Properties

Label 1008.6.a.k.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
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)
 
\(f(q)\) \(=\) \(q-24.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q-24.0000 q^{5} -49.0000 q^{7} +66.0000 q^{11} +98.0000 q^{13} +216.000 q^{17} +340.000 q^{19} -1038.00 q^{23} -2549.00 q^{25} +2490.00 q^{29} +7048.00 q^{31} +1176.00 q^{35} -12238.0 q^{37} -6468.00 q^{41} +15412.0 q^{43} +20604.0 q^{47} +2401.00 q^{49} -32490.0 q^{53} -1584.00 q^{55} +34224.0 q^{59} +35654.0 q^{61} -2352.00 q^{65} -12680.0 q^{67} -42642.0 q^{71} +33734.0 q^{73} -3234.00 q^{77} +85108.0 q^{79} -106764. q^{83} -5184.00 q^{85} -34884.0 q^{89} -4802.00 q^{91} -8160.00 q^{95} +18662.0 q^{97} +O(q^{100})\)

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
\(5\) −24.0000 −0.429325 −0.214663 0.976688i \(-0.568865\pi\)
−0.214663 + 0.976688i \(0.568865\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 66.0000 0.164461 0.0822304 0.996613i \(-0.473796\pi\)
0.0822304 + 0.996613i \(0.473796\pi\)
\(12\) 0 0
\(13\) 98.0000 0.160830 0.0804151 0.996761i \(-0.474375\pi\)
0.0804151 + 0.996761i \(0.474375\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 216.000 0.181272 0.0906362 0.995884i \(-0.471110\pi\)
0.0906362 + 0.995884i \(0.471110\pi\)
\(18\) 0 0
\(19\) 340.000 0.216070 0.108035 0.994147i \(-0.465544\pi\)
0.108035 + 0.994147i \(0.465544\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1038.00 −0.409145 −0.204573 0.978851i \(-0.565580\pi\)
−0.204573 + 0.978851i \(0.565580\pi\)
\(24\) 0 0
\(25\) −2549.00 −0.815680
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 2490.00 0.549800 0.274900 0.961473i \(-0.411355\pi\)
0.274900 + 0.961473i \(0.411355\pi\)
\(30\) 0 0
\(31\) 7048.00 1.31723 0.658615 0.752480i \(-0.271143\pi\)
0.658615 + 0.752480i \(0.271143\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1176.00 0.162270
\(36\) 0 0
\(37\) −12238.0 −1.46962 −0.734812 0.678271i \(-0.762730\pi\)
−0.734812 + 0.678271i \(0.762730\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6468.00 −0.600911 −0.300456 0.953796i \(-0.597139\pi\)
−0.300456 + 0.953796i \(0.597139\pi\)
\(42\) 0 0
\(43\) 15412.0 1.27112 0.635562 0.772050i \(-0.280768\pi\)
0.635562 + 0.772050i \(0.280768\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 20604.0 1.36053 0.680263 0.732968i \(-0.261866\pi\)
0.680263 + 0.732968i \(0.261866\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −32490.0 −1.58877 −0.794383 0.607417i \(-0.792206\pi\)
−0.794383 + 0.607417i \(0.792206\pi\)
\(54\) 0 0
\(55\) −1584.00 −0.0706071
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 34224.0 1.27997 0.639986 0.768386i \(-0.278940\pi\)
0.639986 + 0.768386i \(0.278940\pi\)
\(60\) 0 0
\(61\) 35654.0 1.22683 0.613414 0.789762i \(-0.289796\pi\)
0.613414 + 0.789762i \(0.289796\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −2352.00 −0.0690484
\(66\) 0 0
\(67\) −12680.0 −0.345090 −0.172545 0.985002i \(-0.555199\pi\)
−0.172545 + 0.985002i \(0.555199\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −42642.0 −1.00390 −0.501951 0.864896i \(-0.667384\pi\)
−0.501951 + 0.864896i \(0.667384\pi\)
\(72\) 0 0
\(73\) 33734.0 0.740902 0.370451 0.928852i \(-0.379203\pi\)
0.370451 + 0.928852i \(0.379203\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3234.00 −0.0621603
\(78\) 0 0
\(79\) 85108.0 1.53427 0.767137 0.641484i \(-0.221681\pi\)
0.767137 + 0.641484i \(0.221681\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −106764. −1.70110 −0.850550 0.525895i \(-0.823730\pi\)
−0.850550 + 0.525895i \(0.823730\pi\)
\(84\) 0 0
\(85\) −5184.00 −0.0778247
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −34884.0 −0.466822 −0.233411 0.972378i \(-0.574989\pi\)
−0.233411 + 0.972378i \(0.574989\pi\)
\(90\) 0 0
\(91\) −4802.00 −0.0607881
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −8160.00 −0.0927644
\(96\) 0 0
\(97\) 18662.0 0.201386 0.100693 0.994918i \(-0.467894\pi\)
