Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1856,4,Mod(1,1856)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1856, 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("1856.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1856 = 2^{6} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1856.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(109.507544971\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 29) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1856.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.757359 | 0.145754 | 0.0728769 | − | 0.997341i | \(-0.476782\pi\) | ||||
0.0728769 | + | 0.997341i | \(0.476782\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 10.6569 | 0.953178 | 0.476589 | − | 0.879126i | \(-0.341873\pi\) | ||||
0.476589 | + | 0.879126i | \(0.341873\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −22.1421 | −1.19556 | −0.597781 | − | 0.801659i | \(-0.703951\pi\) | ||||
−0.597781 | + | 0.801659i | \(0.703951\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.4264 | −0.978756 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −39.3259 | −1.07793 | −0.538964 | − | 0.842329i | \(-0.681184\pi\) | ||||
−0.538964 | + | 0.842329i | \(0.681184\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −23.7696 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.07107 | 0.138929 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.54416 | 0.0648306 | 0.0324153 | − | 0.999474i | \(-0.489680\pi\) | ||||
0.0324153 | + | 0.999474i | \(0.489680\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 155.255 | 1.87463 | 0.937313 | − | 0.348488i | \(-0.113305\pi\) | ||||
0.937313 | + | 0.348488i | \(0.113305\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.7696 | −0.174258 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −41.8823 | −0.379698 | −0.189849 | − | 0.981813i | \(-0.560800\pi\) | ||||
−0.189849 | + | 0.981813i | \(0.560800\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.4315 | −0.0914517 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −40.4630 | −0.288411 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −29.0000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −57.9045 | −0.335483 | −0.167741 | − | 0.985831i | \(-0.553647\pi\) | ||||
−0.167741 | + | 0.985831i | \(0.553647\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −29.7838 | −0.157112 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −235.966 | −1.13958 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −235.196 | −1.04503 | −0.522513 | − | 0.852631i | \(-0.675005\pi\) | ||||
−0.522513 | + | 0.852631i | \(0.675005\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18.0021 | −0.0739139 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −175.161 | −0.667210 | −0.333605 | − | 0.942713i | \(-0.608265\pi\) | ||||
−0.333605 | + | 0.942713i | \(0.608265\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 402.831 | 1.42863 | 0.714315 | − | 0.699824i | \(-0.246738\pi\) | ||||
0.714315 | + | 0.699824i | \(0.246738\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −281.622 | −0.932929 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 227.742 | 0.706800 | 0.353400 | − | 0.935472i | \(-0.385025\pi\) | ||||
0.353400 | + | 0.935472i | \(0.385025\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 147.274 | 0.429371 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.44156 | 0.00944931 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −673.534 | −1.74560 | −0.872802 | − | 0.488074i | \(-0.837699\pi\) | ||||
−0.872802 | + | 0.488074i | \(0.837699\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −419.090 | −1.02746 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 117.584 | 0.273234 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 800.725 | 1.76687 | 0.883437 | − | 0.468551i | \(-0.155224\pi\) | ||||
0.883437 | + | 0.468551i | \(0.155224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 222.270 | 0.466537 | 0.233268 | − | 0.972412i | \(-0.425058\pi\) | ||||
0.233268 | + | 0.972412i | \(0.425058\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 585.137 | 1.17016 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −253.309 | −0.483370 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 524.479 | 0.956349 | 0.478174 | − | 0.878265i | \(-0.341299\pi\) | ||||
0.478174 | + | 0.878265i | \(0.341299\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −31.7199 | −0.0553424 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −281.917 | −0.471230 | −0.235615 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235615 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1229.10 | 1.97061 | 0.985307 | − | 0.170790i | \(-0.0546320\pi\) | ||||
0.985307 | + | 0.170790i | \(0.0546320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.65772 | −0.0133294 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 870.759 | 1.28873 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 611.247 | 0.870514 | 0.435257 | − | 0.900306i | \(-0.356657\pi\) | ||||
0.435257 | + | 0.900306i | \(0.356657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 682.868 | 0.936719 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −515.490 | −0.681716 | −0.340858 | − | 0.940115i | \(-0.610718\pi\) | ||||
−0.340858 | + | 0.940115i | \(0.610718\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 48.4264 | 0.0617951 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.9634 | −0.0270658 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −358.219 | −0.426643 | −0.213321 | − | 0.976982i | \(-0.568428\pi\) | ||||
−0.213321 | + | 0.976982i | \(0.568428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 526.309 | 0.606287 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −43.8545 | −0.0488979 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1654.53 | 1.78685 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 829.415 | 0.868189 | 0.434095 | − | 0.900867i | \(-0.357068\pi\) | ||||
0.434095 | + | 0.900867i | \(0.357068\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1039.24 | 1.05503 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 978.010 | 0.963521 | 0.481761 | − | 0.876303i | \(-0.339997\pi\) | ||||
0.481761 | + | 0.876303i | \(0.339997\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1217.33 | −1.16453 | −0.582266 | − | 0.812998i | \(-0.697834\pi\) | ||||
−0.582266 | + | 0.812998i | \(0.697834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −178.711 | −0.166099 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 707.044 | 0.638808 | 0.319404 | − | 0.947619i | \(-0.396517\pi\) | ||||
