Properties

Label 3024.2.cc.d.881.8
Level $3024$
Weight $2$
Character 3024.881
Analytic conductor $24.147$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3024,2,Mod(881,3024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.cc (of order \(6\), degree \(2\), not 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: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 881.8
Character \(\chi\) \(=\) 3024.881
Dual form 3024.2.cc.d.2897.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.965651 + 1.67256i) q^{5} +(-2.53170 + 0.768427i) q^{7} +O(q^{10})\) \(q+(-0.965651 + 1.67256i) q^{5} +(-2.53170 + 0.768427i) q^{7} +(1.10681 - 0.639015i) q^{11} +(2.52802 + 1.45955i) q^{13} +0.475237 q^{17} +6.10647i q^{19} +(-6.51132 - 3.75931i) q^{23} +(0.635036 + 1.09991i) q^{25} +(-3.76797 + 2.17544i) q^{29} +(4.21872 + 2.43568i) q^{31} +(1.15950 - 4.97645i) q^{35} +1.76145 q^{37} +(1.16103 - 2.01097i) q^{41} +(-4.63638 - 8.03045i) q^{43} +(-4.00447 - 6.93595i) q^{47} +(5.81904 - 3.89086i) q^{49} +10.3345i q^{53} +2.46826i q^{55} +(-1.74272 + 3.01848i) q^{59} +(-4.26195 + 2.46064i) q^{61} +(-4.88237 + 2.81883i) q^{65} +(-0.602527 + 1.04361i) q^{67} +11.2114i q^{71} -1.84336i q^{73} +(-2.31107 + 2.46830i) q^{77} +(-8.54654 - 14.8030i) q^{79} +(-0.225217 - 0.390088i) q^{83} +(-0.458913 + 0.794861i) q^{85} +11.2580 q^{89} +(-7.52175 - 1.75255i) q^{91} +(-10.2134 - 5.89672i) q^{95} +(-9.22775 + 5.32764i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 12 q^{23} - 24 q^{25} + 36 q^{29} - 12 q^{43} + 6 q^{49} - 36 q^{65} + 60 q^{77} + 12 q^{79} + 12 q^{91} - 108 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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
\(5\) −0.965651 + 1.67256i −0.431852 + 0.747990i −0.997033 0.0769771i \(-0.975473\pi\)
0.565181 + 0.824967i \(0.308806\pi\)
\(6\) 0 0
\(7\) −2.53170 + 0.768427i −0.956894 + 0.290438i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.10681 0.639015i 0.333715 0.192670i −0.323774 0.946134i \(-0.604952\pi\)
0.657489 + 0.753464i \(0.271619\pi\)
\(12\) 0 0
\(13\) 2.52802 + 1.45955i 0.701146 + 0.404807i 0.807774 0.589492i \(-0.200672\pi\)
−0.106628 + 0.994299i \(0.534005\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.475237 0.115262 0.0576310 0.998338i \(-0.481645\pi\)
0.0576310 + 0.998338i \(0.481645\pi\)
\(18\) 0 0
\(19\) 6.10647i 1.40092i 0.713691 + 0.700460i \(0.247022\pi\)
−0.713691 + 0.700460i \(0.752978\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.51132 3.75931i −1.35770 0.783871i −0.368390 0.929671i \(-0.620091\pi\)
−0.989314 + 0.145801i \(0.953424\pi\)
\(24\) 0 0
\(25\) 0.635036 + 1.09991i 0.127007 + 0.219983i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −3.76797 + 2.17544i −0.699695 + 0.403969i −0.807234 0.590232i \(-0.799036\pi\)
0.107539 + 0.994201i \(0.465703\pi\)
\(30\) 0 0
\(31\) 4.21872 + 2.43568i 0.757705 + 0.437461i 0.828471 0.560032i \(-0.189211\pi\)
−0.0707660 + 0.997493i \(0.522544\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 1.15950 4.97645i 0.195992 0.841173i
\(36\) 0 0
\(37\) 1.76145 0.289580 0.144790 0.989462i \(-0.453749\pi\)
0.144790 + 0.989462i \(0.453749\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 1.16103 2.01097i 0.181323 0.314060i −0.761009 0.648742i \(-0.775296\pi\)
0.942331 + 0.334682i \(0.108629\pi\)
\(42\) 0 0
\(43\) −4.63638 8.03045i −0.707042 1.22463i −0.965950 0.258730i \(-0.916696\pi\)
0.258908 0.965902i \(-0.416637\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.00447 6.93595i −0.584112 1.01171i −0.994985 0.100020i \(-0.968109\pi\)
0.410873 0.911693i \(-0.365224\pi\)
\(48\) 0 0
\(49\) 5.81904 3.89086i 0.831291 0.555837i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 10.3345i 1.41955i 0.704428 + 0.709775i \(0.251204\pi\)
−0.704428 + 0.709775i \(0.748796\pi\)
\(54\) 0 0
\(55\) 2.46826i 0.332820i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.74272 + 3.01848i −0.226883 + 0.392973i −0.956883 0.290475i \(-0.906187\pi\)
0.730000 + 0.683447i \(0.239520\pi\)
\(60\) 0 0
\(61\) −4.26195 + 2.46064i −0.545686 + 0.315052i −0.747380 0.664396i \(-0.768689\pi\)
0.201694 + 0.979449i \(0.435355\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −4.88237 + 2.81883i −0.605583 + 0.349633i
\(66\) 0 0
\(67\) −0.602527 + 1.04361i −0.0736104 + 0.127497i −0.900481 0.434895i \(-0.856785\pi\)
0.826871 + 0.562392i \(0.190119\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.2114i 1.33055i 0.746598 + 0.665275i \(0.231686\pi\)
−0.746598 + 0.665275i \(0.768314\pi\)
\(72\) 0 0
\(73\) 1.84336i 0.215749i −0.994164 0.107875i \(-0.965595\pi\)
0.994164 0.107875i \(-0.0344045\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.31107 + 2.46830i −0.263371 + 0.281288i
\(78\) 0 0
\(79\) −8.54654 14.8030i −0.961561 1.66547i −0.718584 0.695440i \(-0.755209\pi\)
