Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(1,507)]
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, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.39246\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.83750 | −1.71031 | −0.855157 | − | 0.518368i | \(-0.826540\pi\) | ||||
−0.855157 | + | 0.518368i | \(0.826540\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 15.4014 | 1.92518 | ||||||||
\(5\) | 21.1983 | 1.89603 | 0.948015 | − | 0.318225i | \(-0.103087\pi\) | ||||
0.948015 | + | 0.318225i | \(0.103087\pi\) | |||||||
\(6\) | −14.5125 | −0.987451 | ||||||||
\(7\) | 16.2806 | 0.879070 | 0.439535 | − | 0.898225i | \(-0.355143\pi\) | ||||
0.439535 | + | 0.898225i | \(0.355143\pi\) | |||||||
\(8\) | −35.8043 | −1.58234 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −102.547 | −3.24281 | ||||||||
\(11\) | 30.7532 | 0.842950 | 0.421475 | − | 0.906840i | \(-0.361513\pi\) | ||||
0.421475 | + | 0.906840i | \(0.361513\pi\) | |||||||
\(12\) | 46.2042 | 1.11150 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −78.7575 | −1.50349 | ||||||||
\(15\) | 63.5948 | 1.09467 | ||||||||
\(16\) | 49.9922 | 0.781128 | ||||||||
\(17\) | 46.2371 | 0.659656 | 0.329828 | − | 0.944041i | \(-0.393009\pi\) | ||||
0.329828 | + | 0.944041i | \(0.393009\pi\) | |||||||
\(18\) | −43.5375 | −0.570105 | ||||||||
\(19\) | 144.865 | 1.74917 | 0.874585 | − | 0.484873i | \(-0.161134\pi\) | ||||
0.874585 | + | 0.484873i | \(0.161134\pi\) | |||||||
\(20\) | 326.483 | 3.65019 | ||||||||
\(21\) | 48.8418 | 0.507531 | ||||||||
\(22\) | −148.769 | −1.44171 | ||||||||
\(23\) | 8.38045 | 0.0759758 | 0.0379879 | − | 0.999278i | \(-0.487905\pi\) | ||||
0.0379879 | + | 0.999278i | \(0.487905\pi\) | |||||||
\(24\) | −107.413 | −0.913566 | ||||||||
\(25\) | 324.366 | 2.59493 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 250.744 | 1.69237 | ||||||||
\(29\) | −242.958 | −1.55573 | −0.777865 | − | 0.628431i | \(-0.783697\pi\) | ||||
−0.777865 | + | 0.628431i | \(0.783697\pi\) | |||||||
\(30\) | −307.640 | −1.87224 | ||||||||
\(31\) | 87.9353 | 0.509472 | 0.254736 | − | 0.967011i | \(-0.418011\pi\) | ||||
0.254736 | + | 0.967011i | \(0.418011\pi\) | |||||||
\(32\) | 44.5973 | 0.246368 | ||||||||
\(33\) | 92.2597 | 0.486677 | ||||||||
\(34\) | −223.672 | −1.12822 | ||||||||
\(35\) | 345.121 | 1.66674 | ||||||||
\(36\) | 138.613 | 0.641726 | ||||||||
\(37\) | −49.6950 | −0.220806 | −0.110403 | − | 0.993887i | \(-0.535214\pi\) | ||||
−0.110403 | + | 0.993887i | \(0.535214\pi\) | |||||||
\(38\) | −700.783 | −2.99163 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −758.990 | −3.00017 | ||||||||
\(41\) | −107.947 | −0.411181 | −0.205591 | − | 0.978638i | \(-0.565912\pi\) | ||||
−0.205591 | + | 0.978638i | \(0.565912\pi\) | |||||||
\(42\) | −236.272 | −0.868039 | ||||||||
\(43\) | −35.4166 | −0.125604 | −0.0628021 | − | 0.998026i | \(-0.520004\pi\) | ||||
−0.0628021 | + | 0.998026i | \(0.520004\pi\) | |||||||
\(44\) | 473.643 | 1.62283 | ||||||||
\(45\) | 190.784 | 0.632010 | ||||||||
\(46\) | −40.5404 | −0.129943 | ||||||||
\(47\) | −374.815 | −1.16324 | −0.581621 | − | 0.813460i | \(-0.697581\pi\) | ||||
−0.581621 | + | 0.813460i | \(0.697581\pi\) | |||||||
\(48\) | 149.977 | 0.450985 | ||||||||
\(49\) | −77.9418 | −0.227236 | ||||||||
\(50\) | −1569.12 | −4.43815 | ||||||||
\(51\) | 138.711 | 0.380853 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −348.583 | −0.903426 | −0.451713 | − | 0.892163i | \(-0.649187\pi\) | ||||
−0.451713 | + | 0.892163i | \(0.649187\pi\) | |||||||
\(54\) | −130.613 | −0.329150 | ||||||||
\(55\) | 651.915 | 1.59826 | ||||||||
\(56\) | −582.916 | −1.39099 | ||||||||
\(57\) | 434.594 | 1.00988 | ||||||||
\(58\) | 1175.31 | 2.66079 | ||||||||
\(59\) | −679.430 | −1.49923 | −0.749613 | − | 0.661877i | \(-0.769760\pi\) | ||||
−0.749613 | + | 0.661877i | \(0.769760\pi\) | |||||||
\(60\) | 979.450 | 2.10744 | ||||||||
\(61\) | −230.403 | −0.483608 | −0.241804 | − | 0.970325i | \(-0.577739\pi\) | ||||
−0.241804 | + | 0.970325i | \(0.577739\pi\) | |||||||
\(62\) | −425.387 | −0.871358 | ||||||||
\(63\) | 146.525 | 0.293023 | ||||||||
\(64\) | −615.677 | −1.20249 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −446.306 | −0.832372 | ||||||||
\(67\) | 295.642 | 0.539082 | 0.269541 | − | 0.962989i | \(-0.413128\pi\) | ||||
0.269541 | + | 0.962989i | \(0.413128\pi\) | |||||||
\(68\) | 712.117 | 1.26995 | ||||||||
\(69\) | 25.1413 | 0.0438647 | ||||||||
\(70\) | −1669.52 | −2.85066 | ||||||||
\(71\) | −329.215 | −0.550290 | −0.275145 | − | 0.961403i | \(-0.588726\pi\) | ||||
−0.275145 | + | 0.961403i | \(0.588726\pi\) | |||||||
\(72\) | −322.239 | −0.527448 | ||||||||
\(73\) | −48.9973 | −0.0785575 | −0.0392787 | − | 0.999228i | \(-0.512506\pi\) | ||||
−0.0392787 | + | 0.999228i | \(0.512506\pi\) | |||||||
\(74\) | 240.399 | 0.377647 | ||||||||
\(75\) | 973.099 | 1.49818 | ||||||||
\(76\) | 2231.12 | 3.36746 | ||||||||
\(77\) | 500.681 | 0.741012 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −107.942 | −0.153727 | −0.0768636 | − | 0.997042i | \(-0.524491\pi\) | ||||
−0.0768636 | + | 0.997042i | \(0.524491\pi\) | |||||||
\(80\) | 1059.75 | 1.48104 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 522.192 | 0.703250 | ||||||||
\(83\) | −515.654 | −0.681932 | −0.340966 | − | 0.940076i | \(-0.610754\pi\) | ||||
−0.340966 | + | 0.940076i | \(0.610754\pi\) | |||||||
\(84\) | 752.233 | 0.977088 | ||||||||
\(85\) | 980.147 | 1.25073 | ||||||||
\(86\) | 171.328 | 0.214823 | ||||||||
\(87\) | −728.874 | −0.898201 | ||||||||
\(88\) | −1101.10 | −1.33384 | ||||||||
\(89\) | −984.453 | −1.17249 | −0.586246 | − | 0.810133i | \(-0.699395\pi\) | ||||
−0.586246 | + | 0.810133i | \(0.699395\pi\) | |||||||
\(90\) | −922.919 | −1.08094 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 129.071 | 0.146267 | ||||||||
\(93\) | 263.806 | 0.294144 | ||||||||
\(94\) | 1813.17 | 1.98951 | ||||||||
\(95\) | 3070.88 | 3.31648 | ||||||||
\(96\) | 133.792 | 0.142241 | ||||||||
\(97\) | −487.072 | −0.509842 | −0.254921 | − | 0.966962i | \(-0.582049\pi\) | ||||
−0.254921 | + | 0.966962i | \(0.582049\pi\) | |||||||
\(98\) | 377.043 | 0.388644 | ||||||||
\(99\) | 276.779 | 0.280983 | ||||||||
\(100\) | 4995.70 | 4.99570 | ||||||||
\(101\) | 766.375 | 0.755021 | 0.377511 | − | 0.926005i | \(-0.376780\pi\) | ||||
0.377511 | + | 0.926005i | \(0.376780\pi\) | |||||||
\(102\) | −671.016 | −0.651378 | ||||||||
\(103\) | 1229.87 | 1.17653 | 0.588266 | − | 0.808668i | \(-0.299811\pi\) | ||||
0.588266 | + | 0.808668i | \(0.299811\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1035.36 | 0.962295 | ||||||||
\(106\) | 1686.27 | 1.54514 | ||||||||
\(107\) | 76.8261 | 0.0694117 | 0.0347059 | − | 0.999398i | \(-0.488951\pi\) | ||||
0.0347059 | + | 0.999398i | \(0.488951\pi\) | |||||||
\(108\) | 415.838 | 0.370500 | ||||||||
\(109\) | 626.001 | 0.550092 | 0.275046 | − | 0.961431i | \(-0.411307\pi\) | ||||
0.275046 | + | 0.961431i | \(0.411307\pi\) | |||||||
\(110\) | −3153.64 | −2.73353 | ||||||||
\(111\) | −149.085 | −0.127482 | ||||||||
