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: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
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.d.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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.00000i | 1.06066i | 0.847791 | + | 0.530330i | \(0.177932\pi\) | ||||
−0.847791 | + | 0.530330i | \(0.822068\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | −1.00000 | −0.125000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 9.00000 | 0.612372 | ||||||||
\(7\) | 7.00000i | 0.377964i | 0.981981 | + | 0.188982i | \(0.0605189\pi\) | ||||
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | 21.0000i | 0.928078i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 3.00000i | 0.0721688i | ||||||||
\(13\) | − 16.0000i | − 0.341354i | −0.985327 | − | 0.170677i | \(-0.945405\pi\) | ||||
0.985327 | − | 0.170677i | \(-0.0545955\pi\) | |||||||
\(14\) | −21.0000 | −0.400892 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | − 21.0000i | − 0.299603i | −0.988716 | − | 0.149801i | \(-0.952137\pi\) | ||||
0.988716 | − | 0.149801i | \(-0.0478634\pi\) | |||||||
\(18\) | − 27.0000i | − 0.353553i | ||||||||
\(19\) | −125.000 | −1.50931 | −0.754657 | − | 0.656119i | \(-0.772197\pi\) | ||||
−0.754657 | + | 0.656119i | \(0.772197\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 33.0000i | 0.319801i | ||||||||
\(23\) | − 81.0000i | − 0.734333i | −0.930155 | − | 0.367167i | \(-0.880328\pi\) | ||||
0.930155 | − | 0.367167i | \(-0.119672\pi\) | |||||||
\(24\) | 63.0000 | 0.535826 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 48.0000 | 0.362061 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | − 7.00000i | − 0.0472456i | ||||||||
\(29\) | −186.000 | −1.19101 | −0.595506 | − | 0.803351i | \(-0.703048\pi\) | ||||
−0.595506 | + | 0.803351i | \(0.703048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −58.0000 | −0.336036 | −0.168018 | − | 0.985784i | \(-0.553737\pi\) | ||||
−0.168018 | + | 0.985784i | \(0.553737\pi\) | |||||||
\(32\) | − 45.0000i | − 0.248592i | ||||||||
\(33\) | − 33.0000i | − 0.174078i | ||||||||
\(34\) | 63.0000 | 0.317777 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.00000 | 0.0416667 | ||||||||
\(37\) | 253.000i | 1.12413i | 0.827092 | + | 0.562067i | \(0.189994\pi\) | ||||
−0.827092 | + | 0.562067i | \(0.810006\pi\) | |||||||
\(38\) | − 375.000i | − 1.60087i | ||||||||
\(39\) | −48.0000 | −0.197081 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 63.0000 | 0.239974 | 0.119987 | − | 0.992775i | \(-0.461715\pi\) | ||||
0.119987 | + | 0.992775i | \(0.461715\pi\) | |||||||
\(42\) | 63.0000i | 0.231455i | ||||||||
\(43\) | − 100.000i | − 0.354648i | −0.984153 | − | 0.177324i | \(-0.943256\pi\) | ||||
0.984153 | − | 0.177324i | \(-0.0567440\pi\) | |||||||
\(44\) | −11.0000 | −0.0376889 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 243.000 | 0.778878 | ||||||||
\(47\) | 219.000i | 0.679669i | 0.940485 | + | 0.339834i | \(0.110371\pi\) | ||||
−0.940485 | + | 0.339834i | \(0.889629\pi\) | |||||||
\(48\) | 213.000i | 0.640498i | ||||||||
\(49\) | 294.000 | 0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −63.0000 | −0.172976 | ||||||||
\(52\) | 16.0000i | 0.0426692i | ||||||||
\(53\) | − 192.000i | − 0.497608i | −0.968554 | − | 0.248804i | \(-0.919962\pi\) | ||||
0.968554 | − | 0.248804i | \(-0.0800375\pi\) | |||||||
\(54\) | −81.0000 | −0.204124 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −147.000 | −0.350780 | ||||||||
\(57\) | 375.000i | 0.871403i | ||||||||
\(58\) | − 558.000i | − 1.26326i | ||||||||
\(59\) | −249.000 | −0.549441 | −0.274721 | − | 0.961524i | \(-0.588585\pi\) | ||||
−0.274721 | + | 0.961524i | \(0.588585\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −64.0000 | −0.134334 | −0.0671669 | − | 0.997742i | \(-0.521396\pi\) | ||||
−0.0671669 | + | 0.997742i | \(0.521396\pi\) | |||||||
\(62\) | − 174.000i | − 0.356420i | ||||||||
\(63\) | − 63.0000i | − 0.125988i | ||||||||
\(64\) | −433.000 | −0.845703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 99.0000 | 0.184637 | ||||||||
\(67\) | − 272.000i | − 0.495971i | −0.968764 | − | 0.247986i | \(-0.920231\pi\) | ||||
0.968764 | − | 0.247986i | \(-0.0797686\pi\) | |||||||
\(68\) | 21.0000i | 0.0374504i | ||||||||
\(69\) | −243.000 | −0.423968 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −645.000 | −1.07813 | −0.539066 | − | 0.842263i | \(-0.681223\pi\) | ||||
−0.539066 | + | 0.842263i | \(0.681223\pi\) | |||||||
\(72\) | − 189.000i | − 0.309359i | ||||||||
\(73\) | − 112.000i | − 0.179570i | −0.995961 | − | 0.0897850i | \(-0.971382\pi\) | ||||
0.995961 | − | 0.0897850i | \(-0.0286180\pi\) | |||||||
\(74\) | −759.000 | −1.19232 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 125.000 | 0.188664 | ||||||||
\(77\) | 77.0000i | 0.113961i | ||||||||
\(78\) | − 144.000i | − 0.209036i | ||||||||
\(79\) | −509.000 | −0.724898 | −0.362449 | − | 0.932004i | \(-0.618059\pi\) | ||||
−0.362449 | + | 0.932004i | \(0.618059\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 189.000i | 0.254531i | ||||||||
\(83\) | − 1254.00i | − 1.65837i | −0.558977 | − | 0.829183i | \(-0.688806\pi\) | ||||
0.558977 | − | 0.829183i | \(-0.311194\pi\) | |||||||
\(84\) | −21.0000 | −0.0272772 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 300.000 | 0.376161 | ||||||||
\(87\) | 558.000i | 0.687631i | ||||||||
\(88\) | 231.000i | 0.279826i | ||||||||
\(89\) | −756.000 | −0.900403 | −0.450201 | − | 0.892927i | \(-0.648648\pi\) | ||||
−0.450201 | + | 0.892927i | \(0.648648\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 112.000 | 0.129020 | ||||||||
\(92\) | 81.0000i | 0.0917917i | ||||||||
\(93\) | 174.000i | 0.194010i | ||||||||
\(94\) | −657.000 | −0.720898 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −135.000 | −0.143525 | ||||||||
\(97\) | − 839.000i | − 0.878222i | −0.898433 | − | 0.439111i | \(-0.855293\pi\) | ||||
0.898433 | − | 0.439111i | \(-0.144707\pi\) | |||||||
\(98\) | 882.000i | 0.909137i | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1413.00 | −1.39207 | −0.696033 | − | 0.718009i | \(-0.745053\pi\) | ||||
−0.696033 | + | 0.718009i | \(0.745053\pi\) | |||||||
\(102\) | − 189.000i | − 0.183469i | ||||||||
\(103\) | 1634.00i | 1.56313i | 0.623821 | + | 0.781567i | \(0.285579\pi\) | ||||
−0.623821 | + | 0.781567i | \(0.714421\pi\) | |||||||
\(104\) | 336.000 | 0.316803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 576.000 | 0.527793 | ||||||||
\(107\) | − 726.000i | − 0.655935i | −0.944689 | − | 0.327968i | \(-0.893636\pi\) | ||||
0.944689 | − | 0.327968i | \(-0.106364\pi\) | |||||||
\(108\) | − 27.0000i | − 0.0240563i | ||||||||
\(109\) | −1712.00 | −1.50440 | −0.752201 | − | 0.658934i | \(-0.771008\pi\) | ||||
−0.752201 | + | 0.658934i | \(0.771008\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 759.000 | 0.649019 | ||||||||
\(112\) | − 497.000i | − 0.419304i | ||||||||
\(113\) | − 1128.00i | − 0.939056i | −0.882918 | − | 0.469528i | \(-0.844424\pi\) | ||||
0.882918 | − | 0.469528i | \(-0.155576\pi\) | |||||||
