Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.09927 | −1.78937 | −0.894684 | − | 0.446701i | \(-0.852599\pi\) | ||||
−0.894684 | + | 0.446701i | \(0.852599\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.61970 | −1.17157 | −0.585783 | − | 0.810468i | \(-0.699213\pi\) | ||||
−0.585783 | + | 0.810468i | \(0.699213\pi\) | |||||||
\(6\) | 3.09927 | 1.26527 | ||||||||
\(7\) | −2.12795 | −0.804289 | −0.402144 | − | 0.915576i | \(-0.631735\pi\) | ||||
−0.402144 | + | 0.915576i | \(0.631735\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 6.60550 | 2.20183 | ||||||||
\(10\) | 2.61970 | 0.828422 | ||||||||
\(11\) | 0.148791 | 0.0448623 | 0.0224312 | − | 0.999748i | \(-0.492859\pi\) | ||||
0.0224312 | + | 0.999748i | \(0.492859\pi\) | |||||||
\(12\) | −3.09927 | −0.894684 | ||||||||
\(13\) | 3.47687 | 0.964312 | 0.482156 | − | 0.876085i | \(-0.339854\pi\) | ||||
0.482156 | + | 0.876085i | \(0.339854\pi\) | |||||||
\(14\) | 2.12795 | 0.568718 | ||||||||
\(15\) | 8.11917 | 2.09636 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.38312 | −1.30560 | −0.652799 | − | 0.757531i | \(-0.726405\pi\) | ||||
−0.652799 | + | 0.757531i | \(0.726405\pi\) | |||||||
\(18\) | −6.60550 | −1.55693 | ||||||||
\(19\) | 5.56518 | 1.27674 | 0.638370 | − | 0.769730i | \(-0.279609\pi\) | ||||
0.638370 | + | 0.769730i | \(0.279609\pi\) | |||||||
\(20\) | −2.61970 | −0.585783 | ||||||||
\(21\) | 6.59510 | 1.43917 | ||||||||
\(22\) | −0.148791 | −0.0317225 | ||||||||
\(23\) | 3.85549 | 0.803925 | 0.401963 | − | 0.915656i | \(-0.368328\pi\) | ||||
0.401963 | + | 0.915656i | \(0.368328\pi\) | |||||||
\(24\) | 3.09927 | 0.632637 | ||||||||
\(25\) | 1.86283 | 0.372566 | ||||||||
\(26\) | −3.47687 | −0.681871 | ||||||||
\(27\) | −11.1744 | −2.15052 | ||||||||
\(28\) | −2.12795 | −0.402144 | ||||||||
\(29\) | −5.49729 | −1.02082 | −0.510411 | − | 0.859931i | \(-0.670507\pi\) | ||||
−0.510411 | + | 0.859931i | \(0.670507\pi\) | |||||||
\(30\) | −8.11917 | −1.48235 | ||||||||
\(31\) | 3.00511 | 0.539734 | 0.269867 | − | 0.962898i | \(-0.413020\pi\) | ||||
0.269867 | + | 0.962898i | \(0.413020\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.461146 | −0.0802752 | ||||||||
\(34\) | 5.38312 | 0.923197 | ||||||||
\(35\) | 5.57459 | 0.942277 | ||||||||
\(36\) | 6.60550 | 1.10092 | ||||||||
\(37\) | 9.30172 | 1.52919 | 0.764597 | − | 0.644509i | \(-0.222938\pi\) | ||||
0.764597 | + | 0.644509i | \(0.222938\pi\) | |||||||
\(38\) | −5.56518 | −0.902791 | ||||||||
\(39\) | −10.7758 | −1.72551 | ||||||||
\(40\) | 2.61970 | 0.414211 | ||||||||
\(41\) | 4.64584 | 0.725559 | 0.362779 | − | 0.931875i | \(-0.381828\pi\) | ||||
0.362779 | + | 0.931875i | \(0.381828\pi\) | |||||||
\(42\) | −6.59510 | −1.01765 | ||||||||
\(43\) | −3.45167 | −0.526374 | −0.263187 | − | 0.964745i | \(-0.584774\pi\) | ||||
−0.263187 | + | 0.964745i | \(0.584774\pi\) | |||||||
\(44\) | 0.148791 | 0.0224312 | ||||||||
\(45\) | −17.3044 | −2.57959 | ||||||||
\(46\) | −3.85549 | −0.568461 | ||||||||
\(47\) | −4.44000 | −0.647640 | −0.323820 | − | 0.946119i | \(-0.604967\pi\) | ||||
−0.323820 | + | 0.946119i | \(0.604967\pi\) | |||||||
\(48\) | −3.09927 | −0.447342 | ||||||||
\(49\) | −2.47184 | −0.353120 | ||||||||
\(50\) | −1.86283 | −0.263444 | ||||||||
\(51\) | 16.6838 | 2.33619 | ||||||||
\(52\) | 3.47687 | 0.482156 | ||||||||
\(53\) | −11.9870 | −1.64654 | −0.823271 | − | 0.567649i | \(-0.807853\pi\) | ||||
−0.823271 | + | 0.567649i | \(0.807853\pi\) | |||||||
\(54\) | 11.1744 | 1.52065 | ||||||||
\(55\) | −0.389789 | −0.0525592 | ||||||||
\(56\) | 2.12795 | 0.284359 | ||||||||
\(57\) | −17.2480 | −2.28456 | ||||||||
\(58\) | 5.49729 | 0.721830 | ||||||||
\(59\) | 13.4011 | 1.74468 | 0.872340 | − | 0.488900i | \(-0.162602\pi\) | ||||
0.872340 | + | 0.488900i | \(0.162602\pi\) | |||||||
\(60\) | 8.11917 | 1.04818 | ||||||||
\(61\) | −2.74011 | −0.350835 | −0.175418 | − | 0.984494i | \(-0.556128\pi\) | ||||
−0.175418 | + | 0.984494i | \(0.556128\pi\) | |||||||
\(62\) | −3.00511 | −0.381650 | ||||||||
\(63\) | −14.0562 | −1.77091 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.10837 | −1.12975 | ||||||||
\(66\) | 0.461146 | 0.0567631 | ||||||||
\(67\) | −14.1888 | −1.73344 | −0.866718 | − | 0.498798i | \(-0.833775\pi\) | ||||
−0.866718 | + | 0.498798i | \(0.833775\pi\) | |||||||
\(68\) | −5.38312 | −0.652799 | ||||||||
\(69\) | −11.9492 | −1.43852 | ||||||||
\(70\) | −5.57459 | −0.666291 | ||||||||
\(71\) | −5.84157 | −0.693267 | −0.346633 | − | 0.938001i | \(-0.612675\pi\) | ||||
−0.346633 | + | 0.938001i | \(0.612675\pi\) | |||||||
\(72\) | −6.60550 | −0.778466 | ||||||||
\(73\) | 8.90902 | 1.04272 | 0.521361 | − | 0.853336i | \(-0.325425\pi\) | ||||
0.521361 | + | 0.853336i | \(0.325425\pi\) | |||||||
\(74\) | −9.30172 | −1.08130 | ||||||||
\(75\) | −5.77343 | −0.666658 | ||||||||
\(76\) | 5.56518 | 0.638370 | ||||||||
\(77\) | −0.316621 | −0.0360823 | ||||||||
\(78\) | 10.7758 | 1.22012 | ||||||||
\(79\) | −5.50715 | −0.619602 | −0.309801 | − | 0.950801i | \(-0.600262\pi\) | ||||
−0.309801 | + | 0.950801i | \(0.600262\pi\) | |||||||
\(80\) | −2.61970 | −0.292891 | ||||||||
\(81\) | 14.8162 | 1.64624 | ||||||||
\(82\) | −4.64584 | −0.513048 | ||||||||
\(83\) | −9.90711 | −1.08745 | −0.543723 | − | 0.839265i | \(-0.682986\pi\) | ||||
−0.543723 | + | 0.839265i | \(0.682986\pi\) | |||||||
\(84\) | 6.59510 | 0.719584 | ||||||||
\(85\) | 14.1022 | 1.52959 | ||||||||
\(86\) | 3.45167 | 0.372203 | ||||||||
\(87\) | 17.0376 | 1.82662 | ||||||||
\(88\) | −0.148791 | −0.0158612 | ||||||||
\(89\) | 2.44980 | 0.259678 | 0.129839 | − | 0.991535i | \(-0.458554\pi\) | ||||
0.129839 | + | 0.991535i | \(0.458554\pi\) | |||||||
\(90\) | 17.3044 | 1.82405 | ||||||||
\(91\) | −7.39861 | −0.775585 | ||||||||
\(92\) | 3.85549 | 0.401963 | ||||||||
\(93\) | −9.31367 | −0.965782 | ||||||||
\(94\) | 4.44000 | 0.457951 | ||||||||
\(95\) | −14.5791 | −1.49578 | ||||||||
\(96\) | 3.09927 | 0.316318 | ||||||||
\(97\) | −5.79639 | −0.588534 | −0.294267 | − | 0.955723i | \(-0.595076\pi\) | ||||
−0.294267 | + | 0.955723i | \(0.595076\pi\) | |||||||
\(98\) | 2.47184 | 0.249693 | ||||||||
\(99\) | 0.982843 | 0.0987794 | ||||||||
\(100\) | 1.86283 | 0.186283 | ||||||||
\(101\) | −14.8569 | −1.47832 | −0.739160 | − | 0.673529i | \(-0.764777\pi\) | ||||
−0.739160 | + | 0.673529i | \(0.764777\pi\) | |||||||
\(102\) | −16.6838 | −1.65194 | ||||||||
\(103\) | −2.39252 | −0.235742 | −0.117871 | − | 0.993029i | \(-0.537607\pi\) | ||||
−0.117871 | + | 0.993029i | \(0.537607\pi\) | |||||||
\(104\) | −3.47687 | −0.340936 | ||||||||
\(105\) | −17.2772 | −1.68608 | ||||||||
\(106\) | 11.9870 | 1.16428 | ||||||||
\(107\) | 3.31461 | 0.320436 | 0.160218 | − | 0.987082i | \(-0.448780\pi\) | ||||
0.160218 | + | 0.987082i | \(0.448780\pi\) | |||||||
\(108\) | −11.1744 | −1.07526 | ||||||||
\(109\) | 5.94762 | 0.569678 | 0.284839 | − | 0.958575i | \(-0.408060\pi\) | ||||
0.284839 | + | 0.958575i | \(0.408060\pi\) | |||||||
\(110\) | 0.389789 | 0.0371649 | ||||||||
\(111\) | −28.8286 | −2.73629 | ||||||||
\(112\) | −2.12795 | −0.201072 | ||||||||
