Properties

Label 1296.2.c.b.1295.2
Level $1296$
Weight $2$
Character 1296.1295
Analytic conductor $10.349$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1296,2,Mod(1295,1296)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1296, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("1296.1295");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1296 = 2^{4} \cdot 3^{4} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1296.c (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: \(10.3486121020\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1295.2
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1296.1295
Dual form 1296.2.c.b.1295.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.46410i q^{5} +3.46410i q^{7} -3.00000 q^{11} +4.00000 q^{13} +1.73205i q^{17} +1.73205i q^{19} -7.00000 q^{25} -3.46410i q^{29} -12.0000 q^{35} +2.00000 q^{37} +5.19615i q^{41} -5.19615i q^{43} -12.0000 q^{47} -5.00000 q^{49} -10.3923i q^{55} -15.0000 q^{59} +8.00000 q^{61} +13.8564i q^{65} -8.66025i q^{67} +6.00000 q^{71} -11.0000 q^{73} -10.3923i q^{77} -3.46410i q^{79} +12.0000 q^{83} -6.00000 q^{85} +13.8564i q^{89} +13.8564i q^{91} -6.00000 q^{95} +13.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 6 q^{11} + 8 q^{13} - 14 q^{25} - 24 q^{35} + 4 q^{37} - 24 q^{47} - 10 q^{49} - 30 q^{59} + 16 q^{61} + 12 q^{71} - 22 q^{73} + 24 q^{83} - 12 q^{85} - 12 q^{95} + 26 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1296\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(1135\) \(1217\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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
\(5\) 3.46410i 1.54919i 0.632456 + 0.774597i \(0.282047\pi\)
−0.632456 + 0.774597i \(0.717953\pi\)
\(6\) 0 0
\(7\) 3.46410i 1.30931i 0.755929 + 0.654654i \(0.227186\pi\)
−0.755929 + 0.654654i \(0.772814\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.00000 −0.904534 −0.452267 0.891883i \(-0.649385\pi\)
−0.452267 + 0.891883i \(0.649385\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.73205i 0.420084i 0.977692 + 0.210042i \(0.0673601\pi\)
−0.977692 + 0.210042i \(0.932640\pi\)
\(18\) 0 0
\(19\) 1.73205i 0.397360i 0.980064 + 0.198680i \(0.0636654\pi\)
−0.980064 + 0.198680i \(0.936335\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −7.00000 −1.40000
\(26\) 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
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −12.0000 −2.02837
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 5.19615i 0.811503i 0.913984 + 0.405751i \(0.132990\pi\)
−0.913984 + 0.405751i \(0.867010\pi\)
\(42\) 0 0
\(43\) − 5.19615i − 0.792406i −0.918163 0.396203i \(-0.870328\pi\)
0.918163 0.396203i \(-0.129672\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) 0 0
\(49\) −5.00000 −0.714286
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) − 10.3923i − 1.40130i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −15.0000 −1.95283 −0.976417 0.215894i \(-0.930733\pi\)
−0.976417 + 0.215894i \(0.930733\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 13.8564i 1.71868i
\(66\) 0 0
\(67\) − 8.66025i − 1.05802i −0.848616 0.529009i \(-0.822564\pi\)
0.848616 0.529009i \(-0.177436\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 10.3923i − 1.18431i
\(78\) 0 0
\(79\) − 3.46410i − 0.389742i −0.980829 0.194871i \(-0.937571\pi\)
0.980829 0.194871i \(-0.0624288\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 13.8564i 1.46878i 0.678730 + 0.734388i \(0.262531\pi\)
−0.678730 + 0.734388i \(0.737469\pi\)
\(90\) 0 0
\(91\) 13.8564i 1.45255i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −6.00000 −0.615587
