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: \( 15.8972868045 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-0.464305947\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.587583281\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.160834505\) \(a_{12}=+0.000000000\) \(a_{13}=+0.037572619\) \(a_{14}=+0.000000000\) \(a_{15}=+0.268067163\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.224967172\) \(a_{18}=+0.000000000\) \(a_{19}=+0.478892074\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.339241365\) \(a_{22}=+0.000000000\) \(a_{23}=-1.171233528\) \(a_{24}=+0.000000000\) \(a_{25}=-0.784419988\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+0.247052135\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.866564791\) \(a_{32}=+0.000000000\) \(a_{33}=+0.670208114\) \(a_{34}=+0.000000000\) \(a_{35}=+0.272818411\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.013025294\) \(a_{38}=+0.000000000\) \(a_{39}=-0.021692562\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.597308071\) \(a_{42}=+0.000000000\) \(a_{43}=-0.880478224\) \(a_{44}=+0.000000000\) \(a_{45}=-0.154768649\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.469530870\) \(a_{48}=+0.000000000\) \(a_{49}=-0.654745888\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.707235127\) \(a_{52}=+0.000000000\) \(a_{53}=+0.542034664\) \(a_{54}=+0.000000000\) \(a_{55}=+0.538982364\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.276488468\) \(a_{58}=+0.000000000\) \(a_{59}=+0.907899445\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.797956627\) \(a_{62}=+0.000000000\) \(a_{63}=-0.195861094\) \(a_{64}=+0.000000000\) \(a_{65}=-0.017445191\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.971701447\) \(a_{68}=+0.000000000\) \(a_{69}=+0.676211992\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.573316107\) \(a_{72}=+0.000000000\) \(a_{73}=+0.997081745\) \(a_{74}=+0.000000000\) \(a_{75}=+0.452885091\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.682086947\) \(a_{78}=+0.000000000\) \(a_{79}=-1.190560456\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=+0.604916370\) \(a_{84}=+0.000000000\) \(a_{85}=+0.568759543\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.142635616\) \(a_{88}=+0.000000000\) \(a_{89}=+0.999688666\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.022077043\) \(a_{92}=+0.000000000\) \(a_{93}=+0.500311415\) \(a_{94}=+0.000000000\) \(a_{95}=-0.222352438\)
\(a_{96}=+0.000000000\) \(a_{97}=+1.563485487\) \(a_{98}=+0.000000000\) \(a_{99}=-0.386944835\) \(a_{100}=+0.000000000\)

Showing 100 of 210 available coefficients

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