Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6033,2,Mod(1,6033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6033 = 3 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6033.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: | \(48.1737475394\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 6033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.60707 | −1.84348 | −0.921739 | − | 0.387812i | \(-0.873231\pi\) | ||||
−0.921739 | + | 0.387812i | \(0.873231\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.79682 | 2.39841 | ||||||||
\(5\) | 3.79845 | 1.69872 | 0.849359 | − | 0.527816i | \(-0.176989\pi\) | ||||
0.849359 | + | 0.527816i | \(0.176989\pi\) | |||||||
\(6\) | 2.60707 | 1.06433 | ||||||||
\(7\) | 0.267933 | 0.101269 | 0.0506346 | − | 0.998717i | \(-0.483876\pi\) | ||||
0.0506346 | + | 0.998717i | \(0.483876\pi\) | |||||||
\(8\) | −7.29150 | −2.57794 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −9.90282 | −3.13155 | ||||||||
\(11\) | −3.59805 | −1.08485 | −0.542427 | − | 0.840103i | \(-0.682494\pi\) | ||||
−0.542427 | + | 0.840103i | \(0.682494\pi\) | |||||||
\(12\) | −4.79682 | −1.38472 | ||||||||
\(13\) | −2.40460 | −0.666917 | −0.333458 | − | 0.942765i | \(-0.608216\pi\) | ||||
−0.333458 | + | 0.942765i | \(0.608216\pi\) | |||||||
\(14\) | −0.698520 | −0.186687 | ||||||||
\(15\) | −3.79845 | −0.980755 | ||||||||
\(16\) | 9.41582 | 2.35396 | ||||||||
\(17\) | 4.06799 | 0.986632 | 0.493316 | − | 0.869850i | \(-0.335785\pi\) | ||||
0.493316 | + | 0.869850i | \(0.335785\pi\) | |||||||
\(18\) | −2.60707 | −0.614492 | ||||||||
\(19\) | 5.75949 | 1.32132 | 0.660659 | − | 0.750686i | \(-0.270277\pi\) | ||||
0.660659 | + | 0.750686i | \(0.270277\pi\) | |||||||
\(20\) | 18.2205 | 4.07422 | ||||||||
\(21\) | −0.267933 | −0.0584677 | ||||||||
\(22\) | 9.38038 | 1.99990 | ||||||||
\(23\) | 8.77446 | 1.82960 | 0.914800 | − | 0.403906i | \(-0.132348\pi\) | ||||
0.914800 | + | 0.403906i | \(0.132348\pi\) | |||||||
\(24\) | 7.29150 | 1.48837 | ||||||||
\(25\) | 9.42821 | 1.88564 | ||||||||
\(26\) | 6.26897 | 1.22945 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.28523 | 0.242885 | ||||||||
\(29\) | 3.95909 | 0.735185 | 0.367592 | − | 0.929987i | \(-0.380182\pi\) | ||||
0.367592 | + | 0.929987i | \(0.380182\pi\) | |||||||
\(30\) | 9.90282 | 1.80800 | ||||||||
\(31\) | 9.31418 | 1.67288 | 0.836438 | − | 0.548061i | \(-0.184634\pi\) | ||||
0.836438 | + | 0.548061i | \(0.184634\pi\) | |||||||
\(32\) | −9.96472 | −1.76153 | ||||||||
\(33\) | 3.59805 | 0.626340 | ||||||||
\(34\) | −10.6055 | −1.81883 | ||||||||
\(35\) | 1.01773 | 0.172028 | ||||||||
\(36\) | 4.79682 | 0.799470 | ||||||||
\(37\) | −5.99166 | −0.985024 | −0.492512 | − | 0.870306i | \(-0.663921\pi\) | ||||
−0.492512 | + | 0.870306i | \(0.663921\pi\) | |||||||
\(38\) | −15.0154 | −2.43582 | ||||||||
\(39\) | 2.40460 | 0.385045 | ||||||||
\(40\) | −27.6964 | −4.37918 | ||||||||
\(41\) | 7.35835 | 1.14918 | 0.574591 | − | 0.818441i | \(-0.305161\pi\) | ||||
0.574591 | + | 0.818441i | \(0.305161\pi\) | |||||||
\(42\) | 0.698520 | 0.107784 | ||||||||
\(43\) | 6.70189 | 1.02203 | 0.511015 | − | 0.859572i | \(-0.329270\pi\) | ||||
0.511015 | + | 0.859572i | \(0.329270\pi\) | |||||||
\(44\) | −17.2592 | −2.60192 | ||||||||
\(45\) | 3.79845 | 0.566239 | ||||||||
\(46\) | −22.8756 | −3.37283 | ||||||||
\(47\) | 2.54569 | 0.371326 | 0.185663 | − | 0.982613i | \(-0.440557\pi\) | ||||
0.185663 | + | 0.982613i | \(0.440557\pi\) | |||||||
\(48\) | −9.41582 | −1.35906 | ||||||||
\(49\) | −6.92821 | −0.989745 | ||||||||
\(50\) | −24.5800 | −3.47614 | ||||||||
\(51\) | −4.06799 | −0.569632 | ||||||||
\(52\) | −11.5344 | −1.59954 | ||||||||
\(53\) | 12.1009 | 1.66219 | 0.831095 | − | 0.556130i | \(-0.187714\pi\) | ||||
0.831095 | + | 0.556130i | \(0.187714\pi\) | |||||||
\(54\) | 2.60707 | 0.354777 | ||||||||
\(55\) | −13.6670 | −1.84286 | ||||||||
\(56\) | −1.95363 | −0.261065 | ||||||||
\(57\) | −5.75949 | −0.762863 | ||||||||
\(58\) | −10.3216 | −1.35530 | ||||||||
\(59\) | −3.20680 | −0.417490 | −0.208745 | − | 0.977970i | \(-0.566938\pi\) | ||||
−0.208745 | + | 0.977970i | \(0.566938\pi\) | |||||||
\(60\) | −18.2205 | −2.35225 | ||||||||
\(61\) | −10.5338 | −1.34871 | −0.674356 | − | 0.738406i | \(-0.735579\pi\) | ||||
−0.674356 | + | 0.738406i | \(0.735579\pi\) | |||||||
\(62\) | −24.2827 | −3.08391 | ||||||||
\(63\) | 0.267933 | 0.0337564 | ||||||||
\(64\) | 7.14707 | 0.893384 | ||||||||
\(65\) | −9.13376 | −1.13290 | ||||||||
\(66\) | −9.38038 | −1.15464 | ||||||||
\(67\) | 8.82801 | 1.07851 | 0.539257 | − | 0.842141i | \(-0.318705\pi\) | ||||
0.539257 | + | 0.842141i | \(0.318705\pi\) | |||||||
\(68\) | 19.5134 | 2.36635 | ||||||||
\(69\) | −8.77446 | −1.05632 | ||||||||
\(70\) | −2.65329 | −0.317129 | ||||||||
\(71\) | −11.4169 | −1.35494 | −0.677469 | − | 0.735551i | \(-0.736923\pi\) | ||||
−0.677469 | + | 0.735551i | \(0.736923\pi\) | |||||||
\(72\) | −7.29150 | −0.859312 | ||||||||
\(73\) | 13.4256 | 1.57135 | 0.785673 | − | 0.618642i | \(-0.212317\pi\) | ||||
0.785673 | + | 0.618642i | \(0.212317\pi\) | |||||||
\(74\) | 15.6207 | 1.81587 | ||||||||
\(75\) | −9.42821 | −1.08868 | ||||||||
\(76\) | 27.6272 | 3.16906 | ||||||||
\(77\) | −0.964036 | −0.109862 | ||||||||
\(78\) | −6.26897 | −0.709821 | ||||||||
\(79\) | −12.8664 | −1.44759 | −0.723793 | − | 0.690017i | \(-0.757603\pi\) | ||||
−0.723793 | + | 0.690017i | \(0.757603\pi\) | |||||||
\(80\) | 35.7655 | 3.99871 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −19.1837 | −2.11849 | ||||||||
\(83\) | 5.32736 | 0.584754 | 0.292377 | − | 0.956303i | \(-0.405554\pi\) | ||||
0.292377 | + | 0.956303i | \(0.405554\pi\) | |||||||
\(84\) | −1.28523 | −0.140230 | ||||||||
\(85\) | 15.4520 | 1.67601 | ||||||||
\(86\) | −17.4723 | −1.88409 | ||||||||
\(87\) | −3.95909 | −0.424459 | ||||||||
\(88\) | 26.2352 | 2.79668 | ||||||||
\(89\) | −3.00869 | −0.318920 | −0.159460 | − | 0.987204i | \(-0.550975\pi\) | ||||
−0.159460 | + | 0.987204i | \(0.550975\pi\) | |||||||
\(90\) | −9.90282 | −1.04385 | ||||||||
\(91\) | −0.644272 | −0.0675381 | ||||||||
\(92\) | 42.0895 | 4.38813 | ||||||||
\(93\) | −9.31418 | −0.965836 | ||||||||
\(94\) | −6.63678 | −0.684532 | ||||||||
\(95\) | 21.8771 | 2.24454 | ||||||||
\(96\) | 9.96472 | 1.01702 | ||||||||
\(97\) | −9.03564 | −0.917430 | −0.458715 | − | 0.888583i | \(-0.651690\pi\) | ||||
−0.458715 | + | 0.888583i | \(0.651690\pi\) | |||||||
\(98\) | 18.0623 | 1.82457 | ||||||||
\(99\) | −3.59805 | −0.361618 | ||||||||
\(100\) | 45.2254 | 4.52254 | ||||||||
\(101\) | 4.46532 | 0.444316 | 0.222158 | − | 0.975011i | \(-0.428690\pi\) | ||||
0.222158 | + | 0.975011i | \(0.428690\pi\) | |||||||
\(102\) | 10.6055 | 1.05010 | ||||||||
\(103\) | −4.48598 | −0.442017 | −0.221008 | − | 0.975272i | \(-0.570935\pi\) | ||||
−0.221008 | + | 0.975272i | \(0.570935\pi\) | |||||||
\(104\) | 17.5332 | 1.71927 | ||||||||
\(105\) | −1.01773 | −0.0993202 | ||||||||
\(106\) | −31.5480 | −3.06421 | ||||||||
\(107\) | −3.59497 | −0.347539 | −0.173769 | − | 0.984786i | \(-0.555595\pi\) | ||||
−0.173769 | + | 0.984786i | \(0.555595\pi\) | |||||||
