Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [322,4,Mod(1,322)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(322, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("322.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 322 = 2 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 322.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: | \(18.9986150218\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 92x^{3} - 28x^{2} + 1593x - 1782 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.26012\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 322.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −0.260120 | −0.0500601 | −0.0250301 | − | 0.999687i | \(-0.507968\pi\) | ||||
−0.0250301 | + | 0.999687i | \(0.507968\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 15.2484 | 1.36386 | 0.681931 | − | 0.731416i | \(-0.261140\pi\) | ||||
0.681931 | + | 0.731416i | \(0.261140\pi\) | |||||||
\(6\) | −0.520240 | −0.0353978 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −26.9323 | −0.997494 | ||||||||
\(10\) | 30.4969 | 0.964397 | ||||||||
\(11\) | 63.1379 | 1.73062 | 0.865309 | − | 0.501238i | \(-0.167122\pi\) | ||||
0.865309 | + | 0.501238i | \(0.167122\pi\) | |||||||
\(12\) | −1.04048 | −0.0250301 | ||||||||
\(13\) | 40.8864 | 0.872295 | 0.436148 | − | 0.899875i | \(-0.356343\pi\) | ||||
0.436148 | + | 0.899875i | \(0.356343\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | −3.96643 | −0.0682751 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −57.0717 | −0.814231 | −0.407115 | − | 0.913377i | \(-0.633465\pi\) | ||||
−0.407115 | + | 0.913377i | \(0.633465\pi\) | |||||||
\(18\) | −53.8647 | −0.705335 | ||||||||
\(19\) | 34.4579 | 0.416062 | 0.208031 | − | 0.978122i | \(-0.433294\pi\) | ||||
0.208031 | + | 0.978122i | \(0.433294\pi\) | |||||||
\(20\) | 60.9938 | 0.681931 | ||||||||
\(21\) | 1.82084 | 0.0189209 | ||||||||
\(22\) | 126.276 | 1.22373 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | −2.08096 | −0.0176989 | ||||||||
\(25\) | 107.515 | 0.860121 | ||||||||
\(26\) | 81.7727 | 0.616806 | ||||||||
\(27\) | 14.0289 | 0.0999948 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | 180.951 | 1.15868 | 0.579340 | − | 0.815086i | \(-0.303310\pi\) | ||||
0.579340 | + | 0.815086i | \(0.303310\pi\) | |||||||
\(30\) | −7.93285 | −0.0482778 | ||||||||
\(31\) | −5.92805 | −0.0343455 | −0.0171727 | − | 0.999853i | \(-0.505467\pi\) | ||||
−0.0171727 | + | 0.999853i | \(0.505467\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −16.4234 | −0.0866350 | ||||||||
\(34\) | −114.143 | −0.575748 | ||||||||
\(35\) | −106.739 | −0.515492 | ||||||||
\(36\) | −107.729 | −0.498747 | ||||||||
\(37\) | −161.864 | −0.719196 | −0.359598 | − | 0.933107i | \(-0.617086\pi\) | ||||
−0.359598 | + | 0.933107i | \(0.617086\pi\) | |||||||
\(38\) | 68.9158 | 0.294200 | ||||||||
\(39\) | −10.6354 | −0.0436672 | ||||||||
\(40\) | 121.988 | 0.482198 | ||||||||
\(41\) | −104.432 | −0.397792 | −0.198896 | − | 0.980021i | \(-0.563736\pi\) | ||||
−0.198896 | + | 0.980021i | \(0.563736\pi\) | |||||||
\(42\) | 3.64168 | 0.0133791 | ||||||||
\(43\) | 16.5725 | 0.0587742 | 0.0293871 | − | 0.999568i | \(-0.490644\pi\) | ||||
0.0293871 | + | 0.999568i | \(0.490644\pi\) | |||||||
\(44\) | 252.552 | 0.865309 | ||||||||
\(45\) | −410.676 | −1.36044 | ||||||||
\(46\) | 46.0000 | 0.147442 | ||||||||
\(47\) | 333.754 | 1.03581 | 0.517904 | − | 0.855439i | \(-0.326713\pi\) | ||||
0.517904 | + | 0.855439i | \(0.326713\pi\) | |||||||
\(48\) | −4.16192 | −0.0125150 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 215.030 | 0.608198 | ||||||||
\(51\) | 14.8455 | 0.0407605 | ||||||||
\(52\) | 163.545 | 0.436148 | ||||||||
\(53\) | 296.103 | 0.767412 | 0.383706 | − | 0.923455i | \(-0.374648\pi\) | ||||
0.383706 | + | 0.923455i | \(0.374648\pi\) | |||||||
\(54\) | 28.0578 | 0.0707070 | ||||||||
\(55\) | 962.756 | 2.36033 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | −8.96319 | −0.0208281 | ||||||||
\(58\) | 361.902 | 0.819311 | ||||||||
\(59\) | −805.644 | −1.77773 | −0.888864 | − | 0.458171i | \(-0.848505\pi\) | ||||
−0.888864 | + | 0.458171i | \(0.848505\pi\) | |||||||
\(60\) | −15.8657 | −0.0341376 | ||||||||
\(61\) | 715.603 | 1.50202 | 0.751012 | − | 0.660288i | \(-0.229566\pi\) | ||||
0.751012 | + | 0.660288i | \(0.229566\pi\) | |||||||
\(62\) | −11.8561 | −0.0242859 | ||||||||
\(63\) | 188.526 | 0.377017 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 623.454 | 1.18969 | ||||||||
\(66\) | −32.8469 | −0.0612602 | ||||||||
\(67\) | 301.232 | 0.549275 | 0.274637 | − | 0.961548i | \(-0.411442\pi\) | ||||
0.274637 | + | 0.961548i | \(0.411442\pi\) | |||||||
\(68\) | −228.287 | −0.407115 | ||||||||
\(69\) | −5.98276 | −0.0104383 | ||||||||
\(70\) | −213.478 | −0.364508 | ||||||||
\(71\) | −871.046 | −1.45597 | −0.727987 | − | 0.685591i | \(-0.759544\pi\) | ||||
−0.727987 | + | 0.685591i | \(0.759544\pi\) | |||||||
\(72\) | −215.459 | −0.352667 | ||||||||
\(73\) | 894.771 | 1.43459 | 0.717295 | − | 0.696770i | \(-0.245380\pi\) | ||||
0.717295 | + | 0.696770i | \(0.245380\pi\) | |||||||
\(74\) | −323.728 | −0.508548 | ||||||||
\(75\) | −27.9668 | −0.0430578 | ||||||||
\(76\) | 137.832 | 0.208031 | ||||||||
\(77\) | −441.966 | −0.654112 | ||||||||
\(78\) | −21.2707 | −0.0308774 | ||||||||
\(79\) | −1246.19 | −1.77477 | −0.887386 | − | 0.461028i | \(-0.847481\pi\) | ||||
−0.887386 | + | 0.461028i | \(0.847481\pi\) | |||||||
\(80\) | 243.975 | 0.340966 | ||||||||
\(81\) | 723.524 | 0.992488 | ||||||||
\(82\) | −208.863 | −0.281281 | ||||||||
\(83\) | −1223.93 | −1.61860 | −0.809300 | − | 0.587395i | \(-0.800154\pi\) | ||||
−0.809300 | + | 0.587395i | \(0.800154\pi\) | |||||||
\(84\) | 7.28336 | 0.00946047 | ||||||||
\(85\) | −870.255 | −1.11050 | ||||||||
\(86\) | 33.1451 | 0.0415596 | ||||||||
\(87\) | −47.0690 | −0.0580037 | ||||||||
\(88\) | 505.104 | 0.611866 | ||||||||
\(89\) | −86.3579 | −0.102853 | −0.0514265 | − | 0.998677i | \(-0.516377\pi\) | ||||
−0.0514265 | + | 0.998677i | \(0.516377\pi\) | |||||||
\(90\) | −821.353 | −0.961980 | ||||||||
\(91\) | −286.205 | −0.329697 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 1.54200 | 0.00171934 | ||||||||
\(94\) | 667.507 | 0.732426 | ||||||||
\(95\) | 525.429 | 0.567452 | ||||||||
\(96\) | −8.32384 | −0.00884946 | ||||||||
\(97\) | 343.939 | 0.360018 | 0.180009 | − | 0.983665i | \(-0.442387\pi\) | ||||
0.180009 | + | 0.983665i | \(0.442387\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | −1700.45 | −1.72628 | ||||||||
\(100\) | 430.061 | 0.430061 | ||||||||
\(101\) | 458.505 | 0.451713 | 0.225856 | − | 0.974161i | \(-0.427482\pi\) | ||||
0.225856 | + | 0.974161i | \(0.427482\pi\) | |||||||
\(102\) | 29.6910 | 0.0288220 | ||||||||
\(103\) | −574.886 | −0.549954 | −0.274977 | − | 0.961451i | \(-0.588670\pi\) | ||||
−0.274977 | + | 0.961451i | \(0.588670\pi\) | |||||||
\(104\) | 327.091 | 0.308403 | ||||||||
\(105\) | 27.7650 | 0.0258056 | ||||||||
\(106\) | 592.205 | 0.542642 | ||||||||
\(107\) | −1451.76 | −1.31165 | −0.655825 | − | 0.754913i | \(-0.727679\pi\) | ||||
−0.655825 | + | 0.754913i | \(0.727679\pi\) | |||||||
\(108\) | 56.1155 | 0.0499974 | ||||||||
