Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,4,Mod(1,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2070.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.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: | \(122.133953712\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - 2x^{3} - 60x^{2} - 45x + 108 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 230) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.01192\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.98517 | 0.161184 | 0.0805921 | − | 0.996747i | \(-0.474319\pi\) | ||||
0.0805921 | + | 0.996747i | \(0.474319\pi\) | |||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.0000 | 0.316228 | ||||||||
\(11\) | −68.6262 | −1.88105 | −0.940527 | − | 0.339720i | \(-0.889668\pi\) | ||||
−0.940527 | + | 0.339720i | \(0.889668\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.0028 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(14\) | −5.97035 | −0.113974 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −106.208 | −1.51525 | −0.757623 | − | 0.652693i | \(-0.773639\pi\) | ||||
−0.757623 | + | 0.652693i | \(0.773639\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −48.4891 | −0.585482 | −0.292741 | − | 0.956192i | \(-0.594567\pi\) | ||||
−0.292741 | + | 0.956192i | \(0.594567\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 137.252 | 1.33011 | ||||||||
\(23\) | 23.0000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 24.0055 | 0.181072 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 11.9407 | 0.0805921 | ||||||||
\(29\) | −135.226 | −0.865890 | −0.432945 | − | 0.901420i | \(-0.642526\pi\) | ||||
−0.432945 | + | 0.901420i | \(0.642526\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −230.782 | −1.33709 | −0.668544 | − | 0.743673i | \(-0.733082\pi\) | ||||
−0.668544 | + | 0.743673i | \(0.733082\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 212.416 | 1.07144 | ||||||||
\(35\) | −14.9259 | −0.0720838 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −107.956 | −0.479672 | −0.239836 | − | 0.970813i | \(-0.577094\pi\) | ||||
−0.239836 | + | 0.970813i | \(0.577094\pi\) | |||||||
\(38\) | 96.9782 | 0.413998 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 40.0000 | 0.158114 | ||||||||
\(41\) | −394.637 | −1.50322 | −0.751610 | − | 0.659608i | \(-0.770722\pi\) | ||||
−0.751610 | + | 0.659608i | \(0.770722\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 136.063 | 0.482543 | 0.241272 | − | 0.970458i | \(-0.422436\pi\) | ||||
0.241272 | + | 0.970458i | \(0.422436\pi\) | |||||||
\(44\) | −274.505 | −0.940527 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 50.4512 | 0.156576 | 0.0782880 | − | 0.996931i | \(-0.475055\pi\) | ||||
0.0782880 | + | 0.996931i | \(0.475055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −334.089 | −0.974020 | ||||||||
\(50\) | −50.0000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −48.0110 | −0.128037 | ||||||||
\(53\) | 414.707 | 1.07480 | 0.537400 | − | 0.843327i | \(-0.319406\pi\) | ||||
0.537400 | + | 0.843327i | \(0.319406\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 343.131 | 0.841232 | ||||||||
\(56\) | −23.8814 | −0.0569872 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 270.452 | 0.612277 | ||||||||
\(59\) | 183.586 | 0.405100 | 0.202550 | − | 0.979272i | \(-0.435077\pi\) | ||||
0.202550 | + | 0.979272i | \(0.435077\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −98.4751 | −0.206696 | −0.103348 | − | 0.994645i | \(-0.532956\pi\) | ||||
−0.103348 | + | 0.994645i | \(0.532956\pi\) | |||||||
\(62\) | 461.565 | 0.945464 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 60.0138 | 0.114520 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 136.925 | 0.249672 | 0.124836 | − | 0.992177i | \(-0.460160\pi\) | ||||
0.124836 | + | 0.992177i | \(0.460160\pi\) | |||||||
\(68\) | −424.831 | −0.757623 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 29.8517 | 0.0509709 | ||||||||
\(71\) | 708.800 | 1.18478 | 0.592388 | − | 0.805653i | \(-0.298185\pi\) | ||||
0.592388 | + | 0.805653i | \(0.298185\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −689.605 | −1.10565 | −0.552823 | − | 0.833299i | \(-0.686449\pi\) | ||||
−0.552823 | + | 0.833299i | \(0.686449\pi\) | |||||||
\(74\) | 215.912 | 0.339179 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −193.956 | −0.292741 | ||||||||
\(77\) | −204.861 | −0.303196 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 546.583 | 0.778423 | 0.389212 | − | 0.921148i | \(-0.372748\pi\) | ||||
0.389212 | + | 0.921148i | \(0.372748\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 789.275 | 1.06294 | ||||||||
\(83\) | 20.2622 | 0.0267959 | 0.0133980 | − | 0.999910i | \(-0.495735\pi\) | ||||
0.0133980 | + | 0.999910i | \(0.495735\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 531.039 | 0.677638 | ||||||||
\(86\) | −272.125 | −0.341210 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 549.010 | 0.665053 | ||||||||
\(89\) | 1087.31 | 1.29499 | 0.647495 | − | 0.762069i | \(-0.275817\pi\) | ||||
0.647495 | + | 0.762069i | \(0.275817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −35.8303 | −0.0412751 | ||||||||
\(92\) | 92.0000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −100.902 | −0.110716 | ||||||||
\(95\) | 242.445 | 0.261836 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1115.90 | −1.16807 | −0.584036 | − | 0.811728i | \(-0.698527\pi\) | ||||
−0.584036 | + | 0.811728i | \(0.698527\pi\) | |||||||
\(98\) | 668.177 | 0.688736 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | 134.565 | 0.132572 | 0.0662859 | − | 0.997801i | \(-0.478885\pi\) | ||||
0.0662859 | + | 0.997801i | \(0.478885\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −925.953 | −0.885795 | −0.442898 | − | 0.896572i | \(-0.646049\pi\) | ||||
−0.442898 | + | 0.896572i | \(0.646049\pi\) | |||||||
\(104\) | 96.0221 | 0.0905360 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −829.415 | −0.759999 | ||||||||
\(107\) | −1871.13 | −1.69055 | −0.845273 | − | 0.534334i | \(-0.820562\pi\) | ||||
−0.845273 | + | 0.534334i | \(0.820562\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −978.242 | −0.859620 | −0.429810 | − | 0.902919i | \(-0.641419\pi\) | ||||
−0.429810 | + | 0.902919i | \(0.641419\pi\) | |||||||
\(110\) | −686.262 | −0.594841 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 47.7628 | 0.0402961 | ||||||||
\(113\) | 1760.45 | 1.46557 | 0.732786 | − | 0.680459i | \(-0.238220\pi\) | ||||
0.732786 | + | 0.680459i | \(0.238220\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −115.000 | −0.0932505 | ||||||||
\(116\) | −540.903 | −0.432945 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −367.172 | −0.286449 | ||||||||
