Properties

Label 4032.2.i.c.1889.20
Level $4032$
Weight $2$
Character 4032.1889
Analytic conductor $32.196$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $16$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4032,2,Mod(1889,4032)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4032.1889");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4032.i (of order \(2\), degree \(1\), minimal)

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: no
Analytic conductor: \(32.1956820950\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1889.20
Character \(\chi\) \(=\) 4032.1889
Dual form 4032.2.i.c.1889.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.77767i q^{5} +(-2.39248 - 1.12962i) q^{7} +O(q^{10})\) \(q+1.77767i q^{5} +(-2.39248 - 1.12962i) q^{7} +3.85226 q^{11} -6.59329 q^{13} +4.56507 q^{17} -1.05080 q^{19} -0.0946494i q^{23} +1.83988 q^{25} -4.31746 q^{29} -4.07928i q^{31} +(2.00810 - 4.25305i) q^{35} -4.65110i q^{37} -11.5851 q^{41} +6.28779i q^{43} +6.12926 q^{47} +(4.44791 + 5.40519i) q^{49} -2.44949 q^{53} +6.84805i q^{55} -13.1781i q^{59} +4.58881 q^{61} -11.7207i q^{65} +4.83988i q^{67} -11.5713i q^{71} -2.25280i q^{73} +(-9.21644 - 4.35159i) q^{77} +14.2210 q^{79} +10.6162i q^{83} +8.11521i q^{85} -8.61301 q^{89} +(15.7743 + 7.44791i) q^{91} -1.86797i q^{95} -14.2822i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 80 q^{25} - 16 q^{49}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1793\) \(3781\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 1.77767i 0.795000i 0.917602 + 0.397500i \(0.130122\pi\)
−0.917602 + 0.397500i \(0.869878\pi\)
\(6\) 0 0
\(7\) −2.39248 1.12962i −0.904272 0.426957i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.85226 1.16150 0.580749 0.814082i \(-0.302760\pi\)
0.580749 + 0.814082i \(0.302760\pi\)
\(12\) 0 0
\(13\) −6.59329 −1.82865 −0.914324 0.404983i \(-0.867277\pi\)
−0.914324 + 0.404983i \(0.867277\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.56507 1.10719 0.553596 0.832785i \(-0.313255\pi\)
0.553596 + 0.832785i \(0.313255\pi\)
\(18\) 0 0
\(19\) −1.05080 −0.241069 −0.120535 0.992709i \(-0.538461\pi\)
−0.120535 + 0.992709i \(0.538461\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0.0946494i 0.0197358i −0.999951 0.00986789i \(-0.996859\pi\)
0.999951 0.00986789i \(-0.00314110\pi\)
\(24\) 0 0
\(25\) 1.83988 0.367976
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.31746 −0.801733 −0.400866 0.916137i \(-0.631291\pi\)
−0.400866 + 0.916137i \(0.631291\pi\)
\(30\) 0 0
\(31\) 4.07928i 0.732660i −0.930485 0.366330i \(-0.880614\pi\)
0.930485 0.366330i \(-0.119386\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00810 4.25305i 0.339430 0.718896i
\(36\) 0 0
\(37\) 4.65110i 0.764637i −0.924031 0.382318i \(-0.875126\pi\)
0.924031 0.382318i \(-0.124874\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −11.5851 −1.80929 −0.904645 0.426165i \(-0.859864\pi\)
−0.904645 + 0.426165i \(0.859864\pi\)
\(42\) 0 0
\(43\) 6.28779i 0.958879i 0.877575 + 0.479440i \(0.159160\pi\)
−0.877575 + 0.479440i \(0.840840\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.12926 0.894045 0.447022 0.894523i \(-0.352484\pi\)
0.447022 + 0.894523i \(0.352484\pi\)
\(48\) 0 0
\(49\) 4.44791 + 5.40519i 0.635416 + 0.772170i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.44949 −0.336463 −0.168232 0.985747i \(-0.553806\pi\)
−0.168232 + 0.985747i \(0.553806\pi\)
\(54\) 0 0
\(55\) 6.84805i 0.923391i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 13.1781i 1.71564i −0.513950 0.857820i \(-0.671818\pi\)
0.513950 0.857820i \(-0.328182\pi\)
\(60\) 0 0
\(61\) 4.58881 0.587537 0.293769 0.955877i \(-0.405091\pi\)
0.293769 + 0.955877i \(0.405091\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 11.7207i 1.45377i
\(66\) 0 0
\(67\) 4.83988i 0.591285i 0.955299 + 0.295643i \(0.0955337\pi\)
−0.955299 + 0.295643i \(0.904466\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.5713i 1.37326i −0.727008 0.686629i \(-0.759090\pi\)
0.727008 0.686629i \(-0.240910\pi\)
\(72\) 0 0
\(73\) 2.25280i 0.263670i −0.991272 0.131835i \(-0.957913\pi\)
0.991272 0.131835i \(-0.0420869\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −9.21644 4.35159i −1.05031 0.495910i
\(78\) 0 0
\(79\) 14.2210 1.59999 0.799995 0.600007i \(-0.204835\pi\)
