Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,6,Mod(1,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("147.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.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: | \(23.5764215125\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 59x^{4} + 122x^{3} + 941x^{2} - 1856x - 2338 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 7^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-5.10089\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.38033 | 0.597564 | 0.298782 | − | 0.954321i | \(-0.403420\pi\) | ||||
0.298782 | + | 0.954321i | \(0.403420\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −20.5734 | −0.642918 | ||||||||
\(5\) | −54.5253 | −0.975378 | −0.487689 | − | 0.873017i | \(-0.662160\pi\) | ||||
−0.487689 | + | 0.873017i | \(0.662160\pi\) | |||||||
\(6\) | 30.4230 | 0.345004 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −177.715 | −0.981748 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −184.313 | −0.582850 | ||||||||
\(11\) | 481.911 | 1.20084 | 0.600420 | − | 0.799685i | \(-0.295000\pi\) | ||||
0.600420 | + | 0.799685i | \(0.295000\pi\) | |||||||
\(12\) | −185.160 | −0.371189 | ||||||||
\(13\) | 512.622 | 0.841277 | 0.420638 | − | 0.907228i | \(-0.361806\pi\) | ||||
0.420638 | + | 0.907228i | \(0.361806\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −490.728 | −0.563135 | ||||||||
\(16\) | 57.6111 | 0.0562608 | ||||||||
\(17\) | 590.744 | 0.495766 | 0.247883 | − | 0.968790i | \(-0.420265\pi\) | ||||
0.247883 | + | 0.968790i | \(0.420265\pi\) | |||||||
\(18\) | 273.807 | 0.199188 | ||||||||
\(19\) | 2451.02 | 1.55762 | 0.778811 | − | 0.627259i | \(-0.215823\pi\) | ||||
0.778811 | + | 0.627259i | \(0.215823\pi\) | |||||||
\(20\) | 1121.77 | 0.627088 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1629.02 | 0.717579 | ||||||||
\(23\) | 1774.90 | 0.699609 | 0.349804 | − | 0.936823i | \(-0.386248\pi\) | ||||
0.349804 | + | 0.936823i | \(0.386248\pi\) | |||||||
\(24\) | −1599.44 | −0.566812 | ||||||||
\(25\) | −151.993 | −0.0486379 | ||||||||
\(26\) | 1732.83 | 0.502716 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4246.44 | −0.937627 | −0.468814 | − | 0.883297i | \(-0.655318\pi\) | ||||
−0.468814 | + | 0.883297i | \(0.655318\pi\) | |||||||
\(30\) | −1658.82 | −0.336509 | ||||||||
\(31\) | 9767.37 | 1.82547 | 0.912733 | − | 0.408558i | \(-0.133968\pi\) | ||||
0.912733 | + | 0.408558i | \(0.133968\pi\) | |||||||
\(32\) | 5881.64 | 1.01537 | ||||||||
\(33\) | 4337.20 | 0.693306 | ||||||||
\(34\) | 1996.91 | 0.296252 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1666.44 | −0.214306 | ||||||||
\(37\) | −9969.65 | −1.19722 | −0.598612 | − | 0.801039i | \(-0.704281\pi\) | ||||
−0.598612 | + | 0.801039i | \(0.704281\pi\) | |||||||
\(38\) | 8285.24 | 0.930778 | ||||||||
\(39\) | 4613.60 | 0.485711 | ||||||||
\(40\) | 9689.98 | 0.957575 | ||||||||
\(41\) | −3377.54 | −0.313791 | −0.156896 | − | 0.987615i | \(-0.550149\pi\) | ||||
−0.156896 | + | 0.987615i | \(0.550149\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −18223.4 | −1.50300 | −0.751500 | − | 0.659733i | \(-0.770669\pi\) | ||||
−0.751500 | + | 0.659733i | \(0.770669\pi\) | |||||||
\(44\) | −9914.53 | −0.772042 | ||||||||
\(45\) | −4416.55 | −0.325126 | ||||||||
\(46\) | 5999.76 | 0.418061 | ||||||||
\(47\) | 1320.64 | 0.0872046 | 0.0436023 | − | 0.999049i | \(-0.486117\pi\) | ||||
0.0436023 | + | 0.999049i | \(0.486117\pi\) | |||||||
\(48\) | 518.500 | 0.0324822 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −513.788 | −0.0290642 | ||||||||
\(51\) | 5316.69 | 0.286231 | ||||||||
\(52\) | −10546.4 | −0.540872 | ||||||||
\(53\) | 34837.0 | 1.70353 | 0.851767 | − | 0.523921i | \(-0.175531\pi\) | ||||
0.851767 | + | 0.523921i | \(0.175531\pi\) | |||||||
\(54\) | 2464.26 | 0.115001 | ||||||||
\(55\) | −26276.3 | −1.17127 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 22059.1 | 0.899293 | ||||||||
\(58\) | −14354.4 | −0.560292 | ||||||||
\(59\) | 11592.5 | 0.433558 | 0.216779 | − | 0.976221i | \(-0.430445\pi\) | ||||
0.216779 | + | 0.976221i | \(0.430445\pi\) | |||||||
\(60\) | 10095.9 | 0.362049 | ||||||||
\(61\) | 31406.1 | 1.08066 | 0.540331 | − | 0.841452i | \(-0.318299\pi\) | ||||
0.540331 | + | 0.841452i | \(0.318299\pi\) | |||||||
\(62\) | 33016.9 | 1.09083 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 18038.3 | 0.550486 | ||||||||
\(65\) | −27950.9 | −0.820563 | ||||||||
\(66\) | 14661.2 | 0.414294 | ||||||||
\(67\) | 27555.9 | 0.749942 | 0.374971 | − | 0.927036i | \(-0.377653\pi\) | ||||
0.374971 | + | 0.927036i | \(0.377653\pi\) | |||||||
\(68\) | −12153.6 | −0.318737 | ||||||||
\(69\) | 15974.1 | 0.403919 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −22868.5 | −0.538384 | −0.269192 | − | 0.963086i | \(-0.586757\pi\) | ||||
−0.269192 | + | 0.963086i | \(0.586757\pi\) | |||||||
\(72\) | −14394.9 | −0.327249 | ||||||||
\(73\) | 15936.4 | 0.350012 | 0.175006 | − | 0.984567i | \(-0.444005\pi\) | ||||
0.175006 | + | 0.984567i | \(0.444005\pi\) | |||||||
\(74\) | −33700.7 | −0.715418 | ||||||||
\(75\) | −1367.94 | −0.0280811 | ||||||||
\(76\) | −50425.6 | −1.00142 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 15595.5 | 0.290243 | ||||||||
\(79\) | 87165.3 | 1.57136 | 0.785680 | − | 0.618633i | \(-0.212313\pi\) | ||||
0.785680 | + | 0.618633i | \(0.212313\pi\) | |||||||
\(80\) | −3141.26 | −0.0548755 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −11417.2 | −0.187510 | ||||||||
\(83\) | 90307.5 | 1.43889 | 0.719447 | − | 0.694548i | \(-0.244395\pi\) | ||||
0.719447 | + | 0.694548i | \(0.244395\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −32210.5 | −0.483559 | ||||||||
\(86\) | −61601.2 | −0.898138 | ||||||||
\(87\) | −38218.0 | −0.541339 | ||||||||
\(88\) | −85643.0 | −1.17892 | ||||||||
\(89\) | −126570. | −1.69377 | −0.846884 | − | 0.531777i | \(-0.821524\pi\) | ||||
−0.846884 | + | 0.531777i | \(0.821524\pi\) | |||||||
\(90\) | −14929.4 | −0.194283 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −36515.7 | −0.449791 | ||||||||
\(93\) | 87906.4 | 1.05393 | ||||||||
\(94\) | 4464.20 | 0.0521103 | ||||||||
\(95\) | −133642. | −1.51927 | ||||||||
\(96\) | 52934.7 | 0.586223 | ||||||||
\(97\) | −16573.1 | −0.178844 | −0.0894219 | − | 0.995994i | \(-0.528502\pi\) | ||||
−0.0894219 | + | 0.995994i | \(0.528502\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 39034.8 | 0.400280 | ||||||||
\(100\) | 3127.02 | 0.0312702 | ||||||||
\(101\) | −76610.1 | −0.747279 | −0.373639 | − | 0.927574i | \(-0.621890\pi\) | ||||
−0.373639 | + | 0.927574i | \(0.621890\pi\) | |||||||
\(102\) | 17972.2 | 0.171041 | ||||||||
\(103\) | 80435.8 | 0.747062 | 0.373531 | − | 0.927618i | \(-0.378147\pi\) | ||||
0.373531 | + | 0.927618i | \(0.378147\pi\) | |||||||
\(104\) | −91100.8 | −0.825922 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 117760. | 1.01797 | ||||||||
\(107\) | 148042. | 1.25005 | 0.625023 | − | 0.780606i | \(-0.285090\pi\) | ||||
0.625023 | + | 0.780606i | \(0.285090\pi\) | |||||||
\(108\) | −14998.0 | −0.123730 | ||||||||
\(109\) | −124982. | −1.00759 | −0.503793 | − | 0.863825i | \(-0.668062\pi\) | ||||
