Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1104,6,Mod(1,1104)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1104, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1104.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1104 = 2^{4} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1104.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: | \(177.063737074\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 552) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 1104.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −82.0000 | −1.46686 | −0.733430 | − | 0.679765i | \(-0.762082\pi\) | ||||
−0.733430 | + | 0.679765i | \(0.762082\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 64.0000 | 0.493668 | 0.246834 | − | 0.969058i | \(-0.420610\pi\) | ||||
0.246834 | + | 0.969058i | \(0.420610\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 412.000 | 1.02663 | 0.513317 | − | 0.858199i | \(-0.328417\pi\) | ||||
0.513317 | + | 0.858199i | \(0.328417\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 622.000 | 1.02078 | 0.510390 | − | 0.859943i | \(-0.329501\pi\) | ||||
0.510390 | + | 0.859943i | \(0.329501\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −738.000 | −0.846892 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 466.000 | 0.391078 | 0.195539 | − | 0.980696i | \(-0.437354\pi\) | ||||
0.195539 | + | 0.980696i | \(0.437354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −204.000 | −0.129642 | −0.0648211 | − | 0.997897i | \(-0.520648\pi\) | ||||
−0.0648211 | + | 0.997897i | \(0.520648\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 576.000 | 0.285019 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3599.00 | 1.15168 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1030.00 | 0.227427 | 0.113714 | − | 0.993514i | \(-0.463725\pi\) | ||||
0.113714 | + | 0.993514i | \(0.463725\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5688.00 | −1.06305 | −0.531527 | − | 0.847041i | \(-0.678382\pi\) | ||||
−0.531527 | + | 0.847041i | \(0.678382\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3708.00 | 0.592727 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5248.00 | −0.724142 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7862.00 | 0.944123 | 0.472062 | − | 0.881566i | \(-0.343510\pi\) | ||||
0.472062 | + | 0.881566i | \(0.343510\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5598.00 | 0.589347 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4026.00 | 0.374037 | 0.187018 | − | 0.982356i | \(-0.440118\pi\) | ||||
0.187018 | + | 0.982356i | \(0.440118\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6548.00 | −0.540054 | −0.270027 | − | 0.962853i | \(-0.587033\pi\) | ||||
−0.270027 | + | 0.962853i | \(0.587033\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6642.00 | −0.488954 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 22016.0 | 1.45376 | 0.726882 | − | 0.686763i | \(-0.240969\pi\) | ||||
0.726882 | + | 0.686763i | \(0.240969\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12711.0 | −0.756292 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4194.00 | 0.225789 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4974.00 | 0.243229 | 0.121615 | − | 0.992577i | \(-0.461193\pi\) | ||||
0.121615 | + | 0.992577i | \(0.461193\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −33784.0 | −1.50593 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1836.00 | −0.0748489 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −35972.0 | −1.34535 | −0.672674 | − | 0.739939i | \(-0.734854\pi\) | ||||
−0.672674 | + | 0.739939i | \(0.734854\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 17870.0 | 0.614894 | 0.307447 | − | 0.951565i | \(-0.400525\pi\) | ||||
0.307447 | + | 0.951565i | \(0.400525\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5184.00 | 0.164556 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −51004.0 | −1.49734 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 22708.0 | 0.618005 | 0.309002 | − | 0.951061i | \(-0.400005\pi\) | ||||
0.309002 | + | 0.951061i | \(0.400005\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4761.00 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 59288.0 | 1.39579 | 0.697896 | − | 0.716199i | \(-0.254120\pi\) | ||||
0.697896 | + | 0.716199i | \(0.254120\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −22038.0 | −0.484022 | −0.242011 | − | 0.970274i | \(-0.577807\pi\) | ||||
−0.242011 | + | 0.970274i | \(0.577807\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 32391.0 | 0.664923 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 26368.0 | 0.506816 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −85656.0 | −1.54415 | −0.772076 | − | 0.635530i | \(-0.780782\pi\) | ||||
−0.772076 | + | 0.635530i | \(0.780782\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −59100.0 | −0.941656 | −0.470828 | − | 0.882225i | \(-0.656045\pi\) | ||||
−0.470828 | + | 0.882225i | \(0.656045\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −38212.0 | −0.573657 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9270.00 | 0.131305 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −113174. | −1.51451 | −0.757254 | − | 0.653120i | \(-0.773460\pi\) | ||||
−0.757254 | + | 0.653120i | \(0.773460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 39808.0 | 0.503926 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −51192.0 | −0.613755 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16728.0 | 0.190167 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −75038.0 | −0.809752 | −0.404876 | − | 0.914372i | \(-0.632685\pi\) | ||||
−0.404876 | + | 0.914372i | \(0.632685\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 33372.0 | 0.342211 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −52114.0 | −0.508336 | −0.254168 | − | 0.967160i | \(-0.581802\pi\) | ||||
−0.254168 | + | 0.967160i | \(0.581802\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 69104.0 | 0.641815 | 0.320908 | − | 0.947110i | \(-0.396012\pi\) | ||||
0.320908 | + | 0.947110i | \(0.396012\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −47232.0 | −0.418084 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 116364. | 0.982560 | 0.491280 | − | 0.871002i | \(-0.336529\pi\) | ||||
0.491280 | + | 0.871002i | \(0.336529\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 92430.0 | 0.745155 | 0.372578 | − | 0.928001i | \(-0.378474\pi\) | ||||
