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: | \(1\) |
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 | 1.6 | ||
Root | \(5.59680\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.0089 | 1.76934 | 0.884669 | − | 0.466219i | \(-0.154384\pi\) | ||||
0.884669 | + | 0.466219i | \(0.154384\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 68.1779 | 2.13056 | ||||||||
\(5\) | −70.3512 | −1.25848 | −0.629241 | − | 0.777211i | \(-0.716634\pi\) | ||||
−0.629241 | + | 0.777211i | \(0.716634\pi\) | |||||||
\(6\) | −90.0800 | −1.02153 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 362.101 | 2.00034 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −704.138 | −2.22668 | ||||||||
\(11\) | −731.396 | −1.82251 | −0.911257 | − | 0.411838i | \(-0.864887\pi\) | ||||
−0.911257 | + | 0.411838i | \(0.864887\pi\) | |||||||
\(12\) | −613.601 | −1.23008 | ||||||||
\(13\) | −899.645 | −1.47643 | −0.738215 | − | 0.674566i | \(-0.764331\pi\) | ||||
−0.738215 | + | 0.674566i | \(0.764331\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 633.161 | 0.726584 | ||||||||
\(16\) | 1442.53 | 1.40872 | ||||||||
\(17\) | 1392.39 | 1.16853 | 0.584263 | − | 0.811564i | \(-0.301384\pi\) | ||||
0.584263 | + | 0.811564i | \(0.301384\pi\) | |||||||
\(18\) | 810.720 | 0.589780 | ||||||||
\(19\) | 190.198 | 0.120871 | 0.0604354 | − | 0.998172i | \(-0.480751\pi\) | ||||
0.0604354 | + | 0.998172i | \(0.480751\pi\) | |||||||
\(20\) | −4796.40 | −2.68127 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7320.46 | −3.22464 | ||||||||
\(23\) | 42.9770 | 0.0169401 | 0.00847006 | − | 0.999964i | \(-0.497304\pi\) | ||||
0.00847006 | + | 0.999964i | \(0.497304\pi\) | |||||||
\(24\) | −3258.91 | −1.15490 | ||||||||
\(25\) | 1824.30 | 0.583775 | ||||||||
\(26\) | −9004.45 | −2.61230 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7746.59 | −1.71047 | −0.855236 | − | 0.518239i | \(-0.826588\pi\) | ||||
−0.855236 | + | 0.518239i | \(0.826588\pi\) | |||||||
\(30\) | 6337.24 | 1.28557 | ||||||||
\(31\) | −1179.22 | −0.220390 | −0.110195 | − | 0.993910i | \(-0.535148\pi\) | ||||
−0.110195 | + | 0.993910i | \(0.535148\pi\) | |||||||
\(32\) | 2850.94 | 0.492168 | ||||||||
\(33\) | 6582.56 | 1.05223 | ||||||||
\(34\) | 13936.3 | 2.06752 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5522.41 | 0.710187 | ||||||||
\(37\) | 9288.68 | 1.11545 | 0.557724 | − | 0.830026i | \(-0.311675\pi\) | ||||
0.557724 | + | 0.830026i | \(0.311675\pi\) | |||||||
\(38\) | 1903.67 | 0.213861 | ||||||||
\(39\) | 8096.80 | 0.852417 | ||||||||
\(40\) | −25474.2 | −2.51739 | ||||||||
\(41\) | −13453.4 | −1.24989 | −0.624945 | − | 0.780668i | \(-0.714879\pi\) | ||||
−0.624945 | + | 0.780668i | \(0.714879\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6033.68 | 0.497635 | 0.248818 | − | 0.968550i | \(-0.419958\pi\) | ||||
0.248818 | + | 0.968550i | \(0.419958\pi\) | |||||||
\(44\) | −49865.0 | −3.88297 | ||||||||
\(45\) | −5698.45 | −0.419494 | ||||||||
\(46\) | 430.152 | 0.0299728 | ||||||||
\(47\) | 3244.94 | 0.214270 | 0.107135 | − | 0.994244i | \(-0.465832\pi\) | ||||
0.107135 | + | 0.994244i | \(0.465832\pi\) | |||||||
\(48\) | −12982.8 | −0.813327 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 18259.2 | 1.03289 | ||||||||
\(51\) | −12531.5 | −0.674649 | ||||||||
\(52\) | −61335.9 | −3.14562 | ||||||||
\(53\) | 25675.8 | 1.25555 | 0.627775 | − | 0.778395i | \(-0.283966\pi\) | ||||
0.627775 | + | 0.778395i | \(0.283966\pi\) | |||||||
\(54\) | −7296.48 | −0.340509 | ||||||||
\(55\) | 51454.6 | 2.29360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1711.78 | −0.0697848 | ||||||||
\(58\) | −77534.8 | −3.02640 | ||||||||
\(59\) | 26450.5 | 0.989244 | 0.494622 | − | 0.869108i | \(-0.335306\pi\) | ||||
0.494622 | + | 0.869108i | \(0.335306\pi\) | |||||||
\(60\) | 43167.6 | 1.54803 | ||||||||
\(61\) | 6432.77 | 0.221347 | 0.110673 | − | 0.993857i | \(-0.464699\pi\) | ||||
0.110673 | + | 0.993857i | \(0.464699\pi\) | |||||||
\(62\) | −11802.7 | −0.389944 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −17626.3 | −0.537913 | ||||||||
\(65\) | 63291.1 | 1.85806 | ||||||||
\(66\) | 65884.2 | 1.86175 | ||||||||
\(67\) | −23815.7 | −0.648150 | −0.324075 | − | 0.946031i | \(-0.605053\pi\) | ||||
−0.324075 | + | 0.946031i | \(0.605053\pi\) | |||||||
\(68\) | 94930.2 | 2.48961 | ||||||||
\(69\) | −386.793 | −0.00978039 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −44680.7 | −1.05190 | −0.525949 | − | 0.850516i | \(-0.676290\pi\) | ||||
−0.525949 | + | 0.850516i | \(0.676290\pi\) | |||||||
\(72\) | 29330.2 | 0.666781 | ||||||||
\(73\) | 39601.3 | 0.869765 | 0.434882 | − | 0.900487i | \(-0.356790\pi\) | ||||
0.434882 | + | 0.900487i | \(0.356790\pi\) | |||||||
\(74\) | 92969.4 | 1.97361 | ||||||||
\(75\) | −16418.7 | −0.337042 | ||||||||
\(76\) | 12967.3 | 0.257523 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 81040.0 | 1.50821 | ||||||||
\(79\) | 23123.0 | 0.416846 | 0.208423 | − | 0.978039i | \(-0.433167\pi\) | ||||
0.208423 | + | 0.978039i | \(0.433167\pi\) | |||||||
\(80\) | −101484. | −1.77285 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −134654. | −2.21148 | ||||||||
\(83\) | 17267.2 | 0.275122 | 0.137561 | − | 0.990493i | \(-0.456074\pi\) | ||||
0.137561 | + | 0.990493i | \(0.456074\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −97956.3 | −1.47057 | ||||||||
\(86\) | 60390.4 | 0.880485 | ||||||||
\(87\) | 69719.3 | 0.987541 | ||||||||
\(88\) | −264839. | −3.64565 | ||||||||
\(89\) | −49929.7 | −0.668166 | −0.334083 | − | 0.942544i | \(-0.608427\pi\) | ||||
−0.334083 | + | 0.942544i | \(0.608427\pi\) | |||||||
\(90\) | −57035.2 | −0.742226 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2930.08 | 0.0360920 | ||||||||
\(93\) | 10613.0 | 0.127242 | ||||||||
\(94\) | 32478.3 | 0.379117 | ||||||||
\(95\) | −13380.7 | −0.152114 | ||||||||
\(96\) | −25658.5 | −0.284153 | ||||||||
\(97\) | 16865.0 | 0.181994 | 0.0909970 | − | 0.995851i | \(-0.470995\pi\) | ||||
0.0909970 | + | 0.995851i | \(0.470995\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −59243.1 | −0.607505 | ||||||||
\(100\) | 124377. | 1.24377 | ||||||||
\(101\) | −105449. | −1.02858 | −0.514290 | − | 0.857617i | \(-0.671944\pi\) | ||||
−0.514290 | + | 0.857617i | \(0.671944\pi\) | |||||||
\(102\) | −125426. | −1.19368 | ||||||||
\(103\) | 20355.8 | 0.189058 | 0.0945290 | − | 0.995522i | \(-0.469865\pi\) | ||||
0.0945290 | + | 0.995522i | \(0.469865\pi\) | |||||||
\(104\) | −325762. | −2.95337 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 256986. | 2.22149 | ||||||||
\(107\) | −3775.43 | −0.0318792 | −0.0159396 | − | 0.999873i | \(-0.505074\pi\) | ||||
−0.0159396 | + | 0.999873i | \(0.505074\pi\) | |||||||
\(108\) | −49701.7 | −0.410026 | ||||||||
\(109\) | 8536.98 | 0.0688237 | 0.0344118 | − | 0.999408i | \(-0.489044\pi\) | ||||
0.0344118 | + | 0.999408i | \(0.489044\pi\) | |||||||
\(110\) | 515004. | 4.05815 | ||||||||
\(111\) | −83598.1 | −0.644005 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −100869. | −0.743125 | −0.371562 | − | 0.928408i | \(-0.621178\pi\) | ||||
−0.371562 | + | 0.928408i | \(0.621178\pi\) | |||||||
