Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [867,6,Mod(1,867)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(867, 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("867.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 867 = 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 867.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: | \(139.052771778\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 51) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 867.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.85553 | −0.858345 | −0.429172 | − | 0.903223i | \(-0.641195\pi\) | ||||
−0.429172 | + | 0.903223i | \(0.641195\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | −8.42383 | −0.263245 | ||||||||
\(5\) | 82.3928 | 1.47389 | 0.736943 | − | 0.675955i | \(-0.236268\pi\) | ||||
0.736943 | + | 0.675955i | \(0.236268\pi\) | |||||||
\(6\) | −43.6998 | −0.495565 | ||||||||
\(7\) | 35.3683 | 0.272816 | 0.136408 | − | 0.990653i | \(-0.456444\pi\) | ||||
0.136408 | + | 0.990653i | \(0.456444\pi\) | |||||||
\(8\) | 196.279 | 1.08430 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −400.061 | −1.26510 | ||||||||
\(11\) | −88.9161 | −0.221564 | −0.110782 | − | 0.993845i | \(-0.535336\pi\) | ||||
−0.110782 | + | 0.993845i | \(0.535336\pi\) | |||||||
\(12\) | −75.8144 | −0.151984 | ||||||||
\(13\) | −607.679 | −0.997276 | −0.498638 | − | 0.866810i | \(-0.666166\pi\) | ||||
−0.498638 | + | 0.866810i | \(0.666166\pi\) | |||||||
\(14\) | −171.732 | −0.234170 | ||||||||
\(15\) | 741.535 | 0.850949 | ||||||||
\(16\) | −683.477 | −0.667458 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −393.298 | −0.286115 | ||||||||
\(19\) | 728.381 | 0.462887 | 0.231443 | − | 0.972848i | \(-0.425655\pi\) | ||||
0.231443 | + | 0.972848i | \(0.425655\pi\) | |||||||
\(20\) | −694.062 | −0.387993 | ||||||||
\(21\) | 318.315 | 0.157510 | ||||||||
\(22\) | 431.735 | 0.190178 | ||||||||
\(23\) | 842.921 | 0.332252 | 0.166126 | − | 0.986105i | \(-0.446874\pi\) | ||||
0.166126 | + | 0.986105i | \(0.446874\pi\) | |||||||
\(24\) | 1766.51 | 0.626020 | ||||||||
\(25\) | 3663.57 | 1.17234 | ||||||||
\(26\) | 2950.60 | 0.856007 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | −297.937 | −0.0718173 | ||||||||
\(29\) | −521.365 | −0.115119 | −0.0575595 | − | 0.998342i | \(-0.518332\pi\) | ||||
−0.0575595 | + | 0.998342i | \(0.518332\pi\) | |||||||
\(30\) | −3600.55 | −0.730407 | ||||||||
\(31\) | −1459.76 | −0.272822 | −0.136411 | − | 0.990652i | \(-0.543557\pi\) | ||||
−0.136411 | + | 0.990652i | \(0.543557\pi\) | |||||||
\(32\) | −2962.29 | −0.511390 | ||||||||
\(33\) | −800.245 | −0.127920 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2914.10 | 0.402100 | ||||||||
\(36\) | −682.330 | −0.0877482 | ||||||||
\(37\) | −11600.8 | −1.39310 | −0.696552 | − | 0.717506i | \(-0.745283\pi\) | ||||
−0.696552 | + | 0.717506i | \(0.745283\pi\) | |||||||
\(38\) | −3536.68 | −0.397316 | ||||||||
\(39\) | −5469.11 | −0.575778 | ||||||||
\(40\) | 16172.0 | 1.59813 | ||||||||
\(41\) | −14400.6 | −1.33789 | −0.668944 | − | 0.743313i | \(-0.733253\pi\) | ||||
−0.668944 | + | 0.743313i | \(0.733253\pi\) | |||||||
\(42\) | −1545.59 | −0.135198 | ||||||||
\(43\) | 2446.99 | 0.201818 | 0.100909 | − | 0.994896i | \(-0.467825\pi\) | ||||
0.100909 | + | 0.994896i | \(0.467825\pi\) | |||||||
\(44\) | 749.014 | 0.0583255 | ||||||||
\(45\) | 6673.81 | 0.491296 | ||||||||
\(46\) | −4092.83 | −0.285186 | ||||||||
\(47\) | −25631.6 | −1.69251 | −0.846255 | − | 0.532778i | \(-0.821148\pi\) | ||||
−0.846255 | + | 0.532778i | \(0.821148\pi\) | |||||||
\(48\) | −6151.29 | −0.385357 | ||||||||
\(49\) | −15556.1 | −0.925572 | ||||||||
\(50\) | −17788.6 | −1.00627 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5118.98 | 0.262528 | ||||||||
\(53\) | −2320.07 | −0.113452 | −0.0567260 | − | 0.998390i | \(-0.518066\pi\) | ||||
−0.0567260 | + | 0.998390i | \(0.518066\pi\) | |||||||
\(54\) | −3539.68 | −0.165188 | ||||||||
\(55\) | −7326.05 | −0.326560 | ||||||||
\(56\) | 6942.07 | 0.295814 | ||||||||
\(57\) | 6555.43 | 0.267248 | ||||||||
\(58\) | 2531.50 | 0.0988117 | ||||||||
\(59\) | −37043.5 | −1.38542 | −0.692711 | − | 0.721215i | \(-0.743584\pi\) | ||||
−0.692711 | + | 0.721215i | \(0.743584\pi\) | |||||||
\(60\) | −6246.56 | −0.224008 | ||||||||
\(61\) | 11489.3 | 0.395338 | 0.197669 | − | 0.980269i | \(-0.436663\pi\) | ||||
0.197669 | + | 0.980269i | \(0.436663\pi\) | |||||||
\(62\) | 7087.93 | 0.234175 | ||||||||
\(63\) | 2864.84 | 0.0909386 | ||||||||
\(64\) | 36254.7 | 1.10641 | ||||||||
\(65\) | −50068.3 | −1.46987 | ||||||||
\(66\) | 3885.62 | 0.109799 | ||||||||
\(67\) | −57126.2 | −1.55471 | −0.777353 | − | 0.629065i | \(-0.783438\pi\) | ||||
−0.777353 | + | 0.629065i | \(0.783438\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7586.29 | 0.191826 | ||||||||
\(70\) | −14149.5 | −0.345140 | ||||||||
\(71\) | 62663.3 | 1.47526 | 0.737628 | − | 0.675208i | \(-0.235946\pi\) | ||||
0.737628 | + | 0.675208i | \(0.235946\pi\) | |||||||
\(72\) | 15898.6 | 0.361433 | ||||||||
\(73\) | 31928.3 | 0.701243 | 0.350621 | − | 0.936517i | \(-0.385970\pi\) | ||||
0.350621 | + | 0.936517i | \(0.385970\pi\) | |||||||
\(74\) | 56328.0 | 1.19576 | ||||||||
\(75\) | 32972.1 | 0.676852 | ||||||||
\(76\) | −6135.76 | −0.121852 | ||||||||
\(77\) | −3144.82 | −0.0604461 | ||||||||
\(78\) | 26555.4 | 0.494216 | ||||||||
\(79\) | 51843.7 | 0.934606 | 0.467303 | − | 0.884097i | \(-0.345226\pi\) | ||||
0.467303 | + | 0.884097i | \(0.345226\pi\) | |||||||
\(80\) | −56313.5 | −0.983757 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 69922.4 | 1.14837 | ||||||||
\(83\) | −68331.8 | −1.08875 | −0.544374 | − | 0.838843i | \(-0.683233\pi\) | ||||
−0.544374 | + | 0.838843i | \(0.683233\pi\) | |||||||
\(84\) | −2681.43 | −0.0414637 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −11881.4 | −0.173230 | ||||||||
\(87\) | −4692.29 | −0.0664640 | ||||||||
\(88\) | −17452.4 | −0.240241 | ||||||||
\(89\) | −130403. | −1.74506 | −0.872531 | − | 0.488558i | \(-0.837523\pi\) | ||||
−0.872531 | + | 0.488558i | \(0.837523\pi\) | |||||||
\(90\) | −32404.9 | −0.421701 | ||||||||
\(91\) | −21492.6 | −0.272073 | ||||||||
\(92\) | −7100.62 | −0.0874635 | ||||||||
\(93\) | −13137.9 | −0.157514 | ||||||||
\(94\) | 124455. | 1.45276 | ||||||||
\(95\) | 60013.4 | 0.682243 | ||||||||
\(96\) | −26660.6 | −0.295251 | ||||||||
\(97\) | 53915.3 | 0.581812 | 0.290906 | − | 0.956752i | \(-0.406043\pi\) | ||||
0.290906 | + | 0.956752i | \(0.406043\pi\) | |||||||
\(98\) | 75533.0 | 0.794459 | ||||||||
\(99\) | −7202.21 | −0.0738546 | ||||||||
\(100\) | −30861.3 | −0.308613 | ||||||||
\(101\) | 178516. | 1.74130 | 0.870651 | − | 0.491901i | \(-0.163698\pi\) | ||||
0.870651 | + | 0.491901i | \(0.163698\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 25684.7 | 0.238551 | 0.119275 | − | 0.992861i | \(-0.461943\pi\) | ||||
0.119275 | + | 0.992861i | \(0.461943\pi\) | |||||||
\(104\) | −119275. | −1.08135 | ||||||||
\(105\) | 26226.9 | 0.232152 | ||||||||
\(106\) | 11265.2 | 0.0973808 | ||||||||
\(107\) | −146355. | −1.23580 | −0.617902 | − | 0.786255i | \(-0.712017\pi\) | ||||
−0.617902 | + | 0.786255i | \(0.712017\pi\) | |||||||
\(108\) | −6140.97 | −0.0506614 | ||||||||
