Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(1,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, 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("320.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.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: | \(51.3228223402\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{129}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 32 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.17891\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.1 |
$q$-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 | ||||||||
\(3\) | −16.7156 | −1.07231 | −0.536154 | − | 0.844120i | \(-0.680123\pi\) | ||||
−0.536154 | + | 0.844120i | \(0.680123\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 94.1469 | 0.726208 | 0.363104 | − | 0.931749i | \(-0.381717\pi\) | ||||
0.363104 | + | 0.931749i | \(0.381717\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 36.4124 | 0.149845 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −143.706 | −0.358091 | −0.179046 | − | 0.983841i | \(-0.557301\pi\) | ||||
−0.179046 | + | 0.983841i | \(0.557301\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −421.412 | −0.691590 | −0.345795 | − | 0.938310i | \(-0.612391\pi\) | ||||
−0.345795 | + | 0.938310i | \(0.612391\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 417.891 | 0.479551 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1982.11 | 1.66344 | 0.831718 | − | 0.555198i | \(-0.187358\pi\) | ||||
0.831718 | + | 0.555198i | \(0.187358\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1317.76 | 0.837439 | 0.418720 | − | 0.908116i | \(-0.362479\pi\) | ||||
0.418720 | + | 0.908116i | \(0.362479\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1573.73 | −0.778719 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4020.02 | −1.58456 | −0.792280 | − | 0.610157i | \(-0.791106\pi\) | ||||
−0.792280 | + | 0.610157i | \(0.791106\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3453.24 | 0.911628 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6417.28 | 1.41695 | 0.708477 | − | 0.705734i | \(-0.249383\pi\) | ||||
0.708477 | + | 0.705734i | \(0.249383\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2350.64 | −0.439322 | −0.219661 | − | 0.975576i | \(-0.570495\pi\) | ||||
−0.219661 | + | 0.975576i | \(0.570495\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2402.14 | 0.383984 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2353.67 | −0.324770 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7876.58 | 0.945874 | 0.472937 | − | 0.881096i | \(-0.343194\pi\) | ||||
0.472937 | + | 0.881096i | \(0.343194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7044.18 | 0.741598 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15081.6 | 1.40116 | 0.700582 | − | 0.713572i | \(-0.252924\pi\) | ||||
0.700582 | + | 0.713572i | \(0.252924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1141.40 | −0.0941384 | −0.0470692 | − | 0.998892i | \(-0.514988\pi\) | ||||
−0.0470692 | + | 0.998892i | \(0.514988\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −910.310 | −0.0670128 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −21557.3 | −1.42348 | −0.711738 | − | 0.702445i | \(-0.752092\pi\) | ||||
−0.711738 | + | 0.702445i | \(0.752092\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7943.36 | −0.472622 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −33132.3 | −1.78372 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9560.44 | −0.467507 | −0.233754 | − | 0.972296i | \(-0.575101\pi\) | ||||
−0.233754 | + | 0.972296i | \(0.575101\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3592.65 | 0.160143 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −22027.2 | −0.897993 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −42740.7 | −1.59850 | −0.799248 | − | 0.601002i | \(-0.794768\pi\) | ||||
−0.799248 | + | 0.601002i | \(0.794768\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −32132.1 | −1.10564 | −0.552820 | − | 0.833301i | \(-0.686448\pi\) | ||||
−0.552820 | + | 0.833301i | \(0.686448\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3428.11 | 0.108819 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10535.3 | 0.309289 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30371.4 | 0.826567 | 0.413283 | − | 0.910602i | \(-0.364382\pi\) | ||||
0.413283 | + | 0.910602i | \(0.364382\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 67197.2 | 1.69914 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36006.7 | 0.847692 | 0.423846 | − | 0.905734i | \(-0.360680\pi\) | ||||
0.423846 | + | 0.905734i | \(0.360680\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −63438.0 | −1.39329 | −0.696647 | − | 0.717414i | \(-0.745326\pi\) | ||||
−0.696647 | + | 0.717414i | \(0.745326\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10447.3 | −0.214462 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13529.5 | −0.260049 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −89922.8 | −1.62107 | −0.810536 | − | 0.585689i | \(-0.800824\pi\) | ||||
−0.810536 | + | 0.585689i | \(0.800824\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −66571.4 | −1.12739 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −38211.2 | −0.608829 | −0.304414 | − | 0.952540i | \(-0.598461\pi\) | ||||
−0.304414 | + | 0.952540i | \(0.598461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −49552.8 | −0.743911 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −107269. | −1.51941 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5745.69 | 0.0768895 | 0.0384447 | − | 0.999261i | \(-0.487760\pi\) | ||||
0.0384447 | + | 0.999261i | \(0.487760\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −39674.7 | −0.502238 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 39292.5 | 0.471088 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −32944.1 | −0.374514 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 178780. | 1.92926 | 0.964629 | − | 0.263613i | \(-0.0849140\pi\) | ||||
0.964629 | + | 0.263613i | \(0.0849140\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5232.69 | −0.0536583 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −152223. | −1.48483 | −0.742417 | − | 0.669938i | \(-0.766321\pi\) | ||||
−0.742417 | + | 0.669938i | \(0.766321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −35830.1 | −0.332778 | −0.166389 | − | 0.986060i | \(-0.553211\pi\) | ||||
−0.166389 | + | 0.986060i | \(0.553211\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 39343.1 | 0.348254 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −70030.2 | −0.591324 | −0.295662 | − | 0.955293i | \(-0.595540\pi\) | ||||
