Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,4,Mod(1,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, 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("1638.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.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: | \(96.6451285894\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1638.1 |
$q$-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 | ||||||||
\(5\) | −3.00000 | −0.268328 | −0.134164 | − | 0.990959i | \(-0.542835\pi\) | ||||
−0.134164 | + | 0.990959i | \(0.542835\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.00000 | 0.189737 | ||||||||
\(11\) | 54.0000 | 1.48015 | 0.740073 | − | 0.672526i | \(-0.234791\pi\) | ||||
0.740073 | + | 0.672526i | \(0.234791\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.0000 | 0.277350 | ||||||||
\(14\) | −14.0000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 96.0000 | 1.36961 | 0.684806 | − | 0.728725i | \(-0.259887\pi\) | ||||
0.684806 | + | 0.728725i | \(0.259887\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −151.000 | −1.82325 | −0.911626 | − | 0.411021i | \(-0.865172\pi\) | ||||
−0.911626 | + | 0.411021i | \(0.865172\pi\) | |||||||
\(20\) | −12.0000 | −0.134164 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −108.000 | −1.04662 | ||||||||
\(23\) | −33.0000 | −0.299173 | −0.149586 | − | 0.988749i | \(-0.547794\pi\) | ||||
−0.149586 | + | 0.988749i | \(0.547794\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −116.000 | −0.928000 | ||||||||
\(26\) | −26.0000 | −0.196116 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 28.0000 | 0.188982 | ||||||||
\(29\) | −183.000 | −1.17180 | −0.585901 | − | 0.810383i | \(-0.699259\pi\) | ||||
−0.585901 | + | 0.810383i | \(0.699259\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −331.000 | −1.91772 | −0.958861 | − | 0.283877i | \(-0.908379\pi\) | ||||
−0.958861 | + | 0.283877i | \(0.908379\pi\) | |||||||
\(32\) | −32.0000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −192.000 | −0.968463 | ||||||||
\(35\) | −21.0000 | −0.101419 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −88.0000 | −0.391003 | −0.195501 | − | 0.980703i | \(-0.562633\pi\) | ||||
−0.195501 | + | 0.980703i | \(0.562633\pi\) | |||||||
\(38\) | 302.000 | 1.28923 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.0000 | 0.0948683 | ||||||||
\(41\) | 42.0000 | 0.159983 | 0.0799914 | − | 0.996796i | \(-0.474511\pi\) | ||||
0.0799914 | + | 0.996796i | \(0.474511\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 353.000 | 1.25191 | 0.625953 | − | 0.779860i | \(-0.284710\pi\) | ||||
0.625953 | + | 0.779860i | \(0.284710\pi\) | |||||||
\(44\) | 216.000 | 0.740073 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 66.0000 | 0.211547 | ||||||||
\(47\) | 465.000 | 1.44313 | 0.721566 | − | 0.692345i | \(-0.243423\pi\) | ||||
0.721566 | + | 0.692345i | \(0.243423\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | 232.000 | 0.656195 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 52.0000 | 0.138675 | ||||||||
\(53\) | −195.000 | −0.505383 | −0.252692 | − | 0.967547i | \(-0.581316\pi\) | ||||
−0.252692 | + | 0.967547i | \(0.581316\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −162.000 | −0.397165 | ||||||||
\(56\) | −56.0000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 366.000 | 0.828589 | ||||||||
\(59\) | −552.000 | −1.21804 | −0.609019 | − | 0.793155i | \(-0.708437\pi\) | ||||
−0.609019 | + | 0.793155i | \(0.708437\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 470.000 | 0.986514 | 0.493257 | − | 0.869884i | \(-0.335806\pi\) | ||||
0.493257 | + | 0.869884i | \(0.335806\pi\) | |||||||
\(62\) | 662.000 | 1.35603 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −39.0000 | −0.0744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 254.000 | 0.463150 | 0.231575 | − | 0.972817i | \(-0.425612\pi\) | ||||
0.231575 | + | 0.972817i | \(0.425612\pi\) | |||||||
\(68\) | 384.000 | 0.684806 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 42.0000 | 0.0717137 | ||||||||
\(71\) | −132.000 | −0.220641 | −0.110321 | − | 0.993896i | \(-0.535188\pi\) | ||||
−0.110321 | + | 0.993896i | \(0.535188\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −943.000 | −1.51192 | −0.755958 | − | 0.654621i | \(-0.772828\pi\) | ||||
−0.755958 | + | 0.654621i | \(0.772828\pi\) | |||||||
\(74\) | 176.000 | 0.276481 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −604.000 | −0.911626 | ||||||||
\(77\) | 378.000 | 0.559443 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −727.000 | −1.03537 | −0.517683 | − | 0.855573i | \(-0.673205\pi\) | ||||
−0.517683 | + | 0.855573i | \(0.673205\pi\) | |||||||
\(80\) | −48.0000 | −0.0670820 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −84.0000 | −0.113125 | ||||||||
\(83\) | 1197.00 | 1.58299 | 0.791493 | − | 0.611178i | \(-0.209304\pi\) | ||||
0.791493 | + | 0.611178i | \(0.209304\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −288.000 | −0.367506 | ||||||||
\(86\) | −706.000 | −0.885232 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −432.000 | −0.523311 | ||||||||
\(89\) | −753.000 | −0.896830 | −0.448415 | − | 0.893826i | \(-0.648011\pi\) | ||||
−0.448415 | + | 0.893826i | \(0.648011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 91.0000 | 0.104828 | ||||||||
\(92\) | −132.000 | −0.149586 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −930.000 | −1.02045 | ||||||||
\(95\) | 453.000 | 0.489230 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1037.00 | 1.08548 | 0.542739 | − | 0.839901i | \(-0.317387\pi\) | ||||
0.542739 | + | 0.839901i | \(0.317387\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −464.000 | −0.464000 | ||||||||
\(101\) | −1566.00 | −1.54280 | −0.771400 | − | 0.636350i | \(-0.780443\pi\) | ||||
−0.771400 | + | 0.636350i | \(0.780443\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 416.000 | 0.397958 | 0.198979 | − | 0.980004i | \(-0.436237\pi\) | ||||
0.198979 | + | 0.980004i | \(0.436237\pi\) | |||||||
\(104\) | −104.000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 390.000 | 0.357360 | ||||||||
\(107\) | 660.000 | 0.596305 | 0.298152 | − | 0.954518i | \(-0.403630\pi\) | ||||
0.298152 | + | 0.954518i | \(0.403630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −250.000 | −0.219685 | −0.109842 | − | 0.993949i | \(-0.535035\pi\) | ||||
−0.109842 | + | 0.993949i | \(0.535035\pi\) | |||||||
\(110\) | 324.000 | 0.280838 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 112.000 | 0.0944911 | ||||||||
\(113\) | 1515.00 | 1.26123 | 0.630616 | − | 0.776095i | \(-0.282802\pi\) | ||||
0.630616 | + | 0.776095i | \(0.282802\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 99.0000 | 0.0802765 | ||||||||
