Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 8.19303593168 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.493592650\) \(a_{3}=-0.577350269\) \(a_{4}=-0.756366296\) \(a_{5}=-1.060977119\)
\(a_{6}=-0.284975849\) \(a_{7}=+0.451277637\) \(a_{8}=-0.866929492\) \(a_{9}=+0.333333325\) \(a_{10}=-0.523690462\)
\(a_{11}=+0.865827744\) \(a_{12}=+0.436689668\) \(a_{13}=-1.616217302\) \(a_{14}=+0.222786646\) \(a_{15}=+0.612555425\)
\(a_{16}=+0.328456270\) \(a_{17}=-0.040383047\) \(a_{18}=+0.164530883\) \(a_{19}=-1.403730737\) \(a_{20}=+0.802487334\)
\(a_{21}=-0.260545265\) \(a_{22}=+0.427366333\) \(a_{23}=-0.047995358\) \(a_{24}=+0.500521977\) \(a_{25}=+0.125672446\)
\(a_{26}=-0.797749193\) \(a_{27}=-0.192450090\) \(a_{28}=-0.341331195\) \(a_{29}=+0.259056160\) \(a_{30}=+0.302352855\)
\(a_{31}=+0.060968855\) \(a_{32}=+1.029053095\) \(a_{33}=-0.499886024\) \(a_{34}=-0.019932775\) \(a_{35}=-0.478795247\)
\(a_{36}=-0.252122099\) \(a_{37}=-0.410641768\) \(a_{38}=-0.692871174\) \(a_{39}=+0.933119065\) \(a_{40}=+0.919792356\)
\(a_{41}=+0.544222039\) \(a_{42}=-0.128603228\) \(a_{43}=-0.366256787\) \(a_{44}=-0.654883111\) \(a_{45}=-0.353659040\)
\(a_{46}=-0.023690157\) \(a_{47}=+0.709292303\) \(a_{48}=-0.189634315\) \(a_{49}=-0.796348494\) \(a_{50}=+0.062030994\)
\(a_{51}=+0.023315162\) \(a_{52}=+1.222446496\) \(a_{53}=+0.618272539\) \(a_{54}=-0.094991956\) \(a_{55}=-0.918623701\)
\(a_{56}=-0.391225888\) \(a_{57}=+0.810444351\) \(a_{58}=+0.127868220\) \(a_{59}=-1.600850395\) \(a_{60}=-0.463316278\)
\(a_{61}=+0.741218568\) \(a_{62}=+0.030093779\) \(a_{63}=+0.150425879\) \(a_{64}=+0.179476773\) \(a_{65}=+1.714761436\)
\(a_{66}=-0.246740067\) \(a_{67}=-0.763485301\) \(a_{68}=+0.030544376\) \(a_{69}=+0.027710133\) \(a_{70}=-0.236329815\)
\(a_{71}=-0.320729214\) \(a_{72}=-0.288976497\) \(a_{73}=-0.647953977\) \(a_{74}=-0.202689759\) \(a_{75}=-0.072557022\)
\(a_{76}=+1.061734620\) \(a_{77}=+0.390728813\) \(a_{78}=+0.460580711\) \(a_{79}=+0.238585536\) \(a_{80}=-0.348484591\)
\(a_{81}=+0.111111117\) \(a_{82}=+0.268624008\) \(a_{83}=-1.016313264\) \(a_{84}=+0.197067640\) \(a_{85}=+0.042845483\)
\(a_{86}=-0.180781629\) \(a_{87}=-0.149566117\) \(a_{88}=-0.750611853\) \(a_{89}=+0.974928999\) \(a_{90}=-0.174563494\)
\(a_{91}=-0.729359136\) \(a_{92}=+0.036302130\) \(a_{93}=-0.035200556\) \(a_{94}=+0.350101245\) \(a_{95}=+1.489326360\)
\(a_{96}=-0.594123604\) \(a_{97}=+1.226114887\) \(a_{98}=-0.393072552\) \(a_{99}=+0.288608847\) \(a_{100}=-0.095053283\)

Showing 100 of 5000 available coefficients

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