Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, 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("245.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{11}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 11 \) |
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 | \(-3.31662\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.31662 | −0.819051 | −0.409525 | − | 0.912299i | \(-0.634306\pi\) | ||||
−0.409525 | + | 0.912299i | \(0.634306\pi\) | |||||||
\(3\) | 5.00000 | 0.962250 | 0.481125 | − | 0.876652i | \(-0.340228\pi\) | ||||
0.481125 | + | 0.876652i | \(0.340228\pi\) | |||||||
\(4\) | −2.63325 | −0.329156 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −11.5831 | −0.788132 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 24.6332 | 1.08865 | ||||||||
\(9\) | −2.00000 | −0.0740741 | ||||||||
\(10\) | −11.5831 | −0.366291 | ||||||||
\(11\) | 46.2665 | 1.26817 | 0.634085 | − | 0.773263i | \(-0.281377\pi\) | ||||
0.634085 | + | 0.773263i | \(0.281377\pi\) | |||||||
\(12\) | −13.1662 | −0.316731 | ||||||||
\(13\) | −61.3325 | −1.30851 | −0.654253 | − | 0.756276i | \(-0.727017\pi\) | ||||
−0.654253 | + | 0.756276i | \(0.727017\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 25.0000 | 0.430331 | ||||||||
\(16\) | −36.0000 | −0.562500 | ||||||||
\(17\) | 101.332 | 1.44569 | 0.722845 | − | 0.691010i | \(-0.242834\pi\) | ||||
0.722845 | + | 0.691010i | \(0.242834\pi\) | |||||||
\(18\) | 4.63325 | 0.0606704 | ||||||||
\(19\) | 3.66750 | 0.0442833 | 0.0221417 | − | 0.999755i | \(-0.492952\pi\) | ||||
0.0221417 | + | 0.999755i | \(0.492952\pi\) | |||||||
\(20\) | −13.1662 | −0.147203 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −107.182 | −1.03870 | ||||||||
\(23\) | 84.8655 | 0.769377 | 0.384689 | − | 0.923046i | \(-0.374309\pi\) | ||||
0.384689 | + | 0.923046i | \(0.374309\pi\) | |||||||
\(24\) | 123.166 | 1.04755 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 142.084 | 1.07173 | ||||||||
\(27\) | −145.000 | −1.03353 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 30.1980 | 0.193366 | 0.0966832 | − | 0.995315i | \(-0.469177\pi\) | ||||
0.0966832 | + | 0.995315i | \(0.469177\pi\) | |||||||
\(30\) | −57.9156 | −0.352463 | ||||||||
\(31\) | 188.997 | 1.09500 | 0.547499 | − | 0.836806i | \(-0.315580\pi\) | ||||
0.547499 | + | 0.836806i | \(0.315580\pi\) | |||||||
\(32\) | −113.668 | −0.627930 | ||||||||
\(33\) | 231.332 | 1.22030 | ||||||||
\(34\) | −234.749 | −1.18409 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.26650 | 0.0243819 | ||||||||
\(37\) | 18.0685 | 0.0802823 | 0.0401411 | − | 0.999194i | \(-0.487219\pi\) | ||||
0.0401411 | + | 0.999194i | \(0.487219\pi\) | |||||||
\(38\) | −8.49623 | −0.0362703 | ||||||||
\(39\) | −306.662 | −1.25911 | ||||||||
\(40\) | 123.166 | 0.486857 | ||||||||
\(41\) | 481.662 | 1.83471 | 0.917354 | − | 0.398072i | \(-0.130321\pi\) | ||||
0.917354 | + | 0.398072i | \(0.130321\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −97.7995 | −0.346844 | −0.173422 | − | 0.984848i | \(-0.555482\pi\) | ||||
−0.173422 | + | 0.984848i | \(0.555482\pi\) | |||||||
\(44\) | −121.831 | −0.417426 | ||||||||
\(45\) | −10.0000 | −0.0331269 | ||||||||
\(46\) | −196.602 | −0.630159 | ||||||||
\(47\) | 117.665 | 0.365175 | 0.182587 | − | 0.983190i | \(-0.441553\pi\) | ||||
0.182587 | + | 0.983190i | \(0.441553\pi\) | |||||||
\(48\) | −180.000 | −0.541266 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −57.9156 | −0.163810 | ||||||||
\(51\) | 506.662 | 1.39112 | ||||||||
\(52\) | 161.504 | 0.430703 | ||||||||
\(53\) | 667.995 | 1.73125 | 0.865624 | − | 0.500694i | \(-0.166922\pi\) | ||||
0.865624 | + | 0.500694i | \(0.166922\pi\) | |||||||
\(54\) | 335.911 | 0.846512 | ||||||||
\(55\) | 231.332 | 0.567143 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 18.3375 | 0.0426116 | ||||||||
\(58\) | −69.9574 | −0.158377 | ||||||||
\(59\) | 57.3350 | 0.126515 | 0.0632575 | − | 0.997997i | \(-0.479851\pi\) | ||||
0.0632575 | + | 0.997997i | \(0.479851\pi\) | |||||||
\(60\) | −65.8312 | −0.141646 | ||||||||
\(61\) | 738.997 | 1.55113 | 0.775565 | − | 0.631268i | \(-0.217465\pi\) | ||||
0.775565 | + | 0.631268i | \(0.217465\pi\) | |||||||
\(62\) | −437.836 | −0.896859 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 551.325 | 1.07681 | ||||||||
\(65\) | −306.662 | −0.585182 | ||||||||
\(66\) | −535.911 | −0.999485 | ||||||||
\(67\) | 552.396 | 1.00725 | 0.503626 | − | 0.863922i | \(-0.331999\pi\) | ||||
0.503626 | + | 0.863922i | \(0.331999\pi\) | |||||||
\(68\) | −266.834 | −0.475858 | ||||||||
\(69\) | 424.327 | 0.740334 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −740.264 | −1.23737 | −0.618684 | − | 0.785640i | \(-0.712334\pi\) | ||||
−0.618684 | + | 0.785640i | \(0.712334\pi\) | |||||||
\(72\) | −49.2665 | −0.0806405 | ||||||||
\(73\) | 233.325 | 0.374091 | 0.187045 | − | 0.982351i | \(-0.440109\pi\) | ||||
0.187045 | + | 0.982351i | \(0.440109\pi\) | |||||||
\(74\) | −41.8580 | −0.0657553 | ||||||||
\(75\) | 125.000 | 0.192450 | ||||||||
\(76\) | −9.65745 | −0.0145761 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 710.422 | 1.03127 | ||||||||
\(79\) | −1075.19 | −1.53124 | −0.765619 | − | 0.643294i | \(-0.777567\pi\) | ||||
−0.765619 | + | 0.643294i | \(0.777567\pi\) | |||||||
\(80\) | −180.000 | −0.251558 | ||||||||
\(81\) | −671.000 | −0.920439 | ||||||||
\(82\) | −1115.83 | −1.50272 | ||||||||
\(83\) | 683.325 | 0.903671 | 0.451835 | − | 0.892101i | \(-0.350769\pi\) | ||||
0.451835 | + | 0.892101i | \(0.350769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 506.662 | 0.646532 | ||||||||
\(86\) | 226.565 | 0.284083 | ||||||||
\(87\) | 150.990 | 0.186067 | ||||||||
\(88\) | 1139.69 | 1.38059 | ||||||||
\(89\) | −1380.32 | −1.64397 | −0.821985 | − | 0.569509i | \(-0.807133\pi\) | ||||
−0.821985 | + | 0.569509i | \(0.807133\pi\) | |||||||
\(90\) | 23.1662 | 0.0271326 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −223.472 | −0.253245 | ||||||||
\(93\) | 944.987 | 1.05366 | ||||||||
\(94\) | −272.586 | −0.299096 | ||||||||
\(95\) | 18.3375 | 0.0198041 | ||||||||
\(96\) | −568.338 | −0.604226 | ||||||||
\(97\) | 218.008 | 0.228199 | 0.114100 | − | 0.993469i | \(-0.463602\pi\) | ||||
0.114100 | + | 0.993469i | \(0.463602\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −92.5330 | −0.0939385 | ||||||||
\(100\) | −65.8312 | −0.0658312 | ||||||||
\(101\) | −1474.33 | −1.45249 | −0.726243 | − | 0.687438i | \(-0.758735\pi\) | ||||
−0.726243 | + | 0.687438i | \(0.758735\pi\) | |||||||
\(102\) | −1173.75 | −1.13939 | ||||||||
\(103\) | −810.990 | −0.775818 | −0.387909 | − | 0.921698i | \(-0.626802\pi\) | ||||
−0.387909 | + | 0.921698i | \(0.626802\pi\) | |||||||
\(104\) | −1510.82 | −1.42450 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1547.49 | −1.41798 | ||||||||
\(107\) | 440.660 | 0.398133 | 0.199066 | − | 0.979986i | \(-0.436209\pi\) | ||||
0.199066 | + | 0.979986i | \(0.436209\pi\) | |||||||
\(108\) | 381.821 | 0.340192 | ||||||||
\(109\) | −1906.19 | −1.67504 | −0.837522 | − | 0.546404i | \(-0.815996\pi\) | ||||
