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Properties

Label 4028.2.a.a.1.1
Level $4028$
Weight $2$
Character 4028.1
Self dual yes
Analytic conductor $32.164$
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] = [4028,2,Mod(1,4028)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4028, 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("4028.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4028.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: \(32.1637419342\)
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 \(\chi\) \(=\) 4028.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{3} +4.00000 q^{7} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{3} +4.00000 q^{7} -2.00000 q^{9} +1.00000 q^{11} -6.00000 q^{13} +3.00000 q^{17} +1.00000 q^{19} +4.00000 q^{21} -6.00000 q^{23} -5.00000 q^{25} -5.00000 q^{27} +4.00000 q^{29} +9.00000 q^{31} +1.00000 q^{33} +10.0000 q^{37} -6.00000 q^{39} +10.0000 q^{41} +5.00000 q^{43} +8.00000 q^{47} +9.00000 q^{49} +3.00000 q^{51} +1.00000 q^{53} +1.00000 q^{57} +12.0000 q^{59} +12.0000 q^{61} -8.00000 q^{63} -1.00000 q^{67} -6.00000 q^{69} -15.0000 q^{71} +6.00000 q^{73} -5.00000 q^{75} +4.00000 q^{77} -4.00000 q^{79} +1.00000 q^{81} -6.00000 q^{83} +4.00000 q^{87} +8.00000 q^{89} -24.0000 q^{91} +9.00000 q^{93} +10.0000 q^{97} -2.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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
\(3\) 1.00000 0.577350 0.288675 − 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 0 0
\(5\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) 4.00000 1.51186 0.755929 − 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 1.00000 0.301511 0.150756 − 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) 0 0
\(13\) −6.00000 −1.66410 −0.832050 − 0.554700i \(-0.812833\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3.00000 0.727607 0.363803 − 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 4.00000 0.872872
\(22\) 0 0
\(23\) −6.00000 −1.25109 −0.625543 − 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 0 0
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 − 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 9.00000 1.61645 0.808224 − 0.588875i \(-0.200429\pi\)
0.808224 + 0.588875i \(0.200429\pi\)
\(32\) 0 0
\(33\) 1.00000 0.174078
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.0000 1.64399 0.821995 − 0.569495i \(-0.192861\pi\)
0.821995 + 0.569495i \(0.192861\pi\)
\(38\) 0 0
\(39\) −6.00000 −0.960769
\(40\) 0 0
\(41\) 10.0000 1.56174 0.780869 − 0.624695i \(-0.214777\pi\)
0.780869 + 0.624695i \(0.214777\pi\)
\(42\) 0 0
\(43\) 5.00000 0.762493 0.381246 − 0.924473i \(-0.375495\pi\)
0.381246 + 0.924473i \(0.375495\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.00000 1.16692 0.583460 − 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 3.00000 0.420084
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.00000 0.132453
\(58\) 0 0
\(59\) 12.0000 1.56227 0.781133 − 0.624364i \(-0.214642\pi\)
0.781133 + 0.624364i \(0.214642\pi\)
\(60\) 0 0
\(61\) 12.0000 1.53644 0.768221 − 0.640184i \(-0.221142\pi\)
0.768221 + 0.640184i \(0.221142\pi\)
\(62\) 0 0
\(63\) −8.00000 −1.00791
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −1.00000 −0.122169 −0.0610847 − 0.998133i \(-0.519456\pi\)
−0.0610847 + 0.998133i \(0.519456\pi\)
\(68\) 0 0
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) −15.0000 −1.78017 −0.890086 − 0.455792i \(-0.849356\pi\)
−0.890086 + 0.455792i \(0.849356\pi\)
\(72\) 0 0
\(73\) 6.00000 0.702247 0.351123 − 0.936329i \(-0.385800\pi\)
0.351123 + 0.936329i \(0.385800\pi\)
\(74\) 0 0
\(75\) −5.00000 −0.577350
\(76\) 0 0
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) −4.00000 −0.450035 −0.225018 − 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 − 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 4.00000 0.428845
