Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,4,Mod(1,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, 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("966.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.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: | \(56.9958450655\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 966.1 |
$q$-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 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | −9.00000 | −0.804984 | −0.402492 | − | 0.915423i | \(-0.631856\pi\) | ||||
−0.402492 | + | 0.915423i | \(0.631856\pi\) | |||||||
\(6\) | −6.00000 | −0.408248 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −18.0000 | −0.569210 | ||||||||
\(11\) | −12.0000 | −0.328921 | −0.164461 | − | 0.986384i | \(-0.552588\pi\) | ||||
−0.164461 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 11.0000 | 0.234681 | 0.117340 | − | 0.993092i | \(-0.462563\pi\) | ||||
0.117340 | + | 0.993092i | \(0.462563\pi\) | |||||||
\(14\) | 14.0000 | 0.267261 | ||||||||
\(15\) | 27.0000 | 0.464758 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 96.0000 | 1.36961 | 0.684806 | − | 0.728725i | \(-0.259887\pi\) | ||||
0.684806 | + | 0.728725i | \(0.259887\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | −40.0000 | −0.482980 | −0.241490 | − | 0.970403i | \(-0.577636\pi\) | ||||
−0.241490 | + | 0.970403i | \(0.577636\pi\) | |||||||
\(20\) | −36.0000 | −0.402492 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | −24.0000 | −0.232583 | ||||||||
\(23\) | −23.0000 | −0.208514 | ||||||||
\(24\) | −24.0000 | −0.204124 | ||||||||
\(25\) | −44.0000 | −0.352000 | ||||||||
\(26\) | 22.0000 | 0.165944 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −231.000 | −1.47916 | −0.739580 | − | 0.673069i | \(-0.764976\pi\) | ||||
−0.739580 | + | 0.673069i | \(0.764976\pi\) | |||||||
\(30\) | 54.0000 | 0.328634 | ||||||||
\(31\) | −94.0000 | −0.544610 | −0.272305 | − | 0.962211i | \(-0.587786\pi\) | ||||
−0.272305 | + | 0.962211i | \(0.587786\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 36.0000 | 0.189903 | ||||||||
\(34\) | 192.000 | 0.968463 | ||||||||
\(35\) | −63.0000 | −0.304256 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 47.0000 | 0.208831 | 0.104416 | − | 0.994534i | \(-0.466703\pi\) | ||||
0.104416 | + | 0.994534i | \(0.466703\pi\) | |||||||
\(38\) | −80.0000 | −0.341519 | ||||||||
\(39\) | −33.0000 | −0.135493 | ||||||||
\(40\) | −72.0000 | −0.284605 | ||||||||
\(41\) | −27.0000 | −0.102846 | −0.0514231 | − | 0.998677i | \(-0.516376\pi\) | ||||
−0.0514231 | + | 0.998677i | \(0.516376\pi\) | |||||||
\(42\) | −42.0000 | −0.154303 | ||||||||
\(43\) | 479.000 | 1.69876 | 0.849382 | − | 0.527779i | \(-0.176975\pi\) | ||||
0.849382 | + | 0.527779i | \(0.176975\pi\) | |||||||
\(44\) | −48.0000 | −0.164461 | ||||||||
\(45\) | −81.0000 | −0.268328 | ||||||||
\(46\) | −46.0000 | −0.147442 | ||||||||
\(47\) | 423.000 | 1.31278 | 0.656392 | − | 0.754420i | \(-0.272082\pi\) | ||||
0.656392 | + | 0.754420i | \(0.272082\pi\) | |||||||
\(48\) | −48.0000 | −0.144338 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −88.0000 | −0.248902 | ||||||||
\(51\) | −288.000 | −0.790746 | ||||||||
\(52\) | 44.0000 | 0.117340 | ||||||||
\(53\) | 516.000 | 1.33732 | 0.668661 | − | 0.743568i | \(-0.266868\pi\) | ||||
0.668661 | + | 0.743568i | \(0.266868\pi\) | |||||||
\(54\) | −54.0000 | −0.136083 | ||||||||
\(55\) | 108.000 | 0.264777 | ||||||||
\(56\) | 56.0000 | 0.133631 | ||||||||
\(57\) | 120.000 | 0.278849 | ||||||||
\(58\) | −462.000 | −1.04592 | ||||||||
\(59\) | 882.000 | 1.94621 | 0.973107 | − | 0.230354i | \(-0.0739883\pi\) | ||||
0.973107 | + | 0.230354i | \(0.0739883\pi\) | |||||||
\(60\) | 108.000 | 0.232379 | ||||||||
\(61\) | 842.000 | 1.76733 | 0.883664 | − | 0.468121i | \(-0.155069\pi\) | ||||
0.883664 | + | 0.468121i | \(0.155069\pi\) | |||||||
\(62\) | −188.000 | −0.385097 | ||||||||
\(63\) | 63.0000 | 0.125988 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −99.0000 | −0.188914 | ||||||||
\(66\) | 72.0000 | 0.134282 | ||||||||
\(67\) | −844.000 | −1.53897 | −0.769485 | − | 0.638665i | \(-0.779487\pi\) | ||||
−0.769485 | + | 0.638665i | \(0.779487\pi\) | |||||||
\(68\) | 384.000 | 0.684806 | ||||||||
\(69\) | 69.0000 | 0.120386 | ||||||||
\(70\) | −126.000 | −0.215141 | ||||||||
\(71\) | 654.000 | 1.09318 | 0.546588 | − | 0.837402i | \(-0.315926\pi\) | ||||
0.546588 | + | 0.837402i | \(0.315926\pi\) | |||||||
\(72\) | 72.0000 | 0.117851 | ||||||||
\(73\) | −496.000 | −0.795238 | −0.397619 | − | 0.917551i | \(-0.630163\pi\) | ||||
−0.397619 | + | 0.917551i | \(0.630163\pi\) | |||||||
\(74\) | 94.0000 | 0.147666 | ||||||||
\(75\) | 132.000 | 0.203227 | ||||||||
\(76\) | −160.000 | −0.241490 | ||||||||
\(77\) | −84.0000 | −0.124321 | ||||||||
\(78\) | −66.0000 | −0.0958081 | ||||||||
\(79\) | 260.000 | 0.370282 | 0.185141 | − | 0.982712i | \(-0.440726\pi\) | ||||
0.185141 | + | 0.982712i | \(0.440726\pi\) | |||||||
\(80\) | −144.000 | −0.201246 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −54.0000 | −0.0727232 | ||||||||
\(83\) | −156.000 | −0.206304 | −0.103152 | − | 0.994666i | \(-0.532893\pi\) | ||||
−0.103152 | + | 0.994666i | \(0.532893\pi\) | |||||||
\(84\) | −84.0000 | −0.109109 | ||||||||
\(85\) | −864.000 | −1.10252 | ||||||||
\(86\) | 958.000 | 1.20121 | ||||||||
\(87\) | 693.000 | 0.853993 | ||||||||
\(88\) | −96.0000 | −0.116291 | ||||||||
\(89\) | −414.000 | −0.493078 | −0.246539 | − | 0.969133i | \(-0.579293\pi\) | ||||
−0.246539 | + | 0.969133i | \(0.579293\pi\) | |||||||
\(90\) | −162.000 | −0.189737 | ||||||||
\(91\) | 77.0000 | 0.0887010 | ||||||||
\(92\) | −92.0000 | −0.104257 | ||||||||
\(93\) | 282.000 | 0.314431 | ||||||||
\(94\) | 846.000 | 0.928279 | ||||||||
\(95\) | 360.000 | 0.388792 | ||||||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | 1343.00 | 1.40578 | 0.702892 | − | 0.711297i | \(-0.251892\pi\) | ||||
0.702892 | + | 0.711297i | \(0.251892\pi\) | |||||||
\(98\) | 98.0000 | 0.101015 | ||||||||
\(99\) | −108.000 | −0.109640 | ||||||||
\(100\) | −176.000 | −0.176000 | ||||||||
\(101\) | 270.000 | 0.266000 | 0.133000 | − | 0.991116i | \(-0.457539\pi\) | ||||
0.133000 | + | 0.991116i | \(0.457539\pi\) | |||||||
\(102\) | −576.000 | −0.559142 | ||||||||
\(103\) | 449.000 | 0.429527 | 0.214764 | − | 0.976666i | \(-0.431102\pi\) | ||||
0.214764 | + | 0.976666i | \(0.431102\pi\) | |||||||
\(104\) | 88.0000 | 0.0829722 | ||||||||
\(105\) | 189.000 | 0.175662 | ||||||||
\(106\) | 1032.00 | 0.945629 | ||||||||
\(107\) | 276.000 | 0.249364 | 0.124682 | − | 0.992197i | \(-0.460209\pi\) | ||||
0.124682 | + | 0.992197i | \(0.460209\pi\) | |||||||
\(108\) | −108.000 | −0.0962250 | ||||||||
\(109\) | −589.000 | −0.517578 | −0.258789 | − | 0.965934i | \(-0.583323\pi\) | ||||
−0.258789 | + | 0.965934i | \(0.583323\pi\) | |||||||
\(110\) | 216.000 | 0.187225 | ||||||||
\(111\) | −141.000 | −0.120569 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 1779.00 | 1.48101 | 0.740505 | − | 0.672050i | \(-0.234586\pi\) | ||||
0.740505 | + | 0.672050i | \(0.234586\pi\) | |||||||
