Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,6,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.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: | \(8.01919099065\) |
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 | \(\chi\) | \(=\) | 50.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 26.0000 | 1.66790 | 0.833950 | − | 0.551839i | \(-0.186074\pi\) | ||||
0.833950 | + | 0.551839i | \(0.186074\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 104.000 | 1.17938 | ||||||||
\(7\) | 22.0000 | 0.169698 | 0.0848492 | − | 0.996394i | \(-0.472959\pi\) | ||||
0.0848492 | + | 0.996394i | \(0.472959\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 433.000 | 1.78189 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −768.000 | −1.91372 | −0.956862 | − | 0.290541i | \(-0.906165\pi\) | ||||
−0.956862 | + | 0.290541i | \(0.906165\pi\) | |||||||
\(12\) | 416.000 | 0.833950 | ||||||||
\(13\) | 46.0000 | 0.0754917 | 0.0377459 | − | 0.999287i | \(-0.487982\pi\) | ||||
0.0377459 | + | 0.999287i | \(0.487982\pi\) | |||||||
\(14\) | 88.0000 | 0.119995 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −378.000 | −0.317227 | −0.158613 | − | 0.987341i | \(-0.550702\pi\) | ||||
−0.158613 | + | 0.987341i | \(0.550702\pi\) | |||||||
\(18\) | 1732.00 | 1.25999 | ||||||||
\(19\) | 1100.00 | 0.699051 | 0.349525 | − | 0.936927i | \(-0.386343\pi\) | ||||
0.349525 | + | 0.936927i | \(0.386343\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 572.000 | 0.283040 | ||||||||
\(22\) | −3072.00 | −1.35321 | ||||||||
\(23\) | 1986.00 | 0.782816 | 0.391408 | − | 0.920217i | \(-0.371988\pi\) | ||||
0.391408 | + | 0.920217i | \(0.371988\pi\) | |||||||
\(24\) | 1664.00 | 0.589692 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 184.000 | 0.0533807 | ||||||||
\(27\) | 4940.00 | 1.30412 | ||||||||
\(28\) | 352.000 | 0.0848492 | ||||||||
\(29\) | −5610.00 | −1.23870 | −0.619352 | − | 0.785113i | \(-0.712605\pi\) | ||||
−0.619352 | + | 0.785113i | \(0.712605\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3988.00 | −0.745334 | −0.372667 | − | 0.927965i | \(-0.621557\pi\) | ||||
−0.372667 | + | 0.927965i | \(0.621557\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | −19968.0 | −3.19190 | ||||||||
\(34\) | −1512.00 | −0.224313 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6928.00 | 0.890947 | ||||||||
\(37\) | 142.000 | 0.0170523 | 0.00852617 | − | 0.999964i | \(-0.497286\pi\) | ||||
0.00852617 | + | 0.999964i | \(0.497286\pi\) | |||||||
\(38\) | 4400.00 | 0.494303 | ||||||||
\(39\) | 1196.00 | 0.125913 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1542.00 | 0.143260 | 0.0716300 | − | 0.997431i | \(-0.477180\pi\) | ||||
0.0716300 | + | 0.997431i | \(0.477180\pi\) | |||||||
\(42\) | 2288.00 | 0.200139 | ||||||||
\(43\) | 5026.00 | 0.414526 | 0.207263 | − | 0.978285i | \(-0.433544\pi\) | ||||
0.207263 | + | 0.978285i | \(0.433544\pi\) | |||||||
\(44\) | −12288.0 | −0.956862 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7944.00 | 0.553534 | ||||||||
\(47\) | −24738.0 | −1.63350 | −0.816752 | − | 0.576990i | \(-0.804227\pi\) | ||||
−0.816752 | + | 0.576990i | \(0.804227\pi\) | |||||||
\(48\) | 6656.00 | 0.416975 | ||||||||
\(49\) | −16323.0 | −0.971202 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9828.00 | −0.529102 | ||||||||
\(52\) | 736.000 | 0.0377459 | ||||||||
\(53\) | 14166.0 | 0.692720 | 0.346360 | − | 0.938102i | \(-0.387418\pi\) | ||||
0.346360 | + | 0.938102i | \(0.387418\pi\) | |||||||
\(54\) | 19760.0 | 0.922152 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1408.00 | 0.0599974 | ||||||||
\(57\) | 28600.0 | 1.16595 | ||||||||
\(58\) | −22440.0 | −0.875897 | ||||||||
\(59\) | 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 | \(0.469714\pi\) | |||||||
\(62\) | −15952.0 | −0.527031 | ||||||||
\(63\) | 9526.00 | 0.302384 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −79872.0 | −2.25702 | ||||||||
\(67\) | 24742.0 | 0.673361 | 0.336680 | − | 0.941619i | \(-0.390696\pi\) | ||||
0.336680 | + | 0.941619i | \(0.390696\pi\) | |||||||
\(68\) | −6048.00 | −0.158613 | ||||||||
\(69\) | 51636.0 | 1.30566 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 42372.0 | 0.997546 | 0.498773 | − | 0.866733i | \(-0.333784\pi\) | ||||
0.498773 | + | 0.866733i | \(0.333784\pi\) | |||||||
\(72\) | 27712.0 | 0.629994 | ||||||||
\(73\) | 52126.0 | 1.14485 | 0.572423 | − | 0.819958i | \(-0.306003\pi\) | ||||
0.572423 | + | 0.819958i | \(0.306003\pi\) | |||||||
\(74\) | 568.000 | 0.0120578 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 17600.0 | 0.349525 | ||||||||
\(77\) | −16896.0 | −0.324756 | ||||||||
\(78\) | 4784.00 | 0.0890337 | ||||||||
\(79\) | −39640.0 | −0.714605 | −0.357302 | − | 0.933989i | \(-0.616303\pi\) | ||||
−0.357302 | + | 0.933989i | \(0.616303\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23221.0 | 0.393250 | ||||||||
\(82\) | 6168.00 | 0.101300 | ||||||||
\(83\) | 59826.0 | 0.953223 | 0.476612 | − | 0.879114i | \(-0.341865\pi\) | ||||
0.476612 | + | 0.879114i | \(0.341865\pi\) | |||||||
\(84\) | 9152.00 | 0.141520 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 20104.0 | 0.293114 | ||||||||
\(87\) | −145860. | −2.06604 | ||||||||
\(88\) | −49152.0 | −0.676604 | ||||||||
\(89\) | 57690.0 | 0.772015 | 0.386007 | − | 0.922496i | \(-0.373854\pi\) | ||||
0.386007 | + | 0.922496i | \(0.373854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1012.00 | 0.0128108 | ||||||||
\(92\) | 31776.0 | 0.391408 | ||||||||
\(93\) | −103688. | −1.24314 | ||||||||
\(94\) | −98952.0 | −1.15506 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 26624.0 | 0.294846 | ||||||||
\(97\) | 144382. | 1.55806 | 0.779029 | − | 0.626988i | \(-0.215712\pi\) | ||||
0.779029 | + | 0.626988i | \(0.215712\pi\) | |||||||
\(98\) | −65292.0 | −0.686744 | ||||||||
\(99\) | −332544. | −3.41005 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −141258. | −1.37787 | −0.688937 | − | 0.724821i | \(-0.741922\pi\) | ||||
−0.688937 | + | 0.724821i | \(0.741922\pi\) | |||||||
\(102\) | −39312.0 | −0.374132 | ||||||||
\(103\) | −139814. | −1.29855 | −0.649273 | − | 0.760555i | \(-0.724927\pi\) | ||||
−0.649273 | + | 0.760555i | \(0.724927\pi\) | |||||||
\(104\) | 2944.00 | 0.0266904 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 56664.0 | 0.489827 | ||||||||
\(107\) | −86418.0 | −0.729701 | −0.364850 | − | 0.931066i | \(-0.618880\pi\) | ||||
−0.364850 | + | 0.931066i | \(0.618880\pi\) | |||||||
\(108\) | 79040.0 | 0.652060 | ||||||||
\(109\) | 218450. | 1.76111 | 0.880554 | − | 0.473947i | \(-0.157171\pi\) | ||||
0.880554 | + | 0.473947i | \(0.157171\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3692.00 | 0.0284416 | ||||||||
\(112\) | 5632.00 | 0.0424246 | ||||||||
\(113\) | 28806.0 | 0.212220 | 0.106110 | − | 0.994354i | \(-0.466160\pi\) | ||||
0.106110 | + | 0.994354i | \(0.466160\pi\) | |||||||
\(114\) | 114400. | 0.824449 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −89760.0 | −0.619352 | ||||||||
\(117\) | 19918.0 | 0.134518 | ||||||||
\(118\) | 113520. | 0.750529 | ||||||||
\(119\) | −8316.00 | −0.0538328 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 428773. | 2.66234 | ||||||||
\(122\) | 22088.0 | 0.134356 | ||||||||
\(123\) | 40092.0 | 0.238943 | ||||||||
\(124\) | −63808.0 | −0.372667 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 38104.0 | 0.213818 | ||||||||
\(127\) | 216502. | 1.19111 | 0.595556 | − | 0.803314i | \(-0.296932\pi\) | ||||
0.595556 | + | 0.803314i | \(0.296932\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 130676. | 0.691388 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −244608. | −1.24535 | −0.622676 | − | 0.782479i | \(-0.713955\pi\) | ||||
−0.622676 | + | 0.782479i | \(0.713955\pi\) | |||||||
\(132\) | −319488. | −1.59595 | ||||||||
\(133\) | 24200.0 | 0.118628 | ||||||||
\(134\) | 98968.0 | 0.476138 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24192.0 | −0.112157 | ||||||||
\(137\) | 239502. | 1.09020 | 0.545102 | − | 0.838370i | \(-0.316491\pi\) | ||||
0.545102 | + | 0.838370i | \(0.316491\pi\) | |||||||
\(138\) | 206544. | 0.923241 | ||||||||
\(139\) | 30860.0 | 0.135475 | 0.0677375 | − | 0.997703i | \(-0.478422\pi\) | ||||
0.0677375 | + | 0.997703i | \(0.478422\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −643188. | −2.72452 | ||||||||
\(142\) | 169488. | 0.705372 | ||||||||
\(143\) | −35328.0 | −0.144470 | ||||||||
\(144\) | 110848. | 0.445473 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 208504. | 0.809529 | ||||||||
\(147\) | −424398. | −1.61987 | ||||||||
\(148\) | 2272.00 | 0.00852617 | ||||||||
\(149\) | −100950. | −0.372512 | −0.186256 | − | 0.982501i | \(-0.559635\pi\) | ||||
−0.186256 | + | 0.982501i | \(0.559635\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12452.0 | 0.0444423 | 0.0222212 | − | 0.999753i | \(-0.492926\pi\) | ||||
0.0222212 | + | 0.999753i | \(0.492926\pi\) | |||||||
\(152\) | 70400.0 | 0.247152 | ||||||||
\(153\) | −163674. | −0.565264 | ||||||||
\(154\) | −67584.0 | −0.229637 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 19136.0 | 0.0629564 | ||||||||
\(157\) | 6022.00 | 0.0194981 | 0.00974903 | − | 0.999952i | \(-0.496897\pi\) | ||||
0.00974903 | + | 0.999952i | \(0.496897\pi\) | |||||||
\(158\) | −158560. | −0.505302 | ||||||||
\(159\) | 368316. | 1.15539 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 43692.0 | 0.132843 | ||||||||
\(162\) | 92884.0 | 0.278070 | ||||||||
\(163\) | 500866. | 1.47656 | 0.738282 | − | 0.674492i | \(-0.235637\pi\) | ||||
0.738282 | + | 0.674492i | \(0.235637\pi\) | |||||||
\(164\) | 24672.0 | 0.0716300 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 239304. | 0.674031 | ||||||||
\(167\) | −555258. | −1.54065 | −0.770324 | − | 0.637652i | \(-0.779906\pi\) | ||||
−0.770324 | + | 0.637652i | \(0.779906\pi\) | |||||||
\(168\) | 36608.0 | 0.100070 | ||||||||
\(169\) | −369177. | −0.994301 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 476300. | 1.24563 | ||||||||
\(172\) | 80416.0 | 0.207263 | ||||||||
\(173\) | −417354. | −1.06020 | −0.530102 | − | 0.847934i | \(-0.677846\pi\) | ||||
−0.530102 | + | 0.847934i | \(0.677846\pi\) | |||||||
\(174\) | −583440. | −1.46091 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −196608. | −0.478431 | ||||||||
\(177\) | 737880. | 1.77032 | ||||||||
\(178\) | 230760. | 0.545897 | ||||||||
\(179\) | −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 | \(0.287074\pi\) | |||||||
\(182\) | 4048.00 | 0.00905862 | ||||||||
\(183\) | 143572. | 0.316914 | ||||||||
\(184\) | 127104. | 0.276767 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −414752. | −0.879035 | ||||||||
\(187\) | 290304. | 0.607084 | ||||||||
\(188\) | −395808. | −0.816752 | ||||||||
\(189\) | 108680. | 0.221307 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −452028. | −0.896565 | −0.448283 | − | 0.893892i | \(-0.647964\pi\) | ||||
−0.448283 | + | 0.893892i | \(0.647964\pi\) | |||||||
\(192\) | 106496. | 0.208488 | ||||||||
\(193\) | −485594. | −0.938383 | −0.469191 | − | 0.883097i | \(-0.655455\pi\) | ||||
−0.469191 | + | 0.883097i | \(0.655455\pi\) | |||||||
\(194\) | 577528. | 1.10171 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −261168. | −0.485601 | ||||||||
\(197\) | −1.01018e6 | −1.85452 | −0.927262 | − | 0.374414i | \(-0.877844\pi\) | ||||
−0.927262 | + | 0.374414i | \(0.877844\pi\) | |||||||
\(198\) | −1.33018e6 | −2.41127 | ||||||||
\(199\) | −807640. | −1.44572 | −0.722862 | − | 0.690993i | \(-0.757174\pi\) | ||||
−0.722862 | + | 0.690993i | \(0.757174\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 643292. | 1.12310 | ||||||||
\(202\) | −565032. | −0.974304 | ||||||||
\(203\) | −123420. | −0.210206 | ||||||||
\(204\) | −157248. | −0.264551 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −559256. | −0.918211 | ||||||||
\(207\) | 859938. | 1.39489 | ||||||||
\(208\) | 11776.0 | 0.0188729 | ||||||||
\(209\) | −844800. | −1.33779 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 149552. | 0.231252 | 0.115626 | − | 0.993293i | \(-0.463113\pi\) | ||||
0.115626 | + | 0.993293i | \(0.463113\pi\) | |||||||
\(212\) | 226656. | 0.346360 | ||||||||
\(213\) | 1.10167e6 | 1.66381 | ||||||||
\(214\) | −345672. | −0.515976 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 316160. | 0.461076 | ||||||||
\(217\) | −87736.0 | −0.126482 | ||||||||
\(218\) | 873800. | 1.24529 | ||||||||
\(219\) | 1.35528e6 | 1.90949 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17388.0 | −0.0239480 | ||||||||
\(222\) | 14768.0 | 0.0201113 | ||||||||
\(223\) | 443506. | 0.597224 | 0.298612 | − | 0.954375i | \(-0.403476\pi\) | ||||
0.298612 | + | 0.954375i | \(0.403476\pi\) | |||||||
\(224\) | 22528.0 | 0.0299987 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 115224. | 0.150062 | ||||||||
\(227\) | −420018. | −0.541007 | −0.270504 | − | 0.962719i | \(-0.587190\pi\) | ||||
−0.270504 | + | 0.962719i | \(0.587190\pi\) | |||||||
\(228\) | 457600. | 0.582974 | ||||||||
\(229\) | 1.05875e6 | 1.33415 | 0.667075 | − | 0.744990i | \(-0.267546\pi\) | ||||
0.667075 | + | 0.744990i | \(0.267546\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −439296. | −0.541661 | ||||||||
\(232\) | −359040. | −0.437948 | ||||||||
\(233\) | 1.27345e6 | 1.53671 | 0.768353 | − | 0.640026i | \(-0.221077\pi\) | ||||
0.768353 | + | 0.640026i | \(0.221077\pi\) | |||||||
\(234\) | 79672.0 | 0.0951187 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 454080. | 0.530704 | ||||||||
\(237\) | −1.03064e6 | −1.19189 | ||||||||
\(238\) | −33264.0 | −0.0380655 | ||||||||
\(239\) | −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 | \(0.600750\pi\) | |||||||
\(242\) | 1.71509e6 | 1.88256 | ||||||||
\(243\) | −596674. | −0.648219 | ||||||||