\(109\) | 135166. | 1.08968 | 0.544842 | − | 0.838539i | \(-0.316590\pi\) | ||||
0.544842 | + | 0.838539i | \(0.316590\pi\) | |||||||
\(110\) | 35571.8 | 0.280301 | ||||||||
\(111\) | −104407. | −0.804309 | ||||||||
\(112\) | −24173.4 | −0.182093 | ||||||||
\(113\) | −116529. | −0.858495 | −0.429247 | − | 0.903187i | \(-0.641221\pi\) | ||||
−0.429247 | + | 0.903187i | \(0.641221\pi\) | |||||||
\(114\) | −31830.1 | −0.229391 | ||||||||
\(115\) | 69450.6 | 0.489701 | ||||||||
\(116\) | 4391.89 | 0.0303044 | ||||||||
\(117\) | −49222.0 | −0.332425 | ||||||||
\(118\) | 179866. | 1.18917 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 145548. | 0.922683 | ||||||||
\(121\) | −153145. | −0.950909 | ||||||||
\(122\) | −55786.6 | −0.339336 | ||||||||
\(123\) | −129605. | −0.772430 | ||||||||
\(124\) | 12296.8 | 0.0718188 | ||||||||
\(125\) | 44374.2 | 0.254013 | ||||||||
\(126\) | −13910.3 | −0.0780567 | ||||||||
\(127\) | 234366. | 1.28939 | 0.644695 | − | 0.764440i | \(-0.276984\pi\) | ||||
0.644695 | + | 0.764440i | \(0.276984\pi\) | |||||||
\(128\) | −81242.7 | −0.438288 | ||||||||
\(129\) | 22022.9 | 0.116520 | ||||||||
\(130\) | 243108. | 1.26166 | ||||||||
\(131\) | −35395.7 | −0.180207 | −0.0901037 | − | 0.995932i | \(-0.528720\pi\) | ||||
−0.0901037 | + | 0.995932i | \(0.528720\pi\) | |||||||
\(132\) | 6741.13 | 0.0336742 | ||||||||
\(133\) | 25761.6 | 0.126283 | ||||||||
\(134\) | 277378. | 1.33447 | ||||||||
\(135\) | 60064.3 | 0.283650 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 292411. | 1.33104 | 0.665522 | − | 0.746378i | \(-0.268209\pi\) | ||||
0.665522 | + | 0.746378i | \(0.268209\pi\) | |||||||
\(138\) | −36835.5 | −0.164652 | ||||||||
\(139\) | 281862. | 1.23737 | 0.618685 | − | 0.785639i | \(-0.287666\pi\) | ||||
0.618685 | + | 0.785639i | \(0.287666\pi\) | |||||||
\(140\) | −24547.8 | −0.105851 | ||||||||
\(141\) | −230685. | −0.977171 | ||||||||
\(142\) | −304263. | −1.26628 | ||||||||
\(143\) | 54032.4 | 0.220960 | ||||||||
\(144\) | −55361.6 | −0.222486 | ||||||||
\(145\) | −42956.7 | −0.169672 | ||||||||
\(146\) | −155029. | −0.601908 | ||||||||
\(147\) | −140005. | −0.534379 | ||||||||
\(148\) | 97723.1 | 0.366727 | ||||||||
\(149\) | 124400. | 0.459046 | 0.229523 | − | 0.973303i | \(-0.426283\pi\) | ||||
0.229523 | + | 0.973303i | \(0.426283\pi\) | |||||||
\(150\) | −160097. | −0.580972 | ||||||||
\(151\) | −497288. | −1.77487 | −0.887433 | − | 0.460936i | \(-0.847514\pi\) | ||||
−0.887433 | + | 0.460936i | \(0.847514\pi\) | |||||||
\(152\) | 142966. | 0.501908 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15269.7 | 0.0518836 | ||||||||
\(155\) | −120274. | −0.402108 | ||||||||
\(156\) | 46070.8 | 0.151570 | ||||||||
\(157\) | −471249. | −1.52581 | −0.762906 | − | 0.646510i | \(-0.776228\pi\) | ||||
−0.762906 | + | 0.646510i | \(0.776228\pi\) | |||||||
\(158\) | −251729. | −0.802214 | ||||||||
\(159\) | −20880.7 | −0.0655015 | ||||||||
\(160\) | −244071. | −0.753732 | ||||||||
\(161\) | 29812.7 | 0.0906435 | ||||||||
\(162\) | −31857.1 | −0.0953716 | ||||||||
\(163\) | −429530. | −1.26626 | −0.633132 | − | 0.774044i | \(-0.718231\pi\) | ||||
−0.633132 | + | 0.774044i | \(0.718231\pi\) | |||||||
\(164\) | 121308. | 0.352192 | ||||||||
\(165\) | −65934.4 | −0.188540 | ||||||||
\(166\) | 331787. | 0.934521 | ||||||||
\(167\) | −251418. | −0.697599 | −0.348799 | − | 0.937197i | \(-0.613411\pi\) | ||||
−0.348799 | + | 0.937197i | \(0.613411\pi\) | |||||||
\(168\) | 62478.6 | 0.170788 | ||||||||
\(169\) | −2019.82 | −0.00543997 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 58998.9 | 0.154296 | ||||||||
\(172\) | −20613.0 | −0.0531276 | ||||||||
\(173\) | 364784. | 0.926659 | 0.463330 | − | 0.886186i | \(-0.346655\pi\) | ||||
0.463330 | + | 0.886186i | \(0.346655\pi\) | |||||||
\(174\) | 22783.5 | 0.0570490 | ||||||||
\(175\) | 129574. | 0.319833 | ||||||||
\(176\) | 60772.1 | 0.147884 | ||||||||
\(177\) | −333392. | −0.799874 | ||||||||
\(178\) | 633174. | 1.49787 | ||||||||
\(179\) | −512444. | −1.19540 | −0.597701 | − | 0.801719i | \(-0.703919\pi\) | ||||
−0.597701 | + | 0.801719i | \(0.703919\pi\) | |||||||
\(180\) | −56219.1 | −0.129331 | ||||||||
\(181\) | 593596. | 1.34677 | 0.673387 | − | 0.739290i | \(-0.264839\pi\) | ||||
0.673387 | + | 0.739290i | \(0.264839\pi\) | |||||||
\(182\) | 104358. | 0.233532 | ||||||||
\(183\) | 103404. | 0.228248 | ||||||||
\(184\) | 165448. | 0.360260 | ||||||||
\(185\) | −955822. | −2.05328 | ||||||||
\(186\) | 63791.4 | 0.135201 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 215916. | 0.445544 | ||||||||
\(189\) | 25783.5 | 0.0525034 | ||||||||
\(190\) | −291397. | −0.585599 | ||||||||
\(191\) | 853915. | 1.69368 | 0.846840 | − | 0.531848i | \(-0.178502\pi\) | ||||
0.846840 | + | 0.531848i | \(0.178502\pi\) | |||||||
\(192\) | 326293. | 0.638784 | ||||||||
\(193\) | 619608. | 1.19736 | 0.598679 | − | 0.800989i | \(-0.295692\pi\) | ||||
0.598679 | + | 0.800989i | \(0.295692\pi\) | |||||||
\(194\) | −261787. | −0.499395 | ||||||||
\(195\) | −450615. | −0.848631 | ||||||||
\(196\) | 131042. | 0.243652 | ||||||||
\(197\) | 483204. | 0.887085 | 0.443542 | − | 0.896253i | \(-0.353722\pi\) | ||||
0.443542 | + | 0.896253i | \(0.353722\pi\) | |||||||
\(198\) | 34970.5 | 0.0633927 | ||||||||
\(199\) | −987693. | −1.76803 | −0.884015 | − | 0.467459i | \(-0.845169\pi\) | ||||
−0.884015 | + | 0.467459i | \(0.845169\pi\) | |||||||
\(200\) | 719082. | 1.27117 | ||||||||
\(201\) | −514136. | −0.897610 | ||||||||
\(202\) | −866791. | −1.49464 | ||||||||
\(203\) | −18439.8 | −0.0314063 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.18650e6 | −1.97190 | ||||||||
\(206\) | −124713. | −0.204759 | ||||||||
\(207\) | 68276.6 | 0.110751 | ||||||||
\(208\) | 415334. | 0.665640 | ||||||||
\(209\) | −64764.9 | −0.102559 | ||||||||
\(210\) | −127345. | −0.199267 | ||||||||
\(211\) | 350297. | 0.541665 | 0.270833 | − | 0.962626i | \(-0.412701\pi\) | ||||
0.270833 | + | 0.962626i | \(0.412701\pi\) | |||||||
\(212\) | 19543.9 | 0.0298656 | ||||||||
\(213\) | 563969. | 0.851739 | ||||||||
\(214\) | 710633. | 1.06074 | ||||||||
\(215\) | 201614. | 0.297458 | ||||||||
\(216\) | 143087. | 0.208673 | ||||||||
\(217\) | −51629.5 | −0.0744300 | ||||||||
\(218\) | −656302. | −0.935324 | ||||||||
\(219\) | 287355. | 0.404863 | ||||||||
\(220\) | 61713.4 | 0.0859652 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 506952. | 0.690374 | ||||||||
\(223\) | −460117. | −0.619592 | −0.309796 | − | 0.950803i | \(-0.600261\pi\) | ||||
−0.309796 | + | 0.950803i | \(0.600261\pi\) | |||||||
\(224\) | −104771. | −0.139515 | ||||||||
\(225\) | 296749. | 0.390781 | ||||||||
\(226\) | 565810. | 0.736884 | ||||||||
\(227\) | 180122. | 0.232008 | 0.116004 | − | 0.993249i | \(-0.462991\pi\) | ||||
0.116004 | + | 0.993249i | \(0.462991\pi\) | |||||||
\(228\) | −55221.8 | −0.0703516 | ||||||||
\(229\) | 854469. | 1.07673 | 0.538366 | − | 0.842711i | \(-0.319042\pi\) | ||||
0.538366 | + | 0.842711i | \(0.319042\pi\) | |||||||
\(230\) | −337219. | −0.420333 | ||||||||
\(231\) | −28303.3 | −0.0348986 | ||||||||
\(232\) | −102333. | −0.124823 | ||||||||
\(233\) | −851701. | −1.02777 | −0.513887 | − | 0.857858i | \(-0.671795\pi\) | ||||
−0.513887 | + | 0.857858i | \(0.671795\pi\) | |||||||
\(234\) | 238999. | 0.285336 | ||||||||