−0.837522 | + | 0.546404i | \(0.815996\pi\) | |||||||
\(110\) | −535.911 | −0.464519 | ||||||||
\(111\) | 90.3425 | 0.0772517 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 962.470 | 0.801252 | 0.400626 | − | 0.916242i | \(-0.368793\pi\) | ||||
0.400626 | + | 0.916242i | \(0.368793\pi\) | |||||||
\(114\) | −42.4812 | −0.0349011 | ||||||||
\(115\) | 424.327 | 0.344076 | ||||||||
\(116\) | −79.5188 | −0.0636478 | ||||||||
\(117\) | 122.665 | 0.0969263 | ||||||||
\(118\) | −132.824 | −0.103622 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 615.831 | 0.468479 | ||||||||
\(121\) | 809.589 | 0.608256 | ||||||||
\(122\) | −1711.98 | −1.27045 | ||||||||
\(123\) | 2408.31 | 1.76545 | ||||||||
\(124\) | −497.678 | −0.360426 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1621.74 | −1.13312 | −0.566558 | − | 0.824022i | \(-0.691725\pi\) | ||||
−0.566558 | + | 0.824022i | \(0.691725\pi\) | |||||||
\(128\) | −367.873 | −0.254029 | ||||||||
\(129\) | −488.997 | −0.333751 | ||||||||
\(130\) | 710.422 | 0.479293 | ||||||||
\(131\) | −1380.32 | −0.920602 | −0.460301 | − | 0.887763i | \(-0.652259\pi\) | ||||
−0.460301 | + | 0.887763i | \(0.652259\pi\) | |||||||
\(132\) | −609.156 | −0.401668 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1279.69 | −0.824991 | ||||||||
\(135\) | −725.000 | −0.462208 | ||||||||
\(136\) | 2496.15 | 1.57385 | ||||||||
\(137\) | −1949.66 | −1.21584 | −0.607921 | − | 0.793997i | \(-0.707996\pi\) | ||||
−0.607921 | + | 0.793997i | \(0.707996\pi\) | |||||||
\(138\) | −983.008 | −0.606371 | ||||||||
\(139\) | 2800.00 | 1.70858 | 0.854291 | − | 0.519795i | \(-0.173992\pi\) | ||||
0.854291 | + | 0.519795i | \(0.173992\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 588.325 | 0.351389 | ||||||||
\(142\) | 1714.91 | 1.01347 | ||||||||
\(143\) | −2837.64 | −1.65941 | ||||||||
\(144\) | 72.0000 | 0.0416667 | ||||||||
\(145\) | 150.990 | 0.0864761 | ||||||||
\(146\) | −540.526 | −0.306399 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −47.5789 | −0.0264254 | ||||||||
\(149\) | −1434.12 | −0.788506 | −0.394253 | − | 0.919002i | \(-0.628997\pi\) | ||||
−0.394253 | + | 0.919002i | \(0.628997\pi\) | |||||||
\(150\) | −289.578 | −0.157626 | ||||||||
\(151\) | −1985.58 | −1.07009 | −0.535047 | − | 0.844822i | \(-0.679706\pi\) | ||||
−0.535047 | + | 0.844822i | \(0.679706\pi\) | |||||||
\(152\) | 90.3425 | 0.0482089 | ||||||||
\(153\) | −202.665 | −0.107088 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 944.987 | 0.489698 | ||||||||
\(156\) | 807.519 | 0.414444 | ||||||||
\(157\) | 40.6600 | 0.0206689 | 0.0103345 | − | 0.999947i | \(-0.496710\pi\) | ||||
0.0103345 | + | 0.999947i | \(0.496710\pi\) | |||||||
\(158\) | 2490.80 | 1.25416 | ||||||||
\(159\) | 3339.97 | 1.66589 | ||||||||
\(160\) | −568.338 | −0.280819 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1554.46 | 0.753886 | ||||||||
\(163\) | −3953.98 | −1.90000 | −0.950000 | − | 0.312250i | \(-0.898917\pi\) | ||||
−0.950000 | + | 0.312250i | \(0.898917\pi\) | |||||||
\(164\) | −1268.34 | −0.603906 | ||||||||
\(165\) | 1156.66 | 0.545734 | ||||||||
\(166\) | −1583.01 | −0.740152 | ||||||||
\(167\) | 3380.30 | 1.56632 | 0.783161 | − | 0.621819i | \(-0.213606\pi\) | ||||
0.783161 | + | 0.621819i | \(0.213606\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1564.68 | 0.712187 | ||||||||
\(170\) | −1173.75 | −0.529543 | ||||||||
\(171\) | −7.33501 | −0.00328025 | ||||||||
\(172\) | 257.530 | 0.114166 | ||||||||
\(173\) | 3206.66 | 1.40924 | 0.704619 | − | 0.709586i | \(-0.251118\pi\) | ||||
0.704619 | + | 0.709586i | \(0.251118\pi\) | |||||||
\(174\) | −349.787 | −0.152398 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1665.59 | −0.713346 | ||||||||
\(177\) | 286.675 | 0.121739 | ||||||||
\(178\) | 3197.68 | 1.34649 | ||||||||
\(179\) | 1442.65 | 0.602395 | 0.301198 | − | 0.953562i | \(-0.402614\pi\) | ||||
0.301198 | + | 0.953562i | \(0.402614\pi\) | |||||||
\(180\) | 26.3325 | 0.0109039 | ||||||||
\(181\) | −908.680 | −0.373158 | −0.186579 | − | 0.982440i | \(-0.559740\pi\) | ||||
−0.186579 | + | 0.982440i | \(0.559740\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3694.99 | 1.49258 | ||||||||
\(184\) | 2090.51 | 0.837580 | ||||||||
\(185\) | 90.3425 | 0.0359033 | ||||||||
\(186\) | −2189.18 | −0.863003 | ||||||||
\(187\) | 4688.30 | 1.83338 | ||||||||
\(188\) | −309.841 | −0.120199 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −42.4812 | −0.0162206 | ||||||||
\(191\) | 2474.64 | 0.937479 | 0.468739 | − | 0.883336i | \(-0.344708\pi\) | ||||
0.468739 | + | 0.883336i | \(0.344708\pi\) | |||||||
\(192\) | 2756.62 | 1.03616 | ||||||||
\(193\) | 3533.52 | 1.31787 | 0.658934 | − | 0.752201i | \(-0.271008\pi\) | ||||
0.658934 | + | 0.752201i | \(0.271008\pi\) | |||||||
\(194\) | −505.042 | −0.186907 | ||||||||
\(195\) | −1533.31 | −0.563091 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1952.57 | −0.706165 | −0.353083 | − | 0.935592i | \(-0.614867\pi\) | ||||
−0.353083 | + | 0.935592i | \(0.614867\pi\) | |||||||
\(198\) | 214.364 | 0.0769404 | ||||||||
\(199\) | 4064.67 | 1.44792 | 0.723962 | − | 0.689840i | \(-0.242319\pi\) | ||||
0.723962 | + | 0.689840i | \(0.242319\pi\) | |||||||
\(200\) | 615.831 | 0.217729 | ||||||||
\(201\) | 2761.98 | 0.969229 | ||||||||
\(202\) | 3415.46 | 1.18966 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1334.17 | −0.457895 | ||||||||
\(205\) | 2408.31 | 0.820507 | ||||||||
\(206\) | 1878.76 | 0.635434 | ||||||||
\(207\) | −169.731 | −0.0569909 | ||||||||
\(208\) | 2207.97 | 0.736034 | ||||||||
\(209\) | 169.683 | 0.0561588 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4325.34 | −1.41123 | −0.705613 | − | 0.708598i | \(-0.749328\pi\) | ||||
−0.705613 | + | 0.708598i | \(0.749328\pi\) | |||||||
\(212\) | −1759.00 | −0.569851 | ||||||||
\(213\) | −3701.32 | −1.19066 | ||||||||
\(214\) | −1020.84 | −0.326091 | ||||||||
\(215\) | −488.997 | −0.155113 | ||||||||
\(216\) | −3571.82 | −1.12515 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4415.92 | 1.37194 | ||||||||
\(219\) | 1166.62 | 0.359969 | ||||||||
\(220\) | −609.156 | −0.186679 | ||||||||
\(221\) | −6214.97 | −1.89169 | ||||||||
\(222\) | −209.290 | −0.0632730 | ||||||||
\(223\) | −982.970 | −0.295177 | −0.147589 | − | 0.989049i | \(-0.547151\pi\) | ||||
−0.147589 | + | 0.989049i | \(0.547151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −50.0000 | −0.0148148 | ||||||||
\(226\) | −2229.68 | −0.656266 | ||||||||
\(227\) | −1660.96 | −0.485648 | −0.242824 | − | 0.970070i | \(-0.578074\pi\) | ||||
−0.242824 | + | 0.970070i | \(0.578074\pi\) | |||||||
\(228\) | −48.2873 | −0.0140259 | ||||||||
\(229\) | −574.327 | −0.165732 | −0.0828660 | − | 0.996561i | \(-0.526407\pi\) | ||||
−0.0828660 | + | 0.996561i | \(0.526407\pi\) | |||||||
\(230\) | −983.008 | −0.281816 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 743.875 | 0.210508 | ||||||||
\(233\) | −2316.48 | −0.651320 | −0.325660 | − | 0.945487i | \(-0.605586\pi\) | ||||
−0.325660 | + | 0.945487i | \(0.605586\pi\) | |||||||
\(234\) | −284.169 | −0.0793876 | ||||||||
