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: \( 12.8481421756 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.719058834\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.350476012\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-1.243571768\) \(a_{12}=+0.000000000\) \(a_{13}=-0.022436016\) \(a_{14}=+0.000000000\) \(a_{15}=+0.415148811\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.211743645\) \(a_{18}=+0.000000000\) \(a_{19}=-0.661067241\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.202347420\) \(a_{22}=+0.000000000\) \(a_{23}=+0.766341760\) \(a_{24}=+0.000000000\) \(a_{25}=-0.482954394\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+1.212192014\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.974357975\) \(a_{32}=+0.000000000\) \(a_{33}=-0.717976495\) \(a_{34}=+0.000000000\) \(a_{35}=-0.252012872\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.514005331\) \(a_{38}=+0.000000000\) \(a_{39}=-0.012953440\) \(a_{40}=+0.000000000\)
\(a_{41}=-1.554493686\) \(a_{42}=+0.000000000\) \(a_{43}=-1.230780693\) \(a_{44}=+0.000000000\) \(a_{45}=+0.239686278\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.010562478\) \(a_{48}=+0.000000000\) \(a_{49}=-0.877166565\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.699600520\) \(a_{52}=+0.000000000\) \(a_{53}=-0.814645355\) \(a_{54}=+0.000000000\) \(a_{55}=-0.894201265\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.381667350\) \(a_{58}=+0.000000000\) \(a_{59}=-1.122605766\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.630988477\) \(a_{62}=+0.000000000\) \(a_{63}=-0.116825337\) \(a_{64}=+0.000000000\) \(a_{65}=-0.016132815\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.078575765\) \(a_{68}=+0.000000000\) \(a_{69}=+0.442447621\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.189798221\) \(a_{72}=+0.000000000\) \(a_{73}=-1.704447027\) \(a_{74}=+0.000000000\) \(a_{75}=-0.278833849\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.435842074\) \(a_{78}=+0.000000000\) \(a_{79}=-0.368849192\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=+1.112712338\) \(a_{84}=+0.000000000\) \(a_{85}=-0.871314972\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.699859385\) \(a_{88}=+0.000000000\) \(a_{89}=+0.077938787\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.007863285\) \(a_{92}=+0.000000000\) \(a_{93}=+0.562545839\) \(a_{94}=+0.000000000\) \(a_{95}=-0.475346240\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.775274788\) \(a_{98}=+0.000000000\) \(a_{99}=-0.414523923\) \(a_{100}=+0.000000000\)

Showing 100 of 190 available coefficients

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