Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1296,4,Mod(1,1296)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1296, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1296.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1296 = 2^{4} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1296.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: | \(76.4664753674\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 18) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1296.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 9.00000 | 0.804984 | 0.402492 | − | 0.915423i | \(-0.368144\pi\) | ||||
0.402492 | + | 0.915423i | \(0.368144\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 31.0000 | 1.67384 | 0.836921 | − | 0.547323i | \(-0.184353\pi\) | ||||
0.836921 | + | 0.547323i | \(0.184353\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.0000 | −0.411152 | −0.205576 | − | 0.978641i | \(-0.565907\pi\) | ||||
−0.205576 | + | 0.978641i | \(0.565907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −37.0000 | −0.789381 | −0.394691 | − | 0.918814i | \(-0.629148\pi\) | ||||
−0.394691 | + | 0.918814i | \(0.629148\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 42.0000 | 0.599206 | 0.299603 | − | 0.954064i | \(-0.403146\pi\) | ||||
0.299603 | + | 0.954064i | \(0.403146\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.0000 | 0.338086 | 0.169043 | − | 0.985609i | \(-0.445932\pi\) | ||||
0.169043 | + | 0.985609i | \(0.445932\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 195.000 | 1.76784 | 0.883920 | − | 0.467639i | \(-0.154895\pi\) | ||||
0.883920 | + | 0.467639i | \(0.154895\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −111.000 | −0.710765 | −0.355382 | − | 0.934721i | \(-0.615649\pi\) | ||||
−0.355382 | + | 0.934721i | \(0.615649\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 205.000 | 1.18771 | 0.593856 | − | 0.804571i | \(-0.297605\pi\) | ||||
0.593856 | + | 0.804571i | \(0.297605\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 279.000 | 1.34742 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −166.000 | −0.737574 | −0.368787 | − | 0.929514i | \(-0.620227\pi\) | ||||
−0.368787 | + | 0.929514i | \(0.620227\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 261.000 | 0.994179 | 0.497090 | − | 0.867699i | \(-0.334402\pi\) | ||||
0.497090 | + | 0.867699i | \(0.334402\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.0000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 177.000 | 0.549321 | 0.274661 | − | 0.961541i | \(-0.411434\pi\) | ||||
0.274661 | + | 0.961541i | \(0.411434\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 618.000 | 1.80175 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −114.000 | −0.295455 | −0.147727 | − | 0.989028i | \(-0.547196\pi\) | ||||
−0.147727 | + | 0.989028i | \(0.547196\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −135.000 | −0.330971 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 159.000 | 0.350848 | 0.175424 | − | 0.984493i | \(-0.443870\pi\) | ||||
0.175424 | + | 0.984493i | \(0.443870\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 191.000 | 0.400902 | 0.200451 | − | 0.979704i | \(-0.435759\pi\) | ||||
0.200451 | + | 0.979704i | \(0.435759\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −333.000 | −0.635439 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 421.000 | 0.767662 | 0.383831 | − | 0.923403i | \(-0.374605\pi\) | ||||
0.383831 | + | 0.923403i | \(0.374605\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 156.000 | 0.260758 | 0.130379 | − | 0.991464i | \(-0.458381\pi\) | ||||
0.130379 | + | 0.991464i | \(0.458381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 182.000 | 0.291801 | 0.145901 | − | 0.989299i | \(-0.453392\pi\) | ||||
0.145901 | + | 0.989299i | \(0.453392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −465.000 | −0.688203 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1133.00 | −1.61358 | −0.806788 | − | 0.590841i | \(-0.798796\pi\) | ||||
−0.806788 | + | 0.590841i | \(0.798796\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1083.00 | −1.43223 | −0.716113 | − | 0.697985i | \(-0.754080\pi\) | ||||
−0.716113 | + | 0.697985i | \(0.754080\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 378.000 | 0.482351 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1050.00 | 1.25056 | 0.625280 | − | 0.780401i | \(-0.284985\pi\) | ||||
0.625280 | + | 0.780401i | \(0.284985\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1147.00 | −1.32130 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 252.000 | 0.272154 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −901.000 | −0.943121 | −0.471560 | − | 0.881834i | \(-0.656309\pi\) | ||||
−0.471560 | + | 0.881834i | \(0.656309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −387.000 | −0.381267 | −0.190633 | − | 0.981661i | \(-0.561054\pi\) | ||||
−0.190633 | + | 0.981661i | \(0.561054\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −551.000 | −0.527103 | −0.263552 | − | 0.964645i | \(-0.584894\pi\) | ||||
