↑

Properties

Label 576.6.a.h.1.1
Level $576$
Weight $6$
Character 576.1
Self dual yes
Analytic conductor $92.381$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,6,Mod(1,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 576.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: \(92.3810802123\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 8)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 576.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-74.0000 q^{5} +24.0000 q^{7} +O(q^{10})\) \(q-74.0000 q^{5} +24.0000 q^{7} -124.000 q^{11} -478.000 q^{13} +1198.00 q^{17} +3044.00 q^{19} +184.000 q^{23} +2351.00 q^{25} -3282.00 q^{29} +5728.00 q^{31} -1776.00 q^{35} -10326.0 q^{37} +8886.00 q^{41} -9188.00 q^{43} +23664.0 q^{47} -16231.0 q^{49} +11686.0 q^{53} +9176.00 q^{55} -16876.0 q^{59} +18482.0 q^{61} +35372.0 q^{65} -15532.0 q^{67} -31960.0 q^{71} -4886.00 q^{73} -2976.00 q^{77} -44560.0 q^{79} -67364.0 q^{83} -88652.0 q^{85} -71994.0 q^{89} -11472.0 q^{91} -225256. q^{95} +48866.0 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −74.0000 −1.32375 −0.661876 − 0.749613i \(-0.730240\pi\)
−0.661876 + 0.749613i \(0.730240\pi\)
\(6\) 0 0
\(7\) 24.0000 0.185125 0.0925627 − 0.995707i \(-0.470494\pi\)
0.0925627 + 0.995707i \(0.470494\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −124.000 −0.308987 −0.154493 − 0.987994i \(-0.549375\pi\)
−0.154493 + 0.987994i \(0.549375\pi\)
\(12\) 0 0
\(13\) −478.000 −0.784458 −0.392229 − 0.919868i \(-0.628296\pi\)
−0.392229 + 0.919868i \(0.628296\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1198.00 1.00539 0.502695 − 0.864464i \(-0.332342\pi\)
0.502695 + 0.864464i \(0.332342\pi\)
\(18\) 0 0
\(19\) 3044.00 1.93446 0.967232 − 0.253894i \(-0.0817115\pi\)
0.967232 + 0.253894i \(0.0817115\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 184.000 0.0725268 0.0362634 − 0.999342i \(-0.488454\pi\)
0.0362634 + 0.999342i \(0.488454\pi\)
\(24\) 0 0
\(25\) 2351.00 0.752320
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3282.00 −0.724676 −0.362338 − 0.932047i \(-0.618021\pi\)
−0.362338 + 0.932047i \(0.618021\pi\)
\(30\) 0 0
\(31\) 5728.00 1.07053 0.535265 − 0.844684i \(-0.320212\pi\)
0.535265 + 0.844684i \(0.320212\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −1776.00 −0.245060
\(36\) 0 0
\(37\) −10326.0 −1.24002 −0.620009 − 0.784595i \(-0.712871\pi\)
−0.620009 + 0.784595i \(0.712871\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 8886.00 0.825556 0.412778 − 0.910832i \(-0.364558\pi\)
0.412778 + 0.910832i \(0.364558\pi\)
\(42\) 0 0
\(43\) −9188.00 −0.757792 −0.378896 − 0.925439i \(-0.623696\pi\)
−0.378896 + 0.925439i \(0.623696\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 23664.0 1.56258 0.781292 − 0.624165i \(-0.214561\pi\)
0.781292 + 0.624165i \(0.214561\pi\)
\(48\) 0 0
\(49\) −16231.0 −0.965729
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 11686.0 0.571447 0.285724 − 0.958312i \(-0.407766\pi\)
0.285724 + 0.958312i \(0.407766\pi\)
\(54\) 0 0
\(55\) 9176.00 0.409022
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −16876.0 −0.631160 −0.315580 − 0.948899i \(-0.602199\pi\)
−0.315580 + 0.948899i \(0.602199\pi\)
\(60\) 0 0
\(61\) 18482.0 0.635952 0.317976 − 0.948099i \(-0.396997\pi\)
0.317976 + 0.948099i \(0.396997\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 35372.0 1.03843
\(66\) 0 0
\(67\) −15532.0 −0.422708 −0.211354 − 0.977410i \(-0.567787\pi\)
−0.211354 + 0.977410i \(0.567787\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −31960.0 −0.752421 −0.376210 − 0.926534i \(-0.622773\pi\)
−0.376210 + 0.926534i \(0.622773\pi\)
\(72\) 0 0
\(73\) −4886.00 −0.107312 −0.0536558 − 0.998559i \(-0.517087\pi\)
−0.0536558 + 0.998559i \(0.517087\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2976.00 −0.0572013
\(78\) 0 0
\(79\) −44560.0 −0.803299 −0.401650 − 0.915793i \(-0.631563\pi\)
−0.401650 + 0.915793i \(0.631563\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −67364.0 −1.07333 −0.536664 − 0.843796i \(-0.680316\pi\)
−0.536664 + 0.843796i \(0.680316\pi\)
\(84\) 0 0
\(85\) −88652.0 −1.33089
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −71994.0 −0.963432 −0.481716 − 0.876327i \(-0.659986\pi\)
