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 | 199.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.b.199.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 5.00000i | − 1.76777i | −0.467707 | − | 0.883883i | \(-0.654920\pi\) | ||||
0.467707 | − | 0.883883i | \(-0.345080\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | −17.0000 | −2.12500 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 15.0000 | 1.02062 | ||||||||
\(7\) | − 3.00000i | − 0.161985i | −0.996715 | − | 0.0809924i | \(-0.974191\pi\) | ||||
0.996715 | − | 0.0809924i | \(-0.0258089\pi\) | |||||||
\(8\) | 45.0000i | 1.98874i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | − 51.0000i | − 1.22687i | ||||||||
\(13\) | 32.0000i | 0.682708i | 0.939935 | + | 0.341354i | \(0.110885\pi\) | ||||
−0.939935 | + | 0.341354i | \(0.889115\pi\) | |||||||
\(14\) | −15.0000 | −0.286351 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 89.0000 | 1.39062 | ||||||||
\(17\) | − 33.0000i | − 0.470804i | −0.971898 | − | 0.235402i | \(-0.924359\pi\) | ||||
0.971898 | − | 0.235402i | \(-0.0756407\pi\) | |||||||
\(18\) | 45.0000i | 0.589256i | ||||||||
\(19\) | −47.0000 | −0.567502 | −0.283751 | − | 0.958898i | \(-0.591579\pi\) | ||||
−0.283751 | + | 0.958898i | \(0.591579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.00000 | 0.0935220 | ||||||||
\(22\) | 55.0000i | 0.533002i | ||||||||
\(23\) | 113.000i | 1.02444i | 0.858854 | + | 0.512220i | \(0.171177\pi\) | ||||
−0.858854 | + | 0.512220i | \(0.828823\pi\) | |||||||
\(24\) | −135.000 | −1.14820 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 160.000 | 1.20687 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 51.0000i | 0.344218i | ||||||||
\(29\) | 54.0000 | 0.345778 | 0.172889 | − | 0.984941i | \(-0.444690\pi\) | ||||
0.172889 | + | 0.984941i | \(0.444690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 178.000 | 1.03128 | 0.515641 | − | 0.856805i | \(-0.327554\pi\) | ||||
0.515641 | + | 0.856805i | \(0.327554\pi\) | |||||||
\(32\) | − 85.0000i | − 0.469563i | ||||||||
\(33\) | − 33.0000i | − 0.174078i | ||||||||
\(34\) | −165.000 | −0.832273 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 153.000 | 0.708333 | ||||||||
\(37\) | − 19.0000i | − 0.0844211i | −0.999109 | − | 0.0422106i | \(-0.986560\pi\) | ||||
0.999109 | − | 0.0422106i | \(-0.0134400\pi\) | |||||||
\(38\) | 235.000i | 1.00321i | ||||||||
\(39\) | −96.0000 | −0.394162 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 139.000 | 0.529467 | 0.264734 | − | 0.964322i | \(-0.414716\pi\) | ||||
0.264734 | + | 0.964322i | \(0.414716\pi\) | |||||||
\(42\) | − 45.0000i | − 0.165325i | ||||||||
\(43\) | − 308.000i | − 1.09232i | −0.837682 | − | 0.546158i | \(-0.816090\pi\) | ||||
0.837682 | − | 0.546158i | \(-0.183910\pi\) | |||||||
\(44\) | 187.000 | 0.640712 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 565.000 | 1.81097 | ||||||||
\(47\) | − 195.000i | − 0.605185i | −0.953120 | − | 0.302592i | \(-0.902148\pi\) | ||||
0.953120 | − | 0.302592i | \(-0.0978520\pi\) | |||||||
\(48\) | 267.000i | 0.802878i | ||||||||
\(49\) | 334.000 | 0.973761 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 99.0000 | 0.271819 | ||||||||
\(52\) | − 544.000i | − 1.45075i | ||||||||
\(53\) | 152.000i | 0.393940i | 0.980410 | + | 0.196970i | \(0.0631101\pi\) | ||||
−0.980410 | + | 0.196970i | \(0.936890\pi\) | |||||||
\(54\) | −135.000 | −0.340207 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 135.000 | 0.322145 | ||||||||
\(57\) | − 141.000i | − 0.327647i | ||||||||
\(58\) | − 270.000i | − 0.611254i | ||||||||
\(59\) | 625.000 | 1.37912 | 0.689560 | − | 0.724229i | \(-0.257804\pi\) | ||||
0.689560 | + | 0.724229i | \(0.257804\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 320.000 | 0.671669 | 0.335834 | − | 0.941921i | \(-0.390982\pi\) | ||||
0.335834 | + | 0.941921i | \(0.390982\pi\) | |||||||
\(62\) | − 890.000i | − 1.82307i | ||||||||
\(63\) | 27.0000i | 0.0539949i | ||||||||
\(64\) | 287.000 | 0.560547 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −165.000 | −0.307729 | ||||||||
\(67\) | − 200.000i | − 0.364685i | −0.983235 | − | 0.182342i | \(-0.941632\pi\) | ||||
0.983235 | − | 0.182342i | \(-0.0583679\pi\) | |||||||
\(68\) | 561.000i | 1.00046i | ||||||||
\(69\) | −339.000 | −0.591461 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −947.000 | −1.58293 | −0.791466 | − | 0.611213i | \(-0.790682\pi\) | ||||
−0.791466 | + | 0.611213i | \(0.790682\pi\) | |||||||
\(72\) | − 405.000i | − 0.662913i | ||||||||
\(73\) | − 448.000i | − 0.718280i | −0.933284 | − | 0.359140i | \(-0.883070\pi\) | ||||
0.933284 | − | 0.359140i | \(-0.116930\pi\) | |||||||
\(74\) | −95.0000 | −0.149237 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 799.000 | 1.20594 | ||||||||
\(77\) | 33.0000i | 0.0488402i | ||||||||
\(78\) | 480.000i | 0.696786i | ||||||||
\(79\) | 721.000 | 1.02682 | 0.513410 | − | 0.858143i | \(-0.328382\pi\) | ||||
0.513410 | + | 0.858143i | \(0.328382\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − 695.000i | − 0.935975i | ||||||||
\(83\) | 142.000i | 0.187789i | 0.995582 | + | 0.0938947i | \(0.0299317\pi\) | ||||
−0.995582 | + | 0.0938947i | \(0.970068\pi\) | |||||||
\(84\) | −153.000 | −0.198734 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1540.00 | −1.93096 | ||||||||
\(87\) | 162.000i | 0.199635i | ||||||||
\(88\) | − 495.000i | − 0.599627i | ||||||||
\(89\) | −404.000 | −0.481168 | −0.240584 | − | 0.970628i | \(-0.577339\pi\) | ||||
−0.240584 | + | 0.970628i | \(0.577339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 96.0000 | 0.110588 | ||||||||
\(92\) | − 1921.00i | − 2.17694i | ||||||||
\(93\) | 534.000i | 0.595411i | ||||||||
\(94\) | −975.000 | −1.06983 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 255.000 | 0.271102 | ||||||||
\(97\) | − 79.0000i | − 0.0826931i | −0.999145 | − | 0.0413466i | \(-0.986835\pi\) | ||||
0.999145 | − | 0.0413466i | \(-0.0131648\pi\) | |||||||
\(98\) | − 1670.00i | − 1.72138i | ||||||||
\(99\) | 99.0000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −545.000 | −0.536926 | −0.268463 | − | 0.963290i | \(-0.586516\pi\) | ||||
−0.268463 | + | 0.963290i | \(0.586516\pi\) | |||||||
\(102\) | − 495.000i | − 0.480513i | ||||||||
\(103\) | − 1306.00i | − 1.24936i | −0.780881 | − | 0.624680i | \(-0.785230\pi\) | ||||
0.780881 | − | 0.624680i | \(-0.214770\pi\) | |||||||
\(104\) | −1440.00 | −1.35773 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 760.000 | 0.696394 | ||||||||
\(107\) | − 1938.00i | − 1.75097i | −0.483247 | − | 0.875484i | \(-0.660543\pi\) | ||||
0.483247 | − | 0.875484i | \(-0.339457\pi\) | |||||||
\(108\) | 459.000i | 0.408956i | ||||||||
\(109\) | 576.000 | 0.506154 | 0.253077 | − | 0.967446i | \(-0.418557\pi\) | ||||
0.253077 | + | 0.967446i | \(0.418557\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 57.0000 | 0.0487405 | ||||||||
\(112\) | − 267.000i | − 0.225260i | ||||||||
\(113\) | − 1104.00i | − 0.919076i | −0.888158 | − | 0.459538i | \(-0.848015\pi\) | ||||
0.888158 | − | 0.459538i | \(-0.151985\pi\) | |||||||