0.372578 | + | 0.928001i | \(0.378474\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 70758.0 | 0.545090 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 111138. | 0.818779 | 0.409389 | − | 0.912360i | \(-0.365742\pi\) | ||||
0.409389 | + | 0.912360i | \(0.365742\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 43378.0 | 0.305862 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 50382.0 | 0.340260 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29824.0 | 0.193063 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8693.00 | 0.0539767 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 36234.0 | 0.215950 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −38868.0 | −0.222493 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 156472. | 0.860850 | 0.430425 | − | 0.902626i | \(-0.358364\pi\) | ||||
0.430425 | + | 0.902626i | \(0.358364\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −58932.0 | −0.311801 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 284772. | 1.44984 | 0.724918 | − | 0.688835i | \(-0.241877\pi\) | ||||
0.724918 | + | 0.688835i | \(0.241877\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13056.0 | −0.0640002 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −59778.0 | −0.282297 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 421450. | 1.91842 | 0.959212 | − | 0.282687i | \(-0.0912259\pi\) | ||||
0.959212 | + | 0.282687i | \(0.0912259\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −234836. | −1.03093 | −0.515463 | − | 0.856912i | \(-0.672380\pi\) | ||||
−0.515463 | + | 0.856912i | \(0.672380\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 198144. | 0.839331 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 256264. | 1.04797 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −84460.0 | −0.333604 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −114399. | −0.436645 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22914.0 | −0.0845542 | −0.0422771 | − | 0.999106i | \(-0.513461\pi\) | ||||
−0.0422771 | + | 0.999106i | \(0.513461\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 152704. | 0.545014 | 0.272507 | − | 0.962154i | \(-0.412147\pi\) | ||||
0.272507 | + | 0.962154i | \(0.412147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 37746.0 | 0.130359 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 466416. | 1.55935 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 217230. | 0.703349 | 0.351674 | − | 0.936122i | \(-0.385612\pi\) | ||||
0.351674 | + | 0.936122i | \(0.385612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 44766.0 | 0.140429 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33856.0 | −0.102937 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −161836. | −0.477096 | −0.238548 | − | 0.971131i | \(-0.576671\pi\) | ||||
−0.238548 | + | 0.971131i | \(0.576671\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −304056. | −0.869448 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 470184. | 1.30460 | 0.652299 | − | 0.757962i | \(-0.273805\pi\) | ||||
0.652299 | + | 0.757962i | \(0.273805\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15591.0 | 0.0419911 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16524.0 | −0.0432140 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20134.0 | 0.0511464 | 0.0255732 | − | 0.999673i | \(-0.491859\pi\) | ||||
0.0255732 | + | 0.999673i | \(0.491859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 230336. | 0.568547 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −323748. | −0.776737 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 497780. | 1.16119 | 0.580597 | − | 0.814191i | \(-0.302819\pi\) | ||||
0.580597 | + | 0.814191i | \(0.302819\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −253002. | −0.574021 | −0.287010 | − | 0.957927i | \(-0.592661\pi\) | ||||
−0.287010 | + | 0.957927i | \(0.592661\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 160830. | 0.355009 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −644684. | −1.38490 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 191992. | 0.401494 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 46656.0 | 0.0950064 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 425184. | 0.843322 | 0.421661 | − | 0.906754i | \(-0.361447\pi\) | ||||
0.421661 | + | 0.906754i | \(0.361447\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 443266. | 0.856586 | 0.428293 | − | 0.903640i | \(-0.359115\pi\) | ||||
0.428293 | + | 0.903640i | \(0.359115\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −459036. | −0.864490 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 95502.0 | 0.175326 | 0.0876631 | − | 0.996150i | \(-0.472060\pi\) | ||||
0.0876631 | + | 0.996150i | \(0.472060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 290864. | 0.520664 | 0.260332 | − | 0.965519i | \(-0.416168\pi\) | ||||
0.260332 | + | 0.965519i | \(0.416168\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 204372. | 0.356805 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 65920.0 | 0.112273 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −330132. | −0.548660 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −42849.0 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −84048.0 | −0.133095 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 519700. | 0.803612 | 0.401806 | − | 0.915725i | \(-0.368383\pi\) | ||||
0.401806 | + | 0.915725i | \(0.368383\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 533592. | 0.805861 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 536936. | 0.792185 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −364032. | −0.524796 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −198342. | −0.279450 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 289852. | 0.399205 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 994456. | 1.33913 | 0.669566 | − | 0.742753i | \(-0.266480\pi\) | ||||
0.669566 | + | 0.742753i | \(0.266480\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 291519. | 0.383893 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 523892. | 0.674803 | 0.337402 | − | 0.941361i | \(-0.390452\pi\) | ||||
0.337402 | + | 0.941361i | \(0.390452\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −328250. | −0.413634 | −0.206817 | − | 0.978380i | \(-0.566310\pi\) | ||||
−0.206817 | + | 0.978380i | \(0.566310\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 237312. | 0.292610 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 500778. | 0.604304 | 0.302152 | − | 0.953260i | \(-0.402295\pi\) | ||||
