Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(1,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.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: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 13) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.56155 | 0.552092 | 0.276046 | − | 0.961144i | \(-0.410976\pi\) | ||||
0.276046 | + | 0.961144i | \(0.410976\pi\) | |||||||
\(3\) | 8.68466 | 1.67136 | 0.835682 | − | 0.549214i | \(-0.185073\pi\) | ||||
0.835682 | + | 0.549214i | \(0.185073\pi\) | |||||||
\(4\) | −5.56155 | −0.695194 | ||||||||
\(5\) | 3.56155 | 0.318555 | 0.159277 | − | 0.987234i | \(-0.449084\pi\) | ||||
0.159277 | + | 0.987234i | \(0.449084\pi\) | |||||||
\(6\) | 13.5616 | 0.922747 | ||||||||
\(7\) | 27.1771 | 1.46742 | 0.733712 | − | 0.679460i | \(-0.237786\pi\) | ||||
0.733712 | + | 0.679460i | \(0.237786\pi\) | |||||||
\(8\) | −21.1771 | −0.935904 | ||||||||
\(9\) | 48.4233 | 1.79346 | ||||||||
\(10\) | 5.56155 | 0.175872 | ||||||||
\(11\) | −15.2614 | −0.418316 | −0.209158 | − | 0.977882i | \(-0.567072\pi\) | ||||
−0.209158 | + | 0.977882i | \(0.567072\pi\) | |||||||
\(12\) | −48.3002 | −1.16192 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 42.4384 | 0.810154 | ||||||||
\(15\) | 30.9309 | 0.532421 | ||||||||
\(16\) | 11.4233 | 0.178489 | ||||||||
\(17\) | 44.5464 | 0.635535 | 0.317767 | − | 0.948169i | \(-0.397067\pi\) | ||||
0.317767 | + | 0.948169i | \(0.397067\pi\) | |||||||
\(18\) | 75.6155 | 0.990153 | ||||||||
\(19\) | −23.9697 | −0.289422 | −0.144711 | − | 0.989474i | \(-0.546225\pi\) | ||||
−0.144711 | + | 0.989474i | \(0.546225\pi\) | |||||||
\(20\) | −19.8078 | −0.221458 | ||||||||
\(21\) | 236.024 | 2.45260 | ||||||||
\(22\) | −23.8314 | −0.230949 | ||||||||
\(23\) | 122.739 | 1.11273 | 0.556365 | − | 0.830938i | \(-0.312196\pi\) | ||||
0.556365 | + | 0.830938i | \(0.312196\pi\) | |||||||
\(24\) | −183.916 | −1.56423 | ||||||||
\(25\) | −112.315 | −0.898523 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 186.054 | 1.32615 | ||||||||
\(28\) | −151.147 | −1.02014 | ||||||||
\(29\) | −219.909 | −1.40814 | −0.704071 | − | 0.710130i | \(-0.748636\pi\) | ||||
−0.704071 | + | 0.710130i | \(0.748636\pi\) | |||||||
\(30\) | 48.3002 | 0.293946 | ||||||||
\(31\) | −27.0928 | −0.156968 | −0.0784840 | − | 0.996915i | \(-0.525008\pi\) | ||||
−0.0784840 | + | 0.996915i | \(0.525008\pi\) | |||||||
\(32\) | 187.255 | 1.03445 | ||||||||
\(33\) | −132.540 | −0.699158 | ||||||||
\(34\) | 69.5616 | 0.350874 | ||||||||
\(35\) | 96.7926 | 0.467455 | ||||||||
\(36\) | −269.309 | −1.24680 | ||||||||
\(37\) | −94.1922 | −0.418516 | −0.209258 | − | 0.977860i | \(-0.567105\pi\) | ||||
−0.209258 | + | 0.977860i | \(0.567105\pi\) | |||||||
\(38\) | −37.4299 | −0.159788 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −75.4233 | −0.298137 | ||||||||
\(41\) | 160.354 | 0.610808 | 0.305404 | − | 0.952223i | \(-0.401209\pi\) | ||||
0.305404 | + | 0.952223i | \(0.401209\pi\) | |||||||
\(42\) | 368.563 | 1.35406 | ||||||||
\(43\) | −151.302 | −0.536589 | −0.268295 | − | 0.963337i | \(-0.586460\pi\) | ||||
−0.268295 | + | 0.963337i | \(0.586460\pi\) | |||||||
\(44\) | 84.8769 | 0.290811 | ||||||||
\(45\) | 172.462 | 0.571314 | ||||||||
\(46\) | 191.663 | 0.614329 | ||||||||
\(47\) | −466.948 | −1.44918 | −0.724589 | − | 0.689181i | \(-0.757970\pi\) | ||||
−0.724589 | + | 0.689181i | \(0.757970\pi\) | |||||||
\(48\) | 99.2074 | 0.298320 | ||||||||
\(49\) | 395.594 | 1.15333 | ||||||||
\(50\) | −175.386 | −0.496067 | ||||||||
\(51\) | 386.870 | 1.06221 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −120.847 | −0.313199 | −0.156600 | − | 0.987662i | \(-0.550053\pi\) | ||||
−0.156600 | + | 0.987662i | \(0.550053\pi\) | |||||||
\(54\) | 290.533 | 0.732158 | ||||||||
\(55\) | −54.3542 | −0.133257 | ||||||||
\(56\) | −575.531 | −1.37337 | ||||||||
\(57\) | −208.169 | −0.483730 | ||||||||
\(58\) | −343.400 | −0.777424 | ||||||||
\(59\) | 439.633 | 0.970090 | 0.485045 | − | 0.874489i | \(-0.338803\pi\) | ||||
0.485045 | + | 0.874489i | \(0.338803\pi\) | |||||||
\(60\) | −172.024 | −0.370136 | ||||||||
\(61\) | −137.305 | −0.288198 | −0.144099 | − | 0.989563i | \(-0.546028\pi\) | ||||
−0.144099 | + | 0.989563i | \(0.546028\pi\) | |||||||
\(62\) | −42.3068 | −0.0866609 | ||||||||
\(63\) | 1316.00 | 2.63176 | ||||||||
\(64\) | 201.022 | 0.392621 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −206.968 | −0.386000 | ||||||||
\(67\) | −512.280 | −0.934104 | −0.467052 | − | 0.884230i | \(-0.654684\pi\) | ||||
−0.467052 | + | 0.884230i | \(0.654684\pi\) | |||||||
\(68\) | −247.747 | −0.441820 | ||||||||
\(69\) | 1065.94 | 1.85977 | ||||||||
\(70\) | 151.147 | 0.258078 | ||||||||
\(71\) | −410.719 | −0.686526 | −0.343263 | − | 0.939239i | \(-0.611532\pi\) | ||||
−0.343263 | + | 0.939239i | \(0.611532\pi\) | |||||||
\(72\) | −1025.46 | −1.67850 | ||||||||
\(73\) | 308.004 | 0.493823 | 0.246912 | − | 0.969038i | \(-0.420584\pi\) | ||||
0.246912 | + | 0.969038i | \(0.420584\pi\) | |||||||
\(74\) | −147.086 | −0.231060 | ||||||||
\(75\) | −975.420 | −1.50176 | ||||||||
\(76\) | 133.309 | 0.201205 | ||||||||
\(77\) | −414.759 | −0.613847 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −586.462 | −0.835217 | −0.417608 | − | 0.908627i | \(-0.637132\pi\) | ||||
−0.417608 | + | 0.908627i | \(0.637132\pi\) | |||||||
\(80\) | 40.6847 | 0.0568585 | ||||||||
\(81\) | 308.386 | 0.423027 | ||||||||
\(82\) | 250.401 | 0.337222 | ||||||||
\(83\) | −1354.20 | −1.79088 | −0.895440 | − | 0.445182i | \(-0.853139\pi\) | ||||
−0.895440 | + | 0.445182i | \(0.853139\pi\) | |||||||
\(84\) | −1312.66 | −1.70503 | ||||||||
\(85\) | 158.654 | 0.202453 | ||||||||
\(86\) | −236.266 | −0.296247 | ||||||||
\(87\) | −1909.84 | −2.35352 | ||||||||
\(88\) | 323.191 | 0.391503 | ||||||||
\(89\) | −439.882 | −0.523904 | −0.261952 | − | 0.965081i | \(-0.584366\pi\) | ||||
−0.261952 | + | 0.965081i | \(0.584366\pi\) | |||||||
\(90\) | 269.309 | 0.315418 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −682.617 | −0.773563 | ||||||||
\(93\) | −235.292 | −0.262351 | ||||||||
\(94\) | −729.164 | −0.800080 | ||||||||
\(95\) | −85.3693 | −0.0921969 | ||||||||
\(96\) | 1626.24 | 1.72894 | ||||||||
\(97\) | 1511.27 | 1.58192 | 0.790959 | − | 0.611869i | \(-0.209582\pi\) | ||||
0.790959 | + | 0.611869i | \(0.209582\pi\) | |||||||
\(98\) | 617.740 | 0.636747 | ||||||||
\(99\) | −739.006 | −0.750231 | ||||||||
\(100\) | 624.648 | 0.624648 | ||||||||
\(101\) | 336.260 | 0.331278 | 0.165639 | − | 0.986186i | \(-0.447031\pi\) | ||||
0.165639 | + | 0.986186i | \(0.447031\pi\) | |||||||
\(102\) | 604.118 | 0.586438 | ||||||||
\(103\) | 322.712 | 0.308716 | 0.154358 | − | 0.988015i | \(-0.450669\pi\) | ||||
0.154358 | + | 0.988015i | \(0.450669\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 840.611 | 0.781288 | ||||||||
\(106\) | −188.708 | −0.172915 | ||||||||
\(107\) | 1434.62 | 1.29617 | 0.648083 | − | 0.761570i | \(-0.275571\pi\) | ||||
0.648083 | + | 0.761570i | \(0.275571\pi\) | |||||||
\(108\) | −1034.75 | −0.921933 | ||||||||
\(109\) | −849.147 | −0.746179 | −0.373089 | − | 0.927795i | \(-0.621702\pi\) | ||||
−0.373089 | + | 0.927795i | \(0.621702\pi\) | |||||||
\(110\) | −84.8769 | −0.0735699 | ||||||||
\(111\) | −818.027 | −0.699493 | ||||||||