\(114\) | −17133.0 | −0.123473 | ||||||||
\(115\) | −3023.49 | −0.0213188 | ||||||||
\(116\) | −528147. | −3.64426 | ||||||||
\(117\) | −72871.2 | −0.492143 | ||||||||
\(118\) | 264740. | 1.75031 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 229268. | 1.45342 | ||||||||
\(121\) | 373889. | 2.32156 | ||||||||
\(122\) | 64384.9 | 0.391638 | ||||||||
\(123\) | 121081. | 0.721625 | ||||||||
\(124\) | −80396.9 | −0.469554 | ||||||||
\(125\) | 91506.2 | 0.523812 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −185451. | −1.02028 | −0.510142 | − | 0.860090i | \(-0.670407\pi\) | ||||
−0.510142 | + | 0.860090i | \(0.670407\pi\) | |||||||
\(128\) | −267650. | −1.44392 | ||||||||
\(129\) | −54303.1 | −0.287310 | ||||||||
\(130\) | 633474. | 3.28754 | ||||||||
\(131\) | −124046. | −0.631545 | −0.315773 | − | 0.948835i | \(-0.602264\pi\) | ||||
−0.315773 | + | 0.948835i | \(0.602264\pi\) | |||||||
\(132\) | 448785. | 2.24184 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −238368. | −1.14680 | ||||||||
\(135\) | 51286.0 | 0.242195 | ||||||||
\(136\) | 504185. | 2.33745 | ||||||||
\(137\) | 99520.5 | 0.453013 | 0.226507 | − | 0.974010i | \(-0.427269\pi\) | ||||
0.226507 | + | 0.974010i | \(0.427269\pi\) | |||||||
\(138\) | −3871.37 | −0.0173048 | ||||||||
\(139\) | −254481. | −1.11717 | −0.558583 | − | 0.829449i | \(-0.688655\pi\) | ||||
−0.558583 | + | 0.829449i | \(0.688655\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29204.5 | −0.123709 | ||||||||
\(142\) | −447204. | −1.86116 | ||||||||
\(143\) | 657997. | 2.69081 | ||||||||
\(144\) | 116845. | 0.469575 | ||||||||
\(145\) | 544982. | 2.15260 | ||||||||
\(146\) | 396365. | 1.53891 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 633283. | 2.37653 | ||||||||
\(149\) | −427260. | −1.57662 | −0.788309 | − | 0.615279i | \(-0.789043\pi\) | ||||
−0.788309 | + | 0.615279i | \(0.789043\pi\) | |||||||
\(150\) | −164333. | −0.596342 | ||||||||
\(151\) | −150472. | −0.537047 | −0.268523 | − | 0.963273i | \(-0.586536\pi\) | ||||
−0.268523 | + | 0.963273i | \(0.586536\pi\) | |||||||
\(152\) | 68870.8 | 0.241783 | ||||||||
\(153\) | 112784. | 0.389509 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 82959.8 | 0.277357 | ||||||||
\(156\) | 552023. | 1.81613 | ||||||||
\(157\) | −165831. | −0.536930 | −0.268465 | − | 0.963290i | \(-0.586516\pi\) | ||||
−0.268465 | + | 0.963290i | \(0.586516\pi\) | |||||||
\(158\) | 231435. | 0.737542 | ||||||||
\(159\) | −231082. | −0.724892 | ||||||||
\(160\) | −200567. | −0.619384 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 65668.3 | 0.196593 | ||||||||
\(163\) | 95718.2 | 0.282180 | 0.141090 | − | 0.989997i | \(-0.454939\pi\) | ||||
0.141090 | + | 0.989997i | \(0.454939\pi\) | |||||||
\(164\) | −917224. | −2.66297 | ||||||||
\(165\) | −463091. | −1.32421 | ||||||||
\(166\) | 172825. | 0.486784 | ||||||||
\(167\) | −474209. | −1.31577 | −0.657883 | − | 0.753120i | \(-0.728548\pi\) | ||||
−0.657883 | + | 0.753120i | \(0.728548\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 438068. | 1.17984 | ||||||||
\(170\) | −980434. | −2.60193 | ||||||||
\(171\) | 15406.0 | 0.0402903 | ||||||||
\(172\) | 411363. | 1.06024 | ||||||||
\(173\) | −258876. | −0.657624 | −0.328812 | − | 0.944395i | \(-0.606648\pi\) | ||||
−0.328812 | + | 0.944395i | \(0.606648\pi\) | |||||||
\(174\) | 697813. | 1.74729 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.05506e6 | −2.56742 | ||||||||
\(177\) | −238054. | −0.571140 | ||||||||
\(178\) | −499741. | −1.18221 | ||||||||
\(179\) | −542178. | −1.26476 | −0.632381 | − | 0.774657i | \(-0.717922\pi\) | ||||
−0.632381 | + | 0.774657i | \(0.717922\pi\) | |||||||
\(180\) | −388508. | −0.893756 | ||||||||
\(181\) | −653930. | −1.48366 | −0.741831 | − | 0.670587i | \(-0.766042\pi\) | ||||
−0.741831 | + | 0.670587i | \(0.766042\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −57894.9 | −0.127795 | ||||||||
\(184\) | 15562.0 | 0.0338861 | ||||||||
\(185\) | −653470. | −1.40377 | ||||||||
\(186\) | 106224. | 0.225134 | ||||||||
\(187\) | −1.01839e6 | −2.12965 | ||||||||
\(188\) | 221233. | 0.456516 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −133925. | −0.269141 | ||||||||
\(191\) | 769535. | 1.52632 | 0.763159 | − | 0.646210i | \(-0.223647\pi\) | ||||
0.763159 | + | 0.646210i | \(0.223647\pi\) | |||||||
\(192\) | 158637. | 0.310564 | ||||||||
\(193\) | 814230. | 1.57345 | 0.786727 | − | 0.617301i | \(-0.211774\pi\) | ||||
0.786727 | + | 0.617301i | \(0.211774\pi\) | |||||||
\(194\) | 168800. | 0.322009 | ||||||||
\(195\) | −569620. | −1.07275 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −443688. | −0.814539 | −0.407269 | − | 0.913308i | \(-0.633519\pi\) | ||||
−0.407269 | + | 0.913308i | \(0.633519\pi\) | |||||||
\(198\) | −592957. | −1.07488 | ||||||||
\(199\) | −618941. | −1.10794 | −0.553970 | − | 0.832536i | \(-0.686888\pi\) | ||||
−0.553970 | + | 0.832536i | \(0.686888\pi\) | |||||||
\(200\) | 660579. | 1.16775 | ||||||||
\(201\) | 214341. | 0.374210 | ||||||||
\(202\) | −1.05542e6 | −1.81991 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −854372. | −1.43738 | ||||||||
\(205\) | 946463. | 1.57296 | ||||||||
\(206\) | 203739. | 0.334508 | ||||||||
\(207\) | 3481.14 | 0.00564671 | ||||||||
\(208\) | −1.29777e6 | −2.07988 | ||||||||
\(209\) | −139110. | −0.220289 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 769805. | 1.19035 | 0.595175 | − | 0.803596i | \(-0.297083\pi\) | ||||
0.595175 | + | 0.803596i | \(0.297083\pi\) | |||||||
\(212\) | 1.75052e6 | 2.67502 | ||||||||
\(213\) | 402126. | 0.607314 | ||||||||
\(214\) | −37787.9 | −0.0564050 | ||||||||
\(215\) | −424477. | −0.626264 | ||||||||
\(216\) | −263971. | −0.384966 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 85445.7 | 0.121772 | ||||||||
\(219\) | −356411. | −0.502159 | ||||||||
\(220\) | 3.50807e6 | 4.88665 | ||||||||
\(221\) | −1.25266e6 | −1.72525 | ||||||||
\(222\) | −836724. | −1.13946 | ||||||||
\(223\) | 1.45664e6 | 1.96151 | 0.980755 | − | 0.195244i | \(-0.0625498\pi\) | ||||
0.980755 | + | 0.195244i | \(0.0625498\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 147768. | 0.194592 | ||||||||
\(226\) | −1.00959e6 | −1.31484 | ||||||||
\(227\) | −949905. | −1.22353 | −0.611767 | − | 0.791038i | \(-0.709541\pi\) | ||||
−0.611767 | + | 0.791038i | \(0.709541\pi\) | |||||||
\(228\) | −116706. | −0.148681 | ||||||||
\(229\) | 312283. | 0.393513 | 0.196757 | − | 0.980452i | \(-0.436959\pi\) | ||||
0.196757 | + | 0.980452i | \(0.436959\pi\) | |||||||
\(230\) | −30261.7 | −0.0377202 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.80505e6 | −3.42153 | ||||||||
\(233\) | 396905. | 0.478957 | 0.239479 | − | 0.970902i | \(-0.423023\pi\) | ||||
0.239479 | + | 0.970902i | \(0.423023\pi\) | |||||||
\(234\) | −729360. | −0.870768 | ||||||||
\(235\) | −228286. | −0.269655 | ||||||||
\(236\) | 1.80334e6 | 2.10764 | ||||||||
\(237\) | −208107. | −0.240666 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −87033.3 | −0.0985578 | −0.0492789 | − | 0.998785i | \(-0.515692\pi\) | ||||
−0.0492789 | + | 0.998785i | \(0.515692\pi\) | |||||||