−0.481716 + 0.876327i \(0.659986\pi\)
\(90\) 0 0
\(91\) −11472.0 −0.145223
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −225256. −2.56075
\(96\) 0 0
\(97\) 48866.0 0.527324 0.263662 − 0.964615i \(-0.415070\pi\)
0.263662 + 0.964615i \(0.415070\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 51606.0 0.503381 0.251690 − 0.967808i \(-0.419014\pi\)
0.251690 + 0.967808i \(0.419014\pi\)
\(102\) 0 0
\(103\) −180424. −1.67572 −0.837860 − 0.545886i \(-0.816193\pi\)
−0.837860 + 0.545886i \(0.816193\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 65700.0 0.554761 0.277381 − 0.960760i \(-0.410534\pi\)
0.277381 + 0.960760i \(0.410534\pi\)
\(108\) 0 0
\(109\) 112706. 0.908617 0.454308 − 0.890844i \(-0.349886\pi\)
0.454308 + 0.890844i \(0.349886\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 23502.0 0.173145 0.0865723 − 0.996246i \(-0.472409\pi\)
0.0865723 + 0.996246i \(0.472409\pi\)
\(114\) 0 0
\(115\) −13616.0 −0.0960075
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 28752.0 0.186123
\(120\) 0 0
\(121\) −145675. −0.904527
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 57276.0 0.327867
\(126\) 0 0
\(127\) 94592.0 0.520409 0.260205 − 0.965553i \(-0.416210\pi\)
0.260205 + 0.965553i \(0.416210\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −70292.0 −0.357872 −0.178936 − 0.983861i \(-0.557265\pi\)
−0.178936 + 0.983861i \(0.557265\pi\)
\(132\) 0 0
\(133\) 73056.0 0.358119
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −277290. −1.26221 −0.631107 − 0.775696i \(-0.717399\pi\)
−0.631107 + 0.775696i \(0.717399\pi\)
\(138\) 0 0
\(139\) −130308. −0.572050 −0.286025 − 0.958222i \(-0.592334\pi\)
−0.286025 + 0.958222i \(0.592334\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 59272.0 0.242387
\(144\) 0 0
\(145\) 242868. 0.959291
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −401530. −1.48167 −0.740836 − 0.671685i \(-0.765571\pi\)
−0.740836 + 0.671685i \(0.765571\pi\)
\(150\) 0 0
\(151\) 75976.0 0.271165 0.135583 − 0.990766i \(-0.456709\pi\)
0.135583 + 0.990766i \(0.456709\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −423872. −1.41712
\(156\) 0 0
\(157\) 394322. 1.27674 0.638369 − 0.769730i \(-0.279609\pi\)
0.638369 + 0.769730i \(0.279609\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4416.00 0.0134265
\(162\) 0 0
\(163\) −11724.0 −0.0345626 −0.0172813 − 0.999851i \(-0.505501\pi\)
−0.0172813 + 0.999851i \(0.505501\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −551928. −1.53141 −0.765705 − 0.643192i \(-0.777610\pi\)
−0.765705 + 0.643192i \(0.777610\pi\)
\(168\) 0 0
\(169\) −142809. −0.384626
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 432894. 1.09968 0.549840 − 0.835270i \(-0.314689\pi\)
0.549840 + 0.835270i \(0.314689\pi\)
\(174\) 0 0
\(175\) 56424.0 0.139274
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −559620. −1.30545 −0.652726 − 0.757594i \(-0.726375\pi\)
−0.652726 + 0.757594i \(0.726375\pi\)
\(180\) 0 0
\(181\) −604710. −1.37199 −0.685995 − 0.727607i \(-0.740633\pi\)
−0.685995 + 0.727607i \(0.740633\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 764124. 1.64148
\(186\) 0 0
\(187\) −148552. −0.310652
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −409152. −0.811524 −0.405762 − 0.913979i \(-0.632994\pi\)
−0.405762 + 0.913979i \(0.632994\pi\)
\(192\) 0 0
\(193\) 540866. 1.04519 0.522596 − 0.852580i \(-0.324963\pi\)
0.522596 + 0.852580i \(0.324963\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −629898. −1.15639 −0.578195 − 0.815898i \(-0.696243\pi\)
−0.578195 + 0.815898i \(0.696243\pi\)
\(198\) 0 0
\(199\) −283048. −0.506673 −0.253336 − 0.967378i \(-0.581528\pi\)
−0.253336 + 0.967378i \(0.581528\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −78768.0 −0.134156
\(204\) 0 0
\(205\) −657564. −1.09283
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −377456. −0.597724
\(210\) 0 0
\(211\) 142756. 0.220744 0.110372 − 0.993890i \(-0.464796\pi\)
0.110372 + 0.993890i \(0.464796\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 679912. 1.00313
\(216\) 0 0
\(217\) 137472. 0.198182
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −572644. −0.788686