0.799995 + 0.600007i \(0.204835\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 10.6162i 1.16528i 0.812731 + 0.582639i \(0.197980\pi\)
−0.812731 + 0.582639i \(0.802020\pi\)
\(84\) 0 0
\(85\) 8.11521i 0.880218i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −8.61301 −0.912977 −0.456489 0.889729i \(-0.650893\pi\)
−0.456489 + 0.889729i \(0.650893\pi\)
\(90\) 0 0
\(91\) 15.7743 + 7.44791i 1.65360 + 0.780753i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 1.86797i 0.191650i
\(96\) 0 0
\(97\) 14.2822i 1.45014i −0.688675 0.725070i \(-0.741807\pi\)
0.688675 0.725070i \(-0.258193\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 5.33302i 0.530655i −0.964158 0.265328i \(-0.914520\pi\)
0.964158 0.265328i \(-0.0854801\pi\)
\(102\) 0 0
\(103\) 14.1353i 1.39279i −0.717657 0.696397i \(-0.754785\pi\)
0.717657 0.696397i \(-0.245215\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.5730 1.50550 0.752748 0.658309i \(-0.228728\pi\)
0.752748 + 0.658309i \(0.228728\pi\)
\(108\) 0 0
\(109\) 13.0340i 1.24843i −0.781252 0.624216i \(-0.785418\pi\)
0.781252 0.624216i \(-0.214582\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 15.9633i 1.50171i −0.660470 0.750853i \(-0.729643\pi\)
0.660470 0.750853i \(-0.270357\pi\)
\(114\) 0 0
\(115\) 0.168256 0.0156899
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −10.9218 5.15680i −1.00120 0.472723i
\(120\) 0 0
\(121\) 3.83988 0.349080
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.1591i 1.08754i
\(126\) 0 0
\(127\) 2.27710 0.202060 0.101030 0.994883i \(-0.467786\pi\)
0.101030 + 0.994883i \(0.467786\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0.624051i 0.0545236i 0.999628 + 0.0272618i \(0.00867877\pi\)
−0.999628 + 0.0272618i \(0.991321\pi\)
\(132\) 0 0
\(133\) 2.51401 + 1.18700i 0.217992 + 0.102926i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 15.1826i 1.29714i −0.761157 0.648568i \(-0.775368\pi\)
0.761157 0.648568i \(-0.224632\pi\)
\(138\) 0 0
\(139\) −12.9120 −1.09518 −0.547590 0.836747i \(-0.684454\pi\)
−0.547590 + 0.836747i \(0.684454\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −25.3990 −2.12397
\(144\) 0 0
\(145\) 7.67504i 0.637377i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.02714 0.739532 0.369766 0.929125i \(-0.379438\pi\)
0.369766 + 0.929125i \(0.379438\pi\)
\(150\) 0 0
\(151\) 7.42667 0.604374 0.302187 0.953249i \(-0.402283\pi\)
0.302187 + 0.953249i \(0.402283\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 7.25162 0.582464
\(156\) 0 0
\(157\) −5.46723 −0.436332 −0.218166 0.975912i \(-0.570007\pi\)
−0.218166 + 0.975912i \(0.570007\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −0.106918 + 0.226447i −0.00842632 + 0.0178465i
\(162\) 0 0
\(163\) 0.839878i 0.0657843i 0.999459 + 0.0328922i \(0.0104718\pi\)
−0.999459 + 0.0328922i \(0.989528\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.57392 0.199176 0.0995878 0.995029i \(-0.468248\pi\)
0.0995878 + 0.995029i \(0.468248\pi\)
\(168\) 0 0
\(169\) 30.4714 2.34395
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 17.4921i 1.32990i 0.746888 + 0.664949i \(0.231547\pi\)
−0.746888 + 0.664949i \(0.768453\pi\)
\(174\) 0 0
\(175\) −4.40187 2.07836i −0.332750 0.157110i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 20.3699 1.52252 0.761260 0.648447i \(-0.224581\pi\)
0.761260 + 0.648447i \(0.224581\pi\)
\(180\) 0 0
\(181\) 1.56527 0.116345 0.0581726 0.998307i \(-0.481473\pi\)
0.0581726 + 0.998307i \(0.481473\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 8.26814 0.607886
\(186\) 0 0
\(187\) 17.5858 1.28600
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 4.80433i 0.347629i −0.984778 0.173815i \(-0.944391\pi\)
0.984778 0.173815i \(-0.0556093\pi\)
\(192\) 0 0
\(193\) 6.05595 0.435917 0.217958 0.975958i \(-0.430060\pi\)
0.217958 + 0.975958i \(0.430060\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.4367 0.886082 0.443041 0.896501i \(-0.353900\pi\)
0.443041 + 0.896501i \(0.353900\pi\)
\(198\) 0 0
\(199\) 15.9553i 1.13104i 0.824733 + 0.565522i \(0.191325\pi\)
−0.824733 + 0.565522i \(0.808675\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 10.3294 + 4.87710i 0.724985 + 0.342305i
\(204\) 0 0
\(205\) 20.5945i 1.43839i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −4.04794 −0.280002
