Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34509 | −0.829115 | −0.414557 | − | 0.910023i | \(-0.636064\pi\) | ||||
−0.414557 | + | 0.910023i | \(0.636064\pi\) | |||||||
\(3\) | 2.42890 | 0.467442 | 0.233721 | − | 0.972304i | \(-0.424910\pi\) | ||||
0.233721 | + | 0.972304i | \(0.424910\pi\) | |||||||
\(4\) | −2.50055 | −0.312569 | ||||||||
\(5\) | −18.7081 | −1.67330 | −0.836652 | − | 0.547735i | \(-0.815490\pi\) | ||||
−0.836652 | + | 0.547735i | \(0.815490\pi\) | |||||||
\(6\) | −5.69599 | −0.387563 | ||||||||
\(7\) | −0.512587 | −0.0276771 | −0.0138386 | − | 0.999904i | \(-0.504405\pi\) | ||||
−0.0138386 | + | 0.999904i | \(0.504405\pi\) | |||||||
\(8\) | 24.6247 | 1.08827 | ||||||||
\(9\) | −21.1004 | −0.781498 | ||||||||
\(10\) | 43.8722 | 1.38736 | ||||||||
\(11\) | 5.04244 | 0.138214 | 0.0691070 | − | 0.997609i | \(-0.477985\pi\) | ||||
0.0691070 | + | 0.997609i | \(0.477985\pi\) | |||||||
\(12\) | −6.07358 | −0.146108 | ||||||||
\(13\) | −48.6308 | −1.03752 | −0.518760 | − | 0.854920i | \(-0.673606\pi\) | ||||
−0.518760 | + | 0.854920i | \(0.673606\pi\) | |||||||
\(14\) | 1.20206 | 0.0229475 | ||||||||
\(15\) | −45.4401 | −0.782173 | ||||||||
\(16\) | −37.7429 | −0.589732 | ||||||||
\(17\) | −6.35958 | −0.0907308 | −0.0453654 | − | 0.998970i | \(-0.514445\pi\) | ||||
−0.0453654 | + | 0.998970i | \(0.514445\pi\) | |||||||
\(18\) | 49.4825 | 0.647951 | ||||||||
\(19\) | −123.762 | −1.49436 | −0.747182 | − | 0.664620i | \(-0.768594\pi\) | ||||
−0.747182 | + | 0.664620i | \(0.768594\pi\) | |||||||
\(20\) | 46.7805 | 0.523022 | ||||||||
\(21\) | −1.24502 | −0.0129375 | ||||||||
\(22\) | −11.8250 | −0.114595 | ||||||||
\(23\) | 141.010 | 1.27837 | 0.639185 | − | 0.769053i | \(-0.279272\pi\) | ||||
0.639185 | + | 0.769053i | \(0.279272\pi\) | |||||||
\(24\) | 59.8111 | 0.508703 | ||||||||
\(25\) | 224.993 | 1.79995 | ||||||||
\(26\) | 114.044 | 0.860224 | ||||||||
\(27\) | −116.831 | −0.832747 | ||||||||
\(28\) | 1.28175 | 0.00865100 | ||||||||
\(29\) | 206.672 | 1.32338 | 0.661690 | − | 0.749777i | \(-0.269839\pi\) | ||||
0.661690 | + | 0.749777i | \(0.269839\pi\) | |||||||
\(30\) | 106.561 | 0.648511 | ||||||||
\(31\) | 164.801 | 0.954809 | 0.477405 | − | 0.878684i | \(-0.341578\pi\) | ||||
0.477405 | + | 0.878684i | \(0.341578\pi\) | |||||||
\(32\) | −108.487 | −0.599314 | ||||||||
\(33\) | 12.2476 | 0.0646071 | ||||||||
\(34\) | 14.9138 | 0.0752263 | ||||||||
\(35\) | 9.58954 | 0.0463122 | ||||||||
\(36\) | 52.7627 | 0.244272 | ||||||||
\(37\) | 365.186 | 1.62260 | 0.811300 | − | 0.584630i | \(-0.198760\pi\) | ||||
0.811300 | + | 0.584630i | \(0.198760\pi\) | |||||||
\(38\) | 290.233 | 1.23900 | ||||||||
\(39\) | −118.119 | −0.484981 | ||||||||
\(40\) | −460.682 | −1.82101 | ||||||||
\(41\) | −175.812 | −0.669689 | −0.334844 | − | 0.942273i | \(-0.608684\pi\) | ||||
−0.334844 | + | 0.942273i | \(0.608684\pi\) | |||||||
\(42\) | 2.91969 | 0.0107266 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −12.6089 | −0.0432013 | ||||||||
\(45\) | 394.749 | 1.30768 | ||||||||
\(46\) | −330.680 | −1.05992 | ||||||||
\(47\) | 219.602 | 0.681537 | 0.340768 | − | 0.940147i | \(-0.389313\pi\) | ||||
0.340768 | + | 0.940147i | \(0.389313\pi\) | |||||||
\(48\) | −91.6737 | −0.275666 | ||||||||
\(49\) | −342.737 | −0.999234 | ||||||||
\(50\) | −527.630 | −1.49236 | ||||||||
\(51\) | −15.4468 | −0.0424114 | ||||||||
\(52\) | 121.604 | 0.324296 | ||||||||
\(53\) | 34.4084 | 0.0891765 | 0.0445883 | − | 0.999005i | \(-0.485802\pi\) | ||||
0.0445883 | + | 0.999005i | \(0.485802\pi\) | |||||||
\(54\) | 273.980 | 0.690443 | ||||||||
\(55\) | −94.3346 | −0.231274 | ||||||||
\(56\) | −12.6223 | −0.0301202 | ||||||||
\(57\) | −300.605 | −0.698529 | ||||||||
\(58\) | −484.665 | −1.09723 | ||||||||
\(59\) | −771.285 | −1.70191 | −0.850956 | − | 0.525238i | \(-0.823976\pi\) | ||||
−0.850956 | + | 0.525238i | \(0.823976\pi\) | |||||||
\(60\) | 113.625 | 0.244483 | ||||||||
\(61\) | 432.289 | 0.907360 | 0.453680 | − | 0.891165i | \(-0.350111\pi\) | ||||
0.453680 | + | 0.891165i | \(0.350111\pi\) | |||||||
\(62\) | −386.473 | −0.791647 | ||||||||
\(63\) | 10.8158 | 0.0216296 | ||||||||
\(64\) | 556.356 | 1.08663 | ||||||||
\(65\) | 909.791 | 1.73609 | ||||||||
\(66\) | −28.7217 | −0.0535667 | ||||||||
\(67\) | −644.829 | −1.17580 | −0.587899 | − | 0.808935i | \(-0.700045\pi\) | ||||
−0.587899 | + | 0.808935i | \(0.700045\pi\) | |||||||
\(68\) | 15.9024 | 0.0283596 | ||||||||
\(69\) | 342.498 | 0.597564 | ||||||||
\(70\) | −22.4883 | −0.0383982 | ||||||||
\(71\) | 919.149 | 1.53638 | 0.768190 | − | 0.640222i | \(-0.221158\pi\) | ||||
0.768190 | + | 0.640222i | \(0.221158\pi\) | |||||||
\(72\) | −519.593 | −0.850481 | ||||||||
\(73\) | −98.7029 | −0.158251 | −0.0791253 | − | 0.996865i | \(-0.525213\pi\) | ||||
−0.0791253 | + | 0.996865i | \(0.525213\pi\) | |||||||
\(74\) | −856.394 | −1.34532 | ||||||||
\(75\) | 546.486 | 0.841371 | ||||||||
\(76\) | 309.472 | 0.467091 | ||||||||
\(77\) | −2.58469 | −0.00382536 | ||||||||
\(78\) | 277.001 | 0.402105 | ||||||||
\(79\) | 411.930 | 0.586655 | 0.293327 | − | 0.956012i | \(-0.405237\pi\) | ||||
0.293327 | + | 0.956012i | \(0.405237\pi\) | |||||||
\(80\) | 706.098 | 0.986802 | ||||||||
\(81\) | 285.940 | 0.392237 | ||||||||
\(82\) | 412.295 | 0.555249 | ||||||||
\(83\) | 271.229 | 0.358689 | 0.179345 | − | 0.983786i | \(-0.442602\pi\) | ||||
0.179345 | + | 0.983786i | \(0.442602\pi\) | |||||||
\(84\) | 3.11324 | 0.00404384 | ||||||||
\(85\) | 118.976 | 0.151820 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 501.986 | 0.618604 | ||||||||
\(88\) | 124.169 | 0.150414 | ||||||||
\(89\) | −115.517 | −0.137582 | −0.0687908 | − | 0.997631i | \(-0.521914\pi\) | ||||
−0.0687908 | + | 0.997631i | \(0.521914\pi\) | |||||||
\(90\) | −925.723 | −1.08422 | ||||||||
\(91\) | 24.9276 | 0.0287156 | ||||||||
\(92\) | −352.601 | −0.399578 | ||||||||
\(93\) | 400.285 | 0.446318 | ||||||||
\(94\) | −514.986 | −0.565072 | ||||||||
\(95\) | 2315.35 | 2.50053 | ||||||||
\(96\) | −263.505 | −0.280145 | ||||||||
\(97\) | 623.381 | 0.652523 | 0.326261 | − | 0.945280i | \(-0.394211\pi\) | ||||
0.326261 | + | 0.945280i | \(0.394211\pi\) | |||||||
\(98\) | 803.750 | 0.828480 | ||||||||
\(99\) | −106.398 | −0.108014 | ||||||||
\(100\) | −562.606 | −0.562606 | ||||||||
\(101\) | 134.852 | 0.132854 | 0.0664270 | − | 0.997791i | \(-0.478840\pi\) | ||||
0.0664270 | + | 0.997791i | \(0.478840\pi\) | |||||||
\(102\) | 36.2241 | 0.0351639 | ||||||||
\(103\) | −246.042 | −0.235371 | −0.117686 | − | 0.993051i | \(-0.537547\pi\) | ||||
−0.117686 | + | 0.993051i | \(0.537547\pi\) | |||||||
\(104\) | −1197.52 | −1.12910 | ||||||||
\(105\) | 23.2920 | 0.0216483 | ||||||||
\(106\) | −80.6908 | −0.0739376 | ||||||||
\(107\) | −615.063 | −0.555704 | −0.277852 | − | 0.960624i | \(-0.589623\pi\) | ||||
−0.277852 | + | 0.960624i | \(0.589623\pi\) | |||||||
\(108\) | 292.142 | 0.260291 | ||||||||
\(109\) | 1860.95 | 1.63529 | 0.817646 | − | 0.575721i | \(-0.195279\pi\) | ||||
0.817646 | + | 0.575721i | \(0.195279\pi\) | |||||||
\(110\) | 221.223 | 0.191753 | ||||||||
\(111\) | 887.001 | 0.758472 | ||||||||