−0.242977 0.970032i \(-0.578124\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −0.225217 0.390088i −0.0247208 0.0428177i 0.853400 0.521256i \(-0.174536\pi\)
−0.878121 + 0.478438i \(0.841203\pi\)
\(84\) 0 0
\(85\) −0.458913 + 0.794861i −0.0497761 + 0.0862148i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 11.2580 1.19335 0.596675 0.802483i \(-0.296488\pi\)
0.596675 + 0.802483i \(0.296488\pi\)
\(90\) 0 0
\(91\) −7.52175 1.75255i −0.788493 0.183718i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −10.2134 5.89672i −1.04787 0.604991i
\(96\) 0 0
\(97\) −9.22775 + 5.32764i −0.936936 + 0.540940i −0.888998 0.457910i \(-0.848598\pi\)
−0.0479373 + 0.998850i \(0.515265\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.65330 11.5239i −0.662028 1.14667i −0.980082 0.198594i \(-0.936363\pi\)
0.318054 0.948073i \(-0.396971\pi\)
\(102\) 0 0
\(103\) −16.4947 9.52323i −1.62527 0.938352i −0.985478 0.169806i \(-0.945686\pi\)
−0.639795 0.768546i \(-0.720981\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.1392i 1.56024i −0.625630 0.780120i \(-0.715158\pi\)
0.625630 0.780120i \(-0.284842\pi\)
\(108\) 0 0
\(109\) 3.40434 0.326077 0.163038 0.986620i \(-0.447871\pi\)
0.163038 + 0.986620i \(0.447871\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −3.64150 2.10242i −0.342563 0.197779i 0.318842 0.947808i \(-0.396706\pi\)
−0.661405 + 0.750029i \(0.730040\pi\)
\(114\) 0 0
\(115\) 12.5753 7.26037i 1.17265 0.677033i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.20316 + 0.365185i −0.110293 + 0.0334765i
\(120\) 0 0
\(121\) −4.68332 + 8.11175i −0.425756 + 0.737432i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −12.1094 −1.08310
\(126\) 0 0
\(127\) −17.1828 −1.52473 −0.762363 0.647150i \(-0.775961\pi\)
−0.762363 + 0.647150i \(0.775961\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −4.00420 + 6.93548i −0.349848 + 0.605955i −0.986222 0.165425i \(-0.947100\pi\)
0.636374 + 0.771381i \(0.280434\pi\)
\(132\) 0 0
\(133\) −4.69238 15.4598i −0.406881 1.34053i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.44241 + 4.87423i −0.721284 + 0.416433i −0.815225 0.579144i \(-0.803387\pi\)
0.0939411 + 0.995578i \(0.470053\pi\)
\(138\) 0 0
\(139\) −6.76047 3.90316i −0.573416 0.331062i 0.185097 0.982720i \(-0.440740\pi\)
−0.758513 + 0.651658i \(0.774074\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 3.73070 0.311977
\(144\) 0 0
\(145\) 8.40286i 0.697820i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −9.62284 5.55575i −0.788333 0.455145i 0.0510420 0.998697i \(-0.483746\pi\)
−0.839376 + 0.543552i \(0.817079\pi\)
\(150\) 0 0
\(151\) 1.88730 + 3.26890i 0.153586 + 0.266020i 0.932543 0.361058i \(-0.117584\pi\)
−0.778957 + 0.627077i \(0.784251\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −8.14763 + 4.70404i −0.654433 + 0.377837i
\(156\) 0 0
\(157\) 3.55162 + 2.05053i 0.283450 + 0.163650i 0.634984 0.772525i \(-0.281007\pi\)
−0.351534 + 0.936175i \(0.614340\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 19.3735 + 4.51399i 1.52684 + 0.355752i
\(162\) 0 0
\(163\) 14.3871 1.12689 0.563443 0.826155i \(-0.309477\pi\)
0.563443 + 0.826155i \(0.309477\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.06975 + 13.9772i −0.624456 + 1.08159i 0.364190 + 0.931325i \(0.381346\pi\)
−0.988646 + 0.150265i \(0.951987\pi\)
\(168\) 0 0
\(169\) −2.23942 3.87879i −0.172263 0.298368i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.695376 + 1.20443i 0.0528685 + 0.0915709i 0.891248 0.453515i \(-0.149830\pi\)
−0.838380 + 0.545086i \(0.816497\pi\)
\(174\) 0 0
\(175\) −2.45293 2.29668i −0.185424 0.173613i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.60605i 0.344273i −0.985073 0.172136i \(-0.944933\pi\)
0.985073 0.172136i \(-0.0550669\pi\)
\(180\) 0 0
\(181\) 16.3732i 1.21701i −0.793550 0.608505i \(-0.791769\pi\)
0.793550 0.608505i \(-0.208231\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.70094 + 2.94612i −0.125056 + 0.216603i
\(186\) 0 0
\(187\) 0.525996 0.303684i 0.0384646 0.0222075i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.7953 + 7.38735i −0.925833 + 0.534530i −0.885491 0.464656i \(-0.846178\pi\)
−0.0403419 + 0.999186i \(0.512845\pi\)
\(192\) 0 0
\(193\) 8.91923 15.4486i 0.642020 1.11201i −0.342961 0.939350i \(-0.611430\pi\)
0.984981 0.172662i \(-0.0552369\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 8.00352i 0.570227i −0.958494 0.285113i \(-0.907969\pi\)
0.958494 0.285113i \(-0.0920313\pi\)
\(198\) 0 0
\(199\) 16.3034i 1.15572i 0.816137 + 0.577858i \(0.196111\pi\)
−0.816137 + 0.577858i \(0.803889\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7.86772 8.40298i 0.552205 0.589773i
\(204\) 0 0
\(205\) 2.24230 + 3.88378i 0.156609 + 0.271255i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 3.90213 + 6.75868i 0.269916 + 0.467508i
