Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
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, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 306 x^{11} - 206 x^{10} + 34574 x^{9} + 39928 x^{8} - 1788312 x^{7} - 2591628 x^{6} + \cdots + 522579400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 5^{7} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(4.62206\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.62206 | 0.640296 | 0.320148 | − | 0.947368i | \(-0.396267\pi\) | ||||
0.320148 | + | 0.947368i | \(0.396267\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −18.8807 | −0.590021 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −32.5985 | −0.369675 | ||||||||
\(7\) | 168.040 | 1.29619 | 0.648095 | − | 0.761560i | \(-0.275566\pi\) | ||||
0.648095 | + | 0.761560i | \(0.275566\pi\) | |||||||
\(8\) | −184.293 | −1.01808 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 169.926 | 0.340649 | ||||||||
\(13\) | −155.005 | −0.254383 | −0.127191 | − | 0.991878i | \(-0.540596\pi\) | ||||
−0.127191 | + | 0.991878i | \(0.540596\pi\) | |||||||
\(14\) | 608.652 | 0.829944 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −63.3377 | −0.0618532 | ||||||||
\(17\) | −426.797 | −0.358178 | −0.179089 | − | 0.983833i | \(-0.557315\pi\) | ||||
−0.179089 | + | 0.983833i | \(0.557315\pi\) | |||||||
\(18\) | 293.387 | 0.213432 | ||||||||
\(19\) | −1674.14 | −1.06392 | −0.531959 | − | 0.846770i | \(-0.678544\pi\) | ||||
−0.531959 | + | 0.846770i | \(0.678544\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1512.36 | −0.748355 | ||||||||
\(22\) | 438.269 | 0.193056 | ||||||||
\(23\) | −11.2327 | −0.00442757 | −0.00221379 | − | 0.999998i | \(-0.500705\pi\) | ||||
−0.00221379 | + | 0.999998i | \(0.500705\pi\) | |||||||
\(24\) | 1658.64 | 0.587791 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −561.437 | −0.162880 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −3172.72 | −0.764780 | ||||||||
\(29\) | −1107.81 | −0.244609 | −0.122304 | − | 0.992493i | \(-0.539028\pi\) | ||||
−0.122304 | + | 0.992493i | \(0.539028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7186.50 | 1.34312 | 0.671558 | − | 0.740952i | \(-0.265625\pi\) | ||||
0.671558 | + | 0.740952i | \(0.265625\pi\) | |||||||
\(32\) | 5667.96 | 0.978480 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −1545.88 | −0.229340 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1529.34 | −0.196674 | ||||||||
\(37\) | −4576.30 | −0.549554 | −0.274777 | − | 0.961508i | \(-0.588604\pi\) | ||||
−0.274777 | + | 0.961508i | \(0.588604\pi\) | |||||||
\(38\) | −6063.84 | −0.681222 | ||||||||
\(39\) | 1395.05 | 0.146868 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14041.6 | −1.30454 | −0.652268 | − | 0.757988i | \(-0.726182\pi\) | ||||
−0.652268 | + | 0.757988i | \(0.726182\pi\) | |||||||
\(42\) | −5477.87 | −0.479169 | ||||||||
\(43\) | 20306.0 | 1.67476 | 0.837380 | − | 0.546621i | \(-0.184086\pi\) | ||||
0.837380 | + | 0.546621i | \(0.184086\pi\) | |||||||
\(44\) | −2284.56 | −0.177898 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −40.6856 | −0.00283495 | ||||||||
\(47\) | 10551.8 | 0.696756 | 0.348378 | − | 0.937354i | \(-0.386733\pi\) | ||||
0.348378 | + | 0.937354i | \(0.386733\pi\) | |||||||
\(48\) | 570.039 | 0.0357110 | ||||||||
\(49\) | 11430.6 | 0.680107 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3841.17 | 0.206794 | ||||||||
\(52\) | 2926.60 | 0.150091 | ||||||||
\(53\) | 27069.4 | 1.32370 | 0.661849 | − | 0.749637i | \(-0.269772\pi\) | ||||
0.661849 | + | 0.749637i | \(0.269772\pi\) | |||||||
\(54\) | −2640.48 | −0.123225 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −30968.6 | −1.31963 | ||||||||
\(57\) | 15067.3 | 0.614253 | ||||||||
\(58\) | −4012.57 | −0.156622 | ||||||||
\(59\) | 22773.1 | 0.851709 | 0.425854 | − | 0.904792i | \(-0.359974\pi\) | ||||
0.425854 | + | 0.904792i | \(0.359974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −916.341 | −0.0315306 | −0.0157653 | − | 0.999876i | \(-0.505018\pi\) | ||||
−0.0157653 | + | 0.999876i | \(0.505018\pi\) | |||||||
\(62\) | 26029.9 | 0.859991 | ||||||||
\(63\) | 13611.3 | 0.432063 | ||||||||
\(64\) | 22556.5 | 0.688369 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3944.42 | −0.111461 | ||||||||
\(67\) | −25328.4 | −0.689321 | −0.344660 | − | 0.938727i | \(-0.612006\pi\) | ||||
−0.344660 | + | 0.938727i | \(0.612006\pi\) | |||||||
\(68\) | 8058.22 | 0.211333 | ||||||||
\(69\) | 101.095 | 0.00255626 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16788.6 | −0.395248 | −0.197624 | − | 0.980278i | \(-0.563323\pi\) | ||||
−0.197624 | + | 0.980278i | \(0.563323\pi\) | |||||||
\(72\) | −14927.7 | −0.339361 | ||||||||
\(73\) | −55976.9 | −1.22942 | −0.614712 | − | 0.788752i | \(-0.710728\pi\) | ||||
−0.614712 | + | 0.788752i | \(0.710728\pi\) | |||||||
\(74\) | −16575.6 | −0.351877 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 31608.9 | 0.627735 | ||||||||
\(77\) | 20332.9 | 0.390816 | ||||||||
\(78\) | 5052.94 | 0.0940389 | ||||||||
\(79\) | −47517.8 | −0.856621 | −0.428310 | − | 0.903632i | \(-0.640891\pi\) | ||||
−0.428310 | + | 0.903632i | \(0.640891\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −50859.4 | −0.835289 | ||||||||
\(83\) | −24415.3 | −0.389016 | −0.194508 | − | 0.980901i | \(-0.562311\pi\) | ||||
−0.194508 | + | 0.980901i | \(0.562311\pi\) | |||||||
\(84\) | 28554.5 | 0.441546 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 73549.4 | 1.07234 | ||||||||
\(87\) | 9970.33 | 0.141225 | ||||||||
\(88\) | −22299.4 | −0.306964 | ||||||||
\(89\) | −22081.6 | −0.295499 | −0.147749 | − | 0.989025i | \(-0.547203\pi\) | ||||
−0.147749 | + | 0.989025i | \(0.547203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26047.1 | −0.329728 | ||||||||
\(92\) | 212.082 | 0.00261236 | ||||||||
\(93\) | −64678.5 | −0.775448 | ||||||||
\(94\) | 38219.1 | 0.446130 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −51011.6 | −0.564925 | ||||||||
\(97\) | −15706.3 | −0.169490 | −0.0847449 | − | 0.996403i | \(-0.527008\pi\) | ||||
−0.0847449 | + | 0.996403i | \(0.527008\pi\) | |||||||
\(98\) | 41402.1 | 0.435469 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10765.2 | 0.105007 | 0.0525033 | − | 0.998621i | \(-0.483280\pi\) | ||||
0.0525033 | + | 0.998621i | \(0.483280\pi\) | |||||||
\(102\) | 13913.0 | 0.132409 | ||||||||
\(103\) | −28684.5 | −0.266412 | −0.133206 | − | 0.991088i | \(-0.542527\pi\) | ||||
−0.133206 | + | 0.991088i | \(0.542527\pi\) | |||||||
\(104\) | 28566.3 | 0.258983 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 98046.9 | 0.847558 | ||||||||
\(107\) | 121918. | 1.02946 | 0.514728 | − | 0.857354i | \(-0.327893\pi\) | ||||
0.514728 | + | 0.857354i | \(0.327893\pi\) | |||||||
\(108\) | 13764.0 | 0.113550 | ||||||||
\(109\) | −169782. | −1.36876 | −0.684378 | − | 0.729128i | \(-0.739926\pi\) | ||||
−0.684378 | + | 0.729128i | \(0.739926\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 41186.7 | 0.317285 | ||||||||
\(112\) | −10643.3 | −0.0801735 | ||||||||
