Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7935,2,Mod(1,7935)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7935, 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("7935.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7935 = 3 \cdot 5 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7935.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: | \(63.3612940039\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | no (minimal twist has level 345) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 7935.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.51687 | −1.07259 | −0.536295 | − | 0.844030i | \(-0.680177\pi\) | ||||
−0.536295 | + | 0.844030i | \(0.680177\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0.300900 | 0.150450 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.51687 | 0.619260 | ||||||||
\(7\) | 3.34169 | 1.26304 | 0.631520 | − | 0.775360i | \(-0.282432\pi\) | ||||
0.631520 | + | 0.775360i | \(0.282432\pi\) | |||||||
\(8\) | 2.57732 | 0.911219 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.51687 | 0.479677 | ||||||||
\(11\) | −1.18548 | −0.357435 | −0.178718 | − | 0.983900i | \(-0.557195\pi\) | ||||
−0.178718 | + | 0.983900i | \(0.557195\pi\) | |||||||
\(12\) | −0.300900 | −0.0868625 | ||||||||
\(13\) | 0.915669 | 0.253961 | 0.126980 | − | 0.991905i | \(-0.459471\pi\) | ||||
0.126980 | + | 0.991905i | \(0.459471\pi\) | |||||||
\(14\) | −5.06891 | −1.35472 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −4.51126 | −1.12781 | ||||||||
\(17\) | 2.52173 | 0.611610 | 0.305805 | − | 0.952094i | \(-0.401074\pi\) | ||||
0.305805 | + | 0.952094i | \(0.401074\pi\) | |||||||
\(18\) | −1.51687 | −0.357530 | ||||||||
\(19\) | 8.46827 | 1.94276 | 0.971378 | − | 0.237541i | \(-0.0763413\pi\) | ||||
0.971378 | + | 0.237541i | \(0.0763413\pi\) | |||||||
\(20\) | −0.300900 | −0.0672834 | ||||||||
\(21\) | −3.34169 | −0.729216 | ||||||||
\(22\) | 1.79822 | 0.383382 | ||||||||
\(23\) | 0 | 0 | ||||||||
\(24\) | −2.57732 | −0.526093 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.38895 | −0.272396 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.00552 | 0.190025 | ||||||||
\(29\) | 7.86833 | 1.46111 | 0.730556 | − | 0.682852i | \(-0.239261\pi\) | ||||
0.730556 | + | 0.682852i | \(0.239261\pi\) | |||||||
\(30\) | −1.51687 | −0.276942 | ||||||||
\(31\) | −5.67444 | −1.01916 | −0.509580 | − | 0.860423i | \(-0.670199\pi\) | ||||
−0.509580 | + | 0.860423i | \(0.670199\pi\) | |||||||
\(32\) | 1.68837 | 0.298465 | ||||||||
\(33\) | 1.18548 | 0.206365 | ||||||||
\(34\) | −3.82515 | −0.656008 | ||||||||
\(35\) | −3.34169 | −0.564848 | ||||||||
\(36\) | 0.300900 | 0.0501501 | ||||||||
\(37\) | 5.68722 | 0.934973 | 0.467487 | − | 0.884000i | \(-0.345160\pi\) | ||||
0.467487 | + | 0.884000i | \(0.345160\pi\) | |||||||
\(38\) | −12.8453 | −2.08378 | ||||||||
\(39\) | −0.915669 | −0.146624 | ||||||||
\(40\) | −2.57732 | −0.407510 | ||||||||
\(41\) | 10.1782 | 1.58957 | 0.794787 | − | 0.606888i | \(-0.207582\pi\) | ||||
0.794787 | + | 0.606888i | \(0.207582\pi\) | |||||||
\(42\) | 5.06891 | 0.782150 | ||||||||
\(43\) | 8.92948 | 1.36173 | 0.680866 | − | 0.732408i | \(-0.261604\pi\) | ||||
0.680866 | + | 0.732408i | \(0.261604\pi\) | |||||||
\(44\) | −0.356711 | −0.0537762 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.20823 | −1.05143 | −0.525714 | − | 0.850661i | \(-0.676202\pi\) | ||||
−0.525714 | + | 0.850661i | \(0.676202\pi\) | |||||||
\(48\) | 4.51126 | 0.651144 | ||||||||
\(49\) | 4.16687 | 0.595268 | ||||||||
\(50\) | −1.51687 | −0.214518 | ||||||||
\(51\) | −2.52173 | −0.353113 | ||||||||
\(52\) | 0.275525 | 0.0382085 | ||||||||
\(53\) | 1.10303 | 0.151513 | 0.0757567 | − | 0.997126i | \(-0.475863\pi\) | ||||
0.0757567 | + | 0.997126i | \(0.475863\pi\) | |||||||
\(54\) | 1.51687 | 0.206420 | ||||||||
\(55\) | 1.18548 | 0.159850 | ||||||||
\(56\) | 8.61259 | 1.15091 | ||||||||
\(57\) | −8.46827 | −1.12165 | ||||||||
\(58\) | −11.9353 | −1.56718 | ||||||||
\(59\) | −3.44898 | −0.449018 | −0.224509 | − | 0.974472i | \(-0.572078\pi\) | ||||
−0.224509 | + | 0.974472i | \(0.572078\pi\) | |||||||
\(60\) | 0.300900 | 0.0388461 | ||||||||
\(61\) | 4.49161 | 0.575092 | 0.287546 | − | 0.957767i | \(-0.407161\pi\) | ||||
0.287546 | + | 0.957767i | \(0.407161\pi\) | |||||||
\(62\) | 8.60740 | 1.09314 | ||||||||
\(63\) | 3.34169 | 0.421013 | ||||||||
\(64\) | 6.46148 | 0.807685 | ||||||||
\(65\) | −0.915669 | −0.113575 | ||||||||
\(66\) | −1.79822 | −0.221346 | ||||||||
\(67\) | −0.818172 | −0.0999556 | −0.0499778 | − | 0.998750i | \(-0.515915\pi\) | ||||
−0.0499778 | + | 0.998750i | \(0.515915\pi\) | |||||||
\(68\) | 0.758791 | 0.0920169 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.06891 | 0.605851 | ||||||||
\(71\) | 7.34757 | 0.871996 | 0.435998 | − | 0.899948i | \(-0.356395\pi\) | ||||
0.435998 | + | 0.899948i | \(0.356395\pi\) | |||||||
\(72\) | 2.57732 | 0.303740 | ||||||||
\(73\) | 13.6141 | 1.59341 | 0.796703 | − | 0.604370i | \(-0.206575\pi\) | ||||
0.796703 | + | 0.604370i | \(0.206575\pi\) | |||||||
\(74\) | −8.62678 | −1.00284 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.54811 | 0.292288 | ||||||||
\(77\) | −3.96150 | −0.451455 | ||||||||
\(78\) | 1.38895 | 0.157268 | ||||||||
\(79\) | 15.6680 | 1.76279 | 0.881394 | − | 0.472382i | \(-0.156606\pi\) | ||||
0.881394 | + | 0.472382i | \(0.156606\pi\) | |||||||
\(80\) | 4.51126 | 0.504374 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −15.4391 | −1.70496 | ||||||||
\(83\) | 6.60930 | 0.725465 | 0.362732 | − | 0.931893i | \(-0.381844\pi\) | ||||
0.362732 | + | 0.931893i | \(0.381844\pi\) | |||||||
\(84\) | −1.00552 | −0.109711 | ||||||||
\(85\) | −2.52173 | −0.273521 | ||||||||
\(86\) | −13.5449 | −1.46058 | ||||||||
\(87\) | −7.86833 | −0.843574 | ||||||||
\(88\) | −3.05536 | −0.325702 | ||||||||
\(89\) | −9.17352 | −0.972391 | −0.486195 | − | 0.873850i | \(-0.661616\pi\) | ||||
−0.486195 | + | 0.873850i | \(0.661616\pi\) | |||||||
\(90\) | 1.51687 | 0.159892 | ||||||||
\(91\) | 3.05988 | 0.320763 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.67444 | 0.588412 | ||||||||
\(94\) | 10.9340 | 1.12775 | ||||||||
\(95\) | −8.46827 | −0.868827 | ||||||||
\(96\) | −1.68837 | −0.172319 | ||||||||
\(97\) | −3.08867 | −0.313607 | −0.156804 | − | 0.987630i | \(-0.550119\pi\) | ||||
−0.156804 | + | 0.987630i | \(0.550119\pi\) | |||||||
\(98\) | −6.32062 | −0.638479 | ||||||||
\(99\) | −1.18548 | −0.119145 | ||||||||
\(100\) | 0.300900 | 0.0300900 | ||||||||
\(101\) | 10.0879 | 1.00379 | 0.501894 | − | 0.864929i | \(-0.332637\pi\) | ||||
0.501894 | + | 0.864929i | \(0.332637\pi\) | |||||||
\(102\) | 3.82515 | 0.378746 | ||||||||
\(103\) | −3.01573 | −0.297149 | −0.148575 | − | 0.988901i | \(-0.547469\pi\) | ||||
−0.148575 | + | 0.988901i | \(0.547469\pi\) | |||||||
\(104\) | 2.35997 | 0.231414 | ||||||||
\(105\) | 3.34169 | 0.326115 | ||||||||
\(106\) | −1.67316 | −0.162512 | ||||||||
\(107\) | −1.71816 | −0.166101 | −0.0830503 | − | 0.996545i | \(-0.526466\pi\) | ||||
−0.0830503 | + | 0.996545i | \(0.526466\pi\) | |||||||
\(108\) | −0.300900 | −0.0289542 | ||||||||
