Properties

Label 1008.6.a.bh.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $2$
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: \(2\)
Coefficient field: \(\Q(\sqrt{37}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 504)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.54138\) of defining polynomial
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)
 
\(f(q)\) \(=\) \(q-84.8276 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-84.8276 q^{5} +49.0000 q^{7} +634.124 q^{11} +895.242 q^{13} +2057.46 q^{17} -2451.95 q^{19} +569.186 q^{23} +4070.73 q^{25} +1471.78 q^{29} +2006.65 q^{31} -4156.55 q^{35} +4860.54 q^{37} -17228.4 q^{41} +15481.3 q^{43} -5006.40 q^{47} +2401.00 q^{49} -19560.3 q^{53} -53791.3 q^{55} -14515.6 q^{59} +3572.67 q^{61} -75941.3 q^{65} +41480.7 q^{67} -9247.05 q^{71} -41350.0 q^{73} +31072.1 q^{77} +37962.2 q^{79} -79211.1 q^{83} -174530. q^{85} -92538.5 q^{89} +43866.9 q^{91} +207993. q^{95} +175419. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 48 q^{5} + 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 48 q^{5} + 98 q^{7} + 368 q^{11} - 156 q^{13} + 3312 q^{17} - 3736 q^{19} + 1552 q^{23} + 2302 q^{25} - 1728 q^{29} + 3624 q^{31} - 2352 q^{35} + 6996 q^{37} - 26160 q^{41} + 30184 q^{43} - 11424 q^{47} + 4802 q^{49} + 17376 q^{53} - 63592 q^{55} + 15008 q^{59} + 35564 q^{61} - 114656 q^{65} + 70504 q^{67} + 40752 q^{71} - 53892 q^{73} + 18032 q^{77} + 9744 q^{79} + 31360 q^{83} - 128328 q^{85} - 35952 q^{89} - 7644 q^{91} + 160704 q^{95} + 66652 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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
\(5\) −84.8276 −1.51744 −0.758721 0.651415i \(-0.774176\pi\)
−0.758721 + 0.651415i \(0.774176\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 634.124 1.58013 0.790065 0.613023i \(-0.210047\pi\)
0.790065 + 0.613023i \(0.210047\pi\)
\(12\) 0 0
\(13\) 895.242 1.46920 0.734602 0.678498i \(-0.237369\pi\)
0.734602 + 0.678498i \(0.237369\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2057.46 1.72667 0.863335 0.504630i \(-0.168371\pi\)
0.863335 + 0.504630i \(0.168371\pi\)
\(18\) 0 0
\(19\) −2451.95 −1.55821 −0.779106 0.626892i \(-0.784327\pi\)
−0.779106 + 0.626892i \(0.784327\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 569.186 0.224354 0.112177 0.993688i \(-0.464218\pi\)
0.112177 + 0.993688i \(0.464218\pi\)
\(24\) 0 0
\(25\) 4070.73 1.30263
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 1471.78 0.324974 0.162487 0.986711i \(-0.448049\pi\)
0.162487 + 0.986711i \(0.448049\pi\)
\(30\) 0 0
\(31\) 2006.65 0.375031 0.187515 0.982262i \(-0.439957\pi\)
0.187515 + 0.982262i \(0.439957\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4156.55 −0.573539
\(36\) 0 0
\(37\) 4860.54 0.583687 0.291844 0.956466i \(-0.405731\pi\)
0.291844 + 0.956466i \(0.405731\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −17228.4 −1.60061 −0.800307 0.599591i \(-0.795330\pi\)
−0.800307 + 0.599591i \(0.795330\pi\)
\(42\) 0 0
\(43\) 15481.3 1.27684 0.638420 0.769689i \(-0.279588\pi\)
0.638420 + 0.769689i \(0.279588\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5006.40 −0.330583 −0.165292 0.986245i \(-0.552857\pi\)
−0.165292 + 0.986245i \(0.552857\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −19560.3 −0.956504 −0.478252 0.878223i \(-0.658729\pi\)
−0.478252 + 0.878223i \(0.658729\pi\)
\(54\) 0 0
\(55\) −53791.3 −2.39776
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −14515.6 −0.542881 −0.271441 0.962455i \(-0.587500\pi\)
−0.271441 + 0.962455i \(0.587500\pi\)
\(60\) 0 0
\(61\) 3572.67 0.122933 0.0614664 0.998109i \(-0.480422\pi\)
0.0614664 + 0.998109i \(0.480422\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −75941.3 −2.22943
\(66\) 0 0
\(67\) 41480.7 1.12891 0.564455 0.825464i \(-0.309086\pi\)
0.564455 + 0.825464i \(0.309086\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −9247.05 −0.217700 −0.108850 0.994058i \(-0.534717\pi\)
−0.108850 + 0.994058i \(0.534717\pi\)
\(72\) 0 0