\(114\) | −1125.00 | −0.924262 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 186.000 | 0.148876 | ||||||||
\(117\) | 144.000i | 0.113785i | ||||||||
\(118\) | − 747.000i | − 0.582771i | ||||||||
\(119\) | 147.000 | 0.113239 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | − 192.000i | − 0.142482i | ||||||||
\(123\) | − 189.000i | − 0.138549i | ||||||||
\(124\) | 58.0000 | 0.0420045 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 189.000 | 0.133631 | ||||||||
\(127\) | − 1127.00i | − 0.787442i | −0.919230 | − | 0.393721i | \(-0.871188\pi\) | ||||
0.919230 | − | 0.393721i | \(-0.128812\pi\) | |||||||
\(128\) | − 1659.00i | − 1.14560i | ||||||||
\(129\) | −300.000 | −0.204756 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1122.00 | −0.748318 | −0.374159 | − | 0.927365i | \(-0.622068\pi\) | ||||
−0.374159 | + | 0.927365i | \(0.622068\pi\) | |||||||
\(132\) | 33.0000i | 0.0217597i | ||||||||
\(133\) | − 875.000i | − 0.570467i | ||||||||
\(134\) | 816.000 | 0.526057 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 441.000 | 0.278055 | ||||||||
\(137\) | − 54.0000i | − 0.0336754i | −0.999858 | − | 0.0168377i | \(-0.994640\pi\) | ||||
0.999858 | − | 0.0168377i | \(-0.00535986\pi\) | |||||||
\(138\) | − 729.000i | − 0.449686i | ||||||||
\(139\) | −1748.00 | −1.06664 | −0.533322 | − | 0.845913i | \(-0.679056\pi\) | ||||
−0.533322 | + | 0.845913i | \(0.679056\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 657.000 | 0.392407 | ||||||||
\(142\) | − 1935.00i | − 1.14353i | ||||||||
\(143\) | − 176.000i | − 0.102922i | ||||||||
\(144\) | 639.000 | 0.369792 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 336.000 | 0.190463 | ||||||||
\(147\) | − 882.000i | − 0.494872i | ||||||||
\(148\) | − 253.000i | − 0.140517i | ||||||||
\(149\) | −1797.00 | −0.988027 | −0.494013 | − | 0.869454i | \(-0.664471\pi\) | ||||
−0.494013 | + | 0.869454i | \(0.664471\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1040.00 | 0.560490 | 0.280245 | − | 0.959928i | \(-0.409584\pi\) | ||||
0.280245 | + | 0.959928i | \(0.409584\pi\) | |||||||
\(152\) | − 2625.00i | − 1.40076i | ||||||||
\(153\) | 189.000i | 0.0998676i | ||||||||
\(154\) | −231.000 | −0.120873 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 48.0000 | 0.0246351 | ||||||||
\(157\) | 562.000i | 0.285685i | 0.989745 | + | 0.142842i | \(0.0456242\pi\) | ||||
−0.989745 | + | 0.142842i | \(0.954376\pi\) | |||||||
\(158\) | − 1527.00i | − 0.768871i | ||||||||
\(159\) | −576.000 | −0.287294 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 567.000 | 0.277552 | ||||||||
\(162\) | 243.000i | 0.117851i | ||||||||
\(163\) | 2432.00i | 1.16864i | 0.811522 | + | 0.584322i | \(0.198639\pi\) | ||||
−0.811522 | + | 0.584322i | \(0.801361\pi\) | |||||||
\(164\) | −63.0000 | −0.0299968 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3762.00 | 1.75896 | ||||||||
\(167\) | − 2340.00i | − 1.08428i | −0.840288 | − | 0.542140i | \(-0.817614\pi\) | ||||
0.840288 | − | 0.542140i | \(-0.182386\pi\) | |||||||
\(168\) | 441.000i | 0.202523i | ||||||||
\(169\) | 1941.00 | 0.883477 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1125.00 | 0.503105 | ||||||||
\(172\) | 100.000i | 0.0443310i | ||||||||
\(173\) | 3747.00i | 1.64670i | 0.567534 | + | 0.823350i | \(0.307898\pi\) | ||||
−0.567534 | + | 0.823350i | \(0.692102\pi\) | |||||||
\(174\) | −1674.00 | −0.729343 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −781.000 | −0.334489 | ||||||||
\(177\) | 747.000i | 0.317220i | ||||||||
\(178\) | − 2268.00i | − 0.955021i | ||||||||
\(179\) | 267.000 | 0.111489 | 0.0557445 | − | 0.998445i | \(-0.482247\pi\) | ||||
0.0557445 | + | 0.998445i | \(0.482247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4277.00 | 1.75639 | 0.878196 | − | 0.478301i | \(-0.158747\pi\) | ||||
0.878196 | + | 0.478301i | \(0.158747\pi\) | |||||||
\(182\) | 336.000i | 0.136846i | ||||||||
\(183\) | 192.000i | 0.0775576i | ||||||||
\(184\) | 1701.00 | 0.681518 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −522.000 | −0.205779 | ||||||||
\(187\) | − 231.000i | − 0.0903337i | ||||||||
\(188\) | − 219.000i | − 0.0849586i | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1797.00 | −0.680766 | −0.340383 | − | 0.940287i | \(-0.610557\pi\) | ||||
−0.340383 | + | 0.940287i | \(0.610557\pi\) | |||||||
\(192\) | 1299.00i | 0.488267i | ||||||||
\(193\) | 1988.00i | 0.741448i | 0.928743 | + | 0.370724i | \(0.120890\pi\) | ||||
−0.928743 | + | 0.370724i | \(0.879110\pi\) | |||||||
\(194\) | 2517.00 | 0.931495 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −294.000 | −0.107143 | ||||||||
\(197\) | − 3327.00i | − 1.20324i | −0.798781 | − | 0.601622i | \(-0.794522\pi\) | ||||
0.798781 | − | 0.601622i | \(-0.205478\pi\) | |||||||
\(198\) | − 297.000i | − 0.106600i | ||||||||
\(199\) | 1780.00 | 0.634075 | 0.317037 | − | 0.948413i | \(-0.397312\pi\) | ||||
0.317037 | + | 0.948413i | \(0.397312\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −816.000 | −0.286349 | ||||||||
\(202\) | − 4239.00i | − 1.47651i | ||||||||
\(203\) | − 1302.00i | − 0.450160i | ||||||||
\(204\) | 63.0000 | 0.0216220 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4902.00 | −1.65795 | ||||||||
\(207\) | 729.000i | 0.244778i | ||||||||
\(208\) | 1136.00i | 0.378690i | ||||||||
\(209\) | −1375.00 | −0.455075 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2180.00 | 0.711267 | 0.355634 | − | 0.934625i | \(-0.384265\pi\) | ||||
0.355634 | + | 0.934625i | \(0.384265\pi\) | |||||||
\(212\) | 192.000i | 0.0622010i | ||||||||
\(213\) | 1935.00i | 0.622460i | ||||||||
\(214\) | 2178.00 | 0.695724 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −567.000 | −0.178609 | ||||||||
\(217\) | − 406.000i | − 0.127010i | ||||||||
\(218\) | − 5136.00i | − 1.59566i | ||||||||
\(219\) | −336.000 | −0.103675 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −336.000 | −0.102271 | ||||||||
\(222\) | 2277.00i | 0.688388i | ||||||||
\(223\) | 3848.00i | 1.15552i | 0.816206 | + | 0.577760i | \(0.196073\pi\) | ||||
−0.816206 | + | 0.577760i | \(0.803927\pi\) | |||||||
\(224\) | 315.000 | 0.0939590 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3384.00 | 0.996019 | ||||||||
\(227\) | 1386.00i | 0.405251i | 0.979256 | + | 0.202626i | \(0.0649475\pi\) | ||||
−0.979256 | + | 0.202626i | \(0.935053\pi\) | |||||||
\(228\) | − 375.000i | − 0.108925i | ||||||||
\(229\) | 991.000 | 0.285970 | 0.142985 | − | 0.989725i | \(-0.454330\pi\) | ||||
0.142985 | + | 0.989725i | \(0.454330\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 231.000 | 0.0657952 | ||||||||
\(232\) | − 3906.00i | − 1.10535i | ||||||||
\(233\) | 975.000i | 0.274139i | 0.990561 | + | 0.137069i | \(0.0437684\pi\) | ||||
−0.990561 | + | 0.137069i | \(0.956232\pi\) | |||||||
\(234\) | −432.000 | −0.120687 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 249.000 | 0.0686802 | ||||||||
\(237\) | 1527.00i | 0.418520i | ||||||||
\(238\) | 441.000i | 0.120108i | ||||||||
\(239\) | 1524.00 | 0.412466 | 0.206233 | − | 0.978503i | \(-0.433880\pi\) | ||||
