Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,4,Mod(1,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.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: | \(126.913108422\) |
Analytic rank: | \(0\) |
Dimension: | \(37\) |
Twist minimal: | no (minimal twist has level 239) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 2151.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.79841 | −1.69650 | −0.848248 | − | 0.529600i | \(-0.822342\pi\) | ||||
−0.848248 | + | 0.529600i | \(0.822342\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 15.0248 | 1.87810 | ||||||||
\(5\) | 14.4400 | 1.29155 | 0.645777 | − | 0.763526i | \(-0.276533\pi\) | ||||
0.645777 | + | 0.763526i | \(0.276533\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.92684 | 0.104040 | 0.0520199 | − | 0.998646i | \(-0.483434\pi\) | ||||
0.0520199 | + | 0.998646i | \(0.483434\pi\) | |||||||
\(8\) | −33.7078 | −1.48969 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −69.2892 | −2.19112 | ||||||||
\(11\) | −24.5238 | −0.672201 | −0.336100 | − | 0.941826i | \(-0.609108\pi\) | ||||
−0.336100 | + | 0.941826i | \(0.609108\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.6663 | −0.248895 | −0.124448 | − | 0.992226i | \(-0.539716\pi\) | ||||
−0.124448 | + | 0.992226i | \(0.539716\pi\) | |||||||
\(14\) | −9.24579 | −0.176503 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 41.5456 | 0.649149 | ||||||||
\(17\) | 49.4720 | 0.705807 | 0.352903 | − | 0.935660i | \(-0.385194\pi\) | ||||
0.352903 | + | 0.935660i | \(0.385194\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 106.669 | 1.28798 | 0.643990 | − | 0.765034i | \(-0.277278\pi\) | ||||
0.643990 | + | 0.765034i | \(0.277278\pi\) | |||||||
\(20\) | 216.958 | 2.42566 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 117.675 | 1.14039 | ||||||||
\(23\) | 102.672 | 0.930810 | 0.465405 | − | 0.885098i | \(-0.345909\pi\) | ||||
0.465405 | + | 0.885098i | \(0.345909\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 83.5141 | 0.668113 | ||||||||
\(26\) | 55.9795 | 0.422250 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 28.9504 | 0.195397 | ||||||||
\(29\) | −64.1149 | −0.410546 | −0.205273 | − | 0.978705i | \(-0.565808\pi\) | ||||
−0.205273 | + | 0.978705i | \(0.565808\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −280.276 | −1.62384 | −0.811920 | − | 0.583769i | \(-0.801577\pi\) | ||||
−0.811920 | + | 0.583769i | \(0.801577\pi\) | |||||||
\(32\) | 70.3092 | 0.388407 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −237.387 | −1.19740 | ||||||||
\(35\) | 27.8237 | 0.134373 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −224.640 | −0.998124 | −0.499062 | − | 0.866566i | \(-0.666322\pi\) | ||||
−0.499062 | + | 0.866566i | \(0.666322\pi\) | |||||||
\(38\) | −511.844 | −2.18505 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −486.741 | −1.92401 | ||||||||
\(41\) | 65.1232 | 0.248062 | 0.124031 | − | 0.992278i | \(-0.460418\pi\) | ||||
0.124031 | + | 0.992278i | \(0.460418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.6265 | −0.0412331 | −0.0206166 | − | 0.999787i | \(-0.506563\pi\) | ||||
−0.0206166 | + | 0.999787i | \(0.506563\pi\) | |||||||
\(44\) | −368.465 | −1.26246 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −492.663 | −1.57911 | ||||||||
\(47\) | 171.648 | 0.532711 | 0.266355 | − | 0.963875i | \(-0.414181\pi\) | ||||
0.266355 | + | 0.963875i | \(0.414181\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −339.287 | −0.989176 | ||||||||
\(50\) | −400.735 | −1.13345 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −175.283 | −0.467449 | ||||||||
\(53\) | 347.764 | 0.901302 | 0.450651 | − | 0.892700i | \(-0.351192\pi\) | ||||
0.450651 | + | 0.892700i | \(0.351192\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −354.124 | −0.868184 | ||||||||
\(56\) | −64.9496 | −0.154987 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 307.650 | 0.696490 | ||||||||
\(59\) | −753.785 | −1.66330 | −0.831648 | − | 0.555303i | \(-0.812602\pi\) | ||||
−0.831648 | + | 0.555303i | \(0.812602\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 865.111 | 1.81584 | 0.907919 | − | 0.419145i | \(-0.137670\pi\) | ||||
0.907919 | + | 0.419145i | \(0.137670\pi\) | |||||||
\(62\) | 1344.88 | 2.75484 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −669.737 | −1.30808 | ||||||||
\(65\) | −168.461 | −0.321462 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 664.993 | 1.21257 | 0.606283 | − | 0.795249i | \(-0.292660\pi\) | ||||
0.606283 | + | 0.795249i | \(0.292660\pi\) | |||||||
\(68\) | 743.305 | 1.32557 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −133.509 | −0.227963 | ||||||||
\(71\) | 624.120 | 1.04323 | 0.521616 | − | 0.853180i | \(-0.325329\pi\) | ||||
0.521616 | + | 0.853180i | \(0.325329\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 750.992 | 1.20407 | 0.602034 | − | 0.798470i | \(-0.294357\pi\) | ||||
0.602034 | + | 0.798470i | \(0.294357\pi\) | |||||||
\(74\) | 1077.92 | 1.69331 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1602.68 | 2.41895 | ||||||||
\(77\) | −47.2536 | −0.0699356 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1171.54 | 1.66846 | 0.834231 | − | 0.551415i | \(-0.185912\pi\) | ||||
0.834231 | + | 0.551415i | \(0.185912\pi\) | |||||||
\(80\) | 599.919 | 0.838412 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −312.488 | −0.420836 | ||||||||
\(83\) | −1237.79 | −1.63693 | −0.818466 | − | 0.574554i | \(-0.805175\pi\) | ||||
−0.818466 | + | 0.574554i | \(0.805175\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 714.376 | 0.911588 | ||||||||
\(86\) | 55.7888 | 0.0699518 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 826.643 | 1.00137 | ||||||||
\(89\) | 558.663 | 0.665372 | 0.332686 | − | 0.943038i | \(-0.392045\pi\) | ||||
0.332686 | + | 0.943038i | \(0.392045\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.4791 | −0.0258950 | ||||||||
\(92\) | 1542.63 | 1.74815 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −823.637 | −0.903741 | ||||||||
\(95\) | 1540.31 | 1.66350 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −698.747 | −0.731412 | −0.365706 | − | 0.930730i | \(-0.619172\pi\) | ||||
−0.365706 | + | 0.930730i | \(0.619172\pi\) | |||||||
\(98\) | 1628.04 | 1.67813 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1254.78 | 1.25478 | ||||||||
\(101\) | −1492.55 | −1.47044 | −0.735219 | − | 0.677829i | \(-0.762921\pi\) | ||||
−0.735219 | + | 0.677829i | \(0.762921\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 42.1689 | 0.0403401 | 0.0201700 | − | 0.999797i | \(-0.493579\pi\) | ||||
0.0201700 | + | 0.999797i | \(0.493579\pi\) | |||||||
\(104\) | 393.243 | 0.370776 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1668.71 | −1.52906 | ||||||||
