Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,4,Mod(1,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, 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("21.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(1.23904011012\) |
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 | \(\chi\) | \(=\) | 21.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 8.00000 | 1.00000 | ||||||||
\(5\) | −4.00000 | −0.357771 | −0.178885 | − | 0.983870i | \(-0.557249\pi\) | ||||
−0.178885 | + | 0.983870i | \(0.557249\pi\) | |||||||
\(6\) | −12.0000 | −0.816497 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −16.0000 | −0.505964 | ||||||||
\(11\) | 62.0000 | 1.69943 | 0.849714 | − | 0.527244i | \(-0.176775\pi\) | ||||
0.849714 | + | 0.527244i | \(0.176775\pi\) | |||||||
\(12\) | −24.0000 | −0.577350 | ||||||||
\(13\) | −62.0000 | −1.32275 | −0.661373 | − | 0.750057i | \(-0.730026\pi\) | ||||
−0.661373 | + | 0.750057i | \(0.730026\pi\) | |||||||
\(14\) | −28.0000 | −0.534522 | ||||||||
\(15\) | 12.0000 | 0.206559 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | 84.0000 | 1.19841 | 0.599206 | − | 0.800595i | \(-0.295483\pi\) | ||||
0.599206 | + | 0.800595i | \(0.295483\pi\) | |||||||
\(18\) | 36.0000 | 0.471405 | ||||||||
\(19\) | 100.000 | 1.20745 | 0.603726 | − | 0.797192i | \(-0.293682\pi\) | ||||
0.603726 | + | 0.797192i | \(0.293682\pi\) | |||||||
\(20\) | −32.0000 | −0.357771 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 248.000 | 2.40335 | ||||||||
\(23\) | −42.0000 | −0.380765 | −0.190383 | − | 0.981710i | \(-0.560973\pi\) | ||||
−0.190383 | + | 0.981710i | \(0.560973\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −109.000 | −0.872000 | ||||||||
\(26\) | −248.000 | −1.87065 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −56.0000 | −0.377964 | ||||||||
\(29\) | −10.0000 | −0.0640329 | −0.0320164 | − | 0.999487i | \(-0.510193\pi\) | ||||
−0.0320164 | + | 0.999487i | \(0.510193\pi\) | |||||||
\(30\) | 48.0000 | 0.292119 | ||||||||
\(31\) | −48.0000 | −0.278099 | −0.139049 | − | 0.990285i | \(-0.544405\pi\) | ||||
−0.139049 | + | 0.990285i | \(0.544405\pi\) | |||||||
\(32\) | −256.000 | −1.41421 | ||||||||
\(33\) | −186.000 | −0.981165 | ||||||||
\(34\) | 336.000 | 1.69481 | ||||||||
\(35\) | 28.0000 | 0.135225 | ||||||||
\(36\) | 72.0000 | 0.333333 | ||||||||
\(37\) | −246.000 | −1.09303 | −0.546516 | − | 0.837449i | \(-0.684046\pi\) | ||||
−0.546516 | + | 0.837449i | \(0.684046\pi\) | |||||||
\(38\) | 400.000 | 1.70759 | ||||||||
\(39\) | 186.000 | 0.763688 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −248.000 | −0.944661 | −0.472330 | − | 0.881422i | \(-0.656587\pi\) | ||||
−0.472330 | + | 0.881422i | \(0.656587\pi\) | |||||||
\(42\) | 84.0000 | 0.308607 | ||||||||
\(43\) | 68.0000 | 0.241161 | 0.120580 | − | 0.992704i | \(-0.461524\pi\) | ||||
0.120580 | + | 0.992704i | \(0.461524\pi\) | |||||||
\(44\) | 496.000 | 1.69943 | ||||||||
\(45\) | −36.0000 | −0.119257 | ||||||||
\(46\) | −168.000 | −0.538484 | ||||||||
\(47\) | 324.000 | 1.00554 | 0.502769 | − | 0.864421i | \(-0.332315\pi\) | ||||
0.502769 | + | 0.864421i | \(0.332315\pi\) | |||||||
\(48\) | 192.000 | 0.577350 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −436.000 | −1.23319 | ||||||||
\(51\) | −252.000 | −0.691903 | ||||||||
\(52\) | −496.000 | −1.32275 | ||||||||
\(53\) | 258.000 | 0.668661 | 0.334330 | − | 0.942456i | \(-0.391490\pi\) | ||||
0.334330 | + | 0.942456i | \(0.391490\pi\) | |||||||
\(54\) | −108.000 | −0.272166 | ||||||||
\(55\) | −248.000 | −0.608006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −300.000 | −0.697122 | ||||||||
\(58\) | −40.0000 | −0.0905562 | ||||||||
\(59\) | 120.000 | 0.264791 | 0.132396 | − | 0.991197i | \(-0.457733\pi\) | ||||
0.132396 | + | 0.991197i | \(0.457733\pi\) | |||||||
\(60\) | 96.0000 | 0.206559 | ||||||||
\(61\) | 622.000 | 1.30556 | 0.652778 | − | 0.757549i | \(-0.273603\pi\) | ||||
0.652778 | + | 0.757549i | \(0.273603\pi\) | |||||||
\(62\) | −192.000 | −0.393291 | ||||||||
\(63\) | −63.0000 | −0.125988 | ||||||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 248.000 | 0.473240 | ||||||||
\(66\) | −744.000 | −1.38758 | ||||||||
\(67\) | 904.000 | 1.64838 | 0.824188 | − | 0.566316i | \(-0.191632\pi\) | ||||
0.824188 | + | 0.566316i | \(0.191632\pi\) | |||||||
\(68\) | 672.000 | 1.19841 | ||||||||
\(69\) | 126.000 | 0.219835 | ||||||||
\(70\) | 112.000 | 0.191237 | ||||||||
\(71\) | −678.000 | −1.13329 | −0.566646 | − | 0.823961i | \(-0.691759\pi\) | ||||
−0.566646 | + | 0.823961i | \(0.691759\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −642.000 | −1.02932 | −0.514660 | − | 0.857394i | \(-0.672082\pi\) | ||||
−0.514660 | + | 0.857394i | \(0.672082\pi\) | |||||||
\(74\) | −984.000 | −1.54578 | ||||||||
\(75\) | 327.000 | 0.503449 | ||||||||
\(76\) | 800.000 | 1.20745 | ||||||||
\(77\) | −434.000 | −0.642323 | ||||||||
\(78\) | 744.000 | 1.08002 | ||||||||
\(79\) | 740.000 | 1.05388 | 0.526940 | − | 0.849903i | \(-0.323339\pi\) | ||||
0.526940 | + | 0.849903i | \(0.323339\pi\) | |||||||
\(80\) | 256.000 | 0.357771 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | −992.000 | −1.33595 | ||||||||
\(83\) | 468.000 | 0.618912 | 0.309456 | − | 0.950914i | \(-0.399853\pi\) | ||||
0.309456 | + | 0.950914i | \(0.399853\pi\) | |||||||
\(84\) | 168.000 | 0.218218 | ||||||||
\(85\) | −336.000 | −0.428757 | ||||||||
\(86\) | 272.000 | 0.341052 | ||||||||
\(87\) | 30.0000 | 0.0369694 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 200.000 | 0.238202 | 0.119101 | − | 0.992882i | \(-0.461999\pi\) | ||||
0.119101 | + | 0.992882i | \(0.461999\pi\) | |||||||
\(90\) | −144.000 | −0.168655 | ||||||||
\(91\) | 434.000 | 0.499951 | ||||||||
\(92\) | −336.000 | −0.380765 | ||||||||
\(93\) | 144.000 | 0.160560 | ||||||||
\(94\) | 1296.00 | 1.42204 | ||||||||
\(95\) | −400.000 | −0.431991 | ||||||||
\(96\) | 768.000 | 0.816497 | ||||||||
\(97\) | −1266.00 | −1.32518 | −0.662592 | − | 0.748981i | \(-0.730544\pi\) | ||||
−0.662592 | + | 0.748981i | \(0.730544\pi\) | |||||||
\(98\) | 196.000 | 0.202031 | ||||||||
\(99\) | 558.000 | 0.566476 | ||||||||
\(100\) | −872.000 | −0.872000 | ||||||||
\(101\) | 232.000 | 0.228563 | 0.114281 | − | 0.993448i | \(-0.463543\pi\) | ||||
0.114281 | + | 0.993448i | \(0.463543\pi\) | |||||||
\(102\) | −1008.00 | −0.978499 | ||||||||
\(103\) | −1792.00 | −1.71428 | −0.857141 | − | 0.515082i | \(-0.827761\pi\) | ||||
−0.857141 | + | 0.515082i | \(0.827761\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −84.0000 | −0.0780720 | ||||||||
\(106\) | 1032.00 | 0.945629 | ||||||||
\(107\) | −1906.00 | −1.72206 | −0.861028 | − | 0.508558i | \(-0.830179\pi\) | ||||
−0.861028 | + | 0.508558i | \(0.830179\pi\) | |||||||
\(108\) | −216.000 | −0.192450 | ||||||||
\(109\) | −90.0000 | −0.0790866 | −0.0395433 | − | 0.999218i | \(-0.512590\pi\) | ||||
−0.0395433 | + | 0.999218i | \(0.512590\pi\) | |||||||
\(110\) | −992.000 | −0.859850 | ||||||||
\(111\) | 738.000 | 0.631062 | ||||||||
\(112\) | 448.000 | 0.377964 | ||||||||
\(113\) | 458.000 | 0.381283 | 0.190642 | − | 0.981660i | \(-0.438943\pi\) | ||||
0.190642 | + | 0.981660i | \(0.438943\pi\) | |||||||
\(114\) | −1200.00 | −0.985880 | ||||||||
\(115\) | 168.000 | 0.136227 | ||||||||
\(116\) | −80.0000 | −0.0640329 | ||||||||
\(117\) | −558.000 | −0.440916 | ||||||||
\(118\) | 480.000 | 0.374471 | ||||||||
\(119\) | −588.000 | −0.452957 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2513.00 | 1.88805 | ||||||||
\(122\) | 2488.00 | 1.84634 | ||||||||
\(123\) | 744.000 | 0.545400 | ||||||||
\(124\) | −384.000 | −0.278099 | ||||||||
\(125\) | 936.000 | 0.669747 | ||||||||
\(126\) | −252.000 | −0.178174 | ||||||||
\(127\) | 804.000 | 0.561760 | 0.280880 | − | 0.959743i | \(-0.409374\pi\) | ||||
0.280880 | + | 0.959743i | \(0.409374\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −204.000 | −0.139234 | ||||||||
\(130\) | 992.000 | 0.669263 | ||||||||
\(131\) | 812.000 | 0.541563 | 0.270782 | − | 0.962641i | \(-0.412718\pi\) | ||||
0.270782 | + | 0.962641i | \(0.412718\pi\) | |||||||
\(132\) | −1488.00 | −0.981165 | ||||||||
\(133\) | −700.000 | −0.456374 | ||||||||
\(134\) | 3616.00 | 2.33116 | ||||||||
\(135\) | 108.000 | 0.0688530 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 414.000 | 0.258178 | 0.129089 | − | 0.991633i | \(-0.458795\pi\) | ||||
0.129089 | + | 0.991633i | \(0.458795\pi\) | |||||||
\(138\) | 504.000 | 0.310894 | ||||||||
\(139\) | −1620.00 | −0.988537 | −0.494268 | − | 0.869309i | \(-0.664564\pi\) | ||||
−0.494268 | + | 0.869309i | \(0.664564\pi\) | |||||||
\(140\) | 224.000 | 0.135225 | ||||||||
\(141\) | −972.000 | −0.580547 | ||||||||
\(142\) | −2712.00 | −1.60272 | ||||||||
\(143\) | −3844.00 | −2.24791 | ||||||||
\(144\) | −576.000 | −0.333333 | ||||||||
\(145\) | 40.0000 | 0.0229091 | ||||||||
\(146\) | −2568.00 | −1.45568 | ||||||||
\(147\) | −147.000 | −0.0824786 | ||||||||
\(148\) | −1968.00 | −1.09303 | ||||||||
\(149\) | 2370.00 | 1.30307 | 0.651537 | − | 0.758617i | \(-0.274125\pi\) | ||||
0.651537 | + | 0.758617i | \(0.274125\pi\) | |||||||
\(150\) | 1308.00 | 0.711985 | ||||||||
\(151\) | −568.000 | −0.306114 | −0.153057 | − | 0.988217i | \(-0.548912\pi\) | ||||
−0.153057 | + | 0.988217i | \(0.548912\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 756.000 | 0.399470 | ||||||||
\(154\) | −1736.00 | −0.908382 | ||||||||
\(155\) | 192.000 | 0.0994956 | ||||||||
\(156\) | 1488.00 | 0.763688 | ||||||||
\(157\) | −266.000 | −0.135217 | −0.0676086 | − | 0.997712i | \(-0.521537\pi\) | ||||
−0.0676086 | + | 0.997712i | \(0.521537\pi\) | |||||||
\(158\) | 2960.00 | 1.49041 | ||||||||
\(159\) | −774.000 | −0.386052 | ||||||||
\(160\) | 1024.00 | 0.505964 | ||||||||
\(161\) | 294.000 | 0.143916 | ||||||||
\(162\) | 324.000 | 0.157135 | ||||||||
\(163\) | −272.000 | −0.130704 | −0.0653518 | − | 0.997862i | \(-0.520817\pi\) | ||||
−0.0653518 | + | 0.997862i | \(0.520817\pi\) | |||||||
\(164\) | −1984.00 | −0.944661 | ||||||||
\(165\) | 744.000 | 0.351032 | ||||||||
\(166\) | 1872.00 | 0.875273 | ||||||||
\(167\) | −1876.00 | −0.869277 | −0.434638 | − | 0.900605i | \(-0.643124\pi\) | ||||
−0.434638 | + | 0.900605i | \(0.643124\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1647.00 | 0.749659 | ||||||||
\(170\) | −1344.00 | −0.606353 | ||||||||
\(171\) | 900.000 | 0.402484 | ||||||||
\(172\) | 544.000 | 0.241161 | ||||||||
\(173\) | −152.000 | −0.0667997 | −0.0333998 | − | 0.999442i | \(-0.510633\pi\) | ||||
−0.0333998 | + | 0.999442i | \(0.510633\pi\) | |||||||
\(174\) | 120.000 | 0.0522826 | ||||||||
\(175\) | 763.000 | 0.329585 | ||||||||
\(176\) | −3968.00 | −1.69943 | ||||||||
\(177\) | −360.000 | −0.152877 | ||||||||
\(178\) | 800.000 | 0.336868 | ||||||||
\(179\) | 610.000 | 0.254713 | 0.127356 | − | 0.991857i | \(-0.459351\pi\) | ||||
0.127356 | + | 0.991857i | \(0.459351\pi\) | |||||||
\(180\) | −288.000 | −0.119257 | ||||||||
\(181\) | 1042.00 | 0.427907 | 0.213954 | − | 0.976844i | \(-0.431366\pi\) | ||||
0.213954 | + | 0.976844i | \(0.431366\pi\) | |||||||
\(182\) | 1736.00 | 0.707038 | ||||||||
\(183\) | −1866.00 | −0.753763 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 984.000 | 0.391055 | ||||||||
\(186\) | 576.000 | 0.227067 | ||||||||
\(187\) | 5208.00 | 2.03661 | ||||||||
\(188\) | 2592.00 | 1.00554 | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | −1600.00 | −0.610927 | ||||||||
\(191\) | −2038.00 | −0.772065 | −0.386033 | − | 0.922485i | \(-0.626155\pi\) | ||||
−0.386033 | + | 0.922485i | \(0.626155\pi\) | |||||||
\(192\) | 1536.00 | 0.577350 | ||||||||
\(193\) | −2602.00 | −0.970446 | −0.485223 | − | 0.874390i | \(-0.661262\pi\) | ||||
−0.485223 | + | 0.874390i | \(0.661262\pi\) | |||||||
\(194\) | −5064.00 | −1.87409 | ||||||||
\(195\) | −744.000 | −0.273225 | ||||||||
\(196\) | 392.000 | 0.142857 | ||||||||
\(197\) | 2354.00 | 0.851348 | 0.425674 | − | 0.904877i | \(-0.360037\pi\) | ||||
0.425674 | + | 0.904877i | \(0.360037\pi\) | |||||||
\(198\) | 2232.00 | 0.801118 | ||||||||
\(199\) | 1680.00 | 0.598452 | 0.299226 | − | 0.954182i | \(-0.403271\pi\) | ||||
0.299226 | + | 0.954182i | \(0.403271\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2712.00 | −0.951690 | ||||||||
\(202\) | 928.000 | 0.323237 | ||||||||
\(203\) | 70.0000 | 0.0242022 | ||||||||
\(204\) | −2016.00 | −0.691903 | ||||||||
\(205\) | 992.000 | 0.337972 | ||||||||
\(206\) | −7168.00 | −2.42436 | ||||||||
\(207\) | −378.000 | −0.126922 | ||||||||
\(208\) | 3968.00 | 1.32275 | ||||||||
\(209\) | 6200.00 | 2.05198 | ||||||||
\(210\) | −336.000 | −0.110410 | ||||||||
\(211\) | −668.000 | −0.217948 | −0.108974 | − | 0.994045i | \(-0.534757\pi\) | ||||
−0.108974 | + | 0.994045i | \(0.534757\pi\) | |||||||
\(212\) | 2064.00 | 0.668661 | ||||||||
\(213\) | 2034.00 | 0.654307 | ||||||||
\(214\) | −7624.00 | −2.43535 | ||||||||
\(215\) | −272.000 | −0.0862802 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 336.000 | 0.105111 | ||||||||
\(218\) | −360.000 | −0.111845 | ||||||||
\(219\) | 1926.00 | 0.594279 | ||||||||
\(220\) | −1984.00 | −0.608006 | ||||||||
\(221\) | −5208.00 | −1.58519 | ||||||||
\(222\) | 2952.00 | 0.892456 | ||||||||
\(223\) | −1832.00 | −0.550134 | −0.275067 | − | 0.961425i | \(-0.588700\pi\) | ||||
−0.275067 | + | 0.961425i | \(0.588700\pi\) | |||||||
\(224\) | 1792.00 | 0.534522 | ||||||||
\(225\) | −981.000 | −0.290667 | ||||||||
\(226\) | 1832.00 | 0.539216 | ||||||||
\(227\) | 4944.00 | 1.44557 | 0.722786 | − | 0.691072i | \(-0.242861\pi\) | ||||
0.722786 | + | 0.691072i | \(0.242861\pi\) | |||||||
\(228\) | −2400.00 | −0.697122 | ||||||||
\(229\) | −5470.00 | −1.57846 | −0.789231 | − | 0.614096i | \(-0.789521\pi\) | ||||
−0.789231 | + | 0.614096i | \(0.789521\pi\) | |||||||
\(230\) | 672.000 | 0.192654 | ||||||||
\(231\) | 1302.00 | 0.370846 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2802.00 | −0.787833 | −0.393917 | − | 0.919146i | \(-0.628880\pi\) | ||||
−0.393917 | + | 0.919146i | \(0.628880\pi\) | |||||||
\(234\) | −2232.00 | −0.623549 | ||||||||
\(235\) | −1296.00 | −0.359752 | ||||||||
\(236\) | 960.000 | 0.264791 | ||||||||
\(237\) | −2220.00 | −0.608458 | ||||||||
\(238\) | −2352.00 | −0.640578 | ||||||||
\(239\) | −1170.00 | −0.316657 | −0.158328 | − | 0.987386i | \(-0.550610\pi\) | ||||
−0.158328 | + | 0.987386i | \(0.550610\pi\) | |||||||
\(240\) | −768.000 | −0.206559 | ||||||||
\(241\) | −2338.00 | −0.624912 | −0.312456 | − | 0.949932i | \(-0.601152\pi\) | ||||
