Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1350,4,Mod(1,1350)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1350, 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("1350.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1350 = 2 \cdot 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1350.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: | \(79.6525785077\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1350.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −19.0000 | −1.02590 | −0.512952 | − | 0.858417i | \(-0.671448\pi\) | ||||
−0.512952 | + | 0.858417i | \(0.671448\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.0000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 50.0000 | 1.06673 | 0.533366 | − | 0.845885i | \(-0.320927\pi\) | ||||
0.533366 | + | 0.845885i | \(0.320927\pi\) | |||||||
\(14\) | −38.0000 | −0.725423 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −126.000 | −1.79762 | −0.898808 | − | 0.438342i | \(-0.855566\pi\) | ||||
−0.898808 | + | 0.438342i | \(0.855566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29.0000 | 0.350161 | 0.175080 | − | 0.984554i | \(-0.443981\pi\) | ||||
0.175080 | + | 0.984554i | \(0.443981\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 24.0000 | 0.232583 | ||||||||
\(23\) | 18.0000 | 0.163185 | 0.0815926 | − | 0.996666i | \(-0.473999\pi\) | ||||
0.0815926 | + | 0.996666i | \(0.473999\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 100.000 | 0.754293 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −76.0000 | −0.512952 | ||||||||
\(29\) | 102.000 | 0.653135 | 0.326568 | − | 0.945174i | \(-0.394108\pi\) | ||||
0.326568 | + | 0.945174i | \(0.394108\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −265.000 | −1.53534 | −0.767668 | − | 0.640848i | \(-0.778583\pi\) | ||||
−0.767668 | + | 0.640848i | \(0.778583\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −252.000 | −1.27111 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 65.0000 | 0.288809 | 0.144405 | − | 0.989519i | \(-0.453873\pi\) | ||||
0.144405 | + | 0.989519i | \(0.453873\pi\) | |||||||
\(38\) | 58.0000 | 0.247601 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 240.000 | 0.914188 | 0.457094 | − | 0.889418i | \(-0.348890\pi\) | ||||
0.457094 | + | 0.889418i | \(0.348890\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −367.000 | −1.30156 | −0.650779 | − | 0.759267i | \(-0.725557\pi\) | ||||
−0.650779 | + | 0.759267i | \(0.725557\pi\) | |||||||
\(44\) | 48.0000 | 0.164461 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 36.0000 | 0.115389 | ||||||||
\(47\) | −72.0000 | −0.223453 | −0.111726 | − | 0.993739i | \(-0.535638\pi\) | ||||
−0.111726 | + | 0.993739i | \(0.535638\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.0000 | 0.0524781 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 200.000 | 0.533366 | ||||||||
\(53\) | −636.000 | −1.64833 | −0.824163 | − | 0.566352i | \(-0.808354\pi\) | ||||
−0.824163 | + | 0.566352i | \(0.808354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −152.000 | −0.362712 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 204.000 | 0.461836 | ||||||||
\(59\) | 102.000 | 0.225072 | 0.112536 | − | 0.993648i | \(-0.464103\pi\) | ||||
0.112536 | + | 0.993648i | \(0.464103\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −103.000 | −0.216193 | −0.108097 | − | 0.994140i | \(-0.534476\pi\) | ||||
−0.108097 | + | 0.994140i | \(0.534476\pi\) | |||||||
\(62\) | −530.000 | −1.08565 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −52.0000 | −0.0948181 | −0.0474090 | − | 0.998876i | \(-0.515096\pi\) | ||||
−0.0474090 | + | 0.998876i | \(0.515096\pi\) | |||||||
\(68\) | −504.000 | −0.898808 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −582.000 | −0.972827 | −0.486413 | − | 0.873729i | \(-0.661695\pi\) | ||||
−0.486413 | + | 0.873729i | \(0.661695\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 65.0000 | 0.104215 | 0.0521074 | − | 0.998641i | \(-0.483406\pi\) | ||||
0.0521074 | + | 0.998641i | \(0.483406\pi\) | |||||||
\(74\) | 130.000 | 0.204219 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 116.000 | 0.175080 | ||||||||
\(77\) | −228.000 | −0.337442 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 173.000 | 0.246380 | 0.123190 | − | 0.992383i | \(-0.460688\pi\) | ||||
0.123190 | + | 0.992383i | \(0.460688\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 480.000 | 0.646428 | ||||||||
\(83\) | 498.000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −734.000 | −0.920340 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 96.0000 | 0.116291 | ||||||||
\(89\) | −822.000 | −0.979009 | −0.489505 | − | 0.872001i | \(-0.662822\pi\) | ||||
−0.489505 | + | 0.872001i | \(0.662822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −950.000 | −1.09436 | ||||||||
\(92\) | 72.0000 | 0.0815926 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −144.000 | −0.158005 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 821.000 | 0.859381 | 0.429690 | − | 0.902976i | \(-0.358623\pi\) | ||||
0.429690 | + | 0.902976i | \(0.358623\pi\) | |||||||
\(98\) | 36.0000 | 0.0371076 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1200.00 | −1.18222 | −0.591111 | − | 0.806590i | \(-0.701311\pi\) | ||||
−0.591111 | + | 0.806590i | \(0.701311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2041.00 | −1.95248 | −0.976241 | − | 0.216686i | \(-0.930475\pi\) | ||||
−0.976241 | + | 0.216686i | \(0.930475\pi\) | |||||||
\(104\) | 400.000 | 0.377146 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1272.00 | −1.16554 | ||||||||
\(107\) | −1278.00 | −1.15466 | −0.577331 | − | 0.816510i | \(-0.695906\pi\) | ||||
−0.577331 | + | 0.816510i | \(0.695906\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −205.000 | −0.180142 | −0.0900708 | − | 0.995935i | \(-0.528709\pi\) | ||||
−0.0900708 | + | 0.995935i | \(0.528709\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −304.000 | −0.256476 | ||||||||
\(113\) | −1500.00 | −1.24874 | −0.624372 | − | 0.781127i | \(-0.714645\pi\) | ||||
