Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,6,Mod(1,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, 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("720.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.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: | \(115.476350265\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 720.1 |
$q$-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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 22.0000 | 0.169698 | 0.0848492 | − | 0.996394i | \(-0.472959\pi\) | ||||
0.0848492 | + | 0.996394i | \(0.472959\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −768.000 | −1.91372 | −0.956862 | − | 0.290541i | \(-0.906165\pi\) | ||||
−0.956862 | + | 0.290541i | \(0.906165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −46.0000 | −0.0754917 | −0.0377459 | − | 0.999287i | \(-0.512018\pi\) | ||||
−0.0377459 | + | 0.999287i | \(0.512018\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −378.000 | −0.317227 | −0.158613 | − | 0.987341i | \(-0.550702\pi\) | ||||
−0.158613 | + | 0.987341i | \(0.550702\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1100.00 | −0.699051 | −0.349525 | − | 0.936927i | \(-0.613657\pi\) | ||||
−0.349525 | + | 0.936927i | \(0.613657\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1986.00 | −0.782816 | −0.391408 | − | 0.920217i | \(-0.628012\pi\) | ||||
−0.391408 | + | 0.920217i | \(0.628012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5610.00 | 1.23870 | 0.619352 | − | 0.785113i | \(-0.287395\pi\) | ||||
0.619352 | + | 0.785113i | \(0.287395\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3988.00 | 0.745334 | 0.372667 | − | 0.927965i | \(-0.378443\pi\) | ||||
0.372667 | + | 0.927965i | \(0.378443\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 550.000 | 0.0758914 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −142.000 | −0.0170523 | −0.00852617 | − | 0.999964i | \(-0.502714\pi\) | ||||
−0.00852617 | + | 0.999964i | \(0.502714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1542.00 | −0.143260 | −0.0716300 | − | 0.997431i | \(-0.522820\pi\) | ||||
−0.0716300 | + | 0.997431i | \(0.522820\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5026.00 | 0.414526 | 0.207263 | − | 0.978285i | \(-0.433544\pi\) | ||||
0.207263 | + | 0.978285i | \(0.433544\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 24738.0 | 1.63350 | 0.816752 | − | 0.576990i | \(-0.195773\pi\) | ||||
0.816752 | + | 0.576990i | \(0.195773\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16323.0 | −0.971202 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 14166.0 | 0.692720 | 0.346360 | − | 0.938102i | \(-0.387418\pi\) | ||||
0.346360 | + | 0.938102i | \(0.387418\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19200.0 | −0.855844 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 28380.0 | 1.06141 | 0.530704 | − | 0.847557i | \(-0.321928\pi\) | ||||
0.530704 | + | 0.847557i | \(0.321928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5522.00 | 0.190008 | 0.0950040 | − | 0.995477i | \(-0.469714\pi\) | ||||
0.0950040 | + | 0.995477i | \(0.469714\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1150.00 | −0.0337609 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 24742.0 | 0.673361 | 0.336680 | − | 0.941619i | \(-0.390696\pi\) | ||||
0.336680 | + | 0.941619i | \(0.390696\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42372.0 | 0.997546 | 0.498773 | − | 0.866733i | \(-0.333784\pi\) | ||||
0.498773 | + | 0.866733i | \(0.333784\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −52126.0 | −1.14485 | −0.572423 | − | 0.819958i | \(-0.693997\pi\) | ||||
−0.572423 | + | 0.819958i | \(0.693997\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16896.0 | −0.324756 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39640.0 | 0.714605 | 0.357302 | − | 0.933989i | \(-0.383697\pi\) | ||||
0.357302 | + | 0.933989i | \(0.383697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −59826.0 | −0.953223 | −0.476612 | − | 0.879114i | \(-0.658135\pi\) | ||||
−0.476612 | + | 0.879114i | \(0.658135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9450.00 | −0.141868 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −57690.0 | −0.772015 | −0.386007 | − | 0.922496i | \(-0.626146\pi\) | ||||
−0.386007 | + | 0.922496i | \(0.626146\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1012.00 | −0.0128108 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −27500.0 | −0.312625 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −144382. | −1.55806 | −0.779029 | − | 0.626988i | \(-0.784288\pi\) | ||||
−0.779029 | + | 0.626988i | \(0.784288\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 141258. | 1.37787 | 0.688937 | − | 0.724821i | \(-0.258078\pi\) | ||||
0.688937 | + | 0.724821i | \(0.258078\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −139814. | −1.29855 | −0.649273 | − | 0.760555i | \(-0.724927\pi\) | ||||
−0.649273 | + | 0.760555i | \(0.724927\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 86418.0 | 0.729701 | 0.364850 | − | 0.931066i | \(-0.381120\pi\) | ||||
