Properties

Label 1008.6.a.bd.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $1$
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: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{345}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 86 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 3 \)
Twist minimal: no (minimal twist has level 56)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(9.78709\) 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)
 
\(f(q)\) \(=\) \(q-96.7225 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-96.7225 q^{5} +49.0000 q^{7} +281.445 q^{11} -269.393 q^{13} -1719.45 q^{17} +1172.84 q^{19} +785.341 q^{23} +6230.25 q^{25} -6149.46 q^{29} +7006.58 q^{31} -4739.40 q^{35} -11499.9 q^{37} +13245.3 q^{41} +19824.2 q^{43} +6887.96 q^{47} +2401.00 q^{49} -8654.97 q^{53} -27222.1 q^{55} -47856.6 q^{59} +52762.1 q^{61} +26056.4 q^{65} +24040.2 q^{67} +12540.9 q^{71} +4079.29 q^{73} +13790.8 q^{77} +11919.1 q^{79} +81916.2 q^{83} +166309. q^{85} +96968.7 q^{89} -13200.2 q^{91} -113440. q^{95} -26410.7 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 82 q^{5} + 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 82 q^{5} + 98 q^{7} + 340 q^{11} + 910 q^{13} - 3216 q^{17} + 674 q^{19} - 1104 q^{23} + 3322 q^{25} - 8064 q^{29} + 6212 q^{31} - 4018 q^{35} - 8512 q^{37} + 1304 q^{41} + 10004 q^{43} - 12748 q^{47} + 4802 q^{49} + 11220 q^{53} - 26360 q^{55} - 12018 q^{59} + 102738 q^{61} + 43420 q^{65} - 24136 q^{67} + 89720 q^{71} - 55588 q^{73} + 16660 q^{77} - 48824 q^{79} + 35782 q^{83} + 144276 q^{85} + 18300 q^{89} + 44590 q^{91} - 120784 q^{95} - 69984 q^{97}+O(q^{100}) \) 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
\(5\) −96.7225 −1.73023 −0.865113 0.501578i \(-0.832753\pi\)
−0.865113 + 0.501578i \(0.832753\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 281.445 0.701313 0.350657 0.936504i \(-0.385958\pi\)
0.350657 + 0.936504i \(0.385958\pi\)
\(12\) 0 0
\(13\) −269.393 −0.442107 −0.221054 0.975262i \(-0.570950\pi\)
−0.221054 + 0.975262i \(0.570950\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1719.45 −1.44300 −0.721499 0.692415i \(-0.756547\pi\)
−0.721499 + 0.692415i \(0.756547\pi\)
\(18\) 0 0
\(19\) 1172.84 0.745339 0.372670 0.927964i \(-0.378442\pi\)
0.372670 + 0.927964i \(0.378442\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 785.341 0.309555 0.154778 0.987949i \(-0.450534\pi\)
0.154778 + 0.987949i \(0.450534\pi\)
\(24\) 0 0
\(25\) 6230.25 1.99368
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6149.46 −1.35782 −0.678909 0.734222i \(-0.737547\pi\)
−0.678909 + 0.734222i \(0.737547\pi\)
\(30\) 0 0
\(31\) 7006.58 1.30949 0.654744 0.755851i \(-0.272776\pi\)
0.654744 + 0.755851i \(0.272776\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4739.40 −0.653964
\(36\) 0 0
\(37\) −11499.9 −1.38099 −0.690495 0.723337i \(-0.742607\pi\)
−0.690495 + 0.723337i \(0.742607\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 13245.3 1.23056 0.615279 0.788310i \(-0.289043\pi\)
0.615279 + 0.788310i \(0.289043\pi\)
\(42\) 0 0
\(43\) 19824.2 1.63502 0.817512 0.575911i \(-0.195353\pi\)
0.817512 + 0.575911i \(0.195353\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6887.96 0.454827 0.227413 0.973798i \(-0.426973\pi\)
0.227413 + 0.973798i \(0.426973\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8654.97 −0.423229 −0.211615 0.977353i \(-0.567872\pi\)
−0.211615 + 0.977353i \(0.567872\pi\)
\(54\) 0 0
\(55\) −27222.1 −1.21343
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −47856.6 −1.78983 −0.894915 0.446236i \(-0.852764\pi\)
−0.894915 + 0.446236i \(0.852764\pi\)
\(60\) 0 0
\(61\) 52762.1 1.81550 0.907752 0.419507i \(-0.137797\pi\)
0.907752 + 0.419507i \(0.137797\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 26056.4 0.764945
\(66\) 0 0
\(67\) 24040.2 0.654261 0.327130 0.944979i \(-0.393918\pi\)
0.327130 + 0.944979i \(0.393918\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 12540.9 0.295246 0.147623 0.989044i \(-0.452838\pi\)
0.147623 + 0.989044i \(0.452838\pi\)
\(72\) 0 0