0.302152 | + | 0.953260i | \(0.402295\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.80531e6 | −2.13247 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −770904. | −0.891517 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 642256. | 0.727300 | 0.363650 | − | 0.931536i | \(-0.381530\pi\) | ||||
0.363650 | + | 0.931536i | \(0.381530\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −533710. | −0.591920 | −0.295960 | − | 0.955200i | \(-0.595639\pi\) | ||||
−0.295960 | + | 0.955200i | \(0.595639\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.04230e6 | 1.10937 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −126888. | −0.132336 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −531900. | −0.543665 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.76898e6 | −1.77231 | −0.886153 | − | 0.463393i | \(-0.846632\pi\) | ||||
−0.886153 | + | 0.463393i | \(0.846632\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −217948. | −0.214068 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −343908. | −0.331201 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.45005e6 | 1.36946 | 0.684731 | − | 0.728796i | \(-0.259920\pi\) | ||||
0.684731 | + | 0.728796i | \(0.259920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 503168. | 0.466083 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 83430.0 | 0.0758090 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.14442e6 | 1.02023 | 0.510114 | − | 0.860107i | \(-0.329603\pi\) | ||||
0.510114 | + | 0.860107i | \(0.329603\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −407868. | −0.356784 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.01857e6 | −0.874402 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −991050. | −0.835055 | −0.417527 | − | 0.908664i | \(-0.637103\pi\) | ||||
−0.417527 | + | 0.908664i | \(0.637103\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 381608. | 0.315642 | 0.157821 | − | 0.987468i | \(-0.449553\pi\) | ||||
0.157821 | + | 0.987468i | \(0.449553\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 358272. | 0.290942 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.48279e6 | 1.18235 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −266698. | −0.208843 | −0.104422 | − | 0.994533i | \(-0.533299\pi\) | ||||
−0.104422 | + | 0.994533i | \(0.533299\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −460728. | −0.354351 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.92398e6 | 1.45356 | 0.726782 | − | 0.686868i | \(-0.241015\pi\) | ||||
0.726782 | + | 0.686868i | \(0.241015\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.60927e6 | −1.19443 | −0.597217 | − | 0.802080i | \(-0.703727\pi\) | ||||
−0.597217 | + | 0.802080i | \(0.703727\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 150552. | 0.109793 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 257664. | 0.184650 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.20270e6 | −0.847058 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −675342. | −0.467510 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18274.0 | −0.0124355 | −0.00621777 | − | 0.999981i | \(-0.501979\pi\) | ||||
−0.00621777 | + | 0.999981i | \(0.501979\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.94970e6 | 1.97344 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 300348. | 0.197576 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −329038. | −0.212847 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −419072. | −0.266608 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −469026. | −0.293488 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.46534e6 | −0.901963 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.07756e6 | 0.652520 | 0.326260 | − | 0.945280i | \(-0.394211\pi\) | ||||
0.326260 | + | 0.945280i | \(0.394211\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 621936. | 0.370552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.63745e6 | −0.959990 | −0.479995 | − | 0.877271i | \(-0.659361\pi\) | ||||
−0.479995 | + | 0.877271i | \(0.659361\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.15535e6 | 1.82049 | 0.910243 | − | 0.414075i | \(-0.135895\pi\) | ||||
0.910243 | + | 0.414075i | \(0.135895\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −425088. | −0.241381 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.34585e6 | −1.31115 | −0.655575 | − | 0.755130i | \(-0.727573\pi\) | ||||
−0.655575 | + | 0.755130i | \(0.727573\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 424360. | 0.233484 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.04728e6 | 0.567281 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −95064.0 | −0.0507002 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.23858e6 | 1.17561 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 831870. | 0.430216 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.40902e6 | 0.717676 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.11260e6 | −0.558171 | −0.279086 | − | 0.960266i | \(-0.590031\pi\) | ||||
−0.279086 | + | 0.960266i | \(0.590031\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 636822. | 0.314708 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.86206e6 | −0.906527 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.15944e6 | −0.556125 | −0.278063 | − | 0.960563i | \(-0.589692\pi\) | ||||
−0.278063 | + | 0.960563i | \(0.589692\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.00024e6 | 0.472722 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.34346e6 | −1.09137 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.88915e6 | −0.867025 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 390402. | 0.176589 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7724.00 | 0.00344365 | 0.00172182 | − | 0.999999i | \(-0.499452\pi\) | ||||
0.00172182 | + | 0.999999i | \(0.499452\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.99435e6 | 0.876472 | 0.438236 | − | 0.898860i | \(-0.355604\pi\) | ||||
0.438236 | + | 0.898860i | \(0.355604\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 453438. | 0.196449 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −614622. | −0.262525 | −0.131263 | − | 0.991348i | \(-0.541903\pi\) | ||||
−0.131263 | + | 0.991348i | \(0.541903\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.86162e6 | −2.04743 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 268416. | 0.111465 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.56982e6 | 0.642854 | 0.321427 | − | 0.946934i | \(-0.395837\pi\) | ||||
