Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,5,Mod(161,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.161");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.d (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(83.7296700979\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | no (minimal twist has level 90) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.8 | ||
Character | \(\chi\) | \(=\) | 810.161 |
Dual form | 810.5.d.c.161.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | −0.500000 | ||||||||
\(5\) | 11.1803i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 49.1951 | 1.00398 | 0.501991 | − | 0.864873i | \(-0.332601\pi\) | ||||
0.501991 | + | 0.864873i | \(0.332601\pi\) | |||||||
\(8\) | − 22.6274i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −31.6228 | −0.316228 | ||||||||
\(11\) | 96.2002i | 0.795043i | 0.917593 | + | 0.397521i | \(0.130130\pi\) | ||||
−0.917593 | + | 0.397521i | \(0.869870\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −113.983 | −0.674453 | −0.337227 | − | 0.941423i | \(-0.609489\pi\) | ||||
−0.337227 | + | 0.941423i | \(0.609489\pi\) | |||||||
\(14\) | 139.145i | 0.709922i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 64.0000 | 0.250000 | ||||||||
\(17\) | − 351.453i | − 1.21610i | −0.793899 | − | 0.608050i | \(-0.791952\pi\) | ||||
0.793899 | − | 0.608050i | \(-0.208048\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −253.282 | −0.701613 | −0.350806 | − | 0.936448i | \(-0.614092\pi\) | ||||
−0.350806 | + | 0.936448i | \(0.614092\pi\) | |||||||
\(20\) | − 89.4427i | − 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −272.095 | −0.562180 | ||||||||
\(23\) | 313.171i | 0.592006i | 0.955187 | + | 0.296003i | \(0.0956538\pi\) | ||||
−0.955187 | + | 0.296003i | \(0.904346\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −125.000 | −0.200000 | ||||||||
\(26\) | − 322.392i | − 0.476911i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −393.561 | −0.501991 | ||||||||
\(29\) | − 1127.36i | − 1.34050i | −0.742135 | − | 0.670251i | \(-0.766187\pi\) | ||||
0.742135 | − | 0.670251i | \(-0.233813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 340.531 | 0.354351 | 0.177175 | − | 0.984179i | \(-0.443304\pi\) | ||||
0.177175 | + | 0.984179i | \(0.443304\pi\) | |||||||
\(32\) | 181.019i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 994.058 | 0.859912 | ||||||||
\(35\) | 550.018i | 0.448994i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 75.9627 | 0.0554878 | 0.0277439 | − | 0.999615i | \(-0.491168\pi\) | ||||
0.0277439 | + | 0.999615i | \(0.491168\pi\) | |||||||
\(38\) | − 716.390i | − 0.496115i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 252.982 | 0.158114 | ||||||||
\(41\) | 1144.61i | 0.680910i | 0.940261 | + | 0.340455i | \(0.110581\pi\) | ||||
−0.940261 | + | 0.340455i | \(0.889419\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2591.02 | −1.40131 | −0.700653 | − | 0.713502i | \(-0.747108\pi\) | ||||
−0.700653 | + | 0.713502i | \(0.747108\pi\) | |||||||
\(44\) | − 769.601i | − 0.397521i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −885.781 | −0.418611 | ||||||||
\(47\) | 3558.29i | 1.61081i | 0.592722 | + | 0.805407i | \(0.298053\pi\) | ||||
−0.592722 | + | 0.805407i | \(0.701947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.1598 | 0.00797991 | ||||||||
\(50\) | − 353.553i | − 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 911.861 | 0.337227 | ||||||||
\(53\) | − 2926.47i | − 1.04182i | −0.853612 | − | 0.520910i | \(-0.825593\pi\) | ||||
0.853612 | − | 0.520910i | \(-0.174407\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1075.55 | −0.355554 | ||||||||
\(56\) | − 1113.16i | − 0.354961i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3188.66 | 0.947877 | ||||||||
\(59\) | 130.797i | 0.0375747i | 0.999824 | + | 0.0187873i | \(0.00598055\pi\) | ||||
−0.999824 | + | 0.0187873i | \(0.994019\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5629.54 | −1.51291 | −0.756456 | − | 0.654045i | \(-0.773071\pi\) | ||||
−0.756456 | + | 0.654045i | \(0.773071\pi\) | |||||||
\(62\) | 963.168i | 0.250564i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −512.000 | −0.125000 | ||||||||
\(65\) | − 1274.36i | − 0.301625i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2670.08 | 0.594806 | 0.297403 | − | 0.954752i | \(-0.403879\pi\) | ||||
0.297403 | + | 0.954752i | \(0.403879\pi\) | |||||||
\(68\) | 2811.62i | 0.608050i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1555.69 | −0.317487 | ||||||||
\(71\) | − 2279.92i | − 0.452275i | −0.974095 | − | 0.226137i | \(-0.927390\pi\) | ||||
0.974095 | − | 0.226137i | \(-0.0726098\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8045.40 | −1.50974 | −0.754869 | − | 0.655875i | \(-0.772300\pi\) | ||||
−0.754869 | + | 0.655875i | \(0.772300\pi\) | |||||||
\(74\) | 214.855i | 0.0392358i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2026.26 | 0.350806 | ||||||||
\(77\) | 4732.58i | 0.798209i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8420.23 | −1.34918 | −0.674589 | − | 0.738193i | \(-0.735679\pi\) | ||||
−0.674589 | + | 0.738193i | \(0.735679\pi\) | |||||||
\(80\) | 715.542i | 0.111803i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3237.45 | −0.481476 | ||||||||
\(83\) | 12679.3i | 1.84052i | 0.391313 | + | 0.920258i | \(0.372021\pi\) | ||||
−0.391313 | + | 0.920258i | \(0.627979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3929.36 | 0.543856 | ||||||||
\(86\) | − 7328.50i | − 0.990874i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2176.76 | 0.281090 | ||||||||
\(89\) | − 10724.8i | − 1.35397i | −0.735997 | − | 0.676985i | \(-0.763286\pi\) | ||||
0.735997 | − | 0.676985i | \(-0.236714\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5607.39 | −0.677139 | ||||||||
\(92\) | − 2505.37i | − 0.296003i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10064.4 | −1.13902 | ||||||||
\(95\) | − 2831.78i | − 0.313771i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11723.3 | 1.24596 | 0.622982 | − | 0.782237i | \(-0.285921\pi\) | ||||
0.622982 | + | 0.782237i | \(0.285921\pi\) | |||||||
\(98\) | 54.1920i | 0.00564265i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1000.00 | 0.100000 | ||||||||
\(101\) | − 12192.5i | − 1.19522i | −0.801786 | − | 0.597612i | \(-0.796116\pi\) | ||||
0.801786 | − | 0.597612i | \(-0.203884\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8197.62 | −0.772704 | −0.386352 | − | 0.922351i | \(-0.626265\pi\) | ||||
−0.386352 | + | 0.922351i | \(0.626265\pi\) | |||||||
\(104\) | 2579.13i | 0.238455i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8277.31 | 0.736678 | ||||||||
\(107\) | − 21177.8i | − 1.84975i | −0.380270 | − | 0.924876i | \(-0.624169\pi\) | ||||
0.380270 | − | 0.924876i | \(-0.375831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14536.2 | 1.22348 | 0.611740 | − | 0.791059i | \(-0.290470\pi\) | ||||
