Properties

Label 2001.2.a.c.1.1
Level $2001$
Weight $2$
Character 2001.1
Self dual yes
Analytic conductor $15.978$
Analytic rank $1$
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] = [2001,2,Mod(1,2001)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2001, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("2001.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2001 = 3 \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2001.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: \(15.9780654445\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 2001.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} -2.00000 q^{4} +1.00000 q^{9} -4.00000 q^{11} -2.00000 q^{12} +3.00000 q^{13} +4.00000 q^{16} +3.00000 q^{17} -7.00000 q^{19} +1.00000 q^{23} -5.00000 q^{25} +1.00000 q^{27} -1.00000 q^{29} +2.00000 q^{31} -4.00000 q^{33} -2.00000 q^{36} +1.00000 q^{37} +3.00000 q^{39} -6.00000 q^{41} -11.0000 q^{43} +8.00000 q^{44} +10.0000 q^{47} +4.00000 q^{48} -7.00000 q^{49} +3.00000 q^{51} -6.00000 q^{52} -6.00000 q^{53} -7.00000 q^{57} -11.0000 q^{59} +14.0000 q^{61} -8.00000 q^{64} -6.00000 q^{68} +1.00000 q^{69} -15.0000 q^{71} -12.0000 q^{73} -5.00000 q^{75} +14.0000 q^{76} +1.00000 q^{79} +1.00000 q^{81} -2.00000 q^{83} -1.00000 q^{87} +7.00000 q^{89} -2.00000 q^{92} +2.00000 q^{93} -14.0000 q^{97} -4.00000 q^{99} +O(q^{100})\)

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 \(0.5\pi\)
\(3\) 1.00000 0.577350
\(4\) −2.00000 −1.00000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) −2.00000 −0.577350
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.00000 1.00000
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) −7.00000 −1.60591 −0.802955 0.596040i \(-0.796740\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0 0
\(33\) −4.00000 −0.696311
\(34\) 0 0
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) 1.00000 0.164399 0.0821995 0.996616i \(-0.473806\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) 0 0
\(39\) 3.00000 0.480384
\(40\) 0 0
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 0 0
\(43\) −11.0000 −1.67748 −0.838742 0.544529i \(-0.816708\pi\)
−0.838742 + 0.544529i \(0.816708\pi\)
\(44\) 8.00000 1.20605
\(45\) 0 0
\(46\) 0 0
\(47\) 10.0000 1.45865 0.729325 0.684167i \(-0.239834\pi\)
0.729325 + 0.684167i \(0.239834\pi\)
\(48\) 4.00000 0.577350
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) −6.00000 −0.832050
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −7.00000 −0.927173
\(58\) 0 0
\(59\) −11.0000 −1.43208 −0.716039 0.698060i \(-0.754047\pi\)
−0.716039 + 0.698060i \(0.754047\pi\)
\(60\) 0 0
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) −6.00000 −0.727607
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −15.0000 −1.78017 −0.890086 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 0 0
\(73\) −12.0000 −1.40449 −0.702247 0.711934i \(-0.747820\pi\)
−0.702247 + 0.711934i \(0.747820\pi\)
\(74\) 0 0
\(75\) −5.00000 −0.577350
\(76\) 14.0000 1.60591
\(77\) 0 0
\(78\) 0 0
\(79\) 1.00000 0.112509 0.0562544 0.998416i \(-0.482084\pi\)
0.0562544 + 0.998416i \(0.482084\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.00000 −0.107211
\(88\) 0 0
\(89\) 7.00000 0.741999 0.370999 0.928633i \(-0.379015\pi\)
0.370999 + 0.928633i \(0.379015\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) 2.00000 0.207390
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) −4.00000 −0.402015
\(100\) 10.0000 1.00000
\(101\) −8.00000 −0.796030 −0.398015 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(102\) 0 0
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.00000 −0.193347 −0.0966736 0.995316i \(-0.530820\pi\)
