Properties

Label 1008.6.a.bx.1.2
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: \(\Q(\sqrt{429}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 107 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
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 1.2
Root \(-9.85616\) 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)
 
\(f(q)\) \(=\) \(q+81.4246 q^{5} -49.0000 q^{7} +O(q^{10})\) \(q+81.4246 q^{5} -49.0000 q^{7} -340.274 q^{11} -1100.79 q^{13} +197.369 q^{17} +2338.79 q^{19} +2606.58 q^{23} +3504.97 q^{25} -7915.83 q^{29} +9044.32 q^{31} -3989.81 q^{35} -5472.73 q^{37} +15249.0 q^{41} +3828.88 q^{43} +1940.82 q^{47} +2401.00 q^{49} -26291.9 q^{53} -27706.7 q^{55} -45841.3 q^{59} -43407.8 q^{61} -89631.8 q^{65} -15855.3 q^{67} -24120.6 q^{71} +69057.5 q^{73} +16673.4 q^{77} -60934.9 q^{79} +52245.0 q^{83} +16070.7 q^{85} -100507. q^{89} +53938.9 q^{91} +190435. q^{95} +64941.4 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 80 q^{5} - 98 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 80 q^{5} - 98 q^{7} - 432 q^{11} - 876 q^{13} - 848 q^{17} + 3352 q^{19} + 5296 q^{23} + 382 q^{25} - 256 q^{29} + 856 q^{31} - 3920 q^{35} + 3636 q^{37} - 3056 q^{41} + 26216 q^{43} - 2912 q^{47} + 4802 q^{49} - 27232 q^{53} - 27576 q^{55} - 59040 q^{59} - 40420 q^{61} - 89952 q^{65} - 52920 q^{67} + 52752 q^{71} + 18812 q^{73} + 21168 q^{77} - 50288 q^{79} + 66048 q^{83} + 17560 q^{85} - 131504 q^{89} + 42924 q^{91} + 188992 q^{95} + 164348 q^{97}+O(q^{100}) \) 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
\(5\) 81.4246 1.45657 0.728284 0.685275i \(-0.240318\pi\)
0.728284 + 0.685275i \(0.240318\pi\)
\(6\) 0 0
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −340.274 −0.847904 −0.423952 0.905685i \(-0.639358\pi\)
−0.423952 + 0.905685i \(0.639358\pi\)
\(12\) 0 0
\(13\) −1100.79 −1.80654 −0.903270 0.429072i \(-0.858841\pi\)
−0.903270 + 0.429072i \(0.858841\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 197.369 0.165637 0.0828186 0.996565i \(-0.473608\pi\)
0.0828186 + 0.996565i \(0.473608\pi\)
\(18\) 0 0
\(19\) 2338.79 1.48631 0.743153 0.669122i \(-0.233330\pi\)
0.743153 + 0.669122i \(0.233330\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2606.58 1.02743 0.513713 0.857962i \(-0.328270\pi\)
0.513713 + 0.857962i \(0.328270\pi\)
\(24\) 0 0
\(25\) 3504.97 1.12159
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −7915.83 −1.74784 −0.873920 0.486070i \(-0.838430\pi\)
−0.873920 + 0.486070i \(0.838430\pi\)
\(30\) 0 0
\(31\) 9044.32 1.69033 0.845166 0.534504i \(-0.179502\pi\)
0.845166 + 0.534504i \(0.179502\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3989.81 −0.550531
\(36\) 0 0
\(37\) −5472.73 −0.657204 −0.328602 0.944469i \(-0.606577\pi\)
−0.328602 + 0.944469i \(0.606577\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 15249.0 1.41671 0.708355 0.705856i \(-0.249438\pi\)
0.708355 + 0.705856i \(0.249438\pi\)
\(42\) 0 0
\(43\) 3828.88 0.315792 0.157896 0.987456i \(-0.449529\pi\)
0.157896 + 0.987456i \(0.449529\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1940.82 0.128156 0.0640782 0.997945i \(-0.479589\pi\)
0.0640782 + 0.997945i \(0.479589\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −26291.9 −1.28568 −0.642840 0.766000i \(-0.722244\pi\)
−0.642840 + 0.766000i \(0.722244\pi\)
\(54\) 0 0
\(55\) −27706.7 −1.23503
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −45841.3 −1.71446 −0.857229 0.514935i \(-0.827816\pi\)
−0.857229 + 0.514935i \(0.827816\pi\)
\(60\) 0 0
\(61\) −43407.8 −1.49363 −0.746815 0.665032i \(-0.768418\pi\)
−0.746815 + 0.665032i \(0.768418\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −89631.8 −2.63135
\(66\) 0 0
\(67\) −15855.3 −0.431506 −0.215753 0.976448i \(-0.569221\pi\)
−0.215753 + 0.976448i \(0.569221\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −24120.6 −0.567862 −0.283931 0.958845i \(-0.591639\pi\)
−0.283931 + 0.958845i \(0.591639\pi\)
\(72\) 0 0
\(73\) 69057.5 1.51671 0.758357 0.651840i \(-0.226003\pi\)