0.321427 | + | 0.946934i | \(0.395837\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.43448e6 | −0.983193 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 78237.0 | 0.0311635 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.80712e6 | 0.709993 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.96092e6 | −0.759967 | −0.379983 | − | 0.924993i | \(-0.624070\pi\) | ||||
−0.379983 | + | 0.924993i | \(0.624070\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 326106. | 0.124679 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 318336. | 0.120075 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.19076e6 | 1.55963 | 0.779813 | − | 0.626012i | \(-0.215314\pi\) | ||||
0.779813 | + | 0.626012i | \(0.215314\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −349812. | −0.128457 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 640660. | 0.232153 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 566236. | 0.202488 | 0.101244 | − | 0.994862i | \(-0.467718\pi\) | ||||
0.101244 | + | 0.994862i | \(0.467718\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.40825e6 | 0.497012 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.50262e6 | 0.871763 | 0.435882 | − | 0.900004i | \(-0.356437\pi\) | ||||
0.435882 | + | 0.900004i | \(0.356437\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.16218e6 | −0.743429 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −530388. | −0.180018 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.25294e6 | 0.754877 | 0.377438 | − | 0.926035i | \(-0.376805\pi\) | ||||
0.377438 | + | 0.926035i | \(0.376805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −246514. | −0.0815454 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.56295e6 | 0.837064 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.02379e6 | 2.26506 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.49513e6 | 1.11298 | 0.556490 | − | 0.830854i | \(-0.312148\pi\) | ||||
0.556490 | + | 0.830854i | \(0.312148\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −117504. | −0.0369505 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.22811e6 | −0.381396 | −0.190698 | − | 0.981649i | \(-0.561075\pi\) | ||||
−0.190698 | + | 0.981649i | \(0.561075\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.53794e6 | −1.08514 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −538002. | −0.162985 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.23914e6 | 0.969269 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.13379e6 | 0.335137 | 0.167569 | − | 0.985860i | \(-0.446408\pi\) | ||||
0.167569 | + | 0.985860i | \(0.446408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.79305e6 | 1.10760 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.30221e6 | −0.664155 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.84620e6 | 1.38128 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.11352e6 | −0.595206 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.81525e6 | 1.06167 | 0.530833 | − | 0.847476i | \(-0.321879\pi\) | ||||
0.530833 | + | 0.847476i | \(0.321879\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.40509e6 | 1.76125 | 0.880624 | − | 0.473817i | \(-0.157124\pi\) | ||||
0.880624 | + | 0.473817i | \(0.157124\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.78330e6 | 0.484588 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.67713e6 | 0.450397 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.14368e6 | 0.303553 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.30638e6 | 0.605044 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.98662e6 | 0.515137 | 0.257568 | − | 0.966260i | \(-0.417079\pi\) | ||||
0.257568 | + | 0.966260i | \(0.417079\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.02181e6 | 0.261909 | 0.130954 | − | 0.991388i | \(-0.458196\pi\) | ||||
0.130954 | + | 0.991388i | \(0.458196\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −760140. | −0.192606 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 107916. | 0.0270323 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −234928. | −0.0581800 | −0.0290900 | − | 0.999577i | \(-0.509261\pi\) | ||||
−0.0290900 | + | 0.999577i | \(0.509261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.02959e6 | −0.252097 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.13954e6 | −0.760075 | −0.380038 | − | 0.924971i | \(-0.624089\pi\) | ||||
−0.380038 | + | 0.924971i | \(0.624089\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.28027e6 | 2.22157 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −206226. | −0.0488174 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.98430e6 | −0.698597 | −0.349299 | − | 0.937011i | \(-0.613580\pi\) | ||||
−0.349299 | + | 0.937011i | \(0.613580\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.65871e6 | 0.383999 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.37434e6 | 0.314664 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.26426e6 | −0.739189 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.83614e6 | 0.635239 | 0.317619 | − | 0.948218i | \(-0.397117\pi\) | ||||
0.317619 | + | 0.948218i | \(0.397117\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 339714. | 0.0752630 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.82111e6 | −0.618256 | −0.309128 | − | 0.951020i | \(-0.600037\pi\) | ||||
−0.309128 | + | 0.951020i | \(0.600037\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50177e6 | 0.542369 | 0.271184 | − | 0.962527i | \(-0.412585\pi\) | ||||
0.271184 | + | 0.962527i | \(0.412585\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.19774e6 | 0.900292 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.37399e6 | 0.715898 | 0.357949 | − | 0.933741i | \(-0.383476\pi\) | ||||
0.357949 | + | 0.933741i | \(0.383476\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.45331e6 | 0.305089 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.95507e6 | 0.406079 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.69778e6 | −0.554438 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −734196. | −0.149306 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 402894. | 0.0810765 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.99102e6 | 0.595636 | 0.297818 | − | 0.954623i | \(-0.403741\pi\) | ||||
0.297818 | + | 0.954623i | \(0.403741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.89016e6 | 0.963742 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −304704. | −0.0594306 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.15312e6 | 1.18779 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.38898e6 | −0.456446 | −0.228223 | − | 0.973609i | \(-0.573292\pi\) | ||||
