Properties

Label 6011.2.a.b.1.1
Level $6011$
Weight $2$
Character 6011.1
Self dual yes
Analytic conductor $47.998$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6011,2,Mod(1,6011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6011, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6011.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6011 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6011.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: \(47.9980766550\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 6011.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} +6.00000 q^{9} +O(q^{10})\) \(q+3.00000 q^{3} -2.00000 q^{4} +1.00000 q^{5} -1.00000 q^{7} +6.00000 q^{9} +6.00000 q^{11} -6.00000 q^{12} +3.00000 q^{15} +4.00000 q^{16} +2.00000 q^{19} -2.00000 q^{20} -3.00000 q^{21} -4.00000 q^{25} +9.00000 q^{27} +2.00000 q^{28} +2.00000 q^{29} +8.00000 q^{31} +18.0000 q^{33} -1.00000 q^{35} -12.0000 q^{36} +2.00000 q^{37} +6.00000 q^{41} -5.00000 q^{43} -12.0000 q^{44} +6.00000 q^{45} -8.00000 q^{47} +12.0000 q^{48} -6.00000 q^{49} -6.00000 q^{53} +6.00000 q^{55} +6.00000 q^{57} +5.00000 q^{59} -6.00000 q^{60} -6.00000 q^{63} -8.00000 q^{64} +1.00000 q^{67} +3.00000 q^{71} -11.0000 q^{73} -12.0000 q^{75} -4.00000 q^{76} -6.00000 q^{77} +17.0000 q^{79} +4.00000 q^{80} +9.00000 q^{81} -3.00000 q^{83} +6.00000 q^{84} +6.00000 q^{87} +12.0000 q^{89} +24.0000 q^{93} +2.00000 q^{95} +5.00000 q^{97} +36.0000 q^{99} +O(q^{100})\)

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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(3\) 3.00000 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) −2.00000 −1.00000
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) 6.00000 2.00000
\(10\) 0 0
\(11\) 6.00000 1.80907 0.904534 0.426401i \(-0.140219\pi\)
0.904534 + 0.426401i \(0.140219\pi\)
\(12\) −6.00000 −1.73205
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 3.00000 0.774597
\(16\) 4.00000 1.00000
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) −2.00000 −0.447214
\(21\) −3.00000 −0.654654
\(22\) 0 0
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) 0 0
\(25\) −4.00000 −0.800000
\(26\) 0 0
\(27\) 9.00000 1.73205
\(28\) 2.00000 0.377964
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 0 0
\(33\) 18.0000 3.13340
\(34\) 0 0
\(35\) −1.00000 −0.169031
\(36\) −12.0000 −2.00000
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −5.00000 −0.762493 −0.381246 0.924473i \(-0.624505\pi\)
−0.381246 + 0.924473i \(0.624505\pi\)
\(44\) −12.0000 −1.80907
\(45\) 6.00000 0.894427
\(46\) 0 0
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 12.0000 1.73205
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 6.00000 0.809040
\(56\) 0 0
\(57\) 6.00000 0.794719
\(58\) 0 0
\(59\) 5.00000 0.650945 0.325472 0.945552i \(-0.394477\pi\)
0.325472 + 0.945552i \(0.394477\pi\)
\(60\) −6.00000 −0.774597
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) −6.00000 −0.755929
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 1.00000 0.122169 0.0610847 0.998133i \(-0.480544\pi\)
0.0610847 + 0.998133i \(0.480544\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 0 0
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) 0 0
\(75\) −12.0000 −1.38564
\(76\) −4.00000 −0.458831
\(77\) −6.00000 −0.683763
\(78\) 0 0
\(79\) 17.0000 1.91265 0.956325 0.292306i \(-0.0944227\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 4.00000 0.447214
\(81\) 9.00000 1.00000
\(82\) 0 0
\(83\) −3.00000 −0.329293 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) 6.00000 0.654654
\(85\) 0 0
\(86\) 0 0
\(87\) 6.00000 0.643268
\(88\) 0 0
\(89\) 12.0000 1.27200 0.635999 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 24.0000 2.48868
\(94\) 0 0
\(95\) 2.00000 0.205196
\(96\) 0 0
