Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("825.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(48.6765757547\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3368.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 15x + 11 \) |
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 | \(4.03932\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.03932 | −1.42811 | −0.714057 | − | 0.700087i | \(-0.753144\pi\) | ||||
−0.714057 | + | 0.700087i | \(0.753144\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | 8.31608 | 1.03951 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −12.1180 | −0.824522 | ||||||||
\(7\) | 6.49923 | 0.350925 | 0.175463 | − | 0.984486i | \(-0.443858\pi\) | ||||
0.175463 | + | 0.984486i | \(0.443858\pi\) | |||||||
\(8\) | −1.27677 | −0.0564257 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 24.9483 | 0.600162 | ||||||||
\(13\) | −30.5385 | −0.651528 | −0.325764 | − | 0.945451i | \(-0.605622\pi\) | ||||
−0.325764 | + | 0.945451i | \(0.605622\pi\) | |||||||
\(14\) | −26.2524 | −0.501161 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −61.3714 | −0.958928 | ||||||||
\(17\) | 43.1314 | 0.615347 | 0.307674 | − | 0.951492i | \(-0.400450\pi\) | ||||
0.307674 | + | 0.951492i | \(0.400450\pi\) | |||||||
\(18\) | −36.3539 | −0.476038 | ||||||||
\(19\) | −6.46044 | −0.0780066 | −0.0390033 | − | 0.999239i | \(-0.512418\pi\) | ||||
−0.0390033 | + | 0.999239i | \(0.512418\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 19.4977 | 0.202607 | ||||||||
\(22\) | −44.4325 | −0.430593 | ||||||||
\(23\) | −108.104 | −0.980054 | −0.490027 | − | 0.871707i | \(-0.663013\pi\) | ||||
−0.490027 | + | 0.871707i | \(0.663013\pi\) | |||||||
\(24\) | −3.83030 | −0.0325774 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 123.355 | 0.930457 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 54.0481 | 0.364791 | ||||||||
\(29\) | −274.857 | −1.75999 | −0.879995 | − | 0.474984i | \(-0.842454\pi\) | ||||
−0.879995 | + | 0.474984i | \(0.842454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −68.5519 | −0.397170 | −0.198585 | − | 0.980084i | \(-0.563635\pi\) | ||||
−0.198585 | + | 0.980084i | \(0.563635\pi\) | |||||||
\(32\) | 258.113 | 1.42588 | ||||||||
\(33\) | 33.0000 | 0.174078 | ||||||||
\(34\) | −174.221 | −0.878786 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 74.8448 | 0.346504 | ||||||||
\(37\) | 402.200 | 1.78706 | 0.893530 | − | 0.449004i | \(-0.148221\pi\) | ||||
0.893530 | + | 0.449004i | \(0.148221\pi\) | |||||||
\(38\) | 26.0958 | 0.111402 | ||||||||
\(39\) | −91.6156 | −0.376160 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −268.450 | −1.02256 | −0.511280 | − | 0.859414i | \(-0.670828\pi\) | ||||
−0.511280 | + | 0.859414i | \(0.670828\pi\) | |||||||
\(42\) | −78.7573 | −0.289346 | ||||||||
\(43\) | 30.5334 | 0.108286 | 0.0541431 | − | 0.998533i | \(-0.482757\pi\) | ||||
0.0541431 | + | 0.998533i | \(0.482757\pi\) | |||||||
\(44\) | 91.4769 | 0.313424 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 436.666 | 1.39963 | ||||||||
\(47\) | −31.5850 | −0.0980243 | −0.0490121 | − | 0.998798i | \(-0.515607\pi\) | ||||
−0.0490121 | + | 0.998798i | \(0.515607\pi\) | |||||||
\(48\) | −184.114 | −0.553638 | ||||||||
\(49\) | −300.760 | −0.876851 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 129.394 | 0.355271 | ||||||||
\(52\) | −253.961 | −0.677271 | ||||||||
\(53\) | −252.497 | −0.654398 | −0.327199 | − | 0.944956i | \(-0.606105\pi\) | ||||
−0.327199 | + | 0.944956i | \(0.606105\pi\) | |||||||
\(54\) | −109.062 | −0.274841 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.29800 | −0.0198012 | ||||||||
\(57\) | −19.3813 | −0.0450372 | ||||||||
\(58\) | 1110.24 | 2.51347 | ||||||||
\(59\) | −558.331 | −1.23201 | −0.616004 | − | 0.787743i | \(-0.711250\pi\) | ||||
−0.616004 | + | 0.787743i | \(0.711250\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 335.270 | 0.703719 | 0.351860 | − | 0.936053i | \(-0.385549\pi\) | ||||
0.351860 | + | 0.936053i | \(0.385549\pi\) | |||||||
\(62\) | 276.903 | 0.567205 | ||||||||
\(63\) | 58.4930 | 0.116975 | ||||||||
\(64\) | −551.628 | −1.07740 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −133.297 | −0.248603 | ||||||||
\(67\) | −28.7521 | −0.0524273 | −0.0262136 | − | 0.999656i | \(-0.508345\pi\) | ||||
−0.0262136 | + | 0.999656i | \(0.508345\pi\) | |||||||
\(68\) | 358.684 | 0.639660 | ||||||||
\(69\) | −324.312 | −0.565834 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 89.0081 | 0.148779 | 0.0743895 | − | 0.997229i | \(-0.476299\pi\) | ||||
0.0743895 | + | 0.997229i | \(0.476299\pi\) | |||||||
\(72\) | −11.4909 | −0.0188086 | ||||||||
\(73\) | 717.622 | 1.15057 | 0.575283 | − | 0.817954i | \(-0.304892\pi\) | ||||
0.575283 | + | 0.817954i | \(0.304892\pi\) | |||||||
\(74\) | −1624.61 | −2.55213 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −53.7256 | −0.0810887 | ||||||||
\(77\) | 71.4915 | 0.105808 | ||||||||
\(78\) | 370.065 | 0.537200 | ||||||||
\(79\) | 200.702 | 0.285832 | 0.142916 | − | 0.989735i | \(-0.454352\pi\) | ||||
0.142916 | + | 0.989735i | \(0.454352\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1084.36 | 1.46033 | ||||||||
\(83\) | −243.681 | −0.322258 | −0.161129 | − | 0.986933i | \(-0.551514\pi\) | ||||
−0.161129 | + | 0.986933i | \(0.551514\pi\) | |||||||
\(84\) | 162.144 | 0.210612 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −123.334 | −0.154645 | ||||||||
\(87\) | −824.571 | −1.01613 | ||||||||
\(88\) | −14.0444 | −0.0170130 | ||||||||
\(89\) | −312.832 | −0.372585 | −0.186293 | − | 0.982494i | \(-0.559647\pi\) | ||||
−0.186293 | + | 0.982494i | \(0.559647\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −198.477 | −0.228638 | ||||||||
\(92\) | −899.002 | −1.01878 | ||||||||
\(93\) | −205.656 | −0.229306 | ||||||||
\(94\) | 127.582 | 0.139990 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 774.338 | 0.823235 | ||||||||
\(97\) | −27.9996 | −0.0293085 | −0.0146543 | − | 0.999893i | \(-0.504665\pi\) | ||||
−0.0146543 | + | 0.999893i | \(0.504665\pi\) | |||||||
\(98\) | 1214.87 | 1.25224 | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −228.278 | −0.224896 | −0.112448 | − | 0.993658i | \(-0.535869\pi\) | ||||
−0.112448 | + | 0.993658i | \(0.535869\pi\) | |||||||
\(102\) | −522.664 | −0.507367 | ||||||||
\(103\) | 800.328 | 0.765618 | 0.382809 | − | 0.923827i | \(-0.374957\pi\) | ||||
0.382809 | + | 0.923827i | \(0.374957\pi\) | |||||||
\(104\) | 38.9906 | 0.0367629 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1019.91 | 0.934555 | ||||||||
\(107\) | 1046.89 | 0.945857 | 0.472929 | − | 0.881101i | \(-0.343197\pi\) | ||||
0.472929 | + | 0.881101i | \(0.343197\pi\) | |||||||
\(108\) | 224.534 | 0.200054 | ||||||||
\(109\) | 317.023 | 0.278581 | 0.139291 | − | 0.990252i | \(-0.455518\pi\) | ||||
0.139291 | + | 0.990252i | \(0.455518\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1206.60 | 1.03176 | ||||||||