\(109\) | 7.24743 | 0.694178 | 0.347089 | − | 0.937832i | \(-0.387170\pi\) | ||||
0.347089 | + | 0.937832i | \(0.387170\pi\) | |||||||
\(110\) | −1.79822 | −0.171454 | ||||||||
\(111\) | −5.68722 | −0.539807 | ||||||||
\(112\) | −15.0752 | −1.42447 | ||||||||
\(113\) | −15.8405 | −1.49015 | −0.745073 | − | 0.666983i | \(-0.767585\pi\) | ||||
−0.745073 | + | 0.666983i | \(0.767585\pi\) | |||||||
\(114\) | 12.8453 | 1.20307 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.36758 | 0.219825 | ||||||||
\(117\) | 0.915669 | 0.0846537 | ||||||||
\(118\) | 5.23166 | 0.481613 | ||||||||
\(119\) | 8.42685 | 0.772488 | ||||||||
\(120\) | 2.57732 | 0.235276 | ||||||||
\(121\) | −9.59464 | −0.872240 | ||||||||
\(122\) | −6.81320 | −0.616838 | ||||||||
\(123\) | −10.1782 | −0.917741 | ||||||||
\(124\) | −1.70744 | −0.153333 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −5.06891 | −0.451575 | ||||||||
\(127\) | −7.50750 | −0.666183 | −0.333091 | − | 0.942895i | \(-0.608092\pi\) | ||||
−0.333091 | + | 0.942895i | \(0.608092\pi\) | |||||||
\(128\) | −13.1780 | −1.16478 | ||||||||
\(129\) | −8.92948 | −0.786197 | ||||||||
\(130\) | 1.38895 | 0.121819 | ||||||||
\(131\) | −18.3185 | −1.60050 | −0.800248 | − | 0.599669i | \(-0.795299\pi\) | ||||
−0.800248 | + | 0.599669i | \(0.795299\pi\) | |||||||
\(132\) | 0.356711 | 0.0310477 | ||||||||
\(133\) | 28.2983 | 2.45378 | ||||||||
\(134\) | 1.24106 | 0.107211 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 6.49931 | 0.557311 | ||||||||
\(137\) | 13.4737 | 1.15113 | 0.575567 | − | 0.817754i | \(-0.304781\pi\) | ||||
0.575567 | + | 0.817754i | \(0.304781\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.2453 | 1.46272 | 0.731362 | − | 0.681990i | \(-0.238885\pi\) | ||||
0.731362 | + | 0.681990i | \(0.238885\pi\) | |||||||
\(140\) | −1.00552 | −0.0849815 | ||||||||
\(141\) | 7.20823 | 0.607042 | ||||||||
\(142\) | −11.1453 | −0.935295 | ||||||||
\(143\) | −1.08551 | −0.0907747 | ||||||||
\(144\) | −4.51126 | −0.375938 | ||||||||
\(145\) | −7.86833 | −0.653430 | ||||||||
\(146\) | −20.6508 | −1.70907 | ||||||||
\(147\) | −4.16687 | −0.343678 | ||||||||
\(148\) | 1.71129 | 0.140667 | ||||||||
\(149\) | −4.72490 | −0.387079 | −0.193539 | − | 0.981092i | \(-0.561997\pi\) | ||||
−0.193539 | + | 0.981092i | \(0.561997\pi\) | |||||||
\(150\) | 1.51687 | 0.123852 | ||||||||
\(151\) | 4.22106 | 0.343505 | 0.171753 | − | 0.985140i | \(-0.445057\pi\) | ||||
0.171753 | + | 0.985140i | \(0.445057\pi\) | |||||||
\(152\) | 21.8254 | 1.77028 | ||||||||
\(153\) | 2.52173 | 0.203870 | ||||||||
\(154\) | 6.00909 | 0.484226 | ||||||||
\(155\) | 5.67444 | 0.455782 | ||||||||
\(156\) | −0.275525 | −0.0220597 | ||||||||
\(157\) | 19.1706 | 1.52998 | 0.764991 | − | 0.644041i | \(-0.222743\pi\) | ||||
0.764991 | + | 0.644041i | \(0.222743\pi\) | |||||||
\(158\) | −23.7664 | −1.89075 | ||||||||
\(159\) | −1.10303 | −0.0874763 | ||||||||
\(160\) | −1.68837 | −0.133477 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.51687 | −0.119177 | ||||||||
\(163\) | −18.2402 | −1.42868 | −0.714341 | − | 0.699797i | \(-0.753274\pi\) | ||||
−0.714341 | + | 0.699797i | \(0.753274\pi\) | |||||||
\(164\) | 3.06264 | 0.239152 | ||||||||
\(165\) | −1.18548 | −0.0922894 | ||||||||
\(166\) | −10.0255 | −0.778126 | ||||||||
\(167\) | 3.94892 | 0.305576 | 0.152788 | − | 0.988259i | \(-0.451175\pi\) | ||||
0.152788 | + | 0.988259i | \(0.451175\pi\) | |||||||
\(168\) | −8.61259 | −0.664475 | ||||||||
\(169\) | −12.1615 | −0.935504 | ||||||||
\(170\) | 3.82515 | 0.293375 | ||||||||
\(171\) | 8.46827 | 0.647585 | ||||||||
\(172\) | 2.68688 | 0.204873 | ||||||||
\(173\) | 4.41696 | 0.335815 | 0.167908 | − | 0.985803i | \(-0.446299\pi\) | ||||
0.167908 | + | 0.985803i | \(0.446299\pi\) | |||||||
\(174\) | 11.9353 | 0.904809 | ||||||||
\(175\) | 3.34169 | 0.252608 | ||||||||
\(176\) | 5.34801 | 0.403121 | ||||||||
\(177\) | 3.44898 | 0.259241 | ||||||||
\(178\) | 13.9151 | 1.04298 | ||||||||
\(179\) | −6.29312 | −0.470370 | −0.235185 | − | 0.971951i | \(-0.575570\pi\) | ||||
−0.235185 | + | 0.971951i | \(0.575570\pi\) | |||||||
\(180\) | −0.300900 | −0.0224278 | ||||||||
\(181\) | 12.9253 | 0.960728 | 0.480364 | − | 0.877069i | \(-0.340505\pi\) | ||||
0.480364 | + | 0.877069i | \(0.340505\pi\) | |||||||
\(182\) | −4.64145 | −0.344047 | ||||||||
\(183\) | −4.49161 | −0.332029 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.68722 | −0.418133 | ||||||||
\(186\) | −8.60740 | −0.631125 | ||||||||
\(187\) | −2.98946 | −0.218611 | ||||||||
\(188\) | −2.16896 | −0.158188 | ||||||||
\(189\) | −3.34169 | −0.243072 | ||||||||
\(190\) | 12.8453 | 0.931895 | ||||||||
\(191\) | −26.5082 | −1.91806 | −0.959031 | − | 0.283300i | \(-0.908571\pi\) | ||||
−0.959031 | + | 0.283300i | \(0.908571\pi\) | |||||||
\(192\) | −6.46148 | −0.466317 | ||||||||
\(193\) | 7.46115 | 0.537065 | 0.268532 | − | 0.963271i | \(-0.413461\pi\) | ||||
0.268532 | + | 0.963271i | \(0.413461\pi\) | |||||||
\(194\) | 4.68512 | 0.336372 | ||||||||
\(195\) | 0.915669 | 0.0655724 | ||||||||
\(196\) | 1.25381 | 0.0895582 | ||||||||
\(197\) | −7.88559 | −0.561825 | −0.280913 | − | 0.959733i | \(-0.590637\pi\) | ||||
−0.280913 | + | 0.959733i | \(0.590637\pi\) | |||||||
\(198\) | 1.79822 | 0.127794 | ||||||||
\(199\) | −17.7491 | −1.25820 | −0.629100 | − | 0.777324i | \(-0.716576\pi\) | ||||
−0.629100 | + | 0.777324i | \(0.716576\pi\) | |||||||
\(200\) | 2.57732 | 0.182244 | ||||||||
\(201\) | 0.818172 | 0.0577094 | ||||||||
\(202\) | −15.3021 | −1.07665 | ||||||||
\(203\) | 26.2935 | 1.84544 | ||||||||
\(204\) | −0.758791 | −0.0531260 | ||||||||
\(205\) | −10.1782 | −0.710879 | ||||||||
\(206\) | 4.57448 | 0.318719 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.13082 | −0.286421 | ||||||||
\(209\) | −10.0390 | −0.694410 | ||||||||
\(210\) | −5.06891 | −0.349788 | ||||||||
\(211\) | 1.12533 | 0.0774707 | 0.0387353 | − | 0.999250i | \(-0.487667\pi\) | ||||
0.0387353 | + | 0.999250i | \(0.487667\pi\) | |||||||
\(212\) | 0.331903 | 0.0227952 | ||||||||
\(213\) | −7.34757 | −0.503447 | ||||||||
\(214\) | 2.60622 | 0.178158 | ||||||||
\(215\) | −8.92948 | −0.608985 | ||||||||
\(216\) | −2.57732 | −0.175364 | ||||||||
\(217\) | −18.9622 | −1.28724 | ||||||||
\(218\) | −10.9934 | −0.744569 | ||||||||
\(219\) | −13.6141 | −0.919954 | ||||||||
\(220\) | 0.356711 | 0.0240495 | ||||||||
\(221\) | 2.30907 | 0.155325 | ||||||||
\(222\) | 8.62678 | 0.578992 | ||||||||
\(223\) | −4.70094 | −0.314798 | −0.157399 | − | 0.987535i | \(-0.550311\pi\) | ||||
−0.157399 | + | 0.987535i | \(0.550311\pi\) | |||||||
\(224\) | 5.64201 | 0.376972 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 24.0280 | 1.59832 | ||||||||
\(227\) | 11.6840 | 0.775497 | 0.387748 | − | 0.921765i | \(-0.373253\pi\) | ||||
0.387748 | + | 0.921765i | \(0.373253\pi\) | |||||||
\(228\) | −2.54811 | −0.168753 | ||||||||
\(229\) | −19.7306 | −1.30384 | −0.651918 | − | 0.758289i | \(-0.726035\pi\) | ||||
−0.651918 | + | 0.758289i | \(0.726035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.96150 | 0.260648 | ||||||||
\(232\) | 20.2792 | 1.33139 | ||||||||
\(233\) | 3.50451 | 0.229588 | 0.114794 | − | 0.993389i | \(-0.463379\pi\) | ||||
