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: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.3144.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 16x - 8 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.526440\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.52644 | 0.539678 | 0.269839 | − | 0.962905i | \(-0.413030\pi\) | ||||
0.269839 | + | 0.962905i | \(0.413030\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −5.66998 | −0.708748 | ||||||||
\(5\) | 19.3400 | 1.72982 | 0.864909 | − | 0.501928i | \(-0.167376\pi\) | ||||
0.864909 | + | 0.501928i | \(0.167376\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.84136 | −0.261409 | −0.130704 | − | 0.991421i | \(-0.541724\pi\) | ||||
−0.130704 | + | 0.991421i | \(0.541724\pi\) | |||||||
\(8\) | −20.8664 | −0.922173 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 29.5213 | 0.933545 | ||||||||
\(11\) | −61.0728 | −1.67401 | −0.837006 | − | 0.547194i | \(-0.815696\pi\) | ||||
−0.837006 | + | 0.547194i | \(0.815696\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −7.39005 | −0.141077 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.5085 | 0.211071 | ||||||||
\(17\) | 41.7885 | 0.596188 | 0.298094 | − | 0.954537i | \(-0.403649\pi\) | ||||
0.298094 | + | 0.954537i | \(0.403649\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 107.561 | 1.29875 | 0.649374 | − | 0.760469i | \(-0.275031\pi\) | ||||
0.649374 | + | 0.760469i | \(0.275031\pi\) | |||||||
\(20\) | −109.657 | −1.22601 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −93.2239 | −0.903427 | ||||||||
\(23\) | −28.5138 | −0.258502 | −0.129251 | − | 0.991612i | \(-0.541257\pi\) | ||||
−0.129251 | + | 0.991612i | \(0.541257\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 249.034 | 1.99227 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 27.4504 | 0.185273 | ||||||||
\(29\) | 89.8886 | 0.575583 | 0.287791 | − | 0.957693i | \(-0.407079\pi\) | ||||
0.287791 | + | 0.957693i | \(0.407079\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −183.108 | −1.06087 | −0.530437 | − | 0.847724i | \(-0.677972\pi\) | ||||
−0.530437 | + | 0.847724i | \(0.677972\pi\) | |||||||
\(32\) | 187.551 | 1.03608 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 63.7876 | 0.321750 | ||||||||
\(35\) | −93.6318 | −0.452190 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −418.029 | −1.85739 | −0.928696 | − | 0.370843i | \(-0.879069\pi\) | ||||
−0.928696 | + | 0.370843i | \(0.879069\pi\) | |||||||
\(38\) | 164.185 | 0.700905 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −403.555 | −1.59519 | ||||||||
\(41\) | −142.674 | −0.543460 | −0.271730 | − | 0.962373i | \(-0.587596\pi\) | ||||
−0.271730 | + | 0.962373i | \(0.587596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −71.0935 | −0.252132 | −0.126066 | − | 0.992022i | \(-0.540235\pi\) | ||||
−0.126066 | + | 0.992022i | \(0.540235\pi\) | |||||||
\(44\) | 346.281 | 1.18645 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −43.5246 | −0.139508 | ||||||||
\(47\) | 323.711 | 1.00464 | 0.502321 | − | 0.864681i | \(-0.332480\pi\) | ||||
0.502321 | + | 0.864681i | \(0.332480\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −319.561 | −0.931665 | ||||||||
\(50\) | 380.136 | 1.07519 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25.1047 | 0.0650641 | 0.0325321 | − | 0.999471i | \(-0.489643\pi\) | ||||
0.0325321 | + | 0.999471i | \(0.489643\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1181.15 | −2.89574 | ||||||||
\(56\) | 101.022 | 0.241064 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 137.210 | 0.310629 | ||||||||
\(59\) | −684.508 | −1.51043 | −0.755215 | − | 0.655477i | \(-0.772467\pi\) | ||||
−0.755215 | + | 0.655477i | \(0.772467\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 308.125 | 0.646744 | 0.323372 | − | 0.946272i | \(-0.395184\pi\) | ||||
0.323372 | + | 0.946272i | \(0.395184\pi\) | |||||||
\(62\) | −279.503 | −0.572531 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 178.217 | 0.348081 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −672.808 | −1.22681 | −0.613407 | − | 0.789767i | \(-0.710202\pi\) | ||||
−0.613407 | + | 0.789767i | \(0.710202\pi\) | |||||||
\(68\) | −236.940 | −0.422547 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −142.923 | −0.244037 | ||||||||
\(71\) | −326.837 | −0.546315 | −0.273158 | − | 0.961969i | \(-0.588068\pi\) | ||||
−0.273158 | + | 0.961969i | \(0.588068\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −24.3058 | −0.0389695 | −0.0194847 | − | 0.999810i | \(-0.506203\pi\) | ||||
−0.0194847 | + | 0.999810i | \(0.506203\pi\) | |||||||
\(74\) | −638.095 | −1.00239 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −609.869 | −0.920484 | ||||||||
\(77\) | 295.675 | 0.437602 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 166.810 | 0.237565 | 0.118783 | − | 0.992920i | \(-0.462101\pi\) | ||||
0.118783 | + | 0.992920i | \(0.462101\pi\) | |||||||
\(80\) | 261.255 | 0.365115 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −217.783 | −0.293294 | ||||||||
\(83\) | −201.093 | −0.265938 | −0.132969 | − | 0.991120i | \(-0.542451\pi\) | ||||
−0.132969 | + | 0.991120i | \(0.542451\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 808.188 | 1.03130 | ||||||||
\(86\) | −108.520 | −0.136070 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1274.37 | 1.54373 | ||||||||
\(89\) | 108.834 | 0.129622 | 0.0648109 | − | 0.997898i | \(-0.479356\pi\) | ||||
0.0648109 | + | 0.997898i | \(0.479356\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 161.673 | 0.183212 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 494.126 | 0.542183 | ||||||||
\(95\) | 2080.23 | 2.24660 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1157.95 | −1.21208 | −0.606041 | − | 0.795434i | \(-0.707243\pi\) | ||||
−0.606041 | + | 0.795434i | \(0.707243\pi\) | |||||||
\(98\) | −487.791 | −0.502799 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1412.02 | −1.41202 | ||||||||
\(101\) | −1702.75 | −1.67752 | −0.838761 | − | 0.544500i | \(-0.816719\pi\) | ||||
−0.838761 | + | 0.544500i | \(0.816719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1455.14 | −1.39203 | −0.696015 | − | 0.718027i | \(-0.745045\pi\) | ||||
−0.696015 | + | 0.718027i | \(0.745045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 38.3209 | 0.0351137 | ||||||||
\(107\) | 822.762 | 0.743359 | 0.371679 | − | 0.928361i | \(-0.378782\pi\) | ||||
0.371679 | + | 0.928361i | \(0.378782\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −457.264 | −0.401816 | −0.200908 | − | 0.979610i | \(-0.564389\pi\) | ||||