\(88\) 0 0
\(89\) 8.00000 0.847998 0.423999 − 0.905663i \(-0.360626\pi\)
0.423999 + 0.905663i \(0.360626\pi\)
\(90\) 0 0
\(91\) −24.0000 −2.51588
\(92\) 0 0
\(93\) 9.00000 0.933257
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 10.0000 1.01535 0.507673 − 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 0 0
\(99\) −2.00000 −0.201008
\(100\) 0 0
\(101\) −4.00000 −0.398015 −0.199007 − 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 0 0
\(103\) 19.0000 1.87213 0.936063 − 0.351833i \(-0.114441\pi\)
0.936063 + 0.351833i \(0.114441\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.00000 0.386695 0.193347 − 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 − 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) −16.0000 −1.50515 −0.752577 − 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 12.0000 1.10940
\(118\) 0 0
\(119\) 12.0000 1.10004
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 0 0
\(123\) 10.0000 0.901670
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −11.0000 −0.976092 −0.488046 − 0.872818i \(-0.662290\pi\)
−0.488046 + 0.872818i \(0.662290\pi\)
\(128\) 0 0
\(129\) 5.00000 0.440225
\(130\) 0 0
\(131\) 7.00000 0.611593 0.305796 − 0.952097i \(-0.401077\pi\)
0.305796 + 0.952097i \(0.401077\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.0000 0.854358 0.427179 − 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) −2.00000 −0.169638 −0.0848189 − 0.996396i \(-0.527031\pi\)
−0.0848189 + 0.996396i \(0.527031\pi\)
\(140\) 0 0
\(141\) 8.00000 0.673722
\(142\) 0 0
\(143\) −6.00000 −0.501745
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 9.00000 0.742307
\(148\) 0 0
\(149\) −6.00000 −0.491539 −0.245770 − 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) −16.0000 −1.30206 −0.651031 − 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 18.0000 1.43656 0.718278 − 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 0 0
\(159\) 1.00000 0.0793052
\(160\) 0 0
\(161\) −24.0000 −1.89146
\(162\) 0 0
\(163\) −9.00000 −0.704934 −0.352467 − 0.935824i \(-0.614657\pi\)
−0.352467 + 0.935824i \(0.614657\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.00000 0.696441 0.348220 − 0.937413i \(-0.386786\pi\)
0.348220 + 0.937413i \(0.386786\pi\)
\(168\) 0 0
\(169\) 23.0000 1.76923
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) 0 0
\(173\) 9.00000 0.684257 0.342129 − 0.939653i \(-0.388852\pi\)
0.342129 + 0.939653i \(0.388852\pi\)
\(174\) 0 0
\(175\) −20.0000 −1.51186
\(176\) 0 0
\(177\) 12.0000 0.901975
\(178\) 0 0
\(179\) −15.0000 −1.12115 −0.560576 − 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 − 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 12.0000 0.887066
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3.00000 0.219382
\(188\) 0 0
\(189\) −20.0000 −1.45479
\(190\) 0 0
\(191\) 4.00000 0.289430 0.144715 − 0.989473i \(-0.453773\pi\)
0.144715 + 0.989473i \(0.453773\pi\)
\(192\) 0 0
\(193\) −19.0000 −1.36765 −0.683825 − 0.729646i \(-0.739685\pi\)
−0.683825 + 0.729646i \(0.739685\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 22.0000 1.56744 0.783718 − 0.621117i \(-0.213321\pi\)
0.783718 + 0.621117i \(0.213321\pi\)
\(198\) 0 0
\(199\) −11.0000 −0.779769 −0.389885 − 0.920864i \(-0.627485\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0 0
\(201\) −1.00000 −0.0705346
\(202\) 0 0
\(203\) 16.0000 1.12298
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 12.0000 0.834058
\(208\) 0 0
\(209\) 1.00000 0.0691714
\(210\) 0 0
\(211\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) −15.0000 −1.02778
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 36.0000 2.44384
\(218\) 0 0
\(219\) 6.00000 0.405442
\(220\) 0 0
\(221\) −18.0000 −1.21081
