Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,6,Mod(1,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.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: | \(30.7936934041\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{31}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 96) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.56776\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −107.084 | −1.91558 | −0.957790 | − | 0.287467i | \(-0.907187\pi\) | ||||
−0.957790 | + | 0.287467i | \(0.907187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −149.084 | −1.14997 | −0.574985 | − | 0.818164i | \(-0.694992\pi\) | ||||
−0.574985 | + | 0.818164i | \(0.694992\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −434.505 | −1.08271 | −0.541357 | − | 0.840793i | \(-0.682089\pi\) | ||||
−0.541357 | + | 0.840793i | \(0.682089\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 392.505 | 0.644150 | 0.322075 | − | 0.946714i | \(-0.395620\pi\) | ||||
0.322075 | + | 0.946714i | \(0.395620\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −963.758 | −1.10596 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 803.495 | 0.674312 | 0.337156 | − | 0.941449i | \(-0.390535\pi\) | ||||
0.337156 | + | 0.941449i | \(0.390535\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 854.842 | 0.543253 | 0.271626 | − | 0.962403i | \(-0.412438\pi\) | ||||
0.271626 | + | 0.962403i | \(0.412438\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1341.76 | −0.663936 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4592.53 | 1.81022 | 0.905112 | − | 0.425174i | \(-0.139787\pi\) | ||||
0.905112 | + | 0.425174i | \(0.139787\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8342.03 | 2.66945 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6798.60 | −1.50115 | −0.750576 | − | 0.660784i | \(-0.770224\pi\) | ||||
−0.750576 | + | 0.660784i | \(0.770224\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4798.58 | 0.896826 | 0.448413 | − | 0.893826i | \(-0.351989\pi\) | ||||
0.448413 | + | 0.893826i | \(0.351989\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3910.55 | −0.625105 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 15964.6 | 2.20286 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 909.075 | 0.109168 | 0.0545840 | − | 0.998509i | \(-0.482617\pi\) | ||||
0.0545840 | + | 0.998509i | \(0.482617\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3532.55 | 0.371900 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2372.21 | −0.220391 | −0.110195 | − | 0.993910i | \(-0.535148\pi\) | ||||
−0.110195 | + | 0.993910i | \(0.535148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8664.95 | −0.714652 | −0.357326 | − | 0.933980i | \(-0.616312\pi\) | ||||
−0.357326 | + | 0.933980i | \(0.616312\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8673.82 | −0.638527 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −16878.7 | −1.11454 | −0.557268 | − | 0.830333i | \(-0.688150\pi\) | ||||
−0.557268 | + | 0.830333i | \(0.688150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5419.11 | 0.322432 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7231.45 | 0.389314 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10831.0 | −0.529637 | −0.264818 | − | 0.964298i | \(-0.585312\pi\) | ||||
−0.264818 | + | 0.964298i | \(0.585312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 46528.7 | 2.07402 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7693.58 | 0.313647 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8305.81 | 0.310636 | 0.155318 | − | 0.987865i | \(-0.450360\pi\) | ||||
0.155318 | + | 0.987865i | \(0.450360\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35998.0 | 1.23867 | 0.619333 | − | 0.785128i | \(-0.287403\pi\) | ||||
0.619333 | + | 0.785128i | \(0.287403\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12075.8 | −0.383323 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −42031.1 | −1.23392 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 25077.1 | 0.682481 | 0.341240 | − | 0.939976i | \(-0.389153\pi\) | ||||
0.341240 | + | 0.939976i | \(0.389153\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 41332.7 | 1.04513 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 57850.9 | 1.36196 | 0.680980 | − | 0.732302i | \(-0.261554\pi\) | ||||
0.680980 | + | 0.732302i | \(0.261554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −68092.5 | −1.49552 | −0.747760 | − | 0.663969i | \(-0.768871\pi\) | ||||
−0.747760 | + | 0.663969i | \(0.768871\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75078.3 | 1.54121 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 64777.9 | 1.24509 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 98723.8 | 1.77973 | 0.889865 | − | 0.456223i | \(-0.150798\pi\) | ||||
0.889865 | + | 0.456223i | \(0.150798\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 34859.3 | 0.555422 | 0.277711 | − | 0.960665i | \(-0.410424\pi\) | ||||
0.277711 | + | 0.960665i | \(0.410424\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −86041.6 | −1.29170 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −61187.4 | −0.866690 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 34678.2 | 0.464068 | 0.232034 | − | 0.972708i | \(-0.425462\pi\) | ||||
0.232034 | + | 0.972708i | \(0.425462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −58516.4 | −0.740754 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 43187.2 | 0.517783 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −91540.1 | −1.04064 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 39891.1 | 0.430473 | 0.215237 | − | 0.976562i | \(-0.430948\pi\) | ||||
0.215237 | + | 0.976562i | \(0.430948\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −35194.9 | −0.360904 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −35341.5 | −0.344732 | −0.172366 | − | 0.985033i | \(-0.555141\pi\) | ||||
−0.172366 | + | 0.985033i | \(0.555141\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −37097.4 | −0.344549 | −0.172274 | − | 0.985049i | \(-0.555112\pi\) | ||||
−0.172274 | + | 0.985049i | \(0.555112\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 143681. | 1.27182 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 153566. | 1.29669 | 0.648345 | − | 0.761347i | \(-0.275462\pi\) | ||||
0.648345 | + | 0.761347i | \(0.275462\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 106749. | 0.860590 | 0.430295 | − | 0.902688i | \(-0.358410\pi\) | ||||
0.430295 | + | 0.902688i | \(0.358410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8181.68 | 0.0630282 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −102232. | −0.753168 | −0.376584 | − | 0.926383i | \(-0.622901\pi\) | ||||
