Properties

Label 1008.6.a.d.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 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)
 
\(f(q)\) \(=\) \(q-76.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-76.0000 q^{5} +49.0000 q^{7} +650.000 q^{11} +762.000 q^{13} +556.000 q^{17} +2452.00 q^{19} -2950.00 q^{23} +2651.00 q^{25} +674.000 q^{29} +3024.00 q^{31} -3724.00 q^{35} +7730.00 q^{37} +17016.0 q^{41} -21836.0 q^{43} -23940.0 q^{47} +2401.00 q^{49} -15594.0 q^{53} -49400.0 q^{55} +5608.00 q^{59} +150.000 q^{61} -57912.0 q^{65} +43784.0 q^{67} -39178.0 q^{71} -23570.0 q^{73} +31850.0 q^{77} +17892.0 q^{79} +38972.0 q^{83} -42256.0 q^{85} -6024.00 q^{89} +37338.0 q^{91} -186352. q^{95} +108430. q^{97} +O(q^{100})\)

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
\(5\) −76.0000 −1.35953 −0.679765 0.733430i \(-0.737918\pi\)
−0.679765 + 0.733430i \(0.737918\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 650.000 1.61969 0.809845 0.586645i \(-0.199551\pi\)
0.809845 + 0.586645i \(0.199551\pi\)
\(12\) 0 0
\(13\) 762.000 1.25054 0.625269 0.780410i \(-0.284989\pi\)
0.625269 + 0.780410i \(0.284989\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 556.000 0.466608 0.233304 0.972404i \(-0.425046\pi\)
0.233304 + 0.972404i \(0.425046\pi\)
\(18\) 0 0
\(19\) 2452.00 1.55825 0.779124 0.626870i \(-0.215664\pi\)
0.779124 + 0.626870i \(0.215664\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2950.00 −1.16279 −0.581397 0.813620i \(-0.697493\pi\)
−0.581397 + 0.813620i \(0.697493\pi\)
\(24\) 0 0
\(25\) 2651.00 0.848320
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 674.000 0.148821 0.0744106 0.997228i \(-0.476292\pi\)
0.0744106 + 0.997228i \(0.476292\pi\)
\(30\) 0 0
\(31\) 3024.00 0.565168 0.282584 0.959243i \(-0.408808\pi\)
0.282584 + 0.959243i \(0.408808\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3724.00 −0.513854
\(36\) 0 0
\(37\) 7730.00 0.928272 0.464136 0.885764i \(-0.346365\pi\)
0.464136 + 0.885764i \(0.346365\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 17016.0 1.58088 0.790438 0.612542i \(-0.209853\pi\)
0.790438 + 0.612542i \(0.209853\pi\)
\(42\) 0 0
\(43\) −21836.0 −1.80095 −0.900476 0.434907i \(-0.856781\pi\)
−0.900476 + 0.434907i \(0.856781\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −23940.0 −1.58081 −0.790405 0.612585i \(-0.790130\pi\)
−0.790405 + 0.612585i \(0.790130\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −15594.0 −0.762549 −0.381275 0.924462i \(-0.624515\pi\)
−0.381275 + 0.924462i \(0.624515\pi\)
\(54\) 0 0
\(55\) −49400.0 −2.20201
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5608.00 0.209738 0.104869 0.994486i \(-0.466558\pi\)
0.104869 + 0.994486i \(0.466558\pi\)
\(60\) 0 0
\(61\) 150.000 0.00516139 0.00258069 0.999997i \(-0.499179\pi\)
0.00258069 + 0.999997i \(0.499179\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −57912.0 −1.70014
\(66\) 0 0
\(67\) 43784.0 1.19159 0.595797 0.803135i \(-0.296836\pi\)
0.595797 + 0.803135i \(0.296836\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −39178.0 −0.922351 −0.461176 0.887309i \(-0.652572\pi\)
−0.461176 + 0.887309i \(0.652572\pi\)
\(72\) 0 0
\(73\) −23570.0 −0.517669 −0.258835 0.965922i \(-0.583338\pi\)
−0.258835 + 0.965922i \(0.583338\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 31850.0 0.612185
\(78\) 0 0
\(79\) 17892.0 0.322546 0.161273 0.986910i \(-0.448440\pi\)
0.161273 + 0.986910i \(0.448440\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 38972.0 0.620951 0.310476 0.950581i \(-0.399512\pi\)
0.310476 + 0.950581i \(0.399512\pi\)
\(84\) 0 0
\(85\) −42256.0 −0.634368
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6024.00 −0.0806139 −0.0403070 0.999187i \(-0.512834\pi\)
−0.0403070 + 0.999187i \(0.512834\pi\)
\(90\) 0 0
\(91\) 37338.0 0.472659
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −186352. −2.11848
\(96\) 0 0
\(97\) 108430. 1.17009 0.585046 0.811000i \(-0.301076\pi\)
