Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,6,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, 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("10.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(1.60383819813\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 | \(-0.813926\pi\) | ||||
−0.833950 | + | 0.551839i | \(0.813926\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 104.000 | 1.17938 | ||||||||
\(7\) | −22.0000 | −0.169698 | −0.0848492 | − | 0.996394i | \(-0.527041\pi\) | ||||
−0.0848492 | + | 0.996394i | \(0.527041\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 433.000 | 1.78189 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | −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 | \(-0.512018\pi\) | ||||
−0.0377459 | + | 0.999287i | \(0.512018\pi\) | |||||||
\(14\) | 88.0000 | 0.119995 | ||||||||
\(15\) | 650.000 | 0.745908 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 378.000 | 0.317227 | 0.158613 | − | 0.987341i | \(-0.449298\pi\) | ||||
0.158613 | + | 0.987341i | \(0.449298\pi\) | |||||||
\(18\) | −1732.00 | −1.25999 | ||||||||
\(19\) | 1100.00 | 0.699051 | 0.349525 | − | 0.936927i | \(-0.386343\pi\) | ||||
0.349525 | + | 0.936927i | \(0.386343\pi\) | |||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | 572.000 | 0.283040 | ||||||||
\(22\) | 3072.00 | 1.35321 | ||||||||
\(23\) | −1986.00 | −0.782816 | −0.391408 | − | 0.920217i | \(-0.628012\pi\) | ||||
−0.391408 | + | 0.920217i | \(0.628012\pi\) | |||||||
\(24\) | 1664.00 | 0.589692 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 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 | \(0.712605\pi\) | |||||||
\(30\) | −2600.00 | −0.527437 | ||||||||
\(31\) | −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 | ||||||||
\(35\) | 550.000 | 0.0758914 | ||||||||
\(36\) | 6928.00 | 0.890947 | ||||||||
\(37\) | −142.000 | −0.0170523 | −0.00852617 | − | 0.999964i | \(-0.502714\pi\) | ||||
−0.00852617 | + | 0.999964i | \(0.502714\pi\) | |||||||
\(38\) | −4400.00 | −0.494303 | ||||||||
\(39\) | 1196.00 | 0.125913 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | 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 | \(-0.566456\pi\) | ||||
−0.207263 | + | 0.978285i | \(0.566456\pi\) | |||||||
\(44\) | −12288.0 | −0.956862 | ||||||||
\(45\) | −10825.0 | −0.796887 | ||||||||
\(46\) | 7944.00 | 0.553534 | ||||||||
\(47\) | 24738.0 | 1.63350 | 0.816752 | − | 0.576990i | \(-0.195773\pi\) | ||||
0.816752 | + | 0.576990i | \(0.195773\pi\) | |||||||
\(48\) | −6656.00 | −0.416975 | ||||||||
\(49\) | −16323.0 | −0.971202 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −9828.00 | −0.529102 | ||||||||
\(52\) | −736.000 | −0.0377459 | ||||||||
\(53\) | −14166.0 | −0.692720 | −0.346360 | − | 0.938102i | \(-0.612582\pi\) | ||||
−0.346360 | + | 0.938102i | \(0.612582\pi\) | |||||||
\(54\) | 19760.0 | 0.922152 | ||||||||
\(55\) | 19200.0 | 0.855844 | ||||||||
\(56\) | 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 | \(0.321928\pi\) | |||||||
\(60\) | 10400.0 | 0.372954 | ||||||||
\(61\) | 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 | ||||||||
\(65\) | 1150.00 | 0.0337609 | ||||||||
\(66\) | −79872.0 | −2.25702 | ||||||||
\(67\) | −24742.0 | −0.673361 | −0.336680 | − | 0.941619i | \(-0.609304\pi\) | ||||
−0.336680 | + | 0.941619i | \(0.609304\pi\) | |||||||
\(68\) | 6048.00 | 0.158613 | ||||||||
\(69\) | 51636.0 | 1.30566 | ||||||||
\(70\) | −2200.00 | −0.0536633 | ||||||||
\(71\) | 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 | \(-0.693997\pi\) | ||||
−0.572423 | + | 0.819958i | \(0.693997\pi\) | |||||||
\(74\) | 568.000 | 0.0120578 | ||||||||
\(75\) | −16250.0 | −0.333580 | ||||||||
\(76\) | 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 | \(0.616303\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | 23221.0 | 0.393250 | ||||||||
\(82\) | −6168.00 | −0.101300 | ||||||||
\(83\) | −59826.0 | −0.953223 | −0.476612 | − | 0.879114i | \(-0.658135\pi\) | ||||
−0.476612 | + | 0.879114i | \(0.658135\pi\) | |||||||
\(84\) | 9152.00 | 0.141520 | ||||||||
\(85\) | −9450.00 | −0.141868 | ||||||||
\(86\) | 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 | \(0.373854\pi\) | |||||||
\(90\) | 43300.0 | 0.563484 | ||||||||
\(91\) | 1012.00 | 0.0128108 | ||||||||
\(92\) | −31776.0 | −0.391408 | ||||||||
\(93\) | 103688. | 1.24314 | ||||||||
\(94\) | −98952.0 | −1.15506 | ||||||||
\(95\) | −27500.0 | −0.312625 | ||||||||
\(96\) | 26624.0 | 0.294846 | ||||||||
\(97\) | −144382. | −1.55806 | −0.779029 | − | 0.626988i | \(-0.784288\pi\) | ||||
−0.779029 | + | 0.626988i | \(0.784288\pi\) | |||||||
\(98\) | 65292.0 | 0.686744 | ||||||||
\(99\) | −332544. | −3.41005 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −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 | \(-0.275073\pi\) | ||||
0.649273 | + | 0.760555i | \(0.275073\pi\) | |||||||
\(104\) | 2944.00 | 0.0266904 | ||||||||
\(105\) | −14300.0 | −0.126579 | ||||||||
\(106\) | 56664.0 | 0.489827 | ||||||||
\(107\) | 86418.0 | 0.729701 | 0.364850 | − | 0.931066i | \(-0.381120\pi\) | ||||
0.364850 | + | 0.931066i | \(0.381120\pi\) | |||||||
\(108\) | −79040.0 | −0.652060 | ||||||||
\(109\) | 218450. | 1.76111 | 0.880554 | − | 0.473947i | \(-0.157171\pi\) | ||||
0.880554 | + | 0.473947i | \(0.157171\pi\) | |||||||
\(110\) | −76800.0 | −0.605173 | ||||||||
\(111\) | 3692.00 | 0.0284416 | ||||||||
\(112\) | −5632.00 | −0.0424246 | ||||||||
\(113\) | −28806.0 | −0.212220 | −0.106110 | − | 0.994354i | \(-0.533840\pi\) | ||||
−0.106110 | + | 0.994354i | \(0.533840\pi\) | |||||||
\(114\) | 114400. | 0.824449 | ||||||||
\(115\) | 49650.0 | 0.350086 | ||||||||
\(116\) | −89760.0 | −0.619352 | ||||||||
\(117\) | −19918.0 | −0.134518 | ||||||||
\(118\) | −113520. | −0.750529 | ||||||||
\(119\) | −8316.00 | −0.0538328 | ||||||||
\(120\) | −41600.0 | −0.263718 | ||||||||
