Properties

Label 2960.2.a.a.1.1
Level $2960$
Weight $2$
Character 2960.1
Self dual yes
Analytic conductor $23.636$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2960,2,Mod(1,2960)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2960, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2960.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2960.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: \(23.6357189983\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 740)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2960.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.00000 q^{3} -1.00000 q^{5} +3.00000 q^{7} +6.00000 q^{9} +O(q^{10})\) \(q-3.00000 q^{3} -1.00000 q^{5} +3.00000 q^{7} +6.00000 q^{9} -5.00000 q^{11} +2.00000 q^{13} +3.00000 q^{15} +4.00000 q^{17} +4.00000 q^{19} -9.00000 q^{21} -6.00000 q^{23} +1.00000 q^{25} -9.00000 q^{27} +6.00000 q^{29} +4.00000 q^{31} +15.0000 q^{33} -3.00000 q^{35} -1.00000 q^{37} -6.00000 q^{39} -9.00000 q^{41} -10.0000 q^{43} -6.00000 q^{45} +11.0000 q^{47} +2.00000 q^{49} -12.0000 q^{51} -11.0000 q^{53} +5.00000 q^{55} -12.0000 q^{57} +8.00000 q^{59} -8.00000 q^{61} +18.0000 q^{63} -2.00000 q^{65} +8.00000 q^{67} +18.0000 q^{69} -3.00000 q^{71} +7.00000 q^{73} -3.00000 q^{75} -15.0000 q^{77} -8.00000 q^{79} +9.00000 q^{81} +9.00000 q^{83} -4.00000 q^{85} -18.0000 q^{87} -16.0000 q^{89} +6.00000 q^{91} -12.0000 q^{93} -4.00000 q^{95} +12.0000 q^{97} -30.0000 q^{99} +O(q^{100})\)

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
\(3\) −3.00000 −1.73205 −0.866025 0.500000i \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 3.00000 1.13389 0.566947 0.823754i \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) 0 0
\(9\) 6.00000 2.00000
\(10\) 0 0
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 0 0
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −9.00000 −1.96396
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −9.00000 −1.73205
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 0 0
\(33\) 15.0000 2.61116
\(34\) 0 0
\(35\) −3.00000 −0.507093
\(36\) 0 0
\(37\) −1.00000 −0.164399
\(38\) 0 0
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) −9.00000 −1.40556 −0.702782 0.711405i \(-0.748059\pi\)
−0.702782 + 0.711405i \(0.748059\pi\)
\(42\) 0 0
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 0 0
\(45\) −6.00000 −0.894427
\(46\) 0 0
\(47\) 11.0000 1.60451 0.802257 0.596978i \(-0.203632\pi\)
0.802257 + 0.596978i \(0.203632\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 0 0
\(51\) −12.0000 −1.68034
\(52\) 0 0
\(53\) −11.0000 −1.51097 −0.755483 0.655168i \(-0.772598\pi\)
−0.755483 + 0.655168i \(0.772598\pi\)
\(54\) 0 0
\(55\) 5.00000 0.674200
\(56\) 0 0
\(57\) −12.0000 −1.58944
\(58\) 0 0
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) 0 0
\(61\) −8.00000 −1.02430 −0.512148 0.858898i \(-0.671150\pi\)
−0.512148 + 0.858898i \(0.671150\pi\)
\(62\) 0 0
\(63\) 18.0000 2.26779
\(64\) 0 0
\(65\) −2.00000 −0.248069
\(66\) 0 0
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) 0 0
\(69\) 18.0000 2.16695
\(70\) 0 0
\(71\) −3.00000 −0.356034 −0.178017 0.984027i \(-0.556968\pi\)
−0.178017 + 0.984027i \(0.556968\pi\)
\(72\) 0 0
\(73\) 7.00000 0.819288 0.409644 0.912245i \(-0.365653\pi\)
0.409644 + 0.912245i \(0.365653\pi\)
\(74\) 0 0
\(75\) −3.00000 −0.346410
\(76\) 0 0
\(77\) −15.0000 −1.70941
\(78\) 0 0
\(79\) −8.00000 −0.900070 −0.450035 0.893011i \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) 9.00000 0.987878 0.493939 0.869496i \(-0.335557\pi\)
0.493939 + 0.869496i \(0.335557\pi\)
\(84\) 0 0
\(85\) −4.00000 −0.433861
\(86\) 0 0
\(87\) −18.0000 −1.92980
\(88\) 0 0
\(89\) −16.0000 −1.69600 −0.847998 0.529999i \(-0.822192\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(90\) 0 0
\(91\) 6.00000 0.628971
\(92\) 0 0