\(222\) 0 0
\(223\) −889696. −1.19806 −0.599031 − 0.800726i \(-0.704447\pi\)
−0.599031 + 0.800726i \(0.704447\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.14316e6 −1.47245 −0.736226 − 0.676736i \(-0.763394\pi\)
−0.736226 + 0.676736i \(0.763394\pi\)
\(228\) 0 0
\(229\) 695786. 0.876773 0.438386 − 0.898787i \(-0.355550\pi\)
0.438386 + 0.898787i \(0.355550\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 347126. 0.418887 0.209444 − 0.977821i \(-0.432835\pi\)
0.209444 + 0.977821i \(0.432835\pi\)
\(234\) 0 0
\(235\) −1.75114e6 −2.06847
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.64296e6 −1.86051 −0.930255 − 0.366912i \(-0.880415\pi\)
−0.930255 + 0.366912i \(0.880415\pi\)
\(240\) 0 0
\(241\) −1.16744e6 −1.29477 −0.647383 − 0.762165i \(-0.724137\pi\)
−0.647383 + 0.762165i \(0.724137\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.20109e6 1.27839
\(246\) 0 0
\(247\) −1.45503e6 −1.51751
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 790612. 0.792098 0.396049 − 0.918229i \(-0.370381\pi\)
0.396049 + 0.918229i \(0.370381\pi\)
\(252\) 0 0
\(253\) −22816.0 −0.0224098
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 129790. 0.122577 0.0612884 − 0.998120i \(-0.480479\pi\)
0.0612884 + 0.998120i \(0.480479\pi\)
\(258\) 0 0
\(259\) −247824. −0.229559
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 70888.0 0.0631951 0.0315975 − 0.999501i \(-0.489941\pi\)
0.0315975 + 0.999501i \(0.489941\pi\)
\(264\) 0 0
\(265\) −864764. −0.756455
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.79017e6 1.50839 0.754197 − 0.656649i \(-0.228027\pi\)
0.754197 + 0.656649i \(0.228027\pi\)
\(270\) 0 0
\(271\) 1.77362e6 1.46702 0.733511 − 0.679678i \(-0.237880\pi\)
0.733511 + 0.679678i \(0.237880\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −291524. −0.232457
\(276\) 0 0
\(277\) 275450. 0.215697 0.107848 − 0.994167i \(-0.465604\pi\)
0.107848 + 0.994167i \(0.465604\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −594170. −0.448895 −0.224448 − 0.974486i \(-0.572058\pi\)
−0.224448 + 0.974486i \(0.572058\pi\)
\(282\) 0 0
\(283\) 1.09243e6 0.810824 0.405412 − 0.914134i \(-0.367128\pi\)
0.405412 + 0.914134i \(0.367128\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 213264. 0.152831
\(288\) 0 0
\(289\) 15347.0 0.0108088
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 333654. 0.227053 0.113527 − 0.993535i \(-0.463785\pi\)
0.113527 + 0.993535i \(0.463785\pi\)
\(294\) 0 0
\(295\) 1.24882e6 0.835500
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −87952.0 −0.0568942
\(300\) 0 0
\(301\) −220512. −0.140287
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.36767e6 −0.841843
\(306\) 0 0
\(307\) 1.05997e6 0.641872 0.320936 − 0.947101i \(-0.396003\pi\)
0.320936 + 0.947101i \(0.396003\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.33649e6 −0.783545 −0.391773 − 0.920062i \(-0.628138\pi\)
−0.391773 + 0.920062i \(0.628138\pi\)
\(312\) 0 0
\(313\) 1.64419e6 0.948615 0.474308 − 0.880359i \(-0.342698\pi\)
0.474308 + 0.880359i \(0.342698\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.72370e6 −0.963414 −0.481707 − 0.876332i \(-0.659983\pi\)
−0.481707 + 0.876332i \(0.659983\pi\)
\(318\) 0 0
\(319\) 406968. 0.223915
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.64671e6 1.94489
\(324\) 0 0
\(325\) −1.12378e6 −0.590163
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 567936. 0.289274
\(330\) 0 0
\(331\) 2.74963e6 1.37944 0.689722 − 0.724074i \(-0.257733\pi\)
0.689722 + 0.724074i \(0.257733\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.14937e6 0.559561
\(336\) 0 0
\(337\) −3.41489e6 −1.63796 −0.818978 − 0.573824i \(-0.805459\pi\)
−0.818978 + 0.573824i \(0.805459\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −710272. −0.330780
\(342\) 0 0
\(343\) −792912. −0.363906
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −730764. −0.325802 −0.162901 − 0.986642i \(-0.552085\pi\)
−0.162901 + 0.986642i \(0.552085\pi\)
\(348\) 0 0
\(349\) 2.29749e6 1.00969 0.504847 − 0.863209i \(-0.331549\pi\)
0.504847 + 0.863209i \(0.331549\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.17072e6 0.500052 0.250026 − 0.968239i \(-0.419561\pi\)
