Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,6,Mod(1,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, 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("84.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.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: | \(13.4722408643\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{5569}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1392 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(37.8129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.1 |
$q$-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 | ||||||||
\(5\) | −77.6257 | −1.38861 | −0.694306 | − | 0.719680i | \(-0.744288\pi\) | ||||
−0.694306 | + | 0.719680i | \(0.744288\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −49.0000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 477.380 | 1.18955 | 0.594775 | − | 0.803892i | \(-0.297241\pi\) | ||||
0.594775 | + | 0.803892i | \(0.297241\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −63.7544 | −0.104629 | −0.0523145 | − | 0.998631i | \(-0.516660\pi\) | ||||
−0.0523145 | + | 0.998631i | \(0.516660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 698.632 | 0.801715 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1037.63 | 0.870800 | 0.435400 | − | 0.900237i | \(-0.356607\pi\) | ||||
0.435400 | + | 0.900237i | \(0.356607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −667.018 | −0.423890 | −0.211945 | − | 0.977282i | \(-0.567980\pi\) | ||||
−0.211945 | + | 0.977282i | \(0.567980\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 441.000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3251.63 | 1.28168 | 0.640842 | − | 0.767673i | \(-0.278585\pi\) | ||||
0.640842 | + | 0.767673i | \(0.278585\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2900.75 | 0.928241 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2300.97 | 0.508061 | 0.254031 | − | 0.967196i | \(-0.418244\pi\) | ||||
0.254031 | + | 0.967196i | \(0.418244\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3717.05 | 0.694696 | 0.347348 | − | 0.937736i | \(-0.387082\pi\) | ||||
0.347348 | + | 0.937736i | \(0.387082\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4296.42 | −0.686787 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3803.66 | 0.524846 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12245.9 | 1.47057 | 0.735284 | − | 0.677759i | \(-0.237049\pi\) | ||||
0.735284 | + | 0.677759i | \(0.237049\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 573.790 | 0.0604075 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1829.65 | −0.169984 | −0.0849920 | − | 0.996382i | \(-0.527086\pi\) | ||||
−0.0849920 | + | 0.996382i | \(0.527086\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −20794.2 | −1.71503 | −0.857513 | − | 0.514463i | \(-0.827991\pi\) | ||||
−0.857513 | + | 0.514463i | \(0.827991\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6287.68 | −0.462870 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4283.37 | −0.282840 | −0.141420 | − | 0.989950i | \(-0.545167\pi\) | ||||
−0.141420 | + | 0.989950i | \(0.545167\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9338.63 | −0.502757 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 25718.4 | 1.25764 | 0.628818 | − | 0.777553i | \(-0.283539\pi\) | ||||
0.628818 | + | 0.777553i | \(0.283539\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −37057.0 | −1.65182 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6003.16 | 0.244733 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2838.71 | −0.106167 | −0.0530837 | − | 0.998590i | \(-0.516905\pi\) | ||||
−0.0530837 | + | 0.998590i | \(0.516905\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16803.2 | 0.578186 | 0.289093 | − | 0.957301i | \(-0.406646\pi\) | ||||
0.289093 | + | 0.957301i | \(0.406646\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3969.00 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4948.98 | 0.145289 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −62535.1 | −1.70191 | −0.850955 | − | 0.525238i | \(-0.823976\pi\) | ||||
−0.850955 | + | 0.525238i | \(0.823976\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −29264.6 | −0.739981 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 72301.0 | 1.70215 | 0.851077 | − | 0.525042i | \(-0.175950\pi\) | ||||
0.851077 | + | 0.525042i | \(0.175950\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55676.9 | −1.22283 | −0.611417 | − | 0.791308i | \(-0.709400\pi\) | ||||
−0.611417 | + | 0.791308i | \(0.709400\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −26106.8 | −0.535920 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −23391.6 | −0.449608 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3989.19 | −0.0719146 | −0.0359573 | − | 0.999353i | \(-0.511448\pi\) | ||||
−0.0359573 | + | 0.999353i | \(0.511448\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −46092.2 | −0.734400 | −0.367200 | − | 0.930142i | \(-0.619684\pi\) | ||||
−0.367200 | + | 0.930142i | \(0.619684\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −80546.5 | −1.20920 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −20708.7 | −0.293329 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 135385. | 1.81173 | 0.905867 | − | 0.423562i | \(-0.139220\pi\) | ||||
0.905867 | + | 0.423562i | \(0.139220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3123.97 | 0.0395460 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −33453.5 | −0.401083 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 51777.7 | 0.588619 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 142878. | 1.54183 | 0.770914 | − | 0.636939i | \(-0.219800\pi\) | ||||
0.770914 | + | 0.636939i | \(0.219800\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 38667.8 | 0.396517 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 44467.1 | 0.433746 | 0.216873 | − | 0.976200i | \(-0.430414\pi\) | ||||
0.216873 | + | 0.976200i | \(0.430414\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 202619. | 1.88186 | 0.940931 | − | 0.338598i | \(-0.109953\pi\) | ||||
0.940931 | + | 0.338598i | \(0.109953\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −34232.9 | −0.303020 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 99525.9 | 0.840382 | 0.420191 | − | 0.907436i | \(-0.361963\pi\) | ||||
0.420191 | + | 0.907436i | \(0.361963\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 220930. | 1.78110 | 0.890551 | − | 0.454883i | \(-0.150319\pi\) | ||||
0.890551 | + | 0.454883i | \(0.150319\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −110213. | −0.849033 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 29623.1 | 0.218240 | 0.109120 | − | 0.994029i | \(-0.465197\pi\) | ||||
