Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(70.7292645375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 187x^{4} + 9570x^{2} - 135576 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-4.88952\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.88952 | −0.864353 | −0.432177 | − | 0.901789i | \(-0.642254\pi\) | ||||
−0.432177 | + | 0.901789i | \(0.642254\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.09260 | −0.252894 | ||||||||
\(5\) | −42.7504 | −0.764743 | −0.382371 | − | 0.924009i | \(-0.624892\pi\) | ||||
−0.382371 | + | 0.924009i | \(0.624892\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 196.034 | 1.08294 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 209.029 | 0.661008 | ||||||||
\(11\) | −710.878 | −1.77139 | −0.885693 | − | 0.464271i | \(-0.846316\pi\) | ||||
−0.885693 | + | 0.464271i | \(0.846316\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −885.624 | −1.45342 | −0.726709 | − | 0.686945i | \(-0.758951\pi\) | ||||
−0.726709 | + | 0.686945i | \(0.758951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −699.547 | −0.683151 | ||||||||
\(17\) | −701.317 | −0.588562 | −0.294281 | − | 0.955719i | \(-0.595080\pi\) | ||||
−0.294281 | + | 0.955719i | \(0.595080\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1255.89 | 0.798120 | 0.399060 | − | 0.916925i | \(-0.369336\pi\) | ||||
0.399060 | + | 0.916925i | \(0.369336\pi\) | |||||||
\(20\) | 345.962 | 0.193399 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3475.85 | 1.53110 | ||||||||
\(23\) | 1046.18 | 0.412371 | 0.206186 | − | 0.978513i | \(-0.433895\pi\) | ||||
0.206186 | + | 0.978513i | \(0.433895\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1297.40 | −0.415169 | ||||||||
\(26\) | 4330.27 | 1.25627 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6150.88 | −1.35813 | −0.679067 | − | 0.734077i | \(-0.737615\pi\) | ||||
−0.679067 | + | 0.734077i | \(0.737615\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2294.24 | −0.428780 | −0.214390 | − | 0.976748i | \(-0.568776\pi\) | ||||
−0.214390 | + | 0.976748i | \(0.568776\pi\) | |||||||
\(32\) | −2852.63 | −0.492459 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3429.10 | 0.508725 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 404.109 | 0.0485282 | 0.0242641 | − | 0.999706i | \(-0.492276\pi\) | ||||
0.0242641 | + | 0.999706i | \(0.492276\pi\) | |||||||
\(38\) | −6140.71 | −0.689858 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8380.51 | −0.828172 | ||||||||
\(41\) | −17891.4 | −1.66221 | −0.831103 | − | 0.556119i | \(-0.812290\pi\) | ||||
−0.831103 | + | 0.556119i | \(0.812290\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −14604.8 | −1.20455 | −0.602275 | − | 0.798289i | \(-0.705739\pi\) | ||||
−0.602275 | + | 0.798289i | \(0.705739\pi\) | |||||||
\(44\) | 5752.85 | 0.447973 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5115.34 | −0.356434 | ||||||||
\(47\) | −21137.3 | −1.39574 | −0.697870 | − | 0.716225i | \(-0.745868\pi\) | ||||
−0.697870 | + | 0.716225i | \(0.745868\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6343.67 | 0.358852 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7167.00 | 0.367560 | ||||||||
\(53\) | −107.213 | −0.00524272 | −0.00262136 | − | 0.999997i | \(-0.500834\pi\) | ||||
−0.00262136 | + | 0.999997i | \(0.500834\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 30390.3 | 1.35465 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 30074.9 | 1.17391 | ||||||||
\(59\) | −44498.8 | −1.66425 | −0.832124 | − | 0.554590i | \(-0.812875\pi\) | ||||
−0.832124 | + | 0.554590i | \(0.812875\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23212.4 | 0.798720 | 0.399360 | − | 0.916794i | \(-0.369232\pi\) | ||||
0.399360 | + | 0.916794i | \(0.369232\pi\) | |||||||
\(62\) | 11217.7 | 0.370617 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 36333.5 | 1.10881 | ||||||||
\(65\) | 37860.8 | 1.11149 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6671.32 | −0.181562 | −0.0907809 | − | 0.995871i | \(-0.528936\pi\) | ||||
−0.0907809 | + | 0.995871i | \(0.528936\pi\) | |||||||
\(68\) | 5675.48 | 0.148844 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −25110.5 | −0.591166 | −0.295583 | − | 0.955317i | \(-0.595514\pi\) | ||||
−0.295583 | + | 0.955317i | \(0.595514\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9474.97 | −0.208099 | −0.104050 | − | 0.994572i | \(-0.533180\pi\) | ||||
−0.104050 | + | 0.994572i | \(0.533180\pi\) | |||||||
\(74\) | −1975.90 | −0.0419455 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10163.4 | −0.201840 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −26476.1 | −0.477295 | −0.238647 | − | 0.971106i | \(-0.576704\pi\) | ||||
−0.238647 | + | 0.971106i | \(0.576704\pi\) | |||||||
\(80\) | 29905.9 | 0.522435 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 87480.3 | 1.43673 | ||||||||
\(83\) | −7494.03 | −0.119404 | −0.0597022 | − | 0.998216i | \(-0.519015\pi\) | ||||
−0.0597022 | + | 0.998216i | \(0.519015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29981.6 | 0.450098 | ||||||||
\(86\) | 71410.5 | 1.04116 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −139356. | −1.91831 | ||||||||
\(89\) | 32171.3 | 0.430520 | 0.215260 | − | 0.976557i | \(-0.430940\pi\) | ||||
0.215260 | + | 0.976557i | \(0.430940\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8466.35 | −0.104286 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 103351. | 1.20641 | ||||||||
\(95\) | −53689.9 | −0.610357 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 155070. | 1.67340 | 0.836699 | − | 0.547664i | \(-0.184483\pi\) | ||||
0.836699 | + | 0.547664i | \(0.184483\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 10499.4 | 0.104994 | ||||||||
\(101\) | −111922. | −1.09172 | −0.545860 | − | 0.837876i | \(-0.683797\pi\) | ||||
−0.545860 | + | 0.837876i | \(0.683797\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 60684.3 | 0.563616 | 0.281808 | − | 0.959471i | \(-0.409066\pi\) | ||||
0.281808 | + | 0.959471i | \(0.409066\pi\) | |||||||
\(104\) | −173612. | −1.57397 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 524.219 | 0.00453156 | ||||||||
\(107\) | −112533. | −0.950210 | −0.475105 | − | 0.879929i | \(-0.657590\pi\) | ||||
−0.475105 | + | 0.879929i | \(0.657590\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7623.35 | −0.0614581 | −0.0307291 | − | 0.999528i | \(-0.509783\pi\) | ||||
