Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4029,2,Mod(1,4029)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4029, 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("4029.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4029 = 3 \cdot 17 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4029.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1717269744\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4029.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.77670 | −1.96342 | −0.981711 | − | 0.190380i | \(-0.939028\pi\) | ||||
−0.981711 | + | 0.190380i | \(0.939028\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 5.71004 | 2.85502 | ||||||||
\(5\) | −0.322981 | −0.144441 | −0.0722207 | − | 0.997389i | \(-0.523009\pi\) | ||||
−0.0722207 | + | 0.997389i | \(0.523009\pi\) | |||||||
\(6\) | 2.77670 | 1.13358 | ||||||||
\(7\) | −2.70395 | −1.02200 | −0.510999 | − | 0.859581i | \(-0.670724\pi\) | ||||
−0.510999 | + | 0.859581i | \(0.670724\pi\) | |||||||
\(8\) | −10.3017 | −3.64219 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.896820 | 0.283599 | ||||||||
\(11\) | −4.20627 | −1.26824 | −0.634120 | − | 0.773235i | \(-0.718637\pi\) | ||||
−0.634120 | + | 0.773235i | \(0.718637\pi\) | |||||||
\(12\) | −5.71004 | −1.64835 | ||||||||
\(13\) | −3.21667 | −0.892144 | −0.446072 | − | 0.894997i | \(-0.647177\pi\) | ||||
−0.446072 | + | 0.894997i | \(0.647177\pi\) | |||||||
\(14\) | 7.50806 | 2.00661 | ||||||||
\(15\) | 0.322981 | 0.0833933 | ||||||||
\(16\) | 17.1845 | 4.29613 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −2.77670 | −0.654474 | ||||||||
\(19\) | 1.38003 | 0.316600 | 0.158300 | − | 0.987391i | \(-0.449399\pi\) | ||||
0.158300 | + | 0.987391i | \(0.449399\pi\) | |||||||
\(20\) | −1.84424 | −0.412384 | ||||||||
\(21\) | 2.70395 | 0.590051 | ||||||||
\(22\) | 11.6795 | 2.49009 | ||||||||
\(23\) | −4.75086 | −0.990623 | −0.495312 | − | 0.868715i | \(-0.664946\pi\) | ||||
−0.495312 | + | 0.868715i | \(0.664946\pi\) | |||||||
\(24\) | 10.3017 | 2.10282 | ||||||||
\(25\) | −4.89568 | −0.979137 | ||||||||
\(26\) | 8.93172 | 1.75165 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −15.4397 | −2.91783 | ||||||||
\(29\) | 1.17961 | 0.219047 | 0.109524 | − | 0.993984i | \(-0.465067\pi\) | ||||
0.109524 | + | 0.993984i | \(0.465067\pi\) | |||||||
\(30\) | −0.896820 | −0.163736 | ||||||||
\(31\) | 1.07662 | 0.193366 | 0.0966831 | − | 0.995315i | \(-0.469177\pi\) | ||||
0.0966831 | + | 0.995315i | \(0.469177\pi\) | |||||||
\(32\) | −27.1129 | −4.79292 | ||||||||
\(33\) | 4.20627 | 0.732218 | ||||||||
\(34\) | 2.77670 | 0.476200 | ||||||||
\(35\) | 0.873325 | 0.147619 | ||||||||
\(36\) | 5.71004 | 0.951674 | ||||||||
\(37\) | −5.29347 | −0.870242 | −0.435121 | − | 0.900372i | \(-0.643294\pi\) | ||||
−0.435121 | + | 0.900372i | \(0.643294\pi\) | |||||||
\(38\) | −3.83191 | −0.621618 | ||||||||
\(39\) | 3.21667 | 0.515079 | ||||||||
\(40\) | 3.32724 | 0.526083 | ||||||||
\(41\) | −7.96803 | −1.24440 | −0.622198 | − | 0.782860i | \(-0.713760\pi\) | ||||
−0.622198 | + | 0.782860i | \(0.713760\pi\) | |||||||
\(42\) | −7.50806 | −1.15852 | ||||||||
\(43\) | 11.0562 | 1.68605 | 0.843024 | − | 0.537877i | \(-0.180773\pi\) | ||||
0.843024 | + | 0.537877i | \(0.180773\pi\) | |||||||
\(44\) | −24.0180 | −3.62085 | ||||||||
\(45\) | −0.322981 | −0.0481472 | ||||||||
\(46\) | 13.1917 | 1.94501 | ||||||||
\(47\) | −10.9703 | −1.60018 | −0.800090 | − | 0.599879i | \(-0.795215\pi\) | ||||
−0.800090 | + | 0.599879i | \(0.795215\pi\) | |||||||
\(48\) | −17.1845 | −2.48037 | ||||||||
\(49\) | 0.311361 | 0.0444801 | ||||||||
\(50\) | 13.5938 | 1.92246 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −18.3673 | −2.54709 | ||||||||
\(53\) | −3.46843 | −0.476426 | −0.238213 | − | 0.971213i | \(-0.576562\pi\) | ||||
−0.238213 | + | 0.971213i | \(0.576562\pi\) | |||||||
\(54\) | 2.77670 | 0.377861 | ||||||||
\(55\) | 1.35855 | 0.183186 | ||||||||
\(56\) | 27.8552 | 3.72231 | ||||||||
\(57\) | −1.38003 | −0.182789 | ||||||||
\(58\) | −3.27541 | −0.430082 | ||||||||
\(59\) | −9.56511 | −1.24527 | −0.622636 | − | 0.782512i | \(-0.713938\pi\) | ||||
−0.622636 | + | 0.782512i | \(0.713938\pi\) | |||||||
\(60\) | 1.84424 | 0.238090 | ||||||||
\(61\) | −12.7275 | −1.62958 | −0.814792 | − | 0.579753i | \(-0.803149\pi\) | ||||
−0.814792 | + | 0.579753i | \(0.803149\pi\) | |||||||
\(62\) | −2.98944 | −0.379659 | ||||||||
\(63\) | −2.70395 | −0.340666 | ||||||||
\(64\) | 40.9152 | 5.11440 | ||||||||
\(65\) | 1.03892 | 0.128863 | ||||||||
\(66\) | −11.6795 | −1.43765 | ||||||||
\(67\) | −6.97214 | −0.851782 | −0.425891 | − | 0.904774i | \(-0.640039\pi\) | ||||
−0.425891 | + | 0.904774i | \(0.640039\pi\) | |||||||
\(68\) | −5.71004 | −0.692445 | ||||||||
\(69\) | 4.75086 | 0.571937 | ||||||||
\(70\) | −2.42496 | −0.289838 | ||||||||
\(71\) | −5.38554 | −0.639147 | −0.319573 | − | 0.947562i | \(-0.603540\pi\) | ||||
−0.319573 | + | 0.947562i | \(0.603540\pi\) | |||||||
\(72\) | −10.3017 | −1.21406 | ||||||||
\(73\) | −8.17791 | −0.957152 | −0.478576 | − | 0.878046i | \(-0.658847\pi\) | ||||
−0.478576 | + | 0.878046i | \(0.658847\pi\) | |||||||
\(74\) | 14.6984 | 1.70865 | ||||||||
\(75\) | 4.89568 | 0.565305 | ||||||||
\(76\) | 7.88001 | 0.903899 | ||||||||
\(77\) | 11.3736 | 1.29614 | ||||||||
\(78\) | −8.93172 | −1.01132 | ||||||||
\(79\) | 1.00000 | 0.112509 | ||||||||
\(80\) | −5.55027 | −0.620539 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 22.1248 | 2.44328 | ||||||||
\(83\) | 6.37240 | 0.699462 | 0.349731 | − | 0.936850i | \(-0.386273\pi\) | ||||
0.349731 | + | 0.936850i | \(0.386273\pi\) | |||||||
\(84\) | 15.4397 | 1.68461 | ||||||||
\(85\) | 0.322981 | 0.0350322 | ||||||||
\(86\) | −30.6996 | −3.31042 | ||||||||
\(87\) | −1.17961 | −0.126467 | ||||||||
\(88\) | 43.3316 | 4.61917 | ||||||||
\(89\) | 12.3288 | 1.30685 | 0.653426 | − | 0.756991i | \(-0.273331\pi\) | ||||
0.653426 | + | 0.756991i | \(0.273331\pi\) | |||||||
\(90\) | 0.896820 | 0.0945331 | ||||||||
\(91\) | 8.69772 | 0.911769 | ||||||||
\(92\) | −27.1276 | −2.82825 | ||||||||
\(93\) | −1.07662 | −0.111640 | ||||||||
\(94\) | 30.4612 | 3.14183 | ||||||||
\(95\) | −0.445722 | −0.0457301 | ||||||||
\(96\) | 27.1129 | 2.76720 | ||||||||
\(97\) | 6.91187 | 0.701794 | 0.350897 | − | 0.936414i | \(-0.385877\pi\) | ||||
0.350897 | + | 0.936414i | \(0.385877\pi\) | |||||||
\(98\) | −0.864554 | −0.0873332 | ||||||||
\(99\) | −4.20627 | −0.422746 | ||||||||
\(100\) | −27.9546 | −2.79546 | ||||||||
\(101\) | −0.0359402 | −0.00357618 | −0.00178809 | − | 0.999998i | \(-0.500569\pi\) | ||||
−0.00178809 | + | 0.999998i | \(0.500569\pi\) | |||||||
\(102\) | −2.77670 | −0.274934 | ||||||||
\(103\) | 4.41580 | 0.435102 | 0.217551 | − | 0.976049i | \(-0.430193\pi\) | ||||
0.217551 | + | 0.976049i | \(0.430193\pi\) | |||||||
\(104\) | 33.1371 | 3.24936 | ||||||||
\(105\) | −0.873325 | −0.0852278 | ||||||||
\(106\) | 9.63078 | 0.935424 | ||||||||
\(107\) | −10.2768 | −0.993494 | −0.496747 | − | 0.867895i | \(-0.665472\pi\) | ||||
−0.496747 | + | 0.867895i | \(0.665472\pi\) | |||||||
\(108\) | −5.71004 | −0.549449 | ||||||||
