Properties

Label 1008.6.a.a.1.1
Level $1008$
Weight $6$
Character 1008.1
Self dual yes
Analytic conductor $161.667$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,6,Mod(1,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1008.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(161.666890371\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 1008.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-94.0000 q^{5} +49.0000 q^{7} +O(q^{10})\) \(q-94.0000 q^{5} +49.0000 q^{7} +52.0000 q^{11} -770.000 q^{13} +2022.00 q^{17} -1732.00 q^{19} -576.000 q^{23} +5711.00 q^{25} -5518.00 q^{29} -6336.00 q^{31} -4606.00 q^{35} -7338.00 q^{37} +3262.00 q^{41} -5420.00 q^{43} +864.000 q^{47} +2401.00 q^{49} -4182.00 q^{53} -4888.00 q^{55} -11220.0 q^{59} -45602.0 q^{61} +72380.0 q^{65} -1396.00 q^{67} +18720.0 q^{71} +46362.0 q^{73} +2548.00 q^{77} -97424.0 q^{79} -81228.0 q^{83} -190068. q^{85} +3182.00 q^{89} -37730.0 q^{91} +162808. q^{95} +4914.00 q^{97} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −94.0000 −1.68152 −0.840762 0.541406i \(-0.817892\pi\)
−0.840762 + 0.541406i \(0.817892\pi\)
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 52.0000 0.129575 0.0647876 0.997899i \(-0.479363\pi\)
0.0647876 + 0.997899i \(0.479363\pi\)
\(12\) 0 0
\(13\) −770.000 −1.26367 −0.631833 0.775104i \(-0.717697\pi\)
−0.631833 + 0.775104i \(0.717697\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2022.00 1.69691 0.848455 0.529267i \(-0.177533\pi\)
0.848455 + 0.529267i \(0.177533\pi\)
\(18\) 0 0
\(19\) −1732.00 −1.10069 −0.550344 0.834938i \(-0.685503\pi\)
−0.550344 + 0.834938i \(0.685503\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −576.000 −0.227040 −0.113520 0.993536i \(-0.536213\pi\)
−0.113520 + 0.993536i \(0.536213\pi\)
\(24\) 0 0
\(25\) 5711.00 1.82752
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5518.00 −1.21839 −0.609196 0.793020i \(-0.708508\pi\)
−0.609196 + 0.793020i \(0.708508\pi\)
\(30\) 0 0
\(31\) −6336.00 −1.18416 −0.592081 0.805879i \(-0.701693\pi\)
−0.592081 + 0.805879i \(0.701693\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4606.00 −0.635556
\(36\) 0 0
\(37\) −7338.00 −0.881198 −0.440599 0.897704i \(-0.645234\pi\)
−0.440599 + 0.897704i \(0.645234\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3262.00 0.303057 0.151528 0.988453i \(-0.451580\pi\)
0.151528 + 0.988453i \(0.451580\pi\)
\(42\) 0 0
\(43\) −5420.00 −0.447021 −0.223511 0.974701i \(-0.571752\pi\)
−0.223511 + 0.974701i \(0.571752\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 864.000 0.0570518 0.0285259 0.999593i \(-0.490919\pi\)
0.0285259 + 0.999593i \(0.490919\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4182.00 −0.204500 −0.102250 0.994759i \(-0.532604\pi\)
−0.102250 + 0.994759i \(0.532604\pi\)
\(54\) 0 0
\(55\) −4888.00 −0.217884
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −11220.0 −0.419626 −0.209813 0.977741i \(-0.567286\pi\)
−0.209813 + 0.977741i \(0.567286\pi\)
\(60\) 0 0
\(61\) −45602.0 −1.56913 −0.784566 0.620046i \(-0.787114\pi\)
−0.784566 + 0.620046i \(0.787114\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 72380.0 2.12488
\(66\) 0 0
\(67\) −1396.00 −0.0379925 −0.0189963 0.999820i \(-0.506047\pi\)
−0.0189963 + 0.999820i \(0.506047\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 18720.0 0.440717 0.220359 0.975419i \(-0.429277\pi\)
0.220359 + 0.975419i \(0.429277\pi\)
\(72\) 0 0
\(73\) 46362.0 1.01825 0.509126 0.860692i \(-0.329969\pi\)
0.509126 + 0.860692i \(0.329969\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2548.00 0.0489748
\(78\) 0 0
\(79\) −97424.0 −1.75630 −0.878149 0.478387i \(-0.841222\pi\)
−0.878149 + 0.478387i \(0.841222\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −81228.0 −1.29423 −0.647114 0.762394i \(-0.724024\pi\)
−0.647114 + 0.762394i \(0.724024\pi\)
\(84\) 0 0
\(85\) −190068. −2.85339
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 3182.00 0.0425819 0.0212910 0.999773i \(-0.493222\pi\)
0.0212910 + 0.999773i \(0.493222\pi\)
\(90\) 0 0
\(91\) −37730.0 −0.477621
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 162808. 1.85083
\(96\) 0 0
\(97\) 4914.00 0.0530281 0.0265140 0.999648i \(-0.491559\pi\)
0.0265140 + 0.999648i \(0.491559\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 166354. 1.62267 0.811334 0.584583i \(-0.198742\pi\)
0.811334 + 0.584583i \(0.198742\pi\)
\(102\) 0 0
\(103\) −157160. −1.45965 −0.729825 0.683634i \(-0.760399\pi\)
−0.729825 + 0.683634i \(0.760399\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −6764.00 −0.0571142 −0.0285571 0.999592i \(-0.509091\pi\)
−0.0285571 + 0.999592i \(0.509091\pi\)
\(108\) 0 0
\(109\) 178398. 1.43821 0.719107 0.694899i \(-0.244551\pi\)
0.719107 + 0.694899i \(0.244551\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 45134.0 0.332512 0.166256 0.986083i \(-0.446832\pi\)
0.166256 + 0.986083i \(0.446832\pi\)
\(114\) 0 0
\(115\) 54144.0 0.381773
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 99078.0 0.641372
\(120\) 0 0
\(121\) −158347. −0.983210
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −243084. −1.39149
\(126\) 0 0
\(127\) 205056. 1.12814 0.564070 0.825727i \(-0.309235\pi\)
0.564070 + 0.825727i \(0.309235\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 72964.0 0.371476 0.185738 0.982599i \(-0.440532\pi\)
0.185738 + 0.982599i \(0.440532\pi\)
\(132\) 0 0
\(133\) −84868.0 −0.416021
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 94182.0 0.428713 0.214356 0.976756i \(-0.431235\pi\)
0.214356 + 0.976756i \(0.431235\pi\)
\(138\) 0 0
\(139\) 47796.0 0.209824 0.104912 0.994482i \(-0.466544\pi\)
0.104912 + 0.994482i \(0.466544\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −40040.0 −0.163740
\(144\) 0 0
\(145\) 518692. 2.04875
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 124266. 0.458550 0.229275 0.973362i \(-0.426364\pi\)
0.229275 + 0.973362i \(0.426364\pi\)
\(150\) 0 0
\(151\) 446296. 1.59287 0.796436 0.604723i \(-0.206716\pi\)
0.796436 + 0.604723i \(0.206716\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 595584. 1.99119
\(156\) 0 0
\(157\) −159746. −0.517227 −0.258613 0.965981i \(-0.583266\pi\)
−0.258613 + 0.965981i \(0.583266\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −28224.0 −0.0858132
\(162\) 0 0
\(163\) −247252. −0.728905 −0.364452 0.931222i \(-0.618744\pi\)
−0.364452 + 0.931222i \(0.618744\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −684488. −1.89922 −0.949609 0.313438i \(-0.898519\pi\)
−0.949609 + 0.313438i \(0.898519\pi\)
\(168\) 0 0
\(169\) 221607. 0.596852
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 610474. 1.55079 0.775393 0.631479i \(-0.217552\pi\)
0.775393 + 0.631479i \(0.217552\pi\)
\(174\) 0 0
\(175\) 279839. 0.690738
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 662252. 1.54487 0.772433 0.635097i \(-0.219040\pi\)
0.772433 + 0.635097i \(0.219040\pi\)
\(180\) 0 0
\(181\) 154630. 0.350830 0.175415 0.984495i \(-0.443873\pi\)
0.175415 + 0.984495i \(0.443873\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 689772. 1.48175
\(186\) 0 0
\(187\) 105144. 0.219877
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 486904. 0.965739 0.482870 0.875692i \(-0.339594\pi\)
0.482870 + 0.875692i \(0.339594\pi\)
\(192\) 0 0
\(193\) 620546. 1.19917 0.599585 0.800311i \(-0.295332\pi\)
0.599585 + 0.800311i \(0.295332\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 236570. 0.434304 0.217152 0.976138i \(-0.430323\pi\)
0.217152 + 0.976138i \(0.430323\pi\)
\(198\) 0 0
\(199\) −82104.0 −0.146971 −0.0734855 0.997296i \(-0.523412\pi\)
−0.0734855 + 0.997296i \(0.523412\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −270382. −0.460509
\(204\) 0 0
\(205\) −306628. −0.509597
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −90064.0 −0.142622
\(210\) 0 0
\(211\) −99892.0 −0.154463 −0.0772315 0.997013i \(-0.524608\pi\)
−0.0772315 + 0.997013i \(0.524608\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 509480. 0.751677
\(216\) 0 0
\(217\) −310464. −0.447571
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −1.55694e6 −2.14433
\(222\) 0 0
\(223\) 186704. 0.251415 0.125708 0.992067i \(-0.459880\pi\)
0.125708 + 0.992067i \(0.459880\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 336372. 0.433267 0.216633 0.976253i \(-0.430492\pi\)
0.216633 + 0.976253i \(0.430492\pi\)
\(228\) 0 0
\(229\) −926314. −1.16727 −0.583633 0.812018i \(-0.698369\pi\)
−0.583633 + 0.812018i \(0.698369\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.25711e6 −1.51700 −0.758499 0.651675i \(-0.774067\pi\)
−0.758499 + 0.651675i \(0.774067\pi\)
\(234\) 0 0
\(235\) −81216.0 −0.0959339
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −347016. −0.392966 −0.196483 0.980507i \(-0.562952\pi\)
−0.196483 + 0.980507i \(0.562952\pi\)
\(240\) 0 0
\(241\) 99170.0 0.109986 0.0549930 0.998487i \(-0.482486\pi\)
0.0549930 + 0.998487i \(0.482486\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −225694. −0.240218
\(246\) 0 0
\(247\) 1.33364e6 1.39090
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 344428. 0.345076 0.172538 0.985003i \(-0.444803\pi\)
0.172538 + 0.985003i \(0.444803\pi\)
\(252\) 0 0
\(253\) −29952.0 −0.0294188
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −295130. −0.278728 −0.139364 0.990241i \(-0.544506\pi\)
−0.139364 + 0.990241i \(0.544506\pi\)
\(258\) 0 0
\(259\) −359562. −0.333061
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −1.27246e6 −1.13437 −0.567187 0.823589i \(-0.691968\pi\)
−0.567187 + 0.823589i \(0.691968\pi\)
\(264\) 0 0
\(265\) 393108. 0.343872
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −276774. −0.233209 −0.116604 0.993178i \(-0.537201\pi\)
−0.116604 + 0.993178i \(0.537201\pi\)
\(270\) 0 0
\(271\) 1.28994e6 1.06695 0.533476 0.845815i \(-0.320885\pi\)
0.533476 + 0.845815i \(0.320885\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 296972. 0.236801
\(276\) 0 0
\(277\) 1.71655e6 1.34418 0.672089 0.740470i \(-0.265397\pi\)
0.672089 + 0.740470i \(0.265397\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.47218e6 1.11223 0.556116 0.831104i \(-0.312291\pi\)
0.556116 + 0.831104i \(0.312291\pi\)
\(282\) 0 0
\(283\) −1.02881e6 −0.763607 −0.381804 0.924244i \(-0.624697\pi\)
−0.381804 + 0.924244i \(0.624697\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 159838. 0.114545
\(288\) 0 0
\(289\) 2.66863e6 1.87950
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.18607e6 0.807123 0.403562 0.914952i \(-0.367772\pi\)
0.403562 + 0.914952i \(0.367772\pi\)
\(294\) 0 0
\(295\) 1.05468e6 0.705612
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 443520. 0.286903
\(300\) 0 0
\(301\) −265580. −0.168958
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.28659e6 2.63853
\(306\) 0 0
\(307\) −1.51892e6 −0.919788 −0.459894 0.887974i \(-0.652113\pi\)
−0.459894 + 0.887974i \(0.652113\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 212808. 0.124763 0.0623817 0.998052i \(-0.480130\pi\)
0.0623817 + 0.998052i \(0.480130\pi\)
\(312\) 0 0
\(313\) −1894.00 −0.00109275 −0.000546373 1.00000i \(-0.500174\pi\)
−0.000546373 1.00000i \(0.500174\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.57898e6 0.882527 0.441263 0.897378i \(-0.354530\pi\)
0.441263 + 0.897378i \(0.354530\pi\)
\(318\) 0 0
\(319\) −286936. −0.157873
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.50210e6 −1.86777
\(324\) 0 0
\(325\) −4.39747e6 −2.30938
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 42336.0 0.0215635
\(330\) 0 0
\(331\) 3.39471e6 1.70307 0.851535 0.524298i \(-0.175672\pi\)
0.851535 + 0.524298i \(0.175672\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 131224. 0.0638853
\(336\) 0 0
\(337\) 2.02731e6 0.972403 0.486201 0.873847i \(-0.338382\pi\)
0.486201 + 0.873847i \(0.338382\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −329472. −0.153438
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.48885e6 1.55546 0.777730 0.628598i \(-0.216371\pi\)
0.777730 + 0.628598i \(0.216371\pi\)
\(348\) 0 0
\(349\) 965566. 0.424344 0.212172 0.977232i \(-0.431946\pi\)
0.212172 + 0.977232i \(0.431946\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.15393e6 −0.492882 −0.246441 0.969158i \(-0.579261\pi\)
−0.246441 + 0.969158i \(0.579261\pi\)
\(354\) 0 0
\(355\) −1.75968e6 −0.741076
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 1.61110e6 0.659762 0.329881 0.944022i \(-0.392991\pi\)
0.329881 + 0.944022i \(0.392991\pi\)
\(360\) 0 0
\(361\) 523725. 0.211512
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −4.35803e6 −1.71221
\(366\) 0 0
\(367\) −3.67747e6 −1.42523 −0.712614 0.701557i \(-0.752489\pi\)
−0.712614 + 0.701557i \(0.752489\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −204918. −0.0772939
\(372\) 0 0
\(373\) 649766. 0.241816 0.120908 0.992664i \(-0.461419\pi\)
0.120908 + 0.992664i \(0.461419\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.24886e6 1.53964
\(378\) 0 0
\(379\) −320700. −0.114683 −0.0573417 0.998355i \(-0.518262\pi\)
−0.0573417 + 0.998355i \(0.518262\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.36189e6 −0.822740 −0.411370 0.911469i \(-0.634950\pi\)
−0.411370 + 0.911469i \(0.634950\pi\)
\(384\) 0 0
\(385\) −239512. −0.0823522
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3.53390e6 1.18408 0.592039 0.805910i \(-0.298323\pi\)
0.592039 + 0.805910i \(0.298323\pi\)
\(390\) 0 0
\(391\) −1.16467e6 −0.385267
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 9.15786e6 2.95326
\(396\) 0 0
\(397\) 4.04811e6 1.28907 0.644534 0.764575i \(-0.277051\pi\)
0.644534 + 0.764575i \(0.277051\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2.07645e6 −0.644853 −0.322426 0.946595i \(-0.604498\pi\)
−0.322426 + 0.946595i \(0.604498\pi\)
\(402\) 0 0
\(403\) 4.87872e6 1.49638
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −381576. −0.114181
\(408\) 0 0
\(409\) 2.57431e6 0.760945 0.380472 0.924792i \(-0.375761\pi\)
0.380472 + 0.924792i \(0.375761\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −549780. −0.158604
\(414\) 0 0
\(415\) 7.63543e6 2.17627
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 848148. 0.236013 0.118007 0.993013i \(-0.462350\pi\)
0.118007 + 0.993013i \(0.462350\pi\)
\(420\) 0 0
\(421\) 1.43682e6 0.395092 0.197546 0.980294i \(-0.436703\pi\)
0.197546 + 0.980294i \(0.436703\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.15476e7 3.10114
\(426\) 0 0
\(427\) −2.23450e6 −0.593076
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.35438e6 0.610496 0.305248 0.952273i \(-0.401261\pi\)
0.305248 + 0.952273i \(0.401261\pi\)
\(432\) 0 0
\(433\) −3.78808e6 −0.970955 −0.485478 0.874249i \(-0.661354\pi\)
−0.485478 + 0.874249i \(0.661354\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 997632. 0.249900
\(438\) 0 0
\(439\) 3.64322e6 0.902245 0.451123 0.892462i \(-0.351024\pi\)
0.451123 + 0.892462i \(0.351024\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.48389e6 0.601345 0.300672 0.953728i \(-0.402789\pi\)
0.300672 + 0.953728i \(0.402789\pi\)
\(444\) 0 0
\(445\) −299108. −0.0716025
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.63177e6 0.616074 0.308037 0.951374i \(-0.400328\pi\)
0.308037 + 0.951374i \(0.400328\pi\)
\(450\) 0 0
\(451\) 169624. 0.0392686
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.54662e6 0.803131
\(456\) 0 0
\(457\) −1.16130e6 −0.260109 −0.130054 0.991507i \(-0.541515\pi\)
−0.130054 + 0.991507i \(0.541515\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −2.81385e6 −0.616663 −0.308332 0.951279i \(-0.599771\pi\)
−0.308332 + 0.951279i \(0.599771\pi\)
\(462\) 0 0
\(463\) −6.84299e6 −1.48352 −0.741760 0.670665i \(-0.766009\pi\)
−0.741760 + 0.670665i \(0.766009\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.34314e6 0.709353 0.354676 0.934989i \(-0.384591\pi\)
0.354676 + 0.934989i \(0.384591\pi\)
\(468\) 0 0
\(469\) −68404.0 −0.0143598
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −281840. −0.0579228
\(474\) 0 0
\(475\) −9.89145e6 −2.01153
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −4.28248e6 −0.852818 −0.426409 0.904530i \(-0.640222\pi\)
−0.426409 + 0.904530i \(0.640222\pi\)
\(480\) 0 0
\(481\) 5.65026e6 1.11354
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −461916. −0.0891679
\(486\) 0 0
\(487\) 8.93175e6 1.70653 0.853266 0.521477i \(-0.174619\pi\)
0.853266 + 0.521477i \(0.174619\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.75306e6 0.515361 0.257681 0.966230i \(-0.417042\pi\)
0.257681 + 0.966230i \(0.417042\pi\)
\(492\) 0 0
\(493\) −1.11574e7 −2.06750
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 917280. 0.166575
\(498\) 0 0
\(499\) −4.80408e6 −0.863693 −0.431846 0.901947i \(-0.642138\pi\)
−0.431846 + 0.901947i \(0.642138\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −6.02465e6 −1.06172 −0.530862 0.847458i \(-0.678132\pi\)
−0.530862 + 0.847458i \(0.678132\pi\)
\(504\) 0 0
\(505\) −1.56373e7 −2.72855
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 8.42987e6 1.44220 0.721101 0.692830i \(-0.243636\pi\)
0.721101 + 0.692830i \(0.243636\pi\)
\(510\) 0 0
\(511\) 2.27174e6 0.384863
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 1.47730e7 2.45444
\(516\) 0 0
\(517\) 44928.0 0.00739249
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −9.25058e6 −1.49305 −0.746525 0.665357i \(-0.768279\pi\)
−0.746525 + 0.665357i \(0.768279\pi\)
\(522\) 0 0
\(523\) −5.84494e6 −0.934385 −0.467192 0.884156i \(-0.654734\pi\)
−0.467192 + 0.884156i \(0.654734\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.28114e7 −2.00942
\(528\) 0 0
\(529\) −6.10457e6 −0.948453
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.51174e6 −0.382963
\(534\) 0 0
\(535\) 635816. 0.0960389
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 124852. 0.0185107
\(540\) 0 0
\(541\) 9.22533e6 1.35515 0.677577 0.735452i \(-0.263030\pi\)
0.677577 + 0.735452i \(0.263030\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.67694e7 −2.41839
\(546\) 0 0
\(547\) 6.44337e6 0.920757 0.460378 0.887723i \(-0.347714\pi\)
0.460378 + 0.887723i \(0.347714\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 9.55718e6 1.34107
\(552\) 0 0
\(553\) −4.77378e6 −0.663818
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −3.74213e6 −0.511070 −0.255535 0.966800i \(-0.582252\pi\)
−0.255535 + 0.966800i \(0.582252\pi\)
\(558\) 0 0
\(559\) 4.17340e6 0.564886
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.46384e7 −1.94635 −0.973176 0.230060i \(-0.926108\pi\)
−0.973176 + 0.230060i \(0.926108\pi\)
\(564\) 0 0
\(565\) −4.24260e6 −0.559127
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −1.41805e7 −1.83616 −0.918078 0.396400i \(-0.870259\pi\)
−0.918078 + 0.396400i \(0.870259\pi\)
\(570\) 0 0
\(571\) 1.25160e6 0.160648 0.0803242 0.996769i \(-0.474404\pi\)
0.0803242 + 0.996769i \(0.474404\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −3.28954e6 −0.414921
\(576\) 0 0
\(577\) 5.94378e6 0.743230 0.371615 0.928387i \(-0.378804\pi\)
0.371615 + 0.928387i \(0.378804\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −3.98017e6 −0.489172
\(582\) 0 0
\(583\) −217464. −0.0264982
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.46192e6 −0.774046 −0.387023 0.922070i \(-0.626497\pi\)
−0.387023 + 0.922070i \(0.626497\pi\)
\(588\) 0 0
\(589\) 1.09740e7 1.30339
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 2.34605e6 0.273969 0.136984 0.990573i \(-0.456259\pi\)
0.136984 + 0.990573i \(0.456259\pi\)
\(594\) 0 0
\(595\) −9.31333e6 −1.07848
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.34959e7 −1.53686 −0.768432 0.639931i \(-0.778963\pi\)
−0.768432 + 0.639931i \(0.778963\pi\)
\(600\) 0 0
\(601\) 3.87849e6 0.438002 0.219001 0.975725i \(-0.429720\pi\)
0.219001 + 0.975725i \(0.429720\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.48846e7 1.65329
\(606\) 0 0
\(607\) 533488. 0.0587696 0.0293848 0.999568i \(-0.490645\pi\)
0.0293848 + 0.999568i \(0.490645\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −665280. −0.0720944
\(612\) 0 0
\(613\) 5.14610e6 0.553130 0.276565 0.960995i \(-0.410804\pi\)
0.276565 + 0.960995i \(0.410804\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.37860e6 0.251541 0.125770 0.992059i \(-0.459860\pi\)
0.125770 + 0.992059i \(0.459860\pi\)
\(618\) 0 0
\(619\) −1.60023e7 −1.67863 −0.839317 0.543642i \(-0.817045\pi\)
−0.839317 + 0.543642i \(0.817045\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 155918. 0.0160944
\(624\) 0 0
\(625\) 5.00302e6 0.512309
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −1.48374e7 −1.49531
\(630\) 0 0
\(631\) −1.23459e7 −1.23439 −0.617193 0.786812i \(-0.711730\pi\)
−0.617193 + 0.786812i \(0.711730\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.92753e7 −1.89699
\(636\) 0 0
\(637\) −1.84877e6 −0.180524
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 3.43755e6 0.330449 0.165224 0.986256i \(-0.447165\pi\)
0.165224 + 0.986256i \(0.447165\pi\)
\(642\) 0 0
\(643\) 1.62191e7 1.54703 0.773515 0.633778i \(-0.218497\pi\)
0.773515 + 0.633778i \(0.218497\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.19929e7 1.12632 0.563160 0.826348i \(-0.309585\pi\)
0.563160 + 0.826348i \(0.309585\pi\)
\(648\) 0 0
\(649\) −583440. −0.0543731
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.58009e6 −0.145011 −0.0725053 0.997368i \(-0.523099\pi\)
−0.0725053 + 0.997368i \(0.523099\pi\)
\(654\) 0 0
\(655\) −6.85862e6 −0.624645
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.98358e6 0.626419 0.313209 0.949684i \(-0.398596\pi\)
0.313209 + 0.949684i \(0.398596\pi\)
\(660\) 0 0
\(661\) 3.69602e6 0.329027 0.164513 0.986375i \(-0.447395\pi\)
0.164513 + 0.986375i \(0.447395\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7.97759e6 0.699548
\(666\) 0 0
\(667\) 3.17837e6 0.276624
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2.37130e6 −0.203320
\(672\) 0 0
\(673\) 1.84688e6 0.157182 0.0785908 0.996907i \(-0.474958\pi\)
0.0785908 + 0.996907i \(0.474958\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7.68501e6 0.644426 0.322213 0.946667i \(-0.395573\pi\)
0.322213 + 0.946667i \(0.395573\pi\)
\(678\) 0 0
\(679\) 240786. 0.0200427
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 7.12180e6 0.584168 0.292084 0.956393i \(-0.405651\pi\)
0.292084 + 0.956393i \(0.405651\pi\)
\(684\) 0 0
\(685\) −8.85311e6 −0.720891
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.22014e6 0.258420
\(690\) 0 0
\(691\) 3.23787e6 0.257967 0.128983 0.991647i \(-0.458829\pi\)
0.128983 + 0.991647i \(0.458829\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.49282e6 −0.352823
\(696\) 0 0
\(697\) 6.59576e6 0.514260
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 7.39163e6 0.568127 0.284063 0.958805i \(-0.408317\pi\)
0.284063 + 0.958805i \(0.408317\pi\)
\(702\) 0 0
\(703\) 1.27094e7 0.969923
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.15135e6 0.613311
\(708\) 0 0
\(709\) −5.33361e6 −0.398479 −0.199240 0.979951i \(-0.563847\pi\)
−0.199240 + 0.979951i \(0.563847\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.64954e6 0.268852
\(714\) 0 0
\(715\) 3.76376e6 0.275332
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.14564e7 −0.826468 −0.413234 0.910625i \(-0.635601\pi\)
−0.413234 + 0.910625i \(0.635601\pi\)
\(720\) 0 0
\(721\) −7.70084e6 −0.551696
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3.15133e7 −2.22663
\(726\) 0 0
\(727\) 2.49540e7 1.75107 0.875536 0.483153i \(-0.160508\pi\)
0.875536 + 0.483153i \(0.160508\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.09592e7 −0.758555
\(732\) 0 0
\(733\) −1.43398e7 −0.985789 −0.492894 0.870089i \(-0.664061\pi\)
−0.492894 + 0.870089i \(0.664061\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −72592.0 −0.00492289
\(738\) 0 0
\(739\) −922932. −0.0621668 −0.0310834 0.999517i \(-0.509896\pi\)
−0.0310834 + 0.999517i \(0.509896\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9.38995e6 −0.624010 −0.312005 0.950081i \(-0.601001\pi\)
−0.312005 + 0.950081i \(0.601001\pi\)
\(744\) 0 0
\(745\) −1.16810e7 −0.771062
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −331436. −0.0215871
\(750\) 0 0
\(751\) 408032. 0.0263994 0.0131997 0.999913i \(-0.495798\pi\)
0.0131997 + 0.999913i \(0.495798\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4.19518e7 −2.67845
\(756\) 0 0
\(757\) 2.59605e7 1.64654 0.823271 0.567649i \(-0.192147\pi\)
0.823271 + 0.567649i \(0.192147\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −1.83554e7 −1.14895 −0.574477 0.818521i \(-0.694794\pi\)
−0.574477 + 0.818521i \(0.694794\pi\)
\(762\) 0 0
\(763\) 8.74150e6 0.543594
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.63940e6 0.530268
\(768\) 0 0
\(769\) −747166. −0.0455618 −0.0227809 0.999740i \(-0.507252\pi\)
−0.0227809 + 0.999740i \(0.507252\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.02692e7 −1.22008 −0.610038 0.792372i \(-0.708846\pi\)
−0.610038 + 0.792372i \(0.708846\pi\)
\(774\) 0 0
\(775\) −3.61849e7 −2.16408
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.64978e6 −0.333571
\(780\) 0 0
\(781\) 973440. 0.0571060
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 1.50161e7 0.869729
\(786\) 0 0
\(787\) 4.69982e6 0.270486 0.135243 0.990812i \(-0.456819\pi\)
0.135243 + 0.990812i \(0.456819\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.21157e6 0.125678
\(792\) 0 0
\(793\) 3.51135e7 1.98286
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −584710. −0.0326058 −0.0163029 0.999867i \(-0.505190\pi\)
−0.0163029 + 0.999867i \(0.505190\pi\)
\(798\) 0 0
\(799\) 1.74701e6 0.0968117
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 2.41082e6 0.131940
\(804\) 0 0
\(805\) 2.65306e6 0.144297
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.64013e7 0.881061 0.440531 0.897738i \(-0.354790\pi\)
0.440531 + 0.897738i \(0.354790\pi\)
\(810\) 0 0
\(811\) 304948. 0.0162807 0.00814036 0.999967i \(-0.497409\pi\)
0.00814036 + 0.999967i \(0.497409\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 2.32417e7 1.22567
\(816\) 0 0
\(817\) 9.38744e6 0.492031
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −3.43428e7 −1.77819 −0.889095 0.457722i \(-0.848665\pi\)
−0.889095 + 0.457722i \(0.848665\pi\)
\(822\) 0 0
\(823\) −1.56684e7 −0.806351 −0.403176 0.915123i \(-0.632094\pi\)
−0.403176 + 0.915123i \(0.632094\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −2.96886e7 −1.50948 −0.754738 0.656026i \(-0.772236\pi\)
−0.754738 + 0.656026i \(0.772236\pi\)
\(828\) 0 0
\(829\) −2.30708e7 −1.16594 −0.582970 0.812494i \(-0.698110\pi\)
−0.582970 + 0.812494i \(0.698110\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 4.85482e6 0.242416
\(834\) 0 0
\(835\) 6.43419e7 3.19358
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 2.32642e7 1.14100 0.570498 0.821299i \(-0.306750\pi\)
0.570498 + 0.821299i \(0.306750\pi\)
\(840\) 0 0
\(841\) 9.93718e6 0.484477
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −2.08311e7 −1.00362
\(846\) 0 0
\(847\) −7.75900e6 −0.371619
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.22669e6 0.200067
\(852\) 0 0
\(853\) 1.91515e7 0.901219 0.450610 0.892721i \(-0.351207\pi\)
0.450610 + 0.892721i \(0.351207\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 5.34683e6 0.248682 0.124341 0.992240i \(-0.460318\pi\)
0.124341 + 0.992240i \(0.460318\pi\)
\(858\) 0 0
\(859\) −3.95858e7 −1.83045 −0.915223 0.402948i \(-0.867986\pi\)
−0.915223 + 0.402948i \(0.867986\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −2.50284e7 −1.14395 −0.571973 0.820272i \(-0.693822\pi\)
−0.571973 + 0.820272i \(0.693822\pi\)
\(864\) 0 0
\(865\) −5.73846e7 −2.60768
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −5.06605e6 −0.227573
\(870\) 0 0
\(871\) 1.07492e6 0.0480099
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −1.19111e7 −0.525935
\(876\) 0 0
\(877\) −5.02589e6 −0.220655 −0.110328 0.993895i \(-0.535190\pi\)
−0.110328 + 0.993895i \(0.535190\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 2.60490e7 1.13071 0.565356 0.824847i \(-0.308739\pi\)
0.565356 + 0.824847i \(0.308739\pi\)
\(882\) 0 0
\(883\) 6.82462e6 0.294562 0.147281 0.989095i \(-0.452948\pi\)
0.147281 + 0.989095i \(0.452948\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 2.33835e7 0.997931 0.498965 0.866622i \(-0.333713\pi\)
0.498965 + 0.866622i \(0.333713\pi\)
\(888\) 0 0
\(889\) 1.00477e7 0.426397
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.49645e6 −0.0627961
\(894\) 0 0
\(895\) −6.22517e7 −2.59773
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.49620e7 1.44277
\(900\) 0 0
\(901\) −8.45600e6 −0.347019
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.45352e7 −0.589930
\(906\) 0 0
\(907\) −3.95959e7 −1.59820 −0.799102 0.601196i \(-0.794691\pi\)
−0.799102 + 0.601196i \(0.794691\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −4.67570e6 −0.186660 −0.0933300 0.995635i \(-0.529751\pi\)
−0.0933300 + 0.995635i \(0.529751\pi\)
\(912\) 0 0
\(913\) −4.22386e6 −0.167700
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 3.57524e6 0.140405
\(918\) 0 0
\(919\) 4.92594e6 0.192398 0.0961990 0.995362i \(-0.469331\pi\)
0.0961990 + 0.995362i \(0.469331\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −1.44144e7 −0.556919
\(924\) 0 0
\(925\) −4.19073e7 −1.61041
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 3.23688e7 1.23052 0.615258 0.788326i \(-0.289052\pi\)
0.615258 + 0.788326i \(0.289052\pi\)
\(930\) 0 0
\(931\) −4.15853e6 −0.157241
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −9.88354e6 −0.369729
\(936\) 0 0
\(937\) −3.32337e7 −1.23660 −0.618301 0.785941i \(-0.712179\pi\)
−0.618301 + 0.785941i \(0.712179\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 2.66426e7 0.980852 0.490426 0.871483i \(-0.336841\pi\)
0.490426 + 0.871483i \(0.336841\pi\)
\(942\) 0 0
\(943\) −1.87891e6 −0.0688061
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 3.14663e7 1.14017 0.570086 0.821585i \(-0.306910\pi\)
0.570086 + 0.821585i \(0.306910\pi\)
\(948\) 0 0
\(949\) −3.56987e7 −1.28673
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 1.34516e7 0.479779 0.239890 0.970800i \(-0.422889\pi\)
0.239890 + 0.970800i \(0.422889\pi\)
\(954\) 0 0
\(955\) −4.57690e7 −1.62391
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 4.61492e6 0.162038
\(960\) 0 0
\(961\) 1.15157e7 0.402238
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −5.83313e7 −2.01643
\(966\) 0 0
\(967\) 2.84963e7 0.979992 0.489996 0.871725i \(-0.336998\pi\)
0.489996 + 0.871725i \(0.336998\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 1.81858e7 0.618990 0.309495 0.950901i \(-0.399840\pi\)
0.309495 + 0.950901i \(0.399840\pi\)
\(972\) 0 0
\(973\) 2.34200e6 0.0793059
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.20941e7 −1.07569 −0.537847 0.843042i \(-0.680762\pi\)
−0.537847 + 0.843042i \(0.680762\pi\)
\(978\) 0 0
\(979\) 165464. 0.00551756
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.56154e7 0.515429 0.257715 0.966221i \(-0.417031\pi\)
0.257715 + 0.966221i \(0.417031\pi\)
\(984\) 0 0
\(985\) −2.22376e7 −0.730293
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3.12192e6 0.101492
\(990\) 0 0
\(991\) −4.84499e7 −1.56714 −0.783572 0.621301i \(-0.786605\pi\)
−0.783572 + 0.621301i \(0.786605\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 7.71778e6 0.247135
\(996\) 0 0
\(997\) −4.54336e7 −1.44757 −0.723784 0.690027i \(-0.757599\pi\)
−0.723784 + 0.690027i \(0.757599\pi\)
\(998\) 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.a.1.1 1
3.2 odd 2 336.6.a.i.1.1 1
4.3 odd 2 63.6.a.b.1.1 1
12.11 even 2 21.6.a.c.1.1 1
28.27 even 2 441.6.a.c.1.1 1
60.23 odd 4 525.6.d.c.274.1 2
60.47 odd 4 525.6.d.c.274.2 2
60.59 even 2 525.6.a.b.1.1 1
84.11 even 6 147.6.e.c.79.1 2
84.23 even 6 147.6.e.c.67.1 2
84.47 odd 6 147.6.e.d.67.1 2
84.59 odd 6 147.6.e.d.79.1 2
84.83 odd 2 147.6.a.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
21.6.a.c.1.1 1 12.11 even 2
63.6.a.b.1.1 1 4.3 odd 2
147.6.a.f.1.1 1 84.83 odd 2
147.6.e.c.67.1 2 84.23 even 6
147.6.e.c.79.1 2 84.11 even 6
147.6.e.d.67.1 2 84.47 odd 6
147.6.e.d.79.1 2 84.59 odd 6
336.6.a.i.1.1 1 3.2 odd 2
441.6.a.c.1.1 1 28.27 even 2
525.6.a.b.1.1 1 60.59 even 2
525.6.d.c.274.1 2 60.23 odd 4
525.6.d.c.274.2 2 60.47 odd 4
1008.6.a.a.1.1 1 1.1 even 1 trivial