Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,4,Mod(1,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, 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("1386.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.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: | \(81.7766472680\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 154) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1386.1 |
$q$-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 | ||||||||
\(5\) | −2.00000 | −0.178885 | −0.0894427 | − | 0.995992i | \(-0.528509\pi\) | ||||
−0.0894427 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.00000 | −0.126491 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 26.0000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 46.0000 | 0.656273 | 0.328136 | − | 0.944630i | \(-0.393579\pi\) | ||||
0.328136 | + | 0.944630i | \(0.393579\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −48.0000 | −0.579577 | −0.289788 | − | 0.957091i | \(-0.593585\pi\) | ||||
−0.289788 | + | 0.957091i | \(0.593585\pi\) | |||||||
\(20\) | −8.00000 | −0.0894427 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −22.0000 | −0.213201 | ||||||||
\(23\) | 128.000 | 1.16043 | 0.580214 | − | 0.814464i | \(-0.302969\pi\) | ||||
0.580214 | + | 0.814464i | \(0.302969\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −121.000 | −0.968000 | ||||||||
\(26\) | 52.0000 | 0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | 146.000 | 0.934880 | 0.467440 | − | 0.884025i | \(-0.345176\pi\) | ||||
0.467440 | + | 0.884025i | \(0.345176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −128.000 | −0.741596 | −0.370798 | − | 0.928714i | \(-0.620916\pi\) | ||||
−0.370798 | + | 0.928714i | \(0.620916\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 92.0000 | 0.464055 | ||||||||
\(35\) | 14.0000 | 0.0676123 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −26.0000 | −0.115524 | −0.0577618 | − | 0.998330i | \(-0.518396\pi\) | ||||
−0.0577618 | + | 0.998330i | \(0.518396\pi\) | |||||||
\(38\) | −96.0000 | −0.409823 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −16.0000 | −0.0632456 | ||||||||
\(41\) | −10.0000 | −0.0380912 | −0.0190456 | − | 0.999819i | \(-0.506063\pi\) | ||||
−0.0190456 | + | 0.999819i | \(0.506063\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.0000 | 0.184417 | 0.0922084 | − | 0.995740i | \(-0.470607\pi\) | ||||
0.0922084 | + | 0.995740i | \(0.470607\pi\) | |||||||
\(44\) | −44.0000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 256.000 | 0.820547 | ||||||||
\(47\) | 544.000 | 1.68831 | 0.844155 | − | 0.536099i | \(-0.180103\pi\) | ||||
0.844155 | + | 0.536099i | \(0.180103\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −242.000 | −0.684479 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 104.000 | 0.277350 | ||||||||
\(53\) | −318.000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 22.0000 | 0.0539360 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 292.000 | 0.661060 | ||||||||
\(59\) | 48.0000 | 0.105916 | 0.0529582 | − | 0.998597i | \(-0.483135\pi\) | ||||
0.0529582 | + | 0.998597i | \(0.483135\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 466.000 | 0.978118 | 0.489059 | − | 0.872251i | \(-0.337340\pi\) | ||||
0.489059 | + | 0.872251i | \(0.337340\pi\) | |||||||
\(62\) | −256.000 | −0.524388 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −52.0000 | −0.0992278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 516.000 | 0.940887 | 0.470444 | − | 0.882430i | \(-0.344094\pi\) | ||||
0.470444 | + | 0.882430i | \(0.344094\pi\) | |||||||
\(68\) | 184.000 | 0.328136 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 28.0000 | 0.0478091 | ||||||||
\(71\) | 392.000 | 0.655237 | 0.327619 | − | 0.944810i | \(-0.393754\pi\) | ||||
0.327619 | + | 0.944810i | \(0.393754\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 754.000 | 1.20889 | 0.604445 | − | 0.796647i | \(-0.293395\pi\) | ||||
0.604445 | + | 0.796647i | \(0.293395\pi\) | |||||||
\(74\) | −52.0000 | −0.0816875 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −192.000 | −0.289788 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −32.0000 | −0.0447214 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −20.0000 | −0.0269345 | ||||||||
\(83\) | −624.000 | −0.825216 | −0.412608 | − | 0.910909i | \(-0.635382\pi\) | ||||
−0.412608 | + | 0.910909i | \(0.635382\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −92.0000 | −0.117398 | ||||||||
\(86\) | 104.000 | 0.130402 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −88.0000 | −0.106600 | ||||||||
\(89\) | 1590.00 | 1.89370 | 0.946852 | − | 0.321669i | \(-0.104244\pi\) | ||||
0.946852 | + | 0.321669i | \(0.104244\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −182.000 | −0.209657 | ||||||||
\(92\) | 512.000 | 0.580214 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1088.00 | 1.19382 | ||||||||
\(95\) | 96.0000 | 0.103678 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1018.00 | 1.06559 | 0.532795 | − | 0.846244i | \(-0.321142\pi\) | ||||
0.532795 | + | 0.846244i | \(0.321142\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −484.000 | −0.484000 | ||||||||
\(101\) | −474.000 | −0.466978 | −0.233489 | − | 0.972359i | \(-0.575014\pi\) | ||||
−0.233489 | + | 0.972359i | \(0.575014\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −984.000 | −0.941324 | −0.470662 | − | 0.882314i | \(-0.655985\pi\) | ||||
−0.470662 | + | 0.882314i | \(0.655985\pi\) | |||||||
\(104\) | 208.000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −636.000 | −0.582772 | ||||||||
\(107\) | −92.0000 | −0.0831213 | −0.0415606 | − | 0.999136i | \(-0.513233\pi\) | ||||
−0.0415606 | + | 0.999136i | \(0.513233\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1246.00 | 1.09491 | 0.547455 | − | 0.836835i | \(-0.315597\pi\) | ||||
0.547455 | + | 0.836835i | \(0.315597\pi\) | |||||||
\(110\) | 44.0000 | 0.0381385 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −112.000 | −0.0944911 | ||||||||
\(113\) | 1630.00 | 1.35697 | 0.678485 | − | 0.734615i | \(-0.262637\pi\) | ||||
0.678485 | + | 0.734615i | \(0.262637\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −256.000 | −0.207584 | ||||||||
\(116\) | 584.000 | 0.467440 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 96.0000 | 0.0748942 | ||||||||
\(119\) | −322.000 | −0.248048 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 932.000 | 0.691634 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −512.000 | −0.370798 | ||||||||
