Properties

Label 1008.6.a.z.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 168)
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)
 
\(f(q)\) \(=\) \(q+64.0000 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+64.0000 q^{5} -49.0000 q^{7} -54.0000 q^{11} +738.000 q^{13} +848.000 q^{17} +1604.00 q^{19} -3670.00 q^{23} +971.000 q^{25} +4330.00 q^{29} +4760.00 q^{31} -3136.00 q^{35} -2094.00 q^{37} +6116.00 q^{41} -7916.00 q^{43} +6572.00 q^{47} +2401.00 q^{49} +7894.00 q^{53} -3456.00 q^{55} -41664.0 q^{59} -26570.0 q^{61} +47232.0 q^{65} +41736.0 q^{67} +83574.0 q^{71} -42314.0 q^{73} +2646.00 q^{77} -508.000 q^{79} -8364.00 q^{83} +54272.0 q^{85} +49220.0 q^{89} -36162.0 q^{91} +102656. q^{95} +159670. q^{97} +O(q^{100})\)

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
\(5\) 64.0000 1.14487 0.572433 0.819951i \(-0.306000\pi\)
0.572433 + 0.819951i \(0.306000\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −54.0000 −0.134559 −0.0672794 0.997734i \(-0.521432\pi\)
−0.0672794 + 0.997734i \(0.521432\pi\)
\(12\) 0 0
\(13\) 738.000 1.21115 0.605575 0.795788i \(-0.292943\pi\)
0.605575 + 0.795788i \(0.292943\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 848.000 0.711662 0.355831 0.934550i \(-0.384198\pi\)
0.355831 + 0.934550i \(0.384198\pi\)
\(18\) 0 0
\(19\) 1604.00 1.01934 0.509672 0.860369i \(-0.329767\pi\)
0.509672 + 0.860369i \(0.329767\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3670.00 −1.44659 −0.723297 0.690537i \(-0.757374\pi\)
−0.723297 + 0.690537i \(0.757374\pi\)
\(24\) 0 0
\(25\) 971.000 0.310720
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4330.00 0.956077 0.478039 0.878339i \(-0.341348\pi\)
0.478039 + 0.878339i \(0.341348\pi\)
\(30\) 0 0
\(31\) 4760.00 0.889616 0.444808 0.895626i \(-0.353272\pi\)
0.444808 + 0.895626i \(0.353272\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3136.00 −0.432719
\(36\) 0 0
\(37\) −2094.00 −0.251462 −0.125731 0.992064i \(-0.540128\pi\)
−0.125731 + 0.992064i \(0.540128\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6116.00 0.568209 0.284104 0.958793i \(-0.408304\pi\)
0.284104 + 0.958793i \(0.408304\pi\)
\(42\) 0 0
\(43\) −7916.00 −0.652882 −0.326441 0.945218i \(-0.605849\pi\)
−0.326441 + 0.945218i \(0.605849\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6572.00 0.433963 0.216982 0.976176i \(-0.430379\pi\)
0.216982 + 0.976176i \(0.430379\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7894.00 0.386018 0.193009 0.981197i \(-0.438175\pi\)
0.193009 + 0.981197i \(0.438175\pi\)
\(54\) 0 0
\(55\) −3456.00 −0.154052
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −41664.0 −1.55823 −0.779114 0.626882i \(-0.784331\pi\)
−0.779114 + 0.626882i \(0.784331\pi\)
\(60\) 0 0
\(61\) −26570.0 −0.914254 −0.457127 0.889401i \(-0.651122\pi\)
−0.457127 + 0.889401i \(0.651122\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 47232.0 1.38661
\(66\) 0 0
\(67\) 41736.0 1.13586 0.567929 0.823078i \(-0.307745\pi\)
0.567929 + 0.823078i \(0.307745\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 83574.0 1.96755 0.983774 0.179412i \(-0.0574196\pi\)
0.983774 + 0.179412i \(0.0574196\pi\)
\(72\) 0 0
\(73\) −42314.0 −0.929345 −0.464672 0.885483i \(-0.653828\pi\)
−0.464672 + 0.885483i \(0.653828\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2646.00 0.0508584
\(78\) 0 0
\(79\) −508.000 −0.00915790 −0.00457895 0.999990i \(-0.501458\pi\)
−0.00457895 + 0.999990i \(0.501458\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −8364.00 −0.133266 −0.0666329 0.997778i \(-0.521226\pi\)
−0.0666329 + 0.997778i \(0.521226\pi\)
\(84\) 0 0
\(85\) 54272.0 0.814758
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 49220.0 0.658668 0.329334 0.944213i \(-0.393176\pi\)
0.329334 + 0.944213i \(0.393176\pi\)
\(90\) 0 0
\(91\) −36162.0 −0.457772
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 102656. 1.16701
\(96\) 0 0