0.114794 | + | 0.993389i | \(0.463379\pi\) | |||||||
\(234\) | −1.38895 | −0.0907987 | ||||||||
\(235\) | 7.20823 | 0.470213 | ||||||||
\(236\) | −1.03780 | −0.0675549 | ||||||||
\(237\) | −15.6680 | −1.01775 | ||||||||
\(238\) | −12.7824 | −0.828563 | ||||||||
\(239\) | −5.64390 | −0.365074 | −0.182537 | − | 0.983199i | \(-0.558431\pi\) | ||||
−0.182537 | + | 0.983199i | \(0.558431\pi\) | |||||||
\(240\) | −4.51126 | −0.291201 | ||||||||
\(241\) | 9.80570 | 0.631641 | 0.315820 | − | 0.948819i | \(-0.397720\pi\) | ||||
0.315820 | + | 0.948819i | \(0.397720\pi\) | |||||||
\(242\) | 14.5538 | 0.935556 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.35153 | 0.0865227 | ||||||||
\(245\) | −4.16687 | −0.266212 | ||||||||
\(246\) | 15.4391 | 0.984360 | ||||||||
\(247\) | 7.75414 | 0.493384 | ||||||||
\(248\) | −14.6248 | −0.928677 | ||||||||
\(249\) | −6.60930 | −0.418847 | ||||||||
\(250\) | 1.51687 | 0.0959354 | ||||||||
\(251\) | −15.8115 | −0.998013 | −0.499007 | − | 0.866598i | \(-0.666302\pi\) | ||||
−0.499007 | + | 0.866598i | \(0.666302\pi\) | |||||||
\(252\) | 1.00552 | 0.0633415 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 11.3879 | 0.714541 | ||||||||
\(255\) | 2.52173 | 0.157917 | ||||||||
\(256\) | 7.06634 | 0.441647 | ||||||||
\(257\) | −23.3700 | −1.45778 | −0.728891 | − | 0.684630i | \(-0.759964\pi\) | ||||
−0.728891 | + | 0.684630i | \(0.759964\pi\) | |||||||
\(258\) | 13.5449 | 0.843267 | ||||||||
\(259\) | 19.0049 | 1.18091 | ||||||||
\(260\) | −0.275525 | −0.0170874 | ||||||||
\(261\) | 7.86833 | 0.487038 | ||||||||
\(262\) | 27.7869 | 1.71668 | ||||||||
\(263\) | 19.2160 | 1.18491 | 0.592455 | − | 0.805604i | \(-0.298159\pi\) | ||||
0.592455 | + | 0.805604i | \(0.298159\pi\) | |||||||
\(264\) | 3.05536 | 0.188044 | ||||||||
\(265\) | −1.10303 | −0.0677589 | ||||||||
\(266\) | −42.9249 | −2.63190 | ||||||||
\(267\) | 9.17352 | 0.561410 | ||||||||
\(268\) | −0.246188 | −0.0150383 | ||||||||
\(269\) | −24.7222 | −1.50734 | −0.753669 | − | 0.657254i | \(-0.771718\pi\) | ||||
−0.753669 | + | 0.657254i | \(0.771718\pi\) | |||||||
\(270\) | −1.51687 | −0.0923139 | ||||||||
\(271\) | −13.6555 | −0.829511 | −0.414756 | − | 0.909933i | \(-0.636133\pi\) | ||||
−0.414756 | + | 0.909933i | \(0.636133\pi\) | |||||||
\(272\) | −11.3762 | −0.689783 | ||||||||
\(273\) | −3.05988 | −0.185192 | ||||||||
\(274\) | −20.4379 | −1.23470 | ||||||||
\(275\) | −1.18548 | −0.0714871 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.90029 | 0.354514 | 0.177257 | − | 0.984165i | \(-0.443278\pi\) | ||||
0.177257 | + | 0.984165i | \(0.443278\pi\) | |||||||
\(278\) | −26.1589 | −1.56890 | ||||||||
\(279\) | −5.67444 | −0.339720 | ||||||||
\(280\) | −8.61259 | −0.514700 | ||||||||
\(281\) | −18.6057 | −1.10992 | −0.554961 | − | 0.831876i | \(-0.687267\pi\) | ||||
−0.554961 | + | 0.831876i | \(0.687267\pi\) | |||||||
\(282\) | −10.9340 | −0.651108 | ||||||||
\(283\) | −11.9011 | −0.707449 | −0.353725 | − | 0.935350i | \(-0.615085\pi\) | ||||
−0.353725 | + | 0.935350i | \(0.615085\pi\) | |||||||
\(284\) | 2.21089 | 0.131192 | ||||||||
\(285\) | 8.46827 | 0.501617 | ||||||||
\(286\) | 1.64658 | 0.0973640 | ||||||||
\(287\) | 34.0125 | 2.00769 | ||||||||
\(288\) | 1.68837 | 0.0994882 | ||||||||
\(289\) | −10.6409 | −0.625933 | ||||||||
\(290\) | 11.9353 | 0.700862 | ||||||||
\(291\) | 3.08867 | 0.181061 | ||||||||
\(292\) | 4.09648 | 0.239728 | ||||||||
\(293\) | −6.70436 | −0.391673 | −0.195837 | − | 0.980637i | \(-0.562742\pi\) | ||||
−0.195837 | + | 0.980637i | \(0.562742\pi\) | |||||||
\(294\) | 6.32062 | 0.368626 | ||||||||
\(295\) | 3.44898 | 0.200807 | ||||||||
\(296\) | 14.6578 | 0.851965 | ||||||||
\(297\) | 1.18548 | 0.0687885 | ||||||||
\(298\) | 7.16707 | 0.415177 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.300900 | −0.0173725 | ||||||||
\(301\) | 29.8395 | 1.71992 | ||||||||
\(302\) | −6.40281 | −0.368440 | ||||||||
\(303\) | −10.0879 | −0.579537 | ||||||||
\(304\) | −38.2026 | −2.19107 | ||||||||
\(305\) | −4.49161 | −0.257189 | ||||||||
\(306\) | −3.82515 | −0.218669 | ||||||||
\(307\) | −6.77351 | −0.386585 | −0.193292 | − | 0.981141i | \(-0.561917\pi\) | ||||
−0.193292 | + | 0.981141i | \(0.561917\pi\) | |||||||
\(308\) | −1.19202 | −0.0679215 | ||||||||
\(309\) | 3.01573 | 0.171559 | ||||||||
\(310\) | −8.60740 | −0.488867 | ||||||||
\(311\) | 23.7189 | 1.34497 | 0.672487 | − | 0.740109i | \(-0.265226\pi\) | ||||
0.672487 | + | 0.740109i | \(0.265226\pi\) | |||||||
\(312\) | −2.35997 | −0.133607 | ||||||||
\(313\) | 5.87032 | 0.331810 | 0.165905 | − | 0.986142i | \(-0.446945\pi\) | ||||
0.165905 | + | 0.986142i | \(0.446945\pi\) | |||||||
\(314\) | −29.0794 | −1.64104 | ||||||||
\(315\) | −3.34169 | −0.188283 | ||||||||
\(316\) | 4.71451 | 0.265212 | ||||||||
\(317\) | 1.26758 | 0.0711944 | 0.0355972 | − | 0.999366i | \(-0.488667\pi\) | ||||
0.0355972 | + | 0.999366i | \(0.488667\pi\) | |||||||
\(318\) | 1.67316 | 0.0938262 | ||||||||
\(319\) | −9.32775 | −0.522254 | ||||||||
\(320\) | −6.46148 | −0.361208 | ||||||||
\(321\) | 1.71816 | 0.0958982 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.3547 | 1.18821 | ||||||||
\(324\) | 0.300900 | 0.0167167 | ||||||||
\(325\) | 0.915669 | 0.0507922 | ||||||||
\(326\) | 27.6680 | 1.53239 | ||||||||
\(327\) | −7.24743 | −0.400784 | ||||||||
\(328\) | 26.2326 | 1.44845 | ||||||||
\(329\) | −24.0877 | −1.32800 | ||||||||
\(330\) | 1.79822 | 0.0989888 | ||||||||
\(331\) | −0.0750196 | −0.00412345 | −0.00206172 | − | 0.999998i | \(-0.500656\pi\) | ||||
−0.00206172 | + | 0.999998i | \(0.500656\pi\) | |||||||
\(332\) | 1.98874 | 0.109146 | ||||||||
\(333\) | 5.68722 | 0.311658 | ||||||||
\(334\) | −5.99000 | −0.327758 | ||||||||
\(335\) | 0.818172 | 0.0447015 | ||||||||
\(336\) | 15.0752 | 0.822421 | ||||||||
\(337\) | 5.29621 | 0.288503 | 0.144252 | − | 0.989541i | \(-0.453923\pi\) | ||||
0.144252 | + | 0.989541i | \(0.453923\pi\) | |||||||
\(338\) | 18.4475 | 1.00341 | ||||||||
\(339\) | 15.8405 | 0.860336 | ||||||||
\(340\) | −0.758791 | −0.0411512 | ||||||||
\(341\) | 6.72693 | 0.364284 | ||||||||
\(342\) | −12.8453 | −0.694594 | ||||||||
\(343\) | −9.46742 | −0.511193 | ||||||||
\(344\) | 23.0141 | 1.24084 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.69996 | −0.360192 | ||||||||
\(347\) | 10.3576 | 0.556027 | 0.278013 | − | 0.960577i | \(-0.410324\pi\) | ||||
0.278013 | + | 0.960577i | \(0.410324\pi\) | |||||||
\(348\) | −2.36758 | −0.126916 | ||||||||
\(349\) | −9.36736 | −0.501424 | −0.250712 | − | 0.968062i | \(-0.580665\pi\) | ||||
−0.250712 | + | 0.968062i | \(0.580665\pi\) | |||||||
\(350\) | −5.06891 | −0.270945 | ||||||||
\(351\) | −0.915669 | −0.0488748 | ||||||||
\(352\) | −2.00153 | −0.106682 | ||||||||
\(353\) | 0.463085 | 0.0246475 | 0.0123238 | − | 0.999924i | \(-0.496077\pi\) | ||||
0.0123238 | + | 0.999924i | \(0.496077\pi\) | |||||||
\(354\) | −5.23166 | −0.278059 | ||||||||
\(355\) | −7.34757 | −0.389969 | ||||||||
\(356\) | −2.76032 | −0.146296 | ||||||||
\(357\) | −8.42685 | −0.445996 | ||||||||
\(358\) | 9.54586 | 0.504514 | ||||||||
\(359\) | −30.2683 | −1.59750 | −0.798749 | − | 0.601665i | \(-0.794504\pi\) | ||||
−0.798749 | + | 0.601665i | \(0.794504\pi\) | |||||||
\(360\) | −2.57732 | −0.135837 | ||||||||
\(361\) | 52.7117 | 2.77430 | ||||||||
\(362\) | −19.6060 | −1.03047 | ||||||||
\(363\) | 9.59464 | 0.503588 | ||||||||
\(364\) | 0.920719 | 0.0482588 | ||||||||
\(365\) | −13.6141 | −0.712593 | ||||||||
\(366\) | 6.81320 | 0.356132 | ||||||||
\(367\) | −7.18380 | −0.374991 | −0.187496 | − | 0.982265i | \(-0.560037\pi\) | ||||
−0.187496 | + | 0.982265i | \(0.560037\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.1782 | 0.529858 | ||||||||
\(370\) | 8.62678 | 0.448485 | ||||||||
\(371\) | 3.68600 | 0.191367 | ||||||||
\(372\) | 1.70744 | 0.0885267 | ||||||||
\(373\) | −0.741630 | −0.0384001 | −0.0192001 | − | 0.999816i | \(-0.506112\pi\) | ||||
−0.0192001 | + | 0.999816i | \(0.506112\pi\) | |||||||
\(374\) | 4.53463 | 0.234480 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −18.5779 | −0.958081 | ||||||||
\(377\) | 7.20479 | 0.371066 | ||||||||
\(378\) | 5.06891 | 0.260717 | ||||||||
\(379\) | −25.9624 | −1.33360 | −0.666800 | − | 0.745237i | \(-0.732336\pi\) | ||||
−0.666800 | + | 0.745237i | \(0.732336\pi\) | |||||||
\(380\) | −2.54811 | −0.130715 | ||||||||
\(381\) | 7.50750 | 0.384621 | ||||||||
\(382\) | 40.2095 | 2.05730 | ||||||||
\(383\) | 2.26902 | 0.115942 | 0.0579708 | − | 0.998318i | \(-0.481537\pi\) | ||||
0.0579708 | + | 0.998318i | \(0.481537\pi\) | |||||||
\(384\) | 13.1780 | 0.672486 | ||||||||
\(385\) | 3.96150 | 0.201897 | ||||||||
\(386\) | −11.3176 | −0.576051 | ||||||||
\(387\) | 8.92948 | 0.453911 | ||||||||
\(388\) | −0.929383 | −0.0471823 | ||||||||
\(389\) | 0.331625 | 0.0168140 | 0.00840702 | − | 0.999965i | \(-0.497324\pi\) | ||||
0.00840702 | + | 0.999965i | \(0.497324\pi\) | |||||||
\(390\) | −1.38895 | −0.0703324 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 10.7394 | 0.542419 | ||||||||
\(393\) | 18.3185 | 0.924047 | ||||||||
\(394\) | 11.9614 | 0.602608 | ||||||||
\(395\) | −15.6680 | −0.788343 | ||||||||
\(396\) | −0.356711 | −0.0179254 | ||||||||
\(397\) | −33.6099 | −1.68683 | −0.843417 | − | 0.537260i | \(-0.819459\pi\) | ||||
−0.843417 | + | 0.537260i | \(0.819459\pi\) | |||||||
\(398\) | 26.9231 | 1.34953 | ||||||||
\(399\) | −28.2983 | −1.41669 | ||||||||
\(400\) | −4.51126 | −0.225563 | ||||||||
\(401\) | −2.75774 | −0.137715 | −0.0688576 | − | 0.997626i | \(-0.521935\pi\) | ||||
−0.0688576 | + | 0.997626i | \(0.521935\pi\) | |||||||
\(402\) | −1.24106 | −0.0618985 | ||||||||
\(403\) | −5.19591 | −0.258827 | ||||||||
\(404\) | 3.03546 | 0.151020 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | −39.8839 | −1.97940 | ||||||||
\(407\) | −6.74208 | −0.334193 | ||||||||
\(408\) | −6.49931 | −0.321764 | ||||||||
\(409\) | 24.9515 | 1.23377 | 0.616886 | − | 0.787052i | \(-0.288394\pi\) | ||||
0.616886 | + | 0.787052i | \(0.288394\pi\) | |||||||
\(410\) | 15.4391 | 0.762482 | ||||||||
\(411\) | −13.4737 | −0.664608 | ||||||||
\(412\) | −0.907436 | −0.0447062 | ||||||||
\(413\) | −11.5254 | −0.567128 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.60930 | −0.324438 | ||||||||
\(416\) | 1.54599 | 0.0757983 | ||||||||
\(417\) | −17.2453 | −0.844504 | ||||||||
\(418\) | 15.2278 | 0.744817 | ||||||||
\(419\) | −26.2127 | −1.28058 | −0.640288 | − | 0.768135i | \(-0.721185\pi\) | ||||
−0.640288 | + | 0.768135i | \(0.721185\pi\) | |||||||
\(420\) | 1.00552 | 0.0490641 | ||||||||
\(421\) | 25.2032 | 1.22833 | 0.614164 | − | 0.789178i | \(-0.289493\pi\) | ||||
0.614164 | + | 0.789178i | \(0.289493\pi\) | |||||||
\(422\) | −1.70698 | −0.0830943 | ||||||||
\(423\) | −7.20823 | −0.350476 | ||||||||
\(424\) | 2.84287 | 0.138062 | ||||||||
\(425\) | 2.52173 | 0.122322 | ||||||||
\(426\) | 11.1453 | 0.539993 | ||||||||
\(427\) | 15.0096 | 0.726364 | ||||||||
\(428\) | −0.516994 | −0.0249899 | ||||||||
\(429\) | 1.08551 | 0.0524088 | ||||||||
\(430\) | 13.5449 | 0.653192 | ||||||||
\(431\) | 10.6296 | 0.512010 | 0.256005 | − | 0.966675i | \(-0.417594\pi\) | ||||
0.256005 | + | 0.966675i | \(0.417594\pi\) | |||||||
\(432\) | 4.51126 | 0.217048 | ||||||||
\(433\) | 4.76299 | 0.228895 | 0.114447 | − | 0.993429i | \(-0.463490\pi\) | ||||
0.114447 | + | 0.993429i | \(0.463490\pi\) | |||||||
\(434\) | 28.7632 | 1.38068 | ||||||||
\(435\) | 7.86833 | 0.377258 | ||||||||
\(436\) | 2.18076 | 0.104439 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 20.6508 | 0.986734 | ||||||||
\(439\) | 24.9611 | 1.19133 | 0.595665 | − | 0.803233i | \(-0.296889\pi\) | ||||
0.595665 | + | 0.803233i | \(0.296889\pi\) | |||||||
\(440\) | 3.05536 | 0.145658 | ||||||||
\(441\) | 4.16687 | 0.198423 | ||||||||
\(442\) | −3.50257 | −0.166600 | ||||||||
\(443\) | −11.1218 | −0.528413 | −0.264206 | − | 0.964466i | \(-0.585110\pi\) | ||||
−0.264206 | + | 0.964466i | \(0.585110\pi\) | |||||||
\(444\) | −1.71129 | −0.0812141 | ||||||||
\(445\) | 9.17352 | 0.434866 | ||||||||
\(446\) | 7.13073 | 0.337650 | ||||||||
\(447\) | 4.72490 | 0.223480 | ||||||||
\(448\) | 21.5922 | 1.02014 | ||||||||
\(449\) | 19.7792 | 0.933436 | 0.466718 | − | 0.884406i | \(-0.345436\pi\) | ||||
0.466718 | + | 0.884406i | \(0.345436\pi\) | |||||||
\(450\) | −1.51687 | −0.0715060 | ||||||||
\(451\) | −12.0661 | −0.568170 | ||||||||
\(452\) | −4.76640 | −0.224193 | ||||||||
\(453\) | −4.22106 | −0.198323 | ||||||||
\(454\) | −17.7232 | −0.831791 | ||||||||
\(455\) | −3.05988 | −0.143449 | ||||||||
\(456\) | −21.8254 | −1.02207 | ||||||||
\(457\) | 4.78689 | 0.223921 | 0.111961 | − | 0.993713i | \(-0.464287\pi\) | ||||
0.111961 | + | 0.993713i | \(0.464287\pi\) | |||||||
\(458\) | 29.9288 | 1.39848 | ||||||||
\(459\) | −2.52173 | −0.117704 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15.4721 | −0.720607 | −0.360303 | − | 0.932835i | \(-0.617327\pi\) | ||||
−0.360303 | + | 0.932835i | \(0.617327\pi\) | |||||||
\(462\) | −6.00909 | −0.279568 | ||||||||
\(463\) | 36.9213 | 1.71588 | 0.857940 | − | 0.513751i | \(-0.171744\pi\) | ||||
0.857940 | + | 0.513751i | \(0.171744\pi\) | |||||||
\(464\) | −35.4961 | −1.64786 | ||||||||
\(465\) | −5.67444 | −0.263146 | ||||||||
\(466\) | −5.31590 | −0.246254 | ||||||||
\(467\) | 12.8660 | 0.595369 | 0.297685 | − | 0.954664i | \(-0.403786\pi\) | ||||
0.297685 | + | 0.954664i | \(0.403786\pi\) | |||||||
\(468\) | 0.275525 | 0.0127362 | ||||||||
\(469\) | −2.73407 | −0.126248 | ||||||||
\(470\) | −10.9340 | −0.504346 | ||||||||
\(471\) | −19.1706 | −0.883336 | ||||||||
\(472\) | −8.88910 | −0.409154 | ||||||||
\(473\) | −10.5857 | −0.486731 | ||||||||
\(474\) | 23.7664 | 1.09162 | ||||||||
\(475\) | 8.46827 | 0.388551 | ||||||||
\(476\) | 2.53564 | 0.116221 | ||||||||
\(477\) | 1.10303 | 0.0505045 | ||||||||
\(478\) | 8.56107 | 0.391574 | ||||||||
\(479\) | −9.74079 | −0.445068 | −0.222534 | − | 0.974925i | \(-0.571433\pi\) | ||||
−0.222534 | + | 0.974925i | \(0.571433\pi\) | |||||||
\(480\) | 1.68837 | 0.0770632 | ||||||||
\(481\) | 5.20761 | 0.237447 | ||||||||
\(482\) | −14.8740 | −0.677492 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.88703 | −0.131229 | ||||||||
\(485\) | 3.08867 | 0.140249 | ||||||||
\(486\) | 1.51687 | 0.0688067 | ||||||||