\(125\) | 492.000 | 0.352047 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1016.00 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −104.000 | −0.0701646 | ||||||||
\(131\) | 1920.00 | 1.28054 | 0.640272 | − | 0.768149i | \(-0.278822\pi\) | ||||
0.640272 | + | 0.768149i | \(0.278822\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 336.000 | 0.219059 | ||||||||
\(134\) | 1032.00 | 0.665308 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 368.000 | 0.232027 | ||||||||
\(137\) | −1482.00 | −0.924203 | −0.462101 | − | 0.886827i | \(-0.652904\pi\) | ||||
−0.462101 | + | 0.886827i | \(0.652904\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2608.00 | −1.59142 | −0.795711 | − | 0.605676i | \(-0.792903\pi\) | ||||
−0.795711 | + | 0.605676i | \(0.792903\pi\) | |||||||
\(140\) | 56.0000 | 0.0338062 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 784.000 | 0.463323 | ||||||||
\(143\) | −286.000 | −0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −292.000 | −0.167236 | ||||||||
\(146\) | 1508.00 | 0.854815 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −104.000 | −0.0577618 | ||||||||
\(149\) | −1310.00 | −0.720264 | −0.360132 | − | 0.932901i | \(-0.617268\pi\) | ||||
−0.360132 | + | 0.932901i | \(0.617268\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −192.000 | −0.103475 | −0.0517375 | − | 0.998661i | \(-0.516476\pi\) | ||||
−0.0517375 | + | 0.998661i | \(0.516476\pi\) | |||||||
\(152\) | −384.000 | −0.204911 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 154.000 | 0.0805823 | ||||||||
\(155\) | 256.000 | 0.132661 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 658.000 | 0.334485 | 0.167242 | − | 0.985916i | \(-0.446514\pi\) | ||||
0.167242 | + | 0.985916i | \(0.446514\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −64.0000 | −0.0316228 | ||||||||
\(161\) | −896.000 | −0.438601 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2236.00 | 1.07446 | 0.537230 | − | 0.843436i | \(-0.319471\pi\) | ||||
0.537230 | + | 0.843436i | \(0.319471\pi\) | |||||||
\(164\) | −40.0000 | −0.0190456 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1248.00 | −0.583516 | ||||||||
\(167\) | 1664.00 | 0.771043 | 0.385522 | − | 0.922699i | \(-0.374022\pi\) | ||||
0.385522 | + | 0.922699i | \(0.374022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1521.00 | −0.692308 | ||||||||
\(170\) | −184.000 | −0.0830127 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 208.000 | 0.0922084 | ||||||||
\(173\) | 662.000 | 0.290930 | 0.145465 | − | 0.989363i | \(-0.453532\pi\) | ||||
0.145465 | + | 0.989363i | \(0.453532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 847.000 | 0.365870 | ||||||||
\(176\) | −176.000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3180.00 | 1.33905 | ||||||||
\(179\) | 2540.00 | 1.06061 | 0.530303 | − | 0.847808i | \(-0.322078\pi\) | ||||
0.530303 | + | 0.847808i | \(0.322078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2762.00 | 1.13424 | 0.567121 | − | 0.823634i | \(-0.308057\pi\) | ||||
0.567121 | + | 0.823634i | \(0.308057\pi\) | |||||||
\(182\) | −364.000 | −0.148250 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1024.00 | 0.410273 | ||||||||
\(185\) | 52.0000 | 0.0206655 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −506.000 | −0.197874 | ||||||||
\(188\) | 2176.00 | 0.844155 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 192.000 | 0.0733113 | ||||||||
\(191\) | 16.0000 | 0.00606136 | 0.00303068 | − | 0.999995i | \(-0.499035\pi\) | ||||
0.00303068 | + | 0.999995i | \(0.499035\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5138.00 | 1.91628 | 0.958138 | − | 0.286306i | \(-0.0924275\pi\) | ||||
0.958138 | + | 0.286306i | \(0.0924275\pi\) | |||||||
\(194\) | 2036.00 | 0.753486 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −4350.00 | −1.57322 | −0.786611 | − | 0.617449i | \(-0.788166\pi\) | ||||
−0.786611 | + | 0.617449i | \(0.788166\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4040.00 | −1.43914 | −0.719568 | − | 0.694422i | \(-0.755660\pi\) | ||||
−0.719568 | + | 0.694422i | \(0.755660\pi\) | |||||||
\(200\) | −968.000 | −0.342240 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −948.000 | −0.330203 | ||||||||
\(203\) | −1022.00 | −0.353351 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.0000 | 0.00681395 | ||||||||
\(206\) | −1968.00 | −0.665617 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 416.000 | 0.138675 | ||||||||
\(209\) | 528.000 | 0.174749 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1820.00 | −0.593810 | −0.296905 | − | 0.954907i | \(-0.595955\pi\) | ||||
−0.296905 | + | 0.954907i | \(0.595955\pi\) | |||||||
\(212\) | −1272.00 | −0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −184.000 | −0.0587756 | ||||||||
\(215\) | −104.000 | −0.0329895 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 896.000 | 0.280297 | ||||||||
\(218\) | 2492.00 | 0.774218 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 88.0000 | 0.0269680 | ||||||||
\(221\) | 1196.00 | 0.364035 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2360.00 | −0.708687 | −0.354344 | − | 0.935115i | \(-0.615296\pi\) | ||||
−0.354344 | + | 0.935115i | \(0.615296\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3260.00 | 0.959522 | ||||||||
\(227\) | 6416.00 | 1.87597 | 0.937984 | − | 0.346678i | \(-0.112690\pi\) | ||||
0.937984 | + | 0.346678i | \(0.112690\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1558.00 | −0.449588 | −0.224794 | − | 0.974406i | \(-0.572171\pi\) | ||||
−0.224794 | + | 0.974406i | \(0.572171\pi\) | |||||||
\(230\) | −512.000 | −0.146784 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1168.00 | 0.330530 | ||||||||
\(233\) | −522.000 | −0.146770 | −0.0733849 | − | 0.997304i | \(-0.523380\pi\) | ||||
−0.0733849 | + | 0.997304i | \(0.523380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1088.00 | −0.302014 | ||||||||
\(236\) | 192.000 | 0.0529582 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −644.000 | −0.175396 | ||||||||
\(239\) | −2152.00 | −0.582432 | −0.291216 | − | 0.956657i | \(-0.594060\pi\) | ||||
−0.291216 | + | 0.956657i | \(0.594060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −606.000 | −0.161975 | −0.0809873 | − | 0.996715i | \(-0.525807\pi\) | ||||
−0.0809873 | + | 0.996715i | \(0.525807\pi\) | |||||||
\(242\) | 242.000 | 0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1864.00 | 0.489059 | ||||||||
\(245\) | −98.0000 | −0.0255551 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1248.00 | −0.321491 | ||||||||
\(248\) | −1024.00 | −0.262194 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 984.000 | 0.248934 | ||||||||
\(251\) | 1608.00 | 0.404367 | 0.202183 | − | 0.979348i | \(-0.435196\pi\) | ||||
0.202183 | + | 0.979348i | \(0.435196\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1408.00 | −0.349882 | ||||||||
\(254\) | 2032.00 | 0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 4446.00 | 1.07912 | 0.539560 | − | 0.841947i | \(-0.318591\pi\) | ||||
0.539560 | + | 0.841947i | \(0.318591\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 182.000 | 0.0436638 | ||||||||
\(260\) | −208.000 | −0.0496139 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3840.00 | 0.905481 | ||||||||
\(263\) | −6600.00 | −1.54743 | −0.773714 | − | 0.633535i | \(-0.781603\pi\) | ||||
−0.773714 | + | 0.633535i | \(0.781603\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 636.000 | 0.147431 | ||||||||
\(266\) | 672.000 | 0.154898 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2064.00 | 0.470444 | ||||||||
\(269\) | 1854.00 | 0.420224 | 0.210112 | − | 0.977677i | \(-0.432617\pi\) | ||||
0.210112 | + | 0.977677i | \(0.432617\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −272.000 | −0.0609698 | −0.0304849 | − | 0.999535i | \(-0.509705\pi\) | ||||
−0.0304849 | + | 0.999535i | \(0.509705\pi\) | |||||||
\(272\) | 736.000 | 0.164068 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2964.00 | −0.653510 | ||||||||
\(275\) | 1331.00 | 0.291863 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5010.00 | −1.08672 | −0.543361 | − | 0.839499i | \(-0.682848\pi\) | ||||
−0.543361 | + | 0.839499i | \(0.682848\pi\) | |||||||
\(278\) | −5216.00 | −1.12531 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 112.000 | 0.0239046 | ||||||||
\(281\) | −314.000 | −0.0666607 | −0.0333304 | − | 0.999444i | \(-0.510611\pi\) | ||||
−0.0333304 | + | 0.999444i | \(0.510611\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3480.00 | 0.730970 | 0.365485 | − | 0.930817i | \(-0.380903\pi\) | ||||
0.365485 | + | 0.930817i | \(0.380903\pi\) | |||||||
\(284\) | 1568.00 | 0.327619 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −572.000 | −0.118262 | ||||||||
\(287\) | 70.0000 | 0.0143971 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2797.00 | −0.569306 | ||||||||
\(290\) | −584.000 | −0.118254 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3016.00 | 0.604445 | ||||||||
\(293\) | 4230.00 | 0.843410 | 0.421705 | − | 0.906733i | \(-0.361432\pi\) | ||||
0.421705 | + | 0.906733i | \(0.361432\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −96.0000 | −0.0189469 | ||||||||
\(296\) | −208.000 | −0.0408438 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2620.00 | −0.509304 | ||||||||
\(299\) | 3328.00 | 0.643690 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −364.000 | −0.0697030 | ||||||||
\(302\) | −384.000 | −0.0731679 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −768.000 | −0.144894 | ||||||||
\(305\) | −932.000 | −0.174971 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1552.00 | −0.288525 | −0.144263 | − | 0.989539i | \(-0.546081\pi\) | ||||
−0.144263 | + | 0.989539i | \(0.546081\pi\) | |||||||
\(308\) | 308.000 | 0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 512.000 | 0.0938053 | ||||||||
\(311\) | 4864.00 | 0.886856 | 0.443428 | − | 0.896310i | \(-0.353762\pi\) | ||||
0.443428 | + | 0.896310i | \(0.353762\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4786.00 | 0.864283 | 0.432142 | − | 0.901806i | \(-0.357758\pi\) | ||||
0.432142 | + | 0.901806i | \(0.357758\pi\) | |||||||
\(314\) | 1316.00 | 0.236516 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1530.00 | 0.271083 | 0.135542 | − | 0.990772i | \(-0.456723\pi\) | ||||
0.135542 | + | 0.990772i | \(0.456723\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1606.00 | −0.281877 | ||||||||
\(320\) | −128.000 | −0.0223607 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1792.00 | −0.310137 | ||||||||
\(323\) | −2208.00 | −0.380360 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3146.00 | −0.536950 | ||||||||
\(326\) | 4472.00 | 0.759758 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −80.0000 | −0.0134673 | ||||||||
\(329\) | −3808.00 | −0.638121 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10844.0 | −1.80073 | −0.900363 | − | 0.435140i | \(-0.856699\pi\) | ||||
−0.900363 | + | 0.435140i | \(0.856699\pi\) | |||||||
\(332\) | −2496.00 | −0.412608 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3328.00 | 0.545210 | ||||||||
\(335\) | −1032.00 | −0.168311 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 402.000 | 0.0649802 | 0.0324901 | − | 0.999472i | \(-0.489656\pi\) | ||||
0.0324901 | + | 0.999472i | \(0.489656\pi\) | |||||||
\(338\) | −3042.00 | −0.489535 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −368.000 | −0.0586988 | ||||||||
\(341\) | 1408.00 | 0.223600 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 416.000 | 0.0652012 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1324.00 | 0.205719 | ||||||||
\(347\) | 5980.00 | 0.925139 | 0.462569 | − | 0.886583i | \(-0.346928\pi\) | ||||
0.462569 | + | 0.886583i | \(0.346928\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3094.00 | −0.474550 | −0.237275 | − | 0.971442i | \(-0.576254\pi\) | ||||
−0.237275 | + | 0.971442i | \(0.576254\pi\) | |||||||
\(350\) | 1694.00 | 0.258709 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −352.000 | −0.0533002 | ||||||||
\(353\) | 4494.00 | 0.677596 | 0.338798 | − | 0.940859i | \(-0.389980\pi\) | ||||
0.338798 | + | 0.940859i | \(0.389980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −784.000 | −0.117212 | ||||||||
\(356\) | 6360.00 | 0.946852 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5080.00 | 0.749962 | ||||||||
\(359\) | 2752.00 | 0.404582 | 0.202291 | − | 0.979325i | \(-0.435161\pi\) | ||||
0.202291 | + | 0.979325i | \(0.435161\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4555.00 | −0.664091 | ||||||||
\(362\) | 5524.00 | 0.802030 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −728.000 | −0.104828 | ||||||||
\(365\) | −1508.00 | −0.216253 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2024.00 | −0.287880 | −0.143940 | − | 0.989586i | \(-0.545977\pi\) | ||||
−0.143940 | + | 0.989586i | \(0.545977\pi\) | |||||||
\(368\) | 2048.00 | 0.290107 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 104.000 | 0.0146127 | ||||||||
\(371\) | 2226.00 | 0.311504 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5246.00 | 0.728224 | 0.364112 | − | 0.931355i | \(-0.381373\pi\) | ||||
0.364112 | + | 0.931355i | \(0.381373\pi\) | |||||||
\(374\) | −1012.00 | −0.139918 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4352.00 | 0.596908 | ||||||||
\(377\) | 3796.00 | 0.518578 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3892.00 | 0.527490 | 0.263745 | − | 0.964592i | \(-0.415042\pi\) | ||||
0.263745 | + | 0.964592i | \(0.415042\pi\) | |||||||
\(380\) | 384.000 | 0.0518389 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 32.0000 | 0.00428603 | ||||||||
\(383\) | −6752.00 | −0.900812 | −0.450406 | − | 0.892824i | \(-0.648721\pi\) | ||||
−0.450406 | + | 0.892824i | \(0.648721\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −154.000 | −0.0203859 | ||||||||
\(386\) | 10276.0 | 1.35501 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4072.00 | 0.532795 | ||||||||
\(389\) | −12486.0 | −1.62742 | −0.813709 | − | 0.581273i | \(-0.802555\pi\) | ||||
−0.813709 | + | 0.581273i | \(0.802555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5888.00 | 0.761557 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8700.00 | −1.11244 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1938.00 | 0.245001 | 0.122501 | − | 0.992468i | \(-0.460909\pi\) | ||||
0.122501 | + | 0.992468i | \(0.460909\pi\) | |||||||
\(398\) | −8080.00 | −1.01762 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1936.00 | −0.242000 | ||||||||
\(401\) | −4530.00 | −0.564133 | −0.282067 | − | 0.959395i | \(-0.591020\pi\) | ||||
−0.282067 | + | 0.959395i | \(0.591020\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3328.00 | −0.411363 | ||||||||
\(404\) | −1896.00 | −0.233489 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2044.00 | −0.249857 | ||||||||
\(407\) | 286.000 | 0.0348317 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13718.0 | −1.65846 | −0.829232 | − | 0.558905i | \(-0.811222\pi\) | ||||
−0.829232 | + | 0.558905i | \(0.811222\pi\) | |||||||
\(410\) | 40.0000 | 0.00481819 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3936.00 | −0.470662 | ||||||||
\(413\) | −336.000 | −0.0400326 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1248.00 | 0.147619 | ||||||||
\(416\) | 832.000 | 0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1056.00 | 0.123566 | ||||||||
\(419\) | −15280.0 | −1.78157 | −0.890784 | − | 0.454427i | \(-0.849844\pi\) | ||||
−0.890784 | + | 0.454427i | \(0.849844\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 478.000 | 0.0553356 | 0.0276678 | − | 0.999617i | \(-0.491192\pi\) | ||||
0.0276678 | + | 0.999617i | \(0.491192\pi\) | |||||||
\(422\) | −3640.00 | −0.419887 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2544.00 | −0.291386 | ||||||||
\(425\) | −5566.00 | −0.635272 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3262.00 | −0.369694 | ||||||||
\(428\) | −368.000 | −0.0415606 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −208.000 | −0.0233271 | ||||||||
\(431\) | −6280.00 | −0.701849 | −0.350925 | − | 0.936404i | \(-0.614133\pi\) | ||||
−0.350925 | + | 0.936404i | \(0.614133\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13802.0 | 1.53183 | 0.765914 | − | 0.642943i | \(-0.222287\pi\) | ||||
0.765914 | + | 0.642943i | \(0.222287\pi\) | |||||||
\(434\) | 1792.00 | 0.198200 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4984.00 | 0.547455 | ||||||||
\(437\) | −6144.00 | −0.672557 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8728.00 | 0.948895 | 0.474447 | − | 0.880284i | \(-0.342648\pi\) | ||||
0.474447 | + | 0.880284i | \(0.342648\pi\) | |||||||
\(440\) | 176.000 | 0.0190693 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2392.00 | 0.257411 | ||||||||
\(443\) | 3540.00 | 0.379662 | 0.189831 | − | 0.981817i | \(-0.439206\pi\) | ||||
0.189831 | + | 0.981817i | \(0.439206\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3180.00 | −0.338756 | ||||||||
\(446\) | −4720.00 | −0.501118 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −448.000 | −0.0472456 | ||||||||
\(449\) | −4194.00 | −0.440818 | −0.220409 | − | 0.975408i | \(-0.570739\pi\) | ||||
−0.220409 | + | 0.975408i | \(0.570739\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 110.000 | 0.0114849 | ||||||||
\(452\) | 6520.00 | 0.678485 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 12832.0 | 1.32651 | ||||||||
\(455\) | 364.000 | 0.0375046 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14134.0 | −1.44674 | −0.723370 | − | 0.690460i | \(-0.757408\pi\) | ||||
−0.723370 | + | 0.690460i | \(0.757408\pi\) | |||||||
\(458\) | −3116.00 | −0.317906 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1024.00 | −0.103792 | ||||||||
\(461\) | −234.000 | −0.0236409 | −0.0118205 | − | 0.999930i | \(-0.503763\pi\) | ||||
−0.0118205 | + | 0.999930i | \(0.503763\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13696.0 | 1.37475 | 0.687373 | − | 0.726305i | \(-0.258764\pi\) | ||||
0.687373 | + | 0.726305i | \(0.258764\pi\) | |||||||
\(464\) | 2336.00 | 0.233720 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1044.00 | −0.103782 | ||||||||
\(467\) | −16104.0 | −1.59573 | −0.797863 | − | 0.602839i | \(-0.794036\pi\) | ||||
−0.797863 | + | 0.602839i | \(0.794036\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3612.00 | −0.355622 | ||||||||
\(470\) | −2176.00 | −0.213556 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 384.000 | 0.0374471 | ||||||||
\(473\) | −572.000 | −0.0556038 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5808.00 | 0.561030 | ||||||||
\(476\) | −1288.00 | −0.124024 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4304.00 | −0.411842 | ||||||||
\(479\) | 11272.0 | 1.07522 | 0.537610 | − | 0.843193i | \(-0.319327\pi\) | ||||
0.537610 | + | 0.843193i | \(0.319327\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −676.000 | −0.0640810 | ||||||||
\(482\) | −1212.00 | −0.114533 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 484.000 | 0.0454545 | ||||||||
\(485\) | −2036.00 | −0.190619 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −304.000 | −0.0282866 | −0.0141433 | − | 0.999900i | \(-0.504502\pi\) | ||||
−0.0141433 | + | 0.999900i | \(0.504502\pi\) | |||||||
\(488\) | 3728.00 | 0.345817 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −196.000 | −0.0180702 | ||||||||
\(491\) | −10572.0 | −0.971706 | −0.485853 | − | 0.874041i | \(-0.661491\pi\) | ||||
−0.485853 | + | 0.874041i | \(0.661491\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6716.00 | 0.613536 | ||||||||
\(494\) | −2496.00 | −0.227329 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2048.00 | −0.185399 | ||||||||
\(497\) | −2744.00 | −0.247656 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15004.0 | −1.34603 | −0.673017 | − | 0.739627i | \(-0.735002\pi\) | ||||
−0.673017 | + | 0.739627i | \(0.735002\pi\) | |||||||
\(500\) | 1968.00 | 0.176023 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3216.00 | 0.285930 | ||||||||
\(503\) | −16872.0 | −1.49560 | −0.747799 | − | 0.663926i | \(-0.768889\pi\) | ||||
−0.747799 | + | 0.663926i | \(0.768889\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 948.000 | 0.0835355 | ||||||||
\(506\) | −2816.00 | −0.247404 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4064.00 | 0.354943 | ||||||||
\(509\) | −818.000 | −0.0712322 | −0.0356161 | − | 0.999366i | \(-0.511339\pi\) | ||||
−0.0356161 | + | 0.999366i | \(0.511339\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5278.00 | −0.456918 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8892.00 | 0.763053 | ||||||||
\(515\) | 1968.00 | 0.168389 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5984.00 | −0.509045 | ||||||||
\(518\) | 364.000 | 0.0308750 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −416.000 | −0.0350823 | ||||||||
\(521\) | 2270.00 | 0.190884 | 0.0954419 | − | 0.995435i | \(-0.469574\pi\) | ||||
0.0954419 | + | 0.995435i | \(0.469574\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12776.0 | 1.06817 | 0.534087 | − | 0.845429i | \(-0.320655\pi\) | ||||
0.534087 | + | 0.845429i | \(0.320655\pi\) | |||||||
\(524\) | 7680.00 | 0.640272 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13200.0 | −1.09420 | ||||||||
\(527\) | −5888.00 | −0.486689 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4217.00 | 0.346593 | ||||||||
\(530\) | 1272.00 | 0.104249 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1344.00 | 0.109530 | ||||||||
\(533\) | −260.000 | −0.0211292 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 184.000 | 0.0148692 | ||||||||
\(536\) | 4128.00 | 0.332654 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3708.00 | 0.297144 | ||||||||
\(539\) | −539.000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23050.0 | −1.83179 | −0.915894 | − | 0.401421i | \(-0.868516\pi\) | ||||
−0.915894 | + | 0.401421i | \(0.868516\pi\) | |||||||
\(542\) | −544.000 | −0.0431122 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1472.00 | 0.116014 | ||||||||
\(545\) | −2492.00 | −0.195863 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6564.00 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | −5928.00 | −0.462101 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2662.00 | 0.206378 | ||||||||
\(551\) | −7008.00 | −0.541835 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10020.0 | −0.768428 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10432.0 | −0.795711 | ||||||||
\(557\) | 4522.00 | 0.343992 | 0.171996 | − | 0.985098i | \(-0.444978\pi\) | ||||
0.171996 | + | 0.985098i | \(0.444978\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1352.00 | 0.102296 | ||||||||
\(560\) | 224.000 | 0.0169031 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −628.000 | −0.0471363 | ||||||||
\(563\) | 20440.0 | 1.53009 | 0.765047 | − | 0.643974i | \(-0.222716\pi\) | ||||
0.765047 | + | 0.643974i | \(0.222716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3260.00 | −0.242742 | ||||||||
\(566\) | 6960.00 | 0.516874 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3136.00 | 0.231661 | ||||||||
\(569\) | 16518.0 | 1.21700 | 0.608498 | − | 0.793556i | \(-0.291772\pi\) | ||||
0.608498 | + | 0.793556i | \(0.291772\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8828.00 | −0.647006 | −0.323503 | − | 0.946227i | \(-0.604861\pi\) | ||||
−0.323503 | + | 0.946227i | \(0.604861\pi\) | |||||||
\(572\) | −1144.00 | −0.0836242 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 140.000 | 0.0101803 | ||||||||
\(575\) | −15488.0 | −1.12329 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15550.0 | −1.12193 | −0.560966 | − | 0.827839i | \(-0.689570\pi\) | ||||
−0.560966 | + | 0.827839i | \(0.689570\pi\) | |||||||
\(578\) | −5594.00 | −0.402560 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1168.00 | −0.0836182 | ||||||||
\(581\) | 4368.00 | 0.311902 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3498.00 | 0.248495 | ||||||||
\(584\) | 6032.00 | 0.427407 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8460.00 | 0.596381 | ||||||||
\(587\) | 4536.00 | 0.318945 | 0.159473 | − | 0.987202i | \(-0.449021\pi\) | ||||
0.159473 | + | 0.987202i | \(0.449021\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6144.00 | 0.429812 | ||||||||
\(590\) | −192.000 | −0.0133975 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −416.000 | −0.0288809 | ||||||||
\(593\) | 11142.0 | 0.771580 | 0.385790 | − | 0.922587i | \(-0.373929\pi\) | ||||
0.385790 | + | 0.922587i | \(0.373929\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 644.000 | 0.0443721 | ||||||||
\(596\) | −5240.00 | −0.360132 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 6656.00 | 0.455157 | ||||||||
\(599\) | 16248.0 | 1.10831 | 0.554153 | − | 0.832415i | \(-0.313042\pi\) | ||||
0.554153 | + | 0.832415i | \(0.313042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9646.00 | −0.654690 | −0.327345 | − | 0.944905i | \(-0.606154\pi\) | ||||
−0.327345 | + | 0.944905i | \(0.606154\pi\) | |||||||
\(602\) | −728.000 | −0.0492875 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −768.000 | −0.0517375 | ||||||||
\(605\) | −242.000 | −0.0162623 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4064.00 | 0.271751 | 0.135875 | − | 0.990726i | \(-0.456615\pi\) | ||||
0.135875 | + | 0.990726i | \(0.456615\pi\) | |||||||
\(608\) | −1536.00 | −0.102456 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1864.00 | −0.123723 | ||||||||
\(611\) | 14144.0 | 0.936506 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15098.0 | −0.994784 | −0.497392 | − | 0.867526i | \(-0.665709\pi\) | ||||
−0.497392 | + | 0.867526i | \(0.665709\pi\) | |||||||
\(614\) | −3104.00 | −0.204018 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 616.000 | 0.0402911 | ||||||||
\(617\) | 4470.00 | 0.291662 | 0.145831 | − | 0.989310i | \(-0.453414\pi\) | ||||
0.145831 | + | 0.989310i | \(0.453414\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21184.0 | −1.37554 | −0.687768 | − | 0.725931i | \(-0.741409\pi\) | ||||
−0.687768 | + | 0.725931i | \(0.741409\pi\) | |||||||
\(620\) | 1024.00 | 0.0663304 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9728.00 | 0.627102 | ||||||||
\(623\) | −11130.0 | −0.715753 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14141.0 | 0.905024 | ||||||||
\(626\) | 9572.00 | 0.611141 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2632.00 | 0.167242 | ||||||||
\(629\) | −1196.00 | −0.0758150 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8760.00 | −0.552663 | −0.276331 | − | 0.961062i | \(-0.589119\pi\) | ||||
−0.276331 | + | 0.961062i | \(0.589119\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3060.00 | 0.191685 | ||||||||
\(635\) | −2032.00 | −0.126988 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1274.00 | 0.0792429 | ||||||||
\(638\) | −3212.00 | −0.199317 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −256.000 | −0.0158114 | ||||||||
\(641\) | 3582.00 | 0.220718 | 0.110359 | − | 0.993892i | \(-0.464800\pi\) | ||||
0.110359 | + | 0.993892i | \(0.464800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23168.0 | −1.42093 | −0.710464 | − | 0.703734i | \(-0.751515\pi\) | ||||
−0.710464 | + | 0.703734i | \(0.751515\pi\) | |||||||
\(644\) | −3584.00 | −0.219300 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4416.00 | −0.268955 | ||||||||
\(647\) | −30216.0 | −1.83603 | −0.918017 | − | 0.396542i | \(-0.870210\pi\) | ||||
−0.918017 | + | 0.396542i | \(0.870210\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −528.000 | −0.0319350 | ||||||||
\(650\) | −6292.00 | −0.379681 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8944.00 | 0.537230 | ||||||||
\(653\) | −8158.00 | −0.488893 | −0.244447 | − | 0.969663i | \(-0.578606\pi\) | ||||
−0.244447 | + | 0.969663i | \(0.578606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3840.00 | −0.229071 | ||||||||
\(656\) | −160.000 | −0.00952279 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7616.00 | −0.451220 | ||||||||
\(659\) | −11932.0 | −0.705318 | −0.352659 | − | 0.935752i | \(-0.614722\pi\) | ||||
−0.352659 | + | 0.935752i | \(0.614722\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26882.0 | 1.58183 | 0.790914 | − | 0.611927i | \(-0.209605\pi\) | ||||
0.790914 | + | 0.611927i | \(0.209605\pi\) | |||||||
\(662\) | −21688.0 | −1.27331 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4992.00 | −0.291758 | ||||||||
\(665\) | −672.000 | −0.0391865 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18688.0 | 1.08486 | ||||||||
\(668\) | 6656.00 | 0.385522 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2064.00 | −0.119014 | ||||||||
\(671\) | −5126.00 | −0.294914 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13090.0 | 0.749751 | 0.374875 | − | 0.927075i | \(-0.377685\pi\) | ||||
0.374875 | + | 0.927075i | \(0.377685\pi\) | |||||||
\(674\) | 804.000 | 0.0459480 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6084.00 | −0.346154 | ||||||||
\(677\) | 33790.0 | 1.91825 | 0.959125 | − | 0.282983i | \(-0.0913240\pi\) | ||||
0.959125 | + | 0.282983i | \(0.0913240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7126.00 | −0.402755 | ||||||||
\(680\) | −736.000 | −0.0415063 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2816.00 | 0.158109 | ||||||||
\(683\) | −24588.0 | −1.37750 | −0.688751 | − | 0.724998i | \(-0.741841\pi\) | ||||
−0.688751 | + | 0.724998i | \(0.741841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2964.00 | 0.165326 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 832.000 | 0.0461042 | ||||||||
\(689\) | −8268.00 | −0.457164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1128.00 | −0.0621001 | −0.0310500 | − | 0.999518i | \(-0.509885\pi\) | ||||
−0.0310500 | + | 0.999518i | \(0.509885\pi\) | |||||||
\(692\) | 2648.00 | 0.145465 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 11960.0 | 0.654172 | ||||||||
\(695\) | 5216.00 | 0.284682 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −460.000 | −0.0249982 | ||||||||
\(698\) | −6188.00 | −0.335558 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3388.00 | 0.182935 | ||||||||
\(701\) | 18786.0 | 1.01218 | 0.506089 | − | 0.862481i | \(-0.331091\pi\) | ||||
0.506089 | + | 0.862481i | \(0.331091\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1248.00 | 0.0669548 | ||||||||
\(704\) | −704.000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8988.00 | 0.479133 | ||||||||
\(707\) | 3318.00 | 0.176501 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12102.0 | 0.641044 | 0.320522 | − | 0.947241i | \(-0.396142\pi\) | ||||
0.320522 | + | 0.947241i | \(0.396142\pi\) | |||||||
\(710\) | −1568.00 | −0.0828817 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12720.0 | 0.669525 | ||||||||
\(713\) | −16384.0 | −0.860569 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 572.000 | 0.0299183 | ||||||||
\(716\) | 10160.0 | 0.530303 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5504.00 | 0.286083 | ||||||||
\(719\) | −18112.0 | −0.939449 | −0.469724 | − | 0.882813i | \(-0.655647\pi\) | ||||
−0.469724 | + | 0.882813i | \(0.655647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6888.00 | 0.355787 | ||||||||
\(722\) | −9110.00 | −0.469583 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11048.0 | 0.567121 | ||||||||
\(725\) | −17666.0 | −0.904964 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12728.0 | 0.649320 | 0.324660 | − | 0.945831i | \(-0.394750\pi\) | ||||
0.324660 | + | 0.945831i | \(0.394750\pi\) | |||||||
\(728\) | −1456.00 | −0.0741249 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3016.00 | −0.152914 | ||||||||
\(731\) | 2392.00 | 0.121028 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17138.0 | 0.863583 | 0.431792 | − | 0.901973i | \(-0.357882\pi\) | ||||
0.431792 | + | 0.901973i | \(0.357882\pi\) | |||||||
\(734\) | −4048.00 | −0.203562 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4096.00 | 0.205137 | ||||||||
\(737\) | −5676.00 | −0.283688 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8340.00 | −0.415145 | −0.207572 | − | 0.978220i | \(-0.566556\pi\) | ||||
−0.207572 | + | 0.978220i | \(0.566556\pi\) | |||||||
\(740\) | 208.000 | 0.0103327 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4452.00 | 0.220267 | ||||||||
\(743\) | −8304.00 | −0.410019 | −0.205010 | − | 0.978760i | \(-0.565723\pi\) | ||||
−0.205010 | + | 0.978760i | \(0.565723\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2620.00 | 0.128845 | ||||||||
\(746\) | 10492.0 | 0.514932 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2024.00 | −0.0989369 | ||||||||
\(749\) | 644.000 | 0.0314169 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2152.00 | 0.104564 | 0.0522820 | − | 0.998632i | \(-0.483351\pi\) | ||||
0.0522820 | + | 0.998632i | \(0.483351\pi\) | |||||||
\(752\) | 8704.00 | 0.422077 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7592.00 | 0.366690 | ||||||||
\(755\) | 384.000 | 0.0185102 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25594.0 | −1.22884 | −0.614419 | − | 0.788980i | \(-0.710609\pi\) | ||||
−0.614419 | + | 0.788980i | \(0.710609\pi\) | |||||||
\(758\) | 7784.00 | 0.372992 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 768.000 | 0.0366556 | ||||||||
\(761\) | 17190.0 | 0.818840 | 0.409420 | − | 0.912346i | \(-0.365731\pi\) | ||||
0.409420 | + | 0.912346i | \(0.365731\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8722.00 | −0.413837 | ||||||||
\(764\) | 64.0000 | 0.00303068 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13504.0 | −0.636970 | ||||||||
\(767\) | 1248.00 | 0.0587518 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15086.0 | −0.707432 | −0.353716 | − | 0.935353i | \(-0.615082\pi\) | ||||
−0.353716 | + | 0.935353i | \(0.615082\pi\) | |||||||
\(770\) | −308.000 | −0.0144150 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20552.0 | 0.958138 | ||||||||
\(773\) | −14178.0 | −0.659699 | −0.329849 | − | 0.944034i | \(-0.606998\pi\) | ||||
−0.329849 | + | 0.944034i | \(0.606998\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15488.0 | 0.717865 | ||||||||
\(776\) | 8144.00 | 0.376743 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24972.0 | −1.15076 | ||||||||
\(779\) | 480.000 | 0.0220767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4312.00 | −0.197561 | ||||||||
\(782\) | 11776.0 | 0.538502 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −1316.00 | −0.0598345 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18304.0 | −0.829056 | −0.414528 | − | 0.910037i | \(-0.636053\pi\) | ||||
−0.414528 | + | 0.910037i | \(0.636053\pi\) | |||||||
\(788\) | −17400.0 | −0.786611 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11410.0 | −0.512886 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12116.0 | 0.542562 | ||||||||
\(794\) | 3876.00 | 0.173242 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16160.0 | −0.719568 | ||||||||
\(797\) | 38206.0 | 1.69803 | 0.849013 | − | 0.528373i | \(-0.177198\pi\) | ||||
0.849013 | + | 0.528373i | \(0.177198\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 25024.0 | 1.10799 | ||||||||
\(800\) | −3872.00 | −0.171120 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9060.00 | −0.398902 | ||||||||
\(803\) | −8294.00 | −0.364494 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1792.00 | 0.0784593 | ||||||||
\(806\) | −6656.00 | −0.290878 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3792.00 | −0.165102 | ||||||||
\(809\) | −7146.00 | −0.310556 | −0.155278 | − | 0.987871i | \(-0.549627\pi\) | ||||
−0.155278 | + | 0.987871i | \(0.549627\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21256.0 | −0.920344 | −0.460172 | − | 0.887830i | \(-0.652212\pi\) | ||||
−0.460172 | + | 0.887830i | \(0.652212\pi\) | |||||||
\(812\) | −4088.00 | −0.176676 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 572.000 | 0.0246297 | ||||||||
\(815\) | −4472.00 | −0.192205 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2496.00 | −0.106884 | ||||||||
\(818\) | −27436.0 | −1.17271 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 80.0000 | 0.00340698 | ||||||||
\(821\) | −38670.0 | −1.64384 | −0.821920 | − | 0.569603i | \(-0.807097\pi\) | ||||
−0.821920 | + | 0.569603i | \(0.807097\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21112.0 | −0.894190 | −0.447095 | − | 0.894487i | \(-0.647541\pi\) | ||||
−0.447095 | + | 0.894487i | \(0.647541\pi\) | |||||||
\(824\) | −7872.00 | −0.332808 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −672.000 | −0.0283073 | ||||||||
\(827\) | 3172.00 | 0.133375 | 0.0666876 | − | 0.997774i | \(-0.478757\pi\) | ||||
0.0666876 | + | 0.997774i | \(0.478757\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30346.0 | 1.27136 | 0.635682 | − | 0.771951i | \(-0.280719\pi\) | ||||
0.635682 | + | 0.771951i | \(0.280719\pi\) | |||||||
\(830\) | 2496.00 | 0.104382 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1664.00 | 0.0693375 | ||||||||
\(833\) | 2254.00 | 0.0937533 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3328.00 | −0.137928 | ||||||||
\(836\) | 2112.00 | 0.0873745 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −30560.0 | −1.25976 | ||||||||
\(839\) | 9480.00 | 0.390091 | 0.195045 | − | 0.980794i | \(-0.437515\pi\) | ||||
0.195045 | + | 0.980794i | \(0.437515\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3073.00 | −0.125999 | ||||||||
\(842\) | 956.000 | 0.0391282 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7280.00 | −0.296905 | ||||||||
\(845\) | 3042.00 | 0.123844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −847.000 | −0.0343604 | ||||||||
\(848\) | −5088.00 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −11132.0 | −0.449205 | ||||||||
\(851\) | −3328.00 | −0.134057 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24958.0 | −1.00181 | −0.500906 | − | 0.865502i | \(-0.667000\pi\) | ||||
−0.500906 | + | 0.865502i | \(0.667000\pi\) | |||||||
\(854\) | −6524.00 | −0.261413 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −736.000 | −0.0293878 | ||||||||
\(857\) | 26806.0 | 1.06847 | 0.534233 | − | 0.845337i | \(-0.320600\pi\) | ||||
0.534233 | + | 0.845337i | \(0.320600\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23128.0 | 0.918646 | 0.459323 | − | 0.888269i | \(-0.348092\pi\) | ||||
0.459323 | + | 0.888269i | \(0.348092\pi\) | |||||||
\(860\) | −416.000 | −0.0164947 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12560.0 | −0.496282 | ||||||||
\(863\) | −12496.0 | −0.492895 | −0.246448 | − | 0.969156i | \(-0.579263\pi\) | ||||
−0.246448 | + | 0.969156i | \(0.579263\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1324.00 | −0.0520432 | ||||||||
\(866\) | 27604.0 | 1.08317 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3584.00 | 0.140148 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13416.0 | 0.521910 | ||||||||
\(872\) | 9968.00 | 0.387109 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12288.0 | −0.475570 | ||||||||
\(875\) | −3444.00 | −0.133061 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30478.0 | 1.17351 | 0.586755 | − | 0.809764i | \(-0.300405\pi\) | ||||
0.586755 | + | 0.809764i | \(0.300405\pi\) | |||||||
\(878\) | 17456.0 | 0.670970 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 352.000 | 0.0134840 | ||||||||
\(881\) | −25506.0 | −0.975390 | −0.487695 | − | 0.873014i | \(-0.662162\pi\) | ||||
−0.487695 | + | 0.873014i | \(0.662162\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13244.0 | −0.504752 | −0.252376 | − | 0.967629i | \(-0.581212\pi\) | ||||
−0.252376 | + | 0.967629i | \(0.581212\pi\) | |||||||
\(884\) | 4784.00 | 0.182017 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7080.00 | 0.268462 | ||||||||
\(887\) | −25456.0 | −0.963618 | −0.481809 | − | 0.876276i | \(-0.660020\pi\) | ||||
−0.481809 | + | 0.876276i | \(0.660020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7112.00 | −0.268311 | ||||||||
\(890\) | −6360.00 | −0.239537 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9440.00 | −0.354344 | ||||||||
\(893\) | −26112.0 | −0.978505 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5080.00 | −0.189727 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8388.00 | −0.311705 | ||||||||
\(899\) | −18688.0 | −0.693303 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14628.0 | −0.540876 | ||||||||
\(902\) | 220.000 | 0.00812106 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13040.0 | 0.479761 | ||||||||
\(905\) | −5524.00 | −0.202899 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −51652.0 | −1.89093 | −0.945467 | − | 0.325719i | \(-0.894394\pi\) | ||||
−0.945467 | + | 0.325719i | \(0.894394\pi\) | |||||||
\(908\) | 25664.0 | 0.937984 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 728.000 | 0.0265197 | ||||||||
\(911\) | 46392.0 | 1.68720 | 0.843598 | − | 0.536975i | \(-0.180433\pi\) | ||||
0.843598 | + | 0.536975i | \(0.180433\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6864.00 | 0.248812 | ||||||||
\(914\) | −28268.0 | −1.02300 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6232.00 | −0.224794 | ||||||||
\(917\) | −13440.0 | −0.484000 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17832.0 | 0.640069 | 0.320034 | − | 0.947406i | \(-0.396305\pi\) | ||||
0.320034 | + | 0.947406i | \(0.396305\pi\) | |||||||
\(920\) | −2048.00 | −0.0733919 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −468.000 | −0.0167167 | ||||||||
\(923\) | 10192.0 | 0.363460 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3146.00 | 0.111827 | ||||||||
\(926\) | 27392.0 | 0.972092 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4672.00 | 0.165265 | ||||||||
\(929\) | 41334.0 | 1.45977 | 0.729884 | − | 0.683571i | \(-0.239574\pi\) | ||||
0.729884 | + | 0.683571i | \(0.239574\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2352.00 | −0.0827967 | ||||||||
\(932\) | −2088.00 | −0.0733849 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32208.0 | −1.12835 | ||||||||
\(935\) | 1012.00 | 0.0353967 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23058.0 | 0.803919 | 0.401959 | − | 0.915657i | \(-0.368329\pi\) | ||||
0.401959 | + | 0.915657i | \(0.368329\pi\) | |||||||
\(938\) | −7224.00 | −0.251463 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4352.00 | −0.151007 | ||||||||
\(941\) | 11678.0 | 0.404561 | 0.202281 | − | 0.979328i | \(-0.435165\pi\) | ||||
0.202281 | + | 0.979328i | \(0.435165\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1280.00 | −0.0442021 | ||||||||
\(944\) | 768.000 | 0.0264791 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1144.00 | −0.0393178 | ||||||||
\(947\) | 36436.0 | 1.25028 | 0.625138 | − | 0.780514i | \(-0.285043\pi\) | ||||
0.625138 | + | 0.780514i | \(0.285043\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19604.0 | 0.670572 | ||||||||
\(950\) | 11616.0 | 0.396708 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2576.00 | −0.0876982 | ||||||||
\(953\) | −21098.0 | −0.717137 | −0.358568 | − | 0.933503i | \(-0.616735\pi\) | ||||
−0.358568 | + | 0.933503i | \(0.616735\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −32.0000 | −0.00108429 | ||||||||
\(956\) | −8608.00 | −0.291216 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 22544.0 | 0.760296 | ||||||||
\(959\) | 10374.0 | 0.349316 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13407.0 | −0.450035 | ||||||||
\(962\) | −1352.00 | −0.0453121 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2424.00 | −0.0809873 | ||||||||
\(965\) | −10276.0 | −0.342794 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7184.00 | 0.238906 | 0.119453 | − | 0.992840i | \(-0.461886\pi\) | ||||
0.119453 | + | 0.992840i | \(0.461886\pi\) | |||||||
\(968\) | 968.000 | 0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4072.00 | −0.134788 | ||||||||
\(971\) | 40048.0 | 1.32359 | 0.661793 | − | 0.749687i | \(-0.269796\pi\) | ||||
0.661793 | + | 0.749687i | \(0.269796\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18256.0 | 0.601501 | ||||||||
\(974\) | −608.000 | −0.0200016 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7456.00 | 0.244529 | ||||||||
\(977\) | −51938.0 | −1.70076 | −0.850381 | − | 0.526168i | \(-0.823628\pi\) | ||||
−0.850381 | + | 0.526168i | \(0.823628\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17490.0 | −0.570973 | ||||||||
\(980\) | −392.000 | −0.0127775 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21144.0 | −0.687100 | ||||||||
\(983\) | 28968.0 | 0.939914 | 0.469957 | − | 0.882689i | \(-0.344269\pi\) | ||||
0.469957 | + | 0.882689i | \(0.344269\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8700.00 | 0.281426 | ||||||||
\(986\) | 13432.0 | 0.433836 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4992.00 | −0.160746 | ||||||||
\(989\) | 6656.00 | 0.214003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37504.0 | 1.20217 | 0.601087 | − | 0.799184i | \(-0.294735\pi\) | ||||
0.601087 | + | 0.799184i | \(0.294735\pi\) | |||||||
\(992\) | −4096.00 | −0.131097 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5488.00 | −0.175120 | ||||||||
\(995\) | 8080.00 | 0.257440 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20298.0 | 0.644778 | 0.322389 | − | 0.946607i | \(-0.395514\pi\) | ||||
0.322389 | + | 0.946607i | \(0.395514\pi\) | |||||||
\(998\) | −30008.0 | −0.951790 | ||||||||
\(999\) | 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 | 1386.4.a.j.1.1 | 1 | ||
3.2 | odd | 2 | 154.4.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 1232.4.a.e.1.1 | 1 | |||
21.20 | even | 2 | 1078.4.a.b.1.1 | 1 | |||
33.32 | even | 2 | 1694.4.a.f.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.4.a.b.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1078.4.a.b.1.1 | 1 | 21.20 | even | 2 | |||
1232.4.a.e.1.1 | 1 | 12.11 | even | 2 | |||
1386.4.a.j.1.1 | 1 | 1.1 | even | 1 | trivial | ||
1694.4.a.f.1.1 | 1 | 33.32 | even | 2 |