Properties

Label 1080.4.a.f.1.2
Level $1080$
Weight $4$
Character 1080.1
Self dual yes
Analytic conductor $63.722$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1080,4,Mod(1,1080)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1080, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1080.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1080 = 2^{3} \cdot 3^{3} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1080.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(63.7220628062\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.1765.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 11x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.89055\) of defining polynomial
Character \(\chi\) \(=\) 1080.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.00000 q^{5} -5.60585 q^{7} +O(q^{10})\) \(q-5.00000 q^{5} -5.60585 q^{7} +53.5556 q^{11} +29.6866 q^{13} -109.192 q^{17} -67.6070 q^{19} -87.4550 q^{23} +25.0000 q^{25} +141.980 q^{29} -219.193 q^{31} +28.0293 q^{35} +436.534 q^{37} +68.7309 q^{41} +16.9311 q^{43} +566.322 q^{47} -311.574 q^{49} +95.0703 q^{53} -267.778 q^{55} +306.600 q^{59} -744.914 q^{61} -148.433 q^{65} +521.489 q^{67} -678.577 q^{71} -879.486 q^{73} -300.225 q^{77} -698.634 q^{79} -1191.92 q^{83} +545.959 q^{85} -840.998 q^{89} -166.419 q^{91} +338.035 q^{95} -1045.59 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 15 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 15 q^{5} + 27 q^{11} - 3 q^{13} + 15 q^{17} - 78 q^{19} + 105 q^{23} + 75 q^{25} + 117 q^{29} - 207 q^{31} - 120 q^{37} + 300 q^{41} - 483 q^{43} + 303 q^{47} - 15 q^{49} - 492 q^{53} - 135 q^{55} + 240 q^{59} - 444 q^{61} + 15 q^{65} - 522 q^{67} - 168 q^{71} - 876 q^{73} - 150 q^{77} - 2103 q^{79} - 42 q^{83} - 75 q^{85} - 2268 q^{89} - 1596 q^{91} + 390 q^{95} - 1392 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −5.00000 −0.447214
\(6\) 0 0
\(7\) −5.60585 −0.302688 −0.151344 0.988481i \(-0.548360\pi\)
−0.151344 + 0.988481i \(0.548360\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 53.5556 1.46796 0.733982 0.679168i \(-0.237659\pi\)
0.733982 + 0.679168i \(0.237659\pi\)
\(12\) 0 0
\(13\) 29.6866 0.633352 0.316676 0.948534i \(-0.397433\pi\)
0.316676 + 0.948534i \(0.397433\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −109.192 −1.55782 −0.778909 0.627137i \(-0.784227\pi\)
−0.778909 + 0.627137i \(0.784227\pi\)
\(18\) 0 0
\(19\) −67.6070 −0.816322 −0.408161 0.912910i \(-0.633830\pi\)
−0.408161 + 0.912910i \(0.633830\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −87.4550 −0.792854 −0.396427 0.918066i \(-0.629750\pi\)
−0.396427 + 0.918066i \(0.629750\pi\)
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 141.980 0.909140 0.454570 0.890711i \(-0.349793\pi\)
0.454570 + 0.890711i \(0.349793\pi\)
\(30\) 0 0
\(31\) −219.193 −1.26994 −0.634971 0.772536i \(-0.718988\pi\)
−0.634971 + 0.772536i \(0.718988\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 28.0293 0.135366
\(36\) 0 0
\(37\) 436.534 1.93961 0.969806 0.243876i \(-0.0784190\pi\)
0.969806 + 0.243876i \(0.0784190\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 68.7309 0.261804 0.130902 0.991395i \(-0.458213\pi\)
0.130902 + 0.991395i \(0.458213\pi\)
\(42\) 0 0
\(43\) 16.9311 0.0600456 0.0300228 0.999549i \(-0.490442\pi\)
0.0300228 + 0.999549i \(0.490442\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 566.322 1.75759 0.878793 0.477203i \(-0.158349\pi\)
0.878793 + 0.477203i \(0.158349\pi\)
\(48\) 0 0
\(49\) −311.574 −0.908380
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 95.0703 0.246395 0.123197 0.992382i \(-0.460685\pi\)
0.123197 + 0.992382i \(0.460685\pi\)
\(54\) 0 0
\(55\) −267.778 −0.656494
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 306.600 0.676541 0.338271 0.941049i \(-0.390158\pi\)
0.338271 + 0.941049i \(0.390158\pi\)
\(60\) 0 0
\(61\) −744.914 −1.56355 −0.781774 0.623562i \(-0.785685\pi\)
−0.781774 + 0.623562i \(0.785685\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −148.433 −0.283243