0.758357 + 0.651840i \(0.226003\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 16673.4 0.320478
\(78\) 0 0
\(79\) −60934.9 −1.09850 −0.549248 0.835660i \(-0.685086\pi\)
−0.549248 + 0.835660i \(0.685086\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 52245.0 0.832434 0.416217 0.909265i \(-0.363356\pi\)
0.416217 + 0.909265i \(0.363356\pi\)
\(84\) 0 0
\(85\) 16070.7 0.241262
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −100507. −1.34500 −0.672500 0.740097i \(-0.734780\pi\)
−0.672500 + 0.740097i \(0.734780\pi\)
\(90\) 0 0
\(91\) 53938.9 0.682808
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 190435. 2.16490
\(96\) 0 0
\(97\) 64941.4 0.700797 0.350398 0.936601i \(-0.386046\pi\)
0.350398 + 0.936601i \(0.386046\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −35889.9 −0.350081 −0.175041 0.984561i \(-0.556006\pi\)
−0.175041 + 0.984561i \(0.556006\pi\)
\(102\) 0 0
\(103\) −121284. −1.12645 −0.563223 0.826305i \(-0.690439\pi\)
−0.563223 + 0.826305i \(0.690439\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −54535.5 −0.460490 −0.230245 0.973133i \(-0.573953\pi\)
−0.230245 + 0.973133i \(0.573953\pi\)
\(108\) 0 0
\(109\) −105311. −0.848999 −0.424499 0.905428i \(-0.639550\pi\)
−0.424499 + 0.905428i \(0.639550\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 68204.7 0.502479 0.251240 0.967925i \(-0.419162\pi\)
0.251240 + 0.967925i \(0.419162\pi\)
\(114\) 0 0
\(115\) 212239. 1.49652
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −9671.10 −0.0626049
\(120\) 0 0
\(121\) −45264.7 −0.281058
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 30939.0 0.177105
\(126\) 0 0
\(127\) 213149. 1.17266 0.586332 0.810071i \(-0.300572\pi\)
0.586332 + 0.810071i \(0.300572\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 285781. 1.45497 0.727486 0.686123i \(-0.240689\pi\)
0.727486 + 0.686123i \(0.240689\pi\)
\(132\) 0 0
\(133\) −114601. −0.561771
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −340712. −1.55091 −0.775453 0.631405i \(-0.782479\pi\)
−0.775453 + 0.631405i \(0.782479\pi\)
\(138\) 0 0
\(139\) −335029. −1.47077 −0.735387 0.677648i \(-0.763000\pi\)
−0.735387 + 0.677648i \(0.763000\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 374571. 1.53177
\(144\) 0 0
\(145\) −644544. −2.54585
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 66133.2 0.244036 0.122018 0.992528i \(-0.461063\pi\)
0.122018 + 0.992528i \(0.461063\pi\)
\(150\) 0 0
\(151\) −29502.2 −0.105296 −0.0526480 0.998613i \(-0.516766\pi\)
−0.0526480 + 0.998613i \(0.516766\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 736431. 2.46208
\(156\) 0 0
\(157\) −426148. −1.37978 −0.689892 0.723912i \(-0.742342\pi\)
−0.689892 + 0.723912i \(0.742342\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −127722. −0.388331
\(162\) 0 0
\(163\) −640985. −1.88964 −0.944819 0.327593i \(-0.893763\pi\)
−0.944819 + 0.327593i \(0.893763\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 211785. 0.587629 0.293815 0.955862i \(-0.405075\pi\)
0.293815 + 0.955862i \(0.405075\pi\)
\(168\) 0 0
\(169\) 840455. 2.26359
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 311274. 0.790730 0.395365 0.918524i \(-0.370618\pi\)
0.395365 + 0.918524i \(0.370618\pi\)
\(174\) 0 0
\(175\) −171744. −0.423921
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −803487. −1.87433 −0.937165 0.348886i \(-0.886560\pi\)
−0.937165 + 0.348886i \(0.886560\pi\)
\(180\) 0 0
\(181\) 36730.7 0.0833359 0.0416680 0.999132i \(-0.486733\pi\)
0.0416680 + 0.999132i \(0.486733\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −445615. −0.957262
\(186\) 0 0
\(187\) −67159.7 −0.140444
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 352538. 0.699234 0.349617 0.936893i \(-0.386312\pi\)
0.349617 + 0.936893i \(0.386312\pi\)
\(192\) 0 0
\(193\) −467781. −0.903961 −0.451981 0.892028i \(-0.649282\pi\)
−0.451981 + 0.892028i \(0.649282\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −200981. −0.368969 −0.184485 0.982835i \(-0.559062\pi\)
−0.184485 + 0.982835i \(0.559062\pi\)
