Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [832,4,Mod(1,832)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(832, 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("832.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 832 = 2^{6} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 832.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: | \(49.0895891248\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
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 | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 832.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −8.68466 | −1.67136 | −0.835682 | − | 0.549214i | \(-0.814927\pi\) | ||||
−0.835682 | + | 0.549214i | \(0.814927\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.56155 | 0.318555 | 0.159277 | − | 0.987234i | \(-0.449084\pi\) | ||||
0.159277 | + | 0.987234i | \(0.449084\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −27.1771 | −1.46742 | −0.733712 | − | 0.679460i | \(-0.762214\pi\) | ||||
−0.733712 | + | 0.679460i | \(0.762214\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 48.4233 | 1.79346 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.2614 | −0.418316 | −0.209158 | − | 0.977882i | \(-0.567072\pi\) | ||||
−0.209158 | + | 0.977882i | \(0.567072\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −30.9309 | −0.532421 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 44.5464 | 0.635535 | 0.317767 | − | 0.948169i | \(-0.397067\pi\) | ||||
0.317767 | + | 0.948169i | \(0.397067\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −23.9697 | −0.289422 | −0.144711 | − | 0.989474i | \(-0.546225\pi\) | ||||
−0.144711 | + | 0.989474i | \(0.546225\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 236.024 | 2.45260 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 122.739 | 1.11273 | 0.556365 | − | 0.830938i | \(-0.312196\pi\) | ||||
0.556365 | + | 0.830938i | \(0.312196\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −112.315 | −0.898523 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −186.054 | −1.32615 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 219.909 | 1.40814 | 0.704071 | − | 0.710130i | \(-0.251364\pi\) | ||||
0.704071 | + | 0.710130i | \(0.251364\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 27.0928 | 0.156968 | 0.0784840 | − | 0.996915i | \(-0.474992\pi\) | ||||
0.0784840 | + | 0.996915i | \(0.474992\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 132.540 | 0.699158 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −96.7926 | −0.467455 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −94.1922 | −0.418516 | −0.209258 | − | 0.977860i | \(-0.567105\pi\) | ||||
−0.209258 | + | 0.977860i | \(0.567105\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −112.901 | −0.463553 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −160.354 | −0.610808 | −0.305404 | − | 0.952223i | \(-0.598791\pi\) | ||||
−0.305404 | + | 0.952223i | \(0.598791\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 151.302 | 0.536589 | 0.268295 | − | 0.963337i | \(-0.413540\pi\) | ||||
0.268295 | + | 0.963337i | \(0.413540\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 172.462 | 0.571314 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 466.948 | 1.44918 | 0.724589 | − | 0.689181i | \(-0.242030\pi\) | ||||
0.724589 | + | 0.689181i | \(0.242030\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 395.594 | 1.15333 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −386.870 | −1.06221 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 120.847 | 0.313199 | 0.156600 | − | 0.987662i | \(-0.449947\pi\) | ||||
0.156600 | + | 0.987662i | \(0.449947\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −54.3542 | −0.133257 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 208.169 | 0.483730 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 439.633 | 0.970090 | 0.485045 | − | 0.874489i | \(-0.338803\pi\) | ||||
0.485045 | + | 0.874489i | \(0.338803\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 137.305 | 0.288198 | 0.144099 | − | 0.989563i | \(-0.453972\pi\) | ||||
0.144099 | + | 0.989563i | \(0.453972\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1316.00 | −2.63176 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 46.3002 | 0.0883513 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −512.280 | −0.934104 | −0.467052 | − | 0.884230i | \(-0.654684\pi\) | ||||
−0.467052 | + | 0.884230i | \(0.654684\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1065.94 | −1.85977 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 410.719 | 0.686526 | 0.343263 | − | 0.939239i | \(-0.388468\pi\) | ||||
0.343263 | + | 0.939239i | \(0.388468\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −308.004 | −0.493823 | −0.246912 | − | 0.969038i | \(-0.579416\pi\) | ||||
−0.246912 | + | 0.969038i | \(0.579416\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 975.420 | 1.50176 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 414.759 | 0.613847 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −586.462 | −0.835217 | −0.417608 | − | 0.908627i | \(-0.637132\pi\) | ||||
−0.417608 | + | 0.908627i | \(0.637132\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 308.386 | 0.423027 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1354.20 | −1.79088 | −0.895440 | − | 0.445182i | \(-0.853139\pi\) | ||||
−0.895440 | + | 0.445182i | \(0.853139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 158.654 | 0.202453 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1909.84 | −2.35352 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 439.882 | 0.523904 | 0.261952 | − | 0.965081i | \(-0.415634\pi\) | ||||
0.261952 | + | 0.965081i | \(0.415634\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −353.302 | −0.406990 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −235.292 | −0.262351 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −85.3693 | −0.0921969 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1511.27 | −1.58192 | −0.790959 | − | 0.611869i | \(-0.790418\pi\) | ||||
−0.790959 | + | 0.611869i | \(0.790418\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −739.006 | −0.750231 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −336.260 | −0.331278 | −0.165639 | − | 0.986186i | \(-0.552969\pi\) | ||||
−0.165639 | + | 0.986186i | \(0.552969\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 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 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1434.62 | −1.29617 | −0.648083 | − | 0.761570i | \(-0.724429\pi\) | ||||