−0.263552 | + | 0.964645i | \(0.584894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −0.0108419 | −0.00542095 | − | 0.999985i | \(-0.501726\pi\) | ||||
−0.00542095 | + | 0.999985i | \(0.501726\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −502.000 | −0.441127 | −0.220564 | − | 0.975373i | \(-0.570790\pi\) | ||||
−0.220564 | + | 0.975373i | \(0.570790\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1401.00 | 1.16633 | 0.583164 | − | 0.812355i | \(-0.301815\pi\) | ||||
0.583164 | + | 0.812355i | \(0.301815\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1755.00 | 1.42308 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1302.00 | 1.00298 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1106.00 | −0.830954 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1521.00 | −1.08834 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 880.000 | 0.614861 | 0.307431 | − | 0.951571i | \(-0.400531\pi\) | ||||
0.307431 | + | 0.951571i | \(0.400531\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1503.00 | 1.00243 | 0.501213 | − | 0.865324i | \(-0.332887\pi\) | ||||
0.501213 | + | 0.865324i | \(0.332887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 868.000 | 0.565903 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2661.00 | 1.65945 | 0.829725 | − | 0.558173i | \(-0.188497\pi\) | ||||
0.829725 | + | 0.558173i | \(0.188497\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 121.000 | 0.0738352 | 0.0369176 | − | 0.999318i | \(-0.488246\pi\) | ||||
0.0369176 | + | 0.999318i | \(0.488246\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 555.000 | 0.324555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −999.000 | −0.572155 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2829.00 | 1.55544 | 0.777721 | − | 0.628610i | \(-0.216376\pi\) | ||||
0.777721 | + | 0.628610i | \(0.216376\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −461.000 | −0.248448 | −0.124224 | − | 0.992254i | \(-0.539644\pi\) | ||||
−0.124224 | + | 0.992254i | \(0.539644\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1845.00 | 0.956090 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2977.00 | −1.51332 | −0.756658 | − | 0.653811i | \(-0.773169\pi\) | ||||
−0.756658 | + | 0.653811i | \(0.773169\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6045.00 | 2.95909 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3316.00 | 1.59343 | 0.796715 | − | 0.604355i | \(-0.206569\pi\) | ||||
0.796715 | + | 0.604355i | \(0.206569\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −681.000 | −0.315553 | −0.157777 | − | 0.987475i | \(-0.550433\pi\) | ||||
−0.157777 | + | 0.987475i | \(0.550433\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −828.000 | −0.376878 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3981.00 | 1.74954 | 0.874768 | − | 0.484541i | \(-0.161014\pi\) | ||||
0.874768 | + | 0.484541i | \(0.161014\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1364.00 | −0.589193 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2004.00 | 0.836793 | 0.418397 | − | 0.908264i | \(-0.362592\pi\) | ||||
0.418397 | + | 0.908264i | \(0.362592\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1274.00 | 0.523181 | 0.261590 | − | 0.965179i | \(-0.415753\pi\) | ||||
0.261590 | + | 0.965179i | \(0.415753\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1494.00 | −0.593735 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −630.000 | −0.246365 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1161.00 | 0.439827 | 0.219914 | − | 0.975519i | \(-0.429422\pi\) | ||||
0.219914 | + | 0.975519i | \(0.429422\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3611.00 | 1.34676 | 0.673382 | − | 0.739295i | \(-0.264841\pi\) | ||||
0.673382 | + | 0.739295i | \(0.264841\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2046.00 | −0.739957 | −0.369978 | − | 0.929040i | \(-0.620635\pi\) | ||||
−0.369978 | + | 0.929040i | \(0.620635\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2996.00 | −1.06724 | −0.533620 | − | 0.845724i | \(-0.679169\pi\) | ||||
−0.533620 | + | 0.845724i | \(0.679169\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3441.00 | −1.18971 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2349.00 | 0.800299 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −420.000 | −0.139005 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −755.000 | −0.246333 | −0.123167 | − | 0.992386i | \(-0.539305\pi\) | ||||
−0.123167 | + | 0.992386i | \(0.539305\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 387.000 | 0.122759 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6355.00 | 1.98804 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1554.00 | −0.473002 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3463.00 | 1.03991 | 0.519954 | − | 0.854194i | \(-0.325949\pi\) | ||||
0.519954 | + | 0.854194i | \(0.325949\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6225.00 | 1.82012 | 0.910061 | − | 0.414474i | \(-0.136034\pi\) | ||||
0.910061 | + | 0.414474i | \(0.136034\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1465.00 | −0.422751 | −0.211375 | − | 0.977405i | \(-0.567794\pi\) | ||||
