0.219978 | ||||||||
\(83\) | −9.65775 | −1.06008 | −0.530038 | − | 0.847974i | \(-0.677822\pi\) | ||||
−0.530038 | + | 0.847974i | \(0.677822\pi\) | |||||||
\(84\) | −3.55996 | −0.388423 | ||||||||
\(85\) | 4.53247 | 0.491615 | ||||||||
\(86\) | 25.3816 | 2.73697 | ||||||||
\(87\) | −8.42255 | −0.902993 | ||||||||
\(88\) | −16.0562 | −1.71160 | ||||||||
\(89\) | −3.78900 | −0.401633 | −0.200817 | − | 0.979629i | \(-0.564360\pi\) | ||||
−0.200817 | + | 0.979629i | \(0.564360\pi\) | |||||||
\(90\) | 3.37587 | 0.355848 | ||||||||
\(91\) | 6.27913 | 0.658232 | ||||||||
\(92\) | −31.0764 | −3.23993 | ||||||||
\(93\) | 3.52801 | 0.365838 | ||||||||
\(94\) | 24.5085 | 2.52786 | ||||||||
\(95\) | 3.42362 | 0.351256 | ||||||||
\(96\) | 3.69383 | 0.377000 | ||||||||
\(97\) | −5.91028 | −0.600098 | −0.300049 | − | 0.953924i | \(-0.597003\pi\) | ||||
−0.300049 | + | 0.953924i | \(0.597003\pi\) | |||||||
\(98\) | 2.35796 | 0.238189 | ||||||||
\(99\) | −4.36512 | −0.438711 | ||||||||
\(100\) | −10.5028 | −1.05028 | ||||||||
\(101\) | −4.86006 | −0.483594 | −0.241797 | − | 0.970327i | \(-0.577737\pi\) | ||||
−0.241797 | + | 0.970327i | \(0.577737\pi\) | |||||||
\(102\) | −7.46485 | −0.739130 | ||||||||
\(103\) | −12.2098 | −1.20307 | −0.601534 | − | 0.798847i | \(-0.705443\pi\) | ||||
−0.601534 | + | 0.798847i | \(0.705443\pi\) | |||||||
\(104\) | 23.0966 | 2.26480 | ||||||||
\(105\) | −1.43169 | −0.139719 | ||||||||
\(106\) | −14.3238 | −1.39125 | ||||||||
\(107\) | 4.40730 | 0.426070 | 0.213035 | − | 0.977045i | \(-0.431665\pi\) | ||||
0.213035 | + | 0.977045i | \(0.431665\pi\) | |||||||
\(108\) | −3.55996 | −0.342557 | ||||||||
\(109\) | −12.9720 | −1.24250 | −0.621248 | − | 0.783614i | \(-0.713374\pi\) | ||||
−0.621248 | + | 0.783614i | \(0.713374\pi\) | |||||||
\(110\) | −14.7360 | −1.40503 | ||||||||
\(111\) | −9.12536 | −0.866141 | ||||||||
\(112\) | 1.55337 | 0.146780 | ||||||||
\(113\) | 10.4743 | 0.985343 | 0.492672 | − | 0.870215i | \(-0.336020\pi\) | ||||
0.492672 | + | 0.870215i | \(0.336020\pi\) | |||||||
\(114\) | −5.63860 | −0.528103 | ||||||||
\(115\) | −12.4978 | −1.16543 | ||||||||
\(116\) | 29.9839 | 2.78394 | ||||||||
\(117\) | 6.27913 | 0.580506 | ||||||||
\(118\) | 26.7891 | 2.46613 | ||||||||
\(119\) | 3.16581 | 0.290210 | ||||||||
\(120\) | −5.26620 | −0.480736 | ||||||||
\(121\) | 8.05423 | 0.732203 | ||||||||
\(122\) | −7.60822 | −0.688816 | ||||||||
\(123\) | −0.844792 | −0.0761724 | ||||||||
\(124\) | −12.5596 | −1.12788 | ||||||||
\(125\) | −11.3823 | −1.01807 | ||||||||
\(126\) | 2.35796 | 0.210063 | ||||||||
\(127\) | −5.32100 | −0.472162 | −0.236081 | − | 0.971733i | \(-0.575863\pi\) | ||||
−0.236081 | + | 0.971733i | \(0.575863\pi\) | |||||||
\(128\) | −20.4754 | −1.80979 | ||||||||
\(129\) | −10.7642 | −0.947739 | ||||||||
\(130\) | 21.1975 | 1.85915 | ||||||||
\(131\) | −17.1349 | −1.49708 | −0.748540 | − | 0.663089i | \(-0.769245\pi\) | ||||
−0.748540 | + | 0.663089i | \(0.769245\pi\) | |||||||
\(132\) | 15.5396 | 1.35255 | ||||||||
\(133\) | 2.39131 | 0.207353 | ||||||||
\(134\) | 0.0133356 | 0.00115202 | ||||||||
\(135\) | −1.43169 | −0.123220 | ||||||||
\(136\) | 11.6448 | 0.998536 | ||||||||
\(137\) | −0.450551 | −0.0384932 | −0.0192466 | − | 0.999815i | \(-0.506127\pi\) | ||||
−0.0192466 | + | 0.999815i | \(0.506127\pi\) | |||||||
\(138\) | 20.5836 | 1.75219 | ||||||||
\(139\) | −10.3729 | −0.879814 | −0.439907 | − | 0.898043i | \(-0.644989\pi\) | ||||
−0.439907 | + | 0.898043i | \(0.644989\pi\) | |||||||
\(140\) | 5.09676 | 0.430755 | ||||||||
\(141\) | −10.3940 | −0.875331 | ||||||||
\(142\) | 17.4390 | 1.46345 | ||||||||
\(143\) | −27.4091 | −2.29207 | ||||||||
\(144\) | 1.55337 | 0.129447 | ||||||||
\(145\) | 12.0585 | 1.00140 | ||||||||
\(146\) | 30.6399 | 2.53577 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 32.4859 | 2.67032 | ||||||||
\(149\) | 19.3145 | 1.58230 | 0.791151 | − | 0.611621i | \(-0.209482\pi\) | ||||
0.791151 | + | 0.611621i | \(0.209482\pi\) | |||||||
\(150\) | 6.95658 | 0.568002 | ||||||||
\(151\) | 7.29518 | 0.593673 | 0.296836 | − | 0.954928i | \(-0.404068\pi\) | ||||
0.296836 | + | 0.954928i | \(0.404068\pi\) | |||||||
\(152\) | 8.79596 | 0.713446 | ||||||||
\(153\) | 3.16581 | 0.255941 | ||||||||
\(154\) | −10.2927 | −0.829413 | ||||||||
\(155\) | −5.05103 | −0.405708 | ||||||||
\(156\) | −22.3534 | −1.78971 | ||||||||
\(157\) | 8.62254 | 0.688154 | 0.344077 | − | 0.938941i | \(-0.388192\pi\) | ||||
0.344077 | + | 0.938941i | \(0.388192\pi\) | |||||||
\(158\) | 29.6066 | 2.35538 | ||||||||
\(159\) | 6.07467 | 0.481753 | ||||||||
\(160\) | −5.28843 | −0.418087 | ||||||||
\(161\) | −8.72942 | −0.687975 | ||||||||
\(162\) | 2.35796 | 0.185258 | ||||||||
\(163\) | 5.99453 | 0.469528 | 0.234764 | − | 0.972052i | \(-0.424568\pi\) | ||||
0.234764 | + | 0.972052i | \(0.424568\pi\) | |||||||
\(164\) | 3.00742 | 0.234840 | ||||||||
\(165\) | 6.24950 | 0.486523 | ||||||||
\(166\) | −22.7726 | −1.76749 | ||||||||
\(167\) | 5.72338 | 0.442888 | 0.221444 | − | 0.975173i | \(-0.428923\pi\) | ||||
0.221444 | + | 0.975173i | \(0.428923\pi\) | |||||||
\(168\) | −3.67830 | −0.283787 | ||||||||
\(169\) | 26.4275 | 2.03289 | ||||||||
\(170\) | 10.6874 | 0.819683 | ||||||||
\(171\) | 2.39131 | 0.182868 | ||||||||
\(172\) | 38.3202 | 2.92189 | ||||||||
\(173\) | 12.1863 | 0.926509 | 0.463254 | − | 0.886225i | \(-0.346682\pi\) | ||||
0.463254 | + | 0.886225i | \(0.346682\pi\) | |||||||
\(174\) | −19.8600 | −1.50558 | ||||||||
\(175\) | −2.95026 | −0.223019 | ||||||||
\(176\) | −6.78064 | −0.511110 | ||||||||
\(177\) | −11.3611 | −0.853956 | ||||||||
\(178\) | −8.93430 | −0.669654 | ||||||||
\(179\) | 7.86630 | 0.587955 | 0.293978 | − | 0.955812i | \(-0.405021\pi\) | ||||
0.293978 | + | 0.955812i | \(0.405021\pi\) | |||||||
\(180\) | 5.09676 | 0.379890 | ||||||||
\(181\) | 0.251159 | 0.0186685 | 0.00933425 | − | 0.999956i | \(-0.497029\pi\) | ||||
0.00933425 | + | 0.999956i | \(0.497029\pi\) | |||||||
\(182\) | 14.8059 | 1.09749 | ||||||||
\(183\) | 3.22662 | 0.238518 | ||||||||
\(184\) | −32.1095 | −2.36714 | ||||||||
\(185\) | 13.0647 | 0.960536 | ||||||||
\(186\) | 8.31889 | 0.609971 | ||||||||
\(187\) | −13.8191 | −1.01056 | ||||||||
\(188\) | 37.0021 | 2.69866 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 8.07273 | 0.585658 | ||||||||
\(191\) | −23.2271 | −1.68065 | −0.840326 | − | 0.542082i | \(-0.817636\pi\) | ||||
−0.840326 | + | 0.542082i | \(0.817636\pi\) | |||||||
