Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6047,2,Mod(1,6047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6047 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6047.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: | \(48.2855381023\) |
Analytic rank: | \(0\) |
Dimension: | \(287\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69052 | −1.90249 | −0.951244 | − | 0.308439i | \(-0.900193\pi\) | ||||
−0.951244 | + | 0.308439i | \(0.900193\pi\) | |||||||
\(3\) | −1.22455 | −0.706994 | −0.353497 | − | 0.935436i | \(-0.615008\pi\) | ||||
−0.353497 | + | 0.935436i | \(0.615008\pi\) | |||||||
\(4\) | 5.23892 | 2.61946 | ||||||||
\(5\) | 3.48449 | 1.55831 | 0.779156 | − | 0.626830i | \(-0.215648\pi\) | ||||
0.779156 | + | 0.626830i | \(0.215648\pi\) | |||||||
\(6\) | 3.29468 | 1.34505 | ||||||||
\(7\) | 4.74165 | 1.79218 | 0.896088 | − | 0.443877i | \(-0.146397\pi\) | ||||
0.896088 | + | 0.443877i | \(0.146397\pi\) | |||||||
\(8\) | −8.71440 | −3.08100 | ||||||||
\(9\) | −1.50048 | −0.500159 | ||||||||
\(10\) | −9.37511 | −2.96467 | ||||||||
\(11\) | −0.101858 | −0.0307113 | −0.0153556 | − | 0.999882i | \(-0.504888\pi\) | ||||
−0.0153556 | + | 0.999882i | \(0.504888\pi\) | |||||||
\(12\) | −6.41532 | −1.85194 | ||||||||
\(13\) | 3.70807 | 1.02843 | 0.514217 | − | 0.857660i | \(-0.328082\pi\) | ||||
0.514217 | + | 0.857660i | \(0.328082\pi\) | |||||||
\(14\) | −12.7575 | −3.40959 | ||||||||
\(15\) | −4.26693 | −1.10172 | ||||||||
\(16\) | 12.9685 | 3.24211 | ||||||||
\(17\) | 1.84612 | 0.447749 | 0.223875 | − | 0.974618i | \(-0.428129\pi\) | ||||
0.223875 | + | 0.974618i | \(0.428129\pi\) | |||||||
\(18\) | 4.03707 | 0.951547 | ||||||||
\(19\) | 6.19824 | 1.42197 | 0.710987 | − | 0.703205i | \(-0.248249\pi\) | ||||
0.710987 | + | 0.703205i | \(0.248249\pi\) | |||||||
\(20\) | 18.2550 | 4.08194 | ||||||||
\(21\) | −5.80639 | −1.26706 | ||||||||
\(22\) | 0.274051 | 0.0584279 | ||||||||
\(23\) | −0.771298 | −0.160827 | −0.0804134 | − | 0.996762i | \(-0.525624\pi\) | ||||
−0.0804134 | + | 0.996762i | \(0.525624\pi\) | |||||||
\(24\) | 10.6712 | 2.17825 | ||||||||
\(25\) | 7.14168 | 1.42834 | ||||||||
\(26\) | −9.97666 | −1.95658 | ||||||||
\(27\) | 5.51106 | 1.06060 | ||||||||
\(28\) | 24.8411 | 4.69453 | ||||||||
\(29\) | −7.94169 | −1.47474 | −0.737368 | − | 0.675492i | \(-0.763931\pi\) | ||||
−0.737368 | + | 0.675492i | \(0.763931\pi\) | |||||||
\(30\) | 11.4803 | 2.09600 | ||||||||
\(31\) | 9.88585 | 1.77555 | 0.887776 | − | 0.460276i | \(-0.152250\pi\) | ||||
0.887776 | + | 0.460276i | \(0.152250\pi\) | |||||||
\(32\) | −17.4631 | −3.08708 | ||||||||
\(33\) | 0.124730 | 0.0217127 | ||||||||
\(34\) | −4.96702 | −0.851837 | ||||||||
\(35\) | 16.5222 | 2.79277 | ||||||||
\(36\) | −7.86088 | −1.31015 | ||||||||
\(37\) | 8.20300 | 1.34856 | 0.674282 | − | 0.738474i | \(-0.264453\pi\) | ||||
0.674282 | + | 0.738474i | \(0.264453\pi\) | |||||||
\(38\) | −16.6765 | −2.70529 | ||||||||
\(39\) | −4.54072 | −0.727098 | ||||||||
\(40\) | −30.3652 | −4.80116 | ||||||||
\(41\) | 0.0528848 | 0.00825922 | 0.00412961 | − | 0.999991i | \(-0.498686\pi\) | ||||
0.00412961 | + | 0.999991i | \(0.498686\pi\) | |||||||
\(42\) | 15.6222 | 2.41056 | ||||||||
\(43\) | −5.27439 | −0.804337 | −0.402168 | − | 0.915566i | \(-0.631743\pi\) | ||||
−0.402168 | + | 0.915566i | \(0.631743\pi\) | |||||||
\(44\) | −0.533625 | −0.0804470 | ||||||||
\(45\) | −5.22840 | −0.779404 | ||||||||
\(46\) | 2.07520 | 0.305971 | ||||||||
\(47\) | −10.3434 | −1.50874 | −0.754372 | − | 0.656448i | \(-0.772058\pi\) | ||||
−0.754372 | + | 0.656448i | \(0.772058\pi\) | |||||||
\(48\) | −15.8805 | −2.29216 | ||||||||
\(49\) | 15.4832 | 2.21189 | ||||||||
\(50\) | −19.2149 | −2.71739 | ||||||||
\(51\) | −2.26066 | −0.316556 | ||||||||
\(52\) | 19.4263 | 2.69394 | ||||||||
\(53\) | 2.93474 | 0.403117 | 0.201559 | − | 0.979476i | \(-0.435399\pi\) | ||||
0.201559 | + | 0.979476i | \(0.435399\pi\) | |||||||
\(54\) | −14.8276 | −2.01779 | ||||||||
\(55\) | −0.354923 | −0.0478578 | ||||||||
\(56\) | −41.3206 | −5.52170 | ||||||||
\(57\) | −7.59005 | −1.00533 | ||||||||
\(58\) | 21.3673 | 2.80567 | ||||||||
\(59\) | −2.85944 | −0.372267 | −0.186134 | − | 0.982524i | \(-0.559596\pi\) | ||||
−0.186134 | + | 0.982524i | \(0.559596\pi\) | |||||||
\(60\) | −22.3541 | −2.88591 | ||||||||
\(61\) | −7.44599 | −0.953362 | −0.476681 | − | 0.879076i | \(-0.658160\pi\) | ||||
−0.476681 | + | 0.879076i | \(0.658160\pi\) | |||||||
\(62\) | −26.5981 | −3.37797 | ||||||||
\(63\) | −7.11474 | −0.896373 | ||||||||
\(64\) | 21.0481 | 2.63101 | ||||||||
\(65\) | 12.9208 | 1.60262 | ||||||||
\(66\) | −0.335589 | −0.0413082 | ||||||||
\(67\) | −8.72133 | −1.06548 | −0.532740 | − | 0.846279i | \(-0.678838\pi\) | ||||
−0.532740 | + | 0.846279i | \(0.678838\pi\) | |||||||
\(68\) | 9.67166 | 1.17286 | ||||||||
\(69\) | 0.944493 | 0.113704 | ||||||||
\(70\) | −44.4535 | −5.31321 | ||||||||
\(71\) | 16.6740 | 1.97884 | 0.989422 | − | 0.145067i | \(-0.0463399\pi\) | ||||
0.989422 | + | 0.145067i | \(0.0463399\pi\) | |||||||
\(72\) | 13.0758 | 1.54099 | ||||||||
\(73\) | −4.16063 | −0.486965 | −0.243482 | − | 0.969905i | \(-0.578290\pi\) | ||||
−0.243482 | + | 0.969905i | \(0.578290\pi\) | |||||||
\(74\) | −22.0704 | −2.56563 | ||||||||
\(75\) | −8.74534 | −1.00982 | ||||||||
\(76\) | 32.4721 | 3.72480 | ||||||||
\(77\) | −0.482974 | −0.0550400 | ||||||||
\(78\) | 12.2169 | 1.38329 | ||||||||
\(79\) | 7.63338 | 0.858823 | 0.429411 | − | 0.903109i | \(-0.358721\pi\) | ||||
0.429411 | + | 0.903109i | \(0.358721\pi\) | |||||||
\(80\) | 45.1885 | 5.05222 | ||||||||
\(81\) | −2.24714 | −0.249682 | ||||||||
\(82\) | −0.142288 | −0.0157131 | ||||||||
\(83\) | −2.61134 | −0.286632 | −0.143316 | − | 0.989677i | \(-0.545776\pi\) | ||||
−0.143316 | + | 0.989677i | \(0.545776\pi\) | |||||||
\(84\) | −30.4192 | −3.31901 | ||||||||
\(85\) | 6.43278 | 0.697733 | ||||||||
\(86\) | 14.1909 | 1.53024 | ||||||||
\(87\) | 9.72500 | 1.04263 | ||||||||
\(88\) | 0.887630 | 0.0946216 | ||||||||
\(89\) | 5.30060 | 0.561862 | 0.280931 | − | 0.959728i | \(-0.409357\pi\) | ||||
0.280931 | + | 0.959728i | \(0.409357\pi\) | |||||||
\(90\) | 14.0671 | 1.48281 | ||||||||
\(91\) | 17.5824 | 1.84314 | ||||||||
\(92\) | −4.04077 | −0.421279 | ||||||||
\(93\) | −12.1057 | −1.25530 | ||||||||
\(94\) | 27.8292 | 2.87037 | ||||||||
\(95\) | 21.5977 | 2.21588 | ||||||||
\(96\) | 21.3845 | 2.18255 | ||||||||
\(97\) | 11.8985 | 1.20810 | 0.604052 | − | 0.796945i | \(-0.293552\pi\) | ||||
0.604052 | + | 0.796945i | \(0.293552\pi\) | |||||||
\(98\) | −41.6580 | −4.20810 | ||||||||
\(99\) | 0.152835 | 0.0153605 | ||||||||
\(100\) | 37.4147 | 3.74147 | ||||||||
\(101\) | 9.08359 | 0.903851 | 0.451925 | − | 0.892056i | \(-0.350737\pi\) | ||||
0.451925 | + | 0.892056i | \(0.350737\pi\) | |||||||
\(102\) | 6.08237 | 0.602244 | ||||||||
\(103\) | −3.89449 | −0.383735 | −0.191868 | − | 0.981421i | \(-0.561454\pi\) | ||||
−0.191868 | + | 0.981421i | \(0.561454\pi\) | |||||||
\(104\) | −32.3136 | −3.16861 | ||||||||
\(105\) | −20.2323 | −1.97447 | ||||||||
\(106\) | −7.89598 | −0.766925 | ||||||||
\(107\) | −12.4086 | −1.19959 | −0.599793 | − | 0.800155i | \(-0.704750\pi\) | ||||
−0.599793 | + | 0.800155i | \(0.704750\pi\) | |||||||
\(108\) | 28.8720 | 2.77821 | ||||||||
\(109\) | −15.3937 | −1.47445 | −0.737223 | − | 0.675650i | \(-0.763863\pi\) | ||||
−0.737223 | + | 0.675650i | \(0.763863\pi\) | |||||||
\(110\) | 0.954928 | 0.0910488 | ||||||||
\(111\) | −10.0450 | −0.953427 | ||||||||
\(112\) | 61.4919 | 5.81043 | ||||||||
\(113\) | 8.93885 | 0.840896 | 0.420448 | − | 0.907317i | \(-0.361873\pi\) | ||||
0.420448 | + | 0.907317i | \(0.361873\pi\) | |||||||
\(114\) | 20.4212 | 1.91262 | ||||||||
\(115\) | −2.68758 | −0.250618 | ||||||||
\(116\) | −41.6059 | −3.86301 | ||||||||
\(117\) | −5.56388 | −0.514381 | ||||||||
\(118\) | 7.69339 | 0.708234 | ||||||||
\(119\) | 8.75364 | 0.802445 | ||||||||
\(120\) | 37.1837 | 3.39440 | ||||||||
\(121\) | −10.9896 | −0.999057 | ||||||||
\(122\) | 20.0336 | 1.81376 | ||||||||
\(123\) | −0.0647601 | −0.00583922 | ||||||||
\(124\) | 51.7912 | 4.65099 | ||||||||
\(125\) | 7.46265 | 0.667480 | ||||||||
\(126\) | 19.1424 | 1.70534 | ||||||||
\(127\) | 16.3849 | 1.45393 | 0.726964 | − | 0.686675i | \(-0.240931\pi\) | ||||
0.726964 | + | 0.686675i | \(0.240931\pi\) | |||||||
\(128\) | −21.7042 | −1.91839 | ||||||||
\(129\) | 6.45875 | 0.568662 | ||||||||
\(130\) | −34.7636 | −3.04897 | ||||||||
\(131\) | 10.4649 | 0.914323 | 0.457162 | − | 0.889384i | \(-0.348866\pi\) | ||||
0.457162 | + | 0.889384i | \(0.348866\pi\) | |||||||
\(132\) | 0.653451 | 0.0568756 | ||||||||
\(133\) | 29.3899 | 2.54843 | ||||||||
\(134\) | 23.4649 | 2.02706 | ||||||||
\(135\) | 19.2032 | 1.65275 | ||||||||
\(136\) | −16.0878 | −1.37952 | ||||||||
\(137\) | 8.26403 | 0.706044 | 0.353022 | − | 0.935615i | \(-0.385154\pi\) | ||||
0.353022 | + | 0.935615i | \(0.385154\pi\) | |||||||
\(138\) | −2.54118 | −0.216320 | ||||||||
\(139\) | −21.4749 | −1.82148 | −0.910740 | − | 0.412981i | \(-0.864488\pi\) | ||||
−0.910740 | + | 0.412981i | \(0.864488\pi\) | |||||||
\(140\) | 86.5587 | 7.31554 | ||||||||
\(141\) | 12.6660 | 1.06667 | ||||||||
\(142\) | −44.8619 | −3.76473 | ||||||||
\(143\) | −0.377696 | −0.0315846 | ||||||||
\(144\) | −19.4589 | −1.62157 | ||||||||
\(145\) | −27.6728 | −2.29810 | ||||||||
\(146\) | 11.1943 | 0.926445 | ||||||||
\(147\) | −18.9600 | −1.56379 | ||||||||
\(148\) | 42.9748 | 3.53251 | ||||||||
\(149\) | 9.35958 | 0.766767 | 0.383383 | − | 0.923589i | \(-0.374759\pi\) | ||||
0.383383 | + | 0.923589i | \(0.374759\pi\) | |||||||
\(150\) | 23.5296 | 1.92118 | ||||||||
\(151\) | 15.1816 | 1.23546 | 0.617731 | − | 0.786390i | \(-0.288052\pi\) | ||||
0.617731 | + | 0.786390i | \(0.288052\pi\) | |||||||
\(152\) | −54.0139 | −4.38111 | ||||||||
\(153\) | −2.77006 | −0.223946 | ||||||||
\(154\) | 1.29945 | 0.104713 | ||||||||
\(155\) | 34.4472 | 2.76686 | ||||||||
\(156\) | −23.7885 | −1.90460 | ||||||||
\(157\) | −15.4687 | −1.23454 | −0.617270 | − | 0.786752i | \(-0.711761\pi\) | ||||
−0.617270 | + | 0.786752i | \(0.711761\pi\) | |||||||
\(158\) | −20.5378 | −1.63390 | ||||||||
\(159\) | −3.59373 | −0.285001 | ||||||||
\(160\) | −60.8502 | −4.81063 | ||||||||
\(161\) | −3.65723 | −0.288230 | ||||||||
\(162\) | 6.04598 | 0.475017 | ||||||||
\(163\) | 14.0081 | 1.09720 | 0.548601 | − | 0.836085i | \(-0.315161\pi\) | ||||
0.548601 | + | 0.836085i | \(0.315161\pi\) | |||||||
\(164\) | 0.277059 | 0.0216347 | ||||||||
\(165\) | 0.434621 | 0.0338352 | ||||||||
\(166\) | 7.02587 | 0.545313 | ||||||||
\(167\) | 6.61321 | 0.511746 | 0.255873 | − | 0.966710i | \(-0.417637\pi\) | ||||
0.255873 | + | 0.966710i | \(0.417637\pi\) | |||||||
\(168\) | 50.5992 | 3.90381 | ||||||||
\(169\) | 0.749815 | 0.0576781 | ||||||||
\(170\) | −17.3075 | −1.32743 | ||||||||
\(171\) | −9.30032 | −0.711213 | ||||||||
\(172\) | −27.6321 | −2.10693 | ||||||||
\(173\) | −11.5099 | −0.875081 | −0.437540 | − | 0.899199i | \(-0.644150\pi\) | ||||
−0.437540 | + | 0.899199i | \(0.644150\pi\) | |||||||
\(174\) | −26.1654 | −1.98359 | ||||||||
\(175\) | 33.8633 | 2.55983 | ||||||||
\(176\) | −1.32094 | −0.0995695 | ||||||||
\(177\) | 3.50152 | 0.263191 | ||||||||
\(178\) | −14.2614 | −1.06894 | ||||||||
\(179\) | −4.51739 | −0.337645 | −0.168823 | − | 0.985646i | \(-0.553997\pi\) | ||||
−0.168823 | + | 0.985646i | \(0.553997\pi\) | |||||||
\(180\) | −27.3912 | −2.04162 | ||||||||
\(181\) | −9.54177 | −0.709234 | −0.354617 | − | 0.935012i | \(-0.615389\pi\) | ||||
−0.354617 | + | 0.935012i | \(0.615389\pi\) | |||||||
\(182\) | −47.3058 | −3.50654 | ||||||||
\(183\) | 9.11799 | 0.674021 | ||||||||
\(184\) | 6.72140 | 0.495508 | ||||||||
\(185\) | 28.5833 | 2.10148 | ||||||||
\(186\) | 32.5707 | 2.38820 | ||||||||
\(187\) | −0.188041 | −0.0137510 | ||||||||
\(188\) | −54.1884 | −3.95209 | ||||||||
\(189\) | 26.1315 | 1.90079 | ||||||||
\(190\) | −58.1092 | −4.21568 | ||||||||
\(191\) | 6.36925 | 0.460863 | 0.230431 | − | 0.973089i | \(-0.425986\pi\) | ||||
0.230431 | + | 0.973089i | \(0.425986\pi\) | |||||||
\(192\) | −25.7745 | −1.86011 | ||||||||
\(193\) | 14.3046 | 1.02967 | 0.514835 | − | 0.857290i | \(-0.327853\pi\) | ||||
0.514835 | + | 0.857290i | \(0.327853\pi\) | |||||||
\(194\) | −32.0131 | −2.29840 | ||||||||
\(195\) | −15.8221 | −1.13304 | ||||||||
\(196\) | 81.1155 | 5.79396 | ||||||||
\(197\) | 9.00492 | 0.641574 | 0.320787 | − | 0.947151i | \(-0.396053\pi\) | ||||
0.320787 | + | 0.947151i | \(0.396053\pi\) | |||||||
\(198\) | −0.411207 | −0.0292232 | ||||||||
\(199\) | −10.3462 | −0.733424 | −0.366712 | − | 0.930335i | \(-0.619517\pi\) | ||||
−0.366712 | + | 0.930335i | \(0.619517\pi\) | |||||||
\(200\) | −62.2354 | −4.40071 | ||||||||
\(201\) | 10.6797 | 0.753288 | ||||||||
\(202\) | −24.4396 | −1.71957 | ||||||||
\(203\) | −37.6567 | −2.64298 | ||||||||
\(204\) | −11.8434 | −0.829206 | ||||||||
\(205\) | 0.184277 | 0.0128704 | ||||||||
\(206\) | 10.4782 | 0.730051 | ||||||||
\(207\) | 1.15732 | 0.0804390 | ||||||||
\(208\) | 48.0880 | 3.33430 | ||||||||
\(209\) | −0.631339 | −0.0436707 | ||||||||
\(210\) | 54.4355 | 3.75641 | ||||||||
\(211\) | −9.06806 | −0.624271 | −0.312136 | − | 0.950038i | \(-0.601044\pi\) | ||||
−0.312136 | + | 0.950038i | \(0.601044\pi\) | |||||||
\(212\) | 15.3749 | 1.05595 | ||||||||
\(213\) | −20.4182 | −1.39903 | ||||||||
\(214\) | 33.3857 | 2.28220 | ||||||||
\(215\) | −18.3786 | −1.25341 | ||||||||
\(216\) | −48.0256 | −3.26773 | ||||||||
\(217\) | 46.8753 | 3.18210 | ||||||||
\(218\) | 41.4170 | 2.80511 | ||||||||
\(219\) | 5.09490 | 0.344281 | ||||||||
\(220\) | −1.85941 | −0.125362 | ||||||||
\(221\) | 6.84554 | 0.460481 | ||||||||
\(222\) | 27.0263 | 1.81388 | ||||||||
\(223\) | −11.5714 | −0.774878 | −0.387439 | − | 0.921895i | \(-0.626640\pi\) | ||||
−0.387439 | + | 0.921895i | \(0.626640\pi\) | |||||||
\(224\) | −82.8041 | −5.53258 | ||||||||
\(225\) | −10.7159 | −0.714395 | ||||||||
\(226\) | −24.0502 | −1.59979 | ||||||||
\(227\) | 16.7767 | 1.11351 | 0.556755 | − | 0.830677i | \(-0.312046\pi\) | ||||
0.556755 | + | 0.830677i | \(0.312046\pi\) | |||||||
\(228\) | −39.7637 | −2.63341 | ||||||||
\(229\) | −8.12271 | −0.536764 | −0.268382 | − | 0.963313i | \(-0.586489\pi\) | ||||
