Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [150,6,Mod(1,150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("150.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 150 = 2 \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 150.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: | \(24.0575729719\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1249}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 312 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 5 \) |
Twist minimal: | no (minimal twist has level 30) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-17.1706\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 150.1 |
$q$-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 | ||||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 36.0000 | 0.408248 | ||||||||
\(7\) | 119.706 | 0.923359 | 0.461680 | − | 0.887047i | \(-0.347247\pi\) | ||||
0.461680 | + | 0.887047i | \(0.347247\pi\) | |||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 263.706 | 0.657110 | 0.328555 | − | 0.944485i | \(-0.393438\pi\) | ||||
0.328555 | + | 0.944485i | \(0.393438\pi\) | |||||||
\(12\) | −144.000 | −0.288675 | ||||||||
\(13\) | −851.118 | −1.39679 | −0.698395 | − | 0.715712i | \(-0.746102\pi\) | ||||
−0.698395 | + | 0.715712i | \(0.746102\pi\) | |||||||
\(14\) | −478.824 | −0.652914 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1287.12 | −1.08018 | −0.540090 | − | 0.841607i | \(-0.681610\pi\) | ||||
−0.540090 | + | 0.841607i | \(0.681610\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | 2060.47 | 1.30943 | 0.654716 | − | 0.755875i | \(-0.272788\pi\) | ||||
0.654716 | + | 0.755875i | \(0.272788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1077.35 | −0.533102 | ||||||||
\(22\) | −1054.82 | −0.464647 | ||||||||
\(23\) | −55.5284 | −0.0218875 | −0.0109437 | − | 0.999940i | \(-0.503484\pi\) | ||||
−0.0109437 | + | 0.999940i | \(0.503484\pi\) | |||||||
\(24\) | 576.000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3404.47 | 0.987680 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 1915.30 | 0.461680 | ||||||||
\(29\) | −5986.06 | −1.32174 | −0.660870 | − | 0.750500i | \(-0.729813\pi\) | ||||
−0.660870 | + | 0.750500i | \(0.729813\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4781.76 | 0.893684 | 0.446842 | − | 0.894613i | \(-0.352549\pi\) | ||||
0.446842 | + | 0.894613i | \(0.352549\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −2373.35 | −0.379383 | ||||||||
\(34\) | 5148.47 | 0.763802 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | 12150.4 | 1.45911 | 0.729553 | − | 0.683924i | \(-0.239728\pi\) | ||||
0.729553 | + | 0.683924i | \(0.239728\pi\) | |||||||
\(38\) | −8241.89 | −0.925908 | ||||||||
\(39\) | 7660.06 | 0.806438 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 18500.0 | 1.71875 | 0.859374 | − | 0.511348i | \(-0.170854\pi\) | ||||
0.859374 | + | 0.511348i | \(0.170854\pi\) | |||||||
\(42\) | 4309.41 | 0.376960 | ||||||||
\(43\) | 2188.47 | 0.180496 | 0.0902482 | − | 0.995919i | \(-0.471234\pi\) | ||||
0.0902482 | + | 0.995919i | \(0.471234\pi\) | |||||||
\(44\) | 4219.30 | 0.328555 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 222.113 | 0.0154768 | ||||||||
\(47\) | 5597.76 | 0.369632 | 0.184816 | − | 0.982773i | \(-0.440831\pi\) | ||||
0.184816 | + | 0.982773i | \(0.440831\pi\) | |||||||
\(48\) | −2304.00 | −0.144338 | ||||||||
\(49\) | −2477.48 | −0.147408 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11584.1 | 0.623642 | ||||||||
\(52\) | −13617.9 | −0.698395 | ||||||||
\(53\) | 26463.4 | 1.29406 | 0.647031 | − | 0.762463i | \(-0.276010\pi\) | ||||
0.647031 | + | 0.762463i | \(0.276010\pi\) | |||||||
\(54\) | 2916.00 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7661.18 | −0.326457 | ||||||||
\(57\) | −18544.2 | −0.756000 | ||||||||
\(58\) | 23944.2 | 0.934612 | ||||||||
\(59\) | 20825.6 | 0.778875 | 0.389437 | − | 0.921053i | \(-0.372669\pi\) | ||||
0.389437 | + | 0.921053i | \(0.372669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 45525.8 | 1.56651 | 0.783254 | − | 0.621702i | \(-0.213558\pi\) | ||||
0.783254 | + | 0.621702i | \(0.213558\pi\) | |||||||
\(62\) | −19127.1 | −0.631930 | ||||||||
\(63\) | 9696.18 | 0.307786 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9493.41 | 0.268264 | ||||||||
\(67\) | 34354.7 | 0.934974 | 0.467487 | − | 0.884000i | \(-0.345160\pi\) | ||||
0.467487 | + | 0.884000i | \(0.345160\pi\) | |||||||
\(68\) | −20593.9 | −0.540090 | ||||||||
\(69\) | 499.755 | 0.0126367 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −57489.6 | −1.35345 | −0.676726 | − | 0.736235i | \(-0.736602\pi\) | ||||
−0.676726 | + | 0.736235i | \(0.736602\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | 26956.8 | 0.592054 | 0.296027 | − | 0.955180i | \(-0.404338\pi\) | ||||
0.296027 | + | 0.955180i | \(0.404338\pi\) | |||||||
\(74\) | −48601.7 | −1.03174 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 32967.5 | 0.654716 | ||||||||
\(77\) | 31567.2 | 0.606749 | ||||||||
\(78\) | −30640.2 | −0.570237 | ||||||||
\(79\) | 42097.8 | 0.758912 | 0.379456 | − | 0.925210i | \(-0.376111\pi\) | ||||
0.379456 | + | 0.925210i | \(0.376111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −74000.0 | −1.21534 | ||||||||
\(83\) | −101733. | −1.62094 | −0.810469 | − | 0.585781i | \(-0.800788\pi\) | ||||
−0.810469 | + | 0.585781i | \(0.800788\pi\) | |||||||
\(84\) | −17237.7 | −0.266551 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8753.86 | −0.127630 | ||||||||
\(87\) | 53874.6 | 0.763107 | ||||||||
\(88\) | −16877.2 | −0.232324 | ||||||||
\(89\) | −65551.2 | −0.877214 | −0.438607 | − | 0.898679i | \(-0.644528\pi\) | ||||
−0.438607 | + | 0.898679i | \(0.644528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −101884. | −1.28974 | ||||||||
\(92\) | −888.454 | −0.0109437 | ||||||||
\(93\) | −43035.9 | −0.515969 | ||||||||
\(94\) | −22391.1 | −0.261370 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9216.00 | 0.102062 | ||||||||
\(97\) | 82780.7 | 0.893305 | 0.446653 | − | 0.894708i | \(-0.352616\pi\) | ||||
0.446653 | + | 0.894708i | \(0.352616\pi\) | |||||||
\(98\) | 9909.92 | 0.104233 | ||||||||
\(99\) | 21360.2 | 0.219037 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14644.9 | 0.142851 | 0.0714255 | − | 0.997446i | \(-0.477245\pi\) | ||||
0.0714255 | + | 0.997446i | \(0.477245\pi\) | |||||||
\(102\) | −46336.2 | −0.440982 | ||||||||
\(103\) | 199927. | 1.85686 | 0.928429 | − | 0.371511i | \(-0.121160\pi\) | ||||
0.928429 | + | 0.371511i | \(0.121160\pi\) | |||||||
\(104\) | 54471.5 | 0.493840 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −105853. | −0.915041 | ||||||||
\(107\) | −34770.4 | −0.293596 | −0.146798 | − | 0.989166i | \(-0.546897\pi\) | ||||
−0.146798 | + | 0.989166i | \(0.546897\pi\) | |||||||
\(108\) | −11664.0 | −0.0962250 | ||||||||
\(109\) | −19636.5 | −0.158306 | −0.0791529 | − | 0.996862i | \(-0.525222\pi\) | ||||
−0.0791529 | + | 0.996862i | \(0.525222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −109354. | −0.842415 | ||||||||
\(112\) | 30644.7 | 0.230840 | ||||||||
