Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1617,4,Mod(1,1617)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1617, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1617.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1617 = 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1617.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: | \(95.4060884793\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 92 x^{14} + 346 x^{13} + 3385 x^{12} - 11756 x^{11} - 63875 x^{10} + 199850 x^{9} + \cdots + 5479424 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(4.13448\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1617.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.13448 | 1.46176 | 0.730879 | − | 0.682507i | \(-0.239110\pi\) | ||||
0.730879 | + | 0.682507i | \(0.239110\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 9.09391 | 1.13674 | ||||||||
\(5\) | −10.9590 | −0.980205 | −0.490103 | − | 0.871665i | \(-0.663041\pi\) | ||||
−0.490103 | + | 0.871665i | \(0.663041\pi\) | |||||||
\(6\) | 12.4034 | 0.843947 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 4.52277 | 0.199880 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −45.3099 | −1.43282 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 27.2817 | 0.656297 | ||||||||
\(13\) | 55.7486 | 1.18937 | 0.594687 | − | 0.803957i | \(-0.297276\pi\) | ||||
0.594687 | + | 0.803957i | \(0.297276\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −32.8771 | −0.565922 | ||||||||
\(16\) | −54.0520 | −0.844563 | ||||||||
\(17\) | −55.2997 | −0.788949 | −0.394475 | − | 0.918907i | \(-0.629073\pi\) | ||||
−0.394475 | + | 0.918907i | \(0.629073\pi\) | |||||||
\(18\) | 37.2103 | 0.487253 | ||||||||
\(19\) | 116.629 | 1.40824 | 0.704118 | − | 0.710083i | \(-0.251343\pi\) | ||||
0.704118 | + | 0.710083i | \(0.251343\pi\) | |||||||
\(20\) | −99.6605 | −1.11424 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 45.4793 | 0.440737 | ||||||||
\(23\) | −74.0341 | −0.671182 | −0.335591 | − | 0.942008i | \(-0.608936\pi\) | ||||
−0.335591 | + | 0.942008i | \(0.608936\pi\) | |||||||
\(24\) | 13.5683 | 0.115401 | ||||||||
\(25\) | −4.89972 | −0.0391978 | ||||||||
\(26\) | 230.491 | 1.73858 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 189.891 | 1.21593 | 0.607965 | − | 0.793964i | \(-0.291986\pi\) | ||||
0.607965 | + | 0.793964i | \(0.291986\pi\) | |||||||
\(30\) | −135.930 | −0.827241 | ||||||||
\(31\) | 142.372 | 0.824862 | 0.412431 | − | 0.910989i | \(-0.364680\pi\) | ||||
0.412431 | + | 0.910989i | \(0.364680\pi\) | |||||||
\(32\) | −259.659 | −1.43443 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | −228.635 | −1.15325 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 81.8452 | 0.378913 | ||||||||
\(37\) | 241.223 | 1.07180 | 0.535902 | − | 0.844280i | \(-0.319972\pi\) | ||||
0.535902 | + | 0.844280i | \(0.319972\pi\) | |||||||
\(38\) | 482.199 | 2.05850 | ||||||||
\(39\) | 167.246 | 0.686686 | ||||||||
\(40\) | −49.5651 | −0.195923 | ||||||||
\(41\) | 215.447 | 0.820664 | 0.410332 | − | 0.911936i | \(-0.365413\pi\) | ||||
0.410332 | + | 0.911936i | \(0.365413\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −252.189 | −0.894384 | −0.447192 | − | 0.894438i | \(-0.647576\pi\) | ||||
−0.447192 | + | 0.894438i | \(0.647576\pi\) | |||||||
\(44\) | 100.033 | 0.342740 | ||||||||
\(45\) | −98.6312 | −0.326735 | ||||||||
\(46\) | −306.093 | −0.981106 | ||||||||
\(47\) | 557.633 | 1.73062 | 0.865311 | − | 0.501236i | \(-0.167121\pi\) | ||||
0.865311 | + | 0.501236i | \(0.167121\pi\) | |||||||
\(48\) | −162.156 | −0.487609 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −20.2578 | −0.0572977 | ||||||||
\(51\) | −165.899 | −0.455500 | ||||||||
\(52\) | 506.973 | 1.35201 | ||||||||
\(53\) | 170.675 | 0.442339 | 0.221169 | − | 0.975235i | \(-0.429013\pi\) | ||||
0.221169 | + | 0.975235i | \(0.429013\pi\) | |||||||
\(54\) | 111.631 | 0.281316 | ||||||||
\(55\) | −120.549 | −0.295543 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 349.886 | 0.813045 | ||||||||
\(58\) | 785.102 | 1.77740 | ||||||||
\(59\) | 791.190 | 1.74583 | 0.872917 | − | 0.487869i | \(-0.162226\pi\) | ||||
0.872917 | + | 0.487869i | \(0.162226\pi\) | |||||||
\(60\) | −298.981 | −0.643305 | ||||||||
\(61\) | −257.636 | −0.540769 | −0.270384 | − | 0.962752i | \(-0.587151\pi\) | ||||
−0.270384 | + | 0.962752i | \(0.587151\pi\) | |||||||
\(62\) | 588.633 | 1.20575 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −641.139 | −1.25222 | ||||||||
\(65\) | −610.950 | −1.16583 | ||||||||
\(66\) | 136.438 | 0.254460 | ||||||||
\(67\) | 219.083 | 0.399482 | 0.199741 | − | 0.979849i | \(-0.435990\pi\) | ||||
0.199741 | + | 0.979849i | \(0.435990\pi\) | |||||||
\(68\) | −502.890 | −0.896830 | ||||||||
\(69\) | −222.102 | −0.387507 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.4721 | −0.0208475 | −0.0104237 | − | 0.999946i | \(-0.503318\pi\) | ||||
−0.0104237 | + | 0.999946i | \(0.503318\pi\) | |||||||
\(72\) | 40.7049 | 0.0666266 | ||||||||
\(73\) | −107.351 | −0.172116 | −0.0860578 | − | 0.996290i | \(-0.527427\pi\) | ||||
−0.0860578 | + | 0.996290i | \(0.527427\pi\) | |||||||
\(74\) | 997.330 | 1.56672 | ||||||||
\(75\) | −14.6992 | −0.0226308 | ||||||||
\(76\) | 1060.61 | 1.60080 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 691.474 | 1.00377 | ||||||||
\(79\) | 11.9028 | 0.0169515 | 0.00847575 | − | 0.999964i | \(-0.497302\pi\) | ||||
0.00847575 | + | 0.999964i | \(0.497302\pi\) | |||||||
\(80\) | 592.358 | 0.827845 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 890.763 | 1.19961 | ||||||||
\(83\) | −509.214 | −0.673415 | −0.336708 | − | 0.941609i | \(-0.609313\pi\) | ||||
−0.336708 | + | 0.941609i | \(0.609313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 606.030 | 0.773332 | ||||||||
\(86\) | −1042.67 | −1.30737 | ||||||||
\(87\) | 569.674 | 0.702017 | ||||||||
\(88\) | 49.7504 | 0.0602661 | ||||||||
\(89\) | 1357.83 | 1.61719 | 0.808597 | − | 0.588363i | \(-0.200227\pi\) | ||||
0.808597 | + | 0.588363i | \(0.200227\pi\) | |||||||
\(90\) | −407.789 | −0.477608 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −673.260 | −0.762959 | ||||||||
\(93\) | 427.115 | 0.476234 | ||||||||
\(94\) | 2305.52 | 2.52975 | ||||||||
\(95\) | −1278.14 | −1.38036 | ||||||||
\(96\) | −778.977 | −0.828167 | ||||||||
\(97\) | −405.813 | −0.424785 | −0.212392 | − | 0.977184i | \(-0.568125\pi\) | ||||
−0.212392 | + | 0.977184i | \(0.568125\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | −44.5576 | −0.0445576 | ||||||||
\(101\) | −618.367 | −0.609206 | −0.304603 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304603 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(102\) | −685.906 | −0.665831 | ||||||||
\(103\) | −1220.77 | −1.16783 | −0.583914 | − | 0.811815i | \(-0.698480\pi\) | ||||
−0.583914 | + | 0.811815i | \(0.698480\pi\) | |||||||
\(104\) | 252.138 | 0.237732 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 705.651 | 0.646593 | ||||||||
