Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,6,Mod(1,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("845.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.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: | \(135.524327742\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 845.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | −0.353553 | −0.176777 | − | 0.984251i | \(-0.556567\pi\) | ||||
−0.176777 | + | 0.984251i | \(0.556567\pi\) | |||||||
\(3\) | −4.00000 | −0.256600 | −0.128300 | − | 0.991735i | \(-0.540952\pi\) | ||||
−0.128300 | + | 0.991735i | \(0.540952\pi\) | |||||||
\(4\) | −28.0000 | −0.875000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 8.00000 | 0.0907218 | ||||||||
\(7\) | −192.000 | −1.48100 | −0.740502 | − | 0.672054i | \(-0.765412\pi\) | ||||
−0.740502 | + | 0.672054i | \(0.765412\pi\) | |||||||
\(8\) | 120.000 | 0.662913 | ||||||||
\(9\) | −227.000 | −0.934156 | ||||||||
\(10\) | 50.0000 | 0.158114 | ||||||||
\(11\) | 148.000 | 0.368791 | 0.184395 | − | 0.982852i | \(-0.440967\pi\) | ||||
0.184395 | + | 0.982852i | \(0.440967\pi\) | |||||||
\(12\) | 112.000 | 0.224525 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 384.000 | 0.523614 | ||||||||
\(15\) | 100.000 | 0.114755 | ||||||||
\(16\) | 656.000 | 0.640625 | ||||||||
\(17\) | −1678.00 | −1.40822 | −0.704109 | − | 0.710092i | \(-0.748653\pi\) | ||||
−0.704109 | + | 0.710092i | \(0.748653\pi\) | |||||||
\(18\) | 454.000 | 0.330274 | ||||||||
\(19\) | −1060.00 | −0.673631 | −0.336815 | − | 0.941571i | \(-0.609350\pi\) | ||||
−0.336815 | + | 0.941571i | \(0.609350\pi\) | |||||||
\(20\) | 700.000 | 0.391312 | ||||||||
\(21\) | 768.000 | 0.380026 | ||||||||
\(22\) | −296.000 | −0.130387 | ||||||||
\(23\) | 2976.00 | 1.17304 | 0.586521 | − | 0.809934i | \(-0.300497\pi\) | ||||
0.586521 | + | 0.809934i | \(0.300497\pi\) | |||||||
\(24\) | −480.000 | −0.170103 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1880.00 | 0.496305 | ||||||||
\(28\) | 5376.00 | 1.29588 | ||||||||
\(29\) | −3410.00 | −0.752938 | −0.376469 | − | 0.926429i | \(-0.622862\pi\) | ||||
−0.376469 | + | 0.926429i | \(0.622862\pi\) | |||||||
\(30\) | −200.000 | −0.0405720 | ||||||||
\(31\) | 2448.00 | 0.457517 | 0.228758 | − | 0.973483i | \(-0.426533\pi\) | ||||
0.228758 | + | 0.973483i | \(0.426533\pi\) | |||||||
\(32\) | −5152.00 | −0.889408 | ||||||||
\(33\) | −592.000 | −0.0946317 | ||||||||
\(34\) | 3356.00 | 0.497880 | ||||||||
\(35\) | 4800.00 | 0.662325 | ||||||||
\(36\) | 6356.00 | 0.817387 | ||||||||
\(37\) | −182.000 | −0.0218558 | −0.0109279 | − | 0.999940i | \(-0.503479\pi\) | ||||
−0.0109279 | + | 0.999940i | \(0.503479\pi\) | |||||||
\(38\) | 2120.00 | 0.238164 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3000.00 | −0.296464 | ||||||||
\(41\) | 9398.00 | 0.873124 | 0.436562 | − | 0.899674i | \(-0.356196\pi\) | ||||
0.436562 | + | 0.899674i | \(0.356196\pi\) | |||||||
\(42\) | −1536.00 | −0.134359 | ||||||||
\(43\) | −1244.00 | −0.102600 | −0.0513002 | − | 0.998683i | \(-0.516337\pi\) | ||||
−0.0513002 | + | 0.998683i | \(0.516337\pi\) | |||||||
\(44\) | −4144.00 | −0.322692 | ||||||||
\(45\) | 5675.00 | 0.417767 | ||||||||
\(46\) | −5952.00 | −0.414733 | ||||||||
\(47\) | 12088.0 | 0.798196 | 0.399098 | − | 0.916908i | \(-0.369323\pi\) | ||||
0.399098 | + | 0.916908i | \(0.369323\pi\) | |||||||
\(48\) | −2624.00 | −0.164384 | ||||||||
\(49\) | 20057.0 | 1.19337 | ||||||||
\(50\) | −1250.00 | −0.0707107 | ||||||||
\(51\) | 6712.00 | 0.361349 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 23846.0 | 1.16607 | 0.583037 | − | 0.812446i | \(-0.301864\pi\) | ||||
0.583037 | + | 0.812446i | \(0.301864\pi\) | |||||||
\(54\) | −3760.00 | −0.175470 | ||||||||
\(55\) | −3700.00 | −0.164928 | ||||||||
\(56\) | −23040.0 | −0.981776 | ||||||||
\(57\) | 4240.00 | 0.172854 | ||||||||
\(58\) | 6820.00 | 0.266204 | ||||||||
\(59\) | 20020.0 | 0.748745 | 0.374373 | − | 0.927278i | \(-0.377858\pi\) | ||||
0.374373 | + | 0.927278i | \(0.377858\pi\) | |||||||
\(60\) | −2800.00 | −0.100411 | ||||||||
\(61\) | 32302.0 | 1.11149 | 0.555744 | − | 0.831353i | \(-0.312433\pi\) | ||||
0.555744 | + | 0.831353i | \(0.312433\pi\) | |||||||
\(62\) | −4896.00 | −0.161757 | ||||||||
\(63\) | 43584.0 | 1.38349 | ||||||||
\(64\) | −10688.0 | −0.326172 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1184.00 | 0.0334574 | ||||||||
\(67\) | −60972.0 | −1.65937 | −0.829685 | − | 0.558231i | \(-0.811480\pi\) | ||||
−0.829685 | + | 0.558231i | \(0.811480\pi\) | |||||||
\(68\) | 46984.0 | 1.23219 | ||||||||
\(69\) | −11904.0 | −0.301003 | ||||||||
\(70\) | −9600.00 | −0.234167 | ||||||||
\(71\) | 32648.0 | 0.768618 | 0.384309 | − | 0.923204i | \(-0.374440\pi\) | ||||
0.384309 | + | 0.923204i | \(0.374440\pi\) | |||||||
\(72\) | −27240.0 | −0.619264 | ||||||||
\(73\) | 38774.0 | 0.851596 | 0.425798 | − | 0.904818i | \(-0.359993\pi\) | ||||
0.425798 | + | 0.904818i | \(0.359993\pi\) | |||||||
\(74\) | 364.000 | 0.00772720 | ||||||||
\(75\) | −2500.00 | −0.0513200 | ||||||||
\(76\) | 29680.0 | 0.589427 | ||||||||
\(77\) | −28416.0 | −0.546180 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −33360.0 | −0.601393 | −0.300696 | − | 0.953720i | \(-0.597219\pi\) | ||||
−0.300696 | + | 0.953720i | \(0.597219\pi\) | |||||||
\(80\) | −16400.0 | −0.286496 | ||||||||
\(81\) | 47641.0 | 0.806805 | ||||||||
\(82\) | −18796.0 | −0.308696 | ||||||||
\(83\) | −16716.0 | −0.266340 | −0.133170 | − | 0.991093i | \(-0.542516\pi\) | ||||
−0.133170 | + | 0.991093i | \(0.542516\pi\) | |||||||
\(84\) | −21504.0 | −0.332522 | ||||||||
\(85\) | 41950.0 | 0.629774 | ||||||||
\(86\) | 2488.00 | 0.0362747 | ||||||||
\(87\) | 13640.0 | 0.193204 | ||||||||
\(88\) | 17760.0 | 0.244476 | ||||||||
\(89\) | −101370. | −1.35655 | −0.678273 | − | 0.734810i | \(-0.737271\pi\) | ||||
−0.678273 | + | 0.734810i | \(0.737271\pi\) | |||||||
\(90\) | −11350.0 | −0.147703 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −83328.0 | −1.02641 | ||||||||
\(93\) | −9792.00 | −0.117399 | ||||||||
\(94\) | −24176.0 | −0.282205 | ||||||||
\(95\) | 26500.0 | 0.301257 | ||||||||
\(96\) | 20608.0 | 0.228222 | ||||||||
\(97\) | 119038. | 1.28457 | 0.642283 | − | 0.766468i | \(-0.277987\pi\) | ||||
0.642283 | + | 0.766468i | \(0.277987\pi\) | |||||||
\(98\) | −40114.0 | −0.421921 | ||||||||
\(99\) | −33596.0 | −0.344508 | ||||||||
\(100\) | −17500.0 | −0.175000 | ||||||||
\(101\) | −89898.0 | −0.876893 | −0.438446 | − | 0.898757i | \(-0.644471\pi\) | ||||
−0.438446 | + | 0.898757i | \(0.644471\pi\) | |||||||
\(102\) | −13424.0 | −0.127756 | ||||||||
\(103\) | −19504.0 | −0.181147 | −0.0905734 | − | 0.995890i | \(-0.528870\pi\) | ||||
−0.0905734 | + | 0.995890i | \(0.528870\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −19200.0 | −0.169953 | ||||||||
\(106\) | −47692.0 | −0.412269 | ||||||||
\(107\) | 158292. | 1.33659 | 0.668297 | − | 0.743895i | \(-0.267024\pi\) | ||||
0.668297 | + | 0.743895i | \(0.267024\pi\) | |||||||
\(108\) | −52640.0 | −0.434267 | ||||||||
\(109\) | −36830.0 | −0.296917 | −0.148459 | − | 0.988919i | \(-0.547431\pi\) | ||||
−0.148459 | + | 0.988919i | \(0.547431\pi\) | |||||||
\(110\) | 7400.00 | 0.0583109 | ||||||||
\(111\) | 728.000 | 0.00560821 | ||||||||
\(112\) | −125952. | −0.948768 | ||||||||