\(108\) | −4.79682 | −0.461574 | ||||||||
\(109\) | −11.9929 | −1.14871 | −0.574355 | − | 0.818607i | \(-0.694747\pi\) | ||||
−0.574355 | + | 0.818607i | \(0.694747\pi\) | |||||||
\(110\) | 35.6309 | 3.39727 | ||||||||
\(111\) | 5.99166 | 0.568704 | ||||||||
\(112\) | 2.52281 | 0.238383 | ||||||||
\(113\) | −15.7023 | −1.47715 | −0.738573 | − | 0.674173i | \(-0.764500\pi\) | ||||
−0.738573 | + | 0.674173i | \(0.764500\pi\) | |||||||
\(114\) | 15.0154 | 1.40632 | ||||||||
\(115\) | 33.3293 | 3.10798 | ||||||||
\(116\) | 18.9910 | 1.76327 | ||||||||
\(117\) | −2.40460 | −0.222306 | ||||||||
\(118\) | 8.36036 | 0.769634 | ||||||||
\(119\) | 1.08995 | 0.0999154 | ||||||||
\(120\) | 27.6964 | 2.52832 | ||||||||
\(121\) | 1.94598 | 0.176907 | ||||||||
\(122\) | 27.4623 | 2.48632 | ||||||||
\(123\) | −7.35835 | −0.663480 | ||||||||
\(124\) | 44.6784 | 4.01224 | ||||||||
\(125\) | 16.8203 | 1.50446 | ||||||||
\(126\) | −0.698520 | −0.0622291 | ||||||||
\(127\) | 2.24302 | 0.199036 | 0.0995180 | − | 0.995036i | \(-0.468270\pi\) | ||||
0.0995180 | + | 0.995036i | \(0.468270\pi\) | |||||||
\(128\) | 1.29651 | 0.114596 | ||||||||
\(129\) | −6.70189 | −0.590069 | ||||||||
\(130\) | 23.8124 | 2.08848 | ||||||||
\(131\) | 18.5651 | 1.62204 | 0.811022 | − | 0.585016i | \(-0.198912\pi\) | ||||
0.811022 | + | 0.585016i | \(0.198912\pi\) | |||||||
\(132\) | 17.2592 | 1.50222 | ||||||||
\(133\) | 1.54316 | 0.133809 | ||||||||
\(134\) | −23.0153 | −1.98822 | ||||||||
\(135\) | −3.79845 | −0.326918 | ||||||||
\(136\) | −29.6617 | −2.54347 | ||||||||
\(137\) | −21.4624 | −1.83366 | −0.916830 | − | 0.399278i | \(-0.869261\pi\) | ||||
−0.916830 | + | 0.399278i | \(0.869261\pi\) | |||||||
\(138\) | 22.8756 | 1.94730 | ||||||||
\(139\) | −3.50028 | −0.296890 | −0.148445 | − | 0.988921i | \(-0.547427\pi\) | ||||
−0.148445 | + | 0.988921i | \(0.547427\pi\) | |||||||
\(140\) | 4.88186 | 0.412593 | ||||||||
\(141\) | −2.54569 | −0.214385 | ||||||||
\(142\) | 29.7647 | 2.49780 | ||||||||
\(143\) | 8.65188 | 0.723507 | ||||||||
\(144\) | 9.41582 | 0.784652 | ||||||||
\(145\) | 15.0384 | 1.24887 | ||||||||
\(146\) | −35.0014 | −2.89674 | ||||||||
\(147\) | 6.92821 | 0.571429 | ||||||||
\(148\) | −28.7409 | −2.36249 | ||||||||
\(149\) | 13.5304 | 1.10845 | 0.554227 | − | 0.832366i | \(-0.313014\pi\) | ||||
0.554227 | + | 0.832366i | \(0.313014\pi\) | |||||||
\(150\) | 24.5800 | 2.00695 | ||||||||
\(151\) | 2.21669 | 0.180392 | 0.0901959 | − | 0.995924i | \(-0.471251\pi\) | ||||
0.0901959 | + | 0.995924i | \(0.471251\pi\) | |||||||
\(152\) | −41.9953 | −3.40627 | ||||||||
\(153\) | 4.06799 | 0.328877 | ||||||||
\(154\) | 2.51331 | 0.202528 | ||||||||
\(155\) | 35.3794 | 2.84175 | ||||||||
\(156\) | 11.5344 | 0.923494 | ||||||||
\(157\) | −12.7142 | −1.01470 | −0.507350 | − | 0.861740i | \(-0.669375\pi\) | ||||
−0.507350 | + | 0.861740i | \(0.669375\pi\) | |||||||
\(158\) | 33.5437 | 2.66859 | ||||||||
\(159\) | −12.1009 | −0.959666 | ||||||||
\(160\) | −37.8505 | −2.99234 | ||||||||
\(161\) | 2.35097 | 0.185282 | ||||||||
\(162\) | −2.60707 | −0.204831 | ||||||||
\(163\) | 6.00276 | 0.470172 | 0.235086 | − | 0.971975i | \(-0.424463\pi\) | ||||
0.235086 | + | 0.971975i | \(0.424463\pi\) | |||||||
\(164\) | 35.2967 | 2.75621 | ||||||||
\(165\) | 13.6670 | 1.06398 | ||||||||
\(166\) | −13.8888 | −1.07798 | ||||||||
\(167\) | 20.8557 | 1.61386 | 0.806931 | − | 0.590646i | \(-0.201127\pi\) | ||||
0.806931 | + | 0.590646i | \(0.201127\pi\) | |||||||
\(168\) | 1.95363 | 0.150726 | ||||||||
\(169\) | −7.21789 | −0.555222 | ||||||||
\(170\) | −40.2846 | −3.08969 | ||||||||
\(171\) | 5.75949 | 0.440439 | ||||||||
\(172\) | 32.1478 | 2.45124 | ||||||||
\(173\) | 2.72129 | 0.206896 | 0.103448 | − | 0.994635i | \(-0.467012\pi\) | ||||
0.103448 | + | 0.994635i | \(0.467012\pi\) | |||||||
\(174\) | 10.3216 | 0.782481 | ||||||||
\(175\) | 2.52613 | 0.190957 | ||||||||
\(176\) | −33.8786 | −2.55370 | ||||||||
\(177\) | 3.20680 | 0.241038 | ||||||||
\(178\) | 7.84387 | 0.587923 | ||||||||
\(179\) | −18.9231 | −1.41438 | −0.707190 | − | 0.707024i | \(-0.750037\pi\) | ||||
−0.707190 | + | 0.707024i | \(0.750037\pi\) | |||||||
\(180\) | 18.2205 | 1.35807 | ||||||||
\(181\) | −14.5059 | −1.07821 | −0.539107 | − | 0.842237i | \(-0.681238\pi\) | ||||
−0.539107 | + | 0.842237i | \(0.681238\pi\) | |||||||
\(182\) | 1.67966 | 0.124505 | ||||||||
\(183\) | 10.5338 | 0.778679 | ||||||||
\(184\) | −63.9790 | −4.71659 | ||||||||
\(185\) | −22.7590 | −1.67328 | ||||||||
\(186\) | 24.2827 | 1.78050 | ||||||||
\(187\) | −14.6368 | −1.07035 | ||||||||
\(188\) | 12.2112 | 0.890593 | ||||||||
\(189\) | −0.267933 | −0.0194892 | ||||||||
\(190\) | −57.0352 | −4.13777 | ||||||||
\(191\) | −12.5931 | −0.911208 | −0.455604 | − | 0.890183i | \(-0.650577\pi\) | ||||
−0.455604 | + | 0.890183i | \(0.650577\pi\) | |||||||
\(192\) | −7.14707 | −0.515796 | ||||||||
\(193\) | −15.3829 | −1.10729 | −0.553643 | − | 0.832754i | \(-0.686763\pi\) | ||||
−0.553643 | + | 0.832754i | \(0.686763\pi\) | |||||||
\(194\) | 23.5565 | 1.69126 | ||||||||
\(195\) | 9.13376 | 0.654082 | ||||||||
\(196\) | −33.2334 | −2.37381 | ||||||||
\(197\) | −3.62152 | −0.258023 | −0.129011 | − | 0.991643i | \(-0.541180\pi\) | ||||
−0.129011 | + | 0.991643i | \(0.541180\pi\) | |||||||
\(198\) | 9.38038 | 0.666634 | ||||||||
\(199\) | −10.1713 | −0.721023 | −0.360512 | − | 0.932755i | \(-0.617398\pi\) | ||||
−0.360512 | + | 0.932755i | \(0.617398\pi\) | |||||||
\(200\) | −68.7458 | −4.86106 | ||||||||
\(201\) | −8.82801 | −0.622680 | ||||||||
\(202\) | −11.6414 | −0.819087 | ||||||||
\(203\) | 1.06077 | 0.0744515 | ||||||||
\(204\) | −19.5134 | −1.36621 | ||||||||
\(205\) | 27.9503 | 1.95213 | ||||||||
\(206\) | 11.6953 | 0.814848 | ||||||||
\(207\) | 8.77446 | 0.609867 | ||||||||
\(208\) | −22.6413 | −1.56989 | ||||||||
\(209\) | −20.7229 | −1.43344 | ||||||||
\(210\) | 2.65329 | 0.183095 | ||||||||
\(211\) | −4.30673 | −0.296488 | −0.148244 | − | 0.988951i | \(-0.547362\pi\) | ||||
−0.148244 | + | 0.988951i | \(0.547362\pi\) | |||||||
\(212\) | 58.0459 | 3.98661 | ||||||||
\(213\) | 11.4169 | 0.782274 | ||||||||
\(214\) | 9.37234 | 0.640680 | ||||||||
\(215\) | 25.4568 | 1.73614 | ||||||||
\(216\) | 7.29150 | 0.496124 | ||||||||
\(217\) | 2.49558 | 0.169411 | ||||||||
\(218\) | 31.2663 | 2.11762 | ||||||||
\(219\) | −13.4256 | −0.907217 | ||||||||
\(220\) | −65.5582 | −4.41993 | ||||||||
\(221\) | −9.78189 | −0.658001 | ||||||||
\(222\) | −15.6207 | −1.04839 | ||||||||
\(223\) | 21.8837 | 1.46544 | 0.732721 | − | 0.680529i | \(-0.238250\pi\) | ||||
0.732721 | + | 0.680529i | \(0.238250\pi\) | |||||||
\(224\) | −2.66988 | −0.178389 | ||||||||
\(225\) | 9.42821 | 0.628547 | ||||||||
\(226\) | 40.9370 | 2.72309 | ||||||||
\(227\) | 6.65746 | 0.441871 | 0.220935 | − | 0.975288i | \(-0.429089\pi\) | ||||
0.220935 | + | 0.975288i | \(0.429089\pi\) | |||||||
\(228\) | −27.6272 | −1.82966 | ||||||||
\(229\) | 12.3710 | 0.817497 | 0.408748 | − | 0.912647i | \(-0.365965\pi\) | ||||
0.408748 | + | 0.912647i | \(0.365965\pi\) | |||||||
\(230\) | −86.8919 | −5.72948 | ||||||||
\(231\) | 0.964036 | 0.0634289 | ||||||||
