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: | \(1\) |
Dimension: | \(217\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65451 | −1.87702 | −0.938510 | − | 0.345253i | \(-0.887793\pi\) | ||||
−0.938510 | + | 0.345253i | \(0.887793\pi\) | |||||||
\(3\) | −2.99510 | −1.72922 | −0.864612 | − | 0.502440i | \(-0.832436\pi\) | ||||
−0.864612 | + | 0.502440i | \(0.832436\pi\) | |||||||
\(4\) | 5.04641 | 2.52320 | ||||||||
\(5\) | −2.08040 | −0.930382 | −0.465191 | − | 0.885210i | \(-0.654014\pi\) | ||||
−0.465191 | + | 0.885210i | \(0.654014\pi\) | |||||||
\(6\) | 7.95052 | 3.24579 | ||||||||
\(7\) | −1.11556 | −0.421644 | −0.210822 | − | 0.977524i | \(-0.567614\pi\) | ||||
−0.210822 | + | 0.977524i | \(0.567614\pi\) | |||||||
\(8\) | −8.08670 | −2.85908 | ||||||||
\(9\) | 5.97065 | 1.99022 | ||||||||
\(10\) | 5.52243 | 1.74635 | ||||||||
\(11\) | 3.38425 | 1.02039 | 0.510195 | − | 0.860059i | \(-0.329573\pi\) | ||||
0.510195 | + | 0.860059i | \(0.329573\pi\) | |||||||
\(12\) | −15.1145 | −4.36318 | ||||||||
\(13\) | −3.23622 | −0.897567 | −0.448784 | − | 0.893640i | \(-0.648143\pi\) | ||||
−0.448784 | + | 0.893640i | \(0.648143\pi\) | |||||||
\(14\) | 2.96127 | 0.791434 | ||||||||
\(15\) | 6.23101 | 1.60884 | ||||||||
\(16\) | 11.3734 | 2.84335 | ||||||||
\(17\) | 4.29870 | 1.04259 | 0.521293 | − | 0.853378i | \(-0.325450\pi\) | ||||
0.521293 | + | 0.853378i | \(0.325450\pi\) | |||||||
\(18\) | −15.8491 | −3.73567 | ||||||||
\(19\) | 0.715567 | 0.164162 | 0.0820811 | − | 0.996626i | \(-0.473843\pi\) | ||||
0.0820811 | + | 0.996626i | \(0.473843\pi\) | |||||||
\(20\) | −10.4985 | −2.34754 | ||||||||
\(21\) | 3.34123 | 0.729117 | ||||||||
\(22\) | −8.98352 | −1.91529 | ||||||||
\(23\) | 0.981717 | 0.204702 | 0.102351 | − | 0.994748i | \(-0.467363\pi\) | ||||
0.102351 | + | 0.994748i | \(0.467363\pi\) | |||||||
\(24\) | 24.2205 | 4.94399 | ||||||||
\(25\) | −0.671946 | −0.134389 | ||||||||
\(26\) | 8.59058 | 1.68475 | ||||||||
\(27\) | −8.89739 | −1.71230 | ||||||||
\(28\) | −5.62959 | −1.06389 | ||||||||
\(29\) | −2.22960 | −0.414027 | −0.207014 | − | 0.978338i | \(-0.566374\pi\) | ||||
−0.207014 | + | 0.978338i | \(0.566374\pi\) | |||||||
\(30\) | −16.5402 | −3.01982 | ||||||||
\(31\) | 0.355075 | 0.0637734 | 0.0318867 | − | 0.999491i | \(-0.489848\pi\) | ||||
0.0318867 | + | 0.999491i | \(0.489848\pi\) | |||||||
\(32\) | −14.0173 | −2.47794 | ||||||||
\(33\) | −10.1362 | −1.76448 | ||||||||
\(34\) | −11.4109 | −1.95696 | ||||||||
\(35\) | 2.32082 | 0.392290 | ||||||||
\(36\) | 30.1303 | 5.02172 | ||||||||
\(37\) | 11.1937 | 1.84024 | 0.920118 | − | 0.391641i | \(-0.128092\pi\) | ||||
0.920118 | + | 0.391641i | \(0.128092\pi\) | |||||||
\(38\) | −1.89948 | −0.308136 | ||||||||
\(39\) | 9.69283 | 1.55209 | ||||||||
\(40\) | 16.8236 | 2.66004 | ||||||||
\(41\) | −1.13870 | −0.177834 | −0.0889172 | − | 0.996039i | \(-0.528341\pi\) | ||||
−0.0889172 | + | 0.996039i | \(0.528341\pi\) | |||||||
\(42\) | −8.86932 | −1.36857 | ||||||||
\(43\) | −6.13987 | −0.936321 | −0.468160 | − | 0.883643i | \(-0.655083\pi\) | ||||
−0.468160 | + | 0.883643i | \(0.655083\pi\) | |||||||
\(44\) | 17.0783 | 2.57465 | ||||||||
\(45\) | −12.4213 | −1.85166 | ||||||||
\(46\) | −2.60597 | −0.384230 | ||||||||
\(47\) | −2.54799 | −0.371662 | −0.185831 | − | 0.982582i | \(-0.559498\pi\) | ||||
−0.185831 | + | 0.982582i | \(0.559498\pi\) | |||||||
\(48\) | −34.0645 | −4.91679 | ||||||||
\(49\) | −5.75552 | −0.822216 | ||||||||
\(50\) | 1.78369 | 0.252251 | ||||||||
\(51\) | −12.8750 | −1.80287 | ||||||||
\(52\) | −16.3313 | −2.26474 | ||||||||
\(53\) | −12.6824 | −1.74206 | −0.871028 | − | 0.491233i | \(-0.836546\pi\) | ||||
−0.871028 | + | 0.491233i | \(0.836546\pi\) | |||||||
\(54\) | 23.6182 | 3.21403 | ||||||||
\(55\) | −7.04059 | −0.949353 | ||||||||
\(56\) | 9.02124 | 1.20551 | ||||||||
\(57\) | −2.14320 | −0.283873 | ||||||||
\(58\) | 5.91850 | 0.777137 | ||||||||
\(59\) | 12.1366 | 1.58005 | 0.790027 | − | 0.613072i | \(-0.210067\pi\) | ||||
0.790027 | + | 0.613072i | \(0.210067\pi\) | |||||||
\(60\) | 31.4442 | 4.05943 | ||||||||
\(61\) | 7.65047 | 0.979543 | 0.489771 | − | 0.871851i | \(-0.337080\pi\) | ||||
0.489771 | + | 0.871851i | \(0.337080\pi\) | |||||||
\(62\) | −0.942549 | −0.119704 | ||||||||
\(63\) | −6.66064 | −0.839162 | ||||||||
\(64\) | 14.4624 | 1.80779 | ||||||||
\(65\) | 6.73263 | 0.835080 | ||||||||
\(66\) | 26.9066 | 3.31197 | ||||||||
\(67\) | −9.28979 | −1.13493 | −0.567464 | − | 0.823398i | \(-0.692076\pi\) | ||||
−0.567464 | + | 0.823398i | \(0.692076\pi\) | |||||||
\(68\) | 21.6930 | 2.63066 | ||||||||
\(69\) | −2.94034 | −0.353976 | ||||||||
\(70\) | −6.16063 | −0.736336 | ||||||||
\(71\) | −3.24012 | −0.384531 | −0.192266 | − | 0.981343i | \(-0.561584\pi\) | ||||
−0.192266 | + | 0.981343i | \(0.561584\pi\) | |||||||
\(72\) | −48.2828 | −5.69019 | ||||||||
\(73\) | −4.55854 | −0.533537 | −0.266769 | − | 0.963761i | \(-0.585956\pi\) | ||||
−0.266769 | + | 0.963761i | \(0.585956\pi\) | |||||||
\(74\) | −29.7138 | −3.45416 | ||||||||
\(75\) | 2.01255 | 0.232389 | ||||||||
\(76\) | 3.61104 | 0.414215 | ||||||||
\(77\) | −3.77535 | −0.430241 | ||||||||
\(78\) | −25.7297 | −2.91331 | ||||||||
\(79\) | −2.45178 | −0.275847 | −0.137924 | − | 0.990443i | \(-0.544043\pi\) | ||||
−0.137924 | + | 0.990443i | \(0.544043\pi\) | |||||||
\(80\) | −23.6612 | −2.64540 | ||||||||
\(81\) | 8.73667 | 0.970742 | ||||||||
\(82\) | 3.02268 | 0.333799 | ||||||||
\(83\) | 7.49212 | 0.822367 | 0.411184 | − | 0.911553i | \(-0.365115\pi\) | ||||
0.411184 | + | 0.911553i | \(0.365115\pi\) | |||||||
\(84\) | 16.8612 | 1.83971 | ||||||||
\(85\) | −8.94300 | −0.970004 | ||||||||
\(86\) | 16.2983 | 1.75749 | ||||||||
\(87\) | 6.67790 | 0.715946 | ||||||||
\(88\) | −27.3675 | −2.91738 | ||||||||
\(89\) | 11.6238 | 1.23212 | 0.616059 | − | 0.787700i | \(-0.288728\pi\) | ||||
0.616059 | + | 0.787700i | \(0.288728\pi\) | |||||||
\(90\) | 32.9725 | 3.47560 | ||||||||
\(91\) | 3.61022 | 0.378454 | ||||||||
\(92\) | 4.95414 | 0.516505 | ||||||||
\(93\) | −1.06349 | −0.110278 | ||||||||
\(94\) | 6.76364 | 0.697617 | ||||||||
\(95\) | −1.48866 | −0.152734 | ||||||||
\(96\) | 41.9834 | 4.28491 | ||||||||
\(97\) | −10.6560 | −1.08196 | −0.540979 | − | 0.841036i | \(-0.681946\pi\) | ||||
−0.540979 | + | 0.841036i | \(0.681946\pi\) | |||||||
\(98\) | 15.2781 | 1.54332 | ||||||||
\(99\) | 20.2062 | 2.03080 | ||||||||
\(100\) | −3.39091 | −0.339091 | ||||||||
\(101\) | 4.79542 | 0.477162 | 0.238581 | − | 0.971123i | \(-0.423318\pi\) | ||||
0.238581 | + | 0.971123i | \(0.423318\pi\) | |||||||
\(102\) | 34.1769 | 3.38402 | ||||||||
\(103\) | −15.0541 | −1.48332 | −0.741662 | − | 0.670774i | \(-0.765962\pi\) | ||||
−0.741662 | + | 0.670774i | \(0.765962\pi\) | |||||||
\(104\) | 26.1704 | 2.56622 | ||||||||
\(105\) | −6.95109 | −0.678357 | ||||||||
\(106\) | 33.6654 | 3.26987 | ||||||||
\(107\) | 4.83698 | 0.467609 | 0.233804 | − | 0.972284i | \(-0.424882\pi\) | ||||
0.233804 | + | 0.972284i | \(0.424882\pi\) | |||||||
\(108\) | −44.8998 | −4.32049 | ||||||||
\(109\) | −10.7199 | −1.02678 | −0.513390 | − | 0.858156i | \(-0.671610\pi\) | ||||