−0.503793 | + | 0.863825i | \(0.668062\pi\) | |||||||
\(110\) | −88822.7 | −0.699910 | ||||||||
\(111\) | −89726.9 | −0.691218 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −194474. | −1.43273 | −0.716366 | − | 0.697724i | \(-0.754196\pi\) | ||||
−0.716366 | + | 0.697724i | \(0.754196\pi\) | |||||||
\(114\) | 74567.2 | 0.537385 | ||||||||
\(115\) | −96777.1 | −0.682383 | ||||||||
\(116\) | 87363.6 | 0.602817 | ||||||||
\(117\) | 41522.4 | 0.280426 | ||||||||
\(118\) | 39186.5 | 0.259078 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 87209.8 | 0.552856 | ||||||||
\(121\) | 71187.4 | 0.442018 | ||||||||
\(122\) | 106163. | 0.645765 | ||||||||
\(123\) | −30397.9 | −0.181168 | ||||||||
\(124\) | −200948. | −1.17362 | ||||||||
\(125\) | 178679. | 1.02282 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 239766. | 1.31910 | 0.659551 | − | 0.751660i | \(-0.270746\pi\) | ||||
0.659551 | + | 0.751660i | \(0.270746\pi\) | |||||||
\(128\) | −127237. | −0.686417 | ||||||||
\(129\) | −164011. | −0.867758 | ||||||||
\(130\) | −94483.2 | −0.490339 | ||||||||
\(131\) | −349576. | −1.77977 | −0.889883 | − | 0.456188i | \(-0.849214\pi\) | ||||
−0.889883 | + | 0.456188i | \(0.849214\pi\) | |||||||
\(132\) | −89230.8 | −0.445738 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 93148.1 | 0.448138 | ||||||||
\(135\) | −39748.9 | −0.187712 | ||||||||
\(136\) | −104984. | −0.486717 | ||||||||
\(137\) | −280966. | −1.27894 | −0.639472 | − | 0.768814i | \(-0.720847\pi\) | ||||
−0.639472 | + | 0.768814i | \(0.720847\pi\) | |||||||
\(138\) | 53997.8 | 0.241367 | ||||||||
\(139\) | 50042.9 | 0.219688 | 0.109844 | − | 0.993949i | \(-0.464965\pi\) | ||||
0.109844 | + | 0.993949i | \(0.464965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11885.8 | 0.0503476 | ||||||||
\(142\) | −77303.2 | −0.321719 | ||||||||
\(143\) | 247038. | 1.01024 | ||||||||
\(144\) | 4666.50 | 0.0187536 | ||||||||
\(145\) | 231538. | 0.914541 | ||||||||
\(146\) | 53870.3 | 0.209155 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 205109. | 0.769717 | ||||||||
\(149\) | −328813. | −1.21334 | −0.606671 | − | 0.794953i | \(-0.707495\pi\) | ||||
−0.606671 | + | 0.794953i | \(0.707495\pi\) | |||||||
\(150\) | −4624.09 | −0.0167802 | ||||||||
\(151\) | 511304. | 1.82489 | 0.912445 | − | 0.409200i | \(-0.134192\pi\) | ||||
0.912445 | + | 0.409200i | \(0.134192\pi\) | |||||||
\(152\) | −435583. | −1.52919 | ||||||||
\(153\) | 47850.2 | 0.165255 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −532569. | −1.78052 | ||||||||
\(156\) | −94917.3 | −0.312272 | ||||||||
\(157\) | −75442.1 | −0.244267 | −0.122134 | − | 0.992514i | \(-0.538974\pi\) | ||||
−0.122134 | + | 0.992514i | \(0.538974\pi\) | |||||||
\(158\) | 294647. | 0.938988 | ||||||||
\(159\) | 313533. | 0.983536 | ||||||||
\(160\) | −320698. | −0.990367 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 22178.3 | 0.0663960 | ||||||||
\(163\) | 340753. | 1.00455 | 0.502274 | − | 0.864709i | \(-0.332497\pi\) | ||||
0.502274 | + | 0.864709i | \(0.332497\pi\) | |||||||
\(164\) | 69487.4 | 0.201742 | ||||||||
\(165\) | −236487. | −0.676235 | ||||||||
\(166\) | 305269. | 0.859831 | ||||||||
\(167\) | −132392. | −0.367342 | −0.183671 | − | 0.982988i | \(-0.558798\pi\) | ||||
−0.183671 | + | 0.982988i | \(0.558798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −108512. | −0.292253 | ||||||||
\(170\) | −108882. | −0.288957 | ||||||||
\(171\) | 198532. | 0.519207 | ||||||||
\(172\) | 374917. | 0.966306 | ||||||||
\(173\) | 449322. | 1.14141 | 0.570706 | − | 0.821154i | \(-0.306670\pi\) | ||||
0.570706 | + | 0.821154i | \(0.306670\pi\) | |||||||
\(174\) | −129189. | −0.323485 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 27763.4 | 0.0675602 | ||||||||
\(177\) | 104332. | 0.250315 | ||||||||
\(178\) | −427847. | −1.01213 | ||||||||
\(179\) | −93666.8 | −0.218501 | −0.109250 | − | 0.994014i | \(-0.534845\pi\) | ||||
−0.109250 | + | 0.994014i | \(0.534845\pi\) | |||||||
\(180\) | 90863.3 | 0.209029 | ||||||||
\(181\) | 399795. | 0.907071 | 0.453535 | − | 0.891238i | \(-0.350163\pi\) | ||||
0.453535 | + | 0.891238i | \(0.350163\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 282655. | 0.623921 | ||||||||
\(184\) | −315428. | −0.686839 | ||||||||
\(185\) | 543598. | 1.16775 | ||||||||
\(186\) | 297153. | 0.629792 | ||||||||
\(187\) | 284686. | 0.595336 | ||||||||
\(188\) | −27170.0 | −0.0560654 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −451755. | −0.907861 | ||||||||
\(191\) | 27822.7 | 0.0551844 | 0.0275922 | − | 0.999619i | \(-0.491216\pi\) | ||||
0.0275922 | + | 0.999619i | \(0.491216\pi\) | |||||||
\(192\) | 162345. | 0.317823 | ||||||||
\(193\) | −66464.3 | −0.128438 | −0.0642192 | − | 0.997936i | \(-0.520456\pi\) | ||||
−0.0642192 | + | 0.997936i | \(0.520456\pi\) | |||||||
\(194\) | −56022.5 | −0.106871 | ||||||||
\(195\) | −251558. | −0.473752 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −492506. | −0.904162 | −0.452081 | − | 0.891977i | \(-0.649318\pi\) | ||||
−0.452081 | + | 0.891977i | \(0.649318\pi\) | |||||||
\(198\) | 131951. | 0.239193 | ||||||||
\(199\) | 349206. | 0.625099 | 0.312549 | − | 0.949902i | \(-0.398817\pi\) | ||||
0.312549 | + | 0.949902i | \(0.398817\pi\) | |||||||
\(200\) | 27011.6 | 0.0477501 | ||||||||
\(201\) | 248003. | 0.432979 | ||||||||
\(202\) | −258967. | −0.446547 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −109382. | −0.184023 | ||||||||
\(205\) | 184161. | 0.306065 | ||||||||
\(206\) | 271900. | 0.446417 | ||||||||
\(207\) | 143767. | 0.233203 | ||||||||
\(208\) | 29532.7 | 0.0473309 | ||||||||
\(209\) | 1.18117e6 | 1.87046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −218250. | −0.337480 | −0.168740 | − | 0.985661i | \(-0.553970\pi\) | ||||
−0.168740 | + | 0.985661i | \(0.553970\pi\) | |||||||
\(212\) | −716714. | −1.09523 | ||||||||
\(213\) | −205817. | −0.310836 | ||||||||
\(214\) | 500431. | 0.746982 | ||||||||
\(215\) | 993638. | 1.46599 | ||||||||
\(216\) | −129554. | −0.188937 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −422481. | −0.602096 | ||||||||
\(219\) | 143428. | 0.202080 | ||||||||
\(220\) | 540593. | 0.753032 | ||||||||
\(221\) | 302828. | 0.417076 | ||||||||
\(222\) | −303306. | −0.413047 | ||||||||
\(223\) | 1.24807e6 | 1.68065 | 0.840324 | − | 0.542084i | \(-0.182365\pi\) | ||||
0.840324 | + | 0.542084i | \(0.182365\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12311.5 | −0.0162126 | ||||||||
\(226\) | −657386. | −0.856149 | ||||||||
\(227\) | −520973. | −0.671044 | −0.335522 | − | 0.942032i | \(-0.608913\pi\) | ||||
−0.335522 | + | 0.942032i | \(0.608913\pi\) | |||||||
\(228\) | −453831. | −0.578172 | ||||||||
\(229\) | −525651. | −0.662383 | −0.331191 | − | 0.943564i | \(-0.607451\pi\) | ||||
−0.331191 | + | 0.943564i | \(0.607451\pi\) | |||||||
\(230\) | −327139. | −0.407767 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 754658. | 0.920514 | ||||||||
\(233\) | 210205. | 0.253661 | 0.126831 | − | 0.991924i | \(-0.459520\pi\) | ||||
0.126831 | + | 0.991924i | \(0.459520\pi\) | |||||||
\(234\) | 140359. | 0.167572 | ||||||||
\(235\) | −72008.2 | −0.0850575 | ||||||||
\(236\) | −238497. | −0.278742 | ||||||||