\(210\) 0 0
\(211\) 0.608035i 0.0418589i 0.999781 + 0.0209294i \(0.00666253\pi\)
−0.999781 + 0.0209294i \(0.993337\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −11.1776 −0.762309
\(216\) 0 0
\(217\) −4.60804 + 9.75958i −0.312814 + 0.662524i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −30.0988 −2.02467
\(222\) 0 0
\(223\) 7.28726i 0.487991i −0.969776 0.243996i \(-0.921542\pi\)
0.969776 0.243996i \(-0.0784582\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 19.3361i 1.28338i −0.766963 0.641692i \(-0.778233\pi\)
0.766963 0.641692i \(-0.221767\pi\)
\(228\) 0 0
\(229\) 2.95322 0.195154 0.0975771 0.995228i \(-0.468891\pi\)
0.0975771 + 0.995228i \(0.468891\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.9472i 0.782684i −0.920245 0.391342i \(-0.872011\pi\)
0.920245 0.391342i \(-0.127989\pi\)
\(234\) 0 0
\(235\) 10.8958i 0.710765i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 28.3255i 1.83222i −0.400923 0.916112i \(-0.631310\pi\)
0.400923 0.916112i \(-0.368690\pi\)
\(240\) 0 0
\(241\) 22.9910i 1.48098i −0.672067 0.740491i \(-0.734593\pi\)
0.672067 0.740491i \(-0.265407\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −9.60866 + 7.90694i −0.613875 + 0.505156i
\(246\) 0 0
\(247\) 6.92820 0.440831
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 20.8222i 1.31428i −0.753767 0.657142i \(-0.771765\pi\)
0.753767 0.657142i \(-0.228235\pi\)
\(252\) 0 0
\(253\) 0.364614i 0.0229231i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −17.7432 −1.10679 −0.553394 0.832920i \(-0.686668\pi\)
−0.553394 + 0.832920i \(0.686668\pi\)
\(258\) 0 0
\(259\) −5.25398 + 11.1277i −0.326467 + 0.691440i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 16.4703i 1.01560i 0.861475 + 0.507800i \(0.169541\pi\)
−0.861475 + 0.507800i \(0.830459\pi\)
\(264\) 0 0
\(265\) 4.35439i 0.267488i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.67822i 0.102323i 0.998690 + 0.0511613i \(0.0162923\pi\)
−0.998690 + 0.0511613i \(0.983708\pi\)
\(270\) 0 0
\(271\) 22.8034i 1.38521i 0.721318 + 0.692604i \(0.243537\pi\)
−0.721318 + 0.692604i \(0.756463\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 7.08768 0.427403
\(276\) 0 0
\(277\) 5.47349i 0.328870i −0.986388 0.164435i \(-0.947420\pi\)
0.986388 0.164435i \(-0.0525801\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.03960i 0.539258i −0.962964 0.269629i \(-0.913099\pi\)
0.962964 0.269629i \(-0.0869010\pi\)
\(282\) 0 0
\(283\) −5.55639 −0.330293 −0.165147 0.986269i \(-0.552810\pi\)
−0.165147 + 0.986269i \(0.552810\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 27.7171 + 13.0868i 1.63609 + 0.772489i
\(288\) 0 0
\(289\) 3.83988 0.225875
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 10.3814i 0.606488i −0.952913 0.303244i \(-0.901930\pi\)
0.952913 0.303244i \(-0.0980696\pi\)
\(294\) 0 0
\(295\) 23.4263 1.36393
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.624051i 0.0360898i
\(300\) 0 0
\(301\) 7.10282 15.0434i 0.409400 0.867088i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.15741i 0.467092i
\(306\) 0 0
\(307\) 23.8906 1.36351 0.681754 0.731581i \(-0.261217\pi\)
0.681754 + 0.731581i \(0.261217\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 33.1208 1.87811 0.939053 0.343772i \(-0.111705\pi\)
0.939053 + 0.343772i \(0.111705\pi\)
\(312\) 0 0
\(313\) 25.8239i 1.45966i 0.683631 + 0.729828i \(0.260400\pi\)
−0.683631 + 0.729828i \(0.739600\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −26.2970 −1.47699 −0.738493 0.674261i \(-0.764462\pi\)
−0.738493 + 0.674261i \(0.764462\pi\)
\(318\) 0 0
\(319\) −16.6320 −0.931212
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.79696 −0.266910
\(324\) 0 0
\(325\) −12.1308 −0.672898
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −14.6641 6.92374i −0.808460 0.381718i
\(330\) 0 0
\(331\) 15.9675i 0.877656i 0.898571 + 0.438828i \(0.144606\pi\)
−0.898571 + 0.438828i \(0.855394\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −8.60372 −0.470072
\(336\) 0 0
\(337\) −13.7917 −0.751279 −0.375640 0.926766i \(-0.622577\pi\)
−0.375640 + 0.926766i \(0.622577\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.7144i 0.850983i
\(342\) 0 0
\(343\) −4.53572 17.9563i −0.244906 0.969547i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 3.85226 0.206800 0.103400 0.994640i \(-0.467028\pi\)
