Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,4,Mod(1,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, 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("882.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.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: | \(52.0396846251\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 882.1 |
$q$-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 | ||||||||
\(5\) | −7.00000 | −0.626099 | −0.313050 | − | 0.949737i | \(-0.601351\pi\) | ||||
−0.313050 | + | 0.949737i | \(0.601351\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.0000 | −0.442719 | ||||||||
\(11\) | −35.0000 | −0.959354 | −0.479677 | − | 0.877445i | \(-0.659246\pi\) | ||||
−0.479677 | + | 0.877445i | \(0.659246\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 66.0000 | 1.40809 | 0.704043 | − | 0.710158i | \(-0.251376\pi\) | ||||
0.704043 | + | 0.710158i | \(0.251376\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | −59.0000 | −0.841741 | −0.420871 | − | 0.907121i | \(-0.638275\pi\) | ||||
−0.420871 | + | 0.907121i | \(0.638275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 137.000 | 1.65421 | 0.827104 | − | 0.562049i | \(-0.189987\pi\) | ||||
0.827104 | + | 0.562049i | \(0.189987\pi\) | |||||||
\(20\) | −28.0000 | −0.313050 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −70.0000 | −0.678366 | ||||||||
\(23\) | 7.00000 | 0.0634609 | 0.0317305 | − | 0.999496i | \(-0.489898\pi\) | ||||
0.0317305 | + | 0.999496i | \(0.489898\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −76.0000 | −0.608000 | ||||||||
\(26\) | 132.000 | 0.995667 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −106.000 | −0.678748 | −0.339374 | − | 0.940651i | \(-0.610215\pi\) | ||||
−0.339374 | + | 0.940651i | \(0.610215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 75.0000 | 0.434529 | 0.217264 | − | 0.976113i | \(-0.430287\pi\) | ||||
0.217264 | + | 0.976113i | \(0.430287\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −118.000 | −0.595201 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.0000 | 0.0488754 | 0.0244377 | − | 0.999701i | \(-0.492220\pi\) | ||||
0.0244377 | + | 0.999701i | \(0.492220\pi\) | |||||||
\(38\) | 274.000 | 1.16970 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −56.0000 | −0.221359 | ||||||||
\(41\) | 498.000 | 1.89694 | 0.948470 | − | 0.316867i | \(-0.102631\pi\) | ||||
0.948470 | + | 0.316867i | \(0.102631\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 260.000 | 0.922084 | 0.461042 | − | 0.887378i | \(-0.347476\pi\) | ||||
0.461042 | + | 0.887378i | \(0.347476\pi\) | |||||||
\(44\) | −140.000 | −0.479677 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.0000 | 0.0448736 | ||||||||
\(47\) | 171.000 | 0.530700 | 0.265350 | − | 0.964152i | \(-0.414512\pi\) | ||||
0.265350 | + | 0.964152i | \(0.414512\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −152.000 | −0.429921 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 264.000 | 0.704043 | ||||||||
\(53\) | 417.000 | 1.08074 | 0.540371 | − | 0.841427i | \(-0.318284\pi\) | ||||
0.540371 | + | 0.841427i | \(0.318284\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 245.000 | 0.600651 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −212.000 | −0.479948 | ||||||||
\(59\) | 17.0000 | 0.0375121 | 0.0187560 | − | 0.999824i | \(-0.494029\pi\) | ||||
0.0187560 | + | 0.999824i | \(0.494029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 51.0000 | 0.107047 | 0.0535236 | − | 0.998567i | \(-0.482955\pi\) | ||||
0.0535236 | + | 0.998567i | \(0.482955\pi\) | |||||||
\(62\) | 150.000 | 0.307258 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −462.000 | −0.881601 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 439.000 | 0.800483 | 0.400242 | − | 0.916410i | \(-0.368926\pi\) | ||||
0.400242 | + | 0.916410i | \(0.368926\pi\) | |||||||
\(68\) | −236.000 | −0.420871 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 784.000 | 1.31047 | 0.655237 | − | 0.755423i | \(-0.272569\pi\) | ||||
0.655237 | + | 0.755423i | \(0.272569\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 295.000 | 0.472974 | 0.236487 | − | 0.971635i | \(-0.424004\pi\) | ||||
0.236487 | + | 0.971635i | \(0.424004\pi\) | |||||||
\(74\) | 22.0000 | 0.0345601 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 548.000 | 0.827104 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −495.000 | −0.704960 | −0.352480 | − | 0.935819i | \(-0.614662\pi\) | ||||
−0.352480 | + | 0.935819i | \(0.614662\pi\) | |||||||
\(80\) | −112.000 | −0.156525 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 996.000 | 1.34134 | ||||||||
\(83\) | −932.000 | −1.23253 | −0.616267 | − | 0.787537i | \(-0.711356\pi\) | ||||
−0.616267 | + | 0.787537i | \(0.711356\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 413.000 | 0.527013 | ||||||||
\(86\) | 520.000 | 0.652012 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −280.000 | −0.339183 | ||||||||
\(89\) | 873.000 | 1.03975 | 0.519875 | − | 0.854242i | \(-0.325978\pi\) | ||||
0.519875 | + | 0.854242i | \(0.325978\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 28.0000 | 0.0317305 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 342.000 | 0.375262 | ||||||||
\(95\) | −959.000 | −1.03570 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −290.000 | −0.303557 | −0.151779 | − | 0.988415i | \(-0.548500\pi\) | ||||
−0.151779 | + | 0.988415i | \(0.548500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −304.000 | −0.304000 | ||||||||
\(101\) | 1085.00 | 1.06893 | 0.534463 | − | 0.845192i | \(-0.320514\pi\) | ||||
0.534463 | + | 0.845192i | \(0.320514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1553.00 | 1.48565 | 0.742823 | − | 0.669487i | \(-0.233486\pi\) | ||||
0.742823 | + | 0.669487i | \(0.233486\pi\) | |||||||
\(104\) | 528.000 | 0.497833 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 834.000 | 0.764200 | ||||||||
\(107\) | −129.000 | −0.116550 | −0.0582752 | − | 0.998301i | \(-0.518560\pi\) | ||||
−0.0582752 | + | 0.998301i | \(0.518560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −965.000 | −0.847984 | −0.423992 | − | 0.905666i | \(-0.639372\pi\) | ||||
−0.423992 | + | 0.905666i | \(0.639372\pi\) | |||||||
\(110\) | 490.000 | 0.424724 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 50.0000 | 0.0416248 | 0.0208124 | − | 0.999783i | \(-0.493375\pi\) | ||||
0.0208124 | + | 0.999783i | \(0.493375\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −49.0000 | −0.0397328 | ||||||||
