Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,6,Mod(1,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, 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("325.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.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: | \(52.1247414392\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 257 x^{9} + 1165 x^{8} + 22234 x^{7} - 90282 x^{6} - 751180 x^{5} + 2564400 x^{4} + \cdots + 44115200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(6.07859\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.07859 | −1.07455 | −0.537276 | − | 0.843406i | \(-0.680547\pi\) | ||||
−0.537276 | + | 0.843406i | \(0.680547\pi\) | |||||||
\(3\) | −25.6203 | −1.64354 | −0.821770 | − | 0.569819i | \(-0.807013\pi\) | ||||
−0.821770 | + | 0.569819i | \(0.807013\pi\) | |||||||
\(4\) | 4.94922 | 0.154663 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 155.735 | 1.76607 | ||||||||
\(7\) | −137.301 | −1.05908 | −0.529539 | − | 0.848286i | \(-0.677635\pi\) | ||||
−0.529539 | + | 0.848286i | \(0.677635\pi\) | |||||||
\(8\) | 164.431 | 0.908359 | ||||||||
\(9\) | 413.398 | 1.70122 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 169.031 | 0.421196 | 0.210598 | − | 0.977573i | \(-0.432459\pi\) | ||||
0.210598 | + | 0.977573i | \(0.432459\pi\) | |||||||
\(12\) | −126.800 | −0.254195 | ||||||||
\(13\) | −169.000 | −0.277350 | ||||||||
\(14\) | 834.595 | 1.13804 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1157.88 | −1.13074 | ||||||||
\(17\) | 487.128 | 0.408810 | 0.204405 | − | 0.978886i | \(-0.434474\pi\) | ||||
0.204405 | + | 0.978886i | \(0.434474\pi\) | |||||||
\(18\) | −2512.87 | −1.82806 | ||||||||
\(19\) | 2385.49 | 1.51598 | 0.757990 | − | 0.652267i | \(-0.226182\pi\) | ||||
0.757990 | + | 0.652267i | \(0.226182\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3517.68 | 1.74064 | ||||||||
\(22\) | −1027.47 | −0.452597 | ||||||||
\(23\) | −4144.47 | −1.63361 | −0.816807 | − | 0.576911i | \(-0.804258\pi\) | ||||
−0.816807 | + | 0.576911i | \(0.804258\pi\) | |||||||
\(24\) | −4212.75 | −1.49292 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1027.28 | 0.298027 | ||||||||
\(27\) | −4365.63 | −1.15249 | ||||||||
\(28\) | −679.532 | −0.163800 | ||||||||
\(29\) | −4570.45 | −1.00917 | −0.504585 | − | 0.863362i | \(-0.668354\pi\) | ||||
−0.504585 | + | 0.863362i | \(0.668354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2957.68 | −0.552774 | −0.276387 | − | 0.961046i | \(-0.589137\pi\) | ||||
−0.276387 | + | 0.961046i | \(0.589137\pi\) | |||||||
\(32\) | 1776.50 | 0.306683 | ||||||||
\(33\) | −4330.61 | −0.692252 | ||||||||
\(34\) | −2961.05 | −0.439287 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2046.00 | 0.263117 | ||||||||
\(37\) | −5733.02 | −0.688461 | −0.344230 | − | 0.938885i | \(-0.611860\pi\) | ||||
−0.344230 | + | 0.938885i | \(0.611860\pi\) | |||||||
\(38\) | −14500.4 | −1.62900 | ||||||||
\(39\) | 4329.82 | 0.455836 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1705.07 | −0.158410 | −0.0792051 | − | 0.996858i | \(-0.525238\pi\) | ||||
−0.0792051 | + | 0.996858i | \(0.525238\pi\) | |||||||
\(42\) | −21382.5 | −1.87041 | ||||||||
\(43\) | −10922.2 | −0.900821 | −0.450410 | − | 0.892822i | \(-0.648722\pi\) | ||||
−0.450410 | + | 0.892822i | \(0.648722\pi\) | |||||||
\(44\) | 836.570 | 0.0651434 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 25192.5 | 1.75540 | ||||||||
\(47\) | 7912.12 | 0.522454 | 0.261227 | − | 0.965277i | \(-0.415873\pi\) | ||||
0.261227 | + | 0.965277i | \(0.415873\pi\) | |||||||
\(48\) | 29665.2 | 1.85842 | ||||||||
\(49\) | 2044.52 | 0.121647 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12480.4 | −0.671895 | ||||||||
\(52\) | −836.418 | −0.0428958 | ||||||||
\(53\) | −26431.1 | −1.29249 | −0.646244 | − | 0.763131i | \(-0.723661\pi\) | ||||
−0.646244 | + | 0.763131i | \(0.723661\pi\) | |||||||
\(54\) | 26536.9 | 1.23841 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −22576.4 | −0.962023 | ||||||||
\(57\) | −61116.8 | −2.49157 | ||||||||
\(58\) | 27781.9 | 1.08441 | ||||||||
\(59\) | 11248.5 | 0.420692 | 0.210346 | − | 0.977627i | \(-0.432541\pi\) | ||||
0.210346 | + | 0.977627i | \(0.432541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40298.6 | −1.38665 | −0.693323 | − | 0.720627i | \(-0.743854\pi\) | ||||
−0.693323 | + | 0.720627i | \(0.743854\pi\) | |||||||
\(62\) | 17978.5 | 0.593984 | ||||||||
\(63\) | −56759.8 | −1.80173 | ||||||||
\(64\) | 26253.6 | 0.801195 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 26324.0 | 0.743861 | ||||||||
\(67\) | 64887.2 | 1.76592 | 0.882962 | − | 0.469444i | \(-0.155546\pi\) | ||||
0.882962 | + | 0.469444i | \(0.155546\pi\) | |||||||
\(68\) | 2410.91 | 0.0632278 | ||||||||
\(69\) | 106182. | 2.68491 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −47076.1 | −1.10829 | −0.554147 | − | 0.832419i | \(-0.686955\pi\) | ||||
−0.554147 | + | 0.832419i | \(0.686955\pi\) | |||||||
\(72\) | 67975.2 | 1.54532 | ||||||||
\(73\) | −42771.8 | −0.939400 | −0.469700 | − | 0.882826i | \(-0.655638\pi\) | ||||
−0.469700 | + | 0.882826i | \(0.655638\pi\) | |||||||
\(74\) | 34848.7 | 0.739787 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11806.3 | 0.234466 | ||||||||
\(77\) | −23208.1 | −0.446079 | ||||||||
\(78\) | −26319.2 | −0.489820 | ||||||||
\(79\) | 90057.0 | 1.62349 | 0.811745 | − | 0.584012i | \(-0.198518\pi\) | ||||
0.811745 | + | 0.584012i | \(0.198518\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11392.9 | 0.192941 | ||||||||
\(82\) | 10364.4 | 0.170220 | ||||||||
\(83\) | 16427.0 | 0.261735 | 0.130868 | − | 0.991400i | \(-0.458224\pi\) | ||||
0.130868 | + | 0.991400i | \(0.458224\pi\) | |||||||
\(84\) | 17409.8 | 0.269212 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 66391.5 | 0.967979 | ||||||||
\(87\) | 117096. | 1.65861 | ||||||||
\(88\) | 27793.8 | 0.382597 | ||||||||
\(89\) | −35632.7 | −0.476841 | −0.238421 | − | 0.971162i | \(-0.576630\pi\) | ||||
−0.238421 | + | 0.971162i | \(0.576630\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 23203.8 | 0.293735 | ||||||||
\(92\) | −20511.9 | −0.252660 | ||||||||
\(93\) | 75776.6 | 0.908506 | ||||||||
\(94\) | −48094.5 | −0.561405 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −45514.4 | −0.504046 | ||||||||
\(97\) | 121030. | 1.30606 | 0.653029 | − | 0.757333i | \(-0.273498\pi\) | ||||
0.653029 | + | 0.757333i | \(0.273498\pi\) | |||||||
\(98\) | −12427.8 | −0.130716 | ||||||||
\(99\) | 69876.9 | 0.716549 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −33043.6 | −0.322318 | −0.161159 | − | 0.986928i | \(-0.551523\pi\) | ||||
−0.161159 | + | 0.986928i | \(0.551523\pi\) | |||||||
\(102\) | 75862.9 | 0.721987 | ||||||||
\(103\) | 198815. | 1.84653 | 0.923265 | − | 0.384164i | \(-0.125510\pi\) | ||||
0.923265 | + | 0.384164i | \(0.125510\pi\) | |||||||
\(104\) | −27788.8 | −0.251933 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 160664. | 1.38885 | ||||||||
\(107\) | −183355. | −1.54822 | −0.774112 | − | 0.633049i | \(-0.781803\pi\) | ||||