\(119\) | −317.049 | −0.244234 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3378.56 | 2.53836 | ||||||||
\(122\) | 196.950 | 0.146156 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −923.129 | −0.668544 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1260.87 | −0.880980 | −0.440490 | − | 0.897758i | \(-0.645195\pi\) | ||||
−0.440490 | + | 0.897758i | \(0.645195\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −120.028 | −0.0809778 | ||||||||
\(131\) | −444.283 | −0.296314 | −0.148157 | − | 0.988964i | \(-0.547334\pi\) | ||||
−0.148157 | + | 0.988964i | \(0.547334\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −144.748 | −0.0943705 | ||||||||
\(134\) | −273.849 | −0.176545 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 849.662 | 0.535720 | ||||||||
\(137\) | −429.072 | −0.267577 | −0.133789 | − | 0.991010i | \(-0.542714\pi\) | ||||
−0.133789 | + | 0.991010i | \(0.542714\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −249.755 | −0.152402 | −0.0762012 | − | 0.997092i | \(-0.524279\pi\) | ||||
−0.0762012 | + | 0.997092i | \(0.524279\pi\) | |||||||
\(140\) | −59.7035 | −0.0360419 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1417.60 | −0.837763 | ||||||||
\(143\) | 823.704 | 0.481689 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 676.129 | 0.387238 | ||||||||
\(146\) | 1379.21 | 0.781809 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −431.824 | −0.239836 | ||||||||
\(149\) | 1564.18 | 0.860020 | 0.430010 | − | 0.902824i | \(-0.358510\pi\) | ||||
0.430010 | + | 0.902824i | \(0.358510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1860.04 | −1.00244 | −0.501219 | − | 0.865321i | \(-0.667115\pi\) | ||||
−0.501219 | + | 0.865321i | \(0.667115\pi\) | |||||||
\(152\) | 387.913 | 0.206999 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 409.722 | 0.214392 | ||||||||
\(155\) | 1153.91 | 0.597964 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2834.52 | 1.44089 | 0.720445 | − | 0.693512i | \(-0.243938\pi\) | ||||
0.720445 | + | 0.693512i | \(0.243938\pi\) | |||||||
\(158\) | −1093.17 | −0.550428 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 160.000 | 0.0790569 | ||||||||
\(161\) | 68.6590 | 0.0336092 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2114.51 | 1.01608 | 0.508041 | − | 0.861333i | \(-0.330370\pi\) | ||||
0.508041 | + | 0.861333i | \(0.330370\pi\) | |||||||
\(164\) | −1578.55 | −0.751610 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −40.5244 | −0.0189476 | ||||||||
\(167\) | −2487.41 | −1.15258 | −0.576291 | − | 0.817244i | \(-0.695501\pi\) | ||||
−0.576291 | + | 0.817244i | \(0.695501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2052.93 | −0.934426 | ||||||||
\(170\) | −1062.08 | −0.479163 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 544.251 | 0.241272 | ||||||||
\(173\) | −3672.32 | −1.61388 | −0.806939 | − | 0.590634i | \(-0.798878\pi\) | ||||
−0.806939 | + | 0.590634i | \(0.798878\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 74.6293 | 0.0322368 | ||||||||
\(176\) | −1098.02 | −0.470263 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2174.61 | −0.915697 | ||||||||
\(179\) | 3224.63 | 1.34648 | 0.673240 | − | 0.739424i | \(-0.264902\pi\) | ||||
0.673240 | + | 0.739424i | \(0.264902\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2224.23 | −0.913401 | −0.456700 | − | 0.889621i | \(-0.650969\pi\) | ||||
−0.456700 | + | 0.889621i | \(0.650969\pi\) | |||||||
\(182\) | 71.6606 | 0.0291859 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | 539.780 | 0.214516 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7288.64 | 2.85026 | ||||||||
\(188\) | 201.805 | 0.0782880 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −484.891 | −0.185146 | ||||||||
\(191\) | −3273.53 | −1.24013 | −0.620063 | − | 0.784552i | \(-0.712893\pi\) | ||||
−0.620063 | + | 0.784552i | \(0.712893\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5126.86 | 1.91212 | 0.956062 | − | 0.293166i | \(-0.0947089\pi\) | ||||
0.956062 | + | 0.293166i | \(0.0947089\pi\) | |||||||
\(194\) | 2231.81 | 0.825951 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1336.35 | −0.487010 | ||||||||
\(197\) | −3262.57 | −1.17994 | −0.589971 | − | 0.807425i | \(-0.700861\pi\) | ||||
−0.589971 | + | 0.807425i | \(0.700861\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −168.282 | −0.0599457 | −0.0299728 | − | 0.999551i | \(-0.509542\pi\) | ||||
−0.0299728 | + | 0.999551i | \(0.509542\pi\) | |||||||
\(200\) | −200.000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −269.131 | −0.0937424 | ||||||||
\(203\) | −403.673 | −0.139568 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1973.19 | 0.672260 | ||||||||
\(206\) | 1851.91 | 0.626352 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −192.044 | −0.0640186 | ||||||||
\(209\) | 3327.62 | 1.10132 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4197.01 | 1.36936 | 0.684678 | − | 0.728846i | \(-0.259943\pi\) | ||||
0.684678 | + | 0.728846i | \(0.259943\pi\) | |||||||
\(212\) | 1658.83 | 0.537400 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3742.25 | 1.19540 | ||||||||
\(215\) | −680.313 | −0.215800 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −688.925 | −0.215518 | ||||||||
\(218\) | 1956.48 | 0.607843 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1372.52 | 0.420616 | ||||||||
\(221\) | 1274.79 | 0.388015 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5192.66 | 1.55931 | 0.779656 | − | 0.626208i | \(-0.215394\pi\) | ||||
0.779656 | + | 0.626208i | \(0.215394\pi\) | |||||||
\(224\) | −95.5256 | −0.0284936 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3520.91 | −1.03632 | ||||||||
\(227\) | −4701.24 | −1.37459 | −0.687295 | − | 0.726378i | \(-0.741202\pi\) | ||||
−0.687295 | + | 0.726378i | \(0.741202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2125.17 | −0.613255 | −0.306628 | − | 0.951830i | \(-0.599201\pi\) | ||||
−0.306628 | + | 0.951830i | \(0.599201\pi\) | |||||||
\(230\) | 230.000 | 0.0659380 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1081.81 | 0.306138 | ||||||||
\(233\) | 1646.67 | 0.462992 | 0.231496 | − | 0.972836i | \(-0.425638\pi\) | ||||
0.231496 | + | 0.972836i | \(0.425638\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −252.256 | −0.0700229 | ||||||||
\(236\) | 734.345 | 0.202550 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 634.097 | 0.172699 | ||||||||
\(239\) | −2877.88 | −0.778888 | −0.389444 | − | 0.921050i | \(-0.627333\pi\) | ||||
−0.389444 | + | 0.921050i | \(0.627333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4244.54 | −1.13450 | −0.567251 | − | 0.823545i | \(-0.691993\pi\) | ||||