\(113\) | 11186.0 | 0.0824098 | 0.0412049 | − | 0.999151i | \(-0.486880\pi\) | ||||
0.0412049 | + | 0.999151i | \(0.486880\pi\) | |||||||
\(114\) | −8480.00 | −0.0611130 | ||||||||
\(115\) | −74400.0 | −0.524600 | ||||||||
\(116\) | 95480.0 | 0.658821 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −40040.0 | −0.264721 | ||||||||
\(119\) | 322176. | 2.08557 | ||||||||
\(120\) | 12000.0 | 0.0760726 | ||||||||
\(121\) | −139147. | −0.863993 | ||||||||
\(122\) | −64604.0 | −0.392970 | ||||||||
\(123\) | −37592.0 | −0.224044 | ||||||||
\(124\) | −68544.0 | −0.400327 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −87168.0 | −0.489137 | ||||||||
\(127\) | 70552.0 | 0.388150 | 0.194075 | − | 0.980987i | \(-0.437829\pi\) | ||||
0.194075 | + | 0.980987i | \(0.437829\pi\) | |||||||
\(128\) | 186240. | 1.00473 | ||||||||
\(129\) | 4976.00 | 0.0263273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 76452.0 | 0.389234 | 0.194617 | − | 0.980879i | \(-0.437654\pi\) | ||||
0.194617 | + | 0.980879i | \(0.437654\pi\) | |||||||
\(132\) | 16576.0 | 0.0828028 | ||||||||
\(133\) | 203520. | 0.997650 | ||||||||
\(134\) | 121944. | 0.586676 | ||||||||
\(135\) | −47000.0 | −0.221954 | ||||||||
\(136\) | −201360. | −0.933525 | ||||||||
\(137\) | 144918. | 0.659661 | 0.329831 | − | 0.944040i | \(-0.393008\pi\) | ||||
0.329831 | + | 0.944040i | \(0.393008\pi\) | |||||||
\(138\) | 23808.0 | 0.106420 | ||||||||
\(139\) | 112220. | 0.492644 | 0.246322 | − | 0.969188i | \(-0.420778\pi\) | ||||
0.246322 | + | 0.969188i | \(0.420778\pi\) | |||||||
\(140\) | −134400. | −0.579534 | ||||||||
\(141\) | −48352.0 | −0.204817 | ||||||||
\(142\) | −65296.0 | −0.271748 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −148912. | −0.598444 | ||||||||
\(145\) | 85250.0 | 0.336724 | ||||||||
\(146\) | −77548.0 | −0.301085 | ||||||||
\(147\) | −80228.0 | −0.306219 | ||||||||
\(148\) | 5096.00 | 0.0191238 | ||||||||
\(149\) | −403750. | −1.48986 | −0.744932 | − | 0.667140i | \(-0.767518\pi\) | ||||
−0.744932 | + | 0.667140i | \(0.767518\pi\) | |||||||
\(150\) | 5000.00 | 0.0181444 | ||||||||
\(151\) | 446648. | 1.59413 | 0.797064 | − | 0.603895i | \(-0.206385\pi\) | ||||
0.797064 | + | 0.603895i | \(0.206385\pi\) | |||||||
\(152\) | −127200. | −0.446558 | ||||||||
\(153\) | 380906. | 1.31550 | ||||||||
\(154\) | 56832.0 | 0.193104 | ||||||||
\(155\) | −61200.0 | −0.204608 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −262258. | −0.849141 | −0.424570 | − | 0.905395i | \(-0.639575\pi\) | ||||
−0.424570 | + | 0.905395i | \(0.639575\pi\) | |||||||
\(158\) | 66720.0 | 0.212625 | ||||||||
\(159\) | −95384.0 | −0.299215 | ||||||||
\(160\) | 128800. | 0.397755 | ||||||||
\(161\) | −571392. | −1.73728 | ||||||||
\(162\) | −95282.0 | −0.285248 | ||||||||
\(163\) | 154564. | 0.455658 | 0.227829 | − | 0.973701i | \(-0.426837\pi\) | ||||
0.227829 | + | 0.973701i | \(0.426837\pi\) | |||||||
\(164\) | −263144. | −0.763983 | ||||||||
\(165\) | 14800.0 | 0.0423206 | ||||||||
\(166\) | 33432.0 | 0.0941656 | ||||||||
\(167\) | −396672. | −1.10063 | −0.550314 | − | 0.834958i | \(-0.685492\pi\) | ||||
−0.550314 | + | 0.834958i | \(0.685492\pi\) | |||||||
\(168\) | 92160.0 | 0.251924 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −83900.0 | −0.222659 | ||||||||
\(171\) | 240620. | 0.629276 | ||||||||
\(172\) | 34832.0 | 0.0897754 | ||||||||
\(173\) | −573474. | −1.45680 | −0.728398 | − | 0.685155i | \(-0.759735\pi\) | ||||
−0.728398 | + | 0.685155i | \(0.759735\pi\) | |||||||
\(174\) | −27280.0 | −0.0683079 | ||||||||
\(175\) | −120000. | −0.296201 | ||||||||
\(176\) | 97088.0 | 0.236257 | ||||||||
\(177\) | −80080.0 | −0.192128 | ||||||||
\(178\) | 202740. | 0.479611 | ||||||||
\(179\) | −594460. | −1.38672 | −0.693362 | − | 0.720589i | \(-0.743871\pi\) | ||||
−0.693362 | + | 0.720589i | \(0.743871\pi\) | |||||||
\(180\) | −158900. | −0.365547 | ||||||||
\(181\) | −107098. | −0.242988 | −0.121494 | − | 0.992592i | \(-0.538769\pi\) | ||||
−0.121494 | + | 0.992592i | \(0.538769\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −129208. | −0.285208 | ||||||||
\(184\) | 357120. | 0.777624 | ||||||||
\(185\) | 4550.00 | 0.00977422 | ||||||||
\(186\) | 19584.0 | 0.0415068 | ||||||||
\(187\) | −248344. | −0.519337 | ||||||||
\(188\) | −338464. | −0.698422 | ||||||||
\(189\) | −360960. | −0.735029 | ||||||||
\(190\) | −53000.0 | −0.106510 | ||||||||
\(191\) | 469552. | 0.931323 | 0.465661 | − | 0.884963i | \(-0.345816\pi\) | ||||
0.465661 | + | 0.884963i | \(0.345816\pi\) | |||||||
\(192\) | 42752.0 | 0.0836957 | ||||||||
\(193\) | −52706.0 | −0.101851 | −0.0509257 | − | 0.998702i | \(-0.516217\pi\) | ||||
−0.0509257 | + | 0.998702i | \(0.516217\pi\) | |||||||
\(194\) | −238076. | −0.454163 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −561596. | −1.04420 | ||||||||
\(197\) | −455862. | −0.836889 | −0.418444 | − | 0.908242i | \(-0.637425\pi\) | ||||
−0.418444 | + | 0.908242i | \(0.637425\pi\) | |||||||
\(198\) | 67192.0 | 0.121802 | ||||||||
\(199\) | 865000. | 1.54840 | 0.774200 | − | 0.632940i | \(-0.218152\pi\) | ||||
0.774200 | + | 0.632940i | \(0.218152\pi\) | |||||||
\(200\) | 75000.0 | 0.132583 | ||||||||
\(201\) | 243888. | 0.425795 | ||||||||
\(202\) | 179796. | 0.310028 | ||||||||
\(203\) | 654720. | 1.11510 | ||||||||
\(204\) | −187936. | −0.316180 | ||||||||
\(205\) | −234950. | −0.390473 | ||||||||
\(206\) | 39008.0 | 0.0640451 | ||||||||
\(207\) | −675552. | −1.09580 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −156880. | −0.248429 | ||||||||
\(210\) | 38400.0 | 0.0600873 | ||||||||
\(211\) | 1.10565e6 | 1.70967 | 0.854835 | − | 0.518900i | \(-0.173658\pi\) | ||||
0.854835 | + | 0.518900i | \(0.173658\pi\) | |||||||
\(212\) | −667688. | −1.02031 | ||||||||
\(213\) | −130592. | −0.197228 | ||||||||
\(214\) | −316584. | −0.472557 | ||||||||
\(215\) | 31100.0 | 0.0458843 | ||||||||
\(216\) | 225600. | 0.329007 | ||||||||
\(217\) | −470016. | −0.677584 | ||||||||
\(218\) | 73660.0 | 0.104976 | ||||||||
\(219\) | −155096. | −0.218520 | ||||||||
\(220\) | 103600. | 0.144312 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1456.00 | −0.00198280 | ||||||||
\(223\) | −1.12158e6 | −1.51031 | −0.755156 | − | 0.655545i | \(-0.772439\pi\) | ||||
−0.755156 | + | 0.655545i | \(0.772439\pi\) | |||||||
\(224\) | 989184. | 1.31722 | ||||||||
\(225\) | −141875. | −0.186831 | ||||||||
\(226\) | −22372.0 | −0.0291363 | ||||||||
\(227\) | 23348.0 | 0.0300736 | 0.0150368 | − | 0.999887i | \(-0.495213\pi\) | ||||
0.0150368 | + | 0.999887i | \(0.495213\pi\) | |||||||
\(228\) | −118720. | −0.151247 | ||||||||
\(229\) | 596010. | 0.751043 | 0.375522 | − | 0.926814i | \(-0.377464\pi\) | ||||
0.375522 | + | 0.926814i | \(0.377464\pi\) | |||||||
\(230\) | 148800. | 0.185474 | ||||||||
\(231\) | 113664. | 0.140150 | ||||||||
\(232\) | −409200. | −0.499132 | ||||||||
\(233\) | −485334. | −0.585667 | −0.292834 | − | 0.956163i | \(-0.594598\pi\) | ||||
−0.292834 | + | 0.956163i | \(0.594598\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −302200. | −0.356964 | ||||||||
\(236\) | −560560. | −0.655152 | ||||||||
\(237\) | 133440. | 0.154317 | ||||||||
\(238\) | −644352. | −0.737362 | ||||||||
\(239\) | 48880.0 | 0.0553524 | 0.0276762 | − | 0.999617i | \(-0.491189\pi\) | ||||