−0.295662 | + | 0.955293i | \(0.595540\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −38466.9 | −0.310114 | −0.155057 | − | 0.987906i | \(-0.549556\pi\) | ||||
−0.155057 | + | 0.987906i | \(0.549556\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −131662. | −1.01427 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 39951.6 | 0.294333 | 0.147166 | − | 0.989112i | \(-0.452985\pi\) | ||||
0.147166 | + | 0.989112i | \(0.452985\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 100501. | 0.708637 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15344.6 | −0.103632 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 186610. | 1.20800 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −140400. | −0.871771 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −252099. | −1.50248 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −233239. | −1.28319 | −0.641596 | − | 0.767043i | \(-0.721727\pi\) | ||||
−0.641596 | + | 0.767043i | \(0.721727\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 19079.2 | 0.100945 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −55237.0 | −0.281224 | −0.140612 | − | 0.990065i | \(-0.544907\pi\) | ||||
−0.140612 | + | 0.990065i | \(0.544907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 124063. | 0.608155 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −86331.1 | −0.407692 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 261520. | 1.19043 | 0.595215 | − | 0.803566i | \(-0.297067\pi\) | ||||
0.595215 | + | 0.803566i | \(0.297067\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −293366. | −1.28787 | −0.643935 | − | 0.765080i | \(-0.722699\pi\) | ||||
−0.643935 | + | 0.765080i | \(0.722699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 360345. | 1.52641 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 60559.6 | 0.247653 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −160432. | −0.633681 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 132778. | 0.506797 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 304505. | 1.12364 | 0.561822 | − | 0.827258i | \(-0.310101\pi\) | ||||
0.561822 | + | 0.827258i | \(0.310101\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −337909. | −1.20603 | −0.603015 | − | 0.797730i | \(-0.706034\pi\) | ||||
−0.603015 | + | 0.797730i | \(0.706034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 72173.5 | 0.249258 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 58766.1 | 0.196471 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −68385.9 | −0.221420 | −0.110710 | − | 0.993853i | \(-0.535313\pi\) | ||||
−0.110710 | + | 0.993853i | \(0.535313\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 159809. | 0.501312 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −378473. | −1.15072 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 404471. | 1.19239 | 0.596195 | − | 0.802840i | \(-0.296678\pi\) | ||||
0.596195 | + | 0.802840i | \(0.296678\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −60053.5 | −0.171723 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 411733. | 1.14242 | 0.571209 | − | 0.820805i | \(-0.306475\pi\) | ||||
0.571209 | + | 0.820805i | \(0.306475\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −193705. | −0.521703 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 47982.9 | 0.125486 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 162247. | 0.412155 | 0.206077 | − | 0.978536i | \(-0.433930\pi\) | ||||
0.206077 | + | 0.978536i | \(0.433930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 58841.8 | 0.145242 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 714438. | 1.71408 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −384396. | −0.896698 | −0.448349 | − | 0.893859i | \(-0.647988\pi\) | ||||
−0.448349 | + | 0.893859i | \(0.647988\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −579219. | −1.31415 | −0.657077 | − | 0.753823i | \(-0.728208\pi\) | ||||
−0.657077 | + | 0.753823i | \(0.728208\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 537108. | 1.18559 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −196914. | −0.423008 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −284842. | −0.595662 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 325112. | 0.662031 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 142455. | 0.282550 | 0.141275 | − | 0.989970i | \(-0.454880\pi\) | ||||
0.141275 | + | 0.989970i | \(0.454880\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 267272. | 0.516487 | 0.258244 | − | 0.966080i | \(-0.416856\pi\) | ||||
0.258244 | + | 0.966080i | \(0.416856\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −176104. | −0.331653 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −14189.5 | −0.0260496 | −0.0130248 | − | 0.999915i | \(-0.504146\pi\) | ||||
−0.0130248 | + | 0.999915i | \(0.504146\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 169198. | 0.302875 | 0.151437 | − | 0.988467i | \(-0.451610\pi\) | ||||
0.151437 | + | 0.988467i | \(0.451610\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −507677. | −0.886335 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 604167. | 1.02900 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −377041. | −0.626619 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −146379. | −0.237439 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −189371. | −0.299880 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 407591. | 0.630259 | 0.315129 | − | 0.949049i | \(-0.397952\pi\) | ||||
0.315129 | + | 0.949049i | \(0.397952\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −601875. | −0.908987 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 28535.0 | 0.0421000 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −221306. | −0.319039 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.06041e6 | 1.49404 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −835287. | −1.15042 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −103743. | −0.139700 | −0.0698500 | − | 0.997558i | \(-0.522252\pi\) | ||||
−0.0698500 | + | 0.997558i | \(0.522252\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 22757.7 | 0.0299691 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 803726. | 1.03524 | 0.517622 | − | 0.855609i | \(-0.326817\pi\) | ||||
0.517622 | + | 0.855609i | \(0.326817\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.35955e6 | −1.71319 | −0.856596 | − | 0.515988i | \(-0.827425\pi\) | ||||
−0.856596 | + | 0.515988i | \(0.827425\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 226154. | 0.278852 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −622827. | −0.751584 | −0.375792 | − | 0.926704i | \(-0.622629\pi\) | ||||
