Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,4,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(26.0198423125\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.6257832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 19x^{2} + 42 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 63) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.59805\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.59805 | −0.564998 | −0.282499 | − | 0.959268i | \(-0.591163\pi\) | ||||
−0.282499 | + | 0.959268i | \(0.591163\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.44622 | −0.680778 | ||||||||
\(5\) | 18.2917 | 1.63606 | 0.818029 | − | 0.575177i | \(-0.195067\pi\) | ||||
0.818029 | + | 0.575177i | \(0.195067\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 21.4878 | 0.949635 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −29.2311 | −0.924369 | ||||||||
\(11\) | 61.2673 | 1.67934 | 0.839672 | − | 0.543094i | \(-0.182747\pi\) | ||||
0.839672 | + | 0.543094i | \(0.182747\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.4462 | 0.692228 | 0.346114 | − | 0.938192i | \(-0.387501\pi\) | ||||
0.346114 | + | 0.938192i | \(0.387501\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.23111 | 0.144236 | ||||||||
\(17\) | −81.3289 | −1.16030 | −0.580152 | − | 0.814509i | \(-0.697007\pi\) | ||||
−0.580152 | + | 0.814509i | \(0.697007\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.9084 | −0.252459 | −0.126230 | − | 0.992001i | \(-0.540288\pi\) | ||||
−0.126230 | + | 0.992001i | \(0.540288\pi\) | |||||||
\(20\) | −99.6206 | −1.11379 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −97.9084 | −0.948825 | ||||||||
\(23\) | −33.7310 | −0.305800 | −0.152900 | − | 0.988242i | \(-0.548861\pi\) | ||||
−0.152900 | + | 0.988242i | \(0.548861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 209.586 | 1.67669 | ||||||||
\(26\) | −51.8508 | −0.391107 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 52.0227 | 0.333116 | 0.166558 | − | 0.986032i | \(-0.446735\pi\) | ||||
0.166558 | + | 0.986032i | \(0.446735\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 193.924 | 1.12354 | 0.561772 | − | 0.827292i | \(-0.310120\pi\) | ||||
0.561772 | + | 0.827292i | \(0.310120\pi\) | |||||||
\(32\) | −186.654 | −1.03113 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 129.968 | 0.655568 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −267.156 | −1.18703 | −0.593515 | − | 0.804823i | \(-0.702260\pi\) | ||||
−0.593515 | + | 0.804823i | \(0.702260\pi\) | |||||||
\(38\) | 33.4128 | 0.142639 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 393.048 | 1.55366 | ||||||||
\(41\) | 203.176 | 0.773921 | 0.386960 | − | 0.922096i | \(-0.373525\pi\) | ||||
0.386960 | + | 0.922096i | \(0.373525\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.9520 | −0.0778523 | −0.0389262 | − | 0.999242i | \(-0.512394\pi\) | ||||
−0.0389262 | + | 0.999242i | \(0.512394\pi\) | |||||||
\(44\) | −333.675 | −1.14326 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 53.9040 | 0.172776 | ||||||||
\(47\) | −247.921 | −0.769427 | −0.384713 | − | 0.923036i | \(-0.625700\pi\) | ||||
−0.384713 | + | 0.923036i | \(0.625700\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −334.929 | −0.947324 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −176.709 | −0.471253 | ||||||||
\(53\) | 140.826 | 0.364981 | 0.182490 | − | 0.983208i | \(-0.441584\pi\) | ||||
0.182490 | + | 0.983208i | \(0.441584\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1120.68 | 2.74750 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −83.1351 | −0.188210 | ||||||||
\(59\) | −221.468 | −0.488689 | −0.244344 | − | 0.969689i | \(-0.578573\pi\) | ||||
−0.244344 | + | 0.969689i | \(0.578573\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 652.526 | 1.36963 | 0.684815 | − | 0.728717i | \(-0.259883\pi\) | ||||
0.684815 | + | 0.728717i | \(0.259883\pi\) | |||||||
\(62\) | −309.902 | −0.634800 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 224.435 | 0.438349 | ||||||||
\(65\) | 593.496 | 1.13253 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 604.478 | 1.10222 | 0.551110 | − | 0.834432i | \(-0.314204\pi\) | ||||
0.551110 | + | 0.834432i | \(0.314204\pi\) | |||||||
\(68\) | 442.935 | 0.789909 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 716.031 | 1.19686 | 0.598431 | − | 0.801174i | \(-0.295791\pi\) | ||||
0.598431 | + | 0.801174i | \(0.295791\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 388.876 | 0.623487 | 0.311743 | − | 0.950166i | \(-0.399087\pi\) | ||||
0.311743 | + | 0.950166i | \(0.399087\pi\) | |||||||
\(74\) | 426.929 | 0.670669 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 113.872 | 0.171869 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −289.741 | −0.412639 | −0.206319 | − | 0.978485i | \(-0.566149\pi\) | ||||
−0.206319 | + | 0.978485i | \(0.566149\pi\) | |||||||
\(80\) | 168.853 | 0.235979 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −324.686 | −0.437263 | ||||||||
\(83\) | −115.652 | −0.152946 | −0.0764728 | − | 0.997072i | \(-0.524366\pi\) | ||||
−0.0764728 | + | 0.997072i | \(0.524366\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1487.64 | −1.89832 | ||||||||
\(86\) | 35.0805 | 0.0439864 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1316.50 | 1.59476 | ||||||||
\(89\) | 939.363 | 1.11879 | 0.559395 | − | 0.828901i | \(-0.311033\pi\) | ||||
0.559395 | + | 0.828901i | \(0.311033\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 183.707 | 0.208182 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 396.192 | 0.434724 | ||||||||
\(95\) | −382.451 | −0.413038 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 120.394 | 0.126022 | 0.0630110 | − | 0.998013i | \(-0.479930\pi\) | ||||
0.0630110 | + | 0.998013i | \(0.479930\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1141.45 | −1.14145 | ||||||||
\(101\) | 1281.00 | 1.26203 | 0.631013 | − | 0.775772i | \(-0.282640\pi\) | ||||
0.631013 | + | 0.775772i | \(0.282640\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 531.339 | 0.508295 | 0.254147 | − | 0.967166i | \(-0.418205\pi\) | ||||
0.254147 | + | 0.967166i | \(0.418205\pi\) | |||||||
\(104\) | 697.198 | 0.657364 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −225.048 | −0.206213 | ||||||||
\(107\) | 133.352 | 0.120482 | 0.0602411 | − | 0.998184i | \(-0.480813\pi\) | ||||