−0.312456 | + | 0.949932i | \(0.601152\pi\) | |||||||
\(242\) | 10052.0 | 2.67011 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 4976.00 | 1.30556 | ||||||||
\(245\) | −196.000 | −0.0511101 | ||||||||
\(246\) | 2976.00 | 0.771312 | ||||||||
\(247\) | −6200.00 | −1.59715 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1404.00 | −0.357329 | ||||||||
\(250\) | 3744.00 | 0.947165 | ||||||||
\(251\) | 2792.00 | 0.702109 | 0.351055 | − | 0.936355i | \(-0.385823\pi\) | ||||
0.351055 | + | 0.936355i | \(0.385823\pi\) | |||||||
\(252\) | −504.000 | −0.125988 | ||||||||
\(253\) | −2604.00 | −0.647083 | ||||||||
\(254\) | 3216.00 | 0.794448 | ||||||||
\(255\) | 1008.00 | 0.247543 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 7024.00 | 1.70484 | 0.852422 | − | 0.522854i | \(-0.175133\pi\) | ||||
0.852422 | + | 0.522854i | \(0.175133\pi\) | |||||||
\(258\) | −816.000 | −0.196907 | ||||||||
\(259\) | 1722.00 | 0.413127 | ||||||||
\(260\) | 1984.00 | 0.473240 | ||||||||
\(261\) | −90.0000 | −0.0213443 | ||||||||
\(262\) | 3248.00 | 0.765886 | ||||||||
\(263\) | 2438.00 | 0.571610 | 0.285805 | − | 0.958288i | \(-0.407739\pi\) | ||||
0.285805 | + | 0.958288i | \(0.407739\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1032.00 | −0.239227 | ||||||||
\(266\) | −2800.00 | −0.645410 | ||||||||
\(267\) | −600.000 | −0.137526 | ||||||||
\(268\) | 7232.00 | 1.64838 | ||||||||
\(269\) | −6780.00 | −1.53674 | −0.768372 | − | 0.640004i | \(-0.778933\pi\) | ||||
−0.768372 | + | 0.640004i | \(0.778933\pi\) | |||||||
\(270\) | 432.000 | 0.0973729 | ||||||||
\(271\) | −1928.00 | −0.432168 | −0.216084 | − | 0.976375i | \(-0.569329\pi\) | ||||
−0.216084 | + | 0.976375i | \(0.569329\pi\) | |||||||
\(272\) | −5376.00 | −1.19841 | ||||||||
\(273\) | −1302.00 | −0.288647 | ||||||||
\(274\) | 1656.00 | 0.365119 | ||||||||
\(275\) | −6758.00 | −1.48190 | ||||||||
\(276\) | 1008.00 | 0.219835 | ||||||||
\(277\) | 5554.00 | 1.20472 | 0.602360 | − | 0.798224i | \(-0.294227\pi\) | ||||
0.602360 | + | 0.798224i | \(0.294227\pi\) | |||||||
\(278\) | −6480.00 | −1.39800 | ||||||||
\(279\) | −432.000 | −0.0926995 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1942.00 | 0.412278 | 0.206139 | − | 0.978523i | \(-0.433910\pi\) | ||||
0.206139 | + | 0.978523i | \(0.433910\pi\) | |||||||
\(282\) | −3888.00 | −0.821018 | ||||||||
\(283\) | 4828.00 | 1.01412 | 0.507058 | − | 0.861912i | \(-0.330733\pi\) | ||||
0.507058 | + | 0.861912i | \(0.330733\pi\) | |||||||
\(284\) | −5424.00 | −1.13329 | ||||||||
\(285\) | 1200.00 | 0.249410 | ||||||||
\(286\) | −15376.0 | −3.17903 | ||||||||
\(287\) | 1736.00 | 0.357048 | ||||||||
\(288\) | −2304.00 | −0.471405 | ||||||||
\(289\) | 2143.00 | 0.436190 | ||||||||
\(290\) | 160.000 | 0.0323984 | ||||||||
\(291\) | 3798.00 | 0.765095 | ||||||||
\(292\) | −5136.00 | −1.02932 | ||||||||
\(293\) | −6152.00 | −1.22663 | −0.613317 | − | 0.789837i | \(-0.710165\pi\) | ||||
−0.613317 | + | 0.789837i | \(0.710165\pi\) | |||||||
\(294\) | −588.000 | −0.116642 | ||||||||
\(295\) | −480.000 | −0.0947345 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1674.00 | −0.327055 | ||||||||
\(298\) | 9480.00 | 1.84282 | ||||||||
\(299\) | 2604.00 | 0.503656 | ||||||||
\(300\) | 2616.00 | 0.503449 | ||||||||
\(301\) | −476.000 | −0.0911501 | ||||||||
\(302\) | −2272.00 | −0.432910 | ||||||||
\(303\) | −696.000 | −0.131961 | ||||||||
\(304\) | −6400.00 | −1.20745 | ||||||||
\(305\) | −2488.00 | −0.467090 | ||||||||
\(306\) | 3024.00 | 0.564937 | ||||||||
\(307\) | 5884.00 | 1.09387 | 0.546934 | − | 0.837176i | \(-0.315795\pi\) | ||||
0.546934 | + | 0.837176i | \(0.315795\pi\) | |||||||
\(308\) | −3472.00 | −0.642323 | ||||||||
\(309\) | 5376.00 | 0.989741 | ||||||||
\(310\) | 768.000 | 0.140708 | ||||||||
\(311\) | 9132.00 | 1.66504 | 0.832521 | − | 0.553993i | \(-0.186897\pi\) | ||||
0.832521 | + | 0.553993i | \(0.186897\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9382.00 | −1.69426 | −0.847128 | − | 0.531389i | \(-0.821670\pi\) | ||||
−0.847128 | + | 0.531389i | \(0.821670\pi\) | |||||||
\(314\) | −1064.00 | −0.191226 | ||||||||
\(315\) | 252.000 | 0.0450749 | ||||||||
\(316\) | 5920.00 | 1.05388 | ||||||||
\(317\) | 3114.00 | 0.551734 | 0.275867 | − | 0.961196i | \(-0.411035\pi\) | ||||
0.275867 | + | 0.961196i | \(0.411035\pi\) | |||||||
\(318\) | −3096.00 | −0.545959 | ||||||||
\(319\) | −620.000 | −0.108819 | ||||||||
\(320\) | 2048.00 | 0.357771 | ||||||||
\(321\) | 5718.00 | 0.994229 | ||||||||
\(322\) | 1176.00 | 0.203528 | ||||||||
\(323\) | 8400.00 | 1.44702 | ||||||||
\(324\) | 648.000 | 0.111111 | ||||||||
\(325\) | 6758.00 | 1.15344 | ||||||||
\(326\) | −1088.00 | −0.184843 | ||||||||
\(327\) | 270.000 | 0.0456607 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2268.00 | −0.380057 | ||||||||
\(330\) | 2976.00 | 0.496435 | ||||||||
\(331\) | 1532.00 | 0.254400 | 0.127200 | − | 0.991877i | \(-0.459401\pi\) | ||||
0.127200 | + | 0.991877i | \(0.459401\pi\) | |||||||
\(332\) | 3744.00 | 0.618912 | ||||||||
\(333\) | −2214.00 | −0.364344 | ||||||||
\(334\) | −7504.00 | −1.22934 | ||||||||
\(335\) | −3616.00 | −0.589741 | ||||||||
\(336\) | −1344.00 | −0.218218 | ||||||||
\(337\) | −4166.00 | −0.673402 | −0.336701 | − | 0.941612i | \(-0.609311\pi\) | ||||
−0.336701 | + | 0.941612i | \(0.609311\pi\) | |||||||
\(338\) | 6588.00 | 1.06018 | ||||||||
\(339\) | −1374.00 | −0.220134 | ||||||||
\(340\) | −2688.00 | −0.428757 | ||||||||
\(341\) | −2976.00 | −0.472608 | ||||||||
\(342\) | 3600.00 | 0.569198 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −504.000 | −0.0786506 | ||||||||
\(346\) | −608.000 | −0.0944690 | ||||||||
\(347\) | −11366.0 | −1.75838 | −0.879191 | − | 0.476469i | \(-0.841917\pi\) | ||||
−0.879191 | + | 0.476469i | \(0.841917\pi\) | |||||||
\(348\) | 240.000 | 0.0369694 | ||||||||
\(349\) | 9310.00 | 1.42795 | 0.713973 | − | 0.700174i | \(-0.246894\pi\) | ||||
0.713973 | + | 0.700174i | \(0.246894\pi\) | |||||||
\(350\) | 3052.00 | 0.466104 | ||||||||
\(351\) | 1674.00 | 0.254563 | ||||||||
\(352\) | −15872.0 | −2.40335 | ||||||||
\(353\) | −8572.00 | −1.29247 | −0.646234 | − | 0.763139i | \(-0.723657\pi\) | ||||
−0.646234 | + | 0.763139i | \(0.723657\pi\) | |||||||
\(354\) | −1440.00 | −0.216201 | ||||||||
\(355\) | 2712.00 | 0.405459 | ||||||||
\(356\) | 1600.00 | 0.238202 | ||||||||
\(357\) | 1764.00 | 0.261515 | ||||||||
\(358\) | 2440.00 | 0.360218 | ||||||||
\(359\) | −4790.00 | −0.704196 | −0.352098 | − | 0.935963i | \(-0.614532\pi\) | ||||
−0.352098 | + | 0.935963i | \(0.614532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3141.00 | 0.457938 | ||||||||
\(362\) | 4168.00 | 0.605153 | ||||||||
\(363\) | −7539.00 | −1.09007 | ||||||||
\(364\) | 3472.00 | 0.499951 | ||||||||
\(365\) | 2568.00 | 0.368261 | ||||||||
\(366\) | −7464.00 | −1.06598 | ||||||||
\(367\) | 5424.00 | 0.771473 | 0.385736 | − | 0.922609i | \(-0.373947\pi\) | ||||
0.385736 | + | 0.922609i | \(0.373947\pi\) | |||||||
\(368\) | 2688.00 | 0.380765 | ||||||||
\(369\) | −2232.00 | −0.314887 | ||||||||
\(370\) | 3936.00 | 0.553035 | ||||||||
\(371\) | −1806.00 | −0.252730 | ||||||||
\(372\) | 1152.00 | 0.160560 | ||||||||
\(373\) | 1838.00 | 0.255142 | 0.127571 | − | 0.991829i | \(-0.459282\pi\) | ||||
0.127571 | + | 0.991829i | \(0.459282\pi\) | |||||||
\(374\) | 20832.0 | 2.88021 | ||||||||
\(375\) | −2808.00 | −0.386679 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 620.000 | 0.0846993 | ||||||||
\(378\) | 756.000 | 0.102869 | ||||||||
\(379\) | −4260.00 | −0.577365 | −0.288683 | − | 0.957425i | \(-0.593217\pi\) | ||||
−0.288683 | + | 0.957425i | \(0.593217\pi\) | |||||||
\(380\) | −3200.00 | −0.431991 | ||||||||
\(381\) | −2412.00 | −0.324332 | ||||||||
\(382\) | −8152.00 | −1.09187 | ||||||||
\(383\) | 9048.00 | 1.20713 | 0.603566 | − | 0.797313i | \(-0.293746\pi\) | ||||
0.603566 | + | 0.797313i | \(0.293746\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1736.00 | 0.229805 | ||||||||
\(386\) | −10408.0 | −1.37242 | ||||||||
\(387\) | 612.000 | 0.0803868 | ||||||||
\(388\) | −10128.0 | −1.32518 | ||||||||
\(389\) | −11490.0 | −1.49760 | −0.748800 | − | 0.662796i | \(-0.769369\pi\) | ||||
−0.748800 | + | 0.662796i | \(0.769369\pi\) | |||||||
\(390\) | −2976.00 | −0.386399 | ||||||||
\(391\) | −3528.00 | −0.456314 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2436.00 | −0.312672 | ||||||||
\(394\) | 9416.00 | 1.20399 | ||||||||
\(395\) | −2960.00 | −0.377048 | ||||||||
\(396\) | 4464.00 | 0.566476 | ||||||||
\(397\) | −1866.00 | −0.235899 | −0.117949 | − | 0.993020i | \(-0.537632\pi\) | ||||
−0.117949 | + | 0.993020i | \(0.537632\pi\) | |||||||
\(398\) | 6720.00 | 0.846340 | ||||||||
\(399\) | 2100.00 | 0.263487 | ||||||||
\(400\) | 6976.00 | 0.872000 | ||||||||
\(401\) | 13662.0 | 1.70137 | 0.850683 | − | 0.525679i | \(-0.176189\pi\) | ||||
0.850683 | + | 0.525679i | \(0.176189\pi\) | |||||||
\(402\) | −10848.0 | −1.34589 | ||||||||
\(403\) | 2976.00 | 0.367854 | ||||||||
\(404\) | 1856.00 | 0.228563 | ||||||||
\(405\) | −324.000 | −0.0397523 | ||||||||
\(406\) | 280.000 | 0.0342270 | ||||||||
\(407\) | −15252.0 | −1.85753 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13210.0 | −1.59705 | −0.798524 | − | 0.601963i | \(-0.794385\pi\) | ||||
−0.798524 | + | 0.601963i | \(0.794385\pi\) | |||||||
\(410\) | 3968.00 | 0.477965 | ||||||||
\(411\) | −1242.00 | −0.149059 | ||||||||
\(412\) | −14336.0 | −1.71428 | ||||||||
\(413\) | −840.000 | −0.100082 | ||||||||
\(414\) | −1512.00 | −0.179495 | ||||||||
\(415\) | −1872.00 | −0.221429 | ||||||||
\(416\) | 15872.0 | 1.87065 | ||||||||
\(417\) | 4860.00 | 0.570732 | ||||||||
\(418\) | 24800.0 | 2.90193 | ||||||||
\(419\) | 6960.00 | 0.811499 | 0.405750 | − | 0.913984i | \(-0.367010\pi\) | ||||
0.405750 | + | 0.913984i | \(0.367010\pi\) | |||||||
\(420\) | −672.000 | −0.0780720 | ||||||||
\(421\) | 8162.00 | 0.944873 | 0.472437 | − | 0.881365i | \(-0.343375\pi\) | ||||
0.472437 | + | 0.881365i | \(0.343375\pi\) | |||||||
\(422\) | −2672.00 | −0.308225 | ||||||||
\(423\) | 2916.00 | 0.335179 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9156.00 | −1.04501 | ||||||||
\(426\) | 8136.00 | 0.925330 | ||||||||
\(427\) | −4354.00 | −0.493454 | ||||||||
\(428\) | −15248.0 | −1.72206 | ||||||||
\(429\) | 11532.0 | 1.29783 | ||||||||
\(430\) | −1088.00 | −0.122019 | ||||||||
\(431\) | 16602.0 | 1.85543 | 0.927715 | − | 0.373290i | \(-0.121770\pi\) | ||||
0.927715 | + | 0.373290i | \(0.121770\pi\) | |||||||
\(432\) | 1728.00 | 0.192450 | ||||||||
\(433\) | 7738.00 | 0.858810 | 0.429405 | − | 0.903112i | \(-0.358723\pi\) | ||||
0.429405 | + | 0.903112i | \(0.358723\pi\) | |||||||
\(434\) | 1344.00 | 0.148650 | ||||||||
\(435\) | −120.000 | −0.0132266 | ||||||||
\(436\) | −720.000 | −0.0790866 | ||||||||
\(437\) | −4200.00 | −0.459756 | ||||||||
\(438\) | 7704.00 | 0.840437 | ||||||||
\(439\) | −840.000 | −0.0913235 | −0.0456617 | − | 0.998957i | \(-0.514540\pi\) | ||||
−0.0456617 | + | 0.998957i | \(0.514540\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | −20832.0 | −2.24180 | ||||||||
\(443\) | 6618.00 | 0.709776 | 0.354888 | − | 0.934909i | \(-0.384519\pi\) | ||||
0.354888 | + | 0.934909i | \(0.384519\pi\) | |||||||
\(444\) | 5904.00 | 0.631062 | ||||||||
\(445\) | −800.000 | −0.0852217 | ||||||||
\(446\) | −7328.00 | −0.778006 | ||||||||
\(447\) | −7110.00 | −0.752330 | ||||||||
\(448\) | 3584.00 | 0.377964 | ||||||||
\(449\) | 3090.00 | 0.324780 | 0.162390 | − | 0.986727i | \(-0.448080\pi\) | ||||
0.162390 | + | 0.986727i | \(0.448080\pi\) | |||||||
\(450\) | −3924.00 | −0.411065 | ||||||||
\(451\) | −15376.0 | −1.60538 | ||||||||
\(452\) | 3664.00 | 0.381283 | ||||||||
\(453\) | 1704.00 | 0.176735 | ||||||||
\(454\) | 19776.0 | 2.04435 | ||||||||
\(455\) | −1736.00 | −0.178868 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5914.00 | 0.605351 | 0.302675 | − | 0.953094i | \(-0.402120\pi\) | ||||
0.302675 | + | 0.953094i | \(0.402120\pi\) | |||||||
\(458\) | −21880.0 | −2.23228 | ||||||||
\(459\) | −2268.00 | −0.230634 | ||||||||
\(460\) | 1344.00 | 0.136227 | ||||||||
\(461\) | −15968.0 | −1.61324 | −0.806620 | − | 0.591070i | \(-0.798706\pi\) | ||||
−0.806620 | + | 0.591070i | \(0.798706\pi\) | |||||||
\(462\) | 5208.00 | 0.524455 | ||||||||
\(463\) | −1172.00 | −0.117640 | −0.0588202 | − | 0.998269i | \(-0.518734\pi\) | ||||
−0.0588202 | + | 0.998269i | \(0.518734\pi\) | |||||||
\(464\) | 640.000 | 0.0640329 | ||||||||
\(465\) | −576.000 | −0.0574438 | ||||||||
\(466\) | −11208.0 | −1.11416 | ||||||||
\(467\) | 5304.00 | 0.525567 | 0.262784 | − | 0.964855i | \(-0.415359\pi\) | ||||
0.262784 | + | 0.964855i | \(0.415359\pi\) | |||||||
\(468\) | −4464.00 | −0.440916 | ||||||||
\(469\) | −6328.00 | −0.623027 | ||||||||
\(470\) | −5184.00 | −0.508766 | ||||||||
\(471\) | 798.000 | 0.0780677 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4216.00 | 0.409835 | ||||||||
\(474\) | −8880.00 | −0.860489 | ||||||||
\(475\) | −10900.0 | −1.05290 | ||||||||
\(476\) | −4704.00 | −0.452957 | ||||||||
\(477\) | 2322.00 | 0.222887 | ||||||||
\(478\) | −4680.00 | −0.447821 | ||||||||
\(479\) | 5740.00 | 0.547531 | 0.273765 | − | 0.961796i | \(-0.411731\pi\) | ||||
0.273765 | + | 0.961796i | \(0.411731\pi\) | |||||||
\(480\) | −3072.00 | −0.292119 | ||||||||
\(481\) | 15252.0 | 1.44580 | ||||||||
\(482\) | −9352.00 | −0.883759 | ||||||||
\(483\) | −882.000 | −0.0830898 | ||||||||
\(484\) | 20104.0 | 1.88805 | ||||||||
\(485\) | 5064.00 | 0.474112 | ||||||||
\(486\) | −972.000 | −0.0907218 | ||||||||
\(487\) | 8944.00 | 0.832220 | 0.416110 | − | 0.909314i | \(-0.363393\pi\) | ||||
0.416110 | + | 0.909314i | \(0.363393\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 816.000 | 0.0754617 | ||||||||
\(490\) | −784.000 | −0.0722806 | ||||||||
\(491\) | −5558.00 | −0.510853 | −0.255427 | − | 0.966828i | \(-0.582216\pi\) | ||||
−0.255427 | + | 0.966828i | \(0.582216\pi\) | |||||||
\(492\) | 5952.00 | 0.545400 | ||||||||
\(493\) | −840.000 | −0.0767377 | ||||||||
\(494\) | −24800.0 | −2.25871 | ||||||||
\(495\) | −2232.00 | −0.202669 | ||||||||
\(496\) | 3072.00 | 0.278099 | ||||||||
\(497\) | 4746.00 | 0.428344 | ||||||||
\(498\) | −5616.00 | −0.505339 | ||||||||
\(499\) | −19820.0 | −1.77809 | −0.889043 | − | 0.457823i | \(-0.848629\pi\) | ||||
−0.889043 | + | 0.457823i | \(0.848629\pi\) | |||||||
\(500\) | 7488.00 | 0.669747 | ||||||||
\(501\) | 5628.00 | 0.501877 | ||||||||
\(502\) | 11168.0 | 0.992933 | ||||||||
\(503\) | 1848.00 | 0.163814 | 0.0819068 | − | 0.996640i | \(-0.473899\pi\) | ||||
0.0819068 | + | 0.996640i | \(0.473899\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −928.000 | −0.0817732 | ||||||||
\(506\) | −10416.0 | −0.915114 | ||||||||
\(507\) | −4941.00 | −0.432816 | ||||||||
\(508\) | 6432.00 | 0.561760 | ||||||||
\(509\) | 340.000 | 0.0296075 | 0.0148038 | − | 0.999890i | \(-0.495288\pi\) | ||||
0.0148038 | + | 0.999890i | \(0.495288\pi\) | |||||||
\(510\) | 4032.00 | 0.350078 | ||||||||
\(511\) | 4494.00 | 0.389047 | ||||||||
\(512\) | 16384.0 | 1.41421 | ||||||||
\(513\) | −2700.00 | −0.232374 | ||||||||
\(514\) | 28096.0 | 2.41101 | ||||||||
\(515\) | 7168.00 | 0.613320 | ||||||||
\(516\) | −1632.00 | −0.139234 | ||||||||
\(517\) | 20088.0 | 1.70884 | ||||||||
\(518\) | 6888.00 | 0.584250 | ||||||||
\(519\) | 456.000 | 0.0385668 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10212.0 | 0.858725 | 0.429363 | − | 0.903132i | \(-0.358738\pi\) | ||||
0.429363 | + | 0.903132i | \(0.358738\pi\) | |||||||
\(522\) | −360.000 | −0.0301854 | ||||||||
\(523\) | −9332.00 | −0.780229 | −0.390115 | − | 0.920766i | \(-0.627565\pi\) | ||||
−0.390115 | + | 0.920766i | \(0.627565\pi\) | |||||||
\(524\) | 6496.00 | 0.541563 | ||||||||
\(525\) | −2289.00 | −0.190286 | ||||||||
\(526\) | 9752.00 | 0.808379 | ||||||||
\(527\) | −4032.00 | −0.333276 | ||||||||
\(528\) | 11904.0 | 0.981165 | ||||||||
\(529\) | −10403.0 | −0.855018 | ||||||||
\(530\) | −4128.00 | −0.338319 | ||||||||
\(531\) | 1080.00 | 0.0882637 | ||||||||
\(532\) | −5600.00 | −0.456374 | ||||||||
\(533\) | 15376.0 | 1.24955 | ||||||||
\(534\) | −2400.00 | −0.194491 | ||||||||
\(535\) | 7624.00 | 0.616101 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1830.00 | −0.147058 | ||||||||
\(538\) | −27120.0 | −2.17328 | ||||||||
\(539\) | 3038.00 | 0.242775 | ||||||||
\(540\) | 864.000 | 0.0688530 | ||||||||
\(541\) | −8998.00 | −0.715073 | −0.357536 | − | 0.933899i | \(-0.616383\pi\) | ||||
−0.357536 | + | 0.933899i | \(0.616383\pi\) | |||||||
\(542\) | −7712.00 | −0.611179 | ||||||||
\(543\) | −3126.00 | −0.247052 | ||||||||
\(544\) | −21504.0 | −1.69481 | ||||||||
\(545\) | 360.000 | 0.0282949 | ||||||||
\(546\) | −5208.00 | −0.408208 | ||||||||
\(547\) | −3416.00 | −0.267016 | −0.133508 | − | 0.991048i | \(-0.542624\pi\) | ||||
−0.133508 | + | 0.991048i | \(0.542624\pi\) | |||||||
\(548\) | 3312.00 | 0.258178 | ||||||||
\(549\) | 5598.00 | 0.435185 | ||||||||
\(550\) | −27032.0 | −2.09572 | ||||||||
\(551\) | −1000.00 | −0.0773166 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5180.00 | −0.398329 | ||||||||
\(554\) | 22216.0 | 1.70373 | ||||||||
\(555\) | −2952.00 | −0.225776 | ||||||||
\(556\) | −12960.0 | −0.988537 | ||||||||
\(557\) | −526.000 | −0.0400132 | −0.0200066 | − | 0.999800i | \(-0.506369\pi\) | ||||
−0.0200066 | + | 0.999800i | \(0.506369\pi\) | |||||||
\(558\) | −1728.00 | −0.131097 | ||||||||
\(559\) | −4216.00 | −0.318994 | ||||||||
\(560\) | −1792.00 | −0.135225 | ||||||||
\(561\) | −15624.0 | −1.17584 | ||||||||
\(562\) | 7768.00 | 0.583049 | ||||||||
\(563\) | −6712.00 | −0.502446 | −0.251223 | − | 0.967929i | \(-0.580833\pi\) | ||||
−0.251223 | + | 0.967929i | \(0.580833\pi\) | |||||||
\(564\) | −7776.00 | −0.580547 | ||||||||
\(565\) | −1832.00 | −0.136412 | ||||||||
\(566\) | 19312.0 | 1.43418 | ||||||||
\(567\) | −567.000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4190.00 | 0.308706 | 0.154353 | − | 0.988016i | \(-0.450671\pi\) | ||||
0.154353 | + | 0.988016i | \(0.450671\pi\) | |||||||
\(570\) | 4800.00 | 0.352719 | ||||||||
\(571\) | 3032.00 | 0.222216 | 0.111108 | − | 0.993808i | \(-0.464560\pi\) | ||||
0.111108 | + | 0.993808i | \(0.464560\pi\) | |||||||
\(572\) | −30752.0 | −2.24791 | ||||||||
\(573\) | 6114.00 | 0.445752 | ||||||||
\(574\) | 6944.00 | 0.504942 | ||||||||
\(575\) | 4578.00 | 0.332027 | ||||||||
\(576\) | −4608.00 | −0.333333 | ||||||||
\(577\) | 5434.00 | 0.392063 | 0.196032 | − | 0.980598i | \(-0.437195\pi\) | ||||
0.196032 | + | 0.980598i | \(0.437195\pi\) | |||||||
\(578\) | 8572.00 | 0.616865 | ||||||||
\(579\) | 7806.00 | 0.560287 | ||||||||
\(580\) | 320.000 | 0.0229091 | ||||||||
\(581\) | −3276.00 | −0.233927 | ||||||||
\(582\) | 15192.0 | 1.08201 | ||||||||
\(583\) | 15996.0 | 1.13634 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2232.00 | 0.157747 | ||||||||
\(586\) | −24608.0 | −1.73472 | ||||||||
\(587\) | 464.000 | 0.0326258 | 0.0163129 | − | 0.999867i | \(-0.494807\pi\) | ||||
0.0163129 | + | 0.999867i | \(0.494807\pi\) | |||||||
\(588\) | −1176.00 | −0.0824786 | ||||||||
\(589\) | −4800.00 | −0.335790 | ||||||||
\(590\) | −1920.00 | −0.133975 | ||||||||
\(591\) | −7062.00 | −0.491526 | ||||||||
\(592\) | 15744.0 | 1.09303 | ||||||||
\(593\) | 11748.0 | 0.813546 | 0.406773 | − | 0.913529i | \(-0.366654\pi\) | ||||
0.406773 | + | 0.913529i | \(0.366654\pi\) | |||||||
\(594\) | −6696.00 | −0.462526 | ||||||||
\(595\) | 2352.00 | 0.162055 | ||||||||
\(596\) | 18960.0 | 1.30307 | ||||||||
\(597\) | −5040.00 | −0.345517 | ||||||||
\(598\) | 10416.0 | 0.712277 | ||||||||
\(599\) | 7650.00 | 0.521821 | 0.260910 | − | 0.965363i | \(-0.415977\pi\) | ||||
0.260910 | + | 0.965363i | \(0.415977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22878.0 | −1.55277 | −0.776384 | − | 0.630261i | \(-0.782948\pi\) | ||||
−0.776384 | + | 0.630261i | \(0.782948\pi\) | |||||||
\(602\) | −1904.00 | −0.128906 | ||||||||
\(603\) | 8136.00 | 0.549459 | ||||||||
\(604\) | −4544.00 | −0.306114 | ||||||||
\(605\) | −10052.0 | −0.675491 | ||||||||
\(606\) | −2784.00 | −0.186621 | ||||||||
\(607\) | 704.000 | 0.0470749 | 0.0235375 | − | 0.999723i | \(-0.492507\pi\) | ||||
0.0235375 | + | 0.999723i | \(0.492507\pi\) | |||||||
\(608\) | −25600.0 | −1.70759 | ||||||||
\(609\) | −210.000 | −0.0139731 | ||||||||
\(610\) | −9952.00 | −0.660565 | ||||||||
\(611\) | −20088.0 | −1.33007 | ||||||||
\(612\) | 6048.00 | 0.399470 | ||||||||
\(613\) | 24958.0 | 1.64444 | 0.822222 | − | 0.569167i | \(-0.192734\pi\) | ||||
0.822222 | + | 0.569167i | \(0.192734\pi\) | |||||||
\(614\) | 23536.0 | 1.54696 | ||||||||
\(615\) | −2976.00 | −0.195128 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8826.00 | −0.575886 | −0.287943 | − | 0.957648i | \(-0.592971\pi\) | ||||
−0.287943 | + | 0.957648i | \(0.592971\pi\) | |||||||
\(618\) | 21504.0 | 1.39971 | ||||||||
\(619\) | 21220.0 | 1.37787 | 0.688937 | − | 0.724821i | \(-0.258078\pi\) | ||||
0.688937 | + | 0.724821i | \(0.258078\pi\) | |||||||
\(620\) | 1536.00 | 0.0994956 | ||||||||
\(621\) | 1134.00 | 0.0732783 | ||||||||
\(622\) | 36528.0 | 2.35473 | ||||||||
\(623\) | −1400.00 | −0.0900318 | ||||||||
\(624\) | −11904.0 | −0.763688 | ||||||||
\(625\) | 9881.00 | 0.632384 | ||||||||
\(626\) | −37528.0 | −2.39604 | ||||||||
\(627\) | −18600.0 | −1.18471 | ||||||||
\(628\) | −2128.00 | −0.135217 | ||||||||
\(629\) | −20664.0 | −1.30990 | ||||||||
\(630\) | 1008.00 | 0.0637455 | ||||||||
\(631\) | −3268.00 | −0.206176 | −0.103088 | − | 0.994672i | \(-0.532872\pi\) | ||||
−0.103088 | + | 0.994672i | \(0.532872\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2004.00 | 0.125832 | ||||||||
\(634\) | 12456.0 | 0.780270 | ||||||||
\(635\) | −3216.00 | −0.200981 | ||||||||
\(636\) | −6192.00 | −0.386052 | ||||||||
\(637\) | −3038.00 | −0.188964 | ||||||||
\(638\) | −2480.00 | −0.153894 | ||||||||
\(639\) | −6102.00 | −0.377764 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13062.0 | 0.804864 | 0.402432 | − | 0.915450i | \(-0.368165\pi\) | ||||
0.402432 | + | 0.915450i | \(0.368165\pi\) | |||||||
\(642\) | 22872.0 | 1.40605 | ||||||||
\(643\) | −28012.0 | −1.71802 | −0.859009 | − | 0.511961i | \(-0.828919\pi\) | ||||
−0.859009 | + | 0.511961i | \(0.828919\pi\) | |||||||
\(644\) | 2352.00 | 0.143916 | ||||||||
\(645\) | 816.000 | 0.0498139 | ||||||||
\(646\) | 33600.0 | 2.04640 | ||||||||
\(647\) | 3844.00 | 0.233575 | 0.116788 | − | 0.993157i | \(-0.462740\pi\) | ||||
0.116788 | + | 0.993157i | \(0.462740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7440.00 | 0.449993 | ||||||||
\(650\) | 27032.0 | 1.63120 | ||||||||
\(651\) | −1008.00 | −0.0606861 | ||||||||
\(652\) | −2176.00 | −0.130704 | ||||||||
\(653\) | −28482.0 | −1.70687 | −0.853436 | − | 0.521198i | \(-0.825485\pi\) | ||||
−0.853436 | + | 0.521198i | \(0.825485\pi\) | |||||||
\(654\) | 1080.00 | 0.0645739 | ||||||||
\(655\) | −3248.00 | −0.193756 | ||||||||
\(656\) | 15872.0 | 0.944661 | ||||||||
\(657\) | −5778.00 | −0.343107 | ||||||||
\(658\) | −9072.00 | −0.537482 | ||||||||
\(659\) | −9330.00 | −0.551510 | −0.275755 | − | 0.961228i | \(-0.588928\pi\) | ||||
−0.275755 | + | 0.961228i | \(0.588928\pi\) | |||||||
\(660\) | 5952.00 | 0.351032 | ||||||||
\(661\) | 8782.00 | 0.516763 | 0.258381 | − | 0.966043i | \(-0.416811\pi\) | ||||
0.258381 | + | 0.966043i | \(0.416811\pi\) | |||||||
\(662\) | 6128.00 | 0.359776 | ||||||||
\(663\) | 15624.0 | 0.915212 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2800.00 | 0.163277 | ||||||||
\(666\) | −8856.00 | −0.515260 | ||||||||
\(667\) | 420.000 | 0.0243815 | ||||||||
\(668\) | −15008.0 | −0.869277 | ||||||||
\(669\) | 5496.00 | 0.317620 | ||||||||
\(670\) | −14464.0 | −0.834020 | ||||||||
\(671\) | 38564.0 | 2.21870 | ||||||||
\(672\) | −5376.00 | −0.308607 | ||||||||
\(673\) | −10562.0 | −0.604956 | −0.302478 | − | 0.953156i | \(-0.597814\pi\) | ||||
−0.302478 | + | 0.953156i | \(0.597814\pi\) | |||||||
\(674\) | −16664.0 | −0.952334 | ||||||||
\(675\) | 2943.00 | 0.167816 | ||||||||
\(676\) | 13176.0 | 0.749659 | ||||||||
\(677\) | −26016.0 | −1.47692 | −0.738461 | − | 0.674296i | \(-0.764447\pi\) | ||||
−0.738461 | + | 0.674296i | \(0.764447\pi\) | |||||||
\(678\) | −5496.00 | −0.311317 | ||||||||
\(679\) | 8862.00 | 0.500872 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14832.0 | −0.834601 | ||||||||
\(682\) | −11904.0 | −0.668369 | ||||||||
\(683\) | 8898.00 | 0.498496 | 0.249248 | − | 0.968440i | \(-0.419817\pi\) | ||||
0.249248 | + | 0.968440i | \(0.419817\pi\) | |||||||
\(684\) | 7200.00 | 0.402484 | ||||||||
\(685\) | −1656.00 | −0.0923686 | ||||||||
\(686\) | −1372.00 | −0.0763604 | ||||||||
\(687\) | 16410.0 | 0.911325 | ||||||||
\(688\) | −4352.00 | −0.241161 | ||||||||
\(689\) | −15996.0 | −0.884469 | ||||||||
\(690\) | −2016.00 | −0.111229 | ||||||||
\(691\) | 30572.0 | 1.68309 | 0.841544 | − | 0.540189i | \(-0.181647\pi\) | ||||
0.841544 | + | 0.540189i | \(0.181647\pi\) | |||||||
\(692\) | −1216.00 | −0.0667997 | ||||||||
\(693\) | −3906.00 | −0.214108 | ||||||||
\(694\) | −45464.0 | −2.48673 | ||||||||
\(695\) | 6480.00 | 0.353670 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20832.0 | −1.13209 | ||||||||
\(698\) | 37240.0 | 2.01942 | ||||||||
\(699\) | 8406.00 | 0.454856 | ||||||||
\(700\) | 6104.00 | 0.329585 | ||||||||
\(701\) | −30618.0 | −1.64968 | −0.824840 | − | 0.565366i | \(-0.808735\pi\) | ||||
−0.824840 | + | 0.565366i | \(0.808735\pi\) | |||||||
\(702\) | 6696.00 | 0.360006 | ||||||||
\(703\) | −24600.0 | −1.31978 | ||||||||
\(704\) | −31744.0 | −1.69943 | ||||||||
\(705\) | 3888.00 | 0.207703 | ||||||||
\(706\) | −34288.0 | −1.82783 | ||||||||
\(707\) | −1624.00 | −0.0863887 | ||||||||
\(708\) | −2880.00 | −0.152877 | ||||||||
\(709\) | −8130.00 | −0.430647 | −0.215323 | − | 0.976543i | \(-0.569081\pi\) | ||||
−0.215323 | + | 0.976543i | \(0.569081\pi\) | |||||||
\(710\) | 10848.0 | 0.573406 | ||||||||
\(711\) | 6660.00 | 0.351293 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2016.00 | 0.105890 | ||||||||
\(714\) | 7056.00 | 0.369838 | ||||||||
\(715\) | 15376.0 | 0.804237 | ||||||||
\(716\) | 4880.00 | 0.254713 | ||||||||
\(717\) | 3510.00 | 0.182822 | ||||||||
\(718\) | −19160.0 | −0.995884 | ||||||||
\(719\) | −27840.0 | −1.44403 | −0.722014 | − | 0.691878i | \(-0.756784\pi\) | ||||
−0.722014 | + | 0.691878i | \(0.756784\pi\) | |||||||
\(720\) | 2304.00 | 0.119257 | ||||||||
\(721\) | 12544.0 | 0.647938 | ||||||||
\(722\) | 12564.0 | 0.647623 | ||||||||
\(723\) | 7014.00 | 0.360793 | ||||||||
\(724\) | 8336.00 | 0.427907 | ||||||||
\(725\) | 1090.00 | 0.0558367 | ||||||||
\(726\) | −30156.0 | −1.54159 | ||||||||
\(727\) | 14624.0 | 0.746044 | 0.373022 | − | 0.927822i | \(-0.378322\pi\) | ||||
0.373022 | + | 0.927822i | \(0.378322\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 10272.0 | 0.520800 | ||||||||
\(731\) | 5712.00 | 0.289010 | ||||||||
\(732\) | −14928.0 | −0.753763 | ||||||||
\(733\) | −20862.0 | −1.05124 | −0.525618 | − | 0.850721i | \(-0.676166\pi\) | ||||
−0.525618 | + | 0.850721i | \(0.676166\pi\) | |||||||
\(734\) | 21696.0 | 1.09103 | ||||||||
\(735\) | 588.000 | 0.0295084 | ||||||||
\(736\) | 10752.0 | 0.538484 | ||||||||
\(737\) | 56048.0 | 2.80130 | ||||||||
\(738\) | −8928.00 | −0.445317 | ||||||||
\(739\) | −13920.0 | −0.692903 | −0.346452 | − | 0.938068i | \(-0.612614\pi\) | ||||
−0.346452 | + | 0.938068i | \(0.612614\pi\) | |||||||
\(740\) | 7872.00 | 0.391055 | ||||||||
\(741\) | 18600.0 | 0.922116 | ||||||||
\(742\) | −7224.00 | −0.357414 | ||||||||
\(743\) | 25578.0 | 1.26294 | 0.631471 | − | 0.775400i | \(-0.282452\pi\) | ||||
0.631471 | + | 0.775400i | \(0.282452\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9480.00 | −0.466202 | ||||||||
\(746\) | 7352.00 | 0.360826 | ||||||||
\(747\) | 4212.00 | 0.206304 | ||||||||
\(748\) | 41664.0 | 2.03661 | ||||||||
\(749\) | 13342.0 | 0.650876 | ||||||||
\(750\) | −11232.0 | −0.546846 | ||||||||
\(751\) | 33472.0 | 1.62638 | 0.813189 | − | 0.581999i | \(-0.197729\pi\) | ||||
0.813189 | + | 0.581999i | \(0.197729\pi\) | |||||||
\(752\) | −20736.0 | −1.00554 | ||||||||
\(753\) | −8376.00 | −0.405363 | ||||||||
\(754\) | 2480.00 | 0.119783 | ||||||||
\(755\) | 2272.00 | 0.109519 | ||||||||
\(756\) | 1512.00 | 0.0727393 | ||||||||
\(757\) | 25934.0 | 1.24516 | 0.622581 | − | 0.782556i | \(-0.286084\pi\) | ||||
0.622581 | + | 0.782556i | \(0.286084\pi\) | |||||||
\(758\) | −17040.0 | −0.816518 | ||||||||
\(759\) | 7812.00 | 0.373594 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26952.0 | 1.28385 | 0.641925 | − | 0.766768i | \(-0.278136\pi\) | ||||
0.641925 | + | 0.766768i | \(0.278136\pi\) | |||||||
\(762\) | −9648.00 | −0.458675 | ||||||||
\(763\) | 630.000 | 0.0298919 | ||||||||
\(764\) | −16304.0 | −0.772065 | ||||||||
\(765\) | −3024.00 | −0.142919 | ||||||||