\(109\) | −1812.89 | −1.59306 | −0.796530 | − | 0.604598i | \(-0.793334\pi\) | ||||
−0.796530 | + | 0.604598i | \(0.793334\pi\) | |||||||
\(110\) | 1925.51 | 1.66900 | ||||||||
\(111\) | 42.1040 | 0.0360030 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | −1693.79 | −1.41007 | −0.705035 | − | 0.709173i | \(-0.749069\pi\) | ||||
−0.705035 | + | 0.709173i | \(0.749069\pi\) | |||||||
\(114\) | −17.9264 | −0.0147277 | ||||||||
\(115\) | 350.714 | 0.284385 | ||||||||
\(116\) | 723.804 | 0.579340 | ||||||||
\(117\) | −1101.17 | −0.870109 | ||||||||
\(118\) | −1611.29 | −1.25704 | ||||||||
\(119\) | 399.502 | 0.307750 | ||||||||
\(120\) | −31.7314 | −0.0241389 | ||||||||
\(121\) | 2655.40 | 1.99504 | ||||||||
\(122\) | 1431.21 | 1.06209 | ||||||||
\(123\) | 27.1647 | 0.0199135 | ||||||||
\(124\) | −23.7122 | −0.0171727 | ||||||||
\(125\) | −266.616 | −0.190775 | ||||||||
\(126\) | 377.053 | 0.266591 | ||||||||
\(127\) | 251.950 | 0.176039 | 0.0880194 | − | 0.996119i | \(-0.471946\pi\) | ||||
0.0880194 | + | 0.996119i | \(0.471946\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −4.31085 | −0.00294224 | ||||||||
\(130\) | 1246.91 | 0.841238 | ||||||||
\(131\) | −1844.44 | −1.23015 | −0.615074 | − | 0.788469i | \(-0.710874\pi\) | ||||
−0.615074 | + | 0.788469i | \(0.710874\pi\) | |||||||
\(132\) | −65.6938 | −0.0433175 | ||||||||
\(133\) | −241.205 | −0.157257 | ||||||||
\(134\) | 602.465 | 0.388396 | ||||||||
\(135\) | 213.919 | 0.136379 | ||||||||
\(136\) | −456.574 | −0.287874 | ||||||||
\(137\) | −1169.93 | −0.729592 | −0.364796 | − | 0.931087i | \(-0.618861\pi\) | ||||
−0.364796 | + | 0.931087i | \(0.618861\pi\) | |||||||
\(138\) | −11.9655 | −0.00738096 | ||||||||
\(139\) | −1618.44 | −0.987585 | −0.493792 | − | 0.869580i | \(-0.664390\pi\) | ||||
−0.493792 | + | 0.869580i | \(0.664390\pi\) | |||||||
\(140\) | −426.957 | −0.257746 | ||||||||
\(141\) | −86.8160 | −0.0518526 | ||||||||
\(142\) | −1742.09 | −1.02953 | ||||||||
\(143\) | 2581.48 | 1.50961 | ||||||||
\(144\) | −430.917 | −0.249373 | ||||||||
\(145\) | 2759.22 | 1.58028 | ||||||||
\(146\) | 1789.54 | 1.01441 | ||||||||
\(147\) | −12.7459 | −0.00715144 | ||||||||
\(148\) | −647.455 | −0.359598 | ||||||||
\(149\) | −1745.63 | −0.959785 | −0.479892 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479892 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(150\) | −55.9337 | −0.0304464 | ||||||||
\(151\) | −2520.41 | −1.35833 | −0.679167 | − | 0.733984i | \(-0.737659\pi\) | ||||
−0.679167 | + | 0.733984i | \(0.737659\pi\) | |||||||
\(152\) | 275.663 | 0.147100 | ||||||||
\(153\) | 1537.07 | 0.812190 | ||||||||
\(154\) | −883.931 | −0.462527 | ||||||||
\(155\) | −90.3936 | −0.0468425 | ||||||||
\(156\) | −42.5414 | −0.0218336 | ||||||||
\(157\) | 1122.56 | 0.570635 | 0.285318 | − | 0.958433i | \(-0.407901\pi\) | ||||
0.285318 | + | 0.958433i | \(0.407901\pi\) | |||||||
\(158\) | −2492.37 | −1.25495 | ||||||||
\(159\) | −77.0222 | −0.0384167 | ||||||||
\(160\) | 487.950 | 0.241099 | ||||||||
\(161\) | −161.000 | −0.0788110 | ||||||||
\(162\) | 1447.05 | 0.701795 | ||||||||
\(163\) | 149.438 | 0.0718091 | 0.0359045 | − | 0.999355i | \(-0.488569\pi\) | ||||
0.0359045 | + | 0.999355i | \(0.488569\pi\) | |||||||
\(164\) | −417.726 | −0.198896 | ||||||||
\(165\) | −250.432 | −0.118158 | ||||||||
\(166\) | −2447.86 | −1.14452 | ||||||||
\(167\) | 1950.78 | 0.903927 | 0.451963 | − | 0.892037i | \(-0.350724\pi\) | ||||
0.451963 | + | 0.892037i | \(0.350724\pi\) | |||||||
\(168\) | 14.5667 | 0.00668956 | ||||||||
\(169\) | −525.306 | −0.239101 | ||||||||
\(170\) | −1740.51 | −0.785241 | ||||||||
\(171\) | −928.032 | −0.415020 | ||||||||
\(172\) | 66.2902 | 0.0293871 | ||||||||
\(173\) | 2850.79 | 1.25284 | 0.626420 | − | 0.779486i | \(-0.284520\pi\) | ||||
0.626420 | + | 0.779486i | \(0.284520\pi\) | |||||||
\(174\) | −94.1379 | −0.0410148 | ||||||||
\(175\) | −752.606 | −0.325095 | ||||||||
\(176\) | 1010.21 | 0.432655 | ||||||||
\(177\) | 209.564 | 0.0889933 | ||||||||
\(178\) | −172.716 | −0.0727280 | ||||||||
\(179\) | 1847.62 | 0.771493 | 0.385747 | − | 0.922605i | \(-0.373944\pi\) | ||||
0.385747 | + | 0.922605i | \(0.373944\pi\) | |||||||
\(180\) | −1642.71 | −0.680222 | ||||||||
\(181\) | 3260.42 | 1.33892 | 0.669461 | − | 0.742847i | \(-0.266525\pi\) | ||||
0.669461 | + | 0.742847i | \(0.266525\pi\) | |||||||
\(182\) | −572.409 | −0.233131 | ||||||||
\(183\) | −186.143 | −0.0751915 | ||||||||
\(184\) | 184.000 | 0.0737210 | ||||||||
\(185\) | −2468.17 | −0.980884 | ||||||||
\(186\) | 3.08401 | 0.00121576 | ||||||||
\(187\) | −3603.39 | −1.40912 | ||||||||
\(188\) | 1335.01 | 0.517904 | ||||||||
\(189\) | −98.2021 | −0.0377945 | ||||||||
\(190\) | 1050.86 | 0.401249 | ||||||||
\(191\) | 1616.13 | 0.612247 | 0.306123 | − | 0.951992i | \(-0.400968\pi\) | ||||
0.306123 | + | 0.951992i | \(0.400968\pi\) | |||||||
\(192\) | −16.6477 | −0.00625751 | ||||||||
\(193\) | −4746.87 | −1.77040 | −0.885200 | − | 0.465211i | \(-0.845979\pi\) | ||||
−0.885200 | + | 0.465211i | \(0.845979\pi\) | |||||||
\(194\) | 687.878 | 0.254571 | ||||||||
\(195\) | −162.173 | −0.0595560 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −1471.77 | −0.532280 | −0.266140 | − | 0.963934i | \(-0.585748\pi\) | ||||
−0.266140 | + | 0.963934i | \(0.585748\pi\) | |||||||
\(198\) | −3400.90 | −1.22067 | ||||||||
\(199\) | 3296.74 | 1.17437 | 0.587184 | − | 0.809453i | \(-0.300236\pi\) | ||||
0.587184 | + | 0.809453i | \(0.300236\pi\) | |||||||
\(200\) | 860.121 | 0.304099 | ||||||||
\(201\) | −78.3566 | −0.0274967 | ||||||||
\(202\) | 917.011 | 0.319409 | ||||||||
\(203\) | −1266.66 | −0.437940 | ||||||||
\(204\) | 59.3820 | 0.0203802 | ||||||||
\(205\) | −1592.42 | −0.542533 | ||||||||
\(206\) | −1149.77 | −0.388876 | ||||||||
\(207\) | −619.444 | −0.207992 | ||||||||
\(208\) | 654.182 | 0.218074 | ||||||||
\(209\) | 2175.60 | 0.720045 | ||||||||
\(210\) | 55.5300 | 0.0182473 | ||||||||
\(211\) | −2436.09 | −0.794821 | −0.397410 | − | 0.917641i | \(-0.630091\pi\) | ||||
−0.397410 | + | 0.917641i | \(0.630091\pi\) | |||||||
\(212\) | 1184.41 | 0.383706 | ||||||||
\(213\) | 226.577 | 0.0728862 | ||||||||
\(214\) | −2903.51 | −0.927477 | ||||||||
\(215\) | 252.706 | 0.0801599 | ||||||||
\(216\) | 112.231 | 0.0353535 | ||||||||
\(217\) | 41.4964 | 0.0129814 | ||||||||
\(218\) | −3625.79 | −1.12646 | ||||||||
\(219\) | −232.748 | −0.0718157 | ||||||||
\(220\) | 3851.02 | 1.18016 | ||||||||
\(221\) | −2333.45 | −0.710250 | ||||||||
\(222\) | 84.2080 | 0.0254580 | ||||||||
\(223\) | 1464.12 | 0.439662 | 0.219831 | − | 0.975538i | \(-0.429449\pi\) | ||||
0.219831 | + | 0.975538i | \(0.429449\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | −2895.64 | −0.857966 | ||||||||
\(226\) | −3387.57 | −0.997070 | ||||||||
\(227\) | −3419.39 | −0.999794 | −0.499897 | − | 0.866085i | \(-0.666629\pi\) | ||||
−0.499897 | + | 0.866085i | \(0.666629\pi\) | |||||||
\(228\) | −35.8527 | −0.0104141 | ||||||||
\(229\) | −3437.40 | −0.991922 | −0.495961 | − | 0.868345i | \(-0.665184\pi\) | ||||
−0.495961 | + | 0.868345i | \(0.665184\pi\) | |||||||
\(230\) | 701.429 | 0.201091 | ||||||||
\(231\) | 114.964 | 0.0327449 | ||||||||
\(232\) | 1447.61 | 0.409656 | ||||||||