\(112\) | 310.452 | 0.261919 | ||||||||
\(113\) | 1614.53 | 1.34409 | 0.672044 | − | 0.740511i | \(-0.265417\pi\) | ||||
0.672044 | + | 0.740511i | \(0.265417\pi\) | |||||||
\(114\) | −325.066 | −0.267064 | ||||||||
\(115\) | 437.140 | 0.354465 | ||||||||
\(116\) | 1223.04 | 0.978931 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 686.509 | 0.535579 | ||||||||
\(119\) | 1210.64 | 0.932599 | ||||||||
\(120\) | −655.026 | −0.498295 | ||||||||
\(121\) | −1098.09 | −0.825012 | ||||||||
\(122\) | −214.409 | −0.159112 | ||||||||
\(123\) | 1392.62 | 1.02088 | ||||||||
\(124\) | 150.678 | 0.109123 | ||||||||
\(125\) | −845.211 | −0.604784 | ||||||||
\(126\) | 2055.01 | 1.45297 | ||||||||
\(127\) | 865.174 | 0.604502 | 0.302251 | − | 0.953228i | \(-0.402262\pi\) | ||||
0.302251 | + | 0.953228i | \(0.402262\pi\) | |||||||
\(128\) | −1184.13 | −0.817683 | ||||||||
\(129\) | −1314.01 | −0.896836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −281.400 | −0.187680 | −0.0938400 | − | 0.995587i | \(-0.529914\pi\) | ||||
−0.0938400 | + | 0.995587i | \(0.529914\pi\) | |||||||
\(132\) | 737.127 | 0.486050 | ||||||||
\(133\) | −651.426 | −0.424705 | ||||||||
\(134\) | −799.953 | −0.515712 | ||||||||
\(135\) | 662.641 | 0.422452 | ||||||||
\(136\) | −943.363 | −0.594799 | ||||||||
\(137\) | 2641.43 | 1.64725 | 0.823624 | − | 0.567137i | \(-0.191949\pi\) | ||||
0.823624 | + | 0.567137i | \(0.191949\pi\) | |||||||
\(138\) | 1664.53 | 1.02677 | ||||||||
\(139\) | −1998.64 | −1.21958 | −0.609791 | − | 0.792562i | \(-0.708747\pi\) | ||||
−0.609791 | + | 0.792562i | \(0.708747\pi\) | |||||||
\(140\) | −538.317 | −0.324972 | ||||||||
\(141\) | −4055.28 | −2.42210 | ||||||||
\(142\) | −641.359 | −0.379026 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 553.153 | 0.320112 | ||||||||
\(145\) | −783.218 | −0.448570 | ||||||||
\(146\) | 480.964 | 0.272636 | ||||||||
\(147\) | 3435.60 | 1.92764 | ||||||||
\(148\) | 523.855 | 0.290950 | ||||||||
\(149\) | 1752.98 | 0.963824 | 0.481912 | − | 0.876220i | \(-0.339942\pi\) | ||||
0.481912 | + | 0.876220i | \(0.339942\pi\) | |||||||
\(150\) | −1523.17 | −0.829109 | ||||||||
\(151\) | 2794.64 | 1.50613 | 0.753063 | − | 0.657949i | \(-0.228576\pi\) | ||||
0.753063 | + | 0.657949i | \(0.228576\pi\) | |||||||
\(152\) | 507.608 | 0.270871 | ||||||||
\(153\) | 2157.08 | 1.13980 | ||||||||
\(154\) | −647.669 | −0.338900 | ||||||||
\(155\) | −96.4924 | −0.0500030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3244.87 | 1.64949 | 0.824743 | − | 0.565508i | \(-0.191320\pi\) | ||||
0.824743 | + | 0.565508i | \(0.191320\pi\) | |||||||
\(158\) | −915.792 | −0.461117 | ||||||||
\(159\) | −1049.51 | −0.523470 | ||||||||
\(160\) | 666.918 | 0.329528 | ||||||||
\(161\) | 3335.68 | 1.63285 | ||||||||
\(162\) | 481.562 | 0.233550 | ||||||||
\(163\) | −3281.47 | −1.57684 | −0.788418 | − | 0.615139i | \(-0.789100\pi\) | ||||
−0.788418 | + | 0.615139i | \(0.789100\pi\) | |||||||
\(164\) | −891.818 | −0.424630 | ||||||||
\(165\) | −472.047 | −0.222720 | ||||||||
\(166\) | −2114.66 | −0.988731 | ||||||||
\(167\) | 3126.52 | 1.44873 | 0.724364 | − | 0.689418i | \(-0.242134\pi\) | ||||
0.724364 | + | 0.689418i | \(0.242134\pi\) | |||||||
\(168\) | −4998.29 | −2.29540 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 247.747 | 0.111773 | ||||||||
\(171\) | −1160.69 | −0.519066 | ||||||||
\(172\) | 841.474 | 0.373034 | ||||||||
\(173\) | 97.5698 | 0.0428792 | 0.0214396 | − | 0.999770i | \(-0.493175\pi\) | ||||
0.0214396 | + | 0.999770i | \(0.493175\pi\) | |||||||
\(174\) | −2982.31 | −1.29936 | ||||||||
\(175\) | −3052.40 | −1.31851 | ||||||||
\(176\) | −174.335 | −0.0746648 | ||||||||
\(177\) | 3818.06 | 1.62137 | ||||||||
\(178\) | −686.900 | −0.289243 | ||||||||
\(179\) | −34.7150 | −0.0144956 | −0.00724782 | − | 0.999974i | \(-0.502307\pi\) | ||||
−0.00724782 | + | 0.999974i | \(0.502307\pi\) | |||||||
\(180\) | −959.157 | −0.397174 | ||||||||
\(181\) | −1229.35 | −0.504843 | −0.252422 | − | 0.967617i | \(-0.581227\pi\) | ||||
−0.252422 | + | 0.967617i | \(0.581227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1192.45 | −0.481684 | ||||||||
\(184\) | −2599.25 | −1.04141 | ||||||||
\(185\) | −335.471 | −0.133320 | ||||||||
\(186\) | −367.420 | −0.144842 | ||||||||
\(187\) | −679.839 | −0.265854 | ||||||||
\(188\) | 2596.96 | 1.00746 | ||||||||
\(189\) | 5056.40 | 1.94603 | ||||||||
\(190\) | −133.309 | −0.0509012 | ||||||||
\(191\) | 4280.80 | 1.62172 | 0.810858 | − | 0.585243i | \(-0.199001\pi\) | ||||
0.810858 | + | 0.585243i | \(0.199001\pi\) | |||||||
\(192\) | 1745.81 | 0.656212 | ||||||||
\(193\) | −472.320 | −0.176157 | −0.0880786 | − | 0.996114i | \(-0.528073\pi\) | ||||
−0.0880786 | + | 0.996114i | \(0.528073\pi\) | |||||||
\(194\) | 2359.93 | 0.873365 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2200.12 | −0.801791 | ||||||||
\(197\) | 4484.37 | 1.62182 | 0.810908 | − | 0.585173i | \(-0.198974\pi\) | ||||
0.810908 | + | 0.585173i | \(0.198974\pi\) | |||||||
\(198\) | −1154.00 | −0.414197 | ||||||||
\(199\) | −366.240 | −0.130463 | −0.0652314 | − | 0.997870i | \(-0.520779\pi\) | ||||
−0.0652314 | + | 0.997870i | \(0.520779\pi\) | |||||||
\(200\) | 2378.51 | 0.840931 | ||||||||
\(201\) | −4448.98 | −1.56123 | ||||||||
\(202\) | 525.087 | 0.182896 | ||||||||
\(203\) | −5976.49 | −2.06634 | ||||||||
\(204\) | −2151.60 | −0.738442 | ||||||||
\(205\) | 571.110 | 0.194576 | ||||||||
\(206\) | 503.932 | 0.170440 | ||||||||
\(207\) | 5943.41 | 1.99563 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 365.810 | 0.121070 | ||||||||
\(210\) | 1312.66 | 0.431343 | ||||||||
\(211\) | 2122.55 | 0.692524 | 0.346262 | − | 0.938138i | \(-0.387451\pi\) | ||||
0.346262 | + | 0.938138i | \(0.387451\pi\) | |||||||
\(212\) | 672.095 | 0.217734 | ||||||||
\(213\) | −3566.95 | −1.14743 | ||||||||
\(214\) | 2240.23 | 0.715603 | ||||||||
\(215\) | −538.870 | −0.170933 | ||||||||
\(216\) | −3940.08 | −1.24115 | ||||||||
\(217\) | −736.303 | −0.230339 | ||||||||
\(218\) | −1325.99 | −0.411960 | ||||||||
\(219\) | 2674.91 | 0.825358 | ||||||||
\(220\) | 302.294 | 0.0926392 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1277.39 | −0.386185 | ||||||||
\(223\) | 5926.42 | 1.77965 | 0.889826 | − | 0.456301i | \(-0.150826\pi\) | ||||
0.889826 | + | 0.456301i | \(0.150826\pi\) | |||||||
\(224\) | 5089.04 | 1.51797 | ||||||||
\(225\) | −5438.68 | −1.61146 | ||||||||
\(226\) | 2521.17 | 0.742060 | ||||||||
\(227\) | 895.661 | 0.261881 | 0.130941 | − | 0.991390i | \(-0.458200\pi\) | ||||
0.130941 | + | 0.991390i | \(0.458200\pi\) | |||||||
\(228\) | 1157.74 | 0.336286 | ||||||||
\(229\) | −627.717 | −0.181138 | −0.0905692 | − | 0.995890i | \(-0.528869\pi\) | ||||
−0.0905692 | + | 0.995890i | \(0.528869\pi\) | |||||||
\(230\) | 682.617 | 0.195698 | ||||||||
\(231\) | −3602.04 | −1.02596 | ||||||||
\(232\) | 4657.03 | 1.31788 | ||||||||
\(233\) | 2303.72 | 0.647734 | 0.323867 | − | 0.946103i | \(-0.395017\pi\) | ||||
0.323867 | + | 0.946103i | \(0.395017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1663.06 | −0.461643 | ||||||||
\(236\) | −2445.04 | −0.674401 | ||||||||
\(237\) | −5093.22 | −1.39595 | ||||||||
\(238\) | 1890.48 | 0.514881 | ||||||||
\(239\) | −544.622 | −0.147400 | −0.0737001 | − | 0.997280i | \(-0.523481\pi\) | ||||