−0.200908 | + | 0.979610i | \(0.564389\pi\) | |||||||
\(110\) | −1802.95 | −1.56277 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −65.3998 | −0.0551759 | ||||||||
\(113\) | 381.693 | 0.317758 | 0.158879 | − | 0.987298i | \(-0.449212\pi\) | ||||
0.158879 | + | 0.987298i | \(0.449212\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −551.456 | −0.447161 | ||||||||
\(116\) | −509.667 | −0.407943 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1044.86 | −0.815146 | ||||||||
\(119\) | −202.313 | −0.155849 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2398.88 | 1.80232 | ||||||||
\(122\) | 470.334 | 0.349033 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1038.22 | 0.751892 | ||||||||
\(125\) | 2398.82 | 1.71645 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1129.09 | −0.788905 | −0.394452 | − | 0.918916i | \(-0.629066\pi\) | ||||
−0.394452 | + | 0.918916i | \(0.629066\pi\) | |||||||
\(128\) | −1228.37 | −0.848232 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 852.761 | 0.568749 | 0.284374 | − | 0.958713i | \(-0.408214\pi\) | ||||
0.284374 | + | 0.958713i | \(0.408214\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −520.742 | −0.339504 | ||||||||
\(134\) | −1027.00 | −0.662085 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −871.975 | −0.549789 | ||||||||
\(137\) | −488.903 | −0.304889 | −0.152445 | − | 0.988312i | \(-0.548715\pi\) | ||||
−0.152445 | + | 0.988312i | \(0.548715\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 407.123 | 0.248430 | 0.124215 | − | 0.992255i | \(-0.460359\pi\) | ||||
0.124215 | + | 0.992255i | \(0.460359\pi\) | |||||||
\(140\) | 530.890 | 0.320489 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −498.897 | −0.294834 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1738.44 | 0.995654 | ||||||||
\(146\) | −37.1013 | −0.0210310 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2370.21 | 1.31642 | ||||||||
\(149\) | 1717.63 | 0.944388 | 0.472194 | − | 0.881495i | \(-0.343462\pi\) | ||||
0.472194 | + | 0.881495i | \(0.343462\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1341.79 | −0.723133 | −0.361567 | − | 0.932346i | \(-0.617758\pi\) | ||||
−0.361567 | + | 0.932346i | \(0.617758\pi\) | |||||||
\(152\) | −2244.41 | −1.19767 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 451.331 | 0.236164 | ||||||||
\(155\) | −3541.30 | −1.83512 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −760.546 | −0.386612 | −0.193306 | − | 0.981138i | \(-0.561921\pi\) | ||||
−0.193306 | + | 0.981138i | \(0.561921\pi\) | |||||||
\(158\) | 254.626 | 0.128209 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3627.23 | 1.79224 | ||||||||
\(161\) | 138.046 | 0.0675746 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2712.09 | −1.30323 | −0.651616 | − | 0.758549i | \(-0.725909\pi\) | ||||
−0.651616 | + | 0.758549i | \(0.725909\pi\) | |||||||
\(164\) | 808.957 | 0.385176 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −306.957 | −0.143521 | ||||||||
\(167\) | 1551.69 | 0.719004 | 0.359502 | − | 0.933144i | \(-0.382947\pi\) | ||||
0.359502 | + | 0.933144i | \(0.382947\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 1233.65 | 0.556568 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 403.099 | 0.178698 | ||||||||
\(173\) | 3970.26 | 1.74482 | 0.872409 | − | 0.488777i | \(-0.162557\pi\) | ||||
0.872409 | + | 0.488777i | \(0.162557\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1205.66 | −0.520798 | ||||||||
\(176\) | −825.004 | −0.353335 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 166.128 | 0.0699540 | ||||||||
\(179\) | 2690.95 | 1.12364 | 0.561818 | − | 0.827261i | \(-0.310102\pi\) | ||||
0.561818 | + | 0.827261i | \(0.310102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4371.10 | −1.79503 | −0.897517 | − | 0.440980i | \(-0.854631\pi\) | ||||
−0.897517 | + | 0.440980i | \(0.854631\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 594.980 | 0.238383 | ||||||||
\(185\) | −8084.66 | −3.21295 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2552.14 | −0.998026 | ||||||||
\(188\) | −1835.44 | −0.712038 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3175.34 | 1.21244 | ||||||||
\(191\) | −1408.47 | −0.533578 | −0.266789 | − | 0.963755i | \(-0.585963\pi\) | ||||
−0.266789 | + | 0.963755i | \(0.585963\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4131.69 | 1.54096 | 0.770481 | − | 0.637463i | \(-0.220016\pi\) | ||||
0.770481 | + | 0.637463i | \(0.220016\pi\) | |||||||
\(194\) | −1767.54 | −0.654134 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1811.91 | 0.660316 | ||||||||
\(197\) | −3401.23 | −1.23009 | −0.615045 | − | 0.788492i | \(-0.710862\pi\) | ||||
−0.615045 | + | 0.788492i | \(0.710862\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3520.74 | −1.25416 | −0.627081 | − | 0.778954i | \(-0.715751\pi\) | ||||
−0.627081 | + | 0.778954i | \(0.715751\pi\) | |||||||
\(200\) | −5196.45 | −1.83722 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2599.14 | −0.905321 | ||||||||
\(203\) | −435.183 | −0.150463 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2759.30 | −0.940088 | ||||||||
\(206\) | −2221.18 | −0.751248 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6569.05 | −2.17412 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2245.22 | −0.732545 | −0.366272 | − | 0.930508i | \(-0.619366\pi\) | ||||
−0.366272 | + | 0.930508i | \(0.619366\pi\) | |||||||
\(212\) | −142.343 | −0.0461141 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1255.90 | 0.401174 | ||||||||
\(215\) | −1374.95 | −0.436142 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 886.490 | 0.277322 | ||||||||
\(218\) | −697.986 | −0.216851 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6697.07 | 2.05235 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3431.26 | −1.03038 | −0.515188 | − | 0.857077i | \(-0.672278\pi\) | ||||
−0.515188 | + | 0.857077i | \(0.672278\pi\) | |||||||
\(224\) | −908.003 | −0.270842 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 582.631 | 0.171487 | ||||||||
\(227\) | −4757.91 | −1.39116 | −0.695581 | − | 0.718448i | \(-0.744853\pi\) | ||||
−0.695581 | + | 0.718448i | \(0.744853\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4368.93 | 1.26073 | 0.630364 | − | 0.776300i | \(-0.282906\pi\) | ||||
0.630364 | + | 0.776300i | \(0.282906\pi\) | |||||||
\(230\) | −841.764 | −0.241323 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1875.65 | −0.530787 | ||||||||
\(233\) | 3642.00 | 1.02401 | 0.512007 | − | 0.858981i | \(-0.328902\pi\) | ||||