\(192\) | 11.8166 | 0.852792 | ||||||||
\(193\) | 8.22253 | 0.591871 | 0.295935 | − | 0.955208i | \(-0.404369\pi\) | ||||
0.295935 | + | 0.955208i | \(0.404369\pi\) | |||||||
\(194\) | −13.9362 | −1.00056 | ||||||||
\(195\) | −8.98978 | −0.643772 | ||||||||
\(196\) | 3.55996 | 0.254283 | ||||||||
\(197\) | −22.0586 | −1.57161 | −0.785805 | − | 0.618475i | \(-0.787751\pi\) | ||||
−0.785805 | + | 0.618475i | \(0.787751\pi\) | |||||||
\(198\) | −10.2927 | −0.731474 | ||||||||
\(199\) | 22.8099 | 1.61695 | 0.808476 | − | 0.588529i | \(-0.200293\pi\) | ||||
0.808476 | + | 0.588529i | \(0.200293\pi\) | |||||||
\(200\) | −10.8519 | −0.767349 | ||||||||
\(201\) | −0.00565557 | −0.000398913 0 | ||||||||
\(202\) | −11.4598 | −0.806309 | ||||||||
\(203\) | 8.42255 | 0.591147 | ||||||||
\(204\) | −11.2702 | −0.789069 | ||||||||
\(205\) | 1.20948 | 0.0844739 | ||||||||
\(206\) | −28.7902 | −2.00591 | ||||||||
\(207\) | −8.72942 | −0.606737 | ||||||||
\(208\) | 9.75382 | 0.676306 | ||||||||
\(209\) | −10.4383 | −0.722035 | ||||||||
\(210\) | −3.37587 | −0.232957 | ||||||||
\(211\) | −12.4881 | −0.859717 | −0.429859 | − | 0.902896i | \(-0.641437\pi\) | ||||
−0.429859 | + | 0.902896i | \(0.641437\pi\) | |||||||
\(212\) | −21.6256 | −1.48525 | ||||||||
\(213\) | −7.39583 | −0.506754 | ||||||||
\(214\) | 10.3922 | 0.710397 | ||||||||
\(215\) | 15.4111 | 1.05103 | ||||||||
\(216\) | −3.67830 | −0.250277 | ||||||||
\(217\) | −3.52801 | −0.239497 | ||||||||
\(218\) | −30.5875 | −2.07165 | ||||||||
\(219\) | −12.9942 | −0.878070 | ||||||||
\(220\) | −22.2479 | −1.49996 | ||||||||
\(221\) | 19.8786 | 1.33718 | ||||||||
\(222\) | −21.5172 | −1.44414 | ||||||||
\(223\) | 18.4713 | 1.23693 | 0.618466 | − | 0.785811i | \(-0.287754\pi\) | ||||
0.618466 | + | 0.785811i | \(0.287754\pi\) | |||||||
\(224\) | −3.69383 | −0.246805 | ||||||||
\(225\) | −2.95026 | −0.196684 | ||||||||
\(226\) | 24.6980 | 1.64289 | ||||||||
\(227\) | −15.0873 | −1.00138 | −0.500689 | − | 0.865627i | \(-0.666920\pi\) | ||||
−0.500689 | + | 0.865627i | \(0.666920\pi\) | |||||||
\(228\) | −8.51295 | −0.563784 | ||||||||
\(229\) | 15.6421 | 1.03366 | 0.516830 | − | 0.856088i | \(-0.327112\pi\) | ||||
0.516830 | + | 0.856088i | \(0.327112\pi\) | |||||||
\(230\) | −29.4694 | −1.94315 | ||||||||
\(231\) | 4.36512 | 0.287203 | ||||||||
\(232\) | 30.9807 | 2.03398 | ||||||||
\(233\) | −2.89412 | −0.189600 | −0.0948000 | − | 0.995496i | \(-0.530221\pi\) | ||||
−0.0948000 | + | 0.995496i | \(0.530221\pi\) | |||||||
\(234\) | 14.8059 | 0.967893 | ||||||||
\(235\) | 14.8810 | 0.970728 | ||||||||
\(236\) | 40.4452 | 2.63276 | ||||||||
\(237\) | −12.5561 | −0.815604 | ||||||||
\(238\) | 7.46485 | 0.483874 | ||||||||
\(239\) | 13.5783 | 0.878310 | 0.439155 | − | 0.898411i | \(-0.355278\pi\) | ||||
0.439155 | + | 0.898411i | \(0.355278\pi\) | |||||||
\(240\) | −2.22395 | −0.143555 | ||||||||
\(241\) | 0.304916 | 0.0196414 | 0.00982070 | − | 0.999952i | \(-0.496874\pi\) | ||||
0.00982070 | + | 0.999952i | \(0.496874\pi\) | |||||||
\(242\) | 18.9915 | 1.22082 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −11.4866 | −0.735355 | ||||||||
\(245\) | 1.43169 | 0.0914674 | ||||||||
\(246\) | −1.99198 | −0.127004 | ||||||||
\(247\) | 15.0153 | 0.955403 | ||||||||
\(248\) | −12.9771 | −0.824047 | ||||||||
\(249\) | 9.65775 | 0.612035 | ||||||||
\(250\) | −26.8390 | −1.69745 | ||||||||
\(251\) | −28.2439 | −1.78274 | −0.891369 | − | 0.453278i | \(-0.850254\pi\) | ||||
−0.891369 | + | 0.453278i | \(0.850254\pi\) | |||||||
\(252\) | 3.55996 | 0.224256 | ||||||||
\(253\) | 38.1049 | 2.39564 | ||||||||
\(254\) | −12.5467 | −0.787248 | ||||||||
\(255\) | −4.53247 | −0.283834 | ||||||||
\(256\) | −24.6469 | −1.54043 | ||||||||
\(257\) | 11.0519 | 0.689401 | 0.344701 | − | 0.938713i | \(-0.387980\pi\) | ||||
0.344701 | + | 0.938713i | \(0.387980\pi\) | |||||||
\(258\) | −25.3816 | −1.58019 | ||||||||
\(259\) | 9.12536 | 0.567022 | ||||||||
\(260\) | 32.0032 | 1.98476 | ||||||||
\(261\) | 8.42255 | 0.521343 | ||||||||
\(262\) | −40.4033 | −2.49612 | ||||||||
\(263\) | −14.6634 | −0.904185 | −0.452093 | − | 0.891971i | \(-0.649322\pi\) | ||||
−0.452093 | + | 0.891971i | \(0.649322\pi\) | |||||||
\(264\) | 16.0562 | 0.988192 | ||||||||
\(265\) | −8.69706 | −0.534256 | ||||||||
\(266\) | 5.63860 | 0.345725 | ||||||||
\(267\) | 3.78900 | 0.231883 | ||||||||
\(268\) | 0.0201336 | 0.00122985 | ||||||||
\(269\) | −19.6117 | −1.19575 | −0.597874 | − | 0.801590i | \(-0.703988\pi\) | ||||
−0.597874 | + | 0.801590i | \(0.703988\pi\) | |||||||
\(270\) | −3.37587 | −0.205449 | ||||||||
\(271\) | −6.71460 | −0.407883 | −0.203941 | − | 0.978983i | \(-0.565375\pi\) | ||||
−0.203941 | + | 0.978983i | \(0.565375\pi\) | |||||||
\(272\) | 4.91768 | 0.298178 | ||||||||
\(273\) | −6.27913 | −0.380030 | ||||||||
\(274\) | −1.06238 | −0.0641807 | ||||||||
\(275\) | 12.8782 | 0.776586 | ||||||||
\(276\) | 31.0764 | 1.87058 | ||||||||
\(277\) | −2.80019 | −0.168247 | −0.0841235 | − | 0.996455i | \(-0.526809\pi\) | ||||
−0.0841235 | + | 0.996455i | \(0.526809\pi\) | |||||||
\(278\) | −24.4587 | −1.46694 | ||||||||
\(279\) | −3.52801 | −0.211217 | ||||||||
\(280\) | 5.26620 | 0.314716 | ||||||||
\(281\) | 5.34685 | 0.318967 | 0.159483 | − | 0.987201i | \(-0.449017\pi\) | ||||
0.159483 | + | 0.987201i | \(0.449017\pi\) | |||||||
\(282\) | −24.5085 | −1.45946 | ||||||||
\(283\) | 26.6453 | 1.58390 | 0.791948 | − | 0.610589i | \(-0.209067\pi\) | ||||
0.791948 | + | 0.610589i | \(0.209067\pi\) | |||||||
\(284\) | 26.3288 | 1.56233 | ||||||||
\(285\) | −3.42362 | −0.202797 | ||||||||
\(286\) | −64.6295 | −3.82163 | ||||||||
\(287\) | 0.844792 | 0.0498665 | ||||||||
\(288\) | −3.69383 | −0.217661 | ||||||||
\(289\) | −6.97762 | −0.410449 | ||||||||
\(290\) | 28.4334 | 1.66967 | ||||||||
\(291\) | 5.91028 | 0.346467 | ||||||||
\(292\) | 46.2589 | 2.70710 | ||||||||
\(293\) | −21.6035 | −1.26209 | −0.631046 | − | 0.775745i | \(-0.717374\pi\) | ||||
−0.631046 | + | 0.775745i | \(0.717374\pi\) | |||||||
\(294\) | −2.35796 | −0.137519 | ||||||||
\(295\) | 16.2657 | 0.947023 | ||||||||
\(296\) | 33.5658 | 1.95098 | ||||||||
\(297\) | 4.36512 | 0.253290 | ||||||||
\(298\) | 45.5426 | 2.63821 | ||||||||
\(299\) | −54.8132 | −3.16993 | ||||||||
\(300\) | 10.5028 | 0.606379 | ||||||||
\(301\) | 10.7642 | 0.620441 | ||||||||
\(302\) | 17.2017 | 0.989847 | ||||||||
\(303\) | 4.86006 | 0.279203 | ||||||||
\(304\) | 3.71458 | 0.213046 | ||||||||