\(112\) | −398.867 | −0.336512 | ||||||||
\(113\) | −1333.82 | −1.11040 | −0.555198 | − | 0.831718i | \(-0.687358\pi\) | ||||
−0.555198 | + | 0.831718i | \(0.687358\pi\) | |||||||
\(114\) | 78.2873 | 0.0643182 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2285.74 | −1.82953 | ||||||||
\(117\) | −274.847 | −0.217176 | ||||||||
\(118\) | 2255.28 | 1.75945 | ||||||||
\(119\) | 280.321 | 0.215941 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −1354.26 | −1.00499 | ||||||||
\(123\) | −805.351 | −0.590375 | ||||||||
\(124\) | −570.083 | −0.412863 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −236.272 | −0.167054 | ||||||||
\(127\) | −564.888 | −0.394691 | −0.197345 | − | 0.980334i | \(-0.563232\pi\) | ||||
−0.197345 | + | 0.980334i | \(0.563232\pi\) | |||||||
\(128\) | 163.299 | 0.112763 | ||||||||
\(129\) | 91.6003 | 0.0625190 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −214.082 | −0.142782 | −0.0713908 | − | 0.997448i | \(-0.522744\pi\) | ||||
−0.0713908 | + | 0.997448i | \(0.522744\pi\) | |||||||
\(132\) | 274.431 | 0.180956 | ||||||||
\(133\) | −41.9879 | −0.0273745 | ||||||||
\(134\) | 116.139 | 0.0748721 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −55.0688 | −0.0347214 | ||||||||
\(137\) | 65.2288 | 0.0406779 | 0.0203389 | − | 0.999793i | \(-0.493525\pi\) | ||||
0.0203389 | + | 0.999793i | \(0.493525\pi\) | |||||||
\(138\) | 1310.00 | 0.808076 | ||||||||
\(139\) | −407.084 | −0.248406 | −0.124203 | − | 0.992257i | \(-0.539637\pi\) | ||||
−0.124203 | + | 0.992257i | \(0.539637\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −94.7549 | −0.0565943 | ||||||||
\(142\) | −359.532 | −0.212474 | ||||||||
\(143\) | −335.924 | −0.196443 | ||||||||
\(144\) | −552.343 | −0.319643 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2898.70 | −1.64314 | ||||||||
\(147\) | −902.280 | −0.506250 | ||||||||
\(148\) | 3344.73 | 1.85767 | ||||||||
\(149\) | 792.092 | 0.435508 | 0.217754 | − | 0.976004i | \(-0.430127\pi\) | ||||
0.217754 | + | 0.976004i | \(0.430127\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2861.80 | −1.54232 | −0.771159 | − | 0.636642i | \(-0.780323\pi\) | ||||
−0.771159 | + | 0.636642i | \(0.780323\pi\) | |||||||
\(152\) | 8.24848 | 0.00440158 | ||||||||
\(153\) | 388.183 | 0.205116 | ||||||||
\(154\) | −288.777 | −0.151106 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −761.883 | −0.391022 | ||||||||
\(157\) | −2991.55 | −1.52071 | −0.760355 | − | 0.649507i | \(-0.774975\pi\) | ||||
−0.760355 | + | 0.649507i | \(0.774975\pi\) | |||||||
\(158\) | −810.698 | −0.408201 | ||||||||
\(159\) | −757.490 | −0.377817 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −702.592 | −0.343926 | ||||||||
\(162\) | −327.185 | −0.158679 | ||||||||
\(163\) | −2907.60 | −1.39718 | −0.698592 | − | 0.715520i | \(-0.746190\pi\) | ||||
−0.698592 | + | 0.715520i | \(0.746190\pi\) | |||||||
\(164\) | −2232.46 | −1.06296 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 984.304 | 0.460222 | ||||||||
\(167\) | −1100.39 | −0.509885 | −0.254942 | − | 0.966956i | \(-0.582056\pi\) | ||||
−0.254942 | + | 0.966956i | \(0.582056\pi\) | |||||||
\(168\) | −24.8940 | −0.0114322 | ||||||||
\(169\) | −1264.40 | −0.575511 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −58.1439 | −0.0260022 | ||||||||
\(172\) | 253.919 | 0.112565 | ||||||||
\(173\) | −3754.75 | −1.65011 | −0.825054 | − | 0.565054i | \(-0.808855\pi\) | ||||
−0.825054 | + | 0.565054i | \(0.808855\pi\) | |||||||
\(174\) | 3330.71 | 1.45115 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −675.086 | −0.289128 | ||||||||
\(177\) | −1674.99 | −0.711301 | ||||||||
\(178\) | 1263.63 | 0.532094 | ||||||||
\(179\) | −3218.79 | −1.34404 | −0.672021 | − | 0.740532i | \(-0.734574\pi\) | ||||
−0.672021 | + | 0.740532i | \(0.734574\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −456.885 | −0.187624 | −0.0938121 | − | 0.995590i | \(-0.529905\pi\) | ||||
−0.0938121 | + | 0.995590i | \(0.529905\pi\) | |||||||
\(182\) | 801.711 | 0.326521 | ||||||||
\(183\) | 1005.81 | 0.406292 | ||||||||
\(184\) | 138.024 | 0.0553002 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 830.709 | 0.327476 | ||||||||
\(187\) | 474.445 | 0.185534 | ||||||||
\(188\) | −262.663 | −0.101897 | ||||||||
\(189\) | 175.479 | 0.0675356 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4907.11 | −1.85899 | −0.929493 | − | 0.368841i | \(-0.879755\pi\) | ||||
−0.929493 | + | 0.368841i | \(0.879755\pi\) | |||||||
\(192\) | −1654.88 | −0.622036 | ||||||||
\(193\) | −1462.17 | −0.545333 | −0.272667 | − | 0.962109i | \(-0.587906\pi\) | ||||
−0.272667 | + | 0.962109i | \(0.587906\pi\) | |||||||
\(194\) | 113.099 | 0.0418559 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2501.15 | −0.911496 | ||||||||
\(197\) | −2210.10 | −0.799307 | −0.399653 | − | 0.916666i | \(-0.630869\pi\) | ||||
−0.399653 | + | 0.916666i | \(0.630869\pi\) | |||||||
\(198\) | −399.892 | −0.143531 | ||||||||
\(199\) | −395.272 | −0.140804 | −0.0704022 | − | 0.997519i | \(-0.522428\pi\) | ||||
−0.0704022 | + | 0.997519i | \(0.522428\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −86.2563 | −0.0302689 | ||||||||
\(202\) | 922.086 | 0.321177 | ||||||||
\(203\) | −1786.36 | −0.617625 | ||||||||
\(204\) | 1076.05 | 0.369308 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3232.78 | −1.09339 | ||||||||
\(207\) | −972.936 | −0.326685 | ||||||||
\(208\) | 1874.19 | 0.624769 | ||||||||
\(209\) | −71.0648 | −0.0235199 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1559.98 | 0.508974 | 0.254487 | − | 0.967076i | \(-0.418093\pi\) | ||||
0.254487 | + | 0.967076i | \(0.418093\pi\) | |||||||
\(212\) | −2099.78 | −0.680253 | ||||||||
\(213\) | 267.024 | 0.0858976 | ||||||||
\(214\) | −4228.72 | −1.35079 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −34.4727 | −0.0108591 | ||||||||
\(217\) | −445.534 | −0.139377 | ||||||||
\(218\) | −1280.56 | −0.397846 | ||||||||
\(219\) | 2152.87 | 0.664280 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1317.17 | −0.400916 | ||||||||
\(222\) | −4873.84 | −1.47347 | ||||||||
\(223\) | −756.215 | −0.227085 | −0.113542 | − | 0.993533i | \(-0.536220\pi\) | ||||
−0.113542 | + | 0.993533i | \(0.536220\pi\) | |||||||
\(224\) | 1677.53 | 0.500379 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5387.70 | 1.58577 | ||||||||
\(227\) | 5758.69 | 1.68378 | 0.841890 | − | 0.539649i | \(-0.181443\pi\) | ||||
0.841890 | + | 0.539649i | \(0.181443\pi\) | |||||||
\(228\) | −161.177 | −0.0468166 | ||||||||
\(229\) | −1912.63 | −0.551921 | −0.275961 | − | 0.961169i | \(-0.588996\pi\) | ||||
−0.275961 | + | 0.961169i | \(0.588996\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 214.474 | 0.0610882 | ||||||||
\(232\) | 350.929 | 0.0993086 | ||||||||
\(233\) | −1034.86 | −0.290970 | −0.145485 | − | 0.989360i | \(-0.546474\pi\) | ||||
−0.145485 | + | 0.989360i | \(0.546474\pi\) | |||||||
