Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,4,Mod(1,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, 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("354.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(20.8866761420\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −10.5826 | −0.946534 | −0.473267 | − | 0.880919i | \(-0.656925\pi\) | ||||
−0.473267 | + | 0.880919i | \(0.656925\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | −18.3739 | −0.992095 | −0.496048 | − | 0.868295i | \(-0.665216\pi\) | ||||
−0.496048 | + | 0.868295i | \(0.665216\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 21.1652 | 0.669301 | ||||||||
\(11\) | 47.3303 | 1.29733 | 0.648665 | − | 0.761074i | \(-0.275328\pi\) | ||||
0.648665 | + | 0.761074i | \(0.275328\pi\) | |||||||
\(12\) | 12.0000 | 0.288675 | ||||||||
\(13\) | 63.5735 | 1.35632 | 0.678158 | − | 0.734916i | \(-0.262778\pi\) | ||||
0.678158 | + | 0.734916i | \(0.262778\pi\) | |||||||
\(14\) | 36.7477 | 0.701517 | ||||||||
\(15\) | −31.7477 | −0.546482 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 60.7822 | 0.867168 | 0.433584 | − | 0.901113i | \(-0.357249\pi\) | ||||
0.433584 | + | 0.901113i | \(0.357249\pi\) | |||||||
\(18\) | −18.0000 | −0.235702 | ||||||||
\(19\) | −155.443 | −1.87690 | −0.938448 | − | 0.345421i | \(-0.887736\pi\) | ||||
−0.938448 | + | 0.345421i | \(0.887736\pi\) | |||||||
\(20\) | −42.3303 | −0.473267 | ||||||||
\(21\) | −55.1216 | −0.572787 | ||||||||
\(22\) | −94.6606 | −0.917350 | ||||||||
\(23\) | −120.695 | −1.09420 | −0.547101 | − | 0.837066i | \(-0.684269\pi\) | ||||
−0.547101 | + | 0.837066i | \(0.684269\pi\) | |||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −13.0091 | −0.104073 | ||||||||
\(26\) | −127.147 | −0.959060 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −73.4955 | −0.496048 | ||||||||
\(29\) | −42.8784 | −0.274563 | −0.137281 | − | 0.990532i | \(-0.543836\pi\) | ||||
−0.137281 | + | 0.990532i | \(0.543836\pi\) | |||||||
\(30\) | 63.4955 | 0.386421 | ||||||||
\(31\) | −135.383 | −0.784371 | −0.392185 | − | 0.919886i | \(-0.628281\pi\) | ||||
−0.392185 | + | 0.919886i | \(0.628281\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 141.991 | 0.749013 | ||||||||
\(34\) | −121.564 | −0.613180 | ||||||||
\(35\) | 194.443 | 0.939052 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | −223.025 | −0.990950 | −0.495475 | − | 0.868622i | \(-0.665006\pi\) | ||||
−0.495475 | + | 0.868622i | \(0.665006\pi\) | |||||||
\(38\) | 310.886 | 1.32717 | ||||||||
\(39\) | 190.720 | 0.783070 | ||||||||
\(40\) | 84.6606 | 0.334650 | ||||||||
\(41\) | 75.7133 | 0.288401 | 0.144200 | − | 0.989549i | \(-0.453939\pi\) | ||||
0.144200 | + | 0.989549i | \(0.453939\pi\) | |||||||
\(42\) | 110.243 | 0.405021 | ||||||||
\(43\) | −354.964 | −1.25887 | −0.629435 | − | 0.777053i | \(-0.716714\pi\) | ||||
−0.629435 | + | 0.777053i | \(0.716714\pi\) | |||||||
\(44\) | 189.321 | 0.648665 | ||||||||
\(45\) | −95.2432 | −0.315511 | ||||||||
\(46\) | 241.390 | 0.773718 | ||||||||
\(47\) | −269.484 | −0.836348 | −0.418174 | − | 0.908367i | \(-0.637330\pi\) | ||||
−0.418174 | + | 0.908367i | \(0.637330\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | −5.40114 | −0.0157468 | ||||||||
\(50\) | 26.0182 | 0.0735905 | ||||||||
\(51\) | 182.347 | 0.500659 | ||||||||
\(52\) | 254.294 | 0.678158 | ||||||||
\(53\) | −70.4265 | −0.182525 | −0.0912625 | − | 0.995827i | \(-0.529090\pi\) | ||||
−0.0912625 | + | 0.995827i | \(0.529090\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | −500.877 | −1.22797 | ||||||||
\(56\) | 146.991 | 0.350759 | ||||||||
\(57\) | −466.328 | −1.08363 | ||||||||
\(58\) | 85.7568 | 0.194145 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | −126.991 | −0.273241 | ||||||||
\(61\) | −244.410 | −0.513009 | −0.256504 | − | 0.966543i | \(-0.582571\pi\) | ||||
−0.256504 | + | 0.966543i | \(0.582571\pi\) | |||||||
\(62\) | 270.766 | 0.554634 | ||||||||
\(63\) | −165.365 | −0.330698 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −672.771 | −1.28380 | ||||||||
\(66\) | −283.982 | −0.529633 | ||||||||
\(67\) | 340.717 | 0.621271 | 0.310636 | − | 0.950529i | \(-0.399458\pi\) | ||||
0.310636 | + | 0.950529i | \(0.399458\pi\) | |||||||
\(68\) | 243.129 | 0.433584 | ||||||||
\(69\) | −362.085 | −0.631738 | ||||||||
\(70\) | −388.886 | −0.664010 | ||||||||
\(71\) | 581.951 | 0.972744 | 0.486372 | − | 0.873752i | \(-0.338320\pi\) | ||||
0.486372 | + | 0.873752i | \(0.338320\pi\) | |||||||
\(72\) | −72.0000 | −0.117851 | ||||||||
\(73\) | −230.181 | −0.369051 | −0.184525 | − | 0.982828i | \(-0.559075\pi\) | ||||
−0.184525 | + | 0.982828i | \(0.559075\pi\) | |||||||
\(74\) | 446.051 | 0.700707 | ||||||||
\(75\) | −39.0273 | −0.0600864 | ||||||||
\(76\) | −621.771 | −0.938448 | ||||||||
\(77\) | −869.641 | −1.28707 | ||||||||
\(78\) | −381.441 | −0.553714 | ||||||||
\(79\) | −1016.88 | −1.44820 | −0.724098 | − | 0.689697i | \(-0.757744\pi\) | ||||
−0.724098 | + | 0.689697i | \(0.757744\pi\) | |||||||
\(80\) | −169.321 | −0.236634 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −151.427 | −0.203930 | ||||||||
\(83\) | 383.971 | 0.507786 | 0.253893 | − | 0.967232i | \(-0.418289\pi\) | ||||
0.253893 | + | 0.967232i | \(0.418289\pi\) | |||||||
\(84\) | −220.486 | −0.286393 | ||||||||
\(85\) | −643.232 | −0.820804 | ||||||||
\(86\) | 709.927 | 0.890156 | ||||||||
\(87\) | −128.635 | −0.158519 | ||||||||
\(88\) | −378.642 | −0.458675 | ||||||||
\(89\) | 23.2413 | 0.0276806 | 0.0138403 | − | 0.999904i | \(-0.495594\pi\) | ||||
0.0138403 | + | 0.999904i | \(0.495594\pi\) | |||||||
\(90\) | 190.486 | 0.223100 | ||||||||
\(91\) | −1168.09 | −1.34560 | ||||||||
\(92\) | −482.780 | −0.547101 | ||||||||
\(93\) | −406.149 | −0.452857 | ||||||||
\(94\) | 538.969 | 0.591387 | ||||||||
\(95\) | 1644.99 | 1.77655 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 746.670 | 0.781575 | 0.390788 | − | 0.920481i | \(-0.372203\pi\) | ||||
0.390788 | + | 0.920481i | \(0.372203\pi\) | |||||||
\(98\) | 10.8023 | 0.0111346 | ||||||||
\(99\) | 425.973 | 0.432443 | ||||||||
\(100\) | −52.0364 | −0.0520364 | ||||||||
\(101\) | −854.014 | −0.841362 | −0.420681 | − | 0.907209i | \(-0.638209\pi\) | ||||
−0.420681 | + | 0.907209i | \(0.638209\pi\) | |||||||
\(102\) | −364.693 | −0.354020 | ||||||||
\(103\) | 327.739 | 0.313525 | 0.156762 | − | 0.987636i | \(-0.449894\pi\) | ||||
0.156762 | + | 0.987636i | \(0.449894\pi\) | |||||||
\(104\) | −508.588 | −0.479530 | ||||||||
\(105\) | 583.328 | 0.542162 | ||||||||
\(106\) | 140.853 | 0.129065 | ||||||||
\(107\) | −523.922 | −0.473359 | −0.236679 | − | 0.971588i | \(-0.576059\pi\) | ||||
−0.236679 | + | 0.971588i | \(0.576059\pi\) | |||||||
\(108\) | 108.000 | 0.0962250 | ||||||||
\(109\) | 170.325 | 0.149671 | 0.0748355 | − | 0.997196i | \(-0.476157\pi\) | ||||
0.0748355 | + | 0.997196i | \(0.476157\pi\) | |||||||
\(110\) | 1001.75 | 0.868304 | ||||||||
\(111\) | −669.076 | −0.572125 | ||||||||
\(112\) | −293.982 | −0.248024 | ||||||||
\(113\) | −1264.30 | −1.05252 | −0.526261 | − | 0.850323i | \(-0.676406\pi\) | ||||