−0.513390 | + | 0.858156i | \(0.671610\pi\) | |||||||
\(110\) | 18.6893 | 1.78195 | ||||||||
\(111\) | −33.5264 | −3.18218 | ||||||||
\(112\) | −12.6878 | −1.19888 | ||||||||
\(113\) | −7.17112 | −0.674602 | −0.337301 | − | 0.941397i | \(-0.609514\pi\) | ||||
−0.337301 | + | 0.941397i | \(0.609514\pi\) | |||||||
\(114\) | 5.68913 | 0.532836 | ||||||||
\(115\) | −2.04236 | −0.190451 | ||||||||
\(116\) | −11.2515 | −1.04467 | ||||||||
\(117\) | −19.3223 | −1.78635 | ||||||||
\(118\) | −32.2167 | −2.96579 | ||||||||
\(119\) | −4.79547 | −0.439600 | ||||||||
\(120\) | −50.3883 | −4.59980 | ||||||||
\(121\) | 0.453170 | 0.0411973 | ||||||||
\(122\) | −20.3082 | −1.83862 | ||||||||
\(123\) | 3.41051 | 0.307516 | ||||||||
\(124\) | 1.79185 | 0.160913 | ||||||||
\(125\) | 11.7999 | 1.05542 | ||||||||
\(126\) | 17.6807 | 1.57512 | ||||||||
\(127\) | 17.7855 | 1.57821 | 0.789106 | − | 0.614258i | \(-0.210544\pi\) | ||||
0.789106 | + | 0.614258i | \(0.210544\pi\) | |||||||
\(128\) | −10.3557 | −0.915325 | ||||||||
\(129\) | 18.3895 | 1.61911 | ||||||||
\(130\) | −17.8718 | −1.56746 | ||||||||
\(131\) | −3.25337 | −0.284248 | −0.142124 | − | 0.989849i | \(-0.545393\pi\) | ||||
−0.142124 | + | 0.989849i | \(0.545393\pi\) | |||||||
\(132\) | −51.1513 | −4.45215 | ||||||||
\(133\) | −0.798261 | −0.0692180 | ||||||||
\(134\) | 24.6598 | 2.13028 | ||||||||
\(135\) | 18.5101 | 1.59310 | ||||||||
\(136\) | −34.7623 | −2.98084 | ||||||||
\(137\) | 10.0179 | 0.855884 | 0.427942 | − | 0.903806i | \(-0.359239\pi\) | ||||
0.427942 | + | 0.903806i | \(0.359239\pi\) | |||||||
\(138\) | 7.80516 | 0.664420 | ||||||||
\(139\) | −12.9376 | −1.09735 | −0.548676 | − | 0.836035i | \(-0.684868\pi\) | ||||
−0.548676 | + | 0.836035i | \(0.684868\pi\) | |||||||
\(140\) | 11.7118 | 0.989827 | ||||||||
\(141\) | 7.63148 | 0.642687 | ||||||||
\(142\) | 8.60092 | 0.721773 | ||||||||
\(143\) | −10.9522 | −0.915869 | ||||||||
\(144\) | 67.9065 | 5.65888 | ||||||||
\(145\) | 4.63846 | 0.385203 | ||||||||
\(146\) | 12.1007 | 1.00146 | ||||||||
\(147\) | 17.2384 | 1.42180 | ||||||||
\(148\) | 56.4880 | 4.64329 | ||||||||
\(149\) | 18.6786 | 1.53021 | 0.765105 | − | 0.643906i | \(-0.222687\pi\) | ||||
0.765105 | + | 0.643906i | \(0.222687\pi\) | |||||||
\(150\) | −5.34232 | −0.436199 | ||||||||
\(151\) | −14.4072 | −1.17244 | −0.586221 | − | 0.810151i | \(-0.699385\pi\) | ||||
−0.586221 | + | 0.810151i | \(0.699385\pi\) | |||||||
\(152\) | −5.78657 | −0.469353 | ||||||||
\(153\) | 25.6660 | 2.07497 | ||||||||
\(154\) | 10.0217 | 0.807572 | ||||||||
\(155\) | −0.738697 | −0.0593336 | ||||||||
\(156\) | 48.9139 | 3.91625 | ||||||||
\(157\) | 16.7766 | 1.33892 | 0.669458 | − | 0.742850i | \(-0.266526\pi\) | ||||
0.669458 | + | 0.742850i | \(0.266526\pi\) | |||||||
\(158\) | 6.50828 | 0.517771 | ||||||||
\(159\) | 37.9850 | 3.01241 | ||||||||
\(160\) | 29.1617 | 2.30543 | ||||||||
\(161\) | −1.09517 | −0.0863114 | ||||||||
\(162\) | −23.1916 | −1.82210 | ||||||||
\(163\) | 4.31063 | 0.337635 | 0.168817 | − | 0.985647i | \(-0.446005\pi\) | ||||
0.168817 | + | 0.985647i | \(0.446005\pi\) | |||||||
\(164\) | −5.74632 | −0.448712 | ||||||||
\(165\) | 21.0873 | 1.64164 | ||||||||
\(166\) | −19.8879 | −1.54360 | ||||||||
\(167\) | −14.3337 | −1.10917 | −0.554587 | − | 0.832126i | \(-0.687124\pi\) | ||||
−0.554587 | + | 0.832126i | \(0.687124\pi\) | |||||||
\(168\) | −27.0196 | −2.08460 | ||||||||
\(169\) | −2.52685 | −0.194373 | ||||||||
\(170\) | 23.7392 | 1.82072 | ||||||||
\(171\) | 4.27239 | 0.326718 | ||||||||
\(172\) | −30.9843 | −2.36253 | ||||||||
\(173\) | −7.50239 | −0.570396 | −0.285198 | − | 0.958469i | \(-0.592059\pi\) | ||||
−0.285198 | + | 0.958469i | \(0.592059\pi\) | |||||||
\(174\) | −17.7265 | −1.34384 | ||||||||
\(175\) | 0.749600 | 0.0566644 | ||||||||
\(176\) | 38.4905 | 2.90133 | ||||||||
\(177\) | −36.3504 | −2.73227 | ||||||||
\(178\) | −30.8554 | −2.31271 | ||||||||
\(179\) | −2.38194 | −0.178035 | −0.0890173 | − | 0.996030i | \(-0.528373\pi\) | ||||
−0.0890173 | + | 0.996030i | \(0.528373\pi\) | |||||||
\(180\) | −62.6830 | −4.67211 | ||||||||
\(181\) | −2.47823 | −0.184205 | −0.0921026 | − | 0.995750i | \(-0.529359\pi\) | ||||
−0.0921026 | + | 0.995750i | \(0.529359\pi\) | |||||||
\(182\) | −9.58335 | −0.710365 | ||||||||
\(183\) | −22.9140 | −1.69385 | ||||||||
\(184\) | −7.93886 | −0.585260 | ||||||||
\(185\) | −23.2874 | −1.71212 | ||||||||
\(186\) | 2.82303 | 0.206995 | ||||||||
\(187\) | 14.5479 | 1.06385 | ||||||||
\(188\) | −12.8582 | −0.937778 | ||||||||
\(189\) | 9.92562 | 0.721982 | ||||||||
\(190\) | 3.95167 | 0.286684 | ||||||||
\(191\) | −1.92863 | −0.139551 | −0.0697754 | − | 0.997563i | \(-0.522228\pi\) | ||||
−0.0697754 | + | 0.997563i | \(0.522228\pi\) | |||||||
\(192\) | −43.3162 | −3.12608 | ||||||||
\(193\) | 10.2727 | 0.739447 | 0.369723 | − | 0.929142i | \(-0.379452\pi\) | ||||
0.369723 | + | 0.929142i | \(0.379452\pi\) | |||||||
\(194\) | 28.2866 | 2.03086 | ||||||||
\(195\) | −20.1649 | −1.44404 | ||||||||
\(196\) | −29.0447 | −2.07462 | ||||||||
\(197\) | 22.7684 | 1.62218 | 0.811090 | − | 0.584922i | \(-0.198875\pi\) | ||||
0.811090 | + | 0.584922i | \(0.198875\pi\) | |||||||
\(198\) | −53.6374 | −3.81185 | ||||||||
\(199\) | 20.5648 | 1.45780 | 0.728900 | − | 0.684621i | \(-0.240032\pi\) | ||||
0.728900 | + | 0.684621i | \(0.240032\pi\) | |||||||
\(200\) | 5.43383 | 0.384230 | ||||||||
\(201\) | 27.8239 | 1.96255 | ||||||||
\(202\) | −12.7295 | −0.895643 | ||||||||
\(203\) | 2.48727 | 0.174572 | ||||||||
\(204\) | −64.9727 | −4.54900 | ||||||||
\(205\) | 2.36894 | 0.165454 | ||||||||
\(206\) | 39.9612 | 2.78423 | ||||||||
\(207\) | 5.86149 | 0.407401 | ||||||||
\(208\) | −36.8069 | −2.55210 | ||||||||
\(209\) | 2.42166 | 0.167510 | ||||||||
\(210\) | 18.4517 | 1.27329 | ||||||||
\(211\) | −11.0025 | −0.757446 | −0.378723 | − | 0.925510i | \(-0.623637\pi\) | ||||
−0.378723 | + | 0.925510i | \(0.623637\pi\) | |||||||
\(212\) | −64.0003 | −4.39556 | ||||||||
\(213\) | 9.70449 | 0.664941 | ||||||||
\(214\) | −12.8398 | −0.877711 | ||||||||
\(215\) | 12.7734 | 0.871136 | ||||||||
\(216\) | 71.9506 | 4.89562 | ||||||||
\(217\) | −0.396109 | −0.0268897 | ||||||||
\(218\) | 28.4560 | 1.92728 | ||||||||
\(219\) | 13.6533 | 0.922605 | ||||||||
\(220\) | −35.5297 | −2.39541 | ||||||||
\(221\) | −13.9115 | −0.935792 | ||||||||
\(222\) | 88.9959 | 5.97302 | ||||||||
\(223\) | 22.3094 | 1.49395 | 0.746973 | − | 0.664854i | \(-0.231506\pi\) | ||||
0.746973 | + | 0.664854i | \(0.231506\pi\) | |||||||
\(224\) | 15.6373 | 1.04481 | ||||||||
\(225\) | −4.01195 | −0.267464 | ||||||||
\(226\) | 19.0358 | 1.26624 | ||||||||
\(227\) | −5.76706 | −0.382773 | −0.191387 | − | 0.981515i | \(-0.561298\pi\) | ||||
−0.191387 | + | 0.981515i | \(0.561298\pi\) | |||||||
\(228\) | −10.8154 | −0.716270 | ||||||||
\(229\) | −10.0640 | −0.665048 | −0.332524 | − | 0.943095i | \(-0.607900\pi\) | ||||
−0.332524 | + | 0.943095i | \(0.607900\pi\) | |||||||
\(230\) | 5.42146 | 0.357481 | ||||||||
\(231\) | 11.3076 | 0.743984 | ||||||||
\(232\) | 18.0301 | 1.18374 | ||||||||