\(114\) | 240.000 | 0.197176 | ||||||||
\(115\) | 207.000 | 0.167851 | ||||||||
\(116\) | −924.000 | −0.739580 | ||||||||
\(117\) | 99.0000 | 0.0782270 | ||||||||
\(118\) | 1764.00 | 1.37618 | ||||||||
\(119\) | 672.000 | 0.517665 | ||||||||
\(120\) | 216.000 | 0.164317 | ||||||||
\(121\) | −1187.00 | −0.891811 | ||||||||
\(122\) | 1684.00 | 1.24969 | ||||||||
\(123\) | 81.0000 | 0.0593782 | ||||||||
\(124\) | −376.000 | −0.272305 | ||||||||
\(125\) | 1521.00 | 1.08834 | ||||||||
\(126\) | 126.000 | 0.0890871 | ||||||||
\(127\) | 773.000 | 0.540100 | 0.270050 | − | 0.962846i | \(-0.412960\pi\) | ||||
0.270050 | + | 0.962846i | \(0.412960\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −1437.00 | −0.980781 | ||||||||
\(130\) | −198.000 | −0.133583 | ||||||||
\(131\) | 570.000 | 0.380161 | 0.190081 | − | 0.981768i | \(-0.439125\pi\) | ||||
0.190081 | + | 0.981768i | \(0.439125\pi\) | |||||||
\(132\) | 144.000 | 0.0949514 | ||||||||
\(133\) | −280.000 | −0.182549 | ||||||||
\(134\) | −1688.00 | −1.08822 | ||||||||
\(135\) | 243.000 | 0.154919 | ||||||||
\(136\) | 768.000 | 0.484231 | ||||||||
\(137\) | 2355.00 | 1.46862 | 0.734311 | − | 0.678813i | \(-0.237505\pi\) | ||||
0.734311 | + | 0.678813i | \(0.237505\pi\) | |||||||
\(138\) | 138.000 | 0.0851257 | ||||||||
\(139\) | 2333.00 | 1.42361 | 0.711807 | − | 0.702375i | \(-0.247877\pi\) | ||||
0.711807 | + | 0.702375i | \(0.247877\pi\) | |||||||
\(140\) | −252.000 | −0.152128 | ||||||||
\(141\) | −1269.00 | −0.757937 | ||||||||
\(142\) | 1308.00 | 0.772992 | ||||||||
\(143\) | −132.000 | −0.0771916 | ||||||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | 2079.00 | 1.19070 | ||||||||
\(146\) | −992.000 | −0.562319 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | 188.000 | 0.104416 | ||||||||
\(149\) | −2220.00 | −1.22060 | −0.610300 | − | 0.792170i | \(-0.708951\pi\) | ||||
−0.610300 | + | 0.792170i | \(0.708951\pi\) | |||||||
\(150\) | 264.000 | 0.143703 | ||||||||
\(151\) | −2827.00 | −1.52356 | −0.761781 | − | 0.647834i | \(-0.775675\pi\) | ||||
−0.761781 | + | 0.647834i | \(0.775675\pi\) | |||||||
\(152\) | −320.000 | −0.170759 | ||||||||
\(153\) | 864.000 | 0.456538 | ||||||||
\(154\) | −168.000 | −0.0879080 | ||||||||
\(155\) | 846.000 | 0.438402 | ||||||||
\(156\) | −132.000 | −0.0677465 | ||||||||
\(157\) | 1928.00 | 0.980071 | 0.490036 | − | 0.871702i | \(-0.336984\pi\) | ||||
0.490036 | + | 0.871702i | \(0.336984\pi\) | |||||||
\(158\) | 520.000 | 0.261829 | ||||||||
\(159\) | −1548.00 | −0.772103 | ||||||||
\(160\) | −288.000 | −0.142302 | ||||||||
\(161\) | −161.000 | −0.0788110 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | −1996.00 | −0.959134 | −0.479567 | − | 0.877505i | \(-0.659206\pi\) | ||||
−0.479567 | + | 0.877505i | \(0.659206\pi\) | |||||||
\(164\) | −108.000 | −0.0514231 | ||||||||
\(165\) | −324.000 | −0.152869 | ||||||||
\(166\) | −312.000 | −0.145879 | ||||||||
\(167\) | 1140.00 | 0.528239 | 0.264119 | − | 0.964490i | \(-0.414919\pi\) | ||||
0.264119 | + | 0.964490i | \(0.414919\pi\) | |||||||
\(168\) | −168.000 | −0.0771517 | ||||||||
\(169\) | −2076.00 | −0.944925 | ||||||||
\(170\) | −1728.00 | −0.779597 | ||||||||
\(171\) | −360.000 | −0.160993 | ||||||||
\(172\) | 1916.00 | 0.849382 | ||||||||
\(173\) | 3618.00 | 1.59001 | 0.795004 | − | 0.606604i | \(-0.207469\pi\) | ||||
0.795004 | + | 0.606604i | \(0.207469\pi\) | |||||||
\(174\) | 1386.00 | 0.603864 | ||||||||
\(175\) | −308.000 | −0.133043 | ||||||||
\(176\) | −192.000 | −0.0822304 | ||||||||
\(177\) | −2646.00 | −1.12365 | ||||||||
\(178\) | −828.000 | −0.348659 | ||||||||
\(179\) | 939.000 | 0.392090 | 0.196045 | − | 0.980595i | \(-0.437190\pi\) | ||||
0.196045 | + | 0.980595i | \(0.437190\pi\) | |||||||
\(180\) | −324.000 | −0.134164 | ||||||||
\(181\) | −3598.00 | −1.47755 | −0.738777 | − | 0.673950i | \(-0.764596\pi\) | ||||
−0.738777 | + | 0.673950i | \(0.764596\pi\) | |||||||
\(182\) | 154.000 | 0.0627211 | ||||||||
\(183\) | −2526.00 | −1.02037 | ||||||||
\(184\) | −184.000 | −0.0737210 | ||||||||
\(185\) | −423.000 | −0.168106 | ||||||||
\(186\) | 564.000 | 0.222336 | ||||||||
\(187\) | −1152.00 | −0.450495 | ||||||||
\(188\) | 1692.00 | 0.656392 | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 720.000 | 0.274917 | ||||||||
\(191\) | −5004.00 | −1.89569 | −0.947845 | − | 0.318732i | \(-0.896743\pi\) | ||||
−0.947845 | + | 0.318732i | \(0.896743\pi\) | |||||||
\(192\) | −192.000 | −0.0721688 | ||||||||
\(193\) | 3095.00 | 1.15432 | 0.577158 | − | 0.816633i | \(-0.304162\pi\) | ||||
0.577158 | + | 0.816633i | \(0.304162\pi\) | |||||||
\(194\) | 2686.00 | 0.994039 | ||||||||
\(195\) | 297.000 | 0.109070 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | −621.000 | −0.224591 | −0.112295 | − | 0.993675i | \(-0.535820\pi\) | ||||
−0.112295 | + | 0.993675i | \(0.535820\pi\) | |||||||
\(198\) | −216.000 | −0.0775275 | ||||||||
\(199\) | 3191.00 | 1.13670 | 0.568352 | − | 0.822786i | \(-0.307581\pi\) | ||||
0.568352 | + | 0.822786i | \(0.307581\pi\) | |||||||
\(200\) | −352.000 | −0.124451 | ||||||||
\(201\) | 2532.00 | 0.888525 | ||||||||
\(202\) | 540.000 | 0.188090 | ||||||||
\(203\) | −1617.00 | −0.559070 | ||||||||
\(204\) | −1152.00 | −0.395373 | ||||||||
\(205\) | 243.000 | 0.0827895 | ||||||||
\(206\) | 898.000 | 0.303721 | ||||||||
\(207\) | −207.000 | −0.0695048 | ||||||||
\(208\) | 176.000 | 0.0586702 | ||||||||
\(209\) | 480.000 | 0.158863 | ||||||||
\(210\) | 378.000 | 0.124212 | ||||||||
\(211\) | 80.0000 | 0.0261016 | 0.0130508 | − | 0.999915i | \(-0.495846\pi\) | ||||
0.0130508 | + | 0.999915i | \(0.495846\pi\) | |||||||
\(212\) | 2064.00 | 0.668661 | ||||||||
\(213\) | −1962.00 | −0.631146 | ||||||||
\(214\) | 552.000 | 0.176327 | ||||||||
\(215\) | −4311.00 | −1.36748 | ||||||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | −658.000 | −0.205843 | ||||||||
\(218\) | −1178.00 | −0.365983 | ||||||||
\(219\) | 1488.00 | 0.459131 | ||||||||
\(220\) | 432.000 | 0.132388 | ||||||||
\(221\) | 1056.00 | 0.321422 | ||||||||
\(222\) | −282.000 | −0.0852550 | ||||||||
\(223\) | 2606.00 | 0.782559 | 0.391280 | − | 0.920272i | \(-0.372033\pi\) | ||||
0.391280 | + | 0.920272i | \(0.372033\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | −396.000 | −0.117333 | ||||||||
\(226\) | 3558.00 | 1.04723 | ||||||||
\(227\) | −3699.00 | −1.08155 | −0.540774 | − | 0.841168i | \(-0.681868\pi\) | ||||
−0.540774 | + | 0.841168i | \(0.681868\pi\) | |||||||
\(228\) | 480.000 | 0.139424 | ||||||||
\(229\) | −6712.00 | −1.93686 | −0.968431 | − | 0.249281i | \(-0.919806\pi\) | ||||
−0.968431 | + | 0.249281i | \(0.919806\pi\) | |||||||
\(230\) | 414.000 | 0.118688 | ||||||||
\(231\) | 252.000 | 0.0717765 | ||||||||
\(232\) | −1848.00 | −0.522962 | ||||||||
\(233\) | 5190.00 | 1.45926 | 0.729631 | − | 0.683841i | \(-0.239692\pi\) | ||||
0.729631 | + | 0.683841i | \(0.239692\pi\) | |||||||
\(234\) | 198.000 | 0.0553148 | ||||||||
\(235\) | −3807.00 | −1.05677 | ||||||||
\(236\) | 3528.00 | 0.973107 | ||||||||
\(237\) | −780.000 | −0.213782 | ||||||||
\(238\) | 1344.00 | 0.366044 | ||||||||