−0.211375 | + | 0.977405i | \(0.567794\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2634.00 | −0.740597 | −0.370298 | − | 0.928913i | \(-0.620745\pi\) | ||||
−0.370298 | + | 0.928913i | \(0.620745\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1593.00 | 0.442195 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6915.00 | 1.87152 | 0.935762 | − | 0.352633i | \(-0.114713\pi\) | ||||
0.935762 | + | 0.352633i | \(0.114713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1489.00 | −0.397987 | −0.198994 | − | 0.980001i | \(-0.563767\pi\) | ||||
−0.198994 | + | 0.980001i | \(0.563767\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5562.00 | 1.45038 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1036.00 | −0.266879 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4620.00 | −1.16180 | −0.580900 | − | 0.813975i | \(-0.697299\pi\) | ||||
−0.580900 | + | 0.813975i | \(0.697299\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2925.00 | −0.726850 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3351.00 | −0.813345 | −0.406672 | − | 0.913574i | \(-0.633311\pi\) | ||||
−0.406672 | + | 0.913574i | \(0.633311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5146.00 | −1.23458 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −603.000 | −0.141379 | −0.0706893 | − | 0.997498i | \(-0.522520\pi\) | ||||
−0.0706893 | + | 0.997498i | \(0.522520\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1026.00 | −0.237837 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1470.00 | 0.333188 | 0.166594 | − | 0.986026i | \(-0.446723\pi\) | ||||
0.166594 | + | 0.986026i | \(0.446723\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2072.00 | −0.464447 | −0.232223 | − | 0.972662i | \(-0.574600\pi\) | ||||
−0.232223 | + | 0.972662i | \(0.574600\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 660.000 | 0.144725 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7139.00 | 1.54852 | 0.774262 | − | 0.632866i | \(-0.218121\pi\) | ||||
0.774262 | + | 0.632866i | \(0.218121\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8427.00 | −1.78901 | −0.894507 | − | 0.447055i | \(-0.852473\pi\) | ||||
−0.894507 | + | 0.447055i | \(0.852473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 457.000 | 0.0959923 | 0.0479962 | − | 0.998848i | \(-0.484716\pi\) | ||||
0.0479962 | + | 0.998848i | \(0.484716\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8091.00 | 1.66410 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3149.00 | −0.640953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5889.00 | 1.17419 | 0.587097 | − | 0.809516i | \(-0.300271\pi\) | ||||
0.587097 | + | 0.809516i | \(0.300271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1431.00 | 0.282427 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7215.00 | −1.39550 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1333.00 | 0.255259 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1719.00 | 0.322720 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1204.00 | 0.223830 | 0.111915 | − | 0.993718i | \(-0.464302\pi\) | ||||
0.111915 | + | 0.993718i | \(0.464302\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3285.00 | −0.598956 | −0.299478 | − | 0.954103i | \(-0.596812\pi\) | ||||
−0.299478 | + | 0.954103i | \(0.596812\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10057.0 | −1.81615 | −0.908075 | − | 0.418807i | \(-0.862449\pi\) | ||||
−0.908075 | + | 0.418807i | \(0.862449\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2295.00 | −0.406625 | −0.203312 | − | 0.979114i | \(-0.565171\pi\) | ||||
−0.203312 | + | 0.979114i | \(0.565171\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1665.00 | 0.292232 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1176.00 | 0.202583 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1628.00 | 0.277862 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5487.00 | 0.919478 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6679.00 | 1.10910 | 0.554548 | − | 0.832151i | \(-0.312891\pi\) | ||||
0.554548 | + | 0.832151i | \(0.312891\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3789.00 | 0.617956 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2183.00 | 0.352865 | 0.176433 | − | 0.984313i | \(-0.443544\pi\) | ||||
0.176433 | + | 0.984313i | \(0.443544\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3075.00 | −0.488330 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8525.00 | 1.34200 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3891.00 | 0.601959 | 0.300980 | − | 0.953631i | \(-0.402686\pi\) | ||||
0.300980 | + | 0.953631i | \(0.402686\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2795.00 | 0.428690 | 0.214345 | − | 0.976758i | \(-0.431238\pi\) | ||||
0.214345 | + | 0.976758i | \(0.431238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4755.00 | −0.716949 | −0.358475 | − | 0.933539i | \(-0.616703\pi\) | ||||
−0.358475 | + | 0.933539i | \(0.616703\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1404.00 | 0.209906 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4608.00 | 0.677440 | 0.338720 | − | 0.940887i | \(-0.390006\pi\) | ||||
