Properties

Label 2880.2.d.f.289.1
Level $2880$
Weight $2$
Character 2880.289
Analytic conductor $22.997$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2880,2,Mod(289,2880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2880.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2880.d (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(22.9969157821\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 289.1
Root \(0.965926 - 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 2880.289
Dual form 2880.2.d.f.289.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.41421 - 1.73205i) q^{5} -2.82843i q^{7} +O(q^{10})\) \(q+(-1.41421 - 1.73205i) q^{5} -2.82843i q^{7} +2.00000i q^{11} +2.82843 q^{13} -4.89898i q^{17} -5.65685i q^{23} +(-1.00000 + 4.89898i) q^{25} -3.46410i q^{29} -3.46410 q^{31} +(-4.89898 + 4.00000i) q^{35} +2.82843 q^{37} -8.00000 q^{41} +9.79796 q^{43} -1.00000 q^{49} +8.48528 q^{53} +(3.46410 - 2.82843i) q^{55} +10.0000i q^{59} -6.92820i q^{61} +(-4.00000 - 4.89898i) q^{65} -9.79796 q^{67} -13.8564 q^{71} -9.79796i q^{73} +5.65685 q^{77} +3.46410 q^{79} -9.79796 q^{83} +(-8.48528 + 6.92820i) q^{85} -16.0000 q^{89} -8.00000i q^{91} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{25} - 64 q^{41} - 8 q^{49} - 32 q^{65} - 128 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(2431\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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
\(5\) −1.41421 1.73205i −0.632456 0.774597i
\(6\) 0 0
\(7\) 2.82843i 1.06904i −0.845154 0.534522i \(-0.820491\pi\)
0.845154 0.534522i \(-0.179509\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000i 0.603023i 0.953463 + 0.301511i \(0.0974911\pi\)
−0.953463 + 0.301511i \(0.902509\pi\)
\(12\) 0 0
\(13\) 2.82843 0.784465 0.392232 0.919866i \(-0.371703\pi\)
0.392232 + 0.919866i \(0.371703\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.89898i 1.18818i −0.804400 0.594089i \(-0.797513\pi\)
0.804400 0.594089i \(-0.202487\pi\)
\(18\) 0 0
\(19\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.65685i 1.17954i −0.807573 0.589768i \(-0.799219\pi\)
0.807573 0.589768i \(-0.200781\pi\)
\(24\) 0 0
\(25\) −1.00000 + 4.89898i −0.200000 + 0.979796i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.46410i 0.643268i −0.946864 0.321634i \(-0.895768\pi\)
0.946864 0.321634i \(-0.104232\pi\)
\(30\) 0 0
\(31\) −3.46410 −0.622171 −0.311086 0.950382i \(-0.600693\pi\)
−0.311086 + 0.950382i \(0.600693\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.89898 + 4.00000i −0.828079 + 0.676123i
\(36\) 0 0
\(37\) 2.82843 0.464991 0.232495 0.972598i \(-0.425311\pi\)
0.232495 + 0.972598i \(0.425311\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.00000 −1.24939 −0.624695 0.780869i \(-0.714777\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) 9.79796 1.49417 0.747087 0.664726i \(-0.231452\pi\)
0.747087 + 0.664726i \(0.231452\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(48\) 0 0
\(49\) −1.00000 −0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 8.48528 1.16554 0.582772 0.812636i \(-0.301968\pi\)
0.582772 + 0.812636i \(0.301968\pi\)
\(54\) 0 0
\(55\) 3.46410 2.82843i 0.467099 0.381385i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 10.0000i 1.30189i 0.759125 + 0.650945i \(0.225627\pi\)
−0.759125 + 0.650945i \(0.774373\pi\)
\(60\) 0 0
\(61\) 6.92820i 0.887066i −0.896258 0.443533i \(-0.853725\pi\)
0.896258 0.443533i \(-0.146275\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.00000 4.89898i −0.496139 0.607644i
\(66\) 0 0
\(67\) −9.79796 −1.19701 −0.598506 0.801119i \(-0.704239\pi\)
−0.598506 + 0.801119i \(0.704239\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −13.8564 −1.64445 −0.822226 0.569160i \(-0.807268\pi\)
−0.822226 + 0.569160i \(0.807268\pi\)
\(72\) 0 0
\(73\) 9.79796i 1.14676i −0.819288 0.573382i \(-0.805631\pi\)
0.819288 0.573382i \(-0.194369\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.65685 0.644658
\(78\) 0 0
\(79\) 3.46410 0.389742 0.194871 0.980829i \(-0.437571\pi\)
