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: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
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 | ||||||||
\(3\) | −4.00000 | −0.256600 | −0.128300 | − | 0.991735i | \(-0.540952\pi\) | ||||
−0.128300 | + | 0.991735i | \(0.540952\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −192.000 | −1.48100 | −0.740502 | − | 0.672054i | \(-0.765412\pi\) | ||||
−0.740502 | + | 0.672054i | \(0.765412\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −227.000 | −0.934156 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −148.000 | −0.368791 | −0.184395 | − | 0.982852i | \(-0.559033\pi\) | ||||
−0.184395 | + | 0.982852i | \(0.559033\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −286.000 | −0.469362 | −0.234681 | − | 0.972072i | \(-0.575405\pi\) | ||||
−0.234681 | + | 0.972072i | \(0.575405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 100.000 | 0.114755 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1678.00 | −1.40822 | −0.704109 | − | 0.710092i | \(-0.748653\pi\) | ||||
−0.704109 | + | 0.710092i | \(0.748653\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1060.00 | 0.673631 | 0.336815 | − | 0.941571i | \(-0.390650\pi\) | ||||
0.336815 | + | 0.941571i | \(0.390650\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 768.000 | 0.380026 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2976.00 | −1.17304 | −0.586521 | − | 0.809934i | \(-0.699503\pi\) | ||||
−0.586521 | + | 0.809934i | \(0.699503\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1880.00 | 0.496305 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3410.00 | 0.752938 | 0.376469 | − | 0.926429i | \(-0.377138\pi\) | ||||
0.376469 | + | 0.926429i | \(0.377138\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2448.00 | 0.457517 | 0.228758 | − | 0.973483i | \(-0.426533\pi\) | ||||
0.228758 | + | 0.973483i | \(0.426533\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 592.000 | 0.0946317 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4800.00 | 0.662325 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −182.000 | −0.0218558 | −0.0109279 | − | 0.999940i | \(-0.503479\pi\) | ||||
−0.0109279 | + | 0.999940i | \(0.503479\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1144.00 | 0.120438 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9398.00 | −0.873124 | −0.436562 | − | 0.899674i | \(-0.643804\pi\) | ||||
−0.436562 | + | 0.899674i | \(0.643804\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1244.00 | −0.102600 | −0.0513002 | − | 0.998683i | \(-0.516337\pi\) | ||||
−0.0513002 | + | 0.998683i | \(0.516337\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5675.00 | 0.417767 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12088.0 | 0.798196 | 0.399098 | − | 0.916908i | \(-0.369323\pi\) | ||||
0.399098 | + | 0.916908i | \(0.369323\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20057.0 | 1.19337 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6712.00 | 0.361349 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −23846.0 | −1.16607 | −0.583037 | − | 0.812446i | \(-0.698136\pi\) | ||||
−0.583037 | + | 0.812446i | \(0.698136\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3700.00 | 0.164928 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4240.00 | −0.172854 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −20020.0 | −0.748745 | −0.374373 | − | 0.927278i | \(-0.622142\pi\) | ||||
−0.374373 | + | 0.927278i | \(0.622142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −32302.0 | −1.11149 | −0.555744 | − | 0.831353i | \(-0.687567\pi\) | ||||
−0.555744 | + | 0.831353i | \(0.687567\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 43584.0 | 1.38349 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7150.00 | 0.209905 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 60972.0 | 1.65937 | 0.829685 | − | 0.558231i | \(-0.188520\pi\) | ||||
0.829685 | + | 0.558231i | \(0.188520\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11904.0 | 0.301003 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 32648.0 | 0.768618 | 0.384309 | − | 0.923204i | \(-0.374440\pi\) | ||||
0.384309 | + | 0.923204i | \(0.374440\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −38774.0 | −0.851596 | −0.425798 | − | 0.904818i | \(-0.640007\pi\) | ||||
−0.425798 | + | 0.904818i | \(0.640007\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2500.00 | −0.0513200 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 28416.0 | 0.546180 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 33360.0 | 0.601393 | 0.300696 | − | 0.953720i | \(-0.402781\pi\) | ||||
0.300696 | + | 0.953720i | \(0.402781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 47641.0 | 0.806805 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16716.0 | 0.266340 | 0.133170 | − | 0.991093i | \(-0.457484\pi\) | ||||
0.133170 | + | 0.991093i | \(0.457484\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41950.0 | 0.629774 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13640.0 | −0.193204 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 101370. | 1.35655 | 0.678273 | − | 0.734810i | \(-0.262729\pi\) | ||||
0.678273 | + | 0.734810i | \(0.262729\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 54912.0 | 0.695126 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −9792.00 | −0.117399 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26500.0 | −0.301257 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −119038. | −1.28457 | −0.642283 | − | 0.766468i | \(-0.722013\pi\) | ||||
−0.642283 | + | 0.766468i | \(0.722013\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 33596.0 | 0.344508 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 89898.0 | 0.876893 | 0.438446 | − | 0.898757i | \(-0.355529\pi\) | ||||
0.438446 | + | 0.898757i | \(0.355529\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19504.0 | 0.181147 | 0.0905734 | − | 0.995890i | \(-0.471130\pi\) | ||||
0.0905734 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −19200.0 | −0.169953 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 158292. | 1.33659 | 0.668297 | − | 0.743895i | \(-0.267024\pi\) | ||||
0.668297 | + | 0.743895i | \(0.267024\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −36830.0 | −0.296917 | −0.148459 | − | 0.988919i | \(-0.547431\pi\) | ||||
−0.148459 | + | 0.988919i | \(0.547431\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 728.000 | 0.00560821 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11186.0 | 0.0824098 | 0.0412049 | − | 0.999151i | \(-0.486880\pi\) | ||||