0.512007 | + | 0.858981i | \(0.328902\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6260.57 | 1.73785 | ||||||||
\(236\) | 3881.15 | 1.07051 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −308.819 | −0.0841082 | ||||||||
\(239\) | 2236.17 | 0.605213 | 0.302606 | − | 0.953116i | \(-0.402143\pi\) | ||||
0.302606 | + | 0.953116i | \(0.402143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6538.78 | −1.74772 | −0.873858 | − | 0.486181i | \(-0.838390\pi\) | ||||
−0.873858 | + | 0.486181i | \(0.838390\pi\) | |||||||
\(242\) | 3661.75 | 0.972670 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1747.06 | −0.458378 | ||||||||
\(245\) | −6180.30 | −1.61161 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3820.80 | 0.978310 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3661.65 | 0.926332 | ||||||||
\(251\) | −2507.12 | −0.630470 | −0.315235 | − | 0.949014i | \(-0.602083\pi\) | ||||
−0.315235 | + | 0.949014i | \(0.602083\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1741.42 | 0.432735 | ||||||||
\(254\) | −1723.49 | −0.425755 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3300.77 | −0.805853 | ||||||||
\(257\) | 808.131 | 0.196147 | 0.0980735 | − | 0.995179i | \(-0.468732\pi\) | ||||
0.0980735 | + | 0.995179i | \(0.468732\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2023.83 | 0.485539 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1301.69 | 0.306941 | ||||||||
\(263\) | −2940.70 | −0.689472 | −0.344736 | − | 0.938700i | \(-0.612032\pi\) | ||||
−0.344736 | + | 0.938700i | \(0.612032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 485.525 | 0.112549 | ||||||||
\(266\) | −794.881 | −0.183223 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3814.81 | 0.869502 | ||||||||
\(269\) | −7111.50 | −1.61188 | −0.805940 | − | 0.591997i | \(-0.798340\pi\) | ||||
−0.805940 | + | 0.591997i | \(0.798340\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2034.96 | −0.456145 | −0.228072 | − | 0.973644i | \(-0.573242\pi\) | ||||
−0.228072 | + | 0.973644i | \(0.573242\pi\) | |||||||
\(272\) | 564.502 | 0.125838 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −746.281 | −0.164542 | ||||||||
\(275\) | −15209.2 | −3.33509 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2723.20 | 0.590689 | 0.295345 | − | 0.955391i | \(-0.404566\pi\) | ||||
0.295345 | + | 0.955391i | \(0.404566\pi\) | |||||||
\(278\) | 621.449 | 0.134072 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1953.76 | 0.416998 | ||||||||
\(281\) | 3265.56 | 0.693263 | 0.346632 | − | 0.938001i | \(-0.387325\pi\) | ||||
0.346632 | + | 0.938001i | \(0.387325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1144.02 | 0.240299 | 0.120150 | − | 0.992756i | \(-0.461663\pi\) | ||||
0.120150 | + | 0.992756i | \(0.461663\pi\) | |||||||
\(284\) | 1853.16 | 0.387200 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 690.735 | 0.142065 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3166.72 | −0.644560 | ||||||||
\(290\) | 2653.63 | 0.537333 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 137.813 | 0.0276195 | ||||||||
\(293\) | −1677.35 | −0.334444 | −0.167222 | − | 0.985919i | \(-0.553480\pi\) | ||||
−0.167222 | + | 0.985919i | \(0.553480\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13238.4 | −2.61277 | ||||||||
\(296\) | 8722.75 | 1.71284 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2621.86 | 0.509666 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 344.190 | 0.0659095 | ||||||||
\(302\) | −2048.16 | −0.390259 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1452.99 | 0.274128 | ||||||||
\(305\) | 5959.13 | 1.11875 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7207.70 | −1.33995 | −0.669975 | − | 0.742383i | \(-0.733695\pi\) | ||||
−0.669975 | + | 0.742383i | \(0.733695\pi\) | |||||||
\(308\) | −1676.47 | −0.310149 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5405.57 | −0.990374 | ||||||||
\(311\) | −412.963 | −0.0752958 | −0.0376479 | − | 0.999291i | \(-0.511987\pi\) | ||||
−0.0376479 | + | 0.999291i | \(0.511987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2936.39 | 0.530270 | 0.265135 | − | 0.964211i | \(-0.414583\pi\) | ||||
0.265135 | + | 0.964211i | \(0.414583\pi\) | |||||||
\(314\) | −1160.93 | −0.208646 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −945.812 | −0.168374 | ||||||||
\(317\) | 377.956 | 0.0669657 | 0.0334828 | − | 0.999439i | \(-0.489340\pi\) | ||||
0.0334828 | + | 0.999439i | \(0.489340\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5489.75 | −0.963533 | ||||||||
\(320\) | 3446.71 | 0.602116 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 210.718 | 0.0364685 | ||||||||
\(323\) | 4494.81 | 0.774298 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4139.83 | −0.703326 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2977.09 | 0.501165 | ||||||||
\(329\) | −1567.20 | −0.262622 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4428.17 | 0.735330 | 0.367665 | − | 0.929958i | \(-0.380157\pi\) | ||||
0.367665 | + | 0.929958i | \(0.380157\pi\) | |||||||
\(332\) | 1140.20 | 0.188483 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2368.57 | 0.388031 | ||||||||
\(335\) | −13012.1 | −2.12217 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1768.76 | −0.285907 | −0.142953 | − | 0.989729i | \(-0.545660\pi\) | ||||
−0.142953 | + | 0.989729i | \(0.545660\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4582.41 | −0.730930 | ||||||||
\(341\) | 11182.9 | 1.77592 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3207.70 | 0.504955 | ||||||||
\(344\) | 1483.47 | 0.232509 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6060.36 | 0.941639 | ||||||||
\(347\) | −2412.97 | −0.373300 | −0.186650 | − | 0.982426i | \(-0.559763\pi\) | ||||
−0.186650 | + | 0.982426i | \(0.559763\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9967.45 | 1.52878 | 0.764392 | − | 0.644752i | \(-0.223039\pi\) | ||||
0.764392 | + | 0.644752i | \(0.223039\pi\) | |||||||
\(350\) | −1840.37 | −0.281063 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −11454.3 | −1.73442 | ||||||||
\(353\) | 4516.30 | 0.680959 | 0.340479 | − | 0.940252i | \(-0.389411\pi\) | ||||
0.340479 | + | 0.940252i | \(0.389411\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6321.01 | −0.945027 | ||||||||
\(356\) | −617.084 | −0.0918691 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4107.57 | 0.606401 | ||||||||
\(359\) | 12159.8 | 1.78767 | 0.893833 | − | 0.448400i | \(-0.148006\pi\) | ||||
0.893833 | + | 0.448400i | \(0.148006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4710.38 | 0.686745 | ||||||||
