Properties

Level $63$
Weight $0$
Character 63.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 63 = 3^{2} \cdot 7 \)
Weight: \( 0 \)
Character: 63.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.92400721823 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.378351052\) \(a_{3}=+0.000000000\) \(a_{4}=-0.856850481\) \(a_{5}=-0.526858200\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.377964473\) \(a_{8}=+0.702541334\) \(a_{9}=+0.000000000\) \(a_{10}=+0.199337354\)
\(a_{11}=-0.293224136\) \(a_{12}=+0.000000000\) \(a_{13}=+0.344102309\) \(a_{14}=-0.143003256\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.591043228\) \(a_{17}=+1.185899707\) \(a_{18}=+0.000000000\) \(a_{19}=-0.387933322\) \(a_{20}=+0.451438702\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.110941661\) \(a_{23}=+0.387942068\) \(a_{24}=+0.000000000\) \(a_{25}=-0.722420437\)
\(a_{26}=-0.130191471\) \(a_{27}=+0.000000000\) \(a_{28}=-0.323859041\) \(a_{29}=-1.795710314\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.242013027\) \(a_{32}=-0.926163161\) \(a_{33}=+0.000000000\) \(a_{34}=-0.448686402\) \(a_{35}=-0.199133682\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.842517923\) \(a_{38}=+0.146774981\) \(a_{39}=+0.000000000\) \(a_{40}=-0.370139662\)
\(a_{41}=-0.034460560\) \(a_{42}=+0.000000000\) \(a_{43}=+0.657715161\) \(a_{44}=+0.251249242\) \(a_{45}=+0.000000000\)
\(a_{46}=-0.146778290\) \(a_{47}=+1.220230557\) \(a_{48}=+0.000000000\) \(a_{49}=+0.142857143\) \(a_{50}=+0.273328533\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.294844229\) \(a_{53}=+0.039758451\) \(a_{54}=+0.000000000\) \(a_{55}=+0.154487541\)
\(a_{56}=+0.265535665\) \(a_{57}=+0.000000000\) \(a_{58}=+0.679408887\) \(a_{59}=+0.113229057\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.002747748\) \(a_{62}=-0.469916936\) \(a_{63}=+0.000000000\) \(a_{64}=-0.240628422\) \(a_{65}=-0.181293123\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.104528136\) \(a_{68}=-1.016138735\) \(a_{69}=+0.000000000\) \(a_{70}=+0.075342438\)
\(a_{71}=+1.854174946\) \(a_{72}=+0.000000000\) \(a_{73}=-0.679742133\) \(a_{74}=+0.318767543\) \(a_{75}=+0.000000000\)
\(a_{76}=+0.332400854\) \(a_{77}=-0.110828306\) \(a_{78}=+0.000000000\) \(a_{79}=-0.443896771\) \(a_{80}=-0.311395971\)
\(a_{81}=+0.000000000\) \(a_{82}=+0.013038189\) \(a_{83}=+0.346650245\) \(a_{84}=+0.000000000\) \(a_{85}=-0.624800985\)
\(a_{86}=-0.248847223\) \(a_{87}=+0.000000000\) \(a_{88}=-0.206002076\) \(a_{89}=-0.774701762\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.130058448\) \(a_{92}=-0.332408348\) \(a_{93}=+0.000000000\) \(a_{94}=-0.461675515\) \(a_{95}=+0.204385852\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.668992169\) \(a_{98}=-0.054050150\) \(a_{99}=+0.000000000\) \(a_{100}=+0.619006299\)

Showing 100 of 448 available coefficients

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