Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, 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("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.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: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 56x^{7} - 27x^{6} + 945x^{5} + 763x^{4} - 4139x^{3} - 2478x^{2} + 63x + 27 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 13^{2} \) |
Twist minimal: | no (minimal twist has level 507) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.27560\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.52257 | −1.95253 | −0.976263 | − | 0.216591i | \(-0.930506\pi\) | ||||
−0.976263 | + | 0.216591i | \(0.930506\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 22.4988 | 2.81235 | ||||||||
\(5\) | 6.08065 | 0.543870 | 0.271935 | − | 0.962316i | \(-0.412336\pi\) | ||||
0.271935 | + | 0.962316i | \(0.412336\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 20.2718 | 1.09458 | 0.547288 | − | 0.836944i | \(-0.315660\pi\) | ||||
0.547288 | + | 0.836944i | \(0.315660\pi\) | |||||||
\(8\) | −80.0709 | −3.53867 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −33.5808 | −1.06192 | ||||||||
\(11\) | 48.8284 | 1.33839 | 0.669196 | − | 0.743086i | \(-0.266639\pi\) | ||||
0.669196 | + | 0.743086i | \(0.266639\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −111.953 | −2.13719 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 262.207 | 4.09698 | ||||||||
\(17\) | 37.7513 | 0.538591 | 0.269295 | − | 0.963058i | \(-0.413209\pi\) | ||||
0.269295 | + | 0.963058i | \(0.413209\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 120.837 | 1.45905 | 0.729524 | − | 0.683955i | \(-0.239742\pi\) | ||||
0.729524 | + | 0.683955i | \(0.239742\pi\) | |||||||
\(20\) | 136.807 | 1.52955 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −269.658 | −2.61324 | ||||||||
\(23\) | −74.8543 | −0.678617 | −0.339309 | − | 0.940675i | \(-0.610193\pi\) | ||||
−0.339309 | + | 0.940675i | \(0.610193\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −88.0257 | −0.704206 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 456.092 | 3.07834 | ||||||||
\(29\) | 112.710 | 0.721715 | 0.360858 | − | 0.932621i | \(-0.382484\pi\) | ||||
0.360858 | + | 0.932621i | \(0.382484\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 113.134 | 0.655465 | 0.327733 | − | 0.944770i | \(-0.393715\pi\) | ||||
0.327733 | + | 0.944770i | \(0.393715\pi\) | |||||||
\(32\) | −807.490 | −4.46079 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −208.485 | −1.05161 | ||||||||
\(35\) | 123.266 | 0.595307 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −85.7704 | −0.381096 | −0.190548 | − | 0.981678i | \(-0.561027\pi\) | ||||
−0.190548 | + | 0.981678i | \(0.561027\pi\) | |||||||
\(38\) | −667.331 | −2.84883 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −486.883 | −1.92457 | ||||||||
\(41\) | 133.993 | 0.510395 | 0.255197 | − | 0.966889i | \(-0.417860\pi\) | ||||
0.255197 | + | 0.966889i | \(0.417860\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −319.135 | −1.13181 | −0.565903 | − | 0.824472i | \(-0.691472\pi\) | ||||
−0.565903 | + | 0.824472i | \(0.691472\pi\) | |||||||
\(44\) | 1098.58 | 3.76403 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 413.388 | 1.32502 | ||||||||
\(47\) | 401.982 | 1.24755 | 0.623777 | − | 0.781602i | \(-0.285597\pi\) | ||||
0.623777 | + | 0.781602i | \(0.285597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 67.9471 | 0.198096 | ||||||||
\(50\) | 486.129 | 1.37498 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 384.493 | 0.996494 | 0.498247 | − | 0.867035i | \(-0.333977\pi\) | ||||
0.498247 | + | 0.867035i | \(0.333977\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 296.908 | 0.727911 | ||||||||
\(56\) | −1623.18 | −3.87334 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −622.450 | −1.40917 | ||||||||
\(59\) | 121.629 | 0.268385 | 0.134192 | − | 0.990955i | \(-0.457156\pi\) | ||||
0.134192 | + | 0.990955i | \(0.457156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 220.043 | 0.461864 | 0.230932 | − | 0.972970i | \(-0.425823\pi\) | ||||
0.230932 | + | 0.972970i | \(0.425823\pi\) | |||||||
\(62\) | −624.790 | −1.27981 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2361.77 | 4.61283 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 975.363 | 1.77850 | 0.889250 | − | 0.457421i | \(-0.151227\pi\) | ||||
0.889250 | + | 0.457421i | \(0.151227\pi\) | |||||||
\(68\) | 849.361 | 1.51471 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −680.745 | −1.16235 | ||||||||
\(71\) | −106.725 | −0.178394 | −0.0891969 | − | 0.996014i | \(-0.528430\pi\) | ||||
−0.0891969 | + | 0.996014i | \(0.528430\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 43.2566 | 0.0693535 | 0.0346767 | − | 0.999399i | \(-0.488960\pi\) | ||||
0.0346767 | + | 0.999399i | \(0.488960\pi\) | |||||||
\(74\) | 473.673 | 0.744100 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2718.69 | 4.10336 | ||||||||
\(77\) | 989.841 | 1.46497 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 539.339 | 0.768106 | 0.384053 | − | 0.923311i | \(-0.374528\pi\) | ||||
0.384053 | + | 0.923311i | \(0.374528\pi\) | |||||||
\(80\) | 1594.39 | 2.22822 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −739.986 | −0.996558 | ||||||||
\(83\) | −811.183 | −1.07276 | −0.536379 | − | 0.843977i | \(-0.680208\pi\) | ||||
−0.536379 | + | 0.843977i | \(0.680208\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 229.553 | 0.292923 | ||||||||
\(86\) | 1762.45 | 2.20988 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3909.73 | −4.73612 | ||||||||
\(89\) | 1130.64 | 1.34661 | 0.673304 | − | 0.739366i | \(-0.264875\pi\) | ||||
0.673304 | + | 0.739366i | \(0.264875\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1684.13 | −1.90851 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2219.98 | −2.43588 | ||||||||
\(95\) | 734.767 | 0.793532 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −229.088 | −0.239797 | −0.119899 | − | 0.992786i | \(-0.538257\pi\) | ||||
−0.119899 | + | 0.992786i | \(0.538257\pi\) | |||||||
\(98\) | −375.243 | −0.386788 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1980.48 | −1.98048 | ||||||||
\(101\) | 845.077 | 0.832557 | 0.416279 | − | 0.909237i | \(-0.363334\pi\) | ||||
0.416279 | + | 0.909237i | \(0.363334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1095.09 | −1.04760 | −0.523800 | − | 0.851841i | \(-0.675486\pi\) | ||||
−0.523800 | + | 0.851841i | \(0.675486\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2123.39 | −1.94568 | ||||||||