\(114\) | −705.000 | −0.579204 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −918.000 | −0.734777 | ||||||||
\(117\) | − 288.000i | − 0.227569i | ||||||||
\(118\) | − 3125.00i | − 2.43796i | ||||||||
\(119\) | −99.0000 | −0.0762632 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | − 1600.00i | − 1.18735i | ||||||||
\(123\) | 417.000i | 0.305688i | ||||||||
\(124\) | −3026.00 | −2.19147 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 135.000 | 0.0954504 | ||||||||
\(127\) | 1739.00i | 1.21505i | 0.794301 | + | 0.607525i | \(0.207837\pi\) | ||||
−0.794301 | + | 0.607525i | \(0.792163\pi\) | |||||||
\(128\) | − 2115.00i | − 1.46048i | ||||||||
\(129\) | 924.000 | 0.630649 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1818.00 | 1.21251 | 0.606257 | − | 0.795269i | \(-0.292670\pi\) | ||||
0.606257 | + | 0.795269i | \(0.292670\pi\) | |||||||
\(132\) | 561.000i | 0.369915i | ||||||||
\(133\) | 141.000i | 0.0919267i | ||||||||
\(134\) | −1000.00 | −0.644678 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1485.00 | 0.936307 | ||||||||
\(137\) | − 870.000i | − 0.542548i | −0.962502 | − | 0.271274i | \(-0.912555\pi\) | ||||
0.962502 | − | 0.271274i | \(-0.0874450\pi\) | |||||||
\(138\) | 1695.00i | 1.04557i | ||||||||
\(139\) | 636.000 | 0.388092 | 0.194046 | − | 0.980992i | \(-0.437839\pi\) | ||||
0.194046 | + | 0.980992i | \(0.437839\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 585.000 | 0.349403 | ||||||||
\(142\) | 4735.00i | 2.79826i | ||||||||
\(143\) | − 352.000i | − 0.205844i | ||||||||
\(144\) | −801.000 | −0.463542 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2240.00 | −1.26975 | ||||||||
\(147\) | 1002.00i | 0.562201i | ||||||||
\(148\) | 323.000i | 0.179395i | ||||||||
\(149\) | 239.000 | 0.131407 | 0.0657035 | − | 0.997839i | \(-0.479071\pi\) | ||||
0.0657035 | + | 0.997839i | \(0.479071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1208.00 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | − 2115.00i | − 1.12861i | ||||||||
\(153\) | 297.000i | 0.156935i | ||||||||
\(154\) | 165.000 | 0.0863382 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1632.00 | 0.837593 | ||||||||
\(157\) | 1874.00i | 0.952621i | 0.879277 | + | 0.476310i | \(0.158026\pi\) | ||||
−0.879277 | + | 0.476310i | \(0.841974\pi\) | |||||||
\(158\) | − 3605.00i | − 1.81518i | ||||||||
\(159\) | −456.000 | −0.227441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 339.000 | 0.165944 | ||||||||
\(162\) | − 405.000i | − 0.196419i | ||||||||
\(163\) | − 1904.00i | − 0.914925i | −0.889229 | − | 0.457463i | \(-0.848758\pi\) | ||||
0.889229 | − | 0.457463i | \(-0.151242\pi\) | |||||||
\(164\) | −2363.00 | −1.12512 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 710.000 | 0.331968 | ||||||||
\(167\) | 1180.00i | 0.546773i | 0.961904 | + | 0.273387i | \(0.0881438\pi\) | ||||
−0.961904 | + | 0.273387i | \(0.911856\pi\) | |||||||
\(168\) | 405.000i | 0.185991i | ||||||||
\(169\) | 1173.00 | 0.533910 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 423.000 | 0.189167 | ||||||||
\(172\) | 5236.00i | 2.32117i | ||||||||
\(173\) | − 3177.00i | − 1.39620i | −0.716000 | − | 0.698101i | \(-0.754029\pi\) | ||||
0.716000 | − | 0.698101i | \(-0.245971\pi\) | |||||||
\(174\) | 810.000 | 0.352908 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −979.000 | −0.419289 | ||||||||
\(177\) | 1875.00i | 0.796235i | ||||||||
\(178\) | 2020.00i | 0.850592i | ||||||||
\(179\) | −1787.00 | −0.746182 | −0.373091 | − | 0.927795i | \(-0.621702\pi\) | ||||
−0.373091 | + | 0.927795i | \(0.621702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −835.000 | −0.342901 | −0.171450 | − | 0.985193i | \(-0.554845\pi\) | ||||
−0.171450 | + | 0.985193i | \(0.554845\pi\) | |||||||
\(182\) | − 480.000i | − 0.195494i | ||||||||
\(183\) | 960.000i | 0.387788i | ||||||||
\(184\) | −5085.00 | −2.03734 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2670.00 | 1.05255 | ||||||||
\(187\) | 363.000i | 0.141953i | ||||||||
\(188\) | 3315.00i | 1.28602i | ||||||||
\(189\) | −81.0000 | −0.0311740 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3613.00 | 1.36873 | 0.684365 | − | 0.729139i | \(-0.260079\pi\) | ||||
0.684365 | + | 0.729139i | \(0.260079\pi\) | |||||||
\(192\) | 861.000i | 0.323632i | ||||||||
\(193\) | 4204.00i | 1.56793i | 0.620805 | + | 0.783965i | \(0.286806\pi\) | ||||
−0.620805 | + | 0.783965i | \(0.713194\pi\) | |||||||
\(194\) | −395.000 | −0.146182 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5678.00 | −2.06924 | ||||||||
\(197\) | 4517.00i | 1.63362i | 0.576908 | + | 0.816809i | \(0.304259\pi\) | ||||
−0.576908 | + | 0.816809i | \(0.695741\pi\) | |||||||
\(198\) | − 495.000i | − 0.177667i | ||||||||
\(199\) | −4164.00 | −1.48331 | −0.741654 | − | 0.670783i | \(-0.765958\pi\) | ||||
−0.741654 | + | 0.670783i | \(0.765958\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 600.000 | 0.210551 | ||||||||
\(202\) | 2725.00i | 0.949160i | ||||||||
\(203\) | − 162.000i | − 0.0560107i | ||||||||
\(204\) | −1683.00 | −0.577616 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6530.00 | −2.20858 | ||||||||
\(207\) | − 1017.00i | − 0.341480i | ||||||||
\(208\) | 2848.00i | 0.949391i | ||||||||
\(209\) | 517.000 | 0.171108 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4660.00 | 1.52042 | 0.760208 | − | 0.649680i | \(-0.225097\pi\) | ||||
0.760208 | + | 0.649680i | \(0.225097\pi\) | |||||||
\(212\) | − 2584.00i | − 0.837122i | ||||||||
\(213\) | − 2841.00i | − 0.913907i | ||||||||
\(214\) | −9690.00 | −3.09530 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1215.00 | 0.382733 | ||||||||
\(217\) | − 534.000i | − 0.167052i | ||||||||
\(218\) | − 2880.00i | − 0.894762i | ||||||||
\(219\) | 1344.00 | 0.414699 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1056.00 | 0.321422 | ||||||||
\(222\) | − 285.000i | − 0.0861619i | ||||||||
\(223\) | 3560.00i | 1.06904i | 0.845157 | + | 0.534518i | \(0.179507\pi\) | ||||
−0.845157 | + | 0.534518i | \(0.820493\pi\) | |||||||
\(224\) | −255.000 | −0.0760621 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5520.00 | −1.62471 | ||||||||
\(227\) | 4678.00i | 1.36780i | 0.729577 | + | 0.683898i | \(0.239717\pi\) | ||||
−0.729577 | + | 0.683898i | \(0.760283\pi\) | |||||||
\(228\) | 2397.00i | 0.696251i | ||||||||
\(229\) | 4447.00 | 1.28326 | 0.641629 | − | 0.767015i | \(-0.278259\pi\) | ||||
0.641629 | + | 0.767015i | \(0.278259\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −99.0000 | −0.0281979 | ||||||||
\(232\) | 2430.00i | 0.687661i | ||||||||
\(233\) | 411.000i | 0.115560i | 0.998329 | + | 0.0577801i | \(0.0184022\pi\) | ||||
−0.998329 | + | 0.0577801i | \(0.981598\pi\) | |||||||
\(234\) | −1440.00 | −0.402290 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10625.0 | −2.93063 | ||||||||
\(237\) | 2163.00i | 0.592835i | ||||||||
\(238\) | 495.000i | 0.134815i | ||||||||
\(239\) | 6380.00 | 1.72673 | 0.863364 | − | 0.504582i | \(-0.168353\pi\) | ||||