\(109\) | 9.01915 | 0.863878 | 0.431939 | − | 0.901903i | \(-0.357830\pi\) | ||||
0.431939 | + | 0.901903i | \(0.357830\pi\) | |||||||
\(110\) | −3.77227 | −0.359672 | ||||||||
\(111\) | 5.29347 | 0.502434 | ||||||||
\(112\) | −46.4661 | −4.39064 | ||||||||
\(113\) | −11.7906 | −1.10916 | −0.554582 | − | 0.832129i | \(-0.687122\pi\) | ||||
−0.554582 | + | 0.832129i | \(0.687122\pi\) | |||||||
\(114\) | 3.83191 | 0.358891 | ||||||||
\(115\) | 1.53444 | 0.143087 | ||||||||
\(116\) | 6.73561 | 0.625385 | ||||||||
\(117\) | −3.21667 | −0.297381 | ||||||||
\(118\) | 26.5594 | 2.44499 | ||||||||
\(119\) | 2.70395 | 0.247871 | ||||||||
\(120\) | −3.32724 | −0.303734 | ||||||||
\(121\) | 6.69274 | 0.608431 | ||||||||
\(122\) | 35.3403 | 3.19956 | ||||||||
\(123\) | 7.96803 | 0.718453 | ||||||||
\(124\) | 6.14753 | 0.552065 | ||||||||
\(125\) | 3.19612 | 0.285869 | ||||||||
\(126\) | 7.50806 | 0.668871 | ||||||||
\(127\) | 5.14488 | 0.456534 | 0.228267 | − | 0.973599i | \(-0.426694\pi\) | ||||
0.228267 | + | 0.973599i | \(0.426694\pi\) | |||||||
\(128\) | −59.3833 | −5.24879 | ||||||||
\(129\) | −11.0562 | −0.973440 | ||||||||
\(130\) | −2.88477 | −0.253011 | ||||||||
\(131\) | 14.5680 | 1.27281 | 0.636406 | − | 0.771354i | \(-0.280420\pi\) | ||||
0.636406 | + | 0.771354i | \(0.280420\pi\) | |||||||
\(132\) | 24.0180 | 2.09050 | ||||||||
\(133\) | −3.73152 | −0.323564 | ||||||||
\(134\) | 19.3595 | 1.67241 | ||||||||
\(135\) | 0.322981 | 0.0277978 | ||||||||
\(136\) | 10.3017 | 0.883361 | ||||||||
\(137\) | −15.2209 | −1.30041 | −0.650205 | − | 0.759759i | \(-0.725317\pi\) | ||||
−0.650205 | + | 0.759759i | \(0.725317\pi\) | |||||||
\(138\) | −13.1917 | −1.12295 | ||||||||
\(139\) | −12.7423 | −1.08079 | −0.540396 | − | 0.841411i | \(-0.681725\pi\) | ||||
−0.540396 | + | 0.841411i | \(0.681725\pi\) | |||||||
\(140\) | 4.98673 | 0.421455 | ||||||||
\(141\) | 10.9703 | 0.923865 | ||||||||
\(142\) | 14.9540 | 1.25491 | ||||||||
\(143\) | 13.5302 | 1.13145 | ||||||||
\(144\) | 17.1845 | 1.43204 | ||||||||
\(145\) | −0.380990 | −0.0316395 | ||||||||
\(146\) | 22.7076 | 1.87929 | ||||||||
\(147\) | −0.311361 | −0.0256806 | ||||||||
\(148\) | −30.2260 | −2.48456 | ||||||||
\(149\) | −8.30491 | −0.680365 | −0.340182 | − | 0.940360i | \(-0.610489\pi\) | ||||
−0.340182 | + | 0.940360i | \(0.610489\pi\) | |||||||
\(150\) | −13.5938 | −1.10993 | ||||||||
\(151\) | 14.8951 | 1.21215 | 0.606074 | − | 0.795408i | \(-0.292744\pi\) | ||||
0.606074 | + | 0.795408i | \(0.292744\pi\) | |||||||
\(152\) | −14.2166 | −1.15312 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | −31.5809 | −2.54487 | ||||||||
\(155\) | −0.347727 | −0.0279301 | ||||||||
\(156\) | 18.3673 | 1.47056 | ||||||||
\(157\) | −7.55980 | −0.603338 | −0.301669 | − | 0.953413i | \(-0.597544\pi\) | ||||
−0.301669 | + | 0.953413i | \(0.597544\pi\) | |||||||
\(158\) | −2.77670 | −0.220902 | ||||||||
\(159\) | 3.46843 | 0.275064 | ||||||||
\(160\) | 8.75694 | 0.692297 | ||||||||
\(161\) | 12.8461 | 1.01242 | ||||||||
\(162\) | −2.77670 | −0.218158 | ||||||||
\(163\) | −6.29159 | −0.492796 | −0.246398 | − | 0.969169i | \(-0.579247\pi\) | ||||
−0.246398 | + | 0.969169i | \(0.579247\pi\) | |||||||
\(164\) | −45.4978 | −3.55278 | ||||||||
\(165\) | −1.35855 | −0.105763 | ||||||||
\(166\) | −17.6942 | −1.37334 | ||||||||
\(167\) | −7.31128 | −0.565764 | −0.282882 | − | 0.959155i | \(-0.591290\pi\) | ||||
−0.282882 | + | 0.959155i | \(0.591290\pi\) | |||||||
\(168\) | −27.8552 | −2.14908 | ||||||||
\(169\) | −2.65304 | −0.204080 | ||||||||
\(170\) | −0.896820 | −0.0687830 | ||||||||
\(171\) | 1.38003 | 0.105533 | ||||||||
\(172\) | 63.1311 | 4.81370 | ||||||||
\(173\) | −14.7177 | −1.11897 | −0.559483 | − | 0.828842i | \(-0.689000\pi\) | ||||
−0.559483 | + | 0.828842i | \(0.689000\pi\) | |||||||
\(174\) | 3.27541 | 0.248308 | ||||||||
\(175\) | 13.2377 | 1.00068 | ||||||||
\(176\) | −72.2828 | −5.44852 | ||||||||
\(177\) | 9.56511 | 0.718958 | ||||||||
\(178\) | −34.2334 | −2.56590 | ||||||||
\(179\) | −14.0508 | −1.05021 | −0.525103 | − | 0.851038i | \(-0.675973\pi\) | ||||
−0.525103 | + | 0.851038i | \(0.675973\pi\) | |||||||
\(180\) | −1.84424 | −0.137461 | ||||||||
\(181\) | −10.5713 | −0.785759 | −0.392880 | − | 0.919590i | \(-0.628521\pi\) | ||||
−0.392880 | + | 0.919590i | \(0.628521\pi\) | |||||||
\(182\) | −24.1509 | −1.79019 | ||||||||
\(183\) | 12.7275 | 0.940841 | ||||||||
\(184\) | 48.9418 | 3.60804 | ||||||||
\(185\) | 1.70969 | 0.125699 | ||||||||
\(186\) | 2.98944 | 0.219196 | ||||||||
\(187\) | 4.20627 | 0.307593 | ||||||||
\(188\) | −62.6408 | −4.56855 | ||||||||
\(189\) | 2.70395 | 0.196684 | ||||||||
\(190\) | 1.23763 | 0.0897874 | ||||||||
\(191\) | −2.37252 | −0.171670 | −0.0858348 | − | 0.996309i | \(-0.527356\pi\) | ||||
−0.0858348 | + | 0.996309i | \(0.527356\pi\) | |||||||
\(192\) | −40.9152 | −2.95280 | ||||||||
\(193\) | −22.6178 | −1.62806 | −0.814031 | − | 0.580821i | \(-0.802732\pi\) | ||||
−0.814031 | + | 0.580821i | \(0.802732\pi\) | |||||||
\(194\) | −19.1922 | −1.37792 | ||||||||
\(195\) | −1.03892 | −0.0743988 | ||||||||
\(196\) | 1.77788 | 0.126992 | ||||||||
\(197\) | 14.8804 | 1.06019 | 0.530094 | − | 0.847939i | \(-0.322157\pi\) | ||||
0.530094 | + | 0.847939i | \(0.322157\pi\) | |||||||
\(198\) | 11.6795 | 0.830029 | ||||||||
\(199\) | −2.02098 | −0.143263 | −0.0716316 | − | 0.997431i | \(-0.522821\pi\) | ||||
−0.0716316 | + | 0.997431i | \(0.522821\pi\) | |||||||
\(200\) | 50.4337 | 3.56620 | ||||||||
\(201\) | 6.97214 | 0.491777 | ||||||||
\(202\) | 0.0997951 | 0.00702156 | ||||||||
\(203\) | −3.18960 | −0.223866 | ||||||||
\(204\) | 5.71004 | 0.399783 | ||||||||
\(205\) | 2.57352 | 0.179743 | ||||||||
\(206\) | −12.2613 | −0.854289 | ||||||||
\(207\) | −4.75086 | −0.330208 | ||||||||
\(208\) | −55.2769 | −3.83277 | ||||||||
\(209\) | −5.80476 | −0.401524 | ||||||||
\(210\) | 2.42496 | 0.167338 | ||||||||
\(211\) | −9.24121 | −0.636191 | −0.318096 | − | 0.948059i | \(-0.603043\pi\) | ||||
−0.318096 | + | 0.948059i | \(0.603043\pi\) | |||||||
\(212\) | −19.8049 | −1.36021 | ||||||||
\(213\) | 5.38554 | 0.369011 | ||||||||
\(214\) | 28.5355 | 1.95065 | ||||||||
\(215\) | −3.57093 | −0.243535 | ||||||||
\(216\) | 10.3017 | 0.700940 | ||||||||
\(217\) | −2.91112 | −0.197620 | ||||||||
\(218\) | −25.0435 | −1.69616 | ||||||||
\(219\) | 8.17791 | 0.552612 | ||||||||
\(220\) | 7.75736 | 0.523001 | ||||||||
\(221\) | 3.21667 | 0.216377 | ||||||||
\(222\) | −14.6984 | −0.986490 | ||||||||
\(223\) | 8.34638 | 0.558915 | 0.279457 | − | 0.960158i | \(-0.409845\pi\) | ||||
0.279457 | + | 0.960158i | \(0.409845\pi\) | |||||||
\(224\) | 73.3119 | 4.89836 | ||||||||
\(225\) | −4.89568 | −0.326379 | ||||||||
\(226\) | 32.7388 | 2.17775 | ||||||||
\(227\) | −18.3929 | −1.22078 | −0.610389 | − | 0.792102i | \(-0.708987\pi\) | ||||
−0.610389 | + | 0.792102i | \(0.708987\pi\) | |||||||
\(228\) | −7.88001 | −0.521866 | ||||||||
\(229\) | −15.0245 | −0.992845 | −0.496422 | − | 0.868081i | \(-0.665353\pi\) | ||||
−0.496422 | + | 0.868081i | \(0.665353\pi\) | |||||||
\(230\) | −4.26067 | −0.280940 | ||||||||
\(231\) | −11.3736 | −0.748326 | ||||||||
