Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.44156 | −1.57033 | −0.785164 | − | 0.619288i | \(-0.787421\pi\) | ||||
−0.785164 | + | 0.619288i | \(0.787421\pi\) | |||||||
\(3\) | −2.04104 | −0.392797 | −0.196399 | − | 0.980524i | \(-0.562925\pi\) | ||||
−0.196399 | + | 0.980524i | \(0.562925\pi\) | |||||||
\(4\) | 11.7274 | 1.46593 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 9.06537 | 0.616821 | ||||||||
\(7\) | −16.0963 | −0.869121 | −0.434560 | − | 0.900643i | \(-0.643096\pi\) | ||||
−0.434560 | + | 0.900643i | \(0.643096\pi\) | |||||||
\(8\) | −16.5556 | −0.731659 | ||||||||
\(9\) | −22.8342 | −0.845710 | ||||||||
\(10\) | 22.2078 | 0.702272 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | −23.9361 | −0.575813 | ||||||||
\(13\) | −2.33044 | −0.0497190 | −0.0248595 | − | 0.999691i | \(-0.507914\pi\) | ||||
−0.0248595 | + | 0.999691i | \(0.507914\pi\) | |||||||
\(14\) | 71.4928 | 1.36480 | ||||||||
\(15\) | 10.2052 | 0.175664 | ||||||||
\(16\) | −20.2869 | −0.316983 | ||||||||
\(17\) | −20.5265 | −0.292848 | −0.146424 | − | 0.989222i | \(-0.546776\pi\) | ||||
−0.146424 | + | 0.989222i | \(0.546776\pi\) | |||||||
\(18\) | 101.419 | 1.32804 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | −58.6371 | −0.655583 | ||||||||
\(21\) | 32.8532 | 0.341388 | ||||||||
\(22\) | −48.8571 | −0.473472 | ||||||||
\(23\) | 134.968 | 1.22360 | 0.611799 | − | 0.791013i | \(-0.290446\pi\) | ||||
0.611799 | + | 0.791013i | \(0.290446\pi\) | |||||||
\(24\) | 33.7905 | 0.287394 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 10.3508 | 0.0780751 | ||||||||
\(27\) | 101.713 | 0.724990 | ||||||||
\(28\) | −188.769 | −1.27407 | ||||||||
\(29\) | −229.308 | −1.46832 | −0.734162 | − | 0.678975i | \(-0.762425\pi\) | ||||
−0.734162 | + | 0.678975i | \(0.762425\pi\) | |||||||
\(30\) | −45.3269 | −0.275851 | ||||||||
\(31\) | 151.778 | 0.879361 | 0.439681 | − | 0.898154i | \(-0.355092\pi\) | ||||
0.439681 | + | 0.898154i | \(0.355092\pi\) | |||||||
\(32\) | 222.550 | 1.22943 | ||||||||
\(33\) | −22.4514 | −0.118433 | ||||||||
\(34\) | 91.1697 | 0.459867 | ||||||||
\(35\) | 80.4817 | 0.388683 | ||||||||
\(36\) | −267.786 | −1.23975 | ||||||||
\(37\) | 87.5858 | 0.389163 | 0.194581 | − | 0.980886i | \(-0.437665\pi\) | ||||
0.194581 | + | 0.980886i | \(0.437665\pi\) | |||||||
\(38\) | 84.3896 | 0.360258 | ||||||||
\(39\) | 4.75650 | 0.0195295 | ||||||||
\(40\) | 82.7778 | 0.327208 | ||||||||
\(41\) | 361.861 | 1.37837 | 0.689185 | − | 0.724585i | \(-0.257969\pi\) | ||||
0.689185 | + | 0.724585i | \(0.257969\pi\) | |||||||
\(42\) | −145.919 | −0.536092 | ||||||||
\(43\) | −267.170 | −0.947514 | −0.473757 | − | 0.880656i | \(-0.657103\pi\) | ||||
−0.473757 | + | 0.880656i | \(0.657103\pi\) | |||||||
\(44\) | 129.002 | 0.441994 | ||||||||
\(45\) | 114.171 | 0.378213 | ||||||||
\(46\) | −599.468 | −1.92145 | ||||||||
\(47\) | 95.5432 | 0.296519 | 0.148260 | − | 0.988948i | \(-0.452633\pi\) | ||||
0.148260 | + | 0.988948i | \(0.452633\pi\) | |||||||
\(48\) | 41.4063 | 0.124510 | ||||||||
\(49\) | −83.9077 | −0.244629 | ||||||||
\(50\) | −111.039 | −0.314065 | ||||||||
\(51\) | 41.8954 | 0.115030 | ||||||||
\(52\) | −27.3300 | −0.0728844 | ||||||||
\(53\) | 33.9282 | 0.0879321 | 0.0439661 | − | 0.999033i | \(-0.486001\pi\) | ||||
0.0439661 | + | 0.999033i | \(0.486001\pi\) | |||||||
\(54\) | −451.765 | −1.13847 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 266.484 | 0.635900 | ||||||||
\(57\) | 38.7797 | 0.0901139 | ||||||||
\(58\) | 1018.48 | 2.30575 | ||||||||
\(59\) | −618.143 | −1.36399 | −0.681995 | − | 0.731357i | \(-0.738887\pi\) | ||||
−0.681995 | + | 0.731357i | \(0.738887\pi\) | |||||||
\(60\) | 119.680 | 0.257511 | ||||||||
\(61\) | −148.528 | −0.311755 | −0.155877 | − | 0.987776i | \(-0.549820\pi\) | ||||
−0.155877 | + | 0.987776i | \(0.549820\pi\) | |||||||
\(62\) | −674.132 | −1.38089 | ||||||||
\(63\) | 367.547 | 0.735024 | ||||||||
\(64\) | −826.173 | −1.61362 | ||||||||
\(65\) | 11.6522 | 0.0222350 | ||||||||
\(66\) | 99.7191 | 0.185978 | ||||||||
\(67\) | 672.521 | 1.22629 | 0.613145 | − | 0.789970i | \(-0.289904\pi\) | ||||
0.613145 | + | 0.789970i | \(0.289904\pi\) | |||||||
\(68\) | −240.723 | −0.429294 | ||||||||
\(69\) | −275.474 | −0.480626 | ||||||||
\(70\) | −357.464 | −0.610359 | ||||||||
\(71\) | 287.835 | 0.481123 | 0.240561 | − | 0.970634i | \(-0.422668\pi\) | ||||
0.240561 | + | 0.970634i | \(0.422668\pi\) | |||||||
\(72\) | 378.033 | 0.618772 | ||||||||
\(73\) | 696.551 | 1.11678 | 0.558391 | − | 0.829578i | \(-0.311419\pi\) | ||||
0.558391 | + | 0.829578i | \(0.311419\pi\) | |||||||
\(74\) | −389.017 | −0.611113 | ||||||||
\(75\) | −51.0259 | −0.0785595 | ||||||||
\(76\) | −222.821 | −0.336307 | ||||||||
\(77\) | −177.060 | −0.262050 | ||||||||
\(78\) | −21.1263 | −0.0306677 | ||||||||
\(79\) | 1189.08 | 1.69345 | 0.846723 | − | 0.532034i | \(-0.178572\pi\) | ||||
0.846723 | + | 0.532034i | \(0.178572\pi\) | |||||||
\(80\) | 101.435 | 0.141759 | ||||||||
\(81\) | 408.922 | 0.560936 | ||||||||
\(82\) | −1607.23 | −2.16449 | ||||||||
\(83\) | 599.331 | 0.792591 | 0.396296 | − | 0.918123i | \(-0.370296\pi\) | ||||
0.396296 | + | 0.918123i | \(0.370296\pi\) | |||||||
\(84\) | 385.283 | 0.500451 | ||||||||
\(85\) | 102.633 | 0.130966 | ||||||||
\(86\) | 1186.65 | 1.48791 | ||||||||
\(87\) | 468.025 | 0.576754 | ||||||||
\(88\) | −182.111 | −0.220604 | ||||||||
\(89\) | −679.190 | −0.808921 | −0.404461 | − | 0.914555i | \(-0.632541\pi\) | ||||
−0.404461 | + | 0.914555i | \(0.632541\pi\) | |||||||
\(90\) | −507.096 | −0.593918 | ||||||||
\(91\) | 37.5115 | 0.0432118 | ||||||||
\(92\) | 1582.83 | 1.79371 | ||||||||
\(93\) | −309.785 | −0.345411 | ||||||||
\(94\) | −424.360 | −0.465632 | ||||||||
\(95\) | 95.0000 | 0.102598 | ||||||||
\(96\) | −454.232 | −0.482916 | ||||||||
\(97\) | 1396.16 | 1.46142 | 0.730712 | − | 0.682686i | \(-0.239188\pi\) | ||||
0.730712 | + | 0.682686i | \(0.239188\pi\) | |||||||
\(98\) | 372.681 | 0.384148 | ||||||||
\(99\) | −251.176 | −0.254991 | ||||||||
\(100\) | 293.186 | 0.293186 | ||||||||
\(101\) | −236.571 | −0.233066 | −0.116533 | − | 0.993187i | \(-0.537178\pi\) | ||||
−0.116533 | + | 0.993187i | \(0.537178\pi\) | |||||||
\(102\) | −186.081 | −0.180635 | ||||||||
\(103\) | −582.182 | −0.556933 | −0.278467 | − | 0.960446i | \(-0.589826\pi\) | ||||
−0.278467 | + | 0.960446i | \(0.589826\pi\) | |||||||
\(104\) | 38.5817 | 0.0363774 | ||||||||
\(105\) | −164.266 | −0.152674 | ||||||||
\(106\) | −150.694 | −0.138082 | ||||||||
\(107\) | 1558.45 | 1.40805 | 0.704023 | − | 0.710177i | \(-0.251385\pi\) | ||||
0.704023 | + | 0.710177i | \(0.251385\pi\) | |||||||
\(108\) | 1192.84 | 1.06278 | ||||||||
\(109\) | 145.056 | 0.127466 | 0.0637331 | − | 0.997967i | \(-0.479699\pi\) | ||||
0.0637331 | + | 0.997967i | \(0.479699\pi\) | |||||||
\(110\) | 244.286 | 0.211743 | ||||||||
\(111\) | −178.766 | −0.152862 | ||||||||
\(112\) | 326.545 | 0.275497 | ||||||||
\(113\) | −1687.19 | −1.40458 | −0.702290 | − | 0.711890i | \(-0.747839\pi\) | ||||
−0.702290 | + | 0.711890i | \(0.747839\pi\) | |||||||
\(114\) | −172.242 | −0.141508 | ||||||||
\(115\) | −674.840 | −0.547210 | ||||||||
\(116\) | −2689.19 | −2.15246 | ||||||||
\(117\) | 53.2136 | 0.0420478 | ||||||||
\(118\) | 2745.52 | 2.14191 | ||||||||
\(119\) | 330.402 | 0.254520 | ||||||||
\(120\) | −168.952 | −0.128526 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 659.695 | 0.489557 | ||||||||
\(123\) | −738.571 | −0.541420 | ||||||||
\(124\) | 1779.97 | 1.28908 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −1632.48 | −1.15423 | ||||||||
\(127\) | 2331.61 | 1.62911 | 0.814555 | − | 0.580087i | \(-0.196981\pi\) | ||||
0.814555 | + | 0.580087i | \(0.196981\pi\) | |||||||
\(128\) | 1889.09 | 1.30448 | ||||||||
\(129\) | 545.304 | 0.372181 | ||||||||
\(130\) | −51.7538 | −0.0349162 | ||||||||
\(131\) | −862.636 | −0.575335 | −0.287668 | − | 0.957730i | \(-0.592880\pi\) | ||||
−0.287668 | + | 0.957730i | \(0.592880\pi\) | |||||||
\(132\) | −263.297 | −0.173614 | ||||||||
\(133\) | 305.831 | 0.199390 | ||||||||
\(134\) | −2987.04 | −1.92568 | ||||||||
\(135\) | −508.567 | −0.324225 | ||||||||
\(136\) | 339.828 | 0.214265 | ||||||||
\(137\) | 2891.24 | 1.80303 | 0.901515 | − | 0.432748i | \(-0.142456\pi\) | ||||
0.901515 | + | 0.432748i | \(0.142456\pi\) | |||||||
\(138\) | 1223.53 | 0.754740 | ||||||||
\(139\) | −2422.62 | −1.47830 | −0.739151 | − | 0.673540i | \(-0.764773\pi\) | ||||
−0.739151 | + | 0.673540i | \(0.764773\pi\) | |||||||
\(140\) | 943.843 | 0.569781 | ||||||||
\(141\) | −195.007 | −0.116472 | ||||||||
\(142\) | −1278.44 | −0.755520 | ||||||||
\(143\) | −25.6348 | −0.0149908 | ||||||||
\(144\) | 463.235 | 0.268076 | ||||||||
\(145\) | 1146.54 | 0.656654 | ||||||||
\(146\) | −3093.77 | −1.75371 | ||||||||
\(147\) | 171.259 | 0.0960896 | ||||||||
\(148\) | 1027.16 | 0.570485 | ||||||||
\(149\) | −1259.23 | −0.692352 | −0.346176 | − | 0.938170i | \(-0.612520\pi\) | ||||
−0.346176 | + | 0.938170i | \(0.612520\pi\) | |||||||
\(150\) | 226.634 | 0.123364 | ||||||||
\(151\) | 3181.06 | 1.71438 | 0.857190 | − | 0.515001i | \(-0.172208\pi\) | ||||
0.857190 | + | 0.515001i | \(0.172208\pi\) | |||||||
\(152\) | 314.556 | 0.167854 | ||||||||
\(153\) | 468.706 | 0.247664 | ||||||||
\(154\) | 786.421 | 0.411504 | ||||||||
\(155\) | −758.892 | −0.393262 | ||||||||
\(156\) | 55.7815 | 0.0286288 | ||||||||
\(157\) | −3168.41 | −1.61062 | −0.805308 | − | 0.592857i | \(-0.798000\pi\) | ||||
−0.805308 | + | 0.592857i | \(0.798000\pi\) | |||||||
\(158\) | −5281.38 | −2.65926 | ||||||||
\(159\) | −69.2487 | −0.0345395 | ||||||||
\(160\) | −1112.75 | −0.549816 | ||||||||
\(161\) | −2172.49 | −1.06345 | ||||||||
\(162\) | −1816.25 | −0.880853 | ||||||||
\(163\) | 2163.57 | 1.03966 | 0.519828 | − | 0.854271i | \(-0.325996\pi\) | ||||
0.519828 | + | 0.854271i | \(0.325996\pi\) | |||||||
\(164\) | 4243.70 | 2.02059 | ||||||||
\(165\) | 112.257 | 0.0529648 | ||||||||
\(166\) | −2661.96 | −1.24463 | ||||||||
\(167\) | −3510.58 | −1.62669 | −0.813343 | − | 0.581784i | \(-0.802355\pi\) | ||||
−0.813343 | + | 0.581784i | \(0.802355\pi\) | |||||||
\(168\) | −543.903 | −0.249780 | ||||||||
\(169\) | −2191.57 | −0.997528 | ||||||||
\(170\) | −455.849 | −0.205659 | ||||||||
\(171\) | 433.849 | 0.194019 | ||||||||
\(172\) | −3133.22 | −1.38899 | ||||||||
\(173\) | −3830.63 | −1.68345 | −0.841726 | − | 0.539905i | \(-0.818460\pi\) | ||||
−0.841726 | + | 0.539905i | \(0.818460\pi\) | |||||||
\(174\) | −2078.76 | −0.905692 | ||||||||
\(175\) | −402.409 | −0.173824 | ||||||||
\(176\) | −223.156 | −0.0955740 | ||||||||
\(177\) | 1261.65 | 0.535772 | ||||||||
\(178\) | 3016.66 | 1.27027 | ||||||||
\(179\) | −130.792 | −0.0546139 | −0.0273070 | − | 0.999627i | \(-0.508693\pi\) | ||||
−0.0273070 | + | 0.999627i | \(0.508693\pi\) | |||||||
\(180\) | 1338.93 | 0.554433 | ||||||||
\(181\) | −1828.32 | −0.750819 | −0.375410 | − | 0.926859i | \(-0.622498\pi\) | ||||
−0.375410 | + | 0.926859i | \(0.622498\pi\) | |||||||
\(182\) | −166.609 | −0.0678567 | ||||||||
\(183\) | 303.150 | 0.122456 | ||||||||
\(184\) | −2234.47 | −0.895257 | ||||||||
\(185\) | −437.929 | −0.174039 | ||||||||
\(186\) | 1375.93 | 0.542408 | ||||||||
\(187\) | −225.792 | −0.0882970 | ||||||||
\(188\) | 1120.48 | 0.434676 | ||||||||
\(189\) | −1637.21 | −0.630104 | ||||||||
\(190\) | −421.948 | −0.161112 | ||||||||
\(191\) | −117.373 | −0.0444649 | −0.0222324 | − | 0.999753i | \(-0.507077\pi\) | ||||
−0.0222324 | + | 0.999753i | \(0.507077\pi\) | |||||||
\(192\) | 1686.25 | 0.633825 | ||||||||
\(193\) | −4920.91 | −1.83531 | −0.917654 | − | 0.397380i | \(-0.869920\pi\) | ||||
−0.917654 | + | 0.397380i | \(0.869920\pi\) | |||||||
\(194\) | −6201.11 | −2.29492 | ||||||||
\(195\) | −23.7825 | −0.00873385 | ||||||||
\(196\) | −984.022 | −0.358608 | ||||||||
\(197\) | −279.079 | −0.100932 | −0.0504659 | − | 0.998726i | \(-0.516071\pi\) | ||||
−0.0504659 | + | 0.998726i | \(0.516071\pi\) | |||||||
\(198\) | 1115.61 | 0.400420 | ||||||||
\(199\) | 985.493 | 0.351054 | 0.175527 | − | 0.984475i | \(-0.443837\pi\) | ||||
0.175527 | + | 0.984475i | \(0.443837\pi\) | |||||||
\(200\) | −413.889 | −0.146332 | ||||||||
\(201\) | −1372.64 | −0.481684 | ||||||||
\(202\) | 1050.74 | 0.365990 | ||||||||
\(203\) | 3691.02 | 1.27615 | ||||||||
\(204\) | 491.325 | 0.168626 | ||||||||
\(205\) | −1809.31 | −0.616426 | ||||||||
\(206\) | 2585.80 | 0.874567 | ||||||||
\(207\) | −3081.88 | −1.03481 | ||||||||
\(208\) | 47.2774 | 0.0157601 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | 729.597 | 0.239747 | ||||||||
\(211\) | −4028.03 | −1.31422 | −0.657111 | − | 0.753794i | \(-0.728222\pi\) | ||||
−0.657111 | + | 0.753794i | \(0.728222\pi\) | |||||||
\(212\) | 397.891 | 0.128902 | ||||||||
\(213\) | −587.481 | −0.188984 | ||||||||
\(214\) | −6921.94 | −2.21109 | ||||||||
\(215\) | 1335.85 | 0.423741 | ||||||||
\(216\) | −1683.92 | −0.530446 | ||||||||
\(217\) | −2443.08 | −0.764271 | ||||||||
\(218\) | −644.273 | −0.200164 | ||||||||
\(219\) | −1421.68 | −0.438669 | ||||||||
\(220\) | −645.008 | −0.197666 | ||||||||
\(221\) | 47.8358 | 0.0145601 | ||||||||
\(222\) | 793.998 | 0.240044 | ||||||||
\(223\) | 1174.67 | 0.352742 | 0.176371 | − | 0.984324i | \(-0.443564\pi\) | ||||
0.176371 | + | 0.984324i | \(0.443564\pi\) | |||||||
\(224\) | −3582.24 | −1.06852 | ||||||||
\(225\) | −570.854 | −0.169142 | ||||||||
\(226\) | 7493.76 | 2.20565 | ||||||||
\(227\) | −4567.75 | −1.33556 | −0.667781 | − | 0.744358i | \(-0.732756\pi\) | ||||
−0.667781 | + | 0.744358i | \(0.732756\pi\) | |||||||
\(228\) | 454.786 | 0.132100 | ||||||||
\(229\) | 4847.79 | 1.39891 | 0.699457 | − | 0.714675i | \(-0.253425\pi\) | ||||
0.699457 | + | 0.714675i | \(0.253425\pi\) | |||||||
\(230\) | 2997.34 | 0.859298 | ||||||||
\(231\) | 361.385 | 0.102932 | ||||||||
\(232\) | 3796.32 | 1.07431 | ||||||||
\(233\) | 1014.64 | 0.285284 | 0.142642 | − | 0.989774i | \(-0.454440\pi\) | ||||
0.142642 | + | 0.989774i | \(0.454440\pi\) | |||||||
\(234\) | −236.351 | −0.0660289 | ||||||||
\(235\) | −477.716 | −0.132607 | ||||||||
\(236\) | −7249.23 | −1.99951 | ||||||||
\(237\) | −2426.96 | −0.665181 | ||||||||
\(238\) | −1467.50 | −0.399680 | ||||||||
\(239\) | −6565.39 | −1.77690 | −0.888452 | − | 0.458970i | \(-0.848218\pi\) | ||||
−0.888452 | + | 0.458970i | \(0.848218\pi\) | |||||||
\(240\) | −207.032 | −0.0556826 | ||||||||
\(241\) | −1965.73 | −0.525409 | −0.262705 | − | 0.964876i | \(-0.584615\pi\) | ||||
−0.262705 | + | 0.964876i | \(0.584615\pi\) | |||||||
\(242\) | −537.428 | −0.142757 | ||||||||
\(243\) | −3580.88 | −0.945324 | ||||||||
\(244\) | −1741.85 | −0.457010 | ||||||||
\(245\) | 419.539 | 0.109401 | ||||||||
\(246\) | 3280.41 | 0.850207 | ||||||||
\(247\) | 44.2783 | 0.0114063 | ||||||||
\(248\) | −2512.78 | −0.643393 | ||||||||
\(249\) | −1223.25 | −0.311328 | ||||||||
\(250\) | 555.195 | 0.140454 | ||||||||
\(251\) | 1937.29 | 0.487173 | 0.243587 | − | 0.969879i | \(-0.421676\pi\) | ||||
0.243587 | + | 0.969879i | \(0.421676\pi\) | |||||||
\(252\) | 4310.38 | 1.07749 | ||||||||
\(253\) | 1484.65 | 0.368929 | ||||||||
\(254\) | −10356.0 | −2.55824 | ||||||||
\(255\) | −209.477 | −0.0514429 | ||||||||
\(256\) | −1781.13 | −0.434847 | ||||||||
\(257\) | 6482.31 | 1.57337 | 0.786683 | − | 0.617357i | \(-0.211796\pi\) | ||||
0.786683 | + | 0.617357i | \(0.211796\pi\) | |||||||
\(258\) | −2422.00 | −0.584446 | ||||||||
\(259\) | −1409.81 | −0.338229 | ||||||||
\(260\) | 136.650 | 0.0325949 | ||||||||
\(261\) | 5236.05 | 1.24178 | ||||||||
\(262\) | 3831.45 | 0.903464 | ||||||||
\(263\) | −8166.78 | −1.91477 | −0.957387 | − | 0.288809i | \(-0.906741\pi\) | ||||
−0.957387 | + | 0.288809i | \(0.906741\pi\) | |||||||
\(264\) | 371.695 | 0.0866525 | ||||||||
\(265\) | −169.641 | −0.0393244 | ||||||||
\(266\) | −1358.36 | −0.313108 | ||||||||
\(267\) | 1386.25 | 0.317742 | ||||||||
\(268\) | 7886.94 | 1.79765 | ||||||||
\(269\) | −4545.78 | −1.03034 | −0.515169 | − | 0.857089i | \(-0.672271\pi\) | ||||
−0.515169 | + | 0.857089i | \(0.672271\pi\) | |||||||
\(270\) | 2258.83 | 0.509140 | ||||||||
\(271\) | −142.040 | −0.0318389 | −0.0159195 | − | 0.999873i | \(-0.505068\pi\) | ||||
−0.0159195 | + | 0.999873i | \(0.505068\pi\) | |||||||
\(272\) | 416.420 | 0.0928279 | ||||||||
\(273\) | −76.5623 | −0.0169735 | ||||||||
\(274\) | −12841.6 | −2.83135 | ||||||||
\(275\) | 275.000 | 0.0603023 | ||||||||
\(276\) | −3230.60 | −0.704563 | ||||||||
\(277\) | 8413.20 | 1.82491 | 0.912455 | − | 0.409176i | \(-0.134184\pi\) | ||||
0.912455 | + | 0.409176i | \(0.134184\pi\) | |||||||
\(278\) | 10760.2 | 2.32142 | ||||||||
\(279\) | −3465.73 | −0.743685 | ||||||||
\(280\) | −1332.42 | −0.284383 | ||||||||
\(281\) | 3314.38 | 0.703627 | 0.351814 | − | 0.936070i | \(-0.385565\pi\) | ||||
0.351814 | + | 0.936070i | \(0.385565\pi\) | |||||||
\(282\) | 866.134 | 0.182899 | ||||||||
\(283\) | −2798.04 | −0.587725 | −0.293863 | − | 0.955848i | \(-0.594941\pi\) | ||||
−0.293863 | + | 0.955848i | \(0.594941\pi\) | |||||||
\(284\) | 3375.56 | 0.705292 | ||||||||
\(285\) | −193.898 | −0.0403002 | ||||||||
\(286\) | 113.858 | 0.0235405 | ||||||||
\(287\) | −5824.64 | −1.19797 | ||||||||
\(288\) | −5081.75 | −1.03974 | ||||||||
\(289\) | −4491.66 | −0.914240 | ||||||||
\(290\) | −5092.42 | −1.03116 | ||||||||
\(291\) | −2849.60 | −0.574044 | ||||||||
\(292\) | 8168.74 | 1.63712 | ||||||||
\(293\) | −7617.14 | −1.51876 | −0.759382 | − | 0.650645i | \(-0.774499\pi\) | ||||
−0.759382 | + | 0.650645i | \(0.774499\pi\) | |||||||
\(294\) | −760.655 | −0.150892 | ||||||||
\(295\) | 3090.72 | 0.609995 | ||||||||
\(296\) | −1450.03 | −0.284735 | ||||||||
\(297\) | 1118.85 | 0.218593 | ||||||||
\(298\) | 5592.96 | 1.08722 | ||||||||
\(299\) | −314.534 | −0.0608361 | ||||||||
\(300\) | −598.402 | −0.115163 | ||||||||
\(301\) | 4300.47 | 0.823504 | ||||||||
\(302\) | −14128.9 | −2.69214 | ||||||||
\(303\) | 482.849 | 0.0915477 | ||||||||
\(304\) | 385.451 | 0.0727209 | ||||||||
\(305\) | 742.639 | 0.139421 | ||||||||
\(306\) | −2081.79 | −0.388914 | ||||||||
\(307\) | 6442.47 | 1.19769 | 0.598845 | − | 0.800865i | \(-0.295626\pi\) | ||||
0.598845 | + | 0.800865i | \(0.295626\pi\) | |||||||
\(308\) | −2076.45 | −0.384146 | ||||||||
\(309\) | 1188.25 | 0.218762 | ||||||||
\(310\) | 3370.66 | 0.617551 | ||||||||
\(311\) | 3836.29 | 0.699472 | 0.349736 | − | 0.936848i | \(-0.386271\pi\) | ||||
0.349736 | + | 0.936848i | \(0.386271\pi\) | |||||||
\(312\) | −78.7466 | −0.0142889 | ||||||||
\(313\) | 10822.8 | 1.95444 | 0.977218 | − | 0.212237i | \(-0.0680749\pi\) | ||||
0.977218 | + | 0.212237i | \(0.0680749\pi\) | |||||||
\(314\) | 14072.7 | 2.52919 | ||||||||
\(315\) | −1837.73 | −0.328713 | ||||||||
\(316\) | 13944.9 | 2.48247 | ||||||||
\(317\) | −7916.77 | −1.40268 | −0.701341 | − | 0.712826i | \(-0.747415\pi\) | ||||
−0.701341 | + | 0.712826i | \(0.747415\pi\) | |||||||
\(318\) | 307.572 | 0.0542383 | ||||||||
\(319\) | −2522.39 | −0.442716 | ||||||||
\(320\) | 4130.87 | 0.721632 | ||||||||
\(321\) | −3180.85 | −0.553077 | ||||||||
\(322\) | 9649.24 | 1.66997 | ||||||||
\(323\) | 390.004 | 0.0671839 | ||||||||
\(324\) | 4795.60 | 0.822292 | ||||||||
\(325\) | −58.2609 | −0.00994380 | ||||||||
\(326\) | −9609.62 | −1.63260 | ||||||||
\(327\) | −296.064 | −0.0500684 | ||||||||
\(328\) | −5990.81 | −1.00850 | ||||||||
\(329\) | −1537.90 | −0.257711 | ||||||||
\(330\) | −498.596 | −0.0831721 | ||||||||
\(331\) | −9141.12 | −1.51795 | −0.758975 | − | 0.651120i | \(-0.774300\pi\) | ||||
−0.758975 | + | 0.651120i | \(0.774300\pi\) | |||||||
\(332\) | 7028.60 | 1.16188 | ||||||||
\(333\) | −1999.95 | −0.329119 | ||||||||
\(334\) | 15592.4 | 2.55443 | ||||||||
\(335\) | −3362.60 | −0.548414 | ||||||||
\(336\) | −666.490 | −0.108214 | ||||||||
\(337\) | −5397.86 | −0.872523 | −0.436261 | − | 0.899820i | \(-0.643698\pi\) | ||||
−0.436261 | + | 0.899820i | \(0.643698\pi\) | |||||||
\(338\) | 9733.98 | 1.56645 | ||||||||
\(339\) | 3443.62 | 0.551716 | ||||||||
\(340\) | 1203.62 | 0.191986 | ||||||||
\(341\) | 1669.56 | 0.265137 | ||||||||
\(342\) | −1926.97 | −0.304674 | ||||||||
\(343\) | 6871.65 | 1.08173 | ||||||||
\(344\) | 4423.16 | 0.693258 | ||||||||
\(345\) | 1377.37 | 0.214943 | ||||||||
\(346\) | 17013.9 | 2.64357 | ||||||||
\(347\) | −11464.3 | −1.77359 | −0.886794 | − | 0.462165i | \(-0.847073\pi\) | ||||
−0.886794 | + | 0.462165i | \(0.847073\pi\) | |||||||
\(348\) | 5488.73 | 0.845479 | ||||||||
\(349\) | −1438.79 | −0.220679 | −0.110339 | − | 0.993894i | \(-0.535194\pi\) | ||||
−0.110339 | + | 0.993894i | \(0.535194\pi\) | |||||||
\(350\) | 1787.32 | 0.272961 | ||||||||
\(351\) | −237.036 | −0.0360458 | ||||||||
\(352\) | 2448.05 | 0.370686 | ||||||||
\(353\) | 6497.89 | 0.979739 | 0.489870 | − | 0.871796i | \(-0.337044\pi\) | ||||
0.489870 | + | 0.871796i | \(0.337044\pi\) | |||||||
\(354\) | −5603.70 | −0.841337 | ||||||||
\(355\) | −1439.17 | −0.215165 | ||||||||
\(356\) | −7965.15 | −1.18582 | ||||||||
\(357\) | −674.362 | −0.0999749 | ||||||||
\(358\) | 580.922 | 0.0857617 | ||||||||
\(359\) | −10283.9 | −1.51188 | −0.755941 | − | 0.654640i | \(-0.772820\pi\) | ||||
−0.755941 | + | 0.654640i | \(0.772820\pi\) | |||||||
\(360\) | −1890.16 | −0.276723 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 8120.61 | 1.17903 | ||||||||
\(363\) | −246.965 | −0.0357089 | ||||||||
\(364\) | 439.913 | 0.0633454 | ||||||||
\(365\) | −3482.75 | −0.499440 | ||||||||
\(366\) | −1346.46 | −0.192297 | ||||||||
\(367\) | 6174.57 | 0.878228 | 0.439114 | − | 0.898431i | \(-0.355292\pi\) | ||||
0.439114 | + | 0.898431i | \(0.355292\pi\) | |||||||
\(368\) | −2738.08 | −0.387860 | ||||||||
\(369\) | −8262.80 | −1.16570 | ||||||||
\(370\) | 1945.09 | 0.273298 | ||||||||
\(371\) | −546.121 | −0.0764236 | ||||||||
\(372\) | −3632.98 | −0.506348 | ||||||||
\(373\) | −7009.97 | −0.973090 | −0.486545 | − | 0.873656i | \(-0.661743\pi\) | ||||
−0.486545 | + | 0.873656i | \(0.661743\pi\) | |||||||
\(374\) | 1002.87 | 0.138655 | ||||||||
\(375\) | 255.129 | 0.0351329 | ||||||||
\(376\) | −1581.77 | −0.216951 | ||||||||
\(377\) | 534.387 | 0.0730035 | ||||||||
\(378\) | 7271.77 | 0.989470 | ||||||||
\(379\) | −848.127 | −0.114948 | −0.0574741 | − | 0.998347i | \(-0.518305\pi\) | ||||
−0.0574741 | + | 0.998347i | \(0.518305\pi\) | |||||||
\(380\) | 1114.11 | 0.150401 | ||||||||
\(381\) | −4758.90 | −0.639910 | ||||||||
\(382\) | 521.318 | 0.0698244 | ||||||||
\(383\) | −2084.78 | −0.278140 | −0.139070 | − | 0.990283i | \(-0.544411\pi\) | ||||
−0.139070 | + | 0.990283i | \(0.544411\pi\) | |||||||
\(384\) | −3855.71 | −0.512398 | ||||||||
\(385\) | 885.299 | 0.117192 | ||||||||
\(386\) | 21856.5 | 2.88203 | ||||||||
\(387\) | 6100.62 | 0.801322 | ||||||||
\(388\) | 16373.3 | 2.14234 | ||||||||
\(389\) | −3027.01 | −0.394539 | −0.197269 | − | 0.980349i | \(-0.563207\pi\) | ||||
−0.197269 | + | 0.980349i | \(0.563207\pi\) | |||||||
\(390\) | 105.631 | 0.0137150 | ||||||||
\(391\) | −2770.42 | −0.358328 | ||||||||
\(392\) | 1389.14 | 0.178985 | ||||||||
\(393\) | 1760.67 | 0.225990 | ||||||||
\(394\) | 1239.54 | 0.158496 | ||||||||
\(395\) | −5945.41 | −0.757332 | ||||||||
\(396\) | −2945.65 | −0.373799 | ||||||||
\(397\) | 6308.80 | 0.797555 | 0.398778 | − | 0.917048i | \(-0.369435\pi\) | ||||
0.398778 | + | 0.917048i | \(0.369435\pi\) | |||||||
\(398\) | −4377.12 | −0.551270 | ||||||||
\(399\) | −624.211 | −0.0783199 | ||||||||
\(400\) | −507.173 | −0.0633966 | ||||||||
\(401\) | −2907.43 | −0.362070 | −0.181035 | − | 0.983477i | \(-0.557945\pi\) | ||||
−0.181035 | + | 0.983477i | \(0.557945\pi\) | |||||||
\(402\) | 6096.65 | 0.756401 | ||||||||
\(403\) | −353.710 | −0.0437210 | ||||||||
\(404\) | −2774.36 | −0.341658 | ||||||||
\(405\) | −2044.61 | −0.250858 | ||||||||
\(406\) | −16393.9 | −2.00397 | ||||||||
\(407\) | 963.444 | 0.117337 | ||||||||
\(408\) | −693.602 | −0.0841627 | ||||||||
\(409\) | −10316.6 | −1.24724 | −0.623621 | − | 0.781727i | \(-0.714339\pi\) | ||||
−0.623621 | + | 0.781727i | \(0.714339\pi\) | |||||||
\(410\) | 8036.13 | 0.967991 | ||||||||
\(411\) | −5901.12 | −0.708225 | ||||||||
\(412\) | −6827.50 | −0.816424 | ||||||||
\(413\) | 9949.85 | 1.18547 | ||||||||
\(414\) | 13688.4 | 1.62499 | ||||||||
\(415\) | −2996.65 | −0.354458 | ||||||||
\(416\) | −518.639 | −0.0611258 | ||||||||
\(417\) | 4944.65 | 0.580673 | ||||||||
\(418\) | 928.285 | 0.108622 | ||||||||
\(419\) | 383.904 | 0.0447611 | 0.0223806 | − | 0.999750i | \(-0.492875\pi\) | ||||
0.0223806 | + | 0.999750i | \(0.492875\pi\) | |||||||
\(420\) | −1926.42 | −0.223808 | ||||||||
\(421\) | 4149.92 | 0.480414 | 0.240207 | − | 0.970722i | \(-0.422785\pi\) | ||||
0.240207 | + | 0.970722i | \(0.422785\pi\) | |||||||
\(422\) | 17890.7 | 2.06376 | ||||||||
\(423\) | −2181.65 | −0.250769 | ||||||||
\(424\) | −561.701 | −0.0643364 | ||||||||
\(425\) | −513.163 | −0.0585696 | ||||||||
\(426\) | 2609.33 | 0.296767 | ||||||||
\(427\) | 2390.75 | 0.270952 | ||||||||
\(428\) | 18276.6 | 2.06409 | ||||||||
\(429\) | 52.3215 | 0.00588836 | ||||||||
\(430\) | −5933.26 | −0.665412 | ||||||||
\(431\) | 7268.73 | 0.812349 | 0.406174 | − | 0.913796i | \(-0.366863\pi\) | ||||
0.406174 | + | 0.913796i | \(0.366863\pi\) | |||||||
\(432\) | −2063.45 | −0.229810 | ||||||||
\(433\) | 9973.04 | 1.10687 | 0.553434 | − | 0.832893i | \(-0.313317\pi\) | ||||
0.553434 | + | 0.832893i | \(0.313317\pi\) | |||||||
\(434\) | 10851.1 | 1.20016 | ||||||||
\(435\) | −2340.13 | −0.257932 | ||||||||
\(436\) | 1701.13 | 0.186856 | ||||||||
\(437\) | −2564.39 | −0.280713 | ||||||||
\(438\) | 6314.49 | 0.688854 | ||||||||
\(439\) | 6329.47 | 0.688130 | 0.344065 | − | 0.938946i | \(-0.388196\pi\) | ||||
0.344065 | + | 0.938946i | \(0.388196\pi\) | |||||||
\(440\) | 910.556 | 0.0986569 | ||||||||
\(441\) | 1915.96 | 0.206885 | ||||||||
\(442\) | −212.465 | −0.0228641 | ||||||||
\(443\) | 6231.93 | 0.668370 | 0.334185 | − | 0.942507i | \(-0.391539\pi\) | ||||
0.334185 | + | 0.942507i | \(0.391539\pi\) | |||||||
\(444\) | −2096.46 | −0.224085 | ||||||||
\(445\) | 3395.95 | 0.361761 | ||||||||
\(446\) | −5217.35 | −0.553921 | ||||||||
\(447\) | 2570.14 | 0.271954 | ||||||||
\(448\) | 13298.4 | 1.40243 | ||||||||
\(449\) | 12107.2 | 1.27255 | 0.636275 | − | 0.771462i | \(-0.280474\pi\) | ||||
0.636275 | + | 0.771462i | \(0.280474\pi\) | |||||||
\(450\) | 2535.48 | 0.265608 | ||||||||
\(451\) | 3980.47 | 0.415594 | ||||||||
\(452\) | −19786.4 | −2.05901 | ||||||||
\(453\) | −6492.66 | −0.673404 | ||||||||
\(454\) | 20287.9 | 2.09727 | ||||||||
\(455\) | −187.558 | −0.0193249 | ||||||||
\(456\) | −642.019 | −0.0659327 | ||||||||
\(457\) | −5197.12 | −0.531972 | −0.265986 | − | 0.963977i | \(-0.585697\pi\) | ||||
−0.265986 | + | 0.963977i | \(0.585697\pi\) | |||||||
\(458\) | −21531.7 | −2.19675 | ||||||||
\(459\) | −2087.82 | −0.212312 | ||||||||
\(460\) | −7914.13 | −0.802170 | ||||||||
\(461\) | 9997.95 | 1.01009 | 0.505045 | − | 0.863093i | \(-0.331476\pi\) | ||||
0.505045 | + | 0.863093i | \(0.331476\pi\) | |||||||
\(462\) | −1605.11 | −0.161638 | ||||||||
\(463\) | 11324.6 | 1.13671 | 0.568356 | − | 0.822783i | \(-0.307580\pi\) | ||||
0.568356 | + | 0.822783i | \(0.307580\pi\) | |||||||
\(464\) | 4651.95 | 0.465434 | ||||||||
\(465\) | 1548.93 | 0.154472 | ||||||||
\(466\) | −4506.57 | −0.447989 | ||||||||
\(467\) | −1526.29 | −0.151239 | −0.0756193 | − | 0.997137i | \(-0.524093\pi\) | ||||
−0.0756193 | + | 0.997137i | \(0.524093\pi\) | |||||||
\(468\) | 624.058 | 0.0616391 | ||||||||
\(469\) | −10825.1 | −1.06579 | ||||||||
\(470\) | 2121.80 | 0.208237 | ||||||||
\(471\) | 6466.84 | 0.632646 | ||||||||
\(472\) | 10233.7 | 0.997976 | ||||||||
\(473\) | −2938.87 | −0.285686 | ||||||||
\(474\) | 10779.5 | 1.04455 | ||||||||
\(475\) | −475.000 | −0.0458831 | ||||||||
\(476\) | 3874.77 | 0.373108 | ||||||||
\(477\) | −774.723 | −0.0743651 | ||||||||
\(478\) | 29160.6 | 2.79032 | ||||||||
\(479\) | −4558.69 | −0.434847 | −0.217423 | − | 0.976077i | \(-0.569765\pi\) | ||||
−0.217423 | + | 0.976077i | \(0.569765\pi\) | |||||||
\(480\) | 2271.16 | 0.215966 | ||||||||
\(481\) | −204.113 | −0.0193488 | ||||||||
\(482\) | 8730.89 | 0.825065 | ||||||||
\(483\) | 4434.13 | 0.417722 | ||||||||
\(484\) | 1419.02 | 0.133266 | ||||||||
\(485\) | −6980.78 | −0.653569 | ||||||||
\(486\) | 15904.7 | 1.48447 | ||||||||
\(487\) | −1686.04 | −0.156883 | −0.0784413 | − | 0.996919i | \(-0.524994\pi\) | ||||
−0.0784413 | + | 0.996919i | \(0.524994\pi\) | |||||||
\(488\) | 2458.96 | 0.228098 | ||||||||
\(489\) | −4415.93 | −0.408374 | ||||||||
\(490\) | −1863.40 | −0.171796 | ||||||||
\(491\) | −11377.5 | −1.04574 | −0.522870 | − | 0.852412i | \(-0.675139\pi\) | ||||
−0.522870 | + | 0.852412i | \(0.675139\pi\) | |||||||
\(492\) | −8661.54 | −0.793683 | ||||||||
\(493\) | 4706.89 | 0.429995 | ||||||||
\(494\) | −196.665 | −0.0179116 | ||||||||
\(495\) | 1255.88 | 0.114036 | ||||||||
\(496\) | −3079.12 | −0.278743 | ||||||||
\(497\) | −4633.09 | −0.418154 | ||||||||
\(498\) | 5433.16 | 0.488887 | ||||||||
\(499\) | 18283.0 | 1.64020 | 0.820099 | − | 0.572221i | \(-0.193918\pi\) | ||||
0.820099 | + | 0.572221i | \(0.193918\pi\) | |||||||
\(500\) | −1465.93 | −0.131117 | ||||||||
\(501\) | 7165.21 | 0.638958 | ||||||||
\(502\) | −8604.57 | −0.765021 | ||||||||
\(503\) | −3646.66 | −0.323254 | −0.161627 | − | 0.986852i | \(-0.551674\pi\) | ||||
−0.161627 | + | 0.986852i | \(0.551674\pi\) | |||||||
\(504\) | −6084.94 | −0.537788 | ||||||||
\(505\) | 1182.85 | 0.104230 | ||||||||
\(506\) | −6594.14 | −0.579339 | ||||||||
\(507\) | 4473.07 | 0.391826 | ||||||||
\(508\) | 27343.8 | 2.38816 | ||||||||
\(509\) | −2257.30 | −0.196568 | −0.0982839 | − | 0.995158i | \(-0.531335\pi\) | ||||
−0.0982839 | + | 0.995158i | \(0.531335\pi\) | |||||||
\(510\) | 930.403 | 0.0807823 | ||||||||
\(511\) | −11211.9 | −0.970618 | ||||||||
\(512\) | −7201.75 | −0.621631 | ||||||||
\(513\) | −1932.55 | −0.166324 | ||||||||
\(514\) | −28791.5 | −2.47070 | ||||||||
\(515\) | 2910.91 | 0.249068 | ||||||||
\(516\) | 6395.01 | 0.545591 | ||||||||
\(517\) | 1050.97 | 0.0894039 | ||||||||
\(518\) | 6261.76 | 0.531131 | ||||||||
\(519\) | 7818.45 | 0.661256 | ||||||||
\(520\) | −192.908 | −0.0162685 | ||||||||
\(521\) | −18156.6 | −1.52679 | −0.763394 | − | 0.645933i | \(-0.776469\pi\) | ||||
−0.763394 | + | 0.645933i | \(0.776469\pi\) | |||||||
\(522\) | −23256.2 | −1.94999 | ||||||||
\(523\) | −16592.6 | −1.38728 | −0.693638 | − | 0.720324i | \(-0.743993\pi\) | ||||
−0.693638 | + | 0.720324i | \(0.743993\pi\) | |||||||
\(524\) | −10116.5 | −0.843400 | ||||||||
\(525\) | 821.330 | 0.0682777 | ||||||||
\(526\) | 36273.2 | 3.00682 | ||||||||
\(527\) | −3115.48 | −0.257519 | ||||||||
\(528\) | 455.470 | 0.0375412 | ||||||||
\(529\) | 6049.34 | 0.497193 | ||||||||
\(530\) | 753.471 | 0.0617522 | ||||||||
\(531\) | 14114.8 | 1.15354 | ||||||||
\(532\) | 3586.60 | 0.292291 | ||||||||
\(533\) | −843.294 | −0.0685312 | ||||||||
\(534\) | −6157.11 | −0.498959 | ||||||||
\(535\) | −7792.24 | −0.629697 | ||||||||
\(536\) | −11134.0 | −0.897227 | ||||||||
\(537\) | 266.952 | 0.0214522 | ||||||||
\(538\) | 20190.3 | 1.61797 | ||||||||
\(539\) | −922.985 | −0.0737584 | ||||||||
\(540\) | −5964.18 | −0.475291 | ||||||||
\(541\) | 6540.32 | 0.519760 | 0.259880 | − | 0.965641i | \(-0.416317\pi\) | ||||
0.259880 | + | 0.965641i | \(0.416317\pi\) | |||||||
\(542\) | 630.881 | 0.0499975 | ||||||||
\(543\) | 3731.67 | 0.294920 | ||||||||
\(544\) | −4568.18 | −0.360035 | ||||||||
\(545\) | −725.279 | −0.0570046 | ||||||||
\(546\) | 340.056 | 0.0266539 | ||||||||
\(547\) | 2700.43 | 0.211082 | 0.105541 | − | 0.994415i | \(-0.466343\pi\) | ||||
0.105541 | + | 0.994415i | \(0.466343\pi\) | |||||||
\(548\) | 33906.8 | 2.64311 | ||||||||
\(549\) | 3391.51 | 0.263654 | ||||||||
\(550\) | −1221.43 | −0.0946943 | ||||||||
\(551\) | 4356.85 | 0.336856 | ||||||||
\(552\) | 4560.63 | 0.351655 | ||||||||
\(553\) | −19139.9 | −1.47181 | ||||||||
\(554\) | −37367.7 | −2.86571 | ||||||||
\(555\) | 893.829 | 0.0683620 | ||||||||
\(556\) | −28411.1 | −2.16708 | ||||||||
\(557\) | −16081.4 | −1.22332 | −0.611662 | − | 0.791119i | \(-0.709499\pi\) | ||||
−0.611662 | + | 0.791119i | \(0.709499\pi\) | |||||||
\(558\) | 15393.3 | 1.16783 | ||||||||
\(559\) | 622.624 | 0.0471094 | ||||||||
\(560\) | −1632.73 | −0.123206 | ||||||||
\(561\) | 460.849 | 0.0346828 | ||||||||
\(562\) | −14721.0 | −1.10493 | ||||||||
\(563\) | 17435.4 | 1.30518 | 0.652589 | − | 0.757712i | \(-0.273683\pi\) | ||||
0.652589 | + | 0.757712i | \(0.273683\pi\) | |||||||
\(564\) | −2286.93 | −0.170740 | ||||||||
\(565\) | 8435.96 | 0.628148 | ||||||||
\(566\) | 12427.7 | 0.922921 | ||||||||
\(567\) | −6582.15 | −0.487521 | ||||||||
\(568\) | −4765.27 | −0.352018 | ||||||||
\(569\) | 21828.1 | 1.60823 | 0.804114 | − | 0.594476i | \(-0.202640\pi\) | ||||
0.804114 | + | 0.594476i | \(0.202640\pi\) | |||||||
\(570\) | 861.210 | 0.0632845 | ||||||||
\(571\) | 12874.9 | 0.943606 | 0.471803 | − | 0.881704i | \(-0.343603\pi\) | ||||
0.471803 | + | 0.881704i | \(0.343603\pi\) | |||||||
\(572\) | −300.630 | −0.0219755 | ||||||||
\(573\) | 239.562 | 0.0174657 | ||||||||
\(574\) | 25870.5 | 1.88121 | ||||||||
\(575\) | 3374.20 | 0.244720 | ||||||||
\(576\) | 18865.0 | 1.36465 | ||||||||
\(577\) | −11684.3 | −0.843020 | −0.421510 | − | 0.906824i | \(-0.638500\pi\) | ||||
−0.421510 | + | 0.906824i | \(0.638500\pi\) | |||||||
\(578\) | 19950.0 | 1.43566 | ||||||||
\(579\) | 10043.7 | 0.720904 | ||||||||
\(580\) | 13445.9 | 0.962608 | ||||||||
\(581\) | −9647.03 | −0.688858 | ||||||||
\(582\) | 12656.7 | 0.901437 | ||||||||
\(583\) | 373.211 | 0.0265125 | ||||||||
\(584\) | −11531.8 | −0.817104 | ||||||||
\(585\) | −266.068 | −0.0188044 | ||||||||
\(586\) | 33831.9 | 2.38496 | ||||||||
\(587\) | −10055.1 | −0.707013 | −0.353507 | − | 0.935432i | \(-0.615011\pi\) | ||||
−0.353507 | + | 0.935432i | \(0.615011\pi\) | |||||||
\(588\) | 2008.42 | 0.140860 | ||||||||
\(589\) | −2883.79 | −0.201739 | ||||||||
\(590\) | −13727.6 | −0.957892 | ||||||||
\(591\) | 569.610 | 0.0396457 | ||||||||
\(592\) | −1776.85 | −0.123358 | ||||||||
\(593\) | 23154.8 | 1.60346 | 0.801730 | − | 0.597686i | \(-0.203913\pi\) | ||||
0.801730 | + | 0.597686i | \(0.203913\pi\) | |||||||
\(594\) | −4969.42 | −0.343262 | ||||||||
\(595\) | −1652.01 | −0.113825 | ||||||||
\(596\) | −14767.6 | −1.01494 | ||||||||
\(597\) | −2011.43 | −0.137893 | ||||||||
\(598\) | 1397.02 | 0.0955325 | ||||||||
\(599\) | −14377.2 | −0.980694 | −0.490347 | − | 0.871527i | \(-0.663130\pi\) | ||||
−0.490347 | + | 0.871527i | \(0.663130\pi\) | |||||||
\(600\) | 844.762 | 0.0574788 | ||||||||
\(601\) | −9628.46 | −0.653499 | −0.326750 | − | 0.945111i | \(-0.605953\pi\) | ||||
−0.326750 | + | 0.945111i | \(0.605953\pi\) | |||||||
\(602\) | −19100.8 | −1.29317 | ||||||||
\(603\) | −15356.5 | −1.03709 | ||||||||
\(604\) | 37305.7 | 2.51316 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | −2144.60 | −0.143760 | ||||||||
\(607\) | −13382.7 | −0.894869 | −0.447435 | − | 0.894317i | \(-0.647662\pi\) | ||||
−0.447435 | + | 0.894317i | \(0.647662\pi\) | |||||||
\(608\) | −4228.45 | −0.282050 | ||||||||
\(609\) | −7533.49 | −0.501269 | ||||||||
\(610\) | −3298.47 | −0.218937 | ||||||||
\(611\) | −222.657 | −0.0147426 | ||||||||
\(612\) | 5496.72 | 0.363058 | ||||||||
\(613\) | −6404.88 | −0.422008 | −0.211004 | − | 0.977485i | \(-0.567673\pi\) | ||||
−0.211004 | + | 0.977485i | \(0.567673\pi\) | |||||||
\(614\) | −28614.6 | −1.88077 | ||||||||
\(615\) | 3692.86 | 0.242131 | ||||||||
\(616\) | 2931.32 | 0.191731 | ||||||||
\(617\) | 2024.21 | 0.132077 | 0.0660385 | − | 0.997817i | \(-0.478964\pi\) | ||||
0.0660385 | + | 0.997817i | \(0.478964\pi\) | |||||||
\(618\) | −5277.70 | −0.343528 | ||||||||
\(619\) | 14886.1 | 0.966596 | 0.483298 | − | 0.875456i | \(-0.339439\pi\) | ||||
0.483298 | + | 0.875456i | \(0.339439\pi\) | |||||||
\(620\) | −8899.85 | −0.576494 | ||||||||
\(621\) | 13728.0 | 0.887097 | ||||||||
\(622\) | −17039.1 | −1.09840 | ||||||||
\(623\) | 10932.5 | 0.703050 | ||||||||
\(624\) | −96.4948 | −0.00619052 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −48069.9 | −3.06910 | ||||||||
\(627\) | 426.576 | 0.0271704 | ||||||||
\(628\) | −37157.3 | −2.36105 | ||||||||
\(629\) | −1797.83 | −0.113966 | ||||||||
\(630\) | 8162.40 | 0.516187 | ||||||||
\(631\) | −26067.9 | −1.64461 | −0.822303 | − | 0.569050i | \(-0.807311\pi\) | ||||
−0.822303 | + | 0.569050i | \(0.807311\pi\) | |||||||
\(632\) | −19685.9 | −1.23903 | ||||||||
\(633\) | 8221.34 | 0.516223 | ||||||||
\(634\) | 35162.8 | 2.20267 | ||||||||
\(635\) | −11658.0 | −0.728560 | ||||||||
\(636\) | −812.109 | −0.0506324 | ||||||||
\(637\) | 195.542 | 0.0121627 | ||||||||
\(638\) | 11203.3 | 0.695209 | ||||||||
\(639\) | −6572.47 | −0.406891 | ||||||||
\(640\) | −9445.47 | −0.583383 | ||||||||
\(641\) | −22131.1 | −1.36369 | −0.681846 | − | 0.731496i | \(-0.738823\pi\) | ||||
−0.681846 | + | 0.731496i | \(0.738823\pi\) | |||||||
\(642\) | 14127.9 | 0.868511 | ||||||||
\(643\) | −5655.76 | −0.346876 | −0.173438 | − | 0.984845i | \(-0.555488\pi\) | ||||
−0.173438 | + | 0.984845i | \(0.555488\pi\) | |||||||
\(644\) | −25477.7 | −1.55895 | ||||||||
\(645\) | −2726.52 | −0.166444 | ||||||||
\(646\) | −1732.23 | −0.105501 | ||||||||
\(647\) | −19352.8 | −1.17595 | −0.587973 | − | 0.808881i | \(-0.700074\pi\) | ||||
−0.587973 | + | 0.808881i | \(0.700074\pi\) | |||||||
\(648\) | −6769.94 | −0.410414 | ||||||||
\(649\) | −6799.58 | −0.411258 | ||||||||
\(650\) | 258.769 | 0.0156150 | ||||||||
\(651\) | 4986.41 | 0.300204 | ||||||||
\(652\) | 25373.1 | 1.52406 | ||||||||
\(653\) | −12448.3 | −0.746004 | −0.373002 | − | 0.927831i | \(-0.621672\pi\) | ||||
−0.373002 | + | 0.927831i | \(0.621672\pi\) | |||||||
\(654\) | 1314.98 | 0.0786238 | ||||||||
\(655\) | 4313.18 | 0.257298 | ||||||||
\(656\) | −7341.05 | −0.436920 | ||||||||
\(657\) | −15905.2 | −0.944474 | ||||||||
\(658\) | 6830.65 | 0.404691 | ||||||||
\(659\) | −849.200 | −0.0501975 | −0.0250987 | − | 0.999685i | \(-0.507990\pi\) | ||||
−0.0250987 | + | 0.999685i | \(0.507990\pi\) | |||||||
\(660\) | 1316.48 | 0.0776426 | ||||||||
\(661\) | −3793.75 | −0.223237 | −0.111619 | − | 0.993751i | \(-0.535603\pi\) | ||||
−0.111619 | + | 0.993751i | \(0.535603\pi\) | |||||||
\(662\) | 40600.8 | 2.38368 | ||||||||
\(663\) | −97.6345 | −0.00571917 | ||||||||
\(664\) | −9922.26 | −0.579907 | ||||||||
\(665\) | −1529.15 | −0.0891699 | ||||||||
\(666\) | 8882.89 | 0.516824 | ||||||||
\(667\) | −30949.2 | −1.79664 | ||||||||
\(668\) | −41170.0 | −2.38461 | ||||||||
\(669\) | −2397.54 | −0.138556 | ||||||||
\(670\) | 14935.2 | 0.861189 | ||||||||
\(671\) | −1633.81 | −0.0939976 | ||||||||
\(672\) | 7311.48 | 0.419712 | ||||||||
\(673\) | −12440.3 | −0.712540 | −0.356270 | − | 0.934383i | \(-0.615952\pi\) | ||||
−0.356270 | + | 0.934383i | \(0.615952\pi\) | |||||||
\(674\) | 23974.9 | 1.37015 | ||||||||
\(675\) | 2542.83 | 0.144998 | ||||||||
\(676\) | −25701.5 | −1.46230 | ||||||||
\(677\) | 8522.43 | 0.483816 | 0.241908 | − | 0.970299i | \(-0.422227\pi\) | ||||
0.241908 | + | 0.970299i | \(0.422227\pi\) | |||||||
\(678\) | −15295.0 | −0.866374 | ||||||||
\(679\) | −22473.0 | −1.27015 | ||||||||
\(680\) | −1699.14 | −0.0958222 | ||||||||
\(681\) | 9322.95 | 0.524605 | ||||||||
\(682\) | −7415.46 | −0.416353 | ||||||||
\(683\) | 22802.3 | 1.27746 | 0.638731 | − | 0.769430i | \(-0.279460\pi\) | ||||
0.638731 | + | 0.769430i | \(0.279460\pi\) | |||||||
\(684\) | 5087.93 | 0.284418 | ||||||||
\(685\) | −14456.2 | −0.806339 | ||||||||
\(686\) | −30520.8 | −1.69867 | ||||||||
\(687\) | −9894.52 | −0.549490 | ||||||||
\(688\) | 5420.07 | 0.300346 | ||||||||
\(689\) | −79.0676 | −0.00437190 | ||||||||
\(690\) | −6117.67 | −0.337530 | ||||||||
\(691\) | −11655.7 | −0.641686 | −0.320843 | − | 0.947132i | \(-0.603966\pi\) | ||||
−0.320843 | + | 0.947132i | \(0.603966\pi\) | |||||||
\(692\) | −44923.4 | −2.46782 | ||||||||
\(693\) | 4043.01 | 0.221618 | ||||||||
\(694\) | 50919.3 | 2.78511 | ||||||||
\(695\) | 12113.1 | 0.661117 | ||||||||
\(696\) | −7748.42 | −0.421987 | ||||||||
\(697\) | −7427.75 | −0.403653 | ||||||||
\(698\) | 6390.49 | 0.346538 | ||||||||
\(699\) | −2070.91 | −0.112059 | ||||||||
\(700\) | −4719.22 | −0.254814 | ||||||||
\(701\) | 29100.5 | 1.56792 | 0.783960 | − | 0.620811i | \(-0.213197\pi\) | ||||
0.783960 | + | 0.620811i | \(0.213197\pi\) | |||||||
\(702\) | 1052.81 | 0.0566037 | ||||||||
\(703\) | −1664.13 | −0.0892801 | ||||||||
\(704\) | −9087.90 | −0.486525 | ||||||||
\(705\) | 975.035 | 0.0520879 | ||||||||
\(706\) | −28860.8 | −1.53851 | ||||||||
\(707\) | 3807.92 | 0.202562 | ||||||||
\(708\) | 14795.9 | 0.785403 | ||||||||
\(709\) | 28240.3 | 1.49589 | 0.747944 | − | 0.663761i | \(-0.231041\pi\) | ||||
0.747944 | + | 0.663761i | \(0.231041\pi\) | |||||||
\(710\) | 6392.18 | 0.337879 | ||||||||
\(711\) | −27151.7 | −1.43216 | ||||||||
\(712\) | 11244.4 | 0.591855 | ||||||||
\(713\) | 20485.2 | 1.07599 | ||||||||
\(714\) | 2995.22 | 0.156993 | ||||||||
\(715\) | 128.174 | 0.00670411 | ||||||||
\(716\) | −1533.86 | −0.0800601 | ||||||||
\(717\) | 13400.2 | 0.697963 | ||||||||
\(718\) | 45676.7 | 2.37415 | ||||||||
\(719\) | 26917.3 | 1.39617 | 0.698086 | − | 0.716014i | \(-0.254035\pi\) | ||||
0.698086 | + | 0.716014i | \(0.254035\pi\) | |||||||
\(720\) | −2316.18 | −0.119887 | ||||||||
\(721\) | 9371.01 | 0.484042 | ||||||||
\(722\) | −1603.40 | −0.0826488 | ||||||||
\(723\) | 4012.12 | 0.206379 | ||||||||
\(724\) | −21441.5 | −1.10065 | ||||||||
\(725\) | −5732.69 | −0.293665 | ||||||||
\(726\) | 1096.91 | 0.0560746 | ||||||||
\(727\) | 7401.00 | 0.377562 | 0.188781 | − | 0.982019i | \(-0.439546\pi\) | ||||
0.188781 | + | 0.982019i | \(0.439546\pi\) | |||||||
\(728\) | −621.024 | −0.0316163 | ||||||||
\(729\) | −3732.19 | −0.189615 | ||||||||
\(730\) | 15468.8 | 0.784284 | ||||||||
\(731\) | 5484.08 | 0.277478 | ||||||||
\(732\) | 3555.17 | 0.179512 | ||||||||
\(733\) | 14809.9 | 0.746272 | 0.373136 | − | 0.927777i | \(-0.378282\pi\) | ||||
0.373136 | + | 0.927777i | \(0.378282\pi\) | |||||||
\(734\) | −27424.7 | −1.37911 | ||||||||
\(735\) | −856.293 | −0.0429726 | ||||||||
\(736\) | 30037.1 | 1.50432 | ||||||||
\(737\) | 7397.73 | 0.369741 | ||||||||
\(738\) | 36699.7 | 1.83053 | ||||||||
\(739\) | −23335.1 | −1.16156 | −0.580781 | − | 0.814060i | \(-0.697253\pi\) | ||||
−0.580781 | + | 0.814060i | \(0.697253\pi\) | |||||||
\(740\) | −5135.78 | −0.255128 | ||||||||
\(741\) | −90.3735 | −0.00448037 | ||||||||
\(742\) | 2425.63 | 0.120010 | ||||||||
\(743\) | −14279.1 | −0.705045 | −0.352522 | − | 0.935803i | \(-0.614676\pi\) | ||||
−0.352522 | + | 0.935803i | \(0.614676\pi\) | |||||||
\(744\) | 5128.67 | 0.252723 | ||||||||
\(745\) | 6296.17 | 0.309629 | ||||||||
\(746\) | 31135.2 | 1.52807 | ||||||||
\(747\) | −13685.2 | −0.670303 | ||||||||
\(748\) | −2647.96 | −0.129437 | ||||||||
\(749\) | −25085.3 | −1.22376 | ||||||||
\(750\) | −1133.17 | −0.0551701 | ||||||||
\(751\) | 1425.69 | 0.0692734 | 0.0346367 | − | 0.999400i | \(-0.488973\pi\) | ||||
0.0346367 | + | 0.999400i | \(0.488973\pi\) | |||||||
\(752\) | −1938.28 | −0.0939916 | ||||||||
\(753\) | −3954.07 | −0.191360 | ||||||||
\(754\) | −2373.51 | −0.114639 | ||||||||
\(755\) | −15905.3 | −0.766694 | ||||||||
\(756\) | −19200.3 | −0.923687 | ||||||||
\(757\) | 23916.6 | 1.14830 | 0.574151 | − | 0.818749i | \(-0.305332\pi\) | ||||
0.574151 | + | 0.818749i | \(0.305332\pi\) | |||||||
\(758\) | 3767.00 | 0.180506 | ||||||||
\(759\) | −3030.22 | −0.144914 | ||||||||
\(760\) | −1572.78 | −0.0750667 | ||||||||
\(761\) | −22441.1 | −1.06897 | −0.534486 | − | 0.845177i | \(-0.679495\pi\) | ||||
−0.534486 | + | 0.845177i | \(0.679495\pi\) | |||||||
\(762\) | 21136.9 | 1.00487 | ||||||||
\(763\) | −2334.87 | −0.110784 | ||||||||
\(764\) | −1376.48 | −0.0651823 | ||||||||
\(765\) | −2343.53 | −0.110759 | ||||||||
\(766\) | 9259.68 | 0.436770 | ||||||||
\(767\) | 1440.54 | 0.0678162 | ||||||||
\(768\) | 3635.36 | 0.170807 | ||||||||
\(769\) | −2966.80 | −0.139123 | −0.0695615 | − | 0.997578i | \(-0.522160\pi\) | ||||
−0.0695615 | + | 0.997578i | \(0.522160\pi\) | |||||||
\(770\) | −3932.10 | −0.184030 | ||||||||
\(771\) | −13230.6 | −0.618014 | ||||||||
\(772\) | −57709.5 | −2.69043 | ||||||||
\(773\) | 18391.6 | 0.855758 | 0.427879 | − | 0.903836i | \(-0.359261\pi\) | ||||
0.427879 | + | 0.903836i | \(0.359261\pi\) | |||||||
\(774\) | −27096.2 | −1.25834 | ||||||||
\(775\) | 3794.46 | 0.175872 | ||||||||
\(776\) | −23114.2 | −1.06927 | ||||||||
\(777\) | 2877.48 | 0.132856 | ||||||||
\(778\) | 13444.6 | 0.619555 | ||||||||
\(779\) | −6875.36 | −0.316220 | ||||||||
\(780\) | −278.908 | −0.0128032 | ||||||||
\(781\) | 3166.18 | 0.145064 | ||||||||
\(782\) | 12305.0 | 0.562693 | ||||||||
\(783\) | −23323.6 | −1.06452 | ||||||||
\(784\) | 1702.23 | 0.0775433 | ||||||||
\(785\) | 15842.1 | 0.720289 | ||||||||
\(786\) | −7820.12 | −0.354879 | ||||||||
\(787\) | 4993.78 | 0.226187 | 0.113093 | − | 0.993584i | \(-0.463924\pi\) | ||||
0.113093 | + | 0.993584i | \(0.463924\pi\) | |||||||
\(788\) | −3272.88 | −0.147959 | ||||||||
\(789\) | 16668.7 | 0.752118 | ||||||||
\(790\) | 26406.9 | 1.18926 | ||||||||
\(791\) | 27157.6 | 1.22075 | ||||||||
\(792\) | 4158.36 | 0.186567 | ||||||||
\(793\) | 346.135 | 0.0155001 | ||||||||
\(794\) | −28020.9 | −1.25242 | ||||||||
\(795\) | 346.244 | 0.0154465 | ||||||||
\(796\) | 11557.3 | 0.514620 | ||||||||
\(797\) | −27110.3 | −1.20489 | −0.602443 | − | 0.798162i | \(-0.705806\pi\) | ||||
−0.602443 | + | 0.798162i | \(0.705806\pi\) | |||||||
\(798\) | 2772.47 | 0.122988 | ||||||||
\(799\) | −1961.17 | −0.0868350 | ||||||||
\(800\) | 5563.75 | 0.245885 | ||||||||
\(801\) | 15508.7 | 0.684113 | ||||||||
\(802\) | 12913.5 | 0.568568 | ||||||||
\(803\) | 7662.06 | 0.336722 | ||||||||
\(804\) | −16097.5 | −0.706114 | ||||||||
\(805\) | 10862.5 | 0.475591 | ||||||||
\(806\) | 1571.02 | 0.0686562 | ||||||||
\(807\) | 9278.09 | 0.404714 | ||||||||
\(808\) | 3916.56 | 0.170525 | ||||||||
\(809\) | 14651.2 | 0.636721 | 0.318361 | − | 0.947970i | \(-0.396868\pi\) | ||||
0.318361 | + | 0.947970i | \(0.396868\pi\) | |||||||
\(810\) | 9081.26 | 0.393929 | ||||||||
\(811\) | −16985.0 | −0.735418 | −0.367709 | − | 0.929941i | \(-0.619858\pi\) | ||||
−0.367709 | + | 0.929941i | \(0.619858\pi\) | |||||||
\(812\) | 43286.1 | 1.87074 | ||||||||
\(813\) | 289.910 | 0.0125062 | ||||||||
\(814\) | −4279.19 | −0.184257 | ||||||||
\(815\) | −10817.9 | −0.464948 | ||||||||
\(816\) | −849.928 | −0.0364625 | ||||||||
\(817\) | 5076.24 | 0.217375 | ||||||||
\(818\) | 45821.7 | 1.95858 | ||||||||
\(819\) | −856.544 | −0.0365447 | ||||||||
\(820\) | −21218.5 | −0.903636 | ||||||||
\(821\) | 18345.3 | 0.779847 | 0.389923 | − | 0.920847i | \(-0.372501\pi\) | ||||
0.389923 | + | 0.920847i | \(0.372501\pi\) | |||||||
\(822\) | 26210.1 | 1.11215 | ||||||||
\(823\) | 1129.79 | 0.0478517 | 0.0239258 | − | 0.999714i | \(-0.492383\pi\) | ||||
0.0239258 | + | 0.999714i | \(0.492383\pi\) | |||||||
\(824\) | 9638.36 | 0.407485 | ||||||||
\(825\) | −561.285 | −0.0236866 | ||||||||
\(826\) | −44192.8 | −1.86158 | ||||||||
\(827\) | −42737.9 | −1.79703 | −0.898514 | − | 0.438944i | \(-0.855353\pi\) | ||||
−0.898514 | + | 0.438944i | \(0.855353\pi\) | |||||||
\(828\) | −36142.5 | −1.51696 | ||||||||
\(829\) | −32743.8 | −1.37182 | −0.685910 | − | 0.727686i | \(-0.740596\pi\) | ||||
−0.685910 | + | 0.727686i | \(0.740596\pi\) | |||||||
\(830\) | 13309.8 | 0.556614 | ||||||||
\(831\) | −17171.6 | −0.716820 | ||||||||
\(832\) | 1925.34 | 0.0802275 | ||||||||
\(833\) | 1722.33 | 0.0716391 | ||||||||
\(834\) | −21962.0 | −0.911847 | ||||||||
\(835\) | 17552.9 | 0.727476 | ||||||||
\(836\) | −2451.03 | −0.101400 | ||||||||
\(837\) | 15437.9 | 0.637528 | ||||||||
\(838\) | −1705.13 | −0.0702896 | ||||||||
\(839\) | −11541.7 | −0.474926 | −0.237463 | − | 0.971397i | \(-0.576316\pi\) | ||||
−0.237463 | + | 0.971397i | \(0.576316\pi\) | |||||||
\(840\) | 2719.52 | 0.111705 | ||||||||
\(841\) | 28193.0 | 1.15597 | ||||||||
\(842\) | −18432.1 | −0.754408 | ||||||||
\(843\) | −6764.76 | −0.276383 | ||||||||
\(844\) | −47238.4 | −1.92655 | ||||||||
\(845\) | 10957.8 | 0.446108 | ||||||||
\(846\) | 9689.92 | 0.393790 | ||||||||
\(847\) | −1947.66 | −0.0790110 | ||||||||
\(848\) | −688.300 | −0.0278730 | ||||||||
\(849\) | 5710.90 | 0.230857 | ||||||||
\(850\) | 2279.24 | 0.0919734 | ||||||||
\(851\) | 11821.3 | 0.476179 | ||||||||
\(852\) | −6889.64 | −0.277037 | ||||||||
\(853\) | 18224.8 | 0.731543 | 0.365771 | − | 0.930705i | \(-0.380805\pi\) | ||||
0.365771 | + | 0.930705i | \(0.380805\pi\) | |||||||
\(854\) | −10618.7 | −0.425484 | ||||||||
\(855\) | −2169.25 | −0.0867680 | ||||||||
\(856\) | −25801.0 | −1.03021 | ||||||||
\(857\) | −7004.17 | −0.279181 | −0.139590 | − | 0.990209i | \(-0.544579\pi\) | ||||
−0.139590 | + | 0.990209i | \(0.544579\pi\) | |||||||
\(858\) | −232.389 | −0.00924666 | ||||||||
\(859\) | 49926.8 | 1.98310 | 0.991549 | − | 0.129733i | \(-0.0414119\pi\) | ||||
0.991549 | + | 0.129733i | \(0.0414119\pi\) | |||||||
\(860\) | 15666.1 | 0.621174 | ||||||||
\(861\) | 11888.3 | 0.470560 | ||||||||
\(862\) | −32284.5 | −1.27565 | ||||||||
\(863\) | −23919.2 | −0.943477 | −0.471738 | − | 0.881739i | \(-0.656373\pi\) | ||||
−0.471738 | + | 0.881739i | \(0.656373\pi\) | |||||||
\(864\) | 22636.3 | 0.891322 | ||||||||
\(865\) | 19153.1 | 0.752863 | ||||||||
\(866\) | −44295.8 | −1.73814 | ||||||||
\(867\) | 9167.64 | 0.359111 | ||||||||
\(868\) | −28651.0 | −1.12037 | ||||||||
\(869\) | 13079.9 | 0.510593 | ||||||||
\(870\) | 10393.8 | 0.405038 | ||||||||
\(871\) | −1567.27 | −0.0609699 | ||||||||
\(872\) | −2401.48 | −0.0932619 | ||||||||
\(873\) | −31880.1 | −1.23594 | ||||||||
\(874\) | 11389.9 | 0.440811 | ||||||||
\(875\) | 2012.04 | 0.0777365 | ||||||||
\(876\) | −16672.7 | −0.643057 | ||||||||
\(877\) | −41369.1 | −1.59286 | −0.796429 | − | 0.604732i | \(-0.793280\pi\) | ||||
−0.796429 | + | 0.604732i | \(0.793280\pi\) | |||||||
\(878\) | −28112.7 | −1.08059 | ||||||||
\(879\) | 15546.8 | 0.596567 | ||||||||
\(880\) | 1115.78 | 0.0427420 | ||||||||
\(881\) | −1043.41 | −0.0399017 | −0.0199508 | − | 0.999801i | \(-0.506351\pi\) | ||||
−0.0199508 | + | 0.999801i | \(0.506351\pi\) | |||||||
\(882\) | −8509.86 | −0.324878 | ||||||||
\(883\) | 29290.9 | 1.11633 | 0.558163 | − | 0.829731i | \(-0.311506\pi\) | ||||
0.558163 | + | 0.829731i | \(0.311506\pi\) | |||||||
\(884\) | 560.990 | 0.0213441 | ||||||||
\(885\) | −6308.26 | −0.239604 | ||||||||
\(886\) | −27679.5 | −1.04956 | ||||||||
\(887\) | 33779.7 | 1.27870 | 0.639352 | − | 0.768914i | \(-0.279203\pi\) | ||||
0.639352 | + | 0.768914i | \(0.279203\pi\) | |||||||
\(888\) | 2959.57 | 0.111843 | ||||||||
\(889\) | −37530.4 | −1.41589 | ||||||||
\(890\) | −15083.3 | −0.568082 | ||||||||
\(891\) | 4498.15 | 0.169129 | ||||||||
\(892\) | 13775.8 | 0.517095 | ||||||||
\(893\) | −1815.32 | −0.0680262 | ||||||||
\(894\) | −11415.4 | −0.427057 | ||||||||
\(895\) | 653.962 | 0.0244241 | ||||||||
\(896\) | −30407.5 | −1.13375 | ||||||||
\(897\) | 641.975 | 0.0238962 | ||||||||
\(898\) | −53774.9 | −1.99832 | ||||||||
\(899\) | −34804.0 | −1.29119 | ||||||||
\(900\) | −6694.65 | −0.247950 | ||||||||
\(901\) | −696.429 | −0.0257507 | ||||||||
\(902\) | −17679.5 | −0.652619 | ||||||||
\(903\) | −8777.41 | −0.323470 | ||||||||
\(904\) | 27932.4 | 1.02767 | ||||||||
\(905\) | 9141.62 | 0.335777 | ||||||||
\(906\) | 28837.5 | 1.05746 | ||||||||
\(907\) | −19281.2 | −0.705866 | −0.352933 | − | 0.935649i | \(-0.614816\pi\) | ||||
−0.352933 | + | 0.935649i | \(0.614816\pi\) | |||||||
\(908\) | −53568.0 | −1.95784 | ||||||||
\(909\) | 5401.90 | 0.197106 | ||||||||
\(910\) | 833.047 | 0.0303464 | ||||||||
\(911\) | −9931.37 | −0.361187 | −0.180593 | − | 0.983558i | \(-0.557802\pi\) | ||||
−0.180593 | + | 0.983558i | \(0.557802\pi\) | |||||||
\(912\) | −786.720 | −0.0285646 | ||||||||
\(913\) | 6592.64 | 0.238975 | ||||||||
\(914\) | 23083.3 | 0.835370 | ||||||||
\(915\) | −1515.75 | −0.0547642 | ||||||||
\(916\) | 56852.1 | 2.05071 | ||||||||
\(917\) | 13885.3 | 0.500036 | ||||||||
\(918\) | 9273.18 | 0.333399 | ||||||||
\(919\) | 22360.2 | 0.802606 | 0.401303 | − | 0.915945i | \(-0.368557\pi\) | ||||
0.401303 | + | 0.915945i | \(0.368557\pi\) | |||||||
\(920\) | 11172.4 | 0.400371 | ||||||||
\(921\) | −13149.3 | −0.470450 | ||||||||
\(922\) | −44406.5 | −1.58617 | ||||||||
\(923\) | −670.781 | −0.0239209 | ||||||||
\(924\) | 4238.12 | 0.150892 | ||||||||
\(925\) | 2189.65 | 0.0778326 | ||||||||
\(926\) | −50298.8 | −1.78501 | ||||||||
\(927\) | 13293.7 | 0.471004 | ||||||||
\(928\) | −51032.4 | −1.80520 | ||||||||
\(929\) | −22123.5 | −0.781323 | −0.390661 | − | 0.920534i | \(-0.627754\pi\) | ||||
−0.390661 | + | 0.920534i | \(0.627754\pi\) | |||||||
\(930\) | −6879.64 | −0.242572 | ||||||||
\(931\) | 1594.25 | 0.0561217 | ||||||||
\(932\) | 11899.1 | 0.418206 | ||||||||
\(933\) | −7830.00 | −0.274751 | ||||||||
\(934\) | 6779.12 | 0.237494 | ||||||||
\(935\) | 1128.96 | 0.0394876 | ||||||||
\(936\) | −880.981 | −0.0307647 | ||||||||
\(937\) | 34597.4 | 1.20624 | 0.603121 | − | 0.797650i | \(-0.293924\pi\) | ||||
0.603121 | + | 0.797650i | \(0.293924\pi\) | |||||||
\(938\) | 48080.4 | 1.67365 | ||||||||
\(939\) | −22089.6 | −0.767698 | ||||||||
\(940\) | −5602.38 | −0.194393 | ||||||||
\(941\) | 19146.3 | 0.663284 | 0.331642 | − | 0.943405i | \(-0.392397\pi\) | ||||
0.331642 | + | 0.943405i | \(0.392397\pi\) | |||||||
\(942\) | −28722.8 | −0.993461 | ||||||||
\(943\) | 48839.6 | 1.68657 | ||||||||
\(944\) | 12540.2 | 0.432362 | ||||||||
\(945\) | 8186.06 | 0.281791 | ||||||||
\(946\) | 13053.2 | 0.448621 | ||||||||
\(947\) | −34120.7 | −1.17083 | −0.585414 | − | 0.810734i | \(-0.699068\pi\) | ||||
−0.585414 | + | 0.810734i | \(0.699068\pi\) | |||||||
\(948\) | −28462.0 | −0.975107 | ||||||||
\(949\) | −1623.27 | −0.0555253 | ||||||||
\(950\) | 2109.74 | 0.0720516 | ||||||||
\(951\) | 16158.4 | 0.550970 | ||||||||
\(952\) | −5469.99 | −0.186222 | ||||||||
\(953\) | −7005.75 | −0.238131 | −0.119065 | − | 0.992886i | \(-0.537990\pi\) | ||||
−0.119065 | + | 0.992886i | \(0.537990\pi\) | |||||||
\(954\) | 3440.98 | 0.116778 | ||||||||
\(955\) | 586.864 | 0.0198853 | ||||||||
\(956\) | −76995.1 | −2.60481 | ||||||||
\(957\) | 5148.28 | 0.173898 | ||||||||
\(958\) | 20247.7 | 0.682852 | ||||||||
\(959\) | −46538.3 | −1.56705 | ||||||||
\(960\) | −8431.24 | −0.283455 | ||||||||
\(961\) | −6754.32 | −0.226723 | ||||||||
\(962\) | 906.580 | 0.0303839 | ||||||||
\(963\) | −35585.9 | −1.19080 | ||||||||
\(964\) | −23052.9 | −0.770212 | ||||||||
\(965\) | 24604.5 | 0.820775 | ||||||||
\(966\) | −19694.4 | −0.655961 | ||||||||
\(967\) | −19648.3 | −0.653408 | −0.326704 | − | 0.945127i | \(-0.605938\pi\) | ||||
−0.326704 | + | 0.945127i | \(0.605938\pi\) | |||||||
\(968\) | −2003.22 | −0.0665145 | ||||||||
\(969\) | −796.012 | −0.0263897 | ||||||||
\(970\) | 31005.5 | 1.02632 | ||||||||
\(971\) | 6388.43 | 0.211138 | 0.105569 | − | 0.994412i | \(-0.466334\pi\) | ||||
0.105569 | + | 0.994412i | \(0.466334\pi\) | |||||||
\(972\) | −41994.5 | −1.38578 | ||||||||
\(973\) | 38995.3 | 1.28482 | ||||||||
\(974\) | 7488.65 | 0.246357 | ||||||||
\(975\) | 118.913 | 0.00390590 | ||||||||
\(976\) | 3013.17 | 0.0988210 | ||||||||
\(977\) | −33593.0 | −1.10004 | −0.550019 | − | 0.835152i | \(-0.685379\pi\) | ||||
−0.550019 | + | 0.835152i | \(0.685379\pi\) | |||||||
\(978\) | 19613.6 | 0.641281 | ||||||||
\(979\) | −7471.09 | −0.243899 | ||||||||
\(980\) | 4920.11 | 0.160375 | ||||||||
\(981\) | −3312.23 | −0.107800 | ||||||||
\(982\) | 50533.7 | 1.64215 | ||||||||
\(983\) | −16401.3 | −0.532167 | −0.266083 | − | 0.963950i | \(-0.585730\pi\) | ||||
−0.266083 | + | 0.963950i | \(0.585730\pi\) | |||||||
\(984\) | 12227.5 | 0.396135 | ||||||||
\(985\) | 1395.39 | 0.0451380 | ||||||||
\(986\) | −20905.9 | −0.675234 | ||||||||
\(987\) | 3138.90 | 0.101228 | ||||||||
\(988\) | 519.270 | 0.0167208 | ||||||||
\(989\) | −36059.4 | −1.15938 | ||||||||
\(990\) | −5578.06 | −0.179073 | ||||||||
\(991\) | −52043.2 | −1.66822 | −0.834111 | − | 0.551597i | \(-0.814019\pi\) | ||||
−0.834111 | + | 0.551597i | \(0.814019\pi\) | |||||||
\(992\) | 33778.3 | 1.08111 | ||||||||
\(993\) | 18657.3 | 0.596247 | ||||||||
\(994\) | 20578.1 | 0.656639 | ||||||||
\(995\) | −4927.46 | −0.156996 | ||||||||
\(996\) | −14345.6 | −0.456384 | ||||||||
\(997\) | −16321.1 | −0.518448 | −0.259224 | − | 0.965817i | \(-0.583467\pi\) | ||||
−0.259224 | + | 0.965817i | \(0.583467\pi\) | |||||||
\(998\) | −81204.9 | −2.57565 | ||||||||
\(999\) | 8908.64 | 0.282139 |
(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 | 1045.4.a.f.1.4 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.f.1.4 | ✓ | 23 | 1.1 | even | 1 | trivial |