0.863364 | + | 0.504582i | \(0.168353\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7282.00 | 1.94637 | 0.973184 | − | 0.230027i | \(-0.0738813\pi\) | ||||
0.973184 | + | 0.230027i | \(0.0738813\pi\) | |||||||
\(242\) | − 605.000i | − 0.160706i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | −5440.00 | −1.42730 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2085.00 | 0.540385 | ||||||||
\(247\) | − 1504.00i | − 0.387438i | ||||||||
\(248\) | 8010.00i | 2.05095i | ||||||||
\(249\) | −426.000 | −0.108420 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4728.00 | −1.18896 | −0.594480 | − | 0.804111i | \(-0.702642\pi\) | ||||
−0.594480 | + | 0.804111i | \(0.702642\pi\) | |||||||
\(252\) | − 459.000i | − 0.114739i | ||||||||
\(253\) | − 1243.00i | − 0.308880i | ||||||||
\(254\) | 8695.00 | 2.14792 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8279.00 | −2.02124 | ||||||||
\(257\) | − 5418.00i | − 1.31504i | −0.753437 | − | 0.657521i | \(-0.771605\pi\) | ||||
0.753437 | − | 0.657521i | \(-0.228395\pi\) | |||||||
\(258\) | − 4620.00i | − 1.11484i | ||||||||
\(259\) | −57.0000 | −0.0136749 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −486.000 | −0.115259 | ||||||||
\(262\) | − 9090.00i | − 2.14344i | ||||||||
\(263\) | − 3354.00i | − 0.786375i | −0.919458 | − | 0.393187i | \(-0.871372\pi\) | ||||
0.919458 | − | 0.393187i | \(-0.128628\pi\) | |||||||
\(264\) | 1485.00 | 0.346195 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 705.000 | 0.162505 | ||||||||
\(267\) | − 1212.00i | − 0.277802i | ||||||||
\(268\) | 3400.00i | 0.774955i | ||||||||
\(269\) | −1062.00 | −0.240711 | −0.120356 | − | 0.992731i | \(-0.538403\pi\) | ||||
−0.120356 | + | 0.992731i | \(0.538403\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4821.00 | −1.08065 | −0.540323 | − | 0.841458i | \(-0.681698\pi\) | ||||
−0.540323 | + | 0.841458i | \(0.681698\pi\) | |||||||
\(272\) | − 2937.00i | − 0.654712i | ||||||||
\(273\) | 288.000i | 0.0638482i | ||||||||
\(274\) | −4350.00 | −0.959099 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5763.00 | 1.25685 | ||||||||
\(277\) | − 4.00000i | 0 0.000867642i | −1.00000 | 0.000433821i | \(-0.999862\pi\) | |||||
1.00000 | 0.000433821i | \(-0.000138089\pi\) | ||||||||
\(278\) | − 3180.00i | − 0.686057i | ||||||||
\(279\) | −1602.00 | −0.343761 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4647.00 | 0.986537 | 0.493268 | − | 0.869877i | \(-0.335802\pi\) | ||||
0.493268 | + | 0.869877i | \(0.335802\pi\) | |||||||
\(282\) | − 2925.00i | − 0.617664i | ||||||||
\(283\) | − 4283.00i | − 0.899639i | −0.893119 | − | 0.449820i | \(-0.851488\pi\) | ||||
0.893119 | − | 0.449820i | \(-0.148512\pi\) | |||||||
\(284\) | 16099.0 | 3.36373 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1760.00 | −0.363885 | ||||||||
\(287\) | − 417.000i | − 0.0857656i | ||||||||
\(288\) | 765.000i | 0.156521i | ||||||||
\(289\) | 3824.00 | 0.778343 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 237.000 | 0.0477429 | ||||||||
\(292\) | 7616.00i | 1.52634i | ||||||||
\(293\) | − 6811.00i | − 1.35803i | −0.734124 | − | 0.679015i | \(-0.762407\pi\) | ||||
0.734124 | − | 0.679015i | \(-0.237593\pi\) | |||||||
\(294\) | 5010.00 | 0.993841 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 855.000 | 0.167891 | ||||||||
\(297\) | 297.000i | 0.0580259i | ||||||||
\(298\) | − 1195.00i | − 0.232297i | ||||||||
\(299\) | −3616.00 | −0.699394 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −924.000 | −0.176938 | ||||||||
\(302\) | − 6040.00i | − 1.15087i | ||||||||
\(303\) | − 1635.00i | − 0.309994i | ||||||||
\(304\) | −4183.00 | −0.789183 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1485.00 | 0.277424 | ||||||||
\(307\) | 460.000i | 0.0855166i | 0.999085 | + | 0.0427583i | \(0.0136145\pi\) | ||||
−0.999085 | + | 0.0427583i | \(0.986385\pi\) | |||||||
\(308\) | − 561.000i | − 0.103786i | ||||||||
\(309\) | 3918.00 | 0.721318 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8328.00 | 1.51845 | 0.759224 | − | 0.650829i | \(-0.225579\pi\) | ||||
0.759224 | + | 0.650829i | \(0.225579\pi\) | |||||||
\(312\) | − 4320.00i | − 0.783884i | ||||||||
\(313\) | − 5929.00i | − 1.07069i | −0.844633 | − | 0.535346i | \(-0.820181\pi\) | ||||
0.844633 | − | 0.535346i | \(-0.179819\pi\) | |||||||
\(314\) | 9370.00 | 1.68401 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12257.0 | −2.18199 | ||||||||
\(317\) | − 5040.00i | − 0.892980i | −0.894789 | − | 0.446490i | \(-0.852674\pi\) | ||||
0.894789 | − | 0.446490i | \(-0.147326\pi\) | |||||||
\(318\) | 2280.00i | 0.402063i | ||||||||
\(319\) | −594.000 | −0.104256 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5814.00 | 1.01092 | ||||||||
\(322\) | − 1695.00i | − 0.293350i | ||||||||
\(323\) | 1551.00i | 0.267183i | ||||||||
\(324\) | −1377.00 | −0.236111 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9520.00 | −1.61737 | ||||||||
\(327\) | 1728.00i | 0.292228i | ||||||||
\(328\) | 6255.00i | 1.05297i | ||||||||
\(329\) | −585.000 | −0.0980307 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10396.0 | 1.72633 | 0.863166 | − | 0.504920i | \(-0.168478\pi\) | ||||
0.863166 | + | 0.504920i | \(0.168478\pi\) | |||||||
\(332\) | − 2414.00i | − 0.399053i | ||||||||
\(333\) | 171.000i | 0.0281404i | ||||||||
\(334\) | 5900.00 | 0.966568 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 801.000 | 0.130054 | ||||||||
\(337\) | 7236.00i | 1.16964i | 0.811162 | + | 0.584822i | \(0.198836\pi\) | ||||
−0.811162 | + | 0.584822i | \(0.801164\pi\) | |||||||
\(338\) | − 5865.00i | − 0.943828i | ||||||||
\(339\) | 3312.00 | 0.530629 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1958.00 | −0.310943 | ||||||||
\(342\) | − 2115.00i | − 0.334404i | ||||||||
\(343\) | − 2031.00i | − 0.319719i | ||||||||
\(344\) | 13860.0 | 2.17233 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15885.0 | −2.46816 | ||||||||
\(347\) | − 1468.00i | − 0.227108i | −0.993532 | − | 0.113554i | \(-0.963777\pi\) | ||||
0.993532 | − | 0.113554i | \(-0.0362234\pi\) | |||||||
\(348\) | − 2754.00i | − 0.424224i | ||||||||
\(349\) | −5690.00 | −0.872718 | −0.436359 | − | 0.899773i | \(-0.643732\pi\) | ||||
−0.436359 | + | 0.899773i | \(0.643732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 864.000 | 0.131387 | ||||||||
\(352\) | 935.000i | 0.141579i | ||||||||
\(353\) | 5376.00i | 0.810582i | 0.914188 | + | 0.405291i | \(0.132830\pi\) | ||||
−0.914188 | + | 0.405291i | \(0.867170\pi\) | |||||||
\(354\) | 9375.00 | 1.40756 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6868.00 | 1.02248 | ||||||||
\(357\) | − 297.000i | − 0.0440306i | ||||||||
\(358\) | 8935.00i | 1.31908i | ||||||||
\(359\) | −3734.00 | −0.548950 | −0.274475 | − | 0.961594i | \(-0.588504\pi\) | ||||
−0.274475 | + | 0.961594i | \(0.588504\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4650.00 | −0.677941 | ||||||||
\(362\) | 4175.00i | 0.606169i | ||||||||
\(363\) | 363.000i | 0.0524864i | ||||||||
\(364\) | −1632.00 | −0.235000 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4800.00 | 0.685519 | ||||||||
