Properties

Label 576.2.r.c.481.2
Level $576$
Weight $2$
Character 576.481
Analytic conductor $4.599$
Analytic rank $0$
Dimension $8$
CM discriminant -8
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [576,2,Mod(97,576)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(576, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("576.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.r (of order \(6\), degree \(2\), 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: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
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: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label 481.2
Root \(0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 576.481
Dual form 576.2.r.c.97.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.158919 + 1.72474i) q^{3} +(-2.94949 - 0.548188i) q^{9} +O(q^{10})\) \(q+(-0.158919 + 1.72474i) q^{3} +(-2.94949 - 0.548188i) q^{9} +(-4.71940 + 2.72474i) q^{11} -1.89898 q^{17} +8.34847i q^{19} +(-2.50000 - 4.33013i) q^{25} +(1.41421 - 5.00000i) q^{27} +(-3.94949 - 8.57277i) q^{33} +(-6.39898 + 11.0834i) q^{41} +(-2.03383 + 1.17423i) q^{43} +(3.50000 - 6.06218i) q^{49} +(0.301783 - 3.27526i) q^{51} +(-14.3990 - 1.32673i) q^{57} +(-8.00853 - 4.62372i) q^{59} +(12.4261 + 7.17423i) q^{67} +13.6969 q^{73} +(7.86566 - 3.62372i) q^{75} +(8.39898 + 3.23375i) q^{81} +(-15.5885 + 9.00000i) q^{83} +18.0000 q^{89} +(9.84847 + 17.0580i) q^{97} +(15.4135 - 5.44949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{9} + 24 q^{17} - 20 q^{25} - 12 q^{33} - 12 q^{41} + 28 q^{49} - 76 q^{57} - 8 q^{73} + 28 q^{81} + 144 q^{89} + 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

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
\(3\) −0.158919 + 1.72474i −0.0917517 + 0.995782i
\(4\) 0 0
\(5\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(6\) 0 0
\(7\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(8\) 0 0
\(9\) −2.94949 0.548188i −0.983163 0.182729i
\(10\) 0 0
\(11\) −4.71940 + 2.72474i −1.42295 + 0.821541i −0.996550 0.0829925i \(-0.973552\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(12\) 0 0
\(13\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.89898 −0.460570 −0.230285 0.973123i \(-0.573966\pi\)
−0.230285 + 0.973123i \(0.573966\pi\)
\(18\) 0 0
\(19\) 8.34847i 1.91527i 0.287984 + 0.957635i \(0.407015\pi\)
−0.287984 + 0.957635i \(0.592985\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) 0 0
\(25\) −2.50000 4.33013i −0.500000 0.866025i
\(26\) 0 0
\(27\) 1.41421 5.00000i 0.272166 0.962250i
\(28\) 0 0
\(29\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(30\) 0 0
\(31\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(32\) 0 0
\(33\) −3.94949 8.57277i −0.687518 1.49233i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.39898 + 11.0834i −0.999353 + 1.73093i −0.468521 + 0.883452i \(0.655213\pi\)
−0.530831 + 0.847477i \(0.678120\pi\)
\(42\) 0 0
\(43\) −2.03383 + 1.17423i −0.310157 + 0.179069i −0.646997 0.762493i \(-0.723975\pi\)
0.336840 + 0.941562i \(0.390642\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 3.50000 6.06218i 0.500000 0.866025i
\(50\) 0 0
\(51\) 0.301783 3.27526i 0.0422581 0.458627i
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −14.3990 1.32673i −1.90719 0.175729i
\(58\) 0 0
\(59\) −8.00853 4.62372i −1.04262 0.601958i −0.122047 0.992524i \(-0.538946\pi\)