\(210\) 0 0
\(211\) 10.1930 17.6548i 0.701717 1.21541i −0.266147 0.963933i \(-0.585751\pi\)
0.967863 0.251476i \(-0.0809161\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 17.9085 1.22135
\(216\) 0 0
\(217\) −12.5522 2.92464i −0.852099 0.198537i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.20141 + 0.693633i 0.0808154 + 0.0466588i
\(222\) 0 0
\(223\) 1.95301 1.12757i 0.130783 0.0755078i −0.433181 0.901307i \(-0.642609\pi\)
0.563964 + 0.825799i \(0.309276\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 10.8916 + 18.8648i 0.722899 + 1.25210i 0.959833 + 0.280572i \(0.0905243\pi\)
−0.236934 + 0.971526i \(0.576142\pi\)
\(228\) 0 0
\(229\) 10.4832 + 6.05247i 0.692748 + 0.399958i 0.804641 0.593762i \(-0.202358\pi\)
−0.111893 + 0.993720i \(0.535691\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 21.9876i 1.44046i −0.693736 0.720229i \(-0.744037\pi\)
0.693736 0.720229i \(-0.255963\pi\)
\(234\) 0 0
\(235\) 15.4677 1.00900
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 18.7861 + 10.8462i 1.21517 + 0.701581i 0.963882 0.266330i \(-0.0858111\pi\)
0.251292 + 0.967911i \(0.419144\pi\)
\(240\) 0 0
\(241\) −23.1674 + 13.3757i −1.49234 + 0.861604i −0.999961 0.00877651i \(-0.997206\pi\)
−0.492380 + 0.870380i \(0.663873\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.888520 + 13.4899i 0.0567655 + 0.861837i
\(246\) 0 0
\(247\) −8.91271 + 15.4373i −0.567102 + 0.982250i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.75601 −0.110839 −0.0554193 0.998463i \(-0.517650\pi\)
−0.0554193 + 0.998463i \(0.517650\pi\)
\(252\) 0 0
\(253\) −9.60903 −0.604114
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.9860 + 25.9565i −0.934800 + 1.61912i −0.159809 + 0.987148i \(0.551088\pi\)
−0.774991 + 0.631972i \(0.782246\pi\)
\(258\) 0 0
\(259\) −4.45946 + 1.35354i −0.277097 + 0.0841050i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −13.4273 + 7.75223i −0.827960 + 0.478023i −0.853154 0.521659i \(-0.825313\pi\)
0.0251934 + 0.999683i \(0.491980\pi\)
\(264\) 0 0
\(265\) −17.2850 9.97951i −1.06181 0.613036i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.412404 −0.0251447 −0.0125724 0.999921i \(-0.504002\pi\)
−0.0125724 + 0.999921i \(0.504002\pi\)
\(270\) 0 0
\(271\) 0.360056i 0.0218718i 0.999940 + 0.0109359i \(0.00348108\pi\)
−0.999940 + 0.0109359i \(0.996519\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.40572 + 0.811595i 0.0847683 + 0.0489410i
\(276\) 0 0
\(277\) −3.03617 5.25881i −0.182426 0.315971i 0.760280 0.649595i \(-0.225062\pi\)
−0.942706 + 0.333624i \(0.891728\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.22494 4.74867i 0.490659 0.283282i −0.234189 0.972191i \(-0.575243\pi\)
0.724848 + 0.688909i \(0.241910\pi\)
\(282\) 0 0
\(283\) 9.81761 + 5.66820i 0.583596 + 0.336939i 0.762561 0.646916i \(-0.223942\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.39411 + 5.98333i −0.0822915 + 0.353185i
\(288\) 0 0
\(289\) −16.7741 −0.986715
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −9.22450 + 15.9773i −0.538901 + 0.933404i 0.460062 + 0.887887i \(0.347827\pi\)
−0.998964 + 0.0455177i \(0.985506\pi\)
\(294\) 0 0
\(295\) −3.36572 5.82960i −0.195960 0.339412i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −10.9738 19.0072i −0.634632 1.09922i
\(300\) 0 0
\(301\) 17.9088 + 16.7680i 1.03224 + 0.966491i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 9.50447i 0.544224i
\(306\) 0 0
\(307\) 11.0961i 0.633285i −0.948545 0.316643i \(-0.897444\pi\)
0.948545 0.316643i \(-0.102556\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.06866 1.85097i 0.0605979 0.104959i −0.834135 0.551560i \(-0.814033\pi\)
0.894733 + 0.446602i \(0.147366\pi\)
\(312\) 0 0
\(313\) 22.3161 12.8842i 1.26138 0.728259i 0.288039 0.957619i \(-0.406997\pi\)
0.973342 + 0.229360i \(0.0736634\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.82524 3.36320i 0.327178 0.188896i −0.327409 0.944883i \(-0.606176\pi\)
0.654588 + 0.755986i \(0.272842\pi\)
\(318\) 0 0
\(319\) −2.78028 + 4.81558i −0.155666 + 0.269621i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.90202i 0.161473i
\(324\) 0 0
\(325\) 3.70747i 0.205653i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 15.4679 + 14.4826i 0.852773 + 0.798453i
\(330\) 0 0
\(331\) 12.0006 + 20.7857i 0.659615 + 1.14249i 0.980715 + 0.195441i \(0.0626139\pi\)
−0.321101 + 0.947045i \(0.604053\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.16366 2.01552i −0.0635777 0.110120i
\(336\) 0 0
\(337\) −1.07839 + 1.86783i −0.0587438 + 0.101747i −0.893902 0.448263i \(-0.852043\pi\)
0.835158 + 0.550010i \(0.185376\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.22575 0.337143
\(342\) 0 0
\(343\) −11.7422 + 14.3220i −0.634021 + 0.773316i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.31897 + 4.22561i 0.392903 + 0.226843i 0.683417 0.730028i \(-0.260493\pi\)