\(233\) | 3049.48 | 0.857415 | 0.428708 | − | 0.903443i | \(-0.358969\pi\) | ||||
0.428708 | + | 0.903443i | \(0.358969\pi\) | |||||||
\(234\) | −2202.33 | −0.615260 | ||||||||
\(235\) | 5089.22 | 1.41270 | ||||||||
\(236\) | −3222.58 | −0.888864 | ||||||||
\(237\) | 324.158 | 0.0888453 | ||||||||
\(238\) | 799.004 | 0.217612 | ||||||||
\(239\) | 1961.10 | 0.530767 | 0.265383 | − | 0.964143i | \(-0.414501\pi\) | ||||
0.265383 | + | 0.964143i | \(0.414501\pi\) | |||||||
\(240\) | −63.4628 | −0.0170688 | ||||||||
\(241\) | 6121.70 | 1.63624 | 0.818119 | − | 0.575049i | \(-0.195017\pi\) | ||||
0.818119 | + | 0.575049i | \(0.195017\pi\) | |||||||
\(242\) | 5310.80 | 1.41071 | ||||||||
\(243\) | −566.983 | −0.149679 | ||||||||
\(244\) | 2862.41 | 0.751012 | ||||||||
\(245\) | 747.174 | 0.194838 | ||||||||
\(246\) | 54.3295 | 0.0140810 | ||||||||
\(247\) | 1408.86 | 0.362929 | ||||||||
\(248\) | −47.4244 | −0.0121430 | ||||||||
\(249\) | 318.369 | 0.0810273 | ||||||||
\(250\) | −533.233 | −0.134898 | ||||||||
\(251\) | 4112.95 | 1.03429 | 0.517145 | − | 0.855898i | \(-0.326995\pi\) | ||||
0.517145 | + | 0.855898i | \(0.326995\pi\) | |||||||
\(252\) | 754.105 | 0.188509 | ||||||||
\(253\) | 1452.17 | 0.360859 | ||||||||
\(254\) | 503.899 | 0.124478 | ||||||||
\(255\) | 226.371 | 0.0555917 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2135.52 | −0.518328 | −0.259164 | − | 0.965833i | \(-0.583447\pi\) | ||||
−0.259164 | + | 0.965833i | \(0.583447\pi\) | |||||||
\(258\) | −8.62170 | −0.00208048 | ||||||||
\(259\) | 1133.05 | 0.271830 | ||||||||
\(260\) | 2493.81 | 0.594845 | ||||||||
\(261\) | −4873.43 | −1.15578 | ||||||||
\(262\) | −3688.88 | −0.869846 | ||||||||
\(263\) | 7005.80 | 1.64257 | 0.821286 | − | 0.570517i | \(-0.193257\pi\) | ||||
0.821286 | + | 0.570517i | \(0.193257\pi\) | |||||||
\(264\) | −131.388 | −0.0306301 | ||||||||
\(265\) | 4515.10 | 1.04664 | ||||||||
\(266\) | −482.410 | −0.111197 | ||||||||
\(267\) | 22.4634 | 0.00514883 | ||||||||
\(268\) | 1204.93 | 0.274637 | ||||||||
\(269\) | 6566.34 | 1.48831 | 0.744157 | − | 0.668004i | \(-0.232851\pi\) | ||||
0.744157 | + | 0.668004i | \(0.232851\pi\) | |||||||
\(270\) | 427.837 | 0.0964346 | ||||||||
\(271\) | −5759.43 | −1.29100 | −0.645499 | − | 0.763761i | \(-0.723351\pi\) | ||||
−0.645499 | + | 0.763761i | \(0.723351\pi\) | |||||||
\(272\) | −913.147 | −0.203558 | ||||||||
\(273\) | 74.4475 | 0.0165046 | ||||||||
\(274\) | −2339.87 | −0.515900 | ||||||||
\(275\) | 6788.29 | 1.48854 | ||||||||
\(276\) | −23.9310 | −0.00521913 | ||||||||
\(277\) | 356.886 | 0.0774123 | 0.0387061 | − | 0.999251i | \(-0.487676\pi\) | ||||
0.0387061 | + | 0.999251i | \(0.487676\pi\) | |||||||
\(278\) | −3236.88 | −0.698328 | ||||||||
\(279\) | 159.656 | 0.0342594 | ||||||||
\(280\) | −853.913 | −0.182254 | ||||||||
\(281\) | −925.745 | −0.196531 | −0.0982657 | − | 0.995160i | \(-0.531329\pi\) | ||||
−0.0982657 | + | 0.995160i | \(0.531329\pi\) | |||||||
\(282\) | −173.632 | −0.0366654 | ||||||||
\(283\) | 6928.18 | 1.45526 | 0.727629 | − | 0.685971i | \(-0.240622\pi\) | ||||
0.727629 | + | 0.685971i | \(0.240622\pi\) | |||||||
\(284\) | −3484.19 | −0.727987 | ||||||||
\(285\) | −136.675 | −0.0284067 | ||||||||
\(286\) | 5162.96 | 1.06746 | ||||||||
\(287\) | 731.021 | 0.150351 | ||||||||
\(288\) | −861.835 | −0.176334 | ||||||||
\(289\) | −1655.82 | −0.337028 | ||||||||
\(290\) | 5518.44 | 1.11743 | ||||||||
\(291\) | −89.4655 | −0.0180225 | ||||||||
\(292\) | 3579.08 | 0.717295 | ||||||||
\(293\) | 148.190 | 0.0295472 | 0.0147736 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147736 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(294\) | −25.4918 | −0.00505684 | ||||||||
\(295\) | −12284.8 | −2.42458 | ||||||||
\(296\) | −1294.91 | −0.254274 | ||||||||
\(297\) | 885.755 | 0.173053 | ||||||||
\(298\) | −3491.27 | −0.678670 | ||||||||
\(299\) | 940.386 | 0.181886 | ||||||||
\(300\) | −111.867 | −0.0215289 | ||||||||
\(301\) | −116.008 | −0.0222145 | ||||||||
\(302\) | −5040.83 | −0.960487 | ||||||||
\(303\) | −119.266 | −0.0226128 | ||||||||
\(304\) | 551.326 | 0.104016 | ||||||||
\(305\) | 10911.8 | 2.04856 | ||||||||
\(306\) | 3074.15 | 0.574305 | ||||||||
\(307\) | −10096.8 | −1.87705 | −0.938527 | − | 0.345207i | \(-0.887809\pi\) | ||||
−0.938527 | + | 0.345207i | \(0.887809\pi\) | |||||||
\(308\) | −1767.86 | −0.327056 | ||||||||
\(309\) | 149.539 | 0.0275308 | ||||||||
\(310\) | −180.787 | −0.0331227 | ||||||||
\(311\) | −1063.81 | −0.193965 | −0.0969826 | − | 0.995286i | \(-0.530919\pi\) | ||||
−0.0969826 | + | 0.995286i | \(0.530919\pi\) | |||||||
\(312\) | −85.0829 | −0.0154387 | ||||||||
\(313\) | 1953.88 | 0.352844 | 0.176422 | − | 0.984315i | \(-0.443548\pi\) | ||||
0.176422 | + | 0.984315i | \(0.443548\pi\) | |||||||
\(314\) | 2245.11 | 0.403500 | ||||||||
\(315\) | 2874.73 | 0.514200 | ||||||||
\(316\) | −4984.75 | −0.887386 | ||||||||
\(317\) | −2939.51 | −0.520819 | −0.260409 | − | 0.965498i | \(-0.583858\pi\) | ||||
−0.260409 | + | 0.965498i | \(0.583858\pi\) | |||||||
\(318\) | −154.044 | −0.0271647 | ||||||||
\(319\) | 11424.9 | 2.00523 | ||||||||
\(320\) | 975.901 | 0.170483 | ||||||||
\(321\) | 377.631 | 0.0656614 | ||||||||
\(322\) | −322.000 | −0.0557278 | ||||||||
\(323\) | −1966.57 | −0.338771 | ||||||||
\(324\) | 2894.10 | 0.496244 | ||||||||
\(325\) | 4395.90 | 0.750280 | ||||||||
\(326\) | 298.876 | 0.0507767 | ||||||||
\(327\) | 471.570 | 0.0797488 | ||||||||
\(328\) | −835.452 | −0.140641 | ||||||||
\(329\) | −2336.27 | −0.391498 | ||||||||
\(330\) | −500.864 | −0.0835505 | ||||||||
\(331\) | −8808.46 | −1.46271 | −0.731354 | − | 0.681998i | \(-0.761111\pi\) | ||||
−0.731354 | + | 0.681998i | \(0.761111\pi\) | |||||||
\(332\) | −4895.72 | −0.809300 | ||||||||
\(333\) | 4359.37 | 0.717393 | ||||||||
\(334\) | 3901.56 | 0.639173 | ||||||||
\(335\) | 4593.33 | 0.749135 | ||||||||
\(336\) | 29.1334 | 0.00473024 | ||||||||
\(337\) | 3966.73 | 0.641191 | 0.320596 | − | 0.947216i | \(-0.396117\pi\) | ||||
0.320596 | + | 0.947216i | \(0.396117\pi\) | |||||||
\(338\) | −1050.61 | −0.169070 | ||||||||
\(339\) | 440.587 | 0.0705883 | ||||||||
\(340\) | −3481.02 | −0.555250 | ||||||||
\(341\) | −374.285 | −0.0594389 | ||||||||
\(342\) | −1856.06 | −0.293463 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 132.580 | 0.0207798 | ||||||||
\(345\) | −91.2278 | −0.0142363 | ||||||||
\(346\) | 5701.57 | 0.885891 | ||||||||
\(347\) | 5747.24 | 0.889129 | 0.444565 | − | 0.895747i | \(-0.353358\pi\) | ||||
0.444565 | + | 0.895747i | \(0.353358\pi\) | |||||||
\(348\) | −188.276 | −0.0290018 | ||||||||
\(349\) | 8367.21 | 1.28334 | 0.641671 | − | 0.766980i | \(-0.278241\pi\) | ||||
0.641671 | + | 0.766980i | \(0.278241\pi\) | |||||||
\(350\) | −1505.21 | −0.229877 | ||||||||
\(351\) | 573.590 | 0.0872249 | ||||||||
\(352\) | 2020.41 | 0.305933 | ||||||||
\(353\) | 4056.10 | 0.611571 | 0.305785 | − | 0.952100i | \(-0.401081\pi\) | ||||
0.305785 | + | 0.952100i | \(0.401081\pi\) | |||||||
\(354\) | 419.128 | 0.0629278 | ||||||||
\(355\) | −13282.1 | −1.98575 | ||||||||
\(356\) | −345.431 | −0.0514265 | ||||||||
\(357\) | −103.918 | −0.0154060 | ||||||||
\(358\) | 3695.23 | 0.545528 | ||||||||