−0.0737001 | + | 0.997280i | \(0.523481\pi\) | |||||||
\(240\) | 353.332 | 0.0950313 | ||||||||
\(241\) | −5426.10 | −1.45031 | −0.725157 | − | 0.688584i | \(-0.758233\pi\) | ||||
−0.725157 | + | 0.688584i | \(0.758233\pi\) | |||||||
\(242\) | −1714.73 | −0.455483 | ||||||||
\(243\) | −2345.23 | −0.619121 | ||||||||
\(244\) | 763.629 | 0.200354 | ||||||||
\(245\) | 1408.93 | 0.367400 | ||||||||
\(246\) | 2174.65 | 0.563621 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 573.746 | 0.146907 | ||||||||
\(249\) | −11760.8 | −2.99321 | ||||||||
\(250\) | −1319.84 | −0.333897 | ||||||||
\(251\) | −5221.22 | −1.31299 | −0.656494 | − | 0.754331i | \(-0.727961\pi\) | ||||
−0.656494 | + | 0.754331i | \(0.727961\pi\) | |||||||
\(252\) | −7319.02 | −1.82958 | ||||||||
\(253\) | −1873.16 | −0.465472 | ||||||||
\(254\) | 1351.02 | 0.333741 | ||||||||
\(255\) | 1377.86 | 0.338372 | ||||||||
\(256\) | −3457.26 | −0.844057 | ||||||||
\(257\) | 658.206 | 0.159758 | 0.0798789 | − | 0.996805i | \(-0.474547\pi\) | ||||
0.0798789 | + | 0.996805i | \(0.474547\pi\) | |||||||
\(258\) | −2051.89 | −0.495136 | ||||||||
\(259\) | −2559.87 | −0.614141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10648.7 | −2.52544 | ||||||||
\(262\) | −439.422 | −0.103617 | ||||||||
\(263\) | 3246.45 | 0.761160 | 0.380580 | − | 0.924748i | \(-0.375724\pi\) | ||||
0.380580 | + | 0.924748i | \(0.375724\pi\) | |||||||
\(264\) | 2806.81 | 0.654344 | ||||||||
\(265\) | −430.401 | −0.0997711 | ||||||||
\(266\) | −1017.24 | −0.234477 | ||||||||
\(267\) | −3820.23 | −0.875634 | ||||||||
\(268\) | 2849.07 | 0.649384 | ||||||||
\(269\) | −2585.80 | −0.586093 | −0.293047 | − | 0.956098i | \(-0.594669\pi\) | ||||
−0.293047 | + | 0.956098i | \(0.594669\pi\) | |||||||
\(270\) | 1034.75 | 0.233233 | ||||||||
\(271\) | −988.933 | −0.221673 | −0.110836 | − | 0.993839i | \(-0.535353\pi\) | ||||
−0.110836 | + | 0.993839i | \(0.535353\pi\) | |||||||
\(272\) | 508.867 | 0.113436 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4124.74 | 0.909433 | ||||||||
\(275\) | 1714.09 | 0.375866 | ||||||||
\(276\) | −5928.30 | −1.29290 | ||||||||
\(277\) | 8142.40 | 1.76617 | 0.883086 | − | 0.469211i | \(-0.155462\pi\) | ||||
0.883086 | + | 0.469211i | \(0.155462\pi\) | |||||||
\(278\) | −3120.97 | −0.673322 | ||||||||
\(279\) | −1311.92 | −0.281515 | ||||||||
\(280\) | −2049.78 | −0.437493 | ||||||||
\(281\) | −1534.21 | −0.325705 | −0.162853 | − | 0.986650i | \(-0.552070\pi\) | ||||
−0.162853 | + | 0.986650i | \(0.552070\pi\) | |||||||
\(282\) | −6332.54 | −1.33722 | ||||||||
\(283\) | −6965.00 | −1.46299 | −0.731495 | − | 0.681847i | \(-0.761177\pi\) | ||||
−0.731495 | + | 0.681847i | \(0.761177\pi\) | |||||||
\(284\) | 2284.23 | 0.477269 | ||||||||
\(285\) | −741.403 | −0.154095 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4357.96 | 0.896314 | ||||||||
\(288\) | 9067.49 | 1.85523 | ||||||||
\(289\) | −2928.62 | −0.596096 | ||||||||
\(290\) | −1223.04 | −0.247652 | ||||||||
\(291\) | 13124.9 | 2.64396 | ||||||||
\(292\) | −1712.98 | −0.343303 | ||||||||
\(293\) | −640.029 | −0.127614 | −0.0638070 | − | 0.997962i | \(-0.520324\pi\) | ||||
−0.0638070 | + | 0.997962i | \(0.520324\pi\) | |||||||
\(294\) | 5364.87 | 1.06424 | ||||||||
\(295\) | 1565.77 | 0.309027 | ||||||||
\(296\) | 1994.72 | 0.391691 | ||||||||
\(297\) | −2839.44 | −0.554750 | ||||||||
\(298\) | 2737.37 | 0.532120 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5424.85 | 1.04401 | ||||||||
\(301\) | −4111.95 | −0.787404 | ||||||||
\(302\) | 4363.99 | 0.831520 | ||||||||
\(303\) | 2920.30 | 0.553686 | ||||||||
\(304\) | −273.813 | −0.0516587 | ||||||||
\(305\) | −489.019 | −0.0918070 | ||||||||
\(306\) | 3368.40 | 0.629276 | ||||||||
\(307\) | 100.406 | 0.0186660 | 0.00933299 | − | 0.999956i | \(-0.497029\pi\) | ||||
0.00933299 | + | 0.999956i | \(0.497029\pi\) | |||||||
\(308\) | 2306.71 | 0.426743 | ||||||||
\(309\) | 2802.64 | 0.515977 | ||||||||
\(310\) | −150.678 | −0.0276062 | ||||||||
\(311\) | −3878.92 | −0.707245 | −0.353623 | − | 0.935388i | \(-0.615050\pi\) | ||||
−0.353623 | + | 0.935388i | \(0.615050\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3789.39 | −0.684311 | −0.342155 | − | 0.939643i | \(-0.611157\pi\) | ||||
−0.342155 | + | 0.939643i | \(0.611157\pi\) | |||||||
\(314\) | 5067.04 | 0.910668 | ||||||||
\(315\) | 4687.02 | 0.838360 | ||||||||
\(316\) | 3261.64 | 0.580638 | ||||||||
\(317\) | −4406.81 | −0.780791 | −0.390396 | − | 0.920647i | \(-0.627662\pi\) | ||||
−0.390396 | + | 0.920647i | \(0.627662\pi\) | |||||||
\(318\) | −1638.87 | −0.289004 | ||||||||
\(319\) | 3356.11 | 0.589048 | ||||||||
\(320\) | 715.950 | 0.125071 | ||||||||
\(321\) | 12459.2 | 2.16636 | ||||||||
\(322\) | 5208.84 | 0.901482 | ||||||||
\(323\) | −1067.76 | −0.183938 | ||||||||
\(324\) | −1715.11 | −0.294086 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5124.19 | −0.870559 | ||||||||
\(327\) | −7374.55 | −1.24714 | ||||||||
\(328\) | −3395.83 | −0.571657 | ||||||||
\(329\) | −12690.3 | −2.12656 | ||||||||
\(330\) | −737.127 | −0.122962 | ||||||||
\(331\) | 4131.49 | 0.686064 | 0.343032 | − | 0.939324i | \(-0.388546\pi\) | ||||
0.343032 | + | 0.939324i | \(0.388546\pi\) | |||||||
\(332\) | 7531.47 | 1.24501 | ||||||||
\(333\) | −4561.10 | −0.750591 | ||||||||
\(334\) | 4882.23 | 0.799831 | ||||||||
\(335\) | −1824.51 | −0.297564 | ||||||||
\(336\) | 2696.17 | 0.437762 | ||||||||
\(337\) | −4560.82 | −0.737221 | −0.368611 | − | 0.929584i | \(-0.620166\pi\) | ||||
−0.368611 | + | 0.929584i | \(0.620166\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14021.6 | 2.24646 | ||||||||
\(340\) | −882.365 | −0.140744 | ||||||||
\(341\) | 413.473 | 0.0656622 | ||||||||
\(342\) | −1812.48 | −0.286572 | ||||||||
\(343\) | 1429.34 | 0.225007 | ||||||||
\(344\) | 3204.14 | 0.502196 | ||||||||
\(345\) | 3796.41 | 0.592441 | ||||||||
\(346\) | 152.360 | 0.0236733 | ||||||||
\(347\) | 10069.4 | 1.55779 | 0.778896 | − | 0.627153i | \(-0.215780\pi\) | ||||
0.778896 | + | 0.627153i | \(0.215780\pi\) | |||||||
\(348\) | 10621.6 | 1.63615 | ||||||||
\(349\) | −5879.32 | −0.901757 | −0.450878 | − | 0.892585i | \(-0.648889\pi\) | ||||
−0.450878 | + | 0.892585i | \(0.648889\pi\) | |||||||
\(350\) | −4766.49 | −0.727942 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2857.76 | −0.432725 | ||||||||
\(353\) | 9142.56 | 1.37850 | 0.689249 | − | 0.724525i | \(-0.257941\pi\) | ||||
0.689249 | + | 0.724525i | \(0.257941\pi\) | |||||||
\(354\) | 5962.10 | 0.895147 | ||||||||
\(355\) | −1462.80 | −0.218696 | ||||||||
\(356\) | 2446.43 | 0.364215 | ||||||||
\(357\) | 10514.0 | 1.55871 | ||||||||
\(358\) | −54.2093 | −0.00800293 | ||||||||
\(359\) | 2754.32 | 0.404924 | 0.202462 | − | 0.979290i | \(-0.435106\pi\) | ||||
0.202462 | + | 0.979290i | \(0.435106\pi\) | |||||||
\(360\) | −3652.24 | −0.534695 | ||||||||
\(361\) | −6284.45 | −0.916235 | ||||||||
\(362\) | −1919.69 | −0.278720 | ||||||||
\(363\) | −9536.54 | −1.37889 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1096.97 | 0.157310 | ||||||||
\(366\) | −1862.07 | −0.265934 | ||||||||
\(367\) | 3040.19 | 0.432416 | 0.216208 | − | 0.976347i | \(-0.430631\pi\) | ||||
0.216208 | + | 0.976347i | \(0.430631\pi\) | |||||||
\(368\) | 1402.08 | 0.198610 | ||||||||
\(369\) | 7764.88 | 1.09546 | ||||||||
\(370\) | −523.855 | −0.0736052 | ||||||||
\(371\) | −3284.26 | −0.459596 | ||||||||
\(372\) | 1308.59 | 0.182385 | ||||||||
\(373\) | −5384.72 | −0.747481 | −0.373740 | − | 0.927533i | \(-0.621925\pi\) | ||||
−0.373740 | + | 0.927533i | \(0.621925\pi\) | |||||||
\(374\) | −1061.60 | −0.146776 | ||||||||
\(375\) | −7340.37 | −1.01081 | ||||||||
\(376\) | 9888.59 | 1.35629 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 7895.84 | 1.07439 | ||||||||
\(379\) | 3424.27 | 0.464097 | 0.232049 | − | 0.972704i | \(-0.425457\pi\) | ||||
0.232049 | + | 0.972704i | \(0.425457\pi\) | |||||||
\(380\) | 474.786 | 0.0640948 | ||||||||
\(381\) | 7513.74 | 1.01034 | ||||||||
\(382\) | 6684.69 | 0.895336 | ||||||||
\(383\) | 382.985 | 0.0510956 | 0.0255478 | − | 0.999674i | \(-0.491867\pi\) | ||||
0.0255478 | + | 0.999674i | \(0.491867\pi\) | |||||||
\(384\) | −10283.8 | −1.36665 | ||||||||
\(385\) | −1477.19 | −0.195544 | ||||||||
\(386\) | −737.553 | −0.0972551 | ||||||||
\(387\) | −7326.54 | −0.962349 | ||||||||
\(388\) | −8405.00 | −1.09974 | ||||||||
\(389\) | 8588.34 | 1.11940 | 0.559699 | − | 0.828696i | \(-0.310917\pi\) | ||||
0.559699 | + | 0.828696i | \(0.310917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5467.56 | 0.707178 | ||||||||
\(392\) | −8377.52 | −1.07941 | ||||||||
\(393\) | −2443.87 | −0.313681 | ||||||||
\(394\) | 7002.57 | 0.895392 | ||||||||
\(395\) | −2088.72 | −0.266063 | ||||||||
\(396\) | 4110.02 | 0.521556 | ||||||||
\(397\) | 7239.16 | 0.915171 | 0.457586 | − | 0.889166i | \(-0.348714\pi\) | ||||
0.457586 | + | 0.889166i | \(0.348714\pi\) | |||||||
\(398\) | −571.904 | −0.0720275 | ||||||||
\(399\) | −5657.41 | −0.709837 | ||||||||
\(400\) | −1283.01 | −0.160376 | ||||||||
\(401\) | −4269.62 | −0.531708 | −0.265854 | − | 0.964013i | \(-0.585654\pi\) | ||||
−0.265854 | + | 0.964013i | \(0.585654\pi\) | |||||||
\(402\) | −6947.32 | −0.861942 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1870.12 | −0.230302 | ||||||||
\(405\) | 1098.33 | 0.134757 | ||||||||
\(406\) | −9332.60 | −1.14081 | ||||||||
\(407\) | 1437.50 | 0.175072 | ||||||||
\(408\) | −8192.78 | −0.994125 | ||||||||
\(409\) | −13562.5 | −1.63967 | −0.819834 | − | 0.572602i | \(-0.805934\pi\) | ||||
−0.819834 | + | 0.572602i | \(0.805934\pi\) | |||||||
\(410\) | 891.818 | 0.107424 | ||||||||
\(411\) | 22939.9 | 2.75315 | ||||||||
\(412\) | −1794.78 | −0.214618 | ||||||||
\(413\) | 11947.9 | 1.42353 | ||||||||
\(414\) | 9280.95 | 1.10177 | ||||||||
\(415\) | −4823.06 | −0.570494 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17357.5 | −2.03837 | ||||||||
\(418\) | 571.232 | 0.0668418 | ||||||||
\(419\) | −14576.9 | −1.69959 | −0.849794 | − | 0.527114i | \(-0.823274\pi\) | ||||
−0.849794 | + | 0.527114i | \(0.823274\pi\) | |||||||
\(420\) | −4675.10 | −0.543147 | ||||||||
\(421\) | −15848.4 | −1.83469 | −0.917343 | − | 0.398099i | \(-0.869670\pi\) | ||||
−0.917343 | + | 0.398099i | \(0.869670\pi\) | |||||||
\(422\) | 3314.48 | 0.382337 | ||||||||
\(423\) | −22611.2 | −2.59904 | ||||||||
\(424\) | 2559.18 | 0.293124 | ||||||||
\(425\) | −5003.24 | −0.571042 | ||||||||
\(426\) | −5569.98 | −0.633490 | ||||||||
\(427\) | −3731.55 | −0.422909 | ||||||||
\(428\) | −7978.70 | −0.901087 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −841.474 | −0.0943709 | ||||||||
\(431\) | −10694.7 | −1.19524 | −0.597618 | − | 0.801781i | \(-0.703886\pi\) | ||||
−0.597618 | + | 0.801781i | \(0.703886\pi\) | |||||||
\(432\) | 2125.35 | 0.236703 | ||||||||
\(433\) | −16079.0 | −1.78454 | −0.892272 | − | 0.451498i | \(-0.850890\pi\) | ||||
−0.892272 | + | 0.451498i | \(0.850890\pi\) | |||||||
\(434\) | −1149.78 | −0.127168 | ||||||||
\(435\) | −6801.98 | −0.749724 | ||||||||
\(436\) | 4722.57 | 0.518739 | ||||||||
\(437\) | −2942.01 | −0.322049 | ||||||||
\(438\) | 4177.01 | 0.455674 | ||||||||
\(439\) | 6035.80 | 0.656203 | 0.328101 | − | 0.944643i | \(-0.393591\pi\) | ||||
0.328101 | + | 0.944643i | \(0.393591\pi\) | |||||||
\(440\) | 1151.06 | 0.124715 | ||||||||
\(441\) | 19156.0 | 2.06845 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10201.3 | 1.09409 | 0.547043 | − | 0.837105i | \(-0.315753\pi\) | ||||
0.547043 | + | 0.837105i | \(0.315753\pi\) | |||||||
\(444\) | 4549.50 | 0.486283 | ||||||||
\(445\) | −1566.66 | −0.166892 | ||||||||
\(446\) | 9254.41 | 0.982532 | ||||||||
\(447\) | 15224.0 | 1.61090 | ||||||||
\(448\) | 5463.19 | 0.576141 | ||||||||
\(449\) | 5822.54 | 0.611988 | 0.305994 | − | 0.952033i | \(-0.401011\pi\) | ||||
0.305994 | + | 0.952033i | \(0.401011\pi\) | |||||||
\(450\) | −8492.78 | −0.889675 | ||||||||
\(451\) | −2447.22 | −0.255511 | ||||||||
\(452\) | −8979.27 | −0.934402 | ||||||||
\(453\) | 24270.5 | 2.51728 | ||||||||
\(454\) | 1398.62 | 0.144583 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4408.40 | 0.452724 | ||||||||
\(457\) | −4621.60 | −0.473062 | −0.236531 | − | 0.971624i | \(-0.576010\pi\) | ||||
−0.236531 | + | 0.971624i | \(0.576010\pi\) | |||||||
\(458\) | −980.213 | −0.100005 | ||||||||
\(459\) | 8288.03 | 0.842816 | ||||||||
\(460\) | −2431.18 | −0.246422 | ||||||||
\(461\) | −5127.77 | −0.518056 | −0.259028 | − | 0.965870i | \(-0.583402\pi\) | ||||
−0.259028 | + | 0.965870i | \(0.583402\pi\) | |||||||
\(462\) | −5624.78 | −0.566425 | ||||||||
\(463\) | −6486.27 | −0.651064 | −0.325532 | − | 0.945531i | \(-0.605543\pi\) | ||||
−0.325532 | + | 0.945531i | \(0.605543\pi\) | |||||||
\(464\) | −2512.09 | −0.251338 | ||||||||
\(465\) | −838.004 | −0.0835731 | ||||||||
\(466\) | 3597.39 | 0.357609 | ||||||||
\(467\) | 12978.0 | 1.28598 | 0.642990 | − | 0.765875i | \(-0.277694\pi\) | ||||
0.642990 | + | 0.765875i | \(0.277694\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13922.3 | −1.37073 | ||||||||
\(470\) | −2596.96 | −0.254869 | ||||||||
\(471\) | 28180.6 | 2.75689 | ||||||||
\(472\) | −9310.13 | −0.907910 | ||||||||
\(473\) | 2309.08 | 0.224464 | ||||||||
\(474\) | −7953.34 | −0.770694 | ||||||||
\(475\) | 2692.16 | 0.260053 | ||||||||
\(476\) | −6733.04 | −0.648337 | ||||||||
\(477\) | −5851.79 | −0.561709 | ||||||||
\(478\) | −850.456 | −0.0813786 | ||||||||
\(479\) | 5808.96 | 0.554109 | 0.277055 | − | 0.960854i | \(-0.410642\pi\) | ||||
0.277055 | + | 0.960854i | \(0.410642\pi\) | |||||||
\(480\) | 5791.95 | 0.550761 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −8473.14 | −0.800707 | ||||||||
\(483\) | 28969.2 | 2.72908 | ||||||||
\(484\) | 6107.09 | 0.573543 | ||||||||
\(485\) | 5382.46 | 0.503928 | ||||||||
\(486\) | −3662.20 | −0.341812 | ||||||||
\(487\) | 5387.14 | 0.501262 | 0.250631 | − | 0.968083i | \(-0.419362\pi\) | ||||
0.250631 | + | 0.968083i | \(0.419362\pi\) | |||||||
\(488\) | 2907.72 | 0.269726 | ||||||||
\(489\) | −28498.4 | −2.63547 | ||||||||
\(490\) | 2200.12 | 0.202839 | ||||||||
\(491\) | 15259.1 | 1.40251 | 0.701255 | − | 0.712911i | \(-0.252624\pi\) | ||||
0.701255 | + | 0.712911i | \(0.252624\pi\) | |||||||
\(492\) | −7745.14 | −0.709711 | ||||||||
\(493\) | −9796.16 | −0.894922 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2632.01 | −0.238990 | ||||||||
\(496\) | −309.489 | −0.0280171 | ||||||||
\(497\) | −11162.1 | −1.00742 | ||||||||
\(498\) | −18365.1 | −1.65253 | ||||||||
\(499\) | −1856.04 | −0.166509 | −0.0832544 | − | 0.996528i | \(-0.526531\pi\) | ||||