\(235\) | −2.11186e6 | −2.49457 | ||||||||
\(236\) | 312048. | 0.364705 | ||||||||
\(237\) | 466593. | 0.539595 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 53163.9 | 0.0602036 | 0.0301018 | − | 0.999547i | \(-0.490417\pi\) | ||||
0.0301018 | + | 0.999547i | \(0.490417\pi\) | |||||||
\(240\) | −506822. | −0.567972 | ||||||||
\(241\) | 1839.35 | 0.00203996 | 0.00101998 | − | 0.999999i | \(-0.499675\pi\) | ||||
0.00101998 | + | 0.999999i | \(0.499675\pi\) | |||||||
\(242\) | 743600. | 0.816208 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −96783.8 | −0.104071 | ||||||||
\(245\) | −1.28171e6 | −1.36419 | ||||||||
\(246\) | 629301. | 0.663011 | ||||||||
\(247\) | −442622. | −0.461626 | ||||||||
\(248\) | −286521. | −0.295820 | ||||||||
\(249\) | −614986. | −0.628589 | ||||||||
\(250\) | −215460. | −0.218030 | ||||||||
\(251\) | −510288. | −0.511247 | −0.255624 | − | 0.966776i | \(-0.582281\pi\) | ||||
−0.255624 | + | 0.966776i | \(0.582281\pi\) | |||||||
\(252\) | −24132.9 | −0.0239391 | ||||||||
\(253\) | −74949.3 | −0.0736150 | ||||||||
\(254\) | −1.13797e6 | −1.10674 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −765675. | −0.730205 | ||||||||
\(257\) | −635023. | −0.599731 | −0.299866 | − | 0.953981i | \(-0.596942\pi\) | ||||
−0.299866 | + | 0.953981i | \(0.596942\pi\) | |||||||
\(258\) | −106933. | −0.100014 | ||||||||
\(259\) | −410301. | −0.380061 | ||||||||
\(260\) | 421767. | 0.386936 | ||||||||
\(261\) | −42230.6 | −0.0383730 | ||||||||
\(262\) | 171865. | 0.154680 | ||||||||
\(263\) | 658997. | 0.587481 | 0.293741 | − | 0.955885i | \(-0.405100\pi\) | ||||
0.293741 | + | 0.955885i | \(0.405100\pi\) | |||||||
\(264\) | −157071. | −0.138703 | ||||||||
\(265\) | −191157. | −0.167215 | ||||||||
\(266\) | −125086. | −0.108394 | ||||||||
\(267\) | −1.17362e6 | −1.00751 | ||||||||
\(268\) | 481221. | 0.409268 | ||||||||
\(269\) | −755566. | −0.636637 | −0.318318 | − | 0.947984i | \(-0.603118\pi\) | ||||
−0.318318 | + | 0.947984i | \(0.603118\pi\) | |||||||
\(270\) | −291644. | −0.243469 | ||||||||
\(271\) | −171275. | −0.141668 | −0.0708340 | − | 0.997488i | \(-0.522566\pi\) | ||||
−0.0708340 | + | 0.997488i | \(0.522566\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −193433. | −0.157081 | ||||||||
\(274\) | −1.41981e6 | −1.14249 | ||||||||
\(275\) | −325750. | −0.259749 | ||||||||
\(276\) | −63905.6 | −0.0504971 | ||||||||
\(277\) | −1.49471e6 | −1.17046 | −0.585230 | − | 0.810867i | \(-0.698996\pi\) | ||||
−0.585230 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(278\) | −1.36859e6 | −1.06209 | ||||||||
\(279\) | −118241. | −0.0909405 | ||||||||
\(280\) | 571976. | 0.435996 | ||||||||
\(281\) | 690053. | 0.521335 | 0.260667 | − | 0.965429i | \(-0.416057\pi\) | ||||
0.260667 | + | 0.965429i | \(0.416057\pi\) | |||||||
\(282\) | 1.12010e6 | 0.838750 | ||||||||
\(283\) | 361859. | 0.268580 | 0.134290 | − | 0.990942i | \(-0.457125\pi\) | ||||
0.134290 | + | 0.990942i | \(0.457125\pi\) | |||||||
\(284\) | −527864. | −0.388353 | ||||||||
\(285\) | 540120. | 0.393893 | ||||||||
\(286\) | −262356. | −0.189660 | ||||||||
\(287\) | −509324. | −0.364997 | ||||||||
\(288\) | −239945. | −0.170463 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 208578. | 0.145637 | ||||||||
\(291\) | 485238. | 0.335909 | ||||||||
\(292\) | −268958. | −0.184598 | ||||||||
\(293\) | −817433. | −0.556267 | −0.278133 | − | 0.960542i | \(-0.589716\pi\) | ||||
−0.278133 | + | 0.960542i | \(0.589716\pi\) | |||||||
\(294\) | 679797. | 0.458681 | ||||||||
\(295\) | −3.05212e6 | −2.04196 | ||||||||
\(296\) | −2.27699e6 | −1.51054 | ||||||||
\(297\) | −64819.9 | −0.0426400 | ||||||||
\(298\) | −604030. | −0.394020 | ||||||||
\(299\) | −512225. | −0.331347 | ||||||||
\(300\) | −277751. | −0.178178 | ||||||||
\(301\) | 86545.9 | 0.0550593 | ||||||||
\(302\) | 2.41460e6 | 1.52345 | ||||||||
\(303\) | 1.60665e6 | 1.00534 | ||||||||
\(304\) | −497832. | −0.308957 | ||||||||
\(305\) | 946634. | 0.582683 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.22091e6 | −1.34488 | −0.672442 | − | 0.740149i | \(-0.734755\pi\) | ||||
−0.672442 | + | 0.740149i | \(0.734755\pi\) | |||||||
\(308\) | 26491.4 | 0.0159121 | ||||||||
\(309\) | 231162. | 0.137727 | ||||||||
\(310\) | 583994. | 0.345147 | ||||||||
\(311\) | 22862.3 | 0.0134035 | 0.00670177 | − | 0.999978i | \(-0.497867\pi\) | ||||
0.00670177 | + | 0.999978i | \(0.497867\pi\) | |||||||
\(312\) | −1.07347e6 | −0.624315 | ||||||||
\(313\) | −1.65461e6 | −0.954632 | −0.477316 | − | 0.878732i | \(-0.658390\pi\) | ||||
−0.477316 | + | 0.878732i | \(0.658390\pi\) | |||||||
\(314\) | 2.28816e6 | 1.30967 | ||||||||
\(315\) | 236042. | 0.134033 | ||||||||
\(316\) | −436722. | −0.246030 | ||||||||
\(317\) | 1.06021e6 | 0.592574 | 0.296287 | − | 0.955099i | \(-0.404252\pi\) | ||||
0.296287 | + | 0.955099i | \(0.404252\pi\) | |||||||
\(318\) | 101387. | 0.0562229 | ||||||||
\(319\) | 46357.8 | 0.0255062 | ||||||||
\(320\) | 2.98713e6 | 1.63072 | ||||||||
\(321\) | −1.31720e6 | −0.713491 | ||||||||
\(322\) | −144757. | −0.0778034 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −55268.7 | −0.0292494 | ||||||||
\(325\) | −2.22627e6 | −1.16915 | ||||||||
\(326\) | 2.08559e6 | 1.08689 | ||||||||
\(327\) | 1.21649e6 | 0.629129 | ||||||||
\(328\) | −2.82653e6 | −1.45067 | ||||||||
\(329\) | −906548. | −0.461744 | ||||||||
\(330\) | 320147. | 0.161832 | ||||||||
\(331\) | 532449. | 0.267121 | 0.133561 | − | 0.991041i | \(-0.457359\pi\) | ||||
0.133561 | + | 0.991041i | \(0.457359\pi\) | |||||||
\(332\) | 575615. | 0.286607 | ||||||||
\(333\) | −939665. | −0.464368 | ||||||||
\(334\) | 1.22077e6 | 0.598780 | ||||||||
\(335\) | −4.70678e6 | −2.29146 | ||||||||
\(336\) | −217561. | −0.105131 | ||||||||
\(337\) | −1.17270e6 | −0.562489 | −0.281244 | − | 0.959636i | \(-0.590747\pi\) | ||||
−0.281244 | + | 0.959636i | \(0.590747\pi\) | |||||||
\(338\) | 9807.31 | 0.00466937 | ||||||||
\(339\) | −1.04876e6 | −0.495652 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 129797. | 0.0604474 | ||||||||
\(342\) | −286471. | −0.132439 | ||||||||
\(343\) | −1.14463e6 | −0.525326 | ||||||||
\(344\) | 480293. | 0.218832 | ||||||||
\(345\) | 625055. | 0.282729 | ||||||||
\(346\) | −1.77122e6 | −0.795393 | ||||||||
\(347\) | −3.27941e6 | −1.46208 | −0.731042 | − | 0.682332i | \(-0.760966\pi\) | ||||
−0.731042 | + | 0.682332i | \(0.760966\pi\) | |||||||
\(348\) | 39527.0 | 0.0174963 | ||||||||
\(349\) | −3.56553e6 | −1.56697 | −0.783485 | − | 0.621411i | \(-0.786560\pi\) | ||||
−0.783485 | + | 0.621411i | \(0.786560\pi\) | |||||||
\(350\) | −629152. | −0.274527 | ||||||||
\(351\) | −442998. | −0.191926 | ||||||||
\(352\) | 263395. | 0.113306 | ||||||||
\(353\) | −2.40109e6 | −1.02559 | −0.512793 | − | 0.858512i | \(-0.671389\pi\) | ||||
−0.512793 | + | 0.858512i | \(0.671389\pi\) | |||||||
\(354\) | 1.61879e6 | 0.686568 | ||||||||
\(355\) | 5.16300e6 | 2.17436 | ||||||||
\(356\) | 1.09849e6 | 0.459378 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.48819e6 | 1.02607 | ||||||||
\(359\) | 18532.7 | 0.00758930 | 0.00379465 | − | 0.999993i | \(-0.498792\pi\) | ||||
0.00379465 | + | 0.999993i | \(0.498792\pi\) | |||||||
\(360\) | 1.30993e6 | 0.532711 | ||||||||
\(361\) | −1.94556e6 | −0.785736 | ||||||||
\(362\) | −2.88223e6 | −1.15600 | ||||||||