\(107\) | −1183.33 | −1.06913 | −0.534563 | − | 0.845129i | \(-0.679524\pi\) | ||||
−0.534563 | + | 0.845129i | \(0.679524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −239.968 | −0.210870 | −0.105435 | − | 0.994426i | \(-0.533623\pi\) | ||||
−0.105435 | + | 0.994426i | \(0.533623\pi\) | |||||||
\(110\) | −1639.70 | −1.42126 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5315.41 | 4.48446 | ||||||||
\(113\) | 1031.22 | 0.858490 | 0.429245 | − | 0.903188i | \(-0.358780\pi\) | ||||
0.429245 | + | 0.903188i | \(0.358780\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −455.162 | −0.369079 | ||||||||
\(116\) | 2535.85 | 2.02972 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −671.703 | −0.524028 | ||||||||
\(119\) | 765.288 | 0.589528 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1053.21 | 0.791294 | ||||||||
\(122\) | −1215.21 | −0.901800 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2545.38 | 1.84340 | ||||||||
\(125\) | −1295.33 | −0.926866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.0201 | −0.0125908 | −0.00629539 | − | 0.999980i | \(-0.502004\pi\) | ||||
−0.00629539 | + | 0.999980i | \(0.502004\pi\) | |||||||
\(128\) | −6583.12 | −4.54587 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1282.52 | 0.855378 | 0.427689 | − | 0.903926i | \(-0.359328\pi\) | ||||
0.427689 | + | 0.903926i | \(0.359328\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2449.59 | 1.59704 | ||||||||
\(134\) | −5386.51 | −3.47257 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3022.78 | −1.90589 | ||||||||
\(137\) | −1547.36 | −0.964965 | −0.482482 | − | 0.875906i | \(-0.660265\pi\) | ||||
−0.482482 | + | 0.875906i | \(0.660265\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3096.87 | −1.88973 | −0.944867 | − | 0.327455i | \(-0.893809\pi\) | ||||
−0.944867 | + | 0.327455i | \(0.893809\pi\) | |||||||
\(140\) | 2773.34 | 1.67421 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 589.398 | 0.348318 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 685.351 | 0.392519 | ||||||||
\(146\) | −238.888 | −0.135414 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1929.73 | −1.07178 | ||||||||
\(149\) | −420.879 | −0.231408 | −0.115704 | − | 0.993284i | \(-0.536912\pi\) | ||||
−0.115704 | + | 0.993284i | \(0.536912\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2801.17 | −1.50964 | −0.754821 | − | 0.655931i | \(-0.772276\pi\) | ||||
−0.754821 | + | 0.655931i | \(0.772276\pi\) | |||||||
\(152\) | −9675.52 | −5.16308 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5466.47 | −2.86039 | ||||||||
\(155\) | 687.927 | 0.356488 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2344.20 | −1.19164 | −0.595820 | − | 0.803118i | \(-0.703173\pi\) | ||||
−0.595820 | + | 0.803118i | \(0.703173\pi\) | |||||||
\(158\) | −2978.54 | −1.49975 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4910.06 | −2.42609 | ||||||||
\(161\) | −1517.43 | −0.742798 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3658.41 | 1.75797 | 0.878984 | − | 0.476851i | \(-0.158222\pi\) | ||||
0.878984 | + | 0.476851i | \(0.158222\pi\) | |||||||
\(164\) | 3014.68 | 1.43541 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4479.82 | 2.09459 | ||||||||
\(167\) | −1987.85 | −0.921105 | −0.460552 | − | 0.887632i | \(-0.652349\pi\) | ||||
−0.460552 | + | 0.887632i | \(0.652349\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1267.72 | −0.571940 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7180.17 | −3.18304 | ||||||||
\(173\) | 3577.11 | 1.57204 | 0.786019 | − | 0.618202i | \(-0.212139\pi\) | ||||
0.786019 | + | 0.618202i | \(0.212139\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1784.44 | −0.770807 | ||||||||
\(176\) | 12803.1 | 5.48337 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6244.07 | −2.62928 | ||||||||
\(179\) | −770.144 | −0.321582 | −0.160791 | − | 0.986988i | \(-0.551405\pi\) | ||||
−0.160791 | + | 0.986988i | \(0.551405\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1895.69 | −0.778482 | −0.389241 | − | 0.921136i | \(-0.627263\pi\) | ||||
−0.389241 | + | 0.921136i | \(0.627263\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5993.65 | 2.40140 | ||||||||
\(185\) | −521.539 | −0.207267 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1843.34 | 0.720846 | ||||||||
\(188\) | 9044.12 | 3.50857 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4057.81 | −1.54939 | ||||||||
\(191\) | −2203.83 | −0.834887 | −0.417443 | − | 0.908703i | \(-0.637074\pi\) | ||||
−0.417443 | + | 0.908703i | \(0.637074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1016.38 | 0.379069 | 0.189534 | − | 0.981874i | \(-0.439302\pi\) | ||||
0.189534 | + | 0.981874i | \(0.439302\pi\) | |||||||
\(194\) | 1265.15 | 0.468210 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1528.73 | 0.557117 | ||||||||
\(197\) | −4318.58 | −1.56186 | −0.780930 | − | 0.624619i | \(-0.785254\pi\) | ||||
−0.780930 | + | 0.624619i | \(0.785254\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1363.40 | 0.485672 | 0.242836 | − | 0.970067i | \(-0.421922\pi\) | ||||
0.242836 | + | 0.970067i | \(0.421922\pi\) | |||||||
\(200\) | 7048.30 | 2.49195 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4667.00 | −1.62559 | ||||||||
\(203\) | 2284.84 | 0.789972 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 814.764 | 0.277588 | ||||||||
\(206\) | 6047.74 | 2.04546 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5900.28 | 1.95278 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5288.34 | 1.72542 | 0.862711 | − | 0.505697i | \(-0.168765\pi\) | ||||
0.862711 | + | 0.505697i | \(0.168765\pi\) | |||||||
\(212\) | 8650.64 | 2.80249 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6535.00 | 2.08749 | ||||||||
\(215\) | −1940.55 | −0.615555 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2293.43 | 0.717457 | ||||||||
\(218\) | 1325.24 | 0.411728 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6680.09 | 2.04714 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1258.01 | −0.377769 | −0.188884 | − | 0.981999i | \(-0.560487\pi\) | ||||
−0.188884 | + | 0.981999i | \(0.560487\pi\) | |||||||
\(224\) | −16369.3 | −4.88268 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5695.01 | −1.67622 | ||||||||
\(227\) | −1135.21 | −0.331922 | −0.165961 | − | 0.986132i | \(-0.553073\pi\) | ||||
−0.165961 | + | 0.986132i | \(0.553073\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −218.002 | −0.0629083 | −0.0314541 | − | 0.999505i | \(-0.510014\pi\) | ||||