0.250026 + 0.968239i \(0.419561\pi\)
\(354\) 0 0
\(355\) 2.36504e6 0.996019
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.88654e6 1.59157 0.795787 − 0.605577i \(-0.207058\pi\)
0.795787 + 0.605577i \(0.207058\pi\)
\(360\) 0 0
\(361\) 6.78984e6 2.74215
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 361564. 0.142054
\(366\) 0 0
\(367\) −933040. −0.361606 −0.180803 − 0.983519i \(-0.557870\pi\)
−0.180803 + 0.983519i \(0.557870\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 280464. 0.105789
\(372\) 0 0
\(373\) 392218. 0.145967 0.0729836 − 0.997333i \(-0.476748\pi\)
0.0729836 + 0.997333i \(0.476748\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.56880e6 0.568477
\(378\) 0 0
\(379\) −4.72930e6 −1.69122 −0.845608 − 0.533805i \(-0.820762\pi\)
−0.845608 + 0.533805i \(0.820762\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.89734e6 0.660920 0.330460 − 0.943820i \(-0.392796\pi\)
0.330460 + 0.943820i \(0.392796\pi\)
\(384\) 0 0
\(385\) 220224. 0.0757204
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.72295e6 −1.24742 −0.623711 − 0.781655i \(-0.714376\pi\)
−0.623711 + 0.781655i \(0.714376\pi\)
\(390\) 0 0
\(391\) 220432. 0.0729177
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.29744e6 1.06337
\(396\) 0 0
\(397\) −3.33808e6 −1.06297 −0.531484 − 0.847068i \(-0.678365\pi\)
−0.531484 + 0.847068i \(0.678365\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.27490e6 −1.32759 −0.663796 − 0.747913i \(-0.731056\pi\)
−0.663796 + 0.747913i \(0.731056\pi\)
\(402\) 0 0
\(403\) −2.73798e6 −0.839785
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.28042e6 0.383149
\(408\) 0 0
\(409\) −2.57319e6 −0.760613 −0.380306 − 0.924861i \(-0.624181\pi\)
−0.380306 + 0.924861i \(0.624181\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −405024. −0.116844
\(414\) 0 0
\(415\) 4.98494e6 1.42082
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.26828e6 −1.46600 −0.732999 − 0.680230i \(-0.761880\pi\)
−0.732999 + 0.680230i \(0.761880\pi\)
\(420\) 0 0
\(421\) 973354. 0.267649 0.133824 − 0.991005i \(-0.457274\pi\)
0.133824 + 0.991005i \(0.457274\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.81650e6 0.756375
\(426\) 0 0
\(427\) 443568. 0.117731
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 3.55736e6 0.922433 0.461216 − 0.887288i \(-0.347413\pi\)
0.461216 + 0.887288i \(0.347413\pi\)
\(432\) 0 0
\(433\) −1.95496e6 −0.501092 −0.250546 − 0.968105i \(-0.580610\pi\)
−0.250546 + 0.968105i \(0.580610\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 560096. 0.140300
\(438\) 0 0
\(439\) 3.29681e6 0.816455 0.408228 − 0.912880i \(-0.366147\pi\)
0.408228 + 0.912880i \(0.366147\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.05820e6 1.22458 0.612289 − 0.790634i \(-0.290249\pi\)
0.612289 + 0.790634i \(0.290249\pi\)
\(444\) 0 0
\(445\) 5.32756e6 1.27535
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.12730e6 −0.497981 −0.248990 − 0.968506i \(-0.580099\pi\)
−0.248990 + 0.968506i \(0.580099\pi\)
\(450\) 0 0
\(451\) −1.10186e6 −0.255086
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 848928. 0.192239
\(456\) 0 0
\(457\) 289130. 0.0647594 0.0323797 − 0.999476i \(-0.489691\pi\)
0.0323797 + 0.999476i \(0.489691\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.66870e6 0.584854 0.292427 − 0.956288i \(-0.405537\pi\)
0.292427 + 0.956288i \(0.405537\pi\)
\(462\) 0 0
\(463\) −7.58619e6 −1.64464 −0.822321 − 0.569024i \(-0.807321\pi\)
−0.822321 + 0.569024i \(0.807321\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.41961e6 0.301216 0.150608 − 0.988594i \(-0.451877\pi\)
0.150608 + 0.988594i \(0.451877\pi\)
\(468\) 0 0
\(469\) −372768. −0.0782540
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.13931e6 0.234148
\(474\) 0 0
\(475\) 7.15644e6 1.45534
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.88406e6 −0.375195 −0.187597 − 0.982246i \(-0.560070\pi\)
−0.187597 + 0.982246i \(0.560070\pi\)
\(480\) 0 0
\(481\) 4.93583e6 0.972741
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.61608e6 −0.698046
\(486\) 0 0
\(487\) 6.01388e6 1.14903 0.574516 − 0.818493i \(-0.305190\pi\)