\(232\) | −12.1519 | −0.797812 | ||||||||
\(233\) | 21.0029 | 1.37594 | 0.687972 | − | 0.725737i | \(-0.258501\pi\) | ||||
0.687972 | + | 0.725737i | \(0.258501\pi\) | |||||||
\(234\) | 8.93172 | 0.583885 | ||||||||
\(235\) | 3.54319 | 0.231132 | ||||||||
\(236\) | −54.6172 | −3.55528 | ||||||||
\(237\) | −1.00000 | −0.0649570 | ||||||||
\(238\) | −7.50806 | −0.486675 | ||||||||
\(239\) | −18.4947 | −1.19632 | −0.598160 | − | 0.801377i | \(-0.704101\pi\) | ||||
−0.598160 | + | 0.801377i | \(0.704101\pi\) | |||||||
\(240\) | 5.55027 | 0.358269 | ||||||||
\(241\) | 17.6246 | 1.13530 | 0.567651 | − | 0.823269i | \(-0.307852\pi\) | ||||
0.567651 | + | 0.823269i | \(0.307852\pi\) | |||||||
\(242\) | −18.5837 | −1.19461 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −72.6744 | −4.65250 | ||||||||
\(245\) | −0.100564 | −0.00642477 | ||||||||
\(246\) | −22.1248 | −1.41063 | ||||||||
\(247\) | −4.43909 | −0.282452 | ||||||||
\(248\) | −11.0910 | −0.704276 | ||||||||
\(249\) | −6.37240 | −0.403834 | ||||||||
\(250\) | −8.87465 | −0.561282 | ||||||||
\(251\) | 14.9045 | 0.940762 | 0.470381 | − | 0.882463i | \(-0.344117\pi\) | ||||
0.470381 | + | 0.882463i | \(0.344117\pi\) | |||||||
\(252\) | −15.4397 | −0.972609 | ||||||||
\(253\) | 19.9834 | 1.25635 | ||||||||
\(254\) | −14.2858 | −0.896369 | ||||||||
\(255\) | −0.322981 | −0.0202259 | ||||||||
\(256\) | 83.0590 | 5.19119 | ||||||||
\(257\) | 10.3361 | 0.644749 | 0.322375 | − | 0.946612i | \(-0.395519\pi\) | ||||
0.322375 | + | 0.946612i | \(0.395519\pi\) | |||||||
\(258\) | 30.6996 | 1.91127 | ||||||||
\(259\) | 14.3133 | 0.889385 | ||||||||
\(260\) | 5.93230 | 0.367905 | ||||||||
\(261\) | 1.17961 | 0.0730158 | ||||||||
\(262\) | −40.4509 | −2.49906 | ||||||||
\(263\) | 27.3781 | 1.68821 | 0.844104 | − | 0.536180i | \(-0.180133\pi\) | ||||
0.844104 | + | 0.536180i | \(0.180133\pi\) | |||||||
\(264\) | −43.3316 | −2.66688 | ||||||||
\(265\) | 1.12024 | 0.0688156 | ||||||||
\(266\) | 10.3613 | 0.635293 | ||||||||
\(267\) | −12.3288 | −0.754511 | ||||||||
\(268\) | −39.8112 | −2.43186 | ||||||||
\(269\) | 8.86101 | 0.540265 | 0.270133 | − | 0.962823i | \(-0.412932\pi\) | ||||
0.270133 | + | 0.962823i | \(0.412932\pi\) | |||||||
\(270\) | −0.896820 | −0.0545787 | ||||||||
\(271\) | 10.2725 | 0.624007 | 0.312004 | − | 0.950081i | \(-0.399000\pi\) | ||||
0.312004 | + | 0.950081i | \(0.399000\pi\) | |||||||
\(272\) | −17.1845 | −1.04196 | ||||||||
\(273\) | −8.69772 | −0.526410 | ||||||||
\(274\) | 42.2638 | 2.55325 | ||||||||
\(275\) | 20.5926 | 1.24178 | ||||||||
\(276\) | 27.1276 | 1.63289 | ||||||||
\(277\) | −16.9199 | −1.01662 | −0.508310 | − | 0.861174i | \(-0.669730\pi\) | ||||
−0.508310 | + | 0.861174i | \(0.669730\pi\) | |||||||
\(278\) | 35.3816 | 2.12205 | ||||||||
\(279\) | 1.07662 | 0.0644554 | ||||||||
\(280\) | −8.99671 | −0.537656 | ||||||||
\(281\) | 29.1419 | 1.73846 | 0.869231 | − | 0.494406i | \(-0.164614\pi\) | ||||
0.869231 | + | 0.494406i | \(0.164614\pi\) | |||||||
\(282\) | −30.4612 | −1.81394 | ||||||||
\(283\) | 0.580483 | 0.0345061 | 0.0172531 | − | 0.999851i | \(-0.494508\pi\) | ||||
0.0172531 | + | 0.999851i | \(0.494508\pi\) | |||||||
\(284\) | −30.7517 | −1.82478 | ||||||||
\(285\) | 0.445722 | 0.0264023 | ||||||||
\(286\) | −37.5692 | −2.22152 | ||||||||
\(287\) | 21.5452 | 1.27177 | ||||||||
\(288\) | −27.1129 | −1.59764 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 1.05789 | 0.0621217 | ||||||||
\(291\) | −6.91187 | −0.405181 | ||||||||
\(292\) | −46.6962 | −2.73269 | ||||||||
\(293\) | −20.3726 | −1.19018 | −0.595089 | − | 0.803660i | \(-0.702883\pi\) | ||||
−0.595089 | + | 0.803660i | \(0.702883\pi\) | |||||||
\(294\) | 0.864554 | 0.0504218 | ||||||||
\(295\) | 3.08935 | 0.179869 | ||||||||
\(296\) | 54.5316 | 3.16959 | ||||||||
\(297\) | 4.20627 | 0.244073 | ||||||||
\(298\) | 23.0602 | 1.33584 | ||||||||
\(299\) | 15.2820 | 0.883778 | ||||||||
\(300\) | 27.9546 | 1.61396 | ||||||||
\(301\) | −29.8953 | −1.72314 | ||||||||
\(302\) | −41.3592 | −2.37996 | ||||||||
\(303\) | 0.0359402 | 0.00206471 | ||||||||
\(304\) | 23.7151 | 1.36015 | ||||||||
\(305\) | 4.11073 | 0.235380 | ||||||||
\(306\) | 2.77670 | 0.158733 | ||||||||
\(307\) | 12.8136 | 0.731313 | 0.365656 | − | 0.930750i | \(-0.380845\pi\) | ||||
0.365656 | + | 0.930750i | \(0.380845\pi\) | |||||||
\(308\) | 64.9436 | 3.70050 | ||||||||
\(309\) | −4.41580 | −0.251206 | ||||||||
\(310\) | 0.965532 | 0.0548385 | ||||||||
\(311\) | 30.6229 | 1.73646 | 0.868232 | − | 0.496159i | \(-0.165257\pi\) | ||||
0.868232 | + | 0.496159i | \(0.165257\pi\) | |||||||
\(312\) | −33.1371 | −1.87602 | ||||||||
\(313\) | −11.3555 | −0.641852 | −0.320926 | − | 0.947104i | \(-0.603994\pi\) | ||||
−0.320926 | + | 0.947104i | \(0.603994\pi\) | |||||||
\(314\) | 20.9913 | 1.18461 | ||||||||
\(315\) | 0.873325 | 0.0492063 | ||||||||
\(316\) | 5.71004 | 0.321215 | ||||||||
\(317\) | 7.81235 | 0.438785 | 0.219393 | − | 0.975637i | \(-0.429592\pi\) | ||||
0.219393 | + | 0.975637i | \(0.429592\pi\) | |||||||
\(318\) | −9.63078 | −0.540067 | ||||||||
\(319\) | −4.96175 | −0.277805 | ||||||||
\(320\) | −13.2148 | −0.738731 | ||||||||
\(321\) | 10.2768 | 0.573594 | ||||||||
\(322\) | −35.6697 | −1.98780 | ||||||||
\(323\) | −1.38003 | −0.0767867 | ||||||||
\(324\) | 5.71004 | 0.317225 | ||||||||
\(325\) | 15.7478 | 0.873531 | ||||||||
\(326\) | 17.4698 | 0.967565 | ||||||||
\(327\) | −9.01915 | −0.498760 | ||||||||
\(328\) | 82.0840 | 4.53233 | ||||||||
\(329\) | 29.6631 | 1.63538 | ||||||||
\(330\) | 3.77227 | 0.207657 | ||||||||
\(331\) | 32.6427 | 1.79421 | 0.897104 | − | 0.441820i | \(-0.145667\pi\) | ||||
0.897104 | + | 0.441820i | \(0.145667\pi\) | |||||||
\(332\) | 36.3867 | 1.99698 | ||||||||
\(333\) | −5.29347 | −0.290081 | ||||||||
\(334\) | 20.3012 | 1.11083 | ||||||||
\(335\) | 2.25187 | 0.123033 | ||||||||
\(336\) | 46.4661 | 2.53494 | ||||||||
\(337\) | 0.144926 | 0.00789460 | 0.00394730 | − | 0.999992i | \(-0.498744\pi\) | ||||
0.00394730 | + | 0.999992i | \(0.498744\pi\) | |||||||
\(338\) | 7.36668 | 0.400694 | ||||||||
\(339\) | 11.7906 | 0.640376 | ||||||||
\(340\) | 1.84424 | 0.100018 | ||||||||
\(341\) | −4.52855 | −0.245235 | ||||||||
\(342\) | −3.83191 | −0.207206 | ||||||||
\(343\) | 18.0858 | 0.976540 | ||||||||
\(344\) | −113.897 | −6.14090 | ||||||||
\(345\) | −1.53444 | −0.0826114 | ||||||||
\(346\) | 40.8666 | 2.19700 | ||||||||
\(347\) | 15.4928 | 0.831694 | 0.415847 | − | 0.909434i | \(-0.363485\pi\) | ||||
0.415847 | + | 0.909434i | \(0.363485\pi\) | |||||||
\(348\) | −6.73561 | −0.361066 | ||||||||
\(349\) | −36.9254 | −1.97657 | −0.988285 | − | 0.152621i | \(-0.951229\pi\) | ||||
−0.988285 | + | 0.152621i | \(0.951229\pi\) | |||||||
\(350\) | −36.7571 | −1.96475 | ||||||||
\(351\) | 3.21667 | 0.171693 | ||||||||
\(352\) | 114.044 | 6.07857 | ||||||||
\(353\) | 19.1010 | 1.01664 | 0.508322 | − | 0.861167i | \(-0.330266\pi\) | ||||
0.508322 | + | 0.861167i | \(0.330266\pi\) | |||||||
\(354\) | −26.5594 | −1.41162 | ||||||||
\(355\) | 1.73943 | 0.0923193 | ||||||||
\(356\) | 70.3981 | 3.73109 | ||||||||
\(357\) | −2.70395 | −0.143108 | ||||||||
\(358\) | 39.0148 | 2.06200 | ||||||||