\(237\) | 784488. | 0.907225 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 805791. | 0.912489 | 0.456244 | − | 0.889855i | \(-0.349194\pi\) | ||||
0.456244 | + | 0.889855i | \(0.349194\pi\) | |||||||
\(240\) | −28271.3 | −0.0316824 | ||||||||
\(241\) | 1.13795e6 | 1.26206 | 0.631030 | − | 0.775758i | \(-0.282632\pi\) | ||||
0.631030 | + | 0.775758i | \(0.282632\pi\) | |||||||
\(242\) | 240637. | 0.264134 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −646130. | −0.694777 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −102755. | −0.108259 | ||||||||
\(247\) | 1.25644e6 | 1.31039 | ||||||||
\(248\) | −1.73581e6 | −1.79215 | ||||||||
\(249\) | 812768. | 0.830746 | ||||||||
\(250\) | 603994. | 0.611199 | ||||||||
\(251\) | −1.16566e6 | −1.16785 | −0.583927 | − | 0.811806i | \(-0.698484\pi\) | ||||
−0.583927 | + | 0.811806i | \(0.698484\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 855346. | 0.840118 | ||||||||
\(254\) | 810489. | 0.788248 | ||||||||
\(255\) | −289894. | −0.279183 | ||||||||
\(256\) | −1.00733e6 | −0.960664 | ||||||||
\(257\) | −1.02881e6 | −0.971635 | −0.485817 | − | 0.874060i | \(-0.661478\pi\) | ||||
−0.485817 | + | 0.874060i | \(0.661478\pi\) | |||||||
\(258\) | −554411. | −0.518540 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 575043. | 0.527554 | ||||||||
\(261\) | −343962. | −0.312542 | ||||||||
\(262\) | −1.18168e6 | −1.06352 | ||||||||
\(263\) | −657345. | −0.586009 | −0.293004 | − | 0.956111i | \(-0.594655\pi\) | ||||
−0.293004 | + | 0.956111i | \(0.594655\pi\) | |||||||
\(264\) | −770787. | −0.680651 | ||||||||
\(265\) | −1.89950e6 | −1.66159 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.13913e6 | −0.977898 | ||||||||
\(268\) | −566918. | −0.482151 | ||||||||
\(269\) | 5475.86 | 0.00461393 | 0.00230697 | − | 0.999997i | \(-0.499266\pi\) | ||||
0.00230697 | + | 0.999997i | \(0.499266\pi\) | |||||||
\(270\) | −134365. | −0.112170 | ||||||||
\(271\) | −769147. | −0.636189 | −0.318094 | − | 0.948059i | \(-0.603043\pi\) | ||||
−0.318094 | + | 0.948059i | \(0.603043\pi\) | |||||||
\(272\) | 34033.4 | 0.0278922 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −949757. | −0.764251 | ||||||||
\(275\) | −73247.3 | −0.0584063 | ||||||||
\(276\) | −328642. | −0.259687 | ||||||||
\(277\) | −1.17384e6 | −0.919196 | −0.459598 | − | 0.888127i | \(-0.652007\pi\) | ||||
−0.459598 | + | 0.888127i | \(0.652007\pi\) | |||||||
\(278\) | 169162. | 0.131277 | ||||||||
\(279\) | 791157. | 0.608488 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 837649. | 0.632843 | 0.316422 | − | 0.948619i | \(-0.397519\pi\) | ||||
0.316422 | + | 0.948619i | \(0.397519\pi\) | |||||||
\(282\) | 40177.8 | 0.0300859 | ||||||||
\(283\) | −597221. | −0.443271 | −0.221635 | − | 0.975130i | \(-0.571139\pi\) | ||||
−0.221635 | + | 0.975130i | \(0.571139\pi\) | |||||||
\(284\) | 470483. | 0.346137 | ||||||||
\(285\) | −1.20278e6 | −0.877151 | ||||||||
\(286\) | 835071. | 0.603682 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 476412. | 0.338456 | ||||||||
\(289\) | −1.07088e6 | −0.754216 | ||||||||
\(290\) | 782677. | 0.546496 | ||||||||
\(291\) | −149158. | −0.103256 | ||||||||
\(292\) | −327866. | −0.225029 | ||||||||
\(293\) | −851321. | −0.579328 | −0.289664 | − | 0.957128i | \(-0.593543\pi\) | ||||
−0.289664 | + | 0.957128i | \(0.593543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −632084. | −0.422883 | ||||||||
\(296\) | 1.77176e6 | 1.17537 | ||||||||
\(297\) | 351313. | 0.231102 | ||||||||
\(298\) | −1.11150e6 | −0.725049 | ||||||||
\(299\) | 909855. | 0.588565 | ||||||||
\(300\) | 28143.1 | 0.0180538 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.72838e6 | 1.09049 | ||||||||
\(303\) | −689491. | −0.431441 | ||||||||
\(304\) | 141206. | 0.0876331 | ||||||||
\(305\) | −1.71243e6 | −1.05405 | ||||||||
\(306\) | 161750. | 0.0987506 | ||||||||
\(307\) | −600906. | −0.363882 | −0.181941 | − | 0.983309i | \(-0.558238\pi\) | ||||
−0.181941 | + | 0.983309i | \(0.558238\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 723923. | 0.431316 | ||||||||
\(310\) | −1.80026e6 | −1.06397 | ||||||||
\(311\) | −465866. | −0.273124 | −0.136562 | − | 0.990632i | \(-0.543605\pi\) | ||||
−0.136562 | + | 0.990632i | \(0.543605\pi\) | |||||||
\(312\) | −819907. | −0.476846 | ||||||||
\(313\) | −2.97366e6 | −1.71565 | −0.857827 | − | 0.513938i | \(-0.828186\pi\) | ||||
−0.857827 | + | 0.513938i | \(0.828186\pi\) | |||||||
\(314\) | −255019. | −0.145965 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.79328e6 | −1.01026 | ||||||||
\(317\) | 2.55521e6 | 1.42816 | 0.714082 | − | 0.700062i | \(-0.246844\pi\) | ||||
0.714082 | + | 0.700062i | \(0.246844\pi\) | |||||||
\(318\) | 1.05984e6 | 0.587725 | ||||||||
\(319\) | −2.04641e6 | −1.12594 | ||||||||
\(320\) | −983544. | −0.536932 | ||||||||
\(321\) | 1.33238e6 | 0.721714 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.44792e6 | 0.772216 | ||||||||
\(324\) | −134982. | −0.0714353 | ||||||||
\(325\) | −77915.2 | −0.0409179 | ||||||||
\(326\) | 1.15186e6 | 0.600281 | ||||||||
\(327\) | −1.12484e6 | −0.581730 | ||||||||
\(328\) | 600241. | 0.308064 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −799405. | −0.404093 | ||||||||
\(331\) | 2.56138e6 | 1.28500 | 0.642502 | − | 0.766284i | \(-0.277896\pi\) | ||||
0.642502 | + | 0.766284i | \(0.277896\pi\) | |||||||
\(332\) | −1.85793e6 | −0.925090 | ||||||||
\(333\) | −807542. | −0.399075 | ||||||||
\(334\) | −447528. | −0.219510 | ||||||||
\(335\) | −1.50249e6 | −0.731477 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.21525e6 | −0.582894 | −0.291447 | − | 0.956587i | \(-0.594137\pi\) | ||||
−0.291447 | + | 0.956587i | \(0.594137\pi\) | |||||||
\(338\) | −366805. | −0.174640 | ||||||||
\(339\) | −1.75026e6 | −0.827188 | ||||||||
\(340\) | 662678. | 0.310889 | ||||||||
\(341\) | 4.70701e6 | 2.19209 | ||||||||
\(342\) | 671105. | 0.310259 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.23858e6 | 1.47557 | ||||||||
\(345\) | −870994. | −0.393974 | ||||||||
\(346\) | 1.51886e6 | 0.682066 | ||||||||
\(347\) | 1.25318e6 | 0.558714 | 0.279357 | − | 0.960187i | \(-0.409879\pi\) | ||||
0.279357 | + | 0.960187i | \(0.409879\pi\) | |||||||
\(348\) | 786272. | 0.348037 | ||||||||
\(349\) | 450403. | 0.197942 | 0.0989709 | − | 0.995090i | \(-0.468445\pi\) | ||||
0.0989709 | + | 0.995090i | \(0.468445\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 373702. | 0.161904 | ||||||||
\(352\) | 2.83443e6 | 1.21929 | ||||||||
\(353\) | 545281. | 0.232907 | 0.116454 | − | 0.993196i | \(-0.462847\pi\) | ||||
0.116454 | + | 0.993196i | \(0.462847\pi\) | |||||||
\(354\) | 352678. | 0.149579 | ||||||||
\(355\) | 1.24691e6 | 0.525128 | ||||||||
\(356\) | 2.60396e6 | 1.08895 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −316625. | −0.130568 | ||||||||
\(359\) | −1.01159e6 | −0.414254 | −0.207127 | − | 0.978314i | \(-0.566411\pi\) | ||||
−0.207127 | + | 0.978314i | \(0.566411\pi\) | |||||||
\(360\) | 784888. | 0.319192 | ||||||||
\(361\) | 3.53138e6 | 1.42619 | ||||||||
\(362\) | 1.35144e6 | 0.542033 | ||||||||
\(363\) | 640686. | 0.255199 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −868937. | −0.341394 | ||||||||