\(107\) | 1047.79 | 0.946667 | 0.473334 | − | 0.880883i | \(-0.343051\pi\) | ||||
0.473334 | + | 0.880883i | \(0.343051\pi\) | |||||||
\(108\) | 245.536 | 0.218766 | ||||||||
\(109\) | −519.147 | −0.456195 | −0.228098 | − | 0.973638i | \(-0.573251\pi\) | ||||
−0.228098 | + | 0.973638i | \(0.573251\pi\) | |||||||
\(110\) | −498.409 | −0.432013 | ||||||||
\(111\) | 723.668 | 0.618806 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2341.62 | 1.94939 | 0.974694 | − | 0.223542i | \(-0.0717621\pi\) | ||||
0.974694 | + | 0.223542i | \(0.0717621\pi\) | |||||||
\(114\) | 1446.60 | 1.18848 | ||||||||
\(115\) | 811.342 | 0.657896 | ||||||||
\(116\) | 1726.86 | 1.38219 | ||||||||
\(117\) | 501.737 | 0.396458 | ||||||||
\(118\) | 3271.16 | 2.55199 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −148.695 | −0.113116 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1065.19 | −0.790473 | ||||||||
\(123\) | 646.342 | 0.473811 | ||||||||
\(124\) | 1294.72 | 0.937653 | ||||||||
\(125\) | 1423.57 | 1.01863 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1468.50 | −1.02605 | −0.513025 | − | 0.858374i | \(-0.671475\pi\) | ||||
−0.513025 | + | 0.858374i | \(0.671475\pi\) | |||||||
\(128\) | −573.502 | −0.396022 | ||||||||
\(129\) | −756.568 | −0.516373 | ||||||||
\(130\) | −2525.96 | −1.70416 | ||||||||
\(131\) | 2128.17 | 1.41938 | 0.709692 | − | 0.704512i | \(-0.248834\pi\) | ||||
0.709692 | + | 0.704512i | \(0.248834\pi\) | |||||||
\(132\) | 300.099 | 0.197881 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 905.795 | 0.583946 | ||||||||
\(135\) | −295.894 | −0.188641 | ||||||||
\(136\) | −250.107 | −0.157695 | ||||||||
\(137\) | −1654.03 | −1.03149 | −0.515743 | − | 0.856743i | \(-0.672484\pi\) | ||||
−0.515743 | + | 0.856743i | \(0.672484\pi\) | |||||||
\(138\) | −918.278 | −0.566442 | ||||||||
\(139\) | 2311.64 | 1.41058 | 0.705290 | − | 0.708919i | \(-0.250817\pi\) | ||||
0.705290 | + | 0.708919i | \(0.250817\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1672.90 | 0.999175 | ||||||||
\(142\) | −51.5657 | −0.0304740 | ||||||||
\(143\) | 613.234 | 0.358610 | ||||||||
\(144\) | −486.468 | −0.281521 | ||||||||
\(145\) | −2081.03 | −1.19186 | ||||||||
\(146\) | −443.839 | −0.251592 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2193.66 | 1.21836 | ||||||||
\(149\) | −1496.00 | −0.822528 | −0.411264 | − | 0.911516i | \(-0.634913\pi\) | ||||
−0.411264 | + | 0.911516i | \(0.634913\pi\) | |||||||
\(150\) | −60.7734 | −0.0330808 | ||||||||
\(151\) | 37.2530 | 0.0200769 | 0.0100384 | − | 0.999950i | \(-0.496805\pi\) | ||||
0.0100384 | + | 0.999950i | \(0.496805\pi\) | |||||||
\(152\) | 527.485 | 0.281478 | ||||||||
\(153\) | −497.697 | −0.262983 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1560.26 | −0.808534 | ||||||||
\(156\) | 1520.92 | 0.780583 | ||||||||
\(157\) | 539.971 | 0.274486 | 0.137243 | − | 0.990537i | \(-0.456176\pi\) | ||||
0.137243 | + | 0.990537i | \(0.456176\pi\) | |||||||
\(158\) | 49.2118 | 0.0247790 | ||||||||
\(159\) | 512.024 | 0.255384 | ||||||||
\(160\) | 2845.61 | 1.40603 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 334.893 | 0.162418 | ||||||||
\(163\) | −2002.98 | −0.962487 | −0.481244 | − | 0.876587i | \(-0.659815\pi\) | ||||
−0.481244 | + | 0.876587i | \(0.659815\pi\) | |||||||
\(164\) | 1959.26 | 0.932881 | ||||||||
\(165\) | −361.648 | −0.170632 | ||||||||
\(166\) | −2105.33 | −0.984371 | ||||||||
\(167\) | 3346.12 | 1.55048 | 0.775241 | − | 0.631666i | \(-0.217629\pi\) | ||||
0.775241 | + | 0.631666i | \(0.217629\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 910.901 | 0.414611 | ||||||||
\(170\) | 2505.62 | 1.13043 | ||||||||
\(171\) | 1049.66 | 0.469412 | ||||||||
\(172\) | −2293.39 | −1.01668 | ||||||||
\(173\) | 2538.50 | 1.11560 | 0.557799 | − | 0.829976i | \(-0.311646\pi\) | ||||
0.557799 | + | 0.829976i | \(0.311646\pi\) | |||||||
\(174\) | 2355.31 | 1.02618 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −594.572 | −0.254645 | ||||||||
\(177\) | 2373.57 | 1.00796 | ||||||||
\(178\) | 5613.94 | 2.36395 | ||||||||
\(179\) | −4575.15 | −1.91041 | −0.955203 | − | 0.295951i | \(-0.904363\pi\) | ||||
−0.955203 | + | 0.295951i | \(0.904363\pi\) | |||||||
\(180\) | −896.944 | −0.371413 | ||||||||
\(181\) | −495.478 | −0.203473 | −0.101736 | − | 0.994811i | \(-0.532440\pi\) | ||||
−0.101736 | + | 0.994811i | \(0.532440\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −772.907 | −0.312213 | ||||||||
\(184\) | −334.839 | −0.134156 | ||||||||
\(185\) | −2643.57 | −1.05059 | ||||||||
\(186\) | 1765.90 | 0.696140 | ||||||||
\(187\) | −608.296 | −0.237877 | ||||||||
\(188\) | 5071.07 | 1.96726 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5284.43 | −2.01775 | ||||||||
\(191\) | 1787.89 | 0.677314 | 0.338657 | − | 0.940910i | \(-0.390027\pi\) | ||||
0.338657 | + | 0.940910i | \(0.390027\pi\) | |||||||
\(192\) | −1923.42 | −0.722972 | ||||||||
\(193\) | −4947.29 | −1.84515 | −0.922575 | − | 0.385818i | \(-0.873919\pi\) | ||||
−0.922575 | + | 0.385818i | \(0.873919\pi\) | |||||||
\(194\) | −1677.83 | −0.620933 | ||||||||
\(195\) | −1832.85 | −0.673093 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2792.79 | 1.01004 | 0.505020 | − | 0.863108i | \(-0.331485\pi\) | ||||
0.505020 | + | 0.863108i | \(0.331485\pi\) | |||||||
\(198\) | 409.313 | 0.146912 | ||||||||
\(199\) | −2512.22 | −0.894907 | −0.447454 | − | 0.894307i | \(-0.647669\pi\) | ||||
−0.447454 | + | 0.894307i | \(0.647669\pi\) | |||||||
\(200\) | −22.1603 | −0.00783484 | ||||||||
\(201\) | 657.249 | 0.230641 | ||||||||
\(202\) | −2556.62 | −0.890512 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1508.67 | −0.517785 | ||||||||
\(205\) | −2361.09 | −0.804419 | ||||||||
\(206\) | −5047.26 | −1.70708 | ||||||||
\(207\) | −666.307 | −0.223727 | ||||||||
\(208\) | −3013.32 | −1.00450 | ||||||||
\(209\) | 1282.92 | 0.424599 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3069.47 | 1.00147 | 0.500736 | − | 0.865600i | \(-0.333063\pi\) | ||||
0.500736 | + | 0.865600i | \(0.333063\pi\) | |||||||
\(212\) | 1552.10 | 0.502824 | ||||||||
\(213\) | −37.4164 | −0.0120363 | ||||||||
\(214\) | 4332.05 | 1.38380 | ||||||||
\(215\) | 2763.75 | 0.876680 | ||||||||
\(216\) | 122.115 | 0.0384669 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2146.40 | −0.666847 | ||||||||
\(219\) | −322.052 | −0.0993710 | ||||||||
\(220\) | −1096.27 | −0.335955 | ||||||||
\(221\) | −3082.88 | −0.938356 | ||||||||
\(222\) | 2991.99 | 0.904546 | ||||||||
\(223\) | −6545.98 | −1.96570 | −0.982850 | − | 0.184407i | \(-0.940964\pi\) | ||||
−0.982850 | + | 0.184407i | \(0.940964\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −44.0975 | −0.0130659 | ||||||||
\(226\) | 9681.37 | 2.84954 | ||||||||
\(227\) | −431.720 | −0.126230 | −0.0631151 | − | 0.998006i | \(-0.520104\pi\) | ||||
−0.0631151 | + | 0.998006i | \(0.520104\pi\) | |||||||
\(228\) | 3181.84 | 0.924220 | ||||||||
\(229\) | −1091.44 | −0.314953 | −0.157477 | − | 0.987523i | \(-0.550336\pi\) | ||||