−0.0307291 | + | 0.999528i | \(0.509783\pi\) | |||||||
\(110\) | −148594. | −1.17090 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −41498.7 | −0.305730 | −0.152865 | − | 0.988247i | \(-0.548850\pi\) | ||||
−0.152865 | + | 0.988247i | \(0.548850\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −44724.8 | −0.315358 | ||||||||
\(116\) | 49776.6 | 0.343463 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 217578. | 1.43850 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 344297. | 2.13781 | ||||||||
\(122\) | −113497. | −0.690376 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18566.3 | 0.108436 | ||||||||
\(125\) | 189060. | 1.08224 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 94796.7 | 0.521535 | 0.260768 | − | 0.965402i | \(-0.416024\pi\) | ||||
0.260768 | + | 0.965402i | \(0.416024\pi\) | |||||||
\(128\) | −86369.2 | −0.465944 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −185121. | −0.960721 | ||||||||
\(131\) | 211095. | 1.07473 | 0.537365 | − | 0.843350i | \(-0.319420\pi\) | ||||
0.537365 | + | 0.843350i | \(0.319420\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 32619.5 | 0.156934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −137482. | −0.637379 | ||||||||
\(137\) | −96193.1 | −0.437867 | −0.218934 | − | 0.975740i | \(-0.570258\pi\) | ||||
−0.218934 | + | 0.975740i | \(0.570258\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 401994. | 1.76475 | 0.882375 | − | 0.470548i | \(-0.155944\pi\) | ||||
0.882375 | + | 0.470548i | \(0.155944\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 122778. | 0.510976 | ||||||||
\(143\) | 629570. | 2.57457 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 262953. | 1.03862 | ||||||||
\(146\) | 46328.1 | 0.179871 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3270.29 | −0.0122725 | ||||||||
\(149\) | 75300.1 | 0.277862 | 0.138931 | − | 0.990302i | \(-0.455633\pi\) | ||||
0.138931 | + | 0.990302i | \(0.455633\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −490594. | −1.75098 | −0.875488 | − | 0.483240i | \(-0.839460\pi\) | ||||
−0.875488 | + | 0.483240i | \(0.839460\pi\) | |||||||
\(152\) | 246197. | 0.864318 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 98079.6 | 0.327906 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 461015. | 1.49268 | 0.746339 | − | 0.665566i | \(-0.231810\pi\) | ||||
0.746339 | + | 0.665566i | \(0.231810\pi\) | |||||||
\(158\) | 129455. | 0.412551 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 121951. | 0.376604 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −478444. | −1.41046 | −0.705232 | − | 0.708977i | \(-0.749157\pi\) | ||||
−0.705232 | + | 0.708977i | \(0.749157\pi\) | |||||||
\(164\) | 144788. | 0.420361 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 36642.2 | 0.103208 | ||||||||
\(167\) | 498852. | 1.38414 | 0.692070 | − | 0.721830i | \(-0.256699\pi\) | ||||
0.692070 | + | 0.721830i | \(0.256699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 413036. | 1.11243 | ||||||||
\(170\) | −146596. | −0.389044 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 118191. | 0.304623 | ||||||||
\(173\) | −260643. | −0.662112 | −0.331056 | − | 0.943611i | \(-0.607405\pi\) | ||||
−0.331056 | + | 0.943611i | \(0.607405\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 497292. | 1.21012 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −157302. | −0.372121 | ||||||||
\(179\) | 533418. | 1.24433 | 0.622164 | − | 0.782887i | \(-0.286254\pi\) | ||||
0.622164 | + | 0.782887i | \(0.286254\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −185798. | −0.421546 | −0.210773 | − | 0.977535i | \(-0.567598\pi\) | ||||
−0.210773 | + | 0.977535i | \(0.567598\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 205087. | 0.446574 | ||||||||
\(185\) | −17275.8 | −0.0371115 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 498551. | 1.04257 | ||||||||
\(188\) | 171055. | 0.352974 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 262518. | 0.527564 | ||||||||
\(191\) | −708837. | −1.40593 | −0.702964 | − | 0.711226i | \(-0.748140\pi\) | ||||
−0.702964 | + | 0.711226i | \(0.748140\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −723504. | −1.39813 | −0.699065 | − | 0.715058i | \(-0.746400\pi\) | ||||
−0.699065 | + | 0.715058i | \(0.746400\pi\) | |||||||
\(194\) | −758219. | −1.44641 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −147313. | −0.270443 | −0.135222 | − | 0.990815i | \(-0.543175\pi\) | ||||
−0.135222 | + | 0.990815i | \(0.543175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1420.98 | −0.00254364 | −0.00127182 | − | 0.999999i | \(-0.500405\pi\) | ||||
−0.00127182 | + | 0.999999i | \(0.500405\pi\) | |||||||
\(200\) | −254334. | −0.449604 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 547244. | 0.943632 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 764865. | 1.27116 | ||||||||
\(206\) | −296717. | −0.487163 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 619535. | 0.992905 | ||||||||
\(209\) | −892786. | −1.41378 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −30296.2 | −0.0468470 | −0.0234235 | − | 0.999726i | \(-0.507457\pi\) | ||||
−0.0234235 | + | 0.999726i | \(0.507457\pi\) | |||||||
\(212\) | 867.630 | 0.00132585 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 550231. | 0.821317 | ||||||||
\(215\) | 624362. | 0.921171 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 37274.5 | 0.0531215 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −245937. | −0.342584 | ||||||||
\(221\) | 621103. | 0.855427 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 147864. | 0.199114 | 0.0995570 | − | 0.995032i | \(-0.468257\pi\) | ||||
0.0995570 | + | 0.995032i | \(0.468257\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 202908. | 0.264259 | ||||||||
\(227\) | 813445. | 1.04776 | 0.523882 | − | 0.851791i | \(-0.324483\pi\) | ||||
0.523882 | + | 0.851791i | \(0.324483\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.28219e6 | −1.61571 | −0.807854 | − | 0.589382i | \(-0.799371\pi\) | ||||
−0.807854 | + | 0.589382i | \(0.799371\pi\) | |||||||
\(230\) | 218683. | 0.272581 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.20578e6 | −1.47078 | ||||||||
\(233\) | 1.23570e6 | 1.49116 | 0.745578 | − | 0.666418i | \(-0.232173\pi\) | ||||