\(113\) | 19716.6 | 0.145256 | 0.0726282 | − | 0.997359i | \(-0.476861\pi\) | ||||
0.0726282 | + | 0.997359i | \(0.476861\pi\) | |||||||
\(114\) | 74177.0 | 0.534573 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −95777.0 | −0.660870 | ||||||||
\(117\) | −68940.6 | −0.465597 | ||||||||
\(118\) | −83302.4 | −0.550748 | ||||||||
\(119\) | −154076. | −0.997394 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −91510.2 | −0.568206 | ||||||||
\(122\) | −182103. | −1.10769 | ||||||||
\(123\) | −166500. | −0.992320 | ||||||||
\(124\) | 76508.2 | 0.446842 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −38784.7 | −0.217638 | ||||||||
\(127\) | 55823.7 | 0.307121 | 0.153560 | − | 0.988139i | \(-0.450926\pi\) | ||||
0.153560 | + | 0.988139i | \(0.450926\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −19696.2 | −0.104210 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 136377. | 0.694326 | 0.347163 | − | 0.937805i | \(-0.387145\pi\) | ||||
0.347163 | + | 0.937805i | \(0.387145\pi\) | |||||||
\(132\) | −37973.7 | −0.189691 | ||||||||
\(133\) | 246651. | 1.20908 | ||||||||
\(134\) | −137419. | −0.661126 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 82375.5 | 0.381901 | ||||||||
\(137\) | 134387. | 0.611722 | 0.305861 | − | 0.952076i | \(-0.401056\pi\) | ||||
0.305861 | + | 0.952076i | \(0.401056\pi\) | |||||||
\(138\) | −1999.02 | −0.00893551 | ||||||||
\(139\) | −305523. | −1.34124 | −0.670620 | − | 0.741801i | \(-0.733972\pi\) | ||||
−0.670620 | + | 0.741801i | \(0.733972\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −50379.9 | −0.213407 | ||||||||
\(142\) | 229958. | 0.957036 | ||||||||
\(143\) | −224445. | −0.917846 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −107827. | −0.418646 | ||||||||
\(147\) | 22297.3 | 0.0851059 | ||||||||
\(148\) | 194407. | 0.729553 | ||||||||
\(149\) | 349387. | 1.28926 | 0.644630 | − | 0.764494i | \(-0.277011\pi\) | ||||
0.644630 | + | 0.764494i | \(0.277011\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −314525. | −1.12257 | −0.561284 | − | 0.827623i | \(-0.689692\pi\) | ||||
−0.561284 | + | 0.827623i | \(0.689692\pi\) | |||||||
\(152\) | −131870. | −0.462954 | ||||||||
\(153\) | −104257. | −0.360060 | ||||||||
\(154\) | −126269. | −0.429036 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 122561. | 0.403219 | ||||||||
\(157\) | 131302. | 0.425132 | 0.212566 | − | 0.977147i | \(-0.431818\pi\) | ||||
0.212566 | + | 0.977147i | \(0.431818\pi\) | |||||||
\(158\) | −168391. | −0.536632 | ||||||||
\(159\) | −238170. | −0.747128 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6647.08 | −0.0202100 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | 633204. | 1.86670 | 0.933351 | − | 0.358966i | \(-0.116871\pi\) | ||||
0.933351 | + | 0.358966i | \(0.116871\pi\) | |||||||
\(164\) | 296000. | 0.859374 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 406932. | 1.14618 | ||||||||
\(167\) | −137690. | −0.382042 | −0.191021 | − | 0.981586i | \(-0.561180\pi\) | ||||
−0.191021 | + | 0.981586i | \(0.561180\pi\) | |||||||
\(168\) | 68950.6 | 0.188480 | ||||||||
\(169\) | 353109. | 0.951024 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 166898. | 0.436477 | ||||||||
\(172\) | 35015.5 | 0.0902482 | ||||||||
\(173\) | 90278.1 | 0.229333 | 0.114667 | − | 0.993404i | \(-0.463420\pi\) | ||||
0.114667 | + | 0.993404i | \(0.463420\pi\) | |||||||
\(174\) | −215498. | −0.539598 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 67508.7 | 0.164278 | ||||||||
\(177\) | −187430. | −0.449684 | ||||||||
\(178\) | 262205. | 0.620284 | ||||||||
\(179\) | 601579. | 1.40333 | 0.701665 | − | 0.712507i | \(-0.252440\pi\) | ||||
0.701665 | + | 0.712507i | \(0.252440\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 447746. | 1.01586 | 0.507931 | − | 0.861398i | \(-0.330410\pi\) | ||||
0.507931 | + | 0.861398i | \(0.330410\pi\) | |||||||
\(182\) | 407536. | 0.911984 | ||||||||
\(183\) | −409732. | −0.904424 | ||||||||
\(184\) | 3553.81 | 0.00773838 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 172144. | 0.364845 | ||||||||
\(187\) | −339421. | −0.709797 | ||||||||
\(188\) | 89564.2 | 0.184816 | ||||||||
\(189\) | −87265.7 | −0.177701 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 673846. | 1.33653 | 0.668263 | − | 0.743925i | \(-0.267038\pi\) | ||||
0.668263 | + | 0.743925i | \(0.267038\pi\) | |||||||
\(192\) | −36864.0 | −0.0721688 | ||||||||
\(193\) | −255962. | −0.494632 | −0.247316 | − | 0.968935i | \(-0.579549\pi\) | ||||
−0.247316 | + | 0.968935i | \(0.579549\pi\) | |||||||
\(194\) | −331123. | −0.631662 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −39639.7 | −0.0737038 | ||||||||
\(197\) | −196202. | −0.360195 | −0.180097 | − | 0.983649i | \(-0.557641\pi\) | ||||
−0.180097 | + | 0.983649i | \(0.557641\pi\) | |||||||
\(198\) | −85440.7 | −0.154882 | ||||||||
\(199\) | 118265. | 0.211702 | 0.105851 | − | 0.994382i | \(-0.466243\pi\) | ||||
0.105851 | + | 0.994382i | \(0.466243\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −309192. | −0.539807 | ||||||||
\(202\) | −58579.7 | −0.101011 | ||||||||
\(203\) | −716567. | −1.22044 | ||||||||
\(204\) | 185345. | 0.311821 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −799708. | −1.31300 | ||||||||
\(207\) | −4497.80 | −0.00729582 | ||||||||
\(208\) | −217886. | −0.349198 | ||||||||
\(209\) | 543359. | 0.860441 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 910278. | 1.40756 | 0.703781 | − | 0.710417i | \(-0.251493\pi\) | ||||
0.703781 | + | 0.710417i | \(0.251493\pi\) | |||||||
\(212\) | 423414. | 0.647031 | ||||||||
\(213\) | 517406. | 0.781416 | ||||||||
\(214\) | 139082. | 0.207604 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 46656.0 | 0.0680414 | ||||||||
\(217\) | 572406. | 0.825191 | ||||||||
\(218\) | 78545.9 | 0.111939 | ||||||||
\(219\) | −242611. | −0.341823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.09549e6 | 1.50879 | ||||||||
\(222\) | 437415. | 0.595677 | ||||||||
\(223\) | −1.04513e6 | −1.40737 | −0.703683 | − | 0.710514i | \(-0.748462\pi\) | ||||
−0.703683 | + | 0.710514i | \(0.748462\pi\) | |||||||
\(224\) | −122579. | −0.163228 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −78866.3 | −0.102712 | ||||||||
\(227\) | −869120. | −1.11948 | −0.559739 | − | 0.828669i | \(-0.689098\pi\) | ||||
−0.559739 | + | 0.828669i | \(0.689098\pi\) | |||||||
\(228\) | −296708. | −0.378000 | ||||||||
\(229\) | −1.39907e6 | −1.76299 | −0.881494 | − | 0.472195i | \(-0.843462\pi\) | ||||
−0.881494 | + | 0.472195i | \(0.843462\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −284105. | −0.350307 | ||||||||
\(232\) | 383108. | 0.467306 | ||||||||
\(233\) | 403494. | 0.486908 | 0.243454 | − | 0.969912i | \(-0.421720\pi\) | ||||
0.243454 | + | 0.969912i | \(0.421720\pi\) | |||||||
\(234\) | 275762. | 0.329227 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 333210. | 0.389437 | ||||||||
\(237\) | −378880. | −0.438158 | ||||||||
\(238\) | 616303. | 0.705264 | ||||||||
\(239\) | −611076. | −0.691991 | −0.345995 | − | 0.938236i | \(-0.612459\pi\) | ||||
−0.345995 | + | 0.938236i | \(0.612459\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.50639e6 | −1.67068 | −0.835342 | − | 0.549730i | \(-0.814730\pi\) | ||||
−0.835342 | + | 0.549730i | \(0.814730\pi\) | |||||||
\(242\) | 366041. | 0.401782 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 728412. | 0.783254 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 666000. | 0.701676 | ||||||||
\(247\) | −1.75370e6 | −1.82900 | ||||||||
\(248\) | −306033. | −0.315965 | ||||||||
\(249\) | 915597. | 0.935849 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 558727. | 0.559777 | 0.279889 | − | 0.960032i | \(-0.409702\pi\) | ||||
0.279889 | + | 0.960032i | \(0.409702\pi\) | |||||||
\(252\) | 155139. | 0.153893 | ||||||||
\(253\) | −14643.2 | −0.0143825 | ||||||||
\(254\) | −223295. | −0.217167 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −680108. | −0.642310 | −0.321155 | − | 0.947027i | \(-0.604071\pi\) | ||||
−0.321155 | + | 0.947027i | \(0.604071\pi\) | |||||||
\(258\) | 78784.8 | 0.0736874 | ||||||||
\(259\) | 1.45448e6 | 1.34728 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −484871. | −0.440580 | ||||||||
\(262\) | −545508. | −0.490962 | ||||||||
\(263\) | 428668. | 0.382148 | 0.191074 | − | 0.981576i | \(-0.438803\pi\) | ||||
0.191074 | + | 0.981576i | \(0.438803\pi\) | |||||||
\(264\) | 151895. | 0.134132 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −986603. | −0.854945 | ||||||||
\(267\) | 589961. | 0.506460 | ||||||||
\(268\) | 549675. | 0.467487 | ||||||||
\(269\) | −1.51936e6 | −1.28020 | −0.640101 | − | 0.768291i | \(-0.721108\pi\) | ||||
−0.640101 | + | 0.768291i | \(0.721108\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.34595e6 | −1.11329 | −0.556643 | − | 0.830752i | \(-0.687911\pi\) | ||||
−0.556643 | + | 0.830752i | \(0.687911\pi\) | |||||||
\(272\) | −329502. | −0.270045 | ||||||||
\(273\) | 916955. | 0.744632 | ||||||||
\(274\) | −537546. | −0.432553 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7996.08 | 0.00631836 | ||||||||
\(277\) | 885541. | 0.693440 | 0.346720 | − | 0.937969i | \(-0.387295\pi\) | ||||
0.346720 | + | 0.937969i | \(0.387295\pi\) | |||||||
\(278\) | 1.22209e6 | 0.948400 | ||||||||
\(279\) | 387323. | 0.297895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.26803e6 | −0.957999 | −0.478999 | − | 0.877815i | \(-0.659000\pi\) | ||||
−0.478999 | + | 0.877815i | \(0.659000\pi\) | |||||||
\(282\) | 201520. | 0.150902 | ||||||||
\(283\) | −685833. | −0.509040 | −0.254520 | − | 0.967067i | \(-0.581918\pi\) | ||||
−0.254520 | + | 0.967067i | \(0.581918\pi\) | |||||||
\(284\) | −919833. | −0.676726 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 897779. | 0.649015 | ||||||||
\(287\) | 2.21456e6 | 1.58702 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 236816. | 0.166788 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −745026. | −0.515750 | ||||||||
\(292\) | 431309. | 0.296027 | ||||||||
\(293\) | 1.66857e6 | 1.13547 | 0.567736 | − | 0.823211i | \(-0.307819\pi\) | ||||
0.567736 | + | 0.823211i | \(0.307819\pi\) | |||||||
\(294\) | −89189.3 | −0.0601789 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −777626. | −0.515872 | ||||||||
\(297\) | −192242. | −0.126461 | ||||||||
\(298\) | −1.39755e6 | −0.911645 | ||||||||
\(299\) | 47261.2 | 0.0305722 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 261972. | 0.166663 | ||||||||
\(302\) | 1.25810e6 | 0.793776 | ||||||||
\(303\) | −131804. | −0.0824751 | ||||||||
\(304\) | 527481. | 0.327358 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 417026. | 0.254601 | ||||||||
\(307\) | 560776. | 0.339581 | 0.169790 | − | 0.985480i | \(-0.445691\pi\) | ||||
0.169790 | + | 0.985480i | \(0.445691\pi\) | |||||||
\(308\) | 505075. | 0.303374 | ||||||||
\(309\) | −1.79934e6 | −1.07206 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.33943e6 | −0.785268 | −0.392634 | − | 0.919695i | \(-0.628436\pi\) | ||||
−0.392634 | + | 0.919695i | \(0.628436\pi\) | |||||||
\(312\) | −490244. | −0.285119 | ||||||||
\(313\) | −621225. | −0.358417 | −0.179208 | − | 0.983811i | \(-0.557354\pi\) | ||||
−0.179208 | + | 0.983811i | \(0.557354\pi\) | |||||||
\(314\) | −525210. | −0.300614 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 673565. | 0.379456 | ||||||||
\(317\) | −300282. | −0.167834 | −0.0839172 | − | 0.996473i | \(-0.526743\pi\) | ||||
−0.0839172 | + | 0.996473i | \(0.526743\pi\) | |||||||
\(318\) | 952681. | 0.528299 | ||||||||
\(319\) | −1.57856e6 | −0.868529 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 312934. | 0.169508 | ||||||||
\(322\) | 26588.3 | 0.0142906 | ||||||||
\(323\) | −2.65207e6 | −1.41442 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.53282e6 | −1.31996 | ||||||||
\(327\) | 176728. | 0.0913979 | ||||||||
\(328\) | −1.18400e6 | −0.607669 | ||||||||
\(329\) | 670086. | 0.341303 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.94914e6 | −0.977851 | −0.488925 | − | 0.872326i | \(-0.662611\pi\) | ||||
−0.488925 | + | 0.872326i | \(0.662611\pi\) | |||||||
\(332\) | −1.62773e6 | −0.810469 | ||||||||
\(333\) | 984183. | 0.486369 | ||||||||
\(334\) | 550760. | 0.270145 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −275803. | −0.133275 | ||||||||
\(337\) | −253373. | −0.121530 | −0.0607652 | − | 0.998152i | \(-0.519354\pi\) | ||||
−0.0607652 | + | 0.998152i | \(0.519354\pi\) | |||||||
\(338\) | −1.41243e6 | −0.672476 | ||||||||
\(339\) | −177449. | −0.0838638 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.26098e6 | 0.587249 | ||||||||
\(342\) | −667593. | −0.308636 | ||||||||
\(343\) | −2.30847e6 | −1.05947 | ||||||||
\(344\) | −140062. | −0.0638151 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −361112. | −0.162163 | ||||||||
\(347\) | −1.60688e6 | −0.716406 | −0.358203 | − | 0.933644i | \(-0.616610\pi\) | ||||
−0.358203 | + | 0.933644i | \(0.616610\pi\) | |||||||
\(348\) | 861993. | 0.381554 | ||||||||
\(349\) | −608374. | −0.267367 | −0.133683 | − | 0.991024i | \(-0.542680\pi\) | ||||
−0.133683 | + | 0.991024i | \(0.542680\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 620465. | 0.268813 | ||||||||
\(352\) | −270035. | −0.116162 | ||||||||
\(353\) | 3.83773e6 | 1.63922 | 0.819612 | − | 0.572919i | \(-0.194189\pi\) | ||||
0.819612 | + | 0.572919i | \(0.194189\pi\) | |||||||
\(354\) | 749722. | 0.317974 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.04882e6 | −0.438607 | ||||||||
\(357\) | 1.38668e6 | 0.575846 | ||||||||
\(358\) | −2.40632e6 | −0.992305 | ||||||||
\(359\) | 2.13850e6 | 0.875738 | 0.437869 | − | 0.899039i | \(-0.355733\pi\) | ||||
0.437869 | + | 0.899039i | \(0.355733\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.76944e6 | 0.714610 | ||||||||
\(362\) | −1.79098e6 | −0.718323 | ||||||||
\(363\) | 823591. | 0.328054 | ||||||||
\(364\) | −1.63014e6 | −0.644870 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.63893e6 | 0.639524 | ||||||||
\(367\) | −4.50396e6 | −1.74554 | −0.872769 | − | 0.488133i | \(-0.837678\pi\) | ||||
−0.872769 | + | 0.488133i | \(0.837678\pi\) | |||||||
\(368\) | −14215.3 | −0.00547186 | ||||||||