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 − 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 10.0000 0.666667
\(226\) 0 0
\(227\) −18.0000 −1.19470 −0.597351 − 0.801980i \(-0.703780\pi\)
−0.597351 + 0.801980i \(0.703780\pi\)
\(228\) 0 0
\(229\) 17.0000 1.12339 0.561696 − 0.827344i \(-0.310149\pi\)
0.561696 + 0.827344i \(0.310149\pi\)
\(230\) 0 0
\(231\) 4.00000 0.263181
\(232\) 0 0
\(233\) −24.0000 −1.57229 −0.786146 − 0.618041i \(-0.787927\pi\)
−0.786146 + 0.618041i \(0.787927\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −4.00000 −0.259828
\(238\) 0 0
\(239\) −18.0000 −1.16432 −0.582162 − 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) 0 0
\(241\) 14.0000 0.901819 0.450910 − 0.892570i \(-0.351100\pi\)
0.450910 + 0.892570i \(0.351100\pi\)
\(242\) 0 0
\(243\) 16.0000 1.02640
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.00000 −0.381771
\(248\) 0 0
\(249\) −6.00000 −0.380235
\(250\) 0 0
\(251\) −6.00000 −0.378717 −0.189358 − 0.981908i \(-0.560641\pi\)
−0.189358 + 0.981908i \(0.560641\pi\)
\(252\) 0 0
\(253\) −6.00000 −0.377217
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −3.00000 −0.187135 −0.0935674 − 0.995613i \(-0.529827\pi\)
−0.0935674 + 0.995613i \(0.529827\pi\)
\(258\) 0 0
\(259\) 40.0000 2.48548
\(260\) 0 0
\(261\) −8.00000 −0.495188
\(262\) 0 0
\(263\) 30.0000 1.84988 0.924940 − 0.380114i \(-0.124115\pi\)
0.924940 + 0.380114i \(0.124115\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 8.00000 0.489592
\(268\) 0 0
\(269\) −12.0000 −0.731653 −0.365826 − 0.930683i \(-0.619214\pi\)
−0.365826 + 0.930683i \(0.619214\pi\)
\(270\) 0 0
\(271\) −3.00000 −0.182237 −0.0911185 − 0.995840i \(-0.529044\pi\)
−0.0911185 + 0.995840i \(0.529044\pi\)
\(272\) 0 0
\(273\) −24.0000 −1.45255
\(274\) 0 0
\(275\) −5.00000 −0.301511
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 − 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) 0 0
\(279\) −18.0000 −1.07763
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 − 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 0 0
\(283\) −6.00000 −0.356663 −0.178331 − 0.983970i \(-0.557070\pi\)
−0.178331 + 0.983970i \(0.557070\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 40.0000 2.36113
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 10.0000 0.586210
\(292\) 0 0
\(293\) −16.0000 −0.934730 −0.467365 − 0.884064i \(-0.654797\pi\)
−0.467365 + 0.884064i \(0.654797\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.00000 −0.290129
\(298\) 0 0
\(299\) 36.0000 2.08193
\(300\) 0 0
\(301\) 20.0000 1.15278
\(302\) 0 0
\(303\) −4.00000 −0.229794
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 32.0000 1.82634 0.913168 − 0.407583i \(-0.133628\pi\)
0.913168 + 0.407583i \(0.133628\pi\)
\(308\) 0 0
\(309\) 19.0000 1.08087
\(310\) 0 0
\(311\) 9.00000 0.510343 0.255172 − 0.966896i \(-0.417868\pi\)
0.255172 + 0.966896i \(0.417868\pi\)
\(312\) 0 0
\(313\) −26.0000 −1.46961 −0.734803 − 0.678280i \(-0.762726\pi\)
−0.734803 + 0.678280i \(0.762726\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −30.0000 −1.68497 −0.842484 − 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) 0 0
\(319\) 4.00000 0.223957
\(320\) 0 0
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) 3.00000 0.166924
\(324\) 0 0
\(325\) 30.0000 1.66410
\(326\) 0 0
\(327\) −10.0000 −0.553001
\(328\) 0 0
\(329\) 32.0000 1.76422
\(330\) 0 0
\(331\) 34.0000 1.86881 0.934405 − 0.356214i \(-0.115932\pi\)
0.934405 + 0.356214i \(0.115932\pi\)
\(332\) 0 0
\(333\) −20.0000 −1.09599
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −13.0000 −0.708155 −0.354078 − 0.935216i \(-0.615205\pi\)
−0.354078 + 0.935216i \(0.615205\pi\)
\(338\) 0 0
\(339\) −16.0000 −0.869001
\(340\) 0 0
\(341\) 9.00000 0.487377
\(342\) 0 0
\(343\) 8.00000 0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 21.0000 1.12734 0.563670 − 0.826000i \(-0.309389\pi\)
