Properties

Label 1008.6.a.p.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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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: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
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)
 
\(f(q)\) \(=\) \(q-4.00000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-4.00000 q^{5} -49.0000 q^{7} -240.000 q^{11} -744.000 q^{13} +1042.00 q^{17} +986.000 q^{19} +184.000 q^{23} -3109.00 q^{25} +734.000 q^{29} -5140.00 q^{31} +196.000 q^{35} -6054.00 q^{37} -7598.00 q^{41} -13016.0 q^{43} +14668.0 q^{47} +2401.00 q^{49} +14522.0 q^{53} +960.000 q^{55} -13362.0 q^{59} +9676.00 q^{61} +2976.00 q^{65} +62124.0 q^{67} -2112.00 q^{71} -28910.0 q^{73} +11760.0 q^{77} +101768. q^{79} -23922.0 q^{83} -4168.00 q^{85} -141674. q^{89} +36456.0 q^{91} -3944.00 q^{95} +99982.0 q^{97} +O(q^{100})\)

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
\(5\) −4.00000 −0.0715542 −0.0357771 0.999360i \(-0.511391\pi\)
−0.0357771 + 0.999360i \(0.511391\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −240.000 −0.598039 −0.299020 0.954247i \(-0.596660\pi\)
−0.299020 + 0.954247i \(0.596660\pi\)
\(12\) 0 0
\(13\) −744.000 −1.22100 −0.610498 0.792017i \(-0.709031\pi\)
−0.610498 + 0.792017i \(0.709031\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1042.00 0.874471 0.437236 0.899347i \(-0.355958\pi\)
0.437236 + 0.899347i \(0.355958\pi\)
\(18\) 0 0
\(19\) 986.000 0.626604 0.313302 0.949654i \(-0.398565\pi\)
0.313302 + 0.949654i \(0.398565\pi\)
\(20\) 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
\(25\) −3109.00 −0.994880
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 734.000 0.162069 0.0810347 0.996711i \(-0.474178\pi\)
0.0810347 + 0.996711i \(0.474178\pi\)
\(30\) 0 0
\(31\) −5140.00 −0.960636 −0.480318 0.877094i \(-0.659479\pi\)
−0.480318 + 0.877094i \(0.659479\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 196.000 0.0270449
\(36\) 0 0
\(37\) −6054.00 −0.727006 −0.363503 0.931593i \(-0.618419\pi\)
−0.363503 + 0.931593i \(0.618419\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7598.00 −0.705894 −0.352947 0.935643i \(-0.614820\pi\)
−0.352947 + 0.935643i \(0.614820\pi\)
\(42\) 0 0
\(43\) −13016.0 −1.07351 −0.536755 0.843738i \(-0.680350\pi\)
−0.536755 + 0.843738i \(0.680350\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 14668.0 0.968559 0.484280 0.874913i \(-0.339082\pi\)
0.484280 + 0.874913i \(0.339082\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 14522.0 0.710128 0.355064 0.934842i \(-0.384459\pi\)
0.355064 + 0.934842i \(0.384459\pi\)
\(54\) 0 0
\(55\) 960.000 0.0427922
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −13362.0 −0.499737 −0.249868 0.968280i \(-0.580387\pi\)
−0.249868 + 0.968280i \(0.580387\pi\)
\(60\) 0 0
\(61\) 9676.00 0.332944 0.166472 0.986046i \(-0.446762\pi\)
0.166472 + 0.986046i \(0.446762\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2976.00 0.0873674
\(66\) 0 0
\(67\) 62124.0 1.69072 0.845361 0.534195i \(-0.179385\pi\)
0.845361 + 0.534195i \(0.179385\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2112.00 −0.0497219 −0.0248610 0.999691i \(-0.507914\pi\)
−0.0248610 + 0.999691i \(0.507914\pi\)
\(72\) 0 0
\(73\) −28910.0 −0.634952 −0.317476 0.948266i \(-0.602835\pi\)
−0.317476 + 0.948266i \(0.602835\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 11760.0 0.226038
\(78\) 0 0
\(79\) 101768. 1.83461 0.917304 0.398186i \(-0.130360\pi\)
0.917304 + 0.398186i \(0.130360\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −23922.0 −0.381156 −0.190578 0.981672i \(-0.561036\pi\)
−0.190578 + 0.981672i \(0.561036\pi\)
\(84\) 0 0
\(85\) −4168.00 −0.0625721
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −141674. −1.89590 −0.947949 0.318421i \(-0.896847\pi\)
−0.947949 + 0.318421i \(0.896847\pi\)
\(90\) 0 0
\(91\) 36456.0 0.461493
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3944.00 −0.0448361
\(96\) 0 0
