Properties

Level $27$
Weight $0$
Character 27.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 27 = 3^{3} \)
Weight: \( 0 \)
Character: 27.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 1.45034943837 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.901075184\) \(a_{3}=+0.000000000\) \(a_{4}=-0.188063510\) \(a_{5}=+0.403991636\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.864719577\) \(a_{8}=+1.070534551\) \(a_{9}=+0.000000000\) \(a_{10}=-0.364026845\)
\(a_{11}=-0.633330787\) \(a_{12}=+0.000000000\) \(a_{13}=-0.158019261\) \(a_{14}=-0.779177363\) \(a_{15}=+0.000000000\)
\(a_{16}=-0.776568605\) \(a_{17}=-0.588942151\) \(a_{18}=+0.000000000\) \(a_{19}=+1.188427074\) \(a_{20}=-0.075976085\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.570678649\) \(a_{23}=+1.341503054\) \(a_{24}=+0.000000000\) \(a_{25}=-0.836790752\)
\(a_{26}=+0.142387213\) \(a_{27}=+0.000000000\) \(a_{28}=-0.162622150\) \(a_{29}=+0.784841243\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.630486507\) \(a_{32}=-0.370787789\) \(a_{33}=+0.000000000\) \(a_{34}=+0.530681164\) \(a_{35}=+0.349339446\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.134192737\) \(a_{38}=-1.070862145\) \(a_{39}=+0.000000000\) \(a_{40}=+0.432487060\)
\(a_{41}=-1.391897646\) \(a_{42}=+0.000000000\) \(a_{43}=+1.290888414\) \(a_{44}=+0.119106349\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.208795126\) \(a_{47}=-0.101682375\) \(a_{48}=+0.000000000\) \(a_{49}=-0.252260038\) \(a_{50}=+0.754011349\)
\(a_{51}=+0.000000000\) \(a_{52}=+0.029717592\) \(a_{53}=-0.489466728\) \(a_{54}=+0.000000000\) \(a_{55}=-0.255860308\)
\(a_{56}=+0.925712227\) \(a_{57}=+0.000000000\) \(a_{58}=-0.707200946\) \(a_{59}=+0.944222964\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.044089810\) \(a_{62}=+0.568115626\) \(a_{63}=+0.000000000\) \(a_{64}=+1.110676359\) \(a_{65}=-0.063838403\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.152721885\) \(a_{68}=+0.110758573\) \(a_{69}=+0.000000000\) \(a_{70}=-0.314781155\)
\(a_{71}=-0.891682821\) \(a_{72}=+0.000000000\) \(a_{73}=-0.217937412\) \(a_{74}=+0.120917675\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.223499746\) \(a_{77}=-0.547653552\) \(a_{78}=+0.000000000\) \(a_{79}=-1.536090732\) \(a_{80}=-0.313727200\)
\(a_{81}=+0.000000000\) \(a_{82}=+1.254204389\) \(a_{83}=-1.146603004\) \(a_{84}=+0.000000000\) \(a_{85}=-0.237927637\)
\(a_{86}=-1.163187421\) \(a_{87}=+0.000000000\) \(a_{88}=-0.678002556\) \(a_{89}=+1.293465576\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.136642340\) \(a_{92}=-0.252287863\) \(a_{93}=+0.000000000\) \(a_{94}=+0.091623365\) \(a_{95}=+0.480114602\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.883359914\) \(a_{98}=+0.227305333\) \(a_{99}=+0.000000000\) \(a_{100}=+0.157369839\)

Showing 100 of 2000 available coefficients

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