−0.648083 | + | 0.761570i | \(0.724429\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −849.147 | −0.746179 | −0.373089 | − | 0.927795i | \(-0.621702\pi\) | ||||
−0.373089 | + | 0.927795i | \(0.621702\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 818.027 | 0.699493 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1614.53 | 1.34409 | 0.672044 | − | 0.740511i | \(-0.265417\pi\) | ||||
0.672044 | + | 0.740511i | \(0.265417\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 437.140 | 0.354465 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 629.503 | 0.497415 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1210.64 | −0.932599 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1098.09 | −0.825012 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1392.62 | 1.02088 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −845.211 | −0.604784 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 865.174 | 0.604502 | 0.302251 | − | 0.953228i | \(-0.402262\pi\) | ||||
0.302251 | + | 0.953228i | \(0.402262\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1314.01 | −0.896836 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 281.400 | 0.187680 | 0.0938400 | − | 0.995587i | \(-0.470086\pi\) | ||||
0.0938400 | + | 0.995587i | \(0.470086\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 651.426 | 0.424705 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −662.641 | −0.422452 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2641.43 | −1.64725 | −0.823624 | − | 0.567137i | \(-0.808051\pi\) | ||||
−0.823624 | + | 0.567137i | \(0.808051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1998.64 | 1.21958 | 0.609791 | − | 0.792562i | \(-0.291253\pi\) | ||||
0.609791 | + | 0.792562i | \(0.291253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4055.28 | −2.42210 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −198.398 | −0.116020 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 783.218 | 0.448570 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3435.60 | −1.92764 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1752.98 | 0.963824 | 0.481912 | − | 0.876220i | \(-0.339942\pi\) | ||||
0.481912 | + | 0.876220i | \(0.339942\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2794.64 | −1.50613 | −0.753063 | − | 0.657949i | \(-0.771424\pi\) | ||||
−0.753063 | + | 0.657949i | \(0.771424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2157.08 | 1.13980 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 96.4924 | 0.0500030 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3244.87 | −1.64949 | −0.824743 | − | 0.565508i | \(-0.808680\pi\) | ||||
−0.824743 | + | 0.565508i | \(0.808680\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1049.51 | −0.523470 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3335.68 | −1.63285 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3281.47 | −1.57684 | −0.788418 | − | 0.615139i | \(-0.789100\pi\) | ||||
−0.788418 | + | 0.615139i | \(0.789100\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 472.047 | 0.222720 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3126.52 | −1.44873 | −0.724364 | − | 0.689418i | \(-0.757866\pi\) | ||||
−0.724364 | + | 0.689418i | \(0.757866\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1160.69 | −0.519066 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −97.5698 | −0.0428792 | −0.0214396 | − | 0.999770i | \(-0.506825\pi\) | ||||
−0.0214396 | + | 0.999770i | \(0.506825\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3052.40 | 1.31851 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3818.06 | −1.62137 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 34.7150 | 0.0144956 | 0.00724782 | − | 0.999974i | \(-0.497693\pi\) | ||||
0.00724782 | + | 0.999974i | \(0.497693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1229.35 | 0.504843 | 0.252422 | − | 0.967617i | \(-0.418773\pi\) | ||||
0.252422 | + | 0.967617i | \(0.418773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1192.45 | −0.481684 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −335.471 | −0.133320 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −679.839 | −0.265854 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5056.40 | 1.94603 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4280.80 | 1.62172 | 0.810858 | − | 0.585243i | \(-0.199001\pi\) | ||||
0.810858 | + | 0.585243i | \(0.199001\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 472.320 | 0.176157 | 0.0880786 | − | 0.996114i | \(-0.471927\pi\) | ||||
0.0880786 | + | 0.996114i | \(0.471927\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −402.101 | −0.147667 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4484.37 | 1.62182 | 0.810908 | − | 0.585173i | \(-0.198974\pi\) | ||||
0.810908 | + | 0.585173i | \(0.198974\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −366.240 | −0.130463 | −0.0652314 | − | 0.997870i | \(-0.520779\pi\) | ||||
−0.0652314 | + | 0.997870i | \(0.520779\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4448.98 | 1.56123 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5976.49 | −2.06634 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −571.110 | −0.194576 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5943.41 | 1.99563 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 365.810 | 0.121070 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2122.55 | −0.692524 | −0.346262 | − | 0.938138i | \(-0.612549\pi\) | ||||
−0.346262 | + | 0.938138i | \(0.612549\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3566.95 | −1.14743 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 538.870 | 0.170933 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −736.303 | −0.230339 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2674.91 | 0.825358 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 579.103 | 0.176266 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5926.42 | −1.77965 | −0.889826 | − | 0.456301i | \(-0.849174\pi\) | ||||
−0.889826 | + | 0.456301i | \(0.849174\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5438.68 | −1.61146 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 895.661 | 0.261881 | 0.130941 | − | 0.991390i | \(-0.458200\pi\) | ||||
0.130941 | + | 0.991390i | \(0.458200\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −627.717 | −0.181138 | −0.0905692 | − | 0.995890i | \(-0.528869\pi\) | ||||
−0.0905692 | + | 0.995890i | \(0.528869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3602.04 | −1.02596 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 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 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5093.22 | 1.39595 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 544.622 | 0.147400 | 0.0737001 | − | 0.997280i | \(-0.476519\pi\) | ||||