\(234\) | 1110.19 | 0.310152 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4643.13 | −1.28069 | ||||||||
\(237\) | 602.105 | 0.165025 | ||||||||
\(238\) | −1132.30 | −0.308388 | ||||||||
\(239\) | 2647.23 | 0.716465 | 0.358232 | − | 0.933632i | \(-0.383380\pi\) | ||||
0.358232 | + | 0.933632i | \(0.383380\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6734.00 | 1.79990 | 0.899948 | − | 0.435996i | \(-0.143604\pi\) | ||||
0.899948 | + | 0.435996i | \(0.143604\pi\) | |||||||
\(242\) | −488.757 | −0.129829 | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | 2788.13 | 0.731523 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3253.07 | 0.843123 | ||||||||
\(247\) | 197.292 | 0.0508235 | ||||||||
\(248\) | 87.5248 | 0.0224106 | ||||||||
\(249\) | −731.043 | −0.186056 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5377.57 | −1.35231 | −0.676154 | − | 0.736761i | \(-0.736354\pi\) | ||||
−0.676154 | + | 0.736761i | \(0.736354\pi\) | |||||||
\(252\) | 486.433 | 0.121597 | ||||||||
\(253\) | −1189.14 | −0.295497 | ||||||||
\(254\) | 2281.76 | 0.563663 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3753.41 | 0.916360 | ||||||||
\(257\) | −5882.33 | −1.42774 | −0.713871 | − | 0.700278i | \(-0.753060\pi\) | ||||
−0.713871 | + | 0.700278i | \(0.753060\pi\) | |||||||
\(258\) | −370.003 | −0.0892843 | ||||||||
\(259\) | 2613.99 | 0.627124 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2473.71 | −0.586663 | ||||||||
\(262\) | 864.744 | 0.203909 | ||||||||
\(263\) | 4001.67 | 0.938227 | 0.469113 | − | 0.883138i | \(-0.344574\pi\) | ||||
0.469113 | + | 0.883138i | \(0.344574\pi\) | |||||||
\(264\) | −42.1333 | −0.00982245 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 169.602 | 0.0390939 | ||||||||
\(267\) | −938.495 | −0.215112 | ||||||||
\(268\) | −239.105 | −0.0544987 | ||||||||
\(269\) | −1758.29 | −0.398530 | −0.199265 | − | 0.979946i | \(-0.563856\pi\) | ||||
−0.199265 | + | 0.979946i | \(0.563856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6018.44 | 1.34906 | 0.674528 | − | 0.738249i | \(-0.264347\pi\) | ||||
0.674528 | + | 0.738249i | \(0.264347\pi\) | |||||||
\(272\) | −2647.03 | −0.590074 | ||||||||
\(273\) | −595.431 | −0.132004 | ||||||||
\(274\) | −263.480 | −0.0580927 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2697.01 | −0.588191 | ||||||||
\(277\) | −2910.30 | −0.631275 | −0.315637 | − | 0.948880i | \(-0.602218\pi\) | ||||
−0.315637 | + | 0.948880i | \(0.602218\pi\) | |||||||
\(278\) | 1644.34 | 0.354752 | ||||||||
\(279\) | −616.967 | −0.132390 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6893.19 | 1.46339 | 0.731697 | − | 0.681631i | \(-0.238729\pi\) | ||||
0.731697 | + | 0.681631i | \(0.238729\pi\) | |||||||
\(282\) | 382.745 | 0.0808232 | ||||||||
\(283\) | −3120.16 | −0.655385 | −0.327693 | − | 0.944784i | \(-0.606271\pi\) | ||||
−0.327693 | + | 0.944784i | \(0.606271\pi\) | |||||||
\(284\) | 740.199 | 0.154657 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1356.90 | 0.280543 | ||||||||
\(287\) | −1744.72 | −0.358842 | ||||||||
\(288\) | 2323.01 | 0.475295 | ||||||||
\(289\) | −3052.68 | −0.621348 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −83.9988 | −0.0169213 | ||||||||
\(292\) | 5967.81 | 1.19603 | ||||||||
\(293\) | −8869.62 | −1.76849 | −0.884247 | − | 0.467020i | \(-0.845328\pi\) | ||||
−0.884247 | + | 0.467020i | \(0.845328\pi\) | |||||||
\(294\) | 3644.60 | 0.722983 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −513.515 | −0.100836 | ||||||||
\(297\) | 297.000 | 0.0580259 | ||||||||
\(298\) | −3199.51 | −0.621955 | ||||||||
\(299\) | 3301.34 | 0.638533 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 198.444 | 0.0380003 | ||||||||
\(302\) | 11559.7 | 2.20261 | ||||||||
\(303\) | −684.833 | −0.129844 | ||||||||
\(304\) | 396.486 | 0.0748028 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1567.99 | −0.292929 | ||||||||
\(307\) | 5713.42 | 1.06216 | 0.531078 | − | 0.847323i | \(-0.321787\pi\) | ||||
0.531078 | + | 0.847323i | \(0.321787\pi\) | |||||||
\(308\) | 594.529 | 0.109988 | ||||||||
\(309\) | 2400.98 | 0.442030 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1984.01 | 0.361746 | 0.180873 | − | 0.983506i | \(-0.442108\pi\) | ||||
0.180873 | + | 0.983506i | \(0.442108\pi\) | |||||||
\(312\) | 116.972 | 0.0212251 | ||||||||
\(313\) | 2675.50 | 0.483156 | 0.241578 | − | 0.970381i | \(-0.422335\pi\) | ||||
0.241578 | + | 0.970381i | \(0.422335\pi\) | |||||||
\(314\) | 12083.8 | 2.17175 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1669.05 | 0.297125 | ||||||||
\(317\) | 7083.76 | 1.25509 | 0.627545 | − | 0.778580i | \(-0.284060\pi\) | ||||
0.627545 | + | 0.778580i | \(0.284060\pi\) | |||||||
\(318\) | 3059.74 | 0.539565 | ||||||||
\(319\) | −3023.43 | −0.530657 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3140.67 | 0.546091 | ||||||||
\(322\) | 2837.99 | 0.491165 | ||||||||
\(323\) | −278.648 | −0.0480012 | ||||||||
\(324\) | 673.603 | 0.115501 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11744.7 | 1.99534 | ||||||||
\(327\) | 951.070 | 0.160839 | ||||||||
\(328\) | 342.749 | 0.0576986 | ||||||||
\(329\) | −205.278 | −0.0343992 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7812.39 | 1.29730 | 0.648652 | − | 0.761085i | \(-0.275333\pi\) | ||||
0.648652 | + | 0.761085i | \(0.275333\pi\) | |||||||
\(332\) | −2026.47 | −0.334991 | ||||||||
\(333\) | 3619.80 | 0.595686 | ||||||||
\(334\) | 4444.82 | 0.728173 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1196.60 | −0.194285 | ||||||||
\(337\) | 11866.4 | 1.91811 | 0.959056 | − | 0.283218i | \(-0.0914019\pi\) | ||||
0.959056 | + | 0.283218i | \(0.0914019\pi\) | |||||||
\(338\) | 5107.30 | 0.821895 | ||||||||
\(339\) | −4001.45 | −0.641088 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −754.071 | −0.119751 | ||||||||
\(342\) | 234.862 | 0.0371341 | ||||||||
\(343\) | −4183.94 | −0.658635 | ||||||||
\(344\) | −38.9841 | −0.00611012 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 15166.6 | 2.35654 | ||||||||
\(347\) | −3485.50 | −0.539225 | −0.269613 | − | 0.962969i | \(-0.586896\pi\) | ||||
−0.269613 | + | 0.962969i | \(0.586896\pi\) | |||||||
\(348\) | −6857.21 | −1.05628 | ||||||||
\(349\) | −6366.76 | −0.976518 | −0.488259 | − | 0.872699i | \(-0.662368\pi\) | ||||
−0.488259 | + | 0.872699i | \(0.662368\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −824.541 | −0.125387 | ||||||||
\(352\) | 2839.24 | 0.429920 | ||||||||
\(353\) | −8223.15 | −1.23987 | −0.619935 | − | 0.784653i | \(-0.712841\pi\) | ||||
−0.619935 | + | 0.784653i | \(0.712841\pi\) | |||||||
\(354\) | 6765.83 | 1.01582 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2601.54 | −0.387306 | ||||||||
\(357\) | 840.962 | 0.124674 | ||||||||
\(358\) | 13001.7 | 1.91945 | ||||||||
\(359\) | −9377.54 | −1.37863 | −0.689314 | − | 0.724462i | \(-0.742088\pi\) | ||||
−0.689314 | + | 0.724462i | \(0.742088\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6817.26 | −0.993915 | ||||||||