\(359\) | −2580.13 | −0.379315 | −0.189658 | − | 0.981850i | \(-0.560738\pi\) | ||||
−0.189658 | + | 0.981850i | \(0.560738\pi\) | |||||||
\(360\) | −3285.41 | −0.480990 | ||||||||
\(361\) | −5671.65 | −0.826892 | ||||||||
\(362\) | 6520.83 | 0.946761 | ||||||||
\(363\) | −690.722 | −0.0998720 | ||||||||
\(364\) | −1144.82 | −0.164848 | ||||||||
\(365\) | 13643.9 | 1.95658 | ||||||||
\(366\) | −372.285 | −0.0531684 | ||||||||
\(367\) | 938.253 | 0.133451 | 0.0667254 | − | 0.997771i | \(-0.478745\pi\) | ||||
0.0667254 | + | 0.997771i | \(0.478745\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 2812.59 | 0.396795 | ||||||||
\(370\) | −4936.34 | −0.693590 | ||||||||
\(371\) | −2072.72 | −0.290054 | ||||||||
\(372\) | 6.16802 | 0.000859669 0 | ||||||||
\(373\) | 10951.6 | 1.52025 | 0.760125 | − | 0.649777i | \(-0.225138\pi\) | ||||
0.760125 | + | 0.649777i | \(0.225138\pi\) | |||||||
\(374\) | −7206.78 | −0.996401 | ||||||||
\(375\) | 69.3522 | 0.00955023 | ||||||||
\(376\) | 2670.03 | 0.366213 | ||||||||
\(377\) | 7398.42 | 1.01071 | ||||||||
\(378\) | −196.404 | −0.0267247 | ||||||||
\(379\) | 9520.76 | 1.29037 | 0.645183 | − | 0.764028i | \(-0.276781\pi\) | ||||
0.645183 | + | 0.764028i | \(0.276781\pi\) | |||||||
\(380\) | 2101.72 | 0.283726 | ||||||||
\(381\) | −65.5371 | −0.00881252 | ||||||||
\(382\) | 3232.26 | 0.432924 | ||||||||
\(383\) | −3099.25 | −0.413484 | −0.206742 | − | 0.978396i | \(-0.566286\pi\) | ||||
−0.206742 | + | 0.978396i | \(0.566286\pi\) | |||||||
\(384\) | −33.2954 | −0.00442473 | ||||||||
\(385\) | −6739.29 | −0.892119 | ||||||||
\(386\) | −9493.74 | −1.25186 | ||||||||
\(387\) | −446.337 | −0.0586269 | ||||||||
\(388\) | 1375.76 | 0.180009 | ||||||||
\(389\) | 4368.35 | 0.569368 | 0.284684 | − | 0.958621i | \(-0.408111\pi\) | ||||
0.284684 | + | 0.958621i | \(0.408111\pi\) | |||||||
\(390\) | −324.345 | −0.0421125 | ||||||||
\(391\) | −1312.65 | −0.169779 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | 479.775 | 0.0615813 | ||||||||
\(394\) | −2943.54 | −0.376379 | ||||||||
\(395\) | −19002.4 | −2.42054 | ||||||||
\(396\) | −6801.81 | −0.863141 | ||||||||
\(397\) | 6306.06 | 0.797210 | 0.398605 | − | 0.917123i | \(-0.369495\pi\) | ||||
0.398605 | + | 0.917123i | \(0.369495\pi\) | |||||||
\(398\) | 6593.47 | 0.830404 | ||||||||
\(399\) | 62.7423 | 0.00787229 | ||||||||
\(400\) | 1720.24 | 0.215030 | ||||||||
\(401\) | −83.0874 | −0.0103471 | −0.00517355 | − | 0.999987i | \(-0.501647\pi\) | ||||
−0.00517355 | + | 0.999987i | \(0.501647\pi\) | |||||||
\(402\) | −156.713 | −0.0194431 | ||||||||
\(403\) | −242.376 | −0.0299594 | ||||||||
\(404\) | 1834.02 | 0.225856 | ||||||||
\(405\) | 11032.6 | 1.35362 | ||||||||
\(406\) | −2533.31 | −0.309671 | ||||||||
\(407\) | −10219.7 | −1.24465 | ||||||||
\(408\) | 118.764 | 0.0144110 | ||||||||
\(409\) | 1594.33 | 0.192750 | 0.0963749 | − | 0.995345i | \(-0.469275\pi\) | ||||
0.0963749 | + | 0.995345i | \(0.469275\pi\) | |||||||
\(410\) | −3184.84 | −0.383629 | ||||||||
\(411\) | 304.323 | 0.0365235 | ||||||||
\(412\) | −2299.55 | −0.274977 | ||||||||
\(413\) | 5639.51 | 0.671918 | ||||||||
\(414\) | −1238.89 | −0.147072 | ||||||||
\(415\) | −18663.0 | −2.20755 | ||||||||
\(416\) | 1308.36 | 0.154201 | ||||||||
\(417\) | 420.988 | 0.0494386 | ||||||||
\(418\) | 4351.20 | 0.509149 | ||||||||
\(419\) | −3260.67 | −0.380177 | −0.190089 | − | 0.981767i | \(-0.560878\pi\) | ||||
−0.190089 | + | 0.981767i | \(0.560878\pi\) | |||||||
\(420\) | 111.060 | 0.0129028 | ||||||||
\(421\) | −7104.66 | −0.822471 | −0.411235 | − | 0.911529i | \(-0.634903\pi\) | ||||
−0.411235 | + | 0.911529i | \(0.634903\pi\) | |||||||
\(422\) | −4872.18 | −0.562023 | ||||||||
\(423\) | −8988.76 | −1.03321 | ||||||||
\(424\) | 2368.82 | 0.271321 | ||||||||
\(425\) | −6136.08 | −0.700337 | ||||||||
\(426\) | 453.153 | 0.0515384 | ||||||||
\(427\) | −5009.22 | −0.567712 | ||||||||
\(428\) | −5807.02 | −0.655825 | ||||||||
\(429\) | −671.495 | −0.0755712 | ||||||||
\(430\) | 505.411 | 0.0566816 | ||||||||
\(431\) | 10760.4 | 1.20258 | 0.601290 | − | 0.799031i | \(-0.294654\pi\) | ||||
0.601290 | + | 0.799031i | \(0.294654\pi\) | |||||||
\(432\) | 224.462 | 0.0249987 | ||||||||
\(433\) | −11537.4 | −1.28049 | −0.640245 | − | 0.768171i | \(-0.721167\pi\) | ||||
−0.640245 | + | 0.768171i | \(0.721167\pi\) | |||||||
\(434\) | 82.9927 | 0.00917921 | ||||||||
\(435\) | −717.729 | −0.0791091 | ||||||||
\(436\) | −7251.57 | −0.796530 | ||||||||
\(437\) | 792.532 | 0.0867550 | ||||||||
\(438\) | −465.496 | −0.0507814 | ||||||||
\(439\) | −10785.2 | −1.17255 | −0.586277 | − | 0.810111i | \(-0.699407\pi\) | ||||
−0.586277 | + | 0.810111i | \(0.699407\pi\) | |||||||
\(440\) | 7702.05 | 0.834501 | ||||||||
\(441\) | −1319.68 | −0.142499 | ||||||||
\(442\) | −4666.91 | −0.502222 | ||||||||
\(443\) | 2483.46 | 0.266349 | 0.133175 | − | 0.991093i | \(-0.457483\pi\) | ||||
0.133175 | + | 0.991093i | \(0.457483\pi\) | |||||||
\(444\) | 168.416 | 0.0180015 | ||||||||
\(445\) | −1316.82 | −0.140277 | ||||||||
\(446\) | 2928.24 | 0.310888 | ||||||||
\(447\) | 454.074 | 0.0480469 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | −3010.79 | −0.316454 | −0.158227 | − | 0.987403i | \(-0.550578\pi\) | ||||
−0.158227 | + | 0.987403i | \(0.550578\pi\) | |||||||
\(450\) | −5791.27 | −0.606674 | ||||||||
\(451\) | −6593.59 | −0.688426 | ||||||||
\(452\) | −6775.14 | −0.705035 | ||||||||
\(453\) | 655.610 | 0.0679983 | ||||||||
\(454\) | −6838.79 | −0.706961 | ||||||||
\(455\) | −4364.17 | −0.449661 | ||||||||
\(456\) | −71.7055 | −0.00736385 | ||||||||
\(457\) | −12906.5 | −1.32110 | −0.660549 | − | 0.750783i | \(-0.729677\pi\) | ||||
−0.660549 | + | 0.750783i | \(0.729677\pi\) | |||||||
\(458\) | −6874.81 | −0.701395 | ||||||||
\(459\) | −800.652 | −0.0814188 | ||||||||
\(460\) | 1402.86 | 0.142193 | ||||||||
\(461\) | 1928.01 | 0.194786 | 0.0973931 | − | 0.995246i | \(-0.468950\pi\) | ||||
0.0973931 | + | 0.995246i | \(0.468950\pi\) | |||||||
\(462\) | 229.928 | 0.0231542 | ||||||||
\(463\) | 2880.38 | 0.289121 | 0.144560 | − | 0.989496i | \(-0.453823\pi\) | ||||
0.144560 | + | 0.989496i | \(0.453823\pi\) | |||||||
\(464\) | 2895.22 | 0.289670 | ||||||||
\(465\) | 23.5132 | 0.00234494 | ||||||||
\(466\) | 6098.95 | 0.606284 | ||||||||
\(467\) | 6861.47 | 0.679895 | 0.339947 | − | 0.940444i | \(-0.389591\pi\) | ||||
0.339947 | + | 0.940444i | \(0.389591\pi\) | |||||||
\(468\) | −4404.66 | −0.435055 | ||||||||
\(469\) | −2108.63 | −0.207606 | ||||||||
\(470\) | 10178.4 | 0.998929 | ||||||||
\(471\) | −291.999 | −0.0285661 | ||||||||
\(472\) | −6445.16 | −0.628522 | ||||||||
\(473\) | 1046.36 | 0.101716 | ||||||||
\(474\) | 648.316 | 0.0628231 | ||||||||
\(475\) | 3704.75 | 0.357864 | ||||||||
\(476\) | 1598.01 | 0.153875 | ||||||||
\(477\) | −7974.73 | −0.765488 | ||||||||
\(478\) | 3922.21 | 0.375309 | ||||||||
\(479\) | −4580.05 | −0.436885 | −0.218443 | − | 0.975850i | \(-0.570098\pi\) | ||||
−0.218443 | + | 0.975850i | \(0.570098\pi\) | |||||||
\(480\) | −126.926 | −0.0120695 | ||||||||
\(481\) | −6618.02 | −0.627351 | ||||||||
\(482\) | 12243.4 | 1.15700 | ||||||||
\(483\) | 41.8793 | 0.00394529 | ||||||||
\(484\) | 10621.6 | 0.997521 | ||||||||