\(239\) | 4800.00 | 1.29911 | 0.649553 | − | 0.760317i | \(-0.274956\pi\) | ||||
0.649553 | + | 0.760317i | \(0.274956\pi\) | |||||||
\(240\) | 432.000 | 0.116190 | ||||||||
\(241\) | 7229.00 | 1.93220 | 0.966101 | − | 0.258163i | \(-0.0831173\pi\) | ||||
0.966101 | + | 0.258163i | \(0.0831173\pi\) | |||||||
\(242\) | −2374.00 | −0.630605 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 3368.00 | 0.883664 | ||||||||
\(245\) | −441.000 | −0.114998 | ||||||||
\(246\) | 162.000 | 0.0419868 | ||||||||
\(247\) | −440.000 | −0.113346 | ||||||||
\(248\) | −752.000 | −0.192549 | ||||||||
\(249\) | 468.000 | 0.119110 | ||||||||
\(250\) | 3042.00 | 0.769572 | ||||||||
\(251\) | −123.000 | −0.0309310 | −0.0154655 | − | 0.999880i | \(-0.504923\pi\) | ||||
−0.0154655 | + | 0.999880i | \(0.504923\pi\) | |||||||
\(252\) | 252.000 | 0.0629941 | ||||||||
\(253\) | 276.000 | 0.0685849 | ||||||||
\(254\) | 1546.00 | 0.381908 | ||||||||
\(255\) | 2592.00 | 0.636539 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | 5886.00 | 1.42863 | 0.714316 | − | 0.699823i | \(-0.246738\pi\) | ||||
0.714316 | + | 0.699823i | \(0.246738\pi\) | |||||||
\(258\) | −2874.00 | −0.693517 | ||||||||
\(259\) | 329.000 | 0.0789308 | ||||||||
\(260\) | −396.000 | −0.0944572 | ||||||||
\(261\) | −2079.00 | −0.493053 | ||||||||
\(262\) | 1140.00 | 0.268815 | ||||||||
\(263\) | 357.000 | 0.0837018 | 0.0418509 | − | 0.999124i | \(-0.486675\pi\) | ||||
0.0418509 | + | 0.999124i | \(0.486675\pi\) | |||||||
\(264\) | 288.000 | 0.0671408 | ||||||||
\(265\) | −4644.00 | −1.07652 | ||||||||
\(266\) | −560.000 | −0.129082 | ||||||||
\(267\) | 1242.00 | 0.284679 | ||||||||
\(268\) | −3376.00 | −0.769485 | ||||||||
\(269\) | −8418.00 | −1.90801 | −0.954005 | − | 0.299792i | \(-0.903083\pi\) | ||||
−0.954005 | + | 0.299792i | \(0.903083\pi\) | |||||||
\(270\) | 486.000 | 0.109545 | ||||||||
\(271\) | 4172.00 | 0.935170 | 0.467585 | − | 0.883948i | \(-0.345124\pi\) | ||||
0.467585 | + | 0.883948i | \(0.345124\pi\) | |||||||
\(272\) | 1536.00 | 0.342403 | ||||||||
\(273\) | −231.000 | −0.0512116 | ||||||||
\(274\) | 4710.00 | 1.03847 | ||||||||
\(275\) | 528.000 | 0.115780 | ||||||||
\(276\) | 276.000 | 0.0601929 | ||||||||
\(277\) | −760.000 | −0.164852 | −0.0824259 | − | 0.996597i | \(-0.526267\pi\) | ||||
−0.0824259 | + | 0.996597i | \(0.526267\pi\) | |||||||
\(278\) | 4666.00 | 1.00665 | ||||||||
\(279\) | −846.000 | −0.181537 | ||||||||
\(280\) | −504.000 | −0.107571 | ||||||||
\(281\) | −9339.00 | −1.98263 | −0.991313 | − | 0.131522i | \(-0.958014\pi\) | ||||
−0.991313 | + | 0.131522i | \(0.958014\pi\) | |||||||
\(282\) | −2538.00 | −0.535942 | ||||||||
\(283\) | −6262.00 | −1.31533 | −0.657663 | − | 0.753312i | \(-0.728455\pi\) | ||||
−0.657663 | + | 0.753312i | \(0.728455\pi\) | |||||||
\(284\) | 2616.00 | 0.546588 | ||||||||
\(285\) | −1080.00 | −0.224469 | ||||||||
\(286\) | −264.000 | −0.0545827 | ||||||||
\(287\) | −189.000 | −0.0388722 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 4303.00 | 0.875840 | ||||||||
\(290\) | 4158.00 | 0.841952 | ||||||||
\(291\) | −4029.00 | −0.811629 | ||||||||
\(292\) | −1984.00 | −0.397619 | ||||||||
\(293\) | −5754.00 | −1.14728 | −0.573639 | − | 0.819108i | \(-0.694469\pi\) | ||||
−0.573639 | + | 0.819108i | \(0.694469\pi\) | |||||||
\(294\) | −294.000 | −0.0583212 | ||||||||
\(295\) | −7938.00 | −1.56667 | ||||||||
\(296\) | 376.000 | 0.0738330 | ||||||||
\(297\) | 324.000 | 0.0633010 | ||||||||
\(298\) | −4440.00 | −0.863095 | ||||||||
\(299\) | −253.000 | −0.0489343 | ||||||||
\(300\) | 528.000 | 0.101614 | ||||||||
\(301\) | 3353.00 | 0.642072 | ||||||||
\(302\) | −5654.00 | −1.07732 | ||||||||
\(303\) | −810.000 | −0.153575 | ||||||||
\(304\) | −640.000 | −0.120745 | ||||||||
\(305\) | −7578.00 | −1.42267 | ||||||||
\(306\) | 1728.00 | 0.322821 | ||||||||
\(307\) | 3971.00 | 0.738231 | 0.369116 | − | 0.929384i | \(-0.379661\pi\) | ||||
0.369116 | + | 0.929384i | \(0.379661\pi\) | |||||||
\(308\) | −336.000 | −0.0621603 | ||||||||
\(309\) | −1347.00 | −0.247988 | ||||||||
\(310\) | 1692.00 | 0.309997 | ||||||||
\(311\) | 6156.00 | 1.12243 | 0.561213 | − | 0.827671i | \(-0.310335\pi\) | ||||
0.561213 | + | 0.827671i | \(0.310335\pi\) | |||||||
\(312\) | −264.000 | −0.0479040 | ||||||||
\(313\) | −4210.00 | −0.760266 | −0.380133 | − | 0.924932i | \(-0.624122\pi\) | ||||
−0.380133 | + | 0.924932i | \(0.624122\pi\) | |||||||
\(314\) | 3856.00 | 0.693015 | ||||||||
\(315\) | −567.000 | −0.101419 | ||||||||
\(316\) | 1040.00 | 0.185141 | ||||||||
\(317\) | −1329.00 | −0.235470 | −0.117735 | − | 0.993045i | \(-0.537563\pi\) | ||||
−0.117735 | + | 0.993045i | \(0.537563\pi\) | |||||||
\(318\) | −3096.00 | −0.545959 | ||||||||
\(319\) | 2772.00 | 0.486527 | ||||||||
\(320\) | −576.000 | −0.100623 | ||||||||
\(321\) | −828.000 | −0.143970 | ||||||||
\(322\) | −322.000 | −0.0557278 | ||||||||
\(323\) | −3840.00 | −0.661496 | ||||||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | −484.000 | −0.0826077 | ||||||||
\(326\) | −3992.00 | −0.678210 | ||||||||
\(327\) | 1767.00 | 0.298824 | ||||||||
\(328\) | −216.000 | −0.0363616 | ||||||||
\(329\) | 2961.00 | 0.496186 | ||||||||
\(330\) | −648.000 | −0.108095 | ||||||||
\(331\) | −7444.00 | −1.23613 | −0.618065 | − | 0.786127i | \(-0.712083\pi\) | ||||
−0.618065 | + | 0.786127i | \(0.712083\pi\) | |||||||
\(332\) | −624.000 | −0.103152 | ||||||||
\(333\) | 423.000 | 0.0696104 | ||||||||
\(334\) | 2280.00 | 0.373521 | ||||||||
\(335\) | 7596.00 | 1.23885 | ||||||||
\(336\) | −336.000 | −0.0545545 | ||||||||
\(337\) | 9596.00 | 1.55112 | 0.775560 | − | 0.631274i | \(-0.217468\pi\) | ||||
0.775560 | + | 0.631274i | \(0.217468\pi\) | |||||||
\(338\) | −4152.00 | −0.668163 | ||||||||
\(339\) | −5337.00 | −0.855062 | ||||||||
\(340\) | −3456.00 | −0.551259 | ||||||||
\(341\) | 1128.00 | 0.179134 | ||||||||
\(342\) | −720.000 | −0.113840 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 3832.00 | 0.600603 | ||||||||
\(345\) | −621.000 | −0.0969087 | ||||||||
\(346\) | 7236.00 | 1.12431 | ||||||||
\(347\) | 2079.00 | 0.321633 | 0.160816 | − | 0.986984i | \(-0.448587\pi\) | ||||
0.160816 | + | 0.986984i | \(0.448587\pi\) | |||||||
\(348\) | 2772.00 | 0.426997 | ||||||||
\(349\) | −1582.00 | −0.242643 | −0.121322 | − | 0.992613i | \(-0.538713\pi\) | ||||
−0.121322 | + | 0.992613i | \(0.538713\pi\) | |||||||
\(350\) | −616.000 | −0.0940760 | ||||||||
\(351\) | −297.000 | −0.0451644 | ||||||||
\(352\) | −384.000 | −0.0581456 | ||||||||
\(353\) | 4191.00 | 0.631911 | 0.315955 | − | 0.948774i | \(-0.397675\pi\) | ||||
0.315955 | + | 0.948774i | \(0.397675\pi\) | |||||||
\(354\) | −5292.00 | −0.794538 | ||||||||
\(355\) | −5886.00 | −0.879990 | ||||||||
\(356\) | −1656.00 | −0.246539 | ||||||||
\(357\) | −2016.00 | −0.298874 | ||||||||
\(358\) | 1878.00 | 0.277250 | ||||||||
\(359\) | −11721.0 | −1.72315 | −0.861575 | − | 0.507631i | \(-0.830521\pi\) | ||||
−0.861575 | + | 0.507631i | \(0.830521\pi\) | |||||||
\(360\) | −648.000 | −0.0948683 | ||||||||
\(361\) | −5259.00 | −0.766730 | ||||||||
\(362\) | −7196.00 | −1.04479 | ||||||||