\(362\) | −6672.22 | −0.968740 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −470.072 | −0.0674102 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2674.25 | −0.380367 | −0.190183 | − | 0.981749i | \(-0.560908\pi\) | ||||
−0.190183 | + | 0.981749i | \(0.560908\pi\) | |||||||
\(368\) | −385.180 | −0.0545622 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12340.7 | −1.73396 | ||||||||
\(371\) | −121.541 | −0.0170083 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9601.74 | 1.33287 | 0.666433 | − | 0.745564i | \(-0.267820\pi\) | ||||
0.666433 | + | 0.745564i | \(0.267820\pi\) | |||||||
\(374\) | −3895.69 | −0.538613 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6754.69 | −0.926454 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9019.65 | −1.22245 | −0.611225 | − | 0.791457i | \(-0.709323\pi\) | ||||
−0.611225 | + | 0.791457i | \(0.709323\pi\) | |||||||
\(380\) | −11794.9 | −1.59227 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2149.95 | −0.287960 | ||||||||
\(383\) | −4015.34 | −0.535703 | −0.267852 | − | 0.963460i | \(-0.586314\pi\) | ||||
−0.267852 | + | 0.963460i | \(0.586314\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5718.35 | 0.756972 | ||||||||
\(386\) | 6306.78 | 0.831623 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6565.55 | 0.859060 | ||||||||
\(389\) | 2725.35 | 0.355221 | 0.177610 | − | 0.984101i | \(-0.443163\pi\) | ||||
0.177610 | + | 0.984101i | \(0.443163\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1191.55 | −0.154115 | ||||||||
\(392\) | 6668.09 | 0.859157 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5191.78 | −0.663853 | ||||||||
\(395\) | 3226.11 | 0.410945 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4391.59 | 0.555182 | 0.277591 | − | 0.960699i | \(-0.410464\pi\) | ||||
0.277591 | + | 0.960699i | \(0.410464\pi\) | |||||||
\(398\) | −5374.19 | −0.676844 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3364.09 | 0.420511 | ||||||||
\(401\) | 3762.48 | 0.468552 | 0.234276 | − | 0.972170i | \(-0.424728\pi\) | ||||
0.234276 | + | 0.972170i | \(0.424728\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 9654.55 | 1.18894 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −664.281 | −0.0812013 | ||||||||
\(407\) | 25530.2 | 3.10930 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6797.81 | 0.821833 | 0.410917 | − | 0.911673i | \(-0.365209\pi\) | ||||
0.410917 | + | 0.911673i | \(0.365209\pi\) | |||||||
\(410\) | −4211.91 | −0.507345 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8250.61 | 0.986599 | ||||||||
\(413\) | 3313.95 | 0.394840 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3889.14 | −0.460025 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10027.3 | −1.17332 | ||||||||
\(419\) | 12594.2 | 1.46841 | 0.734207 | − | 0.678925i | \(-0.237554\pi\) | ||||
0.734207 | + | 0.678925i | \(0.237554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6888.04 | −0.797393 | −0.398697 | − | 0.917083i | \(-0.630537\pi\) | ||||
−0.398697 | + | 0.917083i | \(0.630537\pi\) | |||||||
\(422\) | −3427.19 | −0.395338 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −523.845 | −0.0600004 | ||||||||
\(425\) | 10406.8 | 1.18777 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1491.74 | −0.169065 | ||||||||
\(428\) | −4665.04 | −0.526854 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2098.77 | −0.235376 | ||||||||
\(431\) | −7384.53 | −0.825291 | −0.412645 | − | 0.910892i | \(-0.635395\pi\) | ||||
−0.412645 | + | 0.910892i | \(0.635395\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9068.33 | 1.00646 | 0.503229 | − | 0.864153i | \(-0.332145\pi\) | ||||
0.503229 | + | 0.864153i | \(0.332145\pi\) | |||||||
\(434\) | 1353.17 | 0.149665 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2592.68 | 0.284786 | ||||||||
\(437\) | −3066.97 | −0.335728 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16875.4 | 1.83466 | 0.917331 | − | 0.398125i | \(-0.130339\pi\) | ||||
0.917331 | + | 0.398125i | \(0.130339\pi\) | |||||||
\(440\) | 24646.3 | 2.67037 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6766.18 | 0.725668 | 0.362834 | − | 0.931854i | \(-0.381809\pi\) | ||||
0.362834 | + | 0.931854i | \(0.381809\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2104.84 | 0.224222 | ||||||||
\(446\) | −5237.61 | −0.556072 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −862.814 | −0.0909914 | ||||||||
\(449\) | 140.944 | 0.0148141 | 0.00740706 | − | 0.999973i | \(-0.497642\pi\) | ||||
0.00740706 | + | 0.999973i | \(0.497642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8713.47 | 0.909759 | ||||||||
\(452\) | −2164.19 | −0.225210 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7262.67 | −0.750779 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17733.1 | 1.81514 | 0.907571 | − | 0.419898i | \(-0.137934\pi\) | ||||
0.907571 | + | 0.419898i | \(0.137934\pi\) | |||||||
\(458\) | 6668.90 | 0.680387 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3126.74 | 0.316924 | ||||||||
\(461\) | 2293.37 | 0.231699 | 0.115849 | − | 0.993267i | \(-0.463041\pi\) | ||||
0.115849 | + | 0.993267i | \(0.463041\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13770.9 | −1.38226 | −0.691129 | − | 0.722731i | \(-0.742887\pi\) | ||||
−0.691129 | + | 0.722731i | \(0.742887\pi\) | |||||||
\(464\) | 1214.27 | 0.121489 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5559.29 | 0.552638 | ||||||||
\(467\) | 3477.37 | 0.344568 | 0.172284 | − | 0.985047i | \(-0.444885\pi\) | ||||
0.172284 | + | 0.985047i | \(0.444885\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3257.31 | 0.320700 | ||||||||
\(470\) | 9556.38 | 0.937879 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14283.2 | 1.39288 | ||||||||
\(473\) | 4341.88 | 0.422072 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26786.4 | 2.58746 | ||||||||
\(476\) | 1147.11 | 0.110458 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3413.38 | 0.326620 | ||||||||
\(479\) | −3137.39 | −0.299271 | −0.149636 | − | 0.988741i | \(-0.547810\pi\) | ||||
−0.149636 | + | 0.988741i | \(0.547810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9981.05 | −0.943204 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13601.6 | −1.27739 | ||||||||
\(485\) | −22394.7 | −2.09668 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5996.52 | −0.557964 | −0.278982 | − | 0.960296i | \(-0.589997\pi\) | ||||
−0.278982 | + | 0.960296i | \(0.589997\pi\) | |||||||
\(488\) | −6429.46 | −0.596410 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9433.86 | −0.869752 | ||||||||
