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: \( 16.8153068636 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-0.243030751\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.473404670\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.204727451\) \(a_{12}=+0.000000000\) \(a_{13}=-0.875764923\) \(a_{14}=+0.000000000\) \(a_{15}=+0.140313869\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.116290484\) \(a_{18}=+0.000000000\) \(a_{19}=-1.226812660\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.273320313\) \(a_{22}=+0.000000000\) \(a_{23}=+0.794353437\) \(a_{24}=+0.000000000\) \(a_{25}=-0.940936054\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-0.698074691\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.083500939\) \(a_{32}=+0.000000000\) \(a_{33}=-0.695549718\) \(a_{34}=+0.000000000\) \(a_{35}=-0.115051892\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.250494784\) \(a_{38}=+0.000000000\) \(a_{39}=+0.505623114\) \(a_{40}=+0.000000000\)
\(a_{41}=+0.402396149\) \(a_{42}=+0.000000000\) \(a_{43}=+0.898855973\) \(a_{44}=+0.000000000\) \(a_{45}=-0.081010250\)
\(a_{46}=+0.000000000\) \(a_{47}=-0.679780928\) \(a_{48}=+0.000000000\) \(a_{49}=-0.775888019\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.644490612\) \(a_{52}=+0.000000000\) \(a_{53}=-1.299799827\) \(a_{54}=+0.000000000\) \(a_{55}=-0.292785817\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.708300620\) \(a_{58}=+0.000000000\) \(a_{59}=+0.522488946\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.152074672\) \(a_{62}=+0.000000000\) \(a_{63}=+0.157801557\) \(a_{64}=+0.000000000\) \(a_{65}=+0.212837807\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.289404358\) \(a_{68}=+0.000000000\) \(a_{69}=-0.458620170\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.415204229\) \(a_{72}=+0.000000000\) \(a_{73}=+1.966557061\) \(a_{74}=+0.000000000\) \(a_{75}=+0.543249684\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.570323601\) \(a_{78}=+0.000000000\) \(a_{79}=+1.912174643\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=+0.036246836\) \(a_{84}=+0.000000000\) \(a_{85}=-0.271292914\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.403033611\) \(a_{88}=+0.000000000\) \(a_{89}=+1.517738569\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.414591204\) \(a_{92}=+0.000000000\) \(a_{93}=+0.048209290\) \(a_{94}=+0.000000000\) \(a_{95}=+0.298153202\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.269107287\) \(a_{98}=+0.000000000\) \(a_{99}=+0.401575817\) \(a_{100}=+0.000000000\)

Showing 100 of 222 available coefficients

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