0.563670 + 0.826000i \(0.309389\pi\)
\(348\) 0 0
\(349\) −12.0000 −0.642345 −0.321173 − 0.947021i \(-0.604077\pi\)
−0.321173 + 0.947021i \(0.604077\pi\)
\(350\) 0 0
\(351\) 30.0000 1.60128
\(352\) 0 0
\(353\) 8.00000 0.425797 0.212899 − 0.977074i \(-0.431710\pi\)
0.212899 + 0.977074i \(0.431710\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 12.0000 0.635107
\(358\) 0 0
\(359\) 24.0000 1.26667 0.633336 − 0.773877i \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −10.0000 −0.524864
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −5.00000 −0.260998 −0.130499 − 0.991448i \(-0.541658\pi\)
−0.130499 + 0.991448i \(0.541658\pi\)
\(368\) 0 0
\(369\) −20.0000 −1.04116
\(370\) 0 0
\(371\) 4.00000 0.207670
\(372\) 0 0
\(373\) 29.0000 1.50156 0.750782 − 0.660551i \(-0.229677\pi\)
0.750782 + 0.660551i \(0.229677\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −24.0000 −1.23606
\(378\) 0 0
\(379\) 33.0000 1.69510 0.847548 − 0.530719i \(-0.178078\pi\)
0.847548 + 0.530719i \(0.178078\pi\)
\(380\) 0 0
\(381\) −11.0000 −0.563547
\(382\) 0 0
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −10.0000 −0.508329
\(388\) 0 0
\(389\) −24.0000 −1.21685 −0.608424 − 0.793612i \(-0.708198\pi\)
−0.608424 + 0.793612i \(0.708198\pi\)
\(390\) 0 0
\(391\) −18.0000 −0.910299
\(392\) 0 0
\(393\) 7.00000 0.353103
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 8.00000 0.401508 0.200754 − 0.979642i \(-0.435661\pi\)
0.200754 + 0.979642i \(0.435661\pi\)
\(398\) 0 0
\(399\) 4.00000 0.200250
\(400\) 0 0
\(401\) −37.0000 −1.84769 −0.923846 − 0.382765i \(-0.874972\pi\)
−0.923846 + 0.382765i \(0.874972\pi\)
\(402\) 0 0
\(403\) −54.0000 −2.68993
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 10.0000 0.495682
\(408\) 0 0
\(409\) 24.0000 1.18672 0.593362 − 0.804936i \(-0.297800\pi\)
0.593362 + 0.804936i \(0.297800\pi\)
\(410\) 0 0
\(411\) 10.0000 0.493264
\(412\) 0 0
\(413\) 48.0000 2.36193
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −2.00000 −0.0979404
\(418\) 0 0
\(419\) −32.0000 −1.56330 −0.781651 − 0.623716i \(-0.785622\pi\)
−0.781651 + 0.623716i \(0.785622\pi\)
\(420\) 0 0
\(421\) 27.0000 1.31590 0.657950 − 0.753062i \(-0.271424\pi\)
0.657950 + 0.753062i \(0.271424\pi\)
\(422\) 0 0
\(423\) −16.0000 −0.777947
\(424\) 0 0
\(425\) −15.0000 −0.727607
\(426\) 0 0
\(427\) 48.0000 2.32288
\(428\) 0 0
\(429\) −6.00000 −0.289683
\(430\) 0 0
\(431\) −24.0000 −1.15604 −0.578020 − 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 0 0
\(433\) 30.0000 1.44171 0.720854 − 0.693087i \(-0.243750\pi\)
0.720854 + 0.693087i \(0.243750\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −6.00000 −0.287019
\(438\) 0 0
\(439\) −10.0000 −0.477274 −0.238637 − 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 0 0
\(441\) −18.0000 −0.857143
\(442\) 0 0
\(443\) −34.0000 −1.61539 −0.807694 − 0.589601i \(-0.799285\pi\)
−0.807694 + 0.589601i \(0.799285\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −6.00000 −0.283790
\(448\) 0 0
\(449\) −12.0000 −0.566315 −0.283158 − 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 10.0000 0.470882
\(452\) 0 0
\(453\) −16.0000 −0.751746
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −18.0000 −0.842004 −0.421002 − 0.907060i \(-0.638322\pi\)
−0.421002 + 0.907060i \(0.638322\pi\)
\(458\) 0 0
\(459\) −15.0000 −0.700140
\(460\) 0 0
\(461\) −25.0000 −1.16437 −0.582183 − 0.813058i \(-0.697801\pi\)
−0.582183 + 0.813058i \(0.697801\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 − 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −15.0000 −0.694117 −0.347059 − 0.937843i \(-0.612820\pi\)
−0.347059 + 0.937843i \(0.612820\pi\)
\(468\) 0 0
\(469\) −4.00000 −0.184703
\(470\) 0 0
\(471\) 18.0000 0.829396
\(472\) 0 0
\(473\) 5.00000 0.229900
\(474\) 0 0
\(475\) −5.00000 −0.229416