\(363\) | 3561.00 | 0.514887 | ||||||||
\(364\) | 308.000 | 0.0443505 | ||||||||
\(365\) | 4464.00 | 0.640155 | ||||||||
\(366\) | −5052.00 | −0.721509 | ||||||||
\(367\) | 9899.00 | 1.40797 | 0.703983 | − | 0.710217i | \(-0.251403\pi\) | ||||
0.703983 | + | 0.710217i | \(0.251403\pi\) | |||||||
\(368\) | −368.000 | −0.0521286 | ||||||||
\(369\) | −243.000 | −0.0342820 | ||||||||
\(370\) | −846.000 | −0.118869 | ||||||||
\(371\) | 3612.00 | 0.505460 | ||||||||
\(372\) | 1128.00 | 0.157215 | ||||||||
\(373\) | −8170.00 | −1.13412 | −0.567060 | − | 0.823677i | \(-0.691919\pi\) | ||||
−0.567060 | + | 0.823677i | \(0.691919\pi\) | |||||||
\(374\) | −2304.00 | −0.318548 | ||||||||
\(375\) | −4563.00 | −0.628353 | ||||||||
\(376\) | 3384.00 | 0.464140 | ||||||||
\(377\) | −2541.00 | −0.347130 | ||||||||
\(378\) | −378.000 | −0.0514344 | ||||||||
\(379\) | −6163.00 | −0.835282 | −0.417641 | − | 0.908612i | \(-0.637143\pi\) | ||||
−0.417641 | + | 0.908612i | \(0.637143\pi\) | |||||||
\(380\) | 1440.00 | 0.194396 | ||||||||
\(381\) | −2319.00 | −0.311827 | ||||||||
\(382\) | −10008.0 | −1.34046 | ||||||||
\(383\) | −9168.00 | −1.22314 | −0.611570 | − | 0.791190i | \(-0.709462\pi\) | ||||
−0.611570 | + | 0.791190i | \(0.709462\pi\) | |||||||
\(384\) | −384.000 | −0.0510310 | ||||||||
\(385\) | 756.000 | 0.100076 | ||||||||
\(386\) | 6190.00 | 0.816225 | ||||||||
\(387\) | 4311.00 | 0.566254 | ||||||||
\(388\) | 5372.00 | 0.702892 | ||||||||
\(389\) | 6834.00 | 0.890739 | 0.445370 | − | 0.895347i | \(-0.353072\pi\) | ||||
0.445370 | + | 0.895347i | \(0.353072\pi\) | |||||||
\(390\) | 594.000 | 0.0771240 | ||||||||
\(391\) | −2208.00 | −0.285584 | ||||||||
\(392\) | 392.000 | 0.0505076 | ||||||||
\(393\) | −1710.00 | −0.219486 | ||||||||
\(394\) | −1242.00 | −0.158810 | ||||||||
\(395\) | −2340.00 | −0.298071 | ||||||||
\(396\) | −432.000 | −0.0548202 | ||||||||
\(397\) | −5698.00 | −0.720339 | −0.360169 | − | 0.932887i | \(-0.617281\pi\) | ||||
−0.360169 | + | 0.932887i | \(0.617281\pi\) | |||||||
\(398\) | 6382.00 | 0.803771 | ||||||||
\(399\) | 840.000 | 0.105395 | ||||||||
\(400\) | −704.000 | −0.0880000 | ||||||||
\(401\) | −942.000 | −0.117310 | −0.0586549 | − | 0.998278i | \(-0.518681\pi\) | ||||
−0.0586549 | + | 0.998278i | \(0.518681\pi\) | |||||||
\(402\) | 5064.00 | 0.628282 | ||||||||
\(403\) | −1034.00 | −0.127809 | ||||||||
\(404\) | 1080.00 | 0.133000 | ||||||||
\(405\) | −729.000 | −0.0894427 | ||||||||
\(406\) | −3234.00 | −0.395322 | ||||||||
\(407\) | −564.000 | −0.0686890 | ||||||||
\(408\) | −2304.00 | −0.279571 | ||||||||
\(409\) | −12976.0 | −1.56876 | −0.784379 | − | 0.620282i | \(-0.787018\pi\) | ||||
−0.784379 | + | 0.620282i | \(0.787018\pi\) | |||||||
\(410\) | 486.000 | 0.0585410 | ||||||||
\(411\) | −7065.00 | −0.847909 | ||||||||
\(412\) | 1796.00 | 0.214764 | ||||||||
\(413\) | 6174.00 | 0.735600 | ||||||||
\(414\) | −414.000 | −0.0491473 | ||||||||
\(415\) | 1404.00 | 0.166071 | ||||||||
\(416\) | 352.000 | 0.0414861 | ||||||||
\(417\) | −6999.00 | −0.821924 | ||||||||
\(418\) | 960.000 | 0.112333 | ||||||||
\(419\) | 36.0000 | 0.00419741 | 0.00209871 | − | 0.999998i | \(-0.499332\pi\) | ||||
0.00209871 | + | 0.999998i | \(0.499332\pi\) | |||||||
\(420\) | 756.000 | 0.0878310 | ||||||||
\(421\) | 659.000 | 0.0762891 | 0.0381445 | − | 0.999272i | \(-0.487855\pi\) | ||||
0.0381445 | + | 0.999272i | \(0.487855\pi\) | |||||||
\(422\) | 160.000 | 0.0184566 | ||||||||
\(423\) | 3807.00 | 0.437595 | ||||||||
\(424\) | 4128.00 | 0.472815 | ||||||||
\(425\) | −4224.00 | −0.482104 | ||||||||
\(426\) | −3924.00 | −0.446287 | ||||||||
\(427\) | 5894.00 | 0.667987 | ||||||||
\(428\) | 1104.00 | 0.124682 | ||||||||
\(429\) | 396.000 | 0.0445666 | ||||||||
\(430\) | −8622.00 | −0.966953 | ||||||||
\(431\) | 15573.0 | 1.74043 | 0.870215 | − | 0.492673i | \(-0.163980\pi\) | ||||
0.870215 | + | 0.492673i | \(0.163980\pi\) | |||||||
\(432\) | −432.000 | −0.0481125 | ||||||||
\(433\) | −15727.0 | −1.74548 | −0.872738 | − | 0.488188i | \(-0.837658\pi\) | ||||
−0.872738 | + | 0.488188i | \(0.837658\pi\) | |||||||
\(434\) | −1316.00 | −0.145553 | ||||||||
\(435\) | −6237.00 | −0.687451 | ||||||||
\(436\) | −2356.00 | −0.258789 | ||||||||
\(437\) | 920.000 | 0.100708 | ||||||||
\(438\) | 2976.00 | 0.324655 | ||||||||
\(439\) | 11666.0 | 1.26831 | 0.634155 | − | 0.773206i | \(-0.281348\pi\) | ||||
0.634155 | + | 0.773206i | \(0.281348\pi\) | |||||||
\(440\) | 864.000 | 0.0936127 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 2112.00 | 0.227280 | ||||||||
\(443\) | 14457.0 | 1.55050 | 0.775251 | − | 0.631653i | \(-0.217623\pi\) | ||||
0.775251 | + | 0.631653i | \(0.217623\pi\) | |||||||
\(444\) | −564.000 | −0.0602844 | ||||||||
\(445\) | 3726.00 | 0.396920 | ||||||||
\(446\) | 5212.00 | 0.553353 | ||||||||
\(447\) | 6660.00 | 0.704714 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | 5886.00 | 0.618658 | 0.309329 | − | 0.950955i | \(-0.399896\pi\) | ||||
0.309329 | + | 0.950955i | \(0.399896\pi\) | |||||||
\(450\) | −792.000 | −0.0829672 | ||||||||
\(451\) | 324.000 | 0.0338283 | ||||||||
\(452\) | 7116.00 | 0.740505 | ||||||||
\(453\) | 8481.00 | 0.879629 | ||||||||
\(454\) | −7398.00 | −0.764769 | ||||||||
\(455\) | −693.000 | −0.0714029 | ||||||||
\(456\) | 960.000 | 0.0985880 | ||||||||
\(457\) | −7540.00 | −0.771786 | −0.385893 | − | 0.922543i | \(-0.626107\pi\) | ||||
−0.385893 | + | 0.922543i | \(0.626107\pi\) | |||||||
\(458\) | −13424.0 | −1.36957 | ||||||||
\(459\) | −2592.00 | −0.263582 | ||||||||
\(460\) | 828.000 | 0.0839254 | ||||||||
\(461\) | 1266.00 | 0.127903 | 0.0639517 | − | 0.997953i | \(-0.479630\pi\) | ||||
0.0639517 | + | 0.997953i | \(0.479630\pi\) | |||||||
\(462\) | 504.000 | 0.0507537 | ||||||||
\(463\) | −12265.0 | −1.23111 | −0.615554 | − | 0.788095i | \(-0.711068\pi\) | ||||
−0.615554 | + | 0.788095i | \(0.711068\pi\) | |||||||
\(464\) | −3696.00 | −0.369790 | ||||||||
\(465\) | −2538.00 | −0.253112 | ||||||||
\(466\) | 10380.0 | 1.03185 | ||||||||
\(467\) | 10491.0 | 1.03954 | 0.519770 | − | 0.854306i | \(-0.326017\pi\) | ||||
0.519770 | + | 0.854306i | \(0.326017\pi\) | |||||||
\(468\) | 396.000 | 0.0391135 | ||||||||
\(469\) | −5908.00 | −0.581676 | ||||||||
\(470\) | −7614.00 | −0.747250 | ||||||||
\(471\) | −5784.00 | −0.565844 | ||||||||
\(472\) | 7056.00 | 0.688091 | ||||||||
\(473\) | −5748.00 | −0.558760 | ||||||||
\(474\) | −1560.00 | −0.151167 | ||||||||
\(475\) | 1760.00 | 0.170009 | ||||||||
\(476\) | 2688.00 | 0.258833 | ||||||||
\(477\) | 4644.00 | 0.445774 | ||||||||
\(478\) | 9600.00 | 0.918606 | ||||||||
\(479\) | 10062.0 | 0.959801 | 0.479900 | − | 0.877323i | \(-0.340673\pi\) | ||||
0.479900 | + | 0.877323i | \(0.340673\pi\) | |||||||
\(480\) | 864.000 | 0.0821584 | ||||||||
\(481\) | 517.000 | 0.0490087 | ||||||||
\(482\) | 14458.0 | 1.36627 | ||||||||
\(483\) | 483.000 | 0.0455016 | ||||||||
\(484\) | −4748.00 | −0.445905 | ||||||||
\(485\) | −12087.0 | −1.13163 | ||||||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 13967.0 | 1.29960 | 0.649800 | − | 0.760105i | \(-0.274853\pi\) | ||||
0.649800 | + | 0.760105i | \(0.274853\pi\) | |||||||
