Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,4,Mod(1,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(1.23904011012\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.27492 | −1.86496 | −0.932482 | − | 0.361215i | \(-0.882362\pi\) | ||||
−0.932482 | + | 0.361215i | \(0.882362\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 19.8248 | 2.47809 | ||||||||
\(5\) | 10.5498 | 0.943606 | 0.471803 | − | 0.881704i | \(-0.343603\pi\) | ||||
0.471803 | + | 0.881704i | \(0.343603\pi\) | |||||||
\(6\) | −15.8248 | −1.07674 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −62.3746 | −2.75659 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −55.6495 | −1.75979 | ||||||||
\(11\) | 34.7492 | 0.952479 | 0.476240 | − | 0.879316i | \(-0.342000\pi\) | ||||
0.476240 | + | 0.879316i | \(0.342000\pi\) | |||||||
\(12\) | 59.4743 | 1.43073 | ||||||||
\(13\) | −37.2990 | −0.795760 | −0.397880 | − | 0.917437i | \(-0.630254\pi\) | ||||
−0.397880 | + | 0.917437i | \(0.630254\pi\) | |||||||
\(14\) | −36.9244 | −0.704890 | ||||||||
\(15\) | 31.6495 | 0.544791 | ||||||||
\(16\) | 170.423 | 2.66286 | ||||||||
\(17\) | −10.5498 | −0.150512 | −0.0752562 | − | 0.997164i | \(-0.523977\pi\) | ||||
−0.0752562 | + | 0.997164i | \(0.523977\pi\) | |||||||
\(18\) | −47.4743 | −0.621655 | ||||||||
\(19\) | −58.5980 | −0.707542 | −0.353771 | − | 0.935332i | \(-0.615101\pi\) | ||||
−0.353771 | + | 0.935332i | \(0.615101\pi\) | |||||||
\(20\) | 209.148 | 2.33834 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | −183.299 | −1.77634 | ||||||||
\(23\) | −125.347 | −1.13638 | −0.568189 | − | 0.822898i | \(-0.692356\pi\) | ||||
−0.568189 | + | 0.822898i | \(0.692356\pi\) | |||||||
\(24\) | −187.124 | −1.59152 | ||||||||
\(25\) | −13.7010 | −0.109608 | ||||||||
\(26\) | 196.749 | 1.48406 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 138.773 | 0.936631 | ||||||||
\(29\) | −35.4020 | −0.226689 | −0.113345 | − | 0.993556i | \(-0.536156\pi\) | ||||
−0.113345 | + | 0.993556i | \(0.536156\pi\) | |||||||
\(30\) | −166.949 | −1.01602 | ||||||||
\(31\) | 291.794 | 1.69057 | 0.845286 | − | 0.534313i | \(-0.179430\pi\) | ||||
0.845286 | + | 0.534313i | \(0.179430\pi\) | |||||||
\(32\) | −399.969 | −2.20954 | ||||||||
\(33\) | 104.248 | 0.549914 | ||||||||
\(34\) | 55.6495 | 0.280700 | ||||||||
\(35\) | 73.8488 | 0.356649 | ||||||||
\(36\) | 178.423 | 0.826031 | ||||||||
\(37\) | −259.897 | −1.15478 | −0.577389 | − | 0.816469i | \(-0.695928\pi\) | ||||
−0.577389 | + | 0.816469i | \(0.695928\pi\) | |||||||
\(38\) | 309.100 | 1.31954 | ||||||||
\(39\) | −111.897 | −0.459432 | ||||||||
\(40\) | −658.042 | −2.60114 | ||||||||
\(41\) | −338.248 | −1.28842 | −0.644212 | − | 0.764847i | \(-0.722815\pi\) | ||||
−0.644212 | + | 0.764847i | \(0.722815\pi\) | |||||||
\(42\) | −110.773 | −0.406969 | ||||||||
\(43\) | 6.80397 | 0.0241301 | 0.0120651 | − | 0.999927i | \(-0.496159\pi\) | ||||
0.0120651 | + | 0.999927i | \(0.496159\pi\) | |||||||
\(44\) | 688.894 | 2.36033 | ||||||||
\(45\) | 94.9485 | 0.314535 | ||||||||
\(46\) | 661.196 | 2.11931 | ||||||||
\(47\) | 250.694 | 0.778033 | 0.389016 | − | 0.921231i | \(-0.372815\pi\) | ||||
0.389016 | + | 0.921231i | \(0.372815\pi\) | |||||||
\(48\) | 511.268 | 1.53740 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 72.2716 | 0.204415 | ||||||||
\(51\) | −31.6495 | −0.0868984 | ||||||||
\(52\) | −739.444 | −1.97197 | ||||||||
\(53\) | −536.900 | −1.39149 | −0.695745 | − | 0.718289i | \(-0.744925\pi\) | ||||
−0.695745 | + | 0.718289i | \(0.744925\pi\) | |||||||
\(54\) | −142.423 | −0.358913 | ||||||||
\(55\) | 366.598 | 0.898765 | ||||||||
\(56\) | −436.622 | −1.04189 | ||||||||
\(57\) | −175.794 | −0.408500 | ||||||||
\(58\) | 186.743 | 0.422767 | ||||||||
\(59\) | −35.8904 | −0.0791955 | −0.0395977 | − | 0.999216i | \(-0.512608\pi\) | ||||
−0.0395977 | + | 0.999216i | \(0.512608\pi\) | |||||||
\(60\) | 627.444 | 1.35004 | ||||||||
\(61\) | 57.7940 | 0.121308 | 0.0606538 | − | 0.998159i | \(-0.480681\pi\) | ||||
0.0606538 | + | 0.998159i | \(0.480681\pi\) | |||||||
\(62\) | −1539.19 | −3.15286 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 746.423 | 1.45786 | ||||||||
\(65\) | −393.498 | −0.750884 | ||||||||
\(66\) | −549.897 | −1.02557 | ||||||||
\(67\) | 481.691 | 0.878327 | 0.439164 | − | 0.898407i | \(-0.355275\pi\) | ||||
0.439164 | + | 0.898407i | \(0.355275\pi\) | |||||||
\(68\) | −209.148 | −0.372984 | ||||||||
\(69\) | −376.042 | −0.656088 | ||||||||
\(70\) | −389.547 | −0.665139 | ||||||||
\(71\) | 363.752 | 0.608021 | 0.304010 | − | 0.952669i | \(-0.401674\pi\) | ||||
0.304010 | + | 0.952669i | \(0.401674\pi\) | |||||||
\(72\) | −561.371 | −0.918864 | ||||||||
\(73\) | 581.299 | 0.931999 | 0.465999 | − | 0.884785i | \(-0.345695\pi\) | ||||
0.465999 | + | 0.884785i | \(0.345695\pi\) | |||||||
\(74\) | 1370.94 | 2.15362 | ||||||||
\(75\) | −41.1030 | −0.0632822 | ||||||||
\(76\) | −1161.69 | −1.75336 | ||||||||
\(77\) | 243.244 | 0.360003 | ||||||||
\(78\) | 590.248 | 0.856825 | ||||||||
\(79\) | −693.691 | −0.987928 | −0.493964 | − | 0.869482i | \(-0.664453\pi\) | ||||
−0.493964 | + | 0.869482i | \(0.664453\pi\) | |||||||
\(80\) | 1797.93 | 2.51269 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1784.23 | 2.40287 | ||||||||
\(83\) | 1334.39 | 1.76468 | 0.882341 | − | 0.470611i | \(-0.155967\pi\) | ||||
0.882341 | + | 0.470611i | \(0.155967\pi\) | |||||||
\(84\) | 416.320 | 0.540764 | ||||||||
\(85\) | −111.299 | −0.142024 | ||||||||
\(86\) | −35.8904 | −0.0450019 | ||||||||
\(87\) | −106.206 | −0.130879 | ||||||||
\(88\) | −2167.47 | −2.62560 | ||||||||
\(89\) | −353.038 | −0.420472 | −0.210236 | − | 0.977651i | \(-0.567423\pi\) | ||||
−0.210236 | + | 0.977651i | \(0.567423\pi\) | |||||||
\(90\) | −500.846 | −0.586597 | ||||||||
\(91\) | −261.093 | −0.300769 | ||||||||
\(92\) | −2484.98 | −2.81605 | ||||||||
\(93\) | 875.382 | 0.976053 | ||||||||
\(94\) | −1322.39 | −1.45100 | ||||||||
\(95\) | −618.199 | −0.667641 | ||||||||
\(96\) | −1199.91 | −1.27568 | ||||||||
\(97\) | 1445.88 | 1.51347 | 0.756735 | − | 0.653722i | \(-0.226793\pi\) | ||||
0.756735 | + | 0.653722i | \(0.226793\pi\) | |||||||
\(98\) | −258.471 | −0.266424 | ||||||||
\(99\) | 312.743 | 0.317493 | ||||||||
\(100\) | −271.619 | −0.271619 | ||||||||
\(101\) | 474.852 | 0.467817 | 0.233909 | − | 0.972259i | \(-0.424848\pi\) | ||||
0.233909 | + | 0.972259i | \(0.424848\pi\) | |||||||
\(102\) | 166.949 | 0.162062 | ||||||||
\(103\) | −1999.59 | −1.91287 | −0.956433 | − | 0.291951i | \(-0.905696\pi\) | ||||
−0.956433 | + | 0.291951i | \(0.905696\pi\) | |||||||
\(104\) | 2326.51 | 2.19359 | ||||||||
\(105\) | 221.547 | 0.205912 | ||||||||
\(106\) | 2832.10 | 2.59508 | ||||||||
\(107\) | 1166.74 | 1.05414 | 0.527068 | − | 0.849823i | \(-0.323291\pi\) | ||||
0.527068 | + | 0.849823i | \(0.323291\pi\) | |||||||
\(108\) | 535.268 | 0.476909 | ||||||||
\(109\) | −1337.18 | −1.17503 | −0.587515 | − | 0.809213i | \(-0.699894\pi\) | ||||
−0.587515 | + | 0.809213i | \(0.699894\pi\) | |||||||
\(110\) | −1933.77 | −1.67616 | ||||||||
\(111\) | −779.691 | −0.666712 | ||||||||
\(112\) | 1192.96 | 1.00646 | ||||||||
\(113\) | 906.578 | 0.754723 | 0.377361 | − | 0.926066i | \(-0.376831\pi\) | ||||
0.377361 | + | 0.926066i | \(0.376831\pi\) | |||||||
\(114\) | 927.299 | 0.761838 | ||||||||