\(476\) 0 0
\(477\) −2.00000 −0.0915737
\(478\) 0 0
\(479\) −18.0000 −0.822441 −0.411220 − 0.911536i \(-0.634897\pi\)
−0.411220 + 0.911536i \(0.634897\pi\)
\(480\) 0 0
\(481\) −60.0000 −2.73576
\(482\) 0 0
\(483\) −24.0000 −1.09204
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −38.0000 −1.72194 −0.860972 − 0.508652i \(-0.830144\pi\)
−0.860972 + 0.508652i \(0.830144\pi\)
\(488\) 0 0
\(489\) −9.00000 −0.406994
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 − 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 0 0
\(493\) 12.0000 0.540453
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −60.0000 −2.69137
\(498\) 0 0
\(499\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) 9.00000 0.402090
\(502\) 0 0
\(503\) 26.0000 1.15928 0.579641 − 0.814872i \(-0.303193\pi\)
0.579641 + 0.814872i \(0.303193\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 23.0000 1.02147
\(508\) 0 0
\(509\) 6.00000 0.265945 0.132973 − 0.991120i \(-0.457548\pi\)
0.132973 + 0.991120i \(0.457548\pi\)
\(510\) 0 0
\(511\) 24.0000 1.06170
\(512\) 0 0
\(513\) −5.00000 −0.220755
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 8.00000 0.351840
\(518\) 0 0
\(519\) 9.00000 0.395056
\(520\) 0 0
\(521\) 12.0000 0.525730 0.262865 − 0.964833i \(-0.415333\pi\)
0.262865 + 0.964833i \(0.415333\pi\)
\(522\) 0 0
\(523\) 24.0000 1.04945 0.524723 − 0.851273i \(-0.324169\pi\)
0.524723 + 0.851273i \(0.324169\pi\)
\(524\) 0 0
\(525\) −20.0000 −0.872872
\(526\) 0 0
\(527\) 27.0000 1.17614
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) −24.0000 −1.04151
\(532\) 0 0
\(533\) −60.0000 −2.59889
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −15.0000 −0.647298
\(538\) 0 0
\(539\) 9.00000 0.387657
\(540\) 0 0
\(541\) −17.0000 −0.730887 −0.365444 − 0.930834i \(-0.619083\pi\)
−0.365444 + 0.930834i \(0.619083\pi\)
\(542\) 0 0
\(543\) −7.00000 −0.300399
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 22.0000 0.940652 0.470326 − 0.882493i \(-0.344136\pi\)
0.470326 + 0.882493i \(0.344136\pi\)
\(548\) 0 0
\(549\) −24.0000 −1.02430
\(550\) 0 0
\(551\) 4.00000 0.170406
\(552\) 0 0
\(553\) −16.0000 −0.680389
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 36.0000 1.52537 0.762684 − 0.646771i \(-0.223881\pi\)
0.762684 + 0.646771i \(0.223881\pi\)
\(558\) 0 0
\(559\) −30.0000 −1.26886
\(560\) 0 0
\(561\) 3.00000 0.126660
\(562\) 0 0
\(563\) −13.0000 −0.547885 −0.273942 − 0.961746i \(-0.588328\pi\)
−0.273942 + 0.961746i \(0.588328\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 4.00000 0.167984
\(568\) 0 0
\(569\) 1.00000 0.0419222 0.0209611 − 0.999780i \(-0.493327\pi\)
0.0209611 + 0.999780i \(0.493327\pi\)
\(570\) 0 0
\(571\) 16.0000 0.669579 0.334790 − 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) 0 0
\(573\) 4.00000 0.167102
\(574\) 0 0
\(575\) 30.0000 1.25109
\(576\) 0 0
\(577\) −35.0000 −1.45707 −0.728535 − 0.685009i \(-0.759798\pi\)
−0.728535 + 0.685009i \(0.759798\pi\)
\(578\) 0 0
\(579\) −19.0000 −0.789613
\(580\) 0 0
\(581\) −24.0000 −0.995688
\(582\) 0 0
\(583\) 1.00000 0.0414158
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −28.0000 −1.15568 −0.577842 − 0.816149i \(-0.696105\pi\)
−0.577842 + 0.816149i \(0.696105\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) 0 0
\(591\) 22.0000 0.904959
\(592\) 0 0
\(593\) −23.0000 −0.944497 −0.472248 − 0.881466i \(-0.656557\pi\)
−0.472248 + 0.881466i \(0.656557\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −11.0000 −0.450200
\(598\) 0 0
\(599\) 10.0000 0.408589 0.204294 − 0.978909i \(-0.434510\pi\)
0.204294 + 0.978909i \(0.434510\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 − 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 0 0
\(603\) 2.00000 0.0814463
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 12.0000 0.487065 0.243532 − 0.969893i \(-0.421694\pi\)