0.0602411 | + | 0.998184i | \(0.480813\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −217.769 | −0.191362 | −0.0956811 | − | 0.995412i | \(-0.530503\pi\) | ||||
−0.0956811 | + | 0.995412i | \(0.530503\pi\) | |||||||
\(110\) | −1790.91 | −1.55233 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2006.09 | −1.67006 | −0.835031 | − | 0.550204i | \(-0.814550\pi\) | ||||
−0.835031 | + | 0.550204i | \(0.814550\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −616.997 | −0.500307 | ||||||||
\(116\) | −283.327 | −0.226778 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 353.917 | 0.276108 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2422.68 | 1.82019 | ||||||||
\(122\) | −1042.77 | −0.773838 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1056.16 | −0.764884 | ||||||||
\(125\) | 1547.22 | 1.10710 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1638.92 | 1.14512 | 0.572562 | − | 0.819861i | \(-0.305950\pi\) | ||||
0.572562 | + | 0.819861i | \(0.305950\pi\) | |||||||
\(128\) | 1134.57 | 0.783462 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −948.439 | −0.639874 | ||||||||
\(131\) | 91.7511 | 0.0611933 | 0.0305967 | − | 0.999532i | \(-0.490259\pi\) | ||||
0.0305967 | + | 0.999532i | \(0.490259\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −965.989 | −0.622752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1747.58 | −1.10186 | ||||||||
\(137\) | −1867.13 | −1.16438 | −0.582188 | − | 0.813054i | \(-0.697803\pi\) | ||||
−0.582188 | + | 0.813054i | \(0.697803\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 639.778 | 0.390397 | 0.195199 | − | 0.980764i | \(-0.437465\pi\) | ||||
0.195199 | + | 0.980764i | \(0.437465\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1144.26 | −0.676224 | ||||||||
\(143\) | 1987.89 | 1.16249 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 951.583 | 0.544998 | ||||||||
\(146\) | −621.446 | −0.352269 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1454.99 | 0.808103 | ||||||||
\(149\) | −3136.53 | −1.72453 | −0.862264 | − | 0.506460i | \(-0.830954\pi\) | ||||
−0.862264 | + | 0.506460i | \(0.830954\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2721.37 | −1.46663 | −0.733317 | − | 0.679887i | \(-0.762029\pi\) | ||||
−0.733317 | + | 0.679887i | \(0.762029\pi\) | |||||||
\(152\) | −449.276 | −0.239744 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3547.20 | 1.83818 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2879.75 | 1.46388 | 0.731939 | − | 0.681370i | \(-0.238616\pi\) | ||||
0.731939 | + | 0.681370i | \(0.238616\pi\) | |||||||
\(158\) | 463.022 | 0.233140 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3414.22 | −1.68699 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 646.142 | 0.310489 | 0.155245 | − | 0.987876i | \(-0.450383\pi\) | ||||
0.155245 | + | 0.987876i | \(0.450383\pi\) | |||||||
\(164\) | −1106.54 | −0.526868 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 184.819 | 0.0864139 | ||||||||
\(167\) | −3765.03 | −1.74459 | −0.872296 | − | 0.488979i | \(-0.837370\pi\) | ||||
−0.872296 | + | 0.488979i | \(0.837370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1144.24 | −0.520821 | ||||||||
\(170\) | 2377.33 | 1.07255 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 119.555 | 0.0530001 | ||||||||
\(173\) | 2308.98 | 1.01473 | 0.507366 | − | 0.861731i | \(-0.330619\pi\) | ||||
0.507366 | + | 0.861731i | \(0.330619\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 565.565 | 0.242222 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1501.15 | −0.632114 | ||||||||
\(179\) | 3033.76 | 1.26678 | 0.633390 | − | 0.773833i | \(-0.281663\pi\) | ||||
0.633390 | + | 0.773833i | \(0.281663\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4079.71 | −1.67537 | −0.837686 | − | 0.546152i | \(-0.816092\pi\) | ||||
−0.837686 | + | 0.546152i | \(0.816092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −724.805 | −0.290399 | ||||||||
\(185\) | −4886.73 | −1.94205 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4982.80 | −1.94855 | ||||||||
\(188\) | 1350.24 | 0.523809 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 611.177 | 0.233365 | ||||||||
\(191\) | −877.109 | −0.332279 | −0.166140 | − | 0.986102i | \(-0.553130\pi\) | ||||
−0.166140 | + | 0.986102i | \(0.553130\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1458.71 | −0.544043 | −0.272022 | − | 0.962291i | \(-0.587692\pi\) | ||||
−0.272022 | + | 0.962291i | \(0.587692\pi\) | |||||||
\(194\) | −192.396 | −0.0712021 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −952.250 | −0.344391 | −0.172195 | − | 0.985063i | \(-0.555086\pi\) | ||||
−0.172195 | + | 0.985063i | \(0.555086\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3342.22 | 1.19057 | 0.595285 | − | 0.803515i | \(-0.297039\pi\) | ||||
0.595285 | + | 0.803515i | \(0.297039\pi\) | |||||||
\(200\) | 4503.54 | 1.59224 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2047.11 | −0.713041 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3716.43 | 1.26618 | ||||||||
\(206\) | −849.108 | −0.287185 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 299.515 | 0.0998442 | ||||||||
\(209\) | −1281.00 | −0.423966 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1439.27 | 0.469589 | 0.234794 | − | 0.972045i | \(-0.424558\pi\) | ||||
0.234794 | + | 0.972045i | \(0.424558\pi\) | |||||||
\(212\) | −766.971 | −0.248471 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −213.103 | −0.0680721 | ||||||||
\(215\) | −401.539 | −0.127371 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 348.007 | 0.108119 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6103.48 | −1.87044 | ||||||||
\(221\) | −2638.82 | −0.803194 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1009.86 | 0.303253 | 0.151626 | − | 0.988438i | \(-0.451549\pi\) | ||||
0.151626 | + | 0.988438i | \(0.451549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3205.84 | 0.943580 | ||||||||
\(227\) | 2948.60 | 0.862140 | 0.431070 | − | 0.902319i | \(-0.358136\pi\) | ||||
0.431070 | + | 0.902319i | \(0.358136\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4038.85 | −1.16548 | −0.582739 | − | 0.812659i | \(-0.698019\pi\) | ||||
−0.582739 | + | 0.812659i | \(0.698019\pi\) | |||||||
\(230\) | 985.995 | 0.282672 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1117.85 | 0.316339 | ||||||||