−0.774112 | + | 0.633049i | \(0.781803\pi\) | |||||||
\(108\) | −21606.5 | −0.178248 | ||||||||
\(109\) | −178328. | −1.43765 | −0.718827 | − | 0.695189i | \(-0.755321\pi\) | ||||
−0.718827 | + | 0.695189i | \(0.755321\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 146881. | 1.13151 | ||||||||
\(112\) | 158978. | 1.19754 | ||||||||
\(113\) | 22426.7 | 0.165223 | 0.0826114 | − | 0.996582i | \(-0.473674\pi\) | ||||
0.0826114 | + | 0.996582i | \(0.473674\pi\) | |||||||
\(114\) | 371504. | 2.67733 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −22620.2 | −0.156081 | ||||||||
\(117\) | −69864.2 | −0.471835 | ||||||||
\(118\) | −68374.9 | −0.452056 | ||||||||
\(119\) | −66883.1 | −0.432961 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −132480. | −0.822594 | ||||||||
\(122\) | 244959. | 1.49002 | ||||||||
\(123\) | 43684.4 | 0.260354 | ||||||||
\(124\) | −14638.2 | −0.0854937 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 345020. | 1.93605 | ||||||||
\(127\) | −90854.6 | −0.499847 | −0.249924 | − | 0.968266i | \(-0.580406\pi\) | ||||
−0.249924 | + | 0.968266i | \(0.580406\pi\) | |||||||
\(128\) | −216433. | −1.16761 | ||||||||
\(129\) | 279829. | 1.48054 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −78399.9 | −0.399151 | −0.199575 | − | 0.979882i | \(-0.563956\pi\) | ||||
−0.199575 | + | 0.979882i | \(0.563956\pi\) | |||||||
\(132\) | −21433.1 | −0.107066 | ||||||||
\(133\) | −327530. | −1.60554 | ||||||||
\(134\) | −394423. | −1.89758 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 80098.8 | 0.371346 | ||||||||
\(137\) | 111261. | 0.506456 | 0.253228 | − | 0.967407i | \(-0.418508\pi\) | ||||
0.253228 | + | 0.967407i | \(0.418508\pi\) | |||||||
\(138\) | −645439. | −2.88508 | ||||||||
\(139\) | −226363. | −0.993728 | −0.496864 | − | 0.867828i | \(-0.665515\pi\) | ||||
−0.496864 | + | 0.867828i | \(0.665515\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −202711. | −0.858675 | ||||||||
\(142\) | 286156. | 1.19092 | ||||||||
\(143\) | −28566.2 | −0.116819 | ||||||||
\(144\) | −478665. | −1.92365 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 259992. | 1.00943 | ||||||||
\(147\) | −52381.1 | −0.199931 | ||||||||
\(148\) | −28374.0 | −0.106479 | ||||||||
\(149\) | 443036. | 1.63483 | 0.817416 | − | 0.576047i | \(-0.195406\pi\) | ||||
0.817416 | + | 0.576047i | \(0.195406\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1334.00 | −0.00476118 | −0.00238059 | − | 0.999997i | \(-0.500758\pi\) | ||||
−0.00238059 | + | 0.999997i | \(0.500758\pi\) | |||||||
\(152\) | 392247. | 1.37705 | ||||||||
\(153\) | 201378. | 0.695477 | ||||||||
\(154\) | 141072. | 0.479336 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 21429.2 | 0.0705010 | ||||||||
\(157\) | −66009.4 | −0.213726 | −0.106863 | − | 0.994274i | \(-0.534081\pi\) | ||||
−0.106863 | + | 0.994274i | \(0.534081\pi\) | |||||||
\(158\) | −547419. | −1.74453 | ||||||||
\(159\) | 677173. | 2.12425 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 569039. | 1.73012 | ||||||||
\(162\) | −69253.0 | −0.207325 | ||||||||
\(163\) | −57419.5 | −0.169274 | −0.0846371 | − | 0.996412i | \(-0.526973\pi\) | ||||
−0.0846371 | + | 0.996412i | \(0.526973\pi\) | |||||||
\(164\) | −8438.78 | −0.0245002 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −99852.7 | −0.281248 | ||||||||
\(167\) | −298875. | −0.829275 | −0.414637 | − | 0.909987i | \(-0.636092\pi\) | ||||
−0.414637 | + | 0.909987i | \(0.636092\pi\) | |||||||
\(168\) | 578414. | 1.58112 | ||||||||
\(169\) | 28561.0 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 986155. | 2.57902 | ||||||||
\(172\) | −54056.3 | −0.139324 | ||||||||
\(173\) | −16389.5 | −0.0416342 | −0.0208171 | − | 0.999783i | \(-0.506627\pi\) | ||||
−0.0208171 | + | 0.999783i | \(0.506627\pi\) | |||||||
\(174\) | −711779. | −1.78226 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −195717. | −0.476264 | ||||||||
\(177\) | −288189. | −0.691424 | ||||||||
\(178\) | 216596. | 0.512391 | ||||||||
\(179\) | 420541. | 0.981015 | 0.490507 | − | 0.871437i | \(-0.336811\pi\) | ||||
0.490507 | + | 0.871437i | \(0.336811\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −598369. | −1.35760 | −0.678801 | − | 0.734322i | \(-0.737500\pi\) | ||||
−0.678801 | + | 0.734322i | \(0.737500\pi\) | |||||||
\(182\) | −141047. | −0.315634 | ||||||||
\(183\) | 1.03246e6 | 2.27901 | ||||||||
\(184\) | −681477. | −1.48391 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −460615. | −0.976237 | ||||||||
\(187\) | 82339.7 | 0.172189 | ||||||||
\(188\) | 39158.8 | 0.0808044 | ||||||||
\(189\) | 599405. | 1.22058 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 207706. | 0.411971 | 0.205985 | − | 0.978555i | \(-0.433960\pi\) | ||||
0.205985 | + | 0.978555i | \(0.433960\pi\) | |||||||
\(192\) | −672623. | −1.31680 | ||||||||
\(193\) | −545285. | −1.05373 | −0.526867 | − | 0.849948i | \(-0.676633\pi\) | ||||
−0.526867 | + | 0.849948i | \(0.676633\pi\) | |||||||
\(194\) | −735690. | −1.40343 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10118.8 | 0.0188143 | ||||||||
\(197\) | 559003. | 1.02624 | 0.513119 | − | 0.858317i | \(-0.328490\pi\) | ||||
0.513119 | + | 0.858317i | \(0.328490\pi\) | |||||||
\(198\) | −424753. | −0.769969 | ||||||||
\(199\) | −800588. | −1.43310 | −0.716549 | − | 0.697536i | \(-0.754280\pi\) | ||||
−0.716549 | + | 0.697536i | \(0.754280\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.66243e6 | −2.90237 | ||||||||
\(202\) | 200858. | 0.346347 | ||||||||
\(203\) | 627527. | 1.06879 | ||||||||
\(204\) | −61768.0 | −0.103917 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.20851e6 | −1.98419 | ||||||||
\(207\) | −1.71331e6 | −2.77914 | ||||||||
\(208\) | 195682. | 0.313612 | ||||||||
\(209\) | 403221. | 0.638524 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −971904. | −1.50285 | −0.751427 | − | 0.659816i | \(-0.770634\pi\) | ||||
−0.751427 | + | 0.659816i | \(0.770634\pi\) | |||||||
\(212\) | −130814. | −0.199900 | ||||||||
\(213\) | 1.20610e6 | 1.82153 | ||||||||
\(214\) | 1.11454e6 | 1.66365 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −717843. | −1.04688 | ||||||||
\(217\) | 406092. | 0.585431 | ||||||||
\(218\) | 1.08398e6 | 1.54483 | ||||||||
\(219\) | 1.09582e6 | 1.54394 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −82324.7 | −0.113383 | ||||||||
\(222\) | −892831. | −1.21587 | ||||||||
\(223\) | 401286. | 0.540371 | 0.270186 | − | 0.962808i | \(-0.412915\pi\) | ||||
0.270186 | + | 0.962808i | \(0.412915\pi\) | |||||||
\(224\) | −243915. | −0.324802 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −136323. | −0.177541 | ||||||||
\(227\) | 1.30062e6 | 1.67527 | 0.837637 | − | 0.546227i | \(-0.183936\pi\) | ||||
0.837637 | + | 0.546227i | \(0.183936\pi\) | |||||||
\(228\) | −302481. | −0.385354 | ||||||||
\(229\) | −864830. | −1.08979 | −0.544894 | − | 0.838505i | \(-0.683430\pi\) | ||||
−0.544894 | + | 0.838505i | \(0.683430\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 594596. | 0.733149 | ||||||||
\(232\) | −751521. | −0.916688 | ||||||||