\(73\) 4079.29 0.0895936 0.0447968 0.998996i \(-0.485736\pi\)
0.0447968 + 0.998996i \(0.485736\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 13790.8 0.265071
\(78\) 0 0
\(79\) 11919.1 0.214870 0.107435 0.994212i \(-0.465736\pi\)
0.107435 + 0.994212i \(0.465736\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 81916.2 1.30519 0.652596 0.757706i \(-0.273680\pi\)
0.652596 + 0.757706i \(0.273680\pi\)
\(84\) 0 0
\(85\) 166309. 2.49671
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 96968.7 1.29765 0.648824 0.760939i \(-0.275261\pi\)
0.648824 + 0.760939i \(0.275261\pi\)
\(90\) 0 0
\(91\) −13200.2 −0.167101
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −113440. −1.28960
\(96\) 0 0
\(97\) −26410.7 −0.285004 −0.142502 0.989795i \(-0.545515\pi\)
−0.142502 + 0.989795i \(0.545515\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 73137.7 0.713408 0.356704 0.934217i \(-0.383901\pi\)
0.356704 + 0.934217i \(0.383901\pi\)
\(102\) 0 0
\(103\) −87649.5 −0.814060 −0.407030 0.913415i \(-0.633435\pi\)
−0.407030 + 0.913415i \(0.633435\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −115438. −0.974743 −0.487372 0.873195i \(-0.662044\pi\)
−0.487372 + 0.873195i \(0.662044\pi\)
\(108\) 0 0
\(109\) −117303. −0.945675 −0.472837 0.881150i \(-0.656770\pi\)
−0.472837 + 0.881150i \(0.656770\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −181535. −1.33741 −0.668705 0.743528i \(-0.733151\pi\)
−0.668705 + 0.743528i \(0.733151\pi\)
\(114\) 0 0
\(115\) −75960.1 −0.535601
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −84252.8 −0.545402
\(120\) 0 0
\(121\) −81839.7 −0.508160
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −300347. −1.71929
\(126\) 0 0
\(127\) −106111. −0.583780 −0.291890 0.956452i \(-0.594284\pi\)
−0.291890 + 0.956452i \(0.594284\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 300334. 1.52907 0.764534 0.644584i \(-0.222969\pi\)
0.764534 + 0.644584i \(0.222969\pi\)
\(132\) 0 0
\(133\) 57469.1 0.281712
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 91892.5 0.418291 0.209146 0.977885i \(-0.432932\pi\)
0.209146 + 0.977885i \(0.432932\pi\)
\(138\) 0 0
\(139\) −153133. −0.672252 −0.336126 0.941817i \(-0.609117\pi\)
−0.336126 + 0.941817i \(0.609117\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −75819.3 −0.310056
\(144\) 0 0
\(145\) 594791. 2.34933
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −498602. −1.83987 −0.919937 0.392066i \(-0.871760\pi\)
−0.919937 + 0.392066i \(0.871760\pi\)
\(150\) 0 0
\(151\) −209609. −0.748114 −0.374057 0.927406i \(-0.622034\pi\)
−0.374057 + 0.927406i \(0.622034\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −677694. −2.26571
\(156\) 0 0
\(157\) −7381.72 −0.0239006 −0.0119503 0.999929i \(-0.503804\pi\)
−0.0119503 + 0.999929i \(0.503804\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 38481.7 0.117001
\(162\) 0 0
\(163\) −388154. −1.14429 −0.572144 0.820153i \(-0.693888\pi\)
−0.572144 + 0.820153i \(0.693888\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −168240. −0.466808 −0.233404 0.972380i \(-0.574987\pi\)
−0.233404 + 0.972380i \(0.574987\pi\)
\(168\) 0 0
\(169\) −298720. −0.804541
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −321513. −0.816740 −0.408370 0.912817i \(-0.633903\pi\)
−0.408370 + 0.912817i \(0.633903\pi\)
\(174\) 0 0
\(175\) 305282. 0.753540
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −611906. −1.42742 −0.713710 0.700441i \(-0.752987\pi\)
−0.713710 + 0.700441i \(0.752987\pi\)
\(180\) 0 0
\(181\) 261474. 0.593242 0.296621 0.954995i \(-0.404140\pi\)
0.296621 + 0.954995i \(0.404140\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.11230e6 2.38943
\(186\) 0 0
\(187\) −483929. −1.01199
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 703301. 1.39495 0.697474 0.716610i \(-0.254307\pi\)
0.697474 + 0.716610i \(0.254307\pi\)
\(192\) 0 0
\(193\) 516411. 0.997934 0.498967 0.866621i \(-0.333713\pi\)
0.498967 + 0.866621i \(0.333713\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −142579. −0.261752 −0.130876 0.991399i \(-0.541779\pi\)
−0.130876 + 0.991399i \(0.541779\pi\)
\(198\) 0 0