\(488\) | 6736.00 | 0.624845 | ||||||||
\(489\) | 5988.00 | 0.553756 | ||||||||
\(490\) | −882.000 | −0.0813157 | ||||||||
\(491\) | 9732.00 | 0.894499 | 0.447250 | − | 0.894409i | \(-0.352404\pi\) | ||||
0.447250 | + | 0.894409i | \(0.352404\pi\) | |||||||
\(492\) | 324.000 | 0.0296891 | ||||||||
\(493\) | −22176.0 | −2.02588 | ||||||||
\(494\) | −880.000 | −0.0801479 | ||||||||
\(495\) | 972.000 | 0.0882589 | ||||||||
\(496\) | −1504.00 | −0.136152 | ||||||||
\(497\) | 4578.00 | 0.413182 | ||||||||
\(498\) | 936.000 | 0.0842232 | ||||||||
\(499\) | −6190.00 | −0.555316 | −0.277658 | − | 0.960680i | \(-0.589558\pi\) | ||||
−0.277658 | + | 0.960680i | \(0.589558\pi\) | |||||||
\(500\) | 6084.00 | 0.544170 | ||||||||
\(501\) | −3420.00 | −0.304979 | ||||||||
\(502\) | −246.000 | −0.0218715 | ||||||||
\(503\) | 10026.0 | 0.888742 | 0.444371 | − | 0.895843i | \(-0.353427\pi\) | ||||
0.444371 | + | 0.895843i | \(0.353427\pi\) | |||||||
\(504\) | 504.000 | 0.0445435 | ||||||||
\(505\) | −2430.00 | −0.214126 | ||||||||
\(506\) | 552.000 | 0.0484968 | ||||||||
\(507\) | 6228.00 | 0.545553 | ||||||||
\(508\) | 3092.00 | 0.270050 | ||||||||
\(509\) | −14640.0 | −1.27487 | −0.637433 | − | 0.770506i | \(-0.720004\pi\) | ||||
−0.637433 | + | 0.770506i | \(0.720004\pi\) | |||||||
\(510\) | 5184.00 | 0.450101 | ||||||||
\(511\) | −3472.00 | −0.300572 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 1080.00 | 0.0929496 | ||||||||
\(514\) | 11772.0 | 1.01020 | ||||||||
\(515\) | −4041.00 | −0.345763 | ||||||||
\(516\) | −5748.00 | −0.490391 | ||||||||
\(517\) | −5076.00 | −0.431803 | ||||||||
\(518\) | 658.000 | 0.0558125 | ||||||||
\(519\) | −10854.0 | −0.917992 | ||||||||
\(520\) | −792.000 | −0.0667913 | ||||||||
\(521\) | 11682.0 | 0.982337 | 0.491169 | − | 0.871065i | \(-0.336570\pi\) | ||||
0.491169 | + | 0.871065i | \(0.336570\pi\) | |||||||
\(522\) | −4158.00 | −0.348641 | ||||||||
\(523\) | −20254.0 | −1.69339 | −0.846697 | − | 0.532075i | \(-0.821413\pi\) | ||||
−0.846697 | + | 0.532075i | \(0.821413\pi\) | |||||||
\(524\) | 2280.00 | 0.190081 | ||||||||
\(525\) | 924.000 | 0.0768127 | ||||||||
\(526\) | 714.000 | 0.0591861 | ||||||||
\(527\) | −9024.00 | −0.745904 | ||||||||
\(528\) | 576.000 | 0.0474757 | ||||||||
\(529\) | 529.000 | 0.0434783 | ||||||||
\(530\) | −9288.00 | −0.761217 | ||||||||
\(531\) | 7938.00 | 0.648738 | ||||||||
\(532\) | −1120.00 | −0.0912747 | ||||||||
\(533\) | −297.000 | −0.0241360 | ||||||||
\(534\) | 2484.00 | 0.201298 | ||||||||
\(535\) | −2484.00 | −0.200734 | ||||||||
\(536\) | −6752.00 | −0.544108 | ||||||||
\(537\) | −2817.00 | −0.226373 | ||||||||
\(538\) | −16836.0 | −1.34917 | ||||||||
\(539\) | −588.000 | −0.0469888 | ||||||||
\(540\) | 972.000 | 0.0774597 | ||||||||
\(541\) | −6712.00 | −0.533404 | −0.266702 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266702 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(542\) | 8344.00 | 0.661265 | ||||||||
\(543\) | 10794.0 | 0.853066 | ||||||||
\(544\) | 3072.00 | 0.242116 | ||||||||
\(545\) | 5301.00 | 0.416642 | ||||||||
\(546\) | −462.000 | −0.0362120 | ||||||||
\(547\) | 10658.0 | 0.833095 | 0.416548 | − | 0.909114i | \(-0.363240\pi\) | ||||
0.416548 | + | 0.909114i | \(0.363240\pi\) | |||||||
\(548\) | 9420.00 | 0.734311 | ||||||||
\(549\) | 7578.00 | 0.589110 | ||||||||
\(550\) | 1056.00 | 0.0818691 | ||||||||
\(551\) | 9240.00 | 0.714405 | ||||||||
\(552\) | 552.000 | 0.0425628 | ||||||||
\(553\) | 1820.00 | 0.139953 | ||||||||
\(554\) | −1520.00 | −0.116568 | ||||||||
\(555\) | 1269.00 | 0.0970559 | ||||||||
\(556\) | 9332.00 | 0.711807 | ||||||||
\(557\) | 12972.0 | 0.986789 | 0.493394 | − | 0.869806i | \(-0.335756\pi\) | ||||
0.493394 | + | 0.869806i | \(0.335756\pi\) | |||||||
\(558\) | −1692.00 | −0.128366 | ||||||||
\(559\) | 5269.00 | 0.398667 | ||||||||
\(560\) | −1008.00 | −0.0760639 | ||||||||
\(561\) | 3456.00 | 0.260093 | ||||||||
\(562\) | −18678.0 | −1.40193 | ||||||||
\(563\) | 16329.0 | 1.22235 | 0.611177 | − | 0.791494i | \(-0.290696\pi\) | ||||
0.611177 | + | 0.791494i | \(0.290696\pi\) | |||||||
\(564\) | −5076.00 | −0.378968 | ||||||||
\(565\) | −16011.0 | −1.19219 | ||||||||
\(566\) | −12524.0 | −0.930076 | ||||||||
\(567\) | 567.000 | 0.0419961 | ||||||||
\(568\) | 5232.00 | 0.386496 | ||||||||
\(569\) | −2823.00 | −0.207990 | −0.103995 | − | 0.994578i | \(-0.533163\pi\) | ||||
−0.103995 | + | 0.994578i | \(0.533163\pi\) | |||||||
\(570\) | −2160.00 | −0.158724 | ||||||||
\(571\) | −21580.0 | −1.58160 | −0.790801 | − | 0.612073i | \(-0.790336\pi\) | ||||
−0.790801 | + | 0.612073i | \(0.790336\pi\) | |||||||
\(572\) | −528.000 | −0.0385958 | ||||||||
\(573\) | 15012.0 | 1.09448 | ||||||||
\(574\) | −378.000 | −0.0274868 | ||||||||
\(575\) | 1012.00 | 0.0733971 | ||||||||
\(576\) | 576.000 | 0.0416667 | ||||||||
\(577\) | 11354.0 | 0.819191 | 0.409595 | − | 0.912267i | \(-0.365670\pi\) | ||||
0.409595 | + | 0.912267i | \(0.365670\pi\) | |||||||
\(578\) | 8606.00 | 0.619312 | ||||||||
\(579\) | −9285.00 | −0.666445 | ||||||||
\(580\) | 8316.00 | 0.595350 | ||||||||
\(581\) | −1092.00 | −0.0779755 | ||||||||
\(582\) | −8058.00 | −0.573909 | ||||||||
\(583\) | −6192.00 | −0.439874 | ||||||||
\(584\) | −3968.00 | −0.281159 | ||||||||
\(585\) | −891.000 | −0.0629715 | ||||||||
\(586\) | −11508.0 | −0.811248 | ||||||||
\(587\) | 16872.0 | 1.18634 | 0.593170 | − | 0.805077i | \(-0.297876\pi\) | ||||
0.593170 | + | 0.805077i | \(0.297876\pi\) | |||||||
\(588\) | −588.000 | −0.0412393 | ||||||||
\(589\) | 3760.00 | 0.263036 | ||||||||
\(590\) | −15876.0 | −1.10780 | ||||||||
\(591\) | 1863.00 | 0.129668 | ||||||||
\(592\) | 752.000 | 0.0522078 | ||||||||
\(593\) | −19527.0 | −1.35224 | −0.676120 | − | 0.736792i | \(-0.736340\pi\) | ||||
−0.676120 | + | 0.736792i | \(0.736340\pi\) | |||||||
\(594\) | 648.000 | 0.0447605 | ||||||||
\(595\) | −6048.00 | −0.416712 | ||||||||
\(596\) | −8880.00 | −0.610300 | ||||||||
\(597\) | −9573.00 | −0.656276 | ||||||||
\(598\) | −506.000 | −0.0346018 | ||||||||
\(599\) | 14076.0 | 0.960150 | 0.480075 | − | 0.877227i | \(-0.340609\pi\) | ||||
0.480075 | + | 0.877227i | \(0.340609\pi\) | |||||||
\(600\) | 1056.00 | 0.0718517 | ||||||||
\(601\) | −7264.00 | −0.493020 | −0.246510 | − | 0.969140i | \(-0.579284\pi\) | ||||
−0.246510 | + | 0.969140i | \(0.579284\pi\) | |||||||
\(602\) | 6706.00 | 0.454014 | ||||||||
\(603\) | −7596.00 | −0.512990 | ||||||||
\(604\) | −11308.0 | −0.761781 | ||||||||
\(605\) | 10683.0 | 0.717894 | ||||||||
\(606\) | −1620.00 | −0.108594 | ||||||||
\(607\) | −18394.0 | −1.22997 | −0.614983 | − | 0.788540i | \(-0.710837\pi\) | ||||
−0.614983 | + | 0.788540i | \(0.710837\pi\) | |||||||
\(608\) | −1280.00 | −0.0853797 | ||||||||
\(609\) | 4851.00 | 0.322779 | ||||||||
\(610\) | −15156.0 | −1.00598 | ||||||||
\(611\) | 4653.00 | 0.308085 | ||||||||
\(612\) | 3456.00 | 0.228269 | ||||||||
\(613\) | −8527.00 | −0.561831 | −0.280915 | − | 0.959733i | \(-0.590638\pi\) | ||||
−0.280915 | + | 0.959733i | \(0.590638\pi\) | |||||||
\(614\) | 7942.00 | 0.522008 | ||||||||
\(615\) | −729.000 | −0.0477986 | ||||||||