\(113\) | −6.35860 | −0.598167 | −0.299083 | − | 0.954227i | \(-0.596681\pi\) | ||||
−0.299083 | + | 0.954227i | \(0.596681\pi\) | |||||||
\(114\) | 17.2480 | 1.61543 | ||||||||
\(115\) | −10.1002 | −0.941851 | ||||||||
\(116\) | −5.49729 | −0.510411 | ||||||||
\(117\) | 22.9665 | 2.12325 | ||||||||
\(118\) | −13.4011 | −1.23367 | ||||||||
\(119\) | 11.4550 | 1.05008 | ||||||||
\(120\) | −8.11917 | −0.741176 | ||||||||
\(121\) | −10.9779 | −0.997987 | ||||||||
\(122\) | 2.74011 | 0.248078 | ||||||||
\(123\) | −14.3987 | −1.29829 | ||||||||
\(124\) | 3.00511 | 0.269867 | ||||||||
\(125\) | 8.21844 | 0.735080 | ||||||||
\(126\) | 14.0562 | 1.25222 | ||||||||
\(127\) | 14.2280 | 1.26253 | 0.631266 | − | 0.775566i | \(-0.282536\pi\) | ||||
0.631266 | + | 0.775566i | \(0.282536\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 10.6977 | 0.941877 | ||||||||
\(130\) | 9.10837 | 0.798857 | ||||||||
\(131\) | −8.78974 | −0.767963 | −0.383982 | − | 0.923341i | \(-0.625447\pi\) | ||||
−0.383982 | + | 0.923341i | \(0.625447\pi\) | |||||||
\(132\) | −0.461146 | −0.0401376 | ||||||||
\(133\) | −11.8424 | −1.02687 | ||||||||
\(134\) | 14.1888 | 1.22573 | ||||||||
\(135\) | 29.2737 | 2.51948 | ||||||||
\(136\) | 5.38312 | 0.461599 | ||||||||
\(137\) | −2.13472 | −0.182382 | −0.0911909 | − | 0.995833i | \(-0.529067\pi\) | ||||
−0.0911909 | + | 0.995833i | \(0.529067\pi\) | |||||||
\(138\) | 11.9492 | 1.01719 | ||||||||
\(139\) | 21.7640 | 1.84600 | 0.923001 | − | 0.384798i | \(-0.125729\pi\) | ||||
0.923001 | + | 0.384798i | \(0.125729\pi\) | |||||||
\(140\) | 5.57459 | 0.471139 | ||||||||
\(141\) | 13.7608 | 1.15887 | ||||||||
\(142\) | 5.84157 | 0.490214 | ||||||||
\(143\) | 0.517329 | 0.0432613 | ||||||||
\(144\) | 6.60550 | 0.550459 | ||||||||
\(145\) | 14.4013 | 1.19596 | ||||||||
\(146\) | −8.90902 | −0.737315 | ||||||||
\(147\) | 7.66090 | 0.631860 | ||||||||
\(148\) | 9.30172 | 0.764597 | ||||||||
\(149\) | 9.16194 | 0.750575 | 0.375288 | − | 0.926908i | \(-0.377544\pi\) | ||||
0.375288 | + | 0.926908i | \(0.377544\pi\) | |||||||
\(150\) | 5.77343 | 0.471398 | ||||||||
\(151\) | 8.39943 | 0.683536 | 0.341768 | − | 0.939784i | \(-0.388974\pi\) | ||||
0.341768 | + | 0.939784i | \(0.388974\pi\) | |||||||
\(152\) | −5.56518 | −0.451396 | ||||||||
\(153\) | −35.5582 | −2.87471 | ||||||||
\(154\) | 0.316621 | 0.0255140 | ||||||||
\(155\) | −7.87249 | −0.632334 | ||||||||
\(156\) | −10.7758 | −0.862754 | ||||||||
\(157\) | −7.42604 | −0.592662 | −0.296331 | − | 0.955085i | \(-0.595763\pi\) | ||||
−0.296331 | + | 0.955085i | \(0.595763\pi\) | |||||||
\(158\) | 5.50715 | 0.438125 | ||||||||
\(159\) | 37.1510 | 2.94627 | ||||||||
\(160\) | 2.61970 | 0.207106 | ||||||||
\(161\) | −8.20428 | −0.646588 | ||||||||
\(162\) | −14.8162 | −1.16407 | ||||||||
\(163\) | 11.6891 | 0.915559 | 0.457779 | − | 0.889066i | \(-0.348645\pi\) | ||||
0.457779 | + | 0.889066i | \(0.348645\pi\) | |||||||
\(164\) | 4.64584 | 0.362779 | ||||||||
\(165\) | 1.20806 | 0.0940476 | ||||||||
\(166\) | 9.90711 | 0.768941 | ||||||||
\(167\) | 17.5163 | 1.35545 | 0.677725 | − | 0.735315i | \(-0.262966\pi\) | ||||
0.677725 | + | 0.735315i | \(0.262966\pi\) | |||||||
\(168\) | −6.59510 | −0.508823 | ||||||||
\(169\) | −0.911340 | −0.0701031 | ||||||||
\(170\) | −14.1022 | −1.08159 | ||||||||
\(171\) | 36.7608 | 2.81117 | ||||||||
\(172\) | −3.45167 | −0.263187 | ||||||||
\(173\) | −18.4618 | −1.40362 | −0.701812 | − | 0.712362i | \(-0.747625\pi\) | ||||
−0.701812 | + | 0.712362i | \(0.747625\pi\) | |||||||
\(174\) | −17.0376 | −1.29162 | ||||||||
\(175\) | −3.96401 | −0.299651 | ||||||||
\(176\) | 0.148791 | 0.0112156 | ||||||||
\(177\) | −41.5338 | −3.12187 | ||||||||
\(178\) | −2.44980 | −0.183620 | ||||||||
\(179\) | −24.4519 | −1.82762 | −0.913809 | − | 0.406144i | \(-0.866873\pi\) | ||||
−0.913809 | + | 0.406144i | \(0.866873\pi\) | |||||||
\(180\) | −17.3044 | −1.28980 | ||||||||
\(181\) | −19.7749 | −1.46985 | −0.734927 | − | 0.678147i | \(-0.762783\pi\) | ||||
−0.734927 | + | 0.678147i | \(0.762783\pi\) | |||||||
\(182\) | 7.39861 | 0.548421 | ||||||||
\(183\) | 8.49235 | 0.627773 | ||||||||
\(184\) | −3.85549 | −0.284230 | ||||||||
\(185\) | −24.3677 | −1.79155 | ||||||||
\(186\) | 9.31367 | 0.682911 | ||||||||
\(187\) | −0.800962 | −0.0585722 | ||||||||
\(188\) | −4.44000 | −0.323820 | ||||||||
\(189\) | 23.7786 | 1.72964 | ||||||||
\(190\) | 14.5791 | 1.05768 | ||||||||
\(191\) | 15.3198 | 1.10850 | 0.554252 | − | 0.832349i | \(-0.313005\pi\) | ||||
0.554252 | + | 0.832349i | \(0.313005\pi\) | |||||||
\(192\) | −3.09927 | −0.223671 | ||||||||
\(193\) | −6.32568 | −0.455333 | −0.227666 | − | 0.973739i | \(-0.573110\pi\) | ||||
−0.227666 | + | 0.973739i | \(0.573110\pi\) | |||||||
\(194\) | 5.79639 | 0.416157 | ||||||||
\(195\) | 28.2293 | 2.02155 | ||||||||
\(196\) | −2.47184 | −0.176560 | ||||||||
\(197\) | −1.16579 | −0.0830594 | −0.0415297 | − | 0.999137i | \(-0.513223\pi\) | ||||
−0.0415297 | + | 0.999137i | \(0.513223\pi\) | |||||||
\(198\) | −0.982843 | −0.0698476 | ||||||||
\(199\) | −2.03661 | −0.144372 | −0.0721858 | − | 0.997391i | \(-0.522997\pi\) | ||||
−0.0721858 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(200\) | −1.86283 | −0.131722 | ||||||||
\(201\) | 43.9750 | 3.10176 | ||||||||
\(202\) | 14.8569 | 1.04533 | ||||||||
\(203\) | 11.6980 | 0.821035 | ||||||||
\(204\) | 16.6838 | 1.16810 | ||||||||
\(205\) | −12.1707 | −0.850040 | ||||||||
\(206\) | 2.39252 | 0.166694 | ||||||||
\(207\) | 25.4675 | 1.77011 | ||||||||
\(208\) | 3.47687 | 0.241078 | ||||||||
\(209\) | 0.828051 | 0.0572775 | ||||||||
\(210\) | 17.2772 | 1.19224 | ||||||||
\(211\) | −12.2799 | −0.845385 | −0.422692 | − | 0.906273i | \(-0.638915\pi\) | ||||
−0.422692 | + | 0.906273i | \(0.638915\pi\) | |||||||
\(212\) | −11.9870 | −0.823271 | ||||||||
\(213\) | 18.1046 | 1.24051 | ||||||||
\(214\) | −3.31461 | −0.226582 | ||||||||
\(215\) | 9.04234 | 0.616682 | ||||||||
\(216\) | 11.1744 | 0.760325 | ||||||||
\(217\) | −6.39472 | −0.434102 | ||||||||
\(218\) | −5.94762 | −0.402824 | ||||||||
\(219\) | −27.6115 | −1.86581 | ||||||||
\(220\) | −0.389789 | −0.0262796 | ||||||||
\(221\) | −18.7164 | −1.25900 | ||||||||
\(222\) | 28.8286 | 1.93485 | ||||||||
\(223\) | −0.298598 | −0.0199956 | −0.00999779 | − | 0.999950i | \(-0.503182\pi\) | ||||
−0.00999779 | + | 0.999950i | \(0.503182\pi\) | |||||||
\(224\) | 2.12795 | 0.142180 | ||||||||
\(225\) | 12.3049 | 0.820330 | ||||||||
\(226\) | 6.35860 | 0.422968 | ||||||||
\(227\) | 13.7237 | 0.910876 | 0.455438 | − | 0.890267i | \(-0.349483\pi\) | ||||
0.455438 | + | 0.890267i | \(0.349483\pi\) | |||||||
\(228\) | −17.2480 | −1.14228 | ||||||||
\(229\) | 6.54010 | 0.432182 | 0.216091 | − | 0.976373i | \(-0.430669\pi\) | ||||
0.216091 | + | 0.976373i | \(0.430669\pi\) | |||||||
\(230\) | 10.1002 | 0.665989 | ||||||||
\(231\) | 0.981294 | 0.0645644 | ||||||||
\(232\) | 5.49729 | 0.360915 | ||||||||
\(233\) | 15.0625 | 0.986775 | 0.493388 | − | 0.869810i | \(-0.335758\pi\) | ||||
0.493388 | + | 0.869810i | \(0.335758\pi\) | |||||||
\(234\) | −22.9665 | −1.50137 | ||||||||
\(235\) | 11.6315 | 0.758753 | ||||||||