\(362\) | 1845.50 | 0.267949 | ||||||||
\(363\) | 363.000 | 0.0524864 | ||||||||
\(364\) | −1650.55 | −0.237671 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4062.78 | −0.580232 | ||||||||
\(367\) | 310.895 | 0.0442196 | 0.0221098 | − | 0.999756i | \(-0.492962\pi\) | ||||
0.0221098 | + | 0.999756i | \(0.492962\pi\) | |||||||
\(368\) | 6634.49 | 0.939801 | ||||||||
\(369\) | −2416.05 | −0.340853 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1641.03 | −0.229645 | ||||||||
\(372\) | −1710.25 | −0.238366 | ||||||||
\(373\) | 4738.51 | 0.657777 | 0.328889 | − | 0.944369i | \(-0.393326\pi\) | ||||
0.328889 | + | 0.944369i | \(0.393326\pi\) | |||||||
\(374\) | −1916.44 | −0.264964 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 40.3267 | 0.00553109 | ||||||||
\(377\) | 8393.74 | 1.14668 | ||||||||
\(378\) | −708.816 | −0.0964486 | ||||||||
\(379\) | −4735.47 | −0.641806 | −0.320903 | − | 0.947112i | \(-0.603986\pi\) | ||||
−0.320903 | + | 0.947112i | \(0.603986\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1694.66 | −0.227875 | ||||||||
\(382\) | 19821.4 | 2.65484 | ||||||||
\(383\) | −3632.14 | −0.484579 | −0.242289 | − | 0.970204i | \(-0.577898\pi\) | ||||
−0.242289 | + | 0.970204i | \(0.577898\pi\) | |||||||
\(384\) | 489.896 | 0.0651039 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5906.17 | 0.778798 | ||||||||
\(387\) | 274.801 | 0.0360954 | ||||||||
\(388\) | −232.847 | −0.0304665 | ||||||||
\(389\) | 6557.50 | 0.854701 | 0.427350 | − | 0.904086i | \(-0.359447\pi\) | ||||
0.427350 | + | 0.904086i | \(0.359447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4662.68 | −0.603073 | ||||||||
\(392\) | 384.001 | 0.0494769 | ||||||||
\(393\) | −642.245 | −0.0824350 | ||||||||
\(394\) | 8927.31 | 1.14150 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 823.292 | 0.104475 | ||||||||
\(397\) | −4084.97 | −0.516420 | −0.258210 | − | 0.966089i | \(-0.583133\pi\) | ||||
−0.258210 | + | 0.966089i | \(0.583133\pi\) | |||||||
\(398\) | 1596.63 | 0.201085 | ||||||||
\(399\) | −125.964 | −0.0158047 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6676.04 | −0.831386 | −0.415693 | − | 0.909505i | \(-0.636461\pi\) | ||||
−0.415693 | + | 0.909505i | \(0.636461\pi\) | |||||||
\(402\) | 348.417 | 0.0432275 | ||||||||
\(403\) | 2093.47 | 0.258768 | ||||||||
\(404\) | −1898.38 | −0.233782 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7215.67 | 0.882039 | ||||||||
\(407\) | 4424.20 | 0.538819 | ||||||||
\(408\) | −165.206 | −0.0200464 | ||||||||
\(409\) | 1718.56 | 0.207769 | 0.103884 | − | 0.994589i | \(-0.466873\pi\) | ||||
0.103884 | + | 0.994589i | \(0.466873\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 195.686 | 0.0234854 | ||||||||
\(412\) | 6655.60 | 0.795868 | ||||||||
\(413\) | −3628.72 | −0.432343 | ||||||||
\(414\) | 3930.00 | 0.466543 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7882.39 | −0.929004 | ||||||||
\(417\) | −1221.25 | −0.143417 | ||||||||
\(418\) | 287.053 | 0.0335891 | ||||||||
\(419\) | 5732.23 | 0.668348 | 0.334174 | − | 0.942511i | \(-0.391543\pi\) | ||||
0.334174 | + | 0.942511i | \(0.391543\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9647.38 | −1.11683 | −0.558414 | − | 0.829563i | \(-0.688590\pi\) | ||||
−0.558414 | + | 0.829563i | \(0.688590\pi\) | |||||||
\(422\) | −6301.26 | −0.726873 | ||||||||
\(423\) | −284.265 | −0.0326748 | ||||||||
\(424\) | 322.379 | 0.0369248 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1078.60 | −0.122672 | ||||||||
\(427\) | 2178.99 | 0.246953 | ||||||||
\(428\) | 8706.03 | 0.983229 | ||||||||
\(429\) | −1007.77 | −0.113417 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3054.57 | −0.341376 | −0.170688 | − | 0.985325i | \(-0.554599\pi\) | ||||
−0.170688 | + | 0.985325i | \(0.554599\pi\) | |||||||
\(432\) | −1657.03 | −0.184546 | ||||||||
\(433\) | −11022.8 | −1.22337 | −0.611686 | − | 0.791100i | \(-0.709509\pi\) | ||||
−0.611686 | + | 0.791100i | \(0.709509\pi\) | |||||||
\(434\) | 1799.65 | 0.199046 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2636.39 | 0.289588 | ||||||||
\(437\) | 698.399 | 0.0764507 | ||||||||
\(438\) | −8696.11 | −0.948667 | ||||||||
\(439\) | −7589.30 | −0.825097 | −0.412548 | − | 0.910936i | \(-0.635361\pi\) | ||||
−0.412548 | + | 0.910936i | \(0.635361\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2706.84 | −0.292284 | ||||||||
\(442\) | 5320.47 | 0.572554 | ||||||||
\(443\) | −4043.30 | −0.433641 | −0.216821 | − | 0.976211i | \(-0.569569\pi\) | ||||
−0.216821 | + | 0.976211i | \(0.569569\pi\) | |||||||
\(444\) | 10034.2 | 1.07252 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3054.59 | 0.324303 | ||||||||
\(447\) | 2376.28 | 0.251441 | ||||||||
\(448\) | −3585.16 | −0.378086 | ||||||||
\(449\) | 14619.3 | 1.53658 | 0.768291 | − | 0.640101i | \(-0.221107\pi\) | ||||
0.768291 | + | 0.640101i | \(0.221107\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2952.96 | −0.308313 | ||||||||
\(452\) | −11092.1 | −1.15427 | ||||||||
\(453\) | −8585.40 | −0.890458 | ||||||||
\(454\) | −23261.2 | −2.40463 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.7454 | 0.00254125 | ||||||||
\(457\) | 10910.8 | 1.11682 | 0.558411 | − | 0.829565i | \(-0.311411\pi\) | ||||
0.558411 | + | 0.829565i | \(0.311411\pi\) | |||||||
\(458\) | 7725.71 | 0.788207 | ||||||||
\(459\) | 1164.55 | 0.118424 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16371.0 | 1.65395 | 0.826977 | − | 0.562236i | \(-0.190059\pi\) | ||||
0.826977 | + | 0.562236i | \(0.190059\pi\) | |||||||
\(462\) | −866.331 | −0.0872410 | ||||||||
\(463\) | 16023.5 | 1.60837 | 0.804186 | − | 0.594377i | \(-0.202601\pi\) | ||||
0.804186 | + | 0.594377i | \(0.202601\pi\) | |||||||
\(464\) | 16868.4 | 1.68770 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4180.13 | 0.415538 | ||||||||
\(467\) | 15097.3 | 1.49597 | 0.747985 | − | 0.663716i | \(-0.231022\pi\) | ||||
0.747985 | + | 0.663716i | \(0.231022\pi\) | |||||||
\(468\) | −2285.65 | −0.225757 | ||||||||
\(469\) | −186.866 | −0.0183981 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8974.65 | −0.877983 | ||||||||
\(472\) | 712.859 | 0.0695170 | ||||||||
\(473\) | 335.868 | 0.0326495 | ||||||||
\(474\) | −2432.09 | −0.235675 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2331.17 | 0.224473 | ||||||||
\(477\) | −2272.47 | −0.218133 | ||||||||
\(478\) | −10693.0 | −1.02319 | ||||||||
\(479\) | −10459.0 | −0.997667 | −0.498834 | − | 0.866698i | \(-0.666238\pi\) | ||||
−0.498834 | + | 0.866698i | \(0.666238\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12282.6 | −1.16432 | ||||||||
\(482\) | −27200.8 | −2.57046 | ||||||||
\(483\) | −2107.78 | −0.198566 | ||||||||
\(484\) | 1006.25 | 0.0945010 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −981.554 | −0.0916136 | ||||||||
\(487\) | 7939.86 | 0.738788 | 0.369394 | − | 0.929273i | \(-0.379565\pi\) | ||||
0.369394 | + | 0.929273i | \(0.379565\pi\) | |||||||
