Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,4,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(71.7463225670\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{73}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 18 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 38) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.77200\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.227998 | 0.0438783 | 0.0219391 | − | 0.999759i | \(-0.493016\pi\) | ||||
0.0219391 | + | 0.999759i | \(0.493016\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.31601 | −0.743806 | −0.371903 | − | 0.928272i | \(-0.621295\pi\) | ||||
−0.371903 | + | 0.928272i | \(0.621295\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.08801 | −0.436711 | −0.218356 | − | 0.975869i | \(-0.570069\pi\) | ||||
−0.218356 | + | 0.975869i | \(0.570069\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −26.9480 | −0.998075 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −12.7720 | −0.350082 | −0.175041 | − | 0.984561i | \(-0.556006\pi\) | ||||
−0.175041 | + | 0.984561i | \(0.556006\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 47.0360 | 1.00350 | 0.501748 | − | 0.865014i | \(-0.332691\pi\) | ||||
0.501748 | + | 0.865014i | \(0.332691\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.89603 | −0.0326369 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −31.4560 | −0.448776 | −0.224388 | − | 0.974500i | \(-0.572038\pi\) | ||||
−0.224388 | + | 0.974500i | \(0.572038\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.84405 | −0.0191621 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 19.0360 | 0.172578 | 0.0862888 | − | 0.996270i | \(-0.472499\pi\) | ||||
0.0862888 | + | 0.996270i | \(0.472499\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −55.8441 | −0.446752 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −12.3000 | −0.0876720 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −91.2120 | −0.584057 | −0.292028 | − | 0.956410i | \(-0.594330\pi\) | ||||
−0.292028 | + | 0.956410i | \(0.594330\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −293.968 | −1.70317 | −0.851584 | − | 0.524218i | \(-0.824358\pi\) | ||||
−0.851584 | + | 0.524218i | \(0.824358\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.91199 | −0.0153610 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 67.2599 | 0.324829 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −215.616 | −0.958029 | −0.479014 | − | 0.877807i | \(-0.659006\pi\) | ||||
−0.479014 | + | 0.877807i | \(0.659006\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.7241 | 0.0440317 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −67.7200 | −0.257953 | −0.128977 | − | 0.991648i | \(-0.541169\pi\) | ||||
−0.128977 | + | 0.991648i | \(0.541169\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 308.596 | 1.09443 | 0.547214 | − | 0.836992i | \(-0.315688\pi\) | ||||
0.547214 | + | 0.836992i | \(0.315688\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 224.100 | 0.742374 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −108.812 | −0.337700 | −0.168850 | − | 0.985642i | \(-0.554005\pi\) | ||||
−0.168850 | + | 0.985642i | \(0.554005\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −277.584 | −0.809283 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.17191 | −0.0196915 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 682.124 | 1.76787 | 0.883933 | − | 0.467613i | \(-0.154886\pi\) | ||||
0.883933 | + | 0.467613i | \(0.154886\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 106.212 | 0.260393 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.33196 | 0.0100664 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −250.300 | −0.552310 | −0.276155 | − | 0.961113i | \(-0.589060\pi\) | ||||
−0.276155 | + | 0.961113i | \(0.589060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 317.692 | 0.666825 | 0.333412 | − | 0.942781i | \(-0.391800\pi\) | ||||
0.333412 | + | 0.942781i | \(0.391800\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 217.956 | 0.435871 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −391.152 | −0.746406 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 940.444 | 1.71483 | 0.857414 | − | 0.514626i | \(-0.172069\pi\) | ||||
0.857414 | + | 0.514626i | \(0.172069\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.34018 | 0.00757241 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 395.552 | 0.661175 | 0.330587 | − | 0.943775i | \(-0.392753\pi\) | ||||
0.330587 | + | 0.943775i | \(0.392753\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 975.048 | 1.56330 | 0.781649 | − | 0.623718i | \(-0.214379\pi\) | ||||
0.781649 | + | 0.623718i | \(0.214379\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.7323 | −0.0196027 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 103.300 | 0.152885 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −922.776 | −1.31418 | −0.657091 | − | 0.753811i | \(-0.728213\pi\) | ||||
−0.657091 | + | 0.753811i | \(0.728213\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 724.792 | 0.994228 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1163.77 | −1.53904 | −0.769519 | − | 0.638624i | \(-0.779504\pi\) | ||||
−0.769519 | + | 0.638624i | \(0.779504\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 261.588 | 0.333803 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20.7962 | −0.0256274 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 685.136 | 0.816003 | 0.408002 | − | 0.912981i | \(-0.366226\pi\) | ||||
0.408002 | + | 0.912981i | \(0.366226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −380.428 | −0.438238 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −67.0242 | −0.0747321 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −158.004 | −0.170641 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 211.256 | 0.221132 | 0.110566 | − | 0.993869i | \(-0.464734\pi\) | ||||
0.110566 | + | 0.993869i | \(0.464734\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 344.180 | 0.349408 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1703.55 | 1.67831 | 0.839157 | − | 0.543889i | \(-0.183049\pi\) | ||||
0.839157 | + | 0.543889i | \(0.183049\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1393.52 | 1.33308 | 0.666542 | − | 0.745468i | \(-0.267774\pi\) | ||||
0.666542 | + | 0.745468i | \(0.267774\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.3351 | 0.0142529 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 907.996 | 0.820367 | 0.410184 | − | 0.912003i | \(-0.365465\pi\) | ||||
0.410184 | + | 0.912003i | \(0.365465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −862.077 | −0.757541 | −0.378770 | − | 0.925491i | \(-0.623653\pi\) | ||||
