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 | 1.16 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.96328 | −1.04768 | −0.523839 | − | 0.851817i | \(-0.675501\pi\) | ||||
−0.523839 | + | 0.851817i | \(0.675501\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.781040 | 0.0976300 | ||||||||
\(5\) | 9.17370 | 0.820521 | 0.410260 | − | 0.911968i | \(-0.365438\pi\) | ||||
0.410260 | + | 0.911968i | \(0.365438\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.35613 | 0.127219 | 0.0636096 | − | 0.997975i | \(-0.479739\pi\) | ||||
0.0636096 | + | 0.997975i | \(0.479739\pi\) | |||||||
\(8\) | 21.3918 | 0.945394 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −27.1843 | −0.859642 | ||||||||
\(11\) | −14.3796 | −0.394148 | −0.197074 | − | 0.980389i | \(-0.563144\pi\) | ||||
−0.197074 | + | 0.980389i | \(0.563144\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.1470 | 0.323155 | 0.161578 | − | 0.986860i | \(-0.448342\pi\) | ||||
0.161578 | + | 0.986860i | \(0.448342\pi\) | |||||||
\(14\) | −6.98188 | −0.133285 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −69.6383 | −1.08810 | ||||||||
\(17\) | −57.8861 | −0.825849 | −0.412925 | − | 0.910765i | \(-0.635493\pi\) | ||||
−0.412925 | + | 0.910765i | \(0.635493\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 103.148 | 1.24546 | 0.622730 | − | 0.782436i | \(-0.286023\pi\) | ||||
0.622730 | + | 0.782436i | \(0.286023\pi\) | |||||||
\(20\) | 7.16503 | 0.0801074 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 42.6109 | 0.412940 | ||||||||
\(23\) | 82.7139 | 0.749872 | 0.374936 | − | 0.927051i | \(-0.377665\pi\) | ||||
0.374936 | + | 0.927051i | \(0.377665\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −40.8433 | −0.326746 | ||||||||
\(26\) | −44.8848 | −0.338563 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.84023 | 0.0124204 | ||||||||
\(29\) | −82.2294 | −0.526538 | −0.263269 | − | 0.964722i | \(-0.584801\pi\) | ||||
−0.263269 | + | 0.964722i | \(0.584801\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −156.009 | −0.903874 | −0.451937 | − | 0.892050i | \(-0.649267\pi\) | ||||
−0.451937 | + | 0.892050i | \(0.649267\pi\) | |||||||
\(32\) | 35.2234 | 0.194584 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 171.533 | 0.865225 | ||||||||
\(35\) | 21.6144 | 0.104386 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 202.052 | 0.897762 | 0.448881 | − | 0.893591i | \(-0.351823\pi\) | ||||
0.448881 | + | 0.893591i | \(0.351823\pi\) | |||||||
\(38\) | −305.656 | −1.30484 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 196.242 | 0.775715 | ||||||||
\(41\) | −3.54593 | −0.0135069 | −0.00675344 | − | 0.999977i | \(-0.502150\pi\) | ||||
−0.00675344 | + | 0.999977i | \(0.502150\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 357.565 | 1.26810 | 0.634048 | − | 0.773293i | \(-0.281392\pi\) | ||||
0.634048 | + | 0.773293i | \(0.281392\pi\) | |||||||
\(44\) | −11.2311 | −0.0384807 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −245.105 | −0.785624 | ||||||||
\(47\) | 147.712 | 0.458426 | 0.229213 | − | 0.973376i | \(-0.426385\pi\) | ||||
0.229213 | + | 0.973376i | \(0.426385\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −337.449 | −0.983815 | ||||||||
\(50\) | 121.030 | 0.342325 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 11.8304 | 0.0315496 | ||||||||
\(53\) | 160.081 | 0.414885 | 0.207442 | − | 0.978247i | \(-0.433486\pi\) | ||||
0.207442 | + | 0.978247i | \(0.433486\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −131.915 | −0.323406 | ||||||||
\(56\) | 50.4019 | 0.120272 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 243.669 | 0.551643 | ||||||||
\(59\) | −45.9350 | −0.101360 | −0.0506799 | − | 0.998715i | \(-0.516139\pi\) | ||||
−0.0506799 | + | 0.998715i | \(0.516139\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −743.891 | −1.56140 | −0.780701 | − | 0.624905i | \(-0.785138\pi\) | ||||
−0.780701 | + | 0.624905i | \(0.785138\pi\) | |||||||
\(62\) | 462.299 | 0.946969 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 452.730 | 0.884237 | ||||||||
\(65\) | 138.954 | 0.265155 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 165.554 | 0.301876 | 0.150938 | − | 0.988543i | \(-0.451771\pi\) | ||||
0.150938 | + | 0.988543i | \(0.451771\pi\) | |||||||
\(68\) | −45.2114 | −0.0806277 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −64.0497 | −0.109363 | ||||||||
\(71\) | 747.149 | 1.24888 | 0.624439 | − | 0.781074i | \(-0.285328\pi\) | ||||
0.624439 | + | 0.781074i | \(0.285328\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 962.660 | 1.54344 | 0.771718 | − | 0.635965i | \(-0.219398\pi\) | ||||
0.771718 | + | 0.635965i | \(0.219398\pi\) | |||||||
\(74\) | −598.738 | −0.940566 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 80.5627 | 0.121594 | ||||||||
\(77\) | −33.8803 | −0.0501432 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 803.730 | 1.14464 | 0.572321 | − | 0.820030i | \(-0.306043\pi\) | ||||
0.572321 | + | 0.820030i | \(0.306043\pi\) | |||||||
\(80\) | −638.841 | −0.892807 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 10.5076 | 0.0141509 | ||||||||
\(83\) | 588.954 | 0.778869 | 0.389435 | − | 0.921054i | \(-0.372670\pi\) | ||||
0.389435 | + | 0.921054i | \(0.372670\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −531.030 | −0.677626 | ||||||||
\(86\) | −1059.57 | −1.32856 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −307.607 | −0.372625 | ||||||||
\(89\) | −764.364 | −0.910365 | −0.455182 | − | 0.890398i | \(-0.650426\pi\) | ||||
−0.455182 | + | 0.890398i | \(0.650426\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 35.6883 | 0.0411115 | ||||||||
\(92\) | 64.6029 | 0.0732100 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −437.713 | −0.480283 | ||||||||
\(95\) | 946.248 | 1.02193 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −135.843 | −0.142193 | −0.0710966 | − | 0.997469i | \(-0.522650\pi\) | ||||
−0.0710966 | + | 0.997469i | \(0.522650\pi\) | |||||||
\(98\) | 999.955 | 1.03072 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −31.9002 | −0.0319002 | ||||||||
\(101\) | 1641.69 | 1.61737 | 0.808685 | − | 0.588241i | \(-0.200179\pi\) | ||||
0.808685 | + | 0.588241i | \(0.200179\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1733.25 | −1.65808 | −0.829041 | − | 0.559188i | \(-0.811113\pi\) | ||||
−0.829041 | + | 0.559188i | \(0.811113\pi\) | |||||||
\(104\) | 324.021 | 0.305509 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −474.367 | −0.434666 | ||||||||
\(107\) | 1549.33 | 1.39981 | 0.699903 | − | 0.714238i | \(-0.253227\pi\) | ||||
0.699903 | + | 0.714238i | \(0.253227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1886.61 | −1.65784 | −0.828920 | − | 0.559368i | \(-0.811044\pi\) | ||||
−0.828920 | + | 0.559368i | \(0.811044\pi\) | |||||||
\(110\) | 390.900 | 0.338826 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −164.077 | −0.138427 | ||||||||
\(113\) | 177.382 | 0.147670 | 0.0738348 | − | 0.997270i | \(-0.476476\pi\) | ||||
0.0738348 | + | 0.997270i | \(0.476476\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 758.793 | 0.615285 | ||||||||
\(116\) | −64.2244 | −0.0514059 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 136.118 | 0.106192 | ||||||||
\(119\) | −136.387 | −0.105064 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1124.23 | −0.844648 | ||||||||
\(122\) | 2204.36 | 1.63585 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −121.849 | −0.0882452 | ||||||||
\(125\) | −1521.40 | −1.08862 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 465.031 | 0.324920 | 0.162460 | − | 0.986715i | \(-0.448057\pi\) | ||||
0.162460 | + | 0.986715i | \(0.448057\pi\) | |||||||
\(128\) | −1623.35 | −1.12098 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −411.759 | −0.277798 | ||||||||
\(131\) | 91.2048 | 0.0608290 | 0.0304145 | − | 0.999537i | \(-0.490317\pi\) | ||||
0.0304145 | + | 0.999537i | \(0.490317\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 243.030 | 0.158446 | ||||||||
\(134\) | −490.584 | −0.316268 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1238.29 | −0.780753 | ||||||||
\(137\) | 2813.92 | 1.75481 | 0.877406 | − | 0.479748i | \(-0.159272\pi\) | ||||
0.877406 | + | 0.479748i | \(0.159272\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2029.26 | −1.23827 | −0.619136 | − | 0.785284i | \(-0.712517\pi\) | ||||
−0.619136 | + | 0.785284i | \(0.712517\pi\) | |||||||
\(140\) | 16.8817 | 0.0101912 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2214.01 | −1.30842 | ||||||||
\(143\) | −217.808 | −0.127371 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −754.347 | −0.432035 | ||||||||
\(146\) | −2852.63 | −1.61703 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 157.811 | 0.0876485 | ||||||||
\(149\) | −833.802 | −0.458441 | −0.229221 | − | 0.973375i | \(-0.573618\pi\) | ||||
−0.229221 | + | 0.973375i | \(0.573618\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1231.99 | 0.663957 | 0.331979 | − | 0.943287i | \(-0.392284\pi\) | ||||
0.331979 | + | 0.943287i | \(0.392284\pi\) | |||||||
\(152\) | 2206.52 | 1.17745 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 100.397 | 0.0525339 | ||||||||
\(155\) | −1431.18 | −0.741647 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1856.39 | −0.943670 | −0.471835 | − | 0.881687i | \(-0.656408\pi\) | ||||
−0.471835 | + | 0.881687i | \(0.656408\pi\) | |||||||
\(158\) | −2381.68 | −1.19922 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 323.129 | 0.159660 | ||||||||
\(161\) | 194.885 | 0.0953981 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3384.37 | −1.62629 | −0.813143 | − | 0.582064i | \(-0.802245\pi\) | ||||
−0.813143 | + | 0.582064i | \(0.802245\pi\) | |||||||
\(164\) | −2.76952 | −0.00131868 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1745.24 | −0.816005 | ||||||||
\(167\) | −1594.39 | −0.738789 | −0.369394 | − | 0.929273i | \(-0.620435\pi\) | ||||
−0.369394 | + | 0.929273i | \(0.620435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1967.57 | −0.895571 | ||||||||
\(170\) | 1573.59 | 0.709934 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 279.273 | 0.123804 | ||||||||
\(173\) | 1538.64 | 0.676191 | 0.338095 | − | 0.941112i | \(-0.390217\pi\) | ||||
0.338095 | + | 0.941112i | \(0.390217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −96.2321 | −0.0415684 | ||||||||
\(176\) | 1001.37 | 0.428872 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2265.03 | 0.953769 | ||||||||
\(179\) | −418.587 | −0.174786 | −0.0873929 | − | 0.996174i | \(-0.527854\pi\) | ||||
−0.0873929 | + | 0.996174i | \(0.527854\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1821.82 | 0.748149 | 0.374074 | − | 0.927399i | \(-0.377960\pi\) | ||||
0.374074 | + | 0.927399i | \(0.377960\pi\) | |||||||
\(182\) | −105.754 | −0.0430717 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1769.40 | 0.708924 | ||||||||
\(185\) | 1853.57 | 0.736632 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 832.381 | 0.325507 | ||||||||
\(188\) | 115.369 | 0.0447561 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2804.00 | −1.07065 | ||||||||
\(191\) | 1876.74 | 0.710974 | 0.355487 | − | 0.934681i | \(-0.384315\pi\) | ||||
0.355487 | + | 0.934681i | \(0.384315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3743.99 | 1.39637 | 0.698183 | − | 0.715919i | \(-0.253992\pi\) | ||||
0.698183 | + | 0.715919i | \(0.253992\pi\) | |||||||
\(194\) | 402.540 | 0.148973 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −263.561 | −0.0960499 | ||||||||
\(197\) | −22.9050 | −0.00828384 | −0.00414192 | − | 0.999991i | \(-0.501318\pi\) | ||||
−0.00414192 | + | 0.999991i | \(0.501318\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1922.67 | 0.684897 | 0.342448 | − | 0.939537i | \(-0.388744\pi\) | ||||
0.342448 | + | 0.939537i | \(0.388744\pi\) | |||||||
\(200\) | −873.711 | −0.308904 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4864.80 | −1.69448 | ||||||||
\(203\) | −193.743 | −0.0669858 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −32.5293 | −0.0110827 | ||||||||
\(206\) | 5136.11 | 1.73714 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1054.81 | −0.351624 | ||||||||
\(209\) | −1483.23 | −0.490896 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1483.21 | −0.483924 | −0.241962 | − | 0.970286i | \(-0.577791\pi\) | ||||
−0.241962 | + | 0.970286i | \(0.577791\pi\) | |||||||
\(212\) | 125.030 | 0.0405052 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4591.10 | −1.46655 | ||||||||
\(215\) | 3280.19 | 1.04050 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −367.578 | −0.114990 | ||||||||
\(218\) | 5590.56 | 1.73688 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −103.031 | −0.0315742 | ||||||||
\(221\) | −876.799 | −0.266877 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2208.44 | −0.663176 | −0.331588 | − | 0.943424i | \(-0.607584\pi\) | ||||
−0.331588 | + | 0.943424i | \(0.607584\pi\) | |||||||
\(224\) | 82.9910 | 0.0247548 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −525.632 | −0.154710 | ||||||||
\(227\) | 5649.03 | 1.65172 | 0.825858 | − | 0.563879i | \(-0.190691\pi\) | ||||
0.825858 | + | 0.563879i | \(0.190691\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5161.69 | 1.48949 | 0.744747 | − | 0.667347i | \(-0.232570\pi\) | ||||
0.744747 | + | 0.667347i | \(0.232570\pi\) | |||||||
\(230\) | −2248.52 | −0.644621 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1759.04 | −0.497786 | ||||||||
\(233\) | 1290.84 | 0.362943 | 0.181472 | − | 0.983396i | \(-0.441914\pi\) | ||||
0.181472 | + | 0.983396i | \(0.441914\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1355.07 | 0.376148 | ||||||||
\(236\) | −35.8771 | −0.00989575 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 404.154 | 0.110073 | ||||||||
\(239\) | −239.000 | −0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2953.77 | −0.789497 | −0.394749 | − | 0.918789i | \(-0.629168\pi\) | ||||
−0.394749 | + | 0.918789i | \(0.629168\pi\) | |||||||
\(242\) | 3331.40 | 0.884919 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −581.009 | −0.152440 | ||||||||
\(245\) | −3095.65 | −0.807241 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1562.38 | 0.402477 | ||||||||
\(248\) | −3337.32 | −0.854516 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4508.33 | 1.14053 | ||||||||
\(251\) | 3409.90 | 0.857495 | 0.428747 | − | 0.903424i | \(-0.358955\pi\) | ||||
0.428747 | + | 0.903424i | \(0.358955\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1189.40 | −0.295560 | ||||||||
\(254\) | −1378.02 | −0.340412 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1188.61 | 0.290189 | ||||||||
\(257\) | 6809.80 | 1.65286 | 0.826428 | − | 0.563043i | \(-0.190369\pi\) | ||||
0.826428 | + | 0.563043i | \(0.190369\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 476.062 | 0.114213 | ||||||||
\(260\) | 108.528 | 0.0258871 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −270.265 | −0.0637292 | ||||||||
\(263\) | −6686.40 | −1.56768 | −0.783842 | − | 0.620960i | \(-0.786743\pi\) | ||||
−0.783842 | + | 0.620960i | \(0.786743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1468.54 | 0.340421 | ||||||||
\(266\) | −720.167 | −0.166001 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 129.304 | 0.0294721 | ||||||||
\(269\) | −7028.75 | −1.59312 | −0.796562 | − | 0.604557i | \(-0.793350\pi\) | ||||
−0.796562 | + | 0.604557i | \(0.793350\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6307.26 | 1.41380 | 0.706898 | − | 0.707316i | \(-0.250094\pi\) | ||||
0.706898 | + | 0.707316i | \(0.250094\pi\) | |||||||
\(272\) | 4031.09 | 0.898605 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8338.43 | −1.83848 | ||||||||
\(275\) | 587.311 | 0.128786 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 997.811 | 0.216436 | 0.108218 | − | 0.994127i | \(-0.465486\pi\) | ||||
0.108218 | + | 0.994127i | \(0.465486\pi\) | |||||||
\(278\) | 6013.28 | 1.29731 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 462.372 | 0.0986858 | ||||||||
\(281\) | 4367.88 | 0.927281 | 0.463640 | − | 0.886024i | \(-0.346543\pi\) | ||||
0.463640 | + | 0.886024i | \(0.346543\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4659.41 | −0.978705 | −0.489352 | − | 0.872086i | \(-0.662767\pi\) | ||||
−0.489352 | + | 0.872086i | \(0.662767\pi\) | |||||||
\(284\) | 583.553 | 0.121928 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 645.427 | 0.133444 | ||||||||
\(287\) | −8.35469 | −0.00171833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1562.20 | −0.317973 | ||||||||
\(290\) | 2235.34 | 0.452634 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 751.876 | 0.150686 | ||||||||
\(293\) | −1873.11 | −0.373476 | −0.186738 | − | 0.982410i | \(-0.559791\pi\) | ||||
−0.186738 | + | 0.982410i | \(0.559791\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −421.394 | −0.0831677 | ||||||||
\(296\) | 4322.27 | 0.848739 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2470.79 | 0.480299 | ||||||||
\(299\) | 1252.87 | 0.242325 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 842.471 | 0.161326 | ||||||||
\(302\) | −3650.72 | −0.695614 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7183.05 | −1.35518 | ||||||||
\(305\) | −6824.23 | −1.28116 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9380.18 | 1.74383 | 0.871914 | − | 0.489659i | \(-0.162879\pi\) | ||||
0.871914 | + | 0.489659i | \(0.162879\pi\) | |||||||
\(308\) | −26.4619 | −0.00489548 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4241.00 | 0.777008 | ||||||||
\(311\) | −9990.35 | −1.82155 | −0.910773 | − | 0.412908i | \(-0.864513\pi\) | ||||
−0.910773 | + | 0.412908i | \(0.864513\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8829.71 | −1.59452 | −0.797260 | − | 0.603636i | \(-0.793718\pi\) | ||||
−0.797260 | + | 0.603636i | \(0.793718\pi\) | |||||||
\(314\) | 5501.01 | 0.988663 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 627.745 | 0.111751 | ||||||||
\(317\) | 4211.98 | 0.746273 | 0.373136 | − | 0.927776i | \(-0.378282\pi\) | ||||
0.373136 | + | 0.927776i | \(0.378282\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1182.43 | 0.207534 | ||||||||
\(320\) | 4153.20 | 0.725535 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −577.499 | −0.0999465 | ||||||||
\(323\) | −5970.83 | −1.02856 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −618.652 | −0.105590 | ||||||||
\(326\) | 10028.8 | 1.70382 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −75.8539 | −0.0127693 | ||||||||
\(329\) | 348.029 | 0.0583206 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6313.47 | 1.04840 | 0.524199 | − | 0.851596i | \(-0.324365\pi\) | ||||
0.524199 | + | 0.851596i | \(0.324365\pi\) | |||||||
\(332\) | 459.997 | 0.0760410 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4724.63 | 0.774013 | ||||||||
\(335\) | 1518.74 | 0.247695 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7036.97 | −1.13747 | −0.568736 | − | 0.822520i | \(-0.692567\pi\) | ||||
−0.568736 | + | 0.822520i | \(0.692567\pi\) | |||||||
\(338\) | 5830.46 | 0.938270 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −414.755 | −0.0661567 | ||||||||
\(341\) | 2243.36 | 0.356260 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1603.23 | −0.252379 | ||||||||
\(344\) | 7648.96 | 1.19885 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4559.44 | −0.708430 | ||||||||
\(347\) | 10927.9 | 1.69061 | 0.845306 | − | 0.534282i | \(-0.179418\pi\) | ||||
0.845306 | + | 0.534282i | \(0.179418\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4966.40 | 0.761734 | 0.380867 | − | 0.924630i | \(-0.375626\pi\) | ||||
0.380867 | + | 0.924630i | \(0.375626\pi\) | |||||||
\(350\) | 285.163 | 0.0435503 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −506.500 | −0.0766947 | ||||||||
\(353\) | 7853.14 | 1.18408 | 0.592040 | − | 0.805908i | \(-0.298323\pi\) | ||||
0.592040 | + | 0.805908i | \(0.298323\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6854.12 | 1.02473 | ||||||||
\(356\) | −596.999 | −0.0888789 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1240.39 | 0.183119 | ||||||||
\(359\) | 4725.95 | 0.694781 | 0.347390 | − | 0.937721i | \(-0.387068\pi\) | ||||
0.347390 | + | 0.937721i | \(0.387068\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3780.49 | 0.551173 | ||||||||
\(362\) | −5398.57 | −0.783819 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 27.8740 | 0.00401372 | ||||||||
\(365\) | 8831.16 | 1.26642 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11340.8 | 1.61304 | 0.806522 | − | 0.591204i | \(-0.201347\pi\) | ||||
0.806522 | + | 0.591204i | \(0.201347\pi\) | |||||||
\(368\) | −5760.06 | −0.815934 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5492.64 | −0.771754 | ||||||||
\(371\) | 377.173 | 0.0527813 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9963.63 | 1.38310 | 0.691551 | − | 0.722328i | \(-0.256928\pi\) | ||||
0.691551 | + | 0.722328i | \(0.256928\pi\) | |||||||
\(374\) | −2466.58 | −0.341026 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3159.83 | 0.433393 | ||||||||
\(377\) | −1245.53 | −0.170154 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3903.68 | −0.529073 | −0.264536 | − | 0.964376i | \(-0.585219\pi\) | ||||
−0.264536 | + | 0.964376i | \(0.585219\pi\) | |||||||
\(380\) | 739.058 | 0.0997707 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −5561.31 | −0.744872 | ||||||||
\(383\) | 7011.53 | 0.935438 | 0.467719 | − | 0.883877i | \(-0.345076\pi\) | ||||
0.467719 | + | 0.883877i | \(0.345076\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −310.808 | −0.0411435 | ||||||||
\(386\) | −11094.5 | −1.46294 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −106.099 | −0.0138823 | ||||||||
\(389\) | 6380.67 | 0.831652 | 0.415826 | − | 0.909444i | \(-0.363493\pi\) | ||||
0.415826 | + | 0.909444i | \(0.363493\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4787.99 | −0.619281 | ||||||||
\(392\) | −7218.64 | −0.930093 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 67.8741 | 0.00867880 | ||||||||
\(395\) | 7373.18 | 0.939202 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13753.7 | 1.73874 | 0.869370 | − | 0.494162i | \(-0.164525\pi\) | ||||
0.869370 | + | 0.494162i | \(0.164525\pi\) | |||||||
\(398\) | −5697.41 | −0.717552 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2844.25 | 0.355532 | ||||||||
\(401\) | −2550.97 | −0.317679 | −0.158840 | − | 0.987304i | \(-0.550775\pi\) | ||||
−0.158840 | + | 0.987304i | \(0.550775\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2363.07 | −0.292091 | ||||||||
\(404\) | 1282.23 | 0.157904 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 574.116 | 0.0701795 | ||||||||
\(407\) | −2905.44 | −0.353851 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10406.3 | 1.25809 | 0.629047 | − | 0.777367i | \(-0.283445\pi\) | ||||
0.629047 | + | 0.777367i | \(0.283445\pi\) | |||||||
\(410\) | 96.3936 | 0.0116111 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1353.74 | −0.161879 | ||||||||
\(413\) | −108.229 | −0.0128949 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5402.89 | 0.639078 | ||||||||
\(416\) | 533.528 | 0.0628807 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4395.23 | 0.514301 | ||||||||
\(419\) | 15119.5 | 1.76286 | 0.881429 | − | 0.472317i | \(-0.156582\pi\) | ||||
0.881429 | + | 0.472317i | \(0.156582\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8421.52 | −0.974917 | −0.487458 | − | 0.873146i | \(-0.662076\pi\) | ||||
−0.487458 | + | 0.873146i | \(0.662076\pi\) | |||||||
\(422\) | 4395.16 | 0.506997 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3424.43 | 0.392229 | ||||||||
\(425\) | 2364.26 | 0.269843 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1752.71 | −0.198640 | ||||||||
\(428\) | 1210.09 | 0.136663 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9720.14 | −1.09011 | ||||||||
\(431\) | −14275.6 | −1.59544 | −0.797719 | − | 0.603030i | \(-0.793960\pi\) | ||||
−0.797719 | + | 0.603030i | \(0.793960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13380.4 | 1.48504 | 0.742518 | − | 0.669826i | \(-0.233632\pi\) | ||||
0.742518 | + | 0.669826i | \(0.233632\pi\) | |||||||
\(434\) | 1089.24 | 0.120473 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1473.52 | −0.161855 | ||||||||
\(437\) | 8531.77 | 0.933936 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5354.50 | 0.582133 | 0.291067 | − | 0.956703i | \(-0.405990\pi\) | ||||
0.291067 | + | 0.956703i | \(0.405990\pi\) | |||||||
\(440\) | −2821.89 | −0.305746 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2598.20 | 0.279602 | ||||||||
\(443\) | 17239.1 | 1.84889 | 0.924443 | − | 0.381321i | \(-0.124531\pi\) | ||||
0.924443 | + | 0.381321i | \(0.124531\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7012.05 | −0.746973 | ||||||||
\(446\) | 6544.24 | 0.694795 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1066.69 | 0.112492 | ||||||||
\(449\) | −12372.6 | −1.30044 | −0.650220 | − | 0.759746i | \(-0.725323\pi\) | ||||
−0.650220 | + | 0.759746i | \(0.725323\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 50.9893 | 0.00532370 | ||||||||
\(452\) | 138.542 | 0.0144170 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16739.7 | −1.73047 | ||||||||
\(455\) | 327.394 | 0.0337328 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10218.6 | 1.04596 | 0.522982 | − | 0.852343i | \(-0.324819\pi\) | ||||
0.522982 | + | 0.852343i | \(0.324819\pi\) | |||||||
\(458\) | −15295.5 | −1.56051 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 592.648 | 0.0600703 | ||||||||
\(461\) | 10295.4 | 1.04014 | 0.520069 | − | 0.854124i | \(-0.325906\pi\) | ||||
0.520069 | + | 0.854124i | \(0.325906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 624.733 | 0.0627080 | 0.0313540 | − | 0.999508i | \(-0.490018\pi\) | ||||
0.0313540 | + | 0.999508i | \(0.490018\pi\) | |||||||
\(464\) | 5726.31 | 0.572925 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3825.12 | −0.380248 | ||||||||
\(467\) | 3096.27 | 0.306805 | 0.153403 | − | 0.988164i | \(-0.450977\pi\) | ||||
0.153403 | + | 0.988164i | \(0.450977\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 390.067 | 0.0384044 | ||||||||
\(470\) | −4015.44 | −0.394082 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −982.632 | −0.0958248 | ||||||||
\(473\) | −5141.66 | −0.499817 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4212.90 | −0.406949 | ||||||||
\(476\) | −106.524 | −0.0102574 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 708.224 | 0.0677687 | ||||||||
\(479\) | 3505.65 | 0.334399 | 0.167200 | − | 0.985923i | \(-0.446528\pi\) | ||||
0.167200 | + | 0.985923i | \(0.446528\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3060.48 | 0.290116 | ||||||||
\(482\) | 8752.84 | 0.827139 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −878.065 | −0.0824629 | ||||||||
\(485\) | −1246.18 | −0.116672 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5020.73 | −0.467168 | −0.233584 | − | 0.972337i | \(-0.575045\pi\) | ||||
−0.233584 | + | 0.972337i | \(0.575045\pi\) | |||||||
\(488\) | −15913.2 | −1.47614 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9173.29 | 0.845729 | ||||||||
\(491\) | 7985.83 | 0.734003 | 0.367002 | − | 0.930220i | \(-0.380384\pi\) | ||||
0.367002 | + | 0.930220i | \(0.380384\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4759.94 | 0.434841 | ||||||||
\(494\) | −4629.77 | −0.421666 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10864.2 | 0.983504 | ||||||||
\(497\) | 1760.38 | 0.158881 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19646.0 | −1.76248 | −0.881240 | − | 0.472669i | \(-0.843291\pi\) | ||||
−0.881240 | + | 0.472669i | \(0.843291\pi\) | |||||||
\(500\) | −1188.27 | −0.106282 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10104.5 | −0.898379 | ||||||||
\(503\) | −8830.82 | −0.782797 | −0.391398 | − | 0.920221i | \(-0.628009\pi\) | ||||
−0.391398 | + | 0.920221i | \(0.628009\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15060.4 | 1.32709 | ||||||||
\(506\) | 3524.52 | 0.309652 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 363.208 | 0.0317220 | ||||||||
\(509\) | −11339.0 | −0.987413 | −0.493707 | − | 0.869628i | \(-0.664358\pi\) | ||||
−0.493707 | + | 0.869628i | \(0.664358\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2268.16 | 0.196355 | ||||||||
\(512\) | 9464.62 | 0.816955 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20179.4 | −1.73166 | ||||||||
\(515\) | −15900.3 | −1.36049 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2124.05 | −0.180688 | ||||||||
\(518\) | −1410.71 | −0.119658 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2972.47 | 0.250676 | ||||||||
\(521\) | 10393.5 | 0.873985 | 0.436992 | − | 0.899465i | \(-0.356044\pi\) | ||||
0.436992 | + | 0.899465i | \(0.356044\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4010.67 | 0.335324 | 0.167662 | − | 0.985845i | \(-0.446378\pi\) | ||||
0.167662 | + | 0.985845i | \(0.446378\pi\) | |||||||
\(524\) | 71.2346 | 0.00593874 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19813.7 | 1.64243 | ||||||||
\(527\) | 9030.77 | 0.746464 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5325.40 | −0.437692 | ||||||||
\(530\) | −4351.70 | −0.356652 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 189.816 | 0.0154691 | ||||||||
\(533\) | −53.7102 | −0.00436481 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14213.1 | 1.14857 | ||||||||
\(536\) | 3541.50 | 0.285391 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20828.2 | 1.66908 | ||||||||
\(539\) | 4852.39 | 0.387769 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23915.0 | 1.90053 | 0.950264 | − | 0.311445i | \(-0.100813\pi\) | ||||
0.950264 | + | 0.311445i | \(0.100813\pi\) | |||||||
\(542\) | −18690.2 | −1.48120 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2038.94 | −0.160697 | ||||||||
\(545\) | −17307.2 | −1.36029 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 569.608 | 0.0445241 | 0.0222621 | − | 0.999752i | \(-0.492913\pi\) | ||||
0.0222621 | + | 0.999752i | \(0.492913\pi\) | |||||||
\(548\) | 2197.78 | 0.171322 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1740.37 | −0.134927 | ||||||||
\(551\) | −8481.79 | −0.655783 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1893.69 | 0.145620 | ||||||||
\(554\) | −2956.79 | −0.226755 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1584.94 | −0.120893 | ||||||||
\(557\) | 4270.83 | 0.324885 | 0.162442 | − | 0.986718i | \(-0.448063\pi\) | ||||
0.162442 | + | 0.986718i | \(0.448063\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5416.03 | 0.409792 | ||||||||
\(560\) | −1505.19 | −0.113582 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12943.3 | −0.971492 | ||||||||
\(563\) | −13696.2 | −1.02527 | −0.512633 | − | 0.858608i | \(-0.671330\pi\) | ||||
−0.512633 | + | 0.858608i | \(0.671330\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1627.25 | 0.121166 | ||||||||
\(566\) | 13807.2 | 1.02537 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15982.9 | 1.18068 | ||||||||
\(569\) | 5737.72 | 0.422738 | 0.211369 | − | 0.977406i | \(-0.432208\pi\) | ||||
0.211369 | + | 0.977406i | \(0.432208\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9931.62 | 0.727890 | 0.363945 | − | 0.931420i | \(-0.381430\pi\) | ||||
0.363945 | + | 0.931420i | \(0.381430\pi\) | |||||||
\(572\) | −170.117 | −0.0124352 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 24.7573 | 0.00180026 | ||||||||
\(575\) | −3378.31 | −0.245018 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1313.36 | 0.0947591 | 0.0473796 | − | 0.998877i | \(-0.484913\pi\) | ||||
0.0473796 | + | 0.998877i | \(0.484913\pi\) | |||||||
\(578\) | 4629.24 | 0.333133 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −589.176 | −0.0421796 | ||||||||
\(581\) | 1387.65 | 0.0990871 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2301.91 | −0.163526 | ||||||||
\(584\) | 20593.1 | 1.45915 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5550.56 | 0.391282 | ||||||||
\(587\) | 14304.2 | 1.00579 | 0.502894 | − | 0.864348i | \(-0.332268\pi\) | ||||
0.502894 | + | 0.864348i | \(0.332268\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16092.0 | −1.12574 | ||||||||
\(590\) | 1248.71 | 0.0871331 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −14070.6 | −0.976854 | ||||||||
\(593\) | 4557.38 | 0.315597 | 0.157799 | − | 0.987471i | \(-0.449560\pi\) | ||||
0.157799 | + | 0.987471i | \(0.449560\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1251.18 | −0.0862071 | ||||||||
\(596\) | −651.233 | −0.0447576 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3712.60 | −0.253878 | ||||||||
\(599\) | 26296.5 | 1.79373 | 0.896867 | − | 0.442300i | \(-0.145837\pi\) | ||||
0.896867 | + | 0.442300i | \(0.145837\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19846.9 | 1.34704 | 0.673520 | − | 0.739169i | \(-0.264781\pi\) | ||||
0.673520 | + | 0.739169i | \(0.264781\pi\) | |||||||
\(602\) | −2496.48 | −0.169018 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 962.230 | 0.0648222 | ||||||||
\(605\) | −10313.3 | −0.693051 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18072.3 | −1.20846 | −0.604228 | − | 0.796812i | \(-0.706518\pi\) | ||||
−0.604228 | + | 0.796812i | \(0.706518\pi\) | |||||||
\(608\) | 3633.22 | 0.242346 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20222.1 | 1.34225 | ||||||||
\(611\) | 2237.39 | 0.148143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12103.1 | 0.797457 | 0.398729 | − | 0.917069i | \(-0.369451\pi\) | ||||
0.398729 | + | 0.917069i | \(0.369451\pi\) | |||||||
\(614\) | −27796.1 | −1.82697 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −724.762 | −0.0474050 | ||||||||
\(617\) | −20613.6 | −1.34502 | −0.672508 | − | 0.740090i | \(-0.734783\pi\) | ||||
−0.672508 | + | 0.740090i | \(0.734783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1056.49 | −0.0686007 | −0.0343004 | − | 0.999412i | \(-0.510920\pi\) | ||||
−0.0343004 | + | 0.999412i | \(0.510920\pi\) | |||||||
\(620\) | −1117.81 | −0.0724070 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 29604.2 | 1.90839 | ||||||||
\(623\) | −1800.94 | −0.115816 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8851.42 | −0.566491 | ||||||||
\(626\) | 26164.9 | 1.67054 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1449.92 | −0.0921305 | ||||||||
\(629\) | −11696.0 | −0.741416 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8013.19 | −0.505547 | −0.252773 | − | 0.967526i | \(-0.581343\pi\) | ||||
−0.252773 | + | 0.967526i | \(0.581343\pi\) | |||||||
\(632\) | 17193.2 | 1.08214 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12481.3 | −0.781854 | ||||||||
\(635\) | 4266.06 | 0.266604 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5111.33 | −0.317925 | ||||||||
\(638\) | −3503.87 | −0.217429 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −14892.1 | −0.919787 | ||||||||
\(641\) | 21822.2 | 1.34466 | 0.672328 | − | 0.740254i | \(-0.265295\pi\) | ||||
0.672328 | + | 0.740254i | \(0.265295\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6406.87 | −0.392943 | −0.196472 | − | 0.980510i | \(-0.562948\pi\) | ||||
−0.196472 | + | 0.980510i | \(0.562948\pi\) | |||||||
\(644\) | 152.213 | 0.00931371 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17693.3 | 1.07760 | ||||||||
\(647\) | −13195.9 | −0.801830 | −0.400915 | − | 0.916115i | \(-0.631308\pi\) | ||||
−0.400915 | + | 0.916115i | \(0.631308\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 660.529 | 0.0399507 | ||||||||
\(650\) | 1833.24 | 0.110624 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2643.33 | −0.158774 | ||||||||
\(653\) | 21736.7 | 1.30264 | 0.651319 | − | 0.758804i | \(-0.274216\pi\) | ||||
0.651319 | + | 0.758804i | \(0.274216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 836.685 | 0.0499114 | ||||||||
\(656\) | 246.933 | 0.0146968 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1031.31 | −0.0611012 | ||||||||
\(659\) | −16114.2 | −0.952534 | −0.476267 | − | 0.879301i | \(-0.658010\pi\) | ||||
−0.476267 | + | 0.879301i | \(0.658010\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3118.43 | 0.183499 | 0.0917496 | − | 0.995782i | \(-0.470754\pi\) | ||||
0.0917496 | + | 0.995782i | \(0.470754\pi\) | |||||||
\(662\) | −18708.6 | −1.09838 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12598.8 | 0.736338 | ||||||||
\(665\) | 2229.49 | 0.130009 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6801.51 | −0.394836 | ||||||||
\(668\) | −1245.28 | −0.0721279 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4500.47 | −0.259505 | ||||||||
\(671\) | 10696.9 | 0.615423 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7726.86 | −0.442569 | −0.221284 | − | 0.975209i | \(-0.571025\pi\) | ||||
−0.221284 | + | 0.975209i | \(0.571025\pi\) | |||||||
\(674\) | 20852.5 | 1.19171 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1536.75 | −0.0874346 | ||||||||
\(677\) | 32338.1 | 1.83583 | 0.917914 | − | 0.396780i | \(-0.129873\pi\) | ||||
0.917914 | + | 0.396780i | \(0.129873\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −320.063 | −0.0180897 | ||||||||
\(680\) | −11359.7 | −0.640624 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6647.70 | −0.373246 | ||||||||
\(683\) | 31880.4 | 1.78604 | 0.893022 | − | 0.450013i | \(-0.148581\pi\) | ||||
0.893022 | + | 0.450013i | \(0.148581\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 25814.0 | 1.43986 | ||||||||
\(686\) | 4750.81 | 0.264412 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24900.2 | −1.37981 | ||||||||
\(689\) | 2424.75 | 0.134072 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11724.0 | −0.645447 | −0.322723 | − | 0.946493i | \(-0.604598\pi\) | ||||
−0.322723 | + | 0.946493i | \(0.604598\pi\) | |||||||
\(692\) | 1201.74 | 0.0660165 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32382.6 | −1.77122 | ||||||||
\(695\) | −18615.8 | −1.01603 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 205.260 | 0.0111546 | ||||||||
\(698\) | −14716.8 | −0.798052 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −75.1611 | −0.00405832 | ||||||||
\(701\) | −14029.1 | −0.755880 | −0.377940 | − | 0.925830i | \(-0.623367\pi\) | ||||
−0.377940 | + | 0.925830i | \(0.623367\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20841.3 | 1.11813 | ||||||||
\(704\) | −6510.09 | −0.348520 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23271.1 | −1.24054 | ||||||||
\(707\) | 3868.04 | 0.205761 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15232.8 | −0.806881 | −0.403440 | − | 0.915006i | \(-0.632186\pi\) | ||||
−0.403440 | + | 0.915006i | \(0.632186\pi\) | |||||||
\(710\) | −20310.7 | −1.07359 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16351.1 | −0.860653 | ||||||||
\(713\) | −12904.1 | −0.677789 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1998.11 | −0.104510 | ||||||||
\(716\) | −326.933 | −0.0170643 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −14004.3 | −0.727907 | ||||||||
\(719\) | 33270.0 | 1.72568 | 0.862838 | − | 0.505481i | \(-0.168685\pi\) | ||||
0.862838 | + | 0.505481i | \(0.168685\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4083.77 | −0.210940 | ||||||||
\(722\) | −11202.7 | −0.577452 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1422.92 | 0.0730418 | ||||||||
\(725\) | 3358.51 | 0.172044 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16319.6 | −0.832543 | −0.416272 | − | 0.909240i | \(-0.636663\pi\) | ||||
−0.416272 | + | 0.909240i | \(0.636663\pi\) | |||||||
\(728\) | 763.437 | 0.0388666 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −26169.2 | −1.32680 | ||||||||
\(731\) | −20698.0 | −1.04726 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32024.7 | 1.61372 | 0.806862 | − | 0.590741i | \(-0.201164\pi\) | ||||
0.806862 | + | 0.590741i | \(0.201164\pi\) | |||||||
\(734\) | −33606.1 | −1.68995 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2913.47 | 0.145913 | ||||||||
\(737\) | −2380.61 | −0.118984 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9196.88 | −0.457798 | −0.228899 | − | 0.973450i | \(-0.573513\pi\) | ||||
−0.228899 | + | 0.973450i | \(0.573513\pi\) | |||||||
\(740\) | 1447.71 | 0.0719174 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1117.67 | −0.0552978 | ||||||||
\(743\) | −33744.1 | −1.66615 | −0.833075 | − | 0.553160i | \(-0.813422\pi\) | ||||
−0.833075 | + | 0.553160i | \(0.813422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7649.05 | −0.376160 | ||||||||
\(746\) | −29525.0 | −1.44905 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 650.123 | 0.0317792 | ||||||||
\(749\) | 3650.42 | 0.178082 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11732.9 | 0.570091 | 0.285046 | − | 0.958514i | \(-0.407991\pi\) | ||||
0.285046 | + | 0.958514i | \(0.407991\pi\) | |||||||
\(752\) | −10286.4 | −0.498813 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3690.85 | 0.178266 | ||||||||
\(755\) | 11301.9 | 0.544791 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15986.7 | 0.767563 | 0.383781 | − | 0.923424i | \(-0.374622\pi\) | ||||
0.383781 | + | 0.923424i | \(0.374622\pi\) | |||||||
\(758\) | 11567.7 | 0.554298 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20242.0 | 0.966122 | ||||||||
\(761\) | −19860.3 | −0.946039 | −0.473019 | − | 0.881052i | \(-0.656836\pi\) | ||||
−0.473019 | + | 0.881052i | \(0.656836\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4445.10 | −0.210909 | ||||||||
\(764\) | 1465.81 | 0.0694124 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20777.2 | −0.980038 | ||||||||
\(767\) | −695.776 | −0.0327549 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11902.2 | 0.558133 | 0.279067 | − | 0.960272i | \(-0.409975\pi\) | ||||
0.279067 | + | 0.960272i | \(0.409975\pi\) | |||||||
\(770\) | 921.012 | 0.0431051 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2924.21 | 0.136327 | ||||||||
\(773\) | 36404.0 | 1.69387 | 0.846935 | − | 0.531696i | \(-0.178445\pi\) | ||||
0.846935 | + | 0.531696i | \(0.178445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6371.93 | 0.295337 | ||||||||
\(776\) | −2905.92 | −0.134428 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18907.7 | −0.871304 | ||||||||
\(779\) | −365.756 | −0.0168223 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10743.7 | −0.492242 | ||||||||
\(782\) | 14188.2 | 0.648807 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23499.3 | 1.07049 | ||||||||
\(785\) | −17030.0 | −0.774301 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14540.7 | −0.658603 | −0.329301 | − | 0.944225i | \(-0.606813\pi\) | ||||
−0.329301 | + | 0.944225i | \(0.606813\pi\) | |||||||
\(788\) | −17.8898 | −0.000808752 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21848.8 | −0.983982 | ||||||||
\(791\) | 417.935 | 0.0187864 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11267.7 | −0.504575 | ||||||||
\(794\) | −40756.2 | −1.82164 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1501.68 | 0.0668665 | ||||||||
\(797\) | 25877.1 | 1.15008 | 0.575040 | − | 0.818125i | \(-0.304986\pi\) | ||||
0.575040 | + | 0.818125i | \(0.304986\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8550.48 | −0.378591 | ||||||||
\(800\) | −1438.64 | −0.0635794 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7559.25 | 0.332826 | ||||||||
\(803\) | −13842.7 | −0.608342 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1787.82 | 0.0782761 | ||||||||
\(806\) | 7002.44 | 0.306018 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 35118.8 | 1.52905 | ||||||||
\(809\) | −7017.33 | −0.304965 | −0.152482 | − | 0.988306i | \(-0.548727\pi\) | ||||
−0.152482 | + | 0.988306i | \(0.548727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9683.99 | −0.419298 | −0.209649 | − | 0.977777i | \(-0.567232\pi\) | ||||
−0.209649 | + | 0.977777i | \(0.567232\pi\) | |||||||
\(812\) | −151.321 | −0.00653982 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8609.64 | 0.370722 | ||||||||
\(815\) | −31047.2 | −1.33440 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 36882.1 | 1.57936 | ||||||||
\(818\) | −30836.9 | −1.31808 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −25.4067 | −0.00108200 | ||||||||
\(821\) | 27788.1 | 1.18125 | 0.590627 | − | 0.806944i | \(-0.298880\pi\) | ||||
0.590627 | + | 0.806944i | \(0.298880\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −33251.1 | −1.40834 | −0.704168 | − | 0.710034i | \(-0.748680\pi\) | ||||
−0.704168 | + | 0.710034i | \(0.748680\pi\) | |||||||
\(824\) | −37077.4 | −1.56754 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 320.713 | 0.0135097 | ||||||||
\(827\) | −44335.1 | −1.86419 | −0.932093 | − | 0.362218i | \(-0.882020\pi\) | ||||
−0.932093 | + | 0.362218i | \(0.882020\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −37480.4 | −1.57026 | −0.785132 | − | 0.619328i | \(-0.787405\pi\) | ||||
−0.785132 | + | 0.619328i | \(0.787405\pi\) | |||||||
\(830\) | −16010.3 | −0.669548 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6857.48 | 0.285746 | ||||||||
\(833\) | 19533.6 | 0.812483 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14626.5 | −0.606191 | ||||||||
\(836\) | −1158.46 | −0.0479261 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −44803.4 | −1.84691 | ||||||||
\(839\) | −28545.7 | −1.17462 | −0.587310 | − | 0.809362i | \(-0.699813\pi\) | ||||
−0.587310 | + | 0.809362i | \(0.699813\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17627.3 | −0.722757 | ||||||||
\(842\) | 24955.3 | 1.02140 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1158.44 | −0.0472456 | ||||||||
\(845\) | −18049.9 | −0.734834 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2648.82 | −0.107455 | ||||||||
\(848\) | −11147.8 | −0.451435 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7005.96 | −0.282709 | ||||||||
\(851\) | 16712.5 | 0.673206 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10701.2 | 0.429546 | 0.214773 | − | 0.976664i | \(-0.431099\pi\) | ||||
0.214773 | + | 0.976664i | \(0.431099\pi\) | |||||||
\(854\) | 5193.76 | 0.208111 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 33142.9 | 1.32337 | ||||||||
\(857\) | −31267.6 | −1.24630 | −0.623152 | − | 0.782101i | \(-0.714148\pi\) | ||||
−0.623152 | + | 0.782101i | \(0.714148\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.6688 | −0.00141677 | −0.000708385 | − | 1.00000i | \(-0.500225\pi\) | ||||
−0.000708385 | 1.00000i | \(0.500225\pi\) | ||||||||
\(860\) | 2561.96 | 0.101584 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 42302.8 | 1.67151 | ||||||||
\(863\) | −6916.71 | −0.272825 | −0.136412 | − | 0.990652i | \(-0.543557\pi\) | ||||
−0.136412 | + | 0.990652i | \(0.543557\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14115.1 | 0.554828 | ||||||||
\(866\) | −39649.9 | −1.55584 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −287.093 | −0.0112265 | ||||||||
\(869\) | −11557.4 | −0.451158 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2507.65 | 0.0975526 | ||||||||
\(872\) | −40358.0 | −1.56731 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −25282.0 | −0.978464 | ||||||||
\(875\) | −3584.61 | −0.138494 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2327.68 | 0.0896239 | 0.0448120 | − | 0.998995i | \(-0.485731\pi\) | ||||
0.0448120 | + | 0.998995i | \(0.485731\pi\) | |||||||
\(878\) | −15866.9 | −0.609888 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9186.30 | 0.351898 | ||||||||
\(881\) | −2343.54 | −0.0896205 | −0.0448103 | − | 0.998996i | \(-0.514268\pi\) | ||||
−0.0448103 | + | 0.998996i | \(0.514268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19558.9 | −0.745424 | −0.372712 | − | 0.927947i | \(-0.621572\pi\) | ||||
−0.372712 | + | 0.927947i | \(0.621572\pi\) | |||||||
\(884\) | −684.815 | −0.0260552 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −51084.4 | −1.93704 | ||||||||
\(887\) | −10331.5 | −0.391091 | −0.195546 | − | 0.980695i | \(-0.562648\pi\) | ||||
−0.195546 | + | 0.980695i | \(0.562648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1095.68 | 0.0413361 | ||||||||
\(890\) | 20778.7 | 0.782587 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1724.88 | −0.0647459 | ||||||||
\(893\) | 15236.2 | 0.570952 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3839.99 | −0.143415 | ||||||||
\(896\) | −3824.83 | −0.142610 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36663.4 | 1.36244 | ||||||||
\(899\) | 12828.5 | 0.475924 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9266.49 | −0.342632 | ||||||||
\(902\) | −151.096 | −0.00557753 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3794.52 | 0.139606 | ||||||||
\(905\) | 16712.8 | 0.613871 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52052.2 | 1.90559 | 0.952793 | − | 0.303621i | \(-0.0981957\pi\) | ||||
0.952793 | + | 0.303621i | \(0.0981957\pi\) | |||||||
\(908\) | 4412.12 | 0.161257 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −970.159 | −0.0353412 | ||||||||
\(911\) | −10108.8 | −0.367639 | −0.183820 | − | 0.982960i | \(-0.558846\pi\) | ||||
−0.183820 | + | 0.982960i | \(0.558846\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8468.95 | −0.306990 | ||||||||
\(914\) | −30280.6 | −1.09583 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4031.48 | 0.145419 | ||||||||
\(917\) | 214.890 | 0.00773861 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34840.7 | 1.25059 | 0.625293 | − | 0.780390i | \(-0.284979\pi\) | ||||
0.625293 | + | 0.780390i | \(0.284979\pi\) | |||||||
\(920\) | 16232.0 | 0.581687 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30508.1 | −1.08973 | ||||||||
\(923\) | 11317.0 | 0.403581 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8252.48 | −0.293340 | ||||||||
\(926\) | −1851.26 | −0.0656978 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2896.40 | −0.102456 | ||||||||
\(929\) | −39014.1 | −1.37784 | −0.688919 | − | 0.724838i | \(-0.741915\pi\) | ||||
−0.688919 | + | 0.724838i | \(0.741915\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34807.1 | −1.22530 | ||||||||
\(932\) | 1008.20 | 0.0354342 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9175.11 | −0.321433 | ||||||||
\(935\) | 7636.02 | 0.267085 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23368.1 | −0.814729 | −0.407364 | − | 0.913266i | \(-0.633552\pi\) | ||||
−0.407364 | + | 0.913266i | \(0.633552\pi\) | |||||||
\(938\) | −1155.88 | −0.0402354 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1058.36 | 0.0367233 | ||||||||
\(941\) | −6990.35 | −0.242167 | −0.121083 | − | 0.992642i | \(-0.538637\pi\) | ||||
−0.121083 | + | 0.992642i | \(0.538637\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −293.298 | −0.0101284 | ||||||||
\(944\) | 3198.83 | 0.110289 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15236.2 | 0.523648 | ||||||||
\(947\) | 34940.9 | 1.19897 | 0.599486 | − | 0.800385i | \(-0.295372\pi\) | ||||
0.599486 | + | 0.800385i | \(0.295372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14581.4 | 0.498769 | ||||||||
\(950\) | 12484.0 | 0.426352 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2917.57 | −0.0993267 | ||||||||
\(953\) | 49498.4 | 1.68249 | 0.841244 | − | 0.540655i | \(-0.181824\pi\) | ||||
0.841244 | + | 0.540655i | \(0.181824\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17216.6 | 0.583369 | ||||||||
\(956\) | −186.669 | −0.00631516 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10388.2 | −0.350343 | ||||||||
\(959\) | 6629.96 | 0.223246 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5452.12 | −0.183012 | ||||||||
\(962\) | −9069.07 | −0.303949 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2307.01 | −0.0770786 | ||||||||
\(965\) | 34346.3 | 1.14575 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22271.8 | −0.740655 | −0.370328 | − | 0.928901i | \(-0.620755\pi\) | ||||
−0.370328 | + | 0.928901i | \(0.620755\pi\) | |||||||
\(968\) | −24049.2 | −0.798524 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3692.78 | 0.122235 | ||||||||
\(971\) | −16361.7 | −0.540753 | −0.270376 | − | 0.962755i | \(-0.587148\pi\) | ||||
−0.270376 | + | 0.962755i | \(0.587148\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4781.21 | −0.157532 | ||||||||
\(974\) | 14877.8 | 0.489442 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 51803.3 | 1.69896 | ||||||||
\(977\) | −13731.6 | −0.449654 | −0.224827 | − | 0.974399i | \(-0.572182\pi\) | ||||
−0.224827 | + | 0.974399i | \(0.572182\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10991.3 | 0.358818 | ||||||||
\(980\) | −2417.83 | −0.0788109 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −23664.3 | −0.768999 | ||||||||
\(983\) | −41619.1 | −1.35040 | −0.675200 | − | 0.737634i | \(-0.735943\pi\) | ||||
−0.675200 | + | 0.737634i | \(0.735943\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −210.124 | −0.00679706 | ||||||||
\(986\) | −14105.0 | −0.455574 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1220.28 | 0.0392938 | ||||||||
\(989\) | 29575.6 | 0.950910 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15749.0 | 0.504827 | 0.252413 | − | 0.967619i | \(-0.418776\pi\) | ||||
0.252413 | + | 0.967619i | \(0.418776\pi\) | |||||||
\(992\) | −5495.18 | −0.175879 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5216.51 | −0.166456 | ||||||||
\(995\) | 17638.0 | 0.561972 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16722.9 | −0.531212 | −0.265606 | − | 0.964082i | \(-0.585572\pi\) | ||||
−0.265606 | + | 0.964082i | \(0.585572\pi\) | |||||||
\(998\) | 58216.8 | 1.84651 | ||||||||
\(999\) | 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.1.16 | yes | 59 | |
3.2 | odd | 2 | 2151.4.a.g.1.44 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.4.a.g.1.44 | ✓ | 59 | 3.2 | odd | 2 | ||
2151.4.a.h.1.16 | yes | 59 | 1.1 | even | 1 | trivial |