0.745578 | + | 0.666418i | \(0.232173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 903627. | 1.06738 | ||||||||
\(236\) | 360111. | 0.420878 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −874240. | −0.990001 | −0.495001 | − | 0.868893i | \(-0.664832\pi\) | ||||
−0.495001 | + | 0.868893i | \(0.664832\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 979610. | 1.08645 | 0.543226 | − | 0.839586i | \(-0.317203\pi\) | ||||
0.543226 | + | 0.839586i | \(0.317203\pi\) | |||||||
\(242\) | −1.68344e6 | −1.84782 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −187848. | −0.201991 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.11225e6 | −1.16000 | ||||||||
\(248\) | −449747. | −0.464344 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −924410. | −0.935437 | ||||||||
\(251\) | −213005. | −0.213406 | −0.106703 | − | 0.994291i | \(-0.534029\pi\) | ||||
−0.106703 | + | 0.994291i | \(0.534029\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −743709. | −0.730469 | ||||||||
\(254\) | −463510. | −0.450791 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −740367. | −0.706069 | ||||||||
\(257\) | 1.57901e6 | 1.49126 | 0.745629 | − | 0.666362i | \(-0.232149\pi\) | ||||
0.745629 | + | 0.666362i | \(0.232149\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −306392. | −0.281089 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.03215e6 | −0.928947 | ||||||||
\(263\) | −289087. | −0.257715 | −0.128857 | − | 0.991663i | \(-0.541131\pi\) | ||||
−0.128857 | + | 0.991663i | \(0.541131\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4583.39 | 0.00400933 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 53988.3 | 0.0459159 | ||||||||
\(269\) | −2.04489e6 | −1.72301 | −0.861506 | − | 0.507747i | \(-0.830479\pi\) | ||||
−0.861506 | + | 0.507747i | \(0.830479\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 605963. | 0.501213 | 0.250607 | − | 0.968089i | \(-0.419370\pi\) | ||||
0.250607 | + | 0.968089i | \(0.419370\pi\) | |||||||
\(272\) | 490604. | 0.402077 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 470338. | 0.378472 | ||||||||
\(275\) | 922295. | 0.735424 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.22275e6 | 0.957499 | 0.478750 | − | 0.877951i | \(-0.341090\pi\) | ||||
0.478750 | + | 0.877951i | \(0.341090\pi\) | |||||||
\(278\) | −1.96556e6 | −1.52537 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −639205. | −0.482919 | −0.241460 | − | 0.970411i | \(-0.577626\pi\) | ||||
−0.241460 | + | 0.970411i | \(0.577626\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −473655. | −0.351557 | −0.175779 | − | 0.984430i | \(-0.556244\pi\) | ||||
−0.175779 | + | 0.984430i | \(0.556244\pi\) | |||||||
\(284\) | 203209. | 0.149502 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.07830e6 | −2.22533 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −928011. | −0.653595 | ||||||||
\(290\) | −1.28571e6 | −0.897737 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 76677.1 | 0.0526270 | ||||||||
\(293\) | −829294. | −0.564338 | −0.282169 | − | 0.959365i | \(-0.591054\pi\) | ||||
−0.282169 | + | 0.959365i | \(0.591054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.90234e6 | 1.27272 | ||||||||
\(296\) | 79218.8 | 0.0525532 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −368181. | −0.240171 | ||||||||
\(299\) | −926525. | −0.599348 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.39877e6 | 1.51346 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −878555. | −0.545237 | ||||||||
\(305\) | −992338. | −0.610815 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.63715e6 | −0.991385 | −0.495693 | − | 0.868498i | \(-0.665086\pi\) | ||||
−0.495693 | + | 0.868498i | \(0.665086\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −479562. | −0.283427 | ||||||||
\(311\) | 607458. | 0.356135 | 0.178068 | − | 0.984018i | \(-0.443015\pi\) | ||||
0.178068 | + | 0.984018i | \(0.443015\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.57802e6 | −0.910443 | −0.455222 | − | 0.890378i | \(-0.650440\pi\) | ||||
−0.455222 | + | 0.890378i | \(0.650440\pi\) | |||||||
\(314\) | −2.25414e6 | −1.29020 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 214261. | 0.120705 | ||||||||
\(317\) | 2.18686e6 | 1.22228 | 0.611142 | − | 0.791521i | \(-0.290710\pi\) | ||||
0.611142 | + | 0.791521i | \(0.290710\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.37253e6 | 2.40578 | ||||||||
\(320\) | −1.55327e6 | −0.847954 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −880779. | −0.469743 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.14901e6 | 0.603414 | ||||||||
\(326\) | 2.33936e6 | 1.21914 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.50731e6 | −1.80007 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.76869e6 | −1.38901 | −0.694503 | − | 0.719490i | \(-0.744376\pi\) | ||||
−0.694503 | + | 0.719490i | \(0.744376\pi\) | |||||||
\(332\) | 60646.2 | 0.0301966 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.43915e6 | −1.19639 | ||||||||
\(335\) | 285202. | 0.138848 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.45187e6 | −1.17604 | −0.588021 | − | 0.808846i | \(-0.700093\pi\) | ||||
−0.588021 | + | 0.808846i | \(0.700093\pi\) | |||||||
\(338\) | −2.01955e6 | −0.961529 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −242629. | −0.113827 | ||||||||
\(341\) | 1.63092e6 | 0.759534 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −2.86303e6 | −1.30446 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.27442e6 | 0.572298 | ||||||||
\(347\) | 1.48100e6 | 0.660284 | 0.330142 | − | 0.943931i | \(-0.392903\pi\) | ||||
0.330142 | + | 0.943931i | \(0.392903\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.28643e6 | 0.565357 | 0.282678 | − | 0.959215i | \(-0.408777\pi\) | ||||
0.282678 | + | 0.959215i | \(0.408777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.02787e6 | 0.872335 | ||||||||
\(353\) | 2.25124e6 | 0.961580 | 0.480790 | − | 0.876836i | \(-0.340350\pi\) | ||||
0.480790 | + | 0.876836i | \(0.340350\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.07348e6 | 0.452090 | ||||||||
\(356\) | −260349. | −0.108876 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.60816e6 | −1.07554 | ||||||||
\(359\) | 725864. | 0.297248 | 0.148624 | − | 0.988894i | \(-0.452516\pi\) | ||||
0.148624 | + | 0.988894i | \(0.452516\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −898834. | −0.363004 | ||||||||
\(362\) | 908464. | 0.364365 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 405059. | 0.159142 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.42764e6 | −1.32840 | −0.664202 | − | 0.747553i | \(-0.731229\pi\) | ||||
−0.664202 | + | 0.747553i | \(0.731229\pi\) | |||||||
\(368\) | −731854. | −0.281712 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 84470.4 | 0.0320775 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.09304e6 | −0.406786 | −0.203393 | − | 0.979097i | \(-0.565197\pi\) | ||||
−0.203393 | + | 0.979097i | \(0.565197\pi\) | |||||||
\(374\) | −2.43767e6 | −0.901149 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.14361e6 | −1.51151 | ||||||||
\(377\) | 5.44737e6 | 1.97394 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.92579e6 | −1.04627 | −0.523137 | − | 0.852249i | \(-0.675238\pi\) | ||||
−0.523137 | + | 0.852249i | \(0.675238\pi\) | |||||||
\(380\) | 434491. | 0.154355 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.46587e6 | 1.21522 | ||||||||
\(383\) | −103933. | −0.0362038 | −0.0181019 | − | 0.999836i | \(-0.505762\pi\) | ||||
−0.0181019 | + | 0.999836i | \(0.505762\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.53759e6 | 1.20848 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.25492e6 | −0.423192 | ||||||||
\(389\) | −172931. | −0.0579428 | −0.0289714 | − | 0.999580i | \(-0.509223\pi\) | ||||
−0.0289714 | + | 0.999580i | \(0.509223\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −733707. | −0.242706 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 720291. | 0.233759 | ||||||||
\(395\) | 1.13186e6 | 0.365008 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.59965e6 | −0.827826 | −0.413913 | − | 0.910316i | \(-0.635838\pi\) | ||||
−0.413913 | + | 0.910316i | \(0.635838\pi\) | |||||||
\(398\) | 6947.91 | 0.00219860 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 907594. | 0.283623 | ||||||||
\(401\) | −3.45011e6 | −1.07145 | −0.535726 | − | 0.844392i | \(-0.679962\pi\) | ||||
−0.535726 | + | 0.844392i | \(0.679962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.03183e6 | 0.623196 | ||||||||
\(404\) | 905738. | 0.276089 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −287272. | −0.0859621 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.44275e6 | 0.426464 | 0.213232 | − | 0.977002i | \(-0.431601\pi\) | ||||
0.213232 | + | 0.977002i | \(0.431601\pi\) | |||||||
\(410\) | −3.73982e6 | −1.09873 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −491093. | −0.142535 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 320373. | 0.0913136 | ||||||||
\(416\) | 2.52635e6 | 0.715749 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.36530e6 | 1.22200 | ||||||||
\(419\) | −5.10039e6 | −1.41928 | −0.709641 | − | 0.704564i | \(-0.751143\pi\) | ||||
−0.709641 | + | 0.704564i | \(0.751143\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.08241e6 | 1.39754 | 0.698771 | − | 0.715346i | \(-0.253731\pi\) | ||||
0.698771 | + | 0.715346i | \(0.253731\pi\) | |||||||
\(422\) | 148134. | 0.0404923 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −21017.3 | −0.00567757 | ||||||||
\(425\) | 909891. | 0.244353 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 910683. | 0.240302 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.05283e6 | −0.796217 | ||||||||
\(431\) | −2.47441e6 | −0.641620 | −0.320810 | − | 0.947144i | \(-0.603955\pi\) | ||||
−0.320810 | + | 0.947144i | \(0.603955\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 331952. | 0.0850855 | 0.0425428 | − | 0.999095i | \(-0.486454\pi\) | ||||
0.0425428 | + | 0.999095i | \(0.486454\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 61692.7 | 0.0155424 | ||||||||
\(437\) | 1.31389e6 | 0.329122 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.11220e6 | 1.01839 | 0.509193 | − | 0.860652i | \(-0.329944\pi\) | ||||
0.509193 | + | 0.860652i | \(0.329944\pi\) | |||||||
\(440\) | 5.95752e6 | 1.46701 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.03690e6 | −0.739391 | ||||||||
\(443\) | −5.85348e6 | −1.41712 | −0.708558 | − | 0.705653i | \(-0.750654\pi\) | ||||
−0.708558 | + | 0.705653i | \(0.750654\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.37534e6 | −0.329237 | ||||||||
\(446\) | −722986. | −0.172105 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.86497e6 | 0.904754 | 0.452377 | − | 0.891827i | \(-0.350576\pi\) | ||||
0.452377 | + | 0.891827i | \(0.350576\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.27186e7 | 2.94441 | ||||||||
\(452\) | 335832. | 0.0773172 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.97736e6 | −0.905638 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.39046e6 | −1.20736 | −0.603678 | − | 0.797228i | \(-0.706299\pi\) | ||||
−0.603678 | + | 0.797228i | \(0.706299\pi\) | |||||||
\(458\) | 6.26928e6 | 1.39654 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 361940. | 0.0797520 | ||||||||
\(461\) | 1.17429e6 | 0.257350 | 0.128675 | − | 0.991687i | \(-0.458928\pi\) | ||||
0.128675 | + | 0.991687i | \(0.458928\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.03702e6 | 0.875203 | 0.437601 | − | 0.899169i | \(-0.355828\pi\) | ||||
0.437601 | + | 0.899169i | \(0.355828\pi\) | |||||||
\(464\) | 4.30283e6 | 0.927810 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.04198e6 | −1.28889 | ||||||||
\(467\) | 1.43710e6 | 0.304926 | 0.152463 | − | 0.988309i | \(-0.451279\pi\) | ||||
0.152463 | + | 0.988309i | \(0.451279\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.41830e6 | −0.922594 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.72325e6 | −1.80229 | ||||||||
\(473\) | 1.03822e7 | 2.13372 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.62940e6 | −0.331355 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.27461e6 | 0.855711 | ||||||||
\(479\) | −2.37217e6 | −0.472396 | −0.236198 | − | 0.971705i | \(-0.575901\pi\) | ||||
−0.236198 | + | 0.971705i | \(0.575901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −357888. | −0.0705317 | ||||||||
\(482\) | −4.78982e6 | −0.939079 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.78625e6 | −0.540639 | ||||||||
\(485\) | −6.62932e6 | −1.27972 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 669068. | 0.127834 | 0.0639172 | − | 0.997955i | \(-0.479641\pi\) | ||||
0.0639172 | + | 0.997955i | \(0.479641\pi\) | |||||||