\(363\) | −1.37830e6 | −0.549008 | ||||||||
\(364\) | 181050. | 0.0716217 | ||||||||
\(365\) | 2.63066e6 | 1.03355 | ||||||||
\(366\) | −502079. | −0.195916 | ||||||||
\(367\) | 3.01002e6 | 1.16655 | 0.583275 | − | 0.812275i | \(-0.301771\pi\) | ||||
0.583275 | + | 0.812275i | \(0.301771\pi\) | |||||||
\(368\) | −576117. | −0.221764 | ||||||||
\(369\) | −1.16645e6 | −0.445963 | ||||||||
\(370\) | 4.64102e6 | 1.76242 | ||||||||
\(371\) | −82057.1 | −0.0309515 | ||||||||
\(372\) | 110671. | 0.0414646 | ||||||||
\(373\) | −1.79099e6 | −0.666534 | −0.333267 | − | 0.942833i | \(-0.608151\pi\) | ||||
−0.333267 | + | 0.942833i | \(0.608151\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 399367. | 0.146654 | ||||||||
\(376\) | −5.03095e6 | −1.83519 | ||||||||
\(377\) | 316822. | 0.114805 | ||||||||
\(378\) | −125193. | −0.0450660 | ||||||||
\(379\) | 1.04095e6 | 0.372248 | 0.186124 | − | 0.982526i | \(-0.440407\pi\) | ||||
0.186124 | + | 0.982526i | \(0.440407\pi\) | |||||||
\(380\) | −505542. | −0.179597 | ||||||||
\(381\) | 2.10929e6 | 0.744430 | ||||||||
\(382\) | −4.14621e6 | −1.45376 | ||||||||
\(383\) | 315801. | 0.110006 | 0.0550030 | − | 0.998486i | \(-0.482483\pi\) | ||||
0.0550030 | + | 0.998486i | \(0.482483\pi\) | |||||||
\(384\) | −731184. | −0.253046 | ||||||||
\(385\) | −259110. | −0.0890907 | ||||||||
\(386\) | −3.00853e6 | −1.02775 | ||||||||
\(387\) | 198206. | 0.0672728 | ||||||||
\(388\) | −454173. | −0.153159 | ||||||||
\(389\) | 2.24538e6 | 0.752343 | 0.376172 | − | 0.926550i | \(-0.377240\pi\) | ||||
0.376172 | + | 0.926550i | \(0.377240\pi\) | |||||||
\(390\) | 2.18797e6 | 0.728418 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.05333e6 | −1.00360 | ||||||||
\(393\) | −318562. | −0.104043 | ||||||||
\(394\) | −2.34621e6 | −0.761425 | ||||||||
\(395\) | 4.27155e6 | 1.37750 | ||||||||
\(396\) | 60670.1 | 0.0194418 | ||||||||
\(397\) | 1.40448e6 | 0.447239 | 0.223619 | − | 0.974677i | \(-0.428213\pi\) | ||||
0.223619 | + | 0.974677i | \(0.428213\pi\) | |||||||
\(398\) | 4.79577e6 | 1.51758 | ||||||||
\(399\) | 231855. | 0.0729094 | ||||||||
\(400\) | −2.50396e6 | −0.782489 | ||||||||
\(401\) | 6.09175e6 | 1.89182 | 0.945912 | − | 0.324423i | \(-0.105170\pi\) | ||||
0.945912 | + | 0.324423i | \(0.105170\pi\) | |||||||
\(402\) | 2.49640e6 | 0.770459 | ||||||||
\(403\) | 887068. | 0.272078 | ||||||||
\(404\) | −1.50379e6 | −0.458388 | ||||||||
\(405\) | 540579. | 0.163765 | ||||||||
\(406\) | 89535.1 | 0.0269574 | ||||||||
\(407\) | 1.03150e6 | 0.308661 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.15158e6 | −0.635989 | −0.317995 | − | 0.948093i | \(-0.603009\pi\) | ||||
−0.317995 | + | 0.948093i | \(0.603009\pi\) | |||||||
\(410\) | 5.76110e6 | 1.69257 | ||||||||
\(411\) | 2.63170e6 | 0.768479 | ||||||||
\(412\) | −216363. | −0.0627973 | ||||||||
\(413\) | −1.31017e6 | −0.377965 | ||||||||
\(414\) | −331519. | −0.0950622 | ||||||||
\(415\) | −5.63004e6 | −1.60469 | ||||||||
\(416\) | 1.80012e6 | 0.509998 | ||||||||
\(417\) | 2.53676e6 | 0.714396 | ||||||||
\(418\) | 314468. | 0.0880310 | ||||||||
\(419\) | −3.76613e6 | −1.04800 | −0.523999 | − | 0.851719i | \(-0.675561\pi\) | ||||
−0.523999 | + | 0.851719i | \(0.675561\pi\) | |||||||
\(420\) | −220931. | −0.0611128 | ||||||||
\(421\) | 5.15676e6 | 1.41798 | 0.708992 | − | 0.705217i | \(-0.249150\pi\) | ||||
0.708992 | + | 0.705217i | \(0.249150\pi\) | |||||||
\(422\) | −1.70088e6 | −0.464935 | ||||||||
\(423\) | −2.07616e6 | −0.564170 | ||||||||
\(424\) | −455382. | −0.123016 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.73837e6 | −0.731086 | ||||||||
\(427\) | 406357. | 0.107854 | ||||||||
\(428\) | 1.23287e6 | 0.325318 | ||||||||
\(429\) | 486292. | 0.127572 | ||||||||
\(430\) | −978944. | −0.255321 | ||||||||
\(431\) | 4.63311e6 | 1.20138 | 0.600689 | − | 0.799483i | \(-0.294893\pi\) | ||||
0.600689 | + | 0.799483i | \(0.294893\pi\) | |||||||
\(432\) | −498255. | −0.128452 | ||||||||
\(433\) | 1485.21 | 0.000380686 0 | 0.000190343 | − | 1.00000i | \(-0.499939\pi\) | ||||
0.000190343 | 1.00000i | \(0.499939\pi\) | ||||||||
\(434\) | 250688. | 0.0638866 | ||||||||
\(435\) | −386610. | −0.0979604 | ||||||||
\(436\) | −1.13861e6 | −0.286853 | ||||||||
\(437\) | 613968. | 0.153795 | ||||||||
\(438\) | −1.39526e6 | −0.347512 | ||||||||
\(439\) | −7.02203e6 | −1.73901 | −0.869504 | − | 0.493926i | \(-0.835561\pi\) | ||||
−0.869504 | + | 0.493926i | \(0.835561\pi\) | |||||||
\(440\) | −1.43795e6 | −0.354089 | ||||||||
\(441\) | −1.26004e6 | −0.308524 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.06390e6 | 1.22596 | 0.612979 | − | 0.790099i | \(-0.289971\pi\) | ||||
0.612979 | + | 0.790099i | \(0.289971\pi\) | |||||||
\(444\) | 879508. | 0.211730 | ||||||||
\(445\) | −1.07442e7 | −2.57203 | ||||||||
\(446\) | 2.23411e6 | 0.531824 | ||||||||
\(447\) | 1.11960e6 | 0.265030 | ||||||||
\(448\) | 1.28227e6 | 0.301845 | ||||||||
\(449\) | −1.36157e6 | −0.318731 | −0.159366 | − | 0.987220i | \(-0.550945\pi\) | ||||
−0.159366 | + | 0.987220i | \(0.550945\pi\) | |||||||
\(450\) | −1.44087e6 | −0.335424 | ||||||||
\(451\) | 1.28044e6 | 0.296428 | ||||||||
\(452\) | 981620. | 0.225994 | ||||||||
\(453\) | −4.47559e6 | −1.02472 | ||||||||
\(454\) | −874589. | −0.199143 | ||||||||
\(455\) | −1.77083e6 | −0.401004 | ||||||||
\(456\) | 1.28669e6 | 0.289777 | ||||||||
\(457\) | −41544.6 | −0.00930515 | −0.00465258 | − | 0.999989i | \(-0.501481\pi\) | ||||
−0.00465258 | + | 0.999989i | \(0.501481\pi\) | |||||||
\(458\) | −4.14890e6 | −0.924207 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −585040. | −0.128911 | ||||||||
\(461\) | 349314. | 0.0765534 | 0.0382767 | − | 0.999267i | \(-0.487813\pi\) | ||||
0.0382767 | + | 0.999267i | \(0.487813\pi\) | |||||||
\(462\) | 137428. | 0.0299550 | ||||||||
\(463\) | −7.95491e6 | −1.72458 | −0.862289 | − | 0.506417i | \(-0.830970\pi\) | ||||
−0.862289 | + | 0.506417i | \(0.830970\pi\) | |||||||
\(464\) | 356341. | 0.0768370 | ||||||||
\(465\) | −1.08247e6 | −0.232157 | ||||||||
\(466\) | 4.13546e6 | 0.882184 | ||||||||
\(467\) | −3.16371e6 | −0.671281 | −0.335641 | − | 0.941990i | \(-0.608953\pi\) | ||||
−0.335641 | + | 0.941990i | \(0.608953\pi\) | |||||||
\(468\) | 414637. | 0.0875092 | ||||||||
\(469\) | −2.02046e6 | −0.424148 | ||||||||
\(470\) | 1.02542e7 | 2.14120 | ||||||||
\(471\) | −4.24124e6 | −0.880928 | ||||||||
\(472\) | −7.27087e6 | −1.50221 | ||||||||
\(473\) | −217577. | −0.0447157 | ||||||||
\(474\) | −2.26556e6 | −0.463158 | ||||||||
\(475\) | 2.66848e6 | 0.542662 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −187926. | −0.0378173 | ||||||||
\(478\) | −258139. | −0.0516754 | ||||||||
\(479\) | 1.20473e6 | 0.239912 | 0.119956 | − | 0.992779i | \(-0.461725\pi\) | ||||
0.119956 | + | 0.992779i | \(0.461725\pi\) | |||||||
\(480\) | −2.19664e6 | −0.435167 | ||||||||
\(481\) | 7.04955e6 | 1.38931 | ||||||||
\(482\) | −8931.03 | −0.00175099 | ||||||||
\(483\) | 268314. | 0.0523331 | ||||||||
\(484\) | 1.29007e6 | 0.250322 | ||||||||
\(485\) | 4.44223e6 | 0.857525 | ||||||||
\(486\) | −286714. | −0.0550628 | ||||||||
\(487\) | −855818. | −0.163516 | −0.0817578 | − | 0.996652i | \(-0.526053\pi\) | ||||
−0.0817578 | + | 0.996652i | \(0.526053\pi\) | |||||||
\(488\) | 2.25511e6 | 0.428665 | ||||||||