\(235\) | 588.325 | 0.163311 | ||||||||
\(236\) | −150.977 | −0.0416432 | ||||||||
\(237\) | −5375.93 | −1.47343 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3659.31 | −0.990382 | −0.495191 | − | 0.868784i | \(-0.664902\pi\) | ||||
−0.495191 | + | 0.868784i | \(0.664902\pi\) | |||||||
\(240\) | −900.000 | −0.242061 | ||||||||
\(241\) | 2446.33 | 0.653868 | 0.326934 | − | 0.945047i | \(-0.393985\pi\) | ||||
0.326934 | + | 0.945047i | \(0.393985\pi\) | |||||||
\(242\) | −1875.51 | −0.498193 | ||||||||
\(243\) | 560.000 | 0.147835 | ||||||||
\(244\) | −1945.96 | −0.510564 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5579.16 | −1.44599 | ||||||||
\(247\) | −224.937 | −0.0579450 | ||||||||
\(248\) | 4655.62 | 1.19207 | ||||||||
\(249\) | 3416.62 | 0.869557 | ||||||||
\(250\) | −289.578 | −0.0732581 | ||||||||
\(251\) | −2909.29 | −0.731605 | −0.365802 | − | 0.930693i | \(-0.619205\pi\) | ||||
−0.365802 | + | 0.930693i | \(0.619205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3926.43 | 0.975702 | ||||||||
\(254\) | 3756.95 | 0.928080 | ||||||||
\(255\) | 2533.31 | 0.622126 | ||||||||
\(256\) | −3558.38 | −0.868744 | ||||||||
\(257\) | 168.680 | 0.0409415 | 0.0204708 | − | 0.999790i | \(-0.493483\pi\) | ||||
0.0204708 | + | 0.999790i | \(0.493483\pi\) | |||||||
\(258\) | 1132.82 | 0.273359 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 807.519 | 0.192616 | ||||||||
\(261\) | −60.3960 | −0.0143234 | ||||||||
\(262\) | 3197.68 | 0.754020 | ||||||||
\(263\) | −3244.47 | −0.760695 | −0.380347 | − | 0.924844i | \(-0.624196\pi\) | ||||
−0.380347 | + | 0.924844i | \(0.624196\pi\) | |||||||
\(264\) | 5698.47 | 1.32847 | ||||||||
\(265\) | 3339.97 | 0.774238 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6901.59 | −1.58191 | ||||||||
\(268\) | −1454.60 | −0.331543 | ||||||||
\(269\) | −2848.65 | −0.645671 | −0.322836 | − | 0.946455i | \(-0.604636\pi\) | ||||
−0.322836 | + | 0.946455i | \(0.604636\pi\) | |||||||
\(270\) | 1679.55 | 0.378572 | ||||||||
\(271\) | −2850.98 | −0.639057 | −0.319529 | − | 0.947577i | \(-0.603525\pi\) | ||||
−0.319529 | + | 0.947577i | \(0.603525\pi\) | |||||||
\(272\) | −3647.97 | −0.813201 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4516.62 | 0.995837 | ||||||||
\(275\) | 1156.66 | 0.253634 | ||||||||
\(276\) | −1117.36 | −0.243685 | ||||||||
\(277\) | 2298.63 | 0.498597 | 0.249298 | − | 0.968427i | \(-0.419800\pi\) | ||||
0.249298 | + | 0.968427i | \(0.419800\pi\) | |||||||
\(278\) | −6486.55 | −1.39942 | ||||||||
\(279\) | −377.995 | −0.0811110 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6109.20 | 1.29695 | 0.648477 | − | 0.761234i | \(-0.275406\pi\) | ||||
0.648477 | + | 0.761234i | \(0.275406\pi\) | |||||||
\(282\) | −1362.93 | −0.287806 | ||||||||
\(283\) | 5854.95 | 1.22983 | 0.614913 | − | 0.788595i | \(-0.289191\pi\) | ||||
0.614913 | + | 0.788595i | \(0.289191\pi\) | |||||||
\(284\) | 1949.30 | 0.407288 | ||||||||
\(285\) | 91.6876 | 0.0190565 | ||||||||
\(286\) | 6573.75 | 1.35914 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 227.335 | 0.0465133 | ||||||||
\(289\) | 5355.27 | 1.09002 | ||||||||
\(290\) | −349.787 | −0.0708283 | ||||||||
\(291\) | 1090.04 | 0.219585 | ||||||||
\(292\) | −614.403 | −0.123134 | ||||||||
\(293\) | −5135.34 | −1.02392 | −0.511962 | − | 0.859008i | \(-0.671081\pi\) | ||||
−0.511962 | + | 0.859008i | \(0.671081\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 286.675 | 0.0565792 | ||||||||
\(296\) | 445.086 | 0.0873990 | ||||||||
\(297\) | −6708.64 | −1.31069 | ||||||||
\(298\) | 3322.31 | 0.645827 | ||||||||
\(299\) | −5205.01 | −1.00673 | ||||||||
\(300\) | −329.156 | −0.0633461 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4599.85 | 0.876462 | ||||||||
\(303\) | −7371.64 | −1.39766 | ||||||||
\(304\) | −132.030 | −0.0249094 | ||||||||
\(305\) | 3694.99 | 0.693686 | ||||||||
\(306\) | 469.499 | 0.0877106 | ||||||||
\(307\) | 2102.97 | 0.390954 | 0.195477 | − | 0.980708i | \(-0.437375\pi\) | ||||
0.195477 | + | 0.980708i | \(0.437375\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4054.95 | −0.746531 | ||||||||
\(310\) | −2189.18 | −0.401088 | ||||||||
\(311\) | −5764.30 | −1.05101 | −0.525504 | − | 0.850791i | \(-0.676123\pi\) | ||||
−0.525504 | + | 0.850791i | \(0.676123\pi\) | |||||||
\(312\) | −7554.09 | −1.37073 | ||||||||
\(313\) | −1360.01 | −0.245599 | −0.122799 | − | 0.992432i | \(-0.539187\pi\) | ||||
−0.122799 | + | 0.992432i | \(0.539187\pi\) | |||||||
\(314\) | −94.1939 | −0.0169289 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2831.23 | 0.504017 | ||||||||
\(317\) | 5138.95 | 0.910511 | 0.455256 | − | 0.890361i | \(-0.349548\pi\) | ||||
0.455256 | + | 0.890361i | \(0.349548\pi\) | |||||||
\(318\) | −7737.47 | −1.36445 | ||||||||
\(319\) | 1397.16 | 0.245222 | ||||||||
\(320\) | 2756.62 | 0.481563 | ||||||||
\(321\) | 2203.30 | 0.383103 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 371.637 | 0.0640200 | ||||||||
\(324\) | 1766.91 | 0.302968 | ||||||||
\(325\) | −1533.31 | −0.261701 | ||||||||
\(326\) | 9159.90 | 1.55620 | ||||||||
\(327\) | −9530.94 | −1.61181 | ||||||||
\(328\) | 11864.9 | 1.99735 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2679.55 | −0.446983 | ||||||||
\(331\) | 1825.70 | 0.303171 | 0.151585 | − | 0.988444i | \(-0.451562\pi\) | ||||
0.151585 | + | 0.988444i | \(0.451562\pi\) | |||||||
\(332\) | −1799.37 | −0.297449 | ||||||||
\(333\) | −36.1370 | −0.00594684 | ||||||||
\(334\) | −7830.90 | −1.28290 | ||||||||
\(335\) | 2761.98 | 0.450457 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 153.985 | 0.0248905 | 0.0124452 | − | 0.999923i | \(-0.496038\pi\) | ||||
0.0124452 | + | 0.999923i | \(0.496038\pi\) | |||||||
\(338\) | −3624.76 | −0.583317 | ||||||||
\(339\) | 4812.35 | 0.771005 | ||||||||
\(340\) | −1334.17 | −0.212810 | ||||||||
\(341\) | 8744.25 | 1.38864 | ||||||||
\(342\) | 16.9925 | 0.00268669 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2409.12 | −0.377590 | ||||||||
\(345\) | 2121.64 | 0.331087 | ||||||||
\(346\) | −7428.63 | −1.15424 | ||||||||
\(347\) | 4359.39 | 0.674421 | 0.337211 | − | 0.941429i | \(-0.390517\pi\) | ||||
0.337211 | + | 0.941429i | \(0.390517\pi\) | |||||||
\(348\) | −397.594 | −0.0612451 | ||||||||
\(349\) | 1689.00 | 0.259054 | 0.129527 | − | 0.991576i | \(-0.458654\pi\) | ||||
0.129527 | + | 0.991576i | \(0.458654\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8893.21 | 1.35238 | ||||||||
\(352\) | −5259.00 | −0.796322 | ||||||||
\(353\) | −3921.36 | −0.591254 | −0.295627 | − | 0.955303i | \(-0.595529\pi\) | ||||
−0.295627 | + | 0.955303i | \(0.595529\pi\) | |||||||
\(354\) | −664.119 | −0.0997105 | ||||||||
\(355\) | −3701.32 | −0.553368 | ||||||||
\(356\) | 3634.72 | 0.541123 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3342.08 | −0.493392 | ||||||||
\(359\) | −2867.86 | −0.421616 | −0.210808 | − | 0.977528i | \(-0.567609\pi\) | ||||
−0.210808 | + | 0.977528i | \(0.567609\pi\) | |||||||
\(360\) | −246.332 | −0.0360635 | ||||||||
\(361\) | −6845.55 | −0.998039 | ||||||||
\(362\) | 2105.07 | 0.305636 | ||||||||
\(363\) | 4047.94 | 0.585295 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1166.62 | 0.167298 | ||||||||
\(366\) | −8559.90 | −1.22249 | ||||||||
\(367\) | 11503.0 | 1.63611 | 0.818054 | − | 0.575142i | \(-0.195053\pi\) | ||||
0.818054 | + | 0.575142i | \(0.195053\pi\) | |||||||
\(368\) | −3055.16 | −0.432775 | ||||||||
\(369\) | −963.325 | −0.135904 | ||||||||
\(370\) | −209.290 | −0.0294066 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2488.39 | −0.346820 | ||||||||
\(373\) | 5086.43 | 0.706073 | 0.353037 | − | 0.935610i | \(-0.385149\pi\) | ||||
0.353037 | + | 0.935610i | \(0.385149\pi\) | |||||||
\(374\) | −10861.0 | −1.50163 | ||||||||
\(375\) | 625.000 | 0.0860663 | ||||||||
\(376\) | 2898.47 | 0.397546 | ||||||||
\(377\) | −1852.12 | −0.253021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 954.827 | 0.129409 | 0.0647047 | − | 0.997904i | \(-0.479389\pi\) | ||||
0.0647047 | + | 0.997904i | \(0.479389\pi\) | |||||||
\(380\) | −48.2873 | −0.00651864 | ||||||||
\(381\) | −8108.68 | −1.09034 | ||||||||
\(382\) | −5732.81 | −0.767843 | ||||||||
\(383\) | 3083.91 | 0.411437 | 0.205719 | − | 0.978611i | \(-0.434047\pi\) | ||||
0.205719 | + | 0.978611i | \(0.434047\pi\) | |||||||
\(384\) | −1839.37 | −0.244439 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8185.84 | −1.07940 | ||||||||
\(387\) | 195.599 | 0.0256921 | ||||||||
\(388\) | −574.068 | −0.0751131 | ||||||||
\(389\) | −6331.15 | −0.825198 | −0.412599 | − | 0.910913i | \(-0.635379\pi\) | ||||
−0.412599 | + | 0.910913i | \(0.635379\pi\) | |||||||
\(390\) | 3552.11 | 0.461200 | ||||||||
\(391\) | 8599.63 | 1.11228 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6901.59 | −0.885850 | ||||||||
\(394\) | 4523.36 | 0.578385 | ||||||||
\(395\) | −5375.93 | −0.684791 | ||||||||
\(396\) | 243.662 | 0.0309205 | ||||||||
\(397\) | −12133.2 | −1.53388 | −0.766939 | − | 0.641720i | \(-0.778221\pi\) | ||||
−0.766939 | + | 0.641720i | \(0.778221\pi\) | |||||||
\(398\) | −9416.32 | −1.18592 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −900.000 | −0.112500 | ||||||||
\(401\) | −270.669 | −0.0337072 | −0.0168536 | − | 0.999858i | \(-0.505365\pi\) | ||||
−0.0168536 | + | 0.999858i | \(0.505365\pi\) | |||||||
\(402\) | −6398.47 | −0.793848 | ||||||||
\(403\) | −11591.7 | −1.43281 | ||||||||
\(404\) | 3882.27 | 0.478095 | ||||||||
\(405\) | −3355.00 | −0.411633 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 835.967 | 0.101812 | ||||||||
\(408\) | 12480.7 | 1.51443 | ||||||||
\(409\) | 4019.92 | 0.485996 | 0.242998 | − | 0.970027i | \(-0.421869\pi\) | ||||
0.242998 | + | 0.970027i | \(0.421869\pi\) | |||||||
\(410\) | −5579.16 | −0.672036 | ||||||||
\(411\) | −9748.29 | −1.16995 | ||||||||
\(412\) | 2135.54 | 0.255365 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 393.203 | 0.0466784 | ||||||||
\(415\) | 3416.62 | 0.404134 | ||||||||
\(416\) | 6971.51 | 0.821650 | ||||||||
\(417\) | 14000.0 | 1.64408 | ||||||||
\(418\) | −393.091 | −0.0459969 | ||||||||
\(419\) | 2437.28 | 0.284175 | 0.142087 | − | 0.989854i | \(-0.454619\pi\) | ||||
0.142087 | + | 0.989854i | \(0.454619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4751.36 | −0.550041 | −0.275020 | − | 0.961438i | \(-0.588685\pi\) | ||||
−0.275020 | + | 0.961438i | \(0.588685\pi\) | |||||||
\(422\) | 10020.2 | 1.15586 | ||||||||
\(423\) | −235.330 | −0.0270500 | ||||||||
\(424\) | 16454.9 | 1.88472 | ||||||||
\(425\) | 2533.31 | 0.289138 | ||||||||
\(426\) | 8574.57 | 0.975210 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1160.37 | −0.131048 | ||||||||
\(429\) | −14188.2 | −1.59677 | ||||||||
\(430\) | 1132.82 | 0.127046 | ||||||||
\(431\) | 7925.19 | 0.885714 | 0.442857 | − | 0.896592i | \(-0.353965\pi\) | ||||
0.442857 | + | 0.896592i | \(0.353965\pi\) | |||||||
\(432\) | 5220.00 | 0.581360 | ||||||||
\(433\) | −11487.3 | −1.27492 | −0.637462 | − | 0.770481i | \(-0.720016\pi\) | ||||
−0.637462 | + | 0.770481i | \(0.720016\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 754.950 | 0.0832117 | ||||||||
\(436\) | 5019.47 | 0.551351 | ||||||||
\(437\) | 311.245 | 0.0340706 | ||||||||
\(438\) | −2702.63 | −0.294833 | ||||||||
\(439\) | −9147.92 | −0.994548 | −0.497274 | − | 0.867594i | \(-0.665666\pi\) | ||||
−0.497274 | + | 0.867594i | \(0.665666\pi\) | |||||||
\(440\) | 5698.47 | 0.617418 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14397.8 | 1.54939 | ||||||||
\(443\) | 1864.35 | 0.199950 | 0.0999752 | − | 0.994990i | \(-0.468124\pi\) | ||||
0.0999752 | + | 0.994990i | \(0.468124\pi\) | |||||||
\(444\) | −237.894 | −0.0254279 | ||||||||
\(445\) | −6901.59 | −0.735206 | ||||||||
\(446\) | 2277.17 | 0.241765 | ||||||||
\(447\) | −7170.58 | −0.758741 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4490.88 | 0.472022 | 0.236011 | − | 0.971750i | \(-0.424160\pi\) | ||||
0.236011 | + | 0.971750i | \(0.424160\pi\) | |||||||
\(450\) | 115.831 | 0.0121341 | ||||||||
\(451\) | 22284.8 | 2.32672 | ||||||||
\(452\) | −2534.42 | −0.263737 | ||||||||
\(453\) | −9927.91 | −1.02970 | ||||||||
\(454\) | 3847.83 | 0.397770 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 451.713 | 0.0463890 | ||||||||
\(457\) | −14343.8 | −1.46822 | −0.734109 | − | 0.679032i | \(-0.762400\pi\) | ||||
−0.734109 | + | 0.679032i | \(0.762400\pi\) | |||||||
\(458\) | 1330.50 | 0.135743 | ||||||||
\(459\) | −14693.2 | −1.49416 | ||||||||
\(460\) | −1117.36 | −0.113255 | ||||||||
\(461\) | −14558.7 | −1.47086 | −0.735429 | − | 0.677602i | \(-0.763019\pi\) | ||||
−0.735429 | + | 0.677602i | \(0.763019\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1809.56 | −0.181636 | −0.0908178 | − | 0.995868i | \(-0.528948\pi\) | ||||
−0.0908178 | + | 0.995868i | \(0.528948\pi\) | |||||||
\(464\) | −1087.13 | −0.108769 | ||||||||
\(465\) | 4724.94 | 0.471212 | ||||||||
\(466\) | 5366.41 | 0.533464 | ||||||||
\(467\) | 5981.65 | 0.592715 | 0.296357 | − | 0.955077i | \(-0.404228\pi\) | ||||
0.296357 | + | 0.955077i | \(0.404228\pi\) | |||||||
\(468\) | −323.008 | −0.0319039 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1362.93 | −0.133760 | ||||||||
\(471\) | 203.300 | 0.0198887 | ||||||||
\(472\) | 1412.35 | 0.137730 | ||||||||
\(473\) | −4524.84 | −0.439857 | ||||||||
\(474\) | 12454.0 | 1.20682 | ||||||||
\(475\) | 91.6876 | 0.00885666 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1335.99 | −0.128241 | ||||||||
\(478\) | 8477.25 | 0.811173 | ||||||||
\(479\) | 11527.5 | 1.09959 | 0.549796 | − | 0.835299i | \(-0.314705\pi\) | ||||
0.549796 | + | 0.835299i | \(0.314705\pi\) | |||||||
\(480\) | −2841.69 | −0.270218 | ||||||||
\(481\) | −1108.19 | −0.105050 | ||||||||
\(482\) | −5667.23 | −0.535551 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2131.85 | −0.200211 | ||||||||
\(485\) | 1090.04 | 0.102054 | ||||||||
\(486\) | −1297.31 | −0.121085 | ||||||||
\(487\) | 15791.5 | 1.46936 | 0.734682 | − | 0.678411i | \(-0.237331\pi\) | ||||
0.734682 | + | 0.678411i | \(0.237331\pi\) | |||||||
\(488\) | 18203.9 | 1.68863 | ||||||||