0.364850 | + | 0.931066i | \(0.381120\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 218450. | 1.76111 | 0.880554 | − | 0.473947i | \(-0.157171\pi\) | ||||
0.880554 | + | 0.473947i | \(0.157171\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 28806.0 | 0.212220 | 0.106110 | − | 0.994354i | \(-0.466160\pi\) | ||||
0.106110 | + | 0.994354i | \(0.466160\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −49650.0 | −0.350086 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8316.00 | −0.0538328 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 428773. | 2.66234 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 216502. | 1.19111 | 0.595556 | − | 0.803314i | \(-0.296932\pi\) | ||||
0.595556 | + | 0.803314i | \(0.296932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −244608. | −1.24535 | −0.622676 | − | 0.782479i | \(-0.713955\pi\) | ||||
−0.622676 | + | 0.782479i | \(0.713955\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24200.0 | −0.118628 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 239502. | 1.09020 | 0.545102 | − | 0.838370i | \(-0.316491\pi\) | ||||
0.545102 | + | 0.838370i | \(0.316491\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −30860.0 | −0.135475 | −0.0677375 | − | 0.997703i | \(-0.521578\pi\) | ||||
−0.0677375 | + | 0.997703i | \(0.521578\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 35328.0 | 0.144470 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 140250. | 0.553966 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 100950. | 0.372512 | 0.186256 | − | 0.982501i | \(-0.440365\pi\) | ||||
0.186256 | + | 0.982501i | \(0.440365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12452.0 | −0.0444423 | −0.0222212 | − | 0.999753i | \(-0.507074\pi\) | ||||
−0.0222212 | + | 0.999753i | \(0.507074\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 99700.0 | 0.333323 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6022.00 | −0.0194981 | −0.00974903 | − | 0.999952i | \(-0.503103\pi\) | ||||
−0.00974903 | + | 0.999952i | \(0.503103\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −43692.0 | −0.132843 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 500866. | 1.47656 | 0.738282 | − | 0.674492i | \(-0.235637\pi\) | ||||
0.738282 | + | 0.674492i | \(0.235637\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 555258. | 1.54065 | 0.770324 | − | 0.637652i | \(-0.220094\pi\) | ||||
0.770324 | + | 0.637652i | \(0.220094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −369177. | −0.994301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −417354. | −1.06020 | −0.530102 | − | 0.847934i | \(-0.677846\pi\) | ||||
−0.530102 | + | 0.847934i | \(0.677846\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13750.0 | 0.0339397 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −52380.0 | −0.122189 | −0.0610946 | − | 0.998132i | \(-0.519459\pi\) | ||||
−0.0610946 | + | 0.998132i | \(0.519459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 546662. | 1.24029 | 0.620144 | − | 0.784488i | \(-0.287074\pi\) | ||||
0.620144 | + | 0.784488i | \(0.287074\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3550.00 | −0.00762604 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 290304. | 0.607084 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −452028. | −0.896565 | −0.448283 | − | 0.893892i | \(-0.647964\pi\) | ||||
−0.448283 | + | 0.893892i | \(0.647964\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 485594. | 0.938383 | 0.469191 | − | 0.883097i | \(-0.344545\pi\) | ||||
0.469191 | + | 0.883097i | \(0.344545\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.01018e6 | −1.85452 | −0.927262 | − | 0.374414i | \(-0.877844\pi\) | ||||
−0.927262 | + | 0.374414i | \(0.877844\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 807640. | 1.44572 | 0.722862 | − | 0.690993i | \(-0.242826\pi\) | ||||
0.722862 | + | 0.690993i | \(0.242826\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 123420. | 0.210206 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −38550.0 | −0.0640678 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 844800. | 1.33779 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −149552. | −0.231252 | −0.115626 | − | 0.993293i | \(-0.536887\pi\) | ||||
−0.115626 | + | 0.993293i | \(0.536887\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 125650. | 0.185381 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 87736.0 | 0.126482 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17388.0 | 0.0239480 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 443506. | 0.597224 | 0.298612 | − | 0.954375i | \(-0.403476\pi\) | ||||
0.298612 | + | 0.954375i | \(0.403476\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 420018. | 0.541007 | 0.270504 | − | 0.962719i | \(-0.412810\pi\) | ||||
0.270504 | + | 0.962719i | \(0.412810\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.05875e6 | 1.33415 | 0.667075 | − | 0.744990i | \(-0.267546\pi\) | ||||
0.667075 | + | 0.744990i | \(0.267546\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.27345e6 | 1.53671 | 0.768353 | − | 0.640026i | \(-0.221077\pi\) | ||||