\(233\) | −8.36503 | −0.548011 | −0.274006 | − | 0.961728i | \(-0.588349\pi\) | ||||
−0.274006 | + | 0.961728i | \(0.588349\pi\) | |||||||
\(234\) | 51.2913 | 3.35302 | ||||||||
\(235\) | 5.30082 | 0.345788 | ||||||||
\(236\) | 61.2463 | 3.98679 | ||||||||
\(237\) | 7.34335 | 0.477002 | ||||||||
\(238\) | 12.7296 | 0.825138 | ||||||||
\(239\) | 11.2520 | 0.727832 | 0.363916 | − | 0.931432i | \(-0.381440\pi\) | ||||
0.363916 | + | 0.931432i | \(0.381440\pi\) | |||||||
\(240\) | 70.8677 | 4.57449 | ||||||||
\(241\) | −7.91275 | −0.509705 | −0.254853 | − | 0.966980i | \(-0.582027\pi\) | ||||
−0.254853 | + | 0.966980i | \(0.582027\pi\) | |||||||
\(242\) | −1.20294 | −0.0773281 | ||||||||
\(243\) | 0.524932 | 0.0336744 | ||||||||
\(244\) | 38.6074 | 2.47158 | ||||||||
\(245\) | 11.9738 | 0.764975 | ||||||||
\(246\) | −9.05323 | −0.577213 | ||||||||
\(247\) | −2.31573 | −0.147347 | ||||||||
\(248\) | −2.87139 | −0.182333 | ||||||||
\(249\) | −22.4397 | −1.42206 | ||||||||
\(250\) | −31.3229 | −1.98104 | ||||||||
\(251\) | 5.57587 | 0.351946 | 0.175973 | − | 0.984395i | \(-0.443693\pi\) | ||||
0.175973 | + | 0.984395i | \(0.443693\pi\) | |||||||
\(252\) | −33.6123 | −2.11738 | ||||||||
\(253\) | 3.32238 | 0.208876 | ||||||||
\(254\) | −47.2118 | −2.96233 | ||||||||
\(255\) | 26.7852 | 1.67735 | ||||||||
\(256\) | −1.43539 | −0.0897121 | ||||||||
\(257\) | 25.4249 | 1.58596 | 0.792979 | − | 0.609248i | \(-0.208529\pi\) | ||||
0.792979 | + | 0.609248i | \(0.208529\pi\) | |||||||
\(258\) | −48.8151 | −3.03910 | ||||||||
\(259\) | −12.4873 | −0.775924 | ||||||||
\(260\) | 33.9756 | 2.10708 | ||||||||
\(261\) | −13.3122 | −0.824003 | ||||||||
\(262\) | 8.63608 | 0.533539 | ||||||||
\(263\) | 15.9468 | 0.983324 | 0.491662 | − | 0.870786i | \(-0.336390\pi\) | ||||
0.491662 | + | 0.870786i | \(0.336390\pi\) | |||||||
\(264\) | 81.9684 | 5.04480 | ||||||||
\(265\) | 26.3844 | 1.62078 | ||||||||
\(266\) | 2.11899 | 0.129924 | ||||||||
\(267\) | −34.8144 | −2.13061 | ||||||||
\(268\) | −46.8801 | −2.86366 | ||||||||
\(269\) | 14.3454 | 0.874657 | 0.437329 | − | 0.899302i | \(-0.355925\pi\) | ||||
0.437329 | + | 0.899302i | \(0.355925\pi\) | |||||||
\(270\) | −49.1352 | −2.99027 | ||||||||
\(271\) | 17.8005 | 1.08130 | 0.540651 | − | 0.841247i | \(-0.318178\pi\) | ||||
0.540651 | + | 0.841247i | \(0.318178\pi\) | |||||||
\(272\) | 48.8908 | 2.96444 | ||||||||
\(273\) | −10.8130 | −0.654431 | ||||||||
\(274\) | −26.5925 | −1.60651 | ||||||||
\(275\) | −2.27404 | −0.137130 | ||||||||
\(276\) | −14.8382 | −0.893153 | ||||||||
\(277\) | 1.67238 | 0.100484 | 0.0502419 | − | 0.998737i | \(-0.484001\pi\) | ||||
0.0502419 | + | 0.998737i | \(0.484001\pi\) | |||||||
\(278\) | 34.3429 | 2.05975 | ||||||||
\(279\) | 2.12003 | 0.126923 | ||||||||
\(280\) | −18.7678 | −1.12159 | ||||||||
\(281\) | −10.7527 | −0.641453 | −0.320727 | − | 0.947172i | \(-0.603927\pi\) | ||||
−0.320727 | + | 0.947172i | \(0.603927\pi\) | |||||||
\(282\) | −20.2578 | −1.20634 | ||||||||
\(283\) | 24.5654 | 1.46026 | 0.730130 | − | 0.683308i | \(-0.239459\pi\) | ||||
0.730130 | + | 0.683308i | \(0.239459\pi\) | |||||||
\(284\) | −16.3510 | −0.970251 | ||||||||
\(285\) | 4.45870 | 0.264111 | ||||||||
\(286\) | 29.0727 | 1.71910 | ||||||||
\(287\) | 1.27029 | 0.0749828 | ||||||||
\(288\) | −83.6926 | −4.93164 | ||||||||
\(289\) | 1.47878 | 0.0869873 | ||||||||
\(290\) | −12.3128 | −0.723034 | ||||||||
\(291\) | 31.9160 | 1.87095 | ||||||||
\(292\) | −23.0043 | −1.34622 | ||||||||
\(293\) | −3.89252 | −0.227403 | −0.113702 | − | 0.993515i | \(-0.536271\pi\) | ||||
−0.113702 | + | 0.993515i | \(0.536271\pi\) | |||||||
\(294\) | −45.7594 | −2.66874 | ||||||||
\(295\) | −25.2490 | −1.47005 | ||||||||
\(296\) | −90.5203 | −5.26139 | ||||||||
\(297\) | −30.1110 | −1.74722 | ||||||||
\(298\) | −49.5824 | −2.87223 | ||||||||
\(299\) | −3.17706 | −0.183734 | ||||||||
\(300\) | 10.1561 | 0.586365 | ||||||||
\(301\) | 6.84942 | 0.394794 | ||||||||
\(302\) | 38.2440 | 2.20070 | ||||||||
\(303\) | −14.3628 | −0.825120 | ||||||||
\(304\) | 8.13842 | 0.466770 | ||||||||
\(305\) | −15.9160 | −0.911349 | ||||||||
\(306\) | −68.1305 | −3.89476 | ||||||||
\(307\) | 6.84135 | 0.390457 | 0.195228 | − | 0.980758i | \(-0.437455\pi\) | ||||
0.195228 | + | 0.980758i | \(0.437455\pi\) | |||||||
\(308\) | −19.0520 | −1.08559 | ||||||||
\(309\) | 45.0886 | 2.56500 | ||||||||
\(310\) | 1.96088 | 0.111370 | ||||||||
\(311\) | 26.9202 | 1.52650 | 0.763252 | − | 0.646101i | \(-0.223602\pi\) | ||||
0.763252 | + | 0.646101i | \(0.223602\pi\) | |||||||
\(312\) | −78.3830 | −4.43756 | ||||||||
\(313\) | −9.98612 | −0.564449 | −0.282224 | − | 0.959348i | \(-0.591072\pi\) | ||||
−0.282224 | + | 0.959348i | \(0.591072\pi\) | |||||||
\(314\) | −44.5335 | −2.51317 | ||||||||
\(315\) | 13.8568 | 0.780741 | ||||||||
\(316\) | −12.3727 | −0.696019 | ||||||||
\(317\) | 17.0621 | 0.958302 | 0.479151 | − | 0.877732i | \(-0.340945\pi\) | ||||
0.479151 | + | 0.877732i | \(0.340945\pi\) | |||||||
\(318\) | −100.831 | −5.65434 | ||||||||
\(319\) | −7.54555 | −0.422469 | ||||||||
\(320\) | −30.0874 | −1.68194 | ||||||||
\(321\) | −14.4873 | −0.808600 | ||||||||
\(322\) | 2.90713 | 0.162008 | ||||||||
\(323\) | 3.07600 | 0.171153 | ||||||||
\(324\) | 44.0888 | 2.44938 | ||||||||
\(325\) | 2.17457 | 0.120623 | ||||||||
\(326\) | −11.4426 | −0.633747 | ||||||||
\(327\) | 32.1072 | 1.77553 | ||||||||
\(328\) | 9.20830 | 0.508443 | ||||||||
\(329\) | 2.84244 | 0.156709 | ||||||||
\(330\) | −55.9764 | −3.08140 | ||||||||
\(331\) | 12.4753 | 0.685707 | 0.342853 | − | 0.939389i | \(-0.388607\pi\) | ||||
0.342853 | + | 0.939389i | \(0.388607\pi\) | |||||||
\(332\) | 37.8083 | 2.07500 | ||||||||
\(333\) | 66.8337 | 3.66247 | ||||||||
\(334\) | 38.0488 | 2.08194 | ||||||||
\(335\) | 19.3265 | 1.05592 | ||||||||
\(336\) | 38.0012 | 2.07313 | ||||||||
\(337\) | −4.17402 | −0.227374 | −0.113687 | − | 0.993517i | \(-0.536266\pi\) | ||||
−0.113687 | + | 0.993517i | \(0.536266\pi\) | |||||||
\(338\) | 6.70755 | 0.364843 | ||||||||
\(339\) | 21.4782 | 1.16654 | ||||||||
\(340\) | −45.1300 | −2.44752 | ||||||||
\(341\) | 1.20166 | 0.0650738 | ||||||||
\(342\) | −11.3411 | −0.613256 | ||||||||
\(343\) | 14.2296 | 0.768326 | ||||||||
\(344\) | 49.6513 | 2.67702 | ||||||||
\(345\) | 6.11709 | 0.329333 | ||||||||
\(346\) | 19.9152 | 1.07065 | ||||||||
\(347\) | −1.54513 | −0.0829468 | −0.0414734 | − | 0.999140i | \(-0.513205\pi\) | ||||
−0.0414734 | + | 0.999140i | \(0.513205\pi\) | |||||||
\(348\) | 33.6994 | 1.80648 | ||||||||
\(349\) | 15.9650 | 0.854589 | 0.427295 | − | 0.904112i | \(-0.359467\pi\) | ||||
0.427295 | + | 0.904112i | \(0.359467\pi\) | |||||||
\(350\) | −1.98982 | −0.106360 | ||||||||
\(351\) | 28.7940 | 1.53691 | ||||||||
\(352\) | −47.4383 | −2.52847 | ||||||||
\(353\) | −20.0161 | −1.06535 | −0.532675 | − | 0.846320i | \(-0.678813\pi\) | ||||
−0.532675 | + | 0.846320i | \(0.678813\pi\) | |||||||
\(354\) | 96.4925 | 5.12852 | ||||||||
\(355\) | 6.74074 | 0.357761 | ||||||||
\(356\) | 58.6583 | 3.10888 | ||||||||
\(357\) | 14.3629 | 0.760167 | ||||||||
\(358\) | 6.32288 | 0.334174 | ||||||||