\(488\) | 4.55040e6 | 0.864968 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.58134e6 | −1.79359 | −0.896794 | − | 0.442448i | \(-0.854110\pi\) | ||||
−0.896794 | + | 0.442448i | \(0.854110\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.31372e6 | 0.799346 | ||||||||
\(494\) | 5.43836e6 | 1.00265 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.60493e6 | 0.292921 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.17805e6 | −0.391576 | −0.195788 | − | 0.980646i | \(-0.562726\pi\) | ||||
−0.195788 | + | 0.980646i | \(0.562726\pi\) | |||||||
\(500\) | −1.52998e6 | −0.273692 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.04149e6 | 0.184458 | ||||||||
\(503\) | 5.11108e6 | 0.900726 | 0.450363 | − | 0.892846i | \(-0.351295\pi\) | ||||
0.450363 | + | 0.892846i | \(0.351295\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.78470e6 | 0.834885 | ||||||||
\(506\) | 3.63638e6 | 0.631383 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −767151. | −0.131893 | ||||||||
\(509\) | −7.08669e6 | −1.21241 | −0.606204 | − | 0.795309i | \(-0.707309\pi\) | ||||
−0.606204 | + | 0.795309i | \(0.707309\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 6.38385e6 | 1.07624 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.72061e6 | −1.28897 | ||||||||
\(515\) | −2.59428e6 | −0.431021 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.50260e7 | 2.47239 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.42198e6 | 1.20368 | ||||||||
\(521\) | 3.45387e6 | 0.557457 | 0.278729 | − | 0.960370i | \(-0.410087\pi\) | ||||
0.278729 | + | 0.960370i | \(0.410087\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 557199. | 0.0890751 | 0.0445375 | − | 0.999008i | \(-0.485819\pi\) | ||||
0.0445375 | + | 0.999008i | \(0.485819\pi\) | |||||||
\(524\) | −1.70831e6 | −0.271793 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.41350e6 | 0.222757 | ||||||||
\(527\) | 1.60899e6 | 0.252363 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.34184e6 | −0.829950 | ||||||||
\(530\) | −22410.6 | −0.00346548 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.58450e7 | 2.41588 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.81082e6 | 0.726666 | ||||||||
\(536\) | −1.30780e6 | −0.196621 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.99851e6 | 1.48929 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.78728e6 | 0.703227 | 0.351614 | − | 0.936145i | \(-0.385633\pi\) | ||||
0.351614 | + | 0.936145i | \(0.385633\pi\) | |||||||
\(542\) | −2.96287e6 | −0.433225 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00060e6 | 0.289843 | ||||||||
\(545\) | 325901. | 0.0469997 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.30360e6 | 0.329184 | 0.164592 | − | 0.986362i | \(-0.447369\pi\) | ||||
0.164592 | + | 0.986362i | \(0.447369\pi\) | |||||||
\(548\) | 778452. | 0.110734 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.50958e6 | −0.635666 | ||||||||
\(551\) | −7.72485e6 | −1.08395 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −5.97866e6 | −0.827617 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.25318e6 | −0.446294 | ||||||||
\(557\) | −1.38851e7 | −1.89631 | −0.948156 | − | 0.317805i | \(-0.897054\pi\) | ||||
−0.948156 | + | 0.317805i | \(0.897054\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.29344e7 | 1.75072 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.12541e6 | 0.417413 | ||||||||
\(563\) | −3.95924e6 | −0.526430 | −0.263215 | − | 0.964737i | \(-0.584783\pi\) | ||||
−0.263215 | + | 0.964737i | \(0.584783\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.77408e6 | 0.233805 | ||||||||
\(566\) | 2.31595e6 | 0.303870 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.92250e6 | −0.640199 | ||||||||
\(569\) | 9.51079e6 | 1.23150 | 0.615752 | − | 0.787940i | \(-0.288852\pi\) | ||||
0.615752 | + | 0.787940i | \(0.288852\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.07955e6 | −1.16540 | −0.582699 | − | 0.812688i | \(-0.698003\pi\) | ||||
−0.582699 | + | 0.812688i | \(0.698003\pi\) | |||||||
\(572\) | −5.09486e6 | −0.651092 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.35732e6 | −0.171204 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.58386e6 | 0.448138 | 0.224069 | − | 0.974573i | \(-0.428066\pi\) | ||||
0.224069 | + | 0.974573i | \(0.428066\pi\) | |||||||
\(578\) | 4.53753e6 | 0.564937 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.12797e6 | −0.262661 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 76215.2 | 0.00928689 | ||||||||
\(584\) | −1.85741e6 | −0.225360 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.05485e6 | 0.487788 | ||||||||
\(587\) | −6.14848e6 | −0.736499 | −0.368250 | − | 0.929727i | \(-0.620043\pi\) | ||||
−0.368250 | + | 0.929727i | \(0.620043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.88131e6 | −0.342218 | ||||||||
\(590\) | −9.30153e6 | −1.10008 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −282693. | −0.0331521 | ||||||||
\(593\) | 1.32996e7 | 1.55311 | 0.776554 | − | 0.630051i | \(-0.216966\pi\) | ||||
0.776554 | + | 0.630051i | \(0.216966\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −609373. | −0.0702697 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.53026e6 | 0.518048 | ||||||||
\(599\) | −4.61463e6 | −0.525497 | −0.262748 | − | 0.964864i | \(-0.584629\pi\) | ||||
−0.262748 | + | 0.964864i | \(0.584629\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.17563e6 | −0.923284 | −0.461642 | − | 0.887066i | \(-0.652740\pi\) | ||||
−0.461642 | + | 0.887066i | \(0.652740\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.97018e6 | 0.442811 | ||||||||
\(605\) | −1.47188e7 | −1.63487 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.36988e6 | 0.481391 | 0.240696 | − | 0.970601i | \(-0.422624\pi\) | ||||
0.240696 | + | 0.970601i | \(0.422624\pi\) | |||||||
\(608\) | −3.58259e6 | −0.393041 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.85205e6 | 0.527960 | ||||||||
\(611\) | 1.87197e7 | 2.02859 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.44920e6 | 0.585708 | 0.292854 | − | 0.956157i | \(-0.405395\pi\) | ||||
0.292854 | + | 0.956157i | \(0.405395\pi\) | |||||||
\(614\) | 8.00488e6 | 0.856907 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.32758e7 | −1.40394 | −0.701969 | − | 0.712208i | \(-0.747695\pi\) | ||||
−0.701969 | + | 0.712208i | \(0.747695\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.46285e6 | 0.468150 | 0.234075 | − | 0.972219i | \(-0.424794\pi\) | ||||
0.234075 | + | 0.972219i | \(0.424794\pi\) | |||||||
\(620\) | −793719. | −0.0829254 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.97018e6 | −0.307827 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.02799e6 | −0.412466 | ||||||||
\(626\) | 7.71578e6 | 0.786945 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.73081e6 | −0.377489 | ||||||||
\(629\) | −283408. | −0.0285618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.00421e6 | 0.800286 | 0.400143 | − | 0.916453i | \(-0.368960\pi\) | ||||
0.400143 | + | 0.916453i | \(0.368960\pi\) | |||||||
\(632\) | −5.19021e6 | −0.516883 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.06927e7 | −1.05649 | ||||||||
\(635\) | −4.05260e6 | −0.398840 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.13796e7 | −2.07944 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.69232e6 | 0.356327 | ||||||||
\(641\) | 3.88910e6 | 0.373855 | 0.186928 | − | 0.982374i | \(-0.440147\pi\) | ||||
0.186928 | + | 0.982374i | \(0.440147\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.77478e7 | 1.69285 | 0.846423 | − | 0.532511i | \(-0.178751\pi\) | ||||
0.846423 | + | 0.532511i | \(0.178751\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.30659e6 | 0.406024 | ||||||||
\(647\) | −8.72276e6 | −0.819206 | −0.409603 | − | 0.912264i | \(-0.634333\pi\) | ||||
−0.409603 | + | 0.912264i | \(0.634333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.16332e7 | 2.94803 | ||||||||
\(650\) | −5.61811e6 | −0.521563 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.87185e6 | 0.356697 | ||||||||
\(653\) | −1.42992e6 | −0.131228 | −0.0656141 | − | 0.997845i | \(-0.520901\pi\) | ||||
−0.0656141 | + | 0.997845i | \(0.520901\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.02440e6 | −0.821892 | ||||||||
\(656\) | 1.25159e7 | 1.13554 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.20182e6 | 0.825392 | 0.412696 | − | 0.910869i | \(-0.364587\pi\) | ||||
0.412696 | + | 0.910869i | \(0.364587\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.43513e6 | −0.127758 | −0.0638790 | − | 0.997958i | \(-0.520347\pi\) | ||||
−0.0638790 | + | 0.997958i | \(0.520347\pi\) | |||||||
\(662\) | 1.35376e7 | 1.20059 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.46908e6 | −0.129308 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.43495e6 | −0.560055 | ||||||||
\(668\) | −4.03701e6 | −0.350040 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.39450e6 | −0.120014 | ||||||||
\(671\) | −1.65012e7 | −1.41484 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.10985e7 | 1.79562 | 0.897808 | − | 0.440388i | \(-0.145159\pi\) | ||||
0.897808 | + | 0.440388i | \(0.145159\pi\) | |||||||
\(674\) | 1.19885e7 | 1.01652 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.34254e6 | −0.281326 | ||||||||
\(677\) | −2.33670e7 | −1.95944 | −0.979720 | − | 0.200372i | \(-0.935785\pi\) | ||||
−0.979720 | + | 0.200372i | \(0.935785\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 5.87740e6 | 0.487431 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.97443e6 | −0.656506 | ||||||||
\(683\) | −1.33489e7 | −1.09495 | −0.547474 | − | 0.836823i | \(-0.684411\pi\) | ||||
−0.547474 | + | 0.836823i | \(0.684411\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.11229e6 | 0.334856 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.02168e7 | 0.822890 | ||||||||
\(689\) | 94950.1 | 0.00761987 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.31469e7 | −1.04743 | −0.523717 | − | 0.851892i | \(-0.675455\pi\) | ||||
−0.523717 | + | 0.851892i | \(0.675455\pi\) | |||||||
\(692\) | 2.10928e6 | 0.167444 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.24137e6 | −0.570718 | ||||||||
\(695\) | −1.71854e7 | −1.34958 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.25475e7 | 0.978311 | ||||||||
\(698\) | −6.29002e6 | −0.488668 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.87304e6 | 0.605128 | 0.302564 | − | 0.953129i | \(-0.402157\pi\) | ||||
0.302564 | + | 0.953129i | \(0.402157\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 507517. | 0.0387313 | ||||||||
\(704\) | −2.58287e7 | −1.96413 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.10075e7 | −0.831144 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.49458e7 | −1.11661 | −0.558306 | − | 0.829635i | \(-0.688548\pi\) | ||||
−0.558306 | + | 0.829635i | \(0.688548\pi\) | |||||||
\(710\) | −5.24882e6 | −0.390765 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.30665e6 | 0.466229 | ||||||||
\(713\) | −2.40019e6 | −0.176816 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.69144e7 | −1.96888 | ||||||||
\(716\) | −4.31674e6 | −0.314683 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.54913e6 | −0.256927 | ||||||||
\(719\) | 355825. | 0.0256693 | 0.0128347 | − | 0.999918i | \(-0.495914\pi\) | ||||
0.0128347 | + | 0.999918i | \(0.495914\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 4.39487e6 | 0.313764 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.50359e6 | 0.106606 | ||||||||
\(725\) | 7.98017e6 | 0.563855 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.16451e7 | 0.817160 | 0.408580 | − | 0.912722i | \(-0.366024\pi\) | ||||
0.408580 | + | 0.912722i | \(0.366024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.98054e6 | −0.137555 | ||||||||
\(731\) | 1.02426e7 | 0.708953 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.56892e7 | −1.07855 | −0.539275 | − | 0.842130i | \(-0.681302\pi\) | ||||
−0.539275 | + | 0.842130i | \(0.681302\pi\) | |||||||
\(734\) | 1.67595e7 | 1.14821 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.98437e6 | −0.203076 | ||||||||
\(737\) | 4.74249e6 | 0.321616 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.49707e7 | 1.00839 | 0.504197 | − | 0.863589i | \(-0.331789\pi\) | ||||
0.504197 | + | 0.863589i | \(0.331789\pi\) | |||||||
\(740\) | 139806. | 0.00938528 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.51503e7 | 1.00682 | 0.503408 | − | 0.864049i | \(-0.332079\pi\) | ||||
0.503408 | + | 0.864049i | \(0.332079\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.21911e6 | −0.212493 | ||||||||
\(746\) | 5.34446e6 | 0.351606 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.03457e6 | −0.263660 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.13714e7 | 1.38272 | 0.691359 | − | 0.722512i | \(-0.257013\pi\) | ||||
0.691359 | + | 0.722512i | \(0.257013\pi\) | |||||||
\(752\) | 1.47865e7 | 0.953501 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.66350e7 | −1.70618 | ||||||||
\(755\) | 2.09731e7 | 1.33905 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.74578e7 | −1.10726 | −0.553632 | − | 0.832762i | \(-0.686758\pi\) | ||||
−0.553632 | + | 0.832762i | \(0.686758\pi\) | |||||||
\(758\) | 1.43057e7 | 0.904350 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.05250e7 | −0.660981 | ||||||||
\(761\) | 1.22517e7 | 0.766895 | 0.383448 | − | 0.923563i | \(-0.374737\pi\) | ||||
0.383448 | + | 0.923563i | \(0.374737\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 5.73633e6 | 0.355550 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 508180. | 0.0312929 | ||||||||
\(767\) | 3.94092e7 | 2.41885 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.26941e6 | −0.443285 | −0.221643 | − | 0.975128i | \(-0.571142\pi\) | ||||
−0.221643 | + | 0.975128i | \(0.571142\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.85503e6 | 0.353578 | ||||||||
\(773\) | 2.02144e6 | 0.121678 | 0.0608389 | − | 0.998148i | \(-0.480622\pi\) | ||||
0.0608389 | + | 0.998148i | \(0.480622\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.97655e6 | 0.178016 | ||||||||
\(776\) | 3.03990e7 | 1.81219 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 845550. | 0.0500830 | ||||||||
\(779\) | −2.24697e7 | −1.32664 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.78505e7 | 1.04718 | ||||||||
\(782\) | 3.58747e6 | 0.209784 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.97086e7 | −1.14151 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.21113e7 | 0.697035 | 0.348517 | − | 0.937302i | \(-0.386685\pi\) | ||||
0.348517 | + | 0.937302i | \(0.386685\pi\) | |||||||
\(788\) | 1.19215e6 | 0.0683934 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.53428e6 | −0.315495 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.05574e7 | −1.16087 | ||||||||
\(794\) | 1.27111e7 | 0.715534 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11499.4 | 0.000643270 0 | ||||||||
\(797\) | −2.45062e7 | −1.36657 | −0.683283 | − | 0.730154i | \(-0.739448\pi\) | ||||
−0.683283 | + | 0.730154i | \(0.739448\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.48239e7 | 0.821479 | ||||||||
\(800\) | 3.70100e6 | 0.204454 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.68694e7 | 0.926112 | ||||||||
\(803\) | 6.73555e6 | 0.368624 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.93468e6 | −0.538662 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.19404e7 | −1.18227 | ||||||||
\(809\) | −5.98754e6 | −0.321645 | −0.160823 | − | 0.986983i | \(-0.551415\pi\) | ||||
−0.160823 | + | 0.986983i | \(0.551415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.57094e7 | −0.838699 | −0.419350 | − | 0.907825i | \(-0.637742\pi\) | ||||
−0.419350 | + | 0.907825i | \(0.637742\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.40462e6 | 0.0743016 | ||||||||
\(815\) | 2.04537e7 | 1.07864 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.83421e7 | −0.961376 | ||||||||
\(818\) | −7.05435e6 | −0.368615 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.18974e6 | −0.321468 | ||||||||
\(821\) | −111158. | −0.00575547 | −0.00287774 | − | 0.999996i | \(-0.500916\pi\) | ||||
−0.00287774 | + | 0.999996i | \(0.500916\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.43892e6 | 0.176980 | 0.0884898 | − | 0.996077i | \(-0.471796\pi\) | ||||
0.0884898 | + | 0.996077i | \(0.471796\pi\) | |||||||
\(824\) | 1.18961e7 | 0.610363 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.87782e7 | 0.954751 | 0.477375 | − | 0.878700i | \(-0.341588\pi\) | ||||
0.477375 | + | 0.878700i | \(0.341588\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.53778e6 | −0.380940 | −0.190470 | − | 0.981693i | \(-0.561001\pi\) | ||||
−0.190470 | + | 0.981693i | \(0.561001\pi\) | |||||||
\(830\) | −1.56647e6 | −0.0789272 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.21778e7 | −1.61156 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.13261e7 | −1.05851 | ||||||||
\(836\) | 7.22496e6 | 0.357536 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.49385e7 | 1.22676 | ||||||||
\(839\) | 1.65147e7 | 0.809962 | 0.404981 | − | 0.914325i | \(-0.367278\pi\) | ||||
0.404981 | + | 0.914325i | \(0.367278\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.73222e7 | 0.844527 | ||||||||
\(842\) | −2.48506e7 | −1.20797 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 245175. | 0.0118473 | ||||||||
\(845\) | −1.76575e7 | −0.850720 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 75000.3 | 0.00358157 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.44893e6 | −0.211207 | ||||||||
\(851\) | 422772. | 0.0200116 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.36772e7 | −1.11418 | −0.557092 | − | 0.830451i | \(-0.688083\pi\) | ||||
−0.557092 | + | 0.830451i | \(0.688083\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.20602e7 | −1.02902 | ||||||||
\(857\) | −296551. | −0.0137927 | −0.00689633 | − | 0.999976i | \(-0.502195\pi\) | ||||
−0.00689633 | + | 0.999976i | \(0.502195\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.21295e7 | −0.560866 | −0.280433 | − | 0.959874i | \(-0.590478\pi\) | ||||
−0.280433 | + | 0.959874i | \(0.590478\pi\) | |||||||
\(860\) | −5.05271e6 | −0.232958 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.20987e7 | 0.554586 | ||||||||
\(863\) | −1.30180e7 | −0.595000 | −0.297500 | − | 0.954722i | \(-0.596153\pi\) | ||||
−0.297500 | + | 0.954722i | \(0.596153\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.11426e7 | 0.506345 | ||||||||
\(866\) | −1.62309e6 | −0.0735440 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.88213e7 | 0.845473 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.90828e6 | 0.263885 | ||||||||
\(872\) | −1.49443e6 | −0.0665556 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.42431e6 | −0.284478 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.08926e6 | −0.0917260 | −0.0458630 | − | 0.998948i | \(-0.514604\pi\) | ||||
−0.0458630 | + | 0.998948i | \(0.514604\pi\) | |||||||
\(878\) | −2.01067e7 | −0.880245 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.12595e7 | −0.925434 | ||||||||
\(881\) | 2.84897e6 | 0.123665 | 0.0618327 | − | 0.998087i | \(-0.480305\pi\) | ||||
0.0618327 | + | 0.998087i | \(0.480305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.75998e7 | −0.759636 | −0.379818 | − | 0.925061i | \(-0.624013\pi\) | ||||
−0.379818 | + | 0.925061i | \(0.624013\pi\) | |||||||
\(884\) | −5.02634e6 | −0.216332 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.86207e7 | 1.22489 | ||||||||
\(887\) | −2.37318e7 | −1.01279 | −0.506397 | − | 0.862300i | \(-0.669023\pi\) | ||||
−0.506397 | + | 0.862300i | \(0.669023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 6.72473e6 | 0.284577 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.19661e6 | −0.0503547 | ||||||||
\(893\) | −2.65461e7 | −1.11397 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.28038e7 | −0.951591 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.88979e7 | −0.782027 | ||||||||
\(899\) | 1.41116e7 | 0.582340 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 75190.1 | 0.00308567 | ||||||||
\(902\) | −6.21878e7 | −2.54501 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.13513e6 | −0.331088 | ||||||||
\(905\) | 7.94295e6 | 0.322374 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.47626e7 | −0.999489 | −0.499744 | − | 0.866173i | \(-0.666573\pi\) | ||||
−0.499744 | + | 0.866173i | \(0.666573\pi\) | |||||||
\(908\) | −6.58288e6 | −0.264973 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.67991e7 | −0.670639 | −0.335320 | − | 0.942104i | \(-0.608844\pi\) | ||||
−0.335320 | + | 0.942104i | \(0.608844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.32734e6 | 0.211511 | ||||||||
\(914\) | 2.63568e7 | 1.04358 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.03762e7 | 0.408602 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.41649e7 | 0.553256 | 0.276628 | − | 0.960977i | \(-0.410783\pi\) | ||||
0.276628 | + | 0.960977i | \(0.410783\pi\) | |||||||
\(920\) | −8.76756e6 | −0.341514 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.74174e6 | −0.222442 | ||||||||
\(923\) | 2.22384e7 | 0.859212 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −524292. | −0.0201474 | ||||||||
\(926\) | −1.97391e7 | −0.756484 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.75462e7 | 0.668825 | ||||||||
\(929\) | 2.95554e7 | 1.12356 | 0.561781 | − | 0.827286i | \(-0.310116\pi\) | ||||
0.561781 | + | 0.827286i | \(0.310116\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.00000e7 | −0.377104 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.02672e6 | −0.263564 | ||||||||
\(935\) | −2.13133e7 | −0.797298 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.20477e7 | −1.19247 | −0.596235 | − | 0.802810i | \(-0.703337\pi\) | ||||
−0.596235 | + | 0.802810i | \(0.703337\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.31269e6 | −0.269934 | ||||||||
\(941\) | −3.68947e7 | −1.35828 | −0.679141 | − | 0.734008i | \(-0.737647\pi\) | ||||
−0.679141 | + | 0.734008i | \(0.737647\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.87177e7 | −0.685446 | ||||||||
\(944\) | 3.11290e7 | 1.13693 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.07642e7 | −1.84429 | ||||||||
\(947\) | 1.45741e7 | 0.528087 | 0.264044 | − | 0.964511i | \(-0.414944\pi\) | ||||
0.264044 | + | 0.964511i | \(0.414944\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.39126e6 | 0.302456 | ||||||||
\(950\) | 7.96697e6 | 0.286407 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.34882e7 | −0.837757 | −0.418878 | − | 0.908042i | \(-0.637577\pi\) | ||||
−0.418878 | + | 0.908042i | \(0.637577\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.03031e7 | 1.07517 | ||||||||
\(956\) | 7.07487e6 | 0.250365 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.15988e7 | 0.408317 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.33656e7 | −0.816148 | ||||||||
\(962\) | 1.74990e6 | 0.0609643 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.92759e6 | −0.274757 | ||||||||
\(965\) | 3.09301e7 | 1.06921 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.25237e7 | −0.774593 | −0.387296 | − | 0.921955i | \(-0.626591\pi\) | ||||
−0.387296 | + | 0.921955i | \(0.626591\pi\) | |||||||
\(968\) | 6.74937e7 | 2.31513 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.24142e7 | 1.10613 | ||||||||
\(971\) | 5.31726e7 | 1.80984 | 0.904920 | − | 0.425583i | \(-0.139931\pi\) | ||||
0.904920 | + | 0.425583i | \(0.139931\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −3.27142e6 | −0.110494 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.62381e7 | −0.545646 | ||||||||
\(977\) | −2.82218e7 | −0.945905 | −0.472953 | − | 0.881088i | \(-0.656812\pi\) | ||||
−0.472953 | + | 0.881088i | \(0.656812\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.28699e7 | −0.762618 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.68482e7 | 1.55029 | ||||||||
\(983\) | 1.71614e7 | 0.566461 | 0.283230 | − | 0.959052i | \(-0.408594\pi\) | ||||
0.283230 | + | 0.959052i | \(0.408594\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.29771e6 | 0.206820 | ||||||||
\(986\) | −2.10920e7 | −0.690917 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9.00097e6 | 0.293357 | ||||||||
\(989\) | −1.52793e7 | −0.496722 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.05742e7 | 0.988941 | 0.494471 | − | 0.869194i | \(-0.335362\pi\) | ||||
0.494471 | + | 0.869194i | \(0.335362\pi\) | |||||||
\(992\) | 6.54460e6 | 0.211156 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 60747.5 | 0.00194523 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.75481e7 | −1.51494 | −0.757470 | − | 0.652870i | \(-0.773565\pi\) | ||||
−0.757470 | + | 0.652870i | \(0.773565\pi\) | |||||||
\(998\) | 1.06496e7 | 0.338460 | ||||||||
\(999\) | 0 | 0 |
(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 | 441.6.a.bd.1.3 | 6 | ||
3.2 | odd | 2 | inner | 441.6.a.bd.1.4 | 6 | ||
7.3 | odd | 6 | 63.6.e.f.37.4 | yes | 12 | ||
7.5 | odd | 6 | 63.6.e.f.46.4 | yes | 12 | ||
7.6 | odd | 2 | 441.6.a.bc.1.3 | 6 | |||
21.5 | even | 6 | 63.6.e.f.46.3 | yes | 12 | ||
21.17 | even | 6 | 63.6.e.f.37.3 | ✓ | 12 | ||
21.20 | even | 2 | 441.6.a.bc.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.6.e.f.37.3 | ✓ | 12 | 21.17 | even | 6 | ||
63.6.e.f.37.4 | yes | 12 | 7.3 | odd | 6 | ||
63.6.e.f.46.3 | yes | 12 | 21.5 | even | 6 | ||
63.6.e.f.46.4 | yes | 12 | 7.5 | odd | 6 | ||
441.6.a.bc.1.3 | 6 | 7.6 | odd | 2 | |||
441.6.a.bc.1.4 | 6 | 21.20 | even | 2 | |||
441.6.a.bd.1.3 | 6 | 1.1 | even | 1 | trivial | ||
441.6.a.bd.1.4 | 6 | 3.2 | odd | 2 | inner |