0.768353 | + | 0.640026i | \(0.221077\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 618450. | 0.730525 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −370680. | −0.419763 | −0.209882 | − | 0.977727i | \(-0.567308\pi\) | ||||
−0.209882 | + | 0.977727i | \(0.567308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −561298. | −0.622517 | −0.311258 | − | 0.950325i | \(-0.600750\pi\) | ||||
−0.311258 | + | 0.950325i | \(0.600750\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −408075. | −0.434335 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 50600.0 | 0.0527726 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 577152. | 0.578237 | 0.289119 | − | 0.957293i | \(-0.406638\pi\) | ||||
0.289119 | + | 0.957293i | \(0.406638\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.52525e6 | 1.49809 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 651462. | 0.615257 | 0.307628 | − | 0.951507i | \(-0.400465\pi\) | ||||
0.307628 | + | 0.951507i | \(0.400465\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3124.00 | −0.00289375 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 917574. | 0.817997 | 0.408999 | − | 0.912535i | \(-0.365878\pi\) | ||||
0.408999 | + | 0.912535i | \(0.365878\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 354150. | 0.309794 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 735390. | 0.619637 | 0.309818 | − | 0.950796i | \(-0.399732\pi\) | ||||
0.309818 | + | 0.950796i | \(0.399732\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.12131e6 | 0.927474 | 0.463737 | − | 0.885973i | \(-0.346508\pi\) | ||||
0.463737 | + | 0.885973i | \(0.346508\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −480000. | −0.382745 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.66034e6 | −1.30016 | −0.650082 | − | 0.759864i | \(-0.725265\pi\) | ||||
−0.650082 | + | 0.759864i | \(0.725265\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.45210e6 | −1.09706 | −0.548531 | − | 0.836130i | \(-0.684813\pi\) | ||||
−0.548531 | + | 0.836130i | \(0.684813\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −309014. | −0.229357 | −0.114679 | − | 0.993403i | \(-0.536584\pi\) | ||||
−0.114679 | + | 0.993403i | \(0.536584\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −33924.0 | −0.0243110 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.27697e6 | −0.899367 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.59301e6 | 1.08405 | 0.542024 | − | 0.840363i | \(-0.317658\pi\) | ||||
0.542024 | + | 0.840363i | \(0.317658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 709500. | 0.474676 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 91356.0 | 0.0590961 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 110572. | 0.0703443 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 138050. | 0.0849741 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.24726e6 | −0.755284 | −0.377642 | − | 0.925952i | \(-0.623265\pi\) | ||||
−0.377642 | + | 0.925952i | \(0.623265\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −665988. | −0.390450 | −0.195225 | − | 0.980758i | \(-0.562544\pi\) | ||||
−0.195225 | + | 0.980758i | \(0.562544\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −591286. | −0.341143 | −0.170572 | − | 0.985345i | \(-0.554561\pi\) | ||||
−0.170572 | + | 0.985345i | \(0.554561\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 516342. | 0.288595 | 0.144298 | − | 0.989534i | \(-0.453908\pi\) | ||||
0.144298 | + | 0.989534i | \(0.453908\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.30848e6 | −2.37054 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 415800. | 0.221757 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −28750.0 | −0.0150983 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 544236. | 0.277203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.29577e6 | 1.65343 | 0.826717 | − | 0.562619i | \(-0.190206\pi\) | ||||
0.826717 | + | 0.562619i | \(0.190206\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 618550. | 0.301136 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.91098e6 | 0.916602 | 0.458301 | − | 0.888797i | \(-0.348458\pi\) | ||||
0.458301 | + | 0.888797i | \(0.348458\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.06278e6 | −1.42636 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −728860. | −0.334510 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.42006e6 | 1.07895 | 0.539476 | − | 0.842001i | \(-0.318622\pi\) | ||||
0.539476 | + | 0.842001i | \(0.318622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.50727e6 | 1.10189 | 0.550944 | − | 0.834542i | \(-0.314268\pi\) | ||||
0.550944 | + | 0.834542i | \(0.314268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 413166. | 0.176477 | 0.0882384 | − | 0.996099i | \(-0.471876\pi\) | ||||
0.0882384 | + | 0.996099i | \(0.471876\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.05930e6 | 0.446116 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.73772e6 | 0.711613 | 0.355806 | − | 0.934560i | \(-0.384206\pi\) | ||||
0.355806 | + | 0.934560i | \(0.384206\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.26610e6 | −0.511328 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.30315e6 | −0.511991 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.16098e6 | −0.449944 | −0.224972 | − | 0.974365i | \(-0.572229\pi\) | ||||