0.338720 | + | 0.940887i | \(0.390006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6075.00 | −0.885698 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1638.00 | 0.234895 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3845.00 | −0.546887 | −0.273443 | − | 0.961888i | \(-0.588163\pi\) | ||||
−0.273443 | + | 0.961888i | \(0.588163\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3534.00 | −0.494545 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8317.00 | −1.15453 | −0.577263 | − | 0.816559i | \(-0.695879\pi\) | ||||
−0.577263 | + | 0.816559i | \(0.695879\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4107.00 | 0.561064 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12560.0 | −1.70228 | −0.851140 | − | 0.524939i | \(-0.824088\pi\) | ||||
−0.851140 | + | 0.524939i | \(0.824088\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12087.0 | 1.61258 | 0.806288 | − | 0.591523i | \(-0.201473\pi\) | ||||
0.806288 | + | 0.591523i | \(0.201473\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4185.00 | −0.553993 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8541.00 | 1.11323 | 0.556614 | − | 0.830771i | \(-0.312100\pi\) | ||||
0.556614 | + | 0.830771i | \(0.312100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8190.00 | 1.05930 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10197.0 | −1.29890 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13174.0 | −1.66545 | −0.832726 | − | 0.553686i | \(-0.813221\pi\) | ||||
−0.832726 | + | 0.553686i | \(0.813221\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9603.00 | −1.19589 | −0.597944 | − | 0.801538i | \(-0.704015\pi\) | ||||
−0.597944 | + | 0.801538i | \(0.704015\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7585.00 | −0.937558 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2490.00 | 0.303255 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11471.0 | 1.38681 | 0.693404 | − | 0.720549i | \(-0.256110\pi\) | ||||
0.693404 | + | 0.720549i | \(0.256110\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4929.00 | 0.587264 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9747.00 | −1.15292 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5973.00 | −0.696420 | −0.348210 | − | 0.937416i | \(-0.613210\pi\) | ||||
−0.348210 | + | 0.937416i | \(0.613210\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8905.00 | −1.03089 | −0.515443 | − | 0.856924i | \(-0.672373\pi\) | ||||
−0.515443 | + | 0.856924i | \(0.672373\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1848.00 | −0.210920 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5921.00 | 0.671047 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1416.00 | 0.158251 | 0.0791257 | − | 0.996865i | \(-0.474787\pi\) | ||||
0.0791257 | + | 0.996865i | \(0.474787\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10766.0 | 1.19488 | 0.597438 | − | 0.801915i | \(-0.296186\pi\) | ||||
0.597438 | + | 0.801915i | \(0.296186\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5460.00 | 0.597682 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4349.00 | −0.472817 | −0.236408 | − | 0.971654i | \(-0.575970\pi\) | ||||
−0.236408 | + | 0.971654i | \(0.575970\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14547.0 | −1.56016 | −0.780078 | − | 0.625683i | \(-0.784820\pi\) | ||||
−0.780078 | + | 0.625683i | \(0.784820\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9450.00 | 1.00668 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3330.00 | 0.350005 | 0.175003 | − | 0.984568i | \(-0.444007\pi\) | ||||
0.175003 | + | 0.984568i | \(0.444007\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3915.00 | −0.408759 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10323.0 | −1.06363 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8147.00 | 0.833918 | 0.416959 | − | 0.908925i | \(-0.363096\pi\) | ||||
0.416959 | + | 0.908925i | \(0.363096\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8031.00 | −0.811369 | −0.405684 | − | 0.914013i | \(-0.632967\pi\) | ||||
−0.405684 | + | 0.914013i | \(0.632967\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4283.00 | −0.429909 | −0.214955 | − | 0.976624i | \(-0.568960\pi\) | ||||
−0.214955 | + | 0.976624i | \(0.568960\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5460.00 | 0.541025 | 0.270512 | − | 0.962716i | \(-0.412807\pi\) | ||||
0.270512 | + | 0.962716i | \(0.412807\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13051.0 | 1.28494 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −645.000 | −0.0627001 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1232.00 | −0.119006 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 429.000 | 0.0409217 | 0.0204609 | − | 0.999791i | \(-0.493487\pi\) | ||||
0.0204609 | + | 0.999791i | \(0.493487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6142.00 | 0.582227 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8109.00 | −0.759197 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11296.0 | 1.05107 | 0.525535 | − | 0.850772i | \(-0.323865\pi\) | ||||