\(97\) 5.00000 0.507673 0.253837 0.967247i \(-0.418307\pi\)
0.253837 + 0.967247i \(0.418307\pi\)
\(98\) 0 0
\(99\) 36.0000 3.61814
\(100\) 8.00000 0.800000
\(101\) 9.00000 0.895533 0.447767 0.894150i \(-0.352219\pi\)
0.447767 + 0.894150i \(0.352219\pi\)
\(102\) 0 0
\(103\) 9.00000 0.886796 0.443398 0.896325i \(-0.353773\pi\)
0.443398 + 0.896325i \(0.353773\pi\)
\(104\) 0 0
\(105\) −3.00000 −0.292770
\(106\) 0 0
\(107\) −4.00000 −0.386695 −0.193347 0.981130i \(-0.561934\pi\)
−0.193347 + 0.981130i \(0.561934\pi\)
\(108\) −18.0000 −1.73205
\(109\) −15.0000 −1.43674 −0.718370 0.695662i \(-0.755111\pi\)
−0.718370 + 0.695662i \(0.755111\pi\)
\(110\) 0 0
\(111\) 6.00000 0.569495
\(112\) −4.00000 −0.377964
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −4.00000 −0.371391
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 25.0000 2.27273
\(122\) 0 0
\(123\) 18.0000 1.62301
\(124\) −16.0000 −1.43684
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 0 0
\(129\) −15.0000 −1.32068
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) −36.0000 −3.13340
\(133\) −2.00000 −0.173422
\(134\) 0 0
\(135\) 9.00000 0.774597
\(136\) 0 0
\(137\) −11.0000 −0.939793 −0.469897 0.882721i \(-0.655709\pi\)
−0.469897 + 0.882721i \(0.655709\pi\)
\(138\) 0 0
\(139\) −14.0000 −1.18746 −0.593732 0.804663i \(-0.702346\pi\)
−0.593732 + 0.804663i \(0.702346\pi\)
\(140\) 2.00000 0.169031
\(141\) −24.0000 −2.02116
\(142\) 0 0
\(143\) 0 0
\(144\) 24.0000 2.00000
\(145\) 2.00000 0.166091
\(146\) 0 0
\(147\) −18.0000 −1.48461
\(148\) −4.00000 −0.328798
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) 0 0
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 0 0
\(159\) −18.0000 −1.42749
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −8.00000 −0.626608 −0.313304 0.949653i \(-0.601436\pi\)
−0.313304 + 0.949653i \(0.601436\pi\)
\(164\) −12.0000 −0.937043
\(165\) 18.0000 1.40130
\(166\) 0 0
\(167\) 9.00000 0.696441 0.348220 0.937413i \(-0.386786\pi\)
0.348220 + 0.937413i \(0.386786\pi\)
\(168\) 0 0
\(169\) −13.0000 −1.00000
\(170\) 0 0
\(171\) 12.0000 0.917663
\(172\) 10.0000 0.762493
\(173\) 18.0000 1.36851 0.684257 0.729241i \(-0.260127\pi\)
0.684257 + 0.729241i \(0.260127\pi\)
\(174\) 0 0
\(175\) 4.00000 0.302372
\(176\) 24.0000 1.80907
\(177\) 15.0000 1.12747
\(178\) 0 0
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) −12.0000 −0.894427
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.00000 0.147043
\(186\) 0 0
\(187\) 0 0
\(188\) 16.0000 1.16692
\(189\) −9.00000 −0.654654
\(190\) 0 0
\(191\) −4.00000 −0.289430 −0.144715 0.989473i \(-0.546227\pi\)
−0.144715 + 0.989473i \(0.546227\pi\)
\(192\) −24.0000 −1.73205
\(193\) −14.0000 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 12.0000 0.857143
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 3.00000 0.211604
\(202\) 0 0
\(203\) −2.00000 −0.140372
\(204\) 0 0
\(205\) 6.00000 0.419058
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 22.0000 1.51454 0.757271 0.653101i \(-0.226532\pi\)
0.757271 + 0.653101i \(0.226532\pi\)
\(212\) 12.0000 0.824163
\(213\) 9.00000 0.616670
\(214\) 0 0
\(215\) −5.00000 −0.340997
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) 0 0
\(219\) −33.0000 −2.22993
\(220\) −12.0000 −0.809040
\(221\) 0 0
\(222\) 0 0
\(223\) 2.00000 0.133930 0.0669650 0.997755i \(-0.478668\pi\)
0.0669650 + 0.997755i \(0.478668\pi\)
\(224\) 0 0
\(225\) −24.0000 −1.60000
\(226\) 0 0
\(227\) 12.0000 0.796468 0.398234 0.917284i \(-0.369623\pi\)
0.398234 + 0.917284i \(0.369623\pi\)
\(228\) −12.0000 −0.794719
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 0 0
\(231\) −18.0000 −1.18431
\(232\) 0 0
\(233\) −8.00000 −0.524097 −0.262049 0.965055i \(-0.584398\pi\)
−0.262049 + 0.965055i \(0.584398\pi\)
\(234\) 0 0
\(235\) −8.00000 −0.521862