\(233\) | −1.19230e6 | −1.43878 | −0.719390 | − | 0.694606i | \(-0.755579\pi\) | ||||
−0.719390 | + | 0.694606i | \(0.755579\pi\) | |||||||
\(234\) | 424676. | 0.507011 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 55671.3 | 0.0650655 | ||||||||
\(237\) | −2.30728e6 | −2.66827 | ||||||||
\(238\) | 406555. | 0.465240 | ||||||||
\(239\) | −1.23057e6 | −1.39352 | −0.696759 | − | 0.717305i | \(-0.745375\pi\) | ||||
−0.696759 | + | 0.717305i | \(0.745375\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.64306e6 | 1.82226 | 0.911129 | − | 0.412122i | \(-0.135212\pi\) | ||||
0.911129 | + | 0.412122i | \(0.135212\pi\) | |||||||
\(242\) | 805289. | 0.883921 | ||||||||
\(243\) | 768958. | 0.835385 | ||||||||
\(244\) | −199447. | −0.214463 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −265539. | −0.279764 | ||||||||
\(247\) | −403148. | −0.420457 | ||||||||
\(248\) | −486333. | −0.502117 | ||||||||
\(249\) | −420863. | −0.430172 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −447259. | −0.448100 | −0.224050 | − | 0.974578i | \(-0.571928\pi\) | ||||
−0.224050 | + | 0.974578i | \(0.571928\pi\) | |||||||
\(252\) | −280917. | −0.278661 | ||||||||
\(253\) | −700543. | −0.688071 | ||||||||
\(254\) | 552267. | 0.537112 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 475490. | 0.453463 | ||||||||
\(257\) | −465085. | −0.439237 | −0.219619 | − | 0.975586i | \(-0.570481\pi\) | ||||
−0.219619 | + | 0.975586i | \(0.570481\pi\) | |||||||
\(258\) | −1.70097e6 | −1.59091 | ||||||||
\(259\) | 787148. | 0.729134 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.88941e6 | −1.71682 | ||||||||
\(262\) | 476560. | 0.428909 | ||||||||
\(263\) | 1.88192e6 | 1.67769 | 0.838846 | − | 0.544369i | \(-0.183231\pi\) | ||||
0.838846 | + | 0.544369i | \(0.183231\pi\) | |||||||
\(264\) | −712085. | −0.628813 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.99092e6 | 1.72524 | ||||||||
\(267\) | 912919. | 0.783707 | ||||||||
\(268\) | 321141. | 0.273123 | ||||||||
\(269\) | 39508.5 | 0.0332897 | 0.0166448 | − | 0.999861i | \(-0.494702\pi\) | ||||
0.0166448 | + | 0.999861i | \(0.494702\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.01156e6 | 1.66383 | 0.831916 | − | 0.554902i | \(-0.187244\pi\) | ||||
0.831916 | + | 0.554902i | \(0.187244\pi\) | |||||||
\(272\) | −564036. | −0.462258 | ||||||||
\(273\) | −594488. | −0.482766 | ||||||||
\(274\) | −676310. | −0.544214 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 525520. | 0.415256 | ||||||||
\(277\) | 750989. | 0.588077 | 0.294039 | − | 0.955794i | \(-0.405001\pi\) | ||||
0.294039 | + | 0.955794i | \(0.405001\pi\) | |||||||
\(278\) | 1.37596e6 | 1.06781 | ||||||||
\(279\) | −1.22270e6 | −0.940392 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −116949. | −0.0883550 | −0.0441775 | − | 0.999024i | \(-0.514067\pi\) | ||||
−0.0441775 | + | 0.999024i | \(0.514067\pi\) | |||||||
\(282\) | 1.23219e6 | 0.922691 | ||||||||
\(283\) | −1.08953e6 | −0.808671 | −0.404335 | − | 0.914611i | \(-0.632497\pi\) | ||||
−0.404335 | + | 0.914611i | \(0.632497\pi\) | |||||||
\(284\) | −232990. | −0.171412 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 173642. | 0.125528 | ||||||||
\(287\) | 234108. | 0.167769 | ||||||||
\(288\) | 734400. | 0.521737 | ||||||||
\(289\) | −1.18256e6 | −0.832875 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.10081e6 | −2.14656 | ||||||||
\(292\) | −211687. | −0.145290 | ||||||||
\(293\) | 2.35419e6 | 1.60204 | 0.801020 | − | 0.598638i | \(-0.204291\pi\) | ||||
0.801020 | + | 0.598638i | \(0.204291\pi\) | |||||||
\(294\) | 318403. | 0.214837 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −942683. | −0.625369 | ||||||||
\(297\) | −737926. | −0.485424 | ||||||||
\(298\) | −2.69303e6 | −1.75671 | ||||||||
\(299\) | 700415. | 0.453083 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.49963e6 | 0.954040 | ||||||||
\(302\) | 8108.85 | 0.00511613 | ||||||||
\(303\) | 846585. | 0.529742 | ||||||||
\(304\) | −2.76211e6 | −1.71418 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.22409e6 | −0.747327 | ||||||||
\(307\) | 1.40614e6 | 0.851495 | 0.425748 | − | 0.904842i | \(-0.360011\pi\) | ||||
0.425748 | + | 0.904842i | \(0.360011\pi\) | |||||||
\(308\) | −114862. | −0.0689920 | ||||||||
\(309\) | −5.09369e6 | −3.03485 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.46661e6 | 0.859832 | 0.429916 | − | 0.902869i | \(-0.358543\pi\) | ||||
0.429916 | + | 0.902869i | \(0.358543\pi\) | |||||||
\(312\) | 711955. | 0.414063 | ||||||||
\(313\) | −310576. | −0.179187 | −0.0895935 | − | 0.995978i | \(-0.528557\pi\) | ||||
−0.0895935 | + | 0.995978i | \(0.528557\pi\) | |||||||
\(314\) | 401244. | 0.229659 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 445712. | 0.251094 | ||||||||
\(317\) | −2.21756e6 | −1.23944 | −0.619721 | − | 0.784822i | \(-0.712754\pi\) | ||||
−0.619721 | + | 0.784822i | \(0.712754\pi\) | |||||||
\(318\) | −4.11625e6 | −2.28262 | ||||||||
\(319\) | −772546. | −0.425058 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.69761e6 | 2.54457 | ||||||||
\(322\) | −3.45895e6 | −1.85911 | ||||||||
\(323\) | 1.16204e6 | 0.619747 | ||||||||
\(324\) | 56386.2 | 0.0298408 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 349030. | 0.181894 | ||||||||
\(327\) | 4.56882e6 | 2.36284 | ||||||||
\(328\) | −280366. | −0.143893 | ||||||||
\(329\) | −1.08634e6 | −0.553320 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 439684. | 0.220582 | 0.110291 | − | 0.993899i | \(-0.464822\pi\) | ||||
0.110291 | + | 0.993899i | \(0.464822\pi\) | |||||||
\(332\) | 81300.7 | 0.0404808 | ||||||||
\(333\) | −2.37002e6 | −1.17123 | ||||||||
\(334\) | 1.81674e6 | 0.891099 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.07306e6 | −1.96821 | ||||||||
\(337\) | −65125.6 | −0.0312376 | −0.0156188 | − | 0.999878i | \(-0.504972\pi\) | ||||
−0.0156188 | + | 0.999878i | \(0.504972\pi\) | |||||||
\(338\) | −173611. | −0.0826579 | ||||||||
\(339\) | −574579. | −0.271550 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −499939. | −0.232826 | ||||||||
\(342\) | −5.99443e6 | −2.77129 | ||||||||
\(343\) | 2.02690e6 | 0.930245 | ||||||||
\(344\) | −1.79594e6 | −0.818269 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 99625.0 | 0.0447382 | ||||||||
\(347\) | 3.63163e6 | 1.61912 | 0.809558 | − | 0.587039i | \(-0.199707\pi\) | ||||
0.809558 | + | 0.587039i | \(0.199707\pi\) | |||||||
\(348\) | 579534. | 0.256526 | ||||||||
\(349\) | 755061. | 0.331832 | 0.165916 | − | 0.986140i | \(-0.446942\pi\) | ||||
0.165916 | + | 0.986140i | \(0.446942\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 737791. | 0.319643 | ||||||||
\(352\) | 300283. | 0.129174 | ||||||||
\(353\) | 3.06050e6 | 1.30724 | 0.653620 | − | 0.756823i | \(-0.273249\pi\) | ||||
0.653620 | + | 0.756823i | \(0.273249\pi\) | |||||||
\(354\) | 1.75178e6 | 0.742972 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −176354. | −0.0737497 | ||||||||
\(357\) | 1.71356e6 | 0.711590 | ||||||||
\(358\) | −2.55629e6 | −1.05415 | ||||||||
\(359\) | 3.68034e6 | 1.50713 | 0.753567 | − | 0.657371i | \(-0.228332\pi\) | ||||