\(232\) | −28.8677 | −1.89526 | ||||||||
\(233\) | −0.436822 | −0.0286172 | −0.0143086 | − | 0.999898i | \(-0.504555\pi\) | ||||
−0.0143086 | + | 0.999898i | \(0.504555\pi\) | |||||||
\(234\) | 6.26897 | 0.409815 | ||||||||
\(235\) | 9.66965 | 0.630779 | ||||||||
\(236\) | −15.3825 | −1.00131 | ||||||||
\(237\) | 12.8664 | 0.835765 | ||||||||
\(238\) | −2.84157 | −0.184192 | ||||||||
\(239\) | 22.6043 | 1.46215 | 0.731075 | − | 0.682298i | \(-0.239019\pi\) | ||||
0.731075 | + | 0.682298i | \(0.239019\pi\) | |||||||
\(240\) | −35.7655 | −2.30865 | ||||||||
\(241\) | −6.62056 | −0.426468 | −0.213234 | − | 0.977001i | \(-0.568400\pi\) | ||||
−0.213234 | + | 0.977001i | \(0.568400\pi\) | |||||||
\(242\) | −5.07330 | −0.326124 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −50.5286 | −3.23476 | ||||||||
\(245\) | −26.3165 | −1.68130 | ||||||||
\(246\) | 19.1837 | 1.22311 | ||||||||
\(247\) | −13.8493 | −0.881209 | ||||||||
\(248\) | −67.9144 | −4.31257 | ||||||||
\(249\) | −5.32736 | −0.337608 | ||||||||
\(250\) | −43.8518 | −2.77343 | ||||||||
\(251\) | 8.28948 | 0.523227 | 0.261614 | − | 0.965173i | \(-0.415745\pi\) | ||||
0.261614 | + | 0.965173i | \(0.415745\pi\) | |||||||
\(252\) | 1.28523 | 0.0809616 | ||||||||
\(253\) | −31.5710 | −1.98485 | ||||||||
\(254\) | −5.84771 | −0.366918 | ||||||||
\(255\) | −15.4520 | −0.967644 | ||||||||
\(256\) | −17.6742 | −1.10464 | ||||||||
\(257\) | 28.5492 | 1.78085 | 0.890424 | − | 0.455132i | \(-0.150408\pi\) | ||||
0.890424 | + | 0.455132i | \(0.150408\pi\) | |||||||
\(258\) | 17.4723 | 1.08778 | ||||||||
\(259\) | −1.60536 | −0.0997525 | ||||||||
\(260\) | −43.8130 | −2.71717 | ||||||||
\(261\) | 3.95909 | 0.245062 | ||||||||
\(262\) | −48.4006 | −2.99020 | ||||||||
\(263\) | −22.4246 | −1.38276 | −0.691379 | − | 0.722493i | \(-0.742996\pi\) | ||||
−0.691379 | + | 0.722493i | \(0.742996\pi\) | |||||||
\(264\) | −26.2352 | −1.61466 | ||||||||
\(265\) | 45.9647 | 2.82359 | ||||||||
\(266\) | −4.02312 | −0.246673 | ||||||||
\(267\) | 3.00869 | 0.184129 | ||||||||
\(268\) | 42.3464 | 2.58672 | ||||||||
\(269\) | 19.4430 | 1.18546 | 0.592732 | − | 0.805400i | \(-0.298049\pi\) | ||||
0.592732 | + | 0.805400i | \(0.298049\pi\) | |||||||
\(270\) | 9.90282 | 0.602667 | ||||||||
\(271\) | −18.4821 | −1.12271 | −0.561353 | − | 0.827577i | \(-0.689719\pi\) | ||||
−0.561353 | + | 0.827577i | \(0.689719\pi\) | |||||||
\(272\) | 38.3035 | 2.32249 | ||||||||
\(273\) | 0.644272 | 0.0389931 | ||||||||
\(274\) | 55.9541 | 3.38031 | ||||||||
\(275\) | −33.9232 | −2.04564 | ||||||||
\(276\) | −42.0895 | −2.53349 | ||||||||
\(277\) | 14.3715 | 0.863498 | 0.431749 | − | 0.901994i | \(-0.357897\pi\) | ||||
0.431749 | + | 0.901994i | \(0.357897\pi\) | |||||||
\(278\) | 9.12548 | 0.547310 | ||||||||
\(279\) | 9.31418 | 0.557626 | ||||||||
\(280\) | −7.42077 | −0.443476 | ||||||||
\(281\) | 26.1043 | 1.55725 | 0.778626 | − | 0.627488i | \(-0.215917\pi\) | ||||
0.778626 | + | 0.627488i | \(0.215917\pi\) | |||||||
\(282\) | 6.63678 | 0.395215 | ||||||||
\(283\) | 11.6766 | 0.694105 | 0.347052 | − | 0.937846i | \(-0.387183\pi\) | ||||
0.347052 | + | 0.937846i | \(0.387183\pi\) | |||||||
\(284\) | −54.7648 | −3.24970 | ||||||||
\(285\) | −21.8771 | −1.29589 | ||||||||
\(286\) | −22.5561 | −1.33377 | ||||||||
\(287\) | 1.97154 | 0.116377 | ||||||||
\(288\) | −9.96472 | −0.587177 | ||||||||
\(289\) | −0.451471 | −0.0265571 | ||||||||
\(290\) | −39.2062 | −2.30227 | ||||||||
\(291\) | 9.03564 | 0.529678 | ||||||||
\(292\) | 64.4001 | 3.76873 | ||||||||
\(293\) | −7.43455 | −0.434331 | −0.217166 | − | 0.976135i | \(-0.569681\pi\) | ||||
−0.217166 | + | 0.976135i | \(0.569681\pi\) | |||||||
\(294\) | −18.0623 | −1.05342 | ||||||||
\(295\) | −12.1809 | −0.709198 | ||||||||
\(296\) | 43.6882 | 2.53933 | ||||||||
\(297\) | 3.59805 | 0.208780 | ||||||||
\(298\) | −35.2747 | −2.04341 | ||||||||
\(299\) | −21.0991 | −1.22019 | ||||||||
\(300\) | −45.2254 | −2.61109 | ||||||||
\(301\) | 1.79566 | 0.103500 | ||||||||
\(302\) | −5.77907 | −0.332548 | ||||||||
\(303\) | −4.46532 | −0.256526 | ||||||||
\(304\) | 54.2303 | 3.11032 | ||||||||
\(305\) | −40.0120 | −2.29108 | ||||||||
\(306\) | −10.6055 | −0.606278 | ||||||||
\(307\) | −7.28317 | −0.415672 | −0.207836 | − | 0.978164i | \(-0.566642\pi\) | ||||
−0.207836 | + | 0.978164i | \(0.566642\pi\) | |||||||
\(308\) | −4.62431 | −0.263494 | ||||||||
\(309\) | 4.48598 | 0.255198 | ||||||||
\(310\) | −92.2367 | −5.23869 | ||||||||
\(311\) | 29.4235 | 1.66846 | 0.834228 | − | 0.551420i | \(-0.185914\pi\) | ||||
0.834228 | + | 0.551420i | \(0.185914\pi\) | |||||||
\(312\) | −17.5332 | −0.992620 | ||||||||
\(313\) | 5.41969 | 0.306339 | 0.153170 | − | 0.988200i | \(-0.451052\pi\) | ||||
0.153170 | + | 0.988200i | \(0.451052\pi\) | |||||||
\(314\) | 33.1467 | 1.87058 | ||||||||
\(315\) | 1.01773 | 0.0573425 | ||||||||
\(316\) | −61.7179 | −3.47190 | ||||||||
\(317\) | −17.7986 | −0.999668 | −0.499834 | − | 0.866121i | \(-0.666606\pi\) | ||||
−0.499834 | + | 0.866121i | \(0.666606\pi\) | |||||||
\(318\) | 31.5480 | 1.76912 | ||||||||
\(319\) | −14.2450 | −0.797568 | ||||||||
\(320\) | 27.1478 | 1.51761 | ||||||||
\(321\) | 3.59497 | 0.200652 | ||||||||
\(322\) | −6.12913 | −0.341563 | ||||||||
\(323\) | 23.4295 | 1.30365 | ||||||||
\(324\) | 4.79682 | 0.266490 | ||||||||
\(325\) | −22.6711 | −1.25757 | ||||||||
\(326\) | −15.6496 | −0.866752 | ||||||||
\(327\) | 11.9929 | 0.663208 | ||||||||
\(328\) | −53.6534 | −2.96251 | ||||||||
\(329\) | 0.682073 | 0.0376039 | ||||||||
\(330\) | −35.6309 | −1.96141 | ||||||||
\(331\) | −15.2761 | −0.839648 | −0.419824 | − | 0.907605i | \(-0.637908\pi\) | ||||
−0.419824 | + | 0.907605i | \(0.637908\pi\) | |||||||
\(332\) | 25.5544 | 1.40248 | ||||||||
\(333\) | −5.99166 | −0.328341 | ||||||||
\(334\) | −54.3722 | −2.97512 | ||||||||
\(335\) | 33.5328 | 1.83209 | ||||||||
\(336\) | −2.52281 | −0.137631 | ||||||||
\(337\) | 11.5829 | 0.630962 | 0.315481 | − | 0.948932i | \(-0.397834\pi\) | ||||
0.315481 | + | 0.948932i | \(0.397834\pi\) | |||||||
\(338\) | 18.8175 | 1.02354 | ||||||||
\(339\) | 15.7023 | 0.852831 | ||||||||
\(340\) | 74.1206 | 4.01976 | ||||||||
\(341\) | −33.5129 | −1.81483 | ||||||||
\(342\) | −15.0154 | −0.811939 | ||||||||
\(343\) | −3.73183 | −0.201500 | ||||||||
\(344\) | −48.8669 | −2.63472 | ||||||||
\(345\) | −33.3293 | −1.79439 | ||||||||
\(346\) | −7.09460 | −0.381408 | ||||||||
\(347\) | 34.6954 | 1.86255 | 0.931273 | − | 0.364323i | \(-0.118700\pi\) | ||||
0.931273 | + | 0.364323i | \(0.118700\pi\) | |||||||
\(348\) | −18.9910 | −1.01803 | ||||||||
\(349\) | −3.01573 | −0.161428 | −0.0807141 | − | 0.996737i | \(-0.525720\pi\) | ||||
−0.0807141 | + | 0.996737i | \(0.525720\pi\) | |||||||
\(350\) | −6.58579 | −0.352025 | ||||||||
\(351\) | 2.40460 | 0.128348 | ||||||||
\(352\) | 35.8536 | 1.91100 | ||||||||
\(353\) | 16.4090 | 0.873364 | 0.436682 | − | 0.899616i | \(-0.356153\pi\) | ||||
0.436682 | + | 0.899616i | \(0.356153\pi\) | |||||||
\(354\) | −8.36036 | −0.444348 | ||||||||
\(355\) | −43.3666 | −2.30166 | ||||||||
\(356\) | −14.4321 | −0.764901 | ||||||||
