Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1250,4,Mod(1,1250)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1250, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1250.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1250 = 2 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1250.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: | \(73.7523875072\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 145x^{4} + 120x^{3} + 5125x^{2} - 2431x - 1069 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(8.28587\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1250.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | −5.66784 | −1.09078 | −0.545388 | − | 0.838184i | \(-0.683618\pi\) | ||||
−0.545388 | + | 0.838184i | \(0.683618\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 11.3357 | 0.771295 | ||||||||
\(7\) | −16.6100 | −0.896857 | −0.448428 | − | 0.893819i | \(-0.648016\pi\) | ||||
−0.448428 | + | 0.893819i | \(0.648016\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 5.12438 | 0.189792 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.04838 | 0.0835565 | 0.0417783 | − | 0.999127i | \(-0.486698\pi\) | ||||
0.0417783 | + | 0.999127i | \(0.486698\pi\) | |||||||
\(12\) | −22.6714 | −0.545388 | ||||||||
\(13\) | −15.4682 | −0.330008 | −0.165004 | − | 0.986293i | \(-0.552764\pi\) | ||||
−0.165004 | + | 0.986293i | \(0.552764\pi\) | |||||||
\(14\) | 33.2200 | 0.634173 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −43.5583 | −0.621437 | −0.310719 | − | 0.950502i | \(-0.600570\pi\) | ||||
−0.310719 | + | 0.950502i | \(0.600570\pi\) | |||||||
\(18\) | −10.2488 | −0.134203 | ||||||||
\(19\) | −24.2031 | −0.292241 | −0.146121 | − | 0.989267i | \(-0.546679\pi\) | ||||
−0.146121 | + | 0.989267i | \(0.546679\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 94.1429 | 0.978270 | ||||||||
\(22\) | −6.09676 | −0.0590834 | ||||||||
\(23\) | −195.996 | −1.77687 | −0.888434 | − | 0.459003i | \(-0.848207\pi\) | ||||
−0.888434 | + | 0.459003i | \(0.848207\pi\) | |||||||
\(24\) | 45.3427 | 0.385647 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 30.9364 | 0.233351 | ||||||||
\(27\) | 123.987 | 0.883755 | ||||||||
\(28\) | −66.4401 | −0.448428 | ||||||||
\(29\) | 10.3063 | 0.0659941 | 0.0329970 | − | 0.999455i | \(-0.489495\pi\) | ||||
0.0329970 | + | 0.999455i | \(0.489495\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −105.236 | −0.609706 | −0.304853 | − | 0.952399i | \(-0.598607\pi\) | ||||
−0.304853 | + | 0.952399i | \(0.598607\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | −17.2777 | −0.0911414 | ||||||||
\(34\) | 87.1165 | 0.439422 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 20.4975 | 0.0948960 | ||||||||
\(37\) | −266.960 | −1.18616 | −0.593080 | − | 0.805144i | \(-0.702088\pi\) | ||||
−0.593080 | + | 0.805144i | \(0.702088\pi\) | |||||||
\(38\) | 48.4063 | 0.206646 | ||||||||
\(39\) | 87.6713 | 0.359965 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 33.7935 | 0.128724 | 0.0643618 | − | 0.997927i | \(-0.479499\pi\) | ||||
0.0643618 | + | 0.997927i | \(0.479499\pi\) | |||||||
\(42\) | −188.286 | −0.691741 | ||||||||
\(43\) | 430.248 | 1.52587 | 0.762933 | − | 0.646478i | \(-0.223759\pi\) | ||||
0.762933 | + | 0.646478i | \(0.223759\pi\) | |||||||
\(44\) | 12.1935 | 0.0417783 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 391.992 | 1.25644 | ||||||||
\(47\) | −556.466 | −1.72700 | −0.863498 | − | 0.504352i | \(-0.831731\pi\) | ||||
−0.863498 | + | 0.504352i | \(0.831731\pi\) | |||||||
\(48\) | −90.6854 | −0.272694 | ||||||||
\(49\) | −67.1073 | −0.195648 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 246.881 | 0.677849 | ||||||||
\(52\) | −61.8728 | −0.165004 | ||||||||
\(53\) | −659.826 | −1.71008 | −0.855038 | − | 0.518565i | \(-0.826466\pi\) | ||||
−0.855038 | + | 0.518565i | \(0.826466\pi\) | |||||||
\(54\) | −247.975 | −0.624909 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 132.880 | 0.317087 | ||||||||
\(57\) | 137.179 | 0.318769 | ||||||||
\(58\) | −20.6126 | −0.0466649 | ||||||||
\(59\) | −162.048 | −0.357575 | −0.178787 | − | 0.983888i | \(-0.557217\pi\) | ||||
−0.178787 | + | 0.983888i | \(0.557217\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −197.885 | −0.415353 | −0.207677 | − | 0.978198i | \(-0.566590\pi\) | ||||
−0.207677 | + | 0.978198i | \(0.566590\pi\) | |||||||
\(62\) | 210.471 | 0.431127 | ||||||||
\(63\) | −85.1161 | −0.170216 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 34.5555 | 0.0644467 | ||||||||
\(67\) | −155.284 | −0.283149 | −0.141575 | − | 0.989928i | \(-0.545217\pi\) | ||||
−0.141575 | + | 0.989928i | \(0.545217\pi\) | |||||||
\(68\) | −174.233 | −0.310719 | ||||||||
\(69\) | 1110.87 | 1.93817 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 860.300 | 1.43801 | 0.719006 | − | 0.695004i | \(-0.244597\pi\) | ||||
0.719006 | + | 0.695004i | \(0.244597\pi\) | |||||||
\(72\) | −40.9951 | −0.0671016 | ||||||||
\(73\) | −359.057 | −0.575678 | −0.287839 | − | 0.957679i | \(-0.592937\pi\) | ||||
−0.287839 | + | 0.957679i | \(0.592937\pi\) | |||||||
\(74\) | 533.919 | 0.838741 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −96.8125 | −0.146121 | ||||||||
\(77\) | −50.6337 | −0.0749382 | ||||||||
\(78\) | −175.343 | −0.254534 | ||||||||
\(79\) | −1110.76 | −1.58190 | −0.790951 | − | 0.611879i | \(-0.790414\pi\) | ||||
−0.790951 | + | 0.611879i | \(0.790414\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −841.099 | −1.15377 | ||||||||
\(82\) | −67.5871 | −0.0910213 | ||||||||
\(83\) | 476.911 | 0.630696 | 0.315348 | − | 0.948976i | \(-0.397879\pi\) | ||||
0.315348 | + | 0.948976i | \(0.397879\pi\) | |||||||
\(84\) | 376.572 | 0.489135 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −860.496 | −1.07895 | ||||||||
\(87\) | −58.4143 | −0.0719847 | ||||||||
\(88\) | −24.3871 | −0.0295417 | ||||||||
\(89\) | −1444.77 | −1.72074 | −0.860368 | − | 0.509673i | \(-0.829766\pi\) | ||||
−0.860368 | + | 0.509673i | \(0.829766\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 256.927 | 0.295970 | ||||||||
\(92\) | −783.984 | −0.888434 | ||||||||
\(93\) | 596.459 | 0.665053 | ||||||||
\(94\) | 1112.93 | 1.22117 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 181.371 | 0.192824 | ||||||||
\(97\) | −645.160 | −0.675321 | −0.337660 | − | 0.941268i | \(-0.609635\pi\) | ||||
−0.337660 | + | 0.941268i | \(0.609635\pi\) | |||||||
\(98\) | 134.215 | 0.138344 | ||||||||
\(99\) | 15.6211 | 0.0158584 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 991.112 | 0.976429 | 0.488214 | − | 0.872724i | \(-0.337648\pi\) | ||||
0.488214 | + | 0.872724i | \(0.337648\pi\) | |||||||
\(102\) | −493.762 | −0.479311 | ||||||||
\(103\) | −1463.05 | −1.39960 | −0.699798 | − | 0.714341i | \(-0.746727\pi\) | ||||
−0.699798 | + | 0.714341i | \(0.746727\pi\) | |||||||
\(104\) | 123.746 | 0.116676 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1319.65 | 1.20921 | ||||||||