\(66\) 0 0
\(67\) 521.489 0.950896 0.475448 0.879744i \(-0.342286\pi\)
0.475448 + 0.879744i \(0.342286\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −678.577 −1.13426 −0.567129 0.823629i \(-0.691946\pi\)
−0.567129 + 0.823629i \(0.691946\pi\)
\(72\) 0 0
\(73\) −879.486 −1.41008 −0.705041 0.709166i \(-0.749071\pi\)
−0.705041 + 0.709166i \(0.749071\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −300.225 −0.444335
\(78\) 0 0
\(79\) −698.634 −0.994968 −0.497484 0.867473i \(-0.665743\pi\)
−0.497484 + 0.867473i \(0.665743\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1191.92 −1.57627 −0.788134 0.615504i \(-0.788952\pi\)
−0.788134 + 0.615504i \(0.788952\pi\)
\(84\) 0 0
\(85\) 545.959 0.696678
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −840.998 −1.00164 −0.500818 0.865553i \(-0.666967\pi\)
−0.500818 + 0.865553i \(0.666967\pi\)
\(90\) 0 0
\(91\) −166.419 −0.191708
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 338.035 0.365070
\(96\) 0 0
\(97\) −1045.59 −1.09447 −0.547234 0.836980i \(-0.684319\pi\)
−0.547234 + 0.836980i \(0.684319\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −754.304 −0.743129 −0.371565 0.928407i \(-0.621179\pi\)
−0.371565 + 0.928407i \(0.621179\pi\)
\(102\) 0 0
\(103\) −1807.06 −1.72869 −0.864346 0.502898i \(-0.832267\pi\)
−0.864346 + 0.502898i \(0.832267\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 657.832 0.594346 0.297173 0.954824i \(-0.403956\pi\)
0.297173 + 0.954824i \(0.403956\pi\)
\(108\) 0 0
\(109\) −981.839 −0.862781 −0.431390 0.902165i \(-0.641977\pi\)
−0.431390 + 0.902165i \(0.641977\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 850.655 0.708167 0.354084 0.935214i \(-0.384793\pi\)
0.354084 + 0.935214i \(0.384793\pi\)
\(114\) 0 0
\(115\) 437.275 0.354575
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 612.113 0.471532
\(120\) 0 0
\(121\) 1537.20 1.15492
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) −226.985 −0.158596 −0.0792978 0.996851i \(-0.525268\pi\)
−0.0792978 + 0.996851i \(0.525268\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1217.09 0.811735 0.405867 0.913932i \(-0.366969\pi\)
0.405867 + 0.913932i \(0.366969\pi\)
\(132\) 0 0
\(133\) 378.995 0.247090
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −509.696 −0.317856 −0.158928 0.987290i \(-0.550804\pi\)
−0.158928 + 0.987290i \(0.550804\pi\)
\(138\) 0 0
\(139\) −845.621 −0.516005 −0.258002 0.966144i \(-0.583064\pi\)
−0.258002 + 0.966144i \(0.583064\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 1589.88 0.929738
\(144\) 0 0
\(145\) −709.901 −0.406580
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1036.04 −0.569638 −0.284819 0.958581i \(-0.591934\pi\)
−0.284819 + 0.958581i \(0.591934\pi\)
\(150\) 0 0
\(151\) −1837.56 −0.990321 −0.495161 0.868801i \(-0.664891\pi\)
−0.495161 + 0.868801i \(0.664891\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1095.97 0.567936
\(156\) 0 0
\(157\) −3080.72 −1.56604 −0.783020 0.621996i \(-0.786322\pi\)
−0.783020 + 0.621996i \(0.786322\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 490.260 0.239987
\(162\) 0 0
\(163\) −606.209 −0.291300 −0.145650 0.989336i \(-0.546527\pi\)
−0.145650 + 0.989336i \(0.546527\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −250.692 −0.116162 −0.0580812 0.998312i \(-0.518498\pi\)
−0.0580812 + 0.998312i \(0.518498\pi\)
\(168\) 0 0
\(169\) −1315.71 −0.598866
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1264.31 0.555629 0.277815 0.960635i \(-0.410390\pi\)
0.277815 + 0.960635i \(0.410390\pi\)
\(174\) 0 0
\(175\) −140.146 −0.0605375
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 558.174 0.233072 0.116536 0.993186i \(-0.462821\pi\)
0.116536 + 0.993186i \(0.462821\pi\)
\(180\) 0 0
\(181\) −4377.85 −1.79781 −0.898904 0.438146i \(-0.855635\pi\)
−0.898904 + 0.438146i \(0.855635\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −2182.67 −0.867421
\(186\) 0 0
\(187\) −5847.83 −2.28682
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1983.68 −0.751489 −0.375744 0.926723i \(-0.622613\pi\)
−0.375744 + 0.926723i \(0.622613\pi\)
\(192\) 0 0
\(193\) 1092.75 0.407555 0.203778 0.979017i \(-0.434678\pi\)
0.203778 + 0.979017i \(0.434678\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 917.082 0.331672 0.165836 0.986153i \(-0.446968\pi\)
0.165836 + 0.986153i \(0.446968\pi\)
\(198\) 0 0
\(199\) 1672.55 0.595797 0.297899 0.954598i \(-0.403714\pi\)
0.297899 + 0.954598i \(0.403714\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −795.920 −0.275185
\(204\) 0 0
\(205\) −343.655 −0.117082
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3620.73 −1.19833
\(210\) 0 0
\(211\) 4890.34 1.59557 0.797785 0.602942i \(-0.206005\pi\)
0.797785 + 0.602942i \(0.206005\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −84.6553 −0.0268532
\(216\) 0 0
\(217\) 1228.76 0.384396
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −3241.53 −0.986647
\(222\) 0 0
\(223\) 25.4162 0.00763227 0.00381614 0.999993i \(-0.498785\pi\)
0.00381614 + 0.999993i \(0.498785\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6185.05 1.80844 0.904220 0.427067i \(-0.140453\pi\)
0.904220 + 0.427067i \(0.140453\pi\)
\(228\) 0 0
\(229\) −633.968 −0.182942 −0.0914712 0.995808i \(-0.529157\pi\)
−0.0914712 + 0.995808i \(0.529157\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −5585.10 −1.57035 −0.785176 0.619273i \(-0.787427\pi\)
−0.785176 + 0.619273i \(0.787427\pi\)
\(234\) 0 0
\(235\) −2831.61 −0.786016
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2686.83 0.727181 0.363591 0.931559i \(-0.381551\pi\)
0.363591 + 0.931559i \(0.381551\pi\)
\(240\) 0 0
\(241\) −1601.60 −0.428084 −0.214042 0.976824i \(-0.568663\pi\)
−0.214042 + 0.976824i \(0.568663\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 1557.87 0.406240
\(246\) 0 0
\(247\) −2007.02 −0.517019
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4955.28 1.24611 0.623057 0.782177i \(-0.285891\pi\)
0.623057 + 0.782177i \(0.285891\pi\)
\(252\) 0 0
\(253\) −4683.70 −1.16388
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6161.72 1.49556 0.747778 0.663949i \(-0.231121\pi\)
0.747778 + 0.663949i \(0.231121\pi\)
\(258\) 0 0
\(259\) −2447.14 −0.587097
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 768.688 0.180226 0.0901128 0.995932i \(-0.471277\pi\)
0.0901128 + 0.995932i \(0.471277\pi\)
\(264\) 0 0
\(265\) −475.351 −0.110191
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −7989.19 −1.81082 −0.905408 0.424542i \(-0.860435\pi\)
−0.905408 + 0.424542i \(0.860435\pi\)
\(270\) 0 0
\(271\) −3875.39 −0.868683 −0.434341 0.900748i \(-0.643019\pi\)
−0.434341 + 0.900748i \(0.643019\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1338.89 0.293593
\(276\) 0 0
\(277\) 1121.71 0.243311 0.121656 0.992572i \(-0.461180\pi\)
0.121656 + 0.992572i \(0.461180\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 5681.52 1.20616 0.603081 0.797680i \(-0.293940\pi\)
0.603081 + 0.797680i \(0.293940\pi\)
\(282\) 0 0
\(283\) 6366.11 1.33719 0.668597 0.743625i \(-0.266895\pi\)
0.668597 + 0.743625i \(0.266895\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −385.296 −0.0792449
\(288\) 0 0
\(289\) 7009.86 1.42680
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −5316.63 −1.06007 −0.530035 0.847976i \(-0.677821\pi\)
−0.530035 + 0.847976i \(0.677821\pi\)
\(294\) 0 0
\(295\) −1533.00 −0.302558
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2596.24 −0.502155
\(300\) 0 0
\(301\) −94.9130 −0.0181751
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 3724.57 0.699240
\(306\) 0 0
\(307\) 2310.21 0.429480 0.214740 0.976671i \(-0.431110\pi\)
0.214740 + 0.976671i \(0.431110\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2874.98 0.524197 0.262099 0.965041i \(-0.415585\pi\)
0.262099 + 0.965041i \(0.415585\pi\)
\(312\) 0 0
\(313\) −7587.20 −1.37014 −0.685070 0.728478i \(-0.740228\pi\)
−0.685070 + 0.728478i \(0.740228\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −7699.56 −1.36420 −0.682099 0.731260i \(-0.738933\pi\)
−0.682099 + 0.731260i \(0.738933\pi\)
\(318\) 0 0
\(319\) 7603.83 1.33459
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7382.14 1.27168
\(324\) 0 0
\(325\) 742.164 0.126670
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3174.72 −0.531999
\(330\) 0 0
\(331\) −5469.00 −0.908168 −0.454084 0.890959i \(-0.650033\pi\)
−0.454084 + 0.890959i \(0.650033\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −2607.45 −0.425254
\(336\) 0 0
\(337\) 6073.73 0.981772 0.490886 0.871224i \(-0.336673\pi\)
0.490886 + 0.871224i \(0.336673\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −11739.0 −1.86423
\(342\) 0 0
\(343\) 3669.45 0.577643
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −6463.73 −0.999975 −0.499988 0.866033i \(-0.666662\pi\)
−0.499988 + 0.866033i \(0.666662\pi\)
\(348\) 0 0
\(349\) −1630.31 −0.250053 −0.125026 0.992153i \(-0.539902\pi\)
−0.125026 + 0.992153i \(0.539902\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8136.15 −1.22675 −0.613376 0.789791i \(-0.710189\pi\)
−0.613376 + 0.789791i \(0.710189\pi\)
\(354\) 0 0
\(355\) 3392.88 0.507255
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8847.53 1.30071 0.650355 0.759631i \(-0.274620\pi\)
0.650355 + 0.759631i \(0.274620\pi\)
\(360\) 0 0
\(361\) −2288.29 −0.333619
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4397.43 0.630608
\(366\) 0 0
\(367\) 6938.76 0.986922 0.493461 0.869768i \(-0.335732\pi\)
0.493461 + 0.869768i \(0.335732\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −532.950 −0.0745806
\(372\) 0 0
\(373\) 7950.83 1.10369 0.551847 0.833945i \(-0.313923\pi\)
0.551847 + 0.833945i \(0.313923\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4214.90 0.575805
\(378\) 0 0
\(379\) −11947.9 −1.61932 −0.809659 0.586901i \(-0.800348\pi\)
−0.809659 + 0.586901i \(0.800348\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1499.09 −0.199999 −0.0999997 0.994987i \(-0.531884\pi\)
−0.0999997 + 0.994987i \(0.531884\pi\)
\(384\) 0 0
\(385\) 1501.12 0.198713
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 708.852 0.0923913 0.0461956 0.998932i \(-0.485290\pi\)
0.0461956 + 0.998932i \(0.485290\pi\)
\(390\) 0 0
\(391\) 9549.38 1.23512
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3493.17 0.444963
\(396\) 0 0
\(397\) 2541.17 0.321253 0.160626 0.987015i \(-0.448649\pi\)
0.160626 + 0.987015i \(0.448649\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −2135.53 −0.265944 −0.132972 0.991120i \(-0.542452\pi\)
−0.132972 + 0.991120i \(0.542452\pi\)
\(402\) 0 0
\(403\) −6507.09 −0.804321
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 23378.8 2.84728
\(408\) 0 0
\(409\) 7921.49 0.957684 0.478842 0.877901i \(-0.341057\pi\)
0.478842 + 0.877901i \(0.341057\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1718.76 −0.204781
\(414\) 0 0
\(415\) 5959.60 0.704928
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −13067.7 −1.52362 −0.761811 0.647799i \(-0.775690\pi\)
−0.761811 + 0.647799i \(0.775690\pi\)
\(420\) 0 0
\(421\) 14532.5 1.68235 0.841175 0.540762i \(-0.181864\pi\)
0.841175 + 0.540762i \(0.181864\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −2729.80 −0.311564
\(426\) 0 0
\(427\) 4175.88 0.473267
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1363.94 0.152433 0.0762164 0.997091i \(-0.475716\pi\)
0.0762164 + 0.997091i \(0.475716\pi\)
\(432\) 0 0
\(433\) 10621.2 1.17880 0.589401 0.807841i \(-0.299364\pi\)
0.589401 + 0.807841i \(0.299364\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5912.57 0.647224
\(438\) 0 0
\(439\) −9505.12 −1.03338 −0.516691 0.856172i \(-0.672836\pi\)
−0.516691 + 0.856172i \(0.672836\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 377.897 0.0405292 0.0202646 0.999795i \(-0.493549\pi\)
0.0202646 + 0.999795i \(0.493549\pi\)
\(444\) 0 0
\(445\) 4204.99 0.447945
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1424.29 −0.149703 −0.0748513 0.997195i \(-0.523848\pi\)
−0.0748513 + 0.997195i \(0.523848\pi\)
\(450\) 0 0
\(451\) 3680.93 0.384319
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 832.093 0.0857343
\(456\) 0 0
\(457\) −10979.1 −1.12381 −0.561903 0.827203i \(-0.689931\pi\)
−0.561903 + 0.827203i \(0.689931\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −10729.6 −1.08401 −0.542003 0.840377i \(-0.682334\pi\)
−0.542003 + 0.840377i \(0.682334\pi\)
\(462\) 0 0
\(463\) 1314.85 0.131979 0.0659895 0.997820i \(-0.478980\pi\)
0.0659895 + 0.997820i \(0.478980\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 7772.33 0.770151 0.385075 0.922885i \(-0.374175\pi\)
0.385075 + 0.922885i \(0.374175\pi\)
\(468\) 0 0
\(469\) −2923.39 −0.287824
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 906.753 0.0881449
\(474\) 0 0
\(475\) −1690.18 −0.163264
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −17266.5 −1.64702 −0.823512 0.567299i \(-0.807988\pi\)
−0.823512 + 0.567299i \(0.807988\pi\)
\(480\) 0 0
\(481\) 12959.2 1.22846
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5227.94 0.489461
\(486\) 0 0
\(487\) −123.244 −0.0114676 −0.00573380 0.999984i \(-0.501825\pi\)
−0.00573380 + 0.999984i \(0.501825\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 13322.6 1.22453 0.612263 0.790654i \(-0.290259\pi\)
0.612263 + 0.790654i \(0.290259\pi\)
\(492\) 0 0
\(493\) −15503.1 −1.41627
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3804.00 0.343326
\(498\) 0 0
\(499\) 5106.10 0.458077 0.229039 0.973417i \(-0.426442\pi\)
0.229039 + 0.973417i \(0.426442\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −856.862 −0.0759554 −0.0379777 0.999279i \(-0.512092\pi\)
−0.0379777 + 0.999279i \(0.512092\pi\)
\(504\) 0 0
\(505\) 3771.52 0.332338
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 568.382 0.0494953 0.0247476 0.999694i \(-0.492122\pi\)
0.0247476 + 0.999694i \(0.492122\pi\)
\(510\) 0 0
\(511\) 4930.27 0.426814
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 9035.32 0.773095
\(516\) 0 0
\(517\) 30329.7 2.58007
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 3341.28 0.280968 0.140484 0.990083i \(-0.455134\pi\)
0.140484 + 0.990083i \(0.455134\pi\)
\(522\) 0 0
\(523\) 20342.2 1.70077 0.850383 0.526165i \(-0.176370\pi\)
0.850383 + 0.526165i \(0.176370\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 23934.1 1.97834
\(528\) 0 0
\(529\) −4518.62 −0.371383
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 2040.39 0.165814
\(534\) 0 0
\(535\) −3289.16 −0.265800
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −16686.5 −1.33347
\(540\) 0 0
\(541\) 5490.90 0.436363 0.218181 0.975908i \(-0.429988\pi\)
0.218181 + 0.975908i \(0.429988\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 4909.19 0.385847
\(546\) 0 0
\(547\) 13539.2 1.05831 0.529153 0.848527i \(-0.322510\pi\)
0.529153 + 0.848527i \(0.322510\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −9598.86 −0.742151
\(552\) 0 0
\(553\) 3916.44 0.301164
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −9817.92 −0.746856 −0.373428 0.927659i \(-0.621818\pi\)
−0.373428 + 0.927659i \(0.621818\pi\)
\(558\) 0 0
\(559\) 502.625 0.0380300
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −8971.81 −0.671610 −0.335805 0.941931i \(-0.609008\pi\)
−0.335805 + 0.941931i \(0.609008\pi\)
\(564\) 0 0
\(565\) −4253.28 −0.316702
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13876.7 1.02239 0.511195 0.859464i \(-0.329203\pi\)
0.511195 + 0.859464i \(0.329203\pi\)
\(570\) 0 0
\(571\) −3513.33 −0.257492 −0.128746 0.991678i \(-0.541095\pi\)
−0.128746 + 0.991678i \(0.541095\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −2186.38 −0.158571
\(576\) 0 0
\(577\) −17636.6 −1.27248 −0.636241 0.771491i \(-0.719511\pi\)
−0.636241 + 0.771491i \(0.719511\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 6681.73 0.477117
\(582\) 0 0
\(583\) 5091.54 0.361698
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1129.54 −0.0794229 −0.0397114 0.999211i \(-0.512644\pi\)
−0.0397114 + 0.999211i \(0.512644\pi\)
\(588\) 0 0
\(589\) 14819.0 1.03668
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −25431.4 −1.76111 −0.880557 0.473940i \(-0.842831\pi\)
−0.880557 + 0.473940i \(0.842831\pi\)
\(594\) 0 0
\(595\) −3060.57 −0.210876
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −24719.7 −1.68618 −0.843089 0.537775i \(-0.819265\pi\)
−0.843089 + 0.537775i \(0.819265\pi\)
\(600\) 0 0
\(601\) −24379.3 −1.65466 −0.827331 0.561714i \(-0.810142\pi\)
−0.827331 + 0.561714i \(0.810142\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −7686.00 −0.516496
\(606\) 0 0
\(607\) 16258.8 1.08719 0.543596 0.839347i \(-0.317063\pi\)
0.543596 + 0.839347i \(0.317063\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 16812.2 1.11317
\(612\) 0 0
\(613\) −13069.4 −0.861124 −0.430562 0.902561i \(-0.641685\pi\)
−0.430562 + 0.902561i \(0.641685\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 20592.5 1.34363 0.671816 0.740718i \(-0.265515\pi\)
0.671816 + 0.740718i \(0.265515\pi\)
\(618\) 0 0
\(619\) 24687.2 1.60301 0.801504 0.597989i \(-0.204033\pi\)
0.801504 + 0.597989i \(0.204033\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4714.51 0.303183
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −47665.9 −3.02157
\(630\) 0 0
\(631\) 18847.2 1.18906 0.594529 0.804074i \(-0.297338\pi\)
0.594529 + 0.804074i \(0.297338\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1134.92 0.0709261
\(636\) 0 0
\(637\) −9249.57 −0.575324
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −3418.42 −0.210639 −0.105319 0.994438i \(-0.533586\pi\)
−0.105319 + 0.994438i \(0.533586\pi\)
\(642\) 0 0
\(643\) 20369.8 1.24931 0.624656 0.780900i \(-0.285239\pi\)
0.624656 + 0.780900i \(0.285239\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 15267.3 0.927699 0.463849 0.885914i \(-0.346468\pi\)
0.463849 + 0.885914i \(0.346468\pi\)
\(648\) 0 0
\(649\) 16420.1 0.993139
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −10839.6 −0.649595 −0.324797 0.945784i \(-0.605296\pi\)
−0.324797 + 0.945784i \(0.605296\pi\)
\(654\) 0 0
\(655\) −6085.43 −0.363019
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1589.00 −0.0939282 −0.0469641 0.998897i \(-0.514955\pi\)
−0.0469641 + 0.998897i \(0.514955\pi\)
\(660\) 0 0
\(661\) −15061.5 −0.886272 −0.443136 0.896454i \(-0.646134\pi\)
−0.443136 + 0.896454i \(0.646134\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1894.98 −0.110502
\(666\) 0 0
\(667\) −12416.9 −0.720815
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −39894.3 −2.29523
\(672\) 0 0
\(673\) 18477.3 1.05832 0.529159 0.848523i \(-0.322508\pi\)
0.529159 + 0.848523i \(0.322508\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 28782.1 1.63395 0.816975 0.576673i \(-0.195649\pi\)
0.816975 + 0.576673i \(0.195649\pi\)
\(678\) 0 0
\(679\) 5861.42 0.331282
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1542.58 −0.0864205 −0.0432103 0.999066i \(-0.513759\pi\)
−0.0432103 + 0.999066i \(0.513759\pi\)
\(684\) 0 0
\(685\) 2548.48 0.142149
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2822.31 0.156054
\(690\) 0 0
\(691\) −8037.73 −0.442503 −0.221252 0.975217i \(-0.571014\pi\)
−0.221252 + 0.975217i \(0.571014\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 4228.11 0.230764
\(696\) 0 0
\(697\) −7504.86 −0.407843
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −3686.72 −0.198639 −0.0993193 0.995056i \(-0.531667\pi\)
−0.0993193 + 0.995056i \(0.531667\pi\)
\(702\) 0 0
\(703\) −29512.7 −1.58335
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4228.52 0.224936
\(708\) 0 0
\(709\) 20887.3 1.10640 0.553200 0.833049i \(-0.313407\pi\)
0.553200 + 0.833049i \(0.313407\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 19169.5 1.00688
\(714\) 0 0
\(715\) −7949.41 −0.415791
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 30381.8 1.57587 0.787935 0.615758i \(-0.211150\pi\)
0.787935 + 0.615758i \(0.211150\pi\)
\(720\) 0 0
\(721\) 10130.1 0.523254
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3549.50 0.181828
\(726\) 0 0
\(727\) −36256.3 −1.84962 −0.924810 0.380430i \(-0.875776\pi\)
−0.924810 + 0.380430i \(0.875776\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1848.73 −0.0935402
\(732\) 0 0
\(733\) 206.568 0.0104089 0.00520447 0.999986i \(-0.498343\pi\)
0.00520447 + 0.999986i \(0.498343\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 27928.7 1.39588
\(738\) 0 0
\(739\) −28859.8 −1.43657 −0.718285 0.695749i \(-0.755073\pi\)
−0.718285 + 0.695749i \(0.755073\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −9452.34 −0.466720 −0.233360 0.972390i \(-0.574972\pi\)
−0.233360 + 0.972390i \(0.574972\pi\)
\(744\) 0 0
\(745\) 5180.22 0.254750
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3687.71 −0.179901
\(750\) 0 0
\(751\) −13833.5 −0.672160 −0.336080 0.941833i \(-0.609101\pi\)
−0.336080 + 0.941833i \(0.609101\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 9187.80 0.442885
\(756\) 0 0
\(757\) −4267.28 −0.204884 −0.102442 0.994739i \(-0.532666\pi\)
−0.102442 + 0.994739i \(0.532666\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 21502.5 1.02426 0.512131 0.858907i \(-0.328856\pi\)
0.512131 + 0.858907i \(0.328856\pi\)
\(762\) 0 0
\(763\) 5504.04 0.261153
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9101.91 0.428489
\(768\) 0 0
\(769\) 17936.2 0.841086 0.420543 0.907273i \(-0.361840\pi\)
0.420543 + 0.907273i \(0.361840\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 13672.3 0.636167 0.318083 0.948063i \(-0.396961\pi\)
0.318083 + 0.948063i \(0.396961\pi\)
\(774\) 0 0
\(775\) −5479.83 −0.253989
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −4646.69 −0.213716
\(780\) 0 0
\(781\) −36341.6 −1.66505
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 15403.6 0.700354
\(786\) 0 0
\(787\) 14681.1 0.664963 0.332482 0.943110i \(-0.392114\pi\)
0.332482 + 0.943110i \(0.392114\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −4768.65 −0.214353
\(792\) 0 0
\(793\) −22113.9 −0.990276
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11761.8 0.522740 0.261370 0.965239i \(-0.415826\pi\)
0.261370 + 0.965239i \(0.415826\pi\)
\(798\) 0 0
\(799\) −61837.7 −2.73800
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −47101.4 −2.06995
\(804\) 0 0
\(805\) −2451.30 −0.107325
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −18821.1 −0.817941 −0.408971 0.912548i \(-0.634112\pi\)
−0.408971 + 0.912548i \(0.634112\pi\)
\(810\) 0 0
\(811\) 13804.6 0.597713 0.298856 0.954298i \(-0.403395\pi\)
0.298856 + 0.954298i \(0.403395\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 3031.05 0.130274
\(816\) 0 0
\(817\) −1144.66 −0.0490166
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −21364.1 −0.908176 −0.454088 0.890957i \(-0.650035\pi\)
−0.454088 + 0.890957i \(0.650035\pi\)
\(822\) 0 0
\(823\) 30739.7 1.30197 0.650983 0.759092i \(-0.274357\pi\)
0.650983 + 0.759092i \(0.274357\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 3820.31 0.160635 0.0803176 0.996769i \(-0.474407\pi\)
0.0803176 + 0.996769i \(0.474407\pi\)
\(828\) 0 0
\(829\) 22902.8 0.959526 0.479763 0.877398i \(-0.340723\pi\)
0.479763 + 0.877398i \(0.340723\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 34021.4 1.41509
\(834\) 0 0
\(835\) 1253.46 0.0519494
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −32660.2 −1.34393 −0.671963 0.740585i \(-0.734549\pi\)
−0.671963 + 0.740585i \(0.734549\pi\)
\(840\) 0 0
\(841\) −4230.63 −0.173465
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 6578.54 0.267821
\(846\) 0 0
\(847\) −8617.31 −0.349580
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −38177.1 −1.53783
\(852\) 0 0
\(853\) 3474.35 0.139460 0.0697301 0.997566i \(-0.477786\pi\)
0.0697301 + 0.997566i \(0.477786\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 36755.3 1.46504 0.732519 0.680746i \(-0.238344\pi\)
0.732519 + 0.680746i \(0.238344\pi\)
\(858\) 0 0
\(859\) −20322.2 −0.807201 −0.403600 0.914935i \(-0.632241\pi\)
−0.403600 + 0.914935i \(0.632241\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −8541.33 −0.336907 −0.168453 0.985710i \(-0.553877\pi\)
−0.168453 + 0.985710i \(0.553877\pi\)
\(864\) 0 0
\(865\) −6321.56 −0.248485
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −37415.7 −1.46058
\(870\) 0 0
\(871\) 15481.2 0.602252
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 700.732 0.0270732
\(876\) 0 0
\(877\) −30963.2 −1.19219 −0.596096 0.802913i \(-0.703282\pi\)
−0.596096 + 0.802913i \(0.703282\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 25296.4 0.967376 0.483688 0.875241i \(-0.339297\pi\)
0.483688 + 0.875241i \(0.339297\pi\)
\(882\) 0 0
\(883\) −20261.1 −0.772187 −0.386094 0.922460i \(-0.626176\pi\)
−0.386094 + 0.922460i \(0.626176\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 6869.30 0.260032 0.130016 0.991512i \(-0.458497\pi\)
0.130016 + 0.991512i \(0.458497\pi\)
\(888\) 0 0
\(889\) 1272.44 0.0480049
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −38287.3 −1.43476
\(894\) 0 0
\(895\) −2790.87 −0.104233
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −31121.1 −1.15456
\(900\) 0 0
\(901\) −10380.9 −0.383838
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 21889.3 0.804004
\(906\) 0 0
\(907\) 11567.2 0.423465 0.211733 0.977328i \(-0.432089\pi\)
0.211733 + 0.977328i \(0.432089\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −27971.1 −1.01726 −0.508631 0.860985i \(-0.669848\pi\)
−0.508631 + 0.860985i \(0.669848\pi\)
\(912\) 0 0
\(913\) −63834.0 −2.31391
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −6822.80 −0.245702
\(918\) 0 0
\(919\) −254.867 −0.00914828 −0.00457414 0.999990i \(-0.501456\pi\)
−0.00457414 + 0.999990i \(0.501456\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −20144.6 −0.718384
\(924\) 0 0
\(925\) 10913.3 0.387923
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −8347.83 −0.294815 −0.147408 0.989076i \(-0.547093\pi\)
−0.147408 + 0.989076i \(0.547093\pi\)
\(930\) 0 0
\(931\) 21064.6 0.741531
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 29239.2 1.02270
\(936\) 0 0
\(937\) 4128.98 0.143957 0.0719786 0.997406i \(-0.477069\pi\)
0.0719786 + 0.997406i \(0.477069\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 43760.0 1.51598 0.757988 0.652268i \(-0.226182\pi\)
0.757988 + 0.652268i \(0.226182\pi\)
\(942\) 0 0
\(943\) −6010.87 −0.207572
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 8035.72 0.275740 0.137870 0.990450i \(-0.455974\pi\)
0.137870 + 0.990450i \(0.455974\pi\)
\(948\) 0 0
\(949\) −26108.9 −0.893078
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 10733.9 0.364854 0.182427 0.983219i \(-0.441605\pi\)
0.182427 + 0.983219i \(0.441605\pi\)
\(954\) 0 0
\(955\) 9918.42 0.336076
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 2857.28 0.0962110
\(960\) 0 0
\(961\) 18254.6 0.612755
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −5463.77 −0.182264
\(966\) 0 0
\(967\) −5800.85 −0.192909 −0.0964543 0.995337i \(-0.530750\pi\)
−0.0964543 + 0.995337i \(0.530750\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 47046.8 1.55490 0.777448 0.628947i \(-0.216514\pi\)
0.777448 + 0.628947i \(0.216514\pi\)
\(972\) 0 0
\(973\) 4740.43 0.156188
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 32043.6 1.04930 0.524649 0.851318i \(-0.324196\pi\)
0.524649 + 0.851318i \(0.324196\pi\)
\(978\) 0 0
\(979\) −45040.1 −1.47037
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −25178.5 −0.816957 −0.408478 0.912768i \(-0.633940\pi\)
−0.408478 + 0.912768i \(0.633940\pi\)
\(984\) 0 0
\(985\) −4585.41 −0.148328
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −1480.71 −0.0476074
\(990\) 0 0
\(991\) 18011.8 0.577360 0.288680 0.957426i \(-0.406784\pi\)
0.288680 + 0.957426i \(0.406784\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −8362.73 −0.266449
\(996\) 0 0
\(997\) −31687.1 −1.00656 −0.503281 0.864123i \(-0.667874\pi\)
−0.503281 + 0.864123i \(0.667874\pi\)
\(998\) 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 1080.4.a.f.1.2 3
3.2 odd 2 1080.4.a.l.1.2 yes 3
4.3 odd 2 2160.4.a.bh.1.2 3
12.11 even 2 2160.4.a.bp.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1080.4.a.f.1.2 3 1.1 even 1 trivial
1080.4.a.l.1.2 yes 3 3.2 odd 2
2160.4.a.bh.1.2 3 4.3 odd 2
2160.4.a.bp.1.2 3 12.11 even 2