\(97\) 99982.0 1.07893 0.539464 0.842009i \(-0.318627\pi\)
0.539464 + 0.842009i \(0.318627\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 108684. 1.06014 0.530069 0.847955i \(-0.322166\pi\)
0.530069 + 0.847955i \(0.322166\pi\)
\(102\) 0 0
\(103\) −87396.0 −0.811706 −0.405853 0.913938i \(-0.633025\pi\)
−0.405853 + 0.913938i \(0.633025\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 71892.0 0.607045 0.303523 0.952824i \(-0.401837\pi\)
0.303523 + 0.952824i \(0.401837\pi\)
\(108\) 0 0
\(109\) −118166. −0.952634 −0.476317 0.879274i \(-0.658029\pi\)
−0.476317 + 0.879274i \(0.658029\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −252774. −1.86224 −0.931121 0.364709i \(-0.881168\pi\)
−0.931121 + 0.364709i \(0.881168\pi\)
\(114\) 0 0
\(115\) −736.000 −0.00518959
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −51058.0 −0.330519
\(120\) 0 0
\(121\) −103451. −0.642349
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 24936.0 0.142742
\(126\) 0 0
\(127\) 3592.00 0.0197618 0.00988091 0.999951i \(-0.496855\pi\)
0.00988091 + 0.999951i \(0.496855\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 364534. 1.85592 0.927961 0.372677i \(-0.121560\pi\)
0.927961 + 0.372677i \(0.121560\pi\)
\(132\) 0 0
\(133\) −48314.0 −0.236834
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 77246.0 0.351621 0.175810 0.984424i \(-0.443745\pi\)
0.175810 + 0.984424i \(0.443745\pi\)
\(138\) 0 0
\(139\) 122742. 0.538835 0.269418 0.963023i \(-0.413169\pi\)
0.269418 + 0.963023i \(0.413169\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 178560. 0.730204
\(144\) 0 0
\(145\) −2936.00 −0.0115967
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 469234. 1.73151 0.865753 0.500472i \(-0.166840\pi\)
0.865753 + 0.500472i \(0.166840\pi\)
\(150\) 0 0
\(151\) 411584. 1.46898 0.734490 0.678619i \(-0.237421\pi\)
0.734490 + 0.678619i \(0.237421\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 20560.0 0.0687375
\(156\) 0 0
\(157\) −574632. −1.86055 −0.930274 0.366867i \(-0.880431\pi\)
−0.930274 + 0.366867i \(0.880431\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −9016.00 −0.0274125
\(162\) 0 0
\(163\) 264704. 0.780354 0.390177 0.920740i \(-0.372414\pi\)
0.390177 + 0.920740i \(0.372414\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 343356. 0.952694 0.476347 0.879257i \(-0.341961\pi\)
0.476347 + 0.879257i \(0.341961\pi\)
\(168\) 0 0
\(169\) 182243. 0.490833
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 303296. 0.770462 0.385231 0.922820i \(-0.374122\pi\)
0.385231 + 0.922820i \(0.374122\pi\)
\(174\) 0 0
\(175\) 152341. 0.376029
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −362756. −0.846218 −0.423109 0.906079i \(-0.639061\pi\)
−0.423109 + 0.906079i \(0.639061\pi\)
\(180\) 0 0
\(181\) −146560. −0.332521 −0.166260 0.986082i \(-0.553169\pi\)
−0.166260 + 0.986082i \(0.553169\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 24216.0 0.0520203
\(186\) 0 0
\(187\) −250080. −0.522968
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 552536. 1.09592 0.547958 0.836506i \(-0.315405\pi\)
0.547958 + 0.836506i \(0.315405\pi\)
\(192\) 0 0
\(193\) 305358. 0.590087 0.295043 0.955484i \(-0.404666\pi\)
0.295043 + 0.955484i \(0.404666\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −743838. −1.36557 −0.682783 0.730621i \(-0.739231\pi\)
−0.682783 + 0.730621i \(0.739231\pi\)
\(198\) 0 0
\(199\) −286220. −0.512351 −0.256175 0.966630i \(-0.582462\pi\)
−0.256175 + 0.966630i \(0.582462\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −35966.0 −0.0612565
\(204\) 0 0
\(205\) 30392.0 0.0505097
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −236640. −0.374733
\(210\) 0 0
\(211\) 895372. 1.38451 0.692257 0.721651i \(-0.256616\pi\)
0.692257 + 0.721651i \(0.256616\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 52064.0 0.0768142
\(216\) 0 0
\(217\) 251860. 0.363086
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −775248. −1.06773
\(222\) 0 0
\(223\) 1.18812e6 1.59992 0.799960 0.600054i \(-0.204854\pi\)
0.799960 + 0.600054i \(0.204854\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 808822. 1.04181 0.520905 0.853615i \(-0.325595\pi\)
0.520905 + 0.853615i \(0.325595\pi\)
\(228\) 0 0
\(229\) −344344. −0.433914 −0.216957 0.976181i \(-0.569613\pi\)
−0.216957 + 0.976181i \(0.569613\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 334022. 0.403074 0.201537 0.979481i \(-0.435406\pi\)
0.201537 + 0.979481i \(0.435406\pi\)
\(234\) 0 0
\(235\) −58672.0 −0.0693045
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −954272. −1.08063 −0.540316 0.841463i \(-0.681695\pi\)
−0.540316 + 0.841463i \(0.681695\pi\)
\(240\) 0 0
\(241\) −272882. −0.302644 −0.151322 0.988485i \(-0.548353\pi\)
−0.151322 + 0.988485i \(0.548353\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −9604.00 −0.0102220
\(246\) 0 0
\(247\) −733584. −0.765081
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 43754.0 0.0438363 0.0219181 0.999760i \(-0.493023\pi\)
0.0219181 + 0.999760i \(0.493023\pi\)
\(252\) 0 0
\(253\) −44160.0 −0.0433738
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.73201e6 1.63576 0.817878 0.575391i \(-0.195150\pi\)
0.817878 + 0.575391i \(0.195150\pi\)
\(258\) 0 0
\(259\) 296646. 0.274783
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 613248. 0.546697 0.273349 0.961915i \(-0.411869\pi\)
0.273349 + 0.961915i \(0.411869\pi\)
\(264\) 0 0
\(265\) −58088.0 −0.0508126
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.01360e6 1.69665 0.848325 0.529475i \(-0.177611\pi\)
0.848325 + 0.529475i \(0.177611\pi\)
\(270\) 0 0
\(271\) 1.22138e6 1.01024 0.505122 0.863048i \(-0.331448\pi\)
0.505122 + 0.863048i \(0.331448\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 746160. 0.594977
\(276\) 0 0
\(277\) 2.11821e6 1.65871 0.829355 0.558722i \(-0.188708\pi\)
0.829355 + 0.558722i \(0.188708\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.64516e6 1.24292 0.621458 0.783447i \(-0.286541\pi\)
0.621458 + 0.783447i \(0.286541\pi\)
\(282\) 0 0
\(283\) −1.66393e6 −1.23501 −0.617504 0.786567i \(-0.711856\pi\)
−0.617504 + 0.786567i \(0.711856\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 372302. 0.266803
\(288\) 0 0
\(289\) −334093. −0.235300
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.15732e6 0.787559 0.393779 0.919205i \(-0.371167\pi\)
0.393779 + 0.919205i \(0.371167\pi\)
\(294\) 0 0
\(295\) 53448.0 0.0357583
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −136896. −0.0885549
\(300\) 0 0
\(301\) 637784. 0.405749
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −38704.0 −0.0238235
\(306\) 0 0
\(307\) −344998. −0.208915 −0.104458 0.994529i \(-0.533311\pi\)
−0.104458 + 0.994529i \(0.533311\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 3.28798e6 1.92765 0.963824 0.266540i \(-0.0858804\pi\)
0.963824 + 0.266540i \(0.0858804\pi\)
\(312\) 0 0
\(313\) −2.21063e6 −1.27542 −0.637712 0.770275i \(-0.720119\pi\)
−0.637712 + 0.770275i \(0.720119\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.19631e6 −0.668645 −0.334322 0.942459i \(-0.608507\pi\)
−0.334322 + 0.942459i \(0.608507\pi\)
\(318\) 0 0
\(319\) −176160. −0.0969238
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.02741e6 0.547947
\(324\) 0 0
\(325\) 2.31310e6 1.21475
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −718732. −0.366081
\(330\) 0 0
\(331\) −2.12828e6 −1.06772 −0.533862 0.845572i \(-0.679260\pi\)
−0.533862 + 0.845572i \(0.679260\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −248496. −0.120978
\(336\) 0 0
\(337\) 1.89841e6 0.910576 0.455288 0.890344i \(-0.349536\pi\)
0.455288 + 0.890344i \(0.349536\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.23360e6 0.574498
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.17548e6 0.969910 0.484955 0.874539i \(-0.338836\pi\)
0.484955 + 0.874539i \(0.338836\pi\)
\(348\) 0 0
\(349\) 2.12950e6 0.935869 0.467934 0.883763i \(-0.344998\pi\)
0.467934 + 0.883763i \(0.344998\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.54144e6 1.08553 0.542766 0.839884i \(-0.317377\pi\)