−0.0966736 + 0.995316i \(0.530820\pi\)
\(108\) −2.00000 −0.192450
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 1.00000 0.0949158
\(112\) 0 0
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 2.00000 0.185695
\(117\) 3.00000 0.277350
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 0.454545
\(122\) 0 0
\(123\) −6.00000 −0.541002
\(124\) −4.00000 −0.359211
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) −11.0000 −0.968496
\(130\) 0 0
\(131\) −16.0000 −1.39793 −0.698963 0.715158i \(-0.746355\pi\)
−0.698963 + 0.715158i \(0.746355\pi\)
\(132\) 8.00000 0.696311
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 15.0000 1.28154 0.640768 0.767734i \(-0.278616\pi\)
0.640768 + 0.767734i \(0.278616\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) 10.0000 0.842152
\(142\) 0 0
\(143\) −12.0000 −1.00349
\(144\) 4.00000 0.333333
\(145\) 0 0
\(146\) 0 0
\(147\) −7.00000 −0.577350
\(148\) −2.00000 −0.164399
\(149\) 20.0000 1.63846 0.819232 0.573462i \(-0.194400\pi\)
0.819232 + 0.573462i \(0.194400\pi\)
\(150\) 0 0
\(151\) 11.0000 0.895167 0.447584 0.894242i \(-0.352285\pi\)
0.447584 + 0.894242i \(0.352285\pi\)
\(152\) 0 0
\(153\) 3.00000 0.242536
\(154\) 0 0
\(155\) 0 0
\(156\) −6.00000 −0.480384
\(157\) −11.0000 −0.877896 −0.438948 0.898513i \(-0.644649\pi\)
−0.438948 + 0.898513i \(0.644649\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 12.0000 0.937043
\(165\) 0 0
\(166\) 0 0
\(167\) −9.00000 −0.696441 −0.348220 0.937413i \(-0.613214\pi\)
−0.348220 + 0.937413i \(0.613214\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) −7.00000 −0.535303
\(172\) 22.0000 1.67748
\(173\) 1.00000 0.0760286 0.0380143 0.999277i \(-0.487897\pi\)
0.0380143 + 0.999277i \(0.487897\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −16.0000 −1.20605
\(177\) −11.0000 −0.826811
\(178\) 0 0
\(179\) 3.00000 0.224231 0.112115 0.993695i \(-0.464237\pi\)
0.112115 + 0.993695i \(0.464237\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −12.0000 −0.877527
\(188\) −20.0000 −1.45865
\(189\) 0 0
\(190\) 0 0
\(191\) −11.0000 −0.795932 −0.397966 0.917400i \(-0.630284\pi\)
−0.397966 + 0.917400i \(0.630284\pi\)
\(192\) −8.00000 −0.577350
\(193\) −18.0000 −1.29567 −0.647834 0.761781i \(-0.724325\pi\)
−0.647834 + 0.761781i \(0.724325\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 14.0000 1.00000
\(197\) 13.0000 0.926212 0.463106 0.886303i \(-0.346735\pi\)
0.463106 + 0.886303i \(0.346735\pi\)
\(198\) 0 0
\(199\) 18.0000 1.27599 0.637993 0.770042i \(-0.279765\pi\)
0.637993 + 0.770042i \(0.279765\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) −6.00000 −0.420084
\(205\) 0 0
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 12.0000 0.832050
\(209\) 28.0000 1.93680
\(210\) 0 0
\(211\) −18.0000 −1.23917 −0.619586 0.784929i \(-0.712699\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(212\) 12.0000 0.824163
\(213\) −15.0000 −1.02778
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −12.0000 −0.810885
\(220\) 0 0
\(221\) 9.00000 0.605406
\(222\) 0 0
\(223\) −7.00000 −0.468755 −0.234377 0.972146i \(-0.575305\pi\)
−0.234377 + 0.972146i \(0.575305\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) 0 0
\(227\) 14.0000 0.929213 0.464606 0.885517i \(-0.346196\pi\)
0.464606 + 0.885517i \(0.346196\pi\)
\(228\) 14.0000 0.927173
\(229\) 23.0000 1.51988 0.759941 0.649992i \(-0.225228\pi\)
0.759941 + 0.649992i \(0.225228\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 22.0000 1.43208
\(237\) 1.00000 0.0649570
\(238\) 0 0
\(239\) 15.0000 0.970269 0.485135 0.874439i \(-0.338771\pi\)
0.485135 + 0.874439i \(0.338771\pi\)