−0.228223 | + | 0.973609i | \(0.573292\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.45652e6 | −0.275452 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.04552e6 | 0.382912 | 0.191456 | − | 0.981501i | \(-0.438679\pi\) | ||||
0.191456 | + | 0.981501i | \(0.438679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 479980. | 0.0889418 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.73650e6 | −0.501976 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.79443e6 | 0.689058 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −486860. | −0.0875292 | −0.0437646 | − | 0.999042i | \(-0.513935\pi\) | ||||
−0.0437646 | + | 0.999042i | \(0.513935\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.23166e6 | 0.753210 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.60946e6 | −0.636096 | −0.318048 | − | 0.948075i | \(-0.603027\pi\) | ||||
−0.318048 | + | 0.948075i | \(0.603027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.27335e6 | 0.745658 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 140319. | 0.0242436 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.10137e6 | −1.55708 | −0.778542 | − | 0.627592i | \(-0.784041\pi\) | ||||
−0.778542 | + | 0.627592i | \(0.784041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.41043e6 | −0.238946 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −148716. | −0.0249496 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.66653e6 | −0.941454 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.07059e6 | 1.49248 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 181206. | 0.0295294 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.42750e6 | 0.391800 | 0.195900 | − | 0.980624i | \(-0.437237\pi\) | ||||
0.195900 | + | 0.980624i | \(0.437237\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.84472e6 | −0.774488 | −0.387244 | − | 0.921977i | \(-0.626573\pi\) | ||||
−0.387244 | + | 0.921977i | \(0.626573\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.07302e6 | 0.328251 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.65061e6 | −0.415737 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.91373e6 | −0.448449 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.50417e6 | 0.381809 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.54185e6 | −1.44128 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.48002e6 | 0.670416 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.23693e6 | −0.776435 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.35670e6 | 0.199293 | 0.0996463 | − | 0.995023i | \(-0.468229\pi\) | ||||
0.0996463 | + | 0.995023i | \(0.468229\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.27702e6 | −0.331411 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.57926e6 | −1.09304 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.35672e6 | 1.33707 | 0.668537 | − | 0.743679i | \(-0.266921\pi\) | ||||
0.668537 | + | 0.743679i | \(0.266921\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.44747e6 | 0.204965 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −210120. | −0.0294841 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.48198e6 | −0.762298 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.80216e6 | −0.799571 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −483498. | −0.0660323 | −0.0330162 | − | 0.999455i | \(-0.510511\pi\) | ||||
−0.0330162 | + | 0.999455i | \(0.510511\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.07286e6 | −0.551277 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.72793e6 | 0.231803 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26916.0 | 0.00357882 | 0.00178941 | − | 0.999998i | \(-0.499430\pi\) | ||||
0.00178941 | + | 0.999998i | \(0.499430\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.11332e6 | −1.20103 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 419904. | 0.0548520 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.43231e6 | 0.444433 | 0.222217 | − | 0.974997i | \(-0.428671\pi\) | ||||
0.222217 | + | 0.974997i | \(0.428671\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.89055e6 | −1.26949 | −0.634746 | − | 0.772721i | \(-0.718895\pi\) | ||||
−0.634746 | + | 0.772721i | \(0.718895\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.82666e6 | 0.486892 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.90387e6 | −0.240142 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.31833e6 | −1.04015 | −0.520076 | − | 0.854120i | \(-0.674096\pi\) | ||||
−0.520076 | + | 0.854120i | \(0.674096\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.98939e6 | 0.494550 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.78240e6 | −0.464865 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.04929e6 | 0.249708 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.13132e6 | −0.499114 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.13469e7 | 1.35919 | 0.679597 | − | 0.733585i | \(-0.262155\pi\) | ||||
0.679597 | + | 0.733585i | \(0.262155\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.16035e6 | 0.137817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 859518. | 0.101225 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.18069e6 | −1.07211 | −0.536054 | − | 0.844184i | \(-0.680086\pi\) | ||||
−0.536054 | + | 0.844184i | \(0.680086\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.44557e6 | −0.283196 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.61778e6 | 0.300605 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.72775e6 | 0.652255 | 0.326127 | − | 0.945326i | \(-0.394256\pi\) | ||||
0.326127 | + | 0.945326i | \(0.394256\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.63309e6 | −0.410290 | −0.205145 | − | 0.978732i | \(-0.565767\pi\) | ||||
−0.205145 | + | 0.978732i | \(0.565767\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.83935e6 | 0.206002 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −712826. | −0.0791763 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.50751e7 | 1.66069 | 0.830343 | − | 0.557253i | \(-0.188145\pi\) | ||||
0.830343 | + | 0.557253i | \(0.188145\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 593280. | 0.0648211 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.36940e7 | 1.48397 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.32798e7 | −1.42739 | −0.713694 | − | 0.700458i | \(-0.752979\pi\) | ||||