\(491\) | 9401.49 | 0.864121 | 0.432060 | − | 0.901845i | \(-0.357787\pi\) | ||||
0.432060 | + | 0.901845i | \(0.357787\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3756.31 | 0.343156 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2473.52 | −0.223920 | ||||||||
\(497\) | 1582.34 | 0.142812 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5052.33 | 0.453253 | 0.226626 | − | 0.973982i | \(-0.427230\pi\) | ||||
0.226626 | + | 0.973982i | \(0.427230\pi\) | |||||||
\(500\) | −13601.2 | −1.21653 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3826.96 | −0.340251 | ||||||||
\(503\) | −8184.02 | −0.725462 | −0.362731 | − | 0.931894i | \(-0.618156\pi\) | ||||
−0.362731 | + | 0.931894i | \(0.618156\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −32931.1 | −2.90181 | ||||||||
\(506\) | 2658.17 | 0.233537 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6401.94 | 0.559134 | ||||||||
\(509\) | 6039.12 | 0.525892 | 0.262946 | − | 0.964811i | \(-0.415306\pi\) | ||||
0.262946 | + | 0.964811i | \(0.415306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 117.673 | 0.0101870 | ||||||||
\(512\) | 4788.54 | 0.413331 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1233.56 | 0.105856 | ||||||||
\(515\) | −28142.3 | −2.40796 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19770.0 | −1.68178 | ||||||||
\(518\) | 3089.25 | 0.262035 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14602.5 | 1.22792 | 0.613960 | − | 0.789337i | \(-0.289576\pi\) | ||||
0.613960 | + | 0.789337i | \(0.289576\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8910.70 | 0.745005 | 0.372502 | − | 0.928031i | \(-0.378500\pi\) | ||||
0.372502 | + | 0.928031i | \(0.378500\pi\) | |||||||
\(524\) | −4835.14 | −0.403099 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4488.80 | −0.372093 | ||||||||
\(527\) | −7651.79 | −0.632481 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11354.0 | −0.933177 | ||||||||
\(530\) | 741.124 | 0.0607403 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2952.60 | 0.240623 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15912.2 | 1.28588 | ||||||||
\(536\) | 14039.1 | 1.13134 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10855.3 | −0.869897 | ||||||||
\(539\) | 19516.5 | 1.55962 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13313.6 | 1.05803 | 0.529017 | − | 0.848611i | \(-0.322561\pi\) | ||||
0.529017 | + | 0.848611i | \(0.322561\pi\) | |||||||
\(542\) | −3106.25 | −0.246171 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7837.48 | 0.617701 | ||||||||
\(545\) | −8843.47 | −0.695069 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4116.94 | −0.321806 | −0.160903 | − | 0.986970i | \(-0.551441\pi\) | ||||
−0.160903 | + | 0.986970i | \(0.551441\pi\) | |||||||
\(548\) | 2772.07 | 0.216090 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −23215.9 | −1.79987 | ||||||||
\(551\) | 9668.52 | 0.747537 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −807.590 | −0.0621016 | ||||||||
\(554\) | 4156.79 | 0.318782 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2308.38 | −0.176074 | ||||||||
\(557\) | −6888.37 | −0.524003 | −0.262002 | − | 0.965067i | \(-0.584383\pi\) | ||||
−0.262002 | + | 0.965067i | \(0.584383\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −1264.83 | −0.0954443 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4984.68 | 0.374139 | ||||||||
\(563\) | −10537.1 | −0.788782 | −0.394391 | − | 0.918943i | \(-0.629045\pi\) | ||||
−0.394391 | + | 0.918943i | \(0.629045\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7381.92 | 0.549664 | ||||||||
\(566\) | 1746.27 | 0.129684 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6819.91 | 0.503798 | ||||||||
\(569\) | −26930.1 | −1.98413 | −0.992065 | − | 0.125722i | \(-0.959875\pi\) | ||||
−0.992065 | + | 0.125722i | \(0.959875\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3125.60 | −0.229076 | −0.114538 | − | 0.993419i | \(-0.536539\pi\) | ||||
−0.114538 | + | 0.993419i | \(0.536539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1054.36 | 0.0766696 | ||||||||
\(575\) | −7100.91 | −0.515006 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4787.13 | −0.345391 | −0.172696 | − | 0.984975i | \(-0.555248\pi\) | ||||
−0.172696 | + | 0.984975i | \(0.555248\pi\) | |||||||
\(578\) | −4833.81 | −0.347855 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9856.94 | −0.705668 | ||||||||
\(581\) | 973.566 | 0.0695186 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1533.22 | −0.108918 | ||||||||
\(584\) | 507.174 | 0.0359366 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2560.38 | −0.180492 | ||||||||
\(587\) | 18380.8 | 1.29243 | 0.646214 | − | 0.763156i | \(-0.276351\pi\) | ||||
0.646214 | + | 0.763156i | \(0.276351\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19695.3 | −1.37781 | ||||||||
\(590\) | −20207.6 | −1.41005 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5646.96 | −0.392042 | ||||||||
\(593\) | −13831.7 | −0.957843 | −0.478922 | − | 0.877858i | \(-0.658972\pi\) | ||||
−0.478922 | + | 0.877858i | \(0.658972\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3912.73 | −0.269590 | ||||||||
\(596\) | −9738.94 | −0.669333 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12248.6 | −0.835502 | −0.417751 | − | 0.908562i | \(-0.637182\pi\) | ||||
−0.417751 | + | 0.908562i | \(0.637182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9719.56 | 0.659682 | 0.329841 | − | 0.944036i | \(-0.393005\pi\) | ||||
0.329841 | + | 0.944036i | \(0.393005\pi\) | |||||||
\(602\) | 525.385 | 0.0355699 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7607.91 | 0.512519 | ||||||||
\(605\) | 46394.3 | 3.11768 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1607.83 | 0.107512 | 0.0537560 | − | 0.998554i | \(-0.482881\pi\) | ||||
0.0537560 | + | 0.998554i | \(0.482881\pi\) | |||||||
\(608\) | 20173.2 | 1.34561 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9096.25 | 0.603764 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14731.1 | −0.970610 | −0.485305 | − | 0.874345i | \(-0.661291\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661291\pi\) | |||||||
\(614\) | −11002.1 | −0.723142 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6169.68 | −0.403545 | ||||||||
\(617\) | 27951.8 | 1.82382 | 0.911909 | − | 0.410392i | \(-0.134608\pi\) | ||||
0.911909 | + | 0.410392i | \(0.134608\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16200.2 | −1.05192 | −0.525961 | − | 0.850509i | \(-0.676294\pi\) | ||||
−0.525961 | + | 0.850509i | \(0.676294\pi\) | |||||||