\(305\) | −4.61952 | −0.264513 | ||||||||
\(306\) | 7.46485 | 0.426737 | ||||||||
\(307\) | 15.4644 | 0.882600 | 0.441300 | − | 0.897360i | \(-0.354517\pi\) | ||||
0.441300 | + | 0.897360i | \(0.354517\pi\) | |||||||
\(308\) | −15.5396 | −0.885452 | ||||||||
\(309\) | 12.2098 | 0.694591 | ||||||||
\(310\) | −11.9101 | −0.676448 | ||||||||
\(311\) | −15.3382 | −0.869749 | −0.434875 | − | 0.900491i | \(-0.643207\pi\) | ||||
−0.434875 | + | 0.900491i | \(0.643207\pi\) | |||||||
\(312\) | −23.0966 | −1.30759 | ||||||||
\(313\) | −9.21957 | −0.521121 | −0.260561 | − | 0.965458i | \(-0.583907\pi\) | ||||
−0.260561 | + | 0.965458i | \(0.583907\pi\) | |||||||
\(314\) | 20.3316 | 1.14738 | ||||||||
\(315\) | 1.43169 | 0.0806667 | ||||||||
\(316\) | 44.6990 | 2.51452 | ||||||||
\(317\) | 13.0864 | 0.735005 | 0.367502 | − | 0.930023i | \(-0.380213\pi\) | ||||
0.367502 | + | 0.930023i | \(0.380213\pi\) | |||||||
\(318\) | 14.3238 | 0.803240 | ||||||||
\(319\) | −36.7654 | −2.05847 | ||||||||
\(320\) | −16.9178 | −0.945733 | ||||||||
\(321\) | −4.40730 | −0.245991 | ||||||||
\(322\) | −20.5836 | −1.14708 | ||||||||
\(323\) | 7.57043 | 0.421230 | ||||||||
\(324\) | 3.55996 | 0.197775 | ||||||||
\(325\) | −18.5251 | −1.02759 | ||||||||
\(326\) | 14.1348 | 0.782856 | ||||||||
\(327\) | 12.9720 | 0.717355 | ||||||||
\(328\) | 3.10740 | 0.171578 | ||||||||
\(329\) | 10.3940 | 0.573039 | ||||||||
\(330\) | 14.7360 | 0.811193 | ||||||||
\(331\) | 0.953807 | 0.0524260 | 0.0262130 | − | 0.999656i | \(-0.491655\pi\) | ||||
0.0262130 | + | 0.999656i | \(0.491655\pi\) | |||||||
\(332\) | −34.3812 | −1.88691 | ||||||||
\(333\) | 9.12536 | 0.500066 | ||||||||
\(334\) | 13.4955 | 0.738439 | ||||||||
\(335\) | 0.00809704 | 0.000442389 0 | ||||||||
\(336\) | −1.55337 | −0.0847433 | ||||||||
\(337\) | 10.0332 | 0.546541 | 0.273271 | − | 0.961937i | \(-0.411895\pi\) | ||||
0.273271 | + | 0.961937i | \(0.411895\pi\) | |||||||
\(338\) | 62.3149 | 3.38949 | ||||||||
\(339\) | −10.4743 | −0.568888 | ||||||||
\(340\) | 16.1354 | 0.875064 | ||||||||
\(341\) | 15.4002 | 0.833966 | ||||||||
\(342\) | 5.63860 | 0.304900 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 39.5942 | 2.13478 | ||||||||
\(345\) | 12.4978 | 0.672861 | ||||||||
\(346\) | 28.7348 | 1.54479 | ||||||||
\(347\) | −33.7742 | −1.81309 | −0.906546 | − | 0.422107i | \(-0.861291\pi\) | ||||
−0.906546 | + | 0.422107i | \(0.861291\pi\) | |||||||
\(348\) | −29.9839 | −1.60731 | ||||||||
\(349\) | 30.8933 | 1.65368 | 0.826839 | − | 0.562438i | \(-0.190137\pi\) | ||||
0.826839 | + | 0.562438i | \(0.190137\pi\) | |||||||
\(350\) | −6.95658 | −0.371845 | ||||||||
\(351\) | −6.27913 | −0.335155 | ||||||||
\(352\) | 16.1240 | 0.859412 | ||||||||
\(353\) | −34.2916 | −1.82516 | −0.912578 | − | 0.408903i | \(-0.865911\pi\) | ||||
−0.912578 | + | 0.408903i | \(0.865911\pi\) | |||||||
\(354\) | −26.7891 | −1.42382 | ||||||||
\(355\) | 10.5885 | 0.561982 | ||||||||
\(356\) | −13.4887 | −0.714898 | ||||||||
\(357\) | −3.16581 | −0.167553 | ||||||||
\(358\) | 18.5484 | 0.980313 | ||||||||
\(359\) | 36.5397 | 1.92849 | 0.964246 | − | 0.265007i | \(-0.0853744\pi\) | ||||
0.964246 | + | 0.265007i | \(0.0853744\pi\) | |||||||
\(360\) | 5.26620 | 0.277553 | ||||||||
\(361\) | −13.2816 | −0.699034 | ||||||||
\(362\) | 0.592222 | 0.0311265 | ||||||||
\(363\) | −8.05423 | −0.422737 | ||||||||
\(364\) | 22.3534 | 1.17164 | ||||||||
\(365\) | 18.6038 | 0.973765 | ||||||||
\(366\) | 7.60822 | 0.397688 | ||||||||
\(367\) | −12.5989 | −0.657657 | −0.328828 | − | 0.944390i | \(-0.606654\pi\) | ||||
−0.328828 | + | 0.944390i | \(0.606654\pi\) | |||||||
\(368\) | −13.5600 | −0.706865 | ||||||||
\(369\) | 0.844792 | 0.0439781 | ||||||||
\(370\) | 30.8060 | 1.60153 | ||||||||
\(371\) | −6.07467 | −0.315381 | ||||||||
\(372\) | 12.5596 | 0.651183 | ||||||||
\(373\) | −6.35656 | −0.329130 | −0.164565 | − | 0.986366i | \(-0.552622\pi\) | ||||
−0.164565 | + | 0.986366i | \(0.552622\pi\) | |||||||
\(374\) | −32.5849 | −1.68493 | ||||||||
\(375\) | 11.3823 | 0.587780 | ||||||||
\(376\) | 38.2322 | 1.97168 | ||||||||
\(377\) | 52.8863 | 2.72379 | ||||||||
\(378\) | −2.35796 | −0.121280 | ||||||||
\(379\) | −7.48695 | −0.384579 | −0.192289 | − | 0.981338i | \(-0.561591\pi\) | ||||
−0.192289 | + | 0.981338i | \(0.561591\pi\) | |||||||
\(380\) | 12.1879 | 0.625227 | ||||||||
\(381\) | 5.32100 | 0.272603 | ||||||||
\(382\) | −54.7684 | −2.80220 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | 20.4754 | 1.04488 | ||||||||
\(385\) | −6.24950 | −0.318504 | ||||||||
\(386\) | 19.3884 | 0.986842 | ||||||||
\(387\) | 10.7642 | 0.547178 | ||||||||
\(388\) | −21.0403 | −1.06816 | ||||||||
\(389\) | 33.6092 | 1.70405 | 0.852026 | − | 0.523499i | \(-0.175374\pi\) | ||||
0.852026 | + | 0.523499i | \(0.175374\pi\) | |||||||
\(390\) | −21.1975 | −1.07338 | ||||||||
\(391\) | −27.6357 | −1.39760 | ||||||||
\(392\) | 3.67830 | 0.185782 | ||||||||
\(393\) | 17.1349 | 0.864340 | ||||||||
\(394\) | −52.0132 | −2.62039 | ||||||||
\(395\) | 17.9764 | 0.904491 | ||||||||
\(396\) | −15.5396 | −0.780895 | ||||||||
\(397\) | 17.9351 | 0.900137 | 0.450069 | − | 0.892994i | \(-0.351400\pi\) | ||||
0.450069 | + | 0.892994i | \(0.351400\pi\) | |||||||
\(398\) | 53.7848 | 2.69599 | ||||||||
\(399\) | −2.39131 | −0.119715 | ||||||||
\(400\) | −4.58284 | −0.229142 | ||||||||
\(401\) | 25.2975 | 1.26330 | 0.631649 | − | 0.775254i | \(-0.282378\pi\) | ||||
0.631649 | + | 0.775254i | \(0.282378\pi\) | |||||||
\(402\) | −0.0133356 | −0.000665119 0 | ||||||||
\(403\) | −22.1529 | −1.10351 | ||||||||
\(404\) | −17.3016 | −0.860786 | ||||||||
\(405\) | 1.43169 | 0.0711413 | ||||||||
\(406\) | 19.8600 | 0.985636 | ||||||||
\(407\) | −39.8332 | −1.97446 | ||||||||
\(408\) | −11.6448 | −0.576505 | ||||||||
\(409\) | 2.27955 | 0.112716 | 0.0563582 | − | 0.998411i | \(-0.482051\pi\) | ||||
0.0563582 | + | 0.998411i | \(0.482051\pi\) | |||||||
\(410\) | 2.85191 | 0.140846 | ||||||||
\(411\) | 0.450551 | 0.0222240 | ||||||||
\(412\) | −43.4663 | −2.14143 | ||||||||
\(413\) | 11.3611 | 0.559045 | ||||||||
\(414\) | −20.5836 | −1.01163 | ||||||||
\(415\) | −13.8269 | −0.678737 | ||||||||
\(416\) | −23.1941 | −1.13718 | ||||||||
\(417\) | 10.3729 | 0.507961 | ||||||||
\(418\) | −24.6131 | −1.20387 | ||||||||
\(419\) | 8.46522 | 0.413553 | 0.206776 | − | 0.978388i | \(-0.433703\pi\) | ||||
0.206776 | + | 0.978388i | \(0.433703\pi\) | |||||||
\(420\) | −5.09676 | −0.248696 | ||||||||