\(107\) | −680.282 | −0.614629 | −0.307315 | − | 0.951608i | \(-0.599430\pi\) | ||||
−0.307315 | + | 0.951608i | \(0.599430\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1890.61 | 1.66135 | 0.830675 | − | 0.556757i | \(-0.187955\pi\) | ||||
0.830675 | + | 0.556757i | \(0.187955\pi\) | |||||||
\(110\) | 1699.23 | 1.47287 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 80.0518 | 0.0675374 | ||||||||
\(113\) | 1819.51 | 1.51473 | 0.757367 | − | 0.652989i | \(-0.226485\pi\) | ||||
0.757367 | + | 0.652989i | \(0.226485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1482.59 | 1.20219 | ||||||||
\(116\) | −963.312 | −0.771045 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3616.97 | 2.82178 | ||||||||
\(119\) | 95.3248 | 0.0734320 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −729.582 | −0.548146 | ||||||||
\(122\) | −4151.16 | −3.08056 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4211.08 | −3.04973 | ||||||||
\(125\) | −599.057 | −0.428651 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1034.80 | 0.723019 | 0.361509 | − | 0.932369i | \(-0.382262\pi\) | ||||
0.361509 | + | 0.932369i | \(0.382262\pi\) | |||||||
\(128\) | 2651.20 | 1.83075 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 808.346 | 0.545358 | ||||||||
\(131\) | −1271.02 | −0.847704 | −0.423852 | − | 0.905732i | \(-0.639322\pi\) | ||||
−0.423852 | + | 0.905732i | \(0.639322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 205.535 | 0.134001 | ||||||||
\(134\) | −3190.91 | −2.05711 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1667.59 | −1.05143 | ||||||||
\(137\) | 1067.27 | 0.665571 | 0.332786 | − | 0.943003i | \(-0.392011\pi\) | ||||
0.332786 | + | 0.943003i | \(0.392011\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1148.09 | 0.700574 | 0.350287 | − | 0.936642i | \(-0.386084\pi\) | ||||
0.350287 | + | 0.936642i | \(0.386084\pi\) | |||||||
\(140\) | 418.044 | 0.252366 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2994.79 | −1.76984 | ||||||||
\(143\) | 286.101 | 0.167308 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −925.821 | −0.530243 | ||||||||
\(146\) | −3603.57 | −2.04270 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3375.16 | −1.87457 | ||||||||
\(149\) | 2430.70 | 1.33645 | 0.668223 | − | 0.743961i | \(-0.267055\pi\) | ||||
0.668223 | + | 0.743961i | \(0.267055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1720.37 | 0.927165 | 0.463582 | − | 0.886054i | \(-0.346564\pi\) | ||||
0.463582 | + | 0.886054i | \(0.346564\pi\) | |||||||
\(152\) | −3595.59 | −1.91869 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 226.742 | 0.118645 | ||||||||
\(155\) | −4047.19 | −2.09728 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −346.753 | −0.176267 | −0.0881335 | − | 0.996109i | \(-0.528090\pi\) | ||||
−0.0881335 | + | 0.996109i | \(0.528090\pi\) | |||||||
\(158\) | −5621.53 | −2.83054 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1015.27 | 0.501649 | ||||||||
\(161\) | 197.833 | 0.0968413 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1373.55 | −0.660027 | −0.330014 | − | 0.943976i | \(-0.607053\pi\) | ||||
−0.330014 | + | 0.943976i | \(0.607053\pi\) | |||||||
\(164\) | 978.461 | 0.465884 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5939.44 | 2.77705 | ||||||||
\(167\) | 1252.43 | 0.580336 | 0.290168 | − | 0.956976i | \(-0.406289\pi\) | ||||
0.290168 | + | 0.956976i | \(0.406289\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2060.90 | −0.938051 | ||||||||
\(170\) | −3427.87 | −1.54650 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −174.686 | −0.0774398 | ||||||||
\(173\) | 3957.84 | 1.73936 | 0.869679 | − | 0.493619i | \(-0.164326\pi\) | ||||
0.869679 | + | 0.493619i | \(0.164326\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 160.919 | 0.0695103 | ||||||||
\(176\) | −1018.86 | −0.436359 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2680.69 | −1.12880 | ||||||||
\(179\) | −1886.60 | −0.787774 | −0.393887 | − | 0.919159i | \(-0.628870\pi\) | ||||
−0.393887 | + | 0.919159i | \(0.628870\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1706.92 | −0.700964 | −0.350482 | − | 0.936569i | \(-0.613982\pi\) | ||||
−0.350482 | + | 0.936569i | \(0.613982\pi\) | |||||||
\(182\) | 107.864 | 0.0439308 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3460.85 | −1.38661 | ||||||||
\(185\) | −3243.80 | −1.28913 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1213.24 | −0.474444 | ||||||||
\(188\) | 2578.97 | 1.00048 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7391.03 | −2.82212 | ||||||||
\(191\) | −1407.60 | −0.533247 | −0.266623 | − | 0.963801i | \(-0.585908\pi\) | ||||
−0.266623 | + | 0.963801i | \(0.585908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4498.42 | −1.67774 | −0.838868 | − | 0.544334i | \(-0.816782\pi\) | ||||
−0.838868 | + | 0.544334i | \(0.816782\pi\) | |||||||
\(194\) | 3352.87 | 1.24084 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5097.71 | −1.85777 | ||||||||
\(197\) | 2768.03 | 1.00109 | 0.500543 | − | 0.865712i | \(-0.333134\pi\) | ||||
0.500543 | + | 0.865712i | \(0.333134\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5558.62 | 1.98010 | 0.990051 | − | 0.140706i | \(-0.0449373\pi\) | ||||
0.990051 | + | 0.140706i | \(0.0449373\pi\) | |||||||
\(200\) | −2815.07 | −0.995278 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7161.87 | 2.49459 | ||||||||
\(203\) | −123.539 | −0.0427132 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 940.380 | 0.320385 | ||||||||
\(206\) | −202.344 | −0.0684368 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −484.681 | −0.161570 | ||||||||
\(209\) | −2615.94 | −0.865782 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −960.310 | −0.313320 | −0.156660 | − | 0.987653i | \(-0.550073\pi\) | ||||
−0.156660 | + | 0.987653i | \(0.550073\pi\) | |||||||
\(212\) | 5225.07 | 1.69273 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3264.27 | 1.04272 | ||||||||
\(215\) | −167.887 | −0.0532548 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −540.048 | −0.168944 | ||||||||
\(218\) | −9071.91 | −2.81847 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5320.64 | −1.63053 | ||||||||
\(221\) | −577.153 | −0.175672 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 614.790 | 0.184616 | 0.0923080 | − | 0.995731i | \(-0.470576\pi\) | ||||
0.0923080 | + | 0.995731i | \(0.470576\pi\) | |||||||
\(224\) | 135.475 | 0.0404098 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8730.75 | −2.56974 | ||||||||
\(227\) | −893.396 | −0.261219 | −0.130610 | − | 0.991434i | \(-0.541693\pi\) | ||||
−0.130610 | + | 0.991434i | \(0.541693\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4864.05 | 1.40360 | 0.701802 | − | 0.712372i | \(-0.252379\pi\) | ||||