\(489\) | −3.86577e6 | −0.731078 | ||||||||
\(490\) | 6.22337e6 | 1.17094 | ||||||||
\(491\) | −7.91330e6 | −1.48134 | −0.740668 | − | 0.671871i | \(-0.765491\pi\) | ||||
−0.740668 | + | 0.671871i | \(0.765491\pi\) | |||||||
\(492\) | 1.09177e6 | 0.203338 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 2.14916e6 | 0.396234 | ||||||||
\(495\) | −593410. | −0.108853 | ||||||||
\(496\) | 997715. | 0.182097 | ||||||||
\(497\) | 2.21630e6 | 0.402473 | ||||||||
\(498\) | 2.98608e6 | 0.539546 | ||||||||
\(499\) | 2.98471e6 | 0.536600 | 0.268300 | − | 0.963335i | \(-0.413538\pi\) | ||||
0.268300 | + | 0.963335i | \(0.413538\pi\) | |||||||
\(500\) | −373800. | −0.0668674 | ||||||||
\(501\) | −2.26276e6 | −0.402759 | ||||||||
\(502\) | 2.47772e6 | 0.438826 | ||||||||
\(503\) | −4.87638e6 | −0.859366 | −0.429683 | − | 0.902980i | \(-0.641375\pi\) | ||||
−0.429683 | + | 0.902980i | \(0.641375\pi\) | |||||||
\(504\) | 562307. | 0.0986047 | ||||||||
\(505\) | 1.47084e7 | 2.56648 | ||||||||
\(506\) | 363918. | 0.0631870 | ||||||||
\(507\) | −18178.4 | −0.00314077 | ||||||||
\(508\) | −1.97426e6 | −0.339425 | ||||||||
\(509\) | −6.74014e6 | −1.15312 | −0.576560 | − | 0.817055i | \(-0.695605\pi\) | ||||
−0.576560 | + | 0.817055i | \(0.695605\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.12925e6 | 0.191310 | ||||||||
\(512\) | 6.31753e6 | 1.06506 | ||||||||
\(513\) | 530990. | 0.0890826 | ||||||||
\(514\) | 3.08337e6 | 0.514776 | ||||||||
\(515\) | 2.11623e6 | 0.351597 | ||||||||
\(516\) | −185517. | −0.0306732 | ||||||||
\(517\) | 2.27906e6 | 0.374999 | ||||||||
\(518\) | 1.99223e6 | 0.326223 | ||||||||
\(519\) | 3.28305e6 | 0.535007 | ||||||||
\(520\) | −9.82736e6 | −1.59378 | ||||||||
\(521\) | 2.60824e6 | 0.420973 | 0.210486 | − | 0.977597i | \(-0.432495\pi\) | ||||
0.210486 | + | 0.977597i | \(0.432495\pi\) | |||||||
\(522\) | 205052. | 0.0329372 | ||||||||
\(523\) | −5.70267e6 | −0.911641 | −0.455821 | − | 0.890072i | \(-0.650654\pi\) | ||||
−0.455821 | + | 0.890072i | \(0.650654\pi\) | |||||||
\(524\) | 298167. | 0.0474386 | ||||||||
\(525\) | 1.16617e6 | 0.184656 | ||||||||
\(526\) | −3.19978e6 | −0.504261 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 546949. | 0.0853812 | ||||||||
\(529\) | −5.72583e6 | −0.889609 | ||||||||
\(530\) | 928170. | 0.143528 | ||||||||
\(531\) | −3.00053e6 | −0.461808 | ||||||||
\(532\) | −217012. | −0.0332433 | ||||||||
\(533\) | 8.75091e6 | 1.33424 | ||||||||
\(534\) | 5.69856e6 | 0.864793 | ||||||||
\(535\) | −1.20586e7 | −1.82143 | ||||||||
\(536\) | −1.12127e7 | −1.68577 | ||||||||
\(537\) | −4.61200e6 | −0.690166 | ||||||||
\(538\) | 3.66867e6 | 0.546454 | ||||||||
\(539\) | 1.38319e6 | 0.205073 | ||||||||
\(540\) | −505972. | −0.0746692 | ||||||||
\(541\) | −1.21066e7 | −1.77840 | −0.889202 | − | 0.457514i | \(-0.848740\pi\) | ||||
−0.889202 | + | 0.457514i | \(0.848740\pi\) | |||||||
\(542\) | 831633. | 0.121600 | ||||||||
\(543\) | 5.34237e6 | 0.777560 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.11367e7 | 1.60607 | ||||||||
\(546\) | 939221. | 0.134830 | ||||||||
\(547\) | 6.64964e6 | 0.950232 | 0.475116 | − | 0.879923i | \(-0.342406\pi\) | ||||
0.475116 | + | 0.879923i | \(0.342406\pi\) | |||||||
\(548\) | −2.46322e6 | −0.350390 | ||||||||
\(549\) | 930632. | 0.131779 | ||||||||
\(550\) | 1.58169e6 | 0.222954 | ||||||||
\(551\) | −379753. | −0.0532871 | ||||||||
\(552\) | 1.48903e6 | 0.207996 | ||||||||
\(553\) | 1.83363e6 | 0.254975 | ||||||||
\(554\) | 7.25759e6 | 1.00466 | ||||||||
\(555\) | −8.60240e6 | −1.18546 | ||||||||
\(556\) | −2.37436e6 | −0.325731 | ||||||||
\(557\) | 3.95921e6 | 0.540718 | 0.270359 | − | 0.962760i | \(-0.412858\pi\) | ||||
0.270359 | + | 0.962760i | \(0.412858\pi\) | |||||||
\(558\) | 574123. | 0.0780583 | ||||||||
\(559\) | −1.48698e6 | −0.201269 | ||||||||
\(560\) | −1.99172e6 | −0.268384 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.35057e6 | −0.447485 | ||||||||
\(563\) | 1.31190e7 | 1.74433 | 0.872164 | − | 0.489213i | \(-0.162716\pi\) | ||||
0.872164 | + | 0.489213i | \(0.162716\pi\) | |||||||
\(564\) | 1.94325e6 | 0.257235 | ||||||||
\(565\) | −9.60114e6 | −1.26532 | ||||||||
\(566\) | −1.75702e6 | −0.230534 | ||||||||
\(567\) | 232052. | 0.0303129 | ||||||||
\(568\) | 1.22995e7 | 1.59962 | ||||||||
\(569\) | −3.91300e6 | −0.506674 | −0.253337 | − | 0.967378i | \(-0.581528\pi\) | ||||
−0.253337 | + | 0.967378i | \(0.581528\pi\) | |||||||
\(570\) | −2.62257e6 | −0.338096 | ||||||||
\(571\) | 2.09705e6 | 0.269165 | 0.134583 | − | 0.990902i | \(-0.457031\pi\) | ||||
0.134583 | + | 0.990902i | \(0.457031\pi\) | |||||||
\(572\) | −455160. | −0.0581666 | ||||||||
\(573\) | 7.68523e6 | 0.977846 | ||||||||
\(574\) | 2.47304e6 | 0.313293 | ||||||||
\(575\) | 3.08810e6 | 0.389513 | ||||||||
\(576\) | 2.93663e6 | 0.368802 | ||||||||
\(577\) | 8.68859e6 | 1.08645 | 0.543225 | − | 0.839587i | \(-0.317203\pi\) | ||||
0.543225 | + | 0.839587i | \(0.317203\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.57648e6 | 0.691295 | ||||||||
\(580\) | 361860. | 0.0446653 | ||||||||
\(581\) | −2.41678e6 | −0.297028 | ||||||||
\(582\) | −2.35609e6 | −0.288326 | ||||||||
\(583\) | 206292. | 0.0251368 | ||||||||
\(584\) | 6.26685e6 | 0.760357 | ||||||||
\(585\) | −4.05553e6 | −0.489957 | ||||||||
\(586\) | 3.96907e6 | 0.477469 | ||||||||
\(587\) | 6.01409e6 | 0.720402 | 0.360201 | − | 0.932875i | \(-0.382708\pi\) | ||||
0.360201 | + | 0.932875i | \(0.382708\pi\) | |||||||
\(588\) | 1.17938e6 | 0.140672 | ||||||||
\(589\) | −1.06327e6 | −0.126286 | ||||||||
\(590\) | 1.48197e7 | 1.75270 | ||||||||
\(591\) | 4.34884e6 | 0.512159 | ||||||||
\(592\) | 7.92887e6 | 0.929838 | ||||||||
\(593\) | 1.55176e7 | 1.81212 | 0.906062 | − | 0.423144i | \(-0.139074\pi\) | ||||
0.906062 | + | 0.423144i | \(0.139074\pi\) | |||||||
\(594\) | 314735. | 0.0365998 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.04793e6 | −0.120841 | ||||||||
\(597\) | −8.88924e6 | −1.02077 | ||||||||
\(598\) | 2.48712e6 | 0.284410 | ||||||||
\(599\) | 5.72200e6 | 0.651600 | 0.325800 | − | 0.945439i | \(-0.394366\pi\) | ||||
0.325800 | + | 0.945439i | \(0.394366\pi\) | |||||||
\(600\) | 6.47174e6 | 0.733910 | ||||||||
\(601\) | −4.06450e6 | −0.459009 | −0.229505 | − | 0.973308i | \(-0.573711\pi\) | ||||
−0.229505 | + | 0.973308i | \(0.573711\pi\) | |||||||
\(602\) | −420226. | −0.0472598 | ||||||||
\(603\) | −4.62722e6 | −0.518235 | ||||||||
\(604\) | 4.18907e6 | 0.467224 | ||||||||
\(605\) | −1.26180e7 | −1.40153 | ||||||||
\(606\) | −7.80111e6 | −0.862929 | ||||||||
\(607\) | 1.44495e7 | 1.59177 | 0.795887 | − | 0.605445i | \(-0.207005\pi\) | ||||
0.795887 | + | 0.605445i | \(0.207005\pi\) | |||||||
\(608\) | −2.15768e6 | −0.236716 | ||||||||
\(609\) | −165958. | −0.0181324 | ||||||||
\(610\) | −4.59641e6 | −0.500143 | ||||||||
\(611\) | 1.55758e7 | 1.68790 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.87340e6 | −0.953759 | −0.476880 | − | 0.878969i | \(-0.658232\pi\) | ||||
−0.476880 | + | 0.878969i | \(0.658232\pi\) | |||||||
\(614\) | 1.07837e7 | 1.15437 | ||||||||
\(615\) | −1.06785e7 | −1.13847 | ||||||||
\(616\) | −617262. | −0.0655417 | ||||||||
\(617\) | −1.67988e7 | −1.77650 | −0.888252 | − | 0.459357i | \(-0.848080\pi\) | ||||
−0.888252 | + | 0.459357i | \(0.848080\pi\) | |||||||