\(244\) | 88352.0 | 0.0950040 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 160368. | 0.168958 | ||||||||
\(247\) | 50600.0 | 0.0527726 | ||||||||
\(248\) | −255232. | −0.263515 | ||||||||
\(249\) | 1.55548e6 | 1.58988 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 577152. | 0.578237 | 0.289119 | − | 0.957293i | \(-0.406638\pi\) | ||||
0.289119 | + | 0.957293i | \(0.406638\pi\) | |||||||
\(252\) | 152416. | 0.151192 | ||||||||
\(253\) | −1.52525e6 | −1.49809 | ||||||||
\(254\) | 866008. | 0.842243 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 651462. | 0.615257 | 0.307628 | − | 0.951507i | \(-0.400465\pi\) | ||||
0.307628 | + | 0.951507i | \(0.400465\pi\) | |||||||
\(258\) | 522704. | 0.488885 | ||||||||
\(259\) | 3124.00 | 0.00289375 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.42913e6 | −2.20724 | ||||||||
\(262\) | −978432. | −0.880597 | ||||||||
\(263\) | −917574. | −0.817997 | −0.408999 | − | 0.912535i | \(-0.634122\pi\) | ||||
−0.408999 | + | 0.912535i | \(0.634122\pi\) | |||||||
\(264\) | −1.27795e6 | −1.12851 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 96800.0 | 0.0838825 | ||||||||
\(267\) | 1.49994e6 | 1.28764 | ||||||||
\(268\) | 395872. | 0.336680 | ||||||||
\(269\) | −735390. | −0.619637 | −0.309818 | − | 0.950796i | \(-0.600268\pi\) | ||||
−0.309818 | + | 0.950796i | \(0.600268\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.12131e6 | −0.927474 | −0.463737 | − | 0.885973i | \(-0.653492\pi\) | ||||
−0.463737 | + | 0.885973i | \(0.653492\pi\) | |||||||
\(272\) | −96768.0 | −0.0793066 | ||||||||
\(273\) | 26312.0 | 0.0213672 | ||||||||
\(274\) | 958008. | 0.770891 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 826176. | 0.652830 | ||||||||
\(277\) | 1.66034e6 | 1.30016 | 0.650082 | − | 0.759864i | \(-0.274735\pi\) | ||||
0.650082 | + | 0.759864i | \(0.274735\pi\) | |||||||
\(278\) | 123440. | 0.0957952 | ||||||||
\(279\) | −1.72680e6 | −1.32811 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.45210e6 | 1.09706 | 0.548531 | − | 0.836130i | \(-0.315187\pi\) | ||||
0.548531 | + | 0.836130i | \(0.315187\pi\) | |||||||
\(282\) | −2.57275e6 | −1.92653 | ||||||||
\(283\) | −309014. | −0.229357 | −0.114679 | − | 0.993403i | \(-0.536584\pi\) | ||||
−0.114679 | + | 0.993403i | \(0.536584\pi\) | |||||||
\(284\) | 677952. | 0.498773 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −141312. | −0.102156 | ||||||||
\(287\) | 33924.0 | 0.0243110 | ||||||||
\(288\) | 443392. | 0.314997 | ||||||||
\(289\) | −1.27697e6 | −0.899367 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.75393e6 | 2.59869 | ||||||||
\(292\) | 834016. | 0.572423 | ||||||||
\(293\) | 1.59301e6 | 1.08405 | 0.542024 | − | 0.840363i | \(-0.317658\pi\) | ||||
0.542024 | + | 0.840363i | \(0.317658\pi\) | |||||||
\(294\) | −1.69759e6 | −1.14542 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9088.00 | 0.00602891 | ||||||||
\(297\) | −3.79392e6 | −2.49573 | ||||||||
\(298\) | −403800. | −0.263406 | ||||||||
\(299\) | 91356.0 | 0.0590961 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 110572. | 0.0703443 | ||||||||
\(302\) | 49808.0 | 0.0314255 | ||||||||
\(303\) | −3.67271e6 | −2.29816 | ||||||||
\(304\) | 281600. | 0.174763 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −654696. | −0.399702 | ||||||||
\(307\) | −1.24726e6 | −0.755284 | −0.377642 | − | 0.925952i | \(-0.623265\pi\) | ||||
−0.377642 | + | 0.925952i | \(0.623265\pi\) | |||||||
\(308\) | −270336. | −0.162378 | ||||||||
\(309\) | −3.63516e6 | −2.16585 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −665988. | −0.390450 | −0.195225 | − | 0.980758i | \(-0.562544\pi\) | ||||
−0.195225 | + | 0.980758i | \(0.562544\pi\) | |||||||
\(312\) | 76544.0 | 0.0445169 | ||||||||
\(313\) | 591286. | 0.341143 | 0.170572 | − | 0.985345i | \(-0.445439\pi\) | ||||
0.170572 | + | 0.985345i | \(0.445439\pi\) | |||||||
\(314\) | 24088.0 | 0.0137872 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −634240. | −0.357302 | ||||||||
\(317\) | 516342. | 0.288595 | 0.144298 | − | 0.989534i | \(-0.453908\pi\) | ||||
0.144298 | + | 0.989534i | \(0.453908\pi\) | |||||||
\(318\) | 1.47326e6 | 0.816983 | ||||||||
\(319\) | 4.30848e6 | 2.37054 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.24687e6 | −1.21707 | ||||||||
\(322\) | 174768. | 0.0939339 | ||||||||
\(323\) | −415800. | −0.221757 | ||||||||
\(324\) | 371536. | 0.196625 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00346e6 | 1.04409 | ||||||||
\(327\) | 5.67970e6 | 2.93735 | ||||||||
\(328\) | 98688.0 | 0.0506500 | ||||||||
\(329\) | −544236. | −0.277203 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.29577e6 | −1.65343 | −0.826717 | − | 0.562619i | \(-0.809794\pi\) | ||||
−0.826717 | + | 0.562619i | \(0.809794\pi\) | |||||||
\(332\) | 957216. | 0.476612 | ||||||||
\(333\) | 61486.0 | 0.0303854 | ||||||||
\(334\) | −2.22103e6 | −1.08940 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 146432. | 0.0707600 | ||||||||
\(337\) | −1.91098e6 | −0.916602 | −0.458301 | − | 0.888797i | \(-0.651542\pi\) | ||||
−0.458301 | + | 0.888797i | \(0.651542\pi\) | |||||||
\(338\) | −1.47671e6 | −0.703077 | ||||||||
\(339\) | 748956. | 0.353962 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.06278e6 | 1.42636 | ||||||||
\(342\) | 1.90520e6 | 0.880796 | ||||||||
\(343\) | −728860. | −0.334510 | ||||||||
\(344\) | 321664. | 0.146557 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.66942e6 | −0.749677 | ||||||||
\(347\) | −2.42006e6 | −1.07895 | −0.539476 | − | 0.842001i | \(-0.681378\pi\) | ||||
−0.539476 | + | 0.842001i | \(0.681378\pi\) | |||||||
\(348\) | −2.33376e6 | −1.03302 | ||||||||
\(349\) | 2.50727e6 | 1.10189 | 0.550944 | − | 0.834542i | \(-0.314268\pi\) | ||||
0.550944 | + | 0.834542i | \(0.314268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 227240. | 0.0984503 | ||||||||
\(352\) | −786432. | −0.338302 | ||||||||
\(353\) | 413166. | 0.176477 | 0.0882384 | − | 0.996099i | \(-0.471876\pi\) | ||||
0.0882384 | + | 0.996099i | \(0.471876\pi\) | |||||||
\(354\) | 2.95152e6 | 1.25181 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 923040. | 0.386007 | ||||||||
\(357\) | −216216. | −0.0897878 | ||||||||
\(358\) | −209520. | −0.0864008 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 2.18665e6 | 0.877016 | ||||||||
\(363\) | 1.11481e7 | 4.44052 | ||||||||
\(364\) | 16192.0 | 0.00640541 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 574288. | 0.224092 | ||||||||
\(367\) | −1.16098e6 | −0.449944 | −0.224972 | − | 0.974365i | \(-0.572229\pi\) | ||||
−0.224972 | + | 0.974365i | \(0.572229\pi\) | |||||||
\(368\) | 508416. | 0.195704 | ||||||||
\(369\) | 667686. | 0.255274 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 311652. | 0.117553 | ||||||||
\(372\) | −1.65901e6 | −0.621572 | ||||||||
\(373\) | −343754. | −0.127931 | −0.0639655 | − | 0.997952i | \(-0.520375\pi\) | ||||
−0.0639655 | + | 0.997952i | \(0.520375\pi\) | |||||||
