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: \( 7.3417508929 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=-0.577350265\) \(a_{4}=+0.000000000\) \(a_{5}=+0.593449055\)
\(a_{6}=+0.000000000\) \(a_{7}=+0.486970206\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.913810317\) \(a_{12}=+0.000000000\) \(a_{13}=-1.752978741\) \(a_{14}=+0.000000000\) \(a_{15}=-0.342627971\)
\(a_{16}=+0.000000000\) \(a_{17}=-1.068392614\) \(a_{18}=+0.000000000\) \(a_{19}=+0.811499690\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.281152397\) \(a_{22}=+0.000000000\) \(a_{23}=-1.144628867\) \(a_{24}=+0.000000000\) \(a_{25}=-0.647818204\)
\(a_{26}=+0.000000000\) \(a_{27}=-0.192450032\) \(a_{28}=+0.000000000\) \(a_{29}=+1.409064566\) \(a_{30}=+0.000000000\)
\(a_{31}=-0.372443194\) \(a_{32}=+0.000000000\) \(a_{33}=+0.527588632\) \(a_{34}=+0.000000000\) \(a_{35}=+0.288992026\)
\(a_{36}=+0.000000000\) \(a_{37}=-1.674071362\) \(a_{38}=+0.000000000\) \(a_{39}=+1.012082719\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.837124833\) \(a_{42}=+0.000000000\) \(a_{43}=-0.600355502\) \(a_{44}=+0.000000000\) \(a_{45}=+0.197816359\)
\(a_{46}=+0.000000000\) \(a_{47}=+1.360515648\) \(a_{48}=+0.000000000\) \(a_{49}=-0.762860028\) \(a_{50}=+0.000000000\)
\(a_{51}=+0.616836839\) \(a_{52}=+0.000000000\) \(a_{53}=+1.129299147\) \(a_{54}=+0.000000000\) \(a_{55}=-0.542299823\)
\(a_{56}=+0.000000000\) \(a_{57}=-0.468519579\) \(a_{58}=+0.000000000\) \(a_{59}=+0.165564424\) \(a_{60}=+0.000000000\)
\(a_{61}=-1.682761638\) \(a_{62}=+0.000000000\) \(a_{63}=+0.162323431\) \(a_{64}=+0.000000000\) \(a_{65}=-1.040303533\)
\(a_{66}=+0.000000000\) \(a_{67}=+1.248975996\) \(a_{68}=+0.000000000\) \(a_{69}=+0.660851783\) \(a_{70}=+0.000000000\)
\(a_{71}=+0.639163656\) \(a_{72}=+0.000000000\) \(a_{73}=-0.321328413\) \(a_{74}=+0.000000000\) \(a_{75}=+0.374018084\)
\(a_{76}=+0.000000000\) \(a_{77}=-0.444998340\) \(a_{78}=+0.000000000\) \(a_{79}=+0.642468281\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111128\) \(a_{82}=+0.000000000\) \(a_{83}=+0.063132952\) \(a_{84}=+0.000000000\) \(a_{85}=-0.634036538\)
\(a_{86}=+0.000000000\) \(a_{87}=-0.813523814\) \(a_{88}=+0.000000000\) \(a_{89}=-0.068357705\) \(a_{90}=+0.000000000\)
\(a_{91}=-0.853648396\) \(a_{92}=+0.000000000\) \(a_{93}=+0.215030191\) \(a_{94}=+0.000000000\) \(a_{95}=+0.481583755\)
\(a_{96}=+0.000000000\) \(a_{97}=-0.578944848\) \(a_{98}=+0.000000000\) \(a_{99}=-0.304603445\) \(a_{100}=+0.000000000\)

Showing 100 of 2000 available coefficients

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