\(93\) −12.0000 −1.24434
\(94\) 0 0
\(95\) −4.00000 −0.410391
\(96\) 0 0
\(97\) 12.0000 1.21842 0.609208 0.793011i \(-0.291488\pi\)
0.609208 + 0.793011i \(0.291488\pi\)
\(98\) 0 0
\(99\) −30.0000 −3.01511
\(100\) 0 0
\(101\) −9.00000 −0.895533 −0.447767 0.894150i \(-0.647781\pi\)
−0.447767 + 0.894150i \(0.647781\pi\)
\(102\) 0 0
\(103\) 6.00000 0.591198 0.295599 0.955312i \(-0.404481\pi\)
0.295599 + 0.955312i \(0.404481\pi\)
\(104\) 0 0
\(105\) 9.00000 0.878310
\(106\) 0 0
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) 0 0
\(109\) 12.0000 1.14939 0.574696 0.818367i \(-0.305120\pi\)
0.574696 + 0.818367i \(0.305120\pi\)
\(110\) 0 0
\(111\) 3.00000 0.284747
\(112\) 0 0
\(113\) 14.0000 1.31701 0.658505 0.752577i \(-0.271189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 0 0
\(115\) 6.00000 0.559503
\(116\) 0 0
\(117\) 12.0000 1.10940
\(118\) 0 0
\(119\) 12.0000 1.10004
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 0 0
\(123\) 27.0000 2.43451
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 13.0000 1.15356 0.576782 0.816898i \(-0.304308\pi\)
0.576782 + 0.816898i \(0.304308\pi\)
\(128\) 0 0
\(129\) 30.0000 2.64135
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 12.0000 1.04053
\(134\) 0 0
\(135\) 9.00000 0.774597
\(136\) 0 0
\(137\) 18.0000 1.53784 0.768922 0.639343i \(-0.220793\pi\)
0.768922 + 0.639343i \(0.220793\pi\)
\(138\) 0 0
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −33.0000 −2.77910
\(142\) 0 0
\(143\) −10.0000 −0.836242
\(144\) 0 0
\(145\) −6.00000 −0.498273
\(146\) 0 0
\(147\) −6.00000 −0.494872
\(148\) 0 0
\(149\) −1.00000 −0.0819232 −0.0409616 0.999161i \(-0.513042\pi\)
−0.0409616 + 0.999161i \(0.513042\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 24.0000 1.94029
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) 3.00000 0.239426 0.119713 0.992809i \(-0.461803\pi\)
0.119713 + 0.992809i \(0.461803\pi\)
\(158\) 0 0
\(159\) 33.0000 2.61707
\(160\) 0 0
\(161\) −18.0000 −1.41860
\(162\) 0 0
\(163\) 10.0000 0.783260 0.391630 0.920123i \(-0.371911\pi\)
0.391630 + 0.920123i \(0.371911\pi\)
\(164\) 0 0
\(165\) −15.0000 −1.16775
\(166\) 0 0
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 24.0000 1.83533
\(172\) 0 0
\(173\) −11.0000 −0.836315 −0.418157 0.908375i \(-0.637324\pi\)
−0.418157 + 0.908375i \(0.637324\pi\)
\(174\) 0 0
\(175\) 3.00000 0.226779
\(176\) 0 0
\(177\) −24.0000 −1.80395
\(178\) 0 0
\(179\) 2.00000 0.149487 0.0747435 0.997203i \(-0.476186\pi\)
0.0747435 + 0.997203i \(0.476186\pi\)
\(180\) 0 0
\(181\) 25.0000 1.85824 0.929118 0.369784i \(-0.120568\pi\)
0.929118 + 0.369784i \(0.120568\pi\)
\(182\) 0 0
\(183\) 24.0000 1.77413
\(184\) 0 0
\(185\) 1.00000 0.0735215
\(186\) 0 0
\(187\) −20.0000 −1.46254
\(188\) 0 0
\(189\) −27.0000 −1.96396
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) 26.0000 1.87152 0.935760 0.352636i \(-0.114715\pi\)
0.935760 + 0.352636i \(0.114715\pi\)
\(194\) 0 0
\(195\) 6.00000 0.429669
\(196\) 0 0
\(197\) 23.0000 1.63868 0.819341 0.573306i \(-0.194340\pi\)
0.819341 + 0.573306i \(0.194340\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) 0 0
\(201\) −24.0000 −1.69283
\(202\) 0 0
\(203\) 18.0000 1.26335
\(204\) 0 0
\(205\) 9.00000 0.628587
\(206\) 0 0
\(207\) −36.0000 −2.50217
\(208\) 0 0
\(209\) −20.0000 −1.38343
\(210\) 0 0
\(211\) 11.0000 0.757271 0.378636 0.925546i \(-0.376393\pi\)
0.378636 + 0.925546i \(0.376393\pi\)
\(212\) 0 0
\(213\) 9.00000 0.616670
\(214\) 0 0
\(215\) 10.0000 0.681994
\(216\) 0 0
\(217\) 12.0000 0.814613
\(218\) 0 0
\(219\) −21.0000 −1.41905
\(220\) 0 0
\(221\) 8.00000 0.538138
\(222\) 0 0
\(223\) −5.00000 −0.334825 −0.167412 0.985887i \(-0.553541\pi\)
−0.167412 + 0.985887i \(0.553541\pi\)
\(224\) 0 0
\(225\) 6.00000 0.400000
\(226\) 0 0
\(227\) 16.0000 1.06196 0.530979 0.847385i \(-0.321824\pi\)
0.530979 + 0.847385i \(0.321824\pi\)
\(228\) 0 0
\(229\) −21.0000 −1.38772 −0.693860 0.720110i \(-0.744091\pi\)
−0.693860 + 0.720110i \(0.744091\pi\)
\(230\) 0 0
\(231\) 45.0000 2.96078
\(232\) 0 0
\(233\) 14.0000 0.917170 0.458585 0.888650i \(-0.348356\pi\)
0.458585 + 0.888650i \(0.348356\pi\)
\(234\) 0 0
\(235\) −11.0000 −0.717561
\(236\) 0 0
\(237\) 24.0000 1.55897
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.00000 −0.127775
\(246\) 0 0
\(247\) 8.00000 0.509028
\(248\) 0 0
\(249\) −27.0000 −1.71106
\(250\) 0 0
\(251\) 10.0000 0.631194 0.315597 0.948893i \(-0.397795\pi\)
0.315597 + 0.948893i \(0.397795\pi\)
\(252\) 0 0
\(253\) 30.0000 1.88608
\(254\) 0 0
\(255\) 12.0000 0.751469
\(256\) 0 0
\(257\) −16.0000 −0.998053 −0.499026 0.866587i \(-0.666309\pi\)
−0.499026 + 0.866587i \(0.666309\pi\)
\(258\) 0 0
\(259\) −3.00000 −0.186411
\(260\) 0 0
\(261\) 36.0000 2.22834
\(262\) 0 0
\(263\) 23.0000 1.41824 0.709120 0.705087i \(-0.249092\pi\)
0.709120 + 0.705087i \(0.249092\pi\)
\(264\) 0 0
\(265\) 11.0000 0.675725
\(266\) 0 0
\(267\) 48.0000 2.93755
\(268\) 0 0
\(269\) −22.0000 −1.34136 −0.670682 0.741745i \(-0.733998\pi\)
−0.670682 + 0.741745i \(0.733998\pi\)
\(270\) 0 0
\(271\) 5.00000 0.303728 0.151864 0.988401i \(-0.451472\pi\)
0.151864 + 0.988401i \(0.451472\pi\)
\(272\) 0 0
\(273\) −18.0000 −1.08941
\(274\) 0 0
\(275\) −5.00000 −0.301511
\(276\) 0 0
\(277\) −4.00000 −0.240337 −0.120168 0.992754i \(-0.538343\pi\)
−0.120168 + 0.992754i \(0.538343\pi\)
\(278\) 0 0
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 0 0
\(283\) −4.00000 −0.237775 −0.118888 0.992908i \(-0.537933\pi\)
−0.118888 + 0.992908i \(0.537933\pi\)
\(284\) 0 0
\(285\) 12.0000 0.710819
\(286\) 0 0
\(287\) −27.0000 −1.59376
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) −36.0000 −2.11036
\(292\) 0 0
\(293\) 30.0000 1.75262 0.876309 0.481749i \(-0.159998\pi\)
0.876309 + 0.481749i \(0.159998\pi\)
\(294\) 0 0
\(295\) −8.00000 −0.465778
\(296\) 0 0
\(297\) 45.0000 2.61116
\(298\) 0 0
\(299\) −12.0000 −0.693978
\(300\) 0 0
\(301\) −30.0000 −1.72917
\(302\) 0 0
\(303\) 27.0000 1.55111
\(304\) 0 0
\(305\) 8.00000 0.458079
\(306\) 0 0
\(307\) 23.0000 1.31268 0.656340 0.754466i \(-0.272104\pi\)
0.656340 + 0.754466i \(0.272104\pi\)
\(308\) 0 0
\(309\) −18.0000 −1.02398
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) 0 0
\(313\) −22.0000 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(314\) 0 0
\(315\) −18.0000 −1.01419
\(316\) 0 0
\(317\) 14.0000 0.786318 0.393159 0.919470i \(-0.371382\pi\)
0.393159 + 0.919470i \(0.371382\pi\)
\(318\) 0 0
\(319\) −30.0000 −1.67968
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 16.0000 0.890264
\(324\) 0 0
\(325\) 2.00000 0.110940
\(326\) 0 0
\(327\) −36.0000 −1.99080
\(328\) 0 0
\(329\) 33.0000 1.81935
\(330\) 0 0
\(331\) 22.0000 1.20923 0.604615 0.796518i \(-0.293327\pi\)
0.604615 + 0.796518i \(0.293327\pi\)
\(332\) 0 0
\(333\) −6.00000 −0.328798
\(334\) 0 0
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) 7.00000 0.381314 0.190657 0.981657i \(-0.438938\pi\)
0.190657 + 0.981657i \(0.438938\pi\)
\(338\) 0 0
\(339\) −42.0000 −2.28113
\(340\) 0 0
\(341\) −20.0000 −1.08306
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) 0 0
\(345\) −18.0000 −0.969087
\(346\) 0 0
\(347\) −10.0000 −0.536828 −0.268414 0.963304i \(-0.586500\pi\)
−0.268414 + 0.963304i \(0.586500\pi\)
\(348\) 0 0
\(349\) 30.0000 1.60586 0.802932 0.596071i \(-0.203272\pi\)
0.802932 + 0.596071i \(0.203272\pi\)
\(350\) 0 0
\(351\) −18.0000 −0.960769
\(352\) 0 0
\(353\) −12.0000 −0.638696 −0.319348 0.947638i \(-0.603464\pi\)
−0.319348 + 0.947638i \(0.603464\pi\)
\(354\) 0 0
\(355\) 3.00000 0.159223
\(356\) 0 0
\(357\) −36.0000 −1.90532
\(358\) 0 0
\(359\) 21.0000 1.10834 0.554169 0.832404i \(-0.313036\pi\)