−0.268382 | + | 0.963313i | \(0.586489\pi\) | |||||||
\(230\) | 7.23100 | 0.476798 | ||||||||
\(231\) | 0.591426 | 0.0389130 | ||||||||
\(232\) | 69.2071 | 4.54367 | ||||||||
\(233\) | 15.2388 | 0.998328 | 0.499164 | − | 0.866507i | \(-0.333640\pi\) | ||||
0.499164 | + | 0.866507i | \(0.333640\pi\) | |||||||
\(234\) | 14.9698 | 0.978604 | ||||||||
\(235\) | −36.0416 | −2.35109 | ||||||||
\(236\) | −14.9804 | −0.975139 | ||||||||
\(237\) | −9.34746 | −0.607183 | ||||||||
\(238\) | −23.5519 | −1.52664 | ||||||||
\(239\) | −27.7155 | −1.79276 | −0.896382 | − | 0.443282i | \(-0.853814\pi\) | ||||
−0.896382 | + | 0.443282i | \(0.853814\pi\) | |||||||
\(240\) | −55.3355 | −3.57189 | ||||||||
\(241\) | −15.5764 | −1.00336 | −0.501682 | − | 0.865052i | \(-0.667285\pi\) | ||||
−0.501682 | + | 0.865052i | \(0.667285\pi\) | |||||||
\(242\) | 29.5679 | 1.90069 | ||||||||
\(243\) | −13.7814 | −0.884080 | ||||||||
\(244\) | −39.0090 | −2.49729 | ||||||||
\(245\) | 53.9512 | 3.44682 | ||||||||
\(246\) | 0.174239 | 0.0111090 | ||||||||
\(247\) | 22.9835 | 1.46241 | ||||||||
\(248\) | −86.1492 | −5.47048 | ||||||||
\(249\) | 3.19771 | 0.202647 | ||||||||
\(250\) | −20.0784 | −1.26987 | ||||||||
\(251\) | −7.64429 | −0.482503 | −0.241252 | − | 0.970463i | \(-0.577558\pi\) | ||||
−0.241252 | + | 0.970463i | \(0.577558\pi\) | |||||||
\(252\) | −37.2735 | −2.34801 | ||||||||
\(253\) | 0.0785628 | 0.00493920 | ||||||||
\(254\) | −44.0841 | −2.76608 | ||||||||
\(255\) | −7.87726 | −0.493293 | ||||||||
\(256\) | 16.2993 | 1.01871 | ||||||||
\(257\) | 5.08550 | 0.317225 | 0.158613 | − | 0.987341i | \(-0.449298\pi\) | ||||
0.158613 | + | 0.987341i | \(0.449298\pi\) | |||||||
\(258\) | −17.3774 | −1.08187 | ||||||||
\(259\) | 38.8957 | 2.41686 | ||||||||
\(260\) | 67.6908 | 4.19800 | ||||||||
\(261\) | 11.9163 | 0.737602 | ||||||||
\(262\) | −28.1561 | −1.73949 | ||||||||
\(263\) | 14.3888 | 0.887252 | 0.443626 | − | 0.896212i | \(-0.353692\pi\) | ||||
0.443626 | + | 0.896212i | \(0.353692\pi\) | |||||||
\(264\) | −1.08695 | −0.0668970 | ||||||||
\(265\) | 10.2261 | 0.628182 | ||||||||
\(266\) | −79.0742 | −4.84835 | ||||||||
\(267\) | −6.49085 | −0.397234 | ||||||||
\(268\) | −45.6904 | −2.79098 | ||||||||
\(269\) | 1.68319 | 0.102626 | 0.0513130 | − | 0.998683i | \(-0.483659\pi\) | ||||
0.0513130 | + | 0.998683i | \(0.483659\pi\) | |||||||
\(270\) | −51.6668 | −3.14434 | ||||||||
\(271\) | −23.7938 | −1.44537 | −0.722686 | − | 0.691177i | \(-0.757093\pi\) | ||||
−0.722686 | + | 0.691177i | \(0.757093\pi\) | |||||||
\(272\) | 23.9413 | 1.45165 | ||||||||
\(273\) | −21.5305 | −1.30309 | ||||||||
\(274\) | −22.2346 | −1.34324 | ||||||||
\(275\) | −0.727436 | −0.0438660 | ||||||||
\(276\) | 4.94813 | 0.297842 | ||||||||
\(277\) | −1.13517 | −0.0682057 | −0.0341028 | − | 0.999418i | \(-0.510857\pi\) | ||||
−0.0341028 | + | 0.999418i | \(0.510857\pi\) | |||||||
\(278\) | 57.7788 | 3.46534 | ||||||||
\(279\) | −14.8335 | −0.888058 | ||||||||
\(280\) | −143.981 | −8.60453 | ||||||||
\(281\) | −9.92821 | −0.592268 | −0.296134 | − | 0.955146i | \(-0.595697\pi\) | ||||
−0.296134 | + | 0.955146i | \(0.595697\pi\) | |||||||
\(282\) | −34.0783 | −2.02933 | ||||||||
\(283\) | 8.82254 | 0.524445 | 0.262223 | − | 0.965007i | \(-0.415545\pi\) | ||||
0.262223 | + | 0.965007i | \(0.415545\pi\) | |||||||
\(284\) | 87.3539 | 5.18350 | ||||||||
\(285\) | −26.4475 | −1.56661 | ||||||||
\(286\) | 1.01620 | 0.0600893 | ||||||||
\(287\) | 0.250761 | 0.0148020 | ||||||||
\(288\) | 26.2030 | 1.54403 | ||||||||
\(289\) | −13.5919 | −0.799521 | ||||||||
\(290\) | 74.4542 | 4.37210 | ||||||||
\(291\) | −14.5702 | −0.854123 | ||||||||
\(292\) | −21.7972 | −1.27559 | ||||||||
\(293\) | −9.50459 | −0.555264 | −0.277632 | − | 0.960688i | \(-0.589550\pi\) | ||||
−0.277632 | + | 0.960688i | \(0.589550\pi\) | |||||||
\(294\) | 51.0124 | 2.97510 | ||||||||
\(295\) | −9.96369 | −0.580108 | ||||||||
\(296\) | −71.4841 | −4.15493 | ||||||||
\(297\) | −0.561345 | −0.0325725 | ||||||||
\(298\) | −25.1822 | −1.45876 | ||||||||
\(299\) | −2.86003 | −0.165400 | ||||||||
\(300\) | −45.8161 | −2.64520 | ||||||||
\(301\) | −25.0093 | −1.44151 | ||||||||
\(302\) | −40.8465 | −2.35045 | ||||||||
\(303\) | −11.1233 | −0.639017 | ||||||||
\(304\) | 80.3816 | 4.61020 | ||||||||
\(305\) | −25.9455 | −1.48563 | ||||||||
\(306\) | 7.45290 | 0.426054 | ||||||||
\(307\) | 8.38054 | 0.478302 | 0.239151 | − | 0.970982i | \(-0.423131\pi\) | ||||
0.239151 | + | 0.970982i | \(0.423131\pi\) | |||||||
\(308\) | −2.53026 | −0.144175 | ||||||||
\(309\) | 4.76899 | 0.271299 | ||||||||
\(310\) | −92.6809 | −5.26392 | ||||||||
\(311\) | −22.5970 | −1.28136 | −0.640680 | − | 0.767808i | \(-0.721347\pi\) | ||||
−0.640680 | + | 0.767808i | \(0.721347\pi\) | |||||||
\(312\) | 39.5697 | 2.24019 | ||||||||
\(313\) | −1.68212 | −0.0950790 | −0.0475395 | − | 0.998869i | \(-0.515138\pi\) | ||||
−0.0475395 | + | 0.998869i | \(0.515138\pi\) | |||||||
\(314\) | 41.6190 | 2.34870 | ||||||||
\(315\) | −24.7912 | −1.39683 | ||||||||
\(316\) | 39.9907 | 2.24965 | ||||||||
\(317\) | −18.2743 | −1.02639 | −0.513194 | − | 0.858272i | \(-0.671538\pi\) | ||||
−0.513194 | + | 0.858272i | \(0.671538\pi\) | |||||||
\(318\) | 9.66902 | 0.542212 | ||||||||
\(319\) | 0.808924 | 0.0452910 | ||||||||
\(320\) | 73.3419 | 4.09994 | ||||||||
\(321\) | 15.1950 | 0.848101 | ||||||||
\(322\) | 9.83986 | 0.548354 | ||||||||
\(323\) | 11.4427 | 0.636687 | ||||||||
\(324\) | −11.7726 | −0.654032 | ||||||||
\(325\) | 26.4819 | 1.46895 | ||||||||
\(326\) | −37.6892 | −2.08741 | ||||||||
\(327\) | 18.8503 | 1.04242 | ||||||||
\(328\) | −0.460859 | −0.0254467 | ||||||||
\(329\) | −49.0449 | −2.70393 | ||||||||
\(330\) | −1.16936 | −0.0643710 | ||||||||
\(331\) | −9.89268 | −0.543751 | −0.271875 | − | 0.962332i | \(-0.587644\pi\) | ||||
−0.271875 | + | 0.962332i | \(0.587644\pi\) | |||||||
\(332\) | −13.6806 | −0.750820 | ||||||||
\(333\) | −12.3084 | −0.674497 | ||||||||
\(334\) | −17.7930 | −0.973590 | ||||||||
\(335\) | −30.3894 | −1.66035 | ||||||||
\(336\) | −75.2999 | −4.10794 | ||||||||
\(337\) | −6.25247 | −0.340594 | −0.170297 | − | 0.985393i | \(-0.554473\pi\) | ||||
−0.170297 | + | 0.985393i | \(0.554473\pi\) | |||||||
\(338\) | −2.01740 | −0.109732 | ||||||||
\(339\) | −10.9461 | −0.594509 | ||||||||
\(340\) | 33.7008 | 1.82768 | ||||||||
\(341\) | −1.00695 | −0.0545295 | ||||||||
\(342\) | 25.0227 | 1.35307 | ||||||||
\(343\) | 40.2246 | 2.17192 | ||||||||
\(344\) | 45.9631 | 2.47817 | ||||||||
\(345\) | 3.29108 | 0.177186 | ||||||||
\(346\) | 30.9676 | 1.66483 | ||||||||
\(347\) | 17.1445 | 0.920364 | 0.460182 | − | 0.887824i | \(-0.347784\pi\) | ||||
0.460182 | + | 0.887824i | \(0.347784\pi\) | |||||||
\(348\) | 50.9485 | 2.73113 | ||||||||
\(349\) | −32.4368 | −1.73630 | −0.868150 | − | 0.496302i | \(-0.834691\pi\) | ||||
−0.868150 | + | 0.496302i | \(0.834691\pi\) | |||||||
\(350\) | −91.1101 | −4.87004 | ||||||||
\(351\) | 20.4354 | 1.09076 | ||||||||
\(352\) | 1.77876 | 0.0948081 | ||||||||
\(353\) | 25.9028 | 1.37867 | 0.689333 | − | 0.724445i | \(-0.257904\pi\) | ||||
0.689333 | + | 0.724445i | \(0.257904\pi\) | |||||||
\(354\) | −9.42094 | −0.500717 | ||||||||
\(355\) | 58.1005 | 3.08366 | ||||||||
\(356\) | 27.7694 | 1.47178 | ||||||||
\(357\) | −10.7193 | −0.567324 | ||||||||
\(358\) | 12.1541 | 0.642366 | ||||||||
\(359\) | −9.41033 | −0.496658 | −0.248329 | − | 0.968676i | \(-0.579881\pi\) | ||||
−0.248329 | + | 0.968676i | \(0.579881\pi\) | |||||||
\(360\) | 45.5623 | 2.40135 | ||||||||
\(361\) | 19.4182 | 1.02201 | ||||||||
\(362\) | 25.6724 | 1.34931 | ||||||||
\(363\) | 13.4573 | 0.706327 | ||||||||
\(364\) | 92.1127 | 4.82802 | ||||||||
\(365\) | −14.4977 | −0.758843 | ||||||||
\(366\) | −24.5322 | −1.28232 | ||||||||
\(367\) | 7.98013 | 0.416559 | 0.208280 | − | 0.978069i | \(-0.433214\pi\) | ||||
0.208280 | + | 0.978069i | \(0.433214\pi\) | |||||||
\(368\) | −10.0025 | −0.521419 | ||||||||
\(369\) | −0.0793524 | −0.00413092 | ||||||||
\(370\) | −76.9040 | −3.99805 | ||||||||
\(371\) | 13.9155 | 0.722456 | ||||||||
\(372\) | −63.4209 | −3.28822 | ||||||||
\(373\) | −27.7050 | −1.43451 | −0.717255 | − | 0.696811i | \(-0.754602\pi\) | ||||
−0.717255 | + | 0.696811i | \(0.754602\pi\) | |||||||
\(374\) | 0.505930 | 0.0261610 | ||||||||
\(375\) | −9.13839 | −0.471904 | ||||||||
\(376\) | 90.1367 | 4.64844 | ||||||||
\(377\) | −29.4484 | −1.51667 | ||||||||
\(378\) | −70.3075 | −3.61623 | ||||||||
\(379\) | 8.04396 | 0.413191 | 0.206595 | − | 0.978426i | \(-0.433762\pi\) | ||||
0.206595 | + | 0.978426i | \(0.433762\pi\) | |||||||
\(380\) | 113.149 | 5.80441 | ||||||||
\(381\) | −20.0642 | −1.02792 | ||||||||
\(382\) | −17.1366 | −0.876786 | ||||||||
\(383\) | −5.00399 | −0.255692 | −0.127846 | − | 0.991794i | \(-0.540806\pi\) | ||||
−0.127846 | + | 0.991794i | \(0.540806\pi\) | |||||||
\(384\) | 26.5778 | 1.35629 | ||||||||
\(385\) | −1.68292 | −0.0857695 | ||||||||
\(386\) | −38.4869 | −1.95893 | ||||||||
\(387\) | 7.91410 | 0.402296 | ||||||||
\(388\) | 62.3350 | 3.16458 | ||||||||
\(389\) | −25.6084 | −1.29840 | −0.649200 | − | 0.760618i | \(-0.724896\pi\) | ||||
−0.649200 | + | 0.760618i | \(0.724896\pi\) | |||||||
\(390\) | 42.5698 | 2.15560 | ||||||||
\(391\) | −1.42391 | −0.0720101 | ||||||||
\(392\) | −134.927 | −6.81485 | ||||||||
\(393\) | −12.8148 | −0.646421 | ||||||||
\(394\) | −24.2280 | −1.22059 | ||||||||
\(395\) | 26.5985 | 1.33831 | ||||||||
\(396\) | 0.800692 | 0.0402363 | ||||||||
\(397\) | 30.9302 | 1.55234 | 0.776172 | − | 0.630521i | \(-0.217159\pi\) | ||||
0.776172 | + | 0.630521i | \(0.217159\pi\) | |||||||
\(398\) | 27.8367 | 1.39533 | ||||||||
\(399\) | −35.9894 | −1.80172 | ||||||||
\(400\) | 92.6165 | 4.63082 | ||||||||
\(401\) | 12.6558 | 0.632001 | 0.316001 | − | 0.948759i | \(-0.397660\pi\) | ||||
0.316001 | + | 0.948759i | \(0.397660\pi\) | |||||||
\(402\) | −28.7340 | −1.43312 | ||||||||
\(403\) | 36.6575 | 1.82604 | ||||||||
\(404\) | 47.5882 | 2.36760 | ||||||||
\(405\) | −7.83013 | −0.389082 | ||||||||
\(406\) | 101.316 | 5.02825 | ||||||||
\(407\) | −0.835539 | −0.0414162 | ||||||||
\(408\) | 19.7003 | 0.975310 | ||||||||
\(409\) | 31.2671 | 1.54606 | 0.773029 | − | 0.634370i | \(-0.218740\pi\) | ||||
0.773029 | + | 0.634370i | \(0.218740\pi\) | |||||||
\(410\) | −0.495801 | −0.0244858 | ||||||||
\(411\) | −10.1197 | −0.499169 | ||||||||
\(412\) | −20.4029 | −1.00518 | ||||||||
\(413\) | −13.5585 | −0.667168 | ||||||||
\(414\) | −3.11379 | −0.153034 | ||||||||
\(415\) | −9.09918 | −0.446661 | ||||||||
\(416\) | −64.7546 | −3.17486 | ||||||||
\(417\) | 26.2971 | 1.28778 | ||||||||
\(418\) | 1.69863 | 0.0830829 | ||||||||
\(419\) | 11.9524 | 0.583911 | 0.291955 | − | 0.956432i | \(-0.405694\pi\) | ||||
0.291955 | + | 0.956432i | \(0.405694\pi\) | |||||||
\(420\) | −105.995 | −5.17205 | ||||||||
\(421\) | 30.4104 | 1.48211 | 0.741057 | − | 0.671442i | \(-0.234325\pi\) | ||||
0.741057 | + | 0.671442i | \(0.234325\pi\) | |||||||
\(422\) | 24.3978 | 1.18767 | ||||||||
\(423\) | 15.5201 | 0.754612 | ||||||||
\(424\) | −25.5745 | −1.24201 | ||||||||
\(425\) | 13.1844 | 0.639536 | ||||||||
\(426\) | 54.9356 | 2.66164 | ||||||||
\(427\) | −35.3063 | −1.70859 | ||||||||
\(428\) | −65.0078 | −3.14227 | ||||||||
\(429\) | 0.462508 | 0.0223301 | ||||||||
\(430\) | 49.4480 | 2.38459 | ||||||||
\(431\) | −10.8315 | −0.521735 | −0.260868 | − | 0.965375i | \(-0.584009\pi\) | ||||
−0.260868 | + | 0.965375i | \(0.584009\pi\) | |||||||
\(432\) | 71.4699 | 3.43860 | ||||||||
\(433\) | 28.8223 | 1.38511 | 0.692555 | − | 0.721365i | \(-0.256485\pi\) | ||||
0.692555 | + | 0.721365i | \(0.256485\pi\) | |||||||
\(434\) | −126.119 | −6.05391 | ||||||||
\(435\) | 33.8867 | 1.62474 | ||||||||
\(436\) | −80.6462 | −3.86225 | ||||||||
\(437\) | −4.78069 | −0.228691 | ||||||||
\(438\) | −13.7079 | −0.654991 | ||||||||
\(439\) | 2.88085 | 0.137496 | 0.0687478 | − | 0.997634i | \(-0.478100\pi\) | ||||
0.0687478 | + | 0.997634i | \(0.478100\pi\) | |||||||
\(440\) | 3.09294 | 0.147450 | ||||||||
\(441\) | −23.2323 | −1.10630 | ||||||||
\(442\) | −18.4181 | −0.876059 | ||||||||
\(443\) | −31.0601 | −1.47571 | −0.737855 | − | 0.674959i | \(-0.764161\pi\) | ||||
−0.737855 | + | 0.674959i | \(0.764161\pi\) | |||||||
\(444\) | −52.6248 | −2.49746 | ||||||||
\(445\) | 18.4699 | 0.875557 | ||||||||
\(446\) | 31.1331 | 1.47420 | ||||||||
\(447\) | −11.4613 | −0.542100 | ||||||||
\(448\) | 99.8027 | 4.71524 | ||||||||
\(449\) | −8.93178 | −0.421517 | −0.210758 | − | 0.977538i | \(-0.567593\pi\) | ||||
−0.210758 | + | 0.977538i | \(0.567593\pi\) | |||||||
\(450\) | 28.8315 | 1.35913 | ||||||||
\(451\) | −0.00538673 | −0.000253651 0 | ||||||||
\(452\) | 46.8299 | 2.20269 | ||||||||
\(453\) | −18.5906 | −0.873464 | ||||||||
\(454\) | −45.1381 | −2.11844 | ||||||||
\(455\) | 61.2657 | 2.87218 | ||||||||
\(456\) | 66.1427 | 3.09742 | ||||||||
\(457\) | −27.6639 | −1.29406 | −0.647032 | − | 0.762463i | \(-0.723990\pi\) | ||||
−0.647032 | + | 0.762463i | \(0.723990\pi\) | |||||||
\(458\) | 21.8544 | 1.02119 | ||||||||
\(459\) | 10.1741 | 0.474884 | ||||||||
\(460\) | −14.0800 | −0.656485 | ||||||||
\(461\) | 28.3363 | 1.31975 | 0.659877 | − | 0.751374i | \(-0.270608\pi\) | ||||
0.659877 | + | 0.751374i | \(0.270608\pi\) | |||||||
\(462\) | −1.59125 | −0.0740315 | ||||||||
\(463\) | −24.3654 | −1.13236 | −0.566179 | − | 0.824282i | \(-0.691579\pi\) | ||||
−0.566179 | + | 0.824282i | \(0.691579\pi\) | |||||||
\(464\) | −102.991 | −4.78126 | ||||||||
\(465\) | −42.1823 | −1.95616 | ||||||||
\(466\) | −41.0004 | −1.89931 | ||||||||
\(467\) | 16.6816 | 0.771933 | 0.385967 | − | 0.922513i | \(-0.373868\pi\) | ||||
0.385967 | + | 0.922513i | \(0.373868\pi\) | |||||||
\(468\) | −29.1487 | −1.34740 | ||||||||
\(469\) | −41.3535 | −1.90953 | ||||||||
\(470\) | 96.9707 | 4.47292 | ||||||||
\(471\) | 18.9422 | 0.872812 | ||||||||
\(472\) | 24.9183 | 1.14696 | ||||||||
\(473\) | 0.537238 | 0.0247022 | ||||||||
\(474\) | 25.1496 | 1.15516 | ||||||||
\(475\) | 44.2658 | 2.03106 | ||||||||
\(476\) | 45.8596 | 2.10197 | ||||||||
\(477\) | −4.40350 | −0.201623 | ||||||||
\(478\) | 74.5691 | 3.41071 | ||||||||
\(479\) | −23.1977 | −1.05993 | −0.529964 | − | 0.848020i | \(-0.677795\pi\) | ||||
−0.529964 | + | 0.848020i | \(0.677795\pi\) | |||||||
\(480\) | 74.5141 | 3.40109 | ||||||||