0.0412049 | + | 0.999151i | \(0.486880\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 74400.0 | 0.524600 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 64922.0 | 0.438457 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 322176. | 2.08557 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −139147. | −0.863993 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 37592.0 | 0.224044 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −70552.0 | −0.388150 | −0.194075 | − | 0.980987i | \(-0.562171\pi\) | ||||
−0.194075 | + | 0.980987i | \(0.562171\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4976.00 | 0.0263273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 76452.0 | 0.389234 | 0.194617 | − | 0.980879i | \(-0.437654\pi\) | ||||
0.194617 | + | 0.980879i | \(0.437654\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −203520. | −0.997650 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −47000.0 | −0.221954 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −144918. | −0.659661 | −0.329831 | − | 0.944040i | \(-0.606992\pi\) | ||||
−0.329831 | + | 0.944040i | \(0.606992\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 112220. | 0.492644 | 0.246322 | − | 0.969188i | \(-0.420778\pi\) | ||||
0.246322 | + | 0.969188i | \(0.420778\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −48352.0 | −0.204817 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 42328.0 | 0.173096 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −85250.0 | −0.336724 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −80228.0 | −0.306219 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −403750. | −1.48986 | −0.744932 | − | 0.667140i | \(-0.767518\pi\) | ||||
−0.744932 | + | 0.667140i | \(0.767518\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 446648. | 1.59413 | 0.797064 | − | 0.603895i | \(-0.206385\pi\) | ||||
0.797064 | + | 0.603895i | \(0.206385\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 380906. | 1.31550 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −61200.0 | −0.204608 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 262258. | 0.849141 | 0.424570 | − | 0.905395i | \(-0.360425\pi\) | ||||
0.424570 | + | 0.905395i | \(0.360425\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 95384.0 | 0.299215 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 571392. | 1.73728 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −154564. | −0.455658 | −0.227829 | − | 0.973701i | \(-0.573163\pi\) | ||||
−0.227829 | + | 0.973701i | \(0.573163\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −14800.0 | −0.0423206 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −396672. | −1.10063 | −0.550314 | − | 0.834958i | \(-0.685492\pi\) | ||||
−0.550314 | + | 0.834958i | \(0.685492\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −289497. | −0.779700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −240620. | −0.629276 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 573474. | 1.45680 | 0.728398 | − | 0.685155i | \(-0.240265\pi\) | ||||
0.728398 | + | 0.685155i | \(0.240265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −120000. | −0.296201 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 80080.0 | 0.192128 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −594460. | −1.38672 | −0.693362 | − | 0.720589i | \(-0.743871\pi\) | ||||
−0.693362 | + | 0.720589i | \(0.743871\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 107098. | 0.242988 | 0.121494 | − | 0.992592i | \(-0.461231\pi\) | ||||
0.121494 | + | 0.992592i | \(0.461231\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 129208. | 0.285208 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4550.00 | 0.00977422 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 248344. | 0.519337 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −360960. | −0.735029 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −469552. | −0.931323 | −0.465661 | − | 0.884963i | \(-0.654184\pi\) | ||||
−0.465661 | + | 0.884963i | \(0.654184\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 52706.0 | 0.101851 | 0.0509257 | − | 0.998702i | \(-0.483783\pi\) | ||||
0.0509257 | + | 0.998702i | \(0.483783\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −28600.0 | −0.0538616 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −455862. | −0.836889 | −0.418444 | − | 0.908242i | \(-0.637425\pi\) | ||||
−0.418444 | + | 0.908242i | \(0.637425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −865000. | −1.54840 | −0.774200 | − | 0.632940i | \(-0.781848\pi\) | ||||
−0.774200 | + | 0.632940i | \(0.781848\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −243888. | −0.425795 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −654720. | −1.11510 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 234950. | 0.390473 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 675552. | 1.09580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −156880. | −0.248429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.10565e6 | 1.70967 | 0.854835 | − | 0.518900i | \(-0.173658\pi\) | ||||
0.854835 | + | 0.518900i | \(0.173658\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −130592. | −0.197228 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31100.0 | 0.0458843 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −470016. | −0.677584 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 155096. | 0.218520 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 479908. | 0.660963 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.12158e6 | −1.51031 | −0.755156 | − | 0.655545i | \(-0.772439\pi\) | ||||
−0.755156 | + | 0.655545i | \(0.772439\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −141875. | −0.186831 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23348.0 | −0.0300736 | −0.0150368 | − | 0.999887i | \(-0.504787\pi\) | ||||
−0.0150368 | + | 0.999887i | \(0.504787\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 596010. | 0.751043 | 0.375522 | − | 0.926814i | \(-0.377464\pi\) | ||||
0.375522 | + | 0.926814i | \(0.377464\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −113664. | −0.140150 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −485334. | −0.585667 | −0.292834 | − | 0.956163i | \(-0.594598\pi\) | ||||
−0.292834 | + | 0.956163i | \(0.594598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −302200. | −0.356964 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −133440. | −0.154317 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 48880.0 | 0.0553524 | 0.0276762 | − | 0.999617i | \(-0.491189\pi\) | ||||
0.0276762 | + | 0.999617i | \(0.491189\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −110798. | −0.122882 | −0.0614411 | − | 0.998111i | \(-0.519570\pi\) | ||||