\(485\) | 5244.54 | 0.491015 | ||||||||
\(486\) | −1133.97 | −0.105839 | ||||||||
\(487\) | 8844.29 | 0.822943 | 0.411471 | − | 0.911423i | \(-0.365015\pi\) | ||||
0.411471 | + | 0.911423i | \(0.365015\pi\) | |||||||
\(488\) | 5724.82 | 0.531046 | ||||||||
\(489\) | −38.8718 | −0.00359477 | ||||||||
\(490\) | 1494.35 | 0.137771 | ||||||||
\(491\) | −4687.22 | −0.430817 | −0.215408 | − | 0.976524i | \(-0.569108\pi\) | ||||
−0.215408 | + | 0.976524i | \(0.569108\pi\) | |||||||
\(492\) | 108.659 | 0.00995675 | ||||||||
\(493\) | −10327.2 | −0.943434 | ||||||||
\(494\) | 2817.72 | 0.256630 | ||||||||
\(495\) | −25929.3 | −2.35441 | ||||||||
\(496\) | −94.8488 | −0.00858637 | ||||||||
\(497\) | 6097.32 | 0.550307 | ||||||||
\(498\) | 636.738 | 0.0572950 | ||||||||
\(499\) | −10245.1 | −0.919107 | −0.459553 | − | 0.888150i | \(-0.651991\pi\) | ||||
−0.459553 | + | 0.888150i | \(0.651991\pi\) | |||||||
\(500\) | −1066.47 | −0.0953876 | ||||||||
\(501\) | −507.436 | −0.0452507 | ||||||||
\(502\) | 8225.89 | 0.731354 | ||||||||
\(503\) | −10020.9 | −0.888286 | −0.444143 | − | 0.895956i | \(-0.646492\pi\) | ||||
−0.444143 | + | 0.895956i | \(0.646492\pi\) | |||||||
\(504\) | 1508.21 | 0.133296 | ||||||||
\(505\) | 6991.50 | 0.616074 | ||||||||
\(506\) | 2904.35 | 0.255166 | ||||||||
\(507\) | 136.643 | 0.0119694 | ||||||||
\(508\) | 1007.80 | 0.0880194 | ||||||||
\(509\) | −15666.6 | −1.36427 | −0.682133 | − | 0.731228i | \(-0.738947\pi\) | ||||
−0.682133 | + | 0.731228i | \(0.738947\pi\) | |||||||
\(510\) | 452.741 | 0.0393093 | ||||||||
\(511\) | −6263.40 | −0.542224 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 483.406 | 0.0416041 | ||||||||
\(514\) | −4271.05 | −0.366513 | ||||||||
\(515\) | −8766.13 | −0.750062 | ||||||||
\(516\) | −17.2434 | −0.00147112 | ||||||||
\(517\) | 21072.5 | 1.79259 | ||||||||
\(518\) | 2266.09 | 0.192213 | ||||||||
\(519\) | −741.546 | −0.0627173 | ||||||||
\(520\) | 4987.63 | 0.420619 | ||||||||
\(521\) | 12571.8 | 1.05716 | 0.528581 | − | 0.848883i | \(-0.322724\pi\) | ||||
0.528581 | + | 0.848883i | \(0.322724\pi\) | |||||||
\(522\) | −9746.86 | −0.817258 | ||||||||
\(523\) | 12266.4 | 1.02557 | 0.512785 | − | 0.858517i | \(-0.328614\pi\) | ||||
0.512785 | + | 0.858517i | \(0.328614\pi\) | |||||||
\(524\) | −7377.76 | −0.615074 | ||||||||
\(525\) | 195.768 | 0.0162743 | ||||||||
\(526\) | 14011.6 | 1.16147 | ||||||||
\(527\) | 338.324 | 0.0279651 | ||||||||
\(528\) | −262.775 | −0.0216587 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 9030.21 | 0.740089 | ||||||||
\(531\) | 21697.9 | 1.77327 | ||||||||
\(532\) | −964.821 | −0.0786284 | ||||||||
\(533\) | −4269.83 | −0.346992 | ||||||||
\(534\) | 44.9268 | 0.00364077 | ||||||||
\(535\) | −22137.0 | −1.78891 | ||||||||
\(536\) | 2409.86 | 0.194198 | ||||||||
\(537\) | −480.602 | −0.0386210 | ||||||||
\(538\) | 13132.7 | 1.05240 | ||||||||
\(539\) | 3093.76 | 0.247231 | ||||||||
\(540\) | 855.675 | 0.0681896 | ||||||||
\(541\) | −17141.8 | −1.36226 | −0.681131 | − | 0.732161i | \(-0.738512\pi\) | ||||
−0.681131 | + | 0.732161i | \(0.738512\pi\) | |||||||
\(542\) | −11518.9 | −0.912874 | ||||||||
\(543\) | −848.100 | −0.0670266 | ||||||||
\(544\) | −1826.29 | −0.143937 | ||||||||
\(545\) | −27643.8 | −2.17272 | ||||||||
\(546\) | 148.895 | 0.0116705 | ||||||||
\(547\) | −13619.5 | −1.06459 | −0.532294 | − | 0.846560i | \(-0.678670\pi\) | ||||
−0.532294 | + | 0.846560i | \(0.678670\pi\) | |||||||
\(548\) | −4679.73 | −0.364796 | ||||||||
\(549\) | −19272.8 | −1.49826 | ||||||||
\(550\) | 13576.6 | 1.05256 | ||||||||
\(551\) | 6235.19 | 0.482083 | ||||||||
\(552\) | −47.8621 | −0.00369048 | ||||||||
\(553\) | 8723.31 | 0.670801 | ||||||||
\(554\) | 713.772 | 0.0547387 | ||||||||
\(555\) | 642.021 | 0.0491032 | ||||||||
\(556\) | −6473.76 | −0.493792 | ||||||||
\(557\) | −14755.1 | −1.12243 | −0.561214 | − | 0.827671i | \(-0.689666\pi\) | ||||
−0.561214 | + | 0.827671i | \(0.689666\pi\) | |||||||
\(558\) | 319.313 | 0.0242251 | ||||||||
\(559\) | 677.591 | 0.0512684 | ||||||||
\(560\) | −1707.83 | −0.128873 | ||||||||
\(561\) | 937.314 | 0.0705409 | ||||||||
\(562\) | −1851.49 | −0.138969 | ||||||||
\(563\) | 21018.7 | 1.57341 | 0.786706 | − | 0.617327i | \(-0.211785\pi\) | ||||
0.786706 | + | 0.617327i | \(0.211785\pi\) | |||||||
\(564\) | −347.264 | −0.0259263 | ||||||||
\(565\) | −25827.6 | −1.92314 | ||||||||
\(566\) | 13856.4 | 1.02902 | ||||||||
\(567\) | −5064.67 | −0.375125 | ||||||||
\(568\) | −6968.37 | −0.514765 | ||||||||
\(569\) | 13750.9 | 1.01313 | 0.506563 | − | 0.862203i | \(-0.330916\pi\) | ||||
0.506563 | + | 0.862203i | \(0.330916\pi\) | |||||||
\(570\) | −273.349 | −0.0200866 | ||||||||
\(571\) | 10636.3 | 0.779535 | 0.389768 | − | 0.920913i | \(-0.372555\pi\) | ||||
0.389768 | + | 0.920913i | \(0.372555\pi\) | |||||||
\(572\) | 10325.9 | 0.754805 | ||||||||
\(573\) | −420.388 | −0.0306491 | ||||||||
\(574\) | 1462.04 | 0.106314 | ||||||||
\(575\) | 2472.85 | 0.179348 | ||||||||
\(576\) | −1723.67 | −0.124687 | ||||||||
\(577\) | 7290.64 | 0.526019 | 0.263010 | − | 0.964793i | \(-0.415285\pi\) | ||||
0.263010 | + | 0.964793i | \(0.415285\pi\) | |||||||
\(578\) | −3311.64 | −0.238315 | ||||||||
\(579\) | 1234.76 | 0.0886264 | ||||||||
\(580\) | 11036.9 | 0.790141 | ||||||||
\(581\) | 8567.52 | 0.611774 | ||||||||
\(582\) | −178.931 | −0.0127439 | ||||||||
\(583\) | 18695.3 | 1.32810 | ||||||||
\(584\) | 7158.17 | 0.507204 | ||||||||
\(585\) | −16791.1 | −1.18671 | ||||||||
\(586\) | 296.379 | 0.0208930 | ||||||||
\(587\) | −6315.96 | −0.444102 | −0.222051 | − | 0.975035i | \(-0.571275\pi\) | ||||
−0.222051 | + | 0.975035i | \(0.571275\pi\) | |||||||
\(588\) | −50.9835 | −0.00357572 | ||||||||
\(589\) | −204.268 | −0.0142899 | ||||||||
\(590\) | −24569.7 | −1.71444 | ||||||||
\(591\) | 382.836 | 0.0266460 | ||||||||
\(592\) | −2589.82 | −0.179799 | ||||||||
\(593\) | 19795.1 | 1.37081 | 0.685403 | − | 0.728164i | \(-0.259626\pi\) | ||||
0.685403 | + | 0.728164i | \(0.259626\pi\) | |||||||
\(594\) | 1771.51 | 0.122367 | ||||||||
\(595\) | 6091.79 | 0.419729 | ||||||||
\(596\) | −6982.54 | −0.479892 | ||||||||
\(597\) | −857.547 | −0.0587890 | ||||||||
\(598\) | 1880.77 | 0.128613 | ||||||||
\(599\) | 27201.1 | 1.85544 | 0.927720 | − | 0.373277i | \(-0.121766\pi\) | ||||
0.927720 | + | 0.373277i | \(0.121766\pi\) | |||||||
\(600\) | −223.735 | −0.0152232 | ||||||||
\(601\) | 11695.1 | 0.793763 | 0.396882 | − | 0.917870i | \(-0.370092\pi\) | ||||
0.396882 | + | 0.917870i | \(0.370092\pi\) | |||||||
\(602\) | −232.016 | −0.0157081 | ||||||||
\(603\) | −8112.89 | −0.547898 | ||||||||
\(604\) | −10081.7 | −0.679167 | ||||||||
\(605\) | 40490.7 | 2.72096 | ||||||||
\(606\) | −238.533 | −0.0159897 | ||||||||
\(607\) | −4523.78 | −0.302495 | −0.151247 | − | 0.988496i | \(-0.548329\pi\) | ||||
−0.151247 | + | 0.988496i | \(0.548329\pi\) | |||||||
\(608\) | 1102.65 | 0.0735501 | ||||||||
\(609\) | 329.483 | 0.0219233 | ||||||||
\(610\) | 21823.7 | 1.44855 | ||||||||
\(611\) | 13646.0 | 0.903530 | ||||||||
\(612\) | 6148.30 | 0.406095 | ||||||||
\(613\) | 27979.4 | 1.84352 | 0.921758 | − | 0.387765i | \(-0.126753\pi\) | ||||
0.921758 | + | 0.387765i | \(0.126753\pi\) | |||||||
\(614\) | −20193.6 | −1.32728 | ||||||||
\(615\) | 414.220 | 0.0271593 | ||||||||
\(616\) | −3535.72 | −0.231264 | ||||||||
\(617\) | 27419.8 | 1.78911 | 0.894553 | − | 0.446961i | \(-0.147494\pi\) | ||||
0.894553 | + | 0.446961i | \(0.147494\pi\) | |||||||
\(618\) | 299.079 | 0.0194672 | ||||||||
\(619\) | 4941.83 | 0.320887 | 0.160443 | − | 0.987045i | \(-0.448708\pi\) | ||||
0.160443 | + | 0.987045i | \(0.448708\pi\) | |||||||
\(620\) | −361.574 | −0.0234213 | ||||||||
\(621\) | 322.664 | 0.0208504 | ||||||||
\(622\) | −2127.62 | −0.137154 | ||||||||
\(623\) | 604.505 | 0.0388748 | ||||||||
\(624\) | −170.166 | −0.0109168 | ||||||||
\(625\) | −17504.9 | −1.12031 | ||||||||
\(626\) | 3907.77 | 0.249498 | ||||||||
\(627\) | −565.917 | −0.0360455 | ||||||||
\(628\) | 4490.22 | 0.285318 | ||||||||
\(629\) | 9237.84 | 0.585591 | ||||||||
\(630\) | 5749.47 | 0.363594 | ||||||||
\(631\) | −13077.3 | −0.825037 | −0.412519 | − | 0.910949i | \(-0.635351\pi\) | ||||
−0.412519 | + | 0.910949i | \(0.635351\pi\) | |||||||
\(632\) | −9969.49 | −0.627477 | ||||||||
\(633\) | 633.675 | 0.0397888 | ||||||||
\(634\) | −5879.03 | −0.368274 | ||||||||
\(635\) | 3841.84 | 0.240093 | ||||||||
\(636\) | −308.089 | −0.0192084 | ||||||||
\(637\) | 2003.43 | 0.124614 | ||||||||
\(638\) | 22849.7 | 1.41792 | ||||||||
\(639\) | 23459.3 | 1.45233 | ||||||||
\(640\) | 1951.80 | 0.120550 | ||||||||
\(641\) | −1272.72 | −0.0784235 | −0.0392117 | − | 0.999231i | \(-0.512485\pi\) | ||||
−0.0392117 | + | 0.999231i | \(0.512485\pi\) | |||||||
\(642\) | 755.262 | 0.0464296 | ||||||||
\(643\) | 113.036 | 0.00693269 | 0.00346634 | − | 0.999994i | \(-0.498897\pi\) | ||||
0.00346634 | + | 0.999994i | \(0.498897\pi\) | |||||||
\(644\) | −644.000 | −0.0394055 | ||||||||
\(645\) | −65.7338 | −0.00401281 | ||||||||
\(646\) | −3933.14 | −0.239547 | ||||||||
\(647\) | −1829.78 | −0.111184 | −0.0555919 | − | 0.998454i | \(-0.517705\pi\) | ||||
−0.0555919 | + | 0.998454i | \(0.517705\pi\) | |||||||
\(648\) | 5788.19 | 0.350898 | ||||||||
\(649\) | −50866.7 | −3.07657 | ||||||||
\(650\) | 8791.81 | 0.530528 | ||||||||
\(651\) | −10.7940 | −0.000649849 0 | ||||||||
\(652\) | 597.751 | 0.0359045 | ||||||||
\(653\) | 1936.86 | 0.116072 | 0.0580361 | − | 0.998314i | \(-0.481516\pi\) | ||||
0.0580361 | + | 0.998314i | \(0.481516\pi\) | |||||||
\(654\) | 943.139 | 0.0563909 | ||||||||
\(655\) | −28124.8 | −1.67775 | ||||||||
\(656\) | −1670.90 | −0.0994480 | ||||||||
\(657\) | −24098.3 | −1.43099 | ||||||||
\(658\) | −4672.55 | −0.276831 | ||||||||
\(659\) | −22889.3 | −1.35302 | −0.676509 | − | 0.736434i | \(-0.736508\pi\) | ||||
−0.676509 | + | 0.736434i | \(0.736508\pi\) | |||||||
\(660\) | −1001.73 | −0.0590791 | ||||||||
\(661\) | 17818.0 | 1.04847 | 0.524237 | − | 0.851573i | \(-0.324351\pi\) | ||||
0.524237 | + | 0.851573i | \(0.324351\pi\) | |||||||
\(662\) | −17616.9 | −1.03429 | ||||||||
\(663\) | 606.978 | 0.0355552 | ||||||||
\(664\) | −9791.45 | −0.572262 | ||||||||
\(665\) | −3678.01 | −0.214477 | ||||||||
\(666\) | 8718.74 | 0.507274 | ||||||||
\(667\) | 4161.87 | 0.241602 | ||||||||
\(668\) | 7803.11 | 0.451963 | ||||||||
\(669\) | −380.847 | −0.0220095 | ||||||||
\(670\) | 9186.65 | 0.529718 | ||||||||
\(671\) | 45181.7 | 2.59943 | ||||||||
\(672\) | 58.2669 | 0.00334478 | ||||||||
\(673\) | 20993.6 | 1.20244 | 0.601222 | − | 0.799082i | \(-0.294681\pi\) | ||||
0.601222 | + | 0.799082i | \(0.294681\pi\) | |||||||
\(674\) | 7933.46 | 0.453391 | ||||||||
\(675\) | 1508.32 | 0.0860076 | ||||||||
\(676\) | −2101.22 | −0.119551 | ||||||||
\(677\) | 5364.75 | 0.304555 | 0.152278 | − | 0.988338i | \(-0.451339\pi\) | ||||
0.152278 | + | 0.988338i | \(0.451339\pi\) | |||||||
\(678\) | 881.175 | 0.0499134 | ||||||||
\(679\) | −2407.57 | −0.136074 | ||||||||
\(680\) | −6962.04 | −0.392621 | ||||||||
\(681\) | 889.453 | 0.0500498 | ||||||||
\(682\) | −748.570 | −0.0420297 | ||||||||
\(683\) | −31720.5 | −1.77709 | −0.888543 | − | 0.458793i | \(-0.848282\pi\) | ||||
−0.888543 | + | 0.458793i | \(0.848282\pi\) | |||||||
\(684\) | −3712.13 | −0.207510 | ||||||||
\(685\) | −17839.7 | −0.995063 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 894.138 | 0.0496557 | ||||||||
\(688\) | 265.161 | 0.0146935 | ||||||||
\(689\) | 12106.6 | 0.669409 | ||||||||
\(690\) | −182.456 | −0.0100666 | ||||||||
\(691\) | −12501.1 | −0.688228 | −0.344114 | − | 0.938928i | \(-0.611821\pi\) | ||||
−0.344114 | + | 0.938928i | \(0.611821\pi\) | |||||||
\(692\) | 11403.1 | 0.626420 | ||||||||
\(693\) | 11903.2 | 0.652473 | ||||||||
\(694\) | 11494.5 | 0.628709 | ||||||||
\(695\) | −24678.7 | −1.34693 | ||||||||
\(696\) | −376.552 | −0.0205074 | ||||||||
\(697\) | 5960.09 | 0.323894 | ||||||||
\(698\) | 16734.4 | 0.907460 | ||||||||
\(699\) | −793.230 | −0.0429223 | ||||||||
\(700\) | −3010.43 | −0.162548 | ||||||||
\(701\) | −4917.13 | −0.264932 | −0.132466 | − | 0.991188i | \(-0.542290\pi\) | ||||
−0.132466 | + | 0.991188i | \(0.542290\pi\) | |||||||
\(702\) | 1147.18 | 0.0616773 | ||||||||
\(703\) | −5577.48 | −0.299230 | ||||||||
\(704\) | 4040.83 | 0.216327 | ||||||||
\(705\) | −1323.81 | −0.0707199 | ||||||||
\(706\) | 8112.20 | 0.432446 | ||||||||
\(707\) | −3209.54 | −0.170731 | ||||||||
\(708\) | 838.257 | 0.0444966 | ||||||||
\(709\) | 2043.21 | 0.108229 | 0.0541145 | − | 0.998535i | \(-0.482766\pi\) | ||||
0.0541145 | + | 0.998535i | \(0.482766\pi\) | |||||||
\(710\) | −26564.2 | −1.40414 | ||||||||
\(711\) | 33562.7 | 1.77032 | ||||||||
\(712\) | −690.863 | −0.0363640 | ||||||||
\(713\) | −136.345 | −0.00716153 | ||||||||
\(714\) | −207.837 | −0.0108937 | ||||||||
\(715\) | 39363.6 | 2.05890 | ||||||||
\(716\) | 7390.46 | 0.385747 | ||||||||
\(717\) | −510.122 | −0.0265703 | ||||||||
\(718\) | −5160.27 | −0.268216 | ||||||||
\(719\) | 24690.8 | 1.28069 | 0.640343 | − | 0.768089i | \(-0.278792\pi\) | ||||
0.640343 | + | 0.768089i | \(0.278792\pi\) | |||||||
\(720\) | −6570.82 | −0.340111 | ||||||||
\(721\) | 4024.21 | 0.207863 | ||||||||
\(722\) | −11343.3 | −0.584701 | ||||||||
\(723\) | −1592.38 | −0.0819103 | ||||||||
\(724\) | 13041.7 | 0.669461 | ||||||||
\(725\) | 19455.0 | 0.996606 | ||||||||
\(726\) | −1381.44 | −0.0706202 | ||||||||
\(727\) | −23243.0 | −1.18574 | −0.592872 | − | 0.805297i | \(-0.702006\pi\) | ||||
−0.592872 | + | 0.805297i | \(0.702006\pi\) | |||||||
\(728\) | −2289.64 | −0.116565 | ||||||||
\(729\) | −19387.7 | −0.984995 | ||||||||
\(730\) | 27287.7 | 1.38351 | ||||||||
\(731\) | −945.823 | −0.0478557 | ||||||||
\(732\) | −744.570 | −0.0375958 | ||||||||
\(733\) | −35315.4 | −1.77954 | −0.889772 | − | 0.456406i | \(-0.849137\pi\) | ||||
−0.889772 | + | 0.456406i | \(0.849137\pi\) | |||||||
\(734\) | 1876.51 | 0.0943639 | ||||||||
\(735\) | −194.355 | −0.00975359 | ||||||||
\(736\) | 736.000 | 0.0368605 | ||||||||
\(737\) | 19019.2 | 0.950585 | ||||||||
\(738\) | 5625.17 | 0.280576 | ||||||||
\(739\) | 10783.2 | 0.536763 | 0.268382 | − | 0.963313i | \(-0.413511\pi\) | ||||
0.268382 | + | 0.963313i | \(0.413511\pi\) | |||||||
\(740\) | −9872.69 | −0.490442 | ||||||||
\(741\) | −366.472 | −0.0181683 | ||||||||
\(742\) | −4145.44 | −0.205099 | ||||||||
\(743\) | −4972.73 | −0.245534 | −0.122767 | − | 0.992436i | \(-0.539177\pi\) | ||||
−0.122767 | + | 0.992436i | \(0.539177\pi\) | |||||||
\(744\) | 12.3360 | 0.000607878 0 | ||||||||
\(745\) | −26618.2 | −1.30901 | ||||||||
\(746\) | 21903.2 | 1.07498 | ||||||||
\(747\) | 32963.3 | 1.61454 | ||||||||
\(748\) | −14413.6 | −0.704562 | ||||||||
\(749\) | 10162.3 | 0.495757 | ||||||||
\(750\) | 138.704 | 0.00675303 | ||||||||
\(751\) | −29604.7 | −1.43847 | −0.719234 | − | 0.694768i | \(-0.755507\pi\) | ||||
−0.719234 | + | 0.694768i | \(0.755507\pi\) | |||||||
\(752\) | 5340.06 | 0.258952 | ||||||||
\(753\) | −1069.86 | −0.0517767 | ||||||||
\(754\) | 14796.8 | 0.714681 | ||||||||
\(755\) | −38432.4 | −1.85258 | ||||||||
\(756\) | −392.809 | −0.0188972 | ||||||||
\(757\) | −9958.05 | −0.478113 | −0.239056 | − | 0.971006i | \(-0.576838\pi\) | ||||
−0.239056 | + | 0.971006i | \(0.576838\pi\) | |||||||
\(758\) | 19041.5 | 0.912426 | ||||||||
\(759\) | −377.739 | −0.0180646 | ||||||||
\(760\) | 4203.44 | 0.200625 | ||||||||
\(761\) | 28654.4 | 1.36494 | 0.682472 | − | 0.730911i | \(-0.260905\pi\) | ||||
0.682472 | + | 0.730911i | \(0.260905\pi\) | |||||||
\(762\) | −131.074 | −0.00623139 | ||||||||
\(763\) | 12690.2 | 0.602120 | ||||||||
\(764\) | 6464.52 | 0.306123 | ||||||||
\(765\) | 23438.0 | 1.10772 | ||||||||
\(766\) | −6198.50 | −0.292377 | ||||||||
\(767\) | −32939.9 | −1.55070 | ||||||||
\(768\) | −66.5907 | −0.00312876 | ||||||||
\(769\) | 1580.21 | 0.0741011 | 0.0370506 | − | 0.999313i | \(-0.488204\pi\) | ||||
0.0370506 | + | 0.999313i | \(0.488204\pi\) | |||||||
\(770\) | −13478.6 | −0.630824 | ||||||||
\(771\) | 555.493 | 0.0259476 | ||||||||
\(772\) | −18987.5 | −0.885200 | ||||||||
\(773\) | 36297.7 | 1.68892 | 0.844461 | − | 0.535617i | \(-0.179921\pi\) | ||||
0.844461 | + | 0.535617i | \(0.179921\pi\) | |||||||
\(774\) | −892.675 | −0.0414555 | ||||||||
\(775\) | −637.356 | −0.0295413 | ||||||||
\(776\) | 2751.51 | 0.127286 | ||||||||
\(777\) | −294.728 | −0.0136079 | ||||||||
\(778\) | 8736.69 | 0.402604 | ||||||||
\(779\) | −3598.49 | −0.165506 | ||||||||
\(780\) | −648.691 | −0.0297780 | ||||||||
\(781\) | −54996.1 | −2.51974 | ||||||||
\(782\) | −2625.30 | −0.120052 | ||||||||
\(783\) | 2538.54 | 0.115862 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 17117.2 | 0.778268 | ||||||||
\(786\) | 959.551 | 0.0435446 | ||||||||
\(787\) | 3840.61 | 0.173956 | 0.0869778 | − | 0.996210i | \(-0.472279\pi\) | ||||
0.0869778 | + | 0.996210i | \(0.472279\pi\) | |||||||
\(788\) | −5887.07 | −0.266140 | ||||||||
\(789\) | −1822.35 | −0.0822273 | ||||||||
\(790\) | −38004.8 | −1.71158 | ||||||||
\(791\) | 11856.5 | 0.532956 | ||||||||
\(792\) | −13603.6 | −0.610333 | ||||||||
\(793\) | 29258.4 | 1.31021 | ||||||||
\(794\) | 12612.1 | 0.563712 | ||||||||
\(795\) | −1174.47 | −0.0523951 | ||||||||
\(796\) | 13186.9 | 0.587184 | ||||||||
\(797\) | −24193.7 | −1.07526 | −0.537632 | − | 0.843179i | \(-0.680681\pi\) | ||||
−0.537632 | + | 0.843179i | \(0.680681\pi\) | |||||||
\(798\) | 125.485 | 0.00556655 | ||||||||
\(799\) | −19047.9 | −0.843386 | ||||||||
\(800\) | 3440.49 | 0.152049 | ||||||||
\(801\) | 2325.82 | 0.102595 | ||||||||
\(802\) | −166.175 | −0.00731650 | ||||||||
\(803\) | 56494.0 | 2.48273 | ||||||||
\(804\) | −313.426 | −0.0137484 | ||||||||
\(805\) | −2455.00 | −0.107487 | ||||||||
\(806\) | −484.753 | −0.0211845 | ||||||||
\(807\) | −1708.04 | −0.0745052 | ||||||||
\(808\) | 3668.04 | 0.159705 | ||||||||
\(809\) | −16476.8 | −0.716063 | −0.358031 | − | 0.933710i | \(-0.616552\pi\) | ||||
−0.358031 | + | 0.933710i | \(0.616552\pi\) | |||||||
\(810\) | 22065.2 | 0.957152 | ||||||||
\(811\) | 2891.58 | 0.125200 | 0.0625999 | − | 0.998039i | \(-0.480061\pi\) | ||||
0.0625999 | + | 0.998039i | \(0.480061\pi\) | |||||||
\(812\) | −5066.63 | −0.218970 | ||||||||
\(813\) | 1498.14 | 0.0646275 | ||||||||
\(814\) | −20439.5 | −0.880103 | ||||||||
\(815\) | 2278.70 | 0.0979377 | ||||||||
\(816\) | 237.528 | 0.0101901 | ||||||||
\(817\) | 571.055 | 0.0244537 | ||||||||
\(818\) | 3188.66 | 0.136295 | ||||||||
\(819\) | 7708.16 | 0.328870 | ||||||||
\(820\) | −6369.68 | −0.271267 | ||||||||
\(821\) | 36315.1 | 1.54373 | 0.771867 | − | 0.635785i | \(-0.219323\pi\) | ||||
0.771867 | + | 0.635785i | \(0.219323\pi\) | |||||||
\(822\) | 608.646 | 0.0258260 | ||||||||
\(823\) | −18744.4 | −0.793913 | −0.396956 | − | 0.917838i | \(-0.629934\pi\) | ||||
−0.396956 | + | 0.917838i | \(0.629934\pi\) | |||||||
\(824\) | −4599.09 | −0.194438 | ||||||||
\(825\) | −1765.77 | −0.0745166 | ||||||||
\(826\) | 11279.0 | 0.475118 | ||||||||
\(827\) | 25294.4 | 1.06357 | 0.531784 | − | 0.846880i | \(-0.321522\pi\) | ||||
0.531784 | + | 0.846880i | \(0.321522\pi\) | |||||||
\(828\) | −2477.78 | −0.103996 | ||||||||
\(829\) | −39438.4 | −1.65230 | −0.826148 | − | 0.563453i | \(-0.809473\pi\) | ||||
−0.826148 | + | 0.563453i | \(0.809473\pi\) | |||||||
\(830\) | −37326.1 | −1.56097 | ||||||||
\(831\) | −92.8332 | −0.00387527 | ||||||||
\(832\) | 2616.73 | 0.109037 | ||||||||
\(833\) | −2796.51 | −0.116319 | ||||||||
\(834\) | 841.977 | 0.0349584 | ||||||||
\(835\) | 29746.3 | 1.23283 | ||||||||
\(836\) | 8702.40 | 0.360023 | ||||||||
\(837\) | −83.1639 | −0.00343437 | ||||||||
\(838\) | −6521.34 | −0.268826 | ||||||||
\(839\) | −30165.0 | −1.24125 | −0.620627 | − | 0.784106i | \(-0.713122\pi\) | ||||
−0.620627 | + | 0.784106i | \(0.713122\pi\) | |||||||
\(840\) | 222.120 | 0.00912365 | ||||||||
\(841\) | 8354.24 | 0.342541 | ||||||||
\(842\) | −14209.3 | −0.581574 | ||||||||
\(843\) | 240.805 | 0.00983838 | ||||||||
\(844\) | −9744.35 | −0.397410 | ||||||||
\(845\) | −8010.10 | −0.326101 | ||||||||
\(846\) | −17977.5 | −0.730591 | ||||||||
\(847\) | −18587.8 | −0.754055 | ||||||||
\(848\) | 4737.64 | 0.191853 | ||||||||
\(849\) | −1802.16 | −0.0728503 | ||||||||
\(850\) | −12272.2 | −0.495213 | ||||||||
\(851\) | −3722.87 | −0.149963 | ||||||||
\(852\) | 906.306 | 0.0364431 | ||||||||
\(853\) | 8977.27 | 0.360347 | 0.180173 | − | 0.983635i | \(-0.442334\pi\) | ||||
0.180173 | + | 0.983635i | \(0.442334\pi\) | |||||||
\(854\) | −10018.4 | −0.401433 | ||||||||
\(855\) | −14151.0 | −0.566030 | ||||||||
\(856\) | −11614.0 | −0.463738 | ||||||||
\(857\) | −40593.6 | −1.61803 | −0.809015 | − | 0.587789i | \(-0.799999\pi\) | ||||
−0.809015 | + | 0.587789i | \(0.799999\pi\) | |||||||
\(858\) | −1342.99 | −0.0534369 | ||||||||
\(859\) | −14117.7 | −0.560755 | −0.280377 | − | 0.959890i | \(-0.590460\pi\) | ||||
−0.280377 | + | 0.959890i | \(0.590460\pi\) | |||||||
\(860\) | 1010.82 | 0.0400799 | ||||||||
\(861\) | −190.153 | −0.00752660 | ||||||||
\(862\) | 21520.9 | 0.850352 | ||||||||
\(863\) | −7080.02 | −0.279266 | −0.139633 | − | 0.990203i | \(-0.544592\pi\) | ||||
−0.139633 | + | 0.990203i | \(0.544592\pi\) | |||||||
\(864\) | 448.924 | 0.0176767 | ||||||||
\(865\) | 43470.1 | 1.70870 | ||||||||
\(866\) | −23074.8 | −0.905443 | ||||||||
\(867\) | 430.712 | 0.0168717 | ||||||||
\(868\) | 165.985 | 0.00649068 | ||||||||
\(869\) | −78681.7 | −3.07145 | ||||||||
\(870\) | −1435.46 | −0.0559386 | ||||||||
\(871\) | 12316.3 | 0.479129 | ||||||||
\(872\) | −14503.1 | −0.563232 | ||||||||
\(873\) | −9263.09 | −0.359116 | ||||||||
