Properties

Label 1008.6.a.bo.1.2
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $2$
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] = [1008,6,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("1008.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1008.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: \(161.666890371\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{5569}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1392 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 84)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(37.8129\) of defining polynomial
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+77.6257 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q+77.6257 q^{5} +49.0000 q^{7} +477.380 q^{11} -63.7544 q^{13} -1037.63 q^{17} +667.018 q^{19} +3251.63 q^{23} +2900.75 q^{25} -2300.97 q^{29} -3717.05 q^{31} +3803.66 q^{35} +12245.9 q^{37} +1829.65 q^{41} +20794.2 q^{43} -4283.37 q^{47} +2401.00 q^{49} -25718.4 q^{53} +37057.0 q^{55} -2838.71 q^{59} +16803.2 q^{61} -4948.98 q^{65} +62535.1 q^{67} +72301.0 q^{71} -55676.9 q^{73} +23391.6 q^{77} +3989.19 q^{79} -46092.2 q^{83} -80546.5 q^{85} -135385. q^{89} -3123.97 q^{91} +51777.7 q^{95} +142878. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 6 q^{5} + 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 6 q^{5} + 98 q^{7} - 90 q^{11} + 768 q^{13} - 1926 q^{17} - 2248 q^{19} + 6354 q^{23} + 4906 q^{25} - 10572 q^{29} + 3312 q^{31} + 294 q^{35} + 2104 q^{37} - 1266 q^{41} + 5768 q^{43} + 15612 q^{47} + 4802 q^{49} - 16512 q^{53} + 77696 q^{55} - 13140 q^{59} - 5796 q^{61} - 64524 q^{65} + 56116 q^{67} + 11022 q^{71} - 85384 q^{73} - 4410 q^{77} + 19620 q^{79} - 44424 q^{83} - 16916 q^{85} - 211218 q^{89} + 37632 q^{91} + 260568 q^{95} + 44864 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) 77.6257 1.38861 0.694306 0.719680i \(-0.255712\pi\)
0.694306 + 0.719680i \(0.255712\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 477.380 1.18955 0.594775 0.803892i \(-0.297241\pi\)
0.594775 + 0.803892i \(0.297241\pi\)
\(12\) 0 0
\(13\) −63.7544 −0.104629 −0.0523145 0.998631i \(-0.516660\pi\)
−0.0523145 + 0.998631i \(0.516660\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1037.63 −0.870800 −0.435400 0.900237i \(-0.643393\pi\)
−0.435400 + 0.900237i \(0.643393\pi\)
\(18\) 0 0
\(19\) 667.018 0.423890 0.211945 0.977282i \(-0.432020\pi\)
0.211945 + 0.977282i \(0.432020\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3251.63 1.28168 0.640842 0.767673i \(-0.278585\pi\)
0.640842 + 0.767673i \(0.278585\pi\)
\(24\) 0 0
\(25\) 2900.75 0.928241
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2300.97 −0.508061 −0.254031 0.967196i \(-0.581756\pi\)
−0.254031 + 0.967196i \(0.581756\pi\)
\(30\) 0 0
\(31\) −3717.05 −0.694696 −0.347348 0.937736i \(-0.612918\pi\)
−0.347348 + 0.937736i \(0.612918\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3803.66 0.524846
\(36\) 0 0
\(37\) 12245.9 1.47057 0.735284 0.677759i \(-0.237049\pi\)
0.735284 + 0.677759i \(0.237049\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1829.65 0.169984 0.0849920 0.996382i \(-0.472914\pi\)
0.0849920 + 0.996382i \(0.472914\pi\)
\(42\) 0 0
\(43\) 20794.2 1.71503 0.857513 0.514463i \(-0.172009\pi\)
0.857513 + 0.514463i \(0.172009\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4283.37 −0.282840 −0.141420 0.989950i \(-0.545167\pi\)
−0.141420 + 0.989950i \(0.545167\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −25718.4 −1.25764 −0.628818 0.777553i \(-0.716461\pi\)
−0.628818 + 0.777553i \(0.716461\pi\)
\(54\) 0 0
\(55\) 37057.0 1.65182
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −2838.71 −0.106167 −0.0530837 0.998590i \(-0.516905\pi\)
−0.0530837 + 0.998590i \(0.516905\pi\)
\(60\) 0 0
\(61\) 16803.2 0.578186 0.289093 0.957301i \(-0.406646\pi\)
0.289093 + 0.957301i \(0.406646\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4948.98 −0.145289
\(66\) 0 0
\(67\) 62535.1 1.70191 0.850955 0.525238i \(-0.176024\pi\)
0.850955 + 0.525238i \(0.176024\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 72301.0 1.70215 0.851077 0.525042i \(-0.175950\pi\)