\(115\) | −1322.39 | −1.07229 | ||||||||
\(116\) | −701.836 | −0.561757 | ||||||||
\(117\) | −335.691 | −0.265253 | ||||||||
\(118\) | 189.319 | 0.147697 | ||||||||
\(119\) | −73.8488 | −0.0568883 | ||||||||
\(120\) | −1974.12 | −1.50177 | ||||||||
\(121\) | −123.495 | −0.0927836 | ||||||||
\(122\) | −304.859 | −0.226235 | ||||||||
\(123\) | −1014.74 | −0.743872 | ||||||||
\(124\) | 5784.74 | 4.18940 | ||||||||
\(125\) | −1463.27 | −1.04703 | ||||||||
\(126\) | −332.320 | −0.234963 | ||||||||
\(127\) | −1714.89 | −1.19820 | −0.599101 | − | 0.800674i | \(-0.704475\pi\) | ||||
−0.599101 | + | 0.800674i | \(0.704475\pi\) | |||||||
\(128\) | −737.564 | −0.509313 | ||||||||
\(129\) | 20.4119 | 0.0139315 | ||||||||
\(130\) | 2075.67 | 1.40037 | ||||||||
\(131\) | 470.611 | 0.313874 | 0.156937 | − | 0.987609i | \(-0.449838\pi\) | ||||
0.156937 | + | 0.987609i | \(0.449838\pi\) | |||||||
\(132\) | 2066.68 | 1.36274 | ||||||||
\(133\) | −410.186 | −0.267426 | ||||||||
\(134\) | −2540.88 | −1.63805 | ||||||||
\(135\) | 284.846 | 0.181597 | ||||||||
\(136\) | 658.042 | 0.414901 | ||||||||
\(137\) | −443.910 | −0.276831 | −0.138415 | − | 0.990374i | \(-0.544201\pi\) | ||||
−0.138415 | + | 0.990374i | \(0.544201\pi\) | |||||||
\(138\) | 1983.59 | 1.22358 | ||||||||
\(139\) | 1669.98 | 1.01904 | 0.509518 | − | 0.860460i | \(-0.329824\pi\) | ||||
0.509518 | + | 0.860460i | \(0.329824\pi\) | |||||||
\(140\) | 1464.03 | 0.883811 | ||||||||
\(141\) | 752.083 | 0.449197 | ||||||||
\(142\) | −1918.76 | −1.13394 | ||||||||
\(143\) | −1296.11 | −0.757945 | ||||||||
\(144\) | 1533.80 | 0.887619 | ||||||||
\(145\) | −373.485 | −0.213905 | ||||||||
\(146\) | −3066.30 | −1.73814 | ||||||||
\(147\) | 147.000 | 0.0824786 | ||||||||
\(148\) | −5152.39 | −2.86165 | ||||||||
\(149\) | 743.871 | 0.408995 | 0.204497 | − | 0.978867i | \(-0.434444\pi\) | ||||
0.204497 | + | 0.978867i | \(0.434444\pi\) | |||||||
\(150\) | 216.815 | 0.118019 | ||||||||
\(151\) | 606.764 | 0.327005 | 0.163503 | − | 0.986543i | \(-0.447721\pi\) | ||||
0.163503 | + | 0.986543i | \(0.447721\pi\) | |||||||
\(152\) | 3655.03 | 1.95041 | ||||||||
\(153\) | −94.9485 | −0.0501708 | ||||||||
\(154\) | −1283.09 | −0.671393 | ||||||||
\(155\) | 3078.38 | 1.59523 | ||||||||
\(156\) | −2218.33 | −1.13852 | ||||||||
\(157\) | 3114.78 | 1.58336 | 0.791678 | − | 0.610939i | \(-0.209208\pi\) | ||||
0.791678 | + | 0.610939i | \(0.209208\pi\) | |||||||
\(158\) | 3659.16 | 1.84245 | ||||||||
\(159\) | −1610.70 | −0.803377 | ||||||||
\(160\) | −4219.61 | −2.08493 | ||||||||
\(161\) | −877.430 | −0.429511 | ||||||||
\(162\) | −427.268 | −0.207218 | ||||||||
\(163\) | 2413.07 | 1.15955 | 0.579774 | − | 0.814777i | \(-0.303141\pi\) | ||||
0.579774 | + | 0.814777i | \(0.303141\pi\) | |||||||
\(164\) | −6705.67 | −3.19284 | ||||||||
\(165\) | 1099.79 | 0.518902 | ||||||||
\(166\) | −7038.81 | −3.29107 | ||||||||
\(167\) | −610.475 | −0.282874 | −0.141437 | − | 0.989947i | \(-0.545172\pi\) | ||||
−0.141437 | + | 0.989947i | \(0.545172\pi\) | |||||||
\(168\) | −1309.87 | −0.601538 | ||||||||
\(169\) | −805.784 | −0.366766 | ||||||||
\(170\) | 587.093 | 0.264870 | ||||||||
\(171\) | −527.382 | −0.235847 | ||||||||
\(172\) | 134.887 | 0.0597968 | ||||||||
\(173\) | 3793.81 | 1.66727 | 0.833636 | − | 0.552315i | \(-0.186255\pi\) | ||||
0.833636 | + | 0.552315i | \(0.186255\pi\) | |||||||
\(174\) | 560.228 | 0.244085 | ||||||||
\(175\) | −95.9070 | −0.0414279 | ||||||||
\(176\) | 5922.05 | 2.53631 | ||||||||
\(177\) | −107.671 | −0.0457235 | ||||||||
\(178\) | 1862.25 | 0.784165 | ||||||||
\(179\) | −2804.68 | −1.17112 | −0.585562 | − | 0.810627i | \(-0.699126\pi\) | ||||
−0.585562 | + | 0.810627i | \(0.699126\pi\) | |||||||
\(180\) | 1882.33 | 0.779448 | ||||||||
\(181\) | 3106.04 | 1.27553 | 0.637763 | − | 0.770232i | \(-0.279860\pi\) | ||||
0.637763 | + | 0.770232i | \(0.279860\pi\) | |||||||
\(182\) | 1377.24 | 0.560924 | ||||||||
\(183\) | 173.382 | 0.0700370 | ||||||||
\(184\) | 7818.48 | 3.13253 | ||||||||
\(185\) | −2741.87 | −1.08966 | ||||||||
\(186\) | −4617.57 | −1.82030 | ||||||||
\(187\) | −366.598 | −0.143360 | ||||||||
\(188\) | 4969.95 | 1.92804 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 3260.95 | 1.24513 | ||||||||
\(191\) | 261.952 | 0.0992365 | 0.0496182 | − | 0.998768i | \(-0.484200\pi\) | ||||
0.0496182 | + | 0.998768i | \(0.484200\pi\) | |||||||
\(192\) | 2239.27 | 0.841694 | ||||||||
\(193\) | 4051.07 | 1.51089 | 0.755447 | − | 0.655210i | \(-0.227420\pi\) | ||||
0.755447 | + | 0.655210i | \(0.227420\pi\) | |||||||
\(194\) | −7626.88 | −2.82257 | ||||||||
\(195\) | −1180.50 | −0.433523 | ||||||||
\(196\) | 971.413 | 0.354013 | ||||||||
\(197\) | −2874.83 | −1.03971 | −0.519855 | − | 0.854254i | \(-0.674014\pi\) | ||||
−0.519855 | + | 0.854254i | \(0.674014\pi\) | |||||||
\(198\) | −1649.69 | −0.592113 | ||||||||
\(199\) | −3066.97 | −1.09252 | −0.546261 | − | 0.837615i | \(-0.683949\pi\) | ||||
−0.546261 | + | 0.837615i | \(0.683949\pi\) | |||||||
\(200\) | 854.594 | 0.302145 | ||||||||
\(201\) | 1445.07 | 0.507103 | ||||||||
\(202\) | −2504.81 | −0.872463 | ||||||||
\(203\) | −247.814 | −0.0856804 | ||||||||
\(204\) | −627.444 | −0.215342 | ||||||||
\(205\) | −3568.46 | −1.21576 | ||||||||
\(206\) | 10547.7 | 3.56743 | ||||||||
\(207\) | −1128.12 | −0.378793 | ||||||||
\(208\) | −6356.60 | −2.11899 | ||||||||
\(209\) | −2036.23 | −0.673919 | ||||||||
\(210\) | −1168.64 | −0.384018 | ||||||||
\(211\) | 595.422 | 0.194268 | 0.0971340 | − | 0.995271i | \(-0.469032\pi\) | ||||
0.0971340 | + | 0.995271i | \(0.469032\pi\) | |||||||
\(212\) | −10643.9 | −3.44824 | ||||||||
\(213\) | 1091.26 | 0.351041 | ||||||||
\(214\) | −6154.44 | −1.96593 | ||||||||
\(215\) | 71.7808 | 0.0227693 | ||||||||
\(216\) | −1684.11 | −0.530507 | ||||||||
\(217\) | 2042.56 | 0.638976 | ||||||||
\(218\) | 7053.49 | 2.19139 | ||||||||
\(219\) | 1743.90 | 0.538090 | ||||||||
\(220\) | 7267.71 | 2.22722 | ||||||||
\(221\) | 393.498 | 0.119772 | ||||||||
\(222\) | 4112.81 | 1.24339 | ||||||||
\(223\) | −3779.79 | −1.13504 | −0.567520 | − | 0.823360i | \(-0.692097\pi\) | ||||
−0.567520 | + | 0.823360i | \(0.692097\pi\) | |||||||
\(224\) | −2799.79 | −0.835127 | ||||||||
\(225\) | −123.309 | −0.0365360 | ||||||||
\(226\) | −4782.12 | −1.40753 | ||||||||
\(227\) | 1827.62 | 0.534376 | 0.267188 | − | 0.963644i | \(-0.413906\pi\) | ||||
0.267188 | + | 0.963644i | \(0.413906\pi\) | |||||||
\(228\) | −3485.07 | −1.01230 | ||||||||
\(229\) | −850.249 | −0.245354 | −0.122677 | − | 0.992447i | \(-0.539148\pi\) | ||||
−0.122677 | + | 0.992447i | \(0.539148\pi\) | |||||||
\(230\) | 6975.51 | 1.99979 | ||||||||
\(231\) | 729.733 | 0.207848 | ||||||||
\(232\) | 2208.18 | 0.624890 | ||||||||
\(233\) | −6591.10 | −1.85321 | −0.926604 | − | 0.376039i | \(-0.877286\pi\) | ||||
−0.926604 | + | 0.376039i | \(0.877286\pi\) | |||||||
\(234\) | 1770.74 | 0.494688 | ||||||||
\(235\) | 2644.78 | 0.734156 | ||||||||
\(236\) | −711.518 | −0.196254 | ||||||||
\(237\) | −2081.07 | −0.570381 | ||||||||
\(238\) | 389.547 | 0.106095 | ||||||||
\(239\) | −182.556 | −0.0494083 | −0.0247042 | − | 0.999695i | \(-0.507864\pi\) | ||||
−0.0247042 | + | 0.999695i | \(0.507864\pi\) | |||||||
\(240\) | 5393.80 | 1.45070 | ||||||||
\(241\) | 1523.90 | 0.407315 | 0.203657 | − | 0.979042i | \(-0.434717\pi\) | ||||