\(236\) | 13.4011 | 0.872340 | ||||||||
\(237\) | 17.0682 | 1.10870 | ||||||||
\(238\) | −11.4550 | −0.742517 | ||||||||
\(239\) | 23.0423 | 1.49048 | 0.745241 | − | 0.666795i | \(-0.232334\pi\) | ||||
0.745241 | + | 0.666795i | \(0.232334\pi\) | |||||||
\(240\) | 8.11917 | 0.524090 | ||||||||
\(241\) | 16.4598 | 1.06027 | 0.530135 | − | 0.847913i | \(-0.322141\pi\) | ||||
0.530135 | + | 0.847913i | \(0.322141\pi\) | |||||||
\(242\) | 10.9779 | 0.705684 | ||||||||
\(243\) | −12.3960 | −0.795206 | ||||||||
\(244\) | −2.74011 | −0.175418 | ||||||||
\(245\) | 6.47547 | 0.413703 | ||||||||
\(246\) | 14.3987 | 0.918031 | ||||||||
\(247\) | 19.3494 | 1.23118 | ||||||||
\(248\) | −3.00511 | −0.190825 | ||||||||
\(249\) | 30.7049 | 1.94584 | ||||||||
\(250\) | −8.21844 | −0.519780 | ||||||||
\(251\) | 14.2485 | 0.899356 | 0.449678 | − | 0.893191i | \(-0.351539\pi\) | ||||
0.449678 | + | 0.893191i | \(0.351539\pi\) | |||||||
\(252\) | −14.0562 | −0.885455 | ||||||||
\(253\) | 0.573664 | 0.0360660 | ||||||||
\(254\) | −14.2280 | −0.892745 | ||||||||
\(255\) | −43.7065 | −2.73701 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.4295 | −1.46149 | −0.730746 | − | 0.682650i | \(-0.760828\pi\) | ||||
−0.730746 | + | 0.682650i | \(0.760828\pi\) | |||||||
\(258\) | −10.6977 | −0.666008 | ||||||||
\(259\) | −19.7936 | −1.22991 | ||||||||
\(260\) | −9.10837 | −0.564877 | ||||||||
\(261\) | −36.3124 | −2.24768 | ||||||||
\(262\) | 8.78974 | 0.543032 | ||||||||
\(263\) | −14.7623 | −0.910280 | −0.455140 | − | 0.890420i | \(-0.650411\pi\) | ||||
−0.455140 | + | 0.890420i | \(0.650411\pi\) | |||||||
\(264\) | 0.461146 | 0.0283816 | ||||||||
\(265\) | 31.4024 | 1.92903 | ||||||||
\(266\) | 11.8424 | 0.726105 | ||||||||
\(267\) | −7.59260 | −0.464659 | ||||||||
\(268\) | −14.1888 | −0.866718 | ||||||||
\(269\) | 12.8535 | 0.783691 | 0.391846 | − | 0.920031i | \(-0.371837\pi\) | ||||
0.391846 | + | 0.920031i | \(0.371837\pi\) | |||||||
\(270\) | −29.2737 | −1.78154 | ||||||||
\(271\) | 17.6066 | 1.06952 | 0.534761 | − | 0.845003i | \(-0.320402\pi\) | ||||
0.534761 | + | 0.845003i | \(0.320402\pi\) | |||||||
\(272\) | −5.38312 | −0.326400 | ||||||||
\(273\) | 22.9303 | 1.38781 | ||||||||
\(274\) | 2.13472 | 0.128963 | ||||||||
\(275\) | 0.277174 | 0.0167142 | ||||||||
\(276\) | −11.9492 | −0.719259 | ||||||||
\(277\) | −24.0872 | −1.44726 | −0.723630 | − | 0.690188i | \(-0.757528\pi\) | ||||
−0.723630 | + | 0.690188i | \(0.757528\pi\) | |||||||
\(278\) | −21.7640 | −1.30532 | ||||||||
\(279\) | 19.8503 | 1.18841 | ||||||||
\(280\) | −5.57459 | −0.333145 | ||||||||
\(281\) | 22.4219 | 1.33758 | 0.668791 | − | 0.743451i | \(-0.266812\pi\) | ||||
0.668791 | + | 0.743451i | \(0.266812\pi\) | |||||||
\(282\) | −13.7608 | −0.819442 | ||||||||
\(283\) | 6.38848 | 0.379756 | 0.189878 | − | 0.981808i | \(-0.439191\pi\) | ||||
0.189878 | + | 0.981808i | \(0.439191\pi\) | |||||||
\(284\) | −5.84157 | −0.346633 | ||||||||
\(285\) | 45.1847 | 2.67651 | ||||||||
\(286\) | −0.517329 | −0.0305903 | ||||||||
\(287\) | −9.88611 | −0.583559 | ||||||||
\(288\) | −6.60550 | −0.389233 | ||||||||
\(289\) | 11.9780 | 0.704587 | ||||||||
\(290\) | −14.4013 | −0.845671 | ||||||||
\(291\) | 17.9646 | 1.05310 | ||||||||
\(292\) | 8.90902 | 0.521361 | ||||||||
\(293\) | −25.6763 | −1.50003 | −0.750014 | − | 0.661422i | \(-0.769953\pi\) | ||||
−0.750014 | + | 0.661422i | \(0.769953\pi\) | |||||||
\(294\) | −7.66090 | −0.446793 | ||||||||
\(295\) | −35.1070 | −2.04401 | ||||||||
\(296\) | −9.30172 | −0.540651 | ||||||||
\(297\) | −1.66266 | −0.0964775 | ||||||||
\(298\) | −9.16194 | −0.530737 | ||||||||
\(299\) | 13.4051 | 0.775234 | ||||||||
\(300\) | −5.77343 | −0.333329 | ||||||||
\(301\) | 7.34497 | 0.423357 | ||||||||
\(302\) | −8.39943 | −0.483333 | ||||||||
\(303\) | 46.0457 | 2.64526 | ||||||||
\(304\) | 5.56518 | 0.319185 | ||||||||
\(305\) | 7.17827 | 0.411026 | ||||||||
\(306\) | 35.5582 | 2.03273 | ||||||||
\(307\) | −9.42016 | −0.537637 | −0.268818 | − | 0.963191i | \(-0.586633\pi\) | ||||
−0.268818 | + | 0.963191i | \(0.586633\pi\) | |||||||
\(308\) | −0.316621 | −0.0180411 | ||||||||
\(309\) | 7.41506 | 0.421828 | ||||||||
\(310\) | 7.87249 | 0.447128 | ||||||||
\(311\) | 18.4008 | 1.04342 | 0.521708 | − | 0.853124i | \(-0.325295\pi\) | ||||
0.521708 | + | 0.853124i | \(0.325295\pi\) | |||||||
\(312\) | 10.7758 | 0.610059 | ||||||||
\(313\) | 2.65401 | 0.150014 | 0.0750068 | − | 0.997183i | \(-0.476102\pi\) | ||||
0.0750068 | + | 0.997183i | \(0.476102\pi\) | |||||||
\(314\) | 7.42604 | 0.419075 | ||||||||
\(315\) | 36.8230 | 2.07474 | ||||||||
\(316\) | −5.50715 | −0.309801 | ||||||||
\(317\) | −4.05309 | −0.227644 | −0.113822 | − | 0.993501i | \(-0.536309\pi\) | ||||
−0.113822 | + | 0.993501i | \(0.536309\pi\) | |||||||
\(318\) | −37.1510 | −2.08333 | ||||||||
\(319\) | −0.817950 | −0.0457964 | ||||||||
\(320\) | −2.61970 | −0.146446 | ||||||||
\(321\) | −10.2729 | −0.573377 | ||||||||
\(322\) | 8.20428 | 0.457207 | ||||||||
\(323\) | −29.9580 | −1.66691 | ||||||||
\(324\) | 14.8162 | 0.823120 | ||||||||
\(325\) | 6.47683 | 0.359270 | ||||||||
\(326\) | −11.6891 | −0.647398 | ||||||||
\(327\) | −18.4333 | −1.01936 | ||||||||
\(328\) | −4.64584 | −0.256524 | ||||||||
\(329\) | 9.44808 | 0.520890 | ||||||||
\(330\) | −1.20806 | −0.0665017 | ||||||||
\(331\) | −24.7302 | −1.35929 | −0.679646 | − | 0.733540i | \(-0.737867\pi\) | ||||
−0.679646 | + | 0.733540i | \(0.737867\pi\) | |||||||
\(332\) | −9.90711 | −0.543723 | ||||||||
\(333\) | 61.4425 | 3.36703 | ||||||||
\(334\) | −17.5163 | −0.958448 | ||||||||
\(335\) | 37.1704 | 2.03084 | ||||||||
\(336\) | 6.59510 | 0.359792 | ||||||||
\(337\) | 16.6246 | 0.905597 | 0.452799 | − | 0.891613i | \(-0.350426\pi\) | ||||
0.452799 | + | 0.891613i | \(0.350426\pi\) | |||||||
\(338\) | 0.911340 | 0.0495704 | ||||||||
\(339\) | 19.7070 | 1.07034 | ||||||||
\(340\) | 14.1022 | 0.764797 | ||||||||
\(341\) | 0.447135 | 0.0242137 | ||||||||
\(342\) | −36.7608 | −1.98780 | ||||||||
\(343\) | 20.1556 | 1.08830 | ||||||||
\(344\) | 3.45167 | 0.186101 | ||||||||
\(345\) | 31.3034 | 1.68532 | ||||||||
\(346\) | 18.4618 | 0.992512 | ||||||||
\(347\) | 14.3029 | 0.767819 | 0.383909 | − | 0.923371i | \(-0.374577\pi\) | ||||
0.383909 | + | 0.923371i | \(0.374577\pi\) | |||||||
\(348\) | 17.0376 | 0.913312 | ||||||||
\(349\) | 12.6510 | 0.677191 | 0.338596 | − | 0.940932i | \(-0.390048\pi\) | ||||
0.338596 | + | 0.940932i | \(0.390048\pi\) | |||||||
\(350\) | 3.96401 | 0.211885 | ||||||||
\(351\) | −38.8522 | −2.07377 | ||||||||
\(352\) | −0.148791 | −0.00793061 | ||||||||
\(353\) | −19.6704 | −1.04695 | −0.523474 | − | 0.852041i | \(-0.675364\pi\) | ||||
−0.523474 | + | 0.852041i | \(0.675364\pi\) | |||||||
\(354\) | 41.5338 | 2.20750 | ||||||||
\(355\) | 15.3032 | 0.812208 | ||||||||
\(356\) | 2.44980 | 0.129839 | ||||||||
\(357\) | −35.5022 | −1.87898 | ||||||||
\(358\) | 24.4519 | 1.29232 | ||||||||
\(359\) | 7.69351 | 0.406048 | 0.203024 | − | 0.979174i | \(-0.434923\pi\) | ||||
0.203024 | + | 0.979174i | \(0.434923\pi\) | |||||||
\(360\) | 17.3044 | 0.912024 | ||||||||
\(361\) | 11.9712 | 0.630065 | ||||||||