\(481\) | 30.4173 | 1.38691 | ||||||||
\(482\) | 41.9087 | 1.90889 | ||||||||
\(483\) | 4.47846 | 0.203777 | ||||||||
\(484\) | −57.5738 | −2.61699 | ||||||||
\(485\) | 41.4600 | 1.88260 | ||||||||
\(486\) | 37.0793 | 1.68195 | ||||||||
\(487\) | −5.42166 | −0.245679 | −0.122839 | − | 0.992427i | \(-0.539200\pi\) | ||||
−0.122839 | + | 0.992427i | \(0.539200\pi\) | |||||||
\(488\) | 64.8873 | 2.93731 | ||||||||
\(489\) | −17.1537 | −0.775715 | ||||||||
\(490\) | −145.157 | −6.55753 | ||||||||
\(491\) | 35.3271 | 1.59429 | 0.797145 | − | 0.603788i | \(-0.206343\pi\) | ||||
0.797145 | + | 0.603788i | \(0.206343\pi\) | |||||||
\(492\) | −0.339273 | −0.0152956 | ||||||||
\(493\) | −14.6613 | −0.660311 | ||||||||
\(494\) | −61.8378 | −2.78221 | ||||||||
\(495\) | 0.532553 | 0.0239365 | ||||||||
\(496\) | 128.204 | 5.75654 | ||||||||
\(497\) | 79.0624 | 3.54643 | ||||||||
\(498\) | −8.60353 | −0.385533 | ||||||||
\(499\) | −4.73592 | −0.212009 | −0.106004 | − | 0.994366i | \(-0.533806\pi\) | ||||
−0.106004 | + | 0.994366i | \(0.533806\pi\) | |||||||
\(500\) | 39.0962 | 1.74844 | ||||||||
\(501\) | −8.09821 | −0.361801 | ||||||||
\(502\) | 20.5672 | 0.917957 | ||||||||
\(503\) | −26.7346 | −1.19204 | −0.596019 | − | 0.802971i | \(-0.703252\pi\) | ||||
−0.596019 | + | 0.802971i | \(0.703252\pi\) | |||||||
\(504\) | 62.0006 | 2.76173 | ||||||||
\(505\) | 31.6517 | 1.40848 | ||||||||
\(506\) | −0.211375 | −0.00939677 | ||||||||
\(507\) | −0.918186 | −0.0407781 | ||||||||
\(508\) | 85.8394 | 3.80851 | ||||||||
\(509\) | −22.8187 | −1.01142 | −0.505710 | − | 0.862703i | \(-0.668770\pi\) | ||||
−0.505710 | + | 0.862703i | \(0.668770\pi\) | |||||||
\(510\) | 21.1939 | 0.938484 | ||||||||
\(511\) | −19.7282 | −0.872726 | ||||||||
\(512\) | −0.445477 | −0.0196875 | ||||||||
\(513\) | 34.1589 | 1.50815 | ||||||||
\(514\) | −13.6827 | −0.603517 | ||||||||
\(515\) | −13.5703 | −0.597979 | ||||||||
\(516\) | 33.8369 | 1.48959 | ||||||||
\(517\) | 1.05356 | 0.0463355 | ||||||||
\(518\) | −104.650 | −4.59805 | ||||||||
\(519\) | 14.0944 | 0.618677 | ||||||||
\(520\) | −112.597 | −4.93768 | ||||||||
\(521\) | 17.4065 | 0.762592 | 0.381296 | − | 0.924453i | \(-0.375478\pi\) | ||||
0.381296 | + | 0.924453i | \(0.375478\pi\) | |||||||
\(522\) | −32.0612 | −1.40328 | ||||||||
\(523\) | 23.6414 | 1.03377 | 0.516884 | − | 0.856056i | \(-0.327092\pi\) | ||||
0.516884 | + | 0.856056i | \(0.327092\pi\) | |||||||
\(524\) | 54.8248 | 2.39503 | ||||||||
\(525\) | −41.4673 | −1.80978 | ||||||||
\(526\) | −38.7135 | −1.68799 | ||||||||
\(527\) | 18.2504 | 0.795002 | ||||||||
\(528\) | 1.61756 | 0.0703951 | ||||||||
\(529\) | −22.4051 | −0.974135 | ||||||||
\(530\) | −27.5135 | −1.19511 | ||||||||
\(531\) | 4.29052 | 0.186193 | ||||||||
\(532\) | 153.971 | 6.67550 | ||||||||
\(533\) | 0.196101 | 0.00849407 | ||||||||
\(534\) | 17.4638 | 0.755732 | ||||||||
\(535\) | −43.2377 | −1.86933 | ||||||||
\(536\) | 76.0011 | 3.28275 | ||||||||
\(537\) | 5.53176 | 0.238713 | ||||||||
\(538\) | −4.52867 | −0.195245 | ||||||||
\(539\) | −1.57709 | −0.0679301 | ||||||||
\(540\) | 100.604 | 4.32932 | ||||||||
\(541\) | 23.3037 | 1.00190 | 0.500951 | − | 0.865475i | \(-0.332984\pi\) | ||||
0.500951 | + | 0.865475i | \(0.332984\pi\) | |||||||
\(542\) | 64.0179 | 2.74980 | ||||||||
\(543\) | 11.6844 | 0.501424 | ||||||||
\(544\) | −32.2390 | −1.38224 | ||||||||
\(545\) | −53.6391 | −2.29765 | ||||||||
\(546\) | 57.9284 | 2.47911 | ||||||||
\(547\) | −20.2022 | −0.863782 | −0.431891 | − | 0.901926i | \(-0.642153\pi\) | ||||
−0.431891 | + | 0.901926i | \(0.642153\pi\) | |||||||
\(548\) | 43.2946 | 1.84945 | ||||||||
\(549\) | 11.1725 | 0.476833 | ||||||||
\(550\) | 1.95718 | 0.0834546 | ||||||||
\(551\) | −49.2245 | −2.09703 | ||||||||
\(552\) | −8.23069 | −0.350321 | ||||||||
\(553\) | 36.1948 | 1.53916 | ||||||||
\(554\) | 3.05420 | 0.129761 | ||||||||
\(555\) | −35.0016 | −1.48574 | ||||||||
\(556\) | −112.505 | −4.77129 | ||||||||
\(557\) | −25.7948 | −1.09296 | −0.546481 | − | 0.837471i | \(-0.684033\pi\) | ||||
−0.546481 | + | 0.837471i | \(0.684033\pi\) | |||||||
\(558\) | 39.9099 | 1.68952 | ||||||||
\(559\) | −19.5578 | −0.827208 | ||||||||
\(560\) | 214.268 | 9.05447 | ||||||||
\(561\) | 0.230266 | 0.00972185 | ||||||||
\(562\) | 26.7121 | 1.12678 | ||||||||
\(563\) | 22.4751 | 0.947214 | 0.473607 | − | 0.880736i | \(-0.342952\pi\) | ||||
0.473607 | + | 0.880736i | \(0.342952\pi\) | |||||||
\(564\) | 66.3564 | 2.79411 | ||||||||
\(565\) | 31.1473 | 1.31038 | ||||||||
\(566\) | −23.7372 | −0.997751 | ||||||||
\(567\) | −10.6551 | −0.447474 | ||||||||
\(568\) | −145.304 | −6.09683 | ||||||||
\(569\) | −34.5715 | −1.44931 | −0.724657 | − | 0.689110i | \(-0.758002\pi\) | ||||
−0.724657 | + | 0.689110i | \(0.758002\pi\) | |||||||
\(570\) | 71.1576 | 2.98046 | ||||||||
\(571\) | −7.49016 | −0.313454 | −0.156727 | − | 0.987642i | \(-0.550094\pi\) | ||||
−0.156727 | + | 0.987642i | \(0.550094\pi\) | |||||||
\(572\) | −1.97872 | −0.0827345 | ||||||||
\(573\) | −7.79946 | −0.325827 | ||||||||
\(574\) | −0.674679 | −0.0281606 | ||||||||
\(575\) | −5.50836 | −0.229715 | ||||||||
\(576\) | −31.5822 | −1.31593 | ||||||||
\(577\) | −39.4227 | −1.64119 | −0.820594 | − | 0.571512i | \(-0.806357\pi\) | ||||
−0.820594 | + | 0.571512i | \(0.806357\pi\) | |||||||
\(578\) | 36.5692 | 1.52108 | ||||||||
\(579\) | −17.5167 | −0.727970 | ||||||||
\(580\) | −144.975 | −6.01978 | ||||||||
\(581\) | −12.3820 | −0.513694 | ||||||||
\(582\) | 39.2016 | 1.62496 | ||||||||
\(583\) | −0.298926 | −0.0123802 | ||||||||
\(584\) | 36.2574 | 1.50034 | ||||||||
\(585\) | −19.3873 | −0.801566 | ||||||||
\(586\) | 25.5723 | 1.05638 | ||||||||
\(587\) | 8.28897 | 0.342122 | 0.171061 | − | 0.985260i | \(-0.445280\pi\) | ||||
0.171061 | + | 0.985260i | \(0.445280\pi\) | |||||||
\(588\) | −99.3300 | −4.09630 | ||||||||
\(589\) | 61.2749 | 2.52479 | ||||||||
\(590\) | 26.8075 | 1.10365 | ||||||||
\(591\) | −11.0270 | −0.453589 | ||||||||
\(592\) | 106.380 | 4.37220 | ||||||||
\(593\) | 26.7614 | 1.09896 | 0.549480 | − | 0.835507i | \(-0.314826\pi\) | ||||
0.549480 | + | 0.835507i | \(0.314826\pi\) | |||||||
\(594\) | 1.51031 | 0.0619688 | ||||||||
\(595\) | 30.5020 | 1.25046 | ||||||||
\(596\) | 49.0341 | 2.00851 | ||||||||
\(597\) | 12.6695 | 0.518526 | ||||||||
\(598\) | 7.69498 | 0.314671 | ||||||||
\(599\) | −35.3536 | −1.44451 | −0.722255 | − | 0.691627i | \(-0.756894\pi\) | ||||
−0.722255 | + | 0.691627i | \(0.756894\pi\) | |||||||
\(600\) | 76.2104 | 3.11127 | ||||||||
\(601\) | 30.0631 | 1.22630 | 0.613150 | − | 0.789966i | \(-0.289902\pi\) | ||||
0.613150 | + | 0.789966i | \(0.289902\pi\) | |||||||
\(602\) | 67.2882 | 2.74246 | ||||||||
\(603\) | 13.0862 | 0.532909 | ||||||||
\(604\) | 79.5352 | 3.23624 | ||||||||
\(605\) | −38.2932 | −1.55684 | ||||||||
\(606\) | 29.9275 | 1.21572 | ||||||||
\(607\) | −32.4269 | −1.31617 | −0.658084 | − | 0.752945i | \(-0.728633\pi\) | ||||
−0.658084 | + | 0.752945i | \(0.728633\pi\) | |||||||
\(608\) | −108.241 | −4.38974 | ||||||||
\(609\) | 46.1125 | 1.86857 | ||||||||
\(610\) | 69.8070 | 2.82640 | ||||||||
\(611\) | −38.3542 | −1.55164 | ||||||||