−0.567251 | + | 0.823545i | \(0.691993\pi\) | |||||||
\(242\) | −6757.12 | −1.79489 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −393.900 | −0.103348 | ||||||||
\(245\) | 1670.44 | 0.435595 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 582.003 | 0.149927 | ||||||||
\(248\) | 1846.26 | 0.472732 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 250.000 | 0.0632456 | ||||||||
\(251\) | −4401.99 | −1.10698 | −0.553488 | − | 0.832857i | \(-0.686704\pi\) | ||||
−0.553488 | + | 0.832857i | \(0.686704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1578.40 | −0.392227 | ||||||||
\(254\) | 2521.75 | 0.622947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1694.78 | −0.411352 | −0.205676 | − | 0.978620i | \(-0.565939\pi\) | ||||
−0.205676 | + | 0.978620i | \(0.565939\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −322.268 | −0.0773156 | ||||||||
\(260\) | 240.055 | 0.0572600 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 888.566 | 0.209526 | ||||||||
\(263\) | 727.462 | 0.170560 | 0.0852799 | − | 0.996357i | \(-0.472822\pi\) | ||||
0.0852799 | + | 0.996357i | \(0.472822\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2073.54 | −0.480666 | ||||||||
\(266\) | 289.497 | 0.0667300 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 547.698 | 0.124836 | ||||||||
\(269\) | −94.9937 | −0.0215311 | −0.0107656 | − | 0.999942i | \(-0.503427\pi\) | ||||
−0.0107656 | + | 0.999942i | \(0.503427\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5321.54 | 1.19284 | 0.596422 | − | 0.802671i | \(-0.296589\pi\) | ||||
0.596422 | + | 0.802671i | \(0.296589\pi\) | |||||||
\(272\) | −1699.32 | −0.378811 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 858.143 | 0.189206 | ||||||||
\(275\) | −1715.66 | −0.376211 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2561.25 | 0.555562 | 0.277781 | − | 0.960644i | \(-0.410401\pi\) | ||||
0.277781 | + | 0.960644i | \(0.410401\pi\) | |||||||
\(278\) | 499.510 | 0.107765 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 119.407 | 0.0254855 | ||||||||
\(281\) | 8753.73 | 1.85838 | 0.929188 | − | 0.369606i | \(-0.120507\pi\) | ||||
0.929188 | + | 0.369606i | \(0.120507\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2400.14 | −0.504147 | −0.252073 | − | 0.967708i | \(-0.581112\pi\) | ||||
−0.252073 | + | 0.967708i | \(0.581112\pi\) | |||||||
\(284\) | 2835.20 | 0.592388 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1647.41 | −0.340606 | ||||||||
\(287\) | −1178.06 | −0.242295 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6367.09 | 1.29597 | ||||||||
\(290\) | −1352.26 | −0.273818 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2758.42 | −0.552823 | ||||||||
\(293\) | −1045.56 | −0.208472 | −0.104236 | − | 0.994553i | \(-0.533240\pi\) | ||||
−0.104236 | + | 0.994553i | \(0.533240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −917.931 | −0.181166 | ||||||||
\(296\) | 863.649 | 0.169590 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3128.37 | −0.608126 | ||||||||
\(299\) | −276.063 | −0.0533952 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 406.171 | 0.0777784 | ||||||||
\(302\) | 3720.08 | 0.708830 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −775.826 | −0.146371 | ||||||||
\(305\) | 492.376 | 0.0924372 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7905.84 | −1.46974 | −0.734870 | − | 0.678208i | \(-0.762757\pi\) | ||||
−0.734870 | + | 0.678208i | \(0.762757\pi\) | |||||||
\(308\) | −819.445 | −0.151598 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2307.82 | −0.422824 | ||||||||
\(311\) | 9227.63 | 1.68248 | 0.841240 | − | 0.540662i | \(-0.181826\pi\) | ||||
0.841240 | + | 0.540662i | \(0.181826\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2712.57 | 0.489852 | 0.244926 | − | 0.969542i | \(-0.421236\pi\) | ||||
0.244926 | + | 0.969542i | \(0.421236\pi\) | |||||||
\(314\) | −5669.05 | −1.01886 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2186.33 | 0.389212 | ||||||||
\(317\) | 3440.29 | 0.609546 | 0.304773 | − | 0.952425i | \(-0.401419\pi\) | ||||
0.304773 | + | 0.952425i | \(0.401419\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9280.04 | 1.62879 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −137.318 | −0.0237653 | ||||||||
\(323\) | 5149.92 | 0.887149 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −300.069 | −0.0512149 | ||||||||
\(326\) | −4229.03 | −0.718479 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3157.10 | 0.531468 | ||||||||
\(329\) | 150.606 | 0.0252376 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3259.75 | 0.541305 | 0.270652 | − | 0.962677i | \(-0.412761\pi\) | ||||
0.270652 | + | 0.962677i | \(0.412761\pi\) | |||||||
\(332\) | 81.0487 | 0.0133980 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4974.81 | 0.814999 | ||||||||
\(335\) | −684.623 | −0.111657 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7163.38 | 1.15790 | 0.578952 | − | 0.815361i | \(-0.303462\pi\) | ||||
0.578952 | + | 0.815361i | \(0.303462\pi\) | |||||||
\(338\) | 4105.87 | 0.660739 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2124.16 | 0.338819 | ||||||||
\(341\) | 15837.7 | 2.51513 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2021.23 | −0.318181 | ||||||||
\(344\) | −1088.50 | −0.170605 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7344.63 | 1.14118 | ||||||||
\(347\) | 1833.45 | 0.283645 | 0.141822 | − | 0.989892i | \(-0.454704\pi\) | ||||
0.141822 | + | 0.989892i | \(0.454704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10400.3 | −1.59517 | −0.797583 | − | 0.603209i | \(-0.793888\pi\) | ||||
−0.797583 | + | 0.603209i | \(0.793888\pi\) | |||||||
\(350\) | −149.259 | −0.0227949 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2196.04 | 0.332526 | ||||||||
\(353\) | 3156.48 | 0.475928 | 0.237964 | − | 0.971274i | \(-0.423520\pi\) | ||||
0.237964 | + | 0.971274i | \(0.423520\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3544.00 | −0.529848 | ||||||||
\(356\) | 4349.22 | 0.647495 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6449.25 | −0.952105 | ||||||||
\(359\) | 9324.16 | 1.37078 | 0.685390 | − | 0.728176i | \(-0.259632\pi\) | ||||
0.685390 | + | 0.728176i | \(0.259632\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4507.81 | −0.657211 | ||||||||
\(362\) | 4448.45 | 0.645872 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −143.321 | −0.0206376 | ||||||||
\(365\) | 3448.02 | 0.494460 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3802.68 | 0.540867 | 0.270434 | − | 0.962739i | \(-0.412833\pi\) | ||||
0.270434 | + | 0.962739i | \(0.412833\pi\) | |||||||