0.554169 + 0.832404i \(0.313036\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) −42.0000 −2.20443
\(364\) 0 0
\(365\) −7.00000 −0.366397
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 0 0
\(369\) −54.0000 −2.81113
\(370\) 0 0
\(371\) −33.0000 −1.71327
\(372\) 0 0
\(373\) 1.00000 0.0517780 0.0258890 0.999665i \(-0.491758\pi\)
0.0258890 + 0.999665i \(0.491758\pi\)
\(374\) 0 0
\(375\) 3.00000 0.154919
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) −17.0000 −0.873231 −0.436616 0.899648i \(-0.643823\pi\)
−0.436616 + 0.899648i \(0.643823\pi\)
\(380\) 0 0
\(381\) −39.0000 −1.99803
\(382\) 0 0
\(383\) −36.0000 −1.83951 −0.919757 0.392488i \(-0.871614\pi\)
−0.919757 + 0.392488i \(0.871614\pi\)
\(384\) 0 0
\(385\) 15.0000 0.764471
\(386\) 0 0
\(387\) −60.0000 −3.04997
\(388\) 0 0
\(389\) 4.00000 0.202808 0.101404 0.994845i \(-0.467667\pi\)
0.101404 + 0.994845i \(0.467667\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 8.00000 0.402524
\(396\) 0 0
\(397\) 7.00000 0.351320 0.175660 0.984451i \(-0.443794\pi\)
0.175660 + 0.984451i \(0.443794\pi\)
\(398\) 0 0
\(399\) −36.0000 −1.80225
\(400\) 0 0
\(401\) −10.0000 −0.499376 −0.249688 0.968326i \(-0.580328\pi\)
−0.249688 + 0.968326i \(0.580328\pi\)
\(402\) 0 0
\(403\) 8.00000 0.398508
\(404\) 0 0
\(405\) −9.00000 −0.447214
\(406\) 0 0
\(407\) 5.00000 0.247841
\(408\) 0 0
\(409\) −4.00000 −0.197787 −0.0988936 0.995098i \(-0.531530\pi\)
−0.0988936 + 0.995098i \(0.531530\pi\)
\(410\) 0 0
\(411\) −54.0000 −2.66362
\(412\) 0 0
\(413\) 24.0000 1.18096
\(414\) 0 0
\(415\) −9.00000 −0.441793
\(416\) 0 0
\(417\) −12.0000 −0.587643
\(418\) 0 0
\(419\) −1.00000 −0.0488532 −0.0244266 0.999702i \(-0.507776\pi\)
−0.0244266 + 0.999702i \(0.507776\pi\)
\(420\) 0 0
\(421\) 36.0000 1.75453 0.877266 0.480004i \(-0.159365\pi\)
0.877266 + 0.480004i \(0.159365\pi\)
\(422\) 0 0
\(423\) 66.0000 3.20903
\(424\) 0 0
\(425\) 4.00000 0.194029
\(426\) 0 0
\(427\) −24.0000 −1.16144
\(428\) 0 0
\(429\) 30.0000 1.44841
\(430\) 0 0
\(431\) 14.0000 0.674356 0.337178 0.941441i \(-0.390528\pi\)
0.337178 + 0.941441i \(0.390528\pi\)
\(432\) 0 0
\(433\) −23.0000 −1.10531 −0.552655 0.833410i \(-0.686385\pi\)
−0.552655 + 0.833410i \(0.686385\pi\)
\(434\) 0 0
\(435\) 18.0000 0.863034
\(436\) 0 0
\(437\) −24.0000 −1.14808
\(438\) 0 0
\(439\) −28.0000 −1.33637 −0.668184 0.743996i \(-0.732928\pi\)
−0.668184 + 0.743996i \(0.732928\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 9.00000 0.427603 0.213801 0.976877i \(-0.431415\pi\)
0.213801 + 0.976877i \(0.431415\pi\)
\(444\) 0 0
\(445\) 16.0000 0.758473
\(446\) 0 0
\(447\) 3.00000 0.141895
\(448\) 0 0
\(449\) −24.0000 −1.13263 −0.566315 0.824189i \(-0.691631\pi\)
−0.566315 + 0.824189i \(0.691631\pi\)
\(450\) 0 0
\(451\) 45.0000 2.11897
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −6.00000 −0.281284
\(456\) 0 0
\(457\) 6.00000 0.280668 0.140334 0.990104i \(-0.455182\pi\)
0.140334 + 0.990104i \(0.455182\pi\)
\(458\) 0 0
\(459\) −36.0000 −1.68034
\(460\) 0 0
\(461\) 10.0000 0.465746 0.232873 0.972507i \(-0.425187\pi\)
0.232873 + 0.972507i \(0.425187\pi\)
\(462\) 0 0
\(463\) −14.0000 −0.650635 −0.325318 0.945605i \(-0.605471\pi\)
−0.325318 + 0.945605i \(0.605471\pi\)
\(464\) 0 0
\(465\) 12.0000 0.556487
\(466\) 0 0
\(467\) −10.0000 −0.462745 −0.231372 0.972865i \(-0.574322\pi\)
−0.231372 + 0.972865i \(0.574322\pi\)
\(468\) 0 0
\(469\) 24.0000 1.10822
\(470\) 0 0
\(471\) −9.00000 −0.414698
\(472\) 0 0
\(473\) 50.0000 2.29900
\(474\) 0 0
\(475\) 4.00000 0.183533
\(476\) 0 0
\(477\) −66.0000 −3.02193
\(478\) 0 0
\(479\) 14.0000 0.639676 0.319838 0.947472i \(-0.396371\pi\)
0.319838 + 0.947472i \(0.396371\pi\)
\(480\) 0 0
\(481\) −2.00000 −0.0911922
\(482\) 0 0
\(483\) 54.0000 2.45709
\(484\) 0 0
\(485\) −12.0000 −0.544892
\(486\) 0 0
\(487\) 4.00000 0.181257 0.0906287 0.995885i \(-0.471112\pi\)