\(113\) | −220268. | −1.62276 | −0.811380 | − | 0.584519i | \(-0.801283\pi\) | ||||
−0.811380 | + | 0.584519i | \(0.801283\pi\) | |||||||
\(114\) | 54574.6 | 0.393304 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 20916.3 | 0.144324 | ||||||||
\(117\) | −12555.4 | −0.0847942 | ||||||||
\(118\) | 82485.3 | 0.545346 | ||||||||
\(119\) | −71719.1 | −0.464267 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | −3319.04 | −0.0201889 | ||||||||
\(123\) | 126374. | 0.753174 | ||||||||
\(124\) | −135686. | −0.792467 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 49300.8 | 0.276648 | ||||||||
\(127\) | −230988. | −1.27081 | −0.635404 | − | 0.772180i | \(-0.719166\pi\) | ||||
−0.635404 | + | 0.772180i | \(0.719166\pi\) | |||||||
\(128\) | −99673.7 | −0.537720 | ||||||||
\(129\) | −182754. | −0.966923 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 175894. | 0.895513 | 0.447757 | − | 0.894155i | \(-0.352223\pi\) | ||||
0.447757 | + | 0.894155i | \(0.352223\pi\) | |||||||
\(132\) | 20561.1 | 0.102710 | ||||||||
\(133\) | −281323. | −1.37904 | ||||||||
\(134\) | −91741.1 | −0.441369 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 78655.7 | 0.364655 | ||||||||
\(137\) | −8437.54 | −0.0384073 | −0.0192037 | − | 0.999816i | \(-0.506113\pi\) | ||||
−0.0192037 | + | 0.999816i | \(0.506113\pi\) | |||||||
\(138\) | 366.170 | 0.00163676 | ||||||||
\(139\) | −75054.6 | −0.329489 | −0.164744 | − | 0.986336i | \(-0.552680\pi\) | ||||
−0.164744 | + | 0.986336i | \(0.552680\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −94965.9 | −0.402272 | ||||||||
\(142\) | −60809.5 | −0.253076 | ||||||||
\(143\) | −18755.6 | −0.0766992 | ||||||||
\(144\) | −5130.35 | −0.0206177 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −202752. | −0.787194 | ||||||||
\(147\) | −102875. | −0.392660 | ||||||||
\(148\) | 86403.7 | 0.324248 | ||||||||
\(149\) | −119523. | −0.441049 | −0.220524 | − | 0.975381i | \(-0.570777\pi\) | ||||
−0.220524 | + | 0.975381i | \(0.570777\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 372713. | 1.33025 | 0.665124 | − | 0.746733i | \(-0.268379\pi\) | ||||
0.665124 | + | 0.746733i | \(0.268379\pi\) | |||||||
\(152\) | 308532. | 1.08316 | ||||||||
\(153\) | −34570.6 | −0.119393 | ||||||||
\(154\) | 73646.9 | 0.250238 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −26339.4 | −0.0866552 | ||||||||
\(157\) | −407799. | −1.32038 | −0.660188 | − | 0.751101i | \(-0.729523\pi\) | ||||
−0.660188 | + | 0.751101i | \(0.729523\pi\) | |||||||
\(158\) | −172112. | −0.548491 | ||||||||
\(159\) | −243624. | −0.764237 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1887.55 | −0.00573897 | ||||||||
\(162\) | 23764.3 | 0.0711440 | ||||||||
\(163\) | −360328. | −1.06225 | −0.531127 | − | 0.847292i | \(-0.678231\pi\) | ||||
−0.531127 | + | 0.847292i | \(0.678231\pi\) | |||||||
\(164\) | 265115. | 0.769704 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −88433.8 | −0.249085 | ||||||||
\(167\) | −69666.3 | −0.193300 | −0.0966500 | − | 0.995318i | \(-0.530813\pi\) | ||||
−0.0966500 | + | 0.995318i | \(0.530813\pi\) | |||||||
\(168\) | 278718. | 0.761888 | ||||||||
\(169\) | −347266. | −0.935289 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −135605. | −0.354639 | ||||||||
\(172\) | −383391. | −0.988144 | ||||||||
\(173\) | −627131. | −1.59310 | −0.796550 | − | 0.604572i | \(-0.793344\pi\) | ||||
−0.796550 | + | 0.604572i | \(0.793344\pi\) | |||||||
\(174\) | 36113.1 | 0.0904257 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7663.86 | −0.0186494 | ||||||||
\(177\) | −204957. | −0.491734 | ||||||||
\(178\) | −79980.8 | −0.189206 | ||||||||
\(179\) | −662582. | −1.54564 | −0.772818 | − | 0.634628i | \(-0.781154\pi\) | ||||
−0.772818 | + | 0.634628i | \(0.781154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −525680. | −1.19268 | −0.596341 | − | 0.802731i | \(-0.703379\pi\) | ||||
−0.596341 | + | 0.802731i | \(0.703379\pi\) | |||||||
\(182\) | −94344.1 | −0.211123 | ||||||||
\(183\) | 8247.07 | 0.0182042 | ||||||||
\(184\) | 2070.11 | 0.00450764 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −234269. | −0.496516 | ||||||||
\(187\) | −51642.5 | −0.107995 | ||||||||
\(188\) | −199225. | −0.411101 | ||||||||
\(189\) | −122501. | −0.249452 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −824338. | −1.63502 | −0.817508 | − | 0.575918i | \(-0.804645\pi\) | ||||
−0.817508 | + | 0.575918i | \(0.804645\pi\) | |||||||
\(192\) | −203008. | −0.397430 | ||||||||
\(193\) | 783372. | 1.51382 | 0.756911 | − | 0.653518i | \(-0.226707\pi\) | ||||
0.756911 | + | 0.653518i | \(0.226707\pi\) | |||||||
\(194\) | −56889.0 | −0.108524 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −215817. | −0.401278 | ||||||||
\(197\) | 272361. | 0.500010 | 0.250005 | − | 0.968245i | \(-0.419568\pi\) | ||||
0.250005 | + | 0.968245i | \(0.419568\pi\) | |||||||
\(198\) | 35499.8 | 0.0643521 | ||||||||
\(199\) | 982522. | 1.75877 | 0.879386 | − | 0.476109i | \(-0.157953\pi\) | ||||
0.879386 | + | 0.476109i | \(0.157953\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 227956. | 0.397979 | ||||||||
\(202\) | 38992.0 | 0.0672353 | ||||||||
\(203\) | −186157. | −0.317059 | ||||||||
\(204\) | −72524.0 | −0.122013 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −103897. | −0.170583 | ||||||||
\(207\) | −909.851 | −0.00147586 | ||||||||
\(208\) | 9817.66 | 0.0157344 | ||||||||
\(209\) | −202571. | −0.320783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −430400. | −0.665527 | −0.332764 | − | 0.943010i | \(-0.607981\pi\) | ||||
−0.332764 | + | 0.943010i | \(0.607981\pi\) | |||||||
\(212\) | −511089. | −0.781010 | ||||||||
\(213\) | 151098. | 0.228197 | ||||||||
\(214\) | 441593. | 0.659156 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 134349. | 0.195930 | ||||||||
\(217\) | 1.20762e6 | 1.74093 | ||||||||
\(218\) | −614961. | −0.876408 | ||||||||
\(219\) | 503792. | 0.709808 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 66155.7 | 0.0911143 | ||||||||
\(222\) | 149181. | 0.203156 | ||||||||
\(223\) | −532033. | −0.716434 | −0.358217 | − | 0.933638i | \(-0.616615\pi\) | ||||
−0.358217 | + | 0.933638i | \(0.616615\pi\) | |||||||
\(224\) | 952446. | 1.26829 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −797822. | −1.03905 | ||||||||
\(227\) | −792684. | −1.02102 | −0.510512 | − | 0.859871i | \(-0.670544\pi\) | ||||
−0.510512 | + | 0.859871i | \(0.670544\pi\) | |||||||
\(228\) | −284481. | −0.362423 | ||||||||
\(229\) | 286558. | 0.361097 | 0.180549 | − | 0.983566i | \(-0.442213\pi\) | ||||
0.180549 | + | 0.983566i | \(0.442213\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −182996. | −0.225638 | ||||||||
\(232\) | 204162. | 0.249032 | ||||||||
\(233\) | −1.41434e6 | −1.70673 | −0.853366 | − | 0.521312i | \(-0.825443\pi\) | ||||
−0.853366 | + | 0.521312i | \(0.825443\pi\) | |||||||
\(234\) | −45476.4 | −0.0542934 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −429971. | −0.502527 | ||||||||
\(237\) | 427660. | 0.494570 | ||||||||
\(238\) | −259771. | −0.297268 | ||||||||
\(239\) | 1.00694e6 | 1.14028 | 0.570138 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570138 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.08716e6 | 1.20573 | 0.602866 | − | 0.797843i | \(-0.294025\pi\) | ||||
0.602866 | + | 0.797843i | \(0.294025\pi\) | |||||||
\(242\) | 53030.6 | 0.0582087 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 17301.1 | 0.0186037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 457735. | 0.482254 | ||||||||
\(247\) | 259500. | 0.270642 | ||||||||
\(248\) | −1.32442e6 | −1.36740 | ||||||||
\(249\) | 219738. | 0.224598 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 312788. | 0.313376 | 0.156688 | − | 0.987648i | \(-0.449918\pi\) | ||||
0.156688 | + | 0.987648i | \(0.449918\pi\) | |||||||
\(252\) | −256990. | −0.254927 | ||||||||
\(253\) | −1359.16 | −0.00133496 | ||||||||
\(254\) | −836652. | −0.813693 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.08283e6 | −1.03267 | ||||||||
\(257\) | −1.50645e6 | −1.42273 | −0.711366 | − | 0.702822i | \(-0.751923\pi\) | ||||
−0.711366 | + | 0.702822i | \(0.751923\pi\) | |||||||
\(258\) | −661945. | −0.619117 | ||||||||
\(259\) | −769003. | −0.712326 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −89732.9 | −0.0815362 | ||||||||
\(262\) | 637097. | 0.573393 | ||||||||
\(263\) | −189662. | −0.169079 | −0.0845397 | − | 0.996420i | \(-0.526942\pi\) | ||||
−0.0845397 | + | 0.996420i | \(0.526942\pi\) | |||||||
\(264\) | 200695. | 0.177226 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.01897e6 | −0.882993 | ||||||||
\(267\) | 198734. | 0.170606 | ||||||||
\(268\) | 478218. | 0.406714 | ||||||||
\(269\) | 1.60463e6 | 1.35206 | 0.676029 | − | 0.736875i | \(-0.263699\pi\) | ||||
0.676029 | + | 0.736875i | \(0.263699\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.71899e6 | 1.42184 | 0.710921 | − | 0.703272i | \(-0.248278\pi\) | ||||
0.710921 | + | 0.703272i | \(0.248278\pi\) | |||||||
\(272\) | 27032.3 | 0.0221545 | ||||||||
\(273\) | 234424. | 0.190369 | ||||||||
\(274\) | −30561.3 | −0.0245921 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1908.73 | −0.00150825 | ||||||||
\(277\) | −756133. | −0.592105 | −0.296053 | − | 0.955172i | \(-0.595670\pi\) | ||||
−0.296053 | + | 0.955172i | \(0.595670\pi\) | |||||||
\(278\) | −271852. | −0.210970 | ||||||||
\(279\) | 582107. | 0.447705 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 772332. | 0.583497 | 0.291748 | − | 0.956495i | \(-0.405763\pi\) | ||||
0.291748 | + | 0.956495i | \(0.405763\pi\) | |||||||
\(282\) | −343972. | −0.257573 | ||||||||
\(283\) | −1.93103e6 | −1.43325 | −0.716625 | − | 0.697458i | \(-0.754314\pi\) | ||||
−0.716625 | + | 0.697458i | \(0.754314\pi\) | |||||||
\(284\) | 316981. | 0.233205 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −67933.9 | −0.0491102 | ||||||||
\(287\) | −2.35955e6 | −1.69093 | ||||||||
\(288\) | 459105. | 0.326160 | ||||||||
\(289\) | −1.23770e6 | −0.871708 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 141356. | 0.0978550 | ||||||||
\(292\) | 1.05688e6 | 0.725386 | ||||||||
\(293\) | 1.70779e6 | 1.16216 | 0.581080 | − | 0.813847i | \(-0.302630\pi\) | ||||
0.581080 | + | 0.813847i | \(0.302630\pi\) | |||||||
\(294\) | −372619. | −0.251418 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 843379. | 0.559492 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −432920. | −0.282402 | ||||||||
\(299\) | 1741.13 | 0.00112630 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.41222e6 | 2.17081 | ||||||||
\(302\) | 1.34999e6 | 0.851752 | ||||||||
\(303\) | −96886.4 | −0.0606256 | ||||||||
\(304\) | 106036. | 0.0658068 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −125217. | −0.0764467 | ||||||||
\(307\) | 256601. | 0.155386 | 0.0776931 | − | 0.996977i | \(-0.475245\pi\) | ||||
0.0776931 | + | 0.996977i | \(0.475245\pi\) | |||||||
\(308\) | −383899. | −0.230590 | ||||||||
\(309\) | 258160. | 0.153813 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.08034e6 | 1.21964 | 0.609822 | − | 0.792539i | \(-0.291241\pi\) | ||||
0.609822 | + | 0.792539i | \(0.291241\pi\) | |||||||
\(312\) | −257097. | −0.149524 | ||||||||
\(313\) | −1.05439e6 | −0.608331 | −0.304166 | − | 0.952619i | \(-0.598378\pi\) | ||||
−0.304166 | + | 0.952619i | \(0.598378\pi\) | |||||||
\(314\) | −1.47707e6 | −0.845431 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 897169. | 0.505425 | ||||||||
\(317\) | −2.35341e6 | −1.31538 | −0.657688 | − | 0.753291i | \(-0.728465\pi\) | ||||
−0.657688 | + | 0.753291i | \(0.728465\pi\) | |||||||
\(318\) | −882422. | −0.489338 | ||||||||
\(319\) | −134045. | −0.0737523 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.09726e6 | −0.594356 | ||||||||
\(322\) | −6836.82 | −0.00367464 | ||||||||
\(323\) | 714519. | 0.381072 | ||||||||
\(324\) | −123876. | −0.0655579 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.30513e6 | −0.680157 | ||||||||
\(327\) | 1.52804e6 | 0.790251 | ||||||||
\(328\) | 2.58776e6 | 1.32813 | ||||||||
\(329\) | 1.77312e6 | 0.903127 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −376896. | −0.189083 | −0.0945414 | − | 0.995521i | \(-0.530138\pi\) | ||||
−0.0945414 | + | 0.995521i | \(0.530138\pi\) | |||||||
\(332\) | 460978. | 0.229528 | ||||||||
\(333\) | −370680. | −0.183185 | ||||||||
\(334\) | −252336. | −0.123769 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 95789.6 | 0.0462882 | ||||||||
\(337\) | 3.13928e6 | 1.50576 | 0.752879 | − | 0.658159i | \(-0.228665\pi\) | ||||
0.752879 | + | 0.658159i | \(0.228665\pi\) | |||||||
\(338\) | −1.25782e6 | −0.598862 | ||||||||
\(339\) | 1.98241e6 | 0.936901 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 869567. | 0.404965 | ||||||||
\(342\) | −491171. | −0.227074 | ||||||||
\(343\) | −903460. | −0.414642 | ||||||||
\(344\) | −3.74225e6 | −1.70505 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.27151e6 | −1.02006 | ||||||||
\(347\) | −1.74141e6 | −0.776384 | −0.388192 | − | 0.921579i | \(-0.626900\pi\) | ||||
−0.388192 | + | 0.921579i | \(0.626900\pi\) | |||||||
\(348\) | −188247. | −0.0833257 | ||||||||
\(349\) | −4.40916e6 | −1.93772 | −0.968862 | − | 0.247602i | \(-0.920357\pi\) | ||||
−0.968862 | + | 0.247602i | \(0.920357\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 112999. | 0.0489560 | ||||||||
\(352\) | 685823. | 0.295023 | ||||||||
\(353\) | −1.97624e6 | −0.844116 | −0.422058 | − | 0.906569i | \(-0.638692\pi\) | ||||
−0.422058 | + | 0.906569i | \(0.638692\pi\) | |||||||
\(354\) | −742368. | −0.314855 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 416916. | 0.174350 | ||||||||
\(357\) | 645472. | 0.268045 | ||||||||
\(358\) | −2.39991e6 | −0.989664 | ||||||||
\(359\) | 340087. | 0.139269 | 0.0696343 | − | 0.997573i | \(-0.477817\pi\) | ||||
0.0696343 | + | 0.997573i | \(0.477817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 326652. | 0.131922 | ||||||||
\(362\) | −1.90404e6 | −0.763669 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 491787. | 0.194547 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 29871.4 | 0.0116561 | ||||||||