0.100693 + 0.994918i \(0.467894\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −153084. −1.49323 −0.746614 0.665257i \(-0.768322\pi\)
−0.746614 + 0.665257i \(0.768322\pi\)
\(102\) 0 0
\(103\) −35864.0 −0.333093 −0.166547 0.986034i \(-0.553262\pi\)
−0.166547 + 0.986034i \(0.553262\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −95454.0 −0.805999 −0.403000 0.915200i \(-0.632032\pi\)
−0.403000 + 0.915200i \(0.632032\pi\)
\(108\) 0 0
\(109\) 212222. 1.71090 0.855449 0.517887i \(-0.173281\pi\)
0.855449 + 0.517887i \(0.173281\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −62106.0 −0.457549 −0.228774 0.973479i \(-0.573472\pi\)
−0.228774 + 0.973479i \(0.573472\pi\)
\(114\) 0 0
\(115\) 24912.0 0.175656
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10584.0 −0.0685145
\(120\) 0 0
\(121\) −156695. −0.972953
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 136176. 0.779517
\(126\) 0 0
\(127\) 53044.0 0.291828 0.145914 0.989297i \(-0.453388\pi\)
0.145914 + 0.989297i \(0.453388\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 69324.0 0.352944 0.176472 0.984306i \(-0.443532\pi\)
0.176472 + 0.984306i \(0.443532\pi\)
\(132\) 0 0
\(133\) −16660.0 −0.0816669
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −129846. −0.591054 −0.295527 0.955334i \(-0.595495\pi\)
−0.295527 + 0.955334i \(0.595495\pi\)
\(138\) 0 0
\(139\) 104356. 0.458121 0.229061 0.973412i \(-0.426435\pi\)
0.229061 + 0.973412i \(0.426435\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6468.00 0.0264503
\(144\) 0 0
\(145\) −59760.0 −0.236043
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −217194. −0.801461 −0.400730 0.916196i \(-0.631244\pi\)
−0.400730 + 0.916196i \(0.631244\pi\)
\(150\) 0 0
\(151\) −221000. −0.788769 −0.394385 0.918945i \(-0.629042\pi\)
−0.394385 + 0.918945i \(0.629042\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −169152. −0.565520
\(156\) 0 0
\(157\) −378370. −1.22509 −0.612544 0.790436i \(-0.709854\pi\)
−0.612544 + 0.790436i \(0.709854\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 50862.0 0.154642
\(162\) 0 0
\(163\) −104816. −0.309000 −0.154500 0.987993i \(-0.549377\pi\)
−0.154500 + 0.987993i \(0.549377\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −426972. −1.18470 −0.592350 0.805681i \(-0.701800\pi\)
−0.592350 + 0.805681i \(0.701800\pi\)
\(168\) 0 0
\(169\) −361689. −0.974134
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −331068. −0.841012 −0.420506 0.907290i \(-0.638147\pi\)
−0.420506 + 0.907290i \(0.638147\pi\)
\(174\) 0 0
\(175\) 124901. 0.308298
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −400194. −0.933551 −0.466775 0.884376i \(-0.654584\pi\)
−0.466775 + 0.884376i \(0.654584\pi\)
\(180\) 0 0
\(181\) 588098. 1.33430 0.667150 0.744924i \(-0.267514\pi\)
0.667150 + 0.744924i \(0.267514\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 293712. 0.630946
\(186\) 0 0
\(187\) 14256.0 0.0298122
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 939342. 1.86312 0.931559 0.363590i \(-0.118449\pi\)
0.931559 + 0.363590i \(0.118449\pi\)
\(192\) 0 0
\(193\) 338390. 0.653919 0.326960 0.945038i \(-0.393976\pi\)
0.326960 + 0.945038i \(0.393976\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 237942. 0.436823 0.218412 0.975857i \(-0.429912\pi\)
0.218412 + 0.975857i \(0.429912\pi\)
\(198\) 0 0
\(199\) −204464. −0.366003 −0.183001 0.983113i \(-0.558581\pi\)
−0.183001 + 0.983113i \(0.558581\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −122010. −0.207805
\(204\) 0 0
\(205\) 155232. 0.257986
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 22440.0 0.0355351
\(210\) 0 0
\(211\) 348724. 0.539232 0.269616 0.962968i \(-0.413103\pi\)
0.269616 + 0.962968i \(0.413103\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −369888. −0.545725
\(216\) 0 0
\(217\) −345352. −0.497866
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 21168.0 0.0291541
\(222\) 0 0
\(223\) −1.47006e6 −1.97957 −0.989787 0.142554i \(-0.954468\pi\)
−0.989787 + 0.142554i \(0.954468\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −589560. −0.759387 −0.379694 0.925112i \(-0.623971\pi\)
−0.379694 + 0.925112i \(0.623971\pi\)
\(228\) 0 0
\(229\) −1.04534e6 −1.31725 −0.658627 0.752469i \(-0.728863\pi\)
−0.658627 + 0.752469i \(0.728863\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −651222. −0.785849 −0.392925 0.919571i \(-0.628537\pi\)
−0.392925 + 0.919571i \(0.628537\pi\)
\(234\) 0 0
\(235\) −494496. −0.584108
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −513462. −0.581452 −0.290726 0.956806i \(-0.593897\pi\)
−0.290726 + 0.956806i \(0.593897\pi\)
\(240\) 0 0
\(241\) −694714. −0.770484 −0.385242 0.922816i \(-0.625882\pi\)
−0.385242 + 0.922816i \(0.625882\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −57624.0 −0.0613322
\(246\) 0 0
\(247\) 33320.0 0.0347506
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.39608e6 −1.39870 −0.699352 0.714777i \(-0.746528\pi\)
−0.699352 + 0.714777i \(0.746528\pi\)
\(252\) 0 0
\(253\) −68508.0 −0.0672884
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.00520e6 0.949339 0.474670 0.880164i \(-0.342568\pi\)
0.474670 + 0.880164i \(0.342568\pi\)
\(258\) 0 0
\(259\) 599662. 0.555466
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.25301e6 1.11703 0.558515 0.829494i \(-0.311371\pi\)
0.558515 + 0.829494i \(0.311371\pi\)
\(264\) 0 0
\(265\) 779760. 0.682097
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.76069e6 1.48355 0.741774 0.670650i \(-0.233985\pi\)
0.741774 + 0.670650i \(0.233985\pi\)
\(270\) 0 0
\(271\) −770528. −0.637331 −0.318666 0.947867i \(-0.603235\pi\)
−0.318666 + 0.947867i \(0.603235\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −168234. −0.134147
\(276\) 0 0
\(277\) 707738. 0.554208 0.277104 0.960840i \(-0.410625\pi\)
0.277104 + 0.960840i \(0.410625\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −2.30432e6 −1.74091 −0.870456 0.492247i \(-0.836176\pi\)
−0.870456 + 0.492247i \(0.836176\pi\)
\(282\) 0 0
\(283\) −1.60903e6 −1.19426 −0.597128 0.802146i \(-0.703692\pi\)
−0.597128 + 0.802146i \(0.703692\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 316932. 0.227123
\(288\) 0 0
\(289\) −1.37320e6 −0.967140
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −517020. −0.351834 −0.175917 0.984405i \(-0.556289\pi\)
−0.175917 + 0.984405i \(0.556289\pi\)
\(294\) 0 0
\(295\) −821376. −0.549524
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −101724. −0.0658030
\(300\) 0 0
\(301\) −755188. −0.480440
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −855696. −0.526708
\(306\) 0 0
\(307\) −1.35002e6 −0.817512 −0.408756 0.912644i \(-0.634037\pi\)
−0.408756 + 0.912644i \(0.634037\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.34538e6 0.788758 0.394379 0.918948i \(-0.370960\pi\)
0.394379 + 0.918948i \(0.370960\pi\)
\(312\) 0 0
\(313\) 256154. 0.147788 0.0738942 0.997266i \(-0.476457\pi\)
0.0738942 + 0.997266i \(0.476457\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.84629e6 −1.03193 −0.515967 0.856609i \(-0.672567\pi\)
−0.515967 + 0.856609i \(0.672567\pi\)
\(318\) 0 0
\(319\) 164340. 0.0904204
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 73440.0 0.0391675
\(324\) 0 0
\(325\) −249802. −0.131186
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.00960e6 −0.514231
\(330\) 0 0
\(331\) 3.33238e6 1.67180 0.835900 0.548881i \(-0.184946\pi\)
0.835900 + 0.548881i \(0.184946\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 304320. 0.148156
\(336\) 0 0
\(337\) −1.63481e6 −0.784136 −0.392068 0.919936i \(-0.628240\pi\)
−0.392068 + 0.919936i \(0.628240\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 465168. 0.216633
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −841530. −0.375185 −0.187593 0.982247i \(-0.560068\pi\)
−0.187593 + 0.982247i \(0.560068\pi\)
\(348\) 0 0
\(349\) −977242. −0.429476 −0.214738 0.976672i \(-0.568890\pi\)
−0.214738 + 0.976672i \(0.568890\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.45857e6 −1.47727 −0.738634 0.674106i \(-0.764529\pi\)