0.574516 + 0.818493i \(0.305190\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.29232e6 −0.803504 −0.401752 − 0.915749i \(-0.631599\pi\)
−0.401752 + 0.915749i \(0.631599\pi\)
\(492\) 0 0
\(493\) −3.93184e6 −0.728581
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −767040. −0.139292
\(498\) 0 0
\(499\) 1.34509e6 0.241825 0.120912 − 0.992663i \(-0.461418\pi\)
0.120912 + 0.992663i \(0.461418\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 202008. 0.0355999 0.0177999 − 0.999842i \(-0.494334\pi\)
0.0177999 + 0.999842i \(0.494334\pi\)
\(504\) 0 0
\(505\) −3.81884e6 −0.666352
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9.78344e6 1.67377 0.836887 − 0.547375i \(-0.184373\pi\)
0.836887 + 0.547375i \(0.184373\pi\)
\(510\) 0 0
\(511\) −117264. −0.0198661
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.33514e7 2.21824
\(516\) 0 0
\(517\) −2.93434e6 −0.482818
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.04830e7 1.69197 0.845985 − 0.533207i \(-0.179013\pi\)
0.845985 + 0.533207i \(0.179013\pi\)
\(522\) 0 0
\(523\) 6.21017e6 0.992772 0.496386 − 0.868102i \(-0.334660\pi\)
0.496386 + 0.868102i \(0.334660\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.86214e6 1.07630
\(528\) 0 0
\(529\) −6.40249e6 −0.994740
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −4.24751e6 −0.647614
\(534\) 0 0
\(535\) −4.86180e6 −0.734366
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.01264e6 0.298397
\(540\) 0 0
\(541\) −5.08088e6 −0.746355 −0.373178 − 0.927760i \(-0.621732\pi\)
−0.373178 + 0.927760i \(0.621732\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.34024e6 −1.20278
\(546\) 0 0
\(547\) 3.34687e6 0.478267 0.239133 − 0.970987i \(-0.423137\pi\)
0.239133 + 0.970987i \(0.423137\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9.99041e6 −1.40186
\(552\) 0 0
\(553\) −1.06944e6 −0.148711
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.00377e6 0.956520 0.478260 − 0.878218i \(-0.341268\pi\)
0.478260 + 0.878218i \(0.341268\pi\)
\(558\) 0 0
\(559\) 4.39186e6 0.594456
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.29819e7 1.72610 0.863052 − 0.505116i \(-0.168550\pi\)
0.863052 + 0.505116i \(0.168550\pi\)
\(564\) 0 0
\(565\) −1.73915e6 −0.229200
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.89942e6 −0.245946 −0.122973 − 0.992410i \(-0.539243\pi\)
−0.122973 + 0.992410i \(0.539243\pi\)
\(570\) 0 0
\(571\) −1.66300e6 −0.213452 −0.106726 − 0.994288i \(-0.534037\pi\)
−0.106726 + 0.994288i \(0.534037\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 432584. 0.0545633
\(576\) 0 0
\(577\) 8.77344e6 1.09706 0.548530 − 0.836131i \(-0.315188\pi\)
0.548530 + 0.836131i \(0.315188\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.61674e6 −0.198700
\(582\) 0 0
\(583\) −1.44906e6 −0.176570
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −5.18393e6 −0.620961 −0.310480 − 0.950580i \(-0.600490\pi\)
−0.310480 + 0.950580i \(0.600490\pi\)
\(588\) 0 0
\(589\) 1.74360e7 2.07090
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −8.49858e6 −0.992452 −0.496226 − 0.868193i \(-0.665281\pi\)
−0.496226 + 0.868193i \(0.665281\pi\)
\(594\) 0 0
\(595\) −2.12765e6 −0.246381
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.12471e7 1.28078 0.640388 − 0.768051i \(-0.278773\pi\)
0.640388 + 0.768051i \(0.278773\pi\)
\(600\) 0 0
\(601\) −3.46439e6 −0.391238 −0.195619 − 0.980680i \(-0.562672\pi\)
−0.195619 + 0.980680i \(0.562672\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.07799e7 1.19737
\(606\) 0 0
\(607\) 999712. 0.110129 0.0550647 − 0.998483i \(-0.482463\pi\)
0.0550647 + 0.998483i \(0.482463\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.13114e7 −1.22578
\(612\) 0 0
\(613\) −9.81340e6 −1.05480 −0.527398 − 0.849619i \(-0.676832\pi\)
−0.527398 + 0.849619i \(0.676832\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 5.34745e6 0.565501 0.282751 − 0.959193i \(-0.408753\pi\)
0.282751 + 0.959193i \(0.408753\pi\)
\(618\) 0 0
\(619\) −6.82768e6 −0.716221 −0.358110 − 0.933679i \(-0.616579\pi\)
−0.358110 + 0.933679i \(0.616579\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −1.72786e6 −0.178356
\(624\) 0 0
\(625\) −1.15853e7 −1.18633
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.23705e7 −1.24670
\(630\) 0 0
\(631\) 3.60970e6 0.360909 0.180455 − 0.983583i \(-0.442243\pi\)
0.180455 + 0.983583i \(0.442243\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.99981e6 −0.688893
\(636\) 0 0
\(637\) 7.75842e6 0.757573
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.33853e7 1.28672 0.643361 − 0.765563i \(-0.277540\pi\)
0.643361 + 0.765563i \(0.277540\pi\)
\(642\) 0 0
\(643\) −9.91115e6 −0.945358 −0.472679 − 0.881235i \(-0.656713\pi\)
−0.472679 + 0.881235i \(0.656713\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.78359e7 −1.67508 −0.837539 − 0.546378i \(-0.816006\pi\)
−0.837539 + 0.546378i \(0.816006\pi\)
\(648\) 0 0
\(649\) 2.09262e6 0.195020
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −4.32323e6 −0.396758 −0.198379 − 0.980125i \(-0.563568\pi\)
−0.198379 + 0.980125i \(0.563568\pi\)
\(654\) 0 0
\(655\) 5.20161e6 0.473734
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.97858e7 −1.77476 −0.887382 − 0.461035i \(-0.847478\pi\)
−0.887382 + 0.461035i \(0.847478\pi\)
\(660\) 0 0
\(661\) −1.57772e7 −1.40451 −0.702255 − 0.711925i \(-0.747824\pi\)
−0.702255 + 0.711925i \(0.747824\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.40614e6 −0.474060
\(666\) 0 0
\(667\) −603888. −0.0525584
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.29177e6 −0.196501
\(672\) 0 0
\(673\) 6.78762e6 0.577670 0.288835 − 0.957379i \(-0.406732\pi\)
0.288835 + 0.957379i \(0.406732\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.49942e7 −1.25734 −0.628669 − 0.777673i \(-0.716400\pi\)
−0.628669 + 0.777673i \(0.716400\pi\)
\(678\) 0 0
\(679\) 1.17278e6 0.0976211
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.15580e7 −0.948053 −0.474026 − 0.880511i \(-0.657200\pi\)
−0.474026 + 0.880511i \(0.657200\pi\)
\(684\) 0 0
\(685\) 2.05195e7 1.67086
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.58591e6 −0.448276
\(690\) 0 0
\(691\) −220156. −0.0175402 −0.00877012 − 0.999962i \(-0.502792\pi\)
−0.00877012 + 0.999962i \(0.502792\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 9.64279e6 0.757253
\(696\) 0 0
\(697\) 1.06454e7 0.830006
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 4.78933e6 0.368111 0.184056 − 0.982916i \(-0.441077\pi\)
0.184056 + 0.982916i \(0.441077\pi\)
\(702\) 0 0
\(703\) −3.14323e7 −2.39877
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.23854e6 0.0931886
\(708\) 0 0
\(709\) −4.26892e6 −0.318935 −0.159468 − 0.987203i \(-0.550978\pi\)
−0.159468 + 0.987203i \(0.550978\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.05395e6 0.0776421
\(714\) 0 0
\(715\) −4.38613e6 −0.320860
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.61960e7 −1.16838 −0.584190 − 0.811617i \(-0.698588\pi\)
−0.584190 + 0.811617i \(0.698588\pi\)
\(720\) 0 0
\(721\) −4.33018e6 −0.310218
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.71598e6 −0.545188
\(726\) 0 0
\(727\) −6.53426e6 −0.458522 −0.229261 − 0.973365i \(-0.573631\pi\)
−0.229261 + 0.973365i \(0.573631\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.10072e7 −0.761876
\(732\) 0 0
\(733\) −1.31617e7 −0.904800 −0.452400 − 0.891815i \(-0.649432\pi\)
−0.452400 + 0.891815i \(0.649432\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.92597e6 0.130611
\(738\) 0 0
\(739\) −1.42348e7 −0.958825 −0.479412 − 0.877590i \(-0.659150\pi\)
−0.479412 + 0.877590i \(0.659150\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.15835e7 −1.43434 −0.717168 − 0.696901i \(-0.754562\pi\)
−0.717168 + 0.696901i \(0.754562\pi\)
\(744\) 0 0
\(745\) 2.97132e7 1.96137
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.57680e6 0.102700
\(750\) 0 0
\(751\) −1.86594e7 −1.20725 −0.603625 − 0.797268i \(-0.706278\pi\)
−0.603625 + 0.797268i \(0.706278\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −5.62222e6 −0.358956
\(756\) 0 0
\(757\) 2.56681e6 0.162800 0.0813999 − 0.996682i \(-0.474061\pi\)
0.0813999 + 0.996682i \(0.474061\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.59586e7 1.62487 0.812436 − 0.583051i \(-0.198141\pi\)
0.812436 + 0.583051i \(0.198141\pi\)
\(762\) 0 0
\(763\) 2.70494e6 0.168208
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.06673e6 0.495118
\(768\) 0 0
\(769\) 5.53267e6 0.337380 0.168690 − 0.985669i \(-0.446046\pi\)
0.168690 + 0.985669i \(0.446046\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8.32940e6 0.501378 0.250689 − 0.968068i \(-0.419343\pi\)
0.250689 + 0.968068i \(0.419343\pi\)
\(774\) 0 0
\(775\) 1.34665e7 0.805381
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.70490e7 1.59701
\(780\) 0 0
\(781\) 3.96304e6 0.232488
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.91798e7 −1.69009
\(786\) 0 0
\(787\) −1.36523e7 −0.785719 −0.392860 − 0.919598i \(-0.628514\pi\)
−0.392860 + 0.919598i \(0.628514\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 564048. 0.0320535
\(792\) 0 0
\(793\) −8.83440e6 −0.498877
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.54626e6 −0.476574 −0.238287 − 0.971195i \(-0.576586\pi\)
−0.238287 + 0.971195i \(0.576586\pi\)
\(798\) 0 0
\(799\) 2.83495e7 1.57101
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 605864. 0.0331578
\(804\) 0 0
\(805\) −326784. −0.0177734
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −7.58484e6 −0.407451 −0.203725 − 0.979028i \(-0.565305\pi\)
−0.203725 + 0.979028i \(0.565305\pi\)
\(810\) 0 0
\(811\) 6.18473e6 0.330194 0.165097 − 0.986277i \(-0.447206\pi\)
0.165097 + 0.986277i \(0.447206\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 867576. 0.0457524
\(816\) 0 0
\(817\) −2.79683e7 −1.46592
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.78102e6 −0.143995 −0.0719973 − 0.997405i \(-0.522937\pi\)
−0.0719973 + 0.997405i \(0.522937\pi\)
\(822\) 0 0
\(823\) −1.63895e7 −0.843461 −0.421731 − 0.906721i \(-0.638577\pi\)
−0.421731 + 0.906721i \(0.638577\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.29511e7 −1.16692 −0.583459 − 0.812142i \(-0.698301\pi\)
−0.583459 + 0.812142i \(0.698301\pi\)
\(828\) 0 0
\(829\) 3.50136e6 0.176950 0.0884750 − 0.996078i \(-0.471801\pi\)
0.0884750 + 0.996078i \(0.471801\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.94447e7 −0.970934
\(834\) 0 0
\(835\) 4.08427e7 2.02721
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 5.29668e6 0.259776 0.129888 − 0.991529i \(-0.458538\pi\)
0.129888 + 0.991529i \(0.458538\pi\)
\(840\) 0 0
\(841\) −9.73962e6 −0.474845
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.05679e7 0.509150
\(846\) 0 0
\(847\) −3.49620e6 −0.167451
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.89998e6 −0.0899344
\(852\) 0 0
\(853\) 2.02948e7 0.955021 0.477511 − 0.878626i \(-0.341539\pi\)
0.477511 + 0.878626i \(0.341539\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 4.82785e6 0.224544 0.112272 − 0.993678i \(-0.464187\pi\)
0.112272 + 0.993678i \(0.464187\pi\)
\(858\) 0 0
\(859\) −1.30210e7 −0.602092 −0.301046 − 0.953610i \(-0.597336\pi\)
−0.301046 + 0.953610i \(0.597336\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −3.92387e7 −1.79344 −0.896721 − 0.442596i \(-0.854058\pi\)
−0.896721 + 0.442596i \(0.854058\pi\)
\(864\) 0 0
\(865\) −3.20342e7 −1.45570
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5.52544e6 0.248209
\(870\) 0 0
\(871\) 7.42430e6 0.331596
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.37462e6 0.0606965
\(876\) 0 0
\(877\) −1.34622e7 −0.591041 −0.295520 − 0.955336i \(-0.595493\pi\)
−0.295520 + 0.955336i \(0.595493\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 917710. 0.0398351 0.0199175 − 0.999802i \(-0.493660\pi\)
0.0199175 + 0.999802i \(0.493660\pi\)
\(882\) 0 0
\(883\) 2.45488e7 1.05957 0.529784 − 0.848133i \(-0.322273\pi\)
0.529784 + 0.848133i \(0.322273\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.61463e7 −0.689070 −0.344535 − 0.938773i \(-0.611963\pi\)
−0.344535 + 0.938773i \(0.611963\pi\)
\(888\) 0 0
\(889\) 2.27021e6 0.0963410
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 7.20332e7 3.02276
\(894\) 0 0
\(895\) 4.14119e7 1.72809
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −1.87993e7 −0.775787
\(900\) 0 0
\(901\) 1.39998e7 0.574527
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 4.47485e7 1.81617
\(906\) 0 0
\(907\) −2.03361e7 −0.820824 −0.410412 − 0.911900i \(-0.634615\pi\)
−0.410412 + 0.911900i \(0.634615\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.07726e7 0.430054 0.215027 − 0.976608i \(-0.431016\pi\)
