Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, 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("966.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(56.9958450655\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.12197.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 15x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.272991\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 4.81897 | 0.431022 | 0.215511 | − | 0.976501i | \(-0.430858\pi\) | ||||
0.215511 | + | 0.976501i | \(0.430858\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 9.63795 | 0.304779 | ||||||||
\(11\) | 43.0349 | 1.17959 | 0.589796 | − | 0.807553i | \(-0.299208\pi\) | ||||
0.589796 | + | 0.807553i | \(0.299208\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 48.6845 | 1.03866 | 0.519332 | − | 0.854572i | \(-0.326181\pi\) | ||||
0.519332 | + | 0.854572i | \(0.326181\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | −14.4569 | −0.248851 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −24.7735 | −0.353439 | −0.176719 | − | 0.984261i | \(-0.556549\pi\) | ||||
−0.176719 | + | 0.984261i | \(0.556549\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 63.2479 | 0.763687 | 0.381844 | − | 0.924227i | \(-0.375289\pi\) | ||||
0.381844 | + | 0.924227i | \(0.375289\pi\) | |||||||
\(20\) | 19.2759 | 0.215511 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | 86.0698 | 0.834097 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −101.777 | −0.814220 | ||||||||
\(26\) | 97.3689 | 0.734447 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −4.70005 | −0.0300957 | −0.0150479 | − | 0.999887i | \(-0.504790\pi\) | ||||
−0.0150479 | + | 0.999887i | \(0.504790\pi\) | |||||||
\(30\) | −28.9138 | −0.175964 | ||||||||
\(31\) | −88.4310 | −0.512345 | −0.256172 | − | 0.966631i | \(-0.582461\pi\) | ||||
−0.256172 | + | 0.966631i | \(0.582461\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | −129.105 | −0.681037 | ||||||||
\(34\) | −49.5470 | −0.249919 | ||||||||
\(35\) | 33.7328 | 0.162911 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −168.863 | −0.750294 | −0.375147 | − | 0.926965i | \(-0.622408\pi\) | ||||
−0.375147 | + | 0.926965i | \(0.622408\pi\) | |||||||
\(38\) | 126.496 | 0.540009 | ||||||||
\(39\) | −146.053 | −0.599673 | ||||||||
\(40\) | 38.5518 | 0.152389 | ||||||||
\(41\) | 465.750 | 1.77410 | 0.887048 | − | 0.461677i | \(-0.152752\pi\) | ||||
0.887048 | + | 0.461677i | \(0.152752\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | 254.877 | 0.903915 | 0.451958 | − | 0.892039i | \(-0.350726\pi\) | ||||
0.451958 | + | 0.892039i | \(0.350726\pi\) | |||||||
\(44\) | 172.140 | 0.589796 | ||||||||
\(45\) | 43.3708 | 0.143674 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | −513.188 | −1.59268 | −0.796342 | − | 0.604847i | \(-0.793234\pi\) | ||||
−0.796342 | + | 0.604847i | \(0.793234\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −203.555 | −0.575740 | ||||||||
\(51\) | 74.3206 | 0.204058 | ||||||||
\(52\) | 194.738 | 0.519332 | ||||||||
\(53\) | 428.489 | 1.11052 | 0.555259 | − | 0.831677i | \(-0.312619\pi\) | ||||
0.555259 | + | 0.831677i | \(0.312619\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 207.384 | 0.508430 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | −189.744 | −0.440915 | ||||||||
\(58\) | −9.40009 | −0.0212809 | ||||||||
\(59\) | 158.984 | 0.350812 | 0.175406 | − | 0.984496i | \(-0.443876\pi\) | ||||
0.175406 | + | 0.984496i | \(0.443876\pi\) | |||||||
\(60\) | −57.8277 | −0.124425 | ||||||||
\(61\) | −28.2878 | −0.0593752 | −0.0296876 | − | 0.999559i | \(-0.509451\pi\) | ||||
−0.0296876 | + | 0.999559i | \(0.509451\pi\) | |||||||
\(62\) | −176.862 | −0.362282 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 234.609 | 0.447687 | ||||||||
\(66\) | −258.209 | −0.481566 | ||||||||
\(67\) | 797.236 | 1.45370 | 0.726850 | − | 0.686796i | \(-0.240984\pi\) | ||||
0.726850 | + | 0.686796i | \(0.240984\pi\) | |||||||
\(68\) | −99.0941 | −0.176719 | ||||||||
\(69\) | 69.0000 | 0.120386 | ||||||||
\(70\) | 67.4656 | 0.115196 | ||||||||
\(71\) | −778.422 | −1.30115 | −0.650576 | − | 0.759442i | \(-0.725472\pi\) | ||||
−0.650576 | + | 0.759442i | \(0.725472\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | 526.081 | 0.843468 | 0.421734 | − | 0.906720i | \(-0.361422\pi\) | ||||
0.421734 | + | 0.906720i | \(0.361422\pi\) | |||||||
\(74\) | −337.726 | −0.530538 | ||||||||
\(75\) | 305.332 | 0.470090 | ||||||||
\(76\) | 252.992 | 0.381844 | ||||||||
\(77\) | 301.244 | 0.445844 | ||||||||
\(78\) | −292.107 | −0.424033 | ||||||||
\(79\) | −108.025 | −0.153845 | −0.0769223 | − | 0.997037i | \(-0.524509\pi\) | ||||
−0.0769223 | + | 0.997037i | \(0.524509\pi\) | |||||||
\(80\) | 77.1036 | 0.107756 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 931.500 | 1.25448 | ||||||||
\(83\) | 409.259 | 0.541229 | 0.270615 | − | 0.962688i | \(-0.412773\pi\) | ||||
0.270615 | + | 0.962688i | \(0.412773\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | −119.383 | −0.152340 | ||||||||
\(86\) | 509.754 | 0.639165 | ||||||||
\(87\) | 14.1001 | 0.0173758 | ||||||||
\(88\) | 344.279 | 0.417049 | ||||||||
\(89\) | 888.952 | 1.05875 | 0.529375 | − | 0.848388i | \(-0.322427\pi\) | ||||
0.529375 | + | 0.848388i | \(0.322427\pi\) | |||||||
\(90\) | 86.7415 | 0.101593 | ||||||||
\(91\) | 340.791 | 0.392578 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 265.293 | 0.295802 | ||||||||
\(94\) | −1026.38 | −1.12620 | ||||||||
\(95\) | 304.790 | 0.329166 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −255.899 | −0.267862 | −0.133931 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133931 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | 387.314 | 0.393197 | ||||||||
\(100\) | −407.110 | −0.407110 | ||||||||
\(101\) | 726.548 | 0.715784 | 0.357892 | − | 0.933763i | \(-0.383496\pi\) | ||||
0.357892 | + | 0.933763i | \(0.383496\pi\) | |||||||
\(102\) | 148.641 | 0.144291 | ||||||||
\(103\) | 623.121 | 0.596097 | 0.298048 | − | 0.954551i | \(-0.403664\pi\) | ||||
0.298048 | + | 0.954551i | \(0.403664\pi\) | |||||||
\(104\) | 389.476 | 0.367223 | ||||||||
\(105\) | −101.198 | −0.0940567 | ||||||||
\(106\) | 856.978 | 0.785255 | ||||||||
\(107\) | −34.0096 | −0.0307274 | −0.0153637 | − | 0.999882i | \(-0.504891\pi\) | ||||
−0.0153637 | + | 0.999882i | \(0.504891\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −177.207 | −0.155719 | −0.0778596 | − | 0.996964i | \(-0.524809\pi\) | ||||
−0.0778596 | + | 0.996964i | \(0.524809\pi\) | |||||||
\(110\) | 414.768 | 0.359514 | ||||||||
\(111\) | 506.589 | 0.433183 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | −1011.65 | −0.842196 | −0.421098 | − | 0.907015i | \(-0.638355\pi\) | ||||
−0.421098 | + | 0.907015i | \(0.638355\pi\) | |||||||
\(114\) | −379.487 | −0.311774 | ||||||||
\(115\) | −110.836 | −0.0898743 | ||||||||
\(116\) | −18.8002 | −0.0150479 | ||||||||
\(117\) | 438.160 | 0.346222 | ||||||||
\(118\) | 317.967 | 0.248062 | ||||||||
\(119\) | −173.415 | −0.133587 | ||||||||
