Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), not 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: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.c.199.1 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000i | 1.41421i | 0.707107 | + | 0.707107i | \(0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −12.0000 | −0.816497 | ||||||||
\(7\) | − 21.0000i | − 1.13389i | −0.823754 | − | 0.566947i | \(-0.808125\pi\) | ||||
0.823754 | − | 0.566947i | \(-0.191875\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | − 24.0000i | − 0.577350i | ||||||||
\(13\) | − 68.0000i | − 1.45075i | −0.688352 | − | 0.725377i | \(-0.741665\pi\) | ||||
0.688352 | − | 0.725377i | \(-0.258335\pi\) | |||||||
\(14\) | 84.0000 | 1.60357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −64.0000 | −1.00000 | ||||||||
\(17\) | − 21.0000i | − 0.299603i | −0.988716 | − | 0.149801i | \(-0.952137\pi\) | ||||
0.988716 | − | 0.149801i | \(-0.0478634\pi\) | |||||||
\(18\) | − 36.0000i | − 0.471405i | ||||||||
\(19\) | −125.000 | −1.50931 | −0.754657 | − | 0.656119i | \(-0.772197\pi\) | ||||
−0.754657 | + | 0.656119i | \(0.772197\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 63.0000 | 0.654654 | ||||||||
\(22\) | 44.0000i | 0.426401i | ||||||||
\(23\) | 137.000i | 1.24202i | 0.783802 | + | 0.621010i | \(0.213278\pi\) | ||||
−0.783802 | + | 0.621010i | \(0.786722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 272.000 | 2.05168 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 168.000i | 1.13389i | ||||||||
\(29\) | 150.000 | 0.960493 | 0.480247 | − | 0.877134i | \(-0.340547\pi\) | ||||
0.480247 | + | 0.877134i | \(0.340547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 292.000 | 1.69177 | 0.845883 | − | 0.533368i | \(-0.179074\pi\) | ||||
0.845883 | + | 0.533368i | \(0.179074\pi\) | |||||||
\(32\) | − 256.000i | − 1.41421i | ||||||||
\(33\) | 33.0000i | 0.174078i | ||||||||
\(34\) | 84.0000 | 0.423702 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 72.0000 | 0.333333 | ||||||||
\(37\) | 349.000i | 1.55068i | 0.631543 | + | 0.775341i | \(0.282422\pi\) | ||||
−0.631543 | + | 0.775341i | \(0.717578\pi\) | |||||||
\(38\) | − 500.000i | − 2.13449i | ||||||||
\(39\) | 204.000 | 0.837593 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 497.000 | 1.89313 | 0.946565 | − | 0.322512i | \(-0.104527\pi\) | ||||
0.946565 | + | 0.322512i | \(0.104527\pi\) | |||||||
\(42\) | 252.000i | 0.925820i | ||||||||
\(43\) | − 208.000i | − 0.737668i | −0.929495 | − | 0.368834i | \(-0.879757\pi\) | ||||
0.929495 | − | 0.368834i | \(-0.120243\pi\) | |||||||
\(44\) | −88.0000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −548.000 | −1.75648 | ||||||||
\(47\) | 369.000i | 1.14520i | 0.819837 | + | 0.572598i | \(0.194064\pi\) | ||||
−0.819837 | + | 0.572598i | \(0.805936\pi\) | |||||||
\(48\) | − 192.000i | − 0.577350i | ||||||||
\(49\) | −98.0000 | −0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 63.0000 | 0.172976 | ||||||||
\(52\) | 544.000i | 1.45075i | ||||||||
\(53\) | 542.000i | 1.40471i | 0.711829 | + | 0.702353i | \(0.247867\pi\) | ||||
−0.711829 | + | 0.702353i | \(0.752133\pi\) | |||||||
\(54\) | 108.000 | 0.272166 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 375.000i | − 0.871403i | ||||||||
\(58\) | 600.000i | 1.35834i | ||||||||
\(59\) | −235.000 | −0.518549 | −0.259275 | − | 0.965804i | \(-0.583483\pi\) | ||||
−0.259275 | + | 0.965804i | \(0.583483\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 482.000 | 1.01170 | 0.505851 | − | 0.862621i | \(-0.331179\pi\) | ||||
0.505851 | + | 0.862621i | \(0.331179\pi\) | |||||||
\(62\) | 1168.00i | 2.39252i | ||||||||
\(63\) | 189.000i | 0.377964i | ||||||||
\(64\) | 512.000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −132.000 | −0.246183 | ||||||||
\(67\) | 734.000i | 1.33839i | 0.743085 | + | 0.669197i | \(0.233362\pi\) | ||||
−0.743085 | + | 0.669197i | \(0.766638\pi\) | |||||||
\(68\) | 168.000i | 0.299603i | ||||||||
\(69\) | −411.000 | −0.717081 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 587.000 | 0.981184 | 0.490592 | − | 0.871389i | \(-0.336781\pi\) | ||||
0.490592 | + | 0.871389i | \(0.336781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 518.000i | − 0.830511i | −0.909705 | − | 0.415256i | \(-0.863692\pi\) | ||||
0.909705 | − | 0.415256i | \(-0.136308\pi\) | |||||||
\(74\) | −1396.00 | −2.19300 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1000.00 | 1.50931 | ||||||||
\(77\) | − 231.000i | − 0.341882i | ||||||||
\(78\) | 816.000i | 1.18454i | ||||||||
\(79\) | 1045.00 | 1.48825 | 0.744125 | − | 0.668041i | \(-0.232867\pi\) | ||||
0.744125 | + | 0.668041i | \(0.232867\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1988.00i | 2.67729i | ||||||||
\(83\) | − 608.000i | − 0.804056i | −0.915627 | − | 0.402028i | \(-0.868305\pi\) | ||||
0.915627 | − | 0.402028i | \(-0.131695\pi\) | |||||||
\(84\) | −504.000 | −0.654654 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 832.000 | 1.04322 | ||||||||
\(87\) | 450.000i | 0.554541i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 770.000 | 0.917077 | 0.458538 | − | 0.888675i | \(-0.348373\pi\) | ||||
0.458538 | + | 0.888675i | \(0.348373\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1428.00 | −1.64500 | ||||||||
\(92\) | − 1096.00i | − 1.24202i | ||||||||
\(93\) | 876.000i | 0.976742i | ||||||||
\(94\) | −1476.00 | −1.61955 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 768.000 | 0.816497 | ||||||||
\(97\) | − 1541.00i | − 1.61304i | −0.591207 | − | 0.806520i | \(-0.701348\pi\) | ||||
0.591207 | − | 0.806520i | \(-0.298652\pi\) | |||||||
\(98\) | − 392.000i | − 0.404061i | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 827.000 | 0.814748 | 0.407374 | − | 0.913261i | \(-0.366445\pi\) | ||||
0.407374 | + | 0.913261i | \(0.366445\pi\) | |||||||
\(102\) | 252.000i | 0.244625i | ||||||||
\(103\) | − 248.000i | − 0.237244i | −0.992939 | − | 0.118622i | \(-0.962152\pi\) | ||||
0.992939 | − | 0.118622i | \(-0.0378477\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2168.00 | −1.98655 | ||||||||
\(107\) | − 366.000i | − 0.330678i | −0.986237 | − | 0.165339i | \(-0.947128\pi\) | ||||
0.986237 | − | 0.165339i | \(-0.0528718\pi\) | |||||||
\(108\) | 216.000i | 0.192450i | ||||||||
\(109\) | −270.000 | −0.237260 | −0.118630 | − | 0.992939i | \(-0.537850\pi\) | ||||
−0.118630 | + | 0.992939i | \(0.537850\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1047.00 | −0.895287 | ||||||||
\(112\) | 1344.00i | 1.13389i | ||||||||
\(113\) | 1002.00i | 0.834161i | 0.908869 | + | 0.417081i | \(0.136947\pi\) | ||||
−0.908869 | + | 0.417081i | \(0.863053\pi\) | |||||||
\(114\) | 1500.00 | 1.23235 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1200.00 | −0.960493 | ||||||||
\(117\) | 612.000i | 0.483585i | ||||||||