\(121\) | 428773. | 2.66234 | ||||||||
\(122\) | −22088.0 | −0.134356 | ||||||||
\(123\) | −40092.0 | −0.238943 | ||||||||
\(124\) | −63808.0 | −0.372667 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 38104.0 | 0.213818 | ||||||||
\(127\) | −216502. | −1.19111 | −0.595556 | − | 0.803314i | \(-0.703068\pi\) | ||||
−0.595556 | + | 0.803314i | \(0.703068\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | 130676. | 0.691388 | ||||||||
\(130\) | −4600.00 | −0.0238726 | ||||||||
\(131\) | −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 | ||||||||
\(135\) | 123500. | 0.583220 | ||||||||
\(136\) | −24192.0 | −0.112157 | ||||||||
\(137\) | −239502. | −1.09020 | −0.545102 | − | 0.838370i | \(-0.683509\pi\) | ||||
−0.545102 | + | 0.838370i | \(0.683509\pi\) | |||||||
\(138\) | −206544. | −0.923241 | ||||||||
\(139\) | 30860.0 | 0.135475 | 0.0677375 | − | 0.997703i | \(-0.478422\pi\) | ||||
0.0677375 | + | 0.997703i | \(0.478422\pi\) | |||||||
\(140\) | 8800.00 | 0.0379457 | ||||||||
\(141\) | −643188. | −2.72452 | ||||||||
\(142\) | −169488. | −0.705372 | ||||||||
\(143\) | 35328.0 | 0.144470 | ||||||||
\(144\) | 110848. | 0.445473 | ||||||||
\(145\) | 140250. | 0.553966 | ||||||||
\(146\) | 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 | \(0.559635\pi\) | |||||||
\(150\) | 65000.0 | 0.235877 | ||||||||
\(151\) | 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 | ||||||||
\(155\) | 99700.0 | 0.333323 | ||||||||
\(156\) | 19136.0 | 0.0629564 | ||||||||
\(157\) | −6022.00 | −0.0194981 | −0.00974903 | − | 0.999952i | \(-0.503103\pi\) | ||||
−0.00974903 | + | 0.999952i | \(0.503103\pi\) | |||||||
\(158\) | 158560. | 0.505302 | ||||||||
\(159\) | 368316. | 1.15539 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 43692.0 | 0.132843 | ||||||||
\(162\) | −92884.0 | −0.278070 | ||||||||
\(163\) | −500866. | −1.47656 | −0.738282 | − | 0.674492i | \(-0.764363\pi\) | ||||
−0.738282 | + | 0.674492i | \(0.764363\pi\) | |||||||
\(164\) | 24672.0 | 0.0716300 | ||||||||
\(165\) | −499200. | −1.42746 | ||||||||
\(166\) | 239304. | 0.674031 | ||||||||
\(167\) | 555258. | 1.54065 | 0.770324 | − | 0.637652i | \(-0.220094\pi\) | ||||
0.770324 | + | 0.637652i | \(0.220094\pi\) | |||||||
\(168\) | −36608.0 | −0.100070 | ||||||||
\(169\) | −369177. | −0.994301 | ||||||||
\(170\) | 37800.0 | 0.100316 | ||||||||
\(171\) | 476300. | 1.24563 | ||||||||
\(172\) | −80416.0 | −0.207263 | ||||||||
\(173\) | 417354. | 1.06020 | 0.530102 | − | 0.847934i | \(-0.322154\pi\) | ||||
0.530102 | + | 0.847934i | \(0.322154\pi\) | |||||||
\(174\) | −583440. | −1.46091 | ||||||||
\(175\) | −13750.0 | −0.0339397 | ||||||||
\(176\) | −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 | \(0.519459\pi\) | |||||||
\(180\) | −173200. | −0.398443 | ||||||||
\(181\) | 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 | ||||||||
\(185\) | 3550.00 | 0.00762604 | ||||||||
\(186\) | −414752. | −0.879035 | ||||||||
\(187\) | −290304. | −0.607084 | ||||||||
\(188\) | 395808. | 0.816752 | ||||||||
\(189\) | 108680. | 0.221307 | ||||||||
\(190\) | 110000. | 0.221059 | ||||||||
\(191\) | −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 | \(-0.344545\pi\) | ||||
0.469191 | + | 0.883097i | \(0.344545\pi\) | |||||||
\(194\) | 577528. | 1.10171 | ||||||||
\(195\) | −29900.0 | −0.0563099 | ||||||||
\(196\) | −261168. | −0.485601 | ||||||||
\(197\) | 1.01018e6 | 1.85452 | 0.927262 | − | 0.374414i | \(-0.122156\pi\) | ||||
0.927262 | + | 0.374414i | \(0.122156\pi\) | |||||||
\(198\) | 1.33018e6 | 2.41127 | ||||||||
\(199\) | −807640. | −1.44572 | −0.722862 | − | 0.690993i | \(-0.757174\pi\) | ||||
−0.722862 | + | 0.690993i | \(0.757174\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 643292. | 1.12310 | ||||||||
\(202\) | 565032. | 0.974304 | ||||||||
\(203\) | 123420. | 0.210206 | ||||||||
\(204\) | −157248. | −0.264551 | ||||||||
\(205\) | −38550.0 | −0.0640678 | ||||||||
\(206\) | −559256. | −0.918211 | ||||||||
\(207\) | −859938. | −1.39489 | ||||||||
\(208\) | −11776.0 | −0.0188729 | ||||||||
\(209\) | −844800. | −1.33779 | ||||||||
\(210\) | 57200.0 | 0.0895051 | ||||||||
\(211\) | 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 | ||||||||
\(215\) | 125650. | 0.185381 | ||||||||
\(216\) | 316160. | 0.461076 | ||||||||
\(217\) | 87736.0 | 0.126482 | ||||||||
\(218\) | −873800. | −1.24529 | ||||||||
\(219\) | 1.35528e6 | 1.90949 | ||||||||
\(220\) | 307200. | 0.427922 | ||||||||
\(221\) | −17388.0 | −0.0239480 | ||||||||
\(222\) | −14768.0 | −0.0201113 | ||||||||
\(223\) | −443506. | −0.597224 | −0.298612 | − | 0.954375i | \(-0.596524\pi\) | ||||
−0.298612 | + | 0.954375i | \(0.596524\pi\) | |||||||
\(224\) | 22528.0 | 0.0299987 | ||||||||
\(225\) | 270625. | 0.356379 | ||||||||
\(226\) | 115224. | 0.150062 | ||||||||
\(227\) | 420018. | 0.541007 | 0.270504 | − | 0.962719i | \(-0.412810\pi\) | ||||
0.270504 | + | 0.962719i | \(0.412810\pi\) | |||||||
\(228\) | −457600. | −0.582974 | ||||||||
\(229\) | 1.05875e6 | 1.33415 | 0.667075 | − | 0.744990i | \(-0.267546\pi\) | ||||
0.667075 | + | 0.744990i | \(0.267546\pi\) | |||||||
\(230\) | −198600. | −0.247548 | ||||||||
\(231\) | −439296. | −0.541661 | ||||||||
\(232\) | 359040. | 0.437948 | ||||||||
\(233\) | −1.27345e6 | −1.53671 | −0.768353 | − | 0.640026i | \(-0.778923\pi\) | ||||
−0.768353 | + | 0.640026i | \(0.778923\pi\) | |||||||
\(234\) | 79672.0 | 0.0951187 | ||||||||
\(235\) | −618450. | −0.730525 | ||||||||
\(236\) | 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 | \(0.567308\pi\) | |||||||
\(240\) | 166400. | 0.186477 | ||||||||
\(241\) | −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 | ||||||||
\(245\) | 408075. | 0.434335 | ||||||||
\(246\) | 160368. | 0.168958 | ||||||||
\(247\) | −50600.0 | −0.0527726 | ||||||||
\(248\) | 255232. | 0.263515 | ||||||||