−0.0614411 | + | 0.998111i | \(0.519570\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −647404. | −0.703331 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −501425. | −0.533692 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −303160. | −0.316176 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −66864.0 | −0.0683430 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.64375e6 | −1.64684 | −0.823419 | − | 0.567434i | \(-0.807936\pi\) | ||||
−0.823419 | + | 0.567434i | \(0.807936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 440448. | 0.432607 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −167800. | −0.161600 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.30624e6 | 1.23365 | 0.616823 | − | 0.787102i | \(-0.288419\pi\) | ||||
0.616823 | + | 0.787102i | \(0.288419\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 34944.0 | 0.0323685 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −774070. | −0.703362 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.12834e6 | −1.89736 | −0.948682 | − | 0.316231i | \(-0.897583\pi\) | ||||
−0.948682 | + | 0.316231i | \(0.897583\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 596150. | 0.521484 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −405480. | −0.348090 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.44109e6 | 1.21426 | 0.607128 | − | 0.794604i | \(-0.292321\pi\) | ||||
0.607128 | + | 0.794604i | \(0.292321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 93248.0 | 0.0771288 | 0.0385644 | − | 0.999256i | \(-0.487722\pi\) | ||||
0.0385644 | + | 0.999256i | \(0.487722\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −219648. | −0.178370 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −92500.0 | −0.0737581 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 110298. | 0.0863711 | 0.0431855 | − | 0.999067i | \(-0.486249\pi\) | ||||
0.0431855 | + | 0.999067i | \(0.486249\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −555696. | −0.427392 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −192198. | −0.145205 | −0.0726027 | − | 0.997361i | \(-0.523131\pi\) | ||||
−0.0726027 | + | 0.997361i | \(0.523131\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −331884. | −0.246332 | −0.123166 | − | 0.992386i | \(-0.539305\pi\) | ||||
−0.123166 | + | 0.992386i | \(0.539305\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 106000. | 0.0773025 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.80442e6 | 1.29310 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.39583e6 | 0.983076 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 476152. | 0.329620 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.19481e6 | −1.49358 | −0.746788 | − | 0.665063i | \(-0.768405\pi\) | ||||
−0.746788 | + | 0.665063i | \(0.768405\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 500500. | 0.334849 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −278240. | −0.183033 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 851136. | 0.550581 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 238848. | 0.151952 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −359592. | −0.225011 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 807550. | 0.497073 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.37751e6 | −1.43971 | −0.719857 | − | 0.694123i | \(-0.755793\pi\) | ||||
−0.719857 | + | 0.694123i | \(0.755793\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −78016.0 | −0.0464823 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.37305e6 | 1.39125 | 0.695626 | − | 0.718405i | \(-0.255127\pi\) | ||||
0.695626 | + | 0.718405i | \(0.255127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.42941e6 | −0.824702 | −0.412351 | − | 0.911025i | \(-0.635292\pi\) | ||||
−0.412351 | + | 0.911025i | \(0.635292\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.08960e6 | −0.618715 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.12462e6 | −1.18750 | −0.593750 | − | 0.804650i | \(-0.702353\pi\) | ||||
−0.593750 | + | 0.804650i | \(0.702353\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −504680. | −0.277677 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −633168. | −0.342970 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.77868e6 | −0.948618 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −178750. | −0.0938723 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 147320. | 0.0761890 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.32090e6 | −1.18213 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.09985e6 | 1.55515 | 0.777573 | − | 0.628793i | \(-0.216451\pi\) | ||||
0.777573 | + | 0.628793i | \(0.216451\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 41314.0 | 0.0204168 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.52430e6 | −0.742093 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.40008e6 | 1.15120 | 0.575601 | − | 0.817731i | \(-0.304768\pi\) | ||||
0.575601 | + | 0.817731i | \(0.304768\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −44744.0 | −0.0211464 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −362304. | −0.168728 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −624000. | −0.286384 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −297600. | −0.134612 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.77741e6 | 0.792436 | 0.396218 | − | 0.918156i | \(-0.370322\pi\) | ||||
0.396218 | + | 0.918156i | \(0.370322\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.14805e6 | 0.944019 | 0.472010 | − | 0.881593i | \(-0.343529\pi\) | ||||
0.472010 | + | 0.881593i | \(0.343529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −537680. | −0.232946 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −661854. | −0.282700 | −0.141350 | − | 0.989960i | \(-0.545144\pi\) | ||||
−0.141350 | + | 0.989960i | \(0.545144\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −816200. | −0.343737 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.28870e6 | −0.535159 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 259320. | 0.106194 | 0.0530970 | − | 0.998589i | \(-0.483091\pi\) | ||||
0.0530970 | + | 0.998589i | \(0.483091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.35250e6 | −0.546222 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 556588. | 0.221701 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 969350. | 0.380845 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.49993e6 | 0.581307 | 0.290653 | − | 0.956828i | \(-0.406127\pi\) | ||||
0.290653 | + | 0.956828i | \(0.406127\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.13335e6 | 0.815634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.57843e6 | 1.72696 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.23807e6 | 0.832918 | 0.416459 | − | 0.909154i | \(-0.363271\pi\) | ||||