0.611740 | + | 0.791059i | \(0.290470\pi\) | |||||||
\(110\) | − 3042.12i | − 0.251415i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3148.49 | 0.250996 | ||||||||
\(113\) | − 8890.90i | − 0.696288i | −0.937441 | − | 0.348144i | \(-0.886812\pi\) | ||||
0.937441 | − | 0.348144i | \(-0.113188\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3501.36 | −0.264753 | ||||||||
\(116\) | 9018.89i | 0.670251i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −369.951 | −0.0265693 | ||||||||
\(119\) | − 17289.8i | − 1.22094i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5386.53 | 0.367907 | ||||||||
\(122\) | − 15922.7i | − 1.06979i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2724.25 | −0.177175 | ||||||||
\(125\) | − 1397.54i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13893.3 | 0.861385 | 0.430692 | − | 0.902499i | \(-0.358269\pi\) | ||||
0.430692 | + | 0.902499i | \(0.358269\pi\) | |||||||
\(128\) | − 1448.15i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3604.45 | 0.213281 | ||||||||
\(131\) | − 3299.12i | − 0.192245i | −0.995370 | − | 0.0961225i | \(-0.969356\pi\) | ||||
0.995370 | − | 0.0961225i | \(-0.0306440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12460.2 | −0.704407 | ||||||||
\(134\) | 7552.14i | 0.420591i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7952.47 | −0.429956 | ||||||||
\(137\) | − 24473.9i | − 1.30395i | −0.758239 | − | 0.651976i | \(-0.773940\pi\) | ||||
0.758239 | − | 0.651976i | \(-0.226060\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17136.1 | −0.886914 | −0.443457 | − | 0.896296i | \(-0.646248\pi\) | ||||
−0.443457 | + | 0.896296i | \(0.646248\pi\) | |||||||
\(140\) | − 4400.15i | − 0.224497i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6448.58 | 0.319806 | ||||||||
\(143\) | − 10965.1i | − 0.536219i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12604.3 | 0.599490 | ||||||||
\(146\) | − 22755.8i | − 1.06755i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −607.702 | −0.0277439 | ||||||||
\(149\) | − 17433.2i | − 0.785243i | −0.919700 | − | 0.392622i | \(-0.871568\pi\) | ||||
0.919700 | − | 0.392622i | \(-0.128432\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5464.62 | −0.239666 | −0.119833 | − | 0.992794i | \(-0.538236\pi\) | ||||
−0.119833 | + | 0.992794i | \(0.538236\pi\) | |||||||
\(152\) | 5731.12i | 0.248058i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13385.8 | −0.564419 | ||||||||
\(155\) | 3807.25i | 0.158471i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −42494.7 | −1.72399 | −0.861996 | − | 0.506915i | \(-0.830786\pi\) | ||||
−0.861996 | + | 0.506915i | \(0.830786\pi\) | |||||||
\(158\) | − 23816.0i | − 0.954013i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2023.86 | −0.0790569 | ||||||||
\(161\) | 15406.5i | 0.594363i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12868.0 | −0.484323 | −0.242162 | − | 0.970236i | \(-0.577856\pi\) | ||||
−0.242162 | + | 0.970236i | \(0.577856\pi\) | |||||||
\(164\) | − 9156.88i | − 0.340455i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −35862.5 | −1.30144 | ||||||||
\(167\) | − 33203.2i | − 1.19055i | −0.803522 | − | 0.595275i | \(-0.797043\pi\) | ||||
0.803522 | − | 0.595275i | \(-0.202957\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15569.0 | −0.545113 | ||||||||
\(170\) | 11113.9i | 0.384564i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 20728.1 | 0.700653 | ||||||||
\(173\) | 27039.6i | 0.903457i | 0.892156 | + | 0.451728i | \(0.149192\pi\) | ||||
−0.892156 | + | 0.451728i | \(0.850808\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6149.39 | −0.200796 | ||||||||
\(176\) | 6156.81i | 0.198761i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 30334.3 | 0.957401 | ||||||||
\(179\) | 50554.7i | 1.57781i | 0.614513 | + | 0.788906i | \(0.289352\pi\) | ||||
−0.614513 | + | 0.788906i | \(0.710648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4462.41 | −0.136211 | −0.0681054 | − | 0.997678i | \(-0.521695\pi\) | ||||
−0.0681054 | + | 0.997678i | \(0.521695\pi\) | |||||||
\(182\) | − 15860.1i | − 0.478810i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7086.25 | 0.209306 | ||||||||
\(185\) | 849.289i | 0.0248149i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 33809.8 | 0.966851 | ||||||||
\(188\) | − 28466.3i | − 0.805407i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8009.49 | 0.221869 | ||||||||
\(191\) | − 4764.36i | − 0.130598i | −0.997866 | − | 0.0652992i | \(-0.979200\pi\) | ||||
0.997866 | − | 0.0652992i | \(-0.0208002\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 62069.6 | 1.66634 | 0.833172 | − | 0.553015i | \(-0.186523\pi\) | ||||
0.833172 | + | 0.553015i | \(0.186523\pi\) | |||||||
\(194\) | 33158.4i | 0.881029i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −153.278 | −0.00398996 | ||||||||
\(197\) | − 30470.8i | − 0.785148i | −0.919720 | − | 0.392574i | \(-0.871585\pi\) | ||||
0.919720 | − | 0.392574i | \(-0.128415\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26636.9 | 0.672632 | 0.336316 | − | 0.941749i | \(-0.390819\pi\) | ||||
0.336316 | + | 0.941749i | \(0.390819\pi\) | |||||||
\(200\) | 2828.43i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 34485.5 | 0.845150 | ||||||||
\(203\) | − 55460.7i | − 1.34584i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12797.1 | −0.304512 | ||||||||
\(206\) | − 23186.4i | − 0.546384i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −7294.89 | −0.168613 | ||||||||
\(209\) | − 24365.8i | − 0.557812i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −78677.0 | −1.76719 | −0.883594 | − | 0.468253i | \(-0.844884\pi\) | ||||
−0.883594 | + | 0.468253i | \(0.844884\pi\) | |||||||
\(212\) | 23411.8i | 0.520910i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 59899.9 | 1.30797 | ||||||||
\(215\) | − 28968.4i | − 0.626684i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16752.5 | 0.355762 | ||||||||
\(218\) | 41114.5i | 0.865132i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 8604.40 | 0.177777 | ||||||||
\(221\) | 40059.5i | 0.820202i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −85807.7 | −1.72551 | −0.862753 | − | 0.505626i | \(-0.831262\pi\) | ||||
−0.862753 | + | 0.505626i | \(0.831262\pi\) | |||||||
\(224\) | 8905.27i | 0.177481i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 25147.3 | 0.492350 | ||||||||
\(227\) | − 37252.2i | − 0.722936i | −0.932384 | − | 0.361468i | \(-0.882276\pi\) | ||||
0.932384 | − | 0.361468i | \(-0.117724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21434.6 | 0.408737 | 0.204369 | − | 0.978894i | \(-0.434486\pi\) | ||||
0.204369 | + | 0.978894i | \(0.434486\pi\) | |||||||
\(230\) | − 9903.34i | − 0.187209i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −25509.3 | −0.473939 | ||||||||
\(233\) | − 31750.4i | − 0.584840i | −0.956290 | − | 0.292420i | \(-0.905540\pi\) | ||||
0.956290 | − | 0.292420i | \(-0.0944605\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −39782.9 | −0.720378 | ||||||||
\(236\) | − 1046.38i | − 0.0187873i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 48902.8 | 0.863336 | ||||||||
\(239\) | − 61678.6i | − 1.07979i | −0.841733 | − | 0.539894i | \(-0.818464\pi\) | ||||
0.841733 | − | 0.539894i | \(-0.181536\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 70047.7 | 1.20604 | 0.603018 | − | 0.797728i | \(-0.293965\pi\) | ||||
0.603018 | + | 0.797728i | \(0.293965\pi\) | |||||||
\(242\) | 15235.4i | 0.260150i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 45036.3 | 0.756456 | ||||||||
\(245\) | 214.213i | 0.00356872i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 28869.8 | 0.473205 | ||||||||
\(248\) | − 7705.34i | − 0.125282i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3952.85 | 0.0632456 | ||||||||
\(251\) | − 91245.1i | − 1.44831i | −0.689636 | − | 0.724156i | \(-0.742229\pi\) | ||||
0.689636 | − | 0.724156i | \(-0.257771\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30127.1 | −0.470670 | ||||||||
\(254\) | 39296.1i | 0.609091i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 52399.4i | 0.793341i | 0.917961 | + | 0.396671i | \(0.129835\pi\) | ||||
−0.917961 | + | 0.396671i | \(0.870165\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3737.00 | 0.0557087 | ||||||||
\(260\) | 10194.9i | 0.150812i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 9331.31 | 0.135938 | ||||||||
\(263\) | 30655.0i | 0.443189i | 0.975139 | + | 0.221595i | \(0.0711262\pi\) | ||||
−0.975139 | + | 0.221595i | \(0.928874\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32719.0 | 0.465916 | ||||||||
\(266\) | − 35242.9i | − 0.498091i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21360.7 | −0.297403 | ||||||||
\(269\) | − 7299.68i | − 0.100879i | −0.998727 | − | 0.0504393i | \(-0.983938\pi\) | ||||
0.998727 | − | 0.0504393i | \(-0.0160621\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −48800.5 | −0.664486 | −0.332243 | − | 0.943194i | \(-0.607805\pi\) | ||||
−0.332243 | + | 0.943194i | \(0.607805\pi\) | |||||||
\(272\) | − 22493.0i | − 0.304025i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 69222.6 | 0.922034 | ||||||||
\(275\) | − 12025.0i | − 0.159009i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18302.9 | 0.238539 | 0.119270 | − | 0.992862i | \(-0.461945\pi\) | ||||
0.119270 | + | 0.992862i | \(0.461945\pi\) | |||||||
\(278\) | − 48468.1i | − 0.627143i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12445.5 | 0.158743 | ||||||||
\(281\) | − 47262.4i | − 0.598554i | −0.954166 | − | 0.299277i | \(-0.903255\pi\) | ||||
0.954166 | − | 0.299277i | \(-0.0967454\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 116677. | 1.45684 | 0.728420 | − | 0.685131i | \(-0.240255\pi\) | ||||
0.728420 | + | 0.685131i | \(0.240255\pi\) | |||||||
\(284\) | 18239.3i | 0.226137i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 31014.1 | 0.379164 | ||||||||
\(287\) | 56309.2i | 0.683622i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −39998.0 | −0.478897 | ||||||||
\(290\) | 35650.3i | 0.423904i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 64363.2 | 0.754869 | ||||||||
\(293\) | − 24486.2i | − 0.285224i | −0.989779 | − | 0.142612i | \(-0.954450\pi\) | ||||
0.989779 | − | 0.142612i | \(-0.0455501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1462.36 | −0.0168039 | ||||||||
\(296\) | − 1718.84i | − 0.0196179i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 49308.5 | 0.555251 | ||||||||
\(299\) | − 35696.1i | − 0.399280i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −127465. | −1.40689 | ||||||||
\(302\) | − 15456.3i | − 0.169469i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16210.1 | −0.175403 | ||||||||
\(305\) | − 62940.2i | − 0.676594i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −103102. | −1.09394 | −0.546968 | − | 0.837154i | \(-0.684218\pi\) | ||||
−0.546968 | + | 0.837154i | \(0.684218\pi\) | |||||||
\(308\) | − 37860.6i | − 0.399104i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10768.5 | −0.112056 | ||||||||
\(311\) | 88795.7i | 0.918060i | 0.888421 | + | 0.459030i | \(0.151803\pi\) | ||||
−0.888421 | + | 0.459030i | \(0.848197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −69209.6 | −0.706444 | −0.353222 | − | 0.935540i | \(-0.614914\pi\) | ||||
−0.353222 | + | 0.935540i | \(0.614914\pi\) | |||||||
\(314\) | − 120193.i | − 1.21905i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 67361.8 | 0.674589 | ||||||||
\(317\) | − 126817.i | − 1.26200i | −0.775783 | − | 0.630999i | \(-0.782645\pi\) | ||||
0.775783 | − | 0.630999i | \(-0.217355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 108452. | 1.06576 | ||||||||
\(320\) | − 5724.33i | − 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −43576.1 | −0.420278 | ||||||||
\(323\) | 89016.7i | 0.853231i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14247.8 | 0.134891 | ||||||||
\(326\) | − 36396.2i | − 0.342468i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 25899.6 | 0.240738 | ||||||||
\(329\) | 175050.i | 1.61723i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 76584.8 | 0.699015 | 0.349508 | − | 0.936934i | \(-0.386349\pi\) | ||||
0.349508 | + | 0.936934i | \(0.386349\pi\) | |||||||
\(332\) | − 101434.i | − 0.920258i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 93912.9 | 0.841845 | ||||||||
\(335\) | 29852.5i | 0.266005i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −141729. | −1.24795 | −0.623977 | − | 0.781443i | \(-0.714484\pi\) | ||||
−0.623977 | + | 0.781443i | \(0.714484\pi\) | |||||||
\(338\) | − 44035.7i | − 0.385453i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −31434.9 | −0.271928 | ||||||||
\(341\) | 32759.2i | 0.281724i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117175. | −0.995970 | ||||||||
\(344\) | 58628.0i | 0.495437i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −76479.4 | −0.638840 | ||||||||
\(347\) | − 118472.i | − 0.983916i | −0.870619 | − | 0.491958i | \(-0.836281\pi\) | ||||
0.870619 | − | 0.491958i | \(-0.163719\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 85526.1 | 0.702179 | 0.351089 | − | 0.936342i | \(-0.385811\pi\) | ||||
0.351089 | + | 0.936342i | \(0.385811\pi\) | |||||||
\(350\) | − 17393.1i | − 0.141984i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −17414.1 | −0.140545 | ||||||||
\(353\) | 149927.i | 1.20318i | 0.798805 | + | 0.601590i | \(0.205466\pi\) | ||||
−0.798805 | + | 0.601590i | \(0.794534\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25490.2 | 0.202263 | ||||||||
\(356\) | 85798.4i | 0.676985i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −142990. | −1.11568 | ||||||||
\(359\) | 61273.8i | 0.475429i | 0.971335 | + | 0.237715i | \(0.0763983\pi\) | ||||
−0.971335 | + | 0.237715i | \(0.923602\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −66169.1 | −0.507739 | ||||||||
\(362\) | − 12621.6i | − 0.0963156i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 44859.1 | 0.338570 | ||||||||
\(365\) | − 89950.3i | − 0.675176i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8152.67 | 0.0605296 | 0.0302648 | − | 0.999542i | \(-0.490365\pi\) | ||||
0.0302648 | + | 0.999542i | \(0.490365\pi\) | |||||||
\(368\) | 20042.9i | 0.148001i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2402.15 | −0.0175468 | ||||||||
\(371\) | − 143968.i | − 1.04597i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −224482. | −1.61348 | −0.806741 | − | 0.590905i | \(-0.798771\pi\) | ||||
−0.806741 | + | 0.590905i | \(0.798771\pi\) | |||||||
\(374\) | 95628.6i | 0.683667i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 80514.9 | 0.569509 | ||||||||
\(377\) | 128500.i | 0.904106i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20153.1 | −0.140302 | −0.0701509 | − | 0.997536i | \(-0.522348\pi\) | ||||
−0.0701509 | + | 0.997536i | \(0.522348\pi\) | |||||||
\(380\) | 22654.3i | 0.156885i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 13475.7 | 0.0923471 | ||||||||
\(383\) | 63325.6i | 0.431700i | 0.976427 | + | 0.215850i | \(0.0692522\pi\) | ||||
−0.976427 | + | 0.215850i | \(0.930748\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −52911.8 | −0.356970 | ||||||||
\(386\) | 175559.i | 1.17828i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −93786.1 | −0.622982 | ||||||||
\(389\) | 194066.i | 1.28248i | 0.767342 | + | 0.641239i | \(0.221579\pi\) | ||||
−0.767342 | + | 0.641239i | \(0.778421\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 110065. | 0.719937 | ||||||||
\(392\) | − 433.536i | − 0.00282132i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 86184.5 | 0.555184 | ||||||||
\(395\) | − 94141.0i | − 0.603371i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 66142.9 | 0.419665 | 0.209832 | − | 0.977737i | \(-0.432708\pi\) | ||||
0.209832 | + | 0.977737i | \(0.432708\pi\) | |||||||
\(398\) | 75340.5i | 0.475623i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8000.00 | −0.0500000 | ||||||||
\(401\) | 290480.i | 1.80645i | 0.429163 | + | 0.903227i | \(0.358809\pi\) | ||||
−0.429163 | + | 0.903227i | \(0.641191\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −38814.6 | −0.238993 | ||||||||
\(404\) | 97539.8i | 0.597612i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 156866. | 0.951652 | ||||||||
\(407\) | 7307.63i | 0.0441151i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −223523. | −1.33622 | −0.668108 | − | 0.744064i | \(-0.732896\pi\) | ||||
−0.668108 | + | 0.744064i | \(0.732896\pi\) | |||||||
\(410\) | − 36195.7i | − 0.215323i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 65580.9 | 0.386352 | ||||||||
\(413\) | 6434.60i | 0.0377243i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −141759. | −0.823104 | ||||||||
\(416\) | − 20633.1i | − 0.119228i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 68916.9 | 0.394433 | ||||||||
\(419\) | − 111993.i | − 0.637914i | −0.947769 | − | 0.318957i | \(-0.896668\pi\) | ||||
0.947769 | − | 0.318957i | \(-0.103332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −300299. | −1.69430 | −0.847148 | − | 0.531358i | \(-0.821682\pi\) | ||||
−0.847148 | + | 0.531358i | \(0.821682\pi\) | |||||||
\(422\) | − 222532.i | − 1.24959i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −66218.5 | −0.368339 | ||||||||
\(425\) | 43931.6i | 0.243220i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −276946. | −1.51894 | ||||||||
\(428\) | 169422.i | 0.924876i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 81935.1 | 0.443132 | ||||||||
\(431\) | 306017.i | 1.64737i | 0.567048 | + | 0.823685i | \(0.308085\pi\) | ||||
−0.567048 | + | 0.823685i | \(0.691915\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 253079. | 1.34984 | 0.674918 | − | 0.737893i | \(-0.264179\pi\) | ||||
0.674918 | + | 0.737893i | \(0.264179\pi\) | |||||||
\(434\) | 47383.1i | 0.251562i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −116289. | −0.611740 | ||||||||
\(437\) | − 79320.6i | − 0.415359i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 269111. | 1.39638 | 0.698189 | − | 0.715914i | \(-0.253990\pi\) | ||||
0.698189 | + | 0.715914i | \(0.253990\pi\) | |||||||
\(440\) | 24336.9i | 0.125707i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −113305. | −0.579971 | ||||||||
\(443\) | 202671.i | 1.03272i | 0.856371 | + | 0.516361i | \(0.172714\pi\) | ||||
−0.856371 | + | 0.516361i | \(0.827286\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 119907. | 0.605514 | ||||||||
\(446\) | − 242701.i | − 1.22012i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −25187.9 | −0.125498 | ||||||||
\(449\) | 76904.0i | 0.381466i | 0.981642 | + | 0.190733i | \(0.0610865\pi\) | ||||
−0.981642 | + | 0.190733i | \(0.938914\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −110112. | −0.541353 | ||||||||
\(452\) | 71127.2i | 0.348144i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 105365. | 0.511193 | ||||||||
\(455\) | − 62692.5i | − 0.302826i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −220998. | −1.05817 | −0.529085 | − | 0.848569i | \(-0.677465\pi\) | ||||
−0.529085 | + | 0.848569i | \(0.677465\pi\) | |||||||
\(458\) | 60626.2i | 0.289021i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 28010.9 | 0.132376 | ||||||||
\(461\) | 43395.3i | 0.204193i | 0.994775 | + | 0.102096i | \(0.0325550\pi\) | ||||
−0.994775 | + | 0.102096i | \(0.967445\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 77526.9 | 0.361652 | 0.180826 | − | 0.983515i | \(-0.442123\pi\) | ||||
0.180826 | + | 0.983515i | \(0.442123\pi\) | |||||||
\(464\) | − 72151.1i | − 0.335125i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 89803.6 | 0.413544 | ||||||||
\(467\) | 144596.i | 0.663015i | 0.943453 | + | 0.331507i | \(0.107557\pi\) | ||||
−0.943453 | + | 0.331507i | \(0.892443\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 131355. | 0.597175 | ||||||||
\(470\) | − 112523.i | − 0.509384i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2959.61 | 0.0132847 | ||||||||
\(473\) | − 249256.i | − 1.11410i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 31660.3 | 0.140323 | ||||||||
\(476\) | 138318.i | 0.610471i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 174453. | 0.763525 | ||||||||
\(479\) | 136132.i | 0.593322i | 0.954983 | + | 0.296661i | \(0.0958731\pi\) | ||||
−0.954983 | + | 0.296661i | \(0.904127\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8658.43 | −0.0374239 | ||||||||
\(482\) | 198125.i | 0.852796i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −43092.2 | −0.183954 | ||||||||
\(485\) | 131070.i | 0.557212i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −42708.6 | −0.180077 | −0.0900384 | − | 0.995938i | \(-0.528699\pi\) | ||||
−0.0900384 | + | 0.995938i | \(0.528699\pi\) | |||||||
\(488\) | 127382.i | 0.534895i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −605.885 | −0.00252347 | ||||||||
\(491\) | − 154556.i | − 0.641094i | −0.947233 | − | 0.320547i | \(-0.896133\pi\) | ||||
0.947233 | − | 0.320547i | \(-0.103867\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −396214. | −1.63018 | ||||||||
\(494\) | 81656.1i | 0.334607i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21794.0 | 0.0885877 | ||||||||
\(497\) | − 112161.i | − 0.454076i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 51859.2 | 0.208269 | 0.104134 | − | 0.994563i | \(-0.466793\pi\) | ||||
0.104134 | + | 0.994563i | \(0.466793\pi\) | |||||||
\(500\) | 11180.3i | 0.0447214i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 258080. | 1.02411 | ||||||||
\(503\) | 334798.i | 1.32327i | 0.749828 | + | 0.661633i | \(0.230136\pi\) | ||||
−0.749828 | + | 0.661633i | \(0.769864\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 136316. | 0.534520 | ||||||||
\(506\) | − 85212.3i | − 0.332814i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −111146. | −0.430692 | ||||||||
\(509\) | 173371.i | 0.669178i | 0.942364 | + | 0.334589i | \(0.108597\pi\) | ||||
−0.942364 | + | 0.334589i | \(0.891403\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −395794. | −1.51575 | ||||||||
\(512\) | 11585.2i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −148208. | −0.560977 | ||||||||
\(515\) | − 91652.1i | − 0.345564i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −342308. | −1.28067 | ||||||||
\(518\) | 10569.8i | 0.0393920i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −28835.6 | −0.106640 | ||||||||
\(521\) | − 200698.i | − 0.739379i | −0.929155 | − | 0.369690i | \(-0.879464\pi\) | ||||
0.929155 | − | 0.369690i | \(-0.120536\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −303311. | −1.10888 | −0.554441 | − | 0.832223i | \(-0.687068\pi\) | ||||
−0.554441 | + | 0.832223i | \(0.687068\pi\) | |||||||
\(524\) | 26392.9i | 0.0961225i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −86705.4 | −0.313382 | ||||||||
\(527\) | − 119681.i | − 0.430926i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 181765. | 0.649529 | ||||||||
\(530\) | 92543.2i | 0.329452i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 99682.0 | 0.352203 | ||||||||
\(533\) | − 130466.i | − 0.459242i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 236775. | 0.827234 | ||||||||
\(536\) | − 60417.1i | − 0.210296i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20646.6 | 0.0713320 | ||||||||
\(539\) | 1843.17i | 0.00634437i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −127347. | −0.435104 | −0.217552 | − | 0.976049i | \(-0.569807\pi\) | ||||
−0.217552 | + | 0.976049i | \(0.569807\pi\) | |||||||
\(542\) | − 138029.i | − 0.469863i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 63619.7 | 0.214978 | ||||||||
\(545\) | 162519.i | 0.547157i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37960.8 | 0.126870 | 0.0634352 | − | 0.997986i | \(-0.479794\pi\) | ||||
0.0634352 | + | 0.997986i | \(0.479794\pi\) | |||||||
\(548\) | 195791.i | 0.651976i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 34011.9 | 0.112436 | ||||||||
\(551\) | 285541.i | 0.940513i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −414234. | −1.35455 | ||||||||
\(554\) | 51768.4i | 0.168673i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 137088. | 0.443457 | ||||||||
\(557\) | − 309520.i | − 0.997651i | −0.866703 | − | 0.498825i | \(-0.833765\pi\) | ||||
0.866703 | − | 0.498825i | \(-0.166235\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 295331. | 0.945116 | ||||||||
\(560\) | 35201.2i | 0.112249i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 133678. | 0.423241 | ||||||||
\(563\) | 581536.i | 1.83468i | 0.398108 | + | 0.917338i | \(0.369667\pi\) | ||||
−0.398108 | + | 0.917338i | \(0.630333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 99403.3 | 0.311389 | ||||||||
\(566\) | 330012.i | 1.03014i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −51588.6 | −0.159903 | ||||||||
\(569\) | 259660.i | 0.802013i | 0.916075 | + | 0.401006i | \(0.131339\pi\) | ||||
−0.916075 | + | 0.401006i | \(0.868661\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13162.2 | 0.0403697 | 0.0201848 | − | 0.999796i | \(-0.493575\pi\) | ||||
0.0201848 | + | 0.999796i | \(0.493575\pi\) | |||||||
\(572\) | 87721.2i | 0.268110i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −159267. | −0.483393 | ||||||||
\(575\) | − 39146.4i | − 0.118401i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 323202. | 0.970784 | 0.485392 | − | 0.874297i | \(-0.338677\pi\) | ||||
0.485392 | + | 0.874297i | \(0.338677\pi\) | |||||||
\(578\) | − 113131.i | − 0.338631i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −100834. | −0.299745 | ||||||||
\(581\) | 623760.i | 1.84784i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 281527. | 0.828291 | ||||||||
\(584\) | 182047.i | 0.533773i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 69257.4 | 0.201684 | ||||||||
\(587\) | 292720.i | 0.849525i | 0.905305 | + | 0.424763i | \(0.139642\pi\) | ||||
−0.905305 | + | 0.424763i | \(0.860358\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −86250.5 | −0.248617 | ||||||||
\(590\) | − 4136.18i | − 0.0118822i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4861.61 | 0.0138719 | ||||||||
\(593\) | − 328987.i | − 0.935554i | −0.883847 | − | 0.467777i | \(-0.845055\pi\) | ||||
0.883847 | − | 0.467777i | \(-0.154945\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 193305. | 0.546022 | ||||||||
\(596\) | 139465.i | 0.392622i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 100964. | 0.282334 | ||||||||
\(599\) | 250539.i | 0.698266i | 0.937073 | + | 0.349133i | \(0.113524\pi\) | ||||
−0.937073 | + | 0.349133i | \(0.886476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 363868. | 1.00738 | 0.503692 | − | 0.863883i | \(-0.331975\pi\) | ||||
0.503692 | + | 0.863883i | \(0.331975\pi\) | |||||||
\(602\) | − 360527.i | − 0.994819i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 43717.0 | 0.119833 | ||||||||
\(605\) | 60223.2i | 0.164533i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 319447. | 0.867005 | 0.433503 | − | 0.901152i | \(-0.357277\pi\) | ||||
0.433503 | + | 0.901152i | \(0.357277\pi\) | |||||||
\(608\) | − 45849.0i | − 0.124029i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 178022. | 0.478424 | ||||||||
\(611\) | − 405583.i | − 1.08642i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −604584. | −1.60892 | −0.804462 | − | 0.594003i | \(-0.797547\pi\) | ||||
−0.804462 | + | 0.594003i | \(0.797547\pi\) | |||||||
\(614\) | − 291618.i | − 0.773529i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 107086. | 0.282209 | ||||||||
\(617\) | 26.7317i | 0 7.02193e-5i | 1.00000 | 3.51097e-5i | \(1.11758e-5\pi\) | |||||
−1.00000 | 3.51097e-5i | \(0.999989\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 115824. | 0.302285 | 0.151143 | − | 0.988512i | \(-0.451705\pi\) | ||||
0.151143 | + | 0.988512i | \(0.451705\pi\) | |||||||
\(620\) | − 30458.0i | − 0.0792353i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −251152. | −0.649167 | ||||||||
\(623\) | − 527608.i | − 1.35936i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | − 195754.i | − 0.499531i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 339957. | 0.861996 | ||||||||
\(629\) | − 26697.3i | − 0.0674786i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −284115. | −0.713568 | −0.356784 | − | 0.934187i | \(-0.616127\pi\) | ||||
−0.356784 | + | 0.934187i | \(0.616127\pi\) | |||||||
\(632\) | 190528.i | 0.477007i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 358693. | 0.892368 | ||||||||
\(635\) | 155331.i | 0.385223i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2183.88 | −0.00538208 | ||||||||
\(638\) | 306750.i | 0.753603i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16190.9 | 0.0395285 | ||||||||
\(641\) | 87886.0i | 0.213896i | 0.994265 | + | 0.106948i | \(0.0341079\pi\) | ||||
−0.994265 | + | 0.106948i | \(0.965892\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −70340.7 | −0.170132 | −0.0850658 | − | 0.996375i | \(-0.527110\pi\) | ||||
−0.0850658 | + | 0.996375i | \(0.527110\pi\) | |||||||
\(644\) | − 123252.i | − 0.297181i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −251777. | −0.603325 | ||||||||
\(647\) | 251015.i | 0.599640i | 0.953996 | + | 0.299820i | \(0.0969266\pi\) | ||||
−0.953996 | + | 0.299820i | \(0.903073\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12582.7 | −0.0298735 | ||||||||
\(650\) | 40298.9i | 0.0953821i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 102944. | 0.242162 | ||||||||
\(653\) | − 23838.5i | − 0.0559052i | −0.999609 | − | 0.0279526i | \(-0.991101\pi\) | ||||
0.999609 | − | 0.0279526i | \(-0.00889874\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36885.2 | 0.0859746 | ||||||||
\(656\) | 73255.0i | 0.170228i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −495117. | −1.14355 | ||||||||
\(659\) | 374084.i | 0.861386i | 0.902498 | + | 0.430693i | \(0.141731\pi\) | ||||
−0.902498 | + | 0.430693i | \(0.858269\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 829840. | 1.89929 | 0.949645 | − | 0.313327i | \(-0.101443\pi\) | ||||
0.949645 | + | 0.313327i | \(0.101443\pi\) | |||||||
\(662\) | 216615.i | 0.494278i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 286900. | 0.650721 | ||||||||
\(665\) | − 139310.i | − 0.315020i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 353057. | 0.793584 | ||||||||
\(668\) | 265626.i | 0.595275i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −84435.5 | −0.188094 | ||||||||
\(671\) | − 541563.i | − 1.20283i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −476337. | −1.05168 | −0.525841 | − | 0.850583i | \(-0.676249\pi\) | ||||
−0.525841 | + | 0.850583i | \(0.676249\pi\) | |||||||
\(674\) | − 400870.i | − 0.882436i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 124552. | 0.272556 | ||||||||
\(677\) | − 151782.i | − 0.331164i | −0.986196 | − | 0.165582i | \(-0.947050\pi\) | ||||
0.986196 | − | 0.165582i | \(-0.0529503\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 576728. | 1.25092 | ||||||||
\(680\) | − 88911.3i | − 0.192282i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −92656.9 | −0.199209 | ||||||||
\(683\) | − 711647.i | − 1.52554i | −0.646670 | − | 0.762770i | \(-0.723839\pi\) | ||||
0.646670 | − | 0.762770i | \(-0.276161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 273626. | 0.583145 | ||||||||
\(686\) | − 331421.i | − 0.704257i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −165825. | −0.350327 | ||||||||
\(689\) | 333567.i | 0.702659i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −348157. | −0.729153 | −0.364577 | − | 0.931173i | \(-0.618786\pi\) | ||||
−0.364577 | + | 0.931173i | \(0.618786\pi\) | |||||||
\(692\) | − 216316.i | − 0.451728i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 335090. | 0.695733 | ||||||||
\(695\) | − 191587.i | − 0.396640i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 402276. | 0.828054 | ||||||||
\(698\) | 241904.i | 0.496515i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 49195.1 | 0.100398 | ||||||||
\(701\) | − 702624.i | − 1.42984i | −0.699207 | − | 0.714920i | \(-0.746463\pi\) | ||||
0.699207 | − | 0.714920i | \(-0.253537\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −19240.0 | −0.0389309 | ||||||||
\(704\) | − 49254.5i | − 0.0993803i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −424057. | −0.850776 | ||||||||
\(707\) | − 599810.i | − 1.19998i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −855514. | −1.70190 | −0.850951 | − | 0.525244i | \(-0.823974\pi\) | ||||
−0.850951 | + | 0.525244i | \(0.823974\pi\) | |||||||
\(710\) | 72097.3i | 0.143022i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −242674. | −0.478701 | ||||||||
\(713\) | 106644.i | 0.209778i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 122594. | 0.239805 | ||||||||
\(716\) | − 404438.i | − 0.788906i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −173308. | −0.336179 | ||||||||
\(719\) | 628845.i | 1.21643i | 0.793774 | + | 0.608213i | \(0.208114\pi\) | ||||
−0.793774 | + | 0.608213i | \(0.791886\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −403283. | −0.775781 | ||||||||
\(722\) | − 187154.i | − 0.359026i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 35699.2 | 0.0681054 | ||||||||
\(725\) | 140920.i | 0.268100i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −528399. | −0.999754 | −0.499877 | − | 0.866096i | \(-0.666621\pi\) | ||||
−0.499877 | + | 0.866096i | \(0.666621\pi\) | |||||||
\(728\) | 126881.i | 0.239405i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 254418. | 0.477421 | ||||||||
\(731\) | 910620.i | 1.70413i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −897234. | −1.66993 | −0.834964 | − | 0.550304i | \(-0.814512\pi\) | ||||
−0.834964 | + | 0.550304i | \(0.814512\pi\) | |||||||
\(734\) | 23059.2i | 0.0428009i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −56690.0 | −0.104653 | ||||||||
\(737\) | 256863.i | 0.472896i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 592410. | 1.08476 | 0.542380 | − | 0.840133i | \(-0.317523\pi\) | ||||
0.542380 | + | 0.840133i | \(0.317523\pi\) | |||||||
\(740\) | − 6794.31i | − 0.0124074i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 407203. | 0.739611 | ||||||||
\(743\) | − 409669.i | − 0.742088i | −0.928615 | − | 0.371044i | \(-0.879000\pi\) | ||||
0.928615 | − | 0.371044i | \(-0.121000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 194909. | 0.351171 | ||||||||
\(746\) | − 634931.i | − 1.14090i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −270478. | −0.483425 | ||||||||
