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: \( 9.95057272015 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+1.718681124\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.411015292\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=+0.238820771\) \(a_{12}=+0.000000000\) \(a_{13}=-1.212024207\) \(a_{14}=+0.000000000\) \(a_{15}=-0.992281010\)
\(a_{16}=+0.000000000\) \(a_{17}=+1.490403321\) \(a_{18}=+0.000000000\) \(a_{19}=-0.991489548\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.237299790\) \(a_{22}=+0.000000000\) \(a_{23}=+1.238252958\) \(a_{24}=+0.000000000\) \(a_{25}=+1.953864807\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+1.497716386\) \(a_{30}=+0.000000000\)
\(a_{31}=+0.486492798\) \(a_{32}=+0.000000000\) \(a_{33}=-0.137883237\) \(a_{34}=+0.000000000\) \(a_{35}=-0.706404224\)
\(a_{36}=+0.000000000\) \(a_{37}=+0.773252669\) \(a_{38}=+0.000000000\) \(a_{39}=+0.699762504\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.204569549\) \(a_{42}=+0.000000000\) \(a_{43}=-1.093324822\) \(a_{44}=+0.000000000\) \(a_{45}=+0.572893701\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.701134409\) \(a_{48}=+0.000000000\) \(a_{49}=-0.831066438\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.860484784\) \(a_{52}=+0.000000000\) \(a_{53}=-0.713562313\) \(a_{54}=+0.000000000\) \(a_{55}=+0.410456751\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.572436758\) \(a_{58}=+0.000000000\) \(a_{59}=+0.989491526\) \(a_{60}=+0.000000000\)
\(a_{61}=+0.957943124\) \(a_{62}=+0.000000000\) \(a_{63}=-0.137005098\) \(a_{64}=+0.000000000\) \(a_{65}=-2.083083122\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.478779799\) \(a_{68}=+0.000000000\) \(a_{69}=-0.714905680\) \(a_{70}=+0.000000000\)
\(a_{71}=-0.407421833\) \(a_{72}=+0.000000000\) \(a_{73}=+0.935509047\) \(a_{74}=+0.000000000\) \(a_{75}=-1.128064373\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.098158988\) \(a_{78}=+0.000000000\) \(a_{79}=-0.797561750\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111110\) \(a_{82}=+0.000000000\) \(a_{83}=+0.678172606\) \(a_{84}=+0.000000000\) \(a_{85}=+2.561528050\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.864706950\) \(a_{88}=+0.000000000\) \(a_{89}=-0.190249633\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.498160498\) \(a_{92}=+0.000000000\) \(a_{93}=-0.280876740\) \(a_{94}=+0.000000000\) \(a_{95}=-1.704054391\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.958559496\) \(a_{98}=+0.000000000\) \(a_{99}=+0.079606918\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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