Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,4,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, 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("1216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(71.7463225670\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3221.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 152) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(0.218090\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-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 | ||||||||
\(3\) | −4.73435 | −0.911125 | −0.455563 | − | 0.890204i | \(-0.650562\pi\) | ||||
−0.455563 | + | 0.890204i | \(0.650562\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.0754 | 1.61671 | 0.808356 | − | 0.588693i | \(-0.200357\pi\) | ||||
0.808356 | + | 0.588693i | \(0.200357\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.213413 | 0.0115232 | 0.00576162 | − | 0.999983i | \(-0.498166\pi\) | ||||
0.00576162 | + | 0.999983i | \(0.498166\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.58596 | −0.169850 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.39329 | 0.0930106 | 0.0465053 | − | 0.998918i | \(-0.485192\pi\) | ||||
0.0465053 | + | 0.998918i | \(0.485192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 90.7156 | 1.93538 | 0.967692 | − | 0.252135i | \(-0.0811328\pi\) | ||||
0.967692 | + | 0.252135i | \(0.0811328\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −85.5752 | −1.47303 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.59392 | −0.0370069 | −0.0185035 | − | 0.999829i | \(-0.505890\pi\) | ||||
−0.0185035 | + | 0.999829i | \(0.505890\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.01037 | −0.0104991 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 26.6112 | 0.241253 | 0.120626 | − | 0.992698i | \(-0.461510\pi\) | ||||
0.120626 | + | 0.992698i | \(0.461510\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 201.720 | 1.61376 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 149.539 | 1.06588 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −60.1034 | −0.384859 | −0.192430 | − | 0.981311i | \(-0.561637\pi\) | ||||
−0.192430 | + | 0.981311i | \(0.561637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −176.070 | −1.02010 | −0.510050 | − | 0.860145i | \(-0.670373\pi\) | ||||
−0.510050 | + | 0.860145i | \(0.670373\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −16.0650 | −0.0847443 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.85753 | 0.0186298 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 154.115 | 0.684768 | 0.342384 | − | 0.939560i | \(-0.388766\pi\) | ||||
0.342384 | + | 0.939560i | \(0.388766\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −429.479 | −1.76338 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 434.137 | 1.65368 | 0.826839 | − | 0.562439i | \(-0.190137\pi\) | ||||
0.826839 | + | 0.562439i | \(0.190137\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 365.511 | 1.29628 | 0.648138 | − | 0.761523i | \(-0.275548\pi\) | ||||
0.648138 | + | 0.761523i | \(0.275548\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −82.8931 | −0.274599 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 204.021 | 0.633180 | 0.316590 | − | 0.948562i | \(-0.397462\pi\) | ||||
0.316590 | + | 0.948562i | \(0.397462\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −342.954 | −0.999867 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.2805 | 0.0337180 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 135.726 | 0.351763 | 0.175881 | − | 0.984411i | \(-0.443722\pi\) | ||||
0.175881 | + | 0.984411i | \(0.443722\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 61.3351 | 0.150371 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 89.9526 | 0.209027 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −759.895 | −1.67678 | −0.838389 | − | 0.545072i | \(-0.816502\pi\) | ||||
−0.838389 | + | 0.545072i | \(0.816502\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −284.941 | −0.598082 | −0.299041 | − | 0.954240i | \(-0.596667\pi\) | ||||
−0.299041 | + | 0.954240i | \(0.596667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.978705 | −0.00195723 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1639.72 | 3.12896 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −590.922 | −1.07750 | −0.538750 | − | 0.842465i | \(-0.681103\pi\) | ||||
−0.538750 | + | 0.842465i | \(0.681103\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −125.986 | −0.219811 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −972.291 | −1.62521 | −0.812604 | − | 0.582817i | \(-0.801950\pi\) | ||||
−0.812604 | + | 0.582817i | \(0.801950\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 368.462 | 0.590756 | 0.295378 | − | 0.955380i | \(-0.404554\pi\) | ||||
0.295378 | + | 0.955380i | \(0.404554\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −955.013 | −1.47034 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.724174 | 0.00107178 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 204.854 | 0.291745 | 0.145873 | − | 0.989303i | \(-0.453401\pi\) | ||||
0.145873 | + | 0.989303i | \(0.453401\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −584.148 | −0.801300 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 782.229 | 1.03447 | 0.517234 | − | 0.855844i | \(-0.326962\pi\) | ||||
0.517234 | + | 0.855844i | \(0.326962\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −46.8861 | −0.0598296 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 284.550 | 0.350655 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 213.620 | 0.254423 | 0.127211 | − | 0.991876i | \(-0.459397\pi\) | ||||
0.127211 | + | 0.991876i | \(0.459397\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.3599 | 0.0223019 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 833.576 | 0.929438 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −343.433 | −0.370899 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1219.54 | −1.27655 | −0.638274 | − | 0.769809i | \(-0.720351\pi\) | ||||
−0.638274 | + | 0.769809i | \(0.720351\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.5615 | −0.0157979 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 53.9766 | 0.0531770 | 0.0265885 | − | 0.999646i | \(-0.491536\pi\) | ||||
0.0265885 | + | 0.999646i | \(0.491536\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1987.50 | 1.90130 | 0.950652 | − | 0.310260i | \(-0.100416\pi\) | ||||
0.950652 | + | 0.310260i | \(0.100416\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.2629 | −0.0169741 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1076.92 | 0.972991 | 0.486496 | − | 0.873683i | \(-0.338275\pi\) | ||||