\(359\) | −35.3630 | −1.86639 | −0.933195 | − | 0.359371i | \(-0.882991\pi\) | ||||
−0.933195 | + | 0.359371i | \(0.882991\pi\) | |||||||
\(360\) | 3.32724 | 0.175361 | ||||||||
\(361\) | −17.0955 | −0.899765 | ||||||||
\(362\) | 29.3533 | 1.54278 | ||||||||
\(363\) | −6.69274 | −0.351278 | ||||||||
\(364\) | 49.6644 | 2.60312 | ||||||||
\(365\) | 2.64131 | 0.138252 | ||||||||
\(366\) | −35.3403 | −1.84727 | ||||||||
\(367\) | −29.7272 | −1.55174 | −0.775872 | − | 0.630890i | \(-0.782690\pi\) | ||||
−0.775872 | + | 0.630890i | \(0.782690\pi\) | |||||||
\(368\) | −81.6413 | −4.25585 | ||||||||
\(369\) | −7.96803 | −0.414799 | ||||||||
\(370\) | −4.74729 | −0.246800 | ||||||||
\(371\) | 9.37847 | 0.486906 | ||||||||
\(372\) | −6.14753 | −0.318735 | ||||||||
\(373\) | −8.59073 | −0.444811 | −0.222405 | − | 0.974954i | \(-0.571391\pi\) | ||||
−0.222405 | + | 0.974954i | \(0.571391\pi\) | |||||||
\(374\) | −11.6795 | −0.603935 | ||||||||
\(375\) | −3.19612 | −0.165047 | ||||||||
\(376\) | 113.012 | 5.82816 | ||||||||
\(377\) | −3.79440 | −0.195422 | ||||||||
\(378\) | −7.50806 | −0.386173 | ||||||||
\(379\) | −11.0870 | −0.569501 | −0.284750 | − | 0.958602i | \(-0.591911\pi\) | ||||
−0.284750 | + | 0.958602i | \(0.591911\pi\) | |||||||
\(380\) | −2.54509 | −0.130560 | ||||||||
\(381\) | −5.14488 | −0.263580 | ||||||||
\(382\) | 6.58777 | 0.337060 | ||||||||
\(383\) | −22.3446 | −1.14176 | −0.570878 | − | 0.821035i | \(-0.693397\pi\) | ||||
−0.570878 | + | 0.821035i | \(0.693397\pi\) | |||||||
\(384\) | 59.3833 | 3.03039 | ||||||||
\(385\) | −3.67345 | −0.187216 | ||||||||
\(386\) | 62.8027 | 3.19657 | ||||||||
\(387\) | 11.0562 | 0.562016 | ||||||||
\(388\) | 39.4671 | 2.00364 | ||||||||
\(389\) | −8.28320 | −0.419975 | −0.209987 | − | 0.977704i | \(-0.567342\pi\) | ||||
−0.209987 | + | 0.977704i | \(0.567342\pi\) | |||||||
\(390\) | 2.88477 | 0.146076 | ||||||||
\(391\) | 4.75086 | 0.240261 | ||||||||
\(392\) | −3.20754 | −0.162005 | ||||||||
\(393\) | −14.5680 | −0.734858 | ||||||||
\(394\) | −41.3185 | −2.08159 | ||||||||
\(395\) | −0.322981 | −0.0162509 | ||||||||
\(396\) | −24.0180 | −1.20695 | ||||||||
\(397\) | −10.7858 | −0.541324 | −0.270662 | − | 0.962674i | \(-0.587243\pi\) | ||||
−0.270662 | + | 0.962674i | \(0.587243\pi\) | |||||||
\(398\) | 5.61164 | 0.281286 | ||||||||
\(399\) | 3.73152 | 0.186810 | ||||||||
\(400\) | −84.1300 | −4.20650 | ||||||||
\(401\) | −15.5146 | −0.774761 | −0.387381 | − | 0.921920i | \(-0.626620\pi\) | ||||
−0.387381 | + | 0.921920i | \(0.626620\pi\) | |||||||
\(402\) | −19.3595 | −0.965565 | ||||||||
\(403\) | −3.46312 | −0.172510 | ||||||||
\(404\) | −0.205220 | −0.0102101 | ||||||||
\(405\) | −0.322981 | −0.0160491 | ||||||||
\(406\) | 8.85655 | 0.439543 | ||||||||
\(407\) | 22.2658 | 1.10367 | ||||||||
\(408\) | −10.3017 | −0.510009 | ||||||||
\(409\) | 10.1806 | 0.503398 | 0.251699 | − | 0.967806i | \(-0.419011\pi\) | ||||
0.251699 | + | 0.967806i | \(0.419011\pi\) | |||||||
\(410\) | −7.14589 | −0.352910 | ||||||||
\(411\) | 15.2209 | 0.750792 | ||||||||
\(412\) | 25.2144 | 1.24223 | ||||||||
\(413\) | 25.8636 | 1.27267 | ||||||||
\(414\) | 13.1917 | 0.648337 | ||||||||
\(415\) | −2.05816 | −0.101031 | ||||||||
\(416\) | 87.2131 | 4.27598 | ||||||||
\(417\) | 12.7423 | 0.623995 | ||||||||
\(418\) | 16.1181 | 0.788361 | ||||||||
\(419\) | 22.9032 | 1.11889 | 0.559447 | − | 0.828866i | \(-0.311013\pi\) | ||||
0.559447 | + | 0.828866i | \(0.311013\pi\) | |||||||
\(420\) | −4.98673 | −0.243327 | ||||||||
\(421\) | −31.4457 | −1.53257 | −0.766284 | − | 0.642502i | \(-0.777896\pi\) | ||||
−0.766284 | + | 0.642502i | \(0.777896\pi\) | |||||||
\(422\) | 25.6600 | 1.24911 | ||||||||
\(423\) | −10.9703 | −0.533394 | ||||||||
\(424\) | 35.7306 | 1.73523 | ||||||||
\(425\) | 4.89568 | 0.237476 | ||||||||
\(426\) | −14.9540 | −0.724525 | ||||||||
\(427\) | 34.4145 | 1.66543 | ||||||||
\(428\) | −58.6809 | −2.83645 | ||||||||
\(429\) | −13.5302 | −0.653244 | ||||||||
\(430\) | 9.91538 | 0.478162 | ||||||||
\(431\) | 13.7981 | 0.664631 | 0.332315 | − | 0.943168i | \(-0.392170\pi\) | ||||
0.332315 | + | 0.943168i | \(0.392170\pi\) | |||||||
\(432\) | −17.1845 | −0.826791 | ||||||||
\(433\) | 29.9389 | 1.43877 | 0.719385 | − | 0.694612i | \(-0.244424\pi\) | ||||
0.719385 | + | 0.694612i | \(0.244424\pi\) | |||||||
\(434\) | 8.08330 | 0.388011 | ||||||||
\(435\) | 0.380990 | 0.0182671 | ||||||||
\(436\) | 51.4998 | 2.46639 | ||||||||
\(437\) | −6.55631 | −0.313631 | ||||||||
\(438\) | −22.7076 | −1.08501 | ||||||||
\(439\) | 23.9078 | 1.14106 | 0.570528 | − | 0.821278i | \(-0.306738\pi\) | ||||
0.570528 | + | 0.821278i | \(0.306738\pi\) | |||||||
\(440\) | −13.9953 | −0.667200 | ||||||||
\(441\) | 0.311361 | 0.0148267 | ||||||||
\(442\) | −8.93172 | −0.424838 | ||||||||
\(443\) | 21.6491 | 1.02858 | 0.514291 | − | 0.857616i | \(-0.328055\pi\) | ||||
0.514291 | + | 0.857616i | \(0.328055\pi\) | |||||||
\(444\) | 30.2260 | 1.43446 | ||||||||
\(445\) | −3.98197 | −0.188764 | ||||||||
\(446\) | −23.1754 | −1.09739 | ||||||||
\(447\) | 8.30491 | 0.392809 | ||||||||
\(448\) | −110.633 | −5.22690 | ||||||||
\(449\) | −25.7595 | −1.21566 | −0.607832 | − | 0.794065i | \(-0.707961\pi\) | ||||
−0.607832 | + | 0.794065i | \(0.707961\pi\) | |||||||
\(450\) | 13.5938 | 0.640819 | ||||||||
\(451\) | 33.5157 | 1.57819 | ||||||||
\(452\) | −67.3247 | −3.16669 | ||||||||
\(453\) | −14.8951 | −0.699834 | ||||||||
\(454\) | 51.0714 | 2.39690 | ||||||||
\(455\) | −2.80920 | −0.131697 | ||||||||
\(456\) | 14.2166 | 0.665752 | ||||||||
\(457\) | 6.57430 | 0.307533 | 0.153767 | − | 0.988107i | \(-0.450860\pi\) | ||||
0.153767 | + | 0.988107i | \(0.450860\pi\) | |||||||
\(458\) | 41.7184 | 1.94937 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 8.76171 | 0.408517 | ||||||||
\(461\) | −30.7661 | −1.43292 | −0.716460 | − | 0.697629i | \(-0.754239\pi\) | ||||
−0.716460 | + | 0.697629i | \(0.754239\pi\) | |||||||
\(462\) | 31.5809 | 1.46928 | ||||||||
\(463\) | 27.3687 | 1.27193 | 0.635966 | − | 0.771717i | \(-0.280602\pi\) | ||||
0.635966 | + | 0.771717i | \(0.280602\pi\) | |||||||
\(464\) | 20.2710 | 0.941056 | ||||||||
\(465\) | 0.347727 | 0.0161254 | ||||||||
\(466\) | −58.3186 | −2.70156 | ||||||||
\(467\) | 2.36036 | 0.109225 | 0.0546123 | − | 0.998508i | \(-0.482608\pi\) | ||||
0.0546123 | + | 0.998508i | \(0.482608\pi\) | |||||||
\(468\) | −18.3673 | −0.849030 | ||||||||
\(469\) | 18.8523 | 0.870520 | ||||||||
\(470\) | −9.83837 | −0.453810 | ||||||||
\(471\) | 7.55980 | 0.348337 | ||||||||
\(472\) | 98.5366 | 4.53552 | ||||||||
\(473\) | −46.5052 | −2.13831 | ||||||||
\(474\) | 2.77670 | 0.127538 | ||||||||
\(475\) | −6.75617 | −0.309994 | ||||||||
\(476\) | 15.4397 | 0.707677 | ||||||||
\(477\) | −3.46843 | −0.158809 | ||||||||
\(478\) | 51.3541 | 2.34888 | ||||||||
\(479\) | −17.6438 | −0.806167 | −0.403083 | − | 0.915163i | \(-0.632062\pi\) | ||||
−0.403083 | + | 0.915163i | \(0.632062\pi\) | |||||||
\(480\) | −8.75694 | −0.399698 | ||||||||
\(481\) | 17.0274 | 0.776381 | ||||||||
\(482\) | −48.9383 | −2.22908 | ||||||||
\(483\) | −12.8461 | −0.584518 | ||||||||