\(116\) | −424.000 | −0.339374 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 34.0000 | 0.0265250 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −106.000 | −0.0796394 | ||||||||
\(122\) | 102.000 | 0.0756938 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 300.000 | 0.217264 | ||||||||
\(125\) | 1407.00 | 1.00677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 936.000 | 0.653989 | 0.326994 | − | 0.945026i | \(-0.393964\pi\) | ||||
0.326994 | + | 0.945026i | \(0.393964\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −924.000 | −0.623386 | ||||||||
\(131\) | 755.000 | 0.503547 | 0.251773 | − | 0.967786i | \(-0.418986\pi\) | ||||
0.251773 | + | 0.967786i | \(0.418986\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 878.000 | 0.566027 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −472.000 | −0.297600 | ||||||||
\(137\) | 2357.00 | 1.46987 | 0.734935 | − | 0.678138i | \(-0.237213\pi\) | ||||
0.734935 | + | 0.678138i | \(0.237213\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 28.0000 | 0.0170858 | 0.00854291 | − | 0.999964i | \(-0.497281\pi\) | ||||
0.00854291 | + | 0.999964i | \(0.497281\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1568.00 | 0.926645 | ||||||||
\(143\) | −2310.00 | −1.35085 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 742.000 | 0.424964 | ||||||||
\(146\) | 590.000 | 0.334443 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 44.0000 | 0.0244377 | ||||||||
\(149\) | −2295.00 | −1.26184 | −0.630919 | − | 0.775849i | \(-0.717322\pi\) | ||||
−0.630919 | + | 0.775849i | \(0.717322\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1109.00 | −0.597676 | −0.298838 | − | 0.954304i | \(-0.596599\pi\) | ||||
−0.298838 | + | 0.954304i | \(0.596599\pi\) | |||||||
\(152\) | 1096.00 | 0.584851 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −525.000 | −0.272058 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1559.00 | 0.792495 | 0.396248 | − | 0.918144i | \(-0.370312\pi\) | ||||
0.396248 | + | 0.918144i | \(0.370312\pi\) | |||||||
\(158\) | −990.000 | −0.498482 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −224.000 | −0.110680 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2251.00 | −1.08167 | −0.540834 | − | 0.841129i | \(-0.681891\pi\) | ||||
−0.540834 | + | 0.841129i | \(0.681891\pi\) | |||||||
\(164\) | 1992.00 | 0.948470 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1864.00 | −0.871533 | ||||||||
\(167\) | −2788.00 | −1.29187 | −0.645934 | − | 0.763393i | \(-0.723532\pi\) | ||||
−0.645934 | + | 0.763393i | \(0.723532\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2159.00 | 0.982704 | ||||||||
\(170\) | 826.000 | 0.372655 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1040.00 | 0.461042 | ||||||||
\(173\) | −1579.00 | −0.693926 | −0.346963 | − | 0.937879i | \(-0.612787\pi\) | ||||
−0.346963 | + | 0.937879i | \(0.612787\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −560.000 | −0.239839 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1746.00 | 0.735215 | ||||||||
\(179\) | −2451.00 | −1.02344 | −0.511722 | − | 0.859151i | \(-0.670992\pi\) | ||||
−0.511722 | + | 0.859151i | \(0.670992\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1170.00 | −0.480472 | −0.240236 | − | 0.970715i | \(-0.577225\pi\) | ||||
−0.240236 | + | 0.970715i | \(0.577225\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 56.0000 | 0.0224368 | ||||||||
\(185\) | −77.0000 | −0.0306008 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2065.00 | 0.807528 | ||||||||
\(188\) | 684.000 | 0.265350 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1918.00 | −0.732349 | ||||||||
\(191\) | 1275.00 | 0.483014 | 0.241507 | − | 0.970399i | \(-0.422358\pi\) | ||||
0.241507 | + | 0.970399i | \(0.422358\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 35.0000 | 0.0130537 | 0.00652683 | − | 0.999979i | \(-0.497922\pi\) | ||||
0.00652683 | + | 0.999979i | \(0.497922\pi\) | |||||||
\(194\) | −580.000 | −0.214647 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2734.00 | 0.988779 | 0.494389 | − | 0.869241i | \(-0.335392\pi\) | ||||
0.494389 | + | 0.869241i | \(0.335392\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2243.00 | 0.799005 | 0.399503 | − | 0.916732i | \(-0.369183\pi\) | ||||
0.399503 | + | 0.916732i | \(0.369183\pi\) | |||||||
\(200\) | −608.000 | −0.214960 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2170.00 | 0.755845 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3486.00 | −1.18767 | ||||||||
\(206\) | 3106.00 | 1.05051 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1056.00 | 0.352021 | ||||||||
\(209\) | −4795.00 | −1.58697 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1172.00 | 0.382388 | 0.191194 | − | 0.981552i | \(-0.438764\pi\) | ||||
0.191194 | + | 0.981552i | \(0.438764\pi\) | |||||||
\(212\) | 1668.00 | 0.540371 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −258.000 | −0.0824136 | ||||||||
\(215\) | −1820.00 | −0.577316 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1930.00 | −0.599615 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 980.000 | 0.300325 | ||||||||
\(221\) | −3894.00 | −1.18524 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2024.00 | 0.607790 | 0.303895 | − | 0.952706i | \(-0.401713\pi\) | ||||
0.303895 | + | 0.952706i | \(0.401713\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 100.000 | 0.0294332 | ||||||||
\(227\) | −2571.00 | −0.751732 | −0.375866 | − | 0.926674i | \(-0.622655\pi\) | ||||
−0.375866 | + | 0.926674i | \(0.622655\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 895.000 | 0.258268 | 0.129134 | − | 0.991627i | \(-0.458780\pi\) | ||||
0.129134 | + | 0.991627i | \(0.458780\pi\) | |||||||
\(230\) | −98.0000 | −0.0280953 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −848.000 | −0.239974 | ||||||||
\(233\) | −1787.00 | −0.502447 | −0.251224 | − | 0.967929i | \(-0.580833\pi\) | ||||
−0.251224 | + | 0.967929i | \(0.580833\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1197.00 | −0.332271 | ||||||||
\(236\) | 68.0000 | 0.0187560 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 5100.00 | 1.38030 | 0.690150 | − | 0.723667i | \(-0.257545\pi\) | ||||
0.690150 | + | 0.723667i | \(0.257545\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4177.00 | −1.11645 | −0.558225 | − | 0.829690i | \(-0.688517\pi\) | ||||
−0.558225 | + | 0.829690i | \(0.688517\pi\) | |||||||
