Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,6,Mod(1,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, 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("570.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.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: | \(91.4187772934\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 25872x^{2} - 1407374x - 6356280 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-57.4501\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 185.237 | 1.42883 | 0.714417 | − | 0.699720i | \(-0.246692\pi\) | ||||
0.714417 | + | 0.699720i | \(0.246692\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −100.000 | −0.316228 | ||||||||
\(11\) | 132.999 | 0.331410 | 0.165705 | − | 0.986175i | \(-0.447010\pi\) | ||||
0.165705 | + | 0.986175i | \(0.447010\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | 637.513 | 1.04624 | 0.523119 | − | 0.852259i | \(-0.324768\pi\) | ||||
0.523119 | + | 0.852259i | \(0.324768\pi\) | |||||||
\(14\) | −740.947 | −1.01034 | ||||||||
\(15\) | −225.000 | −0.258199 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −2266.20 | −1.90185 | −0.950923 | − | 0.309427i | \(-0.899863\pi\) | ||||
−0.950923 | + | 0.309427i | \(0.899863\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | −1667.13 | −0.824938 | ||||||||
\(22\) | −531.994 | −0.234342 | ||||||||
\(23\) | −1230.65 | −0.485082 | −0.242541 | − | 0.970141i | \(-0.577981\pi\) | ||||
−0.242541 | + | 0.970141i | \(0.577981\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −2550.05 | −0.739803 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 2963.79 | 0.714417 | ||||||||
\(29\) | −6562.92 | −1.44911 | −0.724556 | − | 0.689216i | \(-0.757955\pi\) | ||||
−0.724556 | + | 0.689216i | \(0.757955\pi\) | |||||||
\(30\) | 900.000 | 0.182574 | ||||||||
\(31\) | −9179.09 | −1.71552 | −0.857759 | − | 0.514052i | \(-0.828144\pi\) | ||||
−0.857759 | + | 0.514052i | \(0.828144\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −1196.99 | −0.191340 | ||||||||
\(34\) | 9064.79 | 1.34481 | ||||||||
\(35\) | 4630.92 | 0.638994 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 8686.63 | 1.04315 | 0.521575 | − | 0.853205i | \(-0.325345\pi\) | ||||
0.521575 | + | 0.853205i | \(0.325345\pi\) | |||||||
\(38\) | −1444.00 | −0.162221 | ||||||||
\(39\) | −5737.62 | −0.604046 | ||||||||
\(40\) | −1600.00 | −0.158114 | ||||||||
\(41\) | −4870.80 | −0.452523 | −0.226261 | − | 0.974067i | \(-0.572650\pi\) | ||||
−0.226261 | + | 0.974067i | \(0.572650\pi\) | |||||||
\(42\) | 6668.52 | 0.583319 | ||||||||
\(43\) | −11536.3 | −0.951469 | −0.475735 | − | 0.879589i | \(-0.657818\pi\) | ||||
−0.475735 | + | 0.879589i | \(0.657818\pi\) | |||||||
\(44\) | 2127.98 | 0.165705 | ||||||||
\(45\) | 2025.00 | 0.149071 | ||||||||
\(46\) | 4922.60 | 0.343005 | ||||||||
\(47\) | −15404.7 | −1.01721 | −0.508603 | − | 0.861001i | \(-0.669838\pi\) | ||||
−0.508603 | + | 0.861001i | \(0.669838\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | 17505.6 | 1.04157 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | 20395.8 | 1.09803 | ||||||||
\(52\) | 10200.2 | 0.523119 | ||||||||
\(53\) | −2495.54 | −0.122032 | −0.0610161 | − | 0.998137i | \(-0.519434\pi\) | ||||
−0.0610161 | + | 0.998137i | \(0.519434\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 3324.96 | 0.148211 | ||||||||
\(56\) | −11855.1 | −0.505169 | ||||||||
\(57\) | −3249.00 | −0.132453 | ||||||||
\(58\) | 26251.7 | 1.02468 | ||||||||
\(59\) | 14154.2 | 0.529366 | 0.264683 | − | 0.964335i | \(-0.414733\pi\) | ||||
0.264683 | + | 0.964335i | \(0.414733\pi\) | |||||||
\(60\) | −3600.00 | −0.129099 | ||||||||
\(61\) | −18805.9 | −0.647096 | −0.323548 | − | 0.946212i | \(-0.604876\pi\) | ||||
−0.323548 | + | 0.946212i | \(0.604876\pi\) | |||||||
\(62\) | 36716.4 | 1.21305 | ||||||||
\(63\) | 15004.2 | 0.476278 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 15937.8 | 0.467892 | ||||||||
\(66\) | 4787.95 | 0.135297 | ||||||||
\(67\) | 1965.60 | 0.0534944 | 0.0267472 | − | 0.999642i | \(-0.491485\pi\) | ||||
0.0267472 | + | 0.999642i | \(0.491485\pi\) | |||||||
\(68\) | −36259.2 | −0.950923 | ||||||||
\(69\) | 11075.9 | 0.280062 | ||||||||
\(70\) | −18523.7 | −0.451837 | ||||||||
\(71\) | 31989.3 | 0.753111 | 0.376556 | − | 0.926394i | \(-0.377108\pi\) | ||||
0.376556 | + | 0.926394i | \(0.377108\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | −64181.4 | −1.40962 | −0.704810 | − | 0.709396i | \(-0.748968\pi\) | ||||
−0.704810 | + | 0.709396i | \(0.748968\pi\) | |||||||
\(74\) | −34746.5 | −0.737619 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | 5776.00 | 0.114708 | ||||||||
\(77\) | 24636.2 | 0.473530 | ||||||||
\(78\) | 22950.5 | 0.427125 | ||||||||
\(79\) | 88164.8 | 1.58938 | 0.794690 | − | 0.607016i | \(-0.207634\pi\) | ||||
0.794690 | + | 0.607016i | \(0.207634\pi\) | |||||||
\(80\) | 6400.00 | 0.111803 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 19483.2 | 0.319982 | ||||||||
\(83\) | −12857.4 | −0.204860 | −0.102430 | − | 0.994740i | \(-0.532662\pi\) | ||||
−0.102430 | + | 0.994740i | \(0.532662\pi\) | |||||||
\(84\) | −26674.1 | −0.412469 | ||||||||
\(85\) | −56654.9 | −0.850532 | ||||||||
\(86\) | 46145.1 | 0.672790 | ||||||||
\(87\) | 59066.2 | 0.836645 | ||||||||
\(88\) | −8511.91 | −0.117171 | ||||||||
\(89\) | −60163.6 | −0.805117 | −0.402558 | − | 0.915394i | \(-0.631879\pi\) | ||||
−0.402558 | + | 0.915394i | \(0.631879\pi\) | |||||||
\(90\) | −8100.00 | −0.105409 | ||||||||
\(91\) | 118091. | 1.49490 | ||||||||
\(92\) | −19690.4 | −0.242541 | ||||||||
\(93\) | 82611.8 | 0.990455 | ||||||||
\(94\) | 61618.8 | 0.719273 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | −33842.2 | −0.365198 | −0.182599 | − | 0.983187i | \(-0.558451\pi\) | ||||
−0.182599 | + | 0.983187i | \(0.558451\pi\) | |||||||
\(98\) | −70022.5 | −0.736500 | ||||||||
\(99\) | 10772.9 | 0.110470 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 143321. | 1.39800 | 0.698998 | − | 0.715124i | \(-0.253630\pi\) | ||||
0.698998 | + | 0.715124i | \(0.253630\pi\) | |||||||
\(102\) | −81583.1 | −0.776426 | ||||||||
\(103\) | 92271.7 | 0.856990 | 0.428495 | − | 0.903544i | \(-0.359044\pi\) | ||||
0.428495 | + | 0.903544i | \(0.359044\pi\) | |||||||
\(104\) | −40800.8 | −0.369901 | ||||||||
\(105\) | −41678.3 | −0.368923 | ||||||||
\(106\) | 9982.14 | 0.0862897 | ||||||||
\(107\) | −114505. | −0.966865 | −0.483433 | − | 0.875382i | \(-0.660610\pi\) | ||||
−0.483433 | + | 0.875382i | \(0.660610\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | −239404. | −1.93003 | −0.965016 | − | 0.262190i | \(-0.915555\pi\) | ||||
−0.965016 | + | 0.262190i | \(0.915555\pi\) | |||||||
\(110\) | −13299.9 | −0.104801 | ||||||||
\(111\) | −78179.7 | −0.602263 | ||||||||
\(112\) | 47420.6 | 0.357209 | ||||||||
\(113\) | 204322. | 1.50529 | 0.752644 | − | 0.658428i | \(-0.228778\pi\) | ||||
0.752644 | + | 0.658428i | \(0.228778\pi\) | |||||||
\(114\) | 12996.0 | 0.0936586 | ||||||||
\(115\) | −30766.3 | −0.216935 | ||||||||
\(116\) | −105007. | −0.724556 | ||||||||
\(117\) | 51638.6 | 0.348746 | ||||||||
\(118\) | −56616.9 | −0.374318 | ||||||||
\(119\) | −419783. | −2.71742 | ||||||||