\(120\) | −115.655 | −0.0879820 | ||||||||
\(121\) | 521.001 | 0.391436 | ||||||||
\(122\) | −56.5757 | −0.0419846 | ||||||||
\(123\) | −1397.25 | −1.02427 | ||||||||
\(124\) | −353.724 | −0.256172 | ||||||||
\(125\) | −1092.83 | −0.781969 | ||||||||
\(126\) | 126.000 | 0.0890871 | ||||||||
\(127\) | −1522.05 | −1.06346 | −0.531731 | − | 0.846913i | \(-0.678458\pi\) | ||||
−0.531731 | + | 0.846913i | \(0.678458\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −764.631 | −0.521876 | ||||||||
\(130\) | 469.218 | 0.316563 | ||||||||
\(131\) | 2533.05 | 1.68941 | 0.844707 | − | 0.535228i | \(-0.179774\pi\) | ||||
0.844707 | + | 0.535228i | \(0.179774\pi\) | |||||||
\(132\) | −516.419 | −0.340519 | ||||||||
\(133\) | 442.735 | 0.288647 | ||||||||
\(134\) | 1594.47 | 1.02792 | ||||||||
\(135\) | −130.112 | −0.0829502 | ||||||||
\(136\) | −198.188 | −0.124960 | ||||||||
\(137\) | 18.5942 | 0.0115957 | 0.00579783 | − | 0.999983i | \(-0.498154\pi\) | ||||
0.00579783 | + | 0.999983i | \(0.498154\pi\) | |||||||
\(138\) | 138.000 | 0.0851257 | ||||||||
\(139\) | 2684.26 | 1.63796 | 0.818979 | − | 0.573824i | \(-0.194541\pi\) | ||||
0.818979 | + | 0.573824i | \(0.194541\pi\) | |||||||
\(140\) | 134.931 | 0.0814555 | ||||||||
\(141\) | 1539.56 | 0.919537 | ||||||||
\(142\) | −1556.84 | −0.920053 | ||||||||
\(143\) | 2095.13 | 1.22520 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −22.6494 | −0.0129719 | ||||||||
\(146\) | 1052.16 | 0.596422 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | −675.452 | −0.375147 | ||||||||
\(149\) | 71.6799 | 0.0394111 | 0.0197055 | − | 0.999806i | \(-0.493727\pi\) | ||||
0.0197055 | + | 0.999806i | \(0.493727\pi\) | |||||||
\(150\) | 610.665 | 0.332404 | ||||||||
\(151\) | −1287.00 | −0.693604 | −0.346802 | − | 0.937938i | \(-0.612732\pi\) | ||||
−0.346802 | + | 0.937938i | \(0.612732\pi\) | |||||||
\(152\) | 505.983 | 0.270004 | ||||||||
\(153\) | −222.962 | −0.117813 | ||||||||
\(154\) | 602.488 | 0.315259 | ||||||||
\(155\) | −426.147 | −0.220832 | ||||||||
\(156\) | −584.214 | −0.299837 | ||||||||
\(157\) | −1520.90 | −0.773128 | −0.386564 | − | 0.922262i | \(-0.626338\pi\) | ||||
−0.386564 | + | 0.922262i | \(0.626338\pi\) | |||||||
\(158\) | −216.049 | −0.108785 | ||||||||
\(159\) | −1285.47 | −0.641158 | ||||||||
\(160\) | 154.207 | 0.0761947 | ||||||||
\(161\) | −161.000 | −0.0788110 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 2629.34 | 1.26347 | 0.631736 | − | 0.775184i | \(-0.282343\pi\) | ||||
0.631736 | + | 0.775184i | \(0.282343\pi\) | |||||||
\(164\) | 1863.00 | 0.887048 | ||||||||
\(165\) | −622.152 | −0.293542 | ||||||||
\(166\) | 818.518 | 0.382707 | ||||||||
\(167\) | 254.418 | 0.117889 | 0.0589445 | − | 0.998261i | \(-0.481227\pi\) | ||||
0.0589445 | + | 0.998261i | \(0.481227\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | 173.177 | 0.0788242 | ||||||||
\(170\) | −238.766 | −0.107721 | ||||||||
\(171\) | 569.231 | 0.254562 | ||||||||
\(172\) | 1019.51 | 0.451958 | ||||||||
\(173\) | −1451.24 | −0.637780 | −0.318890 | − | 0.947792i | \(-0.603310\pi\) | ||||
−0.318890 | + | 0.947792i | \(0.603310\pi\) | |||||||
\(174\) | 28.2003 | 0.0122865 | ||||||||
\(175\) | −712.442 | −0.307746 | ||||||||
\(176\) | 688.558 | 0.294898 | ||||||||
\(177\) | −476.951 | −0.202541 | ||||||||
\(178\) | 1777.90 | 0.748649 | ||||||||
\(179\) | 1382.02 | 0.577078 | 0.288539 | − | 0.957468i | \(-0.406830\pi\) | ||||
0.288539 | + | 0.957468i | \(0.406830\pi\) | |||||||
\(180\) | 173.483 | 0.0718370 | ||||||||
\(181\) | 825.918 | 0.339171 | 0.169586 | − | 0.985515i | \(-0.445757\pi\) | ||||
0.169586 | + | 0.985515i | \(0.445757\pi\) | |||||||
\(182\) | 681.582 | 0.277595 | ||||||||
\(183\) | 84.8635 | 0.0342803 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | −813.746 | −0.323393 | ||||||||
\(186\) | 530.586 | 0.209164 | ||||||||
\(187\) | −1066.13 | −0.416914 | ||||||||
\(188\) | −2052.75 | −0.796342 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 609.580 | 0.232756 | ||||||||
\(191\) | 1746.50 | 0.661636 | 0.330818 | − | 0.943695i | \(-0.392675\pi\) | ||||
0.330818 | + | 0.943695i | \(0.392675\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 2592.01 | 0.966720 | 0.483360 | − | 0.875422i | \(-0.339416\pi\) | ||||
0.483360 | + | 0.875422i | \(0.339416\pi\) | |||||||
\(194\) | −511.798 | −0.189407 | ||||||||
\(195\) | −703.827 | −0.258472 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −2101.75 | −0.760120 | −0.380060 | − | 0.924962i | \(-0.624097\pi\) | ||||
−0.380060 | + | 0.924962i | \(0.624097\pi\) | |||||||
\(198\) | 774.628 | 0.278032 | ||||||||
\(199\) | 3228.44 | 1.15004 | 0.575020 | − | 0.818139i | \(-0.304994\pi\) | ||||
0.575020 | + | 0.818139i | \(0.304994\pi\) | |||||||
\(200\) | −814.220 | −0.287870 | ||||||||
\(201\) | −2391.71 | −0.839294 | ||||||||
\(202\) | 1453.10 | 0.506136 | ||||||||
\(203\) | −32.9003 | −0.0113751 | ||||||||
\(204\) | 297.282 | 0.102029 | ||||||||
\(205\) | 2244.44 | 0.764675 | ||||||||
\(206\) | 1246.24 | 0.421504 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | 778.951 | 0.259666 | ||||||||
\(209\) | 2721.87 | 0.900839 | ||||||||
\(210\) | −202.397 | −0.0665082 | ||||||||
\(211\) | −2689.98 | −0.877658 | −0.438829 | − | 0.898570i | \(-0.644607\pi\) | ||||
−0.438829 | + | 0.898570i | \(0.644607\pi\) | |||||||
\(212\) | 1713.96 | 0.555259 | ||||||||
\(213\) | 2335.27 | 0.751220 | ||||||||
\(214\) | −68.0193 | −0.0217276 | ||||||||
\(215\) | 1228.24 | 0.389607 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −619.017 | −0.193648 | ||||||||
\(218\) | −354.415 | −0.110110 | ||||||||
\(219\) | −1578.24 | −0.486976 | ||||||||
\(220\) | 829.536 | 0.254215 | ||||||||
\(221\) | −1206.09 | −0.367105 | ||||||||
\(222\) | 1013.18 | 0.306306 | ||||||||
\(223\) | −2592.25 | −0.778429 | −0.389214 | − | 0.921147i | \(-0.627253\pi\) | ||||
−0.389214 | + | 0.921147i | \(0.627253\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | −915.997 | −0.271407 | ||||||||
\(226\) | −2023.30 | −0.595522 | ||||||||
\(227\) | 5463.45 | 1.59745 | 0.798726 | − | 0.601695i | \(-0.205508\pi\) | ||||
0.798726 | + | 0.601695i | \(0.205508\pi\) | |||||||
\(228\) | −758.975 | −0.220458 | ||||||||
\(229\) | 663.825 | 0.191558 | 0.0957790 | − | 0.995403i | \(-0.469466\pi\) | ||||
0.0957790 | + | 0.995403i | \(0.469466\pi\) | |||||||
\(230\) | −221.673 | −0.0635507 | ||||||||
\(231\) | −903.733 | −0.257408 | ||||||||
\(232\) | −37.6004 | −0.0106405 | ||||||||
\(233\) | −3961.76 | −1.11392 | −0.556961 | − | 0.830539i | \(-0.688033\pi\) | ||||
−0.556961 | + | 0.830539i | \(0.688033\pi\) | |||||||
\(234\) | 876.320 | 0.244816 | ||||||||
\(235\) | −2473.04 | −0.686482 | ||||||||
\(236\) | 635.935 | 0.175406 | ||||||||
\(237\) | 324.074 | 0.0888222 | ||||||||
\(238\) | −346.829 | −0.0944605 | ||||||||
\(239\) | −2991.95 | −0.809763 | −0.404881 | − | 0.914369i | \(-0.632687\pi\) | ||||
−0.404881 | + | 0.914369i | \(0.632687\pi\) | |||||||
\(240\) | −231.311 | −0.0622127 | ||||||||
\(241\) | −5740.49 | −1.53435 | −0.767173 | − | 0.641441i | \(-0.778337\pi\) | ||||