\(242\) | −212.000 | −0.0563135 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 204.000 | 0.0535236 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9042.00 | 2.32927 | ||||||||
\(248\) | 600.000 | 0.153629 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2814.00 | 0.711892 | ||||||||
\(251\) | 4680.00 | 1.17689 | 0.588444 | − | 0.808538i | \(-0.299741\pi\) | ||||
0.588444 | + | 0.808538i | \(0.299741\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −245.000 | −0.0608815 | ||||||||
\(254\) | 1872.00 | 0.462440 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 1749.00 | 0.424512 | 0.212256 | − | 0.977214i | \(-0.431919\pi\) | ||||
0.212256 | + | 0.977214i | \(0.431919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1848.00 | −0.440800 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1510.00 | 0.356061 | ||||||||
\(263\) | 4473.00 | 1.04873 | 0.524367 | − | 0.851492i | \(-0.324302\pi\) | ||||
0.524367 | + | 0.851492i | \(0.324302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2919.00 | −0.676652 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1756.00 | 0.400242 | ||||||||
\(269\) | −1975.00 | −0.447650 | −0.223825 | − | 0.974629i | \(-0.571854\pi\) | ||||
−0.223825 | + | 0.974629i | \(0.571854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8439.00 | −1.89163 | −0.945817 | − | 0.324701i | \(-0.894736\pi\) | ||||
−0.945817 | + | 0.324701i | \(0.894736\pi\) | |||||||
\(272\) | −944.000 | −0.210435 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4714.00 | 1.03935 | ||||||||
\(275\) | 2660.00 | 0.583287 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 527.000 | 0.114312 | 0.0571559 | − | 0.998365i | \(-0.481797\pi\) | ||||
0.0571559 | + | 0.998365i | \(0.481797\pi\) | |||||||
\(278\) | 56.0000 | 0.0120815 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 202.000 | 0.0428837 | 0.0214418 | − | 0.999770i | \(-0.493174\pi\) | ||||
0.0214418 | + | 0.999770i | \(0.493174\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7949.00 | −1.66968 | −0.834839 | − | 0.550494i | \(-0.814439\pi\) | ||||
−0.834839 | + | 0.550494i | \(0.814439\pi\) | |||||||
\(284\) | 3136.00 | 0.655237 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4620.00 | −0.955197 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1432.00 | −0.291472 | ||||||||
\(290\) | 1484.00 | 0.300495 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1180.00 | 0.236487 | ||||||||
\(293\) | −318.000 | −0.0634053 | −0.0317027 | − | 0.999497i | \(-0.510093\pi\) | ||||
−0.0317027 | + | 0.999497i | \(0.510093\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −119.000 | −0.0234863 | ||||||||
\(296\) | 88.0000 | 0.0172801 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4590.00 | −0.892254 | ||||||||
\(299\) | 462.000 | 0.0893584 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2218.00 | −0.422621 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2192.00 | 0.413552 | ||||||||
\(305\) | −357.000 | −0.0670222 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8132.00 | −1.51178 | −0.755892 | − | 0.654696i | \(-0.772797\pi\) | ||||
−0.755892 | + | 0.654696i | \(0.772797\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1050.00 | −0.192374 | ||||||||
\(311\) | 929.000 | 0.169385 | 0.0846925 | − | 0.996407i | \(-0.473009\pi\) | ||||
0.0846925 | + | 0.996407i | \(0.473009\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −209.000 | −0.0377424 | −0.0188712 | − | 0.999822i | \(-0.506007\pi\) | ||||
−0.0188712 | + | 0.999822i | \(0.506007\pi\) | |||||||
\(314\) | 3118.00 | 0.560379 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1980.00 | −0.352480 | ||||||||
\(317\) | −7131.00 | −1.26346 | −0.631730 | − | 0.775188i | \(-0.717655\pi\) | ||||
−0.631730 | + | 0.775188i | \(0.717655\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3710.00 | 0.651160 | ||||||||
\(320\) | −448.000 | −0.0782624 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8083.00 | −1.39242 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5016.00 | −0.856116 | ||||||||
\(326\) | −4502.00 | −0.764855 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3984.00 | 0.670670 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6571.00 | −1.09116 | −0.545581 | − | 0.838058i | \(-0.683691\pi\) | ||||
−0.545581 | + | 0.838058i | \(0.683691\pi\) | |||||||
\(332\) | −3728.00 | −0.616267 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5576.00 | −0.913488 | ||||||||
\(335\) | −3073.00 | −0.501182 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11466.0 | −1.85339 | −0.926696 | − | 0.375813i | \(-0.877364\pi\) | ||||
−0.926696 | + | 0.375813i | \(0.877364\pi\) | |||||||
\(338\) | 4318.00 | 0.694876 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1652.00 | 0.263507 | ||||||||
\(341\) | −2625.00 | −0.416867 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2080.00 | 0.326006 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3158.00 | −0.490680 | ||||||||
\(347\) | 9777.00 | 1.51256 | 0.756278 | − | 0.654251i | \(-0.227016\pi\) | ||||
0.756278 | + | 0.654251i | \(0.227016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11914.0 | 1.82734 | 0.913670 | − | 0.406456i | \(-0.133236\pi\) | ||||
0.913670 | + | 0.406456i | \(0.133236\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1120.00 | −0.169591 | ||||||||
\(353\) | −9123.00 | −1.37555 | −0.687774 | − | 0.725925i | \(-0.741412\pi\) | ||||
−0.687774 | + | 0.725925i | \(0.741412\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5488.00 | −0.820487 | ||||||||
\(356\) | 3492.00 | 0.519875 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4902.00 | −0.723684 | ||||||||
\(359\) | −8149.00 | −1.19802 | −0.599008 | − | 0.800743i | \(-0.704438\pi\) | ||||
−0.599008 | + | 0.800743i | \(0.704438\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11910.0 | 1.73640 | ||||||||
\(362\) | −2340.00 | −0.339745 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2065.00 | −0.296129 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9671.00 | 1.37554 | 0.687769 | − | 0.725930i | \(-0.258590\pi\) | ||||
0.687769 | + | 0.725930i | \(0.258590\pi\) | |||||||
\(368\) | 112.000 | 0.0158652 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −154.000 | −0.0216381 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4109.00 | −0.570391 | −0.285196 | − | 0.958469i | \(-0.592059\pi\) | ||||
−0.285196 | + | 0.958469i | \(0.592059\pi\) | |||||||
\(374\) | 4130.00 | 0.571009 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1368.00 | 0.187631 | ||||||||
