Properties

Level $27$
Weight $0$
Character 27.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 27 = 3^{3} \)
Weight: \( 0 \)
Character: 27.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.45034943833 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.901075184\) \(a_{3}=+0.000000000\) \(a_{4}=-0.188063510\) \(a_{5}=-0.403991641\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.864719577\) \(a_{8}=-1.070534541\) \(a_{9}=+0.000000000\) \(a_{10}=-0.364026837\)
\(a_{11}=+0.633330783\) \(a_{12}=+0.000000000\) \(a_{13}=-0.158019273\) \(a_{14}=+0.779177348\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.776568611\) \(a_{17}=+0.588942167\) \(a_{18}=+0.000000000\) \(a_{19}=+1.188427088\) \(a_{20}=+0.075976084\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.570678658\) \(a_{23}=-1.341503034\) \(a_{24}=+0.000000000\) \(a_{25}=-0.836790742\)
\(a_{26}=-0.142387291\) \(a_{27}=+0.000000000\) \(a_{28}=-0.162622291\) \(a_{29}=-0.784841223\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.630486351\) \(a_{32}=+0.370787858\) \(a_{33}=+0.000000000\) \(a_{34}=+0.530681190\) \(a_{35}=-0.349339459\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.134192709\) \(a_{38}=+1.070862167\) \(a_{39}=+0.000000000\) \(a_{40}=+0.432487019\)
\(a_{41}=+1.391897510\) \(a_{42}=+0.000000000\) \(a_{43}=+1.290888273\) \(a_{44}=-0.119106400\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.208795053\) \(a_{47}=+0.101682414\) \(a_{48}=+0.000000000\) \(a_{49}=-0.252260068\) \(a_{50}=-0.754011406\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.029717672\) \(a_{53}=+0.489466792\) \(a_{54}=+0.000000000\) \(a_{55}=-0.255860356\)
\(a_{56}=-0.925712180\) \(a_{57}=+0.000000000\) \(a_{58}=-0.707200993\) \(a_{59}=-0.944222954\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.044089791\) \(a_{62}=-0.568115612\) \(a_{63}=+0.000000000\) \(a_{64}=+1.110676283\) \(a_{65}=+0.063838457\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.152722086\) \(a_{68}=-0.110758518\) \(a_{69}=+0.000000000\) \(a_{70}=-0.314781152\)
\(a_{71}=+0.891682656\) \(a_{72}=+0.000000000\) \(a_{73}=-0.217937442\) \(a_{74}=-0.120917745\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.223499774\) \(a_{77}=+0.547653490\) \(a_{78}=+0.000000000\) \(a_{79}=-1.536090735\) \(a_{80}=+0.313727242\)
\(a_{81}=+0.000000000\) \(a_{82}=+1.254204330\) \(a_{83}=+1.146603097\) \(a_{84}=+0.000000000\) \(a_{85}=-0.237927705\)
\(a_{86}=+1.163187440\) \(a_{87}=+0.000000000\) \(a_{88}=-0.678002447\) \(a_{89}=-1.293465602\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.136642379\) \(a_{92}=+0.252287745\) \(a_{93}=+0.000000000\) \(a_{94}=+0.091623468\) \(a_{95}=-0.480114597\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.883359896\) \(a_{98}=-0.227305251\) \(a_{99}=+0.000000000\) \(a_{100}=+0.157369839\)

Showing 100 of 2000 available coefficients

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