−0.157477 | + | 0.987523i | \(0.550336\pi\) | |||||||
\(230\) | 3354.48 | 0.961685 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 858.834 | 0.243040 | ||||||||
\(233\) | 722.874 | 0.203249 | 0.101625 | − | 0.994823i | \(-0.467596\pi\) | ||||
0.101625 | + | 0.994823i | \(0.467596\pi\) | |||||||
\(234\) | 2074.42 | 0.579526 | ||||||||
\(235\) | −6111.12 | −1.69636 | ||||||||
\(236\) | 7195.02 | 1.98456 | ||||||||
\(237\) | 35.7084 | 0.00978695 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3029.83 | 0.820015 | 0.410008 | − | 0.912082i | \(-0.365526\pi\) | ||||
0.410008 | + | 0.912082i | \(0.365526\pi\) | |||||||
\(240\) | 1777.07 | 0.477957 | ||||||||
\(241\) | −3604.71 | −0.963484 | −0.481742 | − | 0.876313i | \(-0.659996\pi\) | ||||
−0.481742 | + | 0.876313i | \(0.659996\pi\) | |||||||
\(242\) | 500.272 | 0.132887 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −2342.92 | −0.614713 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2672.29 | 0.692597 | ||||||||
\(247\) | 6501.89 | 1.67492 | ||||||||
\(248\) | 643.914 | 0.164873 | ||||||||
\(249\) | −1527.64 | −0.388796 | ||||||||
\(250\) | 5885.74 | 1.48899 | ||||||||
\(251\) | −1623.57 | −0.408281 | −0.204141 | − | 0.978942i | \(-0.565440\pi\) | ||||
−0.204141 | + | 0.978942i | \(0.565440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −814.375 | −0.202369 | ||||||||
\(254\) | −6071.48 | −1.49984 | ||||||||
\(255\) | 1818.09 | 0.446483 | ||||||||
\(256\) | 2757.98 | 0.673335 | ||||||||
\(257\) | 2385.67 | 0.579043 | 0.289522 | − | 0.957171i | \(-0.406504\pi\) | ||||
0.289522 | + | 0.957171i | \(0.406504\pi\) | |||||||
\(258\) | −3128.02 | −0.754813 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −5555.93 | −1.32525 | ||||||||
\(261\) | 1709.02 | 0.405310 | ||||||||
\(262\) | 8798.88 | 2.07480 | ||||||||
\(263\) | 3806.19 | 0.892393 | 0.446197 | − | 0.894935i | \(-0.352778\pi\) | ||||
0.446197 | + | 0.894935i | \(0.352778\pi\) | |||||||
\(264\) | 149.251 | 0.0347946 | ||||||||
\(265\) | −1870.43 | −0.433583 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4073.50 | 0.933687 | ||||||||
\(268\) | 1992.32 | 0.454106 | ||||||||
\(269\) | −920.445 | −0.208626 | −0.104313 | − | 0.994544i | \(-0.533264\pi\) | ||||
−0.104313 | + | 0.994544i | \(0.533264\pi\) | |||||||
\(270\) | −1223.37 | −0.275747 | ||||||||
\(271\) | −4574.65 | −1.02542 | −0.512712 | − | 0.858560i | \(-0.671359\pi\) | ||||
−0.512712 | + | 0.858560i | \(0.671359\pi\) | |||||||
\(272\) | 2989.06 | 0.666317 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6838.56 | −1.50778 | ||||||||
\(275\) | −53.8969 | −0.0118186 | ||||||||
\(276\) | −2019.78 | −0.440494 | ||||||||
\(277\) | 1236.78 | 0.268271 | 0.134136 | − | 0.990963i | \(-0.457174\pi\) | ||||
0.134136 | + | 0.990963i | \(0.457174\pi\) | |||||||
\(278\) | 9557.41 | 2.06193 | ||||||||
\(279\) | 1281.35 | 0.274954 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4590.07 | −0.974450 | −0.487225 | − | 0.873277i | \(-0.661991\pi\) | ||||
−0.487225 | + | 0.873277i | \(0.661991\pi\) | |||||||
\(282\) | 6916.57 | 1.46055 | ||||||||
\(283\) | 4826.37 | 1.01377 | 0.506887 | − | 0.862012i | \(-0.330796\pi\) | ||||
0.506887 | + | 0.862012i | \(0.330796\pi\) | |||||||
\(284\) | −113.420 | −0.0236981 | ||||||||
\(285\) | −3834.41 | −0.796951 | ||||||||
\(286\) | 2535.40 | 0.524201 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2336.93 | −0.478143 | ||||||||
\(289\) | −1854.95 | −0.377559 | ||||||||
\(290\) | −8603.96 | −1.74221 | ||||||||
\(291\) | −1217.44 | −0.245250 | ||||||||
\(292\) | −976.238 | −0.195651 | ||||||||
\(293\) | −1517.59 | −0.302590 | −0.151295 | − | 0.988489i | \(-0.548344\pi\) | ||||
−0.151295 | + | 0.988489i | \(0.548344\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8670.68 | −1.71128 | ||||||||
\(296\) | 1090.99 | 0.214232 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −6185.16 | −1.20234 | ||||||||
\(299\) | −4127.30 | −0.798287 | ||||||||
\(300\) | −133.673 | −0.0257254 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 154.022 | 0.0293475 | ||||||||
\(303\) | −1855.10 | −0.351725 | ||||||||
\(304\) | −6304.02 | −1.18934 | ||||||||
\(305\) | 2823.44 | 0.530064 | ||||||||
\(306\) | −2057.72 | −0.384418 | ||||||||
\(307\) | 2860.08 | 0.531704 | 0.265852 | − | 0.964014i | \(-0.414347\pi\) | ||||
0.265852 | + | 0.964014i | \(0.414347\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3662.32 | −0.674246 | ||||||||
\(310\) | −6450.85 | −1.18188 | ||||||||
\(311\) | −10151.0 | −1.85084 | −0.925420 | − | 0.378942i | \(-0.876288\pi\) | ||||
−0.925420 | + | 0.378942i | \(0.876288\pi\) | |||||||
\(312\) | 756.413 | 0.137255 | ||||||||
\(313\) | −2693.16 | −0.486347 | −0.243174 | − | 0.969983i | \(-0.578188\pi\) | ||||
−0.243174 | + | 0.969983i | \(0.578188\pi\) | |||||||
\(314\) | 2232.50 | 0.401233 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 108.243 | 0.0192694 | ||||||||
\(317\) | 805.888 | 0.142786 | 0.0713930 | − | 0.997448i | \(-0.477256\pi\) | ||||
0.0713930 | + | 0.997448i | \(0.477256\pi\) | |||||||
\(318\) | 2116.95 | 0.373311 | ||||||||
\(319\) | 2088.81 | 0.366617 | ||||||||
\(320\) | 7026.26 | 1.22744 | ||||||||
\(321\) | 3143.36 | 0.546558 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6449.53 | −1.11103 | ||||||||
\(324\) | 736.607 | 0.126304 | ||||||||
\(325\) | −273.152 | −0.0466208 | ||||||||
\(326\) | −8281.28 | −1.40692 | ||||||||
\(327\) | −1557.44 | −0.263384 | ||||||||
\(328\) | 974.418 | 0.164034 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1495.23 | −0.249423 | ||||||||
\(331\) | 634.320 | 0.105333 | 0.0526667 | − | 0.998612i | \(-0.483228\pi\) | ||||
0.0526667 | + | 0.998612i | \(0.483228\pi\) | |||||||
\(332\) | −4630.74 | −0.765497 | ||||||||
\(333\) | 2171.00 | 0.357268 | ||||||||
\(334\) | 13834.5 | 2.26643 | ||||||||
\(335\) | −2400.94 | −0.391574 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1070.63 | −0.173060 | −0.0865299 | − | 0.996249i | \(-0.527578\pi\) | ||||
−0.0865299 | + | 0.996249i | \(0.527578\pi\) | |||||||
\(338\) | 3766.10 | 0.606062 | ||||||||
\(339\) | 7024.85 | 1.12548 | ||||||||
\(340\) | 5511.19 | 0.879077 | ||||||||
\(341\) | 1566.09 | 0.248705 | ||||||||
\(342\) | 4339.79 | 0.686167 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1140.59 | −0.178769 | ||||||||
\(345\) | 2434.03 | 0.379836 | ||||||||
\(346\) | 10495.4 | 1.63073 | ||||||||
\(347\) | −4767.97 | −0.737631 | −0.368816 | − | 0.929503i | \(-0.620237\pi\) | ||||
−0.368816 | + | 0.929503i | \(0.620237\pi\) | |||||||
\(348\) | 5180.57 | 0.798011 | ||||||||
\(349\) | −5046.40 | −0.774005 | −0.387002 | − | 0.922079i | \(-0.626490\pi\) | ||||
−0.387002 | + | 0.922079i | \(0.626490\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1505.21 | 0.228895 | ||||||||
\(352\) | −2856.25 | −0.432496 | ||||||||
\(353\) | −3080.35 | −0.464449 | −0.232224 | − | 0.972662i | \(-0.574600\pi\) | ||||
−0.232224 | + | 0.972662i | \(0.574600\pi\) | |||||||
\(354\) | 9813.48 | 1.47339 | ||||||||