\(97\) 159670. 1.72303 0.861517 0.507728i \(-0.169515\pi\)
0.861517 + 0.507728i \(0.169515\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 67020.0 0.653734 0.326867 0.945070i \(-0.394007\pi\)
0.326867 + 0.945070i \(0.394007\pi\)
\(102\) 0 0
\(103\) −165768. −1.53960 −0.769800 0.638286i \(-0.779644\pi\)
−0.769800 + 0.638286i \(0.779644\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 103146. 0.870949 0.435475 0.900201i \(-0.356581\pi\)
0.435475 + 0.900201i \(0.356581\pi\)
\(108\) 0 0
\(109\) 60094.0 0.484468 0.242234 0.970218i \(-0.422120\pi\)
0.242234 + 0.970218i \(0.422120\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 126246. 0.930083 0.465041 0.885289i \(-0.346039\pi\)
0.465041 + 0.885289i \(0.346039\pi\)
\(114\) 0 0
\(115\) −234880. −1.65616
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −41552.0 −0.268983
\(120\) 0 0
\(121\) −158135. −0.981894
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −137856. −0.789134
\(126\) 0 0
\(127\) −308636. −1.69800 −0.848999 0.528394i \(-0.822794\pi\)
−0.848999 + 0.528394i \(0.822794\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −61012.0 −0.310625 −0.155313 0.987865i \(-0.549639\pi\)
−0.155313 + 0.987865i \(0.549639\pi\)
\(132\) 0 0
\(133\) −78596.0 −0.385275
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 317242. 1.44407 0.722037 0.691855i \(-0.243206\pi\)
0.722037 + 0.691855i \(0.243206\pi\)
\(138\) 0 0
\(139\) 7236.00 0.0317659 0.0158830 0.999874i \(-0.494944\pi\)
0.0158830 + 0.999874i \(0.494944\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −39852.0 −0.162971
\(144\) 0 0
\(145\) 277120. 1.09458
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −126058. −0.465163 −0.232581 0.972577i \(-0.574717\pi\)
−0.232581 + 0.972577i \(0.574717\pi\)
\(150\) 0 0
\(151\) −200296. −0.714875 −0.357437 0.933937i \(-0.616349\pi\)
−0.357437 + 0.933937i \(0.616349\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 304640. 1.01849
\(156\) 0 0
\(157\) 510894. 1.65418 0.827088 0.562073i \(-0.189996\pi\)
0.827088 + 0.562073i \(0.189996\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 179830. 0.546761
\(162\) 0 0
\(163\) −21184.0 −0.0624509 −0.0312255 0.999512i \(-0.509941\pi\)
−0.0312255 + 0.999512i \(0.509941\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −267180. −0.741332 −0.370666 0.928766i \(-0.620871\pi\)
−0.370666 + 0.928766i \(0.620871\pi\)
\(168\) 0 0
\(169\) 173351. 0.466885
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 91948.0 0.233575 0.116788 0.993157i \(-0.462740\pi\)
0.116788 + 0.993157i \(0.462740\pi\)
\(174\) 0 0
\(175\) −47579.0 −0.117441
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −402826. −0.939691 −0.469845 0.882749i \(-0.655690\pi\)
−0.469845 + 0.882749i \(0.655690\pi\)
\(180\) 0 0
\(181\) −796222. −1.80650 −0.903250 0.429116i \(-0.858825\pi\)
−0.903250 + 0.429116i \(0.858825\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −134016. −0.287890
\(186\) 0 0
\(187\) −45792.0 −0.0957603
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 474934. 0.941998 0.470999 0.882134i \(-0.343894\pi\)
0.470999 + 0.882134i \(0.343894\pi\)
\(192\) 0 0
\(193\) 716022. 1.38367 0.691836 0.722055i \(-0.256802\pi\)
0.691836 + 0.722055i \(0.256802\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 221814. 0.407215 0.203607 0.979053i \(-0.434733\pi\)
0.203607 + 0.979053i \(0.434733\pi\)
\(198\) 0 0
\(199\) 333616. 0.597192 0.298596 0.954380i \(-0.403482\pi\)
0.298596 + 0.954380i \(0.403482\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −212170. −0.361363
\(204\) 0 0
\(205\) 391424. 0.650523
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −86616.0 −0.137162
\(210\) 0 0
\(211\) 176404. 0.272774 0.136387 0.990656i \(-0.456451\pi\)
0.136387 + 0.990656i \(0.456451\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −506624. −0.747463
\(216\) 0 0
\(217\) −233240. −0.336243
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 625824. 0.861929
\(222\) 0 0
\(223\) 125016. 0.168346 0.0841731 0.996451i \(-0.473175\pi\)
0.0841731 + 0.996451i \(0.473175\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −272104. −0.350486 −0.175243 0.984525i \(-0.556071\pi\)
−0.175243 + 0.984525i \(0.556071\pi\)
\(228\) 0 0
\(229\) −325822. −0.410574 −0.205287 0.978702i \(-0.565813\pi\)
−0.205287 + 0.978702i \(0.565813\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 534682. 0.645217 0.322608 0.946533i \(-0.395440\pi\)
0.322608 + 0.946533i \(0.395440\pi\)
\(234\) 0 0
\(235\) 420608. 0.496830
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.48512e6 1.68177 0.840887 0.541211i \(-0.182034\pi\)
0.840887 + 0.541211i \(0.182034\pi\)
\(240\) 0 0
\(241\) 1.17689e6 1.30524 0.652622 0.757684i \(-0.273669\pi\)
0.652622 + 0.757684i \(0.273669\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 153664. 0.163552
\(246\) 0 0
\(247\) 1.18375e6 1.23458
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 14080.0 0.0141065 0.00705324 0.999975i \(-0.497755\pi\)
0.00705324 + 0.999975i \(0.497755\pi\)
\(252\) 0 0
\(253\) 198180. 0.194652
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.86851e6 1.76466 0.882332 0.470627i \(-0.155972\pi\)
0.882332 + 0.470627i \(0.155972\pi\)
\(258\) 0 0
\(259\) 102606. 0.0950437
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 802890. 0.715759 0.357879 0.933768i \(-0.383500\pi\)
0.357879 + 0.933768i \(0.383500\pi\)
\(264\) 0 0
\(265\) 505216. 0.441939
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 197448. 0.166369 0.0831844 0.996534i \(-0.473491\pi\)
0.0831844 + 0.996534i \(0.473491\pi\)
\(270\) 0 0
\(271\) 2.01928e6 1.67022 0.835109 0.550084i \(-0.185404\pi\)
0.835109 + 0.550084i \(0.185404\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −52434.0 −0.0418101
\(276\) 0 0
\(277\) 1.57993e6 1.23720 0.618598 0.785708i \(-0.287701\pi\)
0.618598 + 0.785708i \(0.287701\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.44392e6 −1.09088 −0.545440 0.838150i \(-0.683637\pi\)
−0.545440 + 0.838150i \(0.683637\pi\)
\(282\) 0 0
\(283\) 1.68046e6 1.24727 0.623637 0.781714i \(-0.285654\pi\)
0.623637 + 0.781714i \(0.285654\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −299684. −0.214763
\(288\) 0 0
\(289\) −700753. −0.493538
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.31092e6 1.57259 0.786297 0.617849i \(-0.211996\pi\)
0.786297 + 0.617849i \(0.211996\pi\)
\(294\) 0 0
\(295\) −2.66650e6 −1.78396
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.70846e6 −1.75204
\(300\) 0 0
\(301\) 387884. 0.246766
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −1.70048e6 −1.04670
\(306\) 0 0
\(307\) 793964. 0.480789 0.240395 0.970675i \(-0.422723\pi\)
0.240395 + 0.970675i \(0.422723\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.18376e6 0.694007 0.347004 0.937864i \(-0.387199\pi\)
0.347004 + 0.937864i \(0.387199\pi\)
\(312\) 0 0
\(313\) 994970. 0.574049 0.287025 0.957923i \(-0.407334\pi\)
0.287025 + 0.957923i \(0.407334\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.84619e6 −1.03188 −0.515940 0.856625i \(-0.672557\pi\)
−0.515940 + 0.856625i \(0.672557\pi\)
\(318\) 0 0
\(319\) −233820. −0.128649
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.36019e6 0.725427
\(324\) 0 0
\(325\) 716598. 0.376329
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −322028. −0.164023
\(330\) 0 0
\(331\) 1.55801e6 0.781629 0.390815 0.920469i \(-0.372193\pi\)
0.390815 + 0.920469i \(0.372193\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.67110e6 1.30041
\(336\) 0 0
\(337\) 3.28798e6 1.57708 0.788541 0.614982i \(-0.210837\pi\)
0.788541 + 0.614982i \(0.210837\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −257040. −0.119706
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.66137e6 1.63238 0.816188 0.577786i \(-0.196083\pi\)
0.816188 + 0.577786i \(0.196083\pi\)
\(348\) 0 0
\(349\) −3.76811e6 −1.65600 −0.827998 0.560730i \(-0.810520\pi\)
