Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{18} + 112 x^{16} + 5026 x^{14} + 114847 x^{12} + 1397921 x^{10} + 8545747 x^{8} + 21033277 x^{6} + 6703200 x^{4} + 137781 x^{2} + 729 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 13^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.17 | ||
Root | \(5.39246i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.k.337.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.83750i | 1.71031i | 0.518368 | + | 0.855157i | \(0.326540\pi\) | ||||
−0.518368 | + | 0.855157i | \(0.673460\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −15.4014 | −1.92518 | ||||||||
\(5\) | − 21.1983i | − 1.89603i | −0.318225 | − | 0.948015i | \(-0.603087\pi\) | ||||
0.318225 | − | 0.948015i | \(-0.396913\pi\) | |||||||
\(6\) | 14.5125i | 0.987451i | ||||||||
\(7\) | 16.2806i | 0.879070i | 0.898225 | + | 0.439535i | \(0.144857\pi\) | ||||
−0.898225 | + | 0.439535i | \(0.855143\pi\) | |||||||
\(8\) | − 35.8043i | − 1.58234i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 102.547 | 3.24281 | ||||||||
\(11\) | 30.7532i | 0.842950i | 0.906840 | + | 0.421475i | \(0.138487\pi\) | ||||
−0.906840 | + | 0.421475i | \(0.861513\pi\) | |||||||
\(12\) | −46.2042 | −1.11150 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −78.7575 | −1.50349 | ||||||||
\(15\) | − 63.5948i | − 1.09467i | ||||||||
\(16\) | 49.9922 | 0.781128 | ||||||||
\(17\) | −46.2371 | −0.659656 | −0.329828 | − | 0.944041i | \(-0.606991\pi\) | ||||
−0.329828 | + | 0.944041i | \(0.606991\pi\) | |||||||
\(18\) | 43.5375i | 0.570105i | ||||||||
\(19\) | − 144.865i | − 1.74917i | −0.484873 | − | 0.874585i | \(-0.661134\pi\) | ||||
0.484873 | − | 0.874585i | \(-0.338866\pi\) | |||||||
\(20\) | 326.483i | 3.65019i | ||||||||
\(21\) | 48.8418i | 0.507531i | ||||||||
\(22\) | −148.769 | −1.44171 | ||||||||
\(23\) | −8.38045 | −0.0759758 | −0.0379879 | − | 0.999278i | \(-0.512095\pi\) | ||||
−0.0379879 | + | 0.999278i | \(0.512095\pi\) | |||||||
\(24\) | − 107.413i | − 0.913566i | ||||||||
\(25\) | −324.366 | −2.59493 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | − 250.744i | − 1.69237i | ||||||||
\(29\) | −242.958 | −1.55573 | −0.777865 | − | 0.628431i | \(-0.783697\pi\) | ||||
−0.777865 | + | 0.628431i | \(0.783697\pi\) | |||||||
\(30\) | 307.640 | 1.87224 | ||||||||
\(31\) | − 87.9353i | − 0.509472i | −0.967011 | − | 0.254736i | \(-0.918011\pi\) | ||||
0.967011 | − | 0.254736i | \(-0.0819886\pi\) | |||||||
\(32\) | − 44.5973i | − 0.246368i | ||||||||
\(33\) | 92.2597i | 0.486677i | ||||||||
\(34\) | − 223.672i | − 1.12822i | ||||||||
\(35\) | 345.121 | 1.66674 | ||||||||
\(36\) | −138.613 | −0.641726 | ||||||||
\(37\) | − 49.6950i | − 0.220806i | −0.993887 | − | 0.110403i | \(-0.964786\pi\) | ||||
0.993887 | − | 0.110403i | \(-0.0352141\pi\) | |||||||
\(38\) | 700.783 | 2.99163 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −758.990 | −3.00017 | ||||||||
\(41\) | 107.947i | 0.411181i | 0.978638 | + | 0.205591i | \(0.0659116\pi\) | ||||
−0.978638 | + | 0.205591i | \(0.934088\pi\) | |||||||
\(42\) | −236.272 | −0.868039 | ||||||||
\(43\) | 35.4166 | 0.125604 | 0.0628021 | − | 0.998026i | \(-0.479996\pi\) | ||||
0.0628021 | + | 0.998026i | \(0.479996\pi\) | |||||||
\(44\) | − 473.643i | − 1.62283i | ||||||||
\(45\) | − 190.784i | − 0.632010i | ||||||||
\(46\) | − 40.5404i | − 0.129943i | ||||||||
\(47\) | − 374.815i | − 1.16324i | −0.813460 | − | 0.581621i | \(-0.802419\pi\) | ||||
0.813460 | − | 0.581621i | \(-0.197581\pi\) | |||||||
\(48\) | 149.977 | 0.450985 | ||||||||
\(49\) | 77.9418 | 0.227236 | ||||||||
\(50\) | − 1569.12i | − 4.43815i | ||||||||
\(51\) | −138.711 | −0.380853 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −348.583 | −0.903426 | −0.451713 | − | 0.892163i | \(-0.649187\pi\) | ||||
−0.451713 | + | 0.892163i | \(0.649187\pi\) | |||||||
\(54\) | 130.613i | 0.329150i | ||||||||
\(55\) | 651.915 | 1.59826 | ||||||||
\(56\) | 582.916 | 1.39099 | ||||||||
\(57\) | − 434.594i | − 1.00988i | ||||||||
\(58\) | − 1175.31i | − 2.66079i | ||||||||
\(59\) | − 679.430i | − 1.49923i | −0.661877 | − | 0.749613i | \(-0.730240\pi\) | ||||
0.661877 | − | 0.749613i | \(-0.269760\pi\) | |||||||
\(60\) | 979.450i | 2.10744i | ||||||||
\(61\) | −230.403 | −0.483608 | −0.241804 | − | 0.970325i | \(-0.577739\pi\) | ||||
−0.241804 | + | 0.970325i | \(0.577739\pi\) | |||||||
\(62\) | 425.387 | 0.871358 | ||||||||
\(63\) | 146.525i | 0.293023i | ||||||||
\(64\) | 615.677 | 1.20249 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −446.306 | −0.832372 | ||||||||
\(67\) | − 295.642i | − 0.539082i | −0.962989 | − | 0.269541i | \(-0.913128\pi\) | ||||
0.962989 | − | 0.269541i | \(-0.0868719\pi\) | |||||||
\(68\) | 712.117 | 1.26995 | ||||||||
\(69\) | −25.1413 | −0.0438647 | ||||||||
\(70\) | 1669.52i | 2.85066i | ||||||||
\(71\) | 329.215i | 0.550290i | 0.961403 | + | 0.275145i | \(0.0887259\pi\) | ||||
−0.961403 | + | 0.275145i | \(0.911274\pi\) | |||||||
\(72\) | − 322.239i | − 0.527448i | ||||||||
\(73\) | − 48.9973i | − 0.0785575i | −0.999228 | − | 0.0392787i | \(-0.987494\pi\) | ||||
0.999228 | − | 0.0392787i | \(-0.0125060\pi\) | |||||||
\(74\) | 240.399 | 0.377647 | ||||||||
\(75\) | −973.099 | −1.49818 | ||||||||
\(76\) | 2231.12i | 3.36746i | ||||||||
\(77\) | −500.681 | −0.741012 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −107.942 | −0.153727 | −0.0768636 | − | 0.997042i | \(-0.524491\pi\) | ||||
−0.0768636 | + | 0.997042i | \(0.524491\pi\) | |||||||
\(80\) | − 1059.75i | − 1.48104i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −522.192 | −0.703250 | ||||||||
\(83\) | 515.654i | 0.681932i | 0.940076 | + | 0.340966i | \(0.110754\pi\) | ||||
−0.940076 | + | 0.340966i | \(0.889246\pi\) | |||||||
\(84\) | − 752.233i | − 0.977088i | ||||||||
\(85\) | 980.147i | 1.25073i | ||||||||
\(86\) | 171.328i | 0.214823i | ||||||||
\(87\) | −728.874 | −0.898201 | ||||||||
\(88\) | 1101.10 | 1.33384 | ||||||||
\(89\) | − 984.453i | − 1.17249i | −0.810133 | − | 0.586246i | \(-0.800605\pi\) | ||||
0.810133 | − | 0.586246i | \(-0.199395\pi\) | |||||||
\(90\) | 922.919 | 1.08094 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 129.071 | 0.146267 | ||||||||
\(93\) | − 263.806i | − 0.294144i | ||||||||
\(94\) | 1813.17 | 1.98951 | ||||||||
\(95\) | −3070.88 | −3.31648 | ||||||||
\(96\) | − 133.792i | − 0.142241i | ||||||||
\(97\) | 487.072i | 0.509842i | 0.966962 | + | 0.254921i | \(0.0820494\pi\) | ||||
−0.966962 | + | 0.254921i | \(0.917951\pi\) | |||||||
\(98\) | 377.043i | 0.388644i | ||||||||
\(99\) | 276.779i | 0.280983i | ||||||||
\(100\) | 4995.70 | 4.99570 | ||||||||
\(101\) | −766.375 | −0.755021 | −0.377511 | − | 0.926005i | \(-0.623220\pi\) | ||||
−0.377511 | + | 0.926005i | \(0.623220\pi\) | |||||||
\(102\) | − 671.016i | − 0.651378i | ||||||||
\(103\) | −1229.87 | −1.17653 | −0.588266 | − | 0.808668i | \(-0.700189\pi\) | ||||
−0.588266 | + | 0.808668i | \(0.700189\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1035.36 | 0.962295 | ||||||||
\(106\) | − 1686.27i | − 1.54514i | ||||||||
\(107\) | 76.8261 | 0.0694117 | 0.0347059 | − | 0.999398i | \(-0.488951\pi\) | ||||
0.0347059 | + | 0.999398i | \(0.488951\pi\) | |||||||
\(108\) | −415.838 | −0.370500 | ||||||||