\(355\) | 136.682 | 0.0204348 | ||||||||
\(356\) | 12348.0 | 1.83833 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18915.9 | −2.79255 | ||||||||
\(359\) | −6997.76 | −1.02877 | −0.514384 | − | 0.857560i | \(-0.671979\pi\) | ||||
−0.514384 | + | 0.857560i | \(0.671979\pi\) | |||||||
\(360\) | −446.086 | −0.0653078 | ||||||||
\(361\) | 6743.27 | 0.983128 | ||||||||
\(362\) | −2048.54 | −0.297428 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1176.46 | 0.168709 | ||||||||
\(366\) | −3195.57 | −0.456380 | ||||||||
\(367\) | −2459.20 | −0.349780 | −0.174890 | − | 0.984588i | \(-0.555957\pi\) | ||||
−0.174890 | + | 0.984588i | \(0.555957\pi\) | |||||||
\(368\) | 4001.70 | 0.566855 | ||||||||
\(369\) | 1939.03 | 0.273555 | ||||||||
\(370\) | −10929.8 | −1.53571 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3884.15 | 0.541354 | ||||||||
\(373\) | 9454.51 | 1.31243 | 0.656214 | − | 0.754575i | \(-0.272157\pi\) | ||||
0.656214 | + | 0.754575i | \(0.272157\pi\) | |||||||
\(374\) | −2514.99 | −0.347719 | ||||||||
\(375\) | 4270.72 | 0.588105 | ||||||||
\(376\) | 2522.05 | 0.345916 | ||||||||
\(377\) | 10586.2 | 1.44620 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11712.9 | −1.58747 | −0.793736 | − | 0.608262i | \(-0.791867\pi\) | ||||
−0.793736 | + | 0.608262i | \(0.791867\pi\) | |||||||
\(380\) | −11623.3 | −1.56911 | ||||||||
\(381\) | −4405.50 | −0.592390 | ||||||||
\(382\) | 7391.98 | 0.990069 | ||||||||
\(383\) | −11835.3 | −1.57900 | −0.789498 | − | 0.613753i | \(-0.789659\pi\) | ||||
−0.789498 | + | 0.613753i | \(0.789659\pi\) | |||||||
\(384\) | −1720.51 | −0.228644 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20454.5 | −2.69716 | ||||||||
\(387\) | −2269.70 | −0.298128 | ||||||||
\(388\) | −3690.43 | −0.482869 | ||||||||
\(389\) | −6793.97 | −0.885522 | −0.442761 | − | 0.896640i | \(-0.646001\pi\) | ||||
−0.442761 | + | 0.896640i | \(0.646001\pi\) | |||||||
\(390\) | −7577.88 | −0.983899 | ||||||||
\(391\) | 4094.06 | 0.529528 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6384.52 | 0.819482 | ||||||||
\(394\) | 11546.7 | 1.47644 | ||||||||
\(395\) | −130.443 | −0.0166160 | ||||||||
\(396\) | 900.298 | 0.114247 | ||||||||
\(397\) | 9567.26 | 1.20949 | 0.604745 | − | 0.796420i | \(-0.293275\pi\) | ||||
0.604745 | + | 0.796420i | \(0.293275\pi\) | |||||||
\(398\) | −10386.7 | −1.30814 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 264.840 | 0.0331050 | ||||||||
\(401\) | −5521.26 | −0.687577 | −0.343789 | − | 0.939047i | \(-0.611710\pi\) | ||||
−0.343789 | + | 0.939047i | \(0.611710\pi\) | |||||||
\(402\) | 2717.38 | 0.337141 | ||||||||
\(403\) | 7937.02 | 0.981070 | ||||||||
\(404\) | −5623.38 | −0.692508 | ||||||||
\(405\) | −887.681 | −0.108912 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2653.45 | 0.323161 | ||||||||
\(408\) | −750.322 | −0.0910453 | ||||||||
\(409\) | 2847.96 | 0.344310 | 0.172155 | − | 0.985070i | \(-0.444927\pi\) | ||||
0.172155 | + | 0.985070i | \(0.444927\pi\) | |||||||
\(410\) | −9761.90 | −1.17587 | ||||||||
\(411\) | −4962.10 | −0.595529 | ||||||||
\(412\) | −11101.6 | −1.32752 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2754.83 | −0.327035 | ||||||||
\(415\) | 5580.49 | 0.660085 | ||||||||
\(416\) | −14475.6 | −1.70607 | ||||||||
\(417\) | 6934.91 | 0.814398 | ||||||||
\(418\) | 5304.19 | 0.620661 | ||||||||
\(419\) | 886.838 | 0.103401 | 0.0517003 | − | 0.998663i | \(-0.483536\pi\) | ||||
0.0517003 | + | 0.998663i | \(0.483536\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10167.4 | 1.17702 | 0.588511 | − | 0.808489i | \(-0.299714\pi\) | ||||
0.588511 | + | 0.808489i | \(0.299714\pi\) | |||||||
\(422\) | 12690.6 | 1.46391 | ||||||||
\(423\) | 5018.70 | 0.576874 | ||||||||
\(424\) | 771.921 | 0.0884146 | ||||||||
\(425\) | 270.953 | 0.0309250 | ||||||||
\(426\) | −154.697 | −0.0175941 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 9528.48 | 1.07611 | ||||||||
\(429\) | 1839.70 | 0.207044 | ||||||||
\(430\) | 11426.7 | 1.28150 | ||||||||
\(431\) | −5702.23 | −0.637278 | −0.318639 | − | 0.947876i | \(-0.603226\pi\) | ||||
−0.318639 | + | 0.947876i | \(0.603226\pi\) | |||||||
\(432\) | −1459.40 | −0.162536 | ||||||||
\(433\) | 3981.78 | 0.441922 | 0.220961 | − | 0.975283i | \(-0.429081\pi\) | ||||
0.220961 | + | 0.975283i | \(0.429081\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6243.08 | −0.688121 | ||||||||
\(436\) | −4721.08 | −0.518575 | ||||||||
\(437\) | −8634.51 | −0.945182 | ||||||||
\(438\) | −1331.52 | −0.145256 | ||||||||
\(439\) | −6369.61 | −0.692495 | −0.346247 | − | 0.938143i | \(-0.612544\pi\) | ||||
−0.346247 | + | 0.938143i | \(0.612544\pi\) | |||||||
\(440\) | −545.216 | −0.0590731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12746.1 | −1.37165 | ||||||||
\(443\) | 9283.06 | 0.995602 | 0.497801 | − | 0.867291i | \(-0.334141\pi\) | ||||
0.497801 | + | 0.867291i | \(0.334141\pi\) | |||||||
\(444\) | 6580.97 | 0.703422 | ||||||||
\(445\) | −14880.6 | −1.58518 | ||||||||
\(446\) | −27064.2 | −2.87338 | ||||||||
\(447\) | −4487.99 | −0.474887 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12119.9 | 1.27389 | 0.636943 | − | 0.770911i | \(-0.280199\pi\) | ||||
0.636943 | + | 0.770911i | \(0.280199\pi\) | |||||||
\(450\) | −182.320 | −0.0190992 | ||||||||
\(451\) | 2369.92 | 0.247440 | ||||||||
\(452\) | 21294.5 | 2.21595 | ||||||||
\(453\) | 111.759 | 0.0115914 | ||||||||
\(454\) | −1784.94 | −0.184518 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1582.45 | 0.162511 | ||||||||
\(457\) | 9956.75 | 1.01916 | 0.509581 | − | 0.860423i | \(-0.329800\pi\) | ||||
0.509581 | + | 0.860423i | \(0.329800\pi\) | |||||||
\(458\) | −4512.53 | −0.460386 | ||||||||
\(459\) | −1493.09 | −0.151833 | ||||||||
\(460\) | 7378.28 | 0.747856 | ||||||||
\(461\) | −2985.32 | −0.301606 | −0.150803 | − | 0.988564i | \(-0.548186\pi\) | ||||
−0.150803 | + | 0.988564i | \(0.548186\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4409.74 | 0.442630 | 0.221315 | − | 0.975202i | \(-0.428965\pi\) | ||||
0.221315 | + | 0.975202i | \(0.428965\pi\) | |||||||
\(464\) | −10264.0 | −1.02693 | ||||||||
\(465\) | −4680.77 | −0.466807 | ||||||||
\(466\) | 2988.71 | 0.297101 | ||||||||
\(467\) | 2233.71 | 0.221335 | 0.110668 | − | 0.993857i | \(-0.464701\pi\) | ||||
0.110668 | + | 0.993857i | \(0.464701\pi\) | |||||||
\(468\) | 4562.75 | 0.450670 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −25266.3 | −2.47967 | ||||||||
\(471\) | 1619.91 | 0.158475 | ||||||||
\(472\) | 3578.37 | 0.348957 | ||||||||
\(473\) | −2774.08 | −0.269667 | ||||||||
\(474\) | 147.636 | 0.0143062 | ||||||||
\(475\) | −571.448 | −0.0551997 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1536.07 | 0.147446 | ||||||||
\(478\) | 12526.8 | 1.19866 | ||||||||
\(479\) | 4715.63 | 0.449818 | 0.224909 | − | 0.974380i | \(-0.427792\pi\) | ||||
0.224909 | + | 0.974380i | \(0.427792\pi\) | |||||||
\(480\) | 8536.83 | 0.811774 | ||||||||
\(481\) | 13447.8 | 1.27478 | ||||||||