\(362\) | 19.7749 | 1.03934 | ||||||||
\(363\) | 34.0234 | 1.78577 | ||||||||
\(364\) | −7.39861 | −0.387793 | ||||||||
\(365\) | −23.3390 | −1.22162 | ||||||||
\(366\) | −8.49235 | −0.443902 | ||||||||
\(367\) | 1.40887 | 0.0735427 | 0.0367713 | − | 0.999324i | \(-0.488293\pi\) | ||||
0.0367713 | + | 0.999324i | \(0.488293\pi\) | |||||||
\(368\) | 3.85549 | 0.200981 | ||||||||
\(369\) | 30.6881 | 1.59756 | ||||||||
\(370\) | 24.3677 | 1.26682 | ||||||||
\(371\) | 25.5077 | 1.32430 | ||||||||
\(372\) | −9.31367 | −0.482891 | ||||||||
\(373\) | 32.5569 | 1.68573 | 0.842866 | − | 0.538123i | \(-0.180866\pi\) | ||||
0.842866 | + | 0.538123i | \(0.180866\pi\) | |||||||
\(374\) | 0.800962 | 0.0414168 | ||||||||
\(375\) | −25.4712 | −1.31533 | ||||||||
\(376\) | 4.44000 | 0.228975 | ||||||||
\(377\) | −19.1134 | −0.984390 | ||||||||
\(378\) | −23.7786 | −1.22304 | ||||||||
\(379\) | −1.90954 | −0.0980867 | −0.0490434 | − | 0.998797i | \(-0.515617\pi\) | ||||
−0.0490434 | + | 0.998797i | \(0.515617\pi\) | |||||||
\(380\) | −14.5791 | −0.747892 | ||||||||
\(381\) | −44.0965 | −2.25913 | ||||||||
\(382\) | −15.3198 | −0.783830 | ||||||||
\(383\) | 38.2354 | 1.95374 | 0.976869 | − | 0.213837i | \(-0.0685961\pi\) | ||||
0.976869 | + | 0.213837i | \(0.0685961\pi\) | |||||||
\(384\) | 3.09927 | 0.158159 | ||||||||
\(385\) | 0.829451 | 0.0422727 | ||||||||
\(386\) | 6.32568 | 0.321969 | ||||||||
\(387\) | −22.8000 | −1.15899 | ||||||||
\(388\) | −5.79639 | −0.294267 | ||||||||
\(389\) | −7.12094 | −0.361046 | −0.180523 | − | 0.983571i | \(-0.557779\pi\) | ||||
−0.180523 | + | 0.983571i | \(0.557779\pi\) | |||||||
\(390\) | −28.2293 | −1.42945 | ||||||||
\(391\) | −20.7546 | −1.04960 | ||||||||
\(392\) | 2.47184 | 0.124847 | ||||||||
\(393\) | 27.2418 | 1.37417 | ||||||||
\(394\) | 1.16579 | 0.0587318 | ||||||||
\(395\) | 14.4271 | 0.725905 | ||||||||
\(396\) | 0.982843 | 0.0493897 | ||||||||
\(397\) | −0.699225 | −0.0350931 | −0.0175465 | − | 0.999846i | \(-0.505586\pi\) | ||||
−0.0175465 | + | 0.999846i | \(0.505586\pi\) | |||||||
\(398\) | 2.03661 | 0.102086 | ||||||||
\(399\) | 36.7029 | 1.83744 | ||||||||
\(400\) | 1.86283 | 0.0931416 | ||||||||
\(401\) | −5.06910 | −0.253139 | −0.126569 | − | 0.991958i | \(-0.540397\pi\) | ||||
−0.126569 | + | 0.991958i | \(0.540397\pi\) | |||||||
\(402\) | −43.9750 | −2.19327 | ||||||||
\(403\) | 10.4484 | 0.520472 | ||||||||
\(404\) | −14.8569 | −0.739160 | ||||||||
\(405\) | −38.8139 | −1.92868 | ||||||||
\(406\) | −11.6980 | −0.580560 | ||||||||
\(407\) | 1.38402 | 0.0686032 | ||||||||
\(408\) | −16.6838 | −0.825970 | ||||||||
\(409\) | −31.8131 | −1.57306 | −0.786528 | − | 0.617555i | \(-0.788123\pi\) | ||||
−0.786528 | + | 0.617555i | \(0.788123\pi\) | |||||||
\(410\) | 12.1707 | 0.601069 | ||||||||
\(411\) | 6.61609 | 0.326348 | ||||||||
\(412\) | −2.39252 | −0.117871 | ||||||||
\(413\) | −28.5169 | −1.40323 | ||||||||
\(414\) | −25.4675 | −1.25166 | ||||||||
\(415\) | 25.9537 | 1.27402 | ||||||||
\(416\) | −3.47687 | −0.170468 | ||||||||
\(417\) | −67.4527 | −3.30317 | ||||||||
\(418\) | −0.828051 | −0.0405013 | ||||||||
\(419\) | −10.6895 | −0.522217 | −0.261109 | − | 0.965309i | \(-0.584088\pi\) | ||||
−0.261109 | + | 0.965309i | \(0.584088\pi\) | |||||||
\(420\) | −17.2772 | −0.843040 | ||||||||
\(421\) | −33.9650 | −1.65535 | −0.827676 | − | 0.561206i | \(-0.810337\pi\) | ||||
−0.827676 | + | 0.561206i | \(0.810337\pi\) | |||||||
\(422\) | 12.2799 | 0.597777 | ||||||||
\(423\) | −29.3284 | −1.42600 | ||||||||
\(424\) | 11.9870 | 0.582140 | ||||||||
\(425\) | −10.0278 | −0.486422 | ||||||||
\(426\) | −18.1046 | −0.877172 | ||||||||
\(427\) | 5.83081 | 0.282173 | ||||||||
\(428\) | 3.31461 | 0.160218 | ||||||||
\(429\) | −1.60335 | −0.0774103 | ||||||||
\(430\) | −9.04234 | −0.436060 | ||||||||
\(431\) | −6.40630 | −0.308581 | −0.154290 | − | 0.988026i | \(-0.549309\pi\) | ||||
−0.154290 | + | 0.988026i | \(0.549309\pi\) | |||||||
\(432\) | −11.1744 | −0.537631 | ||||||||
\(433\) | 3.40899 | 0.163826 | 0.0819128 | − | 0.996639i | \(-0.473897\pi\) | ||||
0.0819128 | + | 0.996639i | \(0.473897\pi\) | |||||||
\(434\) | 6.39472 | 0.306956 | ||||||||
\(435\) | −44.6335 | −2.14001 | ||||||||
\(436\) | 5.94762 | 0.284839 | ||||||||
\(437\) | 21.4565 | 1.02640 | ||||||||
\(438\) | 27.6115 | 1.31933 | ||||||||
\(439\) | 0.867169 | 0.0413877 | 0.0206938 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206938 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(440\) | 0.389789 | 0.0185825 | ||||||||
\(441\) | −16.3277 | −0.777511 | ||||||||
\(442\) | 18.7164 | 0.890250 | ||||||||
\(443\) | 25.6977 | 1.22093 | 0.610467 | − | 0.792042i | \(-0.290982\pi\) | ||||
0.610467 | + | 0.792042i | \(0.290982\pi\) | |||||||
\(444\) | −28.8286 | −1.36814 | ||||||||
\(445\) | −6.41774 | −0.304230 | ||||||||
\(446\) | 0.298598 | 0.0141390 | ||||||||
\(447\) | −28.3954 | −1.34305 | ||||||||
\(448\) | −2.12795 | −0.100536 | ||||||||
\(449\) | 34.1999 | 1.61399 | 0.806996 | − | 0.590557i | \(-0.201092\pi\) | ||||
0.806996 | + | 0.590557i | \(0.201092\pi\) | |||||||
\(450\) | −12.3049 | −0.580061 | ||||||||
\(451\) | 0.691262 | 0.0325503 | ||||||||
\(452\) | −6.35860 | −0.299083 | ||||||||
\(453\) | −26.0321 | −1.22310 | ||||||||
\(454\) | −13.7237 | −0.644087 | ||||||||
\(455\) | 19.3821 | 0.908649 | ||||||||
\(456\) | 17.2480 | 0.807713 | ||||||||
\(457\) | 34.9056 | 1.63281 | 0.816407 | − | 0.577477i | \(-0.195963\pi\) | ||||
0.816407 | + | 0.577477i | \(0.195963\pi\) | |||||||
\(458\) | −6.54010 | −0.305599 | ||||||||
\(459\) | 60.1534 | 2.80772 | ||||||||
\(460\) | −10.1002 | −0.470926 | ||||||||
\(461\) | −38.9820 | −1.81557 | −0.907787 | − | 0.419432i | \(-0.862229\pi\) | ||||
−0.907787 | + | 0.419432i | \(0.862229\pi\) | |||||||
\(462\) | −0.981294 | −0.0456539 | ||||||||
\(463\) | −20.1468 | −0.936299 | −0.468150 | − | 0.883649i | \(-0.655079\pi\) | ||||
−0.468150 | + | 0.883649i | \(0.655079\pi\) | |||||||
\(464\) | −5.49729 | −0.255205 | ||||||||
\(465\) | 24.3990 | 1.13148 | ||||||||
\(466\) | −15.0625 | −0.697756 | ||||||||
\(467\) | 9.59834 | 0.444158 | 0.222079 | − | 0.975029i | \(-0.428716\pi\) | ||||
0.222079 | + | 0.975029i | \(0.428716\pi\) | |||||||
\(468\) | 22.9665 | 1.06163 | ||||||||
\(469\) | 30.1930 | 1.39418 | ||||||||
\(470\) | −11.6315 | −0.536519 | ||||||||
\(471\) | 23.0153 | 1.06049 | ||||||||
\(472\) | −13.4011 | −0.616837 | ||||||||
\(473\) | −0.513579 | −0.0236144 | ||||||||
\(474\) | −17.0682 | −0.783966 | ||||||||
\(475\) | 10.3670 | 0.475670 | ||||||||
\(476\) | 11.4550 | 0.525039 | ||||||||
\(477\) | −79.1802 | −3.62541 | ||||||||
\(478\) | −23.0423 | −1.05393 | ||||||||
\(479\) | 31.5889 | 1.44334 | 0.721668 | − | 0.692240i | \(-0.243376\pi\) | ||||
0.721668 | + | 0.692240i | \(0.243376\pi\) | |||||||
\(480\) | −8.11917 | −0.370588 | ||||||||
\(481\) | 32.3409 | 1.47462 | ||||||||
\(482\) | −16.4598 | −0.749725 | ||||||||
\(483\) | 25.4273 | 1.15698 | ||||||||
\(484\) | −10.9779 | −0.498994 | ||||||||
\(485\) | 15.1848 | 0.689507 | ||||||||
\(486\) | 12.3960 | 0.562295 | ||||||||