\(112\) | 19.3465 | 0.0163221 | ||||||||
\(113\) | 2228.96 | 1.85560 | 0.927802 | − | 0.373072i | \(-0.121696\pi\) | ||||
0.927802 | + | 0.373072i | \(0.121696\pi\) | |||||||
\(114\) | 704.947 | 0.579161 | ||||||||
\(115\) | −2638.02 | −2.13910 | ||||||||
\(116\) | −516.793 | −0.413647 | ||||||||
\(117\) | 1026.13 | 0.810820 | ||||||||
\(118\) | 1808.73 | 1.41108 | ||||||||
\(119\) | 3.25984 | 0.00251117 | ||||||||
\(120\) | −1118.95 | −0.851215 | ||||||||
\(121\) | −1305.57 | −0.980897 | ||||||||
\(122\) | −1013.76 | −0.752306 | ||||||||
\(123\) | −427.030 | −0.313041 | ||||||||
\(124\) | −412.092 | −0.298443 | ||||||||
\(125\) | −1870.68 | −1.33855 | ||||||||
\(126\) | −25.3641 | −0.0179334 | ||||||||
\(127\) | 453.295 | 0.316720 | 0.158360 | − | 0.987381i | \(-0.449379\pi\) | ||||
0.158360 | + | 0.987381i | \(0.449379\pi\) | |||||||
\(128\) | −436.806 | −0.301629 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2133.54 | −1.43942 | ||||||||
\(131\) | 995.763 | 0.664124 | 0.332062 | − | 0.943258i | \(-0.392256\pi\) | ||||
0.332062 | + | 0.943258i | \(0.392256\pi\) | |||||||
\(132\) | −30.6257 | −0.0201941 | ||||||||
\(133\) | 63.4388 | 0.0413597 | ||||||||
\(134\) | 1512.18 | 0.974871 | ||||||||
\(135\) | 2185.69 | 1.39344 | ||||||||
\(136\) | −156.603 | −0.0987397 | ||||||||
\(137\) | 2491.26 | 1.55359 | 0.776797 | − | 0.629751i | \(-0.216843\pi\) | ||||
0.776797 | + | 0.629751i | \(0.216843\pi\) | |||||||
\(138\) | −803.189 | −0.495449 | ||||||||
\(139\) | −1951.81 | −1.19101 | −0.595506 | − | 0.803351i | \(-0.703048\pi\) | ||||
−0.595506 | + | 0.803351i | \(0.703048\pi\) | |||||||
\(140\) | −23.9791 | −0.0144757 | ||||||||
\(141\) | 533.391 | 0.318579 | ||||||||
\(142\) | −2155.49 | −1.27384 | ||||||||
\(143\) | −245.218 | −0.143400 | ||||||||
\(144\) | 796.391 | 0.460875 | ||||||||
\(145\) | −3866.44 | −2.21442 | ||||||||
\(146\) | 231.467 | 0.131208 | ||||||||
\(147\) | −832.475 | −0.467084 | ||||||||
\(148\) | −913.165 | −0.507174 | ||||||||
\(149\) | 2006.42 | 1.10317 | 0.551585 | − | 0.834119i | \(-0.314023\pi\) | ||||
0.551585 | + | 0.834119i | \(0.314023\pi\) | |||||||
\(150\) | −1281.56 | −0.697593 | ||||||||
\(151\) | −3455.23 | −1.86213 | −0.931067 | − | 0.364847i | \(-0.881121\pi\) | ||||
−0.931067 | + | 0.364847i | \(0.881121\pi\) | |||||||
\(152\) | −3047.60 | −1.62627 | ||||||||
\(153\) | 134.190 | 0.0709059 | ||||||||
\(154\) | 6.06134 | 0.00317167 | ||||||||
\(155\) | −3083.11 | −1.59769 | ||||||||
\(156\) | 295.363 | 0.151590 | ||||||||
\(157\) | 380.367 | 0.193354 | 0.0966771 | − | 0.995316i | \(-0.469179\pi\) | ||||
0.0966771 | + | 0.995316i | \(0.469179\pi\) | |||||||
\(158\) | −966.013 | −0.486404 | ||||||||
\(159\) | 83.5746 | 0.0416849 | ||||||||
\(160\) | 2029.59 | 1.00283 | ||||||||
\(161\) | −72.2797 | −0.0353816 | ||||||||
\(162\) | −670.556 | −0.325209 | ||||||||
\(163\) | 1067.78 | 0.513096 | 0.256548 | − | 0.966532i | \(-0.417415\pi\) | ||||
0.256548 | + | 0.966532i | \(0.417415\pi\) | |||||||
\(164\) | 439.627 | 0.209324 | ||||||||
\(165\) | −229.129 | −0.108107 | ||||||||
\(166\) | −636.056 | −0.297395 | ||||||||
\(167\) | −4232.47 | −1.96119 | −0.980593 | − | 0.196055i | \(-0.937187\pi\) | ||||
−0.980593 | + | 0.196055i | \(0.937187\pi\) | |||||||
\(168\) | −30.6584 | −0.0140794 | ||||||||
\(169\) | 167.959 | 0.0764490 | ||||||||
\(170\) | −279.009 | −0.125876 | ||||||||
\(171\) | 2611.43 | 1.16784 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3617.39 | −1.58974 | −0.794869 | − | 0.606781i | \(-0.792461\pi\) | ||||
−0.794869 | + | 0.606781i | \(0.792461\pi\) | |||||||
\(174\) | −1177.20 | −0.512894 | ||||||||
\(175\) | −115.329 | −0.0498173 | ||||||||
\(176\) | −190.316 | −0.0815093 | ||||||||
\(177\) | −1873.37 | −0.795545 | ||||||||
\(178\) | 270.897 | 0.114071 | ||||||||
\(179\) | −643.127 | −0.268545 | −0.134272 | − | 0.990944i | \(-0.542870\pi\) | ||||
−0.134272 | + | 0.990944i | \(0.542870\pi\) | |||||||
\(180\) | −987.090 | −0.408741 | ||||||||
\(181\) | 3174.93 | 1.30382 | 0.651909 | − | 0.758297i | \(-0.273968\pi\) | ||||
0.651909 | + | 0.758297i | \(0.273968\pi\) | |||||||
\(182\) | −58.4574 | −0.0238085 | ||||||||
\(183\) | 1049.99 | 0.424138 | ||||||||
\(184\) | 3472.32 | 1.39121 | ||||||||
\(185\) | −6831.94 | −2.71510 | ||||||||
\(186\) | −938.704 | −0.370049 | ||||||||
\(187\) | −32.0678 | −0.0125403 | ||||||||
\(188\) | −549.125 | −0.213027 | ||||||||
\(189\) | 59.8862 | 0.0230480 | ||||||||
\(190\) | −5429.71 | −2.07322 | ||||||||
\(191\) | 464.296 | 0.175892 | 0.0879458 | − | 0.996125i | \(-0.471970\pi\) | ||||
0.0879458 | + | 0.996125i | \(0.471970\pi\) | |||||||
\(192\) | 1351.33 | 0.507938 | ||||||||
\(193\) | −3898.46 | −1.45397 | −0.726987 | − | 0.686651i | \(-0.759080\pi\) | ||||
−0.726987 | + | 0.686651i | \(0.759080\pi\) | |||||||
\(194\) | −1461.88 | −0.541017 | ||||||||
\(195\) | 2209.79 | 0.811521 | ||||||||
\(196\) | 857.031 | 0.312329 | ||||||||
\(197\) | 2153.97 | 0.779005 | 0.389503 | − | 0.921025i | \(-0.372647\pi\) | ||||
0.389503 | + | 0.921025i | \(0.372647\pi\) | |||||||
\(198\) | 249.512 | 0.0895560 | ||||||||
\(199\) | −3038.98 | −1.08255 | −0.541275 | − | 0.840845i | \(-0.682058\pi\) | ||||
−0.541275 | + | 0.840845i | \(0.682058\pi\) | |||||||
\(200\) | 5540.40 | 1.95883 | ||||||||
\(201\) | −1566.23 | −0.549617 | ||||||||
\(202\) | −316.240 | −0.110151 | ||||||||
\(203\) | −105.937 | −0.0366274 | ||||||||
\(204\) | 38.6254 | 0.0132565 | ||||||||
\(205\) | 3289.11 | 1.12059 | ||||||||
\(206\) | 576.990 | 0.195150 | ||||||||
\(207\) | −2975.36 | −0.999043 | ||||||||
\(208\) | 1835.47 | 0.611860 | ||||||||
\(209\) | −624.062 | −0.206542 | ||||||||
\(210\) | −54.6220 | −0.0179489 | ||||||||
\(211\) | 969.498 | 0.316318 | 0.158159 | − | 0.987414i | \(-0.449444\pi\) | ||||
0.158159 | + | 0.987414i | \(0.449444\pi\) | |||||||
\(212\) | −86.0398 | −0.0278738 | ||||||||
\(213\) | 2232.52 | 0.718169 | ||||||||
\(214\) | 1442.38 | 0.460743 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2876.94 | −0.906254 | ||||||||
\(217\) | −84.4748 | −0.0264264 | ||||||||
\(218\) | −4364.10 | −1.35584 | ||||||||
\(219\) | −239.740 | −0.0739730 | ||||||||
\(220\) | 235.888 | 0.0722890 | ||||||||
\(221\) | 309.272 | 0.0941351 | ||||||||
\(222\) | −2080.10 | −0.628860 | ||||||||
\(223\) | 446.780 | 0.134164 | 0.0670821 | − | 0.997747i | \(-0.478631\pi\) | ||||
0.0670821 | + | 0.997747i | \(0.478631\pi\) | |||||||
\(224\) | 55.6093 | 0.0165873 | ||||||||
\(225\) | −4747.46 | −1.40665 | ||||||||
\(226\) | −5227.13 | −1.53851 | ||||||||
\(227\) | −552.010 | −0.161402 | −0.0807009 | − | 0.996738i | \(-0.525716\pi\) | ||||
−0.0807009 | + | 0.996738i | \(0.525716\pi\) | |||||||
\(228\) | 751.678 | 0.218338 | ||||||||
\(229\) | −393.795 | −0.113636 | −0.0568181 | − | 0.998385i | \(-0.518096\pi\) | ||||
−0.0568181 | + | 0.998385i | \(0.518096\pi\) | |||||||
\(230\) | 6186.40 | 1.77356 | ||||||||
\(231\) | −6.27796 | −0.00178814 | ||||||||
\(232\) | 5089.25 | 1.44020 | ||||||||
\(233\) | 335.082 | 0.0942143 | 0.0471071 | − | 0.998890i | \(-0.485000\pi\) | ||||
0.0471071 | + | 0.998890i | \(0.485000\pi\) | |||||||
\(234\) | −2406.37 | −0.672263 | ||||||||