0.319404 | + | 0.947619i | \(0.396517\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1496.14 | 1.31471 | 0.657357 | − | 0.753580i | \(-0.271674\pi\) | ||||
0.657357 | + | 0.753580i | \(0.271674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −178.128 | −0.152317 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1067.23 | −0.888469 | −0.444234 | − | 0.895911i | \(-0.646524\pi\) | ||||
−0.444234 | + | 0.895911i | \(0.646524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −446.333 | −0.361920 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 628.144 | 0.496341 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −100.617 | −0.0775090 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 215.527 | 0.161928 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −132.660 | −0.0972485 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1453.93 | −1.04035 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1179.58 | −0.824177 | −0.412088 | − | 0.911144i | \(-0.635201\pi\) | ||||
−0.412088 | + | 0.911144i | \(0.635201\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 305.087 | 0.208228 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2357.47 | 1.57231 | 0.786156 | − | 0.618028i | \(-0.212068\pi\) | ||||
0.786156 | + | 0.618028i | \(0.212068\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3437.67 | −2.24123 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −431.208 | −0.274907 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 722.489 | 0.450558 | 0.225279 | − | 0.974294i | \(-0.427671\pi\) | ||||
0.225279 | + | 0.974294i | \(0.427671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1398.24 | −0.853219 | −0.426610 | − | 0.904436i | \(-0.640292\pi\) | ||||
−0.426610 | + | 0.904436i | \(0.640292\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 172.483 | 0.103019 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 934.759 | 0.546633 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −309.049 | −0.177001 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 111.539 | 0.0625824 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2830.63 | −1.55634 | −0.778168 | − | 0.628056i | \(-0.783851\pi\) | ||||
−0.778168 | + | 0.628056i | \(0.783851\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1705.58 | 0.919194 | 0.459597 | − | 0.888128i | \(-0.347994\pi\) | ||||
0.459597 | + | 0.888128i | \(0.347994\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −120.086 | −0.0634533 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −617.080 | −0.319775 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2670.84 | 1.35768 | 0.678841 | − | 0.734286i | \(-0.262483\pi\) | ||||
0.678841 | + | 0.734286i | \(0.262483\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −510.107 | −0.254429 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 927.362 | 0.453953 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2151.92 | 1.03406 | 0.517028 | − | 0.855968i | \(-0.327038\pi\) | ||||
0.517028 | + | 0.855968i | \(0.327038\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −317.402 | −0.149756 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 999.387 | 0.463083 | 0.231542 | − | 0.972825i | \(-0.425623\pi\) | ||||
0.231542 | + | 0.972825i | \(0.425623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1632.01 | −0.742835 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4102.83 | −1.83480 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2534.30 | 1.11375 | 0.556877 | − | 0.830595i | \(-0.311999\pi\) | ||||
0.556877 | + | 0.830595i | \(0.311999\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 253.117 | 0.109336 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 606.437 | 0.257529 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3550.27 | −1.48245 | −0.741227 | − | 0.671254i | \(-0.765756\pi\) | ||||
−0.741227 | + | 0.671254i | \(0.765756\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3034.68 | 1.24622 | 0.623110 | − | 0.782135i | \(-0.285869\pi\) | ||||
0.623110 | + | 0.782135i | \(0.285869\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 168.338 | 0.0679996 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2506.45 | −0.996096 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −178.703 | −0.0698827 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 895.937 | 0.344814 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2224.00 | 0.842529 | 0.421265 | − | 0.906938i | \(-0.361586\pi\) | ||||
0.421265 | + | 0.906938i | \(0.361586\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −632.830 | −0.236021 | −0.118011 | − | 0.993012i | \(-0.537652\pi\) | ||||
−0.118011 | + | 0.993012i | \(0.537652\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −191.846 | −0.0704531 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1369.80 | −0.495404 | −0.247702 | − | 0.968836i | \(-0.579675\pi\) | ||||
−0.247702 | + | 0.968836i | \(0.579675\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1416.38 | 0.504544 | 0.252272 | − | 0.967656i | \(-0.418822\pi\) | ||||
0.252272 | + | 0.967656i | \(0.418822\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 397.219 | 0.139391 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 642.122 | 0.222010 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1866.67 | −0.635970 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1106.80 | 0.371632 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6105.54 | −2.02071 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 896.432 | 0.292478 | 0.146239 | − | 0.989249i | \(-0.453283\pi\) | ||||
0.146239 | + | 0.989249i | \(0.453283\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −213.512 | −0.0686837 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4292.91 | 1.36174 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1282.13 | 0.401091 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 930.868 | 0.287225 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −108.013 | −0.0328765 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2268.94 | −0.681344 | −0.340672 | − | 0.940182i | \(-0.610655\pi\) | ||||
−0.340672 | + | 0.940182i | \(0.610655\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 302.092 | 0.0895088 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2078.09 | 0.607610 | 0.303805 | − | 0.952734i | \(-0.401743\pi\) | ||||
0.303805 | + | 0.952734i | \(0.401743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3715.05 | 1.07204 | 0.536020 | − | 0.844205i | \(-0.319927\pi\) | ||||