0.0906287 + 0.995885i \(0.471112\pi\)
\(488\) 0 0
\(489\) −30.0000 −1.35665
\(490\) 0 0
\(491\) −20.0000 −0.902587 −0.451294 0.892375i \(-0.649037\pi\)
−0.451294 + 0.892375i \(0.649037\pi\)
\(492\) 0 0
\(493\) 24.0000 1.08091
\(494\) 0 0
\(495\) 30.0000 1.34840
\(496\) 0 0
\(497\) −9.00000 −0.403705
\(498\) 0 0
\(499\) 44.0000 1.96971 0.984855 0.173379i \(-0.0554684\pi\)
0.984855 + 0.173379i \(0.0554684\pi\)
\(500\) 0 0
\(501\) 24.0000 1.07224
\(502\) 0 0
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 0 0
\(507\) 27.0000 1.19911
\(508\) 0 0
\(509\) 21.0000 0.930809 0.465404 0.885098i \(-0.345909\pi\)
0.465404 + 0.885098i \(0.345909\pi\)
\(510\) 0 0
\(511\) 21.0000 0.928985
\(512\) 0 0
\(513\) −36.0000 −1.58944
\(514\) 0 0
\(515\) −6.00000 −0.264392
\(516\) 0 0
\(517\) −55.0000 −2.41890
\(518\) 0 0
\(519\) 33.0000 1.44854
\(520\) 0 0
\(521\) −41.0000 −1.79624 −0.898121 0.439748i \(-0.855068\pi\)
−0.898121 + 0.439748i \(0.855068\pi\)
\(522\) 0 0
\(523\) 6.00000 0.262362 0.131181 0.991358i \(-0.458123\pi\)
0.131181 + 0.991358i \(0.458123\pi\)
\(524\) 0 0
\(525\) −9.00000 −0.392792
\(526\) 0 0
\(527\) 16.0000 0.696971
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 48.0000 2.08302
\(532\) 0 0
\(533\) −18.0000 −0.779667
\(534\) 0 0
\(535\) 4.00000 0.172935
\(536\) 0 0
\(537\) −6.00000 −0.258919
\(538\) 0 0
\(539\) −10.0000 −0.430730
\(540\) 0 0
\(541\) −36.0000 −1.54776 −0.773880 0.633332i \(-0.781687\pi\)
−0.773880 + 0.633332i \(0.781687\pi\)
\(542\) 0 0
\(543\) −75.0000 −3.21856
\(544\) 0 0
\(545\) −12.0000 −0.514024
\(546\) 0 0
\(547\) −16.0000 −0.684111 −0.342055 0.939680i \(-0.611123\pi\)
−0.342055 + 0.939680i \(0.611123\pi\)
\(548\) 0 0
\(549\) −48.0000 −2.04859
\(550\) 0 0
\(551\) 24.0000 1.02243
\(552\) 0 0
\(553\) −24.0000 −1.02058
\(554\) 0 0
\(555\) −3.00000 −0.127343
\(556\) 0 0
\(557\) −10.0000 −0.423714 −0.211857 0.977301i \(-0.567951\pi\)
−0.211857 + 0.977301i \(0.567951\pi\)
\(558\) 0 0
\(559\) −20.0000 −0.845910
\(560\) 0 0
\(561\) 60.0000 2.53320
\(562\) 0 0
\(563\) −42.0000 −1.77009 −0.885044 0.465506i \(-0.845872\pi\)
−0.885044 + 0.465506i \(0.845872\pi\)
\(564\) 0 0
\(565\) −14.0000 −0.588984
\(566\) 0 0
\(567\) 27.0000 1.13389
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) −33.0000 −1.38101 −0.690504 0.723329i \(-0.742611\pi\)
−0.690504 + 0.723329i \(0.742611\pi\)
\(572\) 0 0
\(573\) −36.0000 −1.50392
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) 0 0
\(577\) 28.0000 1.16566 0.582828 0.812596i \(-0.301946\pi\)
0.582828 + 0.812596i \(0.301946\pi\)
\(578\) 0 0
\(579\) −78.0000 −3.24157
\(580\) 0 0
\(581\) 27.0000 1.12015
\(582\) 0 0
\(583\) 55.0000 2.27787
\(584\) 0 0
\(585\) −12.0000 −0.496139
\(586\) 0 0
\(587\) 36.0000 1.48588 0.742940 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 0 0
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) −69.0000 −2.83828
\(592\) 0 0
\(593\) 43.0000 1.76580 0.882899 0.469563i \(-0.155588\pi\)
0.882899 + 0.469563i \(0.155588\pi\)
\(594\) 0 0
\(595\) −12.0000 −0.491952
\(596\) 0 0
\(597\) −6.00000 −0.245564
\(598\) 0 0
\(599\) 45.0000 1.83865 0.919325 0.393499i \(-0.128735\pi\)
0.919325 + 0.393499i \(0.128735\pi\)
\(600\) 0 0
\(601\) 10.0000 0.407909 0.203954 0.978980i \(-0.434621\pi\)
0.203954 + 0.978980i \(0.434621\pi\)
\(602\) 0 0
\(603\) 48.0000 1.95471
\(604\) 0 0
\(605\) −14.0000 −0.569181
\(606\) 0 0
\(607\) 12.0000 0.487065 0.243532 0.969893i \(-0.421694\pi\)
0.243532 + 0.969893i \(0.421694\pi\)
\(608\) 0 0
\(609\) −54.0000 −2.18819
\(610\) 0 0
\(611\) 22.0000 0.890025
\(612\) 0 0
\(613\) 27.0000 1.09052 0.545260 0.838267i \(-0.316431\pi\)
0.545260 + 0.838267i \(0.316431\pi\)
\(614\) 0 0
\(615\) −27.0000 −1.08875
\(616\) 0 0
\(617\) 9.00000 0.362326 0.181163 0.983453i \(-0.442014\pi\)
0.181163 + 0.983453i \(0.442014\pi\)
\(618\) 0 0
\(619\) −25.0000 −1.00483 −0.502417 0.864625i \(-0.667556\pi\)
−0.502417 + 0.864625i \(0.667556\pi\)
\(620\) 0 0
\(621\) 54.0000 2.16695
\(622\) 0 0
\(623\) −48.0000 −1.92308
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 60.0000 2.39617
\(628\) 0 0
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) 48.0000 1.91085 0.955425 0.295234i \(-0.0953977\pi\)
0.955425 + 0.295234i \(0.0953977\pi\)
\(632\) 0 0
\(633\) −33.0000 −1.31163
\(634\) 0 0
\(635\) −13.0000 −0.515889
\(636\) 0 0
\(637\) 4.00000 0.158486
\(638\) 0 0
\(639\) −18.0000 −0.712069
\(640\) 0 0
\(641\) 47.0000 1.85639 0.928194 0.372096i \(-0.121361\pi\)
0.928194 + 0.372096i \(0.121361\pi\)
\(642\) 0 0
\(643\) −34.0000 −1.34083 −0.670415 0.741987i \(-0.733884\pi\)
−0.670415 + 0.741987i \(0.733884\pi\)
\(644\) 0 0
\(645\) −30.0000 −1.18125
\(646\) 0 0
\(647\) 28.0000 1.10079 0.550397 0.834903i \(-0.314476\pi\)
0.550397 + 0.834903i \(0.314476\pi\)
\(648\) 0 0
\(649\) −40.0000 −1.57014
\(650\) 0 0
\(651\) −36.0000 −1.41095
\(652\) 0 0
\(653\) −8.00000 −0.313064 −0.156532 0.987673i \(-0.550031\pi\)
−0.156532 + 0.987673i \(0.550031\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 42.0000 1.63858
\(658\) 0 0
\(659\) 49.0000 1.90877 0.954384 0.298580i \(-0.0965131\pi\)
0.954384 + 0.298580i \(0.0965131\pi\)
\(660\) 0 0
\(661\) 8.00000 0.311164 0.155582 0.987823i \(-0.450275\pi\)
0.155582 + 0.987823i \(0.450275\pi\)
\(662\) 0 0
\(663\) −24.0000 −0.932083
\(664\) 0 0
\(665\) −12.0000 −0.465340
\(666\) 0 0
\(667\) −36.0000 −1.39393
\(668\) 0 0
\(669\) 15.0000 0.579934
\(670\) 0 0
\(671\) 40.0000 1.54418
\(672\) 0 0
\(673\) 19.0000 0.732396 0.366198 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(674\) 0 0
\(675\) −9.00000 −0.346410
\(676\) 0 0
\(677\) −7.00000 −0.269032 −0.134516 0.990911i \(-0.542948\pi\)
−0.134516 + 0.990911i \(0.542948\pi\)
\(678\) 0 0
\(679\) 36.0000 1.38155
\(680\) 0 0
\(681\) −48.0000 −1.83936
\(682\) 0 0
\(683\) −18.0000 −0.688751 −0.344375 0.938832i \(-0.611909\pi\)
−0.344375 + 0.938832i \(0.611909\pi\)
\(684\) 0 0
\(685\) −18.0000 −0.687745
\(686\) 0 0
\(687\) 63.0000 2.40360
\(688\) 0 0
\(689\) −22.0000 −0.838133
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 0 0
\(693\) −90.0000 −3.41882
\(694\) 0 0
\(695\) −4.00000 −0.151729
\(696\) 0 0
\(697\) −36.0000 −1.36360
\(698\) 0 0
\(699\) −42.0000 −1.58859
\(700\) 0 0
\(701\) 20.0000 0.755390 0.377695 0.925930i \(-0.376717\pi\)
0.377695 + 0.925930i \(0.376717\pi\)
\(702\) 0 0
\(703\) −4.00000 −0.150863
\(704\) 0 0
\(705\) 33.0000 1.24285
\(706\) 0 0
\(707\) −27.0000 −1.01544
\(708\) 0 0
\(709\) 36.0000 1.35201 0.676004 0.736898i \(-0.263710\pi\)
0.676004 + 0.736898i \(0.263710\pi\)
\(710\) 0 0
\(711\) −48.0000 −1.80014
\(712\) 0 0
\(713\) −24.0000 −0.898807
\(714\) 0 0
\(715\) 10.0000 0.373979
\(716\) 0 0
\(717\) 18.0000 0.672222
\(718\) 0 0
\(719\) 19.0000 0.708580 0.354290 0.935136i \(-0.384723\pi\)
0.354290 + 0.935136i \(0.384723\pi\)
\(720\) 0 0
\(721\) 18.0000 0.670355
\(722\) 0 0
\(723\) −42.0000 −1.56200
\(724\) 0 0
\(725\) 6.00000 0.222834
\(726\) 0 0
\(727\) −4.00000 −0.148352 −0.0741759 0.997245i \(-0.523633\pi\)
−0.0741759 + 0.997245i \(0.523633\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −40.0000 −1.47945
\(732\) 0 0
\(733\) 43.0000 1.58824 0.794121 0.607760i \(-0.207932\pi\)
0.794121 + 0.607760i \(0.207932\pi\)
\(734\) 0 0
\(735\) 6.00000 0.221313
\(736\) 0 0
\(737\) −40.0000 −1.47342
\(738\) 0 0
\(739\) 15.0000 0.551784 0.275892 0.961189i \(-0.411027\pi\)
0.275892 + 0.961189i \(0.411027\pi\)
\(740\) 0 0
\(741\) −24.0000 −0.881662
\(742\) 0 0
\(743\) 9.00000 0.330178 0.165089 0.986279i \(-0.447209\pi\)
0.165089 + 0.986279i \(0.447209\pi\)
\(744\) 0 0
\(745\) 1.00000 0.0366372
\(746\) 0 0
\(747\) 54.0000 1.97576
\(748\) 0 0
\(749\) −12.0000 −0.438470
\(750\) 0 0
\(751\) −11.0000 −0.401396 −0.200698 0.979653i \(-0.564321\pi\)
−0.200698 + 0.979653i \(0.564321\pi\)
\(752\) 0 0
\(753\) −30.0000 −1.09326
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 0 0
\(759\) −90.0000 −3.26679
\(760\) 0 0
\(761\) −3.00000 −0.108750 −0.0543750 0.998521i \(-0.517317\pi\)
−0.0543750 + 0.998521i \(0.517317\pi\)
\(762\) 0 0
\(763\) 36.0000 1.30329
\(764\) 0 0
\(765\) −24.0000 −0.867722
\(766\) 0 0
\(767\) 16.0000 0.577727
\(768\) 0 0
\(769\) 42.0000 1.51456 0.757279 0.653091i \(-0.226528\pi\)
0.757279 + 0.653091i \(0.226528\pi\)
\(770\) 0 0
\(771\) 48.0000 1.72868
\(772\) 0 0
\(773\) 35.0000 1.25886 0.629431 0.777056i \(-0.283288\pi\)
0.629431 + 0.777056i \(0.283288\pi\)
\(774\) 0 0
\(775\) 4.00000 0.143684
\(776\) 0 0
\(777\) 9.00000 0.322873
\(778\) 0 0
\(779\) −36.0000 −1.28983
\(780\) 0 0
\(781\) 15.0000 0.536742
\(782\) 0 0
\(783\) −54.0000 −1.92980
\(784\) 0 0
\(785\) −3.00000 −0.107075
\(786\) 0 0
\(787\) −21.0000 −0.748569 −0.374285 0.927314i \(-0.622112\pi\)
−0.374285 + 0.927314i \(0.622112\pi\)
\(788\) 0 0
\(789\) −69.0000 −2.45647
\(790\) 0 0
\(791\) 42.0000 1.49335
\(792\) 0 0
\(793\) −16.0000 −0.568177
\(794\) 0 0
\(795\) −33.0000 −1.17039
\(796\) 0 0
\(797\) 12.0000 0.425062 0.212531 0.977154i \(-0.431829\pi\)
0.212531 + 0.977154i \(0.431829\pi\)
\(798\) 0 0
\(799\) 44.0000 1.55661
\(800\) 0 0
\(801\) −96.0000 −3.39199
\(802\) 0 0
\(803\) −35.0000 −1.23512
\(804\) 0 0
\(805\) 18.0000 0.634417
\(806\) 0 0
\(807\) 66.0000 2.32331
\(808\) 0 0
\(809\) −46.0000 −1.61727 −0.808637 0.588308i \(-0.799794\pi\)
−0.808637 + 0.588308i \(0.799794\pi\)
\(810\) 0 0
\(811\) −49.0000 −1.72062 −0.860311 0.509769i \(-0.829731\pi\)
−0.860311 + 0.509769i \(0.829731\pi\)
\(812\) 0 0
\(813\) −15.0000 −0.526073
\(814\) 0 0
\(815\) −10.0000 −0.350285
\(816\) 0 0
\(817\) −40.0000 −1.39942
\(818\) 0 0
\(819\) 36.0000 1.25794
\(820\) 0 0
\(821\) 21.0000 0.732905 0.366453 0.930437i \(-0.380572\pi\)
0.366453 + 0.930437i \(0.380572\pi\)
\(822\) 0 0
\(823\) −8.00000 −0.278862 −0.139431 0.990232i \(-0.544527\pi\)
−0.139431 + 0.990232i \(0.544527\pi\)
\(824\) 0 0
\(825\) 15.0000 0.522233
\(826\) 0 0
\(827\) 30.0000 1.04320 0.521601 0.853189i \(-0.325335\pi\)
0.521601 + 0.853189i \(0.325335\pi\)
\(828\) 0 0
\(829\) 52.0000 1.80603 0.903017 0.429604i \(-0.141347\pi\)
0.903017 + 0.429604i \(0.141347\pi\)
\(830\) 0 0
\(831\) 12.0000 0.416275
\(832\) 0 0
\(833\) 8.00000 0.277184
\(834\) 0 0
\(835\) 8.00000 0.276851
\(836\) 0 0
\(837\) −36.0000 −1.24434
\(838\) 0 0
\(839\) −12.0000 −0.414286 −0.207143 0.978311i \(-0.566417\pi\)
−0.207143 + 0.978311i \(0.566417\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) 0 0
\(843\) 12.0000 0.413302
\(844\) 0 0
\(845\) 9.00000 0.309609
\(846\) 0 0
\(847\) 42.0000 1.44314
\(848\) 0 0
\(849\) 12.0000 0.411839
\(850\) 0 0
\(851\) 6.00000 0.205677
\(852\) 0 0
\(853\) 10.0000 0.342393 0.171197 0.985237i \(-0.445237\pi\)
0.171197 + 0.985237i \(0.445237\pi\)
\(854\) 0 0
\(855\) −24.0000 −0.820783
\(856\) 0 0
\(857\) −12.0000 −0.409912 −0.204956 0.978771i \(-0.565705\pi\)
−0.204956 + 0.978771i \(0.565705\pi\)
\(858\) 0 0
\(859\) −56.0000 −1.91070 −0.955348 0.295484i \(-0.904519\pi\)
−0.955348 + 0.295484i \(0.904519\pi\)
\(860\) 0 0
\(861\) 81.0000 2.76047
\(862\) 0 0
\(863\) 24.0000 0.816970 0.408485 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 11.0000 0.374011
\(866\) 0 0
\(867\) 3.00000 0.101885
\(868\) 0 0
\(869\) 40.0000 1.35691
\(870\) 0 0
\(871\) 16.0000 0.542139
\(872\) 0 0
\(873\) 72.0000 2.43683
\(874\) 0 0
\(875\) −3.00000 −0.101419
\(876\) 0 0
\(877\) −54.0000 −1.82345 −0.911725 0.410801i \(-0.865249\pi\)
−0.911725 + 0.410801i \(0.865249\pi\)
\(878\) 0 0
\(879\) −90.0000 −3.03562
\(880\) 0 0
\(881\) 42.0000 1.41502 0.707508 0.706705i \(-0.249819\pi\)
0.707508 + 0.706705i \(0.249819\pi\)
\(882\) 0 0
\(883\) 16.0000 0.538443 0.269221 0.963078i \(-0.413234\pi\)
0.269221 + 0.963078i \(0.413234\pi\)
\(884\) 0 0
\(885\) 24.0000 0.806751
\(886\) 0 0
\(887\) 37.0000 1.24234 0.621169 0.783676i \(-0.286658\pi\)
0.621169 + 0.783676i \(0.286658\pi\)
\(888\) 0 0
\(889\) 39.0000 1.30802
\(890\) 0 0
\(891\) −45.0000 −1.50756
\(892\) 0 0
\(893\) 44.0000 1.47240
\(894\) 0 0
\(895\) −2.00000 −0.0668526
\(896\) 0 0
\(897\) 36.0000 1.20201
\(898\) 0 0
\(899\) 24.0000 0.800445
\(900\) 0 0
\(901\) −44.0000 −1.46585
\(902\) 0 0
\(903\) 90.0000 2.99501
\(904\) 0 0
\(905\) −25.0000 −0.831028
\(906\) 0 0
\(907\) −4.00000 −0.132818 −0.0664089 0.997792i \(-0.521154\pi\)
−0.0664089 + 0.997792i \(0.521154\pi\)
\(908\) 0 0
\(909\) −54.0000 −1.79107
\(910\) 0 0
\(911\) −42.0000 −1.39152 −0.695761 0.718273i \(-0.744933\pi\)
−0.695761 + 0.718273i \(0.744933\pi\)
\(912\) 0 0
\(913\) −45.0000 −1.48928
\(914\) 0 0
\(915\) −24.0000 −0.793416
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −14.0000 −0.461817 −0.230909 0.972975i \(-0.574170\pi\)
−0.230909 + 0.972975i \(0.574170\pi\)
\(920\) 0 0
\(921\) −69.0000 −2.27363
\(922\) 0 0
\(923\) −6.00000 −0.197492
\(924\) 0 0
\(925\) −1.00000 −0.0328798
\(926\) 0 0
\(927\) 36.0000 1.18240
\(928\) 0 0
\(929\) 18.0000 0.590561 0.295280 0.955411i \(-0.404587\pi\)
0.295280 + 0.955411i \(0.404587\pi\)
\(930\) 0 0
\(931\) 8.00000 0.262189
\(932\) 0 0
\(933\) 36.0000 1.17859
\(934\) 0 0
\(935\) 20.0000 0.654070
\(936\) 0 0
\(937\) 13.0000 0.424691 0.212346 0.977195i \(-0.431890\pi\)
0.212346 + 0.977195i \(0.431890\pi\)
\(938\) 0 0
\(939\) 66.0000 2.15383
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) 0 0
\(943\) 54.0000 1.75848
\(944\) 0 0
\(945\) 27.0000 0.878310
\(946\) 0 0
\(947\) −8.00000 −0.259965 −0.129983 0.991516i \(-0.541492\pi\)
−0.129983 + 0.991516i \(0.541492\pi\)
\(948\) 0 0
\(949\) 14.0000 0.454459
\(950\) 0 0
\(951\) −42.0000 −1.36194
\(952\) 0 0
\(953\) −51.0000 −1.65205 −0.826026 0.563632i \(-0.809404\pi\)
−0.826026 + 0.563632i \(0.809404\pi\)
\(954\) 0 0
\(955\) −12.0000 −0.388311
\(956\) 0 0
\(957\) 90.0000 2.90929
\(958\) 0 0
\(959\) 54.0000 1.74375
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) −24.0000 −0.773389
\(964\) 0 0
\(965\) −26.0000 −0.836970
\(966\) 0 0
\(967\) 2.00000 0.0643157 0.0321578 0.999483i \(-0.489762\pi\)
0.0321578 + 0.999483i \(0.489762\pi\)
\(968\) 0 0
\(969\) −48.0000 −1.54198
\(970\) 0 0
\(971\) 24.0000 0.770197 0.385098 0.922876i \(-0.374168\pi\)
0.385098 + 0.922876i \(0.374168\pi\)
\(972\) 0 0
\(973\) 12.0000 0.384702
\(974\) 0 0
\(975\) −6.00000 −0.192154
\(976\) 0 0
\(977\) 28.0000 0.895799 0.447900 0.894084i \(-0.352172\pi\)
0.447900 + 0.894084i \(0.352172\pi\)
\(978\) 0 0
\(979\) 80.0000 2.55681
\(980\) 0 0
\(981\) 72.0000 2.29878
\(982\) 0 0
\(983\) −27.0000 −0.861166 −0.430583 0.902551i \(-0.641692\pi\)
−0.430583 + 0.902551i \(0.641692\pi\)
\(984\) 0 0
\(985\) −23.0000 −0.732841
\(986\) 0 0
\(987\) −99.0000 −3.15120
\(988\) 0 0
\(989\) 60.0000 1.90789
\(990\) 0 0
\(991\) 34.0000 1.08005 0.540023 0.841650i \(-0.318416\pi\)
0.540023 + 0.841650i \(0.318416\pi\)
\(992\) 0 0
\(993\) −66.0000 −2.09445
\(994\) 0 0
\(995\) −2.00000 −0.0634043
\(996\) 0 0
\(997\) 46.0000 1.45683 0.728417 0.685134i \(-0.240256\pi\)
0.728417 + 0.685134i \(0.240256\pi\)
\(998\) 0 0
\(999\) 9.00000 0.284747
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 2960.2.a.a.1.1 1
4.3 odd 2 740.2.a.c.1.1 1
12.11 even 2 6660.2.a.b.1.1 1
20.3 even 4 3700.2.d.a.149.2 2
20.7 even 4 3700.2.d.a.149.1 2
20.19 odd 2 3700.2.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
740.2.a.c.1.1 1 4.3 odd 2
2960.2.a.a.1.1 1 1.1 even 1 trivial
3700.2.a.a.1.1 1 20.19 odd 2
3700.2.d.a.149.1 2 20.7 even 4
3700.2.d.a.149.2 2 20.3 even 4
6660.2.a.b.1.1 1 12.11 even 2