\(235\) | −4108.34 | −1.14042 | ||||||||
\(236\) | 1928.64 | 0.531964 | ||||||||
\(237\) | 1000.54 | 0.274227 | ||||||||
\(238\) | −7.64462 | −0.00208205 | ||||||||
\(239\) | −5612.62 | −1.51904 | −0.759520 | − | 0.650485i | \(-0.774566\pi\) | ||||
−0.759520 | + | 0.650485i | \(0.774566\pi\) | |||||||
\(240\) | 1715.04 | 0.461273 | ||||||||
\(241\) | 2947.42 | 0.787800 | 0.393900 | − | 0.919153i | \(-0.371126\pi\) | ||||
0.393900 | + | 0.919153i | \(0.371126\pi\) | |||||||
\(242\) | 3061.69 | 0.813276 | ||||||||
\(243\) | 3848.96 | 1.01610 | ||||||||
\(244\) | −1080.96 | −0.283612 | ||||||||
\(245\) | 6411.97 | 1.67202 | ||||||||
\(246\) | 1001.42 | 0.259547 | ||||||||
\(247\) | 6018.64 | 1.55043 | ||||||||
\(248\) | 4058.18 | 1.03909 | ||||||||
\(249\) | 658.788 | 0.167667 | ||||||||
\(250\) | 4386.93 | 1.10981 | ||||||||
\(251\) | 1443.00 | 0.362874 | 0.181437 | − | 0.983403i | \(-0.441925\pi\) | ||||
0.181437 | + | 0.983403i | \(0.441925\pi\) | |||||||
\(252\) | −27.0455 | −0.00676073 | ||||||||
\(253\) | 711.032 | 0.176689 | ||||||||
\(254\) | −1063.02 | −0.262597 | ||||||||
\(255\) | 288.980 | 0.0709672 | ||||||||
\(256\) | −3426.50 | −0.836547 | ||||||||
\(257\) | −7394.73 | −1.79483 | −0.897414 | − | 0.441189i | \(-0.854557\pi\) | ||||
−0.897414 | + | 0.441189i | \(0.854557\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −187.190 | −0.0449089 | ||||||||
\(260\) | −2274.98 | −0.542646 | ||||||||
\(261\) | −4360.87 | −1.03422 | ||||||||
\(262\) | −2335.16 | −0.550635 | ||||||||
\(263\) | −7763.59 | −1.82024 | −0.910121 | − | 0.414343i | \(-0.864012\pi\) | ||||
−0.910121 | + | 0.414343i | \(0.864012\pi\) | |||||||
\(264\) | 301.594 | 0.0703099 | ||||||||
\(265\) | −643.716 | −0.149219 | ||||||||
\(266\) | −148.770 | −0.0342919 | ||||||||
\(267\) | −280.579 | −0.0643114 | ||||||||
\(268\) | 1612.43 | 0.367517 | ||||||||
\(269\) | 6410.90 | 1.45308 | 0.726541 | − | 0.687123i | \(-0.241127\pi\) | ||||
0.726541 | + | 0.687123i | \(0.241127\pi\) | |||||||
\(270\) | −5125.64 | −1.15532 | ||||||||
\(271\) | 1239.58 | 0.277857 | 0.138929 | − | 0.990302i | \(-0.455634\pi\) | ||||
0.138929 | + | 0.990302i | \(0.455634\pi\) | |||||||
\(272\) | 240.029 | 0.0535069 | ||||||||
\(273\) | 60.5466 | 0.0134229 | ||||||||
\(274\) | −5842.22 | −1.28811 | ||||||||
\(275\) | 1134.52 | 0.248778 | ||||||||
\(276\) | −856.433 | −0.186780 | ||||||||
\(277\) | 1265.98 | 0.274605 | 0.137302 | − | 0.990529i | \(-0.456157\pi\) | ||||
0.137302 | + | 0.990529i | \(0.456157\pi\) | |||||||
\(278\) | 4577.18 | 0.987485 | ||||||||
\(279\) | −3477.37 | −0.746181 | ||||||||
\(280\) | 236.140 | 0.0504002 | ||||||||
\(281\) | −2547.49 | −0.540821 | −0.270410 | − | 0.962745i | \(-0.587159\pi\) | ||||
−0.270410 | + | 0.962745i | \(0.587159\pi\) | |||||||
\(282\) | −1250.85 | −0.264139 | ||||||||
\(283\) | −2198.22 | −0.461733 | −0.230866 | − | 0.972985i | \(-0.574156\pi\) | ||||
−0.230866 | + | 0.972985i | \(0.574156\pi\) | |||||||
\(284\) | −2298.38 | −0.480224 | ||||||||
\(285\) | 5623.76 | 1.16885 | ||||||||
\(286\) | 575.059 | 0.118895 | ||||||||
\(287\) | 90.1191 | 0.0185351 | ||||||||
\(288\) | 2289.13 | 0.468363 | ||||||||
\(289\) | −4872.56 | −0.991768 | ||||||||
\(290\) | 9067.16 | 1.83601 | ||||||||
\(291\) | 1514.13 | 0.305017 | ||||||||
\(292\) | 246.811 | 0.0494642 | ||||||||
\(293\) | 3476.05 | 0.693082 | 0.346541 | − | 0.938035i | \(-0.387356\pi\) | ||||
0.346541 | + | 0.938035i | \(0.387356\pi\) | |||||||
\(294\) | 1952.23 | 0.387266 | ||||||||
\(295\) | 14429.3 | 2.84781 | ||||||||
\(296\) | 8992.61 | 1.76583 | ||||||||
\(297\) | −589.115 | −0.115097 | ||||||||
\(298\) | −4705.24 | −0.914655 | ||||||||
\(299\) | −6857.41 | −1.32634 | ||||||||
\(300\) | −1366.52 | −0.262986 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8102.82 | 1.54392 | ||||||||
\(303\) | 327.542 | 0.0621015 | ||||||||
\(304\) | 4671.13 | 0.881275 | ||||||||
\(305\) | −8087.31 | −1.51829 | ||||||||
\(306\) | −314.688 | −0.0587892 | ||||||||
\(307\) | 1861.37 | 0.346039 | 0.173019 | − | 0.984918i | \(-0.444648\pi\) | ||||
0.173019 | + | 0.984918i | \(0.444648\pi\) | |||||||
\(308\) | 6.46315 | 0.00119569 | ||||||||
\(309\) | −597.611 | −0.110022 | ||||||||
\(310\) | 7230.17 | 1.32467 | ||||||||
\(311\) | −7750.28 | −1.41311 | −0.706556 | − | 0.707657i | \(-0.749752\pi\) | ||||
−0.706556 | + | 0.707657i | \(0.749752\pi\) | |||||||
\(312\) | −2908.66 | −0.527790 | ||||||||
\(313\) | −1674.83 | −0.302451 | −0.151225 | − | 0.988499i | \(-0.548322\pi\) | ||||
−0.151225 | + | 0.988499i | \(0.548322\pi\) | |||||||
\(314\) | −891.996 | −0.160313 | ||||||||
\(315\) | −202.344 | −0.0361929 | ||||||||
\(316\) | −1030.05 | −0.183370 | ||||||||
\(317\) | −4814.34 | −0.852998 | −0.426499 | − | 0.904488i | \(-0.640253\pi\) | ||||
−0.426499 | + | 0.904488i | \(0.640253\pi\) | |||||||
\(318\) | −195.990 | −0.0345616 | ||||||||
\(319\) | 1042.13 | 0.182910 | ||||||||
\(320\) | −10408.4 | −1.81827 | ||||||||
\(321\) | −1493.93 | −0.259760 | ||||||||
\(322\) | 169.502 | 0.0293354 | ||||||||
\(323\) | 787.073 | 0.135585 | ||||||||
\(324\) | −715.008 | −0.122601 | ||||||||
\(325\) | −10941.6 | −1.86748 | ||||||||
\(326\) | −2504.03 | −0.425415 | ||||||||
\(327\) | 4520.07 | 0.764404 | ||||||||
\(328\) | −4329.33 | −0.728802 | ||||||||
\(329\) | −112.565 | −0.0188630 | ||||||||
\(330\) | 537.329 | 0.0896333 | ||||||||
\(331\) | 10848.9 | 1.80154 | 0.900768 | − | 0.434301i | \(-0.143005\pi\) | ||||
0.900768 | + | 0.434301i | \(0.143005\pi\) | |||||||
\(332\) | −678.220 | −0.112115 | ||||||||
\(333\) | −7705.58 | −1.26806 | ||||||||
\(334\) | 9925.52 | 1.62605 | ||||||||
\(335\) | 12063.5 | 1.96747 | ||||||||
\(336\) | 46.9908 | 0.00762964 | ||||||||
\(337\) | −8725.22 | −1.41037 | −0.705183 | − | 0.709026i | \(-0.749135\pi\) | ||||
−0.705183 | + | 0.709026i | \(0.749135\pi\) | |||||||
\(338\) | −393.878 | −0.0633850 | ||||||||
\(339\) | 5413.93 | 0.867388 | ||||||||
\(340\) | −297.504 | −0.0474542 | ||||||||
\(341\) | 830.999 | 0.131968 | ||||||||
\(342\) | −6124.04 | −0.968275 | ||||||||
\(343\) | 351.500 | 0.0553330 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6407.49 | −0.999907 | ||||||||
\(346\) | 8483.10 | 1.31808 | ||||||||
\(347\) | −5950.59 | −0.920589 | −0.460295 | − | 0.887766i | \(-0.652256\pi\) | ||||
−0.460295 | + | 0.887766i | \(0.652256\pi\) | |||||||
\(348\) | −1255.24 | −0.193356 | ||||||||
\(349\) | −5162.99 | −0.791887 | −0.395944 | − | 0.918275i | \(-0.629582\pi\) | ||||
−0.395944 | + | 0.918275i | \(0.629582\pi\) | |||||||
\(350\) | 270.456 | 0.0413043 | ||||||||
\(351\) | 5681.60 | 0.863992 | ||||||||
\(352\) | −547.042 | −0.0828336 | ||||||||
\(353\) | −6312.98 | −0.951859 | −0.475929 | − | 0.879484i | \(-0.657888\pi\) | ||||
−0.475929 | + | 0.879484i | \(0.657888\pi\) | |||||||
\(354\) | 4393.23 | 0.659598 | ||||||||
\(355\) | −17195.5 | −2.57083 | ||||||||
\(356\) | 288.855 | 0.0430037 | ||||||||
\(357\) | 7.91783 | 0.00117383 | ||||||||
\(358\) | 1508.19 | 0.222655 | ||||||||
\(359\) | −2094.51 | −0.307921 | −0.153961 | − | 0.988077i | \(-0.549203\pi\) | ||||
−0.153961 | + | 0.988077i | \(0.549203\pi\) | |||||||