−0.767173 | + | 0.641441i | \(0.778337\pi\) | |||||||
\(242\) | 1042.00 | 0.276787 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −113.151 | −0.0296876 | ||||||||
\(245\) | 236.130 | 0.0615746 | ||||||||
\(246\) | −2794.50 | −0.724272 | ||||||||
\(247\) | 3079.19 | 0.793215 | ||||||||
\(248\) | −707.448 | −0.181141 | ||||||||
\(249\) | −1227.78 | −0.312479 | ||||||||
\(250\) | −2185.67 | −0.552936 | ||||||||
\(251\) | 1505.93 | 0.378698 | 0.189349 | − | 0.981910i | \(-0.439362\pi\) | ||||
0.189349 | + | 0.981910i | \(0.439362\pi\) | |||||||
\(252\) | 252.000 | 0.0629941 | ||||||||
\(253\) | −989.802 | −0.245962 | ||||||||
\(254\) | −3044.09 | −0.751982 | ||||||||
\(255\) | 358.149 | 0.0879535 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5987.31 | −1.45322 | −0.726611 | − | 0.687050i | \(-0.758906\pi\) | ||||
−0.726611 | + | 0.687050i | \(0.758906\pi\) | |||||||
\(258\) | −1529.26 | −0.369022 | ||||||||
\(259\) | −1182.04 | −0.283585 | ||||||||
\(260\) | 938.437 | 0.223844 | ||||||||
\(261\) | −42.3004 | −0.0100319 | ||||||||
\(262\) | 5066.09 | 1.19460 | ||||||||
\(263\) | −1898.18 | −0.445046 | −0.222523 | − | 0.974927i | \(-0.571429\pi\) | ||||
−0.222523 | + | 0.974927i | \(0.571429\pi\) | |||||||
\(264\) | −1032.84 | −0.240783 | ||||||||
\(265\) | 2064.88 | 0.478658 | ||||||||
\(266\) | 885.470 | 0.204104 | ||||||||
\(267\) | −2666.86 | −0.611269 | ||||||||
\(268\) | 3188.94 | 0.726850 | ||||||||
\(269\) | 4317.05 | 0.978496 | 0.489248 | − | 0.872145i | \(-0.337271\pi\) | ||||
0.489248 | + | 0.872145i | \(0.337271\pi\) | |||||||
\(270\) | −260.225 | −0.0586547 | ||||||||
\(271\) | −5978.25 | −1.34005 | −0.670024 | − | 0.742340i | \(-0.733716\pi\) | ||||
−0.670024 | + | 0.742340i | \(0.733716\pi\) | |||||||
\(272\) | −396.376 | −0.0883597 | ||||||||
\(273\) | −1022.37 | −0.226655 | ||||||||
\(274\) | 37.1883 | 0.00819938 | ||||||||
\(275\) | −4379.98 | −0.960447 | ||||||||
\(276\) | 276.000 | 0.0601929 | ||||||||
\(277\) | 4212.43 | 0.913719 | 0.456859 | − | 0.889539i | \(-0.348974\pi\) | ||||
0.456859 | + | 0.889539i | \(0.348974\pi\) | |||||||
\(278\) | 5368.52 | 1.15821 | ||||||||
\(279\) | −795.879 | −0.170782 | ||||||||
\(280\) | 269.863 | 0.0575978 | ||||||||
\(281\) | 4850.74 | 1.02979 | 0.514895 | − | 0.857253i | \(-0.327831\pi\) | ||||
0.514895 | + | 0.857253i | \(0.327831\pi\) | |||||||
\(282\) | 3079.13 | 0.650211 | ||||||||
\(283\) | 689.593 | 0.144848 | 0.0724241 | − | 0.997374i | \(-0.476926\pi\) | ||||
0.0724241 | + | 0.997374i | \(0.476926\pi\) | |||||||
\(284\) | −3113.69 | −0.650576 | ||||||||
\(285\) | −914.370 | −0.190044 | ||||||||
\(286\) | 4190.26 | 0.866347 | ||||||||
\(287\) | 3260.25 | 0.670545 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | −4299.27 | −0.875081 | ||||||||
\(290\) | −45.2988 | −0.00917254 | ||||||||
\(291\) | 767.696 | 0.154650 | ||||||||
\(292\) | 2104.32 | 0.421734 | ||||||||
\(293\) | −1099.32 | −0.219191 | −0.109596 | − | 0.993976i | \(-0.534956\pi\) | ||||
−0.109596 | + | 0.993976i | \(0.534956\pi\) | |||||||
\(294\) | −294.000 | −0.0583212 | ||||||||
\(295\) | 766.138 | 0.151208 | ||||||||
\(296\) | −1350.90 | −0.265269 | ||||||||
\(297\) | −1161.94 | −0.227012 | ||||||||
\(298\) | 143.360 | 0.0278678 | ||||||||
\(299\) | −1119.74 | −0.216577 | ||||||||
\(300\) | 1221.33 | 0.235045 | ||||||||
\(301\) | 1784.14 | 0.341648 | ||||||||
\(302\) | −2573.99 | −0.490452 | ||||||||
\(303\) | −2179.64 | −0.413258 | ||||||||
\(304\) | 1011.97 | 0.190922 | ||||||||
\(305\) | −136.318 | −0.0255920 | ||||||||
\(306\) | −445.923 | −0.0833064 | ||||||||
\(307\) | −3586.44 | −0.666739 | −0.333369 | − | 0.942796i | \(-0.608186\pi\) | ||||
−0.333369 | + | 0.942796i | \(0.608186\pi\) | |||||||
\(308\) | 1204.98 | 0.222922 | ||||||||
\(309\) | −1869.36 | −0.344157 | ||||||||
\(310\) | −852.294 | −0.156152 | ||||||||
\(311\) | 1271.25 | 0.231787 | 0.115894 | − | 0.993262i | \(-0.463027\pi\) | ||||
0.115894 | + | 0.993262i | \(0.463027\pi\) | |||||||
\(312\) | −1168.43 | −0.212017 | ||||||||
\(313\) | −7502.44 | −1.35483 | −0.677417 | − | 0.735599i | \(-0.736901\pi\) | ||||
−0.677417 | + | 0.735599i | \(0.736901\pi\) | |||||||
\(314\) | −3041.80 | −0.546684 | ||||||||
\(315\) | 303.595 | 0.0543037 | ||||||||
\(316\) | −432.099 | −0.0769223 | ||||||||
\(317\) | −7578.44 | −1.34274 | −0.671369 | − | 0.741123i | \(-0.734293\pi\) | ||||
−0.671369 | + | 0.741123i | \(0.734293\pi\) | |||||||
\(318\) | −2570.93 | −0.453367 | ||||||||
\(319\) | −202.266 | −0.0355007 | ||||||||
\(320\) | 308.414 | 0.0538778 | ||||||||
\(321\) | 102.029 | 0.0177405 | ||||||||
\(322\) | −322.000 | −0.0557278 | ||||||||
\(323\) | −1566.87 | −0.269917 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −4954.98 | −0.845701 | ||||||||
\(326\) | 5258.68 | 0.893410 | ||||||||
\(327\) | 531.622 | 0.0899045 | ||||||||
\(328\) | 3726.00 | 0.627238 | ||||||||
\(329\) | −3592.32 | −0.601978 | ||||||||
\(330\) | −1244.30 | −0.207566 | ||||||||
\(331\) | −5168.33 | −0.858240 | −0.429120 | − | 0.903248i | \(-0.641176\pi\) | ||||
−0.429120 | + | 0.903248i | \(0.641176\pi\) | |||||||
\(332\) | 1637.04 | 0.270615 | ||||||||
\(333\) | −1519.77 | −0.250098 | ||||||||
\(334\) | 508.836 | 0.0833601 | ||||||||
\(335\) | 3841.86 | 0.626577 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | −3372.75 | −0.545180 | −0.272590 | − | 0.962130i | \(-0.587880\pi\) | ||||
−0.272590 | + | 0.962130i | \(0.587880\pi\) | |||||||
\(338\) | 346.354 | 0.0557372 | ||||||||
\(339\) | 3034.95 | 0.486242 | ||||||||
\(340\) | −477.532 | −0.0761700 | ||||||||
\(341\) | −3805.62 | −0.604357 | ||||||||
\(342\) | 1138.46 | 0.180003 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 2039.01 | 0.319582 | ||||||||
\(345\) | 332.509 | 0.0518890 | ||||||||
\(346\) | −2902.48 | −0.450978 | ||||||||
\(347\) | 4931.32 | 0.762903 | 0.381451 | − | 0.924389i | \(-0.375424\pi\) | ||||
0.381451 | + | 0.924389i | \(0.375424\pi\) | |||||||
\(348\) | 56.4005 | 0.00868789 | ||||||||
\(349\) | −8112.70 | −1.24431 | −0.622153 | − | 0.782895i | \(-0.713742\pi\) | ||||
−0.622153 | + | 0.782895i | \(0.713742\pi\) | |||||||
\(350\) | −1424.88 | −0.217609 | ||||||||
\(351\) | −1314.48 | −0.199891 | ||||||||
\(352\) | 1377.12 | 0.208524 | ||||||||
\(353\) | 1934.09 | 0.291618 | 0.145809 | − | 0.989313i | \(-0.453421\pi\) | ||||
0.145809 | + | 0.989313i | \(0.453421\pi\) | |||||||
\(354\) | −953.902 | −0.143218 | ||||||||
\(355\) | −3751.20 | −0.560825 | ||||||||
\(356\) | 3555.81 | 0.529375 | ||||||||
\(357\) | 520.244 | 0.0771267 | ||||||||
\(358\) | 2764.04 | 0.408056 | ||||||||
\(359\) | −308.167 | −0.0453049 | −0.0226524 | − | 0.999743i | \(-0.507211\pi\) | ||||
−0.0226524 | + | 0.999743i | \(0.507211\pi\) | |||||||
\(360\) | 346.966 | 0.0507964 | ||||||||
\(361\) | −2858.70 | −0.416782 | ||||||||
\(362\) | 1651.84 | 0.239830 | ||||||||
\(363\) | −1563.00 | −0.225996 | ||||||||
\(364\) | 1363.16 | 0.196289 | ||||||||
\(365\) | 2535.17 | 0.363553 | ||||||||
\(366\) | 169.727 | 0.0242398 | ||||||||