\(112\) | 813.904 | 0.686667 | ||||||||
\(113\) | −1343.21 | −1.11822 | −0.559108 | − | 0.829095i | \(-0.688856\pi\) | ||||
−0.559108 | + | 0.829095i | \(0.688856\pi\) | |||||||
\(114\) | −2102.35 | −1.72722 | ||||||||
\(115\) | 177.651 | 0.144052 | ||||||||
\(116\) | −3741.90 | −2.99506 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3286.74 | 2.56415 | ||||||||
\(119\) | 752.769 | 0.579884 | ||||||||
\(120\) | −2276.97 | −1.73215 | ||||||||
\(121\) | −385.238 | −0.289435 | ||||||||
\(122\) | 1114.58 | 0.827122 | ||||||||
\(123\) | −323.840 | −0.237396 | ||||||||
\(124\) | 1354.33 | 0.980824 | ||||||||
\(125\) | 4226.22 | 3.02404 | ||||||||
\(126\) | −708.817 | −0.501162 | ||||||||
\(127\) | −2146.69 | −1.49990 | −0.749952 | − | 0.661492i | \(-0.769923\pi\) | ||||
−0.749952 | + | 0.661492i | \(0.769923\pi\) | |||||||
\(128\) | 2621.56 | 1.81028 | ||||||||
\(129\) | −106.250 | −0.0725177 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −798.626 | −0.532644 | −0.266322 | − | 0.963884i | \(-0.585808\pi\) | ||||
−0.266322 | + | 0.963884i | \(0.585808\pi\) | |||||||
\(132\) | 1420.93 | 0.936940 | ||||||||
\(133\) | 2358.48 | 1.53764 | ||||||||
\(134\) | −1430.17 | −0.921999 | ||||||||
\(135\) | 572.353 | 0.364891 | ||||||||
\(136\) | −1655.49 | −1.04380 | ||||||||
\(137\) | −601.153 | −0.374891 | −0.187445 | − | 0.982275i | \(-0.560021\pi\) | ||||
−0.187445 | + | 0.982275i | \(0.560021\pi\) | |||||||
\(138\) | −121.621 | −0.0750224 | ||||||||
\(139\) | −2134.18 | −1.30229 | −0.651146 | − | 0.758953i | \(-0.725711\pi\) | ||||
−0.651146 | + | 0.758953i | \(0.725711\pi\) | |||||||
\(140\) | 5315.35 | 3.20878 | ||||||||
\(141\) | −1124.44 | −0.671598 | ||||||||
\(142\) | 1592.58 | 0.941169 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 449.930 | 0.260376 | ||||||||
\(145\) | −5150.29 | −2.94971 | ||||||||
\(146\) | 237.024 | 0.134358 | ||||||||
\(147\) | −233.825 | −0.131194 | ||||||||
\(148\) | −765.373 | −0.425090 | ||||||||
\(149\) | 3439.93 | 1.89134 | 0.945670 | − | 0.325127i | \(-0.105407\pi\) | ||||
0.945670 | + | 0.325127i | \(0.105407\pi\) | |||||||
\(150\) | −4707.37 | −2.56237 | ||||||||
\(151\) | 2224.04 | 1.19861 | 0.599305 | − | 0.800521i | \(-0.295444\pi\) | ||||
0.599305 | + | 0.800521i | \(0.295444\pi\) | |||||||
\(152\) | −5186.78 | −2.76779 | ||||||||
\(153\) | 416.134 | 0.219885 | ||||||||
\(154\) | −2422.05 | −1.26736 | ||||||||
\(155\) | 1864.07 | 0.965975 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2465.32 | 1.25321 | 0.626604 | − | 0.779338i | \(-0.284444\pi\) | ||||
0.626604 | + | 0.779338i | \(0.284444\pi\) | |||||||
\(158\) | 522.171 | 0.262922 | ||||||||
\(159\) | −1045.75 | −0.521593 | ||||||||
\(160\) | 945.386 | 0.467121 | ||||||||
\(161\) | 136.439 | 0.0667881 | ||||||||
\(162\) | −391.838 | −0.190035 | ||||||||
\(163\) | −243.565 | −0.117040 | −0.0585199 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585199 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(164\) | −1662.53 | −0.791597 | ||||||||
\(165\) | 1955.75 | 0.922755 | ||||||||
\(166\) | 2494.47 | 1.16632 | ||||||||
\(167\) | 409.099 | 0.189563 | 0.0947814 | − | 0.995498i | \(-0.469785\pi\) | ||||
0.0947814 | + | 0.995498i | \(0.469785\pi\) | |||||||
\(168\) | −1748.75 | −0.803089 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4741.46 | −2.13914 | ||||||||
\(171\) | 1303.78 | 0.583056 | ||||||||
\(172\) | −545.466 | −0.241810 | ||||||||
\(173\) | −2618.97 | −1.15096 | −0.575481 | − | 0.817815i | \(-0.695185\pi\) | ||||
−0.575481 | + | 0.817815i | \(0.695185\pi\) | |||||||
\(174\) | 3525.93 | 1.53621 | ||||||||
\(175\) | 5280.88 | 2.28113 | ||||||||
\(176\) | 1537.42 | 0.658452 | ||||||||
\(177\) | −2038.29 | −0.865578 | ||||||||
\(178\) | 4762.29 | 2.00533 | ||||||||
\(179\) | 163.311 | 0.0681925 | 0.0340963 | − | 0.999419i | \(-0.489145\pi\) | ||||
0.0340963 | + | 0.999419i | \(0.489145\pi\) | |||||||
\(180\) | 2938.35 | 1.21673 | ||||||||
\(181\) | −3313.07 | −1.36054 | −0.680272 | − | 0.732960i | \(-0.738138\pi\) | ||||
−0.680272 | + | 0.732960i | \(0.738138\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −691.209 | −0.279211 | ||||||||
\(184\) | −300.056 | −0.120220 | ||||||||
\(185\) | −1053.45 | −0.418654 | ||||||||
\(186\) | −1276.16 | −0.503079 | ||||||||
\(187\) | 1421.94 | 0.556057 | ||||||||
\(188\) | −5772.68 | −2.23945 | ||||||||
\(189\) | 439.576 | 0.169177 | ||||||||
\(190\) | −14855.4 | −5.67222 | ||||||||
\(191\) | −4281.90 | −1.62213 | −0.811066 | − | 0.584954i | \(-0.801112\pi\) | ||||
−0.811066 | + | 0.584954i | \(0.801112\pi\) | |||||||
\(192\) | −1847.03 | −0.694261 | ||||||||
\(193\) | 1877.33 | 0.700171 | 0.350086 | − | 0.936718i | \(-0.386152\pi\) | ||||
0.350086 | + | 0.936718i | \(0.386152\pi\) | |||||||
\(194\) | 2356.21 | 0.871990 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1200.41 | −0.437468 | ||||||||
\(197\) | −1991.26 | −0.720158 | −0.360079 | − | 0.932922i | \(-0.617250\pi\) | ||||
−0.360079 | + | 0.932922i | \(0.617250\pi\) | |||||||
\(198\) | −1338.92 | −0.480570 | ||||||||
\(199\) | 1345.05 | 0.479137 | 0.239568 | − | 0.970879i | \(-0.422994\pi\) | ||||
0.239568 | + | 0.970879i | \(0.422994\pi\) | |||||||
\(200\) | −11613.7 | −4.10607 | ||||||||
\(201\) | 886.927 | 0.311239 | ||||||||
\(202\) | −3707.34 | −1.29132 | ||||||||
\(203\) | −3955.51 | −1.36760 | ||||||||
\(204\) | 2136.35 | 0.733208 | ||||||||
\(205\) | −2288.28 | −0.779612 | ||||||||
\(206\) | −5949.50 | −2.01224 | ||||||||
\(207\) | 75.4240 | 0.0253253 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4455.05 | 1.47446 | ||||||||
\(210\) | −5008.56 | −1.64583 | ||||||||
\(211\) | −288.763 | −0.0942147 | −0.0471073 | − | 0.998890i | \(-0.515000\pi\) | ||||
−0.0471073 | + | 0.998890i | \(0.515000\pi\) | |||||||
\(212\) | −5368.67 | −1.73925 | ||||||||
\(213\) | −987.644 | −0.317710 | ||||||||
\(214\) | −371.646 | −0.118716 | ||||||||
\(215\) | −750.771 | −0.238150 | ||||||||
\(216\) | −966.717 | −0.304522 | ||||||||
\(217\) | 1431.64 | 0.447862 | ||||||||
\(218\) | −3028.28 | −0.940830 | ||||||||
\(219\) | −146.992 | −0.0453552 | ||||||||
\(220\) | 10040.4 | 3.07693 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 721.198 | 0.218035 | ||||||||
\(223\) | −1798.41 | −0.540046 | −0.270023 | − | 0.962854i | \(-0.587031\pi\) | ||||
−0.270023 | + | 0.962854i | \(0.587031\pi\) | |||||||
\(224\) | 726.072 | 0.216575 | ||||||||
\(225\) | 2919.30 | 0.864977 | ||||||||
\(226\) | 6497.77 | 1.91250 | ||||||||
\(227\) | 2486.10 | 0.726909 | 0.363454 | − | 0.931612i | \(-0.381597\pi\) | ||||
0.363454 | + | 0.931612i | \(0.381597\pi\) | |||||||
\(228\) | 6693.36 | 1.94420 | ||||||||
\(229\) | 6074.71 | 1.75296 | 0.876480 | − | 0.481438i | \(-0.159885\pi\) | ||||
0.876480 | + | 0.481438i | \(0.159885\pi\) | |||||||
\(230\) | −859.386 | −0.246375 | ||||||||
\(231\) | 1502.04 | 0.427824 | ||||||||
\(232\) | 8698.95 | 2.46170 | ||||||||
\(233\) | 6367.16 | 1.79024 | 0.895121 | − | 0.445822i | \(-0.147089\pi\) | ||||
0.895121 | + | 0.445822i | \(0.147089\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7945.42 | −2.20554 | ||||||||
\(236\) | −10464.2 | −2.88627 | ||||||||
\(237\) | −323.827 | −0.0887544 | ||||||||
\(238\) | −3641.52 | −0.991784 | ||||||||
\(239\) | −1886.43 | −0.510556 | −0.255278 | − | 0.966868i | \(-0.582167\pi\) | ||||
−0.255278 | + | 0.966868i | \(0.582167\pi\) | |||||||
\(240\) | 3179.24 | 0.855081 | ||||||||
\(241\) | 5847.91 | 1.56306 | 0.781529 | − | 0.623869i | \(-0.214440\pi\) | ||||
0.781529 | + | 0.623869i | \(0.214440\pi\) | |||||||
\(242\) | 1863.59 | 0.495025 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −3548.53 | −0.931031 | ||||||||
\(245\) | −1652.23 | −0.430845 | ||||||||
\(246\) | 1566.58 | 0.406021 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3148.46 | −0.806160 | ||||||||
\(249\) | −1546.96 | −0.393713 | ||||||||
\(250\) | −20444.3 | −5.17205 | ||||||||
\(251\) | −2388.65 | −0.600678 | −0.300339 | − | 0.953832i | \(-0.597100\pi\) | ||||
−0.300339 | + | 0.953832i | \(0.597100\pi\) | |||||||
\(252\) | 2256.70 | 0.564122 | ||||||||
\(253\) | 257.726 | 0.0640438 | ||||||||
\(254\) | 10384.6 | 2.56531 | ||||||||
\(255\) | 2940.44 | 0.722108 | ||||||||
\(256\) | −7756.38 | −1.89365 | ||||||||
\(257\) | 4447.21 | 1.07941 | 0.539707 | − | 0.841853i | \(-0.318535\pi\) | ||||
0.539707 | + | 0.841853i | \(0.318535\pi\) | |||||||
\(258\) | 513.984 | 0.124028 | ||||||||
\(259\) | −809.064 | −0.194104 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2186.62 | −0.518577 | ||||||||
\(262\) | 3863.36 | 0.910988 | ||||||||
\(263\) | 7590.87 | 1.77975 | 0.889873 | − | 0.456208i | \(-0.150793\pi\) | ||||
0.889873 | + | 0.456208i | \(0.150793\pi\) | |||||||
\(264\) | −3303.30 | −0.770091 | ||||||||
\(265\) | −7389.36 | −1.71292 | ||||||||
\(266\) | −11409.2 | −2.62985 | ||||||||
\(267\) | −2953.36 | −0.676939 | ||||||||
\(268\) | 4553.31 | 1.03783 | ||||||||
\(269\) | −557.911 | −0.126455 | −0.0632275 | − | 0.997999i | \(-0.520139\pi\) | ||||
−0.0632275 | + | 0.997999i | \(0.520139\pi\) | |||||||
\(270\) | −2768.76 | −0.624079 | ||||||||
\(271\) | −2707.41 | −0.606877 | −0.303439 | − | 0.952851i | \(-0.598135\pi\) | ||||
−0.303439 | + | 0.952851i | \(0.598135\pi\) | |||||||
\(272\) | 2311.50 | 0.515276 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2908.08 | 0.641181 | ||||||||
\(275\) | 9975.31 | 2.18740 | ||||||||
\(276\) | 387.212 | 0.0844472 | ||||||||
\(277\) | −1231.35 | −0.267092 | −0.133546 | − | 0.991043i | \(-0.542636\pi\) | ||||
−0.133546 | + | 0.991043i | \(0.542636\pi\) | |||||||
\(278\) | 10324.1 | 2.22733 | ||||||||
\(279\) | 791.417 | 0.169824 | ||||||||
\(280\) | −12356.8 | −2.63736 | ||||||||
\(281\) | −4601.44 | −0.976864 | −0.488432 | − | 0.872602i | \(-0.662431\pi\) | ||||
−0.488432 | + | 0.872602i | \(0.662431\pi\) | |||||||
\(282\) | 5439.50 | 1.14864 | ||||||||
\(283\) | −54.5677 | −0.0114619 | −0.00573094 | − | 0.999984i | \(-0.501824\pi\) | ||||
−0.00573094 | + | 0.999984i | \(0.501824\pi\) | |||||||
\(284\) | −5070.37 | −1.05941 | ||||||||
\(285\) | 9212.63 | 1.91477 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1757.44 | −0.361457 | ||||||||
\(288\) | 401.376 | 0.0821226 | ||||||||
\(289\) | −2775.13 | −0.564854 | ||||||||
\(290\) | 24914.5 | 5.04494 | ||||||||
\(291\) | −1461.22 | −0.294357 | ||||||||
\(292\) | −754.627 | −0.151237 | ||||||||
\(293\) | 4745.24 | 0.946144 | 0.473072 | − | 0.881024i | \(-0.343145\pi\) | ||||
0.473072 | + | 0.881024i | \(0.343145\pi\) | |||||||
\(294\) | 1131.13 | 0.224384 | ||||||||
\(295\) | −14402.7 | −2.84258 | ||||||||
\(296\) | 1779.30 | 0.349390 | ||||||||
\(297\) | 830.337 | 0.162226 | ||||||||
\(298\) | −16640.6 | −3.23479 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 14987.1 | 2.88427 | ||||||||
\(301\) | −576.604 | −0.110415 | ||||||||
\(302\) | −10758.8 | −2.05000 | ||||||||
\(303\) | 2299.13 | 0.435912 | ||||||||
\(304\) | 7242.10 | 1.36633 | ||||||||
\(305\) | −4884.15 | −0.916936 | ||||||||
\(306\) | −2013.05 | −0.376073 | ||||||||
\(307\) | 1028.82 | 0.191264 | 0.0956320 | − | 0.995417i | \(-0.469513\pi\) | ||||
0.0956320 | + | 0.995417i | \(0.469513\pi\) | |||||||
\(308\) | 7711.20 | 1.42658 | ||||||||
\(309\) | 3689.61 | 0.679271 | ||||||||
\(310\) | −9017.46 | −1.65212 | ||||||||
\(311\) | −2437.84 | −0.444492 | −0.222246 | − | 0.974991i | \(-0.571339\pi\) | ||||
−0.222246 | + | 0.974991i | \(0.571339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7934.20 | 1.43280 | 0.716402 | − | 0.697688i | \(-0.245788\pi\) | ||||
0.716402 | + | 0.697688i | \(0.245788\pi\) | |||||||
\(314\) | −11926.0 | −2.14338 | ||||||||
\(315\) | 3106.09 | 0.555581 | ||||||||
\(316\) | −1662.46 | −0.295952 | ||||||||
\(317\) | 6942.72 | 1.23010 | 0.615050 | − | 0.788488i | \(-0.289136\pi\) | ||||
0.615050 | + | 0.788488i | \(0.289136\pi\) | |||||||
\(318\) | 5058.81 | 0.892089 | ||||||||
\(319\) | −7471.75 | −1.31140 | ||||||||
\(320\) | −13051.3 | −2.27997 | ||||||||
\(321\) | 230.478 | 0.0400749 | ||||||||
\(322\) | −660.023 | −0.114229 | ||||||||
\(323\) | 6698.12 | 1.15385 | ||||||||
\(324\) | 1247.51 | 0.213909 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1178.25 | 0.200175 | ||||||||
\(327\) | 1878.00 | 0.317596 | ||||||||
\(328\) | 3864.96 | 0.650630 | ||||||||
\(329\) | −6102.21 | −1.02257 | ||||||||
\(330\) | −9460.92 | −1.57820 | ||||||||
\(331\) | −5439.27 | −0.903230 | −0.451615 | − | 0.892213i | \(-0.649152\pi\) | ||||
−0.451615 | + | 0.892213i | \(0.649152\pi\) | |||||||
\(332\) | −7941.79 | −1.31284 | ||||||||
\(333\) | −447.255 | −0.0736018 | ||||||||
\(334\) | −1979.01 | −0.324212 | ||||||||
\(335\) | 6267.10 | 1.02211 | ||||||||
\(336\) | 2441.71 | 0.396447 | ||||||||
\(337\) | −1663.87 | −0.268952 | −0.134476 | − | 0.990917i | \(-0.542935\pi\) | ||||
−0.134476 | + | 0.990917i | \(0.542935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4029.63 | −0.645602 | ||||||||
\(340\) | 15095.6 | 2.40787 | ||||||||
\(341\) | 2704.29 | 0.429460 | ||||||||
\(342\) | −6307.04 | −0.997210 | ||||||||
\(343\) | −6853.19 | −1.07883 | ||||||||
\(344\) | 1268.07 | 0.198749 | ||||||||
\(345\) | 532.953 | 0.0831687 | ||||||||
\(346\) | 12669.3 | 1.96851 | ||||||||
\(347\) | 9268.10 | 1.43383 | 0.716913 | − | 0.697163i | \(-0.245554\pi\) | ||||
0.716913 | + | 0.697163i | \(0.245554\pi\) | |||||||
\(348\) | −11225.7 | −1.72920 | ||||||||
\(349\) | 5239.45 | 0.803614 | 0.401807 | − | 0.915724i | \(-0.368382\pi\) | ||||
0.401807 | + | 0.915724i | \(0.368382\pi\) | |||||||
\(350\) | −25546.3 | −3.90144 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1371.51 | 0.207676 | ||||||||
\(353\) | 1218.01 | 0.183649 | 0.0918244 | − | 0.995775i | \(-0.470730\pi\) | ||||
0.0918244 | + | 0.995775i | \(0.470730\pi\) | |||||||
\(354\) | 9860.23 | 1.48041 | ||||||||
\(355\) | −6978.78 | −1.04337 | ||||||||
\(356\) | −15162.0 | −2.25726 | ||||||||
\(357\) | 2258.31 | 0.334796 | ||||||||
\(358\) | −790.018 | −0.116631 | ||||||||
\(359\) | 5316.06 | 0.781534 | 0.390767 | − | 0.920490i | \(-0.372210\pi\) | ||||
0.390767 | + | 0.920490i | \(0.372210\pi\) | |||||||
\(360\) | −6830.91 | −1.00006 | ||||||||
\(361\) | 14126.7 | 2.05959 | ||||||||
\(362\) | 16027.0 | 2.32696 | ||||||||
\(363\) | −1155.72 | −0.167106 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1038.66 | −0.148947 | ||||||||
\(366\) | 3343.73 | 0.477539 | ||||||||
\(367\) | −289.101 | −0.0411197 | −0.0205599 | − | 0.999789i | \(-0.506545\pi\) | ||||
−0.0205599 | + | 0.999789i | \(0.506545\pi\) | |||||||
\(368\) | 418.957 | 0.0593469 | ||||||||
\(369\) | −971.520 | −0.137060 | ||||||||
\(370\) | 5096.05 | 0.716030 | ||||||||
\(371\) | −5675.15 | −0.794175 | ||||||||
\(372\) | 4062.98 | 0.566279 | ||||||||
\(373\) | 6163.98 | 0.855654 | 0.427827 | − | 0.903861i | \(-0.359279\pi\) | ||||
0.427827 | + | 0.903861i | \(0.359279\pi\) | |||||||
\(374\) | −6878.64 | −0.951032 | ||||||||
\(375\) | 12678.7 | 1.74593 | ||||||||
\(376\) | 13420.0 | 1.84065 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2126.45 | −0.289346 | ||||||||
\(379\) | −2440.03 | −0.330702 | −0.165351 | − | 0.986235i | \(-0.552876\pi\) | ||||
−0.165351 | + | 0.986235i | \(0.552876\pi\) | |||||||
\(380\) | 47295.9 | 6.38481 | ||||||||
\(381\) | −6440.06 | −0.865970 | ||||||||
\(382\) | 20713.7 | 2.77436 | ||||||||
\(383\) | −6577.28 | −0.877502 | −0.438751 | − | 0.898609i | \(-0.644579\pi\) | ||||
−0.438751 | + | 0.898609i | \(0.644579\pi\) | |||||||
\(384\) | 7864.68 | 1.04516 | ||||||||
\(385\) | 10613.6 | 1.40498 | ||||||||
\(386\) | −9081.58 | −1.19751 | ||||||||
\(387\) | −318.750 | −0.0418681 | ||||||||
\(388\) | −7501.59 | −0.981535 | ||||||||
\(389\) | 4964.94 | 0.647127 | 0.323563 | − | 0.946206i | \(-0.395119\pi\) | ||||
0.323563 | + | 0.946206i | \(0.395119\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 387.488 | 0.0501179 | ||||||||
\(392\) | 2790.65 | 0.359565 | ||||||||
\(393\) | −2395.88 | −0.307522 | ||||||||
\(394\) | 9632.70 | 1.23170 | ||||||||
\(395\) | −2288.19 | −0.291471 | ||||||||
\(396\) | 4262.79 | 0.540943 | ||||||||
\(397\) | −12073.9 | −1.52637 | −0.763187 | − | 0.646178i | \(-0.776366\pi\) | ||||
−0.763187 | + | 0.646178i | \(0.776366\pi\) | |||||||
\(398\) | −6506.69 | −0.819475 | ||||||||
\(399\) | 7075.45 | 0.887758 | ||||||||
\(400\) | 16215.8 | 2.02697 | ||||||||
\(401\) | −4916.90 | −0.612315 | −0.306158 | − | 0.951981i | \(-0.599043\pi\) | ||||
−0.306158 | + | 0.951981i | \(0.599043\pi\) | |||||||
\(402\) | −4290.51 | −0.532316 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 11803.3 | 1.45355 | ||||||||
\(405\) | 1717.06 | 0.210670 | ||||||||
\(406\) | 19134.8 | 2.33902 | ||||||||
\(407\) | −1528.28 | −0.186128 | ||||||||
\(408\) | −4966.47 | −0.602639 | ||||||||
\(409\) | 15350.9 | 1.85588 | 0.927939 | − | 0.372733i | \(-0.121579\pi\) | ||||
0.927939 | + | 0.372733i | \(0.121579\pi\) | |||||||
\(410\) | 11069.6 | 1.33338 | ||||||||
\(411\) | −1803.46 | −0.216443 | ||||||||
\(412\) | 18941.7 | 2.26503 | ||||||||
\(413\) | −11061.5 | −1.31792 | ||||||||
\(414\) | −364.864 | −0.0433142 | ||||||||
\(415\) | −10931.0 | −1.29296 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6402.53 | −0.751878 | ||||||||
\(418\) | −21551.3 | −2.52179 | ||||||||
\(419\) | −5488.58 | −0.639939 | −0.319970 | − | 0.947428i | \(-0.603673\pi\) | ||||
−0.319970 | + | 0.947428i | \(0.603673\pi\) | |||||||
\(420\) | 15946.0 | 1.85259 | ||||||||
\(421\) | −927.681 | −0.107393 | −0.0536964 | − | 0.998557i | \(-0.517100\pi\) | ||||
−0.0536964 | + | 0.998557i | \(0.517100\pi\) | |||||||
\(422\) | 1396.89 | 0.161137 | ||||||||
\(423\) | −3373.33 | −0.387747 | ||||||||
\(424\) | 12480.8 | 1.42953 | ||||||||
\(425\) | 14997.8 | 1.71176 | ||||||||
\(426\) | 4777.73 | 0.543384 | ||||||||
\(427\) | −3751.10 | −0.425126 | ||||||||
\(428\) | 1183.23 | 0.133630 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3631.85 | 0.407311 | ||||||||
\(431\) | 11002.3 | 1.22961 | 0.614806 | − | 0.788678i | \(-0.289234\pi\) | ||||
0.614806 | + | 0.788678i | \(0.289234\pi\) | |||||||
\(432\) | 1349.79 | 0.150328 | ||||||||
\(433\) | −9596.76 | −1.06511 | −0.532553 | − | 0.846397i | \(-0.678767\pi\) | ||||
−0.532553 | + | 0.846397i | \(0.678767\pi\) | |||||||
\(434\) | −6925.56 | −0.765985 | ||||||||
\(435\) | −15450.9 | −1.70302 | ||||||||
\(436\) | 9641.30 | 1.05902 | ||||||||
\(437\) | 1214.03 | 0.132895 | ||||||||
\(438\) | 711.073 | 0.0775716 | ||||||||
\(439\) | −10346.3 | −1.12483 | −0.562416 | − | 0.826854i | \(-0.690128\pi\) | ||||
−0.562416 | + | 0.826854i | \(0.690128\pi\) | |||||||
\(440\) | −23341.4 | −2.52899 | ||||||||
\(441\) | −701.476 | −0.0757452 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5650.38 | 0.606000 | 0.303000 | − | 0.952991i | \(-0.402012\pi\) | ||||
0.303000 | + | 0.952991i | \(0.402012\pi\) | |||||||
\(444\) | −2296.12 | −0.245426 | ||||||||
\(445\) | −20868.7 | −2.22308 | ||||||||
\(446\) | 8699.80 | 0.923649 | ||||||||
\(447\) | 10319.8 | 1.09197 | ||||||||
\(448\) | −10023.6 | −1.05708 | ||||||||
\(449\) | −11987.8 | −1.25999 | −0.629997 | − | 0.776597i | \(-0.716944\pi\) | ||||
−0.629997 | + | 0.776597i | \(0.716944\pi\) | |||||||
\(450\) | −14122.1 | −1.47938 | ||||||||
\(451\) | −3319.71 | −0.346605 | ||||||||
\(452\) | −20687.3 | −2.15276 | ||||||||
\(453\) | 6672.13 | 0.692018 | ||||||||
\(454\) | −12026.5 | −1.24324 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −15560.3 | −1.59798 | ||||||||
\(457\) | 16437.6 | 1.68253 | 0.841265 | − | 0.540623i | \(-0.181811\pi\) | ||||
0.841265 | + | 0.540623i | \(0.181811\pi\) | |||||||
\(458\) | −29386.4 | −2.99811 | ||||||||
\(459\) | 1248.40 | 0.126951 | ||||||||
\(460\) | 2736.08 | 0.277326 | ||||||||
\(461\) | −8847.70 | −0.893880 | −0.446940 | − | 0.894564i | \(-0.647486\pi\) | ||||
−0.446940 | + | 0.894564i | \(0.647486\pi\) | |||||||
\(462\) | −7266.14 | −0.731713 | ||||||||
\(463\) | −10269.6 | −1.03081 | −0.515407 | − | 0.856945i | \(-0.672359\pi\) | ||||
−0.515407 | + | 0.856945i | \(0.672359\pi\) | |||||||
\(464\) | −12146.0 | −1.21523 | ||||||||
\(465\) | 5592.22 | 0.557706 | ||||||||
\(466\) | −30801.1 | −3.06188 | ||||||||
\(467\) | 14730.4 | 1.45962 | 0.729811 | − | 0.683649i | \(-0.239608\pi\) | ||||
0.729811 | + | 0.683649i | \(0.239608\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4813.24 | 0.473891 | ||||||||
\(470\) | 38436.0 | 3.77217 | ||||||||
\(471\) | 7395.95 | 0.723540 | ||||||||
\(472\) | 24326.6 | 2.37229 | ||||||||
\(473\) | −1089.18 | −0.105878 | ||||||||
\(474\) | 1566.51 | 0.151798 | ||||||||
\(475\) | 46989.2 | 4.53897 | ||||||||
\(476\) | 11593.7 | 1.11638 | ||||||||
\(477\) | −3137.25 | −0.301142 | ||||||||
\(478\) | 9125.59 | 0.873211 | ||||||||
\(479\) | −635.077 | −0.0605792 | −0.0302896 | − | 0.999541i | \(-0.509643\pi\) | ||||
−0.0302896 | + | 0.999541i | \(0.509643\pi\) | |||||||
\(480\) | 2836.16 | 0.269692 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −28289.3 | −2.67332 | ||||||||
\(483\) | 409.316 | 0.0385601 | ||||||||
\(484\) | −5933.22 | −0.557214 | ||||||||
\(485\) | −10325.1 | −0.966675 | ||||||||
\(486\) | −1175.51 | −0.109717 | ||||||||
\(487\) | 16611.1 | 1.54563 | 0.772815 | − | 0.634632i | \(-0.218848\pi\) | ||||
0.772815 | + | 0.634632i | \(0.218848\pi\) | |||||||
\(488\) | 8249.43 | 0.765234 | ||||||||
\(489\) | −730.696 | −0.0675730 | ||||||||
\(490\) | 7992.66 | 0.736881 | ||||||||
\(491\) | −2584.14 | −0.237516 | −0.118758 | − | 0.992923i | \(-0.537891\pi\) | ||||
−0.118758 | + | 0.992923i | \(0.537891\pi\) | |||||||
\(492\) | −4987.59 | −0.457029 | ||||||||
\(493\) | −11233.7 | −1.02625 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5867.24 | 0.532753 | ||||||||
\(496\) | 4396.08 | 0.397963 | ||||||||
\(497\) | −5359.82 | −0.483744 | ||||||||
\(498\) | 7483.42 | 0.673374 | ||||||||
\(499\) | −2183.88 | −0.195919 | −0.0979597 | − | 0.995190i | \(-0.531232\pi\) | ||||
−0.0979597 | + | 0.995190i | \(0.531232\pi\) | |||||||
\(500\) | 65089.8 | 5.82180 | ||||||||
\(501\) | 1227.30 | 0.109444 | ||||||||
\(502\) | 11555.1 | 1.02735 | ||||||||
\(503\) | −17214.9 | −1.52600 | −0.762998 | − | 0.646401i | \(-0.776273\pi\) | ||||
−0.762998 | + | 0.646401i | \(0.776273\pi\) | |||||||
\(504\) | −5246.25 | −0.463664 | ||||||||
\(505\) | 16245.8 | 1.43154 | ||||||||
\(506\) | −1246.75 | −0.109535 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −33062.0 | −2.88758 | ||||||||
\(509\) | −20260.6 | −1.76431 | −0.882157 | − | 0.470955i | \(-0.843909\pi\) | ||||
−0.882157 | + | 0.470955i | \(0.843909\pi\) | |||||||
\(510\) | −14224.4 | −1.23503 | ||||||||
\(511\) | −797.705 | −0.0690575 | ||||||||
\(512\) | 16549.0 | 1.42846 | ||||||||
\(513\) | 3911.34 | 0.336628 | ||||||||
\(514\) | −21513.4 | −1.84614 | ||||||||
\(515\) | 26071.1 | 2.23074 | ||||||||
\(516\) | −1636.40 | −0.139609 | ||||||||
\(517\) | −11526.8 | −0.980554 | ||||||||
\(518\) | 3913.85 | 0.331978 | ||||||||
\(519\) | −7856.90 | −0.664508 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20731.5 | −1.74331 | −0.871653 | − | 0.490124i | \(-0.836952\pi\) | ||||
−0.871653 | + | 0.490124i | \(0.836952\pi\) | |||||||
\(522\) | 10577.8 | 0.886930 | ||||||||
\(523\) | −944.353 | −0.0789554 | −0.0394777 | − | 0.999220i | \(-0.512569\pi\) | ||||
−0.0394777 | + | 0.999220i | \(0.512569\pi\) | |||||||
\(524\) | −12300.0 | −1.02543 | ||||||||
\(525\) | 15842.6 | 1.31701 | ||||||||
\(526\) | −36720.9 | −3.04393 | ||||||||
\(527\) | 4065.87 | 0.336076 | ||||||||
\(528\) | 4612.27 | 0.380158 | ||||||||
\(529\) | −12096.8 | −0.994228 | ||||||||
\(530\) | 35746.0 | 2.92964 | ||||||||
\(531\) | −6114.87 | −0.499742 | ||||||||
\(532\) | 36324.0 | 2.96023 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14286.9 | 1.15778 | ||||||||
\(535\) | 1628.58 | 0.131607 | ||||||||
\(536\) | −10585.3 | −0.853012 | ||||||||
\(537\) | 489.934 | 0.0393710 | ||||||||
\(538\) | 2698.89 | 0.216278 | ||||||||
\(539\) | −2396.96 | −0.191548 | ||||||||
\(540\) | 8815.05 | 0.702480 | ||||||||
\(541\) | −4883.06 | −0.388058 | −0.194029 | − | 0.980996i | \(-0.562156\pi\) | ||||
−0.194029 | + | 0.980996i | \(0.562156\pi\) | |||||||
\(542\) | 13097.1 | 1.03795 | ||||||||
\(543\) | −9939.21 | −0.785511 | ||||||||
\(544\) | 2062.05 | 0.162518 | ||||||||
\(545\) | 13270.1 | 1.04299 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16269.1 | −1.27169 | −0.635847 | − | 0.771815i | \(-0.719349\pi\) | ||||
−0.635847 | + | 0.771815i | \(0.719349\pi\) | |||||||
\(548\) | −9258.61 | −0.721730 | ||||||||
\(549\) | −2073.63 | −0.161203 | ||||||||
\(550\) | −48255.6 | −3.74114 | ||||||||
\(551\) | −35196.0 | −2.72124 | ||||||||
\(552\) | −900.169 | −0.0694090 | ||||||||
\(553\) | −1757.37 | −0.135137 | ||||||||
\(554\) | 5956.63 | 0.456811 | ||||||||
\(555\) | −3160.34 | −0.241710 | ||||||||
\(556\) | −32869.3 | −2.50714 | ||||||||
\(557\) | 15661.0 | 1.19134 | 0.595670 | − | 0.803229i | \(-0.296887\pi\) | ||||
0.595670 | + | 0.803229i | \(0.296887\pi\) | |||||||
\(558\) | −3828.48 | −0.290453 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 17253.3 | 1.30194 | ||||||||
\(561\) | 4265.82 | 0.321040 | ||||||||
\(562\) | 22259.5 | 1.67074 | ||||||||
\(563\) | −9915.18 | −0.742230 | −0.371115 | − | 0.928587i | \(-0.621024\pi\) | ||||
−0.371115 | + | 0.928587i | \(0.621024\pi\) | |||||||
\(564\) | −17318.0 | −1.29294 | ||||||||
\(565\) | −28473.7 | −2.12017 | ||||||||
\(566\) | 263.971 | 0.0196034 | ||||||||
\(567\) | 1318.73 | 0.0976745 | ||||||||
\(568\) | 11787.3 | 0.870748 | ||||||||
\(569\) | −11299.1 | −0.832482 | −0.416241 | − | 0.909254i | \(-0.636653\pi\) | ||||
−0.416241 | + | 0.909254i | \(0.636653\pi\) | |||||||
\(570\) | −44566.1 | −3.27486 | ||||||||
\(571\) | −17619.6 | −1.29134 | −0.645672 | − | 0.763615i | \(-0.723423\pi\) | ||||
−0.645672 | + | 0.763615i | \(0.723423\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12845.7 | −0.936539 | ||||||||
\(574\) | 8501.61 | 0.618206 | ||||||||
\(575\) | 2718.33 | 0.197152 | ||||||||
\(576\) | −5541.10 | −0.400832 | ||||||||
\(577\) | −22153.5 | −1.59837 | −0.799186 | − | 0.601083i | \(-0.794736\pi\) | ||||
−0.799186 | + | 0.601083i | \(0.794736\pi\) | |||||||
\(578\) | 13424.7 | 0.966078 | ||||||||
\(579\) | 5631.99 | 0.404244 | ||||||||
\(580\) | −79321.7 | −5.67872 | ||||||||
\(581\) | −8395.15 | −0.599466 | ||||||||
\(582\) | 7068.63 | 0.503444 | ||||||||
\(583\) | −10720.1 | −0.761543 | ||||||||
\(584\) | 1754.31 | 0.124305 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22955.1 | −1.61820 | ||||||||
\(587\) | −9891.28 | −0.695497 | −0.347748 | − | 0.937588i | \(-0.613054\pi\) | ||||
−0.347748 | + | 0.937588i | \(0.613054\pi\) | |||||||
\(588\) | −3601.24 | −0.252573 | ||||||||
\(589\) | 12738.7 | 0.891153 | ||||||||
\(590\) | 69673.3 | 4.86170 | ||||||||
\(591\) | −5973.77 | −0.415783 | ||||||||
\(592\) | −2484.36 | −0.172477 | ||||||||
\(593\) | −9746.23 | −0.674924 | −0.337462 | − | 0.941339i | \(-0.609568\pi\) | ||||
−0.337462 | + | 0.941339i | \(0.609568\pi\) | |||||||
\(594\) | −4016.76 | −0.277457 | ||||||||
\(595\) | 15957.4 | 1.09948 | ||||||||
\(596\) | 52979.7 | 3.64116 | ||||||||
\(597\) | 4035.16 | 0.276630 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8460.53 | −0.577109 | −0.288554 | − | 0.957464i | \(-0.593175\pi\) | ||||
−0.288554 | + | 0.957464i | \(0.593175\pi\) | |||||||
\(600\) | −34841.2 | −2.37064 | ||||||||
\(601\) | 6792.99 | 0.461052 | 0.230526 | − | 0.973066i | \(-0.425955\pi\) | ||||
0.230526 | + | 0.973066i | \(0.425955\pi\) | |||||||
\(602\) | 2789.32 | 0.188844 | ||||||||
\(603\) | 2660.78 | 0.179694 | ||||||||
\(604\) | 34253.4 | 2.30754 | ||||||||
\(605\) | −8166.38 | −0.548778 | ||||||||
\(606\) | −11122.0 | −0.745546 | ||||||||
\(607\) | 19073.4 | 1.27539 | 0.637697 | − | 0.770287i | \(-0.279887\pi\) | ||||
0.637697 | + | 0.770287i | \(0.279887\pi\) | |||||||
\(608\) | 6460.58 | 0.430939 | ||||||||
\(609\) | −11866.5 | −0.789582 | ||||||||
\(610\) | 23627.1 | 1.56825 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6409.05 | 0.423318 | ||||||||
\(613\) | −14465.2 | −0.953091 | −0.476545 | − | 0.879150i | \(-0.658111\pi\) | ||||
−0.476545 | + | 0.879150i | \(0.658111\pi\) | |||||||
\(614\) | −4976.93 | −0.327122 | ||||||||
\(615\) | −6864.85 | −0.450109 | ||||||||
\(616\) | −17926.6 | −1.17254 | ||||||||
\(617\) | 12897.3 | 0.841536 | 0.420768 | − | 0.907168i | \(-0.361761\pi\) | ||||
0.420768 | + | 0.907168i | \(0.361761\pi\) | |||||||
\(618\) | −17848.5 | −1.16177 | ||||||||
\(619\) | −27735.8 | −1.80096 | −0.900481 | − | 0.434895i | \(-0.856786\pi\) | ||||
−0.900481 | + | 0.434895i | \(0.856786\pi\) | |||||||
\(620\) | 28709.4 | 1.85967 | ||||||||
\(621\) | 226.272 | 0.0146216 | ||||||||
\(622\) | 11793.0 | 0.760222 | ||||||||
\(623\) | −16027.5 | −1.03070 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 49042.7 | 3.13873 | ||||||||
\(626\) | −38381.7 | −2.45055 | ||||||||
\(627\) | 13365.2 | 0.851281 | ||||||||
\(628\) | 37969.3 | 2.41265 | ||||||||
\(629\) | −2297.75 | −0.145656 | ||||||||
\(630\) | −15025.7 | −0.950219 | ||||||||
\(631\) | 28560.1 | 1.80184 | 0.900918 | − | 0.433990i | \(-0.142895\pi\) | ||||
0.900918 | + | 0.433990i | \(0.142895\pi\) | |||||||
\(632\) | 3864.80 | 0.243249 | ||||||||
\(633\) | −866.290 | −0.0543949 | ||||||||
\(634\) | −33585.4 | −2.10386 | ||||||||
\(635\) | −45506.1 | −2.84386 | ||||||||
\(636\) | −16106.0 | −1.00416 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 36144.6 | 2.24291 | ||||||||
\(639\) | −2962.93 | −0.183430 | ||||||||
\(640\) | 55572.5 | 3.43234 | ||||||||
\(641\) | 1862.53 | 0.114767 | 0.0573833 | − | 0.998352i | \(-0.481724\pi\) | ||||
0.0573833 | + | 0.998352i | \(0.481724\pi\) | |||||||
\(642\) | −1114.94 | −0.0685407 | ||||||||
\(643\) | 29495.2 | 1.80899 | 0.904494 | − | 0.426487i | \(-0.140249\pi\) | ||||
0.904494 | + | 0.426487i | \(0.140249\pi\) | |||||||
\(644\) | 2101.35 | 0.128579 | ||||||||
\(645\) | −2252.31 | −0.137496 | ||||||||
\(646\) | −32402.2 | −1.97345 | ||||||||
\(647\) | 27780.7 | 1.68805 | 0.844027 | − | 0.536301i | \(-0.180179\pi\) | ||||
0.844027 | + | 0.536301i | \(0.180179\pi\) | |||||||
\(648\) | −2900.15 | −0.175816 | ||||||||
\(649\) | −20894.7 | −1.26377 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4294.92 | 0.258573 | ||||||||
\(652\) | −3751.25 | −0.225322 | ||||||||
\(653\) | 276.678 | 0.0165808 | 0.00829039 | − | 0.999966i | \(-0.497361\pi\) | ||||
0.00829039 | + | 0.999966i | \(0.497361\pi\) | |||||||
\(654\) | −9084.84 | −0.543188 | ||||||||
\(655\) | −16929.5 | −1.00991 | ||||||||
\(656\) | −5396.49 | −0.321185 | ||||||||
\(657\) | −440.975 | −0.0261858 | ||||||||
\(658\) | 29519.5 | 1.74892 | ||||||||
\(659\) | 18114.9 | 1.07080 | 0.535398 | − | 0.844600i | \(-0.320162\pi\) | ||||
0.535398 | + | 0.844600i | \(0.320162\pi\) | |||||||
\(660\) | 30121.2 | 1.77647 | ||||||||
\(661\) | 27094.4 | 1.59433 | 0.797163 | − | 0.603764i | \(-0.206333\pi\) | ||||
0.797163 | + | 0.603764i | \(0.206333\pi\) | |||||||
\(662\) | 26312.5 | 1.54481 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18462.6 | 1.07905 | ||||||||
\(665\) | 49995.8 | 2.91542 | ||||||||
\(666\) | 2163.60 | 0.125882 | ||||||||
\(667\) | −2036.10 | −0.118198 | ||||||||
\(668\) | 6300.70 | 0.364942 | ||||||||
\(669\) | −5395.23 | −0.311796 | ||||||||
\(670\) | −30317.1 | −1.74814 | ||||||||
\(671\) | −7085.64 | −0.407657 | ||||||||
\(672\) | 2178.22 | 0.125039 | ||||||||
\(673\) | 2410.31 | 0.138054 | 0.0690272 | − | 0.997615i | \(-0.478010\pi\) | ||||
0.0690272 | + | 0.997615i | \(0.478010\pi\) | |||||||
\(674\) | 8048.99 | 0.459993 | ||||||||
\(675\) | 8757.89 | 0.499395 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12508.3 | 0.710091 | 0.355046 | − | 0.934849i | \(-0.384465\pi\) | ||||
0.355046 | + | 0.934849i | \(0.384465\pi\) | |||||||
\(678\) | 19493.3 | 1.10418 | ||||||||
\(679\) | −7929.83 | −0.448187 | ||||||||
\(680\) | −35093.5 | −1.97908 | ||||||||
\(681\) | 7458.30 | 0.419681 | ||||||||
\(682\) | −13082.0 | −0.734511 | ||||||||
\(683\) | −16793.8 | −0.940844 | −0.470422 | − | 0.882442i | \(-0.655898\pi\) | ||||
−0.470422 | + | 0.882442i | \(0.655898\pi\) | |||||||
\(684\) | 20080.1 | 1.12249 | ||||||||
\(685\) | −12743.4 | −0.710804 | ||||||||
\(686\) | 33152.3 | 1.84513 | ||||||||
\(687\) | 18224.1 | 1.01207 | ||||||||
\(688\) | −1770.56 | −0.0981131 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −2578.16 | −0.142245 | ||||||||
\(691\) | −26026.9 | −1.43286 | −0.716432 | − | 0.697657i | \(-0.754226\pi\) | ||||
−0.716432 | + | 0.697657i | \(0.754226\pi\) | |||||||
\(692\) | −40335.8 | −2.21580 | ||||||||
\(693\) | 4506.13 | 0.247004 | ||||||||
\(694\) | −44834.4 | −2.45229 | ||||||||
\(695\) | −45240.8 | −2.46918 | ||||||||
\(696\) | 26096.9 | 1.42126 | ||||||||
\(697\) | −4991.14 | −0.271238 | ||||||||
\(698\) | −25345.8 | −1.37443 | ||||||||
\(699\) | 19101.5 | 1.03360 | ||||||||
\(700\) | 81333.0 | 4.39157 | ||||||||
\(701\) | 5079.08 | 0.273658 | 0.136829 | − | 0.990595i | \(-0.456309\pi\) | ||||
0.136829 | + | 0.990595i | \(0.456309\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7199.04 | −0.386226 | ||||||||
\(704\) | −18934.1 | −1.01364 | ||||||||
\(705\) | −23836.3 | −1.27337 | ||||||||
\(706\) | −5892.11 | −0.314097 | ||||||||
\(707\) | 12477.1 | 0.663717 | ||||||||
\(708\) | −31392.6 | −1.66639 | ||||||||
\(709\) | −2530.72 | −0.134052 | −0.0670262 | − | 0.997751i | \(-0.521351\pi\) | ||||
−0.0670262 | + | 0.997751i | \(0.521351\pi\) | |||||||
\(710\) | 33759.9 | 1.78449 | ||||||||
\(711\) | −971.480 | −0.0512424 | ||||||||
\(712\) | 35247.7 | 1.85529 | ||||||||
\(713\) | 736.937 | 0.0387076 | ||||||||
\(714\) | −10924.6 | −0.572607 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2515.22 | 0.131283 | ||||||||
\(717\) | −5659.28 | −0.294770 | ||||||||
\(718\) | −25716.4 | −1.33667 | ||||||||
\(719\) | 9503.67 | 0.492944 | 0.246472 | − | 0.969150i | \(-0.420729\pi\) | ||||
0.246472 | + | 0.969150i | \(0.420729\pi\) | |||||||
\(720\) | 9537.73 | 0.493681 | ||||||||
\(721\) | 20023.0 | 1.03425 | ||||||||
\(722\) | −68338.2 | −3.52255 | ||||||||
\(723\) | 17543.7 | 0.902432 | ||||||||
\(724\) | −51026.0 | −2.61929 | ||||||||
\(725\) | −78807.4 | −4.03701 | ||||||||
\(726\) | 5590.77 | 0.285803 | ||||||||
\(727\) | 33343.1 | 1.70100 | 0.850500 | − | 0.525975i | \(-0.176300\pi\) | ||||
0.850500 | + | 0.525975i | \(0.176300\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 5024.50 | 0.254747 | ||||||||
\(731\) | −1637.56 | −0.0828556 | ||||||||
\(732\) | −10645.6 | −0.537531 | ||||||||
\(733\) | 32288.1 | 1.62699 | 0.813497 | − | 0.581569i | \(-0.197561\pi\) | ||||
0.813497 | + | 0.581569i | \(0.197561\pi\) | |||||||
\(734\) | 1398.53 | 0.0703277 | ||||||||
\(735\) | −4956.69 | −0.248749 | ||||||||
\(736\) | 373.746 | 0.0187180 | ||||||||
\(737\) | 9091.96 | 0.454419 | ||||||||
\(738\) | 4699.73 | 0.234417 | ||||||||
\(739\) | −14168.8 | −0.705288 | −0.352644 | − | 0.935758i | \(-0.614717\pi\) | ||||
−0.352644 | + | 0.935758i | \(0.614717\pi\) | |||||||
\(740\) | −16224.6 | −0.805983 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 27453.5 | 1.35829 | ||||||||
\(743\) | 13248.6 | 0.654165 | 0.327083 | − | 0.944996i | \(-0.393934\pi\) | ||||
0.327083 | + | 0.944996i | \(0.393934\pi\) | |||||||
\(744\) | −9445.39 | −0.465437 | ||||||||
\(745\) | 72920.5 | 3.58604 | ||||||||
\(746\) | −29818.3 | −1.46344 | ||||||||
\(747\) | −4640.88 | −0.227311 | ||||||||
\(748\) | 21899.9 | 1.07051 | ||||||||
\(749\) | 1250.78 | 0.0610178 | ||||||||
\(750\) | −61333.0 | −2.98609 | ||||||||
\(751\) | 5113.98 | 0.248484 | 0.124242 | − | 0.992252i | \(-0.460350\pi\) | ||||
0.124242 | + | 0.992252i | \(0.460350\pi\) | |||||||
\(752\) | −18737.8 | −0.908641 | ||||||||
\(753\) | −7165.95 | −0.346802 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 47145.9 | 2.27260 | ||||||||
\(756\) | 6770.10 | 0.325696 | ||||||||
\(757\) | 27380.4 | 1.31461 | 0.657303 | − | 0.753626i | \(-0.271697\pi\) | ||||
0.657303 | + | 0.753626i | \(0.271697\pi\) | |||||||
\(758\) | 11803.6 | 0.565604 | ||||||||
\(759\) | 773.178 | 0.0369757 | ||||||||
\(760\) | −109951. | −5.24781 | ||||||||
\(761\) | −10613.8 | −0.505586 | −0.252793 | − | 0.967520i | \(-0.581349\pi\) | ||||
−0.252793 | + | 0.967520i | \(0.581349\pi\) | |||||||
\(762\) | 31153.8 | 1.48108 | ||||||||
\(763\) | 10191.7 | 0.483569 | ||||||||
\(764\) | −65947.3 | −3.12289 | ||||||||
\(765\) | 8821.32 | 0.416909 | ||||||||
\(766\) | 31817.6 | 1.50080 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −23269.2 | −1.09330 | ||||||||
\(769\) | 9172.22 | 0.430115 | 0.215058 | − | 0.976601i | \(-0.431006\pi\) | ||||
0.215058 | + | 0.976601i | \(0.431006\pi\) | |||||||
\(770\) | −51343.2 | −2.40296 | ||||||||
\(771\) | 13341.6 | 0.623200 | ||||||||
\(772\) | 28913.5 | 1.34795 | ||||||||
\(773\) | 14952.1 | 0.695718 | 0.347859 | − | 0.937547i | \(-0.386909\pi\) | ||||
0.347859 | + | 0.937547i | \(0.386909\pi\) | |||||||
\(774\) | 1541.95 | 0.0716076 | ||||||||
\(775\) | 28523.2 | 1.32205 | ||||||||
\(776\) | 17439.3 | 0.806745 | ||||||||
\(777\) | −2427.19 | −0.112066 | ||||||||
\(778\) | −24017.9 | −1.10679 | ||||||||
\(779\) | −15637.7 | −0.719226 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10124.4 | −0.463867 | ||||||||
\(782\) | −1874.47 | −0.0857174 | ||||||||
\(783\) | −6559.87 | −0.299400 | ||||||||
\(784\) | −3896.48 | −0.177500 | ||||||||
\(785\) | 52260.4 | 2.37612 | ||||||||
\(786\) | 11590.1 | 0.525959 | ||||||||
\(787\) | −2671.52 | −0.121003 | −0.0605015 | − | 0.998168i | \(-0.519270\pi\) | ||||
−0.0605015 | + | 0.998168i | \(0.519270\pi\) | |||||||
\(788\) | −30668.1 | −1.38643 | ||||||||
\(789\) | 22772.6 | 1.02754 | ||||||||
\(790\) | 11069.1 | 0.498508 | ||||||||
\(791\) | −21868.3 | −0.982991 | ||||||||
\(792\) | −9909.89 | −0.444612 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 58407.4 | 2.61058 | ||||||||
\(795\) | −22168.1 | −0.988957 | ||||||||
\(796\) | 20715.7 | 0.922423 | ||||||||
\(797\) | −12949.7 | −0.575536 | −0.287768 | − | 0.957700i | \(-0.592913\pi\) | ||||
−0.287768 | + | 0.957700i | \(0.592913\pi\) | |||||||
\(798\) | −34227.5 | −1.51835 | ||||||||
\(799\) | −17330.4 | −0.767339 | ||||||||
\(800\) | 14465.9 | 0.639307 | ||||||||
\(801\) | −8860.08 | −0.390831 | ||||||||
\(802\) | 23785.5 | 1.04725 | ||||||||
\(803\) | −1506.82 | −0.0662200 | ||||||||
\(804\) | 13659.9 | 0.599190 | ||||||||
\(805\) | 2892.27 | 0.126632 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1673.73 | −0.0730089 | ||||||||
\(808\) | −27439.6 | −1.19470 | ||||||||
\(809\) | −11640.4 | −0.505876 | −0.252938 | − | 0.967482i | \(-0.581397\pi\) | ||||
−0.252938 | + | 0.967482i | \(0.581397\pi\) | |||||||
\(810\) | −8306.28 | −0.360312 | ||||||||
\(811\) | 18135.3 | 0.785225 | 0.392613 | − | 0.919704i | \(-0.371571\pi\) | ||||
0.392613 | + | 0.919704i | \(0.371571\pi\) | |||||||
\(812\) | −60920.4 | −2.63286 | ||||||||
\(813\) | −8122.24 | −0.350381 | ||||||||
\(814\) | 7393.06 | 0.318337 | ||||||||
\(815\) | −5163.16 | −0.221911 | ||||||||
\(816\) | 6934.49 | 0.297495 | ||||||||
\(817\) | −5130.61 | −0.219703 | ||||||||
\(818\) | −74260.0 | −3.17413 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −35242.8 | −1.50089 | ||||||||
\(821\) | −10789.1 | −0.458640 | −0.229320 | − | 0.973351i | \(-0.573650\pi\) | ||||
−0.229320 | + | 0.973351i | \(0.573650\pi\) | |||||||
\(822\) | 8724.24 | 0.370186 | ||||||||
\(823\) | −12284.7 | −0.520312 | −0.260156 | − | 0.965567i | \(-0.583774\pi\) | ||||
−0.260156 | + | 0.965567i | \(0.583774\pi\) | |||||||
\(824\) | −44034.7 | −1.86168 | ||||||||
\(825\) | 29925.9 | 1.26289 | ||||||||
\(826\) | 53510.2 | 2.25407 | ||||||||
\(827\) | −36077.2 | −1.51696 | −0.758480 | − | 0.651696i | \(-0.774058\pi\) | ||||
−0.758480 | + | 0.651696i | \(0.774058\pi\) | |||||||
\(828\) | 1161.64 | 0.0487556 | ||||||||
\(829\) | −8861.83 | −0.371271 | −0.185636 | − | 0.982619i | \(-0.559434\pi\) | ||||
−0.185636 | + | 0.982619i | \(0.559434\pi\) | |||||||
\(830\) | 52878.5 | 2.21137 | ||||||||
\(831\) | −3694.04 | −0.154205 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3603.80 | −0.149897 | ||||||||
\(834\) | 30972.2 | 1.28595 | ||||||||
\(835\) | 8672.18 | 0.359417 | ||||||||
\(836\) | 68614.1 | 2.83860 | ||||||||
\(837\) | 2374.25 | 0.0980480 | ||||||||
\(838\) | 26551.0 | 1.09450 | ||||||||
\(839\) | −5833.37 | −0.240036 | −0.120018 | − | 0.992772i | \(-0.538295\pi\) | ||||
−0.120018 | + | 0.992772i | \(0.538295\pi\) | |||||||
\(840\) | −37070.4 | −1.52268 | ||||||||
\(841\) | 34639.6 | 1.42030 | ||||||||
\(842\) | 4487.66 | 0.183676 | ||||||||
\(843\) | −13804.3 | −0.563993 | ||||||||
\(844\) | −4447.37 | −0.181380 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16318.5 | 0.663170 | ||||||||
\(847\) | −6271.92 | −0.254434 | ||||||||
\(848\) | −17426.4 | −0.705692 | ||||||||
\(849\) | −163.703 | −0.00661752 | ||||||||
\(850\) | −72551.7 | −2.92765 | ||||||||
\(851\) | −416.466 | −0.0167759 | ||||||||
\(852\) | −15211.1 | −0.611648 | ||||||||
\(853\) | 28649.5 | 1.14999 | 0.574995 | − | 0.818157i | \(-0.305004\pi\) | ||||
0.574995 | + | 0.818157i | \(0.305004\pi\) | |||||||
\(854\) | 18146.0 | 0.727098 | ||||||||
\(855\) | 27637.9 | 1.10549 | ||||||||
\(856\) | −2750.71 | −0.109833 | ||||||||
\(857\) | 32336.1 | 1.28889 | 0.644445 | − | 0.764651i | \(-0.277089\pi\) | ||||
0.644445 | + | 0.764651i | \(0.277089\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13878.5 | −0.551254 | −0.275627 | − | 0.961265i | \(-0.588885\pi\) | ||||
−0.275627 | + | 0.961265i | \(0.588885\pi\) | |||||||
\(860\) | −11562.9 | −0.458480 | ||||||||
\(861\) | −5272.31 | −0.208688 | ||||||||
\(862\) | −53223.7 | −2.10302 | ||||||||
\(863\) | 32934.7 | 1.29908 | 0.649542 | − | 0.760326i | \(-0.274961\pi\) | ||||
0.649542 | + | 0.760326i | \(0.274961\pi\) | |||||||
\(864\) | 1204.13 | 0.0474135 | ||||||||
\(865\) | −55517.5 | −2.18226 | ||||||||
\(866\) | 46424.3 | 1.82167 | ||||||||
\(867\) | −8325.38 | −0.326119 | ||||||||
\(868\) | 22049.3 | 0.862213 | ||||||||
\(869\) | −3319.57 | −0.129584 | ||||||||
\(870\) | 74743.6 | 2.91270 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −22413.5 | −0.870434 | ||||||||
\(873\) | −4383.65 | −0.169947 | ||||||||
\(874\) | −5872.87 | −0.227292 | ||||||||
\(875\) | 68805.4 | 2.65834 | ||||||||
\(876\) | −2263.88 | −0.0873167 | ||||||||
\(877\) | 18375.7 | 0.707531 | 0.353765 | − | 0.935334i | \(-0.384901\pi\) | ||||
0.353765 | + | 0.935334i | \(0.384901\pi\) | |||||||
\(878\) | 50050.2 | 1.92382 | ||||||||
\(879\) | 14235.7 | 0.546256 | ||||||||
\(880\) | 32590.7 | 1.24845 | ||||||||
\(881\) | 46883.4 | 1.79290 | 0.896448 | − | 0.443150i | \(-0.146139\pi\) | ||||
0.896448 | + | 0.443150i | \(0.146139\pi\) | |||||||
\(882\) | 3393.39 | 0.129548 | ||||||||
\(883\) | 1050.05 | 0.0400194 | 0.0200097 | − | 0.999800i | \(-0.493630\pi\) | ||||
0.0200097 | + | 0.999800i | \(0.493630\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −43208.2 | −1.64116 | ||||||||
\(886\) | −27333.7 | −1.03645 | ||||||||
\(887\) | 27916.8 | 1.05677 | 0.528385 | − | 0.849005i | \(-0.322798\pi\) | ||||
0.528385 | + | 0.849005i | \(0.322798\pi\) | |||||||
\(888\) | 5337.89 | 0.201720 | ||||||||
\(889\) | −34949.4 | −1.31852 | ||||||||
\(890\) | 100952. | 3.80217 | ||||||||
\(891\) | 2491.01 | 0.0936611 | ||||||||
\(892\) | −27698.0 | −1.03968 | ||||||||
\(893\) | −54297.4 | −2.03471 | ||||||||
\(894\) | −49921.9 | −1.86761 | ||||||||
\(895\) | 3461.92 | 0.129295 | ||||||||
\(896\) | 42680.6 | 1.59136 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 57990.8 | 2.15499 | ||||||||
\(899\) | −21364.6 | −0.792601 | ||||||||
\(900\) | 44961.3 | 1.66523 | ||||||||
\(901\) | −16117.5 | −0.595950 | ||||||||
\(902\) | 16059.1 | 0.592804 | ||||||||
\(903\) | −1729.81 | −0.0637481 | ||||||||
\(904\) | 48092.7 | 1.76940 | ||||||||
\(905\) | −70231.3 | −2.57963 | ||||||||
\(906\) | −32276.4 | −1.18357 | ||||||||
\(907\) | 23220.1 | 0.850066 | 0.425033 | − | 0.905178i | \(-0.360263\pi\) | ||||
0.425033 | + | 0.905178i | \(0.360263\pi\) | |||||||
\(908\) | 38289.5 | 1.39943 | ||||||||
\(909\) | 6897.38 | 0.251674 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16344.9 | 0.594435 | 0.297217 | − | 0.954810i | \(-0.403941\pi\) | ||||
0.297217 | + | 0.954810i | \(0.403941\pi\) | |||||||
\(912\) | 21726.3 | 0.788848 | ||||||||
\(913\) | −15858.0 | −0.574834 | ||||||||
\(914\) | −79516.7 | −2.87766 | ||||||||
\(915\) | −14652.4 | −0.529393 | ||||||||
\(916\) | 93559.0 | 3.37476 | ||||||||
\(917\) | −13002.1 | −0.468231 | ||||||||
\(918\) | −6039.15 | −0.217126 | ||||||||
\(919\) | −32931.7 | −1.18206 | −0.591032 | − | 0.806648i | \(-0.701279\pi\) | ||||
−0.591032 | + | 0.806648i | \(0.701279\pi\) | |||||||
\(920\) | −6360.67 | −0.227940 | ||||||||
\(921\) | 3086.47 | 0.110426 | ||||||||
\(922\) | 42800.8 | 1.52882 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 23133.6 | 0.823636 | ||||||||
\(925\) | −16119.4 | −0.572975 | ||||||||
\(926\) | 49679.0 | 1.76302 | ||||||||
\(927\) | 11068.8 | 0.392177 | ||||||||
\(928\) | −10835.3 | −0.383282 | ||||||||
\(929\) | 56305.5 | 1.98851 | 0.994253 | − | 0.107056i | \(-0.0341424\pi\) | ||||
0.994253 | + | 0.107056i | \(0.0341424\pi\) | |||||||
\(930\) | −27052.4 | −0.953852 | ||||||||
\(931\) | −11291.0 | −0.397473 | ||||||||
\(932\) | 98063.3 | 3.44653 | ||||||||
\(933\) | −7313.51 | −0.256628 | ||||||||
\(934\) | −71258.5 | −2.49641 | ||||||||
\(935\) | 30142.7 | 1.05430 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7095.61 | 0.247389 | 0.123695 | − | 0.992320i | \(-0.460526\pi\) | ||||
0.123695 | + | 0.992320i | \(0.460526\pi\) | |||||||
\(938\) | −23284.0 | −0.810502 | ||||||||
\(939\) | 23802.6 | 0.827230 | ||||||||
\(940\) | −122371. | −4.24606 | ||||||||
\(941\) | 5185.17 | 0.179630 | 0.0898150 | − | 0.995958i | \(-0.471372\pi\) | ||||
0.0898150 | + | 0.995958i | \(0.471372\pi\) | |||||||
\(942\) | −35777.9 | −1.23748 | ||||||||
\(943\) | −904.641 | −0.0312398 | ||||||||
\(944\) | −33966.2 | −1.17109 | ||||||||
\(945\) | 9318.26 | 0.320765 | ||||||||
\(946\) | 5268.89 | 0.181085 | ||||||||
\(947\) | −38451.7 | −1.31944 | −0.659722 | − | 0.751510i | \(-0.729326\pi\) | ||||
−0.659722 | + | 0.751510i | \(0.729326\pi\) | |||||||
\(948\) | −4987.39 | −0.170868 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −227310. | −7.76307 | ||||||||
\(951\) | 20828.2 | 0.710199 | ||||||||
\(952\) | −26952.4 | −0.917575 | ||||||||
\(953\) | −20930.5 | −0.711445 | −0.355722 | − | 0.934592i | \(-0.615765\pi\) | ||||
−0.355722 | + | 0.934592i | \(0.615765\pi\) | |||||||
\(954\) | 15176.4 | 0.515048 | ||||||||
\(955\) | −90768.8 | −3.07561 | ||||||||
\(956\) | −29053.7 | −0.982910 | ||||||||
\(957\) | −22415.2 | −0.757139 | ||||||||
\(958\) | 3072.19 | 0.103609 | ||||||||
\(959\) | −9787.14 | −0.329555 | ||||||||
\(960\) | −39153.9 | −1.31634 | ||||||||
\(961\) | −22058.4 | −0.740438 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 691.435 | 0.0231372 | ||||||||
\(964\) | 90066.1 | 3.00916 | ||||||||
\(965\) | 39796.1 | 1.32755 | ||||||||
\(966\) | −1980.07 | −0.0659499 | ||||||||
\(967\) | 50788.1 | 1.68897 | 0.844486 | − | 0.535578i | \(-0.179906\pi\) | ||||
0.844486 | + | 0.535578i | \(0.179906\pi\) | |||||||
\(968\) | 13793.2 | 0.457986 | ||||||||
\(969\) | 20094.4 | 0.666175 | ||||||||
\(970\) | 49947.6 | 1.65332 | ||||||||
\(971\) | 15277.5 | 0.504922 | 0.252461 | − | 0.967607i | \(-0.418760\pi\) | ||||
0.252461 | + | 0.967607i | \(0.418760\pi\) | |||||||
\(972\) | 3742.54 | 0.123500 | ||||||||
\(973\) | −34745.7 | −1.14481 | ||||||||
\(974\) | −80356.3 | −2.64351 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11518.4 | −0.377760 | ||||||||
\(977\) | −1293.19 | −0.0423469 | −0.0211734 | − | 0.999776i | \(-0.506740\pi\) | ||||
−0.0211734 | + | 0.999776i | \(0.506740\pi\) | |||||||
\(978\) | 3534.74 | 0.115571 | ||||||||
\(979\) | −30275.1 | −0.988353 | ||||||||
\(980\) | −25446.7 | −0.829453 | ||||||||
\(981\) | 5634.01 | 0.183364 | ||||||||
\(982\) | 12500.8 | 0.406227 | ||||||||
\(983\) | −8474.63 | −0.274973 | −0.137487 | − | 0.990504i | \(-0.543902\pi\) | ||||
−0.137487 | + | 0.990504i | \(0.543902\pi\) | |||||||
\(984\) | 11594.9 | 0.375641 | ||||||||
\(985\) | −42211.1 | −1.36544 | ||||||||
\(986\) | 54343.0 | 1.75521 | ||||||||
\(987\) | −18306.6 | −0.590382 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −296.807 | −0.00954289 | ||||||||
\(990\) | −28382.8 | −0.911175 | ||||||||
\(991\) | −7080.71 | −0.226969 | −0.113484 | − | 0.993540i | \(-0.536201\pi\) | ||||
−0.113484 | + | 0.993540i | \(0.536201\pi\) | |||||||
\(992\) | 3921.68 | 0.125518 | ||||||||
\(993\) | −16317.8 | −0.521480 | ||||||||
\(994\) | 25928.1 | 0.827354 | ||||||||
\(995\) | 28512.8 | 0.908458 | ||||||||
\(996\) | −23825.4 | −0.757968 | ||||||||
\(997\) | 19423.1 | 0.616985 | 0.308493 | − | 0.951227i | \(-0.400175\pi\) | ||||
0.308493 | + | 0.951227i | \(0.400175\pi\) | |||||||
\(998\) | 10564.5 | 0.335084 | ||||||||
\(999\) | −1341.76 | −0.0424940 |
(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.a.p.1.1 | yes | 9 | |
3.2 | odd | 2 | 1521.4.a.bf.1.9 | 9 | |||
13.5 | odd | 4 | 507.4.b.k.337.17 | 18 | |||
13.8 | odd | 4 | 507.4.b.k.337.2 | 18 | |||
13.12 | even | 2 | 507.4.a.o.1.9 | ✓ | 9 | ||
39.38 | odd | 2 | 1521.4.a.bi.1.1 | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.9 | ✓ | 9 | 13.12 | even | 2 | ||
507.4.a.p.1.1 | yes | 9 | 1.1 | even | 1 | trivial | |
507.4.b.k.337.2 | 18 | 13.8 | odd | 4 | |||
507.4.b.k.337.17 | 18 | 13.5 | odd | 4 | |||
1521.4.a.bf.1.9 | 9 | 3.2 | odd | 2 | |||
1521.4.a.bi.1.1 | 9 | 39.38 | odd | 2 |