−0.738634 + 0.674106i \(0.764529\pi\)
\(354\) 0 0
\(355\) 1.02341e6 0.431001
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.47301e6 −1.42223 −0.711115 0.703076i \(-0.751810\pi\)
−0.711115 + 0.703076i \(0.751810\pi\)
\(360\) 0 0
\(361\) −2.36050e6 −0.953314
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −809616. −0.318088
\(366\) 0 0
\(367\) −3.11994e6 −1.20915 −0.604575 0.796548i \(-0.706657\pi\)
−0.604575 + 0.796548i \(0.706657\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.59201e6 0.600497
\(372\) 0 0
\(373\) −2.01673e6 −0.750543 −0.375272 0.926915i \(-0.622451\pi\)
−0.375272 + 0.926915i \(0.622451\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 244020. 0.0884244
\(378\) 0 0
\(379\) 5.38083e6 1.92420 0.962102 0.272690i \(-0.0879134\pi\)
0.962102 + 0.272690i \(0.0879134\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 807432. 0.281261 0.140630 0.990062i \(-0.455087\pi\)
0.140630 + 0.990062i \(0.455087\pi\)
\(384\) 0 0
\(385\) 77616.0 0.0266870
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −891390. −0.298671 −0.149336 0.988787i \(-0.547714\pi\)
−0.149336 + 0.988787i \(0.547714\pi\)
\(390\) 0 0
\(391\) −224208. −0.0741667
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.04259e6 −0.658702
\(396\) 0 0
\(397\) 1.12345e6 0.357749 0.178875 0.983872i \(-0.442754\pi\)
0.178875 + 0.983872i \(0.442754\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.72037e6 −0.534271 −0.267136 0.963659i \(-0.586077\pi\)
−0.267136 + 0.963659i \(0.586077\pi\)
\(402\) 0 0
\(403\) 690704. 0.211850
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −807708. −0.241695
\(408\) 0 0
\(409\) 77246.0 0.0228332 0.0114166 0.999935i \(-0.496366\pi\)
0.0114166 + 0.999935i \(0.496366\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.67698e6 −0.483784
\(414\) 0 0
\(415\) 2.56234e6 0.730324
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.20615e6 −1.44871 −0.724356 0.689427i \(-0.757863\pi\)
−0.724356 + 0.689427i \(0.757863\pi\)
\(420\) 0 0
\(421\) 1.71847e6 0.472539 0.236270 0.971688i \(-0.424075\pi\)
0.236270 + 0.971688i \(0.424075\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −550584. −0.147860
\(426\) 0 0
\(427\) −1.74705e6 −0.463697
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −580626. −0.150558 −0.0752789 0.997163i \(-0.523985\pi\)
−0.0752789 + 0.997163i \(0.523985\pi\)
\(432\) 0 0
\(433\) 4.15087e6 1.06395 0.531973 0.846761i \(-0.321451\pi\)
0.531973 + 0.846761i \(0.321451\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −352920. −0.0884042
\(438\) 0 0
\(439\) −3.88407e6 −0.961891 −0.480946 0.876750i \(-0.659707\pi\)
−0.480946 + 0.876750i \(0.659707\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.31499e6 −0.560453 −0.280226 0.959934i \(-0.590410\pi\)
−0.280226 + 0.959934i \(0.590410\pi\)
\(444\) 0 0
\(445\) 837216. 0.200418
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.92281e6 0.450113 0.225056 0.974346i \(-0.427743\pi\)
0.225056 + 0.974346i \(0.427743\pi\)
\(450\) 0 0
\(451\) −426888. −0.0988263
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 115248. 0.0260979
\(456\) 0 0
\(457\) 6.86215e6 1.53699 0.768493 0.639858i \(-0.221007\pi\)
0.768493 + 0.639858i \(0.221007\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.97167e6 −0.651250 −0.325625 0.945499i \(-0.605575\pi\)
−0.325625 + 0.945499i \(0.605575\pi\)
\(462\) 0 0
\(463\) −4.87423e6 −1.05670 −0.528352 0.849025i \(-0.677190\pi\)
−0.528352 + 0.849025i \(0.677190\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.17301e6 −1.73416 −0.867081 0.498167i \(-0.834007\pi\)
−0.867081 + 0.498167i \(0.834007\pi\)
\(468\) 0 0
\(469\) 621320. 0.130432
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.01719e6 0.209050
\(474\) 0 0
\(475\) −866660. −0.176244
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.34397e6 0.466782 0.233391 0.972383i \(-0.425018\pi\)
0.233391 + 0.972383i \(0.425018\pi\)
\(480\) 0 0
\(481\) −1.19932e6 −0.236360
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −447888. −0.0864600
\(486\) 0 0
\(487\) −316928. −0.0605534 −0.0302767 0.999542i \(-0.509639\pi\)
−0.0302767 + 0.999542i \(0.509639\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.20041e6 −0.973495 −0.486748 0.873543i \(-0.661817\pi\)
−0.486748 + 0.873543i \(0.661817\pi\)
\(492\) 0 0
\(493\) 537840. 0.0996634
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.08946e6 0.379440
\(498\) 0 0
\(499\) 4.86773e6 0.875135 0.437568 0.899185i \(-0.355840\pi\)
0.437568 + 0.899185i \(0.355840\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 426888. 0.0752305 0.0376153 0.999292i \(-0.488024\pi\)
0.0376153 + 0.999292i \(0.488024\pi\)
\(504\) 0 0
\(505\) 3.67402e6 0.641081
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 9.41621e6 1.61095 0.805474 0.592631i \(-0.201911\pi\)
0.805474 + 0.592631i \(0.201911\pi\)
\(510\) 0 0
\(511\) −1.65297e6 −0.280035
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 860736. 0.143005
\(516\) 0 0
\(517\) 1.35986e6 0.223753
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −1.84039e6 −0.297041 −0.148520 0.988909i \(-0.547451\pi\)
−0.148520 + 0.988909i \(0.547451\pi\)
\(522\) 0 0
\(523\) 979108. 0.156522 0.0782612 0.996933i \(-0.475063\pi\)
0.0782612 + 0.996933i \(0.475063\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.52237e6 0.238777
\(528\) 0 0
\(529\) −5.35890e6 −0.832600
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −633864. −0.0966447
\(534\) 0 0
\(535\) 2.29090e6 0.346036
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 158466. 0.0234944
\(540\) 0 0
\(541\) 5.96117e6 0.875666 0.437833 0.899056i \(-0.355746\pi\)
0.437833 + 0.899056i \(0.355746\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.09333e6 −0.734531
\(546\) 0 0
\(547\) −8.73025e6 −1.24755 −0.623775 0.781604i \(-0.714402\pi\)
−0.623775 + 0.781604i \(0.714402\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 846600. 0.118795
\(552\) 0 0
\(553\) −4.17029e6 −0.579901
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.01066e6 0.411172 0.205586 0.978639i \(-0.434090\pi\)
0.205586 + 0.978639i \(0.434090\pi\)
\(558\) 0 0
\(559\) 1.51038e6 0.204435
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.17573e7 1.56327 0.781637 0.623733i \(-0.214385\pi\)
0.781637 + 0.623733i \(0.214385\pi\)
\(564\) 0 0
\(565\) 1.49054e6 0.196437
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.31578e7 −1.70374 −0.851870 0.523754i \(-0.824531\pi\)
−0.851870 + 0.523754i \(0.824531\pi\)
\(570\) 0 0
\(571\) 1.03344e7 1.32647 0.663234 0.748412i \(-0.269183\pi\)
0.663234 + 0.748412i \(0.269183\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.64586e6 0.333732
\(576\) 0 0
\(577\) −7.88133e6 −0.985508 −0.492754 0.870169i \(-0.664010\pi\)
−0.492754 + 0.870169i \(0.664010\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5.23144e6 0.642955
\(582\) 0 0
\(583\) −2.14434e6 −0.261290
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −554568. −0.0664293 −0.0332146 0.999448i \(-0.510574\pi\)
−0.0332146 + 0.999448i \(0.510574\pi\)
\(588\) 0 0
\(589\) 2.39632e6 0.284614
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9.20369e6 1.07479 0.537397 0.843329i \(-0.319408\pi\)
0.537397 + 0.843329i \(0.319408\pi\)
\(594\) 0 0
\(595\) 254016. 0.0294150
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8.54295e6 0.972839 0.486419 0.873725i \(-0.338303\pi\)
0.486419 + 0.873725i \(0.338303\pi\)
\(600\) 0 0
\(601\) −9.61555e6 −1.08590 −0.542948 0.839767i \(-0.682692\pi\)
−0.542948 + 0.839767i \(0.682692\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 3.76068e6 0.417713
\(606\) 0 0
\(607\) −2.21264e6 −0.243747 −0.121873 0.992546i \(-0.538890\pi\)
−0.121873 + 0.992546i \(0.538890\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.01919e6 0.218814
\(612\) 0 0
\(613\) −7.96215e6 −0.855814 −0.427907 0.903823i \(-0.640749\pi\)
−0.427907 + 0.903823i \(0.640749\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.37397e7 1.45299 0.726497 0.687170i \(-0.241147\pi\)
0.726497 + 0.687170i \(0.241147\pi\)
\(618\) 0 0
\(619\) 8.70113e6 0.912744 0.456372 0.889789i \(-0.349149\pi\)
0.456372 + 0.889789i \(0.349149\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.70932e6 0.176442
\(624\) 0 0
\(625\) 4.69740e6 0.481014
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −2.64341e6 −0.266402
\(630\) 0 0
\(631\) −445412. −0.0445337 −0.0222668 0.999752i \(-0.507088\pi\)
−0.0222668 + 0.999752i \(0.507088\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.27306e6 −0.125289
\(636\) 0 0
\(637\) 235298. 0.0229757
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.00119e6 0.769147 0.384573 0.923094i \(-0.374349\pi\)
0.384573 + 0.923094i \(0.374349\pi\)
\(642\) 0 0
\(643\) 1.58402e7 1.51090 0.755448 0.655209i \(-0.227419\pi\)
0.755448 + 0.655209i \(0.227419\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.30187e6 0.122266 0.0611331 0.998130i \(-0.480529\pi\)
0.0611331 + 0.998130i \(0.480529\pi\)
\(648\) 0 0
\(649\) 2.25878e6 0.210505
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.34149e6 −0.673753 −0.336877 0.941549i \(-0.609371\pi\)
−0.336877 + 0.941549i \(0.609371\pi\)
\(654\) 0 0
\(655\) −1.66378e6 −0.151528
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −6.18934e6 −0.555176 −0.277588 0.960700i \(-0.589535\pi\)
−0.277588 + 0.960700i \(0.589535\pi\)
\(660\) 0 0
\(661\) −1.96690e7 −1.75097 −0.875484 0.483248i \(-0.839457\pi\)
−0.875484 + 0.483248i \(0.839457\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 399840. 0.0350616
\(666\) 0 0
\(667\) −2.58462e6 −0.224948
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.35316e6 0.201765
\(672\) 0 0
\(673\) 7.18259e6 0.611285 0.305642 0.952146i \(-0.401129\pi\)
0.305642 + 0.952146i \(0.401129\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.89192e7 1.58647 0.793234 0.608917i \(-0.208396\pi\)
0.793234 + 0.608917i \(0.208396\pi\)
\(678\) 0 0
\(679\) −914438. −0.0761167
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.12204e7 1.74061 0.870306 0.492512i \(-0.163921\pi\)
0.870306 + 0.492512i \(0.163921\pi\)
\(684\) 0 0
\(685\) 3.11630e6 0.253754
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3.18402e6 −0.255522
\(690\) 0 0
\(691\) −1.63276e7 −1.30085 −0.650424 0.759571i \(-0.725409\pi\)
−0.650424 + 0.759571i \(0.725409\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.50454e6 −0.196683
\(696\) 0 0
\(697\) −1.39709e6 −0.108929
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 5.40470e6 0.415409 0.207705 0.978192i \(-0.433401\pi\)
0.207705 + 0.978192i \(0.433401\pi\)
\(702\) 0 0
\(703\) −4.16092e6 −0.317542
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 7.50112e6 0.564387
\(708\) 0 0
\(709\) 2.21195e7 1.65257 0.826284 0.563253i \(-0.190450\pi\)
0.826284 + 0.563253i \(0.190450\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −7.31582e6 −0.538939
\(714\) 0 0
\(715\) −155232. −0.0113558
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.55819e7 1.84548 0.922742 0.385418i \(-0.125943\pi\)
0.922742 + 0.385418i \(0.125943\pi\)
\(720\) 0 0
\(721\) 1.75734e6 0.125897
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −6.34701e6 −0.448460
\(726\) 0 0
\(727\) 9.29438e6 0.652205 0.326103 0.945334i \(-0.394265\pi\)
0.326103 + 0.945334i \(0.394265\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.32899e6 0.230420
\(732\) 0 0
\(733\) 3.40699e6 0.234213 0.117107 0.993119i \(-0.462638\pi\)
0.117107 + 0.993119i \(0.462638\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −836880. −0.0567537
\(738\) 0 0
\(739\) −2.18135e7 −1.46932 −0.734658 0.678438i \(-0.762657\pi\)
−0.734658 + 0.678438i \(0.762657\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.79246e6 0.252028 0.126014 0.992028i \(-0.459782\pi\)
0.126014 + 0.992028i \(0.459782\pi\)
\(744\) 0 0
\(745\) 5.21266e6 0.344087
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 4.67725e6 0.304639
\(750\) 0 0
\(751\) 2.01483e7 1.30358 0.651790 0.758400i \(-0.274018\pi\)
0.651790 + 0.758400i \(0.274018\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.30400e6 0.338638