0.542766 + 0.839884i \(0.317377\pi\)
\(354\) 0 0
\(355\) 8448.00 0.00355781
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −479280. −0.196270 −0.0981348 0.995173i \(-0.531288\pi\)
−0.0981348 + 0.995173i \(0.531288\pi\)
\(360\) 0 0
\(361\) −1.50390e6 −0.607368
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 115640. 0.0454335
\(366\) 0 0
\(367\) −1.89390e6 −0.733991 −0.366996 0.930223i \(-0.619614\pi\)
−0.366996 + 0.930223i \(0.619614\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −711578. −0.268403
\(372\) 0 0
\(373\) 1.56683e6 0.583109 0.291555 0.956554i \(-0.405828\pi\)
0.291555 + 0.956554i \(0.405828\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −546096. −0.197886
\(378\) 0 0
\(379\) 57360.0 0.0205121 0.0102561 0.999947i \(-0.496735\pi\)
0.0102561 + 0.999947i \(0.496735\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −4.41239e6 −1.53701 −0.768505 0.639844i \(-0.778999\pi\)
−0.768505 + 0.639844i \(0.778999\pi\)
\(384\) 0 0
\(385\) −47040.0 −0.0161739
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 872470. 0.292332 0.146166 0.989260i \(-0.453307\pi\)
0.146166 + 0.989260i \(0.453307\pi\)
\(390\) 0 0
\(391\) 191728. 0.0634225
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −407072. −0.131274
\(396\) 0 0
\(397\) 3.63170e6 1.15647 0.578233 0.815871i \(-0.303742\pi\)
0.578233 + 0.815871i \(0.303742\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.58423e6 1.11310 0.556550 0.830814i \(-0.312125\pi\)
0.556550 + 0.830814i \(0.312125\pi\)
\(402\) 0 0
\(403\) 3.82416e6 1.17293
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.45296e6 0.434778
\(408\) 0 0
\(409\) 2.18309e6 0.645304 0.322652 0.946518i \(-0.395426\pi\)
0.322652 + 0.946518i \(0.395426\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 654738. 0.188883
\(414\) 0 0
\(415\) 95688.0 0.0272733
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −4.91137e6 −1.36668 −0.683342 0.730099i \(-0.739474\pi\)
−0.683342 + 0.730099i \(0.739474\pi\)
\(420\) 0 0
\(421\) 693766. 0.190769 0.0953845 0.995441i \(-0.469592\pi\)
0.0953845 + 0.995441i \(0.469592\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.23958e6 −0.869994
\(426\) 0 0
\(427\) −474124. −0.125841
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.25035e6 −0.324219 −0.162110 0.986773i \(-0.551830\pi\)
−0.162110 + 0.986773i \(0.551830\pi\)
\(432\) 0 0
\(433\) 157750. 0.0404343 0.0202171 0.999796i \(-0.493564\pi\)
0.0202171 + 0.999796i \(0.493564\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 181424. 0.0454455
\(438\) 0 0
\(439\) −263736. −0.0653143 −0.0326571 0.999467i \(-0.510397\pi\)
−0.0326571 + 0.999467i \(0.510397\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −1.50410e6 −0.364139 −0.182070 0.983286i \(-0.558280\pi\)
−0.182070 + 0.983286i \(0.558280\pi\)
\(444\) 0 0
\(445\) 566696. 0.135659
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −2.11128e6 −0.494231 −0.247116 0.968986i \(-0.579483\pi\)
−0.247116 + 0.968986i \(0.579483\pi\)
\(450\) 0 0
\(451\) 1.82352e6 0.422152
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −145824. −0.0330218
\(456\) 0 0
\(457\) 3.99938e6 0.895782 0.447891 0.894088i \(-0.352175\pi\)
0.447891 + 0.894088i \(0.352175\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.24090e6 0.491101 0.245551 0.969384i \(-0.421031\pi\)
0.245551 + 0.969384i \(0.421031\pi\)
\(462\) 0 0
\(463\) 1.47304e6 0.319346 0.159673 0.987170i \(-0.448956\pi\)
0.159673 + 0.987170i \(0.448956\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.50472e6 1.80454 0.902272 0.431166i \(-0.141898\pi\)
0.902272 + 0.431166i \(0.141898\pi\)
\(468\) 0 0
\(469\) −3.04408e6 −0.639033
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.12384e6 0.642001
\(474\) 0 0
\(475\) −3.06547e6 −0.623395
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.56984e6 −1.30833 −0.654163 0.756354i \(-0.726979\pi\)
−0.654163 + 0.756354i \(0.726979\pi\)
\(480\) 0 0
\(481\) 4.50418e6 0.887672