\(612\) | −14.5121 | −0.586617 | ||||||||
\(613\) | 3.78794 | 0.152993 | 0.0764967 | − | 0.997070i | \(-0.475627\pi\) | ||||
0.0764967 | + | 0.997070i | \(0.475627\pi\) | |||||||
\(614\) | −22.5480 | −0.909965 | ||||||||
\(615\) | −0.225656 | −0.00909932 | ||||||||
\(616\) | 4.20883 | 0.169579 | ||||||||
\(617\) | −15.4029 | −0.620098 | −0.310049 | − | 0.950721i | \(-0.600345\pi\) | ||||
−0.310049 | + | 0.950721i | \(0.600345\pi\) | |||||||
\(618\) | −12.8311 | −0.516142 | ||||||||
\(619\) | −28.5500 | −1.14752 | −0.573761 | − | 0.819023i | \(-0.694516\pi\) | ||||
−0.573761 | + | 0.819023i | \(0.694516\pi\) | |||||||
\(620\) | 180.466 | 7.24769 | ||||||||
\(621\) | −4.25067 | −0.170574 | ||||||||
\(622\) | 60.7978 | 2.43777 | ||||||||
\(623\) | 25.1336 | 1.00696 | ||||||||
\(624\) | −58.8861 | −2.35733 | ||||||||
\(625\) | −9.70484 | −0.388194 | ||||||||
\(626\) | 4.52578 | 0.180887 | ||||||||
\(627\) | 0.773107 | 0.0308749 | ||||||||
\(628\) | −81.0395 | −3.23383 | ||||||||
\(629\) | 15.1437 | 0.603818 | ||||||||
\(630\) | 66.7014 | 2.65745 | ||||||||
\(631\) | −28.2180 | −1.12334 | −0.561670 | − | 0.827361i | \(-0.689841\pi\) | ||||
−0.561670 | + | 0.827361i | \(0.689841\pi\) | |||||||
\(632\) | −66.5203 | −2.64604 | ||||||||
\(633\) | 11.1043 | 0.441356 | ||||||||
\(634\) | 49.1675 | 1.95269 | ||||||||
\(635\) | 57.0932 | 2.26567 | ||||||||
\(636\) | −18.8273 | −0.746550 | ||||||||
\(637\) | 57.4130 | 2.27479 | ||||||||
\(638\) | −2.17643 | −0.0861657 | ||||||||
\(639\) | −25.0190 | −0.989737 | ||||||||
\(640\) | −75.6279 | −2.98946 | ||||||||
\(641\) | 14.2454 | 0.562660 | 0.281330 | − | 0.959611i | \(-0.409225\pi\) | ||||
0.281330 | + | 0.959611i | \(0.409225\pi\) | |||||||
\(642\) | −40.8824 | −1.61350 | ||||||||
\(643\) | 30.0818 | 1.18631 | 0.593156 | − | 0.805088i | \(-0.297882\pi\) | ||||
0.593156 | + | 0.805088i | \(0.297882\pi\) | |||||||
\(644\) | −19.1599 | −0.755007 | ||||||||
\(645\) | 22.5055 | 0.886152 | ||||||||
\(646\) | −30.7868 | −1.21129 | ||||||||
\(647\) | −34.1451 | −1.34238 | −0.671192 | − | 0.741284i | \(-0.734217\pi\) | ||||
−0.671192 | + | 0.741284i | \(0.734217\pi\) | |||||||
\(648\) | 19.5824 | 0.769271 | ||||||||
\(649\) | 0.291256 | 0.0114328 | ||||||||
\(650\) | −71.2501 | −2.79466 | ||||||||
\(651\) | −57.4011 | −2.24973 | ||||||||
\(652\) | 73.3875 | 2.87408 | ||||||||
\(653\) | 46.1820 | 1.80724 | 0.903621 | − | 0.428334i | \(-0.140899\pi\) | ||||
0.903621 | + | 0.428334i | \(0.140899\pi\) | |||||||
\(654\) | −50.7172 | −1.98320 | ||||||||
\(655\) | 36.4649 | 1.42480 | ||||||||
\(656\) | 0.685834 | 0.0267773 | ||||||||
\(657\) | 6.24293 | 0.243560 | ||||||||
\(658\) | 131.956 | 5.14420 | ||||||||
\(659\) | −18.2059 | −0.709201 | −0.354600 | − | 0.935018i | \(-0.615383\pi\) | ||||
−0.354600 | + | 0.935018i | \(0.615383\pi\) | |||||||
\(660\) | 2.27694 | 0.0886299 | ||||||||
\(661\) | −22.6590 | −0.881334 | −0.440667 | − | 0.897671i | \(-0.645258\pi\) | ||||
−0.440667 | + | 0.897671i | \(0.645258\pi\) | |||||||
\(662\) | 26.6165 | 1.03448 | ||||||||
\(663\) | −8.38270 | −0.325557 | ||||||||
\(664\) | 22.7562 | 0.883113 | ||||||||
\(665\) | 102.409 | 3.97124 | ||||||||
\(666\) | 33.1161 | 1.28322 | ||||||||
\(667\) | 6.12541 | 0.237177 | ||||||||
\(668\) | 34.6461 | 1.34050 | ||||||||
\(669\) | 14.1698 | 0.547834 | ||||||||
\(670\) | 81.7634 | 3.15880 | ||||||||
\(671\) | 0.758433 | 0.0292790 | ||||||||
\(672\) | 101.398 | 3.91150 | ||||||||
\(673\) | 15.2435 | 0.587592 | 0.293796 | − | 0.955868i | \(-0.405081\pi\) | ||||
0.293796 | + | 0.955868i | \(0.405081\pi\) | |||||||
\(674\) | 16.8224 | 0.647976 | ||||||||
\(675\) | 39.3582 | 1.51490 | ||||||||
\(676\) | 3.92822 | 0.151085 | ||||||||
\(677\) | −12.8476 | −0.493775 | −0.246888 | − | 0.969044i | \(-0.579408\pi\) | ||||
−0.246888 | + | 0.969044i | \(0.579408\pi\) | |||||||
\(678\) | 29.4507 | 1.13105 | ||||||||
\(679\) | 56.4183 | 2.16514 | ||||||||
\(680\) | −56.0578 | −2.14972 | ||||||||
\(681\) | −20.5439 | −0.787245 | ||||||||
\(682\) | 2.70923 | 0.103742 | ||||||||
\(683\) | 11.6100 | 0.444243 | 0.222121 | − | 0.975019i | \(-0.428702\pi\) | ||||
0.222121 | + | 0.975019i | \(0.428702\pi\) | |||||||
\(684\) | −48.7236 | −1.86299 | ||||||||
\(685\) | 28.7959 | 1.10024 | ||||||||
\(686\) | −108.225 | −4.13206 | ||||||||
\(687\) | 9.94667 | 0.379489 | ||||||||
\(688\) | −68.4007 | −2.60775 | ||||||||
\(689\) | 10.8822 | 0.414580 | ||||||||
\(690\) | −8.85473 | −0.337094 | ||||||||
\(691\) | −27.7625 | −1.05614 | −0.528068 | − | 0.849202i | \(-0.677083\pi\) | ||||
−0.528068 | + | 0.849202i | \(0.677083\pi\) | |||||||
\(692\) | −60.2994 | −2.29224 | ||||||||
\(693\) | 0.724692 | 0.0275288 | ||||||||
\(694\) | −46.1277 | −1.75098 | ||||||||
\(695\) | −74.8292 | −2.83843 | ||||||||
\(696\) | −84.7475 | −3.21235 | ||||||||
\(697\) | 0.0976315 | 0.00369806 | ||||||||
\(698\) | 87.2719 | 3.30329 | ||||||||
\(699\) | −18.6607 | −0.705812 | ||||||||
\(700\) | 177.407 | 6.70537 | ||||||||
\(701\) | −32.5900 | −1.23091 | −0.615453 | − | 0.788173i | \(-0.711027\pi\) | ||||
−0.615453 | + | 0.788173i | \(0.711027\pi\) | |||||||
\(702\) | −54.9820 | −2.07516 | ||||||||
\(703\) | 50.8441 | 1.91762 | ||||||||
\(704\) | −2.14391 | −0.0808018 | ||||||||
\(705\) | 44.1347 | 1.66221 | ||||||||
\(706\) | −69.6920 | −2.62289 | ||||||||
\(707\) | 43.0712 | 1.61986 | ||||||||
\(708\) | 18.3442 | 0.689418 | ||||||||
\(709\) | 5.99547 | 0.225165 | 0.112582 | − | 0.993642i | \(-0.464088\pi\) | ||||
0.112582 | + | 0.993642i | \(0.464088\pi\) | |||||||
\(710\) | −156.321 | −5.86662 | ||||||||
\(711\) | −11.4537 | −0.429548 | ||||||||
\(712\) | −46.1915 | −1.73110 | ||||||||
\(713\) | −7.62494 | −0.285556 | ||||||||
\(714\) | 28.8404 | 1.07933 | ||||||||
\(715\) | −1.31608 | −0.0492186 | ||||||||
\(716\) | −23.6662 | −0.884448 | ||||||||
\(717\) | 33.9390 | 1.26747 | ||||||||
\(718\) | 25.3187 | 0.944886 | ||||||||
\(719\) | −37.1135 | −1.38410 | −0.692050 | − | 0.721850i | \(-0.743292\pi\) | ||||
−0.692050 | + | 0.721850i | \(0.743292\pi\) | |||||||
\(720\) | −67.8042 | −2.52691 | ||||||||
\(721\) | −18.4663 | −0.687720 | ||||||||
\(722\) | −52.2451 | −1.94436 | ||||||||
\(723\) | 19.0741 | 0.709372 | ||||||||
\(724\) | −49.9886 | −1.85781 | ||||||||
\(725\) | −56.7170 | −2.10642 | ||||||||
\(726\) | −36.2073 | −1.34378 | ||||||||
\(727\) | −1.46708 | −0.0544110 | −0.0272055 | − | 0.999630i | \(-0.508661\pi\) | ||||
−0.0272055 | + | 0.999630i | \(0.508661\pi\) | |||||||
\(728\) | −153.220 | −5.67871 | ||||||||
\(729\) | 23.6175 | 0.874722 | ||||||||
\(730\) | 39.0063 | 1.44369 | ||||||||
\(731\) | −9.73714 | −0.360141 | ||||||||
\(732\) | 47.7684 | 1.76557 | ||||||||
\(733\) | 40.8976 | 1.51059 | 0.755295 | − | 0.655386i | \(-0.227494\pi\) | ||||
0.755295 | + | 0.655386i | \(0.227494\pi\) | |||||||
\(734\) | −21.4707 | −0.792499 | ||||||||
\(735\) | −66.0660 | −2.43688 | ||||||||
\(736\) | 13.4693 | 0.496485 | ||||||||
\(737\) | 0.888336 | 0.0327223 | ||||||||
\(738\) | 0.213500 | 0.00785903 | ||||||||
\(739\) | 1.22727 | 0.0451457 | 0.0225728 | − | 0.999745i | \(-0.492814\pi\) | ||||
0.0225728 | + | 0.999745i | \(0.492814\pi\) | |||||||