−0.713694 | + | 0.700458i | \(0.752979\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.97119e6 | −0.316769 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.67978e6 | −1.02365 | −0.511826 | − | 0.859089i | \(-0.671031\pi\) | ||||
−0.511826 | + | 0.859089i | \(0.671031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.44042e6 | −0.885396 | −0.442698 | − | 0.896671i | \(-0.645979\pi\) | ||||
−0.442698 | + | 0.896671i | \(0.645979\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −385641. | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.24314e6 | −0.747664 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.05970e6 | −0.825313 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −756432. | −0.0768424 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.66369e6 | 0.369226 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.29554e6 | −0.429481 | −0.214741 | − | 0.976671i | \(-0.568891\pi\) | ||||
−0.214741 | + | 0.976671i | \(0.568891\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.67730e6 | 0.463966 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.28307e7 | −1.26275 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.90624e6 | −0.772008 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.80233e6 | 0.465264 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.36288e6 | 0.419400 | 0.209700 | − | 0.977766i | \(-0.432751\pi\) | ||||
0.209700 | + | 0.977766i | \(0.432751\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.22816e7 | 1.17146 | 0.585732 | − | 0.810505i | \(-0.300807\pi\) | ||||
0.585732 | + | 0.810505i | \(0.300807\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.83242e6 | 0.457368 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.17133e7 | 1.10007 | 0.550034 | − | 0.835142i | \(-0.314615\pi\) | ||||
0.550034 | + | 0.835142i | \(0.314615\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.48205e7 | −1.38118 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.27629e6 | −0.302991 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.92255e7 | −1.76439 | −0.882197 | − | 0.470881i | \(-0.843936\pi\) | ||||
−0.882197 | + | 0.470881i | \(0.843936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.33513e7 | −2.12671 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.78508e6 | −0.161341 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.11372e7 | 0.998991 | 0.499495 | − | 0.866317i | \(-0.333519\pi\) | ||||
0.499495 | + | 0.866317i | \(0.333519\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.07766e6 | −0.184957 | −0.0924784 | − | 0.995715i | \(-0.529479\pi\) | ||||
−0.0924784 | + | 0.995715i | \(0.529479\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.60867e6 | 0.230481 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.07059e6 | 0.0938793 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −544870. | −0.0474218 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.95010e6 | 0.773148 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.36244e6 | 0.631270 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.18233e7 | −1.00624 | −0.503120 | − | 0.864216i | \(-0.667815\pi\) | ||||
−0.503120 | + | 0.864216i | \(0.667815\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.62367e6 | 0.221641 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 194414. | 0.0163026 | 0.00815128 | − | 0.999967i | \(-0.497405\pi\) | ||||
0.00815128 | + | 0.999967i | \(0.497405\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.80243e6 | −0.399748 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.71503e6 | 0.389598 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.15464e7 | 0.947100 | 0.473550 | − | 0.880767i | \(-0.342972\pi\) | ||||
0.473550 | + | 0.880767i | \(0.342972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.45589e7 | −2.81406 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.95425e6 | −0.238812 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.09383e6 | 0.248284 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.43088e6 | −0.353016 | −0.176508 | − | 0.984299i | \(-0.556480\pi\) | ||||
−0.176508 | + | 0.984299i | \(0.556480\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.13581e6 | 0.168939 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.92566e7 | 1.51223 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.87612e6 | 0.146278 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.50700e6 | 0.348895 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.27278e7 | −0.978270 | −0.489135 | − | 0.872208i | \(-0.662688\pi\) | ||||
−0.489135 | + | 0.872208i | \(0.662688\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.60385e6 | −0.122398 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.62478e7 | −1.23118 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.33530e6 | −0.250949 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.15842e7 | −0.865463 | −0.432732 | − | 0.901523i | \(-0.642450\pi\) | ||||
−0.432732 | + | 0.901523i | \(0.642450\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.93814e6 | −0.514717 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.00895e6 | 0.221662 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.10136e7 | −1.53722 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.78030e6 | 0.419907 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.56016e6 | −0.545392 | −0.272696 | − | 0.962100i | \(-0.587915\pi\) | ||||
−0.272696 | + | 0.962100i | \(0.587915\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.42266e6 | 0.316844 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.80339e6 | −0.341745 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.70697e6 | 0.261923 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.64277e7 | 1.15276 | 0.576381 | − | 0.817181i | \(-0.304464\pi\) | ||||
0.576381 | + | 0.817181i | \(0.304464\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.05137e6 | −0.211204 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.91447e6 | −0.612823 | −0.306412 | − | 0.951899i | \(-0.599128\pi\) | ||||
−0.306412 | + | 0.951899i | \(0.599128\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.38072e6 | 0.640498 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.35570e6 | 0.634465 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.68060e6 | −0.382634 | −0.191317 | − | 0.981528i | \(-0.561276\pi\) | ||||
−0.191317 | + | 0.981528i | \(0.561276\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.14199e6 | −0.0764043 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.20087e7 | 1.46259 | 0.731296 | − | 0.682060i | \(-0.238916\pi\) | ||||