0.701802 | + | 0.712372i | \(0.252379\pi\) | |||||||
\(230\) | −7114.07 | −2.03951 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2161.17 | 0.611585 | ||||||||
\(233\) | 3134.42 | 0.881298 | 0.440649 | − | 0.897679i | \(-0.354748\pi\) | ||||
0.440649 | + | 0.897679i | \(0.354748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2478.60 | 0.688025 | ||||||||
\(236\) | −11325.5 | −3.12383 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −457.408 | −0.124577 | ||||||||
\(239\) | 239.000 | 0.0646846 | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −567.016 | −0.151555 | −0.0757774 | − | 0.997125i | \(-0.524144\pi\) | ||||
−0.0757774 | + | 0.997125i | \(0.524144\pi\) | |||||||
\(242\) | 3500.84 | 0.929927 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12998.1 | 3.41032 | ||||||||
\(245\) | −4899.31 | −1.27757 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1244.43 | −0.320572 | ||||||||
\(248\) | 9447.47 | 2.41901 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2874.53 | 0.727204 | ||||||||
\(251\) | 2548.35 | 0.640839 | 0.320419 | − | 0.947276i | \(-0.396176\pi\) | ||||
0.320419 | + | 0.947276i | \(0.396176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2517.91 | −0.625691 | ||||||||
\(254\) | −4965.38 | −1.22660 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7363.67 | −1.79777 | ||||||||
\(257\) | 2265.46 | 0.549866 | 0.274933 | − | 0.961463i | \(-0.411344\pi\) | ||||
0.274933 | + | 0.961463i | \(0.411344\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −432.846 | −0.103845 | ||||||||
\(260\) | −2531.09 | −0.603736 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6098.86 | 1.43813 | ||||||||
\(263\) | −4385.52 | −1.02822 | −0.514111 | − | 0.857723i | \(-0.671878\pi\) | ||||
−0.514111 | + | 0.857723i | \(0.671878\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5021.71 | 1.16408 | ||||||||
\(266\) | −986.243 | −0.227333 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9991.37 | 2.27731 | ||||||||
\(269\) | −132.642 | −0.0300645 | −0.0150322 | − | 0.999887i | \(-0.504785\pi\) | ||||
−0.0150322 | + | 0.999887i | \(0.504785\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4955.89 | 1.11088 | 0.555441 | − | 0.831556i | \(-0.312549\pi\) | ||||
0.555441 | + | 0.831556i | \(0.312549\pi\) | |||||||
\(272\) | 2055.34 | 0.458174 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5121.21 | −1.12914 | ||||||||
\(275\) | −2048.08 | −0.449106 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6105.47 | −1.32434 | −0.662169 | − | 0.749354i | \(-0.730364\pi\) | ||||
−0.662169 | + | 0.749354i | \(0.730364\pi\) | |||||||
\(278\) | −5509.02 | −1.18852 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −937.873 | −0.200174 | ||||||||
\(281\) | −5141.47 | −1.09151 | −0.545755 | − | 0.837945i | \(-0.683757\pi\) | ||||
−0.545755 | + | 0.837945i | \(0.683757\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2162.85 | −0.454304 | −0.227152 | − | 0.973859i | \(-0.572941\pi\) | ||||
−0.227152 | + | 0.973859i | \(0.572941\pi\) | |||||||
\(284\) | 9377.26 | 1.95929 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1372.83 | −0.283837 | ||||||||
\(287\) | 125.482 | 0.0258083 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2465.52 | −0.501837 | ||||||||
\(290\) | 4442.47 | 0.899555 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11283.5 | 2.26136 | ||||||||
\(293\) | −1525.62 | −0.304189 | −0.152095 | − | 0.988366i | \(-0.548602\pi\) | ||||
−0.152095 | + | 0.988366i | \(0.548602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10884.7 | −2.14824 | ||||||||
\(296\) | 7572.11 | 1.48689 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11663.5 | −2.26728 | ||||||||
\(299\) | −1197.80 | −0.231674 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.4025 | −0.00428989 | ||||||||
\(302\) | −8255.06 | −1.57293 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4431.64 | 0.836092 | ||||||||
\(305\) | 12492.2 | 2.34525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1612.54 | −0.299781 | −0.149890 | − | 0.988703i | \(-0.547892\pi\) | ||||
−0.149890 | + | 0.988703i | \(0.547892\pi\) | |||||||
\(308\) | −709.974 | −0.131346 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 19420.1 | 3.55802 | ||||||||
\(311\) | 6087.96 | 1.11002 | 0.555011 | − | 0.831843i | \(-0.312714\pi\) | ||||
0.555011 | + | 0.831843i | \(0.312714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6272.21 | 1.13267 | 0.566336 | − | 0.824175i | \(-0.308361\pi\) | ||||
0.566336 | + | 0.824175i | \(0.308361\pi\) | |||||||
\(314\) | 1663.86 | 0.299036 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17602.1 | 3.13353 | ||||||||
\(317\) | −8710.44 | −1.54330 | −0.771652 | − | 0.636045i | \(-0.780569\pi\) | ||||
−0.771652 | + | 0.636045i | \(0.780569\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1572.34 | 0.275970 | ||||||||
\(320\) | −9671.02 | −1.68946 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −949.286 | −0.164291 | ||||||||
\(323\) | 5277.15 | 0.909066 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −974.297 | −0.166290 | ||||||||
\(326\) | 6590.84 | 1.11973 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2195.16 | −0.369534 | ||||||||
\(329\) | 330.738 | 0.0554231 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3094.97 | 0.513943 | 0.256972 | − | 0.966419i | \(-0.417275\pi\) | ||||
0.256972 | + | 0.966419i | \(0.417275\pi\) | |||||||
\(332\) | −18597.6 | −3.07432 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6009.69 | −0.984537 | ||||||||
\(335\) | 9602.52 | 1.56609 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −907.417 | −0.146677 | −0.0733385 | − | 0.997307i | \(-0.523365\pi\) | ||||
−0.0733385 | + | 0.997307i | \(0.523365\pi\) | |||||||
\(338\) | 9889.04 | 1.59140 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10733.3 | 1.71205 | ||||||||
\(341\) | 6873.43 | 1.09155 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1314.66 | −0.206953 | ||||||||
\(344\) | 391.903 | 0.0614244 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18991.3 | −2.95081 | ||||||||
\(347\) | −1470.59 | −0.227509 | −0.113754 | − | 0.993509i | \(-0.536288\pi\) | ||||
−0.113754 | + | 0.993509i | \(0.536288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12338.1 | −1.89239 | −0.946194 | − | 0.323601i | \(-0.895107\pi\) | ||||
−0.946194 | + | 0.323601i | \(0.895107\pi\) | |||||||
\(350\) | −772.154 | −0.117924 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1724.25 | −0.261088 | ||||||||
\(353\) | −204.115 | −0.0307761 | −0.0153881 | − | 0.999882i | \(-0.504898\pi\) | ||||
−0.0153881 | + | 0.999882i | \(0.504898\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9012.31 | 1.34739 | ||||||||