\(359\) | 3.06598 | 0.161816 | 0.0809080 | − | 0.996722i | \(-0.474218\pi\) | ||||
0.0809080 | + | 0.996722i | \(0.474218\pi\) | |||||||
\(360\) | 100.447 | 5.29405 | ||||||||
\(361\) | −18.4880 | −0.973051 | ||||||||
\(362\) | 6.57847 | 0.345757 | ||||||||
\(363\) | −1.35729 | −0.0712394 | ||||||||
\(364\) | 18.2186 | 0.954915 | ||||||||
\(365\) | 9.48358 | 0.496393 | ||||||||
\(366\) | 60.8253 | 3.17939 | ||||||||
\(367\) | 19.9579 | 1.04179 | 0.520897 | − | 0.853620i | \(-0.325598\pi\) | ||||
0.520897 | + | 0.853620i | \(0.325598\pi\) | |||||||
\(368\) | 11.1655 | 0.582040 | ||||||||
\(369\) | −6.79875 | −0.353929 | ||||||||
\(370\) | 61.8165 | 3.21369 | ||||||||
\(371\) | 14.1480 | 0.734527 | ||||||||
\(372\) | −5.36679 | −0.278255 | ||||||||
\(373\) | −31.2790 | −1.61956 | −0.809781 | − | 0.586732i | \(-0.800414\pi\) | ||||
−0.809781 | + | 0.586732i | \(0.800414\pi\) | |||||||
\(374\) | −38.6174 | −1.99686 | ||||||||
\(375\) | −35.3419 | −1.82505 | ||||||||
\(376\) | 20.6048 | 1.06261 | ||||||||
\(377\) | 7.21550 | 0.371617 | ||||||||
\(378\) | −26.3476 | −1.35518 | ||||||||
\(379\) | 21.2304 | 1.09053 | 0.545267 | − | 0.838262i | \(-0.316428\pi\) | ||||
0.545267 | + | 0.838262i | \(0.316428\pi\) | |||||||
\(380\) | −7.51240 | −0.385378 | ||||||||
\(381\) | −53.2695 | −2.72908 | ||||||||
\(382\) | 5.11956 | 0.261939 | ||||||||
\(383\) | −7.97632 | −0.407571 | −0.203785 | − | 0.979016i | \(-0.565324\pi\) | ||||
−0.203785 | + | 0.979016i | \(0.565324\pi\) | |||||||
\(384\) | 31.0164 | 1.58280 | ||||||||
\(385\) | 7.85424 | 0.400289 | ||||||||
\(386\) | −27.2690 | −1.38796 | ||||||||
\(387\) | −36.6590 | −1.86348 | ||||||||
\(388\) | −53.7747 | −2.73000 | ||||||||
\(389\) | −13.0994 | −0.664168 | −0.332084 | − | 0.943250i | \(-0.607752\pi\) | ||||
−0.332084 | + | 0.943250i | \(0.607752\pi\) | |||||||
\(390\) | 53.5279 | 2.71049 | ||||||||
\(391\) | 4.22010 | 0.213420 | ||||||||
\(392\) | 46.5431 | 2.35078 | ||||||||
\(393\) | 9.74417 | 0.491528 | ||||||||
\(394\) | −60.4388 | −3.04486 | ||||||||
\(395\) | 5.10069 | 0.256643 | ||||||||
\(396\) | 101.969 | 5.12411 | ||||||||
\(397\) | −7.38795 | −0.370790 | −0.185395 | − | 0.982664i | \(-0.559357\pi\) | ||||
−0.185395 | + | 0.982664i | \(0.559357\pi\) | |||||||
\(398\) | −54.5894 | −2.73632 | ||||||||
\(399\) | 2.39087 | 0.119693 | ||||||||
\(400\) | −7.64231 | −0.382116 | ||||||||
\(401\) | −8.17292 | −0.408136 | −0.204068 | − | 0.978957i | \(-0.565416\pi\) | ||||
−0.204068 | + | 0.978957i | \(0.565416\pi\) | |||||||
\(402\) | −73.8587 | −3.68374 | ||||||||
\(403\) | −1.14910 | −0.0572409 | ||||||||
\(404\) | 24.1996 | 1.20398 | ||||||||
\(405\) | −18.1758 | −0.903161 | ||||||||
\(406\) | −6.60247 | −0.327675 | ||||||||
\(407\) | 37.8824 | 1.87776 | ||||||||
\(408\) | 104.117 | 5.15454 | ||||||||
\(409\) | −21.3014 | −1.05329 | −0.526643 | − | 0.850087i | \(-0.676549\pi\) | ||||
−0.526643 | + | 0.850087i | \(0.676549\pi\) | |||||||
\(410\) | −6.28837 | −0.310560 | ||||||||
\(411\) | −30.0045 | −1.48001 | ||||||||
\(412\) | −75.9691 | −3.74273 | ||||||||
\(413\) | −13.5392 | −0.666220 | ||||||||
\(414\) | −15.5594 | −0.764700 | ||||||||
\(415\) | −15.5866 | −0.765116 | ||||||||
\(416\) | 45.3633 | 2.22412 | ||||||||
\(417\) | 38.7494 | 1.89757 | ||||||||
\(418\) | −6.42831 | −0.314419 | ||||||||
\(419\) | −12.8051 | −0.625572 | −0.312786 | − | 0.949824i | \(-0.601262\pi\) | ||||
−0.312786 | + | 0.949824i | \(0.601262\pi\) | |||||||
\(420\) | −35.0780 | −1.71163 | ||||||||
\(421\) | −33.8202 | −1.64830 | −0.824148 | − | 0.566374i | \(-0.808346\pi\) | ||||
−0.824148 | + | 0.566374i | \(0.808346\pi\) | |||||||
\(422\) | 29.2063 | 1.42174 | ||||||||
\(423\) | −15.2131 | −0.739687 | ||||||||
\(424\) | 102.558 | 4.98068 | ||||||||
\(425\) | −2.88849 | −0.140112 | ||||||||
\(426\) | −25.7606 | −1.24811 | ||||||||
\(427\) | −8.53460 | −0.413018 | ||||||||
\(428\) | 24.4094 | 1.17987 | ||||||||
\(429\) | 32.8030 | 1.58374 | ||||||||
\(430\) | −33.9070 | −1.63514 | ||||||||
\(431\) | 1.97569 | 0.0951655 | 0.0475827 | − | 0.998867i | \(-0.484848\pi\) | ||||
0.0475827 | + | 0.998867i | \(0.484848\pi\) | |||||||
\(432\) | −101.194 | −4.86868 | ||||||||
\(433\) | 30.4554 | 1.46359 | 0.731797 | − | 0.681523i | \(-0.238682\pi\) | ||||
0.731797 | + | 0.681523i | \(0.238682\pi\) | |||||||
\(434\) | 1.05147 | 0.0504724 | ||||||||
\(435\) | −13.8927 | −0.666103 | ||||||||
\(436\) | −54.0969 | −2.59077 | ||||||||
\(437\) | 0.702484 | 0.0336044 | ||||||||
\(438\) | −36.2428 | −1.73175 | ||||||||
\(439\) | 36.2092 | 1.72817 | 0.864084 | − | 0.503347i | \(-0.167898\pi\) | ||||
0.864084 | + | 0.503347i | \(0.167898\pi\) | |||||||
\(440\) | 56.9352 | 2.71428 | ||||||||
\(441\) | −34.3641 | −1.63639 | ||||||||
\(442\) | 36.9283 | 1.75650 | ||||||||
\(443\) | −22.2613 | −1.05767 | −0.528834 | − | 0.848725i | \(-0.677371\pi\) | ||||
−0.528834 | + | 0.848725i | \(0.677371\pi\) | |||||||
\(444\) | −169.188 | −8.02929 | ||||||||
\(445\) | −24.1821 | −1.14634 | ||||||||
\(446\) | −59.2204 | −2.80417 | ||||||||
\(447\) | −55.9443 | −2.64607 | ||||||||
\(448\) | −16.1337 | −0.762245 | ||||||||
\(449\) | 26.3429 | 1.24320 | 0.621599 | − | 0.783336i | \(-0.286483\pi\) | ||||
0.621599 | + | 0.783336i | \(0.286483\pi\) | |||||||
\(450\) | 10.6498 | 0.502034 | ||||||||
\(451\) | −3.85364 | −0.181461 | ||||||||
\(452\) | −36.1884 | −1.70216 | ||||||||
\(453\) | 43.1511 | 2.02741 | ||||||||
\(454\) | 15.3087 | 0.718473 | ||||||||
\(455\) | −7.51069 | −0.352106 | ||||||||
\(456\) | 17.3314 | 0.811617 | ||||||||
\(457\) | −41.1676 | −1.92574 | −0.962870 | − | 0.269967i | \(-0.912987\pi\) | ||||
−0.962870 | + | 0.269967i | \(0.912987\pi\) | |||||||
\(458\) | 26.7149 | 1.24831 | ||||||||
\(459\) | −38.2472 | −1.78523 | ||||||||
\(460\) | −10.3066 | −0.480547 | ||||||||
\(461\) | −2.21473 | −0.103150 | −0.0515752 | − | 0.998669i | \(-0.516424\pi\) | ||||
−0.0515752 | + | 0.998669i | \(0.516424\pi\) | |||||||
\(462\) | −30.0160 | −1.39647 | ||||||||
\(463\) | −13.0498 | −0.606476 | −0.303238 | − | 0.952915i | \(-0.598068\pi\) | ||||
−0.303238 | + | 0.952915i | \(0.598068\pi\) | |||||||
\(464\) | −25.3582 | −1.17722 | ||||||||
\(465\) | 2.21248 | 0.102601 | ||||||||
\(466\) | 22.2050 | 1.02863 | ||||||||
\(467\) | 11.2239 | 0.519379 | 0.259689 | − | 0.965692i | \(-0.416380\pi\) | ||||
0.259689 | + | 0.965692i | \(0.416380\pi\) | |||||||
\(468\) | −97.5084 | −4.50733 | ||||||||
\(469\) | 10.3634 | 0.478536 | ||||||||
\(470\) | −14.0711 | −0.649050 | ||||||||
\(471\) | −50.2476 | −2.31529 | ||||||||
\(472\) | −98.1452 | −4.51750 | ||||||||
\(473\) | −20.7789 | −0.955413 | ||||||||
\(474\) | −19.4930 | −0.895342 | ||||||||
\(475\) | −0.480822 | −0.0220616 | ||||||||
\(476\) | −24.1999 | −1.10920 | ||||||||
\(477\) | −75.7219 | −3.46707 | ||||||||
\(478\) | −29.8685 | −1.36616 | ||||||||
\(479\) | −18.5816 | −0.849016 | −0.424508 | − | 0.905424i | \(-0.639553\pi\) | ||||
−0.424508 | + | 0.905424i | \(0.639553\pi\) | |||||||
\(480\) | −87.3422 | −3.98661 | ||||||||
\(481\) | −36.2254 | −1.65174 | ||||||||
\(482\) | 21.0045 | 0.956727 | ||||||||
\(483\) | 3.28014 | 0.149252 | ||||||||
\(484\) | 2.28688 | 0.103949 | ||||||||
\(485\) | 22.1688 | 1.00663 | ||||||||
\(486\) | −1.39343 | −0.0632075 | ||||||||
\(487\) | −36.3379 | −1.64663 | −0.823313 | − | 0.567587i | \(-0.807877\pi\) | ||||
−0.823313 | + | 0.567587i | \(0.807877\pi\) | |||||||
\(488\) | −61.8671 | −2.80059 | ||||||||
\(489\) | −12.9108 | −0.583846 | ||||||||
\(490\) | −31.7844 | −1.43587 | ||||||||
\(491\) | 24.6739 | 1.11352 | 0.556759 | − | 0.830674i | \(-0.312045\pi\) | ||||
0.556759 | + | 0.830674i | \(0.312045\pi\) | |||||||
\(492\) | 17.2108 | 0.775924 | ||||||||
\(493\) | −9.58439 | −0.431659 | ||||||||
\(494\) | 6.14713 | 0.276572 | ||||||||
\(495\) | −42.0369 | −1.88942 | ||||||||
\(496\) | 4.03841 | 0.181330 | ||||||||
\(497\) | 3.61456 | 0.162135 | ||||||||
\(498\) | 59.5663 | 2.66923 | ||||||||
\(499\) | 12.0686 | 0.540266 | 0.270133 | − | 0.962823i | \(-0.412932\pi\) | ||||
0.270133 | + | 0.962823i | \(0.412932\pi\) | |||||||
\(500\) | 59.5471 | 2.66303 | ||||||||
\(501\) | 42.9308 | 1.91801 | ||||||||
\(502\) | −14.8012 | −0.660610 | ||||||||
\(503\) | −35.0987 | −1.56497 | −0.782487 | − | 0.622666i | \(-0.786049\pi\) | ||||
−0.782487 | + | 0.622666i | \(0.786049\pi\) | |||||||
\(504\) | 53.8626 | 2.39923 | ||||||||
\(505\) | −9.97638 | −0.443943 | ||||||||
\(506\) | −8.81928 | −0.392065 | ||||||||
\(507\) | 7.56819 | 0.336115 | ||||||||
\(508\) | 89.7530 | 3.98215 | ||||||||
\(509\) | −23.0318 | −1.02087 | −0.510433 | − | 0.859917i | \(-0.670515\pi\) | ||||
−0.510433 | + | 0.859917i | \(0.670515\pi\) | |||||||
\(510\) | −71.1015 | −3.14843 | ||||||||
\(511\) | 5.08535 | 0.224963 | ||||||||
\(512\) | 24.5217 | 1.08372 | ||||||||
\(513\) | −6.36668 | −0.281096 | ||||||||
\(514\) | −67.4904 | −2.97688 | ||||||||
\(515\) | 31.3185 | 1.38006 | ||||||||
\(516\) | 92.8011 | 4.08534 | ||||||||
\(517\) | −8.62303 | −0.379240 | ||||||||
\(518\) | 33.1477 | 1.45643 | ||||||||
\(519\) | 22.4704 | 0.986343 | ||||||||
\(520\) | −54.4448 | −2.38756 | ||||||||
\(521\) | −20.0094 | −0.876626 | −0.438313 | − | 0.898822i | \(-0.644424\pi\) | ||||
−0.438313 | + | 0.898822i | \(0.644424\pi\) | |||||||
\(522\) | 35.3373 | 1.54667 | ||||||||
\(523\) | −19.1158 | −0.835875 | −0.417937 | − | 0.908476i | \(-0.637247\pi\) | ||||
−0.417937 | + | 0.908476i | \(0.637247\pi\) | |||||||
\(524\) | −16.4178 | −0.717215 | ||||||||
\(525\) | −2.24513 | −0.0979855 | ||||||||
\(526\) | −42.3310 | −1.84572 | ||||||||
\(527\) | 1.52636 | 0.0664893 | ||||||||
\(528\) | −115.283 | −5.01704 | ||||||||
\(529\) | −22.0362 | −0.958097 | ||||||||
\(530\) | −70.0374 | −3.04223 | ||||||||
\(531\) | 72.4635 | 3.14465 | ||||||||
\(532\) | −4.02835 | −0.174651 | ||||||||
\(533\) | 3.68508 | 0.159618 | ||||||||
\(534\) | 92.4151 | 3.99919 | ||||||||
\(535\) | −10.0628 | −0.435055 | ||||||||
\(536\) | 75.1238 | 3.24485 | ||||||||
\(537\) | 7.13416 | 0.307862 | ||||||||
\(538\) | −38.0801 | −1.64175 | ||||||||
\(539\) | −19.4781 | −0.838982 | ||||||||
\(540\) | 93.4095 | 4.01971 | ||||||||
\(541\) | −12.8024 | −0.550417 | −0.275208 | − | 0.961385i | \(-0.588747\pi\) | ||||
−0.275208 | + | 0.961385i | \(0.588747\pi\) | |||||||
\(542\) | −47.2515 | −2.02963 | ||||||||
\(543\) | 7.42255 | 0.318532 | ||||||||
\(544\) | −60.2563 | −2.58347 | ||||||||
\(545\) | 22.3016 | 0.955297 | ||||||||
\(546\) | 28.7031 | 1.22838 | ||||||||
\(547\) | −14.9095 | −0.637486 | −0.318743 | − | 0.947841i | \(-0.603261\pi\) | ||||
−0.318743 | + | 0.947841i | \(0.603261\pi\) | |||||||
\(548\) | 50.5542 | 2.15957 | ||||||||
\(549\) | 45.6783 | 1.94950 | ||||||||
\(550\) | 6.03645 | 0.257395 | ||||||||
\(551\) | −1.59543 | −0.0679676 | ||||||||
\(552\) | 23.7777 | 1.01205 | ||||||||
\(553\) | 2.73512 | 0.116309 | ||||||||
\(554\) | −4.43936 | −0.188610 | ||||||||
\(555\) | 69.7481 | 2.96064 | ||||||||
\(556\) | −65.2883 | −2.76884 | ||||||||
\(557\) | −18.1673 | −0.769774 | −0.384887 | − | 0.922964i | \(-0.625760\pi\) | ||||
−0.384887 | + | 0.922964i | \(0.625760\pi\) | |||||||
\(558\) | −5.62763 | −0.238236 | ||||||||
\(559\) | 19.8700 | 0.840411 | ||||||||
\(560\) | 26.3956 | 1.11542 | ||||||||
\(561\) | −43.5724 | −1.83963 | ||||||||
\(562\) | 28.5432 | 1.20402 | ||||||||
\(563\) | 34.3825 | 1.44905 | 0.724524 | − | 0.689249i | \(-0.242060\pi\) | ||||
0.724524 | + | 0.689249i | \(0.242060\pi\) | |||||||
\(564\) | 38.5115 | 1.62163 | ||||||||
\(565\) | 14.9188 | 0.627637 | ||||||||
\(566\) | −65.2090 | −2.74094 | ||||||||
\(567\) | −9.74633 | −0.409307 | ||||||||
\(568\) | 26.2019 | 1.09941 | ||||||||
\(569\) | 2.33082 | 0.0977129 | 0.0488565 | − | 0.998806i | \(-0.484442\pi\) | ||||
0.0488565 | + | 0.998806i | \(0.484442\pi\) | |||||||
\(570\) | −11.8356 | −0.495741 | ||||||||
\(571\) | 34.3236 | 1.43640 | 0.718200 | − | 0.695837i | \(-0.244966\pi\) | ||||
0.718200 | + | 0.695837i | \(0.244966\pi\) | |||||||
\(572\) | −55.2693 | −2.31092 | ||||||||
\(573\) | 5.77645 | 0.241314 | ||||||||
\(574\) | −3.37199 | −0.140744 | ||||||||
\(575\) | −0.659661 | −0.0275098 | ||||||||
\(576\) | 86.3496 | 3.59790 | ||||||||
\(577\) | −22.6331 | −0.942228 | −0.471114 | − | 0.882072i | \(-0.656148\pi\) | ||||
−0.471114 | + | 0.882072i | \(0.656148\pi\) | |||||||
\(578\) | −3.92544 | −0.163277 | ||||||||
\(579\) | −30.7679 | −1.27867 | ||||||||
\(580\) | 23.4076 | 0.971946 | ||||||||
\(581\) | −8.35795 | −0.346746 | ||||||||
\(582\) | −84.7212 | −3.51180 | ||||||||
\(583\) | −42.9203 | −1.77758 | ||||||||
\(584\) | 36.8636 | 1.52543 | ||||||||
\(585\) | 40.1982 | 1.66199 | ||||||||
\(586\) | 10.3327 | 0.426841 | ||||||||
\(587\) | 12.2595 | 0.506003 | 0.253001 | − | 0.967466i | \(-0.418582\pi\) | ||||
0.253001 | + | 0.967466i | \(0.418582\pi\) | |||||||
\(588\) | 86.9918 | 3.58748 | ||||||||
\(589\) | 0.254080 | 0.0104692 | ||||||||
\(590\) | 67.0236 | 2.75932 | ||||||||
\(591\) | −68.1936 | −2.80511 | ||||||||
\(592\) | 127.311 | 5.23243 | ||||||||
\(593\) | 2.68708 | 0.110345 | 0.0551726 | − | 0.998477i | \(-0.482429\pi\) | ||||
0.0551726 | + | 0.998477i | \(0.482429\pi\) | |||||||
\(594\) | 79.9299 | 3.27956 | ||||||||
\(595\) | 9.97649 | 0.408996 | ||||||||
\(596\) | 94.2597 | 3.86103 | ||||||||
\(597\) | −61.5937 | −2.52086 | ||||||||
\(598\) | 8.43352 | 0.344872 | ||||||||
\(599\) | 12.6420 | 0.516537 | 0.258268 | − | 0.966073i | \(-0.416848\pi\) | ||||
0.258268 | + | 0.966073i | \(0.416848\pi\) | |||||||
\(600\) | −16.2749 | −0.664419 | ||||||||
\(601\) | 4.33060 | 0.176649 | 0.0883244 | − | 0.996092i | \(-0.471849\pi\) | ||||
0.0883244 | + | 0.996092i | \(0.471849\pi\) | |||||||
\(602\) | −18.1818 | −0.741036 | ||||||||
\(603\) | −55.4661 | −2.25875 | ||||||||
\(604\) | −72.7046 | −2.95831 | ||||||||
\(605\) | −0.942774 | −0.0383292 | ||||||||
\(606\) | 38.1261 | 1.54877 | ||||||||
\(607\) | 0.468327 | 0.0190088 | 0.00950441 | − | 0.999955i | \(-0.496975\pi\) | ||||
0.00950441 | + | 0.999955i | \(0.496975\pi\) | |||||||
\(608\) | −10.0303 | −0.406784 | ||||||||
\(609\) | −7.44963 | −0.301874 | ||||||||
\(610\) | 42.2492 | 1.71062 | ||||||||
\(611\) | 8.24585 | 0.333591 | ||||||||
\(612\) | 129.521 | 5.23558 | ||||||||
\(613\) | −13.2115 | −0.533609 | −0.266805 | − | 0.963751i | \(-0.585968\pi\) | ||||
−0.266805 | + | 0.963751i | \(0.585968\pi\) | |||||||
\(614\) | −18.1604 | −0.732895 | ||||||||
\(615\) | −7.09522 | −0.286107 | ||||||||
\(616\) | 30.5302 | 1.23010 | ||||||||
\(617\) | −12.5231 | −0.504163 | −0.252081 | − | 0.967706i | \(-0.581115\pi\) | ||||
−0.252081 | + | 0.967706i | \(0.581115\pi\) | |||||||
\(618\) | −119.688 | −4.81456 | ||||||||
\(619\) | −21.8618 | −0.878701 | −0.439351 | − | 0.898316i | \(-0.644791\pi\) | ||||
−0.439351 | + | 0.898316i | \(0.644791\pi\) | |||||||
\(620\) | −3.72777 | −0.149711 | ||||||||
\(621\) | −8.73472 | −0.350512 | ||||||||
\(622\) | −71.4598 | −2.86528 | ||||||||
\(623\) | −12.9671 | −0.519515 | ||||||||
\(624\) | 110.240 | 4.41315 | ||||||||
\(625\) | −21.1888 | −0.847550 | ||||||||
\(626\) | 26.5082 | 1.05948 | ||||||||
\(627\) | −7.25312 | −0.289662 | ||||||||
\(628\) | 84.6614 | 3.37836 | ||||||||
\(629\) | 48.1184 | 1.91861 | ||||||||
\(630\) | −36.7829 | −1.46547 | ||||||||
\(631\) | −30.6788 | −1.22130 | −0.610652 | − | 0.791899i | \(-0.709093\pi\) | ||||
−0.610652 | + | 0.791899i | \(0.709093\pi\) | |||||||
\(632\) | 19.8269 | 0.788670 | ||||||||
\(633\) | 32.9537 | 1.30979 | ||||||||
\(634\) | −45.2914 | −1.79875 | ||||||||
\(635\) | −37.0010 | −1.46834 | ||||||||
\(636\) | 191.688 | 7.60091 | ||||||||
\(637\) | 18.6261 | 0.737994 | ||||||||
\(638\) | 20.0297 | 0.792983 | ||||||||
\(639\) | −19.3456 | −0.765300 | ||||||||
\(640\) | 21.5440 | 0.851601 | ||||||||
\(641\) | 28.0285 | 1.10706 | 0.553529 | − | 0.832830i | \(-0.313281\pi\) | ||||
0.553529 | + | 0.832830i | \(0.313281\pi\) | |||||||
\(642\) | 38.4565 | 1.51776 | ||||||||
\(643\) | 39.3726 | 1.55270 | 0.776352 | − | 0.630300i | \(-0.217068\pi\) | ||||
0.776352 | + | 0.630300i | \(0.217068\pi\) | |||||||
\(644\) | −5.52667 | −0.217781 | ||||||||
\(645\) | −38.2575 | −1.50639 | ||||||||
\(646\) | −8.16527 | −0.321258 | ||||||||
\(647\) | 2.07740 | 0.0816710 | 0.0408355 | − | 0.999166i | \(-0.486998\pi\) | ||||
0.0408355 | + | 0.999166i | \(0.486998\pi\) | |||||||
\(648\) | −70.6509 | −2.77543 | ||||||||
\(649\) | 41.0734 | 1.61227 | ||||||||
\(650\) | −5.77241 | −0.226412 | ||||||||
\(651\) | 1.18639 | 0.0464982 | ||||||||
\(652\) | 21.7532 | 0.851921 | ||||||||
\(653\) | −10.1212 | −0.396074 | −0.198037 | − | 0.980195i | \(-0.563457\pi\) | ||||
−0.198037 | + | 0.980195i | \(0.563457\pi\) | |||||||
\(654\) | −85.2287 | −3.33271 | ||||||||
\(655\) | 6.76830 | 0.264459 | ||||||||
\(656\) | −12.9508 | −0.505645 | ||||||||
\(657\) | −27.2175 | −1.06185 | ||||||||
\(658\) | −7.54528 | −0.294146 | ||||||||
\(659\) | −14.1521 | −0.551286 | −0.275643 | − | 0.961260i | \(-0.588891\pi\) | ||||
−0.275643 | + | 0.961260i | \(0.588891\pi\) | |||||||
\(660\) | 106.415 | 4.14220 | ||||||||
\(661\) | −36.0369 | −1.40167 | −0.700836 | − | 0.713323i | \(-0.747189\pi\) | ||||
−0.700836 | + | 0.713323i | \(0.747189\pi\) | |||||||
\(662\) | −33.1159 | −1.28708 | ||||||||
\(663\) | 41.6665 | 1.61819 | ||||||||
\(664\) | −60.5866 | −2.35122 | ||||||||
\(665\) | 1.66070 | 0.0643992 | ||||||||
\(666\) | −177.411 | −6.87452 | ||||||||
\(667\) | −2.18884 | −0.0847522 | ||||||||
\(668\) | −72.3335 | −2.79867 | ||||||||
\(669\) | −66.8189 | −2.58337 | ||||||||
\(670\) | −51.3022 | −1.98198 | ||||||||
\(671\) | 25.8911 | 0.999516 | ||||||||
\(672\) | −46.8352 | −1.80671 | ||||||||
\(673\) | 22.0857 | 0.851340 | 0.425670 | − | 0.904878i | \(-0.360038\pi\) | ||||
0.425670 | + | 0.904878i | \(0.360038\pi\) | |||||||
\(674\) | 11.0800 | 0.426785 | ||||||||
\(675\) | 5.97857 | 0.230115 | ||||||||
\(676\) | −12.7515 | −0.490443 | ||||||||
\(677\) | 14.4705 | 0.556146 | 0.278073 | − | 0.960560i | \(-0.410304\pi\) | ||||
0.278073 | + | 0.960560i | \(0.410304\pi\) | |||||||
\(678\) | −57.0141 | −2.18961 | ||||||||
\(679\) | 11.8875 | 0.456201 | ||||||||
\(680\) | 72.3194 | 2.77332 | ||||||||
\(681\) | 17.2730 | 0.661901 | ||||||||
\(682\) | −3.18983 | −0.122145 | ||||||||
\(683\) | −0.0799145 | −0.00305784 | −0.00152892 | − | 0.999999i | \(-0.500487\pi\) | ||||
−0.00152892 | + | 0.999999i | \(0.500487\pi\) | |||||||
\(684\) | 21.5602 | 0.824376 | ||||||||
\(685\) | −20.8411 | −0.796299 | ||||||||
\(686\) | −37.7726 | −1.44216 | ||||||||
\(687\) | 30.1427 | 1.15002 | ||||||||
\(688\) | −69.8311 | −2.66229 | ||||||||
\(689\) | 41.0430 | 1.56361 | ||||||||
\(690\) | −16.2378 | −0.618164 | ||||||||
\(691\) | 6.46607 | 0.245981 | 0.122990 | − | 0.992408i | \(-0.460752\pi\) | ||||
0.122990 | + | 0.992408i | \(0.460752\pi\) | |||||||
\(692\) | −37.8601 | −1.43923 | ||||||||
\(693\) | −22.5413 | −0.856273 | ||||||||
\(694\) | 4.10155 | 0.155693 | ||||||||
\(695\) | 26.9153 | 1.02096 | ||||||||
\(696\) | −54.0022 | −2.04695 | ||||||||
\(697\) | −4.89491 | −0.185408 | ||||||||
\(698\) | −42.3793 | −1.60408 | ||||||||
\(699\) | 25.0541 | 0.947634 | ||||||||
\(700\) | 3.78278 | 0.142976 | ||||||||
\(701\) | 8.66524 | 0.327282 | 0.163641 | − | 0.986520i | \(-0.447676\pi\) | ||||
0.163641 | + | 0.986520i | \(0.447676\pi\) | |||||||
\(702\) | −76.4337 | −2.88481 | ||||||||
\(703\) | 8.00985 | 0.302097 | ||||||||
\(704\) | 48.9443 | 1.84466 | ||||||||
\(705\) | −15.8765 | −0.597944 | ||||||||
\(706\) | 53.1329 | 1.99968 | ||||||||
\(707\) | −5.34960 | −0.201192 | ||||||||
\(708\) | −183.439 | −6.89406 | ||||||||
\(709\) | −3.77392 | −0.141733 | −0.0708663 | − | 0.997486i | \(-0.522576\pi\) | ||||
−0.0708663 | + | 0.997486i | \(0.522576\pi\) | |||||||
\(710\) | −17.8933 | −0.671525 | ||||||||
\(711\) | −14.6387 | −0.548996 | ||||||||
\(712\) | −93.9980 | −3.52273 | ||||||||
\(713\) | 0.348583 | 0.0130545 | ||||||||
\(714\) | −38.1265 | −1.42685 | ||||||||
\(715\) | 22.7849 | 0.852108 | ||||||||
\(716\) | −12.0202 | −0.449217 | ||||||||
\(717\) | −33.7009 | −1.25858 | ||||||||
\(718\) | −8.13866 | −0.303732 | ||||||||
\(719\) | −25.8889 | −0.965492 | −0.482746 | − | 0.875761i | \(-0.660360\pi\) | ||||
−0.482746 | + | 0.875761i | \(0.660360\pi\) | |||||||
\(720\) | −141.273 | −5.26492 | ||||||||
\(721\) | 16.7938 | 0.625435 | ||||||||
\(722\) | 49.0764 | 1.82644 | ||||||||
\(723\) | 23.6995 | 0.881394 | ||||||||
\(724\) | −12.5061 | −0.464787 | ||||||||
\(725\) | 1.49817 | 0.0556408 | ||||||||
\(726\) | 3.60294 | 0.133718 | ||||||||
\(727\) | −32.9660 | −1.22264 | −0.611320 | − | 0.791383i | \(-0.709361\pi\) | ||||
−0.611320 | + | 0.791383i | \(0.709361\pi\) | |||||||
\(728\) | −29.1948 | −1.08203 | ||||||||
\(729\) | −27.7822 | −1.02897 | ||||||||
\(730\) | −25.1742 | −0.931740 | ||||||||
\(731\) | −26.3934 | −0.976196 | ||||||||
\(732\) | −115.633 | −4.27392 | ||||||||
\(733\) | 2.09021 | 0.0772037 | 0.0386018 | − | 0.999255i | \(-0.487710\pi\) | ||||
0.0386018 | + | 0.999255i | \(0.487710\pi\) | |||||||
\(734\) | −52.9784 | −1.95547 | ||||||||
\(735\) | −35.8627 | −1.32281 | ||||||||
\(736\) | −13.7611 | −0.507240 | ||||||||
\(737\) | −31.4390 | −1.15807 | ||||||||
\(738\) | 18.0473 | 0.664331 | ||||||||
\(739\) | −7.31887 | −0.269229 | −0.134614 | − | 0.990898i | \(-0.542980\pi\) | ||||
−0.134614 | + | 0.990898i | \(0.542980\pi\) | |||||||
\(740\) | −117.518 | −4.32003 | ||||||||
\(741\) | 6.93586 | 0.254795 | ||||||||