0.731296 | + | 0.682060i | \(0.238916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.87895e6 | 0.124029 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.78710e6 | −0.313885 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.44730e6 | 0.485058 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.06320e7 | 0.687882 | 0.343941 | − | 0.938991i | \(-0.388238\pi\) | ||||
0.343941 | + | 0.938991i | \(0.388238\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.59208e7 | −1.02324 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.25217e7 | −0.799460 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.53289e7 | −1.60648 | −0.803242 | − | 0.595653i | \(-0.796893\pi\) | ||||
−0.803242 | + | 0.595653i | \(0.796893\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.96153e6 | −0.123592 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.51699e7 | −0.949558 | −0.474779 | − | 0.880105i | \(-0.657472\pi\) | ||||
−0.474779 | + | 0.880105i | \(0.657472\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.91552e6 | 0.367859 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.09517e6 | −0.191219 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.23746e7 | −1.37330 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.33459e6 | 0.0813829 | 0.0406915 | − | 0.999172i | \(-0.487044\pi\) | ||||
0.0406915 | + | 0.999172i | \(0.487044\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.30504e7 | 0.790660 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.45025e7 | 0.872957 | 0.436479 | − | 0.899715i | \(-0.356225\pi\) | ||||
0.436479 | + | 0.899715i | \(0.356225\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.04711e7 | −1.22430 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.52851e6 | 0.269093 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −821304. | −0.0484909 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.44267e7 | 1.43297 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 750870. | 0.0437684 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.78129e7 | −1.03171 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.05487e7 | 1.18263 | 0.591313 | − | 0.806442i | \(-0.298610\pi\) | ||||
0.591313 | + | 0.806442i | \(0.298610\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.02998e7 | 0.589029 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.11283e6 | 0.404205 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.11151e7 | 0.627671 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.67081e6 | −0.205989 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.90155e7 | −1.61802 | −0.809010 | − | 0.587795i | \(-0.799996\pi\) | ||||
−0.809010 | + | 0.587795i | \(0.799996\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.02595e7 | 0.568535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.16709e6 | −0.504836 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.07966e6 | −0.496913 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.77619e6 | 0.150994 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.91945e6 | −0.482119 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.91739e7 | 1.56720 | 0.783599 | − | 0.621267i | \(-0.213382\pi\) | ||||
0.783599 | + | 0.621267i | \(0.213382\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.92976e7 | −1.56415 | −0.782077 | − | 0.623182i | \(-0.785840\pi\) | ||||
−0.782077 | + | 0.623182i | \(0.785840\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.43447e6 | 0.182236 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.32706e7 | 0.699834 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.33579e6 | 0.0700138 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.22445e6 | 0.167975 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.24240e6 | −0.374994 | −0.187497 | − | 0.982265i | \(-0.560038\pi\) | ||||
−0.187497 | + | 0.982265i | \(0.560038\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −186400. | −0.00959282 | −0.00479641 | − | 0.999988i | \(-0.501527\pi\) | ||||
−0.00479641 | + | 0.999988i | \(0.501527\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.33451e7 | 0.682632 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.13311e7 | 0.576115 | 0.288058 | − | 0.957613i | \(-0.406990\pi\) | ||||
0.288058 | + | 0.957613i | \(0.406990\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.18438e6 | 0.160931 | 0.0804653 | − | 0.996757i | \(-0.474359\pi\) | ||||
0.0804653 | + | 0.996757i | \(0.474359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.40028e6 | −0.120576 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.92333e6 | −0.295769 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.85551e7 | −1.91366 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.14655e6 | −0.204585 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.59730e7 | −0.783398 | −0.391699 | − | 0.920093i | \(-0.628113\pi\) | ||||
−0.391699 | + | 0.920093i | \(0.628113\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.94502e7 | −0.948277 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.73158e7 | 0.839216 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.27846e6 | −0.0615951 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 556352. | 0.0266466 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.44834e7 | −0.689607 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.15900e6 | −0.196863 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.41773e7 | 0.667147 | 0.333573 | − | 0.942724i | \(-0.391745\pi\) | ||||
0.333573 | + | 0.942724i | \(0.391745\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.35497e6 | 0.0633890 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.83069e7 | 1.78166 | 0.890829 | − | 0.454338i | \(-0.150124\pi\) | ||||
0.890829 | + | 0.454338i | \(0.150124\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.77458e6 | −0.359496 | −0.179748 | − | 0.983713i | \(-0.557528\pi\) | ||||
−0.179748 | + | 0.983713i | \(0.557528\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.31898e6 | 0.106608 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.94086e6 | 0.134415 | 0.0672075 | − | 0.997739i | \(-0.478591\pi\) | ||||
0.0672075 | + | 0.997739i | \(0.478591\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.65099e6 | −0.0750246 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.08243e7 | −0.489049 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.52903e7 | −1.58528 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.41244e7 | 0.630847 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.07808e6 | −0.269917 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.48755e6 | −0.109838 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.03135e7 | −1.33088 | −0.665438 | − | 0.746453i | \(-0.731755\pi\) | ||||