0.0276762 | + | 0.999617i | \(0.491189\pi\) | |||||||
\(240\) | 65600.0 | 0.0735150 | ||||||||
\(241\) | 110798. | 0.122882 | 0.0614411 | − | 0.998111i | \(-0.480430\pi\) | ||||
0.0614411 | + | 0.998111i | \(0.480430\pi\) | |||||||
\(242\) | 278294. | 0.305468 | ||||||||
\(243\) | −647404. | −0.703331 | ||||||||
\(244\) | −904456. | −0.972552 | ||||||||
\(245\) | −501425. | −0.533692 | ||||||||
\(246\) | 75184.0 | 0.0792114 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 293760. | 0.303294 | ||||||||
\(249\) | 66864.0 | 0.0683430 | ||||||||
\(250\) | 31250.0 | 0.0316228 | ||||||||
\(251\) | −1.64375e6 | −1.64684 | −0.823419 | − | 0.567434i | \(-0.807936\pi\) | ||||
−0.823419 | + | 0.567434i | \(0.807936\pi\) | |||||||
\(252\) | −1.22035e6 | −1.21055 | ||||||||
\(253\) | 440448. | 0.432607 | ||||||||
\(254\) | −141104. | −0.137232 | ||||||||
\(255\) | −167800. | −0.161600 | ||||||||
\(256\) | −30464.0 | −0.0290527 | ||||||||
\(257\) | 1.30624e6 | 1.23365 | 0.616823 | − | 0.787102i | \(-0.288419\pi\) | ||||
0.616823 | + | 0.787102i | \(0.288419\pi\) | |||||||
\(258\) | −9952.00 | −0.00930810 | ||||||||
\(259\) | 34944.0 | 0.0323685 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 774070. | 0.703362 | ||||||||
\(262\) | −152904. | −0.137615 | ||||||||
\(263\) | 2.12834e6 | 1.89736 | 0.948682 | − | 0.316231i | \(-0.102417\pi\) | ||||
0.948682 | + | 0.316231i | \(0.102417\pi\) | |||||||
\(264\) | −71040.0 | −0.0627326 | ||||||||
\(265\) | −596150. | −0.521484 | ||||||||
\(266\) | −407040. | −0.352722 | ||||||||
\(267\) | 405480. | 0.348090 | ||||||||
\(268\) | 1.70722e6 | 1.45195 | ||||||||
\(269\) | −1.44109e6 | −1.21426 | −0.607128 | − | 0.794604i | \(-0.707679\pi\) | ||||
−0.607128 | + | 0.794604i | \(0.707679\pi\) | |||||||
\(270\) | 94000.0 | 0.0784727 | ||||||||
\(271\) | 93248.0 | 0.0771288 | 0.0385644 | − | 0.999256i | \(-0.487722\pi\) | ||||
0.0385644 | + | 0.999256i | \(0.487722\pi\) | |||||||
\(272\) | −1.10077e6 | −0.902139 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −289836. | −0.233225 | ||||||||
\(275\) | 92500.0 | 0.0737581 | ||||||||
\(276\) | 333312. | 0.263377 | ||||||||
\(277\) | −110298. | −0.0863711 | −0.0431855 | − | 0.999067i | \(-0.513751\pi\) | ||||
−0.0431855 | + | 0.999067i | \(0.513751\pi\) | |||||||
\(278\) | −224440. | −0.174176 | ||||||||
\(279\) | −555696. | −0.427392 | ||||||||
\(280\) | 576000. | 0.439064 | ||||||||
\(281\) | 192198. | 0.145205 | 0.0726027 | − | 0.997361i | \(-0.476869\pi\) | ||||
0.0726027 | + | 0.997361i | \(0.476869\pi\) | |||||||
\(282\) | 96704.0 | 0.0724139 | ||||||||
\(283\) | −331884. | −0.246332 | −0.123166 | − | 0.992386i | \(-0.539305\pi\) | ||||
−0.123166 | + | 0.992386i | \(0.539305\pi\) | |||||||
\(284\) | −914144. | −0.672541 | ||||||||
\(285\) | −106000. | −0.0773025 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.80442e6 | −1.29310 | ||||||||
\(288\) | 1.16950e6 | 0.830846 | ||||||||
\(289\) | 1.39583e6 | 0.983076 | ||||||||
\(290\) | −170500. | −0.119050 | ||||||||
\(291\) | −476152. | −0.329620 | ||||||||
\(292\) | −1.08567e6 | −0.745146 | ||||||||
\(293\) | −2.19481e6 | −1.49358 | −0.746788 | − | 0.665063i | \(-0.768405\pi\) | ||||
−0.746788 | + | 0.665063i | \(0.768405\pi\) | |||||||
\(294\) | 160456. | 0.108265 | ||||||||
\(295\) | −500500. | −0.334849 | ||||||||
\(296\) | −21840.0 | −0.0144885 | ||||||||
\(297\) | 278240. | 0.183033 | ||||||||
\(298\) | 807500. | 0.526747 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 70000.0 | 0.0449050 | ||||||||
\(301\) | 238848. | 0.151952 | ||||||||
\(302\) | −893296. | −0.563609 | ||||||||
\(303\) | 359592. | 0.225011 | ||||||||
\(304\) | −695360. | −0.431545 | ||||||||
\(305\) | −807550. | −0.497073 | ||||||||
\(306\) | −761812. | −0.465098 | ||||||||
\(307\) | 2.37751e6 | 1.43971 | 0.719857 | − | 0.694123i | \(-0.244207\pi\) | ||||
0.719857 | + | 0.694123i | \(0.244207\pi\) | |||||||
\(308\) | 795648. | 0.477908 | ||||||||
\(309\) | 78016.0 | 0.0464823 | ||||||||
\(310\) | 122400. | 0.0723398 | ||||||||
\(311\) | −2.37305e6 | −1.39125 | −0.695626 | − | 0.718405i | \(-0.744873\pi\) | ||||
−0.695626 | + | 0.718405i | \(0.744873\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.42941e6 | −0.824702 | −0.412351 | − | 0.911025i | \(-0.635292\pi\) | ||||
−0.412351 | + | 0.911025i | \(0.635292\pi\) | |||||||
\(314\) | 524516. | 0.300217 | ||||||||
\(315\) | −1.08960e6 | −0.618715 | ||||||||
\(316\) | 934080. | 0.526219 | ||||||||
\(317\) | −2.12462e6 | −1.18750 | −0.593750 | − | 0.804650i | \(-0.702353\pi\) | ||||
−0.593750 | + | 0.804650i | \(0.702353\pi\) | |||||||
\(318\) | 190768. | 0.105788 | ||||||||
\(319\) | −504680. | −0.277677 | ||||||||
\(320\) | 267200. | 0.145868 | ||||||||
\(321\) | −633168. | −0.342970 | ||||||||
\(322\) | 1.14278e6 | 0.614221 | ||||||||
\(323\) | 1.77868e6 | 0.948618 | ||||||||
\(324\) | −1.33395e6 | −0.705954 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −309128. | −0.161100 | ||||||||
\(327\) | 147320. | 0.0761890 | ||||||||
\(328\) | 1.12776e6 | 0.578805 | ||||||||
\(329\) | −2.32090e6 | −1.18213 | ||||||||
\(330\) | −29600.0 | −0.0149626 | ||||||||
\(331\) | −3.09985e6 | −1.55515 | −0.777573 | − | 0.628793i | \(-0.783549\pi\) | ||||
−0.777573 | + | 0.628793i | \(0.783549\pi\) | |||||||
\(332\) | 468048. | 0.233048 | ||||||||
\(333\) | 41314.0 | 0.0204168 | ||||||||
\(334\) | 793344. | 0.389131 | ||||||||
\(335\) | 1.52430e6 | 0.742093 | ||||||||
\(336\) | 503808. | 0.243454 | ||||||||
\(337\) | 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 | ||||||||
\(340\) | −1.17460e6 | −0.551052 | ||||||||
\(341\) | 362304. | 0.168728 | ||||||||
\(342\) | −481240. | −0.222483 | ||||||||
\(343\) | −624000. | −0.286384 | ||||||||
\(344\) | −149280. | −0.0680151 | ||||||||
\(345\) | 297600. | 0.134612 | ||||||||
\(346\) | 1.14695e6 | 0.515055 | ||||||||
\(347\) | 1.77741e6 | 0.792436 | 0.396218 | − | 0.918156i | \(-0.370322\pi\) | ||||
0.396218 | + | 0.918156i | \(0.370322\pi\) | |||||||
\(348\) | −381920. | −0.169054 | ||||||||
\(349\) | 2.14805e6 | 0.944019 | 0.472010 | − | 0.881593i | \(-0.343529\pi\) | ||||
0.472010 | + | 0.881593i | \(0.343529\pi\) | |||||||
\(350\) | 240000. | 0.104723 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −762496. | −0.328005 | ||||||||
\(353\) | 661854. | 0.282700 | 0.141350 | − | 0.989960i | \(-0.454856\pi\) | ||||
0.141350 | + | 0.989960i | \(0.454856\pi\) | |||||||
\(354\) | 160160. | 0.0679275 | ||||||||
\(355\) | −816200. | −0.343737 | ||||||||
\(356\) | 2.83836e6 | 1.18698 | ||||||||
\(357\) | −1.28870e6 | −0.535159 | ||||||||
\(358\) | 1.18892e6 | 0.490281 | ||||||||
\(359\) | 259320. | 0.106194 | 0.0530970 | − | 0.998589i | \(-0.483091\pi\) | ||||
0.0530970 | + | 0.998589i | \(0.483091\pi\) | |||||||
\(360\) | 681000. | 0.276943 | ||||||||
\(361\) | −1.35250e6 | −0.546222 | ||||||||
\(362\) | 214196. | 0.0859093 | ||||||||
\(363\) | 556588. | 0.221701 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −969350. | −0.380845 | ||||||||
\(366\) | 258416. | 0.100836 | ||||||||
\(367\) | −1.49993e6 | −0.581307 | −0.290653 | − | 0.956828i | \(-0.593873\pi\) | ||||
−0.290653 | + | 0.956828i | \(0.593873\pi\) | |||||||
\(368\) | 1.95226e6 | 0.751480 | ||||||||
\(369\) | −2.13335e6 | −0.815634 | ||||||||
\(370\) | −9100.00 | −0.00345571 | ||||||||
\(371\) | −4.57843e6 | −1.72696 | ||||||||
\(372\) | 274176. | 0.102724 | ||||||||
\(373\) | −2.23807e6 | −0.832918 | −0.416459 | − | 0.909154i | \(-0.636729\pi\) | ||||
−0.416459 | + | 0.909154i | \(0.636729\pi\) | |||||||
\(374\) | 496688. | 0.183614 | ||||||||
\(375\) | 62500.0 | 0.0229510 | ||||||||
\(376\) | 1.45056e6 | 0.529135 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 721920. | 0.259872 | ||||||||
\(379\) | −3.15934e6 | −1.12979 | −0.564896 | − | 0.825162i | \(-0.691084\pi\) | ||||
−0.564896 | + | 0.825162i | \(0.691084\pi\) | |||||||
\(380\) | −742000. | −0.263600 | ||||||||
\(381\) | −282208. | −0.0995994 | ||||||||
\(382\) | −939104. | −0.329272 | ||||||||
\(383\) | −342216. | −0.119207 | −0.0596037 | − | 0.998222i | \(-0.518984\pi\) | ||||
−0.0596037 | + | 0.998222i | \(0.518984\pi\) | |||||||
\(384\) | −744960. | −0.257813 | ||||||||
\(385\) | 710400. | 0.244259 | ||||||||
\(386\) | 105412. | 0.0360099 | ||||||||
\(387\) | 282388. | 0.0958449 | ||||||||
\(388\) | −3.33306e6 | −1.12399 | ||||||||
\(389\) | 88470.0 | 0.0296430 | 0.0148215 | − | 0.999890i | \(-0.495282\pi\) | ||||
0.0148215 | + | 0.999890i | \(0.495282\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.99373e6 | −1.65190 | ||||||||
\(392\) | 2.40684e6 | 0.791101 | ||||||||
\(393\) | −305808. | −0.0998775 | ||||||||
\(394\) | 911724. | 0.295885 | ||||||||
\(395\) | 834000. | 0.268951 | ||||||||
\(396\) | 940688. | 0.301445 | ||||||||
\(397\) | 5.45674e6 | 1.73763 | 0.868814 | − | 0.495138i | \(-0.164883\pi\) | ||||
0.868814 | + | 0.495138i | \(0.164883\pi\) | |||||||
\(398\) | −1.73000e6 | −0.547442 | ||||||||
\(399\) | −814080. | −0.255997 | ||||||||
\(400\) | 410000. | 0.128125 | ||||||||
\(401\) | −4.04680e6 | −1.25676 | −0.628378 | − | 0.777908i | \(-0.716281\pi\) | ||||
−0.628378 | + | 0.777908i | \(0.716281\pi\) | |||||||
\(402\) | −487776. | −0.150541 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 2.51714e6 | 0.767281 | ||||||||
\(405\) | −1.19102e6 | −0.360814 | ||||||||
\(406\) | −1.30944e6 | −0.394249 | ||||||||
\(407\) | −26936.0 | −0.00806022 | ||||||||
\(408\) | 805440. | 0.239543 | ||||||||
\(409\) | 2.71207e6 | 0.801664 | 0.400832 | − | 0.916151i | \(-0.368721\pi\) | ||||
0.400832 | + | 0.916151i | \(0.368721\pi\) | |||||||
\(410\) | 469900. | 0.138053 | ||||||||
\(411\) | −579672. | −0.169269 | ||||||||
\(412\) | 546112. | 0.158503 | ||||||||
\(413\) | −3.84384e6 | −1.10889 | ||||||||
\(414\) | 1.35110e6 | 0.387425 | ||||||||
\(415\) | 417900. | 0.119111 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −448880. | −0.126413 | ||||||||
\(418\) | 313760. | 0.0878328 | ||||||||
\(419\) | 3.71746e6 | 1.03445 | 0.517227 | − | 0.855848i | \(-0.326964\pi\) | ||||
0.517227 | + | 0.855848i | \(0.326964\pi\) | |||||||
\(420\) | 537600. | 0.148709 | ||||||||
\(421\) | −3.55250e6 | −0.976853 | −0.488426 | − | 0.872605i | \(-0.662429\pi\) | ||||
−0.488426 | + | 0.872605i | \(0.662429\pi\) | |||||||
\(422\) | −2.21130e6 | −0.604460 | ||||||||
\(423\) | −2.74398e6 | −0.745640 | ||||||||
\(424\) | 2.86152e6 | 0.773005 | ||||||||
\(425\) | −1.04875e6 | −0.281643 | ||||||||
\(426\) | 261184. | 0.0697305 | ||||||||
\(427\) | −6.20198e6 | −1.64612 | ||||||||
\(428\) | −4.43218e6 | −1.16952 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −62200.0 | −0.0162226 | ||||||||
\(431\) | 4.06205e6 | 1.05330 | 0.526650 | − | 0.850082i | \(-0.323448\pi\) | ||||
0.526650 | + | 0.850082i | \(0.323448\pi\) | |||||||
\(432\) | 1.23328e6 | 0.317945 | ||||||||
\(433\) | 7.26287e6 | 1.86161 | 0.930804 | − | 0.365518i | \(-0.119108\pi\) | ||||
0.930804 | + | 0.365518i | \(0.119108\pi\) | |||||||
\(434\) | 940032. | 0.239562 | ||||||||
\(435\) | −341000. | −0.0864035 | ||||||||
\(436\) | 1.03124e6 | 0.259803 | ||||||||
\(437\) | −3.15456e6 | −0.790197 | ||||||||
\(438\) | 310192. | 0.0772583 | ||||||||
\(439\) | −5.41028e6 | −1.33986 | −0.669928 | − | 0.742426i | \(-0.733675\pi\) | ||||
−0.669928 | + | 0.742426i | \(0.733675\pi\) | |||||||
\(440\) | −444000. | −0.109333 | ||||||||
\(441\) | −4.55294e6 | −1.11480 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.51524e6 | −1.57733 | −0.788663 | − | 0.614826i | \(-0.789226\pi\) | ||||
−0.788663 | + | 0.614826i | \(0.789226\pi\) | |||||||
\(444\) | −20384.0 | −0.00490718 | ||||||||
\(445\) | 2.53425e6 | 0.606666 | ||||||||
\(446\) | 2.24315e6 | 0.533976 | ||||||||
\(447\) | 1.61500e6 | 0.382299 | ||||||||
\(448\) | 2.05210e6 | 0.483062 | ||||||||
\(449\) | 509950. | 0.119375 | 0.0596873 | − | 0.998217i | \(-0.480990\pi\) | ||||
0.0596873 | + | 0.998217i | \(0.480990\pi\) | |||||||
\(450\) | 283750. | 0.0660548 | ||||||||
\(451\) | 1.39090e6 | 0.322000 | ||||||||
\(452\) | −313208. | −0.0721085 | ||||||||
\(453\) | −1.78659e6 | −0.409053 | ||||||||
\(454\) | −46696.0 | −0.0106326 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 508800. | 0.114587 | ||||||||
\(457\) | −1.22084e6 | −0.273444 | −0.136722 | − | 0.990609i | \(-0.543657\pi\) | ||||
−0.136722 | + | 0.990609i | \(0.543657\pi\) | |||||||
\(458\) | −1.19202e6 | −0.265534 | ||||||||
\(459\) | −3.15464e6 | −0.698905 | ||||||||
\(460\) | 2.08320e6 | 0.459025 | ||||||||
\(461\) | 4.07210e6 | 0.892413 | 0.446207 | − | 0.894930i | \(-0.352775\pi\) | ||||
0.446207 | + | 0.894930i | \(0.352775\pi\) | |||||||
\(462\) | −227328. | −0.0495505 | ||||||||
\(463\) | −2.02294e6 | −0.438561 | −0.219280 | − | 0.975662i | \(-0.570371\pi\) | ||||
−0.219280 | + | 0.975662i | \(0.570371\pi\) | |||||||
\(464\) | −2.23696e6 | −0.482351 | ||||||||
\(465\) | 244800. | 0.0525024 | ||||||||
\(466\) | 970668. | 0.207065 | ||||||||
\(467\) | 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 | ||||||||
\(470\) | 604400. | 0.126206 | ||||||||
\(471\) | 1.04903e6 | 0.217890 | ||||||||
\(472\) | 2.40240e6 | 0.496353 | ||||||||
\(473\) | −184112. | −0.0378381 | ||||||||
\(474\) | −266880. | −0.0545595 | ||||||||
\(475\) | −662500. | −0.134726 | ||||||||
\(476\) | −9.02093e6 | −1.82488 | ||||||||
\(477\) | −5.41304e6 | −1.08929 | ||||||||
\(478\) | −97760.0 | −0.0195700 | ||||||||
\(479\) | 3.27936e6 | 0.653056 | 0.326528 | − | 0.945188i | \(-0.394121\pi\) | ||||
0.326528 | + | 0.945188i | \(0.394121\pi\) | |||||||
\(480\) | −515200. | −0.102064 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −221596. | −0.0434455 | ||||||||
\(483\) | 2.28557e6 | 0.445786 | ||||||||
\(484\) | 3.89612e6 | 0.755994 | ||||||||
\(485\) | −2.97595e6 | −0.574475 | ||||||||
\(486\) | 1.29481e6 | 0.248665 | ||||||||
\(487\) | 8.53197e6 | 1.63015 | 0.815074 | − | 0.579357i | \(-0.196696\pi\) | ||||
0.815074 | + | 0.579357i | \(0.196696\pi\) | |||||||
\(488\) | 3.87624e6 | 0.736819 | ||||||||
\(489\) | −618256. | −0.116922 | ||||||||
\(490\) | 1.00285e6 | 0.188689 | ||||||||
\(491\) | 1.51265e6 | 0.283162 | 0.141581 | − | 0.989927i | \(-0.454781\pi\) | ||||
0.141581 | + | 0.989927i | \(0.454781\pi\) | |||||||
\(492\) | 1.05258e6 | 0.196038 | ||||||||
\(493\) | 5.72198e6 | 1.06030 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 839900. | 0.154069 | ||||||||
\(496\) | 1.60589e6 | 0.293097 | ||||||||
\(497\) | −6.26842e6 | −1.13833 | ||||||||
\(498\) | −133728. | −0.0241629 | ||||||||
\(499\) | 6.49190e6 | 1.16713 | 0.583567 | − | 0.812065i | \(-0.301657\pi\) | ||||
0.583567 | + | 0.812065i | \(0.301657\pi\) | |||||||
\(500\) | 437500. | 0.0782624 | ||||||||
\(501\) | 1.58669e6 | 0.282421 | ||||||||
\(502\) | 3.28750e6 | 0.582245 | ||||||||
\(503\) | 8.61770e6 | 1.51870 | 0.759349 | − | 0.650684i | \(-0.225518\pi\) | ||||
0.759349 | + | 0.650684i | \(0.225518\pi\) | |||||||
\(504\) | 5.23008e6 | 0.917132 | ||||||||
\(505\) | 2.24745e6 | 0.392158 | ||||||||
\(506\) | −880896. | −0.152950 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.97546e6 | −0.339632 | ||||||||
\(509\) | −2.67323e6 | −0.457343 | −0.228671 | − | 0.973504i | \(-0.573438\pi\) | ||||
−0.228671 | + | 0.973504i | \(0.573438\pi\) | |||||||
\(510\) | 335600. | 0.0571342 | ||||||||
\(511\) | −7.44461e6 | −1.26122 | ||||||||
\(512\) | −5.89875e6 | −0.994455 | ||||||||
\(513\) | −1.99280e6 | −0.334326 | ||||||||
\(514\) | −2.61248e6 | −0.436160 | ||||||||
\(515\) | 487600. | 0.0810113 | ||||||||
\(516\) | −139328. | −0.0230364 | ||||||||
\(517\) | 1.78902e6 | 0.294367 | ||||||||
\(518\) | −69888.0 | −0.0114440 | ||||||||
\(519\) | 2.29390e6 | 0.373814 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.18500e6 | 0.998264 | 0.499132 | − | 0.866526i | \(-0.333652\pi\) | ||||
0.499132 | + | 0.866526i | \(0.333652\pi\) | |||||||
\(522\) | −1.54814e6 | −0.248676 | ||||||||
\(523\) | −6.89452e6 | −1.10217 | −0.551087 | − | 0.834448i | \(-0.685787\pi\) | ||||
−0.551087 | + | 0.834448i | \(0.685787\pi\) | |||||||
\(524\) | −2.14066e6 | −0.340580 | ||||||||
\(525\) | 480000. | 0.0760051 | ||||||||
\(526\) | −4.25667e6 | −0.670820 | ||||||||
\(527\) | −4.10774e6 | −0.644283 | ||||||||
\(528\) | −388352. | −0.0606235 | ||||||||
\(529\) | 2.42023e6 | 0.376026 | ||||||||
\(530\) | 1.19230e6 | 0.184372 | ||||||||
\(531\) | −4.54454e6 | −0.699445 | ||||||||
\(532\) | −5.69856e6 | −0.872943 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −810960. | −0.123068 | ||||||||
\(535\) | −3.95730e6 | −0.597743 | ||||||||
\(536\) | −7.31664e6 | −1.10002 | ||||||||
\(537\) | 2.37784e6 | 0.355834 | ||||||||
\(538\) | 2.88218e6 | 0.429304 | ||||||||
\(539\) | 2.96844e6 | 0.440104 | ||||||||
\(540\) | 1.31600e6 | 0.194210 | ||||||||
\(541\) | −155502. | −0.0228425 | −0.0114212 | − | 0.999935i | \(-0.503636\pi\) | ||||
−0.0114212 | + | 0.999935i | \(0.503636\pi\) | |||||||
\(542\) | −186496. | −0.0272691 | ||||||||
\(543\) | 428392. | 0.0623508 | ||||||||
\(544\) | 8.64506e6 | 1.25248 | ||||||||
\(545\) | 920750. | 0.132785 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.26544e7 | 1.80831 | 0.904157 | − | 0.427201i | \(-0.140500\pi\) | ||||
0.904157 | + | 0.427201i | \(0.140500\pi\) | |||||||
\(548\) | −4.05770e6 | −0.577204 | ||||||||
\(549\) | −7.33255e6 | −1.03830 | ||||||||
\(550\) | −185000. | −0.0260774 | ||||||||
\(551\) | 3.61460e6 | 0.507202 | ||||||||
\(552\) | −1.42848e6 | −0.199538 | ||||||||
\(553\) | 6.40512e6 | 0.890665 | ||||||||
\(554\) | 220596. | 0.0305368 | ||||||||
\(555\) | −18200.0 | −0.00250807 | ||||||||
\(556\) | −3.14216e6 | −0.431064 | ||||||||
\(557\) | 7.07786e6 | 0.966638 | 0.483319 | − | 0.875444i | \(-0.339431\pi\) | ||||
0.483319 | + | 0.875444i | \(0.339431\pi\) | |||||||
\(558\) | 1.11139e6 | 0.151106 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.14880e6 | 0.424302 | ||||||||
\(561\) | 993376. | 0.133262 | ||||||||
\(562\) | −384396. | −0.0513379 | ||||||||
\(563\) | 846636. | 0.112571 | 0.0562854 | − | 0.998415i | \(-0.482074\pi\) | ||||
0.0562854 | + | 0.998415i | \(0.482074\pi\) | |||||||
\(564\) | 1.35386e6 | 0.179215 | ||||||||
\(565\) | −279650. | −0.0368548 | ||||||||
\(566\) | 663768. | 0.0870914 | ||||||||
\(567\) | −9.14707e6 | −1.19488 | ||||||||
\(568\) | 3.91776e6 | 0.509527 | ||||||||
\(569\) | 4.96041e6 | 0.642299 | 0.321149 | − | 0.947029i | \(-0.395931\pi\) | ||||
0.321149 | + | 0.947029i | \(0.395931\pi\) | |||||||
\(570\) | 212000. | 0.0273306 | ||||||||
\(571\) | 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 | ||||||||
\(574\) | 3.60883e6 | 0.457180 | ||||||||
\(575\) | 1.86000e6 | 0.234608 | ||||||||
\(576\) | 2.42618e6 | 0.304696 | ||||||||
\(577\) | 2.86080e6 | 0.357724 | 0.178862 | − | 0.983874i | \(-0.442758\pi\) | ||||
0.178862 | + | 0.983874i | \(0.442758\pi\) | |||||||
\(578\) | −2.79165e6 | −0.347570 | ||||||||
\(579\) | 210824. | 0.0261351 | ||||||||
\(580\) | −2.38700e6 | −0.294634 | ||||||||
\(581\) | 3.20947e6 | 0.394451 | ||||||||
\(582\) | 952304. | 0.116538 | ||||||||
\(583\) | 3.52921e6 | 0.430037 | ||||||||
\(584\) | 4.65288e6 | 0.564534 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.38961e6 | 0.528059 | ||||||||
\(587\) | 6.74027e6 | 0.807387 | 0.403694 | − | 0.914894i | \(-0.367726\pi\) | ||||
0.403694 | + | 0.914894i | \(0.367726\pi\) | |||||||
\(588\) | 2.24638e6 | 0.267942 | ||||||||
\(589\) | −2.59488e6 | −0.308197 | ||||||||
\(590\) | 1.00100e6 | 0.118387 | ||||||||
\(591\) | 1.82345e6 | 0.214746 | ||||||||
\(592\) | −119392. | −0.0140014 | ||||||||
\(593\) | 1.78609e6 | 0.208578 | 0.104289 | − | 0.994547i | \(-0.466743\pi\) | ||||
0.104289 | + | 0.994547i | \(0.466743\pi\) | |||||||
\(594\) | −556480. | −0.0647118 | ||||||||
\(595\) | −8.05440e6 | −0.932697 | ||||||||
\(596\) | 1.13050e7 | 1.30363 | ||||||||
\(597\) | −3.46000e6 | −0.397320 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.94620e6 | 0.563254 | 0.281627 | − | 0.959524i | \(-0.409126\pi\) | ||||
0.281627 | + | 0.959524i | \(0.409126\pi\) | |||||||
\(600\) | −300000. | −0.0340207 | ||||||||
\(601\) | −4.58100e6 | −0.517337 | −0.258669 | − | 0.965966i | \(-0.583284\pi\) | ||||
−0.258669 | + | 0.965966i | \(0.583284\pi\) | |||||||
\(602\) | −477696. | −0.0537230 | ||||||||
\(603\) | 1.38406e7 | 1.55011 | ||||||||
\(604\) | −1.25061e7 | −1.39486 | ||||||||
\(605\) | 3.47868e6 | 0.386390 | ||||||||
\(606\) | −719184. | −0.0795533 | ||||||||
\(607\) | 7.07999e6 | 0.779940 | 0.389970 | − | 0.920828i | \(-0.372485\pi\) | ||||
0.389970 | + | 0.920828i | \(0.372485\pi\) | |||||||
\(608\) | 5.46112e6 | 0.599132 | ||||||||
\(609\) | −2.61888e6 | −0.286136 | ||||||||
\(610\) | 1.61510e6 | 0.175742 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −1.06654e7 | −1.15106 | ||||||||
\(613\) | −5.09609e6 | −0.547754 | −0.273877 | − | 0.961765i | \(-0.588306\pi\) | ||||
−0.273877 | + | 0.961765i | \(0.588306\pi\) | |||||||
\(614\) | −4.75502e6 | −0.509016 | ||||||||
\(615\) | 939800. | 0.100195 | ||||||||
\(616\) | −3.40992e6 | −0.362070 | ||||||||
\(617\) | 1.30003e7 | 1.37480 | 0.687400 | − | 0.726279i | \(-0.258752\pi\) | ||||
0.687400 | + | 0.726279i | \(0.258752\pi\) | |||||||
\(618\) | −156032. | −0.0164340 | ||||||||
\(619\) | −4.84406e6 | −0.508139 | −0.254070 | − | 0.967186i | \(-0.581769\pi\) | ||||
−0.254070 | + | 0.967186i | \(0.581769\pi\) | |||||||
\(620\) | 1.71360e6 | 0.179032 | ||||||||
\(621\) | 5.59488e6 | 0.582186 | ||||||||
\(622\) | 4.74610e6 | 0.491882 | ||||||||
\(623\) | 1.94630e7 | 2.00905 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 2.85883e6 | 0.291576 | ||||||||
\(627\) | 627520. | 0.0637468 | ||||||||
\(628\) | 7.34322e6 | 0.742998 | ||||||||
\(629\) | 305396. | 0.0307777 | ||||||||
\(630\) | 2.17920e6 | 0.218749 | ||||||||
\(631\) | −6.22775e6 | −0.622670 | −0.311335 | − | 0.950300i | \(-0.600776\pi\) | ||||
−0.311335 | + | 0.950300i | \(0.600776\pi\) | |||||||
\(632\) | −4.00320e6 | −0.398671 | ||||||||
\(633\) | −4.42261e6 | −0.438702 | ||||||||
\(634\) | 4.24924e6 | 0.419845 | ||||||||
\(635\) | −1.76380e6 | −0.173586 | ||||||||
\(636\) | 2.67075e6 | 0.261813 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.00936e6 | 0.0981735 | ||||||||
\(639\) | −7.41110e6 | −0.718010 | ||||||||
\(640\) | −4.65600e6 | −0.449328 | ||||||||
\(641\) | 1.53280e6 | 0.147347 | 0.0736734 | − | 0.997282i | \(-0.476528\pi\) | ||||
0.0736734 | + | 0.997282i | \(0.476528\pi\) | |||||||
\(642\) | 1.26634e6 | 0.121258 | ||||||||
\(643\) | 1.74382e7 | 1.66332 | 0.831659 | − | 0.555287i | \(-0.187391\pi\) | ||||
0.831659 | + | 0.555287i | \(0.187391\pi\) | |||||||
\(644\) | 1.59990e7 | 1.52012 | ||||||||
\(645\) | −124400. | −0.0117739 | ||||||||
\(646\) | −3.55736e6 | −0.335387 | ||||||||
\(647\) | −4.25469e6 | −0.399583 | −0.199792 | − | 0.979838i | \(-0.564026\pi\) | ||||
−0.199792 | + | 0.979838i | \(0.564026\pi\) | |||||||
\(648\) | 5.71692e6 | 0.534841 | ||||||||
\(649\) | 2.96296e6 | 0.276130 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88006e6 | 0.173868 | ||||||||
\(652\) | −4.32779e6 | −0.398701 | ||||||||
\(653\) | 3.01085e6 | 0.276316 | 0.138158 | − | 0.990410i | \(-0.455882\pi\) | ||||
0.138158 | + | 0.990410i | \(0.455882\pi\) | |||||||
\(654\) | −294640. | −0.0269369 | ||||||||
\(655\) | −1.91130e6 | −0.174071 | ||||||||
\(656\) | 6.16509e6 | 0.559345 | ||||||||
\(657\) | −8.80170e6 | −0.795524 | ||||||||
\(658\) | 4.64179e6 | 0.417947 | ||||||||
\(659\) | −8.11462e6 | −0.727871 | −0.363936 | − | 0.931424i | \(-0.618567\pi\) | ||||
−0.363936 | + | 0.931424i | \(0.618567\pi\) | |||||||
\(660\) | −414400. | −0.0370305 | ||||||||
\(661\) | −2.47370e6 | −0.220213 | −0.110107 | − | 0.993920i | \(-0.535119\pi\) | ||||
−0.110107 | + | 0.993920i | \(0.535119\pi\) | |||||||
\(662\) | 6.19970e6 | 0.549827 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.00592e6 | −0.176560 | ||||||||
\(665\) | −5.08800e6 | −0.446162 | ||||||||
\(666\) | −82628.0 | −0.00721841 | ||||||||
\(667\) | −1.01482e7 | −0.883228 | ||||||||
\(668\) | 1.11068e7 | 0.963049 | ||||||||
\(669\) | 4.48630e6 | 0.387546 | ||||||||
\(670\) | −3.04860e6 | −0.262370 | ||||||||
\(671\) | 4.78070e6 | 0.409907 | ||||||||
\(672\) | −3.95674e6 | −0.337998 | ||||||||
\(673\) | 5.77063e6 | 0.491117 | 0.245559 | − | 0.969382i | \(-0.421029\pi\) | ||||
0.245559 | + | 0.969382i | \(0.421029\pi\) | |||||||
\(674\) | −4.80016e6 | −0.407011 | ||||||||
\(675\) | 1.17500e6 | 0.0992610 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.67197e7 | 1.40203 | 0.701014 | − | 0.713147i | \(-0.252731\pi\) | ||||
0.701014 | + | 0.713147i | \(0.252731\pi\) | |||||||
\(678\) | 89488.0 | 0.00747637 | ||||||||
\(679\) | −2.28553e7 | −1.90245 | ||||||||
\(680\) | 5.03400e6 | 0.417485 | ||||||||
\(681\) | −93392.0 | −0.00771688 | ||||||||
\(682\) | −724608. | −0.0596544 | ||||||||
\(683\) | −7.14532e6 | −0.586097 | −0.293049 | − | 0.956098i | \(-0.594670\pi\) | ||||
−0.293049 | + | 0.956098i | \(0.594670\pi\) | |||||||
\(684\) | −6.73736e6 | −0.550617 | ||||||||
\(685\) | −3.62295e6 | −0.295009 | ||||||||
\(686\) | 1.24800e6 | 0.101252 | ||||||||
\(687\) | −2.38404e6 | −0.192718 | ||||||||
\(688\) | −816064. | −0.0657284 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −595200. | −0.0475927 | ||||||||
\(691\) | 8.78395e6 | 0.699833 | 0.349917 | − | 0.936781i | \(-0.386210\pi\) | ||||
0.349917 | + | 0.936781i | \(0.386210\pi\) | |||||||
\(692\) | 1.60573e7 | 1.27470 | ||||||||
\(693\) | 6.45043e6 | 0.510218 | ||||||||
\(694\) | −3.55482e6 | −0.280169 | ||||||||
\(695\) | −2.80550e6 | −0.220317 | ||||||||
\(696\) | 1.63680e6 | 0.128077 | ||||||||
\(697\) | −1.57698e7 | −1.22955 | ||||||||
\(698\) | −4.29610e6 | −0.333761 | ||||||||
\(699\) | 1.94134e6 | 0.150282 | ||||||||
\(700\) | 3.36000e6 | 0.259176 | ||||||||
\(701\) | −1.60141e7 | −1.23086 | −0.615428 | − | 0.788193i | \(-0.711017\pi\) | ||||
−0.615428 | + | 0.788193i | \(0.711017\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 192920. | 0.0147228 | ||||||||
\(704\) | −1.58182e6 | −0.120289 | ||||||||
\(705\) | 1.20880e6 | 0.0915971 | ||||||||
\(706\) | −1.32371e6 | −0.0999495 | ||||||||
\(707\) | 1.72604e7 | 1.29868 | ||||||||
\(708\) | 2.24224e6 | 0.168112 | ||||||||
\(709\) | 1.91354e7 | 1.42962 | 0.714811 | − | 0.699318i | \(-0.246513\pi\) | ||||
0.714811 | + | 0.699318i | \(0.246513\pi\) | |||||||
\(710\) | 1.63240e6 | 0.121529 | ||||||||
\(711\) | 7.57272e6 | 0.561795 | ||||||||
\(712\) | −1.21644e7 | −0.899271 | ||||||||
\(713\) | 7.28525e6 | 0.536686 | ||||||||
\(714\) | 2.57741e6 | 0.189207 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.66449e7 | 1.21338 | ||||||||
\(717\) | −195520. | −0.0142034 | ||||||||
\(718\) | −518640. | −0.0375452 | ||||||||
\(719\) | 1.02934e7 | 0.742566 | 0.371283 | − | 0.928520i | \(-0.378918\pi\) | ||||
0.371283 | + | 0.928520i | \(0.378918\pi\) | |||||||
\(720\) | 3.72280e6 | 0.267632 | ||||||||
\(721\) | 3.74477e6 | 0.268279 | ||||||||
\(722\) | 2.70500e6 | 0.193119 | ||||||||
\(723\) | −443192. | −0.0315316 | ||||||||
\(724\) | 2.99874e6 | 0.212615 | ||||||||
\(725\) | −2.13125e6 | −0.150588 | ||||||||
\(726\) | −1.11318e6 | −0.0783831 | ||||||||
\(727\) | −1.93264e7 | −1.35618 | −0.678088 | − | 0.734981i | \(-0.737191\pi\) | ||||
−0.678088 | + | 0.734981i | \(0.737191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.98715e6 | −0.626330 | ||||||||
\(730\) | 1.93870e6 | 0.134649 | ||||||||
\(731\) | 2.08743e6 | 0.144484 | ||||||||
\(732\) | 3.61782e6 | 0.249557 | ||||||||
\(733\) | −5.26197e6 | −0.361733 | −0.180866 | − | 0.983508i | \(-0.557890\pi\) | ||||
−0.180866 | + | 0.983508i | \(0.557890\pi\) | |||||||
\(734\) | 2.99986e6 | 0.205523 | ||||||||
\(735\) | 2.00570e6 | 0.136945 | ||||||||
\(736\) | −1.53324e7 | −1.04331 | ||||||||
\(737\) | −9.02386e6 | −0.611961 | ||||||||
\(738\) | 4.26669e6 | 0.288370 | ||||||||
\(739\) | −2.82944e7 | −1.90585 | −0.952927 | − | 0.303199i | \(-0.901945\pi\) | ||||
−0.952927 | + | 0.303199i | \(0.901945\pi\) | |||||||
\(740\) | −127400. | −0.00855244 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 9.15686e6 | 0.610572 | ||||||||
\(743\) | −2.09863e7 | −1.39464 | −0.697321 | − | 0.716759i | \(-0.745625\pi\) | ||||
−0.697321 | + | 0.716759i | \(0.745625\pi\) | |||||||
\(744\) | −1.17504e6 | −0.0778252 | ||||||||
\(745\) | 1.00938e7 | 0.666288 | ||||||||
\(746\) | 4.47615e6 | 0.294481 | ||||||||
\(747\) | 3.79453e6 | 0.248804 | ||||||||
\(748\) | 6.95363e6 | 0.454420 | ||||||||
\(749\) | −3.03921e7 | −1.97950 | ||||||||
\(750\) | −125000. | −0.00811441 | ||||||||
\(751\) | −1.89668e7 | −1.22714 | −0.613572 | − | 0.789639i | \(-0.710268\pi\) | ||||
−0.613572 | + | 0.789639i | \(0.710268\pi\) | |||||||
\(752\) | 7.92973e6 | 0.511345 | ||||||||
\(753\) | 6.57499e6 | 0.422579 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.11662e7 | −0.712915 | ||||||||
\(756\) | 1.01069e7 | 0.643151 | ||||||||
\(757\) | −1.08257e7 | −0.686617 | −0.343309 | − | 0.939223i | \(-0.611548\pi\) | ||||
−0.343309 | + | 0.939223i | \(0.611548\pi\) | |||||||
\(758\) | 6.31868e6 | 0.399442 | ||||||||
\(759\) | −1.76179e6 | −0.111007 | ||||||||
\(760\) | 3.18000e6 | 0.199707 | ||||||||