\(360\) | 9720.60 | 1.42311 | ||||||||
\(361\) | 8457.99 | 1.23312 | ||||||||
\(362\) | −7445.51 | −1.08101 | ||||||||
\(363\) | −3171.11 | −0.458513 | ||||||||
\(364\) | −62.3325 | −0.00897559 | ||||||||
\(365\) | 1846.54 | 0.264801 | ||||||||
\(366\) | −2462.32 | −0.351659 | ||||||||
\(367\) | 11071.4 | 1.57473 | 0.787363 | − | 0.616489i | \(-0.211446\pi\) | ||||
0.787363 | + | 0.616489i | \(0.211446\pi\) | |||||||
\(368\) | −5322.10 | −0.753896 | ||||||||
\(369\) | 3709.71 | 0.523360 | ||||||||
\(370\) | 16021.5 | 2.25113 | ||||||||
\(371\) | −17.6373 | −0.00246815 | ||||||||
\(372\) | −1000.93 | −0.139505 | ||||||||
\(373\) | 1517.88 | 0.210705 | 0.105353 | − | 0.994435i | \(-0.466403\pi\) | ||||
0.105353 | + | 0.994435i | \(0.466403\pi\) | |||||||
\(374\) | 75.2019 | 0.0103973 | ||||||||
\(375\) | −4543.71 | −0.625696 | ||||||||
\(376\) | 5407.64 | 0.741696 | ||||||||
\(377\) | −10050.6 | −1.37303 | ||||||||
\(378\) | −140.439 | −0.0191095 | ||||||||
\(379\) | 13541.0 | 1.83524 | 0.917618 | − | 0.397463i | \(-0.130109\pi\) | ||||
0.917618 | + | 0.397463i | \(0.130109\pi\) | |||||||
\(380\) | −5789.64 | −0.781585 | ||||||||
\(381\) | 1101.01 | 0.148048 | ||||||||
\(382\) | −1088.82 | −0.145834 | ||||||||
\(383\) | 1160.65 | 0.154847 | 0.0774235 | − | 0.996998i | \(-0.475331\pi\) | ||||
0.0774235 | + | 0.996998i | \(0.475331\pi\) | |||||||
\(384\) | −1060.96 | −0.140994 | ||||||||
\(385\) | 48.3547 | 0.00640100 | ||||||||
\(386\) | 9142.24 | 1.20551 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1558.79 | −0.203958 | ||||||||
\(389\) | −2125.41 | −0.277024 | −0.138512 | − | 0.990361i | \(-0.544232\pi\) | ||||
−0.138512 | + | 0.990361i | \(0.544232\pi\) | |||||||
\(390\) | −5182.16 | −0.672844 | ||||||||
\(391\) | −896.761 | −0.115988 | ||||||||
\(392\) | −8439.82 | −1.08744 | ||||||||
\(393\) | 2418.61 | 0.310440 | ||||||||
\(394\) | −5051.26 | −0.645885 | ||||||||
\(395\) | −7706.43 | −0.981652 | ||||||||
\(396\) | 266.053 | 0.0337618 | ||||||||
\(397\) | 1017.45 | 0.128626 | 0.0643128 | − | 0.997930i | \(-0.479514\pi\) | ||||
0.0643128 | + | 0.997930i | \(0.479514\pi\) | |||||||
\(398\) | 7126.69 | 0.897559 | ||||||||
\(399\) | 154.086 | 0.0193333 | ||||||||
\(400\) | −8491.89 | −1.06149 | ||||||||
\(401\) | 4536.33 | 0.564922 | 0.282461 | − | 0.959279i | \(-0.408849\pi\) | ||||
0.282461 | + | 0.959279i | \(0.408849\pi\) | |||||||
\(402\) | 3672.94 | 0.455696 | ||||||||
\(403\) | −8014.40 | −0.990634 | ||||||||
\(404\) | −337.203 | −0.0415260 | ||||||||
\(405\) | −5349.40 | −0.656331 | ||||||||
\(406\) | 248.433 | 0.0303683 | ||||||||
\(407\) | 1841.43 | 0.224266 | ||||||||
\(408\) | −380.373 | −0.0461551 | ||||||||
\(409\) | −12621.0 | −1.52584 | −0.762918 | − | 0.646495i | \(-0.776234\pi\) | ||||
−0.762918 | + | 0.646495i | \(0.776234\pi\) | |||||||
\(410\) | −7713.27 | −0.929100 | ||||||||
\(411\) | 6051.01 | 0.726215 | ||||||||
\(412\) | 615.239 | 0.0735696 | ||||||||
\(413\) | 395.351 | 0.0471040 | ||||||||
\(414\) | 6977.50 | 0.828322 | ||||||||
\(415\) | −5074.18 | −0.600196 | ||||||||
\(416\) | 5275.84 | 0.621801 | ||||||||
\(417\) | −4740.76 | −0.556729 | ||||||||
\(418\) | 1463.48 | 0.171247 | ||||||||
\(419\) | −7940.92 | −0.925869 | −0.462934 | − | 0.886392i | \(-0.653203\pi\) | ||||
−0.462934 | + | 0.886392i | \(0.653203\pi\) | |||||||
\(420\) | −58.2429 | −0.00676657 | ||||||||
\(421\) | 3246.56 | 0.375838 | 0.187919 | − | 0.982185i | \(-0.439826\pi\) | ||||
0.187919 | + | 0.982185i | \(0.439826\pi\) | |||||||
\(422\) | −2273.56 | −0.262264 | ||||||||
\(423\) | −4633.70 | −0.532619 | ||||||||
\(424\) | 847.298 | 0.0970482 | ||||||||
\(425\) | −1430.86 | −0.163311 | ||||||||
\(426\) | −5235.47 | −0.595444 | ||||||||
\(427\) | −221.586 | −0.0251131 | ||||||||
\(428\) | 1537.99 | 0.173696 | ||||||||
\(429\) | −595.611 | −0.0670312 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10024.0 | −1.12028 | −0.560141 | − | 0.828398i | \(-0.689253\pi\) | ||||
−0.560141 | + | 0.828398i | \(0.689253\pi\) | |||||||
\(432\) | 4409.55 | 0.491098 | ||||||||
\(433\) | 9624.64 | 1.06820 | 0.534100 | − | 0.845421i | \(-0.320651\pi\) | ||||
0.534100 | + | 0.845421i | \(0.320651\pi\) | |||||||
\(434\) | 198.101 | 0.0219105 | ||||||||
\(435\) | −9391.21 | −1.03511 | ||||||||
\(436\) | −4653.40 | −0.511141 | ||||||||
\(437\) | −17451.6 | −1.91035 | ||||||||
\(438\) | 562.211 | 0.0613321 | ||||||||
\(439\) | −7330.44 | −0.796954 | −0.398477 | − | 0.917178i | \(-0.630461\pi\) | ||||
−0.398477 | + | 0.917178i | \(0.630461\pi\) | |||||||
\(440\) | −2322.96 | −0.251689 | ||||||||
\(441\) | 7231.91 | 0.780899 | ||||||||
\(442\) | −725.270 | −0.0780488 | ||||||||
\(443\) | −1082.51 | −0.116098 | −0.0580492 | − | 0.998314i | \(-0.518488\pi\) | ||||
−0.0580492 | + | 0.998314i | \(0.518488\pi\) | |||||||
\(444\) | −2217.99 | −0.237074 | ||||||||
\(445\) | 2161.10 | 0.230216 | ||||||||
\(446\) | −1047.74 | −0.111238 | ||||||||
\(447\) | 4873.39 | 0.515668 | ||||||||
\(448\) | −285.181 | −0.0300749 | ||||||||
\(449\) | 5924.49 | 0.622703 | 0.311352 | − | 0.950295i | \(-0.399218\pi\) | ||||
0.311352 | + | 0.950295i | \(0.399218\pi\) | |||||||
\(450\) | 11133.2 | 1.16628 | ||||||||
\(451\) | −886.523 | −0.0925604 | ||||||||
\(452\) | −5573.63 | −0.580004 | ||||||||
\(453\) | −8392.40 | −0.870440 | ||||||||
\(454\) | 1294.51 | 0.133821 | ||||||||
\(455\) | −466.347 | −0.0480499 | ||||||||
\(456\) | −7402.33 | −0.760188 | ||||||||
\(457\) | −9192.85 | −0.940970 | −0.470485 | − | 0.882408i | \(-0.655921\pi\) | ||||
−0.470485 | + | 0.882408i | \(0.655921\pi\) | |||||||
\(458\) | 923.485 | 0.0942175 | ||||||||
\(459\) | 742.997 | 0.0755559 | ||||||||
\(460\) | 6596.50 | 0.668616 | ||||||||
\(461\) | −1014.04 | −0.102448 | −0.0512242 | − | 0.998687i | \(-0.516312\pi\) | ||||
−0.0512242 | + | 0.998687i | \(0.516312\pi\) | |||||||
\(462\) | 14.7224 | 0.00148257 | ||||||||
\(463\) | 11579.2 | 1.16227 | 0.581134 | − | 0.813808i | \(-0.302609\pi\) | ||||
0.581134 | + | 0.813808i | \(0.302609\pi\) | |||||||
\(464\) | −7800.40 | −0.780441 | ||||||||
\(465\) | −7488.57 | −0.746826 | ||||||||
\(466\) | −785.797 | −0.0781145 | ||||||||
\(467\) | −11479.0 | −1.13744 | −0.568721 | − | 0.822530i | \(-0.692562\pi\) | ||||
−0.568721 | + | 0.822530i | \(0.692562\pi\) | |||||||
\(468\) | −2565.89 | −0.253437 | ||||||||
\(469\) | 330.531 | 0.0325427 | ||||||||
\(470\) | 9634.42 | 0.945538 | ||||||||
\(471\) | 923.875 | 0.0903820 | ||||||||
\(472\) | −18992.7 | −1.85214 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −2346.35 | −0.227366 | ||||||||
\(475\) | −27845.6 | −2.68977 | ||||||||
\(476\) | −8.15139 | −0.000784912 0 | ||||||||
\(477\) | −726.032 | −0.0696913 | ||||||||
\(478\) | 13162.1 | 1.25946 | ||||||||
\(479\) | 11310.1 | 1.07886 | 0.539429 | − | 0.842031i | \(-0.318640\pi\) | ||||
0.539429 | + | 0.842031i | \(0.318640\pi\) | |||||||
\(480\) | 4929.68 | 0.468767 | ||||||||
\(481\) | −17759.3 | −1.68348 | ||||||||
\(482\) | −6911.96 | −0.653177 | ||||||||
\(483\) | −175.560 | −0.0165389 | ||||||||
\(484\) | 3264.65 | 0.306597 | ||||||||
\(485\) | −11662.3 | −1.09187 | ||||||||
\(486\) | −9026.17 | −0.842460 | ||||||||