\(484\) | 38.2159 | 1.73709 | ||||||||
\(485\) | −2.23240 | −0.101368 | ||||||||
\(486\) | 2.77670 | 0.125954 | ||||||||
\(487\) | −5.71845 | −0.259128 | −0.129564 | − | 0.991571i | \(-0.541358\pi\) | ||||
−0.129564 | + | 0.991571i | \(0.541358\pi\) | |||||||
\(488\) | 131.114 | 5.93526 | ||||||||
\(489\) | 6.29159 | 0.284516 | ||||||||
\(490\) | 0.279235 | 0.0126145 | ||||||||
\(491\) | 10.3947 | 0.469107 | 0.234554 | − | 0.972103i | \(-0.424637\pi\) | ||||
0.234554 | + | 0.972103i | \(0.424637\pi\) | |||||||
\(492\) | 45.4978 | 2.05120 | ||||||||
\(493\) | −1.17961 | −0.0531268 | ||||||||
\(494\) | 12.3260 | 0.554573 | ||||||||
\(495\) | 1.35855 | 0.0610621 | ||||||||
\(496\) | 18.5012 | 0.830726 | ||||||||
\(497\) | 14.5623 | 0.653207 | ||||||||
\(498\) | 17.6942 | 0.792897 | ||||||||
\(499\) | 20.1594 | 0.902461 | 0.451230 | − | 0.892407i | \(-0.350985\pi\) | ||||
0.451230 | + | 0.892407i | \(0.350985\pi\) | |||||||
\(500\) | 18.2500 | 0.816164 | ||||||||
\(501\) | 7.31128 | 0.326644 | ||||||||
\(502\) | −41.3852 | −1.84711 | ||||||||
\(503\) | 32.1849 | 1.43505 | 0.717527 | − | 0.696531i | \(-0.245274\pi\) | ||||
0.717527 | + | 0.696531i | \(0.245274\pi\) | |||||||
\(504\) | 27.8552 | 1.24077 | ||||||||
\(505\) | 0.0116080 | 0.000516549 0 | ||||||||
\(506\) | −55.4879 | −2.46674 | ||||||||
\(507\) | 2.65304 | 0.117825 | ||||||||
\(508\) | 29.3775 | 1.30342 | ||||||||
\(509\) | 41.3316 | 1.83199 | 0.915995 | − | 0.401189i | \(-0.131403\pi\) | ||||
0.915995 | + | 0.401189i | \(0.131403\pi\) | |||||||
\(510\) | 0.896820 | 0.0397119 | ||||||||
\(511\) | 22.1127 | 0.978207 | ||||||||
\(512\) | −111.863 | −4.94370 | ||||||||
\(513\) | −1.38003 | −0.0609296 | ||||||||
\(514\) | −28.7003 | −1.26591 | ||||||||
\(515\) | −1.42622 | −0.0628468 | ||||||||
\(516\) | −63.1311 | −2.77919 | ||||||||
\(517\) | 46.1440 | 2.02941 | ||||||||
\(518\) | −39.7437 | −1.74624 | ||||||||
\(519\) | 14.7177 | 0.646036 | ||||||||
\(520\) | −10.7026 | −0.469342 | ||||||||
\(521\) | 5.84865 | 0.256234 | 0.128117 | − | 0.991759i | \(-0.459107\pi\) | ||||
0.128117 | + | 0.991759i | \(0.459107\pi\) | |||||||
\(522\) | −3.27541 | −0.143361 | ||||||||
\(523\) | 29.2824 | 1.28043 | 0.640216 | − | 0.768195i | \(-0.278845\pi\) | ||||
0.640216 | + | 0.768195i | \(0.278845\pi\) | |||||||
\(524\) | 83.1839 | 3.63391 | ||||||||
\(525\) | −13.2377 | −0.577740 | ||||||||
\(526\) | −76.0208 | −3.31466 | ||||||||
\(527\) | −1.07662 | −0.0468982 | ||||||||
\(528\) | 72.2828 | 3.14571 | ||||||||
\(529\) | −0.429303 | −0.0186653 | ||||||||
\(530\) | −3.11056 | −0.135114 | ||||||||
\(531\) | −9.56511 | −0.415091 | ||||||||
\(532\) | −21.3072 | −0.923783 | ||||||||
\(533\) | 25.6305 | 1.11018 | ||||||||
\(534\) | 34.2334 | 1.48142 | ||||||||
\(535\) | 3.31921 | 0.143502 | ||||||||
\(536\) | 71.8247 | 3.10235 | ||||||||
\(537\) | 14.0508 | 0.606337 | ||||||||
\(538\) | −24.6043 | −1.06077 | ||||||||
\(539\) | −1.30967 | −0.0564114 | ||||||||
\(540\) | 1.84424 | 0.0793633 | ||||||||
\(541\) | 13.5506 | 0.582587 | 0.291293 | − | 0.956634i | \(-0.405914\pi\) | ||||
0.291293 | + | 0.956634i | \(0.405914\pi\) | |||||||
\(542\) | −28.5235 | −1.22519 | ||||||||
\(543\) | 10.5713 | 0.453658 | ||||||||
\(544\) | 27.1129 | 1.16245 | ||||||||
\(545\) | −2.91301 | −0.124780 | ||||||||
\(546\) | 24.1509 | 1.03356 | ||||||||
\(547\) | −17.3102 | −0.740130 | −0.370065 | − | 0.929006i | \(-0.620665\pi\) | ||||
−0.370065 | + | 0.929006i | \(0.620665\pi\) | |||||||
\(548\) | −86.9120 | −3.71270 | ||||||||
\(549\) | −12.7275 | −0.543195 | ||||||||
\(550\) | −57.1794 | −2.43814 | ||||||||
\(551\) | 1.62789 | 0.0693503 | ||||||||
\(552\) | −48.9418 | −2.08310 | ||||||||
\(553\) | −2.70395 | −0.114984 | ||||||||
\(554\) | 46.9815 | 1.99605 | ||||||||
\(555\) | −1.70969 | −0.0725723 | ||||||||
\(556\) | −72.7593 | −3.08568 | ||||||||
\(557\) | 19.5984 | 0.830410 | 0.415205 | − | 0.909728i | \(-0.363710\pi\) | ||||
0.415205 | + | 0.909728i | \(0.363710\pi\) | |||||||
\(558\) | −2.98944 | −0.126553 | ||||||||
\(559\) | −35.5640 | −1.50420 | ||||||||
\(560\) | 15.0077 | 0.634190 | ||||||||
\(561\) | −4.20627 | −0.177589 | ||||||||
\(562\) | −80.9183 | −3.41333 | ||||||||
\(563\) | 13.2572 | 0.558724 | 0.279362 | − | 0.960186i | \(-0.409877\pi\) | ||||
0.279362 | + | 0.960186i | \(0.409877\pi\) | |||||||
\(564\) | 62.6408 | 2.63765 | ||||||||
\(565\) | 3.80813 | 0.160209 | ||||||||
\(566\) | −1.61183 | −0.0677501 | ||||||||
\(567\) | −2.70395 | −0.113555 | ||||||||
\(568\) | 55.4801 | 2.32789 | ||||||||
\(569\) | 17.7645 | 0.744727 | 0.372363 | − | 0.928087i | \(-0.378548\pi\) | ||||
0.372363 | + | 0.928087i | \(0.378548\pi\) | |||||||
\(570\) | −1.23763 | −0.0518388 | ||||||||
\(571\) | −19.2876 | −0.807161 | −0.403581 | − | 0.914944i | \(-0.632234\pi\) | ||||
−0.403581 | + | 0.914944i | \(0.632234\pi\) | |||||||
\(572\) | 77.2580 | 3.23032 | ||||||||
\(573\) | 2.37252 | 0.0991135 | ||||||||
\(574\) | −59.8244 | −2.49702 | ||||||||
\(575\) | 23.2587 | 0.969956 | ||||||||
\(576\) | 40.9152 | 1.70480 | ||||||||
\(577\) | −10.8820 | −0.453023 | −0.226512 | − | 0.974008i | \(-0.572732\pi\) | ||||
−0.226512 | + | 0.974008i | \(0.572732\pi\) | |||||||
\(578\) | −2.77670 | −0.115495 | ||||||||
\(579\) | 22.6178 | 0.939962 | ||||||||
\(580\) | −2.17547 | −0.0903316 | ||||||||
\(581\) | −17.2307 | −0.714849 | ||||||||
\(582\) | 19.1922 | 0.795540 | ||||||||
\(583\) | 14.5892 | 0.604222 | ||||||||
\(584\) | 84.2461 | 3.48613 | ||||||||
\(585\) | 1.03892 | 0.0429542 | ||||||||
\(586\) | 56.5684 | 2.33682 | ||||||||
\(587\) | −26.6493 | −1.09994 | −0.549968 | − | 0.835186i | \(-0.685360\pi\) | ||||
−0.549968 | + | 0.835186i | \(0.685360\pi\) | |||||||
\(588\) | −1.77788 | −0.0733187 | ||||||||
\(589\) | 1.48576 | 0.0612196 | ||||||||
\(590\) | −8.57819 | −0.353158 | ||||||||
\(591\) | −14.8804 | −0.612099 | ||||||||
\(592\) | −90.9658 | −3.73867 | ||||||||
\(593\) | −22.8892 | −0.939947 | −0.469974 | − | 0.882680i | \(-0.655737\pi\) | ||||
−0.469974 | + | 0.882680i | \(0.655737\pi\) | |||||||
\(594\) | −11.6795 | −0.479218 | ||||||||
\(595\) | −0.873325 | −0.0358028 | ||||||||
\(596\) | −47.4214 | −1.94246 | ||||||||
\(597\) | 2.02098 | 0.0827131 | ||||||||
\(598\) | −42.4334 | −1.73523 | ||||||||
\(599\) | −27.0471 | −1.10511 | −0.552557 | − | 0.833475i | \(-0.686348\pi\) | ||||
−0.552557 | + | 0.833475i | \(0.686348\pi\) | |||||||
\(600\) | −50.4337 | −2.05895 | ||||||||
\(601\) | −21.8731 | −0.892221 | −0.446111 | − | 0.894978i | \(-0.647191\pi\) | ||||
−0.446111 | + | 0.894978i | \(0.647191\pi\) | |||||||
\(602\) | 83.0102 | 3.38324 | ||||||||
\(603\) | −6.97214 | −0.283927 | ||||||||
\(604\) | 85.0518 | 3.46071 | ||||||||
\(605\) | −2.16163 | −0.0878827 | ||||||||
\(606\) | −0.0997951 | −0.00405390 | ||||||||
\(607\) | 15.0848 | 0.612272 | 0.306136 | − | 0.951988i | \(-0.400964\pi\) | ||||
0.306136 | + | 0.951988i | \(0.400964\pi\) | |||||||
\(608\) | −37.4164 | −1.51744 | ||||||||
\(609\) | 3.18960 | 0.129249 | ||||||||
\(610\) | −11.4142 | −0.462149 | ||||||||
\(611\) | 35.2878 | 1.42759 | ||||||||
\(612\) | −5.71004 | −0.230815 | ||||||||
\(613\) | −5.33957 | −0.215663 | −0.107832 | − | 0.994169i | \(-0.534391\pi\) | ||||
−0.107832 | + | 0.994169i | \(0.534391\pi\) | |||||||
\(614\) | −35.5796 | −1.43587 | ||||||||
\(615\) | −2.57352 | −0.103774 | ||||||||
\(616\) | −117.167 | −4.72078 | ||||||||
\(617\) | −23.6745 | −0.953100 | −0.476550 | − | 0.879147i | \(-0.658113\pi\) | ||||
−0.476550 | + | 0.879147i | \(0.658113\pi\) | |||||||
\(618\) | 12.2613 | 0.493224 | ||||||||
\(619\) | 0.369405 | 0.0148477 | 0.00742383 | − | 0.999972i | \(-0.497637\pi\) | ||||
0.00742383 | + | 0.999972i | \(0.497637\pi\) | |||||||
\(620\) | −1.98554 | −0.0797410 | ||||||||
\(621\) | 4.75086 | 0.190646 | ||||||||
\(622\) | −85.0304 | −3.40941 | ||||||||
\(623\) | −33.3365 | −1.33560 | ||||||||
\(624\) | 55.2769 | 2.21285 | ||||||||
\(625\) | 23.4461 | 0.937845 | ||||||||
\(626\) | 31.5309 | 1.26023 | ||||||||
\(627\) | 5.80476 | 0.231820 | ||||||||
\(628\) | −43.1668 | −1.72254 | ||||||||
\(629\) | 5.29347 | 0.211065 | ||||||||
\(630\) | −2.42496 | −0.0966127 | ||||||||
\(631\) | 7.20624 | 0.286876 | 0.143438 | − | 0.989659i | \(-0.454184\pi\) | ||||
0.143438 | + | 0.989659i | \(0.454184\pi\) | |||||||
\(632\) | −10.3017 | −0.409778 | ||||||||
\(633\) | 9.24121 | 0.367305 | ||||||||
\(634\) | −21.6925 | −0.861520 | ||||||||
\(635\) | −1.66170 | −0.0659425 | ||||||||
\(636\) | 19.8049 | 0.785315 | ||||||||
\(637\) | −1.00154 | −0.0396826 | ||||||||
\(638\) | 13.7773 | 0.545447 | ||||||||
\(639\) | −5.38554 | −0.213049 | ||||||||
\(640\) | 19.1797 | 0.758143 | ||||||||
\(641\) | −24.4041 | −0.963905 | −0.481953 | − | 0.876197i | \(-0.660072\pi\) | ||||
−0.481953 | + | 0.876197i | \(0.660072\pi\) | |||||||
\(642\) | −28.5355 | −1.12621 | ||||||||
\(643\) | −4.48266 | −0.176779 | −0.0883895 | − | 0.996086i | \(-0.528172\pi\) | ||||
−0.0883895 | + | 0.996086i | \(0.528172\pi\) | |||||||
\(644\) | 73.3519 | 2.89047 | ||||||||
\(645\) | 3.57093 | 0.140605 | ||||||||
\(646\) | 3.83191 | 0.150765 | ||||||||
\(647\) | 22.9291 | 0.901434 | 0.450717 | − | 0.892667i | \(-0.351168\pi\) | ||||
0.450717 | + | 0.892667i | \(0.351168\pi\) | |||||||
\(648\) | −10.3017 | −0.404688 | ||||||||
\(649\) | 40.2335 | 1.57930 | ||||||||
\(650\) | −43.7269 | −1.71511 | ||||||||
\(651\) | 2.91112 | 0.114096 | ||||||||
\(652\) | −35.9253 | −1.40694 | ||||||||
\(653\) | 13.0680 | 0.511392 | 0.255696 | − | 0.966757i | \(-0.417695\pi\) | ||||
0.255696 | + | 0.966757i | \(0.417695\pi\) | |||||||
\(654\) | 25.0435 | 0.979277 | ||||||||
\(655\) | −4.70518 | −0.183847 | ||||||||
\(656\) | −136.927 | −5.34609 | ||||||||
\(657\) | −8.17791 | −0.319051 | ||||||||
\(658\) | −82.3655 | −3.21094 | ||||||||
\(659\) | 31.0634 | 1.21006 | 0.605030 | − | 0.796203i | \(-0.293161\pi\) | ||||
0.605030 | + | 0.796203i | \(0.293161\pi\) | |||||||
\(660\) | −7.75736 | −0.301955 | ||||||||
\(661\) | −19.4967 | −0.758335 | −0.379168 | − | 0.925328i | \(-0.623790\pi\) | ||||
−0.379168 | + | 0.925328i | \(0.623790\pi\) | |||||||
\(662\) | −90.6390 | −3.52278 | ||||||||
\(663\) | −3.21667 | −0.124925 | ||||||||
\(664\) | −65.6464 | −2.54757 | ||||||||
\(665\) | 1.20521 | 0.0467361 | ||||||||
\(666\) | 14.6984 | 0.569550 | ||||||||
\(667\) | −5.60415 | −0.216994 | ||||||||
\(668\) | −41.7477 | −1.61527 | ||||||||
\(669\) | −8.34638 | −0.322690 | ||||||||
\(670\) | −6.25276 | −0.241565 | ||||||||
\(671\) | 53.5352 | 2.06670 | ||||||||
\(672\) | −73.3119 | −2.82807 | ||||||||
\(673\) | 10.5377 | 0.406197 | 0.203098 | − | 0.979158i | \(-0.434899\pi\) | ||||
0.203098 | + | 0.979158i | \(0.434899\pi\) | |||||||
\(674\) | −0.402415 | −0.0155004 | ||||||||
\(675\) | 4.89568 | 0.188435 | ||||||||
\(676\) | −15.1490 | −0.582652 | ||||||||
\(677\) | 43.3226 | 1.66502 | 0.832511 | − | 0.554009i | \(-0.186903\pi\) | ||||
0.832511 | + | 0.554009i | \(0.186903\pi\) | |||||||
\(678\) | −32.7388 | −1.25733 | ||||||||
\(679\) | −18.6894 | −0.717232 | ||||||||
\(680\) | −3.32724 | −0.127594 | ||||||||
\(681\) | 18.3929 | 0.704816 | ||||||||
\(682\) | 12.5744 | 0.481499 | ||||||||
\(683\) | 5.60647 | 0.214526 | 0.107263 | − | 0.994231i | \(-0.465791\pi\) | ||||
0.107263 | + | 0.994231i | \(0.465791\pi\) | |||||||
\(684\) | 7.88001 | 0.301300 | ||||||||
\(685\) | 4.91606 | 0.187833 | ||||||||
\(686\) | −50.2187 | −1.91736 | ||||||||
\(687\) | 15.0245 | 0.573219 | ||||||||
\(688\) | 189.995 | 7.24348 | ||||||||
\(689\) | 11.1568 | 0.425040 | ||||||||
\(690\) | 4.26067 | 0.162201 | ||||||||
\(691\) | −34.5728 | −1.31521 | −0.657607 | − | 0.753362i | \(-0.728431\pi\) | ||||
−0.657607 | + | 0.753362i | \(0.728431\pi\) | |||||||
\(692\) | −84.0388 | −3.19467 | ||||||||
\(693\) | 11.3736 | 0.432046 | ||||||||
\(694\) | −43.0187 | −1.63297 | ||||||||
\(695\) | 4.11553 | 0.156111 | ||||||||
\(696\) | 12.1519 | 0.460617 | ||||||||
\(697\) | 7.96803 | 0.301811 | ||||||||
\(698\) | 102.531 | 3.88084 | ||||||||
\(699\) | −21.0029 | −0.794401 | ||||||||
\(700\) | 75.5878 | 2.85695 | ||||||||
\(701\) | 43.3848 | 1.63862 | 0.819311 | − | 0.573349i | \(-0.194356\pi\) | ||||
0.819311 | + | 0.573349i | \(0.194356\pi\) | |||||||
\(702\) | −8.93172 | −0.337106 | ||||||||
\(703\) | −7.30513 | −0.275518 | ||||||||
\(704\) | −172.100 | −6.48628 | ||||||||
\(705\) | −3.54319 | −0.133444 | ||||||||
\(706\) | −53.0377 | −1.99610 | ||||||||
\(707\) | 0.0971806 | 0.00365485 | ||||||||
\(708\) | 54.6172 | 2.05264 | ||||||||
\(709\) | 1.24770 | 0.0468585 | 0.0234292 | − | 0.999725i | \(-0.492542\pi\) | ||||
0.0234292 | + | 0.999725i | \(0.492542\pi\) | |||||||
\(710\) | −4.82986 | −0.181262 | ||||||||
\(711\) | 1.00000 | 0.0375029 | ||||||||
\(712\) | −127.007 | −4.75980 | ||||||||
\(713\) | −5.11486 | −0.191553 | ||||||||
\(714\) | 7.50806 | 0.280982 | ||||||||
\(715\) | −4.37000 | −0.163429 | ||||||||
\(716\) | −80.2307 | −2.99836 | ||||||||
\(717\) | 18.4947 | 0.690696 | ||||||||
\(718\) | 98.1924 | 3.66451 | ||||||||
\(719\) | 45.3627 | 1.69174 | 0.845872 | − | 0.533385i | \(-0.179080\pi\) | ||||
0.845872 | + | 0.533385i | \(0.179080\pi\) | |||||||
\(720\) | −5.55027 | −0.206846 | ||||||||
\(721\) | −11.9401 | −0.444673 | ||||||||
\(722\) | 47.4691 | 1.76662 | ||||||||
\(723\) | −17.6246 | −0.655467 | ||||||||
\(724\) | −60.3627 | −2.24336 | ||||||||
\(725\) | −5.77498 | −0.214477 | ||||||||
\(726\) | 18.5837 | 0.689707 | ||||||||
\(727\) | −30.4879 | −1.13073 | −0.565366 | − | 0.824840i | \(-0.691265\pi\) | ||||
−0.565366 | + | 0.824840i | \(0.691265\pi\) | |||||||
\(728\) | −89.6011 | −3.32084 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.33411 | −0.271448 | ||||||||
\(731\) | −11.0562 | −0.408927 | ||||||||
\(732\) | 72.6744 | 2.68612 | ||||||||
\(733\) | 8.39289 | 0.309998 | 0.154999 | − | 0.987915i | \(-0.450462\pi\) | ||||
0.154999 | + | 0.987915i | \(0.450462\pi\) | |||||||
\(734\) | 82.5433 | 3.04673 | ||||||||
\(735\) | 0.100564 | 0.00370934 | ||||||||
\(736\) | 128.810 | 4.74798 | ||||||||
\(737\) | 29.3267 | 1.08026 | ||||||||
\(738\) | 22.1248 | 0.814425 | ||||||||
\(739\) | 4.34300 | 0.159760 | 0.0798800 | − | 0.996804i | \(-0.474546\pi\) | ||||
0.0798800 | + | 0.996804i | \(0.474546\pi\) | |||||||
\(740\) | 9.76241 | 0.358873 | ||||||||
\(741\) | 4.43909 | 0.163074 | ||||||||