\(749\) | − 1.04184e6i | − 1.85712i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 878893. | 1.55832 | 0.779159 | − | 0.626826i | \(-0.215646\pi\) | ||||
0.779159 | + | 0.626826i | \(0.215646\pi\) | |||||||
\(752\) | 227730.i | 0.402703i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −363452. | −0.639299 | ||||||||
\(755\) | − 61096.4i | − 0.107182i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −497041. | −0.867362 | −0.433681 | − | 0.901066i | \(-0.642786\pi\) | ||||
−0.433681 | + | 0.901066i | \(0.642786\pi\) | |||||||
\(758\) | − 57001.6i | − 0.0992084i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −64075.9 | −0.110935 | ||||||||
\(761\) | 73857.1i | 0.127533i | 0.997965 | + | 0.0637665i | \(0.0203113\pi\) | ||||
−0.997965 | + | 0.0637665i | \(0.979689\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 715109. | 1.22835 | ||||||||
\(764\) | 38114.9i | 0.0652992i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −179112. | −0.305258 | ||||||||
\(767\) | − 14908.6i | − 0.0253424i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 540707. | 0.914343 | 0.457172 | − | 0.889379i | \(-0.348863\pi\) | ||||
0.457172 | + | 0.889379i | \(0.348863\pi\) | |||||||
\(770\) | − 149657.i | − 0.252416i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −496557. | −0.833172 | ||||||||
\(773\) | 23921.3i | 0.0400337i | 0.999800 | + | 0.0200169i | \(0.00637199\pi\) | ||||
−0.999800 | + | 0.0200169i | \(0.993628\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42566.4 | −0.0708702 | ||||||||
\(776\) | − 265267.i | − 0.440514i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −548901. | −0.906848 | ||||||||
\(779\) | − 289909.i | − 0.477735i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 219328. | 0.359578 | ||||||||
\(782\) | 311310.i | 0.509073i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1226.23 | 0.00199498 | ||||||||
\(785\) | − 475105.i | − 0.770993i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 236097. | 0.381190 | 0.190595 | − | 0.981669i | \(-0.438958\pi\) | ||||
0.190595 | + | 0.981669i | \(0.438958\pi\) | |||||||
\(788\) | 243767.i | 0.392574i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 266271. | 0.426648 | ||||||||
\(791\) | − 437389.i | − 0.699060i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 641670. | 1.02039 | ||||||||
\(794\) | 187080.i | 0.296748i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −213095. | −0.336316 | ||||||||
\(797\) | − 1.02477e6i | − 1.61329i | −0.591039 | − | 0.806643i | \(-0.701282\pi\) | ||||
0.591039 | − | 0.806643i | \(-0.298718\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.25057e6 | 1.95891 | ||||||||
\(800\) | − 22627.4i | − 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −821601. | −1.27736 | ||||||||
\(803\) | − 773968.i | − 1.20031i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −172250. | −0.265807 | ||||||||
\(806\) | − 109784.i | − 0.168994i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −275884. | −0.422575 | ||||||||
\(809\) | 880763.i | 1.34574i | 0.739759 | + | 0.672871i | \(0.234939\pi\) | ||||
−0.739759 | + | 0.672871i | \(0.765061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 946858. | 1.43960 | 0.719802 | − | 0.694179i | \(-0.244232\pi\) | ||||
0.719802 | + | 0.694179i | \(0.244232\pi\) | |||||||
\(812\) | 443685.i | 0.672919i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20669.1 | −0.0311941 | ||||||||
\(815\) | − 143868.i | − 0.216596i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 656258. | 0.983175 | ||||||||
\(818\) | − 632220.i | − 0.944847i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 102377. | 0.152256 | ||||||||
\(821\) | 890064.i | 1.32049i | 0.751050 | + | 0.660245i | \(0.229548\pi\) | ||||
−0.751050 | + | 0.660245i | \(0.770452\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −543081. | −0.801798 | −0.400899 | − | 0.916122i | \(-0.631302\pi\) | ||||
−0.400899 | + | 0.916122i | \(0.631302\pi\) | |||||||
\(824\) | 185491.i | 0.273192i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18199.8 | −0.0266751 | ||||||||
\(827\) | 177655.i | 0.259756i | 0.991530 | + | 0.129878i | \(0.0414586\pi\) | ||||
−0.991530 | + | 0.129878i | \(0.958541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 743143. | 1.08134 | 0.540672 | − | 0.841234i | \(-0.318170\pi\) | ||||
0.540672 | + | 0.841234i | \(0.318170\pi\) | |||||||
\(830\) | − 400955.i | − 0.582022i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 58359.1 | 0.0843067 | ||||||||
\(833\) | − 6733.75i | − 0.00970436i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 371223. | 0.532430 | ||||||||
\(836\) | 194926.i | 0.278906i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 316763. | 0.451073 | ||||||||
\(839\) | 207462.i | 0.294724i | 0.989083 | + | 0.147362i | \(0.0470782\pi\) | ||||
−0.989083 | + | 0.147362i | \(0.952922\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −563663. | −0.796943 | ||||||||
\(842\) | − 849373.i | − 1.19805i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 629416. | 0.883594 | ||||||||
\(845\) | − 174066.i | − 0.243782i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 264991. | 0.369372 | ||||||||
\(848\) | − 187294.i | − 0.260455i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −124257. | −0.171982 | ||||||||
\(851\) | 23789.3i | 0.0328491i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 327894. | 0.450646 | 0.225323 | − | 0.974284i | \(-0.427656\pi\) | ||||
0.225323 | + | 0.974284i | \(0.427656\pi\) | |||||||
\(854\) | − 783322.i | − 1.07405i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −479199. | −0.653986 | ||||||||
\(857\) | − 871170.i | − 1.18615i | −0.805145 | − | 0.593077i | \(-0.797913\pi\) | ||||
0.805145 | − | 0.593077i | \(-0.202087\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −339809. | −0.460520 | −0.230260 | − | 0.973129i | \(-0.573958\pi\) | ||||
−0.230260 | + | 0.973129i | \(0.573958\pi\) | |||||||
\(860\) | 231748.i | 0.313342i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −865547. | −1.16487 | ||||||||
\(863\) | 379236.i | 0.509199i | 0.967047 | + | 0.254600i | \(0.0819437\pi\) | ||||
−0.967047 | + | 0.254600i | \(0.918056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −302311. | −0.404038 | ||||||||
\(866\) | 715816.i | 0.954478i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −134020. | −0.177881 | ||||||||
\(869\) | − 810027.i | − 1.07265i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −304343. | −0.401169 | ||||||||
\(872\) | − 328916.i | − 0.432566i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 224353. | 0.293703 | ||||||||
\(875\) | − 68752.3i | − 0.0897989i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 95986.1 | 0.124798 | 0.0623992 | − | 0.998051i | \(-0.480125\pi\) | ||||
0.0623992 | + | 0.998051i | \(0.480125\pi\) | |||||||
\(878\) | 761162.i | 0.987388i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −68835.2 | −0.0888885 | ||||||||
\(881\) | 97012.4i | 0.124990i | 0.998045 | + | 0.0624950i | \(0.0199058\pi\) | ||||
−0.998045 | + | 0.0624950i | \(0.980094\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −845225. | −1.08405 | −0.542027 | − | 0.840361i | \(-0.682343\pi\) | ||||
−0.542027 | + | 0.840361i | \(0.682343\pi\) | |||||||
\(884\) | − 320476.i | − 0.410101i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −573239. | −0.730245 | ||||||||
\(887\) | 744606.i | 0.946409i | 0.880953 | + | 0.473205i | \(0.156903\pi\) | ||||
−0.880953 | + | 0.473205i | \(0.843097\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 683481. | 0.864815 | ||||||||
\(890\) | 339148.i | 0.428163i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 686461. | 0.862753 | ||||||||
\(893\) | − 901251.i | − 1.13017i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −565219. | −0.705619 | ||||||||
\(896\) | − 71242.1i | − 0.0887403i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −217517. | −0.269737 | ||||||||
\(899\) | − 383902.i | − 0.475008i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.02852e6 | −1.26696 | ||||||||
\(902\) | − 311443.i | − 0.382794i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −201178. | −0.246175 | ||||||||
\(905\) | − 49891.2i | − 0.0609154i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 736427. | 0.895190 | 0.447595 | − | 0.894236i | \(-0.352281\pi\) | ||||
0.447595 | + | 0.894236i | \(0.352281\pi\) | |||||||
\(908\) | 298018.i | 0.361468i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 177321. | 0.214130 | ||||||||
\(911\) | − 347020.i | − 0.418136i | −0.977901 | − | 0.209068i | \(-0.932957\pi\) | ||||
0.977901 | − | 0.209068i | \(-0.0670430\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.21975e6 | −1.46329 | ||||||||
\(914\) | − 625076.i | − 0.748239i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −171477. | −0.204369 | ||||||||
\(917\) | − 162300.i | − 0.193010i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.51291e6 | 1.79136 | 0.895678 | − | 0.444703i | \(-0.146691\pi\) | ||||
0.895678 | + | 0.444703i | \(0.146691\pi\) | |||||||
\(920\) | 79226.7i | 0.0936043i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −122740. | −0.144386 | ||||||||
\(923\) | 259871.i | 0.305038i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9495.34 | −0.0110976 | ||||||||
\(926\) | 219279.i | 0.255726i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 204074. | 0.236969 | ||||||||
\(929\) | − 1.31258e6i | − 1.52088i | −0.649408 | − | 0.760440i | \(-0.724983\pi\) | ||||
0.649408 | − | 0.760440i | \(-0.275017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4852.83 | −0.00559881 | ||||||||
\(932\) | 254003.i | 0.292420i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −408980. | −0.468822 | ||||||||
\(935\) | 378005.i | 0.432389i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −837419. | −0.953814 | −0.476907 | − | 0.878954i | \(-0.658242\pi\) | ||||
−0.476907 | + | 0.878954i | \(0.658242\pi\) | |||||||
\(938\) | 371528.i | 0.422266i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 318263. | 0.360189 | ||||||||
\(941\) | − 39183.5i | − 0.0442511i | −0.999755 | − | 0.0221256i | \(-0.992957\pi\) | ||||
0.999755 | − | 0.0221256i | \(-0.00704336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −358459. | −0.403103 | ||||||||
\(944\) | 8371.04i | 0.00939367i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 705003. | 0.787787 | ||||||||
\(947\) | 940742.i | 1.04899i | 0.851414 | + | 0.524494i | \(0.175746\pi\) | ||||
−0.851414 | + | 0.524494i | \(0.824254\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 917036. | 1.01825 | ||||||||
\(950\) | 89548.8i | 0.0992230i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −391222. | −0.431668 | ||||||||
\(953\) | 984970.i | 1.08452i | 0.840211 | + | 0.542259i | \(0.182431\pi\) | ||||
−0.840211 | + | 0.542259i | \(0.817569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 53267.2 | 0.0584054 | ||||||||
\(956\) | 493429.i | 0.539894i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −385041. | −0.419542 | ||||||||
\(959\) | − 1.20400e6i | − 1.30915i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −807560. | −0.874435 | ||||||||
\(962\) | − 24489.7i | − 0.0264627i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −560382. | −0.603018 | ||||||||
\(965\) | 693959.i | 0.745211i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.70961e6 | −1.82829 | −0.914143 | − | 0.405392i | \(-0.867135\pi\) | ||||
−0.914143 | + | 0.405392i | \(0.867135\pi\) | |||||||
\(968\) | − 121883.i | − 0.130075i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −370722. | −0.394008 | ||||||||
\(971\) | 717106.i | 0.760580i | 0.924867 | + | 0.380290i | \(0.124176\pi\) | ||||
−0.924867 | + | 0.380290i | \(0.875824\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −843010. | −0.890445 | ||||||||
\(974\) | − 120798.i | − 0.127333i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −360291. | −0.378228 | ||||||||
\(977\) | 289225.i | 0.303003i | 0.988457 | + | 0.151501i | \(0.0484108\pi\) | ||||
−0.988457 | + | 0.151501i | \(0.951589\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.03173e6 | 1.07646 | ||||||||
\(980\) | − 1713.70i | − 0.00178436i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 437149. | 0.453322 | ||||||||
\(983\) | − 1.62065e6i | − 1.67718i | −0.544760 | − | 0.838592i | \(-0.683379\pi\) | ||||
0.544760 | − | 0.838592i | \(-0.316621\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 340674. | 0.351129 | ||||||||
\(986\) | − 1.12066e6i | − 1.15271i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −230958. | −0.236603 | ||||||||
\(989\) | − 811431.i | − 0.829582i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −722454. | −0.735636 | −0.367818 | − | 0.929898i | \(-0.619895\pi\) | ||||
−0.367818 | + | 0.929898i | \(0.619895\pi\) | |||||||
\(992\) | 61642.7i | 0.0626410i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 317239. | 0.321080 | ||||||||
\(995\) | 297810.i | 0.300810i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −602932. | −0.606566 | −0.303283 | − | 0.952900i | \(-0.598083\pi\) | ||||
−0.303283 | + | 0.952900i | \(0.598083\pi\) | |||||||
\(998\) | 146680.i | 0.147268i | ||||||||
\(999\) | 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 | 810.5.d.c.161.8 | 32 | ||
3.2 | odd | 2 | inner | 810.5.d.c.161.7 | 32 | ||
9.2 | odd | 6 | 270.5.h.a.71.3 | 32 | |||
9.4 | even | 3 | 270.5.h.a.251.3 | 32 | |||
9.5 | odd | 6 | 90.5.h.a.11.12 | ✓ | 32 | ||
9.7 | even | 3 | 90.5.h.a.41.12 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.5.h.a.11.12 | ✓ | 32 | 9.5 | odd | 6 | ||
90.5.h.a.41.12 | yes | 32 | 9.7 | even | 3 | ||
270.5.h.a.71.3 | 32 | 9.2 | odd | 6 | |||
270.5.h.a.251.3 | 32 | 9.4 | even | 3 | |||
810.5.d.c.161.7 | 32 | 3.2 | odd | 2 | inner | ||
810.5.d.c.161.8 | 32 | 1.1 | even | 1 | trivial |