\(487\) | 13942.4 | 1.29731 | 0.648657 | − | 0.761081i | \(-0.275331\pi\) | ||||
0.648657 | + | 0.761081i | \(0.275331\pi\) | |||||||
\(488\) | 10645.0 | 0.987453 | ||||||||
\(489\) | 2593.52 | 0.239843 | ||||||||
\(490\) | −15036.6 | −1.38630 | ||||||||
\(491\) | −6614.78 | −0.607986 | −0.303993 | − | 0.952674i | \(-0.598320\pi\) | ||||
−0.303993 | + | 0.952674i | \(0.598320\pi\) | |||||||
\(492\) | 1067.81 | 0.0978467 | ||||||||
\(493\) | −1314.35 | −0.120071 | ||||||||
\(494\) | −14114.3 | −1.28549 | ||||||||
\(495\) | 1990.50 | 0.180740 | ||||||||
\(496\) | −6220.06 | −0.563082 | ||||||||
\(497\) | −471.144 | −0.0425226 | ||||||||
\(498\) | −1544.92 | −0.139015 | ||||||||
\(499\) | −1025.76 | −0.0920229 | −0.0460114 | − | 0.998941i | \(-0.514651\pi\) | ||||
−0.0460114 | + | 0.998941i | \(0.514651\pi\) | |||||||
\(500\) | 4677.74 | 0.418389 | ||||||||
\(501\) | −10280.2 | −0.916741 | ||||||||
\(502\) | −3383.96 | −0.300864 | ||||||||
\(503\) | −3411.78 | −0.302433 | −0.151217 | − | 0.988501i | \(-0.548319\pi\) | ||||
−0.151217 | + | 0.988501i | \(0.548319\pi\) | |||||||
\(504\) | 266.337 | 0.0235389 | ||||||||
\(505\) | −2522.82 | −0.222305 | ||||||||
\(506\) | −1667.44 | −0.146495 | ||||||||
\(507\) | 407.955 | 0.0357355 | ||||||||
\(508\) | −1133.49 | −0.0989967 | ||||||||
\(509\) | −334.899 | −0.0291634 | −0.0145817 | − | 0.999894i | \(-0.504642\pi\) | ||||
−0.0145817 | + | 0.999894i | \(0.504642\pi\) | |||||||
\(510\) | −677.685 | −0.0588400 | ||||||||
\(511\) | 50.5938 | 0.00437992 | ||||||||
\(512\) | 11529.9 | 0.995223 | ||||||||
\(513\) | 14459.2 | 1.24443 | ||||||||
\(514\) | 17341.3 | 1.48812 | ||||||||
\(515\) | 4602.98 | 0.393847 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1107.33 | 0.0941979 | ||||||||
\(518\) | 438.977 | 0.0372346 | ||||||||
\(519\) | −8786.27 | −0.743111 | ||||||||
\(520\) | 22403.4 | 1.88933 | ||||||||
\(521\) | 15973.0 | 1.34317 | 0.671585 | − | 0.740928i | \(-0.265614\pi\) | ||||
0.671585 | + | 0.740928i | \(0.265614\pi\) | |||||||
\(522\) | 10226.6 | 0.857486 | ||||||||
\(523\) | 4623.45 | 0.386557 | 0.193279 | − | 0.981144i | \(-0.438088\pi\) | ||||
0.193279 | + | 0.981144i | \(0.438088\pi\) | |||||||
\(524\) | −2489.95 | −0.207584 | ||||||||
\(525\) | −280.122 | −0.0232867 | ||||||||
\(526\) | 18206.3 | 1.50919 | ||||||||
\(527\) | −1048.06 | −0.0866307 | ||||||||
\(528\) | −462.260 | −0.0381009 | ||||||||
\(529\) | 7716.68 | 0.634230 | ||||||||
\(530\) | 1509.57 | 0.123720 | ||||||||
\(531\) | 16274.5 | 1.33004 | ||||||||
\(532\) | −158.632 | −0.0129277 | ||||||||
\(533\) | 8549.89 | 0.694816 | ||||||||
\(534\) | 657.983 | 0.0533216 | ||||||||
\(535\) | 11506.7 | 0.929862 | ||||||||
\(536\) | −15878.8 | −1.27959 | ||||||||
\(537\) | −1562.09 | −0.125529 | ||||||||
\(538\) | −15034.1 | −1.20477 | ||||||||
\(539\) | −1728.23 | −0.138108 | ||||||||
\(540\) | −5465.42 | −0.435545 | ||||||||
\(541\) | 5776.76 | 0.459080 | 0.229540 | − | 0.973299i | \(-0.426278\pi\) | ||||
0.229540 | + | 0.973299i | \(0.426278\pi\) | |||||||
\(542\) | −2906.93 | −0.230376 | ||||||||
\(543\) | 7711.60 | 0.609459 | ||||||||
\(544\) | 689.934 | 0.0543763 | ||||||||
\(545\) | −34814.9 | −2.73634 | ||||||||
\(546\) | −141.987 | −0.0111291 | ||||||||
\(547\) | 20861.6 | 1.63067 | 0.815334 | − | 0.578990i | \(-0.196553\pi\) | ||||
0.815334 | + | 0.578990i | \(0.196553\pi\) | |||||||
\(548\) | −6229.51 | −0.485605 | ||||||||
\(549\) | −9121.49 | −0.709100 | ||||||||
\(550\) | −2660.54 | −0.206265 | ||||||||
\(551\) | −25578.1 | −1.97761 | ||||||||
\(552\) | 8433.93 | 0.650311 | ||||||||
\(553\) | −211.150 | −0.0162369 | ||||||||
\(554\) | −2968.85 | −0.227679 | ||||||||
\(555\) | −16594.1 | −1.26915 | ||||||||
\(556\) | 4880.60 | 0.372273 | ||||||||
\(557\) | −4932.51 | −0.375219 | −0.187610 | − | 0.982244i | \(-0.560074\pi\) | ||||
−0.187610 | + | 0.982244i | \(0.560074\pi\) | |||||||
\(558\) | 8154.75 | 0.618670 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −361.937 | −0.0273118 | ||||||||
\(561\) | −77.8895 | −0.00586185 | ||||||||
\(562\) | 5974.10 | 0.448403 | ||||||||
\(563\) | −14078.4 | −1.05388 | −0.526939 | − | 0.849903i | \(-0.676660\pi\) | ||||
−0.526939 | + | 0.849903i | \(0.676660\pi\) | |||||||
\(564\) | −1333.77 | −0.0995778 | ||||||||
\(565\) | −41699.7 | −3.10499 | ||||||||
\(566\) | 5155.02 | 0.382830 | ||||||||
\(567\) | −146.569 | −0.0108560 | ||||||||
\(568\) | 22633.8 | 1.67200 | ||||||||
\(569\) | −7165.14 | −0.527905 | −0.263953 | − | 0.964536i | \(-0.585026\pi\) | ||||
−0.263953 | + | 0.964536i | \(0.585026\pi\) | |||||||
\(570\) | −13188.2 | −0.969112 | ||||||||
\(571\) | 15291.1 | 1.12069 | 0.560344 | − | 0.828260i | \(-0.310669\pi\) | ||||
0.560344 | + | 0.828260i | \(0.310669\pi\) | |||||||
\(572\) | 613.180 | 0.0448223 | ||||||||
\(573\) | 1127.73 | 0.0822192 | ||||||||
\(574\) | −211.337 | −0.0153677 | ||||||||
\(575\) | 31726.2 | 2.30100 | ||||||||
\(576\) | −11739.4 | −0.849201 | ||||||||
\(577\) | 10271.5 | 0.741089 | 0.370545 | − | 0.928815i | \(-0.379171\pi\) | ||||
0.370545 | + | 0.928815i | \(0.379171\pi\) | |||||||
\(578\) | 11426.6 | 0.822290 | ||||||||
\(579\) | −9468.97 | −0.679649 | ||||||||
\(580\) | 9668.23 | 0.692157 | ||||||||
\(581\) | −139.028 | −0.00992749 | ||||||||
\(582\) | −3550.77 | −0.252894 | ||||||||
\(583\) | 173.502 | 0.0123254 | ||||||||
\(584\) | −2430.53 | −0.172219 | ||||||||
\(585\) | −19197.0 | −1.35675 | ||||||||
\(586\) | −8151.66 | −0.574645 | ||||||||
\(587\) | 5869.33 | 0.412697 | 0.206349 | − | 0.978479i | \(-0.433842\pi\) | ||||
0.206349 | + | 0.978479i | \(0.433842\pi\) | |||||||
\(588\) | 2081.64 | 0.145996 | ||||||||
\(589\) | −20396.0 | −1.42683 | ||||||||
\(590\) | −33838.0 | −2.36117 | ||||||||
\(591\) | 5231.78 | 0.364140 | ||||||||
\(592\) | −13783.2 | −0.956900 | ||||||||
\(593\) | −13637.1 | −0.944367 | −0.472184 | − | 0.881500i | \(-0.656534\pi\) | ||||
−0.472184 | + | 0.881500i | \(0.656534\pi\) | |||||||
\(594\) | 1381.53 | 0.0954289 | ||||||||
\(595\) | −60.9854 | −0.00420195 | ||||||||
\(596\) | −5017.15 | −0.344816 | ||||||||
\(597\) | −7381.38 | −0.506030 | ||||||||
\(598\) | 16081.3 | 1.09968 | ||||||||
\(599\) | 2989.04 | 0.203888 | 0.101944 | − | 0.994790i | \(-0.467494\pi\) | ||||
0.101944 | + | 0.994790i | \(0.467494\pi\) | |||||||
\(600\) | 13457.1 | 0.915639 | ||||||||
\(601\) | 3752.57 | 0.254693 | 0.127347 | − | 0.991858i | \(-0.459354\pi\) | ||||
0.127347 | + | 0.991858i | \(0.459354\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13606.2 | 0.918883 | ||||||||
\(604\) | 8639.96 | 0.582045 | ||||||||
\(605\) | 24424.8 | 1.64134 | ||||||||
\(606\) | −768.115 | −0.0514893 | ||||||||
\(607\) | −9165.95 | −0.612906 | −0.306453 | − | 0.951886i | \(-0.599142\pi\) | ||||
−0.306453 | + | 0.951886i | \(0.599142\pi\) | |||||||
\(608\) | 13426.6 | 0.895593 | ||||||||
\(609\) | −257.312 | −0.0171212 | ||||||||
\(610\) | 18965.5 | 1.25884 | ||||||||
\(611\) | −10679.4 | −0.707108 | ||||||||
\(612\) | −335.548 | −0.0221630 | ||||||||
\(613\) | 8403.46 | 0.553691 | 0.276846 | − | 0.960914i | \(-0.410711\pi\) | ||||
0.276846 | + | 0.960914i | \(0.410711\pi\) | |||||||
\(614\) | −4365.08 | −0.286906 | ||||||||