−0.378770 | + | 0.925491i | \(0.623653\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −49.1601 | −0.0420366 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1502.72 | 1.25101 | 0.625505 | − | 0.780220i | \(-0.284893\pi\) | ||||
0.625505 | + | 0.780220i | \(0.284893\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −158.304 | −0.128364 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1267.53 | −1.00156 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 254.416 | 0.195986 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1167.88 | −0.877443 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.4400 | −0.0113185 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1503.90 | 1.07610 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −389.280 | −0.271992 | −0.135996 | − | 0.990709i | \(-0.543423\pi\) | ||||
−0.135996 | + | 0.990709i | \(0.543423\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 70.3593 | 0.0480216 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −268.308 | −0.178948 | −0.0894739 | − | 0.995989i | \(-0.528519\pi\) | ||||
−0.0894739 | + | 0.995989i | \(0.528519\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −153.672 | −0.100188 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 102.287 | 0.0652110 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2657.33 | 1.65716 | 0.828580 | − | 0.559871i | \(-0.189149\pi\) | ||||
0.828580 | + | 0.559871i | \(0.189149\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2859.92 | −1.74514 | −0.872572 | − | 0.488486i | \(-0.837549\pi\) | ||||
−0.872572 | + | 0.488486i | \(0.837549\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −24.8090 | −0.0148177 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −600.744 | −0.351306 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 758.520 | 0.434425 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −63.2887 | −0.0355099 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −311.812 | −0.171440 | −0.0857202 | − | 0.996319i | \(-0.527319\pi\) | ||||
−0.0857202 | + | 0.996319i | \(0.527319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1462.32 | 0.788093 | 0.394046 | − | 0.919091i | \(-0.371075\pi\) | ||||
0.394046 | + | 0.919091i | \(0.371075\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 847.677 | 0.447912 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2444.64 | 1.26683 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.38395 | −0.00222852 | −0.00111426 | − | 0.999999i | \(-0.500355\pi\) | ||||
−0.00111426 | + | 0.999999i | \(0.500355\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 155.523 | 0.0775709 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −153.964 | −0.0753666 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1777.89 | −0.854325 | −0.427162 | − | 0.904175i | \(-0.640487\pi\) | ||||
−0.427162 | + | 0.904175i | \(0.640487\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 24.2161 | 0.0114256 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −893.064 | −0.413817 | −0.206908 | − | 0.978360i | \(-0.566340\pi\) | ||||
−0.206908 | + | 0.978360i | \(0.566340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.3876 | 0.00700391 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −512.012 | −0.228974 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2452.56 | 1.07783 | 0.538915 | − | 0.842360i | \(-0.318834\pi\) | ||||
0.538915 | + | 0.842360i | \(0.318834\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 451.667 | 0.195102 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −57.0679 | −0.0242344 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2064.81 | −0.862185 | −0.431092 | − | 0.902308i | \(-0.641872\pi\) | ||||
−0.431092 | + | 0.902308i | \(0.641872\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2518.54 | 1.03426 | 0.517132 | − | 0.855906i | \(-0.327000\pi\) | ||||
0.517132 | + | 0.855906i | \(0.327000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 72.4332 | 0.0292591 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1793.06 | 0.712588 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 401.756 | 0.157109 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 99.4829 | 0.0382874 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4206.38 | 1.59352 | 0.796761 | − | 0.604294i | \(-0.206545\pi\) | ||||
0.796761 | + | 0.604294i | \(0.206545\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3245.82 | 1.21056 | 0.605282 | − | 0.796011i | \(-0.293060\pi\) | ||||
0.605282 | + | 0.796011i | \(0.293060\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −89.1819 | −0.0327510 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1734.71 | 0.627377 | 0.313688 | − | 0.949526i | \(-0.398435\pi\) | ||||
0.313688 | + | 0.949526i | \(0.398435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −380.792 | −0.135646 | −0.0678232 | − | 0.997697i | \(-0.521605\pi\) | ||||
−0.0678232 | + | 0.997697i | \(0.521605\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 214.420 | 0.0752437 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 737.724 | 0.255064 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 563.160 | 0.191867 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −512.983 | −0.172245 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −242.668 | −0.0803143 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1010.44 | 0.329675 | 0.164837 | − | 0.986321i | \(-0.447290\pi\) | ||||
0.164837 | + | 0.986321i | \(0.447290\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 90.1852 | 0.0290112 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2566.29 | −0.814043 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2377.62 | 0.743793 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 222.309 | 0.0685948 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1479.57 | −0.450345 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3398.70 | −1.02060 | −0.510301 | − | 0.859996i | \(-0.670466\pi\) | ||||
−0.510301 | + | 0.859996i | \(0.670466\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1504.89 | 0.445892 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5760.80 | 1.68439 | 0.842197 | − | 0.539169i | \(-0.181262\pi\) | ||||
0.842197 | + | 0.539169i | \(0.181262\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2179.00 | 0.628786 | 0.314393 | − | 0.949293i | \(-0.398199\pi\) | ||||
0.314393 | + | 0.949293i | \(0.398199\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.5522 | 0.00670832 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2808.49 | −0.789659 | −0.394830 | − | 0.918754i | \(-0.629196\pi\) | ||||