0.851077 + 0.525042i \(0.175950\pi\)
\(72\) 0 0
\(73\) −55676.9 −1.22283 −0.611417 0.791308i \(-0.709400\pi\)
−0.611417 + 0.791308i \(0.709400\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 23391.6 0.449608
\(78\) 0 0
\(79\) 3989.19 0.0719146 0.0359573 0.999353i \(-0.488552\pi\)
0.0359573 + 0.999353i \(0.488552\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −46092.2 −0.734400 −0.367200 0.930142i \(-0.619684\pi\)
−0.367200 + 0.930142i \(0.619684\pi\)
\(84\) 0 0
\(85\) −80546.5 −1.20920
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −135385. −1.81173 −0.905867 0.423562i \(-0.860780\pi\)
−0.905867 + 0.423562i \(0.860780\pi\)
\(90\) 0 0
\(91\) −3123.97 −0.0395460
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 51777.7 0.588619
\(96\) 0 0
\(97\) 142878. 1.54183 0.770914 0.636939i \(-0.219800\pi\)
0.770914 + 0.636939i \(0.219800\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −44467.1 −0.433746 −0.216873 0.976200i \(-0.569586\pi\)
−0.216873 + 0.976200i \(0.569586\pi\)
\(102\) 0 0
\(103\) −202619. −1.88186 −0.940931 0.338598i \(-0.890047\pi\)
−0.940931 + 0.338598i \(0.890047\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 99525.9 0.840382 0.420191 0.907436i \(-0.361963\pi\)
0.420191 + 0.907436i \(0.361963\pi\)
\(108\) 0 0
\(109\) 220930. 1.78110 0.890551 0.454883i \(-0.150319\pi\)
0.890551 + 0.454883i \(0.150319\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −29623.1 −0.218240 −0.109120 0.994029i \(-0.534803\pi\)
−0.109120 + 0.994029i \(0.534803\pi\)
\(114\) 0 0
\(115\) 252410. 1.77976
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −50843.7 −0.329131
\(120\) 0 0
\(121\) 66840.8 0.415029
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −17407.2 −0.0996448
\(126\) 0 0
\(127\) 264132. 1.45315 0.726577 0.687086i \(-0.241110\pi\)
0.726577 + 0.687086i \(0.241110\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −77850.1 −0.396352 −0.198176 0.980166i \(-0.563502\pi\)
−0.198176 + 0.980166i \(0.563502\pi\)
\(132\) 0 0
\(133\) 32683.9 0.160215
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −372403. −1.69516 −0.847581 0.530666i \(-0.821942\pi\)
−0.847581 + 0.530666i \(0.821942\pi\)
\(138\) 0 0
\(139\) 274550. 1.20527 0.602636 0.798016i \(-0.294117\pi\)
0.602636 + 0.798016i \(0.294117\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −30435.1 −0.124461
\(144\) 0 0
\(145\) −178615. −0.705500
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 312982. 1.15492 0.577462 0.816417i \(-0.304043\pi\)
0.577462 + 0.816417i \(0.304043\pi\)
\(150\) 0 0
\(151\) −432095. −1.54219 −0.771093 0.636723i \(-0.780290\pi\)
−0.771093 + 0.636723i \(0.780290\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −288539. −0.964662
\(156\) 0 0
\(157\) −84603.7 −0.273930 −0.136965 0.990576i \(-0.543735\pi\)
−0.136965 + 0.990576i \(0.543735\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 159330. 0.484431
\(162\) 0 0
\(163\) −306303. −0.902989 −0.451494 0.892274i \(-0.649109\pi\)
−0.451494 + 0.892274i \(0.649109\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −606514. −1.68287 −0.841433 0.540362i \(-0.818287\pi\)
−0.841433 + 0.540362i \(0.818287\pi\)
\(168\) 0 0
\(169\) −367228. −0.989053
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 288481. 0.732828 0.366414 0.930452i \(-0.380585\pi\)
0.366414 + 0.930452i \(0.380585\pi\)
\(174\) 0 0
\(175\) 142137. 0.350842
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 148858. 0.347248 0.173624 0.984812i \(-0.444452\pi\)
0.173624 + 0.984812i \(0.444452\pi\)
\(180\) 0 0
\(181\) 93377.8 0.211859 0.105930 0.994374i \(-0.466218\pi\)
0.105930 + 0.994374i \(0.466218\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 950594. 2.04205
\(186\) 0 0
\(187\) −495342. −1.03586
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 246915. 0.489738 0.244869 0.969556i \(-0.421255\pi\)
0.244869 + 0.969556i \(0.421255\pi\)
\(192\) 0 0
\(193\) 481437. 0.930349 0.465175 0.885219i \(-0.345992\pi\)
0.465175 + 0.885219i \(0.345992\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 548236. 1.00647 0.503237 0.864149i \(-0.332142\pi\)
0.503237 + 0.864149i \(0.332142\pi\)
\(198\) 0 0
\(199\) −158179. −0.283150 −0.141575 0.989928i \(-0.545217\pi\)
−0.141575 + 0.989928i \(0.545217\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −112748. −0.192029
\(204\) 0 0
\(205\) 142028. 0.236042
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 318421. 0.504238
\(210\) 0 0
\(211\) −283510. −0.438392 −0.219196 0.975681i \(-0.570343\pi\)
−0.219196 + 0.975681i \(0.570343\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.61416e6 2.38150
\(216\) 0 0
\(217\) −182136. −0.262570
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 66153.2 0.0911109
\(222\) 0 0
\(223\) 651135. 0.876817 0.438409 0.898776i \(-0.355542\pi\)
0.438409 + 0.898776i \(0.355542\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −378294. −0.487264 −0.243632 0.969868i \(-0.578339\pi\)
−0.243632 + 0.969868i \(0.578339\pi\)
\(228\) 0 0
\(229\) −22332.8 −0.0281420 −0.0140710 0.999901i \(-0.504479\pi\)
−0.0140710 + 0.999901i \(0.504479\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 908940. 1.09685 0.548423 0.836201i \(-0.315229\pi\)
0.548423 + 0.836201i \(0.315229\pi\)
\(234\) 0 0
\(235\) −332500. −0.392755
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.05363e6 1.19315 0.596573 0.802559i \(-0.296529\pi\)
0.596573 + 0.802559i \(0.296529\pi\)
\(240\) 0 0
\(241\) 1.05233e6 1.16710 0.583550 0.812077i \(-0.301663\pi\)
0.583550 + 0.812077i \(0.301663\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 186379. 0.198373
\(246\) 0 0
\(247\) −42525.3 −0.0443512
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 972876. 0.974705 0.487352 0.873205i \(-0.337963\pi\)
0.487352 + 0.873205i \(0.337963\pi\)
\(252\) 0 0
\(253\) 1.55226e6 1.52463
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.77948e6 −1.68058 −0.840290 0.542137i \(-0.817615\pi\)
−0.840290 + 0.542137i \(0.817615\pi\)
\(258\) 0 0
\(259\) 600047. 0.555822
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 21959.6 0.0195765 0.00978827 0.999952i \(-0.496884\pi\)
0.00978827 + 0.999952i \(0.496884\pi\)
\(264\) 0 0
\(265\) −1.99641e6 −1.74637
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.69111e6 1.42492 0.712461 0.701712i \(-0.247581\pi\)
0.712461 + 0.701712i \(0.247581\pi\)
\(270\) 0 0
\(271\) 467863. 0.386986 0.193493 0.981102i \(-0.438018\pi\)
0.193493 + 0.981102i \(0.438018\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.38476e6 1.10419
\(276\) 0 0
\(277\) 906169. 0.709594 0.354797 0.934943i \(-0.384550\pi\)
0.354797 + 0.934943i \(0.384550\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 781388. 0.590338 0.295169 0.955445i \(-0.404624\pi\)
0.295169 + 0.955445i \(0.404624\pi\)
\(282\) 0 0
\(283\) 1.49843e6 1.11217 0.556085 0.831125i \(-0.312303\pi\)
0.556085 + 0.831125i \(0.312303\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 89652.8 0.0642479
\(288\) 0 0
\(289\) −343190. −0.241707
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.56070e6 1.06206 0.531031 0.847352i \(-0.321805\pi\)
0.531031 + 0.847352i \(0.321805\pi\)
\(294\) 0 0
\(295\) −220357. −0.147425
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −207305. −0.134101
\(300\) 0 0
\(301\) 1.01891e6 0.648219
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.30436e6 0.802875
\(306\) 0 0
\(307\) 889308. 0.538525 0.269263 0.963067i \(-0.413220\pi\)
0.269263 + 0.963067i \(0.413220\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.44826e6 1.43535 0.717674 0.696380i \(-0.245207\pi\)
0.717674 + 0.696380i \(0.245207\pi\)
\(312\) 0 0
\(313\) −2.73102e6 −1.57567 −0.787834 0.615887i \(-0.788798\pi\)
−0.787834 + 0.615887i \(0.788798\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 249603. 0.139509 0.0697545 0.997564i \(-0.477778\pi\)
0.0697545 + 0.997564i \(0.477778\pi\)
\(318\) 0 0
\(319\) −1.09844e6 −0.604364
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −692115. −0.369124
\(324\) 0 0
\(325\) −184936. −0.0971209
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −209885. −0.106903
\(330\) 0 0
\(331\) −646617. −0.324397 −0.162199 0.986758i \(-0.551858\pi\)
−0.162199 + 0.986758i \(0.551858\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.85433e6 2.36329
\(336\) 0 0
\(337\) −1.02782e6 −0.492994 −0.246497 0.969144i \(-0.579280\pi\)
−0.246497 + 0.969144i \(0.579280\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.77445e6 −0.826375
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.64916e6 −0.735256 −0.367628 0.929973i \(-0.619830\pi\)
−0.367628 + 0.929973i \(0.619830\pi\)
\(348\) 0 0
\(349\) 2.21201e6 0.972128 0.486064 0.873923i \(-0.338432\pi\)
0.486064 + 0.873923i \(0.338432\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.10158e6 −0.470520 −0.235260 0.971932i \(-0.575594\pi\)
−0.235260 + 0.971932i \(0.575594\pi\)
\(354\) 0 0
\(355\) 5.61242e6 2.36363
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.29940e6 −0.532116 −0.266058 0.963957i \(-0.585721\pi\)
−0.266058 + 0.963957i \(0.585721\pi\)
\(360\) 0 0
\(361\) −2.03119e6 −0.820317
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.32196e6 −1.69804
\(366\) 0 0
\(367\) −1.55669e6 −0.603305 −0.301652 0.953418i \(-0.597538\pi\)
−0.301652 + 0.953418i \(0.597538\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.26020e6 −0.475341
\(372\) 0 0
\(373\) −3.12660e6 −1.16359 −0.581796 0.813335i \(-0.697650\pi\)
−0.581796 + 0.813335i \(0.697650\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 146697. 0.0531579
\(378\) 0 0
\(379\) 2.96497e6 1.06029 0.530143 0.847908i \(-0.322138\pi\)
0.530143 + 0.847908i \(0.322138\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.74774e6 0.957149 0.478574 0.878047i \(-0.341154\pi\)
0.478574 + 0.878047i \(0.341154\pi\)
\(384\) 0 0
\(385\) 1.81579e6 0.624330
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 611343. 0.204838 0.102419 0.994741i \(-0.467342\pi\)
0.102419 + 0.994741i \(0.467342\pi\)
\(390\) 0 0
\(391\) −3.37397e6 −1.11609
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 309664. 0.0998615
\(396\) 0 0
\(397\) 2.16794e6 0.690352 0.345176 0.938538i \(-0.387819\pi\)
0.345176 + 0.938538i \(0.387819\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.14644e6 0.977143 0.488572 0.872524i \(-0.337518\pi\)
0.488572 + 0.872524i \(0.337518\pi\)
\(402\) 0 0
\(403\) 236978. 0.0726852
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.84593e6 1.74931
\(408\) 0 0
\(409\) 5.58165e6 1.64989 0.824943 0.565215i \(-0.191207\pi\)
0.824943 + 0.565215i \(0.191207\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −139097. −0.0401275
\(414\) 0 0
\(415\) −3.57794e6 −1.01980
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.25054e6 0.626257 0.313128 0.949711i \(-0.398623\pi\)
0.313128 + 0.949711i \(0.398623\pi\)
\(420\) 0 0
\(421\) 3.45914e6 0.951180 0.475590 0.879667i \(-0.342235\pi\)
0.475590 + 0.879667i \(0.342235\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.00990e6 −0.808313
\(426\) 0 0
\(427\) 823356. 0.218534
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −6.55926e6 −1.70083 −0.850417 0.526109i \(-0.823650\pi\)
−0.850417 + 0.526109i \(0.823650\pi\)
\(432\) 0 0
\(433\) 5.05669e6 1.29612 0.648062 0.761587i \(-0.275580\pi\)
0.648062 + 0.761587i \(0.275580\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.16889e6 0.543293
\(438\) 0 0
\(439\) −4.23225e6 −1.04812 −0.524059 0.851682i \(-0.675583\pi\)
−0.524059 + 0.851682i \(0.675583\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.05525e6 −1.46596 −0.732981 0.680249i \(-0.761872\pi\)
−0.732981 + 0.680249i \(0.761872\pi\)
\(444\) 0 0
\(445\) −1.05093e7 −2.51579
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 299186. 0.0700368 0.0350184 0.999387i \(-0.488851\pi\)
0.0350184 + 0.999387i \(0.488851\pi\)
\(450\) 0 0
\(451\) 873438. 0.202204
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −242500. −0.0549140
\(456\) 0 0
\(457\) 3.75177e6 0.840322 0.420161 0.907450i \(-0.361974\pi\)
0.420161 + 0.907450i \(0.361974\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.94525e6 −1.52207 −0.761036 0.648709i \(-0.775309\pi\)
−0.761036 + 0.648709i \(0.775309\pi\)
\(462\) 0 0
\(463\) 9.13226e6 1.97982 0.989910 0.141697i \(-0.0452558\pi\)
0.989910 + 0.141697i \(0.0452558\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −424136. −0.0899940 −0.0449970 0.998987i \(-0.514328\pi\)
−0.0449970 + 0.998987i \(0.514328\pi\)
\(468\) 0 0
\(469\) 3.06422e6 0.643262
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9.92673e6 2.04011
\(474\) 0 0
\(475\) 1.93485e6 0.393472
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.78605e6 −1.55052 −0.775262 0.631640i \(-0.782382\pi\)
−0.775262 + 0.631640i \(0.782382\pi\)
\(480\) 0 0
\(481\) −780727. −0.153864
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.10910e7 2.14100
\(486\) 0 0
\(487\) −2.32259e6 −0.443763 −0.221881 0.975074i \(-0.571220\pi\)
−0.221881 + 0.975074i \(0.571220\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.01036e6 1.12512 0.562558 0.826758i \(-0.309817\pi\)
0.562558 + 0.826758i \(0.309817\pi\)
\(492\) 0 0
\(493\) 2.38755e6 0.442420
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3.54275e6 0.643353
\(498\) 0 0
\(499\) −3.37385e6 −0.606562 −0.303281 0.952901i \(-0.598082\pi\)
−0.303281 + 0.952901i \(0.598082\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.22068e6 −0.215120 −0.107560 0.994199i \(-0.534304\pi\)
−0.107560 + 0.994199i \(0.534304\pi\)
\(504\) 0 0
\(505\) −3.45179e6 −0.602304
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.56897e6 −0.268423 −0.134212 0.990953i \(-0.542850\pi\)
−0.134212 + 0.990953i \(0.542850\pi\)
\(510\) 0 0
\(511\) −2.72817e6 −0.462188
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.57285e7 −2.61318
\(516\) 0 0
\(517\) −2.04480e6 −0.336452
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.06779e7 −1.72342 −0.861708 0.507404i \(-0.830605\pi\)
−0.861708 + 0.507404i \(0.830605\pi\)
\(522\) 0 0
\(523\) 1.21007e7 1.93444 0.967219 0.253943i \(-0.0817275\pi\)
0.967219 + 0.253943i \(0.0817275\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.85691e6 0.604941
\(528\) 0 0
\(529\) 4.13673e6 0.642714
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −116648. −0.0177852
\(534\) 0 0
\(535\) 7.72577e6 1.16696
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.14619e6 0.169936
\(540\) 0 0
\(541\) −3.19805e6 −0.469778 −0.234889 0.972022i \(-0.575473\pi\)
−0.234889 + 0.972022i \(0.575473\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.71499e7 2.47326
\(546\) 0 0
\(547\) −3.97811e6 −0.568471 −0.284235 0.958755i \(-0.591740\pi\)
−0.284235 + 0.958755i \(0.591740\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.53479e6 −0.215362
\(552\) 0 0
\(553\) 195470. 0.0271812
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.14113e7 −1.55847 −0.779236 0.626731i \(-0.784392\pi\)
−0.779236 + 0.626731i \(0.784392\pi\)
\(558\) 0 0
\(559\) −1.32572e6 −0.179441
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −6.46973e6 −0.860231 −0.430115 0.902774i \(-0.641527\pi\)
−0.430115 + 0.902774i \(0.641527\pi\)
\(564\) 0 0
\(565\) −2.29952e6 −0.303051
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −717028. −0.0928444 −0.0464222 0.998922i \(-0.514782\pi\)
−0.0464222 + 0.998922i \(0.514782\pi\)
\(570\) 0 0
\(571\) −6.00286e6 −0.770491 −0.385246 0.922814i \(-0.625883\pi\)
−0.385246 + 0.922814i \(0.625883\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.43217e6 1.18971
\(576\) 0 0
\(577\) 1.55712e7 1.94707 0.973537 0.228531i \(-0.0733922\pi\)
0.973537 + 0.228531i \(0.0733922\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.25852e6 −0.277577
\(582\) 0 0
\(583\) −1.22775e7 −1.49602
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.84621e6 0.939863 0.469931 0.882703i \(-0.344279\pi\)
0.469931 + 0.882703i \(0.344279\pi\)
\(588\) 0 0
\(589\) −2.47934e6 −0.294475
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.33248e7 −1.55605 −0.778026 0.628232i \(-0.783779\pi\)
−0.778026 + 0.628232i \(0.783779\pi\)
\(594\) 0 0
\(595\) −3.94678e6 −0.457036
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.77916e6 −0.885861 −0.442930 0.896556i \(-0.646061\pi\)
−0.442930 + 0.896556i \(0.646061\pi\)
\(600\) 0 0
\(601\) 8.62898e6 0.974480 0.487240 0.873268i \(-0.338004\pi\)
0.487240 + 0.873268i \(0.338004\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 5.18857e6 0.576314
\(606\) 0 0
\(607\) 7.09353e6 0.781431 0.390715 0.920512i \(-0.372228\pi\)
0.390715 + 0.920512i \(0.372228\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 273084. 0.0295932
\(612\) 0 0
\(613\) 4.52640e6 0.486521 0.243261 0.969961i \(-0.421783\pi\)
0.243261 + 0.969961i \(0.421783\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.38009e6 0.886208 0.443104 0.896470i \(-0.353877\pi\)
0.443104 + 0.896470i \(0.353877\pi\)
\(618\) 0 0
\(619\) 168342. 0.0176590 0.00882949 0.999961i \(-0.497189\pi\)
0.00882949 + 0.999961i \(0.497189\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −6.63385e6 −0.684771
\(624\) 0 0
\(625\) −1.04161e7 −1.06661
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.27066e7 −1.28057
\(630\) 0 0
\(631\) −1.66208e7 −1.66180 −0.830899 0.556423i \(-0.812174\pi\)
−0.830899 + 0.556423i \(0.812174\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.05034e7 2.01786
\(636\) 0 0
\(637\) −153074. −0.0149470
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.02473e6 −0.0985068 −0.0492534 0.998786i \(-0.515684\pi\)
−0.0492534 + 0.998786i \(0.515684\pi\)
\(642\) 0 0
\(643\) 1.22962e7 1.17286 0.586428 0.810001i \(-0.300534\pi\)
0.586428 + 0.810001i \(0.300534\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.16537e6 −0.203363 −0.101682 0.994817i \(-0.532422\pi\)
−0.101682 + 0.994817i \(0.532422\pi\)
\(648\) 0 0
\(649\) −1.35515e6 −0.126292
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.22501e7 1.12424 0.562119 0.827056i \(-0.309986\pi\)
0.562119 + 0.827056i \(0.309986\pi\)
\(654\) 0 0
\(655\) −6.04317e6 −0.550379
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.18607e6 0.106389 0.0531944 0.998584i \(-0.483060\pi\)
0.0531944 + 0.998584i \(0.483060\pi\)
\(660\) 0 0
\(661\) −1.45382e7 −1.29421 −0.647107 0.762399i \(-0.724021\pi\)
−0.647107 + 0.762399i \(0.724021\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 2.53711e6 0.222477
\(666\) 0 0
\(667\) −7.48190e6 −0.651174
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.02151e6 0.687781
\(672\) 0 0
\(673\) −5.99405e6 −0.510132 −0.255066 0.966924i \(-0.582097\pi\)
−0.255066 + 0.966924i \(0.582097\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.08389e7 −1.74744 −0.873721 0.486428i \(-0.838300\pi\)
−0.873721 + 0.486428i \(0.838300\pi\)
\(678\) 0 0
\(679\) 7.00102e6 0.582756
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 4.55565e6 0.373679 0.186840 0.982390i \(-0.440176\pi\)
0.186840 + 0.982390i \(0.440176\pi\)
\(684\) 0 0
\(685\) −2.89080e7 −2.35392
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.63966e6 0.131585
\(690\) 0 0
\(691\) −1.68542e6 −0.134281 −0.0671404 0.997744i \(-0.521388\pi\)
−0.0671404 + 0.997744i \(0.521388\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.13122e7 1.67365
\(696\) 0 0
\(697\) −1.89849e6 −0.148022
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −2.45349e6 −0.188577 −0.0942887 0.995545i \(-0.530058\pi\)
−0.0942887 + 0.995545i \(0.530058\pi\)
\(702\) 0 0
\(703\) 8.16820e6 0.623359
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.17889e6 −0.163940
\(708\) 0 0
\(709\) −1.32314e7 −0.988530 −0.494265 0.869311i \(-0.664563\pi\)
−0.494265 + 0.869311i \(0.664563\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.20865e7 −0.890380
\(714\) 0 0
\(715\) −2.36255e6 −0.172828
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.35337e7 0.976324 0.488162 0.872753i \(-0.337667\pi\)
0.488162 + 0.872753i \(0.337667\pi\)
\(720\) 0 0
\(721\) −9.92835e6 −0.711277
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.67455e6 −0.471604
\(726\) 0 0
\(727\) −5.29416e6 −0.371502 −0.185751 0.982597i \(-0.559472\pi\)
−0.185751 + 0.982597i \(0.559472\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.15766e7 −1.49344
\(732\) 0 0
\(733\) −2.25014e7 −1.54685 −0.773426 0.633886i \(-0.781459\pi\)
−0.773426 + 0.633886i \(0.781459\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.98530e7 2.02451
\(738\) 0 0
\(739\) −1.60739e7 −1.08271 −0.541353 0.840795i \(-0.682088\pi\)
−0.541353 + 0.840795i \(0.682088\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.31604e6 −0.153913 −0.0769563 0.997034i \(-0.524520\pi\)
−0.0769563 + 0.997034i \(0.524520\pi\)
\(744\) 0 0
\(745\) 2.42955e7 1.60374
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.87677e6 0.317634
\(750\) 0 0
\(751\) 7.77263e6 0.502885 0.251442 0.967872i \(-0.419095\pi\)
0.251442 + 0.967872i \(0.419095\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −3.35417e7 −2.14150
\(756\) 0 0
\(757\) −1.59716e7 −1.01300 −0.506498 0.862241i \(-0.669060\pi\)
−0.506498 + 0.862241i \(0.669060\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.84940e7 −1.15763 −0.578815 0.815459i \(-0.696485\pi\)
−0.578815 + 0.815459i \(0.696485\pi\)
\(762\) 0 0
\(763\) 1.08256e7 0.673193
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 180980. 0.0111082
\(768\) 0 0
\(769\) −2.33524e7 −1.42402 −0.712009 0.702170i \(-0.752214\pi\)
−0.712009 + 0.702170i \(0.752214\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −7.25262e6 −0.436562 −0.218281 0.975886i \(-0.570045\pi\)
−0.218281 + 0.975886i \(0.570045\pi\)
\(774\) 0 0
\(775\) −1.07823e7 −0.644845
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.22041e6 0.0720546
\(780\) 0 0
\(781\) 3.45151e7 2.02480
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.56742e6 −0.380383
\(786\) 0 0
\(787\) −1.18935e6 −0.0684497 −0.0342248 0.999414i \(-0.510896\pi\)
−0.0342248 + 0.999414i \(0.510896\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.45153e6 −0.0824871
\(792\) 0 0
\(793\) −1.07128e6 −0.0604949
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.14041e7 −1.19358 −0.596790 0.802397i \(-0.703558\pi\)
−0.596790 + 0.802397i \(0.703558\pi\)
\(798\) 0 0
\(799\) 4.44453e6 0.246297
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.65790e7 −1.45462
\(804\) 0 0
\(805\) 1.23681e7 0.672686
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −9.60341e6 −0.515886 −0.257943 0.966160i \(-0.583045\pi\)
−0.257943 + 0.966160i \(0.583045\pi\)
\(810\) 0 0
\(811\) −2.62263e7 −1.40018 −0.700091 0.714054i \(-0.746857\pi\)
−0.700091 + 0.714054i \(0.746857\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.37770e7 −1.25390
\(816\) 0 0
\(817\) 1.38701e7 0.726982
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.65685e7 −1.89343 −0.946715 0.322073i \(-0.895620\pi\)
−0.946715 + 0.322073i \(0.895620\pi\)
\(822\) 0 0
\(823\) 7.73488e6 0.398065 0.199032 0.979993i \(-0.436220\pi\)
0.199032 + 0.979993i \(0.436220\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.47172e7 −0.748277 −0.374138 0.927373i \(-0.622061\pi\)
−0.374138 + 0.927373i \(0.622061\pi\)
\(828\) 0 0
\(829\) −7.41886e6 −0.374931 −0.187465 0.982271i \(-0.560027\pi\)
−0.187465 + 0.982271i \(0.560027\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.49134e6 −0.124400
\(834\) 0 0
\(835\) −4.70811e7 −2.33685
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 116538. 0.00571559 0.00285780 0.999996i \(-0.499090\pi\)
0.00285780 + 0.999996i \(0.499090\pi\)
\(840\) 0 0
\(841\) −1.52167e7 −0.741874
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.85064e7 −1.37341
\(846\) 0 0
\(847\) 3.27520e6 0.156866
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 3.98190e7 1.88480
\(852\) 0 0
\(853\) −1.91763e7 −0.902387 −0.451193 0.892426i \(-0.649002\pi\)
−0.451193 + 0.892426i \(0.649002\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.62548e6 0.0756012 0.0378006 0.999285i \(-0.487965\pi\)
0.0378006 + 0.999285i \(0.487965\pi\)
\(858\) 0 0
\(859\) 1.65931e7 0.767265 0.383632 0.923486i \(-0.374673\pi\)
0.383632 + 0.923486i \(0.374673\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.30415e7 −1.05314 −0.526568 0.850133i \(-0.676521\pi\)
−0.526568 + 0.850133i \(0.676521\pi\)
\(864\) 0 0
\(865\) 2.23935e7 1.01761
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.90436e6 0.0855460
\(870\) 0 0
\(871\) −3.98689e6 −0.178069
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −852954. −0.0376622
\(876\) 0 0
\(877\) 1.84493e7 0.809993 0.404996 0.914318i \(-0.367273\pi\)
0.404996 + 0.914318i \(0.367273\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 3.70548e7 1.60844 0.804219 0.594333i \(-0.202584\pi\)
0.804219 + 0.594333i \(0.202584\pi\)
\(882\) 0 0
\(883\) 5.28466e6 0.228095 0.114047 0.993475i \(-0.463618\pi\)
0.114047 + 0.993475i \(0.463618\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.98545e7 −0.847326 −0.423663 0.905820i \(-0.639256\pi\)
−0.423663 + 0.905820i \(0.639256\pi\)
\(888\) 0 0
\(889\) 1.29425e7 0.549240
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.85708e6 −0.119893
\(894\) 0 0
\(895\) 1.15552e7 0.482193
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 8.55283e6 0.352948
\(900\) 0 0
\(901\) 2.66861e7 1.09515
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 7.24852e6 0.294190
\(906\) 0 0
\(907\) 2.00483e7 0.809207 0.404603 0.914492i \(-0.367410\pi\)
0.404603 + 0.914492i \(0.367410\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −765753. −0.0305698 −0.0152849 0.999883i \(-0.504866\pi\)
−0.0152849 + 0.999883i \(0.504866\pi\)
\(912\) 0 0
\(913\) −2.20035e7 −0.873605
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.81465e6 −0.149807
\(918\) 0 0
\(919\) 1.87846e7 0.733692 0.366846 0.930282i \(-0.380438\pi\)
0.366846 + 0.930282i \(0.380438\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −4.60951e6 −0.178094
\(924\) 0 0
\(925\) 3.55222e7 1.36504
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.56290e7 1.73461 0.867304 0.497778i \(-0.165851\pi\)
0.867304 + 0.497778i \(0.165851\pi\)
\(930\) 0 0
\(931\) 1.60151e6 0.0605557
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −3.84513e7 −1.43841
\(936\) 0 0
\(937\) 6.67800e6 0.248484 0.124242 0.992252i \(-0.460350\pi\)
0.124242 + 0.992252i \(0.460350\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.42716e7 −1.26171 −0.630857 0.775899i \(-0.717297\pi\)
−0.630857 + 0.775899i \(0.717297\pi\)
\(942\) 0 0
\(943\) 5.94933e6 0.217866
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5.28766e7 1.91597 0.957984 0.286821i \(-0.0925984\pi\)
0.957984 + 0.286821i \(0.0925984\pi\)
\(948\) 0 0
\(949\) 3.54965e6 0.127944
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5.33439e6 −0.190262 −0.0951311 0.995465i \(-0.530327\pi\)
−0.0951311 + 0.995465i \(0.530327\pi\)
\(954\) 0 0
\(955\) 1.91669e7 0.680056
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.82477e7 −0.640711
\(960\) 0 0
\(961\) −1.48127e7 −0.517398
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 3.73719e7 1.29189
\(966\) 0 0
\(967\) 1.93877e7 0.666744 0.333372 0.942795i \(-0.391813\pi\)
0.333372 + 0.942795i \(0.391813\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.07463e7 0.365772 0.182886 0.983134i \(-0.441456\pi\)
0.182886 + 0.983134i \(0.441456\pi\)
\(972\) 0 0
\(973\) 1.34530e7 0.455550
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.41051e7 0.807926 0.403963 0.914775i \(-0.367632\pi\)
0.403963 + 0.914775i \(0.367632\pi\)
\(978\) 0 0
\(979\) −6.46300e7 −2.15515
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4.05038e7 −1.33694 −0.668470 0.743739i \(-0.733050\pi\)
−0.668470 + 0.743739i \(0.733050\pi\)
\(984\) 0 0
\(985\) 4.25573e7 1.39760
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.76149e7 2.19812
\(990\) 0 0
\(991\) 4.01588e7 1.29896 0.649482 0.760377i \(-0.274986\pi\)
0.649482 + 0.760377i \(0.274986\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −1.22788e7 −0.393185
\(996\) 0 0
\(997\) −2.72276e7 −0.867505 −0.433753 0.901032i \(-0.642811\pi\)
−0.433753 + 0.901032i \(0.642811\pi\)
\(998\) 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 1008.6.a.bo.1.2 2
3.2 odd 2 336.6.a.x.1.1 2
4.3 odd 2 252.6.a.h.1.2 2
12.11 even 2 84.6.a.c.1.1 2
84.11 even 6 588.6.i.l.373.2 4
84.23 even 6 588.6.i.l.361.2 4
84.47 odd 6 588.6.i.i.361.1 4
84.59 odd 6 588.6.i.i.373.1 4
84.83 odd 2 588.6.a.k.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.6.a.c.1.1 2 12.11 even 2
252.6.a.h.1.2 2 4.3 odd 2
336.6.a.x.1.1 2 3.2 odd 2
588.6.a.k.1.2 2 84.83 odd 2
588.6.i.i.361.1 4 84.47 odd 6
588.6.i.i.373.1 4 84.59 odd 6
588.6.i.l.361.2 4 84.23 even 6
588.6.i.l.373.2 4 84.11 even 6
1008.6.a.bo.1.2 2 1.1 even 1 trivial