\(421\) | −14.6432 | −0.713664 | −0.356832 | − | 0.934169i | \(-0.616143\pi\) | ||||
−0.356832 | + | 0.934169i | \(0.616143\pi\) | |||||||
\(422\) | −29.4464 | −1.43343 | ||||||||
\(423\) | 10.3940 | 0.505373 | ||||||||
\(424\) | −22.3445 | −1.08515 | ||||||||
\(425\) | −9.33997 | −0.453055 | ||||||||
\(426\) | −17.4390 | −0.844924 | ||||||||
\(427\) | −3.22662 | −0.156147 | ||||||||
\(428\) | 15.6898 | 0.758395 | ||||||||
\(429\) | 27.4091 | 1.32333 | ||||||||
\(430\) | 36.3387 | 1.75241 | ||||||||
\(431\) | 4.40023 | 0.211952 | 0.105976 | − | 0.994369i | \(-0.466203\pi\) | ||||
0.105976 | + | 0.994369i | \(0.466203\pi\) | |||||||
\(432\) | −1.55337 | −0.0747365 | ||||||||
\(433\) | −10.8468 | −0.521262 | −0.260631 | − | 0.965438i | \(-0.583931\pi\) | ||||
−0.260631 | + | 0.965438i | \(0.583931\pi\) | |||||||
\(434\) | −8.31889 | −0.399320 | ||||||||
\(435\) | −12.0585 | −0.578161 | ||||||||
\(436\) | −46.1798 | −2.21161 | ||||||||
\(437\) | −20.8747 | −0.998574 | ||||||||
\(438\) | −30.6399 | −1.46403 | ||||||||
\(439\) | 9.67830 | 0.461920 | 0.230960 | − | 0.972963i | \(-0.425813\pi\) | ||||
0.230960 | + | 0.972963i | \(0.425813\pi\) | |||||||
\(440\) | −22.9876 | −1.09589 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 46.8728 | 2.22951 | ||||||||
\(443\) | 7.56987 | 0.359656 | 0.179828 | − | 0.983698i | \(-0.442446\pi\) | ||||
0.179828 | + | 0.983698i | \(0.442446\pi\) | |||||||
\(444\) | −32.4859 | −1.54171 | ||||||||
\(445\) | −5.42468 | −0.257155 | ||||||||
\(446\) | 43.5546 | 2.06237 | ||||||||
\(447\) | −19.3145 | −0.913542 | ||||||||
\(448\) | −11.8166 | −0.558283 | ||||||||
\(449\) | 39.3902 | 1.85894 | 0.929470 | − | 0.368898i | \(-0.120265\pi\) | ||||
0.929470 | + | 0.368898i | \(0.120265\pi\) | |||||||
\(450\) | −6.95658 | −0.327936 | ||||||||
\(451\) | −3.68762 | −0.173643 | ||||||||
\(452\) | 37.2882 | 1.75389 | ||||||||
\(453\) | −7.29518 | −0.342757 | ||||||||
\(454\) | −35.5751 | −1.66962 | ||||||||
\(455\) | 8.98978 | 0.421448 | ||||||||
\(456\) | −8.79596 | −0.411908 | ||||||||
\(457\) | −0.120475 | −0.00563557 | −0.00281779 | − | 0.999996i | \(-0.500897\pi\) | ||||
−0.00281779 | + | 0.999996i | \(0.500897\pi\) | |||||||
\(458\) | 36.8834 | 1.72345 | ||||||||
\(459\) | −3.16581 | −0.147768 | ||||||||
\(460\) | −44.4918 | −2.07444 | ||||||||
\(461\) | −21.3935 | −0.996393 | −0.498197 | − | 0.867064i | \(-0.666004\pi\) | ||||
−0.498197 | + | 0.867064i | \(0.666004\pi\) | |||||||
\(462\) | 10.2927 | 0.478862 | ||||||||
\(463\) | −28.2271 | −1.31182 | −0.655911 | − | 0.754838i | \(-0.727716\pi\) | ||||
−0.655911 | + | 0.754838i | \(0.727716\pi\) | |||||||
\(464\) | 13.0833 | 0.607379 | ||||||||
\(465\) | 5.05103 | 0.234236 | ||||||||
\(466\) | −6.82420 | −0.316125 | ||||||||
\(467\) | −6.84376 | −0.316691 | −0.158346 | − | 0.987384i | \(-0.550616\pi\) | ||||
−0.158346 | + | 0.987384i | \(0.550616\pi\) | |||||||
\(468\) | 22.3534 | 1.03329 | ||||||||
\(469\) | 0.00565557 | 0.000261150 0 | ||||||||
\(470\) | 35.0887 | 1.61852 | ||||||||
\(471\) | −8.62254 | −0.397306 | ||||||||
\(472\) | 41.7897 | 1.92353 | ||||||||
\(473\) | −46.9872 | −2.16047 | ||||||||
\(474\) | −29.6066 | −1.35988 | ||||||||
\(475\) | −7.05498 | −0.323704 | ||||||||
\(476\) | 11.2702 | 0.516567 | ||||||||
\(477\) | −6.07467 | −0.278140 | ||||||||
\(478\) | 32.0171 | 1.46443 | ||||||||
\(479\) | −34.4176 | −1.57258 | −0.786289 | − | 0.617858i | \(-0.788000\pi\) | ||||
−0.786289 | + | 0.617858i | \(0.788000\pi\) | |||||||
\(480\) | 5.28843 | 0.241383 | ||||||||
\(481\) | 57.2993 | 2.61263 | ||||||||
\(482\) | 0.718979 | 0.0327486 | ||||||||
\(483\) | 8.72942 | 0.397203 | ||||||||
\(484\) | 28.6727 | 1.30330 | ||||||||
\(485\) | −8.46169 | −0.384226 | ||||||||
\(486\) | −2.35796 | −0.106959 | ||||||||
\(487\) | −30.1182 | −1.36479 | −0.682393 | − | 0.730985i | \(-0.739061\pi\) | ||||
−0.682393 | + | 0.730985i | \(0.739061\pi\) | |||||||
\(488\) | −11.8685 | −0.537261 | ||||||||
\(489\) | −5.99453 | −0.271082 | ||||||||
\(490\) | 3.37587 | 0.152506 | ||||||||
\(491\) | −18.7145 | −0.844576 | −0.422288 | − | 0.906462i | \(-0.638773\pi\) | ||||
−0.422288 | + | 0.906462i | \(0.638773\pi\) | |||||||
\(492\) | −3.00742 | −0.135585 | ||||||||
\(493\) | 26.6642 | 1.20090 | ||||||||
\(494\) | 35.4055 | 1.59297 | ||||||||
\(495\) | −6.24950 | −0.280894 | ||||||||
\(496\) | −5.48031 | −0.246073 | ||||||||
\(497\) | 7.39583 | 0.331748 | ||||||||
\(498\) | 22.7726 | 1.02046 | ||||||||
\(499\) | −40.2777 | −1.80308 | −0.901539 | − | 0.432699i | \(-0.857561\pi\) | ||||
−0.901539 | + | 0.432699i | \(0.857561\pi\) | |||||||
\(500\) | −40.5205 | −1.81213 | ||||||||
\(501\) | −5.72338 | −0.255702 | ||||||||
\(502\) | −66.5978 | −2.97241 | ||||||||
\(503\) | −10.4253 | −0.464840 | −0.232420 | − | 0.972616i | \(-0.574664\pi\) | ||||
−0.232420 | + | 0.972616i | \(0.574664\pi\) | |||||||
\(504\) | 3.67830 | 0.163845 | ||||||||
\(505\) | −6.95810 | −0.309632 | ||||||||
\(506\) | 89.8498 | 3.99431 | ||||||||
\(507\) | −26.4275 | −1.17369 | ||||||||
\(508\) | −18.9425 | −0.840438 | ||||||||
\(509\) | −15.1562 | −0.671785 | −0.335893 | − | 0.941900i | \(-0.609038\pi\) | ||||
−0.335893 | + | 0.941900i | \(0.609038\pi\) | |||||||
\(510\) | −10.6874 | −0.473244 | ||||||||
\(511\) | 12.9942 | 0.574832 | ||||||||
\(512\) | −17.1654 | −0.758612 | ||||||||
\(513\) | −2.39131 | −0.105579 | ||||||||
\(514\) | 26.0600 | 1.14946 | ||||||||
\(515\) | −17.4807 | −0.770291 | ||||||||
\(516\) | −38.3202 | −1.68695 | ||||||||
\(517\) | −45.3709 | −1.99541 | ||||||||
\(518\) | 21.5172 | 0.945411 | ||||||||
\(519\) | −12.1863 | −0.534920 | ||||||||
\(520\) | 33.0672 | 1.45009 | ||||||||
\(521\) | 13.7355 | 0.601763 | 0.300882 | − | 0.953662i | \(-0.402719\pi\) | ||||
0.300882 | + | 0.953662i | \(0.402719\pi\) | |||||||
\(522\) | 19.8600 | 0.869249 | ||||||||
\(523\) | −4.12892 | −0.180545 | −0.0902725 | − | 0.995917i | \(-0.528774\pi\) | ||||
−0.0902725 | + | 0.995917i | \(0.528774\pi\) | |||||||
\(524\) | −60.9994 | −2.66477 | ||||||||
\(525\) | 2.95026 | 0.128760 | ||||||||
\(526\) | −34.5757 | −1.50757 | ||||||||
\(527\) | −11.1690 | −0.486530 | ||||||||
\(528\) | 6.78064 | 0.295089 | ||||||||
\(529\) | 53.2028 | 2.31317 | ||||||||
\(530\) | −20.5073 | −0.890780 | ||||||||
\(531\) | 11.3611 | 0.493032 | ||||||||
\(532\) | 8.51295 | 0.369083 | ||||||||
\(533\) | 5.30456 | 0.229766 | ||||||||
\(534\) | 8.93430 | 0.386625 | ||||||||
\(535\) | 6.30989 | 0.272801 | ||||||||