\(73\) −41350.0 −0.908172 −0.454086 0.890958i \(-0.650034\pi\)
−0.454086 + 0.890958i \(0.650034\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 31072.1 0.597233
\(78\) 0 0
\(79\) 37962.2 0.684359 0.342179 0.939635i \(-0.388835\pi\)
0.342179 + 0.939635i \(0.388835\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −79211.1 −1.26209 −0.631046 0.775746i \(-0.717374\pi\)
−0.631046 + 0.775746i \(0.717374\pi\)
\(84\) 0 0
\(85\) −174530. −2.62012
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −92538.5 −1.23836 −0.619181 0.785248i \(-0.712535\pi\)
−0.619181 + 0.785248i \(0.712535\pi\)
\(90\) 0 0
\(91\) 43866.9 0.555307
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 207993. 2.36450
\(96\) 0 0
\(97\) 175419. 1.89299 0.946495 0.322720i \(-0.104597\pi\)
0.946495 + 0.322720i \(0.104597\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 56163.2 0.547834 0.273917 0.961753i \(-0.411681\pi\)
0.273917 + 0.961753i \(0.411681\pi\)
\(102\) 0 0
\(103\) 158376. 1.47095 0.735474 0.677553i \(-0.236960\pi\)
0.735474 + 0.677553i \(0.236960\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 23496.4 0.198400 0.0992001 0.995068i \(-0.468372\pi\)
0.0992001 + 0.995068i \(0.468372\pi\)
\(108\) 0 0
\(109\) 205342. 1.65543 0.827715 0.561148i \(-0.189640\pi\)
0.827715 + 0.561148i \(0.189640\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −185993. −1.37025 −0.685125 0.728426i \(-0.740252\pi\)
−0.685125 + 0.728426i \(0.740252\pi\)
\(114\) 0 0
\(115\) −48282.7 −0.340445
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 100816. 0.652620
\(120\) 0 0
\(121\) 241063. 1.49681
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −80223.7 −0.459227
\(126\) 0 0
\(127\) −348363. −1.91656 −0.958281 0.285828i \(-0.907732\pi\)
−0.958281 + 0.285828i \(0.907732\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 294849. 1.50114 0.750571 0.660790i \(-0.229779\pi\)
0.750571 + 0.660790i \(0.229779\pi\)
\(132\) 0 0
\(133\) −120145. −0.588949
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 119607. 0.544446 0.272223 0.962234i \(-0.412241\pi\)
0.272223 + 0.962234i \(0.412241\pi\)
\(138\) 0 0
\(139\) −145630. −0.639312 −0.319656 0.947534i \(-0.603567\pi\)
−0.319656 + 0.947534i \(0.603567\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 567695. 2.32153
\(144\) 0 0
\(145\) −124848. −0.493129
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 49750.8 0.183584 0.0917919 0.995778i \(-0.470741\pi\)
0.0917919 + 0.995778i \(0.470741\pi\)
\(150\) 0 0
\(151\) 214254. 0.764691 0.382346 0.924019i \(-0.375116\pi\)
0.382346 + 0.924019i \(0.375116\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −170219. −0.569088
\(156\) 0 0
\(157\) −197114. −0.638217 −0.319108 0.947718i \(-0.603383\pi\)
−0.319108 + 0.947718i \(0.603383\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 27890.1 0.0847980
\(162\) 0 0
\(163\) −103013. −0.303686 −0.151843 0.988405i \(-0.548521\pi\)
−0.151843 + 0.988405i \(0.548521\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 231396. 0.642044 0.321022 0.947072i \(-0.395974\pi\)
0.321022 + 0.947072i \(0.395974\pi\)
\(168\) 0 0
\(169\) 430165. 1.15856
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −207599. −0.527365 −0.263682 0.964610i \(-0.584937\pi\)
−0.263682 + 0.964610i \(0.584937\pi\)
\(174\) 0 0
\(175\) 199466. 0.492349
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 713483. 1.66438 0.832188 0.554494i \(-0.187088\pi\)
0.832188 + 0.554494i \(0.187088\pi\)
\(180\) 0 0
\(181\) 241894. 0.548818 0.274409 0.961613i \(-0.411518\pi\)
0.274409 + 0.961613i \(0.411518\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −412308. −0.885712
\(186\) 0 0
\(187\) 1.30469e6 2.72836
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 220340. 0.437029 0.218515 0.975834i \(-0.429879\pi\)
0.218515 + 0.975834i \(0.429879\pi\)
\(192\) 0 0
\(193\) −736048. −1.42237 −0.711185 0.703005i \(-0.751841\pi\)
−0.711185 + 0.703005i \(0.751841\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −586422. −1.07658 −0.538288 0.842761i \(-0.680929\pi\)