\(756\) 0 0
\(757\) 1.18427e7 0.751126 0.375563 0.926797i \(-0.377449\pi\)
0.375563 + 0.926797i \(0.377449\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.97791e6 −0.186402 −0.0932008 0.995647i \(-0.529710\pi\)
−0.0932008 + 0.995647i \(0.529710\pi\)
\(762\) 0 0
\(763\) −1.03989e7 −0.646659
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 3.35395e6 0.205858
\(768\) 0 0
\(769\) −2.02441e7 −1.23447 −0.617237 0.786777i \(-0.711748\pi\)
−0.617237 + 0.786777i \(0.711748\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 7.37953e6 0.444202 0.222101 0.975024i \(-0.428709\pi\)
0.222101 + 0.975024i \(0.428709\pi\)
\(774\) 0 0
\(775\) −1.79654e7 −1.07444
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.19912e6 −0.129839
\(780\) 0 0
\(781\) −2.81437e6 −0.165103
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 9.08088e6 0.525961
\(786\) 0 0
\(787\) −1.36289e7 −0.784377 −0.392188 0.919885i \(-0.628282\pi\)
−0.392188 + 0.919885i \(0.628282\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 3.04319e6 0.172937
\(792\) 0 0
\(793\) 3.49409e6 0.197311
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 1.49548e7 0.833938 0.416969 0.908921i \(-0.363092\pi\)
0.416969 + 0.908921i \(0.363092\pi\)
\(798\) 0 0
\(799\) 4.45046e6 0.246626
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.22644e6 0.121849
\(804\) 0 0
\(805\) −1.22069e6 −0.0663919
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −2.87242e7 −1.54304 −0.771519 0.636206i \(-0.780503\pi\)
−0.771519 + 0.636206i \(0.780503\pi\)
\(810\) 0 0
\(811\) 1.52265e7 0.812922 0.406461 0.913668i \(-0.366763\pi\)
0.406461 + 0.913668i \(0.366763\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2.51558e6 0.132661
\(816\) 0 0
\(817\) 5.24008e6 0.274652
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 3.31001e7 1.71384 0.856921 0.515447i \(-0.172374\pi\)
0.856921 + 0.515447i \(0.172374\pi\)
\(822\) 0 0
\(823\) 1.35915e7 0.699470 0.349735 0.936849i \(-0.386272\pi\)
0.349735 + 0.936849i \(0.386272\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3.13936e6 0.159616 0.0798082 0.996810i \(-0.474569\pi\)
0.0798082 + 0.996810i \(0.474569\pi\)
\(828\) 0 0
\(829\) 1.27081e7 0.642234 0.321117 0.947040i \(-0.395942\pi\)
0.321117 + 0.947040i \(0.395942\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 518616. 0.0258960
\(834\) 0 0
\(835\) 1.02473e7 0.508621
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −2.98312e7 −1.46307 −0.731536 0.681803i \(-0.761196\pi\)
−0.731536 + 0.681803i \(0.761196\pi\)
\(840\) 0 0
\(841\) −1.43110e7 −0.697720
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.68054e6 0.418220
\(846\) 0 0
\(847\) 7.67806e6 0.367742
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 1.27030e7 0.601290
\(852\) 0 0
\(853\) −1.92215e7 −0.904515 −0.452257 0.891888i \(-0.649381\pi\)
−0.452257 + 0.891888i \(0.649381\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 2.65655e7 1.23556 0.617782 0.786349i \(-0.288031\pi\)
0.617782 + 0.786349i \(0.288031\pi\)
\(858\) 0 0
\(859\) 9.16844e6 0.423948 0.211974 0.977275i \(-0.432011\pi\)
0.211974 + 0.977275i \(0.432011\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.92196e7 −1.33551 −0.667755 0.744381i \(-0.732745\pi\)
−0.667755 + 0.744381i \(0.732745\pi\)
\(864\) 0 0
\(865\) 7.94563e6 0.361067
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 5.61713e6 0.252328
\(870\) 0 0
\(871\) −1.24264e6 −0.0555009
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −6.67262e6 −0.294630
\(876\) 0 0
\(877\) 9.71286e6 0.426430 0.213215 0.977005i \(-0.431606\pi\)
0.213215 + 0.977005i \(0.431606\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.65372e7 −0.717833 −0.358917 0.933370i \(-0.616854\pi\)
−0.358917 + 0.933370i \(0.616854\pi\)
\(882\) 0 0
\(883\) 2.39487e7 1.03367 0.516833 0.856086i \(-0.327111\pi\)
0.516833 + 0.856086i \(0.327111\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4.62846e6 −0.197527 −0.0987637 0.995111i \(-0.531489\pi\)
−0.0987637 + 0.995111i \(0.531489\pi\)
\(888\) 0 0
\(889\) −2.59916e6 −0.110301
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 7.00536e6 0.293969
\(894\) 0 0
\(895\) 9.60466e6 0.400797
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 1.75495e7 0.724212
\(900\) 0 0
\(901\) −7.01784e6 −0.287999
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.41144e7 −0.572848
\(906\) 0 0
\(907\) −2.06126e7 −0.831983 −0.415991 0.909369i \(-0.636565\pi\)
−0.415991 + 0.909369i \(0.636565\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −3.46749e6 −0.138427 −0.0692133 0.997602i \(-0.522049\pi\)
−0.0692133 + 0.997602i \(0.522049\pi\)
\(912\) 0 0
\(913\) −7.04642e6 −0.279764
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −3.39688e6 −0.133400
\(918\) 0 0
\(919\) 3.61227e7 1.41088 0.705442 0.708767i \(-0.250748\pi\)
0.705442 + 0.708767i \(0.250748\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −4.17892e6 −0.161458
\(924\) 0 0
\(925\) 3.11947e7 1.19874
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.29366e7 −0.491792 −0.245896 0.969296i \(-0.579082\pi\)
−0.245896 + 0.969296i \(0.579082\pi\)
\(930\) 0 0
\(931\) 816340. 0.0308672
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −342144. −0.0127991
\(936\) 0 0
\(937\) 5.01394e7 1.86565 0.932824 0.360332i \(-0.117336\pi\)
0.932824 + 0.360332i \(0.117336\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.05568e7 0.388651 0.194325 0.980937i \(-0.437748\pi\)
0.194325 + 0.980937i \(0.437748\pi\)
\(942\) 0 0
\(943\) 6.71378e6 0.245860
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −3.14684e6 −0.114025 −0.0570124 0.998373i \(-0.518157\pi\)
−0.0570124 + 0.998373i \(0.518157\pi\)
\(948\) 0 0
\(949\) 3.30593e6 0.119159
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −5.22829e7 −1.86478 −0.932389 0.361455i \(-0.882280\pi\)
−0.932389 + 0.361455i \(0.882280\pi\)
\(954\) 0 0
\(955\) −2.25442e7 −0.799883
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6.36245e6 0.223397
\(960\) 0 0
\(961\) 2.10452e7 0.735095
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −8.12136e6 −0.280744
\(966\) 0 0
\(967\) 2.48235e7 0.853682 0.426841 0.904327i \(-0.359626\pi\)
0.426841 + 0.904327i \(0.359626\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.33077e7 0.452956 0.226478 0.974016i \(-0.427279\pi\)
0.226478 + 0.974016i \(0.427279\pi\)
\(972\) 0 0
\(973\) −5.11344e6 −0.173154
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −8.17705e6 −0.274069 −0.137035 0.990566i \(-0.543757\pi\)
−0.137035 + 0.990566i \(0.543757\pi\)
\(978\) 0 0
\(979\) −2.30234e6 −0.0767739
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.32465e7 −0.437238 −0.218619 0.975810i \(-0.570155\pi\)
−0.218619 + 0.975810i \(0.570155\pi\)
\(984\) 0 0
\(985\) −5.71061e6 −0.187539
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.59977e7 −0.520075
\(990\) 0 0
\(991\) 1.48550e7 0.480494 0.240247 0.970712i \(-0.422772\pi\)
0.240247 + 0.970712i \(0.422772\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 4.90714e6 0.157134
\(996\) 0 0
\(997\) −3.33769e6 −0.106343 −0.0531714 0.998585i \(-0.516933\pi\)
−0.0531714 + 0.998585i \(0.516933\pi\)
\(998\) 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.k.1.1 1
3.2 odd 2 336.6.a.g.1.1 1
4.3 odd 2 126.6.a.b.1.1 1
12.11 even 2 42.6.a.f.1.1 1
28.27 even 2 882.6.a.i.1.1 1
60.23 odd 4 1050.6.g.m.799.1 2
60.47 odd 4 1050.6.g.m.799.2 2
60.59 even 2 1050.6.a.a.1.1 1
84.11 even 6 294.6.e.b.79.1 2
84.23 even 6 294.6.e.b.67.1 2
84.47 odd 6 294.6.e.f.67.1 2
84.59 odd 6 294.6.e.f.79.1 2
84.83 odd 2 294.6.a.i.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.f.1.1 1 12.11 even 2
126.6.a.b.1.1 1 4.3 odd 2
294.6.a.i.1.1 1 84.83 odd 2
294.6.e.b.67.1 2 84.23 even 6
294.6.e.b.79.1 2 84.11 even 6
294.6.e.f.67.1 2 84.47 odd 6
294.6.e.f.79.1 2 84.59 odd 6
336.6.a.g.1.1 1 3.2 odd 2
882.6.a.i.1.1 1 28.27 even 2
1008.6.a.k.1.1 1 1.1 even 1 trivial
1050.6.a.a.1.1 1 60.59 even 2
1050.6.g.m.799.1 2 60.23 odd 4
1050.6.g.m.799.2 2 60.47 odd 4