\(489\) | −19769.9 | −1.82828 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13064.9 | 1.20083 | 0.600417 | − | 0.799687i | \(-0.295001\pi\) | ||||
0.600417 | + | 0.799687i | \(0.295001\pi\) | |||||||
\(492\) | −6341.69 | −0.581108 | ||||||||
\(493\) | 3060.04 | 0.279548 | ||||||||
\(494\) | 521.095 | 0.0474599 | ||||||||
\(495\) | −462.665 | −0.0420106 | ||||||||
\(496\) | −6803.91 | −0.615937 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7915.04 | −0.712211 | ||||||||
\(499\) | −20135.8 | −1.80642 | −0.903209 | − | 0.429201i | \(-0.858795\pi\) | ||||
−0.903209 | + | 0.429201i | \(0.858795\pi\) | |||||||
\(500\) | −329.156 | −0.0294406 | ||||||||
\(501\) | 16901.5 | 1.50719 | ||||||||
\(502\) | 6739.73 | 0.599221 | ||||||||
\(503\) | 751.675 | 0.0666313 | 0.0333156 | − | 0.999445i | \(-0.489393\pi\) | ||||
0.0333156 | + | 0.999445i | \(0.489393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7371.64 | −0.649571 | ||||||||
\(506\) | −9096.06 | −0.799149 | ||||||||
\(507\) | 7823.38 | 0.685302 | ||||||||
\(508\) | 4270.44 | 0.372972 | ||||||||
\(509\) | 12334.5 | 1.07410 | 0.537049 | − | 0.843551i | \(-0.319539\pi\) | ||||
0.537049 | + | 0.843551i | \(0.319539\pi\) | |||||||
\(510\) | −5868.73 | −0.509553 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11186.4 | 0.965574 | ||||||||
\(513\) | −531.788 | −0.0457681 | ||||||||
\(514\) | −390.768 | −0.0335332 | ||||||||
\(515\) | −4054.95 | −0.346956 | ||||||||
\(516\) | 1287.65 | 0.109856 | ||||||||
\(517\) | 5443.95 | 0.463104 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16033.3 | 1.35604 | ||||||||
\(520\) | −7554.09 | −0.637056 | ||||||||
\(521\) | 1736.43 | 0.146016 | 0.0730082 | − | 0.997331i | \(-0.476740\pi\) | ||||
0.0730082 | + | 0.997331i | \(0.476740\pi\) | |||||||
\(522\) | 139.915 | 0.0117316 | ||||||||
\(523\) | 1421.42 | 0.118842 | 0.0594210 | − | 0.998233i | \(-0.481075\pi\) | ||||
0.0594210 | + | 0.998233i | \(0.481075\pi\) | |||||||
\(524\) | 3634.72 | 0.303022 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7516.23 | 0.623048 | ||||||||
\(527\) | 19151.6 | 1.58303 | ||||||||
\(528\) | −8327.97 | −0.686417 | ||||||||
\(529\) | −4964.85 | −0.408059 | ||||||||
\(530\) | −7737.47 | −0.634140 | ||||||||
\(531\) | −114.670 | −0.00937148 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29541.6 | −2.40073 | ||||||||
\(534\) | 15988.4 | 1.29567 | ||||||||
\(535\) | 2203.30 | 0.178050 | ||||||||
\(536\) | 13607.3 | 1.09654 | ||||||||
\(537\) | 7213.25 | 0.579655 | ||||||||
\(538\) | 6599.26 | 0.528837 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1909.11 | 0.152139 | ||||||||
\(541\) | 5773.27 | 0.458802 | 0.229401 | − | 0.973332i | \(-0.426323\pi\) | ||||
0.229401 | + | 0.973332i | \(0.426323\pi\) | |||||||
\(542\) | 6604.64 | 0.523420 | ||||||||
\(543\) | −4543.40 | −0.359072 | ||||||||
\(544\) | −11518.2 | −0.907793 | ||||||||
\(545\) | −9530.94 | −0.749102 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3941.30 | −0.308076 | −0.154038 | − | 0.988065i | \(-0.549228\pi\) | ||||
−0.154038 | + | 0.988065i | \(0.549228\pi\) | |||||||
\(548\) | 5133.93 | 0.400202 | ||||||||
\(549\) | −1477.99 | −0.114899 | ||||||||
\(550\) | −2679.55 | −0.207739 | ||||||||
\(551\) | 110.751 | 0.00856291 | ||||||||
\(552\) | 10452.6 | 0.805961 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5325.06 | −0.408376 | ||||||||
\(555\) | 451.713 | 0.0345480 | ||||||||
\(556\) | −7373.10 | −0.562390 | ||||||||
\(557\) | −6951.74 | −0.528823 | −0.264412 | − | 0.964410i | \(-0.585178\pi\) | ||||
−0.264412 | + | 0.964410i | \(0.585178\pi\) | |||||||
\(558\) | 875.673 | 0.0664340 | ||||||||
\(559\) | 5998.29 | 0.453847 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23441.5 | 1.76417 | ||||||||
\(562\) | −14152.7 | −1.06227 | ||||||||
\(563\) | 24284.6 | 1.81789 | 0.908946 | − | 0.416913i | \(-0.136888\pi\) | ||||
0.908946 | + | 0.416913i | \(0.136888\pi\) | |||||||
\(564\) | −1549.21 | −0.115662 | ||||||||
\(565\) | 4812.35 | 0.358331 | ||||||||
\(566\) | −13563.7 | −1.00729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18235.1 | −1.34706 | ||||||||
\(569\) | −21563.4 | −1.58873 | −0.794363 | − | 0.607443i | \(-0.792195\pi\) | ||||
−0.794363 | + | 0.607443i | \(0.792195\pi\) | |||||||
\(570\) | −212.406 | −0.0156082 | ||||||||
\(571\) | −3689.56 | −0.270409 | −0.135204 | − | 0.990818i | \(-0.543169\pi\) | ||||
−0.135204 | + | 0.990818i | \(0.543169\pi\) | |||||||
\(572\) | 7472.21 | 0.546204 | ||||||||
\(573\) | 12373.2 | 0.902090 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2121.64 | 0.153875 | ||||||||
\(576\) | −1102.65 | −0.0797634 | ||||||||
\(577\) | −22183.9 | −1.60057 | −0.800285 | − | 0.599620i | \(-0.795318\pi\) | ||||
−0.800285 | + | 0.599620i | \(0.795318\pi\) | |||||||
\(578\) | −12406.2 | −0.892783 | ||||||||
\(579\) | 17667.6 | 1.26812 | ||||||||
\(580\) | −397.594 | −0.0284641 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2525.21 | −0.179851 | ||||||||
\(583\) | 30905.8 | 2.19552 | ||||||||
\(584\) | 5747.55 | 0.407252 | ||||||||
\(585\) | 613.325 | 0.0433468 | ||||||||
\(586\) | 11896.7 | 0.838646 | ||||||||
\(587\) | 10605.3 | 0.745705 | 0.372852 | − | 0.927891i | \(-0.378380\pi\) | ||||
0.372852 | + | 0.927891i | \(0.378380\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 693.149 | 0.0484902 | ||||||||
\(590\) | −664.119 | −0.0463412 | ||||||||
\(591\) | −9762.83 | −0.679508 | ||||||||
\(592\) | −650.466 | −0.0451588 | ||||||||
\(593\) | 6277.25 | 0.434698 | 0.217349 | − | 0.976094i | \(-0.430259\pi\) | ||||
0.217349 | + | 0.976094i | \(0.430259\pi\) | |||||||
\(594\) | 15541.4 | 1.07352 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3776.39 | 0.259542 | ||||||||
\(597\) | 20323.4 | 1.39327 | ||||||||
\(598\) | 12058.1 | 0.824567 | ||||||||
\(599\) | −9970.73 | −0.680122 | −0.340061 | − | 0.940403i | \(-0.610448\pi\) | ||||
−0.340061 | + | 0.940403i | \(0.610448\pi\) | |||||||
\(600\) | 3079.16 | 0.209510 | ||||||||
\(601\) | −24619.2 | −1.67094 | −0.835472 | − | 0.549533i | \(-0.814806\pi\) | ||||
−0.835472 | + | 0.549533i | \(0.814806\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1104.79 | −0.0746113 | ||||||||
\(604\) | 5228.53 | 0.352228 | ||||||||
\(605\) | 4047.94 | 0.272020 | ||||||||
\(606\) | 17077.3 | 1.14475 | ||||||||
\(607\) | 11252.9 | 0.752460 | 0.376230 | − | 0.926526i | \(-0.377220\pi\) | ||||
0.376230 | + | 0.926526i | \(0.377220\pi\) | |||||||
\(608\) | −416.876 | −0.0278068 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8559.90 | −0.568164 | ||||||||
\(611\) | −7216.69 | −0.477833 | ||||||||
\(612\) | 533.668 | 0.0352487 | ||||||||
\(613\) | −15293.2 | −1.00765 | −0.503824 | − | 0.863807i | \(-0.668074\pi\) | ||||
−0.503824 | + | 0.863807i | \(0.668074\pi\) | |||||||
\(614\) | −4871.79 | −0.320211 | ||||||||
\(615\) | 12041.6 | 0.789533 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17589.4 | −1.14769 | −0.573843 | − | 0.818966i | \(-0.694548\pi\) | ||||
−0.573843 | + | 0.818966i | \(0.694548\pi\) | |||||||
\(618\) | 9393.80 | 0.611446 | ||||||||
\(619\) | −23467.4 | −1.52380 | −0.761900 | − | 0.647694i | \(-0.775733\pi\) | ||||
