Properties

Label 1008.6.a.g.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 $1$

Related objects

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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)
 
\(f(q)\) \(=\) \(q-44.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-44.0000 q^{5} +49.0000 q^{7} -470.000 q^{11} -1158.00 q^{13} -1204.00 q^{17} +2644.00 q^{19} -1190.00 q^{23} -1189.00 q^{25} -3614.00 q^{29} -5616.00 q^{31} -2156.00 q^{35} -6478.00 q^{37} -2856.00 q^{41} +13492.0 q^{43} -18372.0 q^{47} +2401.00 q^{49} +4374.00 q^{53} +20680.0 q^{55} +30248.0 q^{59} +19542.0 q^{61} +50952.0 q^{65} -54328.0 q^{67} -10730.0 q^{71} +35374.0 q^{73} -23030.0 q^{77} +49956.0 q^{79} -26948.0 q^{83} +52976.0 q^{85} -100776. q^{89} -56742.0 q^{91} -116336. q^{95} +77134.0 q^{97} +O(q^{100})\)

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
\(5\) −44.0000 −0.787096 −0.393548 0.919304i \(-0.628752\pi\)
−0.393548 + 0.919304i \(0.628752\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −470.000 −1.17116 −0.585580 0.810615i \(-0.699133\pi\)
−0.585580 + 0.810615i \(0.699133\pi\)
\(12\) 0 0
\(13\) −1158.00 −1.90042 −0.950211 0.311606i \(-0.899133\pi\)
−0.950211 + 0.311606i \(0.899133\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1204.00 −1.01043 −0.505213 0.862995i \(-0.668586\pi\)
−0.505213 + 0.862995i \(0.668586\pi\)
\(18\) 0 0
\(19\) 2644.00 1.68026 0.840132 0.542382i \(-0.182478\pi\)
0.840132 + 0.542382i \(0.182478\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1190.00 −0.469059 −0.234529 0.972109i \(-0.575355\pi\)
−0.234529 + 0.972109i \(0.575355\pi\)
\(24\) 0 0
\(25\) −1189.00 −0.380480
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3614.00 −0.797982 −0.398991 0.916955i \(-0.630640\pi\)
−0.398991 + 0.916955i \(0.630640\pi\)
\(30\) 0 0
\(31\) −5616.00 −1.04960 −0.524799 0.851226i \(-0.675859\pi\)
−0.524799 + 0.851226i \(0.675859\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2156.00 −0.297494
\(36\) 0 0
\(37\) −6478.00 −0.777923 −0.388962 0.921254i \(-0.627166\pi\)
−0.388962 + 0.921254i \(0.627166\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2856.00 −0.265337 −0.132669 0.991160i \(-0.542355\pi\)
−0.132669 + 0.991160i \(0.542355\pi\)
\(42\) 0 0
\(43\) 13492.0 1.11277 0.556385 0.830925i \(-0.312188\pi\)
0.556385 + 0.830925i \(0.312188\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −18372.0 −1.21314 −0.606571 0.795029i \(-0.707456\pi\)
−0.606571 + 0.795029i \(0.707456\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 4374.00 0.213889 0.106945 0.994265i \(-0.465893\pi\)
0.106945 + 0.994265i \(0.465893\pi\)
\(54\) 0 0
\(55\) 20680.0 0.921815
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 30248.0 1.13127 0.565635 0.824655i \(-0.308631\pi\)
0.565635 + 0.824655i \(0.308631\pi\)
\(60\) 0 0
\(61\) 19542.0 0.672426 0.336213 0.941786i \(-0.390854\pi\)
0.336213 + 0.941786i \(0.390854\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 50952.0 1.49581
\(66\) 0 0
\(67\) −54328.0 −1.47855 −0.739276 0.673402i \(-0.764832\pi\)
−0.739276 + 0.673402i \(0.764832\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −10730.0 −0.252612 −0.126306 0.991991i \(-0.540312\pi\)
−0.126306 + 0.991991i \(0.540312\pi\)
\(72\) 0 0
\(73\) 35374.0 0.776921 0.388461 0.921465i \(-0.373007\pi\)
0.388461 + 0.921465i \(0.373007\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −23030.0 −0.442657
\(78\) 0 0
\(79\) 49956.0 0.900575 0.450288 0.892884i \(-0.351321\pi\)
0.450288 + 0.892884i \(0.351321\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −26948.0 −0.429370 −0.214685 0.976683i \(-0.568872\pi\)
−0.214685 + 0.976683i \(0.568872\pi\)
\(84\) 0 0
\(85\) 52976.0 0.795302
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −100776. −1.34860 −0.674298 0.738459i \(-0.735554\pi\)
−0.674298 + 0.738459i \(0.735554\pi\)
\(90\) 0 0
\(91\) −56742.0 −0.718292
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −116336. −1.32253
\(96\) 0 0
\(97\) 77134.0 0.832370 0.416185 0.909280i \(-0.363367\pi\)