−0.0314541 | + | 0.999505i | \(0.510014\pi\) | |||||||
\(230\) | 2513.67 | 0.720636 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9024.80 | −2.55391 | ||||||||
\(233\) | 2.56367 | 0.000720823 0 | 0.000360412 | − | 1.00000i | \(-0.499885\pi\) | ||||
0.000360412 | 1.00000i | \(0.499885\pi\) | ||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2444.31 | 0.678507 | ||||||||
\(236\) | 2736.50 | 0.754793 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4226.36 | −1.15107 | ||||||||
\(239\) | −3971.13 | −1.07477 | −0.537387 | − | 0.843336i | \(-0.680589\pi\) | ||||
−0.537387 | + | 0.843336i | \(0.680589\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −658.032 | −0.175882 | −0.0879411 | − | 0.996126i | \(-0.528029\pi\) | ||||
−0.0879411 | + | 0.996126i | \(0.528029\pi\) | |||||||
\(242\) | −5816.44 | −1.54502 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4950.72 | 1.29892 | ||||||||
\(245\) | 413.162 | 0.107739 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −9058.72 | −2.31947 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7153.58 | 1.80973 | ||||||||
\(251\) | −7091.01 | −1.78319 | −0.891595 | − | 0.452833i | \(-0.850413\pi\) | ||||
−0.891595 | + | 0.452833i | \(0.850413\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3655.01 | −0.908256 | ||||||||
\(254\) | 99.5176 | 0.0245838 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17461.6 | 4.26309 | ||||||||
\(257\) | −792.530 | −0.192361 | −0.0961803 | − | 0.995364i | \(-0.530663\pi\) | ||||
−0.0961803 | + | 0.995364i | \(0.530663\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1738.72 | −0.417139 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7082.83 | −1.67015 | ||||||||
\(263\) | 337.467 | 0.0791221 | 0.0395610 | − | 0.999217i | \(-0.487404\pi\) | ||||
0.0395610 | + | 0.999217i | \(0.487404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2337.97 | 0.541963 | ||||||||
\(266\) | −13528.0 | −3.11826 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 21944.5 | 5.00177 | ||||||||
\(269\) | 3523.93 | 0.798728 | 0.399364 | − | 0.916792i | \(-0.369231\pi\) | ||||
0.399364 | + | 0.916792i | \(0.369231\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8313.62 | 1.86353 | 0.931765 | − | 0.363063i | \(-0.118269\pi\) | ||||
0.931765 | + | 0.363063i | \(0.118269\pi\) | |||||||
\(272\) | 9898.65 | 2.20660 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8545.43 | 1.88412 | ||||||||
\(275\) | −4298.16 | −0.942504 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2500.33 | −0.542347 | −0.271174 | − | 0.962530i | \(-0.587412\pi\) | ||||
−0.271174 | + | 0.962530i | \(0.587412\pi\) | |||||||
\(278\) | 17102.7 | 3.68975 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9870.01 | −2.10659 | ||||||||
\(281\) | 3053.13 | 0.648165 | 0.324083 | − | 0.946029i | \(-0.394944\pi\) | ||||
0.324083 | + | 0.946029i | \(0.394944\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1158.80 | 0.243404 | 0.121702 | − | 0.992567i | \(-0.461165\pi\) | ||||
0.121702 | + | 0.992567i | \(0.461165\pi\) | |||||||
\(284\) | −2401.19 | −0.501706 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2716.28 | 0.558666 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3487.84 | −0.709920 | ||||||||
\(290\) | −3784.90 | −0.766403 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 973.223 | 0.195046 | ||||||||
\(293\) | 8357.45 | 1.66637 | 0.833187 | − | 0.552991i | \(-0.186514\pi\) | ||||
0.833187 | + | 0.552991i | \(0.186514\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 739.581 | 0.145966 | ||||||||
\(296\) | 6867.71 | 1.34857 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2324.33 | 0.451829 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6469.46 | −1.23885 | ||||||||
\(302\) | 15469.7 | 2.94761 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 31684.3 | 5.97769 | ||||||||
\(305\) | 1338.01 | 0.251194 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8429.30 | −1.56705 | −0.783527 | − | 0.621357i | \(-0.786582\pi\) | ||||
−0.783527 | + | 0.621357i | \(0.786582\pi\) | |||||||
\(308\) | 22270.3 | 4.12002 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3799.13 | −0.696051 | ||||||||
\(311\) | −3602.87 | −0.656914 | −0.328457 | − | 0.944519i | \(-0.606529\pi\) | ||||
−0.328457 | + | 0.944519i | \(0.606529\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6626.98 | 1.19674 | 0.598369 | − | 0.801220i | \(-0.295816\pi\) | ||||
0.598369 | + | 0.801220i | \(0.295816\pi\) | |||||||
\(314\) | 12946.0 | 2.32671 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12134.5 | 2.16019 | ||||||||
\(317\) | −3983.87 | −0.705857 | −0.352928 | − | 0.935650i | \(-0.614814\pi\) | ||||
−0.352928 | + | 0.935650i | \(0.614814\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5503.46 | 0.965938 | ||||||||
\(320\) | 14361.1 | 2.50878 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8380.14 | 1.45033 | ||||||||
\(323\) | 4561.76 | 0.785829 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20203.8 | −3.43248 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10728.9 | −1.80612 | ||||||||
\(329\) | 8148.91 | 1.36554 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4172.82 | 0.692927 | 0.346464 | − | 0.938063i | \(-0.387382\pi\) | ||||
0.346464 | + | 0.938063i | \(0.387382\pi\) | |||||||
\(332\) | −18250.7 | −3.01697 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10978.1 | 1.79848 | ||||||||
\(335\) | 5930.84 | 0.967272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4157.51 | 0.672030 | 0.336015 | − | 0.941857i | \(-0.390921\pi\) | ||||
0.336015 | + | 0.941857i | \(0.390921\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5164.66 | 0.823804 | ||||||||
\(341\) | 5524.14 | 0.877270 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5575.83 | −0.877744 | ||||||||
\(344\) | 25553.4 | 4.00509 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19754.9 | −3.06944 | ||||||||
\(347\) | −4667.98 | −0.722162 | −0.361081 | − | 0.932535i | \(-0.617592\pi\) | ||||
−0.361081 | + | 0.932535i | \(0.617592\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11905.6 | 1.82606 | 0.913028 | − | 0.407896i | \(-0.133737\pi\) | ||||
0.913028 | + | 0.407896i | \(0.133737\pi\) | |||||||
\(350\) | 9854.72 | 1.50502 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −39428.4 | −5.97029 | ||||||||
\(353\) | 1662.12 | 0.250610 | 0.125305 | − | 0.992118i | \(-0.460009\pi\) | ||||
0.125305 | + | 0.992118i | \(0.460009\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −648.959 | −0.0970229 | ||||||||