−0.290514 + 0.956871i \(0.593826\pi\)
\(348\) 0 0
\(349\) −11.6656 + 6.73516i −0.624447 + 0.360525i −0.778598 0.627523i \(-0.784069\pi\)
0.154151 + 0.988047i \(0.450736\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −14.8956 25.7999i −0.792813 1.37319i −0.924219 0.381863i \(-0.875282\pi\)
0.131406 0.991329i \(-0.458051\pi\)
\(354\) 0 0
\(355\) −18.7517 10.8263i −0.995239 0.574601i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 8.88758i 0.469068i 0.972108 + 0.234534i \(0.0753565\pi\)
−0.972108 + 0.234534i \(0.924644\pi\)
\(360\) 0 0
\(361\) −18.2890 −0.962579
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.08313 + 1.78005i 0.161378 + 0.0931719i
\(366\) 0 0
\(367\) 32.0068 18.4792i 1.67074 0.964604i 0.703520 0.710675i \(-0.251610\pi\)
0.967223 0.253929i \(-0.0817230\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −7.94130 26.1638i −0.412292 1.35836i
\(372\) 0 0
\(373\) 16.8546 29.1931i 0.872700 1.51156i 0.0135064 0.999909i \(-0.495701\pi\)
0.859193 0.511651i \(-0.170966\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −12.7007 −0.654117
\(378\) 0 0
\(379\) 29.7512 1.52821 0.764107 0.645089i \(-0.223180\pi\)
0.764107 + 0.645089i \(0.223180\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −7.62871 + 13.2133i −0.389809 + 0.675169i −0.992424 0.122863i \(-0.960792\pi\)
0.602615 + 0.798032i \(0.294126\pi\)
\(384\) 0 0
\(385\) −1.89668 6.24891i −0.0966637 0.318474i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.947612 0.547104i 0.0480458 0.0277393i −0.475785 0.879562i \(-0.657836\pi\)
0.523831 + 0.851823i \(0.324503\pi\)
\(390\) 0 0
\(391\) −3.09442 1.78656i −0.156492 0.0903504i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 33.0119 1.66101
\(396\) 0 0
\(397\) 18.2381i 0.915345i 0.889121 + 0.457672i \(0.151317\pi\)
−0.889121 + 0.457672i \(0.848683\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −14.3050 8.25900i −0.714358 0.412435i 0.0983146 0.995155i \(-0.468655\pi\)
−0.812673 + 0.582721i \(0.801988\pi\)
\(402\) 0 0
\(403\) 7.11001 + 12.3149i 0.354175 + 0.613448i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.94958 1.12559i 0.0966371 0.0557934i
\(408\) 0 0
\(409\) −12.3657 7.13935i −0.611445 0.353018i 0.162086 0.986777i \(-0.448178\pi\)
−0.773531 + 0.633759i \(0.781511\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 2.09257 8.98105i 0.102969 0.441928i
\(414\) 0 0
\(415\) 0.869925 0.0427029
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −19.2168 + 33.2845i −0.938804 + 1.62606i −0.171098 + 0.985254i \(0.554732\pi\)
−0.767706 + 0.640802i \(0.778602\pi\)
\(420\) 0 0
\(421\) −5.90196 10.2225i −0.287644 0.498214i 0.685603 0.727976i \(-0.259539\pi\)
−0.973247 + 0.229762i \(0.926205\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.301793 + 0.522720i 0.0146391 + 0.0253557i
\(426\) 0 0
\(427\) 8.89917 9.50460i 0.430661 0.459960i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 33.9984i 1.63765i 0.574047 + 0.818823i \(0.305373\pi\)
−0.574047 + 0.818823i \(0.694627\pi\)
\(432\) 0 0
\(433\) 1.24413i 0.0597893i −0.999553 0.0298946i \(-0.990483\pi\)
0.999553 0.0298946i \(-0.00951718\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 22.9561 39.7612i 1.09814 1.90204i
\(438\) 0 0
\(439\) −10.3661 + 5.98485i −0.494745 + 0.285641i −0.726541 0.687123i \(-0.758873\pi\)
0.231796 + 0.972765i \(0.425540\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 5.07711 2.93127i 0.241221 0.139269i −0.374517 0.927220i \(-0.622191\pi\)
0.615738 + 0.787951i \(0.288858\pi\)
\(444\) 0 0
\(445\) −10.8713 + 18.8297i −0.515351 + 0.892614i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 13.7990i 0.651215i 0.945505 + 0.325607i \(0.105569\pi\)
−0.945505 + 0.325607i \(0.894431\pi\)
\(450\) 0 0
\(451\) 2.96767i 0.139742i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 10.1946 10.8882i 0.477932 0.510446i
\(456\) 0 0
\(457\) 17.6082 + 30.4983i 0.823676 + 1.42665i 0.902927 + 0.429794i \(0.141414\pi\)
−0.0792505 + 0.996855i \(0.525253\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −11.6988 20.2629i −0.544867 0.943736i −0.998615 0.0526068i \(-0.983247\pi\)
0.453749 0.891130i \(-0.350086\pi\)
\(462\) 0 0
\(463\) −2.67980 + 4.64155i −0.124541 + 0.215711i −0.921553 0.388252i \(-0.873079\pi\)
0.797013 + 0.603963i \(0.206412\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −31.3997 −1.45300 −0.726502 0.687164i \(-0.758855\pi\)
−0.726502 + 0.687164i \(0.758855\pi\)
\(468\) 0 0
\(469\) 0.723484 3.10510i 0.0334074 0.143380i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −10.2632 5.92544i −0.471901 0.272452i
\(474\) 0 0
\(475\) −6.71660 + 3.87783i −0.308179 + 0.177927i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 10.7485 + 18.6169i 0.491109 + 0.850626i 0.999948 0.0102359i \(-0.00325824\pi\)
−0.508838 + 0.860862i \(0.669925\pi\)
\(480\) 0 0
\(481\) 4.45296 + 2.57092i 0.203038 + 0.117224i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 20.5786i 0.934425i
\(486\) 0 0
\(487\) −2.61173 −0.118349 −0.0591744 0.998248i \(-0.518847\pi\)
−0.0591744 + 0.998248i \(0.518847\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −11.1818 6.45580i −0.504626 0.291346i 0.225996 0.974128i \(-0.427437\pi\)
−0.730622 + 0.682782i \(0.760770\pi\)
\(492\) 0 0
\(493\) −1.79068 + 1.03385i −0.0806482 + 0.0465622i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −8.61516 28.3840i −0.386443 1.27320i
\(498\) 0 0
\(499\) −0.117182 + 0.202964i −0.00524577 + 0.00908593i −0.868636 0.495450i \(-0.835003\pi\)
0.863391 + 0.504536i \(0.168336\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 13.6460 0.608445 0.304223 0.952601i \(-0.401603\pi\)
0.304223 + 0.952601i \(0.401603\pi\)
\(504\) 0 0
\(505\) 25.6991 1.14359
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.71269 2.96647i 0.0759136 0.131486i −0.825570 0.564300i \(-0.809146\pi\)
0.901483 + 0.432814i \(0.142479\pi\)
\(510\) 0 0
\(511\) 1.41649 + 4.66685i 0.0626619 + 0.206449i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 31.8563 18.3922i 1.40376 0.810459i
\(516\) 0 0
\(517\) −8.86435 5.11784i −0.389854 0.225082i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 37.3500 1.63633 0.818167 0.574981i \(-0.194991\pi\)
0.818167 + 0.574981i \(0.194991\pi\)
\(522\) 0 0
\(523\) 8.99132i 0.393163i 0.980487 + 0.196581i \(0.0629840\pi\)
−0.980487 + 0.196581i \(0.937016\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.00489 + 1.15753i 0.0873346 + 0.0504226i
\(528\) 0 0
\(529\) 16.7648 + 29.0376i 0.728906 + 1.26250i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.87021 3.38917i 0.254267 0.146801i
\(534\) 0 0
\(535\) 26.9938 + 15.5849i 1.16704 + 0.673793i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 3.95423 8.02488i 0.170321 0.345656i
\(540\) 0 0
\(541\) 7.90934 0.340049 0.170025 0.985440i \(-0.445615\pi\)
0.170025 + 0.985440i \(0.445615\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −3.28741 + 5.69396i −0.140817 + 0.243902i
\(546\) 0 0
\(547\) 17.2958 + 29.9573i 0.739516 + 1.28088i 0.952713 + 0.303871i \(0.0982790\pi\)
−0.213197 + 0.977009i \(0.568388\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −13.2843 23.0090i −0.565928 0.980217i
\(552\) 0 0
\(553\) 33.0124 + 30.9095i 1.40383 + 1.31441i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.42861i 0.102903i 0.998675 + 0.0514517i \(0.0163848\pi\)
−0.998675 + 0.0514517i \(0.983615\pi\)
\(558\) 0 0
\(559\) 27.0682i 1.14486i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 8.53869 14.7894i 0.359863 0.623301i −0.628075 0.778153i \(-0.716157\pi\)
0.987938 + 0.154852i \(0.0494901\pi\)
\(564\) 0 0
\(565\) 7.03283 4.06041i 0.295873 0.170823i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −19.9471 + 11.5165i −0.836228 + 0.482796i −0.855980 0.517008i \(-0.827046\pi\)
0.0197523 + 0.999805i \(0.493712\pi\)
\(570\) 0 0
\(571\) −4.11356 + 7.12490i −0.172147 + 0.298168i −0.939170 0.343452i \(-0.888404\pi\)
0.767023 + 0.641619i \(0.221737\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.54919i 0.398229i
\(576\) 0 0
\(577\) 11.3064i 0.470691i 0.971912 + 0.235346i \(0.0756222\pi\)
−0.971912 + 0.235346i \(0.924378\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.869937 + 0.814523i 0.0360911 + 0.0337921i
\(582\) 0 0
\(583\) 6.60389 + 11.4383i 0.273505 + 0.473725i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.2862 29.9407i −0.713480 1.23578i −0.963543 0.267553i \(-0.913785\pi\)
0.250063 0.968229i \(-0.419549\pi\)
\(588\) 0 0
\(589\) −14.8734 + 25.7615i −0.612849 + 1.06149i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −9.64649 −0.396134 −0.198067 0.980188i \(-0.563466\pi\)
−0.198067 + 0.980188i \(0.563466\pi\)
\(594\) 0 0
\(595\) 0.551039 2.36499i 0.0225904 0.0969553i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 5.22049 + 3.01405i 0.213303 + 0.123151i 0.602846 0.797858i \(-0.294033\pi\)
−0.389542 + 0.921009i \(0.627367\pi\)
\(600\) 0 0
\(601\) −23.4624 + 13.5460i −0.957052 + 0.552555i −0.895265 0.445535i \(-0.853014\pi\)
−0.0617879 + 0.998089i \(0.519680\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −9.04491 15.6662i −0.367728 0.636923i
\(606\) 0 0
\(607\) 16.1410 + 9.31904i 0.655145 + 0.378248i 0.790425 0.612559i \(-0.209860\pi\)
−0.135280 + 0.990807i \(0.543193\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 23.3789i 0.945811i
\(612\) 0 0
\(613\) 24.7398 0.999232 0.499616 0.866247i \(-0.333474\pi\)
0.499616 + 0.866247i \(0.333474\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 42.5759 + 24.5812i 1.71404 + 0.989603i 0.928934 + 0.370245i \(0.120726\pi\)
0.785109 + 0.619358i \(0.212607\pi\)
\(618\) 0 0