0.103400 + 0.994640i \(0.467028\pi\)
\(348\) 0 0
\(349\) −4.44816 −0.238104 −0.119052 0.992888i \(-0.537986\pi\)
−0.119052 + 0.992888i \(0.537986\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.39917 −0.447043 −0.223521 0.974699i \(-0.571755\pi\)
−0.223521 + 0.974699i \(0.571755\pi\)
\(354\) 0 0
\(355\) 20.5700 1.09174
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.5713i 0.610709i −0.952239 0.305354i \(-0.901225\pi\)
0.952239 0.305354i \(-0.0987750\pi\)
\(360\) 0 0
\(361\) −17.8958 −0.941886
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 4.00474 0.209618
\(366\) 0 0
\(367\) 9.90826i 0.517207i −0.965984 0.258603i \(-0.916738\pi\)
0.965984 0.258603i \(-0.0832623\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 5.86035 + 2.76699i 0.304254 + 0.143655i
\(372\) 0 0
\(373\) 35.6380i 1.84526i 0.385682 + 0.922632i \(0.373966\pi\)
−0.385682 + 0.922632i \(0.626034\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 28.4663 1.46609
\(378\) 0 0
\(379\) 16.6080i 0.853097i −0.904465 0.426549i \(-0.859729\pi\)
0.904465 0.426549i \(-0.140271\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −1.08089 −0.0552308 −0.0276154 0.999619i \(-0.508791\pi\)
−0.0276154 + 0.999619i \(0.508791\pi\)
\(384\) 0 0
\(385\) 7.73570 16.3838i 0.394248 0.834997i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9.73208 0.493436 0.246718 0.969087i \(-0.420648\pi\)
0.246718 + 0.969087i \(0.420648\pi\)
\(390\) 0 0
\(391\) 0.432081i 0.0218513i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 25.2803i 1.27199i
\(396\) 0 0
\(397\) −30.4524 −1.52836 −0.764181 0.645001i \(-0.776857\pi\)
−0.764181 + 0.645001i \(0.776857\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.226447i 0.0113082i −0.999984 0.00565411i \(-0.998200\pi\)
0.999984 0.00565411i \(-0.00179977\pi\)
\(402\) 0 0
\(403\) 26.8958i 1.33978i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 17.9172i 0.888125i
\(408\) 0 0
\(409\) 17.2664i 0.853767i −0.904307 0.426883i \(-0.859611\pi\)
0.904307 0.426883i \(-0.140389\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −14.8862 + 31.5283i −0.732504 + 1.55141i
\(414\) 0 0
\(415\) −18.8721 −0.926396
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 26.1423i 1.27714i −0.769565 0.638568i \(-0.779527\pi\)
0.769565 0.638568i \(-0.220473\pi\)
\(420\) 0 0
\(421\) 22.2393i 1.08388i 0.840418 + 0.541939i \(0.182310\pi\)
−0.840418 + 0.541939i \(0.817690\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 8.39917 0.407420
\(426\) 0 0
\(427\) −10.9786 5.18362i −0.531293 0.250853i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.15666i 0.296556i 0.988946 + 0.148278i \(0.0473730\pi\)
−0.988946 + 0.148278i \(0.952627\pi\)
\(432\) 0 0
\(433\) 32.7676i 1.57471i 0.616498 + 0.787356i \(0.288551\pi\)
−0.616498 + 0.787356i \(0.711449\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0.0994573i 0.00475769i
\(438\) 0 0
\(439\) 35.0484i 1.67277i −0.548145 0.836383i \(-0.684666\pi\)
0.548145 0.836383i \(-0.315334\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −22.4967 −1.06885 −0.534425 0.845216i \(-0.679472\pi\)
−0.534425 + 0.845216i \(0.679472\pi\)
\(444\) 0 0
\(445\) 15.3111i 0.725817i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 31.8253i 1.50193i −0.660344 0.750964i \(-0.729589\pi\)
0.660344 0.750964i \(-0.270411\pi\)
\(450\) 0 0
\(451\) −44.6288 −2.10149
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −13.2400 + 28.0415i −0.620699 + 1.31461i
\(456\) 0 0
\(457\) 25.7917 1.20648 0.603241 0.797559i \(-0.293876\pi\)
0.603241 + 0.797559i \(0.293876\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 10.4809i 0.488142i −0.969757 0.244071i \(-0.921517\pi\)
0.969757 0.244071i \(-0.0784830\pi\)
\(462\) 0 0
\(463\) 27.8097 1.29243 0.646214 0.763157i \(-0.276352\pi\)
0.646214 + 0.763157i \(0.276352\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.50609i 0.393615i 0.980442 + 0.196808i \(0.0630574\pi\)
−0.980442 + 0.196808i \(0.936943\pi\)
\(468\) 0 0
\(469\) 5.46723 11.5793i 0.252453 0.534683i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 24.2222i 1.11374i
\(474\) 0 0
\(475\) −1.93334 −0.0887076
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −22.9246 −1.04745 −0.523725 0.851887i \(-0.675458\pi\)
−0.523725 + 0.851887i \(0.675458\pi\)
\(480\) 0 0
\(481\) 30.6661i 1.39825i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 25.3891 1.15286
\(486\) 0 0
\(487\) −28.2113 −1.27838 −0.639188 0.769051i \(-0.720729\pi\)
−0.639188 + 0.769051i \(0.720729\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −32.5435 −1.46867 −0.734334 0.678788i \(-0.762506\pi\)
−0.734334 + 0.678788i \(0.762506\pi\)
\(492\) 0 0
\(493\) −19.7095 −0.887673
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −13.0712 + 27.6841i −0.586322 + 1.24180i
\(498\) 0 0
\(499\) 17.0717i 0.764235i −0.924114 0.382118i \(-0.875195\pi\)
0.924114 0.382118i \(-0.124805\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −20.3506 −0.907391 −0.453695 0.891157i \(-0.649895\pi\)
−0.453695 + 0.891157i \(0.649895\pi\)
\(504\) 0 0
\(505\) 9.48037 0.421871
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 22.7394i 1.00791i −0.863731 0.503953i \(-0.831879\pi\)
0.863731 0.503953i \(-0.168121\pi\)
\(510\) 0 0
\(511\) −2.54481 + 5.38977i −0.112576 + 0.238430i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 25.1280 1.10727
\(516\) 0 0
\(517\) 23.6115 1.03843
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −28.9834 −1.26979 −0.634893 0.772600i \(-0.718956\pi\)
−0.634893 + 0.772600i \(0.718956\pi\)
\(522\) 0 0
\(523\) −30.6661 −1.34093 −0.670466 0.741940i \(-0.733906\pi\)
−0.670466 + 0.741940i \(0.733906\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 18.6222i 0.811195i
\(528\) 0 0
\(529\) 22.9910 0.999610
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 76.3839 3.30856
\(534\) 0 0
\(535\) 27.6836i 1.19687i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 17.1345 + 20.8222i 0.738035 + 0.896875i
\(540\) 0 0
\(541\) 20.3268i 0.873919i 0.899481 + 0.436959i \(0.143945\pi\)
−0.899481 + 0.436959i \(0.856055\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 23.1702 0.992503
\(546\) 0 0
\(547\) 5.48037i 0.234324i −0.993113 0.117162i \(-0.962620\pi\)
0.993113 0.117162i \(-0.0373796\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.53678 0.193273
\(552\) 0 0
\(553\) −34.0235 16.0644i −1.44683 0.683126i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −42.1570 −1.78625 −0.893124 0.449810i \(-0.851492\pi\)
−0.893124 + 0.449810i \(0.851492\pi\)
\(558\) 0 0
\(559\) 41.4572i 1.75345i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 3.42389i 0.144300i 0.997394 + 0.0721498i \(0.0229860\pi\)
−0.997394 + 0.0721498i \(0.977014\pi\)
\(564\) 0 0
\(565\) 28.3776 1.19386
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 19.3238i 0.810095i 0.914296 + 0.405048i \(0.132745\pi\)
−0.914296 + 0.405048i \(0.867255\pi\)
\(570\) 0 0
\(571\) 37.5274i 1.57047i −0.619197 0.785235i \(-0.712542\pi\)
0.619197 0.785235i \(-0.287458\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.174143i 0.00726228i
\(576\) 0 0
\(577\) 9.92784i 0.413301i 0.978415 + 0.206651i \(0.0662563\pi\)
−0.978415 + 0.206651i \(0.933744\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 11.9923 25.3990i 0.497523 1.05373i
\(582\) 0 0
\(583\) −9.43606 −0.390802
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.43026i 0.306679i −0.988174 0.153340i \(-0.950997\pi\)
0.988174 0.153340i \(-0.0490029\pi\)
\(588\) 0 0
\(589\) 4.28649i 0.176622i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 21.7911 0.894853 0.447426 0.894321i \(-0.352341\pi\)
0.447426 + 0.894321i \(0.352341\pi\)
\(594\) 0 0
\(595\) 9.16711 19.4155i 0.375815 0.795956i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.47799i 0.182966i 0.995807 + 0.0914828i \(0.0291606\pi\)
−0.995807 + 0.0914828i \(0.970839\pi\)
\(600\) 0 0
\(601\) 12.0294i 0.490691i −0.969436 0.245345i \(-0.921099\pi\)
0.969436 0.245345i \(-0.0789014\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 6.82605i 0.277518i
\(606\) 0 0
\(607\) 31.4083i 1.27482i 0.770524 + 0.637412i \(0.219995\pi\)
−0.770524 + 0.637412i \(0.780005\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −40.4120 −1.63489
\(612\) 0 0
\(613\) 14.5856i 0.589108i 0.955635 + 0.294554i \(0.0951711\pi\)
−0.955635 + 0.294554i \(0.904829\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6.69730i 0.269623i 0.990871 + 0.134812i \(0.0430429\pi\)
−0.990871 + 0.134812i \(0.956957\pi\)
\(618\) 0 0
\(619\) 18.6366 0.749069 0.374535 0.927213i \(-0.377803\pi\)
0.374535 + 0.927213i \(0.377803\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 20.6064 + 9.72944i 0.825580 + 0.389802i
\(624\) 0 0
\(625\) −12.4155 −0.496618
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 21.2326i 0.846600i
\(630\) 0 0
\(631\) 22.7940 0.907415 0.453707 0.891151i \(-0.350101\pi\)
0.453707 + 0.891151i \(0.350101\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.04794i 0.160638i
\(636\) 0 0
\(637\) −29.3264 35.6380i −1.16195 1.41203i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 28.7927i 1.13724i 0.822599 + 0.568622i \(0.192523\pi\)
−0.822599 + 0.568622i \(0.807477\pi\)
\(642\) 0 0
\(643\) −5.89291 −0.232394 −0.116197 0.993226i \(-0.537070\pi\)
−0.116197 + 0.993226i \(0.537070\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 21.2326 0.834740 0.417370 0.908737i \(-0.362952\pi\)
0.417370 + 0.908737i \(0.362952\pi\)
\(648\) 0 0
\(649\) 50.7653i 1.99271i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 2.44949 0.0958559 0.0479280 0.998851i \(-0.484738\pi\)
0.0479280 + 0.998851i \(0.484738\pi\)
\(654\) 0 0
\(655\) −1.10936 −0.0433462
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −16.8066 −0.654693 −0.327347 0.944904i \(-0.606154\pi\)
−0.327347 + 0.944904i \(0.606154\pi\)
\(660\) 0 0
\(661\) 27.6908 1.07705 0.538523 0.842611i \(-0.318983\pi\)
0.538523 + 0.842611i \(0.318983\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.11010 + 4.46909i −0.0818262 + 0.173304i
\(666\) 0 0
\(667\) 0.408645i 0.0158228i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 17.6773 0.682424
\(672\) 0 0
\(673\) −4.95177 −0.190877 −0.0954384 0.995435i \(-0.530425\pi\)
−0.0954384 + 0.995435i \(0.530425\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 10.5803i 0.406634i 0.979113 + 0.203317i \(0.0651722\pi\)
−0.979113 + 0.203317i \(0.934828\pi\)
\(678\) 0 0
\(679\) −16.1335 + 34.1699i −0.619147 + 1.31132i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −47.1718 −1.80498 −0.902489 0.430713i \(-0.858262\pi\)
−0.902489 + 0.430713i \(0.858262\pi\)
\(684\) 0 0
\(685\) 26.9897 1.03122
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 16.1502 0.615273
\(690\) 0 0
\(691\) 24.0589 0.915242 0.457621 0.889147i \(-0.348702\pi\)
0.457621 + 0.889147i \(0.348702\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 22.9533i 0.870667i
\(696\) 0 0
\(697\) −52.8869 −2.00323
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 25.2657 0.954273 0.477136 0.878829i \(-0.341675\pi\)
0.477136 + 0.878829i \(0.341675\pi\)
\(702\) 0 0
\(703\) 4.88737i 0.184330i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −6.02429 + 12.7591i −0.226567 + 0.479857i
\(708\) 0 0
\(709\) 22.3362i 0.838855i 0.907789 + 0.419427i \(0.137769\pi\)
−0.907789 + 0.419427i \(0.862231\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.386101 −0.0144596
\(714\) 0 0
\(715\) 45.1512i 1.68856i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.74032 0.251371 0.125686 0.992070i \(-0.459887\pi\)
0.125686 + 0.992070i \(0.459887\pi\)
\(720\) 0 0
\(721\) −15.9675 + 33.8184i −0.594663 + 1.25946i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −7.94361 −0.295018
\(726\) 0 0
\(727\) 36.4995i 1.35369i 0.736125 + 0.676846i \(0.236654\pi\)
−0.736125 + 0.676846i \(0.763346\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 28.7042i 1.06166i
\(732\) 0 0
\(733\) 36.6065 1.35209 0.676046 0.736860i \(-0.263692\pi\)
0.676046 + 0.736860i \(0.263692\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 18.6444i 0.686777i
\(738\) 0 0
\(739\) 1.36847i 0.0503400i 0.999683 + 0.0251700i \(0.00801270\pi\)
−0.999683 + 0.0251700i \(0.991987\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 7.31969i 0.268534i −0.990945 0.134267i \(-0.957132\pi\)
0.990945 0.134267i \(-0.0428679\pi\)
\(744\) 0 0
\(745\) 16.0473i 0.587928i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −37.2580 17.5915i −1.36138 0.642781i
\(750\) 0 0
\(751\) −2.87247 −0.104818 −0.0524090 0.998626i \(-0.516690\pi\)
−0.0524090 + 0.998626i \(0.516690\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 13.2022i 0.480477i
\(756\) 0 0
\(757\) 50.3167i 1.82879i 0.404819 + 0.914397i \(0.367334\pi\)
−0.404819 + 0.914397i \(0.632666\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 9.68885 0.351220 0.175610 0.984460i \(-0.443810\pi\)