0.585046 + 0.811000i \(0.301076\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 70424.0 0.686938 0.343469 0.939164i \(-0.388398\pi\)
0.343469 + 0.939164i \(0.388398\pi\)
\(102\) 0 0
\(103\) 31552.0 0.293045 0.146522 0.989207i \(-0.453192\pi\)
0.146522 + 0.989207i \(0.453192\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 108282. 0.914317 0.457159 0.889385i \(-0.348867\pi\)
0.457159 + 0.889385i \(0.348867\pi\)
\(108\) 0 0
\(109\) −72146.0 −0.581629 −0.290814 0.956779i \(-0.593926\pi\)
−0.290814 + 0.956779i \(0.593926\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −220906. −1.62746 −0.813732 0.581240i \(-0.802568\pi\)
−0.813732 + 0.581240i \(0.802568\pi\)
\(114\) 0 0
\(115\) 224200. 1.58085
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 27244.0 0.176361
\(120\) 0 0
\(121\) 261449. 1.62339
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 36024.0 0.206213
\(126\) 0 0
\(127\) 239652. 1.31847 0.659237 0.751935i \(-0.270879\pi\)
0.659237 + 0.751935i \(0.270879\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −274172. −1.39587 −0.697935 0.716161i \(-0.745897\pi\)
−0.697935 + 0.716161i \(0.745897\pi\)
\(132\) 0 0
\(133\) 120148. 0.588962
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 391154. 1.78052 0.890259 0.455455i \(-0.150523\pi\)
0.890259 + 0.455455i \(0.150523\pi\)
\(138\) 0 0
\(139\) −339364. −1.48980 −0.744901 0.667175i \(-0.767503\pi\)
−0.744901 + 0.667175i \(0.767503\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 495300. 2.02548
\(144\) 0 0
\(145\) −51224.0 −0.202327
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 29334.0 0.108244 0.0541222 0.998534i \(-0.482764\pi\)
0.0541222 + 0.998534i \(0.482764\pi\)
\(150\) 0 0
\(151\) −71608.0 −0.255575 −0.127788 0.991802i \(-0.540788\pi\)
−0.127788 + 0.991802i \(0.540788\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −229824. −0.768362
\(156\) 0 0
\(157\) 296318. 0.959420 0.479710 0.877427i \(-0.340742\pi\)
0.479710 + 0.877427i \(0.340742\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −144550. −0.439494
\(162\) 0 0
\(163\) 480400. 1.41623 0.708115 0.706097i \(-0.249546\pi\)
0.708115 + 0.706097i \(0.249546\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 160180. 0.444444 0.222222 0.974996i \(-0.428669\pi\)
0.222222 + 0.974996i \(0.428669\pi\)
\(168\) 0 0
\(169\) 209351. 0.563843
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 8984.00 0.0228220 0.0114110 0.999935i \(-0.496368\pi\)
0.0114110 + 0.999935i \(0.496368\pi\)
\(174\) 0 0
\(175\) 129899. 0.320635
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 182886. 0.426627 0.213313 0.976984i \(-0.431575\pi\)
0.213313 + 0.976984i \(0.431575\pi\)
\(180\) 0 0
\(181\) 138330. 0.313848 0.156924 0.987611i \(-0.449842\pi\)
0.156924 + 0.987611i \(0.449842\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −587480. −1.26201
\(186\) 0 0
\(187\) 361400. 0.755760
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 327222. 0.649021 0.324511 0.945882i \(-0.394800\pi\)
0.324511 + 0.945882i \(0.394800\pi\)
\(192\) 0 0
\(193\) 786902. 1.52064 0.760322 0.649547i \(-0.225041\pi\)
0.760322 + 0.649547i \(0.225041\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −423098. −0.776740 −0.388370 0.921504i \(-0.626962\pi\)
−0.388370 + 0.921504i \(0.626962\pi\)
\(198\) 0 0
\(199\) −1.02392e6 −1.83288 −0.916439 0.400175i \(-0.868949\pi\)
−0.916439 + 0.400175i \(0.868949\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 33026.0 0.0562491
\(204\) 0 0
\(205\) −1.29322e6 −2.14925
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.59380e6 2.52388
\(210\) 0 0
\(211\) −461516. −0.713642 −0.356821 0.934173i \(-0.616139\pi\)
−0.356821 + 0.934173i \(0.616139\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.65954e6 2.44845
\(216\) 0 0
\(217\) 148176. 0.213613
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 423672. 0.583511
\(222\) 0 0
\(223\) −995048. −1.33993 −0.669965 0.742393i \(-0.733691\pi\)
−0.669965 + 0.742393i \(0.733691\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −95568.0 −0.123097 −0.0615486 0.998104i \(-0.519604\pi\)