0.194871 + 0.980829i \(0.437571\pi\)
\(80\) 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
\(85\) −8.48528 + 6.92820i −0.920358 + 0.751469i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −16.0000 −1.69600 −0.847998 0.529999i \(-0.822192\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(90\) 0 0
\(91\) 8.00000i 0.838628i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 3.46410i 0.344691i −0.985037 0.172345i \(-0.944865\pi\)
0.985037 0.172345i \(-0.0551346\pi\)
\(102\) 0 0
\(103\) 14.1421i 1.39347i 0.717331 + 0.696733i \(0.245364\pi\)
−0.717331 + 0.696733i \(0.754636\pi\)
\(104\) 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
\(109\) 6.92820i 0.663602i 0.943349 + 0.331801i \(0.107656\pi\)
−0.943349 + 0.331801i \(0.892344\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 14.6969i 1.38257i −0.722581 0.691286i \(-0.757045\pi\)
0.722581 0.691286i \(-0.242955\pi\)
\(114\) 0 0
\(115\) −9.79796 + 8.00000i −0.913664 + 0.746004i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −13.8564 −1.27021
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 9.89949 5.19615i 0.885438 0.464758i
\(126\) 0 0
\(127\) 2.82843i 0.250982i 0.992095 + 0.125491i \(0.0400507\pi\)
−0.992095 + 0.125491i \(0.959949\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 14.0000i 1.22319i 0.791173 + 0.611593i \(0.209471\pi\)
−0.791173 + 0.611593i \(0.790529\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.89898i 0.418548i −0.977857 0.209274i \(-0.932890\pi\)
0.977857 0.209274i \(-0.0671101\pi\)
\(138\) 0 0
\(139\) 8.00000i 0.678551i 0.940687 + 0.339276i \(0.110182\pi\)
−0.940687 + 0.339276i \(0.889818\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 5.65685i 0.473050i
\(144\) 0 0
\(145\) −6.00000 + 4.89898i −0.498273 + 0.406838i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 10.3923i 0.851371i −0.904871 0.425685i \(-0.860033\pi\)
0.904871 0.425685i \(-0.139967\pi\)
\(150\) 0 0
\(151\) −17.3205 −1.40952 −0.704761 0.709444i \(-0.748946\pi\)
−0.704761 + 0.709444i \(0.748946\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.89898 + 6.00000i 0.393496 + 0.481932i
\(156\) 0 0
\(157\) −19.7990 −1.58013 −0.790066 0.613022i \(-0.789954\pi\)
−0.790066 + 0.613022i \(0.789954\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −16.0000 −1.26098
\(162\) 0 0
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 22.6274i 1.75096i −0.483252 0.875481i \(-0.660545\pi\)
0.483252 0.875481i \(-0.339455\pi\)
\(168\) 0 0
\(169\) −5.00000 −0.384615
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −8.48528 −0.645124 −0.322562 0.946548i \(-0.604544\pi\)
−0.322562 + 0.946548i \(0.604544\pi\)
\(174\) 0 0
\(175\) 13.8564 + 2.82843i 1.04745 + 0.213809i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.0000i 1.04641i 0.852207 + 0.523205i \(0.175264\pi\)
−0.852207 + 0.523205i \(0.824736\pi\)
\(180\) 0 0
\(181\) 20.7846i 1.54491i −0.635071 0.772454i \(-0.719029\pi\)
0.635071 0.772454i \(-0.280971\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −4.00000 4.89898i −0.294086 0.360180i
\(186\) 0 0
\(187\) 9.79796 0.716498
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 13.8564 1.00261 0.501307 0.865269i \(-0.332853\pi\)
0.501307 + 0.865269i \(0.332853\pi\)
\(192\) 0 0
\(193\) 9.79796i 0.705273i −0.935760 0.352636i \(-0.885285\pi\)
0.935760 0.352636i \(-0.114715\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 2.82843 0.201517 0.100759 0.994911i \(-0.467873\pi\)
0.100759 + 0.994911i \(0.467873\pi\)
\(198\) 0 0
\(199\) 10.3923 0.736691 0.368345 0.929689i \(-0.379924\pi\)
0.368345 + 0.929689i \(0.379924\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −9.79796 −0.687682
\(204\) 0 0
\(205\) 11.3137 + 13.8564i 0.790184 + 0.967773i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 8.00000i 0.550743i −0.961338 0.275371i \(-0.911199\pi\)
0.961338 0.275371i \(-0.0888008\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −13.8564 16.9706i −0.944999 1.15738i
\(216\) 0 0
\(217\) 9.79796i 0.665129i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 13.8564i 0.932083i
\(222\) 0 0
\(223\) 14.1421i 0.947027i −0.880786 0.473514i \(-0.842985\pi\)
0.880786 0.473514i \(-0.157015\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.79796 0.650313 0.325157 0.945660i \(-0.394583\pi\)
0.325157 + 0.945660i \(0.394583\pi\)
\(228\) 0 0
\(229\) 6.92820i 0.457829i 0.973447 + 0.228914i \(0.0735176\pi\)
−0.973447 + 0.228914i \(0.926482\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 14.6969i 0.962828i −0.876493 0.481414i \(-0.840123\pi\)
0.876493 0.481414i \(-0.159877\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 13.8564 0.896296 0.448148 0.893959i \(-0.352084\pi\)
0.448148 + 0.893959i \(0.352084\pi\)
\(240\) 0 0
\(241\) 18.0000 1.15948 0.579741 0.814801i \(-0.303154\pi\)
0.579741 + 0.814801i \(0.303154\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1.41421 + 1.73205i 0.0903508 + 0.110657i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 14.0000i 0.883672i 0.897096 + 0.441836i \(0.145673\pi\)
−0.897096 + 0.441836i \(0.854327\pi\)
\(252\) 0 0
\(253\) 11.3137 0.711287
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.89898i 0.305590i −0.988258 0.152795i \(-0.951173\pi\)
0.988258 0.152795i \(-0.0488274\pi\)
\(258\) 0 0
\(259\) 8.00000i 0.497096i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.3137i 0.697633i −0.937191 0.348817i \(-0.886584\pi\)
0.937191 0.348817i \(-0.113416\pi\)
\(264\) 0 0
\(265\) −12.0000 14.6969i −0.737154 0.902826i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 3.46410i 0.211210i 0.994408 + 0.105605i \(0.0336779\pi\)
−0.994408 + 0.105605i \(0.966322\pi\)
\(270\) 0 0
\(271\) −31.1769 −1.89386 −0.946931 0.321436i \(-0.895835\pi\)
−0.946931 + 0.321436i \(0.895835\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −9.79796 2.00000i −0.590839 0.120605i
\(276\) 0 0
\(277\) 31.1127 1.86938 0.934690 0.355463i \(-0.115677\pi\)
0.934690 + 0.355463i \(0.115677\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 16.0000 0.954480 0.477240 0.878773i \(-0.341637\pi\)
0.477240 + 0.878773i \(0.341637\pi\)
\(282\) 0 0
\(283\) −9.79796 −0.582428 −0.291214 0.956658i \(-0.594059\pi\)
−0.291214 + 0.956658i \(0.594059\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 22.6274i 1.33565i
\(288\) 0 0
\(289\) −7.00000 −0.411765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.82843 −0.165238 −0.0826192 0.996581i \(-0.526329\pi\)
−0.0826192 + 0.996581i \(0.526329\pi\)
\(294\) 0 0
\(295\) 17.3205 14.1421i 1.00844 0.823387i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 16.0000i 0.925304i
\(300\) 0 0
\(301\) 27.7128i 1.59734i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −12.0000 + 9.79796i −0.687118 + 0.561029i
\(306\) 0 0
\(307\) 19.5959 1.11840 0.559199 0.829033i \(-0.311109\pi\)
0.559199 + 0.829033i \(0.311109\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −13.8564 −0.785725 −0.392862 0.919597i \(-0.628515\pi\)
−0.392862 + 0.919597i \(0.628515\pi\)
\(312\) 0 0
\(313\) 29.3939i 1.66144i 0.556690 + 0.830720i \(0.312071\pi\)
−0.556690 + 0.830720i \(0.687929\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 2.82843 0.158860 0.0794301 0.996840i \(-0.474690\pi\)
0.0794301 + 0.996840i \(0.474690\pi\)
\(318\) 0 0
\(319\) 6.92820 0.387905
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −2.82843 + 13.8564i −0.156893 + 0.768615i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 24.0000i 1.31916i −0.751635 0.659580i \(-0.770734\pi\)
0.751635 0.659580i \(-0.229266\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 13.8564 + 16.9706i 0.757056 + 0.927201i
\(336\) 0 0
\(337\) 9.79796i 0.533729i 0.963734 + 0.266864i \(0.0859876\pi\)
−0.963734 + 0.266864i \(0.914012\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.92820i 0.375183i
\(342\) 0 0
\(343\) 16.9706i 0.916324i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 9.79796 0.525982 0.262991 0.964798i \(-0.415291\pi\)
0.262991 + 0.964798i \(0.415291\pi\)
\(348\) 0 0