0.753567 | + | 0.657371i | \(0.228332\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.21446e6 | 1.29819 | ||||||||
\(362\) | 3.63724e6 | 1.45882 | ||||||||
\(363\) | 3.39416e6 | 1.35197 | ||||||||
\(364\) | 114841. | 0.0454300 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.27591e6 | −2.44891 | ||||||||
\(367\) | 2.22414e6 | 0.861978 | 0.430989 | − | 0.902357i | \(-0.358165\pi\) | ||||
0.430989 | + | 0.902357i | \(0.358165\pi\) | |||||||
\(368\) | 4.79880e6 | 1.84720 | ||||||||
\(369\) | −704873. | −0.269491 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.62902e6 | 1.36885 | ||||||||
\(372\) | 375035. | 0.140512 | ||||||||
\(373\) | −3.73922e6 | −1.39158 | −0.695791 | − | 0.718244i | \(-0.744946\pi\) | ||||
−0.695791 | + | 0.718244i | \(0.744946\pi\) | |||||||
\(374\) | −500509. | −0.185026 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.30099e6 | 0.474576 | ||||||||
\(377\) | 772406. | 0.279893 | ||||||||
\(378\) | −3.64353e6 | −1.31158 | ||||||||
\(379\) | 656559. | 0.234788 | 0.117394 | − | 0.993085i | \(-0.462546\pi\) | ||||
0.117394 | + | 0.993085i | \(0.462546\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.32772e6 | 0.821519 | ||||||||
\(382\) | −1.26256e6 | −0.442684 | ||||||||
\(383\) | −3.33584e6 | −1.16200 | −0.581002 | − | 0.813902i | \(-0.697339\pi\) | ||||
−0.581002 | + | 0.813902i | \(0.697339\pi\) | |||||||
\(384\) | 5.54506e6 | 1.91901 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.31456e6 | 1.13229 | ||||||||
\(387\) | −4.51521e6 | −1.53250 | ||||||||
\(388\) | 599003. | 0.201999 | ||||||||
\(389\) | 4.44083e6 | 1.48796 | 0.743978 | − | 0.668204i | \(-0.232937\pi\) | ||||
0.743978 | + | 0.668204i | \(0.232937\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.01889e6 | −0.667837 | ||||||||
\(392\) | 336181. | 0.110499 | ||||||||
\(393\) | 2.00863e6 | 0.656021 | ||||||||
\(394\) | −3.39795e6 | −1.10275 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 345836. | 0.110824 | ||||||||
\(397\) | −2.72643e6 | −0.868196 | −0.434098 | − | 0.900866i | \(-0.642933\pi\) | ||||
−0.434098 | + | 0.900866i | \(0.642933\pi\) | |||||||
\(398\) | 4.86644e6 | 1.53994 | ||||||||
\(399\) | 8.39139e6 | 2.63877 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.27026e6 | 1.63671 | 0.818353 | − | 0.574715i | \(-0.194887\pi\) | ||||
0.818353 | + | 0.574715i | \(0.194887\pi\) | |||||||
\(402\) | 1.01052e7 | 3.11875 | ||||||||
\(403\) | 499848. | 0.153312 | ||||||||
\(404\) | −163540. | −0.0498506 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.81447e6 | −1.14847 | ||||||||
\(407\) | −969056. | −0.289977 | ||||||||
\(408\) | −2.05215e6 | −0.610322 | ||||||||
\(409\) | 4.58065e6 | 1.35400 | 0.677000 | − | 0.735983i | \(-0.263280\pi\) | ||||
0.677000 | + | 0.735983i | \(0.263280\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.85054e6 | −0.832381 | ||||||||
\(412\) | 983979. | 0.285590 | ||||||||
\(413\) | −1.54443e6 | −0.445546 | ||||||||
\(414\) | 1.04145e7 | 2.98634 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −300228. | −0.0850586 | ||||||||
\(417\) | 5.79947e6 | 1.63323 | ||||||||
\(418\) | −2.45101e6 | −0.686128 | ||||||||
\(419\) | 3.94543e6 | 1.09789 | 0.548945 | − | 0.835858i | \(-0.315030\pi\) | ||||
0.548945 | + | 0.835858i | \(0.315030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.17743e6 | 1.14869 | 0.574347 | − | 0.818612i | \(-0.305256\pi\) | ||||
0.574347 | + | 0.818612i | \(0.305256\pi\) | |||||||
\(422\) | 5.90780e6 | 1.61490 | ||||||||
\(423\) | 3.27085e6 | 0.888812 | ||||||||
\(424\) | −4.34609e6 | −1.17404 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.33140e6 | −1.95732 | ||||||||
\(427\) | 5.53304e6 | 1.46857 | ||||||||
\(428\) | −907465. | −0.239453 | ||||||||
\(429\) | 731873. | 0.191996 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.66563e6 | −1.98772 | −0.993859 | − | 0.110652i | \(-0.964706\pi\) | ||||
−0.993859 | + | 0.110652i | \(0.964706\pi\) | |||||||
\(432\) | 5.05488e6 | 1.30317 | ||||||||
\(433\) | 5.49209e6 | 1.40773 | 0.703863 | − | 0.710336i | \(-0.251457\pi\) | ||||
0.703863 | + | 0.710336i | \(0.251457\pi\) | |||||||
\(434\) | −2.46847e6 | −0.629076 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −882586. | −0.222352 | ||||||||
\(437\) | −9.88658e6 | −2.47652 | ||||||||
\(438\) | −6.66107e6 | −1.65905 | ||||||||
\(439\) | −2.56331e6 | −0.634805 | −0.317403 | − | 0.948291i | \(-0.602811\pi\) | ||||
−0.317403 | + | 0.948291i | \(0.602811\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 845199. | 0.206949 | ||||||||
\(442\) | 500418. | 0.121836 | ||||||||
\(443\) | −1.41896e6 | −0.343526 | −0.171763 | − | 0.985138i | \(-0.554946\pi\) | ||||
−0.171763 | + | 0.985138i | \(0.554946\pi\) | |||||||
\(444\) | 726948. | 0.175003 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.43925e6 | −0.580657 | ||||||||
\(447\) | −1.13507e7 | −2.68691 | ||||||||
\(448\) | −3.60464e6 | −0.848528 | ||||||||
\(449\) | 3.56619e6 | 0.834813 | 0.417406 | − | 0.908720i | \(-0.362939\pi\) | ||||
0.417406 | + | 0.908720i | \(0.362939\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −288210. | −0.0667217 | ||||||||
\(452\) | 110995. | 0.0255539 | ||||||||
\(453\) | 34177.5 | 0.00782519 | ||||||||
\(454\) | −7.90593e6 | −1.80017 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00495e7 | −2.26324 | ||||||||
\(457\) | −3.71538e6 | −0.832172 | −0.416086 | − | 0.909325i | \(-0.636598\pi\) | ||||
−0.416086 | + | 0.909325i | \(0.636598\pi\) | |||||||
\(458\) | 5.25694e6 | 1.17103 | ||||||||
\(459\) | −2.12662e6 | −0.471149 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.74184e6 | 0.820035 | 0.410018 | − | 0.912078i | \(-0.365523\pi\) | ||||
0.410018 | + | 0.912078i | \(0.365523\pi\) | |||||||
\(462\) | −3.61431e6 | −0.787807 | ||||||||
\(463\) | −3.53774e6 | −0.766962 | −0.383481 | − | 0.923549i | \(-0.625275\pi\) | ||||
−0.383481 | + | 0.923549i | \(0.625275\pi\) | |||||||
\(464\) | 5.29203e6 | 1.14111 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.24748e6 | 1.54605 | ||||||||
\(467\) | −1.97789e6 | −0.419671 | −0.209836 | − | 0.977737i | \(-0.567293\pi\) | ||||
−0.209836 | + | 0.977737i | \(0.567293\pi\) | |||||||
\(468\) | −345773. | −0.0729754 | ||||||||
\(469\) | −8.90907e6 | −1.87025 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.69118e6 | 0.351267 | ||||||||
\(472\) | 1.84960e6 | 0.382139 | ||||||||
\(473\) | −1.84619e6 | −0.379422 | ||||||||
\(474\) | 1.40250e7 | 2.86720 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −331019. | −0.0669632 | ||||||||
\(477\) | −1.09266e7 | −2.19881 | ||||||||
\(478\) | 7.48014e6 | 1.49741 | ||||||||
\(479\) | −2.88196e6 | −0.573918 | −0.286959 | − | 0.957943i | \(-0.592644\pi\) | ||||
−0.286959 | + | 0.957943i | \(0.592644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 968880. | 0.190945 | ||||||||
\(482\) | −9.98746e6 | −1.95811 | ||||||||
\(483\) | −1.45789e7 | −2.84353 | ||||||||
\(484\) | −655671. | −0.127225 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.67418e6 | −0.897665 | ||||||||
\(487\) | −2.88578e6 | −0.551366 | −0.275683 | − | 0.961249i | \(-0.588904\pi\) | ||||