0.215027 + 0.976608i \(0.431016\pi\)
\(912\) 0 0
\(913\) 8.35314e6 0.331644
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.68701e6 −0.0662512
\(918\) 0 0
\(919\) −4.18566e7 −1.63484 −0.817419 − 0.576043i \(-0.804596\pi\)
−0.817419 + 0.576043i \(0.804596\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.52769e7 0.590242
\(924\) 0 0
\(925\) −2.42764e7 −0.932890
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.99845e7 −1.13988 −0.569939 − 0.821687i \(-0.693033\pi\)
−0.569939 + 0.821687i \(0.693033\pi\)
\(930\) 0 0
\(931\) −4.94072e7 −1.86817
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.09928e7 0.411227
\(936\) 0 0
\(937\) 1.42402e7 0.529867 0.264934 − 0.964267i \(-0.414650\pi\)
0.264934 + 0.964267i \(0.414650\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −4.14546e7 −1.52615 −0.763077 − 0.646307i \(-0.776313\pi\)
−0.763077 + 0.646307i \(0.776313\pi\)
\(942\) 0 0
\(943\) 1.63502e6 0.0598749
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 1.54079e7 0.558300 0.279150 − 0.960248i \(-0.409947\pi\)
0.279150 + 0.960248i \(0.409947\pi\)
\(948\) 0 0
\(949\) 2.33551e6 0.0841813
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.06328e7 0.735912 0.367956 − 0.929843i \(-0.380058\pi\)
0.367956 + 0.929843i \(0.380058\pi\)
\(954\) 0 0
\(955\) 3.02772e7 1.07426
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6.65496e6 −0.233668
\(960\) 0 0
\(961\) 4.18083e6 0.146034
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −4.00241e7 −1.38358
\(966\) 0 0
\(967\) −1.18724e7 −0.408294 −0.204147 − 0.978940i \(-0.565442\pi\)
−0.204147 + 0.978940i \(0.565442\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.53222e6 −0.0521523 −0.0260761 − 0.999660i \(-0.508301\pi\)
−0.0260761 + 0.999660i \(0.508301\pi\)
\(972\) 0 0
\(973\) −3.12739e6 −0.105901
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −1.74321e7 −0.584269 −0.292135 − 0.956377i \(-0.594365\pi\)
−0.292135 + 0.956377i \(0.594365\pi\)
\(978\) 0 0
\(979\) 8.92726e6 0.297688
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.23270e6 0.0736963 0.0368482 − 0.999321i \(-0.488268\pi\)
0.0368482 + 0.999321i \(0.488268\pi\)
\(984\) 0 0
\(985\) 4.66125e7 1.53078
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.69059e6 −0.0549602
\(990\) 0 0
\(991\) −2.22501e7 −0.719693 −0.359847 − 0.933011i \(-0.617171\pi\)
−0.359847 + 0.933011i \(0.617171\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2.09456e7 0.670709
\(996\) 0 0
\(997\) −5.32662e7 −1.69712 −0.848562 − 0.529095i \(-0.822531\pi\)
−0.848562 + 0.529095i \(0.822531\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 576.6.a.h.1.1 1
3.2 odd 2 64.6.a.g.1.1 1
4.3 odd 2 576.6.a.g.1.1 1
8.3 odd 2 72.6.a.f.1.1 1
8.5 even 2 144.6.a.k.1.1 1
12.11 even 2 64.6.a.a.1.1 1
24.5 odd 2 16.6.a.a.1.1 1
24.11 even 2 8.6.a.a.1.1 ✓ 1
48.5 odd 4 256.6.b.d.129.1 2
48.11 even 4 256.6.b.f.129.2 2
48.29 odd 4 256.6.b.d.129.2 2
48.35 even 4 256.6.b.f.129.1 2
120.29 odd 2 400.6.a.l.1.1 1
120.53 even 4 400.6.c.d.49.1 2
120.59 even 2 200.6.a.a.1.1 1
120.77 even 4 400.6.c.d.49.2 2
120.83 odd 4 200.6.c.a.49.2 2
120.107 odd 4 200.6.c.a.49.1 2
168.11 even 6 392.6.i.b.177.1 2
168.59 odd 6 392.6.i.e.177.1 2
168.83 odd 2 392.6.a.b.1.1 1
168.107 even 6 392.6.i.b.361.1 2
168.125 even 2 784.6.a.l.1.1 1
168.131 odd 6 392.6.i.e.361.1 2
264.131 odd 2 968.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8.6.a.a.1.1 ✓ 1 24.11 even 2
16.6.a.a.1.1 1 24.5 odd 2
64.6.a.a.1.1 1 12.11 even 2
64.6.a.g.1.1 1 3.2 odd 2
72.6.a.f.1.1 1 8.3 odd 2
144.6.a.k.1.1 1 8.5 even 2
200.6.a.a.1.1 1 120.59 even 2
200.6.c.a.49.1 2 120.107 odd 4
200.6.c.a.49.2 2 120.83 odd 4
256.6.b.d.129.1 2 48.5 odd 4
256.6.b.d.129.2 2 48.29 odd 4
256.6.b.f.129.1 2 48.35 even 4
256.6.b.f.129.2 2 48.11 even 4
392.6.a.b.1.1 1 168.83 odd 2
392.6.i.b.177.1 2 168.11 even 6
392.6.i.b.361.1 2 168.107 even 6
392.6.i.e.177.1 2 168.59 odd 6
392.6.i.e.361.1 2 168.131 odd 6
400.6.a.l.1.1 1 120.29 odd 2
400.6.c.d.49.1 2 120.53 even 4
400.6.c.d.49.2 2 120.77 even 4
576.6.a.g.1.1 1 4.3 odd 2
576.6.a.h.1.1 1 1.1 even 1 trivial
784.6.a.l.1.1 1 168.125 even 2
968.6.a.a.1.1 1 264.131 odd 2