−0.224972 | + | 0.974365i | \(0.572229\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 311652. | 0.117553 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 343754. | 0.127931 | 0.0639655 | − | 0.997952i | \(-0.479625\pi\) | ||||
0.0639655 | + | 0.997952i | \(0.479625\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −258060. | −0.0935120 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −573140. | −0.204957 | −0.102478 | − | 0.994735i | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.88055e6 | −1.00341 | −0.501704 | − | 0.865039i | \(-0.667293\pi\) | ||||
−0.501704 | + | 0.865039i | \(0.667293\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −422400. | −0.145235 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.08559e6 | 1.03387 | 0.516933 | − | 0.856026i | \(-0.327074\pi\) | ||||
0.516933 | + | 0.856026i | \(0.327074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 750708. | 0.248330 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 991000. | 0.319581 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 885458. | 0.281963 | 0.140981 | − | 0.990012i | \(-0.454974\pi\) | ||||
0.140981 | + | 0.990012i | \(0.454974\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.75344e6 | 1.16565 | 0.582825 | − | 0.812598i | \(-0.301947\pi\) | ||||
0.582825 | + | 0.812598i | \(0.301947\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −183448. | −0.0562666 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 109056. | 0.0326335 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.94653e6 | −0.575377 | −0.287689 | − | 0.957724i | \(-0.592887\pi\) | ||||
−0.287689 | + | 0.957724i | \(0.592887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 624360. | 0.180119 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.49565e6 | −0.426295 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.99166e6 | −0.832486 | −0.416243 | − | 0.909253i | \(-0.636654\pi\) | ||||
−0.416243 | + | 0.909253i | \(0.636654\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.96660e6 | 1.09072 | 0.545360 | − | 0.838202i | \(-0.316393\pi\) | ||||
0.545360 | + | 0.838202i | \(0.316393\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −236250. | −0.0634453 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 121484. | 0.0322440 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.17115e6 | −1.34089 | −0.670446 | − | 0.741958i | \(-0.733897\pi\) | ||||
−0.670446 | + | 0.741958i | \(0.733897\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.53485e6 | −1.16237 | −0.581183 | − | 0.813773i | \(-0.697410\pi\) | ||||
−0.581183 | + | 0.813773i | \(0.697410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.18460e6 | 0.547228 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.08220e6 | 0.268007 | 0.134004 | − | 0.990981i | \(-0.457217\pi\) | ||||
0.134004 | + | 0.990981i | \(0.457217\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.08079e6 | −0.261656 | −0.130828 | − | 0.991405i | \(-0.541764\pi\) | ||||
−0.130828 | + | 0.991405i | \(0.541764\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.44225e6 | −0.345255 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.61783e6 | −0.612810 | −0.306405 | − | 0.951901i | \(-0.599126\pi\) | ||||
−0.306405 | + | 0.951901i | \(0.599126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.18426e6 | 0.274160 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −25300.0 | −0.00572917 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.59046e6 | 0.356231 | 0.178115 | − | 0.984010i | \(-0.443000\pi\) | ||||
0.178115 | + | 0.984010i | \(0.443000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.25470e6 | −0.932431 | −0.466216 | − | 0.884671i | \(-0.654383\pi\) | ||||
−0.466216 | + | 0.884671i | \(0.654383\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.26605e6 | −0.708061 | −0.354031 | − | 0.935234i | \(-0.615189\pi\) | ||||
−0.354031 | + | 0.935234i | \(0.615189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −601542. | −0.127636 | −0.0638181 | − | 0.997962i | \(-0.520328\pi\) | ||||
−0.0638181 | + | 0.997962i | \(0.520328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 544324. | 0.114268 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.85997e6 | −0.793288 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −687500. | −0.139810 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.57932e6 | −0.911931 | −0.455966 | − | 0.889997i | \(-0.650706\pi\) | ||||
−0.455966 | + | 0.889997i | \(0.650706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6532.00 | 0.00128731 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.60955e6 | −0.696785 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.05226e6 | −1.34743 | −0.673714 | − | 0.738992i | \(-0.735302\pi\) | ||||
−0.673714 | + | 0.738992i | \(0.735302\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.62349e6 | −0.491106 | −0.245553 | − | 0.969383i | \(-0.578970\pi\) | ||||
−0.245553 | + | 0.969383i | \(0.578970\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.12058e6 | −0.392950 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 932184. | 0.169282 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.61234e6 | 0.649437 | 0.324719 | − | 0.945811i | \(-0.394730\pi\) | ||||
0.324719 | + | 0.945811i | \(0.394730\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.15629e6 | 1.61361 | 0.806807 | − | 0.590815i | \(-0.201194\pi\) | ||||
0.806807 | + | 0.590815i | \(0.201194\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.53145e6 | 0.616204 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.26159e6 | −1.24233 | −0.621165 | − | 0.783679i | \(-0.713340\pi\) | ||||
−0.621165 | + | 0.783679i | \(0.713340\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.14677e6 | −0.194279 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.49535e6 | −0.580728 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.89988e7 | −3.12608 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.81020e6 | −0.937771 | −0.468886 | − | 0.883259i | \(-0.655344\pi\) | ||||
−0.468886 | + | 0.883259i | \(0.655344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.17067e6 | 1.30618 | 0.653090 | − | 0.757280i | \(-0.273472\pi\) | ||||
0.653090 | + | 0.757280i | \(0.273472\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.50746e6 | −0.236440 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.49215e6 | −0.387199 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 70932.0 | 0.0108149 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.16045e6 | 0.326332 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.25361e7 | 1.85861 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −817378. | −0.120069 | −0.0600343 | − | 0.998196i | \(-0.519121\pi\) | ||||
−0.0600343 | + | 0.998196i | \(0.519121\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.46125e6 | 0.787591 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.50750e6 | 0.501221 | 0.250611 | − | 0.968088i | \(-0.419369\pi\) | ||||
0.250611 | + | 0.968088i | \(0.419369\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.17100e6 | −0.865918 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 872080. | 0.121267 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.61490e6 | −1.31313 | −0.656563 | − | 0.754271i | \(-0.727991\pi\) | ||||
−0.656563 | + | 0.754271i | \(0.727991\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −231196. | −0.0312933 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.01941e6 | 0.268506 | 0.134253 | − | 0.990947i | \(-0.457136\pi\) | ||||
0.134253 | + | 0.990947i | \(0.457136\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 720150. | 0.0949078 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.37859e6 | −0.178507 | −0.0892533 | − | 0.996009i | \(-0.528448\pi\) | ||||
−0.0892533 | + | 0.996009i | \(0.528448\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.54295e6 | −1.09652 | −0.548261 | − | 0.836307i | \(-0.684710\pi\) | ||||
−0.548261 | + | 0.836307i | \(0.684710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.24125e6 | −0.156563 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.31458e6 | −0.289423 | −0.144711 | − | 0.989474i | \(-0.546225\pi\) | ||||
−0.144711 | + | 0.989474i | \(0.546225\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.31617e6 | −0.161760 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.08795e7 | −1.32568 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 928338. | 0.111202 | 0.0556008 | − | 0.998453i | \(-0.482293\pi\) | ||||
0.0556008 | + | 0.998453i | \(0.482293\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.38680e6 | −0.521026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 909486. | 0.106209 | 0.0531043 | − | 0.998589i | \(-0.483088\pi\) | ||||
0.0531043 | + | 0.998589i | \(0.483088\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −207900. | −0.0240748 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.51136e6 | −0.969241 | −0.484621 | − | 0.874724i | \(-0.661042\pi\) | ||||
−0.484621 | + | 0.874724i | \(0.661042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.12498e6 | 0.691701 | 0.345851 | − | 0.938290i | \(-0.387590\pi\) | ||||
0.345851 | + | 0.938290i | \(0.387590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.07193e7 | 1.19064 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.51646e6 | 0.497538 | 0.248769 | − | 0.968563i | \(-0.419974\pi\) | ||||
0.248769 | + | 0.968563i | \(0.419974\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.13795e6 | −0.123316 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.63979e6 | 1.03614 | 0.518068 | − | 0.855340i | \(-0.326651\pi\) | ||||
0.518068 | + | 0.855340i | \(0.326651\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.92650e6 | 1.04974 | 0.524872 | − | 0.851181i | \(-0.324113\pi\) | ||||
0.524872 | + | 0.851181i | \(0.324113\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.63322e6 | −0.800721 | −0.400360 | − | 0.916358i | \(-0.631115\pi\) | ||||
−0.400360 | + | 0.916358i | \(0.631115\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.26918e6 | −0.131010 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 53676.0 | 0.00540946 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.80314e7 | −1.80284 | −0.901418 | − | 0.432949i | \(-0.857473\pi\) | ||||
−0.901418 | + | 0.432949i | \(0.857473\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.41255e6 | 0.532681 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 750858. | 0.0733178 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.30190e6 | −0.894184 | −0.447092 | − | 0.894488i | \(-0.647540\pi\) | ||||
−0.447092 | + | 0.894488i | \(0.647540\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.38332e7 | 1.31946 | 0.659730 | − | 0.751503i | \(-0.270671\pi\) | ||||
0.659730 | + | 0.751503i | \(0.270671\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.48997e7 | −1.39932 | −0.699658 | − | 0.714478i | \(-0.746664\pi\) | ||||
−0.699658 | + | 0.714478i | \(0.746664\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.17958e7 | −2.03124 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.93306e7 | 1.77403 | 0.887016 | − | 0.461738i | \(-0.152774\pi\) | ||||
0.887016 | + | 0.461738i | \(0.152774\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.11520e6 | −0.556939 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.06110e6 | −0.364276 | −0.182138 | − | 0.983273i | \(-0.558302\pi\) | ||||
−0.182138 | + | 0.983273i | \(0.558302\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.35152e7 | −1.20315 | −0.601575 | − | 0.798816i | \(-0.705460\pi\) | ||||
−0.601575 | + | 0.798816i | \(0.705460\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −605000. | −0.0530519 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.11415e7 | −0.969678 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.24090e6 | −0.363623 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.43520e7 | 1.22144 | 0.610722 | − | 0.791845i | \(-0.290879\pi\) | ||||
0.610722 | + | 0.791845i | \(0.290879\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.89530e6 | −0.158930 | −0.0794650 | − | 0.996838i | \(-0.525321\pi\) | ||||
−0.0794650 | + | 0.996838i | \(0.525321\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.17640e6 | −0.264400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.91641e6 | 0.239220 | 0.119610 | − | 0.992821i | \(-0.461836\pi\) | ||||
0.119610 | + | 0.992821i | \(0.461836\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.98755e6 | 0.487554 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −651636. | −0.0522946 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.44278e7 | −1.14949 | −0.574743 | − | 0.818334i | \(-0.694898\pi\) | ||||
−0.574743 | + | 0.818334i | \(0.694898\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −771500. | −0.0605862 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 582876. | 0.0454458 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.58679e7 | 1.21962 | 0.609811 | − | 0.792547i | \(-0.291246\pi\) | ||||
0.609811 | + | 0.792547i | \(0.291246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 156200. | 0.0119205 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.10768e6 | 0.233823 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −301810. | −0.0225485 | −0.0112743 | − | 0.999936i | \(-0.503589\pi\) | ||||
−0.0112743 | + | 0.999936i | \(0.503589\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.92017e6 | −0.583459 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 883200. | 0.0646091 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.12677e7 | 1.53426 | 0.767130 | − | 0.641492i | \(-0.221684\pi\) | ||||
0.767130 | + | 0.641492i | \(0.221684\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.07591e6 | −0.220361 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.50625e6 | 0.247741 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.55009e7 | −1.08773 | −0.543863 | − | 0.839174i | \(-0.683039\pi\) | ||||
−0.543863 | + | 0.839174i | \(0.683039\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.89983e6 | −0.131499 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.21850e7 | −0.837653 | −0.418827 | − | 0.908066i | \(-0.637559\pi\) | ||||
−0.418827 | + | 0.908066i | \(0.637559\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.90019e7 | −1.28863 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.90282e7 | 1.95528 | 0.977641 | − | 0.210282i | \(-0.0674382\pi\) | ||||
0.977641 | + | 0.210282i | \(0.0674382\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.61145e7 | 1.07089 | 0.535445 | − | 0.844570i | \(-0.320144\pi\) | ||||
0.535445 | + | 0.844570i | \(0.320144\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.52375e6 | 0.166593 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.90120e6 | 0.123829 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.92431e6 | 0.189201 | 0.0946005 | − | 0.995515i | \(-0.469843\pi\) | ||||
0.0946005 | + | 0.995515i | \(0.469843\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −311300. | −0.0198752 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.60325e7 | 1.65111 | 0.825557 | − | 0.564319i | \(-0.190861\pi\) | ||||
0.825557 | + | 0.564319i | \(0.190861\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.63263e7 | −1.02194 | −0.510970 | − | 0.859598i | \(-0.670714\pi\) | ||||
−0.510970 | + | 0.859598i | \(0.670714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.80590e6 | 0.298857 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.30548e6 | −0.0801275 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.58132e7 | 1.57408 | 0.787040 | − | 0.616902i | \(-0.211612\pi\) | ||||
0.787040 | + | 0.616902i | \(0.211612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.90592e7 | 1.14725 | 0.573624 | − | 0.819119i | \(-0.305537\pi\) | ||||
0.573624 | + | 0.819119i | \(0.305537\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.49250e6 | 0.149067 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.69620e6 | 0.100146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.25417e7 | −1.90903 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −150550. | −0.00871980 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.73411e7 | 0.998021 | 0.499011 | − | 0.866596i | \(-0.333697\pi\) | ||||
0.499011 | + | 0.866596i | \(0.333697\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 633732. | 0.0360134 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −254012. | −0.0143440 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.58169e7 | 1.43965 | 0.719827 | − | 0.694153i | \(-0.244221\pi\) | ||||
0.719827 | + | 0.694153i | \(0.244221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.35096e6 | −0.518190 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.00328e7 | 2.19092 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.09230e6 | −0.0594090 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.88489e6 | −0.477288 | −0.238644 | − | 0.971107i | \(-0.576703\pi\) | ||||
−0.238644 | + | 0.971107i | \(0.576703\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.46396e7 | 1.31547 | 0.657735 | − | 0.753249i | \(-0.271515\pi\) | ||||
0.657735 | + | 0.753249i | \(0.271515\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.25216e7 | 0.660340 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.52860e6 | −0.289774 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.13768e7 | −0.589062 | −0.294531 | − | 0.955642i | \(-0.595163\pi\) | ||||
−0.294531 | + | 0.955642i | \(0.595163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.30783e7 | 0.673057 | 0.336529 | − | 0.941673i | \(-0.390747\pi\) | ||||
0.336529 | + | 0.941673i | \(0.390747\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.57188e7 | −1.81607 | −0.908037 | − | 0.418891i | \(-0.862419\pi\) | ||||
−0.908037 | + | 0.418891i | \(0.862419\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.61880e7 | 0.818103 | 0.409052 | − | 0.912511i | \(-0.365860\pi\) | ||||
0.409052 | + | 0.912511i | \(0.365860\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.17009e6 | 0.308091 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.38814e7 | 0.688999 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.55497e7 | −1.25309 | −0.626543 | − | 0.779387i | \(-0.715531\pi\) | ||||
−0.626543 | + | 0.779387i | \(0.715531\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.09610e7 | 0.534390 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.22942e6 | −0.444665 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.43301e6 | 0.451795 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 282012. | 0.0133488 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.22953e7 | −1.04916 | −0.524579 | − | 0.851362i | \(-0.675777\pi\) | ||||
−0.524579 | + | 0.851362i | \(0.675777\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.96872e7 | −0.915656 | −0.457828 | − | 0.889041i | \(-0.651372\pi\) | ||||
−0.457828 | + | 0.889041i | \(0.651372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.77582e6 | −0.313313 | −0.156657 | − | 0.987653i | \(-0.550072\pi\) | ||||
−0.156657 | + | 0.987653i | \(0.550072\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.63804e7 | −1.20574 | −0.602871 | − | 0.797839i | \(-0.705977\pi\) | ||||
−0.602871 | + | 0.797839i | \(0.705977\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.04338e7 | −0.474138 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.04435e7 | −1.36756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.13813e6 | −0.0508332 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 343750. | 0.0151783 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.95161e7 | 1.29587 | 0.647934 | − | 0.761697i | \(-0.275633\pi\) | ||||
0.647934 | + | 0.761697i | \(0.275633\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.48565e7 | 0.644877 | 0.322438 | − | 0.946590i | \(-0.395498\pi\) | ||||
0.322438 | + | 0.946590i | \(0.395498\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.45340e7 | 0.627313 | 0.313656 | − | 0.949537i | \(-0.398446\pi\) | ||||
0.313656 | + | 0.949537i | \(0.398446\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.72028e7 | −0.734160 | −0.367080 | − | 0.930189i | \(-0.619642\pi\) | ||||
−0.367080 | + | 0.930189i | \(0.619642\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.76304e6 | 0.202130 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.72118e7 | −1.14190 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.30950e6 | −0.0546447 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.23727e7 | 0.923249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.35475e6 | −0.219749 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.36666e7 | 0.554674 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.44434e7 | 1.39023 | 0.695116 | − | 0.718897i | \(-0.255353\pi\) | ||||
0.695116 | + | 0.718897i | \(0.255353\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −983748. | −0.0392724 | −0.0196362 | − | 0.999807i | \(-0.506251\pi\) | ||||
−0.0196362 | + | 0.999807i | \(0.506251\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.59464e7 | 1.82421 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.38138e6 | −0.211334 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.08857e7 | −1.20634 | −0.603168 | − | 0.797614i | \(-0.706095\pi\) | ||||
−0.603168 | + | 0.797614i | \(0.706095\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.94911e6 | −0.0753065 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −88750.0 | −0.00341047 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.20874e7 | 1.21982 | 0.609909 | − | 0.792472i | \(-0.291206\pi\) | ||||
0.609909 | + | 0.792472i | \(0.291206\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.79553e7 | 0.678920 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.25760e6 | 0.271496 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.52520e7 | 0.567515 | 0.283757 | − | 0.958896i | \(-0.408419\pi\) | ||||
0.283757 | + | 0.958896i | \(0.408419\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.48166e6 | −0.128178 | −0.0640889 | − | 0.997944i | \(-0.520414\pi\) | ||||
−0.0640889 | + | 0.997944i | \(0.520414\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.06241e6 | 0.112146 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.54010e7 | −0.920398 | −0.460199 | − | 0.887816i | \(-0.652222\pi\) | ||||
−0.460199 | + | 0.887816i | \(0.652222\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.39780e6 | 0.0864265 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.97352e7 | 1.77391 | 0.886955 | − | 0.461856i | \(-0.152816\pi\) | ||||
0.886955 | + | 0.461856i | \(0.152816\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.13007e7 | −0.400956 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.26904e6 | 0.185006 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.27250e7 | −0.444477 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.21398e7 | 0.419658 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.05173e7 | −1.04949 | −0.524747 | − | 0.851258i | \(-0.675840\pi\) | ||||
−0.524747 | + | 0.851258i | \(0.675840\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.19854e7 | 1.08869 | 0.544344 | − | 0.838862i | \(-0.316779\pi\) | ||||
0.544344 | + | 0.838862i | \(0.316779\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −678920. | −0.0229899 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.90786e6 | −0.0974623 | −0.0487312 | − | 0.998812i | \(-0.515518\pi\) | ||||
−0.0487312 | + | 0.998812i | \(0.515518\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.43059e7 | 1.47742 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.49621e7 | 1.15402 | 0.577010 | − | 0.816737i | \(-0.304219\pi\) | ||||
0.577010 | + | 0.816737i | \(0.304219\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.52544e7 | −0.829368 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.98164e6 | −0.324497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.00465e6 | −0.0971874 | −0.0485937 | − | 0.998819i | \(-0.515474\pi\) | ||||
−0.0485937 | + | 0.998819i | \(0.515474\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.01910e7 | 0.646547 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.20789e7 | 1.02207 | 0.511035 | − | 0.859560i | \(-0.329262\pi\) | ||||
0.511035 | + | 0.859560i | \(0.329262\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 720.6.a.r.1.1 | 1 | ||
3.2 | odd | 2 | 80.6.a.h.1.1 | 1 | |||
4.3 | odd | 2 | 90.6.a.f.1.1 | 1 | |||
12.11 | even | 2 | 10.6.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 400.6.c.a.49.1 | 2 | |||
15.8 | even | 4 | 400.6.c.a.49.2 | 2 | |||
15.14 | odd | 2 | 400.6.a.a.1.1 | 1 | |||
20.3 | even | 4 | 450.6.c.o.199.1 | 2 | |||
20.7 | even | 4 | 450.6.c.o.199.2 | 2 | |||
20.19 | odd | 2 | 450.6.a.h.1.1 | 1 | |||
24.5 | odd | 2 | 320.6.a.a.1.1 | 1 | |||
24.11 | even | 2 | 320.6.a.p.1.1 | 1 | |||
60.23 | odd | 4 | 50.6.b.d.49.2 | 2 | |||
60.47 | odd | 4 | 50.6.b.d.49.1 | 2 | |||
60.59 | even | 2 | 50.6.a.g.1.1 | 1 | |||
84.83 | odd | 2 | 490.6.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.a.1.1 | ✓ | 1 | 12.11 | even | 2 | ||
50.6.a.g.1.1 | 1 | 60.59 | even | 2 | |||
50.6.b.d.49.1 | 2 | 60.47 | odd | 4 | |||
50.6.b.d.49.2 | 2 | 60.23 | odd | 4 | |||
80.6.a.h.1.1 | 1 | 3.2 | odd | 2 | |||
90.6.a.f.1.1 | 1 | 4.3 | odd | 2 | |||
320.6.a.a.1.1 | 1 | 24.5 | odd | 2 | |||
320.6.a.p.1.1 | 1 | 24.11 | even | 2 | |||
400.6.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
400.6.c.a.49.1 | 2 | 15.2 | even | 4 | |||
400.6.c.a.49.2 | 2 | 15.8 | even | 4 | |||
450.6.a.h.1.1 | 1 | 20.19 | odd | 2 | |||
450.6.c.o.199.1 | 2 | 20.3 | even | 4 | |||
450.6.c.o.199.2 | 2 | 20.7 | even | 4 | |||
490.6.a.j.1.1 | 1 | 84.83 | odd | 2 | |||
720.6.a.r.1.1 | 1 | 1.1 | even | 1 | trivial |