Properties

Label 6552.2.a.bb.1.1
Level $6552$
Weight $2$
Character 6552.1
Self dual yes
Analytic conductor $52.318$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6552,2,Mod(1,6552)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6552, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("6552.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6552 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6552.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: \(52.3179834043\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{33}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(3.37228\) of defining polynomial
Character \(\chi\) \(=\) 6552.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.37228 q^{5} -1.00000 q^{7} +O(q^{10})\) \(q-4.37228 q^{5} -1.00000 q^{7} +0.372281 q^{11} -1.00000 q^{13} -0.372281 q^{17} +1.62772 q^{19} +4.37228 q^{23} +14.1168 q^{25} -10.3723 q^{29} +0.744563 q^{31} +4.37228 q^{35} -0.372281 q^{37} +6.00000 q^{41} +1.62772 q^{43} +13.4891 q^{47} +1.00000 q^{49} -8.74456 q^{53} -1.62772 q^{55} -8.74456 q^{59} +5.11684 q^{61} +4.37228 q^{65} +12.0000 q^{67} -10.0000 q^{71} +3.62772 q^{73} -0.372281 q^{77} -3.25544 q^{79} +12.7446 q^{83} +1.62772 q^{85} +7.48913 q^{89} +1.00000 q^{91} -7.11684 q^{95} +7.48913 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 3 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 3 q^{5} - 2 q^{7} - 5 q^{11} - 2 q^{13} + 5 q^{17} + 9 q^{19} + 3 q^{23} + 11 q^{25} - 15 q^{29} - 10 q^{31} + 3 q^{35} + 5 q^{37} + 12 q^{41} + 9 q^{43} + 4 q^{47} + 2 q^{49} - 6 q^{53} - 9 q^{55} - 6 q^{59} - 7 q^{61} + 3 q^{65} + 24 q^{67} - 20 q^{71} + 13 q^{73} + 5 q^{77} - 18 q^{79} + 14 q^{83} + 9 q^{85} - 8 q^{89} + 2 q^{91} + 3 q^{95} - 8 q^{97}+O(q^{100}) \) 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
\(5\) −4.37228 −1.95534 −0.977672 0.210138i \(-0.932609\pi\)
−0.977672 + 0.210138i \(0.932609\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 0.372281 0.112247 0.0561235 0.998424i \(-0.482126\pi\)
0.0561235 + 0.998424i \(0.482126\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.372281 −0.0902915 −0.0451457 0.998980i \(-0.514375\pi\)
−0.0451457 + 0.998980i \(0.514375\pi\)
\(18\) 0 0
\(19\) 1.62772 0.373424 0.186712 0.982415i \(-0.440217\pi\)
0.186712 + 0.982415i \(0.440217\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.37228 0.911684 0.455842 0.890061i \(-0.349338\pi\)
0.455842 + 0.890061i \(0.349338\pi\)
\(24\) 0 0
\(25\) 14.1168 2.82337
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −10.3723 −1.92608 −0.963042 0.269351i \(-0.913191\pi\)
−0.963042 + 0.269351i \(0.913191\pi\)
\(30\) 0 0
\(31\) 0.744563 0.133727 0.0668637 0.997762i \(-0.478701\pi\)
0.0668637 + 0.997762i \(0.478701\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.37228 0.739050
\(36\) 0 0
\(37\) −0.372281 −0.0612027 −0.0306013 0.999532i \(-0.509742\pi\)
−0.0306013 + 0.999532i \(0.509742\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 1.62772 0.248225 0.124112 0.992268i \(-0.460392\pi\)
0.124112 + 0.992268i \(0.460392\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 13.4891 1.96759 0.983796 0.179294i \(-0.0573813\pi\)
0.983796 + 0.179294i \(0.0573813\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.74456 −1.20116 −0.600579 0.799565i \(-0.705063\pi\)
−0.600579 + 0.799565i \(0.705063\pi\)
\(54\) 0 0
\(55\) −1.62772 −0.219482
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.74456 −1.13845 −0.569223 0.822183i \(-0.692756\pi\)
−0.569223 + 0.822183i \(0.692756\pi\)
\(60\) 0 0
\(61\) 5.11684 0.655145 0.327572 0.944826i \(-0.393769\pi\)
0.327572 + 0.944826i \(0.393769\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.37228 0.542315
\(66\) 0 0
\(67\) 12.0000 1.46603 0.733017 0.680211i \(-0.238112\pi\)
0.733017 + 0.680211i \(0.238112\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −10.0000 −1.18678 −0.593391 0.804914i \(-0.702211\pi\)
−0.593391 + 0.804914i \(0.702211\pi\)
\(72\) 0 0
\(73\) 3.62772 0.424592 0.212296 0.977205i \(-0.431906\pi\)
0.212296 + 0.977205i \(0.431906\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −0.372281 −0.0424254
\(78\) 0 0
\(79\) −3.25544 −0.366265 −0.183133 0.983088i \(-0.558624\pi\)
−0.183133 + 0.983088i \(0.558624\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.7446 1.39890 0.699449 0.714683i \(-0.253429\pi\)
0.699449 + 0.714683i \(0.253429\pi\)
\(84\) 0 0
\(85\) 1.62772 0.176551
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.48913 0.793846 0.396923 0.917852i \(-0.370078\pi\)
0.396923 + 0.917852i \(0.370078\pi\)
\(90\) 0 0
\(91\) 1.00000 0.104828
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −7.11684 −0.730173
\(96\) 0 0
\(97\) 7.48913 0.760405 0.380203 0.924903i \(-0.375854\pi\)
0.380203 + 0.924903i \(0.375854\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 11.1168 1.09538 0.547688 0.836683i \(-0.315508\pi\)
0.547688 + 0.836683i \(0.315508\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −10.0000 −0.966736 −0.483368 0.875417i \(-0.660587\pi\)
−0.483368 + 0.875417i \(0.660587\pi\)
\(108\) 0 0
\(109\) −13.1168 −1.25637 −0.628183 0.778066i \(-0.716201\pi\)
−0.628183 + 0.778066i \(0.716201\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.48913 −0.892662 −0.446331 0.894868i \(-0.647270\pi\)
−0.446331 + 0.894868i \(0.647270\pi\)
\(114\) 0 0
\(115\) −19.1168 −1.78265
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.372281 0.0341270
\(120\) 0 0
\(121\) −10.8614 −0.987401
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −39.8614 −3.56531
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −18.3723 −1.60519 −0.802597 0.596522i \(-0.796549\pi\)
−0.802597 + 0.596522i \(0.796549\pi\)
\(132\) 0 0
\(133\) −1.62772 −0.141141
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.8614 −1.35513 −0.677566 0.735462i \(-0.736965\pi\)
−0.677566 + 0.735462i \(0.736965\pi\)
\(138\) 0 0
\(139\) 14.2337 1.20729 0.603643 0.797255i \(-0.293715\pi\)
0.603643 + 0.797255i \(0.293715\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.372281 −0.0311317
\(144\) 0 0
\(145\) 45.3505 3.76616
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 5.48913 0.449687 0.224843 0.974395i \(-0.427813\pi\)
0.224843 + 0.974395i \(0.427813\pi\)
\(150\) 0 0
\(151\) −18.3723 −1.49512 −0.747558 0.664197i \(-0.768774\pi\)
−0.747558 + 0.664197i \(0.768774\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −3.25544 −0.261483
\(156\) 0 0
\(157\) 11.6277 0.927993 0.463996 0.885837i \(-0.346415\pi\)
0.463996 + 0.885837i \(0.346415\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.37228 −0.344584
\(162\) 0 0
\(163\) 8.74456 0.684927 0.342464 0.939531i \(-0.388739\pi\)
0.342464 + 0.939531i \(0.388739\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 19.1168 1.47931 0.739653 0.672989i \(-0.234990\pi\)
0.739653 + 0.672989i \(0.234990\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −22.0000 −1.67263 −0.836315 0.548250i \(-0.815294\pi\)
−0.836315 + 0.548250i \(0.815294\pi\)
\(174\) 0 0
\(175\) −14.1168 −1.06713
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.23369 0.615415 0.307707 0.951481i \(-0.400438\pi\)
0.307707 + 0.951481i \(0.400438\pi\)
\(180\) 0 0
\(181\) −23.4891 −1.74593 −0.872966 0.487780i \(-0.837807\pi\)
−0.872966 + 0.487780i \(0.837807\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.62772 0.119672
\(186\) 0 0
\(187\) −0.138593 −0.0101350
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −18.6060 −1.34628 −0.673140 0.739515i \(-0.735055\pi\)
−0.673140 + 0.739515i \(0.735055\pi\)
\(192\) 0 0
\(193\) −19.4891 −1.40286 −0.701429 0.712739i \(-0.747454\pi\)
−0.701429 + 0.712739i \(0.747454\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −7.25544 −0.516929 −0.258464 0.966021i \(-0.583216\pi\)
−0.258464 + 0.966021i \(0.583216\pi\)
\(198\) 0 0
\(199\) −5.62772 −0.398938 −0.199469 0.979904i \(-0.563922\pi\)
−0.199469 + 0.979904i \(0.563922\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 10.3723 0.727991
\(204\) 0 0
\(205\) −26.2337 −1.83224
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.605969 0.0419158
\(210\) 0 0
\(211\) −11.1168 −0.765315 −0.382658 0.923890i \(-0.624991\pi\)
−0.382658 + 0.923890i \(0.624991\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −7.11684 −0.485365
\(216\) 0 0
\(217\) −0.744563 −0.0505442
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.372281 0.0250424
\(222\) 0 0
\(223\) −17.4891 −1.17116 −0.585579 0.810615i \(-0.699133\pi\)
−0.585579 + 0.810615i \(0.699133\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −15.2554 −1.01254 −0.506269 0.862375i \(-0.668976\pi\)
−0.506269 + 0.862375i \(0.668976\pi\)
\(228\) 0 0
\(229\) 19.4891 1.28788 0.643939 0.765077i \(-0.277299\pi\)
0.643939 + 0.765077i \(0.277299\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −12.0000 −0.786146 −0.393073 0.919507i \(-0.628588\pi\)
−0.393073 + 0.919507i \(0.628588\pi\)
\(234\) 0 0
\(235\) −58.9783 −3.84732
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 14.7446 0.953746 0.476873 0.878972i \(-0.341770\pi\)
0.476873 + 0.878972i \(0.341770\pi\)
\(240\) 0 0
\(241\) −3.48913 −0.224754 −0.112377 0.993666i \(-0.535846\pi\)
−0.112377 + 0.993666i \(0.535846\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.37228 −0.279335
\(246\) 0 0
\(247\) −1.62772 −0.103569
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 19.1168 1.20664 0.603322 0.797498i \(-0.293843\pi\)
0.603322 + 0.797498i \(0.293843\pi\)
\(252\) 0 0
\(253\) 1.62772 0.102334
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −0.510875 −0.0318675 −0.0159337 0.999873i \(-0.505072\pi\)
−0.0159337 + 0.999873i \(0.505072\pi\)
\(258\) 0 0
\(259\) 0.372281 0.0231324
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −9.25544 −0.570715 −0.285357 0.958421i \(-0.592112\pi\)
−0.285357 + 0.958421i \(0.592112\pi\)
\(264\) 0 0
\(265\) 38.2337 2.34868
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 15.4891 0.944389 0.472194 0.881494i \(-0.343462\pi\)
0.472194 + 0.881494i \(0.343462\pi\)
\(270\) 0 0
\(271\) −26.2337 −1.59358 −0.796792 0.604254i \(-0.793471\pi\)
−0.796792 + 0.604254i \(0.793471\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.25544 0.316915
\(276\) 0 0
\(277\) 18.7446 1.12625 0.563126 0.826371i \(-0.309599\pi\)
0.563126 + 0.826371i \(0.309599\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 26.2337 1.56497 0.782485 0.622669i \(-0.213952\pi\)
0.782485 + 0.622669i \(0.213952\pi\)
\(282\) 0 0
\(283\) −22.9783 −1.36592 −0.682958 0.730458i \(-0.739307\pi\)
−0.682958 + 0.730458i \(0.739307\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) −16.8614 −0.991847
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −7.48913 −0.437519 −0.218760 0.975779i \(-0.570201\pi\)
−0.218760 + 0.975779i \(0.570201\pi\)
\(294\) 0 0
\(295\) 38.2337 2.22605
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.37228 −0.252856
\(300\) 0 0
\(301\) −1.62772 −0.0938201
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −22.3723 −1.28103
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −4.00000 −0.226819 −0.113410 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −18.2337 −1.02411 −0.512053 0.858954i \(-0.671115\pi\)
−0.512053 + 0.858954i \(0.671115\pi\)
\(318\) 0 0
\(319\) −3.86141 −0.216197
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −0.605969 −0.0337170
\(324\) 0 0
\(325\) −14.1168 −0.783062
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −13.4891 −0.743680
\(330\) 0 0
\(331\) −10.2337 −0.562494 −0.281247 0.959635i \(-0.590748\pi\)
−0.281247 + 0.959635i \(0.590748\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −52.4674 −2.86660
\(336\) 0 0
\(337\) −12.3723 −0.673961 −0.336981 0.941512i \(-0.609406\pi\)
−0.336981 + 0.941512i \(0.609406\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.277187 0.0150105
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −17.2554 −0.926320 −0.463160 0.886275i \(-0.653285\pi\)
−0.463160 + 0.886275i \(0.653285\pi\)
\(348\) 0 0
\(349\) 28.2337 1.51131 0.755657 0.654967i \(-0.227318\pi\)
0.755657 + 0.654967i \(0.227318\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 11.4891 0.611504 0.305752 0.952111i \(-0.401092\pi\)
0.305752 + 0.952111i \(0.401092\pi\)
\(354\) 0 0
\(355\) 43.7228 2.32057
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 4.51087 0.238075 0.119037 0.992890i \(-0.462019\pi\)
0.119037 + 0.992890i \(0.462019\pi\)
\(360\) 0 0
\(361\) −16.3505 −0.860554
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −15.8614 −0.830224
\(366\) 0 0
\(367\) −18.9783 −0.990657 −0.495328 0.868706i \(-0.664952\pi\)
−0.495328 + 0.868706i \(0.664952\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.74456 0.453995
\(372\) 0 0
\(373\) 8.97825 0.464876 0.232438 0.972611i \(-0.425330\pi\)
0.232438 + 0.972611i \(0.425330\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10.3723 0.534200
\(378\) 0 0
\(379\) −10.2337 −0.525669 −0.262835 0.964841i \(-0.584657\pi\)
−0.262835 + 0.964841i \(0.584657\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −19.8614 −1.01487 −0.507435 0.861690i \(-0.669406\pi\)
−0.507435 + 0.861690i \(0.669406\pi\)
\(384\) 0 0
\(385\) 1.62772 0.0829562
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −3.25544 −0.165057 −0.0825286 0.996589i \(-0.526300\pi\)
−0.0825286 + 0.996589i \(0.526300\pi\)
\(390\) 0 0
\(391\) −1.62772 −0.0823173
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 14.2337 0.716175
\(396\) 0 0
\(397\) −8.23369 −0.413237 −0.206618 0.978422i \(-0.566246\pi\)
−0.206618 + 0.978422i \(0.566246\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 10.2337 0.511046 0.255523 0.966803i \(-0.417752\pi\)
0.255523 + 0.966803i \(0.417752\pi\)
\(402\) 0 0
\(403\) −0.744563 −0.0370893
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.138593 −0.00686982
\(408\) 0 0
\(409\) 8.37228 0.413983 0.206991 0.978343i \(-0.433633\pi\)
0.206991 + 0.978343i \(0.433633\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8.74456 0.430292
\(414\) 0 0
\(415\) −55.7228 −2.73533
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −17.6277 −0.861170 −0.430585 0.902550i \(-0.641693\pi\)
−0.430585 + 0.902550i \(0.641693\pi\)
\(420\) 0 0
\(421\) 32.9783 1.60726 0.803631 0.595128i \(-0.202899\pi\)
0.803631 + 0.595128i \(0.202899\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −5.25544 −0.254926
\(426\) 0 0
\(427\) −5.11684 −0.247621
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.51087 −0.409954 −0.204977 0.978767i \(-0.565712\pi\)
−0.204977 + 0.978767i \(0.565712\pi\)
\(432\) 0 0
\(433\) −24.9783 −1.20038 −0.600189 0.799858i \(-0.704908\pi\)
−0.600189 + 0.799858i \(0.704908\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.11684 0.340445
\(438\) 0 0
\(439\) −26.3723 −1.25868 −0.629340 0.777130i \(-0.716675\pi\)
−0.629340 + 0.777130i \(0.716675\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −30.0000 −1.42534 −0.712672 0.701498i \(-0.752515\pi\)
−0.712672 + 0.701498i \(0.752515\pi\)
\(444\) 0 0
\(445\) −32.7446 −1.55224
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 15.1168 0.713408 0.356704 0.934217i \(-0.383900\pi\)
0.356704 + 0.934217i \(0.383900\pi\)
\(450\) 0 0
\(451\) 2.23369 0.105180
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4.37228 −0.204976
\(456\) 0 0
\(457\) 1.25544 0.0587269 0.0293634 0.999569i \(-0.490652\pi\)
0.0293634 + 0.999569i \(0.490652\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −5.11684 −0.238315 −0.119158 0.992875i \(-0.538019\pi\)
−0.119158 + 0.992875i \(0.538019\pi\)
\(462\) 0 0
\(463\) 15.1168 0.702539 0.351270 0.936274i \(-0.385750\pi\)
0.351270 + 0.936274i \(0.385750\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −33.3505 −1.54328 −0.771639 0.636060i \(-0.780563\pi\)
−0.771639 + 0.636060i \(0.780563\pi\)
\(468\) 0 0
\(469\) −12.0000 −0.554109
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.605969 0.0278625
\(474\) 0 0
\(475\) 22.9783 1.05431
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −28.6060 −1.30704 −0.653520 0.756909i \(-0.726708\pi\)
−0.653520 + 0.756909i \(0.726708\pi\)
\(480\) 0 0
\(481\) 0.372281 0.0169746
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −32.7446 −1.48685
\(486\) 0 0
\(487\) −8.00000 −0.362515 −0.181257 0.983436i \(-0.558017\pi\)
−0.181257 + 0.983436i \(0.558017\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 30.7446 1.38748 0.693741 0.720224i \(-0.255961\pi\)
0.693741 + 0.720224i \(0.255961\pi\)
\(492\) 0 0
\(493\) 3.86141 0.173909
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.0000 0.448561
\(498\) 0 0
\(499\) 14.9783 0.670519 0.335259 0.942126i \(-0.391176\pi\)
0.335259 + 0.942126i \(0.391176\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 18.9783 0.846198 0.423099 0.906083i \(-0.360942\pi\)
0.423099 + 0.906083i \(0.360942\pi\)
\(504\) 0 0
\(505\) −8.74456 −0.389128
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0.372281 0.0165011 0.00825054 0.999966i \(-0.497374\pi\)
0.00825054 + 0.999966i \(0.497374\pi\)
\(510\) 0 0
\(511\) −3.62772 −0.160481
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −48.6060 −2.14183
\(516\) 0 0
\(517\) 5.02175 0.220856
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 26.8832 1.17777 0.588886 0.808216i \(-0.299567\pi\)
0.588886 + 0.808216i \(0.299567\pi\)
\(522\) 0 0
\(523\) 23.7228 1.03733 0.518663 0.854979i \(-0.326430\pi\)
0.518663 + 0.854979i \(0.326430\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.277187 −0.0120744
\(528\) 0 0
\(529\) −3.88316 −0.168833
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −6.00000 −0.259889
\(534\) 0 0
\(535\) 43.7228 1.89030
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.372281 0.0160353
\(540\) 0 0
\(541\) 0.372281 0.0160056 0.00800281 0.999968i \(-0.497453\pi\)
0.00800281 + 0.999968i \(0.497453\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 57.3505 2.45663
\(546\) 0 0
\(547\) 14.9783 0.640424 0.320212 0.947346i \(-0.396246\pi\)
0.320212 + 0.947346i \(0.396246\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −16.8832 −0.719247
\(552\) 0 0
\(553\) 3.25544 0.138435
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 8.74456 0.370519 0.185260 0.982690i \(-0.440687\pi\)
0.185260 + 0.982690i \(0.440687\pi\)
\(558\) 0 0
\(559\) −1.62772 −0.0688452
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 11.1168 0.468519 0.234260 0.972174i \(-0.424733\pi\)
0.234260 + 0.972174i \(0.424733\pi\)
\(564\) 0 0
\(565\) 41.4891 1.74546
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 8.74456 0.366591 0.183296 0.983058i \(-0.441323\pi\)
0.183296 + 0.983058i \(0.441323\pi\)
\(570\) 0 0
\(571\) −12.0000 −0.502184 −0.251092 0.967963i \(-0.580790\pi\)
−0.251092 + 0.967963i \(0.580790\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 61.7228 2.57402
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −12.7446 −0.528734
\(582\) 0 0
\(583\) −3.25544 −0.134826
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −19.7228 −0.814048 −0.407024 0.913418i \(-0.633433\pi\)
−0.407024 + 0.913418i \(0.633433\pi\)
\(588\) 0 0
\(589\) 1.21194 0.0499371
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −2.74456 −0.112706 −0.0563528 0.998411i \(-0.517947\pi\)
−0.0563528 + 0.998411i \(0.517947\pi\)
\(594\) 0 0
\(595\) −1.62772 −0.0667300
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 45.1168 1.84342 0.921712 0.387875i \(-0.126791\pi\)
0.921712 + 0.387875i \(0.126791\pi\)
\(600\) 0 0
\(601\) 16.5109 0.673493 0.336746 0.941595i \(-0.390674\pi\)
0.336746 + 0.941595i \(0.390674\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 47.4891 1.93071
\(606\) 0 0
\(607\) 7.11684 0.288864 0.144432 0.989515i \(-0.453865\pi\)
0.144432 + 0.989515i \(0.453865\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −13.4891 −0.545712
\(612\) 0 0
\(613\) 0.372281 0.0150363 0.00751815 0.999972i \(-0.497607\pi\)
0.00751815 + 0.999972i \(0.497607\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 15.8614 0.638556 0.319278 0.947661i \(-0.396560\pi\)
0.319278 + 0.947661i \(0.396560\pi\)
\(618\) 0 0
\(619\) −2.37228 −0.0953500 −0.0476750 0.998863i \(-0.515181\pi\)
−0.0476750 + 0.998863i \(0.515181\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.48913 −0.300045
\(624\) 0 0
\(625\) 103.701 4.14804
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.138593 0.00552608
\(630\) 0 0
\(631\) 16.6060 0.661073 0.330537 0.943793i \(-0.392770\pi\)
0.330537 + 0.943793i \(0.392770\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −34.9783 −1.38807
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 8.74456 0.345389 0.172695 0.984975i \(-0.444753\pi\)
0.172695 + 0.984975i \(0.444753\pi\)
\(642\) 0 0
\(643\) −27.1168 −1.06938 −0.534692 0.845047i \(-0.679572\pi\)
−0.534692 + 0.845047i \(0.679572\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −40.4674 −1.59094 −0.795468 0.605995i \(-0.792775\pi\)
−0.795468 + 0.605995i \(0.792775\pi\)
\(648\) 0 0
\(649\) −3.25544 −0.127787
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 38.8397 1.51991 0.759957 0.649974i \(-0.225220\pi\)
0.759957 + 0.649974i \(0.225220\pi\)
\(654\) 0 0
\(655\) 80.3288 3.13871
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −17.7228 −0.690383 −0.345191 0.938532i \(-0.612186\pi\)
−0.345191 + 0.938532i \(0.612186\pi\)
\(660\) 0 0
\(661\) −24.2337 −0.942581 −0.471291 0.881978i \(-0.656212\pi\)
−0.471291 + 0.881978i \(0.656212\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 7.11684 0.275979
\(666\) 0 0
\(667\) −45.3505 −1.75598
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.90491 0.0735381
\(672\) 0 0
\(673\) 45.1168 1.73913 0.869563 0.493822i \(-0.164400\pi\)
0.869563 + 0.493822i \(0.164400\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 2.00000 0.0768662 0.0384331 0.999261i \(-0.487763\pi\)
0.0384331 + 0.999261i \(0.487763\pi\)
\(678\) 0 0
\(679\) −7.48913 −0.287406
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.60597 0.0997146 0.0498573 0.998756i \(-0.484123\pi\)
0.0498573 + 0.998756i \(0.484123\pi\)
\(684\) 0 0
\(685\) 69.3505 2.64975
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 8.74456 0.333141
\(690\) 0 0
\(691\) 10.9783 0.417632 0.208816 0.977955i \(-0.433039\pi\)
0.208816 + 0.977955i \(0.433039\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −62.2337 −2.36066
\(696\) 0 0
\(697\) −2.23369 −0.0846070
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −36.7446 −1.38782 −0.693911 0.720060i \(-0.744114\pi\)
−0.693911 + 0.720060i \(0.744114\pi\)
\(702\) 0 0
\(703\) −0.605969 −0.0228546
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.00000 −0.0752177
\(708\) 0 0
\(709\) 35.4891 1.33282 0.666411 0.745585i \(-0.267830\pi\)
0.666411 + 0.745585i \(0.267830\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 3.25544 0.121917
\(714\) 0 0
\(715\) 1.62772 0.0608732
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 34.9783 1.30447 0.652234 0.758017i \(-0.273832\pi\)
0.652234 + 0.758017i \(0.273832\pi\)
\(720\) 0 0
\(721\) −11.1168 −0.414013
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −146.424 −5.43805
\(726\) 0 0
\(727\) −49.3505 −1.83031 −0.915155 0.403102i \(-0.867932\pi\)
−0.915155 + 0.403102i \(0.867932\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −0.605969 −0.0224126
\(732\) 0 0
\(733\) 46.7446 1.72655 0.863275 0.504734i \(-0.168409\pi\)
0.863275 + 0.504734i \(0.168409\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 4.46738 0.164558
\(738\) 0 0
\(739\) −16.7446 −0.615959 −0.307979 0.951393i \(-0.599653\pi\)
−0.307979 + 0.951393i \(0.599653\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 26.7446 0.981163 0.490581 0.871395i \(-0.336784\pi\)
0.490581 + 0.871395i \(0.336784\pi\)
\(744\) 0 0
\(745\) −24.0000 −0.879292
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10.0000 0.365392
\(750\) 0 0
\(751\) 10.9783 0.400602 0.200301 0.979734i \(-0.435808\pi\)
0.200301 + 0.979734i \(0.435808\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 80.3288 2.92346
\(756\) 0 0
\(757\) −45.7228 −1.66182 −0.830912 0.556404i \(-0.812181\pi\)
−0.830912 + 0.556404i \(0.812181\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 45.7228 1.65745 0.828725 0.559656i \(-0.189067\pi\)
0.828725 + 0.559656i \(0.189067\pi\)
\(762\) 0 0
\(763\) 13.1168 0.474862
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 8.74456 0.315748
\(768\) 0 0
\(769\) 32.8397 1.18423 0.592114 0.805854i \(-0.298293\pi\)
0.592114 + 0.805854i \(0.298293\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −10.1386 −0.364660 −0.182330 0.983237i \(-0.558364\pi\)
−0.182330 + 0.983237i \(0.558364\pi\)
\(774\) 0 0
\(775\) 10.5109 0.377562
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.76631 0.349914
\(780\) 0 0
\(781\) −3.72281 −0.133213
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −50.8397 −1.81455
\(786\) 0 0
\(787\) −42.3723 −1.51041 −0.755204 0.655489i \(-0.772462\pi\)
−0.755204 + 0.655489i \(0.772462\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9.48913 0.337394
\(792\) 0 0
\(793\) −5.11684 −0.181704
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 3.76631 0.133410 0.0667048 0.997773i \(-0.478751\pi\)
0.0667048 + 0.997773i \(0.478751\pi\)
\(798\) 0 0
\(799\) −5.02175 −0.177657
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 1.35053 0.0476592
\(804\) 0 0
\(805\) 19.1168 0.673780
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −33.2119 −1.16767 −0.583835 0.811872i \(-0.698448\pi\)
−0.583835 + 0.811872i \(0.698448\pi\)
\(810\) 0 0
\(811\) −13.3505 −0.468801 −0.234400 0.972140i \(-0.575313\pi\)
−0.234400 + 0.972140i \(0.575313\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −38.2337 −1.33927
\(816\) 0 0
\(817\) 2.64947 0.0926932
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 9.02175 0.314861 0.157431 0.987530i \(-0.449679\pi\)
0.157431 + 0.987530i \(0.449679\pi\)
\(822\) 0 0
\(823\) −23.7228 −0.826925 −0.413463 0.910521i \(-0.635681\pi\)
−0.413463 + 0.910521i \(0.635681\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 27.3505 0.951071 0.475536 0.879696i \(-0.342254\pi\)
0.475536 + 0.879696i \(0.342254\pi\)
\(828\) 0 0
\(829\) −56.3723 −1.95789 −0.978945 0.204124i \(-0.934566\pi\)
−0.978945 + 0.204124i \(0.934566\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −0.372281 −0.0128988
\(834\) 0 0
\(835\) −83.5842 −2.89255
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −13.4891 −0.465696 −0.232848 0.972513i \(-0.574805\pi\)
−0.232848 + 0.972513i \(0.574805\pi\)
\(840\) 0 0
\(841\) 78.5842 2.70980
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.37228 −0.150411
\(846\) 0 0
\(847\) 10.8614 0.373202
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −1.62772 −0.0557975
\(852\) 0 0
\(853\) −17.7228 −0.606818 −0.303409 0.952860i \(-0.598125\pi\)
−0.303409 + 0.952860i \(0.598125\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 32.9783 1.12652 0.563258 0.826281i \(-0.309548\pi\)
0.563258 + 0.826281i \(0.309548\pi\)
\(858\) 0 0
\(859\) 26.2337 0.895082 0.447541 0.894263i \(-0.352300\pi\)
0.447541 + 0.894263i \(0.352300\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −39.2119 −1.33479 −0.667395 0.744704i \(-0.732591\pi\)
−0.667395 + 0.744704i \(0.732591\pi\)
\(864\) 0 0
\(865\) 96.1902 3.27056
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −1.21194 −0.0411122
\(870\) 0 0
\(871\) −12.0000 −0.406604
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 39.8614 1.34756
\(876\) 0 0
\(877\) −36.9783 −1.24867 −0.624333 0.781158i \(-0.714629\pi\)
−0.624333 + 0.781158i \(0.714629\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −32.3723 −1.09065 −0.545325 0.838225i \(-0.683594\pi\)
−0.545325 + 0.838225i \(0.683594\pi\)
\(882\) 0 0
\(883\) −7.86141 −0.264557 −0.132279 0.991213i \(-0.542229\pi\)
−0.132279 + 0.991213i \(0.542229\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 19.7228 0.662227 0.331114 0.943591i \(-0.392576\pi\)
0.331114 + 0.943591i \(0.392576\pi\)
\(888\) 0 0
\(889\) −8.00000 −0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 21.9565 0.734746
\(894\) 0 0
\(895\) −36.0000 −1.20335
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −7.72281 −0.257570
\(900\) 0 0
\(901\) 3.25544 0.108454
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 102.701 3.41390
\(906\) 0 0
\(907\) 20.0000 0.664089 0.332045 0.943264i \(-0.392262\pi\)
0.332045 + 0.943264i \(0.392262\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −20.3723 −0.674964 −0.337482 0.941332i \(-0.609575\pi\)
−0.337482 + 0.941332i \(0.609575\pi\)
\(912\) 0 0
\(913\) 4.74456 0.157022
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 18.3723 0.606706
\(918\) 0 0
\(919\) 17.7663 0.586057 0.293028 0.956104i \(-0.405337\pi\)
0.293028 + 0.956104i \(0.405337\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 10.0000 0.329154
\(924\) 0 0
\(925\) −5.25544 −0.172798
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 15.4891 0.508182 0.254091 0.967180i \(-0.418224\pi\)
0.254091 + 0.967180i \(0.418224\pi\)
\(930\) 0 0
\(931\) 1.62772 0.0533463
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.605969 0.0198173
\(936\) 0 0
\(937\) −4.51087 −0.147364 −0.0736819 0.997282i \(-0.523475\pi\)
−0.0736819 + 0.997282i \(0.523475\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 0 0
\(943\) 26.2337 0.854286
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18.6060 −0.604613 −0.302306 0.953211i \(-0.597757\pi\)
−0.302306 + 0.953211i \(0.597757\pi\)
\(948\) 0 0
\(949\) −3.62772 −0.117761
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −45.9565 −1.48868 −0.744339 0.667802i \(-0.767235\pi\)
−0.744339 + 0.667802i \(0.767235\pi\)
\(954\) 0 0
\(955\) 81.3505 2.63244
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 15.8614 0.512192
\(960\) 0 0
\(961\) −30.4456 −0.982117
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 85.2119 2.74307
\(966\) 0 0
\(967\) −47.1168 −1.51518 −0.757588 0.652733i \(-0.773622\pi\)
−0.757588 + 0.652733i \(0.773622\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −48.0000 −1.54039 −0.770197 0.637806i \(-0.779842\pi\)
−0.770197 + 0.637806i \(0.779842\pi\)
\(972\) 0 0
\(973\) −14.2337 −0.456311
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.11684 −0.0997167 −0.0498583 0.998756i \(-0.515877\pi\)
−0.0498583 + 0.998756i \(0.515877\pi\)
\(978\) 0 0
\(979\) 2.78806 0.0891068
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −21.6277 −0.689817 −0.344909 0.938636i \(-0.612090\pi\)
−0.344909 + 0.938636i \(0.612090\pi\)
\(984\) 0 0
\(985\) 31.7228 1.01077
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 7.11684 0.226302
\(990\) 0 0
\(991\) −50.7011 −1.61057 −0.805286 0.592886i \(-0.797988\pi\)
−0.805286 + 0.592886i \(0.797988\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 24.6060 0.780062
\(996\) 0 0
\(997\) −38.4674 −1.21827 −0.609137 0.793065i \(-0.708484\pi\)
−0.609137 + 0.793065i \(0.708484\pi\)
\(998\) 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 6552.2.a.bb.1.1 2
3.2 odd 2 6552.2.a.bm.1.2 yes 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6552.2.a.bb.1.1 2 1.1 even 1 trivial
6552.2.a.bm.1.2 yes 2 3.2 odd 2