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −399928. −0.0772018
\(486\) 0 0
\(487\) −7.71038e6 −1.47317 −0.736585 0.676344i \(-0.763563\pi\)
−0.736585 + 0.676344i \(0.763563\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 8.72147e6 1.63262 0.816311 0.577612i \(-0.196015\pi\)
0.816311 + 0.577612i \(0.196015\pi\)
\(492\) 0 0
\(493\) 764828. 0.141725
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 103488. 0.0187931
\(498\) 0 0
\(499\) 7.87430e6 1.41567 0.707833 0.706380i \(-0.249673\pi\)
0.707833 + 0.706380i \(0.249673\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8.68726e6 1.53096 0.765479 0.643461i \(-0.222502\pi\)
0.765479 + 0.643461i \(0.222502\pi\)
\(504\) 0 0
\(505\) −434736. −0.0758573
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.34131e6 0.229475 0.114737 0.993396i \(-0.463397\pi\)
0.114737 + 0.993396i \(0.463397\pi\)
\(510\) 0 0
\(511\) 1.41659e6 0.239989
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 349584. 0.0580809
\(516\) 0 0
\(517\) −3.52032e6 −0.579236
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.00185e6 −0.968704 −0.484352 0.874873i \(-0.660945\pi\)
−0.484352 + 0.874873i \(0.660945\pi\)
\(522\) 0 0
\(523\) −1.19109e7 −1.90410 −0.952048 0.305950i \(-0.901026\pi\)
−0.952048 + 0.305950i \(0.901026\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.35588e6 −0.840048
\(528\) 0 0
\(529\) −6.40249e6 −0.994740
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.65291e6 0.861895
\(534\) 0 0
\(535\) −287568. −0.0434366
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −576240. −0.0854341
\(540\) 0 0
\(541\) −7.20703e6 −1.05868 −0.529338 0.848411i \(-0.677560\pi\)
−0.529338 + 0.848411i \(0.677560\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 472664. 0.0681650
\(546\) 0 0
\(547\) −1.65172e6 −0.236030 −0.118015 0.993012i \(-0.537653\pi\)
−0.118015 + 0.993012i \(0.537653\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 723724. 0.101553
\(552\) 0 0
\(553\) −4.98663e6 −0.693417
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.58171e6 1.03545 0.517725 0.855547i \(-0.326779\pi\)
0.517725 + 0.855547i \(0.326779\pi\)
\(558\) 0 0
\(559\) 9.68390e6 1.31075
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.26568e7 −1.68288 −0.841440 0.540351i \(-0.818292\pi\)
−0.841440 + 0.540351i \(0.818292\pi\)
\(564\) 0 0
\(565\) 1.01110e6 0.133251
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −4.57445e6 −0.592323 −0.296162 0.955138i \(-0.595707\pi\)
−0.296162 + 0.955138i \(0.595707\pi\)
\(570\) 0 0
\(571\) 5.77802e6 0.741632 0.370816 0.928706i \(-0.379078\pi\)
0.370816 + 0.928706i \(0.379078\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −572056. −0.0721554
\(576\) 0 0
\(577\) 5.46520e6 0.683387 0.341693 0.939811i \(-0.389000\pi\)
0.341693 + 0.939811i \(0.389000\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.17218e6 0.144063
\(582\) 0 0
\(583\) −3.48528e6 −0.424684
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.89386e6 1.18514 0.592571 0.805518i \(-0.298113\pi\)
0.592571 + 0.805518i \(0.298113\pi\)
\(588\) 0 0
\(589\) −5.06804e6 −0.601938
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −6.12686e6 −0.715486 −0.357743 0.933820i \(-0.616454\pi\)
−0.357743 + 0.933820i \(0.616454\pi\)
\(594\) 0 0
\(595\) 204232. 0.0236500
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 299432. 0.0340982 0.0170491 0.999855i \(-0.494573\pi\)
0.0170491 + 0.999855i \(0.494573\pi\)
\(600\) 0 0
\(601\) −4.98133e6 −0.562548 −0.281274 0.959628i \(-0.590757\pi\)
−0.281274 + 0.959628i \(0.590757\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 413804. 0.0459628
\(606\) 0 0
\(607\) 1.10694e7 1.21942 0.609709 0.792625i \(-0.291286\pi\)
0.609709 + 0.792625i \(0.291286\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.09130e7 −1.18261
\(612\) 0 0
\(613\) −1.37829e7 −1.48146 −0.740729 0.671804i \(-0.765520\pi\)
−0.740729 + 0.671804i \(0.765520\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.11450e7 −1.17861 −0.589303 0.807912i \(-0.700597\pi\)
−0.589303 + 0.807912i \(0.700597\pi\)
\(618\) 0 0
\(619\) 3.00722e6 0.315456 0.157728 0.987483i \(-0.449583\pi\)
0.157728 + 0.987483i \(0.449583\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.94203e6 0.716582
\(624\) 0 0
\(625\) 9.61588e6 0.984666
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −6.30827e6 −0.635746
\(630\) 0 0
\(631\) 570304. 0.0570208 0.0285104 0.999593i \(-0.490924\pi\)
0.0285104 + 0.999593i \(0.490924\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −14368.0 −0.00141404
\(636\) 0 0
\(637\) −1.78634e6 −0.174428
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.37359e7 −1.32042 −0.660212 0.751080i \(-0.729533\pi\)
−0.660212 + 0.751080i \(0.729533\pi\)
\(642\) 0 0
\(643\) −2.58692e6 −0.246749 −0.123375 0.992360i \(-0.539372\pi\)
−0.123375 + 0.992360i \(0.539372\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6.52446e6 0.612751 0.306375 0.951911i \(-0.400884\pi\)
0.306375 + 0.951911i \(0.400884\pi\)
\(648\) 0 0
\(649\) 3.20688e6 0.298862
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.75793e6 −0.344878 −0.172439 0.985020i \(-0.555165\pi\)
−0.172439 + 0.985020i \(0.555165\pi\)
\(654\) 0 0
\(655\) −1.45814e6 −0.132799
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −6.97436e6 −0.625591 −0.312796 0.949820i \(-0.601266\pi\)
−0.312796 + 0.949820i \(0.601266\pi\)
\(660\) 0 0
\(661\) 1.17059e7 1.04208 0.521042 0.853531i \(-0.325543\pi\)
0.521042 + 0.853531i \(0.325543\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 193256. 0.0169465
\(666\) 0 0
\(667\) 135056. 0.0117544
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.32224e6 −0.199114
\(672\) 0 0
\(673\) −1.82825e7 −1.55596 −0.777980 0.628289i \(-0.783755\pi\)
−0.777980 + 0.628289i \(0.783755\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −2.05661e6 −0.172457 −0.0862283 0.996275i \(-0.527481\pi\)
−0.0862283 + 0.996275i \(0.527481\pi\)
\(678\) 0 0
\(679\) −4.89912e6 −0.407796
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.24913e7 1.02461 0.512303 0.858805i \(-0.328792\pi\)
0.512303 + 0.858805i \(0.328792\pi\)
\(684\) 0 0
\(685\) −308984. −0.0251599
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.08044e7 −0.867064
\(690\) 0 0
\(691\) −176630. −0.0140724 −0.00703622 0.999975i \(-0.502240\pi\)
−0.00703622 + 0.999975i \(0.502240\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −490968. −0.0385559
\(696\) 0 0
\(697\) −7.91712e6 −0.617284
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −4.03111e6 −0.309835 −0.154917 0.987927i \(-0.549511\pi\)
−0.154917 + 0.987927i \(0.549511\pi\)
\(702\) 0 0
\(703\) −5.96924e6 −0.455545
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.32552e6 −0.400694
\(708\) 0 0
\(709\) 1.41839e7 1.05969 0.529847 0.848093i \(-0.322249\pi\)
0.529847 + 0.848093i \(0.322249\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −945760. −0.0696718
\(714\) 0 0
\(715\) −714240. −0.0522491
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −2.46272e7 −1.77661 −0.888306 0.459253i \(-0.848117\pi\)
−0.888306 + 0.459253i \(0.848117\pi\)
\(720\) 0 0
\(721\) 4.28240e6 0.306796
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.28201e6 −0.161240
\(726\) 0 0
\(727\) 1.30482e7 0.915615 0.457808 0.889051i \(-0.348635\pi\)
0.457808 + 0.889051i \(0.348635\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.35627e7 −0.938754
\(732\) 0 0
\(733\) −2.08870e7 −1.43587 −0.717936 0.696109i \(-0.754913\pi\)
−0.717936 + 0.696109i \(0.754913\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.49098e7 −1.01112
\(738\) 0 0
\(739\) 1.47615e7 0.994303 0.497151 0.867664i \(-0.334379\pi\)
0.497151 + 0.867664i \(0.334379\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −4.44570e6 −0.295439 −0.147719 0.989029i \(-0.547193\pi\)
−0.147719 + 0.989029i \(0.547193\pi\)
\(744\) 0 0
\(745\) −1.87694e6 −0.123896
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.52271e6 −0.229442
\(750\) 0 0
\(751\) −1.19094e7 −0.770528 −0.385264 0.922806i \(-0.625890\pi\)
−0.385264 + 0.922806i \(0.625890\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.64634e6 −0.105112
\(756\) 0 0
\(757\) −2.55035e7 −1.61756 −0.808781 0.588110i \(-0.799872\pi\)
−0.808781 + 0.588110i \(0.799872\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.46925e7 0.919675 0.459837 0.888003i \(-0.347908\pi\)
0.459837 + 0.888003i \(0.347908\pi\)
\(762\) 0 0
\(763\) 5.79013e6 0.360062
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.94133e6 0.610177
\(768\) 0 0
\(769\) −1.92779e7 −1.17556 −0.587780 0.809021i \(-0.699998\pi\)
−0.587780 + 0.809021i \(0.699998\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 8.56584e6 0.515610 0.257805 0.966197i \(-0.417001\pi\)
0.257805 + 0.966197i \(0.417001\pi\)
\(774\) 0 0
\(775\) 1.59803e7 0.955718
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.49163e6 −0.442316
\(780\) 0 0
\(781\) 506880. 0.0297357
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.29853e6 0.133130
\(786\) 0 0
\(787\) −1.89027e7 −1.08789 −0.543947 0.839119i \(-0.683071\pi\)
−0.543947 + 0.839119i \(0.683071\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.23859e7 0.703862
\(792\) 0 0
\(793\) −7.19894e6 −0.406524
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.71259e7 0.955010 0.477505 0.878629i \(-0.341541\pi\)
0.477505 + 0.878629i \(0.341541\pi\)
\(798\) 0 0
\(799\) 1.52841e7 0.846977
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 6.93840e6 0.379726
\(804\) 0 0
\(805\) 36064.0 0.00196148
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.84511e7 −1.52837 −0.764185 0.644997i \(-0.776858\pi\)
−0.764185 + 0.644997i \(0.776858\pi\)
\(810\) 0 0
\(811\) −6.55604e6 −0.350017 −0.175009 0.984567i \(-0.555995\pi\)
−0.175009 + 0.984567i \(0.555995\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.05882e6 −0.0558376
\(816\) 0 0
\(817\) −1.28338e7 −0.672666
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 3.14356e6 0.162766 0.0813831 0.996683i \(-0.474066\pi\)
0.0813831 + 0.996683i \(0.474066\pi\)
\(822\) 0 0
\(823\) −1.62191e7 −0.834694 −0.417347 0.908747i \(-0.637040\pi\)
−0.417347 + 0.908747i \(0.637040\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −4.74707e6 −0.241358 −0.120679 0.992692i \(-0.538507\pi\)
−0.120679 + 0.992692i \(0.538507\pi\)
\(828\) 0 0
\(829\) 3.47333e7 1.75533 0.877666 0.479272i \(-0.159099\pi\)
0.877666 + 0.479272i \(0.159099\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.50184e6 0.124924
\(834\) 0 0
\(835\) −1.37342e6 −0.0681692
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −6.10552e6 −0.299445 −0.149723 0.988728i \(-0.547838\pi\)
−0.149723 + 0.988728i \(0.547838\pi\)
\(840\) 0 0
\(841\) −1.99724e7 −0.973734
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −728972. −0.0351212
\(846\) 0 0
\(847\) 5.06910e6 0.242785
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.11394e6 −0.0527274
\(852\) 0 0
\(853\) 2.75613e7 1.29696 0.648481 0.761231i \(-0.275405\pi\)
0.648481 + 0.761231i \(0.275405\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.82100e7 0.846950 0.423475 0.905908i \(-0.360810\pi\)
0.423475 + 0.905908i \(0.360810\pi\)
\(858\) 0 0
\(859\) −3.35920e7 −1.55329 −0.776647 0.629936i \(-0.783081\pi\)
−0.776647 + 0.629936i \(0.783081\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.26084e7 1.49040 0.745199 0.666843i \(-0.232355\pi\)
0.745199 + 0.666843i \(0.232355\pi\)
\(864\) 0 0
\(865\) −1.21318e6 −0.0551298
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.44243e7 −1.09717
\(870\) 0 0
\(871\) −4.62203e7 −2.06437
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.22186e6 −0.0539514
\(876\) 0 0
\(877\) 1.33352e7 0.585463 0.292732 0.956195i \(-0.405436\pi\)
0.292732 + 0.956195i \(0.405436\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.43194e7 −0.621564 −0.310782 0.950481i \(-0.600591\pi\)
−0.310782 + 0.950481i \(0.600591\pi\)
\(882\) 0 0
\(883\) −4.01556e6 −0.173318 −0.0866592 0.996238i \(-0.527619\pi\)
