Properties

Label 1008.6.a.bh.1.2
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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 1.2
Root \(-2.54138\) 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)
 
\(f(q)\) \(=\) \(q+36.8276 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q+36.8276 q^{5} +49.0000 q^{7} -266.124 q^{11} -1051.24 q^{13} +1254.54 q^{17} -1284.05 q^{19} +982.814 q^{23} -1768.73 q^{25} -3199.78 q^{29} +1617.35 q^{31} +1804.55 q^{35} +2135.46 q^{37} -8931.56 q^{41} +14702.7 q^{43} -6417.60 q^{47} +2401.00 q^{49} +36936.3 q^{53} -9800.73 q^{55} +29523.6 q^{59} +31991.3 q^{61} -38714.7 q^{65} +29023.3 q^{67} +49999.1 q^{71} -12542.0 q^{73} -13040.1 q^{77} -28218.2 q^{79} +110571. q^{83} +46201.6 q^{85} +56586.5 q^{89} -51510.9 q^{91} -47288.7 q^{95} -108767. q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 48 q^{5} + 98 q^{7}+O(q^{10}) \) 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
\(5\) 36.8276 0.658793 0.329396 0.944192i \(-0.393155\pi\)
0.329396 + 0.944192i \(0.393155\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −266.124 −0.663137 −0.331568 0.943431i \(-0.607578\pi\)
−0.331568 + 0.943431i \(0.607578\pi\)
\(12\) 0 0
\(13\) −1051.24 −1.72522 −0.862610 0.505870i \(-0.831172\pi\)
−0.862610 + 0.505870i \(0.831172\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1254.54 1.05284 0.526419 0.850225i \(-0.323534\pi\)
0.526419 + 0.850225i \(0.323534\pi\)
\(18\) 0 0
\(19\) −1284.05 −0.816018 −0.408009 0.912978i \(-0.633777\pi\)
−0.408009 + 0.912978i \(0.633777\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 982.814 0.387393 0.193696 0.981062i \(-0.437952\pi\)
0.193696 + 0.981062i \(0.437952\pi\)
\(24\) 0 0
\(25\) −1768.73 −0.565992
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3199.78 −0.706521 −0.353261 0.935525i \(-0.614927\pi\)
−0.353261 + 0.935525i \(0.614927\pi\)
\(30\) 0 0
\(31\) 1617.35 0.302274 0.151137 0.988513i \(-0.451707\pi\)
0.151137 + 0.988513i \(0.451707\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1804.55 0.249000
\(36\) 0 0
\(37\) 2135.46 0.256441 0.128220 0.991746i \(-0.459073\pi\)
0.128220 + 0.991746i \(0.459073\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8931.56 −0.829789 −0.414894 0.909870i \(-0.636181\pi\)
−0.414894 + 0.909870i \(0.636181\pi\)
\(42\) 0 0
\(43\) 14702.7 1.21262 0.606312 0.795227i \(-0.292648\pi\)
0.606312 + 0.795227i \(0.292648\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6417.60 −0.423768 −0.211884 0.977295i \(-0.567960\pi\)
−0.211884 + 0.977295i \(0.567960\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 36936.3 1.80619 0.903097 0.429437i \(-0.141288\pi\)
0.903097 + 0.429437i \(0.141288\pi\)
\(54\) 0 0
\(55\) −9800.73 −0.436870
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 29523.6 1.10418 0.552089 0.833785i \(-0.313831\pi\)
0.552089 + 0.833785i \(0.313831\pi\)
\(60\) 0 0
\(61\) 31991.3 1.10080 0.550399 0.834902i \(-0.314476\pi\)
0.550399 + 0.834902i \(0.314476\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −38714.7 −1.13656
\(66\) 0 0
\(67\) 29023.3 0.789876 0.394938 0.918708i \(-0.370766\pi\)
0.394938 + 0.918708i \(0.370766\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 49999.1 1.17711 0.588553 0.808458i \(-0.299698\pi\)
0.588553 + 0.808458i \(0.299698\pi\)
\(72\) 0 0
\(73\) −12542.0 −0.275461 −0.137731 0.990470i \(-0.543981\pi\)
−0.137731 + 0.990470i \(0.543981\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −13040.1 −0.250642
\(78\) 0 0
\(79\) −28218.2 −0.508700 −0.254350 0.967112i \(-0.581862\pi\)
−0.254350 + 0.967112i \(0.581862\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 110571. 1.76176 0.880879 0.473341i \(-0.156952\pi\)
0.880879 + 0.473341i \(0.156952\pi\)
\(84\) 0 0
\(85\) 46201.6 0.693602
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 56586.5 0.757247 0.378624 0.925551i \(-0.376397\pi\)
0.378624 + 0.925551i \(0.376397\pi\)
\(90\) 0 0
\(91\) −51510.9 −0.652072
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −47288.7 −0.537586
\(96\) 0 0
\(97\) −108767. −1.17373 −0.586866 0.809684i \(-0.699639\pi\)
−0.586866 + 0.809684i \(0.699639\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −120115. −1.17164 −0.585821 0.810441i \(-0.699228\pi\)
−0.585821 + 0.810441i \(0.699228\pi\)
\(102\) 0 0
\(103\) −32768.4 −0.304342 −0.152171 0.988354i \(-0.548626\pi\)
−0.152171 + 0.988354i \(0.548626\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −113560. −0.958887 −0.479444 0.877573i \(-0.659161\pi\)
−0.479444 + 0.877573i \(0.659161\pi\)
\(108\) 0 0
\(109\) 114246. 0.921034 0.460517 0.887651i \(-0.347664\pi\)
0.460517 + 0.887651i \(0.347664\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −114167. −0.841097 −0.420548 0.907270i \(-0.638162\pi\)
−0.420548 + 0.907270i \(0.638162\pi\)
\(114\) 0 0
\(115\) 36194.7 0.255212
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 61472.3 0.397935
\(120\) 0 0
\(121\) −90228.8 −0.560250
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −180224. −1.03166
\(126\) 0 0
\(127\) 153051. 0.842029 0.421015 0.907054i \(-0.361674\pi\)
0.421015 + 0.907054i \(0.361674\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 306431. 1.56011 0.780053 0.625713i \(-0.215192\pi\)
0.780053 + 0.625713i \(0.215192\pi\)
\(132\) 0 0
\(133\) −62918.7 −0.308426
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −237719. −1.08209 −0.541044 0.840995i \(-0.681971\pi\)
−0.541044 + 0.840995i \(0.681971\pi\)
\(138\) 0 0
\(139\) 129214. 0.567246 0.283623 0.958936i \(-0.408463\pi\)
0.283623 + 0.958936i \(0.408463\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 279761. 1.14406
\(144\) 0 0
\(145\) −117840. −0.465451
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −380471. −1.40396 −0.701982 0.712195i \(-0.747701\pi\)
−0.701982 + 0.712195i \(0.747701\pi\)
\(150\) 0 0
\(151\) 222818. 0.795259 0.397629 0.917546i \(-0.369833\pi\)
0.397629 + 0.917546i \(0.369833\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 59563.2 0.199136
\(156\) 0 0
\(157\) 543718. 1.76045 0.880227 0.474554i \(-0.157390\pi\)
0.880227 + 0.474554i \(0.157390\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 48157.9 0.146421
\(162\) 0 0
\(163\) 320541. 0.944964 0.472482 0.881340i \(-0.343358\pi\)
0.472482 + 0.881340i \(0.343358\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −228996. −0.635385 −0.317692 0.948194i \(-0.602908\pi\)
−0.317692 + 0.948194i \(0.602908\pi\)
\(168\) 0 0
\(169\) 733817. 1.97638
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −341153. −0.866629 −0.433315 0.901243i \(-0.642656\pi\)
−0.433315 + 0.901243i \(0.642656\pi\)
\(174\) 0 0
\(175\) −86667.6 −0.213925
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 504261. 1.17631 0.588156 0.808748i \(-0.299854\pi\)
0.588156 + 0.808748i \(0.299854\pi\)
\(180\) 0 0
\(181\) −304290. −0.690384 −0.345192 0.938532i \(-0.612186\pi\)
−0.345192 + 0.938532i \(0.612186\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 78644.0 0.168941
\(186\) 0 0
\(187\) −333863. −0.698175
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 335548. 0.665535 0.332768 0.943009i \(-0.392018\pi\)
0.332768 + 0.943009i \(0.392018\pi\)
\(192\) 0 0
\(193\) 563036. 1.08803 0.544017 0.839074i \(-0.316903\pi\)
0.544017 + 0.839074i \(0.316903\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 149398. 0.274270 0.137135 0.990552i \(-0.456211\pi\)
0.137135 + 0.990552i \(0.456211\pi\)
\(198\) 0 0
\(199\) 133658. 0.239255 0.119628 0.992819i \(-0.461830\pi\)
0.119628 + 0.992819i \(0.461830\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −156789. −0.267040
\(204\) 0 0
\(205\) −328928. −0.546659
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 341718. 0.541131
\(210\) 0 0
\(211\) 1.17939e6 1.82369 0.911846 0.410533i \(-0.134657\pi\)
0.911846 + 0.410533i \(0.134657\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 541466. 0.798868
\(216\) 0 0
\(217\) 79250.2 0.114249
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.31882e6 −1.81638
\(222\) 0 0
\(223\) −540129. −0.727337 −0.363669 0.931528i \(-0.618476\pi\)
−0.363669 + 0.931528i \(0.618476\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −489915. −0.631039 −0.315519 0.948919i \(-0.602179\pi\)
−0.315519 + 0.948919i \(0.602179\pi\)
\(228\) 0 0
\(229\) 462676. 0.583026 0.291513 0.956567i \(-0.405841\pi\)
0.291513 + 0.956567i \(0.405841\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −478011. −0.576831 −0.288415 0.957505i \(-0.593128\pi\)
−0.288415 + 0.957505i \(0.593128\pi\)
\(234\) 0 0
\(235\) −236345. −0.279175
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 692311. 0.783982 0.391991 0.919969i \(-0.371786\pi\)
0.391991 + 0.919969i \(0.371786\pi\)
\(240\) 0 0
\(241\) 527233. 0.584737 0.292368 0.956306i \(-0.405557\pi\)
0.292368 + 0.956306i \(0.405557\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 88423.1 0.0941132
\(246\) 0 0
\(247\) 1.34985e6 1.40781
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 749297. 0.750705 0.375353 0.926882i \(-0.377522\pi\)
0.375353 + 0.926882i \(0.377522\pi\)
\(252\) 0 0
\(253\) −261551. −0.256894
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 505186. 0.477110 0.238555 0.971129i \(-0.423326\pi\)
0.238555 + 0.971129i \(0.423326\pi\)
\(258\) 0 0
\(259\) 104638. 0.0969256
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.36891e6 −1.22035 −0.610175 0.792267i \(-0.708901\pi\)
−0.610175 + 0.792267i \(0.708901\pi\)
\(264\) 0 0
\(265\) 1.36028e6 1.18991
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 88321.5 0.0744193 0.0372097 0.999307i \(-0.488153\pi\)
0.0372097 + 0.999307i \(0.488153\pi\)
\(270\) 0 0
\(271\) 212260. 0.175568 0.0877841 0.996140i \(-0.472021\pi\)
0.0877841 + 0.996140i \(0.472021\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 470701. 0.375330
\(276\) 0 0
\(277\) 428049. 0.335193 0.167596 0.985856i \(-0.446399\pi\)
0.167596 + 0.985856i \(0.446399\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.31549e6 0.993853 0.496927 0.867793i \(-0.334462\pi\)
0.496927 + 0.867793i \(0.334462\pi\)
\(282\) 0 0
\(283\) 1.17914e6 0.875184 0.437592 0.899174i \(-0.355831\pi\)
0.437592 + 0.899174i \(0.355831\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −437646. −0.313631
\(288\) 0 0
\(289\) 154008. 0.108467
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 847126. 0.576473 0.288236 0.957559i \(-0.406931\pi\)
0.288236 + 0.957559i \(0.406931\pi\)
\(294\) 0 0
\(295\) 1.08728e6 0.727425
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.03318e6 −0.668338
\(300\) 0 0
\(301\) 720432. 0.458329
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.17816e6 0.725198
\(306\) 0 0
\(307\) 2.84575e6 1.72326 0.861630 0.507536i \(-0.169444\pi\)
0.861630 + 0.507536i \(0.169444\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.90808e6 1.11865 0.559327 0.828947i \(-0.311060\pi\)
0.559327 + 0.828947i \(0.311060\pi\)
\(312\) 0 0
\(313\) 699063. 0.403325 0.201663 0.979455i \(-0.435366\pi\)
0.201663 + 0.979455i \(0.435366\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.90613e6 1.06538 0.532689 0.846311i \(-0.321182\pi\)
0.532689 + 0.846311i \(0.321182\pi\)
\(318\) 0 0
\(319\) 851540. 0.468520
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.61090e6 −0.859134
\(324\) 0 0
\(325\) 1.85936e6 0.976461
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −314462. −0.160169
\(330\) 0 0
\(331\) −654655. −0.328430 −0.164215 0.986425i \(-0.552509\pi\)
−0.164215 + 0.986425i \(0.552509\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.06886e6 0.520365
\(336\) 0 0
\(337\) −307622. −0.147551 −0.0737755 0.997275i \(-0.523505\pi\)
−0.0737755 + 0.997275i \(0.523505\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −430417. −0.200449
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.29468e6 −1.91473 −0.957364 0.288883i \(-0.906716\pi\)
−0.957364 + 0.288883i \(0.906716\pi\)
\(348\) 0 0
\(349\) 1.65690e6 0.728169 0.364084 0.931366i \(-0.381382\pi\)
0.364084 + 0.931366i \(0.381382\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.11793e6 −0.477507 −0.238753 0.971080i \(-0.576739\pi\)
−0.238753 + 0.971080i \(0.576739\pi\)
\(354\) 0 0
\(355\) 1.84135e6 0.775469
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.65289e6 −1.08638 −0.543192 0.839608i \(-0.682784\pi\)
−0.543192 + 0.839608i \(0.682784\pi\)
\(360\) 0 0
\(361\) −827302. −0.334115
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −461893. −0.181472
\(366\) 0 0
\(367\) −1.69963e6 −0.658704 −0.329352 0.944207i \(-0.606830\pi\)
−0.329352 + 0.944207i \(0.606830\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.80988e6 0.682677
\(372\) 0 0
\(373\) 1.58779e6 0.590910 0.295455 0.955357i \(-0.404529\pi\)
0.295455 + 0.955357i \(0.404529\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.36374e6 1.21890
\(378\) 0 0
\(379\) −3.10464e6 −1.11023 −0.555115 0.831773i \(-0.687326\pi\)
−0.555115 + 0.831773i \(0.687326\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −5.35117e6 −1.86403 −0.932013 0.362424i \(-0.881949\pi\)
−0.932013 + 0.362424i \(0.881949\pi\)
\(384\) 0 0
\(385\) −480236. −0.165121
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.56930e6 1.19594 0.597969 0.801519i \(-0.295975\pi\)
0.597969 + 0.801519i \(0.295975\pi\)
\(390\) 0 0
\(391\) 1.23298e6 0.407862
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −1.03921e6 −0.335128
\(396\) 0 0
\(397\) 5.21853e6 1.66177 0.830887 0.556442i \(-0.187834\pi\)
0.830887 + 0.556442i \(0.187834\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.02167e6 0.317286 0.158643 0.987336i \(-0.449288\pi\)
0.158643 + 0.987336i \(0.449288\pi\)
\(402\) 0 0
\(403\) −1.70023e6 −0.521488
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −568298. −0.170055
\(408\) 0 0
\(409\) −3.21240e6 −0.949558 −0.474779 0.880105i \(-0.657472\pi\)
−0.474779 + 0.880105i \(0.657472\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.44666e6 0.417340
\(414\) 0 0
\(415\) 4.07207e6 1.16063
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −1.93346e6 −0.538022 −0.269011 0.963137i \(-0.586697\pi\)
−0.269011 + 0.963137i \(0.586697\pi\)
\(420\) 0 0
\(421\) 2.25443e6 0.619915 0.309958 0.950750i \(-0.399685\pi\)
0.309958 + 0.950750i \(0.399685\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2.21893e6 −0.595898
\(426\) 0 0
\(427\) 1.56758e6 0.416063
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2.02676e6 −0.525545 −0.262772 0.964858i \(-0.584637\pi\)
−0.262772 + 0.964858i \(0.584637\pi\)
\(432\) 0 0
\(433\) −1.99286e6 −0.510808 −0.255404 0.966834i \(-0.582208\pi\)
−0.255404 + 0.966834i \(0.582208\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.26199e6 −0.316119
\(438\) 0 0
\(439\) 7.82083e6 1.93683 0.968415 0.249344i \(-0.0802149\pi\)
0.968415 + 0.249344i \(0.0802149\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 1.95595e6 0.473531 0.236766 0.971567i \(-0.423913\pi\)
0.236766 + 0.971567i \(0.423913\pi\)
\(444\) 0 0
\(445\) 2.08395e6 0.498869
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 4.25221e6 0.995403 0.497701 0.867348i \(-0.334178\pi\)
0.497701 + 0.867348i \(0.334178\pi\)
\(450\) 0 0
\(451\) 2.37691e6 0.550263
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −1.89702e6 −0.429580
\(456\) 0 0
\(457\) 8.11945e6 1.81860 0.909298 0.416145i \(-0.136619\pi\)
0.909298 + 0.416145i \(0.136619\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −1.57593e6 −0.345370 −0.172685 0.984977i \(-0.555244\pi\)
−0.172685 + 0.984977i \(0.555244\pi\)
\(462\) 0 0
\(463\) −5.62788e6 −1.22009 −0.610046 0.792366i \(-0.708849\pi\)
−0.610046 + 0.792366i \(0.708849\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.42965e6 0.515526 0.257763 0.966208i \(-0.417015\pi\)
0.257763 + 0.966208i \(0.417015\pi\)
\(468\) 0 0
\(469\) 1.42214e6 0.298545
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −3.91275e6 −0.804135
\(474\) 0 0
\(475\) 2.27114e6 0.461860
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.19799e6 1.03513 0.517567 0.855643i \(-0.326838\pi\)
0.517567 + 0.855643i \(0.326838\pi\)
\(480\) 0 0
\(481\) −2.24489e6 −0.442417
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −4.00564e6 −0.773246
\(486\) 0 0
\(487\) 9.12733e6 1.74390 0.871950 0.489596i \(-0.162856\pi\)
0.871950 + 0.489596i \(0.162856\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −2.36226e6 −0.442205 −0.221103 0.975251i \(-0.570966\pi\)
−0.221103 + 0.975251i \(0.570966\pi\)
\(492\) 0 0
\(493\) −4.01425e6 −0.743852
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.44995e6 0.444905
\(498\) 0 0
\(499\) −2.11297e6 −0.379877 −0.189938 0.981796i \(-0.560829\pi\)
−0.189938 + 0.981796i \(0.560829\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −7.06115e6 −1.24439 −0.622194 0.782863i \(-0.713758\pi\)
−0.622194 + 0.782863i \(0.713758\pi\)
\(504\) 0 0
\(505\) −4.42356e6 −0.771869
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −218657. −0.0374084 −0.0187042 0.999825i \(-0.505954\pi\)
−0.0187042 + 0.999825i \(0.505954\pi\)
\(510\) 0 0
\(511\) −614559. −0.104115
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.20678e6 −0.200498
\(516\) 0 0
\(517\) 1.70788e6 0.281016
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 6.02402e6 0.972282 0.486141 0.873880i \(-0.338404\pi\)
0.486141 + 0.873880i \(0.338404\pi\)
\(522\) 0 0
\(523\) −6.80625e6 −1.08806 −0.544031 0.839065i \(-0.683103\pi\)
−0.544031 + 0.839065i \(0.683103\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.02903e6 0.318245
\(528\) 0 0
\(529\) −5.47042e6 −0.849927
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 9.38923e6 1.43157
\(534\) 0 0
\(535\) −4.18216e6 −0.631708
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −638965. −0.0947338
\(540\) 0 0
\(541\) −1.82151e6 −0.267570 −0.133785 0.991010i \(-0.542713\pi\)
−0.133785 + 0.991010i \(0.542713\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4.20742e6 0.606771
\(546\) 0 0
\(547\) 7.79327e6 1.11366 0.556829 0.830627i \(-0.312018\pi\)
0.556829 + 0.830627i \(0.312018\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.10869e6 0.576534
\(552\) 0 0
\(553\) −1.38269e6 −0.192271
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −5.02092e6 −0.685718 −0.342859 0.939387i \(-0.611395\pi\)
−0.342859 + 0.939387i \(0.611395\pi\)
\(558\) 0 0
\(559\) −1.54561e7 −2.09204
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.04957e7 1.39553 0.697765 0.716326i \(-0.254178\pi\)
0.697765 + 0.716326i \(0.254178\pi\)
\(564\) 0 0
\(565\) −4.20451e6 −0.554108
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.33137e7 −1.72392 −0.861960 0.506977i \(-0.830763\pi\)
−0.861960 + 0.506977i \(0.830763\pi\)
\(570\) 0 0
\(571\) −1.20473e7 −1.54633 −0.773163 0.634207i \(-0.781327\pi\)
−0.773163 + 0.634207i \(0.781327\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.73833e6 −0.219261
\(576\) 0 0
\(577\) −613486. −0.0767123 −0.0383562 0.999264i \(-0.512212\pi\)
−0.0383562 + 0.999264i \(0.512212\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 5.41798e6 0.665882
\(582\) 0 0
\(583\) −9.82966e6 −1.19775
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 9.87842e6 1.18329 0.591647 0.806197i \(-0.298478\pi\)
0.591647 + 0.806197i \(0.298478\pi\)
\(588\) 0 0
\(589\) −2.07677e6 −0.246661
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −7.99130e6 −0.933213 −0.466607 0.884465i \(-0.654524\pi\)
−0.466607 + 0.884465i \(0.654524\pi\)
\(594\) 0 0
\(595\) 2.26388e6 0.262157
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.19067e7 1.35589 0.677946 0.735112i \(-0.262870\pi\)
0.677946 + 0.735112i \(0.262870\pi\)
\(600\) 0 0
\(601\) 927318. 0.104723 0.0523616 0.998628i \(-0.483325\pi\)
0.0523616 + 0.998628i \(0.483325\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.32291e6 −0.369088
\(606\) 0 0
\(607\) 902698. 0.0994422 0.0497211 0.998763i \(-0.484167\pi\)
0.0497211 + 0.998763i \(0.484167\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.74645e6 0.731093
\(612\) 0 0
\(613\) 6.30139e6 0.677307 0.338653 0.940911i \(-0.390029\pi\)
0.338653 + 0.940911i \(0.390029\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.65600e7 −1.75124 −0.875621 0.482999i \(-0.839548\pi\)
−0.875621 + 0.482999i \(0.839548\pi\)
\(618\) 0 0
\(619\) 8.45924e6 0.887370 0.443685 0.896183i \(-0.353671\pi\)
0.443685 + 0.896183i \(0.353671\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.77274e6 0.286213
\(624\) 0 0
\(625\) −1.10996e6 −0.113660
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.67902e6 0.269991
\(630\) 0 0
\(631\) 1.84142e6 0.184111 0.0920556 0.995754i \(-0.470656\pi\)
0.0920556 + 0.995754i \(0.470656\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 5.63651e6 0.554723
\(636\) 0 0
\(637\) −2.52403e6 −0.246460
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 7.24440e6 0.696398 0.348199 0.937421i \(-0.386793\pi\)
0.348199 + 0.937421i \(0.386793\pi\)
\(642\) 0 0
\(643\) −126242. −0.0120413 −0.00602067 0.999982i \(-0.501916\pi\)
−0.00602067 + 0.999982i \(0.501916\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.56292e7 1.46783 0.733916 0.679240i \(-0.237690\pi\)
0.733916 + 0.679240i \(0.237690\pi\)
\(648\) 0 0
\(649\) −7.85695e6 −0.732221
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.07641e6 0.190559 0.0952796 0.995451i \(-0.469625\pi\)
0.0952796 + 0.995451i \(0.469625\pi\)
\(654\) 0 0
\(655\) 1.12851e7 1.02779
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.45723e7 −1.30712 −0.653558 0.756876i \(-0.726724\pi\)
−0.653558 + 0.756876i \(0.726724\pi\)
\(660\) 0 0
\(661\) 6.25230e6 0.556591 0.278295 0.960496i \(-0.410231\pi\)
0.278295 + 0.960496i \(0.410231\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.31715e6 −0.203189
\(666\) 0 0
\(667\) −3.14479e6 −0.273701
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8.51368e6 −0.729980
\(672\) 0 0
\(673\) 6.67890e6 0.568417 0.284208 0.958763i \(-0.408269\pi\)
0.284208 + 0.958763i \(0.408269\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.15867e7 −0.971603 −0.485801 0.874069i \(-0.661472\pi\)
−0.485801 + 0.874069i \(0.661472\pi\)
\(678\) 0 0
\(679\) −5.32960e6 −0.443629
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.75672e7 −1.44095 −0.720476 0.693480i \(-0.756077\pi\)
−0.720476 + 0.693480i \(0.756077\pi\)
\(684\) 0 0
\(685\) −8.75462e6 −0.712871
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −3.88290e7 −3.11608
\(690\) 0 0
\(691\) −1.05537e7 −0.840836 −0.420418 0.907331i \(-0.638116\pi\)
−0.420418 + 0.907331i \(0.638116\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4.75864e6 0.373698
\(696\) 0 0
\(697\) −1.12050e7 −0.873633
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.09325e7 0.840277 0.420139 0.907460i \(-0.361981\pi\)
0.420139 + 0.907460i \(0.361981\pi\)
\(702\) 0 0
\(703\) −2.74205e6 −0.209260
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.88565e6 −0.442839
\(708\) 0 0
\(709\) −6.94267e6 −0.518694 −0.259347 0.965784i \(-0.583507\pi\)
−0.259347 + 0.965784i \(0.583507\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 1.58956e6 0.117099
\(714\) 0 0
\(715\) 1.03029e7 0.753696
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.89029e6 0.208507 0.104253 0.994551i \(-0.466755\pi\)
0.104253 + 0.994551i \(0.466755\pi\)
\(720\) 0 0
\(721\) −1.60565e6 −0.115030
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 5.65954e6 0.399886
\(726\) 0 0
\(727\) −2.13282e7 −1.49664 −0.748320 0.663338i \(-0.769139\pi\)
−0.748320 + 0.663338i \(0.769139\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.84451e7 1.27670
\(732\) 0 0
\(733\) −6.35149e6 −0.436632 −0.218316 0.975878i \(-0.570056\pi\)
−0.218316 + 0.975878i \(0.570056\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −7.72380e6 −0.523796
\(738\) 0 0
\(739\) −2.58265e7 −1.73962 −0.869811 0.493385i \(-0.835759\pi\)
−0.869811 + 0.493385i \(0.835759\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.25879e7 1.50108 0.750538 0.660827i \(-0.229794\pi\)
0.750538 + 0.660827i \(0.229794\pi\)
\(744\) 0 0
\(745\) −1.40118e7 −0.924920
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −5.56446e6 −0.362425
\(750\) 0 0
\(751\) 1.02413e7 0.662609 0.331304 0.943524i \(-0.392511\pi\)
0.331304 + 0.943524i \(0.392511\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.20587e6 0.523911
\(756\) 0 0
\(757\) 2.52903e7 1.60404 0.802020 0.597298i \(-0.203759\pi\)
0.802020 + 0.597298i \(0.203759\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4.30933e6 0.269742 0.134871 0.990863i \(-0.456938\pi\)
0.134871 + 0.990863i \(0.456938\pi\)
\(762\) 0 0
\(763\) 5.59807e6 0.348118
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −3.10364e7 −1.90495
\(768\) 0 0
\(769\) −2.62286e7 −1.59941 −0.799705 0.600393i \(-0.795011\pi\)
−0.799705 + 0.600393i \(0.795011\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.55637e7 −1.53878 −0.769389 0.638781i \(-0.779439\pi\)
−0.769389 + 0.638781i \(0.779439\pi\)
\(774\) 0 0
\(775\) −2.86065e6 −0.171085
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 1.14686e7 0.677122
\(780\) 0 0
\(781\) −1.33060e7 −0.780583
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 2.00238e7 1.15977
\(786\) 0 0
\(787\) −7.39343e6 −0.425509 −0.212755 0.977106i \(-0.568244\pi\)
−0.212755 + 0.977106i \(0.568244\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.59420e6 −0.317905
\(792\) 0 0
\(793\) −3.36306e7 −1.89912
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.36502e7 −0.761193 −0.380597 0.924741i \(-0.624281\pi\)
−0.380597 + 0.924741i \(0.624281\pi\)
\(798\) 0 0
\(799\) −8.05112e6 −0.446159
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 3.33774e6 0.182668
\(804\) 0 0
\(805\) 1.77354e6 0.0964609
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.99385e7 1.07108 0.535538 0.844511i \(-0.320109\pi\)
0.535538 + 0.844511i \(0.320109\pi\)
\(810\) 0 0
\(811\) −3.73268e6 −0.199282 −0.0996410 0.995023i \(-0.531769\pi\)
−0.0996410 + 0.995023i \(0.531769\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.18048e7 0.622535
\(816\) 0 0
\(817\) −1.88791e7 −0.989522
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −7.69515e6 −0.398437 −0.199218 0.979955i \(-0.563840\pi\)
−0.199218 + 0.979955i \(0.563840\pi\)
\(822\) 0 0
\(823\) −1.25144e7 −0.644038 −0.322019 0.946733i \(-0.604361\pi\)
−0.322019 + 0.946733i \(0.604361\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.01622e7 −1.02512 −0.512560 0.858651i \(-0.671303\pi\)
−0.512560 + 0.858651i \(0.671303\pi\)
\(828\) 0 0
\(829\) 2.25413e7 1.13918 0.569591 0.821929i \(-0.307102\pi\)
0.569591 + 0.821929i \(0.307102\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.01214e6 0.150405
\(834\) 0 0
\(835\) −8.43338e6 −0.418587
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 1.03142e7 0.505862 0.252931 0.967484i \(-0.418605\pi\)
0.252931 + 0.967484i \(0.418605\pi\)
\(840\) 0 0
\(841\) −1.02726e7 −0.500828
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 2.70247e7 1.30203
\(846\) 0 0
\(847\) −4.42121e6 −0.211755
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 2.09876e6 0.0993434
\(852\) 0 0
\(853\) −1.61040e7 −0.757812 −0.378906 0.925435i \(-0.623700\pi\)
−0.378906 + 0.925435i \(0.623700\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −4.81242e6 −0.223827 −0.111913 0.993718i \(-0.535698\pi\)
−0.111913 + 0.993718i \(0.535698\pi\)
\(858\) 0 0
\(859\) −1.04274e7 −0.482160 −0.241080 0.970505i \(-0.577502\pi\)
−0.241080 + 0.970505i \(0.577502\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −4.31905e6 −0.197407 −0.0987033 0.995117i \(-0.531469\pi\)
−0.0987033 + 0.995117i \(0.531469\pi\)
\(864\) 0 0
\(865\) −1.25638e7 −0.570929
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 7.50956e6 0.337338
\(870\) 0 0
\(871\) −3.05105e7 −1.36271
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −8.83099e6 −0.389932
\(876\) 0 0
\(877\) 4.47176e7 1.96327 0.981633 0.190778i \(-0.0611010\pi\)
0.981633 + 0.190778i \(0.0611010\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.93106e7 1.27229 0.636144 0.771570i \(-0.280528\pi\)
0.636144 + 0.771570i \(0.280528\pi\)
\(882\) 0 0
\(883\) 9.91162e6 0.427802 0.213901 0.976855i \(-0.431383\pi\)
0.213901 + 0.976855i \(0.431383\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 1.22959e7 0.524750 0.262375 0.964966i \(-0.415494\pi\)
0.262375 + 0.964966i \(0.415494\pi\)
\(888\) 0 0
\(889\) 7.49951e6 0.318257
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 8.24055e6 0.345802
\(894\) 0 0
\(895\) 1.85707e7 0.774946
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −5.17517e6 −0.213563
\(900\) 0 0
\(901\) 4.63380e7 1.90163
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.12063e7 −0.454820
\(906\) 0 0
\(907\) −1.43614e7 −0.579666 −0.289833 0.957077i \(-0.593600\pi\)
−0.289833 + 0.957077i \(0.593600\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −3.87113e7 −1.54540 −0.772702 0.634769i \(-0.781095\pi\)
−0.772702 + 0.634769i \(0.781095\pi\)
\(912\) 0 0
\(913\) −2.94257e7 −1.16829
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.50151e7 0.589665
\(918\) 0 0
\(919\) 937251. 0.0366072 0.0183036 0.999832i \(-0.494173\pi\)
0.0183036 + 0.999832i \(0.494173\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −5.25611e7 −2.03077
\(924\) 0 0
\(925\) −3.77705e6 −0.145144
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −2.97659e7 −1.13157 −0.565783 0.824554i \(-0.691426\pi\)
−0.565783 + 0.824554i \(0.691426\pi\)
\(930\) 0 0
\(931\) −3.08302e6 −0.116574
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −1.22954e7 −0.459953
\(936\) 0 0
\(937\) −2.53013e7 −0.941443 −0.470722 0.882282i \(-0.656006\pi\)
−0.470722 + 0.882282i \(0.656006\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −5.32597e7 −1.96076 −0.980380 0.197117i \(-0.936842\pi\)
−0.980380 + 0.197117i \(0.936842\pi\)
\(942\) 0 0
\(943\) −8.77806e6 −0.321454
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 4.84017e7 1.75382 0.876912 0.480651i \(-0.159600\pi\)
0.876912 + 0.480651i \(0.159600\pi\)
\(948\) 0 0
\(949\) 1.31847e7 0.475231
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 4.83953e7 1.72612 0.863060 0.505101i \(-0.168545\pi\)
0.863060 + 0.505101i \(0.168545\pi\)
\(954\) 0 0
\(955\) 1.23574e7 0.438450
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −1.16482e7 −0.408991
\(960\) 0 0
\(961\) −2.60133e7 −0.908631
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 2.07353e7 0.716789
\(966\) 0 0
\(967\) −5.79009e6 −0.199122 −0.0995610 0.995031i \(-0.531744\pi\)
−0.0995610 + 0.995031i \(0.531744\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −8.97051e6 −0.305330 −0.152665 0.988278i \(-0.548786\pi\)
−0.152665 + 0.988278i \(0.548786\pi\)
\(972\) 0 0
\(973\) 6.33147e6 0.214399
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 4.01117e7 1.34442 0.672210 0.740361i \(-0.265345\pi\)
0.672210 + 0.740361i \(0.265345\pi\)
\(978\) 0 0
\(979\) −1.50591e7 −0.502159
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 9.55325e6 0.315332 0.157666 0.987493i \(-0.449603\pi\)
0.157666 + 0.987493i \(0.449603\pi\)
\(984\) 0 0
\(985\) 5.50197e6 0.180687
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.44500e7 0.469762
\(990\) 0 0
\(991\) 4.58578e7 1.48330 0.741650 0.670787i \(-0.234044\pi\)
0.741650 + 0.670787i \(0.234044\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 4.92229e6 0.157619
\(996\) 0 0
\(997\) −6.10854e6 −0.194626 −0.0973128 0.995254i \(-0.531025\pi\)
−0.0973128 + 0.995254i \(0.531025\pi\)
\(998\) 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.1.2 2
3.2 odd 2 1008.6.a.bs.1.1 2
4.3 odd 2 504.6.a.l.1.2 2
12.11 even 2 504.6.a.r.1.1 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.6.a.l.1.2 2 4.3 odd 2
504.6.a.r.1.1 yes 2 12.11 even 2
1008.6.a.bh.1.2 2 1.1 even 1 trivial
1008.6.a.bs.1.1 2 3.2 odd 2