\(482\) | −14903.6 | −1.40838 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1100.36 | 0.103340 | ||||||||
\(485\) | 4447.32 | 0.416376 | ||||||||
\(486\) | 1004.68 | 0.0937719 | ||||||||
\(487\) | −3311.08 | −0.308089 | −0.154045 | − | 0.988064i | \(-0.549230\pi\) | ||||
−0.154045 | + | 0.988064i | \(0.549230\pi\) | |||||||
\(488\) | −1165.23 | −0.108089 | ||||||||
\(489\) | −6008.94 | −0.555692 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18909.3 | 1.73801 | 0.869007 | − | 0.494800i | \(-0.164759\pi\) | ||||
0.869007 | + | 0.494800i | \(0.164759\pi\) | |||||||
\(492\) | 5877.78 | 0.538599 | ||||||||
\(493\) | −10500.9 | −0.959307 | ||||||||
\(494\) | 26881.9 | 2.44833 | ||||||||
\(495\) | −1084.94 | −0.0985143 | ||||||||
\(496\) | −7695.49 | −0.696648 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −6316.00 | −0.568327 | ||||||||
\(499\) | 19151.7 | 1.71813 | 0.859067 | − | 0.511863i | \(-0.171044\pi\) | ||||
0.859067 | + | 0.511863i | \(0.171044\pi\) | |||||||
\(500\) | 12945.9 | 1.15791 | ||||||||
\(501\) | 10038.4 | 0.895171 | ||||||||
\(502\) | −6712.60 | −0.596809 | ||||||||
\(503\) | 5085.07 | 0.450759 | 0.225380 | − | 0.974271i | \(-0.427638\pi\) | ||||
0.225380 | + | 0.974271i | \(0.427638\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6776.70 | 0.597147 | ||||||||
\(506\) | −3367.02 | −0.295815 | ||||||||
\(507\) | 2732.70 | 0.239376 | ||||||||
\(508\) | −13354.4 | −1.16635 | ||||||||
\(509\) | −5714.36 | −0.497612 | −0.248806 | − | 0.968553i | \(-0.580038\pi\) | ||||
−0.248806 | + | 0.968553i | \(0.580038\pi\) | |||||||
\(510\) | 7516.86 | 0.652651 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 15990.8 | 1.38028 | ||||||||
\(513\) | 3148.98 | 0.271015 | ||||||||
\(514\) | 9863.51 | 0.846422 | ||||||||
\(515\) | 13378.5 | 1.14471 | ||||||||
\(516\) | −6880.17 | −0.586982 | ||||||||
\(517\) | 6133.97 | 0.521802 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7615.49 | 0.644091 | ||||||||
\(520\) | −2763.18 | −0.233026 | ||||||||
\(521\) | 4605.81 | 0.387301 | 0.193651 | − | 0.981071i | \(-0.437967\pi\) | ||||
0.193651 | + | 0.981071i | \(0.437967\pi\) | |||||||
\(522\) | 7065.92 | 0.592465 | ||||||||
\(523\) | −1660.38 | −0.138821 | −0.0694103 | − | 0.997588i | \(-0.522112\pi\) | ||||
−0.0694103 | + | 0.997588i | \(0.522112\pi\) | |||||||
\(524\) | 19353.4 | 1.61347 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15736.6 | 1.30446 | ||||||||
\(527\) | −7873.11 | −0.650774 | ||||||||
\(528\) | −1783.72 | −0.147020 | ||||||||
\(529\) | −6685.95 | −0.549515 | ||||||||
\(530\) | −7733.24 | −0.633794 | ||||||||
\(531\) | 7120.71 | 0.581945 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12010.9 | 0.976077 | ||||||||
\(534\) | 16841.8 | 1.36483 | ||||||||
\(535\) | −11482.7 | −0.927928 | ||||||||
\(536\) | 990.862 | 0.0798483 | ||||||||
\(537\) | −13725.4 | −1.10297 | ||||||||
\(538\) | −3805.56 | −0.304962 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2690.83 | −0.214435 | ||||||||
\(541\) | −13229.9 | −1.05138 | −0.525690 | − | 0.850676i | \(-0.676193\pi\) | ||||
−0.525690 | + | 0.850676i | \(0.676193\pi\) | |||||||
\(542\) | −18913.8 | −1.49892 | ||||||||
\(543\) | −1486.43 | −0.117475 | ||||||||
\(544\) | 14359.1 | 1.13169 | ||||||||
\(545\) | 5689.35 | 0.447165 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13908.5 | 1.08718 | 0.543588 | − | 0.839352i | \(-0.317065\pi\) | ||||
0.543588 | + | 0.839352i | \(0.317065\pi\) | |||||||
\(548\) | −15041.6 | −1.17253 | ||||||||
\(549\) | −2318.72 | −0.180256 | ||||||||
\(550\) | −222.836 | −0.0172759 | ||||||||
\(551\) | 22146.8 | 1.71232 | ||||||||
\(552\) | −1004.52 | −0.0774549 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5113.45 | 0.392148 | ||||||||
\(555\) | −7930.70 | −0.606557 | ||||||||
\(556\) | 21021.8 | 1.60346 | ||||||||
\(557\) | −15886.9 | −1.20853 | −0.604264 | − | 0.796784i | \(-0.706533\pi\) | ||||
−0.604264 | + | 0.796784i | \(0.706533\pi\) | |||||||
\(558\) | 5297.70 | 0.401917 | ||||||||
\(559\) | −14059.2 | −1.06376 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1824.89 | −0.137338 | ||||||||
\(562\) | −18977.5 | −1.42441 | ||||||||
\(563\) | −18993.4 | −1.42180 | −0.710901 | − | 0.703292i | \(-0.751713\pi\) | ||||
−0.710901 | + | 0.703292i | \(0.751713\pi\) | |||||||
\(564\) | 15213.2 | 1.13580 | ||||||||
\(565\) | −25661.9 | −1.91080 | ||||||||
\(566\) | 19954.5 | 1.48189 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −56.4085 | −0.00416699 | ||||||||
\(569\) | 5613.98 | 0.413621 | 0.206810 | − | 0.978381i | \(-0.433692\pi\) | ||||
0.206810 | + | 0.978381i | \(0.433692\pi\) | |||||||
\(570\) | −15853.3 | −1.16495 | ||||||||
\(571\) | −14949.8 | −1.09567 | −0.547835 | − | 0.836586i | \(-0.684548\pi\) | ||||
−0.547835 | + | 0.836586i | \(0.684548\pi\) | |||||||
\(572\) | 5576.70 | 0.407646 | ||||||||
\(573\) | 5363.66 | 0.391047 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 362.747 | 0.0263088 | ||||||||
\(576\) | −5770.25 | −0.417408 | ||||||||
\(577\) | 892.541 | 0.0643969 | 0.0321984 | − | 0.999481i | \(-0.489749\pi\) | ||||
0.0321984 | + | 0.999481i | \(0.489749\pi\) | |||||||
\(578\) | −7669.24 | −0.551901 | ||||||||
\(579\) | −14841.9 | −1.06530 | ||||||||
\(580\) | −18924.7 | −1.35483 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5033.48 | −0.358496 | ||||||||
\(583\) | 1877.42 | 0.133370 | ||||||||
\(584\) | −485.522 | −0.0344025 | ||||||||
\(585\) | −5498.55 | −0.388610 | ||||||||
\(586\) | −6274.46 | −0.442313 | ||||||||
\(587\) | 19851.1 | 1.39582 | 0.697908 | − | 0.716187i | \(-0.254114\pi\) | ||||
0.697908 | + | 0.716187i | \(0.254114\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16604.6 | 1.16160 | ||||||||
\(590\) | −35848.7 | −2.50147 | ||||||||
\(591\) | 8378.36 | 0.583147 | ||||||||
\(592\) | −13038.6 | −0.905206 | ||||||||
\(593\) | −6639.01 | −0.459749 | −0.229875 | − | 0.973220i | \(-0.573832\pi\) | ||||
−0.229875 | + | 0.973220i | \(0.573832\pi\) | |||||||
\(594\) | 1227.94 | 0.0848199 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13604.5 | −0.935000 | ||||||||
\(597\) | −7536.66 | −0.516675 | ||||||||
\(598\) | −17064.2 | −1.16690 | ||||||||
\(599\) | −25797.7 | −1.75971 | −0.879856 | − | 0.475241i | \(-0.842361\pi\) | ||||
−0.879856 | + | 0.475241i | \(0.842361\pi\) | |||||||
\(600\) | −66.4809 | −0.00452345 | ||||||||
\(601\) | −26416.1 | −1.79291 | −0.896453 | − | 0.443138i | \(-0.853865\pi\) | ||||
−0.896453 | + | 0.443138i | \(0.853865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1971.75 | 0.133161 | ||||||||
\(604\) | 338.776 | 0.0228222 | ||||||||
\(605\) | −1326.04 | −0.0891096 | ||||||||
\(606\) | −7669.87 | −0.514138 | ||||||||
\(607\) | −4301.46 | −0.287629 | −0.143815 | − | 0.989605i | \(-0.545937\pi\) | ||||
−0.143815 | + | 0.989605i | \(0.545937\pi\) | |||||||
\(608\) | −30283.7 | −2.02001 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 11673.4 | 0.774826 | ||||||||
\(611\) | 31087.3 | 2.05836 | ||||||||
\(612\) | −4526.01 | −0.298943 | ||||||||