−0.761900 | + | 0.647694i | \(0.775733\pi\) | |||||||
\(620\) | −2488.39 | −0.161187 | ||||||||
\(621\) | −12305.5 | −0.795173 | ||||||||
\(622\) | 13353.7 | 0.860829 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 11039.8 | 0.708249 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 3150.64 | 0.201158 | ||||||||
\(627\) | 848.413 | 0.0540388 | ||||||||
\(628\) | −107.068 | −0.00680330 | ||||||||
\(629\) | 1830.93 | 0.116063 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6040.86 | −0.381114 | −0.190557 | − | 0.981676i | \(-0.561029\pi\) | ||||
−0.190557 | + | 0.981676i | \(0.561029\pi\) | |||||||
\(632\) | −26485.3 | −1.66698 | ||||||||
\(633\) | −21626.7 | −1.35795 | ||||||||
\(634\) | −11905.0 | −0.745755 | ||||||||
\(635\) | −8108.68 | −0.506745 | ||||||||
\(636\) | −8794.99 | −0.548340 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −3236.68 | −0.200849 | ||||||||
\(639\) | 1480.53 | 0.0916569 | ||||||||
\(640\) | −1839.37 | −0.113605 | ||||||||
\(641\) | 25111.6 | 1.54735 | 0.773673 | − | 0.633586i | \(-0.218418\pi\) | ||||
0.773673 | + | 0.633586i | \(0.218418\pi\) | |||||||
\(642\) | −5104.22 | −0.313781 | ||||||||
\(643\) | 3095.03 | 0.189823 | 0.0949113 | − | 0.995486i | \(-0.469743\pi\) | ||||
0.0949113 | + | 0.995486i | \(0.469743\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2444.99 | −0.149258 | ||||||||
\(646\) | −860.944 | −0.0524356 | ||||||||
\(647\) | 9178.63 | 0.557727 | 0.278863 | − | 0.960331i | \(-0.410042\pi\) | ||||
0.278863 | + | 0.960331i | \(0.410042\pi\) | |||||||
\(648\) | −16528.9 | −1.00203 | ||||||||
\(649\) | 2652.69 | 0.160443 | ||||||||
\(650\) | 3552.11 | 0.214346 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10411.8 | 0.625397 | ||||||||
\(653\) | −14438.4 | −0.865265 | −0.432632 | − | 0.901570i | \(-0.642415\pi\) | ||||
−0.432632 | + | 0.901570i | \(0.642415\pi\) | |||||||
\(654\) | 22079.6 | 1.32015 | ||||||||
\(655\) | −6901.59 | −0.411706 | ||||||||
\(656\) | −17339.8 | −1.03202 | ||||||||
\(657\) | −466.650 | −0.0277104 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2900.64 | −0.171461 | −0.0857305 | − | 0.996318i | \(-0.527322\pi\) | ||||
−0.0857305 | + | 0.996318i | \(0.527322\pi\) | |||||||
\(660\) | −3045.78 | −0.179632 | ||||||||
\(661\) | 9976.52 | 0.587053 | 0.293526 | − | 0.955951i | \(-0.405171\pi\) | ||||
0.293526 | + | 0.955951i | \(0.405171\pi\) | |||||||
\(662\) | −4229.46 | −0.248312 | ||||||||
\(663\) | −31074.9 | −1.82028 | ||||||||
\(664\) | 16832.5 | 0.983777 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 83.7159 | 0.00487076 | ||||||||
\(667\) | 2562.77 | 0.148772 | ||||||||
\(668\) | −8901.19 | −0.515565 | ||||||||
\(669\) | −4914.85 | −0.284034 | ||||||||
\(670\) | −6398.47 | −0.368947 | ||||||||
\(671\) | 34190.8 | 1.96710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20760.8 | 1.18911 | 0.594554 | − | 0.804055i | \(-0.297329\pi\) | ||||
0.594554 | + | 0.804055i | \(0.297329\pi\) | |||||||
\(674\) | −356.725 | −0.0203866 | ||||||||
\(675\) | −3625.00 | −0.206706 | ||||||||
\(676\) | −4120.18 | −0.234421 | ||||||||
\(677\) | 3209.13 | 0.182181 | 0.0910907 | − | 0.995843i | \(-0.470965\pi\) | ||||
0.0910907 | + | 0.995843i | \(0.470965\pi\) | |||||||
\(678\) | −11148.4 | −0.631492 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12480.7 | 0.703845 | ||||||||
\(681\) | −8304.82 | −0.467315 | ||||||||
\(682\) | −20257.2 | −1.13737 | ||||||||
\(683\) | 4333.57 | 0.242781 | 0.121391 | − | 0.992605i | \(-0.461265\pi\) | ||||
0.121391 | + | 0.992605i | \(0.461265\pi\) | |||||||
\(684\) | 19.3149 | 0.00107971 | ||||||||
\(685\) | −9748.29 | −0.543741 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2871.64 | −0.159476 | ||||||||
\(688\) | 3520.78 | 0.195100 | ||||||||
\(689\) | −40969.8 | −2.26535 | ||||||||
\(690\) | −4915.04 | −0.271177 | ||||||||
\(691\) | −14446.0 | −0.795297 | −0.397649 | − | 0.917538i | \(-0.630174\pi\) | ||||
−0.397649 | + | 0.917538i | \(0.630174\pi\) | |||||||
\(692\) | −8443.94 | −0.463859 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10099.1 | −0.552385 | ||||||||
\(695\) | 14000.0 | 0.764101 | ||||||||
\(696\) | 3719.37 | 0.202561 | ||||||||
\(697\) | 48808.1 | 2.65242 | ||||||||
\(698\) | −3912.77 | −0.212179 | ||||||||
\(699\) | −11582.4 | −0.626733 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −859.801 | −0.0463256 | −0.0231628 | − | 0.999732i | \(-0.507374\pi\) | ||||
−0.0231628 | + | 0.999732i | \(0.507374\pi\) | |||||||
\(702\) | −20602.2 | −1.10767 | ||||||||
\(703\) | 66.2663 | 0.00355517 | ||||||||
\(704\) | 25507.9 | 1.36557 | ||||||||
\(705\) | 2941.62 | 0.157146 | ||||||||
\(706\) | 9084.31 | 0.484267 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −754.887 | −0.0400712 | ||||||||
\(709\) | −7979.13 | −0.422655 | −0.211327 | − | 0.977415i | \(-0.567779\pi\) | ||||
−0.211327 | + | 0.977415i | \(0.567779\pi\) | |||||||
\(710\) | 8574.57 | 0.453236 | ||||||||
\(711\) | 2150.37 | 0.113425 | ||||||||
\(712\) | −34001.7 | −1.78970 | ||||||||
\(713\) | 16039.4 | 0.842467 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14188.2 | −0.742110 | ||||||||
\(716\) | −3798.86 | −0.198282 | ||||||||
\(717\) | −18296.6 | −0.952995 | ||||||||
\(718\) | 6643.76 | 0.345325 | ||||||||
\(719\) | −33703.3 | −1.74815 | −0.874076 | − | 0.485790i | \(-0.838532\pi\) | ||||
−0.874076 | + | 0.485790i | \(0.838532\pi\) | |||||||
\(720\) | 360.000 | 0.0186339 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15858.6 | 0.817444 | ||||||||
\(723\) | 12231.7 | 0.629185 | ||||||||
\(724\) | 2392.78 | 0.122827 | ||||||||
\(725\) | 754.950 | 0.0386733 | ||||||||
\(726\) | −9377.57 | −0.479386 | ||||||||
\(727\) | −30277.0 | −1.54458 | −0.772290 | − | 0.635270i | \(-0.780889\pi\) | ||||
−0.772290 | + | 0.635270i | \(0.780889\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | −2702.63 | −0.137026 | ||||||||
\(731\) | −9910.27 | −0.501429 | ||||||||
\(732\) | −9729.82 | −0.491291 | ||||||||
\(733\) | 19363.9 | 0.975749 | 0.487874 | − | 0.872914i | \(-0.337772\pi\) | ||||
0.487874 | + | 0.872914i | \(0.337772\pi\) | |||||||
\(734\) | −26648.1 | −1.34005 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9646.45 | −0.483115 | ||||||||
\(737\) | 25557.4 | 1.27737 | ||||||||
\(738\) | 2231.66 | 0.111313 | ||||||||
\(739\) | 24952.4 | 1.24207 | 0.621035 | − | 0.783783i | \(-0.286713\pi\) | ||||
0.621035 | + | 0.783783i | \(0.286713\pi\) | |||||||
\(740\) | −237.894 | −0.0118178 | ||||||||
\(741\) | −1124.69 | −0.0557576 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8154.54 | −0.402640 | −0.201320 | − | 0.979526i | \(-0.564523\pi\) | ||||
−0.201320 | + | 0.979526i | \(0.564523\pi\) | |||||||
\(744\) | 23278.1 | 1.14707 | ||||||||
\(745\) | −7170.58 | −0.352631 | ||||||||
\(746\) | −11783.3 | −0.578310 | ||||||||
\(747\) | −1366.65 | −0.0669386 | ||||||||
\(748\) | −12345.5 | −0.603469 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1447.89 | −0.0704926 | ||||||||
\(751\) | −4311.26 | −0.209481 | −0.104740 | − | 0.994500i | \(-0.533401\pi\) | ||||
−0.104740 | + | 0.994500i | \(0.533401\pi\) | |||||||