0.109120 | + | 0.994029i | \(0.465197\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −252410. | −1.77976 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5164.11 | −0.0348763 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −50843.7 | −0.329131 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 66840.8 | 0.415029 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16466.8 | 0.0981403 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 17407.2 | 0.0996448 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −264132. | −1.45315 | −0.726577 | − | 0.687086i | \(-0.758890\pi\) | ||||
−0.726577 | + | 0.687086i | \(0.758890\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 187148. | 0.990170 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −77850.1 | −0.396352 | −0.198176 | − | 0.980166i | \(-0.563502\pi\) | ||||
−0.198176 | + | 0.980166i | \(0.563502\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 32683.9 | 0.160215 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 56589.2 | 0.267238 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 372403. | 1.69516 | 0.847581 | − | 0.530666i | \(-0.178058\pi\) | ||||
0.847581 | + | 0.530666i | \(0.178058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −274550. | −1.20527 | −0.602636 | − | 0.798016i | \(-0.705883\pi\) | ||||
−0.602636 | + | 0.798016i | \(0.705883\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 38550.3 | 0.163298 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −30435.1 | −0.124461 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −178615. | −0.705500 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −21609.0 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −312982. | −1.15492 | −0.577462 | − | 0.816417i | \(-0.695957\pi\) | ||||
−0.577462 | + | 0.816417i | \(0.695957\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 432095. | 1.54219 | 0.771093 | − | 0.636723i | \(-0.219710\pi\) | ||||
0.771093 | + | 0.636723i | \(0.219710\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 84047.7 | 0.290267 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −288539. | −0.964662 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −84603.7 | −0.273930 | −0.136965 | − | 0.990576i | \(-0.543735\pi\) | ||||
−0.136965 | + | 0.990576i | \(0.543735\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −231466. | −0.726096 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −159330. | −0.484431 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 306303. | 0.902989 | 0.451494 | − | 0.892274i | \(-0.350891\pi\) | ||||
0.451494 | + | 0.892274i | \(0.350891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 333513. | 0.953680 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −606514. | −1.68287 | −0.841433 | − | 0.540362i | \(-0.818287\pi\) | ||||
−0.841433 | + | 0.540362i | \(0.818287\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −367228. | −0.989053 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −54028.4 | −0.141297 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −288481. | −0.732828 | −0.366414 | − | 0.930452i | \(-0.619415\pi\) | ||||
−0.366414 | + | 0.930452i | \(0.619415\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −142137. | −0.350842 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25548.4 | 0.0612958 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 148858. | 0.347248 | 0.173624 | − | 0.984812i | \(-0.444452\pi\) | ||||
0.173624 | + | 0.984812i | \(0.444452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 93377.8 | 0.211859 | 0.105930 | − | 0.994374i | \(-0.466218\pi\) | ||||
0.105930 | + | 0.994374i | \(0.466218\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −151229. | −0.333816 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −950594. | −2.04205 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 495342. | 1.03586 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 35721.0 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 246915. | 0.489738 | 0.244869 | − | 0.969556i | \(-0.421255\pi\) | ||||
0.244869 | + | 0.969556i | \(0.421255\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 481437. | 0.930349 | 0.465175 | − | 0.885219i | \(-0.345992\pi\) | ||||
0.465175 | + | 0.885219i | \(0.345992\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −44540.8 | −0.0838826 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −548236. | −1.00647 | −0.503237 | − | 0.864149i | \(-0.667858\pi\) | ||||
−0.503237 | + | 0.864149i | \(0.667858\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 158179. | 0.283150 | 0.141575 | − | 0.989928i | \(-0.454783\pi\) | ||||
0.141575 | + | 0.989928i | \(0.454783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 562816. | 0.982599 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −112748. | −0.192029 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 142028. | 0.236042 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 263382. | 0.427228 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −318421. | −0.504238 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 283510. | 0.438392 | 0.219196 | − | 0.975681i | \(-0.429657\pi\) | ||||
0.219196 | + | 0.975681i | \(0.429657\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −650709. | −0.982739 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.61416e6 | 2.38150 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −182136. | −0.262570 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 501092. | 0.706004 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −66153.2 | −0.0911109 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −651135. | −0.876817 | −0.438409 | − | 0.898776i | \(-0.644458\pi\) | ||||
−0.438409 | + | 0.898776i | \(0.644458\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 234961. | 0.309414 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −378294. | −0.487264 | −0.243632 | − | 0.969868i | \(-0.578339\pi\) | ||||
−0.243632 | + | 0.969868i | \(0.578339\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22332.8 | −0.0281420 | −0.0140710 | − | 0.999901i | \(-0.504479\pi\) | ||||
−0.0140710 | + | 0.999901i | \(0.504479\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 210525. | 0.259581 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −908940. | −1.09685 | −0.548423 | − | 0.836201i | \(-0.684771\pi\) | ||||