\(368\) | 368.000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1079.56 | −0.151686 | ||||||||
\(371\) | 1237.97 | 0.173241 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8928.03 | −1.23935 | −0.619673 | − | 0.784860i | \(-0.712735\pi\) | ||||
−0.619673 | + | 0.784860i | \(0.712735\pi\) | |||||||
\(374\) | −14577.3 | −2.01544 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −403.610 | −0.0553580 | ||||||||
\(377\) | 1623.08 | 0.221732 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3798.13 | 0.514768 | 0.257384 | − | 0.966309i | \(-0.417140\pi\) | ||||
0.257384 | + | 0.966309i | \(0.417140\pi\) | |||||||
\(380\) | 969.782 | 0.130918 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6547.05 | 0.876901 | ||||||||
\(383\) | −1456.41 | −0.194306 | −0.0971530 | − | 0.995269i | \(-0.530974\pi\) | ||||
−0.0971530 | + | 0.995269i | \(0.530974\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1024.31 | 0.135593 | ||||||||
\(386\) | −10253.7 | −1.35208 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4463.62 | −0.584036 | ||||||||
\(389\) | 8211.34 | 1.07026 | 0.535130 | − | 0.844769i | \(-0.320262\pi\) | ||||
0.535130 | + | 0.844769i | \(0.320262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2442.78 | −0.315950 | ||||||||
\(392\) | 2672.71 | 0.344368 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6525.14 | 0.834345 | ||||||||
\(395\) | −2732.92 | −0.348121 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 914.365 | 0.115594 | 0.0577968 | − | 0.998328i | \(-0.481592\pi\) | ||||
0.0577968 | + | 0.998328i | \(0.481592\pi\) | |||||||
\(398\) | 336.564 | 0.0423880 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | −9414.97 | −1.17247 | −0.586236 | − | 0.810140i | \(-0.699391\pi\) | ||||
−0.586236 | + | 0.810140i | \(0.699391\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2770.02 | 0.342394 | ||||||||
\(404\) | 538.261 | 0.0662859 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 807.345 | 0.0986894 | ||||||||
\(407\) | 7408.62 | 0.902289 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3299.41 | 0.398889 | 0.199444 | − | 0.979909i | \(-0.436086\pi\) | ||||
0.199444 | + | 0.979909i | \(0.436086\pi\) | |||||||
\(410\) | −3946.37 | −0.475360 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3703.81 | −0.442898 | ||||||||
\(413\) | 548.037 | 0.0652957 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −101.311 | −0.0119835 | ||||||||
\(416\) | 384.088 | 0.0452680 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6655.25 | −0.778753 | ||||||||
\(419\) | 3554.64 | 0.414452 | 0.207226 | − | 0.978293i | \(-0.433556\pi\) | ||||
0.207226 | + | 0.978293i | \(0.433556\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11655.5 | 1.34930 | 0.674649 | − | 0.738139i | \(-0.264295\pi\) | ||||
0.674649 | + | 0.738139i | \(0.264295\pi\) | |||||||
\(422\) | −8394.02 | −0.968281 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3317.66 | −0.380000 | ||||||||
\(425\) | −2655.19 | −0.303049 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −293.965 | −0.0333161 | ||||||||
\(428\) | −7484.50 | −0.845273 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1360.63 | 0.152594 | ||||||||
\(431\) | −4727.38 | −0.528330 | −0.264165 | − | 0.964478i | \(-0.585096\pi\) | ||||
−0.264165 | + | 0.964478i | \(0.585096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3936.24 | 0.436868 | 0.218434 | − | 0.975852i | \(-0.429905\pi\) | ||||
0.218434 | + | 0.975852i | \(0.429905\pi\) | |||||||
\(434\) | 1377.85 | 0.152394 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3912.97 | −0.429810 | ||||||||
\(437\) | −1115.25 | −0.122081 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6859.77 | 0.745784 | 0.372892 | − | 0.927875i | \(-0.378366\pi\) | ||||
0.372892 | + | 0.927875i | \(0.378366\pi\) | |||||||
\(440\) | −2745.05 | −0.297421 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2549.57 | −0.274368 | ||||||||
\(443\) | −16814.4 | −1.80334 | −0.901668 | − | 0.432430i | \(-0.857656\pi\) | ||||
−0.901668 | + | 0.432430i | \(0.857656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5436.53 | −0.579137 | ||||||||
\(446\) | −10385.3 | −1.10260 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 191.051 | 0.0201480 | ||||||||
\(449\) | −10673.8 | −1.12189 | −0.560943 | − | 0.827855i | \(-0.689561\pi\) | ||||
−0.560943 | + | 0.827855i | \(0.689561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27082.5 | 2.82764 | ||||||||
\(452\) | 7041.82 | 0.732786 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9402.47 | 0.971982 | ||||||||
\(455\) | 179.152 | 0.0184588 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15493.0 | 1.58585 | 0.792926 | − | 0.609318i | \(-0.208557\pi\) | ||||
0.792926 | + | 0.609318i | \(0.208557\pi\) | |||||||
\(458\) | 4250.35 | 0.433637 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −460.000 | −0.0466252 | ||||||||
\(461\) | 10793.0 | 1.09041 | 0.545207 | − | 0.838302i | \(-0.316451\pi\) | ||||
0.545207 | + | 0.838302i | \(0.316451\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6165.87 | −0.618904 | −0.309452 | − | 0.950915i | \(-0.600146\pi\) | ||||
−0.309452 | + | 0.950915i | \(0.600146\pi\) | |||||||
\(464\) | −2163.61 | −0.216473 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3293.34 | −0.327385 | ||||||||
\(467\) | 10736.4 | 1.06386 | 0.531929 | − | 0.846789i | \(-0.321467\pi\) | ||||
0.531929 | + | 0.846789i | \(0.321467\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 408.744 | 0.0402431 | ||||||||
\(470\) | 504.512 | 0.0495137 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1468.69 | −0.143224 | ||||||||
\(473\) | −9337.47 | −0.907690 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1212.23 | −0.117096 | ||||||||
\(476\) | −1268.19 | −0.122117 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5755.75 | 0.550757 | ||||||||
\(479\) | −6333.30 | −0.604125 | −0.302062 | − | 0.953288i | \(-0.597675\pi\) | ||||
−0.302062 | + | 0.953288i | \(0.597675\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1295.77 | 0.122832 | ||||||||
\(482\) | 8489.08 | 0.802213 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13514.2 | 1.26918 | ||||||||
\(485\) | 5579.52 | 0.522377 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16833.3 | −1.56630 | −0.783149 | − | 0.621834i | \(-0.786388\pi\) | ||||
−0.783149 | + | 0.621834i | \(0.786388\pi\) | |||||||
\(488\) | 787.801 | 0.0730780 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3340.89 | −0.308012 | ||||||||
\(491\) | 4.80428 | 0.000441577 0 | 0.000220788 | − | 1.00000i | \(-0.499930\pi\) | ||||