\(233\) | −2995.80 | −0.842323 | −0.421162 | − | 0.906986i | \(-0.638378\pi\) | ||||
−0.421162 | + | 0.906986i | \(0.638378\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4534.90 | −1.25883 | ||||||||
\(236\) | 1206.16 | 0.332688 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1810.28 | 0.489948 | 0.244974 | − | 0.969530i | \(-0.421221\pi\) | ||||
0.244974 | + | 0.969530i | \(0.421221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3749.43 | −1.00217 | −0.501083 | − | 0.865399i | \(-0.667065\pi\) | ||||
−0.501083 | + | 0.865399i | \(0.667065\pi\) | |||||||
\(242\) | −3871.57 | −1.02841 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3553.80 | −0.932414 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −678.400 | −0.174759 | ||||||||
\(248\) | 4167.01 | 1.06696 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2472.54 | −0.625508 | ||||||||
\(251\) | 2706.96 | 0.680724 | 0.340362 | − | 0.940295i | \(-0.389450\pi\) | ||||
0.340362 | + | 0.940295i | \(0.389450\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2066.61 | −0.513544 | ||||||||
\(254\) | −2619.09 | −0.646992 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3608.59 | −0.881003 | ||||||||
\(257\) | −5375.28 | −1.30467 | −0.652337 | − | 0.757929i | \(-0.726211\pi\) | ||||
−0.652337 | + | 0.757929i | \(0.726211\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −3232.31 | −0.770998 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −146.623 | −0.0345741 | ||||||||
\(263\) | −5246.56 | −1.23010 | −0.615051 | − | 0.788487i | \(-0.710865\pi\) | ||||
−0.615051 | + | 0.788487i | \(0.710865\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2575.95 | 0.597129 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3292.12 | −0.750367 | ||||||||
\(269\) | −3013.32 | −0.682993 | −0.341496 | − | 0.939883i | \(-0.610934\pi\) | ||||
−0.341496 | + | 0.939883i | \(0.610934\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6897.25 | 1.54604 | 0.773022 | − | 0.634379i | \(-0.218744\pi\) | ||||
0.773022 | + | 0.634379i | \(0.218744\pi\) | |||||||
\(272\) | −750.756 | −0.167358 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2983.77 | 0.657869 | ||||||||
\(275\) | 12840.7 | 2.81573 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3318.61 | 0.719840 | 0.359920 | − | 0.932983i | \(-0.382804\pi\) | ||||
0.359920 | + | 0.932983i | \(0.382804\pi\) | |||||||
\(278\) | −1022.40 | −0.220574 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6274.14 | −1.33197 | −0.665986 | − | 0.745964i | \(-0.731989\pi\) | ||||
−0.665986 | + | 0.745964i | \(0.731989\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7772.47 | 1.63260 | 0.816300 | − | 0.577629i | \(-0.196022\pi\) | ||||
0.816300 | + | 0.577629i | \(0.196022\pi\) | |||||||
\(284\) | −3899.66 | −0.814797 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3176.76 | −0.656803 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1701.39 | 0.346304 | ||||||||
\(290\) | −1520.68 | −0.307922 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2117.91 | −0.424456 | ||||||||
\(293\) | 854.897 | 0.170456 | 0.0852280 | − | 0.996361i | \(-0.472838\pi\) | ||||
0.0852280 | + | 0.996361i | \(0.472838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4051.02 | −0.799523 | ||||||||
\(296\) | −5740.58 | −1.12725 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5012.35 | 0.974354 | ||||||||
\(299\) | −1094.44 | −0.211683 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4348.89 | 0.828645 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −193.008 | −0.0364137 | ||||||||
\(305\) | 11935.8 | 2.24079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2550.68 | 0.474185 | 0.237092 | − | 0.971487i | \(-0.423806\pi\) | ||||
0.237092 | + | 0.971487i | \(0.423806\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5668.63 | −1.03857 | ||||||||
\(311\) | 7480.50 | 1.36392 | 0.681962 | − | 0.731388i | \(-0.261127\pi\) | ||||
0.681962 | + | 0.731388i | \(0.261127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.24784 | 0.00112827 | 0.000564135 | − | 1.00000i | \(-0.499820\pi\) | ||||
0.000564135 | 1.00000i | \(0.499820\pi\) | ||||||||
\(314\) | −4601.99 | −0.827088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1578.00 | 0.280915 | ||||||||
\(317\) | 965.803 | 0.171120 | 0.0855598 | − | 0.996333i | \(-0.472732\pi\) | ||||
0.0855598 | + | 0.996333i | \(0.472732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3187.29 | 0.559417 | ||||||||
\(320\) | 4105.29 | 0.717164 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1700.46 | 0.292929 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6800.27 | 1.16065 | ||||||||
\(326\) | −1032.57 | −0.175426 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4365.80 | 0.734942 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6710.20 | 1.11428 | 0.557139 | − | 0.830419i | \(-0.311899\pi\) | ||||
0.557139 | + | 0.830419i | \(0.311899\pi\) | |||||||
\(332\) | 629.868 | 0.104122 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6016.72 | 0.985690 | ||||||||
\(335\) | 11056.9 | 1.80330 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −605.546 | −0.0978819 | −0.0489409 | − | 0.998802i | \(-0.515585\pi\) | ||||
−0.0489409 | + | 0.998802i | \(0.515585\pi\) | |||||||
\(338\) | 1828.56 | 0.294262 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8102.03 | 1.29234 | ||||||||
\(341\) | 11881.2 | 1.88682 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −471.700 | −0.0739313 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3689.88 | −0.573321 | ||||||||
\(347\) | 6938.16 | 1.07337 | 0.536686 | − | 0.843782i | \(-0.319676\pi\) | ||||
0.536686 | + | 0.843782i | \(0.319676\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10368.9 | 1.59035 | 0.795176 | − | 0.606378i | \(-0.207378\pi\) | ||||
0.795176 | + | 0.606378i | \(0.207378\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11435.8 | −1.73162 | ||||||||
\(353\) | −5881.76 | −0.886840 | −0.443420 | − | 0.896314i | \(-0.646235\pi\) | ||||
−0.443420 | + | 0.896314i | \(0.646235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13097.4 | 1.95814 | ||||||||
\(356\) | −5115.98 | −0.761647 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4848.11 | −0.715728 | ||||||||
\(359\) | 589.269 | 0.0866307 | 0.0433153 | − | 0.999061i | \(-0.486208\pi\) | ||||