\(377\) | −6996.00 | −0.955736 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3488.00 | −0.472735 | −0.236367 | − | 0.971664i | \(-0.575957\pi\) | ||||
−0.236367 | + | 0.971664i | \(0.575957\pi\) | |||||||
\(380\) | −3836.00 | −0.517849 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2550.00 | 0.341543 | ||||||||
\(383\) | −8717.00 | −1.16297 | −0.581485 | − | 0.813557i | \(-0.697528\pi\) | ||||
−0.581485 | + | 0.813557i | \(0.697528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 70.0000 | 0.00923033 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1160.00 | −0.151779 | ||||||||
\(389\) | −163.000 | −0.0212453 | −0.0106227 | − | 0.999944i | \(-0.503381\pi\) | ||||
−0.0106227 | + | 0.999944i | \(0.503381\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −413.000 | −0.0534177 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5468.00 | 0.699172 | ||||||||
\(395\) | 3465.00 | 0.441375 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 999.000 | 0.126293 | 0.0631466 | − | 0.998004i | \(-0.479886\pi\) | ||||
0.0631466 | + | 0.998004i | \(0.479886\pi\) | |||||||
\(398\) | 4486.00 | 0.564982 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1216.00 | −0.152000 | ||||||||
\(401\) | 14757.0 | 1.83773 | 0.918865 | − | 0.394573i | \(-0.129107\pi\) | ||||
0.918865 | + | 0.394573i | \(0.129107\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4950.00 | 0.611854 | ||||||||
\(404\) | 4340.00 | 0.534463 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −385.000 | −0.0468888 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −133.000 | −0.0160793 | −0.00803964 | − | 0.999968i | \(-0.502559\pi\) | ||||
−0.00803964 | + | 0.999968i | \(0.502559\pi\) | |||||||
\(410\) | −6972.00 | −0.839811 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6212.00 | 0.742823 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6524.00 | 0.771688 | ||||||||
\(416\) | 2112.00 | 0.248917 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9590.00 | −1.12216 | ||||||||
\(419\) | 6420.00 | 0.748538 | 0.374269 | − | 0.927320i | \(-0.377894\pi\) | ||||
0.374269 | + | 0.927320i | \(0.377894\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10266.0 | 1.18844 | 0.594221 | − | 0.804302i | \(-0.297460\pi\) | ||||
0.594221 | + | 0.804302i | \(0.297460\pi\) | |||||||
\(422\) | 2344.00 | 0.270389 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3336.00 | 0.382100 | ||||||||
\(425\) | 4484.00 | 0.511779 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −516.000 | −0.0582752 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3640.00 | −0.408224 | ||||||||
\(431\) | 15213.0 | 1.70020 | 0.850098 | − | 0.526625i | \(-0.176543\pi\) | ||||
0.850098 | + | 0.526625i | \(0.176543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1378.00 | −0.152939 | −0.0764693 | − | 0.997072i | \(-0.524365\pi\) | ||||
−0.0764693 | + | 0.997072i | \(0.524365\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3860.00 | −0.423992 | ||||||||
\(437\) | 959.000 | 0.104978 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2763.00 | −0.300389 | −0.150195 | − | 0.988656i | \(-0.547990\pi\) | ||||
−0.150195 | + | 0.988656i | \(0.547990\pi\) | |||||||
\(440\) | 1960.00 | 0.212362 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7788.00 | −0.838094 | ||||||||
\(443\) | −5849.00 | −0.627301 | −0.313651 | − | 0.949538i | \(-0.601552\pi\) | ||||
−0.313651 | + | 0.949538i | \(0.601552\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6111.00 | −0.650987 | ||||||||
\(446\) | 4048.00 | 0.429772 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4582.00 | −0.481599 | −0.240799 | − | 0.970575i | \(-0.577410\pi\) | ||||
−0.240799 | + | 0.970575i | \(0.577410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17430.0 | −1.81984 | ||||||||
\(452\) | 200.000 | 0.0208124 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5142.00 | −0.531555 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11551.0 | 1.18235 | 0.591174 | − | 0.806544i | \(-0.298665\pi\) | ||||
0.591174 | + | 0.806544i | \(0.298665\pi\) | |||||||
\(458\) | 1790.00 | 0.182623 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −196.000 | −0.0198664 | ||||||||
\(461\) | 9494.00 | 0.959175 | 0.479587 | − | 0.877494i | \(-0.340786\pi\) | ||||
0.479587 | + | 0.877494i | \(0.340786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10160.0 | −1.01982 | −0.509908 | − | 0.860229i | \(-0.670321\pi\) | ||||
−0.509908 | + | 0.860229i | \(0.670321\pi\) | |||||||
\(464\) | −1696.00 | −0.169687 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3574.00 | −0.355284 | ||||||||
\(467\) | 1307.00 | 0.129509 | 0.0647545 | − | 0.997901i | \(-0.479374\pi\) | ||||
0.0647545 | + | 0.997901i | \(0.479374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2394.00 | −0.234951 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 136.000 | 0.0132625 | ||||||||
\(473\) | −9100.00 | −0.884606 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10412.0 | −1.00576 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10200.0 | 0.976019 | ||||||||
\(479\) | −18287.0 | −1.74437 | −0.872186 | − | 0.489174i | \(-0.837298\pi\) | ||||
−0.872186 | + | 0.489174i | \(0.837298\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 726.000 | 0.0688207 | ||||||||
\(482\) | −8354.00 | −0.789449 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −424.000 | −0.0398197 | ||||||||
\(485\) | 2030.00 | 0.190057 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14953.0 | −1.39135 | −0.695673 | − | 0.718359i | \(-0.744894\pi\) | ||||
−0.695673 | + | 0.718359i | \(0.744894\pi\) | |||||||
\(488\) | 408.000 | 0.0378469 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14352.0 | −1.31914 | −0.659569 | − | 0.751644i | \(-0.729261\pi\) | ||||
−0.659569 | + | 0.751644i | \(0.729261\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6254.00 | 0.571331 | ||||||||
\(494\) | 18084.0 | 1.64704 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1200.00 | 0.108632 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5531.00 | −0.496196 | −0.248098 | − | 0.968735i | \(-0.579805\pi\) | ||||
−0.248098 | + | 0.968735i | \(0.579805\pi\) | |||||||
\(500\) | 5628.00 | 0.503384 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 9360.00 | 0.832186 | ||||||||
\(503\) | −8400.00 | −0.744607 | −0.372304 | − | 0.928111i | \(-0.621432\pi\) | ||||
−0.372304 | + | 0.928111i | \(0.621432\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7595.00 | −0.669254 | ||||||||