\(742\) | −37.5559 | −1.37872 | ||||||||
\(743\) | −27.8176 | −1.02053 | −0.510264 | − | 0.860018i | \(-0.670452\pi\) | ||||
−0.510264 | + | 0.860018i | \(0.670452\pi\) | |||||||
\(744\) | 8.60010 | 0.315295 | ||||||||
\(745\) | −38.8589 | −1.42368 | ||||||||
\(746\) | 83.0302 | 3.03995 | ||||||||
\(747\) | 44.7328 | 1.63669 | ||||||||
\(748\) | 73.4145 | 2.68430 | ||||||||
\(749\) | −5.39597 | −0.197164 | ||||||||
\(750\) | 93.8154 | 3.42565 | ||||||||
\(751\) | −10.1157 | −0.369127 | −0.184563 | − | 0.982821i | \(-0.559087\pi\) | ||||
−0.184563 | + | 0.982821i | \(0.559087\pi\) | |||||||
\(752\) | −28.9792 | −1.05676 | ||||||||
\(753\) | −16.7003 | −0.608594 | ||||||||
\(754\) | −19.1536 | −0.697533 | ||||||||
\(755\) | 29.9727 | 1.09082 | ||||||||
\(756\) | 50.0887 | 1.82171 | ||||||||
\(757\) | 50.1035 | 1.82104 | 0.910522 | − | 0.413461i | \(-0.135680\pi\) | ||||
0.910522 | + | 0.413461i | \(0.135680\pi\) | |||||||
\(758\) | −56.3564 | −2.04695 | ||||||||
\(759\) | −9.95087 | −0.361194 | ||||||||
\(760\) | 12.0384 | 0.436678 | ||||||||
\(761\) | −23.9710 | −0.868947 | −0.434473 | − | 0.900685i | \(-0.643066\pi\) | ||||
−0.434473 | + | 0.900685i | \(0.643066\pi\) | |||||||
\(762\) | 141.404 | 5.12254 | ||||||||
\(763\) | 11.9587 | 0.432935 | ||||||||
\(764\) | −9.73265 | −0.352115 | ||||||||
\(765\) | −53.3955 | −1.93052 | ||||||||
\(766\) | 21.1732 | 0.765018 | ||||||||
\(767\) | −39.2768 | −1.41820 | ||||||||
\(768\) | 4.29915 | 0.155132 | ||||||||
\(769\) | −41.4527 | −1.49482 | −0.747412 | − | 0.664361i | \(-0.768704\pi\) | ||||
−0.747412 | + | 0.664361i | \(0.768704\pi\) | |||||||
\(770\) | −20.8491 | −0.751350 | ||||||||
\(771\) | −76.1501 | −2.74248 | ||||||||
\(772\) | 51.8403 | 1.86577 | ||||||||
\(773\) | −41.1687 | −1.48073 | −0.740367 | − | 0.672203i | \(-0.765348\pi\) | ||||
−0.740367 | + | 0.672203i | \(0.765348\pi\) | |||||||
\(774\) | 97.3115 | 3.49779 | ||||||||
\(775\) | −0.238591 | −0.00857046 | ||||||||
\(776\) | 86.1723 | 3.09341 | ||||||||
\(777\) | 37.4008 | 1.34175 | ||||||||
\(778\) | 34.7726 | 1.24666 | ||||||||
\(779\) | −0.814813 | −0.0291937 | ||||||||
\(780\) | −101.760 | −3.64361 | ||||||||
\(781\) | −10.9654 | −0.392372 | ||||||||
\(782\) | −11.2023 | −0.400593 | ||||||||
\(783\) | 19.8377 | 0.708940 | ||||||||
\(784\) | −65.4598 | −2.33785 | ||||||||
\(785\) | −34.9019 | −1.24570 | ||||||||
\(786\) | −25.8660 | −0.922608 | ||||||||
\(787\) | 15.5666 | 0.554891 | 0.277445 | − | 0.960741i | \(-0.410512\pi\) | ||||
0.277445 | + | 0.960741i | \(0.410512\pi\) | |||||||
\(788\) | 114.898 | 4.09309 | ||||||||
\(789\) | −47.7624 | −1.70039 | ||||||||
\(790\) | −13.5398 | −0.481725 | ||||||||
\(791\) | 7.99984 | 0.284442 | ||||||||
\(792\) | −163.401 | −5.80621 | ||||||||
\(793\) | −24.7586 | −0.879205 | ||||||||
\(794\) | 19.6113 | 0.695981 | ||||||||
\(795\) | −79.0239 | −2.80269 | ||||||||
\(796\) | 103.778 | 3.67832 | ||||||||
\(797\) | 21.4327 | 0.759185 | 0.379592 | − | 0.925154i | \(-0.376064\pi\) | ||||
0.379592 | + | 0.925154i | \(0.376064\pi\) | |||||||
\(798\) | −6.34659 | −0.224667 | ||||||||
\(799\) | −10.9530 | −0.387490 | ||||||||
\(800\) | 9.41891 | 0.333009 | ||||||||
\(801\) | 69.4015 | 2.45218 | ||||||||
\(802\) | 21.6951 | 0.766080 | ||||||||
\(803\) | −15.4273 | −0.544417 | ||||||||
\(804\) | 140.411 | 4.95190 | ||||||||
\(805\) | 2.27839 | 0.0803026 | ||||||||
\(806\) | 3.05030 | 0.107442 | ||||||||
\(807\) | −42.9661 | −1.51248 | ||||||||
\(808\) | −38.7791 | −1.36425 | ||||||||
\(809\) | −7.93616 | −0.279020 | −0.139510 | − | 0.990221i | \(-0.544553\pi\) | ||||
−0.139510 | + | 0.990221i | \(0.544553\pi\) | |||||||
\(810\) | 48.2477 | 1.69525 | ||||||||
\(811\) | 19.6150 | 0.688774 | 0.344387 | − | 0.938828i | \(-0.388087\pi\) | ||||
0.344387 | + | 0.938828i | \(0.388087\pi\) | |||||||
\(812\) | 12.5518 | 0.440480 | ||||||||
\(813\) | −53.3143 | −1.86981 | ||||||||
\(814\) | −100.559 | −3.52459 | ||||||||
\(815\) | −8.96783 | −0.314129 | ||||||||
\(816\) | −146.433 | −5.12618 | ||||||||
\(817\) | −4.39348 | −0.153709 | ||||||||
\(818\) | 56.5446 | 1.97704 | ||||||||
\(819\) | 21.5553 | 0.753204 | ||||||||
\(820\) | 11.9546 | 0.417474 | ||||||||
\(821\) | 26.2538 | 0.916263 | 0.458132 | − | 0.888884i | \(-0.348519\pi\) | ||||
0.458132 | + | 0.888884i | \(0.348519\pi\) | |||||||
\(822\) | 79.6472 | 2.77802 | ||||||||
\(823\) | −27.3948 | −0.954921 | −0.477461 | − | 0.878653i | \(-0.658443\pi\) | ||||
−0.477461 | + | 0.878653i | \(0.658443\pi\) | |||||||
\(824\) | 121.738 | 4.24095 | ||||||||
\(825\) | 6.81098 | 0.237128 | ||||||||
\(826\) | 35.9399 | 1.25051 | ||||||||
\(827\) | 18.4701 | 0.642267 | 0.321134 | − | 0.947034i | \(-0.395936\pi\) | ||||
0.321134 | + | 0.947034i | \(0.395936\pi\) | |||||||
\(828\) | 29.5794 | 1.02796 | ||||||||
\(829\) | 25.6304 | 0.890180 | 0.445090 | − | 0.895486i | \(-0.353172\pi\) | ||||
0.445090 | + | 0.895486i | \(0.353172\pi\) | |||||||
\(830\) | 41.3747 | 1.43614 | ||||||||
\(831\) | −5.00897 | −0.173759 | ||||||||
\(832\) | −46.8034 | −1.62262 | ||||||||
\(833\) | −24.7412 | −0.857232 | ||||||||
\(834\) | −102.861 | −3.56177 | ||||||||
\(835\) | 29.8197 | 1.03195 | ||||||||
\(836\) | 12.2207 | 0.422661 | ||||||||
\(837\) | −3.15924 | −0.109199 | ||||||||
\(838\) | 33.9913 | 1.17421 | ||||||||
\(839\) | −20.4166 | −0.704858 | −0.352429 | − | 0.935838i | \(-0.614644\pi\) | ||||
−0.352429 | + | 0.935838i | \(0.614644\pi\) | |||||||
\(840\) | 56.2114 | 1.93948 | ||||||||
\(841\) | −24.0289 | −0.828582 | ||||||||
\(842\) | 89.7760 | 3.09388 | ||||||||
\(843\) | 32.2055 | 1.10922 | ||||||||
\(844\) | −55.5233 | −1.91119 | ||||||||
\(845\) | 5.25686 | 0.180841 | ||||||||
\(846\) | 40.3833 | 1.38841 | ||||||||
\(847\) | −0.505541 | −0.0173706 | ||||||||
\(848\) | −144.242 | −4.95327 | ||||||||
\(849\) | −73.5759 | −2.52512 | ||||||||
\(850\) | 7.66752 | 0.262994 | ||||||||
\(851\) | 10.9891 | 0.376700 | ||||||||
\(852\) | 48.9728 | 1.67778 | ||||||||
\(853\) | 5.62072 | 0.192450 | 0.0962249 | − | 0.995360i | \(-0.469323\pi\) | ||||
0.0962249 | + | 0.995360i | \(0.469323\pi\) | |||||||
\(854\) | 22.6551 | 0.775243 | ||||||||
\(855\) | −8.88828 | −0.303973 | ||||||||
\(856\) | −39.1153 | −1.33693 | ||||||||
\(857\) | −18.7527 | −0.640581 | −0.320290 | − | 0.947319i | \(-0.603781\pi\) | ||||
−0.320290 | + | 0.947319i | \(0.603781\pi\) | |||||||
\(858\) | −87.0757 | −2.97272 | ||||||||
\(859\) | −6.75647 | −0.230528 | −0.115264 | − | 0.993335i | \(-0.536771\pi\) | ||||
−0.115264 | + | 0.993335i | \(0.536771\pi\) | |||||||
\(860\) | 64.4596 | 2.19805 | ||||||||
\(861\) | −3.80465 | −0.129662 | ||||||||
\(862\) | −5.24447 | −0.178627 | ||||||||
\(863\) | 4.92266 | 0.167569 | 0.0837847 | − | 0.996484i | \(-0.473299\pi\) | ||||
0.0837847 | + | 0.996484i | \(0.473299\pi\) | |||||||
\(864\) | 124.718 | 4.24299 | ||||||||
\(865\) | 15.6080 | 0.530687 | ||||||||
\(866\) | −80.8441 | −2.74719 | ||||||||
\(867\) | −4.42911 | −0.150421 | ||||||||
\(868\) | −1.99893 | −0.0678480 | ||||||||
\(869\) | −8.29746 | −0.281472 | ||||||||
\(870\) | 36.8782 | 1.25029 | ||||||||
\(871\) | 30.0639 | 1.01867 | ||||||||