0.0737001 | + | 0.997280i | \(0.476519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5426.10 | 1.45031 | 0.725157 | − | 0.688584i | \(-0.241767\pi\) | ||||
0.725157 | + | 0.688584i | \(0.241767\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2345.23 | 0.619121 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1408.93 | 0.367400 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −311.606 | −0.0802713 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11760.8 | 2.99321 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5221.22 | 1.31299 | 0.656494 | − | 0.754331i | \(-0.272039\pi\) | ||||
0.656494 | + | 0.754331i | \(0.272039\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1873.16 | −0.465472 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1377.86 | −0.338372 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 658.206 | 0.159758 | 0.0798789 | − | 0.996805i | \(-0.474547\pi\) | ||||
0.0798789 | + | 0.996805i | \(0.474547\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2559.87 | 0.614141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10648.7 | 2.52544 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3246.45 | 0.761160 | 0.380580 | − | 0.924748i | \(-0.375724\pi\) | ||||
0.380580 | + | 0.924748i | \(0.375724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 430.401 | 0.0997711 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3820.23 | −0.875634 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2585.80 | 0.586093 | 0.293047 | − | 0.956098i | \(-0.405331\pi\) | ||||
0.293047 | + | 0.956098i | \(0.405331\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 988.933 | 0.221673 | 0.110836 | − | 0.993839i | \(-0.464647\pi\) | ||||
0.110836 | + | 0.993839i | \(0.464647\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3068.31 | 0.680229 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1714.09 | 0.375866 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8142.40 | −1.76617 | −0.883086 | − | 0.469211i | \(-0.844538\pi\) | ||||
−0.883086 | + | 0.469211i | \(0.844538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1311.92 | 0.281515 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1534.21 | 0.325705 | 0.162853 | − | 0.986650i | \(-0.447930\pi\) | ||||
0.162853 | + | 0.986650i | \(0.447930\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6965.00 | 1.46299 | 0.731495 | − | 0.681847i | \(-0.238823\pi\) | ||||
0.731495 | + | 0.681847i | \(0.238823\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 741.403 | 0.154095 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4357.96 | 0.896314 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2928.62 | −0.596096 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13124.9 | 2.64396 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −640.029 | −0.127614 | −0.0638070 | − | 0.997962i | \(-0.520324\pi\) | ||||
−0.0638070 | + | 0.997962i | \(0.520324\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1565.77 | 0.309027 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2839.44 | 0.554750 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1595.60 | 0.308616 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4111.95 | −0.787404 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2920.30 | 0.553686 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 489.019 | 0.0918070 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 100.406 | 0.0186660 | 0.00933299 | − | 0.999956i | \(-0.497029\pi\) | ||||
0.00933299 | + | 0.999956i | \(0.497029\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2802.64 | −0.515977 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −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 | \(0.611157\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4687.02 | −0.838360 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4406.81 | −0.780791 | −0.390396 | − | 0.920647i | \(-0.627662\pi\) | ||||
−0.390396 | + | 0.920647i | \(0.627662\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3356.11 | −0.589048 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12459.2 | 2.16636 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1067.76 | −0.183938 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1460.10 | −0.249205 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7374.55 | 1.24714 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12690.3 | −2.12656 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4131.49 | 0.686064 | 0.343032 | − | 0.939324i | \(-0.388546\pi\) | ||||
0.343032 | + | 0.939324i | \(0.388546\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4561.10 | −0.750591 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1824.51 | −0.297564 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −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 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −413.473 | −0.0656622 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1429.34 | −0.225007 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3796.41 | −0.592441 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10069.4 | −1.55779 | −0.778896 | − | 0.627153i | \(-0.784220\pi\) | ||||
−0.778896 | + | 0.627153i | \(0.784220\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5879.32 | −0.901757 | −0.450878 | − | 0.892585i | \(-0.648889\pi\) | ||||
−0.450878 | + | 0.892585i | \(0.648889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2418.70 | −0.367808 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −9142.56 | −1.37850 | −0.689249 | − | 0.724525i | \(-0.742059\pi\) | ||||
−0.689249 | + | 0.724525i | \(0.742059\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1462.80 | 0.218696 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10514.0 | 1.55871 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2754.32 | −0.404924 | −0.202462 | − | 0.979290i | \(-0.564894\pi\) | ||||
−0.202462 | + | 0.979290i | \(0.564894\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6284.45 | −0.916235 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9536.54 | 1.37889 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1096.97 | −0.157310 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3040.19 | 0.432416 | 0.216208 | − | 0.976347i | \(-0.430631\pi\) | ||||
0.216208 | + | 0.976347i | \(0.430631\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7764.88 | −1.09546 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3284.26 | −0.459596 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5384.72 | 0.747481 | 0.373740 | − | 0.927533i | \(-0.378075\pi\) | ||||