0.203657 | + | 0.979042i | \(0.434717\pi\) | |||||||
\(242\) | 651.426 | 0.173038 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 1145.75 | 0.300612 | ||||||||
\(245\) | 516.942 | 0.134801 | ||||||||
\(246\) | 5352.68 | 1.38730 | ||||||||
\(247\) | 2185.65 | 0.563034 | ||||||||
\(248\) | −18200.5 | −4.66022 | ||||||||
\(249\) | 4003.18 | 1.01884 | ||||||||
\(250\) | 7718.64 | 1.95268 | ||||||||
\(251\) | 2357.73 | 0.592903 | 0.296451 | − | 0.955048i | \(-0.404197\pi\) | ||||
0.296451 | + | 0.955048i | \(0.404197\pi\) | |||||||
\(252\) | 1248.96 | 0.312210 | ||||||||
\(253\) | −4355.71 | −1.08238 | ||||||||
\(254\) | 9045.89 | 2.23460 | ||||||||
\(255\) | −333.897 | −0.0819978 | ||||||||
\(256\) | −2080.79 | −0.508006 | ||||||||
\(257\) | 2782.55 | 0.675372 | 0.337686 | − | 0.941259i | \(-0.390356\pi\) | ||||
0.337686 | + | 0.941259i | \(0.390356\pi\) | |||||||
\(258\) | −107.671 | −0.0259818 | ||||||||
\(259\) | −1819.28 | −0.436465 | ||||||||
\(260\) | −7801.01 | −1.86076 | ||||||||
\(261\) | −318.618 | −0.0755630 | ||||||||
\(262\) | −2482.44 | −0.585364 | ||||||||
\(263\) | 2043.78 | 0.479183 | 0.239591 | − | 0.970874i | \(-0.422987\pi\) | ||||
0.239591 | + | 0.970874i | \(0.422987\pi\) | |||||||
\(264\) | −6502.40 | −1.51589 | ||||||||
\(265\) | −5664.21 | −1.31302 | ||||||||
\(266\) | 2163.70 | 0.498740 | ||||||||
\(267\) | −1059.11 | −0.242759 | ||||||||
\(268\) | 9549.41 | 2.17658 | ||||||||
\(269\) | 3452.84 | 0.782614 | 0.391307 | − | 0.920260i | \(-0.372023\pi\) | ||||
0.391307 | + | 0.920260i | \(0.372023\pi\) | |||||||
\(270\) | −1502.54 | −0.338672 | ||||||||
\(271\) | 2644.29 | 0.592728 | 0.296364 | − | 0.955075i | \(-0.404226\pi\) | ||||
0.296364 | + | 0.955075i | \(0.404226\pi\) | |||||||
\(272\) | −1797.93 | −0.400793 | ||||||||
\(273\) | −783.279 | −0.173649 | ||||||||
\(274\) | 2341.59 | 0.516280 | ||||||||
\(275\) | −476.098 | −0.104399 | ||||||||
\(276\) | −7454.93 | −1.62585 | ||||||||
\(277\) | 2679.49 | 0.581208 | 0.290604 | − | 0.956843i | \(-0.406144\pi\) | ||||
0.290604 | + | 0.956843i | \(0.406144\pi\) | |||||||
\(278\) | −8809.01 | −1.90046 | ||||||||
\(279\) | 2626.15 | 0.563524 | ||||||||
\(280\) | −4606.29 | −0.983138 | ||||||||
\(281\) | −1019.69 | −0.216476 | −0.108238 | − | 0.994125i | \(-0.534521\pi\) | ||||
−0.108238 | + | 0.994125i | \(0.534521\pi\) | |||||||
\(282\) | −3967.18 | −0.837737 | ||||||||
\(283\) | 432.206 | 0.0907844 | 0.0453922 | − | 0.998969i | \(-0.485546\pi\) | ||||
0.0453922 | + | 0.998969i | \(0.485546\pi\) | |||||||
\(284\) | 7211.30 | 1.50673 | ||||||||
\(285\) | −1854.60 | −0.385463 | ||||||||
\(286\) | 6836.87 | 1.41354 | ||||||||
\(287\) | −2367.73 | −0.486979 | ||||||||
\(288\) | −3599.72 | −0.736513 | ||||||||
\(289\) | −4801.70 | −0.977346 | ||||||||
\(290\) | 1970.10 | 0.398926 | ||||||||
\(291\) | 4337.63 | 0.873802 | ||||||||
\(292\) | 11524.1 | 2.30958 | ||||||||
\(293\) | −2245.92 | −0.447809 | −0.223904 | − | 0.974611i | \(-0.571880\pi\) | ||||
−0.223904 | + | 0.974611i | \(0.571880\pi\) | |||||||
\(294\) | −775.413 | −0.153820 | ||||||||
\(295\) | −378.638 | −0.0747293 | ||||||||
\(296\) | 16211.0 | 3.18325 | ||||||||
\(297\) | 938.228 | 0.183305 | ||||||||
\(298\) | −3923.86 | −0.762761 | ||||||||
\(299\) | 4675.33 | 0.904284 | ||||||||
\(300\) | −814.856 | −0.156819 | ||||||||
\(301\) | 47.6278 | 0.00912034 | ||||||||
\(302\) | −3200.63 | −0.609853 | ||||||||
\(303\) | 1424.56 | 0.270094 | ||||||||
\(304\) | −9986.44 | −1.88408 | ||||||||
\(305\) | 609.718 | 0.114467 | ||||||||
\(306\) | 500.846 | 0.0935668 | ||||||||
\(307\) | −3197.08 | −0.594354 | −0.297177 | − | 0.954822i | \(-0.596045\pi\) | ||||
−0.297177 | + | 0.954822i | \(0.596045\pi\) | |||||||
\(308\) | 4822.26 | 0.892122 | ||||||||
\(309\) | −5998.76 | −1.10439 | ||||||||
\(310\) | −16238.2 | −2.97506 | ||||||||
\(311\) | −3355.60 | −0.611829 | −0.305915 | − | 0.952059i | \(-0.598962\pi\) | ||||
−0.305915 | + | 0.952059i | \(0.598962\pi\) | |||||||
\(312\) | 6979.53 | 1.26647 | ||||||||
\(313\) | −2256.39 | −0.407472 | −0.203736 | − | 0.979026i | \(-0.565308\pi\) | ||||
−0.203736 | + | 0.979026i | \(0.565308\pi\) | |||||||
\(314\) | −16430.2 | −2.95290 | ||||||||
\(315\) | 664.640 | 0.118883 | ||||||||
\(316\) | −13752.3 | −2.44818 | ||||||||
\(317\) | −6139.19 | −1.08773 | −0.543866 | − | 0.839172i | \(-0.683040\pi\) | ||||
−0.543866 | + | 0.839172i | \(0.683040\pi\) | |||||||
\(318\) | 8496.31 | 1.49827 | ||||||||
\(319\) | −1230.19 | −0.215917 | ||||||||
\(320\) | 7874.64 | 1.37564 | ||||||||
\(321\) | 3500.21 | 0.608606 | ||||||||
\(322\) | 4628.37 | 0.801022 | ||||||||
\(323\) | 618.199 | 0.106494 | ||||||||
\(324\) | 1605.80 | 0.275344 | ||||||||
\(325\) | 511.033 | 0.0872216 | ||||||||
\(326\) | −12728.8 | −2.16252 | ||||||||
\(327\) | −4011.53 | −0.678404 | ||||||||
\(328\) | 21098.0 | 3.55166 | ||||||||
\(329\) | 1754.86 | 0.294069 | ||||||||
\(330\) | −5801.32 | −0.967734 | ||||||||
\(331\) | 7029.81 | 1.16735 | 0.583676 | − | 0.811987i | \(-0.301614\pi\) | ||||
0.583676 | + | 0.811987i | \(0.301614\pi\) | |||||||
\(332\) | 26454.0 | 4.37305 | ||||||||
\(333\) | −2339.07 | −0.384926 | ||||||||
\(334\) | 3220.21 | 0.527550 | ||||||||
\(335\) | 5081.76 | 0.828795 | ||||||||
\(336\) | 3578.88 | 0.581083 | ||||||||
\(337\) | 10328.4 | 1.66951 | 0.834757 | − | 0.550619i | \(-0.185608\pi\) | ||||
0.834757 | + | 0.550619i | \(0.185608\pi\) | |||||||
\(338\) | 4250.44 | 0.684005 | ||||||||
\(339\) | 2719.73 | 0.435740 | ||||||||
\(340\) | −2206.48 | −0.351950 | ||||||||
\(341\) | 10139.6 | 1.61024 | ||||||||
\(342\) | 2781.90 | 0.439847 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −424.395 | −0.0665170 | ||||||||
\(345\) | −3967.18 | −0.619089 | ||||||||
\(346\) | −20012.0 | −3.10940 | ||||||||
\(347\) | 1967.54 | 0.304389 | 0.152194 | − | 0.988351i | \(-0.451366\pi\) | ||||
0.152194 | + | 0.988351i | \(0.451366\pi\) | |||||||
\(348\) | −2105.51 | −0.324330 | ||||||||
\(349\) | −4365.46 | −0.669564 | −0.334782 | − | 0.942296i | \(-0.608663\pi\) | ||||
−0.334782 | + | 0.942296i | \(0.608663\pi\) | |||||||
\(350\) | 505.901 | 0.0772616 | ||||||||
\(351\) | −1007.07 | −0.153144 | ||||||||
\(352\) | −13898.6 | −2.10454 | ||||||||
\(353\) | −6071.59 | −0.915462 | −0.457731 | − | 0.889091i | \(-0.651338\pi\) | ||||
−0.457731 | + | 0.889091i | \(0.651338\pi\) | |||||||
\(354\) | 567.957 | 0.0852728 | ||||||||
\(355\) | 3837.53 | 0.573732 | ||||||||
\(356\) | −6998.90 | −1.04197 | ||||||||
\(357\) | −221.547 | −0.0328445 | ||||||||
\(358\) | 14794.4 | 2.18411 | ||||||||
\(359\) | 9638.04 | 1.41693 | 0.708463 | − | 0.705748i | \(-0.249389\pi\) | ||||
0.708463 | + | 0.705748i | \(0.249389\pi\) | |||||||
\(360\) | −5922.37 | −0.867046 | ||||||||
\(361\) | −3425.27 | −0.499384 | ||||||||
\(362\) | −16384.1 | −2.37881 | ||||||||
\(363\) | −370.485 | −0.0535687 | ||||||||
\(364\) | −5176.10 | −0.745334 | ||||||||
\(365\) | 6132.61 | 0.879439 | ||||||||
\(366\) | −914.576 | −0.130617 | ||||||||
\(367\) | 522.725 | 0.0743488 | 0.0371744 | − | 0.999309i | \(-0.488164\pi\) | ||||
0.0371744 | + | 0.999309i | \(0.488164\pi\) | |||||||
\(368\) | −21362.0 | −3.02601 | ||||||||
\(369\) | −3044.23 | −0.429475 | ||||||||
\(370\) | 14463.1 | 2.03217 | ||||||||
\(371\) | −3758.30 | −0.525934 | ||||||||
\(372\) | 17354.2 | 2.41875 | ||||||||