\(240\) 0 0
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) −28.0000 −1.79252
\(245\) 0 0
\(246\) 0 0
\(247\) −21.0000 −1.33620
\(248\) 0 0
\(249\) −2.00000 −0.126745
\(250\) 0 0
\(251\) 25.0000 1.57799 0.788993 0.614402i \(-0.210603\pi\)
0.788993 + 0.614402i \(0.210603\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 0 0
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 9.00000 0.561405 0.280702 0.959795i \(-0.409433\pi\)
0.280702 + 0.959795i \(0.409433\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −1.00000 −0.0618984
\(262\) 0 0
\(263\) 28.0000 1.72655 0.863277 0.504730i \(-0.168408\pi\)
0.863277 + 0.504730i \(0.168408\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 7.00000 0.428393
\(268\) 0 0
\(269\) 24.0000 1.46331 0.731653 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 0 0
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) 12.0000 0.727607
\(273\) 0 0
\(274\) 0 0
\(275\) 20.0000 1.20605
\(276\) −2.00000 −0.120386
\(277\) 19.0000 1.14160 0.570800 0.821089i \(-0.306633\pi\)
0.570800 + 0.821089i \(0.306633\pi\)
\(278\) 0 0
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) 24.0000 1.43172 0.715860 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 0 0
\(283\) −10.0000 −0.594438 −0.297219 0.954809i \(-0.596059\pi\)
−0.297219 + 0.954809i \(0.596059\pi\)
\(284\) 30.0000 1.78017
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) −14.0000 −0.820695
\(292\) 24.0000 1.40449
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −4.00000 −0.232104
\(298\) 0 0
\(299\) 3.00000 0.173494
\(300\) 10.0000 0.577350
\(301\) 0 0
\(302\) 0 0
\(303\) −8.00000 −0.459588
\(304\) −28.0000 −1.60591
\(305\) 0 0
\(306\) 0 0
\(307\) 26.0000 1.48390 0.741949 0.670456i \(-0.233902\pi\)
0.741949 + 0.670456i \(0.233902\pi\)
\(308\) 0 0
\(309\) −8.00000 −0.455104
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) 0 0
\(313\) −14.0000 −0.791327 −0.395663 0.918396i \(-0.629485\pi\)
−0.395663 + 0.918396i \(0.629485\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −2.00000 −0.112509
\(317\) −14.0000 −0.786318 −0.393159 0.919470i \(-0.628618\pi\)
−0.393159 + 0.919470i \(0.628618\pi\)
\(318\) 0 0
\(319\) 4.00000 0.223957
\(320\) 0 0
\(321\) −2.00000 −0.111629
\(322\) 0 0
\(323\) −21.0000 −1.16847
\(324\) −2.00000 −0.111111
\(325\) −15.0000 −0.832050
\(326\) 0 0
\(327\) 10.0000 0.553001
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −18.0000 −0.989369 −0.494685 0.869072i \(-0.664716\pi\)
−0.494685 + 0.869072i \(0.664716\pi\)
\(332\) 4.00000 0.219529
\(333\) 1.00000 0.0547997
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −23.0000 −1.25289 −0.626445 0.779466i \(-0.715491\pi\)
−0.626445 + 0.779466i \(0.715491\pi\)
\(338\) 0 0
\(339\) 10.0000 0.543125
\(340\) 0 0
\(341\) −8.00000 −0.433224
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 17.0000 0.912608 0.456304 0.889824i \(-0.349173\pi\)
0.456304 + 0.889824i \(0.349173\pi\)
\(348\) 2.00000 0.107211
\(349\) 19.0000 1.01705 0.508523 0.861048i \(-0.330192\pi\)
0.508523 + 0.861048i \(0.330192\pi\)
\(350\) 0 0
\(351\) 3.00000 0.160128
\(352\) 0 0
\(353\) 10.0000 0.532246 0.266123 0.963939i \(-0.414257\pi\)
0.266123 + 0.963939i \(0.414257\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −14.0000 −0.741999
\(357\) 0 0
\(358\) 0 0
\(359\) −3.00000 −0.158334 −0.0791670 0.996861i \(-0.525226\pi\)
−0.0791670 + 0.996861i \(0.525226\pi\)
\(360\) 0 0
\(361\) 30.0000 1.57895
\(362\) 0 0
\(363\) 5.00000 0.262432
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −4.00000 −0.208798 −0.104399 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) 4.00000 0.208514
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 0 0
\(372\) −4.00000 −0.207390
\(373\) −6.00000 −0.310668 −0.155334 0.987862i \(-0.549645\pi\)
−0.155334 + 0.987862i \(0.549645\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −3.00000 −0.154508
\(378\) 0 0
\(379\) −1.00000 −0.0513665 −0.0256833 0.999670i \(-0.508176\pi\)
−0.0256833 + 0.999670i \(0.508176\pi\)
\(380\) 0 0
\(381\) −16.0000 −0.819705
\(382\) 0 0
\(383\) −30.0000 −1.53293 −0.766464 0.642287i \(-0.777986\pi\)
−0.766464 + 0.642287i \(0.777986\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −11.0000 −0.559161
\(388\) 28.0000 1.42148
\(389\) −15.0000 −0.760530 −0.380265 0.924878i \(-0.624167\pi\)
−0.380265 + 0.924878i \(0.624167\pi\)
\(390\) 0 0
\(391\) 3.00000 0.151717
\(392\) 0 0
\(393\) −16.0000 −0.807093
\(394\) 0 0
\(395\) 0 0
\(396\) 8.00000 0.402015
\(397\) 18.0000 0.903394 0.451697 0.892171i \(-0.350819\pi\)
0.451697 + 0.892171i \(0.350819\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −20.0000 −1.00000
\(401\) −34.0000 −1.69788 −0.848939 0.528490i \(-0.822758\pi\)
−0.848939 + 0.528490i \(0.822758\pi\)
\(402\) 0 0
\(403\) 6.00000 0.298881
\(404\) 16.0000 0.796030
\(405\) 0 0
\(406\) 0 0
\(407\) −4.00000 −0.198273
\(408\) 0 0
\(409\) −8.00000 −0.395575 −0.197787 0.980245i \(-0.563376\pi\)
−0.197787 + 0.980245i \(0.563376\pi\)
\(410\) 0 0
\(411\) 15.0000 0.739895
\(412\) 16.0000 0.788263
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 17.0000 0.828529 0.414265 0.910156i \(-0.364039\pi\)
0.414265 + 0.910156i \(0.364039\pi\)
\(422\) 0 0
\(423\) 10.0000 0.486217
\(424\) 0 0
\(425\) −15.0000 −0.727607
\(426\) 0 0
\(427\) 0 0
\(428\) 4.00000 0.193347
\(429\) −12.0000 −0.579365
\(430\) 0 0
\(431\) 22.0000 1.05970 0.529851 0.848091i \(-0.322248\pi\)
0.529851 + 0.848091i \(0.322248\pi\)
\(432\) 4.00000 0.192450
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −20.0000 −0.957826
\(437\) −7.00000 −0.334855
\(438\) 0 0
\(439\) −35.0000 −1.67046 −0.835229 0.549902i \(-0.814665\pi\)
−0.835229 + 0.549902i \(0.814665\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) −2.00000 −0.0949158
\(445\) 0 0
\(446\) 0 0
\(447\) 20.0000 0.945968
\(448\) 0 0
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 24.0000 1.13012
\(452\) −20.0000 −0.940721
\(453\) 11.0000 0.516825
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 4.00000 0.187112 0.0935561 0.995614i \(-0.470177\pi\)
0.0935561 + 0.995614i \(0.470177\pi\)
\(458\) 0 0
\(459\) 3.00000 0.140028
\(460\) 0 0
\(461\) −28.0000 −1.30409 −0.652045 0.758180i \(-0.726089\pi\)
−0.652045 + 0.758180i \(0.726089\pi\)
\(462\) 0 0
\(463\) −39.0000 −1.81248 −0.906242 0.422760i \(-0.861061\pi\)
−0.906242 + 0.422760i \(0.861061\pi\)
\(464\) −4.00000 −0.185695
\(465\) 0 0
\(466\) 0 0
\(467\) 11.0000 0.509019 0.254510 0.967070i \(-0.418086\pi\)
0.254510 + 0.967070i \(0.418086\pi\)
\(468\) −6.00000 −0.277350
\(469\) 0 0
\(470\) 0 0
\(471\) −11.0000 −0.506853
\(472\) 0 0
\(473\) 44.0000 2.02312
\(474\) 0 0
\(475\) 35.0000 1.60591
\(476\) 0 0
\(477\) −6.00000 −0.274721
\(478\) 0 0
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) 3.00000 0.136788
\(482\) 0 0
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) 0 0
\(486\) 0 0
\(487\) 32.0000 1.45006 0.725029 0.688718i \(-0.241826\pi\)
0.725029 + 0.688718i \(0.241826\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 12.0000 0.541002
\(493\) −3.00000 −0.135113
\(494\) 0 0
\(495\) 0 0
\(496\) 8.00000 0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) 31.0000 1.38775 0.693875 0.720095i \(-0.255902\pi\)
0.693875 + 0.720095i \(0.255902\pi\)
\(500\) 0 0
\(501\) −9.00000 −0.402090
\(502\) 0 0
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −4.00000 −0.177646
\(508\) 32.0000 1.41977
\(509\) −1.00000 −0.0443242 −0.0221621 0.999754i \(-0.507055\pi\)
−0.0221621 + 0.999754i \(0.507055\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −7.00000 −0.309058
\(514\) 0 0
\(515\) 0 0
\(516\) 22.0000 0.968496
\(517\) −40.0000 −1.75920
\(518\) 0 0
\(519\) 1.00000 0.0438951
\(520\) 0 0
\(521\) 20.0000 0.876216 0.438108 0.898922i \(-0.355649\pi\)
0.438108 + 0.898922i \(0.355649\pi\)
\(522\) 0 0
\(523\) 28.0000 1.22435 0.612177 0.790721i \(-0.290294\pi\)
0.612177 + 0.790721i \(0.290294\pi\)
\(524\) 32.0000 1.39793
\(525\) 0 0
\(526\) 0 0
\(527\) 6.00000 0.261364
\(528\) −16.0000 −0.696311
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −11.0000 −0.477359
\(532\) 0 0
\(533\) −18.0000 −0.779667
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 3.00000 0.129460
\(538\) 0 0
\(539\) 28.0000 1.20605
\(540\) 0 0
\(541\) 44.0000 1.89171 0.945854 0.324593i \(-0.105227\pi\)
0.945854 + 0.324593i \(0.105227\pi\)
\(542\) 0 0
\(543\) −2.00000 −0.0858282
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 23.0000 0.983409 0.491704 0.870762i \(-0.336374\pi\)
0.491704 + 0.870762i \(0.336374\pi\)
\(548\) −30.0000 −1.28154
\(549\) 14.0000 0.597505
\(550\) 0 0
\(551\) 7.00000 0.298210
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 26.0000 1.10166 0.550828 0.834619i \(-0.314312\pi\)
0.550828 + 0.834619i \(0.314312\pi\)
\(558\) 0 0
\(559\) −33.0000 −1.39575
\(560\) 0 0
\(561\) −12.0000 −0.506640
\(562\) 0 0
\(563\) −7.00000 −0.295015 −0.147507 0.989061i \(-0.547125\pi\)
−0.147507 + 0.989061i \(0.547125\pi\)
\(564\) −20.0000 −0.842152
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 6.00000 0.251533 0.125767 0.992060i \(-0.459861\pi\)
0.125767 + 0.992060i \(0.459861\pi\)
\(570\) 0 0
\(571\) −18.0000 −0.753277 −0.376638 0.926360i \(-0.622920\pi\)
−0.376638 + 0.926360i \(0.622920\pi\)
\(572\) 24.0000 1.00349
\(573\) −11.0000 −0.459532
\(574\) 0 0
\(575\) −5.00000 −0.208514
\(576\) −8.00000 −0.333333
\(577\) −26.0000 −1.08239 −0.541197 0.840896i \(-0.682029\pi\)
−0.541197 + 0.840896i \(0.682029\pi\)
\(578\) 0 0
\(579\) −18.0000 −0.748054
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 24.0000 0.993978
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −15.0000 −0.619116 −0.309558 0.950881i \(-0.600181\pi\)
−0.309558 + 0.950881i \(0.600181\pi\)
\(588\) 14.0000 0.577350
\(589\) −14.0000 −0.576860
\(590\) 0 0
\(591\) 13.0000 0.534749
\(592\) 4.00000 0.164399
\(593\) −9.00000 −0.369586 −0.184793 0.982777i \(-0.559161\pi\)
−0.184793 + 0.982777i \(0.559161\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −40.0000 −1.63846
\(597\) 18.0000 0.736691
\(598\) 0 0
\(599\) −38.0000 −1.55264 −0.776319 0.630340i \(-0.782915\pi\)
−0.776319 + 0.630340i \(0.782915\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −22.0000 −0.895167
\(605\) 0 0
\(606\) 0 0
\(607\) −20.0000 −0.811775 −0.405887 0.913923i \(-0.633038\pi\)
−0.405887 + 0.913923i \(0.633038\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 30.0000 1.21367
\(612\) −6.00000 −0.242536
\(613\) −2.00000 −0.0807792 −0.0403896 0.999184i \(-0.512860\pi\)
−0.0403896 + 0.999184i \(0.512860\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 34.0000 1.36879 0.684394 0.729112i \(-0.260067\pi\)
0.684394 + 0.729112i \(0.260067\pi\)
\(618\) 0 0
\(619\) 29.0000 1.16561 0.582804 0.812613i \(-0.301955\pi\)
0.582804 + 0.812613i \(0.301955\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 0 0
\(624\) 12.0000 0.480384
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 28.0000 1.11821
\(628\) 22.0000 0.877896
\(629\) 3.00000 0.119618
\(630\) 0 0
\(631\) 34.0000 1.35352 0.676759 0.736204i \(-0.263384\pi\)
0.676759 + 0.736204i \(0.263384\pi\)
\(632\) 0 0
\(633\) −18.0000 −0.715436
\(634\) 0 0
\(635\) 0 0
\(636\) 12.0000 0.475831
\(637\) −21.0000 −0.832050
\(638\) 0 0
\(639\) −15.0000 −0.593391
\(640\) 0 0
\(641\) 17.0000 0.671460 0.335730 0.941958i \(-0.391017\pi\)
0.335730 + 0.941958i \(0.391017\pi\)
\(642\) 0 0
\(643\) −36.0000 −1.41970 −0.709851 0.704352i \(-0.751238\pi\)
−0.709851 + 0.704352i \(0.751238\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −7.00000 −0.275198 −0.137599 0.990488i \(-0.543939\pi\)
−0.137599 + 0.990488i \(0.543939\pi\)
\(648\) 0 0
\(649\) 44.0000 1.72715
\(650\) 0 0
\(651\) 0 0
\(652\) 8.00000 0.313304
\(653\) −14.0000 −0.547862 −0.273931 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −24.0000 −0.937043
\(657\) −12.0000 −0.468165
\(658\) 0 0
\(659\) −19.0000 −0.740135 −0.370067 0.929005i \(-0.620665\pi\)
−0.370067 + 0.929005i \(0.620665\pi\)
\(660\) 0 0
\(661\) −10.0000 −0.388955 −0.194477 0.980907i \(-0.562301\pi\)
−0.194477 + 0.980907i \(0.562301\pi\)
\(662\) 0 0
\(663\) 9.00000 0.349531
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 18.0000 0.696441
\(669\) −7.00000 −0.270636
\(670\) 0 0
\(671\) −56.0000 −2.16186
\(672\) 0 0
\(673\) 37.0000 1.42625 0.713123 0.701039i \(-0.247280\pi\)
0.713123 + 0.701039i \(0.247280\pi\)
\(674\) 0 0
\(675\) −5.00000 −0.192450
\(676\) 8.00000 0.307692
\(677\) −38.0000 −1.46046 −0.730229 0.683202i \(-0.760587\pi\)
−0.730229 + 0.683202i \(0.760587\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 14.0000 0.536481
\(682\) 0 0
\(683\) 44.0000 1.68361 0.841807 0.539779i \(-0.181492\pi\)
0.841807 + 0.539779i \(0.181492\pi\)
\(684\) 14.0000 0.535303
\(685\) 0 0
\(686\) 0 0
\(687\) 23.0000 0.877505
\(688\) −44.0000 −1.67748
\(689\) −18.0000 −0.685745
\(690\) 0 0
\(691\) −20.0000 −0.760836 −0.380418 0.924815i \(-0.624220\pi\)
−0.380418 + 0.924815i \(0.624220\pi\)
\(692\) −2.00000 −0.0760286
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −18.0000 −0.681799
\(698\) 0 0
\(699\) −21.0000 −0.794293
\(700\) 0 0
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) −7.00000 −0.264010
\(704\) 32.0000 1.20605
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 22.0000 0.826811
\(709\) 22.0000 0.826227 0.413114 0.910679i \(-0.364441\pi\)
0.413114 + 0.910679i \(0.364441\pi\)
\(710\) 0 0
\(711\) 1.00000 0.0375029
\(712\) 0 0
\(713\) 2.00000 0.0749006
\(714\) 0 0
\(715\) 0 0
\(716\) −6.00000 −0.224231
\(717\) 15.0000 0.560185
\(718\) 0 0
\(719\) −33.0000 −1.23069 −0.615346 0.788257i \(-0.710984\pi\)
−0.615346 + 0.788257i \(0.710984\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) −18.0000 −0.669427
\(724\) 4.00000 0.148659
\(725\) 5.00000 0.185695
\(726\) 0 0
\(727\) 16.0000 0.593407 0.296704 0.954970i \(-0.404113\pi\)
0.296704 + 0.954970i \(0.404113\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −33.0000 −1.22055
\(732\) −28.0000 −1.03491
\(733\) −14.0000 −0.517102 −0.258551 0.965998i \(-0.583245\pi\)
−0.258551 + 0.965998i \(0.583245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −2.00000 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(740\) 0 0
\(741\) −21.0000 −0.771454
\(742\) 0 0
\(743\) −3.00000 −0.110059 −0.0550297 0.998485i \(-0.517525\pi\)
−0.0550297 + 0.998485i \(0.517525\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.00000 −0.0731762
\(748\) 24.0000 0.877527
\(749\) 0 0
\(750\) 0 0
\(751\) −51.0000 −1.86102 −0.930508 0.366271i \(-0.880634\pi\)
−0.930508 + 0.366271i \(0.880634\pi\)
\(752\) 40.0000 1.45865
\(753\) 25.0000 0.911051
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −29.0000 −1.05402 −0.527011 0.849858i \(-0.676688\pi\)
−0.527011 + 0.849858i \(0.676688\pi\)
\(758\) 0 0
\(759\) −4.00000 −0.145191
\(760\) 0 0
\(761\) 35.0000 1.26875 0.634375 0.773026i \(-0.281258\pi\)
0.634375 + 0.773026i \(0.281258\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 22.0000 0.795932
\(765\) 0 0
\(766\) 0 0
\(767\) −33.0000 −1.19156
\(768\) 16.0000 0.577350
\(769\) −45.0000 −1.62274 −0.811371 0.584532i \(-0.801278\pi\)
−0.811371 + 0.584532i \(0.801278\pi\)
\(770\) 0 0
\(771\) 9.00000 0.324127
\(772\) 36.0000 1.29567
\(773\) 26.0000 0.935155 0.467578 0.883952i \(-0.345127\pi\)
0.467578 + 0.883952i \(0.345127\pi\)
\(774\) 0 0
\(775\) −10.0000 −0.359211
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 42.0000 1.50481
\(780\) 0 0
\(781\) 60.0000 2.14697
\(782\) 0 0
\(783\) −1.00000 −0.0357371
\(784\) −28.0000 −1.00000
\(785\) 0 0
\(786\) 0 0
\(787\) −38.0000 −1.35455 −0.677277 0.735728i \(-0.736840\pi\)
−0.677277 + 0.735728i \(0.736840\pi\)
\(788\) −26.0000 −0.926212
\(789\) 28.0000 0.996826
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 42.0000 1.49146
\(794\) 0 0
\(795\) 0 0
\(796\) −36.0000 −1.27599
\(797\) −30.0000 −1.06265 −0.531327 0.847167i \(-0.678307\pi\)
−0.531327 + 0.847167i \(0.678307\pi\)
\(798\) 0 0
\(799\) 30.0000 1.06132
\(800\) 0 0
\(801\) 7.00000 0.247333
\(802\) 0 0
\(803\) 48.0000 1.69388
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 24.0000 0.844840
\(808\) 0 0
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 0 0
\(811\) 12.0000 0.421377 0.210688 0.977553i \(-0.432429\pi\)
0.210688 + 0.977553i \(0.432429\pi\)
\(812\) 0 0
\(813\) −20.0000 −0.701431
\(814\) 0 0
\(815\) 0 0
\(816\) 12.0000 0.420084
\(817\) 77.0000 2.69389
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 43.0000 1.50071 0.750355 0.661035i \(-0.229882\pi\)
0.750355 + 0.661035i \(0.229882\pi\)
\(822\) 0 0
\(823\) −24.0000 −0.836587 −0.418294 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) 0 0
\(825\) 20.0000 0.696311
\(826\) 0 0
\(827\) −43.0000 −1.49526 −0.747628 0.664117i \(-0.768807\pi\)
−0.747628 + 0.664117i \(0.768807\pi\)
\(828\) −2.00000 −0.0695048
\(829\) −52.0000 −1.80603 −0.903017 0.429604i \(-0.858653\pi\)
−0.903017 + 0.429604i \(0.858653\pi\)
\(830\) 0 0
\(831\) 19.0000 0.659103
\(832\) −24.0000 −0.832050
\(833\) −21.0000 −0.727607
\(834\) 0 0
\(835\) 0 0
\(836\) −56.0000 −1.93680
\(837\) 2.00000 0.0691301
\(838\) 0 0
\(839\) 28.0000 0.966667 0.483334 0.875436i \(-0.339426\pi\)
0.483334 + 0.875436i \(0.339426\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) 24.0000 0.826604
\(844\) 36.0000 1.23917
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −24.0000 −0.824163
\(849\) −10.0000 −0.343199
\(850\) 0 0
\(851\) 1.00000 0.0342796
\(852\) 30.0000 1.02778
\(853\) 14.0000 0.479351 0.239675 0.970853i \(-0.422959\pi\)
0.239675 + 0.970853i \(0.422959\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 18.0000 0.614868 0.307434 0.951569i \(-0.400530\pi\)
0.307434 + 0.951569i \(0.400530\pi\)
\(858\) 0 0
\(859\) −46.0000 −1.56950 −0.784750 0.619813i \(-0.787209\pi\)
−0.784750 + 0.619813i \(0.787209\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 4.00000 0.136162 0.0680808 0.997680i \(-0.478312\pi\)
0.0680808 + 0.997680i \(0.478312\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −8.00000 −0.271694
\(868\) 0 0
\(869\) −4.00000 −0.135691
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −14.0000 −0.473828
\(874\) 0 0
\(875\) 0 0
\(876\) 24.0000 0.810885
\(877\) 23.0000 0.776655 0.388327 0.921521i \(-0.373053\pi\)
0.388327 + 0.921521i \(0.373053\pi\)
\(878\) 0 0
\(879\) 9.00000 0.303562
\(880\) 0 0
\(881\) 11.0000 0.370599 0.185300 0.982682i \(-0.440674\pi\)
0.185300 + 0.982682i \(0.440674\pi\)
\(882\) 0 0
\(883\) −13.0000 −0.437485 −0.218742 0.975783i \(-0.570195\pi\)
−0.218742 + 0.975783i \(0.570195\pi\)
\(884\) −18.0000 −0.605406
\(885\) 0 0
\(886\) 0 0
\(887\) −48.0000 −1.61168 −0.805841 0.592132i \(-0.798286\pi\)
−0.805841 + 0.592132i \(0.798286\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −4.00000 −0.134005
\(892\) 14.0000 0.468755
\(893\) −70.0000 −2.34246
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 3.00000 0.100167
\(898\) 0 0
\(899\) −2.00000 −0.0667037
\(900\) 10.0000 0.333333
\(901\) −18.0000 −0.599667
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −5.00000 −0.166022 −0.0830111 0.996549i \(-0.526454\pi\)
−0.0830111 + 0.996549i \(0.526454\pi\)
\(908\) −28.0000 −0.929213
\(909\) −8.00000 −0.265343
\(910\) 0 0
\(911\) −31.0000 −1.02708 −0.513538 0.858067i \(-0.671665\pi\)
−0.513538 + 0.858067i \(0.671665\pi\)
\(912\) −28.0000 −0.927173
\(913\) 8.00000 0.264761
\(914\) 0 0
\(915\) 0 0
\(916\) −46.0000 −1.51988
\(917\) 0 0
\(918\) 0 0
\(919\) 58.0000 1.91324 0.956622 0.291333i \(-0.0940987\pi\)
0.956622 + 0.291333i \(0.0940987\pi\)
\(920\) 0 0
\(921\) 26.0000 0.856729
\(922\) 0 0
\(923\) −45.0000 −1.48119
\(924\) 0 0
\(925\) −5.00000 −0.164399
\(926\) 0 0
\(927\) −8.00000 −0.262754
\(928\) 0 0
\(929\) −27.0000 −0.885841 −0.442921 0.896561i \(-0.646058\pi\)
−0.442921 + 0.896561i \(0.646058\pi\)
\(930\) 0 0
\(931\) 49.0000 1.60591
\(932\) 42.0000 1.37576
\(933\) 8.00000 0.261908
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) 0 0
\(939\) −14.0000 −0.456873
\(940\) 0 0
\(941\) −12.0000 −0.391189 −0.195594 0.980685i \(-0.562664\pi\)
−0.195594 + 0.980685i \(0.562664\pi\)
\(942\) 0 0
\(943\) −6.00000 −0.195387
\(944\) −44.0000 −1.43208
\(945\) 0 0
\(946\) 0 0
\(947\) 48.0000 1.55979 0.779895 0.625910i \(-0.215272\pi\)
0.779895 + 0.625910i \(0.215272\pi\)
\(948\) −2.00000 −0.0649570
\(949\) −36.0000 −1.16861
\(950\) 0 0
\(951\) −14.0000 −0.453981
\(952\) 0 0
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −30.0000 −0.970269
\(957\) 4.00000 0.129302
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) −2.00000 −0.0644491
\(964\) 36.0000 1.15948
\(965\) 0 0
\(966\) 0 0
\(967\) −42.0000 −1.35063 −0.675314 0.737530i \(-0.735992\pi\)
−0.675314 + 0.737530i \(0.735992\pi\)
\(968\) 0 0
\(969\) −21.0000 −0.674617
\(970\) 0 0
\(971\) −40.0000 −1.28366 −0.641831 0.766846i \(-0.721825\pi\)
−0.641831 + 0.766846i \(0.721825\pi\)
\(972\) −2.00000 −0.0641500
\(973\) 0 0
\(974\) 0 0
\(975\) −15.0000 −0.480384
\(976\) 56.0000 1.79252
\(977\) −52.0000 −1.66363 −0.831814 0.555055i \(-0.812697\pi\)
−0.831814 + 0.555055i \(0.812697\pi\)
\(978\) 0 0
\(979\) −28.0000 −0.894884
\(980\) 0 0
\(981\) 10.0000 0.319275
\(982\) 0 0
\(983\) −27.0000 −0.861166 −0.430583 0.902551i \(-0.641692\pi\)
−0.430583 + 0.902551i \(0.641692\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 42.0000 1.33620
\(989\) −11.0000 −0.349780
\(990\) 0 0
\(991\) −32.0000 −1.01651 −0.508257 0.861206i \(-0.669710\pi\)
−0.508257 + 0.861206i \(0.669710\pi\)
\(992\) 0 0
\(993\) −18.0000 −0.571213
\(994\) 0 0
\(995\) 0 0
\(996\) 4.00000 0.126745
\(997\) 4.00000 0.126681 0.0633406 0.997992i \(-0.479825\pi\)
0.0633406 + 0.997992i \(0.479825\pi\)
\(998\) 0 0
\(999\) 1.00000 0.0316386
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 2001.2.a.c.1.1 1
3.2 odd 2 6003.2.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2001.2.a.c.1.1 1 1.1 even 1 trivial
6003.2.a.b.1.1 1 3.2 odd 2