\(236\) −10.0000 −0.650945
\(237\) 51.0000 3.31281
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 12.0000 0.774597
\(241\) −2.00000 −0.128831 −0.0644157 0.997923i \(-0.520518\pi\)
−0.0644157 + 0.997923i \(0.520518\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −6.00000 −0.383326
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −9.00000 −0.570352
\(250\) 0 0
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) 12.0000 0.755929
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) −7.00000 −0.436648 −0.218324 0.975876i \(-0.570059\pi\)
−0.218324 + 0.975876i \(0.570059\pi\)
\(258\) 0 0
\(259\) −2.00000 −0.124274
\(260\) 0 0
\(261\) 12.0000 0.742781
\(262\) 0 0
\(263\) 12.0000 0.739952 0.369976 0.929041i \(-0.379366\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(264\) 0 0
\(265\) −6.00000 −0.368577
\(266\) 0 0
\(267\) 36.0000 2.20316
\(268\) −2.00000 −0.122169
\(269\) −3.00000 −0.182913 −0.0914566 0.995809i \(-0.529152\pi\)
−0.0914566 + 0.995809i \(0.529152\pi\)
\(270\) 0 0
\(271\) 8.00000 0.485965 0.242983 0.970031i \(-0.421874\pi\)
0.242983 + 0.970031i \(0.421874\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −24.0000 −1.44725
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) 0 0
\(279\) 48.0000 2.87368
\(280\) 0 0
\(281\) −20.0000 −1.19310 −0.596550 0.802576i \(-0.703462\pi\)
−0.596550 + 0.802576i \(0.703462\pi\)
\(282\) 0 0
\(283\) −1.00000 −0.0594438 −0.0297219 0.999558i \(-0.509462\pi\)
−0.0297219 + 0.999558i \(0.509462\pi\)
\(284\) −6.00000 −0.356034
\(285\) 6.00000 0.355409
\(286\) 0 0
\(287\) −6.00000 −0.354169
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 15.0000 0.879316
\(292\) 22.0000 1.28745
\(293\) 6.00000 0.350524 0.175262 0.984522i \(-0.443923\pi\)
0.175262 + 0.984522i \(0.443923\pi\)
\(294\) 0 0
\(295\) 5.00000 0.291111
\(296\) 0 0
\(297\) 54.0000 3.13340
\(298\) 0 0
\(299\) 0 0
\(300\) 24.0000 1.38564
\(301\) 5.00000 0.288195
\(302\) 0 0
\(303\) 27.0000 1.55111
\(304\) 8.00000 0.458831
\(305\) 0 0
\(306\) 0 0
\(307\) −5.00000 −0.285365 −0.142683 0.989769i \(-0.545573\pi\)
−0.142683 + 0.989769i \(0.545573\pi\)
\(308\) 12.0000 0.683763
\(309\) 27.0000 1.53598
\(310\) 0 0
\(311\) 33.0000 1.87126 0.935629 0.352985i \(-0.114833\pi\)
0.935629 + 0.352985i \(0.114833\pi\)
\(312\) 0 0
\(313\) 15.0000 0.847850 0.423925 0.905697i \(-0.360652\pi\)
0.423925 + 0.905697i \(0.360652\pi\)
\(314\) 0 0
\(315\) −6.00000 −0.338062
\(316\) −34.0000 −1.91265
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) 12.0000 0.671871
\(320\) −8.00000 −0.447214
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) −18.0000 −1.00000
\(325\) 0 0
\(326\) 0 0
\(327\) −45.0000 −2.48851
\(328\) 0 0
\(329\) 8.00000 0.441054
\(330\) 0 0
\(331\) 4.00000 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(332\) 6.00000 0.329293
\(333\) 12.0000 0.657596
\(334\) 0 0
\(335\) 1.00000 0.0546358
\(336\) −12.0000 −0.654654
\(337\) −30.0000 −1.63420 −0.817102 0.576493i \(-0.804421\pi\)
−0.817102 + 0.576493i \(0.804421\pi\)
\(338\) 0 0
\(339\) 3.00000 0.162938
\(340\) 0 0
\(341\) 48.0000 2.59935
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −3.00000 −0.161048 −0.0805242 0.996753i \(-0.525659\pi\)
−0.0805242 + 0.996753i \(0.525659\pi\)
\(348\) −12.0000 −0.643268
\(349\) −5.00000 −0.267644 −0.133822 0.991005i \(-0.542725\pi\)
−0.133822 + 0.991005i \(0.542725\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 26.0000 1.38384 0.691920 0.721974i \(-0.256765\pi\)
0.691920 + 0.721974i \(0.256765\pi\)
\(354\) 0 0
\(355\) 3.00000 0.159223
\(356\) −24.0000 −1.27200
\(357\) 0 0
\(358\) 0 0
\(359\) 31.0000 1.63612 0.818059 0.575135i \(-0.195050\pi\)
0.818059 + 0.575135i \(0.195050\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 75.0000 3.93648
\(364\) 0 0
\(365\) −11.0000 −0.575766
