Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [270,4,Mod(1,270)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(270, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("270.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 270 = 2 \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 270.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: | \(15.9305157015\) |
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 | \(\chi\) | \(=\) | 270.1 |
$q$-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 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 14.0000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −10.0000 | −0.316228 | ||||||||
\(11\) | −3.00000 | −0.0822304 | −0.0411152 | − | 0.999154i | \(-0.513091\pi\) | ||||
−0.0411152 | + | 0.999154i | \(0.513091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 47.0000 | 1.00273 | 0.501364 | − | 0.865237i | \(-0.332832\pi\) | ||||
0.501364 | + | 0.865237i | \(0.332832\pi\) | |||||||
\(14\) | 28.0000 | 0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 39.0000 | 0.556405 | 0.278203 | − | 0.960522i | \(-0.410261\pi\) | ||||
0.278203 | + | 0.960522i | \(0.410261\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.0000 | 0.386384 | 0.193192 | − | 0.981161i | \(-0.438116\pi\) | ||||
0.193192 | + | 0.981161i | \(0.438116\pi\) | |||||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.00000 | −0.0581456 | ||||||||
\(23\) | 99.0000 | 0.897519 | 0.448759 | − | 0.893653i | \(-0.351866\pi\) | ||||
0.448759 | + | 0.893653i | \(0.351866\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 94.0000 | 0.709035 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 56.0000 | 0.377964 | ||||||||
\(29\) | −51.0000 | −0.326568 | −0.163284 | − | 0.986579i | \(-0.552209\pi\) | ||||
−0.163284 | + | 0.986579i | \(0.552209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 83.0000 | 0.480879 | 0.240439 | − | 0.970664i | \(-0.422708\pi\) | ||||
0.240439 | + | 0.970664i | \(0.422708\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 78.0000 | 0.393438 | ||||||||
\(35\) | −70.0000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 314.000 | 1.39517 | 0.697585 | − | 0.716502i | \(-0.254258\pi\) | ||||
0.697585 | + | 0.716502i | \(0.254258\pi\) | |||||||
\(38\) | 64.0000 | 0.273215 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −40.0000 | −0.158114 | ||||||||
\(41\) | 108.000 | 0.411385 | 0.205692 | − | 0.978617i | \(-0.434055\pi\) | ||||
0.205692 | + | 0.978617i | \(0.434055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 299.000 | 1.06040 | 0.530199 | − | 0.847874i | \(-0.322117\pi\) | ||||
0.530199 | + | 0.847874i | \(0.322117\pi\) | |||||||
\(44\) | −12.0000 | −0.0411152 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 198.000 | 0.634641 | ||||||||
\(47\) | −531.000 | −1.64796 | −0.823982 | − | 0.566616i | \(-0.808252\pi\) | ||||
−0.823982 | + | 0.566616i | \(0.808252\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −147.000 | −0.428571 | ||||||||
\(50\) | 50.0000 | 0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 188.000 | 0.501364 | ||||||||
\(53\) | −564.000 | −1.46172 | −0.730862 | − | 0.682525i | \(-0.760882\pi\) | ||||
−0.730862 | + | 0.682525i | \(0.760882\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15.0000 | 0.0367745 | ||||||||
\(56\) | 112.000 | 0.267261 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −102.000 | −0.230918 | ||||||||
\(59\) | −12.0000 | −0.0264791 | −0.0132396 | − | 0.999912i | \(-0.504214\pi\) | ||||
−0.0132396 | + | 0.999912i | \(0.504214\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 230.000 | 0.482762 | 0.241381 | − | 0.970430i | \(-0.422400\pi\) | ||||
0.241381 | + | 0.970430i | \(0.422400\pi\) | |||||||
\(62\) | 166.000 | 0.340033 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −235.000 | −0.448433 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −268.000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 156.000 | 0.278203 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −140.000 | −0.239046 | ||||||||
\(71\) | −120.000 | −0.200583 | −0.100291 | − | 0.994958i | \(-0.531978\pi\) | ||||
−0.100291 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1106.00 | 1.77325 | 0.886627 | − | 0.462486i | \(-0.153042\pi\) | ||||
0.886627 | + | 0.462486i | \(0.153042\pi\) | |||||||
\(74\) | 628.000 | 0.986534 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 128.000 | 0.193192 | ||||||||
\(77\) | −42.0000 | −0.0621603 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −739.000 | −1.05246 | −0.526228 | − | 0.850344i | \(-0.676394\pi\) | ||||
−0.526228 | + | 0.850344i | \(0.676394\pi\) | |||||||
\(80\) | −80.0000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 216.000 | 0.290893 | ||||||||
\(83\) | −1086.00 | −1.43619 | −0.718096 | − | 0.695944i | \(-0.754986\pi\) | ||||
−0.718096 | + | 0.695944i | \(0.754986\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −195.000 | −0.248832 | ||||||||
\(86\) | 598.000 | 0.749814 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −24.0000 | −0.0290728 | ||||||||
\(89\) | 120.000 | 0.142921 | 0.0714605 | − | 0.997443i | \(-0.477234\pi\) | ||||
0.0714605 | + | 0.997443i | \(0.477234\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 658.000 | 0.757991 | ||||||||
\(92\) | 396.000 | 0.448759 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1062.00 | −1.16529 | ||||||||
\(95\) | −160.000 | −0.172796 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1642.00 | −1.71876 | −0.859381 | − | 0.511336i | \(-0.829151\pi\) | ||||
−0.859381 | + | 0.511336i | \(0.829151\pi\) | |||||||
\(98\) | −294.000 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 100.000 | 0.100000 | ||||||||
\(101\) | −33.0000 | −0.0325111 | −0.0162556 | − | 0.999868i | \(-0.505175\pi\) | ||||
−0.0162556 | + | 0.999868i | \(0.505175\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1198.00 | −1.14604 | −0.573022 | − | 0.819540i | \(-0.694229\pi\) | ||||
−0.573022 | + | 0.819540i | \(0.694229\pi\) | |||||||
\(104\) | 376.000 | 0.354518 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1128.00 | −1.03359 | ||||||||
\(107\) | 1542.00 | 1.39318 | 0.696592 | − | 0.717467i | \(-0.254699\pi\) | ||||
0.696592 | + | 0.717467i | \(0.254699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −556.000 | −0.488579 | −0.244290 | − | 0.969702i | \(-0.578555\pi\) | ||||
−0.244290 | + | 0.969702i | \(0.578555\pi\) | |||||||
\(110\) | 30.0000 | 0.0260035 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 224.000 | 0.188982 | ||||||||
\(113\) | −1605.00 | −1.33616 | −0.668078 | − | 0.744091i | \(-0.732883\pi\) | ||||
−0.668078 | + | 0.744091i | \(0.732883\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −495.000 | −0.401383 | ||||||||