0.373740 | + | 0.927533i | \(0.378075\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7340.37 | 1.01081 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2858.82 | 0.390548 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3424.27 | 0.464097 | 0.232049 | − | 0.972704i | \(-0.425457\pi\) | ||||
0.232049 | + | 0.972704i | \(0.425457\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7513.74 | −1.01034 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −382.985 | −0.0510956 | −0.0255478 | − | 0.999674i | \(-0.508133\pi\) | ||||
−0.0255478 | + | 0.999674i | \(0.508133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1477.19 | 0.195544 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7326.54 | 0.962349 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8588.34 | −1.11940 | −0.559699 | − | 0.828696i | \(-0.689083\pi\) | ||||
−0.559699 | + | 0.828696i | \(0.689083\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5467.56 | 0.707178 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2443.87 | −0.313681 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2088.72 | −0.266063 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7239.16 | 0.915171 | 0.457586 | − | 0.889166i | \(-0.348714\pi\) | ||||
0.457586 | + | 0.889166i | \(0.348714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −5657.41 | −0.709837 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4269.62 | 0.531708 | 0.265854 | − | 0.964013i | \(-0.414346\pi\) | ||||
0.265854 | + | 0.964013i | \(0.414346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 352.206 | 0.0435351 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1098.33 | 0.134757 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1437.50 | 0.175072 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13562.5 | 1.63967 | 0.819834 | − | 0.572602i | \(-0.194066\pi\) | ||||
0.819834 | + | 0.572602i | \(0.194066\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 22939.9 | 2.75315 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11947.9 | −1.42353 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4823.06 | −0.570494 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −17357.5 | −2.03837 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14576.9 | 1.69959 | 0.849794 | − | 0.527114i | \(-0.176726\pi\) | ||||
0.849794 | + | 0.527114i | \(0.176726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15848.4 | −1.83469 | −0.917343 | − | 0.398099i | \(-0.869670\pi\) | ||||
−0.917343 | + | 0.398099i | \(0.869670\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22611.2 | 2.59904 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5003.24 | −0.571042 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3731.55 | −0.422909 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1723.02 | 0.193912 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10694.7 | 1.19524 | 0.597618 | − | 0.801781i | \(-0.296114\pi\) | ||||
0.597618 | + | 0.801781i | \(0.296114\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16079.0 | −1.78454 | −0.892272 | − | 0.451498i | \(-0.850890\pi\) | ||||
−0.892272 | + | 0.451498i | \(0.850890\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6801.98 | −0.749724 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2942.01 | −0.322049 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6035.80 | 0.656203 | 0.328101 | − | 0.944643i | \(-0.393591\pi\) | ||||
0.328101 | + | 0.944643i | \(0.393591\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19156.0 | 2.06845 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10201.3 | −1.09409 | −0.547043 | − | 0.837105i | \(-0.684247\pi\) | ||||
−0.547043 | + | 0.837105i | \(0.684247\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1566.66 | 0.166892 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15224.0 | −1.61090 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5822.54 | −0.611988 | −0.305994 | − | 0.952033i | \(-0.598989\pi\) | ||||
−0.305994 | + | 0.952033i | \(0.598989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2447.22 | 0.255511 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24270.5 | 2.51728 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1258.30 | −0.129649 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4621.60 | 0.473062 | 0.236531 | − | 0.971624i | \(-0.423990\pi\) | ||||
0.236531 | + | 0.971624i | \(0.423990\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8288.03 | −0.842816 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5127.77 | −0.518056 | −0.259028 | − | 0.965870i | \(-0.583402\pi\) | ||||
−0.259028 | + | 0.965870i | \(0.583402\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6486.27 | 0.651064 | 0.325532 | − | 0.945531i | \(-0.394457\pi\) | ||||
0.325532 | + | 0.945531i | \(0.394457\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −838.004 | −0.0835731 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12978.0 | −1.28598 | −0.642990 | − | 0.765875i | \(-0.722306\pi\) | ||||
−0.642990 | + | 0.765875i | \(0.722306\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13922.3 | 1.37073 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 28180.6 | 2.75689 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2309.08 | −0.224464 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2692.16 | 0.260053 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5851.79 | 0.561709 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5808.96 | −0.554109 | −0.277055 | − | 0.960854i | \(-0.589358\pi\) | ||||
−0.277055 | + | 0.960854i | \(0.589358\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1224.50 | −0.116076 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28969.2 | 2.72908 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5382.46 | −0.503928 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5387.14 | −0.501262 | −0.250631 | − | 0.968083i | \(-0.580638\pi\) | ||||
−0.250631 | + | 0.968083i | \(0.580638\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 28498.4 | 2.63547 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15259.1 | −1.40251 | −0.701255 | − | 0.712911i | \(-0.747376\pi\) | ||||
−0.701255 | + | 0.712911i | \(0.747376\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9796.16 | 0.894922 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2632.01 | −0.238990 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11162.1 | −1.00742 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1856.04 | −0.166509 | −0.0832544 | − | 0.996528i | \(-0.526531\pi\) | ||||
−0.0832544 | + | 0.996528i | \(0.526531\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27152.8 | 2.42135 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1049.46 | 0.0930283 | 0.0465142 | − | 0.998918i | \(-0.485189\pi\) | ||||
0.0465142 | + | 0.998918i | \(0.485189\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1197.61 | −0.105530 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1467.71 | −0.128566 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 551.106 | 0.0479909 | 0.0239954 | − | 0.999712i | \(-0.492361\pi\) | ||||
0.0239954 | + | 0.999712i | \(0.492361\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8370.64 | 0.724649 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4459.66 | 0.383818 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1149.36 | 0.0983431 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7126.26 | −0.606214 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 847.361 | 0.0716667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8995.30 | −0.756413 | −0.378206 | − | 0.925721i | \(-0.623459\pi\) | ||||
−0.378206 | + | 0.925721i | \(0.623459\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2663.91 | −0.222724 | −0.111362 | − | 0.993780i | \(-0.535521\pi\) | ||||
−0.111362 | + | 0.993780i | \(0.535521\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −26509.1 | −2.20372 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1206.89 | 0.0997586 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2897.77 | 0.238167 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21288.5 | 1.73981 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2084.60 | −0.169408 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5109.47 | −0.412900 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −301.488 | −0.0242275 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6037.30 | −0.482458 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6169.23 | 0.490270 | 0.245135 | − | 0.969489i | \(-0.421168\pi\) | ||||
0.245135 | + | 0.969489i | \(0.421168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10676.5 | −0.843776 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3024.28 | −0.237699 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5140.42 | −0.401807 | −0.200904 | − | 0.979611i | \(-0.564388\pi\) | ||||
−0.200904 | + | 0.979611i | \(0.564388\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6648.76 | 0.516871 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5271.15 | −0.407547 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15938.3 | 1.22562 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2913.45 | 0.222827 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2778.56 | −0.211367 | −0.105683 | − | 0.994400i | \(-0.533703\pi\) | ||||
−0.105683 | + | 0.994400i | \(0.533703\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1966.93 | 0.148823 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5904.17 | 0.444339 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4906.14 | −0.367263 | −0.183632 | − | 0.982995i | \(-0.558785\pi\) | ||||
−0.183632 | + | 0.982995i | \(0.558785\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5750.22 | 0.428166 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8381.04 | −0.620759 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9363.15 | −0.689849 | −0.344924 | − | 0.938631i | \(-0.612095\pi\) | ||||
−0.344924 | + | 0.938631i | \(0.612095\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7199.32 | −0.527640 | −0.263820 | − | 0.964572i | \(-0.584982\pi\) | ||||
−0.263820 | + | 0.964572i | \(0.584982\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −37177.3 | −2.71048 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13785.4 | −0.999813 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11449.6 | −0.826086 | −0.413043 | − | 0.910711i | \(-0.635534\pi\) | ||||
−0.413043 | + | 0.910711i | \(0.635534\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4101.94 | −0.294423 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36803.3 | 2.62798 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1844.28 | −0.131016 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2242.01 | 0.158454 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5439.39 | 0.382466 | 0.191233 | − | 0.981545i | \(-0.438751\pi\) | ||||
0.191233 | + | 0.981545i | \(0.438751\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −649.406 | −0.0454301 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −38945.2 | −2.71064 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28405.8 | −1.96709 | −0.983547 | − | 0.180651i | \(-0.942180\pi\) | ||||
−0.983547 | + | 0.180651i | \(0.942180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4311.76 | −0.297084 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3180.67 | 0.218051 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10482.3 | −0.715020 | −0.357510 | − | 0.933909i | \(-0.616374\pi\) | ||||
−0.357510 | + | 0.933909i | \(0.616374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3199.54 | 0.217158 | 0.108579 | − | 0.994088i | \(-0.465370\pi\) | ||||
0.108579 | + | 0.994088i | \(0.465370\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −24806.3 | −1.67527 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3910.91 | −0.262812 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11342.8 | 0.758468 | 0.379234 | − | 0.925301i | \(-0.376188\pi\) | ||||
0.379234 | + | 0.925301i | \(0.376188\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 51903.7 | 3.45361 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6070.32 | 0.401930 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14385.4 | −0.947831 | −0.473916 | − | 0.880570i | \(-0.657160\pi\) | ||||
−0.473916 | + | 0.880570i | \(0.657160\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4959.89 | 0.325207 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 22056.8 | 1.43918 | 0.719588 | − | 0.694401i | \(-0.244331\pi\) | ||||
0.719588 | + | 0.694401i | \(0.244331\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13621.4 | −0.884477 | −0.442238 | − | 0.896898i | \(-0.645815\pi\) | ||||
−0.442238 | + | 0.896898i | \(0.645815\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22836.0 | −1.47565 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11954.7 | −0.768789 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11029.2 | 0.705866 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3176.94 | −0.202352 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4195.92 | −0.265982 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18737.5 | −1.18214 | −0.591068 | − | 0.806622i | \(-0.701293\pi\) | ||||