0.525535 | + | 0.850772i | \(0.323865\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14673.0 | −1.34864 | −0.674321 | − | 0.738438i | \(-0.735564\pi\) | ||||
−0.674321 | + | 0.738438i | \(0.735564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4662.00 | −0.425894 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4836.00 | 0.436467 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13439.0 | −1.20564 | −0.602818 | − | 0.797879i | \(-0.705955\pi\) | ||||
−0.602818 | + | 0.797879i | \(0.705955\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17388.0 | −1.54134 | −0.770669 | − | 0.637236i | \(-0.780078\pi\) | ||||
−0.770669 | + | 0.637236i | \(0.780078\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3483.00 | −0.306914 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3789.00 | 0.329950 | 0.164975 | − | 0.986298i | \(-0.447246\pi\) | ||||
0.164975 | + | 0.986298i | \(0.447246\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5642.00 | 0.488429 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4959.00 | −0.424310 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2655.00 | −0.225854 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9786.00 | −0.822903 | −0.411451 | − | 0.911432i | \(-0.634978\pi\) | ||||
−0.411451 | + | 0.911432i | \(0.634978\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8008.00 | 0.669532 | 0.334766 | − | 0.942301i | \(-0.391343\pi\) | ||||
0.334766 | + | 0.942301i | \(0.391343\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8610.00 | 0.711684 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25858.0 | 2.12526 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9657.00 | −0.784786 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −108.000 | −0.00872756 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9270.00 | −0.740793 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2938.00 | −0.233483 | −0.116742 | − | 0.993162i | \(-0.537245\pi\) | ||||
−0.116742 | + | 0.993162i | \(0.537245\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4518.00 | −0.355101 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10375.0 | 0.810974 | 0.405487 | − | 0.914101i | \(-0.367102\pi\) | ||||
0.405487 | + | 0.914101i | \(0.367102\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3108.00 | −0.240300 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −35123.0 | −2.70087 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3306.00 | −0.251490 | −0.125745 | − | 0.992063i | \(-0.540132\pi\) | ||||
−0.125745 | + | 0.992063i | \(0.540132\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1591.00 | −0.120379 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21093.0 | −1.57898 | −0.789488 | − | 0.613765i | \(-0.789654\pi\) | ||||
−0.789488 | + | 0.613765i | \(0.789654\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12609.0 | 0.938875 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1287.00 | −0.0948222 | −0.0474111 | − | 0.998875i | \(-0.515097\pi\) | ||||
−0.0474111 | + | 0.998875i | \(0.515097\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15035.0 | −1.10192 | −0.550959 | − | 0.834532i | \(-0.685738\pi\) | ||||
−0.550959 | + | 0.834532i | \(0.685738\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8580.00 | −0.622280 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1190.00 | 0.0858585 | 0.0429292 | − | 0.999078i | \(-0.486331\pi\) | ||||
0.0429292 | + | 0.999078i | \(0.486331\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33573.0 | −2.39732 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1710.00 | 0.121477 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17883.0 | −1.25743 | −0.628714 | − | 0.777637i | \(-0.716418\pi\) | ||||
−0.628714 | + | 0.777637i | \(0.716418\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5740.00 | 0.401549 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −20118.0 | −1.39317 | −0.696583 | − | 0.717476i | \(-0.745297\pi\) | ||||
−0.696583 | + | 0.717476i | \(0.745297\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11718.0 | 0.807380 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1065.00 | −0.0726456 | −0.0363228 | − | 0.999340i | \(-0.511564\pi\) | ||||
−0.0363228 | + | 0.999340i | \(0.511564\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20725.0 | −1.40664 | −0.703320 | − | 0.710874i | \(-0.748300\pi\) | ||||
−0.703320 | + | 0.710874i | \(0.748300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9954.00 | −0.668905 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15745.0 | 1.05283 | 0.526417 | − | 0.850227i | \(-0.323535\pi\) | ||||
0.526417 | + | 0.850227i | \(0.323535\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6549.00 | −0.433624 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5042.00 | 0.332210 | 0.166105 | − | 0.986108i | \(-0.446881\pi\) | ||||
0.166105 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10053.0 | 0.655946 | 0.327973 | − | 0.944687i | \(-0.393635\pi\) | ||||
0.327973 | + | 0.944687i | \(0.393635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5983.00 | 0.388493 | 0.194246 | − | 0.980953i | \(-0.437774\pi\) | ||||
