Properties

Level $12$
Weight $0$
Character 12.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 12 = 2^{2} \cdot 3 \)
Weight: \( 0 \)
Character: 12.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 12.1738052763 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-0.888798055\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.740996050\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.998689210\) \(a_{12}=+0.000000000\) \(a_{13}=-1.302548916\) \(a_{14}=+0.000000000\) \(a_{15}=+0.513147796\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.746892666\) \(a_{18}=+0.000000000\) \(a_{19}=-1.387948366\) \(a_{20}=+0.000000000\)
\(a_{21}=+1.005164538\) \(a_{22}=+0.000000000\) \(a_{23}=-1.331963931\) \(a_{24}=+0.000000000\) \(a_{25}=-0.210038017\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-0.581407263\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.458446182\) \(a_{32}=+0.000000000\) \(a_{33}=+0.576593484\) \(a_{34}=+0.000000000\) \(a_{35}=+1.547393903\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.330876686\) \(a_{38}=+0.000000000\) \(a_{39}=+0.752026967\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.343952241\) \(a_{42}=+0.000000000\) \(a_{43}=-0.184253752\) \(a_{44}=+0.000000000\) \(a_{45}=-0.296266018\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.470909188\) \(a_{48}=+0.000000000\) \(a_{49}=+2.031067245\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.431218682\) \(a_{52}=+0.000000000\) \(a_{53}=-0.475459348\) \(a_{54}=+0.000000000\) \(a_{55}=+0.887633028\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.801332363\) \(a_{58}=+0.000000000\) \(a_{59}=-0.685878892\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.940922761\) \(a_{62}=+0.000000000\) \(a_{63}=-0.580332017\) \(a_{64}=+0.000000000\) \(a_{65}=+1.157702943\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.113566695\) \(a_{68}=+0.000000000\) \(a_{69}=+0.769009734\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.332656607\) \(a_{72}=+0.000000000\) \(a_{73}=-0.785244326\) \(a_{74}=+0.000000000\) \(a_{75}=+0.121265506\)
\(a_{76}=+0.000000000\) \(a_{77}=+1.738713970\) \(a_{78}=+0.000000000\) \(a_{79}=-0.690807796\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-1.577061555\) \(a_{84}=+0.000000000\) \(a_{85}=-0.663836749\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.335675640\) \(a_{88}=+0.000000000\) \(a_{89}=-1.434338940\) \(a_{90}=+0.000000000\)
\(a_{91}=+2.267732517\) \(a_{92}=+0.000000000\) \(a_{93}=-0.264684027\) \(a_{94}=+0.000000000\) \(a_{95}=+1.233605807\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.335044436\) \(a_{98}=+0.000000000\) \(a_{99}=-0.332896403\) \(a_{100}=+0.000000000\)

Showing 100 of 190 available coefficients

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