0.000220788 | 1.00000i | \(0.499930\pi\) | ||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14362.0 | 1.31204 | ||||||||
\(494\) | −1164.01 | −0.106014 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3692.52 | −0.334272 | ||||||||
\(497\) | 2115.89 | 0.190967 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21206.9 | 1.90251 | 0.951253 | − | 0.308412i | \(-0.0997975\pi\) | ||||
0.951253 | + | 0.308412i | \(0.0997975\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8803.98 | 0.782750 | ||||||||
\(503\) | −14513.7 | −1.28655 | −0.643275 | − | 0.765635i | \(-0.722425\pi\) | ||||
−0.643275 | + | 0.765635i | \(0.722425\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −672.827 | −0.0592879 | ||||||||
\(506\) | 3156.81 | 0.277346 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5043.49 | −0.440490 | ||||||||
\(509\) | 2545.77 | 0.221689 | 0.110844 | − | 0.993838i | \(-0.464645\pi\) | ||||
0.110844 | + | 0.993838i | \(0.464645\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2058.59 | −0.178213 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3389.56 | 0.290870 | ||||||||
\(515\) | 4629.77 | 0.396140 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3462.28 | −0.294528 | ||||||||
\(518\) | 644.535 | 0.0546704 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −480.110 | −0.0404889 | ||||||||
\(521\) | 21343.1 | 1.79473 | 0.897367 | − | 0.441285i | \(-0.145477\pi\) | ||||
0.897367 | + | 0.441285i | \(0.145477\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −789.191 | −0.0659827 | −0.0329913 | − | 0.999456i | \(-0.510503\pi\) | ||||
−0.0329913 | + | 0.999456i | \(0.510503\pi\) | |||||||
\(524\) | −1777.13 | −0.148157 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1454.92 | −0.120604 | ||||||||
\(527\) | 24510.9 | 2.02602 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | 4147.07 | 0.339882 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −578.994 | −0.0471852 | ||||||||
\(533\) | 4736.74 | 0.384936 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9355.63 | 0.756036 | ||||||||
\(536\) | −1095.40 | −0.0882723 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 189.987 | 0.0152248 | ||||||||
\(539\) | 22927.2 | 1.83218 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13405.1 | 1.06531 | 0.532653 | − | 0.846334i | \(-0.321195\pi\) | ||||
0.532653 | + | 0.846334i | \(0.321195\pi\) | |||||||
\(542\) | −10643.1 | −0.843468 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3398.65 | 0.267860 | ||||||||
\(545\) | 4891.21 | 0.384434 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10088.8 | 0.788605 | 0.394303 | − | 0.918981i | \(-0.370986\pi\) | ||||
0.394303 | + | 0.918981i | \(0.370986\pi\) | |||||||
\(548\) | −1716.29 | −0.133789 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3431.31 | 0.266021 | ||||||||
\(551\) | 6556.98 | 0.506963 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1631.65 | 0.125470 | ||||||||
\(554\) | −5122.50 | −0.392842 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −999.019 | −0.0762012 | ||||||||
\(557\) | 11657.7 | 0.886809 | 0.443405 | − | 0.896322i | \(-0.353770\pi\) | ||||
0.443405 | + | 0.896322i | \(0.353770\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1633.13 | −0.123567 | ||||||||
\(560\) | −238.814 | −0.0180209 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17507.5 | −1.31407 | ||||||||
\(563\) | −4839.43 | −0.362270 | −0.181135 | − | 0.983458i | \(-0.557977\pi\) | ||||
−0.181135 | + | 0.983458i | \(0.557977\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8802.27 | −0.655424 | ||||||||
\(566\) | 4800.28 | 0.356486 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5670.40 | −0.418882 | ||||||||
\(569\) | 646.680 | 0.0476454 | 0.0238227 | − | 0.999716i | \(-0.492416\pi\) | ||||
0.0238227 | + | 0.999716i | \(0.492416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3263.66 | 0.239194 | 0.119597 | − | 0.992822i | \(-0.461840\pi\) | ||||
0.119597 | + | 0.992822i | \(0.461840\pi\) | |||||||
\(572\) | 3294.82 | 0.240845 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2356.12 | 0.171329 | ||||||||
\(575\) | 575.000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8980.46 | −0.647940 | −0.323970 | − | 0.946067i | \(-0.605018\pi\) | ||||
−0.323970 | + | 0.946067i | \(0.605018\pi\) | |||||||
\(578\) | −12734.2 | −0.916388 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2704.52 | 0.193619 | ||||||||
\(581\) | 60.4861 | 0.00431908 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28459.8 | −2.02176 | ||||||||
\(584\) | 5516.84 | 0.390905 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2091.12 | 0.147412 | ||||||||
\(587\) | 6538.05 | 0.459718 | 0.229859 | − | 0.973224i | \(-0.426174\pi\) | ||||
0.229859 | + | 0.973224i | \(0.426174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11190.4 | 0.782841 | ||||||||
\(590\) | 1835.86 | 0.128104 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1727.30 | −0.119918 | ||||||||
\(593\) | −7803.41 | −0.540384 | −0.270192 | − | 0.962806i | \(-0.587087\pi\) | ||||
−0.270192 | + | 0.962806i | \(0.587087\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1585.24 | 0.109225 | ||||||||
\(596\) | 6256.73 | 0.430010 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 552.127 | 0.0377561 | ||||||||
\(599\) | 27812.0 | 1.89711 | 0.948555 | − | 0.316613i | \(-0.102546\pi\) | ||||
0.948555 | + | 0.316613i | \(0.102546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 483.216 | 0.0327966 | 0.0163983 | − | 0.999866i | \(-0.494780\pi\) | ||||
0.0163983 | + | 0.999866i | \(0.494780\pi\) | |||||||
\(602\) | −812.342 | −0.0549976 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −7440.17 | −0.501219 | ||||||||
\(605\) | −16892.8 | −1.13519 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18104.0 | −1.21058 | −0.605289 | − | 0.796006i | \(-0.706942\pi\) | ||||
−0.605289 | + | 0.796006i | \(0.706942\pi\) | |||||||
\(608\) | 1551.65 | 0.103500 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −984.751 | −0.0653630 | ||||||||
\(611\) | −605.554 | −0.0400951 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2191.19 | 0.144374 | 0.0721870 | − | 0.997391i | \(-0.477002\pi\) | ||||
0.0721870 | + | 0.997391i | \(0.477002\pi\) | |||||||
\(614\) | 15811.7 | 1.03926 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1638.89 | 0.107196 | ||||||||
\(617\) | 8243.06 | 0.537849 | 0.268925 | − | 0.963161i | \(-0.413332\pi\) | ||||
0.268925 | + | 0.963161i | \(0.413332\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18298.0 | 1.18814 | 0.594069 | − | 0.804414i | \(-0.297521\pi\) | ||||
0.594069 | + | 0.804414i | \(0.297521\pi\) | |||||||
\(620\) | 4615.65 | 0.298982 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18455.3 | −1.18969 | ||||||||
\(623\) | 3245.80 | 0.208732 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −5425.15 | −0.346378 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11338.1 | 0.720445 | ||||||||
\(629\) | 11465.8 | 0.726821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26472.0 | −1.67010 | −0.835051 | − | 0.550172i | \(-0.814562\pi\) | ||||
−0.835051 | + | 0.550172i | \(0.814562\pi\) | |||||||
\(632\) | −4372.67 | −0.275214 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6880.58 | −0.431014 | ||||||||
\(635\) | 6304.37 | 0.393986 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4009.99 | 0.249421 | ||||||||
\(638\) | −18560.1 | −1.15173 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 640.000 | 0.0395285 | ||||||||
\(641\) | −7411.93 | −0.456714 | −0.228357 | − | 0.973577i | \(-0.573335\pi\) | ||||
−0.228357 | + | 0.973577i | \(0.573335\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8405.96 | 0.515550 | 0.257775 | − | 0.966205i | \(-0.417011\pi\) | ||||
0.257775 | + | 0.966205i | \(0.417011\pi\) | |||||||
\(644\) | 274.636 | 0.0168046 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10299.8 | −0.627309 | ||||||||
\(647\) | −27878.3 | −1.69398 | −0.846992 | − | 0.531605i | \(-0.821589\pi\) | ||||
−0.846992 | + | 0.531605i | \(0.821589\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12598.8 | −0.762014 | ||||||||
\(650\) | 600.138 | 0.0362144 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8458.06 | 0.508041 | ||||||||
\(653\) | 18871.1 | 1.13091 | 0.565455 | − | 0.824779i | \(-0.308701\pi\) | ||||
0.565455 | + | 0.824779i | \(0.308701\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2221.42 | 0.132516 | ||||||||
\(656\) | −6314.20 | −0.375805 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −301.211 | −0.0178457 | ||||||||
\(659\) | 12144.4 | 0.717872 | 0.358936 | − | 0.933362i | \(-0.383140\pi\) | ||||
0.358936 | + | 0.933362i | \(0.383140\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32504.2 | −1.91266 | −0.956328 | − | 0.292295i | \(-0.905581\pi\) | ||||
−0.956328 | + | 0.292295i | \(0.905581\pi\) | |||||||
\(662\) | −6519.49 | −0.382760 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −162.097 | −0.00947380 | ||||||||
\(665\) | 723.742 | 0.0422038 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3110.19 | −0.180551 | ||||||||
\(668\) | −9949.62 | −0.576291 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1369.25 | 0.0789531 | ||||||||
\(671\) | 6757.98 | 0.388806 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21387.8 | −1.22502 | −0.612511 | − | 0.790462i | \(-0.709840\pi\) | ||||
−0.612511 | + | 0.790462i | \(0.709840\pi\) | |||||||
\(674\) | −14326.8 | −0.818762 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8211.74 | −0.467213 | ||||||||
\(677\) | −10494.6 | −0.595776 | −0.297888 | − | 0.954601i | \(-0.596282\pi\) | ||||
−0.297888 | + | 0.954601i | \(0.596282\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3331.17 | −0.188275 | ||||||||
\(680\) | −4248.31 | −0.239581 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −31675.4 | −1.77847 | ||||||||
\(683\) | −24014.2 | −1.34535 | −0.672677 | − | 0.739937i | \(-0.734855\pi\) | ||||
−0.672677 | + | 0.739937i | \(0.734855\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2145.36 | 0.119664 | ||||||||
\(686\) | 4042.45 | 0.224988 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2177.00 | 0.120636 | ||||||||
\(689\) | −4977.63 | −0.275229 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10825.8 | −0.595995 | −0.297997 | − | 0.954567i | \(-0.596319\pi\) | ||||
−0.297997 | + | 0.954567i | \(0.596319\pi\) | |||||||
\(692\) | −14689.3 | −0.806939 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3666.90 | −0.200567 | ||||||||
\(695\) | 1248.77 | 0.0681564 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 41913.6 | 2.27775 | ||||||||
\(698\) | 20800.5 | 1.12795 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 298.517 | 0.0161184 | ||||||||
\(701\) | 171.021 | 0.00921451 | 0.00460726 | − | 0.999989i | \(-0.498533\pi\) | ||||
0.00460726 | + | 0.999989i | \(0.498533\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5234.69 | 0.280840 | ||||||||
\(704\) | −4392.08 | −0.235132 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6312.96 | −0.336532 | ||||||||
\(707\) | 401.701 | 0.0213685 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28732.7 | 1.52197 | 0.760987 | − | 0.648767i | \(-0.224715\pi\) | ||||
0.760987 | + | 0.648767i | \(0.224715\pi\) | |||||||
\(710\) | 7088.00 | 0.374659 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8698.45 | −0.457848 | ||||||||
\(713\) | −5307.99 | −0.278802 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4118.52 | −0.215418 | ||||||||
\(716\) | 12898.5 | 0.673240 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18648.3 | −0.969288 | ||||||||
\(719\) | −6976.22 | −0.361849 | −0.180924 | − | 0.983497i | \(-0.557909\pi\) | ||||
−0.180924 | + | 0.983497i | \(0.557909\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2764.13 | −0.142776 | ||||||||
\(722\) | 9015.61 | 0.464718 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8896.91 | −0.456700 | ||||||||
\(725\) | −3380.65 | −0.173178 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13114.6 | 0.669042 | 0.334521 | − | 0.942388i | \(-0.391426\pi\) | ||||
0.334521 | + | 0.942388i | \(0.391426\pi\) | |||||||
\(728\) | 286.643 | 0.0145930 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6896.05 | −0.349636 | ||||||||
\(731\) | −14450.9 | −0.731172 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22681.7 | −1.14293 | −0.571466 | − | 0.820626i | \(-0.693625\pi\) | ||||
−0.571466 | + | 0.820626i | \(0.693625\pi\) | |||||||
\(734\) | −7605.36 | −0.382451 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | −9396.62 | −0.469646 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24237.8 | 1.20650 | 0.603249 | − | 0.797553i | \(-0.293873\pi\) | ||||
0.603249 | + | 0.797553i | \(0.293873\pi\) | |||||||
\(740\) | 2159.12 | 0.107258 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2475.95 | −0.122500 | ||||||||
\(743\) | −27356.7 | −1.35077 | −0.675384 | − | 0.737466i | \(-0.736022\pi\) | ||||
−0.675384 | + | 0.737466i | \(0.736022\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7820.92 | −0.384612 | ||||||||
\(746\) | 17856.1 | 0.876350 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 29154.6 | 1.42513 | ||||||||
\(749\) | −5585.63 | −0.272489 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22297.8 | 1.08343 | 0.541716 | − | 0.840561i | \(-0.317775\pi\) | ||||
0.541716 | + | 0.840561i | \(0.317775\pi\) | |||||||