−0.591068 | + | 0.806622i | \(0.701293\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18433.7 | 1.15746 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3081.36 | 0.192567 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5142.72 | 0.319877 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 19888.4 | 1.23125 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29798.7 | 1.83616 | 0.918081 | − | 0.396394i | \(-0.129739\pi\) | ||||
0.918081 | + | 0.396394i | \(0.129739\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22983.5 | 1.40961 | 0.704807 | − | 0.709399i | \(-0.251034\pi\) | ||||
0.704807 | + | 0.709399i | \(0.251034\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4679.90 | −0.285692 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24905.4 | −1.51334 | −0.756672 | − | 0.653794i | \(-0.773176\pi\) | ||||
−0.756672 | + | 0.653794i | \(0.773176\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6709.39 | −0.405804 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6394.54 | 0.384980 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −10077.8 | −0.603946 | −0.301973 | − | 0.953316i | \(-0.597645\pi\) | ||||
−0.301973 | + | 0.953316i | \(0.597645\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1002.22 | 0.0597864 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14914.6 | −0.885650 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12334.6 | −0.729116 | −0.364558 | − | 0.931181i | \(-0.618780\pi\) | ||||
−0.364558 | + | 0.931181i | \(0.618780\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12749.1 | 0.750202 | 0.375101 | − | 0.926984i | \(-0.377608\pi\) | ||||
0.375101 | + | 0.926984i | \(0.377608\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5029.31 | −0.294604 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2320.09 | 0.135292 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26991.3 | 1.56688 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 51468.9 | 2.97444 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2095.46 | −0.120558 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13618.2 | −0.780007 | −0.390004 | − | 0.920813i | \(-0.627526\pi\) | ||||
−0.390004 | + | 0.920813i | \(0.627526\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20896.7 | 1.19158 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9655.67 | −0.548150 | −0.274075 | − | 0.961708i | \(-0.588372\pi\) | ||||
−0.274075 | + | 0.961708i | \(0.588372\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 41071.9 | 2.32135 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7778.51 | −0.437699 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16316.8 | −0.914119 | −0.457060 | − | 0.889436i | \(-0.651097\pi\) | ||||
−0.457060 | + | 0.889436i | \(0.651097\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9407.61 | −0.524739 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5451.51 | 0.302748 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1571.01 | 0.0868658 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2350.84 | −0.129421 | −0.0647106 | − | 0.997904i | \(-0.520612\pi\) | ||||
−0.0647106 | + | 0.997904i | \(0.520612\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 20084.0 | 1.10091 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7118.24 | 0.388504 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7143.20 | −0.388189 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20007.1 | −1.08260 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8076.90 | 0.435179 | 0.217589 | − | 0.976040i | \(-0.430181\pi\) | ||||
0.217589 | + | 0.976040i | \(0.430181\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2257.76 | 0.121128 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14443.1 | −0.771573 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9138.55 | 0.486125 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13624.9 | 0.721712 | 0.360856 | − | 0.932622i | \(-0.382485\pi\) | ||||
0.360856 | + | 0.932622i | \(0.382485\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −28398.4 | −1.49792 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3325.33 | 0.174663 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −706.604 | −0.0369587 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4729.86 | −0.246359 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16235.8 | 0.842131 | 0.421066 | − | 0.907030i | \(-0.361656\pi\) | ||||
0.421066 | + | 0.907030i | \(0.361656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8770.37 | −0.453018 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −47123.8 | −2.42400 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24699.2 | −1.26525 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 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 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6739.96 | 0.341021 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3053.70 | −0.153876 | −0.0769379 | − | 0.997036i | \(-0.524514\pi\) | ||||
−0.0769379 | + | 0.997036i | \(0.524514\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12236.1 | −0.614060 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7818.10 | 0.390751 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8033.62 | 0.399894 | 0.199947 | − | 0.979807i | \(-0.435923\pi\) | ||||
0.199947 | + | 0.979807i | \(0.435923\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2706.19 | 0.134163 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16139.6 | −0.796912 | −0.398456 | − | 0.917187i | \(-0.630454\pi\) | ||||
−0.398456 | + | 0.917187i | \(0.630454\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6243.33 | 0.307031 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −65574.9 | −3.21186 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 38988.7 | 1.90202 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18491.1 | −0.898469 | −0.449235 | − | 0.893414i | \(-0.648303\pi\) | ||||
−0.449235 | + | 0.893414i | \(0.648303\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −45344.5 | −2.19448 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9953.28 | −0.479784 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −160.630 | −0.00771227 | −0.00385613 | − | 0.999993i | \(-0.501227\pi\) | ||||
−0.00385613 | + | 0.999993i | \(0.501227\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16267.7 | 0.777973 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26799.1 | 1.27656 | 0.638282 | − | 0.769803i | \(-0.279645\pi\) | ||||
0.638282 | + | 0.769803i | \(0.279645\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23077.3 | 1.09496 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7682.57 | 0.363090 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5715.22 | 0.269054 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5145.82 | −0.241304 | −0.120652 | − | 0.992695i | \(-0.538499\pi\) | ||||
−0.120652 | + | 0.992695i | \(0.538499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5716.29 | −0.267013 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12810.6 | −0.596072 | −0.298036 | − | 0.954555i | \(-0.596332\pi\) | ||||
−0.298036 | + | 0.954555i | \(0.596332\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3042.94 | −0.141039 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −22231.6 | −1.02645 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3843.64 | 0.176781 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6268.13 | −0.287185 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −40915.0 | −1.86741 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11556.8 | −0.525452 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28073.0 | −1.27153 | −0.635764 | − | 0.771883i | \(-0.719315\pi\) | ||||
−0.635764 | + | 0.771883i | \(0.719315\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −28194.3 | −1.27217 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −43878.1 | −1.97235 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1784.96 | 0.0799318 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3737.89 | −0.166754 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −30093.1 | −1.33746 | −0.668729 | − | 0.743507i | \(-0.733161\pi\) | ||||
−0.668729 | + | 0.743507i | \(0.733161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20800.8 | 0.921003 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21300.6 | 0.939598 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4700.56 | 0.206574 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11880.2 | −0.520151 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22456.8 | −0.979575 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24337.1 | −1.05766 | −0.528831 | − | 0.848727i | \(-0.677369\pi\) | ||||
−0.528831 | + | 0.848727i | \(0.677369\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19078.7 | −0.826071 | −0.413035 | − | 0.910715i | \(-0.635531\pi\) | ||||
−0.413035 | + | 0.910715i | \(0.635531\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8588.54 | −0.370496 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11687.1 | −0.502309 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3626.66 | −0.155301 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17108.0 | −0.729919 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2013.92 | −0.0856104 | −0.0428052 | − | 0.999083i | \(-0.513629\pi\) | ||||
−0.0428052 | + | 0.999083i | \(0.513629\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7692.10 | −0.325795 | −0.162898 | − | 0.986643i | \(-0.552084\pi\) | ||||
−0.162898 | + | 0.986643i | \(0.552084\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −14886.2 | −0.628209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4762.76 | 0.200263 | 0.100131 | − | 0.994974i | \(-0.468074\pi\) | ||||
0.100131 | + | 0.994974i | \(0.468074\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19977.7 | −0.836976 | −0.418488 | − | 0.908222i | \(-0.637440\pi\) | ||||
−0.418488 | + | 0.908222i | \(0.637440\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 70714.0 | 2.95191 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 17622.3 | 0.732984 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11135.3 | −0.461499 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5040.72 | −0.208164 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30615.8 | −1.25980 | −0.629901 | − | 0.776676i | \(-0.716905\pi\) | ||||
−0.629901 | + | 0.776676i | \(0.716905\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23971.0 | 0.982861 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13324.1 | −0.544372 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 601.902 | 0.0245042 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29842.9 | 1.21064 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −60488.6 | −2.44519 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11561.0 | −0.465696 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5660.88 | −0.227227 | −0.113614 | − | 0.993525i | \(-0.536243\pi\) | ||||
−0.113614 | + | 0.993525i | \(0.536243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4133.86 | −0.165351 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 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 | \(-0.257021\pi\) | ||||
0.691339 | + | 0.722530i | \(0.257021\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37847.4 | −1.49807 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8360.51 | −0.329774 | −0.164887 | − | 0.986312i | \(-0.552726\pi\) | ||||
−0.164887 | + | 0.986312i | \(0.552726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −347.500 | −0.0136594 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 25434.1 | 0.996293 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8950.21 | 0.349385 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6659.64 | −0.259074 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −73180.6 | −2.83710 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22970.4 | 0.887475 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40579.3 | 1.56245 | 0.781223 | − | 0.624251i | \(-0.214596\pi\) | ||||
0.781223 | + | 0.624251i | \(0.214596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5558.43 | 0.213289 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10445.2 | 0.399442 | 0.199721 | − | 0.979853i | \(-0.435996\pi\) | ||||
0.199721 | + | 0.979853i | \(0.435996\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18227.6 | −0.694685 | −0.347343 | − | 0.937738i | \(-0.612916\pi\) | ||||
−0.347343 | + | 0.937738i | \(0.612916\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13598.2 | −0.516496 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23517.7 | −0.890245 | −0.445122 | − | 0.895470i | \(-0.646840\pi\) | ||||
−0.445122 | + | 0.895470i | \(0.646840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23512.9 | −0.887061 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4706.40 | −0.176959 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11192.6 | −0.419424 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 123.639 | 0.00461766 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −13857.3 | −0.515809 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5957.95 | 0.221033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5383.28 | 0.199049 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 35710.9 | 1.31604 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4378.38 | 0.160820 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30564.6 | 1.11894 | 0.559471 | − | 0.828850i | \(-0.311004\pi\) | ||||
0.559471 | + | 0.828850i | \(0.311004\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −16282.8 | −0.594132 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32766.5 | −1.19166 | −0.595831 | − | 0.803110i | \(-0.703177\pi\) | ||||
−0.595831 | + | 0.803110i | \(0.703177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20667.0 | 0.749154 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4246.96 | −0.153443 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7647.64 | −0.275406 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20686.7 | 0.742538 | 0.371269 | − | 0.928525i | \(-0.378923\pi\) | ||||
0.371269 | + | 0.928525i | \(0.378923\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −871.989 | −0.0311976 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5339.34 | 0.190408 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10579.2 | 0.376047 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 15626.8 | 0.553669 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 45632.2 | 1.61156 | 0.805782 | − | 0.592212i | \(-0.201745\pi\) | ||||
0.805782 | + | 0.592212i | \(0.201745\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9482.26 | −0.333801 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33687.1 | 1.18206 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2421.28 | −0.0846892 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17761.4 | −0.619253 | −0.309626 | − | 0.950858i | \(-0.600204\pi\) | ||||
−0.309626 | + | 0.950858i | \(0.600204\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 32909.6 | 1.14373 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44888.3 | 1.55507 | 0.777534 | − | 0.628841i | \(-0.216470\pi\) | ||||
0.777534 | + | 0.628841i | \(0.216470\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19681.7 | −0.679664 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18008.6 | 0.619917 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16069.6 | −0.551415 | −0.275708 | − | 0.961242i | \(-0.588912\pi\) | ||||
−0.275708 | + | 0.961242i | \(0.588912\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4004.05 | −0.136962 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38271.6 | 1.30499 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3512.03 | 0.119377 | 0.0596883 | − | 0.998217i | \(-0.480989\pi\) | ||||
0.0596883 | + | 0.998217i | \(0.480989\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15246.3 | 0.516605 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 29146.7 | 0.984513 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 71786.5 | 2.41721 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29057.0 | −0.975361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −69468.9 | −2.32461 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1682.19 | 0.0561158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37011.9 | −1.23084 | −0.615421 | − | 0.788199i | \(-0.711014\pi\) | ||||
−0.615421 | + | 0.788199i | \(0.711014\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9273.16 | 0.307427 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19532.3 | −0.645542 | −0.322771 | − | 0.946477i | \(-0.604614\pi\) | ||||
−0.322771 | + | 0.946477i | \(0.604614\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −54317.1 | −1.78965 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 12680.5 | 0.416513 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30201.2 | 0.988970 | 0.494485 | − | 0.869186i | \(-0.335357\pi\) | ||||
0.494485 | + | 0.869186i | \(0.335357\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6713.21 | −0.219157 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −41118.5 | −1.33824 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −38774.9 | −1.25812 | −0.629058 | − | 0.777359i | \(-0.716559\pi\) | ||||
−0.629058 | + | 0.777359i | \(0.716559\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15971.3 | 0.516638 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 110211. | 3.55425 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18570.6 | 0.597079 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27728.9 | −0.888838 | −0.444419 | − | 0.895819i | \(-0.646590\pi\) | ||||
−0.444419 | + | 0.895819i | \(0.646590\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35880.6 | −1.14666 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1304.38 | −0.0415596 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 48918.2 | 1.55392 | 0.776958 | − | 0.629552i | \(-0.216761\pi\) | ||||
0.776958 | + | 0.629552i | \(0.216761\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 832.4.a.s.1.1 | 2 | ||
4.3 | odd | 2 | 832.4.a.z.1.2 | 2 | |||
8.3 | odd | 2 | 208.4.a.h.1.1 | 2 | |||
8.5 | even | 2 | 13.4.a.b.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 117.4.a.d.1.2 | 2 | |||
24.11 | even | 2 | 1872.4.a.bb.1.2 | 2 | |||
40.13 | odd | 4 | 325.4.b.e.274.3 | 4 | |||
40.29 | even | 2 | 325.4.a.f.1.2 | 2 | |||
40.37 | odd | 4 | 325.4.b.e.274.2 | 4 | |||
56.13 | odd | 2 | 637.4.a.b.1.1 | 2 | |||
88.21 | odd | 2 | 1573.4.a.b.1.2 | 2 | |||
104.5 | odd | 4 | 169.4.b.f.168.3 | 4 | |||
104.21 | odd | 4 | 169.4.b.f.168.2 | 4 | |||
104.29 | even | 6 | 169.4.c.g.22.2 | 4 | |||
104.37 | odd | 12 | 169.4.e.f.147.3 | 8 | |||
104.45 | odd | 12 | 169.4.e.f.23.3 | 8 | |||
104.61 | even | 6 | 169.4.c.g.146.2 | 4 | |||
104.69 | even | 6 | 169.4.c.j.146.1 | 4 | |||
104.77 | even | 2 | 169.4.a.g.1.2 | 2 | |||
104.85 | odd | 12 | 169.4.e.f.23.2 | 8 | |||
104.93 | odd | 12 | 169.4.e.f.147.2 | 8 | |||
104.101 | even | 6 | 169.4.c.j.22.1 | 4 | |||
312.77 | odd | 2 | 1521.4.a.r.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.a.b.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
117.4.a.d.1.2 | 2 | 24.5 | odd | 2 | |||
169.4.a.g.1.2 | 2 | 104.77 | even | 2 | |||
169.4.b.f.168.2 | 4 | 104.21 | odd | 4 | |||
169.4.b.f.168.3 | 4 | 104.5 | odd | 4 | |||
169.4.c.g.22.2 | 4 | 104.29 | even | 6 | |||
169.4.c.g.146.2 | 4 | 104.61 | even | 6 | |||
169.4.c.j.22.1 | 4 | 104.101 | even | 6 | |||
169.4.c.j.146.1 | 4 | 104.69 | even | 6 | |||
169.4.e.f.23.2 | 8 | 104.85 | odd | 12 | |||
169.4.e.f.23.3 | 8 | 104.45 | odd | 12 | |||
169.4.e.f.147.2 | 8 | 104.93 | odd | 12 | |||
169.4.e.f.147.3 | 8 | 104.37 | odd | 12 | |||
208.4.a.h.1.1 | 2 | 8.3 | odd | 2 | |||
325.4.a.f.1.2 | 2 | 40.29 | even | 2 | |||
325.4.b.e.274.2 | 4 | 40.37 | odd | 4 | |||
325.4.b.e.274.3 | 4 | 40.13 | odd | 4 | |||
637.4.a.b.1.1 | 2 | 56.13 | odd | 2 | |||
832.4.a.s.1.1 | 2 | 1.1 | even | 1 | trivial | ||
832.4.a.z.1.2 | 2 | 4.3 | odd | 2 | |||
1521.4.a.r.1.1 | 2 | 312.77 | odd | 2 | |||
1573.4.a.b.1.2 | 2 | 88.21 | odd | 2 | |||
1872.4.a.bb.1.2 | 2 | 24.11 | even | 2 |