−0.375792 | + | 0.926704i | \(0.622629\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 538933. | 0.636598 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.50312e6 | 1.73829 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −642843. | −0.727964 | −0.363982 | − | 0.931406i | \(-0.618583\pi\) | ||||
−0.363982 | + | 0.931406i | \(0.618583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.11814e6 | 1.24009 | 0.620046 | − | 0.784566i | \(-0.287114\pi\) | ||||
0.620046 | + | 0.784566i | \(0.287114\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 273644. | 0.297283 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 198584. | 0.211363 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −555322. | −0.579165 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 638724. | 0.652852 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −731067. | −0.732442 | −0.366221 | − | 0.930528i | \(-0.619349\pi\) | ||||
−0.366221 | + | 0.930528i | \(0.619349\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 577702. | 0.567418 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 828307. | 0.797702 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.76622e6 | −1.66806 | −0.834030 | − | 0.551720i | \(-0.813972\pi\) | ||||
−0.834030 | + | 0.551720i | \(0.813972\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 741555. | 0.686901 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 233668. | 0.212324 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.00926e6 | 0.899735 | 0.449868 | − | 0.893095i | \(-0.351471\pi\) | ||||
0.449868 | + | 0.893095i | \(0.351471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 239011. | 0.209076 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −96042.8 | −0.0824492 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 775681. | 0.653585 | 0.326793 | − | 0.945096i | \(-0.394032\pi\) | ||||
0.326793 | + | 0.945096i | \(0.394032\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.21395e6 | 1.00410 | 0.502052 | − | 0.864837i | \(-0.332578\pi\) | ||||
0.502052 | + | 0.864837i | \(0.332578\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 663187. | 0.538554 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −89816.4 | −0.0716183 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 218505. | 0.171104 | 0.0855522 | − | 0.996334i | \(-0.472735\pi\) | ||||
0.0855522 | + | 0.996334i | \(0.472735\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −85592.6 | −0.0658303 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −316219. | −0.238903 | −0.119452 | − | 0.992840i | \(-0.538114\pi\) | ||||
−0.119452 | + | 0.992840i | \(0.538114\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 927934. | 0.688733 | 0.344366 | − | 0.938835i | \(-0.388094\pi\) | ||||
0.344366 | + | 0.938835i | \(0.388094\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 550681. | 0.401595 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.41989e6 | 1.01754 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.50892e6 | 1.76702 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.98842e6 | −2.06876 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −262992. | −0.178967 | −0.0894835 | − | 0.995988i | \(-0.528522\pi\) | ||||
−0.0894835 | + | 0.995988i | \(0.528522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.06852e6 | 0.714869 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −496252. | −0.326446 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.69409e6 | 1.09587 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −107459. | −0.0683640 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.54451e6 | 1.59220 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 803301. | 0.494458 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.15704e6 | −1.30621 | −0.653104 | − | 0.757269i | \(-0.726533\pi\) | ||||
−0.653104 | + | 0.757269i | \(0.726533\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 598923. | 0.356841 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.33078e6 | −1.36647 | −0.683235 | − | 0.730199i | \(-0.739427\pi\) | ||||
−0.683235 | + | 0.730199i | \(0.739427\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.12235e6 | −0.647539 | −0.323769 | − | 0.946136i | \(-0.604950\pi\) | ||||
−0.323769 | + | 0.946136i | \(0.604950\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −85702.9 | −0.0486652 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.27955e6 | 0.715169 | 0.357584 | − | 0.933881i | \(-0.383600\pi\) | ||||
0.357584 | + | 0.933881i | \(0.383600\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −922203. | −0.507399 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.17060e6 | 0.634082 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.61196e6 | 1.39303 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −263383. | −0.138318 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 642998. | 0.332537 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.02956e6 | −1.03374 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.09571e6 | 1.05138 | 0.525691 | − | 0.850675i | \(-0.323807\pi\) | ||||
0.525691 | + | 0.850675i | \(0.323807\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 286805. | 0.141735 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −759285. | −0.369652 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −571289. | −0.274019 | −0.137010 | − | 0.990570i | \(-0.543749\pi\) | ||||
−0.137010 | + | 0.990570i | \(0.543749\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −667817. | −0.315615 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 337802. | 0.157317 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.33017e6 | −1.06943 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.67993e6 | −0.759878 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.24067e6 | −0.998973 | −0.499486 | − | 0.866322i | \(-0.666478\pi\) | ||||
−0.499486 | + | 0.866322i | \(0.666478\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −130448. | −0.0573290 | −0.0286645 | − | 0.999589i | \(-0.509125\pi\) | ||||
−0.0286645 | + | 0.999589i | \(0.509125\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.45524e6 | −0.630473 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.95452e6 | 0.834839 | 0.417420 | − | 0.908714i | \(-0.362935\pi\) | ||||
0.417420 | + | 0.908714i | \(0.362935\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −900168. | −0.379099 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.11930e6 | −1.29535 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −850543. | −0.348305 | −0.174153 | − | 0.984719i | \(-0.555719\pi\) | ||||
−0.174153 | + | 0.984719i | \(0.555719\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −739600. | −0.298696 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.34687e6 | 0.934807 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.58595e6 | 0.623100 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50673e6 | −0.583941 | −0.291970 | − | 0.956427i | \(-0.594311\pi\) | ||||
−0.291970 | + | 0.956427i | \(0.594311\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 549159. | 0.209958 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −900086. | −0.339507 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.90602e6 | −1.08150 | −0.540749 | − | 0.841184i | \(-0.681859\pi\) | ||||
−0.540749 | + | 0.841184i | \(0.681859\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 261182. | 0.0959102 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.70432e6 | −0.979952 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.16710e6 | −1.84777 | −0.923887 | − | 0.382665i | \(-0.875006\pi\) | ||||
−0.923887 | + | 0.382665i | \(0.875006\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.89874e6 | 1.37598 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.85088e6 | 1.34142 | 0.670708 | − | 0.741721i | \(-0.265990\pi\) | ||||
0.670708 | + | 0.741721i | \(0.265990\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 338237. | 0.116297 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −41561.1 | −0.0141062 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.49855e6 | −1.84236 | −0.921179 | − | 0.389138i | \(-0.872773\pi\) | ||||
−0.921179 | + | 0.389138i | \(0.872773\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.96814e6 | −2.63582 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 923321. | 0.301558 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.24807e6 | 0.724965 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.71425e6 | −0.545881 | −0.272941 | − | 0.962031i | \(-0.587996\pi\) | ||||
−0.272941 | + | 0.962031i | \(0.587996\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.07380e6 | −0.652130 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.63329e6 | 1.12834 | 0.564169 | − | 0.825660i | \(-0.309197\pi\) | ||||
0.564169 | + | 0.825660i | \(0.309197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 990591. | 0.303831 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.66428e6 | 0.504185 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.13191e6 | −0.338709 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.38246e6 | −0.408642 | −0.204321 | − | 0.978904i | \(-0.565499\pi\) | ||||
−0.204321 | + | 0.978904i | \(0.565499\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.37148e6 | −1.27651 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.02390e6 | −1.16084 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 955280. | 0.272277 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.90379e6 | 1.38099 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.55435e6 | −0.710795 | −0.355398 | − | 0.934715i | \(-0.615655\pi\) | ||||
−0.355398 | + | 0.934715i | \(0.615655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.68110e6 | 0.462263 | 0.231132 | − | 0.972923i | \(-0.425757\pi\) | ||||
0.231132 | + | 0.972923i | \(0.425757\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −784954. | −0.213301 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.23882e6 | 0.332687 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.02513e6 | −0.802925 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.01229e6 | −0.265560 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.32369e6 | −0.602539 | −0.301269 | − | 0.953539i | \(-0.597410\pi\) | ||||
−0.301269 | + | 0.953539i | \(0.597410\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.06439e6 | −1.04178 | −0.520890 | − | 0.853624i | \(-0.674400\pi\) | ||||
−0.520890 | + | 0.853624i | \(0.674400\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.68172e6 | 0.679502 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.29744e6 | −1.32697 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.39272e6 | 1.58316 | 0.791579 | − | 0.611066i | \(-0.209259\pi\) | ||||
0.791579 | + | 0.611066i | \(0.209259\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −289237. | −0.0708202 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.23515e6 | −0.783222 | −0.391611 | − | 0.920131i | \(-0.628082\pi\) | ||||
−0.391611 | + | 0.920131i | \(0.628082\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −143642. | −0.0343860 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.08999e6 | −1.20489 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.74812e6 | −0.643310 | −0.321655 | − | 0.946857i | \(-0.604239\pi\) | ||||
−0.321655 | + | 0.946857i | \(0.604239\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.16732e6 | −0.501745 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.64837e6 | 1.29324 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 991867. | 0.224608 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.37326e6 | −1.20350 | −0.601751 | − | 0.798684i | \(-0.705530\pi\) | ||||
−0.601751 | + | 0.798684i | \(0.705530\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.84472e6 | 1.51644 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.19928e6 | 1.79690 | 0.898449 | − | 0.439078i | \(-0.144695\pi\) | ||||
0.898449 | + | 0.439078i | \(0.144695\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.76963e6 | 0.817233 | 0.408617 | − | 0.912706i | \(-0.366011\pi\) | ||||
0.408617 | + | 0.912706i | \(0.366011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −982313. | −0.210677 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.03412e6 | −1.28033 | −0.640165 | − | 0.768237i | \(-0.721134\pi\) | ||||
−0.640165 | + | 0.768237i | \(0.721134\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.85937e6 | 0.600259 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.14311e6 | 0.237431 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 164026. | 0.0337101 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 823602. | 0.167488 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −348119. | −0.0700537 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.26406e6 | −1.04829 | −0.524146 | − | 0.851629i | \(-0.675615\pi\) | ||||
−0.524146 | + | 0.851629i | \(0.675615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.31929e6 | −0.654157 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.32641e6 | 1.23393 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.46951e6 | −0.862790 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.19979e6 | −0.420300 | −0.210150 | − | 0.977669i | \(-0.567395\pi\) | ||||
−0.210150 | + | 0.977669i | \(0.567395\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.76099e6 | −1.27861 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.47314e6 | −1.21174 | −0.605872 | − | 0.795562i | \(-0.707176\pi\) | ||||
−0.605872 | + | 0.795562i | \(0.707176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.27198e7 | 2.35701 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 130817. | 0.0239967 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.38992e6 | 0.615600 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.62090e6 | −1.54989 | −0.774946 | − | 0.632028i | \(-0.782223\pi\) | ||||
−0.774946 | + | 0.632028i | \(0.782223\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.88238e6 | −1.22502 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.10557e6 | 1.42845 | 0.714223 | − | 0.699918i | \(-0.246780\pi\) | ||||
0.714223 | + | 0.699918i | \(0.246780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.80559e6 | 0.664038 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.23789e6 | 0.559426 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.39610e6 | 1.09426 | 0.547131 | − | 0.837047i | \(-0.315720\pi\) | ||||
0.547131 | + | 0.837047i | \(0.315720\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.97250e6 | −1.01182 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.55055e6 | 0.763433 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 895752. | 0.148823 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.09792e6 | 0.509735 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.71205e6 | −0.441957 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.53647e6 | 1.21639 | 0.608197 | − | 0.793786i | \(-0.291893\pi\) | ||||
0.608197 | + | 0.793786i | \(0.291893\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.87780e6 | −0.300189 | −0.150095 | − | 0.988672i | \(-0.547958\pi\) | ||||
−0.150095 | + | 0.988672i | \(0.547958\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −983578. | −0.155744 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.65924e6 | −0.730784 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.72424e6 | 1.51083 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.55629e6 | −0.239527 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.35559e6 | −0.969031 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.75075e6 | 0.264448 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.42542e6 | 0.961537 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.14151e6 | 0.169242 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.44482e6 | −0.359131 | −0.179566 | − | 0.983746i | \(-0.557469\pi\) | ||||
−0.179566 | + | 0.983746i | \(0.557469\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.68202e6 | 1.40918 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 961672. | 0.138687 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.09485e7 | 1.56453 | 0.782266 | − | 0.622944i | \(-0.214064\pi\) | ||||
0.782266 | + | 0.622944i | \(0.214064\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.17001e6 | −0.165675 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.45645e6 | 1.18661 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.46595e6 | −1.17723 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.29155e6 | 0.453595 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 768938. | 0.105015 | 0.0525077 | − | 0.998621i | \(-0.483279\pi\) | ||||
0.0525077 | + | 0.998621i | \(0.483279\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 481000. | 0.0651052 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.76131e6 | 0.638733 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.47386e7 | 1.95968 | 0.979838 | − | 0.199792i | \(-0.0640265\pi\) | ||||
0.979838 | + | 0.199792i | \(0.0640265\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −998791. | −0.131630 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.26749e6 | −0.818721 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.33696e6 | −0.432086 | −0.216043 | − | 0.976384i | \(-0.569315\pi\) | ||||
−0.216043 | + | 0.976384i | \(0.569315\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.54413e7 | −1.98195 | −0.990974 | − | 0.134051i | \(-0.957201\pi\) | ||||
−0.990974 | + | 0.134051i | \(0.957201\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.38123e6 | −0.302981 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.51251e6 | −0.316912 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.05636e6 | −0.507221 | −0.253610 | − | 0.967306i | \(-0.581618\pi\) | ||||
−0.253610 | + | 0.967306i | \(0.581618\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.46762e6 | −0.553834 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.59746e6 | −0.442136 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.37389e6 | 0.167410 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 383616. | 0.0463454 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.22567e7 | 1.46818 | 0.734090 | − | 0.679052i | \(-0.237609\pi\) | ||||
0.734090 | + | 0.679052i | \(0.237609\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.09759e6 | −0.367905 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 237186. | 0.0279332 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.58993e6 | 1.00312 | 0.501560 | − | 0.865123i | \(-0.332760\pi\) | ||||
0.501560 | + | 0.865123i | \(0.332760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.66525e6 | −0.540234 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.82825e6 | −0.324775 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.85849e6 | 1.00877 | 0.504386 | − | 0.863479i | \(-0.331719\pi\) | ||||
0.504386 | + | 0.863479i | \(0.331719\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.50579e6 | −0.960569 | −0.480284 | − | 0.877113i | \(-0.659467\pi\) | ||||
−0.480284 | + | 0.877113i | \(0.659467\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.10590e6 | 0.123857 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.50999e6 | 0.389868 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.15481e6 | −0.347537 | −0.173768 | − | 0.984787i | \(-0.555594\pi\) | ||||
−0.173768 | + | 0.984787i | \(0.555594\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.00990e7 | −1.10341 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.08453e6 | 0.984463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.20689e6 | −0.344694 | −0.172347 | − | 0.985036i | \(-0.555135\pi\) | ||||
−0.172347 | + | 0.985036i | \(0.555135\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.30248e6 | 0.671929 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.31916e6 | −0.139504 | −0.0697519 | − | 0.997564i | \(-0.522221\pi\) | ||||
−0.0697519 | + | 0.997564i | \(0.522221\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.36061e6 | 0.352526 | 0.176263 | − | 0.984343i | \(-0.443599\pi\) | ||||
0.176263 | + | 0.984343i | \(0.443599\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.38821e7 | −1.44453 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 540939. | 0.0558377 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.16545e6 | 0.321563 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.56123e7 | 1.57340 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.46547e7 | −1.46522 | −0.732610 | − | 0.680648i | \(-0.761698\pi\) | ||||
−0.732610 | + | 0.680648i | \(0.761698\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.81315e6 | −0.675832 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.83097e6 | 0.573861 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.34743e6 | 0.326861 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.31109e6 | 0.127023 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.67545e6 | −0.545576 | −0.272788 | − | 0.962074i | \(-0.587946\pi\) | ||||
−0.272788 | + | 0.962074i | \(0.587946\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.81422e7 | 1.73047 | 0.865233 | − | 0.501370i | \(-0.167170\pi\) | ||||
0.865233 | + | 0.501370i | \(0.167170\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −476981. | −0.0451442 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 472390. | 0.0443649 | 0.0221825 | − | 0.999754i | \(-0.492939\pi\) | ||||
0.0221825 | + | 0.999754i | \(0.492939\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.14210e6 | 0.572407 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.69927e6 | 0.342108 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.79442e6 | −0.898867 | −0.449434 | − | 0.893314i | \(-0.648374\pi\) | ||||
−0.449434 | + | 0.893314i | \(0.648374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.38092e6 | 0.125767 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.30993e6 | −0.208778 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.83251e6 | 0.881964 | 0.440982 | − | 0.897516i | \(-0.354630\pi\) | ||||
0.440982 | + | 0.897516i | \(0.354630\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.84120e6 | −0.163907 | −0.0819535 | − | 0.996636i | \(-0.526116\pi\) | ||||
−0.0819535 | + | 0.996636i | \(0.526116\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.39624e7 | 1.23360 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.10158e6 | −0.271975 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.57976e7 | −2.24525 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.73413e6 | 0.149802 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.61758e6 | 0.395920 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.02990e7 | −0.876510 | −0.438255 | − | 0.898851i | \(-0.644403\pi\) | ||||
−0.438255 | + | 0.898851i | \(0.644403\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.15828e6 | 0.182326 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.63461e6 | 0.304779 | 0.152390 | − | 0.988320i | \(-0.451303\pi\) | ||||
0.152390 | + | 0.988320i | \(0.451303\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.68316e7 | 1.40104 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.34348e7 | −1.11010 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.78443e6 | 0.802571 | 0.401286 | − | 0.915953i | \(-0.368563\pi\) | ||||
0.401286 | + | 0.915953i | \(0.368563\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.53801e6 | −0.532377 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.27257e7 | 1.83707 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.02889e6 | 0.323323 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.67949e6 | −0.372824 | −0.186412 | − | 0.982472i | \(-0.559686\pi\) | ||||
−0.186412 | + | 0.982472i | \(0.559686\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −492641. | −0.0389671 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.33414e6 | 0.575953 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.98935e7 | 2.33075 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.04110e7 | 0.805930 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 565147. | 0.0434376 | 0.0217188 | − | 0.999764i | \(-0.493086\pi\) | ||||
0.0217188 | + | 0.999764i | \(0.493086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.03795e7 | 0.792112 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.00861e6 | −0.682630 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.43314e7 | −1.07830 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.00907e6 | 0.0753889 | 0.0376944 | − | 0.999289i | \(-0.487999\pi\) | ||||
0.0376944 | + | 0.999289i | \(0.487999\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.27431e6 | −0.242910 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.44964e6 | 0.696132 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.51399e6 | −0.110754 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.07455e7 | 0.780602 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.02329e6 | −0.434522 | −0.217261 | − | 0.976114i | \(-0.569712\pi\) | ||||
−0.217261 | + | 0.976114i | \(0.569712\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.37329e6 | −0.241666 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.86904e7 | −1.32976 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.01080e6 | 0.283391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.30828e6 | −0.161977 | −0.0809883 | − | 0.996715i | \(-0.525808\pi\) | ||||
−0.0809883 | + | 0.996715i | \(0.525808\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.16027e7 | 0.808612 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.26238e6 | −0.156593 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.65224e7 | 1.13583 | 0.567914 | − | 0.823088i | \(-0.307751\pi\) | ||||
0.567914 | + | 0.823088i | \(0.307751\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.31946e6 | −0.226646 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.36456e6 | −0.295986 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.41051e7 | −1.62367 | −0.811834 | − | 0.583888i | \(-0.801531\pi\) | ||||
−0.811834 | + | 0.583888i | \(0.801531\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.28255e6 | 0.621043 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.54593e7 | −1.69190 | −0.845950 | − | 0.533262i | \(-0.820966\pi\) | ||||
−0.845950 | + | 0.533262i | \(0.820966\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.61262e6 | −0.502508 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.39136e6 | −0.0912301 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.59312e6 | −0.429424 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.25073e7 | −0.809215 | −0.404608 | − | 0.914490i | \(-0.632592\pi\) | ||||
−0.404608 | + | 0.914490i | \(0.632592\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.22203e7 | 0.785404 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.44773e6 | 0.539353 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.34914e6 | 0.339269 | 0.169635 | − | 0.985507i | \(-0.445741\pi\) | ||||
0.169635 | + | 0.985507i | \(0.445741\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.65666e6 | −0.608447 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.80369e7 | −1.12901 | −0.564507 | − | 0.825428i | \(-0.690934\pi\) | ||||
−0.564507 | + | 0.825428i | \(0.690934\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.62154e6 | −0.225207 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.80434e6 | −0.111472 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.80115e7 | 1.10550 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.41928e7 | 1.47526 | 0.737632 | − | 0.675203i | \(-0.235944\pi\) | ||||
0.737632 | + | 0.675203i | \(0.235944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.95234e7 | 1.78867 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.22531e6 | 0.194143 | 0.0970716 | − | 0.995277i | \(-0.469052\pi\) | ||||
0.0970716 | + | 0.995277i | \(0.469052\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.46915e6 | −0.0878643 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.23956e7 | −0.736570 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.98740e7 | 1.17339 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.17439e6 | −0.303551 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.21604e7 | 1.29174 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.70965e6 | 0.0990221 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.12227e6 | 0.0645896 | 0.0322948 | − | 0.999478i | \(-0.489718\pi\) | ||||
0.0322948 | + | 0.999478i | \(0.489718\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.68705e7 | −0.964793 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.76132e6 | 0.213747 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.35408e7 | 0.764650 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.99522e6 | −0.224193 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.48763e7 | 0.829560 | 0.414780 | − | 0.909922i | \(-0.363859\pi\) | ||||
0.414780 | + | 0.909922i | \(0.363859\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.27291e7 | −2.36786 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 209214. | 0.0115215 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.11644e6 | 0.498926 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.46182e6 | 0.514618 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.29660e7 | −0.700845 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.86436e7 | 1.00152 | 0.500759 | − | 0.865587i | \(-0.333054\pi\) | ||||
0.500759 | + | 0.865587i | \(0.333054\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.50701e6 | −0.240623 | −0.120311 | − | 0.992736i | \(-0.538389\pi\) | ||||
−0.120311 | + | 0.992736i | \(0.538389\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.02920e7 | −1.07671 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.01118e7 | −0.533253 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.50409e6 | −0.0788352 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.44465e6 | −0.0752580 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.26560e7 | 1.17307 | 0.586537 | − | 0.809922i | \(-0.300491\pi\) | ||||
0.586537 | + | 0.809922i | \(0.300491\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.76806e7 | −1.42454 | −0.712272 | − | 0.701903i | \(-0.752334\pi\) | ||||
−0.712272 | + | 0.701903i | \(0.752334\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.50134e6 | 0.0767969 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.42673e6 | 0.377602 | 0.188801 | − | 0.982015i | \(-0.439540\pi\) | ||||
0.188801 | + | 0.982015i | \(0.439540\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.41770e7 | −1.72722 | −0.863610 | − | 0.504160i | \(-0.831802\pi\) | ||||
−0.863610 | + | 0.504160i | \(0.831802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.65244e6 | −0.183477 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.57446e7 | −0.786177 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.02933e7 | −0.510905 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.11734e6 | −0.400498 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 155990. | 0.00765051 | 0.00382526 | − | 0.999993i | \(-0.498782\pi\) | ||||
0.00382526 | + | 0.999993i | \(0.498782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.06703e7 | 1.00776 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.28580e6 | 0.256178 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.84261e6 | 0.233313 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.32182e7 | −0.633087 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.55110e7 | −0.738534 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.16640e7 | −1.49879 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.52778e7 | 1.18951 | 0.594754 | − | 0.803908i | \(-0.297250\pi\) | ||||
0.594754 | + | 0.803908i | \(0.297250\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.19957e6 | −0.0561192 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.40854e6 | 0.0655112 | 0.0327556 | − | 0.999463i | \(-0.489572\pi\) | ||||
0.0327556 | + | 0.999463i | \(0.489572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 246158. | 0.0113823 | 0.00569116 | − | 0.999984i | \(-0.498188\pi\) | ||||
0.00569116 | + | 0.999984i | \(0.498188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.37344e7 | −1.09111 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.17019e7 | 0.534849 | 0.267424 | − | 0.963579i | \(-0.413827\pi\) | ||||
0.267424 | + | 0.963579i | \(0.413827\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.05616e6 | −0.184321 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.19381e7 | −1.89479 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.29225e7 | 0.580492 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.27989e7 | −0.571646 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.50982e6 | 0.289090 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.47105e6 | −0.0649540 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.85174e6 | 0.344720 | 0.172360 | − | 0.985034i | \(-0.444861\pi\) | ||||
0.172360 | + | 0.985034i | \(0.444861\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.39607e6 | 0.191908 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 105461. | 0.00457777 | 0.00228888 | − | 0.999997i | \(-0.499271\pi\) | ||||
0.00228888 | + | 0.999997i | \(0.499271\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.43760e7 | −0.620491 | −0.310245 | − | 0.950656i | \(-0.600411\pi\) | ||||
−0.310245 | + | 0.950656i | \(0.600411\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.78609e7 | −0.766560 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.71725e7 | 1.15963 | 0.579816 | − | 0.814748i | \(-0.303125\pi\) | ||||
0.579816 | + | 0.814748i | \(0.303125\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.19587e7 | −0.931864 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9.56672e6 | 0.403709 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.84075e7 | −1.19208 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.60990e6 | 0.401016 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.83177e7 | −1.17511 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.50847e7 | −0.622499 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.89499e7 | −0.777668 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.79625e6 | 0.0733073 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.44805e7 | 0.587708 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.25290e6 | 0.212022 | 0.106011 | − | 0.994365i | \(-0.466192\pi\) | ||||
0.106011 | + | 0.994365i | \(0.466192\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.54282e6 | −0.222495 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.68057e7 | 1.07012 | 0.535059 | − | 0.844815i | \(-0.320289\pi\) | ||||
0.535059 | + | 0.844815i | \(0.320289\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.49118e6 | 0.218016 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.34277e7 | −0.530211 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.20039e6 | −0.204227 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.25954e7 | −0.491951 | −0.245976 | − | 0.969276i | \(-0.579108\pi\) | ||||
−0.245976 | + | 0.969276i | \(0.579108\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.60563e7 | 1.40066 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.51737e7 | −0.586255 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.92286e6 | 0.189175 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.30466e6 | −0.0498652 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.23322e7 | −1.22912 | −0.614562 | − | 0.788868i | \(-0.710667\pi\) | ||||
−0.614562 | + | 0.788868i | \(0.710667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.04675e7 | −0.395792 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.89604e7 | 1.46528 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.12105e6 | 0.266388 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.04882e7 | 0.762350 | 0.381175 | − | 0.924503i | \(-0.375519\pi\) | ||||
0.381175 | + | 0.924503i | \(0.375519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.87607e7 | 0.694361 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.87135e6 | 0.216154 | 0.108077 | − | 0.994143i | \(-0.465531\pi\) | ||||
0.108077 | + | 0.994143i | \(0.465531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.06285e7 | −2.22023 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.12780e6 | −0.296069 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.86718e7 | 0.676567 | 0.338284 | − | 0.941044i | \(-0.390154\pi\) | ||||
0.338284 | + | 0.941044i | \(0.390154\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.67336e7 | 0.963588 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.13885e7 | −0.766882 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.55896e7 | 0.556037 | 0.278018 | − | 0.960576i | \(-0.410322\pi\) | ||||
0.278018 | + | 0.960576i | \(0.410322\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.56139e6 | −0.126360 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.54152e7 | 0.544088 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.46213e7 | 0.864500 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.31036e7 | −0.806996 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.54997e6 | −0.0886071 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6.68179e6 | −0.230980 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.24491e7 | −1.11593 | −0.557964 | − | 0.829865i | \(-0.688417\pi\) | ||||
−0.557964 | + | 0.829865i | \(0.688417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.36605e7 | −1.49375 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.73661e7 | −1.27183 | −0.635916 | − | 0.771758i | \(-0.719378\pi\) | ||||
−0.635916 | + | 0.771758i | \(0.719378\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.76195e7 | −0.935261 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.40261e6 | 0.148320 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.23874e7 | −1.75586 | −0.877931 | − | 0.478787i | \(-0.841077\pi\) | ||||
−0.877931 | + | 0.478787i | \(0.841077\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −825691. | −0.0275335 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.40067e6 | −0.0464690 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.75140e7 | −1.56833 | −0.784166 | − | 0.620551i | \(-0.786909\pi\) | ||||
−0.784166 | + | 0.620551i | \(0.786909\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 354737. | 0.0116497 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.39253e7 | 1.10849 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.58846e6 | 0.149168 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.47278e7 | 0.799835 | 0.399918 | − | 0.916551i | \(-0.369039\pi\) | ||||
0.399918 | + | 0.916551i | \(0.369039\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.50311e7 | −1.12741 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.22995e6 | −0.135450 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.25139e7 | −0.398709 | −0.199355 | − | 0.979927i | \(-0.563885\pi\) | ||||
−0.199355 | + | 0.979927i | \(0.563885\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.71997e7 | 0.862285 |
(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 | 320.6.a.w.1.1 | 2 | ||
4.3 | odd | 2 | 320.6.a.q.1.2 | 2 | |||
8.3 | odd | 2 | 80.6.a.i.1.1 | 2 | |||
8.5 | even | 2 | 40.6.a.d.1.2 | ✓ | 2 | ||
24.5 | odd | 2 | 360.6.a.l.1.2 | 2 | |||
24.11 | even | 2 | 720.6.a.z.1.1 | 2 | |||
40.3 | even | 4 | 400.6.c.l.49.2 | 4 | |||
40.13 | odd | 4 | 200.6.c.e.49.3 | 4 | |||
40.19 | odd | 2 | 400.6.a.q.1.2 | 2 | |||
40.27 | even | 4 | 400.6.c.l.49.3 | 4 | |||
40.29 | even | 2 | 200.6.a.g.1.1 | 2 | |||
40.37 | odd | 4 | 200.6.c.e.49.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.a.d.1.2 | ✓ | 2 | 8.5 | even | 2 | ||
80.6.a.i.1.1 | 2 | 8.3 | odd | 2 | |||
200.6.a.g.1.1 | 2 | 40.29 | even | 2 | |||
200.6.c.e.49.2 | 4 | 40.37 | odd | 4 | |||
200.6.c.e.49.3 | 4 | 40.13 | odd | 4 | |||
320.6.a.q.1.2 | 2 | 4.3 | odd | 2 | |||
320.6.a.w.1.1 | 2 | 1.1 | even | 1 | trivial | ||
360.6.a.l.1.2 | 2 | 24.5 | odd | 2 | |||
400.6.a.q.1.2 | 2 | 40.19 | odd | 2 | |||
400.6.c.l.49.2 | 4 | 40.3 | even | 4 | |||
400.6.c.l.49.3 | 4 | 40.27 | even | 4 | |||
720.6.a.z.1.1 | 2 | 24.11 | even | 2 |