\(356\) | 8393.78 | 1.24963 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9052.71 | 1.33645 | ||||||||
\(359\) | 4940.39 | 0.726306 | 0.363153 | − | 0.931729i | \(-0.381700\pi\) | ||||
0.363153 | + | 0.931729i | \(0.381700\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4519.36 | 0.658895 | ||||||||
\(362\) | 8190.52 | 1.18918 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −337.743 | −0.0486333 | ||||||||
\(365\) | 10844.3 | 1.55512 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11947.9 | −1.69939 | −0.849697 | − | 0.527271i | \(-0.823215\pi\) | ||||
−0.849697 | + | 0.527271i | \(0.823215\pi\) | |||||||
\(368\) | 4265.57 | 0.604235 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 15565.1 | 2.18701 | ||||||||
\(371\) | 670.087 | 0.0937713 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4902.14 | 0.680491 | 0.340246 | − | 0.940337i | \(-0.389490\pi\) | ||||
0.340246 | + | 0.940337i | \(0.389490\pi\) | |||||||
\(374\) | 5821.63 | 0.804892 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5785.86 | −0.793572 | ||||||||
\(377\) | 747.981 | 0.102183 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1510.16 | 0.204675 | 0.102338 | − | 0.994750i | \(-0.467368\pi\) | ||||
0.102338 | + | 0.994750i | \(0.467368\pi\) | |||||||
\(380\) | 23142.8 | 3.12421 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6754.23 | 0.904650 | ||||||||
\(383\) | 7967.82 | 1.06302 | 0.531510 | − | 0.847052i | \(-0.321625\pi\) | ||||
0.531510 | + | 0.847052i | \(0.321625\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −682.342 | −0.0903257 | ||||||||
\(386\) | 21585.3 | 2.84627 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10498.5 | −1.37366 | ||||||||
\(389\) | 1896.84 | 0.247233 | 0.123616 | − | 0.992330i | \(-0.460551\pi\) | ||||
0.123616 | + | 0.992330i | \(0.460551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5079.39 | 0.656972 | ||||||||
\(392\) | 11436.6 | 1.47356 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13282.2 | −1.69834 | ||||||||
\(395\) | 16917.1 | 2.15491 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6439.34 | 0.814059 | 0.407029 | − | 0.913415i | \(-0.366565\pi\) | ||||
0.407029 | + | 0.913415i | \(0.366565\pi\) | |||||||
\(398\) | −26672.6 | −3.35924 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3469.64 | 0.433705 | ||||||||
\(401\) | 1714.30 | 0.213487 | 0.106743 | − | 0.994287i | \(-0.465958\pi\) | ||||
0.106743 | + | 0.994287i | \(0.465958\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3269.77 | 0.404166 | ||||||||
\(404\) | −22425.2 | −2.76162 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 592.793 | 0.0724627 | ||||||||
\(407\) | 5509.03 | 0.670940 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6901.15 | 0.834327 | 0.417163 | − | 0.908831i | \(-0.363024\pi\) | ||||
0.417163 | + | 0.908831i | \(0.363024\pi\) | |||||||
\(410\) | −4512.33 | −0.543532 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 633.579 | 0.0757626 | ||||||||
\(413\) | −1452.43 | −0.173049 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17873.8 | −2.11419 | ||||||||
\(416\) | −820.246 | −0.0966727 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 12552.4 | 1.46879 | ||||||||
\(419\) | 6255.85 | 0.729399 | 0.364699 | − | 0.931125i | \(-0.381172\pi\) | ||||
0.364699 | + | 0.931125i | \(0.381172\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4921.75 | 0.569766 | 0.284883 | − | 0.958562i | \(-0.408045\pi\) | ||||
0.284883 | + | 0.958562i | \(0.408045\pi\) | |||||||
\(422\) | 4607.96 | 0.531545 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −11722.3 | −1.34266 | ||||||||
\(425\) | 4131.61 | 0.471558 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1666.93 | 0.188920 | ||||||||
\(428\) | −10221.1 | −1.15433 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 805.591 | 0.0903466 | ||||||||
\(431\) | −841.948 | −0.0940957 | −0.0470478 | − | 0.998893i | \(-0.514981\pi\) | ||||
−0.0470478 | + | 0.998893i | \(0.514981\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14074.4 | 1.56206 | 0.781031 | − | 0.624492i | \(-0.214694\pi\) | ||||
0.781031 | + | 0.624492i | \(0.214694\pi\) | |||||||
\(434\) | 2591.37 | 0.286613 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 28405.9 | 3.12018 | ||||||||
\(437\) | 10952.0 | 1.19887 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3415.28 | −0.371304 | −0.185652 | − | 0.982616i | \(-0.559440\pi\) | ||||
−0.185652 | + | 0.982616i | \(0.559440\pi\) | |||||||
\(440\) | 11936.7 | 1.29332 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2769.42 | 0.298027 | ||||||||
\(443\) | −9565.85 | −1.02593 | −0.512965 | − | 0.858409i | \(-0.671453\pi\) | ||||
−0.512965 | + | 0.858409i | \(0.671453\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8067.10 | 0.859365 | ||||||||
\(446\) | −2950.01 | −0.313200 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1290.48 | −0.136092 | ||||||||
\(449\) | 11487.5 | 1.20741 | 0.603707 | − | 0.797207i | \(-0.293690\pi\) | ||||
0.603707 | + | 0.797207i | \(0.293690\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1597.07 | −0.166747 | ||||||||
\(452\) | 27337.7 | 2.84482 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4286.88 | 0.443157 | ||||||||
\(455\) | −324.598 | −0.0334448 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14153.0 | 1.44869 | 0.724344 | − | 0.689439i | \(-0.242143\pi\) | ||||
0.724344 | + | 0.689439i | \(0.242143\pi\) | |||||||
\(458\) | −23339.7 | −2.38121 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 22275.5 | 2.25783 | ||||||||
\(461\) | −4852.98 | −0.490295 | −0.245147 | − | 0.969486i | \(-0.578836\pi\) | ||||
−0.245147 | + | 0.969486i | \(0.578836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4232.92 | 0.424882 | 0.212441 | − | 0.977174i | \(-0.431859\pi\) | ||||
0.212441 | + | 0.977174i | \(0.431859\pi\) | |||||||
\(464\) | −2663.69 | −0.266506 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15040.2 | −1.49512 | ||||||||
\(467\) | 8525.46 | 0.844778 | 0.422389 | − | 0.906415i | \(-0.361192\pi\) | ||||
0.422389 | + | 0.906415i | \(0.361192\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1281.34 | 0.126155 | ||||||||
\(470\) | −11893.3 | −1.16723 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 25408.4 | 2.47779 | ||||||||
\(473\) | 285.126 | 0.0277169 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8908.40 | 0.860516 | ||||||||
\(476\) | 1432.23 | 0.137912 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1146.82 | −0.109737 | ||||||||
\(479\) | 1731.93 | 0.165207 | 0.0826033 | − | 0.996583i | \(-0.473677\pi\) | ||||
0.0826033 | + | 0.996583i | \(0.473677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2620.71 | 0.248428 | ||||||||
\(482\) | 2720.78 | 0.257112 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10961.8 | −1.02947 | ||||||||
\(485\) | −10089.9 | −0.944658 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12107.2 | 1.12655 | 0.563276 | − | 0.826269i | \(-0.309541\pi\) | ||||
0.563276 | + | 0.826269i | \(0.309541\pi\) | |||||||
\(488\) | −29161.0 | −2.70503 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 23508.9 | 2.16740 | ||||||||
\(491\) | −17318.6 | −1.59180 | −0.795902 | − | 0.605425i | \(-0.793003\pi\) | ||||
−0.795902 | + | 0.605425i | \(0.793003\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3171.89 | −0.289766 | ||||||||
\(494\) | 5971.30 | 0.543849 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11644.2 | −1.05411 | ||||||||
\(497\) | 1202.58 | 0.108538 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10591.8 | 0.950205 | 0.475103 | − | 0.879930i | \(-0.342411\pi\) | ||||
0.475103 | + | 0.879930i | \(0.342411\pi\) | |||||||
\(500\) | −9000.70 | −0.805047 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12228.0 | −1.08718 | ||||||||
\(503\) | −12622.8 | −1.11894 | −0.559468 | − | 0.828852i | \(-0.688994\pi\) | ||||
−0.559468 | + | 0.828852i | \(0.688994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21552.4 | −1.89915 | ||||||||
\(506\) | 12082.0 | 1.06148 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15547.6 | 1.35790 | ||||||||
\(509\) | 21821.7 | 1.90025 | 0.950127 | − | 0.311862i | \(-0.100953\pi\) | ||||
0.950127 | + | 0.311862i | \(0.100953\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1447.04 | 0.125271 | ||||||||
\(512\) | 14124.3 | 1.21916 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10870.6 | −0.932846 | ||||||||
\(515\) | 608.920 | 0.0521014 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4209.46 | −0.358088 | ||||||||
\(518\) | 2076.97 | 0.176172 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5678.44 | 0.478877 | ||||||||
\(521\) | 2616.35 | 0.220008 | 0.110004 | − | 0.993931i | \(-0.464914\pi\) | ||||
0.110004 | + | 0.993931i | \(0.464914\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15427.1 | −1.28983 | −0.644915 | − | 0.764254i | \(-0.723107\pi\) | ||||
−0.644915 | + | 0.764254i | \(0.723107\pi\) | |||||||
\(524\) | −19096.7 | −1.59207 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21043.5 | 1.74438 | ||||||||
\(527\) | −13865.8 | −1.14612 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1625.43 | −0.133593 | ||||||||
\(530\) | −24096.3 | −1.97486 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3088.12 | 0.251667 | ||||||||
\(533\) | −759.744 | −0.0617414 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9823.28 | −0.793827 | ||||||||
\(536\) | −22415.4 | −1.80634 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 636.472 | 0.0510042 | ||||||||
\(539\) | 8320.62 | 0.664925 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12474.7 | 0.991369 | 0.495685 | − | 0.868503i | \(-0.334917\pi\) | ||||
0.495685 | + | 0.868503i | \(0.334917\pi\) | |||||||
\(542\) | −23780.4 | −1.88461 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3478.34 | 0.274140 | ||||||||
\(545\) | 27300.4 | 2.14572 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6216.78 | −0.485942 | −0.242971 | − | 0.970034i | \(-0.578122\pi\) | ||||
−0.242971 | + | 0.970034i | \(0.578122\pi\) | |||||||
\(548\) | 16035.5 | 1.25001 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9827.55 | 0.761906 | ||||||||
\(551\) | −6839.10 | −0.528776 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2257.37 | 0.173586 | ||||||||
\(554\) | 29296.5 | 2.24673 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17249.8 | 1.31575 | ||||||||
\(557\) | 17629.7 | 1.34110 | 0.670551 | − | 0.741864i | \(-0.266058\pi\) | ||||
0.670551 | + | 0.741864i | \(0.266058\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 135.638 | 0.0102627 | ||||||||
\(560\) | 1155.95 | 0.0872282 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 24670.9 | 1.85174 | ||||||||
\(563\) | 8727.05 | 0.653288 | 0.326644 | − | 0.945147i | \(-0.394082\pi\) | ||||
0.326644 | + | 0.945147i | \(0.394082\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26273.7 | 1.95636 | ||||||||
\(566\) | 10378.2 | 0.770725 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −21037.7 | −1.55409 | ||||||||
\(569\) | 917.170 | 0.0675742 | 0.0337871 | − | 0.999429i | \(-0.489243\pi\) | ||||
0.0337871 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10983.3 | −0.804966 | −0.402483 | − | 0.915428i | \(-0.631853\pi\) | ||||
−0.402483 | + | 0.915428i | \(0.631853\pi\) | |||||||
\(572\) | 4298.61 | 0.314220 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −602.116 | −0.0437837 | ||||||||
\(575\) | 8574.57 | 0.621886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11383.1 | −0.821292 | −0.410646 | − | 0.911795i | \(-0.634697\pi\) | ||||
−0.410646 | + | 0.911795i | \(0.634697\pi\) | |||||||
\(578\) | 11830.6 | 0.851364 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −13910.2 | −0.995847 | ||||||||
\(581\) | −2385.03 | −0.170306 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8528.49 | −0.605856 | ||||||||
\(584\) | −25314.2 | −1.79368 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7320.53 | 0.516055 | ||||||||
\(587\) | −18677.0 | −1.31326 | −0.656628 | − | 0.754215i | \(-0.728018\pi\) | ||||
−0.656628 | + | 0.754215i | \(0.728018\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −29896.8 | −2.09147 | ||||||||
\(590\) | 52229.2 | 3.64448 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9332.79 | −0.647932 | ||||||||
\(593\) | −14315.0 | −0.991307 | −0.495653 | − | 0.868520i | \(-0.665071\pi\) | ||||
−0.495653 | + | 0.868520i | \(0.665071\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1376.49 | 0.0948414 | ||||||||
\(596\) | 36520.7 | 2.50998 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5747.54 | 0.393034 | ||||||||
\(599\) | 21968.9 | 1.49854 | 0.749269 | − | 0.662266i | \(-0.230405\pi\) | ||||
0.749269 | + | 0.662266i | \(0.230405\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17018.9 | 1.15510 | 0.577549 | − | 0.816356i | \(-0.304009\pi\) | ||||
0.577549 | + | 0.816356i | \(0.304009\pi\) | |||||||
\(602\) | 107.496 | 0.00727777 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 25848.2 | 1.74131 | ||||||||
\(605\) | −10535.2 | −0.707960 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19695.6 | 1.31700 | 0.658500 | − | 0.752581i | \(-0.271191\pi\) | ||||
0.658500 | + | 0.752581i | \(0.271191\pi\) | |||||||
\(608\) | 7499.84 | 0.500261 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −59942.8 | −3.97871 | ||||||||
\(611\) | −2002.49 | −0.132589 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21790.3 | −1.43573 | −0.717866 | − | 0.696181i | \(-0.754881\pi\) | ||||