0.206233 | + | 0.978503i | \(0.433880\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2230.00 | −0.596045 | −0.298023 | − | 0.954559i | \(-0.596327\pi\) | ||||
−0.298023 | + | 0.954559i | \(0.596327\pi\) | |||||||
\(242\) | 363.000i | 0.0964237i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | 64.0000 | 0.0167917 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 567.000 | 0.146954 | ||||||||
\(247\) | 2000.00i | 0.515210i | ||||||||
\(248\) | − 1218.00i | − 0.311867i | ||||||||
\(249\) | −3762.00 | −0.957458 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3864.00 | 0.971687 | 0.485844 | − | 0.874046i | \(-0.338512\pi\) | ||||
0.485844 | + | 0.874046i | \(0.338512\pi\) | |||||||
\(252\) | 63.0000i | 0.0157485i | ||||||||
\(253\) | − 891.000i | − 0.221410i | ||||||||
\(254\) | 3381.00 | 0.835208 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | 4518.00i | 1.09660i | 0.836283 | + | 0.548298i | \(0.184724\pi\) | ||||
−0.836283 | + | 0.548298i | \(0.815276\pi\) | |||||||
\(258\) | − 900.000i | − 0.217177i | ||||||||
\(259\) | −1771.00 | −0.424883 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1674.00 | 0.397004 | ||||||||
\(262\) | − 3366.00i | − 0.793711i | ||||||||
\(263\) | − 438.000i | − 0.102693i | −0.998681 | − | 0.0513465i | \(-0.983649\pi\) | ||||
0.998681 | − | 0.0513465i | \(-0.0163513\pi\) | |||||||
\(264\) | 693.000 | 0.161558 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2625.00 | 0.605072 | ||||||||
\(267\) | 2268.00i | 0.519848i | ||||||||
\(268\) | 272.000i | 0.0619964i | ||||||||
\(269\) | −4902.00 | −1.11108 | −0.555539 | − | 0.831490i | \(-0.687488\pi\) | ||||
−0.555539 | + | 0.831490i | \(0.687488\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2455.00 | −0.550298 | −0.275149 | − | 0.961402i | \(-0.588727\pi\) | ||||
−0.275149 | + | 0.961402i | \(0.588727\pi\) | |||||||
\(272\) | 1491.00i | 0.332372i | ||||||||
\(273\) | − 336.000i | − 0.0744895i | ||||||||
\(274\) | 162.000 | 0.0357182 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 243.000 | 0.0529959 | ||||||||
\(277\) | − 1868.00i | − 0.405189i | −0.979263 | − | 0.202594i | \(-0.935063\pi\) | ||||
0.979263 | − | 0.202594i | \(-0.0649373\pi\) | |||||||
\(278\) | − 5244.00i | − 1.13135i | ||||||||
\(279\) | 522.000 | 0.112012 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6093.00 | −1.29352 | −0.646758 | − | 0.762695i | \(-0.723876\pi\) | ||||
−0.646758 | + | 0.762695i | \(0.723876\pi\) | |||||||
\(282\) | 1971.00i | 0.416210i | ||||||||
\(283\) | 2543.00i | 0.534154i | 0.963675 | + | 0.267077i | \(0.0860579\pi\) | ||||
−0.963675 | + | 0.267077i | \(0.913942\pi\) | |||||||
\(284\) | 645.000 | 0.134767 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 528.000 | 0.109165 | ||||||||
\(287\) | 441.000i | 0.0907018i | ||||||||
\(288\) | 405.000i | 0.0828641i | ||||||||
\(289\) | 4472.00 | 0.910238 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2517.00 | −0.507042 | ||||||||
\(292\) | 112.000i | 0.0224462i | ||||||||
\(293\) | − 4623.00i | − 0.921770i | −0.887460 | − | 0.460885i | \(-0.847532\pi\) | ||||
0.887460 | − | 0.460885i | \(-0.152468\pi\) | |||||||
\(294\) | 2646.00 | 0.524891 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5313.00 | −1.04328 | ||||||||
\(297\) | 297.000i | 0.0580259i | ||||||||
\(298\) | − 5391.00i | − 1.04796i | ||||||||
\(299\) | −1296.00 | −0.250668 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 700.000 | 0.134044 | ||||||||
\(302\) | 3120.00i | 0.594489i | ||||||||
\(303\) | 4239.00i | 0.803710i | ||||||||
\(304\) | 8875.00 | 1.67440 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −567.000 | −0.105926 | ||||||||
\(307\) | − 644.000i | − 0.119723i | −0.998207 | − | 0.0598616i | \(-0.980934\pi\) | ||||
0.998207 | − | 0.0598616i | \(-0.0190659\pi\) | |||||||
\(308\) | − 77.0000i | − 0.0142451i | ||||||||
\(309\) | 4902.00 | 0.902476 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2616.00 | 0.476977 | 0.238488 | − | 0.971145i | \(-0.423348\pi\) | ||||
0.238488 | + | 0.971145i | \(0.423348\pi\) | |||||||
\(312\) | − 1008.00i | − 0.182906i | ||||||||
\(313\) | 4079.00i | 0.736609i | 0.929705 | + | 0.368305i | \(0.120062\pi\) | ||||
−0.929705 | + | 0.368305i | \(0.879938\pi\) | |||||||
\(314\) | −1686.00 | −0.303014 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 509.000 | 0.0906123 | ||||||||
\(317\) | − 3504.00i | − 0.620834i | −0.950601 | − | 0.310417i | \(-0.899531\pi\) | ||||
0.950601 | − | 0.310417i | \(-0.100469\pi\) | |||||||
\(318\) | − 1728.00i | − 0.304721i | ||||||||
\(319\) | −2046.00 | −0.359103 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2178.00 | −0.378704 | ||||||||
\(322\) | 1701.00i | 0.294388i | ||||||||
\(323\) | 2625.00i | 0.452195i | ||||||||
\(324\) | −81.0000 | −0.0138889 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7296.00 | −1.23953 | ||||||||
\(327\) | 5136.00i | 0.868567i | ||||||||
\(328\) | 1323.00i | 0.222715i | ||||||||
\(329\) | −1533.00 | −0.256891 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4100.00 | 0.680835 | 0.340417 | − | 0.940274i | \(-0.389432\pi\) | ||||
0.340417 | + | 0.940274i | \(0.389432\pi\) | |||||||
\(332\) | 1254.00i | 0.207296i | ||||||||
\(333\) | − 2277.00i | − 0.374711i | ||||||||
\(334\) | 7020.00 | 1.15005 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1491.00 | −0.242085 | ||||||||
\(337\) | 10924.0i | 1.76578i | 0.469579 | + | 0.882891i | \(0.344406\pi\) | ||||
−0.469579 | + | 0.882891i | \(0.655594\pi\) | |||||||
\(338\) | 5823.00i | 0.937069i | ||||||||
\(339\) | −3384.00 | −0.542164 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −638.000 | −0.101319 | ||||||||
\(342\) | 3375.00i | 0.533623i | ||||||||
\(343\) | 4459.00i | 0.701934i | ||||||||
\(344\) | 2100.00 | 0.329141 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11241.0 | −1.74659 | ||||||||
\(347\) | 3612.00i | 0.558796i | 0.960175 | + | 0.279398i | \(0.0901349\pi\) | ||||
−0.960175 | + | 0.279398i | \(0.909865\pi\) | |||||||
\(348\) | − 558.000i | − 0.0859538i | ||||||||
\(349\) | 406.000 | 0.0622713 | 0.0311356 | − | 0.999515i | \(-0.490088\pi\) | ||||
0.0311356 | + | 0.999515i | \(0.490088\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 432.000 | 0.0656936 | ||||||||
\(352\) | − 495.000i | − 0.0749534i | ||||||||
\(353\) | − 816.000i | − 0.123035i | −0.998106 | − | 0.0615174i | \(-0.980406\pi\) | ||||
0.998106 | − | 0.0615174i | \(-0.0195940\pi\) | |||||||
\(354\) | −2241.00 | −0.336463 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 756.000 | 0.112550 | ||||||||
\(357\) | − 441.000i | − 0.0653787i | ||||||||
\(358\) | 801.000i | 0.118252i | ||||||||
\(359\) | −4818.00 | −0.708313 | −0.354156 | − | 0.935186i | \(-0.615232\pi\) | ||||
−0.354156 | + | 0.935186i | \(0.615232\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8766.00 | 1.27803 | ||||||||
\(362\) | 12831.0i | 1.86293i | ||||||||
\(363\) | − 363.000i | − 0.0524864i | ||||||||
\(364\) | −112.000 | −0.0161275 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −576.000 | −0.0822623 | ||||||||