\(118\) | − 940.000i | − 0.733339i | ||||||||
\(119\) | −441.000 | −0.339718 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 1928.00i | 1.43076i | ||||||||
\(123\) | 1491.00i | 1.09300i | ||||||||
\(124\) | −2336.00 | −1.69177 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −756.000 | −0.534522 | ||||||||
\(127\) | 469.000i | 0.327693i | 0.986486 | + | 0.163847i | \(0.0523902\pi\) | ||||
−0.986486 | + | 0.163847i | \(0.947610\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 624.000 | 0.425893 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −408.000 | −0.272115 | −0.136058 | − | 0.990701i | \(-0.543443\pi\) | ||||
−0.136058 | + | 0.990701i | \(0.543443\pi\) | |||||||
\(132\) | − 264.000i | − 0.174078i | ||||||||
\(133\) | 2625.00i | 1.71140i | ||||||||
\(134\) | −2936.00 | −1.89277 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2466.00i | − 1.53784i | −0.639343 | − | 0.768922i | \(-0.720793\pi\) | ||||
0.639343 | − | 0.768922i | \(-0.279207\pi\) | |||||||
\(138\) | − 1644.00i | − 1.01411i | ||||||||
\(139\) | −1020.00 | −0.622412 | −0.311206 | − | 0.950342i | \(-0.600733\pi\) | ||||
−0.311206 | + | 0.950342i | \(0.600733\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1107.00 | −0.661179 | ||||||||
\(142\) | 2348.00i | 1.38760i | ||||||||
\(143\) | − 748.000i | − 0.437419i | ||||||||
\(144\) | 576.000 | 0.333333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2072.00 | 1.17452 | ||||||||
\(147\) | − 294.000i | − 0.164957i | ||||||||
\(148\) | − 2792.00i | − 1.55068i | ||||||||
\(149\) | −5.00000 | −0.00274910 | −0.00137455 | − | 0.999999i | \(-0.500438\pi\) | ||||
−0.00137455 | + | 0.999999i | \(0.500438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 452.000 | 0.243598 | 0.121799 | − | 0.992555i | \(-0.461134\pi\) | ||||
0.121799 | + | 0.992555i | \(0.461134\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 189.000i | 0.0998676i | ||||||||
\(154\) | 924.000 | 0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1632.00 | −0.837593 | ||||||||
\(157\) | − 1766.00i | − 0.897721i | −0.893602 | − | 0.448860i | \(-0.851830\pi\) | ||||
0.893602 | − | 0.448860i | \(-0.148170\pi\) | |||||||
\(158\) | 4180.00i | 2.10470i | ||||||||
\(159\) | −1626.00 | −0.811007 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2877.00 | 1.40832 | ||||||||
\(162\) | 324.000i | 0.157135i | ||||||||
\(163\) | − 2068.00i | − 0.993732i | −0.867827 | − | 0.496866i | \(-0.834484\pi\) | ||||
0.867827 | − | 0.496866i | \(-0.165516\pi\) | |||||||
\(164\) | −3976.00 | −1.89313 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2432.00 | 1.13711 | ||||||||
\(167\) | − 3386.00i | − 1.56896i | −0.620153 | − | 0.784481i | \(-0.712930\pi\) | ||||
0.620153 | − | 0.784481i | \(-0.287070\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2427.00 | −1.10469 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1125.00 | 0.503105 | ||||||||
\(172\) | 1664.00i | 0.737668i | ||||||||
\(173\) | 117.000i | 0.0514182i | 0.999669 | + | 0.0257091i | \(0.00818436\pi\) | ||||
−0.999669 | + | 0.0257091i | \(0.991816\pi\) | |||||||
\(174\) | −1800.00 | −0.784239 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −704.000 | −0.301511 | ||||||||
\(177\) | − 705.000i | − 0.299384i | ||||||||
\(178\) | 3080.00i | 1.29694i | ||||||||
\(179\) | −2995.00 | −1.25060 | −0.625298 | − | 0.780386i | \(-0.715023\pi\) | ||||
−0.625298 | + | 0.780386i | \(0.715023\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4067.00 | 1.67015 | 0.835077 | − | 0.550134i | \(-0.185423\pi\) | ||||
0.835077 | + | 0.550134i | \(0.185423\pi\) | |||||||
\(182\) | − 5712.00i | − 2.32638i | ||||||||
\(183\) | 1446.00i | 0.584106i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3504.00 | −1.38132 | ||||||||
\(187\) | − 231.000i | − 0.0903337i | ||||||||
\(188\) | − 2952.00i | − 1.14520i | ||||||||
\(189\) | −567.000 | −0.218218 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3047.00 | 1.15431 | 0.577155 | − | 0.816635i | \(-0.304163\pi\) | ||||
0.577155 | + | 0.816635i | \(0.304163\pi\) | |||||||
\(192\) | 1536.00i | 0.577350i | ||||||||
\(193\) | 1232.00i | 0.459489i | 0.973251 | + | 0.229744i | \(0.0737890\pi\) | ||||
−0.973251 | + | 0.229744i | \(0.926211\pi\) | |||||||
\(194\) | 6164.00 | 2.28118 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 784.000 | 0.285714 | ||||||||
\(197\) | 4979.00i | 1.80071i | 0.435160 | + | 0.900353i | \(0.356692\pi\) | ||||
−0.435160 | + | 0.900353i | \(0.643308\pi\) | |||||||
\(198\) | − 396.000i | − 0.142134i | ||||||||
\(199\) | −600.000 | −0.213733 | −0.106867 | − | 0.994273i | \(-0.534082\pi\) | ||||
−0.106867 | + | 0.994273i | \(0.534082\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2202.00 | −0.772722 | ||||||||
\(202\) | 3308.00i | 1.15223i | ||||||||
\(203\) | − 3150.00i | − 1.08910i | ||||||||
\(204\) | −504.000 | −0.172976 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 992.000 | 0.335514 | ||||||||
\(207\) | − 1233.00i | − 0.414007i | ||||||||
\(208\) | 4352.00i | 1.45075i | ||||||||
\(209\) | −1375.00 | −0.455075 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2468.00 | −0.805233 | −0.402616 | − | 0.915369i | \(-0.631899\pi\) | ||||
−0.402616 | + | 0.915369i | \(0.631899\pi\) | |||||||
\(212\) | − 4336.00i | − 1.40471i | ||||||||
\(213\) | 1761.00i | 0.566487i | ||||||||
\(214\) | 1464.00 | 0.467649 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 6132.00i | − 1.91828i | ||||||||
\(218\) | − 1080.00i | − 0.335536i | ||||||||
\(219\) | 1554.00 | 0.479496 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1428.00 | −0.434650 | ||||||||
\(222\) | − 4188.00i | − 1.26613i | ||||||||
\(223\) | 5392.00i | 1.61917i | 0.587002 | + | 0.809585i | \(0.300308\pi\) | ||||
−0.587002 | + | 0.809585i | \(0.699692\pi\) | |||||||
\(224\) | −5376.00 | −1.60357 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4008.00 | −1.17968 | ||||||||
\(227\) | − 2366.00i | − 0.691793i | −0.938273 | − | 0.345896i | \(-0.887575\pi\) | ||||
0.938273 | − | 0.345896i | \(-0.112425\pi\) | |||||||
\(228\) | 3000.00i | 0.871403i | ||||||||
\(229\) | 4645.00 | 1.34039 | 0.670197 | − | 0.742183i | \(-0.266210\pi\) | ||||
0.670197 | + | 0.742183i | \(0.266210\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 693.000 | 0.197386 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 513.000i | − 0.144239i | −0.997396 | − | 0.0721196i | \(-0.977024\pi\) | ||||
0.997396 | − | 0.0721196i | \(-0.0229763\pi\) | |||||||
\(234\) | −2448.00 | −0.683892 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1880.00 | 0.518549 | ||||||||
\(237\) | 3135.00i | 0.859241i | ||||||||
\(238\) | − 1764.00i | − 0.480433i | ||||||||
\(239\) | −2690.00 | −0.728040 | −0.364020 | − | 0.931391i | \(-0.618596\pi\) | ||||