\(616\) | −672.000 | −0.0439540 | ||||||||
\(617\) | −17706.0 | −1.15529 | −0.577647 | − | 0.816286i | \(-0.696029\pi\) | ||||
−0.577647 | + | 0.816286i | \(0.696029\pi\) | |||||||
\(618\) | −2694.00 | −0.175354 | ||||||||
\(619\) | 7238.00 | 0.469983 | 0.234992 | − | 0.971997i | \(-0.424494\pi\) | ||||
0.234992 | + | 0.971997i | \(0.424494\pi\) | |||||||
\(620\) | 3384.00 | 0.219201 | ||||||||
\(621\) | 621.000 | 0.0401286 | ||||||||
\(622\) | 12312.0 | 0.793676 | ||||||||
\(623\) | −2898.00 | −0.186366 | ||||||||
\(624\) | −528.000 | −0.0338733 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | −8420.00 | −0.537589 | ||||||||
\(627\) | −1440.00 | −0.0917194 | ||||||||
\(628\) | 7712.00 | 0.490036 | ||||||||
\(629\) | 4512.00 | 0.286018 | ||||||||
\(630\) | −1134.00 | −0.0717137 | ||||||||
\(631\) | 21656.0 | 1.36626 | 0.683131 | − | 0.730296i | \(-0.260618\pi\) | ||||
0.683131 | + | 0.730296i | \(0.260618\pi\) | |||||||
\(632\) | 2080.00 | 0.130914 | ||||||||
\(633\) | −240.000 | −0.0150697 | ||||||||
\(634\) | −2658.00 | −0.166503 | ||||||||
\(635\) | −6957.00 | −0.434772 | ||||||||
\(636\) | −6192.00 | −0.386052 | ||||||||
\(637\) | 539.000 | 0.0335258 | ||||||||
\(638\) | 5544.00 | 0.344027 | ||||||||
\(639\) | 5886.00 | 0.364392 | ||||||||
\(640\) | −1152.00 | −0.0711512 | ||||||||
\(641\) | −18027.0 | −1.11080 | −0.555401 | − | 0.831583i | \(-0.687435\pi\) | ||||
−0.555401 | + | 0.831583i | \(0.687435\pi\) | |||||||
\(642\) | −1656.00 | −0.101802 | ||||||||
\(643\) | −14218.0 | −0.872011 | −0.436006 | − | 0.899944i | \(-0.643607\pi\) | ||||
−0.436006 | + | 0.899944i | \(0.643607\pi\) | |||||||
\(644\) | −644.000 | −0.0394055 | ||||||||
\(645\) | 12933.0 | 0.789514 | ||||||||
\(646\) | −7680.00 | −0.467749 | ||||||||
\(647\) | −18840.0 | −1.14479 | −0.572393 | − | 0.819979i | \(-0.693985\pi\) | ||||
−0.572393 | + | 0.819979i | \(0.693985\pi\) | |||||||
\(648\) | 648.000 | 0.0392837 | ||||||||
\(649\) | −10584.0 | −0.640152 | ||||||||
\(650\) | −968.000 | −0.0584124 | ||||||||
\(651\) | 1974.00 | 0.118844 | ||||||||
\(652\) | −7984.00 | −0.479567 | ||||||||
\(653\) | −7611.00 | −0.456112 | −0.228056 | − | 0.973648i | \(-0.573237\pi\) | ||||
−0.228056 | + | 0.973648i | \(0.573237\pi\) | |||||||
\(654\) | 3534.00 | 0.211300 | ||||||||
\(655\) | −5130.00 | −0.306024 | ||||||||
\(656\) | −432.000 | −0.0257115 | ||||||||
\(657\) | −4464.00 | −0.265079 | ||||||||
\(658\) | 5922.00 | 0.350857 | ||||||||
\(659\) | 30456.0 | 1.80030 | 0.900150 | − | 0.435581i | \(-0.143457\pi\) | ||||
0.900150 | + | 0.435581i | \(0.143457\pi\) | |||||||
\(660\) | −1296.00 | −0.0764344 | ||||||||
\(661\) | 25298.0 | 1.48862 | 0.744310 | − | 0.667834i | \(-0.232778\pi\) | ||||
0.744310 | + | 0.667834i | \(0.232778\pi\) | |||||||
\(662\) | −14888.0 | −0.874076 | ||||||||
\(663\) | −3168.00 | −0.185573 | ||||||||
\(664\) | −1248.00 | −0.0729394 | ||||||||
\(665\) | 2520.00 | 0.146949 | ||||||||
\(666\) | 846.000 | 0.0492220 | ||||||||
\(667\) | 5313.00 | 0.308426 | ||||||||
\(668\) | 4560.00 | 0.264119 | ||||||||
\(669\) | −7818.00 | −0.451811 | ||||||||
\(670\) | 15192.0 | 0.875997 | ||||||||
\(671\) | −10104.0 | −0.581312 | ||||||||
\(672\) | −672.000 | −0.0385758 | ||||||||
\(673\) | 23555.0 | 1.34915 | 0.674575 | − | 0.738206i | \(-0.264327\pi\) | ||||
0.674575 | + | 0.738206i | \(0.264327\pi\) | |||||||
\(674\) | 19192.0 | 1.09681 | ||||||||
\(675\) | 1188.00 | 0.0677424 | ||||||||
\(676\) | −8304.00 | −0.472462 | ||||||||
\(677\) | −15954.0 | −0.905705 | −0.452852 | − | 0.891586i | \(-0.649594\pi\) | ||||
−0.452852 | + | 0.891586i | \(0.649594\pi\) | |||||||
\(678\) | −10674.0 | −0.604620 | ||||||||
\(679\) | 9401.00 | 0.531336 | ||||||||
\(680\) | −6912.00 | −0.389799 | ||||||||
\(681\) | 11097.0 | 0.624432 | ||||||||
\(682\) | 2256.00 | 0.126667 | ||||||||
\(683\) | −10284.0 | −0.576144 | −0.288072 | − | 0.957609i | \(-0.593014\pi\) | ||||
−0.288072 | + | 0.957609i | \(0.593014\pi\) | |||||||
\(684\) | −1440.00 | −0.0804967 | ||||||||
\(685\) | −21195.0 | −1.18222 | ||||||||
\(686\) | 686.000 | 0.0381802 | ||||||||
\(687\) | 20136.0 | 1.11825 | ||||||||
\(688\) | 7664.00 | 0.424691 | ||||||||
\(689\) | 5676.00 | 0.313844 | ||||||||
\(690\) | −1242.00 | −0.0685248 | ||||||||
\(691\) | −193.000 | −0.0106253 | −0.00531264 | − | 0.999986i | \(-0.501691\pi\) | ||||
−0.00531264 | + | 0.999986i | \(0.501691\pi\) | |||||||
\(692\) | 14472.0 | 0.795004 | ||||||||
\(693\) | −756.000 | −0.0414402 | ||||||||
\(694\) | 4158.00 | 0.227429 | ||||||||
\(695\) | −20997.0 | −1.14599 | ||||||||
\(696\) | 5544.00 | 0.301932 | ||||||||
\(697\) | −2592.00 | −0.140859 | ||||||||
\(698\) | −3164.00 | −0.171575 | ||||||||
\(699\) | −15570.0 | −0.842506 | ||||||||
\(700\) | −1232.00 | −0.0665217 | ||||||||
\(701\) | −6840.00 | −0.368535 | −0.184268 | − | 0.982876i | \(-0.558991\pi\) | ||||
−0.184268 | + | 0.982876i | \(0.558991\pi\) | |||||||
\(702\) | −594.000 | −0.0319360 | ||||||||
\(703\) | −1880.00 | −0.100861 | ||||||||
\(704\) | −768.000 | −0.0411152 | ||||||||
\(705\) | 11421.0 | 0.610127 | ||||||||
\(706\) | 8382.00 | 0.446828 | ||||||||
\(707\) | 1890.00 | 0.100539 | ||||||||
\(708\) | −10584.0 | −0.561824 | ||||||||
\(709\) | −10354.0 | −0.548452 | −0.274226 | − | 0.961665i | \(-0.588422\pi\) | ||||
−0.274226 | + | 0.961665i | \(0.588422\pi\) | |||||||
\(710\) | −11772.0 | −0.622247 | ||||||||
\(711\) | 2340.00 | 0.123427 | ||||||||
\(712\) | −3312.00 | −0.174329 | ||||||||
\(713\) | 2162.00 | 0.113559 | ||||||||
\(714\) | −4032.00 | −0.211336 | ||||||||
\(715\) | 1188.00 | 0.0621380 | ||||||||
\(716\) | 3756.00 | 0.196045 | ||||||||
\(717\) | −14400.0 | −0.750039 | ||||||||
\(718\) | −23442.0 | −1.21845 | ||||||||
\(719\) | 9111.00 | 0.472577 | 0.236289 | − | 0.971683i | \(-0.424069\pi\) | ||||
0.236289 | + | 0.971683i | \(0.424069\pi\) | |||||||
\(720\) | −1296.00 | −0.0670820 | ||||||||
\(721\) | 3143.00 | 0.162346 | ||||||||
\(722\) | −10518.0 | −0.542160 | ||||||||
\(723\) | −21687.0 | −1.11556 | ||||||||
\(724\) | −14392.0 | −0.738777 | ||||||||
\(725\) | 10164.0 | 0.520664 | ||||||||
\(726\) | 7122.00 | 0.364080 | ||||||||
\(727\) | −6676.00 | −0.340577 | −0.170288 | − | 0.985394i | \(-0.554470\pi\) | ||||
−0.170288 | + | 0.985394i | \(0.554470\pi\) | |||||||
\(728\) | 616.000 | 0.0313605 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 8928.00 | 0.452658 | ||||||||
\(731\) | 45984.0 | 2.32665 | ||||||||
\(732\) | −10104.0 | −0.510184 | ||||||||
\(733\) | 116.000 | 0.00584524 | 0.00292262 | − | 0.999996i | \(-0.499070\pi\) | ||||
0.00292262 | + | 0.999996i | \(0.499070\pi\) | |||||||
\(734\) | 19798.0 | 0.995582 | ||||||||
\(735\) | 1323.00 | 0.0663940 | ||||||||
\(736\) | −736.000 | −0.0368605 | ||||||||
\(737\) | 10128.0 | 0.506200 | ||||||||
\(738\) | −486.000 | −0.0242411 | ||||||||
\(739\) | 314.000 | 0.0156301 | 0.00781507 | − | 0.999969i | \(-0.497512\pi\) | ||||
0.00781507 | + | 0.999969i | \(0.497512\pi\) | |||||||
\(740\) | −1692.00 | −0.0840529 | ||||||||
\(741\) | 1320.00 | 0.0654405 | ||||||||
\(742\) | 7224.00 | 0.357414 | ||||||||