\(615\) | 7988.93 | 0.523812 | ||||||||
\(616\) | −63.6474 | −0.00416303 | ||||||||
\(617\) | −14381.6 | −0.938380 | −0.469190 | − | 0.883097i | \(-0.655454\pi\) | ||||
−0.469190 | + | 0.883097i | \(0.655454\pi\) | |||||||
\(618\) | 1401.45 | 0.0912212 | ||||||||
\(619\) | 20695.9 | 1.34384 | 0.671921 | − | 0.740623i | \(-0.265470\pi\) | ||||
0.671921 | + | 0.740623i | \(0.265470\pi\) | |||||||
\(620\) | 7709.47 | 0.499386 | ||||||||
\(621\) | −16474.3 | −1.06456 | ||||||||
\(622\) | 18175.1 | 1.17163 | ||||||||
\(623\) | 59.2125 | 0.00380786 | ||||||||
\(624\) | 4458.17 | 0.286009 | ||||||||
\(625\) | 6872.81 | 0.439860 | ||||||||
\(626\) | 3927.64 | 0.250767 | ||||||||
\(627\) | −1515.79 | −0.0965465 | ||||||||
\(628\) | −951.127 | −0.0604365 | ||||||||
\(629\) | −2322.43 | −0.147220 | ||||||||
\(630\) | 474.514 | 0.0300081 | ||||||||
\(631\) | 18686.0 | 1.17889 | 0.589444 | − | 0.807809i | \(-0.299347\pi\) | ||||
0.589444 | + | 0.807809i | \(0.299347\pi\) | |||||||
\(632\) | 10143.7 | 0.638439 | ||||||||
\(633\) | 2354.81 | 0.147860 | ||||||||
\(634\) | 11290.1 | 0.707233 | ||||||||
\(635\) | −8480.29 | −0.529969 | ||||||||
\(636\) | −208.982 | −0.0130294 | ||||||||
\(637\) | 16667.6 | 1.03673 | ||||||||
\(638\) | −2443.89 | −0.151653 | ||||||||
\(639\) | −19394.5 | −1.20068 | ||||||||
\(640\) | 8171.81 | 0.504717 | ||||||||
\(641\) | 2741.94 | 0.168955 | 0.0844774 | − | 0.996425i | \(-0.473078\pi\) | ||||
0.0844774 | + | 0.996425i | \(0.473078\pi\) | |||||||
\(642\) | 3503.39 | 0.215371 | ||||||||
\(643\) | −9202.37 | −0.564395 | −0.282198 | − | 0.959356i | \(-0.591063\pi\) | ||||
−0.282198 | + | 0.959356i | \(0.591063\pi\) | |||||||
\(644\) | 180.739 | 0.0110592 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1845.76 | −0.112415 | ||||||||
\(647\) | −8101.38 | −0.492269 | −0.246135 | − | 0.969236i | \(-0.579161\pi\) | ||||
−0.246135 | + | 0.969236i | \(0.579161\pi\) | |||||||
\(648\) | 7041.21 | 0.426859 | ||||||||
\(649\) | −3889.16 | −0.235228 | ||||||||
\(650\) | 25659.1 | 1.54836 | ||||||||
\(651\) | −205.181 | −0.0123528 | ||||||||
\(652\) | −2670.02 | −0.160378 | ||||||||
\(653\) | −2590.36 | −0.155235 | −0.0776175 | − | 0.996983i | \(-0.524731\pi\) | ||||
−0.0776175 | + | 0.996983i | \(0.524731\pi\) | |||||||
\(654\) | −10600.0 | −0.633779 | ||||||||
\(655\) | −18628.8 | −1.11128 | ||||||||
\(656\) | 6635.66 | 0.394937 | ||||||||
\(657\) | 2082.67 | 0.123673 | ||||||||
\(658\) | 263.976 | 0.0156396 | ||||||||
\(659\) | −5952.63 | −0.351869 | −0.175934 | − | 0.984402i | \(-0.556295\pi\) | ||||
−0.175934 | + | 0.984402i | \(0.556295\pi\) | |||||||
\(660\) | 572.949 | 0.0337909 | ||||||||
\(661\) | −23326.7 | −1.37262 | −0.686311 | − | 0.727309i | \(-0.740771\pi\) | ||||
−0.686311 | + | 0.727309i | \(0.740771\pi\) | |||||||
\(662\) | −25441.6 | −1.49368 | ||||||||
\(663\) | 751.190 | 0.0440027 | ||||||||
\(664\) | 6678.94 | 0.390351 | ||||||||
\(665\) | −1186.82 | −0.0692073 | ||||||||
\(666\) | 18070.3 | 1.05137 | ||||||||
\(667\) | 29142.7 | 1.69177 | ||||||||
\(668\) | 10583.5 | 0.613005 | ||||||||
\(669\) | 1085.19 | 0.0627140 | ||||||||
\(670\) | −28290.1 | −1.63126 | ||||||||
\(671\) | 2179.79 | 0.125410 | ||||||||
\(672\) | 135.069 | 0.00775360 | ||||||||
\(673\) | −20507.9 | −1.17462 | −0.587311 | − | 0.809362i | \(-0.699813\pi\) | ||||
−0.587311 | + | 0.809362i | \(0.699813\pi\) | |||||||
\(674\) | 20461.4 | 1.16935 | ||||||||
\(675\) | −26286.2 | −1.49890 | ||||||||
\(676\) | −419.988 | −0.0238956 | ||||||||
\(677\) | −29831.9 | −1.69355 | −0.846774 | − | 0.531953i | \(-0.821458\pi\) | ||||
−0.846774 | + | 0.531953i | \(0.821458\pi\) | |||||||
\(678\) | −12696.2 | −0.719164 | ||||||||
\(679\) | −319.537 | −0.0180600 | ||||||||
\(680\) | 2929.74 | 0.165221 | ||||||||
\(681\) | −1340.78 | −0.0754460 | ||||||||
\(682\) | −1948.77 | −0.109417 | ||||||||
\(683\) | −6248.79 | −0.350078 | −0.175039 | − | 0.984562i | \(-0.556005\pi\) | ||||
−0.175039 | + | 0.984562i | \(0.556005\pi\) | |||||||
\(684\) | −6530.00 | −0.365031 | ||||||||
\(685\) | −46606.7 | −2.59964 | ||||||||
\(686\) | −824.300 | −0.0458774 | ||||||||
\(687\) | −956.489 | −0.0531184 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1673.31 | −0.0925225 | ||||||||
\(690\) | 15026.2 | 0.829037 | ||||||||
\(691\) | 17494.1 | 0.963107 | 0.481554 | − | 0.876417i | \(-0.340073\pi\) | ||||
0.481554 | + | 0.876417i | \(0.340073\pi\) | |||||||
\(692\) | 9045.45 | 0.496902 | ||||||||
\(693\) | 54.5382 | 0.00298951 | ||||||||
\(694\) | 13954.7 | 0.763274 | ||||||||
\(695\) | 36514.7 | 1.99292 | ||||||||
\(696\) | 12361.3 | 0.673208 | ||||||||
\(697\) | 1118.09 | 0.0607614 | ||||||||
\(698\) | 12107.7 | 0.656566 | ||||||||
\(699\) | 813.880 | 0.0440397 | ||||||||
\(700\) | 288.385 | 0.0155713 | ||||||||
\(701\) | 25115.2 | 1.35319 | 0.676596 | − | 0.736354i | \(-0.263454\pi\) | ||||
0.676596 | + | 0.736354i | \(0.263454\pi\) | |||||||
\(702\) | −13323.9 | −0.716349 | ||||||||
\(703\) | −45196.1 | −2.42476 | ||||||||
\(704\) | 2805.39 | 0.150188 | ||||||||
\(705\) | −9978.74 | −0.533080 | ||||||||
\(706\) | 14804.5 | 0.789200 | ||||||||
\(707\) | −69.1233 | −0.00367701 | ||||||||
\(708\) | 4684.46 | 0.248662 | ||||||||
\(709\) | 18394.0 | 0.974331 | 0.487165 | − | 0.873310i | \(-0.338031\pi\) | ||||
0.487165 | + | 0.873310i | \(0.338031\pi\) | |||||||
\(710\) | 40325.1 | 2.13151 | ||||||||
\(711\) | −8691.90 | −0.458469 | ||||||||
\(712\) | −2844.57 | −0.149726 | ||||||||
\(713\) | 23238.5 | 1.22060 | ||||||||
\(714\) | −18.5680 | −0.000973237 0 | ||||||||
\(715\) | 4587.57 | 0.239952 | ||||||||
\(716\) | 1608.17 | 0.0839387 | ||||||||
\(717\) | −13632.5 | −0.710063 | ||||||||
\(718\) | 4911.81 | 0.255302 | ||||||||
\(719\) | 30052.0 | 1.55876 | 0.779382 | − | 0.626549i | \(-0.215533\pi\) | ||||
0.779382 | + | 0.626549i | \(0.215533\pi\) | |||||||
\(720\) | −14899.0 | −0.771183 | ||||||||
\(721\) | 126.118 | 0.00651439 | ||||||||
\(722\) | −19834.8 | −1.02240 | ||||||||
\(723\) | 7158.99 | 0.368251 | ||||||||
\(724\) | −7939.07 | −0.407532 | ||||||||
\(725\) | 46499.8 | 2.38201 | ||||||||
\(726\) | 7436.54 | 0.380160 | ||||||||
\(727\) | 4166.51 | 0.212555 | 0.106277 | − | 0.994337i | \(-0.466107\pi\) | ||||
0.106277 | + | 0.994337i | \(0.466107\pi\) | |||||||
\(728\) | 613.835 | 0.0312503 | ||||||||
\(729\) | 1628.36 | 0.0827293 | ||||||||
\(730\) | −4330.31 | −0.219551 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −2625.54 | −0.132572 | ||||||||
\(733\) | 23201.4 | 1.16912 | 0.584559 | − | 0.811351i | \(-0.301267\pi\) | ||||
0.584559 | + | 0.811351i | \(0.301267\pi\) | |||||||
\(734\) | −25963.5 | −1.30563 | ||||||||
\(735\) | 15574.0 | 0.781574 | ||||||||
\(736\) | −15297.8 | −0.766145 | ||||||||
\(737\) | −3251.51 | −0.162512 | ||||||||
\(738\) | −8699.62 | −0.433926 | ||||||||
\(739\) | 27055.3 | 1.34675 | 0.673373 | − | 0.739303i | \(-0.264845\pi\) | ||||
0.673373 | + | 0.739303i | \(0.264845\pi\) | |||||||
\(740\) | 17083.6 | 0.848656 | ||||||||
\(741\) | 14618.7 | 0.724738 | ||||||||
\(742\) | 41.3611 | 0.00204638 | ||||||||
\(743\) | 16610.7 | 0.820172 | 0.410086 | − | 0.912047i | \(-0.365499\pi\) | ||||