\(740\) | 149.745 | 5.50475 | ||||||||
\(741\) | −28.1445 | −1.03391 | ||||||||
\(742\) | −37.4400 | −1.37446 | ||||||||
\(743\) | −30.3102 | −1.11197 | −0.555986 | − | 0.831192i | \(-0.687659\pi\) | ||||
−0.555986 | + | 0.831192i | \(0.687659\pi\) | |||||||
\(744\) | 105.494 | 3.86760 | ||||||||
\(745\) | 32.6134 | 1.19486 | ||||||||
\(746\) | 74.5409 | 2.72914 | ||||||||
\(747\) | 3.91825 | 0.143361 | ||||||||
\(748\) | −0.985134 | −0.0360201 | ||||||||
\(749\) | −58.8373 | −2.14987 | ||||||||
\(750\) | 24.5871 | 0.897793 | ||||||||
\(751\) | 25.3132 | 0.923693 | 0.461847 | − | 0.886960i | \(-0.347187\pi\) | ||||
0.461847 | + | 0.886960i | \(0.347187\pi\) | |||||||
\(752\) | −134.138 | −4.89152 | ||||||||
\(753\) | 9.36082 | 0.341127 | ||||||||
\(754\) | 79.2316 | 2.88544 | ||||||||
\(755\) | 52.9001 | 1.92523 | ||||||||
\(756\) | 136.901 | 4.97904 | ||||||||
\(757\) | 14.6495 | 0.532446 | 0.266223 | − | 0.963911i | \(-0.414224\pi\) | ||||
0.266223 | + | 0.963911i | \(0.414224\pi\) | |||||||
\(758\) | −21.6425 | −0.786090 | ||||||||
\(759\) | −0.0962041 | −0.00349199 | ||||||||
\(760\) | −188.211 | −6.82713 | ||||||||
\(761\) | 15.0204 | 0.544487 | 0.272244 | − | 0.962228i | \(-0.412234\pi\) | ||||
0.272244 | + | 0.962228i | \(0.412234\pi\) | |||||||
\(762\) | 53.9832 | 1.95560 | ||||||||
\(763\) | −72.9913 | −2.64246 | ||||||||
\(764\) | 33.3680 | 1.20721 | ||||||||
\(765\) | −9.65223 | −0.348977 | ||||||||
\(766\) | 13.4634 | 0.486451 | ||||||||
\(767\) | −10.6030 | −0.382852 | ||||||||
\(768\) | −19.9594 | −0.720222 | ||||||||
\(769\) | 4.96410 | 0.179010 | 0.0895050 | − | 0.995986i | \(-0.471471\pi\) | ||||
0.0895050 | + | 0.995986i | \(0.471471\pi\) | |||||||
\(770\) | 4.52794 | 0.163175 | ||||||||
\(771\) | −6.22745 | −0.224276 | ||||||||
\(772\) | 74.9408 | 2.69718 | ||||||||
\(773\) | 43.8007 | 1.57540 | 0.787701 | − | 0.616058i | \(-0.211271\pi\) | ||||
0.787701 | + | 0.616058i | \(0.211271\pi\) | |||||||
\(774\) | −21.2931 | −0.765364 | ||||||||
\(775\) | 70.6016 | 2.53608 | ||||||||
\(776\) | −103.688 | −3.72218 | ||||||||
\(777\) | −47.6298 | −1.70871 | ||||||||
\(778\) | 68.9001 | 2.47019 | ||||||||
\(779\) | 0.327793 | 0.0117444 | ||||||||
\(780\) | −82.8908 | −2.96797 | ||||||||
\(781\) | −1.69838 | −0.0607729 | ||||||||
\(782\) | 3.83106 | 0.136998 | ||||||||
\(783\) | −43.7671 | −1.56411 | ||||||||
\(784\) | 200.794 | 7.17120 | ||||||||
\(785\) | −53.9007 | −1.92380 | ||||||||
\(786\) | 34.4785 | 1.22981 | ||||||||
\(787\) | −26.6270 | −0.949152 | −0.474576 | − | 0.880215i | \(-0.657399\pi\) | ||||
−0.474576 | + | 0.880215i | \(0.657399\pi\) | |||||||
\(788\) | 47.1761 | 1.68058 | ||||||||
\(789\) | −17.6198 | −0.627282 | ||||||||
\(790\) | −71.5638 | −2.54612 | ||||||||
\(791\) | 42.3849 | 1.50703 | ||||||||
\(792\) | −1.33187 | −0.0473259 | ||||||||
\(793\) | −27.6103 | −0.980470 | ||||||||
\(794\) | −83.2186 | −2.95332 | ||||||||
\(795\) | −12.5223 | −0.444121 | ||||||||
\(796\) | −54.2030 | −1.92117 | ||||||||
\(797\) | 49.4424 | 1.75134 | 0.875670 | − | 0.482910i | \(-0.160420\pi\) | ||||
0.875670 | + | 0.482910i | \(0.160420\pi\) | |||||||
\(798\) | 96.8303 | 3.42776 | ||||||||
\(799\) | −19.0952 | −0.675538 | ||||||||
\(800\) | −124.716 | −4.40938 | ||||||||
\(801\) | −7.95343 | −0.281021 | ||||||||
\(802\) | −34.0508 | −1.20238 | ||||||||
\(803\) | 0.423793 | 0.0149553 | ||||||||
\(804\) | 55.9501 | 1.97321 | ||||||||
\(805\) | −12.7436 | −0.449152 | ||||||||
\(806\) | −98.6278 | −3.47402 | ||||||||
\(807\) | −2.06115 | −0.0725560 | ||||||||
\(808\) | −79.1580 | −2.78477 | ||||||||
\(809\) | 9.48953 | 0.333634 | 0.166817 | − | 0.985988i | \(-0.446651\pi\) | ||||
0.166817 | + | 0.985988i | \(0.446651\pi\) | |||||||
\(810\) | 21.0671 | 0.740224 | ||||||||
\(811\) | −18.4162 | −0.646681 | −0.323340 | − | 0.946283i | \(-0.604806\pi\) | ||||
−0.323340 | + | 0.946283i | \(0.604806\pi\) | |||||||
\(812\) | −197.281 | −6.92319 | ||||||||
\(813\) | 29.1367 | 1.02187 | ||||||||
\(814\) | 2.24804 | 0.0787937 | ||||||||
\(815\) | 48.8112 | 1.70978 | ||||||||
\(816\) | −29.3173 | −1.02631 | ||||||||
\(817\) | −32.6919 | −1.14375 | ||||||||
\(818\) | −84.1249 | −2.94136 | ||||||||
\(819\) | −26.3820 | −0.921861 | ||||||||
\(820\) | 0.965411 | 0.0337136 | ||||||||
\(821\) | −9.97256 | −0.348045 | −0.174022 | − | 0.984742i | \(-0.555677\pi\) | ||||
−0.174022 | + | 0.984742i | \(0.555677\pi\) | |||||||
\(822\) | 27.2274 | 0.949663 | ||||||||
\(823\) | −15.7357 | −0.548511 | −0.274256 | − | 0.961657i | \(-0.588431\pi\) | ||||
−0.274256 | + | 0.961657i | \(0.588431\pi\) | |||||||
\(824\) | 33.9381 | 1.18229 | ||||||||
\(825\) | 0.890782 | 0.0310130 | ||||||||
\(826\) | 36.4793 | 1.26928 | ||||||||
\(827\) | −38.2246 | −1.32920 | −0.664601 | − | 0.747199i | \(-0.731398\pi\) | ||||
−0.664601 | + | 0.747199i | \(0.731398\pi\) | |||||||
\(828\) | 6.06308 | 0.210707 | ||||||||
\(829\) | 49.3887 | 1.71534 | 0.857670 | − | 0.514200i | \(-0.171911\pi\) | ||||
0.857670 | + | 0.514200i | \(0.171911\pi\) | |||||||
\(830\) | 24.4816 | 0.849768 | ||||||||
\(831\) | 1.39007 | 0.0482210 | ||||||||
\(832\) | 78.0479 | 2.70583 | ||||||||
\(833\) | 28.5839 | 0.990372 | ||||||||
\(834\) | −70.7530 | −2.44998 | ||||||||
\(835\) | 23.0437 | 0.797459 | ||||||||
\(836\) | −3.30754 | −0.114394 | ||||||||
\(837\) | 54.4815 | 1.88316 | ||||||||
\(838\) | −32.1581 | −1.11088 | ||||||||
\(839\) | −18.5985 | −0.642091 | −0.321046 | − | 0.947064i | \(-0.604034\pi\) | ||||
−0.321046 | + | 0.947064i | \(0.604034\pi\) | |||||||
\(840\) | 176.312 | 6.08335 | ||||||||
\(841\) | 34.0705 | 1.17484 | ||||||||
\(842\) | −81.8200 | −2.81970 | ||||||||
\(843\) | 12.1576 | 0.418730 | ||||||||
\(844\) | −47.5069 | −1.63525 | ||||||||
\(845\) | 2.61272 | 0.0898804 | ||||||||
\(846\) | −41.7571 | −1.43564 | ||||||||
\(847\) | −52.1090 | −1.79048 | ||||||||
\(848\) | 38.0590 | 1.30695 | ||||||||
\(849\) | −10.8036 | −0.370780 | ||||||||
\(850\) | −35.4729 | −1.21671 | ||||||||
\(851\) | −6.32696 | −0.216885 | ||||||||
\(852\) | −106.969 | −3.66471 | ||||||||
\(853\) | −52.4880 | −1.79715 | −0.898577 | − | 0.438815i | \(-0.855398\pi\) | ||||
−0.898577 | + | 0.438815i | \(0.855398\pi\) | |||||||
\(854\) | 94.9924 | 3.25057 | ||||||||
\(855\) | −32.4069 | −1.10829 | ||||||||
\(856\) | 108.134 | 3.69593 | ||||||||
\(857\) | 45.9719 | 1.57037 | 0.785185 | − | 0.619262i | \(-0.212568\pi\) | ||||
0.785185 | + | 0.619262i | \(0.212568\pi\) | |||||||
\(858\) | −1.24439 | −0.0424828 | ||||||||
\(859\) | −44.6790 | −1.52443 | −0.762213 | − | 0.647326i | \(-0.775887\pi\) | ||||
−0.762213 | + | 0.647326i | \(0.775887\pi\) | |||||||
\(860\) | −96.2838 | −3.28325 | ||||||||
\(861\) | −0.307070 | −0.0104649 | ||||||||
\(862\) | 29.1424 | 0.992595 | ||||||||
\(863\) | −0.948035 | −0.0322715 | −0.0161357 | − | 0.999870i | \(-0.505136\pi\) | ||||
−0.0161357 | + | 0.999870i | \(0.505136\pi\) | |||||||
\(864\) | −96.2404 | −3.27417 | ||||||||
\(865\) | −40.1061 | −1.36365 | ||||||||
\(866\) | −77.5470 | −2.63516 | ||||||||
\(867\) | 16.6439 | 0.565257 | ||||||||
\(868\) | 245.576 | 8.33538 | ||||||||
\(869\) | −0.777520 | −0.0263756 | ||||||||
\(870\) | −91.1729 | −3.09105 | ||||||||