\(240\) | 913356. | 1.02356 | ||||||||
\(241\) | −1.57173e6 | −1.74315 | −0.871576 | − | 0.490260i | \(-0.836902\pi\) | ||||
−0.871576 | + | 0.490260i | \(0.836902\pi\) | |||||||
\(242\) | 3.74222e6 | 4.10762 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 438573. | 0.471593 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.21188e6 | 1.27680 | ||||||||
\(247\) | −171111. | −0.178457 | ||||||||
\(248\) | −426997. | −0.440855 | ||||||||
\(249\) | −155404. | −0.158842 | ||||||||
\(250\) | 915875. | 0.926801 | ||||||||
\(251\) | −385591. | −0.386316 | −0.193158 | − | 0.981168i | \(-0.561873\pi\) | ||||
−0.193158 | + | 0.981168i | \(0.561873\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −31433.2 | −0.0308736 | ||||||||
\(254\) | −1.85616e6 | −1.80523 | ||||||||
\(255\) | 881607. | 0.849033 | ||||||||
\(256\) | −2.11484e6 | −2.01687 | ||||||||
\(257\) | −441809. | −0.417255 | −0.208627 | − | 0.977995i | \(-0.566900\pi\) | ||||
−0.208627 | + | 0.977995i | \(0.566900\pi\) | |||||||
\(258\) | −543514. | −0.508348 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.31506e6 | 3.95870 | ||||||||
\(261\) | −627474. | −0.570157 | ||||||||
\(262\) | −1.24156e6 | −1.11742 | ||||||||
\(263\) | −600264. | −0.535122 | −0.267561 | − | 0.963541i | \(-0.586218\pi\) | ||||
−0.267561 | + | 0.963541i | \(0.586218\pi\) | |||||||
\(264\) | 2.38355e6 | 2.10482 | ||||||||
\(265\) | −1.80632e6 | −1.58009 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 449368. | 0.385766 | ||||||||
\(268\) | −1.62370e6 | −1.38092 | ||||||||
\(269\) | 325609. | 0.274357 | 0.137178 | − | 0.990546i | \(-0.456197\pi\) | ||||
0.137178 | + | 0.990546i | \(0.456197\pi\) | |||||||
\(270\) | 513316. | 0.428525 | ||||||||
\(271\) | 1.75592e6 | 1.45239 | 0.726193 | − | 0.687491i | \(-0.241288\pi\) | ||||
0.726193 | + | 0.687491i | \(0.241288\pi\) | |||||||
\(272\) | 2.00857e6 | 1.64613 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 996090. | 0.801534 | ||||||||
\(275\) | −1.33428e6 | −1.06394 | ||||||||
\(276\) | −26370.7 | −0.0208377 | ||||||||
\(277\) | −342363. | −0.268094 | −0.134047 | − | 0.990975i | \(-0.542797\pi\) | ||||
−0.134047 | + | 0.990975i | \(0.542797\pi\) | |||||||
\(278\) | −2.54707e6 | −1.97664 | ||||||||
\(279\) | −95517.1 | −0.0734633 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 930671. | 0.703122 | 0.351561 | − | 0.936165i | \(-0.385651\pi\) | ||||
0.351561 | + | 0.936165i | \(0.385651\pi\) | |||||||
\(282\) | −292304. | −0.218883 | ||||||||
\(283\) | −1.64760e6 | −1.22288 | −0.611442 | − | 0.791290i | \(-0.709410\pi\) | ||||
−0.611442 | + | 0.791290i | \(0.709410\pi\) | |||||||
\(284\) | −3.04623e6 | −2.24113 | ||||||||
\(285\) | 120426. | 0.0878229 | ||||||||
\(286\) | 6.58582e6 | 4.76096 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 230926. | 0.164056 | ||||||||
\(289\) | 518891. | 0.365453 | ||||||||
\(290\) | 5.45467e6 | 3.80867 | ||||||||
\(291\) | −151785. | −0.105074 | ||||||||
\(292\) | 2.69993e6 | 1.85309 | ||||||||
\(293\) | −1.14378e6 | −0.778347 | −0.389174 | − | 0.921164i | \(-0.627239\pi\) | ||||
−0.389174 | + | 0.921164i | \(0.627239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.86082e6 | −1.24495 | ||||||||
\(296\) | 3.36344e6 | 2.23128 | ||||||||
\(297\) | 533188. | 0.350743 | ||||||||
\(298\) | −4.27640e6 | −2.78957 | ||||||||
\(299\) | −38664.1 | −0.0250109 | ||||||||
\(300\) | −1.11939e6 | −0.718089 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.50605e6 | −0.950218 | ||||||||
\(303\) | 949038. | 0.593851 | ||||||||
\(304\) | 274367. | 0.170274 | ||||||||
\(305\) | −452553. | −0.278561 | ||||||||
\(306\) | 1.12884e6 | 0.689173 | ||||||||
\(307\) | 2.98831e6 | 1.80959 | 0.904795 | − | 0.425848i | \(-0.140024\pi\) | ||||
0.904795 | + | 0.425848i | \(0.140024\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −183202. | −0.109153 | ||||||||
\(310\) | 830335. | 0.490738 | ||||||||
\(311\) | 2.83751e6 | 1.66355 | 0.831775 | − | 0.555113i | \(-0.187325\pi\) | ||||
0.831775 | + | 0.555113i | \(0.187325\pi\) | |||||||
\(312\) | 2.93186e6 | 1.70513 | ||||||||
\(313\) | −2.14749e6 | −1.23899 | −0.619497 | − | 0.784999i | \(-0.712664\pi\) | ||||
−0.619497 | + | 0.784999i | \(0.712664\pi\) | |||||||
\(314\) | −1.65979e6 | −0.950010 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.57648e6 | 0.888116 | ||||||||
\(317\) | −2.63357e6 | −1.47196 | −0.735982 | − | 0.677001i | \(-0.763279\pi\) | ||||
−0.735982 | + | 0.677001i | \(0.763279\pi\) | |||||||
\(318\) | −2.31288e6 | −1.28258 | ||||||||
\(319\) | 5.66583e6 | 3.11736 | ||||||||
\(320\) | 1.24003e6 | 0.676953 | ||||||||
\(321\) | 33978.9 | 0.0184054 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 264829. | 0.141241 | ||||||||
\(324\) | 447315. | 0.236729 | ||||||||
\(325\) | −1.64122e6 | −0.861902 | ||||||||
\(326\) | 958033. | 0.499271 | ||||||||
\(327\) | −76832.8 | −0.0397354 | ||||||||
\(328\) | −4.87148e6 | −2.50021 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.63503e6 | −2.34298 | ||||||||
\(331\) | 3.28434e6 | 1.64770 | 0.823849 | − | 0.566809i | \(-0.191822\pi\) | ||||
0.823849 | + | 0.566809i | \(0.191822\pi\) | |||||||
\(332\) | 1.17724e6 | 0.586164 | ||||||||
\(333\) | 752383. | 0.371816 | ||||||||
\(334\) | −4.74631e6 | −2.32804 | ||||||||
\(335\) | 1.67546e6 | 0.815685 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −238202. | −0.114254 | −0.0571270 | − | 0.998367i | \(-0.518194\pi\) | ||||
−0.0571270 | + | 0.998367i | \(0.518194\pi\) | |||||||
\(338\) | 4.38457e6 | 2.08754 | ||||||||
\(339\) | 907821. | 0.429043 | ||||||||
\(340\) | −6.67846e6 | −3.13313 | ||||||||
\(341\) | 862479. | 0.401664 | ||||||||
\(342\) | 154197. | 0.0712872 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.18480e6 | 0.995441 | ||||||||
\(345\) | 27211.4 | 0.0123084 | ||||||||
\(346\) | −2.59107e6 | −1.16356 | ||||||||
\(347\) | 1.06436e6 | 0.474532 | 0.237266 | − | 0.971445i | \(-0.423749\pi\) | ||||
0.237266 | + | 0.971445i | \(0.423749\pi\) | |||||||
\(348\) | 4.75332e6 | 2.10402 | ||||||||
\(349\) | −1.85940e6 | −0.817163 | −0.408582 | − | 0.912722i | \(-0.633977\pi\) | ||||
−0.408582 | + | 0.912722i | \(0.633977\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 655841. | 0.284139 | ||||||||
\(352\) | −2.08517e6 | −0.896983 | ||||||||
\(353\) | 1.66487e6 | 0.711123 | 0.355561 | − | 0.934653i | \(-0.384290\pi\) | ||||
0.355561 | + | 0.934653i | \(0.384290\pi\) | |||||||
\(354\) | −2.38266e6 | −1.01054 | ||||||||
\(355\) | 3.14334e6 | 1.32379 | ||||||||
\(356\) | −3.40411e6 | −1.42357 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.42660e6 | −2.23779 | ||||||||
\(359\) | 2.67457e6 | 1.09526 | 0.547632 | − | 0.836720i | \(-0.315530\pi\) | ||||
0.547632 | + | 0.836720i | \(0.315530\pi\) | |||||||
\(360\) | −2.06341e6 | −0.839131 | ||||||||
\(361\) | −2.43992e6 | −0.985390 | ||||||||
\(362\) | −6.54511e6 | −2.62510 | ||||||||
\(363\) | −3.36500e6 | −1.34035 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.78600e6 | −1.09458 | ||||||||
\(366\) | −579464. | −0.226112 | ||||||||
\(367\) | 2.14384e6 | 0.830860 | 0.415430 | − | 0.909625i | \(-0.363631\pi\) | ||||