\(356\) | 25438.2 | 3.78714 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4253.18 | 0.627898 | ||||||||
\(359\) | −12754.4 | −1.87507 | −0.937535 | − | 0.347890i | \(-0.886898\pi\) | ||||
−0.937535 | + | 0.347890i | \(0.886898\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7742.58 | 1.12882 | ||||||||
\(362\) | 10469.1 | 1.52001 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 263.028 | 0.0377192 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4463.81 | 0.634901 | 0.317451 | − | 0.948275i | \(-0.397173\pi\) | ||||
0.317451 | + | 0.948275i | \(0.397173\pi\) | |||||||
\(368\) | −19627.3 | −2.78028 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2880.24 | 0.404693 | ||||||||
\(371\) | 7794.38 | 1.09074 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9454.46 | 1.31242 | 0.656211 | − | 0.754578i | \(-0.272158\pi\) | ||||
0.656211 | + | 0.754578i | \(0.272158\pi\) | |||||||
\(374\) | −10180.0 | −1.40747 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32187.0 | −4.41468 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14085.9 | 1.90908 | 0.954542 | − | 0.298077i | \(-0.0963453\pi\) | ||||
0.954542 | + | 0.298077i | \(0.0963453\pi\) | |||||||
\(380\) | 16531.4 | 2.23169 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12170.8 | 1.63014 | ||||||||
\(383\) | 8663.84 | 1.15588 | 0.577939 | − | 0.816080i | \(-0.303857\pi\) | ||||
0.577939 | + | 0.816080i | \(0.303857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6018.87 | 0.796754 | ||||||||
\(386\) | −5613.01 | −0.740141 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5154.20 | −0.674395 | ||||||||
\(389\) | −5085.58 | −0.662852 | −0.331426 | − | 0.943481i | \(-0.607530\pi\) | ||||
−0.331426 | + | 0.943481i | \(0.607530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2825.85 | −0.365497 | ||||||||
\(392\) | −5440.58 | −0.700997 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 23849.7 | 3.04957 | ||||||||
\(395\) | 3279.53 | 0.417750 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12983.7 | 1.64140 | 0.820700 | − | 0.571360i | \(-0.193584\pi\) | ||||
0.820700 | + | 0.571360i | \(0.193584\pi\) | |||||||
\(398\) | −7529.48 | −0.948288 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −23080.9 | −2.88512 | ||||||||
\(401\) | −6493.66 | −0.808673 | −0.404337 | − | 0.914610i | \(-0.632498\pi\) | ||||
−0.404337 | + | 0.914610i | \(0.632498\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 19013.2 | 2.34145 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12618.2 | −1.54244 | ||||||||
\(407\) | −4188.03 | −0.510056 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12546.2 | −1.51680 | −0.758398 | − | 0.651792i | \(-0.774017\pi\) | ||||
−0.758398 | + | 0.651792i | \(0.774017\pi\) | |||||||
\(410\) | −4499.59 | −0.541998 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −24638.3 | −2.94622 | ||||||||
\(413\) | 2465.63 | 0.293767 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4932.52 | −0.583440 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −32584.7 | −3.81285 | ||||||||
\(419\) | −7945.58 | −0.926413 | −0.463206 | − | 0.886250i | \(-0.653301\pi\) | ||||
−0.463206 | + | 0.886250i | \(0.653301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −284.758 | −0.0329650 | −0.0164825 | − | 0.999864i | \(-0.505247\pi\) | ||||
−0.0164825 | + | 0.999864i | \(0.505247\pi\) | |||||||
\(422\) | −29205.2 | −3.36893 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −30786.7 | −3.52626 | ||||||||
\(425\) | −3323.09 | −0.379279 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4460.68 | 0.505545 | ||||||||
\(428\) | −26623.4 | −3.00676 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10716.8 | 1.20189 | ||||||||
\(431\) | 12512.1 | 1.39835 | 0.699173 | − | 0.714952i | \(-0.253552\pi\) | ||||
0.699173 | + | 0.714952i | \(0.253552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13217.2 | −1.46692 | −0.733460 | − | 0.679732i | \(-0.762096\pi\) | ||||
−0.733460 | + | 0.679732i | \(0.762096\pi\) | |||||||
\(434\) | −12665.6 | −1.40085 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5399.01 | −0.593040 | ||||||||
\(437\) | −9045.16 | −0.990135 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4635.40 | 0.503953 | 0.251977 | − | 0.967733i | \(-0.418919\pi\) | ||||
0.251977 | + | 0.967733i | \(0.418919\pi\) | |||||||
\(440\) | −23773.7 | −2.57583 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2945.92 | 0.315947 | 0.157974 | − | 0.987443i | \(-0.449504\pi\) | ||||
0.157974 | + | 0.987443i | \(0.449504\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6875.05 | 0.732379 | ||||||||
\(446\) | 6947.45 | 0.737603 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 47877.3 | 5.04909 | ||||||||
\(449\) | 8668.29 | 0.911095 | 0.455548 | − | 0.890211i | \(-0.349443\pi\) | ||||
0.455548 | + | 0.890211i | \(0.349443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6542.66 | 0.683108 | ||||||||
\(452\) | 23201.3 | 2.41438 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6269.27 | 0.648087 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5195.36 | −0.531791 | −0.265896 | − | 0.964002i | \(-0.585668\pi\) | ||||
−0.265896 | + | 0.964002i | \(0.585668\pi\) | |||||||
\(458\) | 1203.93 | 0.122830 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10240.6 | −1.03798 | ||||||||
\(461\) | 2931.19 | 0.296136 | 0.148068 | − | 0.988977i | \(-0.452694\pi\) | ||||
0.148068 | + | 0.988977i | \(0.452694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −396.589 | −0.0398079 | −0.0199039 | − | 0.999802i | \(-0.506336\pi\) | ||||
−0.0199039 | + | 0.999802i | \(0.506336\pi\) | |||||||
\(464\) | 29553.4 | 2.95685 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.1581 | −0.00140743 | ||||||||
\(467\) | −16627.5 | −1.64760 | −0.823801 | − | 0.566880i | \(-0.808150\pi\) | ||||
−0.823801 | + | 0.566880i | \(0.808150\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19772.4 | 1.94670 | ||||||||
\(470\) | −13498.9 | −1.32480 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9738.91 | −0.949724 | ||||||||
\(473\) | −15582.9 | −1.51480 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10636.8 | −1.02747 | ||||||||
\(476\) | 17218.1 | 1.65796 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 21930.9 | 2.09852 | ||||||||
\(479\) | −8903.28 | −0.849272 | −0.424636 | − | 0.905364i | \(-0.639598\pi\) | ||||
−0.424636 | + | 0.905364i | \(0.639598\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3634.03 | 0.343414 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 23696.1 | 2.22540 | ||||||||
\(485\) | −1393.00 | −0.130418 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −469.526 | −0.0436884 | −0.0218442 | − | 0.999761i | \(-0.506954\pi\) | ||||
−0.0218442 | + | 0.999761i | \(0.506954\pi\) | |||||||
\(488\) | −17619.1 | −1.63438 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2281.72 | −0.210362 | ||||||||
\(491\) | 18823.8 | 1.73015 | 0.865077 | − | 0.501639i | \(-0.167269\pi\) | ||||
0.865077 | + | 0.501639i | \(0.167269\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4254.96 | 0.388709 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 29664.4 | 2.68543 | ||||||||
\(497\) | −2163.52 | −0.195265 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5651.95 | −0.507046 | −0.253523 | − | 0.967329i | \(-0.581589\pi\) | ||||
−0.253523 | + | 0.967329i | \(0.581589\pi\) | |||||||
\(500\) | −29143.5 | −2.60667 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 39160.7 | 3.48172 | ||||||||
\(503\) | −8022.35 | −0.711131 | −0.355565 | − | 0.934651i | \(-0.615712\pi\) | ||||
−0.355565 | + | 0.934651i | \(0.615712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5138.62 | 0.452803 | ||||||||
\(506\) | 20185.1 | 1.77339 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −405.432 | −0.0354097 | ||||||||
\(509\) | −3940.56 | −0.343148 | −0.171574 | − | 0.985171i | \(-0.554885\pi\) | ||||
−0.171574 | + | 0.985171i | \(0.554885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 876.890 | 0.0759126 | ||||||||
\(512\) | −43768.2 | −3.77793 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4376.81 | 0.375589 | ||||||||
\(515\) | −6658.88 | −0.569758 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 19628.1 | 1.66972 | ||||||||
\(518\) | 9602.22 | 0.814474 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8644.84 | −0.726943 | −0.363472 | − | 0.931605i | \(-0.618409\pi\) | ||||
−0.363472 | + | 0.931605i | \(0.618409\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1956.76 | 0.163600 | 0.0818001 | − | 0.996649i | \(-0.473933\pi\) | ||||
0.0818001 | + | 0.996649i | \(0.473933\pi\) | |||||||
\(524\) | 28855.3 | 2.40563 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1863.69 | −0.154488 | ||||||||
\(527\) | 4270.95 | 0.353028 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6563.84 | −0.539479 | ||||||||
\(530\) | −12911.6 | −1.05820 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 55112.8 | 4.49144 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7195.39 | −0.581465 | ||||||||
\(536\) | −78098.2 | −6.29352 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −19461.2 | −1.55954 | ||||||||
\(539\) | 3317.75 | 0.265131 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7005.37 | 0.556718 | 0.278359 | − | 0.960477i | \(-0.410210\pi\) | ||||
0.278359 | + | 0.960477i | \(0.410210\pi\) | |||||||
\(542\) | −45912.6 | −3.63859 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −30483.8 | −2.40254 | ||||||||
\(545\) | −1459.16 | −0.114686 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23216.7 | 1.81476 | 0.907382 | − | 0.420307i | \(-0.138077\pi\) | ||||
0.907382 | + | 0.420307i | \(0.138077\pi\) | |||||||
\(548\) | −34813.9 | −2.71382 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 23736.9 | 1.84026 | ||||||||
\(551\) | 13619.6 | 1.05302 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10933.4 | 0.840751 | ||||||||
\(554\) | 13808.2 | 1.05895 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −69675.9 | −5.31460 | ||||||||
\(557\) | 14912.9 | 1.13443 | 0.567217 | − | 0.823568i | \(-0.308020\pi\) | ||||
0.567217 | + | 0.823568i | \(0.308020\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 32321.1 | 2.43896 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16861.1 | −1.26556 | ||||||||
\(563\) | −10854.3 | −0.812531 | −0.406266 | − | 0.913755i | \(-0.633169\pi\) | ||||
−0.406266 | + | 0.913755i | \(0.633169\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6270.50 | 0.466906 | ||||||||
\(566\) | −6399.55 | −0.475253 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8545.58 | 0.631276 | ||||||||
\(569\) | −17892.5 | −1.31827 | −0.659134 | − | 0.752026i | \(-0.729077\pi\) | ||||
−0.659134 | + | 0.752026i | \(0.729077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17319.8 | 1.26937 | 0.634686 | − | 0.772770i | \(-0.281130\pi\) | ||||
0.634686 | + | 0.772770i | \(0.281130\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15000.9 | −1.09081 | ||||||||
\(575\) | 6589.10 | 0.477886 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9738.48 | −0.702632 | −0.351316 | − | 0.936257i | \(-0.614266\pi\) | ||||
−0.351316 | + | 0.936257i | \(0.614266\pi\) | |||||||
\(578\) | 19261.8 | 1.38614 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15419.6 | 1.10390 | ||||||||
\(581\) | −16444.2 | −1.17421 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18774.2 | 1.33370 | ||||||||
\(584\) | −3463.59 | −0.245419 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −46154.7 | −3.25364 | ||||||||
\(587\) | 5960.31 | 0.419095 | 0.209547 | − | 0.977799i | \(-0.432801\pi\) | ||||
0.209547 | + | 0.977799i | \(0.432801\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13670.7 | 0.956355 | ||||||||
\(590\) | −4084.39 | −0.285003 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −22489.6 | −1.56134 | ||||||||
\(593\) | 17870.2 | 1.23751 | 0.618753 | − | 0.785586i | \(-0.287638\pi\) | ||||
0.618753 | + | 0.785586i | \(0.287638\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4653.45 | 0.320627 | ||||||||
\(596\) | −9469.28 | −0.650800 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17943.7 | 1.22397 | 0.611987 | − | 0.790868i | \(-0.290371\pi\) | ||||
0.611987 | + | 0.790868i | \(0.290371\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6548.20 | 0.444437 | 0.222219 | − | 0.974997i | \(-0.428670\pi\) | ||||
0.222219 | + | 0.974997i | \(0.428670\pi\) | |||||||
\(602\) | 35728.1 | 2.41888 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −63023.0 | −4.24565 | ||||||||
\(605\) | 6404.21 | 0.430361 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14886.0 | −0.995391 | −0.497696 | − | 0.867352i | \(-0.665820\pi\) | ||||
−0.497696 | + | 0.867352i | \(0.665820\pi\) | |||||||
\(608\) | −97574.6 | −6.50851 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7389.24 | −0.490462 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8774.65 | −0.578148 | −0.289074 | − | 0.957307i | \(-0.593347\pi\) | ||||
−0.289074 | + | 0.957307i | \(0.593347\pi\) | |||||||
\(614\) | 46551.5 | 3.05971 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −79257.4 | −5.18405 | ||||||||
\(617\) | 3810.41 | 0.248625 | 0.124312 | − | 0.992243i | \(-0.460327\pi\) | ||||
0.124312 | + | 0.992243i | \(0.460327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16392.6 | −1.06441 | −0.532207 | − | 0.846614i | \(-0.678637\pi\) | ||||
−0.532207 | + | 0.846614i | \(0.678637\pi\) | |||||||
\(620\) | 15477.5 | 1.00257 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19897.1 | 1.28264 | ||||||||
\(623\) | 22920.2 | 1.47396 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3126.74 | 0.200112 | ||||||||
\(626\) | −36598.0 | −2.33666 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −52741.8 | −3.35131 | ||||||||
\(629\) | −3237.95 | −0.205255 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11077.3 | −0.698858 | −0.349429 | − | 0.936963i | \(-0.613624\pi\) | ||||
−0.349429 | + | 0.936963i | \(0.613624\pi\) | |||||||
\(632\) | −43185.4 | −2.71807 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22001.2 | 1.37820 | ||||||||
\(635\) | −109.574 | −0.00684775 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −30393.2 | −1.88602 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −40029.6 | −2.47236 | ||||||||
\(641\) | 2143.45 | 0.132077 | 0.0660383 | − | 0.997817i | \(-0.478964\pi\) | ||||
0.0660383 | + | 0.997817i | \(0.478964\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9774.93 | 0.599511 | 0.299755 | − | 0.954016i | \(-0.403095\pi\) | ||||
0.299755 | + | 0.954016i | \(0.403095\pi\) | |||||||
\(644\) | −34140.5 | −2.08901 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −25192.6 | −1.53435 | ||||||||
\(647\) | 22447.6 | 1.36400 | 0.681999 | − | 0.731353i | \(-0.261111\pi\) | ||||
0.681999 | + | 0.731353i | \(0.261111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5938.93 | 0.359204 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 82310.0 | 4.94403 | ||||||||
\(653\) | −10582.0 | −0.634157 | −0.317079 | − | 0.948399i | \(-0.602702\pi\) | ||||
−0.317079 | + | 0.948399i | \(0.602702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7798.57 | 0.465214 | ||||||||
\(656\) | 35133.9 | 2.09108 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −45003.0 | −2.66626 | ||||||||
\(659\) | 15114.6 | 0.893445 | 0.446722 | − | 0.894673i | \(-0.352591\pi\) | ||||
0.446722 | + | 0.894673i | \(0.352591\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2229.61 | 0.131198 | 0.0655990 | − | 0.997846i | \(-0.479104\pi\) | ||||
0.0655990 | + | 0.997846i | \(0.479104\pi\) | |||||||
\(662\) | −23044.7 | −1.35296 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 64952.1 | 3.79613 | ||||||||
\(665\) | 14895.1 | 0.868581 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8436.83 | −0.489768 | ||||||||
\(668\) | −44724.3 | −2.59047 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −32753.5 | −1.88862 | ||||||||
\(671\) | 10744.4 | 0.618155 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3588.22 | −0.205521 | −0.102761 | − | 0.994706i | \(-0.532768\pi\) | ||||
−0.102761 | + | 0.994706i | \(0.532768\pi\) | |||||||
\(674\) | −22960.2 | −1.31216 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 26458.4 | 1.50204 | 0.751019 | − | 0.660280i | \(-0.229562\pi\) | ||||
0.751019 | + | 0.660280i | \(0.229562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4644.03 | −0.262476 | ||||||||
\(680\) | −18380.5 | −1.03656 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −30507.5 | −1.71289 | ||||||||
\(683\) | 23598.4 | 1.32206 | 0.661031 | − | 0.750358i | \(-0.270119\pi\) | ||||
0.661031 | + | 0.750358i | \(0.270119\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9408.97 | −0.524815 | ||||||||
\(686\) | 30792.9 | 1.71382 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −83679.4 | −4.63699 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16433.6 | −0.904722 | −0.452361 | − | 0.891835i | \(-0.649418\pi\) | ||||
−0.452361 | + | 0.891835i | \(0.649418\pi\) | |||||||
\(692\) | 80480.8 | 4.42113 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25779.2 | 1.41004 | ||||||||
\(695\) | −18831.0 | −1.02777 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5058.41 | 0.274894 | ||||||||
\(698\) | −65749.7 | −3.56542 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −40147.9 | −2.16778 | ||||||||
\(701\) | −13899.4 | −0.748892 | −0.374446 | − | 0.927249i | \(-0.622167\pi\) | ||||
−0.374446 | + | 0.927249i | \(0.622167\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10364.2 | −0.556038 | ||||||||
\(704\) | 115321. | 6.17377 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9179.16 | −0.489323 | ||||||||
\(707\) | 17131.3 | 0.911297 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32829.6 | 1.73899 | 0.869494 | − | 0.493944i | \(-0.164445\pi\) | ||||
0.869494 | + | 0.493944i | \(0.164445\pi\) | |||||||
\(710\) | 3583.92 | 0.189440 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −90531.7 | −4.76519 | ||||||||
\(713\) | −8468.55 | −0.444810 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17327.3 | −0.904403 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 70437.0 | 3.66112 | ||||||||
\(719\) | 4683.94 | 0.242951 | 0.121475 | − | 0.992594i | \(-0.461237\pi\) | ||||
0.121475 | + | 0.992594i | \(0.461237\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22199.5 | −1.14668 | ||||||||
\(722\) | −42759.0 | −2.20405 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −42650.7 | −2.18937 | ||||||||
\(725\) | −9921.39 | −0.508236 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35368.3 | −1.80432 | −0.902159 | − | 0.431405i | \(-0.858018\pi\) | ||||
−0.902159 | + | 0.431405i | \(0.858018\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1452.59 | −0.0736478 | ||||||||
\(731\) | −12047.8 | −0.609580 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33988.4 | 1.71268 | 0.856338 | − | 0.516416i | \(-0.172734\pi\) | ||||
0.856338 | + | 0.516416i | \(0.172734\pi\) | |||||||
\(734\) | −24651.7 | −1.23966 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 60444.0 | 3.02717 | ||||||||
\(737\) | 47625.4 | 2.38033 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7777.31 | −0.387135 | −0.193568 | − | 0.981087i | \(-0.562006\pi\) | ||||
−0.193568 | + | 0.981087i | \(0.562006\pi\) | |||||||
\(740\) | −11734.0 | −0.582907 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −43045.0 | −2.12969 | ||||||||
\(743\) | 7022.08 | 0.346723 | 0.173361 | − | 0.984858i | \(-0.444537\pi\) | ||||
0.173361 | + | 0.984858i | \(0.444537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2559.22 | −0.125856 | ||||||||
\(746\) | −52212.9 | −2.56254 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 41472.9 | 2.02727 | ||||||||
\(749\) | −23988.2 | −1.17024 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8214.69 | 0.399146 | 0.199573 | − | 0.979883i | \(-0.436045\pi\) | ||||
0.199573 | + | 0.979883i | \(0.436045\pi\) | |||||||
\(752\) | 105402. | 5.11121 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17032.9 | −0.821048 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20846.9 | −1.00092 | −0.500459 | − | 0.865760i | \(-0.666835\pi\) | ||||
−0.500459 | + | 0.865760i | \(0.666835\pi\) | |||||||
\(758\) | −77790.3 | −3.72753 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −58833.5 | −2.80804 | ||||||||
\(761\) | 3563.06 | 0.169725 | 0.0848627 | − | 0.996393i | \(-0.472955\pi\) | ||||
0.0848627 | + | 0.996393i | \(0.472955\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4864.60 | −0.230813 | ||||||||
\(764\) | −49583.6 | −2.34800 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −47846.7 | −2.25688 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32557.9 | 1.52675 | 0.763373 | − | 0.645958i | \(-0.223542\pi\) | ||||
0.763373 | + | 0.645958i | \(0.223542\pi\) | |||||||
\(770\) | −33239.7 | −1.55568 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22867.3 | 1.06608 | ||||||||
\(773\) | −20126.4 | −0.936477 | −0.468238 | − | 0.883602i | \(-0.655111\pi\) | ||||
−0.468238 | + | 0.883602i | \(0.655111\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9958.68 | −0.461583 | ||||||||
\(776\) | 18343.2 | 0.848562 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28085.5 | 1.29423 | ||||||||
\(779\) | 16191.3 | 0.744690 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5211.22 | −0.238761 | ||||||||
\(782\) | 15606.0 | 0.713642 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17816.2 | 0.811597 | ||||||||
\(785\) | −14254.3 | −0.648097 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18828.4 | 0.852806 | 0.426403 | − | 0.904533i | \(-0.359781\pi\) | ||||
0.426403 | + | 0.904533i | \(0.359781\pi\) | |||||||
\(788\) | −97163.1 | −4.39250 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −18111.5 | −0.815667 | ||||||||
\(791\) | 20904.8 | 0.939682 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −71703.7 | −3.20487 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 30674.9 | 1.36588 | ||||||||
\(797\) | −7288.52 | −0.323930 | −0.161965 | − | 0.986796i | \(-0.551783\pi\) | ||||
−0.161965 | + | 0.986796i | \(0.551783\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15175.3 | 0.671921 | ||||||||
\(800\) | 71079.9 | 3.14132 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35861.7 | 1.57896 | ||||||||
\(803\) | 2112.15 | 0.0928221 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9226.97 | −0.403985 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −67666.1 | −2.94614 | ||||||||
\(809\) | 33799.0 | 1.46886 | 0.734430 | − | 0.678684i | \(-0.237449\pi\) | ||||
0.734430 | + | 0.678684i | \(0.237449\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29055.3 | −1.25804 | −0.629019 | − | 0.777390i | \(-0.716543\pi\) | ||||
−0.629019 | + | 0.777390i | \(0.716543\pi\) | |||||||
\(812\) | 51406.2 | 2.22168 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 23128.7 | 0.995898 | ||||||||
\(815\) | 22245.5 | 0.956106 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −38563.3 | −1.65136 | ||||||||
\(818\) | 69287.3 | 2.96158 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18331.2 | 0.780676 | ||||||||
\(821\) | 8921.98 | 0.379268 | 0.189634 | − | 0.981855i | \(-0.439270\pi\) | ||||
0.189634 | + | 0.981855i | \(0.439270\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9148.48 | −0.387480 | −0.193740 | − | 0.981053i | \(-0.562062\pi\) | ||||
−0.193740 | + | 0.981053i | \(0.562062\pi\) | |||||||
\(824\) | 87685.1 | 3.70711 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13616.6 | −0.573588 | ||||||||
\(827\) | 20206.0 | 0.849615 | 0.424807 | − | 0.905284i | \(-0.360342\pi\) | ||||
0.424807 | + | 0.905284i | \(0.360342\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10832.4 | −0.453830 | −0.226915 | − | 0.973915i | \(-0.572864\pi\) | ||||
−0.226915 | + | 0.973915i | \(0.572864\pi\) | |||||||
\(830\) | 27240.2 | 1.13918 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2565.09 | 0.106693 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12087.4 | −0.500961 | ||||||||
\(836\) | 132749. | 5.49190 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 43880.1 | 1.80884 | ||||||||
\(839\) | −7047.44 | −0.289994 | −0.144997 | − | 0.989432i | \(-0.546317\pi\) | ||||
−0.144997 | + | 0.989432i | \(0.546317\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11685.4 | −0.479127 | ||||||||
\(842\) | 1572.60 | 0.0643650 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 118981. | 4.85250 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21350.5 | 0.866132 | ||||||||
\(848\) | 100817. | 4.08262 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18352.0 | 0.740551 | ||||||||
\(851\) | 6420.28 | 0.258618 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24085.5 | −0.966790 | −0.483395 | − | 0.875402i | \(-0.660596\pi\) | ||||
−0.483395 | + | 0.875402i | \(0.660596\pi\) | |||||||
\(854\) | −24634.5 | −0.987089 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 94749.9 | 3.78328 | ||||||||
\(857\) | 4161.31 | 0.165866 | 0.0829332 | − | 0.996555i | \(-0.473571\pi\) | ||||
0.0829332 | + | 0.996555i | \(0.473571\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27387.5 | 1.08784 | 0.543918 | − | 0.839139i | \(-0.316940\pi\) | ||||
0.543918 | + | 0.839139i | \(0.316940\pi\) | |||||||
\(860\) | −43660.1 | −1.73116 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −69099.1 | −2.73031 | ||||||||
\(863\) | 19420.4 | 0.766022 | 0.383011 | − | 0.923744i | \(-0.374887\pi\) | ||||
0.383011 | + | 0.923744i | \(0.374887\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21751.1 | 0.854984 | ||||||||
\(866\) | 72992.8 | 2.86420 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 51599.5 | 2.01774 | ||||||||
\(869\) | 26335.1 | 1.02803 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 19214.5 | 0.746198 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 49952.6 | 1.93326 | ||||||||
\(875\) | −26258.8 | −1.01453 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9908.85 | 0.381526 | 0.190763 | − | 0.981636i | \(-0.438904\pi\) | ||||
0.190763 | + | 0.981636i | \(0.438904\pi\) | |||||||