\(487\) | 39.8060 | 1.80378 | 0.901892 | − | 0.431962i | \(-0.142179\pi\) | ||||
0.901892 | + | 0.431962i | \(0.142179\pi\) | |||||||
\(488\) | 11.5763 | 0.524035 | ||||||||
\(489\) | 18.2402 | 0.824850 | ||||||||
\(490\) | 6.32062 | 0.285536 | ||||||||
\(491\) | 15.6081 | 0.704384 | 0.352192 | − | 0.935928i | \(-0.385436\pi\) | ||||
0.352192 | + | 0.935928i | \(0.385436\pi\) | |||||||
\(492\) | −3.06264 | −0.138074 | ||||||||
\(493\) | 19.8418 | 0.893632 | ||||||||
\(494\) | −11.7620 | −0.529199 | ||||||||
\(495\) | 1.18548 | 0.0532833 | ||||||||
\(496\) | 25.5989 | 1.14942 | ||||||||
\(497\) | 24.5533 | 1.10137 | ||||||||
\(498\) | 10.0255 | 0.449251 | ||||||||
\(499\) | −34.4712 | −1.54314 | −0.771571 | − | 0.636143i | \(-0.780529\pi\) | ||||
−0.771571 | + | 0.636143i | \(0.780529\pi\) | |||||||
\(500\) | −0.300900 | −0.0134567 | ||||||||
\(501\) | −3.94892 | −0.176425 | ||||||||
\(502\) | 23.9840 | 1.07046 | ||||||||
\(503\) | 32.9419 | 1.46881 | 0.734404 | − | 0.678713i | \(-0.237462\pi\) | ||||
0.734404 | + | 0.678713i | \(0.237462\pi\) | |||||||
\(504\) | 8.61259 | 0.383635 | ||||||||
\(505\) | −10.0879 | −0.448907 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.1615 | 0.540113 | ||||||||
\(508\) | −2.25901 | −0.100227 | ||||||||
\(509\) | 19.7488 | 0.875352 | 0.437676 | − | 0.899133i | \(-0.355802\pi\) | ||||
0.437676 | + | 0.899133i | \(0.355802\pi\) | |||||||
\(510\) | −3.82515 | −0.169380 | ||||||||
\(511\) | 45.4940 | 2.01254 | ||||||||
\(512\) | 15.6372 | 0.691074 | ||||||||
\(513\) | −8.46827 | −0.373883 | ||||||||
\(514\) | 35.4493 | 1.56360 | ||||||||
\(515\) | 3.01573 | 0.132889 | ||||||||
\(516\) | −2.68688 | −0.118283 | ||||||||
\(517\) | 8.54521 | 0.375818 | ||||||||
\(518\) | −28.8280 | −1.26663 | ||||||||
\(519\) | −4.41696 | −0.193883 | ||||||||
\(520\) | −2.35997 | −0.103492 | ||||||||
\(521\) | −5.67485 | −0.248620 | −0.124310 | − | 0.992243i | \(-0.539672\pi\) | ||||
−0.124310 | + | 0.992243i | \(0.539672\pi\) | |||||||
\(522\) | −11.9353 | −0.522392 | ||||||||
\(523\) | −24.2711 | −1.06130 | −0.530651 | − | 0.847590i | \(-0.678053\pi\) | ||||
−0.530651 | + | 0.847590i | \(0.678053\pi\) | |||||||
\(524\) | −5.51205 | −0.240795 | ||||||||
\(525\) | −3.34169 | −0.145843 | ||||||||
\(526\) | −29.1482 | −1.27092 | ||||||||
\(527\) | −14.3094 | −0.623329 | ||||||||
\(528\) | −5.34801 | −0.232742 | ||||||||
\(529\) | 0 | 0 | ||||||||
\(530\) | 1.67316 | 0.0726775 | ||||||||
\(531\) | −3.44898 | −0.149673 | ||||||||
\(532\) | 8.51498 | 0.369171 | ||||||||
\(533\) | 9.31990 | 0.403690 | ||||||||
\(534\) | −13.9151 | −0.602163 | ||||||||
\(535\) | 1.71816 | 0.0742824 | ||||||||
\(536\) | −2.10869 | −0.0910814 | ||||||||
\(537\) | 6.29312 | 0.271568 | ||||||||
\(538\) | 37.5004 | 1.61676 | ||||||||
\(539\) | −4.93974 | −0.212770 | ||||||||
\(540\) | 0.300900 | 0.0129487 | ||||||||
\(541\) | −24.7491 | −1.06405 | −0.532023 | − | 0.846730i | \(-0.678568\pi\) | ||||
−0.532023 | + | 0.846730i | \(0.678568\pi\) | |||||||
\(542\) | 20.7136 | 0.889726 | ||||||||
\(543\) | −12.9253 | −0.554677 | ||||||||
\(544\) | 4.25762 | 0.182544 | ||||||||
\(545\) | −7.24743 | −0.310446 | ||||||||
\(546\) | 4.64145 | 0.198636 | ||||||||
\(547\) | 10.0536 | 0.429860 | 0.214930 | − | 0.976629i | \(-0.431048\pi\) | ||||
0.214930 | + | 0.976629i | \(0.431048\pi\) | |||||||
\(548\) | 4.05424 | 0.173188 | ||||||||
\(549\) | 4.49161 | 0.191697 | ||||||||
\(550\) | 1.79822 | 0.0766764 | ||||||||
\(551\) | 66.6312 | 2.83858 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 52.3576 | 2.22647 | ||||||||
\(554\) | −8.94999 | −0.380249 | ||||||||
\(555\) | 5.68722 | 0.241409 | ||||||||
\(556\) | 5.18911 | 0.220067 | ||||||||
\(557\) | 42.0867 | 1.78327 | 0.891635 | − | 0.452755i | \(-0.149559\pi\) | ||||
0.891635 | + | 0.452755i | \(0.149559\pi\) | |||||||
\(558\) | 8.60740 | 0.364380 | ||||||||
\(559\) | 8.17645 | 0.345827 | ||||||||
\(560\) | 15.0752 | 0.637044 | ||||||||
\(561\) | 2.98946 | 0.126215 | ||||||||
\(562\) | 28.2224 | 1.19049 | ||||||||
\(563\) | 34.0940 | 1.43689 | 0.718445 | − | 0.695584i | \(-0.244854\pi\) | ||||
0.718445 | + | 0.695584i | \(0.244854\pi\) | |||||||
\(564\) | 2.16896 | 0.0913297 | ||||||||
\(565\) | 15.8405 | 0.666413 | ||||||||
\(566\) | 18.0525 | 0.758803 | ||||||||
\(567\) | 3.34169 | 0.140338 | ||||||||
\(568\) | 18.9370 | 0.794580 | ||||||||
\(569\) | 4.73609 | 0.198547 | 0.0992736 | − | 0.995060i | \(-0.468348\pi\) | ||||
0.0992736 | + | 0.995060i | \(0.468348\pi\) | |||||||
\(570\) | −12.8453 | −0.538030 | ||||||||
\(571\) | −10.6327 | −0.444966 | −0.222483 | − | 0.974937i | \(-0.571416\pi\) | ||||
−0.222483 | + | 0.974937i | \(0.571416\pi\) | |||||||
\(572\) | −0.326630 | −0.0136571 | ||||||||
\(573\) | 26.5082 | 1.10739 | ||||||||
\(574\) | −51.5926 | −2.15343 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.46148 | 0.269228 | ||||||||
\(577\) | 31.3949 | 1.30699 | 0.653493 | − | 0.756933i | \(-0.273303\pi\) | ||||
0.653493 | + | 0.756933i | \(0.273303\pi\) | |||||||
\(578\) | 16.1408 | 0.671369 | ||||||||
\(579\) | −7.46115 | −0.310075 | ||||||||
\(580\) | −2.36758 | −0.0983086 | ||||||||
\(581\) | 22.0862 | 0.916290 | ||||||||
\(582\) | −4.68512 | −0.194204 | ||||||||
\(583\) | −1.30762 | −0.0541563 | ||||||||
\(584\) | 35.0878 | 1.45194 | ||||||||
\(585\) | −0.915669 | −0.0378583 | ||||||||
\(586\) | 10.1697 | 0.420105 | ||||||||
\(587\) | 37.3199 | 1.54036 | 0.770178 | − | 0.637829i | \(-0.220167\pi\) | ||||
0.770178 | + | 0.637829i | \(0.220167\pi\) | |||||||
\(588\) | −1.25381 | −0.0517064 | ||||||||
\(589\) | −48.0527 | −1.97998 | ||||||||
\(590\) | −5.23166 | −0.215384 | ||||||||
\(591\) | 7.88559 | 0.324370 | ||||||||
\(592\) | −25.6565 | −1.05448 | ||||||||
\(593\) | −12.3873 | −0.508684 | −0.254342 | − | 0.967114i | \(-0.581859\pi\) | ||||
−0.254342 | + | 0.967114i | \(0.581859\pi\) | |||||||
\(594\) | −1.79822 | −0.0737819 | ||||||||
\(595\) | −8.42685 | −0.345467 | ||||||||
\(596\) | −1.42172 | −0.0582361 | ||||||||
\(597\) | 17.7491 | 0.726422 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.67194 | 0.0683137 | 0.0341569 | − | 0.999416i | \(-0.489125\pi\) | ||||
0.0341569 | + | 0.999416i | \(0.489125\pi\) | |||||||
\(600\) | −2.57732 | −0.105219 | ||||||||
\(601\) | 40.3053 | 1.64409 | 0.822043 | − | 0.569425i | \(-0.192834\pi\) | ||||
0.822043 | + | 0.569425i | \(0.192834\pi\) | |||||||
\(602\) | −45.2627 | −1.84477 | ||||||||
\(603\) | −0.818172 | −0.0333185 | ||||||||
\(604\) | 1.27012 | 0.0516804 | ||||||||
\(605\) | 9.59464 | 0.390078 | ||||||||
\(606\) | 15.3021 | 0.621606 | ||||||||
\(607\) | 47.1147 | 1.91233 | 0.956163 | − | 0.292835i | \(-0.0945988\pi\) | ||||
0.956163 | + | 0.292835i | \(0.0945988\pi\) | |||||||
\(608\) | 14.2976 | 0.579844 | ||||||||
\(609\) | −26.2935 | −1.06547 | ||||||||
\(610\) | 6.81320 | 0.275858 | ||||||||
\(611\) | −6.60035 | −0.267022 | ||||||||
\(612\) | 0.758791 | 0.0306723 | ||||||||
\(613\) | 4.11013 | 0.166006 | 0.0830032 | − | 0.996549i | \(-0.473549\pi\) | ||||
0.0830032 | + | 0.996549i | \(0.473549\pi\) | |||||||
\(614\) | 10.2745 | 0.414647 | ||||||||
\(615\) | 10.1782 | 0.410426 | ||||||||
\(616\) | −10.2100 | −0.411374 | ||||||||
\(617\) | 15.5339 | 0.625370 | 0.312685 | − | 0.949857i | \(-0.398772\pi\) | ||||
0.312685 | + | 0.949857i | \(0.398772\pi\) | |||||||
\(618\) | −4.57448 | −0.184013 | ||||||||
\(619\) | 6.49312 | 0.260981 | 0.130490 | − | 0.991450i | \(-0.458345\pi\) | ||||
0.130490 | + | 0.991450i | \(0.458345\pi\) | |||||||
\(620\) | 1.70744 | 0.0685725 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −35.9785 | −1.44261 | ||||||||
\(623\) | −30.6550 | −1.22817 | ||||||||
\(624\) | 4.13082 | 0.165365 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.90452 | −0.355896 | ||||||||
\(627\) | 10.0390 | 0.400918 | ||||||||
\(628\) | 5.76845 | 0.230186 | ||||||||
\(629\) | 14.3417 | 0.571839 | ||||||||
\(630\) | 5.06891 | 0.201950 | ||||||||
\(631\) | 41.2351 | 1.64154 | 0.820772 | − | 0.571256i | \(-0.193544\pi\) | ||||
0.820772 | + | 0.571256i | \(0.193544\pi\) | |||||||
\(632\) | 40.3814 | 1.60629 | ||||||||
\(633\) | −1.12533 | −0.0447277 | ||||||||
\(634\) | −1.92276 | −0.0763625 | ||||||||
\(635\) | 7.50750 | 0.297926 | ||||||||
\(636\) | −0.331903 | −0.0131608 | ||||||||
\(637\) | 3.81548 | 0.151175 | ||||||||
\(638\) | 14.1490 | 0.560164 | ||||||||
\(639\) | 7.34757 | 0.290665 | ||||||||
\(640\) | 13.1780 | 0.520905 | ||||||||
\(641\) | −30.8144 | −1.21710 | −0.608548 | − | 0.793517i | \(-0.708248\pi\) | ||||
−0.608548 | + | 0.793517i | \(0.708248\pi\) | |||||||
\(642\) | −2.60622 | −0.102859 | ||||||||
\(643\) | 4.30931 | 0.169943 | 0.0849713 | − | 0.996383i | \(-0.472920\pi\) | ||||
0.0849713 | + | 0.996383i | \(0.472920\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.92948 | 0.351598 | ||||||||
\(646\) | −32.3924 | −1.27446 | ||||||||
\(647\) | −35.2005 | −1.38388 | −0.691938 | − | 0.721957i | \(-0.743243\pi\) | ||||
−0.691938 | + | 0.721957i | \(0.743243\pi\) | |||||||
\(648\) | 2.57732 | 0.101247 | ||||||||
\(649\) | 4.08869 | 0.160495 | ||||||||
\(650\) | −1.38895 | −0.0544792 | ||||||||
\(651\) | 18.9622 | 0.743187 | ||||||||
\(652\) | −5.48848 | −0.214946 | ||||||||
\(653\) | −39.0783 | −1.52925 | −0.764625 | − | 0.644475i | \(-0.777076\pi\) | ||||
−0.764625 | + | 0.644475i | \(0.777076\pi\) | |||||||
\(654\) | 10.9934 | 0.429877 | ||||||||
\(655\) | 18.3185 | 0.715764 | ||||||||
\(656\) | −45.9167 | −1.79275 | ||||||||
\(657\) | 13.6141 | 0.531136 | ||||||||
\(658\) | 36.5379 | 1.42439 | ||||||||
\(659\) | −44.5911 | −1.73702 | −0.868512 | − | 0.495668i | \(-0.834923\pi\) | ||||
−0.868512 | + | 0.495668i | \(0.834923\pi\) | |||||||
\(660\) | −0.356711 | −0.0138850 | ||||||||
\(661\) | −41.3256 | −1.60738 | −0.803690 | − | 0.595048i | \(-0.797133\pi\) | ||||
−0.803690 | + | 0.595048i | \(0.797133\pi\) | |||||||
\(662\) | 0.113795 | 0.00442277 | ||||||||
\(663\) | −2.30907 | −0.0896770 | ||||||||
\(664\) | 17.0342 | 0.661057 | ||||||||
\(665\) | −28.2983 | −1.09736 | ||||||||
\(666\) | −8.62678 | −0.334281 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 1.18823 | 0.0459740 | ||||||||
\(669\) | 4.70094 | 0.181749 | ||||||||
\(670\) | −1.24106 | −0.0479464 | ||||||||
\(671\) | −5.32471 | −0.205558 | ||||||||
\(672\) | −5.64201 | −0.217645 | ||||||||
\(673\) | −16.0980 | −0.620533 | −0.310267 | − | 0.950650i | \(-0.600418\pi\) | ||||
−0.310267 | + | 0.950650i | \(0.600418\pi\) | |||||||
\(674\) | −8.03368 | −0.309446 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | −3.65942 | −0.140747 | ||||||||
\(677\) | −18.9140 | −0.726924 | −0.363462 | − | 0.931609i | \(-0.618405\pi\) | ||||
−0.363462 | + | 0.931609i | \(0.618405\pi\) | |||||||
\(678\) | −24.0280 | −0.922788 | ||||||||
\(679\) | −10.3214 | −0.396098 | ||||||||
\(680\) | −6.49931 | −0.249237 | ||||||||
\(681\) | −11.6840 | −0.447733 | ||||||||
\(682\) | −10.2039 | −0.390727 | ||||||||
\(683\) | −13.1889 | −0.504660 | −0.252330 | − | 0.967641i | \(-0.581197\pi\) | ||||
−0.252330 | + | 0.967641i | \(0.581197\pi\) | |||||||
\(684\) | 2.54811 | 0.0974293 | ||||||||
\(685\) | −13.4737 | −0.514803 | ||||||||
\(686\) | 14.3609 | 0.548300 | ||||||||
\(687\) | 19.7306 | 0.752770 | ||||||||
\(688\) | −40.2832 | −1.53578 | ||||||||
\(689\) | 1.01001 | 0.0384785 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.2043 | 1.87182 | 0.935911 | − | 0.352238i | \(-0.114579\pi\) | ||||
0.935911 | + | 0.352238i | \(0.114579\pi\) | |||||||
\(692\) | 1.32907 | 0.0505235 | ||||||||
\(693\) | −3.96150 | −0.150485 | ||||||||
\(694\) | −15.7112 | −0.596389 | ||||||||
\(695\) | −17.2453 | −0.654150 | ||||||||
\(696\) | −20.2792 | −0.768681 | ||||||||
\(697\) | 25.6668 | 0.972200 | ||||||||
\(698\) | 14.2091 | 0.537822 | ||||||||
\(699\) | −3.50451 | −0.132553 | ||||||||
\(700\) | 1.00552 | 0.0380049 | ||||||||
\(701\) | −21.9082 | −0.827463 | −0.413731 | − | 0.910399i | \(-0.635775\pi\) | ||||
−0.413731 | + | 0.910399i | \(0.635775\pi\) | |||||||
\(702\) | 1.38895 | 0.0524227 | ||||||||
\(703\) | 48.1609 | 1.81642 | ||||||||
\(704\) | −7.65995 | −0.288695 | ||||||||
\(705\) | −7.20823 | −0.271478 | ||||||||
\(706\) | −0.702440 | −0.0264367 | ||||||||
\(707\) | 33.7107 | 1.26782 | ||||||||
\(708\) | 1.03780 | 0.0390029 | ||||||||
\(709\) | −49.1126 | −1.84446 | −0.922232 | − | 0.386637i | \(-0.873637\pi\) | ||||
−0.922232 | + | 0.386637i | \(0.873637\pi\) | |||||||
\(710\) | 11.1453 | 0.418277 | ||||||||
\(711\) | 15.6680 | 0.587596 | ||||||||
\(712\) | −23.6431 | −0.886061 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 12.7824 | 0.478371 | ||||||||
\(715\) | 1.08551 | 0.0405957 | ||||||||
\(716\) | −1.89360 | −0.0707673 | ||||||||
\(717\) | 5.64390 | 0.210775 | ||||||||
\(718\) | 45.9131 | 1.71346 | ||||||||
\(719\) | 36.9481 | 1.37793 | 0.688966 | − | 0.724793i | \(-0.258065\pi\) | ||||
0.688966 | + | 0.724793i | \(0.258065\pi\) | |||||||
\(720\) | 4.51126 | 0.168125 | ||||||||
\(721\) | −10.0776 | −0.375311 | ||||||||
\(722\) | −79.9568 | −2.97568 | ||||||||
\(723\) | −9.80570 | −0.364678 | ||||||||
\(724\) | 3.88922 | 0.144542 | ||||||||
\(725\) | 7.86833 | 0.292223 | ||||||||
\(726\) | −14.5538 | −0.540144 | ||||||||
\(727\) | 1.56501 | 0.0580429 | 0.0290215 | − | 0.999579i | \(-0.490761\pi\) | ||||
0.0290215 | + | 0.999579i | \(0.490761\pi\) | |||||||
\(728\) | 7.88628 | 0.292285 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 20.6508 | 0.764321 | ||||||||
\(731\) | 22.5178 | 0.832850 | ||||||||
\(732\) | −1.35153 | −0.0499539 | ||||||||
\(733\) | −2.95045 | −0.108977 | −0.0544886 | − | 0.998514i | \(-0.517353\pi\) | ||||
−0.0544886 | + | 0.998514i | \(0.517353\pi\) | |||||||
\(734\) | 10.8969 | 0.402212 | ||||||||
\(735\) | 4.16687 | 0.153697 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.969926 | 0.0357277 | ||||||||
\(738\) | −15.4391 | −0.568321 | ||||||||
\(739\) | 25.2790 | 0.929903 | 0.464951 | − | 0.885336i | \(-0.346072\pi\) | ||||
0.464951 | + | 0.885336i | \(0.346072\pi\) | |||||||
\(740\) | −1.71129 | −0.0629082 | ||||||||
\(741\) | −7.75414 | −0.284855 | ||||||||
\(742\) | −5.59118 | −0.205259 | ||||||||
\(743\) | −37.8488 | −1.38854 | −0.694269 | − | 0.719716i | \(-0.744272\pi\) | ||||
−0.694269 | + | 0.719716i | \(0.744272\pi\) | |||||||
\(744\) | 14.6248 | 0.536172 | ||||||||
\(745\) | 4.72490 | 0.173107 | ||||||||
\(746\) | 1.12496 | 0.0411876 | ||||||||
\(747\) | 6.60930 | 0.241822 | ||||||||
\(748\) | −0.899531 | −0.0328901 | ||||||||
\(749\) | −5.74154 | −0.209791 | ||||||||
\(750\) | −1.51687 | −0.0553883 | ||||||||
\(751\) | −23.3637 | −0.852553 | −0.426277 | − | 0.904593i | \(-0.640175\pi\) | ||||
−0.426277 | + | 0.904593i | \(0.640175\pi\) | |||||||
\(752\) | 32.5182 | 1.18582 | ||||||||
\(753\) | 15.8115 | 0.576203 | ||||||||
\(754\) | −10.9287 | −0.398001 | ||||||||
\(755\) | −4.22106 | −0.153620 | ||||||||
\(756\) | −1.00552 | −0.0365702 | ||||||||
\(757\) | 31.4175 | 1.14189 | 0.570944 | − | 0.820989i | \(-0.306577\pi\) | ||||
0.570944 | + | 0.820989i | \(0.306577\pi\) | |||||||
\(758\) | 39.3816 | 1.43041 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −21.8254 | −0.791691 | ||||||||
\(761\) | 14.6063 | 0.529478 | 0.264739 | − | 0.964320i | \(-0.414714\pi\) | ||||
0.264739 | + | 0.964320i | \(0.414714\pi\) | |||||||
\(762\) | −11.3879 | −0.412541 | ||||||||
\(763\) | 24.2187 | 0.876774 | ||||||||
\(764\) | −7.97631 | −0.288573 | ||||||||
\(765\) | −2.52173 | −0.0911735 | ||||||||
\(766\) | −3.44181 | −0.124358 | ||||||||
\(767\) | −3.15812 | −0.114033 | ||||||||
\(768\) | −7.06634 | −0.254985 | ||||||||
\(769\) | 7.09022 | 0.255680 | 0.127840 | − | 0.991795i | \(-0.459196\pi\) | ||||
0.127840 | + | 0.991795i | \(0.459196\pi\) | |||||||
\(770\) | −6.00909 | −0.216553 | ||||||||
\(771\) | 23.3700 | 0.841651 | ||||||||
\(772\) | 2.24506 | 0.0808015 | ||||||||
\(773\) | −51.5235 | −1.85317 | −0.926586 | − | 0.376082i | \(-0.877271\pi\) | ||||
−0.926586 | + | 0.376082i | \(0.877271\pi\) | |||||||
\(774\) | −13.5449 | −0.486860 | ||||||||
\(775\) | −5.67444 | −0.203832 | ||||||||
\(776\) | −7.96049 | −0.285765 | ||||||||
\(777\) | −19.0049 | −0.681797 | ||||||||
\(778\) | −0.503032 | −0.0180346 | ||||||||
\(779\) | 86.1921 | 3.08815 | ||||||||
\(780\) | 0.275525 | 0.00986539 | ||||||||
\(781\) | −8.71039 | −0.311682 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.86833 | −0.281191 | ||||||||
\(784\) | −18.7979 | −0.671352 | ||||||||
\(785\) | −19.1706 | −0.684229 | ||||||||
\(786\) | −27.7869 | −0.991124 | ||||||||
\(787\) | −19.5456 | −0.696726 | −0.348363 | − | 0.937360i | \(-0.613262\pi\) | ||||
−0.348363 | + | 0.937360i | \(0.613262\pi\) | |||||||
\(788\) | −2.37278 | −0.0845267 | ||||||||
\(789\) | −19.2160 | −0.684108 | ||||||||
\(790\) | 23.7664 | 0.845569 | ||||||||
\(791\) | −52.9339 | −1.88211 | ||||||||
\(792\) | −3.05536 | −0.108567 | ||||||||
\(793\) | 4.11283 | 0.146051 | ||||||||
\(794\) | 50.9819 | 1.80928 | ||||||||
\(795\) | 1.10303 | 0.0391206 | ||||||||
\(796\) | −5.34071 | −0.189296 | ||||||||
\(797\) | −35.1492 | −1.24505 | −0.622525 | − | 0.782600i | \(-0.713893\pi\) | ||||
−0.622525 | + | 0.782600i | \(0.713893\pi\) | |||||||
\(798\) | 42.9249 | 1.51953 | ||||||||
\(799\) | −18.1772 | −0.643065 | ||||||||
\(800\) | 1.68837 | 0.0596929 | ||||||||
\(801\) | −9.17352 | −0.324130 | ||||||||
\(802\) | 4.18315 | 0.147712 | ||||||||
\(803\) | −16.1392 | −0.569540 | ||||||||
\(804\) | 0.246188 | 0.00868239 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.88153 | 0.277615 | ||||||||
\(807\) | 24.7222 | 0.870262 | ||||||||
\(808\) | 25.9998 | 0.914670 | ||||||||
\(809\) | 7.77663 | 0.273412 | 0.136706 | − | 0.990612i | \(-0.456348\pi\) | ||||
0.136706 | + | 0.990612i | \(0.456348\pi\) | |||||||
\(810\) | 1.51687 | 0.0532974 | ||||||||
\(811\) | 27.2727 | 0.957675 | 0.478837 | − | 0.877904i | \(-0.341058\pi\) | ||||
0.478837 | + | 0.877904i | \(0.341058\pi\) | |||||||
\(812\) | 7.91173 | 0.277647 | ||||||||
\(813\) | 13.6555 | 0.478919 | ||||||||
\(814\) | 10.2269 | 0.358452 | ||||||||
\(815\) | 18.2402 | 0.638926 | ||||||||
\(816\) | 11.3762 | 0.398247 | ||||||||
\(817\) | 75.6172 | 2.64551 | ||||||||
\(818\) | −37.8482 | −1.32333 | ||||||||
\(819\) | 3.05988 | 0.106921 | ||||||||
\(820\) | −3.06264 | −0.106952 | ||||||||
\(821\) | −9.64824 | −0.336726 | −0.168363 | − | 0.985725i | \(-0.553848\pi\) | ||||
−0.168363 | + | 0.985725i | \(0.553848\pi\) | |||||||
\(822\) | 20.4379 | 0.712852 | ||||||||
\(823\) | 5.57561 | 0.194353 | 0.0971767 | − | 0.995267i | \(-0.469019\pi\) | ||||
0.0971767 | + | 0.995267i | \(0.469019\pi\) | |||||||
\(824\) | −7.77250 | −0.270768 | ||||||||
\(825\) | 1.18548 | 0.0412731 | ||||||||
\(826\) | 17.4826 | 0.608296 | ||||||||
\(827\) | −9.60982 | −0.334166 | −0.167083 | − | 0.985943i | \(-0.553435\pi\) | ||||
−0.167083 | + | 0.985943i | \(0.553435\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −50.8320 | −1.76547 | −0.882734 | − | 0.469873i | \(-0.844300\pi\) | ||||
−0.882734 | + | 0.469873i | \(0.844300\pi\) | |||||||
\(830\) | 10.0255 | 0.347989 | ||||||||
\(831\) | −5.90029 | −0.204679 | ||||||||
\(832\) | 5.91658 | 0.205120 | ||||||||
\(833\) | 10.5078 | 0.364072 | ||||||||
\(834\) | 26.1589 | 0.905807 | ||||||||
\(835\) | −3.94892 | −0.136658 | ||||||||
\(836\) | −3.02073 | −0.104474 | ||||||||
\(837\) | 5.67444 | 0.196137 | ||||||||
\(838\) | 39.7614 | 1.37353 | ||||||||
\(839\) | −29.6836 | −1.02479 | −0.512396 | − | 0.858749i | \(-0.671242\pi\) | ||||
−0.512396 | + | 0.858749i | \(0.671242\pi\) | |||||||
\(840\) | 8.61259 | 0.297162 | ||||||||
\(841\) | 32.9107 | 1.13485 | ||||||||
\(842\) | −38.2300 | −1.31749 | ||||||||
\(843\) | 18.6057 | 0.640814 | ||||||||
\(844\) | 0.338611 | 0.0116555 | ||||||||
\(845\) | 12.1615 | 0.418370 | ||||||||
\(846\) | 10.9340 | 0.375917 | ||||||||
\(847\) | −32.0623 | −1.10167 | ||||||||
\(848\) | −4.97607 | −0.170879 | ||||||||
\(849\) | 11.9011 | 0.408446 | ||||||||
\(850\) | −3.82515 | −0.131202 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −2.21089 | −0.0757437 | ||||||||
\(853\) | 12.3860 | 0.424087 | 0.212044 | − | 0.977260i | \(-0.431988\pi\) | ||||
0.212044 | + | 0.977260i | \(0.431988\pi\) | |||||||
\(854\) | −22.7676 | −0.779091 | ||||||||
\(855\) | −8.46827 | −0.289609 | ||||||||
\(856\) | −4.42824 | −0.151354 | ||||||||
\(857\) | 29.7484 | 1.01618 | 0.508092 | − | 0.861303i | \(-0.330351\pi\) | ||||
0.508092 | + | 0.861303i | \(0.330351\pi\) | |||||||
\(858\) | −1.64658 | −0.0562132 | ||||||||
\(859\) | 4.56314 | 0.155692 | 0.0778461 | − | 0.996965i | \(-0.475196\pi\) | ||||
0.0778461 | + | 0.996965i | \(0.475196\pi\) | |||||||
\(860\) | −2.68688 | −0.0916220 | ||||||||
\(861\) | −34.0125 | −1.15914 | ||||||||
\(862\) | −16.1237 | −0.549177 | ||||||||
\(863\) | 25.2281 | 0.858775 | 0.429388 | − | 0.903120i | \(-0.358729\pi\) | ||||
0.429388 | + | 0.903120i | \(0.358729\pi\) | |||||||
\(864\) | −1.68837 | −0.0574395 | ||||||||
\(865\) | −4.41696 | −0.150181 | ||||||||
\(866\) | −7.22485 | −0.245510 | ||||||||
\(867\) | 10.6409 | 0.361382 | ||||||||
\(868\) | −5.70574 | −0.193665 | ||||||||
\(869\) | −18.5741 | −0.630083 | ||||||||
\(870\) | −11.9353 | −0.404643 | ||||||||
\(871\) | −0.749175 | −0.0253848 | ||||||||
\(872\) | 18.6789 | 0.632548 | ||||||||
\(873\) | −3.08867 | −0.104536 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.34169 | −0.112970 | ||||||||
\(876\) | −4.09648 | −0.138407 | ||||||||
\(877\) | 24.2627 | 0.819294 | 0.409647 | − | 0.912244i | \(-0.365652\pi\) | ||||