\(752\) | 807.220 | 0.0391440 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3246.17 | −0.156788 | ||||||||
\(755\) | 9300.21 | 0.448304 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16088.4 | −0.772447 | −0.386224 | − | 0.922405i | \(-0.626221\pi\) | ||||
−0.386224 | + | 0.922405i | \(0.626221\pi\) | |||||||
\(758\) | −7596.26 | −0.363996 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1939.56 | −0.0925729 | ||||||||
\(761\) | −22500.2 | −1.07179 | −0.535894 | − | 0.844285i | \(-0.680025\pi\) | ||||
−0.535894 | + | 0.844285i | \(0.680025\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2920.22 | −0.138557 | ||||||||
\(764\) | −13094.1 | −0.620063 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2912.82 | 0.137395 | ||||||||
\(767\) | −2203.54 | −0.103736 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22677.7 | −1.06343 | −0.531716 | − | 0.846923i | \(-0.678453\pi\) | ||||
−0.531716 | + | 0.846923i | \(0.678453\pi\) | |||||||
\(770\) | −2048.61 | −0.0958790 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20507.5 | 0.956062 | ||||||||
\(773\) | −20465.1 | −0.952235 | −0.476118 | − | 0.879382i | \(-0.657956\pi\) | ||||
−0.476118 | + | 0.879382i | \(0.657956\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5769.56 | −0.267418 | ||||||||
\(776\) | 8927.24 | 0.412976 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16422.7 | −0.756789 | ||||||||
\(779\) | 19135.6 | 0.880108 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48642.3 | −2.22863 | ||||||||
\(782\) | 4885.56 | 0.223411 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5345.42 | −0.243505 | ||||||||
\(785\) | −14172.6 | −0.644386 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28850.8 | −1.30676 | −0.653379 | − | 0.757031i | \(-0.726649\pi\) | ||||
−0.653379 | + | 0.757031i | \(0.726649\pi\) | |||||||
\(788\) | −13050.3 | −0.589971 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5465.83 | 0.246159 | ||||||||
\(791\) | 5255.26 | 0.236227 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1181.97 | 0.0529295 | ||||||||
\(794\) | −1828.73 | −0.0817370 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −673.128 | −0.0299728 | ||||||||
\(797\) | 39332.9 | 1.74811 | 0.874054 | − | 0.485828i | \(-0.161482\pi\) | ||||
0.874054 | + | 0.485828i | \(0.161482\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5358.31 | −0.237251 | ||||||||
\(800\) | −800.000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18829.9 | 0.829063 | ||||||||
\(803\) | 47325.0 | 2.07978 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −343.295 | −0.0150305 | ||||||||
\(806\) | −5540.05 | −0.242109 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1076.52 | −0.0468712 | ||||||||
\(809\) | −33946.5 | −1.47527 | −0.737637 | − | 0.675198i | \(-0.764058\pi\) | ||||
−0.737637 | + | 0.675198i | \(0.764058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20772.2 | −0.899398 | −0.449699 | − | 0.893180i | \(-0.648469\pi\) | ||||
−0.449699 | + | 0.893180i | \(0.648469\pi\) | |||||||
\(812\) | −1614.69 | −0.0697839 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −14817.2 | −0.638015 | ||||||||
\(815\) | −10572.6 | −0.454406 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6597.56 | −0.282521 | ||||||||
\(818\) | −6598.83 | −0.282057 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7892.75 | 0.336130 | ||||||||
\(821\) | −6466.37 | −0.274882 | −0.137441 | − | 0.990510i | \(-0.543888\pi\) | ||||
−0.137441 | + | 0.990510i | \(0.543888\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16503.7 | −0.699008 | −0.349504 | − | 0.936935i | \(-0.613650\pi\) | ||||
−0.349504 | + | 0.936935i | \(0.613650\pi\) | |||||||
\(824\) | 7407.63 | 0.313176 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1096.07 | −0.0461710 | ||||||||
\(827\) | −36540.8 | −1.53645 | −0.768227 | − | 0.640177i | \(-0.778861\pi\) | ||||
−0.768227 | + | 0.640177i | \(0.778861\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24874.5 | −1.04213 | −0.521066 | − | 0.853516i | \(-0.674465\pi\) | ||||
−0.521066 | + | 0.853516i | \(0.674465\pi\) | |||||||
\(830\) | 202.622 | 0.00847362 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −768.177 | −0.0320093 | ||||||||
\(833\) | 35482.8 | 1.47588 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12437.0 | 0.515450 | ||||||||
\(836\) | 13310.5 | 0.550662 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7109.28 | −0.293062 | ||||||||
\(839\) | −15814.3 | −0.650741 | −0.325370 | − | 0.945587i | \(-0.605489\pi\) | ||||
−0.325370 | + | 0.945587i | \(0.605489\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6102.97 | −0.250234 | ||||||||
\(842\) | −23311.0 | −0.954097 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16788.0 | 0.684678 | ||||||||
\(845\) | 10264.7 | 0.417888 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10085.6 | 0.409144 | ||||||||
\(848\) | 6635.32 | 0.268700 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5310.39 | 0.214288 | ||||||||
\(851\) | −2482.99 | −0.100019 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31093.2 | −1.24808 | −0.624039 | − | 0.781394i | \(-0.714509\pi\) | ||||
−0.624039 | + | 0.781394i | \(0.714509\pi\) | |||||||
\(854\) | 587.931 | 0.0235580 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14969.0 | 0.597699 | ||||||||
\(857\) | −34212.4 | −1.36368 | −0.681840 | − | 0.731501i | \(-0.738820\pi\) | ||||
−0.681840 | + | 0.731501i | \(0.738820\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4821.57 | 0.191513 | 0.0957567 | − | 0.995405i | \(-0.469473\pi\) | ||||
0.0957567 | + | 0.995405i | \(0.469473\pi\) | |||||||
\(860\) | −2721.25 | −0.107900 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9454.77 | 0.373585 | ||||||||
\(863\) | −19145.6 | −0.755185 | −0.377593 | − | 0.925972i | \(-0.623248\pi\) | ||||
−0.377593 | + | 0.925972i | \(0.623248\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18361.6 | 0.721748 | ||||||||
\(866\) | −7872.49 | −0.308912 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2755.70 | −0.107759 | ||||||||
\(869\) | −37509.9 | −1.46426 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1643.47 | −0.0639345 | ||||||||
\(872\) | 7825.93 | 0.303921 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2230.50 | 0.0863246 | ||||||||
\(875\) | −373.147 | −0.0144168 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16890.8 | 0.650354 | 0.325177 | − | 0.945653i | \(-0.394576\pi\) | ||||
0.325177 | + | 0.945653i | \(0.394576\pi\) | |||||||
\(878\) | −13719.5 | −0.527349 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5490.10 | 0.210308 | ||||||||
\(881\) | 27802.3 | 1.06321 | 0.531603 | − | 0.846994i | \(-0.321590\pi\) | ||||
0.531603 | + | 0.846994i | \(0.321590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9794.15 | 0.373272 | 0.186636 | − | 0.982429i | \(-0.440241\pi\) | ||||
0.186636 | + | 0.982429i | \(0.440241\pi\) | |||||||
\(884\) | 5099.15 | 0.194008 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33628.9 | 1.27515 | ||||||||
\(887\) | 41652.4 | 1.57672 | 0.788360 | − | 0.615214i | \(-0.210930\pi\) | ||||
0.788360 | + | 0.615214i | \(0.210930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3763.93 | −0.142000 | ||||||||
\(890\) | 10873.1 | 0.409512 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20770.7 | 0.779656 | ||||||||
\(893\) | −2446.34 | −0.0916724 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16123.1 | −0.602164 | ||||||||
\(896\) | −382.102 | −0.0142468 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 21347.5 | 0.793293 | ||||||||
\(899\) | 31207.7 | 1.15777 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −44045.2 | −1.62859 | ||||||||
\(902\) | −54164.9 | −1.99944 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −14083.6 | −0.518158 | ||||||||
\(905\) | 11121.1 | 0.408485 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5467.21 | 0.200150 | 0.100075 | − | 0.994980i | \(-0.468092\pi\) | ||||
0.100075 | + | 0.994980i | \(0.468092\pi\) | |||||||
\(908\) | −18804.9 | −0.687295 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −358.303 | −0.0130523 | ||||||||
\(911\) | −33520.9 | −1.21910 | −0.609549 | − | 0.792749i | \(-0.708649\pi\) | ||||
−0.609549 | + | 0.792749i | \(0.708649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1390.52 | −0.0504046 | ||||||||
\(914\) | −30986.1 | −1.12137 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8500.70 | −0.306628 | ||||||||
\(917\) | −1326.26 | −0.0477612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21423.9 | 0.768996 | 0.384498 | − | 0.923126i | \(-0.374375\pi\) | ||||
0.384498 | + | 0.923126i | \(0.374375\pi\) | |||||||
\(920\) | 920.000 | 0.0329690 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21586.0 | −0.771039 | ||||||||
\(923\) | −8507.56 | −0.303391 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2698.90 | −0.0959344 | ||||||||
\(926\) | 12331.7 | 0.437631 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4327.23 | 0.153069 | ||||||||
\(929\) | −25838.9 | −0.912538 | −0.456269 | − | 0.889842i | \(-0.650814\pi\) | ||||
−0.456269 | + | 0.889842i | \(0.650814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16199.7 | 0.570271 | ||||||||
\(932\) | 6586.69 | 0.231496 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21472.8 | −0.752261 | ||||||||
\(935\) | −36443.2 | −1.27467 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48095.9 | 1.67687 | 0.838434 | − | 0.545003i | \(-0.183472\pi\) | ||||
0.838434 | + | 0.545003i | \(0.183472\pi\) | |||||||
\(938\) | −817.487 | −0.0284562 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1009.02 | −0.0350114 | ||||||||
\(941\) | 32450.4 | 1.12418 | 0.562089 | − | 0.827077i | \(-0.309998\pi\) | ||||
0.562089 | + | 0.827077i | \(0.309998\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −9076.66 | −0.313443 | ||||||||
\(944\) | 2937.38 | 0.101275 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18674.9 | 0.641834 | ||||||||
\(947\) | −39067.9 | −1.34059 | −0.670294 | − | 0.742096i | \(-0.733832\pi\) | ||||
−0.670294 | + | 0.742096i | \(0.733832\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8277.16 | 0.283127 | ||||||||
\(950\) | 2424.45 | 0.0827997 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2536.39 | 0.0863496 | ||||||||
\(953\) | −17756.2 | −0.603546 | −0.301773 | − | 0.953380i | \(-0.597578\pi\) | ||||
−0.301773 | + | 0.953380i | \(0.597578\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16367.6 | 0.554601 | ||||||||
\(956\) | −11511.5 | −0.389444 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12666.6 | 0.427181 | ||||||||
\(959\) | −1280.85 | −0.0431292 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23469.5 | 0.787805 | ||||||||
\(962\) | −2591.54 | −0.0868552 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16978.2 | −0.567251 | ||||||||
\(965\) | −25634.3 | −0.855127 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10696.2 | −0.355705 | −0.177853 | − | 0.984057i | \(-0.556915\pi\) | ||||
−0.177853 | + | 0.984057i | \(0.556915\pi\) | |||||||
\(968\) | −27028.5 | −0.897446 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11159.0 | −0.369377 | ||||||||
\(971\) | 53635.1 | 1.77264 | 0.886320 | − | 0.463074i | \(-0.153254\pi\) | ||||
0.886320 | + | 0.463074i | \(0.153254\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −745.561 | −0.0245649 | ||||||||
\(974\) | 33666.5 | 1.10754 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1575.60 | −0.0516740 | ||||||||
\(977\) | 21627.7 | 0.708220 | 0.354110 | − | 0.935204i | \(-0.384784\pi\) | ||||
0.354110 | + | 0.935204i | \(0.384784\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −74617.7 | −2.43595 | ||||||||
\(980\) | 6681.77 | 0.217797 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.60856 | −0.000312242 0 | ||||||||
\(983\) | −12031.4 | −0.390378 | −0.195189 | − | 0.980766i | \(-0.562532\pi\) | ||||
−0.195189 | + | 0.980766i | \(0.562532\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16312.8 | 0.527686 | ||||||||
\(986\) | −28724.1 | −0.927749 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2328.01 | 0.0749635 | ||||||||
\(989\) | 3129.44 | 0.100617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24573.0 | −0.787675 | −0.393838 | − | 0.919180i | \(-0.628853\pi\) | ||||
−0.393838 | + | 0.919180i | \(0.628853\pi\) | |||||||
\(992\) | 7385.03 | 0.236366 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4231.78 | −0.135034 | ||||||||
\(995\) | 841.410 | 0.0268085 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14209.7 | −0.451379 | −0.225690 | − | 0.974199i | \(-0.572464\pi\) | ||||
−0.225690 | + | 0.974199i | \(0.572464\pi\) | |||||||
\(998\) | −42413.8 | −1.34527 | ||||||||
\(999\) | 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 | 2070.4.a.bg.1.2 | 4 | ||
3.2 | odd | 2 | 230.4.a.j.1.2 | ✓ | 4 | ||
12.11 | even | 2 | 1840.4.a.k.1.3 | 4 | |||
15.2 | even | 4 | 1150.4.b.o.599.7 | 8 | |||
15.8 | even | 4 | 1150.4.b.o.599.2 | 8 | |||
15.14 | odd | 2 | 1150.4.a.n.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.4.a.j.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
1150.4.a.n.1.3 | 4 | 15.14 | odd | 2 | |||
1150.4.b.o.599.2 | 8 | 15.8 | even | 4 | |||
1150.4.b.o.599.7 | 8 | 15.2 | even | 4 | |||
1840.4.a.k.1.3 | 4 | 12.11 | even | 2 | |||
2070.4.a.bg.1.2 | 4 | 1.1 | even | 1 | trivial |