0.194246 | + | 0.980953i | \(0.437774\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32550.0 | 2.09324 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6972.00 | −0.441958 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19696.0 | 1.24261 | 0.621304 | − | 0.783570i | \(-0.286603\pi\) | ||||
0.621304 | + | 0.783570i | \(0.286603\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7920.00 | 0.494954 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22866.0 | −1.42227 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10977.0 | 0.676389 | 0.338195 | − | 0.941076i | \(-0.390184\pi\) | ||||
0.338195 | + | 0.941076i | \(0.390184\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15829.0 | 0.970816 | 0.485408 | − | 0.874288i | \(-0.338671\pi\) | ||||
0.485408 | + | 0.874288i | \(0.338671\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28224.0 | 1.71499 | 0.857496 | − | 0.514490i | \(-0.172019\pi\) | ||||
0.857496 | + | 0.514490i | \(0.172019\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2385.00 | −0.144252 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −28167.0 | −1.68799 | −0.843997 | − | 0.536348i | \(-0.819803\pi\) | ||||
−0.843997 | + | 0.536348i | \(0.819803\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13527.0 | 0.806937 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10737.0 | 0.634680 | 0.317340 | − | 0.948312i | \(-0.397210\pi\) | ||||
0.317340 | + | 0.948312i | \(0.397210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10127.0 | 0.595907 | 0.297954 | − | 0.954580i | \(-0.403696\pi\) | ||||
0.297954 | + | 0.954580i | \(0.403696\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7812.00 | 0.455543 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21645.0 | −1.25652 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2865.00 | −0.164832 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 251.000 | 0.0143764 | 0.00718822 | − | 0.999974i | \(-0.497712\pi\) | ||||
0.00718822 | + | 0.999974i | \(0.497712\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8451.00 | −0.479761 | −0.239881 | − | 0.970802i | \(-0.577108\pi\) | ||||
−0.239881 | + | 0.970802i | \(0.577108\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27931.0 | −1.57864 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25884.0 | −1.45011 | −0.725054 | − | 0.688692i | \(-0.758185\pi\) | ||||
−0.725054 | + | 0.688692i | \(0.758185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23949.0 | 1.33583 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4218.00 | 0.233226 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6365.00 | −0.350414 | −0.175207 | − | 0.984532i | \(-0.556059\pi\) | ||||
−0.175207 | + | 0.984532i | \(0.556059\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1089.00 | 0.0594362 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10962.0 | 0.595718 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1122.00 | −0.0604527 | −0.0302264 | − | 0.999543i | \(-0.509623\pi\) | ||||
−0.0302264 | + | 0.999543i | \(0.509623\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4648.00 | −0.249364 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −11997.0 | −0.638181 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4283.00 | 0.226871 | 0.113435 | − | 0.993545i | \(-0.463814\pi\) | ||||
0.113435 | + | 0.993545i | \(0.463814\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 39975.0 | 2.09969 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4995.00 | 0.261262 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4032.00 | 0.209135 | 0.104568 | − | 0.994518i | \(-0.466654\pi\) | ||||
0.104568 | + | 0.994518i | \(0.466654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17081.0 | −0.882288 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4884.00 | 0.250189 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24005.0 | −1.22462 | −0.612308 | − | 0.790619i | \(-0.709759\pi\) | ||||
−0.612308 | + | 0.790619i | \(0.709759\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1806.00 | 0.0913780 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37501.0 | −1.88967 | −0.944837 | − | 0.327541i | \(-0.893780\pi\) | ||||
−0.944837 | + | 0.327541i | \(0.893780\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6315.00 | −0.315626 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 880.000 | 0.0438042 | 0.0219021 | − | 0.999760i | \(-0.493028\pi\) | ||||
0.0219021 | + | 0.999760i | \(0.493028\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1623.00 | 0.0801374 | 0.0400687 | − | 0.999197i | \(-0.487242\pi\) | ||||
0.0400687 | + | 0.999197i | \(0.487242\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 25461.0 | 1.25211 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −372.000 | −0.0181476 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6889.00 | 0.334731 | 0.167366 | − | 0.985895i | \(-0.446474\pi\) | ||||
0.167366 | + | 0.985895i | \(0.446474\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4149.00 | −0.199997 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12850.0 | −0.616963 | −0.308482 | − | 0.951230i | \(-0.599821\pi\) | ||||
−0.308482 | + | 0.951230i | \(0.599821\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4611.00 | −0.219643 | −0.109822 | − | 0.993951i | \(-0.535028\pi\) | ||||
−0.109822 | + | 0.993951i | \(0.535028\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15562.0 | −0.738378 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5883.00 | −0.276953 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2305.00 | −0.108089 | −0.0540445 | − | 0.998539i | \(-0.517211\pi\) | ||||
−0.0540445 | + | 0.998539i | \(0.517211\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34902.0 | 1.62398 | 0.811991 | − | 0.583670i | \(-0.198384\pi\) | ||||
0.811991 | + | 0.583670i | \(0.198384\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9020.00 | −0.418075 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7308.00 | 0.336118 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2340.00 | −0.107211 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26793.0 | −1.21820 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26255.0 | −1.18919 | −0.594593 | − | 0.804027i | \(-0.702687\pi\) | ||||
−0.594593 | + | 0.804027i | \(0.702687\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43431.0 | 1.95225 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7067.00 | −0.316465 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1437.00 | 0.0638659 | 0.0319330 | − | 0.999490i | \(-0.489834\pi\) | ||||
0.0319330 | + | 0.999490i | \(0.489834\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7434.00 | 0.329156 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2730.00 | −0.119975 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 54405.0 | 2.38202 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25734.0 | −1.11837 | −0.559184 | − | 0.829044i | \(-0.688885\pi\) | ||||
−0.559184 | + | 0.829044i | \(0.688885\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3220.00 | 0.139420 | 0.0697099 | − | 0.997567i | \(-0.477793\pi\) | ||||
0.0697099 | + | 0.997567i | \(0.477793\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 29844.0 | 1.28269 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1204.00 | 0.0515577 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44631.0 | −1.89724 | −0.948619 | − | 0.316420i | \(-0.897519\pi\) | ||||
−0.948619 | + | 0.316420i | \(0.897519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24947.0 | −1.05662 | −0.528310 | − | 0.849052i | \(-0.677174\pi\) | ||||
−0.528310 | + | 0.849052i | \(0.677174\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14964.0 | −0.629201 | −0.314601 | − | 0.949224i | \(-0.601871\pi\) | ||||
−0.314601 | + | 0.949224i | \(0.601871\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7462.00 | −0.312625 | −0.156312 | − | 0.987708i | \(-0.549961\pi\) | ||||
−0.156312 | + | 0.987708i | \(0.549961\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25956.0 | 1.07962 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6129.00 | −0.254015 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2697.00 | 0.110978 | 0.0554891 | − | 0.998459i | \(-0.482328\pi\) | ||||
0.0554891 | + | 0.998459i | \(0.482328\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12068.0 | −0.494813 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7452.00 | −0.303381 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34286.0 | −1.39089 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32370.0 | −1.30391 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −39625.0 | −1.59054 | −0.795272 | − | 0.606253i | \(-0.792672\pi\) | ||||
−0.795272 | + | 0.606253i | \(0.792672\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2973.00 | 0.118501 | 0.0592507 | − | 0.998243i | \(-0.481129\pi\) | ||||
0.0592507 | + | 0.998243i | \(0.481129\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 45229.0 | 1.79650 | 0.898250 | − | 0.439485i | \(-0.144839\pi\) | ||||
0.898250 | + | 0.439485i | \(0.144839\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1416.00 | 0.0558531 | 0.0279265 | − | 0.999610i | \(-0.491110\pi\) | ||||
0.0279265 | + | 0.999610i | \(0.491110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35829.0 | 1.40835 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16995.0 | 0.663424 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15577.0 | −0.605978 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −47151.0 | −1.82171 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17555.0 | 0.675930 | 0.337965 | − | 0.941159i | \(-0.390262\pi\) | ||||
0.337965 | + | 0.941159i | \(0.390262\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30030.0 | −1.14840 | −0.574198 | − | 0.818717i | \(-0.694686\pi\) | ||||
−0.574198 | + | 0.818717i | \(0.694686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35740.0 | 1.36211 | 0.681057 | − | 0.732230i | \(-0.261521\pi\) | ||||
0.681057 | + | 0.732230i | \(0.261521\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 747.000 | 0.0282771 | 0.0141386 | − | 0.999900i | \(-0.495499\pi\) | ||||
0.0141386 | + | 0.999900i | \(0.495499\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27280.0 | 1.02918 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4956.00 | 0.185718 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18036.0 | 0.673606 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22755.0 | −0.844184 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4788.00 | −0.177038 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11466.0 | 0.421152 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20539.0 | 0.751914 | 0.375957 | − | 0.926637i | \(-0.377314\pi\) | ||||
0.375957 | + | 0.926637i | \(0.377314\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24123.0 | −0.877311 | −0.438656 | − | 0.898655i | \(-0.644545\pi\) | ||||
−0.438656 | + | 0.898655i | \(0.644545\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16245.0 | 0.588862 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 46593.0 | 1.67790 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23312.0 | −0.836770 | −0.418385 | − | 0.908270i | \(-0.637404\pi\) | ||||
−0.418385 | + | 0.908270i | \(0.637404\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5772.00 | −0.205837 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7304.00 | 0.259626 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18699.0 | −0.660381 | −0.330191 | − | 0.943914i | \(-0.607113\pi\) | ||||
−0.330191 | + | 0.943914i | \(0.607113\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17304.0 | 0.609147 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5670.00 | −0.198320 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −31234.0 | −1.08898 | −0.544488 | − | 0.838769i | \(-0.683276\pi\) | ||||
−0.544488 | + | 0.838769i | \(0.683276\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11751.0 | −0.407090 | −0.203545 | − | 0.979066i | \(-0.565246\pi\) | ||||
−0.203545 | + | 0.979066i | \(0.565246\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 50895.0 | 1.75755 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25887.0 | −0.888294 | −0.444147 | − | 0.895954i | \(-0.646493\pi\) | ||||
−0.444147 | + | 0.895954i | \(0.646493\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6734.00 | −0.230342 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 41130.0 | 1.39804 | 0.699020 | − | 0.715102i | \(-0.253620\pi\) | ||||
0.699020 | + | 0.715102i | \(0.253620\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10449.0 | 0.354054 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 82491.0 | 2.77766 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12234.0 | 0.410661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 32499.0 | 1.08412 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28645.0 | 0.952597 | 0.476298 | − | 0.879284i | \(-0.341978\pi\) | ||||
0.476298 | + | 0.879284i | \(0.341978\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32256.0 | −1.06606 | −0.533030 | − | 0.846096i | \(-0.678947\pi\) | ||||
−0.533030 | + | 0.846096i | \(0.678947\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3751.00 | 0.123588 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9015.00 | −0.295205 | −0.147603 | − | 0.989047i | \(-0.547156\pi\) | ||||
−0.147603 | + | 0.989047i | \(0.547156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15750.0 | −0.514170 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15885.0 | 0.515415 | 0.257707 | − | 0.966223i | \(-0.417033\pi\) | ||||
0.257707 | + | 0.966223i | \(0.417033\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18414.0 | −0.595654 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8385.00 | 0.269593 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34904.0 | −1.11883 | −0.559416 | − | 0.828887i | \(-0.688974\pi\) | ||||
−0.559416 | + | 0.828887i | \(0.688974\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −26964.0 | −0.859112 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35341.0 | −1.12263 | −0.561314 | − | 0.827603i | \(-0.689704\pi\) | ||||
−0.561314 | + | 0.827603i | \(0.689704\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1296.4.a.g.1.1 | 1 | ||
3.2 | odd | 2 | 1296.4.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 162.4.a.a.1.1 | 1 | |||
9.2 | odd | 6 | 144.4.i.a.49.1 | 2 | |||
9.4 | even | 3 | 432.4.i.a.289.1 | 2 | |||
9.5 | odd | 6 | 144.4.i.a.97.1 | 2 | |||
9.7 | even | 3 | 432.4.i.a.145.1 | 2 | |||
12.11 | even | 2 | 162.4.a.d.1.1 | 1 | |||
36.7 | odd | 6 | 54.4.c.a.37.1 | 2 | |||
36.11 | even | 6 | 18.4.c.a.13.1 | yes | 2 | ||
36.23 | even | 6 | 18.4.c.a.7.1 | ✓ | 2 | ||
36.31 | odd | 6 | 54.4.c.a.19.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.4.c.a.7.1 | ✓ | 2 | 36.23 | even | 6 | ||
18.4.c.a.13.1 | yes | 2 | 36.11 | even | 6 | ||
54.4.c.a.19.1 | 2 | 36.31 | odd | 6 | |||
54.4.c.a.37.1 | 2 | 36.7 | odd | 6 | |||
144.4.i.a.49.1 | 2 | 9.2 | odd | 6 | |||
144.4.i.a.97.1 | 2 | 9.5 | odd | 6 | |||
162.4.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
162.4.a.d.1.1 | 1 | 12.11 | even | 2 | |||
432.4.i.a.145.1 | 2 | 9.7 | even | 3 | |||
432.4.i.a.289.1 | 2 | 9.4 | even | 3 | |||
1296.4.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
1296.4.a.g.1.1 | 1 | 1.1 | even | 1 | trivial |