−0.376584 | + | 0.926383i | \(0.622901\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −491787. | −3.46763 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 31792.9 | 0.214717 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −119788. | −0.775438 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27743.9 | 0.172268 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −21349.9 | −0.127243 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −558662. | −3.19797 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 47290.4 | 0.260174 | 0.130087 | − | 0.991503i | \(-0.458474\pi\) | ||||
0.130087 | + | 0.991503i | \(0.458474\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −77984.5 | −0.412605 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −82047.2 | −0.417720 | −0.208860 | − | 0.977946i | \(-0.566975\pi\) | ||||
−0.208860 | + | 0.977946i | \(0.566975\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −127444. | −0.624725 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −78064.4 | −0.368654 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −68984.2 | −0.314013 | −0.157007 | − | 0.987598i | \(-0.550184\pi\) | ||||
−0.157007 | + | 0.987598i | \(0.550184\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 437887. | 1.92232 | 0.961158 | − | 0.275998i | \(-0.0890084\pi\) | ||||
0.961158 | + | 0.275998i | \(0.0890084\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −151908. | −0.643477 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −170546. | −0.697430 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 728023. | 2.87558 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 48772.0 | 0.186156 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 27672.3 | 0.102113 | 0.0510564 | − | 0.998696i | \(-0.483741\pi\) | ||||
0.0510564 | + | 0.998696i | \(0.483741\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 84706.4 | 0.302325 | 0.151162 | − | 0.988509i | \(-0.451698\pi\) | ||||
0.151162 | + | 0.988509i | \(0.451698\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 65083.1 | 0.224771 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −513852. | −1.71794 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 565956. | 1.83246 | 0.916229 | − | 0.400656i | \(-0.131218\pi\) | ||||
0.916229 | + | 0.400656i | \(0.131218\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −97478.8 | −0.305786 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −684673. | −2.08170 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 26326.8 | 0.0776121 | 0.0388060 | − | 0.999247i | \(-0.487645\pi\) | ||||
0.0388060 | + | 0.999247i | \(0.487645\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 418758. | 1.19744 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 268359. | 0.744603 | 0.372301 | − | 0.928112i | \(-0.378569\pi\) | ||||
0.372301 | + | 0.928112i | \(0.378569\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −217233. | −0.585070 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 69242.2 | 0.181084 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −103090. | −0.261879 | −0.130939 | − | 0.991390i | \(-0.541799\pi\) | ||||
−0.130939 | + | 0.991390i | \(0.541799\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.24367e6 | −3.06979 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 74752.3 | 0.179346 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −671994. | −1.56759 | −0.783796 | − | 0.621019i | \(-0.786719\pi\) | ||||
−0.783796 | + | 0.621019i | \(0.786719\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 445972. | 1.01184 | 0.505919 | − | 0.862581i | \(-0.331154\pi\) | ||||
0.505919 | + | 0.862581i | \(0.331154\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 323982. | 0.715144 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −97347.6 | −0.209120 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −349123. | −0.730086 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −108682. | −0.221312 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −420397. | −0.833827 | −0.416914 | − | 0.908946i | \(-0.636888\pi\) | ||||
−0.416914 | + | 0.908946i | \(0.636888\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −148098. | −0.286190 | −0.143095 | − | 0.989709i | \(-0.545705\pi\) | ||||
−0.143095 | + | 0.989709i | \(0.545705\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −378280. | −0.712405 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −399632. | −0.733660 | −0.366830 | − | 0.930288i | \(-0.619557\pi\) | ||||
−0.366830 | + | 0.930288i | \(0.619557\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 639043. | 1.14393 | 0.571963 | − | 0.820280i | \(-0.306182\pi\) | ||||
0.571963 | + | 0.820280i | \(0.306182\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 225694. | 0.394030 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.01356e6 | 1.72628 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 254026. | 0.422177 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 371995. | 0.603408 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −371434. | −0.588187 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 840471. | 1.29962 | 0.649810 | − | 0.760097i | \(-0.274848\pi\) | ||||
0.649810 | + | 0.760097i | \(0.274848\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 520658. | 0.786328 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 927879. | 1.36897 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −715392. | −1.03132 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −612832. | −0.863439 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 315376. | 0.434358 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −436150. | −0.587319 | −0.293659 | − | 0.955910i | \(-0.594873\pi\) | ||||
−0.293659 | + | 0.955910i | \(0.594873\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 675705. | 0.889817 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 656896. | 0.846119 | 0.423060 | − | 0.906102i | \(-0.360956\pi\) | ||||
0.423060 | + | 0.906102i | \(0.360956\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −769622. | −0.969815 | −0.484908 | − | 0.874565i | \(-0.661147\pi\) | ||||
−0.484908 | + | 0.874565i | \(0.661147\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 583001. | 0.718852 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.11414e6 | −1.34446 | −0.672232 | − | 0.740341i | \(-0.734664\pi\) | ||||
−0.672232 | + | 0.740341i | \(0.734664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.80744e6 | 2.13498 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 888515. | 1.02753 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 742802. | 0.841160 | 0.420580 | − | 0.907256i | \(-0.361827\pi\) | ||||
0.420580 | + | 0.907256i | \(0.361827\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 427097. | 0.473679 | 0.236840 | − | 0.971549i | \(-0.423888\pi\) | ||||
0.236840 | + | 0.971549i | \(0.423888\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −580301. | −0.617644 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 335530. | 0.349936 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 313734. | 0.320673 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 714389. | 0.715732 | 0.357866 | − | 0.933773i | \(-0.383505\pi\) | ||||
0.357866 | + | 0.933773i | \(0.383505\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.99548e6 | −1.95995 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −774374. | −0.745763 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.01289e6 | 1.90102 | 0.950511 | − | 0.310691i | \(-0.100561\pi\) | ||||
0.950511 | + | 0.310691i | \(0.100561\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −135529. | −0.125540 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −550687. | −0.500384 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.13759e6 | 1.01413 | 0.507067 | − | 0.861907i | \(-0.330730\pi\) | ||||
0.507067 | + | 0.861907i | \(0.330730\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.15983e6 | 1.01456 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 312104. | 0.267930 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.15018e6 | −0.969138 | −0.484569 | − | 0.874753i | \(-0.661023\pi\) | ||||
−0.484569 | + | 0.874753i | \(0.661023\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −271676. | −0.224713 | −0.112356 | − | 0.993668i | \(-0.535840\pi\) | ||||
−0.112356 | + | 0.993668i | \(0.535840\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −526647. | −0.427674 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.62466e6 | −2.89025 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.20183e6 | 0.941115 | 0.470557 | − | 0.882369i | \(-0.344053\pi\) | ||||
0.470557 | + | 0.882369i | \(0.344053\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 388685. | 0.298942 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.14613e6 | 0.865900 | 0.432950 | − | 0.901418i | \(-0.357473\pi\) | ||||
0.432950 | + | 0.901418i | \(0.357473\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 552547. | 0.410113 | 0.205056 | − | 0.978750i | \(-0.434262\pi\) | ||||
0.205056 | + | 0.978750i | \(0.434262\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −823861. | −0.600817 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 353659. | 0.253443 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −774253. | −0.545304 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 359019. | 0.248534 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −601434. | −0.409278 | −0.204639 | − | 0.978837i | \(-0.565602\pi\) | ||||
−0.204639 | + | 0.978837i | \(0.565602\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −889421. | −0.595048 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −316754. | −0.208368 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.80259e6 | 1.16606 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.29181e6 | 0.821829 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −318074. | −0.199031 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.85482e6 | −2.37277 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −561644. | −0.340107 | −0.170053 | − | 0.985435i | \(-0.554394\pi\) | ||||
−0.170053 | + | 0.985435i | \(0.554394\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −333877. | −0.198925 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.83235e6 | −1.07425 | −0.537126 | − | 0.843502i | \(-0.680490\pi\) | ||||
−0.537126 | + | 0.843502i | \(0.680490\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.63782e6 | 1.52190 | 0.760948 | − | 0.648813i | \(-0.224734\pi\) | ||||
0.760948 | + | 0.648813i | \(0.224734\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.29313e6 | 0.734287 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.11403e6 | 1.18158 | 0.590791 | − | 0.806825i | \(-0.298816\pi\) | ||||
0.590791 | + | 0.806825i | \(0.298816\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.95403e6 | 1.62532 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.38209e6 | 0.748644 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 686861. | 0.366322 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.27429e6 | 1.71953 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 960738. | 0.496862 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.51634e6 | 1.28168 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −432931. | −0.217194 | −0.108597 | − | 0.994086i | \(-0.534636\pi\) | ||||
−0.108597 | + | 0.994086i | \(0.534636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 73635.1 | 0.0363893 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.68536e6 | −1.30735 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −188395. | −0.0903640 | −0.0451820 | − | 0.998979i | \(-0.514387\pi\) | ||||
−0.0451820 | + | 0.998979i | \(0.514387\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −920090. | −0.434842 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.08501e6 | −0.971006 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.69776e6 | 0.779184 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.42608e6 | −2.00204 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.75126e6 | 1.22661 | 0.613306 | − | 0.789845i | \(-0.289839\pi\) | ||||
0.613306 | + | 0.789845i | \(0.289839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.36608e6 | −1.03984 | −0.519919 | − | 0.854216i | \(-0.674038\pi\) | ||||
−0.519919 | + | 0.854216i | \(0.674038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 286136. | 0.123967 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −67235.9 | −0.0287187 | −0.0143593 | − | 0.999897i | \(-0.504571\pi\) | ||||
−0.0143593 | + | 0.999897i | \(0.504571\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.19492e6 | −2.60894 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.07810e6 | −0.447700 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −880277. | −0.360482 | −0.180241 | − | 0.983622i | \(-0.557688\pi\) | ||||
−0.180241 | + | 0.983622i | \(0.557688\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.74534e6 | −0.704876 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 249695. | 0.0994589 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.29163e6 | 2.86479 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.71882e6 | −1.05370 | −0.526848 | − | 0.849959i | \(-0.676626\pi\) | ||||
−0.526848 | + | 0.849959i | \(0.676626\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −192149. | −0.0734637 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.61473e6 | 0.609066 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −111486. | −0.0414904 | −0.0207452 | − | 0.999785i | \(-0.506604\pi\) | ||||
−0.0207452 | + | 0.999785i | \(0.506604\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.02796e6 | −1.84635 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.66849e6 | −0.966967 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.62051e6 | −0.937104 | −0.468552 | − | 0.883436i | \(-0.655224\pi\) | ||||
−0.468552 | + | 0.883436i | \(0.655224\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 425614. | 0.150212 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.82442e6 | −0.635519 | −0.317760 | − | 0.948171i | \(-0.602930\pi\) | ||||
−0.317760 | + | 0.948171i | \(0.602930\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.93669e6 | −2.38507 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −701861. | −0.238217 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 162259. | 0.0543668 | 0.0271834 | − | 0.999630i | \(-0.491346\pi\) | ||||
0.0271834 | + | 0.999630i | \(0.491346\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.69007e6 | 1.22065 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −738425. | −0.241171 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.05718e7 | −3.40922 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.92783e6 | −0.932330 | −0.466165 | − | 0.884698i | \(-0.654365\pi\) | ||||
−0.466165 | + | 0.884698i | \(0.654365\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.14699e6 | −0.360685 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.92259e6 | 1.21818 | 0.609090 | − | 0.793101i | \(-0.291535\pi\) | ||||
0.609090 | + | 0.793101i | \(0.291535\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.88347e6 | 0.577691 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −702580. | −0.212842 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −394998. | −0.118198 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −151551. | −0.0447973 | −0.0223986 | − | 0.999749i | \(-0.507130\pi\) | ||||
−0.0223986 | + | 0.999749i | \(0.507130\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −620858. | −0.181296 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.23826e6 | −0.357222 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.73288e6 | −1.06396 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.94098e6 | 1.10985 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.13904e6 | 0.873497 | 0.436748 | − | 0.899584i | \(-0.356130\pi\) | ||||
0.436748 | + | 0.899584i | \(0.356130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.32328e6 | −0.638847 | −0.319423 | − | 0.947612i | \(-0.603489\pi\) | ||||
−0.319423 | + | 0.947612i | \(0.603489\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.36717e6 | −0.371512 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.70278e6 | 1.80004 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.36674e6 | −1.42443 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.53491e6 | −0.402661 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 998677. | 0.258960 | 0.129480 | − | 0.991582i | \(-0.458669\pi\) | ||||
0.129480 | + | 0.991582i | \(0.458669\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.18444e6 | 1.07255 | 0.536275 | − | 0.844044i | \(-0.319831\pi\) | ||||
0.536275 | + | 0.844044i | \(0.319831\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.55221e6 | 1.66022 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.92589e6 | 0.983409 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.30452e6 | −0.818364 | −0.409182 | − | 0.912453i | \(-0.634186\pi\) | ||||
−0.409182 | + | 0.912453i | \(0.634186\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 438948. | 0.107477 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.11097e6 | 0.995257 | 0.497629 | − | 0.867390i | \(-0.334204\pi\) | ||||
0.497629 | + | 0.867390i | \(0.334204\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.71349e6 | −0.888959 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 249051. | 0.0589548 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.22741e6 | 1.69187 | 0.845934 | − | 0.533287i | \(-0.179043\pi\) | ||||
0.845934 | + | 0.533287i | \(0.179043\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.03074e6 | 0.238620 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 762357. | 0.174547 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.26618e6 | 1.41897 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.11469e6 | −1.36957 | −0.684784 | − | 0.728746i | \(-0.740103\pi\) | ||||
−0.684784 | + | 0.728746i | \(0.740103\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 585748. | 0.129771 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.91568e6 | 0.858134 | 0.429067 | − | 0.903273i | \(-0.358842\pi\) | ||||
0.429067 | + | 0.903273i | \(0.358842\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.39830e6 | 1.38711 | 0.693557 | − | 0.720402i | \(-0.256043\pi\) | ||||
0.693557 | + | 0.720402i | \(0.256043\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.62467e6 | −0.991855 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.54919e6 | 0.753074 | 0.376537 | − | 0.926402i | \(-0.377115\pi\) | ||||
0.376537 | + | 0.926402i | \(0.377115\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.73860e6 | −0.784833 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.09361e6 | 1.05797 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.76497e6 | 0.773764 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.13112e6 | 1.45019 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −877309. | −0.176546 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.52909e6 | −1.10107 | −0.550535 | − | 0.834812i | \(-0.685576\pi\) | ||||
−0.550535 | + | 0.834812i | \(0.685576\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 356817. | 0.0703206 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.16206e6 | −1.20187 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.27170e6 | −0.824606 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.29274e6 | 0.246996 | 0.123498 | − | 0.992345i | \(-0.460589\pi\) | ||||
0.123498 | + | 0.992345i | \(0.460589\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 236941. | 0.0448094 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.06222e6 | −0.947626 | −0.473813 | − | 0.880625i | \(-0.657123\pi\) | ||||
−0.473813 | + | 0.880625i | \(0.657123\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.46264e6 | −1.01224 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.76882e6 | 0.691342 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.62466e6 | −1.56621 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.89211e6 | 0.519951 | 0.259976 | − | 0.965615i | \(-0.416285\pi\) | ||||
0.259976 | + | 0.965615i | \(0.416285\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.41523e6 | 0.429897 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.20037e6 | −0.740231 | −0.370115 | − | 0.928986i | \(-0.620682\pi\) | ||||
−0.370115 | + | 0.928986i | \(0.620682\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.78452e6 | 0.660363 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.95509e6 | −0.337791 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.09356e6 | 0.529255 | 0.264627 | − | 0.964351i | \(-0.414751\pi\) | ||||
0.264627 | + | 0.964351i | \(0.414751\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.01515e7 | 1.71980 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 623180. | 0.104549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.97255e6 | 0.660011 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.33388e6 | 1.20672 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −927807. | −0.151196 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.99447e6 | 1.12891 | 0.564456 | − | 0.825463i | \(-0.309086\pi\) | ||||
0.564456 | + | 0.825463i | \(0.309086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.93493e6 | −0.309322 | −0.154661 | − | 0.987968i | \(-0.549429\pi\) | ||||
−0.154661 | + | 0.987968i | \(0.549429\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.11930e7 | −1.77234 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.85563e6 | 0.604741 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.46550e7 | 2.27691 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 672770. | 0.103545 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −931106. | −0.141965 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.64445e7 | −2.48391 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.04795e6 | −0.905049 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.35463e6 | −0.349101 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.23886e6 | 1.21025 | 0.605124 | − | 0.796131i | \(-0.293124\pi\) | ||||
0.605124 | + | 0.796131i | \(0.293124\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.01375e6 | 0.584185 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.14311e7 | −1.64853 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.16514e6 | 1.30970 | 0.654849 | − | 0.755760i | \(-0.272732\pi\) | ||||
0.654849 | + | 0.755760i | \(0.272732\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.91584e6 | 0.412889 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.81173e6 | −0.815505 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.47182e7 | −2.04664 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −876129. | −0.120736 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.54035e6 | 0.893230 | 0.446615 | − | 0.894726i | \(-0.352629\pi\) | ||||
0.446615 | + | 0.894726i | \(0.352629\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.40104e6 | −0.460344 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.14210e6 | −0.421515 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.50619e6 | −0.599155 | −0.299577 | − | 0.954072i | \(-0.596846\pi\) | ||||
−0.299577 | + | 0.954072i | \(0.596846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.09475e7 | 1.44275 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −978142. | −0.127774 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.55292e6 | 0.460050 | 0.230025 | − | 0.973185i | \(-0.426119\pi\) | ||||
0.230025 | + | 0.973185i | \(0.426119\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.19688e7 | 1.53624 | 0.768122 | − | 0.640304i | \(-0.221192\pi\) | ||||
0.768122 | + | 0.640304i | \(0.221192\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.78357e6 | −0.481410 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.83110e7 | 4.83230 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.21327e7 | −1.51711 | −0.758554 | − | 0.651611i | \(-0.774094\pi\) | ||||
−0.758554 | + | 0.651611i | \(0.774094\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.33288e6 | −0.165232 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.19697e6 | −0.638719 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.70612e6 | 0.573445 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.40452e6 | −0.411307 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.03620e7 | 1.24122 | 0.620612 | − | 0.784118i | \(-0.286884\pi\) | ||||
0.620612 | + | 0.784118i | \(0.286884\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.10203e6 | 0.487204 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.59669e6 | −0.423579 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.01261e7 | −1.18251 | −0.591254 | − | 0.806486i | \(-0.701367\pi\) | ||||
−0.591254 | + | 0.806486i | \(0.701367\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.28274e7 | 1.48541 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.75139e6 | 0.660446 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −313236. | −0.0356701 | −0.0178350 | − | 0.999841i | \(-0.505677\pi\) | ||||
−0.0178350 | + | 0.999841i | \(0.505677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.89443e6 | −0.552734 | −0.276367 | − | 0.961052i | \(-0.589131\pi\) | ||||
−0.276367 | + | 0.961052i | \(0.589131\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.03125e6 | 0.227494 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.97094e6 | −0.329993 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.48909e6 | −0.825006 | −0.412503 | − | 0.910956i | \(-0.635345\pi\) | ||||
−0.412503 | + | 0.910956i | \(0.635345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.12208e6 | 0.996668 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.62497e6 | −0.717928 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.20289e7 | −1.29293 | −0.646466 | − | 0.762942i | \(-0.723754\pi\) | ||||
−0.646466 | + | 0.762942i | \(0.723754\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.28624e6 | 0.243744 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.27115e6 | −0.451681 | −0.225841 | − | 0.974164i | \(-0.572513\pi\) | ||||
−0.225841 | + | 0.974164i | \(0.572513\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.05328e7 | −1.10488 | −0.552442 | − | 0.833552i | \(-0.686304\pi\) | ||||