\(367\) | −6831.82 | −0.971711 | −0.485856 | − | 0.874039i | \(-0.661492\pi\) | ||||
−0.485856 | + | 0.874039i | \(0.661492\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | 4191.75 | 0.591365 | ||||||||
\(370\) | −1627.49 | −0.228674 | ||||||||
\(371\) | 2999.42 | 0.419737 | ||||||||
\(372\) | 1061.17 | 0.147901 | ||||||||
\(373\) | −10390.3 | −1.44232 | −0.721162 | − | 0.692766i | \(-0.756392\pi\) | ||||
−0.721162 | + | 0.692766i | \(0.756392\pi\) | |||||||
\(374\) | −2132.25 | −0.294802 | ||||||||
\(375\) | 3278.50 | 0.451470 | ||||||||
\(376\) | −4105.50 | −0.563099 | ||||||||
\(377\) | −228.819 | −0.0312594 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | 4526.85 | 0.613532 | 0.306766 | − | 0.951785i | \(-0.400753\pi\) | ||||
0.306766 | + | 0.951785i | \(0.400753\pi\) | |||||||
\(380\) | 1219.16 | 0.164583 | ||||||||
\(381\) | 4566.14 | 0.613990 | ||||||||
\(382\) | 3493.00 | 0.467847 | ||||||||
\(383\) | −1271.78 | −0.169674 | −0.0848369 | − | 0.996395i | \(-0.527037\pi\) | ||||
−0.0848369 | + | 0.996395i | \(0.527037\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 1451.69 | 0.192168 | ||||||||
\(386\) | 5184.02 | 0.683575 | ||||||||
\(387\) | 2293.89 | 0.301305 | ||||||||
\(388\) | −1023.60 | −0.133931 | ||||||||
\(389\) | −9955.76 | −1.29763 | −0.648813 | − | 0.760948i | \(-0.724734\pi\) | ||||
−0.648813 | + | 0.760948i | \(0.724734\pi\) | |||||||
\(390\) | −1407.65 | −0.182768 | ||||||||
\(391\) | 569.791 | 0.0736971 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | −7599.14 | −0.975384 | ||||||||
\(394\) | −4203.51 | −0.537486 | ||||||||
\(395\) | −520.568 | −0.0663104 | ||||||||
\(396\) | 1549.26 | 0.196599 | ||||||||
\(397\) | 6168.22 | 0.779784 | 0.389892 | − | 0.920861i | \(-0.372512\pi\) | ||||
0.389892 | + | 0.920861i | \(0.372512\pi\) | |||||||
\(398\) | 6456.88 | 0.813201 | ||||||||
\(399\) | −1328.21 | −0.166650 | ||||||||
\(400\) | −1628.44 | −0.203555 | ||||||||
\(401\) | −5134.86 | −0.639458 | −0.319729 | − | 0.947509i | \(-0.603592\pi\) | ||||
−0.319729 | + | 0.947509i | \(0.603592\pi\) | |||||||
\(402\) | −4783.42 | −0.593470 | ||||||||
\(403\) | −4305.22 | −0.532154 | ||||||||
\(404\) | 2906.19 | 0.357892 | ||||||||
\(405\) | 390.337 | 0.0478913 | ||||||||
\(406\) | −65.8006 | −0.00804343 | ||||||||
\(407\) | −7266.99 | −0.885041 | ||||||||
\(408\) | 594.565 | 0.0721454 | ||||||||
\(409\) | −6805.93 | −0.822816 | −0.411408 | − | 0.911451i | \(-0.634963\pi\) | ||||
−0.411408 | + | 0.911451i | \(0.634963\pi\) | |||||||
\(410\) | 4488.87 | 0.540707 | ||||||||
\(411\) | −55.7825 | −0.00669476 | ||||||||
\(412\) | 2492.49 | 0.298048 | ||||||||
\(413\) | 1112.89 | 0.132594 | ||||||||
\(414\) | −414.000 | −0.0491473 | ||||||||
\(415\) | 1972.21 | 0.233282 | ||||||||
\(416\) | 1557.90 | 0.183612 | ||||||||
\(417\) | −8052.79 | −0.945675 | ||||||||
\(418\) | 5443.73 | 0.636989 | ||||||||
\(419\) | 9403.51 | 1.09640 | 0.548200 | − | 0.836347i | \(-0.315313\pi\) | ||||
0.548200 | + | 0.836347i | \(0.315313\pi\) | |||||||
\(420\) | −404.794 | −0.0470284 | ||||||||
\(421\) | 2153.32 | 0.249279 | 0.124639 | − | 0.992202i | \(-0.460223\pi\) | ||||
0.124639 | + | 0.992202i | \(0.460223\pi\) | |||||||
\(422\) | −5379.96 | −0.620598 | ||||||||
\(423\) | −4618.69 | −0.530895 | ||||||||
\(424\) | 3427.91 | 0.392628 | ||||||||
\(425\) | 2521.39 | 0.287777 | ||||||||
\(426\) | 4670.53 | 0.531193 | ||||||||
\(427\) | −198.015 | −0.0224417 | ||||||||
\(428\) | −136.039 | −0.0153637 | ||||||||
\(429\) | −6285.39 | −0.707369 | ||||||||
\(430\) | 2456.49 | 0.275494 | ||||||||
\(431\) | 6346.56 | 0.709287 | 0.354644 | − | 0.935002i | \(-0.384602\pi\) | ||||
0.354644 | + | 0.935002i | \(0.384602\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −718.947 | −0.0797931 | −0.0398965 | − | 0.999204i | \(-0.512703\pi\) | ||||
−0.0398965 | + | 0.999204i | \(0.512703\pi\) | |||||||
\(434\) | −1238.03 | −0.136930 | ||||||||
\(435\) | 67.9482 | 0.00748935 | ||||||||
\(436\) | −708.830 | −0.0778596 | ||||||||
\(437\) | −1454.70 | −0.159240 | ||||||||
\(438\) | −3156.49 | −0.344344 | ||||||||
\(439\) | 7477.10 | 0.812898 | 0.406449 | − | 0.913673i | \(-0.366767\pi\) | ||||
0.406449 | + | 0.913673i | \(0.366767\pi\) | |||||||
\(440\) | 1659.07 | 0.179757 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −2412.17 | −0.259582 | ||||||||
\(443\) | 12703.0 | 1.36239 | 0.681196 | − | 0.732101i | \(-0.261460\pi\) | ||||
0.681196 | + | 0.732101i | \(0.261460\pi\) | |||||||
\(444\) | 2026.35 | 0.216591 | ||||||||
\(445\) | 4283.84 | 0.456345 | ||||||||
\(446\) | −5184.49 | −0.550432 | ||||||||
\(447\) | −215.040 | −0.0227540 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | 634.326 | 0.0666719 | 0.0333359 | − | 0.999444i | \(-0.489387\pi\) | ||||
0.0333359 | + | 0.999444i | \(0.489387\pi\) | |||||||
\(450\) | −1831.99 | −0.191913 | ||||||||
\(451\) | 20043.5 | 2.09271 | ||||||||
\(452\) | −4046.60 | −0.421098 | ||||||||
\(453\) | 3860.99 | 0.400453 | ||||||||
\(454\) | 10926.9 | 1.12957 | ||||||||
\(455\) | 1642.26 | 0.169210 | ||||||||
\(456\) | −1517.95 | −0.155887 | ||||||||
\(457\) | 1586.41 | 0.162384 | 0.0811918 | − | 0.996698i | \(-0.474127\pi\) | ||||
0.0811918 | + | 0.996698i | \(0.474127\pi\) | |||||||
\(458\) | 1327.65 | 0.135452 | ||||||||
\(459\) | 668.885 | 0.0680194 | ||||||||
\(460\) | −443.346 | −0.0449372 | ||||||||
\(461\) | 12274.6 | 1.24010 | 0.620051 | − | 0.784562i | \(-0.287112\pi\) | ||||
0.620051 | + | 0.784562i | \(0.287112\pi\) | |||||||
\(462\) | −1807.47 | −0.182015 | ||||||||
\(463\) | −11981.2 | −1.20262 | −0.601312 | − | 0.799014i | \(-0.705355\pi\) | ||||
−0.601312 | + | 0.799014i | \(0.705355\pi\) | |||||||
\(464\) | −75.2007 | −0.00752394 | ||||||||
\(465\) | 1278.44 | 0.127497 | ||||||||
\(466\) | −7923.52 | −0.787661 | ||||||||
\(467\) | 4935.51 | 0.489054 | 0.244527 | − | 0.969643i | \(-0.421367\pi\) | ||||
0.244527 | + | 0.969643i | \(0.421367\pi\) | |||||||
\(468\) | 1752.64 | 0.173111 | ||||||||
\(469\) | 5580.65 | 0.549447 | ||||||||
\(470\) | −4946.08 | −0.485416 | ||||||||
\(471\) | 4562.71 | 0.446366 | ||||||||
\(472\) | 1271.87 | 0.124031 | ||||||||
\(473\) | 10968.6 | 1.06625 | ||||||||
\(474\) | 648.148 | 0.0628068 | ||||||||
\(475\) | −6437.21 | −0.621809 | ||||||||
\(476\) | −693.659 | −0.0667937 | ||||||||
\(477\) | 3856.40 | 0.370173 | ||||||||
\(478\) | −5983.91 | −0.572589 | ||||||||
\(479\) | −7814.60 | −0.745424 | −0.372712 | − | 0.927947i | \(-0.621572\pi\) | ||||
−0.372712 | + | 0.927947i | \(0.621572\pi\) | |||||||
\(480\) | −462.621 | −0.0439910 | ||||||||
\(481\) | −8221.00 | −0.779304 | ||||||||
\(482\) | −11481.0 | −1.08495 | ||||||||
\(483\) | 483.000 | 0.0455016 | ||||||||
\(484\) | 2084.00 | 0.195718 | ||||||||
\(485\) | −1233.17 | −0.115454 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −1993.13 | −0.185457 | −0.0927284 | − | 0.995691i | \(-0.529559\pi\) | ||||
−0.0927284 | + | 0.995691i | \(0.529559\pi\) | |||||||
\(488\) | −226.303 | −0.0209923 | ||||||||
\(489\) | −7888.02 | −0.729466 | ||||||||
\(490\) | 472.259 | 0.0435398 | ||||||||