\(618\) | −1.12241e6 | −0.118218 | ||||||||
\(619\) | 8.69167e6 | 0.911751 | 0.455876 | − | 0.890043i | \(-0.349326\pi\) | ||||
0.455876 | + | 0.890043i | \(0.349326\pi\) | |||||||
\(620\) | 1.01317e6 | 0.105853 | ||||||||
\(621\) | 614489. | 0.0639419 | ||||||||
\(622\) | −111009. | −0.0115049 | ||||||||
\(623\) | −4.61212e6 | −0.476081 | ||||||||
\(624\) | 3.73801e6 | 0.384307 | ||||||||
\(625\) | −7.79254e6 | −0.797956 | ||||||||
\(626\) | 8.03403e6 | 0.819403 | ||||||||
\(627\) | −582884. | −0.0592125 | ||||||||
\(628\) | 3.96972e6 | 0.401662 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.14611e6 | −0.115047 | ||||||||
\(631\) | 5.83156e6 | 0.583058 | 0.291529 | − | 0.956562i | \(-0.405836\pi\) | ||||
0.291529 | + | 0.956562i | \(0.405836\pi\) | |||||||
\(632\) | 1.01758e7 | 1.01339 | ||||||||
\(633\) | 3.15268e6 | 0.312731 | ||||||||
\(634\) | −5.14786e6 | −0.508632 | ||||||||
\(635\) | 1.93100e7 | 1.90042 | ||||||||
\(636\) | 175895. | 0.0172429 | ||||||||
\(637\) | 9.45310e6 | 0.923051 | ||||||||
\(638\) | −225092. | −0.0218931 | ||||||||
\(639\) | 5.07572e6 | 0.491752 | ||||||||
\(640\) | −6.69381e6 | −0.645987 | ||||||||
\(641\) | 3.83410e6 | 0.368569 | 0.184284 | − | 0.982873i | \(-0.441003\pi\) | ||||
0.184284 | + | 0.982873i | \(0.441003\pi\) | |||||||
\(642\) | 6.39570e6 | 0.612421 | ||||||||
\(643\) | 1.83408e7 | 1.74941 | 0.874703 | − | 0.484660i | \(-0.161057\pi\) | ||||
0.874703 | + | 0.484660i | \(0.161057\pi\) | |||||||
\(644\) | −251137. | −0.0238614 | ||||||||
\(645\) | 1.81453e6 | 0.171737 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.29974e7 | 1.22066 | 0.610330 | − | 0.792148i | \(-0.291037\pi\) | ||||
0.610330 | + | 0.792148i | \(0.291037\pi\) | |||||||
\(648\) | 1.28779e6 | 0.120478 | ||||||||
\(649\) | 3.29377e6 | 0.306960 | ||||||||
\(650\) | 1.08097e7 | 1.00353 | ||||||||
\(651\) | −464665. | −0.0429722 | ||||||||
\(652\) | 3.61828e6 | 0.333337 | ||||||||
\(653\) | −2.70030e6 | −0.247816 | −0.123908 | − | 0.992294i | \(-0.539543\pi\) | ||||
−0.123908 | + | 0.992294i | \(0.539543\pi\) | |||||||
\(654\) | −5.90672e6 | −0.540010 | ||||||||
\(655\) | −2.91635e6 | −0.265605 | ||||||||
\(656\) | 9.84245e6 | 0.892984 | ||||||||
\(657\) | 2.58619e6 | 0.233748 | ||||||||
\(658\) | 4.40177e6 | 0.396335 | ||||||||
\(659\) | 1.32077e6 | 0.118472 | 0.0592358 | − | 0.998244i | \(-0.481134\pi\) | ||||
0.0592358 | + | 0.998244i | \(0.481134\pi\) | |||||||
\(660\) | 555420. | 0.0496320 | ||||||||
\(661\) | 1.21919e7 | 1.08535 | 0.542673 | − | 0.839944i | \(-0.317412\pi\) | ||||
0.542673 | + | 0.839944i | \(0.317412\pi\) | |||||||
\(662\) | −2.58532e6 | −0.229282 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.34121e7 | −1.18053 | ||||||||
\(665\) | 2.12257e6 | 0.186127 | ||||||||
\(666\) | 4.56257e6 | 0.398588 | ||||||||
\(667\) | −439470. | −0.0382485 | ||||||||
\(668\) | 2.11790e6 | 0.183639 | ||||||||
\(669\) | −4.14105e6 | −0.357722 | ||||||||
\(670\) | 2.28539e7 | 1.96686 | ||||||||
\(671\) | −1.02158e6 | −0.0875926 | ||||||||
\(672\) | −942941. | −0.0805493 | ||||||||
\(673\) | −3.40439e6 | −0.289735 | −0.144868 | − | 0.989451i | \(-0.546276\pi\) | ||||
−0.144868 | + | 0.989451i | \(0.546276\pi\) | |||||||
\(674\) | 5.69410e6 | 0.482809 | ||||||||
\(675\) | 2.67074e6 | 0.225617 | ||||||||
\(676\) | 17014.6 | 0.00143204 | ||||||||
\(677\) | −1.16605e7 | −0.977791 | −0.488895 | − | 0.872342i | \(-0.662600\pi\) | ||||
−0.488895 | + | 0.872342i | \(0.662600\pi\) | |||||||
\(678\) | 5.09229e6 | 0.425440 | ||||||||
\(679\) | 1.90689e6 | 0.158728 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.62110e6 | 0.133950 | ||||||||
\(682\) | −630232. | −0.0518847 | ||||||||
\(683\) | 5.56138e6 | 0.456174 | 0.228087 | − | 0.973641i | \(-0.426753\pi\) | ||||
0.228087 | + | 0.973641i | \(0.426753\pi\) | |||||||
\(684\) | −496996. | −0.0406175 | ||||||||
\(685\) | 2.40926e7 | 1.96181 | ||||||||
\(686\) | 5.55778e6 | 0.450911 | ||||||||
\(687\) | 7.69022e6 | 0.621652 | ||||||||
\(688\) | −1.67246e6 | −0.134705 | ||||||||
\(689\) | 1.40986e6 | 0.113143 | ||||||||
\(690\) | −3.03497e6 | −0.242679 | ||||||||
\(691\) | 2.67455e6 | 0.213086 | 0.106543 | − | 0.994308i | \(-0.466022\pi\) | ||||
0.106543 | + | 0.994308i | \(0.466022\pi\) | |||||||
\(692\) | −3.07287e6 | −0.243938 | ||||||||
\(693\) | −254730. | −0.0201487 | ||||||||
\(694\) | 1.59233e7 | 1.25497 | ||||||||
\(695\) | 2.32234e7 | 1.82374 | ||||||||
\(696\) | −920998. | −0.0720668 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 1.73125e7 | 1.34500 | ||||||||
\(699\) | −7.66531e6 | −0.593385 | ||||||||
\(700\) | −1.09151e6 | −0.0841944 | ||||||||
\(701\) | −1.56726e7 | −1.20460 | −0.602302 | − | 0.798268i | \(-0.705750\pi\) | ||||
−0.602302 | + | 0.798268i | \(0.705750\pi\) | |||||||
\(702\) | 2.15099e6 | 0.164739 | ||||||||
\(703\) | −8.44980e6 | −0.644849 | ||||||||
\(704\) | −3.22363e6 | −0.245140 | ||||||||
\(705\) | −1.90067e7 | −1.44024 | ||||||||
\(706\) | 1.16586e7 | 0.880306 | ||||||||
\(707\) | 6.31382e6 | 0.475055 | ||||||||
\(708\) | 2.80843e6 | 0.210563 | ||||||||
\(709\) | −1.49150e7 | −1.11431 | −0.557156 | − | 0.830408i | \(-0.688108\pi\) | ||||
−0.557156 | + | 0.830408i | \(0.688108\pi\) | |||||||
\(710\) | −2.50691e7 | −1.86635 | ||||||||
\(711\) | 4.19934e6 | 0.311535 | ||||||||
\(712\) | −2.55953e7 | −1.89217 | ||||||||
\(713\) | −1.23047e6 | −0.0906454 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.45188e6 | 0.325671 | ||||||||
\(716\) | 4.31674e6 | 0.314683 | ||||||||
\(717\) | 478475. | 0.0347586 | ||||||||
\(718\) | −89985.9 | −0.00651423 | ||||||||
\(719\) | −1.26695e7 | −0.913978 | −0.456989 | − | 0.889472i | \(-0.651072\pi\) | ||||
−0.456989 | + | 0.889472i | \(0.651072\pi\) | |||||||
\(720\) | −4.56140e6 | −0.327919 | ||||||||
\(721\) | 908425. | 0.0650805 | ||||||||
\(722\) | 9.44672e6 | 0.674432 | ||||||||
\(723\) | 16554.2 | 0.00117777 | ||||||||
\(724\) | −5.00035e6 | −0.354531 | ||||||||
\(725\) | −1.91006e6 | −0.134959 | ||||||||
\(726\) | 6.69240e6 | 0.471238 | ||||||||
\(727\) | 1.07708e6 | 0.0755810 | 0.0377905 | − | 0.999286i | \(-0.487968\pi\) | ||||
0.0377905 | + | 0.999286i | \(0.487968\pi\) | |||||||
\(728\) | −4.21854e6 | −0.295008 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | −1.27732e7 | −0.887144 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −871054. | −0.0600852 | ||||||||
\(733\) | 2.29858e7 | 1.58015 | 0.790077 | − | 0.613008i | \(-0.210041\pi\) | ||||
0.790077 | + | 0.613008i | \(0.210041\pi\) | |||||||
\(734\) | −1.46152e7 | −1.00130 | ||||||||
\(735\) | −1.15354e7 | −0.787614 | ||||||||
\(736\) | −2.49698e6 | −0.169910 | ||||||||
\(737\) | 5.07944e6 | 0.344467 | ||||||||
\(738\) | 5.66371e6 | 0.382790 | ||||||||
\(739\) | −7.07195e6 | −0.476352 | −0.238176 | − | 0.971222i | \(-0.576550\pi\) | ||||
−0.238176 | + | 0.971222i | \(0.576550\pi\) | |||||||
\(740\) | 8.05168e6 | 0.540514 | ||||||||
\(741\) | −3.98360e6 | −0.266520 | ||||||||
\(742\) | 398431. | 0.0265670 | ||||||||
\(743\) | 5.88199e6 | 0.390888 | 0.195444 | − | 0.980715i | \(-0.437385\pi\) | ||||
0.195444 | + | 0.980715i | \(0.437385\pi\) | |||||||
\(744\) | −2.57869e6 | −0.170792 | ||||||||
\(745\) | 1.02497e7 | 0.676582 | ||||||||
\(746\) | 8.69622e6 | 0.572115 | ||||||||