−0.717866 | + | 0.696181i | \(0.754881\pi\) | |||||||
\(614\) | 7737.65 | 0.508577 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1592.81 | 0.104182 | ||||||||
\(617\) | 1280.93 | 0.0835792 | 0.0417896 | − | 0.999126i | \(-0.486694\pi\) | ||||
0.0417896 | + | 0.999126i | \(0.486694\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22357.2 | 1.45171 | 0.725857 | − | 0.687846i | \(-0.241444\pi\) | ||||
0.725857 | + | 0.687846i | \(0.241444\pi\) | |||||||
\(620\) | −60808.0 | −3.93889 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −29212.5 | −1.88315 | ||||||||
\(623\) | 1076.46 | 0.0692252 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19089.7 | −1.22174 | ||||||||
\(626\) | −30096.6 | −1.92157 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5209.88 | −0.331046 | ||||||||
\(629\) | −11113.4 | −0.704483 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 362.824 | 0.0228903 | 0.0114452 | − | 0.999935i | \(-0.496357\pi\) | ||||
0.0114452 | + | 0.999935i | \(0.496357\pi\) | |||||||
\(632\) | −39490.0 | −2.48548 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 41796.3 | 2.61821 | ||||||||
\(635\) | 14942.5 | 0.933818 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3958.21 | 0.246201 | ||||||||
\(638\) | −7544.75 | −0.468181 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 38283.4 | 2.36451 | ||||||||
\(641\) | 10762.7 | 0.663187 | 0.331594 | − | 0.943422i | \(-0.392414\pi\) | ||||
0.331594 | + | 0.943422i | \(0.392414\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19982.4 | −1.22555 | −0.612774 | − | 0.790258i | \(-0.709946\pi\) | ||||
−0.612774 | + | 0.790258i | \(0.709946\pi\) | |||||||
\(644\) | 2972.40 | 0.181877 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25321.9 | −1.54223 | ||||||||
\(647\) | −20270.5 | −1.23171 | −0.615854 | − | 0.787860i | \(-0.711189\pi\) | ||||
−0.615854 | + | 0.787860i | \(0.711189\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 18485.7 | 1.11807 | ||||||||
\(650\) | 4675.08 | 0.282110 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −20637.2 | −1.23959 | ||||||||
\(653\) | 14667.0 | 0.878967 | 0.439483 | − | 0.898251i | \(-0.355162\pi\) | ||||
0.439483 | + | 0.898251i | \(0.355162\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18353.5 | −1.09486 | ||||||||
\(656\) | 2705.58 | 0.161029 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1587.02 | −0.0940250 | ||||||||
\(659\) | 30650.2 | 1.81178 | 0.905890 | − | 0.423513i | \(-0.139203\pi\) | ||||
0.905890 | + | 0.423513i | \(0.139203\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22478.6 | 1.32272 | 0.661360 | − | 0.750069i | \(-0.269980\pi\) | ||||
0.661360 | + | 0.750069i | \(0.269980\pi\) | |||||||
\(662\) | −14851.0 | −0.871902 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 41723.2 | 2.43852 | ||||||||
\(665\) | 2967.93 | 0.173070 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6582.82 | −0.382140 | ||||||||
\(668\) | 18817.5 | 1.08993 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −46076.8 | −2.65687 | ||||||||
\(671\) | −21215.8 | −1.22061 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29582.8 | −1.69440 | −0.847202 | − | 0.531271i | \(-0.821714\pi\) | ||||
−0.847202 | + | 0.531271i | \(0.821714\pi\) | |||||||
\(674\) | 4354.16 | 0.248837 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30964.5 | −1.76175 | ||||||||
\(677\) | 26863.8 | 1.52505 | 0.762526 | − | 0.646957i | \(-0.223959\pi\) | ||||
0.762526 | + | 0.646957i | \(0.223959\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1346.38 | −0.0760960 | ||||||||
\(680\) | −24080.0 | −1.35798 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −32981.6 | −1.85180 | ||||||||
\(683\) | −10052.2 | −0.563159 | −0.281579 | − | 0.959538i | \(-0.590858\pi\) | ||||
−0.281579 | + | 0.959538i | \(0.590858\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15411.4 | 0.859621 | ||||||||
\(686\) | 6308.29 | 0.351096 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −483.030 | −0.0267665 | ||||||||
\(689\) | −4057.10 | −0.224330 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28224.7 | 1.55386 | 0.776930 | − | 0.629587i | \(-0.216776\pi\) | ||||
0.776930 | + | 0.629587i | \(0.216776\pi\) | |||||||
\(692\) | 59465.6 | 3.26668 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7056.51 | 0.385968 | ||||||||
\(695\) | 16578.5 | 0.904830 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3221.77 | 0.175084 | ||||||||
\(698\) | 59203.3 | 3.21043 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2417.77 | 0.130547 | ||||||||
\(701\) | 6567.19 | 0.353837 | 0.176918 | − | 0.984226i | \(-0.443387\pi\) | ||||
0.176918 | + | 0.984226i | \(0.443387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23962.2 | −1.28556 | ||||||||
\(704\) | 16424.5 | 0.879293 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 979.430 | 0.0522115 | ||||||||
\(707\) | −2875.91 | −0.152984 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6459.04 | 0.342136 | 0.171068 | − | 0.985259i | \(-0.445278\pi\) | ||||
0.171068 | + | 0.985259i | \(0.445278\pi\) | |||||||
\(710\) | −43244.8 | −2.28584 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −18831.3 | −0.991196 | ||||||||
\(713\) | −28776.5 | −1.51149 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4131.31 | 0.216087 | ||||||||
\(716\) | −28345.8 | −1.47951 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −23706.0 | −1.23217 | ||||||||
\(719\) | 22411.0 | 1.16243 | 0.581217 | − | 0.813749i | \(-0.302577\pi\) | ||||
0.581217 | + | 0.813749i | \(0.302577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 81.2530 | 0.00419698 | ||||||||
\(722\) | −21685.8 | −1.11781 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25646.1 | −1.31648 | ||||||||
\(725\) | −5354.50 | −0.274291 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10632.3 | 0.542407 | 0.271203 | − | 0.962522i | \(-0.412578\pi\) | ||||
0.271203 | + | 0.962522i | \(0.412578\pi\) | |||||||
\(728\) | 757.719 | 0.0385754 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −52035.6 | −2.63825 | ||||||||
\(731\) | −575.186 | −0.0291026 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9413.78 | 0.474360 | 0.237180 | − | 0.971466i | \(-0.423777\pi\) | ||||
0.237180 | + | 0.971466i | \(0.423777\pi\) | |||||||
\(734\) | 57331.2 | 2.88301 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7218.80 | 0.361533 | ||||||||
\(737\) | −16308.2 | −0.815087 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13114.7 | −0.652819 | −0.326409 | − | 0.945228i | \(-0.605839\pi\) | ||||
−0.326409 | + | 0.945228i | \(0.605839\pi\) | |||||||
\(740\) | −48737.4 | −2.42111 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3215.35 | −0.159083 | ||||||||