0.416185 + 0.909280i \(0.363367\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −99464.0 −0.970203 −0.485101 0.874458i \(-0.661217\pi\)
−0.485101 + 0.874458i \(0.661217\pi\)
\(102\) 0 0
\(103\) −66944.0 −0.621754 −0.310877 0.950450i \(-0.600623\pi\)
−0.310877 + 0.950450i \(0.600623\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −228198. −1.92687 −0.963435 0.267942i \(-0.913656\pi\)
−0.963435 + 0.267942i \(0.913656\pi\)
\(108\) 0 0
\(109\) −95186.0 −0.767374 −0.383687 0.923463i \(-0.625346\pi\)
−0.383687 + 0.923463i \(0.625346\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 261142. 1.92389 0.961946 0.273240i \(-0.0880954\pi\)
0.961946 + 0.273240i \(0.0880954\pi\)
\(114\) 0 0
\(115\) 52360.0 0.369194
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −58996.0 −0.381905
\(120\) 0 0
\(121\) 59849.0 0.371615
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 189816. 1.08657
\(126\) 0 0
\(127\) 167652. 0.922358 0.461179 0.887307i \(-0.347427\pi\)
0.461179 + 0.887307i \(0.347427\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −83068.0 −0.422917 −0.211459 0.977387i \(-0.567821\pi\)
−0.211459 + 0.977387i \(0.567821\pi\)
\(132\) 0 0
\(133\) 129556. 0.635080
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −162254. −0.738574 −0.369287 0.929315i \(-0.620398\pi\)
−0.369287 + 0.929315i \(0.620398\pi\)
\(138\) 0 0
\(139\) 58844.0 0.258324 0.129162 0.991623i \(-0.458771\pi\)
0.129162 + 0.991623i \(0.458771\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 544260. 2.22570
\(144\) 0 0
\(145\) 159016. 0.628088
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −430698. −1.58930 −0.794652 0.607065i \(-0.792347\pi\)
−0.794652 + 0.607065i \(0.792347\pi\)
\(150\) 0 0
\(151\) 500936. 1.78789 0.893943 0.448180i \(-0.147928\pi\)
0.893943 + 0.448180i \(0.147928\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 247104. 0.826134
\(156\) 0 0
\(157\) −280258. −0.907421 −0.453711 0.891149i \(-0.649900\pi\)
−0.453711 + 0.891149i \(0.649900\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −58310.0 −0.177288
\(162\) 0 0
\(163\) 120016. 0.353810 0.176905 0.984228i \(-0.443391\pi\)
0.176905 + 0.984228i \(0.443391\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 546932. 1.51755 0.758774 0.651355i \(-0.225799\pi\)
0.758774 + 0.651355i \(0.225799\pi\)
\(168\) 0 0
\(169\) 969671. 2.61161
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 367096. 0.932533 0.466267 0.884644i \(-0.345599\pi\)
0.466267 + 0.884644i \(0.345599\pi\)
\(174\) 0 0
\(175\) −58261.0 −0.143808
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −88890.0 −0.207358 −0.103679 0.994611i \(-0.533061\pi\)
−0.103679 + 0.994611i \(0.533061\pi\)
\(180\) 0 0
\(181\) −782118. −1.77450 −0.887250 0.461290i \(-0.847387\pi\)
−0.887250 + 0.461290i \(0.847387\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 285032. 0.612300
\(186\) 0 0
\(187\) 565880. 1.18337
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 763350. 1.51405 0.757025 0.653386i \(-0.226652\pi\)
0.757025 + 0.653386i \(0.226652\pi\)
\(192\) 0 0
\(193\) −377002. −0.728535 −0.364267 0.931294i \(-0.618681\pi\)
−0.364267 + 0.931294i \(0.618681\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 68678.0 0.126082 0.0630409 0.998011i \(-0.479920\pi\)
0.0630409 + 0.998011i \(0.479920\pi\)
\(198\) 0 0
\(199\) −182576. −0.326822 −0.163411 0.986558i \(-0.552250\pi\)
−0.163411 + 0.986558i \(0.552250\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −177086. −0.301609
\(204\) 0 0
\(205\) 125664. 0.208846
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.24268e6 −1.96786
\(210\) 0 0
\(211\) −232652. −0.359750 −0.179875 0.983689i \(-0.557569\pi\)
−0.179875 + 0.983689i \(0.557569\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −593648. −0.875856
\(216\) 0 0
\(217\) −275184. −0.396711
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.39423e6 1.92023
\(222\) 0 0
\(223\) −167144. −0.225076 −0.112538 0.993647i \(-0.535898\pi\)
−0.112538 + 0.993647i \(0.535898\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 415728. 0.535482 0.267741 0.963491i \(-0.413723\pi\)
0.267741 + 0.963491i \(0.413723\pi\)
\(228\) 0 0
\(229\) 473482. 0.596643 0.298322 0.954465i \(-0.403573\pi\)
0.298322 + 0.954465i \(0.403573\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.55655e6 1.87833 0.939166 0.343465i \(-0.111601\pi\)
0.939166 + 0.343465i \(0.111601\pi\)
\(234\) 0 0
\(235\) 808368. 0.954859
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 655890. 0.742739 0.371370 0.928485i \(-0.378888\pi\)
0.371370 + 0.928485i \(0.378888\pi\)
\(240\) 0 0
\(241\) −889474. −0.986485 −0.493243 0.869892i \(-0.664189\pi\)
−0.493243 + 0.869892i \(0.664189\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −105644. −0.112442
\(246\) 0 0
\(247\) −3.06175e6 −3.19321
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 131832. 0.132080 0.0660399 0.997817i \(-0.478964\pi\)
0.0660399 + 0.997817i \(0.478964\pi\)
\(252\) 0 0
\(253\) 559300. 0.549343
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.46482e6 1.38341 0.691704 0.722181i \(-0.256860\pi\)
0.691704 + 0.722181i \(0.256860\pi\)
\(258\) 0 0
\(259\) −317422. −0.294027
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.47969e6 1.31911 0.659556 0.751656i \(-0.270745\pi\)
0.659556 + 0.751656i \(0.270745\pi\)
\(264\) 0 0
\(265\) −192456. −0.168351
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 187852. 0.158283 0.0791417 0.996863i \(-0.474782\pi\)
0.0791417 + 0.996863i \(0.474782\pi\)
\(270\) 0 0
\(271\) −193800. −0.160299 −0.0801495 0.996783i \(-0.525540\pi\)
−0.0801495 + 0.996783i \(0.525540\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 558830. 0.445603
\(276\) 0 0
\(277\) −617062. −0.483203 −0.241601 0.970376i \(-0.577673\pi\)
−0.241601 + 0.970376i \(0.577673\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.73129e6 1.30799 0.653994 0.756499i \(-0.273092\pi\)
0.653994 + 0.756499i \(0.273092\pi\)
\(282\) 0 0
\(283\) −356020. −0.264246 −0.132123 0.991233i \(-0.542179\pi\)
−0.132123 + 0.991233i \(0.542179\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −139944. −0.100288
\(288\) 0 0
\(289\) 29759.0 0.0209592
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −536664. −0.365202 −0.182601 0.983187i \(-0.558452\pi\)
−0.182601 + 0.983187i \(0.558452\pi\)
\(294\) 0 0
\(295\) −1.33091e6 −0.890419
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.37802e6 0.891410
\(300\) 0 0
\(301\) 661108. 0.420587
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −859848. −0.529264
\(306\) 0 0
\(307\) 2.88398e6 1.74641 0.873205 0.487353i \(-0.162037\pi\)
0.873205 + 0.487353i \(0.162037\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.02958e6 −0.603614 −0.301807 0.953369i \(-0.597590\pi\)
−0.301807 + 0.953369i \(0.597590\pi\)
\(312\) 0 0
\(313\) 1.39297e6 0.803676 0.401838 0.915711i \(-0.368372\pi\)
0.401838 + 0.915711i \(0.368372\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 780030. 0.435977 0.217988 0.975951i \(-0.430051\pi\)
0.217988 + 0.975951i \(0.430051\pi\)
\(318\) 0 0
\(319\) 1.69858e6 0.934565
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.18338e6 −1.69778
\(324\) 0 0
\(325\) 1.37686e6 0.723073
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −900228. −0.458525
\(330\) 0 0
\(331\) 1.41204e6 0.708399 0.354200 0.935170i \(-0.384753\pi\)
0.354200 + 0.935170i \(0.384753\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.39043e6 1.16376
\(336\) 0 0
\(337\) −634662. −0.304416 −0.152208 0.988348i \(-0.548638\pi\)
−0.152208 + 0.988348i \(0.548638\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.63952e6 1.22925
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.07942e6 1.37292 0.686460 0.727167i \(-0.259163\pi\)
0.686460 + 0.727167i \(0.259163\pi\)
\(348\) 0 0
\(349\) −2.60671e6 −1.14559 −0.572796 0.819698i \(-0.694141\pi\)
−0.572796 + 0.819698i \(0.694141\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 63132.0 0.0269658 0.0134829 0.999909i \(-0.495708\pi\)