−0.526261 | + | 0.850323i | \(0.676406\pi\) | |||||||
\(114\) | 932.657 | 0.766240 | ||||||||
\(115\) | 1277.26 | 1.03570 | ||||||||
\(116\) | −171.514 | −0.137281 | ||||||||
\(117\) | 572.161 | 0.452105 | ||||||||
\(118\) | 118.000 | 0.0920575 | ||||||||
\(119\) | −1116.80 | −0.860313 | ||||||||
\(120\) | 253.982 | 0.193211 | ||||||||
\(121\) | 909.158 | 0.683064 | ||||||||
\(122\) | 488.820 | 0.362752 | ||||||||
\(123\) | 227.140 | 0.166508 | ||||||||
\(124\) | −541.532 | −0.392185 | ||||||||
\(125\) | 1460.49 | 1.04504 | ||||||||
\(126\) | 330.730 | 0.233839 | ||||||||
\(127\) | −2301.47 | −1.60805 | −0.804027 | − | 0.594593i | \(-0.797313\pi\) | ||||
−0.804027 | + | 0.594593i | \(0.797313\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | −1064.89 | −0.726809 | ||||||||
\(130\) | 1345.54 | 0.907784 | ||||||||
\(131\) | 244.628 | 0.163155 | 0.0815773 | − | 0.996667i | \(-0.474004\pi\) | ||||
0.0815773 | + | 0.996667i | \(0.474004\pi\) | |||||||
\(132\) | 567.964 | 0.374507 | ||||||||
\(133\) | 2856.08 | 1.86206 | ||||||||
\(134\) | −681.433 | −0.439305 | ||||||||
\(135\) | −285.730 | −0.182161 | ||||||||
\(136\) | −486.258 | −0.306590 | ||||||||
\(137\) | 2176.57 | 1.35735 | 0.678676 | − | 0.734437i | \(-0.262554\pi\) | ||||
0.678676 | + | 0.734437i | \(0.262554\pi\) | |||||||
\(138\) | 724.170 | 0.446706 | ||||||||
\(139\) | −774.267 | −0.472464 | −0.236232 | − | 0.971697i | \(-0.575912\pi\) | ||||
−0.236232 | + | 0.971697i | \(0.575912\pi\) | |||||||
\(140\) | 777.771 | 0.469526 | ||||||||
\(141\) | −808.453 | −0.482866 | ||||||||
\(142\) | −1163.90 | −0.687834 | ||||||||
\(143\) | 3008.95 | 1.75959 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 453.764 | 0.259883 | ||||||||
\(146\) | 460.363 | 0.260958 | ||||||||
\(147\) | −16.2034 | −0.00909140 | ||||||||
\(148\) | −892.102 | −0.495475 | ||||||||
\(149\) | −1742.93 | −0.958296 | −0.479148 | − | 0.877734i | \(-0.659054\pi\) | ||||
−0.479148 | + | 0.877734i | \(0.659054\pi\) | |||||||
\(150\) | 78.0545 | 0.0424875 | ||||||||
\(151\) | 1290.03 | 0.695237 | 0.347618 | − | 0.937636i | \(-0.386990\pi\) | ||||
0.347618 | + | 0.937636i | \(0.386990\pi\) | |||||||
\(152\) | 1243.54 | 0.663583 | ||||||||
\(153\) | 547.040 | 0.289056 | ||||||||
\(154\) | 1739.28 | 0.910099 | ||||||||
\(155\) | 1432.70 | 0.742434 | ||||||||
\(156\) | 762.882 | 0.391535 | ||||||||
\(157\) | −165.689 | −0.0842258 | −0.0421129 | − | 0.999113i | \(-0.513409\pi\) | ||||
−0.0421129 | + | 0.999113i | \(0.513409\pi\) | |||||||
\(158\) | 2033.75 | 1.02403 | ||||||||
\(159\) | −211.280 | −0.105381 | ||||||||
\(160\) | 338.642 | 0.167325 | ||||||||
\(161\) | 2217.63 | 1.08555 | ||||||||
\(162\) | −162.000 | −0.0785674 | ||||||||
\(163\) | 938.091 | 0.450779 | 0.225389 | − | 0.974269i | \(-0.427635\pi\) | ||||
0.225389 | + | 0.974269i | \(0.427635\pi\) | |||||||
\(164\) | 302.853 | 0.144200 | ||||||||
\(165\) | −1502.63 | −0.708967 | ||||||||
\(166\) | −767.942 | −0.359059 | ||||||||
\(167\) | 2572.71 | 1.19211 | 0.596056 | − | 0.802943i | \(-0.296734\pi\) | ||||
0.596056 | + | 0.802943i | \(0.296734\pi\) | |||||||
\(168\) | 440.973 | 0.202511 | ||||||||
\(169\) | 1844.59 | 0.839594 | ||||||||
\(170\) | 1286.46 | 0.580396 | ||||||||
\(171\) | −1398.99 | −0.625632 | ||||||||
\(172\) | −1419.85 | −0.629435 | ||||||||
\(173\) | −2338.48 | −1.02770 | −0.513848 | − | 0.857881i | \(-0.671781\pi\) | ||||
−0.513848 | + | 0.857881i | \(0.671781\pi\) | |||||||
\(174\) | 257.270 | 0.112090 | ||||||||
\(175\) | 239.027 | 0.103250 | ||||||||
\(176\) | 757.285 | 0.324332 | ||||||||
\(177\) | −177.000 | −0.0751646 | ||||||||
\(178\) | −46.4826 | −0.0195731 | ||||||||
\(179\) | −2618.21 | −1.09326 | −0.546632 | − | 0.837373i | \(-0.684090\pi\) | ||||
−0.546632 | + | 0.837373i | \(0.684090\pi\) | |||||||
\(180\) | −380.973 | −0.157756 | ||||||||
\(181\) | −2858.10 | −1.17371 | −0.586853 | − | 0.809694i | \(-0.699633\pi\) | ||||
−0.586853 | + | 0.809694i | \(0.699633\pi\) | |||||||
\(182\) | 2336.18 | 0.951479 | ||||||||
\(183\) | −733.231 | −0.296186 | ||||||||
\(184\) | 965.561 | 0.386859 | ||||||||
\(185\) | 2360.18 | 0.937968 | ||||||||
\(186\) | 812.298 | 0.320218 | ||||||||
\(187\) | 2876.84 | 1.12500 | ||||||||
\(188\) | −1077.94 | −0.418174 | ||||||||
\(189\) | −496.094 | −0.190929 | ||||||||
\(190\) | −3289.97 | −1.25621 | ||||||||
\(191\) | 4461.29 | 1.69009 | 0.845047 | − | 0.534692i | \(-0.179573\pi\) | ||||
0.845047 | + | 0.534692i | \(0.179573\pi\) | |||||||
\(192\) | 192.000 | 0.0721688 | ||||||||
\(193\) | 3727.85 | 1.39035 | 0.695173 | − | 0.718842i | \(-0.255328\pi\) | ||||
0.695173 | + | 0.718842i | \(0.255328\pi\) | |||||||
\(194\) | −1493.34 | −0.552657 | ||||||||
\(195\) | −2018.31 | −0.741202 | ||||||||
\(196\) | −21.6046 | −0.00787338 | ||||||||
\(197\) | 3200.74 | 1.15758 | 0.578791 | − | 0.815476i | \(-0.303525\pi\) | ||||
0.578791 | + | 0.815476i | \(0.303525\pi\) | |||||||
\(198\) | −851.945 | −0.305783 | ||||||||
\(199\) | −4664.90 | −1.66174 | −0.830869 | − | 0.556469i | \(-0.812156\pi\) | ||||
−0.830869 | + | 0.556469i | \(0.812156\pi\) | |||||||
\(200\) | 104.073 | 0.0367953 | ||||||||
\(201\) | 1022.15 | 0.358691 | ||||||||
\(202\) | 1708.03 | 0.594933 | ||||||||
\(203\) | 787.842 | 0.272392 | ||||||||
\(204\) | 729.386 | 0.250330 | ||||||||
\(205\) | −801.241 | −0.272981 | ||||||||
\(206\) | −655.477 | −0.221695 | ||||||||
\(207\) | −1086.26 | −0.364734 | ||||||||
\(208\) | 1017.18 | 0.339079 | ||||||||
\(209\) | −7357.15 | −2.43495 | ||||||||
\(210\) | −1166.66 | −0.383367 | ||||||||
\(211\) | −4340.78 | −1.41626 | −0.708131 | − | 0.706081i | \(-0.750462\pi\) | ||||
−0.708131 | + | 0.706081i | \(0.750462\pi\) | |||||||
\(212\) | −281.706 | −0.0912625 | ||||||||
\(213\) | 1745.85 | 0.561614 | ||||||||
\(214\) | 1047.84 | 0.334715 | ||||||||
\(215\) | 3756.43 | 1.19156 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 2487.51 | 0.778171 | ||||||||
\(218\) | −340.649 | −0.105833 | ||||||||
\(219\) | −690.544 | −0.213072 | ||||||||
\(220\) | −2003.51 | −0.613983 | ||||||||
\(221\) | 3864.14 | 1.17615 | ||||||||
\(222\) | 1338.15 | 0.404554 | ||||||||
\(223\) | 2562.58 | 0.769521 | 0.384761 | − | 0.923016i | \(-0.374284\pi\) | ||||
0.384761 | + | 0.923016i | \(0.374284\pi\) | |||||||
\(224\) | 587.964 | 0.175379 | ||||||||
\(225\) | −117.082 | −0.0346909 | ||||||||
\(226\) | 2528.59 | 0.744245 | ||||||||
\(227\) | −2062.18 | −0.602958 | −0.301479 | − | 0.953473i | \(-0.597480\pi\) | ||||
−0.301479 | + | 0.953473i | \(0.597480\pi\) | |||||||
\(228\) | −1865.31 | −0.541813 | ||||||||
\(229\) | −5837.14 | −1.68441 | −0.842203 | − | 0.539160i | \(-0.818742\pi\) | ||||
−0.842203 | + | 0.539160i | \(0.818742\pi\) | |||||||
\(230\) | −2554.53 | −0.732351 | ||||||||
\(231\) | −2608.92 | −0.743093 | ||||||||
\(232\) | 343.027 | 0.0970726 | ||||||||
\(233\) | −3673.85 | −1.03297 | −0.516485 | − | 0.856296i | \(-0.672760\pi\) | ||||
−0.516485 | + | 0.856296i | \(0.672760\pi\) | |||||||
\(234\) | −1144.32 | −0.319687 | ||||||||
\(235\) | 2851.84 | 0.791632 | ||||||||
\(236\) | −236.000 | −0.0650945 | ||||||||
\(237\) | −3050.63 | −0.836117 | ||||||||
\(238\) | 2233.61 | 0.608333 | ||||||||
\(239\) | −2455.33 | −0.664527 | −0.332263 | − | 0.943187i | \(-0.607812\pi\) | ||||
−0.332263 | + | 0.943187i | \(0.607812\pi\) | |||||||
\(240\) | −507.964 | −0.136620 | ||||||||
\(241\) | 4882.16 | 1.30493 | 0.652463 | − | 0.757820i | \(-0.273736\pi\) | ||||
0.652463 | + | 0.757820i | \(0.273736\pi\) | |||||||
\(242\) | −1818.32 | −0.482999 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −977.641 | −0.256504 | ||||||||
\(245\) | 57.1580 | 0.0149048 | ||||||||
\(246\) | −454.280 | −0.117739 | ||||||||
\(247\) | −9882.04 | −2.54566 | ||||||||
\(248\) | 1083.06 | 0.277317 | ||||||||
\(249\) | 1151.91 | 0.293171 | ||||||||
\(250\) | −2920.98 | −0.738957 | ||||||||
\(251\) | 6998.75 | 1.75999 | 0.879995 | − | 0.474984i | \(-0.157546\pi\) | ||||
0.879995 | + | 0.474984i | \(0.157546\pi\) | |||||||
\(252\) | −661.459 | −0.165349 | ||||||||
\(253\) | −5712.53 | −1.41954 | ||||||||
\(254\) | 4602.95 | 1.13707 | ||||||||
\(255\) | −1929.70 | −0.473891 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 233.205 | 0.0566027 | 0.0283014 | − | 0.999599i | \(-0.490990\pi\) | ||||
0.0283014 | + | 0.999599i | \(0.490990\pi\) | |||||||
\(258\) | 2129.78 | 0.513932 | ||||||||
\(259\) | 4097.84 | 0.983117 | ||||||||
\(260\) | −2691.08 | −0.641900 | ||||||||
\(261\) | −385.906 | −0.0915209 | ||||||||
\(262\) | −489.256 | −0.115368 | ||||||||
\(263\) | −4695.32 | −1.10086 | −0.550430 | − | 0.834881i | \(-0.685536\pi\) | ||||
−0.550430 | + | 0.834881i | \(0.685536\pi\) | |||||||
\(264\) | −1135.93 | −0.264816 | ||||||||
\(265\) | 745.294 | 0.172766 | ||||||||
\(266\) | −5712.17 | −1.31668 | ||||||||
\(267\) | 69.7239 | 0.0159814 | ||||||||
\(268\) | 1362.87 | 0.310636 | ||||||||
\(269\) | 2959.38 | 0.670769 | 0.335384 | − | 0.942081i | \(-0.391134\pi\) | ||||
0.335384 | + | 0.942081i | \(0.391134\pi\) | |||||||
\(270\) | 571.459 | 0.128807 | ||||||||
\(271\) | −2964.39 | −0.664479 | −0.332240 | − | 0.943195i | \(-0.607804\pi\) | ||||
−0.332240 | + | 0.943195i | \(0.607804\pi\) | |||||||
\(272\) | 972.515 | 0.216792 | ||||||||
\(273\) | −3504.27 | −0.776880 | ||||||||
\(274\) | −4353.15 | −0.959793 | ||||||||
\(275\) | −615.724 | −0.135017 | ||||||||
\(276\) | −1448.34 | −0.315869 | ||||||||
\(277\) | 5834.05 | 1.26547 | 0.632733 | − | 0.774370i | \(-0.281933\pi\) | ||||
0.632733 | + | 0.774370i | \(0.281933\pi\) | |||||||
\(278\) | 1548.53 | 0.334082 | ||||||||
\(279\) | −1218.45 | −0.261457 | ||||||||
\(280\) | −1555.54 | −0.332005 | ||||||||
\(281\) | 6519.85 | 1.38413 | 0.692067 | − | 0.721834i | \(-0.256700\pi\) | ||||
0.692067 | + | 0.721834i | \(0.256700\pi\) | |||||||
\(282\) | 1616.91 | 0.341438 | ||||||||
\(283\) | 5416.05 | 1.13764 | 0.568818 | − | 0.822463i | \(-0.307401\pi\) | ||||
0.568818 | + | 0.822463i | \(0.307401\pi\) | |||||||
\(284\) | 2327.80 | 0.486372 | ||||||||
\(285\) | 4934.96 | 1.02569 | ||||||||
\(286\) | −6017.90 | −1.24422 | ||||||||
\(287\) | −1391.15 | −0.286121 | ||||||||
\(288\) | −288.000 | −0.0589256 | ||||||||
\(289\) | −1218.52 | −0.248020 | ||||||||
\(290\) | −907.528 | −0.183765 | ||||||||
\(291\) | 2240.01 | 0.451243 | ||||||||
\(292\) | −920.726 | −0.184525 | ||||||||
\(293\) | −8096.63 | −1.61437 | −0.807184 | − | 0.590300i | \(-0.799010\pi\) | ||||
−0.807184 | + | 0.590300i | \(0.799010\pi\) | |||||||
\(294\) | 32.4068 | 0.00642859 | ||||||||
\(295\) | 624.372 | 0.123228 | ||||||||
\(296\) | 1784.20 | 0.350354 | ||||||||
\(297\) | 1277.92 | 0.249671 | ||||||||
\(298\) | 3485.85 | 0.677618 | ||||||||
\(299\) | −7673.01 | −1.48409 | ||||||||
\(300\) | −156.109 | −0.0300432 | ||||||||
\(301\) | 6522.05 | 1.24892 | ||||||||
\(302\) | −2580.05 | −0.491607 | ||||||||
\(303\) | −2562.04 | −0.485761 | ||||||||
\(304\) | −2487.08 | −0.469224 | ||||||||
\(305\) | 2586.49 | 0.485580 | ||||||||
\(306\) | −1094.08 | −0.204393 | ||||||||
\(307\) | 8252.18 | 1.53413 | 0.767063 | − | 0.641572i | \(-0.221717\pi\) | ||||
0.767063 | + | 0.641572i | \(0.221717\pi\) | |||||||
\(308\) | −3478.56 | −0.643537 | ||||||||
\(309\) | 983.216 | 0.181014 | ||||||||
\(310\) | −2865.40 | −0.524980 | ||||||||
\(311\) | −3861.70 | −0.704107 | −0.352053 | − | 0.935980i | \(-0.614516\pi\) | ||||
−0.352053 | + | 0.935980i | \(0.614516\pi\) | |||||||
\(312\) | −1525.76 | −0.276857 | ||||||||
\(313\) | 2319.63 | 0.418892 | 0.209446 | − | 0.977820i | \(-0.432834\pi\) | ||||
0.209446 | + | 0.977820i | \(0.432834\pi\) | |||||||
\(314\) | 331.379 | 0.0595566 | ||||||||
\(315\) | 1749.99 | 0.313017 | ||||||||
\(316\) | −4067.51 | −0.724098 | ||||||||
\(317\) | 453.436 | 0.0803391 | 0.0401695 | − | 0.999193i | \(-0.487210\pi\) | ||||
0.0401695 | + | 0.999193i | \(0.487210\pi\) | |||||||
\(318\) | 422.559 | 0.0745155 | ||||||||
\(319\) | −2029.45 | −0.356198 | ||||||||
\(320\) | −677.285 | −0.118317 | ||||||||
\(321\) | −1571.76 | −0.273294 | ||||||||
\(322\) | −4435.27 | −0.767602 | ||||||||
\(323\) | −9448.15 | −1.62758 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −827.033 | −0.141156 | ||||||||
\(326\) | −1876.18 | −0.318749 | ||||||||
\(327\) | 510.974 | 0.0864126 | ||||||||
\(328\) | −605.706 | −0.101965 | ||||||||
\(329\) | 4951.47 | 0.829737 | ||||||||
\(330\) | 3005.26 | 0.501315 | ||||||||
\(331\) | −9235.83 | −1.53368 | −0.766839 | − | 0.641840i | \(-0.778171\pi\) | ||||
−0.766839 | + | 0.641840i | \(0.778171\pi\) | |||||||
\(332\) | 1535.88 | 0.253893 | ||||||||
\(333\) | −2007.23 | −0.330317 | ||||||||
\(334\) | −5145.43 | −0.842950 | ||||||||
\(335\) | −3605.66 | −0.588054 | ||||||||
\(336\) | −881.945 | −0.143197 | ||||||||
\(337\) | 9340.65 | 1.50984 | 0.754922 | − | 0.655814i | \(-0.227675\pi\) | ||||
0.754922 | + | 0.655814i | \(0.227675\pi\) | |||||||
\(338\) | −3689.18 | −0.593683 | ||||||||
\(339\) | −3792.89 | −0.607673 | ||||||||
\(340\) | −2572.93 | −0.410402 | ||||||||
\(341\) | −6407.72 | −1.01759 | ||||||||
\(342\) | 2797.97 | 0.442389 | ||||||||
\(343\) | 6401.47 | 1.00772 | ||||||||
\(344\) | 2839.71 | 0.445078 | ||||||||
\(345\) | 3831.79 | 0.597962 | ||||||||
\(346\) | 4676.96 | 0.726691 | ||||||||
\(347\) | −5432.79 | −0.840482 | −0.420241 | − | 0.907412i | \(-0.638054\pi\) | ||||
−0.420241 | + | 0.907412i | \(0.638054\pi\) | |||||||
\(348\) | −514.541 | −0.0792594 | ||||||||
\(349\) | 7808.17 | 1.19760 | 0.598799 | − | 0.800899i | \(-0.295645\pi\) | ||||
0.598799 | + | 0.800899i | \(0.295645\pi\) | |||||||
\(350\) | −478.055 | −0.0730088 | ||||||||
\(351\) | 1716.48 | 0.261023 | ||||||||
\(352\) | −1514.57 | −0.229338 | ||||||||
\(353\) | −177.412 | −0.0267499 | −0.0133749 | − | 0.999911i | \(-0.504258\pi\) | ||||
−0.0133749 | + | 0.999911i | \(0.504258\pi\) | |||||||
\(354\) | 354.000 | 0.0531494 | ||||||||
\(355\) | −6158.54 | −0.920736 | ||||||||
\(356\) | 92.9651 | 0.0138403 | ||||||||
\(357\) | −3350.41 | −0.496702 | ||||||||
\(358\) | 5236.42 | 0.773055 | ||||||||
\(359\) | −9472.43 | −1.39258 | −0.696289 | − | 0.717761i | \(-0.745167\pi\) | ||||
−0.696289 | + | 0.717761i | \(0.745167\pi\) | |||||||
\(360\) | 761.945 | 0.111550 | ||||||||
\(361\) | 17303.5 | 2.52274 | ||||||||
\(362\) | 5716.19 | 0.829935 | ||||||||
\(363\) | 2727.47 | 0.394367 | ||||||||
\(364\) | −4672.36 | −0.672798 | ||||||||
\(365\) | 2435.91 | 0.349319 | ||||||||
\(366\) | 1466.46 | 0.209435 | ||||||||
\(367\) | −1628.23 | −0.231588 | −0.115794 | − | 0.993273i | \(-0.536941\pi\) | ||||
−0.115794 | + | 0.993273i | \(0.536941\pi\) | |||||||
\(368\) | −1931.12 | −0.273551 | ||||||||
\(369\) | 681.419 | 0.0961335 | ||||||||
\(370\) | −4720.37 | −0.663244 | ||||||||
\(371\) | 1294.01 | 0.181082 | ||||||||
\(372\) | −1624.60 | −0.226428 | ||||||||
\(373\) | 3096.44 | 0.429833 | 0.214916 | − | 0.976632i | \(-0.431052\pi\) | ||||
0.214916 | + | 0.976632i | \(0.431052\pi\) | |||||||
\(374\) | −5753.68 | −0.795496 | ||||||||
\(375\) | 4381.47 | 0.603356 | ||||||||
\(376\) | 2155.88 | 0.295694 | ||||||||
\(377\) | −2725.93 | −0.372394 | ||||||||
\(378\) | 992.189 | 0.135007 | ||||||||
\(379\) | 11197.9 | 1.51767 | 0.758833 | − | 0.651285i | \(-0.225770\pi\) | ||||
0.758833 | + | 0.651285i | \(0.225770\pi\) | |||||||
\(380\) | 6579.94 | 0.888273 | ||||||||
\(381\) | −6904.42 | −0.928411 | ||||||||
\(382\) | −8922.59 | −1.19508 | ||||||||
\(383\) | −6380.04 | −0.851188 | −0.425594 | − | 0.904914i | \(-0.639935\pi\) | ||||
−0.425594 | + | 0.904914i | \(0.639935\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 9203.04 | 1.21826 | ||||||||
\(386\) | −7455.71 | −0.983123 | ||||||||
\(387\) | −3194.67 | −0.419624 | ||||||||
\(388\) | 2986.68 | 0.390788 | ||||||||
\(389\) | 10070.5 | 1.31258 | 0.656291 | − | 0.754508i | \(-0.272124\pi\) | ||||
0.656291 | + | 0.754508i | \(0.272124\pi\) | |||||||
\(390\) | 4036.63 | 0.524109 | ||||||||
\(391\) | −7336.11 | −0.948857 | ||||||||
\(392\) | 43.2091 | 0.00556732 | ||||||||
\(393\) | 733.884 | 0.0941973 | ||||||||
\(394\) | −6401.49 | −0.818534 | ||||||||
\(395\) | 10761.2 | 1.37077 | ||||||||
\(396\) | 1703.89 | 0.216222 | ||||||||
\(397\) | −1609.08 | −0.203419 | −0.101709 | − | 0.994814i | \(-0.532431\pi\) | ||||
−0.101709 | + | 0.994814i | \(0.532431\pi\) | |||||||
\(398\) | 9329.79 | 1.17503 | ||||||||
\(399\) | 8568.25 | 1.07506 | ||||||||
\(400\) | −208.145 | −0.0260182 | ||||||||
\(401\) | 6154.93 | 0.766490 | 0.383245 | − | 0.923647i | \(-0.374806\pi\) | ||||
0.383245 | + | 0.923647i | \(0.374806\pi\) | |||||||
\(402\) | −2044.30 | −0.253633 | ||||||||
\(403\) | −8606.77 | −1.06385 | ||||||||
\(404\) | −3416.06 | −0.420681 | ||||||||
\(405\) | −857.189 | −0.105170 | ||||||||
\(406\) | −1575.68 | −0.192611 | ||||||||
\(407\) | −10555.9 | −1.28559 | ||||||||
\(408\) | −1458.77 | −0.177010 | ||||||||
\(409\) | 5914.12 | 0.714999 | 0.357499 | − | 0.933913i | \(-0.383629\pi\) | ||||
0.357499 | + | 0.933913i | \(0.383629\pi\) | |||||||
\(410\) | 1602.48 | 0.193027 | ||||||||
\(411\) | 6529.72 | 0.783668 | ||||||||
\(412\) | 1310.95 | 0.156762 | ||||||||
\(413\) | 1084.06 | 0.129160 | ||||||||
\(414\) | 2172.51 | 0.257906 | ||||||||
\(415\) | −4063.40 | −0.480637 | ||||||||
\(416\) | −2034.35 | −0.239765 | ||||||||
\(417\) | −2322.80 | −0.272777 | ||||||||
\(418\) | 14714.3 | 1.72177 | ||||||||
\(419\) | −15412.1 | −1.79697 | −0.898486 | − | 0.439002i | \(-0.855332\pi\) | ||||
−0.898486 | + | 0.439002i | \(0.855332\pi\) | |||||||
\(420\) | 2333.31 | 0.271081 | ||||||||
\(421\) | −7496.68 | −0.867852 | −0.433926 | − | 0.900949i | \(-0.642872\pi\) | ||||
−0.433926 | + | 0.900949i | \(0.642872\pi\) | |||||||
\(422\) | 8681.56 | 1.00145 | ||||||||
\(423\) | −2425.36 | −0.278783 | ||||||||
\(424\) | 563.412 | 0.0645323 | ||||||||
\(425\) | −790.721 | −0.0902485 | ||||||||
\(426\) | −3491.70 | −0.397121 | ||||||||
\(427\) | 4490.76 | 0.508953 | ||||||||
\(428\) | −2095.69 | −0.236679 | ||||||||
\(429\) | 9026.86 | 1.01590 | ||||||||
\(430\) | −7512.86 | −0.842563 | ||||||||
\(431\) | −5517.13 | −0.616591 | −0.308295 | − | 0.951291i | \(-0.599759\pi\) | ||||
−0.308295 | + | 0.951291i | \(0.599759\pi\) | |||||||
\(432\) | 432.000 | 0.0481125 | ||||||||
\(433\) | −9974.48 | −1.10703 | −0.553514 | − | 0.832840i | \(-0.686713\pi\) | ||||
−0.553514 | + | 0.832840i | \(0.686713\pi\) | |||||||
\(434\) | −4975.02 | −0.550250 | ||||||||
\(435\) | 1361.29 | 0.150044 | ||||||||
\(436\) | 681.298 | 0.0748355 | ||||||||
\(437\) | 18761.2 | 2.05370 | ||||||||
\(438\) | 1381.09 | 0.150664 | ||||||||
\(439\) | −7993.13 | −0.869000 | −0.434500 | − | 0.900672i | \(-0.643075\pi\) | ||||
−0.434500 | + | 0.900672i | \(0.643075\pi\) | |||||||
\(440\) | 4007.01 | 0.434152 | ||||||||
\(441\) | −48.6102 | −0.00524892 | ||||||||
\(442\) | −7728.27 | −0.831666 | ||||||||
\(443\) | 18221.4 | 1.95423 | 0.977114 | − | 0.212716i | \(-0.0682309\pi\) | ||||
0.977114 | + | 0.212716i | \(0.0682309\pi\) | |||||||
\(444\) | −2676.30 | −0.286063 | ||||||||
\(445\) | −245.953 | −0.0262006 | ||||||||
\(446\) | −5125.17 | −0.544134 | ||||||||
\(447\) | −5228.78 | −0.553273 | ||||||||
\(448\) | −1175.93 | −0.124012 | ||||||||
\(449\) | −11013.4 | −1.15758 | −0.578790 | − | 0.815477i | \(-0.696475\pi\) | ||||
−0.578790 | + | 0.815477i | \(0.696475\pi\) | |||||||
\(450\) | 234.164 | 0.0245302 | ||||||||
\(451\) | 3583.53 | 0.374151 | ||||||||
\(452\) | −5057.18 | −0.526261 | ||||||||
\(453\) | 3870.08 | 0.401395 | ||||||||
\(454\) | 4124.35 | 0.426355 | ||||||||
\(455\) | 12361.4 | 1.27365 | ||||||||
\(456\) | 3730.63 | 0.383120 | ||||||||
\(457\) | 5504.77 | 0.563462 | 0.281731 | − | 0.959493i | \(-0.409091\pi\) | ||||
0.281731 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(458\) | 11674.3 | 1.19105 | ||||||||
\(459\) | 1641.12 | 0.166886 | ||||||||
\(460\) | 5109.06 | 0.517850 | ||||||||
\(461\) | 17623.4 | 1.78049 | 0.890244 | − | 0.455484i | \(-0.150534\pi\) | ||||
0.890244 | + | 0.455484i | \(0.150534\pi\) | |||||||
\(462\) | 5217.84 | 0.525446 | ||||||||
\(463\) | 18820.0 | 1.88907 | 0.944537 | − | 0.328404i | \(-0.106511\pi\) | ||||
0.944537 | + | 0.328404i | \(0.106511\pi\) | |||||||
\(464\) | −686.055 | −0.0686407 | ||||||||
\(465\) | 4298.10 | 0.428644 | ||||||||
\(466\) | 7347.71 | 0.730421 | ||||||||
\(467\) | 2558.84 | 0.253552 | 0.126776 | − | 0.991931i | \(-0.459537\pi\) | ||||
0.126776 | + | 0.991931i | \(0.459537\pi\) | |||||||
\(468\) | 2288.65 | 0.226053 | ||||||||
\(469\) | −6260.28 | −0.616360 | ||||||||
\(470\) | −5703.68 | −0.559768 | ||||||||
\(471\) | −497.068 | −0.0486278 | ||||||||
\(472\) | 472.000 | 0.0460287 | ||||||||
\(473\) | −16800.5 | −1.63317 | ||||||||
\(474\) | 6101.26 | 0.591224 | ||||||||
\(475\) | 2022.17 | 0.195334 | ||||||||
\(476\) | −4467.22 | −0.430156 | ||||||||
\(477\) | −633.839 | −0.0608417 | ||||||||
\(478\) | 4910.65 | 0.469891 | ||||||||
\(479\) | 8222.33 | 0.784317 | 0.392158 | − | 0.919898i | \(-0.371729\pi\) | ||||
0.392158 | + | 0.919898i | \(0.371729\pi\) | |||||||
\(480\) | 1015.93 | 0.0966053 | ||||||||
\(481\) | −14178.5 | −1.34404 | ||||||||
\(482\) | −9764.31 | −0.922722 | ||||||||
\(483\) | 6652.90 | 0.626745 | ||||||||
\(484\) | 3636.63 | 0.341532 | ||||||||
\(485\) | −7901.69 | −0.739788 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | −13014.7 | −1.21099 | −0.605495 | − | 0.795849i | \(-0.707025\pi\) | ||||
−0.605495 | + | 0.795849i | \(0.707025\pi\) | |||||||
\(488\) | 1955.28 | 0.181376 | ||||||||
\(489\) | 2814.27 | 0.260257 | ||||||||
\(490\) | −114.316 | −0.0105393 | ||||||||
\(491\) | 2376.25 | 0.218408 | 0.109204 | − | 0.994019i | \(-0.465170\pi\) | ||||
0.109204 | + | 0.994019i | \(0.465170\pi\) | |||||||
\(492\) | 908.559 | 0.0832541 | ||||||||
\(493\) | −2606.24 | −0.238092 | ||||||||
\(494\) | 19764.1 | 1.80006 | ||||||||
\(495\) | −4507.89 | −0.409322 | ||||||||
\(496\) | −2166.13 | −0.196093 | ||||||||
\(497\) | −10692.7 | −0.965055 | ||||||||
\(498\) | −2303.82 | −0.207303 | ||||||||
\(499\) | −22141.4 | −1.98634 | −0.993172 | − | 0.116662i | \(-0.962781\pi\) | ||||
−0.993172 | + | 0.116662i | \(0.962781\pi\) | |||||||
\(500\) | 5841.97 | 0.522521 | ||||||||
\(501\) | 7718.14 | 0.688266 | ||||||||
\(502\) | −13997.5 | −1.24450 | ||||||||
\(503\) | −15148.8 | −1.34285 | −0.671424 | − | 0.741073i | \(-0.734317\pi\) | ||||
−0.671424 | + | 0.741073i | \(0.734317\pi\) | |||||||
\(504\) | 1322.92 | 0.116920 | ||||||||
\(505\) | 9037.67 | 0.796378 | ||||||||
\(506\) | 11425.1 | 1.00377 | ||||||||
\(507\) | 5533.76 | 0.484740 | ||||||||
\(508\) | −9205.90 | −0.804027 | ||||||||
\(509\) | −11338.3 | −0.987348 | −0.493674 | − | 0.869647i | \(-0.664346\pi\) | ||||
−0.493674 | + | 0.869647i | \(0.664346\pi\) | |||||||
\(510\) | 3859.39 | 0.335092 | ||||||||
\(511\) | 4229.32 | 0.366133 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | −4196.96 | −0.361209 | ||||||||
\(514\) | −466.409 | −0.0400242 | ||||||||
\(515\) | −3468.32 | −0.296762 | ||||||||
\(516\) | −4259.56 | −0.363405 | ||||||||
\(517\) | −12754.8 | −1.08502 | ||||||||
\(518\) | −8195.68 | −0.695169 | ||||||||
\(519\) | −7015.45 | −0.593341 | ||||||||
\(520\) | 5382.17 | 0.453892 | ||||||||
\(521\) | −14243.1 | −1.19770 | −0.598849 | − | 0.800862i | \(-0.704375\pi\) | ||||
−0.598849 | + | 0.800862i | \(0.704375\pi\) | |||||||
\(522\) | 771.811 | 0.0647151 | ||||||||
\(523\) | −15660.8 | −1.30937 | −0.654684 | − | 0.755903i | \(-0.727198\pi\) | ||||
−0.654684 | + | 0.755903i | \(0.727198\pi\) | |||||||
\(524\) | 978.512 | 0.0815773 | ||||||||
\(525\) | 717.082 | 0.0596115 | ||||||||
\(526\) | 9390.65 | 0.778425 | ||||||||
\(527\) | −8228.87 | −0.680181 | ||||||||
\(528\) | 2271.85 | 0.187253 | ||||||||
\(529\) | 2400.30 | 0.197280 | ||||||||
\(530\) | −1490.59 | −0.122164 | ||||||||
\(531\) | −531.000 | −0.0433963 | ||||||||
\(532\) | 11424.3 | 0.931030 | ||||||||
\(533\) | 4813.36 | 0.391162 | ||||||||
\(534\) | −139.448 | −0.0113005 | ||||||||
\(535\) | 5544.44 | 0.448051 | ||||||||
\(536\) | −2725.73 | −0.219653 | ||||||||
\(537\) | −7854.63 | −0.631196 | ||||||||
\(538\) | −5918.77 | −0.474305 | ||||||||
\(539\) | −255.638 | −0.0204287 | ||||||||
\(540\) | −1142.92 | −0.0910803 | ||||||||
\(541\) | 16850.4 | 1.33910 | 0.669551 | − | 0.742766i | \(-0.266487\pi\) | ||||
0.669551 | + | 0.742766i | \(0.266487\pi\) | |||||||
\(542\) | 5928.78 | 0.469858 | ||||||||
\(543\) | −8574.29 | −0.677639 | ||||||||
\(544\) | −1945.03 | −0.153295 | ||||||||
\(545\) | −1802.47 | −0.141669 | ||||||||
\(546\) | 7008.54 | 0.549337 | ||||||||
\(547\) | 23374.5 | 1.82709 | 0.913547 | − | 0.406733i | \(-0.133332\pi\) | ||||
0.913547 | + | 0.406733i | \(0.133332\pi\) | |||||||
\(548\) | 8706.30 | 0.678676 | ||||||||
\(549\) | −2199.69 | −0.171003 | ||||||||
\(550\) | 1231.45 | 0.0954712 | ||||||||
\(551\) | 6665.14 | 0.515326 | ||||||||
\(552\) | 2896.68 | 0.223353 | ||||||||
\(553\) | 18684.0 | 1.43675 | ||||||||
\(554\) | −11668.1 | −0.894819 | ||||||||
\(555\) | 7080.55 | 0.541536 | ||||||||
\(556\) | −3097.07 | −0.236232 | ||||||||
\(557\) | −10403.4 | −0.791396 | −0.395698 | − | 0.918381i | \(-0.629497\pi\) | ||||
−0.395698 | + | 0.918381i | \(0.629497\pi\) | |||||||
\(558\) | 2436.89 | 0.184878 | ||||||||
\(559\) | −22566.3 | −1.70743 | ||||||||
\(560\) | 3111.08 | 0.234763 | ||||||||
\(561\) | 8630.52 | 0.649520 | ||||||||
\(562\) | −13039.7 | −0.978730 | ||||||||
\(563\) | 1918.38 | 0.143606 | 0.0718029 | − | 0.997419i | \(-0.477125\pi\) | ||||
0.0718029 | + | 0.997419i | \(0.477125\pi\) | |||||||
\(564\) | −3233.81 | −0.241433 | ||||||||
\(565\) | 13379.5 | 0.996248 | ||||||||
\(566\) | −10832.1 | −0.804430 | ||||||||
\(567\) | −1488.28 | −0.110233 | ||||||||
\(568\) | −4655.61 | −0.343917 | ||||||||
\(569\) | 20752.9 | 1.52901 | 0.764506 | − | 0.644617i | \(-0.222983\pi\) | ||||
0.764506 | + | 0.644617i | \(0.222983\pi\) | |||||||
\(570\) | −9869.91 | −0.725272 | ||||||||
\(571\) | 19619.5 | 1.43791 | 0.718957 | − | 0.695054i | \(-0.244620\pi\) | ||||
0.718957 | + | 0.695054i | \(0.244620\pi\) | |||||||
\(572\) | 12035.8 | 0.879795 | ||||||||
\(573\) | 13383.9 | 0.975776 | ||||||||
\(574\) | 2782.29 | 0.202318 | ||||||||
\(575\) | 1570.13 | 0.113877 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | −16614.2 | −1.19872 | −0.599358 | − | 0.800481i | \(-0.704577\pi\) | ||||
−0.599358 | + | 0.800481i | \(0.704577\pi\) | |||||||
\(578\) | 2437.05 | 0.175377 | ||||||||
\(579\) | 11183.6 | 0.802717 | ||||||||
\(580\) | 1815.06 | 0.129942 | ||||||||
\(581\) | −7055.03 | −0.503773 | ||||||||
\(582\) | −4480.02 | −0.319077 | ||||||||
\(583\) | −3333.31 | −0.236795 | ||||||||
\(584\) | 1841.45 | 0.130479 | ||||||||
\(585\) | −6054.94 | −0.427933 | ||||||||
\(586\) | 16193.3 | 1.14153 | ||||||||
\(587\) | −4898.71 | −0.344449 | −0.172224 | − | 0.985058i | \(-0.555095\pi\) | ||||
−0.172224 | + | 0.985058i | \(0.555095\pi\) | |||||||
\(588\) | −64.8137 | −0.00454570 | ||||||||
\(589\) | 21044.3 | 1.47218 | ||||||||
\(590\) | −1248.74 | −0.0871355 | ||||||||
\(591\) | 9602.23 | 0.668330 | ||||||||
\(592\) | −3568.41 | −0.247737 | ||||||||
\(593\) | 9958.75 | 0.689641 | 0.344820 | − | 0.938669i | \(-0.387940\pi\) | ||||
0.344820 | + | 0.938669i | \(0.387940\pi\) | |||||||
\(594\) | −2555.84 | −0.176544 | ||||||||
\(595\) | 11818.7 | 0.814316 | ||||||||
\(596\) | −6971.71 | −0.479148 | ||||||||
\(597\) | −13994.7 | −0.959404 | ||||||||
\(598\) | 15346.0 | 1.04941 | ||||||||
\(599\) | 3477.65 | 0.237217 | 0.118609 | − | 0.992941i | \(-0.462157\pi\) | ||||
0.118609 | + | 0.992941i | \(0.462157\pi\) | |||||||
\(600\) | 312.218 | 0.0212438 | ||||||||
\(601\) | 251.900 | 0.0170969 | 0.00854844 | − | 0.999963i | \(-0.497279\pi\) | ||||
0.00854844 | + | 0.999963i | \(0.497279\pi\) | |||||||
\(602\) | −13044.1 | −0.883120 | ||||||||
\(603\) | 3066.45 | 0.207090 | ||||||||
\(604\) | 5160.10 | 0.347618 | ||||||||
\(605\) | −9621.23 | −0.646543 | ||||||||
\(606\) | 5124.09 | 0.343485 | ||||||||
\(607\) | 27085.9 | 1.81117 | 0.905587 | − | 0.424161i | \(-0.139431\pi\) | ||||
0.905587 | + | 0.424161i | \(0.139431\pi\) | |||||||
\(608\) | 4974.17 | 0.331791 | ||||||||
\(609\) | 2363.53 | 0.157266 | ||||||||
\(610\) | −5172.98 | −0.343357 | ||||||||
\(611\) | −17132.1 | −1.13435 | ||||||||
\(612\) | 2188.16 | 0.144528 | ||||||||
\(613\) | 21711.2 | 1.43052 | 0.715258 | − | 0.698861i | \(-0.246309\pi\) | ||||
0.715258 | + | 0.698861i | \(0.246309\pi\) | |||||||
\(614\) | −16504.4 | −1.08479 | ||||||||
\(615\) | −2403.72 | −0.157606 | ||||||||
\(616\) | 6957.12 | 0.455050 | ||||||||
\(617\) | −2582.21 | −0.168486 | −0.0842431 | − | 0.996445i | \(-0.526847\pi\) | ||||
−0.0842431 | + | 0.996445i | \(0.526847\pi\) | |||||||
\(618\) | −1966.43 | −0.127996 | ||||||||
\(619\) | −10035.8 | −0.651654 | −0.325827 | − | 0.945429i | \(-0.605643\pi\) | ||||
−0.325827 | + | 0.945429i | \(0.605643\pi\) | |||||||
\(620\) | 5730.80 | 0.371217 | ||||||||
\(621\) | −3258.77 | −0.210579 | ||||||||
\(622\) | 7723.41 | 0.497879 | ||||||||
\(623\) | −427.032 | −0.0274618 | ||||||||
\(624\) | 3051.53 | 0.195767 | ||||||||
\(625\) | −13829.6 | −0.885096 | ||||||||
\(626\) | −4639.26 | −0.296201 | ||||||||
\(627\) | −22071.5 | −1.40582 | ||||||||
\(628\) | −662.758 | −0.0421129 | ||||||||
\(629\) | −13556.0 | −0.859320 | ||||||||
\(630\) | −3499.97 | −0.221337 | ||||||||
\(631\) | −8839.40 | −0.557672 | −0.278836 | − | 0.960339i | \(-0.589949\pi\) | ||||
−0.278836 | + | 0.960339i | \(0.589949\pi\) | |||||||
\(632\) | 8135.01 | 0.512015 | ||||||||
\(633\) | −13022.3 | −0.817680 | ||||||||
\(634\) | −906.871 | −0.0568083 | ||||||||
\(635\) | 24355.5 | 1.52208 | ||||||||
\(636\) | −845.118 | −0.0526904 | ||||||||
\(637\) | −343.369 | −0.0213576 | ||||||||
\(638\) | 4058.90 | 0.251870 | ||||||||
\(639\) | 5237.56 | 0.324248 | ||||||||
\(640\) | 1354.57 | 0.0836626 | ||||||||
\(641\) | −11130.3 | −0.685836 | −0.342918 | − | 0.939365i | \(-0.611415\pi\) | ||||
−0.342918 | + | 0.939365i | \(0.611415\pi\) | |||||||
\(642\) | 3143.53 | 0.193248 | ||||||||
\(643\) | −15678.6 | −0.961593 | −0.480797 | − | 0.876832i | \(-0.659653\pi\) | ||||
−0.480797 | + | 0.876832i | \(0.659653\pi\) | |||||||
\(644\) | 8870.54 | 0.542777 | ||||||||
\(645\) | 11269.3 | 0.687950 | ||||||||
\(646\) | 18896.3 | 1.15088 | ||||||||
\(647\) | −7444.89 | −0.452379 | −0.226189 | − | 0.974083i | \(-0.572627\pi\) | ||||
−0.226189 | + | 0.974083i | \(0.572627\pi\) | |||||||
\(648\) | −648.000 | −0.0392837 | ||||||||
\(649\) | −2792.49 | −0.168898 | ||||||||
\(650\) | 1654.07 | 0.0998120 | ||||||||
\(651\) | 7462.52 | 0.449277 | ||||||||
\(652\) | 3752.36 | 0.225389 | ||||||||
\(653\) | 21982.0 | 1.31734 | 0.658670 | − | 0.752432i | \(-0.271119\pi\) | ||||
0.658670 | + | 0.752432i | \(0.271119\pi\) | |||||||
\(654\) | −1021.95 | −0.0611029 | ||||||||
\(655\) | −2588.79 | −0.154431 | ||||||||
\(656\) | 1211.41 | 0.0721001 | ||||||||
\(657\) | −2071.63 | −0.123017 | ||||||||
\(658\) | −9902.94 | −0.586713 | ||||||||
\(659\) | 727.025 | 0.0429755 | 0.0214878 | − | 0.999769i | \(-0.493160\pi\) | ||||
0.0214878 | + | 0.999769i | \(0.493160\pi\) | |||||||
\(660\) | −6010.52 | −0.354483 | ||||||||
\(661\) | −12708.7 | −0.747821 | −0.373911 | − | 0.927465i | \(-0.621983\pi\) | ||||
−0.373911 | + | 0.927465i | \(0.621983\pi\) | |||||||
\(662\) | 18471.7 | 1.08447 | ||||||||
\(663\) | 11592.4 | 0.679053 | ||||||||
\(664\) | −3071.77 | −0.179530 | ||||||||
\(665\) | −30224.7 | −1.76250 | ||||||||
\(666\) | 4014.46 | 0.233569 | ||||||||
\(667\) | 5175.21 | 0.300427 | ||||||||
\(668\) | 10290.9 | 0.596056 | ||||||||
\(669\) | 7687.75 | 0.444283 | ||||||||
\(670\) | 7211.32 | 0.415817 | ||||||||
\(671\) | −11568.0 | −0.665541 | ||||||||
\(672\) | 1763.89 | 0.101255 | ||||||||
\(673\) | −5174.21 | −0.296361 | −0.148181 | − | 0.988960i | \(-0.547342\pi\) | ||||
−0.148181 | + | 0.988960i | \(0.547342\pi\) | |||||||
\(674\) | −18681.3 | −1.06762 | ||||||||
\(675\) | −351.245 | −0.0200288 | ||||||||
\(676\) | 7378.35 | 0.419797 | ||||||||
\(677\) | 13165.1 | 0.747377 | 0.373689 | − | 0.927554i | \(-0.378093\pi\) | ||||
0.373689 | + | 0.927554i | \(0.378093\pi\) | |||||||
\(678\) | 7585.77 | 0.429690 | ||||||||
\(679\) | −13719.2 | −0.775397 | ||||||||
\(680\) | 5145.86 | 0.290198 | ||||||||
\(681\) | −6186.53 | −0.348118 | ||||||||
\(682\) | 12815.4 | 0.719543 | ||||||||
\(683\) | 19713.4 | 1.10441 | 0.552206 | − | 0.833708i | \(-0.313786\pi\) | ||||
0.552206 | + | 0.833708i | \(0.313786\pi\) | |||||||
\(684\) | −5595.94 | −0.312816 | ||||||||
\(685\) | −23033.8 | −1.28478 | ||||||||
\(686\) | −12802.9 | −0.712564 | ||||||||
\(687\) | −17511.4 | −0.972492 | ||||||||
\(688\) | −5679.42 | −0.314718 | ||||||||
\(689\) | −4477.26 | −0.247562 | ||||||||
\(690\) | −7663.59 | −0.422823 | ||||||||
\(691\) | −11628.0 | −0.640158 | −0.320079 | − | 0.947391i | \(-0.603709\pi\) | ||||
−0.320079 | + | 0.947391i | \(0.603709\pi\) | |||||||
\(692\) | −9353.93 | −0.513848 | ||||||||
\(693\) | −7826.76 | −0.429025 | ||||||||
\(694\) | 10865.6 | 0.594311 | ||||||||
\(695\) | 8193.74 | 0.447203 | ||||||||
\(696\) | 1029.08 | 0.0560449 | ||||||||
\(697\) | 4602.02 | 0.250092 | ||||||||
\(698\) | −15616.3 | −0.846830 | ||||||||
\(699\) | −11021.6 | −0.596386 | ||||||||
\(700\) | 956.109 | 0.0516250 | ||||||||
\(701\) | −1961.03 | −0.105659 | −0.0528295 | − | 0.998604i | \(-0.516824\pi\) | ||||
−0.0528295 | + | 0.998604i | \(0.516824\pi\) | |||||||
\(702\) | −3432.97 | −0.184571 | ||||||||
\(703\) | 34667.7 | 1.85991 | ||||||||
\(704\) | 3029.14 | 0.162166 | ||||||||
\(705\) | 8555.52 | 0.457049 | ||||||||
\(706\) | 354.825 | 0.0189150 | ||||||||
\(707\) | 15691.5 | 0.834712 | ||||||||
\(708\) | −708.000 | −0.0375823 | ||||||||
\(709\) | 4838.42 | 0.256292 | 0.128146 | − | 0.991755i | \(-0.459097\pi\) | ||||
0.128146 | + | 0.991755i | \(0.459097\pi\) | |||||||
\(710\) | 12317.1 | 0.651059 | ||||||||
\(711\) | −9151.89 | −0.482732 | ||||||||
\(712\) | −185.930 | −0.00978656 | ||||||||
\(713\) | 16340.1 | 0.858261 | ||||||||
\(714\) | 6700.82 | 0.351221 | ||||||||
\(715\) | −31842.5 | −1.66551 | ||||||||
\(716\) | −10472.8 | −0.546632 | ||||||||
\(717\) | −7365.98 | −0.383665 | ||||||||
\(718\) | 18944.9 | 0.984702 | ||||||||
\(719\) | −23993.5 | −1.24452 | −0.622259 | − | 0.782812i | \(-0.713785\pi\) | ||||
−0.622259 | + | 0.782812i | \(0.713785\pi\) | |||||||
\(720\) | −1523.89 | −0.0788779 | ||||||||
\(721\) | −6021.82 | −0.311046 | ||||||||
\(722\) | −34606.9 | −1.78385 | ||||||||
\(723\) | 14646.5 | 0.753400 | ||||||||
\(724\) | −11432.4 | −0.586853 | ||||||||
\(725\) | 557.809 | 0.0285745 | ||||||||
\(726\) | −5454.95 | −0.278860 | ||||||||
\(727\) | −20017.6 | −1.02120 | −0.510600 | − | 0.859819i | \(-0.670577\pi\) | ||||
−0.510600 | + | 0.859819i | \(0.670577\pi\) | |||||||
\(728\) | 9344.72 | 0.475740 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −4871.82 | −0.247006 | ||||||||
\(731\) | −21575.5 | −1.09165 | ||||||||
\(732\) | −2932.92 | −0.148093 | ||||||||
\(733\) | −26043.8 | −1.31235 | −0.656173 | − | 0.754610i | \(-0.727826\pi\) | ||||
−0.656173 | + | 0.754610i | \(0.727826\pi\) | |||||||
\(734\) | 3256.46 | 0.163758 | ||||||||
\(735\) | 171.474 | 0.00860532 | ||||||||
\(736\) | 3862.24 | 0.193430 | ||||||||
\(737\) | 16126.2 | 0.805993 | ||||||||
\(738\) | −1362.84 | −0.0679767 | ||||||||
\(739\) | −17133.2 | −0.852847 | −0.426423 | − | 0.904524i | \(-0.640227\pi\) | ||||
−0.426423 | + | 0.904524i | \(0.640227\pi\) | |||||||
\(740\) | 9440.73 | 0.468984 | ||||||||
\(741\) | −29646.1 | −1.46974 | ||||||||
\(742\) | −2588.01 | −0.128044 | ||||||||
\(743\) | 8594.93 | 0.424384 | 0.212192 | − | 0.977228i | \(-0.431940\pi\) | ||||
0.212192 | + | 0.977228i | \(0.431940\pi\) | |||||||
\(744\) | 3249.19 | 0.160109 | ||||||||
\(745\) | 18444.7 | 0.907060 | ||||||||
\(746\) | −6192.88 | −0.303938 | ||||||||
\(747\) | 3455.74 | 0.169262 | ||||||||
\(748\) | 11507.4 | 0.562501 | ||||||||
\(749\) | 9626.46 | 0.469617 | ||||||||
\(750\) | −8762.95 | −0.426637 | ||||||||
\(751\) | −27804.9 | −1.35102 | −0.675510 | − | 0.737351i | \(-0.736076\pi\) | ||||
−0.675510 | + | 0.737351i | \(0.736076\pi\) | |||||||
\(752\) | −4311.75 | −0.209087 | ||||||||
\(753\) | 20996.3 | 1.01613 | ||||||||
\(754\) | 5451.86 | 0.263322 | ||||||||
\(755\) | −13651.8 | −0.658066 | ||||||||
\(756\) | −1984.38 | −0.0954644 | ||||||||
\(757\) | −4208.30 | −0.202052 | −0.101026 | − | 0.994884i | \(-0.532213\pi\) | ||||
−0.101026 | + | 0.994884i | \(0.532213\pi\) | |||||||
\(758\) | −22395.7 | −1.07315 | ||||||||
\(759\) | −17137.6 | −0.819573 | ||||||||
\(760\) | −13159.9 | −0.628104 | ||||||||
\(761\) | −1448.37 | −0.0689927 | −0.0344964 | − | 0.999405i | \(-0.510983\pi\) | ||||
−0.0344964 | + | 0.999405i | \(0.510983\pi\) | |||||||
\(762\) | 13808.8 | 0.656485 | ||||||||
\(763\) | −3129.52 | −0.148488 | ||||||||
\(764\) | 17845.2 | 0.845047 | ||||||||
\(765\) | −5789.09 | −0.273601 | ||||||||
\(766\) | 12760.1 | 0.601881 | ||||||||
\(767\) | −3750.84 | −0.176577 | ||||||||
\(768\) | 768.000 | 0.0360844 | ||||||||
\(769\) | −14538.5 | −0.681758 | −0.340879 | − | 0.940107i | \(-0.610725\pi\) | ||||
−0.340879 | + | 0.940107i | \(0.610725\pi\) | |||||||
\(770\) | −18406.1 | −0.861440 | ||||||||
\(771\) | 699.614 | 0.0326796 | ||||||||
\(772\) | 14911.4 | 0.695173 | ||||||||
\(773\) | 12173.4 | 0.566423 | 0.283212 | − | 0.959057i | \(-0.408600\pi\) | ||||
0.283212 | + | 0.959057i | \(0.408600\pi\) | |||||||
\(774\) | 6389.35 | 0.296719 | ||||||||
\(775\) | 1761.21 | 0.0816316 | ||||||||
\(776\) | −5973.36 | −0.276329 | ||||||||
\(777\) | 12293.5 | 0.567603 | ||||||||
\(778\) | −20141.0 | −0.928136 | ||||||||
\(779\) | −11769.1 | −0.541298 | ||||||||
\(780\) | −8073.25 | −0.370601 | ||||||||
\(781\) | 27543.9 | 1.26197 | ||||||||
\(782\) | 14672.2 | 0.670943 | ||||||||
\(783\) | −1157.72 | −0.0528396 | ||||||||
\(784\) | −86.4182 | −0.00393669 | ||||||||
\(785\) | 1753.42 | 0.0797226 | ||||||||
\(786\) | −1467.77 | −0.0666076 | ||||||||
\(787\) | −31829.2 | −1.44166 | −0.720832 | − | 0.693110i | \(-0.756240\pi\) | ||||
−0.720832 | + | 0.693110i | \(0.756240\pi\) | |||||||
\(788\) | 12803.0 | 0.578791 | ||||||||
\(789\) | −14086.0 | −0.635582 | ||||||||
\(790\) | −21522.3 | −0.969279 | ||||||||
\(791\) | 23230.0 | 1.04420 | ||||||||
\(792\) | −3407.78 | −0.152892 | ||||||||
\(793\) | −15538.0 | −0.695802 | ||||||||
\(794\) | 3218.15 | 0.143839 | ||||||||
\(795\) | 2235.88 | 0.0997466 | ||||||||
\(796\) | −18659.6 | −0.830869 | ||||||||
\(797\) | 26250.6 | 1.16668 | 0.583339 | − | 0.812229i | \(-0.301746\pi\) | ||||
0.583339 | + | 0.812229i | \(0.301746\pi\) | |||||||
\(798\) | −17136.5 | −0.760183 | ||||||||
\(799\) | −16379.9 | −0.725254 | ||||||||
\(800\) | 416.291 | 0.0183976 | ||||||||
\(801\) | 209.172 | 0.00922686 | ||||||||
\(802\) | −12309.9 | −0.541990 | ||||||||
\(803\) | −10894.6 | −0.478780 | ||||||||
\(804\) | 4088.60 | 0.179346 | ||||||||
\(805\) | −23468.3 | −1.02751 | ||||||||
\(806\) | 17213.5 | 0.752259 | ||||||||
\(807\) | 8878.15 | 0.387268 | ||||||||
\(808\) | 6832.12 | 0.297467 | ||||||||
\(809\) | 20265.6 | 0.880716 | 0.440358 | − | 0.897822i | \(-0.354851\pi\) | ||||
0.440358 | + | 0.897822i | \(0.354851\pi\) | |||||||
\(810\) | 1714.38 | 0.0743668 | ||||||||
\(811\) | −6139.57 | −0.265832 | −0.132916 | − | 0.991127i | \(-0.542434\pi\) | ||||
−0.132916 | + | 0.991127i | \(0.542434\pi\) | |||||||
\(812\) | 3151.37 | 0.136196 | ||||||||
\(813\) | −8893.17 | −0.383637 | ||||||||
\(814\) | 21111.7 | 0.909048 | ||||||||
\(815\) | −9927.41 | −0.426677 | ||||||||
\(816\) | 2917.55 | 0.125165 | ||||||||
\(817\) | 55176.5 | 2.36277 | ||||||||
\(818\) | −11828.2 | −0.505581 | ||||||||
\(819\) | −10512.8 | −0.448532 | ||||||||
\(820\) | −3204.97 | −0.136491 | ||||||||
\(821\) | −44128.0 | −1.87585 | −0.937927 | − | 0.346832i | \(-0.887257\pi\) | ||||
−0.937927 | + | 0.346832i | \(0.887257\pi\) | |||||||
\(822\) | −13059.4 | −0.554137 | ||||||||
\(823\) | 14143.6 | 0.599044 | 0.299522 | − | 0.954089i | \(-0.403173\pi\) | ||||
0.299522 | + | 0.954089i | \(0.403173\pi\) | |||||||
\(824\) | −2621.91 | −0.110848 | ||||||||
\(825\) | −1847.17 | −0.0779519 | ||||||||
\(826\) | −2168.12 | −0.0913298 | ||||||||
\(827\) | −32831.8 | −1.38050 | −0.690251 | − | 0.723570i | \(-0.742500\pi\) | ||||
−0.690251 | + | 0.723570i | \(0.742500\pi\) | |||||||
\(828\) | −4345.02 | −0.182367 | ||||||||
\(829\) | 1172.52 | 0.0491234 | 0.0245617 | − | 0.999698i | \(-0.492181\pi\) | ||||
0.0245617 | + | 0.999698i | \(0.492181\pi\) | |||||||
\(830\) | 8126.80 | 0.339862 | ||||||||
\(831\) | 17502.1 | 0.730617 | ||||||||
\(832\) | 4068.70 | 0.169540 | ||||||||
\(833\) | −328.293 | −0.0136551 | ||||||||
\(834\) | 4645.60 | 0.192882 | ||||||||
\(835\) | −27225.9 | −1.12837 | ||||||||
\(836\) | −29428.6 | −1.21748 | ||||||||
\(837\) | −3655.34 | −0.150952 | ||||||||
\(838\) | 30824.2 | 1.27065 | ||||||||
\(839\) | −696.702 | −0.0286684 | −0.0143342 | − | 0.999897i | \(-0.504563\pi\) | ||||
−0.0143342 | + | 0.999897i | \(0.504563\pi\) | |||||||
\(840\) | −4666.63 | −0.191683 | ||||||||
\(841\) | −22550.4 | −0.924615 | ||||||||
\(842\) | 14993.4 | 0.613664 | ||||||||
\(843\) | 19559.5 | 0.799130 | ||||||||
\(844\) | −17363.1 | −0.708131 | ||||||||
\(845\) | −19520.5 | −0.794704 | ||||||||
\(846\) | 4850.72 | 0.197129 | ||||||||
\(847\) | −16704.7 | −0.677664 | ||||||||
\(848\) | −1126.82 | −0.0456313 | ||||||||
\(849\) | 16248.2 | 0.656815 | ||||||||
\(850\) | 1581.44 | 0.0638153 | ||||||||
\(851\) | 26918.1 | 1.08430 | ||||||||
\(852\) | 6983.41 | 0.280807 | ||||||||
\(853\) | 23022.2 | 0.924110 | 0.462055 | − | 0.886851i | \(-0.347112\pi\) | ||||
0.462055 | + | 0.886851i | \(0.347112\pi\) | |||||||
\(854\) | −8981.52 | −0.359884 | ||||||||
\(855\) | 14804.9 | 0.592182 | ||||||||
\(856\) | 4191.37 | 0.167358 | ||||||||
\(857\) | 40458.2 | 1.61263 | 0.806315 | − | 0.591486i | \(-0.201458\pi\) | ||||
0.806315 | + | 0.591486i | \(0.201458\pi\) | |||||||
\(858\) | −18053.7 | −0.718349 | ||||||||
\(859\) | 25380.9 | 1.00813 | 0.504066 | − | 0.863665i | \(-0.331837\pi\) | ||||
0.504066 | + | 0.863665i | \(0.331837\pi\) | |||||||
\(860\) | 15025.7 | 0.595782 | ||||||||
\(861\) | −4173.44 | −0.165192 | ||||||||
\(862\) | 11034.3 | 0.435996 | ||||||||
\(863\) | 21524.6 | 0.849023 | 0.424512 | − | 0.905422i | \(-0.360446\pi\) | ||||
0.424512 | + | 0.905422i | \(0.360446\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | 24747.2 | 0.972750 | ||||||||
\(866\) | 19949.0 | 0.782786 | ||||||||
\(867\) | −3655.57 | −0.143195 | ||||||||
\(868\) | 9950.03 | 0.389085 | ||||||||
\(869\) | −48129.1 | −1.87879 | ||||||||
\(870\) | −2722.58 | −0.106097 | ||||||||
\(871\) | 21660.5 | 0.842640 | ||||||||
\(872\) | −1362.60 | −0.0529167 | ||||||||
\(873\) | 6720.03 | 0.260525 | ||||||||
\(874\) | −37522.4 | −1.45219 | ||||||||
\(875\) | −26834.9 | −1.03678 | ||||||||
\(876\) | −2762.18 | −0.106536 | ||||||||
\(877\) | −43051.6 | −1.65764 | −0.828820 | − | 0.559515i | \(-0.810987\pi\) | ||||
−0.828820 | + | 0.559515i | \(0.810987\pi\) | |||||||
\(878\) | 15986.3 | 0.614476 | ||||||||
\(879\) | −24289.9 | −0.932056 | ||||||||
\(880\) | −8014.02 | −0.306992 | ||||||||
\(881\) | −40233.2 | −1.53858 | −0.769292 | − | 0.638898i | \(-0.779391\pi\) | ||||
−0.769292 | + | 0.638898i | \(0.779391\pi\) | |||||||
\(882\) | 97.2205 | 0.00371155 | ||||||||
\(883\) | 42342.7 | 1.61375 | 0.806877 | − | 0.590720i | \(-0.201156\pi\) | ||||
0.806877 | + | 0.590720i | \(0.201156\pi\) | |||||||
\(884\) | 15456.5 | 0.588077 | ||||||||
\(885\) | 1873.12 | 0.0711459 | ||||||||
\(886\) | −36442.7 | −1.38185 | ||||||||
\(887\) | 2936.80 | 0.111170 | 0.0555852 | − | 0.998454i | \(-0.482298\pi\) | ||||
0.0555852 | + | 0.998454i | \(0.482298\pi\) | |||||||
\(888\) | 5352.61 | 0.202277 | ||||||||
\(889\) | 42287.0 | 1.59534 | ||||||||
\(890\) | 491.905 | 0.0185266 | ||||||||
\(891\) | 3833.75 | 0.144148 | ||||||||
\(892\) | 10250.3 | 0.384761 | ||||||||
\(893\) | 41889.4 | 1.56974 | ||||||||
\(894\) | 10457.6 | 0.391223 | ||||||||
\(895\) | 27707.4 | 1.03481 | ||||||||
\(896\) | 2351.85 | 0.0876897 | ||||||||
\(897\) | −23019.0 | −0.856837 | ||||||||
\(898\) | 22026.8 | 0.818533 | ||||||||
\(899\) | 5805.01 | 0.215359 | ||||||||
\(900\) | −468.327 | −0.0173455 | ||||||||
\(901\) | −4280.68 | −0.158280 | ||||||||
\(902\) | −7167.06 | −0.264564 | ||||||||
\(903\) | 19566.2 | 0.721064 | ||||||||
\(904\) | 10114.4 | 0.372122 | ||||||||
\(905\) | 30246.0 | 1.11095 | ||||||||
\(906\) | −7740.15 | −0.283829 | ||||||||
\(907\) | −10543.4 | −0.385985 | −0.192993 | − | 0.981200i | \(-0.561819\pi\) | ||||
−0.192993 | + | 0.981200i | \(0.561819\pi\) | |||||||
\(908\) | −8248.70 | −0.301479 | ||||||||
\(909\) | −7686.13 | −0.280454 | ||||||||
\(910\) | −24722.8 | −0.900608 | ||||||||
\(911\) | 14443.2 | 0.525273 | 0.262637 | − | 0.964895i | \(-0.415408\pi\) | ||||
0.262637 | + | 0.964895i | \(0.415408\pi\) | |||||||
\(912\) | −7461.25 | −0.270907 | ||||||||
\(913\) | 18173.5 | 0.658766 | ||||||||
\(914\) | −11009.5 | −0.398428 | ||||||||
\(915\) | 7759.47 | 0.280350 | ||||||||
\(916\) | −23348.6 | −0.842203 | ||||||||
\(917\) | −4494.76 | −0.161865 | ||||||||
\(918\) | −3282.24 | −0.118007 | ||||||||
\(919\) | 32863.3 | 1.17961 | 0.589804 | − | 0.807546i | \(-0.299205\pi\) | ||||
0.589804 | + | 0.807546i | \(0.299205\pi\) | |||||||
\(920\) | −10218.1 | −0.366175 | ||||||||
\(921\) | 24756.5 | 0.885728 | ||||||||
\(922\) | −35246.9 | −1.25900 | ||||||||
\(923\) | 36996.6 | 1.31935 | ||||||||
\(924\) | −10435.7 | −0.371546 | ||||||||
\(925\) | 2901.36 | 0.103131 | ||||||||
\(926\) | −37640.1 | −1.33578 | ||||||||
\(927\) | 2949.65 | 0.104508 | ||||||||
\(928\) | 1372.11 | 0.0485363 | ||||||||
\(929\) | 25233.0 | 0.891140 | 0.445570 | − | 0.895247i | \(-0.353001\pi\) | ||||
0.445570 | + | 0.895247i | \(0.353001\pi\) | |||||||
\(930\) | −8596.20 | −0.303097 | ||||||||
\(931\) | 839.568 | 0.0295550 | ||||||||
\(932\) | −14695.4 | −0.516485 | ||||||||
\(933\) | −11585.1 | −0.406516 | ||||||||
\(934\) | −5117.67 | −0.179288 | ||||||||
\(935\) | −30444.4 | −1.06485 | ||||||||
\(936\) | −4577.29 | −0.159843 | ||||||||
\(937\) | −35290.6 | −1.23041 | −0.615205 | − | 0.788367i | \(-0.710927\pi\) | ||||
−0.615205 | + | 0.788367i | \(0.710927\pi\) | |||||||
\(938\) | 12520.6 | 0.435832 | ||||||||
\(939\) | 6958.89 | 0.241847 | ||||||||
\(940\) | 11407.4 | 0.395816 | ||||||||
\(941\) | 27389.9 | 0.948868 | 0.474434 | − | 0.880291i | \(-0.342653\pi\) | ||||
0.474434 | + | 0.880291i | \(0.342653\pi\) | |||||||
\(942\) | 994.136 | 0.0343850 | ||||||||
\(943\) | −9138.22 | −0.315569 | ||||||||
\(944\) | −944.000 | −0.0325472 | ||||||||
\(945\) | 5249.96 | 0.180721 | ||||||||
\(946\) | 33601.1 | 1.15483 | ||||||||
\(947\) | 57562.9 | 1.97523 | 0.987615 | − | 0.156896i | \(-0.0501487\pi\) | ||||
0.987615 | + | 0.156896i | \(0.0501487\pi\) | |||||||
\(948\) | −12202.5 | −0.418058 | ||||||||
\(949\) | −14633.4 | −0.500549 | ||||||||
\(950\) | −4044.34 | −0.138122 | ||||||||
\(951\) | 1360.31 | 0.0463838 | ||||||||
\(952\) | 8934.43 | 0.304167 | ||||||||
\(953\) | 31567.6 | 1.07301 | 0.536504 | − | 0.843898i | \(-0.319745\pi\) | ||||
0.536504 | + | 0.843898i | \(0.319745\pi\) | |||||||
\(954\) | 1267.68 | 0.0430216 | ||||||||
\(955\) | −47212.0 | −1.59973 | ||||||||
\(956\) | −9821.31 | −0.332263 | ||||||||
\(957\) | −6088.34 | −0.205651 | ||||||||
\(958\) | −16444.7 | −0.554596 | ||||||||
\(959\) | −39992.1 | −1.34662 | ||||||||
\(960\) | −2031.85 | −0.0683102 | ||||||||
\(961\) | −11462.5 | −0.384762 | ||||||||
\(962\) | 28357.0 | 0.950381 | ||||||||
\(963\) | −4715.29 | −0.157786 | ||||||||
\(964\) | 19528.6 | 0.652463 | ||||||||
\(965\) | −39450.3 | −1.31601 | ||||||||
\(966\) | −13305.8 | −0.443175 | ||||||||
\(967\) | 4311.95 | 0.143395 | 0.0716975 | − | 0.997426i | \(-0.477158\pi\) | ||||
0.0716975 | + | 0.997426i | \(0.477158\pi\) | |||||||
\(968\) | −7273.26 | −0.241499 | ||||||||
\(969\) | −28344.5 | −0.939686 | ||||||||
\(970\) | 15803.4 | 0.523109 | ||||||||
\(971\) | 50749.1 | 1.67726 | 0.838628 | − | 0.544705i | \(-0.183358\pi\) | ||||
0.838628 | + | 0.544705i | \(0.183358\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 14226.3 | 0.468729 | ||||||||
\(974\) | 26029.4 | 0.856300 | ||||||||
\(975\) | −2481.10 | −0.0814962 | ||||||||
\(976\) | −3910.56 | −0.128252 | ||||||||
\(977\) | −52342.5 | −1.71401 | −0.857003 | − | 0.515312i | \(-0.827676\pi\) | ||||
−0.857003 | + | 0.515312i | \(0.827676\pi\) | |||||||
\(978\) | −5628.54 | −0.184030 | ||||||||
\(979\) | 1100.02 | 0.0359108 | ||||||||
\(980\) | 228.632 | 0.00745242 | ||||||||
\(981\) | 1532.92 | 0.0498903 | ||||||||
\(982\) | −4752.49 | −0.154438 | ||||||||
\(983\) | 50740.8 | 1.64637 | 0.823184 | − | 0.567775i | \(-0.192196\pi\) | ||||
0.823184 | + | 0.567775i | \(0.192196\pi\) | |||||||
\(984\) | −1817.12 | −0.0588695 | ||||||||
\(985\) | −33872.1 | −1.09569 | ||||||||
\(986\) | 5212.49 | 0.168356 | ||||||||
\(987\) | 14854.4 | 0.479049 | ||||||||
\(988\) | −39528.2 | −1.27283 | ||||||||
\(989\) | 42842.4 | 1.37746 | ||||||||
\(990\) | 9015.78 | 0.289435 | ||||||||
\(991\) | −14693.4 | −0.470989 | −0.235494 | − | 0.971876i | \(-0.575671\pi\) | ||||
−0.235494 | + | 0.971876i | \(0.575671\pi\) | |||||||
\(992\) | 4332.25 | 0.138658 | ||||||||
\(993\) | −27707.5 | −0.885469 | ||||||||
\(994\) | 21385.4 | 0.682397 | ||||||||
\(995\) | 49366.6 | 1.57289 | ||||||||
\(996\) | 4607.65 | 0.146585 | ||||||||
\(997\) | 46107.5 | 1.46463 | 0.732317 | − | 0.680964i | \(-0.238439\pi\) | ||||
0.732317 | + | 0.680964i | \(0.238439\pi\) | |||||||
\(998\) | 44282.8 | 1.40456 | ||||||||
\(999\) | −6021.69 | −0.190708 |
(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 | 354.4.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 1062.4.a.h.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.4.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1062.4.a.h.1.2 | 2 | 3.2 | odd | 2 |