\(367\) | −3.60337e6 | −1.39651 | −0.698254 | − | 0.715850i | \(-0.746039\pi\) | ||||
−0.698254 | + | 0.715850i | \(0.746039\pi\) | |||||||
\(368\) | 711.455 | 0.000273859 0 | ||||||||
\(369\) | −1.13737e6 | −0.434845 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.54875e6 | 1.71576 | ||||||||
\(372\) | 1.22118e6 | 0.457531 | ||||||||
\(373\) | −1.94994e6 | −0.725687 | −0.362844 | − | 0.931850i | \(-0.618194\pi\) | ||||
−0.362844 | + | 0.931850i | \(0.618194\pi\) | |||||||
\(374\) | −187052. | −0.0691486 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.94462e6 | −0.709356 | ||||||||
\(377\) | 171717. | 0.0622242 | ||||||||
\(378\) | −443707. | −0.159723 | ||||||||
\(379\) | 2.15699e6 | 0.771349 | 0.385674 | − | 0.922635i | \(-0.373969\pi\) | ||||
0.385674 | + | 0.922635i | \(0.373969\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.07889e6 | 0.733701 | ||||||||
\(382\) | −2.98580e6 | −1.04689 | ||||||||
\(383\) | 1.66805e6 | 0.581049 | 0.290525 | − | 0.956868i | \(-0.406170\pi\) | ||||
0.290525 | + | 0.956868i | \(0.406170\pi\) | |||||||
\(384\) | 897064. | 0.310453 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.83742e6 | 0.969294 | ||||||||
\(387\) | 1.64478e6 | 0.558253 | ||||||||
\(388\) | 296545. | 0.100003 | ||||||||
\(389\) | 1.58917e6 | 0.532473 | 0.266236 | − | 0.963908i | \(-0.414220\pi\) | ||||
0.266236 | + | 0.963908i | \(0.414220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4794.09 | 0.00158586 | ||||||||
\(392\) | −2.10657e6 | −0.692406 | ||||||||
\(393\) | −1.58304e6 | −0.517025 | ||||||||
\(394\) | 986506. | 0.320154 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −185050. | −0.0592994 | ||||||||
\(397\) | 4.07780e6 | 1.29852 | 0.649261 | − | 0.760566i | \(-0.275078\pi\) | ||||
0.649261 | + | 0.760566i | \(0.275078\pi\) | |||||||
\(398\) | 3.55875e6 | 1.12613 | ||||||||
\(399\) | 2.53191e6 | 0.796189 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.89367e6 | −1.51976 | −0.759878 | − | 0.650066i | \(-0.774741\pi\) | ||||
−0.759878 | + | 0.650066i | \(0.774741\pi\) | |||||||
\(402\) | 825670. | 0.254824 | ||||||||
\(403\) | −1.11394e6 | −0.341665 | ||||||||
\(404\) | −203254. | −0.0619562 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −674273. | −0.203012 | ||||||||
\(407\) | −553732. | −0.165697 | ||||||||
\(408\) | −707901. | −0.210534 | ||||||||
\(409\) | 508943. | 0.150439 | 0.0752196 | − | 0.997167i | \(-0.476034\pi\) | ||||
0.0752196 | + | 0.997167i | \(0.476034\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 75937.8 | 0.0221745 | ||||||||
\(412\) | 541583. | 0.157189 | ||||||||
\(413\) | 3.82679e6 | 1.10398 | ||||||||
\(414\) | −3295.53 | −0.000944985 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −878562. | −0.248908 | ||||||||
\(417\) | 675492. | 0.190230 | ||||||||
\(418\) | −733725. | −0.205396 | ||||||||
\(419\) | 6.78930e6 | 1.88925 | 0.944626 | − | 0.328148i | \(-0.106425\pi\) | ||||
0.944626 | + | 0.328148i | \(0.106425\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.93204e6 | −1.08122 | −0.540608 | − | 0.841275i | \(-0.681806\pi\) | ||||
−0.540608 | + | 0.841275i | \(0.681806\pi\) | |||||||
\(422\) | −1.55893e6 | −0.426134 | ||||||||
\(423\) | 854693. | 0.232252 | ||||||||
\(424\) | −4.98869e6 | −1.34764 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 547285. | 0.146113 | ||||||||
\(427\) | −153982. | −0.0408697 | ||||||||
\(428\) | −2.30189e6 | −0.607401 | ||||||||
\(429\) | 168800. | 0.0442823 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.24173e6 | −0.840589 | −0.420295 | − | 0.907388i | \(-0.638073\pi\) | ||||
−0.420295 | + | 0.907388i | \(0.638073\pi\) | |||||||
\(432\) | 46173.2 | 0.0119037 | ||||||||
\(433\) | −5.96730e6 | −1.52953 | −0.764765 | − | 0.644309i | \(-0.777145\pi\) | ||||
−0.764765 | + | 0.644309i | \(0.777145\pi\) | |||||||
\(434\) | 4.37408e6 | 1.11471 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.20560e6 | 0.807595 | ||||||||
\(437\) | 18805.2 | 0.00471057 | ||||||||
\(438\) | 1.82476e6 | 0.454487 | ||||||||
\(439\) | 2.85969e6 | 0.708203 | 0.354101 | − | 0.935207i | \(-0.384787\pi\) | ||||
0.354101 | + | 0.935207i | \(0.384787\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 925875. | 0.226702 | ||||||||
\(442\) | 239620. | 0.0583401 | ||||||||
\(443\) | 2.52822e6 | 0.612077 | 0.306038 | − | 0.952019i | \(-0.400996\pi\) | ||||
0.306038 | + | 0.952019i | \(0.400996\pi\) | |||||||
\(444\) | −777633. | −0.187205 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.92705e6 | −0.458730 | ||||||||
\(447\) | 1.07571e6 | 0.254640 | ||||||||
\(448\) | 3.79040e6 | 0.892257 | ||||||||
\(449\) | 5.72753e6 | 1.34076 | 0.670380 | − | 0.742018i | \(-0.266131\pi\) | ||||
0.670380 | + | 0.742018i | \(0.266131\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.69903e6 | −0.393333 | ||||||||
\(452\) | 4.15880e6 | 0.957464 | ||||||||
\(453\) | −3.35442e6 | −0.768019 | ||||||||
\(454\) | −2.87115e6 | −0.653757 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.77679e6 | −0.625362 | ||||||||
\(457\) | −4.94045e6 | −1.10656 | −0.553281 | − | 0.832994i | \(-0.686625\pi\) | ||||
−0.553281 | + | 0.832994i | \(0.686625\pi\) | |||||||
\(458\) | 1.03793e6 | 0.231209 | ||||||||
\(459\) | 311135. | 0.0689314 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.18580e6 | 1.35564 | 0.677818 | − | 0.735229i | \(-0.262926\pi\) | ||||
0.677818 | + | 0.735229i | \(0.262926\pi\) | |||||||
\(462\) | −662822. | −0.144475 | ||||||||
\(463\) | −1.23230e6 | −0.267155 | −0.133577 | − | 0.991038i | \(-0.542646\pi\) | ||||
−0.133577 | + | 0.991038i | \(0.542646\pi\) | |||||||
\(464\) | 70166.4 | 0.0151298 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.12284e6 | −1.09281 | ||||||||
\(467\) | −7.74380e6 | −1.64309 | −0.821546 | − | 0.570142i | \(-0.806888\pi\) | ||||
−0.821546 | + | 0.570142i | \(0.806888\pi\) | |||||||
\(468\) | 237055. | 0.0500304 | ||||||||
\(469\) | −4.25620e6 | −0.893490 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.67019e6 | 0.762319 | ||||||||
\(472\) | −4.19691e6 | −0.867111 | ||||||||
\(473\) | 2.45702e6 | 0.504959 | ||||||||
\(474\) | 1.54901e6 | 0.316671 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.35411e6 | 0.273927 | ||||||||
\(477\) | 2.19262e6 | 0.441233 | ||||||||
\(478\) | 3.64721e6 | 0.730114 | ||||||||
\(479\) | −3.36135e6 | −0.669384 | −0.334692 | − | 0.942328i | \(-0.608632\pi\) | ||||
−0.334692 | + | 0.942328i | \(0.608632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 709349. | 0.139797 | ||||||||
\(482\) | 3.93776e6 | 0.772025 | ||||||||
\(483\) | 16988.0 | 0.00331340 | ||||||||
\(484\) | −276432. | −0.0536383 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −213879. | −0.0410750 | ||||||||
\(487\) | 397760. | 0.0759973 | 0.0379987 | − | 0.999278i | \(-0.487902\pi\) | ||||
0.0379987 | + | 0.999278i | \(0.487902\pi\) | |||||||
\(488\) | 168875. | 0.0321008 | ||||||||