\(766\) | 36192.0 | 1.70714 | ||||||||
\(767\) | −7440.00 | −0.350251 | ||||||||
\(768\) | −12288.0 | −0.577350 | ||||||||
\(769\) | 23450.0 | 1.09965 | 0.549824 | − | 0.835281i | \(-0.314695\pi\) | ||||
0.549824 | + | 0.835281i | \(0.314695\pi\) | |||||||
\(770\) | 6944.00 | 0.324993 | ||||||||
\(771\) | −21072.0 | −0.984293 | ||||||||
\(772\) | −20816.0 | −0.970446 | ||||||||
\(773\) | 39568.0 | 1.84109 | 0.920545 | − | 0.390637i | \(-0.127745\pi\) | ||||
0.920545 | + | 0.390637i | \(0.127745\pi\) | |||||||
\(774\) | 2448.00 | 0.113684 | ||||||||
\(775\) | 5232.00 | 0.242502 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5166.00 | −0.238519 | ||||||||
\(778\) | −45960.0 | −2.11793 | ||||||||
\(779\) | −24800.0 | −1.14063 | ||||||||
\(780\) | −5952.00 | −0.273225 | ||||||||
\(781\) | −42036.0 | −1.92595 | ||||||||
\(782\) | −14112.0 | −0.645325 | ||||||||
\(783\) | 270.000 | 0.0123231 | ||||||||
\(784\) | −3136.00 | −0.142857 | ||||||||
\(785\) | 1064.00 | 0.0483768 | ||||||||
\(786\) | −9744.00 | −0.442184 | ||||||||
\(787\) | −12356.0 | −0.559649 | −0.279825 | − | 0.960051i | \(-0.590276\pi\) | ||||
−0.279825 | + | 0.960051i | \(0.590276\pi\) | |||||||
\(788\) | 18832.0 | 0.851348 | ||||||||
\(789\) | −7314.00 | −0.330019 | ||||||||
\(790\) | −11840.0 | −0.533226 | ||||||||
\(791\) | −3206.00 | −0.144112 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38564.0 | −1.72692 | ||||||||
\(794\) | −7464.00 | −0.333611 | ||||||||
\(795\) | 3096.00 | 0.138118 | ||||||||
\(796\) | 13440.0 | 0.598452 | ||||||||
\(797\) | −21736.0 | −0.966033 | −0.483017 | − | 0.875611i | \(-0.660459\pi\) | ||||
−0.483017 | + | 0.875611i | \(0.660459\pi\) | |||||||
\(798\) | 8400.00 | 0.372628 | ||||||||
\(799\) | 27216.0 | 1.20505 | ||||||||
\(800\) | 27904.0 | 1.23319 | ||||||||
\(801\) | 1800.00 | 0.0794006 | ||||||||
\(802\) | 54648.0 | 2.40609 | ||||||||
\(803\) | −39804.0 | −1.74926 | ||||||||
\(804\) | −21696.0 | −0.951690 | ||||||||
\(805\) | −1176.00 | −0.0514889 | ||||||||
\(806\) | 11904.0 | 0.520224 | ||||||||
\(807\) | 20340.0 | 0.887239 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −38310.0 | −1.66490 | −0.832452 | − | 0.554097i | \(-0.813064\pi\) | ||||
−0.832452 | + | 0.554097i | \(0.813064\pi\) | |||||||
\(810\) | −1296.00 | −0.0562183 | ||||||||
\(811\) | 2132.00 | 0.0923115 | 0.0461558 | − | 0.998934i | \(-0.485303\pi\) | ||||
0.0461558 | + | 0.998934i | \(0.485303\pi\) | |||||||
\(812\) | 560.000 | 0.0242022 | ||||||||
\(813\) | 5784.00 | 0.249513 | ||||||||
\(814\) | −61008.0 | −2.62694 | ||||||||
\(815\) | 1088.00 | 0.0467619 | ||||||||
\(816\) | 16128.0 | 0.691903 | ||||||||
\(817\) | 6800.00 | 0.291190 | ||||||||
\(818\) | −52840.0 | −2.25857 | ||||||||
\(819\) | 3906.00 | 0.166650 | ||||||||
\(820\) | 7936.00 | 0.337972 | ||||||||
\(821\) | 5002.00 | 0.212632 | 0.106316 | − | 0.994332i | \(-0.466094\pi\) | ||||
0.106316 | + | 0.994332i | \(0.466094\pi\) | |||||||
\(822\) | −4968.00 | −0.210802 | ||||||||
\(823\) | −3612.00 | −0.152985 | −0.0764923 | − | 0.997070i | \(-0.524372\pi\) | ||||
−0.0764923 | + | 0.997070i | \(0.524372\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20274.0 | 0.855576 | ||||||||
\(826\) | −3360.00 | −0.141537 | ||||||||
\(827\) | −27666.0 | −1.16329 | −0.581645 | − | 0.813443i | \(-0.697591\pi\) | ||||
−0.581645 | + | 0.813443i | \(0.697591\pi\) | |||||||
\(828\) | −3024.00 | −0.126922 | ||||||||
\(829\) | 12890.0 | 0.540034 | 0.270017 | − | 0.962856i | \(-0.412971\pi\) | ||||
0.270017 | + | 0.962856i | \(0.412971\pi\) | |||||||
\(830\) | −7488.00 | −0.313147 | ||||||||
\(831\) | −16662.0 | −0.695546 | ||||||||
\(832\) | 31744.0 | 1.32275 | ||||||||
\(833\) | 4116.00 | 0.171202 | ||||||||
\(834\) | 19440.0 | 0.807137 | ||||||||
\(835\) | 7504.00 | 0.311002 | ||||||||
\(836\) | 49600.0 | 2.05198 | ||||||||
\(837\) | 1296.00 | 0.0535201 | ||||||||
\(838\) | 27840.0 | 1.14763 | ||||||||
\(839\) | −9340.00 | −0.384330 | −0.192165 | − | 0.981363i | \(-0.561551\pi\) | ||||
−0.192165 | + | 0.981363i | \(0.561551\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24289.0 | −0.995900 | ||||||||
\(842\) | 32648.0 | 1.33625 | ||||||||
\(843\) | −5826.00 | −0.238029 | ||||||||
\(844\) | −5344.00 | −0.217948 | ||||||||
\(845\) | −6588.00 | −0.268206 | ||||||||
\(846\) | 11664.0 | 0.474015 | ||||||||
\(847\) | −17591.0 | −0.713617 | ||||||||
\(848\) | −16512.0 | −0.668661 | ||||||||
\(849\) | −14484.0 | −0.585500 | ||||||||
\(850\) | −36624.0 | −1.47787 | ||||||||
\(851\) | 10332.0 | 0.416188 | ||||||||
\(852\) | 16272.0 | 0.654307 | ||||||||
\(853\) | −33082.0 | −1.32791 | −0.663954 | − | 0.747773i | \(-0.731123\pi\) | ||||
−0.663954 | + | 0.747773i | \(0.731123\pi\) | |||||||
\(854\) | −17416.0 | −0.697849 | ||||||||
\(855\) | −3600.00 | −0.143997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7544.00 | 0.300698 | 0.150349 | − | 0.988633i | \(-0.451960\pi\) | ||||
0.150349 | + | 0.988633i | \(0.451960\pi\) | |||||||
\(858\) | 46128.0 | 1.83541 | ||||||||
\(859\) | 8180.00 | 0.324910 | 0.162455 | − | 0.986716i | \(-0.448059\pi\) | ||||
0.162455 | + | 0.986716i | \(0.448059\pi\) | |||||||
\(860\) | −2176.00 | −0.0862802 | ||||||||
\(861\) | −5208.00 | −0.206142 | ||||||||
\(862\) | 66408.0 | 2.62397 | ||||||||
\(863\) | 10518.0 | 0.414875 | 0.207437 | − | 0.978248i | \(-0.433488\pi\) | ||||
0.207437 | + | 0.978248i | \(0.433488\pi\) | |||||||
\(864\) | 6912.00 | 0.272166 | ||||||||
\(865\) | 608.000 | 0.0238990 | ||||||||
\(866\) | 30952.0 | 1.21454 | ||||||||
\(867\) | −6429.00 | −0.251834 | ||||||||
\(868\) | 2688.00 | 0.105111 | ||||||||
\(869\) | 45880.0 | 1.79099 | ||||||||
\(870\) | −480.000 | −0.0187052 | ||||||||
\(871\) | −56048.0 | −2.18038 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −11394.0 | −0.441728 | ||||||||
\(874\) | −16800.0 | −0.650193 | ||||||||
\(875\) | −6552.00 | −0.253141 | ||||||||
\(876\) | 15408.0 | 0.594279 | ||||||||
\(877\) | 14134.0 | 0.544209 | 0.272104 | − | 0.962268i | \(-0.412280\pi\) | ||||
0.272104 | + | 0.962268i | \(0.412280\pi\) | |||||||
\(878\) | −3360.00 | −0.129151 | ||||||||
\(879\) | 18456.0 | 0.708197 | ||||||||
\(880\) | 15872.0 | 0.608006 | ||||||||
\(881\) | 6492.00 | 0.248265 | 0.124132 | − | 0.992266i | \(-0.460385\pi\) | ||||
0.124132 | + | 0.992266i | \(0.460385\pi\) | |||||||
\(882\) | 1764.00 | 0.0673435 | ||||||||
\(883\) | 38228.0 | 1.45694 | 0.728468 | − | 0.685080i | \(-0.240233\pi\) | ||||
0.728468 | + | 0.685080i | \(0.240233\pi\) | |||||||
\(884\) | −41664.0 | −1.58519 | ||||||||
\(885\) | 1440.00 | 0.0546950 | ||||||||
\(886\) | 26472.0 | 1.00377 | ||||||||
\(887\) | −43076.0 | −1.63061 | −0.815305 | − | 0.579032i | \(-0.803431\pi\) | ||||
−0.815305 | + | 0.579032i | \(0.803431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5628.00 | −0.212325 | ||||||||
\(890\) | −3200.00 | −0.120522 | ||||||||
\(891\) | 5022.00 | 0.188825 | ||||||||
\(892\) | −14656.0 | −0.550134 | ||||||||
\(893\) | 32400.0 | 1.21414 | ||||||||
\(894\) | −28440.0 | −1.06396 | ||||||||
\(895\) | −2440.00 | −0.0911287 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7812.00 | −0.290786 | ||||||||
\(898\) | 12360.0 | 0.459308 | ||||||||
\(899\) | 480.000 | 0.0178074 | ||||||||
\(900\) | −7848.00 | −0.290667 | ||||||||
\(901\) | 21672.0 | 0.801331 | ||||||||
\(902\) | −61504.0 | −2.27035 | ||||||||
\(903\) | 1428.00 | 0.0526255 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4168.00 | −0.153093 | ||||||||
\(906\) | 6816.00 | 0.249941 | ||||||||
\(907\) | −32236.0 | −1.18013 | −0.590065 | − | 0.807355i | \(-0.700898\pi\) | ||||
−0.590065 | + | 0.807355i | \(0.700898\pi\) | |||||||
\(908\) | 39552.0 | 1.44557 | ||||||||
\(909\) | 2088.00 | 0.0761877 | ||||||||
\(910\) | −6944.00 | −0.252958 | ||||||||
\(911\) | −46518.0 | −1.69178 | −0.845889 | − | 0.533359i | \(-0.820930\pi\) | ||||
−0.845889 | + | 0.533359i | \(0.820930\pi\) | |||||||
\(912\) | 19200.0 | 0.697122 | ||||||||
\(913\) | 29016.0 | 1.05180 | ||||||||
\(914\) | 23656.0 | 0.856095 | ||||||||
\(915\) | 7464.00 | 0.269675 | ||||||||
\(916\) | −43760.0 | −1.57846 | ||||||||
\(917\) | −5684.00 | −0.204692 | ||||||||
\(918\) | −9072.00 | −0.326166 | ||||||||
\(919\) | 17840.0 | 0.640356 | 0.320178 | − | 0.947357i | \(-0.396257\pi\) | ||||
0.320178 | + | 0.947357i | \(0.396257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17652.0 | −0.631545 | ||||||||
\(922\) | −63872.0 | −2.28147 | ||||||||
\(923\) | 42036.0 | 1.49906 | ||||||||
\(924\) | 10416.0 | 0.370846 | ||||||||
\(925\) | 26814.0 | 0.953123 | ||||||||
\(926\) | −4688.00 | −0.166369 | ||||||||
\(927\) | −16128.0 | −0.571427 | ||||||||
\(928\) | 2560.00 | 0.0905562 | ||||||||
\(929\) | 7000.00 | 0.247215 | 0.123607 | − | 0.992331i | \(-0.460554\pi\) | ||||
0.123607 | + | 0.992331i | \(0.460554\pi\) | |||||||
\(930\) | −2304.00 | −0.0812378 | ||||||||
\(931\) | 4900.00 | 0.172493 | ||||||||
\(932\) | −22416.0 | −0.787833 | ||||||||
\(933\) | −27396.0 | −0.961313 | ||||||||
\(934\) | 21216.0 | 0.743264 | ||||||||
\(935\) | −20832.0 | −0.728641 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36114.0 | 1.25912 | 0.629559 | − | 0.776953i | \(-0.283236\pi\) | ||||
0.629559 | + | 0.776953i | \(0.283236\pi\) | |||||||
\(938\) | −25312.0 | −0.881094 | ||||||||
\(939\) | 28146.0 | 0.978179 | ||||||||
\(940\) | −10368.0 | −0.359752 | ||||||||
\(941\) | −4748.00 | −0.164485 | −0.0822425 | − | 0.996612i | \(-0.526208\pi\) | ||||
−0.0822425 | + | 0.996612i | \(0.526208\pi\) | |||||||
\(942\) | 3192.00 | 0.110404 | ||||||||
\(943\) | 10416.0 | 0.359694 | ||||||||
\(944\) | −7680.00 | −0.264791 | ||||||||
\(945\) | −756.000 | −0.0260240 | ||||||||
\(946\) | 16864.0 | 0.579594 | ||||||||
\(947\) | 42694.0 | 1.46501 | 0.732507 | − | 0.680759i | \(-0.238350\pi\) | ||||
0.732507 | + | 0.680759i | \(0.238350\pi\) | |||||||
\(948\) | −17760.0 | −0.608458 | ||||||||
\(949\) | 39804.0 | 1.36153 | ||||||||
\(950\) | −43600.0 | −1.48902 | ||||||||
\(951\) | −9342.00 | −0.318544 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −16742.0 | −0.569073 | −0.284537 | − | 0.958665i | \(-0.591840\pi\) | ||||
−0.284537 | + | 0.958665i | \(0.591840\pi\) | |||||||
\(954\) | 9288.00 | 0.315210 | ||||||||
\(955\) | 8152.00 | 0.276223 | ||||||||
\(956\) | −9360.00 | −0.316657 | ||||||||
\(957\) | 1860.00 | 0.0628268 | ||||||||
\(958\) | 22960.0 | 0.774326 | ||||||||
\(959\) | −2898.00 | −0.0975822 | ||||||||
\(960\) | −6144.00 | −0.206559 | ||||||||
\(961\) | −27487.0 | −0.922661 | ||||||||
\(962\) | 61008.0 | 2.04467 | ||||||||
\(963\) | −17154.0 | −0.574019 | ||||||||
\(964\) | −18704.0 | −0.624912 | ||||||||
\(965\) | 10408.0 | 0.347197 | ||||||||
\(966\) | −3528.00 | −0.117507 | ||||||||
\(967\) | −9956.00 | −0.331089 | −0.165545 | − | 0.986202i | \(-0.552938\pi\) | ||||
−0.165545 | + | 0.986202i | \(0.552938\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25200.0 | −0.835439 | ||||||||
\(970\) | 20256.0 | 0.670496 | ||||||||
\(971\) | −26388.0 | −0.872123 | −0.436061 | − | 0.899917i | \(-0.643627\pi\) | ||||
−0.436061 | + | 0.899917i | \(0.643627\pi\) | |||||||
\(972\) | −1944.00 | −0.0641500 | ||||||||
\(973\) | 11340.0 | 0.373632 | ||||||||
\(974\) | 35776.0 | 1.17694 | ||||||||
\(975\) | −20274.0 | −0.665936 | ||||||||
\(976\) | −39808.0 | −1.30556 | ||||||||
\(977\) | −786.000 | −0.0257383 | −0.0128692 | − | 0.999917i | \(-0.504096\pi\) | ||||
−0.0128692 | + | 0.999917i | \(0.504096\pi\) | |||||||
\(978\) | 3264.00 | 0.106719 | ||||||||
\(979\) | 12400.0 | 0.404807 | ||||||||
\(980\) | −1568.00 | −0.0511101 | ||||||||
\(981\) | −810.000 | −0.0263622 | ||||||||
\(982\) | −22232.0 | −0.722456 | ||||||||
\(983\) | 51888.0 | 1.68359 | 0.841796 | − | 0.539796i | \(-0.181499\pi\) | ||||
0.841796 | + | 0.539796i | \(0.181499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9416.00 | −0.304588 | ||||||||
\(986\) | −3360.00 | −0.108524 | ||||||||
\(987\) | 6804.00 | 0.219426 | ||||||||
\(988\) | −49600.0 | −1.59715 | ||||||||
\(989\) | −2856.00 | −0.0918256 | ||||||||
\(990\) | −8928.00 | −0.286617 | ||||||||
\(991\) | −51928.0 | −1.66453 | −0.832264 | − | 0.554379i | \(-0.812956\pi\) | ||||
−0.832264 | + | 0.554379i | \(0.812956\pi\) | |||||||
\(992\) | 12288.0 | 0.393291 | ||||||||
\(993\) | −4596.00 | −0.146878 | ||||||||
\(994\) | 18984.0 | 0.605771 | ||||||||
\(995\) | −6720.00 | −0.214109 | ||||||||
\(996\) | −11232.0 | −0.357329 | ||||||||
\(997\) | −386.000 | −0.0122615 | −0.00613076 | − | 0.999981i | \(-0.501951\pi\) | ||||
−0.00613076 | + | 0.999981i | \(0.501951\pi\) | |||||||
\(998\) | −79280.0 | −2.51459 | ||||||||
\(999\) | 6642.00 | 0.210354 |
(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 | 21.4.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 63.4.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 336.4.a.h.1.1 | 1 | |||
5.2 | odd | 4 | 525.4.d.b.274.2 | 2 | |||
5.3 | odd | 4 | 525.4.d.b.274.1 | 2 | |||
5.4 | even | 2 | 525.4.a.b.1.1 | 1 | |||
7.2 | even | 3 | 147.4.e.c.67.1 | 2 | |||
7.3 | odd | 6 | 147.4.e.b.79.1 | 2 | |||
7.4 | even | 3 | 147.4.e.c.79.1 | 2 | |||
7.5 | odd | 6 | 147.4.e.b.67.1 | 2 | |||
7.6 | odd | 2 | 147.4.a.g.1.1 | 1 | |||
8.3 | odd | 2 | 1344.4.a.i.1.1 | 1 | |||
8.5 | even | 2 | 1344.4.a.w.1.1 | 1 | |||
12.11 | even | 2 | 1008.4.a.m.1.1 | 1 | |||
15.14 | odd | 2 | 1575.4.a.k.1.1 | 1 | |||
21.2 | odd | 6 | 441.4.e.m.361.1 | 2 | |||
21.5 | even | 6 | 441.4.e.n.361.1 | 2 | |||
21.11 | odd | 6 | 441.4.e.m.226.1 | 2 | |||
21.17 | even | 6 | 441.4.e.n.226.1 | 2 | |||
21.20 | even | 2 | 441.4.a.b.1.1 | 1 | |||
28.27 | even | 2 | 2352.4.a.l.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
63.4.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
147.4.a.g.1.1 | 1 | 7.6 | odd | 2 | |||
147.4.e.b.67.1 | 2 | 7.5 | odd | 6 | |||
147.4.e.b.79.1 | 2 | 7.3 | odd | 6 | |||
147.4.e.c.67.1 | 2 | 7.2 | even | 3 | |||
147.4.e.c.79.1 | 2 | 7.4 | even | 3 | |||
336.4.a.h.1.1 | 1 | 4.3 | odd | 2 | |||
441.4.a.b.1.1 | 1 | 21.20 | even | 2 | |||
441.4.e.m.226.1 | 2 | 21.11 | odd | 6 | |||
441.4.e.m.361.1 | 2 | 21.2 | odd | 6 | |||
441.4.e.n.226.1 | 2 | 21.17 | even | 6 | |||
441.4.e.n.361.1 | 2 | 21.5 | even | 6 | |||
525.4.a.b.1.1 | 1 | 5.4 | even | 2 | |||
525.4.d.b.274.1 | 2 | 5.3 | odd | 4 | |||
525.4.d.b.274.2 | 2 | 5.2 | odd | 4 | |||
1008.4.a.m.1.1 | 1 | 12.11 | even | 2 | |||
1344.4.a.i.1.1 | 1 | 8.3 | odd | 2 | |||
1344.4.a.w.1.1 | 1 | 8.5 | even | 2 | |||
1575.4.a.k.1.1 | 1 | 15.14 | odd | 2 | |||
2352.4.a.l.1.1 | 1 | 28.27 | even | 2 |