\(198\) 0 0
\(199\) 140758. 0.251966 0.125983 0.992032i \(-0.459792\pi\)
0.125983 + 0.992032i \(0.459792\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 387876. 0.660621
\(204\) 0 0
\(205\) 1.24164e6 2.06353
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −795831. −1.26024
\(210\) 0 0
\(211\) 178072. 0.275352 0.137676 0.990477i \(-0.456037\pi\)
0.137676 + 0.990477i \(0.456037\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 311765. 0.459972
\(216\) 0 0
\(217\) −443172. −0.638885
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −217263. −0.299230
\(222\) 0 0
\(223\) −577918. −0.778223 −0.389111 0.921191i \(-0.627218\pi\)
−0.389111 + 0.921191i \(0.627218\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −46602.0 −0.0600261 −0.0300130 0.999550i \(-0.509555\pi\)
−0.0300130 + 0.999550i \(0.509555\pi\)
\(228\) 0 0
\(229\) −447131. −0.563438 −0.281719 0.959497i \(-0.590905\pi\)
−0.281719 + 0.959497i \(0.590905\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.07326e6 −1.29513 −0.647567 0.762009i \(-0.724213\pi\)
−0.647567 + 0.762009i \(0.724213\pi\)
\(234\) 0 0
\(235\) 158031. 0.186669
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −375795. −0.425555 −0.212778 0.977101i \(-0.568251\pi\)
−0.212778 + 0.977101i \(0.568251\pi\)
\(240\) 0 0
\(241\) −573941. −0.636539 −0.318269 0.948000i \(-0.603102\pi\)
−0.318269 + 0.948000i \(0.603102\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 195501. 0.208081
\(246\) 0 0
\(247\) −2.57453e6 −2.68507
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.56414e6 1.56708 0.783542 0.621338i \(-0.213411\pi\)
0.783542 + 0.621338i \(0.213411\pi\)
\(252\) 0 0
\(253\) −886950. −0.871159
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 254654. 0.240502 0.120251 0.992744i \(-0.461630\pi\)
0.120251 + 0.992744i \(0.461630\pi\)
\(258\) 0 0
\(259\) 268164. 0.248400
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.93115e6 −1.72157 −0.860787 0.508965i \(-0.830028\pi\)
−0.860787 + 0.508965i \(0.830028\pi\)
\(264\) 0 0
\(265\) −2.14081e6 −1.87268
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.90099e6 1.60177 0.800883 0.598821i \(-0.204364\pi\)
0.800883 + 0.598821i \(0.204364\pi\)
\(270\) 0 0
\(271\) 1.09964e6 0.909555 0.454778 0.890605i \(-0.349719\pi\)
0.454778 + 0.890605i \(0.349719\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.19265e6 −0.951002
\(276\) 0 0
\(277\) −1.12622e6 −0.881908 −0.440954 0.897530i \(-0.645360\pi\)
−0.440954 + 0.897530i \(0.645360\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −619287. −0.467871 −0.233936 0.972252i \(-0.575160\pi\)
−0.233936 + 0.972252i \(0.575160\pi\)
\(282\) 0 0
\(283\) 354811. 0.263348 0.131674 0.991293i \(-0.457965\pi\)
0.131674 + 0.991293i \(0.457965\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −747200. −0.535466
\(288\) 0 0
\(289\) −1.38090e6 −0.972564
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.74574e6 1.18798 0.593992 0.804471i \(-0.297551\pi\)
0.593992 + 0.804471i \(0.297551\pi\)
\(294\) 0 0
\(295\) −3.73261e6 −2.49723
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.86930e6 −1.85609
\(300\) 0 0
\(301\) −187615. −0.119358
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −3.53446e6 −2.17557
\(306\) 0 0
\(307\) −2.40315e6 −1.45524 −0.727621 0.685980i \(-0.759374\pi\)
−0.727621 + 0.685980i \(0.759374\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 738921. 0.433208 0.216604 0.976260i \(-0.430502\pi\)
0.216604 + 0.976260i \(0.430502\pi\)
\(312\) 0 0
\(313\) 410140. 0.236631 0.118316 0.992976i \(-0.462251\pi\)
0.118316 + 0.992976i \(0.462251\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.48927e6 0.832385 0.416193 0.909276i \(-0.363364\pi\)
0.416193 + 0.909276i \(0.363364\pi\)
\(318\) 0 0
\(319\) 2.69355e6 1.48200
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 461607. 0.246187
\(324\) 0 0
\(325\) −3.85825e6 −2.02620
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −95100.2 −0.0484386
\(330\) 0 0
\(331\) 397114. 0.199226 0.0996129 0.995026i \(-0.468240\pi\)
0.0996129 + 0.995026i \(0.468240\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.29101e6 −0.628519
\(336\) 0 0
\(337\) −1.31077e6 −0.628712 −0.314356 0.949305i \(-0.601789\pi\)
−0.314356 + 0.949305i \(0.601789\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.07755e6 −1.43324
\(342\) 0 0
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.01372e6 0.897793 0.448896 0.893584i \(-0.351817\pi\)
0.448896 + 0.893584i \(0.351817\pi\)
\(348\) 0 0
\(349\) 2.13139e6 0.936697 0.468349 0.883544i \(-0.344849\pi\)
0.468349 + 0.883544i \(0.344849\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.59455e6 1.10822 0.554109 0.832444i \(-0.313059\pi\)
0.554109 + 0.832444i \(0.313059\pi\)
\(354\) 0 0
\(355\) −1.96401e6 −0.827129
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.92478e6 −1.19772 −0.598862 0.800852i \(-0.704380\pi\)
−0.598862 + 0.800852i \(0.704380\pi\)
\(360\) 0 0
\(361\) 2.99386e6 1.20910
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 5.62298e6 2.20920
\(366\) 0 0
\(367\) −2.86220e6 −1.10926 −0.554631 0.832096i \(-0.687141\pi\)
−0.554631 + 0.832096i \(0.687141\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.28830e6 0.485941
\(372\) 0 0
\(373\) 1.82182e6 0.678005 0.339002 0.940786i \(-0.389911\pi\)
0.339002 + 0.940786i \(0.389911\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.71370e6 3.15754
\(378\) 0 0
\(379\) −111694. −0.0399421 −0.0199711 0.999801i \(-0.506357\pi\)
−0.0199711 + 0.999801i \(0.506357\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 502665. 0.175098 0.0875490 0.996160i \(-0.472097\pi\)
0.0875490 + 0.996160i \(0.472097\pi\)
\(384\) 0 0
\(385\) 1.35763e6 0.466798
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.12977e6 −0.378544 −0.189272 0.981925i \(-0.560613\pi\)
−0.189272 + 0.981925i \(0.560613\pi\)
\(390\) 0 0
\(391\) 514458. 0.170180
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.96160e6 −1.60003
\(396\) 0 0
\(397\) −3.17615e6 −1.01140 −0.505701 0.862709i \(-0.668766\pi\)
−0.505701 + 0.862709i \(0.668766\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −344088. −0.106858 −0.0534291 0.998572i \(-0.517015\pi\)
−0.0534291 + 0.998572i \(0.517015\pi\)
\(402\) 0 0
\(403\) −9.95594e6 −3.05365
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.86223e6 0.557246
\(408\) 0 0
\(409\) 4.09290e6 1.20983 0.604913 0.796292i \(-0.293208\pi\)
0.604913 + 0.796292i \(0.293208\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.24622e6 0.648004
\(414\) 0 0
\(415\) 4.25403e6 1.21250
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.40179e6 0.668345 0.334172 0.942512i \(-0.391543\pi\)
0.334172 + 0.942512i \(0.391543\pi\)
\(420\) 0 0
\(421\) −6.67831e6 −1.83638 −0.918188 0.396146i \(-0.870347\pi\)
−0.918188 + 0.396146i \(0.870347\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 691774. 0.185777
\(426\) 0 0
\(427\) 2.12698e6 0.564539
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.47258e6 −1.15975 −0.579876 0.814705i \(-0.696899\pi\)
−0.579876 + 0.814705i \(0.696899\pi\)
\(432\) 0 0
\(433\) 365188. 0.0936045 0.0468023 0.998904i \(-0.485097\pi\)
0.0468023 + 0.998904i \(0.485097\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 6.09624e6 1.52707
\(438\) 0 0
\(439\) −89090.3 −0.0220632 −0.0110316 0.999939i \(-0.503512\pi\)
−0.0110316 + 0.999939i \(0.503512\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −489817. −0.118583 −0.0592917 0.998241i \(-0.518884\pi\)
−0.0592917 + 0.998241i \(0.518884\pi\)
\(444\) 0 0
\(445\) −8.18377e6 −1.95908
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 744805. 0.174352 0.0871760 0.996193i \(-0.472216\pi\)
0.0871760 + 0.996193i \(0.472216\pi\)
\(450\) 0 0
\(451\) −5.18883e6 −1.20123
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 4.39196e6 0.994557
\(456\) 0 0
\(457\) −5.14670e6 −1.15276 −0.576379 0.817182i \(-0.695535\pi\)
−0.576379 + 0.817182i \(0.695535\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −7.01082e6 −1.53644 −0.768222 0.640184i \(-0.778858\pi\)
−0.768222 + 0.640184i \(0.778858\pi\)
\(462\) 0 0
\(463\) 222601. 0.0482585 0.0241293 0.999709i \(-0.492319\pi\)
0.0241293 + 0.999709i \(0.492319\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.47129e6 −1.16091 −0.580454 0.814293i \(-0.697125\pi\)
−0.580454 + 0.814293i \(0.697125\pi\)
\(468\) 0 0
\(469\) 776909. 0.163094
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.30287e6 −0.267761
\(474\) 0 0
\(475\) 8.19740e6 1.66703
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.46045e6 0.888260 0.444130 0.895962i \(-0.353513\pi\)
0.444130 + 0.895962i \(0.353513\pi\)
\(480\) 0 0
\(481\) 6.02435e6 1.18727
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.28783e6 1.02076
\(486\) 0 0
\(487\) 966691. 0.184699 0.0923497 0.995727i \(-0.470562\pi\)
0.0923497 + 0.995727i \(0.470562\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.43131e6 0.267936 0.133968 0.990986i \(-0.457228\pi\)
0.133968 + 0.990986i \(0.457228\pi\)
\(492\) 0 0
\(493\) −1.56234e6 −0.289507
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.18191e6 0.214632
\(498\) 0 0
\(499\) 6.88711e6 1.23819 0.619093 0.785318i \(-0.287500\pi\)
0.619093 + 0.785318i \(0.287500\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.00139e6 0.881395 0.440697 0.897656i \(-0.354731\pi\)
0.440697 + 0.897656i \(0.354731\pi\)
\(504\) 0 0
\(505\) −2.92232e6 −0.509917
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −381400. −0.0652508 −0.0326254 0.999468i \(-0.510387\pi\)
−0.0326254 + 0.999468i \(0.510387\pi\)
\(510\) 0 0
\(511\) −3.38382e6 −0.573264
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −9.87550e6 −1.64075
\(516\) 0 0
\(517\) −660410. −0.108664
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.45886e6 1.04246 0.521232 0.853415i \(-0.325473\pi\)
0.521232 + 0.853415i \(0.325473\pi\)
\(522\) 0 0
\(523\) −1.57762e6 −0.252202 −0.126101 0.992017i \(-0.540246\pi\)
−0.126101 + 0.992017i \(0.540246\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.78507e6 0.279982
\(528\) 0 0
\(529\) 357892. 0.0556049
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.67860e7 −2.55934
\(534\) 0 0
\(535\) −4.44053e6 −0.670734
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −816998. −0.121129
\(540\) 0 0
\(541\) −5.98175e6 −0.878690 −0.439345 0.898319i \(-0.644789\pi\)
−0.439345 + 0.898319i \(0.644789\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −8.57490e6 −1.23662
\(546\) 0 0
\(547\) 3.52416e6 0.503602 0.251801 0.967779i \(-0.418977\pi\)
0.251801 + 0.967779i \(0.418977\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.85135e7 −2.59782
\(552\) 0 0
\(553\) 2.98581e6 0.415192
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.23769e7 −1.69034 −0.845172 0.534495i \(-0.820502\pi\)
−0.845172 + 0.534495i \(0.820502\pi\)
\(558\) 0 0
\(559\) −4.21481e6 −0.570491
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 630148. 0.0837860 0.0418930 0.999122i \(-0.486661\pi\)
0.0418930 + 0.999122i \(0.486661\pi\)
\(564\) 0 0
\(565\) 5.55354e6 0.731895
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −751980. −0.0973701 −0.0486851 0.998814i \(-0.515503\pi\)
−0.0486851 + 0.998814i \(0.515503\pi\)
\(570\) 0 0
\(571\) −1.16905e7 −1.50052 −0.750259 0.661144i \(-0.770071\pi\)
−0.750259 + 0.661144i \(0.770071\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.13597e6 1.15235
\(576\) 0 0
\(577\) 8.52927e6 1.06653 0.533264 0.845949i \(-0.320965\pi\)
0.533264 + 0.845949i \(0.320965\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −2.56001e6 −0.314630
\(582\) 0 0
\(583\) 8.94646e6 1.09013
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 5.62232e6 0.673473 0.336737 0.941599i \(-0.390677\pi\)
0.336737 + 0.941599i \(0.390677\pi\)
\(588\) 0 0
\(589\) 2.11528e7 2.51235
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.24396e6 −0.262047 −0.131023 0.991379i \(-0.541826\pi\)
−0.131023 + 0.991379i \(0.541826\pi\)
\(594\) 0 0
\(595\) −787466. −0.0911884
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 2.13424e6 0.243039 0.121520 0.992589i \(-0.461223\pi\)
0.121520 + 0.992589i \(0.461223\pi\)
\(600\) 0 0
\(601\) −6.01631e6 −0.679429 −0.339715 0.940529i \(-0.610330\pi\)
−0.339715 + 0.940529i \(0.610330\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.68566e6 −0.409380
\(606\) 0 0
\(607\) −4.33356e6 −0.477390 −0.238695 0.971095i \(-0.576720\pi\)
−0.238695 + 0.971095i \(0.576720\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.13644e6 −0.231520
\(612\) 0 0
\(613\) 1.25876e7 1.35299 0.676493 0.736449i \(-0.263499\pi\)
0.676493 + 0.736449i \(0.263499\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.91124e6 0.202116 0.101058 0.994881i \(-0.467777\pi\)
0.101058 + 0.994881i \(0.467777\pi\)
\(618\) 0 0
\(619\) 1.84569e7 1.93612 0.968058 0.250727i \(-0.0806696\pi\)
0.968058 + 0.250727i \(0.0806696\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.92486e6 0.508362
\(624\) 0 0
\(625\) −8.43384e6 −0.863625
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.08015e6 −0.108857
\(630\) 0 0
\(631\) 2.56432e6 0.256389 0.128194 0.991749i \(-0.459082\pi\)
0.128194 + 0.991749i \(0.459082\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.73556e7 1.70806
\(636\) 0 0
\(637\) −2.64301e6 −0.258077
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.60595e6 −0.154378 −0.0771891 0.997016i \(-0.524595\pi\)
−0.0771891 + 0.997016i \(0.524595\pi\)
\(642\) 0 0
\(643\) 7.63307e6 0.728068 0.364034 0.931386i \(-0.381399\pi\)
0.364034 + 0.931386i \(0.381399\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.79911e6 −0.544629 −0.272314 0.962208i \(-0.587789\pi\)
−0.272314 + 0.962208i \(0.587789\pi\)
\(648\) 0 0
\(649\) 1.55986e7 1.45370
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −8.55249e6 −0.784892 −0.392446 0.919775i \(-0.628371\pi\)
−0.392446 + 0.919775i \(0.628371\pi\)
\(654\) 0 0
\(655\) 2.32696e7 2.11926
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.06831e7 0.958260 0.479130 0.877744i \(-0.340952\pi\)
0.479130 + 0.877744i \(0.340952\pi\)
\(660\) 0 0
\(661\) 8.79509e6 0.782955 0.391477 0.920188i \(-0.371964\pi\)
0.391477 + 0.920188i \(0.371964\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −9.33134e6 −0.818257
\(666\) 0 0
\(667\) −2.06332e7 −1.79578
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.47705e7 1.26646
\(672\) 0 0
\(673\) 1.77607e6 0.151155 0.0755775 0.997140i \(-0.475920\pi\)
0.0755775 + 0.997140i \(0.475920\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.19599e7 −1.00290 −0.501448 0.865188i \(-0.667199\pi\)
−0.501448 + 0.865188i \(0.667199\pi\)
\(678\) 0 0
\(679\) −3.18213e6 −0.264876
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.52201e7 1.24844 0.624218 0.781250i \(-0.285418\pi\)
0.624218 + 0.781250i \(0.285418\pi\)
\(684\) 0 0
\(685\) −2.77423e7 −2.25900
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.89420e7 2.32263
\(690\) 0 0
\(691\) −24706.9 −0.00196844 −0.000984221 1.00000i \(-0.500313\pi\)
−0.000984221 1.00000i \(0.500313\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −2.72796e7 −2.14228
\(696\) 0 0
\(697\) 3.00968e6 0.234660
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 466834. 0.0358813 0.0179406 0.999839i \(-0.494289\pi\)
0.0179406 + 0.999839i \(0.494289\pi\)
\(702\) 0 0
\(703\) −1.27996e7 −0.976805
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.75861e6 0.132318
\(708\) 0 0
\(709\) 9.10361e6 0.680140 0.340070 0.940400i \(-0.389549\pi\)
0.340070 + 0.940400i \(0.389549\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.35747e7 1.73669
\(714\) 0 0
\(715\) 3.04993e7 2.23113
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.88266e7 1.35815 0.679077 0.734067i \(-0.262380\pi\)
0.679077 + 0.734067i \(0.262380\pi\)
\(720\) 0 0
\(721\) 5.94291e6 0.425757
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.77448e7 −1.96036
\(726\) 0 0
\(727\) −1.60515e7 −1.12636 −0.563182 0.826333i \(-0.690423\pi\)
−0.563182 + 0.826333i \(0.690423\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 755705. 0.0523069
\(732\) 0 0
\(733\) −2.72193e7 −1.87119 −0.935593 0.353080i \(-0.885135\pi\)
−0.935593 + 0.353080i \(0.885135\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.39514e6 0.365876
\(738\) 0 0
\(739\) 1.30938e7 0.881974 0.440987 0.897514i \(-0.354629\pi\)
0.440987 + 0.897514i \(0.354629\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.36637e6 0.223712 0.111856 0.993724i \(-0.464320\pi\)
0.111856 + 0.993724i \(0.464320\pi\)
\(744\) 0 0
\(745\) 5.38487e6 0.355455
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 2.67224e6 0.174049
\(750\) 0 0
\(751\) 2.06113e7 1.33354 0.666769 0.745264i \(-0.267677\pi\)
0.666769 + 0.745264i \(0.267677\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −2.40220e6 −0.153371
\(756\) 0 0
\(757\) 157073. 0.00996238 0.00498119 0.999988i \(-0.498414\pi\)
0.00498119 + 0.999988i \(0.498414\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.11164e6 −0.194772 −0.0973862 0.995247i \(-0.531048\pi\)
−0.0973862 + 0.995247i \(0.531048\pi\)
\(762\) 0 0
\(763\) 5.16023e6 0.320891
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 5.04618e7 3.09724
\(768\) 0 0
\(769\) 2.28503e7 1.39340 0.696702 0.717361i \(-0.254650\pi\)
0.696702 + 0.717361i \(0.254650\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.44437e7 0.869420 0.434710 0.900570i \(-0.356851\pi\)
0.434710 + 0.900570i \(0.356851\pi\)
\(774\) 0 0
\(775\) 3.17001e7 1.89586
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 3.56642e7 2.10566
\(780\) 0 0
\(781\) 8.20762e6 0.481493
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.46989e7 −2.00975
\(786\) 0 0
\(787\) 1.13089e7 0.650854 0.325427 0.945567i \(-0.394492\pi\)
0.325427 + 0.945567i \(0.394492\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −3.34203e6 −0.189919
\(792\) 0 0
\(793\) 4.77830e7 2.69830
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.96145e7 −1.65143 −0.825713 0.564091i \(-0.809227\pi\)
−0.825713 + 0.564091i \(0.809227\pi\)
\(798\) 0 0
\(799\) 383059. 0.0212275
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −2.34985e7 −1.28603
\(804\) 0 0
\(805\) −1.03997e7 −0.565630
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −6.90828e6 −0.371106 −0.185553 0.982634i \(-0.559408\pi\)
−0.185553 + 0.982634i \(0.559408\pi\)
\(810\) 0 0
\(811\) 463040. 0.0247210 0.0123605 0.999924i \(-0.496065\pi\)
0.0123605 + 0.999924i \(0.496065\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −5.21919e7 −2.75239
\(816\) 0 0
\(817\) 8.95497e6 0.469363
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 2.79933e7 1.44942 0.724712 0.689052i \(-0.241973\pi\)
0.724712 + 0.689052i \(0.241973\pi\)
\(822\) 0 0
\(823\) 1.71925e7 0.884786 0.442393 0.896821i \(-0.354130\pi\)
0.442393 + 0.896821i \(0.354130\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3.87619e6 0.197079 0.0985397 0.995133i \(-0.468583\pi\)
0.0985397 + 0.995133i \(0.468583\pi\)
\(828\) 0 0
\(829\) −2.36921e7 −1.19734 −0.598670 0.800996i \(-0.704304\pi\)
−0.598670 + 0.800996i \(0.704304\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 473884. 0.0236624
\(834\) 0 0
\(835\) 1.72445e7 0.855922
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −7.48831e6 −0.367265 −0.183632 0.982995i \(-0.558786\pi\)
−0.183632 + 0.982995i \(0.558786\pi\)
\(840\) 0 0
\(841\) 4.21492e7 2.05494
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 6.84337e7 3.29707
\(846\) 0 0
\(847\) 2.21797e6 0.106230
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.42651e7 −0.675229
\(852\) 0 0
\(853\) 2.19918e6 0.103488 0.0517438 0.998660i \(-0.483522\pi\)
0.0517438 + 0.998660i \(0.483522\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −1.10099e7 −0.512071 −0.256035 0.966667i \(-0.582416\pi\)
−0.256035 + 0.966667i \(0.582416\pi\)
\(858\) 0 0
\(859\) −3.31391e7 −1.53235 −0.766175 0.642632i \(-0.777842\pi\)
−0.766175 + 0.642632i \(0.777842\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −3.12254e7 −1.42719 −0.713594 0.700559i \(-0.752934\pi\)
−0.713594 + 0.700559i \(0.752934\pi\)
\(864\) 0 0
\(865\) 2.53454e7 1.15175
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 2.07345e7 0.931419
\(870\) 0 0
\(871\) 1.74534e7 0.779534
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.51601e6 −0.0669394
\(876\) 0 0
\(877\) 5.05675e6 0.222010 0.111005 0.993820i \(-0.464593\pi\)
0.111005 + 0.993820i \(0.464593\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −1.22651e7 −0.532392 −0.266196 0.963919i \(-0.585767\pi\)
−0.266196 + 0.963919i \(0.585767\pi\)
\(882\) 0 0
\(883\) −1.39549e7 −0.602318 −0.301159 0.953574i \(-0.597374\pi\)
−0.301159 + 0.953574i \(0.597374\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.78677e7 1.18930 0.594651 0.803984i \(-0.297290\pi\)
0.594651 + 0.803984i \(0.297290\pi\)
\(888\) 0 0
\(889\) −1.04443e7 −0.443225
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 4.53918e6 0.190480
\(894\) 0 0
\(895\) −6.54236e7 −2.73009
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −7.15933e7 −2.95443
\(900\) 0 0
\(901\) −5.18923e6 −0.212956
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.99078e6 0.121384
\(906\) 0 0
\(907\) −4.03006e7 −1.62665 −0.813323 0.581812i \(-0.802344\pi\)
−0.813323 + 0.581812i \(0.802344\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 3.94303e7 1.57411 0.787053 0.616886i \(-0.211606\pi\)
0.787053 + 0.616886i \(0.211606\pi\)
\(912\) 0 0
\(913\) −1.77776e7 −0.705824
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −1.40032e7 −0.549927
\(918\) 0 0
\(919\) −2.51340e7 −0.981687 −0.490843 0.871248i \(-0.663311\pi\)
−0.490843 + 0.871248i \(0.663311\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 2.65518e7 1.02587
\(924\) 0 0
\(925\) −1.91818e7 −0.737114
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 4.21100e6 0.160083 0.0800416 0.996792i \(-0.474495\pi\)
0.0800416 + 0.996792i \(0.474495\pi\)
\(930\) 0 0
\(931\) 5.61544e6 0.212329
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −5.46845e6 −0.204567
\(936\) 0 0
\(937\) 2.46140e7 0.915870 0.457935 0.888986i \(-0.348589\pi\)
0.457935 + 0.888986i \(0.348589\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.00570e7 0.370250 0.185125 0.982715i \(-0.440731\pi\)
0.185125 + 0.982715i \(0.440731\pi\)
\(942\) 0 0
\(943\) 3.97476e7 1.45557
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.34193e7 −0.486246 −0.243123 0.969996i \(-0.578172\pi\)
−0.243123 + 0.969996i \(0.578172\pi\)
\(948\) 0 0
\(949\) −7.60181e7 −2.74000
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −2.38524e7 −0.850747 −0.425373 0.905018i \(-0.639857\pi\)
−0.425373 + 0.905018i \(0.639857\pi\)
\(954\) 0 0
\(955\) 2.87053e7 1.01848
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.66949e7 0.586187
\(960\) 0 0
\(961\) 5.31706e7 1.85722
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −3.80889e7 −1.31668
\(966\) 0 0
\(967\) 1.07883e7 0.371012 0.185506 0.982643i \(-0.440608\pi\)
0.185506 + 0.982643i \(0.440608\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.97812e7 −1.69440 −0.847202 0.531270i \(-0.821715\pi\)
−0.847202 + 0.531270i \(0.821715\pi\)
\(972\) 0 0
\(973\) 1.64164e7 0.555900
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.09847e7 1.37368 0.686840 0.726809i \(-0.258997\pi\)
0.686840 + 0.726809i \(0.258997\pi\)
\(978\) 0 0
\(979\) 3.42000e7 1.14043
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −4.69345e7 −1.54920 −0.774602 0.632449i \(-0.782050\pi\)
−0.774602 + 0.632449i \(0.782050\pi\)
\(984\) 0 0
\(985\) −1.63648e7 −0.537429
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 9.98027e6 0.324453
\(990\) 0 0
\(991\) −3.80764e6 −0.123161 −0.0615804 0.998102i \(-0.519614\pi\)
−0.0615804 + 0.998102i \(0.519614\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 1.14612e7 0.367006
\(996\) 0 0
\(997\) 1.32091e7 0.420859 0.210430 0.977609i \(-0.432514\pi\)
0.210430 + 0.977609i \(0.432514\pi\)
\(998\) 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.bx.1.2 2
3.2 odd 2 1008.6.a.be.1.1 2
4.3 odd 2 504.6.a.w.1.2 yes 2
12.11 even 2 504.6.a.j.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.j.1.1 2 12.11 even 2
504.6.a.w.1.2 yes 2 4.3 odd 2
1008.6.a.be.1.1 2 3.2 odd 2
1008.6.a.bx.1.2 2 1.1 even 1 trivial