0.409647 | + | 0.912244i | \(0.365652\pi\) | |||||||
\(878\) | −37.8629 | −1.27781 | ||||||||
\(879\) | 6.70436 | 0.226133 | ||||||||
\(880\) | −5.34801 | −0.180281 | ||||||||
\(881\) | 4.19486 | 0.141328 | 0.0706642 | − | 0.997500i | \(-0.477488\pi\) | ||||
0.0706642 | + | 0.997500i | \(0.477488\pi\) | |||||||
\(882\) | −6.32062 | −0.212826 | ||||||||
\(883\) | 18.8715 | 0.635078 | 0.317539 | − | 0.948245i | \(-0.397144\pi\) | ||||
0.317539 | + | 0.948245i | \(0.397144\pi\) | |||||||
\(884\) | 0.694802 | 0.0233687 | ||||||||
\(885\) | −3.44898 | −0.115936 | ||||||||
\(886\) | 16.8703 | 0.566770 | ||||||||
\(887\) | 33.0470 | 1.10961 | 0.554806 | − | 0.831980i | \(-0.312793\pi\) | ||||
0.554806 | + | 0.831980i | \(0.312793\pi\) | |||||||
\(888\) | −14.6578 | −0.491882 | ||||||||
\(889\) | −25.0877 | −0.841415 | ||||||||
\(890\) | −13.9151 | −0.466434 | ||||||||
\(891\) | −1.18548 | −0.0397151 | ||||||||
\(892\) | −1.41452 | −0.0473615 | ||||||||
\(893\) | −61.0413 | −2.04267 | ||||||||
\(894\) | −7.16707 | −0.239703 | ||||||||
\(895\) | 6.29312 | 0.210356 | ||||||||
\(896\) | −44.0367 | −1.47116 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.0024 | −1.00119 | ||||||||
\(899\) | −44.6484 | −1.48911 | ||||||||
\(900\) | 0.300900 | 0.0100300 | ||||||||
\(901\) | 2.78156 | 0.0926672 | ||||||||
\(902\) | 18.3027 | 0.609414 | ||||||||
\(903\) | −29.8395 | −0.992997 | ||||||||
\(904\) | −40.8259 | −1.35785 | ||||||||
\(905\) | −12.9253 | −0.429651 | ||||||||
\(906\) | 6.40281 | 0.212719 | ||||||||
\(907\) | −59.7016 | −1.98236 | −0.991179 | − | 0.132532i | \(-0.957689\pi\) | ||||
−0.991179 | + | 0.132532i | \(0.957689\pi\) | |||||||
\(908\) | 3.51573 | 0.116674 | ||||||||
\(909\) | 10.0879 | 0.334596 | ||||||||
\(910\) | 4.64145 | 0.153862 | ||||||||
\(911\) | 30.7477 | 1.01872 | 0.509358 | − | 0.860554i | \(-0.329883\pi\) | ||||
0.509358 | + | 0.860554i | \(0.329883\pi\) | |||||||
\(912\) | 38.2026 | 1.26501 | ||||||||
\(913\) | −7.83518 | −0.259307 | ||||||||
\(914\) | −7.26110 | −0.240176 | ||||||||
\(915\) | 4.49161 | 0.148488 | ||||||||
\(916\) | −5.93695 | −0.196162 | ||||||||
\(917\) | −61.2148 | −2.02149 | ||||||||
\(918\) | 3.82515 | 0.126249 | ||||||||
\(919\) | −13.9339 | −0.459637 | −0.229818 | − | 0.973234i | \(-0.573813\pi\) | ||||
−0.229818 | + | 0.973234i | \(0.573813\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.77351 | 0.223195 | ||||||||
\(922\) | 23.4692 | 0.772916 | ||||||||
\(923\) | 6.72795 | 0.221453 | ||||||||
\(924\) | 1.19202 | 0.0392145 | ||||||||
\(925\) | 5.68722 | 0.186995 | ||||||||
\(926\) | −56.0049 | −1.84044 | ||||||||
\(927\) | −3.01573 | −0.0990497 | ||||||||
\(928\) | 13.2847 | 0.436090 | ||||||||
\(929\) | −36.4793 | −1.19685 | −0.598423 | − | 0.801180i | \(-0.704206\pi\) | ||||
−0.598423 | + | 0.801180i | \(0.704206\pi\) | |||||||
\(930\) | 8.60740 | 0.282248 | ||||||||
\(931\) | 35.2862 | 1.15646 | ||||||||
\(932\) | 1.05451 | 0.0345416 | ||||||||
\(933\) | −23.7189 | −0.776521 | ||||||||
\(934\) | −19.5161 | −0.638588 | ||||||||
\(935\) | 2.98946 | 0.0977659 | ||||||||
\(936\) | 2.35997 | 0.0771380 | ||||||||
\(937\) | 50.1209 | 1.63738 | 0.818690 | − | 0.574236i | \(-0.194701\pi\) | ||||
0.818690 | + | 0.574236i | \(0.194701\pi\) | |||||||
\(938\) | 4.14724 | 0.135412 | ||||||||
\(939\) | −5.87032 | −0.191571 | ||||||||
\(940\) | 2.16896 | 0.0707437 | ||||||||
\(941\) | −0.994697 | −0.0324262 | −0.0162131 | − | 0.999869i | \(-0.505161\pi\) | ||||
−0.0162131 | + | 0.999869i | \(0.505161\pi\) | |||||||
\(942\) | 29.0794 | 0.947458 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 15.5592 | 0.506410 | ||||||||
\(945\) | 3.34169 | 0.108705 | ||||||||
\(946\) | 16.0572 | 0.522064 | ||||||||
\(947\) | 41.7320 | 1.35611 | 0.678053 | − | 0.735013i | \(-0.262824\pi\) | ||||
0.678053 | + | 0.735013i | \(0.262824\pi\) | |||||||
\(948\) | −4.71451 | −0.153120 | ||||||||
\(949\) | 12.4660 | 0.404663 | ||||||||
\(950\) | −12.8453 | −0.416756 | ||||||||
\(951\) | −1.26758 | −0.0411041 | ||||||||
\(952\) | 21.7187 | 0.703906 | ||||||||
\(953\) | 4.22759 | 0.136945 | 0.0684725 | − | 0.997653i | \(-0.478187\pi\) | ||||
0.0684725 | + | 0.997653i | \(0.478187\pi\) | |||||||
\(954\) | −1.67316 | −0.0541706 | ||||||||
\(955\) | 26.5082 | 0.857784 | ||||||||
\(956\) | −1.69825 | −0.0549254 | ||||||||
\(957\) | 9.32775 | 0.301523 | ||||||||
\(958\) | 14.7755 | 0.477376 | ||||||||
\(959\) | 45.0249 | 1.45393 | ||||||||
\(960\) | 6.46148 | 0.208543 | ||||||||
\(961\) | 1.19927 | 0.0386860 | ||||||||
\(962\) | −7.89928 | −0.254683 | ||||||||
\(963\) | −1.71816 | −0.0553668 | ||||||||
\(964\) | 2.95054 | 0.0950304 | ||||||||
\(965\) | −7.46115 | −0.240183 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.0842 | −0.549392 | −0.274696 | − | 0.961531i | \(-0.588577\pi\) | ||||
−0.274696 | + | 0.961531i | \(0.588577\pi\) | |||||||
\(968\) | −24.7284 | −0.794802 | ||||||||
\(969\) | −21.3547 | −0.686013 | ||||||||
\(970\) | −4.68512 | −0.150430 | ||||||||
\(971\) | −8.32887 | −0.267286 | −0.133643 | − | 0.991030i | \(-0.542668\pi\) | ||||
−0.133643 | + | 0.991030i | \(0.542668\pi\) | |||||||
\(972\) | −0.300900 | −0.00965139 | ||||||||
\(973\) | 57.6283 | 1.84748 | ||||||||
\(974\) | −60.3806 | −1.93472 | ||||||||
\(975\) | −0.915669 | −0.0293249 | ||||||||
\(976\) | −20.2628 | −0.648597 | ||||||||
\(977\) | −38.1165 | −1.21946 | −0.609728 | − | 0.792611i | \(-0.708721\pi\) | ||||
−0.609728 | + | 0.792611i | \(0.708721\pi\) | |||||||
\(978\) | −27.6680 | −0.884727 | ||||||||
\(979\) | 10.8750 | 0.347567 | ||||||||
\(980\) | −1.25381 | −0.0400516 | ||||||||
\(981\) | 7.24743 | 0.231393 | ||||||||
\(982\) | −23.6755 | −0.755516 | ||||||||
\(983\) | −48.0094 | −1.53126 | −0.765632 | − | 0.643279i | \(-0.777573\pi\) | ||||
−0.765632 | + | 0.643279i | \(0.777573\pi\) | |||||||
\(984\) | −26.2326 | −0.836263 | ||||||||
\(985\) | 7.88559 | 0.251256 | ||||||||
\(986\) | −30.0975 | −0.958501 | ||||||||
\(987\) | 24.0877 | 0.766718 | ||||||||
\(988\) | 2.33322 | 0.0742297 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −1.79822 | −0.0571512 | ||||||||
\(991\) | −9.13462 | −0.290171 | −0.145085 | − | 0.989419i | \(-0.546346\pi\) | ||||
−0.145085 | + | 0.989419i | \(0.546346\pi\) | |||||||
\(992\) | −9.58056 | −0.304183 | ||||||||
\(993\) | 0.0750196 | 0.00238067 | ||||||||
\(994\) | −37.2442 | −1.18131 | ||||||||
\(995\) | 17.7491 | 0.562684 | ||||||||
\(996\) | −1.98874 | −0.0630156 | ||||||||
\(997\) | 19.9123 | 0.630629 | 0.315314 | − | 0.948987i | \(-0.397890\pi\) | ||||
0.315314 | + | 0.948987i | \(0.397890\pi\) | |||||||
\(998\) | 52.2884 | 1.65516 | ||||||||
\(999\) | −5.68722 | −0.179936 |
(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 | 7935.2.a.bt.1.7 | 25 | ||
23.5 | odd | 22 | 345.2.m.d.301.2 | yes | 50 | ||
23.14 | odd | 22 | 345.2.m.d.196.2 | ✓ | 50 | ||
23.22 | odd | 2 | 7935.2.a.bu.1.7 | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
345.2.m.d.196.2 | ✓ | 50 | 23.14 | odd | 22 | ||
345.2.m.d.301.2 | yes | 50 | 23.5 | odd | 22 | ||
7935.2.a.bt.1.7 | 25 | 1.1 | even | 1 | trivial | ||
7935.2.a.bu.1.7 | 25 | 23.22 | odd | 2 |