\(367\) | − 2306.00i | − 0.327990i | −0.986461 | − | 0.163995i | \(-0.947562\pi\) | ||||
0.986461 | − | 0.163995i | \(-0.0524380\pi\) | |||||||
\(368\) | 5751.00i | 0.814651i | ||||||||
\(369\) | −567.000 | −0.0799914 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1344.00 | 0.188078 | ||||||||
\(372\) | − 174.000i | − 0.0242513i | ||||||||
\(373\) | 3134.00i | 0.435047i | 0.976055 | + | 0.217523i | \(0.0697978\pi\) | ||||
−0.976055 | + | 0.217523i | \(0.930202\pi\) | |||||||
\(374\) | 693.000 | 0.0958133 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4599.00 | −0.630785 | ||||||||
\(377\) | 2976.00i | 0.406556i | ||||||||
\(378\) | − 567.000i | − 0.0771517i | ||||||||
\(379\) | −7202.00 | −0.976100 | −0.488050 | − | 0.872816i | \(-0.662292\pi\) | ||||
−0.488050 | + | 0.872816i | \(0.662292\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3381.00 | −0.454630 | ||||||||
\(382\) | − 5391.00i | − 0.722062i | ||||||||
\(383\) | 11472.0i | 1.53053i | 0.643717 | + | 0.765263i | \(0.277391\pi\) | ||||
−0.643717 | + | 0.765263i | \(0.722609\pi\) | |||||||
\(384\) | −4977.00 | −0.661410 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5964.00 | −0.786424 | ||||||||
\(387\) | 900.000i | 0.118216i | ||||||||
\(388\) | 839.000i | 0.109778i | ||||||||
\(389\) | 3462.00 | 0.451235 | 0.225617 | − | 0.974216i | \(-0.427560\pi\) | ||||
0.225617 | + | 0.974216i | \(0.427560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1701.00 | −0.220008 | ||||||||
\(392\) | 6174.00i | 0.795495i | ||||||||
\(393\) | 3366.00i | 0.432041i | ||||||||
\(394\) | 9981.00 | 1.27623 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 99.0000 | 0.0125630 | ||||||||
\(397\) | − 2486.00i | − 0.314279i | −0.987576 | − | 0.157140i | \(-0.949773\pi\) | ||||
0.987576 | − | 0.157140i | \(-0.0502272\pi\) | |||||||
\(398\) | 5340.00i | 0.672538i | ||||||||
\(399\) | −2625.00 | −0.329359 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9024.00 | −1.12378 | −0.561892 | − | 0.827211i | \(-0.689926\pi\) | ||||
−0.561892 | + | 0.827211i | \(0.689926\pi\) | |||||||
\(402\) | − 2448.00i | − 0.303719i | ||||||||
\(403\) | 928.000i | 0.114707i | ||||||||
\(404\) | 1413.00 | 0.174008 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3906.00 | 0.477467 | ||||||||
\(407\) | 2783.00i | 0.338939i | ||||||||
\(408\) | − 1323.00i | − 0.160535i | ||||||||
\(409\) | 14488.0 | 1.75155 | 0.875777 | − | 0.482716i | \(-0.160350\pi\) | ||||
0.875777 | + | 0.482716i | \(0.160350\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −162.000 | −0.0194425 | ||||||||
\(412\) | − 1634.00i | − 0.195392i | ||||||||
\(413\) | − 1743.00i | − 0.207669i | ||||||||
\(414\) | −2187.00 | −0.259626 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −720.000 | −0.0848579 | ||||||||
\(417\) | 5244.00i | 0.615827i | ||||||||
\(418\) | − 4125.00i | − 0.482680i | ||||||||
\(419\) | 3201.00 | 0.373220 | 0.186610 | − | 0.982434i | \(-0.440250\pi\) | ||||
0.186610 | + | 0.982434i | \(0.440250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6721.00 | −0.778056 | −0.389028 | − | 0.921226i | \(-0.627189\pi\) | ||||
−0.389028 | + | 0.921226i | \(0.627189\pi\) | |||||||
\(422\) | 6540.00i | 0.754413i | ||||||||
\(423\) | − 1971.00i | − 0.226556i | ||||||||
\(424\) | 4032.00 | 0.461819 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5805.00 | −0.660219 | ||||||||
\(427\) | − 448.000i | − 0.0507734i | ||||||||
\(428\) | 726.000i | 0.0819919i | ||||||||
\(429\) | −528.000 | −0.0594221 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −354.000 | −0.0395628 | −0.0197814 | − | 0.999804i | \(-0.506297\pi\) | ||||
−0.0197814 | + | 0.999804i | \(0.506297\pi\) | |||||||
\(432\) | − 1917.00i | − 0.213499i | ||||||||
\(433\) | 7682.00i | 0.852594i | 0.904583 | + | 0.426297i | \(0.140182\pi\) | ||||
−0.904583 | + | 0.426297i | \(0.859818\pi\) | |||||||
\(434\) | 1218.00 | 0.134714 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1712.00 | 0.188050 | ||||||||
\(437\) | 10125.0i | 1.10834i | ||||||||
\(438\) | − 1008.00i | − 0.109964i | ||||||||
\(439\) | −5465.00 | −0.594146 | −0.297073 | − | 0.954855i | \(-0.596011\pi\) | ||||
−0.297073 | + | 0.954855i | \(0.596011\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2646.00 | −0.285714 | ||||||||
\(442\) | − 1008.00i | − 0.108474i | ||||||||
\(443\) | − 1551.00i | − 0.166344i | −0.996535 | − | 0.0831718i | \(-0.973495\pi\) | ||||
0.996535 | − | 0.0831718i | \(-0.0265050\pi\) | |||||||
\(444\) | −759.000 | −0.0811274 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −11544.0 | −1.22561 | ||||||||
\(447\) | 5391.00i | 0.570437i | ||||||||
\(448\) | − 3031.00i | − 0.319646i | ||||||||
\(449\) | 1092.00 | 0.114777 | 0.0573883 | − | 0.998352i | \(-0.481723\pi\) | ||||
0.0573883 | + | 0.998352i | \(0.481723\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 693.000 | 0.0723550 | ||||||||
\(452\) | 1128.00i | 0.117382i | ||||||||
\(453\) | − 3120.00i | − 0.323599i | ||||||||
\(454\) | −4158.00 | −0.429834 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7875.00 | −0.808730 | ||||||||
\(457\) | − 10046.0i | − 1.02830i | −0.857701 | − | 0.514149i | \(-0.828108\pi\) | ||||
0.857701 | − | 0.514149i | \(-0.171892\pi\) | |||||||
\(458\) | 2973.00i | 0.303317i | ||||||||
\(459\) | 567.000 | 0.0576586 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15510.0 | 1.56697 | 0.783485 | − | 0.621411i | \(-0.213440\pi\) | ||||
0.783485 | + | 0.621411i | \(0.213440\pi\) | |||||||
\(462\) | 693.000i | 0.0697863i | ||||||||
\(463\) | 6878.00i | 0.690384i | 0.938532 | + | 0.345192i | \(0.112186\pi\) | ||||
−0.938532 | + | 0.345192i | \(0.887814\pi\) | |||||||
\(464\) | 13206.0 | 1.32128 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2925.00 | −0.290768 | ||||||||
\(467\) | 16284.0i | 1.61356i | 0.590850 | + | 0.806781i | \(0.298792\pi\) | ||||
−0.590850 | + | 0.806781i | \(0.701208\pi\) | |||||||
\(468\) | − 144.000i | − 0.0142231i | ||||||||
\(469\) | 1904.00 | 0.187460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1686.00 | 0.164940 | ||||||||
\(472\) | − 5229.00i | − 0.509924i | ||||||||
\(473\) | − 1100.00i | − 0.106930i | ||||||||
\(474\) | −4581.00 | −0.443908 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −147.000 | −0.0141549 | ||||||||
\(477\) | 1728.00i | 0.165869i | ||||||||
\(478\) | 4572.00i | 0.437486i | ||||||||
\(479\) | −6732.00 | −0.642156 | −0.321078 | − | 0.947053i | \(-0.604045\pi\) | ||||
−0.321078 | + | 0.947053i | \(0.604045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4048.00 | 0.383727 | ||||||||
\(482\) | − 6690.00i | − 0.632202i | ||||||||
\(483\) | − 1701.00i | − 0.160245i | ||||||||
\(484\) | −121.000 | −0.0113636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 729.000 | 0.0680414 | ||||||||
\(487\) | − 17498.0i | − 1.62815i | −0.580758 | − | 0.814076i | \(-0.697244\pi\) | ||||
0.580758 | − | 0.814076i | \(-0.302756\pi\) | |||||||
\(488\) | − 1344.00i | − 0.124672i | ||||||||
\(489\) | 7296.00 | 0.674717 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2454.00 | 0.225555 | 0.112777 | − | 0.993620i | \(-0.464025\pi\) | ||||
0.112777 | + | 0.993620i | \(0.464025\pi\) | |||||||
\(492\) | 189.000i | 0.0173187i | ||||||||
\(493\) | 3906.00i | 0.356830i | ||||||||
\(494\) | −6000.00 | −0.546463 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4118.00 | 0.372790 | ||||||||
\(497\) | − 4515.00i | − 0.407496i | ||||||||
\(498\) | − 11286.0i | − 1.01554i | ||||||||
\(499\) | 20716.0 | 1.85847 | 0.929234 | − | 0.369492i | \(-0.120468\pi\) | ||||
0.929234 | + | 0.369492i | \(0.120468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7020.00 | −0.626009 | ||||||||
\(502\) | 11592.0i | 1.03063i | ||||||||
\(503\) | − 1956.00i | − 0.173387i | −0.996235 | − | 0.0866936i | \(-0.972370\pi\) | ||||
0.996235 | − | 0.0866936i | \(-0.0276301\pi\) | |||||||
\(504\) | 1323.00 | 0.116927 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2673.00 | 0.234841 | ||||||||
\(507\) | − 5823.00i | − 0.510076i | ||||||||
\(508\) | 1127.00i | 0.0984302i | ||||||||
\(509\) | −18240.0 | −1.58836 | −0.794179 | − | 0.607684i | \(-0.792099\pi\) | ||||
−0.794179 | + | 0.607684i | \(0.792099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 784.000 | 0.0678711 | ||||||||
\(512\) | − 8733.00i | − 0.753804i | ||||||||
\(513\) | − 3375.00i | − 0.290468i | ||||||||
\(514\) | −13554.0 | −1.16312 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 300.000 | 0.0255945 | ||||||||
\(517\) | 2409.00i | 0.204928i | ||||||||
\(518\) | − 5313.00i | − 0.450656i | ||||||||
\(519\) | 11241.0 | 0.950723 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20790.0 | 1.74823 | 0.874114 | − | 0.485721i | \(-0.161443\pi\) | ||||
0.874114 | + | 0.485721i | \(0.161443\pi\) | |||||||
\(522\) | 5022.00i | 0.421086i | ||||||||
\(523\) | 11897.0i | 0.994684i | 0.867555 | + | 0.497342i | \(0.165690\pi\) | ||||
−0.867555 | + | 0.497342i | \(0.834310\pi\) | |||||||
\(524\) | 1122.00 | 0.0935397 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1314.00 | 0.108922 | ||||||||
\(527\) | 1218.00i | 0.100677i | ||||||||
\(528\) | 2343.00i | 0.193117i | ||||||||
\(529\) | 5606.00 | 0.460754 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2241.00 | 0.183147 | ||||||||
\(532\) | 875.000i | 0.0713084i | ||||||||
\(533\) | − 1008.00i | − 0.0819162i | ||||||||
\(534\) | −6804.00 | −0.551382 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5712.00 | 0.460300 | ||||||||
\(537\) | − 801.000i | − 0.0643682i | ||||||||
\(538\) | − 14706.0i | − 1.17848i | ||||||||
\(539\) | 3234.00 | 0.258438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20336.0 | 1.61611 | 0.808053 | − | 0.589110i | \(-0.200522\pi\) | ||||
0.808053 | + | 0.589110i | \(0.200522\pi\) | |||||||
\(542\) | − 7365.00i | − 0.583679i | ||||||||
\(543\) | − 12831.0i | − 1.01405i | ||||||||
\(544\) | −945.000 | −0.0744789 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1008.00 | 0.0790081 | ||||||||
\(547\) | − 16481.0i | − 1.28826i | −0.764917 | − | 0.644129i | \(-0.777220\pi\) | ||||
0.764917 | − | 0.644129i | \(-0.222780\pi\) | |||||||
\(548\) | 54.0000i | 0.00420943i | ||||||||
\(549\) | 576.000 | 0.0447779 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23250.0 | 1.79761 | ||||||||
\(552\) | − 5103.00i | − 0.393475i | ||||||||
\(553\) | − 3563.00i | − 0.273986i | ||||||||
\(554\) | 5604.00 | 0.429767 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1748.00 | 0.133330 | ||||||||
\(557\) | 24618.0i | 1.87271i | 0.351058 | + | 0.936354i | \(0.385822\pi\) | ||||
−0.351058 | + | 0.936354i | \(0.614178\pi\) | |||||||
\(558\) | 1566.00i | 0.118807i | ||||||||
\(559\) | −1600.00 | −0.121060 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −693.000 | −0.0521542 | ||||||||
\(562\) | − 18279.0i | − 1.37198i | ||||||||
\(563\) | 6438.00i | 0.481935i | 0.970533 | + | 0.240967i | \(0.0774647\pi\) | ||||
−0.970533 | + | 0.240967i | \(0.922535\pi\) | |||||||
\(564\) | −657.000 | −0.0490509 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −7629.00 | −0.566556 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | − 13545.0i | − 1.00059i | ||||||||
\(569\) | 18183.0 | 1.33967 | 0.669834 | − | 0.742511i | \(-0.266365\pi\) | ||||
0.669834 | + | 0.742511i | \(0.266365\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17656.0 | −1.29401 | −0.647006 | − | 0.762485i | \(-0.723979\pi\) | ||||
−0.647006 | + | 0.762485i | \(0.723979\pi\) | |||||||
\(572\) | 176.000i | 0.0128653i | ||||||||
\(573\) | 5391.00i | 0.393041i | ||||||||
\(574\) | −1323.00 | −0.0962038 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3897.00 | 0.281901 | ||||||||
\(577\) | 17155.0i | 1.23773i | 0.785496 | + | 0.618867i | \(0.212408\pi\) | ||||
−0.785496 | + | 0.618867i | \(0.787592\pi\) | |||||||
\(578\) | 13416.0i | 0.965453i | ||||||||
\(579\) | 5964.00 | 0.428075 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8778.00 | 0.626803 | ||||||||
\(582\) | − 7551.00i | − 0.537799i | ||||||||
\(583\) | − 2112.00i | − 0.150034i | ||||||||
\(584\) | 2352.00 | 0.166655 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13869.0 | 0.977684 | ||||||||
\(587\) | − 24621.0i | − 1.73121i | −0.500732 | − | 0.865603i | \(-0.666936\pi\) | ||||
0.500732 | − | 0.865603i | \(-0.333064\pi\) | |||||||
\(588\) | 882.000i | 0.0618590i | ||||||||
\(589\) | 7250.00 | 0.507183 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9981.00 | −0.694693 | ||||||||
\(592\) | − 17963.0i | − 1.24709i | ||||||||
\(593\) | − 9066.00i | − 0.627818i | −0.949453 | − | 0.313909i | \(-0.898361\pi\) | ||||
0.949453 | − | 0.313909i | \(-0.101639\pi\) | |||||||
\(594\) | −891.000 | −0.0615457 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1797.00 | 0.123503 | ||||||||
\(597\) | − 5340.00i | − 0.366083i | ||||||||
\(598\) | − 3888.00i | − 0.265873i | ||||||||
\(599\) | −22353.0 | −1.52474 | −0.762370 | − | 0.647142i | \(-0.775964\pi\) | ||||
−0.762370 | + | 0.647142i | \(0.775964\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6304.00 | −0.427863 | −0.213931 | − | 0.976849i | \(-0.568627\pi\) | ||||
−0.213931 | + | 0.976849i | \(0.568627\pi\) | |||||||
\(602\) | 2100.00i | 0.142175i | ||||||||
\(603\) | 2448.00i | 0.165324i | ||||||||
\(604\) | −1040.00 | −0.0700613 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −12717.0 | −0.852463 | ||||||||
\(607\) | − 23672.0i | − 1.58289i | −0.611238 | − | 0.791447i | \(-0.709328\pi\) | ||||
0.611238 | − | 0.791447i | \(-0.290672\pi\) | |||||||
\(608\) | 5625.00i | 0.375204i | ||||||||
\(609\) | −3906.00 | −0.259900 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3504.00 | 0.232008 | ||||||||
\(612\) | − 189.000i | − 0.0124835i | ||||||||
\(613\) | − 3028.00i | − 0.199510i | −0.995012 | − | 0.0997551i | \(-0.968194\pi\) | ||||
0.995012 | − | 0.0997551i | \(-0.0318059\pi\) | |||||||
\(614\) | 1932.00 | 0.126986 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1617.00 | −0.105764 | ||||||||
\(617\) | 1170.00i | 0.0763410i | 0.999271 | + | 0.0381705i | \(0.0121530\pi\) | ||||
−0.999271 | + | 0.0381705i | \(0.987847\pi\) | |||||||
\(618\) | 14706.0i | 0.957220i | ||||||||
\(619\) | −9626.00 | −0.625043 | −0.312521 | − | 0.949911i | \(-0.601174\pi\) | ||||
−0.312521 | + | 0.949911i | \(0.601174\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2187.00 | 0.141323 | ||||||||
\(622\) | 7848.00i | 0.505910i | ||||||||
\(623\) | − 5292.00i | − 0.340320i | ||||||||
\(624\) | 3408.00 | 0.218637 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12237.0 | −0.781292 | ||||||||
\(627\) | 4125.00i | 0.262738i | ||||||||
\(628\) | − 562.000i | − 0.0357106i | ||||||||
\(629\) | 5313.00 | 0.336794 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5794.00 | −0.365540 | −0.182770 | − | 0.983156i | \(-0.558506\pi\) | ||||
−0.182770 | + | 0.983156i | \(0.558506\pi\) | |||||||
\(632\) | − 10689.0i | − 0.672762i | ||||||||
\(633\) | − 6540.00i | − 0.410650i | ||||||||
\(634\) | 10512.0 | 0.658493 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 576.000 | 0.0359118 | ||||||||
\(637\) | − 4704.00i | − 0.292589i | ||||||||
\(638\) | − 6138.00i | − 0.380887i | ||||||||
\(639\) | 5805.00 | 0.359378 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28308.0 | 1.74430 | 0.872152 | − | 0.489235i | \(-0.162724\pi\) | ||||
0.872152 | + | 0.489235i | \(0.162724\pi\) | |||||||
\(642\) | − 6534.00i | − 0.401677i | ||||||||
\(643\) | 2270.00i | 0.139222i | 0.997574 | + | 0.0696112i | \(0.0221759\pi\) | ||||
−0.997574 | + | 0.0696112i | \(0.977824\pi\) | |||||||
\(644\) | −567.000 | −0.0346940 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7875.00 | −0.479625 | ||||||||
\(647\) | − 23361.0i | − 1.41950i | −0.704454 | − | 0.709749i | \(-0.748808\pi\) | ||||
0.704454 | − | 0.709749i | \(-0.251192\pi\) | |||||||
\(648\) | 1701.00i | 0.103120i | ||||||||
\(649\) | −2739.00 | −0.165663 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1218.00 | −0.0733290 | ||||||||
\(652\) | − 2432.00i | − 0.146080i | ||||||||
\(653\) | 12294.0i | 0.736756i | 0.929676 | + | 0.368378i | \(0.120087\pi\) | ||||
−0.929676 | + | 0.368378i | \(0.879913\pi\) | |||||||
\(654\) | −15408.0 | −0.921255 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4473.00 | −0.266222 | ||||||||
\(657\) | 1008.00i | 0.0598567i | ||||||||
\(658\) | − 4599.00i | − 0.272474i | ||||||||
\(659\) | −31896.0 | −1.88542 | −0.942710 | − | 0.333613i | \(-0.891732\pi\) | ||||
−0.942710 | + | 0.333613i | \(0.891732\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13469.0 | 0.792562 | 0.396281 | − | 0.918129i | \(-0.370301\pi\) | ||||
0.396281 | + | 0.918129i | \(0.370301\pi\) | |||||||
\(662\) | 12300.0i | 0.722135i | ||||||||
\(663\) | 1008.00i | 0.0590460i | ||||||||
\(664\) | 26334.0 | 1.53909 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6831.00 | 0.397441 | ||||||||
\(667\) | 15066.0i | 0.874599i | ||||||||
\(668\) | 2340.00i | 0.135535i | ||||||||
\(669\) | 11544.0 | 0.667140 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −704.000 | −0.0405032 | ||||||||
\(672\) | − 945.000i | − 0.0542473i | ||||||||
\(673\) | 13712.0i | 0.785377i | 0.919672 | + | 0.392689i | \(0.128455\pi\) | ||||
−0.919672 | + | 0.392689i | \(0.871545\pi\) | |||||||
\(674\) | −32772.0 | −1.87289 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1941.00 | −0.110435 | ||||||||
\(677\) | 3714.00i | 0.210843i | 0.994428 | + | 0.105421i | \(0.0336192\pi\) | ||||
−0.994428 | + | 0.105421i | \(0.966381\pi\) | |||||||
\(678\) | − 10152.0i | − 0.575052i | ||||||||
\(679\) | 5873.00 | 0.331937 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4158.00 | 0.233972 | ||||||||
\(682\) | − 1914.00i | − 0.107465i | ||||||||
\(683\) | − 13065.0i | − 0.731945i | −0.930626 | − | 0.365972i | \(-0.880736\pi\) | ||||
0.930626 | − | 0.365972i | \(-0.119264\pi\) | |||||||
\(684\) | −1125.00 | −0.0628881 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13377.0 | −0.744513 | ||||||||
\(687\) | − 2973.00i | − 0.165105i | ||||||||
\(688\) | 7100.00i | 0.393437i | ||||||||
\(689\) | −3072.00 | −0.169860 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12512.0 | 0.688826 | 0.344413 | − | 0.938818i | \(-0.388078\pi\) | ||||
0.344413 | + | 0.938818i | \(0.388078\pi\) | |||||||
\(692\) | − 3747.00i | − 0.205838i | ||||||||
\(693\) | − 693.000i | − 0.0379869i | ||||||||
\(694\) | −10836.0 | −0.592693 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −11718.0 | −0.638175 | ||||||||
\(697\) | − 1323.00i | − 0.0718970i | ||||||||
\(698\) | 1218.00i | 0.0660487i | ||||||||
\(699\) | 2925.00 | 0.158274 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33405.0 | 1.79984 | 0.899921 | − | 0.436053i | \(-0.143624\pi\) | ||||
0.899921 | + | 0.436053i | \(0.143624\pi\) | |||||||
\(702\) | 1296.00i | 0.0696786i | ||||||||
\(703\) | − 31625.0i | − 1.69667i | ||||||||
\(704\) | −4763.00 | −0.254989 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2448.00 | 0.130498 | ||||||||
\(707\) | − 9891.00i | − 0.526152i | ||||||||
\(708\) | − 747.000i | − 0.0396525i | ||||||||
\(709\) | −22217.0 | −1.17684 | −0.588418 | − | 0.808557i | \(-0.700249\pi\) | ||||
−0.588418 | + | 0.808557i | \(0.700249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4581.00 | 0.241633 | ||||||||
\(712\) | − 15876.0i | − 0.835644i | ||||||||
\(713\) | 4698.00i | 0.246762i | ||||||||
\(714\) | 1323.00 | 0.0693446 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −267.000 | −0.0139361 | ||||||||
\(717\) | − 4572.00i | − 0.238137i | ||||||||
\(718\) | − 14454.0i | − 0.751279i | ||||||||
\(719\) | −12336.0 | −0.639854 | −0.319927 | − | 0.947442i | \(-0.603658\pi\) | ||||
−0.319927 | + | 0.947442i | \(0.603658\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11438.0 | −0.590809 | ||||||||
\(722\) | 26298.0i | 1.35555i | ||||||||
\(723\) | 6690.00i | 0.344127i | ||||||||
\(724\) | −4277.00 | −0.219549 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1089.00 | 0.0556702 | ||||||||
\(727\) | 10720.0i | 0.546881i | 0.961889 | + | 0.273441i | \(0.0881617\pi\) | ||||
−0.961889 | + | 0.273441i | \(0.911838\pi\) | |||||||
\(728\) | 2352.00i | 0.119740i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2100.00 | −0.106253 | ||||||||
\(732\) | − 192.000i | − 0.00969471i | ||||||||
\(733\) | 10820.0i | 0.545219i | 0.962125 | + | 0.272610i | \(0.0878868\pi\) | ||||
−0.962125 | + | 0.272610i | \(0.912113\pi\) | |||||||
\(734\) | 6918.00 | 0.347886 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3645.00 | −0.182550 | ||||||||
\(737\) | − 2992.00i | − 0.149541i | ||||||||
\(738\) | − 1701.00i | − 0.0848437i | ||||||||
\(739\) | −10127.0 | −0.504097 | −0.252049 | − | 0.967715i | \(-0.581104\pi\) | ||||
−0.252049 | + | 0.967715i | \(0.581104\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6000.00 | 0.297457 | ||||||||
\(742\) | 4032.00i | 0.199487i | ||||||||
\(743\) | − 6000.00i | − 0.296257i | −0.988968 | − | 0.148128i | \(-0.952675\pi\) | ||||
0.988968 | − | 0.148128i | \(-0.0473249\pi\) | |||||||
\(744\) | −3654.00 | −0.180057 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9402.00 | −0.461437 | ||||||||
\(747\) | 11286.0i | 0.552789i | ||||||||
\(748\) | 231.000i | 0.0112917i | ||||||||
\(749\) | 5082.00 | 0.247920 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26132.0 | 1.26973 | 0.634867 | − | 0.772621i | \(-0.281055\pi\) | ||||
0.634867 | + | 0.772621i | \(0.281055\pi\) | |||||||
\(752\) | − 15549.0i | − 0.754008i | ||||||||
\(753\) | − 11592.0i | − 0.561004i | ||||||||
\(754\) | −8928.00 | −0.431218 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 189.000 | 0.00909241 | ||||||||
\(757\) | − 25850.0i | − 1.24113i | −0.784156 | − | 0.620564i | \(-0.786904\pi\) | ||||
0.784156 | − | 0.620564i | \(-0.213096\pi\) | |||||||
\(758\) | − 21606.0i | − 1.03531i | ||||||||
\(759\) | −2673.00 | −0.127831 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3654.00 | −0.174057 | −0.0870285 | − | 0.996206i | \(-0.527737\pi\) | ||||
−0.0870285 | + | 0.996206i | \(0.527737\pi\) | |||||||
\(762\) | − 10143.0i | − 0.482208i | ||||||||
\(763\) | − 11984.0i | − 0.568611i | ||||||||
\(764\) | 1797.00 | 0.0850958 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −34416.0 | −1.62337 | ||||||||
\(767\) | 3984.00i | 0.187554i | ||||||||
\(768\) | − 4539.00i | − 0.213264i | ||||||||
\(769\) | −6248.00 | −0.292989 | −0.146495 | − | 0.989211i | \(-0.546799\pi\) | ||||
−0.146495 | + | 0.989211i | \(0.546799\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13554.0 | 0.633120 | ||||||||
\(772\) | − 1988.00i | − 0.0926809i | ||||||||
\(773\) | − 23952.0i | − 1.11448i | −0.830351 | − | 0.557240i | \(-0.811860\pi\) | ||||
0.830351 | − | 0.557240i | \(-0.188140\pi\) | |||||||
\(774\) | −2700.00 | −0.125387 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 17619.0 | 0.815058 | ||||||||
\(777\) | 5313.00i | 0.245306i | ||||||||
\(778\) | 10386.0i | 0.478607i | ||||||||
\(779\) | −7875.00 | −0.362197 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7095.00 | −0.325069 | ||||||||
\(782\) | − 5103.00i | − 0.233354i | ||||||||
\(783\) | − 5022.00i | − 0.229210i | ||||||||
\(784\) | −20874.0 | −0.950893 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10098.0 | −0.458249 | ||||||||
\(787\) | 39631.0i | 1.79504i | 0.440979 | + | 0.897518i | \(0.354631\pi\) | ||||
−0.440979 | + | 0.897518i | \(0.645369\pi\) | |||||||
\(788\) | 3327.00i | 0.150405i | ||||||||
\(789\) | −1314.00 | −0.0592898 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7896.00 | 0.354930 | ||||||||
\(792\) | − 2079.00i | − 0.0932753i | ||||||||
\(793\) | 1024.00i | 0.0458554i | ||||||||
\(794\) | 7458.00 | 0.333343 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1780.00 | −0.0792593 | ||||||||
\(797\) | 7530.00i | 0.334663i | 0.985901 | + | 0.167331i | \(0.0535150\pi\) | ||||
−0.985901 | + | 0.167331i | \(0.946485\pi\) | |||||||
\(798\) | − 7875.00i | − 0.349338i | ||||||||
\(799\) | 4599.00 | 0.203631 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6804.00 | 0.300134 | ||||||||
\(802\) | − 27072.0i | − 1.19195i | ||||||||
\(803\) | − 1232.00i | − 0.0541424i | ||||||||
\(804\) | 816.000 | 0.0357937 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2784.00 | −0.121665 | ||||||||
\(807\) | 14706.0i | 0.641482i | ||||||||
\(808\) | − 29673.0i | − 1.29195i | ||||||||
\(809\) | 7239.00 | 0.314598 | 0.157299 | − | 0.987551i | \(-0.449721\pi\) | ||||
0.157299 | + | 0.987551i | \(0.449721\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35611.0 | −1.54189 | −0.770944 | − | 0.636903i | \(-0.780215\pi\) | ||||
−0.770944 | + | 0.636903i | \(0.780215\pi\) | |||||||
\(812\) | 1302.00i | 0.0562700i | ||||||||
\(813\) | 7365.00i | 0.317714i | ||||||||
\(814\) | −8349.00 | −0.359499 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4473.00 | 0.191895 | ||||||||
\(817\) | 12500.0i | 0.535275i | ||||||||
\(818\) | 43464.0i | 1.85780i | ||||||||
\(819\) | −1008.00 | −0.0430066 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42054.0 | −1.78769 | −0.893846 | − | 0.448375i | \(-0.852003\pi\) | ||||
−0.893846 | + | 0.448375i | \(0.852003\pi\) | |||||||
\(822\) | − 486.000i | − 0.0206219i | ||||||||
\(823\) | 10172.0i | 0.430831i | 0.976523 | + | 0.215415i | \(0.0691105\pi\) | ||||
−0.976523 | + | 0.215415i | \(0.930889\pi\) | |||||||
\(824\) | −34314.0 | −1.45071 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5229.00 | 0.220267 | ||||||||
\(827\) | − 4560.00i | − 0.191737i | −0.995394 | − | 0.0958686i | \(-0.969437\pi\) | ||||
0.995394 | − | 0.0958686i | \(-0.0305629\pi\) | |||||||
\(828\) | − 729.000i | − 0.0305972i | ||||||||
\(829\) | −13202.0 | −0.553105 | −0.276553 | − | 0.960999i | \(-0.589192\pi\) | ||||
−0.276553 | + | 0.960999i | \(0.589192\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5604.00 | −0.233936 | ||||||||
\(832\) | 6928.00i | 0.288684i | ||||||||
\(833\) | − 6174.00i | − 0.256802i | ||||||||
\(834\) | −15732.0 | −0.653183 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1375.00 | 0.0568844 | ||||||||
\(837\) | − 1566.00i | − 0.0646701i | ||||||||
\(838\) | 9603.00i | 0.395859i | ||||||||
\(839\) | −6216.00 | −0.255781 | −0.127890 | − | 0.991788i | \(-0.540821\pi\) | ||||
−0.127890 | + | 0.991788i | \(0.540821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10207.0 | 0.418508 | ||||||||
\(842\) | − 20163.0i | − 0.825253i | ||||||||
\(843\) | 18279.0i | 0.746812i | ||||||||
\(844\) | −2180.00 | −0.0889084 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5913.00 | 0.240299 | ||||||||
\(847\) | 847.000i | 0.0343604i | ||||||||
\(848\) | 13632.0i | 0.552034i | ||||||||
\(849\) | 7629.00 | 0.308394 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20493.0 | 0.825489 | ||||||||
\(852\) | − 1935.00i | − 0.0778075i | ||||||||
\(853\) | 22718.0i | 0.911899i | 0.890006 | + | 0.455949i | \(0.150700\pi\) | ||||
−0.890006 | + | 0.455949i | \(0.849300\pi\) | |||||||
\(854\) | 1344.00 | 0.0538533 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15246.0 | 0.608759 | ||||||||
\(857\) | 27435.0i | 1.09354i | 0.837284 | + | 0.546769i | \(0.184142\pi\) | ||||
−0.837284 | + | 0.546769i | \(0.815858\pi\) | |||||||
\(858\) | − 1584.00i | − 0.0630267i | ||||||||
\(859\) | −37556.0 | −1.49173 | −0.745864 | − | 0.666098i | \(-0.767963\pi\) | ||||
−0.745864 | + | 0.666098i | \(0.767963\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1323.00 | 0.0523667 | ||||||||
\(862\) | − 1062.00i | − 0.0419627i | ||||||||
\(863\) | − 14976.0i | − 0.590717i | −0.955386 | − | 0.295359i | \(-0.904561\pi\) | ||||
0.955386 | − | 0.295359i | \(-0.0954391\pi\) | |||||||
\(864\) | 1215.00 | 0.0478416 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23046.0 | −0.904313 | ||||||||
\(867\) | − 13416.0i | − 0.525526i | ||||||||
\(868\) | 406.000i | 0.0158762i | ||||||||
\(869\) | −5599.00 | −0.218565 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4352.00 | −0.169302 | ||||||||
\(872\) | − 35952.0i | − 1.39620i | ||||||||
\(873\) | 7551.00i | 0.292741i | ||||||||
\(874\) | −30375.0 | −1.17557 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 336.000 | 0.0129593 | ||||||||
\(877\) | 30718.0i | 1.18275i | 0.806396 | + | 0.591376i | \(0.201415\pi\) | ||||
−0.806396 | + | 0.591376i | \(0.798585\pi\) | |||||||
\(878\) | − 16395.0i | − 0.630187i | ||||||||
\(879\) | −13869.0 | −0.532184 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2916.00 | 0.111513 | 0.0557563 | − | 0.998444i | \(-0.482243\pi\) | ||||
0.0557563 | + | 0.998444i | \(0.482243\pi\) | |||||||
\(882\) | − 7938.00i | − 0.303046i | ||||||||
\(883\) | − 39670.0i | − 1.51189i | −0.654633 | − | 0.755947i | \(-0.727177\pi\) | ||||
0.654633 | − | 0.755947i | \(-0.272823\pi\) | |||||||
\(884\) | 336.000 | 0.0127838 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4653.00 | 0.176434 | ||||||||
\(887\) | 23724.0i | 0.898054i | 0.893518 | + | 0.449027i | \(0.148229\pi\) | ||||
−0.893518 | + | 0.449027i | \(0.851771\pi\) | |||||||
\(888\) | 15939.0i | 0.602340i | ||||||||
\(889\) | 7889.00 | 0.297625 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | − 3848.00i | − 0.144440i | ||||||||
\(893\) | − 27375.0i | − 1.02583i | ||||||||
\(894\) | −16173.0 | −0.605040 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11613.0 | 0.432995 | ||||||||
\(897\) | 3888.00i | 0.144723i | ||||||||
\(898\) | 3276.00i | 0.121739i | ||||||||
\(899\) | 10788.0 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4032.00 | −0.149085 | ||||||||
\(902\) | 2079.00i | 0.0767440i | ||||||||
\(903\) | − 2100.00i | − 0.0773905i | ||||||||
\(904\) | 23688.0 | 0.871517 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 9360.00 | 0.343229 | ||||||||
\(907\) | 42166.0i | 1.54366i | 0.635829 | + | 0.771830i | \(0.280658\pi\) | ||||
−0.635829 | + | 0.771830i | \(0.719342\pi\) | |||||||
\(908\) | − 1386.00i | − 0.0506564i | ||||||||
\(909\) | 12717.0 | 0.464022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32139.0 | 1.16884 | 0.584420 | − | 0.811452i | \(-0.301322\pi\) | ||||
0.584420 | + | 0.811452i | \(0.301322\pi\) | |||||||
\(912\) | − 26625.0i | − 0.966713i | ||||||||
\(913\) | − 13794.0i | − 0.500016i | ||||||||
\(914\) | 30138.0 | 1.09067 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −991.000 | −0.0357462 | ||||||||
\(917\) | − 7854.00i | − 0.282837i | ||||||||
\(918\) | 1701.00i | 0.0611562i | ||||||||
\(919\) | −44525.0 | −1.59820 | −0.799099 | − | 0.601199i | \(-0.794690\pi\) | ||||
−0.799099 | + | 0.601199i | \(0.794690\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1932.00 | −0.0691222 | ||||||||
\(922\) | 46530.0i | 1.66202i | ||||||||
\(923\) | 10320.0i | 0.368025i | ||||||||
\(924\) | −231.000 | −0.00822440 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −20634.0 | −0.732263 | ||||||||
\(927\) | − 14706.0i | − 0.521045i | ||||||||
\(928\) | 8370.00i | 0.296076i | ||||||||
\(929\) | 5964.00 | 0.210627 | 0.105314 | − | 0.994439i | \(-0.466415\pi\) | ||||
0.105314 | + | 0.994439i | \(0.466415\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −36750.0 | −1.29370 | ||||||||
\(932\) | − 975.000i | − 0.0342674i | ||||||||
\(933\) | − 7848.00i | − 0.275383i | ||||||||
\(934\) | −48852.0 | −1.71144 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3024.00 | −0.105601 | ||||||||
\(937\) | − 6662.00i | − 0.232271i | −0.993233 | − | 0.116136i | \(-0.962949\pi\) | ||||
0.993233 | − | 0.116136i | \(-0.0370507\pi\) | |||||||
\(938\) | 5712.00i | 0.198831i | ||||||||
\(939\) | 12237.0 | 0.425282 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42129.0 | −1.45948 | −0.729738 | − | 0.683727i | \(-0.760358\pi\) | ||||
−0.729738 | + | 0.683727i | \(0.760358\pi\) | |||||||
\(942\) | 5058.00i | 0.174945i | ||||||||
\(943\) | − 5103.00i | − 0.176221i | ||||||||
\(944\) | 17679.0 | 0.609536 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3300.00 | 0.113417 | ||||||||
\(947\) | − 23049.0i | − 0.790910i | −0.918485 | − | 0.395455i | \(-0.870587\pi\) | ||||
0.918485 | − | 0.395455i | \(-0.129413\pi\) | |||||||
\(948\) | − 1527.00i | − 0.0523150i | ||||||||
\(949\) | −1792.00 | −0.0612969 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10512.0 | −0.358438 | ||||||||
\(952\) | 3087.00i | 0.105095i | ||||||||
\(953\) | 10221.0i | 0.347419i | 0.984797 | + | 0.173710i | \(0.0555754\pi\) | ||||
−0.984797 | + | 0.173710i | \(0.944425\pi\) | |||||||
\(954\) | −5184.00 | −0.175931 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1524.00 | −0.0515582 | ||||||||
\(957\) | 6138.00i | 0.207328i | ||||||||
\(958\) | − 20196.0i | − 0.681110i | ||||||||
\(959\) | 378.000 | 0.0127281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26427.0 | −0.887080 | ||||||||
\(962\) | 12144.0i | 0.407004i | ||||||||
\(963\) | 6534.00i | 0.218645i | ||||||||
\(964\) | 2230.00 | 0.0745057 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5103.00 | 0.169965 | ||||||||
\(967\) | 1072.00i | 0.0356496i | 0.999841 | + | 0.0178248i | \(0.00567412\pi\) | ||||
−0.999841 | + | 0.0178248i | \(0.994326\pi\) | |||||||
\(968\) | 2541.00i | 0.0843707i | ||||||||
\(969\) | 7875.00 | 0.261075 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −50337.0 | −1.66364 | −0.831818 | − | 0.555048i | \(-0.812700\pi\) | ||||
−0.831818 | + | 0.555048i | \(0.812700\pi\) | |||||||
\(972\) | 243.000i | 0.00801875i | ||||||||
\(973\) | − 12236.0i | − 0.403153i | ||||||||
\(974\) | 52494.0 | 1.72692 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4544.00 | 0.149027 | ||||||||
\(977\) | − 49638.0i | − 1.62545i | −0.582651 | − | 0.812723i | \(-0.697984\pi\) | ||||
0.582651 | − | 0.812723i | \(-0.302016\pi\) | |||||||
\(978\) | 21888.0i | 0.715645i | ||||||||
\(979\) | −8316.00 | −0.271482 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15408.0 | 0.501467 | ||||||||
\(982\) | 7362.00i | 0.239237i | ||||||||
\(983\) | − 1143.00i | − 0.0370865i | −0.999828 | − | 0.0185433i | \(-0.994097\pi\) | ||||
0.999828 | − | 0.0185433i | \(-0.00590284\pi\) | |||||||
\(984\) | 3969.00 | 0.128584 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −11718.0 | −0.378476 | ||||||||
\(987\) | 4599.00i | 0.148316i | ||||||||
\(988\) | − 2000.00i | − 0.0644013i | ||||||||
\(989\) | −8100.00 | −0.260430 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 35060.0 | 1.12383 | 0.561916 | − | 0.827194i | \(-0.310064\pi\) | ||||
0.561916 | + | 0.827194i | \(0.310064\pi\) | |||||||
\(992\) | 2610.00i | 0.0835359i | ||||||||
\(993\) | − 12300.0i | − 0.393080i | ||||||||
\(994\) | 13545.0 | 0.432215 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3762.00 | 0.119682 | ||||||||
\(997\) | 55582.0i | 1.76560i | 0.469752 | + | 0.882798i | \(0.344343\pi\) | ||||
−0.469752 | + | 0.882798i | \(0.655657\pi\) | |||||||
\(998\) | 62148.0i | 1.97120i | ||||||||
\(999\) | −6831.00 | −0.216340 |
(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.d.199.2 | 2 | ||
5.2 | odd | 4 | 825.4.a.c.1.1 | ✓ | 1 | ||
5.3 | odd | 4 | 825.4.a.g.1.1 | yes | 1 | ||
5.4 | even | 2 | inner | 825.4.c.d.199.1 | 2 | ||
15.2 | even | 4 | 2475.4.a.i.1.1 | 1 | |||
15.8 | even | 4 | 2475.4.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.4.a.c.1.1 | ✓ | 1 | 5.2 | odd | 4 | ||
825.4.a.g.1.1 | yes | 1 | 5.3 | odd | 4 | ||
825.4.c.d.199.1 | 2 | 5.4 | even | 2 | inner | ||
825.4.c.d.199.2 | 2 | 1.1 | even | 1 | trivial | ||
2475.4.a.d.1.1 | 1 | 15.8 | even | 4 | |||
2475.4.a.i.1.1 | 1 | 15.2 | even | 4 |