0.0134829 + 0.999909i \(0.495708\pi\)
\(354\) 0 0
\(355\) 472120. 0.198830
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 479270. 0.196266 0.0981328 0.995173i \(-0.468713\pi\)
0.0981328 + 0.995173i \(0.468713\pi\)
\(360\) 0 0
\(361\) 4.51464e6 1.82329
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.55646e6 −0.611512
\(366\) 0 0
\(367\) 1.33451e6 0.517199 0.258599 0.965985i \(-0.416739\pi\)
0.258599 + 0.965985i \(0.416739\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 214326. 0.0808426
\(372\) 0 0
\(373\) −1.69759e6 −0.631774 −0.315887 0.948797i \(-0.602302\pi\)
−0.315887 + 0.948797i \(0.602302\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.18501e6 1.51650
\(378\) 0 0
\(379\) −2.51074e6 −0.897850 −0.448925 0.893569i \(-0.648193\pi\)
−0.448925 + 0.893569i \(0.648193\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 559144. 0.194772 0.0973860 0.995247i \(-0.468952\pi\)
0.0973860 + 0.995247i \(0.468952\pi\)
\(384\) 0 0
\(385\) 1.01332e6 0.348413
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −4.51055e6 −1.51132 −0.755658 0.654966i \(-0.772683\pi\)
−0.755658 + 0.654966i \(0.772683\pi\)
\(390\) 0 0
\(391\) 1.43276e6 0.473949
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.19806e6 −0.708839
\(396\) 0 0
\(397\) 5.19862e6 1.65543 0.827717 0.561145i \(-0.189639\pi\)
0.827717 + 0.561145i \(0.189639\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 6.34816e6 1.97146 0.985728 0.168346i \(-0.0538426\pi\)
0.985728 + 0.168346i \(0.0538426\pi\)
\(402\) 0 0
\(403\) 6.50333e6 1.99468
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.04466e6 0.911072
\(408\) 0 0
\(409\) −181642. −0.0536918 −0.0268459 0.999640i \(-0.508546\pi\)
−0.0268459 + 0.999640i \(0.508546\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.48215e6 0.427580
\(414\) 0 0
\(415\) 1.18571e6 0.337955
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −5.62699e6 −1.56582 −0.782909 0.622136i \(-0.786265\pi\)
−0.782909 + 0.622136i \(0.786265\pi\)
\(420\) 0 0
\(421\) −4.42671e6 −1.21724 −0.608619 0.793462i \(-0.708276\pi\)
−0.608619 + 0.793462i \(0.708276\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.43156e6 0.384447
\(426\) 0 0
\(427\) 957558. 0.254153
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.44163e6 −0.373817 −0.186909 0.982377i \(-0.559847\pi\)
−0.186909 + 0.982377i \(0.559847\pi\)
\(432\) 0 0
\(433\) −3.89661e6 −0.998775 −0.499387 0.866379i \(-0.666442\pi\)
−0.499387 + 0.866379i \(0.666442\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.14636e6 −0.788143
\(438\) 0 0
\(439\) −5.11207e6 −1.26601 −0.633003 0.774149i \(-0.718178\pi\)
−0.633003 + 0.774149i \(0.718178\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.44070e6 1.31718 0.658591 0.752501i \(-0.271153\pi\)
0.658591 + 0.752501i \(0.271153\pi\)
\(444\) 0 0
\(445\) 4.43414e6 1.06147
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.31525e6 0.307887 0.153943 0.988080i \(-0.450803\pi\)
0.153943 + 0.988080i \(0.450803\pi\)
\(450\) 0 0
\(451\) 1.34232e6 0.310753
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 2.49665e6 0.565365
\(456\) 0 0
\(457\) 2.77604e6 0.621778 0.310889 0.950446i \(-0.399373\pi\)
0.310889 + 0.950446i \(0.399373\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −138080. −0.0302607 −0.0151303 0.999886i \(-0.504816\pi\)
−0.0151303 + 0.999886i \(0.504816\pi\)
\(462\) 0 0
\(463\) 364076. 0.0789295 0.0394648 0.999221i \(-0.487435\pi\)
0.0394648 + 0.999221i \(0.487435\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.73897e6 −1.21770 −0.608852 0.793284i \(-0.708370\pi\)
−0.608852 + 0.793284i \(0.708370\pi\)
\(468\) 0 0
\(469\) −2.66207e6 −0.558840
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −6.34124e6 −1.30323
\(474\) 0 0
\(475\) −3.14372e6 −0.639307
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.51996e6 1.09925 0.549625 0.835411i \(-0.314770\pi\)
0.549625 + 0.835411i \(0.314770\pi\)
\(480\) 0 0
\(481\) 7.50152e6 1.47838
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −3.39390e6 −0.655155
\(486\) 0 0
\(487\) −4.23022e6 −0.808241 −0.404121 0.914706i \(-0.632422\pi\)
−0.404121 + 0.914706i \(0.632422\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.21423e6 −1.35047 −0.675237 0.737601i \(-0.735959\pi\)
−0.675237 + 0.737601i \(0.735959\pi\)
\(492\) 0 0
\(493\) 4.35126e6 0.806301
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −525770. −0.0954783
\(498\) 0 0
\(499\) 224804. 0.0404159 0.0202080 0.999796i \(-0.493567\pi\)
0.0202080 + 0.999796i \(0.493567\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.06983e6 0.893457 0.446728 0.894670i \(-0.352589\pi\)
0.446728 + 0.894670i \(0.352589\pi\)
\(504\) 0 0
\(505\) 4.37642e6 0.763643
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −5.48135e6 −0.937763 −0.468881 0.883261i \(-0.655343\pi\)
−0.468881 + 0.883261i \(0.655343\pi\)
\(510\) 0 0
\(511\) 1.73333e6 0.293649
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.94554e6 0.489380
\(516\) 0 0
\(517\) 8.63484e6 1.42078
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.88932e6 −1.27334 −0.636671 0.771136i \(-0.719689\pi\)
−0.636671 + 0.771136i \(0.719689\pi\)
\(522\) 0 0
\(523\) 9.74950e6 1.55858 0.779288 0.626666i \(-0.215581\pi\)
0.779288 + 0.626666i \(0.215581\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.76166e6 1.06054
\(528\) 0 0
\(529\) −5.02024e6 −0.779984
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 3.30725e6 0.504253
\(534\) 0 0
\(535\) 1.00407e7 1.51663
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.12847e6 −0.167309
\(540\) 0 0
\(541\) −4.17454e6 −0.613219 −0.306610 0.951835i \(-0.599195\pi\)
−0.306610 + 0.951835i \(0.599195\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.18818e6 0.603997
\(546\) 0 0
\(547\) 2.72887e6 0.389955 0.194978 0.980808i \(-0.437537\pi\)
0.194978 + 0.980808i \(0.437537\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9.55542e6 −1.34082
\(552\) 0 0
\(553\) 2.44784e6 0.340385
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 7.35103e6 1.00395 0.501973 0.864883i \(-0.332608\pi\)
0.501973 + 0.864883i \(0.332608\pi\)
\(558\) 0 0
\(559\) −1.56237e7 −2.11473
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.37821e7 −1.83250 −0.916248 0.400612i \(-0.868798\pi\)
−0.916248 + 0.400612i \(0.868798\pi\)
\(564\) 0 0
\(565\) −1.14902e7 −1.51429
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −2.71217e6 −0.351186 −0.175593 0.984463i \(-0.556184\pi\)
−0.175593 + 0.984463i \(0.556184\pi\)
\(570\) 0 0
\(571\) −4.94398e6 −0.634580 −0.317290 0.948329i \(-0.602773\pi\)
−0.317290 + 0.948329i \(0.602773\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.41491e6 0.178468
\(576\) 0 0
\(577\) −1.32683e7 −1.65911 −0.829556 0.558424i \(-0.811406\pi\)
−0.829556 + 0.558424i \(0.811406\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.32045e6 −0.162286
\(582\) 0 0
\(583\) −2.05578e6 −0.250499
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.67205e6 0.200287 0.100144 0.994973i \(-0.468070\pi\)
0.100144 + 0.994973i \(0.468070\pi\)
\(588\) 0 0
\(589\) −1.48487e7 −1.76360
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −5.11693e6 −0.597548 −0.298774 0.954324i \(-0.596578\pi\)
−0.298774 + 0.954324i \(0.596578\pi\)
\(594\) 0 0
\(595\) 2.59582e6 0.300596
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −7.15931e6 −0.815275 −0.407638 0.913144i \(-0.633647\pi\)
−0.407638 + 0.913144i \(0.633647\pi\)
\(600\) 0 0
\(601\) −9.63384e6 −1.08796 −0.543980 0.839098i \(-0.683083\pi\)
−0.543980 + 0.839098i \(0.683083\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.63336e6 −0.292497
\(606\) 0 0
\(607\) −5.52115e6 −0.608216 −0.304108 0.952638i \(-0.598358\pi\)
−0.304108 + 0.952638i \(0.598358\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.12748e7 2.30548
\(612\) 0 0
\(613\) 4.79890e6 0.515811 0.257906 0.966170i \(-0.416968\pi\)
0.257906 + 0.966170i \(0.416968\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.71826e6 −0.287461 −0.143730 0.989617i \(-0.545910\pi\)
−0.143730 + 0.989617i \(0.545910\pi\)
\(618\) 0 0
\(619\) 4.34335e6 0.455615 0.227807 0.973706i \(-0.426844\pi\)
0.227807 + 0.973706i \(0.426844\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.93802e6 −0.509722
\(624\) 0 0
\(625\) −4.63628e6 −0.474755
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.79951e6 0.786033
\(630\) 0 0
\(631\) −1.11952e6 −0.111933 −0.0559667 0.998433i \(-0.517824\pi\)
−0.0559667 + 0.998433i \(0.517824\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −7.37669e6 −0.725984
\(636\) 0 0
\(637\) −2.78036e6 −0.271489
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3.96588e6 0.381237 0.190618 0.981664i \(-0.438951\pi\)
0.190618 + 0.981664i \(0.438951\pi\)
\(642\) 0 0
\(643\) −1.92086e7 −1.83218 −0.916092 0.400968i \(-0.868674\pi\)
−0.916092 + 0.400968i \(0.868674\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 4.72739e6 0.443977 0.221989 0.975049i \(-0.428745\pi\)
0.221989 + 0.975049i \(0.428745\pi\)
\(648\) 0 0
\(649\) −1.42166e7 −1.32490
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.21159e7 −1.11192 −0.555958 0.831210i \(-0.687648\pi\)
−0.555958 + 0.831210i \(0.687648\pi\)
\(654\) 0 0
\(655\) 3.65499e6 0.332877
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 5.91457e6 0.530530 0.265265 0.964176i \(-0.414541\pi\)
0.265265 + 0.964176i \(0.414541\pi\)
\(660\) 0 0
\(661\) 1.41779e7 1.26214 0.631072 0.775724i \(-0.282615\pi\)
0.631072 + 0.775724i \(0.282615\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.70046e6 −0.499869
\(666\) 0 0
\(667\) 4.30066e6 0.374301
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −9.18474e6 −0.787518
\(672\) 0 0
\(673\) 1.34245e7 1.14251 0.571256 0.820772i \(-0.306456\pi\)
0.571256 + 0.820772i \(0.306456\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 8.67312e6 0.727283 0.363642 0.931539i \(-0.381533\pi\)
0.363642 + 0.931539i \(0.381533\pi\)
\(678\) 0 0
\(679\) 3.77957e6 0.314606
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.49777e7 1.22855 0.614275 0.789092i \(-0.289448\pi\)
0.614275 + 0.789092i \(0.289448\pi\)
\(684\) 0 0
\(685\) 7.13918e6 0.581329
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −5.06509e6 −0.406480
\(690\) 0 0
\(691\) 8.76742e6 0.698517 0.349258 0.937026i \(-0.386434\pi\)
0.349258 + 0.937026i \(0.386434\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.58914e6 −0.203326
\(696\) 0 0
\(697\) 3.43862e6 0.268104
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.99459e7 1.53306 0.766529 0.642209i \(-0.221982\pi\)
0.766529 + 0.642209i \(0.221982\pi\)
\(702\) 0 0
\(703\) −1.71278e7 −1.30712
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.87374e6 −0.366702
\(708\) 0 0
\(709\) −2.66387e7 −1.99020 −0.995100 0.0988699i \(-0.968477\pi\)
−0.995100 + 0.0988699i \(0.968477\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.68304e6 0.492323
\(714\) 0 0
\(715\) −2.39474e7 −1.75184
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.17408e6 −0.0846985 −0.0423492 0.999103i \(-0.513484\pi\)
−0.0423492 + 0.999103i \(0.513484\pi\)
\(720\) 0 0
\(721\) −3.28026e6 −0.235001
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4.29705e6 0.303616
\(726\) 0 0
\(727\) −1.05734e7 −0.741957 −0.370979 0.928641i \(-0.620978\pi\)
−0.370979 + 0.928641i \(0.620978\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.62444e7 −1.12437
\(732\) 0 0
\(733\) 2.31670e7 1.59261 0.796306 0.604894i \(-0.206785\pi\)
0.796306 + 0.604894i \(0.206785\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.55342e7 1.73162
\(738\) 0 0
\(739\) 1.55334e7 1.04630 0.523148 0.852242i \(-0.324757\pi\)
0.523148 + 0.852242i \(0.324757\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.54630e7 1.69215 0.846074 0.533066i \(-0.178960\pi\)
0.846074 + 0.533066i \(0.178960\pi\)
\(744\) 0 0
\(745\) 1.89507e7 1.25094
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −1.11817e7 −0.728288
\(750\) 0 0
\(751\) −9.88512e6 −0.639561 −0.319781 0.947492i \(-0.603609\pi\)
−0.319781 + 0.947492i \(0.603609\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.20412e7 −1.40724
\(756\) 0 0
\(757\) −6.41980e6 −0.407176 −0.203588 0.979057i \(-0.565260\pi\)
−0.203588 + 0.979057i \(0.565260\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 5.05052e6 0.316136 0.158068 0.987428i \(-0.449473\pi\)
0.158068 + 0.987428i \(0.449473\pi\)
\(762\) 0 0
\(763\) −4.66411e6 −0.290040
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.50272e7 −2.14989
\(768\) 0 0
\(769\) 2.28169e6 0.139136 0.0695682 0.997577i \(-0.477838\pi\)
0.0695682 + 0.997577i \(0.477838\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.73777e7 −1.64797 −0.823984 0.566613i \(-0.808254\pi\)
−0.823984 + 0.566613i \(0.808254\pi\)
\(774\) 0 0
\(775\) 6.67742e6 0.399351
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −7.55126e6 −0.445837
\(780\) 0 0
\(781\) 5.04310e6 0.295849
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.23314e7 0.714227
\(786\) 0 0
\(787\) −2.04263e7 −1.17558 −0.587791 0.809013i \(-0.700002\pi\)
−0.587791 + 0.809013i \(0.700002\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.27960e7 0.727163
\(792\) 0 0
\(793\) −2.26296e7 −1.27789
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.31557e7 −1.29126 −0.645628 0.763652i \(-0.723404\pi\)
−0.645628 + 0.763652i \(0.723404\pi\)
\(798\) 0 0
\(799\) 2.21199e7 1.22579
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.66258e7 −0.909899
\(804\) 0 0
\(805\) 2.56564e6 0.139542
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −1.14894e7 −0.617203 −0.308601 0.951191i \(-0.599861\pi\)
−0.308601 + 0.951191i \(0.599861\pi\)
\(810\) 0 0
\(811\) −1.72443e7 −0.920648 −0.460324 0.887751i \(-0.652267\pi\)
−0.460324 + 0.887751i \(0.652267\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5.28070e6 −0.278482
\(816\) 0 0
\(817\) 3.56728e7 1.86975
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.37077e6 −0.0709752 −0.0354876 0.999370i \(-0.511298\pi\)
−0.0354876 + 0.999370i \(0.511298\pi\)
\(822\) 0 0
\(823\) −8.56851e6 −0.440967 −0.220483 0.975391i \(-0.570763\pi\)
−0.220483 + 0.975391i \(0.570763\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.33258e6 −0.0677533 −0.0338766 0.999426i \(-0.510785\pi\)
−0.0338766 + 0.999426i \(0.510785\pi\)
\(828\) 0 0
\(829\) 6.25659e6 0.316193 0.158096 0.987424i \(-0.449464\pi\)
0.158096 + 0.987424i \(0.449464\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −2.89080e6 −0.144346
\(834\) 0 0
\(835\) −2.40650e7 −1.19446
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −1.61258e6 −0.0790891 −0.0395445 0.999218i \(-0.512591\pi\)
−0.0395445 + 0.999218i \(0.512591\pi\)
\(840\) 0 0
\(841\) −7.45015e6 −0.363225
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.26655e7 −2.05558
\(846\) 0 0
\(847\) 2.93260e6 0.140457
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 7.70882e6 0.364892
\(852\) 0 0
\(853\) −3.44919e7 −1.62310 −0.811548 0.584286i \(-0.801375\pi\)
−0.811548 + 0.584286i \(0.801375\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.85487e7 0.862704 0.431352 0.902184i \(-0.358037\pi\)
0.431352 + 0.902184i \(0.358037\pi\)
\(858\) 0 0
\(859\) 2.56435e7 1.18575 0.592877 0.805293i \(-0.297992\pi\)
0.592877 + 0.805293i \(0.297992\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.49899e7 −1.14219 −0.571093 0.820885i \(-0.693481\pi\)
−0.571093 + 0.820885i \(0.693481\pi\)
\(864\) 0 0
\(865\) −1.61522e7 −0.733993
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −2.34793e7 −1.05472
\(870\) 0 0
\(871\) 6.29118e7 2.80987
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 9.30098e6 0.410685
\(876\) 0 0
\(877\) −3.46337e7 −1.52055 −0.760274 0.649602i \(-0.774935\pi\)
−0.760274 + 0.649602i \(0.774935\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −2.92434e7 −1.26937 −0.634685 0.772771i \(-0.718870\pi\)
−0.634685 + 0.772771i \(0.718870\pi\)
\(882\) 0 0
\(883\) 3.76532e7 1.62518 0.812588 0.582839i \(-0.198058\pi\)
0.812588 + 0.582839i \(0.198058\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.08201e6 −0.0888534 −0.0444267 0.999013i \(-0.514146\pi\)
−0.0444267 + 0.999013i \(0.514146\pi\)
\(888\) 0 0
\(889\) 8.21495e6 0.348618
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −4.85756e7 −2.03840
\(894\) 0 0
\(895\) 3.91116e6 0.163210
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.02962e7 0.837560
\(900\) 0 0
\(901\) −5.26630e6 −0.216119
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 3.44132e7 1.39670
\(906\) 0 0
\(907\) −1.62350e7 −0.655291 −0.327645 0.944801i \(-0.606255\pi\)
−0.327645 + 0.944801i \(0.606255\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.58656e7 −1.03259 −0.516294 0.856412i \(-0.672689\pi\)
−0.516294 + 0.856412i \(0.672689\pi\)
\(912\) 0 0
\(913\) 1.26656e7 0.502860
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −4.07033e6 −0.159848
\(918\) 0 0
\(919\) 1.23266e7 0.481453 0.240726 0.970593i \(-0.422614\pi\)
0.240726 + 0.970593i \(0.422614\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 1.24253e7 0.480069
\(924\) 0 0
\(925\) 7.70234e6 0.295984
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.15128e7 1.57813 0.789064 0.614310i \(-0.210566\pi\)
0.789064 + 0.614310i \(0.210566\pi\)
\(930\) 0 0
\(931\) 6.34824e6 0.240038
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.48987e7 −0.931425
\(936\) 0 0
\(937\) 2.26895e7 0.844260 0.422130 0.906535i \(-0.361283\pi\)
0.422130 + 0.906535i \(0.361283\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −1.58213e7 −0.582464 −0.291232 0.956652i \(-0.594065\pi\)
−0.291232 + 0.956652i \(0.594065\pi\)
\(942\) 0 0
\(943\) 3.39864e6 0.124459
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 5.17579e7 1.87543 0.937716 0.347402i \(-0.112936\pi\)
0.937716 + 0.347402i \(0.112936\pi\)
\(948\) 0 0
\(949\) −4.09631e7 −1.47648
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.29818e7 −0.819695 −0.409848 0.912154i \(-0.634418\pi\)
−0.409848 + 0.912154i \(0.634418\pi\)
\(954\) 0 0
\(955\) −3.35874e7 −1.19170
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −7.95045e6 −0.279155
\(960\) 0 0
\(961\) 2.91030e6 0.101655
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.65881e7 0.573427
\(966\) 0 0
\(967\) −3.20783e7 −1.10318 −0.551588 0.834117i \(-0.685978\pi\)
−0.551588 + 0.834117i \(0.685978\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 7.31101e6 0.248845 0.124423 0.992229i \(-0.460292\pi\)
0.124423 + 0.992229i \(0.460292\pi\)
\(972\) 0 0
\(973\) 2.88336e6 0.0976374
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −7.58600e6 −0.254259 −0.127129 0.991886i \(-0.540576\pi\)
−0.127129 + 0.991886i \(0.540576\pi\)
\(978\) 0 0
\(979\) 4.73647e7 1.57942
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.47823e7 −0.818007 −0.409004 0.912533i \(-0.634124\pi\)
−0.409004 + 0.912533i \(0.634124\pi\)
\(984\) 0 0
\(985\) −3.02183e6 −0.0992384
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1.60555e7 −0.521954
\(990\) 0 0
\(991\) 7.63530e6 0.246969 0.123484 0.992347i \(-0.460593\pi\)
0.123484 + 0.992347i \(0.460593\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 8.03334e6 0.257240
\(996\) 0 0
\(997\) −2.89785e7 −0.923289 −0.461644 0.887065i \(-0.652740\pi\)
−0.461644 + 0.887065i \(0.652740\pi\)
\(998\) 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.g.1.1 1
3.2 odd 2 336.6.a.o.1.1 1
4.3 odd 2 126.6.a.h.1.1 1
12.11 even 2 42.6.a.b.1.1 1
28.27 even 2 882.6.a.v.1.1 1
60.23 odd 4 1050.6.g.l.799.2 2
60.47 odd 4 1050.6.g.l.799.1 2
60.59 even 2 1050.6.a.o.1.1 1
84.11 even 6 294.6.e.o.79.1 2
84.23 even 6 294.6.e.o.67.1 2
84.47 odd 6 294.6.e.k.67.1 2
84.59 odd 6 294.6.e.k.79.1 2
84.83 odd 2 294.6.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.6.a.b.1.1 1 12.11 even 2
126.6.a.h.1.1 1 4.3 odd 2
294.6.a.f.1.1 1 84.83 odd 2
294.6.e.k.67.1 2 84.47 odd 6
294.6.e.k.79.1 2 84.59 odd 6
294.6.e.o.67.1 2 84.23 even 6
294.6.e.o.79.1 2 84.11 even 6
336.6.a.o.1.1 1 3.2 odd 2
882.6.a.v.1.1 1 28.27 even 2
1008.6.a.g.1.1 1 1.1 even 1 trivial
1050.6.a.o.1.1 1 60.59 even 2
1050.6.g.l.799.1 2 60.47 odd 4
1050.6.g.l.799.2 2 60.23 odd 4