\(120\) | 14400.0 | 0.0912871 | ||||||||
\(121\) | −143362. | −0.890168 | ||||||||
\(122\) | 75223.4 | 0.457566 | ||||||||
\(123\) | 43837.2 | 0.261264 | ||||||||
\(124\) | −146865. | −0.857759 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | −60016.7 | −0.336779 | ||||||||
\(127\) | −60036.9 | −0.330300 | −0.165150 | − | 0.986268i | \(-0.552811\pi\) | ||||
−0.165150 | + | 0.986268i | \(0.552811\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 103827. | 0.549331 | ||||||||
\(130\) | −63751.3 | −0.330850 | ||||||||
\(131\) | −191437. | −0.974648 | −0.487324 | − | 0.873221i | \(-0.662027\pi\) | ||||
−0.487324 | + | 0.873221i | \(0.662027\pi\) | |||||||
\(132\) | −19151.8 | −0.0956698 | ||||||||
\(133\) | 66870.4 | 0.327797 | ||||||||
\(134\) | −7862.40 | −0.0378262 | ||||||||
\(135\) | −18225.0 | −0.0860663 | ||||||||
\(136\) | 145037. | 0.672404 | ||||||||
\(137\) | −334152. | −1.52105 | −0.760524 | − | 0.649310i | \(-0.775058\pi\) | ||||
−0.760524 | + | 0.649310i | \(0.775058\pi\) | |||||||
\(138\) | −44303.4 | −0.198034 | ||||||||
\(139\) | 359419. | 1.57784 | 0.788921 | − | 0.614494i | \(-0.210640\pi\) | ||||
0.788921 | + | 0.614494i | \(0.210640\pi\) | |||||||
\(140\) | 74094.7 | 0.319497 | ||||||||
\(141\) | 138642. | 0.587284 | ||||||||
\(142\) | −127957. | −0.532530 | ||||||||
\(143\) | 84788.4 | 0.346734 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | −164073. | −0.648062 | ||||||||
\(146\) | 256726. | 0.996752 | ||||||||
\(147\) | −157551. | −0.601349 | ||||||||
\(148\) | 138986. | 0.521575 | ||||||||
\(149\) | −331091. | −1.22175 | −0.610874 | − | 0.791728i | \(-0.709182\pi\) | ||||
−0.610874 | + | 0.791728i | \(0.709182\pi\) | |||||||
\(150\) | 22500.0 | 0.0816497 | ||||||||
\(151\) | 28606.3 | 0.102099 | 0.0510493 | − | 0.998696i | \(-0.483743\pi\) | ||||
0.0510493 | + | 0.998696i | \(0.483743\pi\) | |||||||
\(152\) | −23104.0 | −0.0811107 | ||||||||
\(153\) | −183562. | −0.633949 | ||||||||
\(154\) | −98544.9 | −0.334836 | ||||||||
\(155\) | −229477. | −0.767203 | ||||||||
\(156\) | −91801.9 | −0.302023 | ||||||||
\(157\) | 96412.0 | 0.312163 | 0.156082 | − | 0.987744i | \(-0.450114\pi\) | ||||
0.156082 | + | 0.987744i | \(0.450114\pi\) | |||||||
\(158\) | −352659. | −1.12386 | ||||||||
\(159\) | 22459.8 | 0.0704553 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −227962. | −0.693102 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −330416. | −0.974076 | −0.487038 | − | 0.873381i | \(-0.661923\pi\) | ||||
−0.487038 | + | 0.873381i | \(0.661923\pi\) | |||||||
\(164\) | −77932.8 | −0.226261 | ||||||||
\(165\) | −29924.7 | −0.0855696 | ||||||||
\(166\) | 51429.5 | 0.144858 | ||||||||
\(167\) | −478346. | −1.32725 | −0.663623 | − | 0.748067i | \(-0.730982\pi\) | ||||
−0.663623 | + | 0.748067i | \(0.730982\pi\) | |||||||
\(168\) | 106696. | 0.291660 | ||||||||
\(169\) | 35130.2 | 0.0946157 | ||||||||
\(170\) | 226620. | 0.601417 | ||||||||
\(171\) | 29241.0 | 0.0764719 | ||||||||
\(172\) | −184581. | −0.475735 | ||||||||
\(173\) | 466943. | 1.18617 | 0.593087 | − | 0.805138i | \(-0.297909\pi\) | ||||
0.593087 | + | 0.805138i | \(0.297909\pi\) | |||||||
\(174\) | −236265. | −0.591597 | ||||||||
\(175\) | 115773. | 0.285767 | ||||||||
\(176\) | 34047.6 | 0.0828524 | ||||||||
\(177\) | −127388. | −0.305630 | ||||||||
\(178\) | 240654. | 0.569303 | ||||||||
\(179\) | −28144.5 | −0.0656540 | −0.0328270 | − | 0.999461i | \(-0.510451\pi\) | ||||
−0.0328270 | + | 0.999461i | \(0.510451\pi\) | |||||||
\(180\) | 32400.0 | 0.0745356 | ||||||||
\(181\) | 758889. | 1.72180 | 0.860898 | − | 0.508777i | \(-0.169902\pi\) | ||||
0.860898 | + | 0.508777i | \(0.169902\pi\) | |||||||
\(182\) | −472363. | −1.05706 | ||||||||
\(183\) | 169253. | 0.373601 | ||||||||
\(184\) | 78761.6 | 0.171502 | ||||||||
\(185\) | 217166. | 0.466511 | ||||||||
\(186\) | −330447. | −0.700357 | ||||||||
\(187\) | −301401. | −0.630290 | ||||||||
\(188\) | −246475. | −0.508603 | ||||||||
\(189\) | −135038. | −0.274979 | ||||||||
\(190\) | −36100.0 | −0.0725476 | ||||||||
\(191\) | 657635. | 1.30437 | 0.652186 | − | 0.758059i | \(-0.273852\pi\) | ||||
0.652186 | + | 0.758059i | \(0.273852\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −983614. | −1.90078 | −0.950389 | − | 0.311063i | \(-0.899315\pi\) | ||||
−0.950389 | + | 0.311063i | \(0.899315\pi\) | |||||||
\(194\) | 135369. | 0.258234 | ||||||||
\(195\) | −143440. | −0.270138 | ||||||||
\(196\) | 280090. | 0.520784 | ||||||||
\(197\) | 352468. | 0.647074 | 0.323537 | − | 0.946216i | \(-0.395128\pi\) | ||||
0.323537 | + | 0.946216i | \(0.395128\pi\) | |||||||
\(198\) | −43091.5 | −0.0781140 | ||||||||
\(199\) | −687176. | −1.23009 | −0.615043 | − | 0.788494i | \(-0.710861\pi\) | ||||
−0.615043 | + | 0.788494i | \(0.710861\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | −17690.4 | −0.0308850 | ||||||||
\(202\) | −573283. | −0.988532 | ||||||||
\(203\) | −1.21569e6 | −2.07054 | ||||||||
\(204\) | 326332. | 0.549016 | ||||||||
\(205\) | −121770. | −0.202374 | ||||||||
\(206\) | −369087. | −0.605983 | ||||||||
\(207\) | −99682.7 | −0.161694 | ||||||||
\(208\) | 163203. | 0.261560 | ||||||||
\(209\) | 48012.5 | 0.0760306 | ||||||||
\(210\) | 166713. | 0.260868 | ||||||||
\(211\) | 242486. | 0.374957 | 0.187478 | − | 0.982269i | \(-0.439969\pi\) | ||||
0.187478 | + | 0.982269i | \(0.439969\pi\) | |||||||
\(212\) | −39928.6 | −0.0610161 | ||||||||
\(213\) | −287904. | −0.434809 | ||||||||
\(214\) | 458021. | 0.683677 | ||||||||
\(215\) | −288407. | −0.425510 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | −1.70030e6 | −2.45119 | ||||||||
\(218\) | 957615. | 1.36474 | ||||||||
\(219\) | 577632. | 0.813844 | ||||||||
\(220\) | 53199.4 | 0.0741055 | ||||||||
\(221\) | −1.44473e6 | −1.98979 | ||||||||
\(222\) | 312719. | 0.425865 | ||||||||
\(223\) | −979581. | −1.31910 | −0.659551 | − | 0.751660i | \(-0.729253\pi\) | ||||
−0.659551 | + | 0.751660i | \(0.729253\pi\) | |||||||
\(224\) | −189682. | −0.252585 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | −817289. | −1.06440 | ||||||||
\(227\) | 364015. | 0.468872 | 0.234436 | − | 0.972132i | \(-0.424676\pi\) | ||||
0.234436 | + | 0.972132i | \(0.424676\pi\) | |||||||
\(228\) | −51984.0 | −0.0662266 | ||||||||
\(229\) | 352408. | 0.444076 | 0.222038 | − | 0.975038i | \(-0.428729\pi\) | ||||
0.222038 | + | 0.975038i | \(0.428729\pi\) | |||||||
\(230\) | 123065. | 0.153396 | ||||||||
\(231\) | −221726. | −0.273392 | ||||||||
\(232\) | 420027. | 0.512338 | ||||||||
\(233\) | −1.52721e6 | −1.84293 | −0.921465 | − | 0.388461i | \(-0.873007\pi\) | ||||
−0.921465 | + | 0.388461i | \(0.873007\pi\) | |||||||
\(234\) | −206554. | −0.246601 | ||||||||
\(235\) | −385118. | −0.454908 | ||||||||
\(236\) | 226468. | 0.264683 | ||||||||
\(237\) | −793483. | −0.917629 | ||||||||
\(238\) | 1.67913e6 | 1.92151 | ||||||||
\(239\) | −997411. | −1.12948 | −0.564741 | − | 0.825268i | \(-0.691024\pi\) | ||||
−0.564741 | + | 0.825268i | \(0.691024\pi\) | |||||||
\(240\) | −57600.0 | −0.0645497 | ||||||||
\(241\) | 113719. | 0.126122 | 0.0630610 | − | 0.998010i | \(-0.479914\pi\) | ||||
0.0630610 | + | 0.998010i | \(0.479914\pi\) | |||||||