\(109\) | − 626.001i | − 0.550092i | −0.961431 | − | 0.275046i | \(-0.911307\pi\) | ||||
0.961431 | − | 0.275046i | \(-0.0886930\pi\) | |||||||
\(110\) | 3153.64i | 2.73353i | ||||||||
\(111\) | − 149.085i | − 0.127482i | ||||||||
\(112\) | 813.904i | 0.686667i | ||||||||
\(113\) | −1343.21 | −1.11822 | −0.559108 | − | 0.829095i | \(-0.688856\pi\) | ||||
−0.559108 | + | 0.829095i | \(0.688856\pi\) | |||||||
\(114\) | 2102.35 | 1.72722 | ||||||||
\(115\) | 177.651i | 0.144052i | ||||||||
\(116\) | 3741.90 | 2.99506 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3286.74 | 2.56415 | ||||||||
\(119\) | − 752.769i | − 0.579884i | ||||||||
\(120\) | −2276.97 | −1.73215 | ||||||||
\(121\) | 385.238 | 0.289435 | ||||||||
\(122\) | − 1114.58i | − 0.827122i | ||||||||
\(123\) | 323.840i | 0.237396i | ||||||||
\(124\) | 1354.33i | 0.980824i | ||||||||
\(125\) | 4226.22i | 3.02404i | ||||||||
\(126\) | −708.817 | −0.501162 | ||||||||
\(127\) | 2146.69 | 1.49990 | 0.749952 | − | 0.661492i | \(-0.230077\pi\) | ||||
0.749952 | + | 0.661492i | \(0.230077\pi\) | |||||||
\(128\) | 2621.56i | 1.81028i | ||||||||
\(129\) | 106.250 | 0.0725177 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −798.626 | −0.532644 | −0.266322 | − | 0.963884i | \(-0.585808\pi\) | ||||
−0.266322 | + | 0.963884i | \(0.585808\pi\) | |||||||
\(132\) | − 1420.93i | − 0.936940i | ||||||||
\(133\) | 2358.48 | 1.53764 | ||||||||
\(134\) | 1430.17 | 0.921999 | ||||||||
\(135\) | − 572.353i | − 0.364891i | ||||||||
\(136\) | 1655.49i | 1.04380i | ||||||||
\(137\) | − 601.153i | − 0.374891i | −0.982275 | − | 0.187445i | \(-0.939979\pi\) | ||||
0.982275 | − | 0.187445i | \(-0.0600207\pi\) | |||||||
\(138\) | − 121.621i | − 0.0750224i | ||||||||
\(139\) | −2134.18 | −1.30229 | −0.651146 | − | 0.758953i | \(-0.725711\pi\) | ||||
−0.651146 | + | 0.758953i | \(0.725711\pi\) | |||||||
\(140\) | −5315.35 | −3.20878 | ||||||||
\(141\) | − 1124.44i | − 0.671598i | ||||||||
\(142\) | −1592.58 | −0.941169 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 449.930 | 0.260376 | ||||||||
\(145\) | 5150.29i | 2.94971i | ||||||||
\(146\) | 237.024 | 0.134358 | ||||||||
\(147\) | 233.825 | 0.131194 | ||||||||
\(148\) | 765.373i | 0.425090i | ||||||||
\(149\) | − 3439.93i | − 1.89134i | −0.325127 | − | 0.945670i | \(-0.605407\pi\) | ||||
0.325127 | − | 0.945670i | \(-0.394593\pi\) | |||||||
\(150\) | − 4707.37i | − 2.56237i | ||||||||
\(151\) | 2224.04i | 1.19861i | 0.800521 | + | 0.599305i | \(0.204556\pi\) | ||||
−0.800521 | + | 0.599305i | \(0.795444\pi\) | |||||||
\(152\) | −5186.78 | −2.76779 | ||||||||
\(153\) | −416.134 | −0.219885 | ||||||||
\(154\) | − 2422.05i | − 1.26736i | ||||||||
\(155\) | −1864.07 | −0.965975 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2465.32 | 1.25321 | 0.626604 | − | 0.779338i | \(-0.284444\pi\) | ||||
0.626604 | + | 0.779338i | \(0.284444\pi\) | |||||||
\(158\) | − 522.171i | − 0.262922i | ||||||||
\(159\) | −1045.75 | −0.521593 | ||||||||
\(160\) | −945.386 | −0.467121 | ||||||||
\(161\) | − 136.439i | − 0.0667881i | ||||||||
\(162\) | 391.838i | 0.190035i | ||||||||
\(163\) | − 243.565i | − 0.117040i | −0.998286 | − | 0.0585199i | \(-0.981362\pi\) | ||||
0.998286 | − | 0.0585199i | \(-0.0186381\pi\) | |||||||
\(164\) | − 1662.53i | − 0.791597i | ||||||||
\(165\) | 1955.75 | 0.922755 | ||||||||
\(166\) | −2494.47 | −1.16632 | ||||||||
\(167\) | 409.099i | 0.189563i | 0.995498 | + | 0.0947814i | \(0.0302152\pi\) | ||||
−0.995498 | + | 0.0947814i | \(0.969785\pi\) | |||||||
\(168\) | 1748.75 | 0.803089 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4741.46 | −2.13914 | ||||||||
\(171\) | − 1303.78i | − 0.583056i | ||||||||
\(172\) | −545.466 | −0.241810 | ||||||||
\(173\) | 2618.97 | 1.15096 | 0.575481 | − | 0.817815i | \(-0.304815\pi\) | ||||
0.575481 | + | 0.817815i | \(0.304815\pi\) | |||||||
\(174\) | − 3525.93i | − 1.53621i | ||||||||
\(175\) | − 5280.88i | − 2.28113i | ||||||||
\(176\) | 1537.42i | 0.658452i | ||||||||
\(177\) | − 2038.29i | − 0.865578i | ||||||||
\(178\) | 4762.29 | 2.00533 | ||||||||
\(179\) | −163.311 | −0.0681925 | −0.0340963 | − | 0.999419i | \(-0.510855\pi\) | ||||
−0.0340963 | + | 0.999419i | \(0.510855\pi\) | |||||||
\(180\) | 2938.35i | 1.21673i | ||||||||
\(181\) | 3313.07 | 1.36054 | 0.680272 | − | 0.732960i | \(-0.261862\pi\) | ||||
0.680272 | + | 0.732960i | \(0.261862\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −691.209 | −0.279211 | ||||||||
\(184\) | 300.056i | 0.120220i | ||||||||
\(185\) | −1053.45 | −0.418654 | ||||||||
\(186\) | 1276.16 | 0.503079 | ||||||||
\(187\) | − 1421.94i | − 0.556057i | ||||||||
\(188\) | 5772.68i | 2.23945i | ||||||||
\(189\) | 439.576i | 0.169177i | ||||||||
\(190\) | − 14855.4i | − 5.67222i | ||||||||
\(191\) | −4281.90 | −1.62213 | −0.811066 | − | 0.584954i | \(-0.801112\pi\) | ||||
−0.811066 | + | 0.584954i | \(0.801112\pi\) | |||||||
\(192\) | 1847.03 | 0.694261 | ||||||||
\(193\) | 1877.33i | 0.700171i | 0.936718 | + | 0.350086i | \(0.113848\pi\) | ||||
−0.936718 | + | 0.350086i | \(0.886152\pi\) | |||||||
\(194\) | −2356.21 | −0.871990 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1200.41 | −0.437468 | ||||||||
\(197\) | 1991.26i | 0.720158i | 0.932922 | + | 0.360079i | \(0.117250\pi\) | ||||
−0.932922 | + | 0.360079i | \(0.882750\pi\) | |||||||
\(198\) | −1338.92 | −0.480570 | ||||||||
\(199\) | −1345.05 | −0.479137 | −0.239568 | − | 0.970879i | \(-0.577006\pi\) | ||||
−0.239568 | + | 0.970879i | \(0.577006\pi\) | |||||||
\(200\) | 11613.7i | 4.10607i | ||||||||
\(201\) | − 886.927i | − 0.311239i | ||||||||
\(202\) | − 3707.34i | − 1.29132i | ||||||||
\(203\) | − 3955.51i | − 1.36760i | ||||||||
\(204\) | 2136.35 | 0.733208 | ||||||||
\(205\) | 2288.28 | 0.779612 | ||||||||
\(206\) | − 5949.50i | − 2.01224i | ||||||||
\(207\) | −75.4240 | −0.0253253 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4455.05 | 1.47446 | ||||||||
\(210\) | 5008.56i | 1.64583i | ||||||||
\(211\) | −288.763 | −0.0942147 | −0.0471073 | − | 0.998890i | \(-0.515000\pi\) | ||||
−0.0471073 | + | 0.998890i | \(0.515000\pi\) | |||||||
\(212\) | 5368.67 | 1.73925 | ||||||||
\(213\) | 987.644i | 0.317710i | ||||||||
\(214\) | 371.646i | 0.118716i | ||||||||
\(215\) | − 750.771i | − 0.238150i | ||||||||
\(216\) | − 966.717i | − 0.304522i | ||||||||
\(217\) | 1431.64 | 0.447862 | ||||||||
\(218\) | 3028.28 | 0.940830 | ||||||||
\(219\) | − 146.992i | − 0.0453552i | ||||||||
\(220\) | −10040.4 | −3.07693 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 721.198 | 0.218035 | ||||||||
\(223\) | 1798.41i | 0.540046i | 0.962854 | + | 0.270023i | \(0.0870314\pi\) | ||||
−0.962854 | + | 0.270023i | \(0.912969\pi\) | |||||||
\(224\) | 726.072 | 0.216575 | ||||||||
\(225\) | −2919.30 | −0.864977 | ||||||||
\(226\) | − 6497.77i | − 1.91250i | ||||||||
\(227\) | − 2486.10i | − 0.726909i | −0.931612 | − | 0.363454i | \(-0.881597\pi\) | ||||
0.931612 | − | 0.363454i | \(-0.118403\pi\) | |||||||
\(228\) | 6693.36i | 1.94420i | ||||||||
\(229\) | 6074.71i | 1.75296i | 0.481438 | + | 0.876480i | \(0.340115\pi\) | ||||
−0.481438 | + | 0.876480i | \(0.659885\pi\) | |||||||
\(230\) | −859.386 | −0.246375 | ||||||||
\(231\) | −1502.04 | −0.427824 | ||||||||
\(232\) | 8698.95i | 2.46170i | ||||||||