\(752\) | −4235.94 | −0.205411 | ||||||||
\(753\) | −14546.4 | −0.703987 | ||||||||
\(754\) | 4290.66 | 0.207237 | ||||||||
\(755\) | −9927.91 | −0.478561 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3624.79 | 0.174036 | 0.0870179 | − | 0.996207i | \(-0.472266\pi\) | ||||
0.0870179 | + | 0.996207i | \(0.472266\pi\) | |||||||
\(758\) | −2211.98 | −0.105993 | ||||||||
\(759\) | 19632.1 | 0.938869 | ||||||||
\(760\) | 451.713 | 0.0215597 | ||||||||
\(761\) | 20576.4 | 0.980150 | 0.490075 | − | 0.871680i | \(-0.336969\pi\) | ||||
0.490075 | + | 0.871680i | \(0.336969\pi\) | |||||||
\(762\) | 18784.8 | 0.893045 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6516.34 | −0.308577 | ||||||||
\(765\) | −1013.32 | −0.0478913 | ||||||||
\(766\) | −7144.26 | −0.336988 | ||||||||
\(767\) | −3516.50 | −0.165546 | ||||||||
\(768\) | −17791.9 | −0.835949 | ||||||||
\(769\) | −3066.14 | −0.143781 | −0.0718907 | − | 0.997413i | \(-0.522903\pi\) | ||||
−0.0718907 | + | 0.997413i | \(0.522903\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 843.400 | 0.0393960 | ||||||||
\(772\) | −9304.64 | −0.433784 | ||||||||
\(773\) | −19387.0 | −0.902074 | −0.451037 | − | 0.892505i | \(-0.648946\pi\) | ||||
−0.451037 | + | 0.892505i | \(0.648946\pi\) | |||||||
\(774\) | −453.129 | −0.0210432 | ||||||||
\(775\) | 4724.94 | 0.219000 | ||||||||
\(776\) | 5370.23 | 0.248428 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14666.9 | 0.675879 | ||||||||
\(779\) | 1766.50 | 0.0812470 | ||||||||
\(780\) | 4037.59 | 0.185345 | ||||||||
\(781\) | −34249.4 | −1.56919 | ||||||||
\(782\) | −19922.1 | −0.911015 | ||||||||
\(783\) | −4378.71 | −0.199850 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 203.300 | 0.00924342 | ||||||||
\(786\) | 15988.4 | 0.725556 | ||||||||
\(787\) | 43363.4 | 1.96409 | 0.982044 | − | 0.188651i | \(-0.0604115\pi\) | ||||
0.982044 | + | 0.188651i | \(0.0604115\pi\) | |||||||
\(788\) | 5141.59 | 0.232439 | ||||||||
\(789\) | −16222.4 | −0.731979 | ||||||||
\(790\) | 12454.0 | 0.560878 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2279.39 | −0.102266 | ||||||||
\(793\) | −45324.6 | −2.02966 | ||||||||
\(794\) | 28108.2 | 1.25632 | ||||||||
\(795\) | 16699.9 | 0.745011 | ||||||||
\(796\) | −10703.3 | −0.476593 | ||||||||
\(797\) | 17132.6 | 0.761439 | 0.380720 | − | 0.924691i | \(-0.375676\pi\) | ||||
0.380720 | + | 0.924691i | \(0.375676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11923.3 | 0.527929 | ||||||||
\(800\) | −2841.69 | −0.125586 | ||||||||
\(801\) | 2760.63 | 0.121776 | ||||||||
\(802\) | 627.039 | 0.0276079 | ||||||||
\(803\) | 10795.1 | 0.474411 | ||||||||
\(804\) | −7272.98 | −0.319028 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26853.6 | 1.17355 | ||||||||
\(807\) | −14243.3 | −0.621297 | ||||||||
\(808\) | −36317.5 | −1.58124 | ||||||||
\(809\) | −1080.49 | −0.0469566 | −0.0234783 | − | 0.999724i | \(-0.507474\pi\) | ||||
−0.0234783 | + | 0.999724i | \(0.507474\pi\) | |||||||
\(810\) | 7772.28 | 0.337148 | ||||||||
\(811\) | 19593.9 | 0.848378 | 0.424189 | − | 0.905574i | \(-0.360559\pi\) | ||||
0.424189 | + | 0.905574i | \(0.360559\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −14254.9 | −0.614933 | ||||||||
\(814\) | −1936.62 | −0.0833889 | ||||||||
\(815\) | −19769.9 | −0.849706 | ||||||||
\(816\) | −18239.8 | −0.782503 | ||||||||
\(817\) | −358.680 | −0.0153594 | ||||||||
\(818\) | −9312.66 | −0.398056 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6341.69 | −0.270075 | ||||||||
\(821\) | 5123.80 | 0.217810 | 0.108905 | − | 0.994052i | \(-0.465266\pi\) | ||||
0.108905 | + | 0.994052i | \(0.465266\pi\) | |||||||
\(822\) | 22583.1 | 0.958244 | ||||||||
\(823\) | −13184.1 | −0.558405 | −0.279202 | − | 0.960232i | \(-0.590070\pi\) | ||||
−0.279202 | + | 0.960232i | \(0.590070\pi\) | |||||||
\(824\) | −19977.3 | −0.844591 | ||||||||
\(825\) | 5783.31 | 0.244060 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24658.7 | 1.03684 | 0.518421 | − | 0.855126i | \(-0.326520\pi\) | ||||
0.518421 | + | 0.855126i | \(0.326520\pi\) | |||||||
\(828\) | 446.944 | 0.0187589 | ||||||||
\(829\) | −28562.3 | −1.19664 | −0.598318 | − | 0.801259i | \(-0.704164\pi\) | ||||
−0.598318 | + | 0.801259i | \(0.704164\pi\) | |||||||
\(830\) | −7915.04 | −0.331006 | ||||||||
\(831\) | 11493.1 | 0.479775 | ||||||||
\(832\) | −33814.1 | −1.40901 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −32432.7 | −1.34659 | ||||||||
\(835\) | 16901.5 | 0.700481 | ||||||||
\(836\) | −446.817 | −0.0184850 | ||||||||
\(837\) | −27404.6 | −1.13171 | ||||||||
\(838\) | −5646.27 | −0.232753 | ||||||||
\(839\) | 31106.0 | 1.27997 | 0.639987 | − | 0.768386i | \(-0.278940\pi\) | ||||
0.639987 | + | 0.768386i | \(0.278940\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23477.1 | −0.962609 | ||||||||
\(842\) | 11007.1 | 0.450511 | ||||||||
\(843\) | 30546.0 | 1.24800 | ||||||||
\(844\) | 11389.7 | 0.464514 | ||||||||
\(845\) | 7823.38 | 0.318500 | ||||||||
\(846\) | 545.171 | 0.0221553 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −24047.8 | −0.973827 | ||||||||
\(849\) | 29274.7 | 1.18340 | ||||||||
\(850\) | −5868.73 | −0.236819 | ||||||||
\(851\) | 1533.39 | 0.0617674 | ||||||||
\(852\) | 9746.50 | 0.391913 | ||||||||
\(853\) | −20567.9 | −0.825596 | −0.412798 | − | 0.910823i | \(-0.635448\pi\) | ||||
−0.412798 | + | 0.910823i | \(0.635448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −36.6750 | −0.00146697 | ||||||||
\(856\) | 10854.9 | 0.433426 | ||||||||
\(857\) | −6459.44 | −0.257468 | −0.128734 | − | 0.991679i | \(-0.541091\pi\) | ||||
−0.128734 | + | 0.991679i | \(0.541091\pi\) | |||||||
\(858\) | 32868.7 | 1.30783 | ||||||||
\(859\) | 48214.4 | 1.91508 | 0.957541 | − | 0.288298i | \(-0.0930895\pi\) | ||||
0.957541 | + | 0.288298i | \(0.0930895\pi\) | |||||||
\(860\) | 1287.65 | 0.0510565 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −18359.7 | −0.725445 | ||||||||
\(863\) | −31709.5 | −1.25076 | −0.625378 | − | 0.780322i | \(-0.715055\pi\) | ||||
−0.625378 | + | 0.780322i | \(0.715055\pi\) | |||||||
\(864\) | 16481.8 | 0.648984 | ||||||||
\(865\) | 16033.3 | 0.630230 | ||||||||
\(866\) | 26611.7 | 1.04423 | ||||||||
\(867\) | 26776.4 | 1.04887 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −49745.1 | −1.94187 | ||||||||
\(870\) | −1748.94 | −0.0681546 | ||||||||
\(871\) | −33879.8 | −1.31800 | ||||||||
\(872\) | −46955.6 | −1.82353 | ||||||||
\(873\) | −436.015 | −0.0169036 | ||||||||
\(874\) | −721.037 | −0.0279055 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3072.01 | −0.118486 | ||||||||
\(877\) | 25654.8 | 0.987799 | 0.493900 | − | 0.869519i | \(-0.335571\pi\) | ||||
0.493900 | + | 0.869519i | \(0.335571\pi\) | |||||||
\(878\) | 21192.3 | 0.814585 | ||||||||
\(879\) | −25676.7 | −0.985272 | ||||||||
\(880\) | −8327.97 | −0.319018 | ||||||||
\(881\) | 11470.4 | 0.438647 | 0.219323 | − | 0.975652i | \(-0.429615\pi\) | ||||
0.219323 | + | 0.975652i | \(0.429615\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39124.0 | 1.49108 | 0.745542 | − | 0.666459i | \(-0.232191\pi\) | ||||