\(366\) | 955468. | 0.372832 | ||||||||
\(367\) | −1.09038e6 | −0.422584 | −0.211292 | − | 0.977423i | \(-0.567767\pi\) | ||||
−0.211292 | + | 0.977423i | \(0.567767\pi\) | |||||||
\(368\) | 102254. | 0.0393605 | ||||||||
\(369\) | −273581. | −0.104597 | ||||||||
\(370\) | 1.83754e6 | 0.697803 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.80853e6 | −0.677592 | ||||||||
\(373\) | −3.13003e6 | −1.16487 | −0.582433 | − | 0.812879i | \(-0.697899\pi\) | ||||
−0.582433 | + | 0.812879i | \(0.697899\pi\) | |||||||
\(374\) | 962333. | 0.355751 | ||||||||
\(375\) | 1.60811e6 | 0.590524 | ||||||||
\(376\) | −234698. | −0.0856130 | ||||||||
\(377\) | −2.17682e6 | −0.788804 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.27933e6 | −0.457492 | −0.228746 | − | 0.973486i | \(-0.573463\pi\) | ||||
−0.228746 | + | 0.973486i | \(0.573463\pi\) | |||||||
\(380\) | 2.74947e6 | 0.976766 | ||||||||
\(381\) | 2.15790e6 | 0.761584 | ||||||||
\(382\) | 94050.0 | 0.0329762 | ||||||||
\(383\) | 1.30666e6 | 0.455161 | 0.227580 | − | 0.973759i | \(-0.426919\pi\) | ||||
0.227580 | + | 0.973759i | \(0.426919\pi\) | |||||||
\(384\) | −1.14513e6 | −0.396303 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −224671. | −0.0767501 | ||||||||
\(387\) | −1.47610e6 | −0.501000 | ||||||||
\(388\) | 340964. | 0.114982 | ||||||||
\(389\) | −36488.2 | −0.0122258 | −0.00611292 | − | 0.999981i | \(-0.501946\pi\) | ||||
−0.00611292 | + | 0.999981i | \(0.501946\pi\) | |||||||
\(390\) | −850348. | −0.283097 | ||||||||
\(391\) | 1.04851e6 | 0.346842 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.14618e6 | −1.02755 | ||||||||
\(394\) | −1.66483e6 | −0.540294 | ||||||||
\(395\) | −4.75271e6 | −1.53267 | ||||||||
\(396\) | −803077. | −0.257347 | ||||||||
\(397\) | 640204. | 0.203865 | 0.101932 | − | 0.994791i | \(-0.467497\pi\) | ||||
0.101932 | + | 0.994791i | \(0.467497\pi\) | |||||||
\(398\) | 1.18043e6 | 0.373536 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8756.50 | −0.00273641 | ||||||||
\(401\) | −2.69149e6 | −0.835858 | −0.417929 | − | 0.908480i | \(-0.637244\pi\) | ||||
−0.417929 | + | 0.908480i | \(0.637244\pi\) | |||||||
\(402\) | 838333. | 0.258733 | ||||||||
\(403\) | 5.00697e6 | 1.53572 | ||||||||
\(404\) | 1.57613e6 | 0.480439 | ||||||||
\(405\) | −357740. | −0.108375 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.80449e6 | −1.43768 | ||||||||
\(408\) | −944858. | −0.281006 | ||||||||
\(409\) | 2.92572e6 | 0.864817 | 0.432409 | − | 0.901678i | \(-0.357664\pi\) | ||||
0.432409 | + | 0.901678i | \(0.357664\pi\) | |||||||
\(410\) | 622526. | 0.182893 | ||||||||
\(411\) | −2.52869e6 | −0.738399 | ||||||||
\(412\) | −1.65484e6 | −0.480299 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 485981. | 0.139354 | ||||||||
\(415\) | −4.92404e6 | −1.40347 | ||||||||
\(416\) | 3.01506e6 | 0.854205 | ||||||||
\(417\) | 450386. | 0.126837 | ||||||||
\(418\) | 3.99275e6 | 1.11772 | ||||||||
\(419\) | −5.52810e6 | −1.53830 | −0.769150 | − | 0.639068i | \(-0.779320\pi\) | ||||
−0.769150 | + | 0.639068i | \(0.779320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.77477e6 | 1.58792 | 0.793961 | − | 0.607968i | \(-0.208015\pi\) | ||||
0.793961 | + | 0.607968i | \(0.208015\pi\) | |||||||
\(422\) | −737756. | −0.201666 | ||||||||
\(423\) | 106972. | 0.0290682 | ||||||||
\(424\) | −6.19106e6 | −1.67244 | ||||||||
\(425\) | −89789.1 | −0.0241130 | ||||||||
\(426\) | −695729. | −0.185744 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −3.04573e6 | −0.803677 | ||||||||
\(429\) | 2.22334e6 | 0.583262 | ||||||||
\(430\) | 3.35882e6 | 0.876024 | ||||||||
\(431\) | 2.20964e6 | 0.572965 | 0.286483 | − | 0.958085i | \(-0.407514\pi\) | ||||
0.286483 | + | 0.958085i | \(0.407514\pi\) | |||||||
\(432\) | 41998.5 | 0.0108274 | ||||||||
\(433\) | 4.97215e6 | 1.27446 | 0.637228 | − | 0.770676i | \(-0.280081\pi\) | ||||
0.637228 | + | 0.770676i | \(0.280081\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.08385e6 | 0.528010 | ||||||||
\(436\) | 2.57130e6 | 0.647794 | ||||||||
\(437\) | 4.35032e6 | 1.08973 | ||||||||
\(438\) | 484833. | 0.120755 | ||||||||
\(439\) | −2.86405e6 | −0.709282 | −0.354641 | − | 0.935002i | \(-0.615397\pi\) | ||||
−0.354641 | + | 0.935002i | \(0.615397\pi\) | |||||||
\(440\) | 4.66971e6 | 1.14990 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.02366e6 | 0.249230 | ||||||||
\(443\) | −5.66234e6 | −1.37084 | −0.685419 | − | 0.728149i | \(-0.740381\pi\) | ||||
−0.685419 | + | 0.728149i | \(0.740381\pi\) | |||||||
\(444\) | 1.84598e6 | 0.444396 | ||||||||
\(445\) | 6.90124e6 | 1.65206 | ||||||||
\(446\) | 4.21889e6 | 1.00429 | ||||||||
\(447\) | −2.95932e6 | −0.700523 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.54480e6 | 1.76617 | 0.883084 | − | 0.469215i | \(-0.155463\pi\) | ||||
0.883084 | + | 0.469215i | \(0.155463\pi\) | |||||||
\(450\) | −41616.8 | −0.00968808 | ||||||||
\(451\) | −1.62767e6 | −0.376813 | ||||||||
\(452\) | 4.00098e6 | 0.921129 | ||||||||
\(453\) | 4.60173e6 | 1.05360 | ||||||||
\(454\) | −1.76106e6 | −0.400991 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.92025e6 | −0.882879 | ||||||||
\(457\) | −589014. | −0.131928 | −0.0659638 | − | 0.997822i | \(-0.521012\pi\) | ||||
−0.0659638 | + | 0.997822i | \(0.521012\pi\) | |||||||
\(458\) | −1.77687e6 | −0.395816 | ||||||||
\(459\) | 430652. | 0.0954102 | ||||||||
\(460\) | 1.99103e6 | 0.438716 | ||||||||
\(461\) | −5.94951e6 | −1.30385 | −0.651927 | − | 0.758282i | \(-0.726039\pi\) | ||||
−0.651927 | + | 0.758282i | \(0.726039\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.16083e6 | −0.468456 | −0.234228 | − | 0.972182i | \(-0.575256\pi\) | ||||
−0.234228 | + | 0.972182i | \(0.575256\pi\) | |||||||
\(464\) | −244642. | −0.0527517 | ||||||||
\(465\) | −4.79312e6 | −1.02798 | ||||||||
\(466\) | 710563. | 0.151579 | ||||||||
\(467\) | 505766. | 0.107314 | 0.0536571 | − | 0.998559i | \(-0.482912\pi\) | ||||
0.0536571 | + | 0.998559i | \(0.482912\pi\) | |||||||
\(468\) | −854255. | −0.180291 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −243412. | −0.0508272 | ||||||||
\(471\) | −678979. | −0.141028 | ||||||||
\(472\) | −2.06016e6 | −0.425644 | ||||||||
\(473\) | −8.78208e6 | −1.80486 | ||||||||
\(474\) | 2.65183e6 | 0.542125 | ||||||||
\(475\) | −372538. | −0.0757594 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.82179e6 | 0.567845 | ||||||||
\(478\) | 2.72384e6 | 0.545270 | ||||||||
\(479\) | −547067. | −0.108944 | −0.0544718 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544718 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(480\) | −2.88628e6 | −0.571789 | ||||||||
\(481\) | −5.11066e6 | −1.00720 | ||||||||
\(482\) | 3.84665e6 | 0.754162 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.46456e6 | −0.284181 | ||||||||
\(485\) | 903652. | 0.174440 | ||||||||
\(486\) | 199605. | 0.0383337 | ||||||||
\(487\) | 2.37889e6 | 0.454519 | 0.227259 | − | 0.973834i | \(-0.427024\pi\) | ||||
0.227259 | + | 0.973834i | \(0.427024\pi\) | |||||||
\(488\) | −5.58135e6 | −1.06094 | ||||||||
\(489\) | 3.06677e6 | 0.579976 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.19719e6 | −1.34728 | −0.673642 | − | 0.739058i | \(-0.735271\pi\) | ||||
−0.673642 | + | 0.739058i | \(0.735271\pi\) | |||||||
\(492\) | 625386. | 0.116476 | ||||||||
\(493\) | −2.50856e6 | −0.464844 | ||||||||
\(494\) | 4.24720e6 | 0.783042 | ||||||||
\(495\) | −2.12838e6 | −0.390424 | ||||||||
\(496\) | 562709. | 0.102702 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 2.74742e6 | 0.496423 | ||||||||
\(499\) | 2.22236e6 | 0.399543 | 0.199771 | − | 0.979843i | \(-0.435980\pi\) | ||||
0.199771 | + | 0.979843i | \(0.435980\pi\) | |||||||
\(500\) | −3.67603e6 | −0.657588 | ||||||||
\(501\) | −1.19153e6 | −0.212085 | ||||||||
\(502\) | −3.94032e6 | −0.697867 | ||||||||
\(503\) | −305857. | −0.0539013 | −0.0269506 | − | 0.999637i | \(-0.508580\pi\) | ||||
−0.0269506 | + | 0.999637i | \(0.508580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.17719e6 | 0.728879 | ||||||||
\(506\) | 2.89135e6 | 0.502024 | ||||||||
\(507\) | −976604. | −0.168732 | ||||||||
\(508\) | −4.93280e6 | −0.848074 | ||||||||
\(509\) | −9.06420e6 | −1.55073 | −0.775363 | − | 0.631516i | \(-0.782433\pi\) | ||||
−0.775363 | + | 0.631516i | \(0.782433\pi\) | |||||||
\(510\) | −979938. | −0.166830 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 666475. | 0.112359 | ||||||||
\(513\) | 1.78679e6 | 0.299764 | ||||||||
\(514\) | −3.47772e6 | −0.580614 | ||||||||
\(515\) | −4.38579e6 | −0.728668 | ||||||||
\(516\) | 3.37426e6 | 0.557897 | ||||||||
\(517\) | 636431. | 0.104719 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.04390e6 | 0.658995 | ||||||||
\(520\) | 4.96730e6 | 0.805586 | ||||||||
\(521\) | 8.44649e6 | 1.36327 | 0.681635 | − | 0.731692i | \(-0.261269\pi\) | ||||
0.681635 | + | 0.731692i | \(0.261269\pi\) | |||||||
\(522\) | −1.16270e6 | −0.186764 | ||||||||
\(523\) | 3.91585e6 | 0.625997 | 0.312998 | − | 0.949754i | \(-0.398667\pi\) | ||||
0.312998 | + | 0.949754i | \(0.398667\pi\) | |||||||
\(524\) | 7.19195e6 | 1.14424 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.22204e6 | −0.350178 | ||||||||
\(527\) | 5.77001e6 | 0.905003 | ||||||||
\(528\) | 249871. | 0.0390059 | ||||||||
\(529\) | −3.28606e6 | −0.510548 | ||||||||
\(530\) | −6.42092e6 | −0.992905 | ||||||||
\(531\) | 938992. | 0.144519 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.73140e6 | −0.263985 | ||||||||
\(534\) | −3.85062e6 | −0.584356 | ||||||||
\(535\) | −8.07204e6 | −1.21927 | ||||||||
\(536\) | −4.89711e6 | −0.736254 | ||||||||
\(537\) | −843001. | −0.126152 | ||||||||
\(538\) | 18510.2 | 0.00275712 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 817769. | 0.120683 | ||||||||
\(541\) | −2.94802e6 | −0.433049 | −0.216524 | − | 0.976277i | \(-0.569472\pi\) | ||||
−0.216524 | + | 0.976277i | \(0.569472\pi\) | |||||||
\(542\) | −2.59997e6 | −0.380163 | ||||||||
\(543\) | 3.59816e6 | 0.523698 | ||||||||
\(544\) | 3.47454e6 | 0.503385 | ||||||||
\(545\) | 6.81469e6 | 0.982776 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.50670e6 | −0.786906 | −0.393453 | − | 0.919345i | \(-0.628720\pi\) | ||||
−0.393453 | + | 0.919345i | \(0.628720\pi\) | |||||||
\(548\) | 5.78041e6 | 0.822256 | ||||||||
\(549\) | 2.54390e6 | 0.360221 | ||||||||
\(550\) | −247600. | −0.0349015 | ||||||||
\(551\) | −1.04081e7 | −1.46047 | ||||||||
\(552\) | −2.83885e6 | −0.396547 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.96796e6 | −0.549278 | ||||||||
\(555\) | 4.89238e6 | 0.674199 | ||||||||
\(556\) | −1.02955e6 | −0.141241 | ||||||||
\(557\) | −4.97235e6 | −0.679085 | −0.339542 | − | 0.940591i | \(-0.610272\pi\) | ||||
−0.339542 | + | 0.940591i | \(0.610272\pi\) | |||||||
\(558\) | 2.67437e6 | 0.363611 | ||||||||
\(559\) | −9.34174e6 | −1.26444 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.56217e6 | 0.343717 | ||||||||
\(562\) | 2.83153e6 | 0.378164 | ||||||||
\(563\) | 1.31397e7 | 1.74709 | 0.873544 | − | 0.486745i | \(-0.161816\pi\) | ||||
0.873544 | + | 0.486745i | \(0.161816\pi\) | |||||||
\(564\) | −244530. | −0.0323694 | ||||||||
\(565\) | 1.06037e7 | 1.39746 | ||||||||
\(566\) | −2.01880e6 | −0.264882 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.06409e6 | 0.528558 | ||||||||
\(569\) | −1.38589e7 | −1.79452 | −0.897261 | − | 0.441500i | \(-0.854447\pi\) | ||||
−0.897261 | + | 0.441500i | \(0.854447\pi\) | |||||||
\(570\) | −4.06580e6 | −0.524154 | ||||||||
\(571\) | −1.06977e7 | −1.37309 | −0.686547 | − | 0.727085i | \(-0.740874\pi\) | ||||
−0.686547 | + | 0.727085i | \(0.740874\pi\) | |||||||
\(572\) | −5.08241e6 | −0.649501 | ||||||||
\(573\) | 250404. | 0.0318607 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −269774. | −0.0340275 | ||||||||
\(576\) | 1.46110e6 | 0.183495 | ||||||||
\(577\) | −5.61898e6 | −0.702616 | −0.351308 | − | 0.936260i | \(-0.614263\pi\) | ||||
−0.351308 | + | 0.936260i | \(0.614263\pi\) | |||||||
\(578\) | −3.61993e6 | −0.450692 | ||||||||
\(579\) | −598178. | −0.0741540 | ||||||||
\(580\) | −4.76353e6 | −0.587975 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −504203. | −0.0617018 | ||||||||
\(583\) | 1.67883e7 | 2.04567 | ||||||||
\(584\) | −2.83214e6 | −0.343624 | ||||||||
\(585\) | −2.26402e6 | −0.273521 | ||||||||
\(586\) | −2.87775e6 | −0.346185 | ||||||||
\(587\) | −6.86832e6 | −0.822726 | −0.411363 | − | 0.911471i | \(-0.634947\pi\) | ||||
−0.411363 | + | 0.911471i | \(0.634947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.39400e7 | 2.84338 | ||||||||
\(590\) | −2.13665e6 | −0.252699 | ||||||||
\(591\) | −4.43256e6 | −0.522018 | ||||||||
\(592\) | −574362. | −0.0673568 | ||||||||
\(593\) | 4.07737e6 | 0.476149 | 0.238075 | − | 0.971247i | \(-0.423484\pi\) | ||||
0.238075 | + | 0.971247i | \(0.423484\pi\) | |||||||
\(594\) | 1.18755e6 | 0.138098 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.76479e6 | 0.780079 | ||||||||
\(597\) | 3.14285e6 | 0.360901 | ||||||||
\(598\) | 3.07561e6 | 0.351705 | ||||||||
\(599\) | 582993. | 0.0663890 | 0.0331945 | − | 0.999449i | \(-0.489432\pi\) | ||||
0.0331945 | + | 0.999449i | \(0.489432\pi\) | |||||||
\(600\) | 243104. | 0.0275686 | ||||||||
\(601\) | −6.87250e6 | −0.776119 | −0.388060 | − | 0.921634i | \(-0.626855\pi\) | ||||
−0.388060 | + | 0.921634i | \(0.626855\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.23203e6 | 0.249981 | ||||||||
\(604\) | −1.05192e7 | −1.17325 | ||||||||
\(605\) | −3.88151e6 | −0.431134 | ||||||||
\(606\) | −2.33071e6 | −0.257814 | ||||||||
\(607\) | −2.40563e6 | −0.265006 | −0.132503 | − | 0.991183i | \(-0.542301\pi\) | ||||
−0.132503 | + | 0.991183i | \(0.542301\pi\) | |||||||
\(608\) | 1.44160e7 | 1.58156 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.78858e6 | −0.629865 | ||||||||
\(611\) | 676989. | 0.0733632 | ||||||||
\(612\) | −984440. | −0.106246 | ||||||||
\(613\) | −1.16245e7 | −1.24946 | −0.624731 | − | 0.780840i | \(-0.714791\pi\) | ||||
−0.624731 | + | 0.780840i | \(0.714791\pi\) | |||||||
\(614\) | −2.03126e6 | −0.217443 | ||||||||
\(615\) | 1.65745e6 | 0.176707 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.37370e7 | −1.45271 | −0.726353 | − | 0.687322i | \(-0.758786\pi\) | ||||
−0.726353 | + | 0.687322i | \(0.758786\pi\) | |||||||
\(618\) | 2.44710e6 | 0.257739 | ||||||||
\(619\) | 1.64008e7 | 1.72044 | 0.860220 | − | 0.509923i | \(-0.170326\pi\) | ||||
0.860220 | + | 0.509923i | \(0.170326\pi\) | |||||||
\(620\) | 1.09567e7 | 1.14473 | ||||||||
\(621\) | 1.29390e6 | 0.134640 | ||||||||
\(622\) | −1.57478e6 | −0.163209 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 265794. | 0.0273265 | ||||||||
\(625\) | −9.26754e6 | −0.948996 | ||||||||
\(626\) | −1.00519e7 | −1.02521 | ||||||||
\(627\) | 1.06305e7 | 1.07991 | ||||||||
\(628\) | 1.55210e6 | 0.157044 | ||||||||
\(629\) | −5.88951e6 | −0.593543 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.28252e6 | −0.728129 | −0.364065 | − | 0.931374i | \(-0.618611\pi\) | ||||
−0.364065 | + | 0.931374i | \(0.618611\pi\) | |||||||
\(632\) | −1.54906e7 | −1.54268 | ||||||||
\(633\) | −1.96425e6 | −0.194844 | ||||||||
\(634\) | 8.63745e6 | 0.853419 | ||||||||
\(635\) | −1.30733e7 | −1.28662 | ||||||||
\(636\) | −6.45042e6 | −0.632332 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.91754e6 | −0.672821 | ||||||||
\(639\) | −1.85235e6 | −0.179461 | ||||||||
\(640\) | 6.93763e6 | 0.669516 | ||||||||
\(641\) | −107514. | −0.0103352 | −0.00516762 | − | 0.999987i | \(-0.501645\pi\) | ||||
−0.00516762 | + | 0.999987i | \(0.501645\pi\) | |||||||
\(642\) | 4.50388e6 | 0.431270 | ||||||||
\(643\) | 9.75913e6 | 0.930858 | 0.465429 | − | 0.885085i | \(-0.345900\pi\) | ||||
0.465429 | + | 0.885085i | \(0.345900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.94274e6 | 0.846392 | ||||||||
\(646\) | 4.89445e6 | 0.461448 | ||||||||
\(647\) | −6.75588e6 | −0.634485 | −0.317243 | − | 0.948344i | \(-0.602757\pi\) | ||||
−0.317243 | + | 0.948344i | \(0.602757\pi\) | |||||||
\(648\) | −1.16599e6 | −0.109083 | ||||||||
\(649\) | 5.58655e6 | 0.520633 | ||||||||
\(650\) | −263379. | −0.0244511 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.01043e6 | −0.645841 | ||||||||
\(653\) | 2.20346e6 | 0.202219 | 0.101110 | − | 0.994875i | \(-0.467761\pi\) | ||||
0.101110 | + | 0.994875i | \(0.467761\pi\) | |||||||
\(654\) | −3.80233e6 | −0.347620 | ||||||||
\(655\) | 1.90607e7 | 1.73595 | ||||||||
\(656\) | −194584. | −0.0176542 | ||||||||
\(657\) | 1.29085e6 | 0.116671 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.39630e7 | −1.25247 | −0.626233 | − | 0.779636i | \(-0.715404\pi\) | ||||
−0.626233 | + | 0.779636i | \(0.715404\pi\) | |||||||
\(660\) | 4.86534e6 | 0.434763 | ||||||||
\(661\) | −51052.8 | −0.00454482 | −0.00227241 | − | 0.999997i | \(-0.500723\pi\) | ||||
−0.00227241 | + | 0.999997i | \(0.500723\pi\) | |||||||
\(662\) | 8.65832e6 | 0.767872 | ||||||||
\(663\) | 2.72545e6 | 0.240799 | ||||||||
\(664\) | −1.60490e7 | −1.41263 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.72976e6 | −0.238473 | ||||||||
\(667\) | −7.53703e6 | −0.655972 | ||||||||
\(668\) | 2.72375e6 | 0.236170 | ||||||||
\(669\) | 1.12326e7 | 0.970323 | ||||||||
\(670\) | −5.07893e6 | −0.437104 | ||||||||
\(671\) | 1.51350e7 | 1.29770 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.71688e6 | 0.571650 | 0.285825 | − | 0.958282i | \(-0.407732\pi\) | ||||
0.285825 | + | 0.958282i | \(0.407732\pi\) | |||||||
\(674\) | −4.10793e6 | −0.348316 | ||||||||
\(675\) | −110803. | −0.00936036 | ||||||||
\(676\) | 2.23245e6 | 0.187895 | ||||||||
\(677\) | 1.45655e7 | 1.22139 | 0.610693 | − | 0.791867i | \(-0.290891\pi\) | ||||
0.610693 | + | 0.791867i | \(0.290891\pi\) | |||||||
\(678\) | −5.91647e6 | −0.494298 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.72429e6 | 0.474733 | ||||||||
\(681\) | −4.68876e6 | −0.387427 | ||||||||
\(682\) | 1.59112e7 | 1.30991 | ||||||||
\(683\) | −1.62565e6 | −0.133344 | −0.0666722 | − | 0.997775i | \(-0.521238\pi\) | ||||
−0.0666722 | + | 0.997775i | \(0.521238\pi\) | |||||||
\(684\) | −4.08448e6 | −0.333808 | ||||||||
\(685\) | 1.53197e7 | 1.24745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.73086e6 | −0.382427 | ||||||||
\(688\) | −1.04987e6 | −0.0845600 | ||||||||
\(689\) | 1.78582e7 | 1.43314 | ||||||||
\(690\) | −2.94425e6 | −0.235424 | ||||||||
\(691\) | −2.81556e6 | −0.224321 | −0.112160 | − | 0.993690i | \(-0.535777\pi\) | ||||
−0.112160 | + | 0.993690i | \(0.535777\pi\) | |||||||
\(692\) | −9.24407e6 | −0.733834 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.23616e6 | 0.333867 | ||||||||
\(695\) | −2.72860e6 | −0.214278 | ||||||||
\(696\) | 6.79192e6 | 0.531459 | ||||||||
\(697\) | −1.99526e6 | −0.155567 | ||||||||
\(698\) | 1.52251e6 | 0.118283 | ||||||||
\(699\) | 1.89185e6 | 0.146451 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.40996e7 | 1.08371 | 0.541855 | − | 0.840472i | \(-0.317722\pi\) | ||||
0.541855 | + | 0.840472i | \(0.317722\pi\) | |||||||
\(702\) | 1.26323e6 | 0.0967478 | ||||||||
\(703\) | −2.44358e7 | −1.86482 | ||||||||
\(704\) | 8.69287e6 | 0.661046 | ||||||||
\(705\) | −648074. | −0.0491079 | ||||||||
\(706\) | 1.84323e6 | 0.139177 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.14647e6 | −0.160932 | ||||||||
\(709\) | −8.44943e6 | −0.631265 | −0.315633 | − | 0.948881i | \(-0.602217\pi\) | ||||
−0.315633 | + | 0.948881i | \(0.602217\pi\) | |||||||
\(710\) | 4.21498e6 | 0.313797 | ||||||||
\(711\) | 7.06039e6 | 0.523787 | ||||||||
\(712\) | 2.24933e7 | 1.66285 | ||||||||
\(713\) | 1.73361e7 | 1.27711 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.34698e7 | −0.985365 | ||||||||
\(716\) | 1.92704e6 | 0.140478 | ||||||||
\(717\) | 7.25212e6 | 0.526826 | ||||||||
\(718\) | −3.41950e6 | −0.247543 | ||||||||
\(719\) | 1.82657e7 | 1.31769 | 0.658846 | − | 0.752278i | \(-0.271045\pi\) | ||||
0.658846 | + | 0.752278i | \(0.271045\pi\) | |||||||
\(720\) | −254442. | −0.0182918 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.19372e7 | 0.852237 | ||||||||
\(723\) | 1.02415e7 | 0.728651 | ||||||||
\(724\) | −8.22513e6 | −0.583172 | ||||||||
\(725\) | 645431. | 0.0456042 | ||||||||
\(726\) | 2.16573e6 | 0.152498 | ||||||||
\(727\) | 1.37476e6 | 0.0964700 | 0.0482350 | − | 0.998836i | \(-0.484640\pi\) | ||||
0.0482350 | + | 0.998836i | \(0.484640\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.93729e6 | −0.204005 | ||||||||
\(731\) | −1.07654e7 | −0.745136 | ||||||||
\(732\) | −5.81517e6 | −0.401130 | ||||||||
\(733\) | 1.64625e7 | 1.13171 | 0.565857 | − | 0.824503i | \(-0.308545\pi\) | ||||
0.565857 | + | 0.824503i | \(0.308545\pi\) | |||||||
\(734\) | −3.68585e6 | −0.252521 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.04393e7 | 0.710360 | ||||||||
\(737\) | 1.32795e7 | 0.900561 | ||||||||
\(738\) | −924793. | −0.0625034 | ||||||||
\(739\) | 2.72997e6 | 0.183885 | 0.0919425 | − | 0.995764i | \(-0.470692\pi\) | ||||
0.0919425 | + | 0.995764i | \(0.470692\pi\) | |||||||
\(740\) | −1.11836e7 | −0.750765 | ||||||||
\(741\) | 1.13080e7 | 0.756555 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.34396e7 | −1.55768 | −0.778839 | − | 0.627224i | \(-0.784191\pi\) | ||||
−0.778839 | + | 0.627224i | \(0.784191\pi\) | |||||||
\(744\) | −1.56223e7 | −1.03470 | ||||||||
\(745\) | 1.79286e7 | 1.18347 | ||||||||
\(746\) | −1.05805e7 | −0.696082 | ||||||||
\(747\) | 7.31491e6 | 0.479631 | ||||||||
\(748\) | −5.85695e6 | −0.382752 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 5.43595e6 | 0.352876 | ||||||||
\(751\) | 1.79407e7 | 1.16075 | 0.580376 | − | 0.814349i | \(-0.302906\pi\) | ||||
0.580376 | + | 0.814349i | \(0.302906\pi\) | |||||||
\(752\) | 76083.4 | 0.00490620 | ||||||||
\(753\) | −1.04910e7 | −0.674260 | ||||||||
\(754\) | −7.35837e6 | −0.471361 | ||||||||
\(755\) | −2.78790e7 | −1.77996 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.30823e7 | −1.46399 | −0.731997 | − | 0.681308i | \(-0.761412\pi\) | ||||
−0.731997 | + | 0.681308i | \(0.761412\pi\) | |||||||
\(758\) | −4.32455e6 | −0.273381 | ||||||||
\(759\) | 7.69811e6 | 0.485043 | ||||||||
\(760\) | 2.37503e7 | 1.49154 | ||||||||
\(761\) | 1.91587e7 | 1.19924 | 0.599618 | − | 0.800286i | \(-0.295319\pi\) | ||||
0.599618 | + | 0.800286i | \(0.295319\pi\) | |||||||
\(762\) | 7.29440e6 | 0.455095 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −572407. | −0.0354790 | ||||||||
\(765\) | −2.60905e6 | −0.161186 | ||||||||
\(766\) | 4.41693e6 | 0.271988 | ||||||||
\(767\) | 5.94257e6 | 0.364742 | ||||||||
\(768\) | −9.06596e6 | −0.554639 | ||||||||
\(769\) | 1.73017e7 | 1.05505 | 0.527526 | − | 0.849539i | \(-0.323120\pi\) | ||||
0.527526 | + | 0.849539i | \(0.323120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.25931e6 | −0.560974 | ||||||||
\(772\) | 1.36739e6 | 0.0825753 | ||||||||
\(773\) | 3.12287e7 | 1.87977 | 0.939885 | − | 0.341491i | \(-0.110932\pi\) | ||||
0.939885 | + | 0.341491i | \(0.110932\pi\) | |||||||
\(774\) | −4.98970e6 | −0.299379 | ||||||||
\(775\) | −1.48458e6 | −0.0887868 | ||||||||
\(776\) | 2.94529e6 | 0.175580 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −123342. | −0.00730572 | ||||||||
\(779\) | −8.27840e6 | −0.488768 | ||||||||
\(780\) | 5.17539e6 | 0.304584 | ||||||||
\(781\) | −1.10206e7 | −0.646514 | ||||||||
\(782\) | 3.54432e6 | 0.207260 | ||||||||
\(783\) | −3.09566e6 | −0.180446 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.11350e6 | 0.238253 | ||||||||
\(786\) | −1.06351e7 | −0.614026 | ||||||||
\(787\) | −2.48691e7 | −1.43128 | −0.715638 | − | 0.698471i | \(-0.753864\pi\) | ||||
−0.715638 | + | 0.698471i | \(0.753864\pi\) | |||||||
\(788\) | 1.01325e7 | 0.581302 | ||||||||
\(789\) | −5.91611e6 | −0.338332 | ||||||||
\(790\) | −1.60657e7 | −0.915868 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.93708e6 | −0.392974 | ||||||||
\(793\) | 1.60995e7 | 0.909136 | ||||||||
\(794\) | 2.16410e6 | 0.121822 | ||||||||
\(795\) | −1.70955e7 | −0.959319 | ||||||||
\(796\) | −7.18433e6 | −0.401887 | ||||||||
\(797\) | 584574. | 0.0325982 | 0.0162991 | − | 0.999867i | \(-0.494812\pi\) | ||||
0.0162991 | + | 0.999867i | \(0.494812\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 780159. | 0.0432331 | ||||||||
\(800\) | −893970. | −0.0493853 | ||||||||
\(801\) | −1.02521e7 | −0.564590 | ||||||||
\(802\) | −9.09814e6 | −0.499478 | ||||||||
\(803\) | 7.67993e6 | 0.420309 | ||||||||
\(804\) | −5.10226e6 | −0.278370 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.69252e7 | 0.917691 | ||||||||
\(807\) | 49282.7 | 0.00266386 | ||||||||
\(808\) | 1.36148e7 | 0.733639 | ||||||||
\(809\) | −1.10552e7 | −0.593878 | −0.296939 | − | 0.954897i | \(-0.595966\pi\) | ||||
−0.296939 | + | 0.954897i | \(0.595966\pi\) | |||||||
\(810\) | −1.20928e6 | −0.0647612 | ||||||||
\(811\) | 1.62780e7 | 0.869060 | 0.434530 | − | 0.900657i | \(-0.356914\pi\) | ||||
0.434530 | + | 0.900657i | \(0.356914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.92232e6 | −0.367304 | ||||||||
\(814\) | −1.62408e7 | −0.859103 | ||||||||
\(815\) | −1.85796e7 | −0.979813 | ||||||||
\(816\) | 306300. | 0.0161036 | ||||||||
\(817\) | −4.46659e7 | −2.34111 | ||||||||
\(818\) | 9.88989e6 | 0.516783 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.78882e6 | −0.196775 | ||||||||
\(821\) | 3.28574e7 | 1.70128 | 0.850638 | − | 0.525752i | \(-0.176216\pi\) | ||||
0.850638 | + | 0.525752i | \(0.176216\pi\) | |||||||
\(822\) | −8.54781e6 | −0.441240 | ||||||||
\(823\) | 1.06046e7 | 0.545752 | 0.272876 | − | 0.962049i | \(-0.412025\pi\) | ||||
0.272876 | + | 0.962049i | \(0.412025\pi\) | |||||||
\(824\) | −1.42947e7 | −0.733426 | ||||||||
\(825\) | −659226. | −0.0337209 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.57582e7 | 0.801203 | 0.400602 | − | 0.916252i | \(-0.368801\pi\) | ||||
0.400602 | + | 0.916252i | \(0.368801\pi\) | |||||||
\(828\) | −2.95777e6 | −0.149930 | ||||||||
\(829\) | −2.70135e7 | −1.36520 | −0.682598 | − | 0.730794i | \(-0.739150\pi\) | ||||
−0.682598 | + | 0.730794i | \(0.739150\pi\) | |||||||
\(830\) | −1.66449e7 | −0.838660 | ||||||||
\(831\) | −1.05645e7 | −0.530698 | ||||||||
\(832\) | 9.24684e6 | 0.463111 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.52245e6 | 0.0757930 | ||||||||
\(835\) | 7.21871e6 | 0.358297 | ||||||||
\(836\) | −2.43007e7 | −1.20255 | ||||||||
\(837\) | 7.12042e6 | 0.351311 | ||||||||
\(838\) | −1.86868e7 | −0.919232 | ||||||||
\(839\) | −3.50490e7 | −1.71898 | −0.859489 | − | 0.511154i | \(-0.829218\pi\) | ||||
−0.859489 | + | 0.511154i | \(0.829218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.47888e6 | −0.120855 | ||||||||
\(842\) | 1.95206e7 | 0.948885 | ||||||||
\(843\) | 7.53884e6 | 0.365372 | ||||||||
\(844\) | 4.49013e6 | 0.216972 | ||||||||
\(845\) | 5.91663e6 | 0.285057 | ||||||||
\(846\) | 361600. | 0.0173701 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.00699e6 | 0.0958422 | ||||||||
\(849\) | −5.37499e6 | −0.255922 | ||||||||
\(850\) | −303517. | −0.0144091 | ||||||||
\(851\) | −1.76952e7 | −0.837589 | ||||||||
\(852\) | 4.23434e6 | 0.199842 | ||||||||
\(853\) | −538313. | −0.0253316 | −0.0126658 | − | 0.999920i | \(-0.504032\pi\) | ||||
−0.0126658 | + | 0.999920i | \(0.504032\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.08250e7 | −0.506423 | ||||||||
\(856\) | −2.63094e7 | −1.22723 | ||||||||
\(857\) | −3.68275e6 | −0.171285 | −0.0856426 | − | 0.996326i | \(-0.527294\pi\) | ||||
−0.0856426 | + | 0.996326i | \(0.527294\pi\) | |||||||
\(858\) | 7.51564e6 | 0.348536 | ||||||||
\(859\) | −1.88883e7 | −0.873394 | −0.436697 | − | 0.899609i | \(-0.643852\pi\) | ||||
−0.436697 | + | 0.899609i | \(0.643852\pi\) | |||||||
\(860\) | −2.04425e7 | −0.942513 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.46931e6 | 0.342383 | ||||||||
\(863\) | 2.78544e7 | 1.27311 | 0.636557 | − | 0.771230i | \(-0.280358\pi\) | ||||
0.636557 | + | 0.771230i | \(0.280358\pi\) | |||||||
\(864\) | 4.28771e6 | 0.195408 | ||||||||
\(865\) | −2.44994e7 | −1.11331 | ||||||||
\(866\) | 1.68075e7 | 0.761568 | ||||||||
\(867\) | −9.63791e6 | −0.435447 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.20059e7 | 1.88695 | ||||||||
\(870\) | 7.04409e6 | 0.315520 | ||||||||
\(871\) | 1.41258e7 | 0.630909 | ||||||||
\(872\) | 2.22113e7 | 0.989195 | ||||||||
\(873\) | −1.34242e6 | −0.0596146 | ||||||||
\(874\) | 1.47055e7 | 0.651180 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.95079e6 | −0.129921 | ||||||||
\(877\) | −1.75052e7 | −0.768544 | −0.384272 | − | 0.923220i | \(-0.625548\pi\) | ||||
−0.384272 | + | 0.923220i | \(0.625548\pi\) | |||||||
\(878\) | −9.68143e6 | −0.423841 | ||||||||
\(879\) | −7.66189e6 | −0.334475 | ||||||||
\(880\) | −1.51381e6 | −0.0658968 | ||||||||
\(881\) | −5.66292e6 | −0.245811 | −0.122905 | − | 0.992418i | \(-0.539221\pi\) | ||||
−0.122905 | + | 0.992418i | \(0.539221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.43933e7 | 0.621239 | 0.310620 | − | 0.950534i | \(-0.399463\pi\) | ||||
0.310620 | + | 0.950534i | \(0.399463\pi\) | |||||||
\(884\) | −6.23020e6 | −0.268146 | ||||||||
\(885\) | −5.68876e6 | −0.244151 | ||||||||
\(886\) | −1.91406e7 | −0.819163 | ||||||||
\(887\) | 5.50193e6 | 0.234804 | 0.117402 | − | 0.993084i | \(-0.462543\pi\) | ||||
0.117402 | + | 0.993084i | \(0.462543\pi\) | |||||||
\(888\) | 1.59458e7 | 0.678602 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 2.33285e7 | 0.987214 | ||||||||
\(891\) | 3.16182e6 | 0.133427 | ||||||||
\(892\) | −2.56770e7 | −1.08052 | ||||||||
\(893\) | 3.23691e6 | 0.135832 | ||||||||
\(894\) | −1.00035e7 | −0.418607 | ||||||||
\(895\) | 5.10721e6 | 0.213121 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.18869e6 | 0.339808 | ||||||||
\(898\) | 2.55039e7 | 1.05540 | ||||||||
\(899\) | −4.14766e7 | −1.71161 | ||||||||
\(900\) | 253288. | 0.0104234 | ||||||||
\(901\) | 2.05797e7 | 0.844554 | ||||||||
\(902\) | −5.50208e6 | −0.225170 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.45610e7 | 1.40658 | ||||||||
\(905\) | −2.17990e7 | −0.884737 | ||||||||
\(906\) | 1.55554e7 | 0.629593 | ||||||||
\(907\) | 6.01555e6 | 0.242805 | 0.121402 | − | 0.992603i | \(-0.461261\pi\) | ||||
0.121402 | + | 0.992603i | \(0.461261\pi\) | |||||||
\(908\) | 1.07182e7 | 0.431426 | ||||||||
\(909\) | −6.20542e6 | −0.249093 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.47513e7 | −0.588892 | −0.294446 | − | 0.955668i | \(-0.595135\pi\) | ||||
−0.294446 | + | 0.955668i | \(0.595135\pi\) | |||||||
\(912\) | 1.27085e6 | 0.0505950 | ||||||||
\(913\) | 4.35202e7 | 1.72788 | ||||||||
\(914\) | −1.99106e6 | −0.0788351 | ||||||||
\(915\) | −1.54119e7 | −0.608559 | ||||||||
\(916\) | 1.08144e7 | 0.425858 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.45575e6 | 0.0570137 | ||||||||
\(919\) | −3.54001e7 | −1.38266 | −0.691331 | − | 0.722538i | \(-0.742976\pi\) | ||||
−0.691331 | + | 0.722538i | \(0.742976\pi\) | |||||||
\(920\) | 1.71988e7 | 0.669928 | ||||||||
\(921\) | −5.40816e6 | −0.210088 | ||||||||
\(922\) | −2.01113e7 | −0.779135 | ||||||||
\(923\) | −1.17229e7 | −0.452930 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.51532e6 | 0.0582305 | ||||||||
\(926\) | −7.30434e6 | −0.279932 | ||||||||
\(927\) | 6.51530e6 | 0.249021 | ||||||||
\(928\) | −2.49760e7 | −0.952036 | ||||||||
\(929\) | −3.83266e7 | −1.45700 | −0.728502 | − | 0.685044i | \(-0.759783\pi\) | ||||
−0.728502 | + | 0.685044i | \(0.759783\pi\) | |||||||
\(930\) | −1.62023e7 | −0.614285 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.32463e6 | −0.163083 | ||||||||
\(933\) | −4.19280e6 | −0.157688 | ||||||||
\(934\) | 1.70966e6 | 0.0641271 | ||||||||
\(935\) | −1.55226e7 | −0.580677 | ||||||||
\(936\) | −7.37917e6 | −0.275307 | ||||||||
\(937\) | 1.48693e7 | 0.553274 | 0.276637 | − | 0.960974i | \(-0.410780\pi\) | ||||
0.276637 | + | 0.960974i | \(0.410780\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.67629e7 | −0.990534 | ||||||||
\(940\) | 1.48145e6 | 0.0546849 | ||||||||
\(941\) | −3.50894e6 | −0.129182 | −0.0645909 | − | 0.997912i | \(-0.520574\pi\) | ||||
−0.0645909 | + | 0.997912i | \(0.520574\pi\) | |||||||
\(942\) | −2.29517e6 | −0.0842730 | ||||||||
\(943\) | −5.99481e6 | −0.219531 | ||||||||
\(944\) | 667856. | 0.0243923 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.96863e7 | −1.07852 | ||||||||
\(947\) | 3.89774e7 | 1.41234 | 0.706168 | − | 0.708044i | \(-0.250422\pi\) | ||||
0.706168 | + | 0.708044i | \(0.250422\pi\) | |||||||
\(948\) | −1.61395e7 | −0.583271 | ||||||||
\(949\) | 8.16935e6 | 0.294457 | ||||||||
\(950\) | −1.25930e6 | −0.0452711 | ||||||||
\(951\) | 2.29969e7 | 0.824551 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.11438e6 | 0.253749 | 0.126875 | − | 0.991919i | \(-0.459505\pi\) | ||||
0.126875 | + | 0.991919i | \(0.459505\pi\) | |||||||
\(954\) | 9.53860e6 | 0.339323 | ||||||||
\(955\) | −1.51704e6 | −0.0538256 | ||||||||
\(956\) | −1.65778e7 | −0.586655 | ||||||||
\(957\) | −1.84177e7 | −0.650062 | ||||||||
\(958\) | −1.84927e6 | −0.0651008 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.85190e6 | −0.309998 | ||||||||
\(961\) | 6.67724e7 | 2.33232 | ||||||||
\(962\) | −1.72757e7 | −0.601865 | ||||||||
\(963\) | 1.19914e7 | 0.416682 | ||||||||
\(964\) | −2.34114e7 | −0.811401 | ||||||||
\(965\) | 3.62398e6 | 0.125276 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.99357e7 | −0.685592 | −0.342796 | − | 0.939410i | \(-0.611374\pi\) | ||||
−0.342796 | + | 0.939410i | \(0.611374\pi\) | |||||||
\(968\) | −1.26511e7 | −0.433950 | ||||||||
\(969\) | 1.30313e7 | 0.445839 | ||||||||
\(970\) | 3.05464e6 | 0.104239 | ||||||||
\(971\) | 4.95888e7 | 1.68786 | 0.843928 | − | 0.536456i | \(-0.180237\pi\) | ||||
0.843928 | + | 0.536456i | \(0.180237\pi\) | |||||||
\(972\) | −1.21484e6 | −0.0412432 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 8.04143e6 | 0.271604 | ||||||||
\(975\) | −701236. | −0.0236240 | ||||||||
\(976\) | 1.80934e6 | 0.0607989 | ||||||||
\(977\) | −355348. | −0.0119102 | −0.00595508 | − | 0.999982i | \(-0.501896\pi\) | ||||
−0.00595508 | + | 0.999982i | \(0.501896\pi\) | |||||||
\(978\) | 1.03667e7 | 0.346572 | ||||||||
\(979\) | −6.09953e7 | −2.03395 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.01236e7 | −0.335862 | ||||||||
\(982\) | −2.43289e7 | −0.805088 | ||||||||
\(983\) | −991754. | −0.0327356 | −0.0163678 | − | 0.999866i | \(-0.505210\pi\) | ||||
−0.0163678 | + | 0.999866i | \(0.505210\pi\) | |||||||
\(984\) | 5.40217e6 | 0.177861 | ||||||||
\(985\) | 2.68541e7 | 0.881900 | ||||||||
\(986\) | −8.47976e6 | −0.277774 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.58493e7 | −0.842474 | ||||||||
\(989\) | −3.23448e7 | −1.05151 | ||||||||
\(990\) | −7.19464e6 | −0.233303 | ||||||||
\(991\) | 1.06674e7 | 0.345045 | 0.172523 | − | 0.985006i | \(-0.444808\pi\) | ||||
0.172523 | + | 0.985006i | \(0.444808\pi\) | |||||||
\(992\) | 5.74481e7 | 1.85352 | ||||||||
\(993\) | 2.30524e7 | 0.741898 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.90405e7 | −0.609707 | ||||||||
\(996\) | −1.67214e7 | −0.534101 | ||||||||
\(997\) | 5.58283e7 | 1.77876 | 0.889379 | − | 0.457171i | \(-0.151137\pi\) | ||||
0.889379 | + | 0.457171i | \(0.151137\pi\) | |||||||
\(998\) | 7.51232e6 | 0.238752 | ||||||||
\(999\) | −7.26788e6 | −0.230406 |
(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 | 147.6.a.o.1.4 | yes | 6 | |
3.2 | odd | 2 | 441.6.a.ba.1.3 | 6 | |||
7.2 | even | 3 | 147.6.e.p.67.3 | 12 | |||
7.3 | odd | 6 | 147.6.e.q.79.3 | 12 | |||
7.4 | even | 3 | 147.6.e.p.79.3 | 12 | |||
7.5 | odd | 6 | 147.6.e.q.67.3 | 12 | |||
7.6 | odd | 2 | 147.6.a.n.1.4 | ✓ | 6 | ||
21.20 | even | 2 | 441.6.a.bb.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.a.n.1.4 | ✓ | 6 | 7.6 | odd | 2 | ||
147.6.a.o.1.4 | yes | 6 | 1.1 | even | 1 | trivial | |
147.6.e.p.67.3 | 12 | 7.2 | even | 3 | |||
147.6.e.p.79.3 | 12 | 7.4 | even | 3 | |||
147.6.e.q.67.3 | 12 | 7.5 | odd | 6 | |||
147.6.e.q.79.3 | 12 | 7.3 | odd | 6 | |||
441.6.a.ba.1.3 | 6 | 3.2 | odd | 2 | |||
441.6.a.bb.1.3 | 6 | 21.20 | even | 2 |