\(357\) | −1.08995 | −0.0576862 | ||||||||
\(358\) | 49.3339 | 2.60738 | ||||||||
\(359\) | −20.2348 | −1.06795 | −0.533975 | − | 0.845500i | \(-0.679302\pi\) | ||||
−0.533975 | + | 0.845500i | \(0.679302\pi\) | |||||||
\(360\) | −27.6964 | −1.45973 | ||||||||
\(361\) | 14.1717 | 0.745879 | ||||||||
\(362\) | 37.8179 | 1.98766 | ||||||||
\(363\) | −1.94598 | −0.102137 | ||||||||
\(364\) | −3.09046 | −0.161984 | ||||||||
\(365\) | 50.9964 | 2.66927 | ||||||||
\(366\) | −27.4623 | −1.43548 | ||||||||
\(367\) | −3.71559 | −0.193952 | −0.0969760 | − | 0.995287i | \(-0.530917\pi\) | ||||
−0.0969760 | + | 0.995287i | \(0.530917\pi\) | |||||||
\(368\) | 82.6188 | 4.30680 | ||||||||
\(369\) | 7.35835 | 0.383060 | ||||||||
\(370\) | 59.3344 | 3.08465 | ||||||||
\(371\) | 3.24224 | 0.168329 | ||||||||
\(372\) | −44.6784 | −2.31647 | ||||||||
\(373\) | −8.11999 | −0.420437 | −0.210219 | − | 0.977654i | \(-0.567418\pi\) | ||||
−0.210219 | + | 0.977654i | \(0.567418\pi\) | |||||||
\(374\) | 38.1593 | 1.97317 | ||||||||
\(375\) | −16.8203 | −0.868598 | ||||||||
\(376\) | −18.5619 | −0.957255 | ||||||||
\(377\) | −9.52004 | −0.490307 | ||||||||
\(378\) | 0.698520 | 0.0359280 | ||||||||
\(379\) | 25.9500 | 1.33296 | 0.666482 | − | 0.745521i | \(-0.267799\pi\) | ||||
0.666482 | + | 0.745521i | \(0.267799\pi\) | |||||||
\(380\) | 104.941 | 5.38334 | ||||||||
\(381\) | −2.24302 | −0.114913 | ||||||||
\(382\) | 32.8312 | 1.67979 | ||||||||
\(383\) | −0.169806 | −0.00867666 | −0.00433833 | − | 0.999991i | \(-0.501381\pi\) | ||||
−0.00433833 | + | 0.999991i | \(0.501381\pi\) | |||||||
\(384\) | −1.29651 | −0.0661622 | ||||||||
\(385\) | −3.66184 | −0.186625 | ||||||||
\(386\) | 40.1043 | 2.04126 | ||||||||
\(387\) | 6.70189 | 0.340676 | ||||||||
\(388\) | −43.3423 | −2.20037 | ||||||||
\(389\) | 19.0406 | 0.965397 | 0.482698 | − | 0.875787i | \(-0.339657\pi\) | ||||
0.482698 | + | 0.875787i | \(0.339657\pi\) | |||||||
\(390\) | −23.8124 | −1.20579 | ||||||||
\(391\) | 35.6944 | 1.80514 | ||||||||
\(392\) | 50.5171 | 2.55150 | ||||||||
\(393\) | −18.5651 | −0.936488 | ||||||||
\(394\) | 9.44156 | 0.475659 | ||||||||
\(395\) | −48.8725 | −2.45904 | ||||||||
\(396\) | −17.2592 | −0.867307 | ||||||||
\(397\) | 24.6932 | 1.23931 | 0.619657 | − | 0.784872i | \(-0.287272\pi\) | ||||
0.619657 | + | 0.784872i | \(0.287272\pi\) | |||||||
\(398\) | 26.5173 | 1.32919 | ||||||||
\(399\) | −1.54316 | −0.0772544 | ||||||||
\(400\) | 88.7744 | 4.43872 | ||||||||
\(401\) | −6.38350 | −0.318777 | −0.159388 | − | 0.987216i | \(-0.550952\pi\) | ||||
−0.159388 | + | 0.987216i | \(0.550952\pi\) | |||||||
\(402\) | 23.0153 | 1.14790 | ||||||||
\(403\) | −22.3969 | −1.11567 | ||||||||
\(404\) | 21.4193 | 1.06565 | ||||||||
\(405\) | 3.79845 | 0.188746 | ||||||||
\(406\) | −2.76550 | −0.137250 | ||||||||
\(407\) | 21.5583 | 1.06861 | ||||||||
\(408\) | 29.6617 | 1.46848 | ||||||||
\(409\) | −7.73191 | −0.382318 | −0.191159 | − | 0.981559i | \(-0.561225\pi\) | ||||
−0.191159 | + | 0.981559i | \(0.561225\pi\) | |||||||
\(410\) | −72.8684 | −3.59872 | ||||||||
\(411\) | 21.4624 | 1.05866 | ||||||||
\(412\) | −21.5184 | −1.06014 | ||||||||
\(413\) | −0.859208 | −0.0422789 | ||||||||
\(414\) | −22.8756 | −1.12428 | ||||||||
\(415\) | 20.2357 | 0.993332 | ||||||||
\(416\) | 23.9612 | 1.17479 | ||||||||
\(417\) | 3.50028 | 0.171410 | ||||||||
\(418\) | 54.0262 | 2.64251 | ||||||||
\(419\) | −10.7078 | −0.523112 | −0.261556 | − | 0.965188i | \(-0.584236\pi\) | ||||
−0.261556 | + | 0.965188i | \(0.584236\pi\) | |||||||
\(420\) | −4.88186 | −0.238210 | ||||||||
\(421\) | −7.22015 | −0.351889 | −0.175944 | − | 0.984400i | \(-0.556298\pi\) | ||||
−0.175944 | + | 0.984400i | \(0.556298\pi\) | |||||||
\(422\) | 11.2280 | 0.546569 | ||||||||
\(423\) | 2.54569 | 0.123775 | ||||||||
\(424\) | −88.2339 | −4.28502 | ||||||||
\(425\) | 38.3538 | 1.86043 | ||||||||
\(426\) | −29.7647 | −1.44210 | ||||||||
\(427\) | −2.82235 | −0.136583 | ||||||||
\(428\) | −17.2444 | −0.833540 | ||||||||
\(429\) | −8.65188 | −0.417717 | ||||||||
\(430\) | −66.3677 | −3.20053 | ||||||||
\(431\) | 22.6822 | 1.09256 | 0.546282 | − | 0.837601i | \(-0.316043\pi\) | ||||
0.546282 | + | 0.837601i | \(0.316043\pi\) | |||||||
\(432\) | −9.41582 | −0.453019 | ||||||||
\(433\) | −30.7398 | −1.47726 | −0.738630 | − | 0.674111i | \(-0.764527\pi\) | ||||
−0.738630 | + | 0.674111i | \(0.764527\pi\) | |||||||
\(434\) | −6.50614 | −0.312305 | ||||||||
\(435\) | −15.0384 | −0.721036 | ||||||||
\(436\) | −57.5276 | −2.75507 | ||||||||
\(437\) | 50.5364 | 2.41748 | ||||||||
\(438\) | 35.0014 | 1.67243 | ||||||||
\(439\) | −18.8919 | −0.901662 | −0.450831 | − | 0.892609i | \(-0.648872\pi\) | ||||
−0.450831 | + | 0.892609i | \(0.648872\pi\) | |||||||
\(440\) | 99.6530 | 4.75077 | ||||||||
\(441\) | −6.92821 | −0.329915 | ||||||||
\(442\) | 25.5021 | 1.21301 | ||||||||
\(443\) | 12.2912 | 0.583973 | 0.291986 | − | 0.956422i | \(-0.405684\pi\) | ||||
0.291986 | + | 0.956422i | \(0.405684\pi\) | |||||||
\(444\) | 28.7409 | 1.36398 | ||||||||
\(445\) | −11.4283 | −0.541756 | ||||||||
\(446\) | −57.0524 | −2.70151 | ||||||||
\(447\) | −13.5304 | −0.639966 | ||||||||
\(448\) | 1.91494 | 0.0904722 | ||||||||
\(449\) | −1.87592 | −0.0885303 | −0.0442651 | − | 0.999020i | \(-0.514095\pi\) | ||||
−0.0442651 | + | 0.999020i | \(0.514095\pi\) | |||||||
\(450\) | −24.5800 | −1.15871 | ||||||||
\(451\) | −26.4757 | −1.24669 | ||||||||
\(452\) | −75.3210 | −3.54280 | ||||||||
\(453\) | −2.21669 | −0.104149 | ||||||||
\(454\) | −17.3565 | −0.814579 | ||||||||
\(455\) | −2.44723 | −0.114728 | ||||||||
\(456\) | 41.9953 | 1.96661 | ||||||||
\(457\) | 41.9744 | 1.96348 | 0.981739 | − | 0.190232i | \(-0.0609241\pi\) | ||||
0.981739 | + | 0.190232i | \(0.0609241\pi\) | |||||||
\(458\) | −32.2520 | −1.50704 | ||||||||
\(459\) | −4.06799 | −0.189877 | ||||||||
\(460\) | 159.875 | 7.45420 | ||||||||
\(461\) | −6.42824 | −0.299393 | −0.149696 | − | 0.988732i | \(-0.547830\pi\) | ||||
−0.149696 | + | 0.988732i | \(0.547830\pi\) | |||||||
\(462\) | −2.51331 | −0.116930 | ||||||||
\(463\) | 28.0027 | 1.30140 | 0.650699 | − | 0.759336i | \(-0.274476\pi\) | ||||
0.650699 | + | 0.759336i | \(0.274476\pi\) | |||||||
\(464\) | 37.2781 | 1.73059 | ||||||||
\(465\) | −35.3794 | −1.64068 | ||||||||
\(466\) | 1.13883 | 0.0527551 | ||||||||
\(467\) | 5.52032 | 0.255450 | 0.127725 | − | 0.991810i | \(-0.459233\pi\) | ||||
0.127725 | + | 0.991810i | \(0.459233\pi\) | |||||||
\(468\) | −11.5344 | −0.533180 | ||||||||
\(469\) | 2.36531 | 0.109220 | ||||||||
\(470\) | −25.2095 | −1.16283 | ||||||||
\(471\) | 12.7142 | 0.585837 | ||||||||
\(472\) | 23.3824 | 1.07626 | ||||||||
\(473\) | −24.1138 | −1.10875 | ||||||||
\(474\) | −33.5437 | −1.54071 | ||||||||
\(475\) | 54.3017 | 2.49153 | ||||||||
\(476\) | 5.22828 | 0.239638 | ||||||||
\(477\) | 12.1009 | 0.554063 | ||||||||
\(478\) | −58.9310 | −2.69544 | ||||||||
\(479\) | 17.1502 | 0.783615 | 0.391807 | − | 0.920047i | \(-0.371850\pi\) | ||||
0.391807 | + | 0.920047i | \(0.371850\pi\) | |||||||
\(480\) | 37.8505 | 1.72763 | ||||||||
\(481\) | 14.4076 | 0.656929 | ||||||||
\(482\) | 17.2603 | 0.786184 | ||||||||
