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: \( 2.7376477992 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.713510788\) \(a_{3}=+0.000000000\) \(a_{4}=+1.936119219\) \(a_{5}=-0.682281347\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.498388759\) \(a_{8}=+1.604050381\) \(a_{9}=+0.000000000\) \(a_{10}=-1.169096448\)
\(a_{11}=-0.740457607\) \(a_{12}=+0.000000000\) \(a_{13}=+1.368965775\) \(a_{14}=+0.853994515\) \(a_{15}=+0.000000000\)
\(a_{16}=+0.812438413\) \(a_{17}=-0.656466572\) \(a_{18}=+0.000000000\) \(a_{19}=-0.492140468\) \(a_{20}=-1.320978028\)
\(a_{21}=+0.000000000\) \(a_{22}=-1.268782098\) \(a_{23}=-0.681731575\) \(a_{24}=+0.000000000\) \(a_{25}=-0.534492164\)
\(a_{26}=+2.345737624\) \(a_{27}=+0.000000000\) \(a_{28}=+0.964940055\) \(a_{29}=+0.670403610\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.964507679\) \(a_{32}=-0.211928397\) \(a_{33}=+0.000000000\) \(a_{34}=-1.124862553\) \(a_{35}=-0.340041354\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.263094663\) \(a_{38}=-0.843288001\) \(a_{39}=+0.000000000\) \(a_{40}=-1.094413654\)
\(a_{41}=+1.267688990\) \(a_{42}=+0.000000000\) \(a_{43}=+0.205721399\) \(a_{44}=-1.433614205\) \(a_{45}=+0.000000000\)
\(a_{46}=-1.168154409\) \(a_{47}=-0.011937054\) \(a_{48}=+0.000000000\) \(a_{49}=-0.751608645\) \(a_{50}=-0.915858089\)
\(a_{51}=+0.000000000\) \(a_{52}=+2.650480949\) \(a_{53}=-0.930669059\) \(a_{54}=+0.000000000\) \(a_{55}=+0.505200414\)
\(a_{56}=+0.799440679\) \(a_{57}=+0.000000000\) \(a_{58}=+1.148743819\) \(a_{59}=+1.005307858\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.333497516\) \(a_{62}=+3.366205100\) \(a_{63}=+0.000000000\) \(a_{64}=-1.175580006\) \(a_{65}=-0.934019813\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.039437242\) \(a_{68}=-1.270997548\) \(a_{69}=+0.000000000\) \(a_{70}=-0.582664529\)
\(a_{71}=-0.422370322\) \(a_{72}=+0.000000000\) \(a_{73}=-0.351896779\) \(a_{74}=+0.450815545\) \(a_{75}=+0.000000000\)
\(a_{76}=-0.952842614\) \(a_{77}=-0.369035755\) \(a_{78}=+0.000000000\) \(a_{79}=+1.199022108\) \(a_{80}=-0.554311601\)
\(a_{81}=+0.000000000\) \(a_{82}=+2.172198732\) \(a_{83}=+0.141766019\) \(a_{84}=+0.000000000\) \(a_{85}=+0.447894894\)
\(a_{86}=+0.352505729\) \(a_{87}=+0.000000000\) \(a_{88}=-1.187731231\) \(a_{89}=-0.969014673\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.682276876\) \(a_{92}=-1.319913183\) \(a_{93}=+0.000000000\) \(a_{94}=-0.020453661\) \(a_{95}=+0.335779425\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.684154357\) \(a_{98}=-1.287890466\) \(a_{99}=+0.000000000\) \(a_{100}=-1.034840491\)

Showing 100 of 2000 available coefficients

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