\(369\) | 1.49850e6 | 0.572916 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.16782e6 | 1.19488 | ||||||||
\(372\) | −688574. | −0.257984 | ||||||||
\(373\) | 1.15223e6 | 0.428811 | 0.214406 | − | 0.976745i | \(-0.431219\pi\) | ||||
0.214406 | + | 0.976745i | \(0.431219\pi\) | |||||||
\(374\) | 1.35768e6 | 0.501902 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −358257. | −0.130685 | ||||||||
\(377\) | 5.09484e6 | 1.84619 | ||||||||
\(378\) | 349063. | 0.125653 | ||||||||
\(379\) | 797740. | 0.285275 | 0.142637 | − | 0.989775i | \(-0.454442\pi\) | ||||
0.142637 | + | 0.989775i | \(0.454442\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −502413. | −0.177316 | ||||||||
\(382\) | −2.69538e6 | −0.945066 | ||||||||
\(383\) | −1.02124e6 | −0.355737 | −0.177869 | − | 0.984054i | \(-0.556920\pi\) | ||||
−0.177869 | + | 0.984054i | \(0.556920\pi\) | |||||||
\(384\) | 147456. | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.02385e6 | 0.349757 | ||||||||
\(387\) | 177266. | 0.0601655 | ||||||||
\(388\) | 1.32449e6 | 0.446653 | ||||||||
\(389\) | −1.06820e6 | −0.357914 | −0.178957 | − | 0.983857i | \(-0.557272\pi\) | ||||
−0.178957 | + | 0.983857i | \(0.557272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 71471.5 | 0.0236424 | ||||||||
\(392\) | 158559. | 0.0521165 | ||||||||
\(393\) | −1.22739e6 | −0.400869 | ||||||||
\(394\) | 784807. | 0.254696 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 341763. | 0.109518 | ||||||||
\(397\) | −109330. | −0.0348148 | −0.0174074 | − | 0.999848i | \(-0.505541\pi\) | ||||
−0.0174074 | + | 0.999848i | \(0.505541\pi\) | |||||||
\(398\) | −473061. | −0.149696 | ||||||||
\(399\) | −2.21986e6 | −0.698060 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.42131e6 | 0.441395 | 0.220697 | − | 0.975342i | \(-0.429167\pi\) | ||||
0.220697 | + | 0.975342i | \(0.429167\pi\) | |||||||
\(402\) | 1.23677e6 | 0.381701 | ||||||||
\(403\) | −4.06985e6 | −1.24829 | ||||||||
\(404\) | 234319. | 0.0714255 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.86627e6 | 0.862982 | ||||||||
\(407\) | 3.20414e6 | 0.958793 | ||||||||
\(408\) | −741380. | −0.220491 | ||||||||
\(409\) | 3.07511e6 | 0.908975 | 0.454487 | − | 0.890753i | \(-0.349823\pi\) | ||||
0.454487 | + | 0.890753i | \(0.349823\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.20948e6 | −0.353178 | ||||||||
\(412\) | 3.19883e6 | 0.928429 | ||||||||
\(413\) | 2.49295e6 | 0.719181 | ||||||||
\(414\) | 17991.2 | 0.00515892 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 871545. | 0.246920 | ||||||||
\(417\) | 2.74971e6 | 0.774365 | ||||||||
\(418\) | −2.17343e6 | −0.608423 | ||||||||
\(419\) | 3.06462e6 | 0.852789 | 0.426395 | − | 0.904537i | \(-0.359783\pi\) | ||||
0.426395 | + | 0.904537i | \(0.359783\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 837782. | 0.230370 | 0.115185 | − | 0.993344i | \(-0.463254\pi\) | ||||
0.115185 | + | 0.993344i | \(0.463254\pi\) | |||||||
\(422\) | −3.64111e6 | −0.995297 | ||||||||
\(423\) | 453419. | 0.123211 | ||||||||
\(424\) | −1.69366e6 | −0.457520 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.06962e6 | −0.552545 | ||||||||
\(427\) | 5.44971e6 | 1.44645 | ||||||||
\(428\) | −556326. | −0.146798 | ||||||||
\(429\) | 2.02000e6 | 0.529918 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.90720e6 | 1.53175 | 0.765876 | − | 0.642988i | \(-0.222306\pi\) | ||||
0.765876 | + | 0.642988i | \(0.222306\pi\) | |||||||
\(432\) | −186624. | −0.0481125 | ||||||||
\(433\) | 1.84995e6 | 0.474177 | 0.237089 | − | 0.971488i | \(-0.423807\pi\) | ||||
0.237089 | + | 0.971488i | \(0.423807\pi\) | |||||||
\(434\) | −2.28962e6 | −0.583498 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −314183. | −0.0791529 | ||||||||
\(437\) | −114415. | −0.0286601 | ||||||||
\(438\) | 970445. | 0.241705 | ||||||||
\(439\) | −2.81172e6 | −0.696323 | −0.348161 | − | 0.937435i | \(-0.613194\pi\) | ||||
−0.348161 | + | 0.937435i | \(0.613194\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −200676. | −0.0491359 | ||||||||
\(442\) | −4.38196e6 | −1.06687 | ||||||||
\(443\) | 2.41386e6 | 0.584391 | 0.292196 | − | 0.956359i | \(-0.405614\pi\) | ||||
0.292196 | + | 0.956359i | \(0.405614\pi\) | |||||||
\(444\) | −1.74966e6 | −0.421208 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.18051e6 | 0.995158 | ||||||||
\(447\) | −3.14448e6 | −0.744355 | ||||||||
\(448\) | 490316. | 0.115420 | ||||||||
\(449\) | −507124. | −0.118713 | −0.0593565 | − | 0.998237i | \(-0.518905\pi\) | ||||
−0.0593565 | + | 0.998237i | \(0.518905\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.87856e6 | 1.12941 | ||||||||
\(452\) | 315465. | 0.0726282 | ||||||||
\(453\) | 2.83072e6 | 0.648115 | ||||||||
\(454\) | 3.47648e6 | 0.791590 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.18683e6 | 0.267286 | ||||||||
\(457\) | 1.09879e6 | 0.246106 | 0.123053 | − | 0.992400i | \(-0.460731\pi\) | ||||
0.123053 | + | 0.992400i | \(0.460731\pi\) | |||||||
\(458\) | 5.59626e6 | 1.24662 | ||||||||
\(459\) | 938309. | 0.207881 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 106066. | 0.0232446 | 0.0116223 | − | 0.999932i | \(-0.496300\pi\) | ||||
0.0116223 | + | 0.999932i | \(0.496300\pi\) | |||||||
\(462\) | 1.13642e6 | 0.247704 | ||||||||
\(463\) | 1.36176e6 | 0.295222 | 0.147611 | − | 0.989045i | \(-0.452842\pi\) | ||||
0.147611 | + | 0.989045i | \(0.452842\pi\) | |||||||
\(464\) | −1.53243e6 | −0.330435 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.61397e6 | −0.344296 | ||||||||
\(467\) | −2.18710e6 | −0.464062 | −0.232031 | − | 0.972708i | \(-0.574537\pi\) | ||||
−0.232031 | + | 0.972708i | \(0.574537\pi\) | |||||||
\(468\) | −1.10305e6 | −0.232798 | ||||||||
\(469\) | 4.11246e6 | 0.863316 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.18172e6 | −0.245450 | ||||||||
\(472\) | −1.33284e6 | −0.275374 | ||||||||
\(473\) | 577111. | 0.118606 | ||||||||
\(474\) | 1.51552e6 | 0.309825 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.46521e6 | −0.498697 | ||||||||
\(477\) | 2.14353e6 | 0.431354 | ||||||||
\(478\) | 2.44430e6 | 0.489311 | ||||||||
\(479\) | 1.01595e6 | 0.202318 | 0.101159 | − | 0.994870i | \(-0.467745\pi\) | ||||
0.101159 | + | 0.994870i | \(0.467745\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.03414e7 | −2.03807 | ||||||||
\(482\) | 6.02555e6 | 1.18135 | ||||||||
\(483\) | 59823.7 | 0.0116682 | ||||||||
\(484\) | −1.46416e6 | −0.284103 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 236196. | 0.0453609 | ||||||||
\(487\) | 2.02339e6 | 0.386596 | 0.193298 | − | 0.981140i | \(-0.438082\pi\) | ||||
0.193298 | + | 0.981140i | \(0.438082\pi\) | |||||||
\(488\) | −2.91365e6 | −0.553844 | ||||||||
\(489\) | −5.69884e6 | −1.07774 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.22487e6 | −0.790878 | −0.395439 | − | 0.918492i | \(-0.629408\pi\) | ||||
−0.395439 | + | 0.918492i | \(0.629408\pi\) | |||||||
\(492\) | −2.66400e6 | −0.496160 | ||||||||
\(493\) | 7.70477e6 | 1.42772 | ||||||||
\(494\) | 7.01482e6 | 1.29330 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.22413e6 | 0.223421 | ||||||||