0.175610 + 0.984460i \(0.443810\pi\)
\(762\) 0 0
\(763\) −14.7235 + 31.1836i −0.533026 + 1.12892i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 86.8868i 3.13730i
\(768\) 0 0
\(769\) 7.82624i 0.282222i 0.989994 + 0.141111i \(0.0450674\pi\)
−0.989994 + 0.141111i \(0.954933\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 17.3926i 0.625569i −0.949824 0.312785i \(-0.898738\pi\)
0.949824 0.312785i \(-0.101262\pi\)
\(774\) 0 0
\(775\) 7.50537i 0.269601i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.1736 0.436164
\(780\) 0 0
\(781\) 44.5755i 1.59504i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 9.71894i 0.346884i
\(786\) 0 0
\(787\) 15.8961 0.566635 0.283318 0.959026i \(-0.408565\pi\)
0.283318 + 0.959026i \(0.408565\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −18.0325 + 38.1920i −0.641163 + 1.35795i
\(792\) 0 0
\(793\) −30.2553 −1.07440
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 28.1581i 0.997412i 0.866771 + 0.498706i \(0.166191\pi\)
−0.866771 + 0.498706i \(0.833809\pi\)
\(798\) 0 0
\(799\) 27.9805 0.989880
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 8.67836i 0.306253i
\(804\) 0 0
\(805\) −0.402548 0.190065i −0.0141880 0.00669892i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 20.4324i 0.718366i 0.933267 + 0.359183i \(0.116945\pi\)
−0.933267 + 0.359183i \(0.883055\pi\)
\(810\) 0 0
\(811\) 17.9977 0.631985 0.315992 0.948762i \(-0.397663\pi\)
0.315992 + 0.948762i \(0.397663\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.49303 −0.0522985
\(816\) 0 0
\(817\) 6.60719i 0.231156i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 26.1600 0.912989 0.456494 0.889726i \(-0.349105\pi\)
0.456494 + 0.889726i \(0.349105\pi\)
\(822\) 0 0
\(823\) −40.2891 −1.40439 −0.702194 0.711986i \(-0.747796\pi\)
−0.702194 + 0.711986i \(0.747796\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −45.3729 −1.57777 −0.788885 0.614541i \(-0.789341\pi\)
−0.788885 + 0.614541i \(0.789341\pi\)
\(828\) 0 0
\(829\) 7.98124 0.277200 0.138600 0.990348i \(-0.455740\pi\)
0.138600 + 0.990348i \(0.455740\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 20.3050 + 24.6751i 0.703528 + 0.854941i
\(834\) 0 0
\(835\) 4.57558i 0.158345i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 9.58515 0.330916 0.165458 0.986217i \(-0.447090\pi\)
0.165458 + 0.986217i \(0.447090\pi\)
\(840\) 0 0
\(841\) −10.3595 −0.357225
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 54.1682i 1.86344i
\(846\) 0 0
\(847\) −9.18683 4.33761i −0.315663 0.149042i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −0.440224 −0.0150907
\(852\) 0 0
\(853\) −45.1676 −1.54651 −0.773254 0.634096i \(-0.781372\pi\)
−0.773254 + 0.634096i \(0.781372\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 50.9055 1.73890 0.869450 0.494021i \(-0.164474\pi\)
0.869450 + 0.494021i \(0.164474\pi\)
\(858\) 0 0
\(859\) −24.1930 −0.825455 −0.412728 0.910855i \(-0.635424\pi\)
−0.412728 + 0.910855i \(0.635424\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 35.6081i 1.21211i 0.795421 + 0.606057i \(0.207250\pi\)
−0.795421 + 0.606057i \(0.792750\pi\)
\(864\) 0 0
\(865\) −31.0952 −1.05727
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 54.7830 1.85839
\(870\) 0 0
\(871\) 31.9107i 1.08125i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 13.7351 29.0903i 0.464332 0.983432i
\(876\) 0 0
\(877\) 8.84069i 0.298529i 0.988797 + 0.149264i \(0.0476906\pi\)
−0.988797 + 0.149264i \(0.952309\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −7.32334 −0.246730 −0.123365 0.992361i \(-0.539369\pi\)
−0.123365 + 0.992361i \(0.539369\pi\)
\(882\) 0 0
\(883\) 51.4390i 1.73106i −0.500858 0.865529i \(-0.666982\pi\)
0.500858 0.865529i \(-0.333018\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 11.6475 0.391084 0.195542 0.980695i \(-0.437353\pi\)
0.195542 + 0.980695i \(0.437353\pi\)
\(888\) 0 0
\(889\) −5.44791 2.57226i −0.182717 0.0862708i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −6.44061 −0.215527
\(894\) 0 0
\(895\) 36.2111i 1.21040i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 17.6121i 0.587397i
\(900\) 0 0
\(901\) −11.1821 −0.372530
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 2.78253i 0.0924945i
\(906\) 0 0
\(907\) 32.6550i 1.08429i 0.840284 + 0.542146i \(0.182388\pi\)
−0.840284 + 0.542146i \(0.817612\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 49.9787i 1.65587i −0.560826 0.827934i \(-0.689516\pi\)
0.560826 0.827934i \(-0.310484\pi\)
\(912\) 0 0
\(913\) 40.8963i 1.35347i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.704941 1.49303i 0.0232792 0.0493041i
\(918\) 0 0
\(919\) 7.15896 0.236152 0.118076 0.993005i \(-0.462327\pi\)
0.118076 + 0.993005i \(0.462327\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 76.2928i 2.51121i
\(924\) 0 0
\(925\) 8.55746i 0.281368i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0.730969 0.0239823 0.0119912 0.999928i \(-0.496183\pi\)
0.0119912 + 0.999928i \(0.496183\pi\)
\(930\) 0 0
\(931\) −4.67385 5.67976i −0.153179 0.186146i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 31.2619i 1.02237i
\(936\) 0 0
\(937\) 39.3748i 1.28632i 0.765732 + 0.643160i \(0.222377\pi\)
−0.765732 + 0.643160i \(0.777623\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 49.1198i 1.60126i 0.599159 + 0.800630i \(0.295502\pi\)
−0.599159 + 0.800630i \(0.704498\pi\)
\(942\) 0 0
\(943\) 1.09652i 0.0357078i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −44.7171 −1.45311 −0.726556 0.687108i \(-0.758880\pi\)
−0.726556 + 0.687108i \(0.758880\pi\)
\(948\) 0 0
\(949\) 14.8533i 0.482160i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 13.1681i 0.426558i 0.976991 + 0.213279i \(0.0684143\pi\)
−0.976991 + 0.213279i \(0.931586\pi\)
\(954\) 0 0
\(955\) 8.54053 0.276365
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −17.1506 + 36.3240i −0.553820 + 1.17296i
\(960\) 0 0
\(961\) 14.3595 0.463210
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 10.7655i 0.346554i
\(966\) 0 0
\(967\) −28.8067 −0.926360 −0.463180 0.886264i \(-0.653292\pi\)
−0.463180 + 0.886264i \(0.653292\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 26.5284i 0.851338i −0.904879 0.425669i \(-0.860039\pi\)
0.904879 0.425669i \(-0.139961\pi\)
\(972\) 0 0
\(973\) 30.8916 + 14.5856i 0.990340 + 0.467594i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 40.3105i 1.28965i 0.764331 + 0.644824i \(0.223069\pi\)
−0.764331 + 0.644824i \(0.776931\pi\)
\(978\) 0 0
\(979\) −33.1795 −1.06042
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −2.57392 −0.0820952 −0.0410476 0.999157i \(-0.513070\pi\)
−0.0410476 + 0.999157i \(0.513070\pi\)
\(984\) 0 0
\(985\) 22.1085i 0.704435i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.595136 0.0189242
\(990\) 0 0
\(991\) −33.0332 −1.04933 −0.524667 0.851308i \(-0.675810\pi\)
−0.524667 + 0.851308i \(0.675810\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −28.3634 −0.899180
\(996\) 0 0
\(997\) 26.8123 0.849156 0.424578 0.905391i \(-0.360423\pi\)
0.424578 + 0.905391i \(0.360423\pi\)
\(998\) 0 0
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4032.2.i.c.1889.20 yes 48
3.2 odd 2 inner 4032.2.i.c.1889.1 48
4.3 odd 2 inner 4032.2.i.c.1889.12 yes 48
7.6 odd 2 inner 4032.2.i.c.1889.37 yes 48
8.3 odd 2 inner 4032.2.i.c.1889.47 yes 48
8.5 even 2 inner 4032.2.i.c.1889.5 yes 48
12.11 even 2 inner 4032.2.i.c.1889.43 yes 48
21.20 even 2 inner 4032.2.i.c.1889.6 yes 48
24.5 odd 2 inner 4032.2.i.c.1889.38 yes 48
24.11 even 2 inner 4032.2.i.c.1889.30 yes 48
28.27 even 2 inner 4032.2.i.c.1889.29 yes 48
56.13 odd 2 inner 4032.2.i.c.1889.2 yes 48
56.27 even 2 inner 4032.2.i.c.1889.44 yes 48
84.83 odd 2 inner 4032.2.i.c.1889.48 yes 48
168.83 odd 2 inner 4032.2.i.c.1889.11 yes 48
168.125 even 2 inner 4032.2.i.c.1889.19 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4032.2.i.c.1889.1 48 3.2 odd 2 inner
4032.2.i.c.1889.2 yes 48 56.13 odd 2 inner
4032.2.i.c.1889.5 yes 48 8.5 even 2 inner
4032.2.i.c.1889.6 yes 48 21.20 even 2 inner
4032.2.i.c.1889.11 yes 48 168.83 odd 2 inner
4032.2.i.c.1889.12 yes 48 4.3 odd 2 inner
4032.2.i.c.1889.19 yes 48 168.125 even 2 inner
4032.2.i.c.1889.20 yes 48 1.1 even 1 trivial
4032.2.i.c.1889.29 yes 48 28.27 even 2 inner
4032.2.i.c.1889.30 yes 48 24.11 even 2 inner
4032.2.i.c.1889.37 yes 48 7.6 odd 2 inner
4032.2.i.c.1889.38 yes 48 24.5 odd 2 inner
4032.2.i.c.1889.43 yes 48 12.11 even 2 inner
4032.2.i.c.1889.44 yes 48 56.27 even 2 inner
4032.2.i.c.1889.47 yes 48 8.3 odd 2 inner
4032.2.i.c.1889.48 yes 48 84.83 odd 2 inner