\(743\) | −14499.7 | −0.715938 | −0.357969 | − | 0.933733i | \(-0.616531\pi\) | ||||
−0.357969 | + | 0.933733i | \(0.616531\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35099.3 | 1.72609 | ||||||||
\(746\) | −23522.5 | −1.15445 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −18228.7 | −0.891051 | ||||||||
\(749\) | −1310.80 | −0.0639459 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13932.1 | −0.676950 | −0.338475 | − | 0.940975i | \(-0.609911\pi\) | ||||
−0.338475 | + | 0.940975i | \(0.609911\pi\) | |||||||
\(752\) | 7131.20 | 0.345809 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3589.12 | −0.173353 | ||||||||
\(755\) | 24842.2 | 1.19748 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15664.4 | 0.752088 | 0.376044 | − | 0.926602i | \(-0.377284\pi\) | ||||
0.376044 | + | 0.926602i | \(0.377284\pi\) | |||||||
\(758\) | −7246.39 | −0.347231 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −51920.3 | −2.47809 | ||||||||
\(761\) | 18040.5 | 0.859353 | 0.429677 | − | 0.902983i | \(-0.358628\pi\) | ||||
0.429677 | + | 0.902983i | \(0.358628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3642.90 | 0.172847 | ||||||||
\(764\) | −21148.8 | −1.00149 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38232.9 | −1.80341 | ||||||||
\(767\) | 8793.86 | 0.413987 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1523.11 | −0.0714238 | −0.0357119 | − | 0.999362i | \(-0.511370\pi\) | ||||
−0.0357119 | + | 0.999362i | \(0.511370\pi\) | |||||||
\(770\) | 3274.16 | 0.153237 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −67587.7 | −3.15095 | ||||||||
\(773\) | 40569.1 | 1.88767 | 0.943836 | − | 0.330414i | \(-0.107189\pi\) | ||||
0.943836 | + | 0.330414i | \(0.107189\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23407.0 | −1.08491 | ||||||||
\(776\) | 23553.2 | 1.08957 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9101.81 | −0.419429 | ||||||||
\(779\) | 6946.65 | 0.319499 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15305.8 | −0.701261 | ||||||||
\(782\) | −24373.0 | −1.11455 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −14095.9 | −0.642123 | ||||||||
\(785\) | −5007.12 | −0.227658 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19586.0 | 0.887124 | 0.443562 | − | 0.896244i | \(-0.353715\pi\) | ||||
0.443562 | + | 0.896244i | \(0.353715\pi\) | |||||||
\(788\) | 41589.0 | 1.88014 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −81175.0 | −3.65579 | ||||||||
\(791\) | 3505.91 | 0.157593 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10092.6 | −0.451954 | ||||||||
\(794\) | −30898.6 | −1.38105 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 83517.1 | 3.71882 | ||||||||
\(797\) | 9014.22 | 0.400628 | 0.200314 | − | 0.979732i | \(-0.435804\pi\) | ||||
0.200314 | + | 0.979732i | \(0.435804\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8491.75 | 0.375991 | ||||||||
\(800\) | 5871.81 | 0.259500 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8225.94 | −0.362180 | ||||||||
\(803\) | −18417.2 | −0.809375 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2856.72 | 0.125076 | ||||||||
\(806\) | −15689.7 | −0.685666 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 50310.5 | 2.19049 | ||||||||
\(809\) | 37058.4 | 1.61051 | 0.805255 | − | 0.592929i | \(-0.202028\pi\) | ||||
0.805255 | + | 0.592929i | \(0.202028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12988.4 | −0.562375 | −0.281187 | − | 0.959653i | \(-0.590728\pi\) | ||||
−0.281187 | + | 0.959653i | \(0.590728\pi\) | |||||||
\(812\) | −1856.15 | −0.0802194 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −26434.6 | −1.13825 | ||||||||
\(815\) | −19834.0 | −0.852461 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1240.19 | −0.0531075 | ||||||||
\(818\) | −33114.6 | −1.41543 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14129.0 | 0.601715 | ||||||||
\(821\) | −37857.7 | −1.60931 | −0.804654 | − | 0.593744i | \(-0.797649\pi\) | ||||
−0.804654 | + | 0.593744i | \(0.797649\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24099.3 | −1.02072 | −0.510358 | − | 0.859962i | \(-0.670487\pi\) | ||||
−0.510358 | + | 0.859962i | \(0.670487\pi\) | |||||||
\(824\) | −1421.42 | −0.0600941 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6969.34 | 0.293577 | ||||||||
\(827\) | −17199.6 | −0.723201 | −0.361601 | − | 0.932333i | \(-0.617770\pi\) | ||||
−0.361601 | + | 0.932333i | \(0.617770\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5547.26 | 0.232406 | 0.116203 | − | 0.993226i | \(-0.462928\pi\) | ||||
0.116203 | + | 0.993226i | \(0.462928\pi\) | |||||||
\(830\) | 85765.6 | 3.58671 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7813.33 | 0.325575 | ||||||||
\(833\) | −16785.2 | −0.698167 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18085.1 | 0.749536 | ||||||||
\(836\) | −39303.9 | −1.62602 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30018.1 | −1.23742 | ||||||||
\(839\) | −11780.4 | −0.484748 | −0.242374 | − | 0.970183i | \(-0.577926\pi\) | ||||
−0.242374 | + | 0.970183i | \(0.577926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20278.3 | −0.831452 | ||||||||
\(842\) | −23616.6 | −0.966605 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14428.4 | −0.588445 | ||||||||
\(845\) | −29759.4 | −1.21154 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1405.79 | −0.0570290 | ||||||||
\(848\) | 14448.0 | 0.585080 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −19825.2 | −0.799997 | ||||||||
\(851\) | −23064.3 | −0.929063 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27508.0 | −1.10417 | −0.552084 | − | 0.833789i | \(-0.686167\pi\) | ||||
−0.552084 | + | 0.833789i | \(0.686167\pi\) | |||||||
\(854\) | −7998.64 | −0.320501 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22930.8 | 0.915605 | ||||||||
\(857\) | 8744.22 | 0.348538 | 0.174269 | − | 0.984698i | \(-0.444244\pi\) | ||||
0.174269 | + | 0.984698i | \(0.444244\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4332.09 | −0.172071 | −0.0860355 | − | 0.996292i | \(-0.527420\pi\) | ||||
−0.0860355 | + | 0.996292i | \(0.527420\pi\) | |||||||
\(860\) | −2522.46 | −0.100018 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4040.02 | 0.159633 | ||||||||
\(863\) | 47669.0 | 1.88027 | 0.940135 | − | 0.340802i | \(-0.110698\pi\) | ||||
0.940135 | + | 0.340802i | \(0.110698\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 57151.2 | 2.24647 | ||||||||
\(866\) | −67534.9 | −2.65003 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8114.09 | −0.317293 | ||||||||
\(869\) | −28730.6 | −1.12154 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7757.99 | −0.301802 | ||||||||
\(872\) | −63728.1 | −2.47489 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −52552.1 | −2.03387 | ||||||||
\(875\) | −1154.29 | −0.0445967 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8876.79 | 0.341788 | 0.170894 | − | 0.985289i | \(-0.445334\pi\) | ||||
0.170894 | + | 0.985289i | \(0.445334\pi\) | |||||||
\(878\) | 16387.9 | 0.629916 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −14712.3 | −0.563581 | ||||||||
\(881\) | −17796.2 | −0.680554 | −0.340277 | − | 0.940325i | \(-0.610521\pi\) | ||||
−0.340277 | + | 0.940325i | \(0.610521\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36680.9 | 1.39797 | 0.698987 | − | 0.715134i | \(-0.253634\pi\) | ||||
0.698987 | + | 0.715134i | \(0.253634\pi\) | |||||||
\(884\) | −8671.59 | −0.329929 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45900.9 | 1.74049 | ||||||||
\(887\) | 21245.9 | 0.804248 | 0.402124 | − | 0.915585i | \(-0.368272\pi\) | ||||
0.402124 | + | 0.915585i | \(0.368272\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1993.89 | 0.0752227 | ||||||||
\(890\) | −38709.3 | −1.45791 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9237.07 | 0.346727 | ||||||||
\(893\) | 18309.6 | 0.686121 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27242.6 | −1.01745 | ||||||||
\(896\) | 5108.45 | 0.190470 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −55121.8 | −2.04837 | ||||||||
\(899\) | 17969.9 | 0.666661 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17204.6 | 0.636145 | ||||||||
\(902\) | 7663.40 | 0.282886 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −61331.5 | −2.25648 | ||||||||
\(905\) | −24648.0 | −0.905333 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22616.2 | 0.827960 | 0.413980 | − | 0.910286i | \(-0.364138\pi\) | ||||
0.413980 | + | 0.910286i | \(0.364138\pi\) | |||||||
\(908\) | −13423.1 | −0.490595 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1557.56 | 0.0567390 | ||||||||
\(911\) | 22225.8 | 0.808315 | 0.404157 | − | 0.914689i | \(-0.367565\pi\) | ||||
0.404157 | + | 0.914689i | \(0.367565\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30355.4 | 1.10035 | ||||||||
\(914\) | −67912.0 | −2.45769 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 73081.2 | 2.63611 | ||||||||
\(917\) | −2449.05 | −0.0881949 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15412.2 | 0.553212 | 0.276606 | − | 0.960983i | \(-0.410790\pi\) | ||||
0.276606 | + | 0.960983i | \(0.410790\pi\) | |||||||
\(920\) | −49974.7 | −1.79089 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 23286.6 | 0.831783 | ||||||||
\(923\) | −7281.15 | −0.259655 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18760.6 | −0.666859 | ||||||||
\(926\) | −20311.3 | −0.720810 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4507.87 | −0.159459 | ||||||||
\(929\) | 53009.2 | 1.87209 | 0.936047 | − | 0.351875i | \(-0.114456\pi\) | ||||
0.936047 | + | 0.351875i | \(0.114456\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36191.6 | −1.27404 | ||||||||
\(932\) | 47093.9 | 1.65516 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −40908.7 | −1.43316 | ||||||||
\(935\) | −17519.2 | −0.612770 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43533.3 | 1.51779 | 0.758896 | − | 0.651212i | \(-0.225739\pi\) | ||||
0.758896 | + | 0.651212i | \(0.225739\pi\) | |||||||
\(938\) | −6148.39 | −0.214021 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 37240.3 | 1.29218 | ||||||||
\(941\) | −15767.1 | −0.546221 | −0.273110 | − | 0.961983i | \(-0.588052\pi\) | ||||
−0.273110 | + | 0.961983i | \(0.588052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6686.34 | 0.230898 | ||||||||
\(944\) | −31316.4 | −1.07973 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1368.15 | −0.0470217 | ||||||||
\(947\) | −10349.7 | −0.355144 | −0.177572 | − | 0.984108i | \(-0.556824\pi\) | ||||
−0.177572 | + | 0.984108i | \(0.556824\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8761.27 | −0.299687 | ||||||||
\(950\) | −42746.2 | −1.45986 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3213.18 | −0.109391 | ||||||||
\(953\) | 31061.4 | 1.05580 | 0.527899 | − | 0.849307i | \(-0.322980\pi\) | ||||
0.527899 | + | 0.849307i | \(0.322980\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20325.7 | −0.688717 | ||||||||
\(956\) | 3590.92 | 0.121484 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8310.53 | −0.280272 | ||||||||
\(959\) | 2056.47 | 0.0692459 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48763.5 | 1.63685 | ||||||||
\(962\) | −12575.2 | −0.421457 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8519.29 | −0.284635 | ||||||||
\(965\) | −64957.2 | −2.16689 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16381.8 | −0.544781 | −0.272390 | − | 0.962187i | \(-0.587814\pi\) | ||||
−0.272390 | + | 0.962187i | \(0.587814\pi\) | |||||||
\(968\) | 24592.6 | 0.816566 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 48415.6 | 1.60261 | ||||||||
\(971\) | −13611.5 | −0.449861 | −0.224930 | − | 0.974375i | \(-0.572215\pi\) | ||||
−0.224930 | + | 0.974375i | \(0.572215\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2212.19 | 0.0728876 | ||||||||
\(974\) | −58095.5 | −1.91119 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 35941.5 | 1.17875 | ||||||||
\(977\) | 24497.0 | 0.802178 | 0.401089 | − | 0.916039i | \(-0.368632\pi\) | ||||
0.401089 | + | 0.916039i | \(0.368632\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13700.5 | −0.447264 | ||||||||
\(980\) | −73611.1 | −2.39941 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 83101.6 | 2.70049 | ||||||||
\(983\) | −16984.8 | −0.551101 | −0.275550 | − | 0.961287i | \(-0.588860\pi\) | ||||
−0.275550 | + | 0.961287i | \(0.588860\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 39970.4 | 1.29296 | ||||||||
\(986\) | 15220.0 | 0.491587 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18697.3 | −0.602066 | ||||||||
\(989\) | −1193.72 | −0.0383802 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47834.1 | −1.53330 | −0.766650 | − | 0.642065i | \(-0.778078\pi\) | ||||
−0.766650 | + | 0.642065i | \(0.778078\pi\) | |||||||
\(992\) | −19706.0 | −0.630711 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5770.49 | −0.184134 | ||||||||
\(995\) | 80266.6 | 2.55741 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2869.40 | 0.0911483 | 0.0455742 | − | 0.998961i | \(-0.485488\pi\) | ||||
0.0455742 | + | 0.998961i | \(0.485488\pi\) | |||||||
\(998\) | −50823.7 | −1.61202 | ||||||||
\(999\) | 0 | 0 |
(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 | 2151.4.a.f.1.5 | 37 | ||
3.2 | odd | 2 | 239.4.a.b.1.33 | ✓ | 37 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
239.4.a.b.1.33 | ✓ | 37 | 3.2 | odd | 2 | ||
2151.4.a.f.1.5 | 37 | 1.1 | even | 1 | trivial |