\(488\) | −428.061 | −0.0397078 | ||||||||
\(489\) | −8722.81 | −0.806665 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11492.7 | 1.05633 | 0.528167 | − | 0.849141i | \(-0.322880\pi\) | ||||
0.528167 | + | 0.849141i | \(0.322880\pi\) | |||||||
\(492\) | −6697.37 | −0.613701 | ||||||||
\(493\) | −11855.0 | −1.08300 | ||||||||
\(494\) | −796.927 | −0.0725818 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4207.13 | 0.380858 | ||||||||
\(497\) | 578.484 | 0.0522103 | ||||||||
\(498\) | 2952.91 | 0.265709 | ||||||||
\(499\) | 4813.54 | 0.431831 | 0.215915 | − | 0.976412i | \(-0.430726\pi\) | ||||
0.215915 | + | 0.976412i | \(0.430726\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3301.17 | −0.294382 | ||||||||
\(502\) | 21721.7 | 1.93125 | ||||||||
\(503\) | −17756.3 | −1.57399 | −0.786993 | − | 0.616962i | \(-0.788363\pi\) | ||||
−0.786993 | + | 0.616962i | \(0.788363\pi\) | |||||||
\(504\) | −74.6820 | −0.00660040 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4803.33 | 0.422004 | ||||||||
\(507\) | −3793.19 | −0.332271 | ||||||||
\(508\) | −4697.66 | −0.410285 | ||||||||
\(509\) | 3183.05 | 0.277183 | 0.138592 | − | 0.990350i | \(-0.455742\pi\) | ||||
0.138592 | + | 0.990350i | \(0.455742\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4663.99 | 0.403763 | ||||||||
\(512\) | −16467.6 | −1.42143 | ||||||||
\(513\) | −174.432 | −0.0150124 | ||||||||
\(514\) | 23760.6 | 2.03898 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 761.756 | 0.0649892 | ||||||||
\(517\) | −347.435 | −0.0295554 | ||||||||
\(518\) | −10558.7 | −0.895605 | ||||||||
\(519\) | −11264.3 | −0.952690 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7246.60 | 0.609365 | 0.304683 | − | 0.952454i | \(-0.401450\pi\) | ||||
0.304683 | + | 0.952454i | \(0.401450\pi\) | |||||||
\(522\) | 9992.12 | 0.837822 | ||||||||
\(523\) | 17985.0 | 1.50369 | 0.751845 | − | 0.659340i | \(-0.229164\pi\) | ||||
0.751845 | + | 0.659340i | \(0.229164\pi\) | |||||||
\(524\) | −1780.32 | −0.148423 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16164.0 | −1.33990 | ||||||||
\(527\) | −2956.74 | −0.244398 | ||||||||
\(528\) | −2025.26 | −0.166928 | ||||||||
\(529\) | −480.530 | −0.0394945 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5024.98 | −0.410670 | ||||||||
\(532\) | −349.175 | −0.0284561 | ||||||||
\(533\) | 8198.09 | 0.666226 | ||||||||
\(534\) | 3790.88 | 0.307205 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 36.7097 | 0.00295825 | ||||||||
\(537\) | −9656.36 | −0.775983 | ||||||||
\(538\) | 7102.28 | 0.569147 | ||||||||
\(539\) | −3308.36 | −0.264381 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14549.3 | −1.15624 | −0.578119 | − | 0.815952i | \(-0.696213\pi\) | ||||
−0.578119 | + | 0.815952i | \(0.696213\pi\) | |||||||
\(542\) | −24310.4 | −1.92661 | ||||||||
\(543\) | −1370.65 | −0.108325 | ||||||||
\(544\) | 11132.8 | 0.877414 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 2405.13 | 0.188517 | ||||||||
\(547\) | −5487.29 | −0.428920 | −0.214460 | − | 0.976733i | \(-0.568799\pi\) | ||||
−0.214460 | + | 0.976733i | \(0.568799\pi\) | |||||||
\(548\) | 542.448 | 0.0422851 | ||||||||
\(549\) | 3017.43 | 0.234573 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1775.70 | 0.137291 | ||||||||
\(552\) | 414.071 | 0.0319276 | ||||||||
\(553\) | 1304.41 | 0.100306 | ||||||||
\(554\) | 11755.6 | 0.901532 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3385.35 | −0.258221 | ||||||||
\(557\) | 7366.60 | 0.560382 | 0.280191 | − | 0.959944i | \(-0.409602\pi\) | ||||
0.280191 | + | 0.959944i | \(0.409602\pi\) | |||||||
\(558\) | 2492.13 | 0.189068 | ||||||||
\(559\) | −932.446 | −0.0705515 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1423.34 | 0.107118 | ||||||||
\(562\) | −27843.8 | −2.08989 | ||||||||
\(563\) | 4516.14 | 0.338068 | 0.169034 | − | 0.985610i | \(-0.445935\pi\) | ||||
0.169034 | + | 0.985610i | \(0.445935\pi\) | |||||||
\(564\) | −787.990 | −0.0588304 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 12603.3 | 0.935965 | ||||||||
\(567\) | 526.437 | 0.0389917 | ||||||||
\(568\) | −113.643 | −0.00839496 | ||||||||
\(569\) | 2174.35 | 0.160200 | 0.0800999 | − | 0.996787i | \(-0.474476\pi\) | ||||
0.0800999 | + | 0.996787i | \(0.474476\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25339.7 | −1.85715 | −0.928575 | − | 0.371145i | \(-0.878965\pi\) | ||||
−0.928575 | + | 0.371145i | \(0.878965\pi\) | |||||||
\(572\) | −2793.57 | −0.204205 | ||||||||
\(573\) | −14721.3 | −1.07329 | ||||||||
\(574\) | 7047.48 | 0.512467 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4964.65 | −0.359133 | ||||||||
\(577\) | 21909.1 | 1.58074 | 0.790370 | − | 0.612630i | \(-0.209888\pi\) | ||||
0.790370 | + | 0.612630i | \(0.209888\pi\) | |||||||
\(578\) | 12330.8 | 0.887356 | ||||||||
\(579\) | −4386.51 | −0.314848 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1583.74 | −0.113089 | ||||||||
\(582\) | 339.298 | 0.0241655 | ||||||||
\(583\) | −2777.46 | −0.197308 | ||||||||
\(584\) | −916.237 | −0.0649215 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 35827.2 | 2.52561 | ||||||||
\(587\) | 922.235 | 0.0648462 | 0.0324231 | − | 0.999474i | \(-0.489678\pi\) | ||||
0.0324231 | + | 0.999474i | \(0.489678\pi\) | |||||||
\(588\) | −7503.44 | −0.526253 | ||||||||
\(589\) | 442.875 | 0.0309819 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6630.31 | −0.461480 | ||||||||
\(592\) | −24683.6 | −1.71366 | ||||||||
\(593\) | 9075.86 | 0.628501 | 0.314250 | − | 0.949340i | \(-0.398247\pi\) | ||||
0.314250 | + | 0.949340i | \(0.398247\pi\) | |||||||
\(594\) | −1199.68 | −0.0828676 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6587.10 | 0.452715 | ||||||||
\(597\) | −1185.82 | −0.0812935 | ||||||||
\(598\) | −13335.2 | −0.911898 | ||||||||
\(599\) | 19987.0 | 1.36335 | 0.681675 | − | 0.731655i | \(-0.261252\pi\) | ||||
0.681675 | + | 0.731655i | \(0.261252\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11116.7 | 0.754509 | 0.377255 | − | 0.926110i | \(-0.376868\pi\) | ||||
0.377255 | + | 0.926110i | \(0.376868\pi\) | |||||||
\(602\) | −801.577 | −0.0542688 | ||||||||
\(603\) | −258.769 | −0.0174758 | ||||||||
\(604\) | −23799.0 | −1.60326 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2766.26 | 0.185432 | ||||||||
\(607\) | −19355.0 | −1.29423 | −0.647114 | − | 0.762393i | \(-0.724024\pi\) | ||||
−0.647114 | + | 0.762393i | \(0.724024\pi\) | |||||||
\(608\) | −1667.52 | −0.111228 | ||||||||
\(609\) | −5359.08 | −0.356586 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 964.559 | 0.0638656 | ||||||||
\(612\) | 3228.16 | 0.213220 | ||||||||
\(613\) | 12325.5 | 0.812111 | 0.406056 | − | 0.913848i | \(-0.366904\pi\) | ||||
0.406056 | + | 0.913848i | \(0.366904\pi\) | |||||||
\(614\) | −23078.3 | −1.51688 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −91.2780 | −0.00597029 | ||||||||
\(617\) | −28207.0 | −1.84047 | −0.920236 | − | 0.391363i | \(-0.872004\pi\) | ||||