\(761\) | −1.90534e7 | −1.19264 | −0.596322 | − | 0.802745i | \(-0.703372\pi\) | ||||
−0.596322 | + | 0.802745i | \(0.703372\pi\) | |||||||
\(762\) | 564416. | 0.0352137 | ||||||||
\(763\) | 7.07136e6 | 0.439736 | ||||||||
\(764\) | −1.31475e7 | −0.814908 | ||||||||
\(765\) | −9.52265e6 | −0.588307 | ||||||||
\(766\) | 684432. | 0.0421462 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 121856. | 0.00745494 | ||||||||
\(769\) | 1.57826e7 | 0.962415 | 0.481208 | − | 0.876607i | \(-0.340198\pi\) | ||||
0.481208 | + | 0.876607i | \(0.340198\pi\) | |||||||
\(770\) | −1.42080e6 | −0.0863587 | ||||||||
\(771\) | −5.22497e6 | −0.316554 | ||||||||
\(772\) | 1.47577e6 | 0.0891199 | ||||||||
\(773\) | 2.44049e7 | 1.46902 | 0.734510 | − | 0.678598i | \(-0.237412\pi\) | ||||
0.734510 | + | 0.678598i | \(0.237412\pi\) | |||||||
\(774\) | −564776. | −0.0338863 | ||||||||
\(775\) | 1.53000e6 | 0.0915034 | ||||||||
\(776\) | 1.42846e7 | 0.851555 | ||||||||
\(777\) | −139776. | −0.00830577 | ||||||||
\(778\) | −176940. | −0.0104804 | ||||||||
\(779\) | −9.96188e6 | −0.588163 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.83190e6 | 0.283459 | ||||||||
\(782\) | 9.98746e6 | 0.584034 | ||||||||
\(783\) | −6.41080e6 | −0.373687 | ||||||||
\(784\) | 1.31574e7 | 0.764504 | ||||||||
\(785\) | 6.55645e6 | 0.379747 | ||||||||
\(786\) | 611616. | 0.0353120 | ||||||||
\(787\) | −3.37607e7 | −1.94301 | −0.971505 | − | 0.237019i | \(-0.923830\pi\) | ||||
−0.971505 | + | 0.237019i | \(0.923830\pi\) | |||||||
\(788\) | 1.27641e7 | 0.732278 | ||||||||
\(789\) | −8.51334e6 | −0.486864 | ||||||||
\(790\) | −1.66800e6 | −0.0950886 | ||||||||
\(791\) | −2.14771e6 | −0.122049 | ||||||||
\(792\) | −4.03152e6 | −0.228379 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −1.09135e7 | −0.614344 | ||||||||
\(795\) | 2.38460e6 | 0.133813 | ||||||||
\(796\) | −2.42200e7 | −1.35485 | ||||||||
\(797\) | 2.19885e7 | 1.22617 | 0.613083 | − | 0.790019i | \(-0.289929\pi\) | ||||
0.613083 | + | 0.790019i | \(0.289929\pi\) | |||||||
\(798\) | 1.62816e6 | 0.0905086 | ||||||||
\(799\) | −2.02837e7 | −1.12403 | ||||||||
\(800\) | −3.22000e6 | −0.177882 | ||||||||
\(801\) | 2.30110e7 | 1.26723 | ||||||||
\(802\) | 8.09360e6 | 0.444330 | ||||||||
\(803\) | 5.73855e6 | 0.314061 | ||||||||
\(804\) | −6.82886e6 | −0.372570 | ||||||||
\(805\) | 1.42848e7 | 0.776935 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.76436e6 | 0.311578 | ||||||||
\(808\) | −1.07878e7 | −0.581303 | ||||||||
\(809\) | −2.93597e7 | −1.57717 | −0.788587 | − | 0.614923i | \(-0.789187\pi\) | ||||
−0.788587 | + | 0.614923i | \(0.789187\pi\) | |||||||
\(810\) | 2.38205e6 | 0.127567 | ||||||||
\(811\) | −3.17703e7 | −1.69617 | −0.848083 | − | 0.529863i | \(-0.822243\pi\) | ||||
−0.848083 | + | 0.529863i | \(0.822243\pi\) | |||||||
\(812\) | −1.83322e7 | −0.975716 | ||||||||
\(813\) | −372992. | −0.0197912 | ||||||||
\(814\) | 53872.0 | 0.00284972 | ||||||||
\(815\) | −3.86410e6 | −0.203777 | ||||||||
\(816\) | 4.40307e6 | 0.231489 | ||||||||
\(817\) | 1.31864e6 | 0.0691148 | ||||||||
\(818\) | −5.42414e6 | −0.283431 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.57860e6 | 0.341664 | ||||||||
\(821\) | 2.71430e6 | 0.140540 | 0.0702699 | − | 0.997528i | \(-0.477614\pi\) | ||||
0.0702699 | + | 0.997528i | \(0.477614\pi\) | |||||||
\(822\) | 1.15934e6 | 0.0598457 | ||||||||
\(823\) | −1.25866e7 | −0.647753 | −0.323877 | − | 0.946099i | \(-0.604986\pi\) | ||||
−0.323877 | + | 0.946099i | \(0.604986\pi\) | |||||||
\(824\) | −2.34048e6 | −0.120084 | ||||||||
\(825\) | −370000. | −0.0189263 | ||||||||
\(826\) | 7.68768e6 | 0.392053 | ||||||||
\(827\) | 8.72355e6 | 0.443537 | 0.221768 | − | 0.975099i | \(-0.428817\pi\) | ||||
0.221768 | + | 0.975099i | \(0.428817\pi\) | |||||||
\(828\) | 1.89155e7 | 0.958829 | ||||||||
\(829\) | −1.06178e7 | −0.536597 | −0.268299 | − | 0.963336i | \(-0.586461\pi\) | ||||
−0.268299 | + | 0.963336i | \(0.586461\pi\) | |||||||
\(830\) | −835800. | −0.0421121 | ||||||||
\(831\) | 441192. | 0.0221628 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.36556e7 | −1.68053 | ||||||||
\(834\) | 897760. | 0.0446936 | ||||||||
\(835\) | 9.91680e6 | 0.492216 | ||||||||
\(836\) | 4.39264e6 | 0.217375 | ||||||||
\(837\) | 4.60224e6 | 0.227068 | ||||||||
\(838\) | −7.43492e6 | −0.365735 | ||||||||
\(839\) | −1.67765e7 | −0.822805 | −0.411403 | − | 0.911454i | \(-0.634961\pi\) | ||||
−0.411403 | + | 0.911454i | \(0.634961\pi\) | |||||||
\(840\) | −2.30400e6 | −0.112664 | ||||||||
\(841\) | −8.88305e6 | −0.433084 | ||||||||
\(842\) | 7.10500e6 | 0.345370 | ||||||||
\(843\) | −768792. | −0.0372597 | ||||||||
\(844\) | −3.09583e7 | −1.49596 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.48795e6 | 0.263624 | ||||||||
\(847\) | 2.67162e7 | 1.27958 | ||||||||
\(848\) | 1.56430e7 | 0.747016 | ||||||||
\(849\) | 1.32754e6 | 0.0632087 | ||||||||
\(850\) | 2.09750e6 | 0.0995760 | ||||||||
\(851\) | −541632. | −0.0256378 | ||||||||
\(852\) | 3.65658e6 | 0.172574 | ||||||||
\(853\) | 2.20186e7 | 1.03613 | 0.518067 | − | 0.855340i | \(-0.326652\pi\) | ||||
0.518067 | + | 0.855340i | \(0.326652\pi\) | |||||||
\(854\) | 1.24040e7 | 0.581991 | ||||||||
\(855\) | −6.01550e6 | −0.281421 | ||||||||
\(856\) | 1.89950e7 | 0.886045 | ||||||||
\(857\) | 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 | \(0.380918\pi\) | |||||||
\(860\) | −870800. | −0.0401488 | ||||||||
\(861\) | 7.21766e6 | 0.331809 | ||||||||
\(862\) | −8.12410e6 | −0.372398 | ||||||||
\(863\) | 1.44287e7 | 0.659476 | 0.329738 | − | 0.944072i | \(-0.393040\pi\) | ||||
0.329738 | + | 0.944072i | \(0.393040\pi\) | |||||||
\(864\) | −9.68576e6 | −0.441417 | ||||||||
\(865\) | 1.43368e7 | 0.651499 | ||||||||
\(866\) | −1.45257e7 | −0.658178 | ||||||||
\(867\) | −5.58331e6 | −0.252257 | ||||||||
\(868\) | 1.31604e7 | 0.592886 | ||||||||
\(869\) | −4.93728e6 | −0.221788 | ||||||||
\(870\) | 682000. | 0.0305482 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −4.41960e6 | −0.196830 | ||||||||
\(873\) | −2.70216e7 | −1.19999 | ||||||||
\(874\) | 6.30912e6 | 0.279377 | ||||||||
\(875\) | 3.00000e6 | 0.132465 | ||||||||
\(876\) | 4.34269e6 | 0.191205 | ||||||||
\(877\) | −247902. | −0.0108838 | −0.00544191 | − | 0.999985i | \(-0.501732\pi\) | ||||
−0.00544191 | + | 0.999985i | \(0.501732\pi\) | |||||||
\(878\) | 1.08206e7 | 0.473711 | ||||||||
\(879\) | 8.77922e6 | 0.383252 | ||||||||
\(880\) | −2.42720e6 | −0.105657 | ||||||||
\(881\) | 4.10268e7 | 1.78085 | 0.890426 | − | 0.455128i | \(-0.150406\pi\) | ||||
0.890426 | + | 0.455128i | \(0.150406\pi\) | |||||||
\(882\) | 9.10588e6 | 0.394140 | ||||||||
\(883\) | 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 | ||||||||
\(886\) | 1.30305e7 | 0.557669 | ||||||||
\(887\) | −2.10476e7 | −0.898241 | −0.449120 | − | 0.893471i | \(-0.648263\pi\) | ||||
−0.449120 | + | 0.893471i | \(0.648263\pi\) | |||||||
\(888\) | 87360.0 | 0.00371775 | ||||||||
\(889\) | −1.35460e7 | −0.574852 | ||||||||
\(890\) | −5.06850e6 | −0.214489 | ||||||||
\(891\) | 7.05087e6 | 0.297542 | ||||||||
\(892\) | 3.14041e7 | 1.32152 | ||||||||
\(893\) | −1.28133e7 | −0.537690 | ||||||||
\(894\) | −3.23000e6 | −0.135163 | ||||||||
\(895\) | 1.48615e7 | 0.620162 | ||||||||
\(896\) | −3.57581e7 | −1.48800 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.01990e6 | −0.0422053 | ||||||||
\(899\) | −8.34768e6 | −0.344482 | ||||||||
\(900\) | 3.97250e6 | 0.163477 | ||||||||
\(901\) | −4.00136e7 | −1.64208 | ||||||||
\(902\) | −2.78181e6 | −0.113844 | ||||||||
\(903\) | −955392. | −0.0389908 | ||||||||
\(904\) | 1.34232e6 | 0.0546305 | ||||||||
\(905\) | 2.67745e6 | 0.108668 | ||||||||
\(906\) | 3.57318e6 | 0.144622 | ||||||||
\(907\) | 7.48309e6 | 0.302039 | 0.151019 | − | 0.988531i | \(-0.451744\pi\) | ||||
0.151019 | + | 0.988531i | \(0.451744\pi\) | |||||||
\(908\) | −653744. | −0.0263144 | ||||||||
\(909\) | 2.04068e7 | 0.819155 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.63165e6 | −0.264744 | −0.132372 | − | 0.991200i | \(-0.542259\pi\) | ||||
−0.132372 | + | 0.991200i | \(0.542259\pi\) | |||||||
\(912\) | 2.78144e6 | 0.110734 | ||||||||
\(913\) | −2.47397e6 | −0.0982239 | ||||||||
\(914\) | 2.44168e6 | 0.0966772 | ||||||||
\(915\) | 3.23020e6 | 0.127549 | ||||||||
\(916\) | −1.66883e7 | −0.657163 | ||||||||
\(917\) | −1.46788e7 | −0.576457 | ||||||||
\(918\) | 6.30928e6 | 0.247100 | ||||||||
\(919\) | −1.68976e7 | −0.659990 | −0.329995 | − | 0.943983i | \(-0.607047\pi\) | ||||
−0.329995 | + | 0.943983i | \(0.607047\pi\) | |||||||
\(920\) | −8.92800e6 | −0.347764 | ||||||||
\(921\) | −9.51003e6 | −0.369431 | ||||||||
\(922\) | −8.14420e6 | −0.315516 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −3.18259e6 | −0.122631 | ||||||||
\(925\) | −113750. | −0.00437116 | ||||||||
\(926\) | 4.04587e6 | 0.155055 | ||||||||
\(927\) | 4.42741e6 | 0.169219 | ||||||||
\(928\) | 1.75683e7 | 0.669669 | ||||||||
\(929\) | 1.28653e7 | 0.489081 | 0.244541 | − | 0.969639i | \(-0.421363\pi\) | ||||
0.244541 | + | 0.969639i | \(0.421363\pi\) | |||||||
\(930\) | −489600. | −0.0185624 | ||||||||
\(931\) | −2.12604e7 | −0.803892 | ||||||||
\(932\) | 1.35894e7 | 0.512459 | ||||||||
\(933\) | 9.49219e6 | 0.356995 | ||||||||
\(934\) | −6.50194e6 | −0.243880 | ||||||||
\(935\) | 6.20860e6 | 0.232255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.06887e7 | 0.397718 | 0.198859 | − | 0.980028i | \(-0.436276\pi\) | ||||
0.198859 | + | 0.980028i | \(0.436276\pi\) | |||||||
\(938\) | −2.34132e7 | −0.868870 | ||||||||
\(939\) | 5.71766e6 | 0.211619 | ||||||||
\(940\) | 8.46160e6 | 0.312344 | ||||||||
\(941\) | −2.82455e7 | −1.03986 | −0.519930 | − | 0.854209i | \(-0.674042\pi\) | ||||
−0.519930 | + | 0.854209i | \(0.674042\pi\) | |||||||
\(942\) | −2.09806e6 | −0.0770356 | ||||||||
\(943\) | 2.79684e7 | 1.02421 | ||||||||
\(944\) | 1.31331e7 | 0.479665 | ||||||||
\(945\) | 9.02400e6 | 0.328715 | ||||||||
\(946\) | 368224. | 0.0133778 | ||||||||
\(947\) | 1.70892e7 | 0.619222 | 0.309611 | − | 0.950863i | \(-0.399801\pi\) | ||||
0.309611 | + | 0.950863i | \(0.399801\pi\) | |||||||
\(948\) | −3.73632e6 | −0.135028 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 1.32500e6 | 0.0476329 | ||||||||
\(951\) | 8.49849e6 | 0.304713 | ||||||||
\(952\) | 3.86611e7 | 1.38255 | ||||||||
\(953\) | 2.22259e7 | 0.792735 | 0.396367 | − | 0.918092i | \(-0.370271\pi\) | ||||
0.396367 | + | 0.918092i | \(0.370271\pi\) | |||||||
\(954\) | 1.08261e7 | 0.385124 | ||||||||
\(955\) | −1.17388e7 | −0.416500 | ||||||||
\(956\) | −1.36864e6 | −0.0484333 | ||||||||
\(957\) | 2.01872e6 | 0.0712519 | ||||||||
\(958\) | −6.55872e6 | −0.230890 | ||||||||
\(959\) | −2.78243e7 | −0.976961 | ||||||||
\(960\) | −1.06880e6 | −0.0374299 | ||||||||
\(961\) | −2.26364e7 | −0.790678 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.59323e7 | −1.24859 | ||||||||
\(964\) | −3.10234e6 | −0.107522 | ||||||||
\(965\) | 1.31765e6 | 0.0455493 | ||||||||
\(966\) | −4.57114e6 | −0.157609 | ||||||||
\(967\) | −2.41551e7 | −0.830696 | −0.415348 | − | 0.909663i | \(-0.636340\pi\) | ||||
−0.415348 | + | 0.909663i | \(0.636340\pi\) | |||||||
\(968\) | −1.66976e7 | −0.572752 | ||||||||
\(969\) | −7.11472e6 | −0.243416 | ||||||||
\(970\) | 5.95190e6 | 0.203108 | ||||||||
\(971\) | −5.48313e7 | −1.86630 | −0.933149 | − | 0.359491i | \(-0.882950\pi\) | ||||
−0.933149 | + | 0.359491i | \(0.882950\pi\) | |||||||
\(972\) | 1.81273e7 | 0.615415 | ||||||||
\(973\) | −2.15462e7 | −0.729608 | ||||||||
\(974\) | −1.70639e7 | −0.576344 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.11901e7 | 0.712047 | ||||||||
\(977\) | 1.56612e7 | 0.524915 | 0.262457 | − | 0.964944i | \(-0.415467\pi\) | ||||
0.262457 | + | 0.964944i | \(0.415467\pi\) | |||||||
\(978\) | 1.23651e6 | 0.0413382 | ||||||||
\(979\) | −1.50028e7 | −0.500281 | ||||||||
\(980\) | 1.40399e7 | 0.466981 | ||||||||
\(981\) | 8.36041e6 | 0.277367 | ||||||||
\(982\) | −3.02530e6 | −0.100113 | ||||||||
\(983\) | 1.63420e7 | 0.539412 | 0.269706 | − | 0.962943i | \(-0.413073\pi\) | ||||
0.269706 | + | 0.962943i | \(0.413073\pi\) | |||||||
\(984\) | −4.51104e6 | −0.148521 | ||||||||
\(985\) | 1.13966e7 | 0.374268 | ||||||||
\(986\) | −1.14440e7 | −0.374873 | ||||||||
\(987\) | 9.28358e6 | 0.303335 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.70214e6 | −0.120355 | ||||||||
\(990\) | −1.67980e6 | −0.0544715 | ||||||||
\(991\) | 1.37576e7 | 0.444997 | 0.222498 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222498 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(992\) | −1.26121e7 | −0.406919 | ||||||||
\(993\) | 1.23994e7 | 0.399050 | ||||||||
\(994\) | 1.25368e7 | 0.402459 | ||||||||
\(995\) | −2.16250e7 | −0.692466 | ||||||||
\(996\) | −1.87219e6 | −0.0598001 | ||||||||
\(997\) | −1.29097e7 | −0.411320 | −0.205660 | − | 0.978624i | \(-0.565934\pi\) | ||||
−0.205660 | + | 0.978624i | \(0.565934\pi\) | |||||||
\(998\) | −1.29838e7 | −0.412644 | ||||||||
\(999\) | −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 | 845.6.a.b.1.1 | 1 | ||
13.12 | even | 2 | 5.6.a.a.1.1 | ✓ | 1 | ||
39.38 | odd | 2 | 45.6.a.b.1.1 | 1 | |||
52.51 | odd | 2 | 80.6.a.e.1.1 | 1 | |||
65.12 | odd | 4 | 25.6.b.a.24.2 | 2 | |||
65.38 | odd | 4 | 25.6.b.a.24.1 | 2 | |||
65.64 | even | 2 | 25.6.a.a.1.1 | 1 | |||
91.90 | odd | 2 | 245.6.a.b.1.1 | 1 | |||
104.51 | odd | 2 | 320.6.a.g.1.1 | 1 | |||
104.77 | even | 2 | 320.6.a.j.1.1 | 1 | |||
143.142 | odd | 2 | 605.6.a.a.1.1 | 1 | |||
156.155 | even | 2 | 720.6.a.a.1.1 | 1 | |||
195.38 | even | 4 | 225.6.b.e.199.2 | 2 | |||
195.77 | even | 4 | 225.6.b.e.199.1 | 2 | |||
195.194 | odd | 2 | 225.6.a.f.1.1 | 1 | |||
260.103 | even | 4 | 400.6.c.j.49.2 | 2 | |||
260.207 | even | 4 | 400.6.c.j.49.1 | 2 | |||
260.259 | odd | 2 | 400.6.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.6.a.a.1.1 | ✓ | 1 | 13.12 | even | 2 | ||
25.6.a.a.1.1 | 1 | 65.64 | even | 2 | |||
25.6.b.a.24.1 | 2 | 65.38 | odd | 4 | |||
25.6.b.a.24.2 | 2 | 65.12 | odd | 4 | |||
45.6.a.b.1.1 | 1 | 39.38 | odd | 2 | |||
80.6.a.e.1.1 | 1 | 52.51 | odd | 2 | |||
225.6.a.f.1.1 | 1 | 195.194 | odd | 2 | |||
225.6.b.e.199.1 | 2 | 195.77 | even | 4 | |||
225.6.b.e.199.2 | 2 | 195.38 | even | 4 | |||
245.6.a.b.1.1 | 1 | 91.90 | odd | 2 | |||
320.6.a.g.1.1 | 1 | 104.51 | odd | 2 | |||
320.6.a.j.1.1 | 1 | 104.77 | even | 2 | |||
400.6.a.g.1.1 | 1 | 260.259 | odd | 2 | |||
400.6.c.j.49.1 | 2 | 260.207 | even | 4 | |||
400.6.c.j.49.2 | 2 | 260.103 | even | 4 | |||
605.6.a.a.1.1 | 1 | 143.142 | odd | 2 | |||
720.6.a.a.1.1 | 1 | 156.155 | even | 2 | |||
845.6.a.b.1.1 | 1 | 1.1 | even | 1 | trivial |