\(619\) −0.334357 + 0.193041i −0.0134389 + 0.00775898i −0.506704 0.862120i \(-0.669136\pi\)
0.493265 + 0.869879i \(0.335803\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −28.5020 + 8.65098i −1.14191 + 0.346594i
\(624\) 0 0
\(625\) 8.51828 14.7541i 0.340731 0.590164i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0.837104 0.0333775
\(630\) 0 0
\(631\) −45.6531 −1.81742 −0.908710 0.417429i \(-0.862931\pi\)
−0.908710 + 0.417429i \(0.862931\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 16.5926 28.7392i 0.658456 1.14048i
\(636\) 0 0
\(637\) 20.3895 1.34297i 0.807863 0.0532104i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 34.2119 19.7523i 1.35129 0.780167i 0.362859 0.931844i \(-0.381801\pi\)
0.988430 + 0.151677i \(0.0484674\pi\)
\(642\) 0 0
\(643\) −23.1404 13.3601i −0.912570 0.526873i −0.0313129 0.999510i \(-0.509969\pi\)
−0.881257 + 0.472637i \(0.843302\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 40.2634 1.58292 0.791459 0.611222i \(-0.209322\pi\)
0.791459 + 0.611222i \(0.209322\pi\)
\(648\) 0 0
\(649\) 4.45450i 0.174854i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 36.6920 + 21.1841i 1.43587 + 0.828998i 0.997559 0.0698266i \(-0.0222446\pi\)
0.438308 + 0.898825i \(0.355578\pi\)
\(654\) 0 0
\(655\) −7.73332 13.3945i −0.302166 0.523366i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 33.3031 19.2276i 1.29731 0.749000i 0.317368 0.948302i \(-0.397201\pi\)
0.979938 + 0.199302i \(0.0638676\pi\)
\(660\) 0 0
\(661\) −14.2400 8.22149i −0.553874 0.319779i 0.196809 0.980442i \(-0.436942\pi\)
−0.750683 + 0.660663i \(0.770275\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 30.3885 + 7.08048i 1.17842 + 0.274569i
\(666\) 0 0
\(667\) 32.7126 1.26664
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.14477 + 5.44690i −0.121402 + 0.210275i
\(672\) 0 0
\(673\) −16.8254 29.1424i −0.648570 1.12336i −0.983465 0.181100i \(-0.942034\pi\)
0.334895 0.942255i \(-0.391299\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 21.0119 + 36.3938i 0.807555 + 1.39873i 0.914553 + 0.404466i \(0.132543\pi\)
−0.106998 + 0.994259i \(0.534124\pi\)
\(678\) 0 0
\(679\) 19.2680 20.5789i 0.739438 0.789744i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 28.0238i 1.07230i −0.844122 0.536151i \(-0.819878\pi\)
0.844122 0.536151i \(-0.180122\pi\)
\(684\) 0 0
\(685\) 18.8272i 0.719351i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −15.0837 + 26.1258i −0.574644 + 0.995312i
\(690\) 0 0
\(691\) 4.58578 2.64760i 0.174451 0.100720i −0.410232 0.911981i \(-0.634552\pi\)
0.584683 + 0.811262i \(0.301219\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 13.0565 7.53818i 0.495262 0.285940i
\(696\) 0 0
\(697\) 0.551765 0.955685i 0.0208996 0.0361992i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 38.6055i 1.45811i 0.684455 + 0.729055i \(0.260040\pi\)
−0.684455 + 0.729055i \(0.739960\pi\)
\(702\) 0 0
\(703\) 10.7562i 0.405678i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 25.6994 + 24.0624i 0.966526 + 0.904960i
\(708\) 0 0
\(709\) 21.9037 + 37.9383i 0.822610 + 1.42480i 0.903732 + 0.428098i \(0.140816\pi\)
−0.0811228 + 0.996704i \(0.525851\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −18.3130 31.7190i −0.685826 1.18789i
\(714\) 0 0
\(715\) −3.60256 + 6.23981i −0.134728 + 0.233356i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −21.2855 −0.793813 −0.396907 0.917859i \(-0.629916\pi\)
−0.396907 + 0.917859i \(0.629916\pi\)
\(720\) 0 0
\(721\) 49.0776 + 11.4350i 1.82775 + 0.425862i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −4.78559 2.76296i −0.177733 0.102614i
\(726\) 0 0
\(727\) −36.2267 + 20.9155i −1.34358 + 0.775713i −0.987330 0.158679i \(-0.949276\pi\)
−0.356245 + 0.934393i \(0.615943\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −2.20338 3.81637i −0.0814950 0.141154i
\(732\) 0 0
\(733\) −36.6457 21.1574i −1.35354 0.781466i −0.364795 0.931088i \(-0.618861\pi\)
−0.988743 + 0.149622i \(0.952194\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.54010i 0.0567302i
\(738\) 0 0
\(739\) −20.4280 −0.751456 −0.375728 0.926730i \(-0.622607\pi\)
−0.375728 + 0.926730i \(0.622607\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −7.44740 4.29976i −0.273219 0.157743i 0.357131 0.934054i \(-0.383755\pi\)
−0.630349 + 0.776312i \(0.717088\pi\)
\(744\) 0 0
\(745\) 18.5846 10.7298i 0.680887 0.393110i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 12.4018 + 40.8598i 0.453153 + 1.49298i
\(750\) 0 0
\(751\) −20.0359 + 34.7032i −0.731120 + 1.26634i 0.225285 + 0.974293i \(0.427669\pi\)
−0.956405 + 0.292043i \(0.905665\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −7.28990 −0.265307
\(756\) 0 0
\(757\) 10.6186 0.385941 0.192970 0.981205i \(-0.438188\pi\)
