Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(0\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.96448 | −1.04810 | −0.524051 | − | 0.851687i | \(-0.675580\pi\) | ||||
−0.524051 | + | 0.851687i | \(0.675580\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.788155 | 0.0985194 | ||||||||
\(5\) | 20.3046 | 1.81610 | 0.908048 | − | 0.418867i | \(-0.137573\pi\) | ||||
0.908048 | + | 0.418867i | \(0.137573\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −25.7042 | −1.38789 | −0.693947 | − | 0.720026i | \(-0.744130\pi\) | ||||
−0.693947 | + | 0.720026i | \(0.744130\pi\) | |||||||
\(8\) | 21.3794 | 0.944844 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −60.1925 | −1.90345 | ||||||||
\(11\) | −49.6129 | −1.35990 | −0.679948 | − | 0.733260i | \(-0.737998\pi\) | ||||
−0.679948 | + | 0.733260i | \(0.737998\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 51.2572 | 1.09355 | 0.546776 | − | 0.837279i | \(-0.315855\pi\) | ||||
0.546776 | + | 0.837279i | \(0.315855\pi\) | |||||||
\(14\) | 76.1995 | 1.45466 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −69.6841 | −1.08881 | ||||||||
\(17\) | −127.732 | −1.82232 | −0.911162 | − | 0.412048i | \(-0.864813\pi\) | ||||
−0.911162 | + | 0.412048i | \(0.864813\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −97.6252 | −1.17878 | −0.589388 | − | 0.807850i | \(-0.700631\pi\) | ||||
−0.589388 | + | 0.807850i | \(0.700631\pi\) | |||||||
\(20\) | 16.0031 | 0.178921 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 147.077 | 1.42531 | ||||||||
\(23\) | −175.901 | −1.59469 | −0.797346 | − | 0.603522i | \(-0.793763\pi\) | ||||
−0.797346 | + | 0.603522i | \(0.793763\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 287.275 | 2.29820 | ||||||||
\(26\) | −151.951 | −1.14616 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −20.2589 | −0.136734 | ||||||||
\(29\) | −16.4948 | −0.105621 | −0.0528104 | − | 0.998605i | \(-0.516818\pi\) | ||||
−0.0528104 | + | 0.998605i | \(0.516818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −289.775 | −1.67888 | −0.839438 | − | 0.543455i | \(-0.817116\pi\) | ||||
−0.839438 | + | 0.543455i | \(0.817116\pi\) | |||||||
\(32\) | 35.5420 | 0.196344 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 378.659 | 1.90998 | ||||||||
\(35\) | −521.912 | −2.52055 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 86.9503 | 0.386339 | 0.193170 | − | 0.981165i | \(-0.438123\pi\) | ||||
0.193170 | + | 0.981165i | \(0.438123\pi\) | |||||||
\(38\) | 289.408 | 1.23548 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 434.099 | 1.71593 | ||||||||
\(41\) | −88.5567 | −0.337323 | −0.168661 | − | 0.985674i | \(-0.553944\pi\) | ||||
−0.168661 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −346.091 | −1.22741 | −0.613703 | − | 0.789537i | \(-0.710321\pi\) | ||||
−0.613703 | + | 0.789537i | \(0.710321\pi\) | |||||||
\(44\) | −39.1027 | −0.133976 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 521.456 | 1.67140 | ||||||||
\(47\) | 346.909 | 1.07664 | 0.538319 | − | 0.842741i | \(-0.319060\pi\) | ||||
0.538319 | + | 0.842741i | \(0.319060\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 317.704 | 0.926250 | ||||||||
\(50\) | −851.622 | −2.40875 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 40.3986 | 0.107736 | ||||||||
\(53\) | −234.823 | −0.608592 | −0.304296 | − | 0.952578i | \(-0.598421\pi\) | ||||
−0.304296 | + | 0.952578i | \(0.598421\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1007.37 | −2.46970 | ||||||||
\(56\) | −549.539 | −1.31134 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 48.8985 | 0.110701 | ||||||||
\(59\) | 427.583 | 0.943501 | 0.471751 | − | 0.881732i | \(-0.343622\pi\) | ||||
0.471751 | + | 0.881732i | \(0.343622\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 170.020 | 0.356866 | 0.178433 | − | 0.983952i | \(-0.442897\pi\) | ||||
0.178433 | + | 0.983952i | \(0.442897\pi\) | |||||||
\(62\) | 859.034 | 1.75964 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 452.109 | 0.883025 | ||||||||
\(65\) | 1040.75 | 1.98600 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 724.407 | 1.32090 | 0.660451 | − | 0.750869i | \(-0.270365\pi\) | ||||
0.660451 | + | 0.750869i | \(0.270365\pi\) | |||||||
\(68\) | −100.672 | −0.179534 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1547.20 | 2.64179 | ||||||||
\(71\) | −29.5053 | −0.0493189 | −0.0246594 | − | 0.999696i | \(-0.507850\pi\) | ||||
−0.0246594 | + | 0.999696i | \(0.507850\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1203.07 | −1.92888 | −0.964442 | − | 0.264294i | \(-0.914861\pi\) | ||||
−0.964442 | + | 0.264294i | \(0.914861\pi\) | |||||||
\(74\) | −257.763 | −0.404923 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −76.9438 | −0.116132 | ||||||||
\(77\) | 1275.26 | 1.88739 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1204.60 | 1.71555 | 0.857775 | − | 0.514025i | \(-0.171846\pi\) | ||||
0.857775 | + | 0.514025i | \(0.171846\pi\) | |||||||
\(80\) | −1414.90 | −1.97739 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 262.525 | 0.353549 | ||||||||
\(83\) | 191.594 | 0.253376 | 0.126688 | − | 0.991943i | \(-0.459565\pi\) | ||||
0.126688 | + | 0.991943i | \(0.459565\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2593.54 | −3.30951 | ||||||||
\(86\) | 1025.98 | 1.28645 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1060.69 | −1.28489 | ||||||||
\(89\) | 1007.77 | 1.20026 | 0.600132 | − | 0.799901i | \(-0.295115\pi\) | ||||
0.600132 | + | 0.799901i | \(0.295115\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1317.52 | −1.51774 | ||||||||
\(92\) | −138.637 | −0.157108 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1028.41 | −1.12843 | ||||||||
\(95\) | −1982.24 | −2.14077 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 58.7645 | 0.0615116 | 0.0307558 | − | 0.999527i | \(-0.490209\pi\) | ||||
0.0307558 | + | 0.999527i | \(0.490209\pi\) | |||||||
\(98\) | −941.828 | −0.970806 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 226.417 | 0.226417 | ||||||||
\(101\) | −145.304 | −0.143151 | −0.0715755 | − | 0.997435i | \(-0.522803\pi\) | ||||
−0.0715755 | + | 0.997435i | \(0.522803\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1887.96 | 1.80608 | 0.903038 | − | 0.429561i | \(-0.141332\pi\) | ||||
0.903038 | + | 0.429561i | \(0.141332\pi\) | |||||||
\(104\) | 1095.85 | 1.03324 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 696.127 | 0.637867 | ||||||||
\(107\) | 971.749 | 0.877967 | 0.438984 | − | 0.898495i | \(-0.355339\pi\) | ||||
0.438984 | + | 0.898495i | \(0.355339\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1672.48 | 1.46968 | 0.734838 | − | 0.678243i | \(-0.237258\pi\) | ||||