−0.920236 | + | 0.391363i | \(0.872004\pi\) | |||||||
\(618\) | −9698.34 | −0.631269 | ||||||||
\(619\) | 17236.9 | 1.11924 | 0.559621 | − | 0.828748i | \(-0.310947\pi\) | ||||
0.559621 | + | 0.828748i | \(0.310947\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2918.81 | −0.188611 | ||||||||
\(622\) | −8014.06 | −0.516615 | ||||||||
\(623\) | −2033.16 | −0.130750 | ||||||||
\(624\) | 5622.58 | 0.360711 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10807.2 | −0.690003 | ||||||||
\(627\) | −213.194 | −0.0135792 | ||||||||
\(628\) | −24878.0 | −1.58080 | ||||||||
\(629\) | 17347.4 | 1.09966 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23582.7 | −1.48782 | −0.743908 | − | 0.668282i | \(-0.767030\pi\) | ||||
−0.743908 | + | 0.668282i | \(0.767030\pi\) | |||||||
\(632\) | −256.250 | −0.0161283 | ||||||||
\(633\) | 4679.94 | 0.293856 | ||||||||
\(634\) | −28613.6 | −1.79241 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6299.35 | −0.392744 | ||||||||
\(637\) | 9184.77 | 0.571294 | ||||||||
\(638\) | 12212.6 | 0.757839 | ||||||||
\(639\) | 801.073 | 0.0495930 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13003.1 | −0.801233 | −0.400617 | − | 0.916246i | \(-0.631204\pi\) | ||||
−0.400617 | + | 0.916246i | \(0.631204\pi\) | |||||||
\(642\) | −12686.2 | −0.779880 | ||||||||
\(643\) | 21269.1 | 1.30446 | 0.652232 | − | 0.758019i | \(-0.273833\pi\) | ||||
0.652232 | + | 0.758019i | \(0.273833\pi\) | |||||||
\(644\) | −5842.82 | −0.357514 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1125.55 | 0.0685511 | ||||||||
\(647\) | −29247.2 | −1.77716 | −0.888582 | − | 0.458717i | \(-0.848309\pi\) | ||||
−0.888582 | + | 0.458717i | \(0.848309\pi\) | |||||||
\(648\) | −103.418 | −0.00626952 | ||||||||
\(649\) | −6141.64 | −0.371465 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1336.60 | −0.0804694 | ||||||||
\(652\) | −24179.9 | −1.45239 | ||||||||
\(653\) | 1678.30 | 0.100577 | 0.0502885 | − | 0.998735i | \(-0.483986\pi\) | ||||
0.0502885 | + | 0.998735i | \(0.483986\pi\) | |||||||
\(654\) | −3841.67 | −0.229696 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 16475.2 | 0.980561 | ||||||||
\(657\) | 6458.60 | 0.383522 | ||||||||
\(658\) | 829.182 | 0.0491260 | ||||||||
\(659\) | −7620.41 | −0.450454 | −0.225227 | − | 0.974306i | \(-0.572312\pi\) | ||||
−0.225227 | + | 0.974306i | \(0.572312\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22762.2 | −1.33941 | −0.669703 | − | 0.742629i | \(-0.733579\pi\) | ||||
−0.669703 | + | 0.742629i | \(0.733579\pi\) | |||||||
\(662\) | −31556.7 | −1.85270 | ||||||||
\(663\) | −3951.51 | −0.231469 | ||||||||
\(664\) | 311.124 | 0.0181837 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14621.5 | −0.850708 | ||||||||
\(667\) | 29713.2 | 1.72488 | ||||||||
\(668\) | −9150.93 | −0.530030 | ||||||||
\(669\) | −2268.65 | −0.131107 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3687.96 | 0.212179 | ||||||||
\(672\) | 5032.60 | 0.288894 | ||||||||
\(673\) | −698.528 | −0.0400093 | −0.0200047 | − | 0.999800i | \(-0.506368\pi\) | ||||
−0.0200047 | + | 0.999800i | \(0.506368\pi\) | |||||||
\(674\) | −47932.1 | −2.73928 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10514.8 | −0.598250 | ||||||||
\(677\) | 10860.1 | 0.616524 | 0.308262 | − | 0.951302i | \(-0.400253\pi\) | ||||
0.308262 | + | 0.951302i | \(0.400253\pi\) | |||||||
\(678\) | 16163.1 | 0.915547 | ||||||||
\(679\) | −181.976 | −0.0102851 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17276.1 | 0.972131 | ||||||||
\(682\) | 3045.93 | 0.171019 | ||||||||
\(683\) | 6534.95 | 0.366110 | 0.183055 | − | 0.983103i | \(-0.441401\pi\) | ||||
0.183055 | + | 0.983103i | \(0.441401\pi\) | |||||||
\(684\) | −483.530 | −0.0270296 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16900.3 | 0.940606 | ||||||||
\(687\) | −5737.88 | −0.318652 | ||||||||
\(688\) | −1873.88 | −0.103839 | ||||||||
\(689\) | 7710.88 | 0.426359 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10915.3 | −0.600924 | −0.300462 | − | 0.953794i | \(-0.597141\pi\) | ||||
−0.300462 | + | 0.953794i | \(0.597141\pi\) | |||||||
\(692\) | −31224.9 | −1.71530 | ||||||||
\(693\) | 643.423 | 0.0352693 | ||||||||
\(694\) | 14079.0 | 0.770076 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1052.79 | 0.0573359 | ||||||||
\(697\) | −11578.6 | −0.629229 | ||||||||
\(698\) | 25717.3 | 1.39458 | ||||||||
\(699\) | −3104.58 | −0.167991 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18405.4 | 0.991674 | 0.495837 | − | 0.868416i | \(-0.334861\pi\) | ||||
0.495837 | + | 0.868416i | \(0.334861\pi\) | |||||||
\(702\) | 3330.58 | 0.179067 | ||||||||
\(703\) | −2598.39 | −0.139403 | ||||||||
\(704\) | −6067.91 | −0.324848 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 33215.9 | 1.77068 | ||||||||
\(707\) | −1483.63 | −0.0789217 | ||||||||
\(708\) | −13929.4 | −0.739405 | ||||||||
\(709\) | −21436.2 | −1.13547 | −0.567737 | − | 0.823210i | \(-0.692181\pi\) | ||||
−0.567737 | + | 0.823210i | \(0.692181\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1806.32 | 0.0952773 | ||||||||
\(712\) | 399.413 | 0.0210234 | ||||||||
\(713\) | 7410.73 | 0.389248 | ||||||||
\(714\) | −3396.91 | −0.178048 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −26767.7 | −1.39715 | ||||||||
\(717\) | 7941.69 | 0.413651 | ||||||||
\(718\) | 37878.9 | 1.96884 | ||||||||
\(719\) | 28641.7 | 1.48561 | 0.742807 | − | 0.669506i | \(-0.233494\pi\) | ||||
0.742807 | + | 0.669506i | \(0.233494\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5201.51 | 0.268675 | ||||||||
\(722\) | 27537.1 | 1.41942 | ||||||||
\(723\) | 20202.0 | 1.03917 | ||||||||
\(724\) | −3799.49 | −0.195037 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1466.27 | −0.0749566 | ||||||||
\(727\) | 1723.13 | 0.0879055 | 0.0439527 | − | 0.999034i | \(-0.486005\pi\) | ||||
0.0439527 | + | 0.999034i | \(0.486005\pi\) | |||||||
\(728\) | 253.409 | 0.0129010 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1316.95 | 0.0666335 | ||||||||
\(732\) | 8364.39 | 0.422345 | ||||||||
\(733\) | 18813.4 | 0.948005 | 0.474003 | − | 0.880523i | \(-0.342809\pi\) | ||||
0.474003 | + | 0.880523i | \(0.342809\pi\) | |||||||
\(734\) | −1255.80 | −0.0631506 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27903.0 | −1.39744 | ||||||||
\(737\) | −316.273 | −0.0158074 | ||||||||
\(738\) | 9759.21 | 0.486777 | ||||||||
\(739\) | −10893.3 | −0.542242 | −0.271121 | − | 0.962545i | \(-0.587394\pi\) | ||||
−0.271121 | + | 0.962545i | \(0.587394\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 591.877 | 0.0293430 | ||||||||
\(742\) | 6628.65 | 0.327959 | ||||||||
\(743\) | −11888.6 | −0.587013 | −0.293507 | − | 0.955957i | \(-0.594822\pi\) | ||||
−0.293507 | + | 0.955957i | \(0.594822\pi\) | |||||||
\(744\) | 262.574 | 0.0129388 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −19140.4 | −0.939381 | ||||||||
\(747\) | −2193.13 | −0.107419 | ||||||||
\(748\) | 3945.53 | 0.192865 | ||||||||
\(749\) | 6803.98 | 0.331925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32134.8 | −1.56140 | −0.780702 | − | 0.624903i | \(-0.785138\pi\) | ||||
−0.780702 | + | 0.624903i | \(0.785138\pi\) | |||||||
\(752\) | 1938.41 | 0.0939982 | ||||||||
\(753\) | −16132.7 | −0.780755 | ||||||||
\(754\) | −33905.0 | −1.63759 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1459.30 | 0.0702040 | ||||||||
\(757\) | −17366.1 | −0.833794 | −0.416897 | − | 0.908954i | \(-0.636882\pi\) | ||||
−0.416897 | + | 0.908954i | \(0.636882\pi\) | |||||||
\(758\) | 19128.1 | 0.916573 | ||||||||
\(759\) | −3567.43 | −0.170605 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27393.9 | −1.30490 | −0.652450 | − | 0.757832i | \(-0.726259\pi\) | ||||
−0.652450 | + | 0.757832i | \(0.726259\pi\) | |||||||
\(762\) | 6845.28 | 0.325431 | ||||||||
\(763\) | 2060.41 | 0.0977611 | ||||||||
\(764\) | −40808.0 | −1.93243 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14671.4 | 0.692034 | ||||||||
\(767\) | 17050.6 | 0.802689 | ||||||||
\(768\) | 11260.2 | 0.529060 | ||||||||
\(769\) | −12091.3 | −0.567000 | −0.283500 | − | 0.958972i | \(-0.591496\pi\) | ||||
−0.283500 | + | 0.958972i | \(0.591496\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17647.0 | −0.824307 | ||||||||
\(772\) | −12159.5 | −0.566879 | ||||||||
\(773\) | −18895.8 | −0.879216 | −0.439608 | − | 0.898190i | \(-0.644883\pi\) | ||||
−0.439608 | + | 0.898190i | \(0.644883\pi\) | |||||||
\(774\) | −1110.01 | −0.0515483 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 35.7490 | 0.00165375 | ||||||||
\(777\) | 7841.96 | 0.362070 | ||||||||
\(778\) | −26487.8 | −1.22061 | ||||||||
\(779\) | 1734.31 | 0.0797664 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 979.089 | 0.0448586 | ||||||||
\(782\) | 18834.0 | 0.861258 | ||||||||
\(783\) | −7421.14 | −0.338710 | ||||||||
\(784\) | 18458.1 | 0.840838 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2594.23 | 0.117727 | ||||||||
\(787\) | −23705.9 | −1.07373 | −0.536863 | − | 0.843669i | \(-0.680391\pi\) | ||||
−0.536863 | + | 0.843669i | \(0.680391\pi\) | |||||||
\(788\) | −18379.4 | −0.830888 | ||||||||
\(789\) | 12005.0 | 0.541685 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8668.77 | −0.389666 | ||||||||
\(792\) | −126.400 | −0.00567100 | ||||||||
\(793\) | −10238.6 | −0.458493 | ||||||||
\(794\) | 16500.5 | 0.737507 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3287.11 | −0.146368 | ||||||||
\(797\) | 37248.0 | 1.65545 | 0.827725 | − | 0.561135i | \(-0.189635\pi\) | ||||
0.827725 | + | 0.561135i | \(0.189635\pi\) | |||||||
\(798\) | 508.807 | 0.0225709 | ||||||||
\(799\) | −1362.30 | −0.0603189 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2815.49 | −0.124195 | ||||||||
\(802\) | 26966.7 | 1.18731 | ||||||||
\(803\) | 7893.84 | 0.346909 | ||||||||
\(804\) | −717.315 | −0.0314648 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8456.21 | −0.369550 | ||||||||
\(807\) | −5274.86 | −0.230092 | ||||||||
\(808\) | 291.458 | 0.0126899 | ||||||||
\(809\) | −24861.0 | −1.08043 | −0.540214 | − | 0.841528i | \(-0.681657\pi\) | ||||
−0.540214 | + | 0.841528i | \(0.681657\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4131.24 | 0.178875 | 0.0894375 | − | 0.995992i | \(-0.471493\pi\) | ||||
0.0894375 | + | 0.995992i | \(0.471493\pi\) | |||||||
\(812\) | −14855.5 | −0.642027 | ||||||||
\(813\) | 18055.3 | 0.778878 | ||||||||
\(814\) | −17870.7 | −0.769495 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7941.10 | −0.340679 | ||||||||
\(817\) | −197.259 | −0.00844704 | ||||||||
\(818\) | −6941.81 | −0.296717 | ||||||||
\(819\) | −1786.29 | −0.0762126 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25297.3 | 1.07537 | 0.537687 | − | 0.843145i | \(-0.319298\pi\) | ||||
0.537687 | + | 0.843145i | \(0.319298\pi\) | |||||||
\(822\) | −790.439 | −0.0335398 | ||||||||
\(823\) | 18155.5 | 0.768969 | 0.384484 | − | 0.923131i | \(-0.374379\pi\) | ||||
0.384484 | + | 0.923131i | \(0.374379\pi\) | |||||||
\(824\) | −1021.83 | −0.0432005 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14657.6 | 0.617435 | ||||||||
\(827\) | 29566.8 | 1.24321 | 0.621607 | − | 0.783329i | \(-0.286480\pi\) | ||||
0.621607 | + | 0.783329i | \(0.286480\pi\) | |||||||
\(828\) | −8091.02 | −0.339592 | ||||||||
\(829\) | 27249.4 | 1.14163 | 0.570814 | − | 0.821079i | \(-0.306628\pi\) | ||||
0.570814 | + | 0.821079i | \(0.306628\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8730.90 | −0.364467 | ||||||||
\(832\) | 16845.9 | 0.701956 | ||||||||
\(833\) | −12972.2 | −0.539568 | ||||||||
\(834\) | 4933.02 | 0.204816 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −590.981 | −0.0244492 | ||||||||
\(837\) | −1850.90 | −0.0764355 | ||||||||
\(838\) | −23154.3 | −0.954478 | ||||||||
\(839\) | −15506.1 | −0.638058 | −0.319029 | − | 0.947745i | \(-0.603357\pi\) | ||||
−0.319029 | + | 0.947745i | \(0.603357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 51157.5 | 2.09756 | ||||||||
\(842\) | 38968.8 | 1.59496 | ||||||||
\(843\) | 20679.6 | 0.844890 | ||||||||
\(844\) | 12972.9 | 0.529084 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1148.24 | 0.0466633 | ||||||||
\(847\) | 786.406 | 0.0319023 | ||||||||
\(848\) | 15496.1 | 0.627520 | ||||||||
\(849\) | −9360.47 | −0.378387 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −43479.4 | −1.75141 | ||||||||
\(852\) | 2220.60 | 0.0892915 | ||||||||
\(853\) | −8698.16 | −0.349143 | −0.174572 | − | 0.984644i | \(-0.555854\pi\) | ||||
−0.174572 | + | 0.984644i | \(0.555854\pi\) | |||||||
\(854\) | −8801.64 | −0.352677 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1336.64 | −0.0533707 | ||||||||
\(857\) | 28468.8 | 1.13474 | 0.567372 | − | 0.823462i | \(-0.307960\pi\) | ||||
0.567372 | + | 0.823462i | \(0.307960\pi\) | |||||||
\(858\) | 4070.71 | 0.161972 | ||||||||
\(859\) | −21154.3 | −0.840251 | −0.420125 | − | 0.907466i | \(-0.638014\pi\) | ||||
−0.420125 | + | 0.907466i | \(0.638014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5234.16 | −0.207177 | ||||||||
\(862\) | 12338.4 | 0.487525 | ||||||||
\(863\) | 45959.5 | 1.81284 | 0.906420 | − | 0.422378i | \(-0.138805\pi\) | ||||
0.906420 | + | 0.422378i | \(0.138805\pi\) | |||||||
\(864\) | 6969.04 | 0.274412 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 44524.5 | 1.74712 | ||||||||
\(867\) | −9158.05 | −0.358735 | ||||||||
\(868\) | −3705.10 | −0.144884 | ||||||||
\(869\) | 2207.72 | 0.0861815 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 878.047 | 0.0341579 | ||||||||
\(872\) | −404.765 | −0.0157191 | ||||||||
\(873\) | −251.996 | −0.00976951 | ||||||||
\(874\) | −2821.06 | −0.109180 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17903.4 | 0.690526 | ||||||||
\(877\) | 7315.10 | 0.281657 | 0.140829 | − | 0.990034i | \(-0.455023\pi\) | ||||
0.140829 | + | 0.990034i | \(0.455023\pi\) | |||||||
\(878\) | 30655.6 | 1.17833 | ||||||||