\(536\) | 0.0208029 | 0.000898550 0 | ||||||||
\(537\) | −7.86630 | −0.339456 | ||||||||
\(538\) | −46.2436 | −1.99370 | ||||||||
\(539\) | −4.36512 | −0.188019 | ||||||||
\(540\) | −5.09676 | −0.219330 | ||||||||
\(541\) | 25.1511 | 1.08133 | 0.540665 | − | 0.841238i | \(-0.318173\pi\) | ||||
0.540665 | + | 0.841238i | \(0.318173\pi\) | |||||||
\(542\) | −15.8327 | −0.680074 | ||||||||
\(543\) | −0.251159 | −0.0107783 | ||||||||
\(544\) | −11.6940 | −0.501375 | ||||||||
\(545\) | −18.5720 | −0.795535 | ||||||||
\(546\) | −14.8059 | −0.633635 | ||||||||
\(547\) | −39.0410 | −1.66927 | −0.834637 | − | 0.550800i | \(-0.814323\pi\) | ||||
−0.834637 | + | 0.550800i | \(0.814323\pi\) | |||||||
\(548\) | −1.60394 | −0.0685170 | ||||||||
\(549\) | −3.22662 | −0.137709 | ||||||||
\(550\) | 30.3663 | 1.29482 | ||||||||
\(551\) | 20.1409 | 0.858032 | ||||||||
\(552\) | 32.1095 | 1.36667 | ||||||||
\(553\) | 12.5561 | 0.533938 | ||||||||
\(554\) | −6.60272 | −0.280523 | ||||||||
\(555\) | −13.0647 | −0.554566 | ||||||||
\(556\) | −36.9269 | −1.56605 | ||||||||
\(557\) | −25.0051 | −1.05950 | −0.529749 | − | 0.848154i | \(-0.677714\pi\) | ||||
−0.529749 | + | 0.848154i | \(0.677714\pi\) | |||||||
\(558\) | −8.31889 | −0.352167 | ||||||||
\(559\) | 67.5902 | 2.85876 | ||||||||
\(560\) | 2.22395 | 0.0939789 | ||||||||
\(561\) | 13.8191 | 0.583445 | ||||||||
\(562\) | 12.6076 | 0.531821 | ||||||||
\(563\) | −19.5582 | −0.824280 | −0.412140 | − | 0.911121i | \(-0.635219\pi\) | ||||
−0.412140 | + | 0.911121i | \(0.635219\pi\) | |||||||
\(564\) | −37.0021 | −1.55807 | ||||||||
\(565\) | 14.9960 | 0.630888 | ||||||||
\(566\) | 62.8283 | 2.64087 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 27.2041 | 1.14146 | ||||||||
\(569\) | 1.18862 | 0.0498294 | 0.0249147 | − | 0.999690i | \(-0.492069\pi\) | ||||
0.0249147 | + | 0.999690i | \(0.492069\pi\) | |||||||
\(570\) | −8.07273 | −0.338130 | ||||||||
\(571\) | −21.5906 | −0.903538 | −0.451769 | − | 0.892135i | \(-0.649207\pi\) | ||||
−0.451769 | + | 0.892135i | \(0.649207\pi\) | |||||||
\(572\) | −97.5753 | −4.07983 | ||||||||
\(573\) | 23.2271 | 0.970325 | ||||||||
\(574\) | 1.99198 | 0.0831438 | ||||||||
\(575\) | 25.7541 | 1.07402 | ||||||||
\(576\) | −11.8166 | −0.492360 | ||||||||
\(577\) | −1.63152 | −0.0679209 | −0.0339604 | − | 0.999423i | \(-0.510812\pi\) | ||||
−0.0339604 | + | 0.999423i | \(0.510812\pi\) | |||||||
\(578\) | −16.4529 | −0.684352 | ||||||||
\(579\) | −8.22253 | −0.341717 | ||||||||
\(580\) | 42.9277 | 1.78248 | ||||||||
\(581\) | −9.65775 | −0.400671 | ||||||||
\(582\) | 13.9362 | 0.577673 | ||||||||
\(583\) | 26.5167 | 1.09821 | ||||||||
\(584\) | 47.7968 | 1.97785 | ||||||||
\(585\) | 8.98978 | 0.371682 | ||||||||
\(586\) | −50.9402 | −2.10432 | ||||||||
\(587\) | 4.83586 | 0.199597 | 0.0997986 | − | 0.995008i | \(-0.468180\pi\) | ||||
0.0997986 | + | 0.995008i | \(0.468180\pi\) | |||||||
\(588\) | −3.55996 | −0.146810 | ||||||||
\(589\) | −8.43656 | −0.347622 | ||||||||
\(590\) | 38.3537 | 1.57900 | ||||||||
\(591\) | 22.0586 | 0.907369 | ||||||||
\(592\) | 14.1751 | 0.582591 | ||||||||
\(593\) | −11.1365 | −0.457322 | −0.228661 | − | 0.973506i | \(-0.573435\pi\) | ||||
−0.228661 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(594\) | 10.2927 | 0.422317 | ||||||||
\(595\) | 4.53247 | 0.185813 | ||||||||
\(596\) | 68.7586 | 2.81646 | ||||||||
\(597\) | −22.8099 | −0.933548 | ||||||||
\(598\) | −129.247 | −5.28531 | ||||||||
\(599\) | −1.22994 | −0.0502541 | −0.0251270 | − | 0.999684i | \(-0.507999\pi\) | ||||
−0.0251270 | + | 0.999684i | \(0.507999\pi\) | |||||||
\(600\) | 10.8519 | 0.443029 | ||||||||
\(601\) | −39.1211 | −1.59578 | −0.797892 | − | 0.602801i | \(-0.794051\pi\) | ||||
−0.797892 | + | 0.602801i | \(0.794051\pi\) | |||||||
\(602\) | 25.3816 | 1.03448 | ||||||||
\(603\) | 0.00565557 | 0.000230313 0 | ||||||||
\(604\) | 25.9705 | 1.05672 | ||||||||
\(605\) | 11.5312 | 0.468809 | ||||||||
\(606\) | 11.4598 | 0.465522 | ||||||||
\(607\) | −40.1687 | −1.63040 | −0.815199 | − | 0.579182i | \(-0.803372\pi\) | ||||
−0.815199 | + | 0.579182i | \(0.803372\pi\) | |||||||
\(608\) | −8.83309 | −0.358229 | ||||||||
\(609\) | −8.42255 | −0.341299 | ||||||||
\(610\) | −10.8926 | −0.441029 | ||||||||
\(611\) | 65.2652 | 2.64035 | ||||||||
\(612\) | 11.2702 | 0.455569 | ||||||||
\(613\) | 32.2727 | 1.30348 | 0.651742 | − | 0.758441i | \(-0.274039\pi\) | ||||
0.651742 | + | 0.758441i | \(0.274039\pi\) | |||||||
\(614\) | 36.4644 | 1.47158 | ||||||||
\(615\) | −1.20948 | −0.0487710 | ||||||||
\(616\) | −16.0562 | −0.646924 | ||||||||
\(617\) | 36.7284 | 1.47863 | 0.739316 | − | 0.673359i | \(-0.235149\pi\) | ||||
0.739316 | + | 0.673359i | \(0.235149\pi\) | |||||||
\(618\) | 28.7902 | 1.15811 | ||||||||
\(619\) | −8.84864 | −0.355657 | −0.177828 | − | 0.984062i | \(-0.556907\pi\) | ||||
−0.177828 | + | 0.984062i | \(0.556907\pi\) | |||||||
\(620\) | −17.9814 | −0.722151 | ||||||||
\(621\) | 8.72942 | 0.350300 | ||||||||
\(622\) | −36.1668 | −1.45016 | ||||||||
\(623\) | −3.78900 | −0.151803 | ||||||||
\(624\) | −9.75382 | −0.390465 | ||||||||
\(625\) | −1.54468 | −0.0617873 | ||||||||
\(626\) | −21.7393 | −0.868879 | ||||||||
\(627\) | 10.4383 | 0.416867 | ||||||||
\(628\) | 30.6959 | 1.22490 | ||||||||
\(629\) | 28.8892 | 1.15189 | ||||||||
\(630\) | 3.37587 | 0.134498 | ||||||||
\(631\) | −27.0343 | −1.07622 | −0.538110 | − | 0.842875i | \(-0.680862\pi\) | ||||
−0.538110 | + | 0.842875i | \(0.680862\pi\) | |||||||
\(632\) | 46.1850 | 1.83714 | ||||||||
\(633\) | 12.4881 | 0.496358 | ||||||||
\(634\) | 30.8571 | 1.22549 | ||||||||
\(635\) | −7.61803 | −0.302312 | ||||||||
\(636\) | 21.6256 | 0.857510 | ||||||||
\(637\) | 6.27913 | 0.248788 | ||||||||
\(638\) | −86.6912 | −3.43214 | ||||||||
\(639\) | 7.39583 | 0.292574 | ||||||||
\(640\) | −29.3145 | −1.15876 | ||||||||
\(641\) | −49.6956 | −1.96286 | −0.981430 | − | 0.191821i | \(-0.938561\pi\) | ||||
−0.981430 | + | 0.191821i | \(0.938561\pi\) | |||||||
\(642\) | −10.3922 | −0.410148 | ||||||||
\(643\) | 16.7004 | 0.658599 | 0.329300 | − | 0.944225i | \(-0.393187\pi\) | ||||
0.329300 | + | 0.944225i | \(0.393187\pi\) | |||||||
\(644\) | −31.0764 | −1.22458 | ||||||||
\(645\) | −15.4111 | −0.606811 | ||||||||
\(646\) | 17.8507 | 0.702328 | ||||||||
\(647\) | 22.6541 | 0.890624 | 0.445312 | − | 0.895376i | \(-0.353093\pi\) | ||||
0.445312 | + | 0.895376i | \(0.353093\pi\) | |||||||
\(648\) | 3.67830 | 0.144497 | ||||||||
\(649\) | −49.5927 | −1.94668 | ||||||||
\(650\) | −43.6813 | −1.71332 | ||||||||
\(651\) | 3.52801 | 0.138274 | ||||||||
\(652\) | 21.3402 | 0.835748 | ||||||||
\(653\) | −18.6236 | −0.728798 | −0.364399 | − | 0.931243i | \(-0.618726\pi\) | ||||
−0.364399 | + | 0.931243i | \(0.618726\pi\) | |||||||
\(654\) | 30.5875 | 1.19606 | ||||||||
\(655\) | −24.5319 | −0.958539 | ||||||||
\(656\) | 1.31228 | 0.0512357 | ||||||||
\(657\) | 12.9942 | 0.506954 | ||||||||
\(658\) | 24.5085 | 0.955443 | ||||||||
\(659\) | −4.58187 | −0.178484 | −0.0892421 | − | 0.996010i | \(-0.528444\pi\) | ||||
−0.0892421 | + | 0.996010i | \(0.528444\pi\) | |||||||
\(660\) | 22.2479 | 0.866000 | ||||||||
\(661\) | 19.7352 | 0.767609 | 0.383805 | − | 0.923414i | \(-0.374614\pi\) | ||||
0.383805 | + | 0.923414i | \(0.374614\pi\) | |||||||
\(662\) | 2.24904 | 0.0874113 | ||||||||
\(663\) | −19.8786 | −0.772020 | ||||||||
\(664\) | −35.5242 | −1.37860 | ||||||||
\(665\) | 3.42362 | 0.132762 | ||||||||
\(666\) | 21.5172 | 0.833774 | ||||||||
\(667\) | −73.5240 | −2.84686 | ||||||||
\(668\) | 20.3750 | 0.788331 | ||||||||
\(669\) | −18.4713 | −0.714143 | ||||||||
\(670\) | 0.0190925 | 0.000737606 0 | ||||||||
\(671\) | 14.0846 | 0.543728 | ||||||||
\(672\) | 3.69383 | 0.142493 | ||||||||
\(673\) | −9.54034 | −0.367753 | −0.183877 | − | 0.982949i | \(-0.558865\pi\) | ||||
−0.183877 | + | 0.982949i | \(0.558865\pi\) | |||||||
\(674\) | 23.6578 | 0.911263 | ||||||||
\(675\) | 2.95026 | 0.113555 | ||||||||
\(676\) | 94.0808 | 3.61849 | ||||||||
\(677\) | 4.83242 | 0.185725 | 0.0928626 | − | 0.995679i | \(-0.470398\pi\) | ||||
0.0928626 | + | 0.995679i | \(0.470398\pi\) | |||||||
\(678\) | −24.6980 | −0.948523 | ||||||||
\(679\) | −5.91028 | −0.226816 | ||||||||
\(680\) | 16.6718 | 0.639335 | ||||||||
\(681\) | 15.0873 | 0.578145 | ||||||||
\(682\) | 36.3129 | 1.39049 | ||||||||
\(683\) | −33.7253 | −1.29046 | −0.645232 | − | 0.763986i | \(-0.723239\pi\) | ||||
−0.645232 | + | 0.763986i | \(0.723239\pi\) | |||||||
\(684\) | 8.51295 | 0.325501 | ||||||||
\(685\) | −0.645050 | −0.0246461 | ||||||||
\(686\) | 2.35796 | 0.0900272 | ||||||||
\(687\) | −15.6421 | −0.596784 | ||||||||
\(688\) | 16.7209 | 0.637477 | ||||||||
\(689\) | −38.1437 | −1.45316 | ||||||||
\(690\) | 29.4694 | 1.12188 | ||||||||
\(691\) | −41.2895 | −1.57073 | −0.785364 | − | 0.619035i | \(-0.787524\pi\) | ||||
−0.785364 | + | 0.619035i | \(0.787524\pi\) | |||||||
\(692\) | 43.3827 | 1.64916 | ||||||||
\(693\) | −4.36512 | −0.165817 | ||||||||
\(694\) | −79.6380 | −3.02302 | ||||||||
\(695\) | −14.8507 | −0.563320 | ||||||||
\(696\) | −30.9807 | −1.17432 | ||||||||
\(697\) | 2.67446 | 0.101302 | ||||||||
\(698\) | 72.8449 | 2.75722 | ||||||||
\(699\) | 2.89412 | 0.109466 | ||||||||
\(700\) | −10.5028 | −0.396968 | ||||||||
\(701\) | −24.2530 | −0.916022 | −0.458011 | − | 0.888947i | \(-0.651438\pi\) | ||||
−0.458011 | + | 0.888947i | \(0.651438\pi\) | |||||||
\(702\) | −14.8059 | −0.558813 | ||||||||
\(703\) | 21.8215 | 0.823015 | ||||||||
\(704\) | 51.5810 | 1.94403 | ||||||||
\(705\) | −14.8810 | −0.560450 | ||||||||
\(706\) | −80.8580 | −3.04313 | ||||||||
\(707\) | −4.86006 | −0.182781 | ||||||||
\(708\) | −40.4452 | −1.52002 | ||||||||
\(709\) | −6.01257 | −0.225807 | −0.112903 | − | 0.993606i | \(-0.536015\pi\) | ||||
−0.112903 | + | 0.993606i | \(0.536015\pi\) | |||||||
\(710\) | 24.9673 | 0.937007 | ||||||||
\(711\) | 12.5561 | 0.470889 | ||||||||
\(712\) | −13.9371 | −0.522315 | ||||||||
\(713\) | 30.7975 | 1.15338 | ||||||||
\(714\) | −7.46485 | −0.279365 | ||||||||
\(715\) | −39.2414 | −1.46755 | ||||||||
\(716\) | 28.0037 | 1.04655 | ||||||||
\(717\) | −13.5783 | −0.507093 | ||||||||
\(718\) | 86.1590 | 3.21543 | ||||||||
\(719\) | 9.58924 | 0.357618 | 0.178809 | − | 0.983884i | \(-0.442776\pi\) | ||||
0.178809 | + | 0.983884i | \(0.442776\pi\) | |||||||
\(720\) | 2.22395 | 0.0828816 | ||||||||
\(721\) | −12.2098 | −0.454717 | ||||||||
\(722\) | −31.3175 | −1.16552 | ||||||||
\(723\) | −0.304916 | −0.0113400 | ||||||||
\(724\) | 0.894114 | 0.0332295 | ||||||||
\(725\) | −24.8487 | −0.922858 | ||||||||
\(726\) | −18.9915 | −0.704841 | ||||||||
\(727\) | −16.6844 | −0.618789 | −0.309395 | − | 0.950934i | \(-0.600126\pi\) | ||||
−0.309395 | + | 0.950934i | \(0.600126\pi\) | |||||||
\(728\) | 23.0966 | 0.856016 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 43.8668 | 1.62358 | ||||||||
\(731\) | 34.0776 | 1.26041 | ||||||||
\(732\) | 11.4866 | 0.424557 | ||||||||
\(733\) | 37.2954 | 1.37754 | 0.688768 | − | 0.724982i | \(-0.258152\pi\) | ||||
0.688768 | + | 0.724982i | \(0.258152\pi\) | |||||||
\(734\) | −29.7076 | −1.09653 | ||||||||
\(735\) | −1.43169 | −0.0528087 | ||||||||
\(736\) | 32.2450 | 1.18857 | ||||||||
\(737\) | −0.0246872 | −0.000909366 0 | ||||||||
\(738\) | 1.99198 | 0.0733259 | ||||||||
\(739\) | 42.5537 | 1.56536 | 0.782682 | − | 0.622421i | \(-0.213851\pi\) | ||||
0.782682 | + | 0.622421i | \(0.213851\pi\) | |||||||
\(740\) | 46.5097 | 1.70973 | ||||||||
\(741\) | −15.0153 | −0.551602 | ||||||||
\(742\) | −14.3238 | −0.525844 | ||||||||
\(743\) | 30.8722 | 1.13259 | 0.566295 | − | 0.824203i | \(-0.308376\pi\) | ||||
0.566295 | + | 0.824203i | \(0.308376\pi\) | |||||||
\(744\) | 12.9771 | 0.475764 | ||||||||
\(745\) | 27.6523 | 1.01310 | ||||||||
\(746\) | −14.9885 | −0.548768 | ||||||||
\(747\) | −9.65775 | −0.353359 | ||||||||
\(748\) | −49.1955 | −1.79877 | ||||||||
\(749\) | 4.40730 | 0.161039 | ||||||||
\(750\) | 26.8390 | 0.980022 | ||||||||
\(751\) | 33.3561 | 1.21718 | 0.608590 | − | 0.793485i | \(-0.291735\pi\) | ||||
0.608590 | + | 0.793485i | \(0.291735\pi\) | |||||||
\(752\) | 16.1457 | 0.588773 | ||||||||
\(753\) | 28.2439 | 1.02926 | ||||||||
\(754\) | 124.704 | 4.54144 | ||||||||
\(755\) | 10.4444 | 0.380112 | ||||||||
\(756\) | −3.55996 | −0.129474 | ||||||||
\(757\) | −34.7387 | −1.26260 | −0.631300 | − | 0.775539i | \(-0.717478\pi\) | ||||
−0.631300 | + | 0.775539i | \(0.717478\pi\) | |||||||
\(758\) | −17.6539 | −0.641218 | ||||||||
\(759\) | −38.1049 | −1.38312 | ||||||||
\(760\) | 12.5931 | 0.456800 | ||||||||
\(761\) | −7.70707 | −0.279381 | −0.139690 | − | 0.990195i | \(-0.544611\pi\) | ||||
−0.139690 | + | 0.990195i | \(0.544611\pi\) | |||||||
\(762\) | 12.5467 | 0.454518 | ||||||||
\(763\) | −12.9720 | −0.469619 | ||||||||
\(764\) | −82.6873 | −2.99152 | ||||||||
\(765\) | 4.53247 | 0.163872 | ||||||||
\(766\) | −2.35796 | −0.0851964 | ||||||||
\(767\) | 71.3381 | 2.57587 | ||||||||
\(768\) | 24.6469 | 0.889368 | ||||||||
\(769\) | 18.8981 | 0.681482 | 0.340741 | − | 0.940157i | \(-0.389322\pi\) | ||||
0.340741 | + | 0.940157i | \(0.389322\pi\) | |||||||
\(770\) | −14.7360 | −0.531050 | ||||||||
\(771\) | −11.0519 | −0.398026 | ||||||||
\(772\) | 29.2719 | 1.05352 | ||||||||
\(773\) | −11.9315 | −0.429147 | −0.214573 | − | 0.976708i | \(-0.568836\pi\) | ||||
−0.214573 | + | 0.976708i | \(0.568836\pi\) | |||||||
\(774\) | 25.3816 | 0.912324 | ||||||||
\(775\) | 10.4085 | 0.373886 | ||||||||
\(776\) | −21.7398 | −0.780413 | ||||||||
\(777\) | −9.12536 | −0.327370 | ||||||||
\(778\) | 79.2489 | 2.84121 | ||||||||
\(779\) | 2.02016 | 0.0723797 | ||||||||
\(780\) | −32.0032 | −1.14590 | ||||||||
\(781\) | −32.2836 | −1.15520 | ||||||||
\(782\) | −65.1638 | −2.33025 | ||||||||
\(783\) | −8.42255 | −0.300998 | ||||||||
\(784\) | 1.55337 | 0.0554775 | ||||||||
\(785\) | 12.3448 | 0.440606 | ||||||||
\(786\) | 40.4033 | 1.44114 | ||||||||
\(787\) | −20.7016 | −0.737934 | −0.368967 | − | 0.929443i | \(-0.620288\pi\) | ||||
−0.368967 | + | 0.929443i | \(0.620288\pi\) | |||||||
\(788\) | −78.5276 | −2.79743 | ||||||||
\(789\) | 14.6634 | 0.522032 | ||||||||
\(790\) | 42.3876 | 1.50808 | ||||||||
\(791\) | 10.4743 | 0.372425 | ||||||||
\(792\) | −16.0562 | −0.570533 | ||||||||
\(793\) | −20.2604 | −0.719466 | ||||||||
\(794\) | 42.2902 | 1.50082 | ||||||||
\(795\) | 8.69706 | 0.308453 | ||||||||
\(796\) | 81.2023 | 2.87814 | ||||||||
\(797\) | −20.5348 | −0.727380 | −0.363690 | − | 0.931520i | \(-0.618483\pi\) | ||||
−0.363690 | + | 0.931520i | \(0.618483\pi\) | |||||||
\(798\) | −5.63860 | −0.199604 | ||||||||
\(799\) | 32.9054 | 1.16411 | ||||||||
\(800\) | 10.8978 | 0.385294 | ||||||||
\(801\) | −3.78900 | −0.133878 | ||||||||
\(802\) | 59.6505 | 2.10633 | ||||||||
\(803\) | −56.7214 | −2.00165 | ||||||||
\(804\) | −0.0201336 | −0.000710057 0 | ||||||||
\(805\) | −12.4978 | −0.440491 | ||||||||
\(806\) | −52.2355 | −1.83992 | ||||||||
\(807\) | 19.6117 | 0.690366 | ||||||||
\(808\) | −17.8768 | −0.628903 | ||||||||
\(809\) | −10.3787 | −0.364895 | −0.182448 | − | 0.983216i | \(-0.558402\pi\) | ||||
−0.182448 | + | 0.983216i | \(0.558402\pi\) | |||||||
\(810\) | 3.37587 | 0.118616 | ||||||||
\(811\) | 45.5446 | 1.59929 | 0.799644 | − | 0.600475i | \(-0.205022\pi\) | ||||
0.799644 | + | 0.600475i | \(0.205022\pi\) | |||||||
\(812\) | 29.9839 | 1.05223 | ||||||||
\(813\) | 6.71460 | 0.235491 | ||||||||
\(814\) | −93.9250 | −3.29207 | ||||||||
\(815\) | 8.58231 | 0.300625 | ||||||||
\(816\) | −4.91768 | −0.172153 | ||||||||
\(817\) | 25.7406 | 0.900551 | ||||||||
\(818\) | 5.37508 | 0.187935 | ||||||||
\(819\) | 6.27913 | 0.219411 | ||||||||
\(820\) | 4.30570 | 0.150362 | ||||||||
\(821\) | 13.1971 | 0.460582 | 0.230291 | − | 0.973122i | \(-0.426032\pi\) | ||||
0.230291 | + | 0.973122i | \(0.426032\pi\) | |||||||
\(822\) | 1.06238 | 0.0370547 | ||||||||
\(823\) | 9.18432 | 0.320145 | 0.160073 | − | 0.987105i | \(-0.448827\pi\) | ||||
0.160073 | + | 0.987105i | \(0.448827\pi\) | |||||||
\(824\) | −44.9114 | −1.56456 | ||||||||
\(825\) | −12.8782 | −0.448362 | ||||||||
\(826\) | 26.7891 | 0.932111 | ||||||||
\(827\) | −0.687392 | −0.0239030 | −0.0119515 | − | 0.999929i | \(-0.503804\pi\) | ||||
−0.0119515 | + | 0.999929i | \(0.503804\pi\) | |||||||
\(828\) | −31.0764 | −1.07998 | ||||||||
\(829\) | −23.8218 | −0.827366 | −0.413683 | − | 0.910421i | \(-0.635758\pi\) | ||||
−0.413683 | + | 0.910421i | \(0.635758\pi\) | |||||||
\(830\) | −32.6033 | −1.13168 | ||||||||
\(831\) | 2.80019 | 0.0971375 | ||||||||
\(832\) | −74.1982 | −2.57236 | ||||||||
\(833\) | 3.16581 | 0.109689 | ||||||||
\(834\) | 24.4587 | 0.846937 | ||||||||
\(835\) | 8.19411 | 0.283569 | ||||||||
\(836\) | −37.1600 | −1.28521 | ||||||||
\(837\) | 3.52801 | 0.121946 | ||||||||
\(838\) | 19.9606 | 0.689528 | ||||||||
\(839\) | −29.6876 | −1.02493 | −0.512465 | − | 0.858708i | \(-0.671268\pi\) | ||||
−0.512465 | + | 0.858708i | \(0.671268\pi\) | |||||||
\(840\) | −5.26620 | −0.181701 | ||||||||
\(841\) | 41.9394 | 1.44619 | ||||||||
\(842\) | −34.5279 | −1.18991 | ||||||||
\(843\) | −5.34685 | −0.184155 | ||||||||
\(844\) | −44.4571 | −1.53028 | ||||||||
\(845\) | 37.8361 | 1.30160 | ||||||||
\(846\) | 24.5085 | 0.842621 | ||||||||
\(847\) | 8.05423 | 0.276747 | ||||||||
\(848\) | −9.43622 | −0.324041 | ||||||||
\(849\) | −26.6453 | −0.914463 | ||||||||
\(850\) | −22.0232 | −0.755391 | ||||||||
\(851\) | −79.6591 | −2.73068 | ||||||||
\(852\) | −26.3288 | −0.902010 | ||||||||
\(853\) | 10.6533 | 0.364762 | 0.182381 | − | 0.983228i | \(-0.441620\pi\) | ||||
0.182381 | + | 0.983228i | \(0.441620\pi\) | |||||||
\(854\) | −7.60822 | −0.260348 | ||||||||
\(855\) | 3.42362 | 0.117085 | ||||||||
\(856\) | 16.2114 | 0.554094 | ||||||||
\(857\) | −52.8448 | −1.80514 | −0.902572 | − | 0.430538i | \(-0.858324\pi\) | ||||
−0.902572 | + | 0.430538i | \(0.858324\pi\) | |||||||
\(858\) | 64.6295 | 2.20642 | ||||||||
\(859\) | −25.1690 | −0.858756 | −0.429378 | − | 0.903125i | \(-0.641267\pi\) | ||||
−0.429378 | + | 0.903125i | \(0.641267\pi\) | |||||||
\(860\) | 54.8628 | 1.87081 | ||||||||
\(861\) | −0.844792 | −0.0287904 | ||||||||
\(862\) | 10.3755 | 0.353392 | ||||||||
\(863\) | −20.7287 | −0.705614 | −0.352807 | − | 0.935696i | \(-0.614773\pi\) | ||||
−0.352807 | + | 0.935696i | \(0.614773\pi\) | |||||||
\(864\) | 3.69383 | 0.125667 | ||||||||
\(865\) | 17.4471 | 0.593218 | ||||||||
\(866\) | −25.5762 | −0.869114 | ||||||||
\(867\) | 6.97762 | 0.236973 | ||||||||
\(868\) | −12.5596 | −0.426299 | ||||||||
\(869\) | −54.8086 | −1.85926 | ||||||||
\(870\) | −28.4334 | −0.963983 | ||||||||
\(871\) | 0.0355121 | 0.00120328 | ||||||||
\(872\) | −47.7151 | −1.61584 | ||||||||
\(873\) | −5.91028 | −0.200033 | ||||||||
\(874\) | −49.2217 | −1.66495 | ||||||||
\(875\) | −11.3823 | −0.384793 | ||||||||
\(876\) | −46.2589 | −1.56294 | ||||||||
\(877\) | −29.2694 | −0.988358 | −0.494179 | − | 0.869360i | \(-0.664531\pi\) | ||||
−0.494179 | + | 0.869360i | \(0.664531\pi\) | |||||||
\(878\) | 22.8210 | 0.770171 | ||||||||
\(879\) | 21.6035 | 0.728670 | ||||||||
\(880\) | −9.70778 | −0.327249 | ||||||||
\(881\) | −30.0684 | −1.01303 | −0.506515 | − | 0.862231i | \(-0.669066\pi\) | ||||
−0.506515 | + | 0.862231i | \(0.669066\pi\) | |||||||
\(882\) | 2.35796 | 0.0793965 | ||||||||
\(883\) | −4.03992 | −0.135954 | −0.0679771 | − | 0.997687i | \(-0.521654\pi\) | ||||
−0.0679771 | + | 0.997687i | \(0.521654\pi\) | |||||||
\(884\) | 70.7668 | 2.38015 | ||||||||
\(885\) | −16.2657 | −0.546764 | ||||||||
\(886\) | 17.8494 | 0.599663 | ||||||||
\(887\) | 30.9608 | 1.03956 | 0.519781 | − | 0.854299i | \(-0.326013\pi\) | ||||
0.519781 | + | 0.854299i | \(0.326013\pi\) | |||||||
\(888\) | −33.5658 | −1.12640 | ||||||||
\(889\) | −5.32100 | −0.178460 | ||||||||
\(890\) | −12.7912 | −0.428761 | ||||||||
\(891\) | −4.36512 | −0.146237 | ||||||||
\(892\) | 65.7571 | 2.20171 | ||||||||
\(893\) | 24.8552 | 0.831748 | ||||||||
\(894\) | −45.5426 | −1.52317 | ||||||||
\(895\) | 11.2621 | 0.376451 | ||||||||
\(896\) | −20.4754 | −0.684036 | ||||||||
\(897\) | 54.8132 | 1.83016 | ||||||||
\(898\) | 92.8804 | 3.09946 | ||||||||
\(899\) | −29.7149 | −0.991046 | ||||||||
\(900\) | −10.5028 | −0.350093 | ||||||||
\(901\) | −19.2313 | −0.640687 | ||||||||
\(902\) | −8.69524 | −0.289520 | ||||||||
\(903\) | −10.7642 | −0.358212 | ||||||||
\(904\) | 38.5278 | 1.28142 | ||||||||
\(905\) | 0.359582 | 0.0119529 | ||||||||
\(906\) | −17.2017 | −0.571488 | ||||||||
\(907\) | 13.6220 | 0.452312 | 0.226156 | − | 0.974091i | \(-0.427384\pi\) | ||||
0.226156 | + | 0.974091i | \(0.427384\pi\) | |||||||
\(908\) | −53.7100 | −1.78243 | ||||||||
\(909\) | −4.86006 | −0.161198 | ||||||||
\(910\) | 21.1975 | 0.702691 | ||||||||
\(911\) | 24.1478 | 0.800053 | 0.400026 | − | 0.916504i | \(-0.369001\pi\) | ||||
0.400026 | + | 0.916504i | \(0.369001\pi\) | |||||||
\(912\) | −3.71458 | −0.123002 | ||||||||
\(913\) | 42.1572 | 1.39520 | ||||||||
\(914\) | −0.284074 | −0.00939634 | ||||||||
\(915\) | 4.61952 | 0.152717 | ||||||||
\(916\) | 55.6852 | 1.83989 | ||||||||
\(917\) | −17.1349 | −0.565843 | ||||||||
\(918\) | −7.46485 | −0.246377 | ||||||||
\(919\) | 24.1235 | 0.795761 | 0.397880 | − | 0.917437i | \(-0.369746\pi\) | ||||
0.397880 | + | 0.917437i | \(0.369746\pi\) | |||||||
\(920\) | −45.9709 | −1.51562 | ||||||||
\(921\) | −15.4644 | −0.509569 | ||||||||
\(922\) | −50.4448 | −1.66131 | ||||||||
\(923\) | 46.4394 | 1.52857 | ||||||||
\(924\) | 15.5396 | 0.511216 | ||||||||
\(925\) | −26.9222 | −0.885195 | ||||||||
\(926\) | −66.5582 | −2.18724 | ||||||||
\(927\) | −12.2098 | −0.401023 | ||||||||
\(928\) | −31.1115 | −1.02129 | ||||||||
\(929\) | 42.8777 | 1.40677 | 0.703386 | − | 0.710808i | \(-0.251671\pi\) | ||||
0.703386 | + | 0.710808i | \(0.251671\pi\) | |||||||
\(930\) | 11.9101 | 0.390547 | ||||||||
\(931\) | 2.39131 | 0.0783719 | ||||||||
\(932\) | −10.3029 | −0.337484 | ||||||||
\(933\) | 15.3382 | 0.502150 | ||||||||
\(934\) | −16.1373 | −0.528028 | ||||||||
\(935\) | −19.7848 | −0.647031 | ||||||||
\(936\) | 23.0966 | 0.754935 | ||||||||
\(937\) | 24.5459 | 0.801880 | 0.400940 | − | 0.916104i | \(-0.368684\pi\) | ||||
0.400940 | + | 0.916104i | \(0.368684\pi\) | |||||||
\(938\) | 0.0133356 | 0.000435423 0 | ||||||||
\(939\) | 9.21957 | 0.300869 | ||||||||
\(940\) | 52.9756 | 1.72787 | ||||||||
\(941\) | −18.2239 | −0.594081 | −0.297040 | − | 0.954865i | \(-0.596000\pi\) | ||||
−0.297040 | + | 0.954865i | \(0.596000\pi\) | |||||||
\(942\) | −20.3316 | −0.662438 | ||||||||
\(943\) | −7.37455 | −0.240148 | ||||||||
\(944\) | 17.6481 | 0.574395 | ||||||||
\(945\) | −1.43169 | −0.0465729 | ||||||||
\(946\) | −110.794 | −3.60221 | ||||||||
\(947\) | −12.0154 | −0.390448 | −0.195224 | − | 0.980759i | \(-0.562543\pi\) | ||||
−0.195224 | + | 0.980759i | \(0.562543\pi\) | |||||||
\(948\) | −44.6990 | −1.45176 | ||||||||
\(949\) | 81.5926 | 2.64861 | ||||||||
\(950\) | −16.6353 | −0.539721 | ||||||||
\(951\) | −13.0864 | −0.424355 | ||||||||
\(952\) | 11.6448 | 0.377411 | ||||||||
\(953\) | −0.106442 | −0.00344799 | −0.00172400 | − | 0.999999i | \(-0.500549\pi\) | ||||
−0.00172400 | + | 0.999999i | \(0.500549\pi\) | |||||||
\(954\) | −14.3238 | −0.463751 | ||||||||
\(955\) | −33.2540 | −1.07607 | ||||||||
\(956\) | 48.3383 | 1.56337 | ||||||||
\(957\) | 36.7654 | 1.18846 | ||||||||
\(958\) | −81.1551 | −2.62200 | ||||||||
\(959\) | −0.450551 | −0.0145491 | ||||||||
\(960\) | 16.9178 | 0.546019 | ||||||||
\(961\) | −18.5531 | −0.598488 | ||||||||
\(962\) | 135.109 | 4.35610 | ||||||||
\(963\) | 4.40730 | 0.142023 | ||||||||
\(964\) | 1.08549 | 0.0349612 | ||||||||
\(965\) | 11.7721 | 0.378958 | ||||||||
\(966\) | 20.5836 | 0.662266 | ||||||||
\(967\) | −38.2788 | −1.23096 | −0.615481 | − | 0.788151i | \(-0.711038\pi\) | ||||
−0.615481 | + | 0.788151i | \(0.711038\pi\) | |||||||
\(968\) | 29.6259 | 0.952213 | ||||||||
\(969\) | −7.57043 | −0.243197 | ||||||||
\(970\) | −19.9523 | −0.640630 | ||||||||
\(971\) | −9.26689 | −0.297389 | −0.148694 | − | 0.988883i | \(-0.547507\pi\) | ||||
−0.148694 | + | 0.988883i | \(0.547507\pi\) | |||||||
\(972\) | −3.55996 | −0.114186 | ||||||||
\(973\) | −10.3729 | −0.332538 | ||||||||
\(974\) | −71.0174 | −2.27554 | ||||||||
\(975\) | 18.5251 | 0.593277 | ||||||||
\(976\) | −5.01213 | −0.160434 | ||||||||
\(977\) | 21.2564 | 0.680054 | 0.340027 | − | 0.940416i | \(-0.389564\pi\) | ||||
0.340027 | + | 0.940416i | \(0.389564\pi\) | |||||||
\(978\) | −14.1348 | −0.451982 | ||||||||
\(979\) | 16.5394 | 0.528602 | ||||||||
\(980\) | 5.09676 | 0.162810 | ||||||||
\(981\) | −12.9720 | −0.414165 | ||||||||
\(982\) | −44.1281 | −1.40818 | ||||||||
\(983\) | −32.5753 | −1.03899 | −0.519496 | − | 0.854473i | \(-0.673880\pi\) | ||||
−0.519496 | + | 0.854473i | \(0.673880\pi\) | |||||||
\(984\) | −3.10740 | −0.0990604 | ||||||||
\(985\) | −31.5811 | −1.00626 | ||||||||
\(986\) | 62.8731 | 2.00229 | ||||||||
\(987\) | −10.3940 | −0.330844 | ||||||||
\(988\) | 53.4539 | 1.70060 | ||||||||
\(989\) | −93.9657 | −2.98794 | ||||||||
\(990\) | −14.7360 | −0.468342 | ||||||||
\(991\) | −30.5541 | −0.970582 | −0.485291 | − | 0.874353i | \(-0.661286\pi\) | ||||
−0.485291 | + | 0.874353i | \(0.661286\pi\) | |||||||
\(992\) | 13.0319 | 0.413763 | ||||||||
\(993\) | −0.953807 | −0.0302682 | ||||||||
\(994\) | 17.4390 | 0.553133 | ||||||||
\(995\) | 32.6568 | 1.03529 | ||||||||
\(996\) | 34.3812 | 1.08941 | ||||||||
\(997\) | −16.8964 | −0.535114 | −0.267557 | − | 0.963542i | \(-0.586216\pi\) | ||||
−0.267557 | + | 0.963542i | \(0.586216\pi\) | |||||||
\(998\) | −94.9730 | −3.00632 | ||||||||
\(999\) | −9.12536 | −0.288714 |
(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 | 8043.2.a.t.1.45 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.t.1.45 | ✓ | 52 | 1.1 | even | 1 | trivial |