\(491\) | −2069.52 | −0.190216 | −0.0951081 | − | 0.995467i | \(-0.530320\pi\) | ||||
−0.0951081 | + | 0.995467i | \(0.530320\pi\) | |||||||
\(492\) | −5589.00 | −0.512137 | ||||||||
\(493\) | 116.437 | 0.0106370 | ||||||||
\(494\) | 6158.38 | 0.560888 | ||||||||
\(495\) | 1866.46 | 0.169477 | ||||||||
\(496\) | −1414.90 | −0.128086 | ||||||||
\(497\) | −5448.96 | −0.491789 | ||||||||
\(498\) | −2455.56 | −0.220956 | ||||||||
\(499\) | −16681.6 | −1.49654 | −0.748268 | − | 0.663397i | \(-0.769114\pi\) | ||||
−0.748268 | + | 0.663397i | \(0.769114\pi\) | |||||||
\(500\) | −4371.34 | −0.390984 | ||||||||
\(501\) | −763.254 | −0.0680632 | ||||||||
\(502\) | 3011.85 | 0.267780 | ||||||||
\(503\) | 547.940 | 0.0485714 | 0.0242857 | − | 0.999705i | \(-0.492269\pi\) | ||||
0.0242857 | + | 0.999705i | \(0.492269\pi\) | |||||||
\(504\) | 504.000 | 0.0445435 | ||||||||
\(505\) | 3501.21 | 0.308519 | ||||||||
\(506\) | −1979.60 | −0.173921 | ||||||||
\(507\) | −519.531 | −0.0455092 | ||||||||
\(508\) | −6088.18 | −0.531731 | ||||||||
\(509\) | 12549.1 | 1.09279 | 0.546395 | − | 0.837528i | \(-0.316000\pi\) | ||||
0.546395 | + | 0.837528i | \(0.316000\pi\) | |||||||
\(510\) | 716.298 | 0.0621925 | ||||||||
\(511\) | 3682.57 | 0.318801 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −1707.69 | −0.146972 | ||||||||
\(514\) | −11974.6 | −1.02758 | ||||||||
\(515\) | 3002.81 | 0.256931 | ||||||||
\(516\) | −3058.52 | −0.260938 | ||||||||
\(517\) | −22085.0 | −1.87872 | ||||||||
\(518\) | −2364.08 | −0.200525 | ||||||||
\(519\) | 4353.73 | 0.368222 | ||||||||
\(520\) | 1876.87 | 0.158281 | ||||||||
\(521\) | 15526.1 | 1.30559 | 0.652794 | − | 0.757536i | \(-0.273597\pi\) | ||||
0.652794 | + | 0.757536i | \(0.273597\pi\) | |||||||
\(522\) | −84.6008 | −0.00709363 | ||||||||
\(523\) | 15227.7 | 1.27316 | 0.636579 | − | 0.771212i | \(-0.280349\pi\) | ||||
0.636579 | + | 0.771212i | \(0.280349\pi\) | |||||||
\(524\) | 10132.2 | 0.844707 | ||||||||
\(525\) | 2137.33 | 0.177677 | ||||||||
\(526\) | −3796.37 | −0.314695 | ||||||||
\(527\) | 2190.75 | 0.181083 | ||||||||
\(528\) | −2065.67 | −0.170259 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 4129.75 | 0.338462 | ||||||||
\(531\) | 1430.85 | 0.116937 | ||||||||
\(532\) | 1770.94 | 0.144323 | ||||||||
\(533\) | 22674.8 | 1.84269 | ||||||||
\(534\) | −5333.71 | −0.432233 | ||||||||
\(535\) | −163.892 | −0.0132442 | ||||||||
\(536\) | 6377.89 | 0.513960 | ||||||||
\(537\) | −4146.06 | −0.333176 | ||||||||
\(538\) | 8634.11 | 0.691901 | ||||||||
\(539\) | 2108.71 | 0.168513 | ||||||||
\(540\) | −520.449 | −0.0414751 | ||||||||
\(541\) | −18557.1 | −1.47473 | −0.737367 | − | 0.675493i | \(-0.763931\pi\) | ||||
−0.737367 | + | 0.675493i | \(0.763931\pi\) | |||||||
\(542\) | −11956.5 | −0.947557 | ||||||||
\(543\) | −2477.75 | −0.195821 | ||||||||
\(544\) | −792.753 | −0.0624798 | ||||||||
\(545\) | −853.958 | −0.0671184 | ||||||||
\(546\) | −2044.75 | −0.160269 | ||||||||
\(547\) | −2032.79 | −0.158895 | −0.0794476 | − | 0.996839i | \(-0.525316\pi\) | ||||
−0.0794476 | + | 0.996839i | \(0.525316\pi\) | |||||||
\(548\) | 74.3766 | 0.00579783 | ||||||||
\(549\) | −254.591 | −0.0197917 | ||||||||
\(550\) | −8759.96 | −0.679138 | ||||||||
\(551\) | −297.268 | −0.0229837 | ||||||||
\(552\) | 552.000 | 0.0425628 | ||||||||
\(553\) | −756.172 | −0.0581478 | ||||||||
\(554\) | 8424.85 | 0.646097 | ||||||||
\(555\) | 2441.24 | 0.186711 | ||||||||
\(556\) | 10737.0 | 0.818979 | ||||||||
\(557\) | −11605.7 | −0.882855 | −0.441428 | − | 0.897297i | \(-0.645528\pi\) | ||||
−0.441428 | + | 0.897297i | \(0.645528\pi\) | |||||||
\(558\) | −1591.76 | −0.120761 | ||||||||
\(559\) | 12408.5 | 0.938865 | ||||||||
\(560\) | 539.725 | 0.0407278 | ||||||||
\(561\) | 3198.38 | 0.240705 | ||||||||
\(562\) | 9701.48 | 0.728171 | ||||||||
\(563\) | 154.171 | 0.0115409 | 0.00577047 | − | 0.999983i | \(-0.498163\pi\) | ||||
0.00577047 | + | 0.999983i | \(0.498163\pi\) | |||||||
\(564\) | 6158.26 | 0.459768 | ||||||||
\(565\) | −4875.12 | −0.363005 | ||||||||
\(566\) | 1379.19 | 0.102423 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | −6227.38 | −0.460026 | ||||||||
\(569\) | −20639.0 | −1.52062 | −0.760309 | − | 0.649562i | \(-0.774952\pi\) | ||||
−0.760309 | + | 0.649562i | \(0.774952\pi\) | |||||||
\(570\) | −1828.74 | −0.134382 | ||||||||
\(571\) | −22691.0 | −1.66303 | −0.831515 | − | 0.555502i | \(-0.812526\pi\) | ||||
−0.831515 | + | 0.555502i | \(0.812526\pi\) | |||||||
\(572\) | 8380.52 | 0.612600 | ||||||||
\(573\) | −5239.51 | −0.381996 | ||||||||
\(574\) | 6520.50 | 0.474147 | ||||||||
\(575\) | 2340.88 | 0.169777 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −53.9391 | −0.00389171 | −0.00194585 | − | 0.999998i | \(-0.500619\pi\) | ||||
−0.00194585 | + | 0.999998i | \(0.500619\pi\) | |||||||
\(578\) | −8598.55 | −0.618776 | ||||||||
\(579\) | −7776.03 | −0.558136 | ||||||||
\(580\) | −90.5976 | −0.00648597 | ||||||||
\(581\) | 2864.81 | 0.204565 | ||||||||
\(582\) | 1535.39 | 0.109354 | ||||||||
\(583\) | 18440.0 | 1.30996 | ||||||||
\(584\) | 4208.65 | 0.298211 | ||||||||
\(585\) | 2111.48 | 0.149229 | ||||||||
\(586\) | −2198.64 | −0.154991 | ||||||||
\(587\) | 17794.4 | 1.25120 | 0.625600 | − | 0.780144i | \(-0.284854\pi\) | ||||
0.625600 | + | 0.780144i | \(0.284854\pi\) | |||||||
\(588\) | −588.000 | −0.0412393 | ||||||||
\(589\) | −5593.08 | −0.391271 | ||||||||
\(590\) | 1532.28 | 0.106920 | ||||||||
\(591\) | 6305.26 | 0.438856 | ||||||||
\(592\) | −2701.81 | −0.187574 | ||||||||
\(593\) | −27738.6 | −1.92089 | −0.960444 | − | 0.278474i | \(-0.910171\pi\) | ||||
−0.960444 | + | 0.278474i | \(0.910171\pi\) | |||||||
\(594\) | −2323.88 | −0.160522 | ||||||||
\(595\) | −835.681 | −0.0575791 | ||||||||
\(596\) | 286.720 | 0.0197055 | ||||||||
\(597\) | −9685.32 | −0.663976 | ||||||||
\(598\) | −2239.49 | −0.153143 | ||||||||
\(599\) | 2927.43 | 0.199686 | 0.0998428 | − | 0.995003i | \(-0.468166\pi\) | ||||
0.0998428 | + | 0.995003i | \(0.468166\pi\) | |||||||
\(600\) | 2442.66 | 0.166202 | ||||||||
\(601\) | −9902.60 | −0.672106 | −0.336053 | − | 0.941843i | \(-0.609092\pi\) | ||||
−0.336053 | + | 0.941843i | \(0.609092\pi\) | |||||||
\(602\) | 3568.28 | 0.241582 | ||||||||
\(603\) | 7175.12 | 0.484567 | ||||||||
\(604\) | −5147.98 | −0.346802 | ||||||||
\(605\) | 2510.69 | 0.168717 | ||||||||
\(606\) | −4359.29 | −0.292218 | ||||||||
\(607\) | 4754.02 | 0.317891 | 0.158946 | − | 0.987287i | \(-0.449191\pi\) | ||||
0.158946 | + | 0.987287i | \(0.449191\pi\) | |||||||
\(608\) | 2023.93 | 0.135002 | ||||||||
\(609\) | 98.7010 | 0.00656743 | ||||||||
\(610\) | −272.637 | −0.0180963 | ||||||||
\(611\) | −24984.3 | −1.65426 | ||||||||
\(612\) | −891.847 | −0.0589065 | ||||||||
\(613\) | −24542.3 | −1.61706 | −0.808529 | − | 0.588457i | \(-0.799736\pi\) | ||||
−0.808529 | + | 0.588457i | \(0.799736\pi\) | |||||||
\(614\) | −7172.88 | −0.471456 | ||||||||
\(615\) | −6733.31 | −0.441485 | ||||||||
\(616\) | 2409.95 | 0.157630 | ||||||||
\(617\) | 24061.2 | 1.56996 | 0.784981 | − | 0.619520i | \(-0.212673\pi\) | ||||
0.784981 | + | 0.619520i | \(0.212673\pi\) | |||||||
\(618\) | −3738.73 | −0.243355 | ||||||||
\(619\) | 668.751 | 0.0434239 | 0.0217119 | − | 0.999764i | \(-0.493088\pi\) | ||||
0.0217119 | + | 0.999764i | \(0.493088\pi\) | |||||||
\(620\) | −1704.59 | −0.110416 | ||||||||
\(621\) | 621.000 | 0.0401286 | ||||||||
\(622\) | 2542.49 | 0.163898 | ||||||||
\(623\) | 6222.66 | 0.400170 | ||||||||
\(624\) | −2336.85 | −0.149918 | ||||||||
\(625\) | 7455.84 | 0.477174 | ||||||||
\(626\) | −15004.9 | −0.958013 | ||||||||
\(627\) | −8165.60 | −0.520100 | ||||||||
\(628\) | −6083.61 | −0.386564 | ||||||||
\(629\) | 4183.33 | 0.265183 | ||||||||
\(630\) | 607.191 | 0.0383985 | ||||||||
\(631\) | −22237.5 | −1.40295 | −0.701476 | − | 0.712693i | \(-0.747475\pi\) | ||||
−0.701476 | + | 0.712693i | \(0.747475\pi\) | |||||||
\(632\) | −864.197 | −0.0543923 | ||||||||
\(633\) | 8069.94 | 0.506716 | ||||||||
\(634\) | −15156.9 | −0.949459 | ||||||||
\(635\) | −7334.70 | −0.458376 | ||||||||
\(636\) | −5141.87 | −0.320579 | ||||||||
\(637\) | 2385.54 | 0.148381 | ||||||||
\(638\) | −404.532 | −0.0251028 | ||||||||
\(639\) | −7005.80 | −0.433717 | ||||||||
\(640\) | 616.829 | 0.0380973 | ||||||||
\(641\) | −6268.56 | −0.386261 | −0.193131 | − | 0.981173i | \(-0.561864\pi\) | ||||
−0.193131 | + | 0.981173i | \(0.561864\pi\) | |||||||
\(642\) | 204.058 | 0.0125444 | ||||||||
\(643\) | −3657.99 | −0.224350 | −0.112175 | − | 0.993688i | \(-0.535782\pi\) | ||||
−0.112175 | + | 0.993688i | \(0.535782\pi\) | |||||||
\(644\) | −644.000 | −0.0394055 | ||||||||
\(645\) | −3684.73 | −0.224940 | ||||||||
\(646\) | −3133.75 | −0.190860 | ||||||||
\(647\) | 29876.0 | 1.81537 | 0.907687 | − | 0.419647i | \(-0.137846\pi\) | ||||
0.907687 | + | 0.419647i | \(0.137846\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | 6841.84 | 0.413815 | ||||||||
\(650\) | −9909.96 | −0.598001 | ||||||||
\(651\) | 1857.05 | 0.111803 | ||||||||
\(652\) | 10517.4 | 0.631736 | ||||||||
\(653\) | −15406.4 | −0.923274 | −0.461637 | − | 0.887069i | \(-0.652738\pi\) | ||||
−0.461637 | + | 0.887069i | \(0.652738\pi\) | |||||||
\(654\) | 1063.24 | 0.0635721 | ||||||||
\(655\) | 12206.7 | 0.728175 | ||||||||
\(656\) | 7452.00 | 0.443524 | ||||||||
\(657\) | 4734.73 | 0.281156 | ||||||||
\(658\) | −7184.63 | −0.425663 | ||||||||
\(659\) | 11969.6 | 0.707543 | 0.353772 | − | 0.935332i | \(-0.384899\pi\) | ||||
0.353772 | + | 0.935332i | \(0.384899\pi\) | |||||||
\(660\) | −2488.61 | −0.146771 | ||||||||
\(661\) | 19192.9 | 1.12938 | 0.564688 | − | 0.825304i | \(-0.308996\pi\) | ||||
0.564688 | + | 0.825304i | \(0.308996\pi\) | |||||||
\(662\) | −10336.7 | −0.606867 | ||||||||
\(663\) | 3618.26 | 0.211948 | ||||||||
\(664\) | 3274.07 | 0.191353 | ||||||||
\(665\) | 2133.53 | 0.124413 | ||||||||
\(666\) | −3039.53 | −0.176846 | ||||||||
\(667\) | 108.101 | 0.00627540 | ||||||||
\(668\) | 1017.67 | 0.0589445 | ||||||||
\(669\) | 7776.74 | 0.449426 | ||||||||
\(670\) | 7683.72 | 0.443057 | ||||||||
\(671\) | −1217.36 | −0.0700385 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | −17503.4 | −1.00253 | −0.501267 | − | 0.865293i | \(-0.667133\pi\) | ||||
−0.501267 | + | 0.865293i | \(0.667133\pi\) | |||||||
\(674\) | −6745.51 | −0.385500 | ||||||||
\(675\) | 2747.99 | 0.156697 | ||||||||
\(676\) | 692.708 | 0.0394121 | ||||||||
\(677\) | −27542.0 | −1.56355 | −0.781776 | − | 0.623560i | \(-0.785686\pi\) | ||||
−0.781776 | + | 0.623560i | \(0.785686\pi\) | |||||||
\(678\) | 6069.91 | 0.343825 | ||||||||
\(679\) | −1791.29 | −0.101242 | ||||||||
\(680\) | −955.064 | −0.0538603 | ||||||||
\(681\) | −16390.3 | −0.922290 | ||||||||
\(682\) | −7611.24 | −0.427345 | ||||||||
\(683\) | 4505.08 | 0.252389 | 0.126195 | − | 0.992005i | \(-0.459724\pi\) | ||||
0.126195 | + | 0.992005i | \(0.459724\pi\) | |||||||
\(684\) | 2276.92 | 0.127281 | ||||||||
\(685\) | 89.6048 | 0.00499799 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | −1991.47 | −0.110596 | ||||||||
\(688\) | 4078.03 | 0.225979 | ||||||||
\(689\) | 20860.8 | 1.15346 | ||||||||
\(690\) | 665.018 | 0.0366910 | ||||||||
\(691\) | −19738.4 | −1.08666 | −0.543332 | − | 0.839518i | \(-0.682838\pi\) | ||||
−0.543332 | + | 0.839518i | \(0.682838\pi\) | |||||||
\(692\) | −5804.97 | −0.318890 | ||||||||
\(693\) | 2711.20 | 0.148615 | ||||||||
\(694\) | 9862.65 | 0.539454 | ||||||||
\(695\) | 12935.4 | 0.705996 | ||||||||
\(696\) | 112.801 | 0.00614327 | ||||||||
\(697\) | −11538.3 | −0.627035 | ||||||||
\(698\) | −16225.4 | −0.879858 | ||||||||
\(699\) | 11885.3 | 0.643123 | ||||||||
\(700\) | −2849.77 | −0.153873 | ||||||||
\(701\) | 16160.7 | 0.870727 | 0.435364 | − | 0.900255i | \(-0.356620\pi\) | ||||
0.435364 | + | 0.900255i | \(0.356620\pi\) | |||||||
\(702\) | −2628.96 | −0.141344 | ||||||||
\(703\) | −10680.2 | −0.572990 | ||||||||
\(704\) | 2754.23 | 0.147449 | ||||||||
\(705\) | 7419.12 | 0.396341 | ||||||||
\(706\) | 3868.18 | 0.206205 | ||||||||
\(707\) | 5085.83 | 0.270541 | ||||||||
\(708\) | −1907.80 | −0.101271 | ||||||||
\(709\) | −19644.9 | −1.04059 | −0.520295 | − | 0.853987i | \(-0.674178\pi\) | ||||
−0.520295 | + | 0.853987i | \(0.674178\pi\) | |||||||
\(710\) | −7502.39 | −0.396563 | ||||||||
\(711\) | −972.222 | −0.0512815 | ||||||||
\(712\) | 7111.62 | 0.374325 | ||||||||
\(713\) | 2033.91 | 0.106831 | ||||||||
\(714\) | 1040.49 | 0.0545368 | ||||||||
\(715\) | 10096.4 | 0.528088 | ||||||||
\(716\) | 5528.08 | 0.288539 | ||||||||
\(717\) | 8975.86 | 0.467517 | ||||||||
\(718\) | −616.334 | −0.0320354 | ||||||||
\(719\) | 8964.56 | 0.464982 | 0.232491 | − | 0.972599i | \(-0.425312\pi\) | ||||
0.232491 | + | 0.972599i | \(0.425312\pi\) | |||||||
\(720\) | 693.932 | 0.0359185 | ||||||||
\(721\) | 4361.85 | 0.225303 | ||||||||
\(722\) | −5717.41 | −0.294709 | ||||||||
\(723\) | 17221.5 | 0.885855 | ||||||||
\(724\) | 3303.67 | 0.169586 | ||||||||
\(725\) | 478.359 | 0.0245046 | ||||||||
\(726\) | −3126.01 | −0.159803 | ||||||||
\(727\) | −10420.1 | −0.531581 | −0.265791 | − | 0.964031i | \(-0.585633\pi\) | ||||
−0.265791 | + | 0.964031i | \(0.585633\pi\) | |||||||
\(728\) | 2726.33 | 0.138797 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 5070.34 | 0.257071 | ||||||||
\(731\) | −6314.20 | −0.319479 | ||||||||
\(732\) | 339.454 | 0.0171401 | ||||||||
\(733\) | −30932.4 | −1.55868 | −0.779341 | − | 0.626600i | \(-0.784446\pi\) | ||||
−0.779341 | + | 0.626600i | \(0.784446\pi\) | |||||||
\(734\) | −13663.6 | −0.687103 | ||||||||
\(735\) | −708.389 | −0.0355501 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 34309.0 | 1.71477 | ||||||||
\(738\) | 8383.50 | 0.418158 | ||||||||
\(739\) | −35846.9 | −1.78437 | −0.892185 | − | 0.451671i | \(-0.850828\pi\) | ||||
−0.892185 | + | 0.451671i | \(0.850828\pi\) | |||||||
\(740\) | −3254.98 | −0.161697 | ||||||||
\(741\) | −9237.57 | −0.457963 | ||||||||
\(742\) | 5998.85 | 0.296799 | ||||||||
\(743\) | −8603.86 | −0.424825 | −0.212412 | − | 0.977180i | \(-0.568132\pi\) | ||||
−0.212412 | + | 0.977180i | \(0.568132\pi\) | |||||||
\(744\) | 2122.34 | 0.104582 | ||||||||
\(745\) | 345.424 | 0.0169870 | ||||||||
\(746\) | −20780.5 | −1.01988 | ||||||||
\(747\) | 3683.33 | 0.180410 | ||||||||
\(748\) | −4264.50 | −0.208457 | ||||||||
\(749\) | −238.067 | −0.0116139 | ||||||||
\(750\) | 6557.01 | 0.319237 | ||||||||
\(751\) | −16424.7 | −0.798065 | −0.399033 | − | 0.916937i | \(-0.630654\pi\) | ||||
−0.399033 | + | 0.916937i | \(0.630654\pi\) | |||||||
\(752\) | −8211.01 | −0.398171 | ||||||||
\(753\) | −4517.78 | −0.218641 | ||||||||
\(754\) | −457.638 | −0.0221037 | ||||||||
\(755\) | −6202.00 | −0.298959 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | 29277.3 | 1.40568 | 0.702842 | − | 0.711346i | \(-0.251914\pi\) | ||||
0.702842 | + | 0.711346i | \(0.251914\pi\) | |||||||
\(758\) | 9053.70 | 0.433833 | ||||||||
\(759\) | 2969.41 | 0.142006 | ||||||||
\(760\) | 2438.32 | 0.116378 | ||||||||
\(761\) | −4987.56 | −0.237580 | −0.118790 | − | 0.992919i | \(-0.537902\pi\) | ||||
−0.118790 | + | 0.992919i | \(0.537902\pi\) | |||||||
\(762\) | 9132.28 | 0.434157 | ||||||||
\(763\) | −1240.45 | −0.0588563 | ||||||||
\(764\) | 6986.01 | 0.330818 | ||||||||
\(765\) | −1074.45 | −0.0507800 | ||||||||
\(766\) | −2543.56 | −0.119977 | ||||||||
\(767\) | 7740.03 | 0.364376 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 23529.1 | 1.10336 | 0.551679 | − | 0.834057i | \(-0.313987\pi\) | ||||
0.551679 | + | 0.834057i | \(0.313987\pi\) | |||||||
\(770\) | 2903.38 | 0.135884 | ||||||||
\(771\) | 17961.9 | 0.839018 | ||||||||
\(772\) | 10368.0 | 0.483360 | ||||||||
\(773\) | 13327.5 | 0.620125 | 0.310063 | − | 0.950716i | \(-0.399650\pi\) | ||||
0.310063 | + | 0.950716i | \(0.399650\pi\) | |||||||
\(774\) | 4587.78 | 0.213055 | ||||||||
\(775\) | 9000.29 | 0.417161 | ||||||||
\(776\) | −2047.19 | −0.0947034 | ||||||||
\(777\) | 3546.12 | 0.163728 | ||||||||
\(778\) | −19911.5 | −0.917561 | ||||||||
\(779\) | 29457.7 | 1.35485 | ||||||||
\(780\) | −2815.31 | −0.129236 | ||||||||
\(781\) | −33499.3 | −1.53483 | ||||||||
\(782\) | 1139.58 | 0.0521117 | ||||||||
\(783\) | 126.901 | 0.00579193 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −7329.19 | −0.333235 | ||||||||
\(786\) | −15198.3 | −0.689701 | ||||||||
\(787\) | 13967.1 | 0.632624 | 0.316312 | − | 0.948655i | \(-0.397555\pi\) | ||||
0.316312 | + | 0.948655i | \(0.397555\pi\) | |||||||
\(788\) | −8407.01 | −0.380060 | ||||||||
\(789\) | 5694.55 | 0.256947 | ||||||||
\(790\) | −1041.14 | −0.0468885 | ||||||||
\(791\) | −7081.56 | −0.318320 | ||||||||
\(792\) | 3098.51 | 0.139016 | ||||||||
\(793\) | −1377.18 | −0.0616709 | ||||||||
\(794\) | 12336.4 | 0.551391 | ||||||||
\(795\) | −6194.63 | −0.276353 | ||||||||
\(796\) | 12913.8 | 0.575020 | ||||||||
\(797\) | 24891.3 | 1.10627 | 0.553133 | − | 0.833093i | \(-0.313432\pi\) | ||||
0.553133 | + | 0.833093i | \(0.313432\pi\) | |||||||
\(798\) | −2656.41 | −0.117840 | ||||||||
\(799\) | 12713.5 | 0.562917 | ||||||||
\(800\) | −3256.88 | −0.143935 | ||||||||
\(801\) | 8000.57 | 0.352917 | ||||||||
\(802\) | −10269.7 | −0.452165 | ||||||||
\(803\) | 22639.8 | 0.994947 | ||||||||
\(804\) | −9566.83 | −0.419647 | ||||||||
\(805\) | −775.855 | −0.0339693 | ||||||||
\(806\) | −8610.43 | −0.376290 | ||||||||
\(807\) | −12951.2 | −0.564935 | ||||||||
\(808\) | 5812.38 | 0.253068 | ||||||||
\(809\) | 44812.2 | 1.94748 | 0.973742 | − | 0.227656i | \(-0.0731061\pi\) | ||||
0.973742 | + | 0.227656i | \(0.0731061\pi\) | |||||||
\(810\) | 780.674 | 0.0338643 | ||||||||
\(811\) | −11709.4 | −0.506994 | −0.253497 | − | 0.967336i | \(-0.581581\pi\) | ||||
−0.253497 | + | 0.967336i | \(0.581581\pi\) | |||||||
\(812\) | −131.601 | −0.00568756 | ||||||||
\(813\) | 17934.8 | 0.773677 | ||||||||
\(814\) | −14534.0 | −0.625818 | ||||||||
\(815\) | 12670.7 | 0.544584 | ||||||||
\(816\) | 1189.13 | 0.0510145 | ||||||||
\(817\) | 16120.4 | 0.690309 | ||||||||
\(818\) | −13611.9 | −0.581819 | ||||||||
\(819\) | 3067.12 | 0.130859 | ||||||||
\(820\) | 8977.75 | 0.382337 | ||||||||
\(821\) | 8677.96 | 0.368895 | 0.184448 | − | 0.982842i | \(-0.440950\pi\) | ||||
0.184448 | + | 0.982842i | \(0.440950\pi\) | |||||||
\(822\) | −111.565 | −0.00473391 | ||||||||
\(823\) | 22764.2 | 0.964169 | 0.482084 | − | 0.876125i | \(-0.339880\pi\) | ||||
0.482084 | + | 0.876125i | \(0.339880\pi\) | |||||||
\(824\) | 4984.97 | 0.210752 | ||||||||
\(825\) | 13139.9 | 0.554514 | ||||||||
\(826\) | 2225.77 | 0.0937585 | ||||||||
\(827\) | −2370.25 | −0.0996634 | −0.0498317 | − | 0.998758i | \(-0.515868\pi\) | ||||
−0.0498317 | + | 0.998758i | \(0.515868\pi\) | |||||||
\(828\) | −828.000 | −0.0347524 | ||||||||
\(829\) | 32978.6 | 1.38166 | 0.690830 | − | 0.723017i | \(-0.257245\pi\) | ||||
0.690830 | + | 0.723017i | \(0.257245\pi\) | |||||||
\(830\) | 3944.42 | 0.164955 | ||||||||
\(831\) | −12637.3 | −0.527536 | ||||||||
\(832\) | 3115.81 | 0.129833 | ||||||||
\(833\) | −1213.90 | −0.0504913 | ||||||||
\(834\) | −16105.6 | −0.668693 | ||||||||
\(835\) | 1226.03 | 0.0508127 | ||||||||
\(836\) | 10887.5 | 0.450420 | ||||||||
\(837\) | 2387.64 | 0.0986008 | ||||||||
\(838\) | 18807.0 | 0.775272 | ||||||||
\(839\) | 21927.5 | 0.902289 | 0.451145 | − | 0.892451i | \(-0.351016\pi\) | ||||
0.451145 | + | 0.892451i | \(0.351016\pi\) | |||||||
\(840\) | −809.588 | −0.0332541 | ||||||||
\(841\) | −24366.9 | −0.999094 | ||||||||
\(842\) | 4306.64 | 0.176267 | ||||||||
\(843\) | −14552.2 | −0.594549 | ||||||||
\(844\) | −10759.9 | −0.438829 | ||||||||
\(845\) | 834.535 | 0.0339750 | ||||||||
\(846\) | −9237.38 | −0.375399 | ||||||||
\(847\) | 3647.01 | 0.147949 | ||||||||
\(848\) | 6855.82 | 0.277630 | ||||||||
\(849\) | −2068.78 | −0.0836282 | ||||||||
\(850\) | 5042.77 | 0.203489 | ||||||||
\(851\) | 3883.85 | 0.156447 | ||||||||
\(852\) | 9341.07 | 0.375610 | ||||||||
\(853\) | −21082.6 | −0.846253 | −0.423126 | − | 0.906071i | \(-0.639067\pi\) | ||||
−0.423126 | + | 0.906071i | \(0.639067\pi\) | |||||||
\(854\) | −396.030 | −0.0158687 | ||||||||
\(855\) | 2743.11 | 0.109722 | ||||||||
\(856\) | −272.077 | −0.0108638 | ||||||||
\(857\) | 34147.1 | 1.36108 | 0.680538 | − | 0.732713i | \(-0.261746\pi\) | ||||
0.680538 | + | 0.732713i | \(0.261746\pi\) | |||||||
\(858\) | −12570.8 | −0.500186 | ||||||||
\(859\) | 15856.5 | 0.629822 | 0.314911 | − | 0.949121i | \(-0.398025\pi\) | ||||
0.314911 | + | 0.949121i | \(0.398025\pi\) | |||||||
\(860\) | 4912.98 | 0.194804 | ||||||||
\(861\) | −9780.75 | −0.387139 | ||||||||
\(862\) | 12693.1 | 0.501542 | ||||||||
\(863\) | −34127.0 | −1.34611 | −0.673057 | − | 0.739590i | \(-0.735019\pi\) | ||||
−0.673057 | + | 0.739590i | \(0.735019\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −6993.50 | −0.274897 | ||||||||
\(866\) | −1437.89 | −0.0564222 | ||||||||
\(867\) | 12897.8 | 0.505228 | ||||||||
\(868\) | −2476.07 | −0.0968240 | ||||||||
\(869\) | −4648.83 | −0.181474 | ||||||||
\(870\) | 135.896 | 0.00529577 | ||||||||
\(871\) | 38813.0 | 1.50991 | ||||||||
\(872\) | −1417.66 | −0.0550551 | ||||||||
\(873\) | −2303.09 | −0.0892872 | ||||||||