\(879\) | −26608.9 | −1.02104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4652.19 | 0.177907 | 0.0889536 | − | 0.996036i | \(-0.471648\pi\) | ||||
0.0889536 | + | 0.996036i | \(0.471648\pi\) | |||||||
\(882\) | 10933.8 | 0.417415 | ||||||||
\(883\) | 38954.3 | 1.48462 | 0.742309 | − | 0.670058i | \(-0.233731\pi\) | ||||
0.742309 | + | 0.670058i | \(0.233731\pi\) | |||||||
\(884\) | −10953.7 | −0.416756 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16332.2 | 0.619289 | ||||||||
\(887\) | 16917.5 | 0.640398 | 0.320199 | − | 0.947350i | \(-0.396250\pi\) | ||||
0.320199 | + | 0.947350i | \(0.396250\pi\) | |||||||
\(888\) | −1540.55 | −0.0582177 | ||||||||
\(889\) | −3671.33 | −0.138507 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | −6288.75 | −0.236057 | ||||||||
\(893\) | 204.053 | 0.00764654 | ||||||||
\(894\) | −9598.53 | −0.359086 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1061.32 | 0.0395715 | ||||||||
\(897\) | 9904.01 | 0.368657 | ||||||||
\(898\) | −59051.8 | −2.19441 | ||||||||
\(899\) | 18842.0 | 0.699016 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10890.5 | −0.402682 | ||||||||
\(902\) | 11927.9 | 0.440306 | ||||||||
\(903\) | 595.331 | 0.0219395 | ||||||||
\(904\) | 1702.97 | 0.0626549 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34679.2 | 1.27168 | ||||||||
\(907\) | −38985.4 | −1.42722 | −0.713610 | − | 0.700543i | \(-0.752941\pi\) | ||||
−0.713610 | + | 0.700543i | \(0.752941\pi\) | |||||||
\(908\) | 47889.8 | 1.75031 | ||||||||
\(909\) | −2054.50 | −0.0749653 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27759.8 | 1.00957 | 0.504787 | − | 0.863244i | \(-0.331571\pi\) | ||||
0.504787 | + | 0.863244i | \(0.331571\pi\) | |||||||
\(912\) | 1189.46 | 0.0431874 | ||||||||
\(913\) | −2680.49 | −0.0971646 | ||||||||
\(914\) | −44072.3 | −1.59495 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −15905.6 | −0.573728 | ||||||||
\(917\) | −1391.37 | −0.0501057 | ||||||||
\(918\) | −4703.98 | −0.169122 | ||||||||
\(919\) | 29705.5 | 1.06626 | 0.533130 | − | 0.846033i | \(-0.321016\pi\) | ||||
0.533130 | + | 0.846033i | \(0.321016\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17140.3 | 0.613236 | ||||||||
\(922\) | −66127.6 | −2.36204 | ||||||||
\(923\) | −2718.18 | −0.0969338 | ||||||||
\(924\) | 1783.59 | 0.0635019 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −64724.1 | −2.29694 | ||||||||
\(927\) | 7202.95 | 0.255206 | ||||||||
\(928\) | −70944.1 | −2.50954 | ||||||||
\(929\) | 2940.01 | 0.103831 | 0.0519153 | − | 0.998651i | \(-0.483467\pi\) | ||||
0.0519153 | + | 0.998651i | \(0.483467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1943.04 | 0.0684002 | ||||||||
\(932\) | −8605.99 | −0.302466 | ||||||||
\(933\) | 5952.04 | 0.208854 | ||||||||
\(934\) | −60982.6 | −2.13642 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 350.916 | 0.0122543 | ||||||||
\(937\) | 20041.9 | 0.698762 | 0.349381 | − | 0.936981i | \(-0.386392\pi\) | ||||
0.349381 | + | 0.936981i | \(0.386392\pi\) | |||||||
\(938\) | 754.813 | 0.0262745 | ||||||||
\(939\) | 8026.49 | 0.278951 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14446.1 | −0.500457 | −0.250229 | − | 0.968187i | \(-0.580506\pi\) | ||||
−0.250229 | + | 0.968187i | \(0.580506\pi\) | |||||||
\(942\) | 36251.4 | 1.25386 | ||||||||
\(943\) | 29020.6 | 1.00216 | ||||||||
\(944\) | 34265.6 | 1.18141 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1356.68 | −0.0466272 | ||||||||
\(947\) | −3901.33 | −0.133871 | −0.0669357 | − | 0.997757i | \(-0.521322\pi\) | ||||
−0.0669357 | + | 0.997757i | \(0.521322\pi\) | |||||||
\(948\) | 5007.16 | 0.171545 | ||||||||
\(949\) | −21915.1 | −0.749626 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21251.3 | 0.724627 | ||||||||
\(952\) | −357.904 | −0.0121846 | ||||||||
\(953\) | −613.963 | −0.0208691 | −0.0104345 | − | 0.999946i | \(-0.503321\pi\) | ||||
−0.0104345 | + | 0.999946i | \(0.503321\pi\) | |||||||
\(954\) | 9179.22 | 0.311518 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 22014.6 | 0.744773 | ||||||||
\(957\) | −9070.29 | −0.306375 | ||||||||
\(958\) | 42247.1 | 1.42478 | ||||||||
\(959\) | 423.937 | 0.0142749 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −25091.6 | −0.842256 | ||||||||
\(962\) | 49613.3 | 1.66278 | ||||||||
\(963\) | 9422.02 | 0.315286 | ||||||||
\(964\) | 56000.5 | 1.87101 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8513.98 | 0.283574 | ||||||||
\(967\) | 20617.4 | 0.685637 | 0.342819 | − | 0.939402i | \(-0.388618\pi\) | ||||
0.342819 | + | 0.939402i | \(0.388618\pi\) | |||||||
\(968\) | −154.489 | −0.00512961 | ||||||||
\(969\) | −835.943 | −0.0277135 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22816.0 | 0.754069 | 0.377035 | − | 0.926199i | \(-0.376944\pi\) | ||||
0.377035 | + | 0.926199i | \(0.376944\pi\) | |||||||
\(972\) | 2020.81 | 0.0666846 | ||||||||
\(973\) | −2645.73 | −0.0871719 | ||||||||
\(974\) | −32071.6 | −1.05507 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20576.0 | −0.674816 | ||||||||
\(977\) | −22650.2 | −0.741702 | −0.370851 | − | 0.928692i | \(-0.620934\pi\) | ||||
−0.370851 | + | 0.928692i | \(0.620934\pi\) | |||||||
\(978\) | 35234.2 | 1.15201 | ||||||||
\(979\) | −3441.15 | −0.112339 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2853.21 | 0.0928604 | ||||||||
\(982\) | −46422.8 | −1.50857 | ||||||||
\(983\) | 8963.01 | 0.290820 | 0.145410 | − | 0.989372i | \(-0.453550\pi\) | ||||
0.145410 | + | 0.989372i | \(0.453550\pi\) | |||||||
\(984\) | 1028.25 | 0.0333123 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 47886.0 | 1.54665 | ||||||||
\(987\) | −615.834 | −0.0198604 | ||||||||
\(988\) | 1640.70 | 0.0528316 | ||||||||
\(989\) | −3300.78 | −0.106126 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 422.204 | 0.0135336 | 0.00676678 | − | 0.999977i | \(-0.497846\pi\) | ||||
0.00676678 | + | 0.999977i | \(0.497846\pi\) | |||||||
\(992\) | −17694.1 | −0.566319 | ||||||||
\(993\) | 23437.2 | 0.748999 | ||||||||
\(994\) | −2336.68 | −0.0745623 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6079.41 | −0.193407 | ||||||||
\(997\) | 12577.3 | 0.399524 | 0.199762 | − | 0.979844i | \(-0.435983\pi\) | ||||
0.199762 | + | 0.979844i | \(0.435983\pi\) | |||||||
\(998\) | −19443.4 | −0.616704 | ||||||||
\(999\) | 10859.4 | 0.343920 |
(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 | 825.4.a.o.1.1 | ✓ | 3 | |
3.2 | odd | 2 | 2475.4.a.y.1.3 | 3 | |||
5.2 | odd | 4 | 825.4.c.n.199.1 | 6 | |||
5.3 | odd | 4 | 825.4.c.n.199.6 | 6 | |||
5.4 | even | 2 | 825.4.a.q.1.3 | yes | 3 | ||
15.14 | odd | 2 | 2475.4.a.v.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.4.a.o.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
825.4.a.q.1.3 | yes | 3 | 5.4 | even | 2 | ||
825.4.c.n.199.1 | 6 | 5.2 | odd | 4 | |||
825.4.c.n.199.6 | 6 | 5.3 | odd | 4 | |||
2475.4.a.v.1.1 | 3 | 15.14 | odd | 2 | |||
2475.4.a.y.1.3 | 3 | 3.2 | odd | 2 |