−0.920575 + 0.390567i \(0.872279\pi\)
\(60\) 0 0
\(61\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 12.4261 + 7.17423i 1.51809 + 0.876472i 0.999773 + 0.0212861i \(0.00677610\pi\)
0.518321 + 0.855186i \(0.326557\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 13.6969 1.60311 0.801553 0.597924i \(-0.204008\pi\)
0.801553 + 0.597924i \(0.204008\pi\)
\(74\) 0 0
\(75\) 7.86566 3.62372i 0.908248 0.418432i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(80\) 0 0
\(81\) 8.39898 + 3.23375i 0.933220 + 0.359306i
\(82\) 0 0
\(83\) −15.5885 + 9.00000i −1.71106 + 0.987878i −0.777913 + 0.628372i \(0.783721\pi\)
−0.933143 + 0.359506i \(0.882945\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 18.0000 1.90800 0.953998 0.299813i \(-0.0969242\pi\)
0.953998 + 0.299813i \(0.0969242\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 9.84847 + 17.0580i 0.999961 + 1.73198i 0.507673 + 0.861550i \(0.330506\pi\)
0.492287 + 0.870433i \(0.336161\pi\)
\(98\) 0 0
\(99\) 15.4135 5.44949i 1.54911 0.547694i
\(100\) 0 0
\(101\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(102\) 0 0
\(103\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 20.1464i 1.94763i −0.227345 0.973814i \(-0.573004\pi\)
0.227345 0.973814i \(-0.426996\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.00000 + 15.5885i −0.846649 + 1.46644i 0.0375328 + 0.999295i \(0.488050\pi\)
−0.884182 + 0.467143i \(0.845283\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 9.34847 16.1920i 0.849861 1.47200i
\(122\) 0 0
\(123\) −18.0990 12.7980i −1.63194 1.15395i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) −1.70204 3.69445i −0.149856 0.325278i
\(130\) 0 0
\(131\) 15.5885 + 9.00000i 1.36197 + 0.786334i 0.989886 0.141865i \(-0.0453100\pi\)
0.372084 + 0.928199i \(0.378643\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.29796 + 14.3725i 0.708942 + 1.22792i 0.965250 + 0.261329i \(0.0841608\pi\)
−0.256307 + 0.966595i \(0.582506\pi\)
\(138\) 0 0
\(139\) 3.16232 + 1.82577i 0.268224 + 0.154859i 0.628080 0.778148i \(-0.283841\pi\)
−0.359856 + 0.933008i \(0.617174\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 9.89949 + 7.00000i 0.816497 + 0.577350i
\(148\) 0 0
\(149\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(150\) 0 0
\(151\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(152\) 0 0
\(153\) 5.60102 + 1.04100i 0.452816 + 0.0841597i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 2.00000i 0.156652i −0.996928 0.0783260i \(-0.975042\pi\)
0.996928 0.0783260i \(-0.0249575\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(168\) 0 0
\(169\) −6.50000 11.2583i −0.500000 0.866025i
\(170\) 0 0
\(171\) 4.57653 24.6237i 0.349976 1.88302i
\(172\) 0 0
\(173\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 9.24745 13.0779i 0.695081 0.982993i
\(178\) 0 0
\(179\) 18.0000i 1.34538i −0.739923 0.672692i \(-0.765138\pi\)
0.739923 0.672692i \(-0.234862\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 8.96204 5.17423i 0.655369 0.378378i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0 0
\(193\) −12.8485 + 22.2542i −0.924853 + 1.60189i −0.133056 + 0.991109i \(0.542479\pi\)
−0.791797 + 0.610784i \(0.790854\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) −14.3485 + 20.2918i −1.01206 + 1.43127i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −22.7474 39.3997i −1.57347 2.72534i
\(210\) 0 0
\(211\) −12.1244 7.00000i −0.834675 0.481900i 0.0207756 0.999784i \(-0.493386\pi\)
−0.855451 + 0.517884i \(0.826720\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −2.17670 + 23.6237i −0.147088 + 1.59634i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(224\) 0 0
\(225\) 5.00000 + 14.1421i 0.333333 + 0.942809i
\(226\) 0 0
\(227\) −10.8691 + 6.27526i −0.721405 + 0.416503i −0.815270 0.579082i \(-0.803411\pi\)
0.0938647 + 0.995585i \(0.470078\pi\)
\(228\) 0 0
\(229\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 19.8990 1.30363 0.651813 0.758380i \(-0.274009\pi\)
0.651813 + 0.758380i \(0.274009\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) −0.848469 1.46959i −0.0546547 0.0946647i 0.837404 0.546585i \(-0.184072\pi\)
−0.892058 + 0.451920i \(0.850739\pi\)
\(242\) 0 0
\(243\) −6.91215 + 13.9722i −0.443415 + 0.896317i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −13.0454 28.3164i −0.826719 1.79448i
\(250\) 0 0
\(251\) 23.9444i 1.51136i 0.654943 + 0.755678i \(0.272693\pi\)
−0.654943 + 0.755678i \(0.727307\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.60102 + 4.50510i −0.162247 + 0.281020i −0.935674 0.352865i \(-0.885208\pi\)
0.773427 + 0.633885i \(0.218541\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −2.86054 + 31.0454i −0.175062 + 1.89995i
\(268\) 0 0
\(269\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 23.5970 + 13.6237i 1.42295 + 0.821541i
\(276\) 0 0
\(277\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −9.00000 15.5885i −0.536895 0.929929i −0.999069 0.0431402i \(-0.986264\pi\)
0.462174 0.886789i \(-0.347070\pi\)
\(282\) 0 0
\(283\) −19.0526 11.0000i −1.13256 0.653882i −0.187980 0.982173i \(-0.560194\pi\)
−0.944577 + 0.328291i \(0.893527\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −13.3939 −0.787875
\(290\) 0 0
\(291\) −30.9859 + 14.2753i −1.81642 + 0.836830i
\(292\) 0 0
\(293\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 6.94949 + 27.4504i 0.403250 + 1.59283i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 9.65153i 0.550842i 0.961324 + 0.275421i \(0.0888172\pi\)
−0.961324 + 0.275421i \(0.911183\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) −12.1969 21.1257i −0.689412 1.19410i −0.972028 0.234863i \(-0.924536\pi\)
0.282617 0.959233i \(-0.408798\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 34.7474 + 3.20164i 1.93941 + 0.178698i
\(322\) 0 0
\(323\) 15.8536i 0.882116i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −22.5167 + 13.0000i −1.23763 + 0.714545i −0.968609 0.248590i \(-0.920033\pi\)
−0.269019 + 0.963135i \(0.586699\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −18.1969 + 31.5180i −0.991250 + 1.71690i −0.381314 + 0.924445i \(0.624528\pi\)
−0.609936 + 0.792451i \(0.708805\pi\)
\(338\) 0 0
\(339\) −25.4558 18.0000i −1.38257 0.977626i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 30.1752 + 17.4217i 1.61989 + 0.935245i 0.986947 + 0.161048i \(0.0514875\pi\)
0.632945 + 0.774197i \(0.281846\pi\)
\(348\) 0 0
\(349\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −17.2980 29.9609i −0.920677 1.59466i −0.798369 0.602168i \(-0.794304\pi\)
−0.122308 0.992492i \(-0.539030\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −50.6969 −2.66826
\(362\) 0 0
\(363\) 26.4415 + 18.6969i 1.38782 + 0.981335i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(368\) 0 0
\(369\) 24.9495 29.1824i 1.29882 1.51918i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 26.3485i 1.35343i −0.736245 0.676715i \(-0.763403\pi\)
0.736245 0.676715i \(-0.236597\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 6.64247 2.34847i 0.337656 0.119379i
\(388\) 0 0
\(389\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −18.0000 + 25.4558i −0.907980 + 1.28408i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 15.6464 27.1004i 0.781345 1.35333i −0.149813 0.988714i \(-0.547867\pi\)
0.931158 0.364615i \(-0.118800\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 9.19694 15.9296i 0.454759 0.787666i −0.543915 0.839140i \(-0.683059\pi\)
0.998674 + 0.0514740i \(0.0163919\pi\)
\(410\) 0 0
\(411\) −26.1076 + 12.0278i −1.28779 + 0.593288i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −3.65153 + 5.16404i −0.178816 + 0.252884i
\(418\) 0 0
\(419\) 15.5885 + 9.00000i 0.761546 + 0.439679i 0.829851 0.557986i \(-0.188426\pi\)
−0.0683046 + 0.997665i \(0.521759\pi\)
\(420\) 0 0
\(421\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 4.74745 + 8.22282i 0.230285 + 0.398865i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 4.30306 0.206792 0.103396 0.994640i \(-0.467029\pi\)
0.103396 + 0.994640i \(0.467029\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) −13.6464 + 15.9617i −0.649830 + 0.760080i
\(442\) 0 0
\(443\) 20.3079 11.7247i 0.964855 0.557059i 0.0671913 0.997740i \(-0.478596\pi\)
0.897664 + 0.440681i \(0.145263\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −16.1010 −0.759854 −0.379927 0.925016i \(-0.624051\pi\)
−0.379927 + 0.925016i \(0.624051\pi\)
\(450\) 0 0
\(451\) 69.7423i 3.28404i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 21.1969 + 36.7142i 0.991551 + 1.71742i 0.608114 + 0.793849i \(0.291926\pi\)
0.383437 + 0.923567i \(0.374740\pi\)
\(458\) 0 0
\(459\) −2.68556 + 9.49490i −0.125351 + 0.443184i
\(460\) 0 0
\(461\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 41.9444i 1.94095i −0.241192 0.970477i \(-0.577538\pi\)
0.241192 0.970477i \(-0.422462\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 6.39898 11.0834i 0.294225 0.509613i
\(474\) 0 0
\(475\) 36.1499 20.8712i 1.65867 0.957635i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0 0
\(489\) 3.44949 + 0.317837i 0.155991 + 0.0143731i
\(490\) 0 0
\(491\) −7.57993 4.37628i −0.342078 0.197499i 0.319113 0.947717i \(-0.396615\pi\)
−0.661190 + 0.750218i \(0.729948\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −25.7576 14.8712i −1.15307 0.665725i −0.203436 0.979088i \(-0.565211\pi\)
−0.949633 + 0.313363i \(0.898544\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 20.4507 9.42168i 0.908248 0.418432i
\(508\) 0 0
\(509\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 41.7423 + 11.8065i 1.84297 + 0.521271i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 42.1918 1.84846 0.924229 0.381839i \(-0.124709\pi\)
0.924229 + 0.381839i \(0.124709\pi\)
\(522\) 0 0
\(523\) 38.0000i 1.66162i 0.556553 + 0.830812i \(0.312124\pi\)
−0.556553 + 0.830812i \(0.687876\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) 21.0864 + 18.0278i 0.915072 + 0.782340i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 31.0454 + 2.86054i 1.33971 + 0.123441i
\(538\) 0 0
\(539\) 38.1464i 1.64308i
\(540\) 0 0
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −13.5546 + 7.82577i −0.579554 + 0.334606i −0.760956 0.648803i \(-0.775270\pi\)
0.181402 + 0.983409i \(0.441936\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 7.50000 + 16.2795i 0.316650 + 0.687321i
\(562\) 0 0
\(563\) −14.5868 8.42168i −0.614760 0.354932i 0.160066 0.987106i \(-0.448829\pi\)
−0.774826 + 0.632175i \(0.782163\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.702041 + 1.21597i 0.0294311 + 0.0509761i 0.880366 0.474295i \(-0.157297\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 0 0
\(571\) 41.3461 + 23.8712i 1.73028 + 0.998978i 0.887745 + 0.460336i \(0.152271\pi\)
0.842535 + 0.538642i \(0.181062\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 12.3939 0.515964 0.257982 0.966150i \(-0.416942\pi\)
0.257982 + 0.966150i \(0.416942\pi\)
\(578\) 0 0
\(579\) −36.3410 25.6969i −1.51028 1.06793i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 33.4644 19.3207i 1.38122 0.797449i 0.388918 0.921272i \(-0.372849\pi\)
0.992304 + 0.123823i \(0.0395156\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 18.0000 0.739171 0.369586 0.929197i \(-0.379500\pi\)
0.369586 + 0.929197i \(0.379500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) −18.8485 32.6465i −0.768845 1.33168i −0.938190 0.346122i \(-0.887498\pi\)
0.169344 0.985557i \(-0.445835\pi\)
\(602\) 0 0
\(603\) −32.7179 27.9722i −1.33238 1.13912i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −24.6464 + 42.6889i −0.992228 + 1.71859i −0.388351 + 0.921512i \(0.626955\pi\)
−0.603877 + 0.797077i \(0.706378\pi\)
\(618\) 0 0
\(619\) −20.5615 + 11.8712i −0.826435 + 0.477143i −0.852631 0.522514i \(-0.824994\pi\)
0.0261952 + 0.999657i \(0.491661\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) 0 0
\(627\) 71.5695 32.9722i 2.85821 1.31678i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 14.0000 19.7990i 0.556450 0.786939i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 22.7474 + 39.3997i 0.898470 + 1.55620i 0.829450 + 0.558581i \(0.188654\pi\)
0.0690201 + 0.997615i \(0.478013\pi\)
\(642\) 0 0
\(643\) −28.0146 16.1742i −1.10479 0.637850i −0.167313 0.985904i \(-0.553509\pi\)
−0.937474 + 0.348054i \(0.886843\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(648\) 0 0
\(649\) 50.3939 1.97813
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −40.3990 7.50850i −1.57611 0.292934i
\(658\) 0 0
\(659\) −15.5885 + 9.00000i −0.607240 + 0.350590i −0.771885 0.635763i \(-0.780686\pi\)
0.164644 + 0.986353i \(0.447352\pi\)
\(660\) 0 0
\(661\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −5.00000 8.66025i −0.192736 0.333828i 0.753420 0.657539i \(-0.228403\pi\)
−0.946156 + 0.323711i \(0.895069\pi\)
\(674\) 0 0
\(675\) −25.1862 + 6.37628i −0.969416 + 0.245423i
\(676\) 0 0
\(677\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −9.09592 19.7436i −0.348556 0.756577i
\(682\) 0 0
\(683\) 5.94439i 0.227456i −0.993512 0.113728i \(-0.963721\pi\)
0.993512 0.113728i \(-0.0362792\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 39.8372 23.0000i 1.51548 0.874961i 0.515642 0.856804i \(-0.327553\pi\)
0.999835 0.0181572i \(-0.00577993\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 12.1515 21.0471i 0.460272 0.797215i
\(698\) 0 0
\(699\) −3.16232 + 34.3207i −0.119610 + 1.29813i
\(700\) 0 0
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 2.66951 1.22985i 0.0992801 0.0457385i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(728\) 0 0
\(729\) −23.0000 14.1421i −0.851852 0.523783i
\(730\) 0 0
\(731\) 3.86221 2.22985i 0.142849 0.0824739i
\(732\) 0 0
\(733\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −78.1918 −2.88023
\(738\) 0 0
\(739\) 53.7423i 1.97694i 0.151403 + 0.988472i \(0.451621\pi\)
−0.151403 + 0.988472i \(0.548379\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 50.9117 18.0000i 1.86276 0.658586i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(752\) 0 0
\(753\) −41.2980 3.80521i −1.50498 0.138670i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 27.0000 46.7654i 0.978749 1.69524i 0.311787 0.950152i \(-0.399073\pi\)
0.666962 0.745091i \(-0.267594\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 11.0000 19.0526i 0.396670 0.687053i −0.596643 0.802507i \(-0.703499\pi\)
0.993313 + 0.115454i \(0.0368323\pi\)
\(770\) 0 0
\(771\) −7.35680 5.20204i −0.264949 0.187347i
\(772\) 0 0
\(773\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −92.5291 53.4217i −3.31520 1.91403i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 43.3013 + 25.0000i 1.54352 + 0.891154i 0.998613 + 0.0526599i \(0.0167699\pi\)
0.544911 + 0.838494i \(0.316563\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −53.0908 9.86739i −1.87587 0.348647i
\(802\) 0 0
\(803\) −64.6413 + 37.3207i −2.28114 + 1.31702i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −45.9898 −1.61692 −0.808458 0.588555i \(-0.799697\pi\)
−0.808458 + 0.588555i \(0.799697\pi\)
\(810\) 0 0
\(811\) 17.7423i 0.623018i 0.950243 + 0.311509i \(0.100834\pi\)
−0.950243 + 0.311509i \(0.899166\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −9.80306 16.9794i −0.342966 0.594034i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(822\) 0 0
\(823\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(824\) 0 0
\(825\) −27.2474 + 38.5337i −0.948634 + 1.34157i
\(826\) 0 0
\(827\) 54.0000i 1.87776i 0.344239 + 0.938882i \(0.388137\pi\)
−0.344239 + 0.938882i \(0.611863\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −6.64643 + 11.5120i −0.230285 + 0.398865i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(840\) 0 0
\(841\) −14.5000 + 25.1147i −0.500000 + 0.866025i
\(842\) 0 0
\(843\) 28.3164 13.0454i 0.975268 0.449308i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 22.0000 31.1127i 0.755038 1.06779i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 27.0000 + 46.7654i 0.922302 + 1.59747i 0.795843 + 0.605503i \(0.207028\pi\)
0.126459 + 0.991972i \(0.459639\pi\)
\(858\) 0 0
\(859\) −18.7508 10.8258i −0.639768 0.369370i 0.144757 0.989467i \(-0.453760\pi\)
−0.784525 + 0.620097i \(0.787093\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 2.12854 23.1010i 0.0722889 0.784552i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −19.6969 55.7114i −0.666640 1.88554i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) 52.4393i 1.76472i 0.470573 + 0.882361i \(0.344047\pi\)
−0.470573 + 0.882361i \(0.655953\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −48.4493 + 7.62372i −1.62311 + 0.255404i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 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
\(905\) 0 0
\(906\) 0 0
\(907\) −40.2176 + 23.2196i −1.33540 + 0.770996i −0.986122 0.166022i \(-0.946908\pi\)
−0.349281 + 0.937018i \(0.613574\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(912\) 0 0
\(913\) 49.0454 84.9491i 1.62317 2.81141i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(920\) 0 0
\(921\) −16.6464 1.53381i −0.548518 0.0505407i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 27.0000 + 46.7654i 0.885841 + 1.53432i 0.844746 + 0.535167i \(0.179751\pi\)
0.0410949 + 0.999155i \(0.486915\pi\)
\(930\) 0 0
\(931\) 50.6099 + 29.2196i 1.65867 + 0.957635i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 34.0000 1.11073 0.555366 0.831606i \(-0.312578\pi\)
0.555366 + 0.831606i \(0.312578\pi\)
\(938\) 0 0
\(939\) 38.3748 17.6793i 1.25231 0.576943i
\(940\) 0 0
\(941\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 27.3147 15.7702i 0.887609 0.512461i 0.0144491 0.999896i \(-0.495401\pi\)
0.873160 + 0.487435i \(0.162067\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −60.1918 −1.94980 −0.974902 0.222633i \(-0.928535\pi\)
−0.974902 + 0.222633i \(0.928535\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 15.5000 + 26.8468i 0.500000 + 0.866025i
\(962\) 0 0
\(963\) −11.0440 + 59.4217i −0.355889 + 1.91484i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(968\) 0 0
\(969\) 27.3434 + 2.51943i 0.878395 + 0.0809357i
\(970\) 0 0
\(971\) 54.0000i 1.73294i 0.499227 + 0.866471i \(0.333617\pi\)
−0.499227 + 0.866471i \(0.666383\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −28.4444 + 49.2671i −0.910017 + 1.57619i −0.0959785 + 0.995383i \(0.530598\pi\)
−0.814038 + 0.580812i \(0.802735\pi\)
\(978\) 0 0
\(979\) −84.9491 + 49.0454i −2.71499 + 1.56750i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) −18.8434 40.9014i −0.597976 1.29797i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(998\) 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 576.2.r.c.481.2 yes 8
3.2 odd 2 1728.2.r.c.1441.4 8
4.3 odd 2 inner 576.2.r.c.481.3 yes 8
8.3 odd 2 CM 576.2.r.c.481.2 yes 8
8.5 even 2 inner 576.2.r.c.481.3 yes 8
9.2 odd 6 1728.2.r.c.289.1 8
9.4 even 3 5184.2.d.l.2593.1 4
9.5 odd 6 5184.2.d.e.2593.4 4
9.7 even 3 inner 576.2.r.c.97.3 yes 8
12.11 even 2 1728.2.r.c.1441.1 8
24.5 odd 2 1728.2.r.c.1441.1 8
24.11 even 2 1728.2.r.c.1441.4 8
36.7 odd 6 inner 576.2.r.c.97.2 8
36.11 even 6 1728.2.r.c.289.4 8
36.23 even 6 5184.2.d.e.2593.1 4
36.31 odd 6 5184.2.d.l.2593.4 4
72.5 odd 6 5184.2.d.e.2593.1 4
72.11 even 6 1728.2.r.c.289.1 8
72.13 even 6 5184.2.d.l.2593.4 4
72.29 odd 6 1728.2.r.c.289.4 8
72.43 odd 6 inner 576.2.r.c.97.3 yes 8
72.59 even 6 5184.2.d.e.2593.4 4
72.61 even 6 inner 576.2.r.c.97.2 8
72.67 odd 6 5184.2.d.l.2593.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
576.2.r.c.97.2 8 36.7 odd 6 inner
576.2.r.c.97.2 8 72.61 even 6 inner
576.2.r.c.97.3 yes 8 9.7 even 3 inner
576.2.r.c.97.3 yes 8 72.43 odd 6 inner
576.2.r.c.481.2 yes 8 1.1 even 1 trivial
576.2.r.c.481.2 yes 8 8.3 odd 2 CM
576.2.r.c.481.3 yes 8 4.3 odd 2 inner
576.2.r.c.481.3 yes 8 8.5 even 2 inner
1728.2.r.c.289.1 8 9.2 odd 6
1728.2.r.c.289.1 8 72.11 even 6
1728.2.r.c.289.4 8 36.11 even 6
1728.2.r.c.289.4 8 72.29 odd 6
1728.2.r.c.1441.1 8 12.11 even 2
1728.2.r.c.1441.1 8 24.5 odd 2
1728.2.r.c.1441.4 8 3.2 odd 2
1728.2.r.c.1441.4 8 24.11 even 2
5184.2.d.e.2593.1 4 36.23 even 6
5184.2.d.e.2593.1 4 72.5 odd 6
5184.2.d.e.2593.4 4 9.5 odd 6
5184.2.d.e.2593.4 4 72.59 even 6
5184.2.d.l.2593.1 4 9.4 even 3
5184.2.d.l.2593.1 4 72.67 odd 6
5184.2.d.l.2593.4 4 36.31 odd 6
5184.2.d.l.2593.4 4 72.13 even 6