0.410086 | + | 0.912047i | \(0.365499\pi\) | |||||||
\(744\) | 9856.91 | 0.485715 | ||||||||
\(745\) | −37536.3 | −1.84594 | ||||||||
\(746\) | −3559.58 | −0.174699 | ||||||||
\(747\) | −5723.05 | −0.280315 | ||||||||
\(748\) | 80.1871 | 0.00391969 | ||||||||
\(749\) | 315.273 | 0.0153803 | ||||||||
\(750\) | 10655.4 | 0.518774 | ||||||||
\(751\) | −5199.15 | −0.252623 | −0.126311 | − | 0.991991i | \(-0.540314\pi\) | ||||
−0.126311 | + | 0.991991i | \(0.540314\pi\) | |||||||
\(752\) | −8288.41 | −0.401924 | ||||||||
\(753\) | 3504.90 | 0.169622 | ||||||||
\(754\) | 23569.7 | 1.13840 | ||||||||
\(755\) | 64640.7 | 3.11592 | ||||||||
\(756\) | −149.748 | −0.00720409 | ||||||||
\(757\) | 30028.9 | 1.44177 | 0.720884 | − | 0.693056i | \(-0.243736\pi\) | ||||
0.720884 | + | 0.693056i | \(0.243736\pi\) | |||||||
\(758\) | −31754.9 | −1.52162 | ||||||||
\(759\) | 1727.03 | 0.0825917 | ||||||||
\(760\) | 57014.9 | 2.72125 | ||||||||
\(761\) | −13045.8 | −0.621433 | −0.310716 | − | 0.950503i | \(-0.600569\pi\) | ||||
−0.310716 | + | 0.950503i | \(0.600569\pi\) | |||||||
\(762\) | −2581.97 | −0.122749 | ||||||||
\(763\) | −953.900 | −0.0452602 | ||||||||
\(764\) | −1161.00 | −0.0549782 | ||||||||
\(765\) | −2510.44 | −0.118647 | ||||||||
\(766\) | −2721.83 | −0.128386 | ||||||||
\(767\) | 37508.2 | 1.76577 | ||||||||
\(768\) | −8322.63 | −0.391038 | ||||||||
\(769\) | 18935.3 | 0.887938 | 0.443969 | − | 0.896042i | \(-0.353570\pi\) | ||||
0.443969 | + | 0.896042i | \(0.353570\pi\) | |||||||
\(770\) | −113.396 | −0.00530716 | ||||||||
\(771\) | −17961.1 | −0.838978 | ||||||||
\(772\) | 9748.28 | 0.454467 | ||||||||
\(773\) | 7052.59 | 0.328155 | 0.164078 | − | 0.986447i | \(-0.447535\pi\) | ||||
0.164078 | + | 0.986447i | \(0.447535\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37079.1 | 1.71861 | ||||||||
\(776\) | 15350.6 | 0.710121 | ||||||||
\(777\) | −454.665 | −0.0209923 | ||||||||
\(778\) | 4984.28 | 0.229685 | ||||||||
\(779\) | 21758.8 | 1.00076 | ||||||||
\(780\) | −5525.69 | −0.253656 | ||||||||
\(781\) | 4634.76 | 0.212349 | ||||||||
\(782\) | 2102.99 | 0.0961670 | ||||||||
\(783\) | −24145.7 | −1.10204 | ||||||||
\(784\) | 12935.9 | 0.589281 | ||||||||
\(785\) | −7115.95 | −0.323540 | ||||||||
\(786\) | −5671.86 | −0.257390 | ||||||||
\(787\) | 31343.9 | 1.41968 | 0.709841 | − | 0.704362i | \(-0.248767\pi\) | ||||
0.709841 | + | 0.704362i | \(0.248767\pi\) | |||||||
\(788\) | −5386.11 | −0.243492 | ||||||||
\(789\) | −18857.0 | −0.850858 | ||||||||
\(790\) | 18072.3 | 0.813902 | ||||||||
\(791\) | −1142.54 | −0.0513578 | ||||||||
\(792\) | −2620.02 | −0.117548 | ||||||||
\(793\) | −21022.6 | −0.941405 | ||||||||
\(794\) | −2386.01 | −0.106645 | ||||||||
\(795\) | −1563.52 | −0.0697515 | ||||||||
\(796\) | 7599.12 | 0.338371 | ||||||||
\(797\) | 35516.9 | 1.57851 | 0.789255 | − | 0.614066i | \(-0.210467\pi\) | ||||
0.789255 | + | 0.614066i | \(0.210467\pi\) | |||||||
\(798\) | −361.347 | −0.0160295 | ||||||||
\(799\) | −1396.58 | −0.0618364 | ||||||||
\(800\) | −24408.9 | −1.07873 | ||||||||
\(801\) | 2437.46 | 0.107520 | ||||||||
\(802\) | −10638.1 | −0.468385 | ||||||||
\(803\) | −497.704 | −0.0218725 | ||||||||
\(804\) | 3916.42 | 0.171793 | ||||||||
\(805\) | 1352.22 | 0.0592042 | ||||||||
\(806\) | 18794.5 | 0.821350 | ||||||||
\(807\) | 15571.4 | 0.679232 | ||||||||
\(808\) | 3320.69 | 0.144581 | ||||||||
\(809\) | −18244.6 | −0.792886 | −0.396443 | − | 0.918059i | \(-0.629756\pi\) | ||||
−0.396443 | + | 0.918059i | \(0.629756\pi\) | |||||||
\(810\) | 12544.8 | 0.544174 | ||||||||
\(811\) | −26372.1 | −1.14186 | −0.570930 | − | 0.820999i | \(-0.693417\pi\) | ||||
−0.570930 | + | 0.820999i | \(0.693417\pi\) | |||||||
\(812\) | 264.902 | 0.0114486 | ||||||||
\(813\) | 3010.82 | 0.129882 | ||||||||
\(814\) | −4318.32 | −0.185942 | ||||||||
\(815\) | −19976.1 | −0.858565 | ||||||||
\(816\) | 583.006 | 0.0250114 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 29597.3 | 1.26509 | ||||||||
\(819\) | −525.982 | −0.0224412 | ||||||||
\(820\) | −8224.58 | −0.350262 | ||||||||
\(821\) | −3948.12 | −0.167832 | −0.0839162 | − | 0.996473i | \(-0.526743\pi\) | ||||
−0.0839162 | + | 0.996473i | \(0.526743\pi\) | |||||||
\(822\) | −14190.2 | −0.602116 | ||||||||
\(823\) | −36600.5 | −1.55020 | −0.775100 | − | 0.631839i | \(-0.782301\pi\) | ||||
−0.775100 | + | 0.631839i | \(0.782301\pi\) | |||||||
\(824\) | −6058.71 | −0.256147 | ||||||||
\(825\) | 2755.63 | 0.116289 | ||||||||
\(826\) | −927.134 | −0.0390546 | ||||||||
\(827\) | 8511.44 | 0.357886 | 0.178943 | − | 0.983859i | \(-0.442732\pi\) | ||||
0.178943 | + | 0.983859i | \(0.442732\pi\) | |||||||
\(828\) | 7440.04 | 0.312270 | ||||||||
\(829\) | −20202.2 | −0.846382 | −0.423191 | − | 0.906041i | \(-0.639090\pi\) | ||||
−0.423191 | + | 0.906041i | \(0.639090\pi\) | |||||||
\(830\) | 11899.4 | 0.497632 | ||||||||
\(831\) | 3074.95 | 0.128362 | ||||||||
\(832\) | −27056.1 | −1.12740 | ||||||||
\(833\) | 2179.66 | 0.0906613 | ||||||||
\(834\) | 11117.5 | 0.461592 | ||||||||
\(835\) | 79181.4 | 3.28166 | ||||||||
\(836\) | 1560.50 | 0.0645585 | ||||||||
\(837\) | −19253.9 | −0.795115 | ||||||||
\(838\) | 18622.2 | 0.767652 | ||||||||
\(839\) | 5893.79 | 0.242522 | 0.121261 | − | 0.992621i | \(-0.461306\pi\) | ||||
0.121261 | + | 0.992621i | \(0.461306\pi\) | |||||||
\(840\) | 573.561 | 0.0235592 | ||||||||
\(841\) | 18324.3 | 0.751336 | ||||||||
\(842\) | −7613.48 | −0.311613 | ||||||||
\(843\) | −6187.61 | −0.252803 | ||||||||
\(844\) | −2424.28 | −0.0988709 | ||||||||
\(845\) | −3142.19 | −0.127922 | ||||||||
\(846\) | 10866.4 | 0.441603 | ||||||||
\(847\) | 669.221 | 0.0271484 | ||||||||
\(848\) | −1298.67 | −0.0525903 | ||||||||
\(849\) | −5339.25 | −0.215833 | ||||||||
\(850\) | 3355.50 | 0.135403 | ||||||||
\(851\) | 51494.7 | 2.07428 | ||||||||
\(852\) | −5582.53 | −0.224477 | ||||||||
\(853\) | 29634.1 | 1.18951 | 0.594756 | − | 0.803906i | \(-0.297249\pi\) | ||||
0.594756 | + | 0.803906i | \(0.297249\pi\) | |||||||
\(854\) | 519.639 | 0.0208217 | ||||||||
\(855\) | −48854.9 | −1.95415 | ||||||||
\(856\) | −15145.8 | −0.604756 | ||||||||
\(857\) | 18851.6 | 0.751411 | 0.375705 | − | 0.926739i | \(-0.377401\pi\) | ||||
0.375705 | + | 0.926739i | \(0.377401\pi\) | |||||||
\(858\) | 1396.76 | 0.0555765 | ||||||||
\(859\) | 8874.89 | 0.352511 | 0.176256 | − | 0.984344i | \(-0.443601\pi\) | ||||
0.176256 | + | 0.984344i | \(0.443601\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 218.890 | 0.00866407 | ||||||||
\(862\) | 23507.3 | 0.928842 | ||||||||
\(863\) | −34956.5 | −1.37883 | −0.689417 | − | 0.724365i | \(-0.742133\pi\) | ||||
−0.689417 | + | 0.724365i | \(0.742133\pi\) | |||||||
\(864\) | 12674.7 | 0.499077 | ||||||||
\(865\) | 67674.5 | 2.66012 | ||||||||
\(866\) | −22570.7 | −0.885660 | ||||||||
\(867\) | −11835.0 | −0.463594 | ||||||||
\(868\) | 211.233 | 0.00826005 | ||||||||
\(869\) | 2077.13 | 0.0810839 | ||||||||
\(870\) | 22023.2 | 0.858227 | ||||||||
\(871\) | 31358.6 | 1.21991 | ||||||||
\(872\) | 45825.4 | 1.77964 | ||||||||
\(873\) | −13153.6 | −0.509945 | ||||||||
\(874\) | 40925.6 | 1.58390 | ||||||||