\(373\) | 3229.84 | 0.448351 | 0.224175 | − | 0.974549i | \(-0.428031\pi\) | ||||
0.224175 | + | 0.974549i | \(0.428031\pi\) | |||||||
\(374\) | 1933.77 | 0.267361 | ||||||||
\(375\) | −4389.82 | −0.604505 | ||||||||
\(376\) | −15637.0 | −2.14472 | ||||||||
\(377\) | 1320.46 | 0.180390 | ||||||||
\(378\) | −996.959 | −0.135656 | ||||||||
\(379\) | 6639.71 | 0.899892 | 0.449946 | − | 0.893056i | \(-0.351443\pi\) | ||||
0.449946 | + | 0.893056i | \(0.351443\pi\) | |||||||
\(380\) | −12255.6 | −1.65448 | ||||||||
\(381\) | −5144.66 | −0.691782 | ||||||||
\(382\) | −1381.77 | −0.185073 | ||||||||
\(383\) | −14224.4 | −1.89774 | −0.948871 | − | 0.315664i | \(-0.897773\pi\) | ||||
−0.948871 | + | 0.315664i | \(0.897773\pi\) | |||||||
\(384\) | −2212.69 | −0.294052 | ||||||||
\(385\) | 2566.19 | 0.339701 | ||||||||
\(386\) | −21369.1 | −2.81777 | ||||||||
\(387\) | 61.2358 | 0.00804338 | ||||||||
\(388\) | 28664.2 | 3.75052 | ||||||||
\(389\) | 2921.82 | 0.380828 | 0.190414 | − | 0.981704i | \(-0.439017\pi\) | ||||
0.190414 | + | 0.981704i | \(0.439017\pi\) | |||||||
\(390\) | 6227.01 | 0.808505 | ||||||||
\(391\) | 1322.39 | 0.171039 | ||||||||
\(392\) | −3056.35 | −0.393799 | ||||||||
\(393\) | 1411.83 | 0.181215 | ||||||||
\(394\) | 15164.5 | 1.93902 | ||||||||
\(395\) | −7318.33 | −0.932215 | ||||||||
\(396\) | 6200.04 | 0.786778 | ||||||||
\(397\) | 811.940 | 0.102645 | 0.0513226 | − | 0.998682i | \(-0.483656\pi\) | ||||
0.0513226 | + | 0.998682i | \(0.483656\pi\) | |||||||
\(398\) | 16178.0 | 2.03751 | ||||||||
\(399\) | −1230.56 | −0.154398 | ||||||||
\(400\) | −2334.96 | −0.291870 | ||||||||
\(401\) | 2338.63 | 0.291237 | 0.145618 | − | 0.989341i | \(-0.453483\pi\) | ||||
0.145618 | + | 0.989341i | \(0.453483\pi\) | |||||||
\(402\) | −7622.64 | −0.945728 | ||||||||
\(403\) | −10883.6 | −1.34529 | ||||||||
\(404\) | 9413.83 | 1.15930 | ||||||||
\(405\) | 854.537 | 0.104845 | ||||||||
\(406\) | 1307.20 | 0.159791 | ||||||||
\(407\) | −9031.21 | −1.09990 | ||||||||
\(408\) | 1974.12 | 0.239543 | ||||||||
\(409\) | −2727.57 | −0.329755 | −0.164877 | − | 0.986314i | \(-0.552723\pi\) | ||||
−0.164877 | + | 0.986314i | \(0.552723\pi\) | |||||||
\(410\) | 18823.3 | 2.26736 | ||||||||
\(411\) | −1331.73 | −0.159828 | ||||||||
\(412\) | −39641.3 | −4.74026 | ||||||||
\(413\) | −251.233 | −0.0299331 | ||||||||
\(414\) | 5950.76 | 0.706435 | ||||||||
\(415\) | 14077.6 | 1.66516 | ||||||||
\(416\) | 14918.5 | 1.75826 | ||||||||
\(417\) | 5009.94 | 0.588340 | ||||||||
\(418\) | 10741.0 | 1.25684 | ||||||||
\(419\) | 13306.3 | 1.55144 | 0.775721 | − | 0.631076i | \(-0.217386\pi\) | ||||
0.775721 | + | 0.631076i | \(0.217386\pi\) | |||||||
\(420\) | 4392.10 | 0.510268 | ||||||||
\(421\) | −11007.5 | −1.27428 | −0.637138 | − | 0.770750i | \(-0.719882\pi\) | ||||
−0.637138 | + | 0.770750i | \(0.719882\pi\) | |||||||
\(422\) | −3140.80 | −0.362303 | ||||||||
\(423\) | 2256.25 | 0.259344 | ||||||||
\(424\) | 33488.9 | 3.83577 | ||||||||
\(425\) | 144.543 | 0.0164974 | ||||||||
\(426\) | −5756.29 | −0.654679 | ||||||||
\(427\) | 404.558 | 0.0458500 | ||||||||
\(428\) | 23130.2 | 2.61225 | ||||||||
\(429\) | −3888.33 | −0.437600 | ||||||||
\(430\) | −378.638 | −0.0424640 | ||||||||
\(431\) | −6525.62 | −0.729300 | −0.364650 | − | 0.931145i | \(-0.618811\pi\) | ||||
−0.364650 | + | 0.931145i | \(0.618811\pi\) | |||||||
\(432\) | 4601.41 | 0.512467 | ||||||||
\(433\) | −11716.3 | −1.30034 | −0.650171 | − | 0.759788i | \(-0.725303\pi\) | ||||
−0.650171 | + | 0.759788i | \(0.725303\pi\) | |||||||
\(434\) | −10774.3 | −1.19167 | ||||||||
\(435\) | −1120.46 | −0.123498 | ||||||||
\(436\) | −26509.2 | −2.91183 | ||||||||
\(437\) | 7345.10 | 0.804036 | ||||||||
\(438\) | −9198.91 | −1.00352 | ||||||||
\(439\) | −14611.4 | −1.58853 | −0.794264 | − | 0.607573i | \(-0.792143\pi\) | ||||
−0.794264 | + | 0.607573i | \(0.792143\pi\) | |||||||
\(440\) | −22866.4 | −2.47753 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −2075.67 | −0.223370 | ||||||||
\(443\) | −15239.8 | −1.63446 | −0.817228 | − | 0.576314i | \(-0.804490\pi\) | ||||
−0.817228 | + | 0.576314i | \(0.804490\pi\) | |||||||
\(444\) | −15457.2 | −1.65217 | ||||||||
\(445\) | −3724.50 | −0.396760 | ||||||||
\(446\) | 19938.1 | 2.11681 | ||||||||
\(447\) | 2231.61 | 0.236133 | ||||||||
\(448\) | 5224.96 | 0.551018 | ||||||||
\(449\) | 10678.8 | 1.12241 | 0.561206 | − | 0.827676i | \(-0.310338\pi\) | ||||
0.561206 | + | 0.827676i | \(0.310338\pi\) | |||||||
\(450\) | 650.444 | 0.0681383 | ||||||||
\(451\) | −11753.8 | −1.22720 | ||||||||
\(452\) | 17972.7 | 1.87027 | ||||||||
\(453\) | 1820.29 | 0.188796 | ||||||||
\(454\) | −9640.53 | −0.996592 | ||||||||
\(455\) | −2754.49 | −0.283807 | ||||||||
\(456\) | 10965.1 | 1.12607 | ||||||||
\(457\) | 4228.23 | 0.432797 | 0.216399 | − | 0.976305i | \(-0.430569\pi\) | ||||
0.216399 | + | 0.976305i | \(0.430569\pi\) | |||||||
\(458\) | 4484.99 | 0.457577 | ||||||||
\(459\) | −284.846 | −0.0289661 | ||||||||
\(460\) | −26216.1 | −2.65724 | ||||||||
\(461\) | 910.121 | 0.0919492 | 0.0459746 | − | 0.998943i | \(-0.485361\pi\) | ||||
0.0459746 | + | 0.998943i | \(0.485361\pi\) | |||||||
\(462\) | −3849.28 | −0.387629 | ||||||||
\(463\) | 4456.16 | 0.447290 | 0.223645 | − | 0.974671i | \(-0.428204\pi\) | ||||
0.223645 | + | 0.974671i | \(0.428204\pi\) | |||||||
\(464\) | −6033.30 | −0.603640 | ||||||||
\(465\) | 9235.14 | 0.921009 | ||||||||
\(466\) | 34767.5 | 3.45617 | ||||||||
\(467\) | −4429.42 | −0.438907 | −0.219453 | − | 0.975623i | \(-0.570427\pi\) | ||||
−0.219453 | + | 0.975623i | \(0.570427\pi\) | |||||||
\(468\) | −6654.99 | −0.657323 | ||||||||
\(469\) | 3371.84 | 0.331977 | ||||||||
\(470\) | −13951.0 | −1.36918 | ||||||||
\(471\) | 9344.35 | 0.914151 | ||||||||
\(472\) | 2238.65 | 0.218310 | ||||||||
\(473\) | 236.432 | 0.0229835 | ||||||||
\(474\) | 10977.5 | 1.06374 | ||||||||
\(475\) | 802.851 | 0.0775523 | ||||||||
\(476\) | −1464.03 | −0.140975 | ||||||||
\(477\) | −4832.10 | −0.463830 | ||||||||
\(478\) | 962.970 | 0.0921448 | ||||||||
\(479\) | 2752.85 | 0.262591 | 0.131296 | − | 0.991343i | \(-0.458086\pi\) | ||||
0.131296 | + | 0.991343i | \(0.458086\pi\) | |||||||
\(480\) | −12658.8 | −1.20374 | ||||||||
\(481\) | 9693.90 | 0.918927 | ||||||||
\(482\) | −8038.43 | −0.759628 | ||||||||
\(483\) | −2632.29 | −0.247978 | ||||||||
\(484\) | −2448.26 | −0.229927 | ||||||||
\(485\) | 15253.8 | 1.42812 | ||||||||
\(486\) | −1281.80 | −0.119638 | ||||||||
\(487\) | −670.598 | −0.0623977 | −0.0311989 | − | 0.999513i | \(-0.509933\pi\) | ||||
−0.0311989 | + | 0.999513i | \(0.509933\pi\) | |||||||
\(488\) | −3604.88 | −0.334396 | ||||||||
\(489\) | 7239.22 | 0.669466 | ||||||||
\(490\) | −2726.83 | −0.251399 | ||||||||
\(491\) | −8244.70 | −0.757797 | −0.378898 | − | 0.925438i | \(-0.623697\pi\) | ||||
−0.378898 | + | 0.925438i | \(0.623697\pi\) | |||||||
\(492\) | −20117.0 | −1.84338 | ||||||||
\(493\) | 373.485 | 0.0341195 | ||||||||
\(494\) | −11529.1 | −1.05004 | ||||||||
\(495\) | 3299.38 | 0.299588 | ||||||||
\(496\) | 49728.3 | 4.50175 | ||||||||
\(497\) | 2546.27 | 0.229810 | ||||||||
\(498\) | −21116.4 | −1.90010 | ||||||||
\(499\) | 8164.91 | 0.732488 | 0.366244 | − | 0.930519i | \(-0.380644\pi\) | ||||
0.366244 | + | 0.930519i | \(0.380644\pi\) | |||||||
\(500\) | −29009.0 | −2.59465 | ||||||||
\(501\) | −1831.43 | −0.163317 | ||||||||
\(502\) | −12436.8 | −1.10574 | ||||||||
\(503\) | 8175.59 | 0.724715 | 0.362357 | − | 0.932039i | \(-0.381972\pi\) | ||||
0.362357 | + | 0.932039i | \(0.381972\pi\) | |||||||
\(504\) | −3929.60 | −0.347298 | ||||||||
\(505\) | 5009.61 | 0.441435 | ||||||||
\(506\) | 22976.0 | 2.01859 | ||||||||
\(507\) | −2417.35 | −0.211752 | ||||||||
\(508\) | −33997.2 | −2.96926 | ||||||||
\(509\) | −878.448 | −0.0764961 | −0.0382480 | − | 0.999268i | \(-0.512178\pi\) | ||||
−0.0382480 | + | 0.999268i | \(0.512178\pi\) | |||||||
\(510\) | 1761.28 | 0.152923 | ||||||||
\(511\) | 4069.09 | 0.352262 | ||||||||
\(512\) | 16876.5 | 1.45673 | ||||||||
\(513\) | −1582.15 | −0.136167 | ||||||||
\(514\) | −14677.7 | −1.25955 | ||||||||
\(515\) | −21095.3 | −1.80499 | ||||||||
\(516\) | 404.661 | 0.0345237 | ||||||||
\(517\) | 8711.42 | 0.741060 | ||||||||
\(518\) | 9596.55 | 0.813992 | ||||||||
\(519\) | 11381.4 | 0.962600 | ||||||||
\(520\) | 24544.3 | 2.06988 | ||||||||
\(521\) | 11712.6 | 0.984910 | 0.492455 | − | 0.870338i | \(-0.336100\pi\) | ||||
0.492455 | + | 0.870338i | \(0.336100\pi\) | |||||||
\(522\) | 1680.68 | 0.140922 | ||||||||
\(523\) | −7341.82 | −0.613834 | −0.306917 | − | 0.951736i | \(-0.599297\pi\) | ||||
−0.306917 | + | 0.951736i | \(0.599297\pi\) | |||||||
\(524\) | 9329.75 | 0.777809 | ||||||||
\(525\) | −287.721 | −0.0239184 | ||||||||
\(526\) | −10780.8 | −0.893659 | ||||||||
\(527\) | −3078.38 | −0.254452 | ||||||||
\(528\) | 17766.1 | 1.46434 | ||||||||
\(529\) | 3544.92 | 0.291355 | ||||||||
\(530\) | 29878.2 | 2.44873 | ||||||||
\(531\) | −323.014 | −0.0263985 | ||||||||
\(532\) | −8131.84 | −0.662707 | ||||||||
\(533\) | 12616.3 | 1.02528 | ||||||||
\(534\) | 5586.74 | 0.452738 | ||||||||
\(535\) | 12308.9 | 0.994690 | ||||||||
\(536\) | −30045.3 | −2.42119 | ||||||||
\(537\) | −8414.03 | −0.676149 | ||||||||
\(538\) | −18213.4 | −1.45955 | ||||||||
\(539\) | 1702.71 | 0.136068 | ||||||||
\(540\) | 5646.99 | 0.450015 | ||||||||
\(541\) | −15868.7 | −1.26109 | −0.630545 | − | 0.776153i | \(-0.717169\pi\) | ||||
−0.630545 | + | 0.776153i | \(0.717169\pi\) | |||||||
\(542\) | −13948.4 | −1.10542 | ||||||||
\(543\) | 9318.13 | 0.736426 | ||||||||
\(544\) | 4219.61 | 0.332563 | ||||||||
\(545\) | −14107.0 | −1.10877 | ||||||||
\(546\) | 4131.73 | 0.323850 | ||||||||
\(547\) | 2315.26 | 0.180975 | 0.0904875 | − | 0.995898i | \(-0.471157\pi\) | ||||
0.0904875 | + | 0.995898i | \(0.471157\pi\) | |||||||
\(548\) | −8800.41 | −0.686013 | ||||||||
\(549\) | 520.146 | 0.0404359 | ||||||||
\(550\) | 2511.38 | 0.194701 | ||||||||
\(551\) | 2074.49 | 0.160392 | ||||||||
\(552\) | 23455.4 | 1.80857 | ||||||||
\(553\) | −4855.84 | −0.373402 | ||||||||
\(554\) | −14134.1 | −1.08393 | ||||||||
\(555\) | −8225.61 | −0.629113 | ||||||||
\(556\) | 33106.9 | 2.52526 | ||||||||
\(557\) | −4819.05 | −0.366588 | −0.183294 | − | 0.983058i | \(-0.558676\pi\) | ||||
−0.183294 | + | 0.983058i | \(0.558676\pi\) | |||||||
\(558\) | −13852.7 | −1.05095 | ||||||||
\(559\) | −253.781 | −0.0192018 | ||||||||
\(560\) | 12585.5 | 0.949706 | ||||||||
\(561\) | −1099.79 | −0.0827689 | ||||||||
\(562\) | 5378.79 | 0.403720 | ||||||||
\(563\) | 2540.86 | 0.190203 | 0.0951017 | − | 0.995468i | \(-0.469682\pi\) | ||||
0.0951017 | + | 0.995468i | \(0.469682\pi\) | |||||||
\(564\) | 14909.9 | 1.11315 | ||||||||
\(565\) | 9564.25 | 0.712161 | ||||||||
\(566\) | −2279.85 | −0.169310 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | −22688.9 | −1.67607 | ||||||||
\(569\) | −24220.0 | −1.78445 | −0.892227 | − | 0.451587i | \(-0.850858\pi\) | ||||
−0.892227 | + | 0.451587i | \(0.850858\pi\) | |||||||
\(570\) | 9782.85 | 0.718875 | ||||||||
\(571\) | −11772.1 | −0.862778 | −0.431389 | − | 0.902166i | \(-0.641976\pi\) | ||||
−0.431389 | + | 0.902166i | \(0.641976\pi\) | |||||||
\(572\) | −25695.1 | −1.87826 | ||||||||
\(573\) | 785.855 | 0.0572942 | ||||||||
\(574\) | 12489.6 | 0.908198 | ||||||||
\(575\) | 1717.38 | 0.124556 | ||||||||
\(576\) | 6717.80 | 0.485952 | ||||||||
\(577\) | 10584.3 | 0.763655 | 0.381827 | − | 0.924234i | \(-0.375295\pi\) | ||||
0.381827 | + | 0.924234i | \(0.375295\pi\) | |||||||
\(578\) | 25328.6 | 1.82272 | ||||||||
\(579\) | 12153.2 | 0.872315 | ||||||||
\(580\) | −7404.25 | −0.530077 | ||||||||
\(581\) | 9340.74 | 0.666987 | ||||||||
\(582\) | −22880.6 | −1.62961 | ||||||||
\(583\) | −18656.8 | −1.32536 | ||||||||
\(584\) | −36258.3 | −2.56914 | ||||||||
\(585\) | −3541.49 | −0.250295 | ||||||||
\(586\) | 11847.0 | 0.835148 | ||||||||
\(587\) | −8712.63 | −0.612621 | −0.306311 | − | 0.951932i | \(-0.599095\pi\) | ||||
−0.306311 | + | 0.951932i | \(0.599095\pi\) | |||||||
\(588\) | 2914.24 | 0.204390 | ||||||||
\(589\) | −17098.6 | −1.19615 | ||||||||
\(590\) | 1997.28 | 0.139368 | ||||||||
\(591\) | −8624.48 | −0.600277 | ||||||||
\(592\) | −44292.4 | −3.07501 | ||||||||
\(593\) | −15362.9 | −1.06387 | −0.531937 | − | 0.846784i | \(-0.678536\pi\) | ||||
−0.531937 | + | 0.846784i | \(0.678536\pi\) | |||||||
\(594\) | −4949.07 | −0.341857 | ||||||||
\(595\) | −779.093 | −0.0536802 | ||||||||
\(596\) | 14747.0 | 1.01353 | ||||||||
\(597\) | −9200.91 | −0.630768 | ||||||||
\(598\) | −24662.0 | −1.68646 | ||||||||
\(599\) | 26003.8 | 1.77377 | 0.886883 | − | 0.461994i | \(-0.152866\pi\) | ||||
0.886883 | + | 0.461994i | \(0.152866\pi\) | |||||||
\(600\) | 2563.78 | 0.174443 | ||||||||
\(601\) | 20567.7 | 1.39596 | 0.697982 | − | 0.716115i | \(-0.254082\pi\) | ||||
0.697982 | + | 0.716115i | \(0.254082\pi\) | |||||||
\(602\) | −251.233 | −0.0170091 | ||||||||
\(603\) | 4335.22 | 0.292776 | ||||||||
\(604\) | 12029.0 | 0.810349 | ||||||||
\(605\) | −1302.85 | −0.0875512 | ||||||||
\(606\) | −7514.42 | −0.503717 | ||||||||
\(607\) | 19642.1 | 1.31342 | 0.656711 | − | 0.754142i | \(-0.271947\pi\) | ||||
0.656711 | + | 0.754142i | \(0.271947\pi\) | |||||||
\(608\) | 23437.4 | 1.56334 | ||||||||
\(609\) | −743.442 | −0.0494676 | ||||||||
\(610\) | −3216.21 | −0.213476 | ||||||||
\(611\) | −9350.65 | −0.619127 | ||||||||
\(612\) | −1882.33 | −0.124328 | ||||||||
\(613\) | 8454.59 | 0.557060 | 0.278530 | − | 0.960428i | \(-0.410153\pi\) | ||||
0.278530 | + | 0.960428i | \(0.410153\pi\) | |||||||
\(614\) | 16864.3 | 1.10845 | ||||||||
\(615\) | −10705.4 | −0.701922 | ||||||||
\(616\) | −15172.3 | −0.992383 | ||||||||
\(617\) | −24168.4 | −1.57696 | −0.788479 | − | 0.615061i | \(-0.789131\pi\) | ||||
−0.788479 | + | 0.615061i | \(0.789131\pi\) | |||||||
\(618\) | 31643.0 | 2.05966 | ||||||||
\(619\) | −2037.56 | −0.132305 | −0.0661523 | − | 0.997810i | \(-0.521072\pi\) | ||||
−0.0661523 | + | 0.997810i | \(0.521072\pi\) | |||||||
\(620\) | 61028.1 | 3.95314 | ||||||||
\(621\) | −3384.37 | −0.218696 | ||||||||
\(622\) | 17700.5 | 1.14104 | ||||||||
\(623\) | −2471.27 | −0.158923 | ||||||||
\(624\) | −19069.8 | −1.22340 | ||||||||
\(625\) | −13724.7 | −0.878378 | ||||||||
\(626\) | 11902.3 | 0.759921 | ||||||||
\(627\) | −6108.70 | −0.389088 | ||||||||
\(628\) | 61749.8 | 3.92370 | ||||||||
\(629\) | 2741.87 | 0.173808 | ||||||||
\(630\) | −3505.92 | −0.221713 | ||||||||
\(631\) | 12339.5 | 0.778489 | 0.389244 | − | 0.921135i | \(-0.372736\pi\) | ||||
0.389244 | + | 0.921135i | \(0.372736\pi\) | |||||||
\(632\) | 43268.7 | 2.72332 | ||||||||