\(878\) | −25599.3 | −0.983981 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 77851.4 | 2.98224 | ||||||||
\(881\) | −20323.3 | −0.777197 | −0.388598 | − | 0.921407i | \(-0.627041\pi\) | ||||
−0.388598 | + | 0.921407i | \(0.627041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12443.3 | 0.474238 | 0.237119 | − | 0.971481i | \(-0.423797\pi\) | ||||
0.237119 | + | 0.971481i | \(0.423797\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16269.0 | −0.616895 | ||||||||
\(887\) | −42313.5 | −1.60174 | −0.800872 | − | 0.598835i | \(-0.795631\pi\) | ||||
−0.800872 | + | 0.598835i | \(0.795631\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −365.301 | −0.0137816 | ||||||||
\(890\) | −37968.0 | −1.42999 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −28303.7 | −1.06242 | ||||||||
\(893\) | 48574.3 | 1.82024 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4682.97 | −0.174899 | ||||||||
\(896\) | −133452. | −4.97580 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −47871.3 | −1.77894 | ||||||||
\(899\) | 12751.3 | 0.473059 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14515.1 | 0.536702 | ||||||||
\(902\) | −36132.3 | −1.33379 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −82571.0 | −3.03791 | ||||||||
\(905\) | −11527.0 | −0.423393 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11002.3 | −0.402786 | −0.201393 | − | 0.979511i | \(-0.564547\pi\) | ||||
−0.201393 | + | 0.979511i | \(0.564547\pi\) | |||||||
\(908\) | −25540.8 | −0.933483 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40803.4 | 1.48395 | 0.741974 | − | 0.670428i | \(-0.233890\pi\) | ||||
0.741974 | + | 0.670428i | \(0.233890\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39608.8 | −1.43577 | ||||||||
\(914\) | 28691.8 | 1.03834 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4904.80 | −0.176920 | ||||||||
\(917\) | 25999.1 | 0.936276 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2642.69 | 0.0948579 | 0.0474290 | − | 0.998875i | \(-0.484897\pi\) | ||||
0.0474290 | + | 0.998875i | \(0.484897\pi\) | |||||||
\(920\) | 36445.3 | 1.30605 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16187.7 | −0.578214 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7550.00 | 0.268370 | ||||||||
\(926\) | 2190.19 | 0.0777258 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −91012.3 | −3.21942 | ||||||||
\(929\) | 12687.7 | 0.448083 | 0.224042 | − | 0.974580i | \(-0.428075\pi\) | ||||
0.224042 | + | 0.974580i | \(0.428075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8210.52 | 0.289032 | ||||||||
\(932\) | 57.6796 | 0.00202721 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 91826.7 | 3.21698 | ||||||||
\(935\) | 11208.7 | 0.392046 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23066.2 | −0.804205 | −0.402103 | − | 0.915595i | \(-0.631721\pi\) | ||||
−0.402103 | + | 0.915595i | \(0.631721\pi\) | |||||||
\(938\) | −109195. | −3.80099 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 54994.1 | 1.90820 | ||||||||
\(941\) | 12660.7 | 0.438605 | 0.219303 | − | 0.975657i | \(-0.429622\pi\) | ||||
0.219303 | + | 0.975657i | \(0.429622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10029.9 | −0.346362 | ||||||||
\(944\) | 31891.8 | 1.09957 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 86057.5 | 2.95769 | ||||||||
\(947\) | 21059.1 | 0.722629 | 0.361315 | − | 0.932444i | \(-0.382328\pi\) | ||||
0.361315 | + | 0.932444i | \(0.382328\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 58742.3 | 2.00616 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −61277.3 | −2.08614 | ||||||||
\(953\) | −35646.2 | −1.21164 | −0.605820 | − | 0.795602i | \(-0.707155\pi\) | ||||
−0.605820 | + | 0.795602i | \(0.707155\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13400.7 | −0.454070 | ||||||||
\(956\) | −89345.8 | −3.02265 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 49169.0 | 1.65822 | ||||||||
\(959\) | −31367.9 | −1.05623 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16991.7 | −0.570365 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14805.0 | −0.494643 | ||||||||
\(965\) | 6180.22 | 0.206164 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −53452.1 | −1.77756 | −0.888782 | − | 0.458329i | \(-0.848448\pi\) | ||||
−0.888782 | + | 0.458329i | \(0.848448\pi\) | |||||||
\(968\) | −84331.7 | −2.80013 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7692.95 | 0.254645 | ||||||||
\(971\) | −6502.60 | −0.214911 | −0.107455 | − | 0.994210i | \(-0.534270\pi\) | ||||
−0.107455 | + | 0.994210i | \(0.534270\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −62779.2 | −2.06846 | ||||||||
\(974\) | 2592.99 | 0.0853027 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 57696.9 | 1.89225 | ||||||||
\(977\) | −4351.84 | −0.142505 | −0.0712527 | − | 0.997458i | \(-0.522700\pi\) | ||||
−0.0712527 | + | 0.997458i | \(0.522700\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 55207.5 | 1.80229 | ||||||||
\(980\) | 9295.67 | 0.302999 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −103956. | −3.37817 | ||||||||
\(983\) | 48698.2 | 1.58009 | 0.790047 | − | 0.613046i | \(-0.210056\pi\) | ||||
0.790047 | + | 0.613046i | \(0.210056\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26259.8 | −0.849448 | ||||||||
\(986\) | −23498.3 | −0.758964 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23888.6 | 0.768063 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46630.0 | 1.49470 | 0.747351 | − | 0.664429i | \(-0.231325\pi\) | ||||
0.747351 | + | 0.664429i | \(0.231325\pi\) | |||||||
\(992\) | −91354.3 | −2.92389 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11948.2 | 0.381261 | ||||||||
\(995\) | 8290.35 | 0.264143 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37175.5 | 1.18090 | 0.590452 | − | 0.807073i | \(-0.298950\pi\) | ||||
0.590452 | + | 0.807073i | \(0.298950\pi\) | |||||||
\(998\) | 31213.3 | 0.990021 | ||||||||
\(999\) | 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 | 1521.4.a.bf.1.1 | 9 | ||
3.2 | odd | 2 | 507.4.a.p.1.9 | yes | 9 | ||
13.12 | even | 2 | 1521.4.a.bi.1.9 | 9 | |||
39.5 | even | 4 | 507.4.b.k.337.1 | 18 | |||
39.8 | even | 4 | 507.4.b.k.337.18 | 18 | |||
39.38 | odd | 2 | 507.4.a.o.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.4.a.o.1.1 | ✓ | 9 | 39.38 | odd | 2 | ||
507.4.a.p.1.9 | yes | 9 | 3.2 | odd | 2 | ||
507.4.b.k.337.1 | 18 | 39.5 | even | 4 | |||
507.4.b.k.337.18 | 18 | 39.8 | even | 4 | |||
1521.4.a.bf.1.1 | 9 | 1.1 | even | 1 | trivial | ||
1521.4.a.bi.1.9 | 9 | 13.12 | even | 2 |