\(874\) | −2909.40 | −0.112600 | ||||||||
\(875\) | −7649.84 | −0.295556 | ||||||||
\(876\) | −6312.97 | −0.243488 | ||||||||
\(877\) | 22085.6 | 0.850373 | 0.425187 | − | 0.905106i | \(-0.360208\pi\) | ||||
0.425187 | + | 0.905106i | \(0.360208\pi\) | |||||||
\(878\) | 14954.2 | 0.574806 | ||||||||
\(879\) | 3297.96 | 0.126550 | ||||||||
\(880\) | 3318.14 | 0.127107 | ||||||||
\(881\) | 17543.1 | 0.670876 | 0.335438 | − | 0.942062i | \(-0.391116\pi\) | ||||
0.335438 | + | 0.942062i | \(0.391116\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | 2720.55 | 0.103685 | 0.0518424 | − | 0.998655i | \(-0.483491\pi\) | ||||
0.0518424 | + | 0.998655i | \(0.483491\pi\) | |||||||
\(884\) | −4824.34 | −0.183552 | ||||||||
\(885\) | −2298.41 | −0.0872998 | ||||||||
\(886\) | 25406.1 | 0.963356 | ||||||||
\(887\) | −9800.00 | −0.370972 | −0.185486 | − | 0.982647i | \(-0.559386\pi\) | ||||
−0.185486 | + | 0.982647i | \(0.559386\pi\) | |||||||
\(888\) | 4052.71 | 0.153153 | ||||||||
\(889\) | −10654.3 | −0.401951 | ||||||||
\(890\) | 8567.67 | 0.322684 | ||||||||
\(891\) | 3485.83 | 0.131066 | ||||||||
\(892\) | −10369.0 | −0.389214 | ||||||||
\(893\) | −32458.1 | −1.21631 | ||||||||
\(894\) | −430.080 | −0.0160895 | ||||||||
\(895\) | 6659.92 | 0.248733 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 3359.23 | 0.125041 | ||||||||
\(898\) | 1268.65 | 0.0471441 | ||||||||
\(899\) | 415.630 | 0.0154194 | ||||||||
\(900\) | −3663.99 | −0.135703 | ||||||||
\(901\) | −10615.2 | −0.392500 | ||||||||
\(902\) | 40087.0 | 1.47977 | ||||||||
\(903\) | −5352.41 | −0.197250 | ||||||||
\(904\) | −8093.21 | −0.297761 | ||||||||
\(905\) | 3980.08 | 0.146190 | ||||||||
\(906\) | 7721.97 | 0.283163 | ||||||||
\(907\) | −22361.9 | −0.818650 | −0.409325 | − | 0.912389i | \(-0.634236\pi\) | ||||
−0.409325 | + | 0.912389i | \(0.634236\pi\) | |||||||
\(908\) | 21853.8 | 0.798726 | ||||||||
\(909\) | 6538.93 | 0.238595 | ||||||||
\(910\) | 3284.53 | 0.119649 | ||||||||
\(911\) | 20460.4 | 0.744109 | 0.372055 | − | 0.928211i | \(-0.378653\pi\) | ||||
0.372055 | + | 0.928211i | \(0.378653\pi\) | |||||||
\(912\) | −3035.90 | −0.110229 | ||||||||
\(913\) | 17612.4 | 0.638429 | ||||||||
\(914\) | 3172.83 | 0.114823 | ||||||||
\(915\) | 408.955 | 0.0147756 | ||||||||
\(916\) | 2655.30 | 0.0957790 | ||||||||
\(917\) | 17731.3 | 0.638539 | ||||||||
\(918\) | 1337.77 | 0.0480969 | ||||||||
\(919\) | 24141.2 | 0.866534 | 0.433267 | − | 0.901266i | \(-0.357361\pi\) | ||||
0.433267 | + | 0.901266i | \(0.357361\pi\) | |||||||
\(920\) | −886.691 | −0.0317754 | ||||||||
\(921\) | 10759.3 | 0.384942 | ||||||||
\(922\) | 24549.3 | 0.876884 | ||||||||
\(923\) | −37897.1 | −1.35146 | ||||||||
\(924\) | −3614.93 | −0.128704 | ||||||||
\(925\) | 17186.4 | 0.610905 | ||||||||
\(926\) | −23962.5 | −0.850384 | ||||||||
\(927\) | 5608.09 | 0.198699 | ||||||||
\(928\) | −150.401 | −0.00532023 | ||||||||
\(929\) | −27309.5 | −0.964475 | −0.482237 | − | 0.876041i | \(-0.660176\pi\) | ||||
−0.482237 | + | 0.876041i | \(0.660176\pi\) | |||||||
\(930\) | 2556.88 | 0.0901542 | ||||||||
\(931\) | 3099.15 | 0.109098 | ||||||||
\(932\) | −15847.0 | −0.556961 | ||||||||
\(933\) | −3813.74 | −0.133822 | ||||||||
\(934\) | 9871.02 | 0.345813 | ||||||||
\(935\) | −5137.63 | −0.179699 | ||||||||
\(936\) | 3505.28 | 0.122408 | ||||||||
\(937\) | −47133.7 | −1.64332 | −0.821659 | − | 0.569979i | \(-0.806951\pi\) | ||||
−0.821659 | + | 0.569979i | \(0.806951\pi\) | |||||||
\(938\) | 11161.3 | 0.388518 | ||||||||
\(939\) | 22507.3 | 0.782214 | ||||||||
\(940\) | −9892.16 | −0.343241 | ||||||||
\(941\) | −20018.7 | −0.693508 | −0.346754 | − | 0.937956i | \(-0.612716\pi\) | ||||
−0.346754 | + | 0.937956i | \(0.612716\pi\) | |||||||
\(942\) | 9125.41 | 0.315628 | ||||||||
\(943\) | −10712.3 | −0.369925 | ||||||||
\(944\) | 2543.74 | 0.0877030 | ||||||||
\(945\) | −910.786 | −0.0313522 | ||||||||
\(946\) | 21937.2 | 0.753953 | ||||||||
\(947\) | −5601.37 | −0.192207 | −0.0961035 | − | 0.995371i | \(-0.530638\pi\) | ||||
−0.0961035 | + | 0.995371i | \(0.530638\pi\) | |||||||
\(948\) | 1296.30 | 0.0444111 | ||||||||
\(949\) | 25612.0 | 0.876080 | ||||||||
\(950\) | −12874.4 | −0.439686 | ||||||||
\(951\) | 22735.3 | 0.775230 | ||||||||
\(952\) | −1387.32 | −0.0472303 | ||||||||
\(953\) | 23276.4 | 0.791182 | 0.395591 | − | 0.918427i | \(-0.370540\pi\) | ||||
0.395591 | + | 0.918427i | \(0.370540\pi\) | |||||||
\(954\) | 7712.80 | 0.261752 | ||||||||
\(955\) | 8416.35 | 0.285180 | ||||||||
\(956\) | −11967.8 | −0.404881 | ||||||||
\(957\) | 606.798 | 0.0204963 | ||||||||
\(958\) | −15629.2 | −0.527094 | ||||||||
\(959\) | 130.159 | 0.00438275 | ||||||||
\(960\) | −925.243 | −0.0311063 | ||||||||
\(961\) | −21971.0 | −0.737503 | ||||||||
\(962\) | −16442.0 | −0.551051 | ||||||||
\(963\) | −306.087 | −0.0102425 | ||||||||
\(964\) | −22961.9 | −0.767173 | ||||||||
\(965\) | 12490.8 | 0.416678 | ||||||||
\(966\) | 966.000 | 0.0321745 | ||||||||
\(967\) | 43459.8 | 1.44527 | 0.722634 | − | 0.691231i | \(-0.242931\pi\) | ||||
0.722634 | + | 0.691231i | \(0.242931\pi\) | |||||||
\(968\) | 4168.01 | 0.138393 | ||||||||
\(969\) | 4700.62 | 0.155837 | ||||||||
\(970\) | −2466.34 | −0.0816385 | ||||||||
\(971\) | −53549.4 | −1.76981 | −0.884904 | − | 0.465774i | \(-0.845776\pi\) | ||||
−0.884904 | + | 0.465774i | \(0.845776\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 18789.8 | 0.619090 | ||||||||
\(974\) | −3986.27 | −0.131138 | ||||||||
\(975\) | 14864.9 | 0.488266 | ||||||||
\(976\) | −452.605 | −0.0148438 | ||||||||
\(977\) | 30132.4 | 0.986717 | 0.493358 | − | 0.869826i | \(-0.335769\pi\) | ||||
0.493358 | + | 0.869826i | \(0.335769\pi\) | |||||||
\(978\) | −15776.0 | −0.515810 | ||||||||
\(979\) | 38255.9 | 1.24889 | ||||||||
\(980\) | 944.519 | 0.0307873 | ||||||||
\(981\) | −1594.87 | −0.0519064 | ||||||||
\(982\) | −4139.04 | −0.134503 | ||||||||
\(983\) | 10266.6 | 0.333117 | 0.166558 | − | 0.986032i | \(-0.446735\pi\) | ||||
0.166558 | + | 0.986032i | \(0.446735\pi\) | |||||||
\(984\) | −11178.0 | −0.362136 | ||||||||
\(985\) | −10128.3 | −0.327629 | ||||||||
\(986\) | 232.873 | 0.00752150 | ||||||||
\(987\) | 10776.9 | 0.347552 | ||||||||
\(988\) | 12316.8 | 0.396608 | ||||||||
\(989\) | −5862.17 | −0.188479 | ||||||||
\(990\) | 3732.91 | 0.119838 | ||||||||
\(991\) | −8356.87 | −0.267876 | −0.133938 | − | 0.990990i | \(-0.542762\pi\) | ||||
−0.133938 | + | 0.990990i | \(0.542762\pi\) | |||||||
\(992\) | −2829.79 | −0.0905706 | ||||||||
\(993\) | 15505.0 | 0.495505 | ||||||||
\(994\) | −10897.9 | −0.347747 | ||||||||
\(995\) | 15557.8 | 0.495693 | ||||||||
\(996\) | −4911.11 | −0.156239 | ||||||||
\(997\) | −25381.3 | −0.806254 | −0.403127 | − | 0.915144i | \(-0.632077\pi\) | ||||
−0.403127 | + | 0.915144i | \(0.632077\pi\) | |||||||
\(998\) | −33363.2 | −1.05821 | ||||||||
\(999\) | 4559.30 | 0.144394 |
(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 | 966.4.a.f.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.f.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial |