Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,6,Mod(1,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, 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("115.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.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: | \(18.4441392785\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} - 220 x^{8} + 541 x^{7} + 15887 x^{6} - 50180 x^{5} - 417450 x^{4} + 1703213 x^{3} + \cdots + 15136200 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(3.17438\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.17438 | −0.737932 | −0.368966 | − | 0.929443i | \(-0.620288\pi\) | ||||
−0.368966 | + | 0.929443i | \(0.620288\pi\) | |||||||
\(3\) | −2.37223 | −0.152179 | −0.0760894 | − | 0.997101i | \(-0.524243\pi\) | ||||
−0.0760894 | + | 0.997101i | \(0.524243\pi\) | |||||||
\(4\) | −14.5746 | −0.455456 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 9.90260 | 0.112298 | ||||||||
\(7\) | 115.757 | 0.892900 | 0.446450 | − | 0.894809i | \(-0.352688\pi\) | ||||
0.446450 | + | 0.894809i | \(0.352688\pi\) | |||||||
\(8\) | 194.420 | 1.07403 | ||||||||
\(9\) | −237.373 | −0.976842 | ||||||||
\(10\) | 104.359 | 0.330013 | ||||||||
\(11\) | 539.278 | 1.34379 | 0.671894 | − | 0.740647i | \(-0.265481\pi\) | ||||
0.671894 | + | 0.740647i | \(0.265481\pi\) | |||||||
\(12\) | 34.5743 | 0.0693107 | ||||||||
\(13\) | 116.796 | 0.191676 | 0.0958381 | − | 0.995397i | \(-0.469447\pi\) | ||||
0.0958381 | + | 0.995397i | \(0.469447\pi\) | |||||||
\(14\) | −483.214 | −0.658900 | ||||||||
\(15\) | 59.3059 | 0.0680565 | ||||||||
\(16\) | −345.195 | −0.337104 | ||||||||
\(17\) | 283.187 | 0.237658 | 0.118829 | − | 0.992915i | \(-0.462086\pi\) | ||||
0.118829 | + | 0.992915i | \(0.462086\pi\) | |||||||
\(18\) | 990.882 | 0.720843 | ||||||||
\(19\) | −1935.09 | −1.22975 | −0.614875 | − | 0.788625i | \(-0.710793\pi\) | ||||
−0.614875 | + | 0.788625i | \(0.710793\pi\) | |||||||
\(20\) | 364.365 | 0.203686 | ||||||||
\(21\) | −274.603 | −0.135881 | ||||||||
\(22\) | −2251.15 | −0.991625 | ||||||||
\(23\) | −529.000 | −0.208514 | ||||||||
\(24\) | −461.209 | −0.163444 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −487.549 | −0.141444 | ||||||||
\(27\) | 1139.56 | 0.300834 | ||||||||
\(28\) | −1687.11 | −0.406676 | ||||||||
\(29\) | −1811.62 | −0.400010 | −0.200005 | − | 0.979795i | \(-0.564096\pi\) | ||||
−0.200005 | + | 0.979795i | \(0.564096\pi\) | |||||||
\(30\) | −247.565 | −0.0502211 | ||||||||
\(31\) | −1602.67 | −0.299530 | −0.149765 | − | 0.988722i | \(-0.547852\pi\) | ||||
−0.149765 | + | 0.988722i | \(0.547852\pi\) | |||||||
\(32\) | −4780.46 | −0.825268 | ||||||||
\(33\) | −1279.29 | −0.204496 | ||||||||
\(34\) | −1182.13 | −0.175375 | ||||||||
\(35\) | −2893.93 | −0.399317 | ||||||||
\(36\) | 3459.61 | 0.444908 | ||||||||
\(37\) | 7108.55 | 0.853644 | 0.426822 | − | 0.904336i | \(-0.359633\pi\) | ||||
0.426822 | + | 0.904336i | \(0.359633\pi\) | |||||||
\(38\) | 8077.78 | 0.907472 | ||||||||
\(39\) | −277.067 | −0.0291691 | ||||||||
\(40\) | −4860.50 | −0.480320 | ||||||||
\(41\) | −18391.4 | −1.70866 | −0.854328 | − | 0.519734i | \(-0.826031\pi\) | ||||
−0.854328 | + | 0.519734i | \(0.826031\pi\) | |||||||
\(42\) | 1146.30 | 0.100271 | ||||||||
\(43\) | −23389.6 | −1.92909 | −0.964545 | − | 0.263920i | \(-0.914985\pi\) | ||||
−0.964545 | + | 0.263920i | \(0.914985\pi\) | |||||||
\(44\) | −7859.75 | −0.612036 | ||||||||
\(45\) | 5934.31 | 0.436857 | ||||||||
\(46\) | 2208.25 | 0.153870 | ||||||||
\(47\) | −24977.0 | −1.64928 | −0.824642 | − | 0.565655i | \(-0.808623\pi\) | ||||
−0.824642 | + | 0.565655i | \(0.808623\pi\) | |||||||
\(48\) | 818.883 | 0.0513002 | ||||||||
\(49\) | −3407.27 | −0.202729 | ||||||||
\(50\) | −2608.99 | −0.147586 | ||||||||
\(51\) | −671.787 | −0.0361665 | ||||||||
\(52\) | −1702.25 | −0.0873000 | ||||||||
\(53\) | −5302.06 | −0.259272 | −0.129636 | − | 0.991562i | \(-0.541381\pi\) | ||||
−0.129636 | + | 0.991562i | \(0.541381\pi\) | |||||||
\(54\) | −4756.94 | −0.221995 | ||||||||
\(55\) | −13481.9 | −0.600960 | ||||||||
\(56\) | 22505.5 | 0.959000 | ||||||||
\(57\) | 4590.48 | 0.187142 | ||||||||
\(58\) | 7562.37 | 0.295181 | ||||||||
\(59\) | 30543.4 | 1.14232 | 0.571159 | − | 0.820839i | \(-0.306494\pi\) | ||||
0.571159 | + | 0.820839i | \(0.306494\pi\) | |||||||
\(60\) | −864.358 | −0.0309967 | ||||||||
\(61\) | 44040.3 | 1.51539 | 0.757697 | − | 0.652607i | \(-0.226325\pi\) | ||||
0.757697 | + | 0.652607i | \(0.226325\pi\) | |||||||
\(62\) | 6690.16 | 0.221033 | ||||||||
\(63\) | −27477.6 | −0.872222 | ||||||||
\(64\) | 31001.7 | 0.946096 | ||||||||
\(65\) | −2919.89 | −0.0857202 | ||||||||
\(66\) | 5340.25 | 0.150904 | ||||||||
\(67\) | −20711.7 | −0.563675 | −0.281838 | − | 0.959462i | \(-0.590944\pi\) | ||||
−0.281838 | + | 0.959462i | \(0.590944\pi\) | |||||||
\(68\) | −4127.34 | −0.108242 | ||||||||
\(69\) | 1254.91 | 0.0317315 | ||||||||
\(70\) | 12080.4 | 0.294669 | ||||||||
\(71\) | 37127.9 | 0.874087 | 0.437044 | − | 0.899440i | \(-0.356026\pi\) | ||||
0.437044 | + | 0.899440i | \(0.356026\pi\) | |||||||
\(72\) | −46149.9 | −1.04916 | ||||||||
\(73\) | 23277.2 | 0.511238 | 0.255619 | − | 0.966778i | \(-0.417721\pi\) | ||||
0.255619 | + | 0.966778i | \(0.417721\pi\) | |||||||
\(74\) | −29673.8 | −0.629931 | ||||||||
\(75\) | −1482.65 | −0.0304358 | ||||||||
\(76\) | 28203.1 | 0.560096 | ||||||||
\(77\) | 62425.3 | 1.19987 | ||||||||
\(78\) | 1156.58 | 0.0215248 | ||||||||
\(79\) | −53752.1 | −0.969009 | −0.484505 | − | 0.874789i | \(-0.661000\pi\) | ||||
−0.484505 | + | 0.874789i | \(0.661000\pi\) | |||||||
\(80\) | 8629.87 | 0.150758 | ||||||||
\(81\) | 54978.2 | 0.931061 | ||||||||
\(82\) | 76772.6 | 1.26087 | ||||||||
\(83\) | −114591. | −1.82581 | −0.912907 | − | 0.408167i | \(-0.866168\pi\) | ||||
−0.912907 | + | 0.408167i | \(0.866168\pi\) | |||||||
\(84\) | 4002.23 | 0.0618876 | ||||||||
\(85\) | −7079.69 | −0.106284 | ||||||||
\(86\) | 97637.1 | 1.42354 | ||||||||
\(87\) | 4297.58 | 0.0608731 | ||||||||
\(88\) | 104846. | 1.44327 | ||||||||
\(89\) | 40980.7 | 0.548409 | 0.274205 | − | 0.961671i | \(-0.411585\pi\) | ||||
0.274205 | + | 0.961671i | \(0.411585\pi\) | |||||||
\(90\) | −24772.1 | −0.322371 | ||||||||
\(91\) | 13519.9 | 0.171148 | ||||||||
\(92\) | 7709.95 | 0.0949691 | ||||||||
\(93\) | 3801.92 | 0.0455822 | ||||||||
\(94\) | 104263. | 1.21706 | ||||||||
\(95\) | 48377.2 | 0.549961 | ||||||||
\(96\) | 11340.4 | 0.125588 | ||||||||
\(97\) | 429.764 | 0.00463768 | 0.00231884 | − | 0.999997i | \(-0.499262\pi\) | ||||
0.00231884 | + | 0.999997i | \(0.499262\pi\) | |||||||
\(98\) | 14223.2 | 0.149601 | ||||||||
\(99\) | −128010. | −1.31267 | ||||||||
\(100\) | −9109.11 | −0.0910911 | ||||||||
\(101\) | −174445. | −1.70159 | −0.850794 | − | 0.525499i | \(-0.823879\pi\) | ||||
−0.850794 | + | 0.525499i | \(0.823879\pi\) | |||||||
\(102\) | 2804.29 | 0.0266884 | ||||||||
\(103\) | 56582.0 | 0.525515 | 0.262757 | − | 0.964862i | \(-0.415368\pi\) | ||||
0.262757 | + | 0.964862i | \(0.415368\pi\) | |||||||
\(104\) | 22707.4 | 0.205866 | ||||||||
\(105\) | 6865.08 | 0.0607676 | ||||||||
\(106\) | 22132.8 | 0.191325 | ||||||||
\(107\) | 17063.3 | 0.144080 | 0.0720398 | − | 0.997402i | \(-0.477049\pi\) | ||||
0.0720398 | + | 0.997402i | \(0.477049\pi\) | |||||||
\(108\) | −16608.6 | −0.137016 | ||||||||
\(109\) | −27832.2 | −0.224378 | −0.112189 | − | 0.993687i | \(-0.535786\pi\) | ||||
−0.112189 | + | 0.993687i | \(0.535786\pi\) | |||||||
\(110\) | 56278.7 | 0.443468 | ||||||||
\(111\) | −16863.1 | −0.129907 | ||||||||
\(112\) | −39958.8 | −0.301001 | ||||||||
\(113\) | −235136. | −1.73230 | −0.866149 | − | 0.499786i | \(-0.833412\pi\) | ||||
−0.866149 | + | 0.499786i | \(0.833412\pi\) | |||||||
\(114\) | −19162.4 | −0.138098 | ||||||||
\(115\) | 13225.0 | 0.0932505 | ||||||||
\(116\) | 26403.5 | 0.182187 | ||||||||
\(117\) | −27724.1 | −0.187237 | ||||||||
\(118\) | −127500. | −0.842954 | ||||||||
\(119\) | 32781.0 | 0.212204 | ||||||||
\(120\) | 11530.2 | 0.0730946 | ||||||||
\(121\) | 129769. | 0.805766 | ||||||||
\(122\) | −183841. | −1.11826 | ||||||||
\(123\) | 43628.7 | 0.260021 | ||||||||
\(124\) | 23358.3 | 0.136423 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 114702. | 0.643641 | ||||||||
\(127\) | −117540. | −0.646659 | −0.323329 | − | 0.946286i | \(-0.604802\pi\) | ||||
−0.323329 | + | 0.946286i | \(0.604802\pi\) | |||||||
\(128\) | 23562.1 | 0.127113 | ||||||||
\(129\) | 55485.7 | 0.293567 | ||||||||
\(130\) | 12188.7 | 0.0632557 | ||||||||
\(131\) | 228906. | 1.16541 | 0.582706 | − | 0.812683i | \(-0.301994\pi\) | ||||
0.582706 | + | 0.812683i | \(0.301994\pi\) | |||||||
\(132\) | 18645.2 | 0.0931389 | ||||||||
\(133\) | −224000. | −1.09804 | ||||||||
\(134\) | 86458.4 | 0.415954 | ||||||||
\(135\) | −28488.9 | −0.134537 | ||||||||
\(136\) | 55057.3 | 0.255251 | ||||||||
\(137\) | −238305. | −1.08476 | −0.542378 | − | 0.840135i | \(-0.682476\pi\) | ||||
−0.542378 | + | 0.840135i | \(0.682476\pi\) | |||||||
\(138\) | −5238.47 | −0.0234157 | ||||||||
\(139\) | −215507. | −0.946070 | −0.473035 | − | 0.881044i | \(-0.656842\pi\) | ||||
−0.473035 | + | 0.881044i | \(0.656842\pi\) | |||||||
\(140\) | 42177.8 | 0.181871 | ||||||||
\(141\) | 59251.3 | 0.250986 | ||||||||
\(142\) | −154986. | −0.645017 | ||||||||
\(143\) | 62985.3 | 0.257572 | ||||||||
\(144\) | 81939.8 | 0.329298 | ||||||||
\(145\) | 45290.4 | 0.178890 | ||||||||
\(146\) | −97167.7 | −0.377259 | ||||||||
\(147\) | 8082.85 | 0.0308511 | ||||||||
\(148\) | −103604. | −0.388797 | ||||||||
\(149\) | −327077. | −1.20693 | −0.603467 | − | 0.797388i | \(-0.706215\pi\) | ||||
−0.603467 | + | 0.797388i | \(0.706215\pi\) | |||||||
\(150\) | 6189.12 | 0.0224595 | ||||||||
\(151\) | 119246. | 0.425598 | 0.212799 | − | 0.977096i | \(-0.431742\pi\) | ||||
0.212799 | + | 0.977096i | \(0.431742\pi\) | |||||||
\(152\) | −376219. | −1.32079 | ||||||||
\(153\) | −67220.9 | −0.232154 | ||||||||
\(154\) | −260587. | −0.885422 | ||||||||
\(155\) | 40066.8 | 0.133954 | ||||||||
\(156\) | 4038.13 | 0.0132852 | ||||||||
\(157\) | 175169. | 0.567165 | 0.283582 | − | 0.958948i | \(-0.408477\pi\) | ||||
0.283582 | + | 0.958948i | \(0.408477\pi\) | |||||||
\(158\) | 224382. | 0.715063 | ||||||||
\(159\) | 12577.7 | 0.0394557 | ||||||||
\(160\) | 119512. | 0.369071 | ||||||||
\(161\) | −61235.6 | −0.186183 | ||||||||
\(162\) | −229500. | −0.687060 | ||||||||
\(163\) | 140575. | 0.414418 | 0.207209 | − | 0.978297i | \(-0.433562\pi\) | ||||
0.207209 | + | 0.978297i | \(0.433562\pi\) | |||||||
\(164\) | 268047. | 0.778217 | ||||||||
\(165\) | 31982.3 | 0.0914535 | ||||||||
\(166\) | 478347. | 1.34733 | ||||||||
\(167\) | −314621. | −0.872964 | −0.436482 | − | 0.899713i | \(-0.643776\pi\) | ||||
−0.436482 | + | 0.899713i | \(0.643776\pi\) | |||||||
\(168\) | −53388.3 | −0.145940 | ||||||||
\(169\) | −357652. | −0.963260 | ||||||||
\(170\) | 29553.3 | 0.0784302 | ||||||||
\(171\) | 459337. | 1.20127 | ||||||||
\(172\) | 340894. | 0.878615 | ||||||||
\(173\) | −173706. | −0.441264 | −0.220632 | − | 0.975357i | \(-0.570812\pi\) | ||||
−0.220632 | + | 0.975357i | \(0.570812\pi\) | |||||||
\(174\) | −17939.7 | −0.0449203 | ||||||||
\(175\) | 72348.2 | 0.178580 | ||||||||
\(176\) | −186156. | −0.452997 | ||||||||
\(177\) | −72456.1 | −0.173837 | ||||||||
\(178\) | −171069. | −0.404689 | ||||||||
\(179\) | −126133. | −0.294235 | −0.147118 | − | 0.989119i | \(-0.547000\pi\) | ||||
−0.147118 | + | 0.989119i | \(0.547000\pi\) | |||||||
\(180\) | −86490.1 | −0.198969 | ||||||||
\(181\) | 362984. | 0.823552 | 0.411776 | − | 0.911285i | \(-0.364909\pi\) | ||||
0.411776 | + | 0.911285i | \(0.364909\pi\) | |||||||
\(182\) | −56437.3 | −0.126295 | ||||||||
\(183\) | −104474. | −0.230611 | ||||||||
\(184\) | −102848. | −0.223950 | ||||||||
\(185\) | −177714. | −0.381761 | ||||||||
\(186\) | −15870.6 | −0.0336366 | ||||||||
\(187\) | 152717. | 0.319361 | ||||||||
\(188\) | 364029. | 0.751176 | ||||||||
\(189\) | 131912. | 0.268614 | ||||||||
\(190\) | −201945. | −0.405834 | ||||||||
\(191\) | −573499. | −1.13749 | −0.568747 | − | 0.822513i | \(-0.692572\pi\) | ||||
−0.568747 | + | 0.822513i | \(0.692572\pi\) | |||||||
\(192\) | −73543.2 | −0.143976 | ||||||||
\(193\) | 358805. | 0.693369 | 0.346685 | − | 0.937982i | \(-0.387307\pi\) | ||||
0.346685 | + | 0.937982i | \(0.387307\pi\) | |||||||
\(194\) | −1794.00 | −0.00342229 | ||||||||
\(195\) | 6926.67 | 0.0130448 | ||||||||
\(196\) | 49659.6 | 0.0923342 | ||||||||
\(197\) | −655906. | −1.20414 | −0.602069 | − | 0.798444i | \(-0.705657\pi\) | ||||
−0.602069 | + | 0.798444i | \(0.705657\pi\) | |||||||
\(198\) | 534361. | 0.968660 | ||||||||
\(199\) | −384463. | −0.688212 | −0.344106 | − | 0.938931i | \(-0.611818\pi\) | ||||
−0.344106 | + | 0.938931i | \(0.611818\pi\) | |||||||
\(200\) | 121512. | 0.214806 | ||||||||
\(201\) | 49133.0 | 0.0857794 | ||||||||
\(202\) | 728198. | 1.25566 | ||||||||
\(203\) | −209708. | −0.357169 | ||||||||
\(204\) | 9791.01 | 0.0164722 | ||||||||
\(205\) | 459785. | 0.764134 | ||||||||
\(206\) | −236194. | −0.387795 | ||||||||
\(207\) | 125570. | 0.203686 | ||||||||
\(208\) | −40317.3 | −0.0646149 | ||||||||
\(209\) | −1.04355e6 | −1.65252 | ||||||||
\(210\) | −28657.4 | −0.0448424 | ||||||||
\(211\) | 309387. | 0.478405 | 0.239203 | − | 0.970970i | \(-0.423114\pi\) | ||||
0.239203 | + | 0.970970i | \(0.423114\pi\) | |||||||
\(212\) | 77275.4 | 0.118087 | ||||||||
\(213\) | −88076.1 | −0.133018 | ||||||||
\(214\) | −71228.4 | −0.106321 | ||||||||
\(215\) | 584741. | 0.862715 | ||||||||
\(216\) | 221552. | 0.323104 | ||||||||
\(217\) | −185521. | −0.267451 | ||||||||
\(218\) | 116182. | 0.165576 | ||||||||
\(219\) | −55218.9 | −0.0777996 | ||||||||
\(220\) | 196494. | 0.273711 | ||||||||
\(221\) | 33075.1 | 0.0455533 | ||||||||
\(222\) | 70393.1 | 0.0958623 | ||||||||
\(223\) | 1.30912e6 | 1.76286 | 0.881432 | − | 0.472311i | \(-0.156580\pi\) | ||||
0.881432 | + | 0.472311i | \(0.156580\pi\) | |||||||
\(224\) | −553373. | −0.736882 | ||||||||
\(225\) | −148358. | −0.195368 | ||||||||
\(226\) | 981545. | 1.27832 | ||||||||
\(227\) | −1.38190e6 | −1.77996 | −0.889981 | − | 0.455998i | \(-0.849283\pi\) | ||||
−0.889981 | + | 0.455998i | \(0.849283\pi\) | |||||||
\(228\) | −66904.4 | −0.0852349 | ||||||||
\(229\) | 1.23238e6 | 1.55294 | 0.776471 | − | 0.630153i | \(-0.217008\pi\) | ||||
0.776471 | + | 0.630153i | \(0.217008\pi\) | |||||||
\(230\) | −55206.1 | −0.0688126 | ||||||||
\(231\) | −148087. | −0.182595 | ||||||||
\(232\) | −352214. | −0.429622 | ||||||||
\(233\) | 1.05461e6 | 1.27263 | 0.636313 | − | 0.771431i | \(-0.280459\pi\) | ||||
0.636313 | + | 0.771431i | \(0.280459\pi\) | |||||||
\(234\) | 115731. | 0.138168 | ||||||||
\(235\) | 624425. | 0.737582 | ||||||||
\(236\) | −445157. | −0.520275 | ||||||||
\(237\) | 127513. | 0.147463 | ||||||||
\(238\) | −136840. | −0.156593 | ||||||||
\(239\) | 1.07816e6 | 1.22093 | 0.610463 | − | 0.792045i | \(-0.290983\pi\) | ||||
0.610463 | + | 0.792045i | \(0.290983\pi\) | |||||||
\(240\) | −20472.1 | −0.0229421 | ||||||||
\(241\) | −391545. | −0.434249 | −0.217124 | − | 0.976144i | \(-0.569668\pi\) | ||||
−0.217124 | + | 0.976144i | \(0.569668\pi\) | |||||||
\(242\) | −541706. | −0.594601 | ||||||||
\(243\) | −407333. | −0.442521 | ||||||||
\(244\) | −641869. | −0.690195 | ||||||||
\(245\) | 85181.8 | 0.0906633 | ||||||||
\(246\) | −182122. | −0.191878 | ||||||||
\(247\) | −226010. | −0.235714 | ||||||||
\(248\) | −311591. | −0.321704 | ||||||||
\(249\) | 271838. | 0.277850 | ||||||||
\(250\) | 65224.6 | 0.0660027 | ||||||||
\(251\) | 919511. | 0.921240 | 0.460620 | − | 0.887597i | \(-0.347627\pi\) | ||||
0.460620 | + | 0.887597i | \(0.347627\pi\) | |||||||
\(252\) | 400474. | 0.397258 | ||||||||
\(253\) | −285278. | −0.280199 | ||||||||
\(254\) | 490655. | 0.477191 | ||||||||
\(255\) | 16794.7 | 0.0161741 | ||||||||
\(256\) | −1.09041e6 | −1.03990 | ||||||||
\(257\) | −286148. | −0.270245 | −0.135123 | − | 0.990829i | \(-0.543143\pi\) | ||||
−0.135123 | + | 0.990829i | \(0.543143\pi\) | |||||||
\(258\) | −231618. | −0.216632 | ||||||||
\(259\) | 822866. | 0.762219 | ||||||||
\(260\) | 42556.2 | 0.0390418 | ||||||||
\(261\) | 430028. | 0.390747 | ||||||||
\(262\) | −955542. | −0.859996 | ||||||||
\(263\) | −557560. | −0.497052 | −0.248526 | − | 0.968625i | \(-0.579946\pi\) | ||||
−0.248526 | + | 0.968625i | \(0.579946\pi\) | |||||||
\(264\) | −248720. | −0.219635 | ||||||||
\(265\) | 132552. | 0.115950 | ||||||||
\(266\) | 935062. | 0.810282 | ||||||||
\(267\) | −97215.9 | −0.0834563 | ||||||||
\(268\) | 301864. | 0.256729 | ||||||||
\(269\) | 401010. | 0.337890 | 0.168945 | − | 0.985626i | \(-0.445964\pi\) | ||||
0.168945 | + | 0.985626i | \(0.445964\pi\) | |||||||
\(270\) | 118923. | 0.0992791 | ||||||||
\(271\) | 2.08406e6 | 1.72380 | 0.861901 | − | 0.507077i | \(-0.169274\pi\) | ||||
0.861901 | + | 0.507077i | \(0.169274\pi\) | |||||||
\(272\) | −97754.9 | −0.0801154 | ||||||||
\(273\) | −32072.5 | −0.0260451 | ||||||||
\(274\) | 994776. | 0.800477 | ||||||||
\(275\) | 337049. | 0.268758 | ||||||||
\(276\) | −18289.8 | −0.0144523 | ||||||||
\(277\) | 1.30265e6 | 1.02007 | 0.510033 | − | 0.860155i | \(-0.329633\pi\) | ||||
0.510033 | + | 0.860155i | \(0.329633\pi\) | |||||||
\(278\) | 899605. | 0.698136 | ||||||||
\(279\) | 380431. | 0.292594 | ||||||||
\(280\) | −562637. | −0.428878 | ||||||||
\(281\) | −1.11215e6 | −0.840232 | −0.420116 | − | 0.907470i | \(-0.638011\pi\) | ||||
−0.420116 | + | 0.907470i | \(0.638011\pi\) | |||||||
\(282\) | −247337. | −0.185211 | ||||||||
\(283\) | −623456. | −0.462743 | −0.231372 | − | 0.972865i | \(-0.574321\pi\) | ||||
−0.231372 | + | 0.972865i | \(0.574321\pi\) | |||||||
\(284\) | −541124. | −0.398108 | ||||||||
\(285\) | −114762. | −0.0836924 | ||||||||
\(286\) | −262924. | −0.190071 | ||||||||
\(287\) | −2.12893e6 | −1.52566 | ||||||||
\(288\) | 1.13475e6 | 0.806156 | ||||||||
\(289\) | −1.33966e6 | −0.943519 | ||||||||
\(290\) | −189059. | −0.132009 | ||||||||
\(291\) | −1019.50 | −0.000705757 0 | ||||||||
\(292\) | −339255. | −0.232846 | ||||||||
\(293\) | −1.15557e6 | −0.786371 | −0.393186 | − | 0.919459i | \(-0.628627\pi\) | ||||
−0.393186 | + | 0.919459i | \(0.628627\pi\) | |||||||
\(294\) | −33740.8 | −0.0227660 | ||||||||
\(295\) | −763585. | −0.510860 | ||||||||
\(296\) | 1.38204e6 | 0.916837 | ||||||||
\(297\) | 614537. | 0.404257 | ||||||||
\(298\) | 1.36534e6 | 0.890636 | ||||||||
\(299\) | −61784.9 | −0.0399673 | ||||||||
\(300\) | 21609.0 | 0.0138621 | ||||||||
\(301\) | −2.70752e6 | −1.72248 | ||||||||
\(302\) | −497776. | −0.314063 | ||||||||
\(303\) | 413824. | 0.258946 | ||||||||
\(304\) | 667982. | 0.414554 | ||||||||
\(305\) | −1.10101e6 | −0.677705 | ||||||||
\(306\) | 280605. | 0.171314 | ||||||||
\(307\) | 2.53752e6 | 1.53661 | 0.768306 | − | 0.640082i | \(-0.221100\pi\) | ||||
0.768306 | + | 0.640082i | \(0.221100\pi\) | |||||||
\(308\) | −909822. | −0.546487 | ||||||||
\(309\) | −134226. | −0.0799723 | ||||||||
\(310\) | −167254. | −0.0988490 | ||||||||
\(311\) | −312766. | −0.183366 | −0.0916829 | − | 0.995788i | \(-0.529225\pi\) | ||||
−0.0916829 | + | 0.995788i | \(0.529225\pi\) | |||||||
\(312\) | −53867.2 | −0.0313284 | ||||||||
\(313\) | −1.12347e6 | −0.648187 | −0.324093 | − | 0.946025i | \(-0.605059\pi\) | ||||
−0.324093 | + | 0.946025i | \(0.605059\pi\) | |||||||
\(314\) | −731223. | −0.418529 | ||||||||
\(315\) | 686939. | 0.390070 | ||||||||
\(316\) | 783415. | 0.441341 | ||||||||
\(317\) | 1.48240e6 | 0.828545 | 0.414272 | − | 0.910153i | \(-0.364036\pi\) | ||||
0.414272 | + | 0.910153i | \(0.364036\pi\) | |||||||
\(318\) | −52504.2 | −0.0291156 | ||||||||
\(319\) | −976964. | −0.537529 | ||||||||
\(320\) | −775042. | −0.423107 | ||||||||
\(321\) | −40478.0 | −0.0219259 | ||||||||
\(322\) | 255620. | 0.137390 | ||||||||
\(323\) | −547993. | −0.292259 | ||||||||
\(324\) | −801285. | −0.424057 | ||||||||
\(325\) | 72997.3 | 0.0383352 | ||||||||
\(326\) | −586813. | −0.305813 | ||||||||
\(327\) | 66024.4 | 0.0341456 | ||||||||
\(328\) | −3.57565e6 | −1.83514 | ||||||||
\(329\) | −2.89127e6 | −1.47265 | ||||||||
\(330\) | −133506. | −0.0674865 | ||||||||
\(331\) | −3.32429e6 | −1.66774 | −0.833871 | − | 0.551960i | \(-0.813880\pi\) | ||||
−0.833871 | + | 0.551960i | \(0.813880\pi\) | |||||||
\(332\) | 1.67012e6 | 0.831578 | ||||||||
\(333\) | −1.68737e6 | −0.833875 | ||||||||
\(334\) | 1.31335e6 | 0.644188 | ||||||||
\(335\) | 517793. | 0.252083 | ||||||||
\(336\) | 94791.6 | 0.0458059 | ||||||||
\(337\) | 3.09137e6 | 1.48278 | 0.741389 | − | 0.671075i | \(-0.234167\pi\) | ||||
0.741389 | + | 0.671075i | \(0.234167\pi\) | |||||||
\(338\) | 1.49297e6 | 0.710821 | ||||||||
\(339\) | 557797. | 0.263619 | ||||||||
\(340\) | 103183. | 0.0484075 | ||||||||
\(341\) | −864286. | −0.402505 | ||||||||
\(342\) | −1.91744e6 | −0.886456 | ||||||||
\(343\) | −2.33995e6 | −1.07392 | ||||||||
\(344\) | −4.54741e6 | −2.07190 | ||||||||
\(345\) | −31372.8 | −0.0141908 | ||||||||
\(346\) | 725113. | 0.325623 | ||||||||
\(347\) | 418312. | 0.186499 | 0.0932494 | − | 0.995643i | \(-0.470275\pi\) | ||||
0.0932494 | + | 0.995643i | \(0.470275\pi\) | |||||||
\(348\) | −62635.4 | −0.0277250 | ||||||||
\(349\) | 1.05103e6 | 0.461905 | 0.230953 | − | 0.972965i | \(-0.425816\pi\) | ||||
0.230953 | + | 0.972965i | \(0.425816\pi\) | |||||||
\(350\) | −302009. | −0.131780 | ||||||||
\(351\) | 133095. | 0.0576626 | ||||||||
\(352\) | −2.57800e6 | −1.10898 | ||||||||
\(353\) | −169070. | −0.0722154 | −0.0361077 | − | 0.999348i | \(-0.511496\pi\) | ||||
−0.0361077 | + | 0.999348i | \(0.511496\pi\) | |||||||
\(354\) | 302459. | 0.128280 | ||||||||
\(355\) | −928198. | −0.390904 | ||||||||
\(356\) | −597277. | −0.249776 | ||||||||
\(357\) | −77764.2 | −0.0322930 | ||||||||
\(358\) | 526525. | 0.217126 | ||||||||
\(359\) | 3.99005e6 | 1.63396 | 0.816982 | − | 0.576663i | \(-0.195645\pi\) | ||||
0.816982 | + | 0.576663i | \(0.195645\pi\) | |||||||
\(360\) | 1.15375e6 | 0.469196 | ||||||||
\(361\) | 1.26847e6 | 0.512284 | ||||||||
\(362\) | −1.51523e6 | −0.607726 | ||||||||
\(363\) | −307843. | −0.122621 | ||||||||
\(364\) | −197047. | −0.0779502 | ||||||||
\(365\) | −581929. | −0.228633 | ||||||||
\(366\) | 436113. | 0.170175 | ||||||||
\(367\) | 90469.6 | 0.0350621 | 0.0175310 | − | 0.999846i | \(-0.494419\pi\) | ||||
0.0175310 | + | 0.999846i | \(0.494419\pi\) | |||||||
\(368\) | 182608. | 0.0702911 | ||||||||
\(369\) | 4.36561e6 | 1.66909 | ||||||||
\(370\) | 741844. | 0.281714 | ||||||||
\(371\) | −613752. | −0.231504 | ||||||||
\(372\) | −55411.3 | −0.0207607 | ||||||||
\(373\) | −1.13536e6 | −0.422535 | −0.211268 | − | 0.977428i | \(-0.567759\pi\) | ||||
−0.211268 | + | 0.977428i | \(0.567759\pi\) | |||||||
\(374\) | −637497. | −0.235667 | ||||||||
\(375\) | 37066.2 | 0.0136113 | ||||||||
\(376\) | −4.85602e6 | −1.77138 | ||||||||
\(377\) | −211589. | −0.0766725 | ||||||||
\(378\) | −550650. | −0.198219 | ||||||||
\(379\) | 1.85101e6 | 0.661927 | 0.330963 | − | 0.943644i | \(-0.392626\pi\) | ||||
0.330963 | + | 0.943644i | \(0.392626\pi\) | |||||||
\(380\) | −705077. | −0.250483 | ||||||||
\(381\) | 278832. | 0.0984078 | ||||||||
\(382\) | 2.39400e6 | 0.839393 | ||||||||
\(383\) | 791473. | 0.275701 | 0.137851 | − | 0.990453i | \(-0.455981\pi\) | ||||
0.137851 | + | 0.990453i | \(0.455981\pi\) | |||||||
\(384\) | −55894.8 | −0.0193439 | ||||||||
\(385\) | −1.56063e6 | −0.536597 | ||||||||
\(386\) | −1.49779e6 | −0.511660 | ||||||||
\(387\) | 5.55206e6 | 1.88441 | ||||||||
\(388\) | −6263.63 | −0.00211226 | ||||||||
\(389\) | −5.47609e6 | −1.83483 | −0.917417 | − | 0.397928i | \(-0.869730\pi\) | ||||
−0.917417 | + | 0.397928i | \(0.869730\pi\) | |||||||
\(390\) | −28914.5 | −0.00962619 | ||||||||
\(391\) | −149806. | −0.0495550 | ||||||||
\(392\) | −662441. | −0.217737 | ||||||||
\(393\) | −543020. | −0.177351 | ||||||||
\(394\) | 2.73800e6 | 0.888572 | ||||||||
\(395\) | 1.34380e6 | 0.433354 | ||||||||
\(396\) | 1.86569e6 | 0.597862 | ||||||||
\(397\) | 856539. | 0.272754 | 0.136377 | − | 0.990657i | \(-0.456454\pi\) | ||||
0.136377 | + | 0.990657i | \(0.456454\pi\) | |||||||
\(398\) | 1.60489e6 | 0.507854 | ||||||||
\(399\) | 531381. | 0.167099 | ||||||||
\(400\) | −215747. | −0.0674209 | ||||||||
\(401\) | 4.82636e6 | 1.49885 | 0.749426 | − | 0.662088i | \(-0.230330\pi\) | ||||
0.749426 | + | 0.662088i | \(0.230330\pi\) | |||||||
\(402\) | −205100. | −0.0632994 | ||||||||
\(403\) | −187185. | −0.0574128 | ||||||||
\(404\) | 2.54246e6 | 0.774998 | ||||||||
\(405\) | −1.37446e6 | −0.416383 | ||||||||
\(406\) | 875398. | 0.263567 | ||||||||
\(407\) | 3.83348e6 | 1.14712 | ||||||||
\(408\) | −130609. | −0.0388438 | ||||||||
\(409\) | −370285. | −0.109453 | −0.0547265 | − | 0.998501i | \(-0.517429\pi\) | ||||
−0.0547265 | + | 0.998501i | \(0.517429\pi\) | |||||||
\(410\) | −1.91931e6 | −0.563880 | ||||||||
\(411\) | 565316. | 0.165077 | ||||||||
\(412\) | −824659. | −0.239349 | ||||||||
\(413\) | 3.53562e6 | 1.01998 | ||||||||
\(414\) | −524177. | −0.150306 | ||||||||
\(415\) | 2.86478e6 | 0.816529 | ||||||||
\(416\) | −558337. | −0.158184 | ||||||||
\(417\) | 511232. | 0.143972 | ||||||||
\(418\) | 4.35617e6 | 1.21945 | ||||||||
\(419\) | 5.03815e6 | 1.40196 | 0.700980 | − | 0.713181i | \(-0.252746\pi\) | ||||
0.700980 | + | 0.713181i | \(0.252746\pi\) | |||||||
\(420\) | −100056. | −0.0276770 | ||||||||
\(421\) | −1.39455e6 | −0.383467 | −0.191733 | − | 0.981447i | \(-0.561411\pi\) | ||||
−0.191733 | + | 0.981447i | \(0.561411\pi\) | |||||||
\(422\) | −1.29150e6 | −0.353031 | ||||||||
\(423\) | 5.92885e6 | 1.61109 | ||||||||
\(424\) | −1.03083e6 | −0.278465 | ||||||||
\(425\) | 176992. | 0.0475315 | ||||||||
\(426\) | 367663. | 0.0981580 | ||||||||
\(427\) | 5.09798e6 | 1.35310 | ||||||||
\(428\) | −248690. | −0.0656218 | ||||||||
\(429\) | −149416. | −0.0391971 | ||||||||
\(430\) | −2.44093e6 | −0.636625 | ||||||||
\(431\) | 2.53332e6 | 0.656897 | 0.328449 | − | 0.944522i | \(-0.393474\pi\) | ||||
0.328449 | + | 0.944522i | \(0.393474\pi\) | |||||||
\(432\) | −393369. | −0.101412 | ||||||||
\(433\) | 2.45088e6 | 0.628205 | 0.314103 | − | 0.949389i | \(-0.398296\pi\) | ||||
0.314103 | + | 0.949389i | \(0.398296\pi\) | |||||||
\(434\) | 774434. | 0.197360 | ||||||||
\(435\) | −107439. | −0.0272233 | ||||||||
\(436\) | 405642. | 0.102194 | ||||||||
\(437\) | 1.02366e6 | 0.256421 | ||||||||
\(438\) | 230505. | 0.0574109 | ||||||||
\(439\) | −5.83082e6 | −1.44400 | −0.722002 | − | 0.691891i | \(-0.756778\pi\) | ||||
−0.722002 | + | 0.691891i | \(0.756778\pi\) | |||||||
\(440\) | −2.62116e6 | −0.645448 | ||||||||
\(441\) | 808793. | 0.198034 | ||||||||
\(442\) | −138068. | −0.0336153 | ||||||||
\(443\) | −4.81423e6 | −1.16551 | −0.582756 | − | 0.812647i | \(-0.698026\pi\) | ||||
−0.582756 | + | 0.812647i | \(0.698026\pi\) | |||||||
\(444\) | 245773. | 0.0591667 | ||||||||
\(445\) | −1.02452e6 | −0.245256 | ||||||||
\(446\) | −5.46478e6 | −1.30087 | ||||||||
\(447\) | 775902. | 0.183670 | ||||||||
\(448\) | 3.58867e6 | 0.844769 | ||||||||
\(449\) | 1.85298e6 | 0.433765 | 0.216882 | − | 0.976198i | \(-0.430411\pi\) | ||||
0.216882 | + | 0.976198i | \(0.430411\pi\) | |||||||
\(450\) | 619301. | 0.144169 | ||||||||
\(451\) | −9.91806e6 | −2.29607 | ||||||||
\(452\) | 3.42701e6 | 0.788985 | ||||||||
\(453\) | −282878. | −0.0647671 | ||||||||
\(454\) | 5.76855e6 | 1.31349 | ||||||||
\(455\) | −337998. | −0.0765396 | ||||||||
\(456\) | 892481. | 0.200996 | ||||||||
\(457\) | 208337. | 0.0466634 | 0.0233317 | − | 0.999728i | \(-0.492573\pi\) | ||||
0.0233317 | + | 0.999728i | \(0.492573\pi\) | |||||||
\(458\) | −5.14441e6 | −1.14597 | ||||||||
\(459\) | 322708. | 0.0714954 | ||||||||
\(460\) | −192749. | −0.0424715 | ||||||||
\(461\) | 4.11958e6 | 0.902820 | 0.451410 | − | 0.892317i | \(-0.350921\pi\) | ||||
0.451410 | + | 0.892317i | \(0.350921\pi\) | |||||||
\(462\) | 618172. | 0.134743 | ||||||||
\(463\) | 2.50227e6 | 0.542478 | 0.271239 | − | 0.962512i | \(-0.412567\pi\) | ||||
0.271239 | + | 0.962512i | \(0.412567\pi\) | |||||||
\(464\) | 625361. | 0.134845 | ||||||||
\(465\) | −95047.9 | −0.0203850 | ||||||||
\(466\) | −4.40232e6 | −0.939112 | ||||||||
\(467\) | −6.57630e6 | −1.39537 | −0.697685 | − | 0.716404i | \(-0.745787\pi\) | ||||
−0.697685 | + | 0.716404i | \(0.745787\pi\) | |||||||
\(468\) | 404067. | 0.0852783 | ||||||||
\(469\) | −2.39753e6 | −0.503306 | ||||||||
\(470\) | −2.60658e6 | −0.544286 | ||||||||
\(471\) | −415543. | −0.0863105 | ||||||||
\(472\) | 5.93824e6 | 1.22688 | ||||||||
\(473\) | −1.26135e7 | −2.59229 | ||||||||
\(474\) | −532286. | −0.108818 | ||||||||
\(475\) | −1.20943e6 | −0.245950 | ||||||||
\(476\) | −477769. | −0.0966497 | ||||||||
\(477\) | 1.25856e6 | 0.253268 | ||||||||
\(478\) | −4.50065e6 | −0.900961 | ||||||||
\(479\) | 4.62529e6 | 0.921086 | 0.460543 | − | 0.887637i | \(-0.347655\pi\) | ||||
0.460543 | + | 0.887637i | \(0.347655\pi\) | |||||||
\(480\) | −283509. | −0.0561648 | ||||||||
\(481\) | 830248. | 0.163623 | ||||||||
\(482\) | 1.63445e6 | 0.320446 | ||||||||
\(483\) | 145265. | 0.0283331 | ||||||||
\(484\) | −1.89133e6 | −0.366991 | ||||||||
\(485\) | −10744.1 | −0.00207403 | ||||||||
\(486\) | 1.70036e6 | 0.326551 | ||||||||
\(487\) | 5.05164e6 | 0.965184 | 0.482592 | − | 0.875845i | \(-0.339695\pi\) | ||||
0.482592 | + | 0.875845i | \(0.339695\pi\) | |||||||
\(488\) | 8.56230e6 | 1.62758 | ||||||||
\(489\) | −333477. | −0.0630657 | ||||||||
\(490\) | −355581. | −0.0669034 | ||||||||
\(491\) | −6.82168e6 | −1.27699 | −0.638495 | − | 0.769626i | \(-0.720443\pi\) | ||||
−0.638495 | + | 0.769626i | \(0.720443\pi\) | |||||||
\(492\) | −635870. | −0.118428 | ||||||||
\(493\) | −513027. | −0.0950655 | ||||||||
\(494\) | 943450. | 0.173941 | ||||||||
\(495\) | 3.20024e6 | 0.587043 | ||||||||
\(496\) | 553235. | 0.100973 | ||||||||
\(497\) | 4.29782e6 | 0.780473 | ||||||||
\(498\) | −1.13475e6 | −0.205035 | ||||||||
\(499\) | 3.98851e6 | 0.717066 | 0.358533 | − | 0.933517i | \(-0.383277\pi\) | ||||
0.358533 | + | 0.933517i | \(0.383277\pi\) | |||||||
\(500\) | 227728. | 0.0407372 | ||||||||
\(501\) | 746354. | 0.132847 | ||||||||
\(502\) | −3.83839e6 | −0.679813 | ||||||||
\(503\) | 4.90799e6 | 0.864935 | 0.432467 | − | 0.901650i | \(-0.357643\pi\) | ||||
0.432467 | + | 0.901650i | \(0.357643\pi\) | |||||||
\(504\) | −5.34219e6 | −0.936791 | ||||||||
\(505\) | 4.36112e6 | 0.760974 | ||||||||
\(506\) | 1.19086e6 | 0.206768 | ||||||||
\(507\) | 848434. | 0.146588 | ||||||||
\(508\) | 1.71309e6 | 0.294524 | ||||||||
\(509\) | 1.74821e6 | 0.299089 | 0.149544 | − | 0.988755i | \(-0.452219\pi\) | ||||
0.149544 | + | 0.988755i | \(0.452219\pi\) | |||||||
\(510\) | −70107.3 | −0.0119354 | ||||||||
\(511\) | 2.69450e6 | 0.456485 | ||||||||
\(512\) | 3.79780e6 | 0.640261 | ||||||||
\(513\) | −2.20514e6 | −0.369950 | ||||||||
\(514\) | 1.19449e6 | 0.199423 | ||||||||
\(515\) | −1.41455e6 | −0.235017 | ||||||||
\(516\) | −808681. | −0.133707 | ||||||||
\(517\) | −1.34695e7 | −2.21629 | ||||||||
\(518\) | −3.43495e6 | −0.562466 | ||||||||
\(519\) | 412071. | 0.0671511 | ||||||||
\(520\) | −567685. | −0.0920659 | ||||||||
\(521\) | −1.06210e7 | −1.71423 | −0.857117 | − | 0.515121i | \(-0.827747\pi\) | ||||
−0.857117 | + | 0.515121i | \(0.827747\pi\) | |||||||
\(522\) | −1.79510e6 | −0.288345 | ||||||||
\(523\) | 2.43090e6 | 0.388609 | 0.194304 | − | 0.980941i | \(-0.437755\pi\) | ||||
0.194304 | + | 0.980941i | \(0.437755\pi\) | |||||||
\(524\) | −3.33622e6 | −0.530794 | ||||||||
\(525\) | −171627. | −0.0271761 | ||||||||
\(526\) | 2.32746e6 | 0.366791 | ||||||||
\(527\) | −453857. | −0.0711856 | ||||||||
\(528\) | 441605. | 0.0689366 | ||||||||
\(529\) | 279841. | 0.0434783 | ||||||||
\(530\) | −553320. | −0.0855632 | ||||||||
\(531\) | −7.25016e6 | −1.11586 | ||||||||
\(532\) | 3.26471e6 | 0.500110 | ||||||||
\(533\) | −2.14803e6 | −0.327509 | ||||||||
\(534\) | 405816. | 0.0615851 | ||||||||
\(535\) | −426581. | −0.0644343 | ||||||||
\(536\) | −4.02677e6 | −0.605403 | ||||||||
\(537\) | 299216. | 0.0447764 | ||||||||
\(538\) | −1.67397e6 | −0.249340 | ||||||||
\(539\) | −1.83747e6 | −0.272425 | ||||||||
\(540\) | 415214. | 0.0612756 | ||||||||
\(541\) | −1.85923e6 | −0.273112 | −0.136556 | − | 0.990632i | \(-0.543603\pi\) | ||||
−0.136556 | + | 0.990632i | \(0.543603\pi\) | |||||||
\(542\) | −8.69966e6 | −1.27205 | ||||||||
\(543\) | −861083. | −0.125327 | ||||||||
\(544\) | −1.35377e6 | −0.196131 | ||||||||
\(545\) | 695804. | 0.100345 | ||||||||
\(546\) | 133882. | 0.0192195 | ||||||||
\(547\) | −4.02968e6 | −0.575841 | −0.287920 | − | 0.957654i | \(-0.592964\pi\) | ||||
−0.287920 | + | 0.957654i | \(0.592964\pi\) | |||||||
\(548\) | 3.47320e6 | 0.494058 | ||||||||
\(549\) | −1.04540e7 | −1.48030 | ||||||||
\(550\) | −1.40697e6 | −0.198325 | ||||||||
\(551\) | 3.50564e6 | 0.491912 | ||||||||
\(552\) | 243980. | 0.0340805 | ||||||||
\(553\) | −6.22220e6 | −0.865229 | ||||||||
\(554\) | −5.43775e6 | −0.752740 | ||||||||
\(555\) | 421579. | 0.0580960 | ||||||||
\(556\) | 3.14092e6 | 0.430893 | ||||||||
\(557\) | −1.74809e6 | −0.238740 | −0.119370 | − | 0.992850i | \(-0.538088\pi\) | ||||
−0.119370 | + | 0.992850i | \(0.538088\pi\) | |||||||
\(558\) | −1.58806e6 | −0.215914 | ||||||||
\(559\) | −2.73181e6 | −0.369761 | ||||||||
\(560\) | 998970. | 0.134612 | ||||||||
\(561\) | −362280. | −0.0486001 | ||||||||
\(562\) | 4.64255e6 | 0.620035 | ||||||||
\(563\) | −5.57963e6 | −0.741882 | −0.370941 | − | 0.928657i | \(-0.620965\pi\) | ||||
−0.370941 | + | 0.928657i | \(0.620965\pi\) | |||||||
\(564\) | −863562. | −0.114313 | ||||||||
\(565\) | 5.87839e6 | 0.774707 | ||||||||
\(566\) | 2.60254e6 | 0.341473 | ||||||||
\(567\) | 6.36413e6 | 0.831345 | ||||||||
\(568\) | 7.21840e6 | 0.938794 | ||||||||
\(569\) | 8.43793e6 | 1.09258 | 0.546292 | − | 0.837595i | \(-0.316039\pi\) | ||||
0.546292 | + | 0.837595i | \(0.316039\pi\) | |||||||
\(570\) | 479060. | 0.0617593 | ||||||||
\(571\) | 3.61998e6 | 0.464639 | 0.232320 | − | 0.972640i | \(-0.425368\pi\) | ||||
0.232320 | + | 0.972640i | \(0.425368\pi\) | |||||||
\(572\) | −917984. | −0.117313 | ||||||||
\(573\) | 1.36047e6 | 0.173102 | ||||||||
\(574\) | 8.88698e6 | 1.12583 | ||||||||
\(575\) | −330625. | −0.0417029 | ||||||||
\(576\) | −7.35895e6 | −0.924186 | ||||||||
\(577\) | −4.14606e6 | −0.518438 | −0.259219 | − | 0.965819i | \(-0.583465\pi\) | ||||
−0.259219 | + | 0.965819i | \(0.583465\pi\) | |||||||
\(578\) | 5.59225e6 | 0.696253 | ||||||||
\(579\) | −851168. | −0.105516 | ||||||||
\(580\) | −660089. | −0.0814765 | ||||||||
\(581\) | −1.32648e7 | −1.63027 | ||||||||
\(582\) | 4255.78 | 0.000520801 0 | ||||||||
\(583\) | −2.85928e6 | −0.348406 | ||||||||
\(584\) | 4.52554e6 | 0.549084 | ||||||||
\(585\) | 693102. | 0.0837351 | ||||||||
\(586\) | 4.82379e6 | 0.580289 | ||||||||
\(587\) | −5.69728e6 | −0.682452 | −0.341226 | − | 0.939981i | \(-0.610842\pi\) | ||||
−0.341226 | + | 0.939981i | \(0.610842\pi\) | |||||||
\(588\) | −117804. | −0.0140513 | ||||||||
\(589\) | 3.10131e6 | 0.368347 | ||||||||
\(590\) | 3.18749e6 | 0.376980 | ||||||||
\(591\) | 1.55596e6 | 0.183244 | ||||||||
\(592\) | −2.45383e6 | −0.287767 | ||||||||
\(593\) | 5.12766e6 | 0.598801 | 0.299401 | − | 0.954127i | \(-0.403213\pi\) | ||||
0.299401 | + | 0.954127i | \(0.403213\pi\) | |||||||
\(594\) | −2.56531e6 | −0.298314 | ||||||||
\(595\) | −819525. | −0.0949007 | ||||||||
\(596\) | 4.76701e6 | 0.549705 | ||||||||
\(597\) | 912037. | 0.104731 | ||||||||
\(598\) | 257913. | 0.0294931 | ||||||||
\(599\) | 9.56173e6 | 1.08885 | 0.544427 | − | 0.838808i | \(-0.316747\pi\) | ||||
0.544427 | + | 0.838808i | \(0.316747\pi\) | |||||||
\(600\) | −288256. | −0.0326889 | ||||||||
\(601\) | −1.68548e7 | −1.90343 | −0.951716 | − | 0.306981i | \(-0.900681\pi\) | ||||
−0.951716 | + | 0.306981i | \(0.900681\pi\) | |||||||
\(602\) | 1.13022e7 | 1.27108 | ||||||||
\(603\) | 4.91639e6 | 0.550621 | ||||||||
\(604\) | −1.73795e6 | −0.193841 | ||||||||
\(605\) | −3.24423e6 | −0.360349 | ||||||||
\(606\) | −1.72746e6 | −0.191085 | ||||||||
\(607\) | −1.23664e7 | −1.36229 | −0.681147 | − | 0.732147i | \(-0.738518\pi\) | ||||
−0.681147 | + | 0.732147i | \(0.738518\pi\) | |||||||
\(608\) | 9.25061e6 | 1.01487 | ||||||||
\(609\) | 497476. | 0.0543536 | ||||||||
\(610\) | 4.59602e6 | 0.500100 | ||||||||
\(611\) | −2.91720e6 | −0.316128 | ||||||||
\(612\) | 979717. | 0.105736 | ||||||||
\(613\) | −750283. | −0.0806443 | −0.0403222 | − | 0.999187i | \(-0.512838\pi\) | ||||
−0.0403222 | + | 0.999187i | \(0.512838\pi\) | |||||||
\(614\) | −1.05926e7 | −1.13392 | ||||||||
\(615\) | −1.09072e6 | −0.116285 | ||||||||
\(616\) | 1.21367e7 | 1.28869 | ||||||||
\(617\) | −3.25829e6 | −0.344569 | −0.172285 | − | 0.985047i | \(-0.555115\pi\) | ||||