\(620\) | 20079.1 | 1.30064 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −630.364 | −0.0406355 | ||||||||
\(623\) | −526.903 | −0.0338843 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15263.8 | 0.976880 | ||||||||
\(626\) | 4482.22 | 0.286175 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4312.28 | 0.274011 | ||||||||
\(629\) | −17468.8 | −1.10735 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12731.8 | −0.803239 | −0.401619 | − | 0.915807i | \(-0.631553\pi\) | ||||
−0.401619 | + | 0.915807i | \(0.631553\pi\) | |||||||
\(632\) | −3480.73 | −0.219076 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 576.927 | 0.0361399 | ||||||||
\(635\) | −21836.6 | −1.36466 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8379.77 | −0.519997 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23756.7 | −1.46729 | ||||||||
\(641\) | 11556.9 | 0.712119 | 0.356059 | − | 0.934463i | \(-0.384120\pi\) | ||||
0.356059 | + | 0.934463i | \(0.384120\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9181.25 | 0.563100 | 0.281550 | − | 0.959547i | \(-0.409152\pi\) | ||||
0.281550 | + | 0.959547i | \(0.409152\pi\) | |||||||
\(644\) | −782.716 | −0.0478934 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6861.06 | 0.417871 | ||||||||
\(647\) | −5244.11 | −0.318651 | −0.159326 | − | 0.987226i | \(-0.550932\pi\) | ||||
−0.159326 | + | 0.987226i | \(0.550932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41804.8 | 2.52848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15377.5 | 0.923663 | ||||||||
\(653\) | 16421.4 | 0.984106 | 0.492053 | − | 0.870565i | \(-0.336247\pi\) | ||||
0.492053 | + | 0.870565i | \(0.336247\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16492.4 | 0.983832 | ||||||||
\(656\) | −1927.31 | −0.114709 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2392.24 | −0.141732 | ||||||||
\(659\) | −1838.11 | −0.108653 | −0.0543266 | − | 0.998523i | \(-0.517301\pi\) | ||||
−0.0543266 | + | 0.998523i | \(0.517301\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5500.93 | 0.323694 | 0.161847 | − | 0.986816i | \(-0.448255\pi\) | ||||
0.161847 | + | 0.986816i | \(0.448255\pi\) | |||||||
\(662\) | 6759.34 | 0.396841 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4196.10 | 0.245241 | ||||||||
\(665\) | −10071.1 | −0.587281 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2563.07 | −0.148789 | ||||||||
\(668\) | −8798.08 | −0.509593 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −19862.2 | −1.14529 | ||||||||
\(671\) | −18818.0 | −1.08266 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25986.7 | −1.48843 | −0.744216 | − | 0.667939i | \(-0.767177\pi\) | ||||
−0.744216 | + | 0.667939i | \(0.767177\pi\) | |||||||
\(674\) | −2699.91 | −0.154298 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11691.3 | 0.663714 | 0.331857 | − | 0.943330i | \(-0.392325\pi\) | ||||
0.331857 | + | 0.943330i | \(0.392325\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5606.05 | 0.316849 | ||||||||
\(680\) | −16864.0 | −0.951035 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 17070.0 | 0.958423 | ||||||||
\(683\) | −11111.5 | −0.622501 | −0.311251 | − | 0.950328i | \(-0.600748\pi\) | ||||
−0.311251 | + | 0.950328i | \(0.600748\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9455.37 | −0.527403 | ||||||||
\(686\) | 4896.36 | 0.272513 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −960.370 | −0.0532177 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7542.55 | 0.415242 | 0.207621 | − | 0.978209i | \(-0.433428\pi\) | ||||
0.207621 | + | 0.978209i | \(0.433428\pi\) | |||||||
\(692\) | −22511.3 | −1.23664 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3683.26 | −0.201462 | ||||||||
\(695\) | 7873.75 | 0.429738 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5962.11 | −0.324005 | ||||||||
\(698\) | 15214.7 | 0.825051 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6836.10 | 0.369114 | ||||||||
\(701\) | 8231.17 | 0.443491 | 0.221745 | − | 0.975105i | \(-0.428825\pi\) | ||||
0.221745 | + | 0.975105i | \(0.428825\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44963.6 | −2.41228 | ||||||||
\(704\) | −10884.2 | −0.582691 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6893.86 | 0.367498 | ||||||||
\(707\) | 8243.61 | 0.438519 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28044.6 | −1.48553 | −0.742764 | − | 0.669554i | \(-0.766485\pi\) | ||||
−0.742764 | + | 0.669554i | \(0.766485\pi\) | |||||||
\(710\) | −9648.64 | −0.510010 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2270.96 | −0.119534 | ||||||||
\(713\) | 5221.09 | 0.274238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15257.6 | −0.796374 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18561.3 | 0.964764 | ||||||||
\(719\) | −29686.4 | −1.53980 | −0.769901 | − | 0.638163i | \(-0.779694\pi\) | ||||
−0.769901 | + | 0.638163i | \(0.779694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7044.86 | 0.363889 | ||||||||
\(722\) | 7190.12 | 0.370621 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 24784.0 | 1.27223 | ||||||||
\(725\) | 22385.3 | 1.14672 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27654.5 | −1.41080 | −0.705398 | − | 0.708812i | \(-0.749232\pi\) | ||||
−0.705398 | + | 0.708812i | \(0.749232\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −717.537 | −0.0363798 | ||||||||
\(731\) | −2970.89 | −0.150318 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13077.5 | 0.658975 | 0.329488 | − | 0.944160i | \(-0.393124\pi\) | ||||
0.329488 | + | 0.944160i | \(0.393124\pi\) | |||||||
\(734\) | −4082.08 | −0.205276 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5347.79 | −0.267829 | ||||||||
\(737\) | 41090.3 | 2.05370 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4218.33 | 0.209978 | 0.104989 | − | 0.994473i | \(-0.466519\pi\) | ||||
0.104989 | + | 0.994473i | \(0.466519\pi\) | |||||||
\(740\) | 45839.9 | 2.27717 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −185.525 | −0.00917903 | ||||||||
\(743\) | 7725.54 | 0.381457 | 0.190728 | − | 0.981643i | \(-0.438915\pi\) | ||||
0.190728 | + | 0.981643i | \(0.438915\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33218.9 | 1.63362 | ||||||||
\(746\) | 14656.5 | 0.719319 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14470.6 | 0.707349 | ||||||||
\(749\) | −3983.29 | −0.194321 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7506.12 | 0.364717 | 0.182358 | − | 0.983232i | \(-0.441627\pi\) | ||||
0.182358 | + | 0.983232i | \(0.441627\pi\) | |||||||