\(743\) | 9744.00 | 0.481121 | 0.240560 | − | 0.970634i | \(-0.422669\pi\) | ||||
0.240560 | + | 0.970634i | \(0.422669\pi\) | |||||||
\(744\) | 2256.00 | 0.111168 | ||||||||
\(745\) | 19980.0 | 0.982565 | ||||||||
\(746\) | −16340.0 | −0.801944 | ||||||||
\(747\) | −1404.00 | −0.0687680 | ||||||||
\(748\) | −4608.00 | −0.225248 | ||||||||
\(749\) | 1932.00 | 0.0942507 | ||||||||
\(750\) | −9126.00 | −0.444313 | ||||||||
\(751\) | −8476.00 | −0.411842 | −0.205921 | − | 0.978569i | \(-0.566019\pi\) | ||||
−0.205921 | + | 0.978569i | \(0.566019\pi\) | |||||||
\(752\) | 6768.00 | 0.328196 | ||||||||
\(753\) | 369.000 | 0.0178580 | ||||||||
\(754\) | −5082.00 | −0.245458 | ||||||||
\(755\) | 25443.0 | 1.22644 | ||||||||
\(756\) | −756.000 | −0.0363696 | ||||||||
\(757\) | −25918.0 | −1.24439 | −0.622197 | − | 0.782861i | \(-0.713760\pi\) | ||||
−0.622197 | + | 0.782861i | \(0.713760\pi\) | |||||||
\(758\) | −12326.0 | −0.590634 | ||||||||
\(759\) | −828.000 | −0.0395975 | ||||||||
\(760\) | 2880.00 | 0.137459 | ||||||||
\(761\) | 12534.0 | 0.597053 | 0.298526 | − | 0.954401i | \(-0.403505\pi\) | ||||
0.298526 | + | 0.954401i | \(0.403505\pi\) | |||||||
\(762\) | −4638.00 | −0.220495 | ||||||||
\(763\) | −4123.00 | −0.195626 | ||||||||
\(764\) | −20016.0 | −0.947845 | ||||||||
\(765\) | −7776.00 | −0.367506 | ||||||||
\(766\) | −18336.0 | −0.864891 | ||||||||
\(767\) | 9702.00 | 0.456739 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | 9179.00 | 0.430433 | 0.215217 | − | 0.976566i | \(-0.430954\pi\) | ||||
0.215217 | + | 0.976566i | \(0.430954\pi\) | |||||||
\(770\) | 1512.00 | 0.0707645 | ||||||||
\(771\) | −17658.0 | −0.824821 | ||||||||
\(772\) | 12380.0 | 0.577158 | ||||||||
\(773\) | −23121.0 | −1.07581 | −0.537907 | − | 0.843004i | \(-0.680785\pi\) | ||||
−0.537907 | + | 0.843004i | \(0.680785\pi\) | |||||||
\(774\) | 8622.00 | 0.400402 | ||||||||
\(775\) | 4136.00 | 0.191703 | ||||||||
\(776\) | 10744.0 | 0.497019 | ||||||||
\(777\) | −987.000 | −0.0455707 | ||||||||
\(778\) | 13668.0 | 0.629848 | ||||||||
\(779\) | 1080.00 | 0.0496727 | ||||||||
\(780\) | 1188.00 | 0.0545349 | ||||||||
\(781\) | −7848.00 | −0.359569 | ||||||||
\(782\) | −4416.00 | −0.201938 | ||||||||
\(783\) | 6237.00 | 0.284664 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | −17352.0 | −0.788942 | ||||||||
\(786\) | −3420.00 | −0.155200 | ||||||||
\(787\) | 16436.0 | 0.744447 | 0.372224 | − | 0.928143i | \(-0.378595\pi\) | ||||
0.372224 | + | 0.928143i | \(0.378595\pi\) | |||||||
\(788\) | −2484.00 | −0.112295 | ||||||||
\(789\) | −1071.00 | −0.0483252 | ||||||||
\(790\) | −4680.00 | −0.210768 | ||||||||
\(791\) | 12453.0 | 0.559770 | ||||||||
\(792\) | −864.000 | −0.0387638 | ||||||||
\(793\) | 9262.00 | 0.414758 | ||||||||
\(794\) | −11396.0 | −0.509356 | ||||||||
\(795\) | 13932.0 | 0.621531 | ||||||||
\(796\) | 12764.0 | 0.568352 | ||||||||
\(797\) | −18669.0 | −0.829724 | −0.414862 | − | 0.909884i | \(-0.636170\pi\) | ||||
−0.414862 | + | 0.909884i | \(0.636170\pi\) | |||||||
\(798\) | 1680.00 | 0.0745255 | ||||||||
\(799\) | 40608.0 | 1.79801 | ||||||||
\(800\) | −1408.00 | −0.0622254 | ||||||||
\(801\) | −3726.00 | −0.164359 | ||||||||
\(802\) | −1884.00 | −0.0829506 | ||||||||
\(803\) | 5952.00 | 0.261571 | ||||||||
\(804\) | 10128.0 | 0.444262 | ||||||||
\(805\) | 1449.00 | 0.0634417 | ||||||||
\(806\) | −2068.00 | −0.0903749 | ||||||||
\(807\) | 25254.0 | 1.10159 | ||||||||
\(808\) | 2160.00 | 0.0940452 | ||||||||
\(809\) | −20616.0 | −0.895946 | −0.447973 | − | 0.894047i | \(-0.647854\pi\) | ||||
−0.447973 | + | 0.894047i | \(0.647854\pi\) | |||||||
\(810\) | −1458.00 | −0.0632456 | ||||||||
\(811\) | −16075.0 | −0.696017 | −0.348008 | − | 0.937491i | \(-0.613142\pi\) | ||||
−0.348008 | + | 0.937491i | \(0.613142\pi\) | |||||||
\(812\) | −6468.00 | −0.279535 | ||||||||
\(813\) | −12516.0 | −0.539920 | ||||||||
\(814\) | −1128.00 | −0.0485705 | ||||||||
\(815\) | 17964.0 | 0.772088 | ||||||||
\(816\) | −4608.00 | −0.197687 | ||||||||
\(817\) | −19160.0 | −0.820469 | ||||||||
\(818\) | −25952.0 | −1.10928 | ||||||||
\(819\) | 693.000 | 0.0295670 | ||||||||
\(820\) | 972.000 | 0.0413948 | ||||||||
\(821\) | −17010.0 | −0.723085 | −0.361543 | − | 0.932356i | \(-0.617750\pi\) | ||||
−0.361543 | + | 0.932356i | \(0.617750\pi\) | |||||||
\(822\) | −14130.0 | −0.599562 | ||||||||
\(823\) | −1699.00 | −0.0719604 | −0.0359802 | − | 0.999353i | \(-0.511455\pi\) | ||||
−0.0359802 | + | 0.999353i | \(0.511455\pi\) | |||||||
\(824\) | 3592.00 | 0.151861 | ||||||||
\(825\) | −1584.00 | −0.0668458 | ||||||||
\(826\) | 12348.0 | 0.520148 | ||||||||
\(827\) | 35106.0 | 1.47612 | 0.738062 | − | 0.674732i | \(-0.235741\pi\) | ||||
0.738062 | + | 0.674732i | \(0.235741\pi\) | |||||||
\(828\) | −828.000 | −0.0347524 | ||||||||
\(829\) | −15070.0 | −0.631366 | −0.315683 | − | 0.948865i | \(-0.602234\pi\) | ||||
−0.315683 | + | 0.948865i | \(0.602234\pi\) | |||||||
\(830\) | 2808.00 | 0.117430 | ||||||||
\(831\) | 2280.00 | 0.0951773 | ||||||||
\(832\) | 704.000 | 0.0293351 | ||||||||
\(833\) | 4704.00 | 0.195659 | ||||||||
\(834\) | −13998.0 | −0.581188 | ||||||||
\(835\) | −10260.0 | −0.425224 | ||||||||
\(836\) | 1920.00 | 0.0794313 | ||||||||
\(837\) | 2538.00 | 0.104810 | ||||||||
\(838\) | 72.0000 | 0.00296802 | ||||||||
\(839\) | 14082.0 | 0.579457 | 0.289729 | − | 0.957109i | \(-0.406435\pi\) | ||||
0.289729 | + | 0.957109i | \(0.406435\pi\) | |||||||
\(840\) | 1512.00 | 0.0621059 | ||||||||
\(841\) | 28972.0 | 1.18791 | ||||||||
\(842\) | 1318.00 | 0.0539445 | ||||||||
\(843\) | 28017.0 | 1.14467 | ||||||||
\(844\) | 320.000 | 0.0130508 | ||||||||
\(845\) | 18684.0 | 0.760650 | ||||||||
\(846\) | 7614.00 | 0.309426 | ||||||||
\(847\) | −8309.00 | −0.337073 | ||||||||
\(848\) | 8256.00 | 0.334330 | ||||||||
\(849\) | 18786.0 | 0.759404 | ||||||||
\(850\) | −8448.00 | −0.340899 | ||||||||
\(851\) | −1081.00 | −0.0435443 | ||||||||
\(852\) | −7848.00 | −0.315573 | ||||||||
\(853\) | 42737.0 | 1.71546 | 0.857730 | − | 0.514101i | \(-0.171874\pi\) | ||||
0.857730 | + | 0.514101i | \(0.171874\pi\) | |||||||
\(854\) | 11788.0 | 0.472338 | ||||||||
\(855\) | 3240.00 | 0.129597 | ||||||||
\(856\) | 2208.00 | 0.0881634 | ||||||||
\(857\) | 28773.0 | 1.14687 | 0.573435 | − | 0.819251i | \(-0.305611\pi\) | ||||
0.573435 | + | 0.819251i | \(0.305611\pi\) | |||||||
\(858\) | 792.000 | 0.0315133 | ||||||||
\(859\) | −4471.00 | −0.177589 | −0.0887943 | − | 0.996050i | \(-0.528301\pi\) | ||||
−0.0887943 | + | 0.996050i | \(0.528301\pi\) | |||||||
\(860\) | −17244.0 | −0.683739 | ||||||||
\(861\) | 567.000 | 0.0224429 | ||||||||
\(862\) | 31146.0 | 1.23067 | ||||||||
\(863\) | 27672.0 | 1.09150 | 0.545751 | − | 0.837948i | \(-0.316245\pi\) | ||||
0.545751 | + | 0.837948i | \(0.316245\pi\) | |||||||
\(864\) | −864.000 | −0.0340207 | ||||||||
\(865\) | −32562.0 | −1.27993 | ||||||||
\(866\) | −31454.0 | −1.23424 | ||||||||
\(867\) | −12909.0 | −0.505666 | ||||||||
\(868\) | −2632.00 | −0.102922 | ||||||||
\(869\) | −3120.00 | −0.121794 | ||||||||
\(870\) | −12474.0 | −0.486101 | ||||||||
\(871\) | −9284.00 | −0.361167 | ||||||||