0.536020 | + | 0.844205i | \(0.319927\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 659.478 | 0.187837 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2521.35 | 0.708923 | 0.354461 | − | 0.935071i | \(-0.384664\pi\) | ||||
0.354461 | + | 0.935071i | \(0.384664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2427.02 | 0.673707 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 462.933 | 0.126881 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3940.04 | 1.06636 | 0.533179 | − | 0.846002i | \(-0.320997\pi\) | ||||
0.533179 | + | 0.846002i | \(0.320997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1973.06 | −0.527369 | −0.263684 | − | 0.964609i | \(-0.584938\pi\) | ||||
−0.263684 | + | 0.964609i | \(0.584938\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1609.68 | 0.424942 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1569.48 | 0.409267 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3690.34 | −0.950650 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −390.411 | −0.0993627 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1236.65 | 0.310982 | 0.155491 | − | 0.987837i | \(-0.450304\pi\) | ||||
0.155491 | + | 0.987837i | \(0.450304\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1647.06 | 0.409287 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 36.6762 | 0.00900687 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2918.10 | 0.708272 | 0.354136 | − | 0.935194i | \(-0.384775\pi\) | ||||
0.354136 | + | 0.935194i | \(0.384775\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5207.74 | 1.24939 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 766.366 | 0.181750 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −310.789 | −0.0728673 | −0.0364336 | − | 0.999336i | \(-0.511600\pi\) | ||||
−0.0364336 | + | 0.999336i | \(0.511600\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7177.75 | −1.66387 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −271.301 | −0.0621848 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1839.98 | 0.417047 | 0.208523 | − | 0.978017i | \(-0.433134\pi\) | ||||
0.208523 | + | 0.978017i | \(0.433134\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5187.35 | 1.16277 | 0.581383 | − | 0.813630i | \(-0.302512\pi\) | ||||
0.581383 | + | 0.813630i | \(0.302512\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 398.605 | 0.0883687 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 449.552 | 0.0985783 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8666.41 | −1.87983 | −0.939917 | − | 0.341403i | \(-0.889098\pi\) | ||||
−0.939917 | + | 0.341403i | \(0.889098\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1530.21 | 0.328356 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7856.96 | 1.66800 | 0.833998 | − | 0.551767i | \(-0.186046\pi\) | ||||
0.833998 | + | 0.551767i | \(0.186046\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3054.71 | 0.641638 | 0.320819 | − | 0.947141i | \(-0.396042\pi\) | ||||
0.320819 | + | 0.947141i | \(0.396042\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1253.07 | 0.260441 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3878.45 | 0.797692 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4892.35 | −0.995797 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 628.166 | 0.126542 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2847.83 | −0.567822 | −0.283911 | − | 0.958851i | \(-0.591632\pi\) | ||||
−0.283911 | + | 0.958851i | \(0.591632\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8533.21 | 1.68414 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1591.24 | 0.310887 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 995.522 | 0.192550 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8919.53 | −1.70802 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 740.705 | 0.140437 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2368.70 | 0.444693 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2470.79 | 0.459334 | 0.229667 | − | 0.973269i | \(-0.426236\pi\) | ||||
0.229667 | + | 0.973269i | \(0.426236\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −921.955 | −0.169735 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5653.29 | −1.03077 | −0.515384 | − | 0.856959i | \(-0.672351\pi\) | ||||
−0.515384 | + | 0.856959i | \(0.672351\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8289.72 | −1.49701 | −0.748503 | − | 0.663132i | \(-0.769227\pi\) | ||||
−0.748503 | + | 0.663132i | \(0.769227\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6235.72 | 1.11537 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2577.06 | −0.456600 | −0.228300 | − | 0.973591i | \(-0.573317\pi\) | ||||
−0.228300 | + | 0.973591i | \(0.573317\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1140.45 | 0.200166 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 535.486 | 0.0931088 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 705.502 | 0.121533 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 271.721 | 0.0463765 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1133.11 | 0.191625 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5042.70 | −0.845024 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7672.12 | −1.27401 | −0.637006 | − | 0.770859i | \(-0.719827\pi\) | ||||
−0.637006 | + | 0.770859i | \(0.719827\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6215.38 | 1.02283 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5589.30 | 0.911570 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3650.77 | 0.590120 | 0.295060 | − | 0.955479i | \(-0.404660\pi\) | ||||
0.295060 | + | 0.955479i | \(0.404660\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −808.280 | −0.129498 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2277.15 | 0.361626 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4333.79 | 0.682223 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −338.034 | −0.0527512 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8737.06 | 1.35167 | 0.675835 | − | 0.737053i | \(-0.263783\pi\) | ||||
0.675835 | + | 0.737053i | \(0.263783\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2143.83 | 0.328816 | 0.164408 | − | 0.986392i | \(-0.447429\pi\) | ||||
0.164408 | + | 0.986392i | \(0.447429\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 961.787 | 0.146258 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5111.17 | −0.770651 | −0.385326 | − | 0.922781i | \(-0.625911\pi\) | ||||
−0.385326 | + | 0.922781i | \(0.625911\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3004.35 | −0.449167 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −76.2035 | −0.0112972 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4520.87 | 0.664630 | 0.332315 | − | 0.943168i | \(-0.392170\pi\) | ||||
0.332315 | + | 0.943168i | \(0.392170\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17245.1 | 2.51422 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 163.231 | 0.0236017 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13098.3 | 1.87835 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −486.272 | −0.0691641 | −0.0345820 | − | 0.999402i | \(-0.511010\pi\) | ||||
−0.0345820 | + | 0.999402i | \(0.511010\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4628.89 | 0.653036 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14913.5 | 2.08698 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10053.1 | −1.39552 | −0.697758 | − | 0.716333i | \(-0.745819\pi\) | ||||
−0.697758 | + | 0.716333i | \(0.745819\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1101.15 | −0.151635 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 689.317 | 0.0941688 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11602.8 | 1.57255 | 0.786273 | − | 0.617879i | \(-0.212008\pi\) | ||||
0.786273 | + | 0.617879i | \(0.212008\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −893.363 | −0.120127 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4161.38 | −0.555187 | −0.277593 | − | 0.960699i | \(-0.589537\pi\) | ||||
−0.277593 | + | 0.960699i | \(0.589537\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9279.56 | 1.22839 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10645.4 | −1.39828 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6843.95 | 0.892036 | 0.446018 | − | 0.895024i | \(-0.352842\pi\) | ||||
0.446018 | + | 0.895024i | \(0.352842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −190.319 | −0.0246160 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1785.45 | 0.229171 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6513.97 | 0.829755 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5474.73 | −0.692112 | −0.346056 | − | 0.938214i | \(-0.612479\pi\) | ||||
−0.346056 | + | 0.938214i | \(0.612479\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2603.55 | −0.326669 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 890.013 | 0.110836 | 0.0554178 | − | 0.998463i | \(-0.482351\pi\) | ||||
0.0554178 | + | 0.998463i | \(0.482351\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1376.37 | 0.170128 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7277.22 | 0.892860 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9249.29 | 1.12646 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8107.81 | 0.980209 | 0.490104 | − | 0.871664i | \(-0.336959\pi\) | ||||
0.490104 | + | 0.871664i | \(0.336959\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 547.184 | 0.0656706 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17729.8 | −2.11241 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5493.51 | −0.649797 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1058.97 | −0.124360 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4237.59 | −0.494080 | −0.247040 | − | 0.969005i | \(-0.579458\pi\) | ||||
−0.247040 | + | 0.969005i | \(0.579458\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 953.634 | 0.110397 | 0.0551987 | − | 0.998475i | \(-0.482421\pi\) | ||||
0.0551987 | + | 0.998475i | \(0.482421\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6018.41 | −0.691785 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −51.9463 | −0.00592886 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4921.53 | −0.557774 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 707.949 | 0.0796738 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10098.8 | −1.12864 | −0.564318 | − | 0.825557i | \(-0.690861\pi\) | ||||
−0.564318 | + | 0.825557i | \(0.690861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12833.1 | −1.42430 | −0.712148 | − | 0.702029i | \(-0.752278\pi\) | ||||
−0.712148 | + | 0.702029i | \(0.752278\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −234.061 | −0.0257985 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6502.42 | −0.711792 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14434.8 | −1.56932 | −0.784662 | − | 0.619924i | \(-0.787164\pi\) | ||||
−0.784662 | + | 0.619924i | \(0.787164\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3891.93 | −0.420249 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7020.65 | 0.752959 | 0.376480 | − | 0.926425i | \(-0.377134\pi\) | ||||
0.376480 | + | 0.926425i | \(0.377134\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3817.49 | −0.406666 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2143.80 | −0.226842 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13210.5 | 1.38851 | 0.694254 | − | 0.719730i | \(-0.255735\pi\) | ||||
0.694254 | + | 0.719730i | \(0.255735\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6888.38 | 0.719205 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1291.74 | 0.133976 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5608.79 | 0.577900 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2811.18 | −0.287749 | −0.143875 | − | 0.989596i | \(-0.545956\pi\) | ||||
−0.143875 | + | 0.989596i | \(0.545956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −183.870 | −0.0186979 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9645.10 | 0.974441 | 0.487220 | − | 0.873279i | \(-0.338011\pi\) | ||||
0.487220 | + | 0.873279i | \(0.338011\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6923.23 | 0.694924 | 0.347462 | − | 0.937694i | \(-0.387044\pi\) | ||||
0.347462 | + | 0.937694i | \(0.387044\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −467.352 | −0.0466084 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 124.351 | 0.0123218 | 0.00616089 | − | 0.999981i | \(-0.498039\pi\) | ||||
0.00616089 | + | 0.999981i | \(0.498039\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11613.1 | −1.14337 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2022.78 | 0.197887 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15841.7 | −1.53996 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1774.79 | −0.171438 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17799.1 | 1.70852 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4461.48 | −0.425575 | −0.212788 | − | 0.977098i | \(-0.568254\pi\) | ||||
−0.212788 | + | 0.977098i | \(0.568254\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5590.50 | 0.529948 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 702.347 | 0.0661654 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8838.96 | 0.827539 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5660.72 | −0.526718 | −0.263359 | − | 0.964698i | \(-0.584830\pi\) | ||||
−0.263359 | + | 0.964698i | \(0.584830\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1629.77 | 0.150718 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5587.50 | −0.513565 | −0.256782 | − | 0.966469i | \(-0.582662\pi\) | ||||
−0.256782 | + | 0.966469i | \(0.582662\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −131.781 | −0.0120387 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11075.1 | 1.00563 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6242.24 | 0.563386 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4210.19 | 0.377703 | 0.188851 | − | 0.982006i | \(-0.439524\pi\) | ||||
0.188851 | + | 0.982006i | \(0.439524\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 756.895 | 0.0674962 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10796.7 | 0.957063 | 0.478532 | − | 0.878070i | \(-0.341169\pi\) | ||||
0.478532 | + | 0.878070i | \(0.341169\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10422.5 | 0.918407 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1236.02 | −0.108271 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −14983.6 | −1.30479 | −0.652395 | − | 0.757879i | \(-0.726236\pi\) | ||||
−0.652395 | + | 0.757879i | \(0.726236\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27214.8 | −2.35599 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6282.07 | −0.540663 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12972.9 | −1.11001 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8956.17 | −0.761880 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1919.38 | 0.162334 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10770.3 | −0.905671 | −0.452836 | − | 0.891594i | \(-0.649588\pi\) | ||||
−0.452836 | + | 0.891594i | \(0.649588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7538.93 | 0.630314 | 0.315157 | − | 0.949040i | \(-0.397943\pi\) | ||||
0.315157 | + | 0.949040i | \(0.397943\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 191.700 | 0.0159362 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −263.127 | −0.0217495 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10412.9 | −0.855829 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21160.3 | −1.72934 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4163.51 | 0.338352 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7534.86 | 0.608898 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2688.83 | −0.216073 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5791.69 | −0.462831 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −595.816 | −0.0473496 | −0.0236748 | − | 0.999720i | \(-0.507537\pi\) | ||||
−0.0236748 | + | 0.999720i | \(0.507537\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2298.34 | 0.181641 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 15944.1 | 1.25316 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12703.4 | −0.992978 | −0.496489 | − | 0.868043i | \(-0.665378\pi\) | ||||
−0.496489 | + | 0.868043i | \(0.665378\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5873.80 | −0.456626 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4502.39 | −0.348109 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13534.3 | −1.04075 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1898.28 | −0.145185 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14973.0 | 1.13901 | 0.569503 | − | 0.821990i | \(-0.307136\pi\) | ||||
0.569503 | + | 0.821990i | \(0.307136\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9575.10 | −0.724479 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −135.342 | −0.0101857 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10439.3 | 0.781466 | 0.390733 | − | 0.920504i | \(-0.372222\pi\) | ||||
0.390733 | + | 0.920504i | \(0.372222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11373.4 | −0.846869 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −15120.2 | −1.11991 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8859.72 | −0.652757 | −0.326379 | − | 0.945239i | \(-0.605828\pi\) | ||||
−0.326379 | + | 0.945239i | \(0.605828\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5078.17 | 0.372180 | 0.186090 | − | 0.982533i | \(-0.440418\pi\) | ||||
0.186090 | + | 0.982533i | \(0.440418\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1684.37 | 0.122802 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 478.775 | 0.0347240 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20457.2 | 1.47599 | 0.737994 | − | 0.674808i | \(-0.235773\pi\) | ||||
0.737994 | + | 0.674808i | \(0.235773\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −479.280 | −0.0344010 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11414.1 | 0.815034 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26487.3 | 1.88164 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6694.04 | 0.473102 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4355.22 | −0.306234 | −0.153117 | − | 0.988208i | \(-0.548931\pi\) | ||||
−0.153117 | + | 0.988208i | \(0.548931\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8989.96 | −0.628905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1037.43 | −0.0722070 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4342.49 | 0.300716 | 0.150358 | − | 0.988632i | \(-0.451957\pi\) | ||||
0.150358 | + | 0.988632i | \(0.451957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1072.26 | −0.0738799 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1072.71 | 0.0735392 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12761.8 | −0.870506 | −0.435253 | − | 0.900308i | \(-0.643341\pi\) | ||||
−0.435253 | + | 0.900308i | \(0.643341\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2804.87 | −0.190371 | −0.0951857 | − | 0.995460i | \(-0.530344\pi\) | ||||
−0.0951857 | + | 0.995460i | \(0.530344\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13860.1 | −0.936032 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2296.84 | 0.154346 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12033.5 | 0.804654 | 0.402327 | − | 0.915496i | \(-0.368202\pi\) | ||||
0.402327 | + | 0.915496i | \(0.368202\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 486.317 | 0.0323589 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5413.33 | −0.358429 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7993.67 | −0.526690 | −0.263345 | − | 0.964702i | \(-0.584826\pi\) | ||||
−0.263345 | + | 0.964702i | \(0.584826\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1413.74 | −0.0926951 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9922.51 | 0.647432 | 0.323716 | − | 0.946154i | \(-0.395068\pi\) | ||||
0.323716 | + | 0.946154i | \(0.395068\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15401.4 | 1.00005 | 0.500027 | − | 0.866010i | \(-0.333324\pi\) | ||||
0.500027 | + | 0.866010i | \(0.333324\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1694.68 | 0.109509 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7931.74 | 0.510078 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14065.4 | −0.900185 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4624.08 | −0.294527 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1068.77 | −0.0677497 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3776.97 | −0.238287 | −0.119143 | − | 0.992877i | \(-0.538015\pi\) | ||||
−0.119143 | + | 0.992877i | \(0.538015\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 678.921 | 0.0426298 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12570.6 | −0.785587 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3500.64 | −0.217740 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7450.05 | 0.461220 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 464.125 | 0.0285988 | 0.0142994 | − | 0.999898i | \(-0.495448\pi\) | ||||
0.0142994 | + | 0.999898i | \(0.495448\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7607.61 | −0.466586 | −0.233293 | − | 0.972406i | \(-0.574950\pi\) | ||||
−0.233293 | + | 0.972406i | \(0.574950\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3251.27 | 0.198479 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7776.85 | 0.472550 | 0.236275 | − | 0.971686i | \(-0.424073\pi\) | ||||
0.236275 | + | 0.971686i | \(0.424073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31489.2 | −1.90456 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 971.033 | 0.0584605 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24486.1 | 1.46740 | 0.733702 | − | 0.679471i | \(-0.237791\pi\) | ||||
0.733702 | + | 0.679471i | \(0.237791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25123.2 | 1.49869 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −32480.6 | −1.92875 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −910.966 | −0.0538486 | −0.0269243 | − | 0.999637i | \(-0.508571\pi\) | ||||
−0.0269243 | + | 0.999637i | \(0.508571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5826.64 | −0.342859 | −0.171430 | − | 0.985196i | \(-0.554839\pi\) | ||||
−0.171430 | + | 0.985196i | \(0.554839\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −81.8043 | −0.00479188 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −36634.8 | −2.13629 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1214.59 | 0.0705081 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1718.40 | −0.0993085 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8740.97 | −0.502893 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27236.0 | 1.55999 | 0.779994 | − | 0.625788i | \(-0.215222\pi\) | ||||
0.779994 | + | 0.625788i | \(0.215222\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 462.551 | 0.0263757 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8989.70 | −0.510343 | −0.255172 | − | 0.966896i | \(-0.582132\pi\) | ||||
−0.255172 | + | 0.966896i | \(0.582132\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18365.0 | −1.03798 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1573.86 | 0.0885616 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6934.65 | −0.388502 | −0.194251 | − | 0.980952i | \(-0.562228\pi\) | ||||
−0.194251 | + | 0.980952i | \(0.562228\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7699.46 | 0.429462 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2813.63 | 0.156254 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16009.6 | 0.885221 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5234.54 | −0.288178 | −0.144089 | − | 0.989565i | \(-0.546025\pi\) | ||||
−0.144089 | + | 0.989565i | \(0.546025\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −23011.0 | −1.26135 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14900.9 | −0.813270 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −795.961 | −0.0432556 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1909.57 | 0.103328 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33713.7 | 1.81647 | 0.908237 | − | 0.418457i | \(-0.137429\pi\) | ||||
0.908237 | + | 0.418457i | \(0.137429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36515.3 | −1.95903 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1838.12 | 0.0981953 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21655.2 | −1.15195 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12687.3 | 0.672049 | 0.336025 | − | 0.941853i | \(-0.390917\pi\) | ||||
0.336025 | + | 0.941853i | \(0.390917\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16153.1 | −0.852021 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2425.17 | 0.127382 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9961.59 | 0.521038 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2984.02 | 0.155426 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30604.9 | 1.58744 | 0.793720 | − | 0.608283i | \(-0.208141\pi\) | ||||
0.793720 | + | 0.608283i | \(0.208141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26954.2 | 1.39227 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1494.31 | −0.0768661 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 331.512 | 0.0169821 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3727.96 | 0.190182 | 0.0950911 | − | 0.995469i | \(-0.469686\pi\) | ||||
0.0950911 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17218.3 | −0.874782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1830.52 | 0.0926189 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1107.21 | −0.0557921 | −0.0278960 | − | 0.999611i | \(-0.508881\pi\) | ||||
−0.0278960 | + | 0.999611i | \(0.508881\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1188.66 | 0.0596522 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −20625.6 | −1.03087 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29127.7 | 1.44991 | 0.724953 | − | 0.688798i | \(-0.241861\pi\) | ||||
0.724953 | + | 0.688798i | \(0.241861\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2794.91 | −0.138561 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12162.8 | 0.600552 | 0.300276 | − | 0.953852i | \(-0.402921\pi\) | ||||
0.300276 | + | 0.953852i | \(0.402921\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30165.6 | −1.48347 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13622.6 | 0.667233 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15655.5 | −0.763736 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25067.6 | −1.21802 | −0.609008 | − | 0.793164i | \(-0.708432\pi\) | ||||
−0.609008 | + | 0.793164i | \(0.708432\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 936.587 | 0.0453269 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18176.1 | 0.876156 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12020.6 | 0.577140 | 0.288570 | − | 0.957459i | \(-0.406820\pi\) | ||||
0.288570 | + | 0.957459i | \(0.406820\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1247.41 | 0.0596552 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9255.42 | 0.440879 | 0.220439 | − | 0.975401i | \(-0.429251\pi\) | ||||
0.220439 | + | 0.975401i | \(0.429251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33127.6 | −1.57182 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1279.74 | −0.0604823 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19032.9 | −0.896007 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28690.1 | 1.34537 | 0.672687 | − | 0.739928i | \(-0.265140\pi\) | ||||
0.672687 | + | 0.739928i | \(0.265140\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2210.05 | 0.103233 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8984.36 | 0.418040 | 0.209020 | − | 0.977911i | \(-0.432973\pi\) | ||||
0.209020 | + | 0.977911i | \(0.432973\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 661.933 | 0.0306804 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3944.13 | 0.182104 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −27194.7 | −1.25077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11086.6 | 0.507952 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1173.43 | 0.0535566 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28462.7 | 1.29411 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5257.13 | 0.238115 | 0.119058 | − | 0.992887i | \(-0.462013\pi\) | ||||
0.119058 | + | 0.992887i | \(0.462013\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −235.379 | −0.0106207 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23630.9 | 1.06222 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5283.26 | −0.236588 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5436.14 | −0.242516 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7623.92 | −0.338837 | −0.169419 | − | 0.985544i | \(-0.554189\pi\) | ||||
−0.169419 | + | 0.985544i | \(0.554189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1034.90 | 0.0458223 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9466.45 | 0.417579 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48335.3 | −2.12418 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9882.77 | 0.432698 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1393.53 | 0.0607862 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28238.7 | −1.22722 | −0.613609 | − | 0.789610i | \(-0.710283\pi\) | ||||
−0.613609 | + | 0.789610i | \(0.710283\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29851.2 | −1.29250 | −0.646251 | − | 0.763125i | \(-0.723664\pi\) | ||||
−0.646251 | + | 0.763125i | \(0.723664\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3928.69 | 0.169478 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22932.7 | 0.985640 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 62541.4 | 2.67815 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13908.4 | −0.593407 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2043.20 | −0.0868552 | −0.0434276 | − | 0.999057i | \(-0.513828\pi\) | ||||
−0.0434276 | + | 0.999057i | \(0.513828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 123.242 | 0.00521988 | 0.00260994 | − | 0.999997i | \(-0.499169\pi\) | ||||
0.00260994 | + | 0.999997i | \(0.499169\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 340.473 | 0.0143682 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34335.2 | −1.44371 | −0.721857 | − | 0.692043i | \(-0.756711\pi\) | ||||
−0.721857 | + | 0.692043i | \(0.756711\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14705.0 | 0.616073 | 0.308037 | − | 0.951375i | \(-0.400328\pi\) | ||||
0.308037 | + | 0.951375i | \(0.400328\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6563.58 | −0.273993 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 669.237 | 0.0278364 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10650.3 | 0.441401 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2342.99 | 0.0967570 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22204.3 | −0.913679 | −0.456840 | − | 0.889549i | \(-0.651019\pi\) | ||||
−0.456840 | + | 0.889549i | \(0.651019\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5950.54 | 0.243117 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17392.1 | −0.708054 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4772.22 | −0.193595 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2313.51 | 0.0935212 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9850.54 | 0.396794 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40095.2 | 1.60942 | 0.804710 | − | 0.593669i | \(-0.202321\pi\) | ||||
0.804710 | + | 0.593669i | \(0.202321\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −43723.2 | −1.74889 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12883.7 | −0.513536 | −0.256768 | − | 0.966473i | \(-0.582658\pi\) | ||||
−0.256768 | + | 0.966473i | \(0.582658\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34336.9 | 1.36386 | 0.681932 | − | 0.731416i | \(-0.261140\pi\) | ||||
0.681932 | + | 0.731416i | \(0.261140\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2937.38 | 0.116267 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10864.2 | 0.428531 | 0.214266 | − | 0.976775i | \(-0.431264\pi\) | ||||
0.214266 | + | 0.976775i | \(0.431264\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27007.7 | 1.06161 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3705.27 | −0.145141 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −24037.8 | −0.938352 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12466.6 | −0.484978 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21918.5 | −0.849745 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32193.1 | 1.24380 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4818.40 | −0.185525 | −0.0927626 | − | 0.995688i | \(-0.529570\pi\) | ||||
−0.0927626 | + | 0.995688i | \(0.529570\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2156.83 | −0.0827623 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30195.7 | −1.15473 | −0.577366 | − | 0.816485i | \(-0.695920\pi\) | ||||
−0.577366 | + | 0.816485i | \(0.695920\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −30734.0 | −1.17133 | −0.585663 | − | 0.810555i | \(-0.699166\pi\) | ||||
−0.585663 | + | 0.810555i | \(0.699166\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6462.71 | 0.245471 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −43409.3 | −1.64323 | −0.821614 | − | 0.570045i | \(-0.806926\pi\) | ||||
−0.821614 | + | 0.570045i | \(0.806926\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26118.3 | 0.985355 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −26854.4 | −1.00972 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35358.1 | 1.32499 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −37834.7 | −1.41304 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 753.968 | 0.0280650 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1679.23 | 0.0622976 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3060.64 | −0.113169 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6755.29 | −0.248950 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32340.1 | 1.18787 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7991.51 | 0.292562 | 0.146281 | − | 0.989243i | \(-0.453270\pi\) | ||||
0.146281 | + | 0.989243i | \(0.453270\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25845.3 | −0.943052 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24188.5 | 0.879694 | 0.439847 | − | 0.898073i | \(-0.355033\pi\) | ||||
0.439847 | + | 0.898073i | \(0.355033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20272.1 | 0.734840 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1793.96 | 0.0648157 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −52199.4 | −1.87980 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 27421.3 | 0.984273 | 0.492136 | − | 0.870518i | \(-0.336216\pi\) | ||||
0.492136 | + | 0.870518i | \(0.336216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1871.28 | 0.0669497 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6701.03 | 0.238968 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2688.63 | 0.0955694 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32169.6 | 1.13979 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9284.12 | −0.327882 | −0.163941 | − | 0.986470i | \(-0.552421\pi\) | ||||
−0.163941 | + | 0.986470i | \(0.552421\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22865.0 | 0.804910 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −4281.57 | −0.150238 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1904.41 | −0.0666106 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1891.00 | −0.0659297 | −0.0329649 | − | 0.999457i | \(-0.510495\pi\) | ||||
−0.0329649 | + | 0.999457i | \(0.510495\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6278.30 | −0.218194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15163.9 | −0.525322 | −0.262661 | − | 0.964888i | \(-0.584600\pi\) | ||||
−0.262661 | + | 0.964888i | \(0.584600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7336.16 | 0.253338 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9547.87 | 0.328669 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31251.8 | 1.07238 | 0.536192 | − | 0.844096i | \(-0.319862\pi\) | ||||
0.536192 | + | 0.844096i | \(0.319862\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29215.1 | −0.999327 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1951.76 | −0.0665512 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12521.4 | −0.425612 | −0.212806 | − | 0.977094i | \(-0.568260\pi\) | ||||
−0.212806 | + | 0.977094i | \(0.568260\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23700.9 | 0.803081 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 863.731 | 0.0291750 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15997.5 | −0.538670 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26438.1 | −0.887451 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −18684.6 | −0.625237 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6743.98 | −0.224970 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18348.5 | −0.610183 | −0.305091 | − | 0.952323i | \(-0.598687\pi\) | ||||
−0.305091 | + | 0.952323i | \(0.598687\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 534.319 | 0.0177139 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27188.0 | −0.898564 | −0.449282 | − | 0.893390i | \(-0.648320\pi\) | ||||
−0.449282 | + | 0.893390i | \(0.648320\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 30960.1 | 1.02008 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 205.790 | 0.00675955 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4733.67 | 0.155009 | 0.0775044 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775044 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14087.3 | 0.459890 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −39537.5 | −1.28678 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −43971.5 | −1.42673 | −0.713363 | − | 0.700795i | \(-0.752829\pi\) | ||||
−0.713363 | + | 0.700795i | \(0.752829\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14597.8 | −0.472208 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3819.13 | −0.123166 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16871.4 | −0.542448 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14031.4 | −0.449769 | −0.224885 | − | 0.974385i | \(-0.572201\pi\) | ||||
−0.224885 | + | 0.974385i | \(0.572201\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5810.56 | −0.185692 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15094.1 | 0.480920 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43177.4 | −1.37156 | −0.685779 | − | 0.727810i | \(-0.740538\pi\) | ||||
−0.685779 | + | 0.727810i | \(0.740538\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9516.73 | 0.301397 |
(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 | 1856.4.a.n.1.1 | 2 | ||
4.3 | odd | 2 | 1856.4.a.h.1.2 | 2 | |||
8.3 | odd | 2 | 464.4.a.f.1.1 | 2 | |||
8.5 | even | 2 | 29.4.a.a.1.1 | ✓ | 2 | ||
24.5 | odd | 2 | 261.4.a.b.1.2 | 2 | |||
40.29 | even | 2 | 725.4.a.b.1.2 | 2 | |||
56.13 | odd | 2 | 1421.4.a.c.1.1 | 2 | |||
232.173 | even | 2 | 841.4.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.a.1.1 | ✓ | 2 | 8.5 | even | 2 | ||
261.4.a.b.1.2 | 2 | 24.5 | odd | 2 | |||
464.4.a.f.1.1 | 2 | 8.3 | odd | 2 | |||
725.4.a.b.1.2 | 2 | 40.29 | even | 2 | |||
841.4.a.a.1.2 | 2 | 232.173 | even | 2 | |||
1421.4.a.c.1.1 | 2 | 56.13 | odd | 2 | |||
1856.4.a.h.1.2 | 2 | 4.3 | odd | 2 | |||
1856.4.a.n.1.1 | 2 | 1.1 | even | 1 | trivial |