\(487\) | 8.47054 | 0.383837 | 0.191918 | − | 0.981411i | \(-0.438529\pi\) | ||||
0.191918 | + | 0.981411i | \(0.438529\pi\) | |||||||
\(488\) | 2.74011 | 0.124039 | ||||||||
\(489\) | −36.2276 | −1.63827 | ||||||||
\(490\) | −6.47547 | −0.292532 | ||||||||
\(491\) | −10.3954 | −0.469136 | −0.234568 | − | 0.972100i | \(-0.575368\pi\) | ||||
−0.234568 | + | 0.972100i | \(0.575368\pi\) | |||||||
\(492\) | −14.3987 | −0.649146 | ||||||||
\(493\) | 29.5926 | 1.33278 | ||||||||
\(494\) | −19.3494 | −0.870572 | ||||||||
\(495\) | −2.57475 | −0.115727 | ||||||||
\(496\) | 3.00511 | 0.134934 | ||||||||
\(497\) | 12.4306 | 0.557587 | ||||||||
\(498\) | −30.7049 | −1.37592 | ||||||||
\(499\) | −11.1163 | −0.497635 | −0.248818 | − | 0.968550i | \(-0.580042\pi\) | ||||
−0.248818 | + | 0.968550i | \(0.580042\pi\) | |||||||
\(500\) | 8.21844 | 0.367540 | ||||||||
\(501\) | −54.2878 | −2.42540 | ||||||||
\(502\) | −14.2485 | −0.635941 | ||||||||
\(503\) | −2.28972 | −0.102093 | −0.0510467 | − | 0.998696i | \(-0.516256\pi\) | ||||
−0.0510467 | + | 0.998696i | \(0.516256\pi\) | |||||||
\(504\) | 14.0562 | 0.626112 | ||||||||
\(505\) | 38.9207 | 1.73195 | ||||||||
\(506\) | −0.573664 | −0.0255025 | ||||||||
\(507\) | 2.82449 | 0.125440 | ||||||||
\(508\) | 14.2280 | 0.631266 | ||||||||
\(509\) | −3.54828 | −0.157275 | −0.0786374 | − | 0.996903i | \(-0.525057\pi\) | ||||
−0.0786374 | + | 0.996903i | \(0.525057\pi\) | |||||||
\(510\) | 43.7065 | 1.93536 | ||||||||
\(511\) | −18.9579 | −0.838649 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −62.1878 | −2.74566 | ||||||||
\(514\) | 23.4295 | 1.03343 | ||||||||
\(515\) | 6.26768 | 0.276187 | ||||||||
\(516\) | 10.6977 | 0.470938 | ||||||||
\(517\) | −0.660634 | −0.0290546 | ||||||||
\(518\) | 19.7936 | 0.869680 | ||||||||
\(519\) | 57.2182 | 2.51160 | ||||||||
\(520\) | 9.10837 | 0.399429 | ||||||||
\(521\) | 45.1801 | 1.97938 | 0.989689 | − | 0.143232i | \(-0.0457495\pi\) | ||||
0.989689 | + | 0.143232i | \(0.0457495\pi\) | |||||||
\(522\) | 36.3124 | 1.58935 | ||||||||
\(523\) | −7.05363 | −0.308434 | −0.154217 | − | 0.988037i | \(-0.549285\pi\) | ||||
−0.154217 | + | 0.988037i | \(0.549285\pi\) | |||||||
\(524\) | −8.78974 | −0.383982 | ||||||||
\(525\) | 12.2856 | 0.536186 | ||||||||
\(526\) | 14.7623 | 0.643665 | ||||||||
\(527\) | −16.1769 | −0.704676 | ||||||||
\(528\) | −0.461146 | −0.0200688 | ||||||||
\(529\) | −8.13520 | −0.353704 | ||||||||
\(530\) | −31.4024 | −1.36403 | ||||||||
\(531\) | 88.5213 | 3.84150 | ||||||||
\(532\) | −11.8424 | −0.513434 | ||||||||
\(533\) | 16.1530 | 0.699665 | ||||||||
\(534\) | 7.59260 | 0.328564 | ||||||||
\(535\) | −8.68329 | −0.375411 | ||||||||
\(536\) | 14.1888 | 0.612863 | ||||||||
\(537\) | 75.7830 | 3.27028 | ||||||||
\(538\) | −12.8535 | −0.554153 | ||||||||
\(539\) | −0.367788 | −0.0158418 | ||||||||
\(540\) | 29.2737 | 1.25974 | ||||||||
\(541\) | 27.5940 | 1.18636 | 0.593179 | − | 0.805071i | \(-0.297873\pi\) | ||||
0.593179 | + | 0.805071i | \(0.297873\pi\) | |||||||
\(542\) | −17.6066 | −0.756266 | ||||||||
\(543\) | 61.2877 | 2.63011 | ||||||||
\(544\) | 5.38312 | 0.230799 | ||||||||
\(545\) | −15.5810 | −0.667416 | ||||||||
\(546\) | −22.9303 | −0.981327 | ||||||||
\(547\) | −39.2307 | −1.67738 | −0.838692 | − | 0.544607i | \(-0.816679\pi\) | ||||
−0.838692 | + | 0.544607i | \(0.816679\pi\) | |||||||
\(548\) | −2.13472 | −0.0911909 | ||||||||
\(549\) | −18.0998 | −0.772481 | ||||||||
\(550\) | −0.277174 | −0.0118187 | ||||||||
\(551\) | −30.5934 | −1.30332 | ||||||||
\(552\) | 11.9492 | 0.508593 | ||||||||
\(553\) | 11.7189 | 0.498339 | ||||||||
\(554\) | 24.0872 | 1.02337 | ||||||||
\(555\) | 75.5223 | 3.20574 | ||||||||
\(556\) | 21.7640 | 0.923001 | ||||||||
\(557\) | −4.43919 | −0.188095 | −0.0940473 | − | 0.995568i | \(-0.529980\pi\) | ||||
−0.0940473 | + | 0.995568i | \(0.529980\pi\) | |||||||
\(558\) | −19.8503 | −0.840329 | ||||||||
\(559\) | −12.0010 | −0.507589 | ||||||||
\(560\) | 5.57459 | 0.235569 | ||||||||
\(561\) | 2.48240 | 0.104807 | ||||||||
\(562\) | −22.4219 | −0.945813 | ||||||||
\(563\) | 36.4136 | 1.53465 | 0.767326 | − | 0.641257i | \(-0.221587\pi\) | ||||
0.767326 | + | 0.641257i | \(0.221587\pi\) | |||||||
\(564\) | 13.7608 | 0.579433 | ||||||||
\(565\) | 16.6576 | 0.700791 | ||||||||
\(566\) | −6.38848 | −0.268528 | ||||||||
\(567\) | −31.5280 | −1.32405 | ||||||||
\(568\) | 5.84157 | 0.245107 | ||||||||
\(569\) | −34.0600 | −1.42787 | −0.713935 | − | 0.700212i | \(-0.753089\pi\) | ||||
−0.713935 | + | 0.700212i | \(0.753089\pi\) | |||||||
\(570\) | −45.1847 | −1.89258 | ||||||||
\(571\) | 38.4969 | 1.61104 | 0.805522 | − | 0.592566i | \(-0.201885\pi\) | ||||
0.805522 | + | 0.592566i | \(0.201885\pi\) | |||||||
\(572\) | 0.517329 | 0.0216306 | ||||||||
\(573\) | −47.4803 | −1.98352 | ||||||||
\(574\) | 9.88611 | 0.412638 | ||||||||
\(575\) | 7.18213 | 0.299516 | ||||||||
\(576\) | 6.60550 | 0.275229 | ||||||||
\(577\) | 27.7448 | 1.15503 | 0.577517 | − | 0.816379i | \(-0.304022\pi\) | ||||
0.577517 | + | 0.816379i | \(0.304022\pi\) | |||||||
\(578\) | −11.9780 | −0.498218 | ||||||||
\(579\) | 19.6050 | 0.814757 | ||||||||
\(580\) | 14.4013 | 0.597980 | ||||||||
\(581\) | 21.0818 | 0.874621 | ||||||||
\(582\) | −17.9646 | −0.744657 | ||||||||
\(583\) | −1.78356 | −0.0738677 | ||||||||
\(584\) | −8.90902 | −0.368658 | ||||||||
\(585\) | −60.1654 | −2.48753 | ||||||||
\(586\) | 25.6763 | 1.06068 | ||||||||
\(587\) | −35.4020 | −1.46120 | −0.730598 | − | 0.682808i | \(-0.760759\pi\) | ||||
−0.730598 | + | 0.682808i | \(0.760759\pi\) | |||||||
\(588\) | 7.66090 | 0.315930 | ||||||||
\(589\) | 16.7240 | 0.689100 | ||||||||
\(590\) | 35.1070 | 1.44533 | ||||||||
\(591\) | 3.61312 | 0.148624 | ||||||||
\(592\) | 9.30172 | 0.382298 | ||||||||
\(593\) | 5.05182 | 0.207453 | 0.103727 | − | 0.994606i | \(-0.466923\pi\) | ||||
0.103727 | + | 0.994606i | \(0.466923\pi\) | |||||||
\(594\) | 1.66266 | 0.0682199 | ||||||||
\(595\) | −30.0087 | −1.23024 | ||||||||
\(596\) | 9.16194 | 0.375288 | ||||||||
\(597\) | 6.31202 | 0.258334 | ||||||||
\(598\) | −13.4051 | −0.548174 | ||||||||
\(599\) | −40.5567 | −1.65710 | −0.828551 | − | 0.559913i | \(-0.810834\pi\) | ||||
−0.828551 | + | 0.559913i | \(0.810834\pi\) | |||||||
\(600\) | 5.77343 | 0.235699 | ||||||||
\(601\) | 10.0840 | 0.411336 | 0.205668 | − | 0.978622i | \(-0.434063\pi\) | ||||
0.205668 | + | 0.978622i | \(0.434063\pi\) | |||||||
\(602\) | −7.34497 | −0.299359 | ||||||||
\(603\) | −93.7241 | −3.81674 | ||||||||
\(604\) | 8.39943 | 0.341768 | ||||||||
\(605\) | 28.7587 | 1.16921 | ||||||||
\(606\) | −46.0457 | −1.87048 | ||||||||
\(607\) | 5.53065 | 0.224482 | 0.112241 | − | 0.993681i | \(-0.464197\pi\) | ||||
0.112241 | + | 0.993681i | \(0.464197\pi\) | |||||||
\(608\) | −5.56518 | −0.225698 | ||||||||
\(609\) | −36.2552 | −1.46913 | ||||||||
\(610\) | −7.17827 | −0.290640 | ||||||||
\(611\) | −15.4373 | −0.624527 | ||||||||
\(612\) | −35.5582 | −1.43736 | ||||||||
\(613\) | −37.5472 | −1.51652 | −0.758258 | − | 0.651955i | \(-0.773949\pi\) | ||||
−0.758258 | + | 0.651955i | \(0.773949\pi\) | |||||||
\(614\) | 9.42016 | 0.380167 | ||||||||