\(116\) | −204.000 | −0.163284 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24.0000 | −0.0187236 | ||||||||
\(119\) | 546.000 | 0.420603 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1322.00 | −0.993238 | ||||||||
\(122\) | 460.000 | 0.341364 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 332.000 | 0.240439 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1334.00 | 0.932074 | 0.466037 | − | 0.884765i | \(-0.345681\pi\) | ||||
0.466037 | + | 0.884765i | \(0.345681\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −470.000 | −0.317090 | ||||||||
\(131\) | 2883.00 | 1.92282 | 0.961408 | − | 0.275127i | \(-0.0887199\pi\) | ||||
0.961408 | + | 0.275127i | \(0.0887199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 448.000 | 0.292079 | ||||||||
\(134\) | −536.000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 312.000 | 0.196719 | ||||||||
\(137\) | −282.000 | −0.175860 | −0.0879302 | − | 0.996127i | \(-0.528025\pi\) | ||||
−0.0879302 | + | 0.996127i | \(0.528025\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2494.00 | −1.52186 | −0.760929 | − | 0.648835i | \(-0.775257\pi\) | ||||
−0.760929 | + | 0.648835i | \(0.775257\pi\) | |||||||
\(140\) | −280.000 | −0.169031 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −240.000 | −0.141833 | ||||||||
\(143\) | −141.000 | −0.0824546 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 255.000 | 0.146045 | ||||||||
\(146\) | 2212.00 | 1.25388 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1256.00 | 0.697585 | ||||||||
\(149\) | −2595.00 | −1.42678 | −0.713392 | − | 0.700766i | \(-0.752842\pi\) | ||||
−0.713392 | + | 0.700766i | \(0.752842\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1229.00 | 0.662348 | 0.331174 | − | 0.943570i | \(-0.392555\pi\) | ||||
0.331174 | + | 0.943570i | \(0.392555\pi\) | |||||||
\(152\) | 256.000 | 0.136608 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −84.0000 | −0.0439540 | ||||||||
\(155\) | −415.000 | −0.215055 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1591.00 | −0.808762 | −0.404381 | − | 0.914591i | \(-0.632513\pi\) | ||||
−0.404381 | + | 0.914591i | \(0.632513\pi\) | |||||||
\(158\) | −1478.00 | −0.744199 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | 1386.00 | 0.678460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −457.000 | −0.219601 | −0.109801 | − | 0.993954i | \(-0.535021\pi\) | ||||
−0.109801 | + | 0.993954i | \(0.535021\pi\) | |||||||
\(164\) | 432.000 | 0.205692 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2172.00 | −1.01554 | ||||||||
\(167\) | 1164.00 | 0.539359 | 0.269680 | − | 0.962950i | \(-0.413082\pi\) | ||||
0.269680 | + | 0.962950i | \(0.413082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.00546199 | ||||||||
\(170\) | −390.000 | −0.175951 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1196.00 | 0.530199 | ||||||||
\(173\) | −3942.00 | −1.73240 | −0.866199 | − | 0.499700i | \(-0.833444\pi\) | ||||
−0.866199 | + | 0.499700i | \(0.833444\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 350.000 | 0.151186 | ||||||||
\(176\) | −48.0000 | −0.0205576 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 240.000 | 0.101060 | ||||||||
\(179\) | 1212.00 | 0.506085 | 0.253042 | − | 0.967455i | \(-0.418569\pi\) | ||||
0.253042 | + | 0.967455i | \(0.418569\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2288.00 | 0.939590 | 0.469795 | − | 0.882776i | \(-0.344328\pi\) | ||||
0.469795 | + | 0.882776i | \(0.344328\pi\) | |||||||
\(182\) | 1316.00 | 0.535980 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 792.000 | 0.317321 | ||||||||
\(185\) | −1570.00 | −0.623939 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −117.000 | −0.0457534 | ||||||||
\(188\) | −2124.00 | −0.823982 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −320.000 | −0.122185 | ||||||||
\(191\) | 1938.00 | 0.734182 | 0.367091 | − | 0.930185i | \(-0.380354\pi\) | ||||
0.367091 | + | 0.930185i | \(0.380354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1498.00 | −0.558696 | −0.279348 | − | 0.960190i | \(-0.590118\pi\) | ||||
−0.279348 | + | 0.960190i | \(0.590118\pi\) | |||||||
\(194\) | −3284.00 | −1.21535 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −588.000 | −0.214286 | ||||||||
\(197\) | 2124.00 | 0.768166 | 0.384083 | − | 0.923299i | \(-0.374518\pi\) | ||||
0.384083 | + | 0.923299i | \(0.374518\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −385.000 | −0.137145 | −0.0685727 | − | 0.997646i | \(-0.521845\pi\) | ||||
−0.0685727 | + | 0.997646i | \(0.521845\pi\) | |||||||
\(200\) | 200.000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −66.0000 | −0.0229888 | ||||||||
\(203\) | −714.000 | −0.246862 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −540.000 | −0.183977 | ||||||||
\(206\) | −2396.00 | −0.810375 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 752.000 | 0.250682 | ||||||||
\(209\) | −96.0000 | −0.0317725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3170.00 | 1.03427 | 0.517137 | − | 0.855903i | \(-0.326998\pi\) | ||||
0.517137 | + | 0.855903i | \(0.326998\pi\) | |||||||
\(212\) | −2256.00 | −0.730862 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3084.00 | 0.985130 | ||||||||
\(215\) | −1495.00 | −0.474224 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1162.00 | 0.363510 | ||||||||
\(218\) | −1112.00 | −0.345478 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 60.0000 | 0.0183873 | ||||||||
\(221\) | 1833.00 | 0.557923 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1388.00 | 0.416804 | 0.208402 | − | 0.978043i | \(-0.433174\pi\) | ||||
0.208402 | + | 0.978043i | \(0.433174\pi\) | |||||||
\(224\) | 448.000 | 0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3210.00 | −0.944805 | ||||||||
\(227\) | 4644.00 | 1.35786 | 0.678928 | − | 0.734205i | \(-0.262445\pi\) | ||||
0.678928 | + | 0.734205i | \(0.262445\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4736.00 | 1.36665 | 0.683327 | − | 0.730113i | \(-0.260532\pi\) | ||||
0.683327 | + | 0.730113i | \(0.260532\pi\) | |||||||
\(230\) | −990.000 | −0.283820 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −408.000 | −0.115459 | ||||||||
\(233\) | −2814.00 | −0.791207 | −0.395604 | − | 0.918421i | \(-0.629465\pi\) | ||||
−0.395604 | + | 0.918421i | \(0.629465\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2655.00 | 0.736992 | ||||||||
\(236\) | −48.0000 | −0.0132396 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1092.00 | 0.297411 | ||||||||
\(239\) | 2202.00 | 0.595965 | 0.297982 | − | 0.954571i | \(-0.403686\pi\) | ||||
0.297982 | + | 0.954571i | \(0.403686\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3485.00 | 0.931488 | 0.465744 | − | 0.884920i | \(-0.345787\pi\) | ||||
0.465744 | + | 0.884920i | \(0.345787\pi\) | |||||||
\(242\) | −2644.00 | −0.702325 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 920.000 | 0.241381 | ||||||||
\(245\) | 735.000 | 0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1504.00 | 0.387438 | ||||||||
\(248\) | 664.000 | 0.170016 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −250.000 | −0.0632456 | ||||||||
\(251\) | 6345.00 | 1.59559 | 0.797795 | − | 0.602929i | \(-0.206000\pi\) | ||||
0.797795 | + | 0.602929i | \(0.206000\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −297.000 | −0.0738033 | ||||||||
\(254\) | 2668.00 | 0.659076 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −525.000 | −0.127426 | −0.0637132 | − | 0.997968i | \(-0.520294\pi\) | ||||
−0.0637132 | + | 0.997968i | \(0.520294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4396.00 | 1.05465 | ||||||||
\(260\) | −940.000 | −0.224217 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5766.00 | 1.35964 | ||||||||
\(263\) | −5196.00 | −1.21825 | −0.609124 | − | 0.793075i | \(-0.708479\pi\) | ||||
−0.609124 | + | 0.793075i | \(0.708479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2820.00 | 0.653703 | ||||||||
\(266\) | 896.000 | 0.206531 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1072.00 | −0.244339 | ||||||||
\(269\) | 7479.00 | 1.69518 | 0.847589 | − | 0.530654i | \(-0.178054\pi\) | ||||
0.847589 | + | 0.530654i | \(0.178054\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −856.000 | −0.191876 | −0.0959378 | − | 0.995387i | \(-0.530585\pi\) | ||||
−0.0959378 | + | 0.995387i | \(0.530585\pi\) | |||||||
\(272\) | 624.000 | 0.139101 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −564.000 | −0.124352 | ||||||||
\(275\) | −75.0000 | −0.0164461 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7054.00 | −1.53009 | −0.765043 | − | 0.643979i | \(-0.777282\pi\) | ||||
−0.765043 | + | 0.643979i | \(0.777282\pi\) | |||||||
\(278\) | −4988.00 | −1.07612 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −560.000 | −0.119523 | ||||||||
\(281\) | −1014.00 | −0.215268 | −0.107634 | − | 0.994191i | \(-0.534327\pi\) | ||||
−0.107634 | + | 0.994191i | \(0.534327\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 992.000 | 0.208368 | 0.104184 | − | 0.994558i | \(-0.466777\pi\) | ||||
0.104184 | + | 0.994558i | \(0.466777\pi\) | |||||||
\(284\) | −480.000 | −0.100291 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −282.000 | −0.0583042 | ||||||||
\(287\) | 1512.00 | 0.310977 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3392.00 | −0.690413 | ||||||||
\(290\) | 510.000 | 0.103270 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4424.00 | 0.886627 | ||||||||
\(293\) | 4950.00 | 0.986970 | 0.493485 | − | 0.869754i | \(-0.335723\pi\) | ||||
0.493485 | + | 0.869754i | \(0.335723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 60.0000 | 0.0118418 | ||||||||
\(296\) | 2512.00 | 0.493267 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5190.00 | −1.00889 | ||||||||
\(299\) | 4653.00 | 0.899966 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4186.00 | 0.801585 | ||||||||
\(302\) | 2458.00 | 0.468351 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 512.000 | 0.0965961 | ||||||||
\(305\) | −1150.00 | −0.215898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4777.00 | −0.888071 | −0.444035 | − | 0.896009i | \(-0.646454\pi\) | ||||
−0.444035 | + | 0.896009i | \(0.646454\pi\) | |||||||
\(308\) | −168.000 | −0.0310802 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −830.000 | −0.152067 | ||||||||
\(311\) | 7692.00 | 1.40249 | 0.701243 | − | 0.712922i | \(-0.252629\pi\) | ||||
0.701243 | + | 0.712922i | \(0.252629\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2932.00 | −0.529477 | −0.264739 | − | 0.964320i | \(-0.585286\pi\) | ||||
−0.264739 | + | 0.964320i | \(0.585286\pi\) | |||||||
\(314\) | −3182.00 | −0.571881 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2956.00 | −0.526228 | ||||||||
\(317\) | −8352.00 | −1.47980 | −0.739898 | − | 0.672720i | \(-0.765126\pi\) | ||||
−0.739898 | + | 0.672720i | \(0.765126\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 153.000 | 0.0268538 | ||||||||
\(320\) | −320.000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2772.00 | 0.479744 | ||||||||
\(323\) | 1248.00 | 0.214986 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1175.00 | 0.200545 | ||||||||
\(326\) | −914.000 | −0.155282 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 864.000 | 0.145446 | ||||||||
\(329\) | −7434.00 | −1.24574 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3070.00 | −0.509796 | −0.254898 | − | 0.966968i | \(-0.582042\pi\) | ||||
−0.254898 | + | 0.966968i | \(0.582042\pi\) | |||||||
\(332\) | −4344.00 | −0.718096 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2328.00 | 0.381385 | ||||||||
\(335\) | 1340.00 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1672.00 | −0.270266 | −0.135133 | − | 0.990827i | \(-0.543146\pi\) | ||||
−0.135133 | + | 0.990827i | \(0.543146\pi\) | |||||||
\(338\) | 24.0000 | 0.00386221 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −780.000 | −0.124416 | ||||||||
\(341\) | −249.000 | −0.0395428 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6860.00 | −1.07990 | ||||||||
\(344\) | 2392.00 | 0.374907 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7884.00 | −1.22499 | ||||||||
\(347\) | 5076.00 | 0.785285 | 0.392643 | − | 0.919691i | \(-0.371561\pi\) | ||||
0.392643 | + | 0.919691i | \(0.371561\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8594.00 | 1.31813 | 0.659063 | − | 0.752087i | \(-0.270953\pi\) | ||||
0.659063 | + | 0.752087i | \(0.270953\pi\) | |||||||
\(350\) | 700.000 | 0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −96.0000 | −0.0145364 | ||||||||
\(353\) | −12711.0 | −1.91654 | −0.958269 | − | 0.285866i | \(-0.907719\pi\) | ||||
−0.958269 | + | 0.285866i | \(0.907719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 600.000 | 0.0897034 | ||||||||
\(356\) | 480.000 | 0.0714605 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2424.00 | 0.357856 | ||||||||
\(359\) | 1464.00 | 0.215228 | 0.107614 | − | 0.994193i | \(-0.465679\pi\) | ||||
0.107614 | + | 0.994193i | \(0.465679\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5835.00 | −0.850707 | ||||||||
\(362\) | 4576.00 | 0.664390 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2632.00 | 0.378995 | ||||||||
\(365\) | −5530.00 | −0.793023 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −7630.00 | −1.08524 | −0.542620 | − | 0.839979i | \(-0.682567\pi\) | ||||
−0.542620 | + | 0.839979i | \(0.682567\pi\) | |||||||
\(368\) | 1584.00 | 0.224380 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3140.00 | −0.441191 | ||||||||
\(371\) | −7896.00 | −1.10496 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3883.00 | −0.539019 | −0.269510 | − | 0.962998i | \(-0.586862\pi\) | ||||
−0.269510 | + | 0.962998i | \(0.586862\pi\) | |||||||
\(374\) | −234.000 | −0.0323525 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4248.00 | −0.582643 | ||||||||
\(377\) | −2397.00 | −0.327458 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13768.0 | −1.86600 | −0.933001 | − | 0.359874i | \(-0.882820\pi\) | ||||
−0.933001 | + | 0.359874i | \(0.882820\pi\) | |||||||
\(380\) | −640.000 | −0.0863982 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3876.00 | 0.519145 | ||||||||
\(383\) | 14139.0 | 1.88634 | 0.943171 | − | 0.332307i | \(-0.107827\pi\) | ||||
0.943171 | + | 0.332307i | \(0.107827\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 210.000 | 0.0277989 | ||||||||
\(386\) | −2996.00 | −0.395058 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6568.00 | −0.859381 | ||||||||
\(389\) | −567.000 | −0.0739024 | −0.0369512 | − | 0.999317i | \(-0.511765\pi\) | ||||
−0.0369512 | + | 0.999317i | \(0.511765\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3861.00 | 0.499384 | ||||||||
\(392\) | −1176.00 | −0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4248.00 | 0.543176 | ||||||||
\(395\) | 3695.00 | 0.470672 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6685.00 | −0.845115 | −0.422557 | − | 0.906336i | \(-0.638867\pi\) | ||||
−0.422557 | + | 0.906336i | \(0.638867\pi\) | |||||||
\(398\) | −770.000 | −0.0969764 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | −4572.00 | −0.569364 | −0.284682 | − | 0.958622i | \(-0.591888\pi\) | ||||
−0.284682 | + | 0.958622i | \(0.591888\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3901.00 | 0.482190 | ||||||||
\(404\) | −132.000 | −0.0162556 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1428.00 | −0.174558 | ||||||||
\(407\) | −942.000 | −0.114725 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −25.0000 | −0.00302242 | −0.00151121 | − | 0.999999i | \(-0.500481\pi\) | ||||
−0.00151121 | + | 0.999999i | \(0.500481\pi\) | |||||||
\(410\) | −1080.00 | −0.130091 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4792.00 | −0.573022 | ||||||||
\(413\) | −168.000 | −0.0200163 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5430.00 | 0.642285 | ||||||||
\(416\) | 1504.00 | 0.177259 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −192.000 | −0.0224666 | ||||||||
\(419\) | −12453.0 | −1.45195 | −0.725977 | − | 0.687719i | \(-0.758612\pi\) | ||||
−0.725977 | + | 0.687719i | \(0.758612\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5048.00 | 0.584381 | 0.292191 | − | 0.956360i | \(-0.405616\pi\) | ||||
0.292191 | + | 0.956360i | \(0.405616\pi\) | |||||||
\(422\) | 6340.00 | 0.731342 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4512.00 | −0.516797 | ||||||||
\(425\) | 975.000 | 0.111281 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3220.00 | 0.364934 | ||||||||
\(428\) | 6168.00 | 0.696592 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2990.00 | −0.335327 | ||||||||
\(431\) | −5400.00 | −0.603501 | −0.301750 | − | 0.953387i | \(-0.597571\pi\) | ||||
−0.301750 | + | 0.953387i | \(0.597571\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6298.00 | −0.698990 | −0.349495 | − | 0.936938i | \(-0.613647\pi\) | ||||
−0.349495 | + | 0.936938i | \(0.613647\pi\) | |||||||
\(434\) | 2324.00 | 0.257040 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2224.00 | −0.244290 | ||||||||
\(437\) | 3168.00 | 0.346787 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6208.00 | −0.674924 | −0.337462 | − | 0.941339i | \(-0.609568\pi\) | ||||
−0.337462 | + | 0.941339i | \(0.609568\pi\) | |||||||
\(440\) | 120.000 | 0.0130018 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3666.00 | 0.394511 | ||||||||
\(443\) | 3360.00 | 0.360358 | 0.180179 | − | 0.983634i | \(-0.442332\pi\) | ||||
0.180179 | + | 0.983634i | \(0.442332\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −600.000 | −0.0639162 | ||||||||
\(446\) | 2776.00 | 0.294725 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 896.000 | 0.0944911 | ||||||||
\(449\) | −14394.0 | −1.51291 | −0.756453 | − | 0.654048i | \(-0.773069\pi\) | ||||
−0.756453 | + | 0.654048i | \(0.773069\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −324.000 | −0.0338283 | ||||||||
\(452\) | −6420.00 | −0.668078 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9288.00 | 0.960149 | ||||||||
\(455\) | −3290.00 | −0.338984 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −916.000 | −0.0937608 | −0.0468804 | − | 0.998901i | \(-0.514928\pi\) | ||||
−0.0468804 | + | 0.998901i | \(0.514928\pi\) | |||||||
\(458\) | 9472.00 | 0.966370 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1980.00 | −0.200691 | ||||||||
\(461\) | −8550.00 | −0.863803 | −0.431902 | − | 0.901921i | \(-0.642157\pi\) | ||||
−0.431902 | + | 0.901921i | \(0.642157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3734.00 | 0.374803 | 0.187401 | − | 0.982283i | \(-0.439993\pi\) | ||||
0.187401 | + | 0.982283i | \(0.439993\pi\) | |||||||
\(464\) | −816.000 | −0.0816419 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5628.00 | −0.559468 | ||||||||
\(467\) | −9840.00 | −0.975034 | −0.487517 | − | 0.873113i | \(-0.662097\pi\) | ||||
−0.487517 | + | 0.873113i | \(0.662097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3752.00 | −0.369406 | ||||||||
\(470\) | 5310.00 | 0.521132 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −96.0000 | −0.00936178 | ||||||||
\(473\) | −897.000 | −0.0871968 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 800.000 | 0.0772769 | ||||||||
\(476\) | 2184.00 | 0.210301 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4404.00 | 0.421411 | ||||||||
\(479\) | 17280.0 | 1.64832 | 0.824158 | − | 0.566360i | \(-0.191649\pi\) | ||||
0.824158 | + | 0.566360i | \(0.191649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14758.0 | 1.39897 | ||||||||
\(482\) | 6970.00 | 0.658661 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5288.00 | −0.496619 | ||||||||
\(485\) | 8210.00 | 0.768653 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4588.00 | −0.426904 | −0.213452 | − | 0.976954i | \(-0.568471\pi\) | ||||
−0.213452 | + | 0.976954i | \(0.568471\pi\) | |||||||
\(488\) | 1840.00 | 0.170682 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1470.00 | 0.135526 | ||||||||
\(491\) | −636.000 | −0.0584568 | −0.0292284 | − | 0.999573i | \(-0.509305\pi\) | ||||
−0.0292284 | + | 0.999573i | \(0.509305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1989.00 | −0.181704 | ||||||||
\(494\) | 3008.00 | 0.273960 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1328.00 | 0.120220 | ||||||||
\(497\) | −1680.00 | −0.151626 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11716.0 | −1.05106 | −0.525531 | − | 0.850774i | \(-0.676133\pi\) | ||||
−0.525531 | + | 0.850774i | \(0.676133\pi\) | |||||||
\(500\) | −500.000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12690.0 | 1.12825 | ||||||||
\(503\) | −4653.00 | −0.412459 | −0.206230 | − | 0.978504i | \(-0.566119\pi\) | ||||
−0.206230 | + | 0.978504i | \(0.566119\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 165.000 | 0.0145394 | ||||||||
\(506\) | −594.000 | −0.0521868 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5336.00 | 0.466037 | ||||||||
\(509\) | −16479.0 | −1.43501 | −0.717504 | − | 0.696555i | \(-0.754715\pi\) | ||||
−0.717504 | + | 0.696555i | \(0.754715\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15484.0 | 1.34045 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1050.00 | −0.0901041 | ||||||||
\(515\) | 5990.00 | 0.512526 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1593.00 | 0.135513 | ||||||||
\(518\) | 8792.00 | 0.745750 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1880.00 | −0.158545 | ||||||||
\(521\) | −3120.00 | −0.262360 | −0.131180 | − | 0.991359i | \(-0.541877\pi\) | ||||
−0.131180 | + | 0.991359i | \(0.541877\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17645.0 | 1.47526 | 0.737631 | − | 0.675204i | \(-0.235944\pi\) | ||||
0.737631 | + | 0.675204i | \(0.235944\pi\) | |||||||
\(524\) | 11532.0 | 0.961408 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10392.0 | −0.861431 | ||||||||
\(527\) | 3237.00 | 0.267563 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2366.00 | −0.194460 | ||||||||
\(530\) | 5640.00 | 0.462238 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1792.00 | 0.146040 | ||||||||
\(533\) | 5076.00 | 0.412507 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7710.00 | −0.623051 | ||||||||
\(536\) | −2144.00 | −0.172774 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14958.0 | 1.19867 | ||||||||
\(539\) | 441.000 | 0.0352416 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2182.00 | −0.173404 | −0.0867019 | − | 0.996234i | \(-0.527633\pi\) | ||||
−0.0867019 | + | 0.996234i | \(0.527633\pi\) | |||||||
\(542\) | −1712.00 | −0.135677 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1248.00 | 0.0983595 | ||||||||
\(545\) | 2780.00 | 0.218499 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4033.00 | −0.315244 | −0.157622 | − | 0.987499i | \(-0.550383\pi\) | ||||
−0.157622 | + | 0.987499i | \(0.550383\pi\) | |||||||
\(548\) | −1128.00 | −0.0879302 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −150.000 | −0.0116291 | ||||||||
\(551\) | −1632.00 | −0.126181 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10346.0 | −0.795582 | ||||||||
\(554\) | −14108.0 | −1.08193 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9976.00 | −0.760929 | ||||||||
\(557\) | 960.000 | 0.0730278 | 0.0365139 | − | 0.999333i | \(-0.488375\pi\) | ||||
0.0365139 | + | 0.999333i | \(0.488375\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14053.0 | 1.06329 | ||||||||
\(560\) | −1120.00 | −0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2028.00 | −0.152217 | ||||||||
\(563\) | 23754.0 | 1.77817 | 0.889087 | − | 0.457739i | \(-0.151340\pi\) | ||||
0.889087 | + | 0.457739i | \(0.151340\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8025.00 | 0.597547 | ||||||||
\(566\) | 1984.00 | 0.147339 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −960.000 | −0.0709167 | ||||||||
\(569\) | 22536.0 | 1.66038 | 0.830192 | − | 0.557478i | \(-0.188231\pi\) | ||||
0.830192 | + | 0.557478i | \(0.188231\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17726.0 | 1.29914 | 0.649571 | − | 0.760301i | \(-0.274949\pi\) | ||||
0.649571 | + | 0.760301i | \(0.274949\pi\) | |||||||
\(572\) | −564.000 | −0.0412273 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3024.00 | 0.219894 | ||||||||
\(575\) | 2475.00 | 0.179504 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17168.0 | 1.23867 | 0.619336 | − | 0.785126i | \(-0.287402\pi\) | ||||
0.619336 | + | 0.785126i | \(0.287402\pi\) | |||||||
\(578\) | −6784.00 | −0.488196 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1020.00 | 0.0730227 | ||||||||
\(581\) | −15204.0 | −1.08566 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1692.00 | 0.120198 | ||||||||
\(584\) | 8848.00 | 0.626940 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9900.00 | 0.697893 | ||||||||
\(587\) | −7542.00 | −0.530309 | −0.265155 | − | 0.964206i | \(-0.585423\pi\) | ||||
−0.265155 | + | 0.964206i | \(0.585423\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2656.00 | 0.185804 | ||||||||
\(590\) | 120.000 | 0.00837343 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5024.00 | 0.348792 | ||||||||
\(593\) | 15543.0 | 1.07635 | 0.538174 | − | 0.842834i | \(-0.319114\pi\) | ||||
0.538174 | + | 0.842834i | \(0.319114\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2730.00 | −0.188099 | ||||||||
\(596\) | −10380.0 | −0.713392 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9306.00 | 0.636372 | ||||||||
\(599\) | −16026.0 | −1.09316 | −0.546581 | − | 0.837406i | \(-0.684071\pi\) | ||||
−0.546581 | + | 0.837406i | \(0.684071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10469.0 | 0.710548 | 0.355274 | − | 0.934762i | \(-0.384388\pi\) | ||||
0.355274 | + | 0.934762i | \(0.384388\pi\) | |||||||
\(602\) | 8372.00 | 0.566806 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4916.00 | 0.331174 | ||||||||
\(605\) | 6610.00 | 0.444190 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8074.00 | −0.539891 | −0.269945 | − | 0.962876i | \(-0.587006\pi\) | ||||
−0.269945 | + | 0.962876i | \(0.587006\pi\) | |||||||
\(608\) | 1024.00 | 0.0683038 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2300.00 | −0.152663 | ||||||||
\(611\) | −24957.0 | −1.65246 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26855.0 | 1.76943 | 0.884717 | − | 0.466128i | \(-0.154351\pi\) | ||||
0.884717 | + | 0.466128i | \(0.154351\pi\) | |||||||
\(614\) | −9554.00 | −0.627961 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −336.000 | −0.0219770 | ||||||||
\(617\) | −24447.0 | −1.59514 | −0.797568 | − | 0.603229i | \(-0.793881\pi\) | ||||
−0.797568 | + | 0.603229i | \(0.793881\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1850.00 | 0.120126 | 0.0600628 | − | 0.998195i | \(-0.480870\pi\) | ||||
0.0600628 | + | 0.998195i | \(0.480870\pi\) | |||||||
\(620\) | −1660.00 | −0.107528 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 15384.0 | 0.991708 | ||||||||
\(623\) | 1680.00 | 0.108038 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −5864.00 | −0.374397 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6364.00 | −0.404381 | ||||||||
\(629\) | 12246.0 | 0.776280 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21728.0 | 1.37081 | 0.685403 | − | 0.728164i | \(-0.259626\pi\) | ||||
0.685403 | + | 0.728164i | \(0.259626\pi\) | |||||||
\(632\) | −5912.00 | −0.372099 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16704.0 | −1.04637 | ||||||||
\(635\) | −6670.00 | −0.416836 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6909.00 | −0.429740 | ||||||||
\(638\) | 306.000 | 0.0189885 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −640.000 | −0.0395285 | ||||||||
\(641\) | −23862.0 | −1.47035 | −0.735173 | − | 0.677879i | \(-0.762899\pi\) | ||||
−0.735173 | + | 0.677879i | \(0.762899\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10523.0 | 0.645391 | 0.322696 | − | 0.946503i | \(-0.395411\pi\) | ||||
0.322696 | + | 0.946503i | \(0.395411\pi\) | |||||||
\(644\) | 5544.00 | 0.339230 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2496.00 | 0.152018 | ||||||||
\(647\) | −5484.00 | −0.333228 | −0.166614 | − | 0.986022i | \(-0.553283\pi\) | ||||
−0.166614 | + | 0.986022i | \(0.553283\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.0000 | 0.00217739 | ||||||||
\(650\) | 2350.00 | 0.141807 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1828.00 | −0.109801 | ||||||||
\(653\) | 26784.0 | 1.60511 | 0.802557 | − | 0.596576i | \(-0.203473\pi\) | ||||
0.802557 | + | 0.596576i | \(0.203473\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14415.0 | −0.859909 | ||||||||
\(656\) | 1728.00 | 0.102846 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14868.0 | −0.880874 | ||||||||
\(659\) | 12120.0 | 0.716431 | 0.358216 | − | 0.933639i | \(-0.383385\pi\) | ||||
0.358216 | + | 0.933639i | \(0.383385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18226.0 | −1.07248 | −0.536240 | − | 0.844066i | \(-0.680156\pi\) | ||||
−0.536240 | + | 0.844066i | \(0.680156\pi\) | |||||||
\(662\) | −6140.00 | −0.360480 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8688.00 | −0.507771 | ||||||||
\(665\) | −2240.00 | −0.130622 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5049.00 | −0.293101 | ||||||||
\(668\) | 4656.00 | 0.269680 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2680.00 | 0.154533 | ||||||||
\(671\) | −690.000 | −0.0396977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11062.0 | −0.633594 | −0.316797 | − | 0.948493i | \(-0.602607\pi\) | ||||
−0.316797 | + | 0.948493i | \(0.602607\pi\) | |||||||
\(674\) | −3344.00 | −0.191107 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 48.0000 | 0.00273100 | ||||||||
\(677\) | 9348.00 | 0.530684 | 0.265342 | − | 0.964154i | \(-0.414515\pi\) | ||||
0.265342 | + | 0.964154i | \(0.414515\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22988.0 | −1.29926 | ||||||||
\(680\) | −1560.00 | −0.0879754 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −498.000 | −0.0279610 | ||||||||
\(683\) | −19248.0 | −1.07834 | −0.539169 | − | 0.842198i | \(-0.681261\pi\) | ||||
−0.539169 | + | 0.842198i | \(0.681261\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1410.00 | 0.0786472 | ||||||||
\(686\) | −13720.0 | −0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4784.00 | 0.265099 | ||||||||
\(689\) | −26508.0 | −1.46571 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17710.0 | −0.974993 | −0.487496 | − | 0.873125i | \(-0.662090\pi\) | ||||
−0.487496 | + | 0.873125i | \(0.662090\pi\) | |||||||
\(692\) | −15768.0 | −0.866199 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10152.0 | 0.555280 | ||||||||
\(695\) | 12470.0 | 0.680596 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4212.00 | 0.228897 | ||||||||
\(698\) | 17188.0 | 0.932056 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1400.00 | 0.0755929 | ||||||||
\(701\) | 19437.0 | 1.04725 | 0.523627 | − | 0.851947i | \(-0.324578\pi\) | ||||
0.523627 | + | 0.851947i | \(0.324578\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10048.0 | 0.539072 | ||||||||
\(704\) | −192.000 | −0.0102788 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −25422.0 | −1.35520 | ||||||||
\(707\) | −462.000 | −0.0245761 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19516.0 | −1.03376 | −0.516882 | − | 0.856057i | \(-0.672907\pi\) | ||||
−0.516882 | + | 0.856057i | \(0.672907\pi\) | |||||||
\(710\) | 1200.00 | 0.0634299 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 960.000 | 0.0505302 | ||||||||
\(713\) | 8217.00 | 0.431598 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 705.000 | 0.0368748 | ||||||||
\(716\) | 4848.00 | 0.253042 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2928.00 | 0.152189 | ||||||||
\(719\) | −17358.0 | −0.900340 | −0.450170 | − | 0.892943i | \(-0.648637\pi\) | ||||
−0.450170 | + | 0.892943i | \(0.648637\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16772.0 | −0.866327 | ||||||||
\(722\) | −11670.0 | −0.601541 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9152.00 | 0.469795 | ||||||||
\(725\) | −1275.00 | −0.0653135 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24428.0 | 1.24620 | 0.623098 | − | 0.782144i | \(-0.285874\pi\) | ||||
0.623098 | + | 0.782144i | \(0.285874\pi\) | |||||||
\(728\) | 5264.00 | 0.267990 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11060.0 | −0.560752 | ||||||||
\(731\) | 11661.0 | 0.590010 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21418.0 | −1.07925 | −0.539626 | − | 0.841905i | \(-0.681434\pi\) | ||||
−0.539626 | + | 0.841905i | \(0.681434\pi\) | |||||||
\(734\) | −15260.0 | −0.767380 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3168.00 | 0.158660 | ||||||||
\(737\) | 804.000 | 0.0401842 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −664.000 | −0.0330523 | −0.0165261 | − | 0.999863i | \(-0.505261\pi\) | ||||
−0.0165261 | + | 0.999863i | \(0.505261\pi\) | |||||||
\(740\) | −6280.00 | −0.311969 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15792.0 | −0.781324 | ||||||||
\(743\) | 34209.0 | 1.68911 | 0.844553 | − | 0.535471i | \(-0.179866\pi\) | ||||
0.844553 | + | 0.535471i | \(0.179866\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12975.0 | 0.638077 | ||||||||
\(746\) | −7766.00 | −0.381144 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −468.000 | −0.0228767 | ||||||||
\(749\) | 21588.0 | 1.05315 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6857.00 | 0.333176 | 0.166588 | − | 0.986027i | \(-0.446725\pi\) | ||||
0.166588 | + | 0.986027i | \(0.446725\pi\) | |||||||
\(752\) | −8496.00 | −0.411991 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4794.00 | −0.231548 | ||||||||
\(755\) | −6145.00 | −0.296211 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23719.0 | −1.13881 | −0.569407 | − | 0.822056i | \(-0.692827\pi\) | ||||
−0.569407 | + | 0.822056i | \(0.692827\pi\) | |||||||
\(758\) | −27536.0 | −1.31946 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1280.00 | −0.0610927 | ||||||||
\(761\) | 14418.0 | 0.686796 | 0.343398 | − | 0.939190i | \(-0.388422\pi\) | ||||
0.343398 | + | 0.939190i | \(0.388422\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7784.00 | −0.369331 | ||||||||
\(764\) | 7752.00 | 0.367091 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28278.0 | 1.33385 | ||||||||
\(767\) | −564.000 | −0.0265513 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4849.00 | −0.227385 | −0.113693 | − | 0.993516i | \(-0.536268\pi\) | ||||
−0.113693 | + | 0.993516i | \(0.536268\pi\) | |||||||
\(770\) | 420.000 | 0.0196568 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5992.00 | −0.279348 | ||||||||
\(773\) | 36258.0 | 1.68708 | 0.843538 | − | 0.537070i | \(-0.180469\pi\) | ||||
0.843538 | + | 0.537070i | \(0.180469\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2075.00 | 0.0961757 | ||||||||
\(776\) | −13136.0 | −0.607674 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1134.00 | −0.0522569 | ||||||||
\(779\) | 3456.00 | 0.158953 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 360.000 | 0.0164940 | ||||||||
\(782\) | 7722.00 | 0.353118 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2352.00 | −0.107143 | ||||||||
\(785\) | 7955.00 | 0.361689 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18877.0 | −0.855009 | −0.427505 | − | 0.904013i | \(-0.640607\pi\) | ||||
−0.427505 | + | 0.904013i | \(0.640607\pi\) | |||||||
\(788\) | 8496.00 | 0.384083 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7390.00 | 0.332816 | ||||||||
\(791\) | −22470.0 | −1.01004 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10810.0 | 0.484079 | ||||||||
\(794\) | −13370.0 | −0.597586 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1540.00 | −0.0685727 | ||||||||
\(797\) | 16200.0 | 0.719992 | 0.359996 | − | 0.932954i | \(-0.382778\pi\) | ||||
0.359996 | + | 0.932954i | \(0.382778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20709.0 | −0.916936 | ||||||||
\(800\) | 800.000 | 0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9144.00 | −0.402601 | ||||||||
\(803\) | −3318.00 | −0.145815 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6930.00 | −0.303417 | ||||||||
\(806\) | 7802.00 | 0.340960 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −264.000 | −0.0114944 | ||||||||
\(809\) | 26760.0 | 1.16296 | 0.581478 | − | 0.813562i | \(-0.302475\pi\) | ||||
0.581478 | + | 0.813562i | \(0.302475\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10510.0 | −0.455063 | −0.227531 | − | 0.973771i | \(-0.573065\pi\) | ||||
−0.227531 | + | 0.973771i | \(0.573065\pi\) | |||||||
\(812\) | −2856.00 | −0.123431 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1884.00 | −0.0811231 | ||||||||
\(815\) | 2285.00 | 0.0982087 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9568.00 | 0.409721 | ||||||||
\(818\) | −50.0000 | −0.00213717 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2160.00 | −0.0919884 | ||||||||
\(821\) | 28230.0 | 1.20004 | 0.600021 | − | 0.799985i | \(-0.295159\pi\) | ||||
0.600021 | + | 0.799985i | \(0.295159\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39868.0 | −1.68859 | −0.844296 | − | 0.535877i | \(-0.819981\pi\) | ||||
−0.844296 | + | 0.535877i | \(0.819981\pi\) | |||||||
\(824\) | −9584.00 | −0.405187 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −336.000 | −0.0141537 | ||||||||
\(827\) | −32394.0 | −1.36209 | −0.681046 | − | 0.732241i | \(-0.738475\pi\) | ||||
−0.681046 | + | 0.732241i | \(0.738475\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34820.0 | 1.45880 | 0.729402 | − | 0.684085i | \(-0.239798\pi\) | ||||
0.729402 | + | 0.684085i | \(0.239798\pi\) | |||||||
\(830\) | 10860.0 | 0.454164 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3008.00 | 0.125341 | ||||||||
\(833\) | −5733.00 | −0.238459 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5820.00 | −0.241209 | ||||||||
\(836\) | −384.000 | −0.0158863 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24906.0 | −1.02669 | ||||||||
\(839\) | 1146.00 | 0.0471565 | 0.0235783 | − | 0.999722i | \(-0.492494\pi\) | ||||
0.0235783 | + | 0.999722i | \(0.492494\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21788.0 | −0.893354 | ||||||||
\(842\) | 10096.0 | 0.413220 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12680.0 | 0.517137 | ||||||||
\(845\) | −60.0000 | −0.00244268 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18508.0 | −0.750817 | ||||||||
\(848\) | −9024.00 | −0.365431 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1950.00 | 0.0786876 | ||||||||
\(851\) | 31086.0 | 1.25219 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19393.0 | −0.778433 | −0.389217 | − | 0.921146i | \(-0.627254\pi\) | ||||
−0.389217 | + | 0.921146i | \(0.627254\pi\) | |||||||
\(854\) | 6440.00 | 0.258047 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12336.0 | 0.492565 | ||||||||
\(857\) | 8430.00 | 0.336013 | 0.168007 | − | 0.985786i | \(-0.446267\pi\) | ||||
0.168007 | + | 0.985786i | \(0.446267\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15470.0 | 0.614470 | 0.307235 | − | 0.951634i | \(-0.400596\pi\) | ||||
0.307235 | + | 0.951634i | \(0.400596\pi\) | |||||||
\(860\) | −5980.00 | −0.237112 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10800.0 | −0.426740 | ||||||||
\(863\) | −5871.00 | −0.231577 | −0.115789 | − | 0.993274i | \(-0.536940\pi\) | ||||
−0.115789 | + | 0.993274i | \(0.536940\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19710.0 | 0.774752 | ||||||||
\(866\) | −12596.0 | −0.494260 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4648.00 | 0.181755 | ||||||||
\(869\) | 2217.00 | 0.0865438 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12596.0 | −0.490011 | ||||||||
\(872\) | −4448.00 | −0.172739 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6336.00 | 0.245216 | ||||||||
\(875\) | −1750.00 | −0.0676123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11299.0 | −0.435051 | −0.217526 | − | 0.976055i | \(-0.569799\pi\) | ||||
−0.217526 | + | 0.976055i | \(0.569799\pi\) | |||||||
\(878\) | −12416.0 | −0.477243 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 240.000 | 0.00919363 | ||||||||
\(881\) | −29682.0 | −1.13509 | −0.567544 | − | 0.823343i | \(-0.692106\pi\) | ||||
−0.567544 | + | 0.823343i | \(0.692106\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40316.0 | 1.53651 | 0.768257 | − | 0.640142i | \(-0.221124\pi\) | ||||
0.768257 | + | 0.640142i | \(0.221124\pi\) | |||||||
\(884\) | 7332.00 | 0.278961 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6720.00 | 0.254811 | ||||||||
\(887\) | 21945.0 | 0.830711 | 0.415356 | − | 0.909659i | \(-0.363657\pi\) | ||||
0.415356 | + | 0.909659i | \(0.363657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18676.0 | 0.704581 | ||||||||
\(890\) | −1200.00 | −0.0451956 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5552.00 | 0.208402 | ||||||||
\(893\) | −16992.0 | −0.636748 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6060.00 | −0.226328 | ||||||||
\(896\) | 1792.00 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28788.0 | −1.06979 | ||||||||
\(899\) | −4233.00 | −0.157039 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21996.0 | −0.813311 | ||||||||
\(902\) | −648.000 | −0.0239202 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12840.0 | −0.472403 | ||||||||
\(905\) | −11440.0 | −0.420197 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24911.0 | 0.911969 | 0.455985 | − | 0.889988i | \(-0.349287\pi\) | ||||
0.455985 | + | 0.889988i | \(0.349287\pi\) | |||||||
\(908\) | 18576.0 | 0.678928 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6580.00 | −0.239698 | ||||||||
\(911\) | −33264.0 | −1.20975 | −0.604877 | − | 0.796319i | \(-0.706778\pi\) | ||||
−0.604877 | + | 0.796319i | \(0.706778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3258.00 | 0.118099 | ||||||||
\(914\) | −1832.00 | −0.0662989 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18944.0 | 0.683327 | ||||||||
\(917\) | 40362.0 | 1.45351 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23191.0 | −0.832427 | −0.416214 | − | 0.909267i | \(-0.636643\pi\) | ||||
−0.416214 | + | 0.909267i | \(0.636643\pi\) | |||||||
\(920\) | −3960.00 | −0.141910 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17100.0 | −0.610801 | ||||||||
\(923\) | −5640.00 | −0.201130 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7850.00 | 0.279034 | ||||||||
\(926\) | 7468.00 | 0.265026 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1632.00 | −0.0577296 | ||||||||
\(929\) | −2160.00 | −0.0762834 | −0.0381417 | − | 0.999272i | \(-0.512144\pi\) | ||||
−0.0381417 | + | 0.999272i | \(0.512144\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4704.00 | −0.165593 | ||||||||
\(932\) | −11256.0 | −0.395604 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −19680.0 | −0.689453 | ||||||||
\(935\) | 585.000 | 0.0204615 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2066.00 | 0.0720312 | 0.0360156 | − | 0.999351i | \(-0.488533\pi\) | ||||
0.0360156 | + | 0.999351i | \(0.488533\pi\) | |||||||
\(938\) | −7504.00 | −0.261209 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10620.0 | 0.368496 | ||||||||
\(941\) | 22233.0 | 0.770218 | 0.385109 | − | 0.922871i | \(-0.374164\pi\) | ||||
0.385109 | + | 0.922871i | \(0.374164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10692.0 | 0.369225 | ||||||||
\(944\) | −192.000 | −0.00661978 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1794.00 | −0.0616575 | ||||||||
\(947\) | 17754.0 | 0.609216 | 0.304608 | − | 0.952478i | \(-0.401475\pi\) | ||||
0.304608 | + | 0.952478i | \(0.401475\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 51982.0 | 1.77809 | ||||||||
\(950\) | 1600.00 | 0.0546430 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4368.00 | 0.148706 | ||||||||
\(953\) | −33891.0 | −1.15198 | −0.575990 | − | 0.817457i | \(-0.695383\pi\) | ||||
−0.575990 | + | 0.817457i | \(0.695383\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9690.00 | −0.328336 | ||||||||
\(956\) | 8808.00 | 0.297982 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 34560.0 | 1.16554 | ||||||||
\(959\) | −3948.00 | −0.132938 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22902.0 | −0.768756 | ||||||||
\(962\) | 29516.0 | 0.989225 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13940.0 | 0.465744 | ||||||||
\(965\) | 7490.00 | 0.249857 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51074.0 | 1.69848 | 0.849239 | − | 0.528008i | \(-0.177061\pi\) | ||||
0.849239 | + | 0.528008i | \(0.177061\pi\) | |||||||
\(968\) | −10576.0 | −0.351163 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16420.0 | 0.543520 | ||||||||
\(971\) | −20967.0 | −0.692959 | −0.346479 | − | 0.938058i | \(-0.612623\pi\) | ||||
−0.346479 | + | 0.938058i | \(0.612623\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −34916.0 | −1.15042 | ||||||||
\(974\) | −9176.00 | −0.301867 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3680.00 | 0.120691 | ||||||||
\(977\) | −31749.0 | −1.03965 | −0.519826 | − | 0.854272i | \(-0.674003\pi\) | ||||
−0.519826 | + | 0.854272i | \(0.674003\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −360.000 | −0.0117525 | ||||||||
\(980\) | 2940.00 | 0.0958315 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1272.00 | −0.0413352 | ||||||||
\(983\) | −47325.0 | −1.53554 | −0.767769 | − | 0.640727i | \(-0.778633\pi\) | ||||
−0.767769 | + | 0.640727i | \(0.778633\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10620.0 | −0.343534 | ||||||||
\(986\) | −3978.00 | −0.128484 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6016.00 | 0.193719 | ||||||||
\(989\) | 29601.0 | 0.951726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2363.00 | 0.0757449 | 0.0378724 | − | 0.999283i | \(-0.487942\pi\) | ||||
0.0378724 | + | 0.999283i | \(0.487942\pi\) | |||||||
\(992\) | 2656.00 | 0.0850081 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3360.00 | −0.107216 | ||||||||
\(995\) | 1925.00 | 0.0613333 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45569.0 | 1.44753 | 0.723764 | − | 0.690048i | \(-0.242411\pi\) | ||||
0.723764 | + | 0.690048i | \(0.242411\pi\) | |||||||
\(998\) | −23432.0 | −0.743213 | ||||||||
\(999\) | 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 | 270.4.a.j.1.1 | yes | 1 | |
3.2 | odd | 2 | 270.4.a.f.1.1 | ✓ | 1 | ||
4.3 | odd | 2 | 2160.4.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 1350.4.c.j.649.2 | 2 | |||
5.3 | odd | 4 | 1350.4.c.j.649.1 | 2 | |||
5.4 | even | 2 | 1350.4.a.e.1.1 | 1 | |||
9.2 | odd | 6 | 810.4.e.n.271.1 | 2 | |||
9.4 | even | 3 | 810.4.e.f.541.1 | 2 | |||
9.5 | odd | 6 | 810.4.e.n.541.1 | 2 | |||
9.7 | even | 3 | 810.4.e.f.271.1 | 2 | |||
12.11 | even | 2 | 2160.4.a.l.1.1 | 1 | |||
15.2 | even | 4 | 1350.4.c.k.649.1 | 2 | |||
15.8 | even | 4 | 1350.4.c.k.649.2 | 2 | |||
15.14 | odd | 2 | 1350.4.a.r.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
270.4.a.f.1.1 | ✓ | 1 | 3.2 | odd | 2 | ||
270.4.a.j.1.1 | yes | 1 | 1.1 | even | 1 | trivial | |
810.4.e.f.271.1 | 2 | 9.7 | even | 3 | |||
810.4.e.f.541.1 | 2 | 9.4 | even | 3 | |||
810.4.e.n.271.1 | 2 | 9.2 | odd | 6 | |||
810.4.e.n.541.1 | 2 | 9.5 | odd | 6 | |||
1350.4.a.e.1.1 | 1 | 5.4 | even | 2 | |||
1350.4.a.r.1.1 | 1 | 15.14 | odd | 2 | |||
1350.4.c.j.649.1 | 2 | 5.3 | odd | 4 | |||
1350.4.c.j.649.2 | 2 | 5.2 | odd | 4 | |||
1350.4.c.k.649.1 | 2 | 15.2 | even | 4 | |||
1350.4.c.k.649.2 | 2 | 15.8 | even | 4 | |||
2160.4.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
2160.4.a.l.1.1 | 1 | 12.11 | even | 2 |