\(613\) | 19926.9 | 1.31295 | 0.656477 | − | 0.754346i | \(-0.272046\pi\) | ||||
0.656477 | + | 0.754346i | \(0.272046\pi\) | |||||||
\(614\) | 11824.9 | 0.777224 | ||||||||
\(615\) | −7083.28 | −0.464432 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20225.1 | −1.31967 | −0.659833 | − | 0.751412i | \(-0.729373\pi\) | ||||
−0.659833 | + | 0.751412i | \(0.729373\pi\) | |||||||
\(618\) | −15141.8 | −0.985585 | ||||||||
\(619\) | 12966.4 | 0.841947 | 0.420974 | − | 0.907073i | \(-0.361689\pi\) | ||||
0.420974 | + | 0.907073i | \(0.361689\pi\) | |||||||
\(620\) | −14188.8 | −0.919093 | ||||||||
\(621\) | −1998.92 | −0.129169 | ||||||||
\(622\) | −41969.2 | −2.70548 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9039.97 | −0.579949 | ||||||||
\(625\) | −14988.5 | −0.959266 | ||||||||
\(626\) | −11134.8 | −0.710922 | ||||||||
\(627\) | 3848.75 | 0.245142 | ||||||||
\(628\) | 4910.45 | 0.312019 | ||||||||
\(629\) | −13339.5 | −0.845599 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18440.1 | 1.16337 | 0.581687 | − | 0.813413i | \(-0.302393\pi\) | ||||
0.581687 | + | 0.813413i | \(0.302393\pi\) | |||||||
\(632\) | 53.8335 | 0.00338826 | ||||||||
\(633\) | 9208.40 | 0.578201 | ||||||||
\(634\) | 3331.92 | 0.208719 | ||||||||
\(635\) | 16093.3 | 1.00574 | ||||||||
\(636\) | 4656.30 | 0.290306 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 8636.12 | 0.535905 | ||||||||
\(639\) | −112.249 | −0.00694915 | ||||||||
\(640\) | 6285.02 | 0.388183 | ||||||||
\(641\) | −11567.3 | −0.712764 | −0.356382 | − | 0.934340i | \(-0.615990\pi\) | ||||
−0.356382 | + | 0.934340i | \(0.615990\pi\) | |||||||
\(642\) | 12996.2 | 0.798937 | ||||||||
\(643\) | −16921.6 | −1.03782 | −0.518912 | − | 0.854827i | \(-0.673663\pi\) | ||||
−0.518912 | + | 0.854827i | \(0.673663\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8291.25 | 0.506152 | ||||||||
\(646\) | −26665.4 | −1.62405 | ||||||||
\(647\) | −1962.25 | −0.119234 | −0.0596168 | − | 0.998221i | \(-0.518988\pi\) | ||||
−0.0596168 | + | 0.998221i | \(0.518988\pi\) | |||||||
\(648\) | 366.344 | 0.0222089 | ||||||||
\(649\) | 8703.09 | 0.526389 | ||||||||
\(650\) | −1129.34 | −0.0681484 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18214.9 | −1.09410 | ||||||||
\(653\) | 19466.5 | 1.16659 | 0.583293 | − | 0.812261i | \(-0.301764\pi\) | ||||
0.583293 | + | 0.812261i | \(0.301764\pi\) | |||||||
\(654\) | −6439.21 | −0.385005 | ||||||||
\(655\) | −23322.7 | −1.39129 | ||||||||
\(656\) | −11645.4 | −0.693103 | ||||||||
\(657\) | −966.156 | −0.0573719 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9995.31 | 0.590838 | 0.295419 | − | 0.955368i | \(-0.404541\pi\) | ||||
0.295419 | + | 0.955368i | \(0.404541\pi\) | |||||||
\(660\) | −3288.80 | −0.193964 | ||||||||
\(661\) | 15473.1 | 0.910492 | 0.455246 | − | 0.890366i | \(-0.349551\pi\) | ||||
0.455246 | + | 0.890366i | \(0.349551\pi\) | |||||||
\(662\) | 2622.58 | 0.153972 | ||||||||
\(663\) | −9248.63 | −0.541760 | ||||||||
\(664\) | −2303.05 | −0.134602 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8975.97 | 0.522240 | ||||||||
\(667\) | −14058.4 | −0.816110 | ||||||||
\(668\) | 30429.3 | 1.76249 | ||||||||
\(669\) | −19637.9 | −1.13490 | ||||||||
\(670\) | −9926.63 | −0.572387 | ||||||||
\(671\) | −2833.99 | −0.163048 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22075.3 | 1.26440 | 0.632200 | − | 0.774805i | \(-0.282152\pi\) | ||||
0.632200 | + | 0.774805i | \(0.282152\pi\) | |||||||
\(674\) | −4426.51 | −0.252972 | ||||||||
\(675\) | −132.292 | −0.00754361 | ||||||||
\(676\) | 8283.66 | 0.471305 | ||||||||
\(677\) | 10736.1 | 0.609489 | 0.304744 | − | 0.952434i | \(-0.401429\pi\) | ||||
0.304744 | + | 0.952434i | \(0.401429\pi\) | |||||||
\(678\) | 29044.1 | 1.64518 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2740.93 | 0.154574 | ||||||||
\(681\) | −1295.16 | −0.0728791 | ||||||||
\(682\) | 6474.96 | 0.363547 | ||||||||
\(683\) | −18453.5 | −1.03383 | −0.516913 | − | 0.856038i | \(-0.672919\pi\) | ||||
−0.516913 | + | 0.856038i | \(0.672919\pi\) | |||||||
\(684\) | 9545.51 | 0.533599 | ||||||||
\(685\) | 18126.6 | 1.01107 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3274.32 | −0.181838 | ||||||||
\(688\) | 13631.4 | 0.755364 | ||||||||
\(689\) | 9514.86 | 0.526107 | ||||||||
\(690\) | 10063.4 | 0.555229 | ||||||||
\(691\) | 9601.59 | 0.528599 | 0.264299 | − | 0.964441i | \(-0.414859\pi\) | ||||
0.264299 | + | 0.964441i | \(0.414859\pi\) | |||||||
\(692\) | 23084.9 | 1.26814 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19713.1 | −1.07824 | ||||||||
\(695\) | −25333.3 | −1.38266 | ||||||||
\(696\) | 2576.50 | 0.140319 | ||||||||
\(697\) | −11914.2 | −0.647462 | ||||||||
\(698\) | −20864.2 | −1.13141 | ||||||||
\(699\) | 2168.62 | 0.117346 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14973.3 | 0.806753 | 0.403377 | − | 0.915034i | \(-0.367836\pi\) | ||||
0.403377 | + | 0.915034i | \(0.367836\pi\) | |||||||
\(702\) | 6223.26 | 0.334590 | ||||||||
\(703\) | 28133.5 | 1.50935 | ||||||||
\(704\) | −7052.53 | −0.377560 | ||||||||
\(705\) | −18333.4 | −0.979396 | ||||||||
\(706\) | −12735.6 | −0.678912 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 21585.1 | 1.14579 | ||||||||
\(709\) | −17611.7 | −0.932895 | −0.466447 | − | 0.884549i | \(-0.654466\pi\) | ||||
−0.466447 | + | 0.884549i | \(0.654466\pi\) | |||||||
\(710\) | 565.110 | 0.0298707 | ||||||||
\(711\) | 107.125 | 0.00565050 | ||||||||
\(712\) | 6141.17 | 0.323244 | ||||||||
\(713\) | −10540.4 | −0.553633 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6720.45 | −0.351511 | ||||||||
\(716\) | −41606.0 | −2.17163 | ||||||||
\(717\) | 9089.50 | 0.473436 | ||||||||
\(718\) | −28932.1 | −1.50381 | ||||||||
\(719\) | −36062.1 | −1.87050 | −0.935249 | − | 0.353990i | \(-0.884825\pi\) | ||||
−0.935249 | + | 0.353990i | \(0.884825\pi\) | |||||||
\(720\) | 5331.22 | 0.275948 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 27879.9 | 1.43710 | ||||||||
\(723\) | −10814.1 | −0.556268 | ||||||||
\(724\) | −4505.83 | −0.231296 | ||||||||
\(725\) | −930.415 | −0.0476617 | ||||||||
\(726\) | 1500.82 | 0.0767224 | ||||||||
\(727\) | 38125.3 | 1.94496 | 0.972482 | − | 0.232978i | \(-0.0748471\pi\) | ||||
0.972482 | + | 0.232978i | \(0.0748471\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 4864.04 | 0.246611 | ||||||||
\(731\) | 13946.0 | 0.705624 | ||||||||
\(732\) | −7028.75 | −0.354905 | ||||||||
\(733\) | 10828.6 | 0.545654 | 0.272827 | − | 0.962063i | \(-0.412041\pi\) | ||||
0.272827 | + | 0.962063i | \(0.412041\pi\) | |||||||
\(734\) | −10167.5 | −0.511293 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19223.6 | 0.962762 | ||||||||
\(737\) | 2409.91 | 0.120448 | ||||||||
\(738\) | 8016.87 | 0.399871 | ||||||||
\(739\) | 31316.5 | 1.55886 | 0.779429 | − | 0.626491i | \(-0.215509\pi\) | ||||
0.779429 | + | 0.626491i | \(0.215509\pi\) | |||||||
\(740\) | −24040.4 | −1.19424 | ||||||||