\(116\) | −732.000 | −0.585901 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1104.00 | 0.861283 | ||||||||
\(119\) | 672.000 | 0.517665 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1585.00 | 1.19083 | ||||||||
\(122\) | −940.000 | −0.697571 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1324.00 | −0.958861 | ||||||||
\(125\) | 723.000 | 0.517337 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1492.00 | −1.04247 | −0.521235 | − | 0.853413i | \(-0.674528\pi\) | ||||
−0.521235 | + | 0.853413i | \(0.674528\pi\) | |||||||
\(128\) | −128.000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 78.0000 | 0.0526235 | ||||||||
\(131\) | −1740.00 | −1.16049 | −0.580246 | − | 0.814441i | \(-0.697044\pi\) | ||||
−0.580246 | + | 0.814441i | \(0.697044\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1057.00 | −0.689124 | ||||||||
\(134\) | −508.000 | −0.327496 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −768.000 | −0.484231 | ||||||||
\(137\) | −2820.00 | −1.75860 | −0.879302 | − | 0.476264i | \(-0.841991\pi\) | ||||
−0.879302 | + | 0.476264i | \(0.841991\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 74.0000 | 0.0451554 | 0.0225777 | − | 0.999745i | \(-0.492813\pi\) | ||||
0.0225777 | + | 0.999745i | \(0.492813\pi\) | |||||||
\(140\) | −84.0000 | −0.0507093 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 264.000 | 0.156017 | ||||||||
\(143\) | 702.000 | 0.410519 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 549.000 | 0.314427 | ||||||||
\(146\) | 1886.00 | 1.06909 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −352.000 | −0.195501 | ||||||||
\(149\) | 342.000 | 0.188038 | 0.0940192 | − | 0.995570i | \(-0.470028\pi\) | ||||
0.0940192 | + | 0.995570i | \(0.470028\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −268.000 | −0.144434 | −0.0722170 | − | 0.997389i | \(-0.523007\pi\) | ||||
−0.0722170 | + | 0.997389i | \(0.523007\pi\) | |||||||
\(152\) | 1208.00 | 0.644617 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −756.000 | −0.395586 | ||||||||
\(155\) | 993.000 | 0.514579 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2104.00 | −1.06954 | −0.534769 | − | 0.844998i | \(-0.679601\pi\) | ||||
−0.534769 | + | 0.844998i | \(0.679601\pi\) | |||||||
\(158\) | 1454.00 | 0.732114 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 96.0000 | 0.0474342 | ||||||||
\(161\) | −231.000 | −0.113077 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1312.00 | −0.630453 | −0.315226 | − | 0.949017i | \(-0.602080\pi\) | ||||
−0.315226 | + | 0.949017i | \(0.602080\pi\) | |||||||
\(164\) | 168.000 | 0.0799914 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2394.00 | −1.11934 | ||||||||
\(167\) | −2469.00 | −1.14405 | −0.572027 | − | 0.820235i | \(-0.693843\pi\) | ||||
−0.572027 | + | 0.820235i | \(0.693843\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 169.000 | 0.0769231 | ||||||||
\(170\) | 576.000 | 0.259866 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1412.00 | 0.625953 | ||||||||
\(173\) | 36.0000 | 0.0158210 | 0.00791049 | − | 0.999969i | \(-0.497482\pi\) | ||||
0.00791049 | + | 0.999969i | \(0.497482\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −812.000 | −0.350751 | ||||||||
\(176\) | 864.000 | 0.370037 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1506.00 | 0.634154 | ||||||||
\(179\) | −1809.00 | −0.755369 | −0.377684 | − | 0.925934i | \(-0.623280\pi\) | ||||
−0.377684 | + | 0.925934i | \(0.623280\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1190.00 | 0.488685 | 0.244343 | − | 0.969689i | \(-0.421428\pi\) | ||||
0.244343 | + | 0.969689i | \(0.421428\pi\) | |||||||
\(182\) | −182.000 | −0.0741249 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 264.000 | 0.105774 | ||||||||
\(185\) | 264.000 | 0.104917 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5184.00 | 2.02723 | ||||||||
\(188\) | 1860.00 | 0.721566 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −906.000 | −0.345938 | ||||||||
\(191\) | 3384.00 | 1.28198 | 0.640989 | − | 0.767550i | \(-0.278525\pi\) | ||||
0.640989 | + | 0.767550i | \(0.278525\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 110.000 | 0.0410258 | 0.0205129 | − | 0.999790i | \(-0.493470\pi\) | ||||
0.0205129 | + | 0.999790i | \(0.493470\pi\) | |||||||
\(194\) | −2074.00 | −0.767549 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 196.000 | 0.0714286 | ||||||||
\(197\) | 3966.00 | 1.43434 | 0.717172 | − | 0.696896i | \(-0.245436\pi\) | ||||
0.717172 | + | 0.696896i | \(0.245436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −88.0000 | −0.0313475 | −0.0156738 | − | 0.999877i | \(-0.504989\pi\) | ||||
−0.0156738 | + | 0.999877i | \(0.504989\pi\) | |||||||
\(200\) | 928.000 | 0.328098 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3132.00 | 1.09092 | ||||||||
\(203\) | −1281.00 | −0.442899 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −126.000 | −0.0429279 | ||||||||
\(206\) | −832.000 | −0.281399 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 208.000 | 0.0693375 | ||||||||
\(209\) | −8154.00 | −2.69868 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −331.000 | −0.107995 | −0.0539976 | − | 0.998541i | \(-0.517196\pi\) | ||||
−0.0539976 | + | 0.998541i | \(0.517196\pi\) | |||||||
\(212\) | −780.000 | −0.252692 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1320.00 | −0.421651 | ||||||||
\(215\) | −1059.00 | −0.335922 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2317.00 | −0.724830 | ||||||||
\(218\) | 500.000 | 0.155341 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −648.000 | −0.198583 | ||||||||
\(221\) | 1248.00 | 0.379862 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4777.00 | −1.43449 | −0.717246 | − | 0.696820i | \(-0.754597\pi\) | ||||
−0.717246 | + | 0.696820i | \(0.754597\pi\) | |||||||
\(224\) | −224.000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3030.00 | −0.891826 | ||||||||
\(227\) | −3396.00 | −0.992953 | −0.496477 | − | 0.868050i | \(-0.665373\pi\) | ||||
−0.496477 | + | 0.868050i | \(0.665373\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5182.00 | −1.49535 | −0.747677 | − | 0.664062i | \(-0.768831\pi\) | ||||
−0.747677 | + | 0.664062i | \(0.768831\pi\) | |||||||
\(230\) | −198.000 | −0.0567641 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1464.00 | 0.414294 | ||||||||
\(233\) | 5001.00 | 1.40612 | 0.703061 | − | 0.711130i | \(-0.251816\pi\) | ||||
0.703061 | + | 0.711130i | \(0.251816\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1395.00 | −0.387233 | ||||||||
\(236\) | −2208.00 | −0.609019 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1344.00 | −0.366044 | ||||||||
\(239\) | −2340.00 | −0.633314 | −0.316657 | − | 0.948540i | \(-0.602560\pi\) | ||||
−0.316657 | + | 0.948540i | \(0.602560\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5645.00 | 1.50882 | 0.754412 | − | 0.656402i | \(-0.227922\pi\) | ||||
0.754412 | + | 0.656402i | \(0.227922\pi\) | |||||||
\(242\) | −3170.00 | −0.842047 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1880.00 | 0.493257 | ||||||||
\(245\) | −147.000 | −0.0383326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1963.00 | −0.505679 | ||||||||
\(248\) | 2648.00 | 0.678017 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1446.00 | −0.365812 | ||||||||
\(251\) | 642.000 | 0.161445 | 0.0807225 | − | 0.996737i | \(-0.474277\pi\) | ||||
0.0807225 | + | 0.996737i | \(0.474277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1782.00 | −0.442820 | ||||||||
\(254\) | 2984.00 | 0.737137 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −2886.00 | −0.700481 | −0.350241 | − | 0.936660i | \(-0.613900\pi\) | ||||
−0.350241 | + | 0.936660i | \(0.613900\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −616.000 | −0.147785 | ||||||||
\(260\) | −156.000 | −0.0372104 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 3480.00 | 0.820592 | ||||||||
\(263\) | −7587.00 | −1.77884 | −0.889419 | − | 0.457093i | \(-0.848891\pi\) | ||||
−0.889419 | + | 0.457093i | \(0.848891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 585.000 | 0.135609 | ||||||||
\(266\) | 2114.00 | 0.487284 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1016.00 | 0.231575 | ||||||||
\(269\) | −120.000 | −0.0271990 | −0.0135995 | − | 0.999908i | \(-0.504329\pi\) | ||||
−0.0135995 | + | 0.999908i | \(0.504329\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 56.0000 | 0.0125526 | 0.00627631 | − | 0.999980i | \(-0.498002\pi\) | ||||
0.00627631 | + | 0.999980i | \(0.498002\pi\) | |||||||
\(272\) | 1536.00 | 0.342403 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5640.00 | 1.24352 | ||||||||
\(275\) | −6264.00 | −1.37358 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −475.000 | −0.103032 | −0.0515162 | − | 0.998672i | \(-0.516405\pi\) | ||||
−0.0515162 | + | 0.998672i | \(0.516405\pi\) | |||||||
\(278\) | −148.000 | −0.0319297 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 168.000 | 0.0358569 | ||||||||
\(281\) | −918.000 | −0.194887 | −0.0974436 | − | 0.995241i | \(-0.531067\pi\) | ||||
−0.0974436 | + | 0.995241i | \(0.531067\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7252.00 | −1.52327 | −0.761637 | − | 0.648004i | \(-0.775604\pi\) | ||||
−0.761637 | + | 0.648004i | \(0.775604\pi\) | |||||||
\(284\) | −528.000 | −0.110321 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1404.00 | −0.290281 | ||||||||
\(287\) | 294.000 | 0.0604678 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4303.00 | 0.875840 | ||||||||
\(290\) | −1098.00 | −0.222334 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3772.00 | −0.755958 | ||||||||
\(293\) | 525.000 | 0.104679 | 0.0523393 | − | 0.998629i | \(-0.483332\pi\) | ||||
0.0523393 | + | 0.998629i | \(0.483332\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1656.00 | 0.326834 | ||||||||
\(296\) | 704.000 | 0.138240 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −684.000 | −0.132963 | ||||||||
\(299\) | −429.000 | −0.0829756 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2471.00 | 0.473176 | ||||||||
\(302\) | 536.000 | 0.102130 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2416.00 | −0.455813 | ||||||||
\(305\) | −1410.00 | −0.264709 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2077.00 | −0.386126 | −0.193063 | − | 0.981186i | \(-0.561842\pi\) | ||||
−0.193063 | + | 0.981186i | \(0.561842\pi\) | |||||||
\(308\) | 1512.00 | 0.279721 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1986.00 | −0.363862 | ||||||||
\(311\) | −1842.00 | −0.335853 | −0.167926 | − | 0.985800i | \(-0.553707\pi\) | ||||
−0.167926 | + | 0.985800i | \(0.553707\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1150.00 | −0.207674 | −0.103837 | − | 0.994594i | \(-0.533112\pi\) | ||||
−0.103837 | + | 0.994594i | \(0.533112\pi\) | |||||||
\(314\) | 4208.00 | 0.756278 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2908.00 | −0.517683 | ||||||||
\(317\) | 1896.00 | 0.335931 | 0.167965 | − | 0.985793i | \(-0.446280\pi\) | ||||
0.167965 | + | 0.985793i | \(0.446280\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9882.00 | −1.73444 | ||||||||
\(320\) | −192.000 | −0.0335410 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 462.000 | 0.0799573 | ||||||||
\(323\) | −14496.0 | −2.49715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1508.00 | −0.257381 | ||||||||
\(326\) | 2624.00 | 0.445797 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −336.000 | −0.0565625 | ||||||||
\(329\) | 3255.00 | 0.545453 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4934.00 | 0.819327 | 0.409663 | − | 0.912237i | \(-0.365646\pi\) | ||||
0.409663 | + | 0.912237i | \(0.365646\pi\) | |||||||
\(332\) | 4788.00 | 0.791493 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4938.00 | 0.808968 | ||||||||
\(335\) | −762.000 | −0.124276 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5839.00 | −0.943830 | −0.471915 | − | 0.881644i | \(-0.656437\pi\) | ||||
−0.471915 | + | 0.881644i | \(0.656437\pi\) | |||||||
\(338\) | −338.000 | −0.0543928 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1152.00 | −0.183753 | ||||||||
\(341\) | −17874.0 | −2.83851 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | −2824.00 | −0.442616 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −72.0000 | −0.0111871 | ||||||||
\(347\) | 456.000 | 0.0705457 | 0.0352729 | − | 0.999378i | \(-0.488770\pi\) | ||||
0.0352729 | + | 0.999378i | \(0.488770\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6451.00 | −0.989439 | −0.494719 | − | 0.869053i | \(-0.664729\pi\) | ||||
−0.494719 | + | 0.869053i | \(0.664729\pi\) | |||||||
\(350\) | 1624.00 | 0.248018 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1728.00 | −0.261655 | ||||||||
\(353\) | 9342.00 | 1.40857 | 0.704284 | − | 0.709918i | \(-0.251268\pi\) | ||||
0.704284 | + | 0.709918i | \(0.251268\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 396.000 | 0.0592042 | ||||||||
\(356\) | −3012.00 | −0.448415 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3618.00 | 0.534126 | ||||||||
\(359\) | −8328.00 | −1.22433 | −0.612166 | − | 0.790729i | \(-0.709701\pi\) | ||||
−0.612166 | + | 0.790729i | \(0.709701\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15942.0 | 2.32425 | ||||||||
\(362\) | −2380.00 | −0.345553 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 364.000 | 0.0524142 | ||||||||
\(365\) | 2829.00 | 0.405689 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2230.00 | −0.317180 | −0.158590 | − | 0.987345i | \(-0.550695\pi\) | ||||
−0.158590 | + | 0.987345i | \(0.550695\pi\) | |||||||
\(368\) | −528.000 | −0.0747932 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −528.000 | −0.0741876 | ||||||||
\(371\) | −1365.00 | −0.191017 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −178.000 | −0.0247091 | −0.0123545 | − | 0.999924i | \(-0.503933\pi\) | ||||
−0.0123545 | + | 0.999924i | \(0.503933\pi\) | |||||||
\(374\) | −10368.0 | −1.43347 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3720.00 | −0.510224 | ||||||||
\(377\) | −2379.00 | −0.324999 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6874.00 | −0.931646 | −0.465823 | − | 0.884878i | \(-0.654242\pi\) | ||||
−0.465823 | + | 0.884878i | \(0.654242\pi\) | |||||||
\(380\) | 1812.00 | 0.244615 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6768.00 | −0.906495 | ||||||||
\(383\) | 10548.0 | 1.40725 | 0.703626 | − | 0.710570i | \(-0.251563\pi\) | ||||
0.703626 | + | 0.710570i | \(0.251563\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1134.00 | −0.150114 | ||||||||
\(386\) | −220.000 | −0.0290096 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4148.00 | 0.542739 | ||||||||
\(389\) | −6054.00 | −0.789075 | −0.394537 | − | 0.918880i | \(-0.629095\pi\) | ||||
−0.394537 | + | 0.918880i | \(0.629095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3168.00 | −0.409751 | ||||||||
\(392\) | −392.000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7932.00 | −1.01423 | ||||||||
\(395\) | 2181.00 | 0.277818 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10195.0 | −1.28885 | −0.644424 | − | 0.764669i | \(-0.722903\pi\) | ||||
−0.644424 | + | 0.764669i | \(0.722903\pi\) | |||||||
\(398\) | 176.000 | 0.0221660 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1856.00 | −0.232000 | ||||||||
\(401\) | 4512.00 | 0.561892 | 0.280946 | − | 0.959724i | \(-0.409352\pi\) | ||||
0.280946 | + | 0.959724i | \(0.409352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4303.00 | −0.531880 | ||||||||
\(404\) | −6264.00 | −0.771400 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2562.00 | 0.313177 | ||||||||
\(407\) | −4752.00 | −0.578742 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9511.00 | −1.14985 | −0.574925 | − | 0.818206i | \(-0.694969\pi\) | ||||
−0.574925 | + | 0.818206i | \(0.694969\pi\) | |||||||
\(410\) | 252.000 | 0.0303546 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1664.00 | 0.198979 | ||||||||
\(413\) | −3864.00 | −0.460375 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3591.00 | −0.424760 | ||||||||
\(416\) | −416.000 | −0.0490290 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16308.0 | 1.90825 | ||||||||
\(419\) | 5190.00 | 0.605127 | 0.302563 | − | 0.953129i | \(-0.402158\pi\) | ||||
0.302563 | + | 0.953129i | \(0.402158\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4192.00 | −0.485286 | −0.242643 | − | 0.970116i | \(-0.578014\pi\) | ||||
−0.242643 | + | 0.970116i | \(0.578014\pi\) | |||||||
\(422\) | 662.000 | 0.0763641 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1560.00 | 0.178680 | ||||||||
\(425\) | −11136.0 | −1.27100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3290.00 | 0.372867 | ||||||||
\(428\) | 2640.00 | 0.298152 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2118.00 | 0.237533 | ||||||||
\(431\) | 9918.00 | 1.10843 | 0.554215 | − | 0.832374i | \(-0.313019\pi\) | ||||
0.554215 | + | 0.832374i | \(0.313019\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5092.00 | −0.565141 | −0.282570 | − | 0.959247i | \(-0.591187\pi\) | ||||
−0.282570 | + | 0.959247i | \(0.591187\pi\) | |||||||
\(434\) | 4634.00 | 0.512533 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1000.00 | −0.109842 | ||||||||
\(437\) | 4983.00 | 0.545467 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 290.000 | 0.0315283 | 0.0157642 | − | 0.999876i | \(-0.494982\pi\) | ||||
0.0157642 | + | 0.999876i | \(0.494982\pi\) | |||||||
\(440\) | 1296.00 | 0.140419 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2496.00 | −0.268603 | ||||||||
\(443\) | 3867.00 | 0.414733 | 0.207366 | − | 0.978263i | \(-0.433511\pi\) | ||||
0.207366 | + | 0.978263i | \(0.433511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2259.00 | 0.240645 | ||||||||
\(446\) | 9554.00 | 1.01434 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 448.000 | 0.0472456 | ||||||||
\(449\) | 4008.00 | 0.421268 | 0.210634 | − | 0.977565i | \(-0.432447\pi\) | ||||
0.210634 | + | 0.977565i | \(0.432447\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2268.00 | 0.236798 | ||||||||
\(452\) | 6060.00 | 0.630616 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6792.00 | 0.702124 | ||||||||
\(455\) | −273.000 | −0.0281284 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7936.00 | −0.812320 | −0.406160 | − | 0.913802i | \(-0.633133\pi\) | ||||
−0.406160 | + | 0.913802i | \(0.633133\pi\) | |||||||
\(458\) | 10364.0 | 1.05738 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 396.000 | 0.0401383 | ||||||||
\(461\) | −9942.00 | −1.00444 | −0.502218 | − | 0.864741i | \(-0.667483\pi\) | ||||
−0.502218 | + | 0.864741i | \(0.667483\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15914.0 | 1.59738 | 0.798689 | − | 0.601744i | \(-0.205527\pi\) | ||||
0.798689 | + | 0.601744i | \(0.205527\pi\) | |||||||
\(464\) | −2928.00 | −0.292950 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10002.0 | −0.994278 | ||||||||
\(467\) | −10434.0 | −1.03389 | −0.516946 | − | 0.856018i | \(-0.672931\pi\) | ||||
−0.516946 | + | 0.856018i | \(0.672931\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1778.00 | 0.175054 | ||||||||
\(470\) | 2790.00 | 0.273815 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4416.00 | 0.430642 | ||||||||
\(473\) | 19062.0 | 1.85301 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17516.0 | 1.69198 | ||||||||
\(476\) | 2688.00 | 0.258833 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4680.00 | 0.447821 | ||||||||
\(479\) | 7155.00 | 0.682506 | 0.341253 | − | 0.939972i | \(-0.389149\pi\) | ||||
0.341253 | + | 0.939972i | \(0.389149\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1144.00 | −0.108445 | ||||||||
\(482\) | −11290.0 | −1.06690 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6340.00 | 0.595417 | ||||||||
\(485\) | −3111.00 | −0.291264 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16882.0 | −1.57083 | −0.785417 | − | 0.618967i | \(-0.787552\pi\) | ||||
−0.785417 | + | 0.618967i | \(0.787552\pi\) | |||||||
\(488\) | −3760.00 | −0.348785 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 294.000 | 0.0271052 | ||||||||
\(491\) | 10140.0 | 0.932000 | 0.466000 | − | 0.884785i | \(-0.345695\pi\) | ||||
0.466000 | + | 0.884785i | \(0.345695\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17568.0 | −1.60491 | ||||||||
\(494\) | 3926.00 | 0.357569 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5296.00 | −0.479430 | ||||||||
\(497\) | −924.000 | −0.0833945 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −9304.00 | −0.834678 | −0.417339 | − | 0.908751i | \(-0.637037\pi\) | ||||
−0.417339 | + | 0.908751i | \(0.637037\pi\) | |||||||
\(500\) | 2892.00 | 0.258668 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1284.00 | −0.114159 | ||||||||
\(503\) | 5898.00 | 0.522821 | 0.261410 | − | 0.965228i | \(-0.415812\pi\) | ||||
0.261410 | + | 0.965228i | \(0.415812\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4698.00 | 0.413977 | ||||||||
\(506\) | 3564.00 | 0.313121 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5968.00 | −0.521235 | ||||||||
\(509\) | 3693.00 | 0.321590 | 0.160795 | − | 0.986988i | \(-0.448594\pi\) | ||||
0.160795 | + | 0.986988i | \(0.448594\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6601.00 | −0.571450 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5772.00 | 0.495315 | ||||||||
\(515\) | −1248.00 | −0.106783 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25110.0 | 2.13605 | ||||||||
\(518\) | 1232.00 | 0.104500 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 312.000 | 0.0263117 | ||||||||
\(521\) | −9924.00 | −0.834507 | −0.417254 | − | 0.908790i | \(-0.637007\pi\) | ||||
−0.417254 | + | 0.908790i | \(0.637007\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19442.0 | 1.62551 | 0.812753 | − | 0.582609i | \(-0.197968\pi\) | ||||
0.812753 | + | 0.582609i | \(0.197968\pi\) | |||||||
\(524\) | −6960.00 | −0.580246 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15174.0 | 1.25783 | ||||||||
\(527\) | −31776.0 | −2.62654 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11078.0 | −0.910496 | ||||||||
\(530\) | −1170.00 | −0.0958897 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4228.00 | −0.344562 | ||||||||
\(533\) | 546.000 | 0.0443713 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1980.00 | −0.160005 | ||||||||
\(536\) | −2032.00 | −0.163748 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 240.000 | 0.0192326 | ||||||||
\(539\) | 2646.00 | 0.211450 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23416.0 | −1.86087 | −0.930437 | − | 0.366453i | \(-0.880572\pi\) | ||||
−0.930437 | + | 0.366453i | \(0.880572\pi\) | |||||||
\(542\) | −112.000 | −0.00887604 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3072.00 | −0.242116 | ||||||||
\(545\) | 750.000 | 0.0589477 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5065.00 | −0.395912 | −0.197956 | − | 0.980211i | \(-0.563430\pi\) | ||||
−0.197956 | + | 0.980211i | \(0.563430\pi\) | |||||||
\(548\) | −11280.0 | −0.879302 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12528.0 | 0.971265 | ||||||||
\(551\) | 27633.0 | 2.13649 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5089.00 | −0.391331 | ||||||||
\(554\) | 950.000 | 0.0728549 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 296.000 | 0.0225777 | ||||||||
\(557\) | −8424.00 | −0.640819 | −0.320410 | − | 0.947279i | \(-0.603821\pi\) | ||||
−0.320410 | + | 0.947279i | \(0.603821\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4589.00 | 0.347216 | ||||||||
\(560\) | −336.000 | −0.0253546 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1836.00 | 0.137806 | ||||||||
\(563\) | −11316.0 | −0.847092 | −0.423546 | − | 0.905875i | \(-0.639215\pi\) | ||||
−0.423546 | + | 0.905875i | \(0.639215\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4545.00 | −0.338424 | ||||||||
\(566\) | 14504.0 | 1.07712 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1056.00 | 0.0780084 | ||||||||
\(569\) | 18849.0 | 1.38874 | 0.694368 | − | 0.719620i | \(-0.255684\pi\) | ||||
0.694368 | + | 0.719620i | \(0.255684\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9281.00 | 0.680206 | 0.340103 | − | 0.940388i | \(-0.389538\pi\) | ||||
0.340103 | + | 0.940388i | \(0.389538\pi\) | |||||||
\(572\) | 2808.00 | 0.205259 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −588.000 | −0.0427572 | ||||||||
\(575\) | 3828.00 | 0.277632 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16306.0 | −1.17648 | −0.588239 | − | 0.808687i | \(-0.700179\pi\) | ||||
−0.588239 | + | 0.808687i | \(0.700179\pi\) | |||||||
\(578\) | −8606.00 | −0.619312 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2196.00 | 0.157214 | ||||||||
\(581\) | 8379.00 | 0.598312 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10530.0 | −0.748041 | ||||||||
\(584\) | 7544.00 | 0.534543 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1050.00 | −0.0740189 | ||||||||
\(587\) | −22971.0 | −1.61519 | −0.807593 | − | 0.589740i | \(-0.799230\pi\) | ||||
−0.807593 | + | 0.589740i | \(0.799230\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49981.0 | 3.49649 | ||||||||
\(590\) | −3312.00 | −0.231107 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1408.00 | −0.0977507 | ||||||||
\(593\) | −10983.0 | −0.760570 | −0.380285 | − | 0.924869i | \(-0.624174\pi\) | ||||
−0.380285 | + | 0.924869i | \(0.624174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2016.00 | −0.138904 | ||||||||
\(596\) | 1368.00 | 0.0940192 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 858.000 | 0.0586726 | ||||||||
\(599\) | −4209.00 | −0.287104 | −0.143552 | − | 0.989643i | \(-0.545852\pi\) | ||||
−0.143552 | + | 0.989643i | \(0.545852\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12958.0 | −0.879481 | −0.439740 | − | 0.898125i | \(-0.644930\pi\) | ||||
−0.439740 | + | 0.898125i | \(0.644930\pi\) | |||||||
\(602\) | −4942.00 | −0.334586 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1072.00 | −0.0722170 | ||||||||
\(605\) | −4755.00 | −0.319534 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −11302.0 | −0.755740 | −0.377870 | − | 0.925859i | \(-0.623343\pi\) | ||||
−0.377870 | + | 0.925859i | \(0.623343\pi\) | |||||||
\(608\) | 4832.00 | 0.322308 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2820.00 | 0.187178 | ||||||||
\(611\) | 6045.00 | 0.400253 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8188.00 | −0.539495 | −0.269747 | − | 0.962931i | \(-0.586940\pi\) | ||||
−0.269747 | + | 0.962931i | \(0.586940\pi\) | |||||||
\(614\) | 4154.00 | 0.273032 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3024.00 | −0.197793 | ||||||||
\(617\) | 7482.00 | 0.488191 | 0.244096 | − | 0.969751i | \(-0.421509\pi\) | ||||