\(633\) | 1786.27 | 0.112161 | ||||||||
\(634\) | 32383.7 | 2.02858 | ||||||||
\(635\) | −18091.8 | −1.13063 | ||||||||
\(636\) | −31931.7 | −1.99084 | ||||||||
\(637\) | −1827.65 | −0.113680 | ||||||||
\(638\) | 6489.15 | 0.402677 | ||||||||
\(639\) | 3273.77 | 0.202674 | ||||||||
\(640\) | −7781.18 | −0.480591 | ||||||||
\(641\) | −10222.6 | −0.629906 | −0.314953 | − | 0.949107i | \(-0.601989\pi\) | ||||
−0.314953 | + | 0.949107i | \(0.601989\pi\) | |||||||
\(642\) | −18463.3 | −1.13503 | ||||||||
\(643\) | −1211.75 | −0.0743187 | −0.0371594 | − | 0.999309i | \(-0.511831\pi\) | ||||
−0.0371594 | + | 0.999309i | \(0.511831\pi\) | |||||||
\(644\) | −17394.8 | −1.06437 | ||||||||
\(645\) | 215.342 | 0.0131459 | ||||||||
\(646\) | −3260.95 | −0.198607 | ||||||||
\(647\) | −2817.22 | −0.171184 | −0.0855922 | − | 0.996330i | \(-0.527278\pi\) | ||||
−0.0855922 | + | 0.996330i | \(0.527278\pi\) | |||||||
\(648\) | −5052.34 | −0.306288 | ||||||||
\(649\) | −1247.16 | −0.0754320 | ||||||||
\(650\) | −2695.66 | −0.162665 | ||||||||
\(651\) | 6127.67 | 0.368913 | ||||||||
\(652\) | 47838.6 | 2.87347 | ||||||||
\(653\) | 20986.2 | 1.25766 | 0.628831 | − | 0.777542i | \(-0.283534\pi\) | ||||
0.628831 | + | 0.777542i | \(0.283534\pi\) | |||||||
\(654\) | 21160.5 | 1.26520 | ||||||||
\(655\) | 4964.87 | 0.296173 | ||||||||
\(656\) | −57645.1 | −3.43089 | ||||||||
\(657\) | 5231.69 | 0.310666 | ||||||||
\(658\) | −9256.74 | −0.548428 | ||||||||
\(659\) | −2384.09 | −0.140927 | −0.0704635 | − | 0.997514i | \(-0.522448\pi\) | ||||
−0.0704635 | + | 0.997514i | \(0.522448\pi\) | |||||||
\(660\) | 21803.1 | 1.28589 | ||||||||
\(661\) | −7577.10 | −0.445862 | −0.222931 | − | 0.974834i | \(-0.571562\pi\) | ||||
−0.222931 | + | 0.974834i | \(0.571562\pi\) | |||||||
\(662\) | −37081.7 | −2.17707 | ||||||||
\(663\) | 1180.50 | 0.0691503 | ||||||||
\(664\) | −83232.2 | −4.86451 | ||||||||
\(665\) | −4327.40 | −0.252345 | ||||||||
\(666\) | 12338.4 | 0.717874 | ||||||||
\(667\) | 4437.54 | 0.257605 | ||||||||
\(668\) | −12102.5 | −0.700989 | ||||||||
\(669\) | −11339.4 | −0.655315 | ||||||||
\(670\) | −26805.9 | −1.54567 | ||||||||
\(671\) | 2008.30 | 0.115543 | ||||||||
\(672\) | −8399.36 | −0.482161 | ||||||||
\(673\) | 11724.6 | 0.671547 | 0.335774 | − | 0.941943i | \(-0.391002\pi\) | ||||
0.335774 | + | 0.941943i | \(0.391002\pi\) | |||||||
\(674\) | −54481.7 | −3.11358 | ||||||||
\(675\) | −369.927 | −0.0210941 | ||||||||
\(676\) | −15974.5 | −0.908880 | ||||||||
\(677\) | 32304.3 | 1.83390 | 0.916952 | − | 0.398997i | \(-0.130642\pi\) | ||||
0.916952 | + | 0.398997i | \(0.130642\pi\) | |||||||
\(678\) | −14346.4 | −0.812639 | ||||||||
\(679\) | 10121.1 | 0.572038 | ||||||||
\(680\) | 6942.23 | 0.391503 | ||||||||
\(681\) | 5482.85 | 0.308522 | ||||||||
\(682\) | −53485.6 | −3.00303 | ||||||||
\(683\) | 33367.1 | 1.86934 | 0.934669 | − | 0.355519i | \(-0.115696\pi\) | ||||
0.934669 | + | 0.355519i | \(0.115696\pi\) | |||||||
\(684\) | −10455.2 | −0.584452 | ||||||||
\(685\) | −4683.18 | −0.261219 | ||||||||
\(686\) | −1809.30 | −0.100699 | ||||||||
\(687\) | −2550.75 | −0.141655 | ||||||||
\(688\) | 1159.55 | 0.0642551 | ||||||||
\(689\) | 20025.8 | 1.10729 | ||||||||
\(690\) | 20926.5 | 1.15458 | ||||||||
\(691\) | −1043.67 | −0.0574577 | −0.0287288 | − | 0.999587i | \(-0.509146\pi\) | ||||
−0.0287288 | + | 0.999587i | \(0.509146\pi\) | |||||||
\(692\) | 75211.3 | 4.13166 | ||||||||
\(693\) | 2189.20 | 0.120001 | ||||||||
\(694\) | −10378.6 | −0.567674 | ||||||||
\(695\) | 17618.0 | 0.961567 | ||||||||
\(696\) | 6624.55 | 0.360780 | ||||||||
\(697\) | 3568.46 | 0.193924 | ||||||||
\(698\) | 23027.4 | 1.24871 | ||||||||
\(699\) | −19773.3 | −1.06995 | ||||||||
\(700\) | −1901.33 | −0.102662 | ||||||||
\(701\) | −11305.7 | −0.609143 | −0.304572 | − | 0.952489i | \(-0.598513\pi\) | ||||
−0.304572 | + | 0.952489i | \(0.598513\pi\) | |||||||
\(702\) | 5312.23 | 0.285608 | ||||||||
\(703\) | 15229.4 | 0.817055 | ||||||||
\(704\) | 25937.6 | 1.38858 | ||||||||
\(705\) | 7934.35 | 0.423865 | ||||||||
\(706\) | 32027.1 | 1.70730 | ||||||||
\(707\) | 3323.97 | 0.176818 | ||||||||
\(708\) | −2134.55 | −0.113307 | ||||||||
\(709\) | −13306.8 | −0.704860 | −0.352430 | − | 0.935838i | \(-0.614645\pi\) | ||||
−0.352430 | + | 0.935838i | \(0.614645\pi\) | |||||||
\(710\) | −20242.6 | −1.06999 | ||||||||
\(711\) | −6243.22 | −0.329309 | ||||||||
\(712\) | 22020.6 | 1.15907 | ||||||||
\(713\) | −36575.6 | −1.92113 | ||||||||
\(714\) | 1168.64 | 0.0612538 | ||||||||
\(715\) | −13673.7 | −0.715201 | ||||||||
\(716\) | −55602.0 | −2.90216 | ||||||||
\(717\) | −547.669 | −0.0285259 | ||||||||
\(718\) | −50839.9 | −2.64252 | ||||||||
\(719\) | 10701.2 | 0.555062 | 0.277531 | − | 0.960717i | \(-0.410484\pi\) | ||||
0.277531 | + | 0.960717i | \(0.410484\pi\) | |||||||
\(720\) | 16181.4 | 0.837562 | ||||||||
\(721\) | −13997.1 | −0.722996 | ||||||||
\(722\) | 18068.0 | 0.931333 | ||||||||
\(723\) | 4571.69 | 0.235163 | ||||||||
\(724\) | 61576.5 | 3.16088 | ||||||||
\(725\) | 485.042 | 0.0248469 | ||||||||
\(726\) | 1954.28 | 0.0999037 | ||||||||
\(727\) | −2121.14 | −0.108210 | −0.0541051 | − | 0.998535i | \(-0.517231\pi\) | ||||
−0.0541051 | + | 0.998535i | \(0.517231\pi\) | |||||||
\(728\) | 16285.6 | 0.829098 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −32349.0 | −1.64012 | ||||||||
\(731\) | −71.7808 | −0.00363189 | ||||||||
\(732\) | 3437.26 | 0.173558 | ||||||||
\(733\) | −21584.0 | −1.08762 | −0.543809 | − | 0.839209i | \(-0.683019\pi\) | ||||
−0.543809 | + | 0.839209i | \(0.683019\pi\) | |||||||
\(734\) | −2757.33 | −0.138658 | ||||||||
\(735\) | 1550.83 | 0.0778273 | ||||||||
\(736\) | 50135.0 | 2.51087 | ||||||||
\(737\) | 16738.4 | 0.836588 | ||||||||
\(738\) | 16058.0 | 0.800955 | ||||||||
\(739\) | −9945.21 | −0.495048 | −0.247524 | − | 0.968882i | \(-0.579617\pi\) | ||||
−0.247524 | + | 0.968882i | \(0.579617\pi\) | |||||||
\(740\) | −54356.9 | −2.70027 | ||||||||
\(741\) | 6556.94 | 0.325068 | ||||||||
\(742\) | 19824.7 | 0.980848 | ||||||||
\(743\) | 2867.01 | 0.141562 | 0.0707808 | − | 0.997492i | \(-0.477451\pi\) | ||||
0.0707808 | + | 0.997492i | \(0.477451\pi\) | |||||||
\(744\) | −54601.6 | −2.69058 | ||||||||
\(745\) | 7847.71 | 0.385930 | ||||||||
\(746\) | −17037.1 | −0.836158 | ||||||||
\(747\) | 12009.5 | 0.588227 | ||||||||
\(748\) | −7267.71 | −0.355259 | ||||||||
\(749\) | 8167.15 | 0.398426 | ||||||||
\(750\) | 23155.9 | 1.12738 | ||||||||
\(751\) | −10824.1 | −0.525934 | −0.262967 | − | 0.964805i | \(-0.584701\pi\) | ||||
−0.262967 | + | 0.964805i | \(0.584701\pi\) | |||||||
\(752\) | 42724.0 | 2.07179 | ||||||||
\(753\) | 7073.19 | 0.342313 | ||||||||
\(754\) | −6965.31 | −0.336421 | ||||||||
\(755\) | 6401.26 | 0.308564 | ||||||||
\(756\) | 3746.88 | 0.180255 | ||||||||
\(757\) | −14512.0 | −0.696761 | −0.348381 | − | 0.937353i | \(-0.613268\pi\) | ||||
−0.348381 | + | 0.937353i | \(0.613268\pi\) | |||||||
\(758\) | −35023.9 | −1.67827 | ||||||||
\(759\) | −13067.1 | −0.624910 | ||||||||
\(760\) | 38559.9 | 1.84042 | ||||||||
\(761\) | −33075.8 | −1.57556 | −0.787778 | − | 0.615959i | \(-0.788769\pi\) | ||||
−0.787778 | + | 0.615959i | \(0.788769\pi\) | |||||||
\(762\) | 27137.7 | 1.29015 | ||||||||
\(763\) | −9360.23 | −0.444120 | ||||||||
\(764\) | 5193.13 | 0.245917 | ||||||||
