Properties

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

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Maass form invariants

Level: \( 12 = 2^{2} \cdot 3 \)
Weight: \( 0 \)
Character: 12.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 15.2642426303 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=-1.843460227\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.229638020\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+1.770744775\) \(a_{12}=+0.000000000\) \(a_{13}=+0.919175703\) \(a_{14}=+0.000000000\) \(a_{15}=+1.064322258\)
\(a_{16}=+0.000000000\) \(a_{17}=+0.167721045\) \(a_{18}=+0.000000000\) \(a_{19}=+0.287370187\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.709931842\) \(a_{22}=+0.000000000\) \(a_{23}=-0.403316083\) \(a_{24}=+0.000000000\) \(a_{25}=+2.398345607\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=-1.400807306\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.352326568\) \(a_{32}=+0.000000000\) \(a_{33}=-1.022339973\) \(a_{34}=+0.000000000\) \(a_{35}=+2.266788782\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.490482406\) \(a_{38}=+0.000000000\) \(a_{39}=-0.530686340\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.648700906\) \(a_{42}=+0.000000000\) \(a_{43}=+0.536783845\) \(a_{44}=+0.000000000\) \(a_{45}=-0.614486742\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.218846002\) \(a_{48}=+0.000000000\) \(a_{49}=+0.512009659\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.096833791\) \(a_{52}=+0.000000000\) \(a_{53}=+0.879319758\) \(a_{54}=+0.000000000\) \(a_{55}=-3.264297565\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.165913255\) \(a_{58}=+0.000000000\) \(a_{59}=-1.654549804\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.193845122\) \(a_{62}=+0.000000000\) \(a_{63}=-0.409879340\) \(a_{64}=+0.000000000\) \(a_{65}=-1.694463850\)
\(a_{66}=+0.000000000\) \(a_{67}=-0.583460450\) \(a_{68}=+0.000000000\) \(a_{69}=+0.232854649\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.821065805\) \(a_{72}=+0.000000000\) \(a_{73}=-0.430714701\) \(a_{74}=+0.000000000\) \(a_{75}=-1.384685482\)
\(a_{76}=+0.000000000\) \(a_{77}=-2.177375099\) \(a_{78}=+0.000000000\) \(a_{79}=-0.376652155\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=+0.576069637\) \(a_{84}=+0.000000000\) \(a_{85}=-0.309187076\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.808756475\) \(a_{88}=+0.000000000\) \(a_{89}=+0.514613829\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.130253392\) \(a_{92}=+0.000000000\) \(a_{93}=+0.203415839\) \(a_{94}=+0.000000000\) \(a_{95}=-0.529755509\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.220206498\) \(a_{98}=+0.000000000\) \(a_{99}=+0.590248258\) \(a_{100}=+0.000000000\)

Showing 100 of 212 available coefficients

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