−0.548423 | + | 0.836201i | \(0.684771\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 332500. | 0.392755 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 35902.7 | 0.0415199 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.05363e6 | 1.19315 | 0.596573 | − | 0.802559i | \(-0.296529\pi\) | ||||
0.596573 | + | 0.802559i | \(0.296529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.05233e6 | 1.16710 | 0.583550 | − | 0.812077i | \(-0.301663\pi\) | ||||
0.583550 | + | 0.812077i | \(0.301663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −186379. | −0.198373 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 42525.3 | 0.0443512 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 414830. | 0.424006 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 972876. | 0.974705 | 0.487352 | − | 0.873205i | \(-0.337963\pi\) | ||||
0.487352 | + | 0.873205i | \(0.337963\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.55226e6 | 1.52463 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 724918. | 0.698134 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.77948e6 | 1.68058 | 0.840290 | − | 0.542137i | \(-0.182385\pi\) | ||||
0.840290 | + | 0.542137i | \(0.182385\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −600047. | −0.555822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 186379. | 0.169354 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21959.6 | 0.0195765 | 0.00978827 | − | 0.999952i | \(-0.496884\pi\) | ||||
0.00978827 | + | 0.999952i | \(0.496884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.99641e6 | −1.74637 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.21846e6 | −1.04601 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.69111e6 | −1.42492 | −0.712461 | − | 0.701712i | \(-0.752419\pi\) | ||||
−0.712461 | + | 0.701712i | \(0.752419\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −467863. | −0.386986 | −0.193493 | − | 0.981102i | \(-0.561982\pi\) | ||||
−0.193493 | + | 0.981102i | \(0.561982\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −28115.7 | −0.0228319 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.38476e6 | 1.10419 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 906169. | 0.709594 | 0.354797 | − | 0.934943i | \(-0.384550\pi\) | ||||
0.354797 | + | 0.934943i | \(0.384550\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 301081. | 0.231565 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −781388. | −0.590338 | −0.295169 | − | 0.955445i | \(-0.595376\pi\) | ||||
−0.295169 | + | 0.955445i | \(0.595376\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.49843e6 | −1.11217 | −0.556085 | − | 0.831125i | \(-0.687697\pi\) | ||||
−0.556085 | + | 0.831125i | \(0.687697\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −466000. | −0.339839 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 89652.8 | 0.0642479 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −343190. | −0.241707 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.28590e6 | −0.890175 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.56070e6 | −1.06206 | −0.531031 | − | 0.847352i | \(-0.678195\pi\) | ||||
−0.531031 | + | 0.847352i | \(0.678195\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 220357. | 0.147425 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −348010. | −0.228929 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −207305. | −0.134101 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.01891e6 | 0.648219 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −400204. | −0.250423 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.30436e6 | −0.802875 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −889308. | −0.538525 | −0.269263 | − | 0.963067i | \(-0.586780\pi\) | ||||
−0.269263 | + | 0.963067i | \(0.586780\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.82357e6 | −1.08649 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.44826e6 | 1.43535 | 0.717674 | − | 0.696380i | \(-0.245207\pi\) | ||||
0.717674 | + | 0.696380i | \(0.245207\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.73102e6 | −1.57567 | −0.787834 | − | 0.615887i | \(-0.788798\pi\) | ||||
−0.787834 | + | 0.615887i | \(0.788798\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 308097. | 0.174949 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −249603. | −0.139509 | −0.0697545 | − | 0.997564i | \(-0.522222\pi\) | ||||
−0.0697545 | + | 0.997564i | \(0.522222\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.09844e6 | 0.604364 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −895733. | −0.485195 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −692115. | −0.369124 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −184936. | −0.0971209 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.98837e6 | −1.02832 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 209885. | 0.106903 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 646617. | 0.324397 | 0.162199 | − | 0.986758i | \(-0.448142\pi\) | ||||
0.162199 | + | 0.986758i | \(0.448142\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 991915. | 0.490189 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.85433e6 | 2.36329 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.02782e6 | −0.492994 | −0.246497 | − | 0.969144i | \(-0.579280\pi\) | ||||
−0.246497 | + | 0.969144i | \(0.579280\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −266608. | −0.126001 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.77445e6 | 0.826375 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −117649. | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.27169e6 | 1.02755 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.64916e6 | −0.735256 | −0.367628 | − | 0.929973i | \(-0.619830\pi\) | ||||
−0.367628 | + | 0.929973i | \(0.619830\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.21201e6 | 0.972128 | 0.486064 | − | 0.873923i | \(-0.338432\pi\) | ||||
0.486064 | + | 0.873923i | \(0.338432\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 46477.0 | 0.0201358 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.10158e6 | 0.470520 | 0.235260 | − | 0.971932i | \(-0.424406\pi\) | ||||
0.235260 | + | 0.971932i | \(0.424406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.61242e6 | −2.36363 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 457593. | 0.190024 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.29940e6 | −0.532116 | −0.266058 | − | 0.963957i | \(-0.585721\pi\) | ||||
−0.266058 | + | 0.963957i | \(0.585721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.03119e6 | −0.820317 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −601567. | −0.239617 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.32196e6 | 1.69804 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.55669e6 | 0.603305 | 0.301652 | − | 0.953418i | \(-0.402462\pi\) | ||||
0.301652 | + | 0.953418i | \(0.402462\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −148202. | −0.0566614 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.26020e6 | −0.475341 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.12660e6 | −1.16359 | −0.581796 | − | 0.813335i | \(-0.697650\pi\) | ||||
−0.581796 | + | 0.813335i | \(0.697650\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −156665. | −0.0575299 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −146697. | −0.0531579 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.96497e6 | −1.06029 | −0.530143 | − | 0.847908i | \(-0.677862\pi\) | ||||
−0.530143 | + | 0.847908i | \(0.677862\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.37719e6 | 0.838978 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.74774e6 | 0.957149 | 0.478574 | − | 0.878047i | \(-0.341154\pi\) | ||||
0.478574 | + | 0.878047i | \(0.341154\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.81579e6 | 0.624330 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.68433e6 | −0.571675 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −611343. | −0.204838 | −0.102419 | − | 0.994741i | \(-0.532658\pi\) | ||||
−0.102419 | + | 0.994741i | \(0.532658\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.37397e6 | 1.11609 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 700651. | 0.228834 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 309664. | 0.0998615 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.16794e6 | 0.690352 | 0.345176 | − | 0.938538i | \(-0.387819\pi\) | ||||
0.345176 | + | 0.938538i | \(0.387819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −294155. | −0.0925004 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.14644e6 | −0.977143 | −0.488572 | − | 0.872524i | \(-0.662482\pi\) | ||||
−0.488572 | + | 0.872524i | \(0.662482\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −236978. | −0.0726852 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −509302. | −0.154290 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.84593e6 | 1.74931 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.58165e6 | 1.64989 | 0.824943 | − | 0.565215i | \(-0.191207\pi\) | ||||
0.824943 | + | 0.565215i | \(0.191207\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.35162e6 | −0.978703 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 139097. | 0.0401275 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.57794e6 | 1.01980 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.47095e6 | 0.695864 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.25054e6 | 0.626257 | 0.313128 | − | 0.949711i | \(-0.398623\pi\) | ||||
0.313128 | + | 0.949711i | \(0.398623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.45914e6 | 0.951180 | 0.475590 | − | 0.879667i | \(-0.342235\pi\) | ||||
0.475590 | + | 0.879667i | \(0.342235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −346953. | −0.0942800 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00990e6 | 0.808313 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −823356. | −0.218534 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 273916. | 0.0718578 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.55926e6 | −1.70083 | −0.850417 | − | 0.526109i | \(-0.823650\pi\) | ||||
−0.850417 | + | 0.526109i | \(0.823650\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.05669e6 | 1.29612 | 0.648062 | − | 0.761587i | \(-0.275580\pi\) | ||||
0.648062 | + | 0.761587i | \(0.275580\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.60753e6 | 0.407320 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.16889e6 | −0.543293 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.23225e6 | 1.04812 | 0.524059 | − | 0.851682i | \(-0.324417\pi\) | ||||
0.524059 | + | 0.851682i | \(0.324417\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 194481. | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.05525e6 | −1.46596 | −0.732981 | − | 0.680249i | \(-0.761872\pi\) | ||||
−0.732981 | + | 0.680249i | \(0.761872\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.05093e7 | −2.51579 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.81684e6 | 0.666796 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −299186. | −0.0700368 | −0.0350184 | − | 0.999387i | \(-0.511149\pi\) | ||||
−0.0350184 | + | 0.999387i | \(0.511149\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −873438. | −0.202204 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.88885e6 | −0.890381 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −242500. | −0.0549140 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.75177e6 | 0.840322 | 0.420161 | − | 0.907450i | \(-0.361974\pi\) | ||||
0.420161 | + | 0.907450i | \(0.361974\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −756429. | −0.167586 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.94525e6 | 1.52207 | 0.761036 | − | 0.648709i | \(-0.224691\pi\) | ||||
0.761036 | + | 0.648709i | \(0.224691\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.13226e6 | −1.97982 | −0.989910 | − | 0.141697i | \(-0.954744\pi\) | ||||
−0.989910 | + | 0.141697i | \(0.954744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.59685e6 | 0.556948 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −424136. | −0.0899940 | −0.0449970 | − | 0.998987i | \(-0.514328\pi\) | ||||
−0.0449970 | + | 0.998987i | \(0.514328\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.06422e6 | 0.643262 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 761433. | 0.158154 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.92673e6 | −2.04011 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.93485e6 | −0.393472 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.08319e6 | 0.419212 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.78605e6 | −1.55052 | −0.775262 | − | 0.631640i | \(-0.782382\pi\) | ||||
−0.775262 | + | 0.631640i | \(0.782382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −780727. | −0.153864 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.43397e6 | 0.279686 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.10910e7 | −2.14100 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.32259e6 | 0.443763 | 0.221881 | − | 0.975074i | \(-0.428780\pi\) | ||||
0.221881 | + | 0.975074i | \(0.428780\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.75673e6 | −0.521341 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.01036e6 | 1.12512 | 0.562558 | − | 0.826758i | \(-0.309817\pi\) | ||||
0.562558 | + | 0.826758i | \(0.309817\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.38755e6 | 0.442420 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.00162e6 | −0.550607 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.54275e6 | −0.643353 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.37385e6 | 0.606562 | 0.303281 | − | 0.952901i | \(-0.401918\pi\) | ||||
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.45862e6 | 0.971603 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.22068e6 | −0.215120 | −0.107560 | − | 0.994199i | \(-0.534304\pi\) | ||||
−0.107560 | + | 0.994199i | \(0.534304\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.45179e6 | −0.602304 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.30506e6 | 0.571030 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.56897e6 | 0.268423 | 0.134212 | − | 0.990953i | \(-0.457150\pi\) | ||||
0.134212 | + | 0.990953i | \(0.457150\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.72817e6 | 0.462188 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 486256. | 0.0815777 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.57285e7 | −2.61318 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.04480e6 | −0.336452 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.59633e6 | 0.423098 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.06779e7 | 1.72342 | 0.861708 | − | 0.507404i | \(-0.169395\pi\) | ||||
0.861708 | + | 0.507404i | \(0.169395\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.21007e7 | −1.93444 | −0.967219 | − | 0.253943i | \(-0.918272\pi\) | ||||
−0.967219 | + | 0.253943i | \(0.918272\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.27923e6 | 0.202559 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.85691e6 | 0.604941 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.13673e6 | 0.642714 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −229936. | −0.0353892 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 116648. | 0.0177852 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.72577e6 | −1.16696 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.33972e6 | −0.200484 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.14619e6 | 0.169936 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.19805e6 | −0.469778 | −0.234889 | − | 0.972022i | \(-0.575473\pi\) | ||||
−0.234889 | + | 0.972022i | \(0.575473\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −840400. | −0.122317 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.71499e7 | −2.47326 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.97811e6 | 0.568471 | 0.284235 | − | 0.958755i | \(-0.408260\pi\) | ||||
0.284235 | + | 0.958755i | \(0.408260\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.36106e6 | 0.192729 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.53479e6 | −0.215362 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 195470. | 0.0271812 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.55534e6 | 1.17898 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.14113e7 | 1.55847 | 0.779236 | − | 0.626731i | \(-0.215608\pi\) | ||||
0.779236 | + | 0.626731i | \(0.215608\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.32572e6 | 0.179441 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.45808e6 | −0.598054 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.46973e6 | −0.860231 | −0.430115 | − | 0.902774i | \(-0.641527\pi\) | ||||
−0.430115 | + | 0.902774i | \(0.641527\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.29952e6 | −0.303051 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −321489. | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 717028. | 0.0928444 | 0.0464222 | − | 0.998922i | \(-0.485218\pi\) | ||||
0.0464222 | + | 0.998922i | \(0.485218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.00286e6 | 0.770491 | 0.385246 | − | 0.922814i | \(-0.374117\pi\) | ||||
0.385246 | + | 0.922814i | \(0.374117\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.22223e6 | −0.282750 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.43217e6 | 1.18971 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.55712e7 | 1.94707 | 0.973537 | − | 0.228531i | \(-0.0733922\pi\) | ||||
0.973537 | + | 0.228531i | \(0.0733922\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.33293e6 | −0.537137 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.25852e6 | 0.277577 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.22775e7 | 1.49602 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 400868. | 0.0484296 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.84621e6 | 0.939863 | 0.469931 | − | 0.882703i | \(-0.344279\pi\) | ||||
0.469931 | + | 0.882703i | \(0.344279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.47934e6 | −0.294475 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.93413e6 | 0.581088 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.33248e7 | 1.55605 | 0.778026 | − | 0.628232i | \(-0.216221\pi\) | ||||
0.778026 | + | 0.628232i | \(0.216221\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.94678e6 | 0.457036 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.42361e6 | −0.163477 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.77916e6 | −0.885861 | −0.442930 | − | 0.896556i | \(-0.646061\pi\) | ||||
−0.442930 | + | 0.896556i | \(0.646061\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.62898e6 | 0.974480 | 0.487240 | − | 0.873268i | \(-0.338004\pi\) | ||||
0.487240 | + | 0.873268i | \(0.338004\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.06534e6 | −0.567304 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.18857e6 | −0.576314 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.09353e6 | −0.781431 | −0.390715 | − | 0.920512i | \(-0.627772\pi\) | ||||
−0.390715 | + | 0.920512i | \(0.627772\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.01473e6 | 0.110868 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 273084. | 0.0295932 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.52640e6 | 0.486521 | 0.243261 | − | 0.969961i | \(-0.421783\pi\) | ||||
0.243261 | + | 0.969961i | \(0.421783\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.27825e6 | −0.136279 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.38009e6 | −0.886208 | −0.443104 | − | 0.896470i | \(-0.646123\pi\) | ||||
−0.443104 | + | 0.896470i | \(0.646123\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −168342. | −0.0176590 | −0.00882949 | − | 0.999961i | \(-0.502811\pi\) | ||||
−0.00882949 | + | 0.999961i | \(0.502811\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.37044e6 | −0.246660 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −6.63385e6 | −0.684771 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.04161e7 | −1.06661 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.86579e6 | 0.291122 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.27066e7 | 1.28057 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.66208e7 | 1.66180 | 0.830899 | − | 0.556423i | \(-0.187826\pi\) | ||||
0.830899 | + | 0.556423i | \(0.187826\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.55159e6 | −0.253106 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.05034e7 | 2.01786 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −153074. | −0.0149470 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.85638e6 | 0.567384 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.02473e6 | 0.0985068 | 0.0492534 | − | 0.998786i | \(-0.484316\pi\) | ||||
0.0492534 | + | 0.998786i | \(0.484316\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.22962e7 | −1.17286 | −0.586428 | − | 0.810001i | \(-0.699466\pi\) | ||||
−0.586428 | + | 0.810001i | \(0.699466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.45275e7 | −1.37496 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.16537e6 | −0.203363 | −0.101682 | − | 0.994817i | \(-0.532422\pi\) | ||||
−0.101682 | + | 0.994817i | \(0.532422\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.35515e6 | −0.126292 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.63922e6 | 0.151595 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.22501e7 | −1.12424 | −0.562119 | − | 0.827056i | \(-0.690014\pi\) | ||||
−0.562119 | + | 0.827056i | \(0.690014\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.04317e6 | 0.550379 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.50983e6 | −0.407612 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.18607e6 | 0.106389 | 0.0531944 | − | 0.998584i | \(-0.483060\pi\) | ||||
0.0531944 | + | 0.998584i | \(0.483060\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.45382e7 | −1.29421 | −0.647107 | − | 0.762399i | \(-0.724021\pi\) | ||||
−0.647107 | + | 0.762399i | \(0.724021\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 595379. | 0.0526029 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.53711e6 | −0.222477 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.48190e6 | 0.651174 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.86022e6 | 0.506231 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.02151e6 | 0.687781 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.99405e6 | −0.510132 | −0.255066 | − | 0.966924i | \(-0.582097\pi\) | ||||
−0.255066 | + | 0.966924i | \(0.582097\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.11465e6 | −0.178640 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.08389e7 | 1.74744 | 0.873721 | − | 0.486428i | \(-0.161700\pi\) | ||||
0.873721 | + | 0.486428i | \(0.161700\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.00102e6 | −0.582756 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.40464e6 | 0.281322 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.55565e6 | 0.373679 | 0.186840 | − | 0.982390i | \(-0.440176\pi\) | ||||
0.186840 | + | 0.982390i | \(0.440176\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.89080e7 | −2.35392 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 200995. | 0.0162478 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.63966e6 | −0.131585 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.68542e6 | 0.134281 | 0.0671404 | − | 0.997744i | \(-0.478612\pi\) | ||||
0.0671404 | + | 0.997744i | \(0.478612\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.89472e6 | −0.149869 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.13122e7 | 1.67365 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.89849e6 | −0.148022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.18046e6 | 0.633264 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.45349e6 | 0.188577 | 0.0942887 | − | 0.995545i | \(-0.469942\pi\) | ||||
0.0942887 | + | 0.995545i | \(0.469942\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.16820e6 | −0.623359 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.99250e6 | −0.226757 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.17889e6 | −0.163940 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.32314e7 | −0.988530 | −0.494265 | − | 0.869311i | \(-0.664563\pi\) | ||||
−0.494265 | + | 0.869311i | \(0.664563\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −323125. | −0.0239715 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.20865e7 | 0.890380 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.36255e6 | 0.172828 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.48267e6 | −0.688863 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.35337e7 | 0.976324 | 0.488162 | − | 0.872753i | \(-0.337667\pi\) | ||||
0.488162 | + | 0.872753i | \(0.337667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.92835e6 | −0.711277 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.47094e6 | −0.673826 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.67455e6 | 0.471604 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.29416e6 | 0.371502 | 0.185751 | − | 0.982597i | \(-0.440528\pi\) | ||||
0.185751 | + | 0.982597i | \(0.440528\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.15766e7 | −1.49344 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.25014e7 | −1.54685 | −0.773426 | − | 0.633886i | \(-0.781459\pi\) | ||||
−0.773426 | + | 0.633886i | \(0.781459\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.67741e6 | 0.114531 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.98530e7 | −2.02451 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.60739e7 | 1.08271 | 0.541353 | − | 0.840795i | \(-0.317912\pi\) | ||||
0.541353 | + | 0.840795i | \(0.317912\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −382728. | −0.0256062 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.31604e6 | −0.153913 | −0.0769563 | − | 0.997034i | \(-0.524520\pi\) | ||||
−0.0769563 | + | 0.997034i | \(0.524520\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.42955e7 | 1.60374 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.73347e6 | −0.244800 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.87677e6 | −0.317634 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.77263e6 | −0.502885 | −0.251442 | − | 0.967872i | \(-0.580905\pi\) | ||||
−0.251442 | + | 0.967872i | \(0.580905\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.75588e6 | −0.562746 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.35417e7 | −2.14150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.59716e7 | −1.01300 | −0.506498 | − | 0.862241i | \(-0.669060\pi\) | ||||
−0.506498 | + | 0.862241i | \(0.669060\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.39704e7 | −0.880244 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.84940e7 | 1.15763 | 0.578815 | − | 0.815459i | \(-0.303515\pi\) | ||||
0.578815 | + | 0.815459i | \(0.303515\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.08256e7 | −0.673193 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.52426e6 | −0.403068 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 180980. | 0.0111082 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.33524e7 | −1.42402 | −0.712009 | − | 0.702170i | \(-0.752214\pi\) | ||||
−0.712009 | + | 0.702170i | \(0.752214\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.60153e7 | −0.970283 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.25262e6 | 0.436562 | 0.218281 | − | 0.975886i | \(-0.429955\pi\) | ||||
0.218281 | + | 0.975886i | \(0.429955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.07823e7 | 0.644845 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.40042e6 | 0.320904 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.22041e6 | 0.0720546 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.45151e7 | 2.02480 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.67741e6 | −0.0977764 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.56742e6 | 0.380383 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.18935e6 | 0.0684497 | 0.0342248 | − | 0.999414i | \(-0.489104\pi\) | ||||
0.0342248 | + | 0.999414i | \(0.489104\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −197637. | −0.0113025 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.45153e6 | −0.0824871 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.07128e6 | −0.0604949 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.79677e7 | 1.00827 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.14041e7 | 1.19358 | 0.596790 | − | 0.802397i | \(-0.296442\pi\) | ||||
0.596790 | + | 0.802397i | \(0.296442\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.44453e6 | −0.246297 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.09662e7 | 0.603911 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.65790e7 | −1.45462 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.23681e7 | 0.672686 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.52200e7 | 0.822679 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.60341e6 | 0.515886 | 0.257943 | − | 0.966160i | \(-0.416955\pi\) | ||||
0.257943 | + | 0.966160i | \(0.416955\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.62263e7 | 1.40018 | 0.700091 | − | 0.714054i | \(-0.253143\pi\) | ||||
0.700091 | + | 0.714054i | \(0.253143\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.21077e6 | 0.223427 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.37770e7 | −1.25390 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.38701e7 | 0.726982 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 253041. | 0.0131820 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.65685e7 | 1.89343 | 0.946715 | − | 0.322073i | \(-0.104380\pi\) | ||||
0.946715 | + | 0.322073i | \(0.104380\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.73488e6 | −0.398065 | −0.199032 | − | 0.979993i | \(-0.563780\pi\) | ||||
−0.199032 | + | 0.979993i | \(0.563780\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.24629e7 | −0.637504 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.47172e7 | −0.748277 | −0.374138 | − | 0.927373i | \(-0.622061\pi\) | ||||
−0.374138 | + | 0.927373i | \(0.622061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.41886e6 | −0.374931 | −0.187465 | − | 0.982271i | \(-0.560027\pi\) | ||||
−0.187465 | + | 0.982271i | \(0.560027\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.15552e6 | −0.409684 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.49134e6 | 0.124400 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.70811e7 | 2.33685 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.70973e6 | −0.133694 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 116538. | 0.00571559 | 0.00285780 | − | 0.999996i | \(-0.499090\pi\) | ||||
0.00285780 | + | 0.999996i | \(0.499090\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.52167e7 | −0.741874 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.03249e6 | 0.340832 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.85064e7 | 1.37341 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.27520e6 | −0.156866 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.34859e7 | 0.642112 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.98190e7 | 1.88480 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.91763e7 | −0.902387 | −0.451193 | − | 0.892426i | \(-0.649002\pi\) | ||||
−0.451193 | + | 0.892426i | \(0.649002\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.19400e6 | 0.196206 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.62548e6 | −0.0756012 | −0.0378006 | − | 0.999285i | \(-0.512035\pi\) | ||||
−0.0378006 | + | 0.999285i | \(0.512035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.65931e7 | −0.767265 | −0.383632 | − | 0.923486i | \(-0.625327\pi\) | ||||
−0.383632 | + | 0.923486i | \(0.625327\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −806875. | −0.0370936 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.30415e7 | −1.05314 | −0.526568 | − | 0.850133i | \(-0.676521\pi\) | ||||
−0.526568 | + | 0.850133i | \(0.676521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.23935e7 | 1.01761 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.08871e6 | 0.139550 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.90436e6 | −0.0855460 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.98689e6 | 0.178069 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.15731e7 | 0.513943 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −852954. | −0.0376622 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.84493e7 | 0.809993 | 0.404996 | − | 0.914318i | \(-0.367273\pi\) | ||||
0.404996 | + | 0.914318i | \(0.367273\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.40463e7 | 0.613182 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.70548e7 | −1.60844 | −0.804219 | − | 0.594333i | \(-0.797416\pi\) | ||||
−0.804219 | + | 0.594333i | \(0.797416\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5.28466e6 | −0.228095 | −0.114047 | − | 0.993475i | \(-0.536382\pi\) | ||||
−0.114047 | + | 0.993475i | \(0.536382\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.98321e6 | −0.0851161 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.98545e7 | −0.847326 | −0.423663 | − | 0.905820i | \(-0.639256\pi\) | ||||
−0.423663 | + | 0.905820i | \(0.639256\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.29425e7 | 0.549240 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.13209e6 | 0.132172 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.85708e6 | 0.119893 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.15552e7 | −0.482193 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.86575e6 | 0.0774234 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.55283e6 | 0.352948 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.66861e7 | 1.09515 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.17023e6 | −0.374249 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.24852e6 | −0.294190 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.00483e7 | −0.809207 | −0.404603 | − | 0.914492i | \(-0.632590\pi\) | ||||
−0.404603 | + | 0.914492i | \(0.632590\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.60183e6 | 0.144582 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −765753. | −0.0305698 | −0.0152849 | − | 0.999883i | \(-0.504866\pi\) | ||||
−0.0152849 | + | 0.999883i | \(0.504866\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.20035e7 | −0.873605 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.17392e7 | 0.463540 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.81465e6 | 0.149807 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.87846e7 | −0.733692 | −0.366846 | − | 0.930282i | \(-0.619562\pi\) | ||||
−0.366846 | + | 0.930282i | \(0.619562\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.00377e6 | 0.310918 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.60951e6 | −0.178094 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.55222e7 | 1.36504 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.64122e7 | 0.627288 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.56290e7 | −1.73461 | −0.867304 | − | 0.497778i | \(-0.834149\pi\) | ||||
−0.867304 | + | 0.497778i | \(0.834149\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.60151e6 | −0.0605557 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.20344e7 | −0.828698 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.84513e7 | −1.43841 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.67800e6 | 0.248484 | 0.124242 | − | 0.992252i | \(-0.460350\pi\) | ||||
0.124242 | + | 0.992252i | \(0.460350\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.45792e7 | 0.909713 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.42716e7 | 1.26171 | 0.630857 | − | 0.775899i | \(-0.282703\pi\) | ||||
0.630857 | + | 0.775899i | \(0.282703\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.94933e6 | −0.217866 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.77287e6 | −0.101007 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.28766e7 | 1.91597 | 0.957984 | − | 0.286821i | \(-0.0925984\pi\) | ||||
0.957984 | + | 0.286821i | \(0.0925984\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.54965e6 | 0.127944 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.24643e6 | 0.0805455 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.33439e6 | 0.190262 | 0.0951311 | − | 0.995465i | \(-0.469673\pi\) | ||||
0.0951311 | + | 0.995465i | \(0.469673\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.91669e7 | −0.680056 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.88594e6 | −0.348930 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.82477e7 | −0.640711 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.48127e7 | −0.517398 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.06160e6 | 0.280127 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.73719e7 | −1.29189 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.93877e7 | −0.666744 | −0.333372 | − | 0.942795i | \(-0.608187\pi\) | ||||
−0.333372 | + | 0.942795i | \(0.608187\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.22903e6 | 0.213114 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.07463e7 | 0.365772 | 0.182886 | − | 0.983134i | \(-0.441456\pi\) | ||||
0.182886 | + | 0.983134i | \(0.441456\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.34530e7 | 0.455550 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.66442e6 | 0.0560728 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.41051e7 | −0.807926 | −0.403963 | − | 0.914775i | \(-0.632368\pi\) | ||||
−0.403963 | + | 0.914775i | \(0.632368\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.46300e7 | 2.15515 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.78953e7 | 0.593701 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.05038e7 | −1.33694 | −0.668470 | − | 0.743739i | \(-0.733050\pi\) | ||||
−0.668470 | + | 0.743739i | \(0.733050\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.25573e7 | 1.39760 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.88897e6 | −0.0617207 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.76149e7 | −2.19812 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.01588e7 | −1.29896 | −0.649482 | − | 0.760377i | \(-0.725014\pi\) | ||||
−0.649482 | + | 0.760377i | \(0.725014\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.81955e6 | −0.187291 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.22788e7 | −0.393185 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.72276e7 | −0.867505 | −0.433753 | − | 0.901032i | \(-0.642811\pi\) | ||||
−0.433753 | + | 0.901032i | \(0.642811\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.92723e6 | −0.283011 |
(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 | 84.6.a.c.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 252.6.a.h.1.2 | 2 | |||
4.3 | odd | 2 | 336.6.a.x.1.1 | 2 | |||
7.2 | even | 3 | 588.6.i.l.361.2 | 4 | |||
7.3 | odd | 6 | 588.6.i.i.373.1 | 4 | |||
7.4 | even | 3 | 588.6.i.l.373.2 | 4 | |||
7.5 | odd | 6 | 588.6.i.i.361.1 | 4 | |||
7.6 | odd | 2 | 588.6.a.k.1.2 | 2 | |||
12.11 | even | 2 | 1008.6.a.bo.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.6.a.c.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
252.6.a.h.1.2 | 2 | 3.2 | odd | 2 | |||
336.6.a.x.1.1 | 2 | 4.3 | odd | 2 | |||
588.6.a.k.1.2 | 2 | 7.6 | odd | 2 | |||
588.6.i.i.361.1 | 4 | 7.5 | odd | 6 | |||
588.6.i.i.373.1 | 4 | 7.3 | odd | 6 | |||
588.6.i.l.361.2 | 4 | 7.2 | even | 3 | |||
588.6.i.l.373.2 | 4 | 7.4 | even | 3 | |||
1008.6.a.bo.1.2 | 2 | 12.11 | even | 2 |