\(96\) 0 0
\(97\) 13.0000 1.31995 0.659975 0.751288i \(-0.270567\pi\)
0.659975 + 0.751288i \(0.270567\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.3923i 1.03407i 0.855963 + 0.517036i \(0.172965\pi\)
−0.855963 + 0.517036i \(0.827035\pi\)
\(102\) 0 0
\(103\) 13.8564i 1.36531i 0.730740 + 0.682656i \(0.239175\pi\)
−0.730740 + 0.682656i \(0.760825\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 0 0
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.92820i 0.651751i 0.945413 + 0.325875i \(0.105659\pi\)
−0.945413 + 0.325875i \(0.894341\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −6.00000 −0.550019
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) − 6.92820i − 0.619677i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 1.73205i − 0.147979i −0.997259 0.0739895i \(-0.976427\pi\)
0.997259 0.0739895i \(-0.0235731\pi\)
\(138\) 0 0
\(139\) 19.0526i 1.61602i 0.589171 + 0.808008i \(0.299454\pi\)
−0.589171 + 0.808008i \(0.700546\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −12.0000 −1.00349
\(144\) 0 0
\(145\) 12.0000 0.996546
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) − 13.8564i − 1.13516i −0.823318 0.567581i \(-0.807880\pi\)
0.823318 0.567581i \(-0.192120\pi\)
\(150\) 0 0
\(151\) 6.92820i 0.563809i 0.959442 + 0.281905i \(0.0909662\pi\)
−0.959442 + 0.281905i \(0.909034\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 8.00000 0.638470 0.319235 0.947676i \(-0.396574\pi\)
0.319235 + 0.947676i \(0.396574\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 3.46410i 0.271329i 0.990755 + 0.135665i \(0.0433170\pi\)
−0.990755 + 0.135665i \(0.956683\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 24.2487i − 1.84360i −0.387671 0.921798i \(-0.626720\pi\)
0.387671 0.921798i \(-0.373280\pi\)
\(174\) 0 0
\(175\) − 24.2487i − 1.83303i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −8.00000 −0.594635 −0.297318 0.954779i \(-0.596092\pi\)
−0.297318 + 0.954779i \(0.596092\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.92820i 0.509372i
\(186\) 0 0
\(187\) − 5.19615i − 0.379980i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 0 0
\(193\) 23.0000 1.65558 0.827788 0.561041i \(-0.189599\pi\)
0.827788 + 0.561041i \(0.189599\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 13.8564i − 0.987228i −0.869681 0.493614i \(-0.835676\pi\)
0.869681 0.493614i \(-0.164324\pi\)
\(198\) 0 0
\(199\) 3.46410i 0.245564i 0.992434 + 0.122782i \(0.0391815\pi\)
−0.992434 + 0.122782i \(0.960818\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 12.0000 0.842235
\(204\) 0 0
\(205\) −18.0000 −1.25717
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) − 5.19615i − 0.359425i
\(210\) 0 0
\(211\) − 17.3205i − 1.19239i −0.802839 0.596196i \(-0.796678\pi\)
0.802839 0.596196i \(-0.203322\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 18.0000 1.22759
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.92820i 0.466041i
\(222\) 0 0
\(223\) 20.7846i 1.39184i 0.718119 + 0.695920i \(0.245003\pi\)
−0.718119 + 0.695920i \(0.754997\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) −26.0000 −1.71813 −0.859064 0.511868i \(-0.828954\pi\)
−0.859064 + 0.511868i \(0.828954\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) − 12.1244i − 0.794293i −0.917755 0.397146i \(-0.870000\pi\)
0.917755 0.397146i \(-0.130000\pi\)
\(234\) 0 0
\(235\) − 41.5692i − 2.71168i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) −17.0000 −1.09507 −0.547533 0.836784i \(-0.684433\pi\)
−0.547533 + 0.836784i \(0.684433\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) − 17.3205i − 1.10657i
\(246\) 0 0
\(247\) 6.92820i 0.440831i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 21.0000 1.32551 0.662754 0.748837i \(-0.269387\pi\)
0.662754 + 0.748837i \(0.269387\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 19.0526i 1.18847i 0.804293 + 0.594233i \(0.202544\pi\)
−0.804293 + 0.594233i \(0.797456\pi\)
\(258\) 0 0
\(259\) 6.92820i 0.430498i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 18.0000 1.10993 0.554964 0.831875i \(-0.312732\pi\)
0.554964 + 0.831875i \(0.312732\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) − 6.92820i − 0.422420i −0.977441 0.211210i \(-0.932260\pi\)
0.977441 0.211210i \(-0.0677404\pi\)
\(270\) 0 0
\(271\) 6.92820i 0.420858i 0.977609 + 0.210429i \(0.0674861\pi\)
−0.977609 + 0.210429i \(0.932514\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 21.0000 1.26635
\(276\) 0 0
\(277\) −8.00000 −0.480673 −0.240337 0.970690i \(-0.577258\pi\)
−0.240337 + 0.970690i \(0.577258\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.92820i 0.413302i 0.978415 + 0.206651i \(0.0662565\pi\)
−0.978415 + 0.206651i \(0.933744\pi\)
\(282\) 0 0
\(283\) − 10.3923i − 0.617758i −0.951101 0.308879i \(-0.900046\pi\)
0.951101 0.308879i \(-0.0999539\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −18.0000 −1.06251
\(288\) 0 0
\(289\) 14.0000 0.823529
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 3.46410i 0.202375i 0.994867 + 0.101187i \(0.0322642\pi\)
−0.994867 + 0.101187i \(0.967736\pi\)
\(294\) 0 0
\(295\) − 51.9615i − 3.02532i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 18.0000 1.03750
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 27.7128i 1.58683i
\(306\) 0 0
\(307\) 25.9808i 1.48280i 0.671063 + 0.741400i \(0.265838\pi\)
−0.671063 + 0.741400i \(0.734162\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 6.00000 0.340229 0.170114 0.985424i \(-0.445586\pi\)
0.170114 + 0.985424i \(0.445586\pi\)
\(312\) 0 0
\(313\) −1.00000 −0.0565233 −0.0282617 0.999601i \(-0.508997\pi\)
−0.0282617 + 0.999601i \(0.508997\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 6.92820i − 0.389127i −0.980890 0.194563i \(-0.937671\pi\)
0.980890 0.194563i \(-0.0623290\pi\)
\(318\) 0 0
\(319\) 10.3923i 0.581857i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −3.00000 −0.166924
\(324\) 0 0
\(325\) −28.0000 −1.55316
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) − 41.5692i − 2.29179i
\(330\) 0 0
\(331\) 24.2487i 1.33283i 0.745581 + 0.666415i \(0.232172\pi\)
−0.745581 + 0.666415i \(0.767828\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 30.0000 1.63908
\(336\) 0 0
\(337\) −11.0000 −0.599208 −0.299604 0.954064i \(-0.596855\pi\)
−0.299604 + 0.954064i \(0.596855\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 6.92820i 0.374088i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −27.0000 −1.44944 −0.724718 0.689046i \(-0.758030\pi\)
−0.724718 + 0.689046i \(0.758030\pi\)
\(348\) 0 0
\(349\) 32.0000 1.71292 0.856460 0.516213i \(-0.172659\pi\)
0.856460 + 0.516213i \(0.172659\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 25.9808i 1.38282i 0.722464 + 0.691408i \(0.243009\pi\)
−0.722464 + 0.691408i \(0.756991\pi\)
\(354\) 0 0
\(355\) 20.7846i 1.10313i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 30.0000 1.58334 0.791670 0.610949i \(-0.209212\pi\)
0.791670 + 0.610949i \(0.209212\pi\)
\(360\) 0 0
\(361\) 16.0000 0.842105
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) − 38.1051i − 1.99451i
\(366\) 0 0
\(367\) 3.46410i 0.180825i 0.995904 + 0.0904123i \(0.0288185\pi\)
−0.995904 + 0.0904123i \(0.971182\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 20.0000 1.03556 0.517780 0.855514i \(-0.326758\pi\)
0.517780 + 0.855514i \(0.326758\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) − 13.8564i − 0.713641i
\(378\) 0 0
\(379\) − 19.0526i − 0.978664i −0.872098 0.489332i \(-0.837241\pi\)
0.872098 0.489332i \(-0.162759\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 18.0000 0.919757 0.459879 0.887982i \(-0.347893\pi\)
0.459879 + 0.887982i \(0.347893\pi\)
\(384\) 0 0
\(385\) 36.0000 1.83473
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) − 10.3923i − 0.526911i −0.964672 0.263455i \(-0.915138\pi\)
0.964672 0.263455i \(-0.0848622\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 12.0000 0.603786
\(396\) 0 0
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8.66025i 0.432472i 0.976341 + 0.216236i \(0.0693781\pi\)
−0.976341 + 0.216236i \(0.930622\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) 0 0
\(409\) −23.0000 −1.13728 −0.568638 0.822588i \(-0.692530\pi\)
−0.568638 + 0.822588i \(0.692530\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) − 51.9615i − 2.55686i
\(414\) 0 0
\(415\) 41.5692i 2.04055i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) − 12.1244i − 0.588118i
\(426\) 0 0
\(427\) 27.7128i 1.34112i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −18.0000 −0.867029 −0.433515 0.901146i \(-0.642727\pi\)
−0.433515 + 0.901146i \(0.642727\pi\)
\(432\) 0 0
\(433\) −31.0000 −1.48976 −0.744882 0.667196i \(-0.767494\pi\)
−0.744882 + 0.667196i \(0.767494\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 20.7846i 0.991995i 0.868324 + 0.495998i \(0.165198\pi\)
−0.868324 + 0.495998i \(0.834802\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.00000 −0.427603 −0.213801 0.976877i \(-0.568585\pi\)
−0.213801 + 0.976877i \(0.568585\pi\)
\(444\) 0 0
\(445\) −48.0000 −2.27542
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 25.9808i 1.22611i 0.790041 + 0.613054i \(0.210059\pi\)
−0.790041 + 0.613054i \(0.789941\pi\)
\(450\) 0 0
\(451\) − 15.5885i − 0.734032i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −48.0000 −2.25027
\(456\) 0 0
\(457\) −11.0000 −0.514558 −0.257279 0.966337i \(-0.582826\pi\)
−0.257279 + 0.966337i \(0.582826\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 20.7846i 0.968036i 0.875058 + 0.484018i \(0.160823\pi\)
−0.875058 + 0.484018i \(0.839177\pi\)
\(462\) 0 0
\(463\) − 17.3205i − 0.804952i −0.915430 0.402476i \(-0.868150\pi\)
0.915430 0.402476i \(-0.131850\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −3.00000 −0.138823 −0.0694117 0.997588i \(-0.522112\pi\)
−0.0694117 + 0.997588i \(0.522112\pi\)
\(468\) 0 0
\(469\) 30.0000 1.38527
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 15.5885i 0.716758i
\(474\) 0 0
\(475\) − 12.1244i − 0.556304i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 45.0333i 2.04486i
\(486\) 0 0
\(487\) − 17.3205i − 0.784867i −0.919780 0.392434i \(-0.871633\pi\)
0.919780 0.392434i \(-0.128367\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 15.0000 0.676941 0.338470 0.940977i \(-0.390091\pi\)
0.338470 + 0.940977i \(0.390091\pi\)
\(492\) 0 0
\(493\) 6.00000 0.270226
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 20.7846i 0.932317i
\(498\) 0 0
\(499\) − 15.5885i − 0.697835i −0.937153 0.348918i \(-0.886549\pi\)
0.937153 0.348918i \(-0.113451\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) −36.0000 −1.60198
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) − 20.7846i − 0.921262i −0.887592 0.460631i \(-0.847623\pi\)
0.887592 0.460631i \(-0.152377\pi\)
\(510\) 0 0
\(511\) − 38.1051i − 1.68567i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −48.0000 −2.11513
\(516\) 0 0
\(517\) 36.0000 1.58328
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) − 15.5885i − 0.682943i −0.939892 0.341471i \(-0.889075\pi\)
0.939892 0.341471i \(-0.110925\pi\)
\(522\) 0 0
\(523\) 17.3205i 0.757373i 0.925525 + 0.378686i \(0.123624\pi\)
−0.925525 + 0.378686i \(0.876376\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 20.7846i 0.900281i
\(534\) 0 0
\(535\) − 10.3923i − 0.449299i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 15.0000 0.646096
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 13.8564i 0.593543i
\(546\) 0 0
\(547\) 8.66025i 0.370286i 0.982712 + 0.185143i \(0.0592748\pi\)
−0.982712 + 0.185143i \(0.940725\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) 12.0000 0.510292
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 38.1051i 1.61457i 0.590165 + 0.807283i \(0.299063\pi\)
−0.590165 + 0.807283i \(0.700937\pi\)
\(558\) 0 0
\(559\) − 20.7846i − 0.879095i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.00000 0.379305 0.189652 0.981851i \(-0.439264\pi\)
0.189652 + 0.981851i \(0.439264\pi\)
\(564\) 0 0
\(565\) −24.0000 −1.00969
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) − 19.0526i − 0.798725i −0.916793 0.399362i \(-0.869232\pi\)
0.916793 0.399362i \(-0.130768\pi\)
\(570\) 0 0
\(571\) 12.1244i 0.507388i 0.967284 + 0.253694i \(0.0816457\pi\)
−0.967284 + 0.253694i \(0.918354\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −7.00000 −0.291414 −0.145707 0.989328i \(-0.546546\pi\)
−0.145707 + 0.989328i \(0.546546\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 41.5692i 1.72458i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.00000 −0.123823 −0.0619116 0.998082i \(-0.519720\pi\)
−0.0619116 + 0.998082i \(0.519720\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) − 6.92820i − 0.284507i −0.989830 0.142254i \(-0.954565\pi\)
0.989830 0.142254i \(-0.0454349\pi\)
\(594\) 0 0
\(595\) − 20.7846i − 0.852086i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 18.0000 0.735460 0.367730 0.929933i \(-0.380135\pi\)
0.367730 + 0.929933i \(0.380135\pi\)
\(600\) 0 0
\(601\) −7.00000 −0.285536 −0.142768 0.989756i \(-0.545600\pi\)
−0.142768 + 0.989756i \(0.545600\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) − 6.92820i − 0.281672i
\(606\) 0 0
\(607\) − 27.7128i − 1.12483i −0.826856 0.562414i \(-0.809873\pi\)
0.826856 0.562414i \(-0.190127\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −48.0000 −1.94187
\(612\) 0 0
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 29.4449i 1.18541i 0.805421 + 0.592703i \(0.201939\pi\)
−0.805421 + 0.592703i \(0.798061\pi\)
\(618\) 0 0
\(619\) − 29.4449i − 1.18349i −0.806126 0.591744i \(-0.798439\pi\)
0.806126 0.591744i \(-0.201561\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −48.0000 −1.92308
\(624\) 0 0
\(625\) −11.0000 −0.440000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 3.46410i 0.138123i
\(630\) 0 0
\(631\) − 3.46410i − 0.137904i −0.997620 0.0689519i \(-0.978035\pi\)
0.997620 0.0689519i \(-0.0219655\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −20.0000 −0.792429
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) − 43.3013i − 1.71030i −0.518383 0.855149i \(-0.673466\pi\)
0.518383 0.855149i \(-0.326534\pi\)
\(642\) 0 0
\(643\) − 25.9808i − 1.02458i −0.858812 0.512291i \(-0.828797\pi\)
0.858812 0.512291i \(-0.171203\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −42.0000 −1.65119 −0.825595 0.564263i \(-0.809160\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(648\) 0 0
\(649\) 45.0000 1.76640
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 31.1769i 1.22005i 0.792383 + 0.610023i \(0.208840\pi\)
−0.792383 + 0.610023i \(0.791160\pi\)
\(654\) 0 0
\(655\) 41.5692i 1.62424i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 24.0000 0.934907 0.467454 0.884018i \(-0.345171\pi\)
0.467454 + 0.884018i \(0.345171\pi\)
\(660\) 0 0
\(661\) 14.0000 0.544537 0.272268 0.962221i \(-0.412226\pi\)
0.272268 + 0.962221i \(0.412226\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) − 20.7846i − 0.805993i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −46.0000 −1.77317 −0.886585 0.462566i \(-0.846929\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 20.7846i 0.798817i 0.916773 + 0.399409i \(0.130785\pi\)
−0.916773 + 0.399409i \(0.869215\pi\)
\(678\) 0 0
\(679\) 45.0333i 1.72822i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 15.0000 0.573959 0.286980 0.957937i \(-0.407349\pi\)
0.286980 + 0.957937i \(0.407349\pi\)
\(684\) 0 0
\(685\) 6.00000 0.229248
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 31.1769i 1.18603i 0.805193 + 0.593013i \(0.202062\pi\)
−0.805193 + 0.593013i \(0.797938\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −66.0000 −2.50352
\(696\) 0 0
\(697\) −9.00000 −0.340899
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) − 27.7128i − 1.04670i −0.852118 0.523349i \(-0.824682\pi\)
0.852118 0.523349i \(-0.175318\pi\)
\(702\) 0 0
\(703\) 3.46410i 0.130651i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −36.0000 −1.35392
\(708\) 0 0
\(709\) 28.0000 1.05156 0.525781 0.850620i \(-0.323773\pi\)
0.525781 + 0.850620i \(0.323773\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) − 41.5692i − 1.55460i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 42.0000 1.56634 0.783168 0.621810i \(-0.213603\pi\)
0.783168 + 0.621810i \(0.213603\pi\)
\(720\) 0 0
\(721\) −48.0000 −1.78761
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 24.2487i 0.900575i
\(726\) 0 0
\(727\) 41.5692i 1.54172i 0.637006 + 0.770859i \(0.280172\pi\)
−0.637006 + 0.770859i \(0.719828\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 9.00000 0.332877
\(732\) 0 0
\(733\) 22.0000 0.812589 0.406294 0.913742i \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 25.9808i 0.957014i
\(738\) 0 0
\(739\) 25.9808i 0.955718i 0.878437 + 0.477859i \(0.158587\pi\)
−0.878437 + 0.477859i \(0.841413\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18.0000 −0.660356 −0.330178 0.943919i \(-0.607109\pi\)
−0.330178 + 0.943919i \(0.607109\pi\)
\(744\) 0 0
\(745\) 48.0000 1.75858
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) − 10.3923i − 0.379727i
\(750\) 0 0
\(751\) 38.1051i 1.39048i 0.718780 + 0.695238i \(0.244701\pi\)
−0.718780 + 0.695238i \(0.755299\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −24.0000 −0.873449
\(756\) 0 0
\(757\) −26.0000 −0.944986 −0.472493 0.881334i \(-0.656646\pi\)
−0.472493 + 0.881334i \(0.656646\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) − 48.4974i − 1.75803i −0.476794 0.879015i \(-0.658201\pi\)
0.476794 0.879015i \(-0.341799\pi\)
\(762\) 0 0
\(763\) 13.8564i 0.501636i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −60.0000 −2.16647
\(768\) 0 0
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.92820i 0.249190i 0.992208 + 0.124595i \(0.0397632\pi\)
−0.992208 + 0.124595i \(0.960237\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.00000 −0.322458
\(780\) 0 0
\(781\) −18.0000 −0.644091
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 27.7128i 0.989113i
\(786\) 0 0
\(787\) 17.3205i 0.617409i 0.951158 + 0.308705i \(0.0998955\pi\)
−0.951158 + 0.308705i \(0.900105\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −24.0000 −0.853342
\(792\) 0 0
\(793\) 32.0000 1.13635
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 3.46410i − 0.122705i −0.998116 0.0613524i \(-0.980459\pi\)
0.998116 0.0613524i \(-0.0195413\pi\)
\(798\) 0 0
\(799\) − 20.7846i − 0.735307i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 33.0000 1.16454
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 19.0526i 0.669852i 0.942244 + 0.334926i \(0.108711\pi\)
−0.942244 + 0.334926i \(0.891289\pi\)
\(810\) 0 0
\(811\) 36.3731i 1.27723i 0.769526 + 0.638616i \(0.220493\pi\)
−0.769526 + 0.638616i \(0.779507\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −12.0000 −0.420342
\(816\) 0 0
\(817\) 9.00000 0.314870
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 3.46410i 0.120898i 0.998171 + 0.0604490i \(0.0192532\pi\)
−0.998171 + 0.0604490i \(0.980747\pi\)
\(822\) 0 0
\(823\) − 24.2487i − 0.845257i −0.906303 0.422628i \(-0.861108\pi\)
0.906303 0.422628i \(-0.138892\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −36.0000 −1.25184 −0.625921 0.779886i \(-0.715277\pi\)
−0.625921 + 0.779886i \(0.715277\pi\)
\(828\) 0 0
\(829\) −26.0000 −0.903017 −0.451509 0.892267i \(-0.649114\pi\)
−0.451509 + 0.892267i \(0.649114\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) − 8.66025i − 0.300060i
\(834\) 0 0
\(835\) − 20.7846i − 0.719281i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 36.0000 1.24286 0.621429 0.783470i \(-0.286552\pi\)
0.621429 + 0.783470i \(0.286552\pi\)
\(840\) 0 0
\(841\) 17.0000 0.586207
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 10.3923i 0.357506i
\(846\) 0 0
\(847\) − 6.92820i − 0.238056i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 32.0000 1.09566 0.547830 0.836590i \(-0.315454\pi\)
0.547830 + 0.836590i \(0.315454\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 34.6410i 1.18331i 0.806190 + 0.591657i \(0.201526\pi\)
−0.806190 + 0.591657i \(0.798474\pi\)
\(858\) 0 0
\(859\) 29.4449i 1.00465i 0.864680 + 0.502323i \(0.167521\pi\)
−0.864680 + 0.502323i \(0.832479\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 30.0000 1.02121 0.510606 0.859815i \(-0.329421\pi\)
0.510606 + 0.859815i \(0.329421\pi\)
\(864\) 0 0
\(865\) 84.0000 2.85609
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 10.3923i 0.352535i
\(870\) 0 0
\(871\) − 34.6410i − 1.17377i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 24.0000 0.811348
\(876\) 0 0
\(877\) −40.0000 −1.35070 −0.675352 0.737496i \(-0.736008\pi\)
−0.675352 + 0.737496i \(0.736008\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) − 20.7846i − 0.700251i −0.936703 0.350126i \(-0.886139\pi\)
0.936703 0.350126i \(-0.113861\pi\)
\(882\) 0 0
\(883\) 8.66025i 0.291441i 0.989326 + 0.145720i \(0.0465500\pi\)
−0.989326 + 0.145720i \(0.953450\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 42.0000 1.41022 0.705111 0.709097i \(-0.250897\pi\)
0.705111 + 0.709097i \(0.250897\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 20.7846i − 0.695530i
\(894\) 0 0
\(895\) 41.5692i 1.38951i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) − 27.7128i − 0.921205i
\(906\) 0 0
\(907\) − 39.8372i − 1.32277i −0.750046 0.661386i \(-0.769969\pi\)
0.750046 0.661386i \(-0.230031\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 24.0000 0.795155 0.397578 0.917568i \(-0.369851\pi\)
0.397578 + 0.917568i \(0.369851\pi\)
\(912\) 0 0
\(913\) −36.0000 −1.19143
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 41.5692i 1.37274i
\(918\) 0 0
\(919\) − 41.5692i − 1.37124i −0.727959 0.685621i \(-0.759531\pi\)
0.727959 0.685621i \(-0.240469\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 24.0000 0.789970
\(924\) 0 0
\(925\) −14.0000 −0.460317
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 6.92820i 0.227307i 0.993520 + 0.113653i \(0.0362554\pi\)
−0.993520 + 0.113653i \(0.963745\pi\)
\(930\) 0 0
\(931\) − 8.66025i − 0.283828i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 18.0000 0.588663
\(936\) 0 0
\(937\) −34.0000 −1.11073 −0.555366 0.831606i \(-0.687422\pi\)
−0.555366 + 0.831606i \(0.687422\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) − 13.8564i − 0.451706i −0.974161 0.225853i \(-0.927483\pi\)
0.974161 0.225853i \(-0.0725169\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 9.00000 0.292461 0.146230 0.989251i \(-0.453286\pi\)
0.146230 + 0.989251i \(0.453286\pi\)
\(948\) 0 0
\(949\) −44.0000 −1.42830
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 12.1244i − 0.392746i −0.980529 0.196373i \(-0.937084\pi\)
0.980529 0.196373i \(-0.0629164\pi\)
\(954\) 0 0
\(955\) 20.7846i 0.672574i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 6.00000 0.193750
\(960\) 0 0
\(961\) 31.0000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 79.6743i 2.56481i
\(966\) 0 0
\(967\) − 24.2487i − 0.779786i −0.920860 0.389893i \(-0.872512\pi\)
0.920860 0.389893i \(-0.127488\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 12.0000 0.385098 0.192549 0.981287i \(-0.438325\pi\)
0.192549 + 0.981287i \(0.438325\pi\)
\(972\) 0 0
\(973\) −66.0000 −2.11586
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 15.5885i 0.498719i 0.968411 + 0.249359i \(0.0802201\pi\)
−0.968411 + 0.249359i \(0.919780\pi\)
\(978\) 0 0
\(979\) − 41.5692i − 1.32856i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −6.00000 −0.191370 −0.0956851 0.995412i \(-0.530504\pi\)
−0.0956851 + 0.995412i \(0.530504\pi\)
\(984\) 0 0
\(985\) 48.0000 1.52941
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) − 48.4974i − 1.54057i −0.637699 0.770286i \(-0.720114\pi\)
0.637699 0.770286i \(-0.279886\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −12.0000 −0.380426
\(996\) 0 0
\(997\) 20.0000 0.633406 0.316703 0.948525i \(-0.397424\pi\)
0.316703 + 0.948525i \(0.397424\pi\)
\(998\) 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 1296.2.c.b.1295.2 2
3.2 odd 2 1296.2.c.d.1295.1 2
4.3 odd 2 1296.2.c.d.1295.2 2
8.3 odd 2 5184.2.c.a.5183.1 2
8.5 even 2 5184.2.c.c.5183.1 2
9.2 odd 6 432.2.s.d.287.1 2
9.4 even 3 432.2.s.c.143.1 2
9.5 odd 6 144.2.s.a.47.1 2
9.7 even 3 144.2.s.d.95.1 yes 2
12.11 even 2 inner 1296.2.c.b.1295.1 2
24.5 odd 2 5184.2.c.a.5183.2 2
24.11 even 2 5184.2.c.c.5183.2 2
36.7 odd 6 144.2.s.a.95.1 yes 2
36.11 even 6 432.2.s.c.287.1 2
36.23 even 6 144.2.s.d.47.1 yes 2
36.31 odd 6 432.2.s.d.143.1 2
72.5 odd 6 576.2.s.d.191.1 2
72.11 even 6 1728.2.s.a.1151.1 2
72.13 even 6 1728.2.s.a.575.1 2
72.29 odd 6 1728.2.s.b.1151.1 2
72.43 odd 6 576.2.s.d.383.1 2
72.59 even 6 576.2.s.a.191.1 2
72.61 even 6 576.2.s.a.383.1 2
72.67 odd 6 1728.2.s.b.575.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.s.a.47.1 2 9.5 odd 6
144.2.s.a.95.1 yes 2 36.7 odd 6
144.2.s.d.47.1 yes 2 36.23 even 6
144.2.s.d.95.1 yes 2 9.7 even 3
432.2.s.c.143.1 2 9.4 even 3
432.2.s.c.287.1 2 36.11 even 6
432.2.s.d.143.1 2 36.31 odd 6
432.2.s.d.287.1 2 9.2 odd 6
576.2.s.a.191.1 2 72.59 even 6
576.2.s.a.383.1 2 72.61 even 6
576.2.s.d.191.1 2 72.5 odd 6
576.2.s.d.383.1 2 72.43 odd 6
1296.2.c.b.1295.1 2 12.11 even 2 inner
1296.2.c.b.1295.2 2 1.1 even 1 trivial
1296.2.c.d.1295.1 2 3.2 odd 2
1296.2.c.d.1295.2 2 4.3 odd 2
1728.2.s.a.575.1 2 72.13 even 6
1728.2.s.a.1151.1 2 72.11 even 6
1728.2.s.b.575.1 2 72.67 odd 6
1728.2.s.b.1151.1 2 72.29 odd 6
5184.2.c.a.5183.1 2 8.3 odd 2
5184.2.c.a.5183.2 2 24.5 odd 2
5184.2.c.c.5183.1 2 8.5 even 2
5184.2.c.c.5183.2 2 24.11 even 2