Properties

Label 5184.2.a.bv.1.2
Level $5184$
Weight $2$
Character 5184.1
Self dual yes
Analytic conductor $41.394$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5184,2,Mod(1,5184)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5184.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5184 = 2^{6} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5184.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: \(41.3944484078\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{6}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - 6 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 2592)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.44949\) of defining polynomial
Character \(\chi\) \(=\) 5184.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{5} +4.89898 q^{7} +O(q^{10})\) \(q+1.00000 q^{5} +4.89898 q^{7} +4.89898 q^{11} -3.00000 q^{13} -5.00000 q^{17} +4.89898 q^{19} -4.89898 q^{23} -4.00000 q^{25} +5.00000 q^{29} +4.89898 q^{35} +5.00000 q^{37} +2.00000 q^{41} +4.89898 q^{43} +9.79796 q^{47} +17.0000 q^{49} +2.00000 q^{53} +4.89898 q^{55} -9.79796 q^{59} +13.0000 q^{61} -3.00000 q^{65} +4.89898 q^{67} +4.89898 q^{71} +3.00000 q^{73} +24.0000 q^{77} -14.6969 q^{79} -9.79796 q^{83} -5.00000 q^{85} -13.0000 q^{89} -14.6969 q^{91} +4.89898 q^{95} -6.00000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{5} - 6 q^{13} - 10 q^{17} - 8 q^{25} + 10 q^{29} + 10 q^{37} + 4 q^{41} + 34 q^{49} + 4 q^{53} + 26 q^{61} - 6 q^{65} + 6 q^{73} + 48 q^{77} - 10 q^{85} - 26 q^{89} - 12 q^{97}+O(q^{100}) \) 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
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) 4.89898 1.85164 0.925820 0.377964i \(-0.123376\pi\)
0.925820 + 0.377964i \(0.123376\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 4.89898 1.47710 0.738549 0.674200i \(-0.235511\pi\)
0.738549 + 0.674200i \(0.235511\pi\)
\(12\) 0 0
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 0 0
\(19\) 4.89898 1.12390 0.561951 0.827170i \(-0.310051\pi\)
0.561951 + 0.827170i \(0.310051\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.89898 −1.02151 −0.510754 0.859727i \(-0.670634\pi\)
−0.510754 + 0.859727i \(0.670634\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.89898 0.828079
\(36\) 0 0
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 4.89898 0.747087 0.373544 0.927613i \(-0.378143\pi\)
0.373544 + 0.927613i \(0.378143\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.79796 1.42918 0.714590 0.699544i \(-0.246613\pi\)
0.714590 + 0.699544i \(0.246613\pi\)
\(48\) 0 0
\(49\) 17.0000 2.42857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 4.89898 0.660578
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −9.79796 −1.27559 −0.637793 0.770208i \(-0.720152\pi\)
−0.637793 + 0.770208i \(0.720152\pi\)
\(60\) 0 0
\(61\) 13.0000 1.66448 0.832240 0.554416i \(-0.187058\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −3.00000 −0.372104
\(66\) 0 0
\(67\) 4.89898 0.598506 0.299253 0.954174i \(-0.403263\pi\)
0.299253 + 0.954174i \(0.403263\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.89898 0.581402 0.290701 0.956814i \(-0.406112\pi\)
0.290701 + 0.956814i \(0.406112\pi\)
\(72\) 0 0
\(73\) 3.00000 0.351123 0.175562 0.984468i \(-0.443826\pi\)
0.175562 + 0.984468i \(0.443826\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 24.0000 2.73505
\(78\) 0 0
\(79\) −14.6969 −1.65353 −0.826767 0.562544i \(-0.809823\pi\)
−0.826767 + 0.562544i \(0.809823\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −9.79796 −1.07547 −0.537733 0.843115i \(-0.680719\pi\)
−0.537733 + 0.843115i \(0.680719\pi\)
\(84\) 0 0
\(85\) −5.00000 −0.542326
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −13.0000 −1.37800 −0.688999 0.724763i \(-0.741949\pi\)
−0.688999 + 0.724763i \(0.741949\pi\)
\(90\) 0 0
\(91\) −14.6969 −1.54066
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.89898 0.502625
\(96\) 0 0
\(97\) −6.00000 −0.609208 −0.304604 0.952479i \(-0.598524\pi\)
−0.304604 + 0.952479i \(0.598524\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) 9.79796 0.965422 0.482711 0.875780i \(-0.339652\pi\)
0.482711 + 0.875780i \(0.339652\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −19.5959 −1.89441 −0.947204 0.320630i \(-0.896105\pi\)
−0.947204 + 0.320630i \(0.896105\pi\)
\(108\) 0 0
\(109\) 9.00000 0.862044 0.431022 0.902342i \(-0.358153\pi\)
0.431022 + 0.902342i \(0.358153\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −1.00000 −0.0940721 −0.0470360 0.998893i \(-0.514978\pi\)
−0.0470360 + 0.998893i \(0.514978\pi\)
\(114\) 0 0
\(115\) −4.89898 −0.456832
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −24.4949 −2.24544
\(120\) 0 0
\(121\) 13.0000 1.18182
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) −4.89898 −0.434714 −0.217357 0.976092i \(-0.569744\pi\)
−0.217357 + 0.976092i \(0.569744\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 14.6969 1.28408 0.642039 0.766672i \(-0.278089\pi\)
0.642039 + 0.766672i \(0.278089\pi\)
\(132\) 0 0
\(133\) 24.0000 2.08106
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −17.0000 −1.45241 −0.726204 0.687479i \(-0.758717\pi\)
−0.726204 + 0.687479i \(0.758717\pi\)
\(138\) 0 0
\(139\) −9.79796 −0.831052 −0.415526 0.909581i \(-0.636402\pi\)
−0.415526 + 0.909581i \(0.636402\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −14.6969 −1.22902
\(144\) 0 0
\(145\) 5.00000 0.415227
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.00000 0.409616 0.204808 0.978802i \(-0.434343\pi\)
0.204808 + 0.978802i \(0.434343\pi\)
\(150\) 0 0
\(151\) 9.79796 0.797347 0.398673 0.917093i \(-0.369471\pi\)
0.398673 + 0.917093i \(0.369471\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −7.00000 −0.558661 −0.279330 0.960195i \(-0.590112\pi\)
−0.279330 + 0.960195i \(0.590112\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −24.0000 −1.89146
\(162\) 0 0
\(163\) 9.79796 0.767435 0.383718 0.923450i \(-0.374644\pi\)
0.383718 + 0.923450i \(0.374644\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.6969 1.13728 0.568642 0.822585i \(-0.307469\pi\)
0.568642 + 0.822585i \(0.307469\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.00000 0.0760286 0.0380143 0.999277i \(-0.487897\pi\)
0.0380143 + 0.999277i \(0.487897\pi\)
\(174\) 0 0
\(175\) −19.5959 −1.48131
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 19.5959 1.46467 0.732334 0.680946i \(-0.238431\pi\)
0.732334 + 0.680946i \(0.238431\pi\)
\(180\) 0 0
\(181\) 18.0000 1.33793 0.668965 0.743294i \(-0.266738\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 5.00000 0.367607
\(186\) 0 0
\(187\) −24.4949 −1.79124
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.89898 0.354478 0.177239 0.984168i \(-0.443283\pi\)
0.177239 + 0.984168i \(0.443283\pi\)
\(192\) 0 0
\(193\) 19.0000 1.36765 0.683825 0.729646i \(-0.260315\pi\)
0.683825 + 0.729646i \(0.260315\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −23.0000 −1.63868 −0.819341 0.573306i \(-0.805660\pi\)
−0.819341 + 0.573306i \(0.805660\pi\)
\(198\) 0 0
\(199\) −19.5959 −1.38912 −0.694559 0.719436i \(-0.744400\pi\)
−0.694559 + 0.719436i \(0.744400\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 24.4949 1.71920
\(204\) 0 0
\(205\) 2.00000 0.139686
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 24.0000 1.66011
\(210\) 0 0
\(211\) 4.89898 0.337260 0.168630 0.985679i \(-0.446066\pi\)
0.168630 + 0.985679i \(0.446066\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.89898 0.334108
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 15.0000 1.00901
\(222\) 0 0
\(223\) 4.89898 0.328060 0.164030 0.986455i \(-0.447551\pi\)
0.164030 + 0.986455i \(0.447551\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.89898 −0.325157 −0.162578 0.986696i \(-0.551981\pi\)
−0.162578 + 0.986696i \(0.551981\pi\)
\(228\) 0 0
\(229\) −3.00000 −0.198246 −0.0991228 0.995075i \(-0.531604\pi\)
−0.0991228 + 0.995075i \(0.531604\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −29.0000 −1.89985 −0.949927 0.312473i \(-0.898843\pi\)
−0.949927 + 0.312473i \(0.898843\pi\)
\(234\) 0 0
\(235\) 9.79796 0.639148
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −9.79796 −0.633777 −0.316889 0.948463i \(-0.602638\pi\)
−0.316889 + 0.948463i \(0.602638\pi\)
\(240\) 0 0
\(241\) 27.0000 1.73922 0.869611 0.493737i \(-0.164369\pi\)
0.869611 + 0.493737i \(0.164369\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 17.0000 1.08609
\(246\) 0 0
\(247\) −14.6969 −0.935144
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 14.6969 0.927663 0.463831 0.885924i \(-0.346474\pi\)
0.463831 + 0.885924i \(0.346474\pi\)
\(252\) 0 0
\(253\) −24.0000 −1.50887
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.00000 0.436648 0.218324 0.975876i \(-0.429941\pi\)
0.218324 + 0.975876i \(0.429941\pi\)
\(258\) 0 0
\(259\) 24.4949 1.52204
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.79796 0.604168 0.302084 0.953281i \(-0.402318\pi\)
0.302084 + 0.953281i \(0.402318\pi\)
\(264\) 0 0
\(265\) 2.00000 0.122859
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.00000 0.0609711 0.0304855 0.999535i \(-0.490295\pi\)
0.0304855 + 0.999535i \(0.490295\pi\)
\(270\) 0 0
\(271\) 4.89898 0.297592 0.148796 0.988868i \(-0.452460\pi\)
0.148796 + 0.988868i \(0.452460\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −19.5959 −1.18168
\(276\) 0 0
\(277\) 18.0000 1.08152 0.540758 0.841178i \(-0.318138\pi\)
0.540758 + 0.841178i \(0.318138\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −13.0000 −0.775515 −0.387757 0.921761i \(-0.626750\pi\)
−0.387757 + 0.921761i \(0.626750\pi\)
\(282\) 0 0
\(283\) −19.5959 −1.16486 −0.582428 0.812882i \(-0.697897\pi\)
−0.582428 + 0.812882i \(0.697897\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 9.79796 0.578355
\(288\) 0 0
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5.00000 0.292103 0.146052 0.989277i \(-0.453343\pi\)
0.146052 + 0.989277i \(0.453343\pi\)
\(294\) 0 0
\(295\) −9.79796 −0.570459
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 14.6969 0.849946
\(300\) 0 0
\(301\) 24.0000 1.38334
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 13.0000 0.744378
\(306\) 0 0
\(307\) −19.5959 −1.11840 −0.559199 0.829033i \(-0.688891\pi\)
−0.559199 + 0.829033i \(0.688891\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −23.0000 −1.29181 −0.645904 0.763418i \(-0.723520\pi\)
−0.645904 + 0.763418i \(0.723520\pi\)
\(318\) 0 0
\(319\) 24.4949 1.37145
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −24.4949 −1.36293
\(324\) 0 0
\(325\) 12.0000 0.665640
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 48.0000 2.64633
\(330\) 0 0
\(331\) 24.4949 1.34636 0.673181 0.739478i \(-0.264928\pi\)
0.673181 + 0.739478i \(0.264928\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 4.89898 0.267660
\(336\) 0 0
\(337\) −6.00000 −0.326841 −0.163420 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 48.9898 2.64520
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −34.2929 −1.84094 −0.920468 0.390817i \(-0.872193\pi\)
−0.920468 + 0.390817i \(0.872193\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.00000 0.106449 0.0532246 0.998583i \(-0.483050\pi\)
0.0532246 + 0.998583i \(0.483050\pi\)
\(354\) 0 0
\(355\) 4.89898 0.260011
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 14.6969 0.775675 0.387837 0.921728i \(-0.373222\pi\)
0.387837 + 0.921728i \(0.373222\pi\)
\(360\) 0 0
\(361\) 5.00000 0.263158
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.00000 0.157027
\(366\) 0 0
\(367\) 19.5959 1.02290 0.511449 0.859313i \(-0.329109\pi\)
0.511449 + 0.859313i \(0.329109\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 9.79796 0.508685
\(372\) 0 0
\(373\) 34.0000 1.76045 0.880227 0.474554i \(-0.157390\pi\)
0.880227 + 0.474554i \(0.157390\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15.0000 −0.772539
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −14.6969 −0.750978 −0.375489 0.926827i \(-0.622525\pi\)
−0.375489 + 0.926827i \(0.622525\pi\)
\(384\) 0 0
\(385\) 24.0000 1.22315
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 2.00000 0.101404 0.0507020 0.998714i \(-0.483854\pi\)
0.0507020 + 0.998714i \(0.483854\pi\)
\(390\) 0 0
\(391\) 24.4949 1.23876
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −14.6969 −0.739483
\(396\) 0 0
\(397\) 13.0000 0.652451 0.326226 0.945292i \(-0.394223\pi\)
0.326226 + 0.945292i \(0.394223\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −29.0000 −1.44819 −0.724095 0.689700i \(-0.757743\pi\)
−0.724095 + 0.689700i \(0.757743\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 24.4949 1.21417
\(408\) 0 0
\(409\) −9.00000 −0.445021 −0.222511 0.974930i \(-0.571425\pi\)
−0.222511 + 0.974930i \(0.571425\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −48.0000 −2.36193
\(414\) 0 0
\(415\) −9.79796 −0.480963
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −19.5959 −0.957323 −0.478662 0.877999i \(-0.658878\pi\)
−0.478662 + 0.877999i \(0.658878\pi\)
\(420\) 0 0
\(421\) −15.0000 −0.731055 −0.365528 0.930800i \(-0.619111\pi\)
−0.365528 + 0.930800i \(0.619111\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 20.0000 0.970143
\(426\) 0 0
\(427\) 63.6867 3.08202
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9.79796 −0.471951 −0.235976 0.971759i \(-0.575829\pi\)
−0.235976 + 0.971759i \(0.575829\pi\)
\(432\) 0 0
\(433\) 19.0000 0.913082 0.456541 0.889702i \(-0.349088\pi\)
0.456541 + 0.889702i \(0.349088\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −24.0000 −1.14808
\(438\) 0 0
\(439\) −29.3939 −1.40289 −0.701447 0.712722i \(-0.747462\pi\)
−0.701447 + 0.712722i \(0.747462\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.79796 −0.465515 −0.232758 0.972535i \(-0.574775\pi\)
−0.232758 + 0.972535i \(0.574775\pi\)
\(444\) 0 0
\(445\) −13.0000 −0.616259
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 26.0000 1.22702 0.613508 0.789689i \(-0.289758\pi\)
0.613508 + 0.789689i \(0.289758\pi\)
\(450\) 0 0
\(451\) 9.79796 0.461368
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −14.6969 −0.689003
\(456\) 0 0
\(457\) 15.0000 0.701670 0.350835 0.936437i \(-0.385898\pi\)
0.350835 + 0.936437i \(0.385898\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −22.0000 −1.02464 −0.512321 0.858794i \(-0.671214\pi\)
−0.512321 + 0.858794i \(0.671214\pi\)
\(462\) 0 0
\(463\) 9.79796 0.455350 0.227675 0.973737i \(-0.426888\pi\)
0.227675 + 0.973737i \(0.426888\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −9.79796 −0.453395 −0.226698 0.973965i \(-0.572793\pi\)
−0.226698 + 0.973965i \(0.572793\pi\)
\(468\) 0 0
\(469\) 24.0000 1.10822
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 24.0000 1.10352
\(474\) 0 0
\(475\) −19.5959 −0.899122
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −24.4949 −1.11920 −0.559600 0.828763i \(-0.689045\pi\)
−0.559600 + 0.828763i \(0.689045\pi\)
\(480\) 0 0
\(481\) −15.0000 −0.683941
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −6.00000 −0.272446
\(486\) 0 0
\(487\) −19.5959 −0.887976 −0.443988 0.896033i \(-0.646437\pi\)
−0.443988 + 0.896033i \(0.646437\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 34.2929 1.54761 0.773807 0.633421i \(-0.218350\pi\)
0.773807 + 0.633421i \(0.218350\pi\)
\(492\) 0 0
\(493\) −25.0000 −1.12594
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 24.0000 1.07655
\(498\) 0 0
\(499\) −24.4949 −1.09654 −0.548271 0.836301i \(-0.684714\pi\)
−0.548271 + 0.836301i \(0.684714\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −39.1918 −1.74748 −0.873739 0.486395i \(-0.838311\pi\)
−0.873739 + 0.486395i \(0.838311\pi\)
\(504\) 0 0
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 26.0000 1.15243 0.576215 0.817298i \(-0.304529\pi\)
0.576215 + 0.817298i \(0.304529\pi\)
\(510\) 0 0
\(511\) 14.6969 0.650154
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 9.79796 0.431750
\(516\) 0 0
\(517\) 48.0000 2.11104
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 34.0000 1.48957 0.744784 0.667306i \(-0.232553\pi\)
0.744784 + 0.667306i \(0.232553\pi\)
\(522\) 0 0
\(523\) 44.0908 1.92796 0.963978 0.265981i \(-0.0856957\pi\)
0.963978 + 0.265981i \(0.0856957\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.00000 −0.259889
\(534\) 0 0
\(535\) −19.5959 −0.847205
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 83.2827 3.58724
\(540\) 0 0
\(541\) −27.0000 −1.16082 −0.580410 0.814324i \(-0.697108\pi\)
−0.580410 + 0.814324i \(0.697108\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 9.00000 0.385518
\(546\) 0 0
\(547\) −29.3939 −1.25679 −0.628396 0.777894i \(-0.716288\pi\)
−0.628396 + 0.777894i \(0.716288\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 24.4949 1.04352
\(552\) 0 0
\(553\) −72.0000 −3.06175
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 17.0000 0.720313 0.360157 0.932892i \(-0.382723\pi\)
0.360157 + 0.932892i \(0.382723\pi\)
\(558\) 0 0
\(559\) −14.6969 −0.621614
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.79796 0.412935 0.206467 0.978453i \(-0.433803\pi\)
0.206467 + 0.978453i \(0.433803\pi\)
\(564\) 0 0
\(565\) −1.00000 −0.0420703
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −17.0000 −0.712677 −0.356339 0.934357i \(-0.615975\pi\)
−0.356339 + 0.934357i \(0.615975\pi\)
\(570\) 0 0
\(571\) −9.79796 −0.410032 −0.205016 0.978759i \(-0.565725\pi\)
−0.205016 + 0.978759i \(0.565725\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 19.5959 0.817206
\(576\) 0 0
\(577\) −1.00000 −0.0416305 −0.0208153 0.999783i \(-0.506626\pi\)
−0.0208153 + 0.999783i \(0.506626\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −48.0000 −1.99138
\(582\) 0 0
\(583\) 9.79796 0.405790
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.6969 −0.606608 −0.303304 0.952894i \(-0.598090\pi\)
−0.303304 + 0.952894i \(0.598090\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −17.0000 −0.698106 −0.349053 0.937103i \(-0.613497\pi\)
−0.349053 + 0.937103i \(0.613497\pi\)
\(594\) 0 0
\(595\) −24.4949 −1.00419
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −19.5959 −0.800668 −0.400334 0.916369i \(-0.631106\pi\)
−0.400334 + 0.916369i \(0.631106\pi\)
\(600\) 0 0
\(601\) −5.00000 −0.203954 −0.101977 0.994787i \(-0.532517\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 13.0000 0.528525
\(606\) 0 0
\(607\) −24.4949 −0.994217 −0.497109 0.867688i \(-0.665605\pi\)
−0.497109 + 0.867688i \(0.665605\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −29.3939 −1.18915
\(612\) 0 0
\(613\) −14.0000 −0.565455 −0.282727 0.959200i \(-0.591239\pi\)
−0.282727 + 0.959200i \(0.591239\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 11.0000 0.442843 0.221422 0.975178i \(-0.428930\pi\)
0.221422 + 0.975178i \(0.428930\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −63.6867 −2.55156
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −25.0000 −0.996815
\(630\) 0 0
\(631\) −29.3939 −1.17015 −0.585076 0.810979i \(-0.698935\pi\)
−0.585076 + 0.810979i \(0.698935\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −4.89898 −0.194410
\(636\) 0 0
\(637\) −51.0000 −2.02069
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 43.0000 1.69840 0.849199 0.528073i \(-0.177085\pi\)
0.849199 + 0.528073i \(0.177085\pi\)
\(642\) 0 0
\(643\) −29.3939 −1.15918 −0.579591 0.814908i \(-0.696788\pi\)
−0.579591 + 0.814908i \(0.696788\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4.89898 −0.192599 −0.0962994 0.995352i \(-0.530701\pi\)
−0.0962994 + 0.995352i \(0.530701\pi\)
\(648\) 0 0
\(649\) −48.0000 −1.88416
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 10.0000 0.391330 0.195665 0.980671i \(-0.437313\pi\)
0.195665 + 0.980671i \(0.437313\pi\)
\(654\) 0 0
\(655\) 14.6969 0.574257
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.89898 0.190837 0.0954186 0.995437i \(-0.469581\pi\)
0.0954186 + 0.995437i \(0.469581\pi\)
\(660\) 0 0
\(661\) 29.0000 1.12797 0.563985 0.825785i \(-0.309268\pi\)
0.563985 + 0.825785i \(0.309268\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 24.0000 0.930680
\(666\) 0 0
\(667\) −24.4949 −0.948446
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 63.6867 2.45860
\(672\) 0 0
\(673\) 11.0000 0.424019 0.212009 0.977268i \(-0.431999\pi\)
0.212009 + 0.977268i \(0.431999\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 34.0000 1.30673 0.653363 0.757045i \(-0.273358\pi\)
0.653363 + 0.757045i \(0.273358\pi\)
\(678\) 0 0
\(679\) −29.3939 −1.12803
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −48.9898 −1.87454 −0.937271 0.348601i \(-0.886657\pi\)
−0.937271 + 0.348601i \(0.886657\pi\)
\(684\) 0 0
\(685\) −17.0000 −0.649537
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) −4.89898 −0.186366 −0.0931830 0.995649i \(-0.529704\pi\)
−0.0931830 + 0.995649i \(0.529704\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −9.79796 −0.371658
\(696\) 0 0
\(697\) −10.0000 −0.378777
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 17.0000 0.642081 0.321041 0.947065i \(-0.395967\pi\)
0.321041 + 0.947065i \(0.395967\pi\)
\(702\) 0 0
\(703\) 24.4949 0.923843
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 48.9898 1.84245
\(708\) 0 0
\(709\) −27.0000 −1.01401 −0.507003 0.861944i \(-0.669247\pi\)
−0.507003 + 0.861944i \(0.669247\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) −14.6969 −0.549634
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 44.0908 1.64431 0.822155 0.569264i \(-0.192772\pi\)
0.822155 + 0.569264i \(0.192772\pi\)
\(720\) 0 0
\(721\) 48.0000 1.78761
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −20.0000 −0.742781
\(726\) 0 0
\(727\) −4.89898 −0.181693 −0.0908465 0.995865i \(-0.528957\pi\)
−0.0908465 + 0.995865i \(0.528957\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −24.4949 −0.905977
\(732\) 0 0
\(733\) −6.00000 −0.221615 −0.110808 0.993842i \(-0.535344\pi\)
−0.110808 + 0.993842i \(0.535344\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.0000 0.884051
\(738\) 0 0
\(739\) −39.1918 −1.44169 −0.720847 0.693094i \(-0.756247\pi\)
−0.720847 + 0.693094i \(0.756247\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 39.1918 1.43781 0.718905 0.695109i \(-0.244644\pi\)
0.718905 + 0.695109i \(0.244644\pi\)
\(744\) 0 0
\(745\) 5.00000 0.183186
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −96.0000 −3.50776
\(750\) 0 0
\(751\) 14.6969 0.536299 0.268149 0.963377i \(-0.413588\pi\)
0.268149 + 0.963377i \(0.413588\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9.79796 0.356584
\(756\) 0 0
\(757\) −30.0000 −1.09037 −0.545184 0.838316i \(-0.683540\pi\)
−0.545184 + 0.838316i \(0.683540\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 23.0000 0.833749 0.416875 0.908964i \(-0.363125\pi\)
0.416875 + 0.908964i \(0.363125\pi\)
\(762\) 0 0
\(763\) 44.0908 1.59619
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 29.3939 1.06135
\(768\) 0 0
\(769\) 11.0000 0.396670 0.198335 0.980134i \(-0.436447\pi\)
0.198335 + 0.980134i \(0.436447\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 41.0000 1.47467 0.737334 0.675529i \(-0.236085\pi\)
0.737334 + 0.675529i \(0.236085\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.79796 0.351048
\(780\) 0 0
\(781\) 24.0000 0.858788
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.00000 −0.249841
\(786\) 0 0
\(787\) −14.6969 −0.523889 −0.261945 0.965083i \(-0.584364\pi\)
−0.261945 + 0.965083i \(0.584364\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4.89898 −0.174188
\(792\) 0 0
\(793\) −39.0000 −1.38493
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −23.0000 −0.814702 −0.407351 0.913272i \(-0.633547\pi\)
−0.407351 + 0.913272i \(0.633547\pi\)
\(798\) 0 0
\(799\) −48.9898 −1.73313
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 14.6969 0.518644
\(804\) 0 0
\(805\) −24.0000 −0.845889
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 23.0000 0.808637 0.404318 0.914618i \(-0.367509\pi\)
0.404318 + 0.914618i \(0.367509\pi\)
\(810\) 0 0
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 9.79796 0.343208
\(816\) 0 0
\(817\) 24.0000 0.839654
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −11.0000 −0.383903 −0.191951 0.981404i \(-0.561482\pi\)
−0.191951 + 0.981404i \(0.561482\pi\)
\(822\) 0 0
\(823\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 4.89898 0.170354 0.0851771 0.996366i \(-0.472854\pi\)
0.0851771 + 0.996366i \(0.472854\pi\)
\(828\) 0 0
\(829\) 42.0000 1.45872 0.729360 0.684130i \(-0.239818\pi\)
0.729360 + 0.684130i \(0.239818\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −85.0000 −2.94508
\(834\) 0 0
\(835\) 14.6969 0.508609
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 14.6969 0.507395 0.253697 0.967284i \(-0.418353\pi\)
0.253697 + 0.967284i \(0.418353\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.00000 −0.137604
\(846\) 0 0
\(847\) 63.6867 2.18830
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −24.4949 −0.839674
\(852\) 0 0
\(853\) 2.00000 0.0684787 0.0342393 0.999414i \(-0.489099\pi\)
0.0342393 + 0.999414i \(0.489099\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −25.0000 −0.853984 −0.426992 0.904255i \(-0.640427\pi\)
−0.426992 + 0.904255i \(0.640427\pi\)
\(858\) 0 0
\(859\) −29.3939 −1.00291 −0.501453 0.865185i \(-0.667201\pi\)
−0.501453 + 0.865185i \(0.667201\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −24.4949 −0.833816 −0.416908 0.908949i \(-0.636886\pi\)
−0.416908 + 0.908949i \(0.636886\pi\)
\(864\) 0 0
\(865\) 1.00000 0.0340010
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −72.0000 −2.44243
\(870\) 0 0
\(871\) −14.6969 −0.497987
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −44.0908 −1.49054
\(876\) 0 0
\(877\) −35.0000 −1.18187 −0.590933 0.806721i \(-0.701240\pi\)
−0.590933 + 0.806721i \(0.701240\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 10.0000 0.336909 0.168454 0.985709i \(-0.446122\pi\)
0.168454 + 0.985709i \(0.446122\pi\)
\(882\) 0 0
\(883\) 29.3939 0.989183 0.494591 0.869126i \(-0.335318\pi\)
0.494591 + 0.869126i \(0.335318\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 14.6969 0.493475 0.246737 0.969082i \(-0.420641\pi\)
0.246737 + 0.969082i \(0.420641\pi\)
\(888\) 0 0
\(889\) −24.0000 −0.804934
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 48.0000 1.60626
\(894\) 0 0
\(895\) 19.5959 0.655019
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) −10.0000 −0.333148
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 18.0000 0.598340
\(906\) 0 0
\(907\) 19.5959 0.650672 0.325336 0.945599i \(-0.394523\pi\)
0.325336 + 0.945599i \(0.394523\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 4.89898 0.162310 0.0811552 0.996701i \(-0.474139\pi\)
0.0811552 + 0.996701i \(0.474139\pi\)
\(912\) 0 0
\(913\) −48.0000 −1.58857
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 72.0000 2.37765
\(918\) 0 0
\(919\) −34.2929 −1.13122 −0.565608 0.824674i \(-0.691359\pi\)
−0.565608 + 0.824674i \(0.691359\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −14.6969 −0.483756
\(924\) 0 0
\(925\) −20.0000 −0.657596
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −5.00000 −0.164045 −0.0820223 0.996630i \(-0.526138\pi\)
−0.0820223 + 0.996630i \(0.526138\pi\)
\(930\) 0 0
\(931\) 83.2827 2.72948
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −24.4949 −0.801069
\(936\) 0 0
\(937\) 19.0000 0.620703 0.310351 0.950622i \(-0.399553\pi\)
0.310351 + 0.950622i \(0.399553\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 41.0000 1.33656 0.668281 0.743909i \(-0.267030\pi\)
0.668281 + 0.743909i \(0.267030\pi\)
\(942\) 0 0
\(943\) −9.79796 −0.319065
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 14.6969 0.477586 0.238793 0.971070i \(-0.423248\pi\)
0.238793 + 0.971070i \(0.423248\pi\)
\(948\) 0 0
\(949\) −9.00000 −0.292152
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 7.00000 0.226752 0.113376 0.993552i \(-0.463833\pi\)
0.113376 + 0.993552i \(0.463833\pi\)
\(954\) 0 0
\(955\) 4.89898 0.158527
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −83.2827 −2.68934
\(960\) 0 0
\(961\) −31.0000 −1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 19.0000 0.611632
\(966\) 0 0
\(967\) −4.89898 −0.157541 −0.0787703 0.996893i \(-0.525099\pi\)
−0.0787703 + 0.996893i \(0.525099\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −4.89898 −0.157216 −0.0786079 0.996906i \(-0.525048\pi\)
−0.0786079 + 0.996906i \(0.525048\pi\)
\(972\) 0 0
\(973\) −48.0000 −1.53881
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −22.0000 −0.703842 −0.351921 0.936030i \(-0.614471\pi\)
−0.351921 + 0.936030i \(0.614471\pi\)
\(978\) 0 0
\(979\) −63.6867 −2.03544
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 19.5959 0.625013 0.312506 0.949916i \(-0.398831\pi\)
0.312506 + 0.949916i \(0.398831\pi\)
\(984\) 0 0
\(985\) −23.0000 −0.732841
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −24.0000 −0.763156
\(990\) 0 0
\(991\) −34.2929 −1.08935 −0.544674 0.838648i \(-0.683347\pi\)
−0.544674 + 0.838648i \(0.683347\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −19.5959 −0.621232
\(996\) 0 0
\(997\) 25.0000 0.791758 0.395879 0.918303i \(-0.370440\pi\)
0.395879 + 0.918303i \(0.370440\pi\)
\(998\) 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 5184.2.a.bv.1.2 2
3.2 odd 2 5184.2.a.bk.1.2 2
4.3 odd 2 inner 5184.2.a.bv.1.1 2
8.3 odd 2 2592.2.a.m.1.1 2
8.5 even 2 2592.2.a.m.1.2 yes 2
12.11 even 2 5184.2.a.bk.1.1 2
24.5 odd 2 2592.2.a.r.1.2 yes 2
24.11 even 2 2592.2.a.r.1.1 yes 2
72.5 odd 6 2592.2.i.z.865.1 4
72.11 even 6 2592.2.i.z.1729.2 4
72.13 even 6 2592.2.i.bd.865.1 4
72.29 odd 6 2592.2.i.z.1729.1 4
72.43 odd 6 2592.2.i.bd.1729.2 4
72.59 even 6 2592.2.i.z.865.2 4
72.61 even 6 2592.2.i.bd.1729.1 4
72.67 odd 6 2592.2.i.bd.865.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2592.2.a.m.1.1 2 8.3 odd 2
2592.2.a.m.1.2 yes 2 8.5 even 2
2592.2.a.r.1.1 yes 2 24.11 even 2
2592.2.a.r.1.2 yes 2 24.5 odd 2
2592.2.i.z.865.1 4 72.5 odd 6
2592.2.i.z.865.2 4 72.59 even 6
2592.2.i.z.1729.1 4 72.29 odd 6
2592.2.i.z.1729.2 4 72.11 even 6
2592.2.i.bd.865.1 4 72.13 even 6
2592.2.i.bd.865.2 4 72.67 odd 6
2592.2.i.bd.1729.1 4 72.61 even 6
2592.2.i.bd.1729.2 4 72.43 odd 6
5184.2.a.bk.1.1 2 12.11 even 2
5184.2.a.bk.1.2 2 3.2 odd 2
5184.2.a.bv.1.1 2 4.3 odd 2 inner
5184.2.a.bv.1.2 2 1.1 even 1 trivial