0.0433153 | + | 0.999061i | \(0.486208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6421.84 | −0.936264 | ||||||||
\(362\) | 6519.60 | 0.946581 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7113.21 | 1.02006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3548.72 | −0.504745 | −0.252373 | − | 0.967630i | \(-0.581211\pi\) | ||||
−0.252373 | + | 0.967630i | \(0.581211\pi\) | |||||||
\(368\) | −311.375 | −0.0441074 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7809.25 | 1.09725 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1581.33 | −0.219513 | −0.109756 | − | 0.993959i | \(-0.535007\pi\) | ||||
−0.109756 | + | 0.993959i | \(0.535007\pi\) | |||||||
\(374\) | 7962.79 | 1.10092 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5327.29 | −0.730675 | ||||||||
\(377\) | 1687.94 | 0.230592 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3057.01 | 0.414322 | 0.207161 | − | 0.978307i | \(-0.433578\pi\) | ||||
0.207161 | + | 0.978307i | \(0.433578\pi\) | |||||||
\(380\) | 2082.91 | 0.281187 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1401.67 | 0.187737 | ||||||||
\(383\) | −10579.7 | −1.41149 | −0.705744 | − | 0.708467i | \(-0.749387\pi\) | ||||
−0.705744 | + | 0.708467i | \(0.749387\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2331.10 | 0.307383 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −655.691 | −0.0857930 | ||||||||
\(389\) | −7393.29 | −0.963637 | −0.481819 | − | 0.876271i | \(-0.660024\pi\) | ||||
−0.481819 | + | 0.876271i | \(0.660024\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2743.31 | 0.354821 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1521.75 | 0.194580 | ||||||||
\(395\) | −5299.86 | −0.675101 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1778.17 | 0.224796 | 0.112398 | − | 0.993663i | \(-0.464147\pi\) | ||||
0.112398 | + | 0.993663i | \(0.464147\pi\) | |||||||
\(398\) | −5341.04 | −0.672669 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1934.71 | 0.241839 | ||||||||
\(401\) | −147.606 | −0.0183818 | −0.00919090 | − | 0.999958i | \(-0.502926\pi\) | ||||
−0.00919090 | + | 0.999958i | \(0.502926\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6292.12 | 0.777748 | ||||||||
\(404\) | −6976.63 | −0.859159 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16367.9 | −1.99343 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2160.05 | −0.261143 | −0.130572 | − | 0.991439i | \(-0.541681\pi\) | ||||
−0.130572 | + | 0.991439i | \(0.541681\pi\) | |||||||
\(410\) | −5939.06 | −0.715388 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2893.79 | −0.346036 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2115.47 | −0.250228 | ||||||||
\(416\) | −6056.22 | −0.713776 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2047.11 | 0.239540 | ||||||||
\(419\) | −13491.0 | −1.57298 | −0.786488 | − | 0.617605i | \(-0.788103\pi\) | ||||
−0.786488 | + | 0.617605i | \(0.788103\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14146.7 | −1.63769 | −0.818847 | − | 0.574012i | \(-0.805386\pi\) | ||||
−0.818847 | + | 0.574012i | \(0.805386\pi\) | |||||||
\(422\) | −2300.03 | −0.265317 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3026.05 | 0.346598 | ||||||||
\(425\) | −17045.4 | −1.94546 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −726.262 | −0.0820215 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 641.682 | 0.0719643 | ||||||||
\(431\) | −9088.52 | −1.01573 | −0.507864 | − | 0.861437i | \(-0.669565\pi\) | ||||
−0.507864 | + | 0.861437i | \(0.669565\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15461.2 | 1.71597 | 0.857986 | − | 0.513673i | \(-0.171716\pi\) | ||||
0.857986 | + | 0.513673i | \(0.171716\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1186.02 | 0.130275 | ||||||||
\(437\) | 705.263 | 0.0772021 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1782.18 | −0.193756 | −0.0968780 | − | 0.995296i | \(-0.530886\pi\) | ||||
−0.0968780 | + | 0.995296i | \(0.530886\pi\) | |||||||
\(440\) | 24081.0 | 2.60913 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4216.97 | 0.453803 | ||||||||
\(443\) | −13424.7 | −1.43979 | −0.719896 | − | 0.694082i | \(-0.755810\pi\) | ||||
−0.719896 | + | 0.694082i | \(0.755810\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17182.5 | 1.83041 | ||||||||
\(446\) | −1613.81 | −0.171337 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −418.639 | −0.0440018 | −0.0220009 | − | 0.999758i | \(-0.507004\pi\) | ||||
−0.0220009 | + | 0.999758i | \(0.507004\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12448.0 | 1.29968 | ||||||||
\(452\) | 10925.6 | 1.13694 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4712.03 | −0.487107 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −708.410 | −0.0725121 | −0.0362560 | − | 0.999343i | \(-0.511543\pi\) | ||||
−0.0362560 | + | 0.999343i | \(0.511543\pi\) | |||||||
\(458\) | 6454.30 | 0.658493 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3360.30 | 0.340598 | ||||||||
\(461\) | −8223.97 | −0.830865 | −0.415432 | − | 0.909624i | \(-0.636370\pi\) | ||||
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9414.17 | −0.944954 | −0.472477 | − | 0.881343i | \(-0.656640\pi\) | ||||
−0.472477 | + | 0.881343i | \(0.656640\pi\) | |||||||
\(464\) | 480.227 | 0.0480474 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4787.45 | 0.475911 | ||||||||
\(467\) | 10821.5 | 1.07229 | 0.536146 | − | 0.844125i | \(-0.319880\pi\) | ||||
0.536146 | + | 0.844125i | \(0.319880\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 7247.02 | 0.711234 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4758.85 | −0.464076 | ||||||||
\(473\) | −1344.94 | −0.130741 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4382.11 | −0.423295 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2892.93 | −0.276819 | ||||||||
\(479\) | −8185.50 | −0.780804 | −0.390402 | − | 0.920644i | \(-0.627664\pi\) | ||||
−0.390402 | + | 0.920644i | \(0.627664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8668.19 | −0.821695 | ||||||||
\(482\) | 5991.79 | 0.566221 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13194.4 | −1.23915 | ||||||||
\(485\) | 2202.21 | 0.206179 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4003.15 | −0.372485 | −0.186242 | − | 0.982504i | \(-0.559631\pi\) | ||||
−0.186242 | + | 0.982504i | \(0.559631\pi\) | |||||||