\(497\) | −6.88184e6 | −1.24972 | ||||||||
\(498\) | −3.66239e6 | −0.661745 | ||||||||
\(499\) | −6.71381e6 | −1.20703 | −0.603515 | − | 0.797352i | \(-0.706233\pi\) | ||||
−0.603515 | + | 0.797352i | \(0.706233\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.23921e6 | 0.220572 | ||||||||
\(502\) | −2.23491e6 | −0.395822 | ||||||||
\(503\) | −5.36486e6 | −0.945450 | −0.472725 | − | 0.881210i | \(-0.656730\pi\) | ||||
−0.472725 | + | 0.881210i | \(0.656730\pi\) | |||||||
\(504\) | −620556. | −0.108819 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 58572.6 | 0.0101699 | ||||||||
\(507\) | −3.17798e6 | −0.549074 | ||||||||
\(508\) | 893179. | 0.153560 | ||||||||
\(509\) | 1.10627e6 | 0.189264 | 0.0946318 | − | 0.995512i | \(-0.469833\pi\) | ||||
0.0946318 | + | 0.995512i | \(0.469833\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.22689e6 | 0.546679 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −1.50208e6 | −0.252000 | ||||||||
\(514\) | 2.72043e6 | 0.454182 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −315139. | −0.0521048 | ||||||||
\(517\) | 1.47616e6 | 0.242889 | ||||||||
\(518\) | −5.81791e6 | −0.952670 | ||||||||
\(519\) | −812503. | −0.132406 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.11641e6 | −0.502991 | −0.251495 | − | 0.967859i | \(-0.580922\pi\) | ||||
−0.251495 | + | 0.967859i | \(0.580922\pi\) | |||||||
\(522\) | 1.93948e6 | 0.311537 | ||||||||
\(523\) | −9.29324e6 | −1.48564 | −0.742819 | − | 0.669492i | \(-0.766512\pi\) | ||||
−0.742819 | + | 0.669492i | \(0.766512\pi\) | |||||||
\(524\) | 2.18203e6 | 0.347163 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.71467e6 | −0.270219 | ||||||||
\(527\) | −6.15469e6 | −0.965339 | ||||||||
\(528\) | −607579. | −0.0948457 | ||||||||
\(529\) | −6.43326e6 | −0.999521 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.68687e6 | 0.259625 | ||||||||
\(532\) | 3.94641e6 | 0.604538 | ||||||||
\(533\) | −1.57457e7 | −2.40073 | ||||||||
\(534\) | −2.35984e6 | −0.358121 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.19870e6 | −0.330563 | ||||||||
\(537\) | −5.41421e6 | −0.810213 | ||||||||
\(538\) | 6.07742e6 | 0.905240 | ||||||||
\(539\) | −653326. | −0.0968631 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.00152e7 | 1.47118 | 0.735592 | − | 0.677425i | \(-0.236904\pi\) | ||||
0.735592 | + | 0.677425i | \(0.236904\pi\) | |||||||
\(542\) | 5.38382e6 | 0.787213 | ||||||||
\(543\) | −4.02971e6 | −0.586509 | ||||||||
\(544\) | 1.31801e6 | 0.190951 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.66782e6 | −0.526534 | ||||||||
\(547\) | 605416. | 0.0865138 | 0.0432569 | − | 0.999064i | \(-0.486227\pi\) | ||||
0.0432569 | + | 0.999064i | \(0.486227\pi\) | |||||||
\(548\) | 2.15018e6 | 0.305861 | ||||||||
\(549\) | 3.68759e6 | 0.522169 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.23341e7 | −1.73073 | ||||||||
\(552\) | −31984.3 | −0.00446776 | ||||||||
\(553\) | 5.03936e6 | 0.700749 | ||||||||
\(554\) | −3.54216e6 | −0.490336 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.88836e6 | −0.670620 | ||||||||
\(557\) | 9.21693e6 | 1.25878 | 0.629388 | − | 0.777091i | \(-0.283306\pi\) | ||||
0.629388 | + | 0.777091i | \(0.283306\pi\) | |||||||
\(558\) | −1.54929e6 | −0.210643 | ||||||||
\(559\) | −1.86264e6 | −0.252116 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.05479e6 | 0.409802 | ||||||||
\(562\) | 5.07213e6 | 0.677407 | ||||||||
\(563\) | 9.44213e6 | 1.25545 | 0.627724 | − | 0.778436i | \(-0.283986\pi\) | ||||
0.627724 | + | 0.778436i | \(0.283986\pi\) | |||||||
\(564\) | −806078. | −0.106704 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.74333e6 | 0.359946 | ||||||||
\(567\) | 785391. | 0.102595 | ||||||||
\(568\) | 3.67933e6 | 0.478518 | ||||||||
\(569\) | −1.24216e6 | −0.160841 | −0.0804206 | − | 0.996761i | \(-0.525626\pi\) | ||||
−0.0804206 | + | 0.996761i | \(0.525626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.35633e7 | −1.74090 | −0.870450 | − | 0.492256i | \(-0.836172\pi\) | ||||
−0.870450 | + | 0.492256i | \(0.836172\pi\) | |||||||
\(572\) | −3.59112e6 | −0.458923 | ||||||||
\(573\) | −6.06462e6 | −0.771644 | ||||||||
\(574\) | −8.85824e6 | −1.12219 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −6.75669e6 | −0.844879 | −0.422440 | − | 0.906391i | \(-0.638826\pi\) | ||||
−0.422440 | + | 0.906391i | \(0.638826\pi\) | |||||||
\(578\) | −947262. | −0.117937 | ||||||||
\(579\) | 2.30366e6 | 0.285576 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.21780e7 | −1.49671 | ||||||||
\(582\) | 2.98011e6 | 0.364690 | ||||||||
\(583\) | 6.97855e6 | 0.850342 | ||||||||
\(584\) | −1.72524e6 | −0.209323 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.67430e6 | −0.802900 | ||||||||
\(587\) | −1.08655e7 | −1.30153 | −0.650764 | − | 0.759280i | \(-0.725551\pi\) | ||||
−0.650764 | + | 0.759280i | \(0.725551\pi\) | |||||||
\(588\) | 356757. | 0.0425529 | ||||||||
\(589\) | 9.85269e6 | 1.17022 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.76582e6 | 0.207959 | ||||||||
\(592\) | 3.11051e6 | 0.364776 | ||||||||
\(593\) | 1.20061e6 | 0.140205 | 0.0701027 | − | 0.997540i | \(-0.477667\pi\) | ||||
0.0701027 | + | 0.997540i | \(0.477667\pi\) | |||||||
\(594\) | 768967. | 0.0894214 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.59019e6 | 0.644630 | ||||||||
\(597\) | −1.06439e6 | −0.122226 | ||||||||
\(598\) | −189045. | −0.0216178 | ||||||||
\(599\) | −6.77826e6 | −0.771882 | −0.385941 | − | 0.922523i | \(-0.626123\pi\) | ||||
−0.385941 | + | 0.922523i | \(0.626123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.32426e6 | 0.714207 | 0.357103 | − | 0.934065i | \(-0.383764\pi\) | ||||
0.357103 | + | 0.934065i | \(0.383764\pi\) | |||||||
\(602\) | −1.04789e6 | −0.117849 | ||||||||
\(603\) | 2.78273e6 | 0.311658 | ||||||||
\(604\) | −5.03240e6 | −0.561284 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 527217. | 0.0583187 | ||||||||
\(607\) | 2.63732e6 | 0.290530 | 0.145265 | − | 0.989393i | \(-0.453596\pi\) | ||||
0.145265 | + | 0.989393i | \(0.453596\pi\) | |||||||
\(608\) | −2.10992e6 | −0.231477 | ||||||||
\(609\) | 6.44911e6 | 0.704622 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.76436e6 | −0.516299 | ||||||||
\(612\) | −1.66810e6 | −0.180030 | ||||||||
\(613\) | 1.43305e7 | 1.54031 | 0.770157 | − | 0.637854i | \(-0.220178\pi\) | ||||
0.770157 | + | 0.637854i | \(0.220178\pi\) | |||||||
\(614\) | −2.24310e6 | −0.240120 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.02030e6 | −0.214518 | ||||||||
\(617\) | 29265.6 | 0.00309489 | 0.00154744 | − | 0.999999i | \(-0.499507\pi\) | ||||
0.00154744 | + | 0.999999i | \(0.499507\pi\) | |||||||
\(618\) | 7.19737e6 | 0.758059 | ||||||||
\(619\) | 7.84138e6 | 0.822557 | 0.411279 | − | 0.911510i | \(-0.365082\pi\) | ||||
0.411279 | + | 0.911510i | \(0.365082\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 40480.2 | 0.00421224 | ||||||||
\(622\) | 5.35771e6 | 0.555269 | ||||||||
\(623\) | −7.84687e6 | −0.809984 | ||||||||
\(624\) | 1.96098e6 | 0.201609 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.48490e6 | 0.253439 | ||||||||
\(627\) | −4.89023e6 | −0.496776 | ||||||||
\(628\) | 2.10084e6 | 0.212566 | ||||||||
\(629\) | −1.56390e7 | −1.57610 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −668942. | −0.0668829 | −0.0334414 | − | 0.999441i | \(-0.510647\pi\) | ||||
−0.0334414 | + | 0.999441i | \(0.510647\pi\) | |||||||
\(632\) | −2.69426e6 | −0.268316 | ||||||||
\(633\) | −8.19250e6 | −0.812657 | ||||||||
\(634\) | 1.20113e6 | 0.118677 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.81072e6 | −0.373564 | ||||||||
\(637\) | 2.10863e6 | 0.205898 | ||||||||
\(638\) | 6.31424e6 | 0.614143 | ||||||||
\(639\) | −4.65665e6 | −0.451151 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.26732e7 | 1.21826 | 0.609130 | − | 0.793070i | \(-0.291519\pi\) | ||||
0.609130 | + | 0.793070i | \(0.291519\pi\) | |||||||
\(642\) | −1.25173e6 | −0.119860 | ||||||||
\(643\) | −6.26256e6 | −0.597344 | −0.298672 | − | 0.954356i | \(-0.596544\pi\) | ||||
−0.298672 | + | 0.954356i | \(0.596544\pi\) | |||||||
\(644\) | −106353. | −0.0101050 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.06083e7 | 1.00015 | ||||||||
\(647\) | 8.69452e6 | 0.816554 | 0.408277 | − | 0.912858i | \(-0.366130\pi\) | ||||
0.408277 | + | 0.912858i | \(0.366130\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 5.49184e6 | 0.511807 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.15165e6 | −0.476424 | ||||||||
\(652\) | 1.01313e7 | 0.933351 | ||||||||
\(653\) | 4.56532e6 | 0.418976 | 0.209488 | − | 0.977811i | \(-0.432820\pi\) | ||||
0.209488 | + | 0.977811i | \(0.432820\pi\) | |||||||
\(654\) | −706913. | −0.0646281 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.73600e6 | 0.429687 | ||||||||
\(657\) | 2.18350e6 | 0.197351 | ||||||||
\(658\) | −2.68034e6 | −0.241338 | ||||||||
\(659\) | 1.00273e7 | 0.899437 | 0.449718 | − | 0.893170i | \(-0.351524\pi\) | ||||
0.449718 | + | 0.893170i | \(0.351524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.14715e6 | −0.725274 | −0.362637 | − | 0.931930i | \(-0.618123\pi\) | ||||
−0.362637 | + | 0.931930i | \(0.618123\pi\) | |||||||
\(662\) | 7.79655e6 | 0.691445 | ||||||||
\(663\) | −9.85940e6 | −0.871097 | ||||||||
\(664\) | 6.51091e6 | 0.573088 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.93673e6 | −0.343915 | ||||||||
\(667\) | 332396. | 0.0289295 | ||||||||
\(668\) | −2.20304e6 | −0.191021 | ||||||||
\(669\) | 9.40614e6 | 0.812543 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.20054e7 | 1.02937 | ||||||||
\(672\) | 1.10321e6 | 0.0942400 | ||||||||
\(673\) | 1.16421e6 | 0.0990818 | 0.0495409 | − | 0.998772i | \(-0.484224\pi\) | ||||
0.0495409 | + | 0.998772i | \(0.484224\pi\) | |||||||
\(674\) | 1.01349e6 | 0.0859350 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.64974e6 | 0.475512 | ||||||||
\(677\) | −1.20869e7 | −1.01355 | −0.506775 | − | 0.862079i | \(-0.669162\pi\) | ||||
−0.506775 | + | 0.862079i | \(0.669162\pi\) | |||||||
\(678\) | 709796. | 0.0593007 | ||||||||
\(679\) | 9.90934e6 | 0.824841 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.82208e6 | 0.646331 | ||||||||
\(682\) | −5.04392e6 | −0.415248 | ||||||||
\(683\) | −7.57524e6 | −0.621362 | −0.310681 | − | 0.950514i | \(-0.600557\pi\) | ||||
−0.310681 | + | 0.950514i | \(0.600557\pi\) | |||||||
\(684\) | 2.67037e6 | 0.218239 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.23387e6 | 0.749158 | ||||||||
\(687\) | 1.25916e7 | 1.01786 | ||||||||
\(688\) | 560247. | 0.0451241 | ||||||||
\(689\) | −2.25234e7 | −1.80753 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.32589e7 | 1.85308 | 0.926539 | − | 0.376198i | \(-0.122769\pi\) | ||||
0.926539 | + | 0.376198i | \(0.122769\pi\) | |||||||
\(692\) | 1.44445e6 | 0.114667 | ||||||||
\(693\) | 2.55694e6 | 0.202250 | ||||||||
\(694\) | 6.42751e6 | 0.506575 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.44797e6 | −0.269799 | ||||||||
\(697\) | −2.38117e7 | −1.85656 | ||||||||
\(698\) | 2.43350e6 | 0.189057 | ||||||||
\(699\) | −3.63144e6 | −0.281116 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.11461e7 | −0.856700 | −0.428350 | − | 0.903613i | \(-0.640905\pi\) | ||||
−0.428350 | + | 0.903613i | \(0.640905\pi\) | |||||||
\(702\) | −2.48186e6 | −0.190079 | ||||||||
\(703\) | 2.50356e7 | 1.91060 | ||||||||
\(704\) | 1.08014e6 | 0.0821388 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.53509e7 | −1.15911 | ||||||||
\(707\) | 1.75308e6 | 0.131903 | ||||||||
\(708\) | −2.99889e6 | −0.224842 | ||||||||
\(709\) | 264391. | 0.0197529 | 0.00987646 | − | 0.999951i | \(-0.496856\pi\) | ||||
0.00987646 | + | 0.999951i | \(0.496856\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.40992e6 | 0.252971 | ||||||||
\(712\) | 4.19528e6 | 0.310142 | ||||||||
\(713\) | −265523. | −0.0195605 | ||||||||
\(714\) | −5.54673e6 | −0.407184 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.62526e6 | 0.701665 | ||||||||
\(717\) | 5.49968e6 | 0.399521 | ||||||||
\(718\) | −8.55402e6 | −0.619240 | ||||||||
\(719\) | 7.09616e6 | 0.511919 | 0.255959 | − | 0.966688i | \(-0.417609\pi\) | ||||
0.255959 | + | 0.966688i | \(0.417609\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.39325e7 | 1.71455 | ||||||||
\(722\) | −7.07778e6 | −0.505305 | ||||||||
\(723\) | 1.35575e7 | 0.964570 | ||||||||
\(724\) | 7.16393e6 | 0.507931 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.29437e6 | −0.231969 | ||||||||
\(727\) | −3.83492e6 | −0.269104 | −0.134552 | − | 0.990907i | \(-0.542960\pi\) | ||||
−0.134552 | + | 0.990907i | \(0.542960\pi\) | |||||||
\(728\) | 6.52057e6 | 0.455992 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.81681e6 | −0.194969 | ||||||||
\(732\) | −6.55571e6 | −0.452212 | ||||||||
\(733\) | −1.25850e7 | −0.865151 | −0.432575 | − | 0.901598i | \(-0.642395\pi\) | ||||
−0.432575 | + | 0.901598i | \(0.642395\pi\) | |||||||
\(734\) | 1.80158e7 | 1.23428 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 56861.0 | 0.00386919 | ||||||||
\(737\) | 9.05954e6 | 0.614381 | ||||||||
\(738\) | −5.99400e6 | −0.405113 | ||||||||
\(739\) | −1.48983e7 | −1.00352 | −0.501761 | − | 0.865006i | \(-0.667314\pi\) | ||||
−0.501761 | + | 0.865006i | \(0.667314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.57833e7 | 1.05597 | ||||||||
\(742\) | −1.26713e7 | −0.844911 | ||||||||
\(743\) | 921340. | 0.0612277 | 0.0306139 | − | 0.999531i | \(-0.490254\pi\) | ||||
0.0306139 | + | 0.999531i | \(0.490254\pi\) | |||||||
\(744\) | 2.75430e6 | 0.182422 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.60891e6 | −0.303215 | ||||||||
\(747\) | −8.24037e6 | −0.540313 | ||||||||
\(748\) | −5.43073e6 | −0.354899 | ||||||||
\(749\) | −4.16222e6 | −0.271095 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.19124e7 | −0.770726 | −0.385363 | − | 0.922765i | \(-0.625924\pi\) | ||||
−0.385363 | + | 0.922765i | \(0.625924\pi\) | |||||||
\(752\) | 1.43303e6 | 0.0924081 | ||||||||
\(753\) | −5.02854e6 | −0.323188 | ||||||||
\(754\) | −2.03794e7 | −1.30546 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.39625e6 | −0.0888503 | ||||||||
\(757\) | 1.43092e7 | 0.907558 | 0.453779 | − | 0.891114i | \(-0.350076\pi\) | ||||
0.453779 | + | 0.891114i | \(0.350076\pi\) | |||||||
\(758\) | −3.19096e6 | −0.201720 | ||||||||
\(759\) | 131788. | 0.00830372 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.78549e6 | −0.111762 | −0.0558812 | − | 0.998437i | \(-0.517797\pi\) | ||||
−0.0558812 | + | 0.998437i | \(0.517797\pi\) | |||||||
\(762\) | 2.00965e6 | 0.125381 | ||||||||
\(763\) | −2.35060e6 | −0.146173 | ||||||||
\(764\) | 1.07815e7 | 0.668263 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.08494e6 | 0.251544 | ||||||||
\(767\) | −1.77250e7 | −1.08792 | ||||||||
\(768\) | −589824. | −0.0360844 | ||||||||
\(769\) | −1.03207e7 | −0.629350 | −0.314675 | − | 0.949200i | \(-0.601895\pi\) | ||||
−0.314675 | + | 0.949200i | \(0.601895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.12097e6 | 0.370838 | ||||||||
\(772\) | −4.09539e6 | −0.247316 | ||||||||
\(773\) | −6.93308e6 | −0.417328 | −0.208664 | − | 0.977987i | \(-0.566911\pi\) | ||||
−0.208664 | + | 0.977987i | \(0.566911\pi\) | |||||||
\(774\) | −709063. | −0.0425434 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.29797e6 | −0.315831 | ||||||||
\(777\) | −1.30903e7 | −0.777852 | ||||||||
\(778\) | 4.27281e6 | 0.253084 | ||||||||
\(779\) | 3.81187e7 | 2.25058 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.51603e7 | −0.889368 | ||||||||
\(782\) | −285886. | −0.0167177 | ||||||||
\(783\) | 4.36384e6 | 0.254369 | ||||||||
\(784\) | −634235. | −0.0368519 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.90958e6 | 0.283457 | ||||||||
\(787\) | 3.05516e7 | 1.75831 | 0.879157 | − | 0.476532i | \(-0.158106\pi\) | ||||
0.879157 | + | 0.476532i | \(0.158106\pi\) | |||||||
\(788\) | −3.13923e6 | −0.180097 | ||||||||
\(789\) | −3.85801e6 | −0.220633 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.36019e6 | 0.134124 | ||||||||
\(792\) | −1.36705e6 | −0.0774412 | ||||||||
\(793\) | −3.87478e7 | −2.18808 | ||||||||
\(794\) | 437321. | 0.0246178 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.89225e6 | 0.105851 | ||||||||
\(797\) | 2.76107e7 | 1.53968 | 0.769841 | − | 0.638236i | \(-0.220336\pi\) | ||||
0.769841 | + | 0.638236i | \(0.220336\pi\) | |||||||
\(798\) | 8.87943e6 | 0.493603 | ||||||||
\(799\) | −7.20498e6 | −0.399269 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.30965e6 | −0.292405 | ||||||||
\(802\) | −5.68523e6 | −0.312113 | ||||||||
\(803\) | 7.10867e6 | 0.389045 | ||||||||
\(804\) | −4.94708e6 | −0.269904 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.62794e7 | 0.882674 | ||||||||
\(807\) | 1.36742e7 | 0.739125 | ||||||||
\(808\) | −937275. | −0.0505055 | ||||||||
\(809\) | 9.60377e6 | 0.515906 | 0.257953 | − | 0.966157i | \(-0.416952\pi\) | ||||
0.257953 | + | 0.966157i | \(0.416952\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.77352e7 | 0.946856 | 0.473428 | − | 0.880832i | \(-0.343016\pi\) | ||||
0.473428 | + | 0.880832i | \(0.343016\pi\) | |||||||
\(812\) | −1.14651e7 | −0.610221 | ||||||||
\(813\) | 1.21136e7 | 0.642756 | ||||||||
\(814\) | −1.28165e7 | −0.677969 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.96552e6 | 0.155911 | ||||||||
\(817\) | 4.50927e6 | 0.236348 | ||||||||
\(818\) | −1.23004e7 | −0.642742 | ||||||||
\(819\) | −8.25260e6 | −0.429913 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.66186e7 | −1.37825 | −0.689125 | − | 0.724643i | \(-0.742005\pi\) | ||||
−0.689125 | + | 0.724643i | \(0.742005\pi\) | |||||||
\(822\) | 4.83791e6 | 0.249735 | ||||||||
\(823\) | 1.38059e7 | 0.710504 | 0.355252 | − | 0.934771i | \(-0.384395\pi\) | ||||
0.355252 | + | 0.934771i | \(0.384395\pi\) | |||||||
\(824\) | −1.27953e7 | −0.656498 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.97180e6 | −0.508538 | ||||||||
\(827\) | 3.25738e7 | 1.65617 | 0.828084 | − | 0.560604i | \(-0.189431\pi\) | ||||
0.828084 | + | 0.560604i | \(0.189431\pi\) | |||||||
\(828\) | −71964.7 | −0.00364791 | ||||||||
\(829\) | 1.67628e7 | 0.847150 | 0.423575 | − | 0.905861i | \(-0.360775\pi\) | ||||
0.423575 | + | 0.905861i | \(0.360775\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.96987e6 | −0.400358 | ||||||||
\(832\) | −3.48618e6 | −0.174599 | ||||||||
\(833\) | 3.18881e6 | 0.159227 | ||||||||
\(834\) | −1.09988e7 | −0.547559 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.69374e6 | 0.430220 | ||||||||
\(837\) | −3.48591e6 | −0.171990 | ||||||||
\(838\) | −1.22585e7 | −0.603013 | ||||||||
\(839\) | −1.54475e6 | −0.0757625 | −0.0378812 | − | 0.999282i | \(-0.512061\pi\) | ||||
−0.0378812 | + | 0.999282i | \(0.512061\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.53218e7 | 0.746998 | ||||||||
\(842\) | −3.35113e6 | −0.162896 | ||||||||
\(843\) | 1.14123e7 | 0.553101 | ||||||||
\(844\) | 1.45644e7 | 0.703781 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.81368e6 | −0.0871232 | ||||||||
\(847\) | −1.09543e7 | −0.524658 | ||||||||
\(848\) | 6.77462e6 | 0.323516 | ||||||||
\(849\) | 6.17249e6 | 0.293895 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −674692. | −0.0319361 | ||||||||
\(852\) | 8.27850e6 | 0.390708 | ||||||||
\(853\) | −2.39801e7 | −1.12844 | −0.564220 | − | 0.825625i | \(-0.690823\pi\) | ||||
−0.564220 | + | 0.825625i | \(0.690823\pi\) | |||||||
\(854\) | −2.17988e7 | −1.02279 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.22531e6 | 0.103802 | ||||||||
\(857\) | −3.48306e7 | −1.61998 | −0.809989 | − | 0.586445i | \(-0.800527\pi\) | ||||
−0.809989 | + | 0.586445i | \(0.800527\pi\) | |||||||
\(858\) | −8.08002e6 | −0.374709 | ||||||||
\(859\) | −1.01532e7 | −0.469482 | −0.234741 | − | 0.972058i | \(-0.575424\pi\) | ||||
−0.234741 | + | 0.972058i | \(0.575424\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.99310e7 | −0.916267 | ||||||||
\(862\) | −2.36288e7 | −1.08311 | ||||||||
\(863\) | 2.71085e7 | 1.23902 | 0.619510 | − | 0.784989i | \(-0.287331\pi\) | ||||
0.619510 | + | 0.784989i | \(0.287331\pi\) | |||||||
\(864\) | 746496. | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.39981e6 | −0.335294 | ||||||||
\(867\) | −2.13134e6 | −0.0962953 | ||||||||
\(868\) | 9.15849e6 | 0.412596 | ||||||||
\(869\) | 1.11014e7 | 0.498689 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.92399e7 | −1.30596 | ||||||||
\(872\) | 1.25673e6 | 0.0559696 | ||||||||
\(873\) | 6.70524e6 | 0.297768 | ||||||||
\(874\) | 457658. | 0.0202658 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.88178e6 | −0.170911 | ||||||||
\(877\) | 5.76852e6 | 0.253259 | 0.126630 | − | 0.991950i | \(-0.459584\pi\) | ||||
0.126630 | + | 0.991950i | \(0.459584\pi\) | |||||||
\(878\) | 1.12469e7 | 0.492374 | ||||||||
\(879\) | −1.50172e7 | −0.655565 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.56949e7 | −1.54941 | −0.774705 | − | 0.632322i | \(-0.782102\pi\) | ||||
−0.774705 | + | 0.632322i | \(0.782102\pi\) | |||||||
\(882\) | 802704. | 0.0347443 | ||||||||
\(883\) | 4.55843e6 | 0.196749 | 0.0983747 | − | 0.995149i | \(-0.468636\pi\) | ||||
0.0983747 | + | 0.995149i | \(0.468636\pi\) | |||||||
\(884\) | 1.75278e7 | 0.754393 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.65546e6 | −0.413227 | ||||||||