0.745542 | + | 0.666459i | \(0.232191\pi\) | |||||||
\(884\) | 16365.6 | 0.622663 | ||||||||
\(885\) | 1433.38 | 0.0544434 | ||||||||
\(886\) | −4319.01 | −0.163770 | ||||||||
\(887\) | −15585.8 | −0.589987 | −0.294994 | − | 0.955499i | \(-0.595318\pi\) | ||||
−0.294994 | + | 0.955499i | \(0.595318\pi\) | |||||||
\(888\) | 2225.43 | 0.0840997 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 15988.4 | 0.602171 | ||||||||
\(891\) | −31044.8 | −1.16727 | ||||||||
\(892\) | 2588.40 | 0.0971594 | ||||||||
\(893\) | 431.537 | 0.0161711 | ||||||||
\(894\) | 16611.6 | 0.621447 | ||||||||
\(895\) | 7213.25 | 0.269399 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26025.1 | −0.968731 | ||||||||
\(898\) | −10403.7 | −0.386610 | ||||||||
\(899\) | 5707.34 | 0.211736 | ||||||||
\(900\) | 131.662 | 0.00487639 | ||||||||
\(901\) | 67689.6 | 2.50285 | ||||||||
\(902\) | −51625.6 | −1.90570 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 23708.8 | 0.872280 | ||||||||
\(905\) | −4543.40 | −0.166881 | ||||||||
\(906\) | 22999.2 | 0.843376 | ||||||||
\(907\) | 27596.1 | 1.01027 | 0.505134 | − | 0.863041i | \(-0.331443\pi\) | ||||
0.505134 | + | 0.863041i | \(0.331443\pi\) | |||||||
\(908\) | 4373.73 | 0.159854 | ||||||||
\(909\) | 2948.65 | 0.107592 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14396.2 | −0.523565 | −0.261782 | − | 0.965127i | \(-0.584310\pi\) | ||||
−0.261782 | + | 0.965127i | \(0.584310\pi\) | |||||||
\(912\) | −660.151 | −0.0239691 | ||||||||
\(913\) | 31615.1 | 1.14601 | ||||||||
\(914\) | 33229.2 | 1.20254 | ||||||||
\(915\) | 18474.9 | 0.667500 | ||||||||
\(916\) | 1512.35 | 0.0545517 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 34038.7 | 1.22379 | ||||||||
\(919\) | 10279.6 | 0.368978 | 0.184489 | − | 0.982835i | \(-0.440937\pi\) | ||||
0.184489 | + | 0.982835i | \(0.440937\pi\) | |||||||
\(920\) | 10452.6 | 0.374577 | ||||||||
\(921\) | 10514.8 | 0.376196 | ||||||||
\(922\) | 33727.0 | 1.20471 | ||||||||
\(923\) | 45402.2 | 1.61910 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 451.713 | 0.0160565 | ||||||||
\(926\) | 4192.06 | 0.148769 | ||||||||
\(927\) | 1621.98 | 0.0574680 | ||||||||
\(928\) | −3432.53 | −0.121421 | ||||||||
\(929\) | 6499.87 | 0.229552 | 0.114776 | − | 0.993391i | \(-0.463385\pi\) | ||||
0.114776 | + | 0.993391i | \(0.463385\pi\) | |||||||
\(930\) | −10945.9 | −0.385947 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 6099.86 | 0.214386 | ||||||||
\(933\) | −28821.5 | −1.01133 | ||||||||
\(934\) | −13857.2 | −0.485463 | ||||||||
\(935\) | 23441.5 | 0.819913 | ||||||||
\(936\) | 3021.64 | 0.105518 | ||||||||
\(937\) | −10269.8 | −0.358056 | −0.179028 | − | 0.983844i | \(-0.557295\pi\) | ||||
−0.179028 | + | 0.983844i | \(0.557295\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6800.06 | −0.236328 | ||||||||
\(940\) | −1549.21 | −0.0537548 | ||||||||
\(941\) | 34396.2 | 1.19159 | 0.595794 | − | 0.803137i | \(-0.296837\pi\) | ||||
0.595794 | + | 0.803137i | \(0.296837\pi\) | |||||||
\(942\) | −470.969 | −0.0162898 | ||||||||
\(943\) | 40876.5 | 1.41158 | ||||||||
\(944\) | −2064.06 | −0.0711647 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10482.4 | 0.360265 | ||||||||
\(947\) | 27192.1 | 0.933078 | 0.466539 | − | 0.884501i | \(-0.345501\pi\) | ||||
0.466539 | + | 0.884501i | \(0.345501\pi\) | |||||||
\(948\) | 14156.2 | 0.484990 | ||||||||
\(949\) | −14310.4 | −0.489500 | ||||||||
\(950\) | −212.406 | −0.00725406 | ||||||||
\(951\) | 25694.7 | 0.876140 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49965.2 | 1.69836 | 0.849178 | − | 0.528107i | \(-0.177098\pi\) | ||||
0.849178 | + | 0.528107i | \(0.177098\pi\) | |||||||
\(954\) | 3094.99 | 0.105036 | ||||||||
\(955\) | 12373.2 | 0.419253 | ||||||||
\(956\) | 9635.88 | 0.325990 | ||||||||
\(957\) | 6985.78 | 0.235965 | ||||||||
\(958\) | −26704.9 | −0.900622 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 13783.1 | 0.463384 | ||||||||
\(961\) | 5929.05 | 0.199022 | ||||||||
\(962\) | 2567.25 | 0.0860411 | ||||||||
\(963\) | −881.320 | −0.0294913 | ||||||||
\(964\) | −6441.80 | −0.215225 | ||||||||
\(965\) | 17667.6 | 0.589368 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16755.5 | −0.557208 | −0.278604 | − | 0.960406i | \(-0.589872\pi\) | ||||
−0.278604 | + | 0.960406i | \(0.589872\pi\) | |||||||
\(968\) | 19942.8 | 0.662176 | ||||||||
\(969\) | 1858.19 | 0.0616033 | ||||||||
\(970\) | −2525.21 | −0.0835872 | ||||||||
\(971\) | −37617.4 | −1.24325 | −0.621626 | − | 0.783314i | \(-0.713528\pi\) | ||||
−0.621626 | + | 0.783314i | \(0.713528\pi\) | |||||||
\(972\) | −1474.62 | −0.0486610 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −36583.0 | −1.20348 | ||||||||
\(975\) | −7666.56 | −0.251822 | ||||||||
\(976\) | −26603.9 | −0.872511 | ||||||||
\(977\) | −27690.9 | −0.906767 | −0.453384 | − | 0.891315i | \(-0.649783\pi\) | ||||
−0.453384 | + | 0.891315i | \(0.649783\pi\) | |||||||
\(978\) | 45799.5 | 1.49745 | ||||||||
\(979\) | −63862.5 | −2.08483 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3812.38 | 0.124077 | ||||||||
\(982\) | −30266.4 | −0.983544 | ||||||||
\(983\) | −22754.2 | −0.738299 | −0.369149 | − | 0.929370i | \(-0.620351\pi\) | ||||
−0.369149 | + | 0.929370i | \(0.620351\pi\) | |||||||
\(984\) | 59324.6 | 1.92195 | ||||||||
\(985\) | −9762.83 | −0.315807 | ||||||||
\(986\) | −7088.96 | −0.228964 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 592.316 | 0.0190729 | ||||||||
\(989\) | −8299.80 | −0.266854 | ||||||||
\(990\) | 1071.82 | 0.0344088 | ||||||||
\(991\) | −55470.9 | −1.77809 | −0.889047 | − | 0.457816i | \(-0.848632\pi\) | ||||
−0.889047 | + | 0.457816i | \(0.848632\pi\) | |||||||
\(992\) | −21482.9 | −0.687583 | ||||||||
\(993\) | 9128.50 | 0.291726 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20323.4 | 0.647531 | ||||||||
\(996\) | −8996.83 | −0.286220 | ||||||||
\(997\) | −15181.9 | −0.482264 | −0.241132 | − | 0.970492i | \(-0.577519\pi\) | ||||
−0.241132 | + | 0.970492i | \(0.577519\pi\) | |||||||
\(998\) | 46647.1 | 1.47955 | ||||||||
\(999\) | −2619.93 | −0.0829740 |
(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 | 245.4.a.j.1.1 | yes | 2 | |
3.2 | odd | 2 | 2205.4.a.w.1.2 | 2 | |||
5.4 | even | 2 | 1225.4.a.p.1.2 | 2 | |||
7.2 | even | 3 | 245.4.e.j.116.2 | 4 | |||
7.3 | odd | 6 | 245.4.e.k.226.2 | 4 | |||
7.4 | even | 3 | 245.4.e.j.226.2 | 4 | |||
7.5 | odd | 6 | 245.4.e.k.116.2 | 4 | |||
7.6 | odd | 2 | 245.4.a.i.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 2205.4.a.x.1.2 | 2 | |||
35.34 | odd | 2 | 1225.4.a.q.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.i.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
245.4.a.j.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
245.4.e.j.116.2 | 4 | 7.2 | even | 3 | |||
245.4.e.j.226.2 | 4 | 7.4 | even | 3 | |||
245.4.e.k.116.2 | 4 | 7.5 | odd | 6 | |||
245.4.e.k.226.2 | 4 | 7.3 | odd | 6 | |||
1225.4.a.p.1.2 | 2 | 5.4 | even | 2 | |||
1225.4.a.q.1.2 | 2 | 35.34 | odd | 2 | |||
2205.4.a.w.1.2 | 2 | 3.2 | odd | 2 | |||
2205.4.a.x.1.2 | 2 | 21.20 | even | 2 |