\(483\) | −2.35097 | −0.106973 | ||||||||
\(484\) | 9.33449 | 0.424295 | ||||||||
\(485\) | −34.3214 | −1.55845 | ||||||||
\(486\) | 2.60707 | 0.118259 | ||||||||
\(487\) | −31.6438 | −1.43392 | −0.716959 | − | 0.697116i | \(-0.754466\pi\) | ||||
−0.716959 | + | 0.697116i | \(0.754466\pi\) | |||||||
\(488\) | 76.8071 | 3.47689 | ||||||||
\(489\) | −6.00276 | −0.271454 | ||||||||
\(490\) | 68.6089 | 3.09943 | ||||||||
\(491\) | −9.26008 | −0.417901 | −0.208951 | − | 0.977926i | \(-0.567005\pi\) | ||||
−0.208951 | + | 0.977926i | \(0.567005\pi\) | |||||||
\(492\) | −35.2967 | −1.59130 | ||||||||
\(493\) | 16.1055 | 0.725357 | ||||||||
\(494\) | 36.1061 | 1.62449 | ||||||||
\(495\) | −13.6670 | −0.614287 | ||||||||
\(496\) | 87.7007 | 3.93788 | ||||||||
\(497\) | −3.05897 | −0.137213 | ||||||||
\(498\) | 13.8888 | 0.622372 | ||||||||
\(499\) | −19.1263 | −0.856212 | −0.428106 | − | 0.903729i | \(-0.640819\pi\) | ||||
−0.428106 | + | 0.903729i | \(0.640819\pi\) | |||||||
\(500\) | 80.6840 | 3.60830 | ||||||||
\(501\) | −20.8557 | −0.931763 | ||||||||
\(502\) | −21.6113 | −0.964557 | ||||||||
\(503\) | 41.0482 | 1.83025 | 0.915125 | − | 0.403171i | \(-0.132092\pi\) | ||||
0.915125 | + | 0.403171i | \(0.132092\pi\) | |||||||
\(504\) | −1.95363 | −0.0870217 | ||||||||
\(505\) | 16.9613 | 0.754768 | ||||||||
\(506\) | 82.3077 | 3.65902 | ||||||||
\(507\) | 7.21789 | 0.320558 | ||||||||
\(508\) | 10.7594 | 0.477369 | ||||||||
\(509\) | −18.8554 | −0.835752 | −0.417876 | − | 0.908504i | \(-0.637225\pi\) | ||||
−0.417876 | + | 0.908504i | \(0.637225\pi\) | |||||||
\(510\) | 40.2846 | 1.78383 | ||||||||
\(511\) | 3.59716 | 0.159129 | ||||||||
\(512\) | 43.4850 | 1.92178 | ||||||||
\(513\) | −5.75949 | −0.254288 | ||||||||
\(514\) | −74.4297 | −3.28295 | ||||||||
\(515\) | −17.0398 | −0.750861 | ||||||||
\(516\) | −32.1478 | −1.41523 | ||||||||
\(517\) | −9.15951 | −0.402835 | ||||||||
\(518\) | 4.18530 | 0.183891 | ||||||||
\(519\) | −2.72129 | −0.119451 | ||||||||
\(520\) | 66.5988 | 2.92055 | ||||||||
\(521\) | 18.0923 | 0.792638 | 0.396319 | − | 0.918113i | \(-0.370287\pi\) | ||||
0.396319 | + | 0.918113i | \(0.370287\pi\) | |||||||
\(522\) | −10.3216 | −0.451765 | ||||||||
\(523\) | −4.96337 | −0.217033 | −0.108517 | − | 0.994095i | \(-0.534610\pi\) | ||||
−0.108517 | + | 0.994095i | \(0.534610\pi\) | |||||||
\(524\) | 89.0536 | 3.89032 | ||||||||
\(525\) | −2.52613 | −0.110249 | ||||||||
\(526\) | 58.4624 | 2.54908 | ||||||||
\(527\) | 37.8900 | 1.65051 | ||||||||
\(528\) | 33.8786 | 1.47438 | ||||||||
\(529\) | 53.9911 | 2.34744 | ||||||||
\(530\) | −119.833 | −5.20523 | ||||||||
\(531\) | −3.20680 | −0.139163 | ||||||||
\(532\) | 7.40224 | 0.320928 | ||||||||
\(533\) | −17.6939 | −0.766408 | ||||||||
\(534\) | −7.84387 | −0.339437 | ||||||||
\(535\) | −13.6553 | −0.590370 | ||||||||
\(536\) | −64.3695 | −2.78034 | ||||||||
\(537\) | 18.9231 | 0.816592 | ||||||||
\(538\) | −50.6894 | −2.18538 | ||||||||
\(539\) | 24.9281 | 1.07373 | ||||||||
\(540\) | −18.2205 | −0.784084 | ||||||||
\(541\) | −1.21030 | −0.0520350 | −0.0260175 | − | 0.999661i | \(-0.508283\pi\) | ||||
−0.0260175 | + | 0.999661i | \(0.508283\pi\) | |||||||
\(542\) | 48.1841 | 2.06968 | ||||||||
\(543\) | 14.5059 | 0.622507 | ||||||||
\(544\) | −40.5364 | −1.73798 | ||||||||
\(545\) | −45.5543 | −1.95133 | ||||||||
\(546\) | −1.67966 | −0.0718829 | ||||||||
\(547\) | 36.3222 | 1.55303 | 0.776513 | − | 0.630102i | \(-0.216987\pi\) | ||||
0.776513 | + | 0.630102i | \(0.216987\pi\) | |||||||
\(548\) | −102.951 | −4.39787 | ||||||||
\(549\) | −10.5338 | −0.449571 | ||||||||
\(550\) | 88.4401 | 3.77110 | ||||||||
\(551\) | 22.8023 | 0.971412 | ||||||||
\(552\) | 63.9790 | 2.72313 | ||||||||
\(553\) | −3.44734 | −0.146596 | ||||||||
\(554\) | −37.4674 | −1.59184 | ||||||||
\(555\) | 22.7590 | 0.966067 | ||||||||
\(556\) | −16.7902 | −0.712064 | ||||||||
\(557\) | −33.6971 | −1.42779 | −0.713896 | − | 0.700252i | \(-0.753071\pi\) | ||||
−0.713896 | + | 0.700252i | \(0.753071\pi\) | |||||||
\(558\) | −24.2827 | −1.02797 | ||||||||
\(559\) | −16.1154 | −0.681608 | ||||||||
\(560\) | 9.58276 | 0.404945 | ||||||||
\(561\) | 14.6368 | 0.617968 | ||||||||
\(562\) | −68.0558 | −2.87076 | ||||||||
\(563\) | −2.14572 | −0.0904314 | −0.0452157 | − | 0.998977i | \(-0.514398\pi\) | ||||
−0.0452157 | + | 0.998977i | \(0.514398\pi\) | |||||||
\(564\) | −12.2112 | −0.514184 | ||||||||
\(565\) | −59.6443 | −2.50926 | ||||||||
\(566\) | −30.4418 | −1.27957 | ||||||||
\(567\) | 0.267933 | 0.0112521 | ||||||||
\(568\) | 83.2464 | 3.49294 | ||||||||
\(569\) | −43.5427 | −1.82541 | −0.912703 | − | 0.408624i | \(-0.866009\pi\) | ||||
−0.912703 | + | 0.408624i | \(0.866009\pi\) | |||||||
\(570\) | 57.0352 | 2.38894 | ||||||||
\(571\) | −20.2154 | −0.845990 | −0.422995 | − | 0.906132i | \(-0.639021\pi\) | ||||
−0.422995 | + | 0.906132i | \(0.639021\pi\) | |||||||
\(572\) | 41.5015 | 1.73527 | ||||||||
\(573\) | 12.5931 | 0.526086 | ||||||||
\(574\) | −5.13995 | −0.214538 | ||||||||
\(575\) | 82.7274 | 3.44997 | ||||||||
\(576\) | 7.14707 | 0.297795 | ||||||||
\(577\) | −32.6414 | −1.35888 | −0.679440 | − | 0.733731i | \(-0.737777\pi\) | ||||
−0.679440 | + | 0.733731i | \(0.737777\pi\) | |||||||
\(578\) | 1.17702 | 0.0489575 | ||||||||
\(579\) | 15.3829 | 0.639292 | ||||||||
\(580\) | 72.1365 | 2.99530 | ||||||||
\(581\) | 1.42738 | 0.0592175 | ||||||||
\(582\) | −23.5565 | −0.976450 | ||||||||
\(583\) | −43.5398 | −1.80323 | ||||||||
\(584\) | −97.8927 | −4.05083 | ||||||||
\(585\) | −9.13376 | −0.377634 | ||||||||
\(586\) | 19.3824 | 0.800680 | ||||||||
\(587\) | −41.0021 | −1.69234 | −0.846169 | − | 0.532914i | \(-0.821097\pi\) | ||||
−0.846169 | + | 0.532914i | \(0.821097\pi\) | |||||||
\(588\) | 33.2334 | 1.37052 | ||||||||
\(589\) | 53.6449 | 2.21040 | ||||||||
\(590\) | 31.7564 | 1.30739 | ||||||||
\(591\) | 3.62152 | 0.148970 | ||||||||
\(592\) | −56.4165 | −2.31870 | ||||||||
\(593\) | −0.790839 | −0.0324759 | −0.0162379 | − | 0.999868i | \(-0.505169\pi\) | ||||
−0.0162379 | + | 0.999868i | \(0.505169\pi\) | |||||||
\(594\) | −9.38038 | −0.384881 | ||||||||
\(595\) | 4.14011 | 0.169728 | ||||||||
\(596\) | 64.9028 | 2.65852 | ||||||||
\(597\) | 10.1713 | 0.416283 | ||||||||
\(598\) | 55.0068 | 2.24940 | ||||||||
\(599\) | −16.9417 | −0.692221 | −0.346110 | − | 0.938194i | \(-0.612498\pi\) | ||||
−0.346110 | + | 0.938194i | \(0.612498\pi\) | |||||||
\(600\) | 68.7458 | 2.80654 | ||||||||
\(601\) | 18.6504 | 0.760764 | 0.380382 | − | 0.924829i | \(-0.375793\pi\) | ||||
0.380382 | + | 0.924829i | \(0.375793\pi\) | |||||||
\(602\) | −4.68141 | −0.190800 | ||||||||
\(603\) | 8.82801 | 0.359504 | ||||||||
\(604\) | 10.6331 | 0.432653 | ||||||||
\(605\) | 7.39169 | 0.300515 | ||||||||
\(606\) | 11.6414 | 0.472900 | ||||||||
\(607\) | 45.2381 | 1.83616 | 0.918079 | − | 0.396396i | \(-0.129739\pi\) | ||||
0.918079 | + | 0.396396i | \(0.129739\pi\) | |||||||
\(608\) | −57.3917 | −2.32754 | ||||||||
\(609\) | −1.06077 | −0.0429846 | ||||||||
\(610\) | 104.314 | 4.22356 | ||||||||
\(611\) | −6.12136 | −0.247644 | ||||||||
\(612\) | 19.5134 | 0.788782 | ||||||||
\(613\) | 29.4103 | 1.18787 | 0.593936 | − | 0.804513i | \(-0.297573\pi\) | ||||
0.593936 | + | 0.804513i | \(0.297573\pi\) | |||||||
\(614\) | 18.9877 | 0.766282 | ||||||||
\(615\) | −27.9503 | −1.12707 | ||||||||
\(616\) | 7.02927 | 0.283217 | ||||||||
\(617\) | −39.0511 | −1.57214 | −0.786069 | − | 0.618139i | \(-0.787887\pi\) | ||||
−0.786069 | + | 0.618139i | \(0.787887\pi\) | |||||||
\(618\) | −11.6953 | −0.470452 | ||||||||
\(619\) | −3.76517 | −0.151335 | −0.0756674 | − | 0.997133i | \(-0.524109\pi\) | ||||
−0.0756674 | + | 0.997133i | \(0.524109\pi\) | |||||||
\(620\) | 169.709 | 6.81567 | ||||||||
\(621\) | −8.77446 | −0.352107 | ||||||||
\(622\) | −76.7092 | −3.07576 | ||||||||
\(623\) | −0.806127 | −0.0322968 | ||||||||
\(624\) | 22.6413 | 0.906378 | ||||||||
\(625\) | 16.7501 | 0.670003 | ||||||||
\(626\) | −14.1295 | −0.564729 | ||||||||
\(627\) | 20.7229 | 0.827594 | ||||||||
\(628\) | −60.9875 | −2.43366 | ||||||||
\(629\) | −24.3740 | −0.971856 | ||||||||
\(630\) | −2.65329 | −0.105710 | ||||||||
\(631\) | 44.9735 | 1.79037 | 0.895183 | − | 0.445699i | \(-0.147045\pi\) | ||||
0.895183 | + | 0.445699i | \(0.147045\pi\) | |||||||
\(632\) | 93.8156 | 3.73178 | ||||||||
\(633\) | 4.30673 | 0.171177 | ||||||||
\(634\) | 46.4021 | 1.84286 | ||||||||
\(635\) | 8.52000 | 0.338106 | ||||||||
\(636\) | −58.0459 | −2.30167 | ||||||||
\(637\) | 16.6596 | 0.660077 | ||||||||
\(638\) | 37.1378 | 1.47030 | ||||||||
\(639\) | −11.4169 | −0.451646 | ||||||||
\(640\) | 4.92472 | 0.194667 | ||||||||
\(641\) | 13.5355 | 0.534620 | 0.267310 | − | 0.963611i | \(-0.413865\pi\) | ||||
0.267310 | + | 0.963611i | \(0.413865\pi\) | |||||||
\(642\) | −9.37234 | −0.369897 | ||||||||
\(643\) | −16.9111 | −0.666909 | −0.333454 | − | 0.942766i | \(-0.608214\pi\) | ||||
−0.333454 | + | 0.942766i | \(0.608214\pi\) | |||||||
\(644\) | 11.2772 | 0.444382 | ||||||||
\(645\) | −25.4568 | −1.00236 | ||||||||
\(646\) | −61.0824 | −2.40326 | ||||||||
\(647\) | −28.3162 | −1.11322 | −0.556612 | − | 0.830773i | \(-0.687899\pi\) | ||||
−0.556612 | + | 0.830773i | \(0.687899\pi\) | |||||||
\(648\) | −7.29150 | −0.286437 | ||||||||
\(649\) | 11.5382 | 0.452916 | ||||||||
\(650\) | 59.1051 | 2.31829 | ||||||||
\(651\) | −2.49558 | −0.0978093 | ||||||||
\(652\) | 28.7941 | 1.12767 | ||||||||
\(653\) | −34.1458 | −1.33623 | −0.668114 | − | 0.744059i | \(-0.732898\pi\) | ||||
−0.668114 | + | 0.744059i | \(0.732898\pi\) | |||||||
\(654\) | −31.2663 | −1.22261 | ||||||||
\(655\) | 70.5187 | 2.75540 | ||||||||
\(656\) | 69.2849 | 2.70512 | ||||||||
\(657\) | 13.4256 | 0.523782 | ||||||||
\(658\) | −1.77821 | −0.0693219 | ||||||||
\(659\) | −26.7867 | −1.04346 | −0.521730 | − | 0.853111i | \(-0.674713\pi\) | ||||
−0.521730 | + | 0.853111i | \(0.674713\pi\) | |||||||
\(660\) | 65.5582 | 2.55185 | ||||||||
\(661\) | −43.3935 | −1.68781 | −0.843906 | − | 0.536491i | \(-0.819750\pi\) | ||||
−0.843906 | + | 0.536491i | \(0.819750\pi\) | |||||||
\(662\) | 39.8258 | 1.54787 | ||||||||
\(663\) | 9.78189 | 0.379897 | ||||||||
\(664\) | −38.8445 | −1.50746 | ||||||||
\(665\) | 5.86160 | 0.227303 | ||||||||
\(666\) | 15.6207 | 0.605290 | ||||||||
\(667\) | 34.7389 | 1.34509 | ||||||||
\(668\) | 100.041 | 3.87070 | ||||||||
\(669\) | −21.8837 | −0.846074 | ||||||||
\(670\) | −87.4223 | −3.37742 | ||||||||
\(671\) | 37.9011 | 1.46316 | ||||||||
\(672\) | 2.66988 | 0.102993 | ||||||||
\(673\) | −9.08056 | −0.350030 | −0.175015 | − | 0.984566i | \(-0.555997\pi\) | ||||
−0.175015 | + | 0.984566i | \(0.555997\pi\) | |||||||
\(674\) | −30.1975 | −1.16316 | ||||||||
\(675\) | −9.42821 | −0.362892 | ||||||||
\(676\) | −34.6229 | −1.33165 | ||||||||
\(677\) | −20.3909 | −0.783685 | −0.391843 | − | 0.920032i | \(-0.628162\pi\) | ||||
−0.391843 | + | 0.920032i | \(0.628162\pi\) | |||||||
\(678\) | −40.9370 | −1.57217 | ||||||||
\(679\) | −2.42094 | −0.0929073 | ||||||||
\(680\) | −112.669 | −4.32064 | ||||||||
\(681\) | −6.65746 | −0.255114 | ||||||||
\(682\) | 87.3705 | 3.34559 | ||||||||
\(683\) | −11.7185 | −0.448395 | −0.224198 | − | 0.974544i | \(-0.571976\pi\) | ||||
−0.224198 | + | 0.974544i | \(0.571976\pi\) | |||||||
\(684\) | 27.6272 | 1.05635 | ||||||||
\(685\) | −81.5239 | −3.11487 | ||||||||
\(686\) | 9.72913 | 0.371460 | ||||||||
\(687\) | −12.3710 | −0.471982 | ||||||||
\(688\) | 63.1038 | 2.40581 | ||||||||
\(689\) | −29.0979 | −1.10854 | ||||||||
\(690\) | 86.8919 | 3.30792 | ||||||||
\(691\) | 40.7391 | 1.54979 | 0.774893 | − | 0.632092i | \(-0.217803\pi\) | ||||
0.774893 | + | 0.632092i | \(0.217803\pi\) | |||||||
\(692\) | 13.0535 | 0.496221 | ||||||||
\(693\) | −0.964036 | −0.0366207 | ||||||||
\(694\) | −90.4533 | −3.43356 | ||||||||
\(695\) | −13.2956 | −0.504332 | ||||||||
\(696\) | 28.8677 | 1.09423 | ||||||||
\(697\) | 29.9337 | 1.13382 | ||||||||
\(698\) | 7.86222 | 0.297589 | ||||||||
\(699\) | 0.436822 | 0.0165221 | ||||||||
\(700\) | 12.1174 | 0.457994 | ||||||||
\(701\) | 37.7045 | 1.42408 | 0.712040 | − | 0.702139i | \(-0.247771\pi\) | ||||
0.712040 | + | 0.702139i | \(0.247771\pi\) | |||||||
\(702\) | −6.26897 | −0.236607 | ||||||||
\(703\) | −34.5089 | −1.30153 | ||||||||
\(704\) | −25.7155 | −0.969191 | ||||||||
\(705\) | −9.66965 | −0.364180 | ||||||||
\(706\) | −42.7795 | −1.61003 | ||||||||
\(707\) | 1.19641 | 0.0449955 | ||||||||
\(708\) | 15.3825 | 0.578108 | ||||||||
\(709\) | 1.18775 | 0.0446071 | 0.0223035 | − | 0.999751i | \(-0.492900\pi\) | ||||
0.0223035 | + | 0.999751i | \(0.492900\pi\) | |||||||
\(710\) | 113.060 | 4.24305 | ||||||||
\(711\) | −12.8664 | −0.482529 | ||||||||
\(712\) | 21.9379 | 0.822156 | ||||||||
\(713\) | 81.7269 | 3.06070 | ||||||||
\(714\) | 2.84157 | 0.106343 | ||||||||
\(715\) | 32.8637 | 1.22903 | ||||||||
\(716\) | −90.7707 | −3.39226 | ||||||||
\(717\) | −22.6043 | −0.844172 | ||||||||
\(718\) | 52.7535 | 1.96874 | ||||||||
\(719\) | 6.66302 | 0.248489 | 0.124244 | − | 0.992252i | \(-0.460349\pi\) | ||||
0.124244 | + | 0.992252i | \(0.460349\pi\) | |||||||
\(720\) | 35.7655 | 1.33290 | ||||||||
\(721\) | −1.20194 | −0.0447626 | ||||||||
\(722\) | −36.9466 | −1.37501 | ||||||||
\(723\) | 6.62056 | 0.246221 | ||||||||
\(724\) | −69.5821 | −2.58600 | ||||||||
\(725\) | 37.3271 | 1.38629 | ||||||||
\(726\) | 5.07330 | 0.188288 | ||||||||
\(727\) | 51.3143 | 1.90314 | 0.951572 | − | 0.307427i | \(-0.0994680\pi\) | ||||
0.951572 | + | 0.307427i | \(0.0994680\pi\) | |||||||
\(728\) | 4.69771 | 0.174109 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −132.951 | −4.92074 | ||||||||
\(731\) | 27.2632 | 1.00837 | ||||||||
\(732\) | 50.5286 | 1.86759 | ||||||||
\(733\) | −16.4742 | −0.608489 | −0.304244 | − | 0.952594i | \(-0.598404\pi\) | ||||
−0.304244 | + | 0.952594i | \(0.598404\pi\) | |||||||
\(734\) | 9.68679 | 0.357546 | ||||||||
\(735\) | 26.3165 | 0.970697 | ||||||||
\(736\) | −87.4350 | −3.22290 | ||||||||
\(737\) | −31.7636 | −1.17003 | ||||||||
\(738\) | −19.1837 | −0.706163 | ||||||||
\(739\) | −28.6876 | −1.05529 | −0.527646 | − | 0.849464i | \(-0.676925\pi\) | ||||
−0.527646 | + | 0.849464i | \(0.676925\pi\) | |||||||
\(740\) | −109.171 | −4.01320 | ||||||||
\(741\) | 13.8493 | 0.508766 | ||||||||
\(742\) | −8.45274 | −0.310310 | ||||||||
\(743\) | 19.5452 | 0.717046 | 0.358523 | − | 0.933521i | \(-0.383281\pi\) | ||||
0.358523 | + | 0.933521i | \(0.383281\pi\) | |||||||
\(744\) | 67.9144 | 2.48986 | ||||||||
\(745\) | 51.3945 | 1.88295 | ||||||||
\(746\) | 21.1694 | 0.775066 | ||||||||
\(747\) | 5.32736 | 0.194918 | ||||||||
\(748\) | −70.2102 | −2.56714 | ||||||||
\(749\) | −0.963211 | −0.0351950 | ||||||||
\(750\) | 43.8518 | 1.60124 | ||||||||
\(751\) | 52.6114 | 1.91982 | 0.959908 | − | 0.280316i | \(-0.0904393\pi\) | ||||
0.959908 | + | 0.280316i | \(0.0904393\pi\) | |||||||
\(752\) | 23.9697 | 0.874086 | ||||||||
\(753\) | −8.28948 | −0.302085 | ||||||||
\(754\) | 24.8194 | 0.903870 | ||||||||
\(755\) | 8.41999 | 0.306435 | ||||||||
\(756\) | −1.28523 | −0.0467432 | ||||||||
\(757\) | −10.0850 | −0.366546 | −0.183273 | − | 0.983062i | \(-0.558669\pi\) | ||||
−0.183273 | + | 0.983062i | \(0.558669\pi\) | |||||||
\(758\) | −67.6536 | −2.45729 | ||||||||
\(759\) | 31.5710 | 1.14595 | ||||||||
\(760\) | −159.517 | −5.78629 | ||||||||
\(761\) | −15.3482 | −0.556372 | −0.278186 | − | 0.960527i | \(-0.589733\pi\) | ||||
−0.278186 | + | 0.960527i | \(0.589733\pi\) | |||||||
\(762\) | 5.84771 | 0.211840 | ||||||||
\(763\) | −3.21329 | −0.116329 | ||||||||
\(764\) | −60.4070 | −2.18545 | ||||||||
\(765\) | 15.4520 | 0.558670 | ||||||||
\(766\) | 0.442695 | 0.0159952 | ||||||||
\(767\) | 7.71109 | 0.278431 | ||||||||
\(768\) | 17.6742 | 0.637764 | ||||||||
\(769\) | 24.1991 | 0.872643 | 0.436322 | − | 0.899791i | \(-0.356281\pi\) | ||||
0.436322 | + | 0.899791i | \(0.356281\pi\) | |||||||
\(770\) | 9.54668 | 0.344039 | ||||||||
\(771\) | −28.5492 | −1.02817 | ||||||||
\(772\) | −73.7890 | −2.65572 | ||||||||
\(773\) | 10.6841 | 0.384279 | 0.192140 | − | 0.981368i | \(-0.438457\pi\) | ||||
0.192140 | + | 0.981368i | \(0.438457\pi\) | |||||||
\(774\) | −17.4723 | −0.628029 | ||||||||
\(775\) | 87.8161 | 3.15445 | ||||||||
\(776\) | 65.8834 | 2.36507 | ||||||||
\(777\) | 1.60536 | 0.0575921 | ||||||||
\(778\) | −49.6402 | −1.77969 | ||||||||
\(779\) | 42.3803 | 1.51843 | ||||||||
\(780\) | 43.8130 | 1.56876 | ||||||||
\(781\) | 41.0786 | 1.46991 | ||||||||
\(782\) | −93.0578 | −3.32774 | ||||||||
\(783\) | −3.95909 | −0.141486 | ||||||||
\(784\) | −65.2348 | −2.32982 | ||||||||
\(785\) | −48.2940 | −1.72369 | ||||||||
\(786\) | 48.4006 | 1.72639 | ||||||||
\(787\) | 20.7417 | 0.739363 | 0.369682 | − | 0.929158i | \(-0.379467\pi\) | ||||
0.369682 | + | 0.929158i | \(0.379467\pi\) | |||||||
\(788\) | −17.3718 | −0.618844 | ||||||||
\(789\) | 22.4246 | 0.798335 | ||||||||
\(790\) | 127.414 | 4.53319 | ||||||||
\(791\) | −4.20716 | −0.149589 | ||||||||
\(792\) | 26.2352 | 0.932227 | ||||||||
\(793\) | 25.3296 | 0.899479 | ||||||||
\(794\) | −64.3768 | −2.28465 | ||||||||
\(795\) | −45.9647 | −1.63020 | ||||||||
\(796\) | −48.7898 | −1.72931 | ||||||||
\(797\) | 4.81693 | 0.170624 | 0.0853122 | − | 0.996354i | \(-0.472811\pi\) | ||||
0.0853122 | + | 0.996354i | \(0.472811\pi\) | |||||||
\(798\) | 4.02312 | 0.142417 | ||||||||
\(799\) | 10.3558 | 0.366363 | ||||||||
\(800\) | −93.9494 | −3.32161 | ||||||||
\(801\) | −3.00869 | −0.106307 | ||||||||
\(802\) | 16.6422 | 0.587658 | ||||||||
\(803\) | −48.3059 | −1.70468 | ||||||||
\(804\) | −42.3464 | −1.49344 | ||||||||
\(805\) | 8.93002 | 0.314742 | ||||||||
\(806\) | 58.3903 | 2.05671 | ||||||||
\(807\) | −19.4430 | −0.684428 | ||||||||
\(808\) | −32.5589 | −1.14542 | ||||||||
\(809\) | 5.68949 | 0.200032 | 0.100016 | − | 0.994986i | \(-0.468111\pi\) | ||||
0.100016 | + | 0.994986i | \(0.468111\pi\) | |||||||
\(810\) | −9.90282 | −0.347950 | ||||||||
\(811\) | −31.3160 | −1.09965 | −0.549827 | − | 0.835279i | \(-0.685306\pi\) | ||||
−0.549827 | + | 0.835279i | \(0.685306\pi\) | |||||||
\(812\) | 5.08832 | 0.178565 | ||||||||
\(813\) | 18.4821 | 0.648194 | ||||||||
\(814\) | −56.2041 | −1.96995 | ||||||||
\(815\) | 22.8012 | 0.798690 | ||||||||
\(816\) | −38.3035 | −1.34089 | ||||||||
\(817\) | 38.5995 | 1.35042 | ||||||||
\(818\) | 20.1576 | 0.704795 | ||||||||
\(819\) | −0.644272 | −0.0225127 | ||||||||
\(820\) | 134.073 | 4.68202 | ||||||||
\(821\) | −12.6840 | −0.442675 | −0.221338 | − | 0.975197i | \(-0.571042\pi\) | ||||
−0.221338 | + | 0.975197i | \(0.571042\pi\) | |||||||
\(822\) | −55.9541 | −1.95162 | ||||||||
\(823\) | 33.1041 | 1.15394 | 0.576968 | − | 0.816767i | \(-0.304236\pi\) | ||||
0.576968 | + | 0.816767i | \(0.304236\pi\) | |||||||
\(824\) | 32.7095 | 1.13949 | ||||||||
\(825\) | 33.9232 | 1.18105 | ||||||||
\(826\) | 2.24002 | 0.0779401 | ||||||||
\(827\) | 41.8492 | 1.45524 | 0.727620 | − | 0.685980i | \(-0.240626\pi\) | ||||
0.727620 | + | 0.685980i | \(0.240626\pi\) | |||||||
\(828\) | 42.0895 | 1.46271 | ||||||||
\(829\) | 0.0492245 | 0.00170964 | 0.000854819 | − | 1.00000i | \(-0.499728\pi\) | ||||
0.000854819 | 1.00000i | \(0.499728\pi\) | ||||||||
\(830\) | −52.7559 | −1.83118 | ||||||||
\(831\) | −14.3715 | −0.498541 | ||||||||
\(832\) | −17.1859 | −0.595813 | ||||||||
\(833\) | −28.1839 | −0.976514 | ||||||||
\(834\) | −9.12548 | −0.315990 | ||||||||
\(835\) | 79.2192 | 2.74149 | ||||||||
\(836\) | −99.4041 | −3.43796 | ||||||||
\(837\) | −9.31418 | −0.321945 | ||||||||
\(838\) | 27.9161 | 0.964344 | ||||||||
\(839\) | −3.31470 | −0.114436 | −0.0572181 | − | 0.998362i | \(-0.518223\pi\) | ||||
−0.0572181 | + | 0.998362i | \(0.518223\pi\) | |||||||
\(840\) | 7.42077 | 0.256041 | ||||||||
\(841\) | −13.3256 | −0.459504 | ||||||||
\(842\) | 18.8234 | 0.648699 | ||||||||
\(843\) | −26.1043 | −0.899080 | ||||||||
\(844\) | −20.6586 | −0.711099 | ||||||||
\(845\) | −27.4168 | −0.943166 | ||||||||
\(846\) | −6.63678 | −0.228177 | ||||||||
\(847\) | 0.521391 | 0.0179152 | ||||||||
\(848\) | 113.940 | 3.91272 | ||||||||
\(849\) | −11.6766 | −0.400741 | ||||||||
\(850\) | −99.9912 | −3.42967 | ||||||||
\(851\) | −52.5736 | −1.80220 | ||||||||
\(852\) | 54.7648 | 1.87621 | ||||||||
\(853\) | −30.4858 | −1.04381 | −0.521907 | − | 0.853002i | \(-0.674779\pi\) | ||||
−0.521907 | + | 0.853002i | \(0.674779\pi\) | |||||||
\(854\) | 7.35806 | 0.251787 | ||||||||
\(855\) | 21.8771 | 0.748182 | ||||||||
\(856\) | 26.2127 | 0.895933 | ||||||||
\(857\) | 30.6216 | 1.04602 | 0.523008 | − | 0.852328i | \(-0.324810\pi\) | ||||
0.523008 | + | 0.852328i | \(0.324810\pi\) | |||||||
\(858\) | 22.5561 | 0.770052 | ||||||||
\(859\) | 9.02237 | 0.307839 | 0.153920 | − | 0.988083i | \(-0.450810\pi\) | ||||
0.153920 | + | 0.988083i | \(0.450810\pi\) | |||||||
\(860\) | 122.112 | 4.16397 | ||||||||
\(861\) | −1.97154 | −0.0671900 | ||||||||
\(862\) | −59.1342 | −2.01412 | ||||||||
\(863\) | −5.08874 | −0.173223 | −0.0866113 | − | 0.996242i | \(-0.527604\pi\) | ||||
−0.0866113 | + | 0.996242i | \(0.527604\pi\) | |||||||
\(864\) | 9.96472 | 0.339007 | ||||||||
\(865\) | 10.3367 | 0.351458 | ||||||||
\(866\) | 80.1408 | 2.72330 | ||||||||
\(867\) | 0.451471 | 0.0153328 | ||||||||
\(868\) | 11.9708 | 0.406316 | ||||||||
\(869\) | 46.2941 | 1.57042 | ||||||||
\(870\) | 39.2062 | 1.32921 | ||||||||
\(871\) | −21.2279 | −0.719279 | ||||||||
\(872\) | 87.4461 | 2.96130 | ||||||||
\(873\) | −9.03564 | −0.305810 | ||||||||
\(874\) | −131.752 | −4.45658 | ||||||||
\(875\) | 4.50672 | 0.152355 | ||||||||
\(876\) | −64.4001 | −2.17588 | ||||||||
\(877\) | −17.0757 | −0.576607 | −0.288304 | − | 0.957539i | \(-0.593091\pi\) | ||||
−0.288304 | + | 0.957539i | \(0.593091\pi\) | |||||||
\(878\) | 49.2526 | 1.66219 | ||||||||
\(879\) | 7.43455 | 0.250761 | ||||||||
\(880\) | −128.686 | −4.33801 | ||||||||
\(881\) | −15.4514 | −0.520572 | −0.260286 | − | 0.965532i | \(-0.583817\pi\) | ||||
−0.260286 | + | 0.965532i | \(0.583817\pi\) | |||||||
\(882\) | 18.0623 | 0.608191 | ||||||||
\(883\) | 12.5842 | 0.423493 | 0.211746 | − | 0.977325i | \(-0.432085\pi\) | ||||
0.211746 | + | 0.977325i | \(0.432085\pi\) | |||||||
\(884\) | −46.9220 | −1.57816 | ||||||||
\(885\) | 12.1809 | 0.409456 | ||||||||
\(886\) | −32.0440 | −1.07654 | ||||||||
\(887\) | 46.3542 | 1.55642 | 0.778212 | − | 0.628002i | \(-0.216127\pi\) | ||||
0.778212 | + | 0.628002i | \(0.216127\pi\) | |||||||
\(888\) | −43.6882 | −1.46608 | ||||||||
\(889\) | 0.600979 | 0.0201562 | ||||||||
\(890\) | 29.7945 | 0.998714 | ||||||||
\(891\) | −3.59805 | −0.120539 | ||||||||
\(892\) | 104.972 | 3.51473 | ||||||||
\(893\) | 14.6618 | 0.490640 | ||||||||
\(894\) | 35.2747 | 1.17976 | ||||||||
\(895\) | −71.8784 | −2.40263 | ||||||||
\(896\) | 0.347378 | 0.0116051 | ||||||||
\(897\) | 21.0991 | 0.704478 | ||||||||
\(898\) | 4.89066 | 0.163204 | ||||||||
\(899\) | 36.8757 | 1.22987 | ||||||||
\(900\) | 45.2254 | 1.50751 | ||||||||
\(901\) | 49.2264 | 1.63997 | ||||||||
\(902\) | 69.0241 | 2.29825 | ||||||||
\(903\) | −1.79566 | −0.0597557 | ||||||||
\(904\) | 114.493 | 3.80799 | ||||||||
\(905\) | −55.0998 | −1.83158 | ||||||||
\(906\) | 5.77907 | 0.191997 | ||||||||
\(907\) | 13.1600 | 0.436970 | 0.218485 | − | 0.975840i | \(-0.429889\pi\) | ||||
0.218485 | + | 0.975840i | \(0.429889\pi\) | |||||||
\(908\) | 31.9346 | 1.05979 | ||||||||
\(909\) | 4.46532 | 0.148105 | ||||||||
\(910\) | 6.38011 | 0.211499 | ||||||||
\(911\) | 1.05810 | 0.0350566 | 0.0175283 | − | 0.999846i | \(-0.494420\pi\) | ||||
0.0175283 | + | 0.999846i | \(0.494420\pi\) | |||||||
\(912\) | −54.2303 | −1.79575 | ||||||||
\(913\) | −19.1681 | −0.634372 | ||||||||
\(914\) | −109.430 | −3.61963 | ||||||||
\(915\) | 40.0120 | 1.32276 | ||||||||
\(916\) | 59.3413 | 1.96069 | ||||||||
\(917\) | 4.97421 | 0.164263 | ||||||||
\(918\) | 10.6055 | 0.350035 | ||||||||
\(919\) | −20.6586 | −0.681465 | −0.340733 | − | 0.940160i | \(-0.610675\pi\) | ||||
−0.340733 | + | 0.940160i | \(0.610675\pi\) | |||||||
\(920\) | −243.021 | −8.01216 | ||||||||
\(921\) | 7.28317 | 0.239988 | ||||||||
\(922\) | 16.7589 | 0.551924 | ||||||||
\(923\) | 27.4531 | 0.903631 | ||||||||
\(924\) | 4.62431 | 0.152129 | ||||||||
\(925\) | −56.4907 | −1.85740 | ||||||||
\(926\) | −73.0051 | −2.39910 | ||||||||
\(927\) | −4.48598 | −0.147339 | ||||||||
\(928\) | −39.4512 | −1.29505 | ||||||||
\(929\) | 7.81780 | 0.256494 | 0.128247 | − | 0.991742i | \(-0.459065\pi\) | ||||
0.128247 | + | 0.991742i | \(0.459065\pi\) | |||||||
\(930\) | 92.2367 | 3.02456 | ||||||||
\(931\) | −39.9030 | −1.30777 | ||||||||
\(932\) | −2.09536 | −0.0686356 | ||||||||
\(933\) | −29.4235 | −0.963283 | ||||||||
\(934\) | −14.3919 | −0.470916 | ||||||||
\(935\) | −55.5972 | −1.81822 | ||||||||
\(936\) | 17.5332 | 0.573089 | ||||||||
\(937\) | 13.1949 | 0.431057 | 0.215529 | − | 0.976498i | \(-0.430853\pi\) | ||||
0.215529 | + | 0.976498i | \(0.430853\pi\) | |||||||
\(938\) | −6.16654 | −0.201345 | ||||||||
\(939\) | −5.41969 | −0.176865 | ||||||||
\(940\) | 46.3836 | 1.51287 | ||||||||
\(941\) | −30.0295 | −0.978933 | −0.489467 | − | 0.872022i | \(-0.662808\pi\) | ||||
−0.489467 | + | 0.872022i | \(0.662808\pi\) | |||||||
\(942\) | −33.1467 | −1.07998 | ||||||||
\(943\) | 64.5655 | 2.10254 | ||||||||
\(944\) | −30.1947 | −0.982754 | ||||||||
\(945\) | −1.01773 | −0.0331067 | ||||||||
\(946\) | 62.8663 | 2.04396 | ||||||||
\(947\) | −30.5887 | −0.994000 | −0.497000 | − | 0.867751i | \(-0.665565\pi\) | ||||
−0.497000 | + | 0.867751i | \(0.665565\pi\) | |||||||
\(948\) | 61.7179 | 2.00451 | ||||||||
\(949\) | −32.2832 | −1.04796 | ||||||||
\(950\) | −141.568 | −4.59308 | ||||||||
\(951\) | 17.7986 | 0.577158 | ||||||||
\(952\) | −7.94736 | −0.257575 | ||||||||
\(953\) | 11.6434 | 0.377168 | 0.188584 | − | 0.982057i | \(-0.439610\pi\) | ||||
0.188584 | + | 0.982057i | \(0.439610\pi\) | |||||||
\(954\) | −31.5480 | −1.02140 | ||||||||
\(955\) | −47.8344 | −1.54788 | ||||||||
\(956\) | 108.429 | 3.50683 | ||||||||
\(957\) | 14.2450 | 0.460476 | ||||||||
\(958\) | −44.7119 | −1.44458 | ||||||||
\(959\) | −5.75049 | −0.185693 | ||||||||
\(960\) | −27.1478 | −0.876191 | ||||||||
\(961\) | 55.7540 | 1.79852 | ||||||||
\(962\) | −37.5616 | −1.21103 | ||||||||
\(963\) | −3.59497 | −0.115846 | ||||||||
\(964\) | −31.7576 | −1.02284 | ||||||||
\(965\) | −58.4312 | −1.88097 | ||||||||
\(966\) | 6.12913 | 0.197202 | ||||||||
\(967\) | 7.65412 | 0.246140 | 0.123070 | − | 0.992398i | \(-0.460726\pi\) | ||||
0.123070 | + | 0.992398i | \(0.460726\pi\) | |||||||
\(968\) | −14.1891 | −0.456055 | ||||||||
\(969\) | −23.4295 | −0.752665 | ||||||||
\(970\) | 89.4783 | 2.87298 | ||||||||
\(971\) | −30.5790 | −0.981327 | −0.490664 | − | 0.871349i | \(-0.663246\pi\) | ||||
−0.490664 | + | 0.871349i | \(0.663246\pi\) | |||||||
\(972\) | −4.79682 | −0.153858 | ||||||||
\(973\) | −0.937841 | −0.0300658 | ||||||||
\(974\) | 82.4976 | 2.64339 | ||||||||
\(975\) | 22.6711 | 0.726056 | ||||||||
\(976\) | −99.1842 | −3.17481 | ||||||||
\(977\) | −50.2007 | −1.60606 | −0.803031 | − | 0.595937i | \(-0.796781\pi\) | ||||
−0.803031 | + | 0.595937i | \(0.796781\pi\) | |||||||
\(978\) | 15.6496 | 0.500420 | ||||||||
\(979\) | 10.8254 | 0.345982 | ||||||||
\(980\) | −126.235 | −4.03244 | ||||||||
\(981\) | −11.9929 | −0.382903 | ||||||||
\(982\) | 24.1417 | 0.770392 | ||||||||
\(983\) | 13.9497 | 0.444925 | 0.222463 | − | 0.974941i | \(-0.428590\pi\) | ||||
0.222463 | + | 0.974941i | \(0.428590\pi\) | |||||||
\(984\) | 53.6534 | 1.71041 | ||||||||
\(985\) | −13.7562 | −0.438308 | ||||||||
\(986\) | −41.9883 | −1.33718 | ||||||||
\(987\) | −0.682073 | −0.0217106 | ||||||||
\(988\) | −66.4325 | −2.11350 | ||||||||
\(989\) | 58.8055 | 1.86991 | ||||||||
\(990\) | 35.6309 | 1.13242 | ||||||||
\(991\) | −27.3164 | −0.867733 | −0.433866 | − | 0.900977i | \(-0.642851\pi\) | ||||
−0.433866 | + | 0.900977i | \(0.642851\pi\) | |||||||
\(992\) | −92.8132 | −2.94682 | ||||||||
\(993\) | 15.2761 | 0.484771 | ||||||||
\(994\) | 7.97494 | 0.252950 | ||||||||
\(995\) | −38.6351 | −1.22482 | ||||||||
\(996\) | −25.5544 | −0.809722 | ||||||||
\(997\) | 45.8837 | 1.45315 | 0.726576 | − | 0.687087i | \(-0.241111\pi\) | ||||
0.726576 | + | 0.687087i | \(0.241111\pi\) | |||||||
\(998\) | 49.8637 | 1.57841 | ||||||||
\(999\) | 5.99166 | 0.189568 |
(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 | 6033.2.a.c.1.3 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6033.2.a.c.1.3 | ✓ | 82 | 1.1 | even | 1 | trivial |