−0.624372 | + | 0.781127i | \(0.714645\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 408.000 | 0.326568 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 204.000 | 0.159150 | ||||||||
\(119\) | 2394.00 | 1.84418 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | −206.000 | −0.152872 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1060.00 | −0.767668 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 416.000 | 0.290662 | 0.145331 | − | 0.989383i | \(-0.453575\pi\) | ||||
0.145331 | + | 0.989383i | \(0.453575\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1902.00 | −1.26854 | −0.634269 | − | 0.773112i | \(-0.718699\pi\) | ||||
−0.634269 | + | 0.773112i | \(0.718699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −551.000 | −0.359231 | ||||||||
\(134\) | −104.000 | −0.0670465 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1008.00 | −0.635554 | ||||||||
\(137\) | −2712.00 | −1.69125 | −0.845627 | − | 0.533774i | \(-0.820773\pi\) | ||||
−0.845627 | + | 0.533774i | \(0.820773\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −367.000 | −0.223946 | −0.111973 | − | 0.993711i | \(-0.535717\pi\) | ||||
−0.111973 | + | 0.993711i | \(0.535717\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1164.00 | −0.687892 | ||||||||
\(143\) | 600.000 | 0.350871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 130.000 | 0.0736909 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 260.000 | 0.144405 | ||||||||
\(149\) | 3006.00 | 1.65276 | 0.826380 | − | 0.563113i | \(-0.190397\pi\) | ||||
0.826380 | + | 0.563113i | \(0.190397\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2651.00 | 1.42871 | 0.714355 | − | 0.699783i | \(-0.246720\pi\) | ||||
0.714355 | + | 0.699783i | \(0.246720\pi\) | |||||||
\(152\) | 232.000 | 0.123801 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −456.000 | −0.238607 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2801.00 | 1.42385 | 0.711924 | − | 0.702257i | \(-0.247824\pi\) | ||||
0.711924 | + | 0.702257i | \(0.247824\pi\) | |||||||
\(158\) | 346.000 | 0.174217 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −342.000 | −0.167412 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1412.00 | 0.678505 | 0.339253 | − | 0.940695i | \(-0.389826\pi\) | ||||
0.339253 | + | 0.940695i | \(0.389826\pi\) | |||||||
\(164\) | 960.000 | 0.457094 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 996.000 | 0.465690 | ||||||||
\(167\) | −2154.00 | −0.998093 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 303.000 | 0.137915 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1468.00 | −0.650779 | ||||||||
\(173\) | 234.000 | 0.102836 | 0.0514182 | − | 0.998677i | \(-0.483626\pi\) | ||||
0.0514182 | + | 0.998677i | \(0.483626\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 192.000 | 0.0822304 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1644.00 | −0.692264 | ||||||||
\(179\) | 2472.00 | 1.03221 | 0.516106 | − | 0.856525i | \(-0.327381\pi\) | ||||
0.516106 | + | 0.856525i | \(0.327381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −190.000 | −0.0780254 | −0.0390127 | − | 0.999239i | \(-0.512421\pi\) | ||||
−0.0390127 | + | 0.999239i | \(0.512421\pi\) | |||||||
\(182\) | −1900.00 | −0.773832 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 144.000 | 0.0576947 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1512.00 | −0.591275 | ||||||||
\(188\) | −288.000 | −0.111726 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1524.00 | 0.577344 | 0.288672 | − | 0.957428i | \(-0.406786\pi\) | ||||
0.288672 | + | 0.957428i | \(0.406786\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3335.00 | 1.24383 | 0.621913 | − | 0.783086i | \(-0.286356\pi\) | ||||
0.621913 | + | 0.783086i | \(0.286356\pi\) | |||||||
\(194\) | 1642.00 | 0.607674 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 72.0000 | 0.0262391 | ||||||||
\(197\) | −4440.00 | −1.60577 | −0.802886 | − | 0.596133i | \(-0.796703\pi\) | ||||
−0.802886 | + | 0.596133i | \(0.796703\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2192.00 | 0.780838 | 0.390419 | − | 0.920637i | \(-0.372330\pi\) | ||||
0.390419 | + | 0.920637i | \(0.372330\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2400.00 | −0.835957 | ||||||||
\(203\) | −1938.00 | −0.670054 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4082.00 | −1.38061 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 800.000 | 0.266683 | ||||||||
\(209\) | 348.000 | 0.115175 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1732.00 | −0.565099 | −0.282549 | − | 0.959253i | \(-0.591180\pi\) | ||||
−0.282549 | + | 0.959253i | \(0.591180\pi\) | |||||||
\(212\) | −2544.00 | −0.824163 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2556.00 | −0.816470 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5035.00 | 1.57511 | ||||||||
\(218\) | −410.000 | −0.127379 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6300.00 | −1.91757 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5989.00 | −1.79844 | −0.899222 | − | 0.437492i | \(-0.855867\pi\) | ||||
−0.899222 | + | 0.437492i | \(0.855867\pi\) | |||||||
\(224\) | −608.000 | −0.181356 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3000.00 | −0.882996 | ||||||||
\(227\) | −3300.00 | −0.964884 | −0.482442 | − | 0.875928i | \(-0.660250\pi\) | ||||
−0.482442 | + | 0.875928i | \(0.660250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4379.00 | 1.26364 | 0.631818 | − | 0.775117i | \(-0.282309\pi\) | ||||
0.631818 | + | 0.775117i | \(0.282309\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 816.000 | 0.230918 | ||||||||
\(233\) | 2958.00 | 0.831695 | 0.415848 | − | 0.909434i | \(-0.363485\pi\) | ||||
0.415848 | + | 0.909434i | \(0.363485\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 408.000 | 0.112536 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4788.00 | 1.30403 | ||||||||
\(239\) | −2676.00 | −0.724251 | −0.362126 | − | 0.932129i | \(-0.617949\pi\) | ||||
−0.362126 | + | 0.932129i | \(0.617949\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3626.00 | 0.969175 | 0.484588 | − | 0.874743i | \(-0.338970\pi\) | ||||
0.484588 | + | 0.874743i | \(0.338970\pi\) | |||||||
\(242\) | −2374.00 | −0.630605 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −412.000 | −0.108097 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1450.00 | 0.373527 | ||||||||
\(248\) | −2120.00 | −0.542823 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2046.00 | −0.514511 | −0.257256 | − | 0.966343i | \(-0.582818\pi\) | ||||
−0.257256 | + | 0.966343i | \(0.582818\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 216.000 | 0.0536751 | ||||||||
\(254\) | 832.000 | 0.205529 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5700.00 | 1.38349 | 0.691744 | − | 0.722143i | \(-0.256843\pi\) | ||||
0.691744 | + | 0.722143i | \(0.256843\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1235.00 | −0.296290 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3804.00 | −0.896992 | ||||||||
\(263\) | −7674.00 | −1.79924 | −0.899618 | − | 0.436678i | \(-0.856155\pi\) | ||||
−0.899618 | + | 0.436678i | \(0.856155\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1102.00 | −0.254015 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −208.000 | −0.0474090 | ||||||||
\(269\) | 4326.00 | 0.980524 | 0.490262 | − | 0.871575i | \(-0.336901\pi\) | ||||
0.490262 | + | 0.871575i | \(0.336901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6473.00 | 1.45095 | 0.725474 | − | 0.688250i | \(-0.241621\pi\) | ||||
0.725474 | + | 0.688250i | \(0.241621\pi\) | |||||||
\(272\) | −2016.00 | −0.449404 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5424.00 | −1.19590 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7825.00 | −1.69732 | −0.848662 | − | 0.528936i | \(-0.822591\pi\) | ||||
−0.848662 | + | 0.528936i | \(0.822591\pi\) | |||||||
\(278\) | −734.000 | −0.158354 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2760.00 | 0.585935 | 0.292968 | − | 0.956122i | \(-0.405357\pi\) | ||||
0.292968 | + | 0.956122i | \(0.405357\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4801.00 | −1.00844 | −0.504222 | − | 0.863574i | \(-0.668221\pi\) | ||||
−0.504222 | + | 0.863574i | \(0.668221\pi\) | |||||||
\(284\) | −2328.00 | −0.486413 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1200.00 | 0.248103 | ||||||||
\(287\) | −4560.00 | −0.937869 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10963.0 | 2.23143 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 260.000 | 0.0521074 | ||||||||
\(293\) | −8166.00 | −1.62820 | −0.814100 | − | 0.580724i | \(-0.802769\pi\) | ||||
−0.814100 | + | 0.580724i | \(0.802769\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 520.000 | 0.102109 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6012.00 | 1.16868 | ||||||||
\(299\) | 900.000 | 0.174075 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6973.00 | 1.33527 | ||||||||
\(302\) | 5302.00 | 1.01025 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 464.000 | 0.0875402 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −577.000 | −0.107268 | −0.0536338 | − | 0.998561i | \(-0.517080\pi\) | ||||
−0.0536338 | + | 0.998561i | \(0.517080\pi\) | |||||||
\(308\) | −912.000 | −0.168721 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7656.00 | −1.39592 | −0.697961 | − | 0.716135i | \(-0.745909\pi\) | ||||
−0.697961 | + | 0.716135i | \(0.745909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2726.00 | 0.492277 | 0.246138 | − | 0.969235i | \(-0.420838\pi\) | ||||
0.246138 | + | 0.969235i | \(0.420838\pi\) | |||||||
\(314\) | 5602.00 | 1.00681 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 692.000 | 0.123190 | ||||||||
\(317\) | −9450.00 | −1.67434 | −0.837169 | − | 0.546945i | \(-0.815791\pi\) | ||||
−0.837169 | + | 0.546945i | \(0.815791\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1224.00 | 0.214830 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −684.000 | −0.118378 | ||||||||
\(323\) | −3654.00 | −0.629455 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2824.00 | 0.479776 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1920.00 | 0.323214 | ||||||||
\(329\) | 1368.00 | 0.229241 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3089.00 | 0.512951 | 0.256476 | − | 0.966551i | \(-0.417439\pi\) | ||||
0.256476 | + | 0.966551i | \(0.417439\pi\) | |||||||
\(332\) | 1992.00 | 0.329293 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4308.00 | −0.705758 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7894.00 | −1.27600 | −0.638002 | − | 0.770034i | \(-0.720239\pi\) | ||||
−0.638002 | + | 0.770034i | \(0.720239\pi\) | |||||||
\(338\) | 606.000 | 0.0975209 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3180.00 | −0.505005 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6175.00 | 0.972066 | ||||||||
\(344\) | −2936.00 | −0.460170 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 468.000 | 0.0727163 | ||||||||
\(347\) | −3450.00 | −0.533734 | −0.266867 | − | 0.963733i | \(-0.585988\pi\) | ||||
−0.266867 | + | 0.963733i | \(0.585988\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2261.00 | 0.346787 | 0.173393 | − | 0.984853i | \(-0.444527\pi\) | ||||
0.173393 | + | 0.984853i | \(0.444527\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 384.000 | 0.0581456 | ||||||||
\(353\) | 11544.0 | 1.74058 | 0.870291 | − | 0.492539i | \(-0.163931\pi\) | ||||
0.870291 | + | 0.492539i | \(0.163931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3288.00 | −0.489505 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4944.00 | 0.729884 | ||||||||
\(359\) | −198.000 | −0.0291087 | −0.0145544 | − | 0.999894i | \(-0.504633\pi\) | ||||
−0.0145544 | + | 0.999894i | \(0.504633\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6018.00 | −0.877387 | ||||||||
\(362\) | −380.000 | −0.0551723 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3800.00 | −0.547182 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10388.0 | 1.47752 | 0.738759 | − | 0.673970i | \(-0.235412\pi\) | ||||
0.738759 | + | 0.673970i | \(0.235412\pi\) | |||||||
\(368\) | 288.000 | 0.0407963 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12084.0 | 1.69102 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4867.00 | −0.675613 | −0.337807 | − | 0.941216i | \(-0.609685\pi\) | ||||
−0.337807 | + | 0.941216i | \(0.609685\pi\) | |||||||
\(374\) | −3024.00 | −0.418094 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −576.000 | −0.0790025 | ||||||||
\(377\) | 5100.00 | 0.696720 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 656.000 | 0.0889089 | 0.0444544 | − | 0.999011i | \(-0.485845\pi\) | ||||
0.0444544 | + | 0.999011i | \(0.485845\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3048.00 | 0.408244 | ||||||||
\(383\) | 3078.00 | 0.410649 | 0.205324 | − | 0.978694i | \(-0.434175\pi\) | ||||
0.205324 | + | 0.978694i | \(0.434175\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6670.00 | 0.879518 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3284.00 | 0.429690 | ||||||||
\(389\) | 1644.00 | 0.214278 | 0.107139 | − | 0.994244i | \(-0.465831\pi\) | ||||
0.107139 | + | 0.994244i | \(0.465831\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2268.00 | −0.293344 | ||||||||
\(392\) | 144.000 | 0.0185538 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8880.00 | −1.13545 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5729.00 | 0.724258 | 0.362129 | − | 0.932128i | \(-0.382050\pi\) | ||||
0.362129 | + | 0.932128i | \(0.382050\pi\) | |||||||
\(398\) | 4384.00 | 0.552136 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1776.00 | −0.221170 | −0.110585 | − | 0.993867i | \(-0.535272\pi\) | ||||
−0.110585 | + | 0.993867i | \(0.535272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13250.0 | −1.63779 | ||||||||
\(404\) | −4800.00 | −0.591111 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3876.00 | −0.473800 | ||||||||
\(407\) | 780.000 | 0.0949955 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12842.0 | 1.55256 | 0.776279 | − | 0.630390i | \(-0.217105\pi\) | ||||
0.776279 | + | 0.630390i | \(0.217105\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8164.00 | −0.976241 | ||||||||
\(413\) | −1938.00 | −0.230903 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1600.00 | 0.188573 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 696.000 | 0.0814413 | ||||||||
\(419\) | −11298.0 | −1.31729 | −0.658644 | − | 0.752455i | \(-0.728870\pi\) | ||||
−0.658644 | + | 0.752455i | \(0.728870\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3431.00 | 0.397189 | 0.198595 | − | 0.980082i | \(-0.436362\pi\) | ||||
0.198595 | + | 0.980082i | \(0.436362\pi\) | |||||||
\(422\) | −3464.00 | −0.399585 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5088.00 | −0.582772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1957.00 | 0.221794 | ||||||||
\(428\) | −5112.00 | −0.577331 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10530.0 | 1.17683 | 0.588413 | − | 0.808560i | \(-0.299753\pi\) | ||||
0.588413 | + | 0.808560i | \(0.299753\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3179.00 | 0.352824 | 0.176412 | − | 0.984316i | \(-0.443551\pi\) | ||||
0.176412 | + | 0.984316i | \(0.443551\pi\) | |||||||
\(434\) | 10070.0 | 1.11377 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −820.000 | −0.0900708 | ||||||||
\(437\) | 522.000 | 0.0571411 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6047.00 | 0.657420 | 0.328710 | − | 0.944431i | \(-0.393386\pi\) | ||||
0.328710 | + | 0.944431i | \(0.393386\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12600.0 | −1.35593 | ||||||||
\(443\) | 16554.0 | 1.77540 | 0.887702 | − | 0.460418i | \(-0.152300\pi\) | ||||
0.887702 | + | 0.460418i | \(0.152300\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11978.0 | −1.27169 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1216.00 | −0.128238 | ||||||||
\(449\) | −4446.00 | −0.467304 | −0.233652 | − | 0.972320i | \(-0.575068\pi\) | ||||
−0.233652 | + | 0.972320i | \(0.575068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2880.00 | 0.300696 | ||||||||
\(452\) | −6000.00 | −0.624372 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6600.00 | −0.682276 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 146.000 | 0.0149444 | 0.00747220 | − | 0.999972i | \(-0.497622\pi\) | ||||
0.00747220 | + | 0.999972i | \(0.497622\pi\) | |||||||
\(458\) | 8758.00 | 0.893525 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9822.00 | 0.992313 | 0.496156 | − | 0.868233i | \(-0.334744\pi\) | ||||
0.496156 | + | 0.868233i | \(0.334744\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7931.00 | 0.796080 | 0.398040 | − | 0.917368i | \(-0.369691\pi\) | ||||
0.398040 | + | 0.917368i | \(0.369691\pi\) | |||||||
\(464\) | 1632.00 | 0.163284 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5916.00 | 0.588097 | ||||||||
\(467\) | 18714.0 | 1.85435 | 0.927174 | − | 0.374631i | \(-0.122230\pi\) | ||||
0.927174 | + | 0.374631i | \(0.122230\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 988.000 | 0.0972742 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 816.000 | 0.0795751 | ||||||||
\(473\) | −4404.00 | −0.428110 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9576.00 | 0.922091 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5352.00 | −0.512123 | ||||||||
\(479\) | 12786.0 | 1.21964 | 0.609820 | − | 0.792540i | \(-0.291242\pi\) | ||||
0.609820 | + | 0.792540i | \(0.291242\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3250.00 | 0.308082 | ||||||||
\(482\) | 7252.00 | 0.685310 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4748.00 | −0.445905 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10400.0 | 0.967698 | 0.483849 | − | 0.875151i | \(-0.339238\pi\) | ||||
0.483849 | + | 0.875151i | \(0.339238\pi\) | |||||||
\(488\) | −824.000 | −0.0764359 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19548.0 | −1.79672 | −0.898359 | − | 0.439261i | \(-0.855240\pi\) | ||||
−0.898359 | + | 0.439261i | \(0.855240\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12852.0 | −1.17409 | ||||||||
\(494\) | 2900.00 | 0.264124 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4240.00 | −0.383834 | ||||||||
\(497\) | 11058.0 | 0.998026 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14939.0 | 1.34020 | 0.670102 | − | 0.742269i | \(-0.266250\pi\) | ||||
0.670102 | + | 0.742269i | \(0.266250\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4092.00 | −0.363815 | ||||||||
\(503\) | 4098.00 | 0.363262 | 0.181631 | − | 0.983367i | \(-0.441862\pi\) | ||||
0.181631 | + | 0.983367i | \(0.441862\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 432.000 | 0.0379540 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1664.00 | 0.145331 | ||||||||
\(509\) | −12216.0 | −1.06378 | −0.531891 | − | 0.846813i | \(-0.678518\pi\) | ||||
−0.531891 | + | 0.846813i | \(0.678518\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1235.00 | −0.106914 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11400.0 | 0.978273 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −864.000 | −0.0734984 | ||||||||
\(518\) | −2470.00 | −0.209509 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18492.0 | 1.55499 | 0.777494 | − | 0.628890i | \(-0.216490\pi\) | ||||
0.777494 | + | 0.628890i | \(0.216490\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5467.00 | −0.457085 | −0.228542 | − | 0.973534i | \(-0.573396\pi\) | ||||
−0.228542 | + | 0.973534i | \(0.573396\pi\) | |||||||
\(524\) | −7608.00 | −0.634269 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15348.0 | −1.27225 | ||||||||
\(527\) | 33390.0 | 2.75995 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11843.0 | −0.973371 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2204.00 | −0.179616 | ||||||||
\(533\) | 12000.0 | 0.975193 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −416.000 | −0.0335233 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8652.00 | 0.693335 | ||||||||
\(539\) | 216.000 | 0.0172612 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6983.00 | 0.554940 | 0.277470 | − | 0.960734i | \(-0.410504\pi\) | ||||
0.277470 | + | 0.960734i | \(0.410504\pi\) | |||||||
\(542\) | 12946.0 | 1.02597 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4032.00 | −0.317777 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9281.00 | 0.725461 | 0.362730 | − | 0.931894i | \(-0.381845\pi\) | ||||
0.362730 | + | 0.931894i | \(0.381845\pi\) | |||||||
\(548\) | −10848.0 | −0.845627 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2958.00 | 0.228702 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3287.00 | −0.252762 | ||||||||
\(554\) | −15650.0 | −1.20019 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1468.00 | −0.111973 | ||||||||
\(557\) | −1986.00 | −0.151076 | −0.0755382 | − | 0.997143i | \(-0.524067\pi\) | ||||
−0.0755382 | + | 0.997143i | \(0.524067\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18350.0 | −1.38841 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5520.00 | 0.414319 | ||||||||
\(563\) | −12672.0 | −0.948599 | −0.474299 | − | 0.880364i | \(-0.657299\pi\) | ||||
−0.474299 | + | 0.880364i | \(0.657299\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9602.00 | −0.713078 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4656.00 | −0.343946 | ||||||||
\(569\) | −8370.00 | −0.616676 | −0.308338 | − | 0.951277i | \(-0.599773\pi\) | ||||
−0.308338 | + | 0.951277i | \(0.599773\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19675.0 | −1.44198 | −0.720992 | − | 0.692943i | \(-0.756314\pi\) | ||||
−0.720992 | + | 0.692943i | \(0.756314\pi\) | |||||||
\(572\) | 2400.00 | 0.175435 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9120.00 | −0.663173 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26951.0 | 1.94451 | 0.972257 | − | 0.233914i | \(-0.0751535\pi\) | ||||
0.972257 | + | 0.233914i | \(0.0751535\pi\) | |||||||
\(578\) | 21926.0 | 1.57786 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9462.00 | −0.675645 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7632.00 | −0.542170 | ||||||||
\(584\) | 520.000 | 0.0368455 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16332.0 | −1.15131 | ||||||||
\(587\) | −10986.0 | −0.772471 | −0.386236 | − | 0.922400i | \(-0.626225\pi\) | ||||
−0.386236 | + | 0.922400i | \(0.626225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7685.00 | −0.537614 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1040.00 | 0.0722023 | ||||||||
\(593\) | −11226.0 | −0.777397 | −0.388699 | − | 0.921365i | \(-0.627075\pi\) | ||||
−0.388699 | + | 0.921365i | \(0.627075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12024.0 | 0.826380 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1800.00 | 0.123089 | ||||||||
\(599\) | −11400.0 | −0.777615 | −0.388807 | − | 0.921319i | \(-0.627113\pi\) | ||||
−0.388807 | + | 0.921319i | \(0.627113\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6469.00 | −0.439062 | −0.219531 | − | 0.975606i | \(-0.570453\pi\) | ||||
−0.219531 | + | 0.975606i | \(0.570453\pi\) | |||||||
\(602\) | 13946.0 | 0.944180 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10604.0 | 0.714355 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6383.00 | 0.426817 | 0.213409 | − | 0.976963i | \(-0.431543\pi\) | ||||
0.213409 | + | 0.976963i | \(0.431543\pi\) | |||||||
\(608\) | 928.000 | 0.0619003 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3600.00 | −0.238364 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10843.0 | −0.714428 | −0.357214 | − | 0.934022i | \(-0.616273\pi\) | ||||
−0.357214 | + | 0.934022i | \(0.616273\pi\) | |||||||
\(614\) | −1154.00 | −0.0758496 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1824.00 | −0.119304 | ||||||||
\(617\) | 25236.0 | 1.64662 | 0.823309 | − | 0.567594i | \(-0.192126\pi\) | ||||
0.823309 | + | 0.567594i | \(0.192126\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24809.0 | 1.61092 | 0.805459 | − | 0.592652i | \(-0.201919\pi\) | ||||
0.805459 | + | 0.592652i | \(0.201919\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15312.0 | −0.987066 | ||||||||
\(623\) | 15618.0 | 1.00437 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 5452.00 | 0.348092 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11204.0 | 0.711924 | ||||||||
\(629\) | −8190.00 | −0.519168 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11476.0 | −0.724013 | −0.362007 | − | 0.932176i | \(-0.617908\pi\) | ||||
−0.362007 | + | 0.932176i | \(0.617908\pi\) | |||||||
\(632\) | 1384.00 | 0.0871085 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18900.0 | −1.18394 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 900.000 | 0.0559801 | ||||||||
\(638\) | 2448.00 | 0.151908 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25350.0 | 1.56204 | 0.781018 | − | 0.624509i | \(-0.214701\pi\) | ||||
0.781018 | + | 0.624509i | \(0.214701\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14164.0 | −0.868699 | −0.434350 | − | 0.900744i | \(-0.643022\pi\) | ||||
−0.434350 | + | 0.900744i | \(0.643022\pi\) | |||||||
\(644\) | −1368.00 | −0.0837061 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7308.00 | −0.445092 | ||||||||
\(647\) | −7536.00 | −0.457915 | −0.228957 | − | 0.973436i | \(-0.573532\pi\) | ||||
−0.228957 | + | 0.973436i | \(0.573532\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1224.00 | 0.0740311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5648.00 | 0.339253 | ||||||||
\(653\) | −432.000 | −0.0258889 | −0.0129445 | − | 0.999916i | \(-0.504120\pi\) | ||||
−0.0129445 | + | 0.999916i | \(0.504120\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3840.00 | 0.228547 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2736.00 | 0.162098 | ||||||||
\(659\) | −10782.0 | −0.637340 | −0.318670 | − | 0.947866i | \(-0.603236\pi\) | ||||
−0.318670 | + | 0.947866i | \(0.603236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26057.0 | 1.53328 | 0.766641 | − | 0.642076i | \(-0.221926\pi\) | ||||
0.766641 | + | 0.642076i | \(0.221926\pi\) | |||||||
\(662\) | 6178.00 | 0.362711 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3984.00 | 0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1836.00 | 0.106582 | ||||||||
\(668\) | −8616.00 | −0.499046 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1236.00 | −0.0711107 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19091.0 | 1.09347 | 0.546734 | − | 0.837306i | \(-0.315871\pi\) | ||||
0.546734 | + | 0.837306i | \(0.315871\pi\) | |||||||
\(674\) | −15788.0 | −0.902272 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1212.00 | 0.0689577 | ||||||||
\(677\) | 1044.00 | 0.0592676 | 0.0296338 | − | 0.999561i | \(-0.490566\pi\) | ||||
0.0296338 | + | 0.999561i | \(0.490566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15599.0 | −0.881642 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6360.00 | −0.357092 | ||||||||
\(683\) | 26046.0 | 1.45918 | 0.729592 | − | 0.683883i | \(-0.239710\pi\) | ||||
0.729592 | + | 0.683883i | \(0.239710\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12350.0 | 0.687355 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5872.00 | −0.325389 | ||||||||
\(689\) | −31800.0 | −1.75832 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28060.0 | −1.54479 | −0.772397 | − | 0.635140i | \(-0.780942\pi\) | ||||
−0.772397 | + | 0.635140i | \(0.780942\pi\) | |||||||
\(692\) | 936.000 | 0.0514182 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6900.00 | −0.377407 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30240.0 | −1.64336 | ||||||||
\(698\) | 4522.00 | 0.245215 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16794.0 | 0.904851 | 0.452426 | − | 0.891802i | \(-0.350559\pi\) | ||||
0.452426 | + | 0.891802i | \(0.350559\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1885.00 | 0.101130 | ||||||||
\(704\) | 768.000 | 0.0411152 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23088.0 | 1.23078 | ||||||||
\(707\) | 22800.0 | 1.21285 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2495.00 | 0.132160 | 0.0660802 | − | 0.997814i | \(-0.478951\pi\) | ||||
0.0660802 | + | 0.997814i | \(0.478951\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6576.00 | −0.346132 | ||||||||
\(713\) | −4770.00 | −0.250544 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9888.00 | 0.516106 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −396.000 | −0.0205830 | ||||||||
\(719\) | 1950.00 | 0.101144 | 0.0505721 | − | 0.998720i | \(-0.483896\pi\) | ||||
0.0505721 | + | 0.998720i | \(0.483896\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 38779.0 | 2.00306 | ||||||||
\(722\) | −12036.0 | −0.620407 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −760.000 | −0.0390127 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16127.0 | 0.822720 | 0.411360 | − | 0.911473i | \(-0.365054\pi\) | ||||
0.411360 | + | 0.911473i | \(0.365054\pi\) | |||||||
\(728\) | −7600.00 | −0.386916 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46242.0 | 2.33970 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12634.0 | −0.636627 | −0.318313 | − | 0.947986i | \(-0.603116\pi\) | ||||
−0.318313 | + | 0.947986i | \(0.603116\pi\) | |||||||
\(734\) | 20776.0 | 1.04476 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 576.000 | 0.0288473 | ||||||||
\(737\) | −624.000 | −0.0311877 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10420.0 | −0.518682 | −0.259341 | − | 0.965786i | \(-0.583505\pi\) | ||||
−0.259341 | + | 0.965786i | \(0.583505\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 24168.0 | 1.19573 | ||||||||
\(743\) | −21936.0 | −1.08311 | −0.541557 | − | 0.840664i | \(-0.682165\pi\) | ||||
−0.541557 | + | 0.840664i | \(0.682165\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9734.00 | −0.477731 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6048.00 | −0.295637 | ||||||||
\(749\) | 24282.0 | 1.18457 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21715.0 | −1.05512 | −0.527558 | − | 0.849519i | \(-0.676892\pi\) | ||||
−0.527558 | + | 0.849519i | \(0.676892\pi\) | |||||||
\(752\) | −1152.00 | −0.0558632 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10200.0 | 0.492655 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19849.0 | −0.953004 | −0.476502 | − | 0.879173i | \(-0.658096\pi\) | ||||
−0.476502 | + | 0.879173i | \(0.658096\pi\) | |||||||
\(758\) | 1312.00 | 0.0628681 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29952.0 | −1.42675 | −0.713377 | − | 0.700781i | \(-0.752835\pi\) | ||||
−0.713377 | + | 0.700781i | \(0.752835\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3895.00 | 0.184808 | ||||||||
\(764\) | 6096.00 | 0.288672 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6156.00 | 0.290372 | ||||||||
\(767\) | 5100.00 | 0.240092 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17582.0 | 0.824477 | 0.412239 | − | 0.911076i | \(-0.364747\pi\) | ||||
0.412239 | + | 0.911076i | \(0.364747\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 13340.0 | 0.621913 | ||||||||
\(773\) | 19194.0 | 0.893092 | 0.446546 | − | 0.894761i | \(-0.352654\pi\) | ||||
0.446546 | + | 0.894761i | \(0.352654\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6568.00 | 0.303837 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3288.00 | 0.151517 | ||||||||
\(779\) | 6960.00 | 0.320113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6984.00 | −0.319984 | ||||||||
\(782\) | −4536.00 | −0.207426 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 288.000 | 0.0131195 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9823.00 | −0.444920 | −0.222460 | − | 0.974942i | \(-0.571409\pi\) | ||||
−0.222460 | + | 0.974942i | \(0.571409\pi\) | |||||||
\(788\) | −17760.0 | −0.802886 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28500.0 | 1.28109 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5150.00 | −0.230620 | ||||||||
\(794\) | 11458.0 | 0.512127 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8768.00 | 0.390419 | ||||||||
\(797\) | 22188.0 | 0.986122 | 0.493061 | − | 0.869995i | \(-0.335878\pi\) | ||||
0.493061 | + | 0.869995i | \(0.335878\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9072.00 | 0.401682 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3552.00 | −0.156391 | ||||||||
\(803\) | 780.000 | 0.0342785 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26500.0 | −1.15809 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9600.00 | −0.417979 | ||||||||
\(809\) | 9654.00 | 0.419551 | 0.209775 | − | 0.977750i | \(-0.432727\pi\) | ||||
0.209775 | + | 0.977750i | \(0.432727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32377.0 | −1.40186 | −0.700931 | − | 0.713229i | \(-0.747232\pi\) | ||||
−0.700931 | + | 0.713229i | \(0.747232\pi\) | |||||||
\(812\) | −7752.00 | −0.335027 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1560.00 | 0.0671720 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10643.0 | −0.455755 | ||||||||
\(818\) | 25684.0 | 1.09782 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23952.0 | 1.01819 | 0.509093 | − | 0.860712i | \(-0.329981\pi\) | ||||
0.509093 | + | 0.860712i | \(0.329981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5072.00 | 0.214822 | 0.107411 | − | 0.994215i | \(-0.465744\pi\) | ||||
0.107411 | + | 0.994215i | \(0.465744\pi\) | |||||||
\(824\) | −16328.0 | −0.690307 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3876.00 | −0.163273 | ||||||||
\(827\) | −3024.00 | −0.127152 | −0.0635760 | − | 0.997977i | \(-0.520251\pi\) | ||||
−0.0635760 | + | 0.997977i | \(0.520251\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3049.00 | −0.127740 | −0.0638698 | − | 0.997958i | \(-0.520344\pi\) | ||||
−0.0638698 | + | 0.997958i | \(0.520344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3200.00 | 0.133341 | ||||||||
\(833\) | −2268.00 | −0.0943356 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1392.00 | 0.0575877 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −22596.0 | −0.931463 | ||||||||
\(839\) | −40374.0 | −1.66134 | −0.830671 | − | 0.556764i | \(-0.812043\pi\) | ||||
−0.830671 | + | 0.556764i | \(0.812043\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13985.0 | −0.573414 | ||||||||
\(842\) | 6862.00 | 0.280855 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6928.00 | −0.282549 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22553.0 | 0.914912 | ||||||||
\(848\) | −10176.0 | −0.412082 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1170.00 | 0.0471294 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 40322.0 | 1.61852 | 0.809261 | − | 0.587449i | \(-0.199868\pi\) | ||||
0.809261 | + | 0.587449i | \(0.199868\pi\) | |||||||
\(854\) | 3914.00 | 0.156832 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10224.0 | −0.408235 | ||||||||
\(857\) | −19932.0 | −0.794474 | −0.397237 | − | 0.917716i | \(-0.630031\pi\) | ||||
−0.397237 | + | 0.917716i | \(0.630031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34553.0 | 1.37245 | 0.686224 | − | 0.727390i | \(-0.259267\pi\) | ||||
0.686224 | + | 0.727390i | \(0.259267\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21060.0 | 0.832142 | ||||||||
\(863\) | 6918.00 | 0.272875 | 0.136438 | − | 0.990649i | \(-0.456435\pi\) | ||||
0.136438 | + | 0.990649i | \(0.456435\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6358.00 | 0.249485 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20140.0 | 0.787553 | ||||||||
\(869\) | 2076.00 | 0.0810397 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2600.00 | −0.101145 | ||||||||
\(872\) | −1640.00 | −0.0636897 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1044.00 | 0.0404048 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6497.00 | 0.250157 | 0.125079 | − | 0.992147i | \(-0.460082\pi\) | ||||
0.125079 | + | 0.992147i | \(0.460082\pi\) | |||||||
\(878\) | 12094.0 | 0.464866 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44082.0 | −1.68577 | −0.842883 | − | 0.538096i | \(-0.819144\pi\) | ||||
−0.842883 | + | 0.538096i | \(0.819144\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10127.0 | 0.385958 | 0.192979 | − | 0.981203i | \(-0.438185\pi\) | ||||