0.243532 + 0.969893i \(0.421694\pi\)
\(608\) 0 0
\(609\) 16.0000 0.648353
\(610\) 0 0
\(611\) −48.0000 −1.94187
\(612\) 0 0
\(613\) 16.0000 0.646234 0.323117 − 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.00000 −0.161034 −0.0805170 − 0.996753i \(-0.525657\pi\)
−0.0805170 + 0.996753i \(0.525657\pi\)
\(618\) 0 0
\(619\) −7.00000 −0.281354 −0.140677 − 0.990056i \(-0.544928\pi\)
−0.140677 + 0.990056i \(0.544928\pi\)
\(620\) 0 0
\(621\) 30.0000 1.20386
\(622\) 0 0
\(623\) 32.0000 1.28205
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) 0 0
\(627\) 1.00000 0.0399362
\(628\) 0 0
\(629\) 30.0000 1.19618
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 − 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −54.0000 −2.13956
\(638\) 0 0
\(639\) 30.0000 1.18678
\(640\) 0 0
\(641\) −26.0000 −1.02694 −0.513469 − 0.858108i \(-0.671640\pi\)
−0.513469 + 0.858108i \(0.671640\pi\)
\(642\) 0 0
\(643\) −13.0000 −0.512670 −0.256335 − 0.966588i \(-0.582515\pi\)
−0.256335 + 0.966588i \(0.582515\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −27.0000 −1.06148 −0.530740 − 0.847535i \(-0.678086\pi\)
−0.530740 + 0.847535i \(0.678086\pi\)
\(648\) 0 0
\(649\) 12.0000 0.471041
\(650\) 0 0
\(651\) 36.0000 1.41095
\(652\) 0 0
\(653\) −9.00000 −0.352197 −0.176099 − 0.984373i \(-0.556348\pi\)
−0.176099 + 0.984373i \(0.556348\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −12.0000 −0.468165
\(658\) 0 0
\(659\) 12.0000 0.467454 0.233727 − 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) 48.0000 1.86698 0.933492 − 0.358599i \(-0.116745\pi\)
0.933492 + 0.358599i \(0.116745\pi\)
\(662\) 0 0
\(663\) −18.0000 −0.699062
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −24.0000 −0.929284
\(668\) 0 0
\(669\) −8.00000 −0.309298
\(670\) 0 0
\(671\) 12.0000 0.463255
\(672\) 0 0
\(673\) 32.0000 1.23351 0.616755 − 0.787155i \(-0.288447\pi\)
0.616755 + 0.787155i \(0.288447\pi\)
\(674\) 0 0
\(675\) 25.0000 0.962250
\(676\) 0 0
\(677\) 37.0000 1.42203 0.711013 − 0.703179i \(-0.248237\pi\)
0.711013 + 0.703179i \(0.248237\pi\)
\(678\) 0 0
\(679\) 40.0000 1.53506
\(680\) 0 0
\(681\) −18.0000 −0.689761
\(682\) 0 0
\(683\) −6.00000 −0.229584 −0.114792 − 0.993390i \(-0.536620\pi\)
−0.114792 + 0.993390i \(0.536620\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 17.0000 0.648590
\(688\) 0 0
\(689\) −6.00000 −0.228582
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 − 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 0 0
\(693\) −8.00000 −0.303895
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 30.0000 1.13633
\(698\) 0 0
\(699\) −24.0000 −0.907763
\(700\) 0 0
\(701\) 6.00000 0.226617 0.113308 − 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) 0 0
\(703\) 10.0000 0.377157
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −16.0000 −0.601742
\(708\) 0 0
\(709\) −26.0000 −0.976450 −0.488225 − 0.872718i \(-0.662356\pi\)
−0.488225 + 0.872718i \(0.662356\pi\)
\(710\) 0 0
\(711\) 8.00000 0.300023
\(712\) 0 0
\(713\) −54.0000 −2.02232
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −18.0000 −0.672222
\(718\) 0 0
\(719\) −30.0000 −1.11881 −0.559406 − 0.828894i \(-0.688971\pi\)
−0.559406 + 0.828894i \(0.688971\pi\)
\(720\) 0 0
\(721\) 76.0000 2.83039
\(722\) 0 0
\(723\) 14.0000 0.520666
\(724\) 0 0
\(725\) −20.0000 −0.742781
\(726\) 0 0
\(727\) 23.0000 0.853023 0.426511 − 0.904482i \(-0.359742\pi\)
0.426511 + 0.904482i \(0.359742\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 15.0000 0.554795
\(732\) 0 0
\(733\) 1.00000 0.0369358 0.0184679 − 0.999829i \(-0.494121\pi\)
0.0184679 + 0.999829i \(0.494121\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −1.00000 −0.0368355
\(738\) 0 0
\(739\) −28.0000 −1.03000 −0.514998 − 0.857191i \(-0.672207\pi\)
−0.514998 + 0.857191i \(0.672207\pi\)
\(740\) 0 0
\(741\) −6.00000 −0.220416
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 − 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 12.0000 0.439057
\(748\) 0 0
\(749\) 16.0000 0.584627
\(750\) 0 0
\(751\) 4.00000 0.145962 0.0729810 − 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 0 0
\(753\) −6.00000 −0.218652
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −14.0000 −0.508839 −0.254419 − 0.967094i \(-0.581884\pi\)
−0.254419 + 0.967094i \(0.581884\pi\)
\(758\) 0 0
\(759\) −6.00000 −0.217786
\(760\) 0 0
\(761\) −4.00000 −0.145000 −0.0724999 − 0.997368i \(-0.523098\pi\)
−0.0724999 + 0.997368i \(0.523098\pi\)
\(762\) 0 0
\(763\) −40.0000 −1.44810
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −72.0000 −2.59977
\(768\) 0 0
\(769\) −2.00000 −0.0721218 −0.0360609 − 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) 0 0
\(771\) −3.00000 −0.108042
\(772\) 0 0
\(773\) −21.0000 −0.755318 −0.377659 − 0.925945i \(-0.623271\pi\)
−0.377659 + 0.925945i \(0.623271\pi\)
\(774\) 0 0
\(775\) −45.0000 −1.61645
\(776\) 0 0
\(777\) 40.0000 1.43499
\(778\) 0 0
\(779\) 10.0000 0.358287
\(780\) 0 0
\(781\) −15.0000 −0.536742
\(782\) 0 0
\(783\) −20.0000 −0.714742
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −4.00000 −0.142585 −0.0712923 − 0.997455i \(-0.522712\pi\)
−0.0712923 + 0.997455i \(0.522712\pi\)
\(788\) 0 0
\(789\) 30.0000 1.06803
\(790\) 0 0
\(791\) −64.0000 −2.27558
\(792\) 0 0
\(793\) −72.0000 −2.55679
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 11.0000 0.389640 0.194820 − 0.980839i \(-0.437588\pi\)
0.194820 + 0.980839i \(0.437588\pi\)
\(798\) 0 0
\(799\) 24.0000 0.849059
\(800\) 0 0
\(801\) −16.0000 −0.565332
\(802\) 0 0
\(803\) 6.00000 0.211735
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −12.0000 −0.422420
\(808\) 0 0
\(809\) 14.0000 0.492214 0.246107 − 0.969243i \(-0.420849\pi\)
0.246107 + 0.969243i \(0.420849\pi\)
\(810\) 0 0
\(811\) 18.0000 0.632065 0.316033 − 0.948748i \(-0.397649\pi\)
0.316033 + 0.948748i \(0.397649\pi\)
\(812\) 0 0
\(813\) −3.00000 −0.105215
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 5.00000 0.174928
\(818\) 0 0
\(819\) 48.0000 1.67726
\(820\) 0 0
\(821\) −10.0000 −0.349002 −0.174501 − 0.984657i \(-0.555831\pi\)
−0.174501 + 0.984657i \(0.555831\pi\)
\(822\) 0 0
\(823\) 13.0000 0.453152 0.226576 − 0.973994i \(-0.427247\pi\)
0.226576 + 0.973994i \(0.427247\pi\)
\(824\) 0 0
\(825\) −5.00000 −0.174078
\(826\) 0 0
\(827\) −25.0000 −0.869335 −0.434668 − 0.900591i \(-0.643134\pi\)
−0.434668 + 0.900591i \(0.643134\pi\)
\(828\) 0 0
\(829\) 19.0000 0.659897 0.329949 − 0.943999i \(-0.392969\pi\)
0.329949 + 0.943999i \(0.392969\pi\)
\(830\) 0 0
\(831\) −2.00000 −0.0693792
\(832\) 0 0
\(833\) 27.0000 0.935495
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −45.0000 −1.55543
\(838\) 0 0
\(839\) −36.0000 −1.24286 −0.621429 − 0.783470i \(-0.713448\pi\)
−0.621429 + 0.783470i \(0.713448\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) 0 0
\(843\) −4.00000 −0.137767
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −40.0000 −1.37442
\(848\) 0 0
\(849\) −6.00000 −0.205919
\(850\) 0 0
\(851\) −60.0000 −2.05677
\(852\) 0 0
\(853\) −22.0000 −0.753266 −0.376633 − 0.926363i \(-0.622918\pi\)
−0.376633 + 0.926363i \(0.622918\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −46.0000 −1.57133 −0.785665 − 0.618652i \(-0.787679\pi\)
−0.785665 + 0.618652i \(0.787679\pi\)
\(858\) 0 0
\(859\) −13.0000 −0.443554 −0.221777 − 0.975097i \(-0.571186\pi\)
−0.221777 + 0.975097i \(0.571186\pi\)
\(860\) 0 0
\(861\) 40.0000 1.36320
\(862\) 0 0
\(863\) 26.0000 0.885050 0.442525 − 0.896756i \(-0.354083\pi\)
0.442525 + 0.896756i \(0.354083\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −8.00000 −0.271694
\(868\) 0 0
\(869\) −4.00000 −0.135691
\(870\) 0 0
\(871\) 6.00000 0.203302