0.244096 | + | 0.969751i | \(0.421509\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18380.0 | 1.19346 | 0.596732 | − | 0.802440i | \(-0.296465\pi\) | ||||
0.596732 | + | 0.802440i | \(0.296465\pi\) | |||||||
\(620\) | 3972.00 | 0.257289 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3684.00 | 0.237484 | ||||||||
\(623\) | −5271.00 | −0.338970 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12331.0 | 0.789184 | ||||||||
\(626\) | 2300.00 | 0.146847 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8416.00 | −0.534769 | ||||||||
\(629\) | −8448.00 | −0.535523 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27470.0 | 1.73306 | 0.866532 | − | 0.499121i | \(-0.166344\pi\) | ||||
0.866532 | + | 0.499121i | \(0.166344\pi\) | |||||||
\(632\) | 5816.00 | 0.366057 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3792.00 | −0.237539 | ||||||||
\(635\) | 4476.00 | 0.279724 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 637.000 | 0.0396214 | ||||||||
\(638\) | 19764.0 | 1.22643 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 384.000 | 0.0237171 | ||||||||
\(641\) | −9417.00 | −0.580264 | −0.290132 | − | 0.956987i | \(-0.593699\pi\) | ||||
−0.290132 | + | 0.956987i | \(0.593699\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2792.00 | 0.171238 | 0.0856188 | − | 0.996328i | \(-0.472713\pi\) | ||||
0.0856188 | + | 0.996328i | \(0.472713\pi\) | |||||||
\(644\) | −924.000 | −0.0565384 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 28992.0 | 1.76575 | ||||||||
\(647\) | 21402.0 | 1.30046 | 0.650231 | − | 0.759736i | \(-0.274672\pi\) | ||||
0.650231 | + | 0.759736i | \(0.274672\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29808.0 | −1.80288 | ||||||||
\(650\) | 3016.00 | 0.181996 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5248.00 | −0.315226 | ||||||||
\(653\) | 7518.00 | 0.450539 | 0.225270 | − | 0.974296i | \(-0.427674\pi\) | ||||
0.225270 | + | 0.974296i | \(0.427674\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5220.00 | 0.311393 | ||||||||
\(656\) | 672.000 | 0.0399957 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6510.00 | −0.385693 | ||||||||
\(659\) | 23097.0 | 1.36530 | 0.682649 | − | 0.730746i | \(-0.260828\pi\) | ||||
0.682649 | + | 0.730746i | \(0.260828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5033.00 | 0.296159 | 0.148079 | − | 0.988975i | \(-0.452691\pi\) | ||||
0.148079 | + | 0.988975i | \(0.452691\pi\) | |||||||
\(662\) | −9868.00 | −0.579352 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9576.00 | −0.559670 | ||||||||
\(665\) | 3171.00 | 0.184911 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6039.00 | 0.350571 | ||||||||
\(668\) | −9876.00 | −0.572027 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1524.00 | 0.0878765 | ||||||||
\(671\) | 25380.0 | 1.46018 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14983.0 | −0.858176 | −0.429088 | − | 0.903263i | \(-0.641165\pi\) | ||||
−0.429088 | + | 0.903263i | \(0.641165\pi\) | |||||||
\(674\) | 11678.0 | 0.667388 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 676.000 | 0.0384615 | ||||||||
\(677\) | −5034.00 | −0.285779 | −0.142889 | − | 0.989739i | \(-0.545639\pi\) | ||||
−0.142889 | + | 0.989739i | \(0.545639\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7259.00 | 0.410272 | ||||||||
\(680\) | 2304.00 | 0.129933 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35748.0 | 2.00713 | ||||||||
\(683\) | 12048.0 | 0.674969 | 0.337485 | − | 0.941331i | \(-0.390424\pi\) | ||||
0.337485 | + | 0.941331i | \(0.390424\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8460.00 | 0.471883 | ||||||||
\(686\) | −686.000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5648.00 | 0.312977 | ||||||||
\(689\) | −2535.00 | −0.140168 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27191.0 | 1.49695 | 0.748476 | − | 0.663161i | \(-0.230786\pi\) | ||||
0.748476 | + | 0.663161i | \(0.230786\pi\) | |||||||
\(692\) | 144.000 | 0.00791049 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −912.000 | −0.0498834 | ||||||||
\(695\) | −222.000 | −0.0121165 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4032.00 | 0.219115 | ||||||||
\(698\) | 12902.0 | 0.699639 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3248.00 | −0.175376 | ||||||||
\(701\) | 21015.0 | 1.13228 | 0.566138 | − | 0.824310i | \(-0.308437\pi\) | ||||
0.566138 | + | 0.824310i | \(0.308437\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13288.0 | 0.712897 | ||||||||
\(704\) | 3456.00 | 0.185018 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18684.0 | −0.996008 | ||||||||
\(707\) | −10962.0 | −0.583124 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30382.0 | −1.60934 | −0.804669 | − | 0.593724i | \(-0.797657\pi\) | ||||
−0.804669 | + | 0.593724i | \(0.797657\pi\) | |||||||
\(710\) | −792.000 | −0.0418637 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6024.00 | 0.317077 | ||||||||
\(713\) | 10923.0 | 0.573730 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2106.00 | −0.110154 | ||||||||
\(716\) | −7236.00 | −0.377684 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16656.0 | 0.865733 | ||||||||
\(719\) | −20322.0 | −1.05408 | −0.527039 | − | 0.849841i | \(-0.676698\pi\) | ||||
−0.527039 | + | 0.849841i | \(0.676698\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2912.00 | 0.150414 | ||||||||
\(722\) | −31884.0 | −1.64349 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4760.00 | 0.244343 | ||||||||
\(725\) | 21228.0 | 1.08743 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27938.0 | 1.42526 | 0.712629 | − | 0.701541i | \(-0.247504\pi\) | ||||
0.712629 | + | 0.701541i | \(0.247504\pi\) | |||||||
\(728\) | −728.000 | −0.0370625 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5658.00 | −0.286866 | ||||||||
\(731\) | 33888.0 | 1.71463 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11117.0 | 0.560185 | 0.280093 | − | 0.959973i | \(-0.409635\pi\) | ||||
0.280093 | + | 0.959973i | \(0.409635\pi\) | |||||||
\(734\) | 4460.00 | 0.224280 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1056.00 | 0.0528868 | ||||||||
\(737\) | 13716.0 | 0.685530 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12314.0 | 0.612961 | 0.306480 | − | 0.951877i | \(-0.400849\pi\) | ||||
0.306480 | + | 0.951877i | \(0.400849\pi\) | |||||||
\(740\) | 1056.00 | 0.0524586 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2730.00 | 0.135069 | ||||||||
\(743\) | −25968.0 | −1.28220 | −0.641099 | − | 0.767458i | \(-0.721521\pi\) | ||||
−0.641099 | + | 0.767458i | \(0.721521\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1026.00 | −0.0504560 | ||||||||
\(746\) | 356.000 | 0.0174720 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20736.0 | 1.01361 | ||||||||
\(749\) | 4620.00 | 0.225382 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35093.0 | 1.70514 | 0.852571 | − | 0.522611i | \(-0.175042\pi\) | ||||
0.852571 | + | 0.522611i | \(0.175042\pi\) | |||||||
\(752\) | 7440.00 | 0.360783 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4758.00 | 0.229809 | ||||||||
\(755\) | 804.000 | 0.0387557 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12701.0 | 0.609809 | 0.304905 | − | 0.952383i | \(-0.401375\pi\) | ||||
0.304905 | + | 0.952383i | \(0.401375\pi\) | |||||||
\(758\) | 13748.0 | 0.658773 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3624.00 | −0.172969 | ||||||||
\(761\) | −35019.0 | −1.66812 | −0.834059 | − | 0.551675i | \(-0.813989\pi\) | ||||
−0.834059 | + | 0.551675i | \(0.813989\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1750.00 | −0.0830331 | ||||||||
\(764\) | 13536.0 | 0.640989 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21096.0 | −0.995078 | ||||||||
\(767\) | −7176.00 | −0.337823 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25247.0 | 1.18391 | 0.591957 | − | 0.805969i | \(-0.298355\pi\) | ||||
0.591957 | + | 0.805969i | \(0.298355\pi\) | |||||||
\(770\) | 2268.00 | 0.106147 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 440.000 | 0.0205129 | ||||||||
\(773\) | −3162.00 | −0.147127 | −0.0735635 | − | 0.997291i | \(-0.523437\pi\) | ||||
−0.0735635 | + | 0.997291i | \(0.523437\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38396.0 | 1.77965 | ||||||||
\(776\) | −8296.00 | −0.383775 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12108.0 | 0.557960 | ||||||||
\(779\) | −6342.00 | −0.291689 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7128.00 | −0.326581 | ||||||||
\(782\) | 6336.00 | 0.289738 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 6312.00 | 0.286987 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15833.0 | 0.717135 | 0.358568 | − | 0.933504i | \(-0.383265\pi\) | ||||
0.358568 | + | 0.933504i | \(0.383265\pi\) | |||||||
\(788\) | 15864.0 | 0.717172 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4362.00 | −0.196447 | ||||||||
\(791\) | 10605.0 | 0.476701 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6110.00 | 0.273610 | ||||||||
\(794\) | 20390.0 | 0.911353 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −352.000 | −0.0156738 | ||||||||
\(797\) | 20946.0 | 0.930923 | 0.465461 | − | 0.885068i | \(-0.345888\pi\) | ||||
0.465461 | + | 0.885068i | \(0.345888\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 44640.0 | 1.97653 | ||||||||
\(800\) | 3712.00 | 0.164049 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9024.00 | −0.397317 | ||||||||
\(803\) | −50922.0 | −2.23786 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 693.000 | 0.0303417 | ||||||||
\(806\) | 8606.00 | 0.376096 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12528.0 | 0.545462 | ||||||||
\(809\) | −1953.00 | −0.0848749 | −0.0424375 | − | 0.999099i | \(-0.513512\pi\) | ||||
−0.0424375 | + | 0.999099i | \(0.513512\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45412.0 | −1.96625 | −0.983126 | − | 0.182928i | \(-0.941443\pi\) | ||||
−0.983126 | + | 0.182928i | \(0.941443\pi\) | |||||||
\(812\) | −5124.00 | −0.221450 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9504.00 | 0.409232 | ||||||||
\(815\) | 3936.00 | 0.169168 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −53303.0 | −2.28254 | ||||||||
\(818\) | 19022.0 | 0.813067 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −504.000 | −0.0214640 | ||||||||
\(821\) | −5766.00 | −0.245109 | −0.122555 | − | 0.992462i | \(-0.539109\pi\) | ||||
−0.122555 | + | 0.992462i | \(0.539109\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14560.0 | −0.616682 | −0.308341 | − | 0.951276i | \(-0.599774\pi\) | ||||
−0.308341 | + | 0.951276i | \(0.599774\pi\) | |||||||
\(824\) | −3328.00 | −0.140699 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7728.00 | 0.325535 | ||||||||
\(827\) | −21240.0 | −0.893092 | −0.446546 | − | 0.894761i | \(-0.647346\pi\) | ||||
−0.446546 | + | 0.894761i | \(0.647346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21922.0 | −0.918435 | −0.459217 | − | 0.888324i | \(-0.651870\pi\) | ||||
−0.459217 | + | 0.888324i | \(0.651870\pi\) | |||||||
\(830\) | 7182.00 | 0.300350 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 832.000 | 0.0346688 | ||||||||
\(833\) | 4704.00 | 0.195659 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7407.00 | 0.306982 | ||||||||
\(836\) | −32616.0 | −1.34934 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10380.0 | −0.427889 | ||||||||
\(839\) | −11040.0 | −0.454283 | −0.227141 | − | 0.973862i | \(-0.572938\pi\) | ||||
−0.227141 | + | 0.973862i | \(0.572938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9100.00 | 0.373119 | ||||||||
\(842\) | 8384.00 | 0.343149 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1324.00 | −0.0539976 | ||||||||
\(845\) | −507.000 | −0.0206406 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11095.0 | 0.450093 | ||||||||
\(848\) | −3120.00 | −0.126346 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22272.0 | 0.898733 | ||||||||
\(851\) | 2904.00 | 0.116977 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27493.0 | −1.10357 | −0.551783 | − | 0.833987i | \(-0.686052\pi\) | ||||
−0.551783 | + | 0.833987i | \(0.686052\pi\) | |||||||
\(854\) | −6580.00 | −0.263657 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5280.00 | −0.210826 | ||||||||
\(857\) | 13314.0 | 0.530686 | 0.265343 | − | 0.964154i | \(-0.414515\pi\) | ||||
0.265343 | + | 0.964154i | \(0.414515\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19550.0 | 0.776528 | 0.388264 | − | 0.921548i | \(-0.373075\pi\) | ||||
0.388264 | + | 0.921548i | \(0.373075\pi\) | |||||||
\(860\) | −4236.00 | −0.167961 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19836.0 | −0.783778 | ||||||||
\(863\) | −10740.0 | −0.423631 | −0.211816 | − | 0.977310i | \(-0.567938\pi\) | ||||
−0.211816 | + | 0.977310i | \(0.567938\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −108.000 | −0.00424521 | ||||||||
\(866\) | 10184.0 | 0.399615 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −9268.00 | −0.362415 | ||||||||
\(869\) | −39258.0 | −1.53249 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3302.00 | 0.128455 | ||||||||
\(872\) | 2000.00 | 0.0776704 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9966.00 | −0.385704 | ||||||||
\(875\) | 5061.00 | 0.195535 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14456.0 | 0.556607 | 0.278304 | − | 0.960493i | \(-0.410228\pi\) | ||||
0.278304 | + | 0.960493i | \(0.410228\pi\) | |||||||
\(878\) | −580.000 | −0.0222939 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2592.00 | −0.0992913 | ||||||||
\(881\) | 9798.00 | 0.374691 | 0.187346 | − | 0.982294i | \(-0.440012\pi\) | ||||
0.187346 | + | 0.982294i | \(0.440012\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 45308.0 | 1.72677 | 0.863384 | − | 0.504548i | \(-0.168341\pi\) | ||||
0.863384 | + | 0.504548i | \(0.168341\pi\) | |||||||
\(884\) | 4992.00 | 0.189931 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7734.00 | −0.293261 | ||||||||
\(887\) | −24684.0 | −0.934394 | −0.467197 | − | 0.884153i | \(-0.654736\pi\) | ||||
−0.467197 | + | 0.884153i | \(0.654736\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10444.0 | −0.394016 | ||||||||
\(890\) | −4518.00 | −0.170161 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19108.0 | −0.717246 | ||||||||
\(893\) | −70215.0 | −2.63119 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5427.00 | 0.202687 | ||||||||
\(896\) | −896.000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8016.00 | −0.297881 | ||||||||
\(899\) | 60573.0 | 2.24719 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18720.0 | −0.692179 | ||||||||
\(902\) | −4536.00 | −0.167442 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12120.0 | −0.445913 | ||||||||
\(905\) | −3570.00 | −0.131128 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13615.0 | −0.498433 | −0.249216 | − | 0.968448i | \(-0.580173\pi\) | ||||
−0.249216 | + | 0.968448i | \(0.580173\pi\) | |||||||
\(908\) | −13584.0 | −0.496477 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 546.000 | 0.0198898 | ||||||||
\(911\) | 15165.0 | 0.551525 | 0.275762 | − | 0.961226i | \(-0.411070\pi\) | ||||
0.275762 | + | 0.961226i | \(0.411070\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 64638.0 | 2.34305 | ||||||||
\(914\) | 15872.0 | 0.574397 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20728.0 | −0.747677 | ||||||||
\(917\) | −12180.0 | −0.438625 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25576.0 | −0.918035 | −0.459018 | − | 0.888427i | \(-0.651799\pi\) | ||||
−0.459018 | + | 0.888427i | \(0.651799\pi\) | |||||||
\(920\) | −792.000 | −0.0283820 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19884.0 | 0.710244 | ||||||||
\(923\) | −1716.00 | −0.0611948 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10208.0 | 0.362851 | ||||||||
\(926\) | −31828.0 | −1.12952 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5856.00 | 0.207147 | ||||||||
\(929\) | −24759.0 | −0.874399 | −0.437199 | − | 0.899365i | \(-0.644030\pi\) | ||||
−0.437199 | + | 0.899365i | \(0.644030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7399.00 | −0.260464 | ||||||||
\(932\) | 20004.0 | 0.703061 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20868.0 | 0.731073 | ||||||||
\(935\) | −15552.0 | −0.543962 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12976.0 | −0.452409 | −0.226205 | − | 0.974080i | \(-0.572632\pi\) | ||||
−0.226205 | + | 0.974080i | \(0.572632\pi\) | |||||||
\(938\) | −3556.00 | −0.123782 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5580.00 | −0.193617 | ||||||||
\(941\) | 4575.00 | 0.158492 | 0.0792459 | − | 0.996855i | \(-0.474749\pi\) | ||||
0.0792459 | + | 0.996855i | \(0.474749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1386.00 | −0.0478625 | ||||||||
\(944\) | −8832.00 | −0.304510 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38124.0 | −1.31027 | ||||||||
\(947\) | 53346.0 | 1.83053 | 0.915265 | − | 0.402852i | \(-0.131981\pi\) | ||||
0.915265 | + | 0.402852i | \(0.131981\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12259.0 | −0.419330 | ||||||||
\(950\) | −35032.0 | −1.19641 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5376.00 | −0.183022 | ||||||||
\(953\) | −52809.0 | −1.79502 | −0.897509 | − | 0.440997i | \(-0.854625\pi\) | ||||
−0.897509 | + | 0.440997i | \(0.854625\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10152.0 | −0.343991 | ||||||||
\(956\) | −9360.00 | −0.316657 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14310.0 | −0.482605 | ||||||||
\(959\) | −19740.0 | −0.664690 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79770.0 | 2.67765 | ||||||||
\(962\) | 2288.00 | 0.0766820 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22580.0 | 0.754412 | ||||||||
\(965\) | −330.000 | −0.0110084 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7346.00 | 0.244293 | 0.122147 | − | 0.992512i | \(-0.461022\pi\) | ||||
0.122147 | + | 0.992512i | \(0.461022\pi\) | |||||||
\(968\) | −12680.0 | −0.421023 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6222.00 | 0.205955 | ||||||||
\(971\) | −37170.0 | −1.22847 | −0.614234 | − | 0.789124i | \(-0.710535\pi\) | ||||
−0.614234 | + | 0.789124i | \(0.710535\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 518.000 | 0.0170671 | ||||||||
\(974\) | 33764.0 | 1.11075 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7520.00 | 0.246628 | ||||||||
\(977\) | 29358.0 | 0.961357 | 0.480678 | − | 0.876897i | \(-0.340390\pi\) | ||||
0.480678 | + | 0.876897i | \(0.340390\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40662.0 | −1.32744 | ||||||||
\(980\) | −588.000 | −0.0191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −20280.0 | −0.659023 | ||||||||
\(983\) | −21777.0 | −0.706590 | −0.353295 | − | 0.935512i | \(-0.614939\pi\) | ||||
−0.353295 | + | 0.935512i | \(0.614939\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11898.0 | −0.384875 | ||||||||
\(986\) | 35136.0 | 1.13485 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7852.00 | −0.252839 | ||||||||
\(989\) | −11649.0 | −0.374537 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10388.0 | 0.332983 | 0.166491 | − | 0.986043i | \(-0.446756\pi\) | ||||
0.166491 | + | 0.986043i | \(0.446756\pi\) | |||||||
\(992\) | 10592.0 | 0.339008 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1848.00 | 0.0589688 | ||||||||
\(995\) | 264.000 | 0.00841142 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27776.0 | 0.882322 | 0.441161 | − | 0.897428i | \(-0.354567\pi\) | ||||
0.441161 | + | 0.897428i | \(0.354567\pi\) | |||||||
\(998\) | 18608.0 | 0.590206 | ||||||||
\(999\) | 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 | 1638.4.a.d.1.1 | 1 | ||
3.2 | odd | 2 | 182.4.a.b.1.1 | ✓ | 1 | ||
12.11 | even | 2 | 1456.4.a.g.1.1 | 1 | |||
21.20 | even | 2 | 1274.4.a.i.1.1 | 1 | |||
39.38 | odd | 2 | 2366.4.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.4.a.b.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
1274.4.a.i.1.1 | 1 | 21.20 | even | 2 | |||
1456.4.a.g.1.1 | 1 | 12.11 | even | 2 | |||
1638.4.a.d.1.1 | 1 | 1.1 | even | 1 | trivial | ||
2366.4.a.a.1.1 | 1 | 39.38 | odd | 2 |