\(872\) | −4712.00 | −0.182991 | ||||||||
\(873\) | 12087.0 | 0.468594 | ||||||||
\(874\) | 1840.00 | 0.0712116 | ||||||||
\(875\) | 10647.0 | 0.411353 | ||||||||
\(876\) | 5952.00 | 0.229566 | ||||||||
\(877\) | 1316.00 | 0.0506707 | 0.0253353 | − | 0.999679i | \(-0.491935\pi\) | ||||
0.0253353 | + | 0.999679i | \(0.491935\pi\) | |||||||
\(878\) | 23332.0 | 0.896830 | ||||||||
\(879\) | 17262.0 | 0.662381 | ||||||||
\(880\) | 1728.00 | 0.0661942 | ||||||||
\(881\) | 34950.0 | 1.33654 | 0.668272 | − | 0.743917i | \(-0.267034\pi\) | ||||
0.668272 | + | 0.743917i | \(0.267034\pi\) | |||||||
\(882\) | 882.000 | 0.0336718 | ||||||||
\(883\) | 15746.0 | 0.600108 | 0.300054 | − | 0.953922i | \(-0.402995\pi\) | ||||
0.300054 | + | 0.953922i | \(0.402995\pi\) | |||||||
\(884\) | 4224.00 | 0.160711 | ||||||||
\(885\) | 23814.0 | 0.904518 | ||||||||
\(886\) | 28914.0 | 1.09637 | ||||||||
\(887\) | −9240.00 | −0.349773 | −0.174887 | − | 0.984589i | \(-0.555956\pi\) | ||||
−0.174887 | + | 0.984589i | \(0.555956\pi\) | |||||||
\(888\) | −1128.00 | −0.0426275 | ||||||||
\(889\) | 5411.00 | 0.204138 | ||||||||
\(890\) | 7452.00 | 0.280665 | ||||||||
\(891\) | −972.000 | −0.0365468 | ||||||||
\(892\) | 10424.0 | 0.391280 | ||||||||
\(893\) | −16920.0 | −0.634050 | ||||||||
\(894\) | 13320.0 | 0.498308 | ||||||||
\(895\) | −8451.00 | −0.315627 | ||||||||
\(896\) | 896.000 | 0.0334077 | ||||||||
\(897\) | 759.000 | 0.0282523 | ||||||||
\(898\) | 11772.0 | 0.437457 | ||||||||
\(899\) | 21714.0 | 0.805564 | ||||||||
\(900\) | −1584.00 | −0.0586667 | ||||||||
\(901\) | 49536.0 | 1.83161 | ||||||||
\(902\) | 648.000 | 0.0239202 | ||||||||
\(903\) | −10059.0 | −0.370701 | ||||||||
\(904\) | 14232.0 | 0.523616 | ||||||||
\(905\) | 32382.0 | 1.18941 | ||||||||
\(906\) | 16962.0 | 0.621992 | ||||||||
\(907\) | −11695.0 | −0.428143 | −0.214072 | − | 0.976818i | \(-0.568673\pi\) | ||||
−0.214072 | + | 0.976818i | \(0.568673\pi\) | |||||||
\(908\) | −14796.0 | −0.540774 | ||||||||
\(909\) | 2430.00 | 0.0886667 | ||||||||
\(910\) | −1386.00 | −0.0504895 | ||||||||
\(911\) | 48495.0 | 1.76368 | 0.881839 | − | 0.471550i | \(-0.156305\pi\) | ||||
0.881839 | + | 0.471550i | \(0.156305\pi\) | |||||||
\(912\) | 1920.00 | 0.0697122 | ||||||||
\(913\) | 1872.00 | 0.0678578 | ||||||||
\(914\) | −15080.0 | −0.545735 | ||||||||
\(915\) | 22734.0 | 0.821380 | ||||||||
\(916\) | −26848.0 | −0.968431 | ||||||||
\(917\) | 3990.00 | 0.143687 | ||||||||
\(918\) | −5184.00 | −0.186381 | ||||||||
\(919\) | 24788.0 | 0.889750 | 0.444875 | − | 0.895593i | \(-0.353248\pi\) | ||||
0.444875 | + | 0.895593i | \(0.353248\pi\) | |||||||
\(920\) | 1656.00 | 0.0593442 | ||||||||
\(921\) | −11913.0 | −0.426218 | ||||||||
\(922\) | 2532.00 | 0.0904414 | ||||||||
\(923\) | 7194.00 | 0.256548 | ||||||||
\(924\) | 1008.00 | 0.0358883 | ||||||||
\(925\) | −2068.00 | −0.0735086 | ||||||||
\(926\) | −24530.0 | −0.870525 | ||||||||
\(927\) | 4041.00 | 0.143176 | ||||||||
\(928\) | −7392.00 | −0.261481 | ||||||||
\(929\) | −32859.0 | −1.16046 | −0.580231 | − | 0.814452i | \(-0.697038\pi\) | ||||
−0.580231 | + | 0.814452i | \(0.697038\pi\) | |||||||
\(930\) | −5076.00 | −0.178977 | ||||||||
\(931\) | −1960.00 | −0.0689972 | ||||||||
\(932\) | 20760.0 | 0.729631 | ||||||||
\(933\) | −18468.0 | −0.648033 | ||||||||
\(934\) | 20982.0 | 0.735066 | ||||||||
\(935\) | 10368.0 | 0.362642 | ||||||||
\(936\) | 792.000 | 0.0276574 | ||||||||
\(937\) | −45817.0 | −1.59741 | −0.798707 | − | 0.601721i | \(-0.794482\pi\) | ||||
−0.798707 | + | 0.601721i | \(0.794482\pi\) | |||||||
\(938\) | −11816.0 | −0.411307 | ||||||||
\(939\) | 12630.0 | 0.438940 | ||||||||
\(940\) | −15228.0 | −0.528386 | ||||||||
\(941\) | −10737.0 | −0.371962 | −0.185981 | − | 0.982553i | \(-0.559546\pi\) | ||||
−0.185981 | + | 0.982553i | \(0.559546\pi\) | |||||||
\(942\) | −11568.0 | −0.400112 | ||||||||
\(943\) | 621.000 | 0.0214449 | ||||||||
\(944\) | 14112.0 | 0.486553 | ||||||||
\(945\) | 1701.00 | 0.0585540 | ||||||||
\(946\) | −11496.0 | −0.395103 | ||||||||
\(947\) | 54225.0 | 1.86069 | 0.930346 | − | 0.366682i | \(-0.119506\pi\) | ||||
0.930346 | + | 0.366682i | \(0.119506\pi\) | |||||||
\(948\) | −3120.00 | −0.106891 | ||||||||
\(949\) | −5456.00 | −0.186627 | ||||||||
\(950\) | 3520.00 | 0.120215 | ||||||||
\(951\) | 3987.00 | 0.135949 | ||||||||
\(952\) | 5376.00 | 0.183022 | ||||||||
\(953\) | −4050.00 | −0.137663 | −0.0688313 | − | 0.997628i | \(-0.521927\pi\) | ||||
−0.0688313 | + | 0.997628i | \(0.521927\pi\) | |||||||
\(954\) | 9288.00 | 0.315210 | ||||||||
\(955\) | 45036.0 | 1.52600 | ||||||||
\(956\) | 19200.0 | 0.649553 | ||||||||
\(957\) | −8316.00 | −0.280897 | ||||||||
\(958\) | 20124.0 | 0.678682 | ||||||||
\(959\) | 16485.0 | 0.555087 | ||||||||
\(960\) | 1728.00 | 0.0580948 | ||||||||
\(961\) | −20955.0 | −0.703400 | ||||||||
\(962\) | 1034.00 | 0.0346544 | ||||||||
\(963\) | 2484.00 | 0.0831213 | ||||||||
\(964\) | 28916.0 | 0.966101 | ||||||||
\(965\) | −27855.0 | −0.929206 | ||||||||
\(966\) | 966.000 | 0.0321745 | ||||||||
\(967\) | −35452.0 | −1.17897 | −0.589483 | − | 0.807781i | \(-0.700668\pi\) | ||||
−0.589483 | + | 0.807781i | \(0.700668\pi\) | |||||||
\(968\) | −9496.00 | −0.315303 | ||||||||
\(969\) | 11520.0 | 0.381915 | ||||||||
\(970\) | −24174.0 | −0.800186 | ||||||||
\(971\) | −48048.0 | −1.58799 | −0.793993 | − | 0.607927i | \(-0.792001\pi\) | ||||
−0.793993 | + | 0.607927i | \(0.792001\pi\) | |||||||
\(972\) | −972.000 | −0.0320750 | ||||||||
\(973\) | 16331.0 | 0.538076 | ||||||||
\(974\) | 27934.0 | 0.918956 | ||||||||
\(975\) | 1452.00 | 0.0476936 | ||||||||
\(976\) | 13472.0 | 0.441832 | ||||||||
\(977\) | 8391.00 | 0.274772 | 0.137386 | − | 0.990518i | \(-0.456130\pi\) | ||||
0.137386 | + | 0.990518i | \(0.456130\pi\) | |||||||
\(978\) | 11976.0 | 0.391565 | ||||||||
\(979\) | 4968.00 | 0.162184 | ||||||||
\(980\) | −1764.00 | −0.0574989 | ||||||||
\(981\) | −5301.00 | −0.172526 | ||||||||
\(982\) | 19464.0 | 0.632506 | ||||||||
\(983\) | −2322.00 | −0.0753411 | −0.0376705 | − | 0.999290i | \(-0.511994\pi\) | ||||
−0.0376705 | + | 0.999290i | \(0.511994\pi\) | |||||||
\(984\) | 648.000 | 0.0209934 | ||||||||
\(985\) | 5589.00 | 0.180792 | ||||||||
\(986\) | −44352.0 | −1.43251 | ||||||||
\(987\) | −8883.00 | −0.286473 | ||||||||
\(988\) | −1760.00 | −0.0566731 | ||||||||
\(989\) | −11017.0 | −0.354217 | ||||||||
\(990\) | 1944.00 | 0.0624085 | ||||||||
\(991\) | 6476.00 | 0.207585 | 0.103793 | − | 0.994599i | \(-0.466902\pi\) | ||||
0.103793 | + | 0.994599i | \(0.466902\pi\) | |||||||
\(992\) | −3008.00 | −0.0962743 | ||||||||
\(993\) | 22332.0 | 0.713680 | ||||||||
\(994\) | 9156.00 | 0.292164 | ||||||||
\(995\) | −28719.0 | −0.915029 | ||||||||
\(996\) | 1872.00 | 0.0595548 | ||||||||
\(997\) | 61238.0 | 1.94526 | 0.972631 | − | 0.232354i | \(-0.0746427\pi\) | ||||
0.972631 | + | 0.232354i | \(0.0746427\pi\) | |||||||
\(998\) | −12380.0 | −0.392667 | ||||||||
\(999\) | −1269.00 | −0.0401896 |
(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 | 966.4.a.b.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial |