Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [352,6,Mod(1,352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(352, 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("352.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 352 = 2^{5} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 352.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: | \(56.4551045742\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 492x^{4} - 880x^{3} + 32838x^{2} + 13500x - 442908 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-16.7550\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 352.1 |
$q$-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 | ||||||||
\(3\) | −16.0835 | −1.03175 | −0.515877 | − | 0.856663i | \(-0.672534\pi\) | ||||
−0.515877 | + | 0.856663i | \(0.672534\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −100.636 | −1.80024 | −0.900118 | − | 0.435645i | \(-0.856520\pi\) | ||||
−0.900118 | + | 0.435645i | \(0.856520\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −99.5357 | −0.767775 | −0.383887 | − | 0.923380i | \(-0.625415\pi\) | ||||
−0.383887 | + | 0.923380i | \(0.625415\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 15.6776 | 0.0645170 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1129.85 | 1.85423 | 0.927114 | − | 0.374780i | \(-0.122282\pi\) | ||||
0.927114 | + | 0.374780i | \(0.122282\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1618.58 | 1.85740 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.49747 | 0.00461360 | 0.00230680 | − | 0.999997i | \(-0.499266\pi\) | ||||
0.00230680 | + | 0.999997i | \(0.499266\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 576.534 | 0.366388 | 0.183194 | − | 0.983077i | \(-0.441356\pi\) | ||||
0.183194 | + | 0.983077i | \(0.441356\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1600.88 | 0.792155 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 961.905 | 0.379151 | 0.189576 | − | 0.981866i | \(-0.439289\pi\) | ||||
0.189576 | + | 0.981866i | \(0.439289\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7002.66 | 2.24085 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3656.13 | 0.965189 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2010.70 | −0.443968 | −0.221984 | − | 0.975050i | \(-0.571253\pi\) | ||||
−0.221984 | + | 0.975050i | \(0.571253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5682.00 | −1.06193 | −0.530967 | − | 0.847393i | \(-0.678171\pi\) | ||||
−0.530967 | + | 0.847393i | \(0.678171\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1946.10 | −0.311086 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 10016.9 | 1.38218 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7369.08 | −0.884930 | −0.442465 | − | 0.896786i | \(-0.645896\pi\) | ||||
−0.442465 | + | 0.896786i | \(0.645896\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −18171.9 | −1.91311 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18926.0 | −1.75833 | −0.879163 | − | 0.476521i | \(-0.841897\pi\) | ||||
−0.879163 | + | 0.476521i | \(0.841897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 21955.7 | 1.81083 | 0.905413 | − | 0.424532i | \(-0.139561\pi\) | ||||
0.905413 | + | 0.424532i | \(0.139561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1577.74 | −0.116146 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20022.7 | 1.32214 | 0.661071 | − | 0.750323i | \(-0.270102\pi\) | ||||
0.661071 | + | 0.750323i | \(0.270102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6899.64 | −0.410522 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −88.4183 | −0.00476011 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9830.41 | −0.480709 | −0.240354 | − | 0.970685i | \(-0.577264\pi\) | ||||
−0.240354 | + | 0.970685i | \(0.577264\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12177.0 | −0.542792 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9272.67 | −0.378022 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3365.53 | −0.125870 | −0.0629352 | − | 0.998018i | \(-0.520046\pi\) | ||||
−0.0629352 | + | 0.998018i | \(0.520046\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28629.3 | 0.985114 | 0.492557 | − | 0.870280i | \(-0.336062\pi\) | ||||
0.492557 | + | 0.870280i | \(0.336062\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1560.49 | −0.0495346 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −113704. | −3.33805 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42601.9 | 1.15942 | 0.579712 | − | 0.814821i | \(-0.303165\pi\) | ||||
0.579712 | + | 0.814821i | \(0.303165\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −15470.8 | −0.391191 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −34117.8 | −0.803221 | −0.401611 | − | 0.915810i | \(-0.631550\pi\) | ||||
−0.401611 | + | 0.915810i | \(0.631550\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5606.36 | −0.123133 | −0.0615664 | − | 0.998103i | \(-0.519610\pi\) | ||||
−0.0615664 | + | 0.998103i | \(0.519610\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −112627. | −2.31201 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12043.8 | −0.231493 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 21585.3 | 0.389127 | 0.194563 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194563 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −62612.9 | −1.06035 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 82926.3 | 1.32129 | 0.660643 | − | 0.750700i | \(-0.270284\pi\) | ||||
0.660643 | + | 0.750700i | \(0.270284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −553.245 | −0.00830558 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 32338.9 | 0.458065 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 104138. | 1.39358 | 0.696792 | − | 0.717273i | \(-0.254610\pi\) | ||||
0.696792 | + | 0.717273i | \(0.254610\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −112461. | −1.42363 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 91386.3 | 1.09565 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −58020.3 | −0.659585 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12807.1 | 0.138205 | 0.0691024 | − | 0.997610i | \(-0.477986\pi\) | ||||
0.0691024 | + | 0.997610i | \(0.477986\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1896.99 | 0.0194526 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −90924.3 | −0.886903 | −0.443452 | − | 0.896298i | \(-0.646246\pi\) | ||||
−0.443452 | + | 0.896298i | \(0.646246\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −167606. | −1.55667 | −0.778336 | − | 0.627848i | \(-0.783936\pi\) | ||||
−0.778336 | + | 0.627848i | \(0.783936\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −161107. | −1.42607 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −131979. | −1.11441 | −0.557206 | − | 0.830374i | \(-0.688127\pi\) | ||||
−0.557206 | + | 0.830374i | \(0.688127\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −47254.7 | −0.380960 | −0.190480 | − | 0.981691i | \(-0.561004\pi\) | ||||
−0.190480 | + | 0.981691i | \(0.561004\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 118520. | 0.913031 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10173.1 | 0.0749476 | 0.0374738 | − | 0.999298i | \(-0.488069\pi\) | ||||
0.0374738 | + | 0.999298i | \(0.488069\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −96802.6 | −0.682562 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17713.4 | 0.119629 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −547.194 | −0.00354221 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 304396. | 1.81416 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −390234. | −2.23383 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 121460. | 0.668225 | 0.334113 | − | 0.942533i | \(-0.391563\pi\) | ||||
0.334113 | + | 0.942533i | \(0.391563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −353124. | −1.86833 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 322828. | 1.64359 | 0.821794 | − | 0.569785i | \(-0.192973\pi\) | ||||
0.821794 | + | 0.569785i | \(0.192973\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −57385.8 | −0.281303 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −367939. | −1.73757 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −415124. | −1.88963 | −0.944814 | − | 0.327608i | \(-0.893758\pi\) | ||||
−0.944814 | + | 0.327608i | \(0.893758\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −96216.7 | −0.422390 | −0.211195 | − | 0.977444i | \(-0.567735\pi\) | ||||
−0.211195 | + | 0.977444i | \(0.567735\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −322035. | −1.36413 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 136712. | 0.559071 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 202349. | 0.799247 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 110970. | 0.423557 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9994.87 | 0.0368817 | 0.0184409 | − | 0.999830i | \(-0.494130\pi\) | ||||
0.0184409 | + | 0.999830i | \(0.494130\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 486380. | 1.73593 | 0.867967 | − | 0.496621i | \(-0.165426\pi\) | ||||
0.867967 | + | 0.496621i | \(0.165426\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 86.1873 | 0.000297656 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 571816. | 1.91173 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −150199. | −0.486315 | −0.243158 | − | 0.969987i | \(-0.578183\pi\) | ||||
−0.243158 | + | 0.969987i | \(0.578183\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 158107. | 0.495973 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −95743.9 | −0.291103 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −339066. | −0.999573 | −0.499787 | − | 0.866148i | \(-0.666588\pi\) | ||||
−0.499787 | + | 0.866148i | \(0.666588\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 195848. | 0.560028 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −464673. | −1.28931 | −0.644653 | − | 0.764475i | \(-0.722998\pi\) | ||||
−0.644653 | + | 0.764475i | \(0.722998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 905271. | 2.43816 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9038.69 | 0.0236383 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −124921. | −0.317338 | −0.158669 | − | 0.987332i | \(-0.550720\pi\) | ||||
−0.158669 | + | 0.987332i | \(0.550720\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −697015. | −1.72047 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 54129.4 | 0.129867 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 391469. | 0.913198 | 0.456599 | − | 0.889673i | \(-0.349067\pi\) | ||||
0.456599 | + | 0.889673i | \(0.349067\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −555178. | −1.25961 | −0.629805 | − | 0.776753i | \(-0.716865\pi\) | ||||
−0.629805 | + | 0.776753i | \(0.716865\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −460459. | −1.01640 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 741597. | 1.59308 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 665.194 | 0.00139105 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −363916. | −0.741048 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −874483. | −1.73447 | −0.867237 | − | 0.497896i | \(-0.834106\pi\) | ||||
−0.867237 | + | 0.497896i | \(0.834106\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 29380.7 | 0.0567765 | 0.0283883 | − | 0.999597i | \(-0.490963\pi\) | ||||
0.0283883 | + | 0.999597i | \(0.490963\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.82875e6 | 3.44405 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 103525. | 0.190056 | 0.0950278 | − | 0.995475i | \(-0.469706\pi\) | ||||
0.0950278 | + | 0.995475i | \(0.469706\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 163131. | 0.292014 | 0.146007 | − | 0.989284i | \(-0.453358\pi\) | ||||
0.146007 | + | 0.989284i | \(0.453358\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −685187. | −1.19624 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 200136. | 0.340867 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.90464e6 | 3.16540 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15080.4 | 0.0244617 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 69760.7 | 0.110470 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 848872. | 1.31261 | 0.656306 | − | 0.754495i | \(-0.272118\pi\) | ||||
0.656306 | + | 0.754495i | \(0.272118\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 548732. | 0.828727 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.20954e6 | −3.25991 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 565562. | 0.815326 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 90169.6 | 0.127043 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6211.32 | 0.00855467 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −382088. | −0.514519 | −0.257260 | − | 0.966342i | \(-0.582820\pi\) | ||||
−0.257260 | + | 0.966342i | \(0.582820\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 109785. | 0.144573 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −850742. | −1.09581 | −0.547903 | − | 0.836542i | \(-0.684574\pi\) | ||||
−0.547903 | + | 0.836542i | \(0.684574\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 461501. | 0.581545 | 0.290773 | − | 0.956792i | \(-0.406088\pi\) | ||||
0.290773 | + | 0.956792i | \(0.406088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 193706. | 0.238844 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 874178. | 1.05490 | 0.527449 | − | 0.849587i | \(-0.323149\pi\) | ||||
0.527449 | + | 0.849587i | \(0.323149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.01501e6 | −2.38017 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −347167. | −0.401483 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.22182e6 | 1.38360 | 0.691802 | − | 0.722087i | \(-0.256817\pi\) | ||||
0.691802 | + | 0.722087i | \(0.256817\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 385792. | 0.427869 | 0.213935 | − | 0.976848i | \(-0.431372\pi\) | ||||
0.213935 | + | 0.976848i | \(0.431372\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 118592. | 0.128837 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 694354. | 0.739036 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 651398. | 0.679366 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.33374e6 | −1.36324 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 283850. | 0.284384 | 0.142192 | − | 0.989839i | \(-0.454585\pi\) | ||||
0.142192 | + | 0.989839i | \(0.454585\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 116391. | 0.114318 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8898.09 | 0.00856932 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.57262e6 | −1.48522 | −0.742610 | − | 0.669724i | \(-0.766412\pi\) | ||||
−0.742610 | + | 0.669724i | \(0.766412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 733487. | 0.679427 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −31522.9 | −0.0286435 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −282196. | −0.251571 | −0.125786 | − | 0.992057i | \(-0.540145\pi\) | ||||
−0.125786 | + | 0.992057i | \(0.540145\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 989296. | 0.865389 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.67489e6 | −1.43784 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.58865e6 | −1.33859 | −0.669297 | − | 0.742995i | \(-0.733405\pi\) | ||||
−0.669297 | + | 0.742995i | \(0.733405\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.26811e6 | −1.04890 | −0.524448 | − | 0.851443i | \(-0.675728\pi\) | ||||
−0.524448 | + | 0.851443i | \(0.675728\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.80876e6 | 1.46884 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 847322. | 0.675642 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −716430. | −0.561015 | −0.280507 | − | 0.959852i | \(-0.590503\pi\) | ||||
−0.280507 | + | 0.959852i | \(0.590503\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −89080.4 | −0.0685128 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.80960e6 | 1.36715 | 0.683576 | − | 0.729880i | \(-0.260424\pi\) | ||||
0.683576 | + | 0.729880i | \(0.260424\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 972811. | 0.722042 | 0.361021 | − | 0.932558i | \(-0.382428\pi\) | ||||
0.361021 | + | 0.932558i | \(0.382428\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 933167. | 0.680530 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.88381e6 | 1.35000 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41983e6 | −0.999979 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −205983. | −0.142593 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.32696e6 | 0.903000 | 0.451500 | − | 0.892271i | \(-0.350889\pi\) | ||||
0.451500 | + | 0.892271i | \(0.350889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 338694. | 0.226596 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 442392. | 0.291015 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.08681e6 | 0.703033 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.18538e6 | −1.39031 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.46238e6 | 0.915066 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.88115e6 | −1.77344 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −564125. | −0.341609 | −0.170805 | − | 0.985305i | \(-0.554637\pi\) | ||||
−0.170805 | + | 0.985305i | \(0.554637\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.69569e6 | 1.60610 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.99389e6 | −1.75523 | −0.877617 | − | 0.479363i | \(-0.840868\pi\) | ||||
−0.877617 | + | 0.479363i | \(0.840868\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.69271e6 | 1.55356 | 0.776781 | − | 0.629771i | \(-0.216851\pi\) | ||||
0.776781 | + | 0.629771i | \(0.216851\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 157041. | 0.0891739 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 671680. | 0.375417 | 0.187709 | − | 0.982225i | \(-0.439894\pi\) | ||||
0.187709 | + | 0.982225i | \(0.439894\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −243294. | −0.133861 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.12268e6 | 1.14980 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3169.48 | 0.00169037 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.91197e6 | 4.15505 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 760019. | 0.393057 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.99298e6 | −1.01511 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 618419. | 0.310251 | 0.155125 | − | 0.987895i | \(-0.450422\pi\) | ||||
0.155125 | + | 0.987895i | \(0.450422\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −115530. | −0.0570931 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.28730e6 | −2.08724 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.62745e6 | 0.780606 | 0.390303 | − | 0.920686i | \(-0.372370\pi\) | ||||
0.390303 | + | 0.920686i | \(0.372370\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −163619. | −0.0773275 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −687522. | −0.320185 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.35966e6 | 1.08296 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.55692e6 | 0.704236 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.80110e6 | 0.802996 | 0.401498 | − | 0.915860i | \(-0.368490\pi\) | ||||
0.401498 | + | 0.915860i | \(0.368490\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.29014e6 | 1.00647 | 0.503233 | − | 0.864151i | \(-0.332144\pi\) | ||||
0.503233 | + | 0.864151i | \(0.332144\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.13088e6 | 1.78968 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.59156e6 | −1.10694 | −0.553470 | − | 0.832869i | \(-0.686697\pi\) | ||||
−0.553470 | + | 0.832869i | \(0.686697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.43349e6 | 1.44599 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8800.78 | 0.00365469 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.04765e6 | 0.429024 | 0.214512 | − | 0.976721i | \(-0.431184\pi\) | ||||
0.214512 | + | 0.976721i | \(0.431184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.14371e6 | −0.865760 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −235478. | −0.0937958 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 564203. | 0.221668 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.72232e6 | −1.44261 | −0.721304 | − | 0.692618i | \(-0.756457\pi\) | ||||
−0.721304 | + | 0.692618i | \(0.756457\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −296715. | −0.113442 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 978477. | 0.369076 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.97449e6 | −1.85130 | −0.925650 | − | 0.378381i | \(-0.876481\pi\) | ||||
−0.925650 | + | 0.378381i | \(0.876481\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.27631e6 | 2.30476 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.27179e6 | −0.823217 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.49702e6 | 0.535341 | 0.267670 | − | 0.963511i | \(-0.413746\pi\) | ||||
0.267670 | + | 0.963511i | \(0.413746\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.95349e6 | −0.689444 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.26503e6 | −1.83402 | −0.917009 | − | 0.398866i | \(-0.869404\pi\) | ||||
−0.917009 | + | 0.398866i | \(0.869404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.21205e6 | 0.416742 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 344214. | 0.116829 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.47145e6 | −1.16315 | −0.581576 | − | 0.813492i | \(-0.697564\pi\) | ||||
−0.581576 | + | 0.813492i | \(0.697564\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5288.04 | 0.00174925 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.19219e6 | −1.69578 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.17227e6 | −0.700521 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.69270e6 | −1.81277 | −0.906383 | − | 0.422456i | \(-0.861168\pi\) | ||||
−0.906383 | + | 0.422456i | \(0.861168\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 922962. | 0.290236 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.32139e6 | 0.410364 | 0.205182 | − | 0.978724i | \(-0.434221\pi\) | ||||
0.205182 | + | 0.978724i | \(0.434221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.41982e6 | −1.96907 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.30113e6 | 1.90889 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −891659. | −0.266817 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 147690. | 0.0436558 | 0.0218279 | − | 0.999762i | \(-0.493051\pi\) | ||||
0.0218279 | + | 0.999762i | \(0.493051\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.67663e6 | 1.94963 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 334991. | 0.0966401 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.34539e6 | −2.37863 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.54750e6 | 0.435803 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −3.96934e6 | −1.10454 | −0.552272 | − | 0.833664i | \(-0.686239\pi\) | ||||
−0.552272 | + | 0.833664i | \(0.686239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.22916e6 | −1.16292 | −0.581459 | − | 0.813576i | \(-0.697518\pi\) | ||||
−0.581459 | + | 0.813576i | \(0.697518\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 313909. | 0.0853007 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 38496.9 | 0.0103384 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.84964e6 | −0.756346 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.19880e6 | −0.576823 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.80166e6 | −0.726479 | −0.363239 | − | 0.931696i | \(-0.618329\pi\) | ||||
−0.363239 | + | 0.931696i | \(0.618329\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.99859e6 | −1.28123 | −0.640615 | − | 0.767862i | \(-0.721321\pi\) | ||||
−0.640615 | + | 0.767862i | \(0.721321\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.25447e6 | −0.824626 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 554571. | 0.138916 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −617298. | −0.152874 | −0.0764370 | − | 0.997074i | \(-0.524354\pi\) | ||||
−0.0764370 | + | 0.997074i | \(0.524354\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −108170. | −0.0264856 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.10619e6 | −0.752002 | −0.376001 | − | 0.926619i | \(-0.622701\pi\) | ||||
−0.376001 | + | 0.926619i | \(0.622701\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.04800e7 | −2.50878 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −160752. | −0.0380529 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.73212e6 | 1.34184 | 0.670919 | − | 0.741531i | \(-0.265900\pi\) | ||||
0.670919 | + | 0.741531i | \(0.265900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.29005e6 | −0.530155 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.82267e6 | −1.79106 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.13176e7 | 2.56287 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −481316. | −0.107805 | −0.0539026 | − | 0.998546i | \(-0.517166\pi\) | ||||
−0.0539026 | + | 0.998546i | \(0.517166\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20099.5 | 0.00445300 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.21739e6 | 0.924254 | 0.462127 | − | 0.886814i | \(-0.347086\pi\) | ||||
0.462127 | + | 0.886814i | \(0.347086\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 989813. | 0.214586 | 0.107293 | − | 0.994227i | \(-0.465782\pi\) | ||||
0.107293 | + | 0.994227i | \(0.465782\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.19678e6 | −1.97244 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.02797e6 | −0.430298 | −0.215149 | − | 0.976581i | \(-0.569024\pi\) | ||||
−0.215149 | + | 0.976581i | \(0.569024\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.24042e6 | −0.890177 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.41572e6 | 0.501758 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.65664e6 | 0.545984 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.03728e6 | 0.821021 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −154118. | −0.0310139 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.70289e6 | −0.737398 | −0.368699 | − | 0.929549i | \(-0.620197\pi\) | ||||
−0.368699 | + | 0.929549i | \(0.620197\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.32597e6 | −1.64086 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.53989e6 | 0.300347 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.28886e6 | −0.248801 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.22043e6 | 1.57062 | 0.785311 | − | 0.619101i | \(-0.212503\pi\) | ||||
0.785311 | + | 0.619101i | \(0.212503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.45335e6 | 1.03131 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −977146. | −0.182918 | −0.0914588 | − | 0.995809i | \(-0.529153\pi\) | ||||
−0.0914588 | + | 0.995809i | \(0.529153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11053.7 | −0.00204829 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −190906. | −0.0350193 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.39594e6 | 0.616693 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.97522e6 | −1.61359 | −0.806796 | − | 0.590830i | \(-0.798800\pi\) | ||||
−0.806796 | + | 0.590830i | \(0.798800\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.47355e6 | 1.33025 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.40004e6 | −0.246729 | −0.123365 | − | 0.992361i | \(-0.539368\pi\) | ||||
−0.123365 | + | 0.992361i | \(0.539368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.15028e6 | 1.59664 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.45599e7 | −2.51558 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.68974e6 | −0.460167 | −0.230083 | − | 0.973171i | \(-0.573900\pi\) | ||||
−0.230083 | + | 0.973171i | \(0.573900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 558033. | 0.0945382 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.10788e6 | 0.353633 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.68673e7 | 2.80238 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.42275e6 | 0.398641 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.00917e6 | 0.327415 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.78645e6 | 1.09534 | 0.547670 | − | 0.836695i | \(-0.315515\pi\) | ||||
0.547670 | + | 0.836695i | \(0.315515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −202631. | −0.0323931 | −0.0161965 | − | 0.999869i | \(-0.505156\pi\) | ||||
−0.0161965 | + | 0.999869i | \(0.505156\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.12104e7 | 1.77510 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31236.6 | −0.00489934 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.51108e6 | −0.856244 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −52763.6 | −0.00812078 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.13836e7 | −3.26034 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.32819e7 | 2.00621 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.29618e6 | −0.942196 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −834856. | −0.123777 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.08517e6 | 0.453196 | 0.226598 | − | 0.973988i | \(-0.427240\pi\) | ||||
0.226598 | + | 0.973988i | \(0.427240\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.92919e6 | 1.29961 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.75554e6 | 0.685817 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.25255e6 | −0.750589 | −0.375294 | − | 0.926906i | \(-0.622458\pi\) | ||||
−0.375294 | + | 0.926906i | \(0.622458\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 448840. | 0.0635566 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.15923e6 | −0.162664 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.14851e6 | −0.298762 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.19274e7 | −1.64367 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.43928e6 | 0.469709 | 0.234855 | − | 0.972030i | \(-0.424539\pi\) | ||||
0.234855 | + | 0.972030i | \(0.424539\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.48067e7 | 3.35768 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10698.6 | −0.00143523 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.10226e7 | −1.46559 | −0.732796 | − | 0.680448i | \(-0.761785\pi\) | ||||
−0.732796 | + | 0.680448i | \(0.761785\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.02378e6 | −0.134923 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.23222e6 | 0.814114 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2.65040e6 | −0.343187 | −0.171593 | − | 0.985168i | \(-0.554892\pi\) | ||||
−0.171593 | + | 0.985168i | \(0.554892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.31534e6 | −1.06731 | −0.533654 | − | 0.845703i | \(-0.679182\pi\) | ||||
−0.533654 | + | 0.845703i | \(0.679182\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.40647e7 | 1.78955 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.73590e6 | 0.849622 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.23879e6 | 0.780119 | 0.390060 | − | 0.920790i | \(-0.372454\pi\) | ||||
0.390060 | + | 0.920790i | \(0.372454\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −472543. | −0.0585794 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.25413e6 | −1.01445 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.18948e6 | −0.144939 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.78261e6 | −0.215361 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.45705e6 | 1.13282 | 0.566409 | − | 0.824124i | \(-0.308332\pi\) | ||||
0.566409 | + | 0.824124i | \(0.308332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.27587e6 | −0.389080 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.66504e6 | −0.196091 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.24162e7 | −1.44995 | −0.724973 | − | 0.688778i | \(-0.758148\pi\) | ||||
−0.724973 | + | 0.688778i | \(0.758148\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 55067.6 | 0.00637682 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.62371e6 | −0.301287 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.42313e6 | −0.275937 | −0.137969 | − | 0.990437i | \(-0.544057\pi\) | ||||
−0.137969 | + | 0.990437i | \(0.544057\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.03836e6 | −0.907781 | −0.453890 | − | 0.891057i | \(-0.649964\pi\) | ||||
−0.453890 | + | 0.891057i | \(0.649964\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 667898. | 0.0748026 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.47342e6 | −0.163658 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.56220e6 | −0.282255 | −0.141127 | − | 0.989991i | \(-0.545073\pi\) | ||||
−0.141127 | + | 0.989991i | \(0.545073\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.21888e6 | −0.351691 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.26227e7 | 2.45155 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.69197e6 | 0.289347 | 0.144673 | − | 0.989479i | \(-0.453787\pi\) | ||||
0.144673 | + | 0.989479i | \(0.453787\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.06332e7 | −3.26592 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.39002e7 | −1.46997 | −0.734984 | − | 0.678084i | \(-0.762811\pi\) | ||||
−0.734984 | + | 0.678084i | \(0.762811\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.63082e6 | −0.171072 | −0.0855360 | − | 0.996335i | \(-0.527260\pi\) | ||||
−0.0855360 | + | 0.996335i | \(0.527260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.51685e6 | 0.365953 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.03654e7 | −1.06996 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.73883e7 | 1.78057 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.12199e6 | −0.113978 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40511.3 | −0.00408272 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.26684e6 | 0.726561 | 0.363280 | − | 0.931680i | \(-0.381657\pi\) | ||||
0.363280 | + | 0.931680i | \(0.381657\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.36528e7 | −1.35429 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.22233e7 | −1.20296 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.79556e6 | −0.761200 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −534887. | −0.0518215 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.03214e6 | −0.195347 | −0.0976737 | − | 0.995218i | \(-0.531140\pi\) | ||||
−0.0976737 | + | 0.995218i | \(0.531140\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.46142e6 | 0.807079 | 0.403539 | − | 0.914962i | \(-0.367780\pi\) | ||||
0.403539 | + | 0.914962i | \(0.367780\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.55371e7 | 3.36343 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.72450e7 | 1.61958 | 0.809788 | − | 0.586722i | \(-0.199582\pi\) | ||||
0.809788 | + | 0.586722i | \(0.199582\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −407229. | −0.0379513 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.09620e6 | −0.841216 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 218182. | 0.0200233 | 0.0100116 | − | 0.999950i | \(-0.496813\pi\) | ||||
0.0100116 | + | 0.999950i | \(0.496813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.24882e7 | −2.95885 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −87894.4 | −0.00794416 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.09287e7 | 0.980287 | 0.490143 | − | 0.871642i | \(-0.336944\pi\) | ||||
0.490143 | + | 0.871642i | \(0.336944\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.01145e6 | −0.0900413 | −0.0450206 | − | 0.998986i | \(-0.514335\pi\) | ||||
−0.0450206 | + | 0.998986i | \(0.514335\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −99899.5 | −0.00882632 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.77509e6 | 0.506413 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.93410e6 | −0.168331 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.14530e6 | 0.530857 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.46415e6 | 0.297023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.74638e7 | 1.48628 | 0.743142 | − | 0.669134i | \(-0.233335\pi\) | ||||
0.743142 | + | 0.669134i | \(0.233335\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.56026e7 | 2.16285 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.41726e6 | 0.621974 | 0.310987 | − | 0.950414i | \(-0.399340\pi\) | ||||
0.310987 | + | 0.950414i | \(0.399340\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.27477e6 | −0.106110 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.36829e7 | 1.13060 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.42076e7 | −1.16538 | −0.582691 | − | 0.812694i | \(-0.698000\pi\) | ||||
−0.582691 | + | 0.812694i | \(0.698000\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.17765e7 | 3.40178 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.42253e6 | −0.600012 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.11069e7 | −0.891343 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.44515e6 | 0.513497 | 0.256749 | − | 0.966478i | \(-0.417349\pi\) | ||||
0.256749 | + | 0.966478i | \(0.417349\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −188819. | −0.0149352 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.68289e6 | 0.760402 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −104045. | −0.00811222 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.40598e7 | −1.08839 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.64220e7 | −1.26221 | −0.631105 | − | 0.775697i | \(-0.717398\pi\) | ||||
−0.631105 | + | 0.775697i | \(0.717398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.24853e6 | −0.324228 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.24084e7 | 2.45575 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.05021e6 | 0.680942 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.34022e7 | 1.74840 | 0.874200 | − | 0.485566i | \(-0.161386\pi\) | ||||
0.874200 | + | 0.485566i | \(0.161386\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 338407. | 0.0251053 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −5.46555e6 | −0.402633 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.37582e7 | −1.00646 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.96511e7 | −1.42754 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 512196. | 0.0369500 | 0.0184750 | − | 0.999829i | \(-0.494119\pi\) | ||||
0.0184750 | + | 0.999829i | \(0.494119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.66828e7 | 1.19517 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.20488e6 | −0.441456 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.40802e7 | −0.994866 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.41905e6 | −0.169750 | −0.0848749 | − | 0.996392i | \(-0.527049\pi\) | ||||
−0.0848749 | + | 0.996392i | \(0.527049\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.33076e7 | 0.927427 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 120701. | 0.00835443 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.52577e6 | 0.173633 | 0.0868167 | − | 0.996224i | \(-0.472331\pi\) | ||||
0.0868167 | + | 0.996224i | \(0.472331\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.11676e7 | −0.762504 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.15484e6 | 0.349580 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.14494e7 | 1.44479 | 0.722393 | − | 0.691483i | \(-0.243042\pi\) | ||||
0.722393 | + | 0.691483i | \(0.243042\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.04767e7 | −0.700939 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.97440e6 | 0.397029 | 0.198514 | − | 0.980098i | \(-0.436388\pi\) | ||||
0.198514 | + | 0.980098i | \(0.436388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.00585e6 | −0.0663959 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.30009e6 | 0.0852455 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.31366e7 | 0.855618 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.90539e7 | 1.23277 | 0.616387 | − | 0.787443i | \(-0.288596\pi\) | ||||
0.616387 | + | 0.787443i | \(0.288596\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.56530e6 | −0.293414 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.89475e7 | −3.12509 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.24379e7 | 0.788874 | 0.394437 | − | 0.918923i | \(-0.370940\pi\) | ||||
0.394437 | + | 0.918923i | \(0.370940\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.87196e6 | −0.117949 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.50491e6 | 0.469768 | 0.234884 | − | 0.972023i | \(-0.424529\pi\) | ||||
0.234884 | + | 0.972023i | \(0.424529\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.70353e6 | 0.292491 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8673.57 | −0.000535851 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.80255e6 | −0.233392 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.13597e7 | −0.692710 | −0.346355 | − | 0.938104i | \(-0.612581\pi\) | ||||
−0.346355 | + | 0.938104i | \(0.612581\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.52932e7 | 1.53238 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.57906e7 | −0.950493 | −0.475247 | − | 0.879853i | \(-0.657641\pi\) | ||||
−0.475247 | + | 0.879853i | \(0.657641\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.97892e7 | −2.37964 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.17970e7 | −0.701002 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.09115e7 | −0.644229 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.12826e6 | −0.242180 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.35136e6 | −0.428512 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.51155e7 | 0.875483 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.96895e6 | 0.343527 | 0.171764 | − | 0.985138i | \(-0.445054\pi\) | ||||
0.171764 | + | 0.985138i | \(0.445054\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.53868e6 | 0.259560 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.01259e6 | −0.0575429 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.23469e7 | 1.82663 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.59113e7 | −0.892869 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.04962e7 | 1.14295 | 0.571476 | − | 0.820619i | \(-0.306371\pi\) | ||||
0.571476 | + | 0.820619i | \(0.306371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 110074. | 0.00609984 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.63263e6 | 0.0899099 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −678369. | −0.0371259 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.63531e6 | 0.524054 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.55511e7 | 1.38110 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.68444e7 | −1.97925 | −0.989625 | − | 0.143674i | \(-0.954108\pi\) | ||||
−0.989625 | + | 0.143674i | \(0.954108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.94791e7 | 1.57384 | 0.786922 | − | 0.617053i | \(-0.211674\pi\) | ||||
0.786922 | + | 0.617053i | \(0.211674\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.03955e7 | 1.08220 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.41223e7 | 1.79947 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.26582e7 | 0.663465 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.76312e6 | −0.0918483 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.59725e7 | −0.827020 | −0.413510 | − | 0.910500i | \(-0.635697\pi\) | ||||
−0.413510 | + | 0.910500i | \(0.635697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.71603e6 | −0.242704 | −0.121352 | − | 0.992610i | \(-0.538723\pi\) | ||||
−0.121352 | + | 0.992610i | \(0.538723\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.36279e7 | −0.697097 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.07195e7 | 0.545016 | 0.272508 | − | 0.962154i | \(-0.412147\pi\) | ||||
0.272508 | + | 0.962154i | \(0.412147\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.14806e7 | 1.59095 | 0.795475 | − | 0.605987i | \(-0.207222\pi\) | ||||
0.795475 | + | 0.605987i | \(0.207222\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.15227e7 | 0.578829 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37930.5 | −0.00189398 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.67630e7 | 2.32106 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.07741e7 | −1.02497 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.69007e6 | −0.328115 | −0.164057 | − | 0.986451i | \(-0.552458\pi\) | ||||
−0.164057 | + | 0.986451i | \(0.552458\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.64683e7 | −0.802893 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.91046e7 | −1.41056 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.11031e7 | −4.38926 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.45730e6 | −0.0697977 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.56462e7 | −0.744970 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.08836e6 | −0.335522 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.91412e7 | −1.37131 | −0.685654 | − | 0.727928i | \(-0.740484\pi\) | ||||
−0.685654 | + | 0.727928i | \(0.740484\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −909621. | −0.0425545 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.11821e7 | −0.985184 | −0.492592 | − | 0.870260i | \(-0.663950\pi\) | ||||
−0.492592 | + | 0.870260i | \(0.663950\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.16226e6 | 0.423662 | 0.211831 | − | 0.977306i | \(-0.432057\pi\) | ||||
0.211831 | + | 0.977306i | \(0.432057\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.02982e7 | −1.39287 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.11789e7 | −1.42506 | −0.712532 | − | 0.701640i | \(-0.752452\pi\) | ||||
−0.712532 | + | 0.701640i | \(0.752452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.25716e7 | 0.571283 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.28357e7 | 1.03173 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.61183e6 | 0.117326 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.81339e7 | 2.14984 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 200786. | 0.00891656 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.88422e7 | 1.71508 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.32059e7 | 1.89690 | 0.948449 | − | 0.316931i | \(-0.102652\pi\) | ||||
0.948449 | + | 0.316931i | \(0.102652\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.13420e7 | −0.931674 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.40150e7 | −1.04242 | −0.521210 | − | 0.853428i | \(-0.674519\pi\) | ||||
−0.521210 | + | 0.853428i | \(0.674519\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.76263e7 | −1.19240 | −0.596200 | − | 0.802836i | \(-0.703323\pi\) | ||||
−0.596200 | + | 0.802836i | \(0.703323\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.44738e6 | −0.233792 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.53944e7 | 0.656984 | 0.328492 | − | 0.944507i | \(-0.393460\pi\) | ||||
0.328492 | + | 0.944507i | \(0.393460\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.20896e7 | −0.513047 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.57616e6 | −0.319709 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.15438e7 | 0.484417 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.93960e7 | −1.64397 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.74797e7 | −0.725357 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.14248e7 | 0.471464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −54042.3 | −0.00221780 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.51485e7 | 1.43445 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.58711e7 | 2.26760 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.15688e7 | −0.466951 | −0.233475 | − | 0.972363i | \(-0.575010\pi\) | ||||
−0.233475 | + | 0.972363i | \(0.575010\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.42548e6 | −0.0572204 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.43936e6 | −0.0973824 | −0.0486912 | − | 0.998814i | \(-0.515505\pi\) | ||||
−0.0486912 | + | 0.998814i | \(0.515505\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.00341e7 | 0.398383 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.63389e7 | 1.82975 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.21329e7 | −1.26191 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.19368e7 | −1.63797 | −0.818986 | − | 0.573814i | \(-0.805463\pi\) | ||||
−0.818986 | + | 0.573814i | \(0.805463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.07309e6 | 0.352457 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.85481e7 | −1.48936 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.16032e7 | −1.98300 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.62767e6 | −0.100432 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.44846e7 | −0.930796 | −0.465398 | − | 0.885101i | \(-0.654089\pi\) | ||||
−0.465398 | + | 0.885101i | \(0.654089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.97788e6 | −0.150410 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.81521e7 | 1.81097 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −66942.6 | −0.00250423 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.50232e7 | 0.559002 | 0.279501 | − | 0.960145i | \(-0.409831\pi\) | ||||
0.279501 | + | 0.960145i | \(0.409831\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.33081e7 | −1.60289 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.07793e7 | −0.764990 | −0.382495 | − | 0.923957i | \(-0.624935\pi\) | ||||
−0.382495 | + | 0.923957i | \(0.624935\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.82050e7 | −0.666672 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.66231e7 | 1.33406 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.09922e7 | 1.48534 | 0.742670 | − | 0.669657i | \(-0.233559\pi\) | ||||
0.742670 | + | 0.669657i | \(0.233559\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.33435e6 | −0.228316 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.08029e7 | −0.387338 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.32155e7 | −0.471359 | −0.235680 | − | 0.971831i | \(-0.575732\pi\) | ||||
−0.235680 | + | 0.971831i | \(0.575732\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.80047e7 | 3.12246 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.91301e6 | 0.138112 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.13197e7 | 1.45081 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.65602e6 | 0.127703 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.06912e6 | −0.0718986 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.95676e6 | −0.102211 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.42092e7 | 0.832557 | 0.416279 | − | 0.909237i | \(-0.363334\pi\) | ||||
0.416279 | + | 0.909237i | \(0.363334\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −50976.2 | −0.00174405 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.87361e7 | −1.65883 | −0.829417 | − | 0.558630i | \(-0.811327\pi\) | ||||
−0.829417 | + | 0.558630i | \(0.811327\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.57700e6 | 0.324300 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.27252e8 | −4.28699 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.53236e6 | 0.285978 | 0.142989 | − | 0.989724i | \(-0.454329\pi\) | ||||
0.142989 | + | 0.989724i | \(0.454329\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.26007e7 | 0.420181 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −740842. | −0.0245784 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.37548e7 | 0.454015 | 0.227008 | − | 0.973893i | \(-0.427106\pi\) | ||||
0.227008 | + | 0.973893i | \(0.427106\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.04184e7 | −0.342145 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.20539e7 | 1.04734 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.11193e7 | 0.686577 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.12861e6 | 0.230580 | 0.115290 | − | 0.993332i | \(-0.463220\pi\) | ||||
0.115290 | + | 0.993332i | \(0.463220\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.94631e6 | −0.320102 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.64169e7 | −0.525694 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.71603e7 | −0.546746 | −0.273373 | − | 0.961908i | \(-0.588139\pi\) | ||||
−0.273373 | + | 0.961908i | \(0.588139\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.69423e7 | −0.854125 |
(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 | 352.6.a.d.1.2 | yes | 6 | |
4.3 | odd | 2 | 352.6.a.b.1.5 | ✓ | 6 | ||
8.3 | odd | 2 | 704.6.a.bc.1.2 | 6 | |||
8.5 | even | 2 | 704.6.a.ba.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
352.6.a.b.1.5 | ✓ | 6 | 4.3 | odd | 2 | ||
352.6.a.d.1.2 | yes | 6 | 1.1 | even | 1 | trivial | |
704.6.a.ba.1.5 | 6 | 8.5 | even | 2 | |||
704.6.a.bc.1.2 | 6 | 8.3 | odd | 2 |