\(506\) | −490.000 | −0.0430497 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3744.00 | 0.326994 | ||||||||
\(509\) | 2385.00 | 0.207688 | 0.103844 | − | 0.994594i | \(-0.466886\pi\) | ||||
0.103844 | + | 0.994594i | \(0.466886\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3498.00 | 0.300175 | ||||||||
\(515\) | −10871.0 | −0.930162 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5985.00 | −0.509130 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3696.00 | −0.311693 | ||||||||
\(521\) | 9153.00 | 0.769674 | 0.384837 | − | 0.922985i | \(-0.374258\pi\) | ||||
0.384837 | + | 0.922985i | \(0.374258\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13807.0 | −1.15437 | −0.577187 | − | 0.816612i | \(-0.695850\pi\) | ||||
−0.577187 | + | 0.816612i | \(0.695850\pi\) | |||||||
\(524\) | 3020.00 | 0.251773 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8946.00 | 0.741567 | ||||||||
\(527\) | −4425.00 | −0.365761 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12118.0 | −0.995973 | ||||||||
\(530\) | −5838.00 | −0.478465 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32868.0 | 2.67105 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 903.000 | 0.0729721 | ||||||||
\(536\) | 3512.00 | 0.283014 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3950.00 | −0.316536 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8175.00 | 0.649669 | 0.324834 | − | 0.945771i | \(-0.394691\pi\) | ||||
0.324834 | + | 0.945771i | \(0.394691\pi\) | |||||||
\(542\) | −16878.0 | −1.33759 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1888.00 | −0.148800 | ||||||||
\(545\) | 6755.00 | 0.530922 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4656.00 | 0.363942 | 0.181971 | − | 0.983304i | \(-0.441752\pi\) | ||||
0.181971 | + | 0.983304i | \(0.441752\pi\) | |||||||
\(548\) | 9428.00 | 0.734935 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5320.00 | 0.412446 | ||||||||
\(551\) | −14522.0 | −1.12279 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1054.00 | 0.0808306 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 112.000 | 0.00854291 | ||||||||
\(557\) | −7003.00 | −0.532723 | −0.266361 | − | 0.963873i | \(-0.585821\pi\) | ||||
−0.266361 | + | 0.963873i | \(0.585821\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17160.0 | 1.29837 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 404.000 | 0.0303233 | ||||||||
\(563\) | 19753.0 | 1.47867 | 0.739334 | − | 0.673339i | \(-0.235141\pi\) | ||||
0.739334 | + | 0.673339i | \(0.235141\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −350.000 | −0.0260613 | ||||||||
\(566\) | −15898.0 | −1.18064 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6272.00 | 0.463323 | ||||||||
\(569\) | 6897.00 | 0.508150 | 0.254075 | − | 0.967185i | \(-0.418229\pi\) | ||||
0.254075 | + | 0.967185i | \(0.418229\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24915.0 | 1.82603 | 0.913013 | − | 0.407932i | \(-0.133750\pi\) | ||||
0.913013 | + | 0.407932i | \(0.133750\pi\) | |||||||
\(572\) | −9240.00 | −0.675426 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −532.000 | −0.0385842 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 127.000 | 0.00916305 | 0.00458152 | − | 0.999990i | \(-0.498542\pi\) | ||||
0.00458152 | + | 0.999990i | \(0.498542\pi\) | |||||||
\(578\) | −2864.00 | −0.206102 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2968.00 | 0.212482 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −14595.0 | −1.03681 | ||||||||
\(584\) | 2360.00 | 0.167222 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −636.000 | −0.0448343 | ||||||||
\(587\) | −9044.00 | −0.635921 | −0.317961 | − | 0.948104i | \(-0.602998\pi\) | ||||
−0.317961 | + | 0.948104i | \(0.602998\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10275.0 | 0.718801 | ||||||||
\(590\) | −238.000 | −0.0166073 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 176.000 | 0.0122188 | ||||||||
\(593\) | 10701.0 | 0.741041 | 0.370521 | − | 0.928824i | \(-0.379179\pi\) | ||||
0.370521 | + | 0.928824i | \(0.379179\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9180.00 | −0.630919 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 924.000 | 0.0631859 | ||||||||
\(599\) | −20799.0 | −1.41874 | −0.709369 | − | 0.704837i | \(-0.751020\pi\) | ||||
−0.709369 | + | 0.704837i | \(0.751020\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1402.00 | −0.0951560 | −0.0475780 | − | 0.998868i | \(-0.515150\pi\) | ||||
−0.0475780 | + | 0.998868i | \(0.515150\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4436.00 | −0.298838 | ||||||||
\(605\) | 742.000 | 0.0498621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6525.00 | 0.436312 | 0.218156 | − | 0.975914i | \(-0.429996\pi\) | ||||
0.218156 | + | 0.975914i | \(0.429996\pi\) | |||||||
\(608\) | 4384.00 | 0.292425 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −714.000 | −0.0473918 | ||||||||
\(611\) | 11286.0 | 0.747271 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15051.0 | 0.991687 | 0.495844 | − | 0.868412i | \(-0.334859\pi\) | ||||
0.495844 | + | 0.868412i | \(0.334859\pi\) | |||||||
\(614\) | −16264.0 | −1.06899 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11150.0 | −0.727524 | −0.363762 | − | 0.931492i | \(-0.618508\pi\) | ||||
−0.363762 | + | 0.931492i | \(0.618508\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3415.00 | 0.221745 | 0.110873 | − | 0.993835i | \(-0.464635\pi\) | ||||
0.110873 | + | 0.993835i | \(0.464635\pi\) | |||||||
\(620\) | −2100.00 | −0.136029 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1858.00 | 0.119773 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −349.000 | −0.0223360 | ||||||||
\(626\) | −418.000 | −0.0266879 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6236.00 | 0.396248 | ||||||||
\(629\) | −649.000 | −0.0411404 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21184.0 | −1.33648 | −0.668242 | − | 0.743944i | \(-0.732953\pi\) | ||||
−0.668242 | + | 0.743944i | \(0.732953\pi\) | |||||||
\(632\) | −3960.00 | −0.249241 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14262.0 | −0.893401 | ||||||||
\(635\) | −6552.00 | −0.409462 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7420.00 | 0.460440 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −896.000 | −0.0553399 | ||||||||
\(641\) | 10705.0 | 0.659629 | 0.329814 | − | 0.944046i | \(-0.393014\pi\) | ||||
0.329814 | + | 0.944046i | \(0.393014\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6860.00 | 0.420734 | 0.210367 | − | 0.977622i | \(-0.432534\pi\) | ||||