−0.0866592 + 0.996238i \(0.527619\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4.29049e7 −1.83104 −0.915520 0.402272i \(-0.868221\pi\)
−0.915520 + 0.402272i \(0.868221\pi\)
\(888\) 0 0
\(889\) −176008. −0.00746927
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.44626e7 0.606903
\(894\) 0 0
\(895\) 1.45102e6 0.0605504
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −3.77276e6 −0.155690
\(900\) 0 0
\(901\) 1.51319e7 0.620987
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 586240. 0.0237933
\(906\) 0 0
\(907\) 3.04706e7 1.22988 0.614940 0.788574i \(-0.289180\pi\)
0.614940 + 0.788574i \(0.289180\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.75748e7 −1.10082 −0.550411 0.834894i \(-0.685529\pi\)
−0.550411 + 0.834894i \(0.685529\pi\)
\(912\) 0 0
\(913\) 5.74128e6 0.227946
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.78622e7 −0.701473
\(918\) 0 0
\(919\) −3.33346e7 −1.30199 −0.650993 0.759084i \(-0.725647\pi\)
−0.650993 + 0.759084i \(0.725647\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.57133e6 0.0607103
\(924\) 0 0
\(925\) 1.88219e7 0.723284
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.08624e7 −0.793096 −0.396548 0.918014i \(-0.629792\pi\)
−0.396548 + 0.918014i \(0.629792\pi\)
\(930\) 0 0
\(931\) 2.36739e6 0.0895148
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.00032e6 0.0374205
\(936\) 0 0
\(937\) −1.66618e7 −0.619975 −0.309987 0.950741i \(-0.600325\pi\)
−0.309987 + 0.950741i \(0.600325\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 3.36202e7 1.23773 0.618865 0.785497i \(-0.287593\pi\)
0.618865 + 0.785497i \(0.287593\pi\)
\(942\) 0 0
\(943\) −1.39803e6 −0.0511962
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.25335e7 −1.54119 −0.770595 0.637325i \(-0.780041\pi\)
−0.770595 + 0.637325i \(0.780041\pi\)
\(948\) 0 0
\(949\) 2.15090e7 0.775274
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −3.20613e7 −1.14353 −0.571767 0.820416i \(-0.693742\pi\)
−0.571767 + 0.820416i \(0.693742\pi\)
\(954\) 0 0
\(955\) −2.21014e6 −0.0784173
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −3.78505e6 −0.132900
\(960\) 0 0
\(961\) −2.20955e6 −0.0771784
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −1.22143e6 −0.0422232
\(966\) 0 0
\(967\) 5.65115e7 1.94344 0.971719 0.236139i \(-0.0758819\pi\)
0.971719 + 0.236139i \(0.0758819\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.41580e7 1.50301 0.751504 0.659729i \(-0.229329\pi\)
0.751504 + 0.659729i \(0.229329\pi\)
\(972\) 0 0
\(973\) −6.01436e6 −0.203661
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.69053e7 0.901782 0.450891 0.892579i \(-0.351106\pi\)
0.450891 + 0.892579i \(0.351106\pi\)
\(978\) 0 0
\(979\) 3.40018e7 1.13382
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 8.68688e6 0.286735 0.143367 0.989670i \(-0.454207\pi\)
0.143367 + 0.989670i \(0.454207\pi\)
\(984\) 0 0
\(985\) 2.97535e6 0.0977120
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −2.39494e6 −0.0778582
\(990\) 0 0
\(991\) 1.54909e7 0.501063 0.250532 0.968108i \(-0.419395\pi\)
0.250532 + 0.968108i \(0.419395\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.14488e6 0.0366608
\(996\) 0 0
\(997\) −4.47588e6 −0.142607 −0.0713034 0.997455i \(-0.522716\pi\)
−0.0713034 + 0.997455i \(0.522716\pi\)
\(998\) 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.p.1.1 1
3.2 odd 2 112.6.a.f.1.1 1
4.3 odd 2 504.6.a.e.1.1 1
12.11 even 2 56.6.a.a.1.1 1
21.20 even 2 784.6.a.e.1.1 1
24.5 odd 2 448.6.a.g.1.1 1
24.11 even 2 448.6.a.j.1.1 1
84.11 even 6 392.6.i.d.177.1 2
84.23 even 6 392.6.i.d.361.1 2
84.47 odd 6 392.6.i.c.361.1 2
84.59 odd 6 392.6.i.c.177.1 2
84.83 odd 2 392.6.a.c.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.6.a.a.1.1 1 12.11 even 2
112.6.a.f.1.1 1 3.2 odd 2
392.6.a.c.1.1 1 84.83 odd 2
392.6.i.c.177.1 2 84.59 odd 6
392.6.i.c.361.1 2 84.47 odd 6
392.6.i.d.177.1 2 84.11 even 6
392.6.i.d.361.1 2 84.23 even 6
448.6.a.g.1.1 1 24.5 odd 2
448.6.a.j.1.1 1 24.11 even 2
504.6.a.e.1.1 1 4.3 odd 2
784.6.a.e.1.1 1 21.20 even 2
1008.6.a.p.1.1 1 1.1 even 1 trivial