\(249\) | 1.55548e6 | 1.58988 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | 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 | ||||||||
\(255\) | 245700. | 0.236622 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −651462. | −0.615257 | −0.307628 | − | 0.951507i | \(-0.599535\pi\) | ||||
−0.307628 | + | 0.951507i | \(0.599535\pi\) | |||||||
\(258\) | −522704. | −0.488885 | ||||||||
\(259\) | 3124.00 | 0.00289375 | ||||||||
\(260\) | 18400.0 | 0.0168805 | ||||||||
\(261\) | −2.42913e6 | −2.20724 | ||||||||
\(262\) | 978432. | 0.880597 | ||||||||
\(263\) | 917574. | 0.817997 | 0.408999 | − | 0.912535i | \(-0.365878\pi\) | ||||
0.408999 | + | 0.912535i | \(0.365878\pi\) | |||||||
\(264\) | −1.27795e6 | −1.12851 | ||||||||
\(265\) | 354150. | 0.309794 | ||||||||
\(266\) | 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 | \(0.600268\pi\) | |||||||
\(270\) | −494000. | −0.412399 | ||||||||
\(271\) | −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 | ||||||||
\(275\) | −480000. | −0.382745 | ||||||||
\(276\) | 826176. | 0.652830 | ||||||||
\(277\) | −1.66034e6 | −1.30016 | −0.650082 | − | 0.759864i | \(-0.725265\pi\) | ||||
−0.650082 | + | 0.759864i | \(0.725265\pi\) | |||||||
\(278\) | −123440. | −0.0957952 | ||||||||
\(279\) | −1.72680e6 | −1.32811 | ||||||||
\(280\) | −35200.0 | −0.0268317 | ||||||||
\(281\) | 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 | \(-0.463416\pi\) | ||||
0.114679 | + | 0.993403i | \(0.463416\pi\) | |||||||
\(284\) | 677952. | 0.498773 | ||||||||
\(285\) | 715000. | 0.521427 | ||||||||
\(286\) | −141312. | −0.102156 | ||||||||
\(287\) | −33924.0 | −0.0243110 | ||||||||
\(288\) | −443392. | −0.314997 | ||||||||
\(289\) | −1.27697e6 | −0.899367 | ||||||||
\(290\) | −561000. | −0.391713 | ||||||||
\(291\) | 3.75393e6 | 2.59869 | ||||||||
\(292\) | −834016. | −0.572423 | ||||||||
\(293\) | −1.59301e6 | −1.08405 | −0.542024 | − | 0.840363i | \(-0.682342\pi\) | ||||
−0.542024 | + | 0.840363i | \(0.682342\pi\) | |||||||
\(294\) | −1.69759e6 | −1.14542 | ||||||||
\(295\) | −709500. | −0.474676 | ||||||||
\(296\) | 9088.00 | 0.00602891 | ||||||||
\(297\) | 3.79392e6 | 2.49573 | ||||||||
\(298\) | 403800. | 0.263406 | ||||||||
\(299\) | 91356.0 | 0.0590961 | ||||||||
\(300\) | −260000. | −0.166790 | ||||||||
\(301\) | 110572. | 0.0703443 | ||||||||
\(302\) | −49808.0 | −0.0314255 | ||||||||
\(303\) | 3.67271e6 | 2.29816 | ||||||||
\(304\) | 281600. | 0.174763 | ||||||||
\(305\) | −138050. | −0.0849741 | ||||||||
\(306\) | −654696. | −0.399702 | ||||||||
\(307\) | 1.24726e6 | 0.755284 | 0.377642 | − | 0.925952i | \(-0.376735\pi\) | ||||
0.377642 | + | 0.925952i | \(0.376735\pi\) | |||||||
\(308\) | 270336. | 0.162378 | ||||||||
\(309\) | −3.63516e6 | −2.16585 | ||||||||
\(310\) | −398800. | −0.235695 | ||||||||
\(311\) | −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 | \(-0.554561\pi\) | ||||
−0.170572 | + | 0.985345i | \(0.554561\pi\) | |||||||
\(314\) | 24088.0 | 0.0137872 | ||||||||
\(315\) | 238150. | 0.135230 | ||||||||
\(316\) | −634240. | −0.357302 | ||||||||
\(317\) | −516342. | −0.288595 | −0.144298 | − | 0.989534i | \(-0.546092\pi\) | ||||
−0.144298 | + | 0.989534i | \(0.546092\pi\) | |||||||
\(318\) | −1.47326e6 | −0.816983 | ||||||||
\(319\) | 4.30848e6 | 2.37054 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | −2.24687e6 | −1.21707 | ||||||||
\(322\) | −174768. | −0.0939339 | ||||||||
\(323\) | 415800. | 0.221757 | ||||||||
\(324\) | 371536. | 0.196625 | ||||||||
\(325\) | −28750.0 | −0.0150983 | ||||||||
\(326\) | 2.00346e6 | 1.04409 | ||||||||
\(327\) | −5.67970e6 | −2.93735 | ||||||||
\(328\) | −98688.0 | −0.0506500 | ||||||||
\(329\) | −544236. | −0.277203 | ||||||||
\(330\) | 1.99680e6 | 1.00937 | ||||||||
\(331\) | −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 | ||||||||
\(335\) | 618550. | 0.301136 | ||||||||
\(336\) | 146432. | 0.0707600 | ||||||||
\(337\) | 1.91098e6 | 0.916602 | 0.458301 | − | 0.888797i | \(-0.348458\pi\) | ||||
0.458301 | + | 0.888797i | \(0.348458\pi\) | |||||||
\(338\) | 1.47671e6 | 0.703077 | ||||||||
\(339\) | 748956. | 0.353962 | ||||||||
\(340\) | −151200. | −0.0709340 | ||||||||
\(341\) | 3.06278e6 | 1.42636 | ||||||||
\(342\) | −1.90520e6 | −0.880796 | ||||||||
\(343\) | 728860. | 0.334510 | ||||||||
\(344\) | 321664. | 0.146557 | ||||||||
\(345\) | −1.29090e6 | −0.583909 | ||||||||
\(346\) | −1.66942e6 | −0.749677 | ||||||||
\(347\) | 2.42006e6 | 1.07895 | 0.539476 | − | 0.842001i | \(-0.318622\pi\) | ||||
0.539476 | + | 0.842001i | \(0.318622\pi\) | |||||||
\(348\) | 2.33376e6 | 1.03302 | ||||||||
\(349\) | 2.50727e6 | 1.10189 | 0.550944 | − | 0.834542i | \(-0.314268\pi\) | ||||
0.550944 | + | 0.834542i | \(0.314268\pi\) | |||||||
\(350\) | 55000.0 | 0.0239990 | ||||||||
\(351\) | 227240. | 0.0984503 | ||||||||
\(352\) | 786432. | 0.338302 | ||||||||
\(353\) | −413166. | −0.176477 | −0.0882384 | − | 0.996099i | \(-0.528124\pi\) | ||||
−0.0882384 | + | 0.996099i | \(0.528124\pi\) | |||||||
\(354\) | 2.95152e6 | 1.25181 | ||||||||
\(355\) | −1.05930e6 | −0.446116 | ||||||||
\(356\) | 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 | \(0.384206\pi\) | |||||||
\(360\) | 692800. | 0.281742 | ||||||||
\(361\) | −1.26610e6 | −0.511328 | ||||||||
\(362\) | −2.18665e6 | −0.877016 | ||||||||
\(363\) | −1.11481e7 | −4.44052 | ||||||||
\(364\) | 16192.0 | 0.00640541 | ||||||||
\(365\) | 1.30315e6 | 0.511991 | ||||||||
\(366\) | 574288. | 0.224092 | ||||||||
\(367\) | 1.16098e6 | 0.449944 | 0.224972 | − | 0.974365i | \(-0.427771\pi\) | ||||
0.224972 | + | 0.974365i | \(0.427771\pi\) | |||||||
\(368\) | −508416. | −0.195704 | ||||||||
\(369\) | 667686. | 0.255274 | ||||||||
\(370\) | −14200.0 | −0.00539242 | ||||||||
\(371\) | 311652. | 0.117553 | ||||||||
\(372\) | 1.65901e6 | 0.621572 | ||||||||
\(373\) | 343754. | 0.127931 | 0.0639655 | − | 0.997952i | \(-0.479625\pi\) | ||||
0.0639655 | + | 0.997952i | \(0.479625\pi\) | |||||||
\(374\) | 1.16122e6 | 0.429273 | ||||||||
\(375\) | 406250. | 0.149182 | ||||||||
\(376\) | −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 | \(0.467323\pi\) | |||||||
\(380\) | −440000. | −0.156312 | ||||||||
\(381\) | 5.62905e6 | 1.98666 | ||||||||
\(382\) | 1.80811e6 | 0.633967 | ||||||||
\(383\) | −2.88055e6 | −1.00341 | −0.501704 | − | 0.865039i | \(-0.667293\pi\) | ||||
−0.501704 | + | 0.865039i | \(0.667293\pi\) | |||||||
\(384\) | 425984. | 0.147423 | ||||||||
\(385\) | −422400. | −0.145235 | ||||||||
\(386\) | −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 | \(0.672926\pi\) | |||||||
\(390\) | 119600. | 0.0398171 | ||||||||
\(391\) | −750708. | −0.248330 | ||||||||
\(392\) | 1.04467e6 | 0.343372 | ||||||||
\(393\) | 6.35981e6 | 2.07712 | ||||||||
\(394\) | −4.04071e6 | −1.31135 | ||||||||
\(395\) | 991000. | 0.319581 | ||||||||
\(396\) | −5.32070e6 | −1.70503 | ||||||||
\(397\) | 885458. | 0.281963 | 0.140981 | − | 0.990012i | \(-0.454974\pi\) | ||||
0.140981 | + | 0.990012i | \(0.454974\pi\) | |||||||
\(398\) | 3.23056e6 | 1.02228 | ||||||||
\(399\) | 629200. | 0.197859 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −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 | ||||||||
\(405\) | −580525. | −0.175867 | ||||||||
\(406\) | −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 | \(0.592887\pi\) | |||||||
\(410\) | 154200. | 0.0453028 | ||||||||
\(411\) | 6.22705e6 | 1.81835 | ||||||||
\(412\) | 2.23702e6 | 0.649273 | ||||||||
\(413\) | −624360. | −0.180119 | ||||||||
\(414\) | 3.43975e6 | 0.986339 | ||||||||
\(415\) | 1.49565e6 | 0.426295 | ||||||||
\(416\) | 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 | \(0.636654\pi\) | |||||||
\(420\) | −228800. | −0.0632897 | ||||||||
\(421\) | 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 | ||||||||
\(425\) | 236250. | 0.0634453 | ||||||||
\(426\) | 4.40669e6 | 1.17649 | ||||||||
\(427\) | −121484. | −0.0322440 | ||||||||
\(428\) | 1.38269e6 | 0.364850 | ||||||||
\(429\) | −918528. | −0.240962 | ||||||||
\(430\) | −502600. | −0.131085 | ||||||||
\(431\) | −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 | \(-0.697410\pi\) | ||||
−0.581183 | + | 0.813773i | \(0.697410\pi\) | |||||||
\(434\) | −350944. | −0.0894362 | ||||||||
\(435\) | −3.64650e6 | −0.923960 | ||||||||
\(436\) | 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 | \(0.542783\pi\) | |||||||
\(440\) | −1.22880e6 | −0.302586 | ||||||||
\(441\) | −7.06786e6 | −1.73058 | ||||||||
\(442\) | 69552.0 | 0.0169338 | ||||||||
\(443\) | −1.08079e6 | −0.261656 | −0.130828 | − | 0.991405i | \(-0.541764\pi\) | ||||
−0.130828 | + | 0.991405i | \(0.541764\pi\) | |||||||
\(444\) | 59072.0 | 0.0142208 | ||||||||
\(445\) | −1.44225e6 | −0.345255 | ||||||||
\(446\) | 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 | \(0.400874\pi\) | |||||||
\(450\) | −1.08250e6 | −0.251998 | ||||||||
\(451\) | −1.18426e6 | −0.274160 | ||||||||
\(452\) | −460896. | −0.106110 | ||||||||
\(453\) | −323752. | −0.0741254 | ||||||||
\(454\) | −1.68007e6 | −0.382550 | ||||||||
\(455\) | −25300.0 | −0.00572917 | ||||||||
\(456\) | 1.83040e6 | 0.412225 | ||||||||
\(457\) | 1.59046e6 | 0.356231 | 0.178115 | − | 0.984010i | \(-0.443000\pi\) | ||||
0.178115 | + | 0.984010i | \(0.443000\pi\) | |||||||
\(458\) | −4.23500e6 | −0.943387 | ||||||||
\(459\) | −1.86732e6 | −0.413701 | ||||||||
\(460\) | 794400. | 0.175043 | ||||||||
\(461\) | 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 | \(-0.384811\pi\) | ||||
0.354031 | + | 0.935234i | \(0.384811\pi\) | |||||||
\(464\) | −1.43616e6 | −0.309676 | ||||||||
\(465\) | −2.59220e6 | −0.555950 | ||||||||
\(466\) | 5.09378e6 | 1.08662 | ||||||||
\(467\) | −601542. | −0.127636 | −0.0638181 | − | 0.997962i | \(-0.520328\pi\) | ||||
−0.0638181 | + | 0.997962i | \(0.520328\pi\) | |||||||
\(468\) | −318688. | −0.0672591 | ||||||||
\(469\) | 544324. | 0.114268 | ||||||||
\(470\) | 2.47380e6 | 0.516559 | ||||||||
\(471\) | 156572. | 0.0325208 | ||||||||
\(472\) | −1.81632e6 | −0.375264 | ||||||||
\(473\) | 3.85997e6 | 0.793288 | ||||||||
\(474\) | −4.12256e6 | −0.842793 | ||||||||
\(475\) | 687500. | 0.139810 | ||||||||
\(476\) | −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 | \(0.650706\pi\) | |||||||
\(480\) | −665600. | −0.131859 | ||||||||
\(481\) | 6532.00 | 0.00128731 | ||||||||
\(482\) | 2.24519e6 | 0.440186 | ||||||||
\(483\) | −1.13599e6 | −0.221568 | ||||||||
\(484\) | 6.86037e6 | 1.33117 | ||||||||
\(485\) | 3.60955e6 | 0.696785 | ||||||||
\(486\) | −2.38670e6 | −0.458360 | ||||||||
\(487\) | 7.05226e6 | 1.34743 | 0.673714 | − | 0.738992i | \(-0.264698\pi\) | ||||
0.673714 | + | 0.738992i | \(0.264698\pi\) | |||||||
\(488\) | −353408. | −0.0671780 | ||||||||
\(489\) | 1.30225e7 | 2.46276 | ||||||||
\(490\) | −1.63230e6 | −0.307121 | ||||||||
\(491\) | −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 | ||||||||
\(495\) | 8.31360e6 | 1.52502 | ||||||||
\(496\) | −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 | \(0.605270\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | −1.44367e7 | −2.56965 | ||||||||
\(502\) | −2.30861e6 | −0.408875 | ||||||||
\(503\) | 9.15629e6 | 1.61361 | 0.806807 | − | 0.590815i | \(-0.201194\pi\) | ||||
0.806807 | + | 0.590815i | \(0.201194\pi\) | |||||||
\(504\) | 609664. | 0.106909 | ||||||||
\(505\) | 3.53145e6 | 0.616204 | ||||||||
\(506\) | −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 | \(0.286660\pi\) | |||||||
\(510\) | −982800. | −0.167317 | ||||||||
\(511\) | 1.14677e6 | 0.194279 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −5.43400e6 | −0.911646 | ||||||||
\(514\) | 2.60585e6 | 0.435052 | ||||||||
\(515\) | −3.49535e6 | −0.580728 | ||||||||
\(516\) | 2.09082e6 | 0.345694 | ||||||||
\(517\) | −1.89988e7 | −3.12608 | ||||||||
\(518\) | −12496.0 | −0.00204619 | ||||||||
\(519\) | −1.08512e7 | −1.76831 | ||||||||
\(520\) | −73600.0 | −0.0119363 | ||||||||
\(521\) | 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 | \(-0.726528\pi\) | ||||
−0.653090 | + | 0.757280i | \(0.726528\pi\) | |||||||
\(524\) | −3.91373e6 | −0.622676 | ||||||||
\(525\) | 357500. | 0.0566080 | ||||||||
\(526\) | −3.67030e6 | −0.578411 | ||||||||
\(527\) | −1.50746e6 | −0.236440 | ||||||||
\(528\) | 5.11181e6 | 0.797976 | ||||||||
\(529\) | −2.49215e6 | −0.387199 | ||||||||
\(530\) | −1.41660e6 | −0.219057 | ||||||||
\(531\) | 1.22885e7 | 1.89132 | ||||||||
\(532\) | −387200. | −0.0593139 | ||||||||
\(533\) | −70932.0 | −0.0108149 | ||||||||
\(534\) | 5.99976e6 | 0.910502 | ||||||||
\(535\) | −2.16045e6 | −0.326332 | ||||||||
\(536\) | 1.58349e6 | 0.238069 | ||||||||
\(537\) | 1.36188e6 | 0.203800 | ||||||||
\(538\) | 2.94156e6 | 0.438149 | ||||||||
\(539\) | 1.25361e7 | 1.85861 | ||||||||
\(540\) | 1.97600e6 | 0.291610 | ||||||||
\(541\) | −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 | ||||||||
\(545\) | −5.46125e6 | −0.787591 | ||||||||
\(546\) | 105248. | 0.0151089 | ||||||||
\(547\) | −3.50750e6 | −0.501221 | −0.250611 | − | 0.968088i | \(-0.580631\pi\) | ||||
−0.250611 | + | 0.968088i | \(0.580631\pi\) | |||||||
\(548\) | −3.83203e6 | −0.545102 | ||||||||
\(549\) | 2.39103e6 | 0.338574 | ||||||||
\(550\) | 1.92000e6 | 0.270642 | ||||||||
\(551\) | −6.17100e6 | −0.865918 | ||||||||
\(552\) | −3.30470e6 | −0.461620 | ||||||||
\(553\) | 872080. | 0.121267 | ||||||||
\(554\) | 6.64137e6 | 0.919355 | ||||||||
\(555\) | −92300.0 | −0.0127195 | ||||||||
\(556\) | 493760. | 0.0677375 | ||||||||
\(557\) | 9.61490e6 | 1.31313 | 0.656563 | − | 0.754271i | \(-0.272009\pi\) | ||||
0.656563 | + | 0.754271i | \(0.272009\pi\) | |||||||
\(558\) | 6.90722e6 | 0.939112 | ||||||||
\(559\) | 231196. | 0.0312933 | ||||||||
\(560\) | 140800. | 0.0189729 | ||||||||
\(561\) | 7.54790e6 | 1.01256 | ||||||||
\(562\) | −5.80841e6 | −0.775740 | ||||||||
\(563\) | 2.01941e6 | 0.268506 | 0.134253 | − | 0.990947i | \(-0.457136\pi\) | ||||
0.134253 | + | 0.990947i | \(0.457136\pi\) | |||||||
\(564\) | −1.02910e7 | −1.36226 | ||||||||
\(565\) | 720150. | 0.0949078 | ||||||||
\(566\) | −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 | \(0.471552\pi\) | |||||||
\(570\) | −2.86000e6 | −0.368705 | ||||||||
\(571\) | 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 | ||||||||
\(575\) | −1.24125e6 | −0.156563 | ||||||||
\(576\) | 1.77357e6 | 0.222737 | ||||||||
\(577\) | −2.31458e6 | −0.289423 | −0.144711 | − | 0.989474i | \(-0.546225\pi\) | ||||
−0.144711 | + | 0.989474i | \(0.546225\pi\) | |||||||
\(578\) | 5.10789e6 | 0.635949 | ||||||||
\(579\) | −1.26254e7 | −1.56513 | ||||||||
\(580\) | 2.24400e6 | 0.276983 | ||||||||
\(581\) | 1.31617e6 | 0.161760 | ||||||||
\(582\) | −1.50157e7 | −1.83755 | ||||||||
\(583\) | 1.08795e7 | 1.32568 | ||||||||
\(584\) | 3.33606e6 | 0.404764 | ||||||||
\(585\) | 497950. | 0.0601584 | ||||||||
\(586\) | 6.37202e6 | 0.766537 | ||||||||
\(587\) | 928338. | 0.111202 | 0.0556008 | − | 0.998453i | \(-0.482293\pi\) | ||||
0.0556008 | + | 0.998453i | \(0.482293\pi\) | |||||||
\(588\) | 6.79037e6 | 0.809935 | ||||||||
\(589\) | −4.38680e6 | −0.521026 | ||||||||
\(590\) | 2.83800e6 | 0.335647 | ||||||||
\(591\) | −2.62646e7 | −3.09316 | ||||||||
\(592\) | −36352.0 | −0.00426309 | ||||||||
\(593\) | −909486. | −0.106209 | −0.0531043 | − | 0.998589i | \(-0.516912\pi\) | ||||
−0.0531043 | + | 0.998589i | \(0.516912\pi\) | |||||||
\(594\) | −1.51757e7 | −1.76475 | ||||||||
\(595\) | 207900. | 0.0240748 | ||||||||
\(596\) | −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 | \(0.661042\pi\) | |||||||
\(600\) | 1.04000e6 | 0.117938 | ||||||||
\(601\) | 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 | ||||||||
\(605\) | −1.07193e7 | −1.19064 | ||||||||
\(606\) | −1.46908e7 | −1.62504 | ||||||||
\(607\) | −4.51646e6 | −0.497538 | −0.248769 | − | 0.968563i | \(-0.580026\pi\) | ||||
−0.248769 | + | 0.968563i | \(0.580026\pi\) | |||||||
\(608\) | −1.12640e6 | −0.123576 | ||||||||
\(609\) | −3.20892e6 | −0.350603 | ||||||||
\(610\) | 552200. | 0.0600858 | ||||||||
\(611\) | −1.13795e6 | −0.123316 | ||||||||
\(612\) | 2.61878e6 | 0.282632 | ||||||||
\(613\) | 9.63979e6 | 1.03614 | 0.518068 | − | 0.855340i | \(-0.326651\pi\) | ||||
0.518068 | + | 0.855340i | \(0.326651\pi\) | |||||||
\(614\) | −4.98903e6 | −0.534067 | ||||||||
\(615\) | 1.00230e6 | 0.106859 | ||||||||
\(616\) | −1.08134e6 | −0.114819 | ||||||||
\(617\) | −9.92650e6 | −1.04974 | −0.524872 | − | 0.851181i | \(-0.675887\pi\) | ||||
−0.524872 | + | 0.851181i | \(0.675887\pi\) | |||||||
\(618\) | 1.45407e7 | 1.53149 | ||||||||
\(619\) | 7.63322e6 | 0.800721 | 0.400360 | − | 0.916358i | \(-0.368885\pi\) | ||||
0.400360 | + | 0.916358i | \(0.368885\pi\) | |||||||
\(620\) | 1.59520e6 | 0.166662 | ||||||||
\(621\) | 9.81084e6 | 1.02089 | ||||||||
\(622\) | 2.66395e6 | 0.276090 | ||||||||
\(623\) | −1.26918e6 | −0.131010 | ||||||||
\(624\) | 306176. | 0.0314782 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 2.36514e6 | 0.241225 | ||||||||
\(627\) | 2.19648e7 | 2.23130 | ||||||||
\(628\) | −96352.0 | −0.00974903 | ||||||||
\(629\) | −53676.0 | −0.00540946 | ||||||||
\(630\) | −952600. | −0.0956223 | ||||||||
\(631\) | 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 | ||||||||
\(635\) | 5.41255e6 | 0.532681 | ||||||||
\(636\) | 5.89306e6 | 0.577694 | ||||||||
\(637\) | 750858. | 0.0733178 | ||||||||
\(638\) | −1.72339e7 | −1.67623 | ||||||||
\(639\) | 1.83471e7 | 1.77752 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | 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 | \(-0.729329\pi\) | ||||
−0.659730 | + | 0.751503i | \(0.729329\pi\) | |||||||
\(644\) | 699072. | 0.0664213 | ||||||||
\(645\) | −3.26690e6 | −0.309198 | ||||||||
\(646\) | −1.66320e6 | −0.156806 | ||||||||
\(647\) | −1.48997e7 | −1.39932 | −0.699658 | − | 0.714478i | \(-0.746664\pi\) | ||||
−0.699658 | + | 0.714478i | \(0.746664\pi\) | |||||||
\(648\) | −1.48614e6 | −0.139035 | ||||||||
\(649\) | −2.17958e7 | −2.03124 | ||||||||
\(650\) | 115000. | 0.0106761 | ||||||||
\(651\) | −2.28114e6 | −0.210959 | ||||||||
\(652\) | −8.01386e6 | −0.738282 | ||||||||
\(653\) | −1.93306e7 | −1.77403 | −0.887016 | − | 0.461738i | \(-0.847226\pi\) | ||||
−0.887016 | + | 0.461738i | \(0.847226\pi\) | |||||||
\(654\) | 2.27188e7 | 2.07702 | ||||||||
\(655\) | 6.11520e6 | 0.556939 | ||||||||
\(656\) | 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 | \(0.558302\pi\) | |||||||
\(660\) | −7.98720e6 | −0.713731 | ||||||||
\(661\) | −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 | ||||||||
\(665\) | 605000. | 0.0530519 | ||||||||
\(666\) | 245944. | 0.0214858 | ||||||||
\(667\) | 1.11415e7 | 0.969678 | ||||||||
\(668\) | 8.88413e6 | 0.770324 | ||||||||
\(669\) | 1.15312e7 | 0.996111 | ||||||||
\(670\) | −2.47420e6 | −0.212935 | ||||||||
\(671\) | −4.24090e6 | −0.363623 | ||||||||
\(672\) | −585728. | −0.0500349 | ||||||||
\(673\) | 1.43520e7 | 1.22144 | 0.610722 | − | 0.791845i | \(-0.290879\pi\) | ||||
0.610722 | + | 0.791845i | \(0.290879\pi\) | |||||||
\(674\) | −7.64391e6 | −0.648136 | ||||||||
\(675\) | −3.08750e6 | −0.260824 | ||||||||
\(676\) | −5.90683e6 | −0.497150 | ||||||||
\(677\) | 1.89530e6 | 0.158930 | 0.0794650 | − | 0.996838i | \(-0.474679\pi\) | ||||
0.0794650 | + | 0.996838i | \(0.474679\pi\) | |||||||
\(678\) | −2.99582e6 | −0.250289 | ||||||||
\(679\) | 3.17640e6 | 0.264400 | ||||||||
\(680\) | 604800. | 0.0501579 | ||||||||
\(681\) | −1.09205e7 | −0.902347 | ||||||||
\(682\) | −1.22511e7 | −1.00859 | ||||||||
\(683\) | 2.91641e6 | 0.239220 | 0.119610 | − | 0.992821i | \(-0.461836\pi\) | ||||
0.119610 | + | 0.992821i | \(0.461836\pi\) | |||||||
\(684\) | 7.62080e6 | 0.622817 | ||||||||
\(685\) | 5.98755e6 | 0.487554 | ||||||||
\(686\) | −2.91544e6 | −0.236534 | ||||||||
\(687\) | −2.75275e7 | −2.22523 | ||||||||
\(688\) | −1.28666e6 | −0.103631 | ||||||||
\(689\) | 651636. | 0.0522946 | ||||||||
\(690\) | 5.16360e6 | 0.412886 | ||||||||
\(691\) | 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 | ||||||||
\(695\) | −771500. | −0.0605862 | ||||||||
\(696\) | −9.33504e6 | −0.730454 | ||||||||
\(697\) | 582876. | 0.0454458 | ||||||||
\(698\) | −1.00291e7 | −0.779153 | ||||||||
\(699\) | 3.31096e7 | 2.56307 | ||||||||
\(700\) | −220000. | −0.0169698 | ||||||||
\(701\) | −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 | ||||||||
\(705\) | 1.60797e7 | 1.21844 | ||||||||
\(706\) | 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 | \(0.503589\pi\) | |||||||
\(710\) | 4.23720e6 | 0.315452 | ||||||||
\(711\) | −1.71641e7 | −1.27335 | ||||||||
\(712\) | −3.69216e6 | −0.272948 | ||||||||
\(713\) | 7.92017e6 | 0.583459 | ||||||||
\(714\) | −864864. | −0.0634896 | ||||||||
\(715\) | −883200. | −0.0646091 | ||||||||
\(716\) | −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 | \(0.221684\pi\) | |||||||
\(720\) | −2.77120e6 | −0.199222 | ||||||||
\(721\) | −3.07591e6 | −0.220361 | ||||||||
\(722\) | 5.06440e6 | 0.361564 | ||||||||
\(723\) | 1.45937e7 | 1.03830 | ||||||||
\(724\) | 8.74659e6 | 0.620144 | ||||||||
\(725\) | −3.50625e6 | −0.247741 | ||||||||
\(726\) | 4.45924e7 | 3.13992 | ||||||||
\(727\) | 1.55009e7 | 1.08773 | 0.543863 | − | 0.839174i | \(-0.316961\pi\) | ||||
0.543863 | + | 0.839174i | \(0.316961\pi\) | |||||||
\(728\) | −64768.0 | −0.00452931 | ||||||||
\(729\) | −2.11562e7 | −1.47441 | ||||||||
\(730\) | −5.21260e6 | −0.362032 | ||||||||
\(731\) | −1.89983e6 | −0.131499 | ||||||||
\(732\) | −2.29715e6 | −0.158457 | ||||||||
\(733\) | −1.21850e7 | −0.837653 | −0.418827 | − | 0.908066i | \(-0.637559\pi\) | ||||
−0.418827 | + | 0.908066i | \(0.637559\pi\) | |||||||
\(734\) | −4.64391e6 | −0.318159 | ||||||||
\(735\) | −1.06100e7 | −0.724428 | ||||||||
\(736\) | 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 | \(0.932562\pi\) | |||||||
\(740\) | 56800.0 | 0.00381302 | ||||||||
\(741\) | 1.31560e6 | 0.0880194 | ||||||||
\(742\) | −1.24661e6 | −0.0831228 | ||||||||
\(743\) | 1.61145e7 | 1.07089 | 0.535445 | − | 0.844570i | \(-0.320144\pi\) | ||||
0.535445 | + | 0.844570i | \(0.320144\pi\) | |||||||
\(744\) | −6.63603e6 | −0.439517 | ||||||||
\(745\) | 2.52375e6 | 0.166593 | ||||||||
\(746\) | −1.37502e6 | −0.0904609 | ||||||||
\(747\) | −2.59047e7 | −1.69854 | ||||||||
\(748\) | −4.64486e6 | −0.303542 | ||||||||
\(749\) | −1.90120e6 | −0.123829 | ||||||||
\(750\) | −1.62500e6 | −0.105487 | ||||||||
\(751\) | −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 | ||||||||
\(755\) | −311300. | −0.0198752 | ||||||||
\(756\) | 1.73888e6 | 0.110653 | ||||||||
\(757\) | 2.60325e7 | 1.65111 | 0.825557 | − | 0.564319i | \(-0.190861\pi\) | ||||
0.825557 | + | 0.564319i | \(0.190861\pi\) | |||||||
\(758\) | −2.29256e6 | −0.144926 | ||||||||
\(759\) | −3.96564e7 | −2.49867 | ||||||||
\(760\) | 1.76000e6 | 0.110530 | ||||||||
\(761\) | 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 | ||||||||
\(765\) | −4.09185e6 | −0.252794 | ||||||||
\(766\) | 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 | \(0.211612\pi\) | |||||||
\(770\) | 1.68960e6 | 0.102697 | ||||||||
\(771\) | 1.69380e7 | 1.02619 | ||||||||
\(772\) | 7.76950e6 | 0.469191 | ||||||||
\(773\) | −1.90592e7 | −1.14725 | −0.573624 | − | 0.819119i | \(-0.694463\pi\) | ||||
−0.573624 | + | 0.819119i | \(0.694463\pi\) | |||||||
\(774\) | 8.70503e6 | 0.522298 | ||||||||
\(775\) | −2.49250e6 | −0.149067 | ||||||||
\(776\) | 9.24045e6 | 0.550857 | ||||||||
\(777\) | −81224.0 | −0.00482649 | ||||||||
\(778\) | 1.23424e7 | 0.731054 | ||||||||
\(779\) | 1.69620e6 | 0.100146 | ||||||||
\(780\) | −478400. | −0.0281549 | ||||||||
\(781\) | −3.25417e7 | −1.90903 | ||||||||
\(782\) | 3.00283e6 | 0.175596 | ||||||||
\(783\) | 2.77134e7 | 1.61542 | ||||||||
\(784\) | −4.17869e6 | −0.242801 | ||||||||
\(785\) | 150550. | 0.00871980 | ||||||||
\(786\) | −2.54392e7 | −1.46875 | ||||||||
\(787\) | −1.73411e7 | −0.998021 | −0.499011 | − | 0.866596i | \(-0.666303\pi\) | ||||
−0.499011 | + | 0.866596i | \(0.666303\pi\) | |||||||
\(788\) | 1.61628e7 | 0.927262 | ||||||||
\(789\) | −2.38569e7 | −1.36434 | ||||||||
\(790\) | −3.96400e6 | −0.225978 | ||||||||
\(791\) | 633732. | 0.0360134 | ||||||||
\(792\) | 2.12828e7 | 1.20564 | ||||||||
\(793\) | −254012. | −0.0143440 | ||||||||
\(794\) | −3.54183e6 | −0.199378 | ||||||||
\(795\) | −9.20790e6 | −0.516705 | ||||||||
\(796\) | −1.29222e7 | −0.722862 | ||||||||
\(797\) | −2.58169e7 | −1.43965 | −0.719827 | − | 0.694153i | \(-0.755779\pi\) | ||||
−0.719827 | + | 0.694153i | \(0.755779\pi\) | |||||||
\(798\) | −2.51680e6 | −0.139908 | ||||||||
\(799\) | 9.35096e6 | 0.518190 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 2.49798e7 | 1.37565 | ||||||||
\(802\) | 1.50138e7 | 0.824239 | ||||||||
\(803\) | 4.00328e7 | 2.19092 | ||||||||
\(804\) | 1.02927e7 | 0.561549 | ||||||||
\(805\) | −1.09230e6 | −0.0594090 | ||||||||
\(806\) | −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 | \(0.423297\pi\) | |||||||
\(810\) | 2.32210e6 | 0.124356 | ||||||||
\(811\) | −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 | ||||||||
\(815\) | 1.25216e7 | 0.660340 | ||||||||
\(816\) | −2.51597e6 | −0.132276 | ||||||||
\(817\) | −5.52860e6 | −0.289774 | ||||||||
\(818\) | 7.78612e6 | 0.406853 | ||||||||
\(819\) | 438196. | 0.0228275 | ||||||||
\(820\) | −616800. | −0.0320339 | ||||||||
\(821\) | 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 | \(-0.609253\pi\) | ||||
−0.336529 | + | 0.941673i | \(0.609253\pi\) | |||||||
\(824\) | −8.94810e6 | −0.459106 | ||||||||
\(825\) | 1.24800e7 | 0.638381 | ||||||||
\(826\) | 2.49744e6 | 0.127363 | ||||||||
\(827\) | −3.57188e7 | −1.81607 | −0.908037 | − | 0.418891i | \(-0.862419\pi\) | ||||
−0.908037 | + | 0.418891i | \(0.862419\pi\) | |||||||
\(828\) | −1.37590e7 | −0.697447 | ||||||||
\(829\) | 1.61880e7 | 0.818103 | 0.409052 | − | 0.912511i | \(-0.365860\pi\) | ||||
0.409052 | + | 0.912511i | \(0.365860\pi\) | |||||||
\(830\) | −5.98260e6 | −0.301436 | ||||||||
\(831\) | 4.31689e7 | 2.16854 | ||||||||
\(832\) | −188416. | −0.00943647 | ||||||||
\(833\) | −6.17009e6 | −0.308091 | ||||||||
\(834\) | 3.20944e6 | 0.159777 | ||||||||
\(835\) | −1.38814e7 | −0.688999 | ||||||||
\(836\) | −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 | \(0.715531\pi\) | |||||||
\(840\) | 915200. | 0.0447526 | ||||||||
\(841\) | 1.09610e7 | 0.534390 | ||||||||
\(842\) | −1.58664e7 | −0.771256 | ||||||||
\(843\) | −3.77547e7 | −1.82979 | ||||||||
\(844\) | 2.39283e6 | 0.115626 | ||||||||
\(845\) | 9.22942e6 | 0.444665 | ||||||||
\(846\) | −4.28462e7 | −2.05820 | ||||||||
\(847\) | −9.43301e6 | −0.451795 | ||||||||
\(848\) | −3.62650e6 | −0.173180 | ||||||||
\(849\) | −8.03436e6 | −0.382545 | ||||||||
\(850\) | −945000. | −0.0448626 | ||||||||
\(851\) | 282012. | 0.0133488 | ||||||||
\(852\) | −1.76268e7 | −0.831904 | ||||||||
\(853\) | −2.22953e7 | −1.04916 | −0.524579 | − | 0.851362i | \(-0.675777\pi\) | ||||
−0.524579 | + | 0.851362i | \(0.675777\pi\) | |||||||
\(854\) | 485936. | 0.0228000 | ||||||||
\(855\) | −1.19075e7 | −0.557064 | ||||||||
\(856\) | −5.53075e6 | −0.257988 | ||||||||
\(857\) | 1.96872e7 | 0.915656 | 0.457828 | − | 0.889041i | \(-0.348628\pi\) | ||||
0.457828 | + | 0.889041i | \(0.348628\pi\) | |||||||
\(858\) | 3.67411e6 | 0.170386 | ||||||||
\(859\) | 6.77582e6 | 0.313313 | 0.156657 | − | 0.987653i | \(-0.449928\pi\) | ||||
0.156657 | + | 0.987653i | \(0.449928\pi\) | |||||||
\(860\) | 2.01040e6 | 0.0926907 | ||||||||
\(861\) | 882024. | 0.0405483 | ||||||||
\(862\) | 2.06846e7 | 0.948154 | ||||||||
\(863\) | −2.63804e7 | −1.20574 | −0.602871 | − | 0.797839i | \(-0.705977\pi\) | ||||
−0.602871 | + | 0.797839i | \(0.705977\pi\) | |||||||
\(864\) | 5.05856e6 | 0.230538 | ||||||||
\(865\) | −1.04338e7 | −0.474138 | ||||||||
\(866\) | 1.81394e7 | 0.821917 | ||||||||
\(867\) | 3.32013e7 | 1.50006 | ||||||||
\(868\) | 1.40378e6 | 0.0632410 | ||||||||
\(869\) | 3.04435e7 | 1.36756 | ||||||||
\(870\) | 1.45860e7 | 0.653338 | ||||||||
\(871\) | 1.13813e6 | 0.0508332 | ||||||||
\(872\) | −1.39808e7 | −0.622645 | ||||||||
\(873\) | −6.25174e7 | −2.77629 | ||||||||
\(874\) | 8.73840e6 | 0.386949 | ||||||||
\(875\) | 343750. | 0.0151783 | ||||||||
\(876\) | 2.16844e7 | 0.954745 | ||||||||
\(877\) | 2.95161e7 | 1.29587 | 0.647934 | − | 0.761697i | \(-0.275633\pi\) | ||||
0.647934 | + | 0.761697i | \(0.275633\pi\) | |||||||
\(878\) | 4.32880e6 | 0.189510 | ||||||||
\(879\) | 4.14182e7 | 1.80808 | ||||||||
\(880\) | 4.91520e6 | 0.213961 | ||||||||
\(881\) | −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 | \(-0.601554\pi\) | ||||
−0.313656 | + | 0.949537i | \(0.601554\pi\) | |||||||
\(884\) | −278208. | −0.0119740 | ||||||||
\(885\) | 1.84470e7 | 0.791713 | ||||||||
\(886\) | 4.32314e6 | 0.185019 | ||||||||
\(887\) | −1.72028e7 | −0.734160 | −0.367080 | − | 0.930189i | \(-0.619642\pi\) | ||||
−0.367080 | + | 0.930189i | \(0.619642\pi\) | |||||||
\(888\) | −236288. | −0.0100556 | ||||||||
\(889\) | 4.76304e6 | 0.202130 | ||||||||
\(890\) | 5.76900e6 | 0.244132 | ||||||||
\(891\) | −1.78337e7 | −0.752572 | ||||||||
\(892\) | −7.09610e6 | −0.298612 | ||||||||
\(893\) | 2.72118e7 | 1.14190 | ||||||||
\(894\) | −1.04988e7 | −0.439335 | ||||||||
\(895\) | 1.30950e6 | 0.0546447 | ||||||||
\(896\) | 360448. | 0.0149994 | ||||||||
\(897\) | −2.37526e6 | −0.0985665 | ||||||||
\(898\) | −1.04713e7 | −0.433322 | ||||||||
\(899\) | 2.23727e7 | 0.923249 | ||||||||
\(900\) | 4.33000e6 | 0.178189 | ||||||||
\(901\) | −5.35475e6 | −0.219749 | ||||||||
\(902\) | 4.73702e6 | 0.193860 | ||||||||
\(903\) | −2.87487e6 | −0.117327 | ||||||||
\(904\) | 1.84358e6 | 0.0750312 | ||||||||
\(905\) | −1.36666e7 | −0.554674 | ||||||||
\(906\) | 1.29501e6 | 0.0524146 | ||||||||
\(907\) | −3.44434e7 | −1.39023 | −0.695116 | − | 0.718897i | \(-0.744647\pi\) | ||||
−0.695116 | + | 0.718897i | \(0.744647\pi\) | |||||||
\(908\) | 6.72029e6 | 0.270504 | ||||||||
\(909\) | −6.11647e7 | −2.45522 | ||||||||
\(910\) | 101200. | 0.00405114 | ||||||||
\(911\) | −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 | ||||||||
\(915\) | 3.58930e6 | 0.141728 | ||||||||
\(916\) | 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 | \(0.293905\pi\) | |||||||
\(920\) | −3.17760e6 | −0.123774 | ||||||||
\(921\) | −3.24287e7 | −1.25974 | ||||||||
\(922\) | −1.70188e7 | −0.659328 | ||||||||
\(923\) | −1.94911e6 | −0.0753065 | ||||||||
\(924\) | −7.02874e6 | −0.270830 | ||||||||
\(925\) | −88750.0 | −0.00341047 | ||||||||
\(926\) | −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 | \(0.708794\pi\) | |||||||
\(930\) | 1.03688e7 | 0.393116 | ||||||||
\(931\) | −1.79553e7 | −0.678920 | ||||||||
\(932\) | −2.03751e7 | −0.768353 | ||||||||
\(933\) | 1.73157e7 | 0.651232 | ||||||||
\(934\) | 2.40617e6 | 0.0902524 | ||||||||
\(935\) | 7.25760e6 | 0.271496 | ||||||||
\(936\) | 1.27475e6 | 0.0475594 | ||||||||
\(937\) | 1.52520e7 | 0.567515 | 0.283757 | − | 0.958896i | \(-0.408419\pi\) | ||||
0.283757 | + | 0.958896i | \(0.408419\pi\) | |||||||
\(938\) | −2.17730e6 | −0.0807998 | ||||||||
\(939\) | 1.53734e7 | 0.568993 | ||||||||
\(940\) | −9.89520e6 | −0.365262 | ||||||||
\(941\) | 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 | ||||||||
\(945\) | −2.71700e6 | −0.0989715 | ||||||||
\(946\) | −1.54399e7 | −0.560939 | ||||||||
\(947\) | −2.54010e7 | −0.920398 | −0.460199 | − | 0.887816i | \(-0.652222\pi\) | ||||
−0.460199 | + | 0.887816i | \(0.652222\pi\) | |||||||
\(948\) | 1.64902e7 | 0.595945 | ||||||||
\(949\) | 2.39780e6 | 0.0864265 | ||||||||
\(950\) | −2.75000e6 | −0.0988607 | ||||||||
\(951\) | 1.34249e7 | 0.481348 | ||||||||
\(952\) | 532224. | 0.0190328 | ||||||||
\(953\) | −4.97352e7 | −1.77391 | −0.886955 | − | 0.461856i | \(-0.847184\pi\) | ||||
−0.886955 | + | 0.461856i | \(0.847184\pi\) | |||||||
\(954\) | 2.45355e7 | 0.872819 | ||||||||
\(955\) | 1.13007e7 | 0.400956 | ||||||||
\(956\) | −5.93088e6 | −0.209882 | ||||||||
\(957\) | −1.12020e8 | −3.95383 | ||||||||
\(958\) | 1.83173e7 | 0.644833 | ||||||||
\(959\) | 5.26904e6 | 0.185006 | ||||||||
\(960\) | 2.66240e6 | 0.0932385 | ||||||||
\(961\) | −1.27250e7 | −0.444477 | ||||||||
\(962\) | −26128.0 | −0.000910266 0 | ||||||||
\(963\) | 3.74190e7 | 1.30025 | ||||||||
\(964\) | −8.98077e6 | −0.311258 | ||||||||
\(965\) | −1.21398e7 | −0.419658 | ||||||||
\(966\) | 4.54397e6 | 0.156672 | ||||||||
\(967\) | 3.05173e7 | 1.04949 | 0.524747 | − | 0.851258i | \(-0.324160\pi\) | ||||
0.524747 | + | 0.851258i | \(0.324160\pi\) | |||||||
\(968\) | −2.74415e7 | −0.941280 | ||||||||
\(969\) | −1.08108e7 | −0.369869 | ||||||||
\(970\) | −1.44382e7 | −0.492701 | ||||||||
\(971\) | 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 | ||||||||
\(975\) | 747500. | 0.0251825 | ||||||||
\(976\) | 1.41363e6 | 0.0475020 | ||||||||
\(977\) | 2.90786e6 | 0.0974623 | 0.0487312 | − | 0.998812i | \(-0.484482\pi\) | ||||
0.0487312 | + | 0.998812i | \(0.484482\pi\) | |||||||
\(978\) | −5.20901e7 | −1.74144 | ||||||||
\(979\) | −4.43059e7 | −1.47742 | ||||||||
\(980\) | 6.52920e6 | 0.217167 | ||||||||
\(981\) | 9.45888e7 | 3.13810 | ||||||||
\(982\) | 1.04940e7 | 0.347264 | ||||||||
\(983\) | 3.49621e7 | 1.15402 | 0.577010 | − | 0.816737i | \(-0.304219\pi\) | ||||
0.577010 | + | 0.816737i | \(0.304219\pi\) | |||||||
\(984\) | 2.56589e6 | 0.0844792 | ||||||||
\(985\) | −2.52544e7 | −0.829368 | ||||||||
\(986\) | 8.48232e6 | 0.277858 | ||||||||
\(987\) | 1.41501e7 | 0.462347 | ||||||||
\(988\) | −809600. | −0.0263863 | ||||||||
\(989\) | 9.98164e6 | 0.324497 | ||||||||
\(990\) | −3.32544e7 | −1.07835 | ||||||||
\(991\) | 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 | ||||||||
\(995\) | 2.01910e7 | 0.646547 | ||||||||
\(996\) | 2.48876e7 | 0.794941 | ||||||||
\(997\) | 3.20789e7 | 1.02207 | 0.511035 | − | 0.859560i | \(-0.329262\pi\) | ||||
0.511035 | + | 0.859560i | \(0.329262\pi\) | |||||||
\(998\) | 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 | 10.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 90.6.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 80.6.a.h.1.1 | 1 | |||
5.2 | odd | 4 | 50.6.b.d.49.1 | 2 | |||
5.3 | odd | 4 | 50.6.b.d.49.2 | 2 | |||
5.4 | even | 2 | 50.6.a.g.1.1 | 1 | |||
7.6 | odd | 2 | 490.6.a.j.1.1 | 1 | |||
8.3 | odd | 2 | 320.6.a.a.1.1 | 1 | |||
8.5 | even | 2 | 320.6.a.p.1.1 | 1 | |||
12.11 | even | 2 | 720.6.a.r.1.1 | 1 | |||
15.2 | even | 4 | 450.6.c.o.199.2 | 2 | |||
15.8 | even | 4 | 450.6.c.o.199.1 | 2 | |||
15.14 | odd | 2 | 450.6.a.h.1.1 | 1 | |||
20.3 | even | 4 | 400.6.c.a.49.2 | 2 | |||
20.7 | even | 4 | 400.6.c.a.49.1 | 2 | |||
20.19 | odd | 2 | 400.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
50.6.a.g.1.1 | 1 | 5.4 | even | 2 | |||
50.6.b.d.49.1 | 2 | 5.2 | odd | 4 | |||
50.6.b.d.49.2 | 2 | 5.3 | odd | 4 | |||
80.6.a.h.1.1 | 1 | 4.3 | odd | 2 | |||
90.6.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
320.6.a.a.1.1 | 1 | 8.3 | odd | 2 | |||
320.6.a.p.1.1 | 1 | 8.5 | even | 2 | |||
400.6.a.a.1.1 | 1 | 20.19 | odd | 2 | |||
400.6.c.a.49.1 | 2 | 20.7 | even | 4 | |||
400.6.c.a.49.2 | 2 | 20.3 | even | 4 | |||
450.6.a.h.1.1 | 1 | 15.14 | odd | 2 | |||
450.6.c.o.199.1 | 2 | 15.8 | even | 4 | |||
450.6.c.o.199.2 | 2 | 15.2 | even | 4 | |||
490.6.a.j.1.1 | 1 | 7.6 | odd | 2 | |||
720.6.a.r.1.1 | 1 | 12.11 | even | 2 |