−0.827998 + 0.560730i \(0.810520\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.97794e6 −0.844842 −0.422421 0.906400i \(-0.638820\pi\)
−0.422421 + 0.906400i \(0.638820\pi\)
\(354\) 0 0
\(355\) 5.34874e6 2.25258
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 3.17410e6 1.29982 0.649912 0.760009i \(-0.274806\pi\)
0.649912 + 0.760009i \(0.274806\pi\)
\(360\) 0 0
\(361\) 96717.0 0.0390602
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.70810e6 −1.06398
\(366\) 0 0
\(367\) −3.62163e6 −1.40359 −0.701793 0.712381i \(-0.747617\pi\)
−0.701793 + 0.712381i \(0.747617\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −386806. −0.145901
\(372\) 0 0
\(373\) −3.65737e6 −1.36112 −0.680561 0.732692i \(-0.738264\pi\)
−0.680561 + 0.732692i \(0.738264\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.19554e6 1.15795
\(378\) 0 0
\(379\) −1.07802e6 −0.385504 −0.192752 0.981248i \(-0.561741\pi\)
−0.192752 + 0.981248i \(0.561741\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.86954e6 1.34792 0.673958 0.738770i \(-0.264593\pi\)
0.673958 + 0.738770i \(0.264593\pi\)
\(384\) 0 0
\(385\) 169344. 0.0582261
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.75845e6 1.25932 0.629658 0.776872i \(-0.283195\pi\)
0.629658 + 0.776872i \(0.283195\pi\)
\(390\) 0 0
\(391\) −3.11216e6 −1.02948
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −32512.0 −0.0104846
\(396\) 0 0
\(397\) −1.47106e6 −0.468440 −0.234220 0.972184i \(-0.575254\pi\)
−0.234220 + 0.972184i \(0.575254\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.30313e6 1.64692 0.823458 0.567378i \(-0.192042\pi\)
0.823458 + 0.567378i \(0.192042\pi\)
\(402\) 0 0
\(403\) 3.51288e6 1.07746
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 113076. 0.0338364
\(408\) 0 0
\(409\) −6.46984e6 −1.91243 −0.956215 0.292666i \(-0.905458\pi\)
−0.956215 + 0.292666i \(0.905458\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.04154e6 0.588955
\(414\) 0 0
\(415\) −535296. −0.152572
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 554024. 0.154168 0.0770839 0.997025i \(-0.475439\pi\)
0.0770839 + 0.997025i \(0.475439\pi\)
\(420\) 0 0
\(421\) −3.37900e6 −0.929143 −0.464572 0.885536i \(-0.653792\pi\)
−0.464572 + 0.885536i \(0.653792\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 823408. 0.221128
\(426\) 0 0
\(427\) 1.30193e6 0.345556
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.90338e6 0.752854 0.376427 0.926446i \(-0.377152\pi\)
0.376427 + 0.926446i \(0.377152\pi\)
\(432\) 0 0
\(433\) −5.05684e6 −1.29616 −0.648081 0.761571i \(-0.724428\pi\)
−0.648081 + 0.761571i \(0.724428\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.88668e6 −1.47457
\(438\) 0 0
\(439\) 2.43257e6 0.602426 0.301213 0.953557i \(-0.402608\pi\)
0.301213 + 0.953557i \(0.402608\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.35832e6 −0.570944 −0.285472 0.958387i \(-0.592150\pi\)
−0.285472 + 0.958387i \(0.592150\pi\)
\(444\) 0 0
\(445\) 3.15008e6 0.754087
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −798466. −0.186913 −0.0934567 0.995623i \(-0.529792\pi\)
−0.0934567 + 0.995623i \(0.529792\pi\)
\(450\) 0 0
\(451\) −330264. −0.0764575
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.31437e6 −0.524088
\(456\) 0 0
\(457\) −3.53337e6 −0.791404 −0.395702 0.918379i \(-0.629499\pi\)
−0.395702 + 0.918379i \(0.629499\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.98709e6 0.435477 0.217739 0.976007i \(-0.430132\pi\)
0.217739 + 0.976007i \(0.430132\pi\)
\(462\) 0 0
\(463\) −6.33175e6 −1.37269 −0.686343 0.727278i \(-0.740785\pi\)
−0.686343 + 0.727278i \(0.740785\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 274560. 0.0582566 0.0291283 0.999576i \(-0.490727\pi\)
0.0291283 + 0.999576i \(0.490727\pi\)
\(468\) 0 0
\(469\) −2.04506e6 −0.429314
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 427464. 0.0878510
\(474\) 0 0
\(475\) 1.55748e6 0.316730
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 933460. 0.185890 0.0929452 0.995671i \(-0.470372\pi\)
0.0929452 + 0.995671i \(0.470372\pi\)
\(480\) 0 0
\(481\) −1.54537e6 −0.304558
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.02189e7 1.97265
\(486\) 0 0
\(487\) 6.05600e6 1.15708 0.578540 0.815654i \(-0.303623\pi\)
0.578540 + 0.815654i \(0.303623\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.65757e6 0.310290 0.155145 0.987892i \(-0.450416\pi\)
0.155145 + 0.987892i \(0.450416\pi\)
\(492\) 0 0
\(493\) 3.67184e6 0.680403
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −4.09513e6 −0.743663
\(498\) 0 0
\(499\) −4.08804e6 −0.734961 −0.367480 0.930031i \(-0.619780\pi\)
−0.367480 + 0.930031i \(0.619780\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7.43036e6 −1.30945 −0.654726 0.755866i \(-0.727216\pi\)
−0.654726 + 0.755866i \(0.727216\pi\)
\(504\) 0 0
\(505\) 4.28928e6 0.748438
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 3.51290e6 0.600996 0.300498 0.953782i \(-0.402847\pi\)
0.300498 + 0.953782i \(0.402847\pi\)
\(510\) 0 0
\(511\) 2.07339e6 0.351259
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.06092e7 −1.76264
\(516\) 0 0
\(517\) −354888. −0.0583936
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −4.81406e6 −0.776994 −0.388497 0.921450i \(-0.627006\pi\)
−0.388497 + 0.921450i \(0.627006\pi\)
\(522\) 0 0
\(523\) 2.42660e6 0.387921 0.193960 0.981009i \(-0.437867\pi\)
0.193960 + 0.981009i \(0.437867\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.03648e6 0.633106
\(528\) 0 0
\(529\) 7.03256e6 1.09263
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 4.51361e6 0.688186
\(534\) 0 0
\(535\) 6.60134e6 0.997121
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −129654. −0.0192227
\(540\) 0 0
\(541\) 4.82543e6 0.708831 0.354415 0.935088i \(-0.384680\pi\)
0.354415 + 0.935088i \(0.384680\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.84602e6 0.554651
\(546\) 0 0
\(547\) −1.34543e6 −0.192262 −0.0961310 0.995369i \(-0.530647\pi\)
−0.0961310 + 0.995369i \(0.530647\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.94532e6 0.974571
\(552\) 0 0
\(553\) 24892.0 0.00346136
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 938438. 0.128164 0.0640822 0.997945i \(-0.479588\pi\)
0.0640822 + 0.997945i \(0.479588\pi\)
\(558\) 0 0
\(559\) −5.84201e6 −0.790738
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.16124e7 1.54402 0.772008 0.635613i \(-0.219253\pi\)
0.772008 + 0.635613i \(0.219253\pi\)
\(564\) 0 0
\(565\) 8.07974e6 1.06482
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.94876e6 0.899760 0.449880 0.893089i \(-0.351467\pi\)
0.449880 + 0.893089i \(0.351467\pi\)
\(570\) 0 0
\(571\) −2.59412e6 −0.332966 −0.166483 0.986044i \(-0.553241\pi\)
−0.166483 + 0.986044i \(0.553241\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.56357e6 −0.449485
\(576\) 0 0
\(577\) −1.51612e7 −1.89581 −0.947906 0.318551i \(-0.896804\pi\)
−0.947906 + 0.318551i \(0.896804\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 409836. 0.0503697
\(582\) 0 0
\(583\) −426276. −0.0519421
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.29826e6 −0.155513 −0.0777567 0.996972i \(-0.524776\pi\)
−0.0777567 + 0.996972i \(0.524776\pi\)
\(588\) 0 0
\(589\) 7.63504e6 0.906824
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.15002e7 −1.34298 −0.671490 0.741014i \(-0.734345\pi\)
−0.671490 + 0.741014i \(0.734345\pi\)
\(594\) 0 0
\(595\) −2.65933e6 −0.307949
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.99854e6 1.13860 0.569298 0.822131i \(-0.307215\pi\)
0.569298 + 0.822131i \(0.307215\pi\)
\(600\) 0 0
\(601\) 8.05405e6 0.909553 0.454777 0.890606i \(-0.349719\pi\)
0.454777 + 0.890606i \(0.349719\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −1.01206e7 −1.12414
\(606\) 0 0
\(607\) −4.03667e6 −0.444684 −0.222342 0.974969i \(-0.571370\pi\)
−0.222342 + 0.974969i \(0.571370\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.85014e6 0.525595
\(612\) 0 0
\(613\) 1.60521e7 1.72536 0.862681 0.505748i \(-0.168784\pi\)
0.862681 + 0.505748i \(0.168784\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.34770e7 −1.42522 −0.712609 0.701561i \(-0.752487\pi\)
−0.712609 + 0.701561i \(0.752487\pi\)
\(618\) 0 0
\(619\) 1.73797e7 1.82312 0.911559 0.411170i \(-0.134880\pi\)
0.911559 + 0.411170i \(0.134880\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −2.41178e6 −0.248953
\(624\) 0 0
\(625\) −1.18572e7 −1.21417
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.77571e6 −0.178956
\(630\) 0 0
\(631\) −1.46908e7 −1.46883 −0.734416 0.678700i \(-0.762544\pi\)
−0.734416 + 0.678700i \(0.762544\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.97527e7 −1.94398
\(636\) 0 0
\(637\) 1.77194e6 0.173021
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.60166e7 −1.53966 −0.769830 0.638249i \(-0.779659\pi\)
−0.769830 + 0.638249i \(0.779659\pi\)
\(642\) 0 0
\(643\) −8.48624e6 −0.809446 −0.404723 0.914439i \(-0.632632\pi\)
−0.404723 + 0.914439i \(0.632632\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.85487e7 −1.74202 −0.871008 0.491269i \(-0.836533\pi\)
−0.871008 + 0.491269i \(0.836533\pi\)
\(648\) 0 0
\(649\) 2.24986e6 0.209673
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 3.01271e6 0.276486 0.138243 0.990398i \(-0.455854\pi\)
0.138243 + 0.990398i \(0.455854\pi\)
\(654\) 0 0
\(655\) −3.90477e6 −0.355625
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −6.06060e6 −0.543628 −0.271814 0.962350i \(-0.587624\pi\)
−0.271814 + 0.962350i \(0.587624\pi\)
\(660\) 0 0
\(661\) 1.42899e7 1.27211 0.636057 0.771642i \(-0.280564\pi\)
0.636057 + 0.771642i \(0.280564\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.03014e6 −0.441089
\(666\) 0 0
\(667\) −1.58911e7 −1.38305
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.43478e6 0.123021
\(672\) 0 0
\(673\) −5.29680e6 −0.450792 −0.225396 0.974267i \(-0.572368\pi\)
−0.225396 + 0.974267i \(0.572368\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.18550e7 −0.994096 −0.497048 0.867723i \(-0.665583\pi\)
−0.497048 + 0.867723i \(0.665583\pi\)
\(678\) 0 0
\(679\) −7.82383e6 −0.651246
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.65625e7 −1.35854 −0.679272 0.733886i \(-0.737704\pi\)
−0.679272 + 0.733886i \(0.737704\pi\)
\(684\) 0 0
\(685\) 2.03035e7 1.65327
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5.82577e6 0.467526
\(690\) 0 0
\(691\) 4.69748e6 0.374257 0.187128 0.982335i \(-0.440082\pi\)
0.187128 + 0.982335i \(0.440082\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 463104. 0.0363678
\(696\) 0 0
\(697\) 5.18637e6 0.404372
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.10890e7 1.62092 0.810458 0.585797i \(-0.199219\pi\)
0.810458 + 0.585797i \(0.199219\pi\)
\(702\) 0 0
\(703\) −3.35878e6 −0.256326
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −3.28398e6 −0.247088
\(708\) 0 0
\(709\) −1.68683e7 −1.26025 −0.630123 0.776495i \(-0.716996\pi\)
−0.630123 + 0.776495i \(0.716996\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.74692e7 −1.28691
\(714\) 0 0
\(715\) −2.55053e6 −0.186580
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.19606e7 −0.862844 −0.431422 0.902150i \(-0.641988\pi\)
−0.431422 + 0.902150i \(0.641988\pi\)
\(720\) 0 0
\(721\) 8.12263e6 0.581914
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4.20443e6 0.297072
\(726\) 0 0
\(727\) 2.20722e6 0.154885 0.0774427 0.996997i \(-0.475325\pi\)
0.0774427 + 0.996997i \(0.475325\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −6.71277e6 −0.464631
\(732\) 0 0
\(733\) −384494. −0.0264320 −0.0132160 0.999913i \(-0.504207\pi\)
−0.0132160 + 0.999913i \(0.504207\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.25374e6 −0.152840
\(738\) 0 0
\(739\) −8.04242e6 −0.541721 −0.270860 0.962619i \(-0.587308\pi\)
−0.270860 + 0.962619i \(0.587308\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.85291e6 −0.123135 −0.0615675 0.998103i \(-0.519610\pi\)
−0.0615675 + 0.998103i \(0.519610\pi\)
\(744\) 0 0
\(745\) −8.06771e6 −0.532549
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.05415e6 −0.329188
\(750\) 0 0
\(751\) −1.19326e7 −0.772034 −0.386017 0.922492i \(-0.626149\pi\)
−0.386017 + 0.922492i \(0.626149\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.28189e7 −0.818436
\(756\) 0 0
\(757\) −5.55886e6 −0.352570 −0.176285 0.984339i \(-0.556408\pi\)
−0.176285 + 0.984339i \(0.556408\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.71599e7 −1.70007 −0.850033 0.526730i \(-0.823418\pi\)
−0.850033 + 0.526730i \(0.823418\pi\)
\(762\) 0 0
\(763\) −2.94461e6 −0.183112
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.07480e7 −1.88725
\(768\) 0 0
\(769\) −8.75668e6 −0.533978 −0.266989 0.963700i \(-0.586029\pi\)
−0.266989 + 0.963700i \(0.586029\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 3.96856e6 0.238883 0.119441 0.992841i \(-0.461890\pi\)
0.119441 + 0.992841i \(0.461890\pi\)
\(774\) 0 0
\(775\) 4.62196e6 0.276422
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.81006e6 0.579200
\(780\) 0 0
\(781\) −4.51300e6 −0.264751
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 3.26972e7 1.89381
\(786\) 0 0
\(787\) 2.11112e7 1.21500 0.607501 0.794319i \(-0.292172\pi\)
0.607501 + 0.794319i \(0.292172\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.18605e6 −0.351538
\(792\) 0 0
\(793\) −1.96087e7 −1.10730
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.95085e7 1.64552 0.822758 0.568392i \(-0.192434\pi\)
0.822758 + 0.568392i \(0.192434\pi\)
\(798\) 0 0
\(799\) 5.57306e6 0.308835
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.28496e6 0.125052
\(804\) 0 0
\(805\) 1.15091e7 0.625968
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −13002.0 −0.000698456 0 −0.000349228 1.00000i \(-0.500111\pi\)
−0.000349228 1.00000i \(0.500111\pi\)
\(810\) 0 0
\(811\) −2.61790e7 −1.39766 −0.698829 0.715289i \(-0.746295\pi\)
−0.698829 + 0.715289i \(0.746295\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.35578e6 −0.0714980
\(816\) 0 0
\(817\) −1.26973e7 −0.665511
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.21209e7 −1.66314 −0.831572 0.555417i \(-0.812559\pi\)
−0.831572 + 0.555417i \(0.812559\pi\)
\(822\) 0 0
\(823\) 2.49758e7 1.28535 0.642674 0.766140i \(-0.277825\pi\)
0.642674 + 0.766140i \(0.277825\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −3.09229e7 −1.57223 −0.786116 0.618079i \(-0.787911\pi\)
−0.786116 + 0.618079i \(0.787911\pi\)
\(828\) 0 0
\(829\) −1.69047e7 −0.854319 −0.427160 0.904176i \(-0.640486\pi\)
−0.427160 + 0.904176i \(0.640486\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.03605e6 0.101666
\(834\) 0 0
\(835\) −1.70995e7 −0.848726
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.77783e7 1.36239 0.681194 0.732103i \(-0.261461\pi\)
0.681194 + 0.732103i \(0.261461\pi\)
\(840\) 0 0
\(841\) −1.76225e6 −0.0859166
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 1.10945e7 0.534521
\(846\) 0 0
\(847\) 7.74862e6 0.371121
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 7.68498e6 0.363763
\(852\) 0 0
\(853\) −1.77504e7 −0.835289 −0.417645 0.908611i \(-0.637144\pi\)
−0.417645 + 0.908611i \(0.637144\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.50040e7 −0.697838 −0.348919 0.937153i \(-0.613451\pi\)
−0.348919 + 0.937153i \(0.613451\pi\)
\(858\) 0 0
\(859\) −910972. −0.0421233 −0.0210616 0.999778i \(-0.506705\pi\)
−0.0210616 + 0.999778i \(0.506705\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 1.48837e7 0.680275 0.340138 0.940376i \(-0.389526\pi\)
0.340138 + 0.940376i \(0.389526\pi\)
\(864\) 0 0
\(865\) 5.88467e6 0.267413
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 27432.0 0.00123228
\(870\) 0 0
\(871\) 3.08012e7 1.37569
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 6.75494e6 0.298265
\(876\) 0 0
\(877\) −2.39951e7 −1.05348 −0.526738 0.850028i \(-0.676585\pi\)
−0.526738 + 0.850028i \(0.676585\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −7.85879e6 −0.341127 −0.170563 0.985347i \(-0.554559\pi\)
−0.170563 + 0.985347i \(0.554559\pi\)
\(882\) 0 0
\(883\) 1.74586e7 0.753541 0.376771 0.926307i \(-0.377034\pi\)
0.376771 + 0.926307i \(0.377034\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −700092. −0.0298776 −0.0149388 0.999888i \(-0.504755\pi\)
−0.0149388 + 0.999888i \(0.504755\pi\)
\(888\) 0 0
\(889\) 1.51232e7 0.641783
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.05415e7 0.442357
\(894\) 0 0
\(895\) −2.57809e7 −1.07582
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.06108e7 0.850542
\(900\) 0 0
\(901\) 6.69411e6 0.274714
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −5.09582e7 −2.06820
\(906\) 0 0
\(907\) −3.72979e7 −1.50545 −0.752724 0.658336i \(-0.771261\pi\)
−0.752724 + 0.658336i \(0.771261\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −2.99873e7 −1.19713 −0.598564 0.801075i \(-0.704262\pi\)
−0.598564 + 0.801075i \(0.704262\pi\)
\(912\) 0 0
\(913\) 451656. 0.0179321
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.98959e6 0.117405
\(918\) 0 0
\(919\) 2.78316e7 1.08705 0.543525 0.839393i \(-0.317089\pi\)
0.543525 + 0.839393i \(0.317089\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 6.16776e7 2.38300
\(924\) 0 0
\(925\) −2.03327e6 −0.0781343
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −1.88191e7 −0.715418 −0.357709 0.933833i \(-0.616442\pi\)
−0.357709 + 0.933833i \(0.616442\pi\)
\(930\) 0 0
\(931\) 3.85120e6 0.145620
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −2.93069e6 −0.109633
\(936\) 0 0
\(937\) 5.39613e6 0.200786 0.100393 0.994948i \(-0.467990\pi\)
0.100393 + 0.994948i \(0.467990\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.99942e7 −1.47239 −0.736194 0.676770i \(-0.763379\pi\)
−0.736194 + 0.676770i \(0.763379\pi\)
\(942\) 0 0
\(943\) −2.24457e7 −0.821967
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.09314e7 1.12079 0.560395 0.828225i \(-0.310649\pi\)
0.560395 + 0.828225i \(0.310649\pi\)
\(948\) 0 0
\(949\) −3.12277e7 −1.12558
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.55848e7 0.555865 0.277933 0.960601i \(-0.410351\pi\)
0.277933 + 0.960601i \(0.410351\pi\)
\(954\) 0 0
\(955\) 3.03958e7 1.07846
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.55449e7 −0.545808
\(960\) 0 0
\(961\) −5.97155e6 −0.208583
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 4.58254e7 1.58412
\(966\) 0 0
\(967\) 2.60131e7 0.894593 0.447297 0.894386i \(-0.352387\pi\)
0.447297 + 0.894386i \(0.352387\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −8.84316e6 −0.300995 −0.150497 0.988610i \(-0.548088\pi\)
−0.150497 + 0.988610i \(0.548088\pi\)
\(972\) 0 0
\(973\) −354564. −0.0120064
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 2.70010e7 0.904988 0.452494 0.891768i \(-0.350534\pi\)
0.452494 + 0.891768i \(0.350534\pi\)
\(978\) 0 0
\(979\) −2.65788e6 −0.0886296
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −1.69892e7 −0.560775 −0.280387 0.959887i \(-0.590463\pi\)
−0.280387 + 0.959887i \(0.590463\pi\)
\(984\) 0 0
\(985\) 1.41961e7 0.466207
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 2.90517e7 0.944455
\(990\) 0 0
\(991\) −3.77922e7 −1.22241 −0.611207 0.791470i \(-0.709316\pi\)
−0.611207 + 0.791470i \(0.709316\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 2.13514e7 0.683706
\(996\) 0 0
\(997\) −5.16921e7 −1.64697 −0.823487 0.567336i \(-0.807974\pi\)
−0.823487 + 0.567336i \(0.807974\pi\)
\(998\) 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.z.1.1 1
3.2 odd 2 336.6.a.c.1.1 1
4.3 odd 2 504.6.a.h.1.1 1
12.11 even 2 168.6.a.d.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
168.6.a.d.1.1 1 12.11 even 2
336.6.a.c.1.1 1 3.2 odd 2
504.6.a.h.1.1 1 4.3 odd 2
1008.6.a.z.1.1 1 1.1 even 1 trivial