\(874\) | 1585.06 | 0.0613450 | ||||||||
\(875\) | 1866.31 | 0.0721062 | ||||||||
\(876\) | −930.991 | −0.0359079 | ||||||||
\(877\) | −29775.4 | −1.14646 | −0.573229 | − | 0.819395i | \(-0.694309\pi\) | ||||
−0.573229 | + | 0.819395i | \(0.694309\pi\) | |||||||
\(878\) | −21570.5 | −0.829120 | ||||||||
\(879\) | −38.5471 | −0.00147914 | ||||||||
\(880\) | 15404.1 | 0.590082 | ||||||||
\(881\) | 32974.9 | 1.26101 | 0.630506 | − | 0.776184i | \(-0.282847\pi\) | ||||
0.630506 | + | 0.776184i | \(0.282847\pi\) | |||||||
\(882\) | −2639.37 | −0.100762 | ||||||||
\(883\) | −8286.80 | −0.315825 | −0.157912 | − | 0.987453i | \(-0.550476\pi\) | ||||
−0.157912 | + | 0.987453i | \(0.550476\pi\) | |||||||
\(884\) | −9333.82 | −0.355125 | ||||||||
\(885\) | 3195.53 | 0.121375 | ||||||||
\(886\) | 4966.91 | 0.188337 | ||||||||
\(887\) | −13354.7 | −0.505533 | −0.252767 | − | 0.967527i | \(-0.581341\pi\) | ||||
−0.252767 | + | 0.967527i | \(0.581341\pi\) | |||||||
\(888\) | 336.832 | 0.0127290 | ||||||||
\(889\) | −1763.65 | −0.0665364 | ||||||||
\(890\) | −2633.65 | −0.0991911 | ||||||||
\(891\) | 45681.8 | 1.71762 | ||||||||
\(892\) | 5856.48 | 0.219831 | ||||||||
\(893\) | 11500.4 | 0.430960 | ||||||||
\(894\) | 908.149 | 0.0339743 | ||||||||
\(895\) | 28173.3 | 1.05221 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | −244.613 | −0.00910524 | ||||||||
\(898\) | −6021.57 | −0.223767 | ||||||||
\(899\) | −1072.69 | −0.0397954 | ||||||||
\(900\) | −11582.5 | −0.428983 | ||||||||
\(901\) | −16899.1 | −0.624850 | ||||||||
\(902\) | −13187.2 | −0.486791 | ||||||||
\(903\) | 30.1759 | 0.00111206 | ||||||||
\(904\) | −13550.3 | −0.498535 | ||||||||
\(905\) | 49716.3 | 1.82611 | ||||||||
\(906\) | 1311.22 | 0.0480821 | ||||||||
\(907\) | 53901.6 | 1.97329 | 0.986645 | − | 0.162885i | \(-0.0520801\pi\) | ||||
0.986645 | + | 0.162885i | \(0.0520801\pi\) | |||||||
\(908\) | −13677.6 | −0.499897 | ||||||||
\(909\) | −12348.6 | −0.450581 | ||||||||
\(910\) | −8728.35 | −0.317958 | ||||||||
\(911\) | −14861.5 | −0.540488 | −0.270244 | − | 0.962792i | \(-0.587104\pi\) | ||||
−0.270244 | + | 0.962792i | \(0.587104\pi\) | |||||||
\(912\) | −143.411 | −0.00520703 | ||||||||
\(913\) | −77276.5 | −2.80118 | ||||||||
\(914\) | −25813.1 | −0.934158 | ||||||||
\(915\) | −2838.38 | −0.102551 | ||||||||
\(916\) | −13749.6 | −0.495961 | ||||||||
\(917\) | 12911.1 | 0.464952 | ||||||||
\(918\) | −1601.30 | −0.0575718 | ||||||||
\(919\) | 39976.2 | 1.43492 | 0.717460 | − | 0.696599i | \(-0.245304\pi\) | ||||
0.717460 | + | 0.696599i | \(0.245304\pi\) | |||||||
\(920\) | 2805.71 | 0.100545 | ||||||||
\(921\) | 2626.38 | 0.0939655 | ||||||||
\(922\) | 3856.02 | 0.137735 | ||||||||
\(923\) | −35613.9 | −1.27004 | ||||||||
\(924\) | 459.856 | 0.0163725 | ||||||||
\(925\) | −17402.8 | −0.618596 | ||||||||
\(926\) | 5760.77 | 0.204439 | ||||||||
\(927\) | 15483.0 | 0.548576 | ||||||||
\(928\) | 5790.43 | 0.204828 | ||||||||
\(929\) | −7480.52 | −0.264185 | −0.132093 | − | 0.991237i | \(-0.542170\pi\) | ||||
−0.132093 | + | 0.991237i | \(0.542170\pi\) | |||||||
\(930\) | 47.0264 | 0.00165812 | ||||||||
\(931\) | 1688.44 | 0.0594375 | ||||||||
\(932\) | 12197.9 | 0.428708 | ||||||||
\(933\) | 276.718 | 0.00970992 | ||||||||
\(934\) | 13722.9 | 0.480758 | ||||||||
\(935\) | −54946.1 | −1.92185 | ||||||||
\(936\) | −8809.32 | −0.307630 | ||||||||
\(937\) | −18057.0 | −0.629558 | −0.314779 | − | 0.949165i | \(-0.601930\pi\) | ||||
−0.314779 | + | 0.949165i | \(0.601930\pi\) | |||||||
\(938\) | −4217.25 | −0.146800 | ||||||||
\(939\) | −508.244 | −0.0176634 | ||||||||
\(940\) | 20356.9 | 0.706350 | ||||||||
\(941\) | −18921.5 | −0.655496 | −0.327748 | − | 0.944765i | \(-0.606290\pi\) | ||||
−0.327748 | + | 0.944765i | \(0.606290\pi\) | |||||||
\(942\) | −583.999 | −0.0201993 | ||||||||
\(943\) | −2401.93 | −0.0829453 | ||||||||
\(944\) | −12890.3 | −0.444432 | ||||||||
\(945\) | −1497.43 | −0.0515465 | ||||||||
\(946\) | 2092.71 | 0.0719238 | ||||||||
\(947\) | −10147.2 | −0.348193 | −0.174097 | − | 0.984729i | \(-0.555701\pi\) | ||||
−0.174097 | + | 0.984729i | \(0.555701\pi\) | |||||||
\(948\) | 1296.63 | 0.0444226 | ||||||||
\(949\) | 36583.9 | 1.25139 | ||||||||
\(950\) | 7409.49 | 0.253048 | ||||||||
\(951\) | 764.626 | 0.0260722 | ||||||||
\(952\) | 3196.02 | 0.108806 | ||||||||
\(953\) | 6284.28 | 0.213607 | 0.106804 | − | 0.994280i | \(-0.465938\pi\) | ||||
0.106804 | + | 0.994280i | \(0.465938\pi\) | |||||||
\(954\) | −15949.5 | −0.541282 | ||||||||
\(955\) | 24643.5 | 0.835020 | ||||||||
\(956\) | 7844.42 | 0.265383 | ||||||||
\(957\) | −2971.84 | −0.100382 | ||||||||
\(958\) | −9160.11 | −0.308925 | ||||||||
\(959\) | 8189.53 | 0.275760 | ||||||||
\(960\) | −253.851 | −0.00853439 | ||||||||
\(961\) | −29755.9 | −0.998820 | ||||||||
\(962\) | −13236.0 | −0.443604 | ||||||||
\(963\) | 39099.2 | 1.30836 | ||||||||
\(964\) | 24486.8 | 0.818119 | ||||||||
\(965\) | −72382.4 | −2.41458 | ||||||||
\(966\) | 83.7586 | 0.00278974 | ||||||||
\(967\) | −10750.9 | −0.357524 | −0.178762 | − | 0.983892i | \(-0.557209\pi\) | ||||
−0.178762 | + | 0.983892i | \(0.557209\pi\) | |||||||
\(968\) | 21243.2 | 0.705354 | ||||||||
\(969\) | 511.544 | 0.0169589 | ||||||||
\(970\) | 10489.1 | 0.347200 | ||||||||
\(971\) | 21337.3 | 0.705198 | 0.352599 | − | 0.935774i | \(-0.385298\pi\) | ||||
0.352599 | + | 0.935774i | \(0.385298\pi\) | |||||||
\(972\) | −2267.93 | −0.0748394 | ||||||||
\(973\) | 11329.1 | 0.373272 | ||||||||
\(974\) | 17688.6 | 0.581908 | ||||||||
\(975\) | −1143.46 | −0.0375591 | ||||||||
\(976\) | 11449.6 | 0.375506 | ||||||||
\(977\) | −713.051 | −0.0233496 | −0.0116748 | − | 0.999932i | \(-0.503716\pi\) | ||||
−0.0116748 | + | 0.999932i | \(0.503716\pi\) | |||||||
\(978\) | −77.7435 | −0.00254189 | ||||||||
\(979\) | −5452.46 | −0.177999 | ||||||||
\(980\) | 2988.70 | 0.0974188 | ||||||||
\(981\) | 48825.4 | 1.58907 | ||||||||
\(982\) | −9374.43 | −0.304634 | ||||||||
\(983\) | 31306.7 | 1.01580 | 0.507898 | − | 0.861417i | \(-0.330423\pi\) | ||||
0.507898 | + | 0.861417i | \(0.330423\pi\) | |||||||
\(984\) | 217.318 | 0.00704049 | ||||||||
\(985\) | −22442.2 | −0.725956 | ||||||||
\(986\) | −20654.4 | −0.667108 | ||||||||
\(987\) | 607.712 | 0.0195985 | ||||||||
\(988\) | 5635.43 | 0.181465 | ||||||||
\(989\) | 381.168 | 0.0122553 | ||||||||
\(990\) | −51858.5 | −1.66482 | ||||||||
\(991\) | 13538.1 | 0.433956 | 0.216978 | − | 0.976176i | \(-0.430380\pi\) | ||||
0.216978 | + | 0.976176i | \(0.430380\pi\) | |||||||
\(992\) | −189.698 | −0.00607148 | ||||||||
\(993\) | 2291.26 | 0.0732234 | ||||||||
\(994\) | 12194.6 | 0.389125 | ||||||||
\(995\) | 50270.1 | 1.60168 | ||||||||
\(996\) | 1273.48 | 0.0405137 | ||||||||
\(997\) | 44983.5 | 1.42893 | 0.714464 | − | 0.699672i | \(-0.246671\pi\) | ||||
0.714464 | + | 0.699672i | \(0.246671\pi\) | |||||||
\(998\) | −20490.2 | −0.649907 | ||||||||
\(999\) | −2270.77 | −0.0719158 |
(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 | 322.4.a.h.1.3 | ✓ | 5 | |
7.6 | odd | 2 | 2254.4.a.l.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
322.4.a.h.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
2254.4.a.l.1.3 | 5 | 7.6 | odd | 2 |