−0.0615486 + 0.998104i \(0.519604\pi\)
\(228\) 0 0
\(229\) −1.04409e6 −1.31567 −0.657836 0.753161i \(-0.728528\pi\)
−0.657836 + 0.753161i \(0.728528\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.16941e6 1.41116 0.705581 0.708629i \(-0.250686\pi\)
0.705581 + 0.708629i \(0.250686\pi\)
\(234\) 0 0
\(235\) 1.81944e6 2.14916
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −27342.0 −0.0309625 −0.0154812 0.999880i \(-0.504928\pi\)
−0.0154812 + 0.999880i \(0.504928\pi\)
\(240\) 0 0
\(241\) −907714. −1.00671 −0.503357 0.864078i \(-0.667902\pi\)
−0.503357 + 0.864078i \(0.667902\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −182476. −0.194218
\(246\) 0 0
\(247\) 1.86842e6 1.94865
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 44088.0 0.0441709 0.0220854 0.999756i \(-0.492969\pi\)
0.0220854 + 0.999756i \(0.492969\pi\)
\(252\) 0 0
\(253\) −1.91750e6 −1.88336
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 829200. 0.783117 0.391558 0.920153i \(-0.371936\pi\)
0.391558 + 0.920153i \(0.371936\pi\)
\(258\) 0 0
\(259\) 378770. 0.350854
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.31947e6 1.17627 0.588137 0.808761i \(-0.299861\pi\)
0.588137 + 0.808761i \(0.299861\pi\)
\(264\) 0 0
\(265\) 1.18514e6 1.03671
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 783788. 0.660416 0.330208 0.943908i \(-0.392881\pi\)
0.330208 + 0.943908i \(0.392881\pi\)
\(270\) 0 0
\(271\) −955080. −0.789981 −0.394990 0.918685i \(-0.629252\pi\)
−0.394990 + 0.918685i \(0.629252\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.72315e6 1.37401
\(276\) 0 0
\(277\) 1.91273e6 1.49780 0.748901 0.662682i \(-0.230582\pi\)
0.748901 + 0.662682i \(0.230582\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.02620e6 0.775295 0.387648 0.921808i \(-0.373288\pi\)
0.387648 + 0.921808i \(0.373288\pi\)
\(282\) 0 0
\(283\) −1.74668e6 −1.29642 −0.648211 0.761461i \(-0.724482\pi\)
−0.648211 + 0.761461i \(0.724482\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 833784. 0.597515
\(288\) 0 0
\(289\) −1.11072e6 −0.782277
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.23212e6 −1.51897 −0.759484 0.650526i \(-0.774548\pi\)
−0.759484 + 0.650526i \(0.774548\pi\)
\(294\) 0 0
\(295\) −426208. −0.285146
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.24790e6 −1.45412
\(300\) 0 0
\(301\) −1.06996e6 −0.680696
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −11400.0 −0.00701706
\(306\) 0 0
\(307\) −1.85324e6 −1.12224 −0.561119 0.827735i \(-0.689629\pi\)
−0.561119 + 0.827735i \(0.689629\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −450956. −0.264383 −0.132191 0.991224i \(-0.542201\pi\)
−0.132191 + 0.991224i \(0.542201\pi\)
\(312\) 0 0
\(313\) 1.60263e6 0.924642 0.462321 0.886713i \(-0.347017\pi\)
0.462321 + 0.886713i \(0.347017\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20862.0 0.0116602 0.00583012 0.999983i \(-0.498144\pi\)
0.00583012 + 0.999983i \(0.498144\pi\)
\(318\) 0 0
\(319\) 438100. 0.241044
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.36331e6 0.727091
\(324\) 0 0
\(325\) 2.02006e6 1.06086
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −1.17306e6 −0.597490
\(330\) 0 0
\(331\) −2.07621e6 −1.04160 −0.520801 0.853678i \(-0.674367\pi\)
−0.520801 + 0.853678i \(0.674367\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.32758e6 −1.62001
\(336\) 0 0
\(337\) 1.20508e6 0.578019 0.289009 0.957326i \(-0.406674\pi\)
0.289009 + 0.957326i \(0.406674\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.96560e6 0.915396
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −876642. −0.390840 −0.195420 0.980720i \(-0.562607\pi\)
−0.195420 + 0.980720i \(0.562607\pi\)
\(348\) 0 0
\(349\) −1.29593e6 −0.569532 −0.284766 0.958597i \(-0.591916\pi\)
−0.284766 + 0.958597i \(0.591916\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.99040e6 1.70443 0.852215 0.523192i \(-0.175259\pi\)
0.852215 + 0.523192i \(0.175259\pi\)
\(354\) 0 0
\(355\) 2.97753e6 1.25396
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.06452e6 1.66446 0.832229 0.554432i \(-0.187064\pi\)
0.832229 + 0.554432i \(0.187064\pi\)
\(360\) 0 0
\(361\) 3.53620e6 1.42814
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.79132e6 0.703787
\(366\) 0 0
\(367\) 1.67243e6 0.648162 0.324081 0.946029i \(-0.394945\pi\)
0.324081 + 0.946029i \(0.394945\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −764106. −0.288216
\(372\) 0 0
\(373\) 3.16769e6 1.17888 0.589441 0.807812i \(-0.299348\pi\)
0.589441 + 0.807812i \(0.299348\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 513588. 0.186106
\(378\) 0 0
\(379\) 4.20388e6 1.50332 0.751662 0.659548i \(-0.229252\pi\)
0.751662 + 0.659548i \(0.229252\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −342616. −0.119347 −0.0596734 0.998218i \(-0.519006\pi\)
−0.0596734 + 0.998218i \(0.519006\pi\)
\(384\) 0 0
\(385\) −2.42060e6 −0.832283
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.83959e6 1.28650 0.643252 0.765654i \(-0.277585\pi\)
0.643252 + 0.765654i \(0.277585\pi\)
\(390\) 0 0
\(391\) −1.64020e6 −0.542569
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.35979e6 −0.438510
\(396\) 0 0
\(397\) 3.43894e6 1.09509 0.547543 0.836777i \(-0.315563\pi\)
0.547543 + 0.836777i \(0.315563\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.89421e6 1.20937 0.604684 0.796466i \(-0.293299\pi\)
0.604684 + 0.796466i \(0.293299\pi\)
\(402\) 0 0
\(403\) 2.30429e6 0.706764
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.02450e6 1.50351
\(408\) 0 0
\(409\) −1.64679e6 −0.486778 −0.243389 0.969929i \(-0.578259\pi\)
−0.243389 + 0.969929i \(0.578259\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 274792. 0.0792737
\(414\) 0 0
\(415\) −2.96187e6 −0.844201
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.67659e6 −0.466544 −0.233272 0.972412i \(-0.574943\pi\)
−0.233272 + 0.972412i \(0.574943\pi\)
\(420\) 0 0
\(421\) −566742. −0.155840 −0.0779202 0.996960i \(-0.524828\pi\)
−0.0779202 + 0.996960i \(0.524828\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.47396e6 0.395833
\(426\) 0 0
\(427\) 7350.00 0.00195082
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.68468e6 1.73335 0.866677 0.498870i \(-0.166251\pi\)
0.866677 + 0.498870i \(0.166251\pi\)
\(432\) 0 0
\(433\) 6.91337e6 1.77203 0.886013 0.463661i \(-0.153464\pi\)
0.886013 + 0.463661i \(0.153464\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.23340e6 −1.81192
\(438\) 0 0
\(439\) 4.56281e6 1.12998 0.564990 0.825098i \(-0.308880\pi\)
0.564990 + 0.825098i \(0.308880\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.59760e6 1.11307 0.556534 0.830825i \(-0.312131\pi\)
0.556534 + 0.830825i \(0.312131\pi\)
\(444\) 0 0
\(445\) 457824. 0.109597
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.70658e6 −0.399494 −0.199747 0.979848i \(-0.564012\pi\)
−0.199747 + 0.979848i \(0.564012\pi\)
\(450\) 0 0
\(451\) 1.10604e7 2.56053
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.83769e6 −0.642593
\(456\) 0 0
\(457\) −6.93916e6 −1.55423 −0.777117 0.629356i \(-0.783319\pi\)
−0.777117 + 0.629356i \(0.783319\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 2.61805e6 0.573753 0.286877 0.957968i \(-0.407383\pi\)
0.286877 + 0.957968i \(0.407383\pi\)
\(462\) 0 0
\(463\) −7.13602e6 −1.54705 −0.773524 0.633767i \(-0.781508\pi\)
−0.773524 + 0.633767i \(0.781508\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.17398e6 −0.461278 −0.230639 0.973039i \(-0.574082\pi\)
−0.230639 + 0.973039i \(0.574082\pi\)
\(468\) 0 0
\(469\) 2.14542e6 0.450380
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.41934e7 −2.91698
\(474\) 0 0
\(475\) 6.50025e6 1.32189
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.63294e6 −0.922609 −0.461305 0.887242i \(-0.652619\pi\)
−0.461305 + 0.887242i \(0.652619\pi\)
\(480\) 0 0
\(481\) 5.89026e6 1.16084
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −8.24068e6 −1.59077
\(486\) 0 0
\(487\) 4.56645e6 0.872481 0.436241 0.899830i \(-0.356310\pi\)
0.436241 + 0.899830i \(0.356310\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −5.31429e6 −0.994813 −0.497407 0.867518i \(-0.665714\pi\)
−0.497407 + 0.867518i \(0.665714\pi\)
\(492\) 0 0
\(493\) 374744. 0.0694412
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.91972e6 −0.348616
\(498\) 0 0
\(499\) 2.46314e6 0.442831 0.221415 0.975180i \(-0.428932\pi\)
0.221415 + 0.975180i \(0.428932\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 2.79924e6 0.493310 0.246655 0.969103i \(-0.420669\pi\)
0.246655 + 0.969103i \(0.420669\pi\)
\(504\) 0 0
\(505\) −5.35222e6 −0.933912
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −1.99914e6 −0.342018 −0.171009 0.985269i \(-0.554703\pi\)
−0.171009 + 0.985269i \(0.554703\pi\)
\(510\) 0 0
\(511\) −1.15493e6 −0.195661
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.39795e6 −0.398403
\(516\) 0 0
\(517\) −1.55610e7 −2.56042
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −3.52160e6 −0.568390 −0.284195 0.958767i \(-0.591726\pi\)
−0.284195 + 0.958767i \(0.591726\pi\)
\(522\) 0 0
\(523\) −2.60685e6 −0.416737 −0.208369 0.978050i \(-0.566815\pi\)
−0.208369 + 0.978050i \(0.566815\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.68134e6 0.263712
\(528\) 0 0
\(529\) 2.26616e6 0.352088
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.29662e7 1.97694
\(534\) 0 0
\(535\) −8.22943e6 −1.24304
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.56065e6 0.231384
\(540\) 0 0
\(541\) −1.37441e6 −0.201894 −0.100947 0.994892i \(-0.532187\pi\)
−0.100947 + 0.994892i \(0.532187\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 5.48310e6 0.790742
\(546\) 0 0
\(547\) 8.78398e6 1.25523 0.627614 0.778524i \(-0.284032\pi\)
0.627614 + 0.778524i \(0.284032\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1.65265e6 0.231900
\(552\) 0 0
\(553\) 876708. 0.121911
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −6.29262e6 −0.859396 −0.429698 0.902973i \(-0.641380\pi\)
−0.429698 + 0.902973i \(0.641380\pi\)
\(558\) 0 0
\(559\) −1.66390e7 −2.25216
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 4.86582e6 0.646971 0.323485 0.946233i \(-0.395145\pi\)
0.323485 + 0.946233i \(0.395145\pi\)
\(564\) 0 0
\(565\) 1.67889e7 2.21259
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.46383e6 0.577998 0.288999 0.957329i \(-0.406678\pi\)
0.288999 + 0.957329i \(0.406678\pi\)
\(570\) 0 0
\(571\) −8.17054e6 −1.04872 −0.524361 0.851496i \(-0.675696\pi\)
−0.524361 + 0.851496i \(0.675696\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −7.82045e6 −0.986421
\(576\) 0 0
\(577\) −5.50343e6 −0.688167 −0.344084 0.938939i \(-0.611810\pi\)
−0.344084 + 0.938939i \(0.611810\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.90963e6 0.234697
\(582\) 0 0
\(583\) −1.01361e7 −1.23509
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 8.14251e6 0.975356 0.487678 0.873024i \(-0.337844\pi\)
0.487678 + 0.873024i \(0.337844\pi\)
\(588\) 0 0
\(589\) 7.41485e6 0.880672
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.73136e6 0.318964 0.159482 0.987201i \(-0.449018\pi\)
0.159482 + 0.987201i \(0.449018\pi\)
\(594\) 0 0
\(595\) −2.07054e6 −0.239768
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.23733e6 0.140902 0.0704510 0.997515i \(-0.477556\pi\)
0.0704510 + 0.997515i \(0.477556\pi\)
\(600\) 0 0
\(601\) −1.59756e7 −1.80414 −0.902071 0.431587i \(-0.857954\pi\)
−0.902071 + 0.431587i \(0.857954\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.98701e7 −2.20705
\(606\) 0 0
\(607\) 1.88275e6 0.207406 0.103703 0.994608i \(-0.466931\pi\)
0.103703 + 0.994608i \(0.466931\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.82423e7 −1.97686
\(612\) 0 0
\(613\) −9.82804e6 −1.05637 −0.528185 0.849130i \(-0.677127\pi\)
−0.528185 + 0.849130i \(0.677127\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.21262e6 0.868498 0.434249 0.900793i \(-0.357014\pi\)
0.434249 + 0.900793i \(0.357014\pi\)
\(618\) 0 0
\(619\) −6.98465e6 −0.732686 −0.366343 0.930480i \(-0.619390\pi\)
−0.366343 + 0.930480i \(0.619390\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −295176. −0.0304692
\(624\) 0 0
\(625\) −1.10222e7 −1.12867
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 4.29788e6 0.433139
\(630\) 0 0
\(631\) −1.26789e7 −1.26767 −0.633837 0.773467i \(-0.718521\pi\)
−0.633837 + 0.773467i \(0.718521\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.82136e7 −1.79250
\(636\) 0 0
\(637\) 1.82956e6 0.178648
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.40324e7 1.34892 0.674460 0.738311i \(-0.264376\pi\)
0.674460 + 0.738311i \(0.264376\pi\)
\(642\) 0 0
\(643\) −1.30368e6 −0.124349 −0.0621745 0.998065i \(-0.519804\pi\)
−0.0621745 + 0.998065i \(0.519804\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.57110e6 0.147551 0.0737757 0.997275i \(-0.476495\pi\)
0.0737757 + 0.997275i \(0.476495\pi\)
\(648\) 0 0
\(649\) 3.64520e6 0.339711
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 8.34115e6 0.765496 0.382748 0.923853i \(-0.374978\pi\)
0.382748 + 0.923853i \(0.374978\pi\)
\(654\) 0 0
\(655\) 2.08371e7 1.89773
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.18334e6 0.554638 0.277319 0.960778i \(-0.410554\pi\)
0.277319 + 0.960778i \(0.410554\pi\)
\(660\) 0 0
\(661\) 928966. 0.0826982 0.0413491 0.999145i \(-0.486834\pi\)
0.0413491 + 0.999145i \(0.486834\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −9.13125e6 −0.800711
\(666\) 0 0
\(667\) −1.98830e6 −0.173048
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 97500.0 0.00835985
\(672\) 0 0
\(673\) 1.79131e7 1.52452 0.762259 0.647272i \(-0.224090\pi\)
0.762259 + 0.647272i \(0.224090\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.96397e6 0.416253 0.208126 0.978102i \(-0.433263\pi\)
0.208126 + 0.978102i \(0.433263\pi\)
\(678\) 0 0
\(679\) 5.31307e6 0.442253
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 89526.0 0.00734340 0.00367170 0.999993i \(-0.498831\pi\)
0.00367170 + 0.999993i \(0.498831\pi\)
\(684\) 0 0
\(685\) −2.97277e7 −2.42067
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.18826e7 −0.953596
\(690\) 0 0
\(691\) 142396. 0.0113450 0.00567248 0.999984i \(-0.498194\pi\)
0.00567248 + 0.999984i \(0.498194\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.57917e7 2.02543
\(696\) 0 0
\(697\) 9.46090e6 0.737650
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.03935e7 −0.798852 −0.399426 0.916765i \(-0.630791\pi\)
−0.399426 + 0.916765i \(0.630791\pi\)
\(702\) 0 0
\(703\) 1.89540e7 1.44648
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.45078e6 0.259638
\(708\) 0 0
\(709\) 4.65503e6 0.347782 0.173891 0.984765i \(-0.444366\pi\)
0.173891 + 0.984765i \(0.444366\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −8.92080e6 −0.657173
\(714\) 0 0
\(715\) −3.76428e7 −2.75370
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6.72134e6 −0.484880 −0.242440 0.970166i \(-0.577948\pi\)
−0.242440 + 0.970166i \(0.577948\pi\)
\(720\) 0 0
\(721\) 1.54605e6 0.110760
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.78677e6 0.126248
\(726\) 0 0
\(727\) 1.24076e7 0.870670 0.435335 0.900269i \(-0.356630\pi\)
0.435335 + 0.900269i \(0.356630\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.21408e7 −0.840339
\(732\) 0 0
\(733\) 1.35958e7 0.934641 0.467321 0.884088i \(-0.345219\pi\)
0.467321 + 0.884088i \(0.345219\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.84596e7 1.93001
\(738\) 0 0
\(739\) −2.56819e6 −0.172988 −0.0864941 0.996252i \(-0.527566\pi\)
−0.0864941 + 0.996252i \(0.527566\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.02133e7 −1.34327 −0.671637 0.740880i \(-0.734409\pi\)
−0.671637 + 0.740880i \(0.734409\pi\)
\(744\) 0 0
\(745\) −2.22938e6 −0.147161
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 5.30582e6 0.345579
\(750\) 0 0
\(751\) −7.04813e6 −0.456010 −0.228005 0.973660i \(-0.573220\pi\)
−0.228005 + 0.973660i \(0.573220\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 5.44221e6 0.347462
\(756\) 0 0
\(757\) −2.04120e7 −1.29463 −0.647315 0.762223i \(-0.724108\pi\)
−0.647315 + 0.762223i \(0.724108\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5.07974e6 0.317965 0.158983 0.987281i \(-0.449179\pi\)
0.158983 + 0.987281i \(0.449179\pi\)
\(762\) 0 0
\(763\) −3.53515e6 −0.219835
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.27330e6 0.262286
\(768\) 0 0
\(769\) 2.33898e7 1.42630 0.713149 0.701012i \(-0.247268\pi\)
0.713149 + 0.701012i \(0.247268\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.11253e6 0.0669672 0.0334836 0.999439i \(-0.489340\pi\)
0.0334836 + 0.999439i \(0.489340\pi\)
\(774\) 0 0
\(775\) 8.01662e6 0.479443
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.17232e7 2.46340
\(780\) 0 0
\(781\) −2.54657e7 −1.49392
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.25202e7 −1.30436
\(786\) 0 0
\(787\) −2.00812e6 −0.115572 −0.0577859 0.998329i \(-0.518404\pi\)
−0.0577859 + 0.998329i \(0.518404\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −1.08244e7 −0.615124
\(792\) 0 0
\(793\) 114300. 0.00645451
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −3.00897e7 −1.67792 −0.838961 0.544191i \(-0.816837\pi\)
−0.838961 + 0.544191i \(0.816837\pi\)
\(798\) 0 0
\(799\) −1.33106e7 −0.737619
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.53205e7 −0.838463
\(804\) 0 0
\(805\) 1.09858e7 0.597506
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.88207e6 0.101103 0.0505515 0.998721i \(-0.483902\pi\)
0.0505515 + 0.998721i \(0.483902\pi\)
\(810\) 0 0
\(811\) −4.88220e6 −0.260654 −0.130327 0.991471i \(-0.541603\pi\)
−0.130327 + 0.991471i \(0.541603\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −3.65104e7 −1.92541
\(816\) 0 0
\(817\) −5.35419e7 −2.80633
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −8.37096e6 −0.433429 −0.216714 0.976235i \(-0.569534\pi\)
−0.216714 + 0.976235i \(0.569534\pi\)
\(822\) 0 0
\(823\) 2.02090e7 1.04003 0.520015 0.854157i \(-0.325926\pi\)
0.520015 + 0.854157i \(0.325926\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.31059e7 −0.666352 −0.333176 0.942865i \(-0.608120\pi\)
−0.333176 + 0.942865i \(0.608120\pi\)
\(828\) 0 0
\(829\) 3.18667e7 1.61046 0.805232 0.592960i \(-0.202041\pi\)
0.805232 + 0.592960i \(0.202041\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1.33496e6 0.0666583
\(834\) 0 0
\(835\) −1.21737e7 −0.604235
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 9.94742e6 0.487872 0.243936 0.969791i \(-0.421561\pi\)
0.243936 + 0.969791i \(0.421561\pi\)
\(840\) 0 0
\(841\) −2.00569e7 −0.977852
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −1.59107e7 −0.766561
\(846\) 0 0
\(847\) 1.28110e7 0.613585
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −2.28035e7 −1.07939
\(852\) 0 0
\(853\) −6.52611e6 −0.307102 −0.153551 0.988141i \(-0.549071\pi\)
−0.153551 + 0.988141i \(0.549071\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 8.76238e6 0.407540 0.203770 0.979019i \(-0.434681\pi\)
0.203770 + 0.979019i \(0.434681\pi\)
\(858\) 0 0
\(859\) −6.47942e6 −0.299608 −0.149804 0.988716i \(-0.547864\pi\)
−0.149804 + 0.988716i \(0.547864\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.83417e7 −0.838323 −0.419162 0.907912i \(-0.637676\pi\)
−0.419162 + 0.907912i \(0.637676\pi\)
\(864\) 0 0
\(865\) −682784. −0.0310272
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.16298e7 0.522424
\(870\) 0 0
\(871\) 3.33634e7 1.49013
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.76518e6 0.0779413
\(876\) 0 0
\(877\) 2.69065e7 1.18129 0.590647 0.806930i \(-0.298873\pi\)
0.590647 + 0.806930i \(0.298873\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.52174e7 0.660542 0.330271 0.943886i \(-0.392860\pi\)
0.330271 + 0.943886i \(0.392860\pi\)
\(882\) 0 0
\(883\) 2.61520e7 1.12877 0.564383 0.825513i \(-0.309114\pi\)
0.564383 + 0.825513i \(0.309114\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −1.08021e7 −0.460997 −0.230499 0.973073i \(-0.574036\pi\)