\(489\) | 3.24295e6 | 0.613293 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −585823. | −0.109664 | −0.0548318 | − | 0.998496i | \(-0.517462\pi\) | ||||
−0.0548318 | + | 0.998496i | \(0.517462\pi\) | |||||||
\(492\) | −2.38603e6 | −0.444389 | ||||||||
\(493\) | 472812. | 0.0876135 | ||||||||
\(494\) | 939926. | 0.173291 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −455177. | −0.0830760 | ||||||||
\(497\) | −2.82117e6 | −0.512316 | ||||||||
\(498\) | 795904. | 0.143809 | ||||||||
\(499\) | 7.82230e6 | 1.40632 | 0.703158 | − | 0.711034i | \(-0.251773\pi\) | ||||
0.703158 | + | 0.711034i | \(0.251773\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 626997. | 0.111602 | ||||||||
\(502\) | 1.13294e6 | 0.200653 | ||||||||
\(503\) | 4.04320e6 | 0.712534 | 0.356267 | − | 0.934384i | \(-0.384049\pi\) | ||||
0.356267 | + | 0.934384i | \(0.384049\pi\) | |||||||
\(504\) | −2.50846e6 | −0.439876 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4922.96 | −0.000854771 0 | ||||||||
\(507\) | 3.12540e6 | 0.539990 | ||||||||
\(508\) | 4.36121e6 | 0.749804 | ||||||||
\(509\) | −1.07585e7 | −1.84060 | −0.920299 | − | 0.391216i | \(-0.872054\pi\) | ||||
−0.920299 | + | 0.391216i | \(0.872054\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.40637e6 | −1.59357 | ||||||||
\(512\) | −732521. | −0.123494 | ||||||||
\(513\) | 1.22045e6 | 0.204751 | ||||||||
\(514\) | −5.45646e6 | −0.910969 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.45052e6 | 0.570505 | ||||||||
\(517\) | 1.27676e6 | 0.210080 | ||||||||
\(518\) | −2.78537e6 | −0.456099 | ||||||||
\(519\) | 5.64418e6 | 0.919777 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.48830e6 | −0.563014 | −0.281507 | − | 0.959559i | \(-0.590834\pi\) | ||||
−0.281507 | + | 0.959559i | \(0.590834\pi\) | |||||||
\(522\) | −325018. | −0.0522073 | ||||||||
\(523\) | 5.47692e6 | 0.875552 | 0.437776 | − | 0.899084i | \(-0.355766\pi\) | ||||
0.437776 | + | 0.899084i | \(0.355766\pi\) | |||||||
\(524\) | −3.32099e6 | −0.528372 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −686967. | −0.108261 | ||||||||
\(527\) | −3.06718e6 | −0.481075 | ||||||||
\(528\) | 68974.7 | 0.0107673 | ||||||||
\(529\) | −6.43622e6 | −0.999980 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.84462e6 | 0.283903 | ||||||||
\(532\) | 5.31158e6 | 0.813663 | ||||||||
\(533\) | 2.17651e6 | 0.331851 | ||||||||
\(534\) | 719828. | 0.109238 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.66785e6 | 0.701786 | ||||||||
\(537\) | 5.96324e6 | 0.892374 | ||||||||
\(538\) | 5.81208e6 | 0.865717 | ||||||||
\(539\) | 1.38310e6 | 0.205060 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.78523e6 | −1.14361 | −0.571806 | − | 0.820389i | \(-0.693757\pi\) | ||||
−0.571806 | + | 0.820389i | \(0.693757\pi\) | |||||||
\(542\) | 6.22630e6 | 0.910399 | ||||||||
\(543\) | 4.73112e6 | 0.688596 | ||||||||
\(544\) | −2.41907e6 | −0.350470 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 849097. | 0.121892 | ||||||||
\(547\) | 3.92034e6 | 0.560215 | 0.280108 | − | 0.959969i | \(-0.409630\pi\) | ||||
0.280108 | + | 0.959969i | \(0.409630\pi\) | |||||||
\(548\) | 159307. | 0.0226612 | ||||||||
\(549\) | −74223.6 | −0.0105102 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.85464e6 | 0.260244 | ||||||||
\(552\) | −18631.0 | −0.00260249 | ||||||||
\(553\) | −7.98491e6 | −1.11034 | ||||||||
\(554\) | −2.73876e6 | −0.379122 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.41708e6 | 0.194405 | ||||||||
\(557\) | 5.56520e6 | 0.760051 | 0.380026 | − | 0.924976i | \(-0.375915\pi\) | ||||
0.380026 | + | 0.924976i | \(0.375915\pi\) | |||||||
\(558\) | 2.10843e6 | 0.286664 | ||||||||
\(559\) | −3.14753e6 | −0.426030 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 464782. | 0.0623508 | ||||||||
\(562\) | 2.79743e6 | 0.373610 | ||||||||
\(563\) | −6.49216e6 | −0.863213 | −0.431607 | − | 0.902062i | \(-0.642053\pi\) | ||||
−0.431607 | + | 0.902062i | \(0.642053\pi\) | |||||||
\(564\) | 1.79302e6 | 0.237349 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.99429e6 | −0.917704 | ||||||||
\(567\) | 1.10251e6 | 0.144021 | ||||||||
\(568\) | 3.09403e6 | 0.402396 | ||||||||
\(569\) | −1.02437e7 | −1.32641 | −0.663204 | − | 0.748439i | \(-0.730804\pi\) | ||||
−0.663204 | + | 0.748439i | \(0.730804\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.42962e7 | −1.83498 | −0.917488 | − | 0.397764i | \(-0.869786\pi\) | ||||
−0.917488 | + | 0.397764i | \(0.869786\pi\) | |||||||
\(572\) | 354119. | 0.0452542 | ||||||||
\(573\) | 7.41904e6 | 0.943976 | ||||||||
\(574\) | −8.54643e6 | −1.08269 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.82708e6 | 0.229456 | ||||||||
\(577\) | −5.37436e6 | −0.672027 | −0.336014 | − | 0.941857i | \(-0.609079\pi\) | ||||
−0.336014 | + | 0.941857i | \(0.609079\pi\) | |||||||
\(578\) | −4.48303e6 | −0.558151 | ||||||||
\(579\) | −7.05035e6 | −0.874006 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.10276e6 | −0.504238 | ||||||||
\(582\) | 512001. | 0.0626561 | ||||||||
\(583\) | 3.27540e6 | 0.399110 | ||||||||
\(584\) | 1.03161e7 | 1.25166 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.18572e6 | 0.744126 | ||||||||
\(587\) | 1.17715e7 | 1.41006 | 0.705030 | − | 0.709178i | \(-0.250934\pi\) | ||||
0.705030 | + | 0.709178i | \(0.250934\pi\) | |||||||
\(588\) | 1.94235e6 | 0.231678 | ||||||||
\(589\) | −1.20312e7 | −1.42897 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.45125e6 | −0.288681 | ||||||||
\(592\) | 289852. | 0.0339917 | ||||||||
\(593\) | −3.16466e6 | −0.369564 | −0.184782 | − | 0.982780i | \(-0.559158\pi\) | ||||
−0.184782 | + | 0.982780i | \(0.559158\pi\) | |||||||
\(594\) | −319498. | −0.0371537 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.25668e6 | 0.260228 | ||||||||
\(597\) | −8.84270e6 | −1.01543 | ||||||||
\(598\) | 6306.47 | 0.000721163 0 | ||||||||
\(599\) | 4.34303e6 | 0.494567 | 0.247284 | − | 0.968943i | \(-0.420462\pi\) | ||||
0.247284 | + | 0.968943i | \(0.420462\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.05946e6 | 0.910165 | 0.455082 | − | 0.890449i | \(-0.349610\pi\) | ||||
0.455082 | + | 0.890449i | \(0.349610\pi\) | |||||||
\(602\) | 1.23593e7 | 1.38996 | ||||||||
\(603\) | −2.05160e6 | −0.229774 | ||||||||
\(604\) | −7.03708e6 | −0.784874 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −350928. | −0.0388183 | ||||||||
\(607\) | −284560. | −0.0313475 | −0.0156737 | − | 0.999877i | \(-0.504989\pi\) | ||||
−0.0156737 | + | 0.999877i | \(0.504989\pi\) | |||||||
\(608\) | −9.48897e6 | −1.04102 | ||||||||
\(609\) | 1.67542e6 | 0.183054 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.63558e6 | −0.177243 | ||||||||
\(612\) | 652716. | 0.0704443 | ||||||||
\(613\) | 1.43183e7 | 1.53901 | 0.769503 | − | 0.638644i | \(-0.220504\pi\) | ||||
0.769503 | + | 0.638644i | \(0.220504\pi\) | |||||||
\(614\) | 929424. | 0.0994931 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.74720e6 | −0.397883 | ||||||||
\(617\) | −1.35489e7 | −1.43282 | −0.716411 | − | 0.697679i | \(-0.754216\pi\) | ||||
−0.716411 | + | 0.697679i | \(0.754216\pi\) | |||||||
\(618\) | 935072. | 0.0984859 | ||||||||
\(619\) | −1.25027e7 | −1.31152 | −0.655762 | − | 0.754968i | \(-0.727652\pi\) | ||||
−0.655762 | + | 0.754968i | \(0.727652\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8188.65 | 0.000852086 0 | ||||||||
\(622\) | 7.53511e6 | 0.780932 | ||||||||
\(623\) | −3.71060e6 | −0.383022 | ||||||||
\(624\) | −88358.9 | −0.00908425 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.81906e6 | −0.389512 | ||||||||
\(627\) | 1.82314e6 | 0.185204 | ||||||||
\(628\) | 7.69953e6 | 0.779050 | ||||||||
\(629\) | 1.95315e6 | 0.196838 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 272233. | 0.0272187 | 0.0136093 | − | 0.999907i | \(-0.495668\pi\) | ||||
0.0136093 | + | 0.999907i | \(0.495668\pi\) | |||||||
\(632\) | 8.75719e6 | 0.872112 | ||||||||
\(633\) | 3.87360e6 | 0.384242 | ||||||||
\(634\) | −8.52419e6 | −0.842229 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.59980e6 | 0.450916 | ||||||||
\(637\) | −1.77179e6 | −0.173007 | ||||||||
\(638\) | −485521. | −0.0472233 | ||||||||
\(639\) | −1.35988e6 | −0.131749 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.57242e7 | 1.51156 | 0.755779 | − | 0.654827i | \(-0.227258\pi\) | ||||
0.755779 | + | 0.654827i | \(0.227258\pi\) | |||||||
\(642\) | −3.97434e6 | −0.380564 | ||||||||
\(643\) | 5.47692e6 | 0.522407 | 0.261203 | − | 0.965284i | \(-0.415881\pi\) | ||||
0.261203 | + | 0.965284i | \(0.415881\pi\) | |||||||
\(644\) | 35638.2 | 0.00338611 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.58803e6 | 0.243999 | ||||||||
\(647\) | 3.91671e6 | 0.367841 | 0.183921 | − | 0.982941i | \(-0.441121\pi\) | ||||
0.183921 | + | 0.982941i | \(0.441121\pi\) | |||||||
\(648\) | −1.20915e6 | −0.113120 | ||||||||
\(649\) | 2.75554e6 | 0.256800 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.08686e7 | −1.00513 | ||||||||
\(652\) | 6.80323e6 | 0.626753 | ||||||||
\(653\) | 1.51457e7 | 1.38997 | 0.694985 | − | 0.719024i | \(-0.255411\pi\) | ||||
0.694985 | + | 0.719024i | \(0.255411\pi\) | |||||||
\(654\) | 5.53465e6 | 0.505995 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 889361. | 0.0806898 | ||||||||
\(657\) | −4.53413e6 | −0.409808 | ||||||||
\(658\) | 6.42235e6 | 0.578269 | ||||||||
\(659\) | 1.56274e6 | 0.140176 | 0.0700880 | − | 0.997541i | \(-0.477672\pi\) | ||||
0.0700880 | + | 0.997541i | \(0.477672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.33712e7 | 1.19033 | 0.595163 | − | 0.803605i | \(-0.297088\pi\) | ||||
0.595163 | + | 0.803605i | \(0.297088\pi\) | |||||||
\(662\) | −1.36514e6 | −0.121069 | ||||||||
\(663\) | −595401. | −0.0526049 | ||||||||
\(664\) | 4.49957e6 | 0.396051 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.34263e6 | −0.117292 | ||||||||
\(667\) | 12443.8 | 0.00108302 | ||||||||
\(668\) | 1.31535e6 | 0.114051 | ||||||||
\(669\) | 4.78829e6 | 0.413633 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −110877. | −0.00950684 | ||||||||
\(672\) | −8.57201e6 | −0.732250 | ||||||||
\(673\) | 1.30303e7 | 1.10896 | 0.554481 | − | 0.832196i | \(-0.312917\pi\) | ||||
0.554481 | + | 0.832196i | \(0.312917\pi\) | |||||||
\(674\) | 1.13707e7 | 0.964130 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.55663e6 | 0.551841 | ||||||||
\(677\) | −1.20799e7 | −1.01296 | −0.506478 | − | 0.862253i | \(-0.669053\pi\) | ||||
−0.506478 | + | 0.862253i | \(0.669053\pi\) | |||||||
\(678\) | 7.18040e6 | 0.599894 | ||||||||
\(679\) | −2.63929e6 | −0.219691 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.13416e6 | 0.589488 | ||||||||
\(682\) | 3.14962e6 | 0.259297 | ||||||||
\(683\) | 1.84029e7 | 1.50950 | 0.754752 | − | 0.656011i | \(-0.227757\pi\) | ||||
0.754752 | + | 0.656011i | \(0.227757\pi\) | |||||||
\(684\) | 2.56032e6 | 0.209245 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.27238e6 | −0.265494 | ||||||||
\(687\) | −2.57903e6 | −0.208480 | ||||||||
\(688\) | −1.28613e6 | −0.103589 | ||||||||
\(689\) | −4.19589e6 | −0.336726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.23001e6 | 0.416684 | 0.208342 | − | 0.978056i | \(-0.433193\pi\) | ||||
0.208342 | + | 0.978056i | \(0.433193\pi\) | |||||||
\(692\) | 1.18407e7 | 0.939963 | ||||||||
\(693\) | 1.64696e6 | 0.130272 | ||||||||
\(694\) | −6.30748e6 | −0.497115 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.83746e6 | −0.143779 | ||||||||
\(697\) | 5.99290e6 | 0.467257 | ||||||||
\(698\) | −1.59702e7 | −1.24072 | ||||||||
\(699\) | 1.27291e7 | 0.985382 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.83055e6 | 0.371280 | 0.185640 | − | 0.982618i | \(-0.440564\pi\) | ||||
0.185640 | + | 0.982618i | \(0.440564\pi\) | |||||||
\(702\) | 409288. | 0.0313463 | ||||||||
\(703\) | 7.66137e6 | 0.584680 | ||||||||
\(704\) | 2.72934e6 | 0.207551 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.15804e6 | −0.540484 | ||||||||
\(707\) | 1.80898e6 | 0.136109 | ||||||||
\(708\) | 3.86974e6 | 0.290134 | ||||||||
\(709\) | −6.13980e6 | −0.458711 | −0.229355 | − | 0.973343i | \(-0.573662\pi\) | ||||
−0.229355 | + | 0.973343i | \(0.573662\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.84894e6 | −0.285540 | ||||||||
\(712\) | 4.06948e6 | 0.300842 | ||||||||
\(713\) | −80724.0 | −0.00594674 | ||||||||
\(714\) | 2.33794e6 | 0.171628 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.25100e7 | 0.911959 | ||||||||
\(717\) | −9.06249e6 | −0.658339 | ||||||||
\(718\) | 1.23181e6 | 0.0891731 | ||||||||
\(719\) | 1.31130e7 | 0.945974 | 0.472987 | − | 0.881069i | \(-0.343176\pi\) | ||||
0.472987 | + | 0.881069i | \(0.343176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.82015e6 | −0.345321 | ||||||||
\(722\) | 1.18315e6 | 0.0844690 | ||||||||
\(723\) | −9.78444e6 | −0.696130 | ||||||||
\(724\) | 9.92520e6 | 0.703708 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −477275. | −0.0336068 | ||||||||
\(727\) | −2.62296e7 | −1.84059 | −0.920293 | − | 0.391229i | \(-0.872050\pi\) | ||||
−0.920293 | + | 0.391229i | \(0.872050\pi\) | |||||||
\(728\) | 4.80029e6 | 0.335691 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.66653e6 | −0.599863 | ||||||||
\(732\) | −155710. | −0.0107409 | ||||||||
\(733\) | 261993. | 0.0180106 | 0.00900532 | − | 0.999959i | \(-0.497133\pi\) | ||||
0.00900532 | + | 0.999959i | \(0.497133\pi\) | |||||||
\(734\) | −1.30516e7 | −0.894178 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −63666.6 | −0.00433229 | ||||||||
\(737\) | −3.06474e6 | −0.207838 | ||||||||
\(738\) | −4.11961e6 | −0.278430 | ||||||||
\(739\) | 2.14527e7 | 1.44501 | 0.722506 | − | 0.691365i | \(-0.242990\pi\) | ||||
0.722506 | + | 0.691365i | \(0.242990\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.33550e6 | −0.156255 | ||||||||
\(742\) | 1.64758e7 | 1.09860 | ||||||||
\(743\) | −1.11848e7 | −0.743283 | −0.371642 | − | 0.928376i | \(-0.621205\pi\) | ||||
−0.371642 | + | 0.928376i | \(0.621205\pi\) | |||||||
\(744\) | 1.19198e7 | 0.789471 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.06280e6 | −0.464654 | ||||||||
\(747\) | −1.97764e6 | −0.129672 | ||||||||