0.210367 | + | 0.977622i | \(0.432534\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16166.0 | −0.984586 | ||||||||
\(647\) | −14463.0 | −0.878824 | −0.439412 | − | 0.898286i | \(-0.644813\pi\) | ||||
−0.439412 | + | 0.898286i | \(0.644813\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −595.000 | −0.0359874 | ||||||||
\(650\) | −10032.0 | −0.605365 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9004.00 | −0.540834 | ||||||||
\(653\) | −5979.00 | −0.358310 | −0.179155 | − | 0.983821i | \(-0.557336\pi\) | ||||
−0.179155 | + | 0.983821i | \(0.557336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5285.00 | −0.315270 | ||||||||
\(656\) | 7968.00 | 0.474235 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6940.00 | 0.410234 | 0.205117 | − | 0.978737i | \(-0.434243\pi\) | ||||
0.205117 | + | 0.978737i | \(0.434243\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13399.0 | 0.788443 | 0.394221 | − | 0.919015i | \(-0.371014\pi\) | ||||
0.394221 | + | 0.919015i | \(0.371014\pi\) | |||||||
\(662\) | −13142.0 | −0.771568 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7456.00 | −0.435766 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −742.000 | −0.0430740 | ||||||||
\(668\) | −11152.0 | −0.645934 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6146.00 | −0.354389 | ||||||||
\(671\) | −1785.00 | −0.102696 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29510.0 | 1.69023 | 0.845117 | − | 0.534582i | \(-0.179531\pi\) | ||||
0.845117 | + | 0.534582i | \(0.179531\pi\) | |||||||
\(674\) | −22932.0 | −1.31055 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8636.00 | 0.491352 | ||||||||
\(677\) | 26001.0 | 1.47607 | 0.738035 | − | 0.674762i | \(-0.235754\pi\) | ||||
0.738035 | + | 0.674762i | \(0.235754\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3304.00 | 0.186327 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5250.00 | −0.294770 | ||||||||
\(683\) | 8805.00 | 0.493285 | 0.246643 | − | 0.969106i | \(-0.420673\pi\) | ||||
0.246643 | + | 0.969106i | \(0.420673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −16499.0 | −0.920284 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4160.00 | 0.230521 | ||||||||
\(689\) | 27522.0 | 1.52178 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28685.0 | 1.57920 | 0.789601 | − | 0.613620i | \(-0.210287\pi\) | ||||
0.789601 | + | 0.613620i | \(0.210287\pi\) | |||||||
\(692\) | −6316.00 | −0.346963 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 19554.0 | 1.06954 | ||||||||
\(695\) | −196.000 | −0.0106974 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −29382.0 | −1.59673 | ||||||||
\(698\) | 23828.0 | 1.29212 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3146.00 | 0.169505 | 0.0847523 | − | 0.996402i | \(-0.472990\pi\) | ||||
0.0847523 | + | 0.996402i | \(0.472990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1507.00 | 0.0808500 | ||||||||
\(704\) | −2240.00 | −0.119919 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18246.0 | −0.972659 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1259.00 | 0.0666893 | 0.0333447 | − | 0.999444i | \(-0.489384\pi\) | ||||
0.0333447 | + | 0.999444i | \(0.489384\pi\) | |||||||
\(710\) | −10976.0 | −0.580172 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6984.00 | 0.367607 | ||||||||
\(713\) | 525.000 | 0.0275756 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16170.0 | 0.845767 | ||||||||
\(716\) | −9804.00 | −0.511722 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16298.0 | −0.847125 | ||||||||
\(719\) | −16425.0 | −0.851946 | −0.425973 | − | 0.904736i | \(-0.640068\pi\) | ||||
−0.425973 | + | 0.904736i | \(0.640068\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 23820.0 | 1.22782 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4680.00 | −0.240236 | ||||||||
\(725\) | 8056.00 | 0.412679 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6032.00 | −0.307723 | −0.153861 | − | 0.988092i | \(-0.549171\pi\) | ||||
−0.153861 | + | 0.988092i | \(0.549171\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4130.00 | −0.209395 | ||||||||
\(731\) | −15340.0 | −0.776156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15243.0 | 0.768094 | 0.384047 | − | 0.923314i | \(-0.374530\pi\) | ||||
0.384047 | + | 0.923314i | \(0.374530\pi\) | |||||||
\(734\) | 19342.0 | 0.972652 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 224.000 | 0.0112184 | ||||||||
\(737\) | −15365.0 | −0.767947 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10053.0 | −0.500414 | −0.250207 | − | 0.968192i | \(-0.580499\pi\) | ||||
−0.250207 | + | 0.968192i | \(0.580499\pi\) | |||||||
\(740\) | −308.000 | −0.0153004 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24384.0 | −1.20399 | −0.601993 | − | 0.798501i | \(-0.705627\pi\) | ||||
−0.601993 | + | 0.798501i | \(0.705627\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16065.0 | 0.790035 | ||||||||
\(746\) | −8218.00 | −0.403328 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8260.00 | 0.403764 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11589.0 | 0.563101 | 0.281550 | − | 0.959546i | \(-0.409151\pi\) | ||||
0.281550 | + | 0.959546i | \(0.409151\pi\) | |||||||
\(752\) | 2736.00 | 0.132675 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13992.0 | −0.675807 | ||||||||
\(755\) | 7763.00 | 0.374205 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14562.0 | 0.699161 | 0.349581 | − | 0.936906i | \(-0.386324\pi\) | ||||
0.349581 | + | 0.936906i | \(0.386324\pi\) | |||||||
\(758\) | −6976.00 | −0.334274 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7672.00 | −0.366175 | ||||||||
\(761\) | 22765.0 | 1.08440 | 0.542201 | − | 0.840249i | \(-0.317591\pi\) | ||||
0.542201 | + | 0.840249i | \(0.317591\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5100.00 | 0.241507 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17434.0 | −0.822345 | ||||||||
\(767\) | 1122.00 | 0.0528202 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3766.00 | 0.176600 | 0.0883000 | − | 0.996094i | \(-0.471857\pi\) | ||||
0.0883000 | + | 0.996094i | \(0.471857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 140.000 | 0.00652683 | ||||||||
\(773\) | 26861.0 | 1.24984 | 0.624918 | − | 0.780691i | \(-0.285132\pi\) | ||||
0.624918 | + | 0.780691i | \(0.285132\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5700.00 | −0.264194 | ||||||||
\(776\) | −2320.00 | −0.107324 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −326.000 | −0.0150227 | ||||||||
\(779\) | 68226.0 | 3.13793 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27440.0 | −1.25721 | ||||||||
\(782\) | −826.000 | −0.0377720 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10913.0 | −0.496180 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2097.00 | −0.0949809 | −0.0474905 | − | 0.998872i | \(-0.515122\pi\) | ||||
−0.0474905 | + | 0.998872i | \(0.515122\pi\) | |||||||
\(788\) | 10936.0 | 0.494389 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6930.00 | 0.312099 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3366.00 | 0.150732 | ||||||||
\(794\) | 1998.00 | 0.0893027 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8972.00 | 0.399503 | ||||||||
\(797\) | 35334.0 | 1.57038 | 0.785191 | − | 0.619254i | \(-0.212565\pi\) | ||||
0.785191 | + | 0.619254i | \(0.212565\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10089.0 | −0.446712 | ||||||||
\(800\) | −2432.00 | −0.107480 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29514.0 | 1.29947 | ||||||||
\(803\) | −10325.0 | −0.453750 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9900.00 | 0.432646 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8680.00 | 0.377922 | ||||||||
\(809\) | −42535.0 | −1.84852 | −0.924259 | − | 0.381766i | \(-0.875316\pi\) | ||||
−0.924259 | + | 0.381766i | \(0.875316\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30676.0 | 1.32821 | 0.664106 | − | 0.747638i | \(-0.268812\pi\) | ||||
0.664106 | + | 0.747638i | \(0.268812\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −770.000 | −0.0331554 | ||||||||
\(815\) | 15757.0 | 0.677231 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35620.0 | 1.52532 | ||||||||
\(818\) | −266.000 | −0.0113698 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13944.0 | −0.593836 | ||||||||
\(821\) | −37343.0 | −1.58743 | −0.793715 | − | 0.608290i | \(-0.791856\pi\) | ||||
−0.793715 | + | 0.608290i | \(0.791856\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2815.00 | 0.119228 | 0.0596141 | − | 0.998222i | \(-0.481013\pi\) | ||||
0.0596141 | + | 0.998222i | \(0.481013\pi\) | |||||||
\(824\) | 12424.0 | 0.525256 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9276.00 | 0.390034 | 0.195017 | − | 0.980800i | \(-0.437524\pi\) | ||||
0.195017 | + | 0.980800i | \(0.437524\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18571.0 | 0.778043 | 0.389021 | − | 0.921229i | \(-0.372813\pi\) | ||||
0.389021 | + | 0.921229i | \(0.372813\pi\) | |||||||
\(830\) | 13048.0 | 0.545666 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4224.00 | 0.176011 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19516.0 | 0.808837 | ||||||||
\(836\) | −19180.0 | −0.793486 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12840.0 | 0.529296 | ||||||||
\(839\) | −29048.0 | −1.19529 | −0.597645 | − | 0.801761i | \(-0.703897\pi\) | ||||
−0.597645 | + | 0.801761i | \(0.703897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13153.0 | −0.539301 | ||||||||
\(842\) | 20532.0 | 0.840356 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4688.00 | 0.191194 | ||||||||
\(845\) | −15113.0 | −0.615270 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6672.00 | 0.270186 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 8968.00 | 0.361882 | ||||||||
\(851\) | 77.0000 | 0.00310168 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32090.0 | 1.28809 | 0.644045 | − | 0.764988i | \(-0.277255\pi\) | ||||
0.644045 | + | 0.764988i | \(0.277255\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1032.00 | −0.0412068 | ||||||||
\(857\) | 24537.0 | 0.978026 | 0.489013 | − | 0.872277i | \(-0.337357\pi\) | ||||
0.489013 | + | 0.872277i | \(0.337357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20825.0 | 0.827171 | 0.413585 | − | 0.910465i | \(-0.364276\pi\) | ||||
0.413585 | + | 0.910465i | \(0.364276\pi\) | |||||||
\(860\) | −7280.00 | −0.288658 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30426.0 | 1.20222 | ||||||||
\(863\) | 22847.0 | 0.901183 | 0.450591 | − | 0.892730i | \(-0.351213\pi\) | ||||
0.450591 | + | 0.892730i | \(0.351213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11053.0 | 0.434466 | ||||||||
\(866\) | −2756.00 | −0.108144 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17325.0 | 0.676307 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 28974.0 | 1.12715 | ||||||||
\(872\) | −7720.00 | −0.299808 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1918.00 | 0.0742303 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −42737.0 | −1.64553 | −0.822763 | − | 0.568385i | \(-0.807568\pi\) | ||||
−0.822763 | + | 0.568385i | \(0.807568\pi\) | |||||||
\(878\) | −5526.00 | −0.212407 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3920.00 | 0.150163 | ||||||||
\(881\) | −6162.00 | −0.235645 | −0.117822 | − | 0.993035i | \(-0.537591\pi\) | ||||
−0.117822 | + | 0.993035i | \(0.537591\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7748.00 | 0.295290 | 0.147645 | − | 0.989040i | \(-0.452831\pi\) | ||||
0.147645 | + | 0.989040i | \(0.452831\pi\) | |||||||
\(884\) | −15576.0 | −0.592622 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11698.0 | −0.443569 | ||||||||
\(887\) | 25923.0 | 0.981296 | 0.490648 | − | 0.871358i | \(-0.336760\pi\) | ||||
0.490648 | + | 0.871358i | \(0.336760\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −12222.0 | −0.460317 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8096.00 | 0.303895 | ||||||||
\(893\) | 23427.0 | 0.877889 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17157.0 | 0.640777 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9164.00 | −0.340542 | ||||||||
\(899\) | −7950.00 | −0.294936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24603.0 | −0.909706 | ||||||||
\(902\) | −34860.0 | −1.28682 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 400.000 | 0.0147166 | ||||||||
\(905\) | 8190.00 | 0.300823 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31935.0 | 1.16911 | 0.584556 | − | 0.811353i | \(-0.301269\pi\) | ||||
0.584556 | + | 0.811353i | \(0.301269\pi\) | |||||||
\(908\) | −10284.0 | −0.375866 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3408.00 | −0.123943 | −0.0619715 | − | 0.998078i | \(-0.519739\pi\) | ||||
−0.0619715 | + | 0.998078i | \(0.519739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32620.0 | 1.18244 | ||||||||
\(914\) | 23102.0 | 0.836046 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3580.00 | 0.129134 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13909.0 | 0.499255 | 0.249628 | − | 0.968342i | \(-0.419692\pi\) | ||||
0.249628 | + | 0.968342i | \(0.419692\pi\) | |||||||
\(920\) | −392.000 | −0.0140477 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18988.0 | 0.678239 | ||||||||
\(923\) | 51744.0 | 1.84526 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −836.000 | −0.0297162 | ||||||||
\(926\) | −20320.0 | −0.721119 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3392.00 | −0.119987 | ||||||||
\(929\) | 24537.0 | 0.866559 | 0.433279 | − | 0.901260i | \(-0.357356\pi\) | ||||
0.433279 | + | 0.901260i | \(0.357356\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −7148.00 | −0.251224 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2614.00 | 0.0915768 | ||||||||
\(935\) | −14455.0 | −0.505593 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −32758.0 | −1.14211 | −0.571055 | − | 0.820912i | \(-0.693466\pi\) | ||||
−0.571055 | + | 0.820912i | \(0.693466\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4788.00 | −0.166135 | ||||||||
\(941\) | 38561.0 | 1.33587 | 0.667934 | − | 0.744220i | \(-0.267179\pi\) | ||||
0.667934 | + | 0.744220i | \(0.267179\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3486.00 | 0.120382 | ||||||||
\(944\) | 272.000 | 0.00937801 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −18200.0 | −0.625511 | ||||||||
\(947\) | −39661.0 | −1.36094 | −0.680470 | − | 0.732776i | \(-0.738224\pi\) | ||||
−0.680470 | + | 0.732776i | \(0.738224\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19470.0 | 0.665988 | ||||||||
\(950\) | −20824.0 | −0.711179 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46618.0 | 1.58458 | 0.792290 | − | 0.610144i | \(-0.208889\pi\) | ||||
0.792290 | + | 0.610144i | \(0.208889\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8925.00 | −0.302415 | ||||||||
\(956\) | 20400.0 | 0.690150 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36574.0 | −1.23346 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24166.0 | −0.811185 | ||||||||
\(962\) | 1452.00 | 0.0486636 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −16708.0 | −0.558225 | ||||||||
\(965\) | −245.000 | −0.00817288 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14816.0 | 0.492710 | 0.246355 | − | 0.969180i | \(-0.420767\pi\) | ||||
0.246355 | + | 0.969180i | \(0.420767\pi\) | |||||||
\(968\) | −848.000 | −0.0281568 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4060.00 | 0.134390 | ||||||||
\(971\) | 16875.0 | 0.557718 | 0.278859 | − | 0.960332i | \(-0.410044\pi\) | ||||
0.278859 | + | 0.960332i | \(0.410044\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −29906.0 | −0.983830 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 816.000 | 0.0267618 | ||||||||
\(977\) | 15837.0 | 0.518598 | 0.259299 | − | 0.965797i | \(-0.416508\pi\) | ||||
0.259299 | + | 0.965797i | \(0.416508\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30555.0 | −0.997489 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −28704.0 | −0.932771 | ||||||||
\(983\) | −9915.00 | −0.321708 | −0.160854 | − | 0.986978i | \(-0.551425\pi\) | ||||
−0.160854 | + | 0.986978i | \(0.551425\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −19138.0 | −0.619073 | ||||||||
\(986\) | 12508.0 | 0.403992 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 36168.0 | 1.16463 | ||||||||
\(989\) | 1820.00 | 0.0585163 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43681.0 | −1.40017 | −0.700087 | − | 0.714057i | \(-0.746856\pi\) | ||||
−0.700087 | + | 0.714057i | \(0.746856\pi\) | |||||||
\(992\) | 2400.00 | 0.0768146 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15701.0 | −0.500256 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47113.0 | −1.49657 | −0.748287 | − | 0.663375i | \(-0.769123\pi\) | ||||
−0.748287 | + | 0.663375i | \(0.769123\pi\) | |||||||
\(998\) | −11062.0 | −0.350863 | ||||||||
\(999\) | 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 | 882.4.a.k.1.1 | 1 | ||
3.2 | odd | 2 | 98.4.a.b.1.1 | 1 | |||
7.2 | even | 3 | 126.4.g.c.109.1 | 2 | |||
7.3 | odd | 6 | 882.4.g.d.667.1 | 2 | |||
7.4 | even | 3 | 126.4.g.c.37.1 | 2 | |||
7.5 | odd | 6 | 882.4.g.d.361.1 | 2 | |||
7.6 | odd | 2 | 882.4.a.p.1.1 | 1 | |||
12.11 | even | 2 | 784.4.a.l.1.1 | 1 | |||
15.14 | odd | 2 | 2450.4.a.bh.1.1 | 1 | |||
21.2 | odd | 6 | 14.4.c.b.11.1 | yes | 2 | ||
21.5 | even | 6 | 98.4.c.e.67.1 | 2 | |||
21.11 | odd | 6 | 14.4.c.b.9.1 | ✓ | 2 | ||
21.17 | even | 6 | 98.4.c.e.79.1 | 2 | |||
21.20 | even | 2 | 98.4.a.c.1.1 | 1 | |||
84.11 | even | 6 | 112.4.i.b.65.1 | 2 | |||
84.23 | even | 6 | 112.4.i.b.81.1 | 2 | |||
84.83 | odd | 2 | 784.4.a.j.1.1 | 1 | |||
105.2 | even | 12 | 350.4.j.d.249.1 | 4 | |||
105.23 | even | 12 | 350.4.j.d.249.2 | 4 | |||
105.32 | even | 12 | 350.4.j.d.149.2 | 4 | |||
105.44 | odd | 6 | 350.4.e.b.151.1 | 2 | |||
105.53 | even | 12 | 350.4.j.d.149.1 | 4 | |||
105.74 | odd | 6 | 350.4.e.b.51.1 | 2 | |||
105.104 | even | 2 | 2450.4.a.bf.1.1 | 1 | |||
168.11 | even | 6 | 448.4.i.d.65.1 | 2 | |||
168.53 | odd | 6 | 448.4.i.c.65.1 | 2 | |||
168.107 | even | 6 | 448.4.i.d.193.1 | 2 | |||
168.149 | odd | 6 | 448.4.i.c.193.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.4.c.b.9.1 | ✓ | 2 | 21.11 | odd | 6 | ||
14.4.c.b.11.1 | yes | 2 | 21.2 | odd | 6 | ||
98.4.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
98.4.a.c.1.1 | 1 | 21.20 | even | 2 | |||
98.4.c.e.67.1 | 2 | 21.5 | even | 6 | |||
98.4.c.e.79.1 | 2 | 21.17 | even | 6 | |||
112.4.i.b.65.1 | 2 | 84.11 | even | 6 | |||
112.4.i.b.81.1 | 2 | 84.23 | even | 6 | |||
126.4.g.c.37.1 | 2 | 7.4 | even | 3 | |||
126.4.g.c.109.1 | 2 | 7.2 | even | 3 | |||
350.4.e.b.51.1 | 2 | 105.74 | odd | 6 | |||
350.4.e.b.151.1 | 2 | 105.44 | odd | 6 | |||
350.4.j.d.149.1 | 4 | 105.53 | even | 12 | |||
350.4.j.d.149.2 | 4 | 105.32 | even | 12 | |||
350.4.j.d.249.1 | 4 | 105.2 | even | 12 | |||
350.4.j.d.249.2 | 4 | 105.23 | even | 12 | |||
448.4.i.c.65.1 | 2 | 168.53 | odd | 6 | |||
448.4.i.c.193.1 | 2 | 168.149 | odd | 6 | |||
448.4.i.d.65.1 | 2 | 168.11 | even | 6 | |||
448.4.i.d.193.1 | 2 | 168.107 | even | 6 | |||
784.4.a.j.1.1 | 1 | 84.83 | odd | 2 | |||
784.4.a.l.1.1 | 1 | 12.11 | even | 2 | |||
882.4.a.k.1.1 | 1 | 1.1 | even | 1 | trivial | ||
882.4.a.p.1.1 | 1 | 7.6 | odd | 2 | |||
882.4.g.d.361.1 | 2 | 7.5 | odd | 6 | |||
882.4.g.d.667.1 | 2 | 7.3 | odd | 6 | |||
2450.4.a.bf.1.1 | 1 | 105.104 | even | 2 | |||
2450.4.a.bh.1.1 | 1 | 15.14 | odd | 2 |