\(242\) | 573450. | 0.629444 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −300894. | −0.323548 | ||||||||
\(245\) | 437641. | 0.465803 | ||||||||
\(246\) | −175349. | −0.184742 | ||||||||
\(247\) | 230142. | 0.240024 | ||||||||
\(248\) | 587462. | 0.606527 | ||||||||
\(249\) | 115716. | 0.118276 | ||||||||
\(250\) | −62500.0 | −0.0632456 | ||||||||
\(251\) | −303569. | −0.304140 | −0.152070 | − | 0.988370i | \(-0.548594\pi\) | ||||
−0.152070 | + | 0.988370i | \(0.548594\pi\) | |||||||
\(252\) | 240067. | 0.238139 | ||||||||
\(253\) | −163675. | −0.160761 | ||||||||
\(254\) | 240148. | 0.233558 | ||||||||
\(255\) | 509894. | 0.491055 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.08192e6 | 1.02179 | 0.510896 | − | 0.859643i | \(-0.329314\pi\) | ||||
0.510896 | + | 0.859643i | \(0.329314\pi\) | |||||||
\(258\) | −415306. | −0.388436 | ||||||||
\(259\) | 1.60908e6 | 1.49049 | ||||||||
\(260\) | 255005. | 0.233946 | ||||||||
\(261\) | −531596. | −0.483037 | ||||||||
\(262\) | 765748. | 0.689180 | ||||||||
\(263\) | −702957. | −0.626670 | −0.313335 | − | 0.949643i | \(-0.601446\pi\) | ||||
−0.313335 | + | 0.949643i | \(0.601446\pi\) | |||||||
\(264\) | 76607.2 | 0.0676487 | ||||||||
\(265\) | −62388.4 | −0.0545744 | ||||||||
\(266\) | −267482. | −0.231788 | ||||||||
\(267\) | 541472. | 0.464834 | ||||||||
\(268\) | 31449.6 | 0.0267472 | ||||||||
\(269\) | 505465. | 0.425903 | 0.212951 | − | 0.977063i | \(-0.431692\pi\) | ||||
0.212951 | + | 0.977063i | \(0.431692\pi\) | |||||||
\(270\) | 72900.0 | 0.0608581 | ||||||||
\(271\) | 510720. | 0.422434 | 0.211217 | − | 0.977439i | \(-0.432257\pi\) | ||||
0.211217 | + | 0.977439i | \(0.432257\pi\) | |||||||
\(272\) | −580147. | −0.475462 | ||||||||
\(273\) | −1.06282e6 | −0.863082 | ||||||||
\(274\) | 1.33661e6 | 1.07554 | ||||||||
\(275\) | 83124.1 | 0.0662820 | ||||||||
\(276\) | 177214. | 0.140031 | ||||||||
\(277\) | 798121. | 0.624984 | 0.312492 | − | 0.949920i | \(-0.398836\pi\) | ||||
0.312492 | + | 0.949920i | \(0.398836\pi\) | |||||||
\(278\) | −1.43767e6 | −1.11570 | ||||||||
\(279\) | −743506. | −0.571839 | ||||||||
\(280\) | −296379. | −0.225919 | ||||||||
\(281\) | 422979. | 0.319561 | 0.159780 | − | 0.987153i | \(-0.448921\pi\) | ||||
0.159780 | + | 0.987153i | \(0.448921\pi\) | |||||||
\(282\) | −554570. | −0.415273 | ||||||||
\(283\) | −2.14117e6 | −1.58923 | −0.794613 | − | 0.607117i | \(-0.792326\pi\) | ||||
−0.794613 | + | 0.607117i | \(0.792326\pi\) | |||||||
\(284\) | 511829. | 0.376556 | ||||||||
\(285\) | −81225.0 | −0.0592349 | ||||||||
\(286\) | −339153. | −0.245178 | ||||||||
\(287\) | −902251. | −0.646580 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 3.71579e6 | 2.61702 | ||||||||
\(290\) | 656292. | 0.458249 | ||||||||
\(291\) | 304580. | 0.210847 | ||||||||
\(292\) | −1.02690e6 | −0.704810 | ||||||||
\(293\) | −1.53788e6 | −1.04653 | −0.523267 | − | 0.852169i | \(-0.675287\pi\) | ||||
−0.523267 | + | 0.852169i | \(0.675287\pi\) | |||||||
\(294\) | 630203. | 0.425218 | ||||||||
\(295\) | 353856. | 0.236740 | ||||||||
\(296\) | −555944. | −0.368810 | ||||||||
\(297\) | −96956.0 | −0.0637798 | ||||||||
\(298\) | 1.32436e6 | 0.863906 | ||||||||
\(299\) | −784556. | −0.507512 | ||||||||
\(300\) | −90000.0 | −0.0577350 | ||||||||
\(301\) | −2.13694e6 | −1.35949 | ||||||||
\(302\) | −114425. | −0.0721946 | ||||||||
\(303\) | −1.28989e6 | −0.807133 | ||||||||
\(304\) | 92416.0 | 0.0573539 | ||||||||
\(305\) | −470146. | −0.289390 | ||||||||
\(306\) | 734248. | 0.448270 | ||||||||
\(307\) | 2.79516e6 | 1.69263 | 0.846314 | − | 0.532684i | \(-0.178817\pi\) | ||||
0.846314 | + | 0.532684i | \(0.178817\pi\) | |||||||
\(308\) | 394179. | 0.236765 | ||||||||
\(309\) | −830445. | −0.494783 | ||||||||
\(310\) | 917909. | 0.542495 | ||||||||
\(311\) | 212876. | 0.124803 | 0.0624017 | − | 0.998051i | \(-0.480124\pi\) | ||||
0.0624017 | + | 0.998051i | \(0.480124\pi\) | |||||||
\(312\) | 367208. | 0.213563 | ||||||||
\(313\) | 2.87678e6 | 1.65976 | 0.829882 | − | 0.557940i | \(-0.188408\pi\) | ||||
0.829882 | + | 0.557940i | \(0.188408\pi\) | |||||||
\(314\) | −385648. | −0.220733 | ||||||||
\(315\) | 375104. | 0.212998 | ||||||||
\(316\) | 1.41064e6 | 0.794690 | ||||||||
\(317\) | −1.92365e6 | −1.07517 | −0.537586 | − | 0.843209i | \(-0.680664\pi\) | ||||
−0.537586 | + | 0.843209i | \(0.680664\pi\) | |||||||
\(318\) | −89839.3 | −0.0498194 | ||||||||
\(319\) | −872858. | −0.480250 | ||||||||
\(320\) | 102400. | 0.0559017 | ||||||||
\(321\) | 1.03055e6 | 0.558220 | ||||||||
\(322\) | 911847. | 0.490097 | ||||||||
\(323\) | −818097. | −0.436314 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 398446. | 0.209248 | ||||||||
\(326\) | 1.32167e6 | 0.688775 | ||||||||
\(327\) | 2.15463e6 | 1.11430 | ||||||||
\(328\) | 311731. | 0.159991 | ||||||||
\(329\) | −2.85352e6 | −1.45342 | ||||||||
\(330\) | 119699. | 0.0605069 | ||||||||
\(331\) | 3.01336e6 | 1.51175 | 0.755876 | − | 0.654714i | \(-0.227211\pi\) | ||||
0.755876 | + | 0.654714i | \(0.227211\pi\) | |||||||
\(332\) | −205718. | −0.102430 | ||||||||
\(333\) | 703617. | 0.347717 | ||||||||
\(334\) | 1.91339e6 | 0.938504 | ||||||||
\(335\) | 49140.0 | 0.0239234 | ||||||||
\(336\) | −426785. | −0.206234 | ||||||||
\(337\) | 266837. | 0.127988 | 0.0639942 | − | 0.997950i | \(-0.479616\pi\) | ||||
0.0639942 | + | 0.997950i | \(0.479616\pi\) | |||||||
\(338\) | −140521. | −0.0669034 | ||||||||
\(339\) | −1.83890e6 | −0.869078 | ||||||||
\(340\) | −906479. | −0.425266 | ||||||||
\(341\) | −1.22081e6 | −0.568540 | ||||||||
\(342\) | −116964. | −0.0540738 | ||||||||
\(343\) | 129412. | 0.0593934 | ||||||||
\(344\) | 738322. | 0.336395 | ||||||||
\(345\) | 276896. | 0.125248 | ||||||||
\(346\) | −1.86777e6 | −0.838752 | ||||||||
\(347\) | 1.10566e6 | 0.492946 | 0.246473 | − | 0.969150i | \(-0.420728\pi\) | ||||
0.246473 | + | 0.969150i | \(0.420728\pi\) | |||||||
\(348\) | 945060. | 0.418322 | ||||||||
\(349\) | 3.51702e6 | 1.54565 | 0.772825 | − | 0.634619i | \(-0.218843\pi\) | ||||
0.772825 | + | 0.634619i | \(0.218843\pi\) | |||||||
\(350\) | −463092. | −0.202068 | ||||||||
\(351\) | −464747. | −0.201349 | ||||||||
\(352\) | −136191. | −0.0585855 | ||||||||
\(353\) | 1.50722e6 | 0.643783 | 0.321892 | − | 0.946776i | \(-0.395681\pi\) | ||||
0.321892 | + | 0.946776i | \(0.395681\pi\) | |||||||
\(354\) | 509552. | 0.216113 | ||||||||
\(355\) | 799733. | 0.336802 | ||||||||
\(356\) | −962618. | −0.402558 | ||||||||
\(357\) | 3.77805e6 | 1.56891 | ||||||||
\(358\) | 112578. | 0.0464244 | ||||||||
\(359\) | 524591. | 0.214825 | 0.107413 | − | 0.994215i | \(-0.465743\pi\) | ||||
0.107413 | + | 0.994215i | \(0.465743\pi\) | |||||||
\(360\) | −129600. | −0.0527046 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | −3.03556e6 | −1.21749 | ||||||||
\(363\) | 1.29026e6 | 0.513938 | ||||||||
\(364\) | 1.88945e6 | 0.747451 | ||||||||
\(365\) | −1.60453e6 | −0.630401 | ||||||||
\(366\) | −677011. | −0.264176 | ||||||||
\(367\) | −4.90971e6 | −1.90279 | −0.951394 | − | 0.307978i | \(-0.900348\pi\) | ||||
−0.951394 | + | 0.307978i | \(0.900348\pi\) | |||||||
\(368\) | −315047. | −0.121271 | ||||||||
\(369\) | −394535. | −0.150841 | ||||||||
\(370\) | −868663. | −0.329873 | ||||||||
\(371\) | −462265. | −0.174364 | ||||||||