0.415430 | + | 0.909625i | \(0.363631\pi\) | |||||||
\(368\) | 61995.8 | 0.0238640 | ||||||||
\(369\) | −1.08972e6 | −0.416630 | ||||||||
\(370\) | −6.54051e6 | −2.48375 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 723573. | 0.271097 | ||||||||
\(373\) | −759867. | −0.282791 | −0.141395 | − | 0.989953i | \(-0.545159\pi\) | ||||
−0.141395 | + | 0.989953i | \(0.545159\pi\) | |||||||
\(374\) | −1.01929e7 | −3.76808 | ||||||||
\(375\) | −823555. | −0.302423 | ||||||||
\(376\) | 1.17500e6 | 0.428614 | ||||||||
\(377\) | 6.96918e6 | 2.52539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.03679e6 | 1.08597 | 0.542984 | − | 0.839743i | \(-0.317294\pi\) | ||||
0.542984 | + | 0.839743i | \(0.317294\pi\) | |||||||
\(380\) | −912265. | −0.324087 | ||||||||
\(381\) | 1.66906e6 | 0.589061 | ||||||||
\(382\) | 7.70220e6 | 2.70057 | ||||||||
\(383\) | −2.50929e6 | −0.874086 | −0.437043 | − | 0.899441i | \(-0.643974\pi\) | ||||
−0.437043 | + | 0.899441i | \(0.643974\pi\) | |||||||
\(384\) | 2.40885e6 | 0.833646 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.14954e6 | 2.78397 | ||||||||
\(387\) | 488728. | 0.165878 | ||||||||
\(388\) | 1.14982e6 | 0.387749 | ||||||||
\(389\) | −985137. | −0.330082 | −0.165041 | − | 0.986287i | \(-0.552776\pi\) | ||||
−0.165041 | + | 0.986287i | \(0.552776\pi\) | |||||||
\(390\) | −5.70127e6 | −1.89806 | ||||||||
\(391\) | 59840.7 | 0.0197950 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.11641e6 | 0.364623 | ||||||||
\(394\) | −4.44082e6 | −1.44119 | ||||||||
\(395\) | −1.62673e6 | −0.524593 | ||||||||
\(396\) | −4.03907e6 | −1.29432 | ||||||||
\(397\) | 2.90510e6 | 0.925092 | 0.462546 | − | 0.886595i | \(-0.346936\pi\) | ||||
0.462546 | + | 0.886595i | \(0.346936\pi\) | |||||||
\(398\) | −6.19491e6 | −1.96032 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.63161e6 | 0.822377 | ||||||||
\(401\) | −4.23124e6 | −1.31404 | −0.657018 | − | 0.753875i | \(-0.728182\pi\) | ||||
−0.657018 | + | 0.753875i | \(0.728182\pi\) | |||||||
\(402\) | 2.14532e6 | 0.662104 | ||||||||
\(403\) | 1.06088e6 | 0.325390 | ||||||||
\(404\) | −7.18927e6 | −2.19145 | ||||||||
\(405\) | −461574. | −0.139831 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.79370e6 | −2.03292 | ||||||||
\(408\) | −4.53767e6 | −1.34953 | ||||||||
\(409\) | 4.13890e6 | 1.22342 | 0.611711 | − | 0.791081i | \(-0.290482\pi\) | ||||
0.611711 | + | 0.791081i | \(0.290482\pi\) | |||||||
\(410\) | 9.47304e6 | 2.78311 | ||||||||
\(411\) | −895684. | −0.261547 | ||||||||
\(412\) | 1.38782e6 | 0.402799 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 34842.3 | 0.00999094 | ||||||||
\(415\) | −1.21477e6 | −0.346236 | ||||||||
\(416\) | −2.56483e6 | −0.726651 | ||||||||
\(417\) | 2.29033e6 | 0.644996 | ||||||||
\(418\) | −1.39234e6 | −0.389766 | ||||||||
\(419\) | 5.99852e6 | 1.66920 | 0.834601 | − | 0.550855i | \(-0.185698\pi\) | ||||
0.834601 | + | 0.550855i | \(0.185698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00759e6 | −0.277062 | −0.138531 | − | 0.990358i | \(-0.544238\pi\) | ||||
−0.138531 | + | 0.990358i | \(0.544238\pi\) | |||||||
\(422\) | 7.70489e6 | 2.10613 | ||||||||
\(423\) | 262840. | 0.0714235 | ||||||||
\(424\) | 9.29722e6 | 2.51153 | ||||||||
\(425\) | 2.54013e6 | 0.682156 | ||||||||
\(426\) | 4.02484e6 | 1.07454 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −257401. | −0.0679205 | ||||||||
\(429\) | −5.92197e6 | −1.55354 | ||||||||
\(430\) | −4.24854e6 | −1.10807 | ||||||||
\(431\) | 303149. | 0.0786073 | 0.0393037 | − | 0.999227i | \(-0.487486\pi\) | ||||
0.0393037 | + | 0.999227i | \(0.487486\pi\) | |||||||
\(432\) | −1.05161e6 | −0.271109 | ||||||||
\(433\) | 3.97130e6 | 1.01792 | 0.508960 | − | 0.860790i | \(-0.330030\pi\) | ||||
0.508960 | + | 0.860790i | \(0.330030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.90484e6 | −1.24280 | ||||||||
\(436\) | 582033. | 0.146633 | ||||||||
\(437\) | 8174.14 | 0.00204757 | ||||||||
\(438\) | −3.56728e6 | −0.888489 | ||||||||
\(439\) | 3.74799e6 | 0.928192 | 0.464096 | − | 0.885785i | \(-0.346379\pi\) | ||||
0.464096 | + | 0.885785i | \(0.346379\pi\) | |||||||
\(440\) | 1.86318e7 | 4.58798 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.25377e7 | −3.05255 | ||||||||
\(443\) | −1.31077e6 | −0.317334 | −0.158667 | − | 0.987332i | \(-0.550720\pi\) | ||||
−0.158667 | + | 0.987332i | \(0.550720\pi\) | |||||||
\(444\) | −5.69954e6 | −1.37209 | ||||||||
\(445\) | 3.51262e6 | 0.840874 | ||||||||
\(446\) | 1.45794e7 | 3.47057 | ||||||||
\(447\) | 3.84534e6 | 0.910261 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.31311e6 | 1.47784 | 0.738920 | − | 0.673793i | \(-0.235336\pi\) | ||||
0.738920 | + | 0.673793i | \(0.235336\pi\) | |||||||
\(450\) | 1.47899e6 | 0.344298 | ||||||||
\(451\) | 9.83976e6 | 2.27794 | ||||||||
\(452\) | −6.87704e6 | −1.58327 | ||||||||
\(453\) | 1.35424e6 | 0.310064 | ||||||||
\(454\) | −9.50750e6 | −2.16484 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −619837. | −0.139594 | ||||||||
\(457\) | −583476. | −0.130687 | −0.0653435 | − | 0.997863i | \(-0.520814\pi\) | ||||
−0.0653435 | + | 0.997863i | \(0.520814\pi\) | |||||||
\(458\) | 3.12561e6 | 0.696259 | ||||||||
\(459\) | −1.01505e6 | −0.224883 | ||||||||
\(460\) | −206135. | −0.0454210 | ||||||||
\(461\) | −2.93381e6 | −0.642953 | −0.321476 | − | 0.946918i | \(-0.604179\pi\) | ||||
−0.321476 | + | 0.946918i | \(0.604179\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.76716e6 | 0.816699 | 0.408349 | − | 0.912826i | \(-0.366105\pi\) | ||||
0.408349 | + | 0.912826i | \(0.366105\pi\) | |||||||
\(464\) | −1.11747e7 | −2.40958 | ||||||||
\(465\) | −746638. | −0.160132 | ||||||||
\(466\) | 3.97258e6 | 0.847438 | ||||||||
\(467\) | −2.90596e6 | −0.616592 | −0.308296 | − | 0.951290i | \(-0.599759\pi\) | ||||
−0.308296 | + | 0.951290i | \(0.599759\pi\) | |||||||
\(468\) | −4.96821e6 | −1.04854 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.28489e6 | −0.477111 | ||||||||
\(471\) | 1.49248e6 | 0.309996 | ||||||||
\(472\) | 9.57774e6 | 1.97883 | ||||||||
\(473\) | −4.41301e6 | −0.906947 | ||||||||
\(474\) | −2.08292e6 | −0.425820 | ||||||||
\(475\) | 346977. | 0.0705613 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.07974e6 | 0.418517 | ||||||||
\(478\) | −871107. | −0.174382 | ||||||||
\(479\) | −7.06622e6 | −1.40718 | −0.703588 | − | 0.710608i | \(-0.748420\pi\) | ||||
−0.703588 | + | 0.710608i | \(0.748420\pi\) | |||||||
\(480\) | 1.80510e6 | 0.357601 | ||||||||
\(481\) | −8.35651e6 | −1.64688 | ||||||||
\(482\) | −1.57313e7 | −3.08423 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.54910e7 | 4.94622 | ||||||||
\(485\) | −1.18647e6 | −0.229036 | ||||||||
\(486\) | −591015. | −0.113503 | ||||||||
\(487\) | 2.72981e6 | 0.521566 | 0.260783 | − | 0.965397i | \(-0.416019\pi\) | ||||
0.260783 | + | 0.965397i | \(0.416019\pi\) | |||||||
\(488\) | 2.32931e6 | 0.442770 | ||||||||
\(489\) | −861464. | −0.162916 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.02859e7 | −1.92548 | −0.962740 | − | 0.270428i | \(-0.912835\pi\) | ||||
−0.962740 | + | 0.270428i | \(0.912835\pi\) | |||||||
\(492\) | 8.25502e6 | 1.53746 | ||||||||