\(367\) | 10274.0i | 1.46130i | 0.682750 | + | 0.730652i | \(0.260784\pi\) | ||||
−0.682750 | + | 0.730652i | \(0.739216\pi\) | |||||||
\(368\) | 10057.0i | 1.42461i | ||||||||
\(369\) | −1251.00 | −0.176489 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 456.000 | 0.0638122 | ||||||||
\(372\) | − 9078.00i | − 1.26525i | ||||||||
\(373\) | 13662.0i | 1.89649i | 0.317537 | + | 0.948246i | \(0.397144\pi\) | ||||
−0.317537 | + | 0.948246i | \(0.602856\pi\) | |||||||
\(374\) | 1815.00 | 0.250940 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8775.00 | 1.20355 | ||||||||
\(377\) | 1728.00i | 0.236065i | ||||||||
\(378\) | 405.000i | 0.0551083i | ||||||||
\(379\) | 7906.00 | 1.07151 | 0.535757 | − | 0.844372i | \(-0.320026\pi\) | ||||
0.535757 | + | 0.844372i | \(0.320026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5217.00 | −0.701509 | ||||||||
\(382\) | − 18065.0i | − 2.41960i | ||||||||
\(383\) | − 3168.00i | − 0.422656i | −0.977415 | − | 0.211328i | \(-0.932221\pi\) | ||||
0.977415 | − | 0.211328i | \(-0.0677788\pi\) | |||||||
\(384\) | 6345.00 | 0.843208 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21020.0 | 2.77174 | ||||||||
\(387\) | 2772.00i | 0.364105i | ||||||||
\(388\) | 1343.00i | 0.175723i | ||||||||
\(389\) | −10770.0 | −1.40375 | −0.701877 | − | 0.712298i | \(-0.747655\pi\) | ||||
−0.701877 | + | 0.712298i | \(0.747655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3729.00 | 0.482311 | ||||||||
\(392\) | 15030.0i | 1.93656i | ||||||||
\(393\) | 5454.00i | 0.700046i | ||||||||
\(394\) | 22585.0 | 2.88786 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1683.00 | −0.213571 | ||||||||
\(397\) | − 5670.00i | − 0.716799i | −0.933568 | − | 0.358399i | \(-0.883323\pi\) | ||||
0.933568 | − | 0.358399i | \(-0.116677\pi\) | |||||||
\(398\) | 20820.0i | 2.62214i | ||||||||
\(399\) | −423.000 | −0.0530739 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 832.000 | 0.103611 | 0.0518056 | − | 0.998657i | \(-0.483502\pi\) | ||||
0.0518056 | + | 0.998657i | \(0.483502\pi\) | |||||||
\(402\) | − 3000.00i | − 0.372205i | ||||||||
\(403\) | 5696.00i | 0.704064i | ||||||||
\(404\) | 9265.00 | 1.14097 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −810.000 | −0.0990139 | ||||||||
\(407\) | 209.000i | 0.0254539i | ||||||||
\(408\) | 4455.00i | 0.540577i | ||||||||
\(409\) | 5712.00 | 0.690563 | 0.345281 | − | 0.938499i | \(-0.387783\pi\) | ||||
0.345281 | + | 0.938499i | \(0.387783\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2610.00 | 0.313240 | ||||||||
\(412\) | 22202.0i | 2.65489i | ||||||||
\(413\) | − 1875.00i | − 0.223396i | ||||||||
\(414\) | −5085.00 | −0.603657 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2720.00 | 0.320574 | ||||||||
\(417\) | 1908.00i | 0.224065i | ||||||||
\(418\) | − 2585.00i | − 0.302480i | ||||||||
\(419\) | 4559.00 | 0.531555 | 0.265778 | − | 0.964034i | \(-0.414371\pi\) | ||||
0.265778 | + | 0.964034i | \(0.414371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6855.00 | 0.793568 | 0.396784 | − | 0.917912i | \(-0.370126\pi\) | ||||
0.396784 | + | 0.917912i | \(0.370126\pi\) | |||||||
\(422\) | − 23300.0i | − 2.68774i | ||||||||
\(423\) | 1755.00i | 0.201728i | ||||||||
\(424\) | −6840.00 | −0.783443 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14205.0 | −1.61557 | ||||||||
\(427\) | − 960.000i | − 0.108800i | ||||||||
\(428\) | 32946.0i | 3.72081i | ||||||||
\(429\) | 1056.00 | 0.118844 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10770.0 | 1.20365 | 0.601824 | − | 0.798628i | \(-0.294441\pi\) | ||||
0.601824 | + | 0.798628i | \(0.294441\pi\) | |||||||
\(432\) | − 2403.00i | − 0.267626i | ||||||||
\(433\) | 8498.00i | 0.943159i | 0.881824 | + | 0.471579i | \(0.156316\pi\) | ||||
−0.881824 | + | 0.471579i | \(0.843684\pi\) | |||||||
\(434\) | −2670.00 | −0.295309 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9792.00 | −1.07558 | ||||||||
\(437\) | − 5311.00i | − 0.581372i | ||||||||
\(438\) | − 6720.00i | − 0.733091i | ||||||||
\(439\) | −9835.00 | −1.06925 | −0.534623 | − | 0.845091i | \(-0.679546\pi\) | ||||
−0.534623 | + | 0.845091i | \(0.679546\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3006.00 | −0.324587 | ||||||||
\(442\) | − 5280.00i | − 0.568199i | ||||||||
\(443\) | − 10745.0i | − 1.15239i | −0.817311 | − | 0.576197i | \(-0.804536\pi\) | ||||
0.817311 | − | 0.576197i | \(-0.195464\pi\) | |||||||
\(444\) | −969.000 | −0.103574 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17800.0 | 1.88981 | ||||||||
\(447\) | 717.000i | 0.0758679i | ||||||||
\(448\) | − 861.000i | − 0.0908001i | ||||||||
\(449\) | −8356.00 | −0.878272 | −0.439136 | − | 0.898421i | \(-0.644715\pi\) | ||||
−0.439136 | + | 0.898421i | \(0.644715\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1529.00 | −0.159640 | ||||||||
\(452\) | 18768.0i | 1.95304i | ||||||||
\(453\) | 3624.00i | 0.375873i | ||||||||
\(454\) | 23390.0 | 2.41795 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6345.00 | 0.651605 | ||||||||
\(457\) | 7058.00i | 0.722449i | 0.932479 | + | 0.361225i | \(0.117641\pi\) | ||||
−0.932479 | + | 0.361225i | \(0.882359\pi\) | |||||||
\(458\) | − 22235.0i | − 2.26850i | ||||||||
\(459\) | −891.000 | −0.0906064 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 646.000 | 0.0652651 | 0.0326326 | − | 0.999467i | \(-0.489611\pi\) | ||||
0.0326326 | + | 0.999467i | \(0.489611\pi\) | |||||||
\(462\) | 495.000i | 0.0498474i | ||||||||
\(463\) | − 8982.00i | − 0.901574i | −0.892631 | − | 0.450787i | \(-0.851143\pi\) | ||||
0.892631 | − | 0.450787i | \(-0.148857\pi\) | |||||||
\(464\) | 4806.00 | 0.480847 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2055.00 | 0.204283 | ||||||||
\(467\) | 13476.0i | 1.33532i | 0.744466 | + | 0.667661i | \(0.232704\pi\) | ||||
−0.744466 | + | 0.667661i | \(0.767296\pi\) | |||||||
\(468\) | 4896.00i | 0.483585i | ||||||||
\(469\) | −600.000 | −0.0590734 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5622.00 | −0.549996 | ||||||||
\(472\) | 28125.0i | 2.74271i | ||||||||
\(473\) | 3388.00i | 0.329345i | ||||||||
\(474\) | 10815.0 | 1.04799 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1683.00 | 0.162059 | ||||||||
\(477\) | − 1368.00i | − 0.131313i | ||||||||
\(478\) | − 31900.0i | − 3.05245i | ||||||||
\(479\) | −12996.0 | −1.23967 | −0.619835 | − | 0.784732i | \(-0.712801\pi\) | ||||
−0.619835 | + | 0.784732i | \(0.712801\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 608.000 | 0.0576350 | ||||||||
\(482\) | − 36410.0i | − 3.44073i | ||||||||
\(483\) | 1017.00i | 0.0958077i | ||||||||
\(484\) | −2057.00 | −0.193182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1215.00 | 0.113402 | ||||||||
\(487\) | 6026.00i | 0.560707i | 0.959897 | + | 0.280353i | \(0.0904516\pi\) | ||||
−0.959897 | + | 0.280353i | \(0.909548\pi\) | |||||||
\(488\) | 14400.0i | 1.33577i | ||||||||
\(489\) | 5712.00 | 0.528232 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11698.0 | 1.07520 | 0.537600 | − | 0.843200i | \(-0.319331\pi\) | ||||
0.537600 | + | 0.843200i | \(0.319331\pi\) | |||||||
\(492\) | − 7089.00i | − 0.649587i | ||||||||
\(493\) | − 1782.00i | − 0.162794i | ||||||||
\(494\) | −7520.00 | −0.684900 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15842.0 | 1.43413 | ||||||||
\(497\) | 2841.00i | 0.256411i | ||||||||
\(498\) | 2130.00i | 0.191662i | ||||||||
\(499\) | 17052.0 | 1.52976 | 0.764882 | − | 0.644170i | \(-0.222797\pi\) | ||||
0.764882 | + | 0.644170i | \(0.222797\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3540.00 | −0.315680 | ||||||||
\(502\) | 23640.0i | 2.10180i | ||||||||
\(503\) | − 932.000i | − 0.0826160i | −0.999146 | − | 0.0413080i | \(-0.986848\pi\) | ||||
0.999146 | − | 0.0413080i | \(-0.0131525\pi\) | |||||||
\(504\) | −1215.00 | −0.107382 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6215.00 | −0.546029 | ||||||||
\(507\) | 3519.00i | 0.308253i | ||||||||
\(508\) | − 29563.0i | − 2.58198i | ||||||||
\(509\) | −4384.00 | −0.381763 | −0.190882 | − | 0.981613i | \(-0.561135\pi\) | ||||
−0.190882 | + | 0.981613i | \(0.561135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1344.00 | −0.116350 | ||||||||
\(512\) | 24475.0i | 2.11260i | ||||||||
\(513\) | 1269.00i | 0.109216i | ||||||||
\(514\) | −27090.0 | −2.32469 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −15708.0 | −1.34013 | ||||||||
\(517\) | 2145.00i | 0.182470i | ||||||||
\(518\) | 285.000i | 0.0241741i | ||||||||
\(519\) | 9531.00 | 0.806097 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2322.00 | −0.195257 | −0.0976283 | − | 0.995223i | \(-0.531126\pi\) | ||||
−0.0976283 | + | 0.995223i | \(0.531126\pi\) | |||||||
\(522\) | 2430.00i | 0.203751i | ||||||||
\(523\) | − 9749.00i | − 0.815094i | −0.913184 | − | 0.407547i | \(-0.866384\pi\) | ||||
0.913184 | − | 0.407547i | \(-0.133616\pi\) | |||||||
\(524\) | −30906.0 | −2.57659 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16770.0 | −1.39013 | ||||||||
\(527\) | − 5874.00i | − 0.485532i | ||||||||
\(528\) | − 2937.00i | − 0.242077i | ||||||||
\(529\) | −602.000 | −0.0494781 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5625.00 | −0.459707 | ||||||||
\(532\) | − 2397.00i | − 0.195344i | ||||||||
\(533\) | 4448.00i | 0.361471i | ||||||||
\(534\) | −6060.00 | −0.491090 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9000.00 | 0.725263 | ||||||||
\(537\) | − 5361.00i | − 0.430809i | ||||||||
\(538\) | 5310.00i | 0.425521i | ||||||||
\(539\) | −3674.00 | −0.293600 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4208.00 | 0.334410 | 0.167205 | − | 0.985922i | \(-0.446526\pi\) | ||||
0.167205 | + | 0.985922i | \(0.446526\pi\) | |||||||
\(542\) | 24105.0i | 1.91033i | ||||||||
\(543\) | − 2505.00i | − 0.197974i | ||||||||
\(544\) | −2805.00 | −0.221072 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1440.00 | 0.112869 | ||||||||
\(547\) | − 10179.0i | − 0.795654i | −0.917461 | − | 0.397827i | \(-0.869764\pi\) | ||||
0.917461 | − | 0.397827i | \(-0.130236\pi\) | |||||||
\(548\) | 14790.0i | 1.15292i | ||||||||
\(549\) | −2880.00 | −0.223890 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2538.00 | −0.196229 | ||||||||
\(552\) | − 15255.0i | − 1.17626i | ||||||||
\(553\) | − 2163.00i | − 0.166329i | ||||||||
\(554\) | −20.0000 | −0.00153379 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10812.0 | −0.824696 | ||||||||
\(557\) | 2314.00i | 0.176028i | 0.996119 | + | 0.0880138i | \(0.0280519\pi\) | ||||
−0.996119 | + | 0.0880138i | \(0.971948\pi\) | |||||||
\(558\) | 8010.00i | 0.607689i | ||||||||
\(559\) | 9856.00 | 0.745732 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1089.00 | −0.0819565 | ||||||||
\(562\) | − 23235.0i | − 1.74397i | ||||||||
\(563\) | 24330.0i | 1.82129i | 0.413188 | + | 0.910646i | \(0.364415\pi\) | ||||
−0.413188 | + | 0.910646i | \(0.635585\pi\) | |||||||
\(564\) | −9945.00 | −0.742482 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21415.0 | −1.59035 | ||||||||
\(567\) | − 243.000i | − 0.0179983i | ||||||||
\(568\) | − 42615.0i | − 3.14804i | ||||||||
\(569\) | −3445.00 | −0.253817 | −0.126909 | − | 0.991914i | \(-0.540505\pi\) | ||||
−0.126909 | + | 0.991914i | \(0.540505\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13056.0 | −0.956877 | −0.478438 | − | 0.878121i | \(-0.658797\pi\) | ||||
−0.478438 | + | 0.878121i | \(0.658797\pi\) | |||||||
\(572\) | 5984.00i | 0.437419i | ||||||||
\(573\) | 10839.0i | 0.790237i | ||||||||
\(574\) | −2085.00 | −0.151614 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2583.00 | −0.186849 | ||||||||
\(577\) | 17347.0i | 1.25159i | 0.779989 | + | 0.625793i | \(0.215225\pi\) | ||||
−0.779989 | + | 0.625793i | \(0.784775\pi\) | |||||||
\(578\) | − 19120.0i | − 1.37593i | ||||||||
\(579\) | −12612.0 | −0.905245 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 426.000 | 0.0304190 | ||||||||
\(582\) | − 1185.00i | − 0.0843983i | ||||||||
\(583\) | − 1672.00i | − 0.118777i | ||||||||
\(584\) | 20160.0 | 1.42847 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −34055.0 | −2.40068 | ||||||||
\(587\) | − 8379.00i | − 0.589162i | −0.955626 | − | 0.294581i | \(-0.904820\pi\) | ||||
0.955626 | − | 0.294581i | \(-0.0951801\pi\) | |||||||
\(588\) | − 17034.0i | − 1.19468i | ||||||||
\(589\) | −8366.00 | −0.585255 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13551.0 | −0.943170 | ||||||||
\(592\) | − 1691.00i | − 0.117398i | ||||||||
\(593\) | 1958.00i | 0.135591i | 0.997699 | + | 0.0677955i | \(0.0215965\pi\) | ||||
−0.997699 | + | 0.0677955i | \(0.978403\pi\) | |||||||
\(594\) | 1485.00 | 0.102576 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4063.00 | −0.279240 | ||||||||
\(597\) | − 12492.0i | − 0.856388i | ||||||||
\(598\) | 18080.0i | 1.23636i | ||||||||
\(599\) | −23583.0 | −1.60864 | −0.804320 | − | 0.594196i | \(-0.797470\pi\) | ||||
−0.804320 | + | 0.594196i | \(0.797470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15328.0 | −1.04034 | −0.520168 | − | 0.854064i | \(-0.674131\pi\) | ||||
−0.520168 | + | 0.854064i | \(0.674131\pi\) | |||||||
\(602\) | 4620.00i | 0.312786i | ||||||||
\(603\) | 1800.00i | 0.121562i | ||||||||
\(604\) | −20536.0 | −1.38344 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8175.00 | −0.547998 | ||||||||
\(607\) | − 160.000i | − 0.0106988i | −0.999986 | − | 0.00534942i | \(-0.998297\pi\) | ||||
0.999986 | − | 0.00534942i | \(-0.00170278\pi\) | |||||||
\(608\) | 3995.00i | 0.266478i | ||||||||
\(609\) | 486.000 | 0.0323378 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6240.00 | 0.413164 | ||||||||
\(612\) | − 5049.00i | − 0.333486i | ||||||||
\(613\) | − 5948.00i | − 0.391904i | −0.980613 | − | 0.195952i | \(-0.937220\pi\) | ||||
0.980613 | − | 0.195952i | \(-0.0627798\pi\) | |||||||
\(614\) | 2300.00 | 0.151173 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1485.00 | −0.0971304 | ||||||||
\(617\) | − 334.000i | − 0.0217931i | −0.999941 | − | 0.0108965i | \(-0.996531\pi\) | ||||
0.999941 | − | 0.0108965i | \(-0.00346855\pi\) | |||||||
\(618\) | − 19590.0i | − 1.27512i | ||||||||
\(619\) | 7202.00 | 0.467646 | 0.233823 | − | 0.972279i | \(-0.424876\pi\) | ||||
0.233823 | + | 0.972279i | \(0.424876\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3051.00 | 0.197154 | ||||||||
\(622\) | − 41640.0i | − 2.68426i | ||||||||
\(623\) | 1212.00i | 0.0779418i | ||||||||
\(624\) | −8544.00 | −0.548131 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −29645.0 | −1.89274 | ||||||||
\(627\) | 1551.00i | 0.0987894i | ||||||||
\(628\) | − 31858.0i | − 2.02432i | ||||||||
\(629\) | −627.000 | −0.0397458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10306.0 | 0.650199 | 0.325099 | − | 0.945680i | \(-0.394602\pi\) | ||||
0.325099 | + | 0.945680i | \(0.394602\pi\) | |||||||
\(632\) | 32445.0i | 2.04208i | ||||||||
\(633\) | 13980.0i | 0.877812i | ||||||||
\(634\) | −25200.0 | −1.57858 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7752.00 | 0.483313 | ||||||||
\(637\) | 10688.0i | 0.664794i | ||||||||
\(638\) | 2970.00i | 0.184300i | ||||||||
\(639\) | 8523.00 | 0.527644 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1228.00 | −0.0756678 | −0.0378339 | − | 0.999284i | \(-0.512046\pi\) | ||||
−0.0378339 | + | 0.999284i | \(0.512046\pi\) | |||||||
\(642\) | − 29070.0i | − 1.78707i | ||||||||
\(643\) | − 18454.0i | − 1.13181i | −0.824470 | − | 0.565906i | \(-0.808527\pi\) | ||||
0.824470 | − | 0.565906i | \(-0.191473\pi\) | |||||||
\(644\) | −5763.00 | −0.352630 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7755.00 | 0.472316 | ||||||||
\(647\) | − 17647.0i | − 1.07230i | −0.844124 | − | 0.536148i | \(-0.819879\pi\) | ||||
0.844124 | − | 0.536148i | \(-0.180121\pi\) | |||||||
\(648\) | 3645.00i | 0.220971i | ||||||||
\(649\) | −6875.00 | −0.415820 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1602.00 | 0.0964475 | ||||||||
\(652\) | 32368.0i | 1.94422i | ||||||||
\(653\) | 25918.0i | 1.55322i | 0.629984 | + | 0.776608i | \(0.283061\pi\) | ||||
−0.629984 | + | 0.776608i | \(0.716939\pi\) | |||||||
\(654\) | 8640.00 | 0.516591 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12371.0 | 0.736290 | ||||||||
\(657\) | 4032.00i | 0.239427i | ||||||||
\(658\) | 2925.00i | 0.173295i | ||||||||
\(659\) | −12864.0 | −0.760410 | −0.380205 | − | 0.924902i | \(-0.624147\pi\) | ||||
−0.380205 | + | 0.924902i | \(0.624147\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11419.0 | −0.671933 | −0.335966 | − | 0.941874i | \(-0.609063\pi\) | ||||
−0.335966 | + | 0.941874i | \(0.609063\pi\) | |||||||
\(662\) | − 51980.0i | − 3.05175i | ||||||||
\(663\) | 3168.00i | 0.185573i | ||||||||
\(664\) | −6390.00 | −0.373464 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 855.000 | 0.0497456 | ||||||||
\(667\) | 6102.00i | 0.354228i | ||||||||
\(668\) | − 20060.0i | − 1.16189i | ||||||||
\(669\) | −10680.0 | −0.617209 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3520.00 | −0.202516 | ||||||||
\(672\) | − 765.000i | − 0.0439145i | ||||||||
\(673\) | 15784.0i | 0.904054i | 0.892004 | + | 0.452027i | \(0.149299\pi\) | ||||
−0.892004 | + | 0.452027i | \(0.850701\pi\) | |||||||
\(674\) | 36180.0 | 2.06766 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19941.0 | −1.13456 | ||||||||
\(677\) | 26050.0i | 1.47885i | 0.673238 | + | 0.739426i | \(0.264903\pi\) | ||||
−0.673238 | + | 0.739426i | \(0.735097\pi\) | |||||||
\(678\) | − 16560.0i | − 0.938028i | ||||||||
\(679\) | −237.000 | −0.0133950 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14034.0 | −0.789698 | ||||||||
\(682\) | 9790.00i | 0.549675i | ||||||||
\(683\) | − 15095.0i | − 0.845672i | −0.906206 | − | 0.422836i | \(-0.861035\pi\) | ||||
0.906206 | − | 0.422836i | \(-0.138965\pi\) | |||||||
\(684\) | −7191.00 | −0.401981 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −10155.0 | −0.565189 | ||||||||
\(687\) | 13341.0i | 0.740889i | ||||||||
\(688\) | − 27412.0i | − 1.51900i | ||||||||
\(689\) | −4864.00 | −0.268946 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15896.0 | 0.875126 | 0.437563 | − | 0.899188i | \(-0.355842\pi\) | ||||
0.437563 | + | 0.899188i | \(0.355842\pi\) | |||||||
\(692\) | 54009.0i | 2.96693i | ||||||||
\(693\) | − 297.000i | − 0.0162801i | ||||||||
\(694\) | −7340.00 | −0.401473 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7290.00 | −0.397021 | ||||||||
\(697\) | − 4587.00i | − 0.249275i | ||||||||
\(698\) | 28450.0i | 1.54276i | ||||||||
\(699\) | −1233.00 | −0.0667187 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10529.0 | 0.567296 | 0.283648 | − | 0.958928i | \(-0.408455\pi\) | ||||
0.283648 | + | 0.958928i | \(0.408455\pi\) | |||||||
\(702\) | − 4320.00i | − 0.232262i | ||||||||
\(703\) | 893.000i | 0.0479092i | ||||||||
\(704\) | −3157.00 | −0.169011 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26880.0 | 1.43292 | ||||||||
\(707\) | 1635.00i | 0.0869738i | ||||||||
\(708\) | − 31875.0i | − 1.69200i | ||||||||
\(709\) | 16087.0 | 0.852130 | 0.426065 | − | 0.904693i | \(-0.359900\pi\) | ||||
0.426065 | + | 0.904693i | \(0.359900\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6489.00 | −0.342274 | ||||||||
\(712\) | − 18180.0i | − 0.956916i | ||||||||
\(713\) | 20114.0i | 1.05649i | ||||||||
\(714\) | −1485.00 | −0.0778358 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 30379.0 | 1.58564 | ||||||||
\(717\) | 19140.0i | 0.996927i | ||||||||
\(718\) | 18670.0i | 0.970415i | ||||||||
\(719\) | −24336.0 | −1.26228 | −0.631140 | − | 0.775669i | \(-0.717413\pi\) | ||||
−0.631140 | + | 0.775669i | \(0.717413\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3918.00 | −0.202377 | ||||||||
\(722\) | 23250.0i | 1.19844i | ||||||||
\(723\) | 21846.0i | 1.12374i | ||||||||
\(724\) | 14195.0 | 0.728664 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1815.00 | 0.0927837 | ||||||||
\(727\) | − 13960.0i | − 0.712170i | −0.934454 | − | 0.356085i | \(-0.884111\pi\) | ||||
0.934454 | − | 0.356085i | \(-0.115889\pi\) | |||||||
\(728\) | 4320.00i | 0.219931i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10164.0 | −0.514267 | ||||||||
\(732\) | − 16320.0i | − 0.824050i | ||||||||
\(733\) | 9252.00i | 0.466208i | 0.972452 | + | 0.233104i | \(0.0748882\pi\) | ||||
−0.972452 | + | 0.233104i | \(0.925112\pi\) | |||||||
\(734\) | 51370.0 | 2.58324 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 9605.00 | 0.481039 | ||||||||
\(737\) | 2200.00i | 0.109957i | ||||||||
\(738\) | 6255.00i | 0.311992i | ||||||||
\(739\) | −28453.0 | −1.41632 | −0.708160 | − | 0.706052i | \(-0.750474\pi\) | ||||
−0.708160 | + | 0.706052i | \(0.750474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4512.00 | 0.223688 | ||||||||
\(742\) | − 2280.00i | − 0.112805i | ||||||||
\(743\) | 512.000i | 0.0252806i | 0.999920 | + | 0.0126403i | \(0.00402363\pi\) | ||||
−0.999920 | + | 0.0126403i | \(0.995976\pi\) | |||||||
\(744\) | −24030.0 | −1.18412 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 68310.0 | 3.35256 | ||||||||
\(747\) | − 1278.00i | − 0.0625965i | ||||||||
\(748\) | − 6171.00i | − 0.301650i | ||||||||
\(749\) | −5814.00 | −0.283630 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 772.000 | 0.0375109 | 0.0187554 | − | 0.999824i | \(-0.494030\pi\) | ||||
0.0187554 | + | 0.999824i | \(0.494030\pi\) | |||||||
\(752\) | − 17355.0i | − 0.841585i | ||||||||
\(753\) | − 14184.0i | − 0.686446i | ||||||||
\(754\) | 8640.00 | 0.417308 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1377.00 | 0.0662447 | ||||||||
\(757\) | − 8058.00i | − 0.386886i | −0.981111 | − | 0.193443i | \(-0.938034\pi\) | ||||
0.981111 | − | 0.193443i | \(-0.0619655\pi\) | |||||||
\(758\) | − 39530.0i | − 1.89419i | ||||||||
\(759\) | 3729.00 | 0.178332 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18650.0 | 0.888386 | 0.444193 | − | 0.895931i | \(-0.353490\pi\) | ||||
0.444193 | + | 0.895931i | \(0.353490\pi\) | |||||||
\(762\) | 26085.0i | 1.24010i | ||||||||
\(763\) | − 1728.00i | − 0.0819893i | ||||||||
\(764\) | −61421.0 | −2.90855 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15840.0 | −0.747157 | ||||||||
\(767\) | 20000.0i | 0.941536i | ||||||||
\(768\) | − 24837.0i | − 1.16696i | ||||||||
\(769\) | 7144.00 | 0.335005 | 0.167503 | − | 0.985872i | \(-0.446430\pi\) | ||||
0.167503 | + | 0.985872i | \(0.446430\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16254.0 | 0.759239 | ||||||||
\(772\) | − 71468.0i | − 3.33185i | ||||||||
\(773\) | − 1904.00i | − 0.0885927i | −0.999018 | − | 0.0442963i | \(-0.985895\pi\) | ||||
0.999018 | − | 0.0442963i | \(-0.0141046\pi\) | |||||||
\(774\) | 13860.0 | 0.643653 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3555.00 | 0.164455 | ||||||||
\(777\) | − 171.000i | − 0.00789523i | ||||||||
\(778\) | 53850.0i | 2.48151i | ||||||||
\(779\) | −6533.00 | −0.300474 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10417.0 | 0.477272 | ||||||||
\(782\) | − 18645.0i | − 0.852614i | ||||||||
\(783\) | − 1458.00i | − 0.0665449i | ||||||||
\(784\) | 29726.0 | 1.35414 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 27270.0 | 1.23752 | ||||||||
\(787\) | − 7555.00i | − 0.342194i | −0.985254 | − | 0.171097i | \(-0.945269\pi\) | ||||
0.985254 | − | 0.171097i | \(-0.0547311\pi\) | |||||||
\(788\) | − 76789.0i | − 3.47144i | ||||||||
\(789\) | 10062.0 | 0.454014 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3312.00 | −0.148876 | ||||||||
\(792\) | 4455.00i | 0.199876i | ||||||||
\(793\) | 10240.0i | 0.458554i | ||||||||
\(794\) | −28350.0 | −1.26713 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 70788.0 | 3.15203 | ||||||||
\(797\) | − 24950.0i | − 1.10888i | −0.832225 | − | 0.554438i | \(-0.812933\pi\) | ||||
0.832225 | − | 0.554438i | \(-0.187067\pi\) | |||||||
\(798\) | 2115.00i | 0.0938223i | ||||||||
\(799\) | −6435.00 | −0.284924 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3636.00 | 0.160389 | ||||||||
\(802\) | − 4160.00i | − 0.183160i | ||||||||
\(803\) | 4928.00i | 0.216570i | ||||||||
\(804\) | −10200.0 | −0.447421 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28480.0 | 1.24462 | ||||||||
\(807\) | − 3186.00i | − 0.138975i | ||||||||
\(808\) | − 24525.0i | − 1.06781i | ||||||||
\(809\) | −19893.0 | −0.864525 | −0.432262 | − | 0.901748i | \(-0.642285\pi\) | ||||
−0.432262 | + | 0.901748i | \(0.642285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34503.0 | 1.49391 | 0.746957 | − | 0.664872i | \(-0.231514\pi\) | ||||
0.746957 | + | 0.664872i | \(0.231514\pi\) | |||||||
\(812\) | 2754.00i | 0.119023i | ||||||||
\(813\) | − 14463.0i | − 0.623911i | ||||||||
\(814\) | 1045.00 | 0.0449966 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8811.00 | 0.377998 | ||||||||
\(817\) | 14476.0i | 0.619891i | ||||||||
\(818\) | − 28560.0i | − 1.22075i | ||||||||
\(819\) | −864.000 | −0.0368628 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16890.0 | 0.717984 | 0.358992 | − | 0.933341i | \(-0.383120\pi\) | ||||
0.358992 | + | 0.933341i | \(0.383120\pi\) | |||||||
\(822\) | − 13050.0i | − 0.553736i | ||||||||
\(823\) | 34692.0i | 1.46936i | 0.678411 | + | 0.734682i | \(0.262669\pi\) | ||||
−0.678411 | + | 0.734682i | \(0.737331\pi\) | |||||||
\(824\) | 58770.0 | 2.48465 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9375.00 | −0.394913 | ||||||||
\(827\) | − 41424.0i | − 1.74178i | −0.491476 | − | 0.870891i | \(-0.663543\pi\) | ||||
0.491476 | − | 0.870891i | \(-0.336457\pi\) | |||||||
\(828\) | 17289.0i | 0.725645i | ||||||||
\(829\) | 18494.0 | 0.774817 | 0.387408 | − | 0.921908i | \(-0.373370\pi\) | ||||
0.387408 | + | 0.921908i | \(0.373370\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0000 | 0.000500933 0 | ||||||||
\(832\) | 9184.00i | 0.382690i | ||||||||
\(833\) | − 11022.0i | − 0.458451i | ||||||||
\(834\) | 9540.00 | 0.396095 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8789.00 | −0.363605 | ||||||||
\(837\) | − 4806.00i | − 0.198470i | ||||||||
\(838\) | − 22795.0i | − 0.939666i | ||||||||
\(839\) | −6680.00 | −0.274874 | −0.137437 | − | 0.990511i | \(-0.543886\pi\) | ||||
−0.137437 | + | 0.990511i | \(0.543886\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21473.0 | −0.880438 | ||||||||
\(842\) | − 34275.0i | − 1.40284i | ||||||||
\(843\) | 13941.0i | 0.569577i | ||||||||
\(844\) | −79220.0 | −3.23088 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 8775.00 | 0.356608 | ||||||||
\(847\) | − 363.000i | − 0.0147259i | ||||||||
\(848\) | 13528.0i | 0.547822i | ||||||||
\(849\) | 12849.0 | 0.519407 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2147.00 | 0.0864844 | ||||||||
\(852\) | 48297.0i | 1.94205i | ||||||||
\(853\) | 43358.0i | 1.74039i | 0.492711 | + | 0.870193i | \(0.336006\pi\) | ||||
−0.492711 | + | 0.870193i | \(0.663994\pi\) | |||||||
\(854\) | −4800.00 | −0.192333 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 87210.0 | 3.48222 | ||||||||
\(857\) | − 15585.0i | − 0.621206i | −0.950540 | − | 0.310603i | \(-0.899469\pi\) | ||||
0.950540 | − | 0.310603i | \(-0.100531\pi\) | |||||||
\(858\) | − 5280.00i | − 0.210089i | ||||||||
\(859\) | 17036.0 | 0.676672 | 0.338336 | − | 0.941025i | \(-0.390136\pi\) | ||||
0.338336 | + | 0.941025i | \(0.390136\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1251.00 | 0.0495168 | ||||||||
\(862\) | − 53850.0i | − 2.12777i | ||||||||
\(863\) | 28064.0i | 1.10696i | 0.832861 | + | 0.553482i | \(0.186701\pi\) | ||||
−0.832861 | + | 0.553482i | \(0.813299\pi\) | |||||||
\(864\) | −2295.00 | −0.0903675 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 42490.0 | 1.66729 | ||||||||
\(867\) | 11472.0i | 0.449377i | ||||||||
\(868\) | 9078.00i | 0.354985i | ||||||||
\(869\) | −7931.00 | −0.309598 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6400.00 | 0.248973 | ||||||||
\(872\) | 25920.0i | 1.00661i | ||||||||
\(873\) | 711.000i | 0.0275644i | ||||||||
\(874\) | −26555.0 | −1.02773 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −22848.0 | −0.881236 | ||||||||
\(877\) | 22654.0i | 0.872259i | 0.899884 | + | 0.436130i | \(0.143651\pi\) | ||||
−0.899884 | + | 0.436130i | \(0.856349\pi\) | |||||||
\(878\) | 49175.0i | 1.89018i | ||||||||
\(879\) | 20433.0 | 0.784059 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22380.0 | −0.855847 | −0.427924 | − | 0.903815i | \(-0.640755\pi\) | ||||
−0.427924 | + | 0.903815i | \(0.640755\pi\) | |||||||
\(882\) | 15030.0i | 0.573794i | ||||||||
\(883\) | 35174.0i | 1.34054i | 0.742116 | + | 0.670271i | \(0.233822\pi\) | ||||
−0.742116 | + | 0.670271i | \(0.766178\pi\) | |||||||
\(884\) | −17952.0 | −0.683022 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −53725.0 | −2.03716 | ||||||||
\(887\) | − 30868.0i | − 1.16848i | −0.811579 | − | 0.584242i | \(-0.801392\pi\) | ||||
0.811579 | − | 0.584242i | \(-0.198608\pi\) | |||||||
\(888\) | 2565.00i | 0.0969322i | ||||||||
\(889\) | 5217.00 | 0.196820 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −891.000 | −0.0335013 | ||||||||
\(892\) | − 60520.0i | − 2.27170i | ||||||||
\(893\) | 9165.00i | 0.343443i | ||||||||
\(894\) | 3585.00 | 0.134117 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6345.00 | −0.236575 | ||||||||
\(897\) | − 10848.0i | − 0.403795i | ||||||||
\(898\) | 41780.0i | 1.55258i | ||||||||
\(899\) | 9612.00 | 0.356594 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5016.00 | 0.185469 | ||||||||
\(902\) | 7645.00i | 0.282207i | ||||||||
\(903\) | − 2772.00i | − 0.102155i | ||||||||
\(904\) | 49680.0 | 1.82780 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18120.0 | 0.664455 | ||||||||
\(907\) | − 10070.0i | − 0.368654i | −0.982865 | − | 0.184327i | \(-0.940990\pi\) | ||||
0.982865 | − | 0.184327i | \(-0.0590105\pi\) | |||||||
\(908\) | − 79526.0i | − 2.90657i | ||||||||
\(909\) | 4905.00 | 0.178975 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1885.00 | 0.0685542 | 0.0342771 | − | 0.999412i | \(-0.489087\pi\) | ||||
0.0342771 | + | 0.999412i | \(0.489087\pi\) | |||||||
\(912\) | − 12549.0i | − 0.455635i | ||||||||
\(913\) | − 1562.00i | − 0.0566207i | ||||||||
\(914\) | 35290.0 | 1.27712 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −75599.0 | −2.72692 | ||||||||
\(917\) | − 5454.00i | − 0.196409i | ||||||||
\(918\) | 4455.00i | 0.160171i | ||||||||
\(919\) | −23703.0 | −0.850805 | −0.425403 | − | 0.905004i | \(-0.639867\pi\) | ||||
−0.425403 | + | 0.905004i | \(0.639867\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1380.00 | −0.0493730 | ||||||||
\(922\) | − 3230.00i | − 0.115374i | ||||||||
\(923\) | − 30304.0i | − 1.08068i | ||||||||
\(924\) | 1683.00 | 0.0599206 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −44910.0 | −1.59377 | ||||||||
\(927\) | 11754.0i | 0.416453i | ||||||||
\(928\) | − 4590.00i | − 0.162364i | ||||||||
\(929\) | −53804.0 | −1.90016 | −0.950082 | − | 0.312001i | \(-0.899001\pi\) | ||||
−0.950082 | + | 0.312001i | \(0.899001\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15698.0 | −0.552611 | ||||||||
\(932\) | − 6987.00i | − 0.245565i | ||||||||
\(933\) | 24984.0i | 0.876677i | ||||||||
\(934\) | 67380.0 | 2.36054 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12960.0 | 0.452576 | ||||||||
\(937\) | − 1326.00i | − 0.0462311i | −0.999733 | − | 0.0231155i | \(-0.992641\pi\) | ||||
0.999733 | − | 0.0231155i | \(-0.00735856\pi\) | |||||||
\(938\) | 3000.00i | 0.104428i | ||||||||
\(939\) | 17787.0 | 0.618165 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27109.0 | −0.939137 | −0.469569 | − | 0.882896i | \(-0.655591\pi\) | ||||
−0.469569 | + | 0.882896i | \(0.655591\pi\) | |||||||
\(942\) | 28110.0i | 0.972265i | ||||||||
\(943\) | 15707.0i | 0.542408i | ||||||||
\(944\) | 55625.0 | 1.91784 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16940.0 | 0.582206 | ||||||||
\(947\) | − 31143.0i | − 1.06865i | −0.845279 | − | 0.534325i | \(-0.820566\pi\) | ||||
0.845279 | − | 0.534325i | \(-0.179434\pi\) | |||||||
\(948\) | − 36771.0i | − 1.25977i | ||||||||
\(949\) | 14336.0 | 0.490375 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15120.0 | 0.515562 | ||||||||
\(952\) | − 4455.00i | − 0.151667i | ||||||||
\(953\) | − 879.000i | − 0.0298779i | −0.999888 | − | 0.0149389i | \(-0.995245\pi\) | ||||
0.999888 | − | 0.0149389i | \(-0.00475539\pi\) | |||||||
\(954\) | −6840.00 | −0.232131 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −108460. | −3.66930 | ||||||||
\(957\) | − 1782.00i | − 0.0601921i | ||||||||
\(958\) | 64980.0i | 2.19145i | ||||||||
\(959\) | −2610.00 | −0.0878846 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1893.00 | 0.0635427 | ||||||||
\(962\) | − 3040.00i | − 0.101885i | ||||||||
\(963\) | 17442.0i | 0.583656i | ||||||||
\(964\) | −123794. | −4.13603 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5085.00 | 0.169366 | ||||||||
\(967\) | 14824.0i | 0.492976i | 0.969146 | + | 0.246488i | \(0.0792766\pi\) | ||||
−0.969146 | + | 0.246488i | \(0.920723\pi\) | |||||||
\(968\) | 5445.00i | 0.180794i | ||||||||
\(969\) | −4653.00 | −0.154258 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34089.0 | 1.12664 | 0.563320 | − | 0.826239i | \(-0.309524\pi\) | ||||
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(972\) | − 4131.00i | − 0.136319i | ||||||||
\(973\) | − 1908.00i | − 0.0628650i | ||||||||
\(974\) | 30130.0 | 0.991199 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28480.0 | 0.934040 | ||||||||
\(977\) | − 33446.0i | − 1.09522i | −0.836733 | − | 0.547611i | \(-0.815537\pi\) | ||||
0.836733 | − | 0.547611i | \(-0.184463\pi\) | |||||||
\(978\) | − 28560.0i | − 0.933792i | ||||||||
\(979\) | 4444.00 | 0.145077 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5184.00 | −0.168718 | ||||||||
\(982\) | − 58490.0i | − 1.90070i | ||||||||
\(983\) | − 52025.0i | − 1.68804i | −0.536315 | − | 0.844018i | \(-0.680184\pi\) | ||||
0.536315 | − | 0.844018i | \(-0.319816\pi\) | |||||||
\(984\) | −18765.0 | −0.607933 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8910.00 | −0.287781 | ||||||||
\(987\) | − 1755.00i | − 0.0565980i | ||||||||
\(988\) | 25568.0i | 0.823306i | ||||||||
\(989\) | 34804.0 | 1.11901 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41260.0 | −1.32257 | −0.661285 | − | 0.750135i | \(-0.729989\pi\) | ||||
−0.661285 | + | 0.750135i | \(0.729989\pi\) | |||||||
\(992\) | − 15130.0i | − 0.484252i | ||||||||
\(993\) | 31188.0i | 0.996698i | ||||||||
\(994\) | 14205.0 | 0.453275 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7242.00 | 0.230393 | ||||||||
\(997\) | 190.000i | 0.00603547i | 0.999995 | + | 0.00301773i | \(0.000960576\pi\) | ||||
−0.999995 | + | 0.00301773i | \(0.999039\pi\) | |||||||
\(998\) | − 85260.0i | − 2.70427i | ||||||||
\(999\) | −513.000 | −0.0162468 |
(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.b.199.1 | 2 | ||
5.2 | odd | 4 | 825.4.a.j.1.1 | yes | 1 | ||
5.3 | odd | 4 | 825.4.a.a.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 825.4.c.b.199.2 | 2 | ||
15.2 | even | 4 | 2475.4.a.a.1.1 | 1 | |||
15.8 | even | 4 | 2475.4.a.k.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.4.a.a.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
825.4.a.j.1.1 | yes | 1 | 5.2 | odd | 4 | ||
825.4.c.b.199.1 | 2 | 1.1 | even | 1 | trivial | ||
825.4.c.b.199.2 | 2 | 5.4 | even | 2 | inner | ||
2475.4.a.a.1.1 | 1 | 15.2 | even | 4 | |||
2475.4.a.k.1.1 | 1 | 15.8 | even | 4 |