0.192979 | + | 0.981203i | \(0.438185\pi\) | |||||||
\(884\) | −25200.0 | −0.958787 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33108.0 | 1.25540 | ||||||||
\(887\) | −12936.0 | −0.489682 | −0.244841 | − | 0.969563i | \(-0.578736\pi\) | ||||
−0.244841 | + | 0.969563i | \(0.578736\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7904.00 | −0.298191 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −23956.0 | −0.899222 | ||||||||
\(893\) | −2088.00 | −0.0782444 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2432.00 | −0.0906779 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8892.00 | −0.330434 | ||||||||
\(899\) | −27030.0 | −1.00278 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 80136.0 | 2.96306 | ||||||||
\(902\) | 5760.00 | 0.212624 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12000.0 | −0.441498 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45853.0 | −1.67864 | −0.839319 | − | 0.543640i | \(-0.817046\pi\) | ||||
−0.839319 | + | 0.543640i | \(0.817046\pi\) | |||||||
\(908\) | −13200.0 | −0.482442 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34530.0 | −1.25580 | −0.627898 | − | 0.778296i | \(-0.716084\pi\) | ||||
−0.627898 | + | 0.778296i | \(0.716084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5976.00 | 0.216623 | ||||||||
\(914\) | 292.000 | 0.0105673 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17516.0 | 0.631818 | ||||||||
\(917\) | 36138.0 | 1.30140 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31015.0 | −1.11326 | −0.556632 | − | 0.830759i | \(-0.687907\pi\) | ||||
−0.556632 | + | 0.830759i | \(0.687907\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19644.0 | 0.701671 | ||||||||
\(923\) | −29100.0 | −1.03774 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15862.0 | 0.562913 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3264.00 | 0.115459 | ||||||||
\(929\) | 36186.0 | 1.27796 | 0.638980 | − | 0.769224i | \(-0.279357\pi\) | ||||
0.638980 | + | 0.769224i | \(0.279357\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 522.000 | 0.0183758 | ||||||||
\(932\) | 11832.0 | 0.415848 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 37428.0 | 1.31122 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1441.00 | −0.0502406 | −0.0251203 | − | 0.999684i | \(-0.507997\pi\) | ||||
−0.0251203 | + | 0.999684i | \(0.507997\pi\) | |||||||
\(938\) | 1976.00 | 0.0687832 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −33168.0 | −1.14904 | −0.574520 | − | 0.818491i | \(-0.694811\pi\) | ||||
−0.574520 | + | 0.818491i | \(0.694811\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4320.00 | 0.149182 | ||||||||
\(944\) | 1632.00 | 0.0562681 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8808.00 | −0.302720 | ||||||||
\(947\) | −42054.0 | −1.44305 | −0.721527 | − | 0.692387i | \(-0.756559\pi\) | ||||
−0.721527 | + | 0.692387i | \(0.756559\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3250.00 | 0.111169 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 19152.0 | 0.652017 | ||||||||
\(953\) | 26460.0 | 0.899395 | 0.449698 | − | 0.893181i | \(-0.351532\pi\) | ||||
0.449698 | + | 0.893181i | \(0.351532\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10704.0 | −0.362126 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 25572.0 | 0.862415 | ||||||||
\(959\) | 51528.0 | 1.73506 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40434.0 | 1.35726 | ||||||||
\(962\) | 6500.00 | 0.217847 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14504.0 | 0.484588 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29239.0 | −0.972350 | −0.486175 | − | 0.873861i | \(-0.661608\pi\) | ||||
−0.486175 | + | 0.873861i | \(0.661608\pi\) | |||||||
\(968\) | −9496.00 | −0.315303 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54288.0 | −1.79422 | −0.897109 | − | 0.441810i | \(-0.854336\pi\) | ||||
−0.897109 | + | 0.441810i | \(0.854336\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6973.00 | 0.229747 | ||||||||
\(974\) | 20800.0 | 0.684266 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1648.00 | −0.0540484 | ||||||||
\(977\) | −38634.0 | −1.26511 | −0.632554 | − | 0.774516i | \(-0.717993\pi\) | ||||
−0.632554 | + | 0.774516i | \(0.717993\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9864.00 | −0.322017 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −39096.0 | −1.27047 | ||||||||
\(983\) | −19548.0 | −0.634267 | −0.317133 | − | 0.948381i | \(-0.602720\pi\) | ||||
−0.317133 | + | 0.948381i | \(0.602720\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −25704.0 | −0.830205 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5800.00 | 0.186764 | ||||||||
\(989\) | −6606.00 | −0.212395 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28445.0 | 0.911791 | 0.455896 | − | 0.890033i | \(-0.349319\pi\) | ||||
0.455896 | + | 0.890033i | \(0.349319\pi\) | |||||||
\(992\) | −8480.00 | −0.271412 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22116.0 | 0.705711 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48706.0 | −1.54718 | −0.773588 | − | 0.633689i | \(-0.781540\pi\) | ||||
−0.773588 | + | 0.633689i | \(0.781540\pi\) | |||||||
\(998\) | 29878.0 | 0.947667 | ||||||||
\(999\) | 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 | 1350.4.a.q.1.1 | yes | 1 | |
3.2 | odd | 2 | 1350.4.a.c.1.1 | ✓ | 1 | ||
5.2 | odd | 4 | 1350.4.c.m.649.2 | 2 | |||
5.3 | odd | 4 | 1350.4.c.m.649.1 | 2 | |||
5.4 | even | 2 | 1350.4.a.k.1.1 | yes | 1 | ||
15.2 | even | 4 | 1350.4.c.h.649.1 | 2 | |||
15.8 | even | 4 | 1350.4.c.h.649.2 | 2 | |||
15.14 | odd | 2 | 1350.4.a.y.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1350.4.a.c.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1350.4.a.k.1.1 | yes | 1 | 5.4 | even | 2 | ||
1350.4.a.q.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
1350.4.a.y.1.1 | yes | 1 | 15.14 | odd | 2 | ||
1350.4.c.h.649.1 | 2 | 15.2 | even | 4 | |||
1350.4.c.h.649.2 | 2 | 15.8 | even | 4 | |||
1350.4.c.m.649.1 | 2 | 5.3 | odd | 4 | |||
1350.4.c.m.649.2 | 2 | 5.2 | odd | 4 |