\(493\) | −1.07863e7 | −1.99873 | ||||||||
\(494\) | −1.71263e6 | −0.315751 | ||||||||
\(495\) | 4.16782e6 | 0.764533 | ||||||||
\(496\) | −1.70107e6 | −0.310469 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.55543e6 | −0.281045 | ||||||||
\(499\) | −3.63591e6 | −0.653674 | −0.326837 | − | 0.945081i | \(-0.605983\pi\) | ||||
−0.326837 | + | 0.945081i | \(0.605983\pi\) | |||||||
\(500\) | 6.23870e6 | 1.11601 | ||||||||
\(501\) | 4.26788e6 | 0.759658 | ||||||||
\(502\) | −3.85934e6 | −0.683524 | ||||||||
\(503\) | −1.65499e6 | −0.291658 | −0.145829 | − | 0.989310i | \(-0.546585\pi\) | ||||
−0.145829 | + | 0.989310i | \(0.546585\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.41845e6 | 1.29445 | ||||||||
\(506\) | −314612. | −0.0546259 | ||||||||
\(507\) | −3.94261e6 | −0.681183 | ||||||||
\(508\) | −1.26437e7 | −2.17377 | ||||||||
\(509\) | 731110. | 0.125080 | 0.0625401 | − | 0.998042i | \(-0.480080\pi\) | ||||
0.0625401 | + | 0.998042i | \(0.480080\pi\) | |||||||
\(510\) | 8.82391e6 | 1.50223 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.26024e7 | −2.12460 | ||||||||
\(513\) | −138654. | −0.0232616 | ||||||||
\(514\) | −4.42202e6 | −0.738265 | ||||||||
\(515\) | −1.43206e6 | −0.237926 | ||||||||
\(516\) | −3.70227e6 | −0.612130 | ||||||||
\(517\) | −2.37334e6 | −0.390511 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.32989e6 | 0.379679 | ||||||||
\(520\) | 2.29178e7 | 3.71675 | ||||||||
\(521\) | −4.73095e6 | −0.763579 | −0.381790 | − | 0.924249i | \(-0.624692\pi\) | ||||
−0.381790 | + | 0.924249i | \(0.624692\pi\) | |||||||
\(522\) | −6.28032e6 | −1.00880 | ||||||||
\(523\) | 9.72563e6 | 1.55476 | 0.777380 | − | 0.629031i | \(-0.216548\pi\) | ||||
0.777380 | + | 0.629031i | \(0.216548\pi\) | |||||||
\(524\) | −8.45719e6 | −1.34554 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00798e6 | −0.946812 | ||||||||
\(527\) | −1.64194e6 | −0.257531 | ||||||||
\(528\) | 9.49557e6 | 1.48230 | ||||||||
\(529\) | −6.43450e6 | −0.999713 | ||||||||
\(530\) | −1.80793e7 | −2.79571 | ||||||||
\(531\) | 2.14249e6 | 0.329748 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.21033e7 | 1.84538 | ||||||||
\(534\) | 4.49767e6 | 0.682550 | ||||||||
\(535\) | 265606. | 0.0401193 | ||||||||
\(536\) | −8.62367e6 | −1.29652 | ||||||||
\(537\) | 4.87960e6 | 0.730211 | ||||||||
\(538\) | 3.25898e6 | 0.485430 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.49658e6 | 0.516010 | ||||||||
\(541\) | 8.19002e6 | 1.20307 | 0.601536 | − | 0.798845i | \(-0.294556\pi\) | ||||
0.601536 | + | 0.798845i | \(0.294556\pi\) | |||||||
\(542\) | 1.75748e7 | 2.56976 | ||||||||
\(543\) | 5.88537e6 | 0.856592 | ||||||||
\(544\) | 3.96962e6 | 0.575111 | ||||||||
\(545\) | −600587. | −0.0866133 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.17136e6 | −0.596087 | −0.298043 | − | 0.954552i | \(-0.596334\pi\) | ||||
−0.298043 | + | 0.954552i | \(0.596334\pi\) | |||||||
\(548\) | 6.78510e6 | 0.965172 | ||||||||
\(549\) | 521054. | 0.0737823 | ||||||||
\(550\) | −1.33547e7 | −1.88247 | ||||||||
\(551\) | −1.47339e6 | −0.206746 | ||||||||
\(552\) | −140058. | −0.0195641 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.42668e6 | −0.474350 | ||||||||
\(555\) | 5.88123e6 | 0.810468 | ||||||||
\(556\) | −1.73500e7 | −2.38019 | ||||||||
\(557\) | −1.26658e6 | −0.172980 | −0.0864899 | − | 0.996253i | \(-0.527565\pi\) | ||||
−0.0864899 | + | 0.996253i | \(0.527565\pi\) | |||||||
\(558\) | −956020. | −0.129981 | ||||||||
\(559\) | −5.42817e6 | −0.734723 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.16549e6 | 1.22956 | ||||||||
\(562\) | 9.31499e6 | 1.24406 | ||||||||
\(563\) | 6.37431e6 | 0.847544 | 0.423772 | − | 0.905769i | \(-0.360706\pi\) | ||||
0.423772 | + | 0.905769i | \(0.360706\pi\) | |||||||
\(564\) | −1.99110e6 | −0.263570 | ||||||||
\(565\) | 7.09626e6 | 0.935208 | ||||||||
\(566\) | −1.64906e7 | −2.16369 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.61789e7 | −2.10416 | ||||||||
\(569\) | 7.64040e6 | 0.989317 | 0.494659 | − | 0.869087i | \(-0.335293\pi\) | ||||
0.494659 | + | 0.869087i | \(0.335293\pi\) | |||||||
\(570\) | 1.20533e6 | 0.155388 | ||||||||
\(571\) | 790914. | 0.101517 | 0.0507585 | − | 0.998711i | \(-0.483836\pi\) | ||||
0.0507585 | + | 0.998711i | \(0.483836\pi\) | |||||||
\(572\) | 4.48608e7 | 5.73294 | ||||||||
\(573\) | −6.92582e6 | −0.881221 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 78402.8 | 0.00988922 | ||||||||
\(576\) | −1.42773e6 | −0.179304 | ||||||||
\(577\) | 8.55670e6 | 1.06996 | 0.534979 | − | 0.844865i | \(-0.320320\pi\) | ||||
0.534979 | + | 0.844865i | \(0.320320\pi\) | |||||||
\(578\) | 5.19352e6 | 0.646610 | ||||||||
\(579\) | −7.32807e6 | −0.908434 | ||||||||
\(580\) | 3.71558e7 | 4.58623 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.51920e6 | −0.185912 | ||||||||
\(583\) | −1.87792e7 | −2.28826 | ||||||||
\(584\) | 1.43396e7 | 1.73983 | ||||||||
\(585\) | 5.12658e6 | 0.619353 | ||||||||
\(586\) | −1.14480e7 | −1.37716 | ||||||||
\(587\) | 1.17153e7 | 1.40333 | 0.701663 | − | 0.712509i | \(-0.252441\pi\) | ||||
0.701663 | + | 0.712509i | \(0.252441\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −224286. | −0.0266387 | ||||||||
\(590\) | −1.86248e7 | −2.20273 | ||||||||
\(591\) | 3.99319e6 | 0.470274 | ||||||||
\(592\) | 1.33992e7 | 1.57136 | ||||||||
\(593\) | −1.55617e7 | −1.81728 | −0.908639 | − | 0.417583i | \(-0.862877\pi\) | ||||
−0.908639 | + | 0.417583i | \(0.862877\pi\) | |||||||
\(594\) | 5.33662e6 | 0.620583 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.91297e7 | −3.35908 | ||||||||
\(597\) | 5.57047e6 | 0.639670 | ||||||||
\(598\) | −386984. | −0.0442528 | ||||||||
\(599\) | −9.18930e6 | −1.04644 | −0.523221 | − | 0.852197i | \(-0.675270\pi\) | ||||
−0.523221 | + | 0.852197i | \(0.675270\pi\) | |||||||
\(600\) | −5.94521e6 | −0.674200 | ||||||||
\(601\) | −1.61226e7 | −1.82075 | −0.910373 | − | 0.413789i | \(-0.864205\pi\) | ||||
−0.910373 | + | 0.413789i | \(0.864205\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.92907e6 | −0.216050 | ||||||||
\(604\) | −1.02588e7 | −1.14421 | ||||||||
\(605\) | −2.63036e7 | −2.92164 | ||||||||
\(606\) | 9.49882e6 | 1.05072 | ||||||||
\(607\) | −1.04056e7 | −1.14629 | −0.573144 | − | 0.819455i | \(-0.694276\pi\) | ||||
−0.573144 | + | 0.819455i | \(0.694276\pi\) | |||||||
\(608\) | 542243. | 0.0594887 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.52956e6 | −0.492868 | ||||||||
\(611\) | −2.91929e6 | −0.316355 | ||||||||
\(612\) | 7.68935e6 | 0.829871 | ||||||||
\(613\) | −1.13921e7 | −1.22449 | −0.612243 | − | 0.790670i | \(-0.709732\pi\) | ||||
−0.612243 | + | 0.790670i | \(0.709732\pi\) | |||||||
\(614\) | 2.99097e7 | 3.20178 | ||||||||
\(615\) | −8.51816e6 | −0.908151 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.20517e6 | 0.656206 | 0.328103 | − | 0.944642i | \(-0.393591\pi\) | ||||
0.328103 | + | 0.944642i | \(0.393591\pi\) | |||||||
\(618\) | −1.83365e6 | −0.193128 | ||||||||
\(619\) | 9.85608e6 | 1.03390 | 0.516949 | − | 0.856016i | \(-0.327068\pi\) | ||||
0.516949 | + | 0.856016i | \(0.327068\pi\) | |||||||
\(620\) | 5.65602e6 | 0.590925 | ||||||||