\(488\) | 14021.3 | 1.30065 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11180.8 | 1.02766 | 0.513831 | − | 0.857891i | \(-0.328226\pi\) | ||||
0.513831 | + | 0.857891i | \(0.328226\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4230.95 | −0.386516 | ||||||||
\(494\) | 1084.12 | 0.0987386 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1790.14 | 0.162056 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3771.08 | −0.338310 | −0.169155 | − | 0.985589i | \(-0.554104\pi\) | ||||
−0.169155 | + | 0.985589i | \(0.554104\pi\) | |||||||
\(500\) | −8426.48 | −0.753688 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4325.87 | −0.384607 | ||||||||
\(503\) | −13597.2 | −1.20531 | −0.602654 | − | 0.798003i | \(-0.705890\pi\) | ||||
−0.602654 | + | 0.798003i | \(0.705890\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23431.7 | 2.06475 | ||||||||
\(506\) | 3302.55 | 0.290151 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8925.93 | −0.779575 | ||||||||
\(509\) | 7360.75 | 0.640982 | 0.320491 | − | 0.947252i | \(-0.396152\pi\) | ||||
0.320491 | + | 0.947252i | \(0.396152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3309.87 | −0.285698 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8590.00 | 0.737137 | ||||||||
\(515\) | 9719.08 | 0.831600 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15189.5 | −1.29213 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12752.9 | 1.07549 | ||||||||
\(521\) | 13798.8 | 1.16034 | 0.580169 | − | 0.814496i | \(-0.302987\pi\) | ||||
0.580169 | + | 0.814496i | \(0.302987\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18847.2 | 1.57577 | 0.787886 | − | 0.615821i | \(-0.211175\pi\) | ||||
0.787886 | + | 0.615821i | \(0.211175\pi\) | |||||||
\(524\) | −499.697 | −0.0416591 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8384.29 | 0.695005 | ||||||||
\(527\) | −15771.7 | −1.30365 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11029.2 | −0.906486 | ||||||||
\(530\) | −4116.51 | −0.337377 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6592.29 | 0.535730 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2439.23 | 0.197116 | ||||||||
\(536\) | 12988.9 | 1.04671 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4815.44 | 0.385889 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14469.5 | −1.14990 | −0.574948 | − | 0.818190i | \(-0.694978\pi\) | ||||
−0.574948 | + | 0.818190i | \(0.694978\pi\) | |||||||
\(542\) | −11022.2 | −0.873511 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 15180.4 | 1.19642 | ||||||||
\(545\) | −3983.36 | −0.313080 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5749.63 | 0.449427 | 0.224713 | − | 0.974425i | \(-0.427855\pi\) | ||||
0.224713 | + | 0.974425i | \(0.427855\pi\) | |||||||
\(548\) | 10168.8 | 0.792681 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20520.2 | −1.59088 | ||||||||
\(551\) | −1087.71 | −0.0840983 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5303.31 | −0.406708 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3484.37 | −0.265774 | ||||||||
\(557\) | 5430.77 | 0.413122 | 0.206561 | − | 0.978434i | \(-0.433773\pi\) | ||||
0.206561 | + | 0.978434i | \(0.433773\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −712.260 | −0.0538915 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10026.4 | 0.752561 | ||||||||
\(563\) | −24130.7 | −1.80637 | −0.903185 | − | 0.429251i | \(-0.858777\pi\) | ||||
−0.903185 | + | 0.429251i | \(0.858777\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36694.7 | −2.73232 | ||||||||
\(566\) | −12420.8 | −0.922415 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15385.9 | 1.13658 | ||||||||
\(569\) | 18048.5 | 1.32976 | 0.664880 | − | 0.746950i | \(-0.268482\pi\) | ||||
0.664880 | + | 0.746950i | \(0.268482\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11274.8 | −0.826336 | −0.413168 | − | 0.910655i | \(-0.635578\pi\) | ||||
−0.413168 | + | 0.910655i | \(0.635578\pi\) | |||||||
\(572\) | −10826.5 | −0.791396 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7069.54 | −0.512731 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24094.9 | −1.73845 | −0.869225 | − | 0.494417i | \(-0.835382\pi\) | ||||
−0.869225 | + | 0.494417i | \(0.835382\pi\) | |||||||
\(578\) | −2718.91 | −0.195661 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5182.53 | −0.371022 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8628.04 | 0.612928 | ||||||||
\(584\) | 8356.10 | 0.592085 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1366.17 | −0.0963072 | ||||||||
\(587\) | 11438.9 | 0.804315 | 0.402157 | − | 0.915571i | \(-0.368260\pi\) | ||||
0.402157 | + | 0.915571i | \(0.368260\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4054.66 | −0.283649 | ||||||||
\(590\) | 6473.74 | 0.451729 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2466.14 | −0.171213 | ||||||||
\(593\) | −4174.44 | −0.289079 | −0.144539 | − | 0.989499i | \(-0.546170\pi\) | ||||
−0.144539 | + | 0.989499i | \(0.546170\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 17082.2 | 1.17402 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1748.98 | 0.119601 | ||||||||
\(599\) | −11455.5 | −0.781403 | −0.390702 | − | 0.920517i | \(-0.627768\pi\) | ||||
−0.390702 | + | 0.920517i | \(0.627768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17539.2 | −1.19042 | −0.595208 | − | 0.803572i | \(-0.702930\pi\) | ||||
−0.595208 | + | 0.803572i | \(0.702930\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14821.2 | 0.998452 | ||||||||
\(605\) | 44314.9 | 2.97794 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3385.72 | 0.226396 | 0.113198 | − | 0.993572i | \(-0.463891\pi\) | ||||
0.113198 | + | 0.993572i | \(0.463891\pi\) | |||||||
\(608\) | 3902.65 | 0.260318 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19074.1 | −1.26604 | ||||||||
\(611\) | −8044.11 | −0.532619 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4271.88 | 0.281468 | 0.140734 | − | 0.990047i | \(-0.455054\pi\) | ||||
0.140734 | + | 0.990047i | \(0.455054\pi\) | |||||||
\(614\) | −4076.12 | −0.267913 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13123.9 | −0.856321 | −0.428160 | − | 0.903703i | \(-0.640838\pi\) | ||||
−0.428160 | + | 0.903703i | \(0.640838\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1893.94 | −0.122979 | −0.0614893 | − | 0.998108i | \(-0.519585\pi\) | ||||
−0.0614893 | + | 0.998108i | \(0.519585\pi\) | |||||||
\(620\) | −19318.9 | −1.25139 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11954.3 | −0.770614 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2102.97 | 0.134590 | ||||||||
\(626\) | −9.98439 | −0.000637470 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15683.7 | −0.996576 | ||||||||
\(629\) | 21727.5 | 1.37731 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20443.8 | 1.28979 | 0.644894 | − | 0.764272i | \(-0.276902\pi\) | ||||
0.644894 | + | 0.764272i | \(0.276902\pi\) | |||||||
\(632\) | −6225.90 | −0.391856 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1543.41 | −0.0966821 | ||||||||
\(635\) | 29978.6 | 1.87349 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5093.46 | −0.316069 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20753.3 | 1.28179 | ||||||||
\(641\) | −19228.5 | −1.18484 | −0.592419 | − | 0.805630i | \(-0.701827\pi\) | ||||
−0.592419 | + | 0.805630i | \(0.701827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18525.1 | −1.13617 | −0.568087 | − | 0.822969i | \(-0.692316\pi\) | ||||
−0.568087 | + | 0.822969i | \(0.692316\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2717.43 | −0.165504 | ||||||||
\(647\) | −8022.39 | −0.487470 | −0.243735 | − | 0.969842i | \(-0.578373\pi\) | ||||
−0.243735 | + | 0.969842i | \(0.578373\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13568.7 | −0.820676 | ||||||||
\(650\) | −10867.2 | −0.655764 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3519.03 | −0.211374 | ||||||||
\(653\) | −2051.69 | −0.122954 | −0.0614769 | − | 0.998109i | \(-0.519581\pi\) | ||||
−0.0614769 | + | 0.998109i | \(0.519581\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1678.28 | 0.100116 | ||||||||
\(656\) | 1875.54 | 0.111627 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14765.2 | −0.872792 | −0.436396 | − | 0.899755i | \(-0.643745\pi\) | ||||
−0.436396 | + | 0.899755i | \(0.643745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 647.064 | 0.0380755 | 0.0190377 | − | 0.999819i | \(-0.493940\pi\) | ||||
0.0190377 | + | 0.999819i | \(0.493940\pi\) | |||||||
\(662\) | −10723.3 | −0.629564 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2485.11 | −0.145243 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1754.78 | −0.101867 | ||||||||
\(668\) | 20505.2 | 1.18768 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17669.6 | −1.01886 | ||||||||
\(671\) | 39978.5 | 2.30008 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22596.6 | −1.29426 | −0.647130 | − | 0.762380i | \(-0.724031\pi\) | ||||
−0.647130 | + | 0.762380i | \(0.724031\pi\) | |||||||
\(674\) | 967.695 | 0.0553030 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6231.80 | 0.354563 | ||||||||
\(677\) | −25204.3 | −1.43084 | −0.715420 | − | 0.698695i | \(-0.753765\pi\) | ||||
−0.715420 | + | 0.698695i | \(0.753765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −31966.2 | −1.80272 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −18986.8 | −1.06605 | ||||||||
\(683\) | 17020.5 | 0.953547 | 0.476774 | − | 0.879026i | \(-0.341806\pi\) | ||||
0.476774 | + | 0.879026i | \(0.341806\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34152.9 | −1.90499 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −202.641 | −0.0112291 | ||||||||
\(689\) | 4569.28 | 0.252650 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19290.5 | −1.06201 | −0.531003 | − | 0.847370i | \(-0.678185\pi\) | ||||
−0.531003 | + | 0.847370i | \(0.678185\pi\) | |||||||
\(692\) | −12575.2 | −0.690806 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11087.6 | −0.606452 | ||||||||
\(695\) | 11702.6 | 0.638713 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16524.1 | −0.897983 | ||||||||
\(698\) | −16570.0 | −0.898545 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28511.4 | 1.53618 | 0.768088 | − | 0.640345i | \(-0.221208\pi\) | ||||
0.768088 | + | 0.640345i | \(0.221208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5585.81 | 0.299677 | ||||||||
\(704\) | 13750.5 | 0.736138 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9399.37 | 0.501062 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28426.5 | 1.50575 | 0.752877 | − | 0.658161i | \(-0.228665\pi\) | ||||
0.752877 | + | 0.658161i | \(0.228665\pi\) | |||||||
\(710\) | −20930.4 | −1.10634 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 20184.8 | 1.06244 | ||||||||
\(713\) | −6541.27 | −0.343580 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36361.9 | 1.90190 | ||||||||
\(716\) | −16522.5 | −0.862396 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −941.683 | −0.0489461 | ||||||||
\(719\) | −21763.3 | −1.12884 | −0.564420 | − | 0.825488i | \(-0.690900\pi\) | ||||
−0.564420 | + | 0.825488i | \(0.690900\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10262.4 | 0.528987 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22219.0 | 1.14056 | ||||||||
\(725\) | 10903.2 | 0.558532 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13422.8 | −0.684763 | −0.342382 | − | 0.939561i | \(-0.611234\pi\) | ||||
−0.342382 | + | 0.939561i | \(0.611234\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11367.3 | −0.576332 | ||||||||
\(731\) | 1785.33 | 0.0903323 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4559.52 | 0.229754 | 0.114877 | − | 0.993380i | \(-0.463353\pi\) | ||||
0.114877 | + | 0.993380i | \(0.463353\pi\) | |||||||
\(734\) | 5671.04 | 0.285180 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6296.04 | 0.315319 | ||||||||
\(737\) | 37034.7 | 1.85101 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36665.4 | −1.82511 | −0.912557 | − | 0.408950i | \(-0.865895\pi\) | ||||
−0.912557 | + | 0.408950i | \(0.865895\pi\) | |||||||
\(740\) | 26614.2 | 1.32210 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10321.3 | −0.509625 | −0.254813 | − | 0.966990i | \(-0.582014\pi\) | ||||
−0.254813 | + | 0.966990i | \(0.582014\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −57372.4 | −2.82143 | ||||||||
\(746\) | 2527.06 | 0.124024 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 27137.4 | 1.32653 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26678.1 | −1.29627 | −0.648134 | − | 0.761526i | \(-0.724450\pi\) | ||||
−0.648134 | + | 0.761526i | \(0.724450\pi\) | |||||||
\(752\) | −2288.59 | −0.110979 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2697.42 | −0.130284 | ||||||||
