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: \( 13.8686943566 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.763411588\)
\(a_{6}=+0.000000000\) \(a_{7}=-1.311957298\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.022344431\) \(a_{12}=+0.000000000\) \(a_{13}=+1.076475845\) \(a_{14}=+0.000000000\) \(a_{15}=-0.440755886\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.766505510\) \(a_{18}=+0.000000000\) \(a_{19}=-1.232260097\) \(a_{20}=+0.000000000\)
\(a_{21}=+0.757458899\) \(a_{22}=+0.000000000\) \(a_{23}=+0.489299589\) \(a_{24}=+0.000000000\) \(a_{25}=-0.417202748\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+1.143793986\) \(a_{30}=+0.000000000\)
\(a_{31}=-1.594862287\) \(a_{32}=+0.000000000\) \(a_{33}=+0.012900563\) \(a_{34}=+0.000000000\) \(a_{35}=-1.001563404\)
\(a_{36}=+0.000000000\) \(a_{37}=-0.641674371\) \(a_{38}=+0.000000000\) \(a_{39}=-0.621503619\) \(a_{40}=+0.000000000\)
\(a_{41}=+1.688438837\) \(a_{42}=+0.000000000\) \(a_{43}=+1.472321151\) \(a_{44}=+0.000000000\) \(a_{45}=+0.254470529\)
\(a_{46}=+0.000000000\) \(a_{47}=+0.145537320\) \(a_{48}=+0.000000000\) \(a_{49}=+0.721231952\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.442542163\) \(a_{52}=+0.000000000\) \(a_{53}=+1.370636249\) \(a_{54}=+0.000000000\) \(a_{55}=-0.017057997\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.711445699\) \(a_{58}=+0.000000000\) \(a_{59}=+1.269192521\) \(a_{60}=+0.000000000\)
\(a_{61}=+1.006507827\) \(a_{62}=+0.000000000\) \(a_{63}=-0.437319099\) \(a_{64}=+0.000000000\) \(a_{65}=+0.821794134\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.587096599\) \(a_{68}=+0.000000000\) \(a_{69}=-0.282497249\) \(a_{70}=+0.000000000\)
\(a_{71}=-1.487928325\) \(a_{72}=+0.000000000\) \(a_{73}=+0.378557535\) \(a_{74}=+0.000000000\) \(a_{75}=+0.240872119\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.029314939\) \(a_{78}=+0.000000000\) \(a_{79}=+1.652416765\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=+0.621733639\) \(a_{84}=+0.000000000\) \(a_{85}=-0.585159189\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.660369765\) \(a_{88}=+0.000000000\) \(a_{89}=+1.033065736\) \(a_{90}=+0.000000000\)
\(a_{91}=-1.412290342\) \(a_{92}=+0.000000000\) \(a_{93}=+0.920794171\) \(a_{94}=+0.000000000\) \(a_{95}=-0.940721639\)
\(a_{96}=+0.000000000\) \(a_{97}=-1.084951487\) \(a_{98}=+0.000000000\) \(a_{99}=-0.007448144\) \(a_{100}=+0.000000000\)

Showing 100 of 192 available coefficients

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