\(621\) | −31330.2 | −0.00326013 | ||||||||
\(622\) | 2.84003e7 | 2.94338 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.16799e7 | 1.20082 | ||||||||
\(625\) | −1.21385e7 | −1.24298 | ||||||||
\(626\) | −2.14940e7 | −2.19220 | ||||||||
\(627\) | 1.25199e6 | 0.127184 | ||||||||
\(628\) | −1.13060e7 | −1.14396 | ||||||||
\(629\) | 1.29335e7 | 1.30343 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.26873e6 | 0.726750 | 0.363375 | − | 0.931643i | \(-0.381624\pi\) | ||||
0.363375 | + | 0.931643i | \(0.381624\pi\) | |||||||
\(632\) | 8.37284e6 | 0.833835 | ||||||||
\(633\) | −6.92824e6 | −0.687248 | ||||||||
\(634\) | −2.63591e7 | −2.60440 | ||||||||
\(635\) | 1.30467e7 | 1.28401 | ||||||||
\(636\) | −1.57547e7 | −1.54443 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.67087e7 | 5.51566 | ||||||||
\(639\) | −3.61913e6 | −0.350633 | ||||||||
\(640\) | 1.88295e7 | 1.81714 | ||||||||
\(641\) | 8.30119e6 | 0.797986 | 0.398993 | − | 0.916954i | \(-0.369360\pi\) | ||||
0.398993 | + | 0.916954i | \(0.369360\pi\) | |||||||
\(642\) | 340091. | 0.0325655 | ||||||||
\(643\) | 4.14322e6 | 0.395194 | 0.197597 | − | 0.980283i | \(-0.436686\pi\) | ||||
0.197597 | + | 0.980283i | \(0.436686\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.82029e6 | 0.361574 | ||||||||
\(646\) | 2.65065e6 | 0.249903 | ||||||||
\(647\) | 1.47906e7 | 1.38907 | 0.694535 | − | 0.719459i | \(-0.255610\pi\) | ||||
0.694535 | + | 0.719459i | \(0.255610\pi\) | |||||||
\(648\) | 2.37574e6 | 0.222260 | ||||||||
\(649\) | −1.93458e7 | −1.80291 | ||||||||
\(650\) | −1.64268e7 | −1.52500 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.52587e6 | 0.601200 | ||||||||
\(653\) | −6.08931e6 | −0.558837 | −0.279419 | − | 0.960169i | \(-0.590142\pi\) | ||||
−0.279419 | + | 0.960169i | \(0.590142\pi\) | |||||||
\(654\) | −769011. | −0.0703053 | ||||||||
\(655\) | 8.72679e6 | 0.794788 | ||||||||
\(656\) | −1.94070e7 | −1.76075 | ||||||||
\(657\) | 3.20770e6 | 0.289922 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.14447e6 | 0.371754 | 0.185877 | − | 0.982573i | \(-0.440487\pi\) | ||||
0.185877 | + | 0.982573i | \(0.440487\pi\) | |||||||
\(660\) | −3.15726e7 | −2.82131 | ||||||||
\(661\) | −1.80378e7 | −1.60576 | −0.802881 | − | 0.596140i | \(-0.796700\pi\) | ||||
−0.802881 | + | 0.596140i | \(0.796700\pi\) | |||||||
\(662\) | 3.28726e7 | 2.91534 | ||||||||
\(663\) | 1.12739e7 | 0.996071 | ||||||||
\(664\) | 6.25245e6 | 0.550339 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.53052e6 | 0.657869 | ||||||||
\(667\) | −332926. | −0.0289756 | ||||||||
\(668\) | −3.23306e7 | −2.80332 | ||||||||
\(669\) | −1.31098e7 | −1.13248 | ||||||||
\(670\) | 1.67695e7 | 1.44322 | ||||||||
\(671\) | −4.70490e6 | −0.403408 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.62885e6 | 0.479051 | 0.239526 | − | 0.970890i | \(-0.423008\pi\) | ||||
0.239526 | + | 0.970890i | \(0.423008\pi\) | |||||||
\(674\) | −2.38414e6 | −0.202154 | ||||||||
\(675\) | −1.32991e6 | −0.112347 | ||||||||
\(676\) | 2.98666e7 | 2.51373 | ||||||||
\(677\) | 1.50877e7 | 1.26518 | 0.632588 | − | 0.774488i | \(-0.281993\pi\) | ||||
0.632588 | + | 0.774488i | \(0.281993\pi\) | |||||||
\(678\) | 9.08628e6 | 0.759123 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.54700e7 | −2.94164 | ||||||||
\(681\) | 8.54915e6 | 0.706407 | ||||||||
\(682\) | 8.63246e6 | 0.710679 | ||||||||
\(683\) | 7.20414e6 | 0.590922 | 0.295461 | − | 0.955355i | \(-0.404527\pi\) | ||||
0.295461 | + | 0.955355i | \(0.404527\pi\) | |||||||
\(684\) | 1.05035e6 | 0.0858408 | ||||||||
\(685\) | −7.00139e6 | −0.570109 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.81055e6 | −0.227195 | ||||||||
\(688\) | 8.70378e6 | 0.701031 | ||||||||
\(689\) | −2.30991e7 | −1.85373 | ||||||||
\(690\) | 272356. | 0.0217778 | ||||||||
\(691\) | −9.08625e6 | −0.723918 | −0.361959 | − | 0.932194i | \(-0.617892\pi\) | ||||
−0.361959 | + | 0.932194i | \(0.617892\pi\) | |||||||
\(692\) | −1.76497e7 | −1.40111 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.06531e7 | 0.839607 | ||||||||
\(695\) | 1.79030e7 | 1.40593 | ||||||||
\(696\) | 2.52454e7 | 1.97542 | ||||||||
\(697\) | −1.87324e7 | −1.46053 | ||||||||
\(698\) | −1.86105e7 | −1.44584 | ||||||||
\(699\) | −3.57215e6 | −0.276526 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.41913e7 | −1.09075 | −0.545376 | − | 0.838192i | \(-0.683613\pi\) | ||||
−0.545376 | + | 0.838192i | \(0.683613\pi\) | |||||||
\(702\) | 6.56424e6 | 0.502738 | ||||||||
\(703\) | 1.76669e6 | 0.134825 | ||||||||
\(704\) | 1.28918e7 | 0.980354 | ||||||||
\(705\) | 2.05457e6 | 0.155686 | ||||||||
\(706\) | 1.66635e7 | 1.25822 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.62300e7 | −1.21685 | ||||||||
\(709\) | −2.21070e6 | −0.165164 | −0.0825819 | − | 0.996584i | \(-0.526317\pi\) | ||||
−0.0825819 | + | 0.996584i | \(0.526317\pi\) | |||||||
\(710\) | 3.14613e7 | 2.34224 | ||||||||
\(711\) | 1.87296e6 | 0.138949 | ||||||||
\(712\) | −1.80796e7 | −1.33656 | ||||||||
\(713\) | −50679.5 | −0.00373343 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.62909e7 | −3.38634 | ||||||||
\(716\) | −3.69645e7 | −2.69465 | ||||||||
\(717\) | 783300. | 0.0569024 | ||||||||
\(718\) | 2.67695e7 | 1.93789 | ||||||||
\(719\) | 2.99082e6 | 0.215758 | 0.107879 | − | 0.994164i | \(-0.465594\pi\) | ||||
0.107879 | + | 0.994164i | \(0.465594\pi\) | |||||||
\(720\) | −8.22021e6 | −0.590951 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2.44209e7 | −1.74349 | ||||||||
\(723\) | 1.41456e7 | 1.00641 | ||||||||
\(724\) | −4.45836e7 | −3.16103 | ||||||||
\(725\) | −1.41321e7 | −0.998530 | ||||||||
\(726\) | −3.36799e7 | −2.37154 | ||||||||
\(727\) | −8.38066e6 | −0.588088 | −0.294044 | − | 0.955792i | \(-0.595001\pi\) | ||||
−0.294044 | + | 0.955792i | \(0.595001\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −2.78847e7 | −1.93669 | ||||||||
\(731\) | 8.40123e6 | 0.581499 | ||||||||
\(732\) | −3.94715e6 | −0.272274 | ||||||||
\(733\) | −7.70245e6 | −0.529504 | −0.264752 | − | 0.964317i | \(-0.585290\pi\) | ||||
−0.264752 | + | 0.964317i | \(0.585290\pi\) | |||||||
\(734\) | 2.14575e7 | 1.47007 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 122525. | 0.00833739 | ||||||||
\(737\) | 1.74187e7 | 1.18126 | ||||||||
\(738\) | −1.09069e7 | −0.737160 | ||||||||
\(739\) | −7.59899e6 | −0.511852 | −0.255926 | − | 0.966696i | \(-0.582380\pi\) | ||||
−0.255926 | + | 0.966696i | \(0.582380\pi\) | |||||||
\(740\) | −4.45522e7 | −2.99082 | ||||||||
\(741\) | 1.53999e6 | 0.103032 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.40124e7 | −1.59574 | −0.797871 | − | 0.602828i | \(-0.794041\pi\) | ||||
−0.797871 | + | 0.602828i | \(0.794041\pi\) | |||||||
\(744\) | 3.84298e6 | 0.254528 | ||||||||
\(745\) | 3.00583e7 | 1.98414 | ||||||||
\(746\) | −7.60543e6 | −0.500353 | ||||||||
\(747\) | 1.39864e6 | 0.0917074 | ||||||||
\(748\) | −6.94316e7 | −4.53736 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.24288e6 | −0.535089 | ||||||||
\(751\) | 1.69479e7 | 1.09652 | 0.548259 | − | 0.836308i | \(-0.315291\pi\) | ||||
0.548259 | + | 0.836308i | \(0.315291\pi\) | |||||||
\(752\) | 4.68094e6 | 0.301848 | ||||||||
\(753\) | 3.47032e6 | 0.223040 | ||||||||
\(754\) | 6.97538e7 | 4.46827 | ||||||||
\(755\) | 1.05859e7 | 0.675863 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.56402e6 | 0.289473 | 0.144736 | − | 0.989470i | \(-0.453767\pi\) | ||||
0.144736 | + | 0.989470i | \(0.453767\pi\) | |||||||
\(758\) | 3.03949e7 | 1.92145 | ||||||||
\(759\) | 282899. | 0.0178249 | ||||||||
\(760\) | −4.84514e6 | −0.304279 | ||||||||
\(761\) | −4.74018e6 | −0.296711 | −0.148355 | − | 0.988934i | \(-0.547398\pi\) | ||||
−0.148355 | + | 0.988934i | \(0.547398\pi\) | |||||||
\(762\) | 1.67055e7 | 1.04225 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.24653e7 | 3.25191 | ||||||||
\(765\) | −7.93446e6 | −0.490189 | ||||||||
\(766\) | −2.51152e7 | −1.54655 | ||||||||
\(767\) | −2.37960e7 | −1.46055 | ||||||||
\(768\) | 1.90335e7 | 1.16444 | ||||||||
\(769\) | −1.39469e7 | −0.850476 | −0.425238 | − | 0.905082i | \(-0.639810\pi\) | ||||
−0.425238 | + | 0.905082i | \(0.639810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.97628e6 | 0.240902 | ||||||||
\(772\) | 5.55125e7 | 3.35234 | ||||||||
\(773\) | 1.49561e7 | 0.900264 | 0.450132 | − | 0.892962i | \(-0.351377\pi\) | ||||
0.450132 | + | 0.892962i | \(0.351377\pi\) | |||||||
\(774\) | 4.89162e6 | 0.293495 | ||||||||
\(775\) | −2.15125e6 | −0.128658 | ||||||||
\(776\) | 6.10683e6 | 0.364050 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.86012e6 | −0.584028 | ||||||||
\(779\) | −2.55881e6 | −0.151075 | ||||||||
\(780\) | −3.88355e7 | −2.28556 | ||||||||
\(781\) | 3.26793e7 | 1.91710 | ||||||||
\(782\) | 598940. | 0.0350240 | ||||||||
\(783\) | 5.64727e6 | 0.329180 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.16664e7 | 0.675716 | ||||||||
\(786\) | 1.11741e7 | 0.645141 | ||||||||
\(787\) | 2.18273e7 | 1.25621 | 0.628105 | − | 0.778128i | \(-0.283831\pi\) | ||||
0.628105 | + | 0.778128i | \(0.283831\pi\) | |||||||
\(788\) | −3.02497e7 | −1.73542 | ||||||||
\(789\) | 5.40238e6 | 0.308953 | ||||||||
\(790\) | −1.62818e7 | −0.928183 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.14520e7 | −1.21522 | ||||||||
\(793\) | −5.78721e6 | −0.326803 | ||||||||
\(794\) | 2.90768e7 | 1.63680 | ||||||||
\(795\) | 1.62569e7 | 0.912263 | ||||||||
\(796\) | −4.21981e7 | −2.36053 | ||||||||
\(797\) | −8.79229e6 | −0.490294 | −0.245147 | − | 0.969486i | \(-0.578836\pi\) | ||||
−0.245147 | + | 0.969486i | \(0.578836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.51822e6 | 0.250381 | ||||||||
\(800\) | 5.20096e6 | 0.287315 | ||||||||
\(801\) | −4.04431e6 | −0.222722 | ||||||||
\(802\) | −4.23501e7 | −2.32497 | ||||||||
\(803\) | −2.89642e7 | −1.58516 | ||||||||
\(804\) | 1.46133e7 | 0.797276 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.06183e7 | 0.575725 | ||||||||
\(807\) | −2.93048e6 | −0.158400 | ||||||||
\(808\) | −3.81831e7 | −2.05751 | ||||||||
\(809\) | −2.87451e6 | −0.154416 | −0.0772081 | − | 0.997015i | \(-0.524601\pi\) | ||||
−0.0772081 | + | 0.997015i | \(0.524601\pi\) | |||||||
\(810\) | −4.61985e6 | −0.247409 | ||||||||
\(811\) | −660356. | −0.0352554 | −0.0176277 | − | 0.999845i | \(-0.505611\pi\) | ||||
−0.0176277 | + | 0.999845i | \(0.505611\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.58033e7 | −0.838535 | ||||||||
\(814\) | −6.79974e7 | −3.59693 | ||||||||
\(815\) | −6.73389e6 | −0.355118 | ||||||||
\(816\) | −1.80771e7 | −0.950394 | ||||||||
\(817\) | 1.14759e6 | 0.0601496 | ||||||||
\(818\) | 4.14258e7 | 2.16465 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.45278e7 | 3.35129 | ||||||||
\(821\) | −3.05738e7 | −1.58304 | −0.791519 | − | 0.611144i | \(-0.790710\pi\) | ||||
−0.791519 | + | 0.611144i | \(0.790710\pi\) | |||||||
\(822\) | −8.96481e6 | −0.462766 | ||||||||
\(823\) | 1.11281e7 | 0.572693 | 0.286346 | − | 0.958126i | \(-0.407559\pi\) | ||||
0.286346 | + | 0.958126i | \(0.407559\pi\) | |||||||
\(824\) | 7.37085e6 | 0.378181 | ||||||||
\(825\) | 1.20085e7 | 0.614264 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.78304e7 | −1.41500 | −0.707500 | − | 0.706714i | \(-0.750177\pi\) | ||||
−0.707500 | + | 0.706714i | \(0.750177\pi\) | |||||||
\(828\) | 237337. | 0.0120307 | ||||||||
\(829\) | 7.06133e6 | 0.356862 | 0.178431 | − | 0.983952i | \(-0.442898\pi\) | ||||
0.178431 | + | 0.983952i | \(0.442898\pi\) | |||||||
\(830\) | −1.21585e7 | −0.612609 | ||||||||
\(831\) | 3.08127e6 | 0.154784 | ||||||||
\(832\) | 1.58574e7 | 0.794190 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.29236e7 | 1.14122 | ||||||||
\(835\) | 3.33612e7 | 1.65587 | ||||||||
\(836\) | −9.48422e6 | −0.469338 | ||||||||
\(837\) | 859654. | 0.0424141 | ||||||||
\(838\) | 6.00385e7 | 2.95338 | ||||||||
\(839\) | −2.27299e7 | −1.11479 | −0.557395 | − | 0.830247i | \(-0.688199\pi\) | ||||
−0.557395 | + | 0.830247i | \(0.688199\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.94986e7 | 1.92571 | ||||||||
\(842\) | −1.00848e7 | −0.490217 | ||||||||
\(843\) | −8.37604e6 | −0.405947 | ||||||||
\(844\) | 5.24837e7 | 2.53611 | ||||||||
\(845\) | −3.08186e7 | −1.48481 | ||||||||
\(846\) | 2.63074e6 | 0.126372 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.70382e7 | 1.76872 | ||||||||
\(849\) | 1.48284e7 | 0.706032 | ||||||||
\(850\) | 2.54239e7 | 1.20696 | ||||||||
\(851\) | 399200. | 0.0188958 | ||||||||
\(852\) | 2.74161e7 | 1.29392 | ||||||||
\(853\) | −7.94309e6 | −0.373781 | −0.186890 | − | 0.982381i | \(-0.559841\pi\) | ||||
−0.186890 | + | 0.982381i | \(0.559841\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.08383e6 | −0.0507046 | ||||||||
\(856\) | −1.36709e6 | −0.0637693 | ||||||||
\(857\) | −9.91766e6 | −0.461272 | −0.230636 | − | 0.973040i | \(-0.574081\pi\) | ||||
−0.230636 | + | 0.973040i | \(0.574081\pi\) | |||||||
\(858\) | −5.92724e7 | −2.74874 | ||||||||
\(859\) | −61754.4 | −0.00285552 | −0.00142776 | − | 0.999999i | \(-0.500454\pi\) | ||||
−0.00142776 | + | 0.999999i | \(0.500454\pi\) | |||||||
\(860\) | −2.89399e7 | −1.33429 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.03419e6 | 0.139083 | ||||||||
\(863\) | 3.99007e7 | 1.82370 | 0.911851 | − | 0.410522i | \(-0.134653\pi\) | ||||
0.911851 | + | 0.410522i | \(0.134653\pi\) | |||||||
\(864\) | −2.07834e6 | −0.0947177 | ||||||||
\(865\) | 1.82123e7 | 0.827607 | ||||||||
\(866\) | 3.97484e7 | 1.80104 | ||||||||
\(867\) | −4.67002e6 | −0.210994 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.69120e7 | −0.759708 | ||||||||
\(870\) | −4.90920e7 | −2.19894 | ||||||||
\(871\) | 2.14256e7 | 0.956949 | ||||||||
\(872\) | 3.09125e6 | 0.137671 | ||||||||
\(873\) | 1.36606e6 | 0.0606647 | ||||||||
\(874\) | 81814.0 | 0.00362284 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.42994e7 | −1.06988 | ||||||||
\(877\) | −1.89184e7 | −0.830586 | −0.415293 | − | 0.909688i | \(-0.636321\pi\) | ||||
−0.415293 | + | 0.909688i | \(0.636321\pi\) | |||||||
\(878\) | 3.75133e7 | 1.64229 | ||||||||
\(879\) | 1.02940e7 | 0.449379 | ||||||||
\(880\) | 7.42250e7 | 3.23105 | ||||||||
\(881\) | 9.12061e6 | 0.395899 | 0.197949 | − | 0.980212i | \(-0.436572\pi\) | ||||
0.197949 | + | 0.980212i | \(0.436572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.49665e7 | −1.94083 | −0.970414 | − | 0.241449i | \(-0.922377\pi\) | ||||
−0.970414 | + | 0.241449i | \(0.922377\pi\) | |||||||
\(884\) | −8.54035e7 | −3.67574 | ||||||||
\(885\) | 1.67474e7 | 0.718769 | ||||||||
\(886\) | −1.31193e7 | −0.561472 | ||||||||
\(887\) | 2.82985e7 | 1.20769 | 0.603845 | − | 0.797102i | \(-0.293635\pi\) | ||||
0.603845 | + | 0.797102i | \(0.293635\pi\) | |||||||
\(888\) | −3.02709e7 | −1.28823 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 3.51574e7 | 1.48779 | ||||||||
\(891\) | −4.79869e6 | −0.202502 | ||||||||
\(892\) | 9.93107e7 | 4.17911 | ||||||||
\(893\) | 617181. | 0.0258990 | ||||||||
\(894\) | 3.84876e7 | 1.61056 | ||||||||
\(895\) | 3.81429e7 | 1.59168 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 347977. | 0.0144401 | ||||||||
\(898\) | 6.31873e7 | 2.61480 | ||||||||
\(899\) | 9.13496e6 | 0.376971 | ||||||||
\(900\) | 1.00745e7 | 0.414589 | ||||||||
\(901\) | 3.57507e7 | 1.46714 | ||||||||
\(902\) | 9.84850e7 | 4.03045 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.65247e7 | −1.48650 | ||||||||
\(905\) | 4.60048e7 | 1.86716 | ||||||||
\(906\) | 1.35545e7 | 0.548608 | ||||||||
\(907\) | −768537. | −0.0310204 | −0.0155102 | − | 0.999880i | \(-0.504937\pi\) | ||||
−0.0155102 | + | 0.999880i | \(0.504937\pi\) | |||||||
\(908\) | −6.47626e7 | −2.60681 | ||||||||
\(909\) | −8.54135e6 | −0.342860 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.45594e6 | 0.137965 | 0.0689827 | − | 0.997618i | \(-0.478025\pi\) | ||||
0.0689827 | + | 0.997618i | \(0.478025\pi\) | |||||||
\(912\) | −2.46930e6 | −0.0983076 | ||||||||
\(913\) | −1.26291e7 | −0.501414 | ||||||||
\(914\) | −5.83994e6 | −0.231229 | ||||||||
\(915\) | 4.07298e6 | 0.160827 | ||||||||
\(916\) | 2.12908e7 | 0.838404 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.01595e7 | −0.397894 | ||||||||
\(919\) | 5.65327e6 | 0.220806 | 0.110403 | − | 0.993887i | \(-0.464786\pi\) | ||||
0.110403 | + | 0.993887i | \(0.464786\pi\) | |||||||
\(920\) | −1.09481e6 | −0.0426450 | ||||||||
\(921\) | −2.68948e7 | −1.04477 | ||||||||
\(922\) | −2.93641e7 | −1.13760 | ||||||||
\(923\) | 4.01967e7 | 1.55305 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.69453e7 | 0.651171 | ||||||||
\(926\) | 3.77051e7 | 1.44502 | ||||||||
\(927\) | 1.64882e6 | 0.0630194 | ||||||||
\(928\) | −2.20851e7 | −0.841839 | ||||||||
\(929\) | 2.42253e7 | 0.920937 | 0.460469 | − | 0.887676i | \(-0.347681\pi\) | ||||
0.460469 | + | 0.887676i | \(0.347681\pi\) | |||||||
\(930\) | −7.47302e6 | −0.283327 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.70602e7 | 1.02045 | ||||||||
\(933\) | −2.55376e7 | −0.960451 | ||||||||
\(934\) | −2.90855e7 | −1.09096 | ||||||||
\(935\) | 7.16448e7 | 2.68013 | ||||||||
\(936\) | −2.63867e7 | −0.984455 | ||||||||
\(937\) | −3.02477e7 | −1.12549 | −0.562746 | − | 0.826630i | \(-0.690255\pi\) | ||||
−0.562746 | + | 0.826630i | \(0.690255\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.93274e7 | 0.715334 | ||||||||
\(940\) | −1.55640e7 | −0.574517 | ||||||||
\(941\) | −1.38949e7 | −0.511541 | −0.255770 | − | 0.966738i | \(-0.582329\pi\) | ||||
−0.255770 | + | 0.966738i | \(0.582329\pi\) | |||||||
\(942\) | 1.49381e7 | 0.548489 | ||||||||
\(943\) | −578187. | −0.0211733 | ||||||||
\(944\) | 3.81557e7 | 1.39357 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.41693e7 | −1.60470 | ||||||||
\(947\) | −1.78680e7 | −0.647441 | −0.323721 | − | 0.946153i | \(-0.604934\pi\) | ||||
−0.323721 | + | 0.946153i | \(0.604934\pi\) | |||||||
\(948\) | −1.41883e7 | −0.512754 | ||||||||
\(949\) | −3.56271e7 | −1.28415 | ||||||||
\(950\) | 3.47286e6 | 0.124847 | ||||||||
\(951\) | 2.37022e7 | 0.849839 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.37348e7 | 0.489880 | 0.244940 | − | 0.969538i | \(-0.421232\pi\) | ||||
0.244940 | + | 0.969538i | \(0.421232\pi\) | |||||||
\(954\) | 2.08159e7 | 0.740498 | ||||||||
\(955\) | −5.41378e7 | −1.92084 | ||||||||
\(956\) | −5.93375e6 | −0.209983 | ||||||||
\(957\) | −5.09924e7 | −1.79981 | ||||||||
\(958\) | −7.07250e7 | −2.48977 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.11603e7 | −0.390839 | ||||||||
\(961\) | −2.72386e7 | −0.951428 | ||||||||
\(962\) | −8.36394e7 | −2.91389 | ||||||||
\(963\) | −305810. | −0.0106264 | ||||||||
\(964\) | −1.07157e8 | −3.71389 | ||||||||
\(965\) | −5.72821e7 | −1.98016 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.63195e6 | −0.262464 | −0.131232 | − | 0.991352i | \(-0.541893\pi\) | ||||
−0.131232 | + | 0.991352i | \(0.541893\pi\) | |||||||
\(968\) | 1.35386e8 | 4.64391 | ||||||||
\(969\) | −2.38346e6 | −0.0815454 | ||||||||
\(970\) | −1.18753e7 | −0.405242 | ||||||||
\(971\) | 2.22480e7 | 0.757257 | 0.378629 | − | 0.925549i | \(-0.376396\pi\) | ||||
0.378629 | + | 0.925549i | \(0.376396\pi\) | |||||||
\(972\) | −4.02584e6 | −0.136675 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.73223e7 | 0.922827 | ||||||||
\(975\) | 1.47710e7 | 0.497619 | ||||||||
\(976\) | 9.27949e6 | 0.311817 | ||||||||
\(977\) | −1.82385e7 | −0.611297 | −0.305648 | − | 0.952144i | \(-0.598873\pi\) | ||||
−0.305648 | + | 0.952144i | \(0.598873\pi\) | |||||||
\(978\) | −8.62230e6 | −0.288254 | ||||||||
\(979\) | 3.65184e7 | 1.21774 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 691495. | 0.0229412 | ||||||||
\(982\) | −1.02951e8 | −3.40683 | ||||||||
\(983\) | 3.84459e7 | 1.26902 | 0.634508 | − | 0.772917i | \(-0.281203\pi\) | ||||
0.634508 | + | 0.772917i | \(0.281203\pi\) | |||||||
\(984\) | 4.38433e7 | 1.44350 | ||||||||
\(985\) | 3.12140e7 | 1.02508 | ||||||||
\(986\) | −1.07959e8 | −3.53643 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.16660e7 | −0.380214 | ||||||||
\(989\) | 259309. | 0.00843000 | ||||||||
\(990\) | 4.17153e7 | 1.35272 | ||||||||
\(991\) | −2.49658e7 | −0.807533 | −0.403767 | − | 0.914862i | \(-0.632299\pi\) | ||||
−0.403767 | + | 0.914862i | \(0.632299\pi\) | |||||||
\(992\) | −3.36189e6 | −0.108469 | ||||||||
\(993\) | −2.95590e7 | −0.951299 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.35433e7 | 1.39432 | ||||||||
\(996\) | −1.05951e7 | −0.338422 | ||||||||
\(997\) | −3.22763e7 | −1.02836 | −0.514181 | − | 0.857682i | \(-0.671904\pi\) | ||||
−0.514181 | + | 0.857682i | \(0.671904\pi\) | |||||||
\(998\) | −3.63914e7 | −1.15657 | ||||||||
\(999\) | −6.77145e6 | −0.214668 |
(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.n.1.6 | ✓ | 6 | |
3.2 | odd | 2 | 441.6.a.bb.1.1 | 6 | |||
7.2 | even | 3 | 147.6.e.q.67.1 | 12 | |||
7.3 | odd | 6 | 147.6.e.p.79.1 | 12 | |||
7.4 | even | 3 | 147.6.e.q.79.1 | 12 | |||
7.5 | odd | 6 | 147.6.e.p.67.1 | 12 | |||
7.6 | odd | 2 | 147.6.a.o.1.6 | yes | 6 | ||
21.20 | even | 2 | 441.6.a.ba.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.6.a.n.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
147.6.a.o.1.6 | yes | 6 | 7.6 | odd | 2 | ||
147.6.e.p.67.1 | 12 | 7.5 | odd | 6 | |||
147.6.e.p.79.1 | 12 | 7.3 | odd | 6 | |||
147.6.e.q.67.1 | 12 | 7.2 | even | 3 | |||
147.6.e.q.79.1 | 12 | 7.4 | even | 3 | |||
441.6.a.ba.1.1 | 6 | 21.20 | even | 2 | |||
441.6.a.bb.1.1 | 6 | 3.2 | odd | 2 |