−0.275683 | + | 0.961249i | \(0.588904\pi\) | |||||||
\(488\) | −6.62632e6 | −1.25957 | ||||||||
\(489\) | 1.47110e6 | 0.278209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.27189e6 | 0.986876 | 0.493438 | − | 0.869781i | \(-0.335740\pi\) | ||||
0.493438 | + | 0.869781i | \(0.335740\pi\) | |||||||
\(492\) | 216204. | 0.0402671 | ||||||||
\(493\) | −2.22640e6 | −0.412558 | ||||||||
\(494\) | 2.45057e6 | 0.451803 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.42464e6 | 0.625045 | ||||||||
\(497\) | 6.46359e6 | 1.17377 | ||||||||
\(498\) | 2.55825e6 | 0.462243 | ||||||||
\(499\) | −308093. | −0.0553898 | −0.0276949 | − | 0.999616i | \(-0.508817\pi\) | ||||
−0.0276949 | + | 0.999616i | \(0.508817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.65725e6 | 1.36295 | ||||||||
\(502\) | 2.71870e6 | 0.481507 | ||||||||
\(503\) | 4.27447e6 | 0.753291 | 0.376645 | − | 0.926358i | \(-0.377078\pi\) | ||||
0.376645 | + | 0.926358i | \(0.377078\pi\) | |||||||
\(504\) | −9.33305e6 | −1.63662 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.25831e6 | 0.739368 | ||||||||
\(507\) | −731740. | −0.126426 | ||||||||
\(508\) | −449659. | −0.0773080 | ||||||||
\(509\) | −405253. | −0.0693317 | −0.0346658 | − | 0.999399i | \(-0.511037\pi\) | ||||
−0.0346658 | + | 0.999399i | \(0.511037\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.87260e6 | 0.994898 | ||||||||
\(512\) | 4.03553e6 | 0.680340 | ||||||||
\(513\) | −1.04142e7 | −1.74715 | ||||||||
\(514\) | 2.82706e6 | 0.471984 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.38494e6 | 0.228984 | ||||||||
\(517\) | 1.33739e6 | 0.220056 | ||||||||
\(518\) | −4.78475e6 | −0.783492 | ||||||||
\(519\) | 419903. | 0.0684275 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.00100e6 | −1.12997 | −0.564983 | − | 0.825102i | \(-0.691117\pi\) | ||||
−0.564983 | + | 0.825102i | \(0.691117\pi\) | |||||||
\(522\) | 1.14850e7 | 1.84482 | ||||||||
\(523\) | −7.78764e6 | −1.24495 | −0.622475 | − | 0.782640i | \(-0.713873\pi\) | ||||
−0.622475 | + | 0.782640i | \(0.713873\pi\) | |||||||
\(524\) | −388018. | −0.0617339 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.14394e7 | −1.80277 | ||||||||
\(527\) | −1.44077e6 | −0.225979 | ||||||||
\(528\) | 5.01433e6 | 0.782759 | ||||||||
\(529\) | 1.07403e7 | 1.66869 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.65010e6 | 0.715692 | ||||||||
\(532\) | −1.62102e6 | −0.248318 | ||||||||
\(533\) | 288157. | 0.0439351 | ||||||||
\(534\) | −5.54926e6 | −0.842135 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.06694e7 | 1.60409 | ||||||||
\(537\) | −1.07744e7 | −1.61234 | ||||||||
\(538\) | −240156. | −0.0357715 | ||||||||
\(539\) | 345586. | 0.0512371 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.36678e6 | 0.494562 | 0.247281 | − | 0.968944i | \(-0.420463\pi\) | ||||
0.247281 | + | 0.968944i | \(0.420463\pi\) | |||||||
\(542\) | −1.22274e7 | −1.78787 | ||||||||
\(543\) | 1.53304e7 | 2.23128 | ||||||||
\(544\) | 865383. | 0.125375 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.61365e6 | 0.518757 | ||||||||
\(547\) | 1.32125e7 | 1.88806 | 0.944030 | − | 0.329860i | \(-0.107001\pi\) | ||||
0.944030 | + | 0.329860i | \(0.107001\pi\) | |||||||
\(548\) | 550656. | 0.0783301 | ||||||||
\(549\) | −1.66594e7 | −2.35900 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.09028e7 | −1.52988 | ||||||||
\(552\) | 1.74596e7 | 2.43886 | ||||||||
\(553\) | −1.23649e7 | −1.71940 | ||||||||
\(554\) | −4.56495e6 | −0.631920 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.12032e6 | −0.153693 | ||||||||
\(557\) | 7.47598e6 | 1.02101 | 0.510505 | − | 0.859875i | \(-0.329459\pi\) | ||||
0.510505 | + | 0.859875i | \(0.329459\pi\) | |||||||
\(558\) | 7.43228e6 | 1.01050 | ||||||||
\(559\) | 1.84585e6 | 0.249843 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.10956e6 | −0.282999 | ||||||||
\(562\) | 710886. | 0.0949421 | ||||||||
\(563\) | 1.32316e7 | 1.75931 | 0.879653 | − | 0.475617i | \(-0.157775\pi\) | ||||
0.879653 | + | 0.475617i | \(0.157775\pi\) | |||||||
\(564\) | −1.00326e6 | −0.132805 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.62278e6 | 0.868959 | ||||||||
\(567\) | −1.56426e6 | −0.204339 | ||||||||
\(568\) | −7.74075e6 | −1.00673 | ||||||||
\(569\) | −9.80441e6 | −1.26952 | −0.634762 | − | 0.772708i | \(-0.718902\pi\) | ||||
−0.634762 | + | 0.772708i | \(0.718902\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.98442e6 | 0.383063 | 0.191532 | − | 0.981486i | \(-0.438655\pi\) | ||||
0.191532 | + | 0.981486i | \(0.438655\pi\) | |||||||
\(572\) | −141380. | −0.0180675 | ||||||||
\(573\) | −5.32149e6 | −0.677091 | ||||||||
\(574\) | −1.42305e6 | −0.180276 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.08532e7 | 1.36301 | ||||||||
\(577\) | −1.47218e7 | −1.84086 | −0.920429 | − | 0.390911i | \(-0.872160\pi\) | ||||
−0.920429 | + | 0.390911i | \(0.872160\pi\) | |||||||
\(578\) | 7.18831e6 | 0.894968 | ||||||||
\(579\) | 1.39704e7 | 1.73185 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.25544e6 | −0.277198 | ||||||||
\(582\) | 1.88486e7 | 2.30659 | ||||||||
\(583\) | −4.46768e6 | −0.544390 | ||||||||
\(584\) | −7.03299e6 | −0.853312 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.43102e7 | −1.72148 | ||||||||
\(587\) | −9.66987e6 | −1.15831 | −0.579156 | − | 0.815217i | \(-0.696618\pi\) | ||||
−0.579156 | + | 0.815217i | \(0.696618\pi\) | |||||||
\(588\) | −259245. | −0.0309220 | ||||||||
\(589\) | −7.05552e6 | −0.837993 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.43218e7 | −1.68666 | ||||||||
\(592\) | 6.63815e6 | 0.778472 | ||||||||
\(593\) | −1.52788e7 | −1.78424 | −0.892121 | − | 0.451797i | \(-0.850783\pi\) | ||||
−0.892121 | + | 0.451797i | \(0.850783\pi\) | |||||||
\(594\) | 4.48554e6 | 0.521614 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.19268e6 | 0.252848 | ||||||||
\(597\) | 2.05113e7 | 2.35536 | ||||||||
\(598\) | −4.25754e6 | −0.486861 | ||||||||
\(599\) | 7.95473e6 | 0.905854 | 0.452927 | − | 0.891548i | \(-0.350380\pi\) | ||||
0.452927 | + | 0.891548i | \(0.350380\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.48231e6 | 0.619123 | 0.309562 | − | 0.950879i | \(-0.399818\pi\) | ||||
0.309562 | + | 0.950879i | \(0.399818\pi\) | |||||||
\(602\) | −9.11560e6 | −1.02517 | ||||||||
\(603\) | 2.68242e7 | 3.00423 | ||||||||
\(604\) | −6602.27 | −0.000736378 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.14604e6 | −0.569235 | ||||||||
\(607\) | −1.49346e6 | −0.164521 | −0.0822605 | − | 0.996611i | \(-0.526214\pi\) | ||||
−0.0822605 | + | 0.996611i | \(0.526214\pi\) | |||||||
\(608\) | 4.23782e6 | 0.464926 | ||||||||
\(609\) | −1.60774e7 | −1.75660 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.33715e6 | −0.144903 | ||||||||
\(612\) | 996663. | 0.107565 | ||||||||
\(613\) | −9.31063e6 | −1.00076 | −0.500378 | − | 0.865807i | \(-0.666805\pi\) | ||||
−0.500378 | + | 0.865807i | \(0.666805\pi\) | |||||||
\(614\) | −8.54733e6 | −0.914976 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.81611e6 | −0.405200 | ||||||||