\(372\) | 1.32179e6 | 0.495227 | ||||||||
\(373\) | −3.84049e6 | −1.42927 | −0.714636 | − | 0.699497i | \(-0.753408\pi\) | ||||
−0.714636 | + | 0.699497i | \(0.753408\pi\) | |||||||
\(374\) | 1.20560e6 | 0.445683 | ||||||||
\(375\) | −140625. | −0.0516398 | ||||||||
\(376\) | 985901. | 0.359637 | ||||||||
\(377\) | −4.18395e6 | −1.51612 | ||||||||
\(378\) | 540150. | 0.194440 | ||||||||
\(379\) | 2.26040e6 | 0.808328 | 0.404164 | − | 0.914687i | \(-0.367563\pi\) | ||||
0.404164 | + | 0.914687i | \(0.367563\pi\) | |||||||
\(380\) | 144400. | 0.0512989 | ||||||||
\(381\) | 540332. | 0.190699 | ||||||||
\(382\) | −2.63054e6 | −0.922331 | ||||||||
\(383\) | −1.52801e6 | −0.532267 | −0.266133 | − | 0.963936i | \(-0.585746\pi\) | ||||
−0.266133 | + | 0.963936i | \(0.585746\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 615905. | 0.211769 | ||||||||
\(386\) | 3.93446e6 | 1.34405 | ||||||||
\(387\) | −934439. | −0.317156 | ||||||||
\(388\) | −541475. | −0.182599 | ||||||||
\(389\) | 3.23044e6 | 1.08240 | 0.541200 | − | 0.840894i | \(-0.317970\pi\) | ||||
0.541200 | + | 0.840894i | \(0.317970\pi\) | |||||||
\(390\) | 573762. | 0.191016 | ||||||||
\(391\) | 2.78890e6 | 0.922552 | ||||||||
\(392\) | −1.12036e6 | −0.368250 | ||||||||
\(393\) | 1.72293e6 | 0.562713 | ||||||||
\(394\) | −1.40987e6 | −0.457550 | ||||||||
\(395\) | 2.20412e6 | 0.710792 | ||||||||
\(396\) | 172366. | 0.0552350 | ||||||||
\(397\) | −492037. | −0.156683 | −0.0783414 | − | 0.996927i | \(-0.524962\pi\) | ||||
−0.0783414 | + | 0.996927i | \(0.524962\pi\) | |||||||
\(398\) | 2.74870e6 | 0.869802 | ||||||||
\(399\) | −601834. | −0.189254 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | 1.92955e6 | 0.599231 | 0.299615 | − | 0.954060i | \(-0.403142\pi\) | ||||
0.299615 | + | 0.954060i | \(0.403142\pi\) | |||||||
\(402\) | 70761.6 | 0.0218390 | ||||||||
\(403\) | −5.85179e6 | −1.79484 | ||||||||
\(404\) | 2.29313e6 | 0.698998 | ||||||||
\(405\) | 164025. | 0.0496904 | ||||||||
\(406\) | 4.86277e6 | 1.46409 | ||||||||
\(407\) | 1.15531e6 | 0.345710 | ||||||||
\(408\) | −1.30533e6 | −0.388213 | ||||||||
\(409\) | 2.13887e6 | 0.632231 | 0.316115 | − | 0.948721i | \(-0.397621\pi\) | ||||
0.316115 | + | 0.948721i | \(0.397621\pi\) | |||||||
\(410\) | 487080. | 0.143100 | ||||||||
\(411\) | 3.00737e6 | 0.878177 | ||||||||
\(412\) | 1.47635e6 | 0.428495 | ||||||||
\(413\) | 2.62188e6 | 0.756377 | ||||||||
\(414\) | 398731. | 0.114335 | ||||||||
\(415\) | −321435. | −0.0916162 | ||||||||
\(416\) | −652814. | −0.184951 | ||||||||
\(417\) | −3.23477e6 | −0.910968 | ||||||||
\(418\) | −192050. | −0.0537618 | ||||||||
\(419\) | −5.76766e6 | −1.60496 | −0.802480 | − | 0.596678i | \(-0.796487\pi\) | ||||
−0.802480 | + | 0.596678i | \(0.796487\pi\) | |||||||
\(420\) | −666852. | −0.184462 | ||||||||
\(421\) | −269913. | −0.0742195 | −0.0371098 | − | 0.999311i | \(-0.511815\pi\) | ||||
−0.0371098 | + | 0.999311i | \(0.511815\pi\) | |||||||
\(422\) | −969946. | −0.265135 | ||||||||
\(423\) | −1.24778e6 | −0.339069 | ||||||||
\(424\) | 159714. | 0.0431449 | ||||||||
\(425\) | −1.41637e6 | −0.380369 | ||||||||
\(426\) | 1.15162e6 | 0.307456 | ||||||||
\(427\) | −3.48353e6 | −0.924592 | ||||||||
\(428\) | −1.83208e6 | −0.483433 | ||||||||
\(429\) | −763095. | −0.200187 | ||||||||
\(430\) | 1.15363e6 | 0.300881 | ||||||||
\(431\) | −6.23095e6 | −1.61570 | −0.807851 | − | 0.589386i | \(-0.799370\pi\) | ||||
−0.807851 | + | 0.589386i | \(0.799370\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 311409. | 0.0798198 | 0.0399099 | − | 0.999203i | \(-0.487293\pi\) | ||||
0.0399099 | + | 0.999203i | \(0.487293\pi\) | |||||||
\(434\) | 6.80122e6 | 1.73325 | ||||||||
\(435\) | 1.47666e6 | 0.374159 | ||||||||
\(436\) | −3.83046e6 | −0.965016 | ||||||||
\(437\) | −444265. | −0.111285 | ||||||||
\(438\) | −2.31053e6 | −0.575475 | ||||||||
\(439\) | 3.18888e6 | 0.789727 | 0.394864 | − | 0.918740i | \(-0.370792\pi\) | ||||
0.394864 | + | 0.918740i | \(0.370792\pi\) | |||||||
\(440\) | −212798. | −0.0524005 | ||||||||
\(441\) | 1.41796e6 | 0.347189 | ||||||||
\(442\) | 5.77892e6 | 1.40699 | ||||||||
\(443\) | −2.36934e6 | −0.573611 | −0.286805 | − | 0.957989i | \(-0.592593\pi\) | ||||
−0.286805 | + | 0.957989i | \(0.592593\pi\) | |||||||
\(444\) | −1.25088e6 | −0.301132 | ||||||||
\(445\) | −1.50409e6 | −0.360059 | ||||||||
\(446\) | 3.91832e6 | 0.932745 | ||||||||
\(447\) | 2.97982e6 | 0.705376 | ||||||||
\(448\) | 758729. | 0.178604 | ||||||||
\(449\) | 6.92922e6 | 1.62207 | 0.811033 | − | 0.585001i | \(-0.198906\pi\) | ||||
0.811033 | + | 0.585001i | \(0.198906\pi\) | |||||||
\(450\) | −202500. | −0.0471405 | ||||||||
\(451\) | −647809. | −0.149971 | ||||||||
\(452\) | 3.26915e6 | 0.752644 | ||||||||
\(453\) | −257457. | −0.0589467 | ||||||||
\(454\) | −1.45606e6 | −0.331542 | ||||||||
\(455\) | 2.95227e6 | 0.668541 | ||||||||
\(456\) | 207936. | 0.0468293 | ||||||||
\(457\) | 1.28266e6 | 0.287291 | 0.143645 | − | 0.989629i | \(-0.454117\pi\) | ||||
0.143645 | + | 0.989629i | \(0.454117\pi\) | |||||||
\(458\) | −1.40963e6 | −0.314009 | ||||||||
\(459\) | 1.65206e6 | 0.366011 | ||||||||
\(460\) | −492260. | −0.108468 | ||||||||
\(461\) | 3.50945e6 | 0.769107 | 0.384554 | − | 0.923103i | \(-0.374355\pi\) | ||||
0.384554 | + | 0.923103i | \(0.374355\pi\) | |||||||
\(462\) | 886904. | 0.193318 | ||||||||
\(463\) | −2.63980e6 | −0.572292 | −0.286146 | − | 0.958186i | \(-0.592374\pi\) | ||||
−0.286146 | + | 0.958186i | \(0.592374\pi\) | |||||||
\(464\) | −1.68011e6 | −0.362278 | ||||||||
\(465\) | 2.06530e6 | 0.442945 | ||||||||
\(466\) | 6.10884e6 | 1.30315 | ||||||||
\(467\) | 173235. | 0.0367572 | 0.0183786 | − | 0.999831i | \(-0.494150\pi\) | ||||
0.0183786 | + | 0.999831i | \(0.494150\pi\) | |||||||
\(468\) | 826217. | 0.174373 | ||||||||
\(469\) | 364101. | 0.0764346 | ||||||||
\(470\) | 1.54047e6 | 0.321669 | ||||||||
\(471\) | −867708. | −0.180228 | ||||||||
\(472\) | −905871. | −0.187159 | ||||||||
\(473\) | −1.53431e6 | −0.315326 | ||||||||
\(474\) | 3.17393e6 | 0.648862 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | −6.71653e6 | −1.35871 | ||||||||
\(477\) | −202138. | −0.0406774 | ||||||||
\(478\) | 3.98964e6 | 0.798664 | ||||||||
\(479\) | −8.27582e6 | −1.64806 | −0.824029 | − | 0.566548i | \(-0.808278\pi\) | ||||
−0.824029 | + | 0.566548i | \(0.808278\pi\) | |||||||
\(480\) | 230400. | 0.0456435 | ||||||||
\(481\) | 5.53784e6 | 1.09138 | ||||||||
\(482\) | −454876. | −0.0891817 | ||||||||
\(483\) | 2.05165e6 | 0.400163 | ||||||||
\(484\) | −2.29380e6 | −0.445084 | ||||||||
\(485\) | −846054. | −0.163322 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 1.83772e6 | 0.351121 | 0.175560 | − | 0.984469i | \(-0.443826\pi\) | ||||
0.175560 | + | 0.984469i | \(0.443826\pi\) | |||||||
\(488\) | 1.20357e6 | 0.228783 | ||||||||
\(489\) | 2.97375e6 | 0.562383 | ||||||||
\(490\) | −1.75056e6 | −0.329373 | ||||||||
\(491\) | −502846. | −0.0941308 | −0.0470654 | − | 0.998892i | \(-0.514987\pi\) | ||||
−0.0470654 | + | 0.998892i | \(0.514987\pi\) | |||||||
\(492\) | 701395. | 0.130632 | ||||||||
\(493\) | 1.48729e7 | 2.75599 | ||||||||
\(494\) | −920569. | −0.169722 | ||||||||
\(495\) | 269322. | 0.0494036 | ||||||||
\(496\) | −2.34985e6 | −0.428880 | ||||||||
\(497\) | 5.92560e6 | 1.07607 | ||||||||
\(498\) | −462866. | −0.0836338 | ||||||||
\(499\) | 4.04170e6 | 0.726629 | 0.363314 | − | 0.931667i | \(-0.381645\pi\) | ||||
0.363314 | + | 0.931667i | \(0.381645\pi\) | |||||||
\(500\) | 250000. | 0.0447214 | ||||||||
\(501\) | 4.30512e6 | 0.766286 | ||||||||
\(502\) | 1.21428e6 | 0.215059 | ||||||||
\(503\) | −9.14324e6 | −1.61131 | −0.805657 | − | 0.592382i | \(-0.798188\pi\) | ||||
−0.805657 | + | 0.592382i | \(0.798188\pi\) | |||||||
\(504\) | −960267. | −0.168390 | ||||||||
\(505\) | 3.58302e6 | 0.625202 | ||||||||
\(506\) | 654699. | 0.113675 | ||||||||
\(507\) | −316171. | −0.0546264 | ||||||||
\(508\) | −960590. | −0.165150 | ||||||||
\(509\) | 5.27340e6 | 0.902187 | 0.451093 | − | 0.892477i | \(-0.351034\pi\) | ||||
0.451093 | + | 0.892477i | \(0.351034\pi\) | |||||||
\(510\) | −2.03958e6 | −0.347228 | ||||||||
\(511\) | −1.18887e7 | −2.01411 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −263169. | −0.0441511 | ||||||||
\(514\) | −4.32768e6 | −0.722516 | ||||||||
\(515\) | 2.30679e6 | 0.383257 | ||||||||
\(516\) | 1.66123e6 | 0.274666 | ||||||||
\(517\) | −2.04880e6 | −0.337112 | ||||||||
\(518\) | −6.43633e6 | −1.05394 | ||||||||
\(519\) | −4.20249e6 | −0.684838 | ||||||||
\(520\) | −1.02002e6 | −0.165425 | ||||||||
\(521\) | 9.30638e6 | 1.50206 | 0.751029 | − | 0.660270i | \(-0.229558\pi\) | ||||
0.751029 | + | 0.660270i | \(0.229558\pi\) | |||||||
\(522\) | 2.12638e6 | 0.341559 | ||||||||
\(523\) | −8.13792e6 | −1.30095 | −0.650473 | − | 0.759529i | \(-0.725429\pi\) | ||||
−0.650473 | + | 0.759529i | \(0.725429\pi\) | |||||||
\(524\) | −3.06299e6 | −0.487324 | ||||||||
\(525\) | −1.04196e6 | −0.164988 | ||||||||
\(526\) | 2.81183e6 | 0.443123 | ||||||||
\(527\) | 2.08016e7 | 3.26265 | ||||||||
\(528\) | −306429. | −0.0478349 | ||||||||
\(529\) | −4.92184e6 | −0.764695 | ||||||||
\(530\) | 249554. | 0.0385899 | ||||||||
\(531\) | 1.14649e6 | 0.176455 | ||||||||
\(532\) | 1.06993e6 | 0.163899 | ||||||||
\(533\) | −3.10520e6 | −0.473447 | ||||||||
\(534\) | −2.16589e6 | −0.328687 | ||||||||
\(535\) | −2.86263e6 | −0.432395 | ||||||||
\(536\) | −125798. | −0.0189131 | ||||||||
\(537\) | 253301. | 0.0379054 | ||||||||
\(538\) | −2.02186e6 | −0.301159 | ||||||||
\(539\) | 2.32822e6 | 0.345186 | ||||||||
\(540\) | −291600. | −0.0430331 | ||||||||
\(541\) | −3.43794e6 | −0.505015 | −0.252508 | − | 0.967595i | \(-0.581255\pi\) | ||||
−0.252508 | + | 0.967595i | \(0.581255\pi\) | |||||||
\(542\) | −2.04288e6 | −0.298706 | ||||||||
\(543\) | −6.83000e6 | −0.994079 | ||||||||
\(544\) | 2.32059e6 | 0.336202 | ||||||||
\(545\) | −5.98509e6 | −0.863137 | ||||||||
\(546\) | 4.25127e6 | 0.610291 | ||||||||
\(547\) | 8.85291e6 | 1.26508 | 0.632539 | − | 0.774528i | \(-0.282013\pi\) | ||||
0.632539 | + | 0.774528i | \(0.282013\pi\) | |||||||
\(548\) | −5.34643e6 | −0.760524 | ||||||||
\(549\) | −1.52327e6 | −0.215699 | ||||||||
\(550\) | −332496. | −0.0468684 | ||||||||
\(551\) | −2.36921e6 | −0.332449 | ||||||||
\(552\) | −708855. | −0.0990170 | ||||||||
\(553\) | 1.63314e7 | 2.27096 | ||||||||
\(554\) | −3.19248e6 | −0.441931 | ||||||||
\(555\) | −1.95449e6 | −0.269340 | ||||||||
\(556\) | 5.75070e6 | 0.788921 | ||||||||
\(557\) | 202563. | 0.0276644 | 0.0138322 | − | 0.999904i | \(-0.495597\pi\) | ||||
0.0138322 | + | 0.999904i | \(0.495597\pi\) | |||||||
\(558\) | 2.97403e6 | 0.404352 | ||||||||
\(559\) | −7.35453e6 | −0.995464 | ||||||||
\(560\) | 1.18551e6 | 0.159749 | ||||||||
\(561\) | 2.71261e6 | 0.363898 | ||||||||
\(562\) | −1.69192e6 | −0.225964 | ||||||||
\(563\) | 1.73026e6 | 0.230059 | 0.115030 | − | 0.993362i | \(-0.463304\pi\) | ||||
0.115030 | + | 0.993362i | \(0.463304\pi\) | |||||||
\(564\) | 2.21828e6 | 0.293642 | ||||||||
\(565\) | 5.10805e6 | 0.673185 | ||||||||
\(566\) | 8.56469e6 | 1.12375 | ||||||||
\(567\) | 1.21534e6 | 0.158759 | ||||||||
\(568\) | −2.04732e6 | −0.266265 | ||||||||
\(569\) | −1.00719e7 | −1.30416 | −0.652081 | − | 0.758149i | \(-0.726104\pi\) | ||||
−0.652081 | + | 0.758149i | \(0.726104\pi\) | |||||||
\(570\) | 324900. | 0.0418854 | ||||||||
\(571\) | 3.76172e6 | 0.482832 | 0.241416 | − | 0.970422i | \(-0.422388\pi\) | ||||
0.241416 | + | 0.970422i | \(0.422388\pi\) | |||||||
\(572\) | 1.35661e6 | 0.173367 | ||||||||
\(573\) | −5.91872e6 | −0.753080 | ||||||||
\(574\) | 3.60900e6 | 0.457201 | ||||||||
\(575\) | −769157. | −0.0970164 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −1.32750e7 | −1.65995 | −0.829973 | − | 0.557803i | \(-0.811644\pi\) | ||||
−0.829973 | + | 0.557803i | \(0.811644\pi\) | |||||||
\(578\) | −1.48632e7 | −1.85051 | ||||||||
\(579\) | 8.85253e6 | 1.09742 | ||||||||
\(580\) | −2.62517e6 | −0.324031 | ||||||||
\(581\) | −2.38166e6 | −0.292711 | ||||||||
\(582\) | −1.21832e6 | −0.149092 | ||||||||
\(583\) | −331903. | −0.0404426 | ||||||||
\(584\) | 4.10761e6 | 0.498376 | ||||||||
\(585\) | 1.29096e6 | 0.155964 | ||||||||
\(586\) | 6.15151e6 | 0.740011 | ||||||||
\(587\) | −513155. | −0.0614686 | −0.0307343 | − | 0.999528i | \(-0.509785\pi\) | ||||
−0.0307343 | + | 0.999528i | \(0.509785\pi\) | |||||||
\(588\) | −2.52081e6 | −0.300675 | ||||||||
\(589\) | −3.31365e6 | −0.393567 | ||||||||
\(590\) | −1.41542e6 | −0.167400 | ||||||||
\(591\) | −3.17221e6 | −0.373588 | ||||||||
\(592\) | 2.22378e6 | 0.260788 | ||||||||
\(593\) | 6.75813e6 | 0.789204 | 0.394602 | − | 0.918852i | \(-0.370882\pi\) | ||||
0.394602 | + | 0.918852i | \(0.370882\pi\) | |||||||
\(594\) | 387824. | 0.0450992 | ||||||||
\(595\) | −1.04946e7 | −1.21527 | ||||||||
\(596\) | −5.29745e6 | −0.610874 | ||||||||
\(597\) | 6.18459e6 | 0.710190 | ||||||||
\(598\) | 3.13822e6 | 0.358865 | ||||||||
\(599\) | −2.71104e6 | −0.308723 | −0.154361 | − | 0.988014i | \(-0.549332\pi\) | ||||
−0.154361 | + | 0.988014i | \(0.549332\pi\) | |||||||
\(600\) | 360000. | 0.0408248 | ||||||||
\(601\) | 5.20578e6 | 0.587895 | 0.293948 | − | 0.955822i | \(-0.405031\pi\) | ||||
0.293948 | + | 0.955822i | \(0.405031\pi\) | |||||||
\(602\) | 8.54777e6 | 0.961306 | ||||||||
\(603\) | 159214. | 0.0178315 | ||||||||
\(604\) | 457701. | 0.0510493 | ||||||||
\(605\) | −3.58406e6 | −0.398095 | ||||||||
\(606\) | 5.15955e6 | 0.570729 | ||||||||
\(607\) | −1.50241e6 | −0.165507 | −0.0827535 | − | 0.996570i | \(-0.526371\pi\) | ||||
−0.0827535 | + | 0.996570i | \(0.526371\pi\) | |||||||
\(608\) | −369664. | −0.0405554 | ||||||||
\(609\) | 1.09412e7 | 1.19543 | ||||||||
\(610\) | 1.88059e6 | 0.204630 | ||||||||
\(611\) | −9.82071e6 | −1.06424 | ||||||||
\(612\) | −2.93699e6 | −0.316974 | ||||||||
\(613\) | −1.09306e7 | −1.17488 | −0.587439 | − | 0.809268i | \(-0.699864\pi\) | ||||
−0.587439 | + | 0.809268i | \(0.699864\pi\) | |||||||
\(614\) | −1.11807e7 | −1.19687 | ||||||||
\(615\) | 1.09593e6 | 0.116841 | ||||||||
\(616\) | −1.57672e6 | −0.167418 | ||||||||
\(617\) | 1.59629e6 | 0.168810 | 0.0844049 | − | 0.996432i | \(-0.473101\pi\) | ||||
0.0844049 | + | 0.996432i | \(0.473101\pi\) | |||||||
\(618\) | 3.32178e6 | 0.349865 | ||||||||
\(619\) | 2.26197e6 | 0.237279 | 0.118640 | − | 0.992937i | \(-0.462147\pi\) | ||||
0.118640 | + | 0.992937i | \(0.462147\pi\) | |||||||
\(620\) | −3.67164e6 | −0.383602 | ||||||||
\(621\) | 897144. | 0.0933541 | ||||||||
\(622\) | −851506. | −0.0882494 | ||||||||
\(623\) | −1.11445e7 | −1.15038 | ||||||||
\(624\) | −1.46883e6 | −0.151012 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.15071e7 | −1.17363 | ||||||||
\(627\) | −432112. | −0.0438963 | ||||||||
\(628\) | 1.54259e6 | 0.156082 | ||||||||
\(629\) | −1.96856e7 | −1.98391 | ||||||||
\(630\) | −1.50042e6 | −0.150612 | ||||||||
\(631\) | −1.16013e7 | −1.15993 | −0.579967 | − | 0.814640i | \(-0.696934\pi\) | ||||
−0.579967 | + | 0.814640i | \(0.696934\pi\) | |||||||
\(632\) | −5.64255e6 | −0.561931 | ||||||||
\(633\) | −2.18238e6 | −0.216481 | ||||||||
\(634\) | 7.69460e6 | 0.760261 | ||||||||
\(635\) | −1.50092e6 | −0.147715 | ||||||||
\(636\) | 359357. | 0.0352276 | ||||||||
\(637\) | 1.11601e7 | 1.08973 | ||||||||
\(638\) | 3.49143e6 | 0.339588 | ||||||||
\(639\) | 2.59113e6 | 0.251037 | ||||||||
\(640\) | −409600. | −0.0395285 | ||||||||
\(641\) | −1.44428e7 | −1.38838 | −0.694189 | − | 0.719793i | \(-0.744237\pi\) | ||||
−0.694189 | + | 0.719793i | \(0.744237\pi\) | |||||||
\(642\) | −4.12219e6 | −0.394721 | ||||||||
\(643\) | −1.24720e7 | −1.18962 | −0.594809 | − | 0.803867i | \(-0.702772\pi\) | ||||
−0.594809 | + | 0.803867i | \(0.702772\pi\) | |||||||
\(644\) | −3.64739e6 | −0.346551 | ||||||||
\(645\) | 2.59566e6 | 0.245668 | ||||||||
\(646\) | 3.27239e6 | 0.308520 | ||||||||
\(647\) | −3.00553e6 | −0.282267 | −0.141134 | − | 0.989991i | \(-0.545075\pi\) | ||||
−0.141134 | + | 0.989991i | \(0.545075\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 1.88249e6 | 0.175437 | ||||||||
\(650\) | −1.59378e6 | −0.147961 | ||||||||
\(651\) | 1.53027e7 | 1.41520 | ||||||||
\(652\) | −5.28666e6 | −0.487038 | ||||||||
\(653\) | −7.77905e6 | −0.713910 | −0.356955 | − | 0.934122i | \(-0.616185\pi\) | ||||
−0.356955 | + | 0.934122i | \(0.616185\pi\) | |||||||
\(654\) | −8.61853e6 | −0.787932 | ||||||||
\(655\) | −4.78593e6 | −0.435876 | ||||||||
\(656\) | −1.24692e6 | −0.113131 | ||||||||
\(657\) | −5.19869e6 | −0.469873 | ||||||||
\(658\) | 1.14141e7 | 1.02772 | ||||||||
\(659\) | 4.55109e6 | 0.408227 | 0.204113 | − | 0.978947i | \(-0.434569\pi\) | ||||
0.204113 | + | 0.978947i | \(0.434569\pi\) | |||||||
\(660\) | −478795. | −0.0427848 | ||||||||
\(661\) | −1.47211e7 | −1.31050 | −0.655252 | − | 0.755411i | \(-0.727437\pi\) | ||||
−0.655252 | + | 0.755411i | \(0.727437\pi\) | |||||||
\(662\) | −1.20534e7 | −1.06897 | ||||||||
\(663\) | 1.30026e7 | 1.14880 | ||||||||
\(664\) | 822873. | 0.0724290 | ||||||||
\(665\) | 1.67176e6 | 0.146595 | ||||||||
\(666\) | −2.81447e6 | −0.245873 | ||||||||
\(667\) | 8.07666e6 | 0.702938 | ||||||||
\(668\) | −7.65354e6 | −0.663623 | ||||||||
\(669\) | 8.81623e6 | 0.761584 | ||||||||
\(670\) | −196560. | −0.0169164 | ||||||||
\(671\) | −2.50115e6 | −0.214454 | ||||||||
\(672\) | 1.70714e6 | 0.145830 | ||||||||
\(673\) | −5.53394e6 | −0.470974 | −0.235487 | − | 0.971877i | \(-0.575669\pi\) | ||||
−0.235487 | + | 0.971877i | \(0.575669\pi\) | |||||||
\(674\) | −1.06735e6 | −0.0905015 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | 562082. | 0.0473079 | ||||||||
\(677\) | −8.48504e6 | −0.711512 | −0.355756 | − | 0.934579i | \(-0.615777\pi\) | ||||
−0.355756 | + | 0.934579i | \(0.615777\pi\) | |||||||
\(678\) | 7.35560e6 | 0.614531 | ||||||||
\(679\) | −6.26881e6 | −0.521808 | ||||||||
\(680\) | 3.62592e6 | 0.300708 | ||||||||
\(681\) | −3.27613e6 | −0.270703 | ||||||||
\(682\) | 4.88322e6 | 0.402018 | ||||||||
\(683\) | −2.24787e7 | −1.84382 | −0.921910 | − | 0.387404i | \(-0.873372\pi\) | ||||
−0.921910 | + | 0.387404i | \(0.873372\pi\) | |||||||
\(684\) | 467856. | 0.0382360 | ||||||||
\(685\) | −8.35380e6 | −0.680233 | ||||||||
\(686\) | −517647. | −0.0419975 | ||||||||
\(687\) | −3.17167e6 | −0.256387 | ||||||||
\(688\) | −2.95329e6 | −0.237867 | ||||||||
\(689\) | −1.59094e6 | −0.127675 | ||||||||
\(690\) | −1.10759e6 | −0.0885635 | ||||||||
\(691\) | −6.37709e6 | −0.508075 | −0.254037 | − | 0.967194i | \(-0.581759\pi\) | ||||
−0.254037 | + | 0.967194i | \(0.581759\pi\) | |||||||
\(692\) | 7.47109e6 | 0.593087 | ||||||||
\(693\) | 1.99553e6 | 0.157843 | ||||||||
\(694\) | −4.42265e6 | −0.348565 | ||||||||
\(695\) | 8.98547e6 | 0.705633 | ||||||||
\(696\) | −3.78024e6 | −0.295799 | ||||||||
\(697\) | 1.10382e7 | 0.860629 | ||||||||
\(698\) | −1.40681e7 | −1.09294 | ||||||||
\(699\) | 1.37449e7 | 1.06402 | ||||||||
\(700\) | 1.85237e6 | 0.142883 | ||||||||
\(701\) | 3.20106e6 | 0.246036 | 0.123018 | − | 0.992404i | \(-0.460743\pi\) | ||||
0.123018 | + | 0.992404i | \(0.460743\pi\) | |||||||
\(702\) | 1.85899e6 | 0.142375 | ||||||||
\(703\) | 3.13587e6 | 0.239315 | ||||||||
\(704\) | 544762. | 0.0414262 | ||||||||
\(705\) | 3.46606e6 | 0.262641 | ||||||||
\(706\) | −6.02888e6 | −0.455224 | ||||||||
\(707\) | 2.65483e7 | 1.99750 | ||||||||
\(708\) | −2.03821e6 | −0.152815 | ||||||||
\(709\) | 1.47460e7 | 1.10168 | 0.550842 | − | 0.834609i | \(-0.314307\pi\) | ||||
0.550842 | + | 0.834609i | \(0.314307\pi\) | |||||||
\(710\) | −3.19893e6 | −0.238155 | ||||||||
\(711\) | 7.14135e6 | 0.529793 | ||||||||
\(712\) | 3.85047e6 | 0.284652 | ||||||||
\(713\) | 1.12963e7 | 0.832167 | ||||||||
\(714\) | −1.51122e7 | −1.10938 | ||||||||
\(715\) | 2.11971e6 | 0.155064 | ||||||||
\(716\) | −450313. | −0.0328270 | ||||||||
\(717\) | 8.97670e6 | 0.652107 | ||||||||
\(718\) | −2.09837e6 | −0.151904 | ||||||||
\(719\) | −5.76458e6 | −0.415858 | −0.207929 | − | 0.978144i | \(-0.566672\pi\) | ||||
−0.207929 | + | 0.978144i | \(0.566672\pi\) | |||||||
\(720\) | 518400. | 0.0372678 | ||||||||
\(721\) | 1.70921e7 | 1.22450 | ||||||||
\(722\) | −521284. | −0.0372161 | ||||||||
\(723\) | −1.02347e6 | −0.0728165 | ||||||||
\(724\) | 1.21422e7 | 0.860898 | ||||||||
\(725\) | −4.10182e6 | −0.289822 | ||||||||
\(726\) | −5.16105e6 | −0.363409 | ||||||||
\(727\) | 2.04059e7 | 1.43192 | 0.715960 | − | 0.698141i | \(-0.245989\pi\) | ||||
0.715960 | + | 0.698141i | \(0.245989\pi\) | |||||||
\(728\) | −7.55781e6 | −0.528528 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 6.41814e6 | 0.445761 | ||||||||
\(731\) | 2.61435e7 | 1.80955 | ||||||||
\(732\) | 2.70804e6 | 0.186800 | ||||||||
\(733\) | −1.49257e7 | −1.02607 | −0.513034 | − | 0.858368i | \(-0.671478\pi\) | ||||
−0.513034 | + | 0.858368i | \(0.671478\pi\) | |||||||
\(734\) | 1.96388e7 | 1.34547 | ||||||||
\(735\) | −3.93877e6 | −0.268932 | ||||||||
\(736\) | 1.26019e6 | 0.0857512 | ||||||||
\(737\) | 261422. | 0.0177286 | ||||||||
\(738\) | 1.57814e6 | 0.106661 | ||||||||
\(739\) | −2.49017e7 | −1.67732 | −0.838662 | − | 0.544652i | \(-0.816662\pi\) | ||||
−0.838662 | + | 0.544652i | \(0.816662\pi\) | |||||||
\(740\) | 3.47465e6 | 0.233256 | ||||||||
\(741\) | −2.07128e6 | −0.138578 | ||||||||
\(742\) | 1.84906e6 | 0.123294 | ||||||||
\(743\) | −9.85812e6 | −0.655122 | −0.327561 | − | 0.944830i | \(-0.606227\pi\) | ||||
−0.327561 | + | 0.944830i | \(0.606227\pi\) | |||||||
\(744\) | −5.28716e6 | −0.350179 | ||||||||
\(745\) | −8.27727e6 | −0.546382 | ||||||||
\(746\) | 1.53620e7 | 1.01065 | ||||||||
\(747\) | −1.04145e6 | −0.0682867 | ||||||||
\(748\) | −4.82242e6 | −0.315145 | ||||||||
\(749\) | −2.12106e7 | −1.38149 | ||||||||
\(750\) | 562500. | 0.0365148 | ||||||||
\(751\) | −1.17506e7 | −0.760254 | −0.380127 | − | 0.924934i | \(-0.624120\pi\) | ||||
−0.380127 | + | 0.924934i | \(0.624120\pi\) | |||||||
\(752\) | −3.94361e6 | −0.254301 | ||||||||
\(753\) | 2.73212e6 | 0.175595 | ||||||||
\(754\) | 1.67358e7 | 1.07206 | ||||||||
\(755\) | 715159. | 0.0456599 | ||||||||
\(756\) | −2.16060e6 | −0.137490 | ||||||||
\(757\) | −1.31194e7 | −0.832100 | −0.416050 | − | 0.909342i | \(-0.636586\pi\) | ||||
−0.416050 | + | 0.909342i | \(0.636586\pi\) | |||||||
\(758\) | −9.04160e6 | −0.571574 | ||||||||
\(759\) | 1.47307e6 | 0.0928154 | ||||||||
\(760\) | −577600. | −0.0362738 | ||||||||
\(761\) | −1.66140e7 | −1.03995 | −0.519974 | − | 0.854182i | \(-0.674058\pi\) | ||||
−0.519974 | + | 0.854182i | \(0.674058\pi\) | |||||||
\(762\) | −2.16133e6 | −0.134844 | ||||||||
\(763\) | −4.43463e7 | −2.75770 | ||||||||
\(764\) | 1.05222e7 | 0.652186 | ||||||||
\(765\) | −4.58905e6 | −0.283511 | ||||||||
\(766\) | 6.11204e6 | 0.376369 | ||||||||
\(767\) | 9.02351e6 | 0.553843 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | 1.24736e7 | 0.760636 | 0.380318 | − | 0.924856i | \(-0.375815\pi\) | ||||
0.380318 | + | 0.924856i | \(0.375815\pi\) | |||||||
\(770\) | −2.46362e6 | −0.149743 | ||||||||
\(771\) | −9.73728e6 | −0.589932 | ||||||||
\(772\) | −1.57378e7 | −0.950389 | ||||||||
\(773\) | −424135. | −0.0255303 | −0.0127651 | − | 0.999919i | \(-0.504063\pi\) | ||||
−0.0127651 | + | 0.999919i | \(0.504063\pi\) | |||||||
\(774\) | 3.73776e6 | 0.224263 | ||||||||
\(775\) | −5.73693e6 | −0.343104 | ||||||||
\(776\) | 2.16590e6 | 0.129117 | ||||||||
\(777\) | −1.44817e7 | −0.860535 | ||||||||
\(778\) | −1.29218e7 | −0.765372 | ||||||||
\(779\) | −1.75836e6 | −0.103816 | ||||||||
\(780\) | −2.29505e6 | −0.135069 | ||||||||
\(781\) | 4.25453e6 | 0.249588 | ||||||||
\(782\) | −1.11556e7 | −0.652343 | ||||||||
\(783\) | 4.78437e6 | 0.278882 | ||||||||
\(784\) | 4.48144e6 | 0.260392 | ||||||||
\(785\) | 2.41030e6 | 0.139604 | ||||||||
\(786\) | −6.89173e6 | −0.397898 | ||||||||
\(787\) | 2.22988e7 | 1.28335 | 0.641675 | − | 0.766977i | \(-0.278240\pi\) | ||||
0.641675 | + | 0.766977i | \(0.278240\pi\) | |||||||
\(788\) | 5.63949e6 | 0.323537 | ||||||||
\(789\) | 6.32661e6 | 0.361808 | ||||||||
\(790\) | −8.81648e6 | −0.502606 | ||||||||
\(791\) | 3.78480e7 | 2.15081 | ||||||||
\(792\) | −689465. | −0.0390570 | ||||||||
\(793\) | −1.19890e7 | −0.677017 | ||||||||
\(794\) | 1.96815e6 | 0.110791 | ||||||||
\(795\) | 561496. | 0.0315086 | ||||||||
\(796\) | −1.09948e7 | −0.615043 | ||||||||
\(797\) | −6.36779e6 | −0.355094 | −0.177547 | − | 0.984112i | \(-0.556816\pi\) | ||||
−0.177547 | + | 0.984112i | \(0.556816\pi\) | |||||||
\(798\) | 2.40734e6 | 0.133823 | ||||||||
\(799\) | 3.49101e7 | 1.93457 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | −4.87325e6 | −0.268372 | ||||||||
\(802\) | −7.71818e6 | −0.423720 | ||||||||
\(803\) | −8.53603e6 | −0.467162 | ||||||||
\(804\) | −283046. | −0.0154425 | ||||||||
\(805\) | −5.69904e6 | −0.309965 | ||||||||
\(806\) | 2.34072e7 | 1.26914 | ||||||||
\(807\) | −4.54918e6 | −0.245895 | ||||||||
\(808\) | −9.17253e6 | −0.494266 | ||||||||
\(809\) | 1.21132e7 | 0.650709 | 0.325354 | − | 0.945592i | \(-0.394516\pi\) | ||||
0.325354 | + | 0.945592i | \(0.394516\pi\) | |||||||
\(810\) | −656100. | −0.0351364 | ||||||||
\(811\) | −2.44812e7 | −1.30701 | −0.653507 | − | 0.756920i | \(-0.726703\pi\) | ||||
−0.653507 | + | 0.756920i | \(0.726703\pi\) | |||||||
\(812\) | −1.94511e7 | −1.03527 | ||||||||
\(813\) | −4.59648e6 | −0.243893 | ||||||||
\(814\) | −4.62124e6 | −0.244454 | ||||||||
\(815\) | −8.26041e6 | −0.435620 | ||||||||
\(816\) | 5.22132e6 | 0.274508 | ||||||||
\(817\) | −4.16460e6 | −0.218282 | ||||||||
\(818\) | −8.55547e6 | −0.447054 | ||||||||
\(819\) | 9.56536e6 | 0.498301 | ||||||||
\(820\) | −1.94832e6 | −0.101187 | ||||||||
\(821\) | −2.53799e6 | −0.131411 | −0.0657056 | − | 0.997839i | \(-0.520930\pi\) | ||||
−0.0657056 | + | 0.997839i | \(0.520930\pi\) | |||||||
\(822\) | −1.20295e7 | −0.620965 | ||||||||
\(823\) | 1.59503e7 | 0.820859 | 0.410430 | − | 0.911892i | \(-0.365379\pi\) | ||||
0.410430 | + | 0.911892i | \(0.365379\pi\) | |||||||
\(824\) | −5.90539e6 | −0.302992 | ||||||||
\(825\) | −748117. | −0.0382679 | ||||||||
\(826\) | −1.04875e7 | −0.534839 | ||||||||
\(827\) | −1.34516e7 | −0.683928 | −0.341964 | − | 0.939713i | \(-0.611092\pi\) | ||||
−0.341964 | + | 0.939713i | \(0.611092\pi\) | |||||||
\(828\) | −1.59492e6 | −0.0808470 | ||||||||
\(829\) | 1.99401e6 | 0.100772 | 0.0503862 | − | 0.998730i | \(-0.483955\pi\) | ||||
0.0503862 | + | 0.998730i | \(0.483955\pi\) | |||||||
\(830\) | 1.28574e6 | 0.0647825 | ||||||||
\(831\) | −7.18309e6 | −0.360835 | ||||||||
\(832\) | 2.61125e6 | 0.130780 | ||||||||
\(833\) | −3.96712e7 | −1.98090 | ||||||||
\(834\) | 1.29391e7 | 0.644151 | ||||||||
\(835\) | −1.19587e7 | −0.593562 | ||||||||
\(836\) | 768200. | 0.0380153 | ||||||||
\(837\) | 6.69156e6 | 0.330152 | ||||||||
\(838\) | 2.30706e7 | 1.13488 | ||||||||
\(839\) | −7.03249e6 | −0.344909 | −0.172454 | − | 0.985017i | \(-0.555170\pi\) | ||||
−0.172454 | + | 0.985017i | \(0.555170\pi\) | |||||||
\(840\) | 2.66741e6 | 0.130434 | ||||||||
\(841\) | 2.25607e7 | 1.09992 | ||||||||
\(842\) | 1.07965e6 | 0.0524811 | ||||||||
\(843\) | −3.80681e6 | −0.184498 | ||||||||
\(844\) | 3.87978e6 | 0.187478 | ||||||||
\(845\) | 878254. | 0.0423134 | ||||||||
\(846\) | 4.99113e6 | 0.239758 | ||||||||
\(847\) | −2.65560e7 | −1.27190 | ||||||||
\(848\) | −638857. | −0.0305080 | ||||||||
\(849\) | 1.92706e7 | 0.917540 | ||||||||
\(850\) | 5.66549e6 | 0.268962 | ||||||||
\(851\) | −1.06902e7 | −0.506014 | ||||||||
\(852\) | −4.60646e6 | −0.217404 | ||||||||
\(853\) | −1.14269e7 | −0.537721 | −0.268861 | − | 0.963179i | \(-0.586647\pi\) | ||||
−0.268861 | + | 0.963179i | \(0.586647\pi\) | |||||||
\(854\) | 1.39341e7 | 0.653786 | ||||||||
\(855\) | 731025. | 0.0341993 | ||||||||
\(856\) | 7.32833e6 | 0.341838 | ||||||||
\(857\) | 2.16028e6 | 0.100475 | 0.0502374 | − | 0.998737i | \(-0.484002\pi\) | ||||
0.0502374 | + | 0.998737i | \(0.484002\pi\) | |||||||
\(858\) | 3.05238e6 | 0.141553 | ||||||||
\(859\) | −1.41213e7 | −0.652968 | −0.326484 | − | 0.945203i | \(-0.605864\pi\) | ||||
−0.326484 | + | 0.945203i | \(0.605864\pi\) | |||||||
\(860\) | −4.61451e6 | −0.212755 | ||||||||
\(861\) | 8.12026e6 | 0.373303 | ||||||||
\(862\) | 2.49238e7 | 1.14247 | ||||||||
\(863\) | 3.85011e7 | 1.75973 | 0.879866 | − | 0.475221i | \(-0.157632\pi\) | ||||
0.879866 | + | 0.475221i | \(0.157632\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 1.16736e7 | 0.530473 | ||||||||
\(866\) | −1.24563e6 | −0.0564411 | ||||||||
\(867\) | −3.34421e7 | −1.51094 | ||||||||
\(868\) | −2.72049e7 | −1.22560 | ||||||||
\(869\) | 1.17258e7 | 0.526736 | ||||||||
\(870\) | −5.90662e6 | −0.264570 | ||||||||
\(871\) | 1.25310e6 | 0.0559679 | ||||||||
\(872\) | 1.53218e7 | 0.682370 | ||||||||
\(873\) | −2.74122e6 | −0.121733 | ||||||||
\(874\) | 1.77706e6 | 0.0786907 | ||||||||
\(875\) | 2.89432e6 | 0.127799 | ||||||||
\(876\) | 9.24212e6 | 0.406922 | ||||||||
\(877\) | 3.66258e7 | 1.60801 | 0.804004 | − | 0.594624i | \(-0.202699\pi\) | ||||
0.804004 | + | 0.594624i | \(0.202699\pi\) | |||||||
\(878\) | −1.27555e7 | −0.558421 | ||||||||
\(879\) | 1.38409e7 | 0.604216 | ||||||||
\(880\) | 851191. | 0.0370527 | ||||||||
\(881\) | 2.85701e7 | 1.24014 | 0.620072 | − | 0.784545i | \(-0.287103\pi\) | ||||
0.620072 | + | 0.784545i | \(0.287103\pi\) | |||||||
\(882\) | −5.67182e6 | −0.245500 | ||||||||
\(883\) | −4.70913e6 | −0.203254 | −0.101627 | − | 0.994823i | \(-0.532405\pi\) | ||||
−0.101627 | + | 0.994823i | \(0.532405\pi\) | |||||||
\(884\) | −2.31157e7 | −0.994893 | ||||||||
\(885\) | −3.18470e6 | −0.136682 | ||||||||
\(886\) | 9.47734e6 | 0.405604 | ||||||||
\(887\) | 3.52406e7 | 1.50395 | 0.751976 | − | 0.659191i | \(-0.229101\pi\) | ||||
0.751976 | + | 0.659191i | \(0.229101\pi\) | |||||||
\(888\) | 5.00350e6 | 0.212932 | ||||||||
\(889\) | −1.11210e7 | −0.471944 | ||||||||
\(890\) | 6.01636e6 | 0.254600 | ||||||||
\(891\) | 872604. | 0.0368233 | ||||||||
\(892\) | −1.56733e7 | −0.659551 | ||||||||
\(893\) | −5.56110e6 | −0.233363 | ||||||||
\(894\) | −1.19193e7 | −0.498776 | ||||||||
\(895\) | −703613. | −0.0293614 | ||||||||
\(896\) | −3.03492e6 | −0.126292 | ||||||||
\(897\) | 7.06101e6 | 0.293012 | ||||||||
\(898\) | −2.77169e7 | −1.14697 | ||||||||
\(899\) | 6.02416e7 | 2.48598 | ||||||||
\(900\) | 810000. | 0.0333333 | ||||||||
\(901\) | 5.65538e6 | 0.232086 | ||||||||
\(902\) | 2.59124e6 | 0.106045 | ||||||||
\(903\) | 1.92325e7 | 0.784903 | ||||||||
\(904\) | −1.30766e7 | −0.532199 | ||||||||
\(905\) | 1.89722e7 | 0.770011 | ||||||||
\(906\) | 1.02983e6 | 0.0416816 | ||||||||
\(907\) | −1.08073e7 | −0.436215 | −0.218108 | − | 0.975925i | \(-0.569988\pi\) | ||||
−0.218108 | + | 0.975925i | \(0.569988\pi\) | |||||||
\(908\) | 5.82423e6 | 0.234436 | ||||||||
\(909\) | 1.16090e7 | 0.465998 | ||||||||
\(910\) | −1.18091e7 | −0.472730 | ||||||||
\(911\) | 3.58414e7 | 1.43083 | 0.715417 | − | 0.698698i | \(-0.246237\pi\) | ||||
0.715417 | + | 0.698698i | \(0.246237\pi\) | |||||||
\(912\) | −831744. | −0.0331133 | ||||||||
\(913\) | −1.71001e6 | −0.0678926 | ||||||||
\(914\) | −5.13065e6 | −0.203145 | ||||||||
\(915\) | 4.23132e6 | 0.167079 | ||||||||
\(916\) | 5.63853e6 | 0.222038 | ||||||||
\(917\) | −3.54612e7 | −1.39261 | ||||||||
\(918\) | −6.60823e6 | −0.258809 | ||||||||
\(919\) | −4.80159e7 | −1.87541 | −0.937705 | − | 0.347432i | \(-0.887054\pi\) | ||||
−0.937705 | + | 0.347432i | \(0.887054\pi\) | |||||||
\(920\) | 1.96904e6 | 0.0766982 | ||||||||
\(921\) | −2.51565e7 | −0.977239 | ||||||||
\(922\) | −1.40378e7 | −0.543841 | ||||||||
\(923\) | 2.03936e7 | 0.787934 | ||||||||
\(924\) | −3.54762e6 | −0.136696 | ||||||||
\(925\) | 5.42915e6 | 0.208630 | ||||||||
\(926\) | 1.05592e7 | 0.404672 | ||||||||
\(927\) | 7.47401e6 | 0.285663 | ||||||||
\(928\) | 6.72043e6 | 0.256169 | ||||||||
\(929\) | 4.20495e7 | 1.59853 | 0.799266 | − | 0.600978i | \(-0.205222\pi\) | ||||
0.799266 | + | 0.600978i | \(0.205222\pi\) | |||||||
\(930\) | −8.26118e6 | −0.313209 | ||||||||
\(931\) | 6.31953e6 | 0.238952 | ||||||||
\(932\) | −2.44354e7 | −0.921465 | ||||||||
\(933\) | −1.91589e6 | −0.0720553 | ||||||||
\(934\) | −692938. | −0.0259913 | ||||||||
\(935\) | −7.53503e6 | −0.281874 | ||||||||
\(936\) | −3.30487e6 | −0.123300 | ||||||||
\(937\) | 1.58814e7 | 0.590936 | 0.295468 | − | 0.955353i | \(-0.404524\pi\) | ||||
0.295468 | + | 0.955353i | \(0.404524\pi\) | |||||||
\(938\) | −1.45640e6 | −0.0540474 | ||||||||
\(939\) | −2.58910e7 | −0.958265 | ||||||||
\(940\) | −6.16188e6 | −0.227454 | ||||||||
\(941\) | 1.60983e7 | 0.592659 | 0.296329 | − | 0.955086i | \(-0.404237\pi\) | ||||
0.296329 | + | 0.955086i | \(0.404237\pi\) | |||||||
\(942\) | 3.47083e6 | 0.127440 | ||||||||
\(943\) | 5.99425e6 | 0.219511 | ||||||||
\(944\) | 3.62348e6 | 0.132342 | ||||||||
\(945\) | −3.37594e6 | −0.122974 | ||||||||
\(946\) | 6.13724e6 | 0.222969 | ||||||||
\(947\) | −1.47834e7 | −0.535673 | −0.267837 | − | 0.963464i | \(-0.586309\pi\) | ||||
−0.267837 | + | 0.963464i | \(0.586309\pi\) | |||||||
\(948\) | −1.26957e7 | −0.458814 | ||||||||
\(949\) | −4.09165e7 | −1.47480 | ||||||||
\(950\) | −902500. | −0.0324443 | ||||||||
\(951\) | 1.73129e7 | 0.620751 | ||||||||
\(952\) | 2.68661e7 | 0.960754 | ||||||||
\(953\) | 3.55908e7 | 1.26942 | 0.634711 | − | 0.772750i | \(-0.281119\pi\) | ||||
0.634711 | + | 0.772750i | \(0.281119\pi\) | |||||||
\(954\) | 808554. | 0.0287632 | ||||||||
\(955\) | 1.64409e7 | 0.583333 | ||||||||
\(956\) | −1.59586e7 | −0.564741 | ||||||||
\(957\) | 7.85573e6 | 0.277272 | ||||||||
\(958\) | 3.31033e7 | 1.16535 | ||||||||
\(959\) | −6.18972e7 | −2.17332 | ||||||||
\(960\) | −921600. | −0.0322749 | ||||||||
\(961\) | 5.56265e7 | 1.94300 | ||||||||
\(962\) | −2.21514e7 | −0.771726 | ||||||||
\(963\) | −9.27492e6 | −0.322288 | ||||||||
\(964\) | 1.81951e6 | 0.0630610 | ||||||||
\(965\) | −2.45904e7 | −0.850054 | ||||||||
\(966\) | −8.20662e6 | −0.282958 | ||||||||
\(967\) | 2.33745e7 | 0.803852 | 0.401926 | − | 0.915672i | \(-0.368341\pi\) | ||||
0.401926 | + | 0.915672i | \(0.368341\pi\) | |||||||
\(968\) | 9.17519e6 | 0.314722 | ||||||||
\(969\) | 7.36288e6 | 0.251906 | ||||||||
\(970\) | 3.38422e6 | 0.115486 | ||||||||
\(971\) | −2.22140e7 | −0.756100 | −0.378050 | − | 0.925785i | \(-0.623405\pi\) | ||||
−0.378050 | + | 0.925785i | \(0.623405\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | 6.65775e7 | 2.25448 | ||||||||
\(974\) | −7.35087e6 | −0.248280 | ||||||||
\(975\) | −3.58601e6 | −0.120809 | ||||||||
\(976\) | −4.81430e6 | −0.161774 | ||||||||
\(977\) | 2.45425e7 | 0.822590 | 0.411295 | − | 0.911502i | \(-0.365077\pi\) | ||||
0.411295 | + | 0.911502i | \(0.365077\pi\) | |||||||
\(978\) | −1.18950e7 | −0.397665 | ||||||||
\(979\) | −8.00167e6 | −0.266823 | ||||||||
\(980\) | 7.00225e6 | 0.232902 | ||||||||
\(981\) | −1.93917e7 | −0.643344 | ||||||||
\(982\) | 2.01139e6 | 0.0665605 | ||||||||
\(983\) | 3.52199e7 | 1.16253 | 0.581265 | − | 0.813714i | \(-0.302558\pi\) | ||||
0.581265 | + | 0.813714i | \(0.302558\pi\) | |||||||
\(984\) | −2.80558e6 | −0.0923709 | ||||||||
\(985\) | 8.81170e6 | 0.289380 | ||||||||
\(986\) | −5.94915e7 | −1.94878 | ||||||||
\(987\) | 2.56817e7 | 0.839132 | ||||||||
\(988\) | 3.68228e6 | 0.120012 | ||||||||
\(989\) | 1.41971e7 | 0.461541 | ||||||||
\(990\) | −1.07729e6 | −0.0349337 | ||||||||
\(991\) | −8.23228e6 | −0.266278 | −0.133139 | − | 0.991097i | \(-0.542506\pi\) | ||||
−0.133139 | + | 0.991097i | \(0.542506\pi\) | |||||||
\(992\) | 9.39939e6 | 0.303264 | ||||||||
\(993\) | −2.71202e7 | −0.872811 | ||||||||
\(994\) | −2.37024e7 | −0.760897 | ||||||||
\(995\) | −1.71794e7 | −0.550111 | ||||||||
\(996\) | 1.85146e6 | 0.0591380 | ||||||||
\(997\) | 3.86043e7 | 1.22998 | 0.614989 | − | 0.788535i | \(-0.289160\pi\) | ||||
0.614989 | + | 0.788535i | \(0.289160\pi\) | |||||||
\(998\) | −1.61668e7 | −0.513804 | ||||||||
\(999\) | −6.33255e6 | −0.200754 |
(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 | 570.6.a.j.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.6.a.j.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial |