Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,6,Mod(1,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, 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("294.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.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: | \(47.1528430250\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.1 |
$q$-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 | ||||||||
\(5\) | 103.497 | 1.85142 | 0.925710 | − | 0.378235i | \(-0.123469\pi\) | ||||
0.925710 | + | 0.378235i | \(0.123469\pi\) | |||||||
\(6\) | −36.0000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −413.990 | −1.30915 | ||||||||
\(11\) | 240.191 | 0.598515 | 0.299257 | − | 0.954172i | \(-0.403261\pi\) | ||||
0.299257 | + | 0.954172i | \(0.403261\pi\) | |||||||
\(12\) | 144.000 | 0.288675 | ||||||||
\(13\) | 805.477 | 1.32189 | 0.660944 | − | 0.750435i | \(-0.270156\pi\) | ||||
0.660944 | + | 0.750435i | \(0.270156\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 931.477 | 1.06892 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −1293.27 | −1.08534 | −0.542670 | − | 0.839946i | \(-0.682586\pi\) | ||||
−0.542670 | + | 0.839946i | \(0.682586\pi\) | |||||||
\(18\) | −324.000 | −0.235702 | ||||||||
\(19\) | −275.377 | −0.175002 | −0.0875011 | − | 0.996164i | \(-0.527888\pi\) | ||||
−0.0875011 | + | 0.996164i | \(0.527888\pi\) | |||||||
\(20\) | 1655.96 | 0.925710 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −960.764 | −0.423214 | ||||||||
\(23\) | 3796.57 | 1.49648 | 0.748242 | − | 0.663426i | \(-0.230898\pi\) | ||||
0.748242 | + | 0.663426i | \(0.230898\pi\) | |||||||
\(24\) | −576.000 | −0.204124 | ||||||||
\(25\) | 7586.73 | 2.42775 | ||||||||
\(26\) | −3221.91 | −0.934717 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1227.52 | 0.271040 | 0.135520 | − | 0.990775i | \(-0.456730\pi\) | ||||
0.135520 | + | 0.990775i | \(0.456730\pi\) | |||||||
\(30\) | −3725.91 | −0.755839 | ||||||||
\(31\) | 5624.86 | 1.05125 | 0.525627 | − | 0.850715i | \(-0.323831\pi\) | ||||
0.525627 | + | 0.850715i | \(0.323831\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 2161.72 | 0.345553 | ||||||||
\(34\) | 5173.06 | 0.767451 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1296.00 | 0.166667 | ||||||||
\(37\) | −9078.49 | −1.09021 | −0.545104 | − | 0.838368i | \(-0.683510\pi\) | ||||
−0.545104 | + | 0.838368i | \(0.683510\pi\) | |||||||
\(38\) | 1101.51 | 0.123745 | ||||||||
\(39\) | 7249.30 | 0.763193 | ||||||||
\(40\) | −6623.84 | −0.654576 | ||||||||
\(41\) | −18207.4 | −1.69156 | −0.845782 | − | 0.533528i | \(-0.820866\pi\) | ||||
−0.845782 | + | 0.533528i | \(0.820866\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11708.2 | −0.965650 | −0.482825 | − | 0.875717i | \(-0.660389\pi\) | ||||
−0.482825 | + | 0.875717i | \(0.660389\pi\) | |||||||
\(44\) | 3843.05 | 0.299257 | ||||||||
\(45\) | 8383.30 | 0.617140 | ||||||||
\(46\) | −15186.3 | −1.05817 | ||||||||
\(47\) | −23048.6 | −1.52195 | −0.760974 | − | 0.648782i | \(-0.775279\pi\) | ||||
−0.760974 | + | 0.648782i | \(0.775279\pi\) | |||||||
\(48\) | 2304.00 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −30346.9 | −1.71668 | ||||||||
\(51\) | −11639.4 | −0.626621 | ||||||||
\(52\) | 12887.6 | 0.660944 | ||||||||
\(53\) | 17662.8 | 0.863714 | 0.431857 | − | 0.901942i | \(-0.357859\pi\) | ||||
0.431857 | + | 0.901942i | \(0.357859\pi\) | |||||||
\(54\) | −2916.00 | −0.136083 | ||||||||
\(55\) | 24859.2 | 1.10810 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2478.39 | −0.101038 | ||||||||
\(58\) | −4910.07 | −0.191654 | ||||||||
\(59\) | 18376.3 | 0.687271 | 0.343636 | − | 0.939103i | \(-0.388342\pi\) | ||||
0.343636 | + | 0.939103i | \(0.388342\pi\) | |||||||
\(60\) | 14903.6 | 0.534459 | ||||||||
\(61\) | 11324.1 | 0.389654 | 0.194827 | − | 0.980838i | \(-0.437586\pi\) | ||||
0.194827 | + | 0.980838i | \(0.437586\pi\) | |||||||
\(62\) | −22499.5 | −0.743349 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 83364.9 | 2.44737 | ||||||||
\(66\) | −8646.87 | −0.244343 | ||||||||
\(67\) | 36079.3 | 0.981910 | 0.490955 | − | 0.871185i | \(-0.336648\pi\) | ||||
0.490955 | + | 0.871185i | \(0.336648\pi\) | |||||||
\(68\) | −20692.3 | −0.542670 | ||||||||
\(69\) | 34169.2 | 0.863996 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −63434.2 | −1.49341 | −0.746703 | − | 0.665158i | \(-0.768364\pi\) | ||||
−0.746703 | + | 0.665158i | \(0.768364\pi\) | |||||||
\(72\) | −5184.00 | −0.117851 | ||||||||
\(73\) | −52982.4 | −1.16366 | −0.581828 | − | 0.813312i | \(-0.697662\pi\) | ||||
−0.581828 | + | 0.813312i | \(0.697662\pi\) | |||||||
\(74\) | 36314.0 | 0.770893 | ||||||||
\(75\) | 68280.5 | 1.40166 | ||||||||
\(76\) | −4406.03 | −0.0875011 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −28997.2 | −0.539659 | ||||||||
\(79\) | −48564.0 | −0.875481 | −0.437741 | − | 0.899101i | \(-0.644221\pi\) | ||||
−0.437741 | + | 0.899101i | \(0.644221\pi\) | |||||||
\(80\) | 26495.4 | 0.462855 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 72829.7 | 1.19612 | ||||||||
\(83\) | 113161. | 1.80303 | 0.901513 | − | 0.432753i | \(-0.142458\pi\) | ||||
0.901513 | + | 0.432753i | \(0.142458\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −133850. | −2.00942 | ||||||||
\(86\) | 46832.9 | 0.682818 | ||||||||
\(87\) | 11047.7 | 0.156485 | ||||||||
\(88\) | −15372.2 | −0.211607 | ||||||||
\(89\) | 108366. | 1.45017 | 0.725083 | − | 0.688662i | \(-0.241801\pi\) | ||||
0.725083 | + | 0.688662i | \(0.241801\pi\) | |||||||
\(90\) | −33533.2 | −0.436384 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 60745.2 | 0.748242 | ||||||||
\(93\) | 50623.8 | 0.606942 | ||||||||
\(94\) | 92194.4 | 1.07618 | ||||||||
\(95\) | −28500.8 | −0.324002 | ||||||||
\(96\) | −9216.00 | −0.102062 | ||||||||
\(97\) | 99641.2 | 1.07525 | 0.537625 | − | 0.843184i | \(-0.319321\pi\) | ||||
0.537625 | + | 0.843184i | \(0.319321\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19455.5 | 0.199505 | ||||||||
\(100\) | 121388. | 1.21388 | ||||||||
\(101\) | 165200. | 1.61141 | 0.805705 | − | 0.592317i | \(-0.201787\pi\) | ||||
0.805705 | + | 0.592317i | \(0.201787\pi\) | |||||||
\(102\) | 46557.6 | 0.443088 | ||||||||
\(103\) | −107247. | −0.996077 | −0.498038 | − | 0.867155i | \(-0.665946\pi\) | ||||
−0.498038 | + | 0.867155i | \(0.665946\pi\) | |||||||
\(104\) | −51550.5 | −0.467358 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −70651.2 | −0.610738 | ||||||||
\(107\) | −97422.3 | −0.822620 | −0.411310 | − | 0.911496i | \(-0.634929\pi\) | ||||
−0.411310 | + | 0.911496i | \(0.634929\pi\) | |||||||
\(108\) | 11664.0 | 0.0962250 | ||||||||
\(109\) | 59307.2 | 0.478125 | 0.239062 | − | 0.971004i | \(-0.423160\pi\) | ||||
0.239062 | + | 0.971004i | \(0.423160\pi\) | |||||||
\(110\) | −99436.6 | −0.783546 | ||||||||
\(111\) | −81706.4 | −0.629432 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 157268. | 1.15863 | 0.579313 | − | 0.815105i | \(-0.303321\pi\) | ||||
0.579313 | + | 0.815105i | \(0.303321\pi\) | |||||||
\(114\) | 9913.56 | 0.0714443 | ||||||||
\(115\) | 392936. | 2.77062 | ||||||||
\(116\) | 19640.3 | 0.135520 | ||||||||
\(117\) | 65243.7 | 0.440630 | ||||||||
\(118\) | −73505.2 | −0.485974 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −59614.5 | −0.377919 | ||||||||
\(121\) | −103359. | −0.641780 | ||||||||
\(122\) | −45296.3 | −0.275527 | ||||||||
\(123\) | −163867. | −0.976625 | ||||||||
\(124\) | 89997.8 | 0.525627 | ||||||||
\(125\) | 461778. | 2.64337 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −92477.3 | −0.508775 | −0.254387 | − | 0.967102i | \(-0.581874\pi\) | ||||
−0.254387 | + | 0.967102i | \(0.581874\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −105374. | −0.557518 | ||||||||
\(130\) | −333459. | −1.73055 | ||||||||
\(131\) | −72328.4 | −0.368240 | −0.184120 | − | 0.982904i | \(-0.558943\pi\) | ||||
−0.184120 | + | 0.982904i | \(0.558943\pi\) | |||||||
\(132\) | 34587.5 | 0.172776 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −144317. | −0.694315 | ||||||||
\(135\) | 75449.7 | 0.356306 | ||||||||
\(136\) | 82769.0 | 0.383725 | ||||||||
\(137\) | 225662. | 1.02720 | 0.513602 | − | 0.858028i | \(-0.328311\pi\) | ||||
0.513602 | + | 0.858028i | \(0.328311\pi\) | |||||||
\(138\) | −136677. | −0.610937 | ||||||||
\(139\) | −327971. | −1.43979 | −0.719894 | − | 0.694084i | \(-0.755810\pi\) | ||||
−0.719894 | + | 0.694084i | \(0.755810\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −207437. | −0.878697 | ||||||||
\(142\) | 253737. | 1.05600 | ||||||||
\(143\) | 193468. | 0.791170 | ||||||||
\(144\) | 20736.0 | 0.0833333 | ||||||||
\(145\) | 127045. | 0.501808 | ||||||||
\(146\) | 211930. | 0.822829 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −145256. | −0.545104 | ||||||||
\(149\) | 164011. | 0.605211 | 0.302606 | − | 0.953116i | \(-0.402144\pi\) | ||||
0.302606 | + | 0.953116i | \(0.402144\pi\) | |||||||
\(150\) | −273122. | −0.991126 | ||||||||
\(151\) | 62308.8 | 0.222386 | 0.111193 | − | 0.993799i | \(-0.464533\pi\) | ||||
0.111193 | + | 0.993799i | \(0.464533\pi\) | |||||||
\(152\) | 17624.1 | 0.0618726 | ||||||||
\(153\) | −104755. | −0.361780 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 582159. | 1.94631 | ||||||||
\(156\) | 115989. | 0.381596 | ||||||||
\(157\) | −239807. | −0.776447 | −0.388224 | − | 0.921565i | \(-0.626911\pi\) | ||||
−0.388224 | + | 0.921565i | \(0.626911\pi\) | |||||||
\(158\) | 194256. | 0.619059 | ||||||||
\(159\) | 158965. | 0.498665 | ||||||||
\(160\) | −105981. | −0.327288 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −26244.0 | −0.0785674 | ||||||||
\(163\) | −436795. | −1.28768 | −0.643841 | − | 0.765160i | \(-0.722660\pi\) | ||||
−0.643841 | + | 0.765160i | \(0.722660\pi\) | |||||||
\(164\) | −291319. | −0.845782 | ||||||||
\(165\) | 223732. | 0.639763 | ||||||||
\(166\) | −452644. | −1.27493 | ||||||||
\(167\) | 38846.7 | 0.107786 | 0.0538931 | − | 0.998547i | \(-0.482837\pi\) | ||||
0.0538931 | + | 0.998547i | \(0.482837\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 277501. | 0.747390 | ||||||||
\(170\) | 535399. | 1.42087 | ||||||||
\(171\) | −22305.5 | −0.0583340 | ||||||||
\(172\) | −187331. | −0.482825 | ||||||||
\(173\) | 396277. | 1.00666 | 0.503331 | − | 0.864093i | \(-0.332108\pi\) | ||||
0.503331 | + | 0.864093i | \(0.332108\pi\) | |||||||
\(174\) | −44190.7 | −0.110652 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 61488.9 | 0.149629 | ||||||||
\(177\) | 165387. | 0.396796 | ||||||||
\(178\) | −433464. | −1.02542 | ||||||||
\(179\) | 243883. | 0.568918 | 0.284459 | − | 0.958688i | \(-0.408186\pi\) | ||||
0.284459 | + | 0.958688i | \(0.408186\pi\) | |||||||
\(180\) | 134133. | 0.308570 | ||||||||
\(181\) | −299273. | −0.679002 | −0.339501 | − | 0.940606i | \(-0.610258\pi\) | ||||
−0.339501 | + | 0.940606i | \(0.610258\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 101917. | 0.224967 | ||||||||
\(184\) | −242981. | −0.529087 | ||||||||
\(185\) | −939601. | −2.01843 | ||||||||
\(186\) | −202495. | −0.429173 | ||||||||
\(187\) | −310631. | −0.649592 | ||||||||
\(188\) | −368778. | −0.760974 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 114003. | 0.229104 | ||||||||
\(191\) | −776996. | −1.54112 | −0.770558 | − | 0.637369i | \(-0.780023\pi\) | ||||
−0.770558 | + | 0.637369i | \(0.780023\pi\) | |||||||
\(192\) | 36864.0 | 0.0721688 | ||||||||
\(193\) | 276421. | 0.534168 | 0.267084 | − | 0.963673i | \(-0.413940\pi\) | ||||
0.267084 | + | 0.963673i | \(0.413940\pi\) | |||||||
\(194\) | −398565. | −0.760317 | ||||||||
\(195\) | 750284. | 1.41299 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −131615. | −0.241624 | −0.120812 | − | 0.992675i | \(-0.538550\pi\) | ||||
−0.120812 | + | 0.992675i | \(0.538550\pi\) | |||||||
\(198\) | −77821.9 | −0.141071 | ||||||||
\(199\) | 564960. | 1.01131 | 0.505656 | − | 0.862735i | \(-0.331250\pi\) | ||||
0.505656 | + | 0.862735i | \(0.331250\pi\) | |||||||
\(200\) | −485551. | −0.858340 | ||||||||
\(201\) | 324714. | 0.566906 | ||||||||
\(202\) | −660799. | −1.13944 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −186230. | −0.313311 | ||||||||
\(205\) | −1.88442e6 | −3.13180 | ||||||||
\(206\) | 428989. | 0.704333 | ||||||||
\(207\) | 307522. | 0.498828 | ||||||||
\(208\) | 206202. | 0.330472 | ||||||||
\(209\) | −66143.0 | −0.104741 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 313637. | 0.484977 | 0.242489 | − | 0.970154i | \(-0.422036\pi\) | ||||
0.242489 | + | 0.970154i | \(0.422036\pi\) | |||||||
\(212\) | 282605. | 0.431857 | ||||||||
\(213\) | −570908. | −0.862218 | ||||||||
\(214\) | 389689. | 0.581680 | ||||||||
\(215\) | −1.21177e6 | −1.78782 | ||||||||
\(216\) | −46656.0 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −237229. | −0.338085 | ||||||||
\(219\) | −476841. | −0.671837 | ||||||||
\(220\) | 397746. | 0.554051 | ||||||||
\(221\) | −1.04170e6 | −1.43470 | ||||||||
\(222\) | 326826. | 0.445076 | ||||||||
\(223\) | −279483. | −0.376351 | −0.188176 | − | 0.982135i | \(-0.560257\pi\) | ||||
−0.188176 | + | 0.982135i | \(0.560257\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 614525. | 0.809251 | ||||||||
\(226\) | −629071. | −0.819273 | ||||||||
\(227\) | −1.22351e6 | −1.57595 | −0.787974 | − | 0.615709i | \(-0.788870\pi\) | ||||
−0.787974 | + | 0.615709i | \(0.788870\pi\) | |||||||
\(228\) | −39654.3 | −0.0505188 | ||||||||
\(229\) | 254775. | 0.321046 | 0.160523 | − | 0.987032i | \(-0.448682\pi\) | ||||
0.160523 | + | 0.987032i | \(0.448682\pi\) | |||||||
\(230\) | −1.57174e6 | −1.95912 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −78561.2 | −0.0958270 | ||||||||
\(233\) | 746173. | 0.900429 | 0.450215 | − | 0.892920i | \(-0.351347\pi\) | ||||
0.450215 | + | 0.892920i | \(0.351347\pi\) | |||||||
\(234\) | −260975. | −0.311572 | ||||||||
\(235\) | −2.38547e6 | −2.81776 | ||||||||
\(236\) | 294021. | 0.343636 | ||||||||
\(237\) | −437076. | −0.505459 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 321036. | 0.363546 | 0.181773 | − | 0.983341i | \(-0.441816\pi\) | ||||
0.181773 | + | 0.983341i | \(0.441816\pi\) | |||||||
\(240\) | 238458. | 0.267229 | ||||||||
\(241\) | 1.24254e6 | 1.37805 | 0.689027 | − | 0.724735i | \(-0.258038\pi\) | ||||
0.689027 | + | 0.724735i | \(0.258038\pi\) | |||||||
\(242\) | 413437. | 0.453807 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 181185. | 0.194827 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 655467. | 0.690578 | ||||||||
\(247\) | −221810. | −0.231333 | ||||||||
\(248\) | −359991. | −0.371675 | ||||||||
\(249\) | 1.01845e6 | 1.04098 | ||||||||
\(250\) | −1.84711e6 | −1.86914 | ||||||||
\(251\) | 690235. | 0.691532 | 0.345766 | − | 0.938321i | \(-0.387619\pi\) | ||||
0.345766 | + | 0.938321i | \(0.387619\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 911902. | 0.895668 | ||||||||
\(254\) | 369909. | 0.359758 | ||||||||
\(255\) | −1.20465e6 | −1.16014 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 13786.7 | 0.0130205 | 0.00651024 | − | 0.999979i | \(-0.497928\pi\) | ||||
0.00651024 | + | 0.999979i | \(0.497928\pi\) | |||||||
\(258\) | 421496. | 0.394225 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.33384e6 | 1.22369 | ||||||||
\(261\) | 99429.0 | 0.0903466 | ||||||||
\(262\) | 289314. | 0.260385 | ||||||||
\(263\) | 574833. | 0.512451 | 0.256226 | − | 0.966617i | \(-0.417521\pi\) | ||||
0.256226 | + | 0.966617i | \(0.417521\pi\) | |||||||
\(264\) | −138350. | −0.122171 | ||||||||
\(265\) | 1.82806e6 | 1.59910 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 975293. | 0.837253 | ||||||||
\(268\) | 577270. | 0.490955 | ||||||||
\(269\) | −1.11893e6 | −0.942804 | −0.471402 | − | 0.881918i | \(-0.656252\pi\) | ||||
−0.471402 | + | 0.881918i | \(0.656252\pi\) | |||||||
\(270\) | −301799. | −0.251946 | ||||||||
\(271\) | 694869. | 0.574751 | 0.287376 | − | 0.957818i | \(-0.407217\pi\) | ||||
0.287376 | + | 0.957818i | \(0.407217\pi\) | |||||||
\(272\) | −331076. | −0.271335 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −902648. | −0.726343 | ||||||||
\(275\) | 1.82226e6 | 1.45305 | ||||||||
\(276\) | 546706. | 0.431998 | ||||||||
\(277\) | −837654. | −0.655941 | −0.327971 | − | 0.944688i | \(-0.606365\pi\) | ||||
−0.327971 | + | 0.944688i | \(0.606365\pi\) | |||||||
\(278\) | 1.31188e6 | 1.01808 | ||||||||
\(279\) | 455614. | 0.350418 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −917687. | −0.693312 | −0.346656 | − | 0.937992i | \(-0.612683\pi\) | ||||
−0.346656 | + | 0.937992i | \(0.612683\pi\) | |||||||
\(282\) | 829750. | 0.621333 | ||||||||
\(283\) | −415263. | −0.308218 | −0.154109 | − | 0.988054i | \(-0.549251\pi\) | ||||
−0.154109 | + | 0.988054i | \(0.549251\pi\) | |||||||
\(284\) | −1.01495e6 | −0.746703 | ||||||||
\(285\) | −256507. | −0.187063 | ||||||||
\(286\) | −773873. | −0.559442 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −82944.0 | −0.0589256 | ||||||||
\(289\) | 252680. | 0.177962 | ||||||||
\(290\) | −508180. | −0.354832 | ||||||||
\(291\) | 896771. | 0.620796 | ||||||||
\(292\) | −847718. | −0.581828 | ||||||||
\(293\) | −1.21491e6 | −0.826752 | −0.413376 | − | 0.910561i | \(-0.635650\pi\) | ||||
−0.413376 | + | 0.910561i | \(0.635650\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.90190e6 | 1.27243 | ||||||||
\(296\) | 581023. | 0.385447 | ||||||||
\(297\) | 175099. | 0.115184 | ||||||||
\(298\) | −656043. | −0.427949 | ||||||||
\(299\) | 3.05805e6 | 1.97819 | ||||||||
\(300\) | 1.09249e6 | 0.700832 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −249235. | −0.157250 | ||||||||
\(303\) | 1.48680e6 | 0.930348 | ||||||||
\(304\) | −70496.5 | −0.0437505 | ||||||||
\(305\) | 1.17201e6 | 0.721412 | ||||||||
\(306\) | 419018. | 0.255817 | ||||||||
\(307\) | −2.60119e6 | −1.57517 | −0.787584 | − | 0.616207i | \(-0.788668\pi\) | ||||
−0.787584 | + | 0.616207i | \(0.788668\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −965225. | −0.575085 | ||||||||
\(310\) | −2.32864e6 | −1.37625 | ||||||||
\(311\) | −819164. | −0.480253 | −0.240126 | − | 0.970742i | \(-0.577189\pi\) | ||||
−0.240126 | + | 0.970742i | \(0.577189\pi\) | |||||||
\(312\) | −463955. | −0.269829 | ||||||||
\(313\) | −881939. | −0.508836 | −0.254418 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254418 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(314\) | 959226. | 0.549031 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −777024. | −0.437741 | ||||||||
\(317\) | −1.60438e6 | −0.896726 | −0.448363 | − | 0.893852i | \(-0.647993\pi\) | ||||
−0.448363 | + | 0.893852i | \(0.647993\pi\) | |||||||
\(318\) | −635861. | −0.352610 | ||||||||
\(319\) | 294839. | 0.162221 | ||||||||
\(320\) | 423926. | 0.231427 | ||||||||
\(321\) | −876801. | −0.474940 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 356135. | 0.189937 | ||||||||
\(324\) | 104976. | 0.0555556 | ||||||||
\(325\) | 6.11094e6 | 3.20922 | ||||||||
\(326\) | 1.74718e6 | 0.910528 | ||||||||
\(327\) | 533765. | 0.276045 | ||||||||
\(328\) | 1.16527e6 | 0.598058 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −894929. | −0.452381 | ||||||||
\(331\) | 1.00308e6 | 0.503229 | 0.251614 | − | 0.967828i | \(-0.419039\pi\) | ||||
0.251614 | + | 0.967828i | \(0.419039\pi\) | |||||||
\(332\) | 1.81058e6 | 0.901513 | ||||||||
\(333\) | −735358. | −0.363403 | ||||||||
\(334\) | −155387. | −0.0762164 | ||||||||
\(335\) | 3.73412e6 | 1.81793 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.62317e6 | −1.25821 | −0.629103 | − | 0.777322i | \(-0.716578\pi\) | ||||
−0.629103 | + | 0.777322i | \(0.716578\pi\) | |||||||
\(338\) | −1.11000e6 | −0.528484 | ||||||||
\(339\) | 1.41541e6 | 0.668933 | ||||||||
\(340\) | −2.14160e6 | −1.00471 | ||||||||
\(341\) | 1.35104e6 | 0.629191 | ||||||||
\(342\) | 89222.1 | 0.0412484 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 749326. | 0.341409 | ||||||||
\(345\) | 3.53642e6 | 1.59962 | ||||||||
\(346\) | −1.58511e6 | −0.711818 | ||||||||
\(347\) | 226234. | 0.100863 | 0.0504317 | − | 0.998728i | \(-0.483940\pi\) | ||||
0.0504317 | + | 0.998728i | \(0.483940\pi\) | |||||||
\(348\) | 176763. | 0.0782424 | ||||||||
\(349\) | −1.46280e6 | −0.642866 | −0.321433 | − | 0.946932i | \(-0.604165\pi\) | ||||
−0.321433 | + | 0.946932i | \(0.604165\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 587193. | 0.254398 | ||||||||
\(352\) | −245955. | −0.105803 | ||||||||
\(353\) | 2.80957e6 | 1.20006 | 0.600031 | − | 0.799977i | \(-0.295155\pi\) | ||||
0.600031 | + | 0.799977i | \(0.295155\pi\) | |||||||
\(354\) | −661547. | −0.280577 | ||||||||
\(355\) | −6.56528e6 | −2.76492 | ||||||||
\(356\) | 1.73385e6 | 0.725083 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −975534. | −0.402286 | ||||||||
\(359\) | −3.69900e6 | −1.51478 | −0.757388 | − | 0.652965i | \(-0.773525\pi\) | ||||
−0.757388 | + | 0.652965i | \(0.773525\pi\) | |||||||
\(360\) | −536531. | −0.218192 | ||||||||
\(361\) | −2.40027e6 | −0.969374 | ||||||||
\(362\) | 1.19709e6 | 0.480127 | ||||||||
\(363\) | −930234. | −0.370532 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.48354e6 | −2.15441 | ||||||||
\(366\) | −407667. | −0.159075 | ||||||||
\(367\) | 1.16925e6 | 0.453148 | 0.226574 | − | 0.973994i | \(-0.427247\pi\) | ||||
0.226574 | + | 0.973994i | \(0.427247\pi\) | |||||||
\(368\) | 971923. | 0.374121 | ||||||||
\(369\) | −1.47480e6 | −0.563855 | ||||||||
\(370\) | 3.75840e6 | 1.42725 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 809980. | 0.303471 | ||||||||
\(373\) | −4.57690e6 | −1.70333 | −0.851666 | − | 0.524084i | \(-0.824408\pi\) | ||||
−0.851666 | + | 0.524084i | \(0.824408\pi\) | |||||||
\(374\) | 1.24252e6 | 0.459331 | ||||||||
\(375\) | 4.15600e6 | 1.52615 | ||||||||
\(376\) | 1.47511e6 | 0.538090 | ||||||||
\(377\) | 988738. | 0.358284 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.35520e6 | −0.842229 | −0.421114 | − | 0.907007i | \(-0.638361\pi\) | ||||
−0.421114 | + | 0.907007i | \(0.638361\pi\) | |||||||
\(380\) | −456013. | −0.162001 | ||||||||
\(381\) | −832295. | −0.293741 | ||||||||
\(382\) | 3.10799e6 | 1.08973 | ||||||||
\(383\) | 3.03946e6 | 1.05876 | 0.529382 | − | 0.848384i | \(-0.322424\pi\) | ||||
0.529382 | + | 0.848384i | \(0.322424\pi\) | |||||||
\(384\) | −147456. | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.10568e6 | −0.377714 | ||||||||
\(387\) | −948366. | −0.321883 | ||||||||
\(388\) | 1.59426e6 | 0.537625 | ||||||||
\(389\) | −459273. | −0.153885 | −0.0769426 | − | 0.997036i | \(-0.524516\pi\) | ||||
−0.0769426 | + | 0.997036i | \(0.524516\pi\) | |||||||
\(390\) | −3.00114e6 | −0.999135 | ||||||||
\(391\) | −4.90998e6 | −1.62419 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −650956. | −0.212603 | ||||||||
\(394\) | 526461. | 0.170854 | ||||||||
\(395\) | −5.02625e6 | −1.62088 | ||||||||
\(396\) | 311287. | 0.0997525 | ||||||||
\(397\) | 5.42500e6 | 1.72752 | 0.863761 | − | 0.503901i | \(-0.168102\pi\) | ||||
0.863761 | + | 0.503901i | \(0.168102\pi\) | |||||||
\(398\) | −2.25984e6 | −0.715106 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.94220e6 | 0.606938 | ||||||||
\(401\) | 2.11127e6 | 0.655667 | 0.327833 | − | 0.944736i | \(-0.393682\pi\) | ||||
0.327833 | + | 0.944736i | \(0.393682\pi\) | |||||||
\(402\) | −1.29886e6 | −0.400863 | ||||||||
\(403\) | 4.53070e6 | 1.38964 | ||||||||
\(404\) | 2.64320e6 | 0.805705 | ||||||||
\(405\) | 679047. | 0.205713 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.18057e6 | −0.652506 | ||||||||
\(408\) | 744921. | 0.221544 | ||||||||
\(409\) | 2.55745e6 | 0.755959 | 0.377980 | − | 0.925814i | \(-0.376619\pi\) | ||||
0.377980 | + | 0.925814i | \(0.376619\pi\) | |||||||
\(410\) | 7.53769e6 | 2.21451 | ||||||||
\(411\) | 2.03096e6 | 0.593057 | ||||||||
\(412\) | −1.71595e6 | −0.498038 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.23009e6 | −0.352725 | ||||||||
\(415\) | 1.17119e7 | 3.33816 | ||||||||
\(416\) | −824809. | −0.233679 | ||||||||
\(417\) | −2.95174e6 | −0.831262 | ||||||||
\(418\) | 264572. | 0.0740633 | ||||||||
\(419\) | 2.17401e6 | 0.604959 | 0.302480 | − | 0.953156i | \(-0.402186\pi\) | ||||
0.302480 | + | 0.953156i | \(0.402186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.47930e6 | −1.50668 | −0.753338 | − | 0.657633i | \(-0.771558\pi\) | ||||
−0.753338 | + | 0.657633i | \(0.771558\pi\) | |||||||
\(422\) | −1.25455e6 | −0.342931 | ||||||||
\(423\) | −1.86694e6 | −0.507316 | ||||||||
\(424\) | −1.13042e6 | −0.305369 | ||||||||
\(425\) | −9.81166e6 | −2.63494 | ||||||||
\(426\) | 2.28363e6 | 0.609680 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.55876e6 | −0.411310 | ||||||||
\(429\) | 1.74121e6 | 0.456782 | ||||||||
\(430\) | 4.84708e6 | 1.26418 | ||||||||
\(431\) | −6.16874e6 | −1.59957 | −0.799785 | − | 0.600286i | \(-0.795053\pi\) | ||||
−0.799785 | + | 0.600286i | \(0.795053\pi\) | |||||||
\(432\) | 186624. | 0.0481125 | ||||||||
\(433\) | 4.89596e6 | 1.25493 | 0.627463 | − | 0.778647i | \(-0.284093\pi\) | ||||
0.627463 | + | 0.778647i | \(0.284093\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.14341e6 | 0.289719 | ||||||||
\(436\) | 948915. | 0.239062 | ||||||||
\(437\) | −1.04549e6 | −0.261888 | ||||||||
\(438\) | 1.90737e6 | 0.475060 | ||||||||
\(439\) | −3.54588e6 | −0.878137 | −0.439069 | − | 0.898454i | \(-0.644691\pi\) | ||||
−0.439069 | + | 0.898454i | \(0.644691\pi\) | |||||||
\(440\) | −1.59099e6 | −0.391773 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.16679e6 | 1.01448 | ||||||||
\(443\) | 6.05652e6 | 1.46627 | 0.733134 | − | 0.680084i | \(-0.238057\pi\) | ||||
0.733134 | + | 0.680084i | \(0.238057\pi\) | |||||||
\(444\) | −1.30730e6 | −0.314716 | ||||||||
\(445\) | 1.12156e7 | 2.68486 | ||||||||
\(446\) | 1.11793e6 | 0.266121 | ||||||||
\(447\) | 1.47610e6 | 0.349419 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.20801e6 | −0.282783 | −0.141392 | − | 0.989954i | \(-0.545158\pi\) | ||||
−0.141392 | + | 0.989954i | \(0.545158\pi\) | |||||||
\(450\) | −2.45810e6 | −0.572227 | ||||||||
\(451\) | −4.37326e6 | −1.01243 | ||||||||
\(452\) | 2.51628e6 | 0.579313 | ||||||||
\(453\) | 560779. | 0.128394 | ||||||||
\(454\) | 4.89403e6 | 1.11436 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 158617. | 0.0357222 | ||||||||
\(457\) | −5.46550e6 | −1.22416 | −0.612082 | − | 0.790794i | \(-0.709668\pi\) | ||||
−0.612082 | + | 0.790794i | \(0.709668\pi\) | |||||||
\(458\) | −1.01910e6 | −0.227014 | ||||||||
\(459\) | −942791. | −0.208874 | ||||||||
\(460\) | 6.28697e6 | 1.38531 | ||||||||
\(461\) | 1.15956e6 | 0.254121 | 0.127061 | − | 0.991895i | \(-0.459446\pi\) | ||||
0.127061 | + | 0.991895i | \(0.459446\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.31335e6 | −0.935108 | −0.467554 | − | 0.883964i | \(-0.654865\pi\) | ||||
−0.467554 | + | 0.883964i | \(0.654865\pi\) | |||||||
\(464\) | 314245. | 0.0677599 | ||||||||
\(465\) | 5.23943e6 | 1.12370 | ||||||||
\(466\) | −2.98469e6 | −0.636700 | ||||||||
\(467\) | −5.98923e6 | −1.27081 | −0.635403 | − | 0.772181i | \(-0.719166\pi\) | ||||
−0.635403 | + | 0.772181i | \(0.719166\pi\) | |||||||
\(468\) | 1.04390e6 | 0.220315 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.54189e6 | 1.99246 | ||||||||
\(471\) | −2.15826e6 | −0.448282 | ||||||||
\(472\) | −1.17608e6 | −0.242987 | ||||||||
\(473\) | −2.81221e6 | −0.577956 | ||||||||
\(474\) | 1.74830e6 | 0.357414 | ||||||||
\(475\) | −2.08921e6 | −0.424862 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.43069e6 | 0.287905 | ||||||||
\(478\) | −1.28415e6 | −0.257066 | ||||||||
\(479\) | 3.54652e6 | 0.706258 | 0.353129 | − | 0.935575i | \(-0.385118\pi\) | ||||
0.353129 | + | 0.935575i | \(0.385118\pi\) | |||||||
\(480\) | −953833. | −0.188960 | ||||||||
\(481\) | −7.31252e6 | −1.44113 | ||||||||
\(482\) | −4.97015e6 | −0.974432 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.65375e6 | −0.320890 | ||||||||
\(485\) | 1.03126e7 | 1.99074 | ||||||||
\(486\) | −236196. | −0.0453609 | ||||||||
\(487\) | −8.78320e6 | −1.67815 | −0.839074 | − | 0.544017i | \(-0.816903\pi\) | ||||
−0.839074 | + | 0.544017i | \(0.816903\pi\) | |||||||
\(488\) | −724742. | −0.137763 | ||||||||
\(489\) | −3.93115e6 | −0.743443 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −586608. | −0.109811 | −0.0549053 | − | 0.998492i | \(-0.517486\pi\) | ||||
−0.0549053 | + | 0.998492i | \(0.517486\pi\) | |||||||
\(492\) | −2.62187e6 | −0.488313 | ||||||||
\(493\) | −1.58751e6 | −0.294170 | ||||||||
\(494\) | 887239. | 0.163577 | ||||||||
\(495\) | 2.01359e6 | 0.369367 | ||||||||
\(496\) | 1.43997e6 | 0.262814 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.07380e6 | −0.736082 | ||||||||
\(499\) | −9.59772e6 | −1.72551 | −0.862753 | − | 0.505626i | \(-0.831262\pi\) | ||||
−0.862753 | + | 0.505626i | \(0.831262\pi\) | |||||||
\(500\) | 7.38844e6 | 1.32168 | ||||||||
\(501\) | 349620. | 0.0622304 | ||||||||
\(502\) | −2.76094e6 | −0.488987 | ||||||||
\(503\) | −7.21481e6 | −1.27147 | −0.635733 | − | 0.771909i | \(-0.719302\pi\) | ||||
−0.635733 | + | 0.771909i | \(0.719302\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.70978e7 | 2.98340 | ||||||||
\(506\) | −3.64761e6 | −0.633333 | ||||||||
\(507\) | 2.49751e6 | 0.431506 | ||||||||
\(508\) | −1.47964e6 | −0.254387 | ||||||||
\(509\) | 4.38419e6 | 0.750058 | 0.375029 | − | 0.927013i | \(-0.377633\pi\) | ||||
0.375029 | + | 0.927013i | \(0.377633\pi\) | |||||||
\(510\) | 4.81859e6 | 0.820342 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | −200750. | −0.0336792 | ||||||||
\(514\) | −55146.8 | −0.00920688 | ||||||||
\(515\) | −1.10998e7 | −1.84416 | ||||||||
\(516\) | −1.68598e6 | −0.278759 | ||||||||
\(517\) | −5.53606e6 | −0.910909 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.56650e6 | 0.581197 | ||||||||
\(520\) | −5.33535e6 | −0.865276 | ||||||||
\(521\) | 2.06581e6 | 0.333424 | 0.166712 | − | 0.986006i | \(-0.446685\pi\) | ||||
0.166712 | + | 0.986006i | \(0.446685\pi\) | |||||||
\(522\) | −397716. | −0.0638847 | ||||||||
\(523\) | 7.96570e6 | 1.27341 | 0.636707 | − | 0.771106i | \(-0.280296\pi\) | ||||
0.636707 | + | 0.771106i | \(0.280296\pi\) | |||||||
\(524\) | −1.15725e6 | −0.184120 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.29933e6 | −0.362358 | ||||||||
\(527\) | −7.27445e6 | −1.14097 | ||||||||
\(528\) | 553400. | 0.0863882 | ||||||||
\(529\) | 7.97762e6 | 1.23946 | ||||||||
\(530\) | −7.31222e6 | −1.13073 | ||||||||
\(531\) | 1.48848e6 | 0.229090 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.46657e7 | −2.23606 | ||||||||
\(534\) | −3.90117e6 | −0.592028 | ||||||||
\(535\) | −1.00830e7 | −1.52301 | ||||||||
\(536\) | −2.30908e6 | −0.347158 | ||||||||
\(537\) | 2.19495e6 | 0.328465 | ||||||||
\(538\) | 4.47571e6 | 0.666663 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.20719e6 | 0.178153 | ||||||||
\(541\) | 8.23423e6 | 1.20957 | 0.604784 | − | 0.796390i | \(-0.293260\pi\) | ||||
0.604784 | + | 0.796390i | \(0.293260\pi\) | |||||||
\(542\) | −2.77948e6 | −0.406411 | ||||||||
\(543\) | −2.69346e6 | −0.392022 | ||||||||
\(544\) | 1.32430e6 | 0.191863 | ||||||||
\(545\) | 6.13815e6 | 0.885209 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.20365e6 | 0.743601 | 0.371800 | − | 0.928313i | \(-0.378741\pi\) | ||||
0.371800 | + | 0.928313i | \(0.378741\pi\) | |||||||
\(548\) | 3.61059e6 | 0.513602 | ||||||||
\(549\) | 917251. | 0.129885 | ||||||||
\(550\) | −7.28905e6 | −1.02746 | ||||||||
\(551\) | −338030. | −0.0474325 | ||||||||
\(552\) | −2.18683e6 | −0.305469 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.35061e6 | 0.463821 | ||||||||
\(555\) | −8.45641e6 | −1.16534 | ||||||||
\(556\) | −5.24754e6 | −0.719894 | ||||||||
\(557\) | −4.09165e6 | −0.558806 | −0.279403 | − | 0.960174i | \(-0.590136\pi\) | ||||
−0.279403 | + | 0.960174i | \(0.590136\pi\) | |||||||
\(558\) | −1.82246e6 | −0.247783 | ||||||||
\(559\) | −9.43070e6 | −1.27648 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.79568e6 | −0.375042 | ||||||||
\(562\) | 3.67075e6 | 0.490246 | ||||||||
\(563\) | −3.59052e6 | −0.477404 | −0.238702 | − | 0.971093i | \(-0.576722\pi\) | ||||
−0.238702 | + | 0.971093i | \(0.576722\pi\) | |||||||
\(564\) | −3.31900e6 | −0.439349 | ||||||||
\(565\) | 1.62768e7 | 2.14510 | ||||||||
\(566\) | 1.66105e6 | 0.217943 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.05979e6 | 0.527999 | ||||||||
\(569\) | 9.79717e6 | 1.26859 | 0.634293 | − | 0.773093i | \(-0.281291\pi\) | ||||
0.634293 | + | 0.773093i | \(0.281291\pi\) | |||||||
\(570\) | 1.02603e6 | 0.132273 | ||||||||
\(571\) | −2.21804e6 | −0.284694 | −0.142347 | − | 0.989817i | \(-0.545465\pi\) | ||||
−0.142347 | + | 0.989817i | \(0.545465\pi\) | |||||||
\(572\) | 3.09549e6 | 0.395585 | ||||||||
\(573\) | −6.99297e6 | −0.889764 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.88036e7 | 3.63309 | ||||||||
\(576\) | 331776. | 0.0416667 | ||||||||
\(577\) | −2.65534e6 | −0.332032 | −0.166016 | − | 0.986123i | \(-0.553090\pi\) | ||||
−0.166016 | + | 0.986123i | \(0.553090\pi\) | |||||||
\(578\) | −1.01072e6 | −0.125838 | ||||||||
\(579\) | 2.48779e6 | 0.308402 | ||||||||
\(580\) | 2.03272e6 | 0.250904 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −3.58708e6 | −0.438969 | ||||||||
\(583\) | 4.24244e6 | 0.516945 | ||||||||
\(584\) | 3.39087e6 | 0.411414 | ||||||||
\(585\) | 6.75255e6 | 0.815790 | ||||||||
\(586\) | 4.85964e6 | 0.584602 | ||||||||
\(587\) | −2.62690e6 | −0.314665 | −0.157332 | − | 0.987546i | \(-0.550289\pi\) | ||||
−0.157332 | + | 0.987546i | \(0.550289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.54896e6 | −0.183972 | ||||||||
\(590\) | −7.60760e6 | −0.899742 | ||||||||
\(591\) | −1.18454e6 | −0.139502 | ||||||||
\(592\) | −2.32409e6 | −0.272552 | ||||||||
\(593\) | −1.15062e7 | −1.34368 | −0.671839 | − | 0.740697i | \(-0.734495\pi\) | ||||
−0.671839 | + | 0.740697i | \(0.734495\pi\) | |||||||
\(594\) | −700397. | −0.0814475 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.62417e6 | 0.302606 | ||||||||
\(597\) | 5.08464e6 | 0.583881 | ||||||||
\(598\) | −1.22322e7 | −1.39879 | ||||||||
\(599\) | 6.46264e6 | 0.735941 | 0.367970 | − | 0.929838i | \(-0.380053\pi\) | ||||
0.367970 | + | 0.929838i | \(0.380053\pi\) | |||||||
\(600\) | −4.36995e6 | −0.495563 | ||||||||
\(601\) | 8.55332e6 | 0.965937 | 0.482968 | − | 0.875638i | \(-0.339559\pi\) | ||||
0.482968 | + | 0.875638i | \(0.339559\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.92243e6 | 0.327303 | ||||||||
\(604\) | 996941. | 0.111193 | ||||||||
\(605\) | −1.06974e7 | −1.18820 | ||||||||
\(606\) | −5.94719e6 | −0.657856 | ||||||||
\(607\) | 2.99042e6 | 0.329428 | 0.164714 | − | 0.986341i | \(-0.447330\pi\) | ||||
0.164714 | + | 0.986341i | \(0.447330\pi\) | |||||||
\(608\) | 281986. | 0.0309363 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.68806e6 | −0.510115 | ||||||||
\(611\) | −1.85651e7 | −2.01185 | ||||||||
\(612\) | −1.67607e6 | −0.180890 | ||||||||
\(613\) | −1.77145e6 | −0.190405 | −0.0952023 | − | 0.995458i | \(-0.530350\pi\) | ||||
−0.0952023 | + | 0.995458i | \(0.530350\pi\) | |||||||
\(614\) | 1.04048e7 | 1.11381 | ||||||||
\(615\) | −1.69598e7 | −1.80814 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.40871e7 | 1.48974 | 0.744869 | − | 0.667210i | \(-0.232512\pi\) | ||||
0.744869 | + | 0.667210i | \(0.232512\pi\) | |||||||
\(618\) | 3.86090e6 | 0.406647 | ||||||||
\(619\) | −1.13430e7 | −1.18988 | −0.594940 | − | 0.803770i | \(-0.702824\pi\) | ||||
−0.594940 | + | 0.803770i | \(0.702824\pi\) | |||||||
\(620\) | 9.31455e6 | 0.973156 | ||||||||
\(621\) | 2.76770e6 | 0.287999 | ||||||||
\(622\) | 3.27666e6 | 0.339590 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.85582e6 | 0.190798 | ||||||||
\(625\) | 2.40843e7 | 2.46623 | ||||||||
\(626\) | 3.52776e6 | 0.359801 | ||||||||
\(627\) | −595287. | −0.0604724 | ||||||||
\(628\) | −3.83690e6 | −0.388224 | ||||||||
\(629\) | 1.17409e7 | 1.18325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.32628e6 | −0.232588 | −0.116294 | − | 0.993215i | \(-0.537102\pi\) | ||||
−0.116294 | + | 0.993215i | \(0.537102\pi\) | |||||||
\(632\) | 3.10810e6 | 0.309529 | ||||||||
\(633\) | 2.82273e6 | 0.280002 | ||||||||
\(634\) | 6.41753e6 | 0.634081 | ||||||||
\(635\) | −9.57116e6 | −0.941956 | ||||||||
\(636\) | 2.54344e6 | 0.249333 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.17935e6 | −0.114708 | ||||||||
\(639\) | −5.13817e6 | −0.497802 | ||||||||
\(640\) | −1.69570e6 | −0.163644 | ||||||||
\(641\) | −2.56385e6 | −0.246461 | −0.123230 | − | 0.992378i | \(-0.539325\pi\) | ||||
−0.123230 | + | 0.992378i | \(0.539325\pi\) | |||||||
\(642\) | 3.50720e6 | 0.335833 | ||||||||
\(643\) | −5.95343e6 | −0.567858 | −0.283929 | − | 0.958845i | \(-0.591638\pi\) | ||||
−0.283929 | + | 0.958845i | \(0.591638\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.09059e7 | −1.03220 | ||||||||
\(646\) | −1.42454e6 | −0.134306 | ||||||||
\(647\) | −1.53522e6 | −0.144182 | −0.0720909 | − | 0.997398i | \(-0.522967\pi\) | ||||
−0.0720909 | + | 0.997398i | \(0.522967\pi\) | |||||||
\(648\) | −419904. | −0.0392837 | ||||||||
\(649\) | 4.41382e6 | 0.411342 | ||||||||
\(650\) | −2.44437e7 | −2.26926 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.98871e6 | −0.643841 | ||||||||
\(653\) | −1.99582e7 | −1.83163 | −0.915815 | − | 0.401600i | \(-0.868454\pi\) | ||||
−0.915815 | + | 0.401600i | \(0.868454\pi\) | |||||||
\(654\) | −2.13506e6 | −0.195194 | ||||||||
\(655\) | −7.48581e6 | −0.681766 | ||||||||
\(656\) | −4.66110e6 | −0.422891 | ||||||||
\(657\) | −4.29157e6 | −0.387885 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.05477e7 | −0.946119 | −0.473060 | − | 0.881030i | \(-0.656850\pi\) | ||||
−0.473060 | + | 0.881030i | \(0.656850\pi\) | |||||||
\(660\) | 3.57972e6 | 0.319881 | ||||||||
\(661\) | −1.22044e7 | −1.08646 | −0.543229 | − | 0.839585i | \(-0.682798\pi\) | ||||
−0.543229 | + | 0.839585i | \(0.682798\pi\) | |||||||
\(662\) | −4.01232e6 | −0.355837 | ||||||||
\(663\) | −9.37527e6 | −0.828323 | ||||||||
\(664\) | −7.24231e6 | −0.637466 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.94143e6 | 0.256964 | ||||||||
\(667\) | 4.66036e6 | 0.405607 | ||||||||
\(668\) | 621548. | 0.0538931 | ||||||||
\(669\) | −2.51535e6 | −0.217287 | ||||||||
\(670\) | −1.49365e7 | −1.28547 | ||||||||
\(671\) | 2.71994e6 | 0.233213 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.97959e6 | −0.679114 | −0.339557 | − | 0.940585i | \(-0.610277\pi\) | ||||
−0.339557 | + | 0.940585i | \(0.610277\pi\) | |||||||
\(674\) | 1.04927e7 | 0.889686 | ||||||||
\(675\) | 5.53072e6 | 0.467221 | ||||||||
\(676\) | 4.44001e6 | 0.373695 | ||||||||
\(677\) | 5.08381e6 | 0.426302 | 0.213151 | − | 0.977019i | \(-0.431627\pi\) | ||||
0.213151 | + | 0.977019i | \(0.431627\pi\) | |||||||
\(678\) | −5.66164e6 | −0.473007 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.56639e6 | 0.710437 | ||||||||
\(681\) | −1.10116e7 | −0.909874 | ||||||||
\(682\) | −5.40416e6 | −0.444905 | ||||||||
\(683\) | −1.60331e7 | −1.31512 | −0.657559 | − | 0.753403i | \(-0.728411\pi\) | ||||
−0.657559 | + | 0.753403i | \(0.728411\pi\) | |||||||
\(684\) | −356888. | −0.0291670 | ||||||||
\(685\) | 2.33554e7 | 1.90179 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.29297e6 | 0.185356 | ||||||||
\(688\) | −2.99730e6 | −0.241412 | ||||||||
\(689\) | 1.42270e7 | 1.14173 | ||||||||
\(690\) | −1.41457e7 | −1.13110 | ||||||||
\(691\) | −1.10131e7 | −0.877438 | −0.438719 | − | 0.898624i | \(-0.644568\pi\) | ||||
−0.438719 | + | 0.898624i | \(0.644568\pi\) | |||||||
\(692\) | 6.34044e6 | 0.503331 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −904935. | −0.0713212 | ||||||||
\(695\) | −3.39442e7 | −2.66565 | ||||||||
\(696\) | −707050. | −0.0553258 | ||||||||
\(697\) | 2.35470e7 | 1.83592 | ||||||||
\(698\) | 5.85119e6 | 0.454575 | ||||||||
\(699\) | 6.71555e6 | 0.519863 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.10660e6 | −0.238776 | −0.119388 | − | 0.992848i | \(-0.538093\pi\) | ||||
−0.119388 | + | 0.992848i | \(0.538093\pi\) | |||||||
\(702\) | −2.34877e6 | −0.179886 | ||||||||
\(703\) | 2.50001e6 | 0.190789 | ||||||||
\(704\) | 983822. | 0.0748143 | ||||||||
\(705\) | −2.14692e7 | −1.62684 | ||||||||
\(706\) | −1.12383e7 | −0.848571 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.64619e6 | 0.198398 | ||||||||
\(709\) | −1.38036e7 | −1.03128 | −0.515640 | − | 0.856805i | \(-0.672446\pi\) | ||||
−0.515640 | + | 0.856805i | \(0.672446\pi\) | |||||||
\(710\) | 2.62611e7 | 1.95509 | ||||||||
\(711\) | −3.93369e6 | −0.291827 | ||||||||
\(712\) | −6.93542e6 | −0.512711 | ||||||||
\(713\) | 2.13552e7 | 1.57319 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00235e7 | 1.46479 | ||||||||
\(716\) | 3.90214e6 | 0.284459 | ||||||||
\(717\) | 2.88933e6 | 0.209893 | ||||||||
\(718\) | 1.47960e7 | 1.07111 | ||||||||
\(719\) | −1.29855e7 | −0.936777 | −0.468389 | − | 0.883523i | \(-0.655165\pi\) | ||||
−0.468389 | + | 0.883523i | \(0.655165\pi\) | |||||||
\(720\) | 2.14612e6 | 0.154285 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 9.60107e6 | 0.685451 | ||||||||
\(723\) | 1.11828e7 | 0.795620 | ||||||||
\(724\) | −4.78837e6 | −0.339501 | ||||||||
\(725\) | 9.31285e6 | 0.658017 | ||||||||
\(726\) | 3.72094e6 | 0.262006 | ||||||||
\(727\) | −8.61224e6 | −0.604338 | −0.302169 | − | 0.953254i | \(-0.597711\pi\) | ||||
−0.302169 | + | 0.953254i | \(0.597711\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 2.19342e7 | 1.52340 | ||||||||
\(731\) | 1.51418e7 | 1.04806 | ||||||||
\(732\) | 1.63067e6 | 0.112483 | ||||||||
\(733\) | 6.02001e6 | 0.413844 | 0.206922 | − | 0.978357i | \(-0.433655\pi\) | ||||
0.206922 | + | 0.978357i | \(0.433655\pi\) | |||||||
\(734\) | −4.67698e6 | −0.320424 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.88769e6 | −0.264544 | ||||||||
\(737\) | 8.66593e6 | 0.587688 | ||||||||
\(738\) | 5.89920e6 | 0.398706 | ||||||||
\(739\) | −93692.5 | −0.00631094 | −0.00315547 | − | 0.999995i | \(-0.501004\pi\) | ||||
−0.00315547 | + | 0.999995i | \(0.501004\pi\) | |||||||
\(740\) | −1.50336e7 | −1.00922 | ||||||||
\(741\) | −1.99629e6 | −0.133560 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.29874e7 | −0.863081 | −0.431541 | − | 0.902094i | \(-0.642030\pi\) | ||||
−0.431541 | + | 0.902094i | \(0.642030\pi\) | |||||||
\(744\) | −3.23992e6 | −0.214586 | ||||||||
\(745\) | 1.69747e7 | 1.12050 | ||||||||
\(746\) | 1.83076e7 | 1.20444 | ||||||||
\(747\) | 9.16605e6 | 0.601008 | ||||||||
\(748\) | −4.97009e6 | −0.324796 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.66240e7 | −1.07915 | ||||||||
\(751\) | −637441. | −0.0412420 | −0.0206210 | − | 0.999787i | \(-0.506564\pi\) | ||||
−0.0206210 | + | 0.999787i | \(0.506564\pi\) | |||||||
\(752\) | −5.90044e6 | −0.380487 | ||||||||
\(753\) | 6.21211e6 | 0.399256 | ||||||||
\(754\) | −3.95495e6 | −0.253345 | ||||||||
\(755\) | 6.44880e6 | 0.411729 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.86768e6 | −0.308732 | −0.154366 | − | 0.988014i | \(-0.549334\pi\) | ||||
−0.154366 | + | 0.988014i | \(0.549334\pi\) | |||||||
\(758\) | 9.42081e6 | 0.595546 | ||||||||
\(759\) | 8.20712e6 | 0.517114 | ||||||||
\(760\) | 1.82405e6 | 0.114552 | ||||||||
\(761\) | 5.81787e6 | 0.364169 | 0.182084 | − | 0.983283i | \(-0.441716\pi\) | ||||
0.182084 | + | 0.983283i | \(0.441716\pi\) | |||||||
\(762\) | 3.32918e6 | 0.207706 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.24319e7 | −0.770558 | ||||||||
\(765\) | −1.08418e7 | −0.669806 | ||||||||
\(766\) | −1.21578e7 | −0.748659 | ||||||||
\(767\) | 1.48017e7 | 0.908496 | ||||||||
\(768\) | 589824. | 0.0360844 | ||||||||
\(769\) | 1.94310e7 | 1.18490 | 0.592448 | − | 0.805609i | \(-0.298161\pi\) | ||||
0.592448 | + | 0.805609i | \(0.298161\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 124080. | 0.00751738 | ||||||||
\(772\) | 4.42274e6 | 0.267084 | ||||||||
\(773\) | 8.24179e6 | 0.496104 | 0.248052 | − | 0.968747i | \(-0.420210\pi\) | ||||
0.248052 | + | 0.968747i | \(0.420210\pi\) | |||||||
\(774\) | 3.79346e6 | 0.227606 | ||||||||
\(775\) | 4.26743e7 | 2.55219 | ||||||||
\(776\) | −6.37704e6 | −0.380159 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.83709e6 | 0.108813 | ||||||||
\(779\) | 5.01390e6 | 0.296027 | ||||||||
\(780\) | 1.20045e7 | 0.706495 | ||||||||
\(781\) | −1.52363e7 | −0.893826 | ||||||||
\(782\) | 1.96399e7 | 1.14848 | ||||||||
\(783\) | 894861. | 0.0521616 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.48194e7 | −1.43753 | ||||||||
\(786\) | 2.60382e6 | 0.150333 | ||||||||
\(787\) | −1.47863e7 | −0.850986 | −0.425493 | − | 0.904962i | \(-0.639899\pi\) | ||||
−0.425493 | + | 0.904962i | \(0.639899\pi\) | |||||||
\(788\) | −2.10585e6 | −0.120812 | ||||||||
\(789\) | 5.17350e6 | 0.295864 | ||||||||
\(790\) | 2.01050e7 | 1.14614 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −1.24515e6 | −0.0705356 | ||||||||
\(793\) | 9.12129e6 | 0.515079 | ||||||||
\(794\) | −2.17000e7 | −1.22154 | ||||||||
\(795\) | 1.64525e7 | 0.923239 | ||||||||
\(796\) | 9.03937e6 | 0.505656 | ||||||||
\(797\) | −1.58158e7 | −0.881956 | −0.440978 | − | 0.897518i | \(-0.645368\pi\) | ||||
−0.440978 | + | 0.897518i | \(0.645368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.98080e7 | 1.65183 | ||||||||
\(800\) | −7.76881e6 | −0.429170 | ||||||||
\(801\) | 8.77764e6 | 0.483389 | ||||||||
\(802\) | −8.44508e6 | −0.463626 | ||||||||
\(803\) | −1.27259e7 | −0.696465 | ||||||||
\(804\) | 5.19543e6 | 0.283453 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.81228e7 | −0.982625 | ||||||||
\(807\) | −1.00704e7 | −0.544328 | ||||||||
\(808\) | −1.05728e7 | −0.569720 | ||||||||
\(809\) | 1.19304e7 | 0.640888 | 0.320444 | − | 0.947267i | \(-0.396168\pi\) | ||||
0.320444 | + | 0.947267i | \(0.396168\pi\) | |||||||
\(810\) | −2.71619e6 | −0.145461 | ||||||||
\(811\) | 1.89393e7 | 1.01114 | 0.505571 | − | 0.862785i | \(-0.331282\pi\) | ||||
0.505571 | + | 0.862785i | \(0.331282\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.25382e6 | 0.331833 | ||||||||
\(814\) | 8.72228e6 | 0.461391 | ||||||||
\(815\) | −4.52071e7 | −2.38404 | ||||||||
\(816\) | −2.97969e6 | −0.156655 | ||||||||
\(817\) | 3.22417e6 | 0.168991 | ||||||||
\(818\) | −1.02298e7 | −0.534544 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.01507e7 | −1.56590 | ||||||||
\(821\) | 3.20087e7 | 1.65733 | 0.828667 | − | 0.559741i | \(-0.189100\pi\) | ||||
0.828667 | + | 0.559741i | \(0.189100\pi\) | |||||||
\(822\) | −8.12383e6 | −0.419354 | ||||||||
\(823\) | 3.61430e7 | 1.86005 | 0.930025 | − | 0.367495i | \(-0.119785\pi\) | ||||
0.930025 | + | 0.367495i | \(0.119785\pi\) | |||||||
\(824\) | 6.86382e6 | 0.352166 | ||||||||
\(825\) | 1.64004e7 | 0.838916 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.45831e7 | −1.24989 | −0.624946 | − | 0.780668i | \(-0.714879\pi\) | ||||
−0.624946 | + | 0.780668i | \(0.714879\pi\) | |||||||
\(828\) | 4.92036e6 | 0.249414 | ||||||||
\(829\) | 2.10424e7 | 1.06343 | 0.531715 | − | 0.846923i | \(-0.321548\pi\) | ||||
0.531715 | + | 0.846923i | \(0.321548\pi\) | |||||||
\(830\) | −4.68475e7 | −2.36043 | ||||||||
\(831\) | −7.53888e6 | −0.378708 | ||||||||
\(832\) | 3.29923e6 | 0.165236 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.18070e7 | 0.587791 | ||||||||
\(835\) | 4.02054e6 | 0.199557 | ||||||||
\(836\) | −1.05829e6 | −0.0523707 | ||||||||
\(837\) | 4.10053e6 | 0.202314 | ||||||||
\(838\) | −8.69604e6 | −0.427771 | ||||||||
\(839\) | 1.12403e7 | 0.551283 | 0.275642 | − | 0.961260i | \(-0.411110\pi\) | ||||
0.275642 | + | 0.961260i | \(0.411110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.90043e7 | −0.926537 | ||||||||
\(842\) | 2.19172e7 | 1.06538 | ||||||||
\(843\) | −8.25918e6 | −0.400284 | ||||||||
\(844\) | 5.01820e6 | 0.242489 | ||||||||
\(845\) | 2.87206e7 | 1.38373 | ||||||||
\(846\) | 7.46775e6 | 0.358727 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.52168e6 | 0.215928 | ||||||||
\(849\) | −3.73737e6 | −0.177950 | ||||||||
\(850\) | 3.92466e7 | 1.86318 | ||||||||
\(851\) | −3.44672e7 | −1.63148 | ||||||||
\(852\) | −9.13453e6 | −0.431109 | ||||||||
\(853\) | −2.63779e7 | −1.24127 | −0.620636 | − | 0.784099i | \(-0.713126\pi\) | ||||
−0.620636 | + | 0.784099i | \(0.713126\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.30856e6 | −0.108001 | ||||||||
\(856\) | 6.23503e6 | 0.290840 | ||||||||
\(857\) | 4.26663e7 | 1.98442 | 0.992208 | − | 0.124595i | \(-0.0397632\pi\) | ||||
0.992208 | + | 0.124595i | \(0.0397632\pi\) | |||||||
\(858\) | −6.96486e6 | −0.322994 | ||||||||
\(859\) | 2.92617e7 | 1.35306 | 0.676530 | − | 0.736415i | \(-0.263483\pi\) | ||||
0.676530 | + | 0.736415i | \(0.263483\pi\) | |||||||
\(860\) | −1.93883e7 | −0.893911 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.46750e7 | 1.13107 | ||||||||
\(863\) | 1.39448e7 | 0.637359 | 0.318680 | − | 0.947862i | \(-0.396761\pi\) | ||||
0.318680 | + | 0.947862i | \(0.396761\pi\) | |||||||
\(864\) | −746496. | −0.0340207 | ||||||||
\(865\) | 4.10137e7 | 1.86375 | ||||||||
\(866\) | −1.95838e7 | −0.887366 | ||||||||
\(867\) | 2.27412e6 | 0.102746 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.16646e7 | −0.523988 | ||||||||
\(870\) | −4.57362e6 | −0.204862 | ||||||||
\(871\) | 2.90611e7 | 1.29798 | ||||||||
\(872\) | −3.79566e6 | −0.169043 | ||||||||
\(873\) | 8.07094e6 | 0.358417 | ||||||||
\(874\) | 4.18195e6 | 0.185183 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.62946e6 | −0.335918 | ||||||||
\(877\) | 3.40772e6 | 0.149611 | 0.0748057 | − | 0.997198i | \(-0.476166\pi\) | ||||
0.0748057 | + | 0.997198i | \(0.476166\pi\) | |||||||
\(878\) | 1.41835e7 | 0.620937 | ||||||||
\(879\) | −1.09342e7 | −0.477325 | ||||||||
\(880\) | 6.36394e6 | 0.277025 | ||||||||
\(881\) | −3.51391e6 | −0.152528 | −0.0762641 | − | 0.997088i | \(-0.524299\pi\) | ||||
−0.0762641 | + | 0.997088i | \(0.524299\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.14895e7 | 0.927524 | 0.463762 | − | 0.885960i | \(-0.346499\pi\) | ||||
0.463762 | + | 0.885960i | \(0.346499\pi\) | |||||||
\(884\) | −1.66671e7 | −0.717349 | ||||||||
\(885\) | 1.71171e7 | 0.734636 | ||||||||
\(886\) | −2.42261e7 | −1.03681 | ||||||||
\(887\) | 2.45357e7 | 1.04710 | 0.523550 | − | 0.851995i | \(-0.324607\pi\) | ||||
0.523550 | + | 0.851995i | \(0.324607\pi\) | |||||||
\(888\) | 5.22921e6 | 0.222538 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −4.48624e7 | −1.89849 | ||||||||
\(891\) | 1.57589e6 | 0.0665016 | ||||||||
\(892\) | −4.47173e6 | −0.188176 | ||||||||
\(893\) | 6.34705e6 | 0.266344 | ||||||||
\(894\) | −5.90439e6 | −0.247076 | ||||||||
\(895\) | 2.52413e7 | 1.05331 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.75225e7 | 1.14211 | ||||||||
\(898\) | 4.83203e6 | 0.199958 | ||||||||
\(899\) | 6.90462e6 | 0.284932 | ||||||||
\(900\) | 9.83240e6 | 0.404625 | ||||||||
\(901\) | −2.28427e7 | −0.937423 | ||||||||
\(902\) | 1.74930e7 | 0.715894 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.00651e7 | −0.409636 | ||||||||
\(905\) | −3.09740e7 | −1.25712 | ||||||||
\(906\) | −2.24312e6 | −0.0907886 | ||||||||
\(907\) | −8.14146e6 | −0.328613 | −0.164306 | − | 0.986409i | \(-0.552539\pi\) | ||||
−0.164306 | + | 0.986409i | \(0.552539\pi\) | |||||||
\(908\) | −1.95761e7 | −0.787974 | ||||||||
\(909\) | 1.33812e7 | 0.537137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.01384e7 | 0.404739 | 0.202370 | − | 0.979309i | \(-0.435136\pi\) | ||||
0.202370 | + | 0.979309i | \(0.435136\pi\) | |||||||
\(912\) | −634468. | −0.0252594 | ||||||||
\(913\) | 2.71803e7 | 1.07914 | ||||||||
\(914\) | 2.18620e7 | 0.865615 | ||||||||
\(915\) | 1.05481e7 | 0.416507 | ||||||||
\(916\) | 4.07639e6 | 0.160523 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.77116e6 | 0.147696 | ||||||||
\(919\) | −1.01176e7 | −0.395175 | −0.197587 | − | 0.980285i | \(-0.563311\pi\) | ||||
−0.197587 | + | 0.980285i | \(0.563311\pi\) | |||||||
\(920\) | −2.51479e7 | −0.979562 | ||||||||
\(921\) | −2.34108e7 | −0.909424 | ||||||||
\(922\) | −4.63824e6 | −0.179691 | ||||||||
\(923\) | −5.10948e7 | −1.97412 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.88760e7 | −2.64676 | ||||||||
\(926\) | 1.72534e7 | 0.661221 | ||||||||
\(927\) | −8.68702e6 | −0.332026 | ||||||||
\(928\) | −1.25698e6 | −0.0479135 | ||||||||
\(929\) | 2.05111e7 | 0.779739 | 0.389870 | − | 0.920870i | \(-0.372520\pi\) | ||||
0.389870 | + | 0.920870i | \(0.372520\pi\) | |||||||
\(930\) | −2.09577e7 | −0.794579 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.19388e7 | 0.450215 | ||||||||
\(933\) | −7.37248e6 | −0.277274 | ||||||||
\(934\) | 2.39569e7 | 0.898595 | ||||||||
\(935\) | −3.21495e7 | −1.20267 | ||||||||
\(936\) | −4.17559e6 | −0.155786 | ||||||||
\(937\) | −1.46527e7 | −0.545218 | −0.272609 | − | 0.962125i | \(-0.587886\pi\) | ||||
−0.272609 | + | 0.962125i | \(0.587886\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.93745e6 | −0.293777 | ||||||||
\(940\) | −3.81676e7 | −1.40888 | ||||||||
\(941\) | 2.59341e7 | 0.954765 | 0.477382 | − | 0.878696i | \(-0.341586\pi\) | ||||
0.477382 | + | 0.878696i | \(0.341586\pi\) | |||||||
\(942\) | 8.63303e6 | 0.316983 | ||||||||
\(943\) | −6.91258e7 | −2.53140 | ||||||||
\(944\) | 4.70433e6 | 0.171818 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.12488e7 | 0.408676 | ||||||||
\(947\) | 1.04490e7 | 0.378615 | 0.189307 | − | 0.981918i | \(-0.439376\pi\) | ||||
0.189307 | + | 0.981918i | \(0.439376\pi\) | |||||||
\(948\) | −6.99322e6 | −0.252730 | ||||||||
\(949\) | −4.26761e7 | −1.53822 | ||||||||
\(950\) | 8.35683e6 | 0.300423 | ||||||||
\(951\) | −1.44394e7 | −0.517725 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.15666e6 | 0.0412548 | 0.0206274 | − | 0.999787i | \(-0.493434\pi\) | ||||
0.0206274 | + | 0.999787i | \(0.493434\pi\) | |||||||
\(954\) | −5.72275e6 | −0.203579 | ||||||||
\(955\) | −8.04172e7 | −2.85325 | ||||||||
\(956\) | 5.13658e6 | 0.181773 | ||||||||
\(957\) | 2.65355e6 | 0.0936585 | ||||||||
\(958\) | −1.41861e7 | −0.499400 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.81533e6 | 0.133615 | ||||||||
\(961\) | 3.00994e6 | 0.105135 | ||||||||
\(962\) | 2.92501e7 | 1.01904 | ||||||||
\(963\) | −7.89121e6 | −0.274207 | ||||||||
\(964\) | 1.98806e7 | 0.689027 | ||||||||
\(965\) | 2.86089e7 | 0.988969 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00516e7 | 0.689577 | 0.344789 | − | 0.938680i | \(-0.387951\pi\) | ||||
0.344789 | + | 0.938680i | \(0.387951\pi\) | |||||||
\(968\) | 6.61500e6 | 0.226904 | ||||||||
\(969\) | 3.20522e6 | 0.109660 | ||||||||
\(970\) | −4.12505e7 | −1.40767 | ||||||||
\(971\) | 6.10209e6 | 0.207697 | 0.103849 | − | 0.994593i | \(-0.466884\pi\) | ||||
0.103849 | + | 0.994593i | \(0.466884\pi\) | |||||||
\(972\) | 944784. | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 3.51328e7 | 1.18663 | ||||||||
\(975\) | 5.49984e7 | 1.85284 | ||||||||
\(976\) | 2.89897e6 | 0.0974134 | ||||||||
\(977\) | 1.36743e7 | 0.458320 | 0.229160 | − | 0.973389i | \(-0.426402\pi\) | ||||
0.229160 | + | 0.973389i | \(0.426402\pi\) | |||||||
\(978\) | 1.57246e7 | 0.525694 | ||||||||
\(979\) | 2.60285e7 | 0.867945 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.80388e6 | 0.159375 | ||||||||
\(982\) | 2.34643e6 | 0.0776478 | ||||||||
\(983\) | −1.67033e7 | −0.551338 | −0.275669 | − | 0.961253i | \(-0.588899\pi\) | ||||
−0.275669 | + | 0.961253i | \(0.588899\pi\) | |||||||
\(984\) | 1.04875e7 | 0.345289 | ||||||||
\(985\) | −1.36219e7 | −0.447348 | ||||||||
\(986\) | 6.35003e6 | 0.208010 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.54896e6 | −0.115667 | ||||||||
\(989\) | −4.44511e7 | −1.44508 | ||||||||
\(990\) | −8.05437e6 | −0.261182 | ||||||||
\(991\) | 5.74906e7 | 1.85957 | 0.929785 | − | 0.368102i | \(-0.119992\pi\) | ||||
0.929785 | + | 0.368102i | \(0.119992\pi\) | |||||||
\(992\) | −5.75986e6 | −0.185837 | ||||||||
\(993\) | 9.02772e6 | 0.290539 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.84720e7 | 1.87236 | ||||||||
\(996\) | 1.62952e7 | 0.520489 | ||||||||
\(997\) | 3.94489e7 | 1.25689 | 0.628444 | − | 0.777855i | \(-0.283692\pi\) | ||||
0.628444 | + | 0.777855i | \(0.283692\pi\) | |||||||
\(998\) | 3.83909e7 | 1.22012 | ||||||||
\(999\) | −6.61822e6 | −0.209811 |
(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 | 294.6.a.q.1.2 | yes | 2 | |
3.2 | odd | 2 | 882.6.a.bk.1.1 | 2 | |||
7.2 | even | 3 | 294.6.e.x.67.1 | 4 | |||
7.3 | odd | 6 | 294.6.e.z.79.2 | 4 | |||
7.4 | even | 3 | 294.6.e.x.79.1 | 4 | |||
7.5 | odd | 6 | 294.6.e.z.67.2 | 4 | |||
7.6 | odd | 2 | 294.6.a.n.1.1 | ✓ | 2 | ||
21.20 | even | 2 | 882.6.a.bu.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.6.a.n.1.1 | ✓ | 2 | 7.6 | odd | 2 | ||
294.6.a.q.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
294.6.e.x.67.1 | 4 | 7.2 | even | 3 | |||
294.6.e.x.79.1 | 4 | 7.4 | even | 3 | |||
294.6.e.z.67.2 | 4 | 7.5 | odd | 6 | |||
294.6.e.z.79.2 | 4 | 7.3 | odd | 6 | |||
882.6.a.bk.1.1 | 2 | 3.2 | odd | 2 | |||
882.6.a.bu.1.2 | 2 | 21.20 | even | 2 |