\(374\) | 1.16122e6 | 0.429273 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.58323e6 | −0.577531 | ||||||||
\(377\) | −258060. | −0.0935120 | ||||||||
\(378\) | 434720. | 0.156488 | ||||||||
\(379\) | 573140. | 0.204957 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.62905e6 | 1.98666 | ||||||||
\(382\) | −1.80811e6 | −0.633967 | ||||||||
\(383\) | 2.88055e6 | 1.00341 | 0.501704 | − | 0.865039i | \(-0.332707\pi\) | ||||
0.501704 | + | 0.865039i | \(0.332707\pi\) | |||||||
\(384\) | 425984. | 0.147423 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.94238e6 | −0.663537 | ||||||||
\(387\) | 2.17626e6 | 0.738640 | ||||||||
\(388\) | 2.31011e6 | 0.779029 | ||||||||
\(389\) | −3.08559e6 | −1.03387 | −0.516933 | − | 0.856026i | \(-0.672926\pi\) | ||||
−0.516933 | + | 0.856026i | \(0.672926\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −750708. | −0.248330 | ||||||||
\(392\) | −1.04467e6 | −0.343372 | ||||||||
\(393\) | −6.35981e6 | −2.07712 | ||||||||
\(394\) | −4.04071e6 | −1.31135 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.32070e6 | −1.70503 | ||||||||
\(397\) | −885458. | −0.281963 | −0.140981 | − | 0.990012i | \(-0.545026\pi\) | ||||
−0.140981 | + | 0.990012i | \(0.545026\pi\) | |||||||
\(398\) | −3.23056e6 | −1.02228 | ||||||||
\(399\) | 629200. | 0.197859 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.75344e6 | −1.16565 | −0.582825 | − | 0.812598i | \(-0.698053\pi\) | ||||
−0.582825 | + | 0.812598i | \(0.698053\pi\) | |||||||
\(402\) | 2.57317e6 | 0.794151 | ||||||||
\(403\) | −183448. | −0.0562666 | ||||||||
\(404\) | −2.26013e6 | −0.688937 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −493680. | −0.148638 | ||||||||
\(407\) | −109056. | −0.0326335 | ||||||||
\(408\) | −628992. | −0.187066 | ||||||||
\(409\) | −1.94653e6 | −0.575377 | −0.287689 | − | 0.957724i | \(-0.592887\pi\) | ||||
−0.287689 | + | 0.957724i | \(0.592887\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.22705e6 | 1.81835 | ||||||||
\(412\) | −2.23702e6 | −0.649273 | ||||||||
\(413\) | 624360. | 0.180119 | ||||||||
\(414\) | 3.43975e6 | 0.986339 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 47104.0 | 0.0133452 | ||||||||
\(417\) | 802360. | 0.225959 | ||||||||
\(418\) | −3.37920e6 | −0.945961 | ||||||||
\(419\) | −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 | \(0.316393\pi\) | |||||||
\(422\) | 598208. | 0.163520 | ||||||||
\(423\) | −1.07116e7 | −2.91073 | ||||||||
\(424\) | 906624. | 0.244913 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.40669e6 | 1.17649 | ||||||||
\(427\) | 121484. | 0.0322440 | ||||||||
\(428\) | −1.38269e6 | −0.364850 | ||||||||
\(429\) | −918528. | −0.240962 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.17115e6 | −1.34089 | −0.670446 | − | 0.741958i | \(-0.733897\pi\) | ||||
−0.670446 | + | 0.741958i | \(0.733897\pi\) | |||||||
\(432\) | 1.26464e6 | 0.326030 | ||||||||
\(433\) | 4.53485e6 | 1.16237 | 0.581183 | − | 0.813773i | \(-0.302590\pi\) | ||||
0.581183 | + | 0.813773i | \(0.302590\pi\) | |||||||
\(434\) | −350944. | −0.0894362 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.49520e6 | 0.880554 | ||||||||
\(437\) | 2.18460e6 | 0.547228 | ||||||||
\(438\) | 5.42110e6 | 1.35021 | ||||||||
\(439\) | −1.08220e6 | −0.268007 | −0.134004 | − | 0.990981i | \(-0.542783\pi\) | ||||
−0.134004 | + | 0.990981i | \(0.542783\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.06786e6 | −1.73058 | ||||||||
\(442\) | −69552.0 | −0.0169338 | ||||||||
\(443\) | 1.08079e6 | 0.261656 | 0.130828 | − | 0.991405i | \(-0.458236\pi\) | ||||
0.130828 | + | 0.991405i | \(0.458236\pi\) | |||||||
\(444\) | 59072.0 | 0.0142208 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.77402e6 | 0.422301 | ||||||||
\(447\) | −2.62470e6 | −0.621314 | ||||||||
\(448\) | 90112.0 | 0.0212123 | ||||||||
\(449\) | 2.61783e6 | 0.612810 | 0.306405 | − | 0.951901i | \(-0.400874\pi\) | ||||
0.306405 | + | 0.951901i | \(0.400874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.18426e6 | −0.274160 | ||||||||
\(452\) | 460896. | 0.106110 | ||||||||
\(453\) | 323752. | 0.0741254 | ||||||||
\(454\) | −1.68007e6 | −0.382550 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.83040e6 | 0.412225 | ||||||||
\(457\) | −1.59046e6 | −0.356231 | −0.178115 | − | 0.984010i | \(-0.557000\pi\) | ||||
−0.178115 | + | 0.984010i | \(0.557000\pi\) | |||||||
\(458\) | 4.23500e6 | 0.943387 | ||||||||
\(459\) | −1.86732e6 | −0.413701 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.25470e6 | 0.932431 | 0.466216 | − | 0.884671i | \(-0.345617\pi\) | ||||
0.466216 | + | 0.884671i | \(0.345617\pi\) | |||||||
\(462\) | −1.75718e6 | −0.383012 | ||||||||
\(463\) | −3.26605e6 | −0.708061 | −0.354031 | − | 0.935234i | \(-0.615189\pi\) | ||||
−0.354031 | + | 0.935234i | \(0.615189\pi\) | |||||||
\(464\) | −1.43616e6 | −0.309676 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.09378e6 | 1.08662 | ||||||||
\(467\) | 601542. | 0.127636 | 0.0638181 | − | 0.997962i | \(-0.479672\pi\) | ||||
0.0638181 | + | 0.997962i | \(0.479672\pi\) | |||||||
\(468\) | 318688. | 0.0672591 | ||||||||
\(469\) | 544324. | 0.114268 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 156572. | 0.0325208 | ||||||||
\(472\) | 1.81632e6 | 0.375264 | ||||||||
\(473\) | −3.85997e6 | −0.793288 | ||||||||
\(474\) | −4.12256e6 | −0.842793 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −133056. | −0.0269164 | ||||||||
\(477\) | 6.13388e6 | 1.23435 | ||||||||
\(478\) | −1.48272e6 | −0.296817 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | −2.24519e6 | −0.440186 | ||||||||
\(483\) | 1.13599e6 | 0.221568 | ||||||||
\(484\) | 6.86037e6 | 1.33117 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.38670e6 | −0.458360 | ||||||||
\(487\) | −7.05226e6 | −1.34743 | −0.673714 | − | 0.738992i | \(-0.735302\pi\) | ||||
−0.673714 | + | 0.738992i | \(0.735302\pi\) | |||||||
\(488\) | 353408. | 0.0671780 | ||||||||
\(489\) | 1.30225e7 | 2.46276 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.62349e6 | −0.491106 | −0.245553 | − | 0.969383i | \(-0.578970\pi\) | ||||
−0.245553 | + | 0.969383i | \(0.578970\pi\) | |||||||
\(492\) | 641472. | 0.119472 | ||||||||
\(493\) | 2.12058e6 | 0.392950 | ||||||||
\(494\) | 202400. | 0.0373158 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.02093e6 | −0.186333 | ||||||||
\(497\) | 932184. | 0.169282 | ||||||||
\(498\) | 6.22190e6 | 1.12422 | ||||||||
\(499\) | −3.61234e6 | −0.649437 | −0.324719 | − | 0.945811i | \(-0.605270\pi\) | ||||
−0.324719 | + | 0.945811i | \(0.605270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.44367e7 | −2.56965 | ||||||||
\(502\) | 2.30861e6 | 0.408875 | ||||||||
\(503\) | −9.15629e6 | −1.61361 | −0.806807 | − | 0.590815i | \(-0.798806\pi\) | ||||
−0.806807 | + | 0.590815i | \(0.798806\pi\) | |||||||