0.734838 | + | 0.678243i | \(0.237258\pi\) | |||||||
\(110\) | 2986.33 | 2.58850 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1791.17 | 1.51116 | ||||||||
\(113\) | −62.9425 | −0.0523994 | −0.0261997 | − | 0.999657i | \(-0.508341\pi\) | ||||
−0.0261997 | + | 0.999657i | \(0.508341\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3571.59 | −2.89611 | ||||||||
\(116\) | −13.0004 | −0.0104057 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1267.56 | −0.988886 | ||||||||
\(119\) | 3283.24 | 2.52919 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1130.44 | 0.849317 | ||||||||
\(122\) | −504.021 | −0.374032 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −228.388 | −0.165402 | ||||||||
\(125\) | 3294.93 | 2.35766 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 802.101 | 0.560432 | 0.280216 | − | 0.959937i | \(-0.409594\pi\) | ||||
0.280216 | + | 0.959937i | \(0.409594\pi\) | |||||||
\(128\) | −1624.60 | −1.12184 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3085.30 | −2.08153 | ||||||||
\(131\) | −366.963 | −0.244746 | −0.122373 | − | 0.992484i | \(-0.539050\pi\) | ||||
−0.122373 | + | 0.992484i | \(0.539050\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2509.37 | 1.63602 | ||||||||
\(134\) | −2147.49 | −1.38444 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2730.83 | −1.72181 | ||||||||
\(137\) | 1591.63 | 0.992568 | 0.496284 | − | 0.868160i | \(-0.334697\pi\) | ||||
0.496284 | + | 0.868160i | \(0.334697\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1268.70 | −0.774168 | −0.387084 | − | 0.922044i | \(-0.626518\pi\) | ||||
−0.387084 | + | 0.922044i | \(0.626518\pi\) | |||||||
\(140\) | −411.347 | −0.248323 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 87.4681 | 0.0516912 | ||||||||
\(143\) | −2543.02 | −1.48712 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −334.919 | −0.191817 | ||||||||
\(146\) | 3566.48 | 2.02167 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 68.5303 | 0.0380619 | ||||||||
\(149\) | −241.701 | −0.132892 | −0.0664459 | − | 0.997790i | \(-0.521166\pi\) | ||||
−0.0664459 | + | 0.997790i | \(0.521166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −211.546 | −0.114009 | −0.0570045 | − | 0.998374i | \(-0.518155\pi\) | ||||
−0.0570045 | + | 0.998374i | \(0.518155\pi\) | |||||||
\(152\) | −2087.17 | −1.11376 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3780.48 | −1.97818 | ||||||||
\(155\) | −5883.76 | −3.04900 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2178.32 | −1.10732 | −0.553658 | − | 0.832744i | \(-0.686768\pi\) | ||||
−0.553658 | + | 0.832744i | \(0.686768\pi\) | |||||||
\(158\) | −3571.03 | −1.79807 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 721.666 | 0.356579 | ||||||||
\(161\) | 4521.39 | 2.21326 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −598.892 | −0.287784 | −0.143892 | − | 0.989593i | \(-0.545962\pi\) | ||||
−0.143892 | + | 0.989593i | \(0.545962\pi\) | |||||||
\(164\) | −69.7964 | −0.0332328 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −567.977 | −0.265564 | ||||||||
\(167\) | −421.028 | −0.195091 | −0.0975453 | − | 0.995231i | \(-0.531099\pi\) | ||||
−0.0975453 | + | 0.995231i | \(0.531099\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 430.298 | 0.195857 | ||||||||
\(170\) | 7688.50 | 3.46871 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −272.774 | −0.120923 | ||||||||
\(173\) | 4319.92 | 1.89848 | 0.949241 | − | 0.314551i | \(-0.101854\pi\) | ||||
0.949241 | + | 0.314551i | \(0.101854\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7384.17 | −3.18966 | ||||||||
\(176\) | 3457.23 | 1.48067 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2987.52 | −1.25800 | ||||||||
\(179\) | −2.38961 | −0.000997808 0 | −0.000498904 | − | 1.00000i | \(-0.500159\pi\) | ||||
−0.000498904 | 1.00000i | \(0.500159\pi\) | ||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1432.19 | −0.588143 | −0.294072 | − | 0.955783i | \(-0.595010\pi\) | ||||
−0.294072 | + | 0.955783i | \(0.595010\pi\) | |||||||
\(182\) | 3905.77 | 1.59074 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3760.66 | −1.50674 | ||||||||
\(185\) | 1765.49 | 0.701628 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6337.14 | 2.47817 | ||||||||
\(188\) | 273.418 | 0.106070 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5876.30 | 2.24375 | ||||||||
\(191\) | −3769.31 | −1.42795 | −0.713973 | − | 0.700173i | \(-0.753106\pi\) | ||||
−0.713973 | + | 0.700173i | \(0.753106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2778.74 | −1.03636 | −0.518182 | − | 0.855270i | \(-0.673391\pi\) | ||||
−0.518182 | + | 0.855270i | \(0.673391\pi\) | |||||||
\(194\) | −174.206 | −0.0644705 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 250.400 | 0.0912536 | ||||||||
\(197\) | 2904.23 | 1.05034 | 0.525172 | − | 0.850996i | \(-0.324001\pi\) | ||||
0.525172 | + | 0.850996i | \(0.324001\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3462.83 | −1.23354 | −0.616768 | − | 0.787145i | \(-0.711558\pi\) | ||||
−0.616768 | + | 0.787145i | \(0.711558\pi\) | |||||||
\(200\) | 6141.77 | 2.17144 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 430.750 | 0.150037 | ||||||||
\(203\) | 423.984 | 0.146590 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1798.10 | −0.612610 | ||||||||
\(206\) | −5596.81 | −1.89295 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3571.81 | −1.19067 | ||||||||
\(209\) | 4843.47 | 1.60301 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2056.51 | −0.670975 | −0.335487 | − | 0.942045i | \(-0.608901\pi\) | ||||
−0.335487 | + | 0.942045i | \(0.608901\pi\) | |||||||
\(212\) | −185.077 | −0.0599581 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2880.73 | −0.920200 | ||||||||
\(215\) | −7027.23 | −2.22908 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7448.43 | 2.33010 | ||||||||
\(218\) | −4958.04 | −1.54037 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −793.962 | −0.243313 | ||||||||
\(221\) | −6547.17 | −1.99281 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 359.449 | 0.107939 | 0.0539697 | − | 0.998543i | \(-0.482813\pi\) | ||||
0.0539697 | + | 0.998543i | \(0.482813\pi\) | |||||||
\(224\) | −913.578 | −0.272505 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 186.592 | 0.0549199 | ||||||||
\(227\) | −3911.17 | −1.14358 | −0.571792 | − | 0.820398i | \(-0.693752\pi\) | ||||
−0.571792 | + | 0.820398i | \(0.693752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2409.64 | −0.695342 | −0.347671 | − | 0.937617i | \(-0.613027\pi\) | ||||
−0.347671 | + | 0.937617i | \(0.613027\pi\) | |||||||
\(230\) | 10587.9 | 3.03542 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −352.648 | −0.0997952 | ||||||||
\(233\) | −102.677 | −0.0288696 | −0.0144348 | − | 0.999896i | \(-0.504595\pi\) | ||||
−0.0144348 | + | 0.999896i | \(0.504595\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7043.84 | 1.95528 | ||||||||
\(236\) | 337.002 | 0.0929531 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9733.10 | −2.65085 | ||||||||
\(239\) | −239.000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1694.91 | −0.453023 | −0.226511 | − | 0.974009i | \(-0.572732\pi\) | ||||
−0.226511 | + | 0.974009i | \(0.572732\pi\) | |||||||
\(242\) | −3351.17 | −0.890171 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 134.002 | 0.0351582 | ||||||||
\(245\) | 6450.84 | 1.68216 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5003.99 | −1.28905 | ||||||||
\(248\) | −6195.22 | −1.58628 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9767.75 | −2.47107 | ||||||||
\(251\) | −7693.01 | −1.93458 | −0.967288 | − | 0.253681i | \(-0.918359\pi\) | ||||
−0.967288 | + | 0.253681i | \(0.918359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8726.96 | 2.16861 | ||||||||
\(254\) | −2377.81 | −0.587391 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1199.24 | 0.292784 | ||||||||
\(257\) | 1383.71 | 0.335851 | 0.167925 | − | 0.985800i | \(-0.446293\pi\) | ||||
0.167925 | + | 0.985800i | \(0.446293\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2234.98 | −0.536198 | ||||||||
\(260\) | 820.276 | 0.195659 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1087.86 | 0.256519 | ||||||||
\(263\) | 7580.93 | 1.77742 | 0.888708 | − | 0.458473i | \(-0.151604\pi\) | ||||
0.888708 | + | 0.458473i | \(0.151604\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4767.97 | −1.10526 | ||||||||
\(266\) | −7438.99 | −1.71471 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 570.945 | 0.130134 | ||||||||
\(269\) | 773.031 | 0.175214 | 0.0876069 | − | 0.996155i | \(-0.472078\pi\) | ||||
0.0876069 | + | 0.996155i | \(0.472078\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6402.73 | 1.43520 | 0.717598 | − | 0.696458i | \(-0.245242\pi\) | ||||
0.717598 | + | 0.696458i | \(0.245242\pi\) | |||||||
\(272\) | 8900.87 | 1.98417 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4718.35 | −1.04031 | ||||||||
\(275\) | −14252.6 | −3.12531 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2367.03 | 0.513434 | 0.256717 | − | 0.966487i | \(-0.417359\pi\) | ||||
0.256717 | + | 0.966487i | \(0.417359\pi\) | |||||||
\(278\) | 3761.03 | 0.811408 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11158.2 | −2.38153 | ||||||||
\(281\) | 3994.73 | 0.848063 | 0.424032 | − | 0.905647i | \(-0.360615\pi\) | ||||
0.424032 | + | 0.905647i | \(0.360615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5609.87 | 1.17835 | 0.589173 | − | 0.808007i | \(-0.299454\pi\) | ||||
0.589173 | + | 0.808007i | \(0.299454\pi\) | |||||||
\(284\) | −23.2548 | −0.00485886 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7538.73 | 1.55865 | ||||||||
\(287\) | 2276.28 | 0.468168 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11402.4 | 2.32086 | ||||||||
\(290\) | 992.862 | 0.201044 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −948.205 | −0.190032 | ||||||||
\(293\) | −3906.04 | −0.778817 | −0.389409 | − | 0.921065i | \(-0.627321\pi\) | ||||
−0.389409 | + | 0.921065i | \(0.627321\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8681.88 | 1.71349 | ||||||||
\(296\) | 1858.94 | 0.365030 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 716.517 | 0.139284 | ||||||||
\(299\) | −9016.19 | −1.74388 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8895.99 | 1.70351 | ||||||||
\(302\) | 627.124 | 0.119493 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6802.92 | 1.28347 | ||||||||
\(305\) | 3452.18 | 0.648103 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2829.34 | −0.525991 | −0.262995 | − | 0.964797i | \(-0.584710\pi\) | ||||
−0.262995 | + | 0.964797i | \(0.584710\pi\) | |||||||
\(308\) | 1005.10 | 0.185945 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 17442.3 | 3.19567 | ||||||||
\(311\) | 7494.76 | 1.36652 | 0.683262 | − | 0.730174i | \(-0.260561\pi\) | ||||
0.683262 | + | 0.730174i | \(0.260561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3199.49 | 0.577782 | 0.288891 | − | 0.957362i | \(-0.406713\pi\) | ||||
0.288891 | + | 0.957362i | \(0.406713\pi\) | |||||||
\(314\) | 6457.58 | 1.16058 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 949.414 | 0.169015 | ||||||||
\(317\) | 1703.90 | 0.301895 | 0.150947 | − | 0.988542i | \(-0.451768\pi\) | ||||
0.150947 | + | 0.988542i | \(0.451768\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 818.354 | 0.143633 | ||||||||
\(320\) | 9179.87 | 1.60366 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −13403.6 | −2.31973 | ||||||||
\(323\) | 12469.8 | 2.14811 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14724.9 | 2.51320 | ||||||||
\(326\) | 1775.41 | 0.301628 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1893.29 | −0.318717 | ||||||||
\(329\) | −8917.02 | −1.49426 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −449.298 | −0.0746092 | −0.0373046 | − | 0.999304i | \(-0.511877\pi\) | ||||
−0.0373046 | + | 0.999304i | \(0.511877\pi\) | |||||||
\(332\) | 151.006 | 0.0249624 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1248.13 | 0.204475 | ||||||||
\(335\) | 14708.8 | 2.39888 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10616.9 | −1.71615 | −0.858073 | − | 0.513528i | \(-0.828338\pi\) | ||||
−0.858073 | + | 0.513528i | \(0.828338\pi\) | |||||||
\(338\) | −1275.61 | −0.205278 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2044.11 | −0.326051 | ||||||||
\(341\) | 14376.6 | 2.28310 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 650.215 | 0.102357 | ||||||||
\(344\) | −7399.22 | −1.15971 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12806.3 | −1.98980 | ||||||||
\(347\) | 2930.04 | 0.453293 | 0.226647 | − | 0.973977i | \(-0.427224\pi\) | ||||
0.226647 | + | 0.973977i | \(0.427224\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6874.66 | −1.05442 | −0.527209 | − | 0.849735i | \(-0.676762\pi\) | ||||
−0.527209 | + | 0.849735i | \(0.676762\pi\) | |||||||
\(350\) | 21890.2 | 3.34309 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1763.34 | −0.267007 | ||||||||
\(353\) | 10603.9 | 1.59883 | 0.799415 | − | 0.600780i | \(-0.205143\pi\) | ||||
0.799415 | + | 0.600780i | \(0.205143\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −599.093 | −0.0895678 | ||||||||
\(356\) | 794.280 | 0.118249 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.08395 | 0.00104581 | ||||||||
\(359\) | 75.6572 | 0.0111227 | 0.00556133 | − | 0.999985i | \(-0.498230\pi\) | ||||
0.00556133 | + | 0.999985i | \(0.498230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2671.67 | 0.389513 | ||||||||
\(362\) | 4245.71 | 0.616435 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1038.41 | −0.149526 | ||||||||
\(365\) | −24427.8 | −3.50304 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3790.84 | −0.539184 | −0.269592 | − | 0.962975i | \(-0.586889\pi\) | ||||
−0.269592 | + | 0.962975i | \(0.586889\pi\) | |||||||
\(368\) | 12257.5 | 1.73632 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5233.76 | −0.735379 | ||||||||
\(371\) | 6035.92 | 0.844661 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1797.32 | −0.249495 | −0.124747 | − | 0.992189i | \(-0.539812\pi\) | ||||
−0.124747 | + | 0.992189i | \(0.539812\pi\) | |||||||
\(374\) | −18786.4 | −2.59738 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7416.71 | 1.01725 | ||||||||
\(377\) | −845.475 | −0.115502 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13319.4 | 1.80520 | 0.902602 | − | 0.430475i | \(-0.141654\pi\) | ||||
0.902602 | + | 0.430475i | \(0.141654\pi\) | |||||||
\(380\) | −1562.31 | −0.210907 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11174.0 | 1.49663 | ||||||||
\(383\) | −1097.73 | −0.146452 | −0.0732260 | − | 0.997315i | \(-0.523329\pi\) | ||||
−0.0732260 | + | 0.997315i | \(0.523329\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25893.6 | 3.42768 | ||||||||
\(386\) | 8237.54 | 1.08622 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 46.3155 | 0.00606009 | ||||||||
\(389\) | 7483.53 | 0.975398 | 0.487699 | − | 0.873012i | \(-0.337836\pi\) | ||||
0.487699 | + | 0.873012i | \(0.337836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 22468.2 | 2.90605 | ||||||||
\(392\) | 6792.31 | 0.875162 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8609.54 | −1.10087 | ||||||||
\(395\) | 24458.9 | 3.11560 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4426.81 | 0.559635 | 0.279818 | − | 0.960053i | \(-0.409726\pi\) | ||||
0.279818 | + | 0.960053i | \(0.409726\pi\) | |||||||
\(398\) | 10265.5 | 1.29287 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −20018.5 | −2.50231 | ||||||||
\(401\) | 7266.49 | 0.904915 | 0.452458 | − | 0.891786i | \(-0.350547\pi\) | ||||
0.452458 | + | 0.891786i | \(0.350547\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14853.1 | −1.83594 | ||||||||
\(404\) | −114.522 | −0.0141031 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1256.89 | −0.153642 | ||||||||
\(407\) | −4313.86 | −0.525381 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 553.982 | 0.0669747 | 0.0334874 | − | 0.999439i | \(-0.489339\pi\) | ||||
0.0334874 | + | 0.999439i | \(0.489339\pi\) | |||||||
\(410\) | 5330.45 | 0.642078 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1488.00 | 0.177933 | ||||||||
\(413\) | −10990.7 | −1.30948 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3890.23 | 0.460154 | ||||||||
\(416\) | 1821.78 | 0.214712 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14358.4 | −1.68012 | ||||||||
\(419\) | 13106.6 | 1.52816 | 0.764079 | − | 0.645123i | \(-0.223194\pi\) | ||||
0.764079 | + | 0.645123i | \(0.223194\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11133.5 | 1.28887 | 0.644434 | − | 0.764660i | \(-0.277093\pi\) | ||||
0.644434 | + | 0.764660i | \(0.277093\pi\) | |||||||
\(422\) | 6096.47 | 0.703250 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5020.36 | −0.575024 | ||||||||
\(425\) | −36694.2 | −4.18807 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4370.22 | −0.495292 | ||||||||
\(428\) | 765.889 | 0.0864968 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 20832.1 | 2.33631 | ||||||||
\(431\) | −14193.7 | −1.58628 | −0.793138 | − | 0.609042i | \(-0.791554\pi\) | ||||
−0.793138 | + | 0.609042i | \(0.791554\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8641.86 | 0.959125 | 0.479562 | − | 0.877508i | \(-0.340795\pi\) | ||||
0.479562 | + | 0.877508i | \(0.340795\pi\) | |||||||
\(434\) | −22080.7 | −2.44219 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1318.17 | 0.144792 | ||||||||
\(437\) | 17172.4 | 1.87978 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6963.77 | −0.757090 | −0.378545 | − | 0.925583i | \(-0.623575\pi\) | ||||
−0.378545 | + | 0.925583i | \(0.623575\pi\) | |||||||
\(440\) | −21536.9 | −2.33348 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19409.0 | 2.08867 | ||||||||
\(443\) | 5282.31 | 0.566524 | 0.283262 | − | 0.959043i | \(-0.408583\pi\) | ||||
0.283262 | + | 0.959043i | \(0.408583\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20462.3 | 2.17979 | ||||||||
\(446\) | −1065.58 | −0.113132 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −11621.1 | −1.22554 | ||||||||
\(449\) | −6696.11 | −0.703806 | −0.351903 | − | 0.936036i | \(-0.614465\pi\) | ||||
−0.351903 | + | 0.936036i | \(0.614465\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4393.55 | 0.458724 | ||||||||
\(452\) | −49.6084 | −0.00516236 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11594.6 | 1.19859 | ||||||||
\(455\) | −26751.7 | −2.75635 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9008.10 | −0.922059 | −0.461030 | − | 0.887385i | \(-0.652520\pi\) | ||||
−0.461030 | + | 0.887385i | \(0.652520\pi\) | |||||||
\(458\) | 7143.33 | 0.728790 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2814.97 | −0.285323 | ||||||||
\(461\) | −5976.41 | −0.603794 | −0.301897 | − | 0.953341i | \(-0.597620\pi\) | ||||
−0.301897 | + | 0.953341i | \(0.597620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17279.0 | −1.73440 | −0.867198 | − | 0.497964i | \(-0.834081\pi\) | ||||
−0.867198 | + | 0.497964i | \(0.834081\pi\) | |||||||
\(464\) | 1149.42 | 0.115001 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 304.385 | 0.0302583 | ||||||||
\(467\) | −11059.4 | −1.09586 | −0.547932 | − | 0.836523i | \(-0.684585\pi\) | ||||
−0.547932 | + | 0.836523i | \(0.684585\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18620.3 | −1.83327 | ||||||||
\(470\) | −20881.3 | −2.04933 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9141.46 | 0.891462 | ||||||||
\(473\) | 17170.6 | 1.66914 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −28045.3 | −2.70906 | ||||||||
\(476\) | 2587.70 | 0.249175 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 708.511 | 0.0677961 | ||||||||
\(479\) | −3287.38 | −0.313579 | −0.156789 | − | 0.987632i | \(-0.550114\pi\) | ||||
−0.156789 | + | 0.987632i | \(0.550114\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4456.83 | 0.422482 | ||||||||
\(482\) | 5024.52 | 0.474815 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 890.962 | 0.0836742 | ||||||||
\(485\) | 1193.19 | 0.111711 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 998.298 | 0.0928896 | 0.0464448 | − | 0.998921i | \(-0.485211\pi\) | ||||
0.0464448 | + | 0.998921i | \(0.485211\pi\) | |||||||
\(488\) | 3634.92 | 0.337183 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −19123.4 | −1.76308 | ||||||||
\(491\) | −12962.9 | −1.19147 | −0.595733 | − | 0.803183i | \(-0.703138\pi\) | ||||
−0.595733 | + | 0.803183i | \(0.703138\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2106.91 | 0.192475 | ||||||||
\(494\) | 14834.2 | 1.35106 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20192.7 | 1.82798 | ||||||||
\(497\) | 758.410 | 0.0684494 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21620.5 | −1.93961 | −0.969807 | − | 0.243873i | \(-0.921582\pi\) | ||||
−0.969807 | + | 0.243873i | \(0.921582\pi\) | |||||||
\(500\) | 2596.91 | 0.232275 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22805.8 | 2.02763 | ||||||||
\(503\) | −10796.7 | −0.957058 | −0.478529 | − | 0.878072i | \(-0.658830\pi\) | ||||
−0.478529 | + | 0.878072i | \(0.658830\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2950.33 | −0.259976 | ||||||||
\(506\) | −25870.9 | −2.27293 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 632.180 | 0.0552135 | ||||||||
\(509\) | 12066.0 | 1.05072 | 0.525359 | − | 0.850880i | \(-0.323931\pi\) | ||||
0.525359 | + | 0.850880i | \(0.323931\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30923.9 | 2.67709 | ||||||||
\(512\) | 9441.70 | 0.814977 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4101.99 | −0.352006 | ||||||||
\(515\) | 38334.1 | 3.28001 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17211.2 | −1.46411 | ||||||||
\(518\) | 6625.57 | 0.561990 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 22250.7 | 1.87646 | ||||||||
\(521\) | 13033.5 | 1.09599 | 0.547994 | − | 0.836482i | \(-0.315392\pi\) | ||||
0.547994 | + | 0.836482i | \(0.315392\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11294.2 | −0.944283 | −0.472141 | − | 0.881523i | \(-0.656519\pi\) | ||||
−0.472141 | + | 0.881523i | \(0.656519\pi\) | |||||||
\(524\) | −289.224 | −0.0241122 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22473.5 | −1.86291 | ||||||||
\(527\) | 37013.5 | 3.05946 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18774.2 | 1.54304 | ||||||||
\(530\) | 14134.6 | 1.15843 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1977.77 | 0.161179 | ||||||||
\(533\) | −4539.17 | −0.368880 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19730.9 | 1.59447 | ||||||||
\(536\) | 15487.4 | 1.24805 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2291.64 | −0.183642 | ||||||||
\(539\) | −15762.2 | −1.25960 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15543.5 | −1.23525 | −0.617624 | − | 0.786474i | \(-0.711905\pi\) | ||||
−0.617624 | + | 0.786474i | \(0.711905\pi\) | |||||||
\(542\) | −18980.8 | −1.50423 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4539.85 | −0.357802 | ||||||||
\(545\) | 33959.0 | 2.66907 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18479.4 | 1.44447 | 0.722233 | − | 0.691650i | \(-0.243116\pi\) | ||||
0.722233 | + | 0.691650i | \(0.243116\pi\) | |||||||
\(548\) | 1254.45 | 0.0977872 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 42251.4 | 3.27565 | ||||||||
\(551\) | 1610.30 | 0.124503 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30963.3 | −2.38100 | ||||||||
\(554\) | −7017.03 | −0.538132 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −999.929 | −0.0762706 | ||||||||
\(557\) | 1232.15 | 0.0937304 | 0.0468652 | − | 0.998901i | \(-0.485077\pi\) | ||||
0.0468652 | + | 0.998901i | \(0.485077\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17739.7 | −1.34223 | ||||||||
\(560\) | 36368.9 | 2.74441 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11842.3 | −0.888858 | ||||||||
\(563\) | 21917.7 | 1.64071 | 0.820356 | − | 0.571853i | \(-0.193775\pi\) | ||||
0.820356 | + | 0.571853i | \(0.193775\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1278.02 | −0.0951623 | ||||||||
\(566\) | −16630.3 | −1.23503 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −630.806 | −0.0465987 | ||||||||
\(569\) | 16714.5 | 1.23147 | 0.615736 | − | 0.787952i | \(-0.288859\pi\) | ||||
0.615736 | + | 0.787952i | \(0.288859\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15191.2 | −1.11337 | −0.556684 | − | 0.830725i | \(-0.687926\pi\) | ||||
−0.556684 | + | 0.830725i | \(0.687926\pi\) | |||||||
\(572\) | −2004.29 | −0.146510 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6747.98 | −0.490688 | ||||||||
\(575\) | −50532.0 | −3.66492 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10638.4 | −0.767563 | −0.383781 | − | 0.923424i | \(-0.625378\pi\) | ||||
−0.383781 | + | 0.923424i | \(0.625378\pi\) | |||||||
\(578\) | −33802.2 | −2.43250 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −263.968 | −0.0188977 | ||||||||
\(581\) | −4924.77 | −0.351659 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11650.2 | 0.827621 | ||||||||
\(584\) | −25720.9 | −1.82250 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11579.4 | 0.816281 | ||||||||
\(587\) | 7932.26 | 0.557750 | 0.278875 | − | 0.960327i | \(-0.410038\pi\) | ||||
0.278875 | + | 0.960327i | \(0.410038\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 28289.4 | 1.97902 | ||||||||
\(590\) | −25737.3 | −1.79591 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6059.05 | −0.420651 | ||||||||
\(593\) | 20361.1 | 1.41000 | 0.704999 | − | 0.709208i | \(-0.250947\pi\) | ||||
0.704999 | + | 0.709208i | \(0.250947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 66664.7 | 4.59325 | ||||||||
\(596\) | −190.498 | −0.0130924 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 26728.3 | 1.82776 | ||||||||
\(599\) | 7549.97 | 0.514997 | 0.257499 | − | 0.966279i | \(-0.417102\pi\) | ||||
0.257499 | + | 0.966279i | \(0.417102\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14106.0 | 0.957398 | 0.478699 | − | 0.877979i | \(-0.341109\pi\) | ||||
0.478699 | + | 0.877979i | \(0.341109\pi\) | |||||||
\(602\) | −26372.0 | −1.78545 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −166.731 | −0.0112321 | ||||||||
\(605\) | 22953.1 | 1.54244 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3652.23 | −0.244216 | −0.122108 | − | 0.992517i | \(-0.538965\pi\) | ||||
−0.122108 | + | 0.992517i | \(0.538965\pi\) | |||||||
\(608\) | −3469.80 | −0.231446 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10233.9 | −0.679278 | ||||||||
\(611\) | 17781.6 | 1.17736 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22961.7 | −1.51291 | −0.756454 | − | 0.654046i | \(-0.773070\pi\) | ||||
−0.756454 | + | 0.654046i | \(0.773070\pi\) | |||||||
\(614\) | 8387.54 | 0.551292 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27264.2 | 1.78329 | ||||||||
\(617\) | 6976.88 | 0.455233 | 0.227616 | − | 0.973751i | \(-0.426907\pi\) | ||||
0.227616 | + | 0.973751i | \(0.426907\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17452.2 | −1.13322 | −0.566610 | − | 0.823986i | \(-0.691745\pi\) | ||||
−0.566610 | + | 0.823986i | \(0.691745\pi\) | |||||||
\(620\) | −4637.32 | −0.300386 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22218.1 | −1.43226 | ||||||||
\(623\) | −25903.9 | −1.66584 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30992.6 | 1.98353 | ||||||||
\(626\) | −9484.83 | −0.605575 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1716.85 | −0.109092 | ||||||||
\(629\) | −11106.3 | −0.704035 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12015.3 | 0.758034 | 0.379017 | − | 0.925390i | \(-0.376262\pi\) | ||||
0.379017 | + | 0.925390i | \(0.376262\pi\) | |||||||
\(632\) | 25753.7 | 1.62093 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5051.19 | −0.316417 | ||||||||
\(635\) | 16286.3 | 1.01780 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16284.6 | 1.01290 | ||||||||
\(638\) | −2425.99 | −0.150542 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −32986.9 | −2.03738 | ||||||||
\(641\) | 3224.56 | 0.198693 | 0.0993467 | − | 0.995053i | \(-0.468325\pi\) | ||||
0.0993467 | + | 0.995053i | \(0.468325\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20969.8 | 1.28611 | 0.643055 | − | 0.765820i | \(-0.277667\pi\) | ||||
0.643055 | + | 0.765820i | \(0.277667\pi\) | |||||||
\(644\) | 3563.56 | 0.218049 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −36966.6 | −2.25144 | ||||||||
\(647\) | −19896.6 | −1.20899 | −0.604493 | − | 0.796610i | \(-0.706624\pi\) | ||||
−0.604493 | + | 0.796610i | \(0.706624\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21213.6 | −1.28306 | ||||||||
\(650\) | −43651.7 | −2.63410 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −472.020 | −0.0283523 | ||||||||
\(653\) | 18417.7 | 1.10374 | 0.551869 | − | 0.833931i | \(-0.313915\pi\) | ||||
0.551869 | + | 0.833931i | \(0.313915\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7451.03 | −0.444482 | ||||||||
\(656\) | 6170.99 | 0.367281 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 26434.3 | 1.56614 | ||||||||
\(659\) | −26225.4 | −1.55022 | −0.775110 | − | 0.631826i | \(-0.782306\pi\) | ||||
−0.775110 | + | 0.631826i | \(0.782306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24662.9 | 1.45125 | 0.725623 | − | 0.688092i | \(-0.241552\pi\) | ||||
0.725623 | + | 0.688092i | \(0.241552\pi\) | |||||||
\(662\) | 1331.94 | 0.0781981 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4096.16 | 0.239401 | ||||||||
\(665\) | 50951.7 | 2.97116 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2901.45 | 0.168433 | ||||||||
\(668\) | −331.835 | −0.0192202 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −43603.9 | −2.51428 | ||||||||
\(671\) | −8435.19 | −0.485301 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −20312.4 | −1.16343 | −0.581713 | − | 0.813394i | \(-0.697617\pi\) | ||||
−0.581713 | + | 0.813394i | \(0.697617\pi\) | |||||||
\(674\) | 31473.7 | 1.79870 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 339.141 | 0.0192957 | ||||||||
\(677\) | −13110.5 | −0.744278 | −0.372139 | − | 0.928177i | \(-0.621375\pi\) | ||||
−0.372139 | + | 0.928177i | \(0.621375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1510.49 | −0.0853716 | ||||||||
\(680\) | −55448.2 | −3.12697 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −42619.2 | −2.39292 | ||||||||
\(683\) | −2293.08 | −0.128466 | −0.0642330 | − | 0.997935i | \(-0.520460\pi\) | ||||
−0.0642330 | + | 0.997935i | \(0.520460\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32317.3 | 1.80260 | ||||||||
\(686\) | −1927.55 | −0.107280 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 24117.0 | 1.33642 | ||||||||
\(689\) | −12036.3 | −0.665527 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5086.75 | 0.280042 | 0.140021 | − | 0.990149i | \(-0.455283\pi\) | ||||
0.140021 | + | 0.990149i | \(0.455283\pi\) | |||||||
\(692\) | 3404.77 | 0.187037 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8686.05 | −0.475098 | ||||||||
\(695\) | −25760.3 | −1.40596 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11311.5 | 0.614711 | ||||||||
\(698\) | 20379.8 | 1.10514 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5819.87 | −0.314243 | ||||||||
\(701\) | 32271.2 | 1.73875 | 0.869376 | − | 0.494151i | \(-0.164521\pi\) | ||||
0.869376 | + | 0.494151i | \(0.164521\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8488.54 | −0.455407 | ||||||||
\(704\) | −22430.4 | −1.20082 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31435.0 | −1.67574 | ||||||||
\(707\) | 3734.91 | 0.198678 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2369.04 | 0.125488 | 0.0627441 | − | 0.998030i | \(-0.480015\pi\) | ||||
0.0627441 | + | 0.998030i | \(0.480015\pi\) | |||||||
\(710\) | 1776.00 | 0.0938762 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 21545.5 | 1.13406 | ||||||||
\(713\) | 50971.8 | 2.67729 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −51634.8 | −2.70075 | ||||||||
\(716\) | −1.88338 | −9.83034e−5 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −224.284 | −0.0116577 | ||||||||
\(719\) | 1461.76 | 0.0758200 | 0.0379100 | − | 0.999281i | \(-0.487930\pi\) | ||||
0.0379100 | + | 0.999281i | \(0.487930\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48528.3 | −2.50664 | ||||||||
\(722\) | −7920.12 | −0.408250 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1128.79 | −0.0579435 | ||||||||
\(725\) | −4738.54 | −0.242738 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12826.8 | 0.654359 | 0.327179 | − | 0.944962i | \(-0.393902\pi\) | ||||
0.327179 | + | 0.944962i | \(0.393902\pi\) | |||||||
\(728\) | −28167.8 | −1.43402 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 72415.7 | 3.67154 | ||||||||
\(731\) | 44206.9 | 2.23673 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23659.8 | −1.19222 | −0.596108 | − | 0.802904i | \(-0.703287\pi\) | ||||
−0.596108 | + | 0.802904i | \(0.703287\pi\) | |||||||
\(734\) | 11237.9 | 0.565120 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6251.89 | −0.313108 | ||||||||
\(737\) | −35939.9 | −1.79629 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23944.7 | 1.19191 | 0.595953 | − | 0.803019i | \(-0.296774\pi\) | ||||
0.595953 | + | 0.803019i | \(0.296774\pi\) | |||||||
\(740\) | 1391.48 | 0.0691240 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17893.4 | −0.885291 | ||||||||
\(743\) | 13425.5 | 0.662900 | 0.331450 | − | 0.943473i | \(-0.392462\pi\) | ||||
0.331450 | + | 0.943473i | \(0.392462\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4907.63 | −0.241344 | ||||||||
\(746\) | 5328.11 | 0.261496 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4994.65 | 0.244148 | ||||||||
\(749\) | −24978.0 | −1.21853 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9964.72 | −0.484178 | −0.242089 | − | 0.970254i | \(-0.577833\pi\) | ||||
−0.242089 | + | 0.970254i | \(0.577833\pi\) | |||||||
\(752\) | −24174.1 | −1.17226 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2506.40 | 0.121058 | ||||||||
\(755\) | −4295.35 | −0.207051 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23792.0 | −1.14232 | −0.571159 | − | 0.820839i | \(-0.693506\pi\) | ||||
−0.571159 | + | 0.820839i | \(0.693506\pi\) | |||||||
\(758\) | −39485.2 | −1.89204 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −42379.0 | −2.02269 | ||||||||
\(761\) | −25279.5 | −1.20418 | −0.602091 | − | 0.798428i | \(-0.705665\pi\) | ||||
−0.602091 | + | 0.798428i | \(0.705665\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −42989.7 | −2.03975 | ||||||||
\(764\) | −2970.80 | −0.140680 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3254.19 | 0.153497 | ||||||||
\(767\) | 21916.7 | 1.03177 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17553.0 | −0.823116 | −0.411558 | − | 0.911384i | \(-0.635015\pi\) | ||||
−0.411558 | + | 0.911384i | \(0.635015\pi\) | |||||||
\(770\) | −76761.0 | −3.59256 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2190.08 | −0.102102 | ||||||||
\(773\) | 29507.6 | 1.37298 | 0.686490 | − | 0.727139i | \(-0.259150\pi\) | ||||
0.686490 | + | 0.727139i | \(0.259150\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −83245.2 | −3.85840 | ||||||||
\(776\) | 1256.35 | 0.0581189 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22184.8 | −1.02232 | ||||||||
\(779\) | 8645.36 | 0.397628 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1463.85 | 0.0670685 | ||||||||
\(782\) | −66606.5 | −3.04583 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −22138.9 | −1.00851 | ||||||||
\(785\) | −44229.7 | −2.01099 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21920.3 | −0.992851 | −0.496426 | − | 0.868079i | \(-0.665354\pi\) | ||||
−0.496426 | + | 0.868079i | \(0.665354\pi\) | |||||||
\(788\) | 2288.98 | 0.103479 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −72508.1 | −3.26547 | ||||||||
\(791\) | 1617.88 | 0.0727248 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8714.75 | 0.390252 | ||||||||
\(794\) | −13123.2 | −0.586555 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2729.25 | −0.121527 | ||||||||
\(797\) | −12991.8 | −0.577408 | −0.288704 | − | 0.957418i | \(-0.593224\pi\) | ||||
−0.288704 | + | 0.957418i | \(0.593224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44311.4 | −1.96198 | ||||||||
\(800\) | 10210.3 | 0.451238 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21541.4 | −0.948444 | ||||||||
\(803\) | 59687.7 | 2.62308 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 91804.8 | 4.01950 | ||||||||
\(806\) | 44031.6 | 1.92425 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3106.50 | −0.135255 | ||||||||
\(809\) | 14922.2 | 0.648502 | 0.324251 | − | 0.945971i | \(-0.394888\pi\) | ||||
0.324251 | + | 0.945971i | \(0.394888\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1662.46 | −0.0719812 | −0.0359906 | − | 0.999352i | \(-0.511459\pi\) | ||||
−0.0359906 | + | 0.999352i | \(0.511459\pi\) | |||||||
\(812\) | 334.165 | 0.0144420 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12788.4 | 0.550653 | ||||||||
\(815\) | −12160.2 | −0.522644 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 33787.2 | 1.44684 | ||||||||
\(818\) | −1642.27 | −0.0701964 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1417.19 | −0.0603540 | ||||||||
\(821\) | −776.061 | −0.0329899 | −0.0164950 | − | 0.999864i | \(-0.505251\pi\) | ||||
−0.0164950 | + | 0.999864i | \(0.505251\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6659.13 | 0.282044 | 0.141022 | − | 0.990006i | \(-0.454961\pi\) | ||||
0.141022 | + | 0.990006i | \(0.454961\pi\) | |||||||
\(824\) | 40363.3 | 1.70646 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 32581.6 | 1.37247 | ||||||||
\(827\) | −26721.8 | −1.12359 | −0.561794 | − | 0.827277i | \(-0.689889\pi\) | ||||
−0.561794 | + | 0.827277i | \(0.689889\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 16455.6 | 0.689416 | 0.344708 | − | 0.938710i | \(-0.387978\pi\) | ||||
0.344708 | + | 0.938710i | \(0.387978\pi\) | |||||||
\(830\) | −11532.5 | −0.482289 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 23173.8 | 0.965634 | ||||||||
\(833\) | −40580.9 | −1.68793 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8548.79 | −0.354303 | ||||||||
\(836\) | 3817.40 | 0.157928 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −38854.2 | −1.60167 | ||||||||
\(839\) | −11792.2 | −0.485235 | −0.242617 | − | 0.970122i | \(-0.578006\pi\) | ||||
−0.242617 | + | 0.970122i | \(0.578006\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24116.9 | −0.988844 | ||||||||
\(842\) | −33005.0 | −1.35087 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1620.84 | −0.0661040 | ||||||||
\(845\) | 8737.01 | 0.355695 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −29057.0 | −1.17876 | ||||||||
\(848\) | 16363.4 | 0.662643 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 108779. | 4.38952 | ||||||||
\(851\) | −15294.7 | −0.616092 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29560.6 | 1.18656 | 0.593281 | − | 0.804996i | \(-0.297832\pi\) | ||||
0.593281 | + | 0.804996i | \(0.297832\pi\) | |||||||
\(854\) | 12955.4 | 0.519117 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20775.4 | 0.829543 | ||||||||
\(857\) | 6745.76 | 0.268881 | 0.134440 | − | 0.990922i | \(-0.457076\pi\) | ||||
0.134440 | + | 0.990922i | \(0.457076\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22311.2 | −0.886202 | −0.443101 | − | 0.896472i | \(-0.646122\pi\) | ||||
−0.443101 | + | 0.896472i | \(0.646122\pi\) | |||||||
\(860\) | −5538.55 | −0.219608 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42076.9 | 1.66258 | ||||||||
\(863\) | −18773.2 | −0.740497 | −0.370248 | − | 0.928933i | \(-0.620727\pi\) | ||||
−0.370248 | + | 0.928933i | \(0.620727\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 87714.0 | 3.44782 | ||||||||
\(866\) | −25618.6 | −1.00526 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5870.52 | 0.229560 | ||||||||
\(869\) | −59763.9 | −2.33297 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37131.1 | 1.44448 | ||||||||
\(872\) | 35756.6 | 1.38861 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −50907.2 | −1.97021 | ||||||||
\(875\) | −84693.3 | −3.27218 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −12134.1 | −0.467207 | −0.233604 | − | 0.972332i | \(-0.575052\pi\) | ||||
−0.233604 | + | 0.972332i | \(0.575052\pi\) | |||||||
\(878\) | 20644.0 | 0.793508 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 70197.5 | 2.68904 | ||||||||
\(881\) | 13766.4 | 0.526449 | 0.263224 | − | 0.964735i | \(-0.415214\pi\) | ||||
0.263224 | + | 0.964735i | \(0.415214\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −51432.3 | −1.96018 | −0.980088 | − | 0.198563i | \(-0.936373\pi\) | ||||
−0.980088 | + | 0.198563i | \(0.936373\pi\) | |||||||
\(884\) | −5160.19 | −0.196330 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15659.3 | −0.593775 | ||||||||
\(887\) | 49720.0 | 1.88211 | 0.941056 | − | 0.338250i | \(-0.109835\pi\) | ||||
0.941056 | + | 0.338250i | \(0.109835\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20617.3 | −0.777821 | ||||||||
\(890\) | −60660.2 | −2.28465 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 283.301 | 0.0106341 | ||||||||
\(893\) | −33867.1 | −1.26911 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −48.5199 | −0.00181211 | ||||||||
\(896\) | 41759.1 | 1.55700 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 19850.5 | 0.737661 | ||||||||
\(899\) | 4779.78 | 0.177324 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29994.3 | 1.10905 | ||||||||
\(902\) | −13024.6 | −0.480790 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1345.67 | −0.0495093 | ||||||||
\(905\) | −29080.0 | −1.06812 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29374.9 | −1.07539 | −0.537695 | − | 0.843139i | \(-0.680705\pi\) | ||||
−0.537695 | + | 0.843139i | \(0.680705\pi\) | |||||||
\(908\) | −3082.61 | −0.112665 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 79305.0 | 2.88894 | ||||||||
\(911\) | 1836.71 | 0.0667981 | 0.0333990 | − | 0.999442i | \(-0.489367\pi\) | ||||
0.0333990 | + | 0.999442i | \(0.489367\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9505.54 | −0.344565 | ||||||||
\(914\) | 26704.3 | 0.966413 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1899.17 | −0.0685047 | ||||||||
\(917\) | 9432.49 | 0.339682 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 41798.7 | 1.50034 | 0.750170 | − | 0.661245i | \(-0.229972\pi\) | ||||
0.750170 | + | 0.661245i | \(0.229972\pi\) | |||||||
\(920\) | −76358.5 | −2.73638 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 17717.0 | 0.632838 | ||||||||
\(923\) | −1512.36 | −0.0539328 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24978.7 | 0.887885 | ||||||||
\(926\) | 51223.4 | 1.81782 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −586.258 | −0.0207380 | ||||||||
\(929\) | 20108.8 | 0.710170 | 0.355085 | − | 0.934834i | \(-0.384452\pi\) | ||||
0.355085 | + | 0.934834i | \(0.384452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31015.9 | −1.09184 | ||||||||
\(932\) | −80.9256 | −0.00284421 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32785.4 | 1.14858 | ||||||||
\(935\) | 128673. | 4.50059 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7701.92 | −0.268528 | −0.134264 | − | 0.990946i | \(-0.542867\pi\) | ||||
−0.134264 | + | 0.990946i | \(0.542867\pi\) | |||||||
\(938\) | 55199.5 | 1.92146 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5551.64 | 0.192633 | ||||||||
\(941\) | 7997.14 | 0.277045 | 0.138523 | − | 0.990359i | \(-0.455765\pi\) | ||||
0.138523 | + | 0.990359i | \(0.455765\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15577.2 | 0.537926 | ||||||||
\(944\) | −29795.7 | −1.02730 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −50901.9 | −1.74943 | ||||||||
\(947\) | −9984.70 | −0.342618 | −0.171309 | − | 0.985217i | \(-0.554800\pi\) | ||||
−0.171309 | + | 0.985217i | \(0.554800\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −61665.9 | −2.10934 | ||||||||
\(950\) | 83139.7 | 2.83938 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 70193.6 | 2.38969 | ||||||||
\(953\) | −26566.4 | −0.903010 | −0.451505 | − | 0.892269i | \(-0.649113\pi\) | ||||
−0.451505 | + | 0.892269i | \(0.649113\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −76534.2 | −2.59328 | ||||||||
\(956\) | −188.369 | −0.00637269 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9745.38 | 0.328663 | ||||||||
\(959\) | −40911.4 | −1.37758 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 54178.7 | 1.81863 | ||||||||
\(962\) | −13212.2 | −0.442805 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1335.85 | −0.0446315 | ||||||||
\(965\) | −56421.2 | −1.88214 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31596.9 | 1.05076 | 0.525382 | − | 0.850867i | \(-0.323923\pi\) | ||||
0.525382 | + | 0.850867i | \(0.323923\pi\) | |||||||
\(968\) | 24168.1 | 0.802472 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3537.18 | −0.117085 | ||||||||
\(971\) | −23395.4 | −0.773218 | −0.386609 | − | 0.922244i | \(-0.626354\pi\) | ||||
−0.386609 | + | 0.922244i | \(0.626354\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32610.8 | 1.07446 | ||||||||
\(974\) | −2959.44 | −0.0973578 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11847.7 | −0.388561 | ||||||||
\(977\) | −31837.4 | −1.04255 | −0.521274 | − | 0.853390i | \(-0.674543\pi\) | ||||
−0.521274 | + | 0.853390i | \(0.674543\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49998.4 | −1.63223 | ||||||||
\(980\) | 5084.26 | 0.165725 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 38428.4 | 1.24878 | ||||||||
\(983\) | 24432.7 | 0.792758 | 0.396379 | − | 0.918087i | \(-0.370267\pi\) | ||||
0.396379 | + | 0.918087i | \(0.370267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 58969.1 | 1.90753 | ||||||||
\(986\) | −6245.89 | −0.201734 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3943.92 | −0.126997 | ||||||||
\(989\) | 60877.8 | 1.95733 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14624.1 | −0.468767 | −0.234384 | − | 0.972144i | \(-0.575307\pi\) | ||||
−0.234384 | + | 0.972144i | \(0.575307\pi\) | |||||||
\(992\) | −10299.2 | −0.329637 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2248.29 | −0.0717420 | ||||||||
\(995\) | −70311.3 | −2.24022 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8431.79 | 0.267841 | 0.133920 | − | 0.990992i | \(-0.457243\pi\) | ||||
0.133920 | + | 0.990992i | \(0.457243\pi\) | |||||||
\(998\) | 64093.7 | 2.03292 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.4.a.h.1.15 | yes | 59 | |
3.2 | odd | 2 | 2151.4.a.g.1.45 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.45 | ✓ | 59 | 3.2 | odd | 2 | ||
2151.4.a.h.1.15 | yes | 59 | 1.1 | even | 1 | trivial |