0.416459 | + | 0.909154i | \(0.363271\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 62500.0 | 0.0229510 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −975260. | −0.353400 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.15934e6 | 1.12979 | 0.564896 | − | 0.825162i | \(-0.308916\pi\) | ||||
0.564896 | + | 0.825162i | \(0.308916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 282208. | 0.0995994 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −342216. | −0.119207 | −0.0596037 | − | 0.998222i | \(-0.518984\pi\) | ||||
−0.0596037 | + | 0.998222i | \(0.518984\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −710400. | −0.244259 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 282388. | 0.0958449 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −88470.0 | −0.0296430 | −0.0148215 | − | 0.999890i | \(-0.504718\pi\) | ||||
−0.0148215 | + | 0.999890i | \(0.504718\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.99373e6 | 1.65190 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −305808. | −0.0998775 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −834000. | −0.268951 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.45674e6 | 1.73763 | 0.868814 | − | 0.495138i | \(-0.164883\pi\) | ||||
0.868814 | + | 0.495138i | \(0.164883\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 814080. | 0.255997 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.04680e6 | 1.25676 | 0.628378 | − | 0.777908i | \(-0.283719\pi\) | ||||
0.628378 | + | 0.777908i | \(0.283719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −700128. | −0.214741 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.19102e6 | −0.360814 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26936.0 | 0.00806022 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.71207e6 | −0.801664 | −0.400832 | − | 0.916151i | \(-0.631279\pi\) | ||||
−0.400832 | + | 0.916151i | \(0.631279\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 579672. | 0.169269 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.84384e6 | 1.10889 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −417900. | −0.119111 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −448880. | −0.126413 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.71746e6 | 1.03445 | 0.517227 | − | 0.855848i | \(-0.326964\pi\) | ||||
0.517227 | + | 0.855848i | \(0.326964\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.55250e6 | −0.976853 | −0.488426 | − | 0.872605i | \(-0.662429\pi\) | ||||
−0.488426 | + | 0.872605i | \(0.662429\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.74398e6 | −0.745640 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.04875e6 | −0.281643 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.20198e6 | 1.64612 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −169312. | −0.0444165 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.06205e6 | 1.05330 | 0.526650 | − | 0.850082i | \(-0.323448\pi\) | ||||
0.526650 | + | 0.850082i | \(0.323448\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.26287e6 | 1.86161 | 0.930804 | − | 0.365518i | \(-0.119108\pi\) | ||||
0.930804 | + | 0.365518i | \(0.119108\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 341000. | 0.0864035 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.15456e6 | −0.790197 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.41028e6 | 1.33986 | 0.669928 | − | 0.742426i | \(-0.266325\pi\) | ||||
0.669928 | + | 0.742426i | \(0.266325\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.55294e6 | −1.11480 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.51524e6 | −1.57733 | −0.788663 | − | 0.614826i | \(-0.789226\pi\) | ||||
−0.788663 | + | 0.614826i | \(0.789226\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.53425e6 | −0.606666 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.61500e6 | 0.382299 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −509950. | −0.119375 | −0.0596873 | − | 0.998217i | \(-0.519010\pi\) | ||||
−0.0596873 | + | 0.998217i | \(0.519010\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.39090e6 | 0.322000 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.78659e6 | −0.409053 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.37280e6 | −0.310870 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.22084e6 | 0.273444 | 0.136722 | − | 0.990609i | \(-0.456343\pi\) | ||||
0.136722 | + | 0.990609i | \(0.456343\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.15464e6 | −0.698905 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.07210e6 | 0.892413 | 0.446207 | − | 0.894930i | \(-0.352775\pi\) | ||||
0.446207 | + | 0.894930i | \(0.352775\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.02294e6 | −0.438561 | −0.219280 | − | 0.975662i | \(-0.570371\pi\) | ||||
−0.219280 | + | 0.975662i | \(0.570371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 244800. | 0.0525024 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.25097e6 | 0.689797 | 0.344898 | − | 0.938640i | \(-0.387913\pi\) | ||||
0.344898 | + | 0.938640i | \(0.387913\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.17066e7 | −2.45753 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.04903e6 | −0.217890 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 184112. | 0.0378381 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 662500. | 0.134726 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.41304e6 | 1.08929 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.27936e6 | 0.653056 | 0.326528 | − | 0.945188i | \(-0.394121\pi\) | ||||
0.326528 | + | 0.945188i | \(0.394121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 52052.0 | 0.0102583 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.28557e6 | −0.445786 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.97595e6 | 0.574475 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.53197e6 | 1.63015 | 0.815074 | − | 0.579357i | \(-0.196696\pi\) | ||||
0.815074 | + | 0.579357i | \(0.196696\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 618256. | 0.116922 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.51265e6 | 0.283162 | 0.141581 | − | 0.989927i | \(-0.454781\pi\) | ||||
0.141581 | + | 0.989927i | \(0.454781\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.72198e6 | −1.06030 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −839900. | −0.154069 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.26842e6 | −1.13833 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.49190e6 | −1.16713 | −0.583567 | − | 0.812065i | \(-0.698343\pi\) | ||||