\(752\) | 4372.87 | 0.212051 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25950.1 | −1.25089 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2741.62 | −0.131632 | −0.0658162 | − | 0.997832i | \(-0.520965\pi\) | ||||
−0.0658162 | + | 0.997832i | \(0.520965\pi\) | |||||||
\(758\) | −13768.0 | −0.659729 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −43406.9 | −2.07175 | ||||||||
\(761\) | 29740.0 | 1.41666 | 0.708328 | − | 0.705883i | \(-0.249450\pi\) | ||||
0.708328 | + | 0.705883i | \(0.249450\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2213.78 | 0.105038 | ||||||||
\(764\) | 7986.01 | 0.378172 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6129.18 | −0.289107 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19896.3 | 0.933004 | 0.466502 | − | 0.884520i | \(-0.345514\pi\) | ||||
0.466502 | + | 0.884520i | \(0.345514\pi\) | |||||||
\(770\) | 8728.72 | 0.408521 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −23426.6 | −1.09215 | ||||||||
\(773\) | −13601.3 | −0.632866 | −0.316433 | − | 0.948615i | \(-0.602485\pi\) | ||||
−0.316433 | + | 0.948615i | \(0.602485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −45600.1 | −2.11355 | ||||||||
\(776\) | 24162.2 | 1.11775 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4160.09 | 0.191705 | ||||||||
\(779\) | −15346.1 | −0.705818 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19960.8 | 0.914539 | ||||||||
\(782\) | −1818.83 | −0.0831727 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4316.81 | −0.196648 | ||||||||
\(785\) | −14708.9 | −0.668770 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1498.29 | 0.0678631 | 0.0339315 | − | 0.999424i | \(-0.489197\pi\) | ||||
0.0339315 | + | 0.999424i | \(0.489197\pi\) | |||||||
\(788\) | 19284.9 | 0.871824 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 4924.46 | 0.221778 | ||||||||
\(791\) | −1847.91 | −0.0830647 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 6703.49 | 0.299620 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19962.5 | 0.888885 | ||||||||
\(797\) | 3713.30 | 0.165034 | 0.0825168 | − | 0.996590i | \(-0.473704\pi\) | ||||
0.0825168 | + | 0.996590i | \(0.473704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13527.4 | 0.598955 | ||||||||
\(800\) | 46706.7 | 2.06416 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5743.20 | 0.252867 | ||||||||
\(803\) | 1484.42 | 0.0652354 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2669.80 | 0.116892 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 35530.2 | 1.54697 | ||||||||
\(809\) | 34527.6 | 1.50053 | 0.750263 | − | 0.661139i | \(-0.229927\pi\) | ||||
0.750263 | + | 0.661139i | \(0.229927\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37279.2 | 1.61412 | 0.807059 | − | 0.590471i | \(-0.201058\pi\) | ||||
0.807059 | + | 0.590471i | \(0.201058\pi\) | |||||||
\(812\) | 2467.48 | 0.106640 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 38970.3 | 1.67802 | ||||||||
\(815\) | −52451.6 | −2.25436 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7646.90 | −0.327455 | ||||||||
\(818\) | 10376.4 | 0.443525 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15645.2 | 0.666285 | ||||||||
\(821\) | 13877.9 | 0.589943 | 0.294972 | − | 0.955506i | \(-0.404690\pi\) | ||||
0.294972 | + | 0.955506i | \(0.404690\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18945.1 | 0.802410 | 0.401205 | − | 0.915988i | \(-0.368592\pi\) | ||||
0.401205 | + | 0.915988i | \(0.368592\pi\) | |||||||
\(824\) | 30363.5 | 1.28369 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5058.55 | 0.213086 | ||||||||
\(827\) | −7804.75 | −0.328171 | −0.164086 | − | 0.986446i | \(-0.552467\pi\) | ||||
−0.164086 | + | 0.986446i | \(0.552467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5784.85 | 0.242360 | 0.121180 | − | 0.992631i | \(-0.461332\pi\) | ||||
0.121180 | + | 0.992631i | \(0.461332\pi\) | |||||||
\(830\) | −5936.54 | −0.248265 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13354.0 | −0.555448 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30009.7 | 1.24375 | ||||||||
\(836\) | 37246.4 | 1.54090 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19224.3 | 0.792471 | ||||||||
\(839\) | −5011.42 | −0.206214 | −0.103107 | − | 0.994670i | \(-0.532878\pi\) | ||||
−0.103107 | + | 0.994670i | \(0.532878\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16309.0 | −0.668704 | ||||||||
\(842\) | −10514.2 | −0.430336 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12730.3 | 0.519190 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11613.9 | −0.471142 | ||||||||
\(848\) | 339.128 | 0.0137332 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15885.3 | 0.641013 | ||||||||
\(851\) | 11919.6 | 0.480138 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22059.0 | 0.885446 | 0.442723 | − | 0.896659i | \(-0.354013\pi\) | ||||
0.442723 | + | 0.896659i | \(0.354013\pi\) | |||||||
\(854\) | −2277.06 | −0.0912404 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17168.1 | −0.685506 | ||||||||
\(857\) | −13956.2 | −0.556283 | −0.278141 | − | 0.960540i | \(-0.589718\pi\) | ||||
−0.278141 | + | 0.960540i | \(0.589718\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12498.5 | 0.496442 | 0.248221 | − | 0.968703i | \(-0.420154\pi\) | ||||
0.248221 | + | 0.968703i | \(0.420154\pi\) | |||||||
\(860\) | 7795.92 | 0.309115 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11272.0 | −0.445391 | ||||||||
\(863\) | −38631.2 | −1.52378 | −0.761890 | − | 0.647707i | \(-0.775728\pi\) | ||||
−0.761890 | + | 0.647707i | \(0.775728\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 76784.7 | 3.01822 | ||||||||
\(866\) | 13842.3 | 0.543163 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5026.38 | −0.196551 | ||||||||
\(869\) | −10187.6 | −0.397687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 9541.46 | 0.370544 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4681.55 | −0.181185 | ||||||||
\(875\) | −11613.5 | −0.448696 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 856.756 | 0.0329881 | 0.0164941 | − | 0.999864i | \(-0.494750\pi\) | ||||
0.0164941 | + | 0.999864i | \(0.494750\pi\) | |||||||
\(878\) | 25759.2 | 0.990127 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −15955.6 | −0.611206 | ||||||||
\(881\) | −33638.6 | −1.28640 | −0.643198 | − | 0.765700i | \(-0.722393\pi\) | ||||
−0.643198 | + | 0.765700i | \(0.722393\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31109.1 | −1.18562 | −0.592811 | − | 0.805342i | \(-0.701982\pi\) | ||||
−0.592811 | + | 0.805342i | \(0.701982\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10328.2 | 0.391627 | ||||||||