−0.394830 | + | 0.918754i | \(0.629196\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 904.882 | 0.251183 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −210.391 | −0.0576640 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6285.67 | −1.70120 | −0.850599 | − | 0.525815i | \(-0.823761\pi\) | ||||
−0.850599 | + | 0.525815i | \(0.823761\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1129.22 | 0.301825 | 0.150912 | − | 0.988547i | \(-0.451779\pi\) | ||||
0.150912 | + | 0.988547i | \(0.451779\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 497.352 | 0.131297 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2308.39 | 0.601950 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 893.684 | 0.230218 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −265.337 | −0.0675303 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2873.73 | −0.722661 | −0.361331 | − | 0.932438i | \(-0.617677\pi\) | ||||
−0.361331 | + | 0.932438i | \(0.617677\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −243.128 | −0.0604163 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 59.6416 | 0.0146467 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3712.18 | −0.901008 | −0.450504 | − | 0.892774i | \(-0.648756\pi\) | ||||
−0.450504 | + | 0.892774i | \(0.648756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1743.90 | 0.418382 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2457.98 | 0.582932 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1263.04 | −0.296130 | −0.148065 | − | 0.988978i | \(-0.547304\pi\) | ||||
−0.148065 | + | 0.988978i | \(0.547304\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5672.55 | −1.31495 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 156.210 | 0.0358048 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5484.39 | 1.24308 | 0.621541 | − | 0.783381i | \(-0.286507\pi\) | ||||
0.621541 | + | 0.783381i | \(0.286507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3217.66 | 0.721251 | 0.360625 | − | 0.932711i | \(-0.382563\pi\) | ||||
0.360625 | + | 0.932711i | \(0.382563\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −86.7368 | −0.0192291 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 713.240 | 0.156400 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7668.13 | −1.66330 | −0.831649 | − | 0.555302i | \(-0.812603\pi\) | ||||
−0.831649 | + | 0.555302i | \(0.812603\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7921.86 | 1.69989 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1126.81 | 0.239216 | 0.119608 | − | 0.992821i | \(-0.461836\pi\) | ||||
0.119608 | + | 0.992821i | \(0.461836\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1502.63 | −0.315625 | −0.157813 | − | 0.987469i | \(-0.550444\pi\) | ||||
−0.157813 | + | 0.987469i | \(0.550444\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −36.0246 | −0.00748742 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 547.720 | 0.112651 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3923.52 | −0.798600 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 48.1659 | 0.00970288 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 452.324 | 0.0901878 | 0.0450939 | − | 0.998983i | \(-0.485641\pi\) | ||||
0.0450939 | + | 0.998983i | \(0.485641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2081.50 | 0.410812 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 157.096 | 0.0306924 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 895.379 | 0.173181 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2495.93 | −0.477950 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 388.407 | 0.0736415 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2641.93 | −0.495988 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2333.46 | −0.433803 | −0.216901 | − | 0.976194i | \(-0.569595\pi\) | ||||
−0.216901 | + | 0.976194i | \(0.569595\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 317.720 | 0.0584934 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10476.1 | −1.91011 | −0.955055 | − | 0.296429i | \(-0.904204\pi\) | ||||
−0.955055 | + | 0.296429i | \(0.904204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4160.33 | 0.751297 | 0.375648 | − | 0.926762i | \(-0.377420\pi\) | ||||
0.375648 | + | 0.926762i | \(0.377420\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1812.52 | −0.324203 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7508.56 | 1.33036 | 0.665178 | − | 0.746685i | \(-0.268356\pi\) | ||||
0.665178 | + | 0.746685i | \(0.268356\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1164.96 | 0.204468 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 207.021 | 0.0359963 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −597.664 | −0.102956 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2626.68 | −0.448314 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −196.552 | −0.0332396 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 880.073 | 0.147477 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10386.8 | 1.72480 | 0.862400 | − | 0.506227i | \(-0.168960\pi\) | ||||
0.862400 | + | 0.506227i | \(0.168960\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5810.43 | 0.956184 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7820.74 | −1.27550 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5618.29 | 0.908153 | 0.454077 | − | 0.890963i | \(-0.349969\pi\) | ||||
0.454077 | + | 0.890963i | \(0.349969\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 342.617 | 0.0548921 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3754.56 | 0.596249 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5019.29 | 0.790135 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −36.0929 | −0.00563240 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1814.32 | 0.280686 | 0.140343 | − | 0.990103i | \(-0.455180\pi\) | ||||
0.140343 | + | 0.990103i | \(0.455180\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 816.757 | 0.125272 | 0.0626361 | − | 0.998036i | \(-0.480049\pi\) | ||||
0.0626361 | + | 0.998036i | \(0.480049\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −578.545 | −0.0879785 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11090.4 | 1.67219 | 0.836095 | − | 0.548585i | \(-0.184833\pi\) | ||||
0.836095 | + | 0.548585i | \(0.184833\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3289.41 | −0.491786 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 58.0064 | 0.00859951 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3211.68 | 0.472161 | 0.236081 | − | 0.971733i | \(-0.424137\pi\) | ||||