\(199\) −984837. −1.76292 −0.881458 0.472262i \(-0.843438\pi\)
−0.881458 + 0.472262i \(0.843438\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −301323. −0.513207
\(204\) 0 0
\(205\) −1.28112e6 −2.12914
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 330089. 0.522716
\(210\) 0 0
\(211\) 242836. 0.375497 0.187748 0.982217i \(-0.439881\pi\)
0.187748 + 0.982217i \(0.439881\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −1.91745e6 −2.82896
\(216\) 0 0
\(217\) 343322. 0.494940
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 463206. 0.637960
\(222\) 0 0
\(223\) 797063. 1.07332 0.536661 0.843798i \(-0.319685\pi\)
0.536661 + 0.843798i \(0.319685\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −26121.4 −0.0336459 −0.0168229 0.999858i \(-0.505355\pi\)
−0.0168229 + 0.999858i \(0.505355\pi\)
\(228\) 0 0
\(229\) −761592. −0.959695 −0.479848 0.877352i \(-0.659308\pi\)
−0.479848 + 0.877352i \(0.659308\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −657852. −0.793850 −0.396925 0.917851i \(-0.629923\pi\)
−0.396925 + 0.917851i \(0.629923\pi\)
\(234\) 0 0
\(235\) −666221. −0.786953
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 965388. 1.09322 0.546609 0.837388i \(-0.315918\pi\)
0.546609 + 0.837388i \(0.315918\pi\)
\(240\) 0 0
\(241\) 35064.2 0.0388885 0.0194443 0.999811i \(-0.493810\pi\)
0.0194443 + 0.999811i \(0.493810\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −232231. −0.247175
\(246\) 0 0
\(247\) −315954. −0.329520
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.31610e6 1.31857 0.659286 0.751892i \(-0.270859\pi\)
0.659286 + 0.751892i \(0.270859\pi\)
\(252\) 0 0
\(253\) 221030. 0.217095
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 529802. 0.500358 0.250179 0.968200i \(-0.419511\pi\)
0.250179 + 0.968200i \(0.419511\pi\)
\(258\) 0 0
\(259\) −563496. −0.521966
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.29457e6 −1.15408 −0.577041 0.816715i \(-0.695793\pi\)
−0.577041 + 0.816715i \(0.695793\pi\)
\(264\) 0 0
\(265\) 837130. 0.732282
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 444336. 0.374396 0.187198 0.982322i \(-0.440059\pi\)
0.187198 + 0.982322i \(0.440059\pi\)
\(270\) 0 0
\(271\) −624757. −0.516759 −0.258379 0.966044i \(-0.583188\pi\)
−0.258379 + 0.966044i \(0.583188\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.75347e6 1.39819
\(276\) 0 0
\(277\) −2.00202e6 −1.56772 −0.783860 0.620938i \(-0.786752\pi\)
−0.783860 + 0.620938i \(0.786752\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −249316. −0.188358 −0.0941792 0.995555i \(-0.530023\pi\)
−0.0941792 + 0.995555i \(0.530023\pi\)
\(282\) 0 0
\(283\) −645136. −0.478835 −0.239417 0.970917i \(-0.576956\pi\)
−0.239417 + 0.970917i \(0.576956\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 649019. 0.465107
\(288\) 0 0
\(289\) 1.53663e6 1.08225
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.00830e6 −1.36666 −0.683328 0.730112i \(-0.739468\pi\)
−0.683328 + 0.730112i \(0.739468\pi\)
\(294\) 0 0
\(295\) 4.62881e6 3.09681
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −211565. −0.136857
\(300\) 0 0
\(301\) 971385. 0.617981
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.10328e6 −3.14123
\(306\) 0 0
\(307\) 1.71113e6 1.03618 0.518092 0.855325i \(-0.326642\pi\)
0.518092 + 0.855325i \(0.326642\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −602050. −0.352965 −0.176483 0.984304i \(-0.556472\pi\)
−0.176483 + 0.984304i \(0.556472\pi\)
\(312\) 0 0
\(313\) −1.34208e6 −0.774318 −0.387159 0.922013i \(-0.626543\pi\)
−0.387159 + 0.922013i \(0.626543\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −1.01803e6 −0.569001 −0.284500 0.958676i \(-0.591828\pi\)
−0.284500 + 0.958676i \(0.591828\pi\)
\(318\) 0 0
\(319\) −1.73073e6 −0.952256
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.01663e6 −1.07552
\(324\) 0 0
\(325\) −1.67838e6 −0.881420
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 337510. 0.171908
\(330\) 0 0
\(331\) 532371. 0.267082 0.133541 0.991043i \(-0.457365\pi\)
0.133541 + 0.991043i \(0.457365\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2.32523e6 −1.13202
\(336\) 0 0
\(337\) −234947. −0.112693 −0.0563463 0.998411i \(-0.517945\pi\)
−0.0563463 + 0.998411i \(0.517945\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 1.97197e6 0.918361
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.90054e6 −0.847330 −0.423665 0.905819i \(-0.639257\pi\)
−0.423665 + 0.905819i \(0.639257\pi\)
\(348\) 0 0
\(349\) 341162. 0.149933 0.0749665 0.997186i \(-0.476115\pi\)
0.0749665 + 0.997186i \(0.476115\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −673122. −0.287513 −0.143756 0.989613i \(-0.545918\pi\)
−0.143756 + 0.989613i \(0.545918\pi\)
\(354\) 0 0
\(355\) −1.21299e6 −0.510842
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.43301e6 0.586833 0.293417 0.955985i \(-0.405208\pi\)
0.293417 + 0.955985i \(0.405208\pi\)
\(360\) 0 0
\(361\) −1.10055e6 −0.444469
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −394559. −0.155017
\(366\) 0 0
\(367\) 2.04781e6 0.793643 0.396822 0.917896i \(-0.370113\pi\)
0.396822 + 0.917896i \(0.370113\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −424093. −0.159966
\(372\) 0 0
\(373\) −3.33578e6 −1.24144 −0.620719 0.784033i \(-0.713159\pi\)
−0.620719 + 0.784033i \(0.713159\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.65662e6 0.600301
\(378\) 0 0
\(379\) −2.29135e6 −0.819394 −0.409697 0.912222i \(-0.634366\pi\)
−0.409697 + 0.912222i \(0.634366\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.84422e6 0.642414 0.321207 0.947009i \(-0.395911\pi\)
0.321207 + 0.947009i \(0.395911\pi\)
\(384\) 0 0
\(385\) −1.33388e6 −0.458633
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.66601e6 −1.22834 −0.614172 0.789172i \(-0.710510\pi\)
−0.614172 + 0.789172i \(0.710510\pi\)
\(390\) 0 0
\(391\) −1.35035e6 −0.446688
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.15284e6 −0.371773
\(396\) 0 0
\(397\) −4.59382e6 −1.46284 −0.731421 0.681926i \(-0.761142\pi\)
−0.731421 + 0.681926i \(0.761142\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.10984e6 0.344666 0.172333 0.985039i \(-0.444870\pi\)
0.172333 + 0.985039i \(0.444870\pi\)
\(402\) 0 0
\(403\) −1.88752e6 −0.578934
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.23660e6 −0.968507
\(408\) 0 0
\(409\) 3.60689e6 1.06617 0.533083 0.846063i \(-0.321033\pi\)
0.533083 + 0.846063i \(0.321033\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −2.34497e6 −0.676492
\(414\) 0 0
\(415\) −7.92314e6 −2.25828
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 5.51790e6 1.53546 0.767731 0.640773i \(-0.221386\pi\)
0.767731 + 0.640773i \(0.221386\pi\)
\(420\) 0 0
\(421\) −2.59092e6 −0.712440 −0.356220 0.934402i \(-0.615935\pi\)
−0.356220 + 0.934402i \(0.615935\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.07126e7 −2.87688
\(426\) 0 0
\(427\) 2.58534e6 0.686196
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −3.45364e6 −0.895537 −0.447769 0.894150i \(-0.647781\pi\)
−0.447769 + 0.894150i \(0.647781\pi\)
\(432\) 0 0
\(433\) 397522. 0.101892 0.0509461 0.998701i \(-0.483776\pi\)
0.0509461 + 0.998701i \(0.483776\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 921077. 0.230724
\(438\) 0 0
\(439\) −1.60903e6 −0.398476 −0.199238 0.979951i \(-0.563847\pi\)
−0.199238 + 0.979951i \(0.563847\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −7.08182e6 −1.71449 −0.857246 0.514906i \(-0.827827\pi\)
−0.857246 + 0.514906i \(0.827827\pi\)
\(444\) 0 0
\(445\) −9.37906e6 −2.24522
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.46156e6 1.51259 0.756295 0.654230i \(-0.227007\pi\)
0.756295 + 0.654230i \(0.227007\pi\)
\(450\) 0 0
\(451\) 3.72782e6 0.863006
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 1.27676e6 0.289122
\(456\) 0 0
\(457\) −3.37073e6 −0.754976 −0.377488 0.926015i \(-0.623212\pi\)
−0.377488 + 0.926015i \(0.623212\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −6.20821e6 −1.36055 −0.680274 0.732958i \(-0.738139\pi\)
−0.680274 + 0.732958i \(0.738139\pi\)
\(462\) 0 0
\(463\) 5.82940e6 1.26378 0.631890 0.775058i \(-0.282279\pi\)
0.631890 + 0.775058i \(0.282279\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −174742. −0.0370770 −0.0185385 0.999828i \(-0.505901\pi\)
−0.0185385 + 0.999828i \(0.505901\pi\)
\(468\) 0 0
\(469\) 1.17797e6 0.247287
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.57942e6 1.14666
\(474\) 0 0
\(475\) 7.30707e6 1.48597
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 371746. 0.0740299 0.0370150 0.999315i \(-0.488215\pi\)
0.0370150 + 0.999315i \(0.488215\pi\)
\(480\) 0 0
\(481\) 3.09800e6 0.610546
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.55451e6 0.493121
\(486\) 0 0
\(487\) 8.71307e6 1.66475 0.832375 0.554213i \(-0.186981\pi\)
0.832375 + 0.554213i \(0.186981\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 6.88530e6 1.28890 0.644450 0.764646i \(-0.277086\pi\)
0.644450 + 0.764646i \(0.277086\pi\)
\(492\) 0 0
\(493\) 1.05737e7 1.95933
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 614506. 0.111592
\(498\) 0 0
\(499\) 45442.7 0.00816982 0.00408491 0.999992i \(-0.498700\pi\)
0.00408491 + 0.999992i \(0.498700\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −623417. −0.109865 −0.0549324 0.998490i \(-0.517494\pi\)
−0.0549324 + 0.998490i \(0.517494\pi\)
\(504\) 0 0
\(505\) −7.07406e6 −1.23436
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7.69092e6 −1.31578 −0.657891 0.753113i \(-0.728551\pi\)
−0.657891 + 0.753113i \(0.728551\pi\)
\(510\) 0 0
\(511\) 199885. 0.0338632
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 8.47768e6 1.40851
\(516\) 0 0
\(517\) 1.93858e6 0.318976
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.32268e6 −1.18189 −0.590943 0.806713i \(-0.701244\pi\)
−0.590943 + 0.806713i \(0.701244\pi\)
\(522\) 0 0
\(523\) −5.17976e6 −0.828047 −0.414024 0.910266i \(-0.635877\pi\)
−0.414024 + 0.910266i \(0.635877\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.20474e7 −1.88959
\(528\) 0 0
\(529\) −5.81958e6 −0.904175
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −3.56819e6 −0.544038
\(534\) 0 0
\(535\) 1.11655e7 1.68653
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 675750. 0.100188
\(540\) 0 0
\(541\) 9.31804e6 1.36877 0.684387 0.729119i \(-0.260070\pi\)
0.684387 + 0.729119i \(0.260070\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.13458e7 1.63623
\(546\) 0 0
\(547\) −1.26417e7 −1.80650 −0.903250 0.429114i \(-0.858826\pi\)
−0.903250 + 0.429114i \(0.858826\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.21232e6 −1.01204
\(552\) 0 0
\(553\) 584035. 0.0812131
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 3.84693e6 0.525384 0.262692 0.964880i \(-0.415390\pi\)
0.262692 + 0.964880i \(0.415390\pi\)
\(558\) 0 0
\(559\) −5.34050e6 −0.722856
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.69193e6 0.490888 0.245444 0.969411i \(-0.421066\pi\)
0.245444 + 0.969411i \(0.421066\pi\)
\(564\) 0 0
\(565\) 1.75585e7 2.31402
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.64173e6 0.860005 0.430002 0.902828i \(-0.358513\pi\)
0.430002 + 0.902828i \(0.358513\pi\)
\(570\) 0 0
\(571\) −292599. −0.0375562 −0.0187781 0.999824i \(-0.505978\pi\)
−0.0187781 + 0.999824i \(0.505978\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 4.89287e6 0.617154
\(576\) 0 0
\(577\) 3.55569e6 0.444615 0.222307 0.974977i \(-0.428641\pi\)
0.222307 + 0.974977i \(0.428641\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 4.01389e6 0.493316
\(582\) 0 0
\(583\) −2.43590e6 −0.296816
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.64810e6 −0.317204 −0.158602 0.987343i \(-0.550699\pi\)
−0.158602 + 0.987343i \(0.550699\pi\)
\(588\) 0 0
\(589\) 8.21758e6 0.976013
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.05356e6 −0.123034 −0.0615168 0.998106i \(-0.519594\pi\)
−0.0615168 + 0.998106i \(0.519594\pi\)
\(594\) 0 0
\(595\) 8.14914e6 0.943669
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 9.19012e6 1.04654 0.523268 0.852168i \(-0.324713\pi\)
0.523268 + 0.852168i \(0.324713\pi\)
\(600\) 0 0
\(601\) 3.46924e6 0.391785 0.195893 0.980625i \(-0.437240\pi\)
0.195893 + 0.980625i \(0.437240\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.91574e6 0.879231
\(606\) 0 0
\(607\) 744150. 0.0819764 0.0409882 0.999160i \(-0.486949\pi\)
0.0409882 + 0.999160i \(0.486949\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −1.85557e6 −0.201082
\(612\) 0 0
\(613\) 1.14578e7 1.23154 0.615772 0.787925i \(-0.288844\pi\)
0.615772 + 0.787925i \(0.288844\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3.90052e6 0.412486 0.206243 0.978501i \(-0.433876\pi\)
0.206243 + 0.978501i \(0.433876\pi\)
\(618\) 0 0
\(619\) −2.65029e6 −0.278014 −0.139007 0.990291i \(-0.544391\pi\)
−0.139007 + 0.990291i \(0.544391\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.75147e6 0.490464
\(624\) 0 0
\(625\) 9.58083e6 0.981077
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.97735e7 1.99277
\(630\) 0 0
\(631\) 8.97599e6 0.897447 0.448723 0.893671i \(-0.351879\pi\)
0.448723 + 0.893671i \(0.351879\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.02633e7 1.01007
\(636\) 0 0
\(637\) −646812. −0.0631582
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.87152e6 0.276036 0.138018 0.990430i \(-0.455927\pi\)
0.138018 + 0.990430i \(0.455927\pi\)
\(642\) 0 0
\(643\) −1.38761e7 −1.32354 −0.661772 0.749705i \(-0.730195\pi\)
−0.661772 + 0.749705i \(0.730195\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7.24853e6 −0.680752 −0.340376 0.940289i \(-0.610554\pi\)
−0.340376 + 0.940289i \(0.610554\pi\)
\(648\) 0 0
\(649\) −1.34690e7 −1.25523
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.23719e7 1.13541 0.567706 0.823231i \(-0.307831\pi\)
0.567706 + 0.823231i \(0.307831\pi\)
\(654\) 0 0
\(655\) −2.90491e7 −2.64563
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −572294. −0.0513341 −0.0256670 0.999671i \(-0.508171\pi\)
−0.0256670 + 0.999671i \(0.508171\pi\)
\(660\) 0 0
\(661\) 6.73679e6 0.599721 0.299861 0.953983i \(-0.403060\pi\)
0.299861 + 0.953983i \(0.403060\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −5.55855e6 −0.487425
\(666\) 0 0
\(667\) −4.82942e6 −0.420320
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.48496e7 1.27324
\(672\) 0 0
\(673\) −1.22608e7 −1.04348 −0.521738 0.853106i \(-0.674716\pi\)
−0.521738 + 0.853106i \(0.674716\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 462085. 0.0387481 0.0193741 0.999812i \(-0.493833\pi\)
0.0193741 + 0.999812i \(0.493833\pi\)
\(678\) 0 0
\(679\) −1.29413e6 −0.107721
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.15378e7 −0.946392 −0.473196 0.880957i \(-0.656900\pi\)
−0.473196 + 0.880957i \(0.656900\pi\)
\(684\) 0 0
\(685\) −8.88807e6 −0.723738
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.33159e6 0.187113
\(690\) 0 0
\(691\) −3.09921e6 −0.246920 −0.123460 0.992350i \(-0.539399\pi\)
−0.123460 + 0.992350i \(0.539399\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.48114e7 1.16315
\(696\) 0 0
\(697\) −2.27746e7 −1.77569
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −5.83889e6 −0.448782 −0.224391 0.974499i \(-0.572039\pi\)
−0.224391 + 0.974499i \(0.572039\pi\)
\(702\) 0 0
\(703\) −1.34876e7 −1.02931
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.58375e6 0.269643
\(708\) 0 0
\(709\) 75435.7 0.00563587 0.00281794 0.999996i \(-0.499103\pi\)
0.00281794 + 0.999996i \(0.499103\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5.50255e6 0.405359
\(714\) 0 0
\(715\) 7.33343e6 0.536466
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.30869e7 −0.944091 −0.472045 0.881574i \(-0.656484\pi\)
−0.472045 + 0.881574i \(0.656484\pi\)
\(720\) 0 0
\(721\) −4.29482e6 −0.307686
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3.83126e7 −2.70705
\(726\) 0 0
\(727\) 3.58160e6 0.251328 0.125664 0.992073i \(-0.459894\pi\)
0.125664 + 0.992073i \(0.459894\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.40866e7 −2.35934
\(732\) 0 0
\(733\) −9.23826e6 −0.635083 −0.317541 0.948244i \(-0.602857\pi\)
−0.317541 + 0.948244i \(0.602857\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.76599e6 0.458842
\(738\) 0 0
\(739\) 1.90444e7 1.28279 0.641397 0.767210i \(-0.278355\pi\)
0.641397 + 0.767210i \(0.278355\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 9.30669e6 0.618477 0.309238 0.950985i \(-0.399926\pi\)
0.309238 + 0.950985i \(0.399926\pi\)
\(744\) 0 0
\(745\) 4.82260e7 3.18340
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.65647e6 −0.368418
\(750\) 0 0
\(751\) −2.56243e7 −1.65788 −0.828939 0.559339i \(-0.811055\pi\)
−0.828939 + 0.559339i \(0.811055\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 2.02739e7 1.29441
\(756\) 0 0
\(757\) 5.60956e6 0.355786 0.177893 0.984050i \(-0.443072\pi\)
0.177893 + 0.984050i \(0.443072\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.83985e7 1.77760 0.888799 0.458298i \(-0.151541\pi\)
0.888799 + 0.458298i \(0.151541\pi\)
\(762\) 0 0
\(763\) −5.74783e6 −0.357432
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.28922e7 0.791297
\(768\) 0 0
\(769\) −2.41205e6 −0.147086 −0.0735429 0.997292i \(-0.523431\pi\)
−0.0735429 + 0.997292i \(0.523431\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −5.93891e6 −0.357485 −0.178743 0.983896i \(-0.557203\pi\)
−0.178743 + 0.983896i \(0.557203\pi\)
\(774\) 0 0
\(775\) 4.36527e7 2.61070
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.55346e7 0.917183
\(780\) 0 0
\(781\) 3.52958e6 0.207060
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 713979. 0.0413534
\(786\) 0 0
\(787\) −2.62637e7 −1.51154 −0.755769 0.654839i \(-0.772737\pi\)
−0.755769 + 0.654839i \(0.772737\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −8.89522e6 −0.505494
\(792\) 0 0
\(793\) −1.42137e7 −0.802648
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 9.33689e6 0.520663 0.260331 0.965519i \(-0.416168\pi\)
0.260331 + 0.965519i \(0.416168\pi\)
\(798\) 0 0
\(799\) −1.18435e7 −0.656315
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.14809e6 0.0628332
\(804\) 0 0
\(805\) −3.72205e6 −0.202438
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 3.43772e7 1.84671 0.923357 0.383942i \(-0.125434\pi\)
0.923357 + 0.383942i \(0.125434\pi\)
\(810\) 0 0
\(811\) 2.02626e7 1.08179 0.540896 0.841090i \(-0.318085\pi\)
0.540896 + 0.841090i \(0.318085\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3.75433e7 1.97988
\(816\) 0 0
\(817\) 2.32506e7 1.21865
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −1.73641e7 −0.899073 −0.449537 0.893262i \(-0.648411\pi\)
−0.449537 + 0.893262i \(0.648411\pi\)
\(822\) 0 0
\(823\) 2.65094e7 1.36427 0.682136 0.731226i \(-0.261051\pi\)
0.682136 + 0.731226i \(0.261051\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.30816e6 −0.117355 −0.0586775 0.998277i \(-0.518688\pi\)
−0.0586775 + 0.998277i \(0.518688\pi\)
\(828\) 0 0
\(829\) −6.14314e6 −0.310459 −0.155230 0.987878i \(-0.549612\pi\)
−0.155230 + 0.987878i \(0.549612\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −4.12839e6 −0.206143
\(834\) 0 0
\(835\) 1.62726e7 0.807684
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.04628e7 0.513150 0.256575 0.966524i \(-0.417406\pi\)
0.256575 + 0.966524i \(0.417406\pi\)
\(840\) 0 0
\(841\) 1.73047e7 0.843671
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.88930e7 1.39204
\(846\) 0 0
\(847\) −4.01014e6 −0.192066
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −9.03136e6 −0.427493
\(852\) 0 0
\(853\) −3.45134e7 −1.62411 −0.812054 0.583583i \(-0.801650\pi\)
−0.812054 + 0.583583i \(0.801650\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.35665e7 0.630978 0.315489 0.948929i \(-0.397831\pi\)
0.315489 + 0.948929i \(0.397831\pi\)
\(858\) 0 0
\(859\) −3.12783e7 −1.44630 −0.723152 0.690688i \(-0.757308\pi\)
−0.723152 + 0.690688i \(0.757308\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.98071e7 −0.905305 −0.452653 0.891687i \(-0.649522\pi\)
−0.452653 + 0.891687i \(0.649522\pi\)
\(864\) 0 0
\(865\) 3.10976e7 1.41314
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 3.35457e6 0.150691
\(870\) 0 0
\(871\) −6.47626e6 −0.289254
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.47170e7 −0.649830
\(876\) 0 0
\(877\) −1.74647e6 −0.0766765 −0.0383383 0.999265i \(-0.512206\pi\)
−0.0383383 + 0.999265i \(0.512206\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.17415e7 −0.509663 −0.254832 0.966985i \(-0.582020\pi\)
−0.254832 + 0.966985i \(0.582020\pi\)
\(882\) 0 0
\(883\) 4.26514e7 1.84091 0.920453 0.390854i \(-0.127820\pi\)
0.920453 + 0.390854i \(0.127820\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −4.28737e7 −1.82971 −0.914854 0.403785i \(-0.867694\pi\)
−0.914854 + 0.403785i \(0.867694\pi\)
\(888\) 0 0
\(889\) −5.19942e6 −0.220648
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 8.07846e6 0.339000
\(894\) 0 0
\(895\) 5.91851e7 2.46976
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −4.30866e7 −1.77805
\(900\) 0 0
\(901\) 1.48817e7 0.610719
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −2.52904e7 −1.02644
\(906\) 0 0
\(907\) 1.99065e7 0.803482 0.401741 0.915753i \(-0.368405\pi\)
0.401741 + 0.915753i \(0.368405\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −1.12063e7 −0.447371 −0.223685 0.974661i \(-0.571809\pi\)
−0.223685 + 0.974661i \(0.571809\pi\)
\(912\) 0 0
\(913\) 2.30549e7 0.915348
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.47164e7 0.577933
\(918\) 0 0
\(919\) −3.38620e7 −1.32259 −0.661293 0.750128i \(-0.729992\pi\)
−0.661293 + 0.750128i \(0.729992\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.37844e6 −0.130530
\(924\) 0 0
\(925\) −7.16474e7 −2.75325
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.29019e7 0.870627 0.435313 0.900279i \(-0.356638\pi\)
0.435313 + 0.900279i \(0.356638\pi\)
\(930\) 0 0
\(931\) 2.81598e6 0.106477
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 4.68069e7 1.75098
\(936\) 0 0
\(937\) 2.97781e7 1.10802 0.554011 0.832510i \(-0.313097\pi\)
0.554011 + 0.832510i \(0.313097\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.30322e7 0.479782 0.239891 0.970800i \(-0.422888\pi\)
0.239891 + 0.970800i \(0.422888\pi\)
\(942\) 0 0
\(943\) 1.04021e7 0.380926
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.66683e7 1.69101 0.845506 0.533966i \(-0.179299\pi\)
0.845506 + 0.533966i \(0.179299\pi\)
\(948\) 0 0
\(949\) −1.09893e6 −0.0396100
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.00948e7 −0.716724 −0.358362 0.933583i \(-0.616665\pi\)
−0.358362 + 0.933583i \(0.616665\pi\)
\(954\) 0 0
\(955\) −6.80251e7 −2.41357
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 4.50273e6 0.158099
\(960\) 0 0
\(961\) 2.04630e7 0.714760
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −4.99485e7 −1.72665
\(966\) 0 0
\(967\) −7.33633e6 −0.252297 −0.126149 0.992011i \(-0.540262\pi\)
−0.126149 + 0.992011i \(0.540262\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 4.01630e7 1.36703 0.683514 0.729937i \(-0.260451\pi\)
0.683514 + 0.729937i \(0.260451\pi\)
\(972\) 0 0
\(973\) −7.50352e6 −0.254087
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −2.65602e7 −0.890216 −0.445108 0.895477i \(-0.646835\pi\)
−0.445108 + 0.895477i \(0.646835\pi\)
\(978\) 0 0
\(979\) 2.72914e7 0.910057
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 2.77362e7 0.915510 0.457755 0.889078i \(-0.348654\pi\)
0.457755 + 0.889078i \(0.348654\pi\)
\(984\) 0 0
\(985\) 1.37906e7 0.452890
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.55687e7 0.506131
\(990\) 0 0
\(991\) 2.35437e7 0.761536 0.380768 0.924671i \(-0.375660\pi\)
0.380768 + 0.924671i \(0.375660\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 9.52559e7 3.05024
\(996\) 0 0
\(997\) −4.05582e7 −1.29223 −0.646117 0.763239i \(-0.723608\pi\)
−0.646117 + 0.763239i \(0.723608\pi\)
\(998\) 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.bd.1.1 2
3.2 odd 2 112.6.a.i.1.1 2
4.3 odd 2 504.6.a.i.1.1 2
12.11 even 2 56.6.a.e.1.2 2
21.20 even 2 784.6.a.u.1.2 2
24.5 odd 2 448.6.a.t.1.2 2
24.11 even 2 448.6.a.v.1.1 2
84.11 even 6 392.6.i.j.177.1 4
84.23 even 6 392.6.i.j.361.1 4
84.47 odd 6 392.6.i.i.361.2 4
84.59 odd 6 392.6.i.i.177.2 4
84.83 odd 2 392.6.a.d.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
56.6.a.e.1.2 2 12.11 even 2
112.6.a.i.1.1 2 3.2 odd 2
392.6.a.d.1.1 2 84.83 odd 2
392.6.i.i.177.2 4 84.59 odd 6
392.6.i.i.361.2 4 84.47 odd 6
392.6.i.j.177.1 4 84.11 even 6
392.6.i.j.361.1 4 84.23 even 6
448.6.a.t.1.2 2 24.5 odd 2
448.6.a.v.1.1 2 24.11 even 2
504.6.a.i.1.1 2 4.3 odd 2
784.6.a.u.1.2 2 21.20 even 2
1008.6.a.bd.1.1 2 1.1 even 1 trivial