\(765\) | −1001.69 | −0.0473415 | ||||||||
\(766\) | 75032.8 | 3.53922 | ||||||||
\(767\) | 1338.68 | 0.0630206 | ||||||||
\(768\) | −6242.38 | −0.293297 | ||||||||
\(769\) | 6728.44 | 0.315518 | 0.157759 | − | 0.987478i | \(-0.449573\pi\) | ||||
0.157759 | + | 0.987478i | \(0.449573\pi\) | |||||||
\(770\) | −13536.4 | −0.633531 | ||||||||
\(771\) | 8347.65 | 0.389926 | ||||||||
\(772\) | 80311.5 | 3.74414 | ||||||||
\(773\) | −24233.3 | −1.12757 | −0.563784 | − | 0.825922i | \(-0.690655\pi\) | ||||
−0.563784 | + | 0.825922i | \(0.690655\pi\) | |||||||
\(774\) | −323.014 | −0.0150006 | ||||||||
\(775\) | −3997.87 | −0.185300 | ||||||||
\(776\) | −90186.0 | −4.17202 | ||||||||
\(777\) | −5457.84 | −0.251993 | ||||||||
\(778\) | −15412.4 | −0.710231 | ||||||||
\(779\) | 19820.6 | 0.911615 | ||||||||
\(780\) | −23403.0 | −1.07431 | ||||||||
\(781\) | 12640.1 | 0.579127 | ||||||||
\(782\) | −6975.51 | −0.318982 | ||||||||
\(783\) | −955.854 | −0.0436263 | ||||||||
\(784\) | 8350.72 | 0.380408 | ||||||||
\(785\) | 32860.5 | 1.49406 | ||||||||
\(786\) | −7447.31 | −0.337960 | ||||||||
\(787\) | −17200.4 | −0.779069 | −0.389535 | − | 0.921012i | \(-0.627364\pi\) | ||||
−0.389535 | + | 0.921012i | \(0.627364\pi\) | |||||||
\(788\) | −56992.7 | −2.57650 | ||||||||
\(789\) | 6131.35 | 0.276656 | ||||||||
\(790\) | 38603.6 | 1.73855 | ||||||||
\(791\) | 6346.05 | 0.285258 | ||||||||
\(792\) | −19507.2 | −0.875199 | ||||||||
\(793\) | −2155.66 | −0.0965318 | ||||||||
\(794\) | −4282.92 | −0.191430 | ||||||||
\(795\) | −16992.6 | −0.758071 | ||||||||
\(796\) | −60801.9 | −2.70737 | ||||||||
\(797\) | −4208.87 | −0.187059 | −0.0935295 | − | 0.995617i | \(-0.529815\pi\) | ||||
−0.0935295 | + | 0.995617i | \(0.529815\pi\) | |||||||
\(798\) | 6491.09 | 0.287948 | ||||||||
\(799\) | −2644.78 | −0.117104 | ||||||||
\(800\) | 5479.98 | 0.242183 | ||||||||
\(801\) | −3177.34 | −0.140157 | ||||||||
\(802\) | −12336.1 | −0.543146 | ||||||||
\(803\) | 20199.7 | 0.887709 | ||||||||
\(804\) | 28648.2 | 1.25665 | ||||||||
\(805\) | −9256.74 | −0.405289 | ||||||||
\(806\) | 57410.2 | 2.50892 | ||||||||
\(807\) | 10358.5 | 0.451842 | ||||||||
\(808\) | −29618.7 | −1.28958 | ||||||||
\(809\) | −23632.1 | −1.02702 | −0.513511 | − | 0.858083i | \(-0.671656\pi\) | ||||
−0.513511 | + | 0.858083i | \(0.671656\pi\) | |||||||
\(810\) | −4507.61 | −0.195532 | ||||||||
\(811\) | 28425.1 | 1.23075 | 0.615377 | − | 0.788233i | \(-0.289004\pi\) | ||||
0.615377 | + | 0.788233i | \(0.289004\pi\) | |||||||
\(812\) | −4912.85 | −0.212324 | ||||||||
\(813\) | 7932.88 | 0.342212 | ||||||||
\(814\) | 47638.9 | 2.05128 | ||||||||
\(815\) | 25457.5 | 1.09416 | ||||||||
\(816\) | −5393.80 | −0.231398 | ||||||||
\(817\) | −398.699 | −0.0170731 | ||||||||
\(818\) | 14387.7 | 0.614981 | ||||||||
\(819\) | −2349.84 | −0.100256 | ||||||||
\(820\) | −70743.7 | −3.01278 | ||||||||
\(821\) | 39409.6 | 1.67528 | 0.837640 | − | 0.546223i | \(-0.183935\pi\) | ||||
0.837640 | + | 0.546223i | \(0.183935\pi\) | |||||||
\(822\) | 7024.77 | 0.298074 | ||||||||
\(823\) | 16346.6 | 0.692352 | 0.346176 | − | 0.938170i | \(-0.387480\pi\) | ||||
0.346176 | + | 0.938170i | \(0.387480\pi\) | |||||||
\(824\) | 124723. | 5.27300 | ||||||||
\(825\) | −1428.29 | −0.0602749 | ||||||||
\(826\) | 1325.23 | 0.0558241 | ||||||||
\(827\) | −3738.87 | −0.157211 | −0.0786054 | − | 0.996906i | \(-0.525047\pi\) | ||||
−0.0786054 | + | 0.996906i | \(0.525047\pi\) | |||||||
\(828\) | −22364.8 | −0.938684 | ||||||||
\(829\) | −45196.2 | −1.89352 | −0.946761 | − | 0.321937i | \(-0.895666\pi\) | ||||
−0.946761 | + | 0.321937i | \(0.895666\pi\) | |||||||
\(830\) | −74258.3 | −3.10547 | ||||||||
\(831\) | 8038.46 | 0.335561 | ||||||||
\(832\) | −27840.8 | −1.16010 | ||||||||
\(833\) | −516.942 | −0.0215018 | ||||||||
\(834\) | −26427.0 | −1.09723 | ||||||||
\(835\) | −6440.41 | −0.266922 | ||||||||
\(836\) | −40367.8 | −1.67004 | ||||||||
\(837\) | 7878.44 | 0.325351 | ||||||||
\(838\) | −70189.5 | −2.89338 | ||||||||
\(839\) | 15899.7 | 0.654254 | 0.327127 | − | 0.944980i | \(-0.393920\pi\) | ||||
0.327127 | + | 0.944980i | \(0.393920\pi\) | |||||||
\(840\) | −13818.9 | −0.567615 | ||||||||
\(841\) | −23135.7 | −0.948612 | ||||||||
\(842\) | 58063.4 | 2.37648 | ||||||||
\(843\) | −3059.07 | −0.124982 | ||||||||
\(844\) | 11804.1 | 0.481414 | ||||||||
\(845\) | −8500.89 | −0.346082 | ||||||||
\(846\) | −11901.5 | −0.483668 | ||||||||
\(847\) | −864.465 | −0.0350689 | ||||||||
\(848\) | −91500.0 | −3.70534 | ||||||||
\(849\) | 1296.62 | 0.0524144 | ||||||||
\(850\) | −762.453 | −0.0307670 | ||||||||
\(851\) | 32577.4 | 1.31227 | ||||||||
\(852\) | 21633.9 | 0.869913 | ||||||||
\(853\) | 33926.7 | 1.36182 | 0.680908 | − | 0.732369i | \(-0.261585\pi\) | ||||
0.680908 | + | 0.732369i | \(0.261585\pi\) | |||||||
\(854\) | −2134.01 | −0.0855086 | ||||||||
\(855\) | −5563.79 | −0.222547 | ||||||||
\(856\) | −72774.7 | −2.90583 | ||||||||
\(857\) | −35432.4 | −1.41231 | −0.706154 | − | 0.708058i | \(-0.749572\pi\) | ||||
−0.706154 | + | 0.708058i | \(0.749572\pi\) | |||||||
\(858\) | 20510.6 | 0.816108 | ||||||||
\(859\) | −6780.17 | −0.269309 | −0.134655 | − | 0.990893i | \(-0.542992\pi\) | ||||
−0.134655 | + | 0.990893i | \(0.542992\pi\) | |||||||
\(860\) | 1423.04 | 0.0564246 | ||||||||
\(861\) | −7103.20 | −0.281157 | ||||||||
\(862\) | 34422.1 | 1.36012 | ||||||||
\(863\) | −30675.1 | −1.20995 | −0.604977 | − | 0.796243i | \(-0.706818\pi\) | ||||
−0.604977 | + | 0.796243i | \(0.706818\pi\) | |||||||
\(864\) | −10799.2 | −0.425226 | ||||||||
\(865\) | 40024.1 | 1.57325 | ||||||||
\(866\) | 61802.4 | 2.42509 | ||||||||
\(867\) | −14405.1 | −0.564271 | ||||||||
\(868\) | 40493.2 | 1.58344 | ||||||||
\(869\) | −24105.2 | −0.940981 | ||||||||
\(870\) | 5910.31 | 0.230320 | ||||||||
\(871\) | −17966.6 | −0.698938 | ||||||||
\(872\) | 83405.8 | 3.23908 | ||||||||
\(873\) | 13012.9 | 0.504490 | ||||||||
\(874\) | −38744.8 | −1.49950 | ||||||||
\(875\) | −10242.9 | −0.395741 | ||||||||
\(876\) | 34572.3 | 1.33344 | ||||||||
\(877\) | 40861.3 | 1.57330 | 0.786652 | − | 0.617397i | \(-0.211813\pi\) | ||||
0.786652 | + | 0.617397i | \(0.211813\pi\) | |||||||
\(878\) | 77073.9 | 2.96255 | ||||||||
\(879\) | −6737.76 | −0.258543 | ||||||||
\(880\) | 62476.6 | 2.39328 | ||||||||
\(881\) | −43839.0 | −1.67647 | −0.838236 | − | 0.545308i | \(-0.816413\pi\) | ||||
−0.838236 | + | 0.545308i | \(0.816413\pi\) | |||||||
\(882\) | −2326.24 | −0.0888079 | ||||||||
\(883\) | 44625.1 | 1.70074 | 0.850371 | − | 0.526183i | \(-0.176377\pi\) | ||||
0.850371 | + | 0.526183i | \(0.176377\pi\) | |||||||
\(884\) | 7801.01 | 0.296806 | ||||||||
\(885\) | −1135.91 | −0.0431450 | ||||||||
\(886\) | 80388.6 | 3.04820 | ||||||||
\(887\) | −43967.5 | −1.66436 | −0.832178 | − | 0.554509i | \(-0.812906\pi\) | ||||
−0.832178 | + | 0.554509i | \(0.812906\pi\) | |||||||
\(888\) | 48632.9 | 1.83785 | ||||||||
\(889\) | −12004.2 | −0.452878 | ||||||||
\(890\) | 19646.4 | 0.739943 | ||||||||
\(891\) | 2814.68 | 0.105831 | ||||||||
\(892\) | −74933.5 | −2.81273 | ||||||||
\(893\) | −14690.2 | −0.550491 | ||||||||
\(894\) | −11771.6 | −0.440380 | ||||||||
\(895\) | −29588.9 | −1.10508 | ||||||||
\(896\) | −5162.95 | −0.192502 | ||||||||
\(897\) | 14026.0 | 0.522089 | ||||||||
\(898\) | −56329.7 | −2.09326 | ||||||||
