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: \( 2.47697015662 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.663558145\) \(a_{3}=+0.000000000\) \(a_{4}=+1.767425703\) \(a_{5}=+0.030694236\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.214402029\) \(a_{8}=+1.276657280\) \(a_{9}=+0.000000000\) \(a_{10}=+0.051061646\)
\(a_{11}=+0.502305547\) \(a_{12}=+0.000000000\) \(a_{13}=-0.070570502\) \(a_{14}=-2.020228388\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.356367913\) \(a_{17}=+0.904557022\) \(a_{18}=+0.000000000\) \(a_{19}=+0.867477060\) \(a_{20}=+0.054249781\)
\(a_{21}=+0.000000000\) \(a_{22}=+0.835614484\) \(a_{23}=+1.437738940\) \(a_{24}=+0.000000000\) \(a_{25}=-0.999057864\)
\(a_{26}=-0.117398134\) \(a_{27}=+0.000000000\) \(a_{28}=-2.146365361\) \(a_{29}=-1.517387266\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.044810032\) \(a_{32}=-0.683818535\) \(a_{33}=+0.000000000\) \(a_{34}=+1.504783202\) \(a_{35}=-0.037275142\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.012478512\) \(a_{38}=+1.443098530\) \(a_{39}=+0.000000000\) \(a_{40}=+0.039186020\)
\(a_{41}=-0.151760484\) \(a_{42}=+0.000000000\) \(a_{43}=-1.077932745\) \(a_{44}=+0.887787734\) \(a_{45}=+0.000000000\)
\(a_{46}=+2.391762325\) \(a_{47}=+0.866084581\) \(a_{48}=+0.000000000\) \(a_{49}=+0.474772289\) \(a_{50}=-1.661990847\)
\(a_{51}=+0.000000000\) \(a_{52}=-0.124728119\) \(a_{53}=-0.746559415\) \(a_{54}=+0.000000000\) \(a_{55}=+0.015417885\)
\(a_{56}=-1.550375191\) \(a_{57}=+0.000000000\) \(a_{58}=-2.524261948\) \(a_{59}=+1.551218715\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.413948155\) \(a_{62}=-0.074544094\) \(a_{63}=+0.000000000\) \(a_{64}=-1.493939803\) \(a_{65}=-0.002166103\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.563627500\) \(a_{68}=+1.598737331\) \(a_{69}=+0.000000000\) \(a_{70}=-0.062009368\)
\(a_{71}=+0.404171555\) \(a_{72}=+0.000000000\) \(a_{73}=+0.730418014\) \(a_{74}=-0.020758767\) \(a_{75}=+0.000000000\)
\(a_{76}=+1.533201293\) \(a_{77}=-0.610000845\) \(a_{78}=+0.000000000\) \(a_{79}=-0.586703532\) \(a_{80}=+0.010938420\)
\(a_{81}=+0.000000000\) \(a_{82}=-0.252462417\) \(a_{83}=-0.909322120\) \(a_{84}=+0.000000000\) \(a_{85}=+0.027764581\)
\(a_{86}=-1.793203784\) \(a_{87}=+0.000000000\) \(a_{88}=+0.641272800\) \(a_{89}=-0.907252757\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.085700961\) \(a_{92}=+2.541099709\) \(a_{93}=+0.000000000\) \(a_{94}=+1.440782471\) \(a_{95}=+0.026631324\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.119487754\) \(a_{98}=+0.789797482\) \(a_{99}=+0.000000000\) \(a_{100}=-1.765757636\)

Showing 100 of 2000 available coefficients

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