−0.552442 | + | 0.833552i | \(0.686304\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.34795e6 | 0.348378 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.16997e6 | −0.533664 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.37550e7 | 3.45651 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.34290e6 | −0.339590 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 730437. | 0.0736133 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.47931e7 | −1.47906 | −0.739532 | − | 0.673122i | \(-0.764953\pi\) | ||||
−0.739532 | + | 0.673122i | \(0.764953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.56424e6 | 0.750336 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.06406e6 | −0.498384 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.12703e6 | 0.207694 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.68592e6 | 0.453986 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.86457e6 | −0.179240 | −0.0896198 | − | 0.995976i | \(-0.528565\pi\) | ||||
−0.0896198 | + | 0.995976i | \(0.528565\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.14368e6 | 0.586004 | 0.293002 | − | 0.956112i | \(-0.405346\pi\) | ||||
0.293002 | + | 0.956112i | \(0.405346\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.35092e6 | 0.790378 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.58318e6 | 0.524350 | 0.262175 | − | 0.965020i | \(-0.415560\pi\) | ||||
0.262175 | + | 0.965020i | \(0.415560\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.60892e6 | −0.336330 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.43853e6 | −0.595435 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.55163e6 | −0.876586 | −0.438293 | − | 0.898832i | \(-0.644417\pi\) | ||||
−0.438293 | + | 0.898832i | \(0.644417\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.78596e6 | 0.800177 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.51549e6 | −0.498507 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.48421e6 | 0.222831 | 0.111415 | − | 0.993774i | \(-0.464462\pi\) | ||||
0.111415 | + | 0.993774i | \(0.464462\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.32567e7 | −1.18013 | −0.590066 | − | 0.807355i | \(-0.700898\pi\) | ||||
−0.590066 | + | 0.807355i | \(0.700898\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.83838e6 | 0.250777 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.36472e7 | 1.19671 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.12228e7 | −2.71742 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.92535e6 | −0.339089 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.56413e7 | −1.34112 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.13191e7 | −0.963327 | −0.481663 | − | 0.876356i | \(-0.659967\pi\) | ||||
−0.481663 | + | 0.876356i | \(0.659967\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.08134e6 | 0.513736 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.27180e6 | 0.442066 | 0.221033 | − | 0.975266i | \(-0.429057\pi\) | ||||
0.221033 | + | 0.975266i | \(0.429057\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.94713e6 | −0.495031 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.91206e6 | 0.488507 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.64351e6 | −0.791013 | −0.395506 | − | 0.918463i | \(-0.629431\pi\) | ||||
−0.395506 | + | 0.918463i | \(0.629431\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.38712e6 | 0.601518 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.92660e6 | −0.559923 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.25122e6 | −0.341166 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.01345e7 | −0.807437 | −0.403719 | − | 0.914883i | \(-0.632283\pi\) | ||||
−0.403719 | + | 0.914883i | \(0.632283\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.24701e6 | 0.415029 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.68908e7 | −3.68235 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.90606e6 | −0.148612 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.00272e7 | −0.776227 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.04002e7 | 1.56797 | 0.783987 | − | 0.620777i | \(-0.213183\pi\) | ||||
0.783987 | + | 0.620777i | \(0.213183\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 777116. | 0.0593059 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.62670e7 | 1.23263 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.26887e6 | 0.396432 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.99117e7 | −1.48762 | −0.743810 | − | 0.668391i | \(-0.766983\pi\) | ||||
−0.743810 | + | 0.668391i | \(0.766983\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.99663e6 | 0.593244 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.20376e7 | 1.62346 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.82628e7 | 1.33598 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.68522e6 | 0.485644 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.41435e7 | −1.02032 | −0.510159 | − | 0.860080i | \(-0.670413\pi\) | ||||
−0.510159 | + | 0.860080i | \(0.670413\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.53064e6 | 0.396221 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.84388e6 | 0.273479 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.67141e7 | −4.00725 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.28420e7 | 0.901146 | 0.450573 | − | 0.892740i | \(-0.351220\pi\) | ||||
0.450573 | + | 0.892740i | \(0.351220\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.96224e6 | −0.481899 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.88331e6 | 0.129468 | 0.0647339 | − | 0.997903i | \(-0.479380\pi\) | ||||
0.0647339 | + | 0.997903i | \(0.479380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.22271e6 | −0.356597 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.08961e7 | −0.738931 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.31690e6 | −0.0887036 | −0.0443518 | − | 0.999016i | \(-0.514122\pi\) | ||||
−0.0443518 | + | 0.999016i | \(0.514122\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.01977e6 | 0.202036 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.87356e7 | 1.90962 | 0.954812 | − | 0.297210i | \(-0.0960563\pi\) | ||||
0.954812 | + | 0.297210i | \(0.0960563\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.96327e6 | −0.195605 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.82360e6 | 0.185141 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.28943e7 | −1.49115 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.33862e6 | −0.474804 | −0.237402 | − | 0.971411i | \(-0.576296\pi\) | ||||
−0.237402 | + | 0.971411i | \(0.576296\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.42950e6 | 0.413228 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.07072e6 | −0.579128 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.05944e7 | 1.30620 | 0.653100 | − | 0.757272i | \(-0.273468\pi\) | ||||
0.653100 | + | 0.757272i | \(0.273468\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.79593e7 | −1.13158 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.08295e7 | −1.30382 | −0.651911 | − | 0.758296i | \(-0.726032\pi\) | ||||
−0.651911 | + | 0.758296i | \(0.726032\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.59145e7 | −0.989653 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.96937e6 | −0.430566 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.26007e6 | 0.200096 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.24343e6 | 0.441701 | 0.220851 | − | 0.975308i | \(-0.429117\pi\) | ||||
0.220851 | + | 0.975308i | \(0.429117\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.81160e7 | 1.09756 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.56360e6 | 0.455281 | 0.227641 | − | 0.973745i | \(-0.426899\pi\) | ||||
0.227641 | + | 0.973745i | \(0.426899\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.00299e7 | 2.39403 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.21976e6 | −0.0724806 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.02787e6 | −0.119728 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.51365e7 | −1.47461 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.95618e6 | −0.288897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.06050e7 | −3.51022 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.74475e7 | −1.00415 | −0.502074 | − | 0.864825i | \(-0.667429\pi\) | ||||
−0.502074 | + | 0.864825i | \(0.667429\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.02383e7 | 0.585510 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.52412e7 | 0.866121 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.41294e7 | 0.797887 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.04384e7 | 0.585758 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.86812e7 | 1.59938 | 0.799689 | − | 0.600414i | \(-0.204998\pi\) | ||||
0.799689 | + | 0.600414i | \(0.204998\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.35619e7 | −0.751544 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.80893e6 | 0.154689 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.95866e7 | 1.61922 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.33177e7 | 3.98767 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.03516e7 | −0.559532 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.18731e7 | 0.637812 | 0.318906 | − | 0.947786i | \(-0.396685\pi\) | ||||
0.318906 | + | 0.947786i | \(0.396685\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.63302e6 | 0.407516 | 0.203758 | − | 0.979021i | \(-0.434684\pi\) | ||||
0.203758 | + | 0.979021i | \(0.434684\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.44508e6 | −0.129738 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.81919e6 | −0.148672 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.40717e6 | −0.388237 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.73983e6 | −0.246918 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.42730e7 | −0.739021 | −0.369511 | − | 0.929227i | \(-0.620475\pi\) | ||||
−0.369511 | + | 0.929227i | \(0.620475\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.71695e7 | −0.883604 | −0.441802 | − | 0.897113i | \(-0.645661\pi\) | ||||
−0.441802 | + | 0.897113i | \(0.645661\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.26219e7 | −1.66869 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.21323e7 | −1.12529 | −0.562644 | − | 0.826699i | \(-0.690216\pi\) | ||||
−0.562644 | + | 0.826699i | \(0.690216\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.55903e7 | −0.787896 | −0.393948 | − | 0.919133i | \(-0.628891\pi\) | ||||
−0.393948 | + | 0.919133i | \(0.628891\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.08164e7 | 0.543353 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.35422e6 | 0.217419 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.87370e7 | −1.42635 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.49816e6 | 0.172594 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.48897e6 | −0.318252 | −0.159126 | − | 0.987258i | \(-0.550868\pi\) | ||||
−0.159126 | + | 0.987258i | \(0.550868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.57098e7 | 1.25346 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.03152e7 | 0.499928 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.32622e7 | 1.12075 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.13618e6 | −0.198103 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.97292e6 | 0.236779 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.17495e6 | 0.197619 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.78176e7 | 1.30902 | 0.654512 | − | 0.756052i | \(-0.272874\pi\) | ||||
0.654512 | + | 0.756052i | \(0.272874\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.41475e6 | −0.346882 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.23818e7 | −0.575880 | −0.287940 | − | 0.957648i | \(-0.592970\pi\) | ||||
−0.287940 | + | 0.957648i | \(0.592970\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.64820e7 | −0.762126 | −0.381063 | − | 0.924549i | \(-0.624442\pi\) | ||||
−0.381063 | + | 0.924549i | \(0.624442\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.18293e6 | 0.146325 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.92492e6 | 0.316510 | 0.158255 | − | 0.987398i | \(-0.449413\pi\) | ||||
0.158255 | + | 0.987398i | \(0.449413\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.10393e7 | 0.501650 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.96828e6 | −0.314831 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.28960e7 | −1.92694 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.84290e6 | 0.439620 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.23118e6 | 0.143491 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 8.32877e7 | 3.67757 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.07951e7 | 0.473943 | 0.236972 | − | 0.971517i | \(-0.423845\pi\) | ||||
0.236972 | + | 0.971517i | \(0.423845\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.41290e6 | −0.236297 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.27616e7 | 0.553942 | 0.276971 | − | 0.960878i | \(-0.410669\pi\) | ||||
0.276971 | + | 0.960878i | \(0.410669\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.93416e6 | 0.299290 | 0.149645 | − | 0.988740i | \(-0.452187\pi\) | ||||
0.149645 | + | 0.988740i | \(0.452187\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.00479e6 | −0.343551 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.18558e7 | −0.932734 | −0.466367 | − | 0.884591i | \(-0.654437\pi\) | ||||
−0.466367 | + | 0.884591i | \(0.654437\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.05026e6 | −0.299192 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.85079e6 | −0.120301 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.44286e7 | −0.605474 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.19600e7 | 3.00285 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.62233e7 | 0.673223 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.26236e7 | −1.34627 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.70263e6 | −0.357140 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.16263e7 | 0.474483 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.77565e7 | −1.93826 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.22111e7 | 1.70376 | 0.851880 | − | 0.523738i | \(-0.175463\pi\) | ||||
0.851880 | + | 0.523738i | \(0.175463\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.86266e6 | −0.114911 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.45953e7 | −0.582661 | −0.291331 | − | 0.956622i | \(-0.594098\pi\) | ||||
−0.291331 | + | 0.956622i | \(0.594098\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.51466e7 | −0.601363 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.46934e7 | −1.36992 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.22319e7 | 0.480366 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.21908e6 | 0.164789 | 0.0823946 | − | 0.996600i | \(-0.473743\pi\) | ||||
0.0823946 | + | 0.996600i | \(0.473743\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.05480e6 | −0.196361 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.27068e7 | 0.877307 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.58354e6 | 0.291419 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.00489e6 | −0.114850 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.76343e7 | 1.05053 | 0.525265 | − | 0.850939i | \(-0.323966\pi\) | ||||
0.525265 | + | 0.850939i | \(0.323966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.63248e6 | 0.175162 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.64911e7 | −0.620220 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.73855e7 | 1.39854 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.61923e7 | −0.974597 | −0.487298 | − | 0.873236i | \(-0.662018\pi\) | ||||
−0.487298 | + | 0.873236i | \(0.662018\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.37404e7 | 0.878667 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.59191e7 | 1.32236 | 0.661182 | − | 0.750226i | \(-0.270055\pi\) | ||||
0.661182 | + | 0.750226i | \(0.270055\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.08944e7 | −0.398957 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.16382e7 | 0.423941 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.21442e7 | 1.16474 | 0.582369 | − | 0.812924i | \(-0.302126\pi\) | ||||
0.582369 | + | 0.812924i | \(0.302126\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.67267e7 | −0.963339 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.90263e7 | 0.682187 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.06599e7 | 1.80689 | 0.903446 | − | 0.428701i | \(-0.141029\pi\) | ||||
0.903446 | + | 0.428701i | \(0.141029\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.50179e7 | 1.59726 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.65863e7 | 0.938377 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.02845e7 | 0.361106 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.60279e6 | −0.195702 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.24389e7 | 0.432230 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.58589e7 | 0.548221 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.48263e7 | 1.54158 | 0.770790 | − | 0.637089i | \(-0.219862\pi\) | ||||
0.770790 | + | 0.637089i | \(0.219862\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.18175e6 | 0.211496 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.77374e7 | −0.944100 | −0.472050 | − | 0.881572i | \(-0.656486\pi\) | ||||
−0.472050 | + | 0.881572i | \(0.656486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.52820e7 | −2.21061 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.94686e7 | 0.992770 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.60277e7 | 1.20754 | 0.603768 | − | 0.797160i | \(-0.293666\pi\) | ||||
0.603768 | + | 0.797160i | \(0.293666\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.50679e7 | −0.502452 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.64664e6 | 0.286863 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.49497e7 | 0.823534 | 0.411767 | − | 0.911289i | \(-0.364912\pi\) | ||||
0.411767 | + | 0.911289i | \(0.364912\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.27943e7 | 1.40539 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.26471e7 | 0.739980 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.97940e7 | −1.29368 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.88166e7 | −0.608636 | −0.304318 | − | 0.952571i | \(-0.598428\pi\) | ||||
−0.304318 | + | 0.952571i | \(0.598428\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.89638e6 | −0.125397 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.84315e7 | −2.19128 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.25880e7 | −1.35691 | −0.678453 | − | 0.734644i | \(-0.737349\pi\) | ||||
−0.678453 | + | 0.734644i | \(0.737349\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 662716. | 0.0210094 |
(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 | 192.6.a.r.1.1 | 2 | ||
3.2 | odd | 2 | 576.6.a.bm.1.2 | 2 | |||
4.3 | odd | 2 | 192.6.a.q.1.1 | 2 | |||
8.3 | odd | 2 | 96.6.a.h.1.2 | yes | 2 | ||
8.5 | even | 2 | 96.6.a.g.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 576.6.a.bn.1.2 | 2 | |||
16.3 | odd | 4 | 768.6.d.s.385.2 | 4 | |||
16.5 | even | 4 | 768.6.d.z.385.1 | 4 | |||
16.11 | odd | 4 | 768.6.d.s.385.3 | 4 | |||
16.13 | even | 4 | 768.6.d.z.385.4 | 4 | |||
24.5 | odd | 2 | 288.6.a.n.1.1 | 2 | |||
24.11 | even | 2 | 288.6.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.6.a.g.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
96.6.a.h.1.2 | yes | 2 | 8.3 | odd | 2 | ||
192.6.a.q.1.1 | 2 | 4.3 | odd | 2 | |||
192.6.a.r.1.1 | 2 | 1.1 | even | 1 | trivial | ||
288.6.a.n.1.1 | 2 | 24.5 | odd | 2 | |||
288.6.a.o.1.1 | 2 | 24.11 | even | 2 | |||
576.6.a.bm.1.2 | 2 | 3.2 | odd | 2 | |||
576.6.a.bn.1.2 | 2 | 12.11 | even | 2 | |||
768.6.d.s.385.2 | 4 | 16.3 | odd | 4 | |||
768.6.d.s.385.3 | 4 | 16.11 | odd | 4 | |||
768.6.d.z.385.1 | 4 | 16.5 | even | 4 | |||
768.6.d.z.385.4 | 4 | 16.13 | even | 4 |