0.236081 | + | 0.971733i | \(0.424137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −266.274 | −0.0385007 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8108.51 | −1.16279 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8077.81 | −1.14893 | −0.574466 | − | 0.818528i | \(-0.694790\pi\) | ||||
−0.574466 | + | 0.818528i | \(0.694790\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1824.92 | 0.257457 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5517.02 | −0.772048 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5088.15 | 0.706312 | 0.353156 | − | 0.935564i | \(-0.385108\pi\) | ||||
0.353156 | + | 0.935564i | \(0.385108\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 342.886 | 0.0472175 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4290.25 | −0.586099 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2547.00 | 0.345199 | 0.172600 | − | 0.984992i | \(-0.444783\pi\) | ||||
0.172600 | + | 0.984992i | \(0.444783\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −88.7550 | −0.0119345 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7056.11 | 0.941384 | 0.470692 | − | 0.882297i | \(-0.344004\pi\) | ||||
0.470692 | + | 0.882297i | \(0.344004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −859.044 | −0.113717 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8316.05 | −1.09232 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4728.25 | −0.616277 | −0.308138 | − | 0.951342i | \(-0.599706\pi\) | ||||
−0.308138 | + | 0.951342i | \(0.599706\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −598.797 | −0.0774488 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −61.1737 | −0.00785192 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7673.81 | 0.977497 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −740.837 | −0.0936563 | −0.0468281 | − | 0.998903i | \(-0.514911\pi\) | ||||
−0.0468281 | + | 0.998903i | \(0.514911\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −35.0370 | −0.00439610 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1879.58 | 0.234070 | 0.117035 | − | 0.993128i | \(-0.462661\pi\) | ||||
0.117035 | + | 0.993128i | \(0.462661\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13827.1 | −1.70912 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6027.37 | −0.739513 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2753.85 | 0.335389 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1715.45 | −0.207393 | −0.103697 | − | 0.994609i | \(-0.533067\pi\) | ||||
−0.103697 | + | 0.994609i | \(0.533067\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 605.866 | 0.0727133 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2024.43 | 0.241200 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9677.90 | 1.14475 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −652.056 | −0.0765739 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2497.15 | 0.291155 | 0.145578 | − | 0.989347i | \(-0.453496\pi\) | ||||
0.145578 | + | 0.989347i | \(0.453496\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6582.52 | −0.762024 | −0.381012 | − | 0.924570i | \(-0.624424\pi\) | ||||
−0.381012 | + | 0.924570i | \(0.624424\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2932.27 | 0.337049 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1756.63 | 0.200492 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2569.50 | −0.291210 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −136.969 | −0.0154147 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8875.72 | −0.991946 | −0.495973 | − | 0.868338i | \(-0.665188\pi\) | ||||
−0.495973 | + | 0.868338i | \(0.665188\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3636.90 | −0.403645 | −0.201822 | − | 0.979422i | \(-0.564686\pi\) | ||||
−0.201822 | + | 0.979422i | \(0.564686\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 172.941 | 0.0190618 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 361.684 | 0.0395920 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10979.4 | 1.19366 | 0.596829 | − | 0.802368i | \(-0.296427\pi\) | ||||
0.596829 | + | 0.802368i | \(0.296427\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7480.34 | 0.807725 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1300.16 | 0.139442 | 0.0697208 | − | 0.997567i | \(-0.477789\pi\) | ||||
0.0697208 | + | 0.997567i | \(0.477789\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5697.60 | −0.606948 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −71.0925 | −0.00752250 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15875.2 | −1.66859 | −0.834296 | − | 0.551317i | \(-0.814125\pi\) | ||||
−0.834296 | + | 0.551317i | \(0.814125\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 864.920 | 0.0903049 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 333.406 | 0.0345801 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3163.64 | 0.325964 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3115.66 | 0.318916 | 0.159458 | − | 0.987205i | \(-0.449025\pi\) | ||||
0.159458 | + | 0.987205i | \(0.449025\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 386.910 | 0.0393451 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13479.7 | −1.36185 | −0.680924 | − | 0.732354i | \(-0.738422\pi\) | ||||
−0.680924 | + | 0.732354i | \(0.738422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7946.19 | −0.797604 | −0.398802 | − | 0.917037i | \(-0.630574\pi\) | ||||
−0.398802 | + | 0.917037i | \(0.630574\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 557.373 | 0.0555862 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9148.37 | −0.906501 | −0.453250 | − | 0.891383i | \(-0.649736\pi\) | ||||
−0.453250 | + | 0.891383i | \(0.649736\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7606.32 | −0.748885 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.999532 | −9.77834e−5 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3941.39 | −0.383140 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1061.04 | −0.102492 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18381.9 | −1.76446 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7664.64 | −0.731120 | −0.365560 | − | 0.930788i | \(-0.619122\pi\) | ||||
−0.365560 | + | 0.930788i | \(0.619122\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10141.7 | −0.961378 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −35.1034 | −0.00330696 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1756.80 | −0.164479 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5347.21 | 0.497547 | 0.248774 | − | 0.968562i | \(-0.419973\pi\) | ||||
0.248774 | + | 0.968562i | \(0.419973\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −405.355 | −0.0374863 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13647.2 | 1.25436 | 0.627178 | − | 0.778876i | \(-0.284210\pi\) | ||||
0.627178 | + | 0.778876i | \(0.284210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2869.17 | 0.262111 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2862.20 | −0.259892 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3199.23 | −0.288743 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19351.6 | −1.73607 | −0.868034 | − | 0.496504i | \(-0.834617\pi\) | ||||
−0.868034 | + | 0.496504i | \(0.834617\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −203.617 | −0.0181576 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19259.1 | 1.70720 | 0.853600 | − | 0.520929i | \(-0.174414\pi\) | ||||
0.853600 | + | 0.520929i | \(0.174414\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14166.7 | −1.24834 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.50834 | 0.000307319 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3595.77 | −0.313123 | −0.156561 | − | 0.987668i | \(-0.550041\pi\) | ||||
−0.156561 | + | 0.987668i | \(0.550041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7886.20 | −0.682710 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −233.701 | −0.0201133 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11588.5 | −0.991556 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1389.75 | 0.118223 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 559.179 | 0.0472933 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15211.0 | −1.27909 | −0.639544 | − | 0.768754i | \(-0.720877\pi\) | ||||
−0.639544 | + | 0.768754i | \(0.720877\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18307.1 | 1.53062 | 0.765310 | − | 0.643662i | \(-0.222586\pi\) | ||||
0.765310 | + | 0.643662i | \(0.222586\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 102.979 | 0.00856073 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9247.06 | 0.764342 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11804.6 | −0.970217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6745.09 | 0.551247 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3185.28 | −0.258855 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7550.90 | −0.610194 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −470.773 | −0.0378312 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3545.31 | 0.283316 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9102.17 | −0.723351 | −0.361676 | − | 0.932304i | \(-0.617795\pi\) | ||||
−0.361676 | + | 0.932304i | \(0.617795\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 574.223 | 0.0453817 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7169.03 | 0.563464 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9218.75 | −0.720595 | −0.360297 | − | 0.932837i | \(-0.617325\pi\) | ||||
−0.360297 | + | 0.932837i | \(0.617325\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8561.17 | −0.665541 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1733.03 | −0.133992 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7463.42 | 0.573918 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 408.815 | 0.0312671 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13435.1 | 1.02202 | 0.511010 | − | 0.859575i | \(-0.329272\pi\) | ||||
0.511010 | + | 0.859575i | \(0.329272\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14515.1 | 1.09825 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 91.5996 | 0.00689365 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11941.5 | 0.893916 | 0.446958 | − | 0.894555i | \(-0.352507\pi\) | ||||
0.446958 | + | 0.894555i | \(0.352507\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12496.6 | −0.930508 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5862.12 | −0.434191 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6378.91 | −0.469979 | −0.234989 | − | 0.971998i | \(-0.575506\pi\) | ||||
−0.234989 | + | 0.971998i | \(0.575506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24903.9 | 1.82521 | 0.912605 | − | 0.408843i | \(-0.134068\pi\) | ||||
0.912605 | + | 0.408843i | \(0.134068\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 959.046 | 0.0699210 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1063.05 | −0.0770995 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11414.7 | −0.823568 | −0.411784 | − | 0.911281i | \(-0.635094\pi\) | ||||
−0.411784 | + | 0.911281i | \(0.635094\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 740.040 | 0.0531175 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9412.57 | 0.672115 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8712.09 | −0.618899 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10540.8 | 0.744969 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20732.1 | 1.45776 | 0.728881 | − | 0.684641i | \(-0.240041\pi\) | ||||
0.728881 | + | 0.684641i | \(0.240041\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5585.39 | −0.390734 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 395.511 | 0.0275282 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18010.5 | 1.24722 | 0.623611 | − | 0.781735i | \(-0.285665\pi\) | ||||
0.623611 | + | 0.781735i | \(0.285665\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2115.73 | −0.145775 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −86.8199 | −0.00595193 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27944.7 | −1.90616 | −0.953080 | − | 0.302719i | \(-0.902106\pi\) | ||||
−0.953080 | + | 0.302719i | \(0.902106\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11598.1 | −0.787179 | −0.393590 | − | 0.919286i | \(-0.628767\pi\) | ||||
−0.393590 | + | 0.919286i | \(0.628767\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −25343.1 | −1.71153 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9712.06 | 0.652647 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −20170.5 | −1.34876 | −0.674379 | − | 0.738385i | \(-0.735589\pi\) | ||||
−0.674379 | + | 0.738385i | \(0.735589\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 168.200 | 0.0111918 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5118.09 | −0.338880 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14618.3 | −0.963174 | −0.481587 | − | 0.876398i | \(-0.659939\pi\) | ||||
−0.481587 | + | 0.876398i | \(0.659939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 128.399 | 0.00841880 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17538.1 | −1.14434 | −0.572171 | − | 0.820134i | \(-0.693899\pi\) | ||||
−0.572171 | + | 0.820134i | \(0.693899\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8815.75 | −0.572431 | −0.286216 | − | 0.958165i | \(-0.592397\pi\) | ||||