−0.665438 | + | 0.746453i | \(0.731755\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −164466. | −0.00717966 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.47840e7 | 1.07580 | 0.537900 | − | 0.843009i | \(-0.319218\pi\) | ||||
0.537900 | + | 0.843009i | \(0.319218\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.88604e6 | −0.426698 | −0.213349 | − | 0.976976i | \(-0.568437\pi\) | ||||
−0.213349 | + | 0.976976i | \(0.568437\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.65473e7 | 1.13936 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.57903e7 | 0.673878 | 0.336939 | − | 0.941526i | \(-0.390608\pi\) | ||||
0.336939 | + | 0.941526i | \(0.390608\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00142e7 | 0.424974 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.70313e6 | 0.114070 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.49126e6 | −0.188469 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.08180e7 | −1.70331 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.96134e6 | −0.122887 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.85864e6 | −0.241767 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.31788e6 | 0.0951217 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.77165e6 | −0.153926 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.07462e7 | 0.842008 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.75470e7 | 0.708245 | 0.354123 | − | 0.935199i | \(-0.384780\pi\) | ||||
0.354123 | + | 0.935199i | \(0.384780\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.22123e6 | −0.169445 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.62301e7 | 1.04714 | 0.523570 | − | 0.851983i | \(-0.324600\pi\) | ||||
0.523570 | + | 0.851983i | \(0.324600\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.43492e7 | −0.966736 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.31881e7 | −0.520749 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.82254e7 | 0.715738 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.35236e7 | −0.528208 | −0.264104 | − | 0.964494i | \(-0.585076\pi\) | ||||
−0.264104 | + | 0.964494i | \(0.585076\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.69800e6 | 0.376733 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.68771e7 | 1.42480 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.82953e7 | 1.08733 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.59742e6 | 0.213938 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15406.0 | −0.000585667 0 | −0.000292833 | − | 1.00000i | \(-0.500093\pi\) | ||||
−0.000292833 | 1.00000i | \(0.500093\pi\) | ||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.59304e6 | 0.0980473 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.47370e7 | −0.554250 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.57433e7 | −0.588936 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.41659e6 | 0.0527101 | 0.0263551 | − | 0.999653i | \(-0.491610\pi\) | ||||
0.0263551 | + | 0.999653i | \(0.491610\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.83982e7 | 1.05106 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.08997e7 | −0.401273 | −0.200637 | − | 0.979666i | \(-0.564301\pi\) | ||||
−0.200637 | + | 0.979666i | \(0.564301\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.12975e6 | −0.0779920 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.82579e6 | −0.139361 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.53470e7 | −0.918440 | −0.459220 | − | 0.888323i | \(-0.651871\pi\) | ||||
−0.459220 | + | 0.888323i | \(0.651871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.37076e7 | −0.494080 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.11126e7 | −0.756992 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.28501e7 | −1.88501 | −0.942504 | − | 0.334195i | \(-0.891536\pi\) | ||||
−0.942504 | + | 0.334195i | \(0.891536\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.48651e7 | −1.23704 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.81924e6 | 0.134802 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.69728e7 | 0.947064 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.72419e6 | 0.130084 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.42548e6 | 0.327520 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.63478e7 | −1.25649 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.77261e6 | 0.301691 | 0.150846 | − | 0.988557i | \(-0.451800\pi\) | ||||
0.150846 | + | 0.988557i | \(0.451800\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −855576. | −0.0292718 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.53929e7 | 0.864300 | 0.432150 | − | 0.901802i | \(-0.357755\pi\) | ||||
0.432150 | + | 0.901802i | \(0.357755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.50295e7 | −0.508935 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.01472e7 | 0.678740 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.23118e7 | 1.41816 | 0.709080 | − | 0.705128i | \(-0.249110\pi\) | ||||
0.709080 | + | 0.705128i | \(0.249110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.66277e7 | −1.55485 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.48683e6 | 0.248385 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.26108e6 | 0.272680 | 0.136340 | − | 0.990662i | \(-0.456466\pi\) | ||||
0.136340 | + | 0.990662i | \(0.456466\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.83116e6 | −0.257179 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.26812e7 | 0.414351 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.46389e6 | 0.112609 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.90652e6 | −0.288087 | −0.144044 | − | 0.989571i | \(-0.546011\pi\) | ||||
−0.144044 | + | 0.989571i | \(0.546011\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.00134e7 | −0.322260 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.38508e7 | −0.763741 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.05454e7 | −0.654603 | −0.327301 | − | 0.944920i | \(-0.606139\pi\) | ||||
−0.327301 | + | 0.944920i | \(0.606139\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.73140e6 | 0.181697 |
(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 | 1104.6.a.b.1.1 | 1 | ||
4.3 | odd | 2 | 552.6.a.a.1.1 | ✓ | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.6.a.a.1.1 | ✓ | 1 | 4.3 | odd | 2 | ||
1104.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial |