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Properties

Label 9200.2.a.s.1.1
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
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] = [9200,2,Mod(1,9200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("9200.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9200.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: \(73.4623698596\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1150)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 9200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{7} -3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{7} -3.00000 q^{9} +3.00000 q^{11} +3.00000 q^{13} +8.00000 q^{17} +7.00000 q^{19} -1.00000 q^{23} +7.00000 q^{29} -10.0000 q^{31} -4.00000 q^{37} +11.0000 q^{41} +5.00000 q^{43} -10.0000 q^{47} -6.00000 q^{49} +6.00000 q^{53} +8.00000 q^{59} -8.00000 q^{61} +3.00000 q^{63} -10.0000 q^{71} +11.0000 q^{73} -3.00000 q^{77} -3.00000 q^{79} +9.00000 q^{81} +1.00000 q^{83} -6.00000 q^{89} -3.00000 q^{91} -14.0000 q^{97} -9.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 − 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 3.00000 0.904534 0.452267 − 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) 3.00000 0.832050 0.416025 − 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 8.00000 1.94029 0.970143 − 0.242536i \(-0.0779791\pi\)
0.970143 + 0.242536i \(0.0779791\pi\)
\(18\) 0 0
\(19\) 7.00000 1.60591 0.802955 − 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.00000 1.29987 0.649934 − 0.759991i \(-0.274797\pi\)
0.649934 + 0.759991i \(0.274797\pi\)
\(30\) 0 0
\(31\) −10.0000 −1.79605 −0.898027 − 0.439941i \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 − 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 11.0000 1.71791 0.858956 − 0.512050i \(-0.171114\pi\)
0.858956 + 0.512050i \(0.171114\pi\)
\(42\) 0 0
\(43\) 5.00000 0.762493 0.381246 − 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −10.0000 −1.45865 −0.729325 − 0.684167i \(-0.760166\pi\)
−0.729325 + 0.684167i \(0.760166\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 8.00000 1.04151 0.520756 − 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 − 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) 3.00000 0.377964
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 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
\(73\) 11.0000 1.28745 0.643726 − 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −3.00000 −0.341882
\(78\) 0 0
\(79\) −3.00000 −0.337526 −0.168763 − 0.985657i \(-0.553977\pi\)
−0.168763 + 0.985657i \(0.553977\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 1.00000 0.109764 0.0548821 − 0.998493i \(-0.482522\pi\)
0.0548821 + 0.998493i \(0.482522\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −6.00000 −0.635999 −0.317999 − 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 0 0
\(91\) −3.00000 −0.314485
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 − 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) −9.00000 −0.904534
\(100\) 0 0
\(101\) 10.0000 0.995037 0.497519 − 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 0 0
\(103\) −7.00000 −0.689730 −0.344865 − 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −20.0000 −1.93347 −0.966736 − 0.255774i \(-0.917670\pi\)
−0.966736 + 0.255774i \(0.917670\pi\)
\(108\) 0 0
\(109\) 20.0000 1.91565 0.957826 − 0.287348i \(-0.0927736\pi\)
0.957826 + 0.287348i \(0.0927736\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 − 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −9.00000 −0.832050
\(118\) 0 0
\(119\) −8.00000 −0.733359
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 − 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 18.0000 1.57267 0.786334 − 0.617802i \(-0.211977\pi\)
0.786334 + 0.617802i \(0.211977\pi\)
\(132\) 0 0
\(133\) −7.00000 −0.606977
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 0.512615 0.256307 − 0.966595i \(-0.417494\pi\)
0.256307 + 0.966595i \(0.417494\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 − 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 9.00000 0.752618
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 6.00000 0.491539 0.245770 − 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 0 0
\(151\) −2.00000 −0.162758 −0.0813788 − 0.996683i \(-0.525932\pi\)
−0.0813788 + 0.996683i \(0.525932\pi\)
\(152\) 0 0
\(153\) −24.0000 −1.94029
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2.00000 0.159617 0.0798087 − 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) −2.00000 −0.156652 −0.0783260 − 0.996928i \(-0.524958\pi\)
−0.0783260 + 0.996928i \(0.524958\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.0000 1.08335 0.541676 − 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) −21.0000 −1.60591
\(172\) 0 0
\(173\) −11.0000 −0.836315 −0.418157 − 0.908375i \(-0.637324\pi\)
−0.418157 + 0.908375i \(0.637324\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 6.00000 0.448461 0.224231 − 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) 0 0
\(181\) −4.00000 −0.297318 −0.148659 − 0.988889i \(-0.547496\pi\)
−0.148659 + 0.988889i \(0.547496\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 24.0000 1.75505
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 15.0000 1.08536 0.542681 − 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) 0 0
\(193\) 6.00000 0.431889 0.215945 − 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 13.0000 0.926212 0.463106 − 0.886303i \(-0.346735\pi\)
0.463106 + 0.886303i \(0.346735\pi\)
\(198\) 0 0
\(199\) 9.00000 0.637993 0.318997 − 0.947756i \(-0.396654\pi\)
0.318997 + 0.947756i \(0.396654\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −7.00000 −0.491304
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.00000 0.208514
\(208\) 0 0
\(209\) 21.0000 1.45260
\(210\) 0 0
\(211\) 10.0000 0.688428 0.344214 − 0.938891i \(-0.388145\pi\)
0.344214 + 0.938891i \(0.388145\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 10.0000 0.678844
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 24.0000 1.61441
\(222\) 0 0
\(223\) 6.00000 0.401790 0.200895 − 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.00000 −0.265489 −0.132745 − 0.991150i \(-0.542379\pi\)
−0.132745 + 0.991150i \(0.542379\pi\)
\(228\) 0 0
\(229\) 18.0000 1.18947 0.594737 − 0.803921i \(-0.297256\pi\)
0.594737 + 0.803921i \(0.297256\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −11.0000 −0.720634 −0.360317 − 0.932830i \(-0.617331\pi\)
−0.360317 + 0.932830i \(0.617331\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 − 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 2.00000 0.128831 0.0644157 − 0.997923i \(-0.479482\pi\)
0.0644157 + 0.997923i \(0.479482\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 21.0000 1.33620
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 16.0000 1.00991 0.504956 − 0.863145i \(-0.331509\pi\)
0.504956 + 0.863145i \(0.331509\pi\)
\(252\) 0 0
\(253\) −3.00000 −0.188608
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.00000 0.124757 0.0623783 − 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) −21.0000 −1.29987
\(262\) 0 0
\(263\) 16.0000 0.986602 0.493301 − 0.869859i \(-0.335790\pi\)
0.493301 + 0.869859i \(0.335790\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −9.00000 −0.548740 −0.274370 − 0.961624i \(-0.588469\pi\)
−0.274370 + 0.961624i \(0.588469\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 − 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −19.0000 −1.14160 −0.570800 − 0.821089i \(-0.693367\pi\)
−0.570800 + 0.821089i \(0.693367\pi\)
\(278\) 0 0
\(279\) 30.0000 1.79605
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 − 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 0 0
\(283\) 24.0000 1.42665 0.713326 − 0.700832i \(-0.247188\pi\)
0.713326 + 0.700832i \(0.247188\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.0000 −0.649309
\(288\) 0 0
\(289\) 47.0000 2.76471
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 24.0000 1.40209 0.701047 − 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −3.00000 −0.173494
\(300\) 0 0
\(301\) −5.00000 −0.288195
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −24.0000 −1.36975 −0.684876 − 0.728659i \(-0.740144\pi\)
−0.684876 + 0.728659i \(0.740144\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 28.0000 1.58773 0.793867 − 0.608091i \(-0.208065\pi\)
0.793867 + 0.608091i \(0.208065\pi\)
\(312\) 0 0
\(313\) −28.0000 −1.58265 −0.791327 − 0.611393i \(-0.790609\pi\)
−0.791327 + 0.611393i \(0.790609\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.00000 −0.168497 −0.0842484 − 0.996445i \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) 0 0
\(319\) 21.0000 1.17577
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 56.0000 3.11592
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 10.0000 0.551318
\(330\) 0 0
\(331\) 14.0000 0.769510 0.384755 − 0.923019i \(-0.374286\pi\)
0.384755 + 0.923019i \(0.374286\pi\)
\(332\) 0 0
\(333\) 12.0000 0.657596
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −30.0000 −1.63420 −0.817102 − 0.576493i \(-0.804421\pi\)
−0.817102 + 0.576493i \(0.804421\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −30.0000 −1.62459
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 32.0000 1.71785 0.858925 − 0.512101i \(-0.171133\pi\)
0.858925 + 0.512101i \(0.171133\pi\)
\(348\) 0 0
\(349\) 11.0000 0.588817 0.294408 − 0.955680i \(-0.404877\pi\)
0.294408 + 0.955680i \(0.404877\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 27.0000 1.43706 0.718532 − 0.695493i \(-0.244814\pi\)
0.718532 + 0.695493i \(0.244814\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 17.0000 0.897226 0.448613 − 0.893726i \(-0.351918\pi\)
0.448613 + 0.893726i \(0.351918\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −17.0000 −0.887393 −0.443696 − 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) 0 0
\(369\) −33.0000 −1.71791
\(370\) 0 0
\(371\) −6.00000 −0.311504
\(372\) 0 0
\(373\) 36.0000 1.86401 0.932005 − 0.362446i \(-0.118058\pi\)
0.932005 + 0.362446i \(0.118058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 21.0000 1.08156
\(378\) 0 0
\(379\) 28.0000 1.43826 0.719132 − 0.694874i \(-0.244540\pi\)
0.719132 + 0.694874i \(0.244540\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −21.0000 −1.07305 −0.536525 − 0.843884i \(-0.680263\pi\)
−0.536525 + 0.843884i \(0.680263\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −15.0000 −0.762493
\(388\) 0 0
\(389\) −30.0000 −1.52106 −0.760530 − 0.649303i \(-0.775061\pi\)
−0.760530 + 0.649303i \(0.775061\pi\)
\(390\) 0 0
\(391\) −8.00000 −0.404577
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −6.00000 −0.301131 −0.150566 − 0.988600i \(-0.548110\pi\)
−0.150566 + 0.988600i \(0.548110\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −8.00000 −0.399501 −0.199750 − 0.979847i \(-0.564013\pi\)
−0.199750 + 0.979847i \(0.564013\pi\)
\(402\) 0 0
\(403\) −30.0000 −1.49441
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −12.0000 −0.594818
\(408\) 0 0
\(409\) 9.00000 0.445021 0.222511 − 0.974930i \(-0.428575\pi\)
0.222511 + 0.974930i \(0.428575\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.00000 −0.393654
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −27.0000 −1.31904 −0.659518 − 0.751689i \(-0.729240\pi\)
−0.659518 + 0.751689i \(0.729240\pi\)
\(420\) 0 0
\(421\) −2.00000 −0.0974740 −0.0487370 − 0.998812i \(-0.515520\pi\)
−0.0487370 + 0.998812i \(0.515520\pi\)
\(422\) 0 0
\(423\) 30.0000 1.45865
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 8.00000 0.387147
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −8.00000 −0.385346 −0.192673 − 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 0 0
\(433\) −16.0000 −0.768911 −0.384455 − 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7.00000 −0.334855
\(438\) 0 0
\(439\) 12.0000 0.572729 0.286364 − 0.958121i \(-0.407553\pi\)
0.286364 + 0.958121i \(0.407553\pi\)
\(440\) 0 0
\(441\) 18.0000 0.857143
\(442\) 0 0
\(443\) −18.0000 −0.855206 −0.427603 − 0.903967i \(-0.640642\pi\)
−0.427603 + 0.903967i \(0.640642\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 − 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) 33.0000 1.55391
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −10.0000 −0.467780 −0.233890 − 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 3.00000 0.139724 0.0698620 − 0.997557i \(-0.477744\pi\)
0.0698620 + 0.997557i \(0.477744\pi\)
\(462\) 0 0
\(463\) −20.0000 −0.929479 −0.464739 − 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −13.0000 −0.601568 −0.300784 − 0.953692i \(-0.597248\pi\)
−0.300784 + 0.953692i \(0.597248\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 15.0000 0.689701
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −18.0000 −0.824163
\(478\) 0 0
\(479\) −17.0000 −0.776750 −0.388375 − 0.921501i \(-0.626963\pi\)
−0.388375 + 0.921501i \(0.626963\pi\)
\(480\) 0 0
\(481\) −12.0000 −0.547153
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 18.0000 0.815658 0.407829 − 0.913058i \(-0.366286\pi\)
0.407829 + 0.913058i \(0.366286\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −24.0000 −1.08310 −0.541552 − 0.840667i \(-0.682163\pi\)
−0.541552 + 0.840667i \(0.682163\pi\)
\(492\) 0 0
\(493\) 56.0000 2.52211
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 10.0000 0.448561
\(498\) 0 0
\(499\) −6.00000 −0.268597 −0.134298 − 0.990941i \(-0.542878\pi\)
−0.134298 + 0.990941i \(0.542878\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −27.0000 −1.20387 −0.601935 − 0.798545i \(-0.705603\pi\)
−0.601935 + 0.798545i \(0.705603\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 18.0000 0.797836 0.398918 − 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) −11.0000 −0.486611
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −30.0000 −1.31940
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −32.0000 −1.40195 −0.700973 − 0.713188i \(-0.747251\pi\)
−0.700973 + 0.713188i \(0.747251\pi\)
\(522\) 0 0
\(523\) −1.00000 −0.0437269 −0.0218635 − 0.999761i \(-0.506960\pi\)
−0.0218635 + 0.999761i \(0.506960\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −80.0000 −3.48485
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −24.0000 −1.04151
\(532\) 0 0
\(533\) 33.0000 1.42939
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) 19.0000 0.816874 0.408437 − 0.912787i \(-0.366074\pi\)
0.408437 + 0.912787i \(0.366074\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 26.0000 1.11168 0.555840 − 0.831289i \(-0.312397\pi\)
0.555840 + 0.831289i \(0.312397\pi\)
\(548\) 0 0
\(549\) 24.0000 1.02430
\(550\) 0 0
\(551\) 49.0000 2.08747
\(552\) 0 0
\(553\) 3.00000 0.127573
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −24.0000 −1.01691 −0.508456 − 0.861088i \(-0.669784\pi\)
−0.508456 + 0.861088i \(0.669784\pi\)
\(558\) 0 0
\(559\) 15.0000 0.634432
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −11.0000 −0.463595 −0.231797 − 0.972764i \(-0.574461\pi\)
−0.231797 + 0.972764i \(0.574461\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −9.00000 −0.377964
\(568\) 0 0
\(569\) 24.0000 1.00613 0.503066 − 0.864248i \(-0.332205\pi\)
0.503066 + 0.864248i \(0.332205\pi\)
\(570\) 0 0
\(571\) −4.00000 −0.167395 −0.0836974 − 0.996491i \(-0.526673\pi\)
−0.0836974 + 0.996491i \(0.526673\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −25.0000 −1.04076 −0.520382 − 0.853934i \(-0.674210\pi\)
−0.520382 + 0.853934i \(0.674210\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.00000 −0.0414870
\(582\) 0 0
\(583\) 18.0000 0.745484
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −32.0000 −1.32078 −0.660391 − 0.750922i \(-0.729609\pi\)
−0.660391 + 0.750922i \(0.729609\pi\)
\(588\) 0 0
\(589\) −70.0000 −2.88430
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.00000 0.0410651 0.0205325 − 0.999789i \(-0.493464\pi\)
0.0205325 + 0.999789i \(0.493464\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 14.0000 0.572024 0.286012 − 0.958226i \(-0.407670\pi\)
0.286012 + 0.958226i \(0.407670\pi\)
\(600\) 0 0
\(601\) 34.0000 1.38689 0.693444 − 0.720510i \(-0.256092\pi\)
0.693444 + 0.720510i \(0.256092\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 38.0000 1.54237 0.771186 − 0.636610i \(-0.219664\pi\)
0.771186 + 0.636610i \(0.219664\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −30.0000 −1.21367
\(612\) 0 0
\(613\) 4.00000 0.161558 0.0807792 − 0.996732i \(-0.474259\pi\)
0.0807792 + 0.996732i \(0.474259\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −12.0000 −0.483102 −0.241551 − 0.970388i \(-0.577656\pi\)
−0.241551 + 0.970388i \(0.577656\pi\)
\(618\) 0 0
\(619\) 44.0000 1.76851 0.884255 − 0.467005i \(-0.154667\pi\)
0.884255 + 0.467005i \(0.154667\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 6.00000 0.240385
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −32.0000 −1.27592
\(630\) 0 0
\(631\) 15.0000 0.597141 0.298570 − 0.954388i \(-0.403490\pi\)
0.298570 + 0.954388i \(0.403490\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −18.0000 −0.713186
\(638\) 0 0
\(639\) 30.0000 1.18678
\(640\) 0 0
\(641\) 24.0000 0.947943 0.473972 − 0.880540i \(-0.342820\pi\)
0.473972 + 0.880540i \(0.342820\pi\)
\(642\) 0 0
\(643\) −35.0000 −1.38027 −0.690133 − 0.723683i \(-0.742448\pi\)
−0.690133 + 0.723683i \(0.742448\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −10.0000 −0.393141 −0.196570 − 0.980490i \(-0.562980\pi\)
−0.196570 + 0.980490i \(0.562980\pi\)
\(648\) 0 0
\(649\) 24.0000 0.942082
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 23.0000 0.900060 0.450030 − 0.893014i \(-0.351413\pi\)
0.450030 + 0.893014i \(0.351413\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −33.0000 −1.28745
\(658\) 0 0
\(659\) 25.0000 0.973862 0.486931 − 0.873441i \(-0.338116\pi\)
0.486931 + 0.873441i \(0.338116\pi\)
\(660\) 0 0
\(661\) 6.00000 0.233373 0.116686 − 0.993169i \(-0.462773\pi\)
0.116686 + 0.993169i \(0.462773\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −7.00000 −0.271041
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) 13.0000 0.501113 0.250557 − 0.968102i \(-0.419386\pi\)
0.250557 + 0.968102i \(0.419386\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −12.0000 −0.461197 −0.230599 − 0.973049i \(-0.574068\pi\)
−0.230599 + 0.973049i \(0.574068\pi\)
\(678\) 0 0
\(679\) 14.0000 0.537271
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −2.00000 −0.0765279 −0.0382639 − 0.999268i \(-0.512183\pi\)
−0.0382639 + 0.999268i \(0.512183\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 18.0000 0.685745
\(690\) 0 0
\(691\) 4.00000 0.152167 0.0760836 − 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) 0 0
\(693\) 9.00000 0.341882
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 88.0000 3.33324
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −20.0000 −0.755390 −0.377695 − 0.925930i \(-0.623283\pi\)
−0.377695 + 0.925930i \(0.623283\pi\)
\(702\) 0 0
\(703\) −28.0000 −1.05604
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −10.0000 −0.376089
\(708\) 0 0
\(709\) 22.0000 0.826227 0.413114 − 0.910679i \(-0.364441\pi\)
0.413114 + 0.910679i \(0.364441\pi\)
\(710\) 0 0
\(711\) 9.00000 0.337526
\(712\) 0 0
\(713\) 10.0000 0.374503
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −8.00000 −0.298350 −0.149175 − 0.988811i \(-0.547662\pi\)
−0.149175 + 0.988811i \(0.547662\pi\)
\(720\) 0 0
\(721\) 7.00000 0.260694
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 16.0000 0.593407 0.296704 − 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 40.0000 1.47945
\(732\) 0 0
\(733\) −34.0000 −1.25582 −0.627909 − 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −38.0000 −1.39785 −0.698926 − 0.715194i \(-0.746338\pi\)
−0.698926 + 0.715194i \(0.746338\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 19.0000 0.697042 0.348521 − 0.937301i \(-0.386684\pi\)
0.348521 + 0.937301i \(0.386684\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −3.00000 −0.109764
\(748\) 0 0
\(749\) 20.0000 0.730784
\(750\) 0 0
\(751\) −33.0000 −1.20419 −0.602094 − 0.798426i \(-0.705667\pi\)
−0.602094 + 0.798426i \(0.705667\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −8.00000 −0.290765 −0.145382 − 0.989376i \(-0.546441\pi\)
−0.145382 + 0.989376i \(0.546441\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −15.0000 −0.543750 −0.271875 − 0.962333i \(-0.587644\pi\)
−0.271875 + 0.962333i \(0.587644\pi\)
\(762\) 0 0
\(763\) −20.0000 −0.724049
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 24.0000 0.866590
\(768\) 0 0
\(769\) 12.0000 0.432731 0.216366 − 0.976312i \(-0.430580\pi\)
0.216366 + 0.976312i \(0.430580\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −20.0000 −0.719350 −0.359675 − 0.933078i \(-0.617112\pi\)
−0.359675 + 0.933078i \(0.617112\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 77.0000 2.75881
\(780\) 0 0
\(781\) −30.0000 −1.07348
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 7.00000 0.249523 0.124762 − 0.992187i \(-0.460183\pi\)
0.124762 + 0.992187i \(0.460183\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −6.00000 −0.213335
\(792\) 0 0
\(793\) −24.0000 −0.852265
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 48.0000 1.70025 0.850124 − 0.526583i \(-0.176527\pi\)
0.850124 + 0.526583i \(0.176527\pi\)
\(798\) 0 0
\(799\) −80.0000 −2.83020
\(800\) 0 0
\(801\) 18.0000 0.635999
\(802\) 0 0
\(803\) 33.0000 1.16454
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 25.0000 0.878953 0.439477 − 0.898254i \(-0.355164\pi\)
0.439477 + 0.898254i \(0.355164\pi\)
\(810\) 0 0
\(811\) 20.0000 0.702295 0.351147 − 0.936320i \(-0.385792\pi\)
0.351147 + 0.936320i \(0.385792\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 35.0000 1.22449
\(818\) 0 0
\(819\) 9.00000 0.314485
\(820\) 0 0
\(821\) −35.0000 −1.22151 −0.610754 − 0.791820i \(-0.709134\pi\)
−0.610754 + 0.791820i \(0.709134\pi\)
\(822\) 0 0
\(823\) −4.00000 −0.139431 −0.0697156 − 0.997567i \(-0.522209\pi\)
−0.0697156 + 0.997567i \(0.522209\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −1.00000 −0.0347734 −0.0173867 − 0.999849i \(-0.505535\pi\)
−0.0173867 + 0.999849i \(0.505535\pi\)
\(828\) 0 0
\(829\) −45.0000 −1.56291 −0.781457 − 0.623959i \(-0.785523\pi\)
−0.781457 + 0.623959i \(0.785523\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −48.0000 −1.66310
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 31.0000 1.07024 0.535119 − 0.844776i \(-0.320267\pi\)
0.535119 + 0.844776i \(0.320267\pi\)
\(840\) 0 0
\(841\) 20.0000 0.689655
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 2.00000 0.0687208
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 4.00000 0.137118
\(852\) 0 0
\(853\) −9.00000 −0.308154 −0.154077 − 0.988059i \(-0.549240\pi\)
−0.154077 + 0.988059i \(0.549240\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 42.0000 1.43469 0.717346 − 0.696717i \(-0.245357\pi\)
0.717346 + 0.696717i \(0.245357\pi\)
\(858\) 0 0
\(859\) 20.0000 0.682391 0.341196 − 0.939992i \(-0.389168\pi\)
0.341196 + 0.939992i \(0.389168\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 18.0000 0.612727 0.306364 − 0.951915i \(-0.400888\pi\)
0.306364 + 0.951915i \(0.400888\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −9.00000 −0.305304
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 42.0000 1.42148
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 38.0000 1.28317 0.641584 − 0.767052i \(-0.278277\pi\)
0.641584 + 0.767052i \(0.278277\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −12.0000 −0.404290 −0.202145 − 0.979356i \(-0.564791\pi\)
−0.202145 + 0.979356i \(0.564791\pi\)
\(882\) 0 0
\(883\) 16.0000 0.538443 0.269221 − 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 36.0000 1.20876 0.604381 − 0.796696i \(-0.293421\pi\)
0.604381 + 0.796696i \(0.293421\pi\)
\(888\) 0 0
\(889\) 16.0000 0.536623
\(890\) 0 0
\(891\) 27.0000 0.904534
\(892\) 0 0
\(893\) −70.0000 −2.34246
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −70.0000 −2.33463
\(900\) 0 0
\(901\) 48.0000 1.59911
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −5.00000 −0.166022 −0.0830111 − 0.996549i \(-0.526454\pi\)
−0.0830111 + 0.996549i \(0.526454\pi\)
\(908\) 0 0
\(909\) −30.0000 −0.995037
\(910\) 0 0
\(911\) 25.0000 0.828287 0.414143 − 0.910212i \(-0.364081\pi\)
0.414143 + 0.910212i \(0.364081\pi\)
\(912\) 0 0
\(913\) 3.00000 0.0992855
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −18.0000 −0.594412
\(918\) 0 0
\(919\) −16.0000 −0.527791 −0.263896 − 0.964551i \(-0.585007\pi\)
−0.263896 + 0.964551i \(0.585007\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −30.0000 −0.987462
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 21.0000 0.689730
\(928\) 0 0
\(929\) −13.0000 −0.426516 −0.213258 − 0.976996i \(-0.568408\pi\)
−0.213258 + 0.976996i \(0.568408\pi\)
\(930\) 0 0
\(931\) −42.0000 −1.37649
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −42.0000 −1.37208 −0.686040 − 0.727564i \(-0.740653\pi\)
−0.686040 + 0.727564i \(0.740653\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −14.0000 −0.456387 −0.228193 − 0.973616i \(-0.573282\pi\)
−0.228193 + 0.973616i \(0.573282\pi\)
\(942\) 0 0
\(943\) −11.0000 −0.358209
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −18.0000 −0.584921 −0.292461 − 0.956278i \(-0.594474\pi\)
−0.292461 + 0.956278i \(0.594474\pi\)
\(948\) 0 0
\(949\) 33.0000 1.07123
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 36.0000 1.16615 0.583077 − 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −6.00000 −0.193750
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 0 0
\(963\) 60.0000 1.93347
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −44.0000 −1.41494 −0.707472 − 0.706741i \(-0.750165\pi\)
−0.707472 + 0.706741i \(0.750165\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −27.0000 −0.866471 −0.433236 − 0.901281i \(-0.642628\pi\)
−0.433236 + 0.901281i \(0.642628\pi\)
\(972\) 0 0
\(973\) −4.00000 −0.128234
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 26.0000 0.831814 0.415907 − 0.909407i \(-0.363464\pi\)
0.415907 + 0.909407i \(0.363464\pi\)
\(978\) 0 0
\(979\) −18.0000 −0.575282
\(980\) 0 0
\(981\) −60.0000 −1.91565
\(982\) 0 0
\(983\) −39.0000 −1.24391 −0.621953 − 0.783054i \(-0.713661\pi\)
−0.621953 + 0.783054i \(0.713661\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −5.00000 −0.158991
\(990\) 0 0
\(991\) −14.0000 −0.444725 −0.222362 − 0.974964i \(-0.571377\pi\)
−0.222362 + 0.974964i \(0.571377\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 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 9200.2.a.s.1.1 1
4.3 odd 2 1150.2.a.b.1.1 ✓ 1
5.4 even 2 9200.2.a.v.1.1 1
20.3 even 4 1150.2.b.c.599.2 2
20.7 even 4 1150.2.b.c.599.1 2
20.19 odd 2 1150.2.a.g.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1150.2.a.b.1.1 ✓ 1 4.3 odd 2
1150.2.a.g.1.1 yes 1 20.19 odd 2
1150.2.b.c.599.1 2 20.7 even 4
1150.2.b.c.599.2 2 20.3 even 4
9200.2.a.s.1.1 1 1.1 even 1 trivial
9200.2.a.v.1.1 1 5.4 even 2