\(899\) | −10330.1 | −0.383234 | ||||||||
\(900\) | −2444.57 | −0.0905396 | ||||||||
\(901\) | 5664.21 | 0.209436 | ||||||||
\(902\) | 62000.4 | 2.28868 | ||||||||
\(903\) | 142.883 | 0.00526563 | ||||||||
\(904\) | −56547.4 | −2.08046 | ||||||||
\(905\) | 32768.2 | 1.20359 | ||||||||
\(906\) | −9601.89 | −0.352099 | ||||||||
\(907\) | −13584.3 | −0.497309 | −0.248654 | − | 0.968592i | \(-0.579988\pi\) | ||||
−0.248654 | + | 0.968592i | \(0.579988\pi\) | |||||||
\(908\) | 36232.1 | 1.32423 | ||||||||
\(909\) | 4273.67 | 0.155939 | ||||||||
\(910\) | 14529.7 | 0.529291 | ||||||||
\(911\) | −16421.6 | −0.597226 | −0.298613 | − | 0.954374i | \(-0.596524\pi\) | ||||
−0.298613 | + | 0.954374i | \(0.596524\pi\) | |||||||
\(912\) | −29959.3 | −1.08778 | ||||||||
\(913\) | 46369.0 | 1.68082 | ||||||||
\(914\) | −22303.6 | −0.807152 | ||||||||
\(915\) | 1829.15 | 0.0660873 | ||||||||
\(916\) | −16856.0 | −0.608010 | ||||||||
\(917\) | 3294.28 | 0.118633 | ||||||||
\(918\) | 1502.54 | 0.0540208 | ||||||||
\(919\) | −29487.3 | −1.05843 | −0.529214 | − | 0.848488i | \(-0.677513\pi\) | ||||
−0.529214 | + | 0.848488i | \(0.677513\pi\) | |||||||
\(920\) | 82483.7 | 2.95588 | ||||||||
\(921\) | −9591.23 | −0.343151 | ||||||||
\(922\) | −4800.81 | −0.171482 | ||||||||
\(923\) | −13567.6 | −0.483839 | ||||||||
\(924\) | 14466.8 | 0.515067 | ||||||||
\(925\) | 3560.85 | 0.126573 | ||||||||
\(926\) | −23505.9 | −0.834181 | ||||||||
\(927\) | −17996.3 | −0.637622 | ||||||||
\(928\) | 14159.7 | 0.500878 | ||||||||
\(929\) | 3441.85 | 0.121554 | 0.0607769 | − | 0.998151i | \(-0.480642\pi\) | ||||
0.0607769 | + | 0.998151i | \(0.480642\pi\) | |||||||
\(930\) | −48714.6 | −1.71765 | ||||||||
\(931\) | −2871.30 | −0.101077 | ||||||||
\(932\) | −130667. | −4.59242 | ||||||||
\(933\) | −10066.8 | −0.353240 | ||||||||
\(934\) | 23364.8 | 0.818545 | ||||||||
\(935\) | −3867.55 | −0.135275 | ||||||||
\(936\) | 20938.6 | 0.731196 | ||||||||
\(937\) | 5646.60 | 0.196869 | 0.0984346 | − | 0.995144i | \(-0.468616\pi\) | ||||
0.0984346 | + | 0.995144i | \(0.468616\pi\) | |||||||
\(938\) | −17786.2 | −0.619125 | ||||||||
\(939\) | −6769.18 | −0.235254 | ||||||||
\(940\) | 52432.2 | 1.81931 | ||||||||
\(941\) | −44680.1 | −1.54785 | −0.773927 | − | 0.633275i | \(-0.781710\pi\) | ||||
−0.773927 | + | 0.633275i | \(0.781710\pi\) | |||||||
\(942\) | −49290.7 | −1.70486 | ||||||||
\(943\) | 42398.4 | 1.46414 | ||||||||
\(944\) | −6116.54 | −0.210886 | ||||||||
\(945\) | 1993.92 | 0.0686372 | ||||||||
\(946\) | −1247.16 | −0.0428633 | ||||||||
\(947\) | −48924.6 | −1.67881 | −0.839406 | − | 0.543505i | \(-0.817097\pi\) | ||||
−0.839406 | + | 0.543505i | \(0.817097\pi\) | |||||||
\(948\) | −41256.8 | −1.41346 | ||||||||
\(949\) | −21681.9 | −0.741647 | ||||||||
\(950\) | −4234.97 | −0.144632 | ||||||||
\(951\) | −18417.6 | −0.628002 | ||||||||
\(952\) | 4606.29 | 0.156818 | ||||||||
\(953\) | 52014.3 | 1.76801 | 0.884003 | − | 0.467482i | \(-0.154839\pi\) | ||||
0.884003 | + | 0.467482i | \(0.154839\pi\) | |||||||
\(954\) | 25488.9 | 0.865026 | ||||||||
\(955\) | 2763.55 | 0.0936401 | ||||||||
\(956\) | −3619.14 | −0.122439 | ||||||||
\(957\) | −3690.57 | −0.124660 | ||||||||
\(958\) | −14521.1 | −0.489723 | ||||||||
\(959\) | −3107.37 | −0.104632 | ||||||||
\(960\) | 23623.9 | 0.794228 | ||||||||
\(961\) | 55352.8 | 1.85804 | ||||||||
\(962\) | −51134.5 | −1.71377 | ||||||||
\(963\) | 10500.6 | 0.351379 | ||||||||
\(964\) | 30210.9 | 1.00936 | ||||||||
\(965\) | 42738.2 | 1.42569 | ||||||||
\(966\) | 13885.1 | 0.462470 | ||||||||
\(967\) | −47117.7 | −1.56691 | −0.783456 | − | 0.621448i | \(-0.786545\pi\) | ||||
−0.783456 | + | 0.621448i | \(0.786545\pi\) | |||||||
\(968\) | 7702.95 | 0.255767 | ||||||||
\(969\) | 1854.60 | 0.0614843 | ||||||||
\(970\) | −80462.3 | −2.66339 | ||||||||
\(971\) | −8195.04 | −0.270846 | −0.135423 | − | 0.990788i | \(-0.543239\pi\) | ||||
−0.135423 | + | 0.990788i | \(0.543239\pi\) | |||||||
\(972\) | 4817.41 | 0.158970 | ||||||||
\(973\) | 11689.9 | 0.385159 | ||||||||
\(974\) | 3537.35 | 0.116370 | ||||||||
\(975\) | 1533.10 | 0.0503574 | ||||||||
\(976\) | 9849.42 | 0.323025 | ||||||||
\(977\) | 4643.51 | 0.152056 | 0.0760282 | − | 0.997106i | \(-0.475776\pi\) | ||||
0.0760282 | + | 0.997106i | \(0.475776\pi\) | |||||||
\(978\) | −38186.3 | −1.24853 | ||||||||
\(979\) | −12267.8 | −0.400490 | ||||||||
\(980\) | 10248.2 | 0.334049 | ||||||||
\(981\) | −12034.6 | −0.391677 | ||||||||
\(982\) | 43490.1 | 1.41326 | ||||||||
\(983\) | 43986.5 | 1.42721 | 0.713607 | − | 0.700546i | \(-0.247060\pi\) | ||||
0.713607 | + | 0.700546i | \(0.247060\pi\) | |||||||
\(984\) | 63294.1 | 2.05055 | ||||||||
\(985\) | −30329.0 | −0.981077 | ||||||||
\(986\) | −1970.10 | −0.0636317 | ||||||||
\(987\) | 5264.58 | 0.169781 | ||||||||
\(988\) | 43329.9 | 1.39525 | ||||||||
\(989\) | −852.859 | −0.0274210 | ||||||||
\(990\) | −17404.0 | −0.558722 | ||||||||
\(991\) | 1595.21 | 0.0511337 | 0.0255668 | − | 0.999673i | \(-0.491861\pi\) | ||||
0.0255668 | + | 0.999673i | \(0.491861\pi\) | |||||||
\(992\) | −116709. | −3.73539 | ||||||||
\(993\) | 21089.4 | 0.673971 | ||||||||
\(994\) | −13431.3 | −0.428588 | ||||||||
\(995\) | −32356.0 | −1.03091 | ||||||||
\(996\) | 79362.0 | 2.52478 | ||||||||
\(997\) | 21501.2 | 0.682998 | 0.341499 | − | 0.939882i | \(-0.389065\pi\) | ||||
0.341499 | + | 0.939882i | \(0.389065\pi\) | |||||||
\(998\) | −43069.2 | −1.36606 | ||||||||
\(999\) | −7017.22 | −0.222237 |
(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 | 21.4.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 63.4.a.e.1.2 | 2 | |||
4.3 | odd | 2 | 336.4.a.m.1.2 | 2 | |||
5.2 | odd | 4 | 525.4.d.g.274.1 | 4 | |||
5.3 | odd | 4 | 525.4.d.g.274.4 | 4 | |||
5.4 | even | 2 | 525.4.a.n.1.2 | 2 | |||
7.2 | even | 3 | 147.4.e.l.67.2 | 4 | |||
7.3 | odd | 6 | 147.4.e.m.79.2 | 4 | |||
7.4 | even | 3 | 147.4.e.l.79.2 | 4 | |||
7.5 | odd | 6 | 147.4.e.m.67.2 | 4 | |||
7.6 | odd | 2 | 147.4.a.i.1.1 | 2 | |||
8.3 | odd | 2 | 1344.4.a.bo.1.1 | 2 | |||
8.5 | even | 2 | 1344.4.a.bg.1.1 | 2 | |||
12.11 | even | 2 | 1008.4.a.ba.1.1 | 2 | |||
15.14 | odd | 2 | 1575.4.a.p.1.1 | 2 | |||
21.2 | odd | 6 | 441.4.e.q.361.1 | 4 | |||
21.5 | even | 6 | 441.4.e.p.361.1 | 4 | |||
21.11 | odd | 6 | 441.4.e.q.226.1 | 4 | |||
21.17 | even | 6 | 441.4.e.p.226.1 | 4 | |||
21.20 | even | 2 | 441.4.a.r.1.2 | 2 | |||
28.27 | even | 2 | 2352.4.a.bz.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
63.4.a.e.1.2 | 2 | 3.2 | odd | 2 | |||
147.4.a.i.1.1 | 2 | 7.6 | odd | 2 | |||
147.4.e.l.67.2 | 4 | 7.2 | even | 3 | |||
147.4.e.l.79.2 | 4 | 7.4 | even | 3 | |||
147.4.e.m.67.2 | 4 | 7.5 | odd | 6 | |||
147.4.e.m.79.2 | 4 | 7.3 | odd | 6 | |||
336.4.a.m.1.2 | 2 | 4.3 | odd | 2 | |||
441.4.a.r.1.2 | 2 | 21.20 | even | 2 | |||
441.4.e.p.226.1 | 4 | 21.17 | even | 6 | |||
441.4.e.p.361.1 | 4 | 21.5 | even | 6 | |||
441.4.e.q.226.1 | 4 | 21.11 | odd | 6 | |||
441.4.e.q.361.1 | 4 | 21.2 | odd | 6 | |||
525.4.a.n.1.2 | 2 | 5.4 | even | 2 | |||
525.4.d.g.274.1 | 4 | 5.2 | odd | 4 | |||
525.4.d.g.274.4 | 4 | 5.3 | odd | 4 | |||
1008.4.a.ba.1.1 | 2 | 12.11 | even | 2 | |||
1344.4.a.bg.1.1 | 2 | 8.5 | even | 2 | |||
1344.4.a.bo.1.1 | 2 | 8.3 | odd | 2 | |||
1575.4.a.p.1.1 | 2 | 15.14 | odd | 2 | |||
2352.4.a.bz.1.1 | 2 | 28.27 | even | 2 |