−0.583567 | + | 0.812065i | \(0.698343\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.58669e6 | 0.282421 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.61770e6 | −1.51870 | −0.759349 | − | 0.650684i | \(-0.774482\pi\) | ||||
−0.759349 | + | 0.650684i | \(0.774482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.24745e6 | −0.392158 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.15799e6 | 0.200071 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.67323e6 | −0.457343 | −0.228671 | − | 0.973504i | \(-0.573438\pi\) | ||||
−0.228671 | + | 0.973504i | \(0.573438\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.44461e6 | 1.26122 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.99280e6 | 0.334326 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −487600. | −0.0810113 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.78902e6 | −0.294367 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.29390e6 | −0.373814 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.18500e6 | 0.998264 | 0.499132 | − | 0.866526i | \(-0.333652\pi\) | ||||
0.499132 | + | 0.866526i | \(0.333652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.89452e6 | −1.10217 | −0.551087 | − | 0.834448i | \(-0.685787\pi\) | ||||
−0.551087 | + | 0.834448i | \(0.685787\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 480000. | 0.0760051 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.10774e6 | −0.644283 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.42023e6 | 0.376026 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.54454e6 | 0.699445 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.68783e6 | 0.409811 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.95730e6 | −0.597743 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.37784e6 | 0.355834 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.96844e6 | −0.440104 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −155502. | −0.0228425 | −0.0114212 | − | 0.999935i | \(-0.503636\pi\) | ||||
−0.0114212 | + | 0.999935i | \(0.503636\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −428392. | −0.0623508 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 920750. | 0.132785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.26544e7 | 1.80831 | 0.904157 | − | 0.427201i | \(-0.140500\pi\) | ||||
0.904157 | + | 0.427201i | \(0.140500\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.33255e6 | 1.03830 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.61460e6 | 0.507202 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.40512e6 | −0.890665 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18200.0 | −0.00250807 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.07786e6 | 0.966638 | 0.483319 | − | 0.875444i | \(-0.339431\pi\) | ||||
0.483319 | + | 0.875444i | \(0.339431\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 355784. | 0.0481567 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −993376. | −0.133262 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 846636. | 0.112571 | 0.0562854 | − | 0.998415i | \(-0.482074\pi\) | ||||
0.0562854 | + | 0.998415i | \(0.482074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −279650. | −0.0368548 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.14707e6 | −1.19488 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.96041e6 | 0.642299 | 0.321149 | − | 0.947029i | \(-0.395931\pi\) | ||||
0.321149 | + | 0.947029i | \(0.395931\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.96505e6 | 1.15070 | 0.575351 | − | 0.817907i | \(-0.304866\pi\) | ||||
0.575351 | + | 0.817907i | \(0.304866\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.87821e6 | 0.238978 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.86000e6 | −0.234608 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.86080e6 | −0.357724 | −0.178862 | − | 0.983874i | \(-0.557242\pi\) | ||||
−0.178862 | + | 0.983874i | \(0.557242\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −210824. | −0.0261351 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.20947e6 | −0.394451 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.52921e6 | 0.430037 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.62305e6 | −0.196084 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.74027e6 | −0.807387 | −0.403694 | − | 0.914894i | \(-0.632274\pi\) | ||||
−0.403694 | + | 0.914894i | \(0.632274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.59488e6 | 0.308197 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.82345e6 | 0.214746 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.78609e6 | −0.208578 | −0.104289 | − | 0.994547i | \(-0.533257\pi\) | ||||
−0.104289 | + | 0.994547i | \(0.533257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.05440e6 | −0.932697 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.46000e6 | 0.397320 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.94620e6 | −0.563254 | −0.281627 | − | 0.959524i | \(-0.590874\pi\) | ||||
−0.281627 | + | 0.959524i | \(0.590874\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.58100e6 | −0.517337 | −0.258669 | − | 0.965966i | \(-0.583284\pi\) | ||||
−0.258669 | + | 0.965966i | \(0.583284\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.38406e7 | −1.55011 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.47868e6 | 0.386390 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.07999e6 | −0.779940 | −0.389970 | − | 0.920828i | \(-0.627515\pi\) | ||||
−0.389970 | + | 0.920828i | \(0.627515\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.61888e6 | 0.286136 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.45717e6 | −0.374643 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.09609e6 | −0.547754 | −0.273877 | − | 0.961765i | \(-0.588306\pi\) | ||||
−0.273877 | + | 0.961765i | \(0.588306\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −939800. | −0.100195 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.30003e7 | −1.37480 | −0.687400 | − | 0.726279i | \(-0.741248\pi\) | ||||
−0.687400 | + | 0.726279i | \(0.741248\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.84406e6 | 0.508139 | 0.254070 | − | 0.967186i | \(-0.418231\pi\) | ||||
0.254070 | + | 0.967186i | \(0.418231\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.59488e6 | −0.582186 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.94630e7 | −2.00905 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 627520. | 0.0637468 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 305396. | 0.0307777 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.22775e6 | −0.622670 | −0.311335 | − | 0.950300i | \(-0.600776\pi\) | ||||
−0.311335 | + | 0.950300i | \(0.600776\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.42261e6 | −0.438702 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.76380e6 | 0.173586 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.73630e6 | −0.560123 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.41110e6 | −0.718010 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.53280e6 | 0.147347 | 0.0736734 | − | 0.997282i | \(-0.476528\pi\) | ||||
0.0736734 | + | 0.997282i | \(0.476528\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.74382e7 | −1.66332 | −0.831659 | − | 0.555287i | \(-0.812609\pi\) | ||||
−0.831659 | + | 0.555287i | \(0.812609\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −124400. | −0.0117739 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.25469e6 | 0.399583 | 0.199792 | − | 0.979838i | \(-0.435974\pi\) | ||||
0.199792 | + | 0.979838i | \(0.435974\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.96296e6 | 0.276130 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88006e6 | 0.173868 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.01085e6 | −0.276316 | −0.138158 | − | 0.990410i | \(-0.544118\pi\) | ||||
−0.138158 | + | 0.990410i | \(0.544118\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.91130e6 | −0.174071 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.80170e6 | 0.795524 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.11462e6 | −0.727871 | −0.363936 | − | 0.931424i | \(-0.618567\pi\) | ||||
−0.363936 | + | 0.931424i | \(0.618567\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.47370e6 | −0.220213 | −0.110107 | − | 0.993920i | \(-0.535119\pi\) | ||||
−0.110107 | + | 0.993920i | \(0.535119\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.91963e6 | −0.169603 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.08800e6 | 0.446162 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.01482e7 | −0.883228 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.48630e6 | 0.387546 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.78070e6 | 0.409907 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.77063e6 | 0.491117 | 0.245559 | − | 0.969382i | \(-0.421029\pi\) | ||||
0.245559 | + | 0.969382i | \(0.421029\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.17500e6 | 0.0992610 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.67197e7 | −1.40203 | −0.701014 | − | 0.713147i | \(-0.747269\pi\) | ||||
−0.701014 | + | 0.713147i | \(0.747269\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.28553e7 | 1.90245 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 93392.0 | 0.00771688 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.14532e6 | 0.586097 | 0.293049 | − | 0.956098i | \(-0.405330\pi\) | ||||
0.293049 | + | 0.956098i | \(0.405330\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.62295e6 | 0.295009 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.38404e6 | −0.192718 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.81996e6 | 0.547310 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.78395e6 | −0.699833 | −0.349917 | − | 0.936781i | \(-0.613790\pi\) | ||||
−0.349917 | + | 0.936781i | \(0.613790\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.45043e6 | −0.510218 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.80550e6 | −0.220317 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.57698e7 | 1.22955 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.94134e6 | 0.150282 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.60141e7 | 1.23086 | 0.615428 | − | 0.788193i | \(-0.288983\pi\) | ||||
0.615428 | + | 0.788193i | \(0.288983\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −192920. | −0.0147228 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.20880e6 | 0.0915971 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.72604e7 | −1.29868 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.91354e7 | 1.42962 | 0.714811 | − | 0.699318i | \(-0.246513\pi\) | ||||
0.714811 | + | 0.699318i | \(0.246513\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.57272e6 | −0.561795 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.28525e6 | −0.536686 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.05820e6 | −0.0774110 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −195520. | −0.0142034 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.02934e7 | −0.742566 | −0.371283 | − | 0.928520i | \(-0.621082\pi\) | ||||
−0.371283 | + | 0.928520i | \(0.621082\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.74477e6 | −0.268279 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 443192. | 0.0315316 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.13125e6 | 0.150588 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.93264e7 | 1.35618 | 0.678088 | − | 0.734981i | \(-0.262809\pi\) | ||||
0.678088 | + | 0.734981i | \(0.262809\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.98715e6 | −0.626330 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.08743e6 | 0.144484 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.26197e6 | −0.361733 | −0.180866 | − | 0.983508i | \(-0.557890\pi\) | ||||
−0.180866 | + | 0.983508i | \(0.557890\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.00570e6 | 0.136945 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.02386e6 | −0.611961 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.82944e7 | 1.90585 | 0.952927 | − | 0.303199i | \(-0.0980548\pi\) | ||||
0.952927 | + | 0.303199i | \(0.0980548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.21264e6 | 0.0811309 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.09863e7 | −1.39464 | −0.697321 | − | 0.716759i | \(-0.745625\pi\) | ||||
−0.697321 | + | 0.716759i | \(0.745625\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.00938e7 | 0.666288 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.79453e6 | −0.248804 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.03921e7 | −1.97950 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.89668e7 | 1.22714 | 0.613572 | − | 0.789639i | \(-0.289732\pi\) | ||||
0.613572 | + | 0.789639i | \(0.289732\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.57499e6 | 0.422579 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.11662e7 | −0.712915 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.08257e7 | 0.686617 | 0.343309 | − | 0.939223i | \(-0.388452\pi\) | ||||
0.343309 | + | 0.939223i | \(0.388452\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.76179e6 | −0.111007 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.90534e7 | 1.19264 | 0.596322 | − | 0.802745i | \(-0.296628\pi\) | ||||
