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: \( 11.024546463 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.489548397\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.612050682\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.833776400\) \(a_{12}=+0.000000000\) \(a_{13}=-1.207993875\) \(a_{14}=+0.000000000\) \(a_{15}=+0.282640899\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.664228239\) \(a_{18}=+0.000000000\) \(a_{19}=+0.411863024\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.353367626\) \(a_{22}=+0.000000000\) \(a_{23}=+0.788987424\) \(a_{24}=+0.000000000\) \(a_{25}=-0.760342367\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-1.697350568\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.928148123\) \(a_{32}=+0.000000000\) \(a_{33}=-0.481381029\) \(a_{34}=+0.000000000\) \(a_{35}=-0.299628430\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.455225383\) \(a_{38}=+0.000000000\) \(a_{39}=-0.697435589\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.890007441\) \(a_{42}=+0.000000000\) \(a_{43}=-0.375753777\) \(a_{44}=+0.000000000\) \(a_{45}=+0.163182799\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.012562051\) \(a_{48}=+0.000000000\) \(a_{49}=-0.625393962\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.383492352\) \(a_{52}=+0.000000000\) \(a_{53}=+0.780577263\) \(a_{54}=+0.000000000\) \(a_{55}=-0.408173900\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.237789228\) \(a_{58}=+0.000000000\) \(a_{59}=+1.355420780\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.150196098\) \(a_{62}=+0.000000000\) \(a_{63}=-0.204016894\) \(a_{64}=+0.000000000\) \(a_{65}=-0.591371465\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.796560805\) \(a_{68}=+0.000000000\) \(a_{69}=+0.455522102\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.032714461\) \(a_{72}=+0.000000000\) \(a_{73}=+1.788982017\) \(a_{74}=+0.000000000\) \(a_{75}=-0.438983870\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.510313415\) \(a_{78}=+0.000000000\) \(a_{79}=+1.004839490\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=-0.930967137\) \(a_{84}=+0.000000000\) \(a_{85}=+0.325171869\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.979965807\) \(a_{88}=+0.000000000\) \(a_{89}=-0.324552368\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.739353475\) \(a_{92}=+0.000000000\) \(a_{93}=-1.113216838\) \(a_{94}=+0.000000000\) \(a_{95}=+0.201626883\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.488096380\) \(a_{98}=+0.000000000\) \(a_{99}=-0.277925467\) \(a_{100}=+0.000000000\)

Showing 100 of 190 available coefficients

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