0.192970 + 0.981205i \(0.438188\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.36550 2.36512i 0.0494993 0.0857354i −0.840214 0.542255i \(-0.817571\pi\)
0.889713 + 0.456519i \(0.150904\pi\)
\(762\) 0 0
\(763\) −8.61878 + 2.61599i −0.312021 + 0.0947052i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.81125 + 5.08718i −0.318156 + 0.183687i
\(768\) 0 0
\(769\) −5.44566 3.14405i −0.196376 0.113377i 0.398588 0.917130i \(-0.369500\pi\)
−0.594964 + 0.803753i \(0.702834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −15.6236 −0.561942 −0.280971 0.959716i \(-0.590656\pi\)
−0.280971 + 0.959716i \(0.590656\pi\)
\(774\) 0 0
\(775\) 6.18698i 0.222243i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 12.2799 + 7.08981i 0.439973 + 0.254019i
\(780\) 0 0
\(781\) 7.16426 + 12.4089i 0.256358 + 0.444024i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.85925 + 3.96019i −0.244817 + 0.141345i
\(786\) 0 0
\(787\) 39.7379 + 22.9427i 1.41650 + 0.817819i 0.995990 0.0894671i \(-0.0285164\pi\)
0.420514 + 0.907286i \(0.361850\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10.8347 + 2.52448i 0.385239 + 0.0897600i
\(792\) 0 0
\(793\) −14.3657 −0.510141
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −14.8057 + 25.6442i −0.524444 + 0.908364i 0.475151 + 0.879904i \(0.342394\pi\)
−0.999595 + 0.0284597i \(0.990940\pi\)
\(798\) 0 0
\(799\) −1.90307 3.29622i −0.0673259 0.116612i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −1.17794 2.04025i −0.0415685 0.0719987i
\(804\) 0 0
\(805\) −26.2579 + 28.0443i −0.925470 + 0.988432i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 27.7761i 0.976556i 0.872688 + 0.488278i \(0.162375\pi\)
−0.872688 + 0.488278i \(0.837625\pi\)
\(810\) 0 0
\(811\) 17.8221i 0.625820i 0.949783 + 0.312910i \(0.101304\pi\)
−0.949783 + 0.312910i \(0.898696\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −13.8929 + 24.0633i −0.486648 + 0.842899i
\(816\) 0 0
\(817\) 49.0377 28.3119i 1.71561 0.990510i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −0.242236 + 0.139855i −0.00845409 + 0.00488097i −0.504221 0.863575i \(-0.668220\pi\)
0.495767 + 0.868456i \(0.334887\pi\)
\(822\) 0 0
\(823\) 5.56224 9.63408i 0.193887 0.335823i −0.752648 0.658423i \(-0.771224\pi\)
0.946535 + 0.322600i \(0.104557\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 22.9832i 0.799205i −0.916688 0.399603i \(-0.869148\pi\)
0.916688 0.399603i \(-0.130852\pi\)
\(828\) 0 0
\(829\) 6.30082i 0.218837i 0.993996 + 0.109418i \(0.0348988\pi\)
−0.993996 + 0.109418i \(0.965101\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 2.76542 1.84908i 0.0958163 0.0640668i
\(834\) 0 0
\(835\) −15.5851 26.9942i −0.539345 0.934174i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 11.7701 + 20.3864i 0.406349 + 0.703816i 0.994477 0.104951i \(-0.0334685\pi\)
−0.588129 + 0.808767i \(0.700135\pi\)
\(840\) 0 0
\(841\) −5.03493 + 8.72075i −0.173618 + 0.300716i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 8.64999 0.297569
\(846\) 0 0
\(847\) 5.62349 24.1353i 0.193225 0.829300i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −11.4693 6.62182i −0.393164 0.226993i
\(852\) 0 0
\(853\) −1.56621 + 0.904252i −0.0536260 + 0.0309610i −0.526573 0.850130i \(-0.676523\pi\)
0.472947 + 0.881091i \(0.343190\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −0.704571 1.22035i −0.0240677 0.0416865i 0.853741 0.520698i \(-0.174328\pi\)
−0.877808 + 0.479012i \(0.840995\pi\)
\(858\) 0 0
\(859\) −35.4862 20.4879i −1.21077 0.699040i −0.247845 0.968800i \(-0.579722\pi\)
−0.962928 + 0.269760i \(0.913056\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 7.34316i 0.249964i −0.992159 0.124982i \(-0.960113\pi\)
0.992159 0.124982i \(-0.0398873\pi\)
\(864\) 0 0
\(865\) −2.68596 −0.0913255
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −18.9187 10.9227i −0.641774 0.370528i
\(870\) 0 0
\(871\) −3.04640 + 1.75884i −0.103223 + 0.0595960i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 30.6574 9.30519i 1.03641 0.314573i
\(876\) 0 0
\(877\) 1.80443 3.12536i 0.0609312 0.105536i −0.833951 0.551839i \(-0.813926\pi\)
0.894882 + 0.446303i \(0.147260\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −12.6937 −0.427660 −0.213830 0.976871i \(-0.568594\pi\)
−0.213830 + 0.976871i \(0.568594\pi\)
\(882\) 0 0
\(883\) 8.55621 0.287939 0.143970 0.989582i \(-0.454013\pi\)
0.143970 + 0.989582i \(0.454013\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −7.45990 + 12.9209i −0.250479 + 0.433842i −0.963658 0.267140i \(-0.913921\pi\)
0.713179 + 0.700982i \(0.247255\pi\)
\(888\) 0 0
\(889\) 43.5017 13.2037i 1.45900 0.442839i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 42.3542 24.4532i 1.41733 0.818295i
\(894\) 0 0
\(895\) 7.70388 + 4.44784i 0.257512 + 0.148675i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −21.1947 −0.706883
\(900\) 0 0