0.596322 | + | 0.802745i | \(0.296628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.07136e6 | 0.439736 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.52265e6 | −0.588307 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.72572e6 | 0.351432 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.57826e7 | −0.962415 | −0.481208 | − | 0.876607i | \(-0.659802\pi\) | ||||
−0.481208 | + | 0.876607i | \(0.659802\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.22497e6 | −0.316554 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.44049e7 | 1.46902 | 0.734510 | − | 0.678598i | \(-0.237412\pi\) | ||||
0.734510 | + | 0.678598i | \(0.237412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.53000e6 | 0.0915034 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −139776. | −0.00830577 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.96188e6 | −0.588163 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.83190e6 | −0.283459 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.41080e6 | 0.373687 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.55645e6 | −0.379747 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.37607e7 | 1.94301 | 0.971505 | − | 0.237019i | \(-0.0761704\pi\) | ||||
0.971505 | + | 0.237019i | \(0.0761704\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.51334e6 | 0.486864 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.14771e6 | −0.122049 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.23837e6 | 0.521690 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.38460e6 | −0.133813 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.19885e7 | −1.22617 | −0.613083 | − | 0.790019i | \(-0.710071\pi\) | ||||
−0.613083 | + | 0.790019i | \(0.710071\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.02837e7 | −1.12403 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.30110e7 | −1.26723 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.73855e6 | 0.314061 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.42848e7 | −0.776935 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.76436e6 | −0.311578 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.93597e7 | −1.57717 | −0.788587 | − | 0.614923i | \(-0.789187\pi\) | ||||
−0.788587 | + | 0.614923i | \(0.789187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.17703e7 | 1.69617 | 0.848083 | − | 0.529863i | \(-0.177757\pi\) | ||||
0.848083 | + | 0.529863i | \(0.177757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −372992. | −0.0197912 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.86410e6 | 0.203777 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.31864e6 | −0.0691148 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.24650e7 | −0.649357 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.71430e6 | 0.140540 | 0.0702699 | − | 0.997528i | \(-0.477614\pi\) | ||||
0.0702699 | + | 0.997528i | \(0.477614\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.25866e7 | 0.647753 | 0.323877 | − | 0.946099i | \(-0.395014\pi\) | ||||
0.323877 | + | 0.946099i | \(0.395014\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 370000. | 0.0189263 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.72355e6 | −0.443537 | −0.221768 | − | 0.975099i | \(-0.571183\pi\) | ||||
−0.221768 | + | 0.975099i | \(0.571183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.06178e7 | 0.536597 | 0.268299 | − | 0.963336i | \(-0.413539\pi\) | ||||
0.268299 | + | 0.963336i | \(0.413539\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −441192. | −0.0221628 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.36556e7 | −1.68053 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.91680e6 | 0.492216 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.60224e6 | 0.227068 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.67765e7 | −0.822805 | −0.411403 | − | 0.911454i | \(-0.634961\pi\) | ||||
−0.411403 | + | 0.911454i | \(0.634961\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.88305e6 | −0.433084 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 768792. | 0.0372597 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.23742e6 | 0.348692 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.67162e7 | 1.27958 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.32754e6 | 0.0632087 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 541632. | 0.0256378 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.20186e7 | 1.03613 | 0.518067 | − | 0.855340i | \(-0.326652\pi\) | ||||
0.518067 | + | 0.855340i | \(0.326652\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.01550e6 | 0.281421 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.16676e7 | 1.47287 | 0.736434 | − | 0.676510i | \(-0.236508\pi\) | ||||
0.736434 | + | 0.676510i | \(0.236508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.58064e7 | 0.730886 | 0.365443 | − | 0.930834i | \(-0.380918\pi\) | ||||
0.365443 | + | 0.930834i | \(0.380918\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.21766e6 | −0.331809 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.44287e7 | 0.659476 | 0.329738 | − | 0.944072i | \(-0.393040\pi\) | ||||
0.329738 | + | 0.944072i | \(0.393040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.43368e7 | −0.651499 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.58331e6 | −0.252257 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.93728e6 | −0.221788 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.74380e7 | −0.778845 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.70216e7 | 1.19999 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.00000e6 | 0.132465 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −247902. | −0.0108838 | −0.00544191 | − | 0.999985i | \(-0.501732\pi\) | ||||
−0.00544191 | + | 0.999985i | \(0.501732\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.77922e6 | 0.383252 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.10268e7 | 1.78085 | 0.890426 | − | 0.455128i | \(-0.150406\pi\) | ||||
0.890426 | + | 0.455128i | \(0.150406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.18015e7 | 1.80422 | 0.902112 | − | 0.431503i | \(-0.142016\pi\) | ||||
0.902112 | + | 0.431503i | \(0.142016\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.00200e6 | −0.0859223 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.10476e7 | 0.898241 | 0.449120 | − | 0.893471i | \(-0.351737\pi\) | ||||
0.449120 | + | 0.893471i | \(0.351737\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.35460e7 | 0.574852 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.05087e6 | −0.297542 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.28133e7 | 0.537690 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.48615e7 | 0.620162 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.40454e6 | −0.141279 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.34768e6 | 0.344482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.00136e7 | 1.64208 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −955392. | −0.0389908 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.67745e6 | −0.108668 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.48309e6 | 0.302039 | 0.151019 | − | 0.988531i | \(-0.451744\pi\) | ||||
0.151019 | + | 0.988531i | \(0.451744\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.04068e7 | −0.819155 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.63165e6 | 0.264744 | 0.132372 | − | 0.991200i | \(-0.457741\pi\) | ||||
0.132372 | + | 0.991200i | \(0.457741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.47397e6 | −0.0982239 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.23020e6 | −0.127549 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.46788e7 | −0.576457 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.68976e7 | 0.659990 | 0.329995 | − | 0.943983i | \(-0.392953\pi\) | ||||
0.329995 | + | 0.943983i | \(0.392953\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.51003e6 | 0.369431 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.33733e6 | −0.360760 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −113750. | −0.00437116 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.42741e6 | −0.169219 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.28653e7 | −0.489081 | −0.244541 | − | 0.969639i | \(-0.578637\pi\) | ||||
−0.244541 | + | 0.969639i | \(0.578637\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.12604e7 | 0.803892 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.49219e6 | −0.356995 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.20860e6 | −0.232255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.06887e7 | 0.397718 | 0.198859 | − | 0.980028i | \(-0.436276\pi\) | ||||
0.198859 | + | 0.980028i | \(0.436276\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.71766e6 | 0.211619 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.82455e7 | −1.03986 | −0.519930 | − | 0.854209i | \(-0.674042\pi\) | ||||
−0.519930 | + | 0.854209i | \(0.674042\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.79684e7 | 1.02421 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.02400e6 | 0.328715 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.70892e7 | −0.619222 | −0.309611 | − | 0.950863i | \(-0.600199\pi\) | ||||
−0.309611 | + | 0.950863i | \(0.600199\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.10894e7 | 0.399706 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.49849e6 | 0.304713 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.22259e7 | 0.792735 | 0.396367 | − | 0.918092i | \(-0.370271\pi\) | ||||
0.396367 | + | 0.918092i | \(0.370271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.17388e7 | 0.416500 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.01872e6 | 0.0712519 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.78243e7 | 0.976961 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.26364e7 | −0.790678 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.59323e7 | −1.24859 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.31765e6 | −0.0455493 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.41551e7 | −0.830696 | −0.415348 | − | 0.909663i | \(-0.636340\pi\) | ||||
−0.415348 | + | 0.909663i | \(0.636340\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.11472e6 | 0.243416 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.48313e7 | −1.86630 | −0.933149 | − | 0.359491i | \(-0.882950\pi\) | ||||
−0.933149 | + | 0.359491i | \(0.882950\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.15462e7 | −0.729608 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 715000. | 0.0240877 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.56612e7 | −0.524915 | −0.262457 | − | 0.964944i | \(-0.584533\pi\) | ||||
−0.262457 | + | 0.964944i | \(0.584533\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.50028e7 | −0.500281 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.36041e6 | 0.277367 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.63420e7 | 0.539412 | 0.269706 | − | 0.962943i | \(-0.413073\pi\) | ||||
0.269706 | + | 0.962943i | \(0.413073\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.13966e7 | 0.374268 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.28358e6 | 0.303335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.70214e6 | 0.120355 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.37576e7 | −0.444997 | −0.222498 | − | 0.974933i | \(-0.571421\pi\) | ||||
−0.222498 | + | 0.974933i | \(0.571421\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.23994e7 | −0.399050 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.16250e7 | 0.692466 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.29097e7 | 0.411320 | 0.205660 | − | 0.978624i | \(-0.434066\pi\) | ||||
0.205660 | + | 0.978624i | \(0.434066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −342160. | −0.0108471 |
(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.g.1.1 | 1 | ||
4.3 | odd | 2 | 320.6.a.j.1.1 | 1 | |||
8.3 | odd | 2 | 5.6.a.a.1.1 | ✓ | 1 | ||
8.5 | even | 2 | 80.6.a.e.1.1 | 1 | |||
24.5 | odd | 2 | 720.6.a.a.1.1 | 1 | |||
24.11 | even | 2 | 45.6.a.b.1.1 | 1 | |||
40.3 | even | 4 | 25.6.b.a.24.1 | 2 | |||
40.13 | odd | 4 | 400.6.c.j.49.2 | 2 | |||
40.19 | odd | 2 | 25.6.a.a.1.1 | 1 | |||
40.27 | even | 4 | 25.6.b.a.24.2 | 2 | |||
40.29 | even | 2 | 400.6.a.g.1.1 | 1 | |||
40.37 | odd | 4 | 400.6.c.j.49.1 | 2 | |||
56.27 | even | 2 | 245.6.a.b.1.1 | 1 | |||
88.43 | even | 2 | 605.6.a.a.1.1 | 1 | |||
104.51 | odd | 2 | 845.6.a.b.1.1 | 1 | |||
120.59 | even | 2 | 225.6.a.f.1.1 | 1 | |||
120.83 | odd | 4 | 225.6.b.e.199.2 | 2 | |||
120.107 | odd | 4 | 225.6.b.e.199.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.6.a.a.1.1 | ✓ | 1 | 8.3 | odd | 2 | ||
25.6.a.a.1.1 | 1 | 40.19 | odd | 2 | |||
25.6.b.a.24.1 | 2 | 40.3 | even | 4 | |||
25.6.b.a.24.2 | 2 | 40.27 | even | 4 | |||
45.6.a.b.1.1 | 1 | 24.11 | even | 2 | |||
80.6.a.e.1.1 | 1 | 8.5 | even | 2 | |||
225.6.a.f.1.1 | 1 | 120.59 | even | 2 | |||
225.6.b.e.199.1 | 2 | 120.107 | odd | 4 | |||
225.6.b.e.199.2 | 2 | 120.83 | odd | 4 | |||
245.6.a.b.1.1 | 1 | 56.27 | even | 2 | |||
320.6.a.g.1.1 | 1 | 1.1 | even | 1 | trivial | ||
320.6.a.j.1.1 | 1 | 4.3 | odd | 2 | |||
400.6.a.g.1.1 | 1 | 40.29 | even | 2 | |||
400.6.c.j.49.1 | 2 | 40.37 | odd | 4 | |||
400.6.c.j.49.2 | 2 | 40.13 | odd | 4 | |||
605.6.a.a.1.1 | 1 | 88.43 | even | 2 | |||
720.6.a.a.1.1 | 1 | 24.5 | odd | 2 | |||
845.6.a.b.1.1 | 1 | 104.51 | odd | 2 |