\(887\) | −26080.3 | −0.987248 | −0.493624 | − | 0.869675i | \(-0.664328\pi\) | ||||
−0.493624 | + | 0.869675i | \(0.664328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5466.35 | 0.206227 | ||||||||
\(890\) | 3212.91 | 0.121008 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19455.2 | 0.730277 | ||||||||
\(893\) | 34818.8 | 1.30478 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52042.8 | 1.94369 | ||||||||
\(896\) | 5946.99 | 0.221736 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 215.142 | 0.00799486 | ||||||||
\(899\) | −16459.3 | −0.610621 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1049.09 | 0.0387905 | ||||||||
\(902\) | 13300.6 | 0.490977 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7964.56 | −0.293028 | ||||||||
\(905\) | −84536.9 | −3.10508 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20169.0 | 0.738369 | 0.369184 | − | 0.929356i | \(-0.379637\pi\) | ||||
0.369184 | + | 0.929356i | \(0.379637\pi\) | |||||||
\(908\) | 26977.3 | 0.985983 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19982.2 | −0.726716 | −0.363358 | − | 0.931650i | \(-0.618370\pi\) | ||||
−0.363358 | + | 0.931650i | \(0.618370\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12281.3 | 0.445184 | ||||||||
\(914\) | 27068.5 | 0.979593 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24771.7 | −0.893538 | ||||||||
\(917\) | −4128.52 | −0.148676 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38513.1 | 1.38241 | 0.691203 | − | 0.722661i | \(-0.257081\pi\) | ||||
0.691203 | + | 0.722661i | \(0.257081\pi\) | |||||||
\(920\) | 11506.9 | 0.412360 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3500.70 | 0.125043 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −104103. | −3.70043 | ||||||||
\(926\) | −21020.4 | −0.745975 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 16858.7 | 0.596352 | ||||||||
\(929\) | 23218.9 | 0.820009 | 0.410005 | − | 0.912083i | \(-0.365527\pi\) | ||||
0.410005 | + | 0.912083i | \(0.365527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34372.3 | −1.21000 | ||||||||
\(932\) | −20650.1 | −0.725768 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5307.99 | 0.185956 | ||||||||
\(935\) | −49358.3 | −1.72640 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11112.9 | −0.387452 | −0.193726 | − | 0.981056i | \(-0.562057\pi\) | ||||
−0.193726 | + | 0.981056i | \(0.562057\pi\) | |||||||
\(938\) | 4972.08 | 0.173075 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −35497.3 | −1.23170 | ||||||||
\(941\) | 45570.4 | 1.57869 | 0.789347 | − | 0.613947i | \(-0.210419\pi\) | ||||
0.789347 | + | 0.613947i | \(0.210419\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4068.16 | 0.140485 | ||||||||
\(944\) | −9246.71 | −0.318808 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6627.62 | 0.227783 | ||||||||
\(947\) | 34903.9 | 1.19770 | 0.598852 | − | 0.800860i | \(-0.295624\pi\) | ||||
0.598852 | + | 0.800860i | \(0.295624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 40887.8 | 1.39640 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4221.55 | 0.143720 | ||||||||
\(953\) | 2886.52 | 0.0981151 | 0.0490575 | − | 0.998796i | \(-0.484378\pi\) | ||||
0.0490575 | + | 0.998796i | \(0.484378\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27239.8 | −0.922994 | ||||||||
\(956\) | −12679.0 | −0.428943 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4789.03 | −0.161510 | ||||||||
\(959\) | 2366.96 | 0.0797008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3737.42 | 0.125455 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 37074.8 | 1.23869 | ||||||||
\(965\) | 79906.8 | 2.66559 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11593.8 | −0.385556 | −0.192778 | − | 0.981242i | \(-0.561750\pi\) | ||||
−0.192778 | + | 0.981242i | \(0.561750\pi\) | |||||||
\(968\) | −50056.1 | −1.66205 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −34184.1 | −1.13153 | ||||||||
\(971\) | 4952.12 | 0.163667 | 0.0818337 | − | 0.996646i | \(-0.473922\pi\) | ||||
0.0818337 | + | 0.996646i | \(0.473922\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1971.03 | −0.0649418 | ||||||||
\(974\) | −9153.33 | −0.301121 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4162.32 | 0.136509 | ||||||||
\(977\) | −19650.1 | −0.643462 | −0.321731 | − | 0.946831i | \(-0.604265\pi\) | ||||
−0.321731 | + | 0.946831i | \(0.604265\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6646.77 | −0.216988 | ||||||||
\(980\) | 35042.2 | 1.14223 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14350.8 | 0.466347 | ||||||||
\(983\) | 56818.4 | 1.84357 | 0.921783 | − | 0.387707i | \(-0.126733\pi\) | ||||
0.921783 | + | 0.387707i | \(0.126733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −65779.7 | −2.12783 | ||||||||
\(986\) | 5733.78 | 0.185193 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2027.15 | 0.0651764 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19120.4 | −0.612897 | −0.306448 | − | 0.951887i | \(-0.599141\pi\) | ||||
−0.306448 | + | 0.951887i | \(0.599141\pi\) | |||||||
\(992\) | −34342.1 | −1.09915 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2415.34 | 0.0770723 | ||||||||
\(995\) | −68090.9 | −2.16947 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38887.9 | 1.23530 | 0.617650 | − | 0.786453i | \(-0.288085\pi\) | ||||
0.617650 | + | 0.786453i | \(0.288085\pi\) | |||||||
\(998\) | 7712.07 | 0.244611 | ||||||||
\(999\) | 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.u.1.2 | 3 | ||
3.2 | odd | 2 | 507.4.a.h.1.2 | 3 | |||
13.12 | even | 2 | 117.4.a.f.1.2 | 3 | |||
39.5 | even | 4 | 507.4.b.g.337.4 | 6 | |||
39.8 | even | 4 | 507.4.b.g.337.3 | 6 | |||
39.38 | odd | 2 | 39.4.a.c.1.2 | ✓ | 3 | ||
52.51 | odd | 2 | 1872.4.a.bk.1.1 | 3 | |||
156.155 | even | 2 | 624.4.a.t.1.3 | 3 | |||
195.194 | odd | 2 | 975.4.a.l.1.2 | 3 | |||
273.272 | even | 2 | 1911.4.a.k.1.2 | 3 | |||
312.77 | odd | 2 | 2496.4.a.bl.1.1 | 3 | |||
312.155 | even | 2 | 2496.4.a.bp.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.a.c.1.2 | ✓ | 3 | 39.38 | odd | 2 | ||
117.4.a.f.1.2 | 3 | 13.12 | even | 2 | |||
507.4.a.h.1.2 | 3 | 3.2 | odd | 2 | |||
507.4.b.g.337.3 | 6 | 39.8 | even | 4 | |||
507.4.b.g.337.4 | 6 | 39.5 | even | 4 | |||
624.4.a.t.1.3 | 3 | 156.155 | even | 2 | |||
975.4.a.l.1.2 | 3 | 195.194 | odd | 2 | |||
1521.4.a.u.1.2 | 3 | 1.1 | even | 1 | trivial | ||
1872.4.a.bk.1.1 | 3 | 52.51 | odd | 2 | |||
1911.4.a.k.1.2 | 3 | 273.272 | even | 2 | |||
2496.4.a.bl.1.1 | 3 | 312.77 | odd | 2 | |||
2496.4.a.bp.1.1 | 3 | 312.155 | even | 2 |