\(872\) | 86.6886 | 2.93565 | ||||||||
\(873\) | −63.6235 | −2.15333 | ||||||||
\(874\) | −1.86475 | −0.0630761 | ||||||||
\(875\) | −13.1636 | −0.445009 | ||||||||
\(876\) | 68.9002 | 2.32792 | ||||||||
\(877\) | 33.4684 | 1.13015 | 0.565074 | − | 0.825040i | \(-0.308848\pi\) | ||||
0.565074 | + | 0.825040i | \(0.308848\pi\) | |||||||
\(878\) | −96.1174 | −3.24381 | ||||||||
\(879\) | 11.6585 | 0.393232 | ||||||||
\(880\) | −80.0754 | −2.69934 | ||||||||
\(881\) | −13.2892 | −0.447723 | −0.223862 | − | 0.974621i | \(-0.571866\pi\) | ||||
−0.223862 | + | 0.974621i | \(0.571866\pi\) | |||||||
\(882\) | 91.2198 | 3.07153 | ||||||||
\(883\) | −5.26124 | −0.177055 | −0.0885274 | − | 0.996074i | \(-0.528216\pi\) | ||||
−0.0885274 | + | 0.996074i | \(0.528216\pi\) | |||||||
\(884\) | −70.2033 | −2.36119 | ||||||||
\(885\) | 75.6234 | 2.54205 | ||||||||
\(886\) | 59.0929 | 1.98526 | ||||||||
\(887\) | −31.6616 | −1.06309 | −0.531547 | − | 0.847029i | \(-0.678389\pi\) | ||||
−0.531547 | + | 0.847029i | \(0.678389\pi\) | |||||||
\(888\) | 271.118 | 9.09811 | ||||||||
\(889\) | −19.8409 | −0.665443 | ||||||||
\(890\) | 64.1915 | 2.15170 | ||||||||
\(891\) | 29.5671 | 0.990536 | ||||||||
\(892\) | 112.582 | 3.76953 | ||||||||
\(893\) | −1.82325 | −0.0610128 | ||||||||
\(894\) | 148.505 | 4.96673 | ||||||||
\(895\) | 4.95538 | 0.165640 | ||||||||
\(896\) | 11.5525 | 0.385941 | ||||||||
\(897\) | 9.51561 | 0.317717 | ||||||||
\(898\) | −69.9274 | −2.33351 | ||||||||
\(899\) | −0.791677 | −0.0264039 | ||||||||
\(900\) | −20.2459 | −0.674865 | ||||||||
\(901\) | −54.5176 | −1.81624 | ||||||||
\(902\) | 10.2295 | 0.340605 | ||||||||
\(903\) | −20.5147 | −0.682687 | ||||||||
\(904\) | 57.9907 | 1.92874 | ||||||||
\(905\) | 5.15570 | 0.171381 | ||||||||
\(906\) | −114.545 | −3.80550 | ||||||||
\(907\) | 7.43424 | 0.246850 | 0.123425 | − | 0.992354i | \(-0.460612\pi\) | ||||
0.123425 | + | 0.992354i | \(0.460612\pi\) | |||||||
\(908\) | −29.1029 | −0.965815 | ||||||||
\(909\) | 28.6318 | 0.949655 | ||||||||
\(910\) | 19.9372 | 0.660911 | ||||||||
\(911\) | −9.25748 | −0.306714 | −0.153357 | − | 0.988171i | \(-0.549008\pi\) | ||||
−0.153357 | + | 0.988171i | \(0.549008\pi\) | |||||||
\(912\) | −24.3754 | −0.807151 | ||||||||
\(913\) | 25.3552 | 0.839136 | ||||||||
\(914\) | 109.280 | 3.61465 | ||||||||
\(915\) | 47.6701 | 1.57593 | ||||||||
\(916\) | −50.7870 | −1.67805 | ||||||||
\(917\) | 3.62934 | 0.119851 | ||||||||
\(918\) | 101.527 | 3.35090 | ||||||||
\(919\) | −2.32860 | −0.0768134 | −0.0384067 | − | 0.999262i | \(-0.512228\pi\) | ||||
−0.0384067 | + | 0.999262i | \(0.512228\pi\) | |||||||
\(920\) | 16.5160 | 0.544516 | ||||||||
\(921\) | −20.4906 | −0.675187 | ||||||||
\(922\) | 5.87903 | 0.193615 | ||||||||
\(923\) | 10.4858 | 0.345143 | ||||||||
\(924\) | 57.0626 | 1.87722 | ||||||||
\(925\) | −7.52158 | −0.247308 | ||||||||
\(926\) | 34.6408 | 1.13837 | ||||||||
\(927\) | −89.8827 | −2.95213 | ||||||||
\(928\) | 31.2531 | 1.02593 | ||||||||
\(929\) | −1.00084 | −0.0328366 | −0.0164183 | − | 0.999865i | \(-0.505226\pi\) | ||||
−0.0164183 | + | 0.999865i | \(0.505226\pi\) | |||||||
\(930\) | −5.87303 | −0.192584 | ||||||||
\(931\) | −4.11845 | −0.134977 | ||||||||
\(932\) | −42.2133 | −1.38274 | ||||||||
\(933\) | −80.6287 | −2.63967 | ||||||||
\(934\) | −29.7938 | −0.974884 | ||||||||
\(935\) | −30.2654 | −0.989783 | ||||||||
\(936\) | 156.254 | 5.10732 | ||||||||
\(937\) | 23.7432 | 0.775658 | 0.387829 | − | 0.921731i | \(-0.373225\pi\) | ||||
0.387829 | + | 0.921731i | \(0.373225\pi\) | |||||||
\(938\) | −27.5096 | −0.898221 | ||||||||
\(939\) | 29.9095 | 0.976059 | ||||||||
\(940\) | 26.7501 | 0.872492 | ||||||||
\(941\) | 3.67235 | 0.119715 | 0.0598576 | − | 0.998207i | \(-0.480935\pi\) | ||||
0.0598576 | + | 0.998207i | \(0.480935\pi\) | |||||||
\(942\) | 133.383 | 4.34584 | ||||||||
\(943\) | −1.11788 | −0.0364031 | ||||||||
\(944\) | 138.035 | 4.49264 | ||||||||
\(945\) | −20.6492 | −0.671719 | ||||||||
\(946\) | 55.1576 | 1.79333 | ||||||||
\(947\) | 43.5506 | 1.41520 | 0.707602 | − | 0.706611i | \(-0.249777\pi\) | ||||
0.707602 | + | 0.706611i | \(0.249777\pi\) | |||||||
\(948\) | 37.0575 | 1.20357 | ||||||||
\(949\) | 14.7525 | 0.478885 | ||||||||
\(950\) | 1.27635 | 0.0414101 | ||||||||
\(951\) | −51.1027 | −1.65712 | ||||||||
\(952\) | 38.7796 | 1.25685 | ||||||||
\(953\) | −14.9357 | −0.483815 | −0.241907 | − | 0.970299i | \(-0.577773\pi\) | ||||
−0.241907 | + | 0.970299i | \(0.577773\pi\) | |||||||
\(954\) | 201.004 | 6.50775 | ||||||||
\(955\) | 4.01232 | 0.129836 | ||||||||
\(956\) | 56.7822 | 1.83647 | ||||||||
\(957\) | 22.5997 | 0.730544 | ||||||||
\(958\) | 49.3251 | 1.59362 | ||||||||
\(959\) | −11.1756 | −0.360878 | ||||||||
\(960\) | 90.1150 | 2.90845 | ||||||||
\(961\) | −30.8739 | −0.995933 | ||||||||
\(962\) | 96.1605 | 3.10034 | ||||||||
\(963\) | 28.8799 | 0.930642 | ||||||||
\(964\) | −39.9310 | −1.28609 | ||||||||
\(965\) | −21.3713 | −0.687968 | ||||||||
\(966\) | −8.70717 | −0.280148 | ||||||||
\(967\) | −2.72744 | −0.0877084 | −0.0438542 | − | 0.999038i | \(-0.513964\pi\) | ||||
−0.0438542 | + | 0.999038i | \(0.513964\pi\) | |||||||
\(968\) | −3.66465 | −0.117786 | ||||||||
\(969\) | −9.21295 | −0.295962 | ||||||||
\(970\) | −58.8473 | −1.88947 | ||||||||
\(971\) | −24.2522 | −0.778289 | −0.389145 | − | 0.921177i | \(-0.627229\pi\) | ||||
−0.389145 | + | 0.921177i | \(0.627229\pi\) | |||||||
\(972\) | 2.64902 | 0.0849673 | ||||||||
\(973\) | 14.4327 | 0.462692 | ||||||||
\(974\) | 96.4591 | 3.09075 | ||||||||
\(975\) | −6.51306 | −0.208585 | ||||||||
\(976\) | 87.0119 | 2.78518 | ||||||||
\(977\) | −18.6446 | −0.596493 | −0.298246 | − | 0.954489i | \(-0.596402\pi\) | ||||
−0.298246 | + | 0.954489i | \(0.596402\pi\) | |||||||
\(978\) | 34.2718 | 1.09589 | ||||||||
\(979\) | 39.3378 | 1.25724 | ||||||||
\(980\) | 60.4244 | 1.93019 | ||||||||
\(981\) | −64.0047 | −2.04351 | ||||||||
\(982\) | −65.4970 | −2.09009 | ||||||||
\(983\) | 47.0685 | 1.50125 | 0.750626 | − | 0.660727i | \(-0.229752\pi\) | ||||
0.750626 | + | 0.660727i | \(0.229752\pi\) | |||||||
\(984\) | −27.5798 | −0.879212 | ||||||||
\(985\) | −47.3673 | −1.50925 | ||||||||
\(986\) | 25.4418 | 0.810233 | ||||||||
\(987\) | −8.51341 | −0.270985 | ||||||||
\(988\) | −11.6861 | −0.371785 | ||||||||
\(989\) | −6.02761 | −0.191667 | ||||||||
\(990\) | 111.587 | 3.54647 | ||||||||
\(991\) | −10.6374 | −0.337907 | −0.168953 | − | 0.985624i | \(-0.554039\pi\) | ||||
−0.168953 | + | 0.985624i | \(0.554039\pi\) | |||||||
\(992\) | −4.97721 | −0.158027 | ||||||||
\(993\) | −37.3649 | −1.18574 | ||||||||
\(994\) | −9.59488 | −0.304331 | ||||||||
\(995\) | −42.7829 | −1.35631 | ||||||||
\(996\) | −113.240 | −3.58814 | ||||||||
\(997\) | 13.9469 | 0.441704 | 0.220852 | − | 0.975307i | \(-0.429116\pi\) | ||||
0.220852 | + | 0.975307i | \(0.429116\pi\) | |||||||
\(998\) | −32.0362 | −1.01409 | ||||||||
\(999\) | −99.5949 | −3.15104 |
(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.a.1.8 | ✓ | 217 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6047.2.a.a.1.8 | ✓ | 217 | 1.1 | even | 1 | trivial |