\(349\) 6.92820i 0.370858i 0.982658 + 0.185429i \(0.0593675\pi\)
−0.982658 + 0.185429i \(0.940632\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 34.2929i 1.82522i 0.408826 + 0.912612i \(0.365938\pi\)
−0.408826 + 0.912612i \(0.634062\pi\)
\(354\) 0 0
\(355\) 19.5959 + 24.0000i 1.04004 + 1.27379i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −27.7128 −1.46263 −0.731313 0.682042i \(-0.761092\pi\)
−0.731313 + 0.682042i \(0.761092\pi\)
\(360\) 0 0
\(361\) 19.0000 1.00000
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −16.9706 + 13.8564i −0.888280 + 0.725277i
\(366\) 0 0
\(367\) 2.82843i 0.147643i 0.997271 + 0.0738213i \(0.0235195\pi\)
−0.997271 + 0.0738213i \(0.976481\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 24.0000i 1.24602i
\(372\) 0 0
\(373\) −19.7990 −1.02515 −0.512576 0.858642i \(-0.671309\pi\)
−0.512576 + 0.858642i \(0.671309\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 9.79796i 0.504621i
\(378\) 0 0
\(379\) 32.0000i 1.64373i 0.569683 + 0.821865i \(0.307066\pi\)
−0.569683 + 0.821865i \(0.692934\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 16.9706i 0.867155i 0.901116 + 0.433578i \(0.142749\pi\)
−0.901116 + 0.433578i \(0.857251\pi\)
\(384\) 0 0
\(385\) −8.00000 9.79796i −0.407718 0.499350i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 24.2487i 1.22946i 0.788738 + 0.614729i \(0.210735\pi\)
−0.788738 + 0.614729i \(0.789265\pi\)
\(390\) 0 0
\(391\) −27.7128 −1.40150
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.89898 6.00000i −0.246494 0.301893i
\(396\) 0 0
\(397\) −14.1421 −0.709773 −0.354887 0.934909i \(-0.615481\pi\)
−0.354887 + 0.934909i \(0.615481\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8.00000 0.399501 0.199750 0.979847i \(-0.435987\pi\)
0.199750 + 0.979847i \(0.435987\pi\)
\(402\) 0 0
\(403\) −9.79796 −0.488071
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.65685i 0.280400i
\(408\) 0 0
\(409\) −2.00000 −0.0988936 −0.0494468 0.998777i \(-0.515746\pi\)
−0.0494468 + 0.998777i \(0.515746\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 28.2843 1.39178
\(414\) 0 0
\(415\) 13.8564 + 16.9706i 0.680184 + 0.833052i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 10.0000i 0.488532i −0.969708 0.244266i \(-0.921453\pi\)
0.969708 0.244266i \(-0.0785470\pi\)
\(420\) 0 0
\(421\) 34.6410i 1.68830i −0.536107 0.844150i \(-0.680106\pi\)
0.536107 0.844150i \(-0.319894\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 24.0000 + 4.89898i 1.16417 + 0.237635i
\(426\) 0 0
\(427\) −19.5959 −0.948313
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 27.7128 1.33488 0.667440 0.744664i \(-0.267390\pi\)
0.667440 + 0.744664i \(0.267390\pi\)
\(432\) 0 0
\(433\) 19.5959i 0.941720i 0.882208 + 0.470860i \(0.156056\pi\)
−0.882208 + 0.470860i \(0.843944\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 10.3923 0.495998 0.247999 0.968760i \(-0.420227\pi\)
0.247999 + 0.968760i \(0.420227\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 29.3939 1.39655 0.698273 0.715832i \(-0.253952\pi\)
0.698273 + 0.715832i \(0.253952\pi\)
\(444\) 0 0
\(445\) 22.6274 + 27.7128i 1.07264 + 1.31371i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 8.00000 0.377543 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) 0 0
\(451\) 16.0000i 0.753411i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −13.8564 + 11.3137i −0.649598 + 0.530395i
\(456\) 0 0
\(457\) 39.1918i 1.83332i −0.399672 0.916658i \(-0.630876\pi\)
0.399672 0.916658i \(-0.369124\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 31.1769i 1.45205i 0.687666 + 0.726027i \(0.258635\pi\)
−0.687666 + 0.726027i \(0.741365\pi\)
\(462\) 0 0
\(463\) 2.82843i 0.131448i 0.997838 + 0.0657241i \(0.0209357\pi\)
−0.997838 + 0.0657241i \(0.979064\pi\)
\(464\) 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
\(469\) 27.7128i 1.27966i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 19.5959i 0.901021i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 41.5692 1.89935 0.949673 0.313243i \(-0.101415\pi\)
0.949673 + 0.313243i \(0.101415\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 2.82843i 0.128168i 0.997944 + 0.0640841i \(0.0204126\pi\)
−0.997944 + 0.0640841i \(0.979587\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 22.0000i 0.992846i −0.868081 0.496423i \(-0.834646\pi\)
0.868081 0.496423i \(-0.165354\pi\)
\(492\) 0 0
\(493\) −16.9706 −0.764316
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 39.1918i 1.75799i
\(498\) 0 0
\(499\) 24.0000i 1.07439i −0.843459 0.537194i \(-0.819484\pi\)
0.843459 0.537194i \(-0.180516\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 33.9411i 1.51336i −0.653785 0.756680i \(-0.726820\pi\)
0.653785 0.756680i \(-0.273180\pi\)
\(504\) 0 0
\(505\) −6.00000 + 4.89898i −0.266996 + 0.218002i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 10.3923i 0.460631i −0.973116 0.230315i \(-0.926024\pi\)
0.973116 0.230315i \(-0.0739758\pi\)
\(510\) 0 0
\(511\) −27.7128 −1.22594
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 24.4949 20.0000i 1.07937 0.881305i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8.00000 0.350486 0.175243 0.984525i \(-0.443929\pi\)
0.175243 + 0.984525i \(0.443929\pi\)
\(522\) 0 0
\(523\) −39.1918 −1.71374 −0.856870 0.515533i \(-0.827594\pi\)
−0.856870 + 0.515533i \(0.827594\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.9706i 0.739249i
\(528\) 0 0
\(529\) −9.00000 −0.391304
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −22.6274 −0.980102
\(534\) 0 0
\(535\) 27.7128 + 33.9411i 1.19813 + 1.46740i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.00000i 0.0861461i
\(540\) 0 0
\(541\) 34.6410i 1.48933i −0.667436 0.744667i \(-0.732608\pi\)
0.667436 0.744667i \(-0.267392\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 12.0000 9.79796i 0.514024 0.419698i
\(546\) 0 0
\(547\) 9.79796 0.418930 0.209465 0.977816i \(-0.432828\pi\)
0.209465 + 0.977816i \(0.432828\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 9.79796i 0.416652i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −42.4264 −1.79766 −0.898832 0.438293i \(-0.855583\pi\)
−0.898832 + 0.438293i \(0.855583\pi\)
\(558\) 0 0
\(559\) 27.7128 1.17213
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 29.3939 1.23880 0.619402 0.785074i \(-0.287375\pi\)
0.619402 + 0.785074i \(0.287375\pi\)
\(564\) 0 0
\(565\) −25.4558 + 20.7846i −1.07094 + 0.874415i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 40.0000 1.67689 0.838444 0.544988i \(-0.183466\pi\)
0.838444 + 0.544988i \(0.183466\pi\)
\(570\) 0 0
\(571\) 24.0000i 1.00437i −0.864761 0.502184i \(-0.832530\pi\)
0.864761 0.502184i \(-0.167470\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 27.7128 + 5.65685i 1.15570 + 0.235907i
\(576\) 0 0
\(577\) 29.3939i 1.22368i −0.790980 0.611842i \(-0.790429\pi\)
0.790980 0.611842i \(-0.209571\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 27.7128i 1.14972i
\(582\) 0 0
\(583\) 16.9706i 0.702849i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 39.1918 1.61762 0.808810 0.588070i \(-0.200112\pi\)
0.808810 + 0.588070i \(0.200112\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.6969i 0.603531i −0.953382 0.301765i \(-0.902424\pi\)
0.953382 0.301765i \(-0.0975760\pi\)
\(594\) 0 0
\(595\) 19.5959 + 24.0000i 0.803354 + 0.983904i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) 18.0000 0.734235 0.367118 0.930175i \(-0.380345\pi\)
0.367118 + 0.930175i \(0.380345\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9.89949 12.1244i −0.402472 0.492925i
\(606\) 0 0
\(607\) 2.82843i 0.114802i −0.998351 0.0574012i \(-0.981719\pi\)
0.998351 0.0574012i \(-0.0182814\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −14.1421 −0.571195 −0.285598 0.958350i \(-0.592192\pi\)
−0.285598 + 0.958350i \(0.592192\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.2929i 1.38058i 0.723534 + 0.690289i \(0.242517\pi\)
−0.723534 + 0.690289i \(0.757483\pi\)
\(618\) 0 0
\(619\) 40.0000i 1.60774i 0.594808 + 0.803868i \(0.297228\pi\)
−0.594808 + 0.803868i \(0.702772\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 45.2548i 1.81310i
\(624\) 0 0
\(625\) −23.0000 9.79796i −0.920000 0.391918i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 13.8564i 0.552491i
\(630\) 0 0
\(631\) −38.1051 −1.51694 −0.758470 0.651707i \(-0.774053\pi\)
−0.758470 + 0.651707i \(0.774053\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.89898 4.00000i 0.194410 0.158735i
\(636\) 0 0
\(637\) −2.82843 −0.112066
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 40.0000 1.57991 0.789953 0.613168i \(-0.210105\pi\)
0.789953 + 0.613168i \(0.210105\pi\)
\(642\) 0 0
\(643\) 19.5959 0.772788 0.386394 0.922334i \(-0.373721\pi\)
0.386394 + 0.922334i \(0.373721\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 33.9411i 1.33436i −0.744895 0.667182i \(-0.767500\pi\)
0.744895 0.667182i \(-0.232500\pi\)
\(648\) 0 0
\(649\) −20.0000 −0.785069
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −19.7990 −0.774794 −0.387397 0.921913i \(-0.626626\pi\)
−0.387397 + 0.921913i \(0.626626\pi\)
\(654\) 0 0
\(655\) 24.2487 19.7990i 0.947476 0.773611i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 46.0000i 1.79191i −0.444149 0.895953i \(-0.646494\pi\)
0.444149 0.895953i \(-0.353506\pi\)
\(660\) 0 0
\(661\) 20.7846i 0.808428i −0.914665 0.404214i \(-0.867545\pi\)
0.914665 0.404214i \(-0.132455\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −19.5959 −0.758757
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 13.8564 0.534921
\(672\) 0 0
\(673\) 19.5959i 0.755367i 0.925935 + 0.377684i \(0.123279\pi\)
−0.925935 + 0.377684i \(0.876721\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −19.7990 −0.760937 −0.380468 0.924794i \(-0.624237\pi\)
−0.380468 + 0.924794i \(0.624237\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.79796 −0.374908 −0.187454 0.982273i \(-0.560024\pi\)
−0.187454 + 0.982273i \(0.560024\pi\)
\(684\) 0 0
\(685\) −8.48528 + 6.92820i −0.324206 + 0.264713i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 13.8564 11.3137i 0.525603 0.429153i
\(696\) 0 0
\(697\) 39.1918i 1.48450i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 17.3205i 0.654187i −0.944992 0.327093i \(-0.893931\pi\)
0.944992 0.327093i \(-0.106069\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −9.79796 −0.368490
\(708\) 0 0
\(709\) 6.92820i 0.260194i 0.991501 + 0.130097i \(0.0415289\pi\)
−0.991501 + 0.130097i \(0.958471\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 19.5959i 0.733873i
\(714\) 0 0
\(715\) 9.79796 8.00000i 0.366423 0.299183i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 27.7128 1.03351 0.516757 0.856132i \(-0.327139\pi\)
0.516757 + 0.856132i \(0.327139\pi\)
\(720\) 0 0
\(721\) 40.0000 1.48968
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 16.9706 + 3.46410i 0.630271 + 0.128654i
\(726\) 0 0
\(727\) 14.1421i 0.524503i 0.965000 + 0.262251i \(0.0844650\pi\)
−0.965000 + 0.262251i \(0.915535\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 48.0000i 1.77534i
\(732\) 0 0
\(733\) 19.7990 0.731292 0.365646 0.930754i \(-0.380848\pi\)
0.365646 + 0.930754i \(0.380848\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19.5959i 0.721825i
\(738\) 0 0
\(739\) 24.0000i 0.882854i −0.897297 0.441427i \(-0.854472\pi\)
0.897297 0.441427i \(-0.145528\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.9706i 0.622590i 0.950313 + 0.311295i \(0.100763\pi\)
−0.950313 + 0.311295i \(0.899237\pi\)
\(744\) 0 0
\(745\) −18.0000 + 14.6969i −0.659469 + 0.538454i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 55.4256i 2.02521i
\(750\) 0 0
\(751\) −31.1769 −1.13766 −0.568831 0.822455i \(-0.692604\pi\)
−0.568831 + 0.822455i \(0.692604\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 24.4949 + 30.0000i 0.891461 + 1.09181i
\(756\) 0 0
\(757\) 31.1127 1.13081 0.565405 0.824813i \(-0.308720\pi\)
0.565405 + 0.824813i \(0.308720\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8.00000 −0.290000 −0.145000 0.989432i \(-0.546318\pi\)
−0.145000 + 0.989432i \(0.546318\pi\)
\(762\) 0 0
\(763\) 19.5959 0.709420
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 28.2843i 1.02129i
\(768\) 0 0
\(769\) 6.00000 0.216366 0.108183 0.994131i \(-0.465497\pi\)
0.108183 + 0.994131i \(0.465497\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −31.1127 −1.11905 −0.559523 0.828815i \(-0.689016\pi\)
−0.559523 + 0.828815i \(0.689016\pi\)
\(774\) 0 0
\(775\) 3.46410 16.9706i 0.124434 0.609601i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 27.7128i 0.991642i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 28.0000 + 34.2929i 0.999363 + 1.22396i
\(786\) 0 0
\(787\) −19.5959 −0.698519 −0.349260 0.937026i \(-0.613567\pi\)
−0.349260 + 0.937026i \(0.613567\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −41.5692 −1.47803
\(792\) 0 0
\(793\) 19.5959i 0.695871i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.4264 1.50282 0.751410 0.659835i \(-0.229374\pi\)
0.751410 + 0.659835i \(0.229374\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 19.5959 0.691525
\(804\) 0 0
\(805\) 22.6274 + 27.7128i 0.797512 + 0.976748i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −8.00000 −0.281265 −0.140633 0.990062i \(-0.544914\pi\)
−0.140633 + 0.990062i \(0.544914\pi\)
\(810\) 0 0
\(811\) 32.0000i 1.12367i −0.827249 0.561836i \(-0.810095\pi\)
0.827249 0.561836i \(-0.189905\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 10.3923i 0.362694i 0.983419 + 0.181347i \(0.0580457\pi\)
−0.983419 + 0.181347i \(0.941954\pi\)
\(822\) 0 0
\(823\) 48.0833i 1.67608i −0.545611 0.838039i \(-0.683702\pi\)
0.545611 0.838039i \(-0.316298\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 19.5959 0.681417 0.340708 0.940169i \(-0.389333\pi\)
0.340708 + 0.940169i \(0.389333\pi\)
\(828\) 0 0
\(829\) 34.6410i 1.20313i 0.798823 + 0.601566i \(0.205456\pi\)
−0.798823 + 0.601566i \(0.794544\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 4.89898i 0.169740i
\(834\) 0 0
\(835\) −39.1918 + 32.0000i −1.35629 + 1.10741i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 17.0000 0.586207
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 7.07107 + 8.66025i 0.243252 + 0.297922i
\(846\) 0 0
\(847\) 19.7990i 0.680301i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 16.0000i 0.548473i
\(852\) 0 0
\(853\) 19.7990 0.677905 0.338952 0.940804i \(-0.389927\pi\)
0.338952 + 0.940804i \(0.389927\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 24.4949i 0.836730i 0.908279 + 0.418365i \(0.137397\pi\)
−0.908279 + 0.418365i \(0.862603\pi\)
\(858\) 0 0
\(859\) 32.0000i 1.09183i 0.837842 + 0.545913i \(0.183817\pi\)
−0.837842 + 0.545913i \(0.816183\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 11.3137i 0.385123i 0.981285 + 0.192562i \(0.0616795\pi\)
−0.981285 + 0.192562i \(0.938320\pi\)
\(864\) 0 0
\(865\) 12.0000 + 14.6969i 0.408012 + 0.499711i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 6.92820i 0.235023i
\(870\) 0 0
\(871\) −27.7128 −0.939013
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −14.6969 28.0000i −0.496847 0.946573i
\(876\) 0 0
\(877\) 2.82843 0.0955092 0.0477546 0.998859i \(-0.484793\pi\)
0.0477546 + 0.998859i \(0.484793\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −16.0000 −0.539054 −0.269527 0.962993i \(-0.586867\pi\)
−0.269527 + 0.962993i \(0.586867\pi\)
\(882\) 0 0
\(883\) 19.5959 0.659455 0.329728 0.944076i \(-0.393043\pi\)
0.329728 + 0.944076i \(0.393043\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 11.3137i 0.379877i 0.981796 + 0.189939i \(0.0608289\pi\)
−0.981796 + 0.189939i \(0.939171\pi\)
\(888\) 0 0
\(889\) 8.00000 0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 24.2487 19.7990i 0.810545 0.661807i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 12.0000i 0.400222i
\(900\) 0 0
\(901\) 41.5692i 1.38487i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −36.0000 + 29.3939i −1.19668 + 0.977086i
\(906\) 0 0
\(907\) 48.9898 1.62668 0.813340 0.581789i \(-0.197647\pi\)
0.813340 + 0.581789i \(0.197647\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 27.7128 0.918166 0.459083 0.888393i \(-0.348178\pi\)
0.459083 + 0.888393i \(0.348178\pi\)
\(912\) 0 0
\(913\) 19.5959i 0.648530i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 39.5980 1.30764
\(918\) 0 0
\(919\) 38.1051 1.25697 0.628486 0.777821i \(-0.283675\pi\)
0.628486 + 0.777821i \(0.283675\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −39.1918 −1.29001
\(924\) 0 0
\(925\) −2.82843 + 13.8564i −0.0929981 + 0.455596i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 8.00000 0.262471 0.131236 0.991351i \(-0.458106\pi\)
0.131236 + 0.991351i \(0.458106\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −13.8564 16.9706i −0.453153 0.554997i
\(936\) 0 0
\(937\) 19.5959i 0.640171i 0.947389 + 0.320085i \(0.103712\pi\)
−0.947389 + 0.320085i \(0.896288\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 38.1051i 1.24219i 0.783735 + 0.621096i \(0.213312\pi\)
−0.783735 + 0.621096i \(0.786688\pi\)
\(942\) 0 0
\(943\) 45.2548i 1.47370i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 19.5959 0.636782 0.318391 0.947960i \(-0.396858\pi\)
0.318391 + 0.947960i \(0.396858\pi\)
\(948\) 0 0
\(949\) 27.7128i 0.899596i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 4.89898i 0.158694i 0.996847 + 0.0793468i \(0.0252834\pi\)
−0.996847 + 0.0793468i \(0.974717\pi\)
\(954\) 0 0
\(955\) −19.5959 24.0000i −0.634109 0.776622i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −13.8564 −0.447447
\(960\) 0 0
\(961\) −19.0000 −0.612903
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −16.9706 + 13.8564i −0.546302 + 0.446054i
\(966\) 0 0
\(967\) 48.0833i 1.54625i −0.634252 0.773127i \(-0.718692\pi\)
0.634252 0.773127i \(-0.281308\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 46.0000i 1.47621i 0.674686 + 0.738105i \(0.264279\pi\)
−0.674686 + 0.738105i \(0.735721\pi\)
\(972\) 0 0
\(973\) 22.6274 0.725402
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 24.4949i 0.783661i −0.920037 0.391831i \(-0.871842\pi\)
0.920037 0.391831i \(-0.128158\pi\)
\(978\) 0 0
\(979\) 32.0000i 1.02272i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 16.9706i 0.541277i 0.962681 + 0.270638i \(0.0872348\pi\)
−0.962681 + 0.270638i \(0.912765\pi\)
\(984\) 0 0
\(985\) −4.00000 4.89898i −0.127451 0.156094i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 55.4256i 1.76243i
\(990\) 0 0
\(991\) −24.2487 −0.770286 −0.385143 0.922857i \(-0.625848\pi\)
−0.385143 + 0.922857i \(0.625848\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −14.6969 18.0000i −0.465924 0.570638i
\(996\) 0 0
\(997\) −48.0833 −1.52281 −0.761406 0.648275i \(-0.775491\pi\)
−0.761406 + 0.648275i \(0.775491\pi\)
\(998\) 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 2880.2.d.f.289.1 8
3.2 odd 2 2880.2.d.h.289.7 yes 8
4.3 odd 2 inner 2880.2.d.f.289.2 yes 8
5.4 even 2 inner 2880.2.d.f.289.6 yes 8
8.3 odd 2 inner 2880.2.d.f.289.8 yes 8
8.5 even 2 inner 2880.2.d.f.289.7 yes 8
12.11 even 2 2880.2.d.h.289.8 yes 8
15.14 odd 2 2880.2.d.h.289.4 yes 8
20.19 odd 2 inner 2880.2.d.f.289.5 yes 8
24.5 odd 2 2880.2.d.h.289.1 yes 8
24.11 even 2 2880.2.d.h.289.2 yes 8
40.19 odd 2 inner 2880.2.d.f.289.3 yes 8
40.29 even 2 inner 2880.2.d.f.289.4 yes 8
60.59 even 2 2880.2.d.h.289.3 yes 8
120.29 odd 2 2880.2.d.h.289.6 yes 8
120.59 even 2 2880.2.d.h.289.5 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2880.2.d.f.289.1 8 1.1 even 1 trivial
2880.2.d.f.289.2 yes 8 4.3 odd 2 inner
2880.2.d.f.289.3 yes 8 40.19 odd 2 inner
2880.2.d.f.289.4 yes 8 40.29 even 2 inner
2880.2.d.f.289.5 yes 8 20.19 odd 2 inner
2880.2.d.f.289.6 yes 8 5.4 even 2 inner
2880.2.d.f.289.7 yes 8 8.5 even 2 inner
2880.2.d.f.289.8 yes 8 8.3 odd 2 inner
2880.2.d.h.289.1 yes 8 24.5 odd 2
2880.2.d.h.289.2 yes 8 24.11 even 2
2880.2.d.h.289.3 yes 8 60.59 even 2
2880.2.d.h.289.4 yes 8 15.14 odd 2
2880.2.d.h.289.5 yes 8 120.59 even 2
2880.2.d.h.289.6 yes 8 120.29 odd 2
2880.2.d.h.289.7 yes 8 3.2 odd 2
2880.2.d.h.289.8 yes 8 12.11 even 2