\(872\) 0 0
\(873\) −20.0000 −0.676897
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 38.0000 1.28317 0.641584 − 0.767052i \(-0.278277\pi\)
0.641584 + 0.767052i \(0.278277\pi\)
\(878\) 0 0
\(879\) −16.0000 −0.539667
\(880\) 0 0
\(881\) −8.00000 −0.269527 −0.134763 − 0.990878i \(-0.543027\pi\)
−0.134763 + 0.990878i \(0.543027\pi\)
\(882\) 0 0
\(883\) 6.00000 0.201916 0.100958 − 0.994891i \(-0.467809\pi\)
0.100958 + 0.994891i \(0.467809\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 56.0000 1.88030 0.940148 − 0.340766i \(-0.110687\pi\)
0.940148 + 0.340766i \(0.110687\pi\)
\(888\) 0 0
\(889\) −44.0000 −1.47571
\(890\) 0 0
\(891\) 1.00000 0.0335013
\(892\) 0 0
\(893\) 8.00000 0.267710
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 36.0000 1.20201
\(898\) 0 0
\(899\) 36.0000 1.20067
\(900\) 0 0
\(901\) 3.00000 0.0999445
\(902\) 0 0
\(903\) 20.0000 0.665558
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 46.0000 1.52740 0.763702 − 0.645568i \(-0.223379\pi\)
0.763702 + 0.645568i \(0.223379\pi\)
\(908\) 0 0
\(909\) 8.00000 0.265343
\(910\) 0 0
\(911\) −2.00000 −0.0662630 −0.0331315 − 0.999451i \(-0.510548\pi\)
−0.0331315 + 0.999451i \(0.510548\pi\)
\(912\) 0 0
\(913\) −6.00000 −0.198571
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 28.0000 0.924641
\(918\) 0 0
\(919\) 20.0000 0.659739 0.329870 − 0.944027i \(-0.392995\pi\)
0.329870 + 0.944027i \(0.392995\pi\)
\(920\) 0 0
\(921\) 32.0000 1.05444
\(922\) 0 0
\(923\) 90.0000 2.96239
\(924\) 0 0
\(925\) −50.0000 −1.64399
\(926\) 0 0
\(927\) −38.0000 −1.24808
\(928\) 0 0
\(929\) −29.0000 −0.951459 −0.475730 − 0.879592i \(-0.657816\pi\)
−0.475730 + 0.879592i \(0.657816\pi\)
\(930\) 0 0
\(931\) 9.00000 0.294963
\(932\) 0 0
\(933\) 9.00000 0.294647
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 31.0000 1.01273 0.506363 − 0.862320i \(-0.330990\pi\)
0.506363 + 0.862320i \(0.330990\pi\)
\(938\) 0 0
\(939\) −26.0000 −0.848478
\(940\) 0 0
\(941\) 40.0000 1.30396 0.651981 − 0.758235i \(-0.273938\pi\)
0.651981 + 0.758235i \(0.273938\pi\)
\(942\) 0 0
\(943\) −60.0000 −1.95387
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 36.0000 1.16984 0.584921 − 0.811090i \(-0.301125\pi\)
0.584921 + 0.811090i \(0.301125\pi\)
\(948\) 0 0
\(949\) −36.0000 −1.16861
\(950\) 0 0
\(951\) −30.0000 −0.972817
\(952\) 0 0
\(953\) −44.0000 −1.42530 −0.712650 − 0.701520i \(-0.752505\pi\)
−0.712650 + 0.701520i \(0.752505\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 4.00000 0.129302
\(958\) 0 0
\(959\) 40.0000 1.29167
\(960\) 0 0
\(961\) 50.0000 1.61290
\(962\) 0 0
\(963\) −8.00000 −0.257796
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −45.0000 −1.44710 −0.723551 − 0.690271i \(-0.757491\pi\)
−0.723551 + 0.690271i \(0.757491\pi\)
\(968\) 0 0
\(969\) 3.00000 0.0963739
\(970\) 0 0
\(971\) −24.0000 −0.770197 −0.385098 − 0.922876i \(-0.625832\pi\)
−0.385098 + 0.922876i \(0.625832\pi\)
\(972\) 0 0
\(973\) −8.00000 −0.256468
\(974\) 0 0
\(975\) 30.0000 0.960769
\(976\) 0 0
\(977\) −10.0000 −0.319928 −0.159964 − 0.987123i \(-0.551138\pi\)
−0.159964 + 0.987123i \(0.551138\pi\)
\(978\) 0 0
\(979\) 8.00000 0.255681
\(980\) 0 0
\(981\) 20.0000 0.638551
\(982\) 0 0
\(983\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 32.0000 1.01857
\(988\) 0 0
\(989\) −30.0000 −0.953945
\(990\) 0 0
\(991\) −8.00000 −0.254128 −0.127064 − 0.991894i \(-0.540555\pi\)
−0.127064 + 0.991894i \(0.540555\pi\)
\(992\) 0 0
\(993\) 34.0000 1.07896
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −45.0000 −1.42516 −0.712582 − 0.701589i \(-0.752474\pi\)
−0.712582 + 0.701589i \(0.752474\pi\)
\(998\) 0 0
\(999\) −50.0000 −1.58193
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 4028.2.a.a.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4028.2.a.a.1.1 ✓ 1 1.1 even 1 trivial