\(366\) 0 0
\(367\) −1.00000 −0.0521996 −0.0260998 0.999659i \(-0.508309\pi\)
−0.0260998 + 0.999659i \(0.508309\pi\)
\(368\) 0 0
\(369\) 36.0000 1.87409
\(370\) 0 0
\(371\) 6.00000 0.311504
\(372\) −48.0000 −2.48868
\(373\) 14.0000 0.724893 0.362446 0.932005i \(-0.381942\pi\)
0.362446 + 0.932005i \(0.381942\pi\)
\(374\) 0 0
\(375\) −27.0000 −1.39427
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −2.00000 −0.102733 −0.0513665 0.998680i \(-0.516358\pi\)
−0.0513665 + 0.998680i \(0.516358\pi\)
\(380\) −4.00000 −0.205196
\(381\) 6.00000 0.307389
\(382\) 0 0
\(383\) −20.0000 −1.02195 −0.510976 0.859595i \(-0.670716\pi\)
−0.510976 + 0.859595i \(0.670716\pi\)
\(384\) 0 0
\(385\) −6.00000 −0.305788
\(386\) 0 0
\(387\) −30.0000 −1.52499
\(388\) −10.0000 −0.507673
\(389\) −11.0000 −0.557722 −0.278861 0.960331i \(-0.589957\pi\)
−0.278861 + 0.960331i \(0.589957\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 17.0000 0.855363
\(396\) −72.0000 −3.61814
\(397\) 10.0000 0.501886 0.250943 0.968002i \(-0.419259\pi\)
0.250943 + 0.968002i \(0.419259\pi\)
\(398\) 0 0
\(399\) −6.00000 −0.300376
\(400\) −16.0000 −0.800000
\(401\) −21.0000 −1.04869 −0.524345 0.851506i \(-0.675690\pi\)
−0.524345 + 0.851506i \(0.675690\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −18.0000 −0.895533
\(405\) 9.00000 0.447214
\(406\) 0 0
\(407\) 12.0000 0.594818
\(408\) 0 0
\(409\) −14.0000 −0.692255 −0.346128 0.938187i \(-0.612504\pi\)
−0.346128 + 0.938187i \(0.612504\pi\)
\(410\) 0 0
\(411\) −33.0000 −1.62777
\(412\) −18.0000 −0.886796
\(413\) −5.00000 −0.246034
\(414\) 0 0
\(415\) −3.00000 −0.147264
\(416\) 0 0
\(417\) −42.0000 −2.05675
\(418\) 0 0
\(419\) 20.0000 0.977064 0.488532 0.872546i \(-0.337533\pi\)
0.488532 + 0.872546i \(0.337533\pi\)
\(420\) 6.00000 0.292770
\(421\) −28.0000 −1.36464 −0.682318 0.731055i \(-0.739028\pi\)
−0.682318 + 0.731055i \(0.739028\pi\)
\(422\) 0 0
\(423\) −48.0000 −2.33384
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 8.00000 0.386695
\(429\) 0 0
\(430\) 0 0
\(431\) 9.00000 0.433515 0.216757 0.976226i \(-0.430452\pi\)
0.216757 + 0.976226i \(0.430452\pi\)
\(432\) 36.0000 1.73205
\(433\) −26.0000 −1.24948 −0.624740 0.780833i \(-0.714795\pi\)
−0.624740 + 0.780833i \(0.714795\pi\)
\(434\) 0 0
\(435\) 6.00000 0.287678
\(436\) 30.0000 1.43674
\(437\) 0 0
\(438\) 0 0
\(439\) −14.0000 −0.668184 −0.334092 0.942541i \(-0.608430\pi\)
−0.334092 + 0.942541i \(0.608430\pi\)
\(440\) 0 0
\(441\) −36.0000 −1.71429
\(442\) 0 0
\(443\) 28.0000 1.33032 0.665160 0.746701i \(-0.268363\pi\)
0.665160 + 0.746701i \(0.268363\pi\)
\(444\) −12.0000 −0.569495
\(445\) 12.0000 0.568855
\(446\) 0 0
\(447\) 30.0000 1.41895
\(448\) 8.00000 0.377964
\(449\) −14.0000 −0.660701 −0.330350 0.943858i \(-0.607167\pi\)
−0.330350 + 0.943858i \(0.607167\pi\)
\(450\) 0 0
\(451\) 36.0000 1.69517
\(452\) −2.00000 −0.0940721
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −20.0000 −0.935561 −0.467780 0.883845i \(-0.654946\pi\)
−0.467780 + 0.883845i \(0.654946\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) −23.0000 −1.06890 −0.534450 0.845200i \(-0.679481\pi\)
−0.534450 + 0.845200i \(0.679481\pi\)
\(464\) 8.00000 0.371391
\(465\) 24.0000 1.11297
\(466\) 0 0
\(467\) −8.00000 −0.370196 −0.185098 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) −1.00000 −0.0461757
\(470\) 0 0
\(471\) 36.0000 1.65879
\(472\) 0 0
\(473\) −30.0000 −1.37940
\(474\) 0 0
\(475\) −8.00000 −0.367065
\(476\) 0 0
\(477\) −36.0000 −1.64833
\(478\) 0 0
\(479\) −16.0000 −0.731059 −0.365529 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −50.0000 −2.27273
\(485\) 5.00000 0.227038
\(486\) 0 0
\(487\) 12.0000 0.543772 0.271886 0.962329i \(-0.412353\pi\)
0.271886 + 0.962329i \(0.412353\pi\)
\(488\) 0 0
\(489\) −24.0000 −1.08532
\(490\) 0 0
\(491\) −17.0000 −0.767199 −0.383600 0.923499i \(-0.625316\pi\)
−0.383600 + 0.923499i \(0.625316\pi\)
\(492\) −36.0000 −1.62301
\(493\) 0 0
\(494\) 0 0
\(495\) 36.0000 1.61808
\(496\) 32.0000 1.43684
\(497\) −3.00000 −0.134568
\(498\) 0 0
\(499\) −19.0000 −0.850557 −0.425278 0.905063i \(-0.639824\pi\)
−0.425278 + 0.905063i \(0.639824\pi\)
\(500\) 18.0000 0.804984
\(501\) 27.0000 1.20627
\(502\) 0 0
\(503\) 15.0000 0.668817 0.334408 0.942428i \(-0.391463\pi\)
0.334408 + 0.942428i \(0.391463\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 0 0
\(507\) −39.0000 −1.73205
\(508\) −4.00000 −0.177471
\(509\) 31.0000 1.37405 0.687025 0.726633i \(-0.258916\pi\)
0.687025 + 0.726633i \(0.258916\pi\)
\(510\) 0 0
\(511\) 11.0000 0.486611
\(512\) 0 0
\(513\) 18.0000 0.794719
\(514\) 0 0
\(515\) 9.00000 0.396587
\(516\) 30.0000 1.32068
\(517\) −48.0000 −2.11104
\(518\) 0 0
\(519\) 54.0000 2.37034
\(520\) 0 0
\(521\) 4.00000 0.175243 0.0876216 0.996154i \(-0.472073\pi\)
0.0876216 + 0.996154i \(0.472073\pi\)
\(522\) 0 0
\(523\) −34.0000 −1.48672 −0.743358 0.668894i \(-0.766768\pi\)
−0.743358 + 0.668894i \(0.766768\pi\)
\(524\) 0 0
\(525\) 12.0000 0.523723
\(526\) 0 0
\(527\) 0 0
\(528\) 72.0000 3.13340
\(529\) −23.0000 −1.00000
\(530\) 0 0
\(531\) 30.0000 1.30189
\(532\) 4.00000 0.173422
\(533\) 0 0
\(534\) 0 0
\(535\) −4.00000 −0.172935
\(536\) 0 0
\(537\) 27.0000 1.16514
\(538\) 0 0
\(539\) −36.0000 −1.55063
\(540\) −18.0000 −0.774597
\(541\) −1.00000 −0.0429934 −0.0214967 0.999769i \(-0.506843\pi\)
−0.0214967 + 0.999769i \(0.506843\pi\)
\(542\) 0 0
\(543\) 15.0000 0.643712
\(544\) 0 0
\(545\) −15.0000 −0.642529
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) 22.0000 0.939793
\(549\) 0 0
\(550\) 0 0
\(551\) 4.00000 0.170406
\(552\) 0 0
\(553\) −17.0000 −0.722914
\(554\) 0 0
\(555\) 6.00000 0.254686
\(556\) 28.0000 1.18746
\(557\) −45.0000 −1.90671 −0.953356 0.301849i \(-0.902396\pi\)
−0.953356 + 0.301849i \(0.902396\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −4.00000 −0.169031
\(561\) 0 0
\(562\) 0 0
\(563\) −20.0000 −0.842900 −0.421450 0.906852i \(-0.638479\pi\)
−0.421450 + 0.906852i \(0.638479\pi\)
\(564\) 48.0000 2.02116
\(565\) 1.00000 0.0420703
\(566\) 0 0
\(567\) −9.00000 −0.377964
\(568\) 0 0
\(569\) 8.00000 0.335377 0.167689 0.985840i \(-0.446370\pi\)
0.167689 + 0.985840i \(0.446370\pi\)
\(570\) 0 0
\(571\) 29.0000 1.21361 0.606806 0.794850i \(-0.292450\pi\)
0.606806 + 0.794850i \(0.292450\pi\)
\(572\) 0 0
\(573\) −12.0000 −0.501307
\(574\) 0 0
\(575\) 0 0
\(576\) −48.0000 −2.00000
\(577\) 24.0000 0.999133 0.499567 0.866276i \(-0.333493\pi\)
0.499567 + 0.866276i \(0.333493\pi\)
\(578\) 0 0
\(579\) −42.0000 −1.74546
\(580\) −4.00000 −0.166091
\(581\) 3.00000 0.124461
\(582\) 0 0
\(583\) −36.0000 −1.49097
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −34.0000 −1.40333 −0.701665 0.712507i \(-0.747560\pi\)
−0.701665 + 0.712507i \(0.747560\pi\)
\(588\) 36.0000 1.48461
\(589\) 16.0000 0.659269
\(590\) 0 0
\(591\) 18.0000 0.740421
\(592\) 8.00000 0.328798
\(593\) −30.0000 −1.23195 −0.615976 0.787765i \(-0.711238\pi\)
−0.615976 + 0.787765i \(0.711238\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −20.0000 −0.819232
\(597\) −48.0000 −1.96451
\(598\) 0 0
\(599\) −39.0000 −1.59350 −0.796748 0.604311i \(-0.793448\pi\)
−0.796748 + 0.604311i \(0.793448\pi\)
\(600\) 0 0
\(601\) −6.00000 −0.244745 −0.122373 0.992484i \(-0.539050\pi\)
−0.122373 + 0.992484i \(0.539050\pi\)
\(602\) 0 0
\(603\) 6.00000 0.244339
\(604\) 0 0
\(605\) 25.0000 1.01639
\(606\) 0 0
\(607\) 10.0000 0.405887 0.202944 0.979190i \(-0.434949\pi\)
0.202944 + 0.979190i \(0.434949\pi\)
\(608\) 0 0
\(609\) −6.00000 −0.243132
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −26.0000 −1.05013 −0.525065 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) 0 0
\(615\) 18.0000 0.725830
\(616\) 0 0
\(617\) −11.0000 −0.442843 −0.221422 0.975178i \(-0.571070\pi\)
−0.221422 + 0.975178i \(0.571070\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) −16.0000 −0.642575
\(621\) 0 0
\(622\) 0 0
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) 11.0000 0.440000
\(626\) 0 0
\(627\) 36.0000 1.43770
\(628\) −24.0000 −0.957704
\(629\) 0 0
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) 0 0
\(633\) 66.0000 2.62326
\(634\) 0 0
\(635\) 2.00000 0.0793676
\(636\) 36.0000 1.42749
\(637\) 0 0
\(638\) 0 0
\(639\) 18.0000 0.712069
\(640\) 0 0
\(641\) 45.0000 1.77739 0.888697 0.458496i \(-0.151612\pi\)
0.888697 + 0.458496i \(0.151612\pi\)
\(642\) 0 0
\(643\) 41.0000 1.61688 0.808441 0.588577i \(-0.200312\pi\)
0.808441 + 0.588577i \(0.200312\pi\)
\(644\) 0 0
\(645\) −15.0000 −0.590624
\(646\) 0 0
\(647\) 12.0000 0.471769 0.235884 0.971781i \(-0.424201\pi\)
0.235884 + 0.971781i \(0.424201\pi\)
\(648\) 0 0
\(649\) 30.0000 1.17760
\(650\) 0 0
\(651\) −24.0000 −0.940634
\(652\) 16.0000 0.626608
\(653\) −35.0000 −1.36966 −0.684828 0.728705i \(-0.740123\pi\)
−0.684828 + 0.728705i \(0.740123\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 24.0000 0.937043
\(657\) −66.0000 −2.57491
\(658\) 0 0
\(659\) 6.00000 0.233727 0.116863 0.993148i \(-0.462716\pi\)
0.116863 + 0.993148i \(0.462716\pi\)
\(660\) −36.0000 −1.40130
\(661\) −10.0000 −0.388955 −0.194477 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.00000 −0.0775567
\(666\) 0 0
\(667\) 0 0
\(668\) −18.0000 −0.696441
\(669\) 6.00000 0.231973
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 0 0
\(675\) −36.0000 −1.38564
\(676\) 26.0000 1.00000
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 0 0
\(679\) −5.00000 −0.191882
\(680\) 0 0
\(681\) 36.0000 1.37952
\(682\) 0 0
\(683\) −31.0000 −1.18618 −0.593091 0.805135i \(-0.702093\pi\)
−0.593091 + 0.805135i \(0.702093\pi\)
\(684\) −24.0000 −0.917663
\(685\) −11.0000 −0.420288
\(686\) 0 0
\(687\) 39.0000 1.48794
\(688\) −20.0000 −0.762493
\(689\) 0 0
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) −36.0000 −1.36851
\(693\) −36.0000 −1.36753
\(694\) 0 0
\(695\) −14.0000 −0.531050
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) −24.0000 −0.907763
\(700\) −8.00000 −0.302372
\(701\) 30.0000 1.13308 0.566542 0.824033i \(-0.308281\pi\)
0.566542 + 0.824033i \(0.308281\pi\)
\(702\) 0 0
\(703\) 4.00000 0.150863
\(704\) −48.0000 −1.80907
\(705\) −24.0000 −0.903892
\(706\) 0 0
\(707\) −9.00000 −0.338480
\(708\) −30.0000 −1.12747
\(709\) −26.0000 −0.976450 −0.488225 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 0 0
\(711\) 102.000 3.82530
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −18.0000 −0.672692
\(717\) 36.0000 1.34444
\(718\) 0 0
\(719\) −20.0000 −0.745874 −0.372937 0.927857i \(-0.621649\pi\)
−0.372937 + 0.927857i \(0.621649\pi\)
\(720\) 24.0000 0.894427
\(721\) −9.00000 −0.335178
\(722\) 0 0
\(723\) −6.00000 −0.223142
\(724\) −10.0000 −0.371647
\(725\) −8.00000 −0.297113
\(726\) 0 0
\(727\) −24.0000 −0.890111 −0.445055 0.895503i \(-0.646816\pi\)
−0.445055 + 0.895503i \(0.646816\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −30.0000 −1.10808 −0.554038 0.832492i \(-0.686914\pi\)
−0.554038 + 0.832492i \(0.686914\pi\)
\(734\) 0 0
\(735\) −18.0000 −0.663940
\(736\) 0 0
\(737\) 6.00000 0.221013
\(738\) 0 0
\(739\) 6.00000 0.220714 0.110357 0.993892i \(-0.464801\pi\)
0.110357 + 0.993892i \(0.464801\pi\)
\(740\) −4.00000 −0.147043
\(741\) 0 0
\(742\) 0 0
\(743\) −49.0000 −1.79764 −0.898818 0.438322i \(-0.855573\pi\)
−0.898818 + 0.438322i \(0.855573\pi\)
\(744\) 0 0
\(745\) 10.0000 0.366372
\(746\) 0 0
\(747\) −18.0000 −0.658586
\(748\) 0 0
\(749\) 4.00000 0.146157
\(750\) 0 0
\(751\) −17.0000 −0.620339 −0.310169 0.950681i \(-0.600386\pi\)
−0.310169 + 0.950681i \(0.600386\pi\)
\(752\) −32.0000 −1.16692
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 18.0000 0.654654
\(757\) −16.0000 −0.581530 −0.290765 0.956795i \(-0.593910\pi\)
−0.290765 + 0.956795i \(0.593910\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 14.0000 0.507500 0.253750 0.967270i \(-0.418336\pi\)
0.253750 + 0.967270i \(0.418336\pi\)
\(762\) 0 0
\(763\) 15.0000 0.543036
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 48.0000 1.73205
\(769\) −30.0000 −1.08183 −0.540914 0.841078i \(-0.681921\pi\)
−0.540914 + 0.841078i \(0.681921\pi\)
\(770\) 0 0
\(771\) −21.0000 −0.756297
\(772\) 28.0000 1.00774
\(773\) −5.00000 −0.179838 −0.0899188 0.995949i \(-0.528661\pi\)
−0.0899188 + 0.995949i \(0.528661\pi\)
\(774\) 0 0
\(775\) −32.0000 −1.14947
\(776\) 0 0
\(777\) −6.00000 −0.215249
\(778\) 0 0
\(779\) 12.0000 0.429945
\(780\) 0 0
\(781\) 18.0000 0.644091
\(782\) 0 0
\(783\) 18.0000 0.643268
\(784\) −24.0000 −0.857143
\(785\) 12.0000 0.428298
\(786\) 0 0
\(787\) −39.0000 −1.39020 −0.695100 0.718913i \(-0.744640\pi\)
−0.695100 + 0.718913i \(0.744640\pi\)
\(788\) −12.0000 −0.427482
\(789\) 36.0000 1.28163
\(790\) 0 0
\(791\) −1.00000 −0.0355559
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −18.0000 −0.638394
\(796\) 32.0000 1.13421
\(797\) 12.0000 0.425062 0.212531 0.977154i \(-0.431829\pi\)
0.212531 + 0.977154i \(0.431829\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 72.0000 2.54399
\(802\) 0 0
\(803\) −66.0000 −2.32909
\(804\) −6.00000 −0.211604
\(805\) 0 0
\(806\) 0 0
\(807\) −9.00000 −0.316815
\(808\) 0 0
\(809\) 25.0000 0.878953 0.439477 0.898254i \(-0.355164\pi\)
0.439477 + 0.898254i \(0.355164\pi\)
\(810\) 0 0
\(811\) 32.0000 1.12367 0.561836 0.827249i \(-0.310095\pi\)
0.561836 + 0.827249i \(0.310095\pi\)
\(812\) 4.00000 0.140372
\(813\) 24.0000 0.841717
\(814\) 0 0
\(815\) −8.00000 −0.280228
\(816\) 0 0
\(817\) −10.0000 −0.349856
\(818\) 0 0
\(819\) 0 0
\(820\) −12.0000 −0.419058
\(821\) −12.0000 −0.418803 −0.209401 0.977830i \(-0.567152\pi\)
−0.209401 + 0.977830i \(0.567152\pi\)
\(822\) 0 0
\(823\) −31.0000 −1.08059 −0.540296 0.841475i \(-0.681688\pi\)
−0.540296 + 0.841475i \(0.681688\pi\)
\(824\) 0 0
\(825\) −72.0000 −2.50672
\(826\) 0 0
\(827\) 6.00000 0.208640 0.104320 0.994544i \(-0.466733\pi\)
0.104320 + 0.994544i \(0.466733\pi\)
\(828\) 0 0
\(829\) −17.0000 −0.590434 −0.295217 0.955430i \(-0.595392\pi\)
−0.295217 + 0.955430i \(0.595392\pi\)
\(830\) 0 0
\(831\) −66.0000 −2.28951
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 9.00000 0.311458
\(836\) −24.0000 −0.830057
\(837\) 72.0000 2.48868
\(838\) 0 0
\(839\) 42.0000 1.45000 0.725001 0.688748i \(-0.241839\pi\)
0.725001 + 0.688748i \(0.241839\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) −60.0000 −2.06651
\(844\) −44.0000 −1.51454
\(845\) −13.0000 −0.447214
\(846\) 0 0
\(847\) −25.0000 −0.859010
\(848\) −24.0000 −0.824163
\(849\) −3.00000 −0.102960
\(850\) 0 0
\(851\) 0 0
\(852\) −18.0000 −0.616670
\(853\) 3.00000 0.102718 0.0513590 0.998680i \(-0.483645\pi\)
0.0513590 + 0.998680i \(0.483645\pi\)
\(854\) 0 0
\(855\) 12.0000 0.410391
\(856\) 0 0
\(857\) −26.0000 −0.888143 −0.444072 0.895991i \(-0.646466\pi\)
−0.444072 + 0.895991i \(0.646466\pi\)
\(858\) 0 0
\(859\) 50.0000 1.70598 0.852989 0.521929i \(-0.174787\pi\)
0.852989 + 0.521929i \(0.174787\pi\)
\(860\) 10.0000 0.340997
\(861\) −18.0000 −0.613438
\(862\) 0 0
\(863\) −4.00000 −0.136162 −0.0680808 0.997680i \(-0.521688\pi\)
−0.0680808 + 0.997680i \(0.521688\pi\)
\(864\) 0 0
\(865\) 18.0000 0.612018
\(866\) 0 0
\(867\) −51.0000 −1.73205
\(868\) 16.0000 0.543075
\(869\) 102.000 3.46011
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 30.0000 1.01535
\(874\) 0 0
\(875\) 9.00000 0.304256
\(876\) 66.0000 2.22993
\(877\) 34.0000 1.14810 0.574049 0.818821i \(-0.305372\pi\)
0.574049 + 0.818821i \(0.305372\pi\)
\(878\) 0 0
\(879\) 18.0000 0.607125
\(880\) 24.0000 0.809040
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 0 0
\(883\) −1.00000 −0.0336527 −0.0168263 0.999858i \(-0.505356\pi\)
−0.0168263 + 0.999858i \(0.505356\pi\)
\(884\) 0 0
\(885\) 15.0000 0.504219
\(886\) 0 0
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 0 0
\(889\) −2.00000 −0.0670778
\(890\) 0 0
\(891\) 54.0000 1.80907
\(892\) −4.00000 −0.133930
\(893\) −16.0000 −0.535420
\(894\) 0 0
\(895\) 9.00000 0.300837
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 16.0000 0.533630
\(900\) 48.0000 1.60000
\(901\) 0 0
\(902\) 0 0
\(903\) 15.0000 0.499169
\(904\) 0 0
\(905\) 5.00000 0.166206
\(906\) 0 0
\(907\) −38.0000 −1.26177 −0.630885 0.775877i \(-0.717308\pi\)
−0.630885 + 0.775877i \(0.717308\pi\)
\(908\) −24.0000 −0.796468
\(909\) 54.0000 1.79107
\(910\) 0 0
\(911\) 37.0000 1.22586 0.612932 0.790135i \(-0.289990\pi\)
0.612932 + 0.790135i \(0.289990\pi\)
\(912\) 24.0000 0.794719
\(913\) −18.0000 −0.595713
\(914\) 0 0
\(915\) 0 0
\(916\) −26.0000 −0.859064
\(917\) 0 0
\(918\) 0 0
\(919\) 11.0000 0.362857 0.181428 0.983404i \(-0.441928\pi\)
0.181428 + 0.983404i \(0.441928\pi\)
\(920\) 0 0
\(921\) −15.0000 −0.494267
\(922\) 0 0
\(923\) 0 0
\(924\) 36.0000 1.18431
\(925\) −8.00000 −0.263038
\(926\) 0 0
\(927\) 54.0000 1.77359
\(928\) 0 0
\(929\) −14.0000 −0.459325 −0.229663 0.973270i \(-0.573762\pi\)
−0.229663 + 0.973270i \(0.573762\pi\)
\(930\) 0 0
\(931\) −12.0000 −0.393284
\(932\) 16.0000 0.524097
\(933\) 99.0000 3.24111
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −3.00000 −0.0980057 −0.0490029 0.998799i \(-0.515604\pi\)
−0.0490029 + 0.998799i \(0.515604\pi\)
\(938\) 0 0
\(939\) 45.0000 1.46852
\(940\) 16.0000 0.521862
\(941\) −17.0000 −0.554184 −0.277092 0.960843i \(-0.589371\pi\)
−0.277092 + 0.960843i \(0.589371\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 20.0000 0.650945
\(945\) −9.00000 −0.292770
\(946\) 0 0
\(947\) −30.0000 −0.974869 −0.487435 0.873160i \(-0.662067\pi\)
−0.487435 + 0.873160i \(0.662067\pi\)
\(948\) −102.000 −3.31281
\(949\) 0 0
\(950\) 0 0
\(951\) −36.0000 −1.16738
\(952\) 0 0
\(953\) −6.00000 −0.194359 −0.0971795 0.995267i \(-0.530982\pi\)
−0.0971795 + 0.995267i \(0.530982\pi\)
\(954\) 0 0
\(955\) −4.00000 −0.129437
\(956\) −24.0000 −0.776215
\(957\) 36.0000 1.16371
\(958\) 0 0
\(959\) 11.0000 0.355209
\(960\) −24.0000 −0.774597
\(961\) 33.0000 1.06452
\(962\) 0 0
\(963\) −24.0000 −0.773389
\(964\) 4.00000 0.128831
\(965\) −14.0000 −0.450676
\(966\) 0 0
\(967\) 16.0000 0.514525 0.257263 0.966342i \(-0.417179\pi\)
0.257263 + 0.966342i \(0.417179\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 14.0000 0.448819
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −62.0000 −1.98356 −0.991778 0.127971i \(-0.959153\pi\)
−0.991778 + 0.127971i \(0.959153\pi\)
\(978\) 0 0
\(979\) 72.0000 2.30113
\(980\) 12.0000 0.383326
\(981\) −90.0000 −2.87348
\(982\) 0 0
\(983\) 21.0000 0.669796 0.334898 0.942254i \(-0.391298\pi\)
0.334898 + 0.942254i \(0.391298\pi\)
\(984\) 0 0
\(985\) 6.00000 0.191176
\(986\) 0 0
\(987\) 24.0000 0.763928
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 30.0000 0.952981 0.476491 0.879180i \(-0.341909\pi\)
0.476491 + 0.879180i \(0.341909\pi\)
\(992\) 0 0
\(993\) 12.0000 0.380808
\(994\) 0 0
\(995\) −16.0000 −0.507234
\(996\) 18.0000 0.570352
\(997\) 14.0000 0.443384 0.221692 0.975117i \(-0.428842\pi\)
0.221692 + 0.975117i \(0.428842\pi\)
\(998\) 0 0
\(999\) 18.0000 0.569495
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 6011.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6011.2.a.b.1.1 1 1.1 even 1 trivial