−0.0832544 | + | 0.996528i | \(0.526531\pi\) | |||||||
\(500\) | 4700.69 | 0.420442 | ||||||||
\(501\) | 27152.8 | 2.42135 | ||||||||
\(502\) | −8153.20 | −0.724891 | ||||||||
\(503\) | 1049.46 | 0.0930283 | 0.0465142 | − | 0.998918i | \(-0.485189\pi\) | ||||
0.0465142 | + | 0.998918i | \(0.485189\pi\) | |||||||
\(504\) | −27869.1 | −2.46307 | ||||||||
\(505\) | 1197.61 | 0.105530 | ||||||||
\(506\) | −2925.04 | −0.256984 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4811.71 | −0.420246 | ||||||||
\(509\) | 551.106 | 0.0479909 | 0.0239954 | − | 0.999712i | \(-0.492361\pi\) | ||||
0.0239954 | + | 0.999712i | \(0.492361\pi\) | |||||||
\(510\) | 2151.60 | 0.186813 | ||||||||
\(511\) | 8370.64 | 0.724649 | ||||||||
\(512\) | 4074.36 | 0.351686 | ||||||||
\(513\) | −4459.66 | −0.383818 | ||||||||
\(514\) | 1027.82 | 0.0882010 | ||||||||
\(515\) | 1149.36 | 0.0983431 | ||||||||
\(516\) | 7307.92 | 0.623475 | ||||||||
\(517\) | 7126.26 | 0.606214 | ||||||||
\(518\) | −3997.37 | −0.339063 | ||||||||
\(519\) | 847.361 | 0.0716667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8995.30 | −0.756413 | −0.378206 | − | 0.925721i | \(-0.623459\pi\) | ||||
−0.378206 | + | 0.925721i | \(0.623459\pi\) | |||||||
\(522\) | −16628.5 | −1.39427 | ||||||||
\(523\) | 2663.91 | 0.222724 | 0.111362 | − | 0.993780i | \(-0.464479\pi\) | ||||
0.111362 | + | 0.993780i | \(0.464479\pi\) | |||||||
\(524\) | 1565.02 | 0.130474 | ||||||||
\(525\) | −26509.1 | −2.20372 | ||||||||
\(526\) | 5069.51 | 0.420230 | ||||||||
\(527\) | −1206.89 | −0.0997586 | ||||||||
\(528\) | −1514.04 | −0.124792 | ||||||||
\(529\) | 2897.77 | 0.238167 | ||||||||
\(530\) | −672.095 | −0.0550829 | ||||||||
\(531\) | 21288.5 | 1.73981 | ||||||||
\(532\) | 3622.94 | 0.295253 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −5965.49 | −0.483431 | ||||||||
\(535\) | 5109.47 | 0.412900 | ||||||||
\(536\) | 10848.6 | 0.874232 | ||||||||
\(537\) | −301.488 | −0.0242275 | ||||||||
\(538\) | −4037.86 | −0.323577 | ||||||||
\(539\) | −6037.30 | −0.482458 | ||||||||
\(540\) | −3685.31 | −0.293686 | ||||||||
\(541\) | 6169.23 | 0.490270 | 0.245135 | − | 0.969489i | \(-0.421168\pi\) | ||||
0.245135 | + | 0.969489i | \(0.421168\pi\) | |||||||
\(542\) | −1544.27 | −0.122384 | ||||||||
\(543\) | −10676.5 | −0.843776 | ||||||||
\(544\) | 8341.52 | 0.657426 | ||||||||
\(545\) | −3024.28 | −0.237699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5140.42 | 0.401807 | 0.200904 | − | 0.979611i | \(-0.435612\pi\) | ||||
0.200904 | + | 0.979611i | \(0.435612\pi\) | |||||||
\(548\) | −14690.5 | −1.14516 | ||||||||
\(549\) | −6648.76 | −0.516871 | ||||||||
\(550\) | 2676.64 | 0.207513 | ||||||||
\(551\) | 5271.15 | 0.407547 | ||||||||
\(552\) | −22573.6 | −1.74057 | ||||||||
\(553\) | −15938.3 | −1.22562 | ||||||||
\(554\) | 12714.8 | 0.975090 | ||||||||
\(555\) | −2913.45 | −0.222827 | ||||||||
\(556\) | 11115.5 | 0.847847 | ||||||||
\(557\) | −2778.56 | −0.211367 | −0.105683 | − | 0.994400i | \(-0.533703\pi\) | ||||
−0.105683 | + | 0.994400i | \(0.533703\pi\) | |||||||
\(558\) | −2048.64 | −0.155422 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1105.69 | 0.0834356 | ||||||||
\(561\) | −5904.17 | −0.444339 | ||||||||
\(562\) | −2395.75 | −0.179819 | ||||||||
\(563\) | 4906.14 | 0.367263 | 0.183632 | − | 0.982995i | \(-0.441215\pi\) | ||||
0.183632 | + | 0.982995i | \(0.441215\pi\) | |||||||
\(564\) | 22553.7 | 1.68383 | ||||||||
\(565\) | 5750.22 | 0.428166 | ||||||||
\(566\) | −10876.2 | −0.807706 | ||||||||
\(567\) | 8381.04 | 0.620759 | ||||||||
\(568\) | 8697.82 | 0.642522 | ||||||||
\(569\) | −9363.15 | −0.689849 | −0.344924 | − | 0.938631i | \(-0.612095\pi\) | ||||
−0.344924 | + | 0.938631i | \(0.612095\pi\) | |||||||
\(570\) | −1157.74 | −0.0850744 | ||||||||
\(571\) | 7199.32 | 0.527640 | 0.263820 | − | 0.964572i | \(-0.415018\pi\) | ||||
0.263820 | + | 0.964572i | \(0.415018\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37177.3 | 2.71048 | ||||||||
\(574\) | 6805.18 | 0.494848 | ||||||||
\(575\) | −13785.4 | −0.999813 | ||||||||
\(576\) | 9734.14 | 0.704148 | ||||||||
\(577\) | 11449.6 | 0.826086 | 0.413043 | − | 0.910711i | \(-0.364466\pi\) | ||||
0.413043 | + | 0.910711i | \(0.364466\pi\) | |||||||
\(578\) | −4573.19 | −0.329100 | ||||||||
\(579\) | −4101.94 | −0.294423 | ||||||||
\(580\) | 4355.91 | 0.311843 | ||||||||
\(581\) | −36803.3 | −2.62798 | ||||||||
\(582\) | 20495.2 | 1.45971 | ||||||||
\(583\) | 1844.28 | 0.131016 | ||||||||
\(584\) | −6522.62 | −0.462171 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −999.439 | −0.0704547 | ||||||||
\(587\) | 5439.39 | 0.382466 | 0.191233 | − | 0.981545i | \(-0.438751\pi\) | ||||
0.191233 | + | 0.981545i | \(0.438751\pi\) | |||||||
\(588\) | −19107.3 | −1.34008 | ||||||||
\(589\) | 649.406 | 0.0454301 | ||||||||
\(590\) | 2445.04 | 0.170611 | ||||||||
\(591\) | 38945.2 | 2.71064 | ||||||||
\(592\) | −1075.99 | −0.0747006 | ||||||||
\(593\) | 28405.8 | 1.96709 | 0.983547 | − | 0.180651i | \(-0.0578204\pi\) | ||||
0.983547 | + | 0.180651i | \(0.0578204\pi\) | |||||||
\(594\) | −4433.93 | −0.306273 | ||||||||
\(595\) | 4311.76 | 0.297084 | ||||||||
\(596\) | −9749.30 | −0.670045 | ||||||||
\(597\) | −3180.67 | −0.218051 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10482.3 | −0.715020 | −0.357510 | − | 0.933909i | \(-0.616374\pi\) | ||||
−0.357510 | + | 0.933909i | \(0.616374\pi\) | |||||||
\(600\) | 20656.6 | 1.40550 | ||||||||
\(601\) | 3199.54 | 0.217158 | 0.108579 | − | 0.994088i | \(-0.465370\pi\) | ||||
0.108579 | + | 0.994088i | \(0.465370\pi\) | |||||||
\(602\) | −6421.02 | −0.434720 | ||||||||
\(603\) | −24806.3 | −1.67527 | ||||||||
\(604\) | −15542.6 | −1.04705 | ||||||||
\(605\) | −3910.91 | −0.262812 | ||||||||
\(606\) | 4560.20 | 0.305686 | ||||||||
\(607\) | 11342.8 | 0.758468 | 0.379234 | − | 0.925301i | \(-0.376188\pi\) | ||||
0.379234 | + | 0.925301i | \(0.376188\pi\) | |||||||
\(608\) | −4488.44 | −0.299392 | ||||||||
\(609\) | −51903.7 | −3.45361 | ||||||||
\(610\) | −763.629 | −0.0506859 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −11996.7 | −0.792384 | ||||||||
\(613\) | −14385.4 | −0.947831 | −0.473916 | − | 0.880570i | \(-0.657160\pi\) | ||||
−0.473916 | + | 0.880570i | \(0.657160\pi\) | |||||||
\(614\) | 156.789 | 0.0103053 | ||||||||
\(615\) | 4959.89 | 0.325207 | ||||||||
\(616\) | 8783.39 | 0.574502 | ||||||||
\(617\) | −22056.8 | −1.43918 | −0.719588 | − | 0.694401i | \(-0.755669\pi\) | ||||
−0.719588 | + | 0.694401i | \(0.755669\pi\) | |||||||
\(618\) | 4376.48 | 0.284867 | ||||||||
\(619\) | −13621.4 | −0.884477 | −0.442238 | − | 0.896898i | \(-0.645815\pi\) | ||||
−0.442238 | + | 0.896898i | \(0.645815\pi\) | |||||||
\(620\) | 536.648 | 0.0347618 | ||||||||
\(621\) | 22836.0 | 1.47565 | ||||||||
\(622\) | −6057.14 | −0.390465 | ||||||||
\(623\) | −11954.7 | −0.768789 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11029.2 | 0.705866 | ||||||||
\(626\) | −5917.34 | −0.377803 | ||||||||
\(627\) | 3176.94 | 0.202352 | ||||||||
\(628\) | −18046.5 | −1.14671 | ||||||||
\(629\) | −4195.92 | −0.265982 | ||||||||
\(630\) | 7319.02 | 0.462852 | ||||||||
\(631\) | 18737.5 | 1.18214 | 0.591068 | − | 0.806622i | \(-0.298707\pi\) | ||||
0.591068 | + | 0.806622i | \(0.298707\pi\) | |||||||
\(632\) | 12419.6 | 0.781683 | ||||||||
\(633\) | 18433.7 | 1.15746 | ||||||||
\(634\) | −6881.46 | −0.431069 | ||||||||
\(635\) | 3081.36 | 0.192567 | ||||||||
\(636\) | 5836.91 | 0.363913 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5240.75 | 0.325209 | ||||||||
\(639\) | −19888.4 | −1.23125 | ||||||||
\(640\) | −4217.35 | −0.260477 | ||||||||
\(641\) | 29798.7 | 1.83616 | 0.918081 | − | 0.396394i | \(-0.129739\pi\) | ||||
0.918081 | + | 0.396394i | \(0.129739\pi\) | |||||||
\(642\) | 19455.6 | 1.19603 | ||||||||
\(643\) | 22983.5 | 1.40961 | 0.704807 | − | 0.709399i | \(-0.251034\pi\) | ||||
0.704807 | + | 0.709399i | \(0.251034\pi\) | |||||||
\(644\) | −18551.5 | −1.13515 | ||||||||
\(645\) | −4679.90 | −0.285692 | ||||||||
\(646\) | −1667.37 | −0.101551 | ||||||||
\(647\) | −24905.4 | −1.51334 | −0.756672 | − | 0.653794i | \(-0.773176\pi\) | ||||
−0.756672 | + | 0.653794i | \(0.773176\pi\) | |||||||
\(648\) | −6530.72 | −0.395912 | ||||||||
\(649\) | −6709.39 | −0.405804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6394.54 | −0.384980 | ||||||||
\(652\) | 18250.1 | 1.09621 | ||||||||
\(653\) | 10077.8 | 0.603946 | 0.301973 | − | 0.953316i | \(-0.402355\pi\) | ||||
0.301973 | + | 0.953316i | \(0.402355\pi\) | |||||||
\(654\) | −11515.7 | −0.688534 | ||||||||
\(655\) | −1002.22 | −0.0597864 | ||||||||
\(656\) | 1831.77 | 0.109022 | ||||||||
\(657\) | 14914.6 | 0.885650 | ||||||||
\(658\) | −19816.5 | −1.17406 | ||||||||
\(659\) | 12334.6 | 0.729116 | 0.364558 | − | 0.931181i | \(-0.381220\pi\) | ||||
0.364558 | + | 0.931181i | \(0.381220\pi\) | |||||||
\(660\) | 2625.32 | 0.154834 | ||||||||
\(661\) | 12749.1 | 0.750202 | 0.375101 | − | 0.926984i | \(-0.377608\pi\) | ||||
0.375101 | + | 0.926984i | \(0.377608\pi\) | |||||||
\(662\) | 6451.54 | 0.378771 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28678.1 | 1.67609 | ||||||||
\(665\) | −2320.09 | −0.135292 | ||||||||
\(666\) | −7122.40 | −0.414395 | ||||||||
\(667\) | −26991.3 | −1.56688 | ||||||||
\(668\) | −17388.3 | −1.00715 | ||||||||
\(669\) | 51468.9 | 2.97444 | ||||||||
\(670\) | −2849.07 | −0.164283 | ||||||||
\(671\) | 2095.46 | 0.120558 | ||||||||
\(672\) | 44196.5 | 2.53708 | ||||||||
\(673\) | −13618.2 | −0.780007 | −0.390004 | − | 0.920813i | \(-0.627526\pi\) | ||||
−0.390004 | + | 0.920813i | \(0.627526\pi\) | |||||||
\(674\) | −7121.96 | −0.407014 | ||||||||
\(675\) | −20896.7 | −1.19158 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9655.67 | 0.548150 | 0.274075 | − | 0.961708i | \(-0.411628\pi\) | ||||
0.274075 | + | 0.961708i | \(0.411628\pi\) | |||||||
\(678\) | 21895.5 | 1.24025 | ||||||||
\(679\) | 41071.9 | 2.32135 | ||||||||
\(680\) | −3359.84 | −0.189476 | ||||||||
\(681\) | 7778.51 | 0.437699 | ||||||||
\(682\) | 645.660 | 0.0362516 | ||||||||
\(683\) | −16316.8 | −0.914119 | −0.457060 | − | 0.889436i | \(-0.651097\pi\) | ||||
−0.457060 | + | 0.889436i | \(0.651097\pi\) | |||||||
\(684\) | 6455.25 | 0.360852 | ||||||||
\(685\) | 9407.61 | 0.524739 | ||||||||
\(686\) | 2232.00 | 0.124225 | ||||||||
\(687\) | −5451.51 | −0.302748 | ||||||||
\(688\) | −1728.37 | −0.0957753 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 5928.30 | 0.327082 | ||||||||
\(691\) | −2350.84 | −0.129421 | −0.0647106 | − | 0.997904i | \(-0.520612\pi\) | ||||
−0.0647106 | + | 0.997904i | \(0.520612\pi\) | |||||||
\(692\) | −542.640 | −0.0298093 | ||||||||
\(693\) | −20084.0 | −1.10091 | ||||||||
\(694\) | 15723.9 | 0.860045 | ||||||||
\(695\) | −7118.24 | −0.388504 | ||||||||
\(696\) | 40444.7 | 2.20266 | ||||||||
\(697\) | 7143.20 | 0.388189 | ||||||||
\(698\) | −9180.88 | −0.497853 | ||||||||
\(699\) | 20007.1 | 1.08260 | ||||||||
\(700\) | 16976.1 | 0.916623 | ||||||||
\(701\) | −8076.90 | −0.435179 | −0.217589 | − | 0.976040i | \(-0.569819\pi\) | ||||
−0.217589 | + | 0.976040i | \(0.569819\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2257.76 | 0.121128 | ||||||||
\(704\) | −3067.87 | −0.164239 | ||||||||
\(705\) | −14443.1 | −0.771573 | ||||||||
\(706\) | 14276.6 | 0.761058 | ||||||||
\(707\) | 9138.55 | 0.486125 | ||||||||
\(708\) | −21234.3 | −1.12717 | ||||||||
\(709\) | 13624.9 | 0.721712 | 0.360856 | − | 0.932622i | \(-0.382485\pi\) | ||||
0.360856 | + | 0.932622i | \(0.382485\pi\) | |||||||
\(710\) | −2284.23 | −0.120741 | ||||||||
\(711\) | −28398.4 | −1.49792 | ||||||||
\(712\) | 9315.43 | 0.490324 | ||||||||
\(713\) | −3325.33 | −0.174663 | ||||||||
\(714\) | 16418.2 | 0.860553 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 193.069 | 0.0100773 | ||||||||
\(717\) | −4729.86 | −0.246359 | ||||||||
\(718\) | 4301.02 | 0.223555 | ||||||||
\(719\) | 16235.8 | 0.842131 | 0.421066 | − | 0.907030i | \(-0.361656\pi\) | ||||
0.421066 | + | 0.907030i | \(0.361656\pi\) | |||||||
\(720\) | 1970.09 | 0.101973 | ||||||||
\(721\) | 8770.37 | 0.453018 | ||||||||
\(722\) | −9813.51 | −0.505846 | ||||||||
\(723\) | −47123.8 | −2.42400 | ||||||||
\(724\) | 6837.08 | 0.350964 | ||||||||
\(725\) | 24699.2 | 1.26525 | ||||||||
\(726\) | −14891.8 | −0.761277 | ||||||||
\(727\) | 24181.2 | 1.23361 | 0.616803 | − | 0.787118i | \(-0.288428\pi\) | ||||
0.616803 | + | 0.787118i | \(0.288428\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28693.9 | −1.45780 | ||||||||
\(730\) | 1712.98 | 0.0868496 | ||||||||
\(731\) | −6739.96 | −0.341021 | ||||||||
\(732\) | 6631.86 | 0.334864 | ||||||||
\(733\) | −3053.70 | −0.153876 | −0.0769379 | − | 0.997036i | \(-0.524514\pi\) | ||||
−0.0769379 | + | 0.997036i | \(0.524514\pi\) | |||||||
\(734\) | 4747.41 | 0.238733 | ||||||||
\(735\) | 12236.1 | 0.614060 | ||||||||
\(736\) | 22983.4 | 1.15106 | ||||||||
\(737\) | 7818.10 | 0.390751 | ||||||||
\(738\) | 12125.3 | 0.604793 | ||||||||
\(739\) | 8033.62 | 0.399894 | 0.199947 | − | 0.979807i | \(-0.435923\pi\) | ||||
0.199947 | + | 0.979807i | \(0.435923\pi\) | |||||||
\(740\) | 1865.74 | 0.0926836 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5128.54 | −0.253739 | ||||||||
\(743\) | 16139.6 | 0.796912 | 0.398456 | − | 0.917187i | \(-0.369546\pi\) | ||||
0.398456 | + | 0.917187i | \(0.369546\pi\) | |||||||
\(744\) | 4982.79 | 0.245535 | ||||||||
\(745\) | 6243.33 | 0.307031 | ||||||||
\(746\) | −8408.53 | −0.412678 | ||||||||
\(747\) | −65574.9 | −3.21186 | ||||||||
\(748\) | 3780.96 | 0.184820 | ||||||||
\(749\) | 38988.7 | 1.90202 | ||||||||
\(750\) | −11462.4 | −0.558062 | ||||||||
\(751\) | −18491.1 | −0.898469 | −0.449235 | − | 0.893414i | \(-0.648303\pi\) | ||||
−0.449235 | + | 0.893414i | \(0.648303\pi\) | |||||||
\(752\) | −5334.08 | −0.258662 | ||||||||
\(753\) | −45344.5 | −2.19448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9953.28 | 0.479784 | ||||||||
\(756\) | −28121.5 | −1.35287 | ||||||||
\(757\) | 160.630 | 0.00771227 | 0.00385613 | − | 0.999993i | \(-0.498773\pi\) | ||||
0.00385613 | + | 0.999993i | \(0.498773\pi\) | |||||||
\(758\) | 5347.17 | 0.256224 | ||||||||
\(759\) | −16267.7 | −0.777973 | ||||||||
\(760\) | 1807.87 | 0.0862874 | ||||||||
\(761\) | −26799.1 | −1.27656 | −0.638282 | − | 0.769803i | \(-0.720355\pi\) | ||||
−0.638282 | + | 0.769803i | \(0.720355\pi\) | |||||||
\(762\) | 11733.1 | 0.557803 | ||||||||
\(763\) | −23077.3 | −1.09496 | ||||||||
\(764\) | −23807.9 | −1.12741 | ||||||||
\(765\) | 7682.57 | 0.363090 | ||||||||
\(766\) | 598.052 | 0.0282095 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −30025.1 | −1.41073 | ||||||||
\(769\) | 5145.82 | 0.241304 | 0.120652 | − | 0.992695i | \(-0.461501\pi\) | ||||
0.120652 | + | 0.992695i | \(0.461501\pi\) | |||||||
\(770\) | −2306.71 | −0.107958 | ||||||||
\(771\) | 5716.29 | 0.267013 | ||||||||
\(772\) | 2626.83 | 0.122463 | ||||||||
\(773\) | −12810.6 | −0.596072 | −0.298036 | − | 0.954555i | \(-0.596332\pi\) | ||||
−0.298036 | + | 0.954555i | \(0.596332\pi\) | |||||||
\(774\) | −11440.8 | −0.531306 | ||||||||
\(775\) | 3042.94 | 0.141039 | ||||||||
\(776\) | −32004.3 | −1.48052 | ||||||||
\(777\) | −22231.6 | −1.02645 | ||||||||
\(778\) | 13411.1 | 0.618011 | ||||||||
\(779\) | −3843.64 | −0.176781 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6268.13 | 0.287185 | ||||||||
\(782\) | 8537.89 | 0.390428 | ||||||||
\(783\) | −40915.0 | −1.86741 | ||||||||
\(784\) | 4518.98 | 0.205857 | ||||||||
\(785\) | 11556.8 | 0.525452 | ||||||||
\(786\) | −3816.23 | −0.173181 | ||||||||
\(787\) | −28073.0 | −1.27153 | −0.635764 | − | 0.771883i | \(-0.719315\pi\) | ||||
−0.635764 | + | 0.771883i | \(0.719315\pi\) | |||||||
\(788\) | −24940.0 | −1.12748 | ||||||||
\(789\) | 28194.3 | 1.27217 | ||||||||
\(790\) | −3261.64 | −0.146891 | ||||||||
\(791\) | 43878.1 | 1.97235 | ||||||||
\(792\) | 15650.0 | 0.702144 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11304.3 | 0.505259 | ||||||||
\(795\) | −3737.89 | −0.166754 | ||||||||
\(796\) | 2036.87 | 0.0906970 | ||||||||
\(797\) | 30093.1 | 1.33746 | 0.668729 | − | 0.743507i | \(-0.266839\pi\) | ||||
0.668729 | + | 0.743507i | \(0.266839\pi\) | |||||||
\(798\) | −8834.35 | −0.391896 | ||||||||
\(799\) | −20800.8 | −0.921003 | ||||||||
\(800\) | −21031.6 | −0.929473 | ||||||||
\(801\) | −21300.6 | −0.939598 | ||||||||
\(802\) | −6667.24 | −0.293552 | ||||||||
\(803\) | −4700.56 | −0.206574 | ||||||||
\(804\) | 24743.2 | 1.08536 | ||||||||
\(805\) | 11880.2 | 0.520151 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22456.8 | −0.979575 | ||||||||
\(808\) | −7120.99 | −0.310044 | ||||||||
\(809\) | −24337.1 | −1.05766 | −0.528831 | − | 0.848727i | \(-0.677369\pi\) | ||||
−0.528831 | + | 0.848727i | \(0.677369\pi\) | |||||||
\(810\) | 1715.11 | 0.0743984 | ||||||||
\(811\) | −19078.7 | −0.826071 | −0.413035 | − | 0.910715i | \(-0.635531\pi\) | ||||
−0.413035 | + | 0.910715i | \(0.635531\pi\) | |||||||
\(812\) | 33238.5 | 1.43651 | ||||||||
\(813\) | −8588.54 | −0.370496 | ||||||||
\(814\) | 2244.74 | 0.0966559 | ||||||||
\(815\) | −11687.1 | −0.502309 | ||||||||
\(816\) | 4419.33 | 0.189593 | ||||||||
\(817\) | 3626.66 | 0.155301 | ||||||||
\(818\) | −21178.6 | −0.905248 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3176.26 | −0.135268 | ||||||||
\(821\) | −2013.92 | −0.0856104 | −0.0428052 | − | 0.999083i | \(-0.513629\pi\) | ||||
−0.0428052 | + | 0.999083i | \(0.513629\pi\) | |||||||
\(822\) | 35821.9 | 1.51999 | ||||||||
\(823\) | −7692.10 | −0.325795 | −0.162898 | − | 0.986643i | \(-0.552084\pi\) | ||||
−0.162898 | + | 0.986643i | \(0.552084\pi\) | |||||||
\(824\) | −6834.10 | −0.288929 | ||||||||
\(825\) | 14886.2 | 0.628209 | ||||||||
\(826\) | 18657.3 | 0.785922 | ||||||||
\(827\) | 4762.76 | 0.200263 | 0.100131 | − | 0.994974i | \(-0.468074\pi\) | ||||
0.100131 | + | 0.994974i | \(0.468074\pi\) | |||||||
\(828\) | −33054.6 | −1.38735 | ||||||||
\(829\) | 19977.7 | 0.836976 | 0.418488 | − | 0.908222i | \(-0.362560\pi\) | ||||
0.418488 | + | 0.908222i | \(0.362560\pi\) | |||||||
\(830\) | −7531.47 | −0.314965 | ||||||||
\(831\) | 70714.0 | 2.95191 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17622.3 | 0.732984 | ||||||||
\(834\) | −27104.6 | −1.12537 | ||||||||
\(835\) | 11135.3 | 0.461499 | ||||||||
\(836\) | −2034.47 | −0.0841671 | ||||||||
\(837\) | −5040.72 | −0.208164 | ||||||||
\(838\) | −22762.6 | −0.938330 | ||||||||
\(839\) | 30615.8 | 1.25980 | 0.629901 | − | 0.776676i | \(-0.283095\pi\) | ||||
0.629901 | + | 0.776676i | \(0.283095\pi\) | |||||||
\(840\) | −17801.7 | −0.731210 | ||||||||
\(841\) | 23971.0 | 0.982861 | ||||||||
\(842\) | −24748.1 | −1.01292 | ||||||||
\(843\) | −13324.1 | −0.544372 | ||||||||
\(844\) | −11804.7 | −0.481439 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −35308.5 | −1.43491 | ||||||||
\(847\) | −29842.9 | −1.21064 | ||||||||
\(848\) | −1380.47 | −0.0559026 | ||||||||
\(849\) | −60488.6 | −2.44519 | ||||||||
\(850\) | −7812.83 | −0.315268 | ||||||||
\(851\) | −11561.0 | −0.465696 | ||||||||
\(852\) | 19837.8 | 0.797690 | ||||||||
\(853\) | −5660.88 | −0.227227 | −0.113614 | − | 0.993525i | \(-0.536243\pi\) | ||||
−0.113614 | + | 0.993525i | \(0.536243\pi\) | |||||||
\(854\) | −5827.01 | −0.233485 | ||||||||
\(855\) | −4133.86 | −0.165351 | ||||||||
\(856\) | −30381.0 | −1.21309 | ||||||||
\(857\) | 41346.1 | 1.64802 | 0.824012 | − | 0.566572i | \(-0.191731\pi\) | ||||
0.824012 | + | 0.566572i | \(0.191731\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34810.5 | −1.38268 | −0.691339 | − | 0.722530i | \(-0.742979\pi\) | ||||
−0.691339 | + | 0.722530i | \(0.742979\pi\) | |||||||
\(860\) | 2996.96 | 0.118832 | ||||||||
\(861\) | 37847.4 | 1.49807 | ||||||||
\(862\) | −16700.4 | −0.659880 | ||||||||
\(863\) | 8360.51 | 0.329774 | 0.164887 | − | 0.986312i | \(-0.447274\pi\) | ||||
0.164887 | + | 0.986312i | \(0.447274\pi\) | |||||||
\(864\) | 34839.5 | 1.37183 | ||||||||
\(865\) | 347.500 | 0.0136594 | ||||||||
\(866\) | −25108.2 | −0.985233 | ||||||||
\(867\) | −25434.1 | −0.996293 | ||||||||
\(868\) | 4094.99 | 0.160130 | ||||||||
\(869\) | 8950.21 | 0.349385 | ||||||||
\(870\) | −10621.6 | −0.413917 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 17982.4 | 0.698352 | ||||||||
\(873\) | 73180.6 | 2.83710 | ||||||||
\(874\) | −4594.10 | −0.177801 | ||||||||
\(875\) | −22970.4 | −0.887475 | ||||||||
\(876\) | −14876.6 | −0.573784 | ||||||||
\(877\) | 40579.3 | 1.56245 | 0.781223 | − | 0.624251i | \(-0.214596\pi\) | ||||
0.781223 | + | 0.624251i | \(0.214596\pi\) | |||||||
\(878\) | 9425.22 | 0.362285 | ||||||||
\(879\) | −5558.43 | −0.213289 | ||||||||
\(880\) | −620.903 | −0.0237848 | ||||||||
\(881\) | 10445.2 | 0.399442 | 0.199721 | − | 0.979853i | \(-0.435996\pi\) | ||||
0.199721 | + | 0.979853i | \(0.435996\pi\) | |||||||
\(882\) | 29913.0 | 1.14198 | ||||||||
\(883\) | 18227.6 | 0.694685 | 0.347343 | − | 0.937738i | \(-0.387084\pi\) | ||||
0.347343 | + | 0.937738i | \(0.387084\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13598.2 | 0.516496 | ||||||||
\(886\) | 15929.9 | 0.604036 | ||||||||
\(887\) | −23517.7 | −0.890245 | −0.445122 | − | 0.895470i | \(-0.646840\pi\) | ||||
−0.445122 | + | 0.895470i | \(0.646840\pi\) | |||||||
\(888\) | 17323.4 | 0.654658 | ||||||||
\(889\) | 23512.9 | 0.887061 | ||||||||
\(890\) | −2446.43 | −0.0921399 | ||||||||
\(891\) | −4706.40 | −0.176959 | ||||||||
\(892\) | −32960.1 | −1.23720 | ||||||||
\(893\) | 11192.6 | 0.419424 | ||||||||
\(894\) | 23773.1 | 0.889366 | ||||||||
\(895\) | −123.639 | −0.00461766 | ||||||||
\(896\) | −32181.2 | −1.19989 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9092.21 | 0.337874 | ||||||||
\(899\) | 5957.95 | 0.221033 | ||||||||
\(900\) | 30247.5 | 1.12028 | ||||||||
\(901\) | −5383.28 | −0.199049 | ||||||||
\(902\) | −3821.47 | −0.141065 | ||||||||
\(903\) | −35710.9 | −1.31604 | ||||||||
\(904\) | −34191.0 | −1.25794 | ||||||||
\(905\) | −4378.38 | −0.160820 | ||||||||
\(906\) | 37899.7 | 1.38977 | ||||||||
\(907\) | −30564.6 | −1.11894 | −0.559471 | − | 0.828850i | \(-0.688996\pi\) | ||||
−0.559471 | + | 0.828850i | \(0.688996\pi\) | |||||||
\(908\) | −4981.26 | −0.182058 | ||||||||
\(909\) | 16282.8 | 0.594132 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32766.5 | −1.19166 | −0.595831 | − | 0.803110i | \(-0.703177\pi\) | ||||
−0.595831 | + | 0.803110i | \(0.703177\pi\) | |||||||
\(912\) | −2377.97 | −0.0863404 | ||||||||
\(913\) | 20667.0 | 0.749154 | ||||||||
\(914\) | −7216.87 | −0.261174 | ||||||||
\(915\) | −4246.96 | −0.153443 | ||||||||
\(916\) | 3491.08 | 0.125926 | ||||||||
\(917\) | −7647.64 | −0.275406 | ||||||||
\(918\) | 12942.2 | 0.465312 | ||||||||
\(919\) | 20686.7 | 0.742538 | 0.371269 | − | 0.928525i | \(-0.378923\pi\) | ||||
0.371269 | + | 0.928525i | \(0.378923\pi\) | |||||||
\(920\) | −9257.35 | −0.331745 | ||||||||
\(921\) | 871.989 | 0.0311976 | ||||||||
\(922\) | −8007.28 | −0.286015 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 20033.0 | 0.713242 | ||||||||
\(925\) | 10579.2 | 0.376047 | ||||||||
\(926\) | −10128.6 | −0.359447 | ||||||||
\(927\) | 15626.8 | 0.553669 | ||||||||
\(928\) | −41179.0 | −1.45665 | ||||||||
\(929\) | −45632.2 | −1.61156 | −0.805782 | − | 0.592212i | \(-0.798255\pi\) | ||||
−0.805782 | + | 0.592212i | \(0.798255\pi\) | |||||||
\(930\) | −1308.59 | −0.0461401 | ||||||||
\(931\) | −9482.26 | −0.333801 | ||||||||
\(932\) | −12812.3 | −0.450301 | ||||||||
\(933\) | −33687.1 | −1.18206 | ||||||||
\(934\) | 20265.9 | 0.709979 | ||||||||
\(935\) | −2421.28 | −0.0846892 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17761.4 | −0.619253 | −0.309626 | − | 0.950858i | \(-0.600204\pi\) | ||||
−0.309626 | + | 0.950858i | \(0.600204\pi\) | |||||||
\(938\) | −21740.4 | −0.756768 | ||||||||
\(939\) | −32909.6 | −1.14373 | ||||||||
\(940\) | 9249.19 | 0.320931 | ||||||||
\(941\) | 44888.3 | 1.55507 | 0.777534 | − | 0.628841i | \(-0.216470\pi\) | ||||
0.777534 | + | 0.628841i | \(0.216470\pi\) | |||||||
\(942\) | 44005.5 | 1.52206 | ||||||||
\(943\) | 19681.7 | 0.679664 | ||||||||
\(944\) | 5022.05 | 0.173150 | ||||||||
\(945\) | 18008.6 | 0.619917 | ||||||||
\(946\) | 3605.74 | 0.123925 | ||||||||
\(947\) | −16069.6 | −0.551415 | −0.275708 | − | 0.961242i | \(-0.588912\pi\) | ||||
−0.275708 | + | 0.961242i | \(0.588912\pi\) | |||||||
\(948\) | 28326.2 | 0.970457 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4203.96 | 0.143573 | ||||||||
\(951\) | −38271.6 | −1.30499 | ||||||||
\(952\) | −25637.8 | −0.872823 | ||||||||
\(953\) | 3512.03 | 0.119377 | 0.0596883 | − | 0.998217i | \(-0.480989\pi\) | ||||
0.0596883 | + | 0.998217i | \(0.480989\pi\) | |||||||
\(954\) | −9137.88 | −0.310115 | ||||||||
\(955\) | 15246.3 | 0.516605 | ||||||||
\(956\) | 3028.94 | 0.102472 | ||||||||
\(957\) | 29146.7 | 0.984513 | ||||||||
\(958\) | 9071.00 | 0.305919 | ||||||||
\(959\) | 71786.5 | 2.41721 | ||||||||
\(960\) | 6217.78 | 0.209040 | ||||||||
\(961\) | −29057.0 | −0.975361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 69468.9 | 2.32461 | ||||||||
\(964\) | 30177.5 | 1.00825 | ||||||||
\(965\) | −1682.19 | −0.0561158 | ||||||||
\(966\) | 45237.0 | 1.50670 | ||||||||
\(967\) | 37011.9 | 1.23084 | 0.615421 | − | 0.788199i | \(-0.288986\pi\) | ||||
0.615421 | + | 0.788199i | \(0.288986\pi\) | |||||||
\(968\) | 23254.4 | 0.772132 | ||||||||
\(969\) | −9273.16 | −0.307427 | ||||||||
\(970\) | 8405.00 | 0.278215 | ||||||||
\(971\) | 19532.3 | 0.645542 | 0.322771 | − | 0.946477i | \(-0.395386\pi\) | ||||
0.322771 | + | 0.946477i | \(0.395386\pi\) | |||||||
\(972\) | 13043.1 | 0.430409 | ||||||||
\(973\) | −54317.1 | −1.78965 | ||||||||
\(974\) | 8412.30 | 0.276743 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1568.47 | −0.0514402 | ||||||||
\(977\) | −30201.2 | −0.988970 | −0.494485 | − | 0.869186i | \(-0.664643\pi\) | ||||
−0.494485 | + | 0.869186i | \(0.664643\pi\) | |||||||
\(978\) | −44501.8 | −1.45502 | ||||||||
\(979\) | 6713.21 | 0.219157 | ||||||||
\(980\) | −7835.83 | −0.255415 | ||||||||
\(981\) | −41118.5 | −1.33824 | ||||||||
\(982\) | 23827.8 | 0.774315 | ||||||||
\(983\) | 38774.9 | 1.25812 | 0.629058 | − | 0.777359i | \(-0.283441\pi\) | ||||
0.629058 | + | 0.777359i | \(0.283441\pi\) | |||||||
\(984\) | −29491.7 | −0.955447 | ||||||||
\(985\) | 15971.3 | 0.516638 | ||||||||
\(986\) | −15297.2 | −0.494080 | ||||||||
\(987\) | −110211. | −3.55425 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18570.6 | −0.597079 | ||||||||
\(990\) | −4110.02 | −0.131944 | ||||||||
\(991\) | −27728.9 | −0.888838 | −0.444419 | − | 0.895819i | \(-0.646590\pi\) | ||||
−0.444419 | + | 0.895819i | \(0.646590\pi\) | |||||||
\(992\) | −5073.25 | −0.162375 | ||||||||
\(993\) | 35880.6 | 1.14666 | ||||||||
\(994\) | −17430.3 | −0.556192 | ||||||||
\(995\) | −1304.38 | −0.0415596 | ||||||||
\(996\) | 65408.2 | 2.08086 | ||||||||
\(997\) | −48918.2 | −1.55392 | −0.776958 | − | 0.629552i | \(-0.783239\pi\) | ||||
−0.776958 | + | 0.629552i | \(0.783239\pi\) | |||||||
\(998\) | −2898.31 | −0.0919283 | ||||||||
\(999\) | −17524.8 | −0.555016 |
(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 | 169.4.a.g.1.2 | 2 | ||
3.2 | odd | 2 | 1521.4.a.r.1.1 | 2 | |||
13.2 | odd | 12 | 169.4.e.f.147.3 | 8 | |||
13.3 | even | 3 | 169.4.c.j.22.1 | 4 | |||
13.4 | even | 6 | 169.4.c.g.146.2 | 4 | |||
13.5 | odd | 4 | 169.4.b.f.168.2 | 4 | |||
13.6 | odd | 12 | 169.4.e.f.23.2 | 8 | |||
13.7 | odd | 12 | 169.4.e.f.23.3 | 8 | |||
13.8 | odd | 4 | 169.4.b.f.168.3 | 4 | |||
13.9 | even | 3 | 169.4.c.j.146.1 | 4 | |||
13.10 | even | 6 | 169.4.c.g.22.2 | 4 | |||
13.11 | odd | 12 | 169.4.e.f.147.2 | 8 | |||
13.12 | even | 2 | 13.4.a.b.1.1 | ✓ | 2 | ||
39.38 | odd | 2 | 117.4.a.d.1.2 | 2 | |||
52.51 | odd | 2 | 208.4.a.h.1.1 | 2 | |||
65.12 | odd | 4 | 325.4.b.e.274.2 | 4 | |||
65.38 | odd | 4 | 325.4.b.e.274.3 | 4 | |||
65.64 | even | 2 | 325.4.a.f.1.2 | 2 | |||
91.90 | odd | 2 | 637.4.a.b.1.1 | 2 | |||
104.51 | odd | 2 | 832.4.a.z.1.2 | 2 | |||
104.77 | even | 2 | 832.4.a.s.1.1 | 2 | |||
143.142 | odd | 2 | 1573.4.a.b.1.2 | 2 | |||
156.155 | even | 2 | 1872.4.a.bb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.1 | ✓ | 2 | 13.12 | even | 2 | ||
117.4.a.d.1.2 | 2 | 39.38 | odd | 2 | |||
169.4.a.g.1.2 | 2 | 1.1 | even | 1 | trivial | ||
169.4.b.f.168.2 | 4 | 13.5 | odd | 4 | |||
169.4.b.f.168.3 | 4 | 13.8 | odd | 4 | |||
169.4.c.g.22.2 | 4 | 13.10 | even | 6 | |||
169.4.c.g.146.2 | 4 | 13.4 | even | 6 | |||
169.4.c.j.22.1 | 4 | 13.3 | even | 3 | |||
169.4.c.j.146.1 | 4 | 13.9 | even | 3 | |||
169.4.e.f.23.2 | 8 | 13.6 | odd | 12 | |||
169.4.e.f.23.3 | 8 | 13.7 | odd | 12 | |||
169.4.e.f.147.2 | 8 | 13.11 | odd | 12 | |||
169.4.e.f.147.3 | 8 | 13.2 | odd | 12 | |||
208.4.a.h.1.1 | 2 | 52.51 | odd | 2 | |||
325.4.a.f.1.2 | 2 | 65.64 | even | 2 | |||
325.4.b.e.274.2 | 4 | 65.12 | odd | 4 | |||
325.4.b.e.274.3 | 4 | 65.38 | odd | 4 | |||
637.4.a.b.1.1 | 2 | 91.90 | odd | 2 | |||
832.4.a.s.1.1 | 2 | 104.77 | even | 2 | |||
832.4.a.z.1.2 | 2 | 104.51 | odd | 2 | |||
1521.4.a.r.1.1 | 2 | 3.2 | odd | 2 | |||
1573.4.a.b.1.2 | 2 | 143.142 | odd | 2 | |||
1872.4.a.bb.1.2 | 2 | 156.155 | even | 2 |