−0.364020 | + | 0.931391i | \(0.618596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3728.00 | −0.996438 | −0.498219 | − | 0.867051i | \(-0.666012\pi\) | ||||
−0.498219 | + | 0.867051i | \(0.666012\pi\) | |||||||
\(242\) | 484.000i | 0.128565i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | −3856.00 | −1.01170 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5964.00 | −1.54573 | ||||||||
\(247\) | 8500.00i | 2.18964i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1824.00 | 0.464222 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2352.00 | 0.591462 | 0.295731 | − | 0.955271i | \(-0.404437\pi\) | ||||
0.295731 | + | 0.955271i | \(0.404437\pi\) | |||||||
\(252\) | − 1512.00i | − 0.377964i | ||||||||
\(253\) | 1507.00i | 0.374483i | ||||||||
\(254\) | −1876.00 | −0.463428 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | − 3846.00i | − 0.933490i | −0.884392 | − | 0.466745i | \(-0.845427\pi\) | ||||
0.884392 | − | 0.466745i | \(-0.154573\pi\) | |||||||
\(258\) | 2496.00i | 0.602303i | ||||||||
\(259\) | 7329.00 | 1.75831 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1350.00 | −0.320164 | ||||||||
\(262\) | − 1632.00i | − 0.384829i | ||||||||
\(263\) | 522.000i | 0.122387i | 0.998126 | + | 0.0611937i | \(0.0194907\pi\) | ||||
−0.998126 | + | 0.0611937i | \(0.980509\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10500.0 | −2.42029 | ||||||||
\(267\) | 2310.00i | 0.529475i | ||||||||
\(268\) | − 5872.00i | − 1.33839i | ||||||||
\(269\) | −4020.00 | −0.911166 | −0.455583 | − | 0.890193i | \(-0.650569\pi\) | ||||
−0.455583 | + | 0.890193i | \(0.650569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6687.00 | 1.49892 | 0.749458 | − | 0.662052i | \(-0.230314\pi\) | ||||
0.749458 | + | 0.662052i | \(0.230314\pi\) | |||||||
\(272\) | 1344.00i | 0.299603i | ||||||||
\(273\) | − 4284.00i | − 0.949742i | ||||||||
\(274\) | 9864.00 | 2.17484 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3288.00 | 0.717081 | ||||||||
\(277\) | − 3746.00i | − 0.812546i | −0.913752 | − | 0.406273i | \(-0.866828\pi\) | ||||
0.913752 | − | 0.406273i | \(-0.133172\pi\) | |||||||
\(278\) | − 4080.00i | − 0.880224i | ||||||||
\(279\) | −2628.00 | −0.563922 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5883.00 | −1.24893 | −0.624467 | − | 0.781051i | \(-0.714684\pi\) | ||||
−0.624467 | + | 0.781051i | \(0.714684\pi\) | |||||||
\(282\) | − 4428.00i | − 0.935048i | ||||||||
\(283\) | − 3943.00i | − 0.828223i | −0.910226 | − | 0.414111i | \(-0.864092\pi\) | ||||
0.910226 | − | 0.414111i | \(-0.135908\pi\) | |||||||
\(284\) | −4696.00 | −0.981184 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2992.00 | 0.618604 | ||||||||
\(287\) | − 10437.0i | − 2.14661i | ||||||||
\(288\) | 2304.00i | 0.471405i | ||||||||
\(289\) | 4472.00 | 0.910238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4623.00 | 0.931289 | ||||||||
\(292\) | 4144.00i | 0.830511i | ||||||||
\(293\) | 1487.00i | 0.296490i | 0.988951 | + | 0.148245i | \(0.0473624\pi\) | ||||
−0.988951 | + | 0.148245i | \(0.952638\pi\) | |||||||
\(294\) | 1176.00 | 0.233285 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 297.000i | − 0.0580259i | ||||||||
\(298\) | − 20.0000i | − 0.00388782i | ||||||||
\(299\) | 9316.00 | 1.80187 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4368.00 | −0.836436 | ||||||||
\(302\) | 1808.00i | 0.344499i | ||||||||
\(303\) | 2481.00i | 0.470395i | ||||||||
\(304\) | 8000.00 | 1.50931 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −756.000 | −0.141234 | ||||||||
\(307\) | 4844.00i | 0.900527i | 0.892896 | + | 0.450263i | \(0.148670\pi\) | ||||
−0.892896 | + | 0.450263i | \(0.851330\pi\) | |||||||
\(308\) | 1848.00i | 0.341882i | ||||||||
\(309\) | 744.000 | 0.136973 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4632.00 | 0.844555 | 0.422278 | − | 0.906467i | \(-0.361231\pi\) | ||||
0.422278 | + | 0.906467i | \(0.361231\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8437.00i | 1.52360i | 0.647811 | + | 0.761801i | \(0.275685\pi\) | ||||
−0.647811 | + | 0.761801i | \(0.724315\pi\) | |||||||
\(314\) | 7064.00 | 1.26957 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8360.00 | −1.48825 | ||||||||
\(317\) | − 3636.00i | − 0.644221i | −0.946702 | − | 0.322111i | \(-0.895608\pi\) | ||||
0.946702 | − | 0.322111i | \(-0.104392\pi\) | |||||||
\(318\) | − 6504.00i | − 1.14694i | ||||||||
\(319\) | 1650.00 | 0.289600 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1098.00 | 0.190917 | ||||||||
\(322\) | 11508.0i | 1.99166i | ||||||||
\(323\) | 2625.00i | 0.452195i | ||||||||
\(324\) | −648.000 | −0.111111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8272.00 | 1.40535 | ||||||||
\(327\) | − 810.000i | − 0.136982i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7749.00 | 1.29853 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −758.000 | −0.125871 | −0.0629357 | − | 0.998018i | \(-0.520046\pi\) | ||||
−0.0629357 | + | 0.998018i | \(0.520046\pi\) | |||||||
\(332\) | 4864.00i | 0.804056i | ||||||||
\(333\) | − 3141.00i | − 0.516894i | ||||||||
\(334\) | 13544.0 | 2.21885 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4032.00 | −0.654654 | ||||||||
\(337\) | 7374.00i | 1.19195i | 0.803003 | + | 0.595975i | \(0.203234\pi\) | ||||
−0.803003 | + | 0.595975i | \(0.796766\pi\) | |||||||
\(338\) | − 9708.00i | − 1.56227i | ||||||||
\(339\) | −3006.00 | −0.481603 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3212.00 | 0.510087 | ||||||||
\(342\) | 4500.00i | 0.711497i | ||||||||
\(343\) | − 5145.00i | − 0.809924i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −468.000 | −0.0727163 | ||||||||
\(347\) | 6524.00i | 1.00930i | 0.863324 | + | 0.504649i | \(0.168378\pi\) | ||||
−0.863324 | + | 0.504649i | \(0.831622\pi\) | |||||||
\(348\) | − 3600.00i | − 0.554541i | ||||||||
\(349\) | −3710.00 | −0.569031 | −0.284515 | − | 0.958671i | \(-0.591833\pi\) | ||||
−0.284515 | + | 0.958671i | \(0.591833\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1836.00 | −0.279198 | ||||||||
\(352\) | − 2816.00i | − 0.426401i | ||||||||
\(353\) | 2832.00i | 0.427003i | 0.976943 | + | 0.213502i | \(0.0684869\pi\) | ||||
−0.976943 | + | 0.213502i | \(0.931513\pi\) | |||||||
\(354\) | 2820.00 | 0.423394 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6160.00 | −0.917077 | ||||||||
\(357\) | − 1323.00i | − 0.196136i | ||||||||
\(358\) | − 11980.0i | − 1.76861i | ||||||||
\(359\) | 7040.00 | 1.03498 | 0.517489 | − | 0.855690i | \(-0.326867\pi\) | ||||
0.517489 | + | 0.855690i | \(0.326867\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8766.00 | 1.27803 | ||||||||
\(362\) | 16268.0i | 2.36195i | ||||||||
\(363\) | 363.000i | 0.0524864i | ||||||||
\(364\) | 11424.0 | 1.64500 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5784.00 | −0.826051 | ||||||||
\(367\) | − 6206.00i | − 0.882699i | −0.897335 | − | 0.441350i | \(-0.854500\pi\) | ||||
0.897335 | − | 0.441350i | \(-0.145500\pi\) | |||||||
\(368\) | − 8768.00i | − 1.24202i | ||||||||
\(369\) | −4473.00 | −0.631044 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11382.0 | 1.59279 | ||||||||
\(372\) | − 7008.00i | − 0.976742i | ||||||||
\(373\) | 1962.00i | 0.272355i | 0.990684 | + | 0.136178i | \(0.0434818\pi\) | ||||
−0.990684 | + | 0.136178i | \(0.956518\pi\) | |||||||
\(374\) | 924.000 | 0.127751 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 10200.0i | − 1.39344i | ||||||||
\(378\) | − 2268.00i | − 0.308607i | ||||||||
\(379\) | 7960.00 | 1.07883 | 0.539417 | − | 0.842039i | \(-0.318645\pi\) | ||||
0.539417 | + | 0.842039i | \(0.318645\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1407.00 | −0.189194 | ||||||||
\(382\) | 12188.0i | 1.63244i | ||||||||
\(383\) | − 7188.00i | − 0.958981i | −0.877547 | − | 0.479490i | \(-0.840822\pi\) | ||||
0.877547 | − | 0.479490i | \(-0.159178\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4928.00 | −0.649815 | ||||||||
\(387\) | 1872.00i | 0.245889i | ||||||||
\(388\) | 12328.0i | 1.61304i | ||||||||
\(389\) | −7920.00 | −1.03229 | −0.516144 | − | 0.856502i | \(-0.672633\pi\) | ||||
−0.516144 | + | 0.856502i | \(0.672633\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2877.00 | 0.372113 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1224.00i | − 0.157106i | ||||||||
\(394\) | −19916.0 | −2.54658 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 792.000 | 0.100504 | ||||||||
\(397\) | 9654.00i | 1.22045i | 0.792226 | + | 0.610227i | \(0.208922\pi\) | ||||
−0.792226 | + | 0.610227i | \(0.791078\pi\) | |||||||
\(398\) | − 2400.00i | − 0.302264i | ||||||||
\(399\) | −7875.00 | −0.988078 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1952.00 | 0.243088 | 0.121544 | − | 0.992586i | \(-0.461215\pi\) | ||||
0.121544 | + | 0.992586i | \(0.461215\pi\) | |||||||
\(402\) | − 8808.00i | − 1.09279i | ||||||||
\(403\) | − 19856.0i | − 2.45434i | ||||||||
\(404\) | −6616.00 | −0.814748 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12600.0 | 1.54022 | ||||||||
\(407\) | 3839.00i | 0.467548i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9690.00 | −1.17149 | −0.585745 | − | 0.810495i | \(-0.699198\pi\) | ||||
−0.585745 | + | 0.810495i | \(0.699198\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7398.00 | 0.887875 | ||||||||
\(412\) | 1984.00i | 0.237244i | ||||||||
\(413\) | 4935.00i | 0.587979i | ||||||||
\(414\) | 4932.00 | 0.585494 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −17408.0 | −2.05168 | ||||||||
\(417\) | − 3060.00i | − 0.359350i | ||||||||
\(418\) | − 5500.00i | − 0.643574i | ||||||||
\(419\) | 2935.00 | 0.342206 | 0.171103 | − | 0.985253i | \(-0.445267\pi\) | ||||
0.171103 | + | 0.985253i | \(0.445267\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12837.0 | 1.48607 | 0.743037 | − | 0.669250i | \(-0.233385\pi\) | ||||
0.743037 | + | 0.669250i | \(0.233385\pi\) | |||||||
\(422\) | − 9872.00i | − 1.13877i | ||||||||
\(423\) | − 3321.00i | − 0.381732i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7044.00 | −0.801134 | ||||||||
\(427\) | − 10122.0i | − 1.14716i | ||||||||
\(428\) | 2928.00i | 0.330678i | ||||||||
\(429\) | 2244.00 | 0.252544 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6108.00 | −0.682626 | −0.341313 | − | 0.939950i | \(-0.610872\pi\) | ||||
−0.341313 | + | 0.939950i | \(0.610872\pi\) | |||||||
\(432\) | 1728.00i | 0.192450i | ||||||||
\(433\) | − 9278.00i | − 1.02973i | −0.857272 | − | 0.514864i | \(-0.827842\pi\) | ||||
0.857272 | − | 0.514864i | \(-0.172158\pi\) | |||||||
\(434\) | 24528.0 | 2.71286 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2160.00 | 0.237260 | ||||||||
\(437\) | − 17125.0i | − 1.87460i | ||||||||
\(438\) | 6216.00i | 0.678110i | ||||||||
\(439\) | −2455.00 | −0.266904 | −0.133452 | − | 0.991055i | \(-0.542606\pi\) | ||||
−0.133452 | + | 0.991055i | \(0.542606\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 882.000 | 0.0952381 | ||||||||
\(442\) | − 5712.00i | − 0.614688i | ||||||||
\(443\) | − 3503.00i | − 0.375694i | −0.982198 | − | 0.187847i | \(-0.939849\pi\) | ||||
0.982198 | − | 0.187847i | \(-0.0601510\pi\) | |||||||
\(444\) | 8376.00 | 0.895287 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −21568.0 | −2.28985 | ||||||||
\(447\) | − 15.0000i | − 0.00158719i | ||||||||
\(448\) | − 10752.0i | − 1.13389i | ||||||||
\(449\) | 7630.00 | 0.801964 | 0.400982 | − | 0.916086i | \(-0.368669\pi\) | ||||
0.400982 | + | 0.916086i | \(0.368669\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5467.00 | 0.570800 | ||||||||
\(452\) | − 8016.00i | − 0.834161i | ||||||||
\(453\) | 1356.00i | 0.140641i | ||||||||
\(454\) | 9464.00 | 0.978343 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7414.00i | 0.758889i | 0.925214 | + | 0.379445i | \(0.123885\pi\) | ||||
−0.925214 | + | 0.379445i | \(0.876115\pi\) | |||||||
\(458\) | 18580.0i | 1.89560i | ||||||||
\(459\) | −567.000 | −0.0576586 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4982.00 | 0.503329 | 0.251665 | − | 0.967814i | \(-0.419022\pi\) | ||||
0.251665 | + | 0.967814i | \(0.419022\pi\) | |||||||
\(462\) | 2772.00i | 0.279145i | ||||||||
\(463\) | 13422.0i | 1.34724i | 0.739077 | + | 0.673621i | \(0.235262\pi\) | ||||
−0.739077 | + | 0.673621i | \(0.764738\pi\) | |||||||
\(464\) | −9600.00 | −0.960493 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2052.00 | 0.203985 | ||||||||
\(467\) | 15804.0i | 1.56600i | 0.622022 | + | 0.783000i | \(0.286311\pi\) | ||||
−0.622022 | + | 0.783000i | \(0.713689\pi\) | |||||||
\(468\) | − 4896.00i | − 0.483585i | ||||||||
\(469\) | 15414.0 | 1.51760 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5298.00 | 0.518299 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 2288.00i | − 0.222415i | ||||||||
\(474\) | −12540.0 | −1.21515 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3528.00 | 0.339718 | ||||||||
\(477\) | − 4878.00i | − 0.468235i | ||||||||
\(478\) | − 10760.0i | − 1.02960i | ||||||||
\(479\) | 9060.00 | 0.864221 | 0.432111 | − | 0.901821i | \(-0.357769\pi\) | ||||
0.432111 | + | 0.901821i | \(0.357769\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 23732.0 | 2.24966 | ||||||||
\(482\) | − 14912.0i | − 1.40918i | ||||||||
\(483\) | 8631.00i | 0.813093i | ||||||||
\(484\) | −968.000 | −0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −972.000 | −0.0907218 | ||||||||
\(487\) | 2854.00i | 0.265559i | 0.991146 | + | 0.132779i | \(0.0423902\pi\) | ||||
−0.991146 | + | 0.132779i | \(0.957610\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6204.00 | 0.573731 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2278.00 | −0.209378 | −0.104689 | − | 0.994505i | \(-0.533385\pi\) | ||||
−0.104689 | + | 0.994505i | \(0.533385\pi\) | |||||||
\(492\) | − 11928.0i | − 1.09300i | ||||||||
\(493\) | − 3150.00i | − 0.287766i | ||||||||
\(494\) | −34000.0 | −3.09662 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −18688.0 | −1.69177 | ||||||||
\(497\) | − 12327.0i | − 1.11256i | ||||||||
\(498\) | 7296.00i | 0.656509i | ||||||||
\(499\) | −13290.0 | −1.19227 | −0.596134 | − | 0.802885i | \(-0.703297\pi\) | ||||
−0.596134 | + | 0.802885i | \(0.703297\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10158.0 | 0.905840 | ||||||||
\(502\) | 9408.00i | 0.836453i | ||||||||
\(503\) | 10762.0i | 0.953984i | 0.878908 | + | 0.476992i | \(0.158273\pi\) | ||||
−0.878908 | + | 0.476992i | \(0.841727\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6028.00 | −0.529599 | ||||||||
\(507\) | − 7281.00i | − 0.637792i | ||||||||
\(508\) | − 3752.00i | − 0.327693i | ||||||||
\(509\) | 1570.00 | 0.136717 | 0.0683586 | − | 0.997661i | \(-0.478224\pi\) | ||||
0.0683586 | + | 0.997661i | \(0.478224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10878.0 | −0.941711 | ||||||||
\(512\) | 16384.0i | 1.41421i | ||||||||
\(513\) | 3375.00i | 0.290468i | ||||||||
\(514\) | 15384.0 | 1.32015 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4992.00 | −0.425893 | ||||||||
\(517\) | 4059.00i | 0.345289i | ||||||||
\(518\) | 29316.0i | 2.48662i | ||||||||
\(519\) | −351.000 | −0.0296863 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22638.0 | −1.90363 | −0.951813 | − | 0.306680i | \(-0.900782\pi\) | ||||
−0.951813 | + | 0.306680i | \(0.900782\pi\) | |||||||
\(522\) | − 5400.00i | − 0.452781i | ||||||||
\(523\) | − 10273.0i | − 0.858904i | −0.903090 | − | 0.429452i | \(-0.858707\pi\) | ||||
0.903090 | − | 0.429452i | \(-0.141293\pi\) | |||||||
\(524\) | 3264.00 | 0.272115 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2088.00 | −0.173082 | ||||||||
\(527\) | − 6132.00i | − 0.506858i | ||||||||
\(528\) | − 2112.00i | − 0.174078i | ||||||||
\(529\) | −6602.00 | −0.542615 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2115.00 | 0.172850 | ||||||||
\(532\) | − 21000.0i | − 1.71140i | ||||||||
\(533\) | − 33796.0i | − 2.74647i | ||||||||
\(534\) | −9240.00 | −0.748790 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 8985.00i | − 0.722032i | ||||||||
\(538\) | − 16080.0i | − 1.28858i | ||||||||
\(539\) | −1078.00 | −0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6628.00 | −0.526728 | −0.263364 | − | 0.964697i | \(-0.584832\pi\) | ||||
−0.263364 | + | 0.964697i | \(0.584832\pi\) | |||||||
\(542\) | 26748.0i | 2.11979i | ||||||||
\(543\) | 12201.0i | 0.964263i | ||||||||
\(544\) | −5376.00 | −0.423702 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 17136.0 | 1.34314 | ||||||||
\(547\) | − 1131.00i | − 0.0884060i | −0.999023 | − | 0.0442030i | \(-0.985925\pi\) | ||||
0.999023 | − | 0.0442030i | \(-0.0140748\pi\) | |||||||
\(548\) | 19728.0i | 1.53784i | ||||||||
\(549\) | −4338.00 | −0.337234 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18750.0 | −1.44969 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 21945.0i | − 1.68752i | ||||||||
\(554\) | 14984.0 | 1.14911 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8160.00 | 0.622412 | ||||||||
\(557\) | 22954.0i | 1.74613i | 0.487607 | + | 0.873063i | \(0.337870\pi\) | ||||
−0.487607 | + | 0.873063i | \(0.662130\pi\) | |||||||
\(558\) | − 10512.0i | − 0.797506i | ||||||||
\(559\) | −14144.0 | −1.07017 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 693.000 | 0.0521542 | ||||||||
\(562\) | − 23532.0i | − 1.76626i | ||||||||
\(563\) | 5532.00i | 0.414114i | 0.978329 | + | 0.207057i | \(0.0663885\pi\) | ||||
−0.978329 | + | 0.207057i | \(0.933611\pi\) | |||||||
\(564\) | 8856.00 | 0.661179 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15772.0 | 1.17128 | ||||||||
\(567\) | − 1701.00i | − 0.125988i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25225.0 | 1.85850 | 0.929250 | − | 0.369450i | \(-0.120454\pi\) | ||||
0.929250 | + | 0.369450i | \(0.120454\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2088.00 | −0.153030 | −0.0765150 | − | 0.997068i | \(-0.524379\pi\) | ||||
−0.0765150 | + | 0.997068i | \(0.524379\pi\) | |||||||
\(572\) | 5984.00i | 0.437419i | ||||||||
\(573\) | 9141.00i | 0.666441i | ||||||||
\(574\) | 41748.0 | 3.03576 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4608.00 | −0.333333 | ||||||||
\(577\) | − 7831.00i | − 0.565007i | −0.959266 | − | 0.282503i | \(-0.908835\pi\) | ||||
0.959266 | − | 0.282503i | \(-0.0911648\pi\) | |||||||
\(578\) | 17888.0i | 1.28727i | ||||||||
\(579\) | −3696.00 | −0.265286 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12768.0 | −0.911714 | ||||||||
\(582\) | 18492.0i | 1.31704i | ||||||||
\(583\) | 5962.00i | 0.423535i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5948.00 | −0.419300 | ||||||||
\(587\) | 8199.00i | 0.576506i | 0.957554 | + | 0.288253i | \(0.0930744\pi\) | ||||
−0.957554 | + | 0.288253i | \(0.906926\pi\) | |||||||
\(588\) | 2352.00i | 0.164957i | ||||||||
\(589\) | −36500.0 | −2.55341 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14937.0 | −1.03964 | ||||||||
\(592\) | − 22336.0i | − 1.55068i | ||||||||
\(593\) | 9542.00i | 0.660781i | 0.943844 | + | 0.330390i | \(0.107180\pi\) | ||||
−0.943844 | + | 0.330390i | \(0.892820\pi\) | |||||||
\(594\) | 1188.00 | 0.0820610 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 40.0000 | 0.00274910 | ||||||||
\(597\) | − 1800.00i | − 0.123399i | ||||||||
\(598\) | 37264.0i | 2.54822i | ||||||||
\(599\) | −24705.0 | −1.68517 | −0.842587 | − | 0.538561i | \(-0.818968\pi\) | ||||
−0.842587 | + | 0.538561i | \(0.818968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15452.0 | 1.04875 | 0.524376 | − | 0.851487i | \(-0.324299\pi\) | ||||
0.524376 | + | 0.851487i | \(0.324299\pi\) | |||||||
\(602\) | − 17472.0i | − 1.18290i | ||||||||
\(603\) | − 6606.00i | − 0.446131i | ||||||||
\(604\) | −3616.00 | −0.243598 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9924.00 | −0.665239 | ||||||||
\(607\) | − 6176.00i | − 0.412975i | −0.978449 | − | 0.206488i | \(-0.933797\pi\) | ||||
0.978449 | − | 0.206488i | \(-0.0662034\pi\) | |||||||
\(608\) | 32000.0i | 2.13449i | ||||||||
\(609\) | 9450.00 | 0.628790 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25092.0 | 1.66140 | ||||||||
\(612\) | − 1512.00i | − 0.0998676i | ||||||||
\(613\) | − 13198.0i | − 0.869596i | −0.900528 | − | 0.434798i | \(-0.856820\pi\) | ||||
0.900528 | − | 0.434798i | \(-0.143180\pi\) | |||||||
\(614\) | −19376.0 | −1.27354 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 19216.0i | − 1.25382i | −0.779092 | − | 0.626910i | \(-0.784319\pi\) | ||||
0.779092 | − | 0.626910i | \(-0.215681\pi\) | |||||||
\(618\) | 2976.00i | 0.193709i | ||||||||
\(619\) | −27700.0 | −1.79864 | −0.899319 | − | 0.437293i | \(-0.855937\pi\) | ||||
−0.899319 | + | 0.437293i | \(0.855937\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3699.00 | 0.239027 | ||||||||
\(622\) | 18528.0i | 1.19438i | ||||||||
\(623\) | − 16170.0i | − 1.03987i | ||||||||
\(624\) | −13056.0 | −0.837593 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −33748.0 | −2.15470 | ||||||||
\(627\) | − 4125.00i | − 0.262738i | ||||||||
\(628\) | 14128.0i | 0.897721i | ||||||||
\(629\) | 7329.00 | 0.464589 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5108.00 | −0.322260 | −0.161130 | − | 0.986933i | \(-0.551514\pi\) | ||||
−0.161130 | + | 0.986933i | \(0.551514\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 7404.00i | − 0.464901i | ||||||||
\(634\) | 14544.0 | 0.911066 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13008.0 | 0.811007 | ||||||||
\(637\) | 6664.00i | 0.414501i | ||||||||
\(638\) | 6600.00i | 0.409556i | ||||||||
\(639\) | −5283.00 | −0.327061 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 322.000 | 0.0198412 | 0.00992062 | − | 0.999951i | \(-0.496842\pi\) | ||||
0.00992062 | + | 0.999951i | \(0.496842\pi\) | |||||||
\(642\) | 4392.00i | 0.269998i | ||||||||
\(643\) | 7432.00i | 0.455816i | 0.973683 | + | 0.227908i | \(0.0731885\pi\) | ||||
−0.973683 | + | 0.227908i | \(0.926812\pi\) | |||||||
\(644\) | −23016.0 | −1.40832 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10500.0 | −0.639500 | ||||||||
\(647\) | 1409.00i | 0.0856159i | 0.999083 | + | 0.0428080i | \(0.0136304\pi\) | ||||
−0.999083 | + | 0.0428080i | \(0.986370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2585.00 | −0.156348 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18396.0 | 1.10752 | ||||||||
\(652\) | 16544.0i | 0.993732i | ||||||||
\(653\) | − 21548.0i | − 1.29133i | −0.763621 | − | 0.645665i | \(-0.776580\pi\) | ||||
0.763621 | − | 0.645665i | \(-0.223420\pi\) | |||||||
\(654\) | 3240.00 | 0.193722 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −31808.0 | −1.89313 | ||||||||
\(657\) | 4662.00i | 0.276837i | ||||||||
\(658\) | 30996.0i | 1.83640i | ||||||||
\(659\) | 13380.0 | 0.790912 | 0.395456 | − | 0.918485i | \(-0.370587\pi\) | ||||
0.395456 | + | 0.918485i | \(0.370587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10907.0 | 0.641805 | 0.320903 | − | 0.947112i | \(-0.396014\pi\) | ||||
0.320903 | + | 0.947112i | \(0.396014\pi\) | |||||||
\(662\) | − 3032.00i | − 0.178009i | ||||||||
\(663\) | − 4284.00i | − 0.250945i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12564.0 | 0.730999 | ||||||||
\(667\) | 20550.0i | 1.19295i | ||||||||
\(668\) | 27088.0i | 1.56896i | ||||||||
\(669\) | −16176.0 | −0.934829 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5302.00 | 0.305039 | ||||||||
\(672\) | − 16128.0i | − 0.925820i | ||||||||
\(673\) | 17522.0i | 1.00360i | 0.864983 | + | 0.501800i | \(0.167329\pi\) | ||||
−0.864983 | + | 0.501800i | \(0.832671\pi\) | |||||||
\(674\) | −29496.0 | −1.68567 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19416.0 | 1.10469 | ||||||||
\(677\) | − 8306.00i | − 0.471530i | −0.971810 | − | 0.235765i | \(-0.924241\pi\) | ||||
0.971810 | − | 0.235765i | \(-0.0757595\pi\) | |||||||
\(678\) | − 12024.0i | − 0.681090i | ||||||||
\(679\) | −32361.0 | −1.82902 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7098.00 | 0.399407 | ||||||||
\(682\) | 12848.0i | 0.721371i | ||||||||
\(683\) | 18427.0i | 1.03234i | 0.856486 | + | 0.516171i | \(0.172643\pi\) | ||||
−0.856486 | + | 0.516171i | \(0.827357\pi\) | |||||||
\(684\) | −9000.00 | −0.503105 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20580.0 | 1.14541 | ||||||||
\(687\) | 13935.0i | 0.773877i | ||||||||
\(688\) | 13312.0i | 0.737668i | ||||||||
\(689\) | 36856.0 | 2.03788 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8278.00 | −0.455731 | −0.227865 | − | 0.973693i | \(-0.573175\pi\) | ||||
−0.227865 | + | 0.973693i | \(0.573175\pi\) | |||||||
\(692\) | − 936.000i | − 0.0514182i | ||||||||
\(693\) | 2079.00i | 0.113961i | ||||||||
\(694\) | −26096.0 | −1.42736 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 10437.0i | − 0.567187i | ||||||||
\(698\) | − 14840.0i | − 0.804731i | ||||||||
\(699\) | 1539.00 | 0.0832766 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21923.0 | −1.18120 | −0.590599 | − | 0.806965i | \(-0.701109\pi\) | ||||
−0.590599 | + | 0.806965i | \(0.701109\pi\) | |||||||
\(702\) | − 7344.00i | − 0.394845i | ||||||||
\(703\) | − 43625.0i | − 2.34047i | ||||||||
\(704\) | 5632.00 | 0.301511 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11328.0 | −0.603874 | ||||||||
\(707\) | − 17367.0i | − 0.923838i | ||||||||
\(708\) | 5640.00i | 0.299384i | ||||||||
\(709\) | 11425.0 | 0.605183 | 0.302592 | − | 0.953120i | \(-0.402148\pi\) | ||||
0.302592 | + | 0.953120i | \(0.402148\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9405.00 | −0.496083 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 40004.0i | 2.10121i | ||||||||
\(714\) | 5292.00 | 0.277378 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 23960.0 | 1.25060 | ||||||||
\(717\) | − 8070.00i | − 0.420334i | ||||||||
\(718\) | 28160.0i | 1.46368i | ||||||||
\(719\) | −7380.00 | −0.382792 | −0.191396 | − | 0.981513i | \(-0.561301\pi\) | ||||
−0.191396 | + | 0.981513i | \(0.561301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5208.00 | −0.269010 | ||||||||
\(722\) | 35064.0i | 1.80741i | ||||||||
\(723\) | − 11184.0i | − 0.575294i | ||||||||
\(724\) | −32536.0 | −1.67015 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1452.00 | −0.0742270 | ||||||||
\(727\) | 10924.0i | 0.557288i | 0.960394 | + | 0.278644i | \(0.0898850\pi\) | ||||
−0.960394 | + | 0.278644i | \(0.910115\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4368.00 | −0.221007 | ||||||||
\(732\) | − 11568.0i | − 0.584106i | ||||||||
\(733\) | − 13578.0i | − 0.684195i | −0.939664 | − | 0.342097i | \(-0.888863\pi\) | ||||
0.939664 | − | 0.342097i | \(-0.111137\pi\) | |||||||
\(734\) | 24824.0 | 1.24833 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 35072.0 | 1.75648 | ||||||||
\(737\) | 8074.00i | 0.403541i | ||||||||
\(738\) | − 17892.0i | − 0.892430i | ||||||||
\(739\) | −2875.00 | −0.143110 | −0.0715552 | − | 0.997437i | \(-0.522796\pi\) | ||||
−0.0715552 | + | 0.997437i | \(0.522796\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25500.0 | −1.26419 | ||||||||
\(742\) | 45528.0i | 2.25254i | ||||||||
\(743\) | − 9568.00i | − 0.472431i | −0.971701 | − | 0.236215i | \(-0.924093\pi\) | ||||
0.971701 | − | 0.236215i | \(-0.0759071\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7848.00 | −0.385168 | ||||||||
\(747\) | 5472.00i | 0.268019i | ||||||||
\(748\) | 1848.00i | 0.0903337i | ||||||||
\(749\) | −7686.00 | −0.374954 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35048.0 | −1.70296 | −0.851478 | − | 0.524391i | \(-0.824293\pi\) | ||||