\(742\) | −26.0412 | −0.956002 | ||||||||
\(743\) | −21.1018 | −0.774151 | −0.387075 | − | 0.922048i | \(-0.626515\pi\) | ||||
−0.387075 | + | 0.922048i | \(0.626515\pi\) | |||||||
\(744\) | 11.0910 | 0.406614 | ||||||||
\(745\) | 2.68233 | 0.0982729 | ||||||||
\(746\) | 23.8538 | 0.873351 | ||||||||
\(747\) | 6.37240 | 0.233154 | ||||||||
\(748\) | 24.0180 | 0.878186 | ||||||||
\(749\) | 27.7879 | 1.01535 | ||||||||
\(750\) | 8.87465 | 0.324056 | ||||||||
\(751\) | −47.8747 | −1.74697 | −0.873487 | − | 0.486848i | \(-0.838146\pi\) | ||||
−0.873487 | + | 0.486848i | \(0.838146\pi\) | |||||||
\(752\) | −188.519 | −6.87459 | ||||||||
\(753\) | −14.9045 | −0.543149 | ||||||||
\(754\) | 10.5359 | 0.383695 | ||||||||
\(755\) | −4.81084 | −0.175084 | ||||||||
\(756\) | 15.4397 | 0.561536 | ||||||||
\(757\) | 14.1261 | 0.513422 | 0.256711 | − | 0.966488i | \(-0.417361\pi\) | ||||
0.256711 | + | 0.966488i | \(0.417361\pi\) | |||||||
\(758\) | 30.7852 | 1.11817 | ||||||||
\(759\) | −19.9834 | −0.725353 | ||||||||
\(760\) | 4.59168 | 0.166558 | ||||||||
\(761\) | −44.8273 | −1.62499 | −0.812493 | − | 0.582970i | \(-0.801890\pi\) | ||||
−0.812493 | + | 0.582970i | \(0.801890\pi\) | |||||||
\(762\) | 14.2858 | 0.517519 | ||||||||
\(763\) | −24.3874 | −0.882882 | ||||||||
\(764\) | −13.5472 | −0.490121 | ||||||||
\(765\) | 0.322981 | 0.0116774 | ||||||||
\(766\) | 62.0442 | 2.24175 | ||||||||
\(767\) | 30.7678 | 1.11096 | ||||||||
\(768\) | −83.0590 | −2.99713 | ||||||||
\(769\) | −45.5633 | −1.64305 | −0.821527 | − | 0.570169i | \(-0.806878\pi\) | ||||
−0.821527 | + | 0.570169i | \(0.806878\pi\) | |||||||
\(770\) | 10.2000 | 0.367584 | ||||||||
\(771\) | −10.3361 | −0.372246 | ||||||||
\(772\) | −129.148 | −4.64816 | ||||||||
\(773\) | 12.0215 | 0.432385 | 0.216193 | − | 0.976351i | \(-0.430636\pi\) | ||||
0.216193 | + | 0.976351i | \(0.430636\pi\) | |||||||
\(774\) | −30.6996 | −1.10347 | ||||||||
\(775\) | −5.27078 | −0.189332 | ||||||||
\(776\) | −71.2038 | −2.55607 | ||||||||
\(777\) | −14.3133 | −0.513487 | ||||||||
\(778\) | 22.9999 | 0.824587 | ||||||||
\(779\) | −10.9961 | −0.393975 | ||||||||
\(780\) | −5.93230 | −0.212410 | ||||||||
\(781\) | 22.6531 | 0.810591 | ||||||||
\(782\) | −13.1917 | −0.471734 | ||||||||
\(783\) | −1.17961 | −0.0421557 | ||||||||
\(784\) | 5.35059 | 0.191092 | ||||||||
\(785\) | 2.44167 | 0.0871470 | ||||||||
\(786\) | 40.4509 | 1.44284 | ||||||||
\(787\) | −0.683217 | −0.0243541 | −0.0121770 | − | 0.999926i | \(-0.503876\pi\) | ||||
−0.0121770 | + | 0.999926i | \(0.503876\pi\) | |||||||
\(788\) | 84.9680 | 3.02686 | ||||||||
\(789\) | −27.3781 | −0.974687 | ||||||||
\(790\) | 0.896820 | 0.0319074 | ||||||||
\(791\) | 31.8811 | 1.13356 | ||||||||
\(792\) | 43.3316 | 1.53972 | ||||||||
\(793\) | 40.9401 | 1.45382 | ||||||||
\(794\) | 29.9489 | 1.06285 | ||||||||
\(795\) | −1.12024 | −0.0397307 | ||||||||
\(796\) | −11.5399 | −0.409020 | ||||||||
\(797\) | 29.2407 | 1.03576 | 0.517879 | − | 0.855454i | \(-0.326722\pi\) | ||||
0.517879 | + | 0.855454i | \(0.326722\pi\) | |||||||
\(798\) | −10.3613 | −0.366786 | ||||||||
\(799\) | 10.9703 | 0.388101 | ||||||||
\(800\) | 132.736 | 4.69293 | ||||||||
\(801\) | 12.3288 | 0.435617 | ||||||||
\(802\) | 43.0793 | 1.52118 | ||||||||
\(803\) | 34.3985 | 1.21390 | ||||||||
\(804\) | 39.8112 | 1.40403 | ||||||||
\(805\) | −4.14905 | −0.146235 | ||||||||
\(806\) | 9.61604 | 0.338711 | ||||||||
\(807\) | −8.86101 | −0.311922 | ||||||||
\(808\) | 0.370244 | 0.0130251 | ||||||||
\(809\) | 5.21190 | 0.183241 | 0.0916203 | − | 0.995794i | \(-0.470795\pi\) | ||||
0.0916203 | + | 0.995794i | \(0.470795\pi\) | |||||||
\(810\) | 0.896820 | 0.0315110 | ||||||||
\(811\) | 46.6702 | 1.63881 | 0.819406 | − | 0.573214i | \(-0.194304\pi\) | ||||
0.819406 | + | 0.573214i | \(0.194304\pi\) | |||||||
\(812\) | −18.2128 | −0.639143 | ||||||||
\(813\) | −10.2725 | −0.360271 | ||||||||
\(814\) | −61.8254 | −2.16698 | ||||||||
\(815\) | 2.03206 | 0.0711801 | ||||||||
\(816\) | 17.1845 | 0.601579 | ||||||||
\(817\) | 15.2578 | 0.533802 | ||||||||
\(818\) | −28.2684 | −0.988381 | ||||||||
\(819\) | 8.69772 | 0.303923 | ||||||||
\(820\) | 14.6949 | 0.513169 | ||||||||
\(821\) | −8.32703 | −0.290615 | −0.145308 | − | 0.989387i | \(-0.546417\pi\) | ||||
−0.145308 | + | 0.989387i | \(0.546417\pi\) | |||||||
\(822\) | −42.2638 | −1.47412 | ||||||||
\(823\) | 8.52116 | 0.297029 | 0.148514 | − | 0.988910i | \(-0.452551\pi\) | ||||
0.148514 | + | 0.988910i | \(0.452551\pi\) | |||||||
\(824\) | −45.4901 | −1.58472 | ||||||||
\(825\) | −20.5926 | −0.716942 | ||||||||
\(826\) | −71.8154 | −2.49878 | ||||||||
\(827\) | −1.12600 | −0.0391549 | −0.0195774 | − | 0.999808i | \(-0.506232\pi\) | ||||
−0.0195774 | + | 0.999808i | \(0.506232\pi\) | |||||||
\(828\) | −27.1276 | −0.942751 | ||||||||
\(829\) | −4.45797 | −0.154832 | −0.0774159 | − | 0.996999i | \(-0.524667\pi\) | ||||
−0.0774159 | + | 0.996999i | \(0.524667\pi\) | |||||||
\(830\) | 5.71490 | 0.198367 | ||||||||
\(831\) | 16.9199 | 0.586946 | ||||||||
\(832\) | −131.611 | −4.56278 | ||||||||
\(833\) | −0.311361 | −0.0107880 | ||||||||
\(834\) | −35.3816 | −1.22516 | ||||||||
\(835\) | 2.36140 | 0.0817197 | ||||||||
\(836\) | −33.1455 | −1.14636 | ||||||||
\(837\) | −1.07662 | −0.0372133 | ||||||||
\(838\) | −63.5953 | −2.19686 | ||||||||
\(839\) | 9.49170 | 0.327690 | 0.163845 | − | 0.986486i | \(-0.447610\pi\) | ||||
0.163845 | + | 0.986486i | \(0.447610\pi\) | |||||||
\(840\) | 8.99671 | 0.310416 | ||||||||
\(841\) | −27.6085 | −0.952018 | ||||||||
\(842\) | 87.3150 | 3.00908 | ||||||||
\(843\) | −29.1419 | −1.00370 | ||||||||
\(844\) | −52.7677 | −1.81634 | ||||||||
\(845\) | 0.856880 | 0.0294776 | ||||||||
\(846\) | 30.4612 | 1.04728 | ||||||||
\(847\) | −18.0969 | −0.621816 | ||||||||
\(848\) | −59.6033 | −2.04679 | ||||||||
\(849\) | −0.580483 | −0.0199221 | ||||||||
\(850\) | −13.5938 | −0.466264 | ||||||||
\(851\) | 25.1486 | 0.862082 | ||||||||
\(852\) | 30.7517 | 1.05354 | ||||||||
\(853\) | −33.7937 | −1.15708 | −0.578538 | − | 0.815656i | \(-0.696376\pi\) | ||||
−0.578538 | + | 0.815656i | \(0.696376\pi\) | |||||||
\(854\) | −95.5585 | −3.26995 | ||||||||
\(855\) | −0.445722 | −0.0152434 | ||||||||
\(856\) | 105.868 | 3.61850 | ||||||||
\(857\) | 41.5764 | 1.42022 | 0.710112 | − | 0.704089i | \(-0.248644\pi\) | ||||
0.710112 | + | 0.704089i | \(0.248644\pi\) | |||||||
\(858\) | 37.5692 | 1.28259 | ||||||||
\(859\) | −15.3064 | −0.522246 | −0.261123 | − | 0.965306i | \(-0.584093\pi\) | ||||
−0.261123 | + | 0.965306i | \(0.584093\pi\) | |||||||
\(860\) | −20.3901 | −0.695298 | ||||||||
\(861\) | −21.5452 | −0.734258 | ||||||||
\(862\) | −38.3131 | −1.30495 | ||||||||
\(863\) | −20.6599 | −0.703271 | −0.351636 | − | 0.936137i | \(-0.614374\pi\) | ||||
−0.351636 | + | 0.936137i | \(0.614374\pi\) | |||||||
\(864\) | 27.1129 | 0.922399 | ||||||||
\(865\) | 4.75354 | 0.161625 | ||||||||
\(866\) | −83.1311 | −2.82491 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −16.6226 | −0.564209 | ||||||||
\(869\) | −4.20627 | −0.142688 | ||||||||
\(870\) | −1.05789 | −0.0358660 | ||||||||
\(871\) | 22.4271 | 0.759912 | ||||||||
\(872\) | −92.9123 | −3.14641 | ||||||||
\(873\) | 6.91187 | 0.233931 | ||||||||
\(874\) | 18.2049 | 0.615789 | ||||||||
\(875\) | −8.64215 | −0.292158 | ||||||||
\(876\) | 46.6962 | 1.57772 | ||||||||
\(877\) | −21.9803 | −0.742222 | −0.371111 | − | 0.928589i | \(-0.621023\pi\) | ||||
−0.371111 | + | 0.928589i | \(0.621023\pi\) | |||||||
\(878\) | −66.3847 | −2.24037 | ||||||||
\(879\) | 20.3726 | 0.687149 | ||||||||
\(880\) | 23.3460 | 0.786993 | ||||||||
\(881\) | −22.1315 | −0.745629 | −0.372814 | − | 0.927906i | \(-0.621607\pi\) | ||||
−0.372814 | + | 0.927906i | \(0.621607\pi\) | |||||||
\(882\) | −0.864554 | −0.0291111 | ||||||||
\(883\) | 55.3958 | 1.86422 | 0.932109 | − | 0.362179i | \(-0.117967\pi\) | ||||
0.932109 | + | 0.362179i | \(0.117967\pi\) | |||||||
\(884\) | 18.3673 | 0.617760 | ||||||||
\(885\) | −3.08935 | −0.103847 | ||||||||
\(886\) | −60.1131 | −2.01954 | ||||||||
\(887\) | 40.3376 | 1.35441 | 0.677203 | − | 0.735797i | \(-0.263192\pi\) | ||||
0.677203 | + | 0.735797i | \(0.263192\pi\) | |||||||
\(888\) | −54.5316 | −1.82996 | ||||||||
\(889\) | −13.9115 | −0.466577 | ||||||||
\(890\) | 11.0567 | 0.370622 | ||||||||
\(891\) | −4.20627 | −0.140915 | ||||||||
\(892\) | 47.6582 | 1.59571 | ||||||||
\(893\) | −15.1393 | −0.506616 | ||||||||
\(894\) | −23.0602 | −0.771249 | ||||||||
\(895\) | 4.53814 | 0.151693 | ||||||||
\(896\) | 160.570 | 5.36425 | ||||||||
\(897\) | −15.2820 | −0.510250 | ||||||||
\(898\) | 71.5263 | 2.38686 | ||||||||
\(899\) | 1.26998 | 0.0423564 | ||||||||
\(900\) | −27.9546 | −0.931819 | ||||||||
\(901\) | 3.46843 | 0.115550 | ||||||||
\(902\) | −93.0630 | −3.09866 | ||||||||
\(903\) | 29.8953 | 0.994854 | ||||||||
\(904\) | 121.463 | 4.03978 | ||||||||
\(905\) | 3.41433 | 0.113496 | ||||||||
\(906\) | 41.3592 | 1.37407 | ||||||||
\(907\) | −15.7630 | −0.523403 | −0.261701 | − | 0.965149i | \(-0.584284\pi\) | ||||
−0.261701 | + | 0.965149i | \(0.584284\pi\) | |||||||
\(908\) | −105.024 | −3.48535 | ||||||||
\(909\) | −0.0359402 | −0.00119206 | ||||||||
\(910\) | 7.80029 | 0.258577 | ||||||||
\(911\) | −5.54103 | −0.183582 | −0.0917912 | − | 0.995778i | \(-0.529259\pi\) | ||||
−0.0917912 | + | 0.995778i | \(0.529259\pi\) | |||||||
\(912\) | −23.7151 | −0.785285 | ||||||||
\(913\) | −26.8041 | −0.887085 | ||||||||
\(914\) | −18.2549 | −0.603817 | ||||||||
\(915\) | −4.11073 | −0.135896 | ||||||||
\(916\) | −85.7904 | −2.83459 | ||||||||
\(917\) | −39.3912 | −1.30081 | ||||||||
\(918\) | −2.77670 | −0.0916446 | ||||||||
\(919\) | −56.7047 | −1.87052 | −0.935258 | − | 0.353967i | \(-0.884832\pi\) | ||||
−0.935258 | + | 0.353967i | \(0.884832\pi\) | |||||||
\(920\) | −15.8073 | −0.521150 | ||||||||
\(921\) | −12.8136 | −0.422223 | ||||||||
\(922\) | 85.4281 | 2.81342 | ||||||||
\(923\) | 17.3235 | 0.570210 | ||||||||
\(924\) | −64.9436 | −2.13649 | ||||||||
\(925\) | 25.9152 | 0.852086 | ||||||||
\(926\) | −75.9946 | −2.49734 | ||||||||
\(927\) | 4.41580 | 0.145034 | ||||||||
\(928\) | −31.9825 | −1.04988 | ||||||||
\(929\) | −53.0109 | −1.73923 | −0.869616 | − | 0.493729i | \(-0.835633\pi\) | ||||
−0.869616 | + | 0.493729i | \(0.835633\pi\) | |||||||
\(930\) | −0.965532 | −0.0316610 | ||||||||
\(931\) | 0.429686 | 0.0140824 | ||||||||
\(932\) | 119.927 | 3.92835 | ||||||||
\(933\) | −30.6229 | −1.00255 | ||||||||
\(934\) | −6.55401 | −0.214454 | ||||||||
\(935\) | −1.35855 | −0.0444292 | ||||||||
\(936\) | 33.1371 | 1.08312 | ||||||||
\(937\) | 25.1532 | 0.821719 | 0.410859 | − | 0.911699i | \(-0.365229\pi\) | ||||
0.410859 | + | 0.911699i | \(0.365229\pi\) | |||||||
\(938\) | −52.3472 | −1.70920 | ||||||||
\(939\) | 11.3555 | 0.370574 | ||||||||
\(940\) | 20.2318 | 0.659888 | ||||||||
\(941\) | −7.94751 | −0.259081 | −0.129541 | − | 0.991574i | \(-0.541350\pi\) | ||||
−0.129541 | + | 0.991574i | \(0.541350\pi\) | |||||||
\(942\) | −20.9913 | −0.683932 | ||||||||
\(943\) | 37.8550 | 1.23273 | ||||||||
\(944\) | −164.372 | −5.34985 | ||||||||
\(945\) | −0.873325 | −0.0284093 | ||||||||
\(946\) | 129.131 | 4.19841 | ||||||||
\(947\) | 41.4271 | 1.34620 | 0.673099 | − | 0.739552i | \(-0.264963\pi\) | ||||
0.673099 | + | 0.739552i | \(0.264963\pi\) | |||||||
\(948\) | −5.71004 | −0.185454 | ||||||||
\(949\) | 26.3056 | 0.853917 | ||||||||
\(950\) | 18.7598 | 0.608649 | ||||||||
\(951\) | −7.81235 | −0.253333 | ||||||||
\(952\) | −27.8552 | −0.902793 | ||||||||
\(953\) | −12.4697 | −0.403934 | −0.201967 | − | 0.979392i | \(-0.564733\pi\) | ||||
−0.201967 | + | 0.979392i | \(0.564733\pi\) | |||||||
\(954\) | 9.63078 | 0.311808 | ||||||||
\(955\) | 0.766279 | 0.0247962 | ||||||||
\(956\) | −105.605 | −3.41552 | ||||||||
\(957\) | 4.96175 | 0.160391 | ||||||||
\(958\) | 48.9916 | 1.58285 | ||||||||
\(959\) | 41.1566 | 1.32902 | ||||||||
\(960\) | 13.2148 | 0.426506 | ||||||||
\(961\) | −29.8409 | −0.962610 | ||||||||
\(962\) | −47.2798 | −1.52436 | ||||||||
\(963\) | −10.2768 | −0.331165 | ||||||||
\(964\) | 100.637 | 3.24131 | ||||||||
\(965\) | 7.30511 | 0.235160 | ||||||||
\(966\) | 35.6697 | 1.14766 | ||||||||
\(967\) | −24.6704 | −0.793346 | −0.396673 | − | 0.917960i | \(-0.629835\pi\) | ||||
−0.396673 | + | 0.917960i | \(0.629835\pi\) | |||||||
\(968\) | −68.9464 | −2.21602 | ||||||||
\(969\) | 1.38003 | 0.0443328 | ||||||||
\(970\) | 6.19870 | 0.199028 | ||||||||
\(971\) | −34.5670 | −1.10931 | −0.554655 | − | 0.832081i | \(-0.687150\pi\) | ||||
−0.554655 | + | 0.832081i | \(0.687150\pi\) | |||||||
\(972\) | −5.71004 | −0.183150 | ||||||||
\(973\) | 34.4547 | 1.10457 | ||||||||
\(974\) | 15.8784 | 0.508776 | ||||||||
\(975\) | −15.7478 | −0.504333 | ||||||||
\(976\) | −218.715 | −7.00091 | ||||||||
\(977\) | −34.2804 | −1.09673 | −0.548364 | − | 0.836240i | \(-0.684749\pi\) | ||||
−0.548364 | + | 0.836240i | \(0.684749\pi\) | |||||||
\(978\) | −17.4698 | −0.558624 | ||||||||
\(979\) | −51.8584 | −1.65740 | ||||||||
\(980\) | −0.574223 | −0.0183429 | ||||||||
\(981\) | 9.01915 | 0.287959 | ||||||||
\(982\) | −28.8630 | −0.921055 | ||||||||
\(983\) | −61.0530 | −1.94729 | −0.973643 | − | 0.228076i | \(-0.926757\pi\) | ||||
−0.973643 | + | 0.228076i | \(0.926757\pi\) | |||||||
\(984\) | −82.0840 | −2.61674 | ||||||||
\(985\) | −4.80610 | −0.153135 | ||||||||
\(986\) | 3.27541 | 0.104310 | ||||||||
\(987\) | −29.6631 | −0.944188 | ||||||||
\(988\) | −25.3474 | −0.806407 | ||||||||
\(989\) | −52.5263 | −1.67024 | ||||||||
\(990\) | −3.77227 | −0.119891 | ||||||||
\(991\) | −56.8013 | −1.80435 | −0.902177 | − | 0.431367i | \(-0.858031\pi\) | ||||
−0.902177 | + | 0.431367i | \(0.858031\pi\) | |||||||
\(992\) | −29.1902 | −0.926789 | ||||||||
\(993\) | −32.6427 | −1.03589 | ||||||||
\(994\) | −40.4350 | −1.28252 | ||||||||
\(995\) | 0.652737 | 0.0206932 | ||||||||
\(996\) | −36.3867 | −1.15296 | ||||||||
\(997\) | −36.5206 | −1.15662 | −0.578310 | − | 0.815817i | \(-0.696288\pi\) | ||||
−0.578310 | + | 0.815817i | \(0.696288\pi\) | |||||||
\(998\) | −55.9767 | −1.77191 | ||||||||
\(999\) | 5.29347 | 0.167478 |
(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 | 4029.2.a.l.1.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4029.2.a.l.1.1 | ✓ | 32 | 1.1 | even | 1 | trivial |