\(901\) 4.91133i 0.163620i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 27.3851 + 15.8108i 0.910312 + 0.525569i
\(906\) 0 0
\(907\) −16.1506 27.9737i −0.536273 0.928852i −0.999101 0.0424034i \(-0.986499\pi\)
0.462828 0.886448i \(-0.346835\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 13.3778 7.72366i 0.443225 0.255896i −0.261740 0.965139i \(-0.584296\pi\)
0.704965 + 0.709242i \(0.250963\pi\)
\(912\) 0 0
\(913\) −0.498544 0.287834i −0.0164994 0.00952593i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4.80803 20.6355i 0.158775 0.681444i
\(918\) 0 0
\(919\) 1.01879 0.0336069 0.0168034 0.999859i \(-0.494651\pi\)
0.0168034 + 0.999859i \(0.494651\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −16.3636 + 28.3427i −0.538616 + 0.932910i
\(924\) 0 0
\(925\) 1.11858 + 1.93744i 0.0367787 + 0.0637026i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −17.5872 30.4619i −0.577016 0.999421i −0.995819 0.0913443i \(-0.970884\pi\)
0.418803 0.908077i \(-0.362450\pi\)
\(930\) 0 0
\(931\) 23.7594 + 35.5338i 0.778684 + 1.16457i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 1.17301i 0.0383615i
\(936\) 0 0
\(937\) 19.5780i 0.639586i −0.947487 0.319793i \(-0.896387\pi\)
0.947487 0.319793i \(-0.103613\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 23.2160 40.2113i 0.756820 1.31085i −0.187645 0.982237i \(-0.560085\pi\)
0.944464 0.328614i \(-0.106581\pi\)
\(942\) 0 0
\(943\) −15.1197 + 8.72936i −0.492365 + 0.284267i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −32.1063 + 18.5366i −1.04331 + 0.602358i −0.920770 0.390105i \(-0.872439\pi\)
−0.122544 + 0.992463i \(0.539105\pi\)
\(948\) 0 0
\(949\) 2.69048 4.66006i 0.0873368 0.151272i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 2.73116i 0.0884709i 0.999021 + 0.0442354i \(0.0140852\pi\)
−0.999021 + 0.0442354i \(0.985915\pi\)
\(954\) 0 0
\(955\) 28.5344i 0.923352i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 17.6282 18.8275i 0.569244 0.607971i
\(960\) 0 0
\(961\) −3.63491 6.29585i −0.117255 0.203092i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 17.2257 + 29.8358i 0.554516 + 0.960450i
\(966\) 0 0
\(967\) −14.6811 + 25.4285i −0.472113 + 0.817724i −0.999491 0.0319070i \(-0.989842\pi\)
0.527378 + 0.849631i \(0.323175\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 17.1103 0.549094 0.274547 0.961574i \(-0.411472\pi\)
0.274547 + 0.961574i \(0.411472\pi\)
\(972\) 0 0
\(973\) 20.1148 + 4.68671i 0.644851 + 0.150249i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −36.4251 21.0301i −1.16534 0.672812i −0.212765 0.977103i \(-0.568247\pi\)
−0.952579 + 0.304292i \(0.901580\pi\)
\(978\) 0 0
\(979\) 12.4605 7.19406i 0.398238 0.229923i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −3.87731 6.71569i −0.123667 0.214197i 0.797544 0.603261i \(-0.206132\pi\)
−0.921211 + 0.389063i \(0.872799\pi\)
\(984\) 0 0
\(985\) 13.3863 + 7.72860i 0.426524 + 0.246254i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 69.7184i 2.21692i
\(990\) 0 0
\(991\) 11.5135 0.365738 0.182869 0.983137i \(-0.441462\pi\)
0.182869 + 0.983137i \(0.441462\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −27.2683 15.7434i −0.864464 0.499099i
\(996\) 0 0
\(997\) 15.0836 8.70850i 0.477701 0.275801i −0.241757 0.970337i \(-0.577724\pi\)
0.719458 + 0.694536i \(0.244390\pi\)
\(998\) 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 3024.2.cc.d.881.8 48
3.2 odd 2 1008.2.cc.d.545.20 48
4.3 odd 2 1512.2.bu.a.881.8 48
7.6 odd 2 inner 3024.2.cc.d.881.17 48
9.2 odd 6 inner 3024.2.cc.d.2897.17 48
9.7 even 3 1008.2.cc.d.209.5 48
12.11 even 2 504.2.bu.a.41.5 48
21.20 even 2 1008.2.cc.d.545.5 48
28.27 even 2 1512.2.bu.a.881.17 48
36.7 odd 6 504.2.bu.a.209.20 yes 48
36.11 even 6 1512.2.bu.a.1385.17 48
36.23 even 6 4536.2.k.a.3401.16 48
36.31 odd 6 4536.2.k.a.3401.33 48
63.20 even 6 inner 3024.2.cc.d.2897.8 48
63.34 odd 6 1008.2.cc.d.209.20 48
84.83 odd 2 504.2.bu.a.41.20 yes 48
252.83 odd 6 1512.2.bu.a.1385.8 48
252.139 even 6 4536.2.k.a.3401.15 48
252.167 odd 6 4536.2.k.a.3401.34 48
252.223 even 6 504.2.bu.a.209.5 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.bu.a.41.5 48 12.11 even 2
504.2.bu.a.41.20 yes 48 84.83 odd 2
504.2.bu.a.209.5 yes 48 252.223 even 6
504.2.bu.a.209.20 yes 48 36.7 odd 6
1008.2.cc.d.209.5 48 9.7 even 3
1008.2.cc.d.209.20 48 63.34 odd 6
1008.2.cc.d.545.5 48 21.20 even 2
1008.2.cc.d.545.20 48 3.2 odd 2
1512.2.bu.a.881.8 48 4.3 odd 2
1512.2.bu.a.881.17 48 28.27 even 2
1512.2.bu.a.1385.8 48 252.83 odd 6
1512.2.bu.a.1385.17 48 36.11 even 6
3024.2.cc.d.881.8 48 1.1 even 1 trivial
3024.2.cc.d.881.17 48 7.6 odd 2 inner
3024.2.cc.d.2897.8 48 63.20 even 6 inner
3024.2.cc.d.2897.17 48 9.2 odd 6 inner
4536.2.k.a.3401.15 48 252.139 even 6
4536.2.k.a.3401.16 48 36.23 even 6
4536.2.k.a.3401.33 48 36.31 odd 6
4536.2.k.a.3401.34 48 252.167 odd 6