−0.851478 | + | 0.524391i | \(0.824293\pi\) | |||||||
\(752\) | − 23616.0i | − 1.14520i | ||||||||
\(753\) | 7056.00i | 0.341481i | ||||||||
\(754\) | 40800.0 | 1.97062 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4536.00 | 0.218218 | ||||||||
\(757\) | − 8226.00i | − 0.394953i | −0.980308 | − | 0.197476i | \(-0.936725\pi\) | ||||
0.980308 | − | 0.197476i | \(-0.0632745\pi\) | |||||||
\(758\) | 31840.0i | 1.52570i | ||||||||
\(759\) | −4521.00 | −0.216208 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6818.00 | −0.324773 | −0.162387 | − | 0.986727i | \(-0.551919\pi\) | ||||
−0.162387 | + | 0.986727i | \(0.551919\pi\) | |||||||
\(762\) | − 5628.00i | − 0.267560i | ||||||||
\(763\) | 5670.00i | 0.269027i | ||||||||
\(764\) | −24376.0 | −1.15431 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28752.0 | 1.35620 | ||||||||
\(767\) | 15980.0i | 0.752287i | ||||||||
\(768\) | 12288.0i | 0.577350i | ||||||||
\(769\) | −29390.0 | −1.37819 | −0.689097 | − | 0.724670i | \(-0.741992\pi\) | ||||
−0.689097 | + | 0.724670i | \(0.741992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11538.0 | 0.538951 | ||||||||
\(772\) | − 9856.00i | − 0.459489i | ||||||||
\(773\) | − 34358.0i | − 1.59867i | −0.600886 | − | 0.799335i | \(-0.705185\pi\) | ||||
0.600886 | − | 0.799335i | \(-0.294815\pi\) | |||||||
\(774\) | −7488.00 | −0.347740 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21987.0i | 1.01516i | ||||||||
\(778\) | − 31680.0i | − 1.45988i | ||||||||
\(779\) | −62125.0 | −2.85733 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6457.00 | 0.295838 | ||||||||
\(782\) | 11508.0i | 0.526247i | ||||||||
\(783\) | − 4050.00i | − 0.184847i | ||||||||
\(784\) | 6272.00 | 0.285714 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4896.00 | 0.222181 | ||||||||
\(787\) | − 14291.0i | − 0.647292i | −0.946178 | − | 0.323646i | \(-0.895091\pi\) | ||||
0.946178 | − | 0.323646i | \(-0.104909\pi\) | |||||||
\(788\) | − 39832.0i | − 1.80071i | ||||||||
\(789\) | −1566.00 | −0.0706604 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 21042.0 | 0.945850 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 32776.0i | − 1.46773i | ||||||||
\(794\) | −38616.0 | −1.72598 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4800.00 | 0.213733 | ||||||||
\(797\) | − 11576.0i | − 0.514483i | −0.966347 | − | 0.257242i | \(-0.917186\pi\) | ||||
0.966347 | − | 0.257242i | \(-0.0828136\pi\) | |||||||
\(798\) | − 31500.0i | − 1.39735i | ||||||||
\(799\) | 7749.00 | 0.343104 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6930.00 | −0.305692 | ||||||||
\(802\) | 7808.00i | 0.343778i | ||||||||
\(803\) | − 5698.00i | − 0.250409i | ||||||||
\(804\) | 17616.0 | 0.772722 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 79424.0 | 3.47096 | ||||||||
\(807\) | − 12060.0i | − 0.526062i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12825.0 | 0.557358 | 0.278679 | − | 0.960384i | \(-0.410103\pi\) | ||||
0.278679 | + | 0.960384i | \(0.410103\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36843.0 | −1.59523 | −0.797616 | − | 0.603166i | \(-0.793906\pi\) | ||||
−0.797616 | + | 0.603166i | \(0.793906\pi\) | |||||||
\(812\) | 25200.0i | 1.08910i | ||||||||
\(813\) | 20061.0i | 0.865400i | ||||||||
\(814\) | −15356.0 | −0.661213 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −4032.00 | −0.172976 | ||||||||
\(817\) | 26000.0i | 1.11337i | ||||||||
\(818\) | − 38760.0i | − 1.65674i | ||||||||
\(819\) | 12852.0 | 0.548334 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43962.0 | 1.86880 | 0.934400 | − | 0.356226i | \(-0.115937\pi\) | ||||
0.934400 | + | 0.356226i | \(0.115937\pi\) | |||||||
\(822\) | 29592.0i | 1.25564i | ||||||||
\(823\) | 33522.0i | 1.41981i | 0.704298 | + | 0.709905i | \(0.251262\pi\) | ||||
−0.704298 | + | 0.709905i | \(0.748738\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −19740.0 | −0.831528 | ||||||||
\(827\) | 1704.00i | 0.0716492i | 0.999358 | + | 0.0358246i | \(0.0114058\pi\) | ||||
−0.999358 | + | 0.0358246i | \(0.988594\pi\) | |||||||
\(828\) | 9864.00i | 0.414007i | ||||||||
\(829\) | −1750.00 | −0.0733173 | −0.0366586 | − | 0.999328i | \(-0.511671\pi\) | ||||
−0.0366586 | + | 0.999328i | \(0.511671\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11238.0 | 0.469124 | ||||||||
\(832\) | − 34816.0i | − 1.45075i | ||||||||
\(833\) | 2058.00i | 0.0856008i | ||||||||
\(834\) | 12240.0 | 0.508197 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11000.0 | 0.455075 | ||||||||
\(837\) | − 7884.00i | − 0.325581i | ||||||||
\(838\) | 11740.0i | 0.483952i | ||||||||
\(839\) | 15260.0 | 0.627931 | 0.313965 | − | 0.949434i | \(-0.398342\pi\) | ||||
0.313965 | + | 0.949434i | \(0.398342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1889.00 | −0.0774530 | ||||||||
\(842\) | 51348.0i | 2.10163i | ||||||||
\(843\) | − 17649.0i | − 0.721072i | ||||||||
\(844\) | 19744.0 | 0.805233 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13284.0 | 0.539850 | ||||||||
\(847\) | − 2541.00i | − 0.103081i | ||||||||
\(848\) | − 34688.0i | − 1.40471i | ||||||||
\(849\) | 11829.0 | 0.478175 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47813.0 | −1.92598 | ||||||||
\(852\) | − 14088.0i | − 0.566487i | ||||||||
\(853\) | − 878.000i | − 0.0352428i | −0.999845 | − | 0.0176214i | \(-0.994391\pi\) | ||||
0.999845 | − | 0.0176214i | \(-0.00560936\pi\) | |||||||
\(854\) | 40488.0 | 1.62233 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35019.0i | 1.39583i | 0.716181 | + | 0.697915i | \(0.245889\pi\) | ||||
−0.716181 | + | 0.697915i | \(0.754111\pi\) | |||||||
\(858\) | 8976.00i | 0.357151i | ||||||||
\(859\) | 1280.00 | 0.0508417 | 0.0254209 | − | 0.999677i | \(-0.491907\pi\) | ||||
0.0254209 | + | 0.999677i | \(0.491907\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31311.0 | 1.23934 | ||||||||
\(862\) | − 24432.0i | − 0.965380i | ||||||||
\(863\) | − 16888.0i | − 0.666135i | −0.942903 | − | 0.333067i | \(-0.891916\pi\) | ||||
0.942903 | − | 0.333067i | \(-0.108084\pi\) | |||||||
\(864\) | −6912.00 | −0.272166 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 37112.0 | 1.45626 | ||||||||
\(867\) | 13416.0i | 0.525526i | ||||||||
\(868\) | 49056.0i | 1.91828i | ||||||||
\(869\) | 11495.0 | 0.448724 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49912.0 | 1.94168 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 13869.0i | 0.537680i | ||||||||
\(874\) | 68500.0 | 2.65108 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12432.0 | −0.479496 | ||||||||
\(877\) | − 29836.0i | − 1.14879i | −0.818578 | − | 0.574396i | \(-0.805237\pi\) | ||||
0.818578 | − | 0.574396i | \(-0.194763\pi\) | |||||||
\(878\) | − 9820.00i | − 0.377459i | ||||||||
\(879\) | −4461.00 | −0.171178 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29292.0 | 1.12017 | 0.560087 | − | 0.828434i | \(-0.310768\pi\) | ||||
0.560087 | + | 0.828434i | \(0.310768\pi\) | |||||||
\(882\) | 3528.00i | 0.134687i | ||||||||
\(883\) | 6532.00i | 0.248946i | 0.992223 | + | 0.124473i | \(0.0397240\pi\) | ||||
−0.992223 | + | 0.124473i | \(0.960276\pi\) | |||||||
\(884\) | 11424.0 | 0.434650 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14012.0 | 0.531312 | ||||||||
\(887\) | − 20476.0i | − 0.775103i | −0.921848 | − | 0.387552i | \(-0.873321\pi\) | ||||
0.921848 | − | 0.387552i | \(-0.126679\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9849.00 | 0.371569 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | − 43136.0i | − 1.61917i | ||||||||
\(893\) | − 46125.0i | − 1.72846i | ||||||||
\(894\) | 60.0000 | 0.00224463 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 27948.0i | 1.04031i | ||||||||
\(898\) | 30520.0i | 1.13415i | ||||||||
\(899\) | 43800.0 | 1.62493 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11382.0 | 0.420854 | ||||||||
\(902\) | 21868.0i | 0.807234i | ||||||||
\(903\) | − 13104.0i | − 0.482917i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5424.00 | −0.198897 | ||||||||
\(907\) | 51914.0i | 1.90052i | 0.311450 | + | 0.950262i | \(0.399185\pi\) | ||||
−0.311450 | + | 0.950262i | \(0.600815\pi\) | |||||||
\(908\) | 18928.0i | 0.691793i | ||||||||
\(909\) | −7443.00 | −0.271583 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −41893.0 | −1.52358 | −0.761788 | − | 0.647827i | \(-0.775678\pi\) | ||||
−0.761788 | + | 0.647827i | \(0.775678\pi\) | |||||||
\(912\) | 24000.0i | 0.871403i | ||||||||
\(913\) | − 6688.00i | − 0.242432i | ||||||||
\(914\) | −29656.0 | −1.07323 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −37160.0 | −1.34039 | ||||||||
\(917\) | 8568.00i | 0.308550i | ||||||||
\(918\) | − 2268.00i | − 0.0815416i | ||||||||
\(919\) | −495.000 | −0.0177677 | −0.00888386 | − | 0.999961i | \(-0.502828\pi\) | ||||
−0.00888386 | + | 0.999961i | \(0.502828\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14532.0 | −0.519919 | ||||||||
\(922\) | 19928.0i | 0.711815i | ||||||||
\(923\) | − 39916.0i | − 1.42346i | ||||||||
\(924\) | −5544.00 | −0.197386 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −53688.0 | −1.90529 | ||||||||
\(927\) | 2232.00i | 0.0790814i | ||||||||
\(928\) | − 38400.0i | − 1.35834i | ||||||||
\(929\) | 16310.0 | 0.576010 | 0.288005 | − | 0.957629i | \(-0.407008\pi\) | ||||
0.288005 | + | 0.957629i | \(0.407008\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12250.0 | 0.431233 | ||||||||
\(932\) | 4104.00i | 0.144239i | ||||||||
\(933\) | 13896.0i | 0.487604i | ||||||||
\(934\) | −63216.0 | −2.21466 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18744.0i | 0.653511i | 0.945109 | + | 0.326755i | \(0.105955\pi\) | ||||
−0.945109 | + | 0.326755i | \(0.894045\pi\) | |||||||
\(938\) | 61656.0i | 2.14620i | ||||||||
\(939\) | −25311.0 | −0.879652 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25553.0 | −0.885233 | −0.442616 | − | 0.896711i | \(-0.645950\pi\) | ||||
−0.442616 | + | 0.896711i | \(0.645950\pi\) | |||||||
\(942\) | 21192.0i | 0.732986i | ||||||||
\(943\) | 68089.0i | 2.35131i | ||||||||
\(944\) | 15040.0 | 0.518549 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9152.00 | 0.314542 | ||||||||
\(947\) | 6879.00i | 0.236048i | 0.993011 | + | 0.118024i | \(0.0376560\pi\) | ||||
−0.993011 | + | 0.118024i | \(0.962344\pi\) | |||||||
\(948\) | − 25080.0i | − 0.859241i | ||||||||
\(949\) | −35224.0 | −1.20487 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10908.0 | 0.371941 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13677.0i | 0.464891i | 0.972609 | + | 0.232446i | \(0.0746728\pi\) | ||||
−0.972609 | + | 0.232446i | \(0.925327\pi\) | |||||||
\(954\) | 19512.0 | 0.662185 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 21520.0 | 0.728040 | ||||||||
\(957\) | 4950.00i | 0.167200i | ||||||||
\(958\) | 36240.0i | 1.22219i | ||||||||
\(959\) | −51786.0 | −1.74375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55473.0 | 1.86207 | ||||||||
\(962\) | 94928.0i | 3.18150i | ||||||||
\(963\) | 3294.00i | 0.110226i | ||||||||
\(964\) | 29824.0 | 0.996438 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −34524.0 | −1.14989 | ||||||||
\(967\) | 26984.0i | 0.897360i | 0.893693 | + | 0.448680i | \(0.148106\pi\) | ||||
−0.893693 | + | 0.448680i | \(0.851894\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7875.00 | −0.261075 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41937.0 | 1.38602 | 0.693008 | − | 0.720929i | \(-0.256285\pi\) | ||||
0.693008 | + | 0.720929i | \(0.256285\pi\) | |||||||
\(972\) | − 1944.00i | − 0.0641500i | ||||||||
\(973\) | 21420.0i | 0.705749i | ||||||||
\(974\) | −11416.0 | −0.375557 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −30848.0 | −1.01170 | ||||||||
\(977\) | 13504.0i | 0.442202i | 0.975251 | + | 0.221101i | \(0.0709650\pi\) | ||||
−0.975251 | + | 0.221101i | \(0.929035\pi\) | |||||||
\(978\) | 24816.0i | 0.811379i | ||||||||
\(979\) | 8470.00 | 0.276509 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2430.00 | 0.0790866 | ||||||||
\(982\) | − 9112.00i | − 0.296106i | ||||||||
\(983\) | − 33353.0i | − 1.08219i | −0.840961 | − | 0.541096i | \(-0.818009\pi\) | ||||
0.840961 | − | 0.541096i | \(-0.181991\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 12600.0 | 0.406963 | ||||||||
\(987\) | 23247.0i | 0.749706i | ||||||||
\(988\) | − 68000.0i | − 2.18964i | ||||||||
\(989\) | 28496.0 | 0.916198 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16978.0 | −0.544222 | −0.272111 | − | 0.962266i | \(-0.587722\pi\) | ||||
−0.272111 | + | 0.962266i | \(0.587722\pi\) | |||||||
\(992\) | − 74752.0i | − 2.39252i | ||||||||
\(993\) | − 2274.00i | − 0.0726719i | ||||||||
\(994\) | 49308.0 | 1.57340 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −14592.0 | −0.464222 | ||||||||
\(997\) | 2714.00i | 0.0862119i | 0.999071 | + | 0.0431059i | \(0.0137253\pi\) | ||||
−0.999071 | + | 0.0431059i | \(0.986275\pi\) | |||||||
\(998\) | − 53160.0i | − 1.68612i | ||||||||
\(999\) | 9423.00 | 0.298429 |
(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 | 825.4.c.c.199.2 | 2 | ||
5.2 | odd | 4 | 825.4.a.b.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 825.4.a.h.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 825.4.c.c.199.1 | 2 | ||
15.2 | even | 4 | 2475.4.a.j.1.1 | 1 | |||
15.8 | even | 4 | 2475.4.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.4.a.b.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
825.4.a.h.1.1 | yes | 1 | 5.3 | odd | 4 | ||
825.4.c.c.199.1 | 2 | 5.4 | even | 2 | inner | ||
825.4.c.c.199.2 | 2 | 1.1 | even | 1 | trivial | ||
2475.4.a.c.1.1 | 1 | 15.8 | even | 4 | |||
2475.4.a.j.1.1 | 1 | 15.2 | even | 4 |