\(755\) | −49778.4 | −2.39950 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11630.8 | −0.558425 | −0.279212 | − | 0.960229i | \(-0.590073\pi\) | ||||
−0.279212 | + | 0.960229i | \(0.590073\pi\) | |||||||
\(758\) | −4885.27 | −0.234091 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8218.02 | −0.392235 | ||||||||
\(761\) | 36091.7 | 1.71921 | 0.859607 | − | 0.510956i | \(-0.170709\pi\) | ||||
0.859607 | + | 0.510956i | \(0.170709\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4776.93 | 0.226208 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16907.0 | 0.797487 | ||||||||
\(767\) | −7185.79 | −0.338284 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33089.3 | 1.55167 | 0.775833 | − | 0.630938i | \(-0.217330\pi\) | ||||
0.775833 | + | 0.630938i | \(0.217330\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7944.47 | 0.370373 | ||||||||
\(773\) | −30990.8 | −1.44199 | −0.720997 | − | 0.692938i | \(-0.756316\pi\) | ||||
−0.720997 | + | 0.692938i | \(0.756316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40643.8 | 1.88383 | ||||||||
\(776\) | 2587.00 | 0.119675 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11814.9 | 0.544453 | ||||||||
\(779\) | −4248.09 | −0.195383 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43869.2 | 2.00994 | ||||||||
\(782\) | −4383.95 | −0.200473 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52675.4 | 2.39499 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25421.2 | −1.15142 | −0.575711 | − | 0.817653i | \(-0.695275\pi\) | ||||
−0.575711 | + | 0.817653i | \(0.695275\pi\) | |||||||
\(788\) | 5186.17 | 0.234454 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8469.46 | 0.381430 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21172.0 | 0.948096 | ||||||||
\(794\) | −2841.62 | −0.127009 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18202.4 | −0.810513 | ||||||||
\(797\) | −20283.3 | −0.901470 | −0.450735 | − | 0.892658i | \(-0.648838\pi\) | ||||
−0.450735 | + | 0.892658i | \(0.648838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20163.2 | 0.892768 | ||||||||
\(800\) | −39120.1 | −1.72888 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 235.883 | 0.0103857 | ||||||||
\(803\) | 23825.4 | 1.04705 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10055.1 | −0.439426 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 27525.9 | 1.19846 | ||||||||
\(809\) | 16431.3 | 0.714086 | 0.357043 | − | 0.934088i | \(-0.383785\pi\) | ||||
0.357043 | + | 0.934088i | \(0.383785\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6371.81 | 0.275887 | 0.137944 | − | 0.990440i | \(-0.455951\pi\) | ||||
0.137944 | + | 0.990440i | \(0.455951\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 26156.8 | 1.12628 | ||||||||
\(815\) | 11819.0 | 0.507979 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 458.982 | 0.0196545 | ||||||||
\(818\) | 3451.88 | 0.147545 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20240.5 | −0.861987 | ||||||||
\(821\) | −5224.48 | −0.222090 | −0.111045 | − | 0.993815i | \(-0.535420\pi\) | ||||
−0.111045 | + | 0.993815i | \(0.535420\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3713.10 | 0.157267 | 0.0786333 | − | 0.996904i | \(-0.474944\pi\) | ||||
0.0786333 | + | 0.996904i | \(0.474944\pi\) | |||||||
\(824\) | 11417.3 | 0.482695 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10202.6 | 0.428996 | 0.214498 | − | 0.976724i | \(-0.431188\pi\) | ||||
0.214498 | + | 0.976724i | \(0.431188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24995.2 | 1.04719 | 0.523594 | − | 0.851968i | \(-0.324591\pi\) | ||||
0.523594 | + | 0.851968i | \(0.324591\pi\) | |||||||
\(830\) | 3380.64 | 0.141378 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7282.06 | 0.303437 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −68868.8 | −2.85425 | ||||||||
\(836\) | 6976.63 | 0.288626 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21559.3 | 0.888728 | ||||||||
\(839\) | 31173.6 | 1.28275 | 0.641377 | − | 0.767226i | \(-0.278363\pi\) | ||||
0.641377 | + | 0.767226i | \(0.278363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21682.6 | −0.889033 | ||||||||
\(842\) | 22607.2 | 0.925293 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7838.57 | −0.319686 | ||||||||
\(845\) | −20930.1 | −0.852093 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1299.98 | 0.0526434 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 27239.4 | 1.09918 | ||||||||
\(851\) | 9011.43 | 0.362994 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25280.7 | −1.01477 | −0.507383 | − | 0.861721i | \(-0.669387\pi\) | ||||
−0.507383 | + | 0.861721i | \(0.669387\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2865.43 | 0.114414 | ||||||||
\(857\) | −27410.7 | −1.09257 | −0.546285 | − | 0.837599i | \(-0.683959\pi\) | ||||
−0.546285 | + | 0.837599i | \(0.683959\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24558.8 | 0.975480 | 0.487740 | − | 0.872989i | \(-0.337821\pi\) | ||||
0.487740 | + | 0.872989i | \(0.337821\pi\) | |||||||
\(860\) | 2186.87 | 0.0867113 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14523.9 | 0.573883 | ||||||||
\(863\) | −7148.35 | −0.281962 | −0.140981 | − | 0.990012i | \(-0.545026\pi\) | ||||
−0.140981 | + | 0.990012i | \(0.545026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42235.1 | 1.66016 | ||||||||
\(866\) | −24707.8 | −0.969520 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17751.7 | −0.692962 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19613.0 | 0.762988 | ||||||||
\(872\) | −4679.37 | −0.181724 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1127.05 | −0.0436190 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28218.5 | −1.08651 | −0.543256 | − | 0.839567i | \(-0.682809\pi\) | ||||
−0.543256 | + | 0.839567i | \(0.682809\pi\) | |||||||
\(878\) | 2848.02 | 0.109472 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10345.1 | 0.396289 | ||||||||
\(881\) | 7431.50 | 0.284192 | 0.142096 | − | 0.989853i | \(-0.454616\pi\) | ||||
0.142096 | + | 0.989853i | \(0.454616\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4937.77 | 0.188187 | 0.0940936 | − | 0.995563i | \(-0.470005\pi\) | ||||
0.0940936 | + | 0.995563i | \(0.470005\pi\) | |||||||
\(884\) | 14371.6 | 0.546797 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 21453.4 | 0.813478 | ||||||||
\(887\) | −41973.7 | −1.58888 | −0.794441 | − | 0.607341i | \(-0.792236\pi\) | ||||
−0.794441 | + | 0.607341i | \(0.792236\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −27458.6 | −1.03417 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5499.93 | −0.206448 | ||||||||
\(893\) | 5183.65 | 0.194249 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 55492.5 | 2.07253 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 669.008 | 0.0248609 | ||||||||
\(899\) | 10088.5 | 0.374271 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11453.2 | −0.423488 | ||||||||
\(902\) | −19892.6 | −0.734315 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −43106.4 | −1.58595 | ||||||||
\(905\) | −74624.7 | −2.74101 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41424.2 | 1.51650 | 0.758252 | − | 0.651961i | \(-0.226054\pi\) | ||||
0.758252 | + | 0.651961i | \(0.226054\pi\) | |||||||
\(908\) | −16058.7 | −0.586925 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −40072.0 | −1.45735 | −0.728675 | − | 0.684860i | \(-0.759864\pi\) | ||||
−0.728675 | + | 0.684860i | \(0.759864\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7085.70 | −0.256848 | ||||||||
\(914\) | 1132.08 | 0.0409691 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21996.5 | 0.793432 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21817.5 | −0.783124 | −0.391562 | − | 0.920152i | \(-0.628065\pi\) | ||||
−0.391562 | + | 0.920152i | \(0.628065\pi\) | |||||||
\(920\) | −13257.9 | −0.475109 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13142.4 | 0.469437 | ||||||||
\(923\) | 23232.5 | 0.828501 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −55992.0 | −1.99028 | ||||||||
\(926\) | 15044.4 | 0.533897 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −9710.26 | −0.343486 | ||||||||
\(929\) | 11977.0 | 0.422986 | 0.211493 | − | 0.977380i | \(-0.432167\pi\) | ||||
0.211493 | + | 0.977380i | \(0.432167\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16315.8 | 0.573435 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17293.4 | −0.605842 | ||||||||
\(935\) | −91143.8 | −3.18794 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15155.2 | −0.528389 | −0.264194 | − | 0.964469i | \(-0.585106\pi\) | ||||
−0.264194 | + | 0.964469i | \(0.585106\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 24698.1 | 0.856981 | ||||||||
\(941\) | −6954.40 | −0.240921 | −0.120461 | − | 0.992718i | \(-0.538437\pi\) | ||||
−0.120461 | + | 0.992718i | \(0.538437\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6853.33 | −0.236665 | ||||||||
\(944\) | −2044.39 | −0.0704865 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2149.29 | 0.0738682 | ||||||||
\(947\) | 9557.49 | 0.327959 | 0.163979 | − | 0.986464i | \(-0.447567\pi\) | ||||
0.163979 | + | 0.986464i | \(0.447567\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12617.6 | 0.431595 | ||||||||
\(950\) | 7002.85 | 0.239161 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8437.24 | −0.286788 | −0.143394 | − | 0.989666i | \(-0.545802\pi\) | ||||
−0.143394 | + | 0.989666i | \(0.545802\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16043.8 | −0.543628 | ||||||||
\(956\) | −9859.21 | −0.333546 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13080.9 | 0.441153 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7815.69 | 0.262351 | ||||||||
\(962\) | 13852.2 | 0.464256 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20420.2 | 0.682252 | ||||||||
\(965\) | −26682.3 | −0.890087 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52344.7 | 1.74074 | 0.870369 | − | 0.492401i | \(-0.163881\pi\) | ||||
0.870369 | + | 0.492401i | \(0.163881\pi\) | |||||||
\(968\) | 52058.0 | 1.72852 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3519.24 | −0.116491 | ||||||||
\(971\) | 36983.0 | 1.22229 | 0.611143 | − | 0.791520i | \(-0.290710\pi\) | ||||
0.611143 | + | 0.791520i | \(0.290710\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6397.25 | 0.210453 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6023.54 | 0.197550 | ||||||||
\(977\) | 17873.0 | 0.585270 | 0.292635 | − | 0.956224i | \(-0.405468\pi\) | ||||
0.292635 | + | 0.956224i | \(0.405468\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 57552.2 | 1.87883 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17867.5 | −0.580627 | ||||||||
\(983\) | 33744.0 | 1.09488 | 0.547440 | − | 0.836845i | \(-0.315602\pi\) | ||||
0.547440 | + | 0.836845i | \(0.315602\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17418.3 | −0.563444 | ||||||||
\(986\) | 6761.29 | 0.218381 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3694.72 | 0.118972 | ||||||||
\(989\) | 740.464 | 0.0238073 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14506.5 | −0.464999 | −0.232499 | − | 0.972597i | \(-0.574690\pi\) | ||||
−0.232499 | + | 0.972597i | \(0.574690\pi\) | |||||||
\(992\) | −36196.8 | −1.15852 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 61134.7 | 1.94784 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42368.8 | −1.34587 | −0.672936 | − | 0.739701i | \(-0.734967\pi\) | ||||
−0.672936 | + | 0.739701i | \(0.734967\pi\) | |||||||
\(998\) | 6026.40 | 0.191145 | ||||||||
\(999\) | 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 | 441.4.a.w.1.2 | 4 | ||
3.2 | odd | 2 | inner | 441.4.a.w.1.3 | 4 | ||
7.2 | even | 3 | 63.4.e.d.46.3 | yes | 8 | ||
7.3 | odd | 6 | 441.4.e.x.226.3 | 8 | |||
7.4 | even | 3 | 63.4.e.d.37.3 | yes | 8 | ||
7.5 | odd | 6 | 441.4.e.x.361.3 | 8 | |||
7.6 | odd | 2 | 441.4.a.v.1.2 | 4 | |||
21.2 | odd | 6 | 63.4.e.d.46.2 | yes | 8 | ||
21.5 | even | 6 | 441.4.e.x.361.2 | 8 | |||
21.11 | odd | 6 | 63.4.e.d.37.2 | ✓ | 8 | ||
21.17 | even | 6 | 441.4.e.x.226.2 | 8 | |||
21.20 | even | 2 | 441.4.a.v.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.e.d.37.2 | ✓ | 8 | 21.11 | odd | 6 | ||
63.4.e.d.37.3 | yes | 8 | 7.4 | even | 3 | ||
63.4.e.d.46.2 | yes | 8 | 21.2 | odd | 6 | ||
63.4.e.d.46.3 | yes | 8 | 7.2 | even | 3 | ||
441.4.a.v.1.2 | 4 | 7.6 | odd | 2 | |||
441.4.a.v.1.3 | 4 | 21.20 | even | 2 | |||
441.4.a.w.1.2 | 4 | 1.1 | even | 1 | trivial | ||
441.4.a.w.1.3 | 4 | 3.2 | odd | 2 | inner | ||
441.4.e.x.226.2 | 8 | 21.17 | even | 6 | |||
441.4.e.x.226.3 | 8 | 7.3 | odd | 6 | |||
441.4.e.x.361.2 | 8 | 21.5 | even | 6 | |||
441.4.e.x.361.3 | 8 | 7.5 | odd | 6 |