\(747\) | −5.53487e6 | −0.362916 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.17635e6 | −0.337147 | ||||||||
\(750\) | −1.93914e6 | −0.125880 | ||||||||
\(751\) | 2.60946e7 | 1.68831 | 0.844153 | − | 0.536102i | \(-0.180104\pi\) | ||||
0.844153 | + | 0.536102i | \(0.180104\pi\) | |||||||
\(752\) | 1.75186e7 | 1.12968 | ||||||||
\(753\) | −4.59259e6 | −0.295169 | ||||||||
\(754\) | −1.53834e6 | −0.0985426 | ||||||||
\(755\) | −4.09729e7 | −2.61595 | ||||||||
\(756\) | −217196. | −0.0138212 | ||||||||
\(757\) | −2.16589e7 | −1.37372 | −0.686859 | − | 0.726791i | \(-0.741011\pi\) | ||||
−0.686859 | + | 0.726791i | \(0.741011\pi\) | |||||||
\(758\) | −5.05438e6 | −0.319517 | ||||||||
\(759\) | −674544. | −0.0425016 | ||||||||
\(760\) | 1.17794e7 | 0.739755 | ||||||||
\(761\) | −1.16283e7 | −0.727869 | −0.363934 | − | 0.931425i | \(-0.618567\pi\) | ||||
−0.363934 | + | 0.931425i | \(0.618567\pi\) | |||||||
\(762\) | −1.02417e7 | −0.638978 | ||||||||
\(763\) | 4.78059e6 | 0.297283 | ||||||||
\(764\) | −7.19323e6 | −0.445852 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.53338e6 | −0.0944231 | ||||||||
\(767\) | 2.25106e7 | 1.38165 | ||||||||
\(768\) | −6.89108e6 | −0.421584 | ||||||||
\(769\) | −1.99396e7 | −1.21591 | −0.607954 | − | 0.793972i | \(-0.708009\pi\) | ||||
−0.607954 | + | 0.793972i | \(0.708009\pi\) | |||||||
\(770\) | 1.25812e6 | 0.0764705 | ||||||||
\(771\) | −5.71521e6 | −0.346255 | ||||||||
\(772\) | −5.21947e6 | −0.315198 | ||||||||
\(773\) | −2.52638e6 | −0.152072 | −0.0760360 | − | 0.997105i | \(-0.524226\pi\) | ||||
−0.0760360 | + | 0.997105i | \(0.524226\pi\) | |||||||
\(774\) | −962396. | −0.0577433 | ||||||||
\(775\) | −5.34795e6 | −0.319840 | ||||||||
\(776\) | 1.05824e7 | 0.630858 | ||||||||
\(777\) | −3.69271e6 | −0.219428 | ||||||||
\(778\) | −1.09025e7 | −0.645770 | ||||||||
\(779\) | −1.04891e7 | −0.619291 | ||||||||
\(780\) | 3.79590e6 | 0.223398 | ||||||||
\(781\) | −5.57178e6 | −0.326863 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −380075. | −0.0221547 | ||||||||
\(784\) | 1.06322e7 | 0.617780 | ||||||||
\(785\) | −3.88275e7 | −2.24887 | ||||||||
\(786\) | 1.54679e6 | 0.0893046 | ||||||||
\(787\) | 1.49359e7 | 0.859597 | 0.429799 | − | 0.902925i | \(-0.358585\pi\) | ||||
0.429799 | + | 0.902925i | \(0.358585\pi\) | |||||||
\(788\) | −4.07043e6 | −0.233520 | ||||||||
\(789\) | 5.93097e6 | 0.339182 | ||||||||
\(790\) | −2.07406e7 | −1.18237 | ||||||||
\(791\) | −4.12144e6 | −0.234211 | ||||||||
\(792\) | −1.41364e6 | −0.0800805 | ||||||||
\(793\) | −6.98179e6 | −0.394261 | ||||||||
\(794\) | −6.81950e6 | −0.383885 | ||||||||
\(795\) | −1.72041e6 | −0.0965418 | ||||||||
\(796\) | 8.32016e6 | 0.465424 | ||||||||
\(797\) | 2.93554e6 | 0.163697 | 0.0818487 | − | 0.996645i | \(-0.473918\pi\) | ||||
0.0818487 | + | 0.996645i | \(0.473918\pi\) | |||||||
\(798\) | −1.12578e6 | −0.0625814 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −1.08526e7 | −0.599524 | ||||||||
\(801\) | −1.05626e7 | −0.581688 | ||||||||
\(802\) | −2.95787e7 | −1.62384 | ||||||||
\(803\) | −2.83894e6 | −0.155370 | ||||||||
\(804\) | 4.33099e6 | 0.236291 | ||||||||
\(805\) | 2.45635e6 | 0.133598 | ||||||||
\(806\) | −4.30718e6 | −0.233537 | ||||||||
\(807\) | −6.80009e6 | −0.367562 | ||||||||
\(808\) | 3.50390e7 | 1.88809 | ||||||||
\(809\) | 9.29691e6 | 0.499422 | 0.249711 | − | 0.968320i | \(-0.419664\pi\) | ||||
0.249711 | + | 0.968320i | \(0.419664\pi\) | |||||||
\(810\) | −2.62480e6 | −0.140567 | ||||||||
\(811\) | −1.86033e7 | −0.993203 | −0.496601 | − | 0.867979i | \(-0.665419\pi\) | ||||
−0.496601 | + | 0.867979i | \(0.665419\pi\) | |||||||
\(812\) | 155334. | 0.00826753 | ||||||||
\(813\) | −1.54148e6 | −0.0817921 | ||||||||
\(814\) | −5.00847e6 | −0.264938 | ||||||||
\(815\) | −3.53901e7 | −1.86633 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.78234e6 | 0.0934191 | ||||||||
\(818\) | 1.04471e7 | 0.545898 | ||||||||
\(819\) | −1.74090e6 | −0.0906909 | ||||||||
\(820\) | 9.99489e6 | 0.519091 | ||||||||
\(821\) | −3.38436e7 | −1.75234 | −0.876170 | − | 0.482002i | \(-0.839910\pi\) | ||||
−0.876170 | + | 0.482002i | \(0.839910\pi\) | |||||||
\(822\) | −1.27783e7 | −0.659620 | ||||||||
\(823\) | 1.55672e7 | 0.801146 | 0.400573 | − | 0.916265i | \(-0.368811\pi\) | ||||
0.400573 | + | 0.916265i | \(0.368811\pi\) | |||||||
\(824\) | 5.04137e6 | 0.258661 | ||||||||
\(825\) | −2.93175e6 | −0.149966 | ||||||||
\(826\) | 6.36156e6 | 0.324424 | ||||||||
\(827\) | −1.89667e7 | −0.964337 | −0.482169 | − | 0.876078i | \(-0.660151\pi\) | ||||
−0.482169 | + | 0.876078i | \(0.660151\pi\) | |||||||
\(828\) | −575150. | −0.0291545 | ||||||||
\(829\) | −6.48044e6 | −0.327505 | −0.163752 | − | 0.986501i | \(-0.552360\pi\) | ||||
−0.163752 | + | 0.986501i | \(0.552360\pi\) | |||||||
\(830\) | 2.73368e7 | 1.37738 | ||||||||
\(831\) | −1.34524e7 | −0.675765 | ||||||||
\(832\) | −2.20312e7 | −1.10339 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.23173e7 | −0.613198 | ||||||||
\(835\) | −2.07150e7 | −1.02818 | ||||||||
\(836\) | 545568. | 0.0269981 | ||||||||
\(837\) | −1.06417e6 | −0.0525045 | ||||||||
\(838\) | 1.82866e7 | 0.899544 | ||||||||
\(839\) | 1.33849e7 | 0.656461 | 0.328230 | − | 0.944598i | \(-0.393548\pi\) | ||||
0.328230 | + | 0.944598i | \(0.393548\pi\) | |||||||
\(840\) | 5.14778e6 | 0.251723 | ||||||||
\(841\) | −2.02393e7 | −0.986748 | ||||||||
\(842\) | −2.50388e7 | −1.21712 | ||||||||
\(843\) | 6.21048e6 | 0.300993 | ||||||||
\(844\) | −2.95085e6 | −0.142590 | ||||||||
\(845\) | −166419. | −0.00801790 | ||||||||
\(846\) | 1.00809e7 | 0.484252 | ||||||||
\(847\) | −5.41648e6 | −0.259423 | ||||||||
\(848\) | 1.58572e6 | 0.0757244 | ||||||||
\(849\) | 3.25673e6 | 0.155065 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.77855e6 | −0.462861 | ||||||||
\(852\) | −4.75078e6 | −0.224216 | ||||||||
\(853\) | −2.08372e7 | −0.980542 | −0.490271 | − | 0.871570i | \(-0.663102\pi\) | ||||
−0.490271 | + | 0.871570i | \(0.663102\pi\) | |||||||
\(854\) | −1.97308e6 | −0.0925763 | ||||||||
\(855\) | 4.86108e6 | 0.227414 | ||||||||
\(856\) | −2.87265e7 | −1.33998 | ||||||||
\(857\) | 1.49036e7 | 0.693168 | 0.346584 | − | 0.938019i | \(-0.387342\pi\) | ||||
0.346584 | + | 0.938019i | \(0.387342\pi\) | |||||||
\(858\) | −2.36120e6 | −0.109500 | ||||||||
\(859\) | 2.27420e7 | 1.05159 | 0.525795 | − | 0.850611i | \(-0.323768\pi\) | ||||
0.525795 | + | 0.850611i | \(0.323768\pi\) | |||||||
\(860\) | −1.69836e6 | −0.0783041 | ||||||||
\(861\) | −4.58392e6 | −0.210731 | ||||||||
\(862\) | −2.24962e7 | −1.03120 | ||||||||
\(863\) | −2.75601e7 | −1.25966 | −0.629830 | − | 0.776733i | \(-0.716875\pi\) | ||||
−0.629830 | + | 0.776733i | \(0.716875\pi\) | |||||||
\(864\) | −2.15951e6 | −0.0984171 | ||||||||
\(865\) | 3.00555e7 | 1.36579 | ||||||||
\(866\) | −7211.46 | −0.000326760 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 434918. | 0.0195933 | ||||||||
\(869\) | −4.60974e6 | −0.207075 | ||||||||
\(870\) | 1.87720e6 | 0.0840837 | ||||||||
\(871\) | 3.47144e7 | 1.55047 | ||||||||
\(872\) | 2.65302e7 | 1.18154 | ||||||||
\(873\) | 4.36714e6 | 0.193937 | ||||||||
\(874\) | −2.98114e6 | −0.132009 | ||||||||
\(875\) | 1.56944e6 | 0.0692986 | ||||||||
\(876\) | −2.42062e6 | −0.106578 | ||||||||
\(877\) | 1.37826e7 | 0.605105 | 0.302553 | − | 0.953133i | \(-0.402161\pi\) | ||||
0.302553 | + | 0.953133i | \(0.402161\pi\) | |||||||
\(878\) | 3.40957e7 | 1.49267 | ||||||||
\(879\) | −7.35690e6 | −0.321161 | ||||||||
\(880\) | 5.00718e6 | 0.217965 | ||||||||
\(881\) | −3.19822e7 | −1.38825 | −0.694127 | − | 0.719853i | \(-0.744209\pi\) | ||||
−0.694127 | + | 0.719853i | \(0.744209\pi\) | |||||||
\(882\) | 6.11817e6 | 0.264820 | ||||||||
\(883\) | 1.86859e7 | 0.806512 | 0.403256 | − | 0.915087i | \(-0.367878\pi\) | ||||
0.403256 | + | 0.915087i | \(0.367878\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.74691e7 | −1.17892 | ||||||||
\(886\) | −2.45879e7 | −1.05229 | ||||||||
\(887\) | 2.25039e7 | 0.960394 | 0.480197 | − | 0.877161i | \(-0.340565\pi\) | ||||
0.480197 | + | 0.877161i | \(0.340565\pi\) | |||||||
\(888\) | −2.04929e7 | −0.872111 | ||||||||
\(889\) | 8.28912e6 | 0.351766 | ||||||||
\(890\) | 5.21689e7 | 2.20768 | ||||||||
\(891\) | −583379. | −0.0246182 | ||||||||
\(892\) | 3.87594e6 | 0.163104 | ||||||||
\(893\) | −1.86696e7 | −0.783441 | ||||||||
\(894\) | −5.43627e6 | −0.227487 | ||||||||
\(895\) | −4.22217e7 | −1.76189 | ||||||||
\(896\) | −2.87342e6 | −0.119572 | ||||||||
\(897\) | −4.61002e6 | −0.191303 | ||||||||
\(898\) | 6.61115e6 | 0.273581 | ||||||||
\(899\) | 761070. | 0.0314069 | ||||||||
\(900\) | −2.49976e6 | −0.102871 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −6.21723e6 | −0.254437 | ||||||||
\(903\) | 778913. | 0.0317885 | ||||||||
\(904\) | −2.28722e7 | −0.930865 | ||||||||
\(905\) | 4.89080e7 | 1.98499 | ||||||||
\(906\) | 2.17314e7 | 0.879562 | ||||||||
\(907\) | −2.78151e7 | −1.12270 | −0.561348 | − | 0.827580i | \(-0.689717\pi\) | ||||
−0.561348 | + | 0.827580i | \(0.689717\pi\) | |||||||
\(908\) | −1.51732e6 | −0.0610748 | ||||||||
\(909\) | 1.44598e7 | 0.580434 | ||||||||
\(910\) | 8.59833e6 | 0.344200 | ||||||||
\(911\) | 2.46855e7 | 0.985476 | 0.492738 | − | 0.870178i | \(-0.335996\pi\) | ||||
0.492738 | + | 0.870178i | \(0.335996\pi\) | |||||||
\(912\) | −4.48049e6 | −0.178377 | ||||||||
\(913\) | 6.07580e6 | 0.241227 | ||||||||
\(914\) | 201721. | 0.00798703 | ||||||||
\(915\) | 8.51971e6 | 0.336412 | ||||||||
\(916\) | −7.19790e6 | −0.283444 | ||||||||
\(917\) | −1.25189e6 | −0.0491634 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.12446e7 | 1.22036 | 0.610178 | − | 0.792264i | \(-0.291098\pi\) | ||||
0.610178 | + | 0.792264i | \(0.291098\pi\) | |||||||
\(920\) | 1.36317e7 | 0.530983 | ||||||||
\(921\) | −1.99882e7 | −0.776470 | ||||||||
\(922\) | −1.69611e6 | −0.0657092 | ||||||||
\(923\) | −3.80791e7 | −1.47124 | ||||||||
\(924\) | 238422. | 0.00918686 | ||||||||
\(925\) | −4.25003e7 | −1.63319 | ||||||||
\(926\) | 3.86253e7 | 1.48028 | ||||||||
\(927\) | 2.08046e6 | 0.0795170 | ||||||||
\(928\) | 1.54443e6 | 0.0588707 | ||||||||
\(929\) | 4.42427e7 | 1.68191 | 0.840955 | − | 0.541106i | \(-0.181994\pi\) | ||||
0.840955 | + | 0.541106i | \(0.181994\pi\) | |||||||
\(930\) | 5.25595e6 | 0.199271 | ||||||||
\(931\) | −1.13308e7 | −0.428435 | ||||||||
\(932\) | 7.17458e6 | 0.270556 | ||||||||
\(933\) | 205761. | 0.00773854 | ||||||||
\(934\) | 1.53615e7 | 0.576191 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.66124e6 | −0.360449 | ||||||||
\(937\) | −2.59918e7 | −0.967137 | −0.483568 | − | 0.875307i | \(-0.660660\pi\) | ||||
−0.483568 | + | 0.875307i | \(0.660660\pi\) | |||||||
\(938\) | 9.81040e6 | 0.364065 | ||||||||
\(939\) | −1.48915e7 | −0.551157 | ||||||||
\(940\) | 1.77899e7 | 0.656682 | ||||||||
\(941\) | −3.49032e7 | −1.28496 | −0.642482 | − | 0.766301i | \(-0.722095\pi\) | ||||
−0.642482 | + | 0.766301i | \(0.722095\pi\) | |||||||
\(942\) | 2.05935e7 | 0.756140 | ||||||||
\(943\) | −1.21385e7 | −0.444516 | ||||||||
\(944\) | 2.53184e7 | 0.924711 | ||||||||
\(945\) | 2.12438e6 | 0.0773841 | ||||||||
\(946\) | 1.05645e6 | 0.0383815 | ||||||||
\(947\) | −4.52987e7 | −1.64139 | −0.820693 | − | 0.571370i | \(-0.806412\pi\) | ||||
−0.820693 | + | 0.571370i | \(0.806412\pi\) | |||||||
\(948\) | −3.93050e6 | −0.142045 | ||||||||
\(949\) | −1.94021e7 | −0.699333 | ||||||||
\(950\) | −1.29569e7 | −0.465791 | ||||||||
\(951\) | 9.54186e6 | 0.342123 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.68954e7 | −0.959281 | −0.479641 | − | 0.877465i | \(-0.659233\pi\) | ||||
−0.479641 | + | 0.877465i | \(0.659233\pi\) | |||||||
\(954\) | 912480. | 0.0324603 | ||||||||
\(955\) | 7.03564e7 | 2.49629 | ||||||||
\(956\) | −447844. | −0.0158483 | ||||||||
\(957\) | 417220. | 0.0147260 | ||||||||
\(958\) | −5.84962e6 | −0.205927 | ||||||||
\(959\) | 1.03421e7 | 0.363130 | ||||||||
\(960\) | 2.68842e7 | 0.941496 | ||||||||
\(961\) | −2.64982e7 | −0.925568 | ||||||||
\(962\) | −3.42293e7 | −1.19251 | ||||||||
\(963\) | −1.18548e7 | −0.411934 | ||||||||
\(964\) | −15494.4 | −0.000537009 0 | ||||||||
\(965\) | 5.10513e7 | 1.76477 | ||||||||
\(966\) | −1.30281e6 | −0.0449198 | ||||||||
\(967\) | 1.29142e7 | 0.444120 | 0.222060 | − | 0.975033i | \(-0.428722\pi\) | ||||
0.222060 | + | 0.975033i | \(0.428722\pi\) | |||||||
\(968\) | −3.00591e7 | −1.03107 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.15694e7 | −0.736052 | ||||||||
\(971\) | 1.33715e7 | 0.455127 | 0.227564 | − | 0.973763i | \(-0.426924\pi\) | ||||
0.227564 | + | 0.973763i | \(0.426924\pi\) | |||||||
\(972\) | −497419. | −0.0168871 | ||||||||
\(973\) | 9.96900e6 | 0.337574 | ||||||||
\(974\) | 4.15545e6 | 0.140353 | ||||||||
\(975\) | −2.00364e7 | −0.675008 | ||||||||
\(976\) | −7.85266e6 | −0.263871 | ||||||||
\(977\) | 1.85797e7 | 0.622733 | 0.311367 | − | 0.950290i | \(-0.399213\pi\) | ||||
0.311367 | + | 0.950290i | \(0.399213\pi\) | |||||||
\(978\) | 1.87703e7 | 0.627516 | ||||||||
\(979\) | 1.15949e7 | 0.386643 | ||||||||
\(980\) | 1.07969e7 | 0.359115 | ||||||||
\(981\) | 1.09484e7 | 0.363228 | ||||||||
\(982\) | 3.84232e7 | 1.27150 | ||||||||
\(983\) | 3.17048e7 | 1.04650 | 0.523252 | − | 0.852178i | \(-0.324719\pi\) | ||||
0.523252 | + | 0.852178i | \(0.324719\pi\) | |||||||
\(984\) | −2.54388e7 | −0.837545 | ||||||||
\(985\) | 3.98125e7 | 1.30746 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.15893e6 | −0.266588 | ||||||||
\(988\) | 3.72857e6 | 0.121521 | ||||||||
\(989\) | 2.06262e6 | 0.0670545 | ||||||||
\(990\) | 2.88132e6 | 0.0934337 | ||||||||
\(991\) | −2.75365e7 | −0.890687 | −0.445344 | − | 0.895360i | \(-0.646918\pi\) | ||||
−0.445344 | + | 0.895360i | \(0.646918\pi\) | |||||||
\(992\) | 4.32425e6 | 0.139518 | ||||||||
\(993\) | 4.79204e6 | 0.154222 | ||||||||
\(994\) | −1.07613e7 | −0.345460 | ||||||||
\(995\) | −8.13788e7 | −2.60587 | ||||||||
\(996\) | 5.18053e6 | 0.165473 | ||||||||
\(997\) | −4.65005e7 | −1.48156 | −0.740781 | − | 0.671747i | \(-0.765544\pi\) | ||||
−0.740781 | + | 0.671747i | \(0.765544\pi\) | |||||||
\(998\) | −1.44924e7 | −0.460588 | ||||||||
\(999\) | −8.45698e6 | −0.268103 |
(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 | 867.6.a.u.1.10 | 28 | ||
17.10 | odd | 16 | 51.6.h.a.49.10 | yes | 56 | ||
17.12 | odd | 16 | 51.6.h.a.25.10 | ✓ | 56 | ||
17.16 | even | 2 | 867.6.a.t.1.10 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
51.6.h.a.25.10 | ✓ | 56 | 17.12 | odd | 16 | ||
51.6.h.a.49.10 | yes | 56 | 17.10 | odd | 16 | ||
867.6.a.t.1.10 | 28 | 17.16 | even | 2 | |||
867.6.a.u.1.10 | 28 | 1.1 | even | 1 | trivial |