\(615\) | 37.7204 | 1.52103 | ||||||||
\(616\) | 0.316621 | 0.0127570 | ||||||||
\(617\) | 19.6377 | 0.790585 | 0.395293 | − | 0.918555i | \(-0.370643\pi\) | ||||
0.395293 | + | 0.918555i | \(0.370643\pi\) | |||||||
\(618\) | −7.41506 | −0.298278 | ||||||||
\(619\) | 13.9631 | 0.561225 | 0.280612 | − | 0.959821i | \(-0.409462\pi\) | ||||
0.280612 | + | 0.959821i | \(0.409462\pi\) | |||||||
\(620\) | −7.87249 | −0.316167 | ||||||||
\(621\) | −43.0830 | −1.72886 | ||||||||
\(622\) | −18.4008 | −0.737807 | ||||||||
\(623\) | −5.21304 | −0.208856 | ||||||||
\(624\) | −10.7758 | −0.431377 | ||||||||
\(625\) | −30.8440 | −1.23376 | ||||||||
\(626\) | −2.65401 | −0.106076 | ||||||||
\(627\) | −2.56636 | −0.102491 | ||||||||
\(628\) | −7.42604 | −0.296331 | ||||||||
\(629\) | −50.0723 | −1.99651 | ||||||||
\(630\) | −36.8230 | −1.46706 | ||||||||
\(631\) | 23.4992 | 0.935488 | 0.467744 | − | 0.883864i | \(-0.345067\pi\) | ||||
0.467744 | + | 0.883864i | \(0.345067\pi\) | |||||||
\(632\) | 5.50715 | 0.219063 | ||||||||
\(633\) | 38.0588 | 1.51270 | ||||||||
\(634\) | 4.05309 | 0.160969 | ||||||||
\(635\) | −37.2731 | −1.47914 | ||||||||
\(636\) | 37.1510 | 1.47313 | ||||||||
\(637\) | −8.59427 | −0.340517 | ||||||||
\(638\) | 0.817950 | 0.0323830 | ||||||||
\(639\) | −38.5865 | −1.52646 | ||||||||
\(640\) | 2.61970 | 0.103553 | ||||||||
\(641\) | −22.9605 | −0.906887 | −0.453443 | − | 0.891285i | \(-0.649805\pi\) | ||||
−0.453443 | + | 0.891285i | \(0.649805\pi\) | |||||||
\(642\) | 10.2729 | 0.405439 | ||||||||
\(643\) | −0.803322 | −0.0316799 | −0.0158400 | − | 0.999875i | \(-0.505042\pi\) | ||||
−0.0158400 | + | 0.999875i | \(0.505042\pi\) | |||||||
\(644\) | −8.20428 | −0.323294 | ||||||||
\(645\) | −28.0247 | −1.10347 | ||||||||
\(646\) | 29.9580 | 1.17868 | ||||||||
\(647\) | 25.3992 | 0.998547 | 0.499273 | − | 0.866445i | \(-0.333600\pi\) | ||||
0.499273 | + | 0.866445i | \(0.333600\pi\) | |||||||
\(648\) | −14.8162 | −0.582034 | ||||||||
\(649\) | 1.99397 | 0.0782704 | ||||||||
\(650\) | −6.47683 | −0.254042 | ||||||||
\(651\) | 19.8190 | 0.776768 | ||||||||
\(652\) | 11.6891 | 0.457779 | ||||||||
\(653\) | −13.3098 | −0.520852 | −0.260426 | − | 0.965494i | \(-0.583863\pi\) | ||||
−0.260426 | + | 0.965494i | \(0.583863\pi\) | |||||||
\(654\) | 18.4333 | 0.720799 | ||||||||
\(655\) | 23.0265 | 0.899719 | ||||||||
\(656\) | 4.64584 | 0.181390 | ||||||||
\(657\) | 58.8485 | 2.29590 | ||||||||
\(658\) | −9.44808 | −0.368325 | ||||||||
\(659\) | −19.7679 | −0.770048 | −0.385024 | − | 0.922907i | \(-0.625807\pi\) | ||||
−0.385024 | + | 0.922907i | \(0.625807\pi\) | |||||||
\(660\) | 1.20806 | 0.0470238 | ||||||||
\(661\) | 18.7619 | 0.729752 | 0.364876 | − | 0.931056i | \(-0.381111\pi\) | ||||
0.364876 | + | 0.931056i | \(0.381111\pi\) | |||||||
\(662\) | 24.7302 | 0.961165 | ||||||||
\(663\) | 58.0074 | 2.25282 | ||||||||
\(664\) | 9.90711 | 0.384470 | ||||||||
\(665\) | 31.0236 | 1.20304 | ||||||||
\(666\) | −61.4425 | −2.38085 | ||||||||
\(667\) | −21.1948 | −0.820664 | ||||||||
\(668\) | 17.5163 | 0.677725 | ||||||||
\(669\) | 0.925436 | 0.0357794 | ||||||||
\(670\) | −37.1704 | −1.43602 | ||||||||
\(671\) | −0.407705 | −0.0157393 | ||||||||
\(672\) | −6.59510 | −0.254411 | ||||||||
\(673\) | −15.8115 | −0.609489 | −0.304745 | − | 0.952434i | \(-0.598571\pi\) | ||||
−0.304745 | + | 0.952434i | \(0.598571\pi\) | |||||||
\(674\) | −16.6246 | −0.640354 | ||||||||
\(675\) | −20.8161 | −0.801213 | ||||||||
\(676\) | −0.911340 | −0.0350516 | ||||||||
\(677\) | −7.89995 | −0.303620 | −0.151810 | − | 0.988410i | \(-0.548510\pi\) | ||||
−0.151810 | + | 0.988410i | \(0.548510\pi\) | |||||||
\(678\) | −19.7070 | −0.756844 | ||||||||
\(679\) | 12.3344 | 0.473351 | ||||||||
\(680\) | −14.1022 | −0.540793 | ||||||||
\(681\) | −42.5336 | −1.62989 | ||||||||
\(682\) | −0.447135 | −0.0171217 | ||||||||
\(683\) | 20.0291 | 0.766393 | 0.383197 | − | 0.923667i | \(-0.374823\pi\) | ||||
0.383197 | + | 0.923667i | \(0.374823\pi\) | |||||||
\(684\) | 36.7608 | 1.40559 | ||||||||
\(685\) | 5.59234 | 0.213672 | ||||||||
\(686\) | −20.1556 | −0.769544 | ||||||||
\(687\) | −20.2696 | −0.773332 | ||||||||
\(688\) | −3.45167 | −0.131594 | ||||||||
\(689\) | −41.6773 | −1.58778 | ||||||||
\(690\) | −31.3034 | −1.19170 | ||||||||
\(691\) | 32.4113 | 1.23298 | 0.616492 | − | 0.787361i | \(-0.288553\pi\) | ||||
0.616492 | + | 0.787361i | \(0.288553\pi\) | |||||||
\(692\) | −18.4618 | −0.701812 | ||||||||
\(693\) | −2.09144 | −0.0794472 | ||||||||
\(694\) | −14.3029 | −0.542930 | ||||||||
\(695\) | −57.0153 | −2.16271 | ||||||||
\(696\) | −17.0376 | −0.645809 | ||||||||
\(697\) | −25.0091 | −0.947288 | ||||||||
\(698\) | −12.6510 | −0.478846 | ||||||||
\(699\) | −46.6827 | −1.76570 | ||||||||
\(700\) | −3.96401 | −0.149826 | ||||||||
\(701\) | −25.8457 | −0.976179 | −0.488089 | − | 0.872794i | \(-0.662306\pi\) | ||||
−0.488089 | + | 0.872794i | \(0.662306\pi\) | |||||||
\(702\) | 38.8522 | 1.46638 | ||||||||
\(703\) | 51.7657 | 1.95238 | ||||||||
\(704\) | 0.148791 | 0.00560779 | ||||||||
\(705\) | −36.0491 | −1.35769 | ||||||||
\(706\) | 19.6704 | 0.740304 | ||||||||
\(707\) | 31.6148 | 1.18900 | ||||||||
\(708\) | −41.5338 | −1.56094 | ||||||||
\(709\) | 1.03874 | 0.0390106 | 0.0195053 | − | 0.999810i | \(-0.493791\pi\) | ||||
0.0195053 | + | 0.999810i | \(0.493791\pi\) | |||||||
\(710\) | −15.3032 | −0.574318 | ||||||||
\(711\) | −36.3775 | −1.36426 | ||||||||
\(712\) | −2.44980 | −0.0918101 | ||||||||
\(713\) | 11.5862 | 0.433906 | ||||||||
\(714\) | 35.5022 | 1.32864 | ||||||||
\(715\) | −1.35525 | −0.0506834 | ||||||||
\(716\) | −24.4519 | −0.913809 | ||||||||
\(717\) | −71.4144 | −2.66702 | ||||||||
\(718\) | −7.69351 | −0.287119 | ||||||||
\(719\) | 2.02707 | 0.0755971 | 0.0377986 | − | 0.999285i | \(-0.487965\pi\) | ||||
0.0377986 | + | 0.999285i | \(0.487965\pi\) | |||||||
\(720\) | −17.3044 | −0.644899 | ||||||||
\(721\) | 5.09115 | 0.189604 | ||||||||
\(722\) | −11.9712 | −0.445523 | ||||||||
\(723\) | −51.0135 | −1.89721 | ||||||||
\(724\) | −19.7749 | −0.734927 | ||||||||
\(725\) | −10.2405 | −0.380324 | ||||||||
\(726\) | −34.0234 | −1.26273 | ||||||||
\(727\) | 41.7019 | 1.54664 | 0.773319 | − | 0.634017i | \(-0.218595\pi\) | ||||
0.773319 | + | 0.634017i | \(0.218595\pi\) | |||||||
\(728\) | 7.39861 | 0.274211 | ||||||||
\(729\) | −6.02979 | −0.223326 | ||||||||
\(730\) | 23.3390 | 0.863813 | ||||||||
\(731\) | 18.5807 | 0.687233 | ||||||||
\(732\) | 8.49235 | 0.313886 | ||||||||
\(733\) | 25.6182 | 0.946229 | 0.473114 | − | 0.881001i | \(-0.343130\pi\) | ||||
0.473114 | + | 0.881001i | \(0.343130\pi\) | |||||||
\(734\) | −1.40887 | −0.0520025 | ||||||||
\(735\) | −20.0693 | −0.740266 | ||||||||
\(736\) | −3.85549 | −0.142115 | ||||||||
\(737\) | −2.11117 | −0.0777660 | ||||||||
\(738\) | −30.6881 | −1.12965 | ||||||||
\(739\) | −7.88359 | −0.290003 | −0.145001 | − | 0.989431i | \(-0.546319\pi\) | ||||
−0.145001 | + | 0.989431i | \(0.546319\pi\) | |||||||
\(740\) | −24.3677 | −0.895775 | ||||||||
\(741\) | −59.9692 | −2.20302 | ||||||||
\(742\) | −25.5077 | −0.936418 | ||||||||
\(743\) | −26.6017 | −0.975921 | −0.487961 | − | 0.872866i | \(-0.662259\pi\) | ||||
−0.487961 | + | 0.872866i | \(0.662259\pi\) | |||||||
\(744\) | 9.31367 | 0.341456 | ||||||||
\(745\) | −24.0015 | −0.879348 | ||||||||
\(746\) | −32.5569 | −1.19199 | ||||||||
\(747\) | −65.4414 | −2.39438 | ||||||||
\(748\) | −0.800962 | −0.0292861 | ||||||||
\(749\) | −7.05332 | −0.257723 | ||||||||
\(750\) | 25.4712 | 0.930077 | ||||||||
\(751\) | −9.52630 | −0.347620 | −0.173810 | − | 0.984779i | \(-0.555608\pi\) | ||||
−0.173810 | + | 0.984779i | \(0.555608\pi\) | |||||||
\(752\) | −4.44000 | −0.161910 | ||||||||
\(753\) | −44.1599 | −1.60928 | ||||||||
\(754\) | 19.1134 | 0.696069 | ||||||||
\(755\) | −22.0040 | −0.800807 | ||||||||
\(756\) | 23.7786 | 0.864821 | ||||||||
\(757\) | 20.2695 | 0.736709 | 0.368355 | − | 0.929685i | \(-0.379921\pi\) | ||||
0.368355 | + | 0.929685i | \(0.379921\pi\) | |||||||
\(758\) | 1.90954 | 0.0693578 | ||||||||
\(759\) | −1.77794 | −0.0645352 | ||||||||
\(760\) | 14.5791 | 0.528840 | ||||||||
\(761\) | 10.4288 | 0.378042 | 0.189021 | − | 0.981973i | \(-0.439469\pi\) | ||||
0.189021 | + | 0.981973i | \(0.439469\pi\) | |||||||
\(762\) | 44.0965 | 1.59745 | ||||||||
\(763\) | −12.6562 | −0.458186 | ||||||||
\(764\) | 15.3198 | 0.554252 | ||||||||
\(765\) | 93.1519 | 3.36791 | ||||||||
\(766\) | −38.2354 | −1.38150 | ||||||||
\(767\) | 46.5941 | 1.68241 | ||||||||
\(768\) | −3.09927 | −0.111835 | ||||||||
\(769\) | 5.13971 | 0.185343 | 0.0926714 | − | 0.995697i | \(-0.470459\pi\) | ||||
0.0926714 | + | 0.995697i | \(0.470459\pi\) | |||||||
\(770\) | −0.829451 | −0.0298913 | ||||||||
\(771\) | 72.6144 | 2.61515 | ||||||||
\(772\) | −6.32568 | −0.227666 | ||||||||
\(773\) | −14.7193 | −0.529416 | −0.264708 | − | 0.964329i | \(-0.585276\pi\) | ||||
−0.264708 | + | 0.964329i | \(0.585276\pi\) | |||||||
\(774\) | 22.8000 | 0.819529 | ||||||||
\(775\) | 5.59802 | 0.201087 | ||||||||
\(776\) | 5.79639 | 0.208078 | ||||||||
\(777\) | 61.3457 | 2.20077 | ||||||||
\(778\) | 7.12094 | 0.255298 | ||||||||
\(779\) | 25.8550 | 0.926350 | ||||||||
\(780\) | 28.2293 | 1.01077 | ||||||||
\(781\) | −0.869176 | −0.0311016 | ||||||||
\(782\) | 20.7546 | 0.742182 | ||||||||
\(783\) | 61.4292 | 2.19530 | ||||||||
\(784\) | −2.47184 | −0.0882799 | ||||||||
\(785\) | 19.4540 | 0.694343 | ||||||||
\(786\) | −27.2418 | −0.971683 | ||||||||
\(787\) | 15.5990 | 0.556043 | 0.278021 | − | 0.960575i | \(-0.410321\pi\) | ||||
0.278021 | + | 0.960575i | \(0.410321\pi\) | |||||||
\(788\) | −1.16579 | −0.0415297 | ||||||||
\(789\) | 45.7523 | 1.62882 | ||||||||
\(790\) | −14.4271 | −0.513292 | ||||||||
\(791\) | 13.5308 | 0.481099 | ||||||||
\(792\) | −0.982843 | −0.0349238 | ||||||||
\(793\) | −9.52702 | −0.338314 | ||||||||
\(794\) | 0.699225 | 0.0248146 | ||||||||
\(795\) | −97.3246 | −3.45175 | ||||||||
\(796\) | −2.03661 | −0.0721858 | ||||||||
\(797\) | 15.5039 | 0.549176 | 0.274588 | − | 0.961562i | \(-0.411458\pi\) | ||||
0.274588 | + | 0.961562i | \(0.411458\pi\) | |||||||
\(798\) | −36.7029 | −1.29927 | ||||||||
\(799\) | 23.9010 | 0.845558 | ||||||||
\(800\) | −1.86283 | −0.0658611 | ||||||||
\(801\) | 16.1821 | 0.571768 | ||||||||
\(802\) | 5.06910 | 0.178996 | ||||||||
\(803\) | 1.32559 | 0.0467789 | ||||||||
\(804\) | 43.9750 | 1.55088 | ||||||||
\(805\) | 21.4928 | 0.757520 | ||||||||
\(806\) | −10.4484 | −0.368029 | ||||||||
\(807\) | −39.8365 | −1.40231 | ||||||||
\(808\) | 14.8569 | 0.522665 | ||||||||
\(809\) | 15.4307 | 0.542514 | 0.271257 | − | 0.962507i | \(-0.412561\pi\) | ||||
0.271257 | + | 0.962507i | \(0.412561\pi\) | |||||||
\(810\) | 38.8139 | 1.36378 | ||||||||
\(811\) | −1.78281 | −0.0626030 | −0.0313015 | − | 0.999510i | \(-0.509965\pi\) | ||||
−0.0313015 | + | 0.999510i | \(0.509965\pi\) | |||||||
\(812\) | 11.6980 | 0.410518 | ||||||||
\(813\) | −54.5676 | −1.91377 | ||||||||
\(814\) | −1.38402 | −0.0485098 | ||||||||
\(815\) | −30.6219 | −1.07264 | ||||||||
\(816\) | 16.6838 | 0.584049 | ||||||||
\(817\) | −19.2092 | −0.672043 | ||||||||
\(818\) | 31.8131 | 1.11232 | ||||||||
\(819\) | −48.8715 | −1.70771 | ||||||||
\(820\) | −12.1707 | −0.425020 | ||||||||
\(821\) | −13.8490 | −0.483335 | −0.241667 | − | 0.970359i | \(-0.577694\pi\) | ||||
−0.241667 | + | 0.970359i | \(0.577694\pi\) | |||||||
\(822\) | −6.61609 | −0.230763 | ||||||||
\(823\) | −52.5376 | −1.83135 | −0.915673 | − | 0.401924i | \(-0.868341\pi\) | ||||
−0.915673 | + | 0.401924i | \(0.868341\pi\) | |||||||
\(824\) | 2.39252 | 0.0833472 | ||||||||
\(825\) | −0.859037 | −0.0299078 | ||||||||
\(826\) | 28.5169 | 0.992231 | ||||||||
\(827\) | −40.6068 | −1.41204 | −0.706019 | − | 0.708193i | \(-0.749511\pi\) | ||||
−0.706019 | + | 0.708193i | \(0.749511\pi\) | |||||||
\(828\) | 25.4675 | 0.885055 | ||||||||
\(829\) | 2.05702 | 0.0714431 | 0.0357216 | − | 0.999362i | \(-0.488627\pi\) | ||||
0.0357216 | + | 0.999362i | \(0.488627\pi\) | |||||||
\(830\) | −25.9537 | −0.900865 | ||||||||
\(831\) | 74.6529 | 2.58968 | ||||||||
\(832\) | 3.47687 | 0.120539 | ||||||||
\(833\) | 13.3062 | 0.461032 | ||||||||
\(834\) | 67.4527 | 2.33570 | ||||||||
\(835\) | −45.8874 | −1.58800 | ||||||||
\(836\) | 0.828051 | 0.0286388 | ||||||||
\(837\) | −33.5805 | −1.16071 | ||||||||
\(838\) | 10.6895 | 0.369263 | ||||||||
\(839\) | −12.4582 | −0.430105 | −0.215053 | − | 0.976602i | \(-0.568992\pi\) | ||||
−0.215053 | + | 0.976602i | \(0.568992\pi\) | |||||||
\(840\) | 17.2772 | 0.596119 | ||||||||
\(841\) | 1.22022 | 0.0420764 | ||||||||
\(842\) | 33.9650 | 1.17051 | ||||||||
\(843\) | −69.4918 | −2.39342 | ||||||||
\(844\) | −12.2799 | −0.422692 | ||||||||
\(845\) | 2.38744 | 0.0821304 | ||||||||
\(846\) | 29.3284 | 1.00833 | ||||||||
\(847\) | 23.3603 | 0.802670 | ||||||||
\(848\) | −11.9870 | −0.411635 | ||||||||
\(849\) | −19.7997 | −0.679523 | ||||||||
\(850\) | 10.0278 | 0.343952 | ||||||||
\(851\) | 35.8627 | 1.22936 | ||||||||
\(852\) | 18.1046 | 0.620254 | ||||||||
\(853\) | 21.6514 | 0.741330 | 0.370665 | − | 0.928767i | \(-0.379130\pi\) | ||||
0.370665 | + | 0.928767i | \(0.379130\pi\) | |||||||
\(854\) | −5.83081 | −0.199526 | ||||||||
\(855\) | −96.3023 | −3.29347 | ||||||||
\(856\) | −3.31461 | −0.113291 | ||||||||
\(857\) | 45.0521 | 1.53895 | 0.769475 | − | 0.638677i | \(-0.220518\pi\) | ||||
0.769475 | + | 0.638677i | \(0.220518\pi\) | |||||||
\(858\) | 1.60335 | 0.0547373 | ||||||||
\(859\) | −33.3169 | −1.13676 | −0.568379 | − | 0.822767i | \(-0.692429\pi\) | ||||
−0.568379 | + | 0.822767i | \(0.692429\pi\) | |||||||
\(860\) | 9.04234 | 0.308341 | ||||||||
\(861\) | 30.6398 | 1.04420 | ||||||||
\(862\) | 6.40630 | 0.218199 | ||||||||
\(863\) | −16.4424 | −0.559704 | −0.279852 | − | 0.960043i | \(-0.590285\pi\) | ||||
−0.279852 | + | 0.960043i | \(0.590285\pi\) | |||||||
\(864\) | 11.1744 | 0.380162 | ||||||||
\(865\) | 48.3644 | 1.64444 | ||||||||
\(866\) | −3.40899 | −0.115842 | ||||||||
\(867\) | −37.1230 | −1.26076 | ||||||||
\(868\) | −6.39472 | −0.217051 | ||||||||
\(869\) | −0.819416 | −0.0277968 | ||||||||
\(870\) | 44.6335 | 1.51322 | ||||||||
\(871\) | −49.3327 | −1.67157 | ||||||||
\(872\) | −5.94762 | −0.201412 | ||||||||
\(873\) | −38.2881 | −1.29585 | ||||||||
\(874\) | −21.4565 | −0.725777 | ||||||||
\(875\) | −17.4884 | −0.591216 | ||||||||
\(876\) | −27.6115 | −0.932906 | ||||||||
\(877\) | 7.83338 | 0.264515 | 0.132257 | − | 0.991215i | \(-0.457777\pi\) | ||||
0.132257 | + | 0.991215i | \(0.457777\pi\) | |||||||
\(878\) | −0.867169 | −0.0292655 | ||||||||
\(879\) | 79.5780 | 2.68410 | ||||||||
\(880\) | −0.389789 | −0.0131398 | ||||||||
\(881\) | −20.3218 | −0.684659 | −0.342329 | − | 0.939580i | \(-0.611216\pi\) | ||||
−0.342329 | + | 0.939580i | \(0.611216\pi\) | |||||||
\(882\) | 16.3277 | 0.549783 | ||||||||
\(883\) | −27.0014 | −0.908668 | −0.454334 | − | 0.890831i | \(-0.650123\pi\) | ||||
−0.454334 | + | 0.890831i | \(0.650123\pi\) | |||||||
\(884\) | −18.7164 | −0.629502 | ||||||||
\(885\) | 108.806 | 3.65748 | ||||||||
\(886\) | −25.6977 | −0.863331 | ||||||||
\(887\) | −17.1338 | −0.575297 | −0.287648 | − | 0.957736i | \(-0.592873\pi\) | ||||
−0.287648 | + | 0.957736i | \(0.592873\pi\) | |||||||
\(888\) | 28.8286 | 0.967424 | ||||||||
\(889\) | −30.2765 | −1.01544 | ||||||||
\(890\) | 6.41774 | 0.215123 | ||||||||
\(891\) | 2.20452 | 0.0738542 | ||||||||
\(892\) | −0.298598 | −0.00999779 | ||||||||
\(893\) | −24.7094 | −0.826868 | ||||||||
\(894\) | 28.3954 | 0.949683 | ||||||||
\(895\) | 64.0566 | 2.14117 | ||||||||
\(896\) | 2.12795 | 0.0710898 | ||||||||
\(897\) | −41.5460 | −1.38718 | ||||||||
\(898\) | −34.1999 | −1.14126 | ||||||||
\(899\) | −16.5200 | −0.550972 | ||||||||
\(900\) | 12.3049 | 0.410165 | ||||||||
\(901\) | 64.5275 | 2.14972 | ||||||||
\(902\) | −0.691262 | −0.0230165 | ||||||||
\(903\) | −22.7641 | −0.757541 | ||||||||
\(904\) | 6.35860 | 0.211484 | ||||||||
\(905\) | 51.8042 | 1.72203 | ||||||||
\(906\) | 26.0321 | 0.864860 | ||||||||
\(907\) | −3.25252 | −0.107998 | −0.0539991 | − | 0.998541i | \(-0.517197\pi\) | ||||
−0.0539991 | + | 0.998541i | \(0.517197\pi\) | |||||||
\(908\) | 13.7237 | 0.455438 | ||||||||
\(909\) | −98.1376 | −3.25502 | ||||||||
\(910\) | −19.3821 | −0.642512 | ||||||||
\(911\) | 17.4018 | 0.576546 | 0.288273 | − | 0.957548i | \(-0.406919\pi\) | ||||
0.288273 | + | 0.957548i | \(0.406919\pi\) | |||||||
\(912\) | −17.2480 | −0.571139 | ||||||||
\(913\) | −1.47409 | −0.0487854 | ||||||||
\(914\) | −34.9056 | −1.15457 | ||||||||
\(915\) | −22.2474 | −0.735477 | ||||||||
\(916\) | 6.54010 | 0.216091 | ||||||||
\(917\) | 18.7041 | 0.617664 | ||||||||
\(918\) | −60.1534 | −1.98536 | ||||||||
\(919\) | 33.9574 | 1.12015 | 0.560076 | − | 0.828441i | \(-0.310772\pi\) | ||||
0.560076 | + | 0.828441i | \(0.310772\pi\) | |||||||
\(920\) | 10.1002 | 0.332995 | ||||||||
\(921\) | 29.1957 | 0.962030 | ||||||||
\(922\) | 38.9820 | 1.28380 | ||||||||
\(923\) | −20.3104 | −0.668525 | ||||||||
\(924\) | 0.981294 | 0.0322822 | ||||||||
\(925\) | 17.3275 | 0.569726 | ||||||||
\(926\) | 20.1468 | 0.662063 | ||||||||
\(927\) | −15.8038 | −0.519064 | ||||||||
\(928\) | 5.49729 | 0.180457 | ||||||||
\(929\) | 48.4272 | 1.58885 | 0.794423 | − | 0.607365i | \(-0.207773\pi\) | ||||
0.794423 | + | 0.607365i | \(0.207773\pi\) | |||||||
\(930\) | −24.3990 | −0.800075 | ||||||||
\(931\) | −13.7562 | −0.450842 | ||||||||
\(932\) | 15.0625 | 0.493388 | ||||||||
\(933\) | −57.0293 | −1.86706 | ||||||||
\(934\) | −9.59834 | −0.314067 | ||||||||
\(935\) | 2.09828 | 0.0686212 | ||||||||
\(936\) | −22.9665 | −0.750684 | ||||||||
\(937\) | −23.8542 | −0.779282 | −0.389641 | − | 0.920967i | \(-0.627401\pi\) | ||||
−0.389641 | + | 0.920967i | \(0.627401\pi\) | |||||||
\(938\) | −30.1930 | −0.985837 | ||||||||
\(939\) | −8.22551 | −0.268429 | ||||||||
\(940\) | 11.6315 | 0.379376 | ||||||||
\(941\) | 7.04030 | 0.229507 | 0.114754 | − | 0.993394i | \(-0.463392\pi\) | ||||
0.114754 | + | 0.993394i | \(0.463392\pi\) | |||||||
\(942\) | −23.0153 | −0.749880 | ||||||||
\(943\) | 17.9120 | 0.583295 | ||||||||
\(944\) | 13.4011 | 0.436170 | ||||||||
\(945\) | −62.2929 | −2.02639 | ||||||||
\(946\) | 0.513579 | 0.0166979 | ||||||||
\(947\) | −39.3170 | −1.27763 | −0.638815 | − | 0.769360i | \(-0.720575\pi\) | ||||
−0.638815 | + | 0.769360i | \(0.720575\pi\) | |||||||
\(948\) | 17.0682 | 0.554348 | ||||||||
\(949\) | 30.9755 | 1.00551 | ||||||||
\(950\) | −10.3670 | −0.336350 | ||||||||
\(951\) | 12.5616 | 0.407339 | ||||||||
\(952\) | −11.4550 | −0.371259 | ||||||||
\(953\) | −16.5384 | −0.535731 | −0.267866 | − | 0.963456i | \(-0.586318\pi\) | ||||
−0.267866 | + | 0.963456i | \(0.586318\pi\) | |||||||
\(954\) | 79.1802 | 2.56355 | ||||||||
\(955\) | −40.1333 | −1.29868 | ||||||||
\(956\) | 23.0423 | 0.745241 | ||||||||
\(957\) | 2.53505 | 0.0819466 | ||||||||
\(958\) | −31.5889 | −1.02059 | ||||||||
\(959\) | 4.54258 | 0.146688 | ||||||||
\(960\) | 8.11917 | 0.262045 | ||||||||
\(961\) | −21.9693 | −0.708687 | ||||||||
\(962\) | −32.3409 | −1.04271 | ||||||||
\(963\) | 21.8947 | 0.705546 | ||||||||
\(964\) | 16.4598 | 0.530135 | ||||||||
\(965\) | 16.5714 | 0.533452 | ||||||||
\(966\) | −25.4273 | −0.818111 | ||||||||
\(967\) | −35.4268 | −1.13925 | −0.569625 | − | 0.821905i | \(-0.692912\pi\) | ||||
−0.569625 | + | 0.821905i | \(0.692912\pi\) | |||||||
\(968\) | 10.9779 | 0.352842 | ||||||||
\(969\) | 92.8482 | 2.98271 | ||||||||
\(970\) | −15.1848 | −0.487555 | ||||||||
\(971\) | −7.58846 | −0.243525 | −0.121763 | − | 0.992559i | \(-0.538855\pi\) | ||||
−0.121763 | + | 0.992559i | \(0.538855\pi\) | |||||||
\(972\) | −12.3960 | −0.397603 | ||||||||
\(973\) | −46.3127 | −1.48472 | ||||||||
\(974\) | −8.47054 | −0.271414 | ||||||||
\(975\) | −20.0735 | −0.642866 | ||||||||
\(976\) | −2.74011 | −0.0877088 | ||||||||
\(977\) | −52.4573 | −1.67826 | −0.839129 | − | 0.543932i | \(-0.816935\pi\) | ||||
−0.839129 | + | 0.543932i | \(0.816935\pi\) | |||||||
\(978\) | 36.2276 | 1.15843 | ||||||||
\(979\) | 0.364509 | 0.0116498 | ||||||||
\(980\) | 6.47547 | 0.206851 | ||||||||
\(981\) | 39.2870 | 1.25434 | ||||||||
\(982\) | 10.3954 | 0.331729 | ||||||||
\(983\) | −1.20544 | −0.0384476 | −0.0192238 | − | 0.999815i | \(-0.506119\pi\) | ||||
−0.0192238 | + | 0.999815i | \(0.506119\pi\) | |||||||
\(984\) | 14.3987 | 0.459015 | ||||||||
\(985\) | 3.05403 | 0.0973095 | ||||||||
\(986\) | −29.5926 | −0.942420 | ||||||||
\(987\) | −29.2822 | −0.932063 | ||||||||
\(988\) | 19.3494 | 0.615588 | ||||||||
\(989\) | −13.3079 | −0.423166 | ||||||||
\(990\) | 2.57475 | 0.0818310 | ||||||||
\(991\) | 33.3344 | 1.05890 | 0.529450 | − | 0.848341i | \(-0.322398\pi\) | ||||
0.529450 | + | 0.848341i | \(0.322398\pi\) | |||||||
\(992\) | −3.00511 | −0.0954124 | ||||||||
\(993\) | 76.6456 | 2.43227 | ||||||||
\(994\) | −12.4306 | −0.394273 | ||||||||
\(995\) | 5.33531 | 0.169141 | ||||||||
\(996\) | 30.7049 | 0.972920 | ||||||||
\(997\) | 38.2398 | 1.21107 | 0.605534 | − | 0.795819i | \(-0.292960\pi\) | ||||
0.605534 | + | 0.795819i | \(0.292960\pi\) | |||||||
\(998\) | 11.1163 | 0.351881 | ||||||||
\(999\) | −103.942 | −3.28857 |
(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 | 4034.2.a.c.1.2 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.c.1.2 | ✓ | 49 | 1.1 | even | 1 | trivial |