\(741\) | 19505.7 | 0.967015 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3528.10 | −0.174204 | −0.0871019 | − | 0.996199i | \(-0.527761\pi\) | ||||
−0.0871019 | + | 0.996199i | \(0.527761\pi\) | |||||||
\(744\) | 1931.74 | 0.0951897 | ||||||||
\(745\) | 16394.7 | 0.806246 | ||||||||
\(746\) | 39089.5 | 1.91845 | ||||||||
\(747\) | −4582.92 | −0.224472 | ||||||||
\(748\) | −5531.79 | −0.270404 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 17657.2 | 0.859667 | ||||||||
\(751\) | −16211.7 | −0.787715 | −0.393858 | − | 0.919171i | \(-0.628860\pi\) | ||||
−0.393858 | + | 0.919171i | \(0.628860\pi\) | |||||||
\(752\) | −30141.2 | −1.46162 | ||||||||
\(753\) | −4870.70 | −0.235721 | ||||||||
\(754\) | 43768.3 | 2.11399 | ||||||||
\(755\) | −408.257 | −0.0196795 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37954.3 | 1.82229 | 0.911144 | − | 0.412088i | \(-0.135200\pi\) | ||||
0.911144 | + | 0.412088i | \(0.135200\pi\) | |||||||
\(758\) | −48426.8 | −2.32050 | ||||||||
\(759\) | −2443.13 | −0.116838 | ||||||||
\(760\) | −5780.72 | −0.275906 | ||||||||
\(761\) | 109.775 | 0.00522907 | 0.00261454 | − | 0.999997i | \(-0.499168\pi\) | ||||
0.00261454 | + | 0.999997i | \(0.499168\pi\) | |||||||
\(762\) | −18214.4 | −0.865931 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 16258.9 | 0.769929 | ||||||||
\(765\) | 5454.27 | 0.257777 | ||||||||
\(766\) | −48932.8 | −2.30811 | ||||||||
\(767\) | 44107.7 | 2.07645 | ||||||||
\(768\) | 8273.94 | 0.388750 | ||||||||
\(769\) | −36591.1 | −1.71587 | −0.857937 | − | 0.513755i | \(-0.828254\pi\) | ||||
−0.857937 | + | 0.513755i | \(0.828254\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7157.02 | 0.334311 | ||||||||
\(772\) | −44990.3 | −2.09745 | ||||||||
\(773\) | 13202.5 | 0.614310 | 0.307155 | − | 0.951659i | \(-0.400623\pi\) | ||||
0.307155 | + | 0.951659i | \(0.400623\pi\) | |||||||
\(774\) | −9384.05 | −0.435791 | ||||||||
\(775\) | −697.582 | −0.0323328 | ||||||||
\(776\) | −1835.40 | −0.0849059 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −28089.5 | −1.29442 | ||||||||
\(779\) | 25127.4 | 1.15569 | ||||||||
\(780\) | −16667.8 | −0.765131 | ||||||||
\(781\) | −137.193 | −0.00628574 | ||||||||
\(782\) | 16926.8 | 0.774043 | ||||||||
\(783\) | 5127.07 | 0.234006 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5917.55 | −0.269053 | ||||||||
\(786\) | 26396.6 | 1.19788 | ||||||||
\(787\) | 8288.79 | 0.375430 | 0.187715 | − | 0.982224i | \(-0.439892\pi\) | ||||
0.187715 | + | 0.982224i | \(0.439892\pi\) | |||||||
\(788\) | 25397.4 | 1.14815 | ||||||||
\(789\) | 11418.6 | 0.515224 | ||||||||
\(790\) | −539.314 | −0.0242885 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 447.754 | 0.0200887 | ||||||||
\(793\) | −14362.8 | −0.643176 | ||||||||
\(794\) | 39555.6 | 1.76798 | ||||||||
\(795\) | −5611.28 | −0.250329 | ||||||||
\(796\) | −22845.9 | −1.01728 | ||||||||
\(797\) | 42473.0 | 1.88767 | 0.943834 | − | 0.330419i | \(-0.107190\pi\) | ||||
0.943834 | + | 0.330419i | \(0.107190\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30836.9 | −1.36537 | ||||||||
\(800\) | 1272.26 | 0.0562263 | ||||||||
\(801\) | 12220.5 | 0.539064 | ||||||||
\(802\) | −22827.5 | −1.00507 | ||||||||
\(803\) | −1180.86 | −0.0518948 | ||||||||
\(804\) | 5976.97 | 0.262178 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32815.4 | 1.43409 | ||||||||
\(807\) | −2761.33 | −0.120451 | ||||||||
\(808\) | −2796.73 | −0.121768 | ||||||||
\(809\) | 23398.9 | 1.01689 | 0.508444 | − | 0.861095i | \(-0.330221\pi\) | ||||
0.508444 | + | 0.861095i | \(0.330221\pi\) | |||||||
\(810\) | −3670.10 | −0.159203 | ||||||||
\(811\) | −40985.0 | −1.77457 | −0.887286 | − | 0.461220i | \(-0.847412\pi\) | ||||
−0.887286 | + | 0.461220i | \(0.847412\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13723.9 | −0.592029 | ||||||||
\(814\) | 10970.6 | 0.472384 | ||||||||
\(815\) | 21950.7 | 0.943435 | ||||||||
\(816\) | 8967.18 | 0.384699 | ||||||||
\(817\) | −29412.5 | −1.25950 | ||||||||
\(818\) | 11774.8 | 0.503298 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21471.6 | −0.914415 | ||||||||
\(821\) | 21819.6 | 0.927538 | 0.463769 | − | 0.885956i | \(-0.346497\pi\) | ||||
0.463769 | + | 0.885956i | \(0.346497\pi\) | |||||||
\(822\) | −20515.7 | −0.870519 | ||||||||
\(823\) | −30412.0 | −1.28809 | −0.644043 | − | 0.764989i | \(-0.722744\pi\) | ||||
−0.644043 | + | 0.764989i | \(0.722744\pi\) | |||||||
\(824\) | −5521.27 | −0.233425 | ||||||||
\(825\) | −161.691 | −0.00682345 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27535.2 | 1.15779 | 0.578896 | − | 0.815401i | \(-0.303484\pi\) | ||||
0.578896 | + | 0.815401i | \(0.303484\pi\) | |||||||
\(828\) | −6059.34 | −0.254320 | ||||||||
\(829\) | 36911.1 | 1.54641 | 0.773206 | − | 0.634155i | \(-0.218652\pi\) | ||||
0.773206 | + | 0.634155i | \(0.218652\pi\) | |||||||
\(830\) | 23072.4 | 0.964885 | ||||||||
\(831\) | 3710.35 | 0.154886 | ||||||||
\(832\) | −35742.6 | −1.48936 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 28672.2 | 1.19045 | ||||||||
\(835\) | −36670.2 | −1.51979 | ||||||||
\(836\) | 11666.7 | 0.482658 | ||||||||
\(837\) | 3844.04 | 0.158745 | ||||||||
\(838\) | 3666.61 | 0.151147 | ||||||||
\(839\) | −9468.89 | −0.389634 | −0.194817 | − | 0.980840i | \(-0.562411\pi\) | ||||
−0.194817 | + | 0.980840i | \(0.562411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11669.8 | 0.478485 | ||||||||
\(842\) | 42036.7 | 1.72052 | ||||||||
\(843\) | −13770.2 | −0.562599 | ||||||||
\(844\) | 27913.5 | 1.13841 | ||||||||
\(845\) | −9982.59 | −0.406404 | ||||||||
\(846\) | 20749.7 | 0.843250 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9225.31 | −0.373583 | ||||||||
\(849\) | 14479.1 | 0.585303 | ||||||||
\(850\) | 1120.25 | 0.0452050 | ||||||||
\(851\) | −17858.7 | −0.719376 | ||||||||
\(852\) | −340.261 | −0.0136821 | ||||||||
\(853\) | 47631.0 | 1.91191 | 0.955953 | − | 0.293520i | \(-0.0948268\pi\) | ||||
0.955953 | + | 0.293520i | \(0.0948268\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −11503.2 | −0.460120 | ||||||||
\(856\) | 4738.89 | 0.189220 | ||||||||
\(857\) | 30786.4 | 1.22712 | 0.613561 | − | 0.789647i | \(-0.289736\pi\) | ||||
0.613561 | + | 0.789647i | \(0.289736\pi\) | |||||||
\(858\) | 7606.21 | 0.302648 | ||||||||
\(859\) | 45755.7 | 1.81742 | 0.908710 | − | 0.417428i | \(-0.137068\pi\) | ||||
0.908710 | + | 0.417428i | \(0.137068\pi\) | |||||||
\(860\) | 25133.3 | 0.996557 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −23575.7 | −0.931546 | ||||||||
\(863\) | −40160.7 | −1.58411 | −0.792054 | − | 0.610451i | \(-0.790988\pi\) | ||||
−0.792054 | + | 0.610451i | \(0.790988\pi\) | |||||||
\(864\) | −7010.80 | −0.276056 | ||||||||
\(865\) | −27819.5 | −1.09351 | ||||||||
\(866\) | 16462.6 | 0.645984 | ||||||||
\(867\) | −5564.84 | −0.217984 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 130.931 | 0.00511107 | ||||||||
\(870\) | −25811.9 | −1.00587 | ||||||||
\(871\) | 12213.6 | 0.475133 | ||||||||
\(872\) | −2347.98 | −0.0911842 | ||||||||
\(873\) | −3652.32 | −0.141595 | ||||||||
\(874\) | −35699.2 | −1.38163 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2928.71 | −0.112959 | ||||||||
\(877\) | −12085.7 | −0.465341 | −0.232671 | − | 0.972556i | \(-0.574746\pi\) | ||||
−0.232671 | + | 0.972556i | \(0.574746\pi\) | |||||||
\(878\) | −26335.0 | −1.01226 | ||||||||
\(879\) | −4552.78 | −0.174700 | ||||||||
\(880\) | 6515.94 | 0.249605 | ||||||||
\(881\) | −43533.0 | −1.66477 | −0.832387 | − | 0.554196i | \(-0.813026\pi\) | ||||
−0.832387 | + | 0.554196i | \(0.813026\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31480.4 | −1.19977 | −0.599887 | − | 0.800084i | \(-0.704788\pi\) | ||||
−0.599887 | + | 0.800084i | \(0.704788\pi\) | |||||||
\(884\) | −28035.4 | −1.06667 | ||||||||
\(885\) | −26012.0 | −0.988005 | ||||||||
\(886\) | 38380.6 | 1.45533 | ||||||||
\(887\) | 22002.2 | 0.832875 | 0.416437 | − | 0.909164i | \(-0.363278\pi\) | ||||
0.416437 | + | 0.909164i | \(0.363278\pi\) | |||||||
\(888\) | 3272.98 | 0.123687 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −61523.3 | −2.31715 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | −59528.6 | −2.23449 | ||||||||
\(893\) | 65036.1 | 2.43712 | ||||||||
\(894\) | −18555.5 | −0.694170 | ||||||||
\(895\) | 50139.2 | 1.87259 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12381.9 | −0.460891 | ||||||||
\(898\) | 50109.6 | 1.86211 | ||||||||
\(899\) | 27035.2 | 1.00297 | ||||||||
\(900\) | −401.019 | −0.0148525 | ||||||||
\(901\) | −9438.25 | −0.348983 | ||||||||
\(902\) | 9798.39 | 0.361697 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10590.6 | 0.389644 | ||||||||
\(905\) | 5429.95 | 0.199445 | ||||||||
\(906\) | 462.065 | 0.0169438 | ||||||||
\(907\) | −48048.1 | −1.75900 | −0.879500 | − | 0.475900i | \(-0.842123\pi\) | ||||
−0.879500 | + | 0.475900i | \(0.842123\pi\) | |||||||
\(908\) | −3926.03 | −0.143491 | ||||||||
\(909\) | −5565.30 | −0.203069 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32477.6 | 1.18115 | 0.590577 | − | 0.806981i | \(-0.298900\pi\) | ||||
0.590577 | + | 0.806981i | \(0.298900\pi\) | |||||||
\(912\) | −18912.1 | −0.686668 | ||||||||
\(913\) | −5601.35 | −0.203042 | ||||||||
\(914\) | 41166.0 | 1.48977 | ||||||||
\(915\) | 8470.31 | 0.306033 | ||||||||
\(916\) | −9925.45 | −0.358020 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6173.15 | −0.221944 | ||||||||
\(919\) | −48705.4 | −1.74825 | −0.874127 | − | 0.485698i | \(-0.838565\pi\) | ||||
−0.874127 | + | 0.485698i | \(0.838565\pi\) | |||||||
\(920\) | 3669.51 | 0.131500 | ||||||||
\(921\) | 8580.23 | 0.306980 | ||||||||
\(922\) | −12342.8 | −0.440876 | ||||||||
\(923\) | −695.303 | −0.0247954 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1181.92 | −0.0420123 | ||||||||
\(926\) | 18232.0 | 0.647019 | ||||||||
\(927\) | −10987.0 | −0.389276 | ||||||||
\(928\) | −49307.0 | −1.74416 | ||||||||
\(929\) | 28313.6 | 0.999933 | 0.499967 | − | 0.866045i | \(-0.333346\pi\) | ||||
0.499967 | + | 0.866045i | \(0.333346\pi\) | |||||||
\(930\) | −19352.5 | −0.682360 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6573.75 | 0.231041 | ||||||||
\(933\) | −30453.1 | −1.06858 | ||||||||
\(934\) | 9235.22 | 0.323539 | ||||||||
\(935\) | 6666.33 | 0.233168 | ||||||||
\(936\) | 2269.24 | 0.0792440 | ||||||||
\(937\) | −3815.98 | −0.133044 | −0.0665222 | − | 0.997785i | \(-0.521190\pi\) | ||||
−0.0665222 | + | 0.997785i | \(0.521190\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8079.49 | −0.280793 | ||||||||
\(940\) | −55574.0 | −1.92832 | ||||||||
\(941\) | −48453.2 | −1.67856 | −0.839282 | − | 0.543696i | \(-0.817024\pi\) | ||||
−0.839282 | + | 0.543696i | \(0.817024\pi\) | |||||||
\(942\) | 6697.49 | 0.231652 | ||||||||
\(943\) | −15950.5 | −0.550815 | ||||||||
\(944\) | −42765.4 | −1.47447 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11469.4 | −0.394188 | ||||||||
\(947\) | −15831.8 | −0.543256 | −0.271628 | − | 0.962402i | \(-0.587562\pi\) | ||||
−0.271628 | + | 0.962402i | \(0.587562\pi\) | |||||||
\(948\) | 324.729 | 0.0111252 | ||||||||
\(949\) | −5984.64 | −0.204710 | ||||||||
\(950\) | −2362.64 | −0.0806886 | ||||||||
\(951\) | 2417.66 | 0.0824375 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26284.5 | 0.893430 | 0.446715 | − | 0.894676i | \(-0.352594\pi\) | ||||
0.446715 | + | 0.894676i | \(0.352594\pi\) | |||||||
\(954\) | 6350.85 | 0.215531 | ||||||||
\(955\) | −19593.5 | −0.663906 | ||||||||
\(956\) | 27553.0 | 0.932143 | ||||||||
\(957\) | 6266.42 | 0.211666 | ||||||||
\(958\) | 19496.7 | 0.657526 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 21078.8 | 0.708661 | ||||||||
\(961\) | −9521.27 | −0.319602 | ||||||||
\(962\) | 55599.7 | 1.86342 | ||||||||
\(963\) | 9430.08 | 0.315556 | ||||||||
\(964\) | −32780.9 | −1.09523 | ||||||||
\(965\) | 54217.5 | 1.80863 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36542.0 | −1.21521 | −0.607607 | − | 0.794238i | \(-0.707870\pi\) | ||||
−0.607607 | + | 0.794238i | \(0.707870\pi\) | |||||||
\(968\) | 547.255 | 0.0181709 | ||||||||
\(969\) | −19348.6 | −0.641451 | ||||||||
\(970\) | 18387.4 | 0.608641 | ||||||||
\(971\) | −24753.7 | −0.818109 | −0.409055 | − | 0.912510i | \(-0.634141\pi\) | ||||
−0.409055 | + | 0.912510i | \(0.634141\pi\) | |||||||
\(972\) | 2209.82 | 0.0729219 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −13689.6 | −0.450352 | ||||||||
\(975\) | −819.457 | −0.0269165 | ||||||||
\(976\) | 13925.7 | 0.456713 | ||||||||
\(977\) | −47421.6 | −1.55287 | −0.776434 | − | 0.630198i | \(-0.782974\pi\) | ||||
−0.776434 | + | 0.630198i | \(0.782974\pi\) | |||||||
\(978\) | −24843.8 | −0.812288 | ||||||||
\(979\) | 14936.2 | 0.487602 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4672.32 | −0.152065 | ||||||||
\(982\) | 78180.1 | 2.54056 | ||||||||
\(983\) | −9479.42 | −0.307575 | −0.153788 | − | 0.988104i | \(-0.549147\pi\) | ||||
−0.153788 | + | 0.988104i | \(0.549147\pi\) | |||||||
\(984\) | 2923.25 | 0.0947052 | ||||||||
\(985\) | −30606.2 | −0.990047 | ||||||||
\(986\) | −43415.9 | −1.40228 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 59127.6 | 1.90395 | ||||||||
\(989\) | 18670.6 | 0.600295 | ||||||||
\(990\) | −4485.68 | −0.144004 | ||||||||
\(991\) | 2290.12 | 0.0734086 | 0.0367043 | − | 0.999326i | \(-0.488314\pi\) | ||||
0.0367043 | + | 0.999326i | \(0.488314\pi\) | |||||||
\(992\) | −36968.1 | −1.18321 | ||||||||
\(993\) | 1902.96 | 0.0608143 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27531.5 | 0.877193 | ||||||||
\(996\) | −13892.2 | −0.441960 | ||||||||
\(997\) | −14477.0 | −0.459871 | −0.229935 | − | 0.973206i | \(-0.573852\pi\) | ||||
−0.229935 | + | 0.973206i | \(0.573852\pi\) | |||||||
\(998\) | 79182.4 | 2.51150 | ||||||||
\(999\) | 6513.01 | 0.206269 |
(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 | 1617.4.a.bf.1.13 | yes | 16 | |
7.6 | odd | 2 | 1617.4.a.be.1.13 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1617.4.a.be.1.13 | ✓ | 16 | 7.6 | odd | 2 | ||
1617.4.a.bf.1.13 | yes | 16 | 1.1 | even | 1 | trivial |