\(875\) | 958.889 | 0.0370473 | ||||||||
\(876\) | 599.480 | 0.0231216 | ||||||||
\(877\) | −21331.6 | −0.821341 | −0.410670 | − | 0.911784i | \(-0.634705\pi\) | ||||
−0.410670 | + | 0.911784i | \(0.634705\pi\) | |||||||
\(878\) | 17190.6 | 0.660767 | ||||||||
\(879\) | 8442.98 | 0.323976 | ||||||||
\(880\) | 3560.46 | 0.136390 | ||||||||
\(881\) | 28864.1 | 1.10381 | 0.551905 | − | 0.833907i | \(-0.313901\pi\) | ||||
0.551905 | + | 0.833907i | \(0.313901\pi\) | |||||||
\(882\) | −16959.5 | −0.647455 | ||||||||
\(883\) | −14623.5 | −0.557327 | −0.278663 | − | 0.960389i | \(-0.589891\pi\) | ||||
−0.278663 | + | 0.960389i | \(0.589891\pi\) | |||||||
\(884\) | −773.349 | −0.0294237 | ||||||||
\(885\) | 35047.3 | 1.33119 | ||||||||
\(886\) | 2538.58 | 0.0962589 | ||||||||
\(887\) | −31615.5 | −1.19678 | −0.598390 | − | 0.801205i | \(-0.704193\pi\) | ||||
−0.598390 | + | 0.801205i | \(0.704193\pi\) | |||||||
\(888\) | 21842.2 | 0.825422 | ||||||||
\(889\) | −232.353 | −0.00876589 | ||||||||
\(890\) | −5067.98 | −0.190875 | ||||||||
\(891\) | 1441.84 | 0.0542126 | ||||||||
\(892\) | −1117.20 | −0.0419355 | ||||||||
\(893\) | −27178.3 | −1.01846 | ||||||||
\(894\) | −11428.6 | −0.427548 | ||||||||
\(895\) | 12031.7 | 0.449357 | ||||||||
\(896\) | 223.901 | 0.00834823 | ||||||||
\(897\) | −16656.0 | −0.619985 | ||||||||
\(898\) | −13893.5 | −0.516293 | ||||||||
\(899\) | 34059.7 | 1.26358 | ||||||||
\(900\) | 11871.2 | 0.439676 | ||||||||
\(901\) | −218.823 | −0.00809106 | ||||||||
\(902\) | 2078.98 | 0.0767432 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 54887.7 | 2.01940 | ||||||||
\(905\) | −59397.0 | −2.18168 | ||||||||
\(906\) | 19681.0 | 0.721695 | ||||||||
\(907\) | −32362.1 | −1.18475 | −0.592373 | − | 0.805664i | \(-0.701809\pi\) | ||||
−0.592373 | + | 0.805664i | \(0.701809\pi\) | |||||||
\(908\) | 1380.33 | 0.0504491 | ||||||||
\(909\) | −2845.43 | −0.103825 | ||||||||
\(910\) | 1093.63 | 0.0398389 | ||||||||
\(911\) | 35154.1 | 1.27849 | 0.639247 | − | 0.769002i | \(-0.279246\pi\) | ||||
0.639247 | + | 0.769002i | \(0.279246\pi\) | |||||||
\(912\) | 11345.7 | 0.411945 | ||||||||
\(913\) | 1367.66 | 0.0495759 | ||||||||
\(914\) | 21558.1 | 0.780172 | ||||||||
\(915\) | −19643.3 | −0.709712 | ||||||||
\(916\) | 984.703 | 0.0355191 | ||||||||
\(917\) | −510.416 | −0.0183810 | ||||||||
\(918\) | −1742.40 | −0.0626445 | ||||||||
\(919\) | −7359.98 | −0.264182 | −0.132091 | − | 0.991238i | \(-0.542169\pi\) | ||||
−0.132091 | + | 0.991238i | \(0.542169\pi\) | |||||||
\(920\) | −64960.6 | −2.32792 | ||||||||
\(921\) | 4521.08 | 0.161753 | ||||||||
\(922\) | 2378.02 | 0.0849415 | ||||||||
\(923\) | −44699.0 | −1.59403 | ||||||||
\(924\) | 15.6983 | 0.000558915 0 | ||||||||
\(925\) | 82164.4 | 2.92059 | ||||||||
\(926\) | −27154.2 | −0.963654 | ||||||||
\(927\) | 5191.59 | 0.183942 | ||||||||
\(928\) | −22421.3 | −0.793121 | ||||||||
\(929\) | −26410.1 | −0.932708 | −0.466354 | − | 0.884598i | \(-0.654433\pi\) | ||||
−0.466354 | + | 0.884598i | \(0.654433\pi\) | |||||||
\(930\) | 17561.4 | 0.619205 | ||||||||
\(931\) | 42417.8 | 1.49322 | ||||||||
\(932\) | −837.888 | −0.0294484 | ||||||||
\(933\) | −18824.7 | −0.660548 | ||||||||
\(934\) | 26919.3 | 0.943070 | ||||||||
\(935\) | 599.928 | 0.0209837 | ||||||||
\(936\) | 25268.2 | 0.882391 | ||||||||
\(937\) | −26123.6 | −0.910800 | −0.455400 | − | 0.890287i | \(-0.650504\pi\) | ||||
−0.455400 | + | 0.890287i | \(0.650504\pi\) | |||||||
\(938\) | −775.126 | −0.0269816 | ||||||||
\(939\) | −4068.00 | −0.141378 | ||||||||
\(940\) | 10273.1 | 0.356459 | ||||||||
\(941\) | 6602.83 | 0.228742 | 0.114371 | − | 0.993438i | \(-0.463515\pi\) | ||||
0.114371 | + | 0.993438i | \(0.463515\pi\) | |||||||
\(942\) | −2166.57 | −0.0749370 | ||||||||
\(943\) | −24791.2 | −0.856110 | ||||||||
\(944\) | 29110.5 | 1.00367 | ||||||||
\(945\) | −1120.36 | −0.0385664 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9913.13 | −0.340162 | −0.170081 | − | 0.985430i | \(-0.554403\pi\) | ||||
−0.170081 | + | 0.985430i | \(0.554403\pi\) | |||||||
\(948\) | −2501.89 | −0.0857148 | ||||||||
\(949\) | 4800.00 | 0.164188 | ||||||||
\(950\) | 65300.4 | 2.23013 | ||||||||
\(951\) | −11693.6 | −0.398727 | ||||||||
\(952\) | 80.2727 | 0.00273283 | ||||||||
\(953\) | 12334.8 | 0.419268 | 0.209634 | − | 0.977780i | \(-0.432773\pi\) | ||||
0.209634 | + | 0.977780i | \(0.432773\pi\) | |||||||
\(954\) | 1702.61 | 0.0577821 | ||||||||
\(955\) | −8686.10 | −0.294320 | ||||||||
\(956\) | 14034.6 | 0.474804 | ||||||||
\(957\) | 2531.24 | 0.0854997 | ||||||||
\(958\) | −26523.3 | −0.894497 | ||||||||
\(959\) | −1276.99 | −0.0429990 | ||||||||
\(960\) | −25280.9 | −0.849935 | ||||||||
\(961\) | −2631.71 | −0.0883389 | ||||||||
\(962\) | 41647.2 | 1.39580 | ||||||||
\(963\) | 12978.1 | 0.434282 | ||||||||
\(964\) | −7370.16 | −0.246242 | ||||||||
\(965\) | 72932.7 | 2.43294 | ||||||||
\(966\) | 411.705 | 0.0137126 | ||||||||
\(967\) | −43542.0 | −1.44800 | −0.724000 | − | 0.689800i | \(-0.757699\pi\) | ||||
−0.724000 | + | 0.689800i | \(0.757699\pi\) | |||||||
\(968\) | −32149.4 | −1.06748 | ||||||||
\(969\) | 1911.72 | 0.0633781 | ||||||||
\(970\) | 27349.1 | 0.905285 | ||||||||
\(971\) | −47860.8 | −1.58180 | −0.790900 | − | 0.611946i | \(-0.790387\pi\) | ||||
−0.790900 | + | 0.611946i | \(0.790387\pi\) | |||||||
\(972\) | −9624.52 | −0.317599 | ||||||||
\(973\) | 1000.47 | 0.0329638 | ||||||||
\(974\) | −32696.3 | −1.07562 | ||||||||
\(975\) | −26576.1 | −0.872940 | ||||||||
\(976\) | −16315.8 | −0.535100 | ||||||||
\(977\) | 2411.64 | 0.0789716 | 0.0394858 | − | 0.999220i | \(-0.487428\pi\) | ||||
0.0394858 | + | 0.999220i | \(0.487428\pi\) | |||||||
\(978\) | −6082.04 | −0.198857 | ||||||||
\(979\) | −582.487 | −0.0190157 | ||||||||
\(980\) | −16033.4 | −0.522621 | ||||||||
\(981\) | −39266.9 | −1.27798 | ||||||||
\(982\) | 15512.3 | 0.504090 | ||||||||
\(983\) | −15548.6 | −0.504500 | −0.252250 | − | 0.967662i | \(-0.581171\pi\) | ||||
−0.252250 | + | 0.967662i | \(0.581171\pi\) | |||||||
\(984\) | −10515.5 | −0.340673 | ||||||||
\(985\) | −40296.7 | −1.30351 | ||||||||
\(986\) | 3082.26 | 0.0995530 | ||||||||
\(987\) | −273.410 | −0.00881735 | ||||||||
\(988\) | −15049.9 | −0.484617 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −4667.91 | −0.149854 | ||||||||
\(991\) | −679.692 | −0.0217872 | −0.0108936 | − | 0.999941i | \(-0.503468\pi\) | ||||
−0.0108936 | + | 0.999941i | \(0.503468\pi\) | |||||||
\(992\) | −17878.8 | −0.572231 | ||||||||
\(993\) | 26350.8 | 0.842114 | ||||||||
\(994\) | 1104.88 | 0.0352561 | ||||||||
\(995\) | 56853.6 | 1.81144 | ||||||||
\(996\) | −1647.33 | −0.0524073 | ||||||||
\(997\) | −42549.5 | −1.35161 | −0.675806 | − | 0.737080i | \(-0.736204\pi\) | ||||
−0.675806 | + | 0.737080i | \(0.736204\pi\) | |||||||
\(998\) | 2405.51 | 0.0762976 | ||||||||
\(999\) | −42665.1 | −1.35122 |
(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 | 1849.4.a.j.1.15 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.36 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.36 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.15 | yes | 50 | 1.1 | even | 1 | trivial |