\(504\) | 609664. | 0.106909 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.10099e6 | −1.05931 | ||||||||
\(507\) | −9.59860e6 | −1.65840 | ||||||||
\(508\) | 3.46403e6 | 0.595556 | ||||||||
\(509\) | 7.26159e6 | 1.24233 | 0.621165 | − | 0.783679i | \(-0.286660\pi\) | ||||
0.621165 | + | 0.783679i | \(0.286660\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.14677e6 | 0.194279 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 5.43400e6 | 0.911646 | ||||||||
\(514\) | 2.60585e6 | 0.435052 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.09082e6 | 0.345694 | ||||||||
\(517\) | 1.89988e7 | 3.12608 | ||||||||
\(518\) | 12496.0 | 0.00204619 | ||||||||
\(519\) | −1.08512e7 | −1.76831 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.81020e6 | 0.937771 | 0.468886 | − | 0.883259i | \(-0.344656\pi\) | ||||
0.468886 | + | 0.883259i | \(0.344656\pi\) | |||||||
\(522\) | −9.71652e6 | −1.56075 | ||||||||
\(523\) | 8.17067e6 | 1.30618 | 0.653090 | − | 0.757280i | \(-0.273472\pi\) | ||||
0.653090 | + | 0.757280i | \(0.273472\pi\) | |||||||
\(524\) | −3.91373e6 | −0.622676 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.67030e6 | −0.578411 | ||||||||
\(527\) | 1.50746e6 | 0.236440 | ||||||||
\(528\) | −5.11181e6 | −0.797976 | ||||||||
\(529\) | −2.49215e6 | −0.387199 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.22885e7 | 1.89132 | ||||||||
\(532\) | 387200. | 0.0593139 | ||||||||
\(533\) | 70932.0 | 0.0108149 | ||||||||
\(534\) | 5.99976e6 | 0.910502 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.58349e6 | 0.238069 | ||||||||
\(537\) | −1.36188e6 | −0.203800 | ||||||||
\(538\) | −2.94156e6 | −0.438149 | ||||||||
\(539\) | 1.25361e7 | 1.85861 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −817378. | −0.120069 | −0.0600343 | − | 0.998196i | \(-0.519121\pi\) | ||||
−0.0600343 | + | 0.998196i | \(0.519121\pi\) | |||||||
\(542\) | −4.48523e6 | −0.655823 | ||||||||
\(543\) | 1.42132e7 | 2.06868 | ||||||||
\(544\) | −387072. | −0.0560783 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 105248. | 0.0151089 | ||||||||
\(547\) | 3.50750e6 | 0.501221 | 0.250611 | − | 0.968088i | \(-0.419369\pi\) | ||||
0.250611 | + | 0.968088i | \(0.419369\pi\) | |||||||
\(548\) | 3.83203e6 | 0.545102 | ||||||||
\(549\) | 2.39103e6 | 0.338574 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.17100e6 | −0.865918 | ||||||||
\(552\) | 3.30470e6 | 0.461620 | ||||||||
\(553\) | −872080. | −0.121267 | ||||||||
\(554\) | 6.64137e6 | 0.919355 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 493760. | 0.0677375 | ||||||||
\(557\) | −9.61490e6 | −1.31313 | −0.656563 | − | 0.754271i | \(-0.727991\pi\) | ||||
−0.656563 | + | 0.754271i | \(0.727991\pi\) | |||||||
\(558\) | −6.90722e6 | −0.939112 | ||||||||
\(559\) | 231196. | 0.0312933 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.54790e6 | 1.01256 | ||||||||
\(562\) | 5.80841e6 | 0.775740 | ||||||||
\(563\) | −2.01941e6 | −0.268506 | −0.134253 | − | 0.990947i | \(-0.542864\pi\) | ||||
−0.134253 | + | 0.990947i | \(0.542864\pi\) | |||||||
\(564\) | −1.02910e7 | −1.36226 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.23606e6 | −0.162180 | ||||||||
\(567\) | 510862. | 0.0667338 | ||||||||
\(568\) | 2.71181e6 | 0.352686 | ||||||||
\(569\) | 1.37859e6 | 0.178507 | 0.0892533 | − | 0.996009i | \(-0.471552\pi\) | ||||
0.0892533 | + | 0.996009i | \(0.471552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.54295e6 | 1.09652 | 0.548261 | − | 0.836307i | \(-0.315290\pi\) | ||||
0.548261 | + | 0.836307i | \(0.315290\pi\) | |||||||
\(572\) | −565248. | −0.0722352 | ||||||||
\(573\) | −1.17527e7 | −1.49538 | ||||||||
\(574\) | 135696. | 0.0171905 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.77357e6 | 0.222737 | ||||||||
\(577\) | 2.31458e6 | 0.289423 | 0.144711 | − | 0.989474i | \(-0.453775\pi\) | ||||
0.144711 | + | 0.989474i | \(0.453775\pi\) | |||||||
\(578\) | −5.10789e6 | −0.635949 | ||||||||
\(579\) | −1.26254e7 | −1.56513 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.31617e6 | 0.161760 | ||||||||
\(582\) | 1.50157e7 | 1.83755 | ||||||||
\(583\) | −1.08795e7 | −1.32568 | ||||||||
\(584\) | 3.33606e6 | 0.404764 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.37202e6 | 0.766537 | ||||||||
\(587\) | −928338. | −0.111202 | −0.0556008 | − | 0.998453i | \(-0.517707\pi\) | ||||
−0.0556008 | + | 0.998453i | \(0.517707\pi\) | |||||||
\(588\) | −6.79037e6 | −0.809935 | ||||||||
\(589\) | −4.38680e6 | −0.521026 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.62646e7 | −3.09316 | ||||||||
\(592\) | 36352.0 | 0.00426309 | ||||||||
\(593\) | 909486. | 0.106209 | 0.0531043 | − | 0.998589i | \(-0.483088\pi\) | ||||
0.0531043 | + | 0.998589i | \(0.483088\pi\) | |||||||
\(594\) | −1.51757e7 | −1.76475 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.61520e6 | −0.186256 | ||||||||
\(597\) | −2.09986e7 | −2.41132 | ||||||||
\(598\) | 365424. | 0.0417873 | ||||||||
\(599\) | −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 | \(0.387590\pi\) | |||||||
\(602\) | 442288. | 0.0497409 | ||||||||
\(603\) | 1.07133e7 | 1.19986 | ||||||||
\(604\) | 199232. | 0.0222212 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.46908e7 | −1.62504 | ||||||||
\(607\) | 4.51646e6 | 0.497538 | 0.248769 | − | 0.968563i | \(-0.419974\pi\) | ||||
0.248769 | + | 0.968563i | \(0.419974\pi\) | |||||||
\(608\) | 1.12640e6 | 0.123576 | ||||||||
\(609\) | −3.20892e6 | −0.350603 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.13795e6 | −0.123316 | ||||||||
\(612\) | −2.61878e6 | −0.282632 | ||||||||
\(613\) | −9.63979e6 | −1.03614 | −0.518068 | − | 0.855340i | \(-0.673349\pi\) | ||||
−0.518068 | + | 0.855340i | \(0.673349\pi\) | |||||||
\(614\) | −4.98903e6 | −0.534067 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.08134e6 | −0.114819 | ||||||||
\(617\) | 9.92650e6 | 1.04974 | 0.524872 | − | 0.851181i | \(-0.324113\pi\) | ||||
0.524872 | + | 0.851181i | \(0.324113\pi\) | |||||||
\(618\) | −1.45407e7 | −1.53149 | ||||||||
\(619\) | 7.63322e6 | 0.800721 | 0.400360 | − | 0.916358i | \(-0.368885\pi\) | ||||
0.400360 | + | 0.916358i | \(0.368885\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.81084e6 | 1.02089 | ||||||||
\(622\) | −2.66395e6 | −0.276090 | ||||||||
\(623\) | 1.26918e6 | 0.131010 | ||||||||
\(624\) | 306176. | 0.0314782 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.36514e6 | 0.241225 | ||||||||
\(627\) | −2.19648e7 | −2.23130 | ||||||||
\(628\) | 96352.0 | 0.00974903 | ||||||||
\(629\) | −53676.0 | −0.00540946 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.80314e7 | 1.80284 | 0.901418 | − | 0.432949i | \(-0.142527\pi\) | ||||
0.901418 | + | 0.432949i | \(0.142527\pi\) | |||||||
\(632\) | −2.53696e6 | −0.252651 | ||||||||
\(633\) | 3.88835e6 | 0.385706 | ||||||||
\(634\) | 2.06537e6 | 0.204068 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.89306e6 | 0.577694 | ||||||||
\(637\) | −750858. | −0.0733178 | ||||||||
\(638\) | 1.72339e7 | 1.67623 | ||||||||
\(639\) | 1.83471e7 | 1.77752 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.30190e6 | 0.894184 | 0.447092 | − | 0.894488i | \(-0.352460\pi\) | ||||
0.447092 | + | 0.894488i | \(0.352460\pi\) | |||||||
\(642\) | −8.98747e6 | −0.860597 | ||||||||
\(643\) | 1.38332e7 | 1.31946 | 0.659730 | − | 0.751503i | \(-0.270671\pi\) | ||||
0.659730 | + | 0.751503i | \(0.270671\pi\) | |||||||
\(644\) | 699072. | 0.0664213 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.66320e6 | −0.156806 | ||||||||
\(647\) | 1.48997e7 | 1.39932 | 0.699658 | − | 0.714478i | \(-0.253336\pi\) | ||||
0.699658 | + | 0.714478i | \(0.253336\pi\) | |||||||
\(648\) | 1.48614e6 | 0.139035 | ||||||||
\(649\) | −2.17958e7 | −2.03124 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.28114e6 | −0.210959 | ||||||||
\(652\) | 8.01386e6 | 0.738282 | ||||||||
\(653\) | 1.93306e7 | 1.77403 | 0.887016 | − | 0.461738i | \(-0.152774\pi\) | ||||
0.887016 | + | 0.461738i | \(0.152774\pi\) | |||||||
\(654\) | 2.27188e7 | 2.07702 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 394752. | 0.0358150 | ||||||||
\(657\) | 2.25706e7 | 2.03999 | ||||||||
\(658\) | −2.17694e6 | −0.196012 | ||||||||
\(659\) | −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 | \(0.705460\pi\) | |||||||
\(662\) | −1.31831e7 | −1.16915 | ||||||||
\(663\) | −452088. | −0.0399429 | ||||||||
\(664\) | 3.82886e6 | 0.337015 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 245944. | 0.0214858 | ||||||||
\(667\) | −1.11415e7 | −0.969678 | ||||||||
\(668\) | −8.88413e6 | −0.770324 | ||||||||
\(669\) | 1.15312e7 | 0.996111 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.24090e6 | −0.363623 | ||||||||
\(672\) | 585728. | 0.0500349 | ||||||||
\(673\) | −1.43520e7 | −1.22144 | −0.610722 | − | 0.791845i | \(-0.709121\pi\) | ||||
−0.610722 | + | 0.791845i | \(0.709121\pi\) | |||||||
\(674\) | −7.64391e6 | −0.648136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.90683e6 | −0.497150 | ||||||||
\(677\) | −1.89530e6 | −0.158930 | −0.0794650 | − | 0.996838i | \(-0.525321\pi\) | ||||
−0.0794650 | + | 0.996838i | \(0.525321\pi\) | |||||||
\(678\) | 2.99582e6 | 0.250289 | ||||||||
\(679\) | 3.17640e6 | 0.264400 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.09205e7 | −0.902347 | ||||||||
\(682\) | 1.22511e7 | 1.00859 | ||||||||
\(683\) | −2.91641e6 | −0.239220 | −0.119610 | − | 0.992821i | \(-0.538164\pi\) | ||||
−0.119610 | + | 0.992821i | \(0.538164\pi\) | |||||||
\(684\) | 7.62080e6 | 0.622817 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.91544e6 | −0.236534 | ||||||||
\(687\) | 2.75275e7 | 2.22523 | ||||||||
\(688\) | 1.28666e6 | 0.103631 | ||||||||
\(689\) | 651636. | 0.0522946 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.44278e7 | 1.14949 | 0.574743 | − | 0.818334i | \(-0.305102\pi\) | ||||
0.574743 | + | 0.818334i | \(0.305102\pi\) | |||||||
\(692\) | −6.67766e6 | −0.530102 | ||||||||
\(693\) | −7.31597e6 | −0.578680 | ||||||||
\(694\) | −9.68023e6 | −0.762934 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.33504e6 | −0.730454 | ||||||||
\(697\) | −582876. | −0.0454458 | ||||||||
\(698\) | 1.00291e7 | 0.779153 | ||||||||
\(699\) | 3.31096e7 | 2.56307 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.58679e7 | −1.21962 | −0.609811 | − | 0.792547i | \(-0.708754\pi\) | ||||
−0.609811 | + | 0.792547i | \(0.708754\pi\) | |||||||
\(702\) | 908960. | 0.0696149 | ||||||||
\(703\) | 156200. | 0.0119205 | ||||||||
\(704\) | −3.14573e6 | −0.239216 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.65266e6 | 0.124788 | ||||||||
\(707\) | −3.10768e6 | −0.233823 | ||||||||
\(708\) | 1.18061e7 | 0.885162 | ||||||||
\(709\) | −301810. | −0.0225485 | −0.0112743 | − | 0.999936i | \(-0.503589\pi\) | ||||
−0.0112743 | + | 0.999936i | \(0.503589\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.71641e7 | −1.27335 | ||||||||
\(712\) | 3.69216e6 | 0.272948 | ||||||||
\(713\) | −7.92017e6 | −0.583459 | ||||||||
\(714\) | −864864. | −0.0634896 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −838080. | −0.0610946 | ||||||||
\(717\) | −9.63768e6 | −0.700123 | ||||||||
\(718\) | 6.95088e6 | 0.503186 | ||||||||
\(719\) | 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 | ||||||||
\(722\) | −5.06440e6 | −0.361564 | ||||||||
\(723\) | −1.45937e7 | −1.03830 | ||||||||
\(724\) | 8.74659e6 | 0.620144 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.45924e7 | 3.13992 | ||||||||
\(727\) | −1.55009e7 | −1.08773 | −0.543863 | − | 0.839174i | \(-0.683039\pi\) | ||||
−0.543863 | + | 0.839174i | \(0.683039\pi\) | |||||||
\(728\) | 64768.0 | 0.00452931 | ||||||||
\(729\) | −2.11562e7 | −1.47441 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.89983e6 | −0.131499 | ||||||||
\(732\) | 2.29715e6 | 0.158457 | ||||||||
\(733\) | 1.21850e7 | 0.837653 | 0.418827 | − | 0.908066i | \(-0.362441\pi\) | ||||
0.418827 | + | 0.908066i | \(0.362441\pi\) | |||||||
\(734\) | −4.64391e6 | −0.318159 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.03366e6 | 0.138384 | ||||||||
\(737\) | −1.90019e7 | −1.28863 | ||||||||
\(738\) | 2.67074e6 | 0.180506 | ||||||||
\(739\) | −2.90282e7 | −1.95528 | −0.977641 | − | 0.210282i | \(-0.932562\pi\) | ||||
−0.977641 | + | 0.210282i | \(0.932562\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.31560e6 | 0.0880194 | ||||||||
\(742\) | 1.24661e6 | 0.0831228 | ||||||||
\(743\) | −1.61145e7 | −1.07089 | −0.535445 | − | 0.844570i | \(-0.679856\pi\) | ||||
−0.535445 | + | 0.844570i | \(0.679856\pi\) | |||||||
\(744\) | −6.63603e6 | −0.439517 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.37502e6 | −0.0904609 | ||||||||
\(747\) | 2.59047e7 | 1.69854 | ||||||||
\(748\) | 4.64486e6 | 0.303542 | ||||||||
\(749\) | −1.90120e6 | −0.123829 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.92431e6 | −0.189201 | −0.0946005 | − | 0.995515i | \(-0.530157\pi\) | ||||
−0.0946005 | + | 0.995515i | \(0.530157\pi\) | |||||||
\(752\) | −6.33293e6 | −0.408376 | ||||||||
\(753\) | 1.50060e7 | 0.964442 | ||||||||
\(754\) | −1.03224e6 | −0.0661230 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.73888e6 | 0.110653 | ||||||||
\(757\) | −2.60325e7 | −1.65111 | −0.825557 | − | 0.564319i | \(-0.809139\pi\) | ||||
−0.825557 | + | 0.564319i | \(0.809139\pi\) | |||||||
\(758\) | 2.29256e6 | 0.144926 | ||||||||
\(759\) | −3.96564e7 | −2.49867 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.63263e7 | 1.02194 | 0.510970 | − | 0.859598i | \(-0.329286\pi\) | ||||
0.510970 | + | 0.859598i | \(0.329286\pi\) | |||||||
\(762\) | 2.25162e7 | 1.40478 | ||||||||
\(763\) | 4.80590e6 | 0.298857 | ||||||||
\(764\) | −7.23245e6 | −0.448283 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.15222e7 | 0.709517 | ||||||||
\(767\) | 1.30548e6 | 0.0801275 | ||||||||
\(768\) | 1.70394e6 | 0.104244 | ||||||||
\(769\) | 2.58132e7 | 1.57408 | 0.787040 | − | 0.616902i | \(-0.211612\pi\) | ||||
0.787040 | + | 0.616902i | \(0.211612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.69380e7 | 1.02619 | ||||||||
\(772\) | −7.76950e6 | −0.469191 | ||||||||
\(773\) | 1.90592e7 | 1.14725 | 0.573624 | − | 0.819119i | \(-0.305537\pi\) | ||||
0.573624 | + | 0.819119i | \(0.305537\pi\) | |||||||
\(774\) | 8.70503e6 | 0.522298 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.24045e6 | 0.550857 | ||||||||
\(777\) | 81224.0 | 0.00482649 | ||||||||
\(778\) | −1.23424e7 | −0.731054 | ||||||||
\(779\) | 1.69620e6 | 0.100146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.25417e7 | −1.90903 | ||||||||
\(782\) | −3.00283e6 | −0.175596 | ||||||||
\(783\) | −2.77134e7 | −1.61542 | ||||||||
\(784\) | −4.17869e6 | −0.242801 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.54392e7 | −1.46875 | ||||||||
\(787\) | 1.73411e7 | 0.998021 | 0.499011 | − | 0.866596i | \(-0.333697\pi\) | ||||
0.499011 | + | 0.866596i | \(0.333697\pi\) | |||||||
\(788\) | −1.61628e7 | −0.927262 | ||||||||
\(789\) | −2.38569e7 | −1.36434 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 633732. | 0.0360134 | ||||||||
\(792\) | −2.12828e7 | −1.20564 | ||||||||
\(793\) | 254012. | 0.0143440 | ||||||||
\(794\) | −3.54183e6 | −0.199378 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.29222e7 | −0.722862 | ||||||||
\(797\) | 2.58169e7 | 1.43965 | 0.719827 | − | 0.694153i | \(-0.244221\pi\) | ||||
0.719827 | + | 0.694153i | \(0.244221\pi\) | |||||||
\(798\) | 2.51680e6 | 0.139908 | ||||||||
\(799\) | 9.35096e6 | 0.518190 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.49798e7 | 1.37565 | ||||||||
\(802\) | −1.50138e7 | −0.824239 | ||||||||
\(803\) | −4.00328e7 | −2.19092 | ||||||||
\(804\) | 1.02927e7 | 0.561549 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −733792. | −0.0397865 | ||||||||
\(807\) | −1.91201e7 | −1.03349 | ||||||||
\(808\) | −9.04051e6 | −0.487152 | ||||||||
\(809\) | 8.88489e6 | 0.477288 | 0.238644 | − | 0.971107i | \(-0.423297\pi\) | ||||
0.238644 | + | 0.971107i | \(0.423297\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.46396e7 | −1.31547 | −0.657735 | − | 0.753249i | \(-0.728485\pi\) | ||||
−0.657735 | + | 0.753249i | \(0.728485\pi\) | |||||||
\(812\) | −1.97472e6 | −0.105103 | ||||||||
\(813\) | −2.91540e7 | −1.54693 | ||||||||
\(814\) | −436224. | −0.0230754 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.51597e6 | −0.132276 | ||||||||
\(817\) | 5.52860e6 | 0.289774 | ||||||||
\(818\) | −7.78612e6 | −0.406853 | ||||||||
\(819\) | 438196. | 0.0228275 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.13768e7 | 0.589062 | 0.294531 | − | 0.955642i | \(-0.404837\pi\) | ||||
0.294531 | + | 0.955642i | \(0.404837\pi\) | |||||||
\(822\) | 2.49082e7 | 1.28577 | ||||||||
\(823\) | 1.30783e7 | 0.673057 | 0.336529 | − | 0.941673i | \(-0.390747\pi\) | ||||
0.336529 | + | 0.941673i | \(0.390747\pi\) | |||||||
\(824\) | −8.94810e6 | −0.459106 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.49744e6 | 0.127363 | ||||||||
\(827\) | 3.57188e7 | 1.81607 | 0.908037 | − | 0.418891i | \(-0.137581\pi\) | ||||
0.908037 | + | 0.418891i | \(0.137581\pi\) | |||||||
\(828\) | 1.37590e7 | 0.697447 | ||||||||
\(829\) | 1.61880e7 | 0.818103 | 0.409052 | − | 0.912511i | \(-0.365860\pi\) | ||||
0.409052 | + | 0.912511i | \(0.365860\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.31689e7 | 2.16854 | ||||||||
\(832\) | 188416. | 0.00943647 | ||||||||
\(833\) | 6.17009e6 | 0.308091 | ||||||||
\(834\) | 3.20944e6 | 0.159777 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.35168e7 | −0.668895 | ||||||||
\(837\) | −1.97007e7 | −0.972005 | ||||||||
\(838\) | −1.19666e7 | −0.588657 | ||||||||
\(839\) | −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 | ||||||||
\(842\) | 1.58664e7 | 0.771256 | ||||||||
\(843\) | 3.77547e7 | 1.82979 | ||||||||
\(844\) | 2.39283e6 | 0.115626 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.28462e7 | −2.05820 | ||||||||
\(847\) | 9.43301e6 | 0.451795 | ||||||||
\(848\) | 3.62650e6 | 0.173180 | ||||||||
\(849\) | −8.03436e6 | −0.382545 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 282012. | 0.0133488 | ||||||||
\(852\) | 1.76268e7 | 0.831904 | ||||||||
\(853\) | 2.22953e7 | 1.04916 | 0.524579 | − | 0.851362i | \(-0.324223\pi\) | ||||
0.524579 | + | 0.851362i | \(0.324223\pi\) | |||||||
\(854\) | 485936. | 0.0228000 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.53075e6 | −0.257988 | ||||||||
\(857\) | −1.96872e7 | −0.915656 | −0.457828 | − | 0.889041i | \(-0.651372\pi\) | ||||
−0.457828 | + | 0.889041i | \(0.651372\pi\) | |||||||
\(858\) | −3.67411e6 | −0.170386 | ||||||||
\(859\) | 6.77582e6 | 0.313313 | 0.156657 | − | 0.987653i | \(-0.449928\pi\) | ||||
0.156657 | + | 0.987653i | \(0.449928\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 882024. | 0.0405483 | ||||||||
\(862\) | −2.06846e7 | −0.948154 | ||||||||
\(863\) | 2.63804e7 | 1.20574 | 0.602871 | − | 0.797839i | \(-0.294023\pi\) | ||||
0.602871 | + | 0.797839i | \(0.294023\pi\) | |||||||
\(864\) | 5.05856e6 | 0.230538 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.81394e7 | 0.821917 | ||||||||
\(867\) | −3.32013e7 | −1.50006 | ||||||||
\(868\) | −1.40378e6 | −0.0632410 | ||||||||
\(869\) | 3.04435e7 | 1.36756 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.13813e6 | 0.0508332 | ||||||||
\(872\) | 1.39808e7 | 0.622645 | ||||||||
\(873\) | 6.25174e7 | 2.77629 | ||||||||
\(874\) | 8.73840e6 | 0.386949 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.16844e7 | 0.954745 | ||||||||
\(877\) | −2.95161e7 | −1.29587 | −0.647934 | − | 0.761697i | \(-0.724367\pi\) | ||||
−0.647934 | + | 0.761697i | \(0.724367\pi\) | |||||||
\(878\) | −4.32880e6 | −0.189510 | ||||||||
\(879\) | 4.14182e7 | 1.80808 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.48565e7 | −0.644877 | −0.322438 | − | 0.946590i | \(-0.604502\pi\) | ||||
−0.322438 | + | 0.946590i | \(0.604502\pi\) | |||||||
\(882\) | −2.82714e7 | −1.22370 | ||||||||
\(883\) | 1.45340e7 | 0.627313 | 0.313656 | − | 0.949537i | \(-0.398446\pi\) | ||||
0.313656 | + | 0.949537i | \(0.398446\pi\) | |||||||
\(884\) | −278208. | −0.0119740 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.32314e6 | 0.185019 | ||||||||
\(887\) | 1.72028e7 | 0.734160 | 0.367080 | − | 0.930189i | \(-0.380358\pi\) | ||||
0.367080 | + | 0.930189i | \(0.380358\pi\) | |||||||
\(888\) | 236288. | 0.0100556 | ||||||||
\(889\) | 4.76304e6 | 0.202130 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.78337e7 | −0.752572 | ||||||||
\(892\) | 7.09610e6 | 0.298612 | ||||||||
\(893\) | −2.72118e7 | −1.14190 | ||||||||
\(894\) | −1.04988e7 | −0.439335 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 360448. | 0.0149994 | ||||||||
\(897\) | 2.37526e6 | 0.0985665 | ||||||||
\(898\) | 1.04713e7 | 0.433322 | ||||||||
\(899\) | 2.23727e7 | 0.923249 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.35475e6 | −0.219749 | ||||||||
\(902\) | −4.73702e6 | −0.193860 | ||||||||
\(903\) | 2.87487e6 | 0.117327 | ||||||||
\(904\) | 1.84358e6 | 0.0750312 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.29501e6 | 0.0524146 | ||||||||
\(907\) | 3.44434e7 | 1.39023 | 0.695116 | − | 0.718897i | \(-0.255353\pi\) | ||||
0.695116 | + | 0.718897i | \(0.255353\pi\) | |||||||
\(908\) | −6.72029e6 | −0.270504 | ||||||||
\(909\) | −6.11647e7 | −2.45522 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −983748. | −0.0392724 | −0.0196362 | − | 0.999807i | \(-0.506251\pi\) | ||||
−0.0196362 | + | 0.999807i | \(0.506251\pi\) | |||||||
\(912\) | 7.32160e6 | 0.291487 | ||||||||
\(913\) | −4.59464e7 | −1.82421 | ||||||||
\(914\) | −6.36183e6 | −0.251893 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.69400e7 | 0.667075 | ||||||||
\(917\) | −5.38138e6 | −0.211334 | ||||||||
\(918\) | −7.46928e6 | −0.292531 | ||||||||
\(919\) | 3.08857e7 | 1.20634 | 0.603168 | − | 0.797614i | \(-0.293905\pi\) | ||||
0.603168 | + | 0.797614i | \(0.293905\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.24287e7 | −1.25974 | ||||||||
\(922\) | 1.70188e7 | 0.659328 | ||||||||
\(923\) | 1.94911e6 | 0.0753065 | ||||||||
\(924\) | −7.02874e6 | −0.270830 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.30642e7 | −0.500675 | ||||||||
\(927\) | −6.05395e7 | −2.31387 | ||||||||
\(928\) | −5.74464e6 | −0.218974 | ||||||||
\(929\) | −3.20874e7 | −1.21982 | −0.609909 | − | 0.792472i | \(-0.708794\pi\) | ||||
−0.609909 | + | 0.792472i | \(0.708794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.79553e7 | −0.678920 | ||||||||
\(932\) | 2.03751e7 | 0.768353 | ||||||||
\(933\) | −1.73157e7 | −0.651232 | ||||||||
\(934\) | 2.40617e6 | 0.0902524 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.27475e6 | 0.0475594 | ||||||||
\(937\) | −1.52520e7 | −0.567515 | −0.283757 | − | 0.958896i | \(-0.591581\pi\) | ||||
−0.283757 | + | 0.958896i | \(0.591581\pi\) | |||||||
\(938\) | 2.17730e6 | 0.0807998 | ||||||||
\(939\) | 1.53734e7 | 0.568993 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.48166e6 | 0.128178 | 0.0640889 | − | 0.997944i | \(-0.479586\pi\) | ||||
0.0640889 | + | 0.997944i | \(0.479586\pi\) | |||||||
\(942\) | 626288. | 0.0229957 | ||||||||
\(943\) | 3.06241e6 | 0.112146 | ||||||||
\(944\) | 7.26528e6 | 0.265352 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.54399e7 | −0.560939 | ||||||||
\(947\) | 2.54010e7 | 0.920398 | 0.460199 | − | 0.887816i | \(-0.347778\pi\) | ||||
0.460199 | + | 0.887816i | \(0.347778\pi\) | |||||||
\(948\) | −1.64902e7 | −0.595945 | ||||||||
\(949\) | 2.39780e6 | 0.0864265 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.34249e7 | 0.481348 | ||||||||
\(952\) | −532224. | −0.0190328 | ||||||||
\(953\) | 4.97352e7 | 1.77391 | 0.886955 | − | 0.461856i | \(-0.152816\pi\) | ||||
0.886955 | + | 0.461856i | \(0.152816\pi\) | |||||||
\(954\) | 2.45355e7 | 0.872819 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.93088e6 | −0.209882 | ||||||||
\(957\) | 1.12020e8 | 3.95383 | ||||||||
\(958\) | −1.83173e7 | −0.644833 | ||||||||
\(959\) | 5.26904e6 | 0.185006 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.27250e7 | −0.444477 | ||||||||
\(962\) | 26128.0 | 0.000910266 0 | ||||||||
\(963\) | −3.74190e7 | −1.30025 | ||||||||
\(964\) | −8.98077e6 | −0.311258 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.54397e6 | 0.156672 | ||||||||
\(967\) | −3.05173e7 | −1.04949 | −0.524747 | − | 0.851258i | \(-0.675840\pi\) | ||||
−0.524747 | + | 0.851258i | \(0.675840\pi\) | |||||||
\(968\) | 2.74415e7 | 0.941280 | ||||||||
\(969\) | −1.08108e7 | −0.369869 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.19854e7 | 1.08869 | 0.544344 | − | 0.838862i | \(-0.316779\pi\) | ||||
0.544344 | + | 0.838862i | \(0.316779\pi\) | |||||||
\(972\) | −9.54678e6 | −0.324109 | ||||||||
\(973\) | 678920. | 0.0229899 | ||||||||
\(974\) | −2.82090e7 | −0.952776 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.41363e6 | 0.0475020 | ||||||||
\(977\) | −2.90786e6 | −0.0974623 | −0.0487312 | − | 0.998812i | \(-0.515518\pi\) | ||||
−0.0487312 | + | 0.998812i | \(0.515518\pi\) | |||||||
\(978\) | 5.20901e7 | 1.74144 | ||||||||
\(979\) | −4.43059e7 | −1.47742 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.45888e7 | 3.13810 | ||||||||
\(982\) | −1.04940e7 | −0.347264 | ||||||||
\(983\) | −3.49621e7 | −1.15402 | −0.577010 | − | 0.816737i | \(-0.695781\pi\) | ||||
−0.577010 | + | 0.816737i | \(0.695781\pi\) | |||||||
\(984\) | 2.56589e6 | 0.0844792 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.48232e6 | 0.277858 | ||||||||
\(987\) | −1.41501e7 | −0.462347 | ||||||||
\(988\) | 809600. | 0.0263863 | ||||||||
\(989\) | 9.98164e6 | 0.324497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.00465e6 | 0.0971874 | 0.0485937 | − | 0.998819i | \(-0.484526\pi\) | ||||
0.0485937 | + | 0.998819i | \(0.484526\pi\) | |||||||
\(992\) | −4.08371e6 | −0.131758 | ||||||||
\(993\) | −8.56900e7 | −2.75776 | ||||||||
\(994\) | 3.72874e6 | 0.119700 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.48876e7 | 0.794941 | ||||||||
\(997\) | −3.20789e7 | −1.02207 | −0.511035 | − | 0.859560i | \(-0.670738\pi\) | ||||
−0.511035 | + | 0.859560i | \(0.670738\pi\) | |||||||
\(998\) | −1.44494e7 | −0.459222 | ||||||||
\(999\) | 701480. | 0.0222383 |
(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 | 50.6.a.g.1.1 | 1 | ||
3.2 | odd | 2 | 450.6.a.h.1.1 | 1 | |||
4.3 | odd | 2 | 400.6.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 50.6.b.d.49.2 | 2 | |||
5.3 | odd | 4 | 50.6.b.d.49.1 | 2 | |||
5.4 | even | 2 | 10.6.a.a.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 450.6.c.o.199.1 | 2 | |||
15.8 | even | 4 | 450.6.c.o.199.2 | 2 | |||
15.14 | odd | 2 | 90.6.a.f.1.1 | 1 | |||
20.3 | even | 4 | 400.6.c.a.49.1 | 2 | |||
20.7 | even | 4 | 400.6.c.a.49.2 | 2 | |||
20.19 | odd | 2 | 80.6.a.h.1.1 | 1 | |||
35.34 | odd | 2 | 490.6.a.j.1.1 | 1 | |||
40.19 | odd | 2 | 320.6.a.a.1.1 | 1 | |||
40.29 | even | 2 | 320.6.a.p.1.1 | 1 | |||
60.59 | even | 2 | 720.6.a.r.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.a.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
50.6.a.g.1.1 | 1 | 1.1 | even | 1 | trivial | ||
50.6.b.d.49.1 | 2 | 5.3 | odd | 4 | |||
50.6.b.d.49.2 | 2 | 5.2 | odd | 4 | |||
80.6.a.h.1.1 | 1 | 20.19 | odd | 2 | |||
90.6.a.f.1.1 | 1 | 15.14 | odd | 2 | |||
320.6.a.a.1.1 | 1 | 40.19 | odd | 2 | |||
320.6.a.p.1.1 | 1 | 40.29 | even | 2 | |||
400.6.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
400.6.c.a.49.1 | 2 | 20.3 | even | 4 | |||
400.6.c.a.49.2 | 2 | 20.7 | even | 4 | |||
450.6.a.h.1.1 | 1 | 3.2 | odd | 2 | |||
450.6.c.o.199.1 | 2 | 15.2 | even | 4 | |||
450.6.c.o.199.2 | 2 | 15.8 | even | 4 | |||
490.6.a.j.1.1 | 1 | 35.34 | odd | 2 | |||
720.6.a.r.1.1 | 1 | 60.59 | even | 2 |