0.486496 | + | 0.873683i | \(0.338275\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1200.57 | 1.05499 | 0.527494 | − | 0.849559i | \(-0.323132\pi\) | ||||
0.527494 | + | 0.849559i | \(0.323132\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −729.636 | −0.623910 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1402.72 | 1.16776 | 0.583880 | − | 0.811840i | \(-0.301534\pi\) | ||||
0.583880 | + | 0.811840i | \(0.301534\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 481.007 | 0.390036 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −416.018 | −0.328726 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.553577 | −0.000426440 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1319.49 | −0.991349 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2055.35 | −1.50671 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1386.75 | 0.992275 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1055.22 | −0.737289 | −0.368644 | − | 0.929570i | \(-0.620178\pi\) | ||||
−0.368644 | + | 0.929570i | \(0.620178\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1730.45 | −1.18107 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1026.98 | 0.684944 | 0.342472 | − | 0.939528i | \(-0.388736\pi\) | ||||
0.342472 | + | 0.939528i | \(0.388736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.05485 | −0.00264361 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2702.98 | 1.72322 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1728.02 | −1.07763 | −0.538813 | − | 0.842425i | \(-0.681127\pi\) | ||||
−0.538813 | + | 0.842425i | \(0.681127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −624.188 | −0.380885 | −0.190442 | − | 0.981698i | \(-0.560992\pi\) | ||||
−0.190442 | + | 0.981698i | \(0.560992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −965.904 | −0.576906 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 307.825 | 0.180011 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1086.39 | −0.622207 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1623.67 | 0.911004 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −57.5590 | −0.0316471 | −0.0158235 | − | 0.999875i | \(-0.505037\pi\) | ||||
−0.0158235 | + | 0.999875i | \(0.505037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2567.35 | −1.38363 | −0.691814 | − | 0.722076i | \(-0.743188\pi\) | ||||
−0.691814 | + | 0.722076i | \(0.743188\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.8956 | 0.00628564 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3182.53 | −1.64921 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3015.67 | 1.53297 | 0.766486 | − | 0.642261i | \(-0.222003\pi\) | ||||
0.766486 | + | 0.642261i | \(0.222003\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −642.575 | −0.320500 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.67918 | 0.00278001 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3331.49 | 1.60088 | 0.800438 | − | 0.599416i | \(-0.204600\pi\) | ||||
0.800438 | + | 0.599416i | \(0.204600\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −290.382 | −0.137007 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2465.56 | 1.14246 | 0.571229 | − | 0.820791i | \(-0.306467\pi\) | ||||
0.571229 | + | 0.820791i | \(0.306467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6032.33 | 2.74571 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 87.1333 | 0.0389664 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 549.111 | 0.241319 | 0.120659 | − | 0.992694i | \(-0.461499\pi\) | ||||
0.120659 | + | 0.992694i | \(0.461499\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 43.0498 | 0.0185958 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3597.61 | 1.52776 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4186.74 | 1.74822 | 0.874110 | − | 0.485728i | \(-0.161445\pi\) | ||||
0.874110 | + | 0.485728i | \(0.161445\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3954.07 | 1.62378 | 0.811890 | − | 0.583811i | \(-0.198439\pi\) | ||||
0.811890 | + | 0.583811i | \(0.198439\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1349.01 | 0.544928 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2785.70 | 1.10707 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.80193 | −0.00344204 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 31.9136 | 0.0122824 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1623.62 | −0.615084 | −0.307542 | − | 0.951535i | \(-0.599506\pi\) | ||||
−0.307542 | + | 0.951535i | \(0.599506\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1817.44 | 0.677833 | 0.338917 | − | 0.940816i | \(-0.389940\pi\) | ||||
0.338917 | + | 0.940816i | \(0.389940\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7763.01 | −2.85088 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −151.771 | −0.0548894 | −0.0274447 | − | 0.999623i | \(-0.508737\pi\) | ||||
−0.0274447 | + | 0.999623i | \(0.508737\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1229.91 | 0.438119 | 0.219060 | − | 0.975711i | \(-0.429701\pi\) | ||||
0.219060 | + | 0.975711i | \(0.429701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2797.63 | 0.981738 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.8269 | −0.00443483 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7847.20 | 2.67352 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −122.038 | −0.0409769 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −64.4726 | −0.0213381 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2998.12 | 0.978194 | 0.489097 | − | 0.872229i | \(-0.337326\pi\) | ||||
0.489097 | + | 0.872229i | \(0.337326\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4603.16 | 1.48077 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6606.75 | 2.09571 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −37.5757 | −0.0117549 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1744.43 | −0.538253 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −235.309 | −0.0716226 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −781.297 | −0.234617 | −0.117308 | − | 0.993096i | \(-0.537427\pi\) | ||||
−0.117308 | + | 0.993096i | \(0.537427\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −925.080 | −0.274098 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2695.16 | 0.788035 | 0.394017 | − | 0.919103i | \(-0.371085\pi\) | ||||
0.394017 | + | 0.919103i | \(0.371085\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3952.95 | −1.14069 | −0.570346 | − | 0.821405i | \(-0.693191\pi\) | ||||
−0.570346 | + | 0.821405i | \(0.693191\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.42849 | −0.000976529 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4315.28 | 1.21332 | 0.606659 | − | 0.794962i | \(-0.292509\pi\) | ||||
0.606659 | + | 0.794962i | \(0.292509\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3687.75 | 1.02367 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −969.849 | −0.265816 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3808.38 | 1.03073 | 0.515363 | − | 0.856972i | \(-0.327657\pi\) | ||||
0.515363 | + | 0.856972i | \(0.327657\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4274.22 | 1.14243 | 0.571217 | − | 0.820799i | \(-0.306471\pi\) | ||||
0.571217 | + | 0.820799i | \(0.306471\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1271.99 | −0.335795 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6199.04 | −1.61650 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1723.60 | −0.444008 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3703.35 | −0.942530 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2552.20 | −0.641806 | −0.320903 | − | 0.947112i | \(-0.603986\pi\) | ||||
−0.320903 | + | 0.947112i | \(0.603986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 90.2995 | 0.0224390 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 221.975 | 0.0545123 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2099.29 | 0.509533 | 0.254766 | − | 0.967003i | \(-0.418001\pi\) | ||||
0.254766 | + | 0.967003i | \(0.418001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 32.8903 | 0.00789075 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 275.632 | 0.0653685 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7691.71 | −1.80339 | −0.901695 | − | 0.432374i | \(-0.857676\pi\) | ||||
−0.901695 | + | 0.432374i | \(0.857676\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2453.31 | 0.568700 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1011.35 | −0.231811 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1460.77 | −0.331096 | −0.165548 | − | 0.986202i | \(-0.552939\pi\) | ||||
−0.165548 | + | 0.986202i | \(0.552939\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3180.10 | 0.712832 | 0.356416 | − | 0.934327i | \(-0.383999\pi\) | ||||
0.356416 | + | 0.934327i | \(0.383999\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −91.6566 | −0.0203198 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 684.495 | 0.150097 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1227.66 | 0.266293 | 0.133146 | − | 0.991096i | \(-0.457492\pi\) | ||||
0.133146 | + | 0.991096i | \(0.457492\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 807.449 | 0.173264 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6497.13 | 1.37931 | 0.689655 | − | 0.724138i | \(-0.257762\pi\) | ||||
0.689655 | + | 0.724138i | \(0.257762\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 48.1723 | 0.0101185 | 0.00505927 | − | 0.999987i | \(-0.498390\pi\) | ||||
0.00505927 | + | 0.999987i | \(0.498390\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1625.93 | 0.337936 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 92.6506 | 0.0190557 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4906.27 | −0.998630 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5773.71 | 1.16310 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1140.74 | −0.227449 | −0.113724 | − | 0.993512i | \(-0.536278\pi\) | ||||
−0.113724 | + | 0.993512i | \(0.536278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13735.4 | −2.71087 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 507.429 | 0.0991382 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2414.05 | 0.466916 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 78.0049 | 0.0149373 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −255.544 | −0.0484509 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5150.43 | −0.966927 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6728.53 | 1.25087 | 0.625435 | − | 0.780276i | \(-0.284921\pi\) | ||||
0.625435 | + | 0.780276i | \(0.284921\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9409.52 | −1.73233 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9758.17 | −1.77921 | −0.889606 | − | 0.456728i | \(-0.849021\pi\) | ||||
−0.889606 | + | 0.456728i | \(0.849021\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1660.82 | −0.299920 | −0.149960 | − | 0.988692i | \(-0.547915\pi\) | ||||
−0.149960 | + | 0.988692i | \(0.547915\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.6905 | −0.00316427 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6578.84 | −1.16563 | −0.582814 | − | 0.812605i | \(-0.698049\pi\) | ||||
−0.582814 | + | 0.812605i | \(0.698049\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −203.948 | −0.0357960 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5098.53 | −0.886517 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 49.2845 | 0.00848997 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18299.2 | 3.12325 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5683.91 | −0.961226 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 43.5407 | 0.00729629 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5522.33 | 0.917024 | 0.458512 | − | 0.888688i | \(-0.348383\pi\) | ||||
0.458512 | + | 0.888688i | \(0.348383\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −706.767 | −0.116308 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10681.1 | −1.74201 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1350.63 | 0.218319 | 0.109159 | − | 0.994024i | \(-0.465184\pi\) | ||||
0.109159 | + | 0.994024i | \(0.465184\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6640.97 | −1.06398 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −597.457 | −0.0948800 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −146.392 | −0.0230450 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2277.26 | −0.355372 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7266.15 | −1.12411 | −0.562057 | − | 0.827099i | \(-0.689990\pi\) | ||||
−0.562057 | + | 0.827099i | \(0.689990\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10360.4 | −1.58905 | −0.794524 | − | 0.607233i | \(-0.792279\pi\) | ||||
−0.794524 | + | 0.607233i | \(0.792279\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13565.5 | 2.06289 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4014.20 | −0.605253 | −0.302626 | − | 0.953109i | \(-0.597863\pi\) | ||||
−0.302626 | + | 0.953109i | \(0.597863\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −17574.5 | −2.62749 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.62083 | 0.000388540 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7120.01 | 1.04674 | 0.523370 | − | 0.852106i | \(-0.324675\pi\) | ||||
0.523370 | + | 0.852106i | \(0.324675\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6246.90 | 0.903243 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6660.09 | 0.955083 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12447.9 | 1.77050 | 0.885251 | − | 0.465114i | \(-0.153987\pi\) | ||||
0.885251 | + | 0.465114i | \(0.153987\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1990.93 | −0.280878 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.9658 | 0.00405345 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2379.11 | 0.330257 | 0.165128 | − | 0.986272i | \(-0.447196\pi\) | ||||
0.165128 | + | 0.986272i | \(0.447196\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −6565.34 | −0.904087 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5452.32 | −0.744850 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10559.0 | −1.43108 | −0.715541 | − | 0.698571i | \(-0.753820\pi\) | ||||
−0.715541 | + | 0.698571i | \(0.753820\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4995.78 | 0.671763 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3074.48 | 0.410180 | 0.205090 | − | 0.978743i | \(-0.434251\pi\) | ||||
0.205090 | + | 0.978743i | \(0.434251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.0897 | 0.00173277 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1676.22 | −0.220173 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7437.27 | −0.969369 | −0.484684 | − | 0.874689i | \(-0.661066\pi\) | ||||
−0.484684 | + | 0.874689i | \(0.661066\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −69.0272 | −0.00892802 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4862.08 | −0.624070 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3702.82 | 0.471668 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10690.7 | 1.35151 | 0.675756 | − | 0.737125i | \(-0.263817\pi\) | ||||
0.675756 | + | 0.737125i | \(0.263817\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.1971 | 0.00240866 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8536.44 | −1.06307 | −0.531533 | − | 0.847038i | \(-0.678384\pi\) | ||||
−0.531533 | + | 0.847038i | \(0.678384\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15972.3 | −1.97428 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10558.7 | −1.29547 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 522.959 | 0.0636907 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5072.21 | 0.613214 | 0.306607 | − | 0.951836i | \(-0.400806\pi\) | ||||
0.306607 | + | 0.951836i | \(0.400806\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8181.05 | 0.981852 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −162.172 | −0.0193219 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14139.1 | 1.67244 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2955.12 | 0.347034 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13968.1 | 1.62861 | 0.814306 | − | 0.580436i | \(-0.197118\pi\) | ||||
0.814306 | + | 0.580436i | \(0.197118\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14983.2 | −1.73453 | −0.867264 | − | 0.497849i | \(-0.834123\pi\) | ||||
−0.867264 | + | 0.497849i | \(0.834123\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −935.630 | −0.107546 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −523.246 | −0.0597203 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −60.8103 | −0.00689184 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1457.35 | −0.164013 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9101.07 | −1.01713 | −0.508565 | − | 0.861023i | \(-0.669824\pi\) | ||||
−0.508565 | + | 0.861023i | \(0.669824\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8406.65 | −0.933020 | −0.466510 | − | 0.884516i | \(-0.654489\pi\) | ||||
−0.466510 | + | 0.884516i | \(0.654489\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5143.36 | 0.566909 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −505.612 | −0.0553472 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4687.92 | 0.509664 | 0.254832 | − | 0.966985i | \(-0.417980\pi\) | ||||
0.254832 | + | 0.966985i | \(0.417980\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1572.78 | 0.169828 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9503.30 | −1.01922 | −0.509611 | − | 0.860405i | \(-0.670211\pi\) | ||||
−0.509611 | + | 0.860405i | \(0.670211\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3861.26 | 0.411329 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 272.504 | 0.0288345 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2589.35 | −0.272159 | −0.136079 | − | 0.990698i | \(-0.543450\pi\) | ||||
−0.136079 | + | 0.990698i | \(0.543450\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1473.15 | 0.153810 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12154.7 | 1.26066 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 349.939 | 0.0360558 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11145.8 | −1.14087 | −0.570436 | − | 0.821342i | \(-0.693226\pi\) | ||||
−0.570436 | + | 0.821342i | \(0.693226\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −387.892 | −0.0394450 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4634.89 | −0.468261 | −0.234131 | − | 0.972205i | \(-0.575224\pi\) | ||||
−0.234131 | + | 0.972205i | \(0.575224\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8329.82 | 0.836112 | 0.418056 | − | 0.908421i | \(-0.362712\pi\) | ||||
0.418056 | + | 0.908421i | \(0.362712\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15067.2 | 1.50264 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13878.1 | −1.37516 | −0.687582 | − | 0.726107i | \(-0.741328\pi\) | ||||
−0.687582 | + | 0.726107i | \(0.741328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −126.111 | −0.0124163 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14277.2 | −1.39673 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1240.29 | 0.120567 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3832.68 | −0.370222 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −622.435 | −0.0597471 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15896.9 | 1.51639 | 0.758194 | − | 0.652029i | \(-0.226082\pi\) | ||||
0.758194 | + | 0.652029i | \(0.226082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13980.7 | 1.32529 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −26.8872 | −0.00253294 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22043.6 | −2.06381 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10987.2 | −1.02233 | −0.511166 | − | 0.859482i | \(-0.670786\pi\) | ||||
−0.511166 | + | 0.859482i | \(0.670786\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15772.4 | −1.45860 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4422.00 | −0.406440 | −0.203220 | − | 0.979133i | \(-0.565141\pi\) | ||||
−0.203220 | + | 0.979133i | \(0.565141\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 155.903 | 0.0142425 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −281.281 | −0.0255406 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −207.500 | −0.0187277 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9203.68 | −0.825678 | −0.412839 | − | 0.910804i | \(-0.635463\pi\) | ||||
−0.412839 | + | 0.910804i | \(0.635463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11672.8 | −1.04092 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5394.92 | −0.478226 | −0.239113 | − | 0.970992i | \(-0.576857\pi\) | ||||
−0.239113 | + | 0.970992i | \(0.576857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 975.649 | 0.0859719 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28559.1 | −2.50169 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14409.8 | −1.25482 | −0.627410 | − | 0.778689i | \(-0.715885\pi\) | ||||
−0.627410 | + | 0.778689i | \(0.715885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 78.6347 | 0.00680742 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2841.24 | −0.244530 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35924.9 | 3.07386 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 692.302 | 0.0588924 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2599.68 | −0.219872 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2249.98 | −0.189201 | −0.0946003 | − | 0.995515i | \(-0.530157\pi\) | ||||
−0.0946003 | + | 0.995515i | \(0.530157\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19298.1 | 1.61348 | 0.806738 | − | 0.590909i | \(-0.201231\pi\) | ||||
0.806738 | + | 0.590909i | \(0.201231\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −203.813 | −0.0169431 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 456.711 | 0.0377507 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11458.8 | −0.941797 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3484.85 | 0.284801 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39383.0 | 3.20050 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19465.8 | 1.57305 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19821.5 | −1.59285 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1163.75 | −0.0929982 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 307.192 | 0.0244126 | 0.0122063 | − | 0.999926i | \(-0.496115\pi\) | ||||
0.0122063 | + | 0.999926i | \(0.496115\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18720.0 | −1.47947 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 21700.8 | 1.70561 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13468.0 | 1.05274 | 0.526371 | − | 0.850255i | \(-0.323552\pi\) | ||||
0.526371 | + | 0.850255i | \(0.323552\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1306.73 | 0.101584 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1141.96 | 0.0882928 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 43.7186 | 0.00336185 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13188.5 | −1.00868 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3808.21 | −0.289693 | −0.144846 | − | 0.989454i | \(-0.546269\pi\) | ||||
−0.144846 | + | 0.989454i | \(0.546269\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33157.5 | 2.50879 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 41.6714 | 0.00313613 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22451.9 | 1.68070 | 0.840351 | − | 0.542042i | \(-0.182349\pi\) | ||||
0.840351 | + | 0.542042i | \(0.182349\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25354.7 | 1.88793 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −124.665 | −0.00923358 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21111.7 | 1.55545 | 0.777723 | − | 0.628607i | \(-0.216375\pi\) | ||||
0.777723 | + | 0.628607i | \(0.216375\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7839.51 | 0.574559 | 0.287279 | − | 0.957847i | \(-0.407249\pi\) | ||||
0.287279 | + | 0.957847i | \(0.407249\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7686.78 | 0.560419 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5368.01 | 0.389324 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2092.09 | −0.150944 | −0.0754720 | − | 0.997148i | \(-0.524046\pi\) | ||||
−0.0754720 | + | 0.997148i | \(0.524046\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8604.37 | −0.617591 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 166.938 | 0.0119204 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 460.559 | 0.0327177 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7519.70 | −0.531455 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19301.8 | 1.35719 | 0.678595 | − | 0.734513i | \(-0.262589\pi\) | ||||
0.678595 | + | 0.734513i | \(0.262589\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3345.33 | 0.234027 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 718.535 | 0.0500111 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22422.7 | −1.55276 | −0.776381 | − | 0.630264i | \(-0.782947\pi\) | ||||
−0.776381 | + | 0.630264i | \(0.782947\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.0061 | −0.000689431 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5822.80 | −0.399182 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6779.52 | −0.462443 | −0.231222 | − | 0.972901i | \(-0.574272\pi\) | ||||
−0.231222 | + | 0.972901i | \(0.574272\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13065.1 | 0.886746 | 0.443373 | − | 0.896337i | \(-0.353782\pi\) | ||||
0.443373 | + | 0.896337i | \(0.353782\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2709.94 | 0.183014 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23850.2 | −1.60273 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17590.3 | −1.17622 | −0.588112 | − | 0.808780i | \(-0.700128\pi\) | ||||
−0.588112 | + | 0.808780i | \(0.700128\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 60.7268 | 0.00404068 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18507.9 | 1.22545 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10723.1 | −0.706530 | −0.353265 | − | 0.935523i | \(-0.614929\pi\) | ||||
−0.353265 | + | 0.935523i | \(0.614929\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −37151.4 | −2.43591 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2406.12 | −0.156997 | −0.0784983 | − | 0.996914i | \(-0.525013\pi\) | ||||
−0.0784983 | + | 0.996914i | \(0.525013\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5375.50 | −0.349046 | −0.174523 | − | 0.984653i | \(-0.555838\pi\) | ||||
−0.174523 | + | 0.984653i | \(0.555838\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3979.40 | 0.257146 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 45.5893 | 0.00293178 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −149.015 | −0.00953698 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 305.236 | 0.0194417 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −399.763 | −0.0253412 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16557.2 | −1.04458 | −0.522291 | − | 0.852767i | \(-0.674923\pi\) | ||||
−0.522291 | + | 0.852767i | \(0.674923\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14194.1 | −0.891258 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19073.5 | −1.19198 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31111.3 | −1.93513 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4458.89 | 0.276042 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1184.92 | −0.0730131 | −0.0365066 | − | 0.999333i | \(-0.511623\pi\) | ||||
−0.0365066 | + | 0.999333i | \(0.511623\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8126.38 | 0.498403 | 0.249202 | − | 0.968452i | \(-0.419832\pi\) | ||||
0.249202 | + | 0.968452i | \(0.419832\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −31278.7 | −1.90945 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16438.6 | 0.998868 | 0.499434 | − | 0.866352i | \(-0.333541\pi\) | ||||
0.499434 | + | 0.866352i | \(0.333541\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2578.55 | −0.155958 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 177.896 | 0.0107101 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10561.8 | 0.632947 | 0.316473 | − | 0.948601i | \(-0.397501\pi\) | ||||
0.316473 | + | 0.948601i | \(0.397501\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18563.1 | 1.10736 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1689.75 | −0.100340 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28057.4 | 1.65851 | 0.829257 | − | 0.558868i | \(-0.188764\pi\) | ||||
0.829257 | + | 0.558868i | \(0.188764\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16123.6 | −0.948769 | −0.474385 | − | 0.880318i | \(-0.657329\pi\) | ||||
−0.474385 | + | 0.880318i | \(0.657329\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1114.03 | 0.0652572 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −73.2931 | −0.00427396 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1599.42 | −0.0928483 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3698.93 | 0.213765 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −966.889 | −0.0556279 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31833.0 | −1.82329 | −0.911643 | − | 0.410982i | \(-0.865186\pi\) | ||||
−0.911643 | + | 0.410982i | \(0.865186\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 30165.0 | 1.72008 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18505.4 | 1.05055 | 0.525273 | − | 0.850934i | \(-0.323963\pi\) | ||||
0.525273 | + | 0.850934i | \(0.323963\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −260.266 | −0.0147100 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12759.8 | −0.717999 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2660.37 | −0.149043 | −0.0745213 | − | 0.997219i | \(-0.523743\pi\) | ||||
−0.0745213 | + | 0.997219i | \(0.523743\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −31234.7 | −1.74221 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18714.6 | 1.03931 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12312.5 | 0.680796 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23883.5 | −1.31487 | −0.657433 | − | 0.753513i | \(-0.728358\pi\) | ||||
−0.657433 | + | 0.753513i | \(0.728358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.32103 | −0.000182043 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11282.5 | −0.615781 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1126.12 | −0.0611975 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −20430.0 | −1.10549 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25949.8 | −1.39816 | −0.699079 | − | 0.715044i | \(-0.746406\pi\) | ||||
−0.699079 | + | 0.715044i | \(0.746406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2928.19 | −0.157097 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17459.1 | −0.932692 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.5193 | 0.000612771 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12320.8 | −0.652633 | −0.326316 | − | 0.945261i | \(-0.605807\pi\) | ||||
−0.326316 | + | 0.945261i | \(0.605807\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −939.452 | −0.0495530 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4685.42 | −0.246102 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5564.06 | 0.291026 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18030.2 | −0.939120 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27252.6 | −1.41356 | −0.706781 | − | 0.707432i | \(-0.749854\pi\) | ||||
−0.706781 | + | 0.707432i | \(0.749854\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 424.159 | 0.0219092 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20235.6 | −1.04090 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12124.1 | −0.621071 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24073.8 | 1.22813 | 0.614063 | − | 0.789257i | \(-0.289534\pi\) | ||||
0.614063 | + | 0.789257i | \(0.289534\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 21794.0 | 1.10725 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −948.105 | −0.0479712 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10232.2 | −0.515600 | −0.257800 | − | 0.966198i | \(-0.582998\pi\) | ||||
−0.257800 | + | 0.966198i | \(0.582998\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29348.4 | 1.47283 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2005.17 | −0.100219 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5327.77 | −0.265203 | −0.132602 | − | 0.991169i | \(-0.542333\pi\) | ||||
−0.132602 | + | 0.991169i | \(0.542333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8160.11 | 0.404547 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20416.6 | 1.00809 | 0.504046 | − | 0.863677i | \(-0.331844\pi\) | ||||
0.504046 | + | 0.863677i | \(0.331844\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1040.40 | −0.0511642 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3587.27 | −0.175705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 229.830 | 0.0112120 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11444.8 | 0.556092 | 0.278046 | − | 0.960568i | \(-0.410313\pi\) | ||||
0.278046 | + | 0.960568i | \(0.410313\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12083.0 | 0.584766 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −46405.8 | −2.23693 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31158.8 | −1.49602 | −0.748009 | − | 0.663689i | \(-0.768990\pi\) | ||||
−0.748009 | + | 0.663689i | \(0.768990\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −427.509 | −0.0204448 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8933.92 | −0.425564 | −0.212782 | − | 0.977100i | \(-0.568252\pi\) | ||||
−0.212782 | + | 0.977100i | \(0.568252\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 256.217 | 0.0121569 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 215.018 | 0.0101621 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −68934.4 | −3.24521 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29688.6 | 1.39220 | 0.696099 | − | 0.717946i | \(-0.254918\pi\) | ||||
0.696099 | + | 0.717946i | \(0.254918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9938.75 | −0.464248 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35704.1 | 1.66130 | 0.830651 | − | 0.556793i | \(-0.187968\pi\) | ||||
0.830651 | + | 0.556793i | \(0.187968\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −35516.8 | −1.64620 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −155.714 | −0.00718946 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8248.60 | −0.379380 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3299.27 | −0.151161 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8987.79 | −0.410214 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 54509.4 | 2.47838 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26828.3 | 1.21515 | 0.607577 | − | 0.794261i | \(-0.292142\pi\) | ||||
0.607577 | + | 0.794261i | \(0.292142\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36415.2 | 1.64311 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 299.360 | 0.0134564 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25848.6 | −1.15752 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11614.8 | −0.518157 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42689.8 | 1.89730 | 0.948650 | − | 0.316327i | \(-0.102450\pi\) | ||||
0.948650 | + | 0.316327i | \(0.102450\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −529.213 | −0.0234320 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −979.651 | −0.0432138 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1250.30 | 0.0549465 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 102.653 | 0.00449448 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6915.81 | 0.301670 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21486.1 | −0.933759 | −0.466880 | − | 0.884321i | \(-0.654622\pi\) | ||||
−0.466880 | + | 0.884321i | \(0.654622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3074.32 | −0.133112 | −0.0665560 | − | 0.997783i | \(-0.521201\pi\) | ||||
−0.0665560 | + | 0.997783i | \(0.521201\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15055.7 | −0.649480 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 60218.1 | 2.58816 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6944.70 | −0.297386 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −88.7839 | −0.00378799 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32460.2 | 1.37987 | 0.689933 | − | 0.723873i | \(-0.257640\pi\) | ||||
0.689933 | + | 0.723873i | \(0.257640\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25382.1 | −1.07505 | −0.537523 | − | 0.843249i | \(-0.680640\pi\) | ||||
−0.537523 | + | 0.843249i | \(0.680640\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3240.64 | −0.136757 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9830.51 | 0.413350 | 0.206675 | − | 0.978410i | \(-0.433736\pi\) | ||||
0.206675 | + | 0.978410i | \(0.433736\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −47474.0 | −1.98895 | −0.994476 | − | 0.104968i | \(-0.966526\pi\) | ||||
−0.994476 | + | 0.104968i | \(0.966526\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5812.18 | −0.242626 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 889.596 | 0.0370020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 44565.9 | 1.84703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26329.3 | −1.08730 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29050.3 | 1.19539 | 0.597693 | − | 0.801725i | \(-0.296084\pi\) | ||||
0.597693 | + | 0.801725i | \(0.296084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20776.6 | −0.851883 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −30759.7 | −1.25673 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 109037. | 4.43903 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −281.596 | −0.0114236 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −228.064 | −0.00921926 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4101.19 | 0.165202 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21804.2 | −0.875217 | −0.437609 | − | 0.899166i | \(-0.644174\pi\) | ||||
−0.437609 | + | 0.899166i | \(0.644174\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1574.97 | 0.0629974 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 30879.5 | 1.23083 | 0.615416 | − | 0.788203i | \(-0.288988\pi\) | ||||
0.615416 | + | 0.788203i | \(0.288988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6065.94 | −0.240940 | −0.120470 | − | 0.992717i | \(-0.538440\pi\) | ||||
−0.120470 | + | 0.992717i | \(0.538440\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −438.640 | −0.0173622 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1527.39 | −0.0602467 | −0.0301233 | − | 0.999546i | \(-0.509590\pi\) | ||||
−0.0301233 | + | 0.999546i | \(0.509590\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9925.40 | 0.390143 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23228.0 | 0.909878 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 695.129 | 0.0271354 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53605.8 | −2.08538 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5592.75 | 0.216822 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 295.950 | 0.0114342 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 565.469 | 0.0217725 | 0.0108863 | − | 0.999941i | \(-0.496535\pi\) | ||||
0.0108863 | + | 0.999941i | \(0.496535\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5400.64 | 0.207234 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28897.8 | −1.10510 | −0.552549 | − | 0.833481i | \(-0.686345\pi\) | ||||
−0.552549 | + | 0.833481i | \(0.686345\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26073.0 | −0.993687 | −0.496844 | − | 0.867840i | \(-0.665508\pi\) | ||||
−0.496844 | + | 0.867840i | \(0.665508\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 65028.2 | 2.46994 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −859.344 | −0.0325298 | −0.0162649 | − | 0.999868i | \(-0.505178\pi\) | ||||
−0.0162649 | + | 0.999868i | \(0.505178\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −225.198 | −0.00849596 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1982.19 | −0.0745294 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3876.39 | −0.145261 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 75676.9 | 2.82637 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11428.9 | −0.425419 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 10582.4 | 0.392595 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −352.063 | −0.0130177 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −369.302 | −0.0136098 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 71471.5 | 2.62519 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36272.4 | −1.32790 | −0.663951 | − | 0.747776i | \(-0.731122\pi\) | ||||
−0.663951 | + | 0.747776i | \(0.731122\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −247.535 | −0.00903213 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20484.7 | −0.744993 | −0.372497 | − | 0.928034i | \(-0.621498\pi\) | ||||
−0.372497 | + | 0.928034i | \(0.621498\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2654.33 | 0.0962165 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 24383.9 | 0.880992 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 219.171 | 0.00789277 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6354.25 | 0.228082 | 0.114041 | − | 0.993476i | \(-0.463620\pi\) | ||||
0.114041 | + | 0.993476i | \(0.463620\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31855.2 | −1.13970 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −88202.0 | −3.14540 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 31088.2 | 1.10505 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9114.60 | −0.322937 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 33316.3 | 1.17661 | 0.588307 | − | 0.808638i | \(-0.299795\pi\) | ||||
0.588307 | + | 0.808638i | \(0.299795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6516.13 | 0.229385 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 46198.6 | 1.62109 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −159.098 | −0.00556478 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6181.13 | −0.215506 | −0.107753 | − | 0.994178i | \(-0.534365\pi\) | ||||
−0.107753 | + | 0.994178i | \(0.534365\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7862.89 | 0.273265 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −609.315 | −0.0211085 | −0.0105543 | − | 0.999944i | \(-0.503360\pi\) | ||||
−0.0105543 | + | 0.999944i | \(0.503360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11552.9 | 0.398954 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 576.851 | 0.0198571 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9348.71 | 0.320794 | 0.160397 | − | 0.987053i | \(-0.448722\pi\) | ||||
0.160397 | + | 0.987053i | \(0.448722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 33425.2 | 1.14334 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31146.5 | 1.06203 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −36990.5 | −1.25734 | −0.628668 | − | 0.777674i | \(-0.716399\pi\) | ||||
−0.628668 | + | 0.777674i | \(0.716399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29347.6 | −0.994414 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 965.563 | 0.0326146 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −368.783 | −0.0124177 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1209.59 | 0.0406027 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4938.73 | −0.165263 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32850.9 | 1.09586 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48806.2 | −1.62306 | −0.811532 | − | 0.584308i | \(-0.801366\pi\) | ||||
−0.811532 | + | 0.584308i | \(0.801366\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −233.330 | −0.00773543 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −401.490 | −0.0132692 | −0.00663462 | − | 0.999978i | \(-0.502112\pi\) | ||||
−0.00663462 | + | 0.999978i | \(0.502112\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −133.210 | −0.00438903 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −86634.6 | −2.84567 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6786.27 | 0.222223 | 0.111112 | − | 0.993808i | \(-0.464559\pi\) | ||||
0.111112 | + | 0.993808i | \(0.464559\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 724.874 | 0.0236640 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5505.76 | −0.179190 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17163.1 | −0.556884 | −0.278442 | − | 0.960453i | \(-0.589818\pi\) | ||||
−0.278442 | + | 0.960453i | \(0.589818\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2743.31 | −0.0887404 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −206.137 | −0.00664783 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9726.67 | 0.312730 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9323.61 | 0.298864 | 0.149432 | − | 0.988772i | \(-0.452255\pi\) | ||||
0.149432 | + | 0.988772i | \(0.452255\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −26144.6 | −0.835524 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22231.0 | 0.708313 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14764.7 | −0.469011 | −0.234506 | − | 0.972115i | \(-0.575347\pi\) | ||||
−0.234506 | + | 0.972115i | \(0.575347\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 23046.3 | 0.729881 |
(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 | 1216.4.a.x.1.1 | 3 | ||
4.3 | odd | 2 | 1216.4.a.q.1.3 | 3 | |||
8.3 | odd | 2 | 304.4.a.j.1.1 | 3 | |||
8.5 | even | 2 | 152.4.a.b.1.3 | ✓ | 3 | ||
24.5 | odd | 2 | 1368.4.a.e.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
152.4.a.b.1.3 | ✓ | 3 | 8.5 | even | 2 | ||
304.4.a.j.1.1 | 3 | 8.3 | odd | 2 | |||
1216.4.a.q.1.3 | 3 | 4.3 | odd | 2 | |||
1216.4.a.x.1.1 | 3 | 1.1 | even | 1 | trivial | ||
1368.4.a.e.1.3 | 3 | 24.5 | odd | 2 |