−0.230499 + 0.973073i \(0.574036\pi\)
\(888\) 0 0
\(889\) 1.17429e7 0.498337
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −5.87009e7 −2.46329
\(894\) 0 0
\(895\) −1.38993e7 −0.580011
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.03818e6 0.0841090
\(900\) 0 0
\(901\) −8.67026e6 −0.355812
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.05131e7 −0.426686
\(906\) 0 0
\(907\) 9.84167e6 0.397238 0.198619 0.980077i \(-0.436354\pi\)
0.198619 + 0.980077i \(0.436354\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 2.72509e7 1.08789 0.543945 0.839121i \(-0.316930\pi\)
0.543945 + 0.839121i \(0.316930\pi\)
\(912\) 0 0
\(913\) 2.53318e7 1.00575
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.34344e7 −0.527589
\(918\) 0 0
\(919\) −2.86432e7 −1.11875 −0.559374 0.828916i \(-0.688958\pi\)
−0.559374 + 0.828916i \(0.688958\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −2.98536e7 −1.15343
\(924\) 0 0
\(925\) 2.04922e7 0.787472
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −6.78492e6 −0.257932 −0.128966 0.991649i \(-0.541166\pi\)
−0.128966 + 0.991649i \(0.541166\pi\)
\(930\) 0 0
\(931\) 5.88725e6 0.222607
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.74664e7 −1.02748
\(936\) 0 0
\(937\) 3.00308e7 1.11742 0.558712 0.829362i \(-0.311296\pi\)
0.558712 + 0.829362i \(0.311296\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −2.30725e7 −0.849415 −0.424707 0.905331i \(-0.639623\pi\)
−0.424707 + 0.905331i \(0.639623\pi\)
\(942\) 0 0
\(943\) −5.01972e7 −1.83823
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 2.71433e7 0.983531 0.491765 0.870728i \(-0.336352\pi\)
0.491765 + 0.870728i \(0.336352\pi\)
\(948\) 0 0
\(949\) −1.79603e7 −0.647365
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.61552e7 0.576209 0.288104 0.957599i \(-0.406975\pi\)
0.288104 + 0.957599i \(0.406975\pi\)
\(954\) 0 0
\(955\) −2.48689e7 −0.882364
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.91665e7 0.672973
\(960\) 0 0
\(961\) −1.94846e7 −0.680585
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −5.98046e7 −2.06736
\(966\) 0 0
\(967\) 3.80323e7 1.30793 0.653967 0.756523i \(-0.273103\pi\)
0.653967 + 0.756523i \(0.273103\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −2.23104e7 −0.759379 −0.379689 0.925114i \(-0.623969\pi\)
−0.379689 + 0.925114i \(0.623969\pi\)
\(972\) 0 0
\(973\) −1.66288e7 −0.563093
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.06930e7 −1.02873 −0.514367 0.857570i \(-0.671973\pi\)
−0.514367 + 0.857570i \(0.671973\pi\)
\(978\) 0 0
\(979\) −3.91560e6 −0.130569
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.52706e7 −0.504048 −0.252024 0.967721i \(-0.581096\pi\)
−0.252024 + 0.967721i \(0.581096\pi\)
\(984\) 0 0
\(985\) 3.21554e7 1.05600
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.44162e7 2.09413
\(990\) 0 0
\(991\) −3.16279e7 −1.02303 −0.511513 0.859276i \(-0.670915\pi\)
−0.511513 + 0.859276i \(0.670915\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 7.78179e7 2.49185
\(996\) 0 0
\(997\) −3.55842e7 −1.13376 −0.566878 0.823802i \(-0.691849\pi\)
−0.566878 + 0.823802i \(0.691849\pi\)
\(998\) 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.d.1.1 1
3.2 odd 2 336.6.a.q.1.1 1
4.3 odd 2 126.6.a.a.1.1 1
12.11 even 2 42.6.a.e.1.1 1
28.27 even 2 882.6.a.j.1.1 1
60.23 odd 4 1050.6.g.h.799.1 2
60.47 odd 4 1050.6.g.h.799.2 2
60.59 even 2 1050.6.a.f.1.1 1
84.11 even 6 294.6.e.d.79.1 2
84.23 even 6 294.6.e.d.67.1 2
84.47 odd 6 294.6.e.c.67.1 2
84.59 odd 6 294.6.e.c.79.1 2
84.83 odd 2 294.6.a.k.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.e.1.1 1 12.11 even 2
126.6.a.a.1.1 1 4.3 odd 2
294.6.a.k.1.1 1 84.83 odd 2
294.6.e.c.67.1 2 84.47 odd 6
294.6.e.c.79.1 2 84.59 odd 6
294.6.e.d.67.1 2 84.23 even 6
294.6.e.d.79.1 2 84.11 even 6
336.6.a.q.1.1 1 3.2 odd 2
882.6.a.j.1.1 1 28.27 even 2
1008.6.a.d.1.1 1 1.1 even 1 trivial
1050.6.a.f.1.1 1 60.59 even 2
1050.6.g.h.799.1 2 60.23 odd 4
1050.6.g.h.799.2 2 60.47 odd 4