−0.172285 | + | 0.985047i | \(0.555115\pi\) | |||||||
\(618\) | 560309. | 0.0590141 | ||||||||
\(619\) | 1.16837e7 | 1.22562 | 0.612808 | − | 0.790232i | \(-0.290040\pi\) | ||||
0.612808 | + | 0.790232i | \(0.290040\pi\) | |||||||
\(620\) | −583957. | −0.0610101 | ||||||||
\(621\) | −602825. | −0.0627281 | ||||||||
\(622\) | 1.30560e6 | 0.135312 | ||||||||
\(623\) | 4.74381e6 | 0.489675 | ||||||||
\(624\) | 95642.0 | 0.00983302 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 4.68978e6 | 0.478318 | ||||||||
\(627\) | 2.47554e6 | 0.251479 | ||||||||
\(628\) | −2.55302e6 | −0.258318 | ||||||||
\(629\) | 2.01305e6 | 0.202875 | ||||||||
\(630\) | −2.86754e6 | −0.287845 | ||||||||
\(631\) | −1.72370e7 | −1.72341 | −0.861706 | − | 0.507408i | \(-0.830604\pi\) | ||||
−0.861706 | + | 0.507408i | \(0.830604\pi\) | |||||||
\(632\) | −1.04505e7 | −1.04074 | ||||||||
\(633\) | −733938. | −0.0728032 | ||||||||
\(634\) | −6.18808e6 | −0.611410 | ||||||||
\(635\) | 2.93849e6 | 0.289195 | ||||||||
\(636\) | −183315. | −0.0179703 | ||||||||
\(637\) | −397955. | −0.0388584 | ||||||||
\(638\) | 4.07822e6 | 0.396660 | ||||||||
\(639\) | −8.81315e6 | −0.853845 | ||||||||
\(640\) | −589052. | −0.0568465 | ||||||||
\(641\) | 1.12975e7 | 1.08602 | 0.543011 | − | 0.839726i | \(-0.317284\pi\) | ||||
0.543011 | + | 0.839726i | \(0.317284\pi\) | |||||||
\(642\) | 168971. | 0.0161798 | ||||||||
\(643\) | 1.03330e7 | 0.985598 | 0.492799 | − | 0.870143i | \(-0.335974\pi\) | ||||
0.492799 | + | 0.870143i | \(0.335974\pi\) | |||||||
\(644\) | 892483. | 0.0847979 | ||||||||
\(645\) | −1.38714e6 | −0.131287 | ||||||||
\(646\) | 2.28753e6 | 0.215668 | ||||||||
\(647\) | 2.08740e6 | 0.196040 | 0.0980198 | − | 0.995184i | \(-0.468749\pi\) | ||||
0.0980198 | + | 0.995184i | \(0.468749\pi\) | |||||||
\(648\) | 1.06889e7 | 0.999986 | ||||||||
\(649\) | 1.64714e7 | 1.53503 | ||||||||
\(650\) | −304718. | −0.0282888 | ||||||||
\(651\) | 440099. | 0.0407003 | ||||||||
\(652\) | −2.04882e6 | −0.188749 | ||||||||
\(653\) | −1.96369e7 | −1.80214 | −0.901072 | − | 0.433670i | \(-0.857218\pi\) | ||||
−0.901072 | + | 0.433670i | \(0.857218\pi\) | |||||||
\(654\) | −275611. | −0.0251972 | ||||||||
\(655\) | −5.72266e6 | −0.521189 | ||||||||
\(656\) | 6.34861e6 | 0.575996 | ||||||||
\(657\) | −5.52536e6 | −0.499399 | ||||||||
\(658\) | 1.20692e7 | 1.08671 | ||||||||
\(659\) | 6.14484e6 | 0.551185 | 0.275592 | − | 0.961275i | \(-0.411126\pi\) | ||||
0.275592 | + | 0.961275i | \(0.411126\pi\) | |||||||
\(660\) | −466129. | −0.0416530 | ||||||||
\(661\) | −8.67957e6 | −0.772671 | −0.386335 | − | 0.922358i | \(-0.626259\pi\) | ||||
−0.386335 | + | 0.922358i | \(0.626259\pi\) | |||||||
\(662\) | 1.38768e7 | 1.23068 | ||||||||
\(663\) | −78461.8 | −0.00693225 | ||||||||
\(664\) | −2.22788e7 | −1.96098 | ||||||||
\(665\) | 5.60001e6 | 0.491060 | ||||||||
\(666\) | 7.04373e6 | 0.615343 | ||||||||
\(667\) | 958345. | 0.0834079 | ||||||||
\(668\) | 4.58547e6 | 0.397596 | ||||||||
\(669\) | −3.10555e6 | −0.268271 | ||||||||
\(670\) | −2.16146e6 | −0.186020 | ||||||||
\(671\) | 2.37499e7 | 2.03637 | ||||||||
\(672\) | 1.31273e6 | 0.112138 | ||||||||
\(673\) | −5.26147e6 | −0.447785 | −0.223893 | − | 0.974614i | \(-0.571876\pi\) | ||||
−0.223893 | + | 0.974614i | \(0.571876\pi\) | |||||||
\(674\) | −1.29045e7 | −1.09419 | ||||||||
\(675\) | 712223. | 0.0601667 | ||||||||
\(676\) | 5.21263e6 | 0.438722 | ||||||||
\(677\) | −1.16182e7 | −0.974245 | −0.487122 | − | 0.873334i | \(-0.661953\pi\) | ||||
−0.487122 | + | 0.873334i | \(0.661953\pi\) | |||||||
\(678\) | −2.32846e6 | −0.194533 | ||||||||
\(679\) | 49748.3 | 0.00414098 | ||||||||
\(680\) | −1.37643e6 | −0.114152 | ||||||||
\(681\) | 3.27818e6 | 0.270873 | ||||||||
\(682\) | 3.60785e6 | 0.297022 | ||||||||
\(683\) | 1.50356e7 | 1.23330 | 0.616651 | − | 0.787237i | \(-0.288489\pi\) | ||||
0.616651 | + | 0.787237i | \(0.288489\pi\) | |||||||
\(684\) | −6.69464e6 | −0.547125 | ||||||||
\(685\) | 5.95763e6 | 0.485118 | ||||||||
\(686\) | 9.76782e6 | 0.792478 | ||||||||
\(687\) | −2.92349e6 | −0.236325 | ||||||||
\(688\) | 8.07398e6 | 0.650304 | ||||||||
\(689\) | −619258. | −0.0496962 | ||||||||
\(690\) | 130962. | 0.0104718 | ||||||||
\(691\) | 1.50895e7 | 1.20221 | 0.601103 | − | 0.799171i | \(-0.294728\pi\) | ||||
0.601103 | + | 0.799171i | \(0.294728\pi\) | |||||||
\(692\) | 2.53169e6 | 0.200976 | ||||||||
\(693\) | −1.48180e7 | −1.17208 | ||||||||
\(694\) | −1.74619e6 | −0.137624 | ||||||||
\(695\) | 5.38766e6 | 0.423096 | ||||||||
\(696\) | 835534. | 0.0653794 | ||||||||
\(697\) | −5.20821e6 | −0.406075 | ||||||||
\(698\) | −4.38741e6 | −0.340855 | ||||||||
\(699\) | −2.50177e6 | −0.193667 | ||||||||
\(700\) | −1.05445e6 | −0.0813353 | ||||||||
\(701\) | 8.96774e6 | 0.689268 | 0.344634 | − | 0.938737i | \(-0.388003\pi\) | ||||
0.344634 | + | 0.938737i | \(0.388003\pi\) | |||||||
\(702\) | −555589. | −0.0425511 | ||||||||
\(703\) | −1.37557e7 | −1.04977 | ||||||||
\(704\) | 1.67185e7 | 1.27135 | ||||||||
\(705\) | −1.48128e6 | −0.112244 | ||||||||
\(706\) | 705762. | 0.0532901 | ||||||||
\(707\) | −2.01932e7 | −1.51935 | ||||||||
\(708\) | 1.05602e6 | 0.0791750 | ||||||||
\(709\) | −3.65113e6 | −0.272779 | −0.136390 | − | 0.990655i | \(-0.543550\pi\) | ||||
−0.136390 | + | 0.990655i | \(0.543550\pi\) | |||||||
\(710\) | 3.87465e6 | 0.288461 | ||||||||
\(711\) | 1.27593e7 | 0.946569 | ||||||||
\(712\) | 7.96747e6 | 0.589007 | ||||||||
\(713\) | 847814. | 0.0624564 | ||||||||
\(714\) | 324617. | 0.0238301 | ||||||||
\(715\) | −1.57463e6 | −0.115190 | ||||||||
\(716\) | 1.83833e6 | 0.134011 | ||||||||
\(717\) | −2.55765e6 | −0.185799 | ||||||||
\(718\) | −1.66560e7 | −1.20576 | ||||||||
\(719\) | −1.69958e7 | −1.22608 | −0.613040 | − | 0.790052i | \(-0.710053\pi\) | ||||
−0.613040 | + | 0.790052i | \(0.710053\pi\) | |||||||
\(720\) | −2.04849e6 | −0.147266 | ||||||||
\(721\) | 6.54977e6 | 0.469232 | ||||||||
\(722\) | −5.29505e6 | −0.378031 | ||||||||
\(723\) | 928835. | 0.0660835 | ||||||||
\(724\) | −5.29034e6 | −0.375091 | ||||||||
\(725\) | −1.13226e6 | −0.0800021 | ||||||||
\(726\) | 1.28505e6 | 0.0904857 | ||||||||
\(727\) | 2.07234e7 | 1.45420 | 0.727100 | − | 0.686531i | \(-0.240868\pi\) | ||||
0.727100 | + | 0.686531i | \(0.240868\pi\) | |||||||
\(728\) | 2.62854e6 | 0.183817 | ||||||||
\(729\) | −1.23934e7 | −0.863719 | ||||||||
\(730\) | 2.42919e6 | 0.168715 | ||||||||
\(731\) | −6.62365e6 | −0.458463 | ||||||||
\(732\) | 1.52266e6 | 0.105033 | ||||||||
\(733\) | −9.13496e6 | −0.627982 | −0.313991 | − | 0.949426i | \(-0.601666\pi\) | ||||
−0.313991 | + | 0.949426i | \(0.601666\pi\) | |||||||
\(734\) | −377654. | −0.0258734 | ||||||||
\(735\) | −202071. | −0.0137970 | ||||||||
\(736\) | 2.52886e6 | 0.172080 | ||||||||
\(737\) | −1.11694e7 | −0.757460 | ||||||||
\(738\) | −1.82237e7 | −1.23167 | ||||||||
\(739\) | 9.40106e6 | 0.633236 | 0.316618 | − | 0.948553i | \(-0.397453\pi\) | ||||
0.316618 | + | 0.948553i | \(0.397453\pi\) | |||||||
\(740\) | 2.59010e6 | 0.173875 | ||||||||
\(741\) | 536148. | 0.0358707 | ||||||||
\(742\) | 2.56203e6 | 0.170834 | ||||||||
\(743\) | −1.23857e7 | −0.823090 | −0.411545 | − | 0.911389i | \(-0.635011\pi\) | ||||
−0.411545 | + | 0.911389i | \(0.635011\pi\) | |||||||
\(744\) | 739168. | 0.0489565 | ||||||||
\(745\) | 8.17692e6 | 0.539758 | ||||||||
\(746\) | 4.73944e6 | 0.311803 | ||||||||
\(747\) | 2.72008e7 | 1.78353 | ||||||||
\(748\) | −2.22578e6 | −0.145455 | ||||||||
\(749\) | 1.97519e6 | 0.128649 | ||||||||
\(750\) | −154728. | −0.0100442 | ||||||||
\(751\) | 1.44266e7 | 0.933391 | 0.466696 | − | 0.884418i | \(-0.345444\pi\) | ||||
0.466696 | + | 0.884418i | \(0.345444\pi\) | |||||||
\(752\) | 8.62193e6 | 0.555981 | ||||||||
\(753\) | −2.18130e6 | −0.140193 | ||||||||
\(754\) | 883252. | 0.0565791 | ||||||||
\(755\) | −2.98114e6 | −0.190333 | ||||||||
\(756\) | −1.92256e6 | −0.122342 | ||||||||
\(757\) | −2.02830e7 | −1.28645 | −0.643226 | − | 0.765677i | \(-0.722404\pi\) | ||||
−0.643226 | + | 0.765677i | \(0.722404\pi\) | |||||||
\(758\) | −7.72680e6 | −0.488457 | ||||||||
\(759\) | 676746. | 0.0426404 | ||||||||
\(760\) | 9.40549e6 | 0.590673 | ||||||||
\(761\) | 1.56925e7 | 0.982271 | 0.491136 | − | 0.871083i | \(-0.336582\pi\) | ||||
0.491136 | + | 0.871083i | \(0.336582\pi\) | |||||||
\(762\) | −1.16395e6 | −0.0726183 | ||||||||
\(763\) | −3.22177e6 | −0.200347 | ||||||||
\(764\) | 8.35850e6 | 0.518078 | ||||||||
\(765\) | 1.68052e6 | 0.103822 | ||||||||
\(766\) | −3.30391e6 | −0.203449 | ||||||||
\(767\) | 3.56734e6 | 0.218955 | ||||||||
\(768\) | 2.58671e6 | 0.158250 | ||||||||
\(769\) | −1.84834e6 | −0.112711 | −0.0563554 | − | 0.998411i | \(-0.517948\pi\) | ||||
−0.0563554 | + | 0.998411i | \(0.517948\pi\) | |||||||
\(770\) | 6.51466e6 | 0.395973 | ||||||||
\(771\) | 678810. | 0.0411256 | ||||||||
\(772\) | −5.22943e6 | −0.315799 | ||||||||
\(773\) | 6.13309e6 | 0.369173 | 0.184587 | − | 0.982816i | \(-0.440905\pi\) | ||||
0.184587 | + | 0.982816i | \(0.440905\pi\) | |||||||
\(774\) | −2.31764e7 | −1.39057 | ||||||||
\(775\) | −1.00167e6 | −0.0599061 | ||||||||
\(776\) | 83554.6 | 0.00498100 | ||||||||
\(777\) | −1.95203e6 | −0.115994 | ||||||||
\(778\) | 2.28593e7 | 1.35398 | ||||||||
\(779\) | 3.55889e7 | 2.10122 | ||||||||
\(780\) | −100953. | −0.00594133 | ||||||||
\(781\) | 2.00223e7 | 1.17459 | ||||||||
\(782\) | 625347. | 0.0365683 | ||||||||
\(783\) | −2.06444e6 | −0.120337 | ||||||||
\(784\) | 1.17617e6 | 0.0683410 | ||||||||
\(785\) | −4.37923e6 | −0.253644 | ||||||||
\(786\) | 2.26677e6 | 0.130873 | ||||||||
\(787\) | 2.40217e6 | 0.138251 | 0.0691253 | − | 0.997608i | \(-0.477979\pi\) | ||||
0.0691253 | + | 0.997608i | \(0.477979\pi\) | |||||||
\(788\) | 9.55956e6 | 0.548431 | ||||||||
\(789\) | 1.32266e6 | 0.0756409 | ||||||||
\(790\) | −5.60954e6 | −0.319786 | ||||||||
\(791\) | −2.72187e7 | −1.54677 | ||||||||
\(792\) | −2.48876e7 | −1.40984 | ||||||||
\(793\) | 5.14371e6 | 0.290465 | ||||||||
\(794\) | −3.57552e6 | −0.201274 | ||||||||
\(795\) | −314443. | −0.0176451 | ||||||||
\(796\) | 5.60339e6 | 0.313450 | ||||||||
\(797\) | −2.29154e7 | −1.27786 | −0.638928 | − | 0.769266i | \(-0.720622\pi\) | ||||
−0.638928 | + | 0.769266i | \(0.720622\pi\) | |||||||
\(798\) | −2.21819e6 | −0.123308 | ||||||||
\(799\) | −7.07317e6 | −0.391965 | ||||||||
\(800\) | −2.98779e6 | −0.165054 | ||||||||
\(801\) | −9.72770e6 | −0.535709 | ||||||||
\(802\) | −2.01470e7 | −1.10605 | ||||||||
\(803\) | 1.25529e7 | 0.686995 | ||||||||
\(804\) | −716093. | −0.0390687 | ||||||||
\(805\) | 1.53089e6 | 0.0832634 | ||||||||
\(806\) | 781382. | 0.0423668 | ||||||||
\(807\) | −951291. | −0.0514197 | ||||||||
\(808\) | −3.39155e7 | −1.82755 | ||||||||
\(809\) | 9.72366e6 | 0.522346 | 0.261173 | − | 0.965292i | \(-0.415891\pi\) | ||||
0.261173 | + | 0.965292i | \(0.415891\pi\) | |||||||
\(810\) | 5.73749e6 | 0.307263 | ||||||||
\(811\) | −6.87112e6 | −0.366839 | −0.183420 | − | 0.983035i | \(-0.558717\pi\) | ||||
−0.183420 | + | 0.983035i | \(0.558717\pi\) | |||||||
\(812\) | 3.05640e6 | 0.162675 | ||||||||
\(813\) | −4.94388e6 | −0.262326 | ||||||||
\(814\) | −1.60024e7 | −0.846494 | ||||||||
\(815\) | −3.51437e6 | −0.185334 | ||||||||
\(816\) | 231897. | 0.0121919 | ||||||||
\(817\) | 4.52610e7 | 2.37230 | ||||||||
\(818\) | 1.54571e6 | 0.0807689 | ||||||||
\(819\) | −3.20926e6 | −0.167184 | ||||||||
\(820\) | −6.70117e6 | −0.348029 | ||||||||
\(821\) | 3.42232e7 | 1.77200 | 0.885998 | − | 0.463688i | \(-0.153474\pi\) | ||||
0.885998 | + | 0.463688i | \(0.153474\pi\) | |||||||
\(822\) | −2.35984e6 | −0.121816 | ||||||||
\(823\) | −1.78367e7 | −0.917941 | −0.458971 | − | 0.888451i | \(-0.651782\pi\) | ||||
−0.458971 | + | 0.888451i | \(0.651782\pi\) | |||||||
\(824\) | 1.10007e7 | 0.564418 | ||||||||
\(825\) | −799558. | −0.0408992 | ||||||||
\(826\) | −1.47590e7 | −0.752674 | ||||||||
\(827\) | −1.64998e7 | −0.838909 | −0.419454 | − | 0.907776i | \(-0.637779\pi\) | ||||
−0.419454 | + | 0.907776i | \(0.637779\pi\) | |||||||
\(828\) | −1.83013e6 | −0.0927697 | ||||||||
\(829\) | 2.49879e7 | 1.26283 | 0.631413 | − | 0.775447i | \(-0.282475\pi\) | ||||
0.631413 | + | 0.775447i | \(0.282475\pi\) | |||||||
\(830\) | −1.19587e7 | −0.602543 | ||||||||
\(831\) | −3.09019e6 | −0.155232 | ||||||||
\(832\) | 3.62086e6 | 0.181344 | ||||||||
\(833\) | −964897. | −0.0481802 | ||||||||
\(834\) | −2.13407e6 | −0.106242 | ||||||||
\(835\) | 7.86552e6 | 0.390401 | ||||||||
\(836\) | 1.52093e7 | 0.752651 | ||||||||
\(837\) | −1.82634e6 | −0.0901088 | ||||||||
\(838\) | −2.10311e7 | −1.03455 | ||||||||
\(839\) | −5.69219e6 | −0.279174 | −0.139587 | − | 0.990210i | \(-0.544577\pi\) | ||||
−0.139587 | + | 0.990210i | \(0.544577\pi\) | |||||||
\(840\) | 1.33471e6 | 0.0652661 | ||||||||
\(841\) | −1.72292e7 | −0.839992 | ||||||||
\(842\) | 5.82136e6 | 0.282972 | ||||||||
\(843\) | 2.63829e6 | 0.127866 | ||||||||
\(844\) | −4.50919e6 | −0.217892 | ||||||||
\(845\) | 8.94129e6 | 0.430783 | ||||||||
\(846\) | −2.47493e7 | −1.18887 | ||||||||
\(847\) | 1.50217e7 | 0.719468 | ||||||||
\(848\) | 1.83025e6 | 0.0874017 | ||||||||
\(849\) | 1.47898e6 | 0.0704197 | ||||||||
\(850\) | −738832. | −0.0350750 | ||||||||
\(851\) | −3.76042e6 | −0.177997 | ||||||||
\(852\) | 1.28367e6 | 0.0605836 | ||||||||
\(853\) | −6.00174e6 | −0.282426 | −0.141213 | − | 0.989979i | \(-0.545100\pi\) | ||||
−0.141213 | + | 0.989979i | \(0.545100\pi\) | |||||||
\(854\) | −2.12809e7 | −0.998493 | ||||||||
\(855\) | −1.14834e7 | −0.537224 | ||||||||
\(856\) | 3.31743e6 | 0.154745 | ||||||||
\(857\) | −3.62438e7 | −1.68571 | −0.842853 | − | 0.538144i | \(-0.819126\pi\) | ||||
−0.842853 | + | 0.538144i | \(0.819126\pi\) | |||||||
\(858\) | 623718. | 0.0289248 | ||||||||
\(859\) | 1.55995e7 | 0.721318 | 0.360659 | − | 0.932698i | \(-0.382552\pi\) | ||||
0.360659 | + | 0.932698i | \(0.382552\pi\) | |||||||
\(860\) | −8.52235e6 | −0.392928 | ||||||||
\(861\) | 5.05033e6 | 0.232173 | ||||||||
\(862\) | −1.05750e7 | −0.484746 | ||||||||
\(863\) | 9.26097e6 | 0.423282 | 0.211641 | − | 0.977348i | \(-0.432119\pi\) | ||||
0.211641 | + | 0.977348i | \(0.432119\pi\) | |||||||
\(864\) | −5.44760e6 | −0.248268 | ||||||||
\(865\) | 4.34264e6 | 0.197339 | ||||||||
\(866\) | −1.02309e7 | −0.463573 | ||||||||
\(867\) | 3.17799e6 | 0.143584 | ||||||||
\(868\) | 2.70389e6 | 0.121812 | ||||||||
\(869\) | −2.89873e7 | −1.30214 | ||||||||
\(870\) | 448493. | 0.0200889 | ||||||||
\(871\) | −2.41904e6 | −0.108043 | ||||||||
\(872\) | −5.41112e6 | −0.240988 | ||||||||
\(873\) | −102014. | −0.00453028 | ||||||||
\(874\) | −4.27315e6 | −0.189221 | ||||||||
\(875\) | −1.80871e6 | −0.0798634 | ||||||||
\(876\) | 804793. | 0.0354343 | ||||||||
\(877\) | −4.39210e7 | −1.92829 | −0.964147 | − | 0.265367i | \(-0.914507\pi\) | ||||
−0.964147 | + | 0.265367i | \(0.914507\pi\) | |||||||
\(878\) | 2.43400e7 | 1.06558 | ||||||||
\(879\) | 2.74129e6 | 0.119669 | ||||||||
\(880\) | 4.65390e6 | 0.202586 | ||||||||
\(881\) | −2.95441e6 | −0.128242 | −0.0641210 | − | 0.997942i | \(-0.520424\pi\) | ||||
−0.0641210 | + | 0.997942i | \(0.520424\pi\) | |||||||
\(882\) | −3.37620e6 | −0.146136 | ||||||||
\(883\) | −4.34926e7 | −1.87721 | −0.938606 | − | 0.344992i | \(-0.887882\pi\) | ||||
−0.938606 | + | 0.344992i | \(0.887882\pi\) | |||||||
\(884\) | −482055. | −0.0207475 | ||||||||
\(885\) | 1.81140e6 | 0.0777422 | ||||||||
\(886\) | 2.00964e7 | 0.860070 | ||||||||
\(887\) | −2.36867e7 | −1.01087 | −0.505436 | − | 0.862864i | \(-0.668668\pi\) | ||||
−0.505436 | + | 0.862864i | \(0.668668\pi\) | |||||||
\(888\) | −3.27853e6 | −0.139523 | ||||||||
\(889\) | −1.36061e7 | −0.577402 | ||||||||
\(890\) | 4.27672e6 | 0.180982 | ||||||||
\(891\) | 2.96485e7 | 1.25115 | ||||||||
\(892\) | −1.90799e7 | −0.802907 | ||||||||
\(893\) | 4.83327e7 | 2.02821 | ||||||||
\(894\) | −3.23891e6 | −0.135536 | ||||||||
\(895\) | 3.15331e6 | 0.131586 | ||||||||
\(896\) | 2.72748e6 | 0.113499 | ||||||||
\(897\) | 146568. | 0.00608217 | ||||||||
\(898\) | −7.73502e6 | −0.320089 | ||||||||
\(899\) | 2.90343e6 | 0.119815 | ||||||||
\(900\) | 2.16225e6 | 0.0889816 | ||||||||
\(901\) | −1.50148e6 | −0.0616179 | ||||||||
\(902\) | 4.14017e7 | 1.69435 | ||||||||
\(903\) | 6.42287e6 | 0.262126 | ||||||||
\(904\) | −4.57151e7 | −1.86054 | ||||||||
\(905\) | −9.07460e6 | −0.368304 | ||||||||
\(906\) | 1.18084e6 | 0.0477937 | ||||||||
\(907\) | 1.45385e7 | 0.586815 | 0.293408 | − | 0.955987i | \(-0.405211\pi\) | ||||
0.293408 | + | 0.955987i | \(0.405211\pi\) | |||||||
\(908\) | 2.01406e7 | 0.810694 | ||||||||
\(909\) | 4.14084e7 | 1.66218 | ||||||||
\(910\) | 1.41093e6 | 0.0564810 | ||||||||
\(911\) | 3.72476e7 | 1.48697 | 0.743486 | − | 0.668752i | \(-0.233171\pi\) | ||||
0.743486 | + | 0.668752i | \(0.233171\pi\) | |||||||
\(912\) | −1.58461e6 | −0.0630864 | ||||||||
\(913\) | −6.17966e7 | −2.45351 | ||||||||
\(914\) | −869677. | −0.0344344 | ||||||||
\(915\) | 2.61185e6 | 0.103132 | ||||||||
\(916\) | −1.79614e7 | −0.707296 | ||||||||
\(917\) | 2.64976e7 | 1.04060 | ||||||||
\(918\) | −1.34710e6 | −0.0527588 | ||||||||
\(919\) | 1.31283e7 | 0.512766 | 0.256383 | − | 0.966575i | \(-0.417469\pi\) | ||||
0.256383 | + | 0.966575i | \(0.417469\pi\) | |||||||
\(920\) | 2.57120e6 | 0.100154 | ||||||||
\(921\) | −6.01960e6 | −0.233840 | ||||||||
\(922\) | −1.71967e7 | −0.666220 | ||||||||
\(923\) | 4.33638e6 | 0.167542 | ||||||||
\(924\) | 2.15831e6 | 0.0831638 | ||||||||
\(925\) | 4.44284e6 | 0.170729 | ||||||||
\(926\) | −1.04454e7 | −0.400312 | ||||||||
\(927\) | −1.34310e7 | −0.513345 | ||||||||
\(928\) | 8.66036e6 | 0.330116 | ||||||||
\(929\) | 2.79278e7 | 1.06169 | 0.530845 | − | 0.847469i | \(-0.321875\pi\) | ||||
0.530845 | + | 0.847469i | \(0.321875\pi\) | |||||||
\(930\) | 396766. | 0.0150427 | ||||||||
\(931\) | 6.59337e6 | 0.249306 | ||||||||
\(932\) | −1.53704e7 | −0.579625 | ||||||||
\(933\) | 741953. | 0.0279044 | ||||||||
\(934\) | 2.74520e7 | 1.02969 | ||||||||
\(935\) | −3.81792e6 | −0.142823 | ||||||||
\(936\) | −5.39011e6 | −0.201098 | ||||||||
\(937\) | 1.21452e7 | 0.451915 | 0.225958 | − | 0.974137i | \(-0.427449\pi\) | ||||
0.225958 | + | 0.974137i | \(0.427449\pi\) | |||||||
\(938\) | 1.00082e7 | 0.371405 | ||||||||
\(939\) | 2.66513e6 | 0.0986404 | ||||||||
\(940\) | −9.10073e6 | −0.335936 | ||||||||
\(941\) | −2.41588e7 | −0.889408 | −0.444704 | − | 0.895678i | \(-0.646691\pi\) | ||||
−0.444704 | + | 0.895678i | \(0.646691\pi\) | |||||||
\(942\) | 1.73463e6 | 0.0636913 | ||||||||
\(943\) | 9.72904e6 | 0.356279 | ||||||||
\(944\) | −1.05434e7 | −0.385081 | ||||||||
\(945\) | −3.29780e6 | −0.120128 | ||||||||
\(946\) | 5.26535e7 | 1.91293 | ||||||||
\(947\) | 2.45375e6 | 0.0889110 | 0.0444555 | − | 0.999011i | \(-0.485845\pi\) | ||||
0.0444555 | + | 0.999011i | \(0.485845\pi\) | |||||||
\(948\) | −1.85844e6 | −0.0671628 | ||||||||
\(949\) | 2.71867e6 | 0.0979922 | ||||||||
\(950\) | 5.04862e6 | 0.181494 | ||||||||
\(951\) | −3.51659e6 | −0.126087 | ||||||||
\(952\) | 6.37327e6 | 0.227914 | ||||||||
\(953\) | 3.13851e7 | 1.11942 | 0.559708 | − | 0.828690i | \(-0.310913\pi\) | ||||
0.559708 | + | 0.828690i | \(0.310913\pi\) | |||||||
\(954\) | −5.25372e6 | −0.186894 | ||||||||
\(955\) | 1.43375e7 | 0.508703 | ||||||||
\(956\) | −1.57138e7 | −0.556078 | ||||||||
\(957\) | 2.31759e6 | 0.0818006 | ||||||||
\(958\) | −1.93077e7 | −0.679699 | ||||||||
\(959\) | −2.75855e7 | −0.968579 | ||||||||
\(960\) | 1.83858e6 | 0.0643880 | ||||||||
\(961\) | −2.60606e7 | −0.910282 | ||||||||
\(962\) | −3.46577e6 | −0.120743 | ||||||||
\(963\) | −4.05035e6 | −0.140743 | ||||||||
\(964\) | 5.70660e6 | 0.197781 | ||||||||
\(965\) | −8.97011e6 | −0.310084 | ||||||||
\(966\) | −606391. | −0.0209079 | ||||||||
\(967\) | −1.52177e7 | −0.523339 | −0.261669 | − | 0.965158i | \(-0.584273\pi\) | ||||
−0.261669 | + | 0.965158i | \(0.584273\pi\) | |||||||
\(968\) | 2.52297e7 | 0.865415 | ||||||||
\(969\) | 1.29997e6 | 0.0444757 | ||||||||
\(970\) | 44849.9 | 0.00153050 | ||||||||
\(971\) | 1.30611e7 | 0.444562 | 0.222281 | − | 0.974983i | \(-0.428650\pi\) | ||||
0.222281 | + | 0.974983i | \(0.428650\pi\) | |||||||
\(972\) | 5.93671e6 | 0.201549 | ||||||||
\(973\) | −2.49464e7 | −0.844746 | ||||||||
\(974\) | −2.10874e7 | −0.712240 | ||||||||
\(975\) | −173167. | −0.00583382 | ||||||||
\(976\) | −1.52025e7 | −0.510846 | ||||||||
\(977\) | 5.15862e7 | 1.72901 | 0.864504 | − | 0.502626i | \(-0.167633\pi\) | ||||
0.864504 | + | 0.502626i | \(0.167633\pi\) | |||||||
\(978\) | 1.39206e6 | 0.0465383 | ||||||||
\(979\) | 2.21000e7 | 0.736945 | ||||||||
\(980\) | −1.24149e6 | −0.0412931 | ||||||||
\(981\) | 6.60659e6 | 0.219182 | ||||||||
\(982\) | 2.84763e7 | 0.942332 | ||||||||
\(983\) | −2.00691e7 | −0.662437 | −0.331219 | − | 0.943554i | \(-0.607460\pi\) | ||||
−0.331219 | + | 0.943554i | \(0.607460\pi\) | |||||||
\(984\) | 8.48228e6 | 0.279270 | ||||||||
\(985\) | 1.63976e7 | 0.538507 | ||||||||
\(986\) | 2.14157e6 | 0.0701519 | ||||||||
\(987\) | 6.85876e6 | 0.224106 | ||||||||
\(988\) | 3.29400e6 | 0.107357 | ||||||||
\(989\) | 1.23731e7 | 0.402243 | ||||||||
\(990\) | −1.33590e7 | −0.433198 | ||||||||
\(991\) | 2.53926e7 | 0.821339 | 0.410669 | − | 0.911784i | \(-0.365295\pi\) | ||||
0.410669 | + | 0.911784i | \(0.365295\pi\) | |||||||
\(992\) | 7.66152e6 | 0.247193 | ||||||||
\(993\) | 7.88599e6 | 0.253795 | ||||||||
\(994\) | −1.79407e7 | −0.575936 | ||||||||
\(995\) | 9.61158e6 | 0.307778 | ||||||||
\(996\) | −3.96192e6 | −0.126549 | ||||||||
\(997\) | 5.48564e6 | 0.174779 | 0.0873895 | − | 0.996174i | \(-0.472148\pi\) | ||||
0.0873895 | + | 0.996174i | \(0.472148\pi\) | |||||||
\(998\) | −1.66495e7 | −0.529146 | ||||||||
\(999\) | 8.10059e6 | 0.256805 |
(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 | 115.6.a.d.1.5 | ✓ | 10 | |
3.2 | odd | 2 | 1035.6.a.j.1.6 | 10 | |||
5.4 | even | 2 | 575.6.a.f.1.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.6.a.d.1.5 | ✓ | 10 | 1.1 | even | 1 | trivial | |
575.6.a.f.1.6 | 10 | 5.4 | even | 2 | |||
1035.6.a.j.1.6 | 10 | 3.2 | odd | 2 |