\(107\) | 816.480 | 0.737684 | 0.368842 | − | 0.929492i | \(-0.379754\pi\) | ||||
0.368842 | + | 0.929492i | \(0.379754\pi\) | |||||||
\(108\) | 495.950 | 0.441878 | ||||||||
\(109\) | 202.993 | 0.178378 | 0.0891889 | − | 0.996015i | \(-0.471573\pi\) | ||||
0.0891889 | + | 0.996015i | \(0.471573\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1513.08 | 1.29383 | ||||||||
\(112\) | −265.760 | −0.224214 | ||||||||
\(113\) | −1305.27 | −1.08663 | −0.543317 | − | 0.839528i | \(-0.682832\pi\) | ||||
−0.543317 | + | 0.839528i | \(0.682832\pi\) | |||||||
\(114\) | −274.359 | −0.225404 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 41.2251 | 0.0329970 | ||||||||
\(117\) | −79.2650 | −0.0626329 | ||||||||
\(118\) | 324.097 | 0.252843 | ||||||||
\(119\) | 723.504 | 0.557340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1321.71 | −0.993018 | ||||||||
\(122\) | 395.770 | 0.293699 | ||||||||
\(123\) | −191.536 | −0.140408 | ||||||||
\(124\) | −420.943 | −0.304853 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 170.232 | 0.120361 | ||||||||
\(127\) | 1453.61 | 1.01565 | 0.507824 | − | 0.861461i | \(-0.330450\pi\) | ||||
0.507824 | + | 0.861461i | \(0.330450\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −2438.58 | −1.66438 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 278.547 | 0.185777 | 0.0928884 | − | 0.995677i | \(-0.470390\pi\) | ||||
0.0928884 | + | 0.995677i | \(0.470390\pi\) | |||||||
\(132\) | −69.1109 | −0.0455707 | ||||||||
\(133\) | 402.015 | 0.262098 | ||||||||
\(134\) | 310.569 | 0.200217 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 348.466 | 0.219711 | ||||||||
\(137\) | −338.479 | −0.211082 | −0.105541 | − | 0.994415i | \(-0.533657\pi\) | ||||
−0.105541 | + | 0.994415i | \(0.533657\pi\) | |||||||
\(138\) | −2221.75 | −1.37049 | ||||||||
\(139\) | −1295.12 | −0.790293 | −0.395146 | − | 0.918618i | \(-0.629306\pi\) | ||||
−0.395146 | + | 0.918618i | \(0.629306\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3153.96 | 1.88377 | ||||||||
\(142\) | −1720.60 | −1.01683 | ||||||||
\(143\) | −47.1530 | −0.0275743 | ||||||||
\(144\) | 81.9901 | 0.0474480 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 718.115 | 0.407066 | ||||||||
\(147\) | 380.353 | 0.213408 | ||||||||
\(148\) | −1067.84 | −0.593080 | ||||||||
\(149\) | −1132.23 | −0.622521 | −0.311261 | − | 0.950325i | \(-0.600751\pi\) | ||||
−0.311261 | + | 0.950325i | \(0.600751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 719.198 | 0.387599 | 0.193800 | − | 0.981041i | \(-0.437919\pi\) | ||||
0.193800 | + | 0.981041i | \(0.437919\pi\) | |||||||
\(152\) | 193.625 | 0.103323 | ||||||||
\(153\) | −223.209 | −0.117944 | ||||||||
\(154\) | 101.267 | 0.0529893 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 350.685 | 0.179983 | ||||||||
\(157\) | 2182.94 | 1.10967 | 0.554833 | − | 0.831962i | \(-0.312782\pi\) | ||||
0.554833 | + | 0.831962i | \(0.312782\pi\) | |||||||
\(158\) | 2221.52 | 1.11857 | ||||||||
\(159\) | 3739.78 | 1.86531 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3255.50 | 1.59360 | ||||||||
\(162\) | 1682.20 | 0.815839 | ||||||||
\(163\) | −3031.50 | −1.45672 | −0.728359 | − | 0.685196i | \(-0.759717\pi\) | ||||
−0.728359 | + | 0.685196i | \(0.759717\pi\) | |||||||
\(164\) | 135.174 | 0.0643618 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −953.822 | −0.445969 | ||||||||
\(167\) | 2072.36 | 0.960265 | 0.480132 | − | 0.877196i | \(-0.340589\pi\) | ||||
0.480132 | + | 0.877196i | \(0.340589\pi\) | |||||||
\(168\) | −753.143 | −0.345871 | ||||||||
\(169\) | −1957.73 | −0.891095 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −124.026 | −0.0554650 | ||||||||
\(172\) | 1720.99 | 0.762933 | ||||||||
\(173\) | −737.782 | −0.324234 | −0.162117 | − | 0.986772i | \(-0.551832\pi\) | ||||
−0.162117 | + | 0.986772i | \(0.551832\pi\) | |||||||
\(174\) | 116.829 | 0.0509009 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 48.7741 | 0.0208891 | ||||||||
\(177\) | 918.464 | 0.390034 | ||||||||
\(178\) | 2889.54 | 1.21674 | ||||||||
\(179\) | −2351.63 | −0.981952 | −0.490976 | − | 0.871173i | \(-0.663360\pi\) | ||||
−0.490976 | + | 0.871173i | \(0.663360\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4327.33 | 1.77706 | 0.888530 | − | 0.458818i | \(-0.151727\pi\) | ||||
0.888530 | + | 0.458818i | \(0.151727\pi\) | |||||||
\(182\) | −513.854 | −0.209282 | ||||||||
\(183\) | 1121.58 | 0.453058 | ||||||||
\(184\) | 1567.97 | 0.628218 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1192.92 | −0.470263 | ||||||||
\(187\) | −132.782 | −0.0519251 | ||||||||
\(188\) | −2225.86 | −0.863498 | ||||||||
\(189\) | −2059.43 | −0.792602 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1764.16 | 0.668325 | 0.334163 | − | 0.942515i | \(-0.391547\pi\) | ||||
0.334163 | + | 0.942515i | \(0.391547\pi\) | |||||||
\(192\) | −362.742 | −0.136347 | ||||||||
\(193\) | 4958.76 | 1.84943 | 0.924714 | − | 0.380662i | \(-0.124304\pi\) | ||||
0.924714 | + | 0.380662i | \(0.124304\pi\) | |||||||
\(194\) | 1290.32 | 0.477524 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −268.429 | −0.0978240 | ||||||||
\(197\) | 3133.00 | 1.13308 | 0.566540 | − | 0.824034i | \(-0.308282\pi\) | ||||
0.566540 | + | 0.824034i | \(0.308282\pi\) | |||||||
\(198\) | −31.2421 | −0.0112135 | ||||||||
\(199\) | 2883.31 | 1.02710 | 0.513549 | − | 0.858060i | \(-0.328330\pi\) | ||||
0.513549 | + | 0.858060i | \(0.328330\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 880.127 | 0.308852 | ||||||||
\(202\) | −1982.22 | −0.690439 | ||||||||
\(203\) | −171.187 | −0.0591872 | ||||||||
\(204\) | 987.525 | 0.338924 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2926.10 | 0.989664 | ||||||||
\(207\) | −1004.36 | −0.337235 | ||||||||
\(208\) | −247.491 | −0.0825021 | ||||||||
\(209\) | −73.7804 | −0.0244186 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5976.93 | 1.95009 | 0.975044 | − | 0.222011i | \(-0.0712622\pi\) | ||||
0.975044 | + | 0.222011i | \(0.0712622\pi\) | |||||||
\(212\) | −2639.30 | −0.855038 | ||||||||
\(213\) | −4876.04 | −1.56855 | ||||||||
\(214\) | −1632.96 | −0.521621 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −991.900 | −0.312455 | ||||||||
\(217\) | 1747.97 | 0.546819 | ||||||||
\(218\) | −405.986 | −0.126132 | ||||||||
\(219\) | 2035.08 | 0.627936 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 673.768 | 0.205079 | ||||||||
\(222\) | −3026.17 | −0.914879 | ||||||||
\(223\) | 3951.70 | 1.18666 | 0.593331 | − | 0.804959i | \(-0.297813\pi\) | ||||
0.593331 | + | 0.804959i | \(0.297813\pi\) | |||||||
\(224\) | 531.521 | 0.158543 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2610.54 | 0.768366 | ||||||||
\(227\) | 2141.61 | 0.626185 | 0.313092 | − | 0.949723i | \(-0.398635\pi\) | ||||
0.313092 | + | 0.949723i | \(0.398635\pi\) | |||||||
\(228\) | 548.718 | 0.159385 | ||||||||
\(229\) | 2122.54 | 0.612494 | 0.306247 | − | 0.951952i | \(-0.400927\pi\) | ||||
0.306247 | + | 0.951952i | \(0.400927\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 286.983 | 0.0817408 | ||||||||
\(232\) | −82.4502 | −0.0233324 | ||||||||
\(233\) | 4051.36 | 1.13911 | 0.569557 | − | 0.821952i | \(-0.307115\pi\) | ||||
0.569557 | + | 0.821952i | \(0.307115\pi\) | |||||||
\(234\) | 158.530 | 0.0442882 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −648.194 | −0.178787 | ||||||||
\(237\) | 6295.61 | 1.72550 | ||||||||
\(238\) | −1447.01 | −0.394099 | ||||||||
\(239\) | −4447.49 | −1.20370 | −0.601850 | − | 0.798609i | \(-0.705569\pi\) | ||||
−0.601850 | + | 0.798609i | \(0.705569\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 571.376 | 0.152720 | 0.0763601 | − | 0.997080i | \(-0.475670\pi\) | ||||
0.0763601 | + | 0.997080i | \(0.475670\pi\) | |||||||
\(242\) | 2643.41 | 0.702170 | ||||||||
\(243\) | 1419.55 | 0.374750 | ||||||||
\(244\) | −791.540 | −0.207677 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 383.073 | 0.0992838 | ||||||||
\(247\) | 374.379 | 0.0964420 | ||||||||
\(248\) | 841.886 | 0.215564 | ||||||||
\(249\) | −2703.05 | −0.687948 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3432.31 | −0.863129 | −0.431565 | − | 0.902082i | \(-0.642038\pi\) | ||||
−0.431565 | + | 0.902082i | \(0.642038\pi\) | |||||||
\(252\) | −340.464 | −0.0851081 | ||||||||
\(253\) | −597.471 | −0.148469 | ||||||||
\(254\) | −2907.22 | −0.718171 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 144.659 | 0.0351112 | 0.0175556 | − | 0.999846i | \(-0.494412\pi\) | ||||
0.0175556 | + | 0.999846i | \(0.494412\pi\) | |||||||
\(258\) | 4877.15 | 1.17689 | ||||||||
\(259\) | 4434.21 | 1.06382 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 52.8133 | 0.0125251 | ||||||||
\(262\) | −557.094 | −0.131364 | ||||||||
\(263\) | 5463.46 | 1.28096 | 0.640478 | − | 0.767977i | \(-0.278736\pi\) | ||||
0.640478 | + | 0.767977i | \(0.278736\pi\) | |||||||
\(264\) | 138.222 | 0.0322234 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −804.029 | −0.185332 | ||||||||
\(267\) | 8188.73 | 1.87694 | ||||||||
\(268\) | −621.137 | −0.141575 | ||||||||
\(269\) | 2797.61 | 0.634101 | 0.317051 | − | 0.948409i | \(-0.397307\pi\) | ||||
0.317051 | + | 0.948409i | \(0.397307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4284.97 | 0.960492 | 0.480246 | − | 0.877134i | \(-0.340547\pi\) | ||||
0.480246 | + | 0.877134i | \(0.340547\pi\) | |||||||
\(272\) | −696.932 | −0.155359 | ||||||||
\(273\) | −1456.22 | −0.322837 | ||||||||
\(274\) | 676.957 | 0.149257 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4443.49 | 0.969083 | ||||||||
\(277\) | −3735.09 | −0.810179 | −0.405089 | − | 0.914277i | \(-0.632760\pi\) | ||||
−0.405089 | + | 0.914277i | \(0.632760\pi\) | |||||||
\(278\) | 2590.24 | 0.558821 | ||||||||
\(279\) | −539.268 | −0.115717 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6712.03 | −1.42493 | −0.712466 | − | 0.701707i | \(-0.752422\pi\) | ||||
−0.712466 | + | 0.701707i | \(0.752422\pi\) | |||||||
\(282\) | −6307.91 | −1.33202 | ||||||||
\(283\) | 535.045 | 0.112386 | 0.0561928 | − | 0.998420i | \(-0.482104\pi\) | ||||
0.0561928 | + | 0.998420i | \(0.482104\pi\) | |||||||
\(284\) | 3441.20 | 0.719006 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 94.3060 | 0.0194980 | ||||||||
\(287\) | −561.311 | −0.115447 | ||||||||
\(288\) | −163.980 | −0.0335508 | ||||||||
\(289\) | −3015.68 | −0.613816 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3656.66 | 0.736623 | ||||||||
\(292\) | −1436.23 | −0.287839 | ||||||||
\(293\) | 9332.20 | 1.86073 | 0.930363 | − | 0.366639i | \(-0.119491\pi\) | ||||
0.930363 | + | 0.366639i | \(0.119491\pi\) | |||||||
\(294\) | −760.706 | −0.150902 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2135.68 | 0.419371 | ||||||||
\(297\) | 377.961 | 0.0738435 | ||||||||
\(298\) | 2264.45 | 0.440189 | ||||||||
\(299\) | 3031.71 | 0.586381 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7146.43 | −1.36848 | ||||||||
\(302\) | −1438.40 | −0.274074 | ||||||||
\(303\) | −5617.46 | −1.06506 | ||||||||
\(304\) | −387.250 | −0.0730603 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 446.418 | 0.0833988 | ||||||||
\(307\) | −2429.22 | −0.451606 | −0.225803 | − | 0.974173i | \(-0.572501\pi\) | ||||
−0.225803 | + | 0.974173i | \(0.572501\pi\) | |||||||
\(308\) | −202.535 | −0.0374691 | ||||||||
\(309\) | 8292.32 | 1.52665 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2332.86 | −0.425351 | −0.212676 | − | 0.977123i | \(-0.568218\pi\) | ||||
−0.212676 | + | 0.977123i | \(0.568218\pi\) | |||||||
\(312\) | −701.370 | −0.127267 | ||||||||
\(313\) | 1872.59 | 0.338163 | 0.169081 | − | 0.985602i | \(-0.445920\pi\) | ||||
0.169081 | + | 0.985602i | \(0.445920\pi\) | |||||||
\(314\) | −4365.88 | −0.784652 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4443.04 | −0.790951 | ||||||||
\(317\) | −4709.54 | −0.834429 | −0.417215 | − | 0.908808i | \(-0.636994\pi\) | ||||
−0.417215 | + | 0.908808i | \(0.636994\pi\) | |||||||
\(318\) | −7479.57 | −1.31897 | ||||||||
\(319\) | 31.4175 | 0.00551423 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4627.68 | −0.804647 | ||||||||
\(322\) | −6510.99 | −1.12684 | ||||||||
\(323\) | 1054.25 | 0.181609 | ||||||||
\(324\) | −3364.40 | −0.576885 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6062.99 | 1.03006 | ||||||||
\(327\) | −1150.53 | −0.194570 | ||||||||
\(328\) | −270.348 | −0.0455106 | ||||||||
\(329\) | 9242.90 | 1.54887 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7114.17 | 1.18136 | 0.590680 | − | 0.806906i | \(-0.298859\pi\) | ||||
0.590680 | + | 0.806906i | \(0.298859\pi\) | |||||||
\(332\) | 1907.64 | 0.315348 | ||||||||
\(333\) | −1368.00 | −0.225124 | ||||||||
\(334\) | −4144.72 | −0.679010 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1506.29 | 0.244567 | ||||||||
\(337\) | −2327.59 | −0.376237 | −0.188119 | − | 0.982146i | \(-0.560239\pi\) | ||||
−0.188119 | + | 0.982146i | \(0.560239\pi\) | |||||||
\(338\) | 3915.47 | 0.630099 | ||||||||
\(339\) | 7398.07 | 1.18527 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −320.799 | −0.0509449 | ||||||||
\(342\) | 248.052 | 0.0392197 | ||||||||
\(343\) | 6811.89 | 1.07232 | ||||||||
\(344\) | −3441.99 | −0.539475 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1475.56 | 0.229268 | ||||||||
\(347\) | 3332.82 | 0.515605 | 0.257803 | − | 0.966198i | \(-0.417002\pi\) | ||||
0.257803 | + | 0.966198i | \(0.417002\pi\) | |||||||
\(348\) | −233.657 | −0.0359924 | ||||||||
\(349\) | −2838.44 | −0.435353 | −0.217677 | − | 0.976021i | \(-0.569848\pi\) | ||||
−0.217677 | + | 0.976021i | \(0.569848\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1917.86 | −0.291647 | ||||||||
\(352\) | −97.5482 | −0.0147708 | ||||||||
\(353\) | −10997.7 | −1.65821 | −0.829107 | − | 0.559091i | \(-0.811150\pi\) | ||||
−0.829107 | + | 0.559091i | \(0.811150\pi\) | |||||||
\(354\) | −1836.93 | −0.275796 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5779.09 | −0.860368 | ||||||||
\(357\) | −4100.70 | −0.607933 | ||||||||
\(358\) | 4703.27 | 0.694345 | ||||||||
\(359\) | 995.709 | 0.146383 | 0.0731915 | − | 0.997318i | \(-0.476682\pi\) | ||||
0.0731915 | + | 0.997318i | \(0.476682\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6273.21 | −0.914595 | ||||||||
\(362\) | −8654.66 | −1.25657 | ||||||||
\(363\) | 7491.22 | 1.08316 | ||||||||
\(364\) | 1027.71 | 0.147985 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2243.16 | −0.320360 | ||||||||
\(367\) | −9187.31 | −1.30674 | −0.653370 | − | 0.757038i | \(-0.726646\pi\) | ||||
−0.653370 | + | 0.757038i | \(0.726646\pi\) | |||||||
\(368\) | −3135.94 | −0.444217 | ||||||||
\(369\) | 173.171 | 0.0244307 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10959.7 | 1.53369 | ||||||||
\(372\) | 2385.84 | 0.332526 | ||||||||
\(373\) | −6058.93 | −0.841072 | −0.420536 | − | 0.907276i | \(-0.638158\pi\) | ||||
−0.420536 | + | 0.907276i | \(0.638158\pi\) | |||||||
\(374\) | 265.564 | 0.0367166 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4451.72 | 0.610585 | ||||||||
\(377\) | −159.420 | −0.0217786 | ||||||||
\(378\) | 4118.87 | 0.560454 | ||||||||
\(379\) | 893.684 | 0.121123 | 0.0605613 | − | 0.998164i | \(-0.480711\pi\) | ||||
0.0605613 | + | 0.998164i | \(0.480711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8238.83 | −1.10784 | ||||||||
\(382\) | −3528.32 | −0.472577 | ||||||||
\(383\) | −5839.47 | −0.779068 | −0.389534 | − | 0.921012i | \(-0.627364\pi\) | ||||
−0.389534 | + | 0.921012i | \(0.627364\pi\) | |||||||
\(384\) | 725.483 | 0.0964119 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9917.53 | −1.30774 | ||||||||
\(387\) | 2204.76 | 0.289597 | ||||||||
\(388\) | −2580.64 | −0.337660 | ||||||||
\(389\) | −4912.83 | −0.640335 | −0.320168 | − | 0.947361i | \(-0.603739\pi\) | ||||
−0.320168 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8537.24 | 1.10421 | ||||||||
\(392\) | 536.858 | 0.0691720 | ||||||||
\(393\) | −1578.76 | −0.202641 | ||||||||
\(394\) | −6266.00 | −0.801209 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 62.4843 | 0.00792918 | ||||||||
\(397\) | 8419.00 | 1.06433 | 0.532163 | − | 0.846642i | \(-0.321379\pi\) | ||||
0.532163 | + | 0.846642i | \(0.321379\pi\) | |||||||
\(398\) | −5766.62 | −0.726268 | ||||||||
\(399\) | −2278.55 | −0.285891 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7353.01 | −0.915690 | −0.457845 | − | 0.889032i | \(-0.651379\pi\) | ||||
−0.457845 | + | 0.889032i | \(0.651379\pi\) | |||||||
\(402\) | −1760.25 | −0.218392 | ||||||||
\(403\) | 1627.81 | 0.201208 | ||||||||
\(404\) | 3964.45 | 0.488214 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 342.375 | 0.0418517 | ||||||||
\(407\) | −813.795 | −0.0991114 | ||||||||
\(408\) | −1975.05 | −0.239656 | ||||||||
\(409\) | −13980.4 | −1.69019 | −0.845096 | − | 0.534615i | \(-0.820457\pi\) | ||||
−0.845096 | + | 0.534615i | \(0.820457\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1918.44 | 0.230243 | ||||||||
\(412\) | −5852.19 | −0.699798 | ||||||||
\(413\) | 2691.63 | 0.320693 | ||||||||
\(414\) | 2008.72 | 0.238461 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 494.982 | 0.0583378 | ||||||||
\(417\) | 7340.53 | 0.862032 | ||||||||
\(418\) | 147.561 | 0.0172666 | ||||||||
\(419\) | −12778.0 | −1.48985 | −0.744923 | − | 0.667150i | \(-0.767514\pi\) | ||||
−0.744923 | + | 0.667150i | \(0.767514\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1708.71 | 0.197809 | 0.0989044 | − | 0.995097i | \(-0.468466\pi\) | ||||
0.0989044 | + | 0.995097i | \(0.468466\pi\) | |||||||
\(422\) | −11953.9 | −1.37892 | ||||||||
\(423\) | −2851.54 | −0.327770 | ||||||||
\(424\) | 5278.60 | 0.604603 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9752.09 | 1.10913 | ||||||||
\(427\) | 3286.87 | 0.372513 | ||||||||
\(428\) | 3265.92 | 0.368842 | ||||||||
\(429\) | 267.255 | 0.0300774 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5049.46 | −0.564325 | −0.282162 | − | 0.959367i | \(-0.591052\pi\) | ||||
−0.282162 | + | 0.959367i | \(0.591052\pi\) | |||||||
\(432\) | 1983.80 | 0.220939 | ||||||||
\(433\) | −10438.4 | −1.15852 | −0.579259 | − | 0.815143i | \(-0.696658\pi\) | ||||
−0.579259 | + | 0.815143i | \(0.696658\pi\) | |||||||
\(434\) | −3495.94 | −0.386660 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 811.971 | 0.0891889 | ||||||||
\(437\) | 4743.72 | 0.519274 | ||||||||
\(438\) | −4070.16 | −0.444018 | ||||||||
\(439\) | 15290.1 | 1.66231 | 0.831156 | − | 0.556040i | \(-0.187680\pi\) | ||||
0.831156 | + | 0.556040i | \(0.187680\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −343.883 | −0.0371324 | ||||||||
\(442\) | −1347.54 | −0.145013 | ||||||||
\(443\) | −866.921 | −0.0929766 | −0.0464883 | − | 0.998919i | \(-0.514803\pi\) | ||||
−0.0464883 | + | 0.998919i | \(0.514803\pi\) | |||||||
\(444\) | 6052.34 | 0.646917 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7903.41 | −0.839097 | ||||||||
\(447\) | 6417.28 | 0.679031 | ||||||||
\(448\) | −1063.04 | −0.112107 | ||||||||
\(449\) | 400.462 | 0.0420913 | 0.0210456 | − | 0.999779i | \(-0.493300\pi\) | ||||
0.0210456 | + | 0.999779i | \(0.493300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 103.016 | 0.0107557 | ||||||||
\(452\) | −5221.09 | −0.543317 | ||||||||
\(453\) | −4076.30 | −0.422784 | ||||||||
\(454\) | −4283.23 | −0.442779 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1097.44 | −0.112702 | ||||||||
\(457\) | 11585.7 | 1.18590 | 0.592949 | − | 0.805240i | \(-0.297964\pi\) | ||||
0.592949 | + | 0.805240i | \(0.297964\pi\) | |||||||
\(458\) | −4245.07 | −0.433099 | ||||||||
\(459\) | −5400.68 | −0.549198 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5722.52 | −0.578144 | −0.289072 | − | 0.957307i | \(-0.593347\pi\) | ||||
−0.289072 | + | 0.957307i | \(0.593347\pi\) | |||||||
\(462\) | −573.967 | −0.0577995 | ||||||||
\(463\) | 16136.2 | 1.61968 | 0.809841 | − | 0.586649i | \(-0.199553\pi\) | ||||
0.809841 | + | 0.586649i | \(0.199553\pi\) | |||||||
\(464\) | 164.900 | 0.0164985 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8102.73 | −0.805476 | ||||||||
\(467\) | −10508.2 | −1.04125 | −0.520623 | − | 0.853787i | \(-0.674300\pi\) | ||||
−0.520623 | + | 0.853787i | \(0.674300\pi\) | |||||||
\(468\) | −317.060 | −0.0313165 | ||||||||
\(469\) | 2579.28 | 0.253944 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12372.5 | −1.21040 | ||||||||
\(472\) | 1296.39 | 0.126422 | ||||||||
\(473\) | 1311.56 | 0.127496 | ||||||||
\(474\) | −12591.2 | −1.22011 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2894.01 | 0.278670 | ||||||||
\(477\) | −3381.20 | −0.324559 | ||||||||
\(478\) | 8894.98 | 0.851144 | ||||||||
\(479\) | −12405.2 | −1.18331 | −0.591656 | − | 0.806191i | \(-0.701526\pi\) | ||||
−0.591656 | + | 0.806191i | \(0.701526\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4129.39 | 0.391442 | ||||||||
\(482\) | −1142.75 | −0.107989 | ||||||||
\(483\) | −18451.6 | −1.73826 | ||||||||
\(484\) | −5286.83 | −0.496509 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2839.10 | −0.264988 | ||||||||
\(487\) | 6720.06 | 0.625288 | 0.312644 | − | 0.949870i | \(-0.398785\pi\) | ||||
0.312644 | + | 0.949870i | \(0.398785\pi\) | |||||||
\(488\) | 1583.08 | 0.146850 | ||||||||
\(489\) | 17182.0 | 1.58895 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3549.65 | 0.326260 | 0.163130 | − | 0.986605i | \(-0.447841\pi\) | ||||
0.163130 | + | 0.986605i | \(0.447841\pi\) | |||||||
\(492\) | −766.145 | −0.0702042 | ||||||||
\(493\) | −448.924 | −0.0410112 | ||||||||
\(494\) | −748.758 | −0.0681948 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1683.77 | −0.152427 | ||||||||
\(497\) | −14289.6 | −1.28969 | ||||||||
\(498\) | 5406.11 | 0.486453 | ||||||||
\(499\) | 15925.4 | 1.42869 | 0.714346 | − | 0.699793i | \(-0.246724\pi\) | ||||
0.714346 | + | 0.699793i | \(0.246724\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11745.8 | −1.04743 | ||||||||
\(502\) | 6864.62 | 0.610324 | ||||||||
\(503\) | 799.366 | 0.0708588 | 0.0354294 | − | 0.999372i | \(-0.488720\pi\) | ||||
0.0354294 | + | 0.999372i | \(0.488720\pi\) | |||||||
\(504\) | 680.929 | 0.0601805 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1194.94 | 0.104983 | ||||||||
\(507\) | 11096.1 | 0.971984 | ||||||||
\(508\) | 5814.45 | 0.507824 | ||||||||
\(509\) | −17678.2 | −1.53943 | −0.769717 | − | 0.638386i | \(-0.779602\pi\) | ||||
−0.769717 | + | 0.638386i | \(0.779602\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5963.95 | 0.516301 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −3000.88 | −0.258270 | ||||||||
\(514\) | −289.318 | −0.0248273 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9754.31 | −0.832189 | ||||||||
\(517\) | −1696.32 | −0.144302 | ||||||||
\(518\) | −8868.41 | −0.752231 | ||||||||
\(519\) | 4181.63 | 0.353667 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5119.04 | −0.430459 | −0.215230 | − | 0.976563i | \(-0.569050\pi\) | ||||
−0.215230 | + | 0.976563i | \(0.569050\pi\) | |||||||
\(522\) | −105.627 | −0.00885661 | ||||||||
\(523\) | 17639.5 | 1.47480 | 0.737402 | − | 0.675455i | \(-0.236053\pi\) | ||||
0.737402 | + | 0.675455i | \(0.236053\pi\) | |||||||
\(524\) | 1114.19 | 0.0928884 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10926.9 | −0.905772 | ||||||||
\(527\) | 4583.89 | 0.378894 | ||||||||
\(528\) | −276.444 | −0.0227854 | ||||||||
\(529\) | 26247.4 | 2.15726 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −830.398 | −0.0678648 | ||||||||
\(532\) | 1608.06 | 0.131049 | ||||||||
\(533\) | −522.725 | −0.0424798 | ||||||||
\(534\) | −16377.5 | −1.32720 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1242.27 | 0.100108 | ||||||||
\(537\) | 13328.7 | 1.07109 | ||||||||
\(538\) | −5595.22 | −0.448377 | ||||||||
\(539\) | −204.569 | −0.0163477 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2856.92 | 0.227040 | 0.113520 | − | 0.993536i | \(-0.463787\pi\) | ||||
0.113520 | + | 0.993536i | \(0.463787\pi\) | |||||||
\(542\) | −8569.93 | −0.679170 | ||||||||
\(543\) | −24526.6 | −1.93837 | ||||||||
\(544\) | 1393.86 | 0.109856 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2912.44 | 0.228280 | ||||||||
\(547\) | 14400.0 | 1.12559 | 0.562796 | − | 0.826596i | \(-0.309726\pi\) | ||||
0.562796 | + | 0.826596i | \(0.309726\pi\) | |||||||
\(548\) | −1353.91 | −0.105541 | ||||||||
\(549\) | −1014.04 | −0.0788308 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −249.444 | −0.0192862 | ||||||||
\(552\) | −8886.99 | −0.685245 | ||||||||
\(553\) | 18449.7 | 1.41874 | ||||||||
\(554\) | 7470.17 | 0.572883 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5180.48 | −0.395146 | ||||||||
\(557\) | 9685.69 | 0.736797 | 0.368398 | − | 0.929668i | \(-0.379906\pi\) | ||||
0.368398 | + | 0.929668i | \(0.379906\pi\) | |||||||
\(558\) | 1078.54 | 0.0818245 | ||||||||
\(559\) | −6655.17 | −0.503548 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 752.588 | 0.0566387 | ||||||||
\(562\) | 13424.1 | 1.00758 | ||||||||
\(563\) | 20951.5 | 1.56838 | 0.784192 | − | 0.620518i | \(-0.213078\pi\) | ||||
0.784192 | + | 0.620518i | \(0.213078\pi\) | |||||||
\(564\) | 12615.8 | 0.941883 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1070.09 | −0.0794686 | ||||||||
\(567\) | 13970.7 | 1.03477 | ||||||||
\(568\) | −6882.40 | −0.508414 | ||||||||
\(569\) | 6768.07 | 0.498651 | 0.249325 | − | 0.968420i | \(-0.419791\pi\) | ||||
0.249325 | + | 0.968420i | \(0.419791\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17740.7 | −1.30022 | −0.650109 | − | 0.759841i | \(-0.725277\pi\) | ||||
−0.650109 | + | 0.759841i | \(0.725277\pi\) | |||||||
\(572\) | −188.612 | −0.0137872 | ||||||||
\(573\) | −9998.97 | −0.728993 | ||||||||
\(574\) | 1122.62 | 0.0816330 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 327.960 | 0.0237240 | ||||||||
\(577\) | 18908.1 | 1.36422 | 0.682110 | − | 0.731249i | \(-0.261062\pi\) | ||||
0.682110 | + | 0.731249i | \(0.261062\pi\) | |||||||
\(578\) | 6031.36 | 0.434033 | ||||||||
\(579\) | −28105.5 | −2.01731 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7921.50 | −0.565644 | ||||||||
\(582\) | −7313.33 | −0.520871 | ||||||||
\(583\) | −2011.40 | −0.142888 | ||||||||
\(584\) | 2872.46 | 0.203533 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18664.4 | −1.31573 | ||||||||
\(587\) | −15584.1 | −1.09579 | −0.547893 | − | 0.836548i | \(-0.684570\pi\) | ||||
−0.547893 | + | 0.836548i | \(0.684570\pi\) | |||||||
\(588\) | 1521.41 | 0.106704 | ||||||||
\(589\) | 2547.03 | 0.178181 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17757.3 | −1.23594 | ||||||||
\(592\) | −4271.36 | −0.296540 | ||||||||
\(593\) | −5757.33 | −0.398694 | −0.199347 | − | 0.979929i | \(-0.563882\pi\) | ||||
−0.199347 | + | 0.979929i | \(0.563882\pi\) | |||||||
\(594\) | −755.922 | −0.0522152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4528.91 | −0.311261 | ||||||||
\(597\) | −16342.1 | −1.12033 | ||||||||
\(598\) | −6063.41 | −0.414634 | ||||||||
\(599\) | −6004.95 | −0.409608 | −0.204804 | − | 0.978803i | \(-0.565656\pi\) | ||||
−0.204804 | + | 0.978803i | \(0.565656\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26366.0 | −1.78951 | −0.894753 | − | 0.446562i | \(-0.852648\pi\) | ||||
−0.894753 | + | 0.446562i | \(0.852648\pi\) | |||||||
\(602\) | 14292.9 | 0.967664 | ||||||||
\(603\) | −795.737 | −0.0537395 | ||||||||
\(604\) | 2876.79 | 0.193800 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11234.9 | 0.753114 | ||||||||
\(607\) | 3986.79 | 0.266588 | 0.133294 | − | 0.991077i | \(-0.457445\pi\) | ||||
0.133294 | + | 0.991077i | \(0.457445\pi\) | |||||||
\(608\) | 774.500 | 0.0516614 | ||||||||
\(609\) | 970.263 | 0.0645600 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8607.52 | 0.569923 | ||||||||
\(612\) | −892.837 | −0.0589719 | ||||||||
\(613\) | −16845.0 | −1.10989 | −0.554947 | − | 0.831886i | \(-0.687261\pi\) | ||||
−0.554947 | + | 0.831886i | \(0.687261\pi\) | |||||||
\(614\) | 4858.45 | 0.319334 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 405.069 | 0.0264947 | ||||||||
\(617\) | −1679.95 | −0.109615 | −0.0548074 | − | 0.998497i | \(-0.517454\pi\) | ||||
−0.0548074 | + | 0.998497i | \(0.517454\pi\) | |||||||
\(618\) | −16584.6 | −1.07950 | ||||||||
\(619\) | 3608.29 | 0.234296 | 0.117148 | − | 0.993114i | \(-0.462625\pi\) | ||||
0.117148 | + | 0.993114i | \(0.462625\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24301.0 | −1.57032 | ||||||||
\(622\) | 4665.72 | 0.300769 | ||||||||
\(623\) | 23997.7 | 1.54325 | ||||||||
\(624\) | 1402.74 | 0.0899913 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3745.18 | −0.239117 | ||||||||
\(627\) | 418.175 | 0.0266353 | ||||||||
\(628\) | 8731.76 | 0.554833 | ||||||||
\(629\) | 11628.3 | 0.737124 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2066.53 | −0.130376 | −0.0651881 | − | 0.997873i | \(-0.520765\pi\) | ||||
−0.0651881 | + | 0.997873i | \(0.520765\pi\) | |||||||
\(632\) | 8886.08 | 0.559287 | ||||||||
\(633\) | −33876.2 | −2.12711 | ||||||||
\(634\) | 9419.08 | 0.590031 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 14959.1 | 0.932655 | ||||||||
\(637\) | 1038.03 | 0.0645655 | ||||||||
\(638\) | −62.8349 | −0.00389915 | ||||||||
\(639\) | 4408.51 | 0.272923 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27937.8 | −1.72149 | −0.860745 | − | 0.509037i | \(-0.830002\pi\) | ||||
−0.860745 | + | 0.509037i | \(0.830002\pi\) | |||||||
\(642\) | 9255.36 | 0.568972 | ||||||||
\(643\) | −27067.1 | −1.66007 | −0.830034 | − | 0.557713i | \(-0.811679\pi\) | ||||
−0.830034 | + | 0.557713i | \(0.811679\pi\) | |||||||
\(644\) | 13022.0 | 0.796798 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2108.49 | −0.128417 | ||||||||
\(647\) | 2460.23 | 0.149493 | 0.0747463 | − | 0.997203i | \(-0.476185\pi\) | ||||
0.0747463 | + | 0.997203i | \(0.476185\pi\) | |||||||
\(648\) | 6728.79 | 0.407920 | ||||||||
\(649\) | −493.985 | −0.0298777 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9907.20 | −0.596457 | ||||||||
\(652\) | −12126.0 | −0.728359 | ||||||||
\(653\) | −7190.60 | −0.430919 | −0.215459 | − | 0.976513i | \(-0.569125\pi\) | ||||
−0.215459 | + | 0.976513i | \(0.569125\pi\) | |||||||
\(654\) | 2301.06 | 0.137582 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 540.697 | 0.0321809 | ||||||||
\(657\) | −1839.95 | −0.109259 | ||||||||
\(658\) | −18485.8 | −1.09522 | ||||||||
\(659\) | −26124.2 | −1.54424 | −0.772121 | − | 0.635475i | \(-0.780804\pi\) | ||||
−0.772121 | + | 0.635475i | \(0.780804\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13907.5 | 0.818362 | 0.409181 | − | 0.912453i | \(-0.365814\pi\) | ||||
0.409181 | + | 0.912453i | \(0.365814\pi\) | |||||||
\(662\) | −14228.3 | −0.835348 | ||||||||
\(663\) | −3818.81 | −0.223696 | ||||||||
\(664\) | −3815.29 | −0.222985 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2736.01 | 0.159186 | ||||||||
\(667\) | −2019.99 | −0.117263 | ||||||||
\(668\) | 8289.45 | 0.480132 | ||||||||
\(669\) | −22397.6 | −1.29438 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −603.229 | −0.0347055 | ||||||||
\(672\) | −3012.57 | −0.172935 | ||||||||
\(673\) | −16079.5 | −0.920982 | −0.460491 | − | 0.887664i | \(-0.652327\pi\) | ||||
−0.460491 | + | 0.887664i | \(0.652327\pi\) | |||||||
\(674\) | 4655.18 | 0.266040 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7830.94 | −0.445547 | ||||||||
\(677\) | 15882.2 | 0.901626 | 0.450813 | − | 0.892618i | \(-0.351134\pi\) | ||||
0.450813 | + | 0.892618i | \(0.351134\pi\) | |||||||
\(678\) | −14796.1 | −0.838115 | ||||||||
\(679\) | 10716.1 | 0.605666 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12138.3 | −0.683027 | ||||||||
\(682\) | 641.597 | 0.0360235 | ||||||||
\(683\) | 308.314 | 0.0172728 | 0.00863640 | − | 0.999963i | \(-0.497251\pi\) | ||||
0.00863640 | + | 0.999963i | \(0.497251\pi\) | |||||||
\(684\) | −496.105 | −0.0277325 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13623.8 | −0.758248 | ||||||||
\(687\) | −12030.2 | −0.668093 | ||||||||
\(688\) | 6883.97 | 0.381466 | ||||||||
\(689\) | 10206.3 | 0.564339 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11388.7 | 0.626988 | 0.313494 | − | 0.949590i | \(-0.398501\pi\) | ||||
0.313494 | + | 0.949590i | \(0.398501\pi\) | |||||||
\(692\) | −2951.13 | −0.162117 | ||||||||
\(693\) | −259.466 | −0.0142227 | ||||||||
\(694\) | −6665.63 | −0.364588 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 467.315 | 0.0254504 | ||||||||
\(697\) | −1471.99 | −0.0799936 | ||||||||
\(698\) | 5676.89 | 0.307841 | ||||||||
\(699\) | −22962.5 | −1.24252 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30888.8 | 1.66427 | 0.832135 | − | 0.554573i | \(-0.187118\pi\) | ||||
0.832135 | + | 0.554573i | \(0.187118\pi\) | |||||||
\(702\) | 3835.73 | 0.206225 | ||||||||
\(703\) | 6461.26 | 0.346645 | ||||||||
\(704\) | 195.096 | 0.0104446 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21995.4 | 1.17253 | ||||||||
\(707\) | −16462.4 | −0.875717 | ||||||||
\(708\) | 3673.86 | 0.195017 | ||||||||
\(709\) | 1748.32 | 0.0926089 | 0.0463044 | − | 0.998927i | \(-0.485256\pi\) | ||||
0.0463044 | + | 0.998927i | \(0.485256\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5691.96 | −0.300232 | ||||||||
\(712\) | 11558.2 | 0.608372 | ||||||||
\(713\) | 20625.8 | 1.08337 | ||||||||
\(714\) | 8201.40 | 0.429874 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9406.53 | −0.490976 | ||||||||
\(717\) | 25207.6 | 1.31297 | ||||||||
\(718\) | −1991.42 | −0.103508 | ||||||||
\(719\) | −9493.76 | −0.492431 | −0.246215 | − | 0.969215i | \(-0.579187\pi\) | ||||
−0.246215 | + | 0.969215i | \(0.579187\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24301.3 | 1.25524 | ||||||||
\(722\) | 12546.4 | 0.646716 | ||||||||
\(723\) | −3238.47 | −0.166584 | ||||||||
\(724\) | 17309.3 | 0.888530 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −14982.4 | −0.765910 | ||||||||
\(727\) | 19255.5 | 0.982321 | 0.491161 | − | 0.871069i | \(-0.336573\pi\) | ||||
0.491161 | + | 0.871069i | \(0.336573\pi\) | |||||||
\(728\) | −2055.42 | −0.104641 | ||||||||
\(729\) | 14663.9 | 0.745003 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18740.9 | −0.948230 | ||||||||
\(732\) | 4486.32 | 0.226529 | ||||||||
\(733\) | 23675.5 | 1.19301 | 0.596503 | − | 0.802611i | \(-0.296556\pi\) | ||||
0.596503 | + | 0.802611i | \(0.296556\pi\) | |||||||
\(734\) | 18374.6 | 0.924005 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6271.87 | 0.314109 | ||||||||
\(737\) | −473.366 | −0.0236590 | ||||||||
\(738\) | −346.342 | −0.0172751 | ||||||||
\(739\) | 14116.4 | 0.702680 | 0.351340 | − | 0.936248i | \(-0.385726\pi\) | ||||
0.351340 | + | 0.936248i | \(0.385726\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2121.92 | −0.105197 | ||||||||
\(742\) | −21919.4 | −1.08448 | ||||||||
\(743\) | 22922.9 | 1.13184 | 0.565921 | − | 0.824459i | \(-0.308521\pi\) | ||||
0.565921 | + | 0.824459i | \(0.308521\pi\) | |||||||
\(744\) | −4771.67 | −0.235132 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 12117.9 | 0.594727 | ||||||||
\(747\) | 2443.87 | 0.119701 | ||||||||
\(748\) | −531.129 | −0.0259626 | ||||||||
\(749\) | −13561.8 | −0.661596 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3611.62 | 0.175486 | 0.0877429 | − | 0.996143i | \(-0.472035\pi\) | ||||
0.0877429 | + | 0.996143i | \(0.472035\pi\) | |||||||
\(752\) | −8903.45 | −0.431749 | ||||||||
\(753\) | 19453.8 | 0.941480 | ||||||||
\(754\) | 318.839 | 0.0153998 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8237.74 | −0.396301 | ||||||||
\(757\) | 22716.3 | 1.09067 | 0.545334 | − | 0.838219i | \(-0.316403\pi\) | ||||
0.545334 | + | 0.838219i | \(0.316403\pi\) | |||||||
\(758\) | −1787.37 | −0.0856466 | ||||||||
\(759\) | 3386.37 | 0.161946 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7913.07 | −0.376936 | −0.188468 | − | 0.982079i | \(-0.560352\pi\) | ||||
−0.188468 | + | 0.982079i | \(0.560352\pi\) | |||||||
\(762\) | 16477.7 | 0.783363 | ||||||||
\(763\) | −3371.71 | −0.159979 | ||||||||
\(764\) | 7056.64 | 0.334163 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11678.9 | 0.550884 | ||||||||
\(767\) | 2506.60 | 0.118003 | ||||||||
\(768\) | −1450.97 | −0.0681735 | ||||||||
\(769\) | −6790.99 | −0.318452 | −0.159226 | − | 0.987242i | \(-0.550900\pi\) | ||||
−0.159226 | + | 0.987242i | \(0.550900\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −819.903 | −0.0382984 | ||||||||
\(772\) | 19835.1 | 0.924714 | ||||||||
\(773\) | −6088.83 | −0.283312 | −0.141656 | − | 0.989916i | \(-0.545243\pi\) | ||||
−0.141656 | + | 0.989916i | \(0.545243\pi\) | |||||||
\(774\) | −4409.51 | −0.204776 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5161.28 | 0.238762 | ||||||||
\(777\) | −25132.4 | −1.16038 | ||||||||
\(778\) | 9825.66 | 0.452785 | ||||||||
\(779\) | −817.910 | −0.0376183 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2622.52 | 0.120155 | ||||||||
\(782\) | −17074.5 | −0.780796 | ||||||||
\(783\) | 1277.85 | 0.0583226 | ||||||||
\(784\) | −1073.72 | −0.0489120 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3157.52 | 0.143289 | ||||||||
\(787\) | −3296.47 | −0.149309 | −0.0746547 | − | 0.997209i | \(-0.523785\pi\) | ||||
−0.0746547 | + | 0.997209i | \(0.523785\pi\) | |||||||
\(788\) | 12532.0 | 0.566540 | ||||||||
\(789\) | −30966.0 | −1.39724 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21680.6 | 0.974555 | ||||||||
\(792\) | −124.969 | −0.00560677 | ||||||||
\(793\) | 3060.92 | 0.137070 | ||||||||
\(794\) | −16838.0 | −0.752593 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11533.2 | 0.513549 | ||||||||
\(797\) | −40635.4 | −1.80600 | −0.902998 | − | 0.429645i | \(-0.858639\pi\) | ||||
−0.902998 | + | 0.429645i | \(0.858639\pi\) | |||||||
\(798\) | 4557.11 | 0.202155 | ||||||||
\(799\) | 24238.7 | 1.07322 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7403.57 | −0.326582 | ||||||||
\(802\) | 14706.0 | 0.647491 | ||||||||
\(803\) | −1094.54 | −0.0481016 | ||||||||
\(804\) | 3520.51 | 0.154426 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3255.62 | −0.142276 | ||||||||
\(807\) | −15856.4 | −0.691663 | ||||||||
\(808\) | −7928.89 | −0.345220 | ||||||||
\(809\) | −3564.32 | −0.154901 | −0.0774505 | − | 0.996996i | \(-0.524678\pi\) | ||||
−0.0774505 | + | 0.996996i | \(0.524678\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41160.2 | −1.78216 | −0.891079 | − | 0.453847i | \(-0.850051\pi\) | ||||
−0.891079 | + | 0.453847i | \(0.850051\pi\) | |||||||
\(812\) | −684.750 | −0.0295936 | ||||||||
\(813\) | −24286.5 | −1.04768 | ||||||||
\(814\) | 1627.59 | 0.0700823 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3950.10 | 0.169462 | ||||||||
\(817\) | −10413.4 | −0.445921 | ||||||||
\(818\) | 27960.9 | 1.19515 | ||||||||
\(819\) | 1316.59 | 0.0561728 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1498.30 | −0.0636919 | −0.0318460 | − | 0.999493i | \(-0.510139\pi\) | ||||
−0.0318460 | + | 0.999493i | \(0.510139\pi\) | |||||||
\(822\) | −3836.88 | −0.162806 | ||||||||
\(823\) | −4166.11 | −0.176454 | −0.0882268 | − | 0.996100i | \(-0.528120\pi\) | ||||
−0.0882268 | + | 0.996100i | \(0.528120\pi\) | |||||||
\(824\) | 11704.4 | 0.494832 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5383.25 | −0.226764 | ||||||||
\(827\) | −28706.4 | −1.20704 | −0.603519 | − | 0.797349i | \(-0.706235\pi\) | ||||
−0.603519 | + | 0.797349i | \(0.706235\pi\) | |||||||
\(828\) | −4017.43 | −0.168618 | ||||||||
\(829\) | 12315.4 | 0.515961 | 0.257980 | − | 0.966150i | \(-0.416943\pi\) | ||||
0.257980 | + | 0.966150i | \(0.416943\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21169.9 | 0.883723 | ||||||||
\(832\) | −989.965 | −0.0412510 | ||||||||
\(833\) | 2923.08 | 0.121583 | ||||||||
\(834\) | −14681.1 | −0.609549 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −295.122 | −0.0122093 | ||||||||
\(837\) | −13047.9 | −0.538831 | ||||||||
\(838\) | 25556.0 | 1.05348 | ||||||||
\(839\) | 7143.26 | 0.293937 | 0.146968 | − | 0.989141i | \(-0.453048\pi\) | ||||
0.146968 | + | 0.989141i | \(0.453048\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24282.8 | −0.995645 | ||||||||
\(842\) | −3417.42 | −0.139872 | ||||||||
\(843\) | 38042.7 | 1.55428 | ||||||||
\(844\) | 23907.7 | 0.975044 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5703.08 | 0.231768 | ||||||||
\(847\) | 21953.6 | 0.890595 | ||||||||
\(848\) | −10557.2 | −0.427519 | ||||||||
\(849\) | −3032.55 | −0.122587 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 52323.0 | 2.10765 | ||||||||
\(852\) | −19504.2 | −0.784275 | ||||||||
\(853\) | −25259.1 | −1.01390 | −0.506949 | − | 0.861976i | \(-0.669227\pi\) | ||||
−0.506949 | + | 0.861976i | \(0.669227\pi\) | |||||||
\(854\) | −6573.74 | −0.263406 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6531.84 | −0.260811 | ||||||||
\(857\) | −32491.3 | −1.29508 | −0.647539 | − | 0.762032i | \(-0.724202\pi\) | ||||
−0.647539 | + | 0.762032i | \(0.724202\pi\) | |||||||
\(858\) | −534.511 | −0.0212680 | ||||||||
\(859\) | 19552.4 | 0.776624 | 0.388312 | − | 0.921528i | \(-0.373058\pi\) | ||||
0.388312 | + | 0.921528i | \(0.373058\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3181.42 | 0.125926 | ||||||||
\(862\) | 10098.9 | 0.399038 | ||||||||
\(863\) | 27438.7 | 1.08230 | 0.541150 | − | 0.840926i | \(-0.317989\pi\) | ||||
0.541150 | + | 0.840926i | \(0.317989\pi\) | |||||||
\(864\) | −3967.60 | −0.156227 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 20876.8 | 0.819196 | ||||||||
\(867\) | 17092.4 | 0.669536 | ||||||||
\(868\) | 6991.87 | 0.273410 | ||||||||
\(869\) | −3386.02 | −0.132178 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2401.97 | 0.0934416 | ||||||||
\(872\) | −1623.94 | −0.0630661 | ||||||||
\(873\) | −3306.05 | −0.128170 | ||||||||
\(874\) | −9487.43 | −0.367182 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8140.32 | 0.313968 | ||||||||
\(877\) | −47003.2 | −1.80979 | −0.904895 | − | 0.425635i | \(-0.860051\pi\) | ||||
−0.904895 | + | 0.425635i | \(0.860051\pi\) | |||||||
\(878\) | −30580.1 | −1.17543 | ||||||||
\(879\) | −52893.4 | −2.02964 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24523.1 | −0.937804 | −0.468902 | − | 0.883250i | \(-0.655350\pi\) | ||||
−0.468902 | + | 0.883250i | \(0.655350\pi\) | |||||||
\(882\) | 687.767 | 0.0262566 | ||||||||
\(883\) | 30961.2 | 1.17999 | 0.589993 | − | 0.807408i | \(-0.299130\pi\) | ||||
0.589993 | + | 0.807408i | \(0.299130\pi\) | |||||||
\(884\) | 2695.07 | 0.102540 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1733.84 | 0.0657444 | ||||||||
\(887\) | −21566.0 | −0.816363 | −0.408182 | − | 0.912901i | \(-0.633837\pi\) | ||||
−0.408182 | + | 0.912901i | \(0.633837\pi\) | |||||||
\(888\) | −12104.7 | −0.457439 | ||||||||
\(889\) | −24144.5 | −0.910890 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2563.99 | −0.0964051 | ||||||||
\(892\) | 15806.8 | 0.593331 | ||||||||
\(893\) | 13468.2 | 0.504699 | ||||||||
\(894\) | −12834.6 | −0.480147 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2126.08 | 0.0792717 | ||||||||
\(897\) | −17183.2 | −0.639611 | ||||||||
\(898\) | −800.924 | −0.0297630 | ||||||||
\(899\) | −1084.59 | −0.0402370 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28740.9 | 1.06270 | ||||||||
\(902\) | −206.031 | −0.00760542 | ||||||||
\(903\) | 40504.8 | 1.49271 | ||||||||
\(904\) | 10442.2 | 0.384183 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8152.60 | 0.298954 | ||||||||
\(907\) | −40311.8 | −1.47578 | −0.737889 | − | 0.674923i | \(-0.764177\pi\) | ||||
−0.737889 | + | 0.674923i | \(0.764177\pi\) | |||||||
\(908\) | 8566.46 | 0.313092 | ||||||||
\(909\) | 5078.84 | 0.185318 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21257.1 | 0.773084 | 0.386542 | − | 0.922272i | \(-0.373669\pi\) | ||||
0.386542 | + | 0.922272i | \(0.373669\pi\) | |||||||
\(912\) | 2194.87 | 0.0796924 | ||||||||
\(913\) | 1453.81 | 0.0526988 | ||||||||
\(914\) | −23171.4 | −0.838556 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8490.14 | 0.306247 | ||||||||
\(917\) | −4626.67 | −0.166615 | ||||||||
\(918\) | 10801.4 | 0.388342 | ||||||||
\(919\) | −5398.84 | −0.193788 | −0.0968940 | − | 0.995295i | \(-0.530891\pi\) | ||||
−0.0968940 | + | 0.995295i | \(0.530891\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13768.5 | 0.492601 | ||||||||
\(922\) | 11445.0 | 0.408810 | ||||||||
\(923\) | −13307.3 | −0.474556 | ||||||||
\(924\) | 1147.93 | 0.0408704 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −32272.4 | −1.14529 | ||||||||
\(927\) | −7497.22 | −0.265632 | ||||||||
\(928\) | −329.801 | −0.0116662 | ||||||||
\(929\) | 28181.3 | 0.995261 | 0.497631 | − | 0.867389i | \(-0.334204\pi\) | ||||
0.497631 | + | 0.867389i | \(0.334204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1624.21 | 0.0571764 | ||||||||
\(932\) | 16205.5 | 0.569557 | ||||||||
\(933\) | 13222.3 | 0.463963 | ||||||||
\(934\) | 21016.4 | 0.736272 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 634.120 | 0.0221441 | ||||||||
\(937\) | 44657.5 | 1.55699 | 0.778494 | − | 0.627652i | \(-0.215984\pi\) | ||||
0.778494 | + | 0.627652i | \(0.215984\pi\) | |||||||
\(938\) | −5158.55 | −0.179566 | ||||||||
\(939\) | −10613.5 | −0.368860 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30715.7 | 1.06408 | 0.532042 | − | 0.846718i | \(-0.321425\pi\) | ||||
0.532042 | + | 0.846718i | \(0.321425\pi\) | |||||||
\(942\) | 24745.1 | 0.855880 | ||||||||
\(943\) | −6623.40 | −0.228725 | ||||||||
\(944\) | −2592.77 | −0.0893937 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2623.12 | −0.0901533 | ||||||||
\(947\) | −7384.38 | −0.253390 | −0.126695 | − | 0.991942i | \(-0.540437\pi\) | ||||
−0.126695 | + | 0.991942i | \(0.540437\pi\) | |||||||
\(948\) | 25182.4 | 0.862750 | ||||||||
\(949\) | 5553.97 | 0.189979 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26692.9 | 0.910175 | ||||||||
\(952\) | −5788.03 | −0.197049 | ||||||||
\(953\) | −45543.4 | −1.54806 | −0.774028 | − | 0.633152i | \(-0.781761\pi\) | ||||
−0.774028 | + | 0.633152i | \(0.781761\pi\) | |||||||
\(954\) | 6762.40 | 0.229498 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −17790.0 | −0.601850 | ||||||||
\(957\) | −178.069 | −0.00601479 | ||||||||
\(958\) | 24810.3 | 0.836728 | ||||||||
\(959\) | 5622.13 | 0.189310 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18716.4 | −0.628258 | ||||||||
\(962\) | −8258.77 | −0.276792 | ||||||||
\(963\) | 4183.96 | 0.140006 | ||||||||
\(964\) | 2285.50 | 0.0763601 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 36903.3 | 1.22913 | ||||||||
\(967\) | −26437.0 | −0.879169 | −0.439584 | − | 0.898201i | \(-0.644874\pi\) | ||||
−0.439584 | + | 0.898201i | \(0.644874\pi\) | |||||||
\(968\) | 10573.7 | 0.351085 | ||||||||
\(969\) | −5975.30 | −0.198095 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47997.0 | 1.58630 | 0.793150 | − | 0.609026i | \(-0.208440\pi\) | ||||
0.793150 | + | 0.609026i | \(0.208440\pi\) | |||||||
\(972\) | 5678.21 | 0.187375 | ||||||||
\(973\) | 21512.0 | 0.708779 | ||||||||
\(974\) | −13440.1 | −0.442145 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3166.16 | −0.103838 | ||||||||
\(977\) | −8794.09 | −0.287971 | −0.143986 | − | 0.989580i | \(-0.545992\pi\) | ||||
−0.143986 | + | 0.989580i | \(0.545992\pi\) | |||||||
\(978\) | −34364.1 | −1.12356 | ||||||||
\(979\) | −4404.22 | −0.143779 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1040.21 | 0.0338547 | ||||||||
\(982\) | −7099.30 | −0.230700 | ||||||||
\(983\) | 46163.7 | 1.49786 | 0.748928 | − | 0.662651i | \(-0.230569\pi\) | ||||
0.748928 | + | 0.662651i | \(0.230569\pi\) | |||||||
\(984\) | 1532.29 | 0.0496419 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 897.847 | 0.0289993 | ||||||||
\(987\) | −52387.3 | −1.68947 | ||||||||
\(988\) | 1497.52 | 0.0482210 | ||||||||
\(989\) | −84326.9 | −2.71126 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1898.54 | −0.0608568 | −0.0304284 | − | 0.999537i | \(-0.509687\pi\) | ||||
−0.0304284 | + | 0.999537i | \(0.509687\pi\) | |||||||
\(992\) | 3367.54 | 0.107782 | ||||||||
\(993\) | −40322.0 | −1.28860 | ||||||||
\(994\) | 28579.2 | 0.911949 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10812.2 | −0.343974 | ||||||||
\(997\) | 44422.1 | 1.41109 | 0.705547 | − | 0.708663i | \(-0.250701\pi\) | ||||
0.705547 | + | 0.708663i | \(0.250701\pi\) | |||||||
\(998\) | −31850.7 | −1.01024 | ||||||||
\(999\) | −33099.7 | −1.04827 |
(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 | 1250.4.a.c.1.2 | ✓ | 6 | |
5.4 | even | 2 | 1250.4.a.f.1.5 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1250.4.a.c.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
1250.4.a.f.1.5 | yes | 6 | 5.4 | even | 2 |