\(871\) | −32.3393 | −1.09578 | ||||||||
\(872\) | 134.146 | 4.54277 | ||||||||
\(873\) | −17.8534 | −0.604245 | ||||||||
\(874\) | 12.8626 | 0.435083 | ||||||||
\(875\) | 35.3853 | 1.19624 | ||||||||
\(876\) | 26.6918 | 0.901831 | ||||||||
\(877\) | −44.1850 | −1.49202 | −0.746011 | − | 0.665933i | \(-0.768034\pi\) | ||||
−0.746011 | + | 0.665933i | \(0.768034\pi\) | |||||||
\(878\) | −7.75100 | −0.261584 | ||||||||
\(879\) | 11.6388 | 0.392568 | ||||||||
\(880\) | −4.60280 | −0.155160 | ||||||||
\(881\) | −38.4387 | −1.29503 | −0.647516 | − | 0.762052i | \(-0.724192\pi\) | ||||
−0.647516 | + | 0.762052i | \(0.724192\pi\) | |||||||
\(882\) | 62.5069 | 2.10472 | ||||||||
\(883\) | 49.9110 | 1.67964 | 0.839819 | − | 0.542866i | \(-0.182661\pi\) | ||||
0.839819 | + | 0.542866i | \(0.182661\pi\) | |||||||
\(884\) | 35.8632 | 1.20621 | ||||||||
\(885\) | 12.2010 | 0.410133 | ||||||||
\(886\) | 83.5680 | 2.80752 | ||||||||
\(887\) | 4.34039 | 0.145736 | 0.0728681 | − | 0.997342i | \(-0.476785\pi\) | ||||
0.0728681 | + | 0.997342i | \(0.476785\pi\) | |||||||
\(888\) | 87.5359 | 2.93751 | ||||||||
\(889\) | 77.6916 | 2.60569 | ||||||||
\(890\) | −49.6937 | −1.66574 | ||||||||
\(891\) | 0.228888 | 0.00766805 | ||||||||
\(892\) | −60.6216 | −2.02976 | ||||||||
\(893\) | −64.1110 | −2.14539 | ||||||||
\(894\) | 30.8368 | 1.03134 | ||||||||
\(895\) | −15.7408 | −0.526157 | ||||||||
\(896\) | −102.914 | −3.43810 | ||||||||
\(897\) | 3.50225 | 0.116937 | ||||||||
\(898\) | 24.0312 | 0.801931 | ||||||||
\(899\) | −78.5104 | −2.61847 | ||||||||
\(900\) | −56.1399 | −1.87133 | ||||||||
\(901\) | 5.41786 | 0.180495 | ||||||||
\(902\) | 0.0144931 | 0.000482569 0 | ||||||||
\(903\) | 30.6252 | 1.01914 | ||||||||
\(904\) | −77.8966 | −2.59080 | ||||||||
\(905\) | −33.2482 | −1.10521 | ||||||||
\(906\) | 50.0185 | 1.66175 | ||||||||
\(907\) | −47.7832 | −1.58662 | −0.793308 | − | 0.608821i | \(-0.791643\pi\) | ||||
−0.793308 | + | 0.608821i | \(0.791643\pi\) | |||||||
\(908\) | 87.8919 | 2.91679 | ||||||||
\(909\) | −13.6297 | −0.452069 | ||||||||
\(910\) | −164.837 | −5.46429 | ||||||||
\(911\) | 45.3177 | 1.50144 | 0.750721 | − | 0.660619i | \(-0.229706\pi\) | ||||
0.750721 | + | 0.660619i | \(0.229706\pi\) | |||||||
\(912\) | −98.4312 | −3.25938 | ||||||||
\(913\) | 0.265985 | 0.00880283 | ||||||||
\(914\) | 74.4305 | 2.46194 | ||||||||
\(915\) | 31.7716 | 1.05034 | ||||||||
\(916\) | −42.5543 | −1.40603 | ||||||||
\(917\) | 49.6209 | 1.63863 | ||||||||
\(918\) | −27.3736 | −0.903462 | ||||||||
\(919\) | 10.9476 | 0.361128 | 0.180564 | − | 0.983563i | \(-0.442208\pi\) | ||||
0.180564 | + | 0.983563i | \(0.442208\pi\) | |||||||
\(920\) | 23.4207 | 0.772156 | ||||||||
\(921\) | −10.2624 | −0.338157 | ||||||||
\(922\) | −76.2396 | −2.51082 | ||||||||
\(923\) | 61.8285 | 2.03511 | ||||||||
\(924\) | 3.09843 | 0.101931 | ||||||||
\(925\) | 58.5831 | 1.92620 | ||||||||
\(926\) | 65.5558 | 2.15430 | ||||||||
\(927\) | 5.84359 | 0.191929 | ||||||||
\(928\) | 138.687 | 4.55262 | ||||||||
\(929\) | 24.3472 | 0.798804 | 0.399402 | − | 0.916776i | \(-0.369218\pi\) | ||||
0.399402 | + | 0.916776i | \(0.369218\pi\) | |||||||
\(930\) | 113.492 | 3.72156 | ||||||||
\(931\) | 95.9688 | 3.14525 | ||||||||
\(932\) | 79.8350 | 2.61508 | ||||||||
\(933\) | 27.6712 | 0.905914 | ||||||||
\(934\) | −44.8823 | −1.46859 | ||||||||
\(935\) | −0.655229 | −0.0214283 | ||||||||
\(936\) | 48.4859 | 1.58481 | ||||||||
\(937\) | 55.8733 | 1.82530 | 0.912650 | − | 0.408742i | \(-0.134032\pi\) | ||||
0.912650 | + | 0.408742i | \(0.134032\pi\) | |||||||
\(938\) | 111.263 | 3.63285 | ||||||||
\(939\) | 2.05984 | 0.0672203 | ||||||||
\(940\) | −188.819 | −6.15859 | ||||||||
\(941\) | 21.7427 | 0.708793 | 0.354396 | − | 0.935095i | \(-0.384686\pi\) | ||||
0.354396 | + | 0.935095i | \(0.384686\pi\) | |||||||
\(942\) | −50.9645 | −1.66051 | ||||||||
\(943\) | −0.0407900 | −0.00132830 | ||||||||
\(944\) | −37.0825 | −1.20693 | ||||||||
\(945\) | 91.0550 | 2.96202 | ||||||||
\(946\) | −1.44545 | −0.0469957 | ||||||||
\(947\) | −23.8511 | −0.775056 | −0.387528 | − | 0.921858i | \(-0.626671\pi\) | ||||
−0.387528 | + | 0.921858i | \(0.626671\pi\) | |||||||
\(948\) | −48.9706 | −1.59049 | ||||||||
\(949\) | −15.4279 | −0.500812 | ||||||||
\(950\) | −119.098 | −3.86406 | ||||||||
\(951\) | 22.3778 | 0.725651 | ||||||||
\(952\) | −76.2827 | −2.47234 | ||||||||
\(953\) | −6.65749 | −0.215657 | −0.107829 | − | 0.994169i | \(-0.534390\pi\) | ||||
−0.107829 | + | 0.994169i | \(0.534390\pi\) | |||||||
\(954\) | 11.8477 | 0.383585 | ||||||||
\(955\) | 22.1936 | 0.718168 | ||||||||
\(956\) | −145.199 | −4.69607 | ||||||||
\(957\) | −0.990568 | −0.0320205 | ||||||||
\(958\) | 62.4139 | 2.01650 | ||||||||
\(959\) | 39.1851 | 1.26535 | ||||||||
\(960\) | −89.8109 | −2.89863 | ||||||||
\(961\) | 66.7301 | 2.15258 | ||||||||
\(962\) | −81.8385 | −2.63858 | ||||||||
\(963\) | 18.6188 | 0.599984 | ||||||||
\(964\) | −81.6035 | −2.62827 | ||||||||
\(965\) | 49.8443 | 1.60455 | ||||||||
\(966\) | −12.0494 | −0.387683 | ||||||||
\(967\) | 40.0480 | 1.28786 | 0.643929 | − | 0.765086i | \(-0.277303\pi\) | ||||
0.643929 | + | 0.765086i | \(0.277303\pi\) | |||||||
\(968\) | 95.7679 | 3.07810 | ||||||||
\(969\) | −14.0121 | −0.450134 | ||||||||
\(970\) | −111.549 | −3.58163 | ||||||||
\(971\) | 34.7644 | 1.11564 | 0.557821 | − | 0.829962i | \(-0.311638\pi\) | ||||
0.557821 | + | 0.829962i | \(0.311638\pi\) | |||||||
\(972\) | −72.1999 | −2.31581 | ||||||||
\(973\) | −101.827 | −3.26441 | ||||||||
\(974\) | 14.5871 | 0.467401 | ||||||||
\(975\) | −32.4284 | −1.03854 | ||||||||
\(976\) | −96.5630 | −3.09091 | ||||||||
\(977\) | −35.3718 | −1.13164 | −0.565822 | − | 0.824527i | \(-0.691441\pi\) | ||||
−0.565822 | + | 0.824527i | \(0.691441\pi\) | |||||||
\(978\) | 46.1523 | 1.47579 | ||||||||
\(979\) | −0.539908 | −0.0172555 | ||||||||
\(980\) | 282.646 | 9.02880 | ||||||||
\(981\) | 23.0978 | 0.737457 | ||||||||
\(982\) | −95.0484 | −3.03312 | ||||||||
\(983\) | 35.0144 | 1.11678 | 0.558392 | − | 0.829577i | \(-0.311418\pi\) | ||||
0.558392 | + | 0.829577i | \(0.311418\pi\) | |||||||
\(984\) | 0.564345 | 0.0179907 | ||||||||
\(985\) | 31.3776 | 0.999772 | ||||||||
\(986\) | 39.4466 | 1.25623 | ||||||||
\(987\) | 60.0579 | 1.91166 | ||||||||
\(988\) | 120.409 | 3.83072 | ||||||||
\(989\) | 4.06813 | 0.129359 | ||||||||
\(990\) | −1.43285 | −0.0455389 | ||||||||
\(991\) | 51.4127 | 1.63318 | 0.816589 | − | 0.577220i | \(-0.195862\pi\) | ||||
0.816589 | + | 0.577220i | \(0.195862\pi\) | |||||||
\(992\) | −172.638 | −5.48126 | ||||||||
\(993\) | 12.1141 | 0.384429 | ||||||||
\(994\) | −212.719 | −6.74705 | ||||||||
\(995\) | −36.0513 | −1.14290 | ||||||||
\(996\) | 16.7526 | 0.530826 | ||||||||
\(997\) | 27.7549 | 0.879007 | 0.439503 | − | 0.898241i | \(-0.355154\pi\) | ||||
0.439503 | + | 0.898241i | \(0.355154\pi\) | |||||||
\(998\) | 12.7421 | 0.403344 | ||||||||
\(999\) | 45.2072 | 1.43029 |
(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 | 6047.2.a.b.1.8 | ✓ | 287 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6047.2.a.b.1.8 | ✓ | 287 | 1.1 | even | 1 | trivial |