\(748\) | 975045. | 0.0637192 | ||||||||
\(749\) | 2.04871e7 | 1.33437 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.63342e6 | 0.364479 | 0.182239 | − | 0.983254i | \(-0.441665\pi\) | ||||
0.182239 | + | 0.983254i | \(0.441665\pi\) | |||||||
\(752\) | −668325. | −0.0430966 | ||||||||
\(753\) | −2.81509e6 | −0.180928 | ||||||||
\(754\) | 621968. | 0.0398419 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.31291e6 | 0.147182 | ||||||||
\(757\) | 7.69867e6 | 0.488288 | 0.244144 | − | 0.969739i | \(-0.421493\pi\) | ||||
0.244144 | + | 0.969739i | \(0.421493\pi\) | |||||||
\(758\) | 7.81276e6 | 0.493891 | ||||||||
\(759\) | 12232.4 | 0.000770741 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.39899e7 | 1.50164 | 0.750822 | − | 0.660505i | \(-0.229658\pi\) | ||||
0.750822 | + | 0.660505i | \(0.229658\pi\) | |||||||
\(762\) | 7.52987e6 | 0.469786 | ||||||||
\(763\) | −2.85303e7 | −1.77417 | ||||||||
\(764\) | 1.55641e7 | 0.964694 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.04179e6 | 0.372043 | ||||||||
\(767\) | −3.52994e6 | −0.216660 | ||||||||
\(768\) | 9.74549e6 | 0.596212 | ||||||||
\(769\) | −2.03436e7 | −1.24054 | −0.620272 | − | 0.784387i | \(-0.712978\pi\) | ||||
−0.620272 | + | 0.784387i | \(0.712978\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.35581e7 | 0.821415 | ||||||||
\(772\) | −1.47906e7 | −0.893188 | ||||||||
\(773\) | 1.86605e7 | 1.12324 | 0.561622 | − | 0.827394i | \(-0.310178\pi\) | ||||
0.561622 | + | 0.827394i | \(0.310178\pi\) | |||||||
\(774\) | 5.95750e6 | 0.357447 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.89455e6 | 0.172555 | ||||||||
\(777\) | 6.92102e6 | 0.411261 | ||||||||
\(778\) | 5.75608e6 | 0.340940 | ||||||||
\(779\) | 2.35076e7 | 1.38792 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.03143e6 | −0.119172 | ||||||||
\(782\) | 17364.5 | 0.00101542 | ||||||||
\(783\) | 807596. | 0.0470750 | ||||||||
\(784\) | −723985. | −0.0420668 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.73388e6 | −0.331049 | ||||||||
\(787\) | 2.98644e7 | 1.71877 | 0.859383 | − | 0.511333i | \(-0.170848\pi\) | ||||
0.859383 | + | 0.511333i | \(0.170848\pi\) | |||||||
\(788\) | −5.14235e6 | −0.295017 | ||||||||
\(789\) | 1.70696e6 | 0.0976180 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.70138e7 | −2.10341 | ||||||||
\(792\) | −1.80625e6 | −0.102321 | ||||||||
\(793\) | 142037. | 0.00802084 | ||||||||
\(794\) | 1.47700e7 | 0.831438 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.85507e7 | −1.03771 | ||||||||
\(797\) | 2.60350e7 | 1.45182 | 0.725909 | − | 0.687791i | \(-0.241419\pi\) | ||||
0.725909 | + | 0.687791i | \(0.241419\pi\) | |||||||
\(798\) | 9.17073e6 | 0.509796 | ||||||||
\(799\) | −4.50346e6 | −0.249563 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.78861e6 | −0.0984995 | ||||||||
\(802\) | −1.77252e7 | −0.973093 | ||||||||
\(803\) | −6.77320e6 | −0.370685 | ||||||||
\(804\) | −4.30396e6 | −0.234816 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.03477e6 | −0.218767 | ||||||||
\(807\) | −1.44417e7 | −0.780611 | ||||||||
\(808\) | −1.98394e6 | −0.106906 | ||||||||
\(809\) | −1.97670e7 | −1.06186 | −0.530932 | − | 0.847414i | \(-0.678158\pi\) | ||||
−0.530932 | + | 0.847414i | \(0.678158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.26108e6 | 0.387658 | 0.193829 | − | 0.981035i | \(-0.437909\pi\) | ||||
0.193829 | + | 0.981035i | \(0.437909\pi\) | |||||||
\(812\) | 3.51478e6 | 0.187072 | ||||||||
\(813\) | −1.54710e7 | −0.820901 | ||||||||
\(814\) | −2.00565e6 | −0.106095 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −243291. | −0.0127909 | ||||||||
\(817\) | −3.39951e7 | −1.78181 | ||||||||
\(818\) | 1.84342e6 | 0.0963256 | ||||||||
\(819\) | −2.10981e6 | −0.109909 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.10030e7 | 1.60526 | 0.802631 | − | 0.596476i | \(-0.203433\pi\) | ||||
0.802631 | + | 0.596476i | \(0.203433\pi\) | |||||||
\(822\) | 275051. | 0.0141982 | ||||||||
\(823\) | −2.56767e7 | −1.32142 | −0.660709 | − | 0.750643i | \(-0.729744\pi\) | ||||
−0.660709 | + | 0.750643i | \(0.729744\pi\) | |||||||
\(824\) | 5.28635e6 | 0.271230 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.38609e7 | 0.706871 | ||||||||
\(827\) | −1.60345e7 | −0.815254 | −0.407627 | − | 0.913149i | \(-0.633644\pi\) | ||||
−0.407627 | + | 0.913149i | \(0.633644\pi\) | |||||||
\(828\) | 17178.6 | 0.000870787 0 | ||||||||
\(829\) | −1.90352e7 | −0.961992 | −0.480996 | − | 0.876723i | \(-0.659725\pi\) | ||||
−0.480996 | + | 0.876723i | \(0.659725\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.80520e6 | 0.341852 | ||||||||
\(832\) | −3.49637e6 | −0.175109 | ||||||||
\(833\) | −4.87853e6 | −0.243599 | ||||||||
\(834\) | 2.44667e6 | 0.121804 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.82468e6 | 0.189269 | ||||||||
\(837\) | −5.23896e6 | −0.258483 | ||||||||
\(838\) | 2.45912e7 | 1.20968 | ||||||||
\(839\) | 2.86604e7 | 1.40565 | 0.702826 | − | 0.711362i | \(-0.251921\pi\) | ||||
0.702826 | + | 0.711362i | \(0.251921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.92839e7 | −0.940167 | ||||||||
\(842\) | −1.42421e7 | −0.692297 | ||||||||
\(843\) | −6.95099e6 | −0.336882 | ||||||||
\(844\) | 8.12625e6 | 0.392676 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.09575e6 | 0.148710 | ||||||||
\(847\) | 2.46028e6 | 0.117835 | ||||||||
\(848\) | −1.71451e6 | −0.0818749 | ||||||||
\(849\) | 1.73792e7 | 0.827488 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51404.3 | 0.00243319 | ||||||||
\(852\) | −2.85283e6 | −0.134641 | ||||||||
\(853\) | −5.22750e6 | −0.245992 | −0.122996 | − | 0.992407i | \(-0.539250\pi\) | ||||
−0.122996 | + | 0.992407i | \(0.539250\pi\) | |||||||
\(854\) | −557733. | −0.0261687 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.24686e7 | −1.04807 | ||||||||
\(857\) | −9.88397e6 | −0.459705 | −0.229853 | − | 0.973225i | \(-0.573824\pi\) | ||||
−0.229853 | + | 0.973225i | \(0.573824\pi\) | |||||||
\(858\) | 611405. | 0.0283538 | ||||||||
\(859\) | −1.37127e7 | −0.634076 | −0.317038 | − | 0.948413i | \(-0.602688\pi\) | ||||
−0.317038 | + | 0.948413i | \(0.602688\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.12360e7 | 0.976257 | ||||||||
\(862\) | −1.17417e7 | −0.538226 | ||||||||
\(863\) | 3.39850e7 | 1.55332 | 0.776659 | − | 0.629921i | \(-0.216913\pi\) | ||||
0.776659 | + | 0.629921i | \(0.216913\pi\) | |||||||
\(864\) | −4.13194e6 | −0.188308 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.16139e7 | −0.979352 | ||||||||
\(867\) | 1.11393e7 | 0.503281 | ||||||||
\(868\) | −2.28007e7 | −1.02719 | ||||||||
\(869\) | −5.74965e6 | −0.258281 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.92603e6 | 0.175351 | ||||||||
\(872\) | 3.12896e7 | 1.39351 | ||||||||
\(873\) | −1.27221e6 | −0.0564966 | ||||||||
\(874\) | 68113.4 | 0.00301616 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9.51193e6 | −0.418802 | ||||||||
\(877\) | 1.66649e7 | 0.731653 | 0.365826 | − | 0.930683i | \(-0.380786\pi\) | ||||
0.365826 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(878\) | 1.03580e7 | 0.453459 | ||||||||
\(879\) | −1.53701e7 | −0.670973 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.85938e7 | −0.807103 | −0.403551 | − | 0.914957i | \(-0.632224\pi\) | ||||
−0.403551 | + | 0.914957i | \(0.632224\pi\) | |||||||
\(882\) | 3.35357e6 | 0.145156 | ||||||||
\(883\) | −1.41760e7 | −0.611859 | −0.305929 | − | 0.952054i | \(-0.598967\pi\) | ||||
−0.305929 | + | 0.952054i | \(0.598967\pi\) | |||||||
\(884\) | −1.24907e6 | −0.0537594 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.15737e6 | 0.391910 | ||||||||
\(887\) | −1.10264e7 | −0.470570 | −0.235285 | − | 0.971926i | \(-0.575602\pi\) | ||||
−0.235285 | + | 0.971926i | \(0.575602\pi\) | |||||||
\(888\) | −7.59041e6 | −0.323023 | ||||||||
\(889\) | −3.88153e7 | −1.64721 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 1.00451e7 | 0.422711 | ||||||||
\(893\) | −1.76652e7 | −0.741291 | ||||||||
\(894\) | 3.89628e6 | 0.163045 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.67492e7 | −0.696986 | ||||||||
\(897\) | −15670.2 | −0.000650268 0 | ||||||||
\(898\) | 2.07454e7 | 0.858483 | ||||||||
\(899\) | −7.96131e6 | −0.328538 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.15531e7 | −0.474120 | ||||||||
\(902\) | −6.15399e6 | −0.251849 | ||||||||
\(903\) | −3.07100e7 | −1.25332 | ||||||||
\(904\) | 4.05937e7 | 1.65211 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.21499e7 | −0.491759 | ||||||||
\(907\) | −1.14062e7 | −0.460388 | −0.230194 | − | 0.973145i | \(-0.573936\pi\) | ||||
−0.230194 | + | 0.973145i | \(0.573936\pi\) | |||||||
\(908\) | 1.49664e7 | 0.602426 | ||||||||
\(909\) | 871978. | 0.0350022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.17910e7 | 0.869922 | 0.434961 | − | 0.900449i | \(-0.356762\pi\) | ||||
0.434961 | + | 0.900449i | \(0.356762\pi\) | |||||||
\(912\) | −954326. | −0.0379935 | ||||||||
\(913\) | −2.95425e6 | −0.117293 | ||||||||
\(914\) | −1.78946e7 | −0.708527 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.41042e6 | −0.213055 | ||||||||
\(917\) | 2.95572e7 | 1.16075 | ||||||||
\(918\) | 1.12695e6 | 0.0441365 | ||||||||
\(919\) | 3.12982e7 | 1.22245 | 0.611225 | − | 0.791457i | \(-0.290677\pi\) | ||||
0.611225 | + | 0.791457i | \(0.290677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.30941e6 | −0.0897123 | ||||||||
\(922\) | 2.24053e7 | 0.868008 | ||||||||
\(923\) | 2.60232e6 | 0.100544 | ||||||||
\(924\) | 3.45509e6 | 0.133131 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.46345e6 | −0.171058 | ||||||||
\(927\) | −2.32344e6 | −0.0888040 | ||||||||
\(928\) | −6.27904e6 | −0.239345 | ||||||||
\(929\) | −3.00058e7 | −1.14069 | −0.570343 | − | 0.821407i | \(-0.693190\pi\) | ||||
−0.570343 | + | 0.821407i | \(0.693190\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.91364e7 | −0.723578 | ||||||||
\(932\) | 2.67038e7 | 1.00701 | ||||||||
\(933\) | −1.87230e7 | −0.704161 | ||||||||
\(934\) | −2.80485e7 | −1.05206 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.31387e6 | 0.0863276 | ||||||||
\(937\) | −2.12772e7 | −0.791711 | −0.395855 | − | 0.918313i | \(-0.629552\pi\) | ||||
−0.395855 | + | 0.918313i | \(0.629552\pi\) | |||||||
\(938\) | −1.54162e7 | −0.572098 | ||||||||
\(939\) | 9.48950e6 | 0.351220 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.12864e7 | 1.51996 | 0.759982 | − | 0.649944i | \(-0.225208\pi\) | ||||
0.759982 | + | 0.649944i | \(0.225208\pi\) | |||||||
\(942\) | 1.32937e7 | 0.488110 | ||||||||
\(943\) | 157725. | 0.00577593 | ||||||||
\(944\) | −1.44239e6 | −0.0526809 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.89948e6 | 0.323323 | ||||||||
\(947\) | −1.15296e7 | −0.417771 | −0.208886 | − | 0.977940i | \(-0.566984\pi\) | ||||
−0.208886 | + | 0.977940i | \(0.566984\pi\) | |||||||
\(948\) | −8.07452e6 | −0.291807 | ||||||||
\(949\) | 8.67670e6 | 0.312744 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.11807e7 | 0.759432 | ||||||||
\(952\) | 1.32173e7 | 0.472663 | ||||||||
\(953\) | 9.67798e6 | 0.345185 | 0.172593 | − | 0.984993i | \(-0.444786\pi\) | ||||
0.172593 | + | 0.984993i | \(0.444786\pi\) | |||||||
\(954\) | 7.94180e6 | 0.282519 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.90118e7 | −0.672788 | ||||||||
\(957\) | 1.20641e6 | 0.0425809 | ||||||||
\(958\) | −1.21750e7 | −0.428604 | ||||||||
\(959\) | −1.41785e6 | −0.0497832 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.30167e7 | 0.803959 | ||||||||
\(962\) | 2.56931e6 | 0.0895113 | ||||||||
\(963\) | 9.87534e6 | 0.343152 | ||||||||
\(964\) | −2.05263e7 | −0.711408 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 61531.4 | 0.00212155 | ||||||||
\(967\) | −3.88946e7 | −1.33759 | −0.668795 | − | 0.743447i | \(-0.733189\pi\) | ||||
−0.668795 | + | 0.743447i | \(0.733189\pi\) | |||||||
\(968\) | −2.69823e6 | −0.0925531 | ||||||||
\(969\) | −6.43067e6 | −0.220012 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.79477e7 | 0.951259 | 0.475629 | − | 0.879646i | \(-0.342220\pi\) | ||||
0.475629 | + | 0.879646i | \(0.342220\pi\) | |||||||
\(972\) | 1.11489e6 | 0.0378499 | ||||||||
\(973\) | −1.26122e7 | −0.427080 | ||||||||
\(974\) | 1.44071e6 | 0.0486608 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 58038.9 | 0.00195027 | ||||||||
\(977\) | −7.01873e6 | −0.235246 | −0.117623 | − | 0.993058i | \(-0.537527\pi\) | ||||
−0.117623 | + | 0.993058i | \(0.537527\pi\) | |||||||
\(978\) | 1.17462e7 | 0.392689 | ||||||||
\(979\) | −2.67187e6 | −0.0890962 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.37524e7 | −0.456252 | ||||||||
\(982\) | −2.12188e6 | −0.0702171 | ||||||||
\(983\) | 4.12903e7 | 1.36290 | 0.681450 | − | 0.731864i | \(-0.261350\pi\) | ||||
0.681450 | + | 0.731864i | \(0.261350\pi\) | |||||||
\(984\) | −2.32899e7 | −0.766795 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.71255e6 | 0.0560985 | ||||||||
\(987\) | −1.59581e7 | −0.521421 | ||||||||
\(988\) | −4.89955e6 | −0.159685 | ||||||||
\(989\) | −228091. | −0.00741512 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.63627e6 | 0.0852717 | 0.0426359 | − | 0.999091i | \(-0.486424\pi\) | ||||
0.0426359 | + | 0.999091i | \(0.486424\pi\) | |||||||
\(992\) | 4.07328e7 | 1.31421 | ||||||||
\(993\) | 3.39207e6 | 0.109167 | ||||||||
\(994\) | −1.02184e7 | −0.328034 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.14880e6 | −0.132518 | ||||||||
\(997\) | −4.09967e7 | −1.30620 | −0.653102 | − | 0.757270i | \(-0.726533\pi\) | ||||
−0.653102 | + | 0.757270i | \(0.726533\pi\) | |||||||
\(998\) | 2.83328e7 | 0.900458 | ||||||||
\(999\) | 3.33612e6 | 0.105762 |
(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 | 825.6.a.v.1.10 | 13 | ||
5.2 | odd | 4 | 165.6.c.b.34.17 | yes | 26 | ||
5.3 | odd | 4 | 165.6.c.b.34.10 | ✓ | 26 | ||
5.4 | even | 2 | 825.6.a.y.1.4 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.10 | ✓ | 26 | 5.3 | odd | 4 | ||
165.6.c.b.34.17 | yes | 26 | 5.2 | odd | 4 | ||
825.6.a.v.1.10 | 13 | 1.1 | even | 1 | trivial | ||
825.6.a.y.1.4 | 13 | 5.4 | even | 2 |