\(617\) | 245403. | 0.0259517 | 0.0129759 | − | 0.999916i | \(-0.495870\pi\) | ||||
0.0129759 | + | 0.999916i | \(0.495870\pi\) | |||||||
\(618\) | 3.09625e7 | 3.26110 | ||||||||
\(619\) | 2.82756e6 | 0.296610 | 0.148305 | − | 0.988942i | \(-0.452618\pi\) | ||||
0.148305 | + | 0.988942i | \(0.452618\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.80932e7 | 1.88272 | ||||||||
\(622\) | −8.91491e6 | −0.923934 | ||||||||
\(623\) | 4.89240e6 | 0.505012 | ||||||||
\(624\) | −5.01342e6 | −0.515433 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.88786e6 | 0.192546 | ||||||||
\(627\) | −1.03306e7 | −1.04944 | ||||||||
\(628\) | −326695. | −0.0330555 | ||||||||
\(629\) | −2.79272e6 | −0.281449 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.53391e7 | −1.53366 | −0.766828 | − | 0.641853i | \(-0.778166\pi\) | ||||
−0.766828 | + | 0.641853i | \(0.778166\pi\) | |||||||
\(632\) | 1.48081e7 | 1.47471 | ||||||||
\(633\) | 2.49004e7 | 2.47000 | ||||||||
\(634\) | 1.34796e7 | 1.33185 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.35148e6 | 0.328544 | ||||||||
\(637\) | −345523. | −0.0337388 | ||||||||
\(638\) | 4.69599e6 | 0.456747 | ||||||||
\(639\) | −1.94612e7 | −1.88546 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.02617e7 | 0.986444 | 0.493222 | − | 0.869904i | \(-0.335819\pi\) | ||||
0.493222 | + | 0.869904i | \(0.335819\pi\) | |||||||
\(642\) | −2.85548e7 | −2.73427 | ||||||||
\(643\) | 5.26807e6 | 0.502486 | 0.251243 | − | 0.967924i | \(-0.419161\pi\) | ||||
0.251243 | + | 0.967924i | \(0.419161\pi\) | |||||||
\(644\) | 2.81630e6 | 0.267586 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.06356e6 | −0.665951 | ||||||||
\(647\) | −2.03948e7 | −1.91540 | −0.957698 | − | 0.287775i | \(-0.907085\pi\) | ||||
−0.957698 | + | 0.287775i | \(0.907085\pi\) | |||||||
\(648\) | 1.87335e6 | 0.175259 | ||||||||
\(649\) | 1.90134e6 | 0.177194 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.04042e7 | −0.962179 | ||||||||
\(652\) | −284182. | −0.0261805 | ||||||||
\(653\) | 8.69527e6 | 0.797994 | 0.398997 | − | 0.916952i | \(-0.369358\pi\) | ||||
0.398997 | + | 0.916952i | \(0.369358\pi\) | |||||||
\(654\) | −2.77720e7 | −2.53900 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.97427e6 | 0.179121 | ||||||||
\(657\) | −1.76818e7 | −1.59813 | ||||||||
\(658\) | 6.60342e6 | 0.594571 | ||||||||
\(659\) | 1.85493e7 | 1.66385 | 0.831926 | − | 0.554886i | \(-0.187238\pi\) | ||||
0.831926 | + | 0.554886i | \(0.187238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.00321e6 | 0.0893078 | 0.0446539 | − | 0.999003i | \(-0.485782\pi\) | ||||
0.0446539 | + | 0.999003i | \(0.485782\pi\) | |||||||
\(662\) | −2.67266e6 | −0.237027 | ||||||||
\(663\) | 2.10918e6 | 0.186350 | ||||||||
\(664\) | 2.70109e6 | 0.237750 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.44063e7 | 1.25854 | ||||||||
\(667\) | 1.89421e7 | 1.64859 | ||||||||
\(668\) | −1.47920e6 | −0.128258 | ||||||||
\(669\) | −1.02811e7 | −0.888122 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.81171e6 | −0.584049 | ||||||||
\(672\) | 6.24916e6 | 0.533824 | ||||||||
\(673\) | 653810. | 0.0556434 | 0.0278217 | − | 0.999613i | \(-0.491143\pi\) | ||||
0.0278217 | + | 0.999613i | \(0.491143\pi\) | |||||||
\(674\) | 395872. | 0.0335664 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 141355. | 0.0118972 | ||||||||
\(677\) | −831237. | −0.0697033 | −0.0348516 | − | 0.999392i | \(-0.511096\pi\) | ||||
−0.0348516 | + | 0.999392i | \(0.511096\pi\) | |||||||
\(678\) | 3.49263e6 | 0.291795 | ||||||||
\(679\) | −1.66175e7 | −1.38322 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.33222e7 | −2.75338 | ||||||||
\(682\) | 3.03892e6 | 0.250184 | ||||||||
\(683\) | 4.86860e6 | 0.399349 | 0.199675 | − | 0.979862i | \(-0.436012\pi\) | ||||
0.199675 | + | 0.979862i | \(0.436012\pi\) | |||||||
\(684\) | 4.88070e6 | 0.398879 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.23207e7 | −0.999597 | ||||||||
\(687\) | 2.21572e7 | 1.79111 | ||||||||
\(688\) | 1.26466e7 | 1.01860 | ||||||||
\(689\) | 4.46686e6 | 0.358471 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.17359e6 | −0.571533 | −0.285767 | − | 0.958299i | \(-0.592248\pi\) | ||||
−0.285767 | + | 0.958299i | \(0.592248\pi\) | |||||||
\(692\) | −81115.2 | −0.00643928 | ||||||||
\(693\) | −9.59416e6 | −0.758881 | ||||||||
\(694\) | −2.20752e7 | −1.73983 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.92542e7 | 1.50661 | ||||||||
\(697\) | −830589. | −0.0647596 | ||||||||
\(698\) | −4.58970e6 | −0.356571 | ||||||||
\(699\) | 3.05470e7 | 2.36469 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.45026e6 | −0.726355 | −0.363177 | − | 0.931720i | \(-0.618308\pi\) | ||||
−0.363177 | + | 0.931720i | \(0.618308\pi\) | |||||||
\(702\) | −4.48473e6 | −0.343474 | ||||||||
\(703\) | −1.36761e7 | −1.04369 | ||||||||
\(704\) | 4.43766e6 | 0.337460 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.86035e7 | −1.40470 | ||||||||
\(707\) | 4.53691e6 | 0.341359 | ||||||||
\(708\) | −1.42631e6 | −0.106938 | ||||||||
\(709\) | −2.98225e6 | −0.222807 | −0.111404 | − | 0.993775i | \(-0.535535\pi\) | ||||
−0.111404 | + | 0.993775i | \(0.535535\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.72293e7 | 2.76192 | ||||||||
\(712\) | −5.85910e6 | −0.433143 | ||||||||
\(713\) | 1.22580e7 | 0.903019 | ||||||||
\(714\) | −1.04160e7 | −0.764640 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.08135e6 | 0.151727 | ||||||||
\(717\) | 3.15276e7 | 2.29030 | ||||||||
\(718\) | −2.23713e7 | −1.61949 | ||||||||
\(719\) | 1.65959e7 | 1.19723 | 0.598617 | − | 0.801036i | \(-0.295717\pi\) | ||||
0.598617 | + | 0.801036i | \(0.295717\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.72975e7 | −1.95562 | ||||||||
\(722\) | −1.95394e7 | −1.39498 | ||||||||
\(723\) | −4.20955e7 | −2.99495 | ||||||||
\(724\) | −2.96146e6 | −0.209971 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.06317e7 | −1.45276 | ||||||||
\(727\) | −47580.6 | −0.00333882 | −0.00166941 | − | 0.999999i | \(-0.500531\pi\) | ||||
−0.00166941 | + | 0.999999i | \(0.500531\pi\) | |||||||
\(728\) | 3.81542e6 | 0.266817 | ||||||||
\(729\) | −2.24694e7 | −1.56593 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.32051e6 | −0.368264 | ||||||||
\(732\) | 5.10988e6 | 0.352479 | ||||||||
\(733\) | −6.02222e6 | −0.413996 | −0.206998 | − | 0.978341i | \(-0.566369\pi\) | ||||
−0.206998 | + | 0.978341i | \(0.566369\pi\) | |||||||
\(734\) | −1.35196e7 | −0.926241 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.36265e6 | −0.501002 | ||||||||
\(737\) | 1.09679e7 | 0.743800 | ||||||||
\(738\) | 4.28463e6 | 0.289583 | ||||||||
\(739\) | 8.15662e6 | 0.549413 | 0.274707 | − | 0.961528i | \(-0.411419\pi\) | ||||
0.274707 | + | 0.961528i | \(0.411419\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.03287e7 | 0.691038 | ||||||||
\(742\) | −2.20593e7 | −1.47090 | ||||||||
\(743\) | −473118. | −0.0314411 | −0.0157205 | − | 0.999876i | \(-0.505004\pi\) | ||||
−0.0157205 | + | 0.999876i | \(0.505004\pi\) | |||||||
\(744\) | 1.24600e7 | 0.825249 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.27292e7 | 1.49533 | ||||||||
\(747\) | 6.79087e6 | 0.445270 | ||||||||
\(748\) | 407517. | 0.0266313 | ||||||||
\(749\) | 2.51748e7 | 1.63969 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.49506e6 | 0.355527 | 0.177764 | − | 0.984073i | \(-0.443114\pi\) | ||||
0.177764 | + | 0.984073i | \(0.443114\pi\) | |||||||
\(752\) | −9.16129e6 | −0.590761 | ||||||||
\(753\) | 1.14589e7 | 0.736470 | ||||||||
\(754\) | −4.69514e6 | −0.300760 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.96659e6 | 0.188778 | ||||||||
\(757\) | −6.82041e6 | −0.432585 | −0.216292 | − | 0.976329i | \(-0.569396\pi\) | ||||
−0.216292 | + | 0.976329i | \(0.569396\pi\) | |||||||
\(758\) | −3.99095e6 | −0.252292 | ||||||||
\(759\) | 1.79481e7 | 1.13087 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.14435e7 | 0.716304 | 0.358152 | − | 0.933663i | \(-0.383407\pi\) | ||||
0.358152 | + | 0.933663i | \(0.383407\pi\) | |||||||
\(762\) | −1.41492e7 | −0.882766 | ||||||||
\(763\) | 2.44846e7 | 1.52259 | ||||||||
\(764\) | 1.02798e6 | 0.0637167 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.02772e7 | 1.24863 | ||||||||
\(767\) | −1.90100e6 | −0.116679 | ||||||||
\(768\) | −1.21822e7 | −0.745284 | ||||||||
\(769\) | −5.05628e6 | −0.308330 | −0.154165 | − | 0.988045i | \(-0.549269\pi\) | ||||
−0.154165 | + | 0.988045i | \(0.549269\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.19156e7 | 0.721904 | ||||||||
\(772\) | −2.69874e6 | −0.162974 | ||||||||
\(773\) | −3.54919e6 | −0.213639 | −0.106820 | − | 0.994278i | \(-0.534067\pi\) | ||||
−0.106820 | + | 0.994278i | \(0.534067\pi\) | |||||||
\(774\) | 2.74461e7 | 1.64675 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.99010e7 | 1.18637 | ||||||||
\(777\) | −2.01669e7 | −1.19836 | ||||||||
\(778\) | −2.69940e7 | −1.59889 | ||||||||
\(779\) | −4.06743e6 | −0.240147 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.95731e6 | −0.466809 | ||||||||
\(782\) | 1.22720e7 | 0.717626 | ||||||||
\(783\) | 1.99529e7 | 1.16306 | ||||||||
\(784\) | −2.36731e6 | −0.137551 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.22096e7 | −0.704929 | ||||||||
\(787\) | −2.14355e7 | −1.23367 | −0.616833 | − | 0.787094i | \(-0.711585\pi\) | ||||
−0.616833 | + | 0.787094i | \(0.711585\pi\) | |||||||
\(788\) | 2.76663e6 | 0.158721 | ||||||||
\(789\) | −4.82153e7 | −2.75735 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.07921e6 | −0.174984 | ||||||||
\(792\) | 1.14899e7 | 0.650883 | ||||||||
\(793\) | 6.81047e6 | 0.384586 | ||||||||
\(794\) | 1.65728e7 | 0.932923 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.96228e6 | −0.221648 | ||||||||
\(797\) | −1.94471e7 | −1.08445 | −0.542223 | − | 0.840235i | \(-0.682417\pi\) | ||||
−0.542223 | + | 0.840235i | \(0.682417\pi\) | |||||||
\(798\) | −5.10078e7 | −2.83550 | ||||||||
\(799\) | 3.85422e6 | 0.213584 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.47305e7 | −0.811214 | ||||||||
\(802\) | −3.20357e7 | −1.75873 | ||||||||
\(803\) | −7.22975e6 | −0.395671 | ||||||||
\(804\) | −8.22772e6 | −0.448889 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.03837e6 | −0.164742 | ||||||||
\(807\) | −1.01222e6 | −0.0547129 | ||||||||
\(808\) | −5.43338e6 | −0.292780 | ||||||||
\(809\) | 1.45681e7 | 0.782585 | 0.391292 | − | 0.920266i | \(-0.372028\pi\) | ||||
0.391292 | + | 0.920266i | \(0.372028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.86252e7 | 0.994371 | 0.497185 | − | 0.867644i | \(-0.334367\pi\) | ||||
0.497185 | + | 0.867644i | \(0.334367\pi\) | |||||||
\(812\) | 3.10577e6 | 0.165302 | ||||||||
\(813\) | −5.15366e7 | −2.73457 | ||||||||
\(814\) | 5.89049e6 | 0.311595 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.44508e7 | 0.759740 | ||||||||
\(817\) | −2.60548e7 | −1.36563 | ||||||||
\(818\) | −2.78439e7 | −1.45494 | ||||||||
\(819\) | 9.59241e6 | 0.499710 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.61122e7 | 0.834252 | 0.417126 | − | 0.908849i | \(-0.363037\pi\) | ||||
0.417126 | + | 0.908849i | \(0.363037\pi\) | |||||||
\(822\) | 1.73272e7 | 0.894438 | ||||||||
\(823\) | 1.15862e7 | 0.596269 | 0.298134 | − | 0.954524i | \(-0.403636\pi\) | ||||
0.298134 | + | 0.954524i | \(0.403636\pi\) | |||||||
\(824\) | 3.26913e7 | 1.67731 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.38794e6 | 0.478762 | ||||||||
\(827\) | −8.40345e6 | −0.427262 | −0.213631 | − | 0.976914i | \(-0.568529\pi\) | ||||
−0.213631 | + | 0.976914i | \(0.568529\pi\) | |||||||
\(828\) | −8.47957e6 | −0.429831 | ||||||||
\(829\) | −4.77193e6 | −0.241161 | −0.120581 | − | 0.992704i | \(-0.538476\pi\) | ||||
−0.120581 | + | 0.992704i | \(0.538476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.92405e7 | −0.966528 | ||||||||
\(832\) | −4.43685e6 | −0.222212 | ||||||||
\(833\) | 995943. | 0.0497304 | ||||||||
\(834\) | −3.52526e7 | −1.75499 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.99563e6 | 0.0987561 | ||||||||
\(837\) | 1.29121e7 | 0.637067 | ||||||||
\(838\) | −2.39826e7 | −1.17974 | ||||||||
\(839\) | −2.32624e7 | −1.14091 | −0.570453 | − | 0.821330i | \(-0.693232\pi\) | ||||
−0.570453 | + | 0.821330i | \(0.693232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 377863. | 0.0184223 | ||||||||
\(842\) | −2.53929e7 | −1.23433 | ||||||||
\(843\) | 2.99627e6 | 0.145215 | ||||||||
\(844\) | −4.81016e6 | −0.232436 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.98822e7 | −0.955075 | ||||||||
\(847\) | 1.81896e7 | 0.871192 | ||||||||
\(848\) | 3.06041e7 | 1.46147 | ||||||||
\(849\) | 2.79140e7 | 1.32908 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.37603e7 | 1.12468 | ||||||||
\(852\) | 5.96927e6 | 0.281723 | ||||||||
\(853\) | 6.88858e6 | 0.324158 | 0.162079 | − | 0.986778i | \(-0.448180\pi\) | ||||
0.162079 | + | 0.986778i | \(0.448180\pi\) | |||||||
\(854\) | −3.36330e7 | −1.57805 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.01492e7 | −1.40634 | ||||||||
\(857\) | −782343. | −0.0363869 | −0.0181935 | − | 0.999834i | \(-0.505791\pi\) | ||||
−0.0181935 | + | 0.999834i | \(0.505791\pi\) | |||||||
\(858\) | −4.44876e6 | −0.206310 | ||||||||
\(859\) | 1.23216e7 | 0.569751 | 0.284875 | − | 0.958565i | \(-0.408048\pi\) | ||||
0.284875 | + | 0.958565i | \(0.408048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.99790e6 | −0.275735 | ||||||||
\(862\) | 4.65962e7 | 2.13591 | ||||||||
\(863\) | 7.42942e6 | 0.339569 | 0.169785 | − | 0.985481i | \(-0.445693\pi\) | ||||
0.169785 | + | 0.985481i | \(0.445693\pi\) | |||||||
\(864\) | −7.75554e6 | −0.353450 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.33842e7 | −1.51268 | ||||||||
\(867\) | 3.02976e7 | 1.36886 | ||||||||
\(868\) | 2.00984e6 | 0.0905445 | ||||||||
\(869\) | 1.52224e7 | 0.683807 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.09659e7 | −0.489779 | ||||||||
\(872\) | −2.93226e7 | −1.30591 | ||||||||
\(873\) | 5.00334e7 | 2.22190 | ||||||||
\(874\) | 6.00965e7 | 2.66116 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.42348e6 | 0.238791 | ||||||||
\(877\) | 7.95778e6 | 0.349376 | 0.174688 | − | 0.984624i | \(-0.444108\pi\) | ||||
0.174688 | + | 0.984624i | \(0.444108\pi\) | |||||||
\(878\) | 1.55813e7 | 0.682132 | ||||||||
\(879\) | −6.03151e7 | −2.63302 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.11775e7 | 1.35333 | 0.676663 | − | 0.736293i | \(-0.263426\pi\) | ||||
0.676663 | + | 0.736293i | \(0.263426\pi\) | |||||||
\(882\) | −5.13761e6 | −0.222377 | ||||||||
\(883\) | 2.20671e7 | 0.952452 | 0.476226 | − | 0.879323i | \(-0.342004\pi\) | ||||
0.476226 | + | 0.879323i | \(0.342004\pi\) | |||||||
\(884\) | −407443. | −0.0175362 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.62524e6 | 0.369137 | ||||||||
\(887\) | 1.08566e6 | 0.0463323 | 0.0231662 | − | 0.999732i | \(-0.492625\pi\) | ||||
0.0231662 | + | 0.999732i | \(0.492625\pi\) | |||||||
\(888\) | 2.41518e7 | 1.02782 | ||||||||
\(889\) | 1.24744e7 | 0.529378 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.92576e6 | 0.0812657 | ||||||||
\(892\) | 1.98605e6 | 0.0835755 | ||||||||
\(893\) | 1.88743e7 | 0.792030 | ||||||||
\(894\) | 6.89962e7 | 2.88723 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.97164e7 | 1.23659 | ||||||||
\(897\) | −1.79448e7 | −0.744660 | ||||||||
\(898\) | −2.16774e7 | −0.897050 | ||||||||
\(899\) | 1.35179e7 | 0.557842 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.28754e7 | −0.528381 | ||||||||
\(902\) | 1.75191e6 | 0.0716960 | ||||||||
\(903\) | −3.84208e7 | −1.56800 | ||||||||
\(904\) | 3.68764e6 | 0.150082 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −207751. | −0.00840857 | ||||||||
\(907\) | 3.82701e7 | 1.54469 | 0.772345 | − | 0.635203i | \(-0.219084\pi\) | ||||
0.772345 | + | 0.635203i | \(0.219084\pi\) | |||||||
\(908\) | 6.43706e6 | 0.259103 | ||||||||
\(909\) | −1.36601e7 | −0.548334 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.01079e7 | −1.60116 | −0.800579 | − | 0.599227i | \(-0.795475\pi\) | ||||
−0.800579 | + | 0.599227i | \(0.795475\pi\) | |||||||
\(912\) | 7.07660e7 | 2.81733 | ||||||||
\(913\) | 2.77666e6 | 0.110242 | ||||||||
\(914\) | 2.25843e7 | 0.894212 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.28023e6 | −0.168550 | ||||||||
\(917\) | 1.07644e7 | 0.422732 | ||||||||
\(918\) | 1.29269e7 | 0.506275 | ||||||||
\(919\) | 1.38759e6 | 0.0541967 | 0.0270984 | − | 0.999633i | \(-0.491373\pi\) | ||||
0.0270984 | + | 0.999633i | \(0.491373\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.60256e7 | −1.39947 | ||||||||
\(922\) | −2.27451e7 | −0.881171 | ||||||||
\(923\) | 7.95587e6 | 0.307385 | ||||||||
\(924\) | 2.94279e6 | 0.113391 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.15045e7 | 0.824141 | ||||||||
\(927\) | 8.21897e7 | 3.14136 | ||||||||
\(928\) | −8.11940e6 | −0.309495 | ||||||||
\(929\) | −7.82980e6 | −0.297654 | −0.148827 | − | 0.988863i | \(-0.547550\pi\) | ||||
−0.148827 | + | 0.988863i | \(0.547550\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.87717e6 | 0.184414 | ||||||||
\(932\) | −5.90094e6 | −0.222526 | ||||||||
\(933\) | −3.75749e7 | −1.41317 | ||||||||
\(934\) | 1.20228e7 | 0.450959 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.14878e7 | −0.428595 | ||||||||
\(937\) | 5.19939e7 | 1.93465 | 0.967327 | − | 0.253532i | \(-0.0815925\pi\) | ||||
0.967327 | + | 0.253532i | \(0.0815925\pi\) | |||||||
\(938\) | 5.41546e7 | 2.00968 | ||||||||
\(939\) | 7.95703e6 | 0.294501 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.54802e7 | 0.938055 | 0.469028 | − | 0.883184i | \(-0.344605\pi\) | ||||
0.469028 | + | 0.883184i | \(0.344605\pi\) | |||||||
\(942\) | −1.02800e7 | −0.377455 | ||||||||
\(943\) | 7.06662e6 | 0.258781 | ||||||||
\(944\) | −1.30244e7 | −0.475694 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.12222e7 | 0.407709 | ||||||||
\(947\) | 6.45145e6 | 0.233767 | 0.116883 | − | 0.993146i | \(-0.462710\pi\) | ||||
0.116883 | + | 0.993146i | \(0.462710\pi\) | |||||||
\(948\) | −1.14193e7 | −0.412683 | ||||||||
\(949\) | 7.22843e6 | 0.260543 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.68143e7 | 2.03707 | ||||||||
\(952\) | −1.09976e7 | −0.393284 | ||||||||
\(953\) | −2.82313e7 | −1.00693 | −0.503465 | − | 0.864016i | \(-0.667942\pi\) | ||||
−0.503465 | + | 0.864016i | \(0.667942\pi\) | |||||||
\(954\) | 6.64181e7 | 2.36274 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −6.09038e6 | −0.215526 | ||||||||
\(957\) | 1.97928e7 | 0.698599 | ||||||||
\(958\) | 1.75183e7 | 0.616705 | ||||||||
\(959\) | −1.52762e7 | −0.536377 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.98813e7 | −0.694441 | ||||||||
\(962\) | −5.88942e6 | −0.205180 | ||||||||
\(963\) | −7.57986e7 | −2.63388 | ||||||||
\(964\) | 8.13185e6 | 0.281836 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 8.86193e7 | 3.05552 | ||||||||
\(967\) | 5.33839e7 | 1.83588 | 0.917939 | − | 0.396722i | \(-0.129852\pi\) | ||||
0.917939 | + | 0.396722i | \(0.129852\pi\) | |||||||
\(968\) | −2.17837e7 | −0.747211 | ||||||||
\(969\) | −2.97717e7 | −1.01858 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.29212e7 | 1.12054 | 0.560270 | − | 0.828310i | \(-0.310697\pi\) | ||||
0.560270 | + | 0.828310i | \(0.310697\pi\) | |||||||
\(972\) | 3.80574e6 | 0.129203 | ||||||||
\(973\) | 3.10798e7 | 1.05244 | ||||||||
\(974\) | 1.75414e7 | 0.592472 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.66610e7 | 1.56794 | ||||||||
\(977\) | 4.57380e7 | 1.53300 | 0.766498 | − | 0.642247i | \(-0.221997\pi\) | ||||
0.766498 | + | 0.642247i | \(0.221997\pi\) | |||||||
\(978\) | −8.94223e6 | −0.298950 | ||||||||
\(979\) | −6.02302e6 | −0.200843 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.37205e7 | −2.44577 | ||||||||
\(982\) | −3.20457e7 | −1.06045 | ||||||||
\(983\) | 5.78671e7 | 1.91006 | 0.955031 | − | 0.296505i | \(-0.0958211\pi\) | ||||
0.955031 | + | 0.296505i | \(0.0958211\pi\) | |||||||
\(984\) | 7.18305e6 | 0.236495 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.35333e7 | 0.443315 | ||||||||
\(987\) | 2.78323e7 | 0.909404 | ||||||||
\(988\) | −1.99527e6 | −0.0650292 | ||||||||
\(989\) | 4.52667e7 | 1.47159 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.51653e7 | −1.46090 | −0.730451 | − | 0.682965i | \(-0.760690\pi\) | ||||
−0.730451 | + | 0.682965i | \(0.760690\pi\) | |||||||
\(992\) | −5.25432e6 | −0.169526 | ||||||||
\(993\) | −1.12648e7 | −0.362536 | ||||||||
\(994\) | −3.92895e7 | −1.26128 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.08294e6 | −0.0665318 | ||||||||
\(997\) | 1.89237e7 | 0.602933 | 0.301467 | − | 0.953477i | \(-0.402524\pi\) | ||||
0.301467 | + | 0.953477i | \(0.402524\pi\) | |||||||
\(998\) | 1.87277e6 | 0.0595193 | ||||||||
\(999\) | 2.50282e7 | 0.793445 |
(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 | 325.6.a.j.1.3 | ✓ | 11 | |
5.2 | odd | 4 | 325.6.b.i.274.5 | 22 | |||
5.3 | odd | 4 | 325.6.b.i.274.18 | 22 | |||
5.4 | even | 2 | 325.6.a.k.1.9 | yes | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.6.a.j.1.3 | ✓ | 11 | 1.1 | even | 1 | trivial | |
325.6.a.k.1.9 | yes | 11 | 5.4 | even | 2 | ||
325.6.b.i.274.5 | 22 | 5.2 | odd | 4 | |||
325.6.b.i.274.18 | 22 | 5.3 | odd | 4 |