−0.538288 + 0.842761i \(0.680929\pi\)
\(198\) 0 0
\(199\) 680230. 1.21765 0.608826 0.793304i \(-0.291641\pi\)
0.608826 + 0.793304i \(0.291641\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 72117.3 0.122828
\(204\) 0 0
\(205\) 1.46145e6 2.42884
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1.55484e6 −2.46218
\(210\) 0 0
\(211\) −142662. −0.220598 −0.110299 0.993898i \(-0.535181\pi\)
−0.110299 + 0.993898i \(0.535181\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.31324e6 −1.93753
\(216\) 0 0
\(217\) 98325.8 0.141748
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.84193e6 2.53683
\(222\) 0 0
\(223\) 1.41803e6 1.90952 0.954760 0.297377i \(-0.0961117\pi\)
0.954760 + 0.297377i \(0.0961117\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −75557.1 −0.0973219 −0.0486610 0.998815i \(-0.515495\pi\)
−0.0486610 + 0.998815i \(0.515495\pi\)
\(228\) 0 0
\(229\) 1.29149e6 1.62743 0.813714 0.581265i \(-0.197442\pi\)
0.813714 + 0.581265i \(0.197442\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −112997. −0.136357 −0.0681783 0.997673i \(-0.521719\pi\)
−0.0681783 + 0.997673i \(0.521719\pi\)
\(234\) 0 0
\(235\) 424681. 0.501641
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 473209. 0.535869 0.267935 0.963437i \(-0.413659\pi\)
0.267935 + 0.963437i \(0.413659\pi\)
\(240\) 0 0
\(241\) −1.39122e6 −1.54296 −0.771478 0.636256i \(-0.780482\pi\)
−0.771478 + 0.636256i \(0.780482\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −203671. −0.216778
\(246\) 0 0
\(247\) −2.19508e6 −2.28933
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −776017. −0.777476 −0.388738 0.921348i \(-0.627089\pi\)
−0.388738 + 0.921348i \(0.627089\pi\)
\(252\) 0 0
\(253\) 360935. 0.354509
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −955090. −0.902011 −0.451005 0.892521i \(-0.648934\pi\)
−0.451005 + 0.892521i \(0.648934\pi\)
\(258\) 0 0
\(259\) 238166. 0.220613
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −190821. −0.170113 −0.0850566 0.996376i \(-0.527107\pi\)
−0.0850566 + 0.996376i \(0.527107\pi\)
\(264\) 0 0
\(265\) 1.65926e6 1.45144
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −224114. −0.188837 −0.0944186 0.995533i \(-0.530099\pi\)
−0.0944186 + 0.995533i \(0.530099\pi\)
\(270\) 0 0
\(271\) −687404. −0.568577 −0.284288 0.958739i \(-0.591757\pi\)
−0.284288 + 0.958739i \(0.591757\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.58135e6 2.05833
\(276\) 0 0
\(277\) −1.14588e6 −0.897302 −0.448651 0.893707i \(-0.648095\pi\)
−0.448651 + 0.893707i \(0.648095\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −755908. −0.571088 −0.285544 0.958366i \(-0.592174\pi\)
−0.285544 + 0.958366i \(0.592174\pi\)
\(282\) 0 0
\(283\) 1.92464e6 1.42851 0.714257 0.699884i \(-0.246765\pi\)
0.714257 + 0.699884i \(0.246765\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −844194. −0.604975
\(288\) 0 0
\(289\) 2.81329e6 1.98139
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.46185e6 0.994795 0.497398 0.867523i \(-0.334289\pi\)
0.497398 + 0.867523i \(0.334289\pi\)
\(294\) 0 0
\(295\) 1.23132e6 0.823791
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 509559. 0.329622
\(300\) 0 0
\(301\) 758584. 0.482600
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −303061. −0.186544
\(306\) 0 0
\(307\) −1.06474e6 −0.644756 −0.322378 0.946611i \(-0.604482\pi\)
−0.322378 + 0.946611i \(0.604482\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.59214e6 −1.51970 −0.759850 0.650098i \(-0.774728\pi\)
−0.759850 + 0.650098i \(0.774728\pi\)
\(312\) 0 0
\(313\) −2.14280e6 −1.23629 −0.618147 0.786063i \(-0.712116\pi\)
−0.618147 + 0.786063i \(0.712116\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.02229e6 1.68923 0.844613 0.535377i \(-0.179830\pi\)
0.844613 + 0.535377i \(0.179830\pi\)
\(318\) 0 0
\(319\) 933292. 0.513501
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −5.04478e6 −2.69052
\(324\) 0 0
\(325\) 3.64428e6 1.91383
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −245314. −0.124949
\(330\) 0 0
\(331\) 1.03801e6 0.520751 0.260376 0.965507i \(-0.416154\pi\)
0.260376 + 0.965507i \(0.416154\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.51871e6 −1.71306
\(336\) 0 0
\(337\) 2.23059e6 1.06991 0.534953 0.844882i \(-0.320329\pi\)
0.534953 + 0.844882i \(0.320329\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.27246e6 0.592598
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.57483e6 1.14795 0.573977 0.818872i \(-0.305400\pi\)
0.573977 + 0.818872i \(0.305400\pi\)
\(348\) 0 0
\(349\) 311098. 0.136721 0.0683604 0.997661i \(-0.478223\pi\)
0.0683604 + 0.997661i \(0.478223\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −3.77642e6 −1.61303 −0.806517 0.591212i \(-0.798650\pi\)
−0.806517 + 0.591212i \(0.798650\pi\)
\(354\) 0 0
\(355\) 784406. 0.330347
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −996020. −0.407880 −0.203940 0.978983i \(-0.565375\pi\)
−0.203940 + 0.978983i \(0.565375\pi\)
\(360\) 0 0
\(361\) 3.53594e6 1.42803
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.50762e6 1.37810
\(366\) 0 0
\(367\) 3.83928e6 1.48794 0.743969 0.668214i \(-0.232941\pi\)
0.743969 + 0.668214i \(0.232941\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −958457. −0.361525
\(372\) 0 0
\(373\) −5.05517e6 −1.88132 −0.940662 0.339344i \(-0.889795\pi\)
−0.940662 + 0.339344i \(0.889795\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.31760e6 0.477453
\(378\) 0 0
\(379\) 3.46825e6 1.24026 0.620129 0.784500i \(-0.287080\pi\)
0.620129 + 0.784500i \(0.287080\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.58445e6 1.24861 0.624304 0.781182i \(-0.285383\pi\)
0.624304 + 0.781182i \(0.285383\pi\)
\(384\) 0 0
\(385\) −2.63577e6 −0.906267
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.86098e6 1.29367 0.646834 0.762630i \(-0.276092\pi\)
0.646834 + 0.762630i \(0.276092\pi\)
\(390\) 0 0
\(391\) 1.17108e6 0.387386
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −3.22025e6 −1.03848
\(396\) 0 0
\(397\) −1.20136e6 −0.382559 −0.191280 0.981536i \(-0.561264\pi\)
−0.191280 + 0.981536i \(0.561264\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 3.88850e6 1.20760 0.603798 0.797138i \(-0.293653\pi\)
0.603798 + 0.797138i \(0.293653\pi\)
\(402\) 0 0
\(403\) 1.79644e6 0.550997
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 3.08219e6 0.922301
\(408\) 0 0
\(409\) 2.63640e6 0.779296 0.389648 0.920964i \(-0.372597\pi\)
0.389648 + 0.920964i \(0.372597\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −711264. −0.205190
\(414\) 0 0
\(415\) 6.71929e6 1.91515
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 432053. 0.120227 0.0601134 0.998192i \(-0.480854\pi\)
0.0601134 + 0.998192i \(0.480854\pi\)
\(420\) 0 0
\(421\) 3.31215e6 0.910763 0.455381 0.890296i \(-0.349503\pi\)
0.455381 + 0.890296i \(0.349503\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.37537e6 2.24922
\(426\) 0 0
\(427\) 175061. 0.0464642
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.30508e6 1.37562 0.687811 0.725890i \(-0.258572\pi\)
0.687811 + 0.725890i \(0.258572\pi\)
\(432\) 0 0
\(433\) −2.86645e6 −0.734723 −0.367362 0.930078i \(-0.619739\pi\)
−0.367362 + 0.930078i \(0.619739\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.39561e6 −0.349592
\(438\) 0 0
\(439\) −758493. −0.187841 −0.0939205 0.995580i \(-0.529940\pi\)
−0.0939205 + 0.995580i \(0.529940\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.02230e6 −0.731693 −0.365846 0.930675i \(-0.619220\pi\)
−0.365846 + 0.930675i \(0.619220\pi\)
\(444\) 0 0
\(445\) 7.84982e6 1.87914
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.55957e6 1.30144 0.650721 0.759317i \(-0.274467\pi\)
0.650721 + 0.759317i \(0.274467\pi\)
\(450\) 0 0
\(451\) −1.09250e7 −2.52918
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −3.72112e6 −0.842646
\(456\) 0 0
\(457\) 1.48117e6 0.331752 0.165876 0.986147i \(-0.446955\pi\)
0.165876 + 0.986147i \(0.446955\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 12329.0 0.00270193 0.00135097 0.999999i \(-0.499570\pi\)
0.00135097 + 0.999999i \(0.499570\pi\)
\(462\) 0 0
\(463\) 1.27201e6 0.275765 0.137882 0.990449i \(-0.455970\pi\)
0.137882 + 0.990449i \(0.455970\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7.15829e6 1.51886 0.759429 0.650590i \(-0.225479\pi\)
0.759429 + 0.650590i \(0.225479\pi\)
\(468\) 0 0
\(469\) 2.03256e6 0.426688
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9.81707e6 2.01757
\(474\) 0 0
\(475\) −9.98120e6 −2.02978
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.01478e6 0.998649 0.499325 0.866415i \(-0.333582\pi\)
0.499325 + 0.866415i \(0.333582\pi\)
\(480\) 0 0
\(481\) 4.35136e6 0.857555
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.48804e7 −2.87250
\(486\) 0 0
\(487\) −6.46712e6 −1.23563 −0.617815 0.786323i \(-0.711982\pi\)
−0.617815 + 0.786323i \(0.711982\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.89564e6 −1.29084 −0.645418 0.763829i \(-0.723317\pi\)
−0.645418 + 0.763829i \(0.723317\pi\)
\(492\) 0 0
\(493\) 3.02813e6 0.561123
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −453106. −0.0822827
\(498\) 0 0
\(499\) 1.00230e7 1.80196 0.900979 0.433862i \(-0.142849\pi\)
0.900979 + 0.433862i \(0.142849\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.02505e7 −1.80644 −0.903220 0.429178i \(-0.858803\pi\)
−0.903220 + 0.429178i \(0.858803\pi\)
\(504\) 0 0
\(505\) −4.76419e6 −0.831306
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.95058e6 0.333710 0.166855 0.985981i \(-0.446639\pi\)
0.166855 + 0.985981i \(0.446639\pi\)
\(510\) 0 0
\(511\) −2.02615e6 −0.343257
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.34347e7 −2.23208
\(516\) 0 0
\(517\) −3.17468e6 −0.522364
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −5.02692e6 −0.811349 −0.405674 0.914018i \(-0.632963\pi\)
−0.405674 + 0.914018i \(0.632963\pi\)
\(522\) 0 0
\(523\) 356811. 0.0570405 0.0285203 0.999593i \(-0.490920\pi\)
0.0285203 + 0.999593i \(0.490920\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 4.12860e6 0.647555
\(528\) 0 0
\(529\) −6.11237e6 −0.949665
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.54236e7 −2.35163
\(534\) 0 0
\(535\) −1.99314e6 −0.301061
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.52253e6 0.225733
\(540\) 0 0
\(541\) −1.16485e7 −1.71111 −0.855555 0.517712i \(-0.826784\pi\)
−0.855555 + 0.517712i \(0.826784\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.74187e7 −2.51202
\(546\) 0 0
\(547\) 2.56657e6 0.366763 0.183382 0.983042i \(-0.441296\pi\)
0.183382 + 0.983042i \(0.441296\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −3.60873e6 −0.506378
\(552\) 0 0
\(553\) 1.86015e6 0.258663
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.19382e6 1.25562 0.627809 0.778367i \(-0.283952\pi\)
0.627809 + 0.778367i \(0.283952\pi\)
\(558\) 0 0
\(559\) 1.38595e7 1.87594
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 2.73412e6 0.363535 0.181768 0.983342i \(-0.441818\pi\)
0.181768 + 0.983342i \(0.441818\pi\)
\(564\) 0 0
\(565\) 1.57773e7 2.07927
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −5.51619e6 −0.714264 −0.357132 0.934054i \(-0.616245\pi\)
−0.357132 + 0.934054i \(0.616245\pi\)
\(570\) 0 0
\(571\) 1.15557e7 1.48322 0.741612 0.670829i \(-0.234062\pi\)
0.741612 + 0.670829i \(0.234062\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 2.31700e6 0.292251
\(576\) 0 0
\(577\) −9.36955e6 −1.17160 −0.585800 0.810456i \(-0.699220\pi\)
−0.585800 + 0.810456i \(0.699220\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.88134e6 −0.477026
\(582\) 0 0
\(583\) −1.24037e7 −1.51140
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3.61313e6 0.432801 0.216400 0.976305i \(-0.430568\pi\)
0.216400 + 0.976305i \(0.430568\pi\)
\(588\) 0 0
\(589\) −4.92019e6 −0.584378
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 9.65554e6 1.12756 0.563780 0.825925i \(-0.309346\pi\)
0.563780 + 0.825925i \(0.309346\pi\)
\(594\) 0 0
\(595\) −8.55195e6 −0.990314
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 7.36706e6 0.838932 0.419466 0.907771i \(-0.362217\pi\)
0.419466 + 0.907771i \(0.362217\pi\)
\(600\) 0 0
\(601\) −9.04647e6 −1.02163 −0.510814 0.859691i \(-0.670656\pi\)
−0.510814 + 0.859691i \(0.670656\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.04488e7 −2.27132
\(606\) 0 0
\(607\) −1.07723e7 −1.18669 −0.593345 0.804948i \(-0.702193\pi\)
−0.593345 + 0.804948i \(0.702193\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −4.48194e6 −0.485694
\(612\) 0 0
\(613\) 5.64815e6 0.607093 0.303547 0.952817i \(-0.401829\pi\)
0.303547 + 0.952817i \(0.401829\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.21062e7 1.28025 0.640123 0.768272i \(-0.278883\pi\)
0.640123 + 0.768272i \(0.278883\pi\)
\(618\) 0 0
\(619\) 3.22164e6 0.337948 0.168974 0.985620i \(-0.445955\pi\)
0.168974 + 0.985620i \(0.445955\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −4.53439e6 −0.468057
\(624\) 0 0
\(625\) −5.91583e6 −0.605781
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.00004e7 1.00784
\(630\) 0 0
\(631\) 8.59962e6 0.859816 0.429908 0.902873i \(-0.358546\pi\)
0.429908 + 0.902873i \(0.358546\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.95508e7 2.90827
\(636\) 0 0
\(637\) 2.14948e6 0.209886
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −8.89346e6 −0.854920 −0.427460 0.904034i \(-0.640592\pi\)
−0.427460 + 0.904034i \(0.640592\pi\)
\(642\) 0 0
\(643\) 6.57628e6 0.627268 0.313634 0.949544i \(-0.398454\pi\)
0.313634 + 0.949544i \(0.398454\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.16128e7 1.09063 0.545313 0.838232i \(-0.316411\pi\)
0.545313 + 0.838232i \(0.316411\pi\)
\(648\) 0 0
\(649\) −9.20470e6 −0.857823
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.03391e6 −0.645527 −0.322763 0.946480i \(-0.604612\pi\)
−0.322763 + 0.946480i \(0.604612\pi\)
\(654\) 0 0
\(655\) −2.50114e7 −2.27790
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.10193e7 −0.988422 −0.494211 0.869342i \(-0.664543\pi\)
−0.494211 + 0.869342i \(0.664543\pi\)
\(660\) 0 0
\(661\) 3.37812e6 0.300726 0.150363 0.988631i \(-0.451956\pi\)
0.150363 + 0.988631i \(0.451956\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.01916e7 0.893696
\(666\) 0 0
\(667\) 837717. 0.0729093
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 2.26552e6 0.194250
\(672\) 0 0
\(673\) −3.46735e6 −0.295094 −0.147547 0.989055i \(-0.547138\pi\)
−0.147547 + 0.989055i \(0.547138\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.81353e7 −1.52074 −0.760369 0.649492i \(-0.774982\pi\)
−0.760369 + 0.649492i \(0.774982\pi\)
\(678\) 0 0
\(679\) 8.59555e6 0.715483
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.60726e7 1.31836 0.659182 0.751983i \(-0.270903\pi\)
0.659182 + 0.751983i \(0.270903\pi\)
\(684\) 0 0
\(685\) −1.01460e7 −0.826166
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −1.75112e7 −1.40530
\(690\) 0 0
\(691\) −779272. −0.0620860 −0.0310430 0.999518i \(-0.509883\pi\)
−0.0310430 + 0.999518i \(0.509883\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.23534e7 0.970120
\(696\) 0 0
\(697\) −3.54469e7 −2.76373
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 616669. 0.0473977 0.0236989 0.999719i \(-0.492456\pi\)
0.0236989 + 0.999719i \(0.492456\pi\)
\(702\) 0 0
\(703\) −1.19178e7 −0.909509
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 2.75200e6 0.207062
\(708\) 0 0
\(709\) 1.94867e7 1.45587 0.727935 0.685646i \(-0.240480\pi\)
0.727935 + 0.685646i \(0.240480\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.14216e6 0.0841398
\(714\) 0 0
\(715\) −4.81562e7 −3.52279
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −6.07365e6 −0.438155 −0.219078 0.975707i \(-0.570305\pi\)
−0.219078 + 0.975707i \(0.570305\pi\)
\(720\) 0 0
\(721\) 7.76044e6 0.555966
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5.99122e6 0.423321
\(726\) 0 0
\(727\) −9.38803e6 −0.658777 −0.329389 0.944194i \(-0.606843\pi\)
−0.329389 + 0.944194i \(0.606843\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 3.18522e7 2.20468
\(732\) 0 0
\(733\) 6.87253e6 0.472451 0.236226 0.971698i \(-0.424090\pi\)
0.236226 + 0.971698i \(0.424090\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.63040e7 1.78383
\(738\) 0 0
\(739\) −3.13208e6 −0.210970 −0.105485 0.994421i \(-0.533640\pi\)
−0.105485 + 0.994421i \(0.533640\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −8.05007e6 −0.534968 −0.267484 0.963562i \(-0.586192\pi\)
−0.267484 + 0.963562i \(0.586192\pi\)
\(744\) 0 0
\(745\) −4.22024e6 −0.278578
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.15132e6 0.0749882
\(750\) 0 0
\(751\) 1.51621e7 0.980976 0.490488 0.871448i \(-0.336819\pi\)
0.490488 + 0.871448i \(0.336819\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.81746e7 −1.16037
\(756\) 0 0
\(757\) 3.86111e6 0.244891 0.122445 0.992475i \(-0.460926\pi\)
0.122445 + 0.992475i \(0.460926\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.74204e7 −1.71638 −0.858188 0.513335i \(-0.828410\pi\)
−0.858188 + 0.513335i \(0.828410\pi\)
\(762\) 0 0
\(763\) 1.00617e7 0.625694
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.29950e7 −0.797603
\(768\) 0 0
\(769\) 7.96097e6 0.485456 0.242728 0.970094i \(-0.421958\pi\)
0.242728 + 0.970094i \(0.421958\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 4.09621e6 0.246566 0.123283 0.992372i \(-0.460658\pi\)
0.123283 + 0.992372i \(0.460658\pi\)
\(774\) 0 0
\(775\) 8.16852e6 0.488527
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.22432e7 2.49410
\(780\) 0 0
\(781\) −5.86378e6 −0.343994
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.67207e7 0.968457
\(786\) 0 0
\(787\) −1.43564e7 −0.826244 −0.413122 0.910676i \(-0.635562\pi\)
−0.413122 + 0.910676i \(0.635562\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.11364e6 −0.517906
\(792\) 0 0
\(793\) 3.19840e6 0.180613
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.61963e7 1.46081 0.730407 0.683012i \(-0.239330\pi\)
0.730407 + 0.683012i \(0.239330\pi\)
\(798\) 0 0
\(799\) −1.03005e7 −0.570809
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.62210e7 −1.43503
\(804\) 0 0
\(805\) −2.36585e6 −0.128676
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 3.31159e6 0.177896 0.0889478 0.996036i \(-0.471650\pi\)
0.0889478 + 0.996036i \(0.471650\pi\)
\(810\) 0 0
\(811\) −6.43440e6 −0.343523 −0.171761 0.985139i \(-0.554946\pi\)
−0.171761 + 0.985139i \(0.554946\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 8.73839e6 0.460826
\(816\) 0 0
\(817\) −3.79593e7 −1.98959
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −2.12076e7 −1.09808 −0.549039 0.835796i \(-0.685006\pi\)
−0.549039 + 0.835796i \(0.685006\pi\)
\(822\) 0 0
\(823\) −1.96206e7 −1.00975 −0.504875 0.863193i \(-0.668461\pi\)
−0.504875 + 0.863193i \(0.668461\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.34210e6 −0.474986 −0.237493 0.971389i \(-0.576326\pi\)
−0.237493 + 0.971389i \(0.576326\pi\)
\(828\) 0 0
\(829\) −8.15436e6 −0.412101 −0.206050 0.978541i \(-0.566061\pi\)
−0.206050 + 0.978541i \(0.566061\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 4.93997e6 0.246667
\(834\) 0 0
\(835\) −1.96288e7 −0.974265
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 4.14558e6 0.203320 0.101660 0.994819i \(-0.467585\pi\)
0.101660 + 0.994819i \(0.467585\pi\)
\(840\) 0 0
\(841\) −1.83450e7 −0.894392
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −3.64899e7 −1.75805
\(846\) 0 0
\(847\) 1.18121e7 0.565741
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.76655e6 0.130953
\(852\) 0 0
\(853\) 3.40559e6 0.160258 0.0801291 0.996784i \(-0.474467\pi\)
0.0801291 + 0.996784i \(0.474467\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −2.26615e6 −0.105399 −0.0526996 0.998610i \(-0.516783\pi\)
−0.0526996 + 0.998610i \(0.516783\pi\)
\(858\) 0 0
\(859\) 1.45799e7 0.674174 0.337087 0.941474i \(-0.390558\pi\)
0.337087 + 0.941474i \(0.390558\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 3.37184e7 1.54113 0.770567 0.637359i \(-0.219973\pi\)
0.770567 + 0.637359i \(0.219973\pi\)
\(864\) 0 0
\(865\) 1.76102e7 0.800245
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2.40728e7 1.08138
\(870\) 0 0
\(871\) 3.71353e7 1.65860
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −3.93096e6 −0.173572
\(876\) 0 0
\(877\) 1.34267e7 0.589481 0.294740 0.955577i \(-0.404767\pi\)
0.294740 + 0.955577i \(0.404767\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 6.01261e6 0.260990 0.130495 0.991449i \(-0.458343\pi\)
0.130495 + 0.991449i \(0.458343\pi\)
\(882\) 0 0
\(883\) 4.30820e7 1.85949 0.929747 0.368200i \(-0.120026\pi\)
0.929747 + 0.368200i \(0.120026\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −2.82279e7 −1.20467 −0.602336 0.798242i \(-0.705763\pi\)
−0.602336 + 0.798242i \(0.705763\pi\)
\(888\) 0 0
\(889\) −1.70698e7 −0.724392
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 1.22754e7 0.515119
\(894\) 0 0
\(895\) −6.05231e7 −2.52559
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 2.95335e6 0.121875
\(900\) 0 0
\(901\) −4.02447e7 −1.65157
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.05193e7 −0.832799
\(906\) 0 0
\(907\) 1.56044e7 0.629836 0.314918 0.949119i \(-0.398023\pi\)
0.314918 + 0.949119i \(0.398023\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 6.33384e6 0.252855 0.126427 0.991976i \(-0.459649\pi\)
0.126427 + 0.991976i \(0.459649\pi\)
\(912\) 0 0
\(913\) −5.02297e7 −1.99427
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.44476e7 0.567378
\(918\) 0 0
\(919\) −2.11662e7 −0.826713 −0.413357 0.910569i \(-0.635644\pi\)
−0.413357 + 0.910569i \(0.635644\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −8.27835e6 −0.319845
\(924\) 0 0
\(925\) 1.97859e7 0.760330
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −3.25377e6 −0.123694 −0.0618468 0.998086i \(-0.519699\pi\)
−0.0618468 + 0.998086i \(0.519699\pi\)
\(930\) 0 0
\(931\) −5.88712e6 −0.222602
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.10674e8 −4.14014
\(936\) 0 0
\(937\) −1.00930e7 −0.375555 −0.187777 0.982212i \(-0.560128\pi\)
−0.187777 + 0.982212i \(0.560128\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −3.04029e7 −1.11929 −0.559643 0.828734i \(-0.689062\pi\)
−0.559643 + 0.828734i \(0.689062\pi\)
\(942\) 0 0
\(943\) −9.80619e6 −0.359105
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.37126e7 −1.58391 −0.791957 0.610577i \(-0.790938\pi\)
−0.791957 + 0.610577i \(0.790938\pi\)
\(948\) 0 0
\(949\) −3.70182e7 −1.33429
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.31900e7 0.827120 0.413560 0.910477i \(-0.364285\pi\)
0.413560 + 0.910477i \(0.364285\pi\)
\(954\) 0 0
\(955\) −1.86909e7 −0.663167
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 5.86074e6 0.205781
\(960\) 0 0
\(961\) −2.46025e7 −0.859352
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 6.24372e7 2.15837
\(966\) 0 0
\(967\) 2.78623e7 0.958188 0.479094 0.877764i \(-0.340965\pi\)
0.479094 + 0.877764i \(0.340965\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3.65933e7 −1.24553 −0.622763 0.782410i \(-0.713990\pi\)
−0.622763 + 0.782410i \(0.713990\pi\)
\(972\) 0 0
\(973\) −7.13586e6 −0.241637
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 1.83769e7 0.615938 0.307969 0.951396i \(-0.400351\pi\)
0.307969 + 0.951396i \(0.400351\pi\)
\(978\) 0 0
\(979\) −5.86809e7 −1.95677
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 5.09387e7 1.68137 0.840687 0.541522i \(-0.182152\pi\)
0.840687 + 0.541522i \(0.182152\pi\)
\(984\) 0 0
\(985\) 4.97448e7 1.63364
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 8.81174e6 0.286465
\(990\) 0 0
\(991\) 946169. 0.0306044 0.0153022 0.999883i \(-0.495129\pi\)
0.0153022 + 0.999883i \(0.495129\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −5.77023e7 −1.84772
\(996\) 0 0
\(997\) 8.61505e6 0.274486 0.137243 0.990537i \(-0.456176\pi\)
0.137243 + 0.990537i \(0.456176\pi\)
\(998\) 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.bh.1.1 2
3.2 odd 2 1008.6.a.bs.1.2 2
4.3 odd 2 504.6.a.l.1.1 2
12.11 even 2 504.6.a.r.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.l.1.1 2 4.3 odd 2
504.6.a.r.1.2 yes 2 12.11 even 2
1008.6.a.bh.1.1 2 1.1 even 1 trivial
1008.6.a.bs.1.2 2 3.2 odd 2