\(233\) | −6367.16 | −1.79024 | −0.895121 | − | 0.445822i | \(-0.852911\pi\) | ||||
−0.895121 | + | 0.445822i | \(0.852911\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7945.42 | −2.20554 | ||||||||
\(236\) | 10464.2i | 2.88627i | ||||||||
\(237\) | −323.827 | −0.0887544 | ||||||||
\(238\) | 3641.52 | 0.991784 | ||||||||
\(239\) | 1886.43i | 0.510556i | 0.966868 | + | 0.255278i | \(0.0821670\pi\) | ||||
−0.966868 | + | 0.255278i | \(0.917833\pi\) | |||||||
\(240\) | − 3179.24i | − 0.855081i | ||||||||
\(241\) | 5847.91i | 1.56306i | 0.623869 | + | 0.781529i | \(0.285560\pi\) | ||||
−0.623869 | + | 0.781529i | \(0.714440\pi\) | |||||||
\(242\) | 1863.59i | 0.495025i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 3548.53 | 0.931031 | ||||||||
\(245\) | − 1652.23i | − 0.430845i | ||||||||
\(246\) | −1566.58 | −0.406021 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3148.46 | −0.806160 | ||||||||
\(249\) | 1546.96i | 0.393713i | ||||||||
\(250\) | −20444.3 | −5.17205 | ||||||||
\(251\) | 2388.65 | 0.600678 | 0.300339 | − | 0.953832i | \(-0.402900\pi\) | ||||
0.300339 | + | 0.953832i | \(0.402900\pi\) | |||||||
\(252\) | − 2256.70i | − 0.564122i | ||||||||
\(253\) | − 257.726i | − 0.0640438i | ||||||||
\(254\) | 10384.6i | 2.56531i | ||||||||
\(255\) | 2940.44i | 0.722108i | ||||||||
\(256\) | −7756.38 | −1.89365 | ||||||||
\(257\) | −4447.21 | −1.07941 | −0.539707 | − | 0.841853i | \(-0.681465\pi\) | ||||
−0.539707 | + | 0.841853i | \(0.681465\pi\) | |||||||
\(258\) | 513.984i | 0.124028i | ||||||||
\(259\) | 809.064 | 0.194104 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2186.62 | −0.518577 | ||||||||
\(262\) | − 3863.36i | − 0.910988i | ||||||||
\(263\) | 7590.87 | 1.77975 | 0.889873 | − | 0.456208i | \(-0.150793\pi\) | ||||
0.889873 | + | 0.456208i | \(0.150793\pi\) | |||||||
\(264\) | 3303.30 | 0.770091 | ||||||||
\(265\) | 7389.36i | 1.71292i | ||||||||
\(266\) | 11409.2i | 2.62985i | ||||||||
\(267\) | − 2953.36i | − 0.676939i | ||||||||
\(268\) | 4553.31i | 1.03783i | ||||||||
\(269\) | −557.911 | −0.126455 | −0.0632275 | − | 0.997999i | \(-0.520139\pi\) | ||||
−0.0632275 | + | 0.997999i | \(0.520139\pi\) | |||||||
\(270\) | 2768.76 | 0.624079 | ||||||||
\(271\) | − 2707.41i | − 0.606877i | −0.952851 | − | 0.303439i | \(-0.901865\pi\) | ||||
0.952851 | − | 0.303439i | \(-0.0981347\pi\) | |||||||
\(272\) | −2311.50 | −0.515276 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2908.08 | 0.641181 | ||||||||
\(275\) | − 9975.31i | − 2.18740i | ||||||||
\(276\) | 387.212 | 0.0844472 | ||||||||
\(277\) | 1231.35 | 0.267092 | 0.133546 | − | 0.991043i | \(-0.457364\pi\) | ||||
0.133546 | + | 0.991043i | \(0.457364\pi\) | |||||||
\(278\) | − 10324.1i | − 2.22733i | ||||||||
\(279\) | − 791.417i | − 0.169824i | ||||||||
\(280\) | − 12356.8i | − 2.63736i | ||||||||
\(281\) | − 4601.44i | − 0.976864i | −0.872602 | − | 0.488432i | \(-0.837569\pi\) | ||||
0.872602 | − | 0.488432i | \(-0.162431\pi\) | |||||||
\(282\) | 5439.50 | 1.14864 | ||||||||
\(283\) | 54.5677 | 0.0114619 | 0.00573094 | − | 0.999984i | \(-0.498176\pi\) | ||||
0.00573094 | + | 0.999984i | \(0.498176\pi\) | |||||||
\(284\) | − 5070.37i | − 1.05941i | ||||||||
\(285\) | −9212.63 | −1.91477 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1757.44 | −0.361457 | ||||||||
\(288\) | − 401.376i | − 0.0821226i | ||||||||
\(289\) | −2775.13 | −0.564854 | ||||||||
\(290\) | −24914.5 | −5.04494 | ||||||||
\(291\) | 1461.22i | 0.294357i | ||||||||
\(292\) | 754.627i | 0.151237i | ||||||||
\(293\) | 4745.24i | 0.946144i | 0.881024 | + | 0.473072i | \(0.156855\pi\) | ||||
−0.881024 | + | 0.473072i | \(0.843145\pi\) | |||||||
\(294\) | 1131.13i | 0.224384i | ||||||||
\(295\) | −14402.7 | −2.84258 | ||||||||
\(296\) | −1779.30 | −0.349390 | ||||||||
\(297\) | 830.337i | 0.162226i | ||||||||
\(298\) | 16640.6 | 3.23479 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 14987.1 | 2.88427 | ||||||||
\(301\) | 576.604i | 0.110415i | ||||||||
\(302\) | −10758.8 | −2.05000 | ||||||||
\(303\) | −2299.13 | −0.435912 | ||||||||
\(304\) | − 7242.10i | − 1.36633i | ||||||||
\(305\) | 4884.15i | 0.916936i | ||||||||
\(306\) | − 2013.05i | − 0.376073i | ||||||||
\(307\) | 1028.82i | 0.191264i | 0.995417 | + | 0.0956320i | \(0.0304872\pi\) | ||||
−0.995417 | + | 0.0956320i | \(0.969513\pi\) | |||||||
\(308\) | 7711.20 | 1.42658 | ||||||||
\(309\) | −3689.61 | −0.679271 | ||||||||
\(310\) | − 9017.46i | − 1.65212i | ||||||||
\(311\) | 2437.84 | 0.444492 | 0.222246 | − | 0.974991i | \(-0.428661\pi\) | ||||
0.222246 | + | 0.974991i | \(0.428661\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7934.20 | 1.43280 | 0.716402 | − | 0.697688i | \(-0.245788\pi\) | ||||
0.716402 | + | 0.697688i | \(0.245788\pi\) | |||||||
\(314\) | 11926.0i | 2.14338i | ||||||||
\(315\) | 3106.09 | 0.555581 | ||||||||
\(316\) | 1662.46 | 0.295952 | ||||||||
\(317\) | − 6942.72i | − 1.23010i | −0.788488 | − | 0.615050i | \(-0.789136\pi\) | ||||
0.788488 | − | 0.615050i | \(-0.210864\pi\) | |||||||
\(318\) | − 5058.81i | − 0.892089i | ||||||||
\(319\) | − 7471.75i | − 1.31140i | ||||||||
\(320\) | − 13051.3i | − 2.27997i | ||||||||
\(321\) | 230.478 | 0.0400749 | ||||||||
\(322\) | 660.023 | 0.114229 | ||||||||
\(323\) | 6698.12i | 1.15385i | ||||||||
\(324\) | −1247.51 | −0.213909 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1178.25 | 0.200175 | ||||||||
\(327\) | − 1878.00i | − 0.317596i | ||||||||
\(328\) | 3864.96 | 0.650630 | ||||||||
\(329\) | 6102.21 | 1.02257 | ||||||||
\(330\) | 9460.92i | 1.57820i | ||||||||
\(331\) | 5439.27i | 0.903230i | 0.892213 | + | 0.451615i | \(0.149152\pi\) | ||||
−0.892213 | + | 0.451615i | \(0.850848\pi\) | |||||||
\(332\) | − 7941.79i | − 1.31284i | ||||||||
\(333\) | − 447.255i | − 0.0736018i | ||||||||
\(334\) | −1979.01 | −0.324212 | ||||||||
\(335\) | −6267.10 | −1.02211 | ||||||||
\(336\) | 2441.71i | 0.396447i | ||||||||
\(337\) | 1663.87 | 0.268952 | 0.134476 | − | 0.990917i | \(-0.457065\pi\) | ||||
0.134476 | + | 0.990917i | \(0.457065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4029.63 | −0.645602 | ||||||||
\(340\) | − 15095.6i | − 2.40787i | ||||||||
\(341\) | 2704.29 | 0.429460 | ||||||||
\(342\) | 6307.04 | 0.997210 | ||||||||
\(343\) | 6853.19i | 1.07883i | ||||||||
\(344\) | − 1268.07i | − 0.198749i | ||||||||
\(345\) | 532.953i | 0.0831687i | ||||||||
\(346\) | 12669.3i | 1.96851i | ||||||||
\(347\) | 9268.10 | 1.43383 | 0.716913 | − | 0.697163i | \(-0.245554\pi\) | ||||
0.716913 | + | 0.697163i | \(0.245554\pi\) | |||||||
\(348\) | 11225.7 | 1.72920 | ||||||||
\(349\) | 5239.45i | 0.803614i | 0.915724 | + | 0.401807i | \(0.131618\pi\) | ||||
−0.915724 | + | 0.401807i | \(0.868382\pi\) | |||||||
\(350\) | 25546.3 | 3.90144 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1371.51 | 0.207676 | ||||||||
\(353\) | − 1218.01i | − 0.183649i | −0.995775 | − | 0.0918244i | \(-0.970730\pi\) | ||||
0.995775 | − | 0.0918244i | \(-0.0292698\pi\) | |||||||
\(354\) | 9860.23 | 1.48041 | ||||||||
\(355\) | 6978.78 | 1.04337 | ||||||||
\(356\) | 15162.0i | 2.25726i | ||||||||
\(357\) | − 2258.31i | − 0.334796i | ||||||||
\(358\) | − 790.018i | − 0.116631i | ||||||||
\(359\) | 5316.06i | 0.781534i | 0.920490 | + | 0.390767i | \(0.127790\pi\) | ||||
−0.920490 | + | 0.390767i | \(0.872210\pi\) | |||||||
\(360\) | −6830.91 | −1.00006 | ||||||||
\(361\) | −14126.7 | −2.05959 | ||||||||
\(362\) | 16027.0i | 2.32696i | ||||||||
\(363\) | 1155.72 | 0.167106 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1038.66 | −0.148947 | ||||||||
\(366\) | − 3343.73i | − 0.477539i | ||||||||
\(367\) | −289.101 | −0.0411197 | −0.0205599 | − | 0.999789i | \(-0.506545\pi\) | ||||
−0.0205599 | + | 0.999789i | \(0.506545\pi\) | |||||||
\(368\) | −418.957 | −0.0593469 | ||||||||
\(369\) | 971.520i | 0.137060i | ||||||||
\(370\) | − 5096.05i | − 0.716030i | ||||||||
\(371\) | − 5675.15i | − 0.794175i | ||||||||
\(372\) | 4062.98i | 0.566279i | ||||||||
\(373\) | 6163.98 | 0.855654 | 0.427827 | − | 0.903861i | \(-0.359279\pi\) | ||||
0.427827 | + | 0.903861i | \(0.359279\pi\) | |||||||
\(374\) | 6878.64 | 0.951032 | ||||||||
\(375\) | 12678.7i | 1.74593i | ||||||||
\(376\) | −13420.0 | −1.84065 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2126.45 | −0.289346 | ||||||||
\(379\) | 2440.03i | 0.330702i | 0.986235 | + | 0.165351i | \(0.0528756\pi\) | ||||
−0.986235 | + | 0.165351i | \(0.947124\pi\) | |||||||
\(380\) | 47295.9 | 6.38481 | ||||||||
\(381\) | 6440.06 | 0.865970 | ||||||||
\(382\) | − 20713.7i | − 2.77436i | ||||||||
\(383\) | 6577.28i | 0.877502i | 0.898609 | + | 0.438751i | \(0.144579\pi\) | ||||
−0.898609 | + | 0.438751i | \(0.855421\pi\) | |||||||
\(384\) | 7864.68i | 1.04516i | ||||||||
\(385\) | 10613.6i | 1.40498i | ||||||||
\(386\) | −9081.58 | −1.19751 | ||||||||
\(387\) | 318.750 | 0.0418681 | ||||||||
\(388\) | − 7501.59i | − 0.981535i | ||||||||
\(389\) | −4964.94 | −0.647127 | −0.323563 | − | 0.946206i | \(-0.604881\pi\) | ||||
−0.323563 | + | 0.946206i | \(0.604881\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 387.488 | 0.0501179 | ||||||||
\(392\) | − 2790.65i | − 0.359565i | ||||||||
\(393\) | −2395.88 | −0.307522 | ||||||||
\(394\) | −9632.70 | −1.23170 | ||||||||
\(395\) | 2288.19i | 0.291471i | ||||||||
\(396\) | − 4262.79i | − 0.540943i | ||||||||
\(397\) | − 12073.9i | − 1.52637i | −0.646178 | − | 0.763187i | \(-0.723634\pi\) | ||||
0.646178 | − | 0.763187i | \(-0.276366\pi\) | |||||||
\(398\) | − 6506.69i | − 0.819475i | ||||||||
\(399\) | 7075.45 | 0.887758 | ||||||||
\(400\) | −16215.8 | −2.02697 | ||||||||
\(401\) | − 4916.90i | − 0.612315i | −0.951981 | − | 0.306158i | \(-0.900957\pi\) | ||||
0.951981 | − | 0.306158i | \(-0.0990434\pi\) | |||||||
\(402\) | 4290.51 | 0.532316 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11803.3 | 1.45355 | ||||||||
\(405\) | − 1717.06i | − 0.210670i | ||||||||
\(406\) | 19134.8 | 2.33902 | ||||||||
\(407\) | 1528.28 | 0.186128 | ||||||||
\(408\) | 4966.47i | 0.602639i | ||||||||
\(409\) | − 15350.9i | − 1.85588i | −0.372733 | − | 0.927939i | \(-0.621579\pi\) | ||||
0.372733 | − | 0.927939i | \(-0.378421\pi\) | |||||||
\(410\) | 11069.6i | 1.33338i | ||||||||
\(411\) | − 1803.46i | − 0.216443i | ||||||||
\(412\) | 18941.7 | 2.26503 | ||||||||
\(413\) | 11061.5 | 1.31792 | ||||||||
\(414\) | − 364.864i | − 0.0433142i | ||||||||
\(415\) | 10931.0 | 1.29296 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6402.53 | −0.751878 | ||||||||
\(418\) | 21551.3i | 2.52179i | ||||||||
\(419\) | −5488.58 | −0.639939 | −0.319970 | − | 0.947428i | \(-0.603673\pi\) | ||||
−0.319970 | + | 0.947428i | \(0.603673\pi\) | |||||||
\(420\) | −15946.0 | −1.85259 | ||||||||
\(421\) | 927.681i | 0.107393i | 0.998557 | + | 0.0536964i | \(0.0171003\pi\) | ||||
−0.998557 | + | 0.0536964i | \(0.982900\pi\) | |||||||
\(422\) | − 1396.89i | − 0.161137i | ||||||||
\(423\) | − 3373.33i | − 0.387747i | ||||||||
\(424\) | 12480.8i | 1.42953i | ||||||||
\(425\) | 14997.8 | 1.71176 | ||||||||
\(426\) | −4777.73 | −0.543384 | ||||||||
\(427\) | − 3751.10i | − 0.425126i | ||||||||
\(428\) | −1183.23 | −0.133630 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3631.85 | 0.407311 | ||||||||
\(431\) | − 11002.3i | − 1.22961i | −0.788678 | − | 0.614806i | \(-0.789234\pi\) | ||||
0.788678 | − | 0.614806i | \(-0.210766\pi\) | |||||||
\(432\) | 1349.79 | 0.150328 | ||||||||
\(433\) | 9596.76 | 1.06511 | 0.532553 | − | 0.846397i | \(-0.321233\pi\) | ||||
0.532553 | + | 0.846397i | \(0.321233\pi\) | |||||||
\(434\) | 6925.56i | 0.765985i | ||||||||
\(435\) | 15450.9i | 1.70302i | ||||||||
\(436\) | 9641.30i | 1.05902i | ||||||||
\(437\) | 1214.03i | 0.132895i | ||||||||
\(438\) | 711.073 | 0.0775716 | ||||||||
\(439\) | 10346.3 | 1.12483 | 0.562416 | − | 0.826854i | \(-0.309872\pi\) | ||||
0.562416 | + | 0.826854i | \(0.309872\pi\) | |||||||
\(440\) | − 23341.4i | − 2.52899i | ||||||||
\(441\) | 701.476 | 0.0757452 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5650.38 | 0.606000 | 0.303000 | − | 0.952991i | \(-0.402012\pi\) | ||||
0.303000 | + | 0.952991i | \(0.402012\pi\) | |||||||
\(444\) | 2296.12i | 0.245426i | ||||||||
\(445\) | −20868.7 | −2.22308 | ||||||||
\(446\) | −8699.80 | −0.923649 | ||||||||
\(447\) | − 10319.8i | − 1.09197i | ||||||||
\(448\) | 10023.6i | 1.05708i | ||||||||
\(449\) | − 11987.8i | − 1.25999i | −0.776597 | − | 0.629997i | \(-0.783056\pi\) | ||||
0.776597 | − | 0.629997i | \(-0.216944\pi\) | |||||||
\(450\) | − 14122.1i | − 1.47938i | ||||||||
\(451\) | −3319.71 | −0.346605 | ||||||||
\(452\) | 20687.3 | 2.15276 | ||||||||
\(453\) | 6672.13i | 0.692018i | ||||||||
\(454\) | 12026.5 | 1.24324 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15560.3 | −1.59798 | ||||||||
\(457\) | − 16437.6i | − 1.68253i | −0.540623 | − | 0.841265i | \(-0.681811\pi\) | ||||
0.540623 | − | 0.841265i | \(-0.318189\pi\) | |||||||
\(458\) | −29386.4 | −2.99811 | ||||||||
\(459\) | −1248.40 | −0.126951 | ||||||||
\(460\) | − 2736.08i | − 0.277326i | ||||||||
\(461\) | 8847.70i | 0.893880i | 0.894564 | + | 0.446940i | \(0.147486\pi\) | ||||
−0.894564 | + | 0.446940i | \(0.852514\pi\) | |||||||
\(462\) | − 7266.14i | − 0.731713i | ||||||||
\(463\) | − 10269.6i | − 1.03081i | −0.856945 | − | 0.515407i | \(-0.827641\pi\) | ||||
0.856945 | − | 0.515407i | \(-0.172359\pi\) | |||||||
\(464\) | −12146.0 | −1.21523 | ||||||||
\(465\) | −5592.22 | −0.557706 | ||||||||
\(466\) | − 30801.1i | − 3.06188i | ||||||||
\(467\) | −14730.4 | −1.45962 | −0.729811 | − | 0.683649i | \(-0.760392\pi\) | ||||
−0.729811 | + | 0.683649i | \(0.760392\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4813.24 | 0.473891 | ||||||||
\(470\) | − 38436.0i | − 3.77217i | ||||||||
\(471\) | 7395.95 | 0.723540 | ||||||||
\(472\) | −24326.6 | −2.37229 | ||||||||
\(473\) | 1089.18i | 0.105878i | ||||||||
\(474\) | − 1566.51i | − 0.151798i | ||||||||
\(475\) | 46989.2i | 4.53897i | ||||||||
\(476\) | 11593.7i | 1.11638i | ||||||||
\(477\) | −3137.25 | −0.301142 | ||||||||
\(478\) | −9125.59 | −0.873211 | ||||||||
\(479\) | − 635.077i | − 0.0605792i | −0.999541 | − | 0.0302896i | \(-0.990357\pi\) | ||||
0.999541 | − | 0.0302896i | \(-0.00964295\pi\) | |||||||
\(480\) | −2836.16 | −0.269692 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −28289.3 | −2.67332 | ||||||||
\(483\) | − 409.316i | − 0.0385601i | ||||||||
\(484\) | −5933.22 | −0.557214 | ||||||||
\(485\) | 10325.1 | 0.966675 | ||||||||
\(486\) | 1175.51i | 0.109717i | ||||||||
\(487\) | − 16611.1i | − 1.54563i | −0.634632 | − | 0.772815i | \(-0.718848\pi\) | ||||
0.634632 | − | 0.772815i | \(-0.281152\pi\) | |||||||
\(488\) | 8249.43i | 0.765234i | ||||||||
\(489\) | − 730.696i | − 0.0675730i | ||||||||
\(490\) | 7992.66 | 0.736881 | ||||||||
\(491\) | 2584.14 | 0.237516 | 0.118758 | − | 0.992923i | \(-0.462109\pi\) | ||||
0.118758 | + | 0.992923i | \(0.462109\pi\) | |||||||
\(492\) | − 4987.59i | − 0.457029i | ||||||||
\(493\) | 11233.7 | 1.02625 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5867.24 | 0.532753 | ||||||||
\(496\) | − 4396.08i | − 0.397963i | ||||||||
\(497\) | −5359.82 | −0.483744 | ||||||||
\(498\) | −7483.42 | −0.673374 | ||||||||
\(499\) | 2183.88i | 0.195919i | 0.995190 | + | 0.0979597i | \(0.0312316\pi\) | ||||
−0.995190 | + | 0.0979597i | \(0.968768\pi\) | |||||||
\(500\) | − 65089.8i | − 5.82180i | ||||||||
\(501\) | 1227.30i | 0.109444i | ||||||||
\(502\) | 11555.1i | 1.02735i | ||||||||
\(503\) | −17214.9 | −1.52600 | −0.762998 | − | 0.646401i | \(-0.776273\pi\) | ||||
−0.762998 | + | 0.646401i | \(0.776273\pi\) | |||||||
\(504\) | 5246.25 | 0.463664 | ||||||||
\(505\) | 16245.8i | 1.43154i | ||||||||
\(506\) | 1246.75 | 0.109535 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −33062.0 | −2.88758 | ||||||||
\(509\) | 20260.6i | 1.76431i | 0.470955 | + | 0.882157i | \(0.343909\pi\) | ||||
−0.470955 | + | 0.882157i | \(0.656091\pi\) | |||||||
\(510\) | −14224.4 | −1.23503 | ||||||||
\(511\) | 797.705 | 0.0690575 | ||||||||
\(512\) | − 16549.0i | − 1.42846i | ||||||||
\(513\) | − 3911.34i | − 0.336628i | ||||||||
\(514\) | − 21513.4i | − 1.84614i | ||||||||
\(515\) | 26071.1i | 2.23074i | ||||||||
\(516\) | −1636.40 | −0.139609 | ||||||||
\(517\) | 11526.8 | 0.980554 | ||||||||
\(518\) | 3913.85i | 0.331978i | ||||||||
\(519\) | 7856.90 | 0.664508 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20731.5 | −1.74331 | −0.871653 | − | 0.490124i | \(-0.836952\pi\) | ||||
−0.871653 | + | 0.490124i | \(0.836952\pi\) | |||||||
\(522\) | − 10577.8i | − 0.886930i | ||||||||
\(523\) | −944.353 | −0.0789554 | −0.0394777 | − | 0.999220i | \(-0.512569\pi\) | ||||
−0.0394777 | + | 0.999220i | \(0.512569\pi\) | |||||||
\(524\) | 12300.0 | 1.02543 | ||||||||
\(525\) | − 15842.6i | − 1.31701i | ||||||||
\(526\) | 36720.9i | 3.04393i | ||||||||
\(527\) | 4065.87i | 0.336076i | ||||||||
\(528\) | 4612.27i | 0.380158i | ||||||||
\(529\) | −12096.8 | −0.994228 | ||||||||
\(530\) | −35746.0 | −2.92964 | ||||||||
\(531\) | − 6114.87i | − 0.499742i | ||||||||
\(532\) | −36324.0 | −2.96023 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14286.9 | 1.15778 | ||||||||
\(535\) | − 1628.58i | − 0.131607i | ||||||||
\(536\) | −10585.3 | −0.853012 | ||||||||
\(537\) | −489.934 | −0.0393710 | ||||||||
\(538\) | − 2698.89i | − 0.216278i | ||||||||
\(539\) | 2396.96i | 0.191548i | ||||||||
\(540\) | 8815.05i | 0.702480i | ||||||||
\(541\) | − 4883.06i | − 0.388058i | −0.980996 | − | 0.194029i | \(-0.937844\pi\) | ||||
0.980996 | − | 0.194029i | \(-0.0621556\pi\) | |||||||
\(542\) | 13097.1 | 1.03795 | ||||||||
\(543\) | 9939.21 | 0.785511 | ||||||||
\(544\) | 2062.05i | 0.162518i | ||||||||
\(545\) | −13270.1 | −1.04299 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16269.1 | −1.27169 | −0.635847 | − | 0.771815i | \(-0.719349\pi\) | ||||
−0.635847 | + | 0.771815i | \(0.719349\pi\) | |||||||
\(548\) | 9258.61i | 0.721730i | ||||||||
\(549\) | −2073.63 | −0.161203 | ||||||||
\(550\) | 48255.6 | 3.74114 | ||||||||
\(551\) | 35196.0i | 2.72124i | ||||||||
\(552\) | 900.169i | 0.0694090i | ||||||||
\(553\) | − 1757.37i | − 0.135137i | ||||||||
\(554\) | 5956.63i | 0.456811i | ||||||||
\(555\) | −3160.34 | −0.241710 | ||||||||
\(556\) | 32869.3 | 2.50714 | ||||||||
\(557\) | 15661.0i | 1.19134i | 0.803229 | + | 0.595670i | \(0.203113\pi\) | ||||
−0.803229 | + | 0.595670i | \(0.796887\pi\) | |||||||
\(558\) | 3828.48 | 0.290453 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 17253.3 | 1.30194 | ||||||||
\(561\) | − 4265.82i | − 0.321040i | ||||||||
\(562\) | 22259.5 | 1.67074 | ||||||||
\(563\) | 9915.18 | 0.742230 | 0.371115 | − | 0.928587i | \(-0.378976\pi\) | ||||
0.371115 | + | 0.928587i | \(0.378976\pi\) | |||||||
\(564\) | 17318.0i | 1.29294i | ||||||||
\(565\) | 28473.7i | 2.12017i | ||||||||
\(566\) | 263.971i | 0.0196034i | ||||||||
\(567\) | 1318.73i | 0.0976745i | ||||||||
\(568\) | 11787.3 | 0.870748 | ||||||||
\(569\) | 11299.1 | 0.832482 | 0.416241 | − | 0.909254i | \(-0.363347\pi\) | ||||
0.416241 | + | 0.909254i | \(0.363347\pi\) | |||||||
\(570\) | − 44566.1i | − 3.27486i | ||||||||
\(571\) | 17619.6 | 1.29134 | 0.645672 | − | 0.763615i | \(-0.276577\pi\) | ||||
0.645672 | + | 0.763615i | \(0.276577\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12845.7 | −0.936539 | ||||||||
\(574\) | − 8501.61i | − 0.618206i | ||||||||
\(575\) | 2718.33 | 0.197152 | ||||||||
\(576\) | 5541.10 | 0.400832 | ||||||||
\(577\) | 22153.5i | 1.59837i | 0.601083 | + | 0.799186i | \(0.294736\pi\) | ||||
−0.601083 | + | 0.799186i | \(0.705264\pi\) | |||||||
\(578\) | − 13424.7i | − 0.966078i | ||||||||
\(579\) | 5631.99i | 0.404244i | ||||||||
\(580\) | − 79321.7i | − 5.67872i | ||||||||
\(581\) | −8395.15 | −0.599466 | ||||||||
\(582\) | −7068.63 | −0.503444 | ||||||||
\(583\) | − 10720.1i | − 0.761543i | ||||||||
\(584\) | −1754.31 | −0.124305 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22955.1 | −1.61820 | ||||||||
\(587\) | 9891.28i | 0.695497i | 0.937588 | + | 0.347748i | \(0.113054\pi\) | ||||
−0.937588 | + | 0.347748i | \(0.886946\pi\) | |||||||
\(588\) | −3601.24 | −0.252573 | ||||||||
\(589\) | −12738.7 | −0.891153 | ||||||||
\(590\) | − 69673.3i | − 4.86170i | ||||||||
\(591\) | 5973.77i | 0.415783i | ||||||||
\(592\) | − 2484.36i | − 0.172477i | ||||||||
\(593\) | − 9746.23i | − 0.674924i | −0.941339 | − | 0.337462i | \(-0.890432\pi\) | ||||
0.941339 | − | 0.337462i | \(-0.109568\pi\) | |||||||
\(594\) | −4016.76 | −0.277457 | ||||||||
\(595\) | −15957.4 | −1.09948 | ||||||||
\(596\) | 52979.7i | 3.64116i | ||||||||
\(597\) | −4035.16 | −0.276630 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8460.53 | −0.577109 | −0.288554 | − | 0.957464i | \(-0.593175\pi\) | ||||
−0.288554 | + | 0.957464i | \(0.593175\pi\) | |||||||
\(600\) | 34841.2i | 2.37064i | ||||||||
\(601\) | 6792.99 | 0.461052 | 0.230526 | − | 0.973066i | \(-0.425955\pi\) | ||||
0.230526 | + | 0.973066i | \(0.425955\pi\) | |||||||
\(602\) | −2789.32 | −0.188844 | ||||||||
\(603\) | − 2660.78i | − 0.179694i | ||||||||
\(604\) | − 34253.4i | − 2.30754i | ||||||||
\(605\) | − 8166.38i | − 0.548778i | ||||||||
\(606\) | − 11122.0i | − 0.745546i | ||||||||
\(607\) | 19073.4 | 1.27539 | 0.637697 | − | 0.770287i | \(-0.279887\pi\) | ||||
0.637697 | + | 0.770287i | \(0.279887\pi\) | |||||||
\(608\) | −6460.58 | −0.430939 | ||||||||
\(609\) | − 11866.5i | − 0.789582i | ||||||||
\(610\) | −23627.1 | −1.56825 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6409.05 | 0.423318 | ||||||||
\(613\) | 14465.2i | 0.953091i | 0.879150 | + | 0.476545i | \(0.158111\pi\) | ||||
−0.879150 | + | 0.476545i | \(0.841889\pi\) | |||||||
\(614\) | −4976.93 | −0.327122 | ||||||||
\(615\) | 6864.85 | 0.450109 | ||||||||
\(616\) | 17926.6i | 1.17254i | ||||||||
\(617\) | − 12897.3i | − 0.841536i | −0.907168 | − | 0.420768i | \(-0.861761\pi\) | ||||
0.907168 | − | 0.420768i | \(-0.138239\pi\) | |||||||
\(618\) | − 17848.5i | − 1.16177i | ||||||||
\(619\) | − 27735.8i | − 1.80096i | −0.434895 | − | 0.900481i | \(-0.643214\pi\) | ||||
0.434895 | − | 0.900481i | \(-0.356786\pi\) | |||||||
\(620\) | 28709.4 | 1.85967 | ||||||||
\(621\) | −226.272 | −0.0146216 | ||||||||
\(622\) | 11793.0i | 0.760222i | ||||||||
\(623\) | 16027.5 | 1.03070 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 49042.7 | 3.13873 | ||||||||
\(626\) | 38381.7i | 2.45055i | ||||||||
\(627\) | 13365.2 | 0.851281 | ||||||||
\(628\) | −37969.3 | −2.41265 | ||||||||
\(629\) | 2297.75i | 0.145656i | ||||||||
\(630\) | 15025.7i | 0.950219i | ||||||||
\(631\) | 28560.1i | 1.80184i | 0.433990 | + | 0.900918i | \(0.357105\pi\) | ||||
−0.433990 | + | 0.900918i | \(0.642895\pi\) | |||||||
\(632\) | 3864.80i | 0.243249i | ||||||||
\(633\) | −866.290 | −0.0543949 | ||||||||
\(634\) | 33585.4 | 2.10386 | ||||||||
\(635\) | − 45506.1i | − 2.84386i | ||||||||
\(636\) | 16106.0 | 1.00416 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36144.6 | 2.24291 | ||||||||
\(639\) | 2962.93i | 0.183430i | ||||||||
\(640\) | 55572.5 | 3.43234 | ||||||||
\(641\) | −1862.53 | −0.114767 | −0.0573833 | − | 0.998352i | \(-0.518276\pi\) | ||||
−0.0573833 | + | 0.998352i | \(0.518276\pi\) | |||||||
\(642\) | 1114.94i | 0.0685407i | ||||||||
\(643\) | − 29495.2i | − 1.80899i | −0.426487 | − | 0.904494i | \(-0.640249\pi\) | ||||
0.426487 | − | 0.904494i | \(-0.359751\pi\) | |||||||
\(644\) | 2101.35i | 0.128579i | ||||||||
\(645\) | − 2252.31i | − 0.137496i | ||||||||
\(646\) | −32402.2 | −1.97345 | ||||||||
\(647\) | −27780.7 | −1.68805 | −0.844027 | − | 0.536301i | \(-0.819821\pi\) | ||||
−0.844027 | + | 0.536301i | \(0.819821\pi\) | |||||||
\(648\) | − 2900.15i | − 0.175816i | ||||||||
\(649\) | 20894.7 | 1.26377 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4294.92 | 0.258573 | ||||||||
\(652\) | 3751.25i | 0.225322i | ||||||||
\(653\) | 276.678 | 0.0165808 | 0.00829039 | − | 0.999966i | \(-0.497361\pi\) | ||||
0.00829039 | + | 0.999966i | \(0.497361\pi\) | |||||||
\(654\) | 9084.84 | 0.543188 | ||||||||
\(655\) | 16929.5i | 1.00991i | ||||||||
\(656\) | 5396.49i | 0.321185i | ||||||||
\(657\) | − 440.975i | − 0.0261858i | ||||||||
\(658\) | 29519.5i | 1.74892i | ||||||||
\(659\) | 18114.9 | 1.07080 | 0.535398 | − | 0.844600i | \(-0.320162\pi\) | ||||
0.535398 | + | 0.844600i | \(0.320162\pi\) | |||||||
\(660\) | −30121.2 | −1.77647 | ||||||||
\(661\) | 27094.4i | 1.59433i | 0.603764 | + | 0.797163i | \(0.293667\pi\) | ||||
−0.603764 | + | 0.797163i | \(0.706333\pi\) | |||||||
\(662\) | −26312.5 | −1.54481 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18462.6 | 1.07905 | ||||||||
\(665\) | − 49995.8i | − 2.91542i | ||||||||
\(666\) | 2163.60 | 0.125882 | ||||||||
\(667\) | 2036.10 | 0.118198 | ||||||||
\(668\) | − 6300.70i | − 0.364942i | ||||||||
\(669\) | 5395.23i | 0.311796i | ||||||||
\(670\) | − 30317.1i | − 1.74814i | ||||||||
\(671\) | − 7085.64i | − 0.407657i | ||||||||
\(672\) | 2178.22 | 0.125039 | ||||||||
\(673\) | −2410.31 | −0.138054 | −0.0690272 | − | 0.997615i | \(-0.521990\pi\) | ||||
−0.0690272 | + | 0.997615i | \(0.521990\pi\) | |||||||
\(674\) | 8048.99i | 0.459993i | ||||||||
\(675\) | −8757.89 | −0.499395 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12508.3 | 0.710091 | 0.355046 | − | 0.934849i | \(-0.384465\pi\) | ||||
0.355046 | + | 0.934849i | \(0.384465\pi\) | |||||||
\(678\) | − 19493.3i | − 1.10418i | ||||||||
\(679\) | −7929.83 | −0.448187 | ||||||||
\(680\) | 35093.5 | 1.97908 | ||||||||
\(681\) | − 7458.30i | − 0.419681i | ||||||||
\(682\) | 13082.0i | 0.734511i | ||||||||
\(683\) | − 16793.8i | − 0.940844i | −0.882442 | − | 0.470422i | \(-0.844102\pi\) | ||||
0.882442 | − | 0.470422i | \(-0.155898\pi\) | |||||||
\(684\) | 20080.1i | 1.12249i | ||||||||
\(685\) | −12743.4 | −0.710804 | ||||||||
\(686\) | −33152.3 | −1.84513 | ||||||||
\(687\) | 18224.1i | 1.01207i | ||||||||
\(688\) | 1770.56 | 0.0981131 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2578.16 | −0.142245 | ||||||||
\(691\) | 26026.9i | 1.43286i | 0.697657 | + | 0.716432i | \(0.254226\pi\) | ||||
−0.697657 | + | 0.716432i | \(0.745774\pi\) | |||||||
\(692\) | −40335.8 | −2.21580 | ||||||||
\(693\) | −4506.13 | −0.247004 | ||||||||
\(694\) | 44834.4i | 2.45229i | ||||||||
\(695\) | 45240.8i | 2.46918i | ||||||||
\(696\) | 26096.9i | 1.42126i | ||||||||
\(697\) | − 4991.14i | − 0.271238i | ||||||||
\(698\) | −25345.8 | −1.37443 | ||||||||
\(699\) | −19101.5 | −1.03360 | ||||||||
\(700\) | 81333.0i | 4.39157i | ||||||||
\(701\) | −5079.08 | −0.273658 | −0.136829 | − | 0.990595i | \(-0.543691\pi\) | ||||
−0.136829 | + | 0.990595i | \(0.543691\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7199.04 | −0.386226 | ||||||||
\(704\) | 18934.1i | 1.01364i | ||||||||
\(705\) | −23836.3 | −1.27337 | ||||||||
\(706\) | 5892.11 | 0.314097 | ||||||||
\(707\) | − 12477.1i | − 0.663717i | ||||||||
\(708\) | 31392.6i | 1.66639i | ||||||||
\(709\) | − 2530.72i | − 0.134052i | −0.997751 | − | 0.0670262i | \(-0.978649\pi\) | ||||
0.997751 | − | 0.0670262i | \(-0.0213511\pi\) | |||||||
\(710\) | 33759.9i | 1.78449i | ||||||||
\(711\) | −971.480 | −0.0512424 | ||||||||
\(712\) | −35247.7 | −1.85529 | ||||||||
\(713\) | 736.937i | 0.0387076i | ||||||||
\(714\) | 10924.6 | 0.572607 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2515.22 | 0.131283 | ||||||||
\(717\) | 5659.28i | 0.294770i | ||||||||
\(718\) | −25716.4 | −1.33667 | ||||||||
\(719\) | −9503.67 | −0.492944 | −0.246472 | − | 0.969150i | \(-0.579271\pi\) | ||||
−0.246472 | + | 0.969150i | \(0.579271\pi\) | |||||||
\(720\) | − 9537.73i | − 0.493681i | ||||||||
\(721\) | − 20023.0i | − 1.03425i | ||||||||
\(722\) | − 68338.2i | − 3.52255i | ||||||||
\(723\) | 17543.7i | 0.902432i | ||||||||
\(724\) | −51026.0 | −2.61929 | ||||||||
\(725\) | 78807.4 | 4.03701 | ||||||||
\(726\) | 5590.77i | 0.285803i | ||||||||
\(727\) | −33343.1 | −1.70100 | −0.850500 | − | 0.525975i | \(-0.823700\pi\) | ||||
−0.850500 | + | 0.525975i | \(0.823700\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | − 5024.50i | − 0.254747i | ||||||||
\(731\) | −1637.56 | −0.0828556 | ||||||||
\(732\) | 10645.6 | 0.537531 | ||||||||
\(733\) | − 32288.1i | − 1.62699i | −0.581569 | − | 0.813497i | \(-0.697561\pi\) | ||||
0.581569 | − | 0.813497i | \(-0.302439\pi\) | |||||||
\(734\) | − 1398.53i | − 0.0703277i | ||||||||
\(735\) | − 4956.69i | − 0.248749i | ||||||||
\(736\) | 373.746i | 0.0187180i | ||||||||
\(737\) | 9091.96 | 0.454419 | ||||||||
\(738\) | −4699.73 | −0.234417 | ||||||||
\(739\) | − 14168.8i | − 0.705288i | −0.935758 | − | 0.352644i | \(-0.885283\pi\) | ||||
0.935758 | − | 0.352644i | \(-0.114717\pi\) | |||||||
\(740\) | 16224.6 | 0.805983 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27453.5 | 1.35829 | ||||||||
\(743\) | − 13248.6i | − 0.654165i | −0.944996 | − | 0.327083i | \(-0.893934\pi\) | ||||
0.944996 | − | 0.327083i | \(-0.106066\pi\) | |||||||
\(744\) | −9445.39 | −0.465437 | ||||||||
\(745\) | −72920.5 | −3.58604 | ||||||||
\(746\) | 29818.3i | 1.46344i | ||||||||
\(747\) | 4640.88i | 0.227311i | ||||||||
\(748\) | 21899.9i | 1.07051i | ||||||||
\(749\) | 1250.78i | 0.0610178i | ||||||||
\(750\) | −61333.0 | −2.98609 | ||||||||
\(751\) | −5113.98 | −0.248484 | −0.124242 | − | 0.992252i | \(-0.539650\pi\) | ||||
−0.124242 | + | 0.992252i | \(0.539650\pi\) | |||||||
\(752\) | − 18737.8i | − 0.908641i | ||||||||
\(753\) | 7165.95 | 0.346802 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47145.9 | 2.27260 | ||||||||
\(756\) | − 6770.10i | − 0.325696i | ||||||||
\(757\) | 27380.4 | 1.31461 | 0.657303 | − | 0.753626i | \(-0.271697\pi\) | ||||
0.657303 | + | 0.753626i | \(0.271697\pi\) | |||||||
\(758\) | −11803.6 | −0.565604 | ||||||||
\(759\) | − 773.178i | − 0.0369757i | ||||||||
\(760\) | 109951.i | 5.24781i | ||||||||
\(761\) | − 10613.8i | − 0.505586i | −0.967520 | − | 0.252793i | \(-0.918651\pi\) | ||||
0.967520 | − | 0.252793i | \(-0.0813492\pi\) | |||||||
\(762\) | 31153.8i | 1.48108i | ||||||||
\(763\) | 10191.7 | 0.483569 | ||||||||
\(764\) | 65947.3 | 3.12289 | ||||||||
\(765\) | 8821.32i | 0.416909i | ||||||||
\(766\) | −31817.6 | −1.50080 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −23269.2 | −1.09330 | ||||||||
\(769\) | − 9172.22i | − 0.430115i | −0.976601 | − | 0.215058i | \(-0.931006\pi\) | ||||
0.976601 | − | 0.215058i | \(-0.0689939\pi\) | |||||||
\(770\) | −51343.2 | −2.40296 | ||||||||
\(771\) | −13341.6 | −0.623200 | ||||||||
\(772\) | − 28913.5i | − 1.34795i | ||||||||
\(773\) | − 14952.1i | − 0.695718i | −0.937547 | − | 0.347859i | \(-0.886909\pi\) | ||||
0.937547 | − | 0.347859i | \(-0.113091\pi\) | |||||||
\(774\) | 1541.95i | 0.0716076i | ||||||||
\(775\) | 28523.2i | 1.32205i | ||||||||
\(776\) | 17439.3 | 0.806745 | ||||||||
\(777\) | 2427.19 | 0.112066 | ||||||||
\(778\) | − 24017.9i | − 1.10679i | ||||||||
\(779\) | 15637.7 | 0.719226 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10124.4 | −0.463867 | ||||||||
\(782\) | 1874.47i | 0.0857174i | ||||||||
\(783\) | −6559.87 | −0.299400 | ||||||||
\(784\) | 3896.48 | 0.177500 | ||||||||
\(785\) | − 52260.4i | − 2.37612i | ||||||||
\(786\) | − 11590.1i | − 0.525959i | ||||||||
\(787\) | − 2671.52i | − 0.121003i | −0.998168 | − | 0.0605015i | \(-0.980730\pi\) | ||||
0.998168 | − | 0.0605015i | \(-0.0192700\pi\) | |||||||
\(788\) | − 30668.1i | − 1.38643i | ||||||||
\(789\) | 22772.6 | 1.02754 | ||||||||
\(790\) | −11069.1 | −0.498508 | ||||||||
\(791\) | − 21868.3i | − 0.982991i | ||||||||
\(792\) | 9909.89 | 0.444612 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 58407.4 | 2.61058 | ||||||||
\(795\) | 22168.1i | 0.988957i | ||||||||
\(796\) | 20715.7 | 0.922423 | ||||||||
\(797\) | 12949.7 | 0.575536 | 0.287768 | − | 0.957700i | \(-0.407087\pi\) | ||||
0.287768 | + | 0.957700i | \(0.407087\pi\) | |||||||
\(798\) | 34227.5i | 1.51835i | ||||||||
\(799\) | 17330.4i | 0.767339i | ||||||||
\(800\) | 14465.9i | 0.639307i | ||||||||
\(801\) | − 8860.08i | − 0.390831i | ||||||||
\(802\) | 23785.5 | 1.04725 | ||||||||
\(803\) | 1506.82 | 0.0662200 | ||||||||
\(804\) | 13659.9i | 0.599190i | ||||||||
\(805\) | −2892.27 | −0.126632 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1673.73 | −0.0730089 | ||||||||
\(808\) | 27439.6i | 1.19470i | ||||||||
\(809\) | −11640.4 | −0.505876 | −0.252938 | − | 0.967482i | \(-0.581397\pi\) | ||||
−0.252938 | + | 0.967482i | \(0.581397\pi\) | |||||||
\(810\) | 8306.28 | 0.360312 | ||||||||
\(811\) | − 18135.3i | − 0.785225i | −0.919704 | − | 0.392613i | \(-0.871571\pi\) | ||||
0.919704 | − | 0.392613i | \(-0.128429\pi\) | |||||||
\(812\) | 60920.4i | 2.63286i | ||||||||
\(813\) | − 8122.24i | − 0.350381i | ||||||||
\(814\) | 7393.06i | 0.318337i | ||||||||
\(815\) | −5163.16 | −0.221911 | ||||||||
\(816\) | −6934.49 | −0.297495 | ||||||||
\(817\) | − 5130.61i | − 0.219703i | ||||||||
\(818\) | 74260.0 | 3.17413 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −35242.8 | −1.50089 | ||||||||
\(821\) | 10789.1i | 0.458640i | 0.973351 | + | 0.229320i | \(0.0736503\pi\) | ||||
−0.973351 | + | 0.229320i | \(0.926350\pi\) | |||||||
\(822\) | 8724.24 | 0.370186 | ||||||||
\(823\) | 12284.7 | 0.520312 | 0.260156 | − | 0.965567i | \(-0.416226\pi\) | ||||
0.260156 | + | 0.965567i | \(0.416226\pi\) | |||||||
\(824\) | 44034.7i | 1.86168i | ||||||||
\(825\) | − 29925.9i | − 1.26289i | ||||||||
\(826\) | 53510.2i | 2.25407i | ||||||||
\(827\) | − 36077.2i | − 1.51696i | −0.651696 | − | 0.758480i | \(-0.725942\pi\) | ||||
0.651696 | − | 0.758480i | \(-0.274058\pi\) | |||||||
\(828\) | 1161.64 | 0.0487556 | ||||||||
\(829\) | 8861.83 | 0.371271 | 0.185636 | − | 0.982619i | \(-0.440566\pi\) | ||||
0.185636 | + | 0.982619i | \(0.440566\pi\) | |||||||
\(830\) | 52878.5i | 2.21137i | ||||||||
\(831\) | 3694.04 | 0.154205 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3603.80 | −0.149897 | ||||||||
\(834\) | − 30972.2i | − 1.28595i | ||||||||
\(835\) | 8672.18 | 0.359417 | ||||||||
\(836\) | −68614.1 | −2.83860 | ||||||||
\(837\) | − 2374.25i | − 0.0980480i | ||||||||
\(838\) | − 26551.0i | − 1.09450i | ||||||||
\(839\) | − 5833.37i | − 0.240036i | −0.992772 | − | 0.120018i | \(-0.961705\pi\) | ||||
0.992772 | − | 0.120018i | \(-0.0382952\pi\) | |||||||
\(840\) | − 37070.4i | − 1.52268i | ||||||||
\(841\) | 34639.6 | 1.42030 | ||||||||
\(842\) | −4487.66 | −0.183676 | ||||||||
\(843\) | − 13804.3i | − 0.563993i | ||||||||
\(844\) | 4447.37 | 0.181380 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16318.5 | 0.663170 | ||||||||
\(847\) | 6271.92i | 0.254434i | ||||||||
\(848\) | −17426.4 | −0.705692 | ||||||||
\(849\) | 163.703 | 0.00661752 | ||||||||
\(850\) | 72551.7i | 2.92765i | ||||||||
\(851\) | 416.466i | 0.0167759i | ||||||||
\(852\) | − 15211.1i | − 0.611648i | ||||||||
\(853\) | 28649.5i | 1.14999i | 0.818157 | + | 0.574995i | \(0.194996\pi\) | ||||
−0.818157 | + | 0.574995i | \(0.805004\pi\) | |||||||
\(854\) | 18146.0 | 0.727098 | ||||||||
\(855\) | −27637.9 | −1.10549 | ||||||||
\(856\) | − 2750.71i | − 0.109833i | ||||||||
\(857\) | −32336.1 | −1.28889 | −0.644445 | − | 0.764651i | \(-0.722911\pi\) | ||||
−0.644445 | + | 0.764651i | \(0.722911\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13878.5 | −0.551254 | −0.275627 | − | 0.961265i | \(-0.588885\pi\) | ||||
−0.275627 | + | 0.961265i | \(0.588885\pi\) | |||||||
\(860\) | 11562.9i | 0.458480i | ||||||||
\(861\) | −5272.31 | −0.208688 | ||||||||
\(862\) | 53223.7 | 2.10302 | ||||||||
\(863\) | − 32934.7i | − 1.29908i | −0.760326 | − | 0.649542i | \(-0.774961\pi\) | ||||
0.760326 | − | 0.649542i | \(-0.225039\pi\) | |||||||
\(864\) | − 1204.13i | − 0.0474135i | ||||||||
\(865\) | − 55517.5i | − 2.18226i | ||||||||
\(866\) | 46424.3i | 1.82167i | ||||||||
\(867\) | −8325.38 | −0.326119 | ||||||||
\(868\) | −22049.3 | −0.862213 | ||||||||
\(869\) | − 3319.57i | − 0.129584i | ||||||||
\(870\) | −74743.6 | −2.91270 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −22413.5 | −0.870434 | ||||||||
\(873\) | 4383.65i | 0.169947i | ||||||||
\(874\) | −5872.87 | −0.227292 | ||||||||
\(875\) | −68805.4 | −2.65834 | ||||||||
\(876\) | 2263.88i | 0.0873167i | ||||||||
\(877\) | − 18375.7i | − 0.707531i | −0.935334 | − | 0.353765i | \(-0.884901\pi\) | ||||
0.935334 | − | 0.353765i | \(-0.115099\pi\) | |||||||
\(878\) | 50050.2i | 1.92382i | ||||||||
\(879\) | 14235.7i | 0.546256i | ||||||||
\(880\) | 32590.7 | 1.24845 | ||||||||
\(881\) | −46883.4 | −1.79290 | −0.896448 | − | 0.443150i | \(-0.853861\pi\) | ||||
−0.896448 | + | 0.443150i | \(0.853861\pi\) | |||||||
\(882\) | 3393.39i | 0.129548i | ||||||||
\(883\) | −1050.05 | −0.0400194 | −0.0200097 | − | 0.999800i | \(-0.506370\pi\) | ||||
−0.0200097 | + | 0.999800i | \(0.506370\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −43208.2 | −1.64116 | ||||||||
\(886\) | 27333.7i | 1.03645i | ||||||||
\(887\) | 27916.8 | 1.05677 | 0.528385 | − | 0.849005i | \(-0.322798\pi\) | ||||
0.528385 | + | 0.849005i | \(0.322798\pi\) | |||||||
\(888\) | −5337.89 | −0.201720 | ||||||||
\(889\) | 34949.4i | 1.31852i | ||||||||
\(890\) | − 100952.i | − 3.80217i | ||||||||
\(891\) | 2491.01i | 0.0936611i | ||||||||
\(892\) | − 27698.0i | − 1.03968i | ||||||||
\(893\) | −54297.4 | −2.03471 | ||||||||
\(894\) | 49921.9 | 1.86761 | ||||||||
\(895\) | 3461.92i | 0.129295i | ||||||||
\(896\) | −42680.6 | −1.59136 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 57990.8 | 2.15499 | ||||||||
\(899\) | 21364.6i | 0.792601i | ||||||||
\(900\) | 44961.3 | 1.66523 | ||||||||
\(901\) | 16117.5 | 0.595950 | ||||||||
\(902\) | − 16059.1i | − 0.592804i | ||||||||
\(903\) | 1729.81i | 0.0637481i | ||||||||
\(904\) | 48092.7i | 1.76940i | ||||||||
\(905\) | − 70231.3i | − 2.57963i | ||||||||
\(906\) | −32276.4 | −1.18357 | ||||||||
\(907\) | −23220.1 | −0.850066 | −0.425033 | − | 0.905178i | \(-0.639737\pi\) | ||||
−0.425033 | + | 0.905178i | \(0.639737\pi\) | |||||||
\(908\) | 38289.5i | 1.39943i | ||||||||
\(909\) | −6897.38 | −0.251674 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16344.9 | 0.594435 | 0.297217 | − | 0.954810i | \(-0.403941\pi\) | ||||
0.297217 | + | 0.954810i | \(0.403941\pi\) | |||||||
\(912\) | − 21726.3i | − 0.788848i | ||||||||
\(913\) | −15858.0 | −0.574834 | ||||||||
\(914\) | 79516.7 | 2.87766 | ||||||||
\(915\) | 14652.4i | 0.529393i | ||||||||
\(916\) | − 93559.0i | − 3.37476i | ||||||||
\(917\) | − 13002.1i | − 0.468231i | ||||||||
\(918\) | − 6039.15i | − 0.217126i | ||||||||
\(919\) | −32931.7 | −1.18206 | −0.591032 | − | 0.806648i | \(-0.701279\pi\) | ||||
−0.591032 | + | 0.806648i | \(0.701279\pi\) | |||||||
\(920\) | 6360.67 | 0.227940 | ||||||||
\(921\) | 3086.47i | 0.110426i | ||||||||
\(922\) | −42800.8 | −1.52882 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 23133.6 | 0.823636 | ||||||||
\(925\) | 16119.4i | 0.572975i | ||||||||
\(926\) | 49679.0 | 1.76302 | ||||||||
\(927\) | −11068.8 | −0.392177 | ||||||||
\(928\) | 10835.3i | 0.383282i | ||||||||
\(929\) | − 56305.5i | − 1.98851i | −0.107056 | − | 0.994253i | \(-0.534142\pi\) | ||||
0.107056 | − | 0.994253i | \(-0.465858\pi\) | |||||||
\(930\) | − 27052.4i | − 0.953852i | ||||||||
\(931\) | − 11291.0i | − 0.397473i | ||||||||
\(932\) | 98063.3 | 3.44653 | ||||||||
\(933\) | 7313.51 | 0.256628 | ||||||||
\(934\) | − 71258.5i | − 2.49641i | ||||||||
\(935\) | −30142.7 | −1.05430 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7095.61 | 0.247389 | 0.123695 | − | 0.992320i | \(-0.460526\pi\) | ||||
0.123695 | + | 0.992320i | \(0.460526\pi\) | |||||||
\(938\) | 23284.0i | 0.810502i | ||||||||
\(939\) | 23802.6 | 0.827230 | ||||||||
\(940\) | 122371. | 4.24606 | ||||||||
\(941\) | − 5185.17i | − 0.179630i | −0.995958 | − | 0.0898150i | \(-0.971372\pi\) | ||||
0.995958 | − | 0.0898150i | \(-0.0286276\pi\) | |||||||
\(942\) | 35777.9i | 1.23748i | ||||||||
\(943\) | − 904.641i | − 0.0312398i | ||||||||
\(944\) | − 33966.2i | − 1.17109i | ||||||||
\(945\) | 9318.26 | 0.320765 | ||||||||
\(946\) | −5268.89 | −0.181085 | ||||||||
\(947\) | − 38451.7i | − 1.31944i | −0.751510 | − | 0.659722i | \(-0.770674\pi\) | ||||
0.751510 | − | 0.659722i | \(-0.229326\pi\) | |||||||
\(948\) | 4987.39 | 0.170868 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −227310. | −7.76307 | ||||||||
\(951\) | − 20828.2i | − 0.710199i | ||||||||
\(952\) | −26952.4 | −0.917575 | ||||||||
\(953\) | 20930.5 | 0.711445 | 0.355722 | − | 0.934592i | \(-0.384235\pi\) | ||||
0.355722 | + | 0.934592i | \(0.384235\pi\) | |||||||
\(954\) | − 15176.4i | − 0.515048i | ||||||||
\(955\) | 90768.8i | 3.07561i | ||||||||
\(956\) | − 29053.7i | − 0.982910i | ||||||||
\(957\) | − 22415.2i | − 0.757139i | ||||||||
\(958\) | 3072.19 | 0.103609 | ||||||||
\(959\) | 9787.14 | 0.329555 | ||||||||
\(960\) | − 39153.9i | − 1.31634i | ||||||||
\(961\) | 22058.4 | 0.740438 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 691.435 | 0.0231372 | ||||||||
\(964\) | − 90066.1i | − 3.00916i | ||||||||
\(965\) | 39796.1 | 1.32755 | ||||||||
\(966\) | 1980.07 | 0.0659499 | ||||||||
\(967\) | − 50788.1i | − 1.68897i | −0.535578 | − | 0.844486i | \(-0.679906\pi\) | ||||
0.535578 | − | 0.844486i | \(-0.320094\pi\) | |||||||
\(968\) | − 13793.2i | − 0.457986i | ||||||||
\(969\) | 20094.4i | 0.666175i | ||||||||
\(970\) | 49947.6i | 1.65332i | ||||||||
\(971\) | 15277.5 | 0.504922 | 0.252461 | − | 0.967607i | \(-0.418760\pi\) | ||||
0.252461 | + | 0.967607i | \(0.418760\pi\) | |||||||
\(972\) | −3742.54 | −0.123500 | ||||||||
\(973\) | − 34745.7i | − 1.14481i | ||||||||
\(974\) | 80356.3 | 2.64351 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11518.4 | −0.377760 | ||||||||
\(977\) | 1293.19i | 0.0423469i | 0.999776 | + | 0.0211734i | \(0.00674022\pi\) | ||||
−0.999776 | + | 0.0211734i | \(0.993260\pi\) | |||||||
\(978\) | 3534.74 | 0.115571 | ||||||||
\(979\) | 30275.1 | 0.988353 | ||||||||
\(980\) | 25446.7i | 0.829453i | ||||||||
\(981\) | − 5634.01i | − 0.183364i | ||||||||
\(982\) | 12500.8i | 0.406227i | ||||||||
\(983\) | − 8474.63i | − 0.274973i | −0.990504 | − | 0.137487i | \(-0.956098\pi\) | ||||
0.990504 | − | 0.137487i | \(-0.0439024\pi\) | |||||||
\(984\) | 11594.9 | 0.375641 | ||||||||
\(985\) | 42211.1 | 1.36544 | ||||||||
\(986\) | 54343.0i | 1.75521i | ||||||||
\(987\) | 18306.6 | 0.590382 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −296.807 | −0.00954289 | ||||||||
\(990\) | 28382.8i | 0.911175i | ||||||||
\(991\) | −7080.71 | −0.226969 | −0.113484 | − | 0.993540i | \(-0.536201\pi\) | ||||
−0.113484 | + | 0.993540i | \(0.536201\pi\) | |||||||
\(992\) | −3921.68 | −0.125518 | ||||||||
\(993\) | 16317.8i | 0.521480i | ||||||||
\(994\) | − 25928.1i | − 0.827354i | ||||||||
\(995\) | 28512.8i | 0.908458i | ||||||||
\(996\) | − 23825.4i | − 0.757968i | ||||||||
\(997\) | 19423.1 | 0.616985 | 0.308493 | − | 0.951227i | \(-0.400175\pi\) | ||||
0.308493 | + | 0.951227i | \(0.400175\pi\) | |||||||
\(998\) | −10564.5 | −0.335084 | ||||||||
\(999\) | − 1341.76i | − 0.0424940i |
(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 | 507.4.b.k.337.17 | 18 | ||
13.5 | odd | 4 | 507.4.a.o.1.9 | ✓ | 9 | ||
13.8 | odd | 4 | 507.4.a.p.1.1 | yes | 9 | ||
13.12 | even | 2 | inner | 507.4.b.k.337.2 | 18 | ||
39.5 | even | 4 | 1521.4.a.bi.1.1 | 9 | |||
39.8 | even | 4 | 1521.4.a.bf.1.9 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.9 | ✓ | 9 | 13.5 | odd | 4 | ||
507.4.a.p.1.1 | yes | 9 | 13.8 | odd | 4 | ||
507.4.b.k.337.2 | 18 | 13.12 | even | 2 | inner | ||
507.4.b.k.337.17 | 18 | 1.1 | even | 1 | trivial | ||
1521.4.a.bf.1.9 | 9 | 39.8 | even | 4 | |||
1521.4.a.bi.1.1 | 9 | 39.5 | even | 4 |