\(887\) | 3.23885e6 | 0.138223 | 0.0691117 | − | 0.997609i | \(-0.477984\pi\) | ||||
0.0691117 | + | 0.997609i | \(0.477984\pi\) | |||||||
\(888\) | 6.99864e6 | 0.297839 | ||||||||
\(889\) | 6.68243e6 | 0.283583 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.73017e6 | 0.0730123 | ||||||||
\(892\) | −1.67220e7 | −0.703683 | ||||||||
\(893\) | 1.15340e7 | 0.484008 | ||||||||
\(894\) | 1.25779e7 | 0.526338 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.96126e6 | −0.0816142 | ||||||||
\(897\) | −425351. | −0.0176509 | ||||||||
\(898\) | 2.02850e6 | 0.0839428 | ||||||||
\(899\) | −2.86239e7 | −1.18122 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.40615e7 | −1.39782 | ||||||||
\(902\) | −1.95142e7 | −0.798611 | ||||||||
\(903\) | −2.35775e6 | −0.0962230 | ||||||||
\(904\) | −1.26186e6 | −0.0513559 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.13229e7 | −0.458287 | ||||||||
\(907\) | −168518. | −0.00680186 | −0.00340093 | − | 0.999994i | \(-0.501083\pi\) | ||||
−0.00340093 | + | 0.999994i | \(0.501083\pi\) | |||||||
\(908\) | −1.39059e7 | −0.559739 | ||||||||
\(909\) | 1.18624e6 | 0.0476170 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.36451e7 | 1.34315 | 0.671577 | − | 0.740935i | \(-0.265617\pi\) | ||||
0.671577 | + | 0.740935i | \(0.265617\pi\) | |||||||
\(912\) | −4.74733e6 | −0.189000 | ||||||||
\(913\) | −2.68276e7 | −1.06514 | ||||||||
\(914\) | −4.39514e6 | −0.174023 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.23851e7 | −0.881494 | ||||||||
\(917\) | 1.63252e7 | 0.641112 | ||||||||
\(918\) | −3.75324e6 | −0.146994 | ||||||||
\(919\) | 6.60944e6 | 0.258152 | 0.129076 | − | 0.991635i | \(-0.458799\pi\) | ||||
0.129076 | + | 0.991635i | \(0.458799\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.04698e6 | −0.196057 | ||||||||
\(922\) | −424262. | −0.0164364 | ||||||||
\(923\) | 4.89304e7 | 1.89049 | ||||||||
\(924\) | −4.54567e6 | −0.175153 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.44706e6 | −0.208754 | ||||||||
\(927\) | 1.61941e7 | 0.618952 | ||||||||
\(928\) | 6.12973e6 | 0.233653 | ||||||||
\(929\) | −4.55946e7 | −1.73330 | −0.866651 | − | 0.498915i | \(-0.833732\pi\) | ||||
−0.866651 | + | 0.498915i | \(0.833732\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.10478e6 | −0.193020 | ||||||||
\(932\) | 6.45590e6 | 0.243454 | ||||||||
\(933\) | 1.20548e7 | 0.453375 | ||||||||
\(934\) | 8.74839e6 | 0.328141 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.41220e6 | 0.164613 | ||||||||
\(937\) | −3.05380e6 | −0.113630 | −0.0568148 | − | 0.998385i | \(-0.518094\pi\) | ||||
−0.0568148 | + | 0.998385i | \(0.518094\pi\) | |||||||
\(938\) | −1.64499e7 | −0.610457 | ||||||||
\(939\) | 5.59103e6 | 0.206932 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.36840e7 | 1.24008 | 0.620040 | − | 0.784570i | \(-0.287116\pi\) | ||||
0.620040 | + | 0.784570i | \(0.287116\pi\) | |||||||
\(942\) | 4.72689e6 | 0.173559 | ||||||||
\(943\) | −1.02727e6 | −0.0376190 | ||||||||
\(944\) | 5.33135e6 | 0.194719 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.30845e6 | −0.0838671 | ||||||||
\(947\) | 5.69161e6 | 0.206234 | 0.103117 | − | 0.994669i | \(-0.467118\pi\) | ||||
0.103117 | + | 0.994669i | \(0.467118\pi\) | |||||||
\(948\) | −6.06208e6 | −0.219079 | ||||||||
\(949\) | −2.29434e7 | −0.826976 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.70254e6 | 0.0968992 | ||||||||
\(952\) | 9.86084e6 | 0.352632 | ||||||||
\(953\) | 1.73627e7 | 0.619278 | 0.309639 | − | 0.950854i | \(-0.399792\pi\) | ||||
0.309639 | + | 0.950854i | \(0.399792\pi\) | |||||||
\(954\) | −8.57413e6 | −0.305014 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.77721e6 | −0.345995 | ||||||||
\(957\) | 1.42070e7 | 0.501446 | ||||||||
\(958\) | −4.06380e6 | −0.143060 | ||||||||
\(959\) | 1.60869e7 | 0.564839 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.76388e6 | −0.201329 | ||||||||
\(962\) | 4.13657e7 | 1.44113 | ||||||||
\(963\) | −2.81640e6 | −0.0978653 | ||||||||
\(964\) | −2.41022e7 | −0.835342 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −239295. | −0.00825069 | ||||||||
\(967\) | −4.93082e7 | −1.69572 | −0.847858 | − | 0.530224i | \(-0.822108\pi\) | ||||
−0.847858 | + | 0.530224i | \(0.822108\pi\) | |||||||
\(968\) | 5.85665e6 | 0.200891 | ||||||||
\(969\) | 2.38686e7 | 0.816616 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.23520e7 | 1.10117 | 0.550584 | − | 0.834780i | \(-0.314405\pi\) | ||||
0.550584 | + | 0.834780i | \(0.314405\pi\) | |||||||
\(972\) | −944784. | −0.0320750 | ||||||||
\(973\) | −3.65729e7 | −1.23845 | ||||||||
\(974\) | −8.09357e6 | −0.273365 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.16546e7 | 0.391627 | ||||||||
\(977\) | −2.61290e7 | −0.875763 | −0.437882 | − | 0.899033i | \(-0.644271\pi\) | ||||
−0.437882 | + | 0.899033i | \(0.644271\pi\) | |||||||
\(978\) | 2.27954e7 | 0.762078 | ||||||||
\(979\) | −1.72862e7 | −0.576426 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.59055e6 | −0.0527686 | ||||||||
\(982\) | 1.68995e7 | 0.559235 | ||||||||
\(983\) | −3.19496e7 | −1.05458 | −0.527292 | − | 0.849684i | \(-0.676793\pi\) | ||||
−0.527292 | + | 0.849684i | \(0.676793\pi\) | |||||||
\(984\) | 1.06560e7 | 0.350838 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.08191e7 | −1.00955 | ||||||||
\(987\) | −6.03077e6 | −0.197052 | ||||||||
\(988\) | −2.80593e7 | −0.914501 | ||||||||
\(989\) | −121522. | −0.00395061 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.14783e7 | 0.371272 | 0.185636 | − | 0.982619i | \(-0.440565\pi\) | ||||
0.185636 | + | 0.982619i | \(0.440565\pi\) | |||||||
\(992\) | −4.89653e6 | −0.157982 | ||||||||
\(993\) | 1.75422e7 | 0.564563 | ||||||||
\(994\) | 2.75274e7 | 0.883688 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.46495e7 | 0.467925 | ||||||||
\(997\) | 5.48929e7 | 1.74895 | 0.874476 | − | 0.485068i | \(-0.161205\pi\) | ||||
0.874476 | + | 0.485068i | \(0.161205\pi\) | |||||||
\(998\) | 2.68552e7 | 0.853499 | ||||||||
\(999\) | −8.85765e6 | −0.280805 |
(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 | 150.6.a.n.1.2 | 2 | ||
3.2 | odd | 2 | 450.6.a.bc.1.2 | 2 | |||
5.2 | odd | 4 | 30.6.c.b.19.1 | ✓ | 4 | ||
5.3 | odd | 4 | 30.6.c.b.19.3 | yes | 4 | ||
5.4 | even | 2 | 150.6.a.o.1.1 | 2 | |||
15.2 | even | 4 | 90.6.c.c.19.4 | 4 | |||
15.8 | even | 4 | 90.6.c.c.19.2 | 4 | |||
15.14 | odd | 2 | 450.6.a.bb.1.1 | 2 | |||
20.3 | even | 4 | 240.6.f.b.49.3 | 4 | |||
20.7 | even | 4 | 240.6.f.b.49.1 | 4 | |||
60.23 | odd | 4 | 720.6.f.i.289.4 | 4 | |||
60.47 | odd | 4 | 720.6.f.i.289.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.6.c.b.19.1 | ✓ | 4 | 5.2 | odd | 4 | ||
30.6.c.b.19.3 | yes | 4 | 5.3 | odd | 4 | ||
90.6.c.c.19.2 | 4 | 15.8 | even | 4 | |||
90.6.c.c.19.4 | 4 | 15.2 | even | 4 | |||
150.6.a.n.1.2 | 2 | 1.1 | even | 1 | trivial | ||
150.6.a.o.1.1 | 2 | 5.4 | even | 2 | |||
240.6.f.b.49.1 | 4 | 20.7 | even | 4 | |||
240.6.f.b.49.3 | 4 | 20.3 | even | 4 | |||
450.6.a.bb.1.1 | 2 | 15.14 | odd | 2 | |||
450.6.a.bc.1.2 | 2 | 3.2 | odd | 2 | |||
720.6.f.i.289.3 | 4 | 60.47 | odd | 4 | |||
720.6.f.i.289.4 | 4 | 60.23 | odd | 4 |