−0.286216 | + | 0.958165i | \(0.592397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −234.144 | −0.0151302 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5541.39 | −0.356358 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5525.94 | −0.353660 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −55.3279 | −0.00352405 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6782.42 | 0.429941 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22170.8 | 1.39874 | 0.699370 | − | 0.714759i | \(-0.253464\pi\) | ||||
0.699370 | + | 0.714759i | \(0.253464\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 230.378 | 0.0144655 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3237.25 | 0.202309 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13056.5 | −0.812112 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10659.3 | −0.659902 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22067.7 | −1.35978 | −0.679891 | − | 0.733313i | \(-0.737973\pi\) | ||||
−0.679891 | + | 0.733313i | \(0.737973\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11795.4 | −0.723428 | −0.361714 | − | 0.932289i | \(-0.617808\pi\) | ||||
−0.361714 | + | 0.932289i | \(0.617808\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −585.108 | −0.0357188 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9716.04 | 0.590382 | 0.295191 | − | 0.955438i | \(-0.404617\pi\) | ||||
0.295191 | + | 0.955438i | \(0.404617\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3196.83 | 0.193354 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 542.092 | 0.0326363 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10311.9 | 0.617969 | 0.308985 | − | 0.951067i | \(-0.400011\pi\) | ||||
0.308985 | + | 0.951067i | \(0.400011\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2231.25 | 0.133102 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −26275.6 | −1.56029 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4019.80 | 0.237616 | 0.118808 | − | 0.992917i | \(-0.462093\pi\) | ||||
0.118808 | + | 0.992917i | \(0.462093\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22702.6 | 1.33590 | 0.667951 | − | 0.744206i | \(-0.267172\pi\) | ||||
0.667951 | + | 0.744206i | \(0.267172\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −337.338 | −0.0197604 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1277.94 | 0.0745208 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1736.31 | −0.100795 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −774.898 | −0.0447822 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4057.57 | −0.233443 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11132.8 | 0.637652 | 0.318826 | − | 0.947813i | \(-0.396711\pi\) | ||||
0.318826 | + | 0.947813i | \(0.396711\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 686.884 | 0.0391677 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13967.0 | 0.792903 | 0.396452 | − | 0.918056i | \(-0.370241\pi\) | ||||
0.396452 | + | 0.918056i | \(0.370241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1708.64 | −0.0965707 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1313.45 | 0.0739083 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1173.88 | 0.0657648 | 0.0328824 | − | 0.999459i | \(-0.489531\pi\) | ||||
0.0328824 | + | 0.999459i | \(0.489531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22098.4 | −1.23261 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 496.807 | 0.0275901 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32084.4 | 1.77405 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8713.33 | 0.479697 | 0.239849 | − | 0.970810i | \(-0.422902\pi\) | ||||
0.239849 | + | 0.970810i | \(0.422902\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2783.73 | −0.152590 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23783.1 | 1.29805 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2130.20 | 0.115763 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −640.331 | −0.0346489 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31003.4 | 1.67045 | 0.835223 | − | 0.549912i | \(-0.185339\pi\) | ||||
0.835223 | + | 0.549912i | \(0.185339\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4096.70 | −0.219787 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 206.311 | 0.0110215 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13778.3 | −0.732939 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12145.1 | 0.643328 | 0.321664 | − | 0.946854i | \(-0.395758\pi\) | ||||
0.321664 | + | 0.946854i | \(0.395758\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24867.0 | 1.31165 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5595.98 | −0.293929 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4995.79 | 0.261304 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1433.12 | −0.0746456 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24787.8 | −1.28572 | −0.642858 | − | 0.765985i | \(-0.722252\pi\) | ||||
−0.642858 | + | 0.765985i | \(0.722252\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11270.8 | −0.582173 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 257.461 | 0.0132435 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5093.65 | 0.260929 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19335.6 | −0.986409 | −0.493204 | − | 0.869914i | \(-0.664174\pi\) | ||||
−0.493204 | + | 0.869914i | \(0.664174\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19456.0 | −0.988467 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9707.19 | −0.491154 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20204.5 | −1.01810 | −0.509052 | − | 0.860735i | \(-0.670004\pi\) | ||||
−0.509052 | + | 0.860735i | \(0.670004\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 526.309 | 0.0264125 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12011.4 | −0.600331 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15643.7 | 0.778706 | 0.389353 | − | 0.921089i | \(-0.372699\pi\) | ||||
0.389353 | + | 0.921089i | \(0.372699\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 203.758 | 0.0101016 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4500.20 | 0.222202 | 0.111101 | − | 0.993809i | \(-0.464562\pi\) | ||||
0.111101 | + | 0.993809i | \(0.464562\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2593.03 | 0.127518 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 31361.2 | 1.53608 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7343.88 | −0.358264 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35080.2 | −1.70452 | −0.852261 | − | 0.523117i | \(-0.824769\pi\) | ||||
−0.852261 | + | 0.523117i | \(0.824769\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −655.204 | −0.0317091 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12160.7 | −0.586188 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10391.8 | 0.498938 | 0.249469 | − | 0.968383i | \(-0.419744\pi\) | ||||
0.249469 | + | 0.968383i | \(0.419744\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −55.4328 | −0.00265096 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11810.5 | 0.562590 | 0.281295 | − | 0.959621i | \(-0.409236\pi\) | ||||
0.281295 | + | 0.959621i | \(0.409236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6972.48 | 0.330827 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7049.28 | −0.333160 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11773.1 | −0.554241 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35125.5 | 1.64715 | 0.823574 | − | 0.567209i | \(-0.191977\pi\) | ||||
0.823574 | + | 0.567209i | \(0.191977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −846.369 | −0.0395347 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20001.5 | −0.930665 | −0.465332 | − | 0.885136i | \(-0.654065\pi\) | ||||
−0.465332 | + | 0.885136i | \(0.654065\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16416.4 | 0.760895 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 397.607 | 0.0183579 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1286.68 | −0.0591786 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5051.99 | −0.231465 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1121.91 | 0.0512055 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 36.4569 | 0.00165758 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13593.3 | 0.615690 | 0.307845 | − | 0.951437i | \(-0.400392\pi\) | ||||
0.307845 | + | 0.951437i | \(0.400392\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −287.970 | −0.0129937 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12154.0 | −0.546330 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14943.0 | 0.669156 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1293.33 | −0.0576977 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6946.75 | 0.308741 | 0.154370 | − | 0.988013i | \(-0.450665\pi\) | ||||
0.154370 | + | 0.988013i | \(0.450665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3422.79 | 0.151552 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −18463.1 | −0.814432 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12453.3 | −0.547283 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1280.36 | 0.0560581 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1250.43 | 0.0545443 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24987.2 | 1.08591 | 0.542955 | − | 0.839762i | \(-0.317305\pi\) | ||||
0.542955 | + | 0.839762i | \(0.317305\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −23172.5 | −1.00332 | −0.501662 | − | 0.865064i | \(-0.667278\pi\) | ||||
−0.501662 | + | 0.865064i | \(0.667278\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 733.621 | 0.0316472 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14784.9 | 0.635452 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5863.32 | 0.251079 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10251.8 | 0.437394 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30703.8 | −1.30520 | −0.652600 | − | 0.757703i | \(-0.726322\pi\) | ||||
−0.652600 | + | 0.757703i | \(0.726322\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15940.1 | 0.675135 | 0.337568 | − | 0.941301i | \(-0.390396\pi\) | ||||
0.337568 | + | 0.941301i | \(0.390396\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 162.617 | 0.00686256 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6662.20 | −0.280130 | −0.140065 | − | 0.990142i | \(-0.544731\pi\) | ||||
−0.140065 | + | 0.990142i | \(0.544731\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20606.0 | 0.863299 | 0.431649 | − | 0.902041i | \(-0.357932\pi\) | ||||
0.431649 | + | 0.902041i | \(0.357932\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1748.32 | −0.0729826 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8731.69 | 0.363187 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7426.73 | 0.307799 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3615.82 | 0.149320 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 45717.9 | 1.88124 | 0.940618 | − | 0.339468i | \(-0.110247\pi\) | ||||
0.940618 | + | 0.339468i | \(0.110247\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16069.4 | −0.658878 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 256.910 | 0.0104964 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −127.963 | −0.00520955 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9445.79 | 0.383189 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −342.597 | −0.0138491 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4104.47 | −0.165334 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17230.4 | −0.691626 | −0.345813 | − | 0.938303i | \(-0.612397\pi\) | ||||
−0.345813 | + | 0.938303i | \(0.612397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4257.90 | 0.170312 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44484.4 | 1.77311 | 0.886557 | − | 0.462619i | \(-0.153090\pi\) | ||||
0.886557 | + | 0.462619i | \(0.153090\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23213.4 | −0.922039 | −0.461019 | − | 0.887390i | \(-0.652516\pi\) | ||||
−0.461019 | + | 0.887390i | \(0.652516\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 124.879 | 0.00494294 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9640.68 | 0.380270 | 0.190135 | − | 0.981758i | \(-0.439107\pi\) | ||||
0.190135 | + | 0.981758i | \(0.439107\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20395.5 | −0.801697 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −894.555 | −0.0350412 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11785.7 | 0.460072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44234.8 | 1.72082 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5692.93 | −0.220706 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12163.6 | −0.469947 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9499.62 | 0.365769 | 0.182885 | − | 0.983134i | \(-0.441457\pi\) | ||||
0.182885 | + | 0.983134i | \(0.441457\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 103.129 | 0.00395729 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8252.54 | −0.315590 | −0.157795 | − | 0.987472i | \(-0.550439\pi\) | ||||
−0.157795 | + | 0.987472i | \(0.550439\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34768.9 | −1.32510 | −0.662552 | − | 0.749016i | \(-0.730526\pi\) | ||||
−0.662552 | + | 0.749016i | \(0.730526\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 474.577 | 0.0180257 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3288.58 | 0.124487 | 0.0622433 | − | 0.998061i | \(-0.480175\pi\) | ||||
0.0622433 | + | 0.998061i | \(0.480175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3148.50 | 0.118782 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9257.05 | −0.348061 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2067.43 | −0.0774736 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17171.0 | 0.641298 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 204.145 | 0.00759888 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26813.4 | 0.994747 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21456.9 | −0.793377 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −569.067 | −0.0209716 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20944.2 | −0.769292 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 37686.1 | 1.37966 | 0.689828 | − | 0.723973i | \(-0.257686\pi\) | ||||
0.689828 | + | 0.723973i | \(0.257686\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −45907.4 | −1.67508 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15090.9 | −0.548828 | −0.274414 | − | 0.961612i | \(-0.588484\pi\) | ||||
−0.274414 | + | 0.961612i | \(0.588484\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14863.7 | 0.538790 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −602.355 | −0.0217631 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2170.08 | 0.0781485 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −43617.4 | −1.56562 | −0.782810 | − | 0.622261i | \(-0.786214\pi\) | ||||
−0.782810 | + | 0.622261i | \(0.786214\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −532.024 | −0.0190345 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18605.2 | 0.663486 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12040.9 | 0.428002 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −37552.6 | −1.33052 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 32446.2 | 1.14588 | 0.572942 | − | 0.819596i | \(-0.305802\pi\) | ||||
0.572942 | + | 0.819596i | \(0.305802\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5274.10 | −0.185662 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2388.53 | −0.0838123 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3341.01 | −0.116858 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28355.4 | −0.988614 | −0.494307 | − | 0.869287i | \(-0.664578\pi\) | ||||
−0.494307 | + | 0.869287i | \(0.664578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 948.548 | 0.0329656 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48970.8 | 1.69650 | 0.848248 | − | 0.529599i | \(-0.177658\pi\) | ||||
0.848248 | + | 0.529599i | \(0.177658\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1289.12 | −0.0445170 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −827.300 | −0.0284784 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9198.84 | −0.315652 | −0.157826 | − | 0.987467i | \(-0.550448\pi\) | ||||
−0.157826 | + | 0.987467i | \(0.550448\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45862.4 | 1.56876 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1711.94 | 0.0583737 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28428.9 | 0.966321 | 0.483160 | − | 0.875532i | \(-0.339489\pi\) | ||||
0.483160 | + | 0.875532i | \(0.339489\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34980.3 | −1.18527 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 265.609 | 0.00897170 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −21492.5 | −0.723700 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56626.2 | 1.90078 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24468.7 | −0.818788 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −26992.2 | −0.900426 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22315.5 | 0.742109 | 0.371054 | − | 0.928611i | \(-0.378996\pi\) | ||||
0.371054 | + | 0.928611i | \(0.378996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −136.266 | −0.00451755 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 208.410 | 0.00688795 | 0.00344398 | − | 0.999994i | \(-0.498904\pi\) | ||||
0.00344398 | + | 0.999994i | \(0.498904\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23131.0 | 0.762124 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −598.879 | −0.0196712 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35744.3 | 1.17048 | 0.585241 | − | 0.810860i | \(-0.301000\pi\) | ||||
0.585241 | + | 0.810860i | \(0.301000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8750.56 | −0.285668 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23231.3 | 0.756082 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36175.5 | 1.17377 | 0.586887 | − | 0.809669i | \(-0.300353\pi\) | ||||
0.586887 | + | 0.809669i | \(0.300353\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14425.9 | −0.466647 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 200.655 | 0.00647104 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5874.44 | 0.188874 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34654.3 | −1.11083 | −0.555413 | − | 0.831575i | \(-0.687440\pi\) | ||||
−0.555413 | + | 0.831575i | \(0.687440\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2368.17 | 0.0756812 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3166.67 | 0.100895 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4756.72 | −0.151100 | −0.0755501 | − | 0.997142i | \(-0.524071\pi\) | ||||
−0.0755501 | + | 0.997142i | \(0.524071\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2652.09 | 0.0839923 |
(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 | 1216.4.a.p.1.1 | 2 | ||
4.3 | odd | 2 | 1216.4.a.g.1.2 | 2 | |||
8.3 | odd | 2 | 38.4.a.c.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 304.4.a.c.1.2 | 2 | |||
24.11 | even | 2 | 342.4.a.h.1.1 | 2 | |||
40.3 | even | 4 | 950.4.b.i.799.1 | 4 | |||
40.19 | odd | 2 | 950.4.a.e.1.2 | 2 | |||
40.27 | even | 4 | 950.4.b.i.799.4 | 4 | |||
56.27 | even | 2 | 1862.4.a.e.1.2 | 2 | |||
152.75 | even | 2 | 722.4.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.a.c.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
304.4.a.c.1.2 | 2 | 8.5 | even | 2 | |||
342.4.a.h.1.1 | 2 | 24.11 | even | 2 | |||
722.4.a.f.1.2 | 2 | 152.75 | even | 2 | |||
950.4.a.e.1.2 | 2 | 40.19 | odd | 2 | |||
950.4.b.i.799.1 | 4 | 40.3 | even | 4 | |||
950.4.b.i.799.4 | 4 | 40.27 | even | 4 | |||
1216.4.a.g.1.2 | 2 | 4.3 | odd | 2 | |||
1216.4.a.p.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1862.4.a.e.1.2 | 2 | 56.27 | even | 2 |