Properties

Level $60$
Weight $0$
Character 60.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( 0 \)
Character: 60.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 0.674711608 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.000000000\) \(a_{3}=+0.577350269\) \(a_{4}=+0.000000000\) \(a_{5}=+0.447213596\)
\(a_{6}=+0.000000000\) \(a_{7}=-0.361675282\) \(a_{8}=+0.000000000\) \(a_{9}=+0.333333333\) \(a_{10}=+0.000000000\)
\(a_{11}=-0.133712407\) \(a_{12}=+0.000000000\) \(a_{13}=-1.705356444\) \(a_{14}=+0.000000000\) \(a_{15}=+0.258198890\)
\(a_{16}=+0.000000000\) \(a_{17}=-0.630465594\) \(a_{18}=+0.000000000\) \(a_{19}=+0.587194005\) \(a_{20}=+0.000000000\)
\(a_{21}=-0.208813322\) \(a_{22}=+0.000000000\) \(a_{23}=-0.239567200\) \(a_{24}=+0.000000000\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.000000000\) \(a_{27}=+0.192450090\) \(a_{28}=+0.000000000\) \(a_{29}=+1.331117580\) \(a_{30}=+0.000000000\)
\(a_{31}=+1.088448726\) \(a_{32}=+0.000000000\) \(a_{33}=-0.077198894\) \(a_{34}=+0.000000000\) \(a_{35}=-0.161746103\)
\(a_{36}=+0.000000000\) \(a_{37}=+1.310479330\) \(a_{38}=+0.000000000\) \(a_{39}=-0.984588002\) \(a_{40}=+0.000000000\)
\(a_{41}=-0.434493450\) \(a_{42}=+0.000000000\) \(a_{43}=+0.496371999\) \(a_{44}=+0.000000000\) \(a_{45}=+0.149071198\)
\(a_{46}=+0.000000000\) \(a_{47}=-1.858554600\) \(a_{48}=+0.000000000\) \(a_{49}=-0.869190990\) \(a_{50}=+0.000000000\)
\(a_{51}=-0.363999480\) \(a_{52}=+0.000000000\) \(a_{53}=+1.310594801\) \(a_{54}=+0.000000000\) \(a_{55}=-0.059798006\)
\(a_{56}=+0.000000000\) \(a_{57}=+0.339016617\) \(a_{58}=+0.000000000\) \(a_{59}=-1.095234700\) \(a_{60}=+0.000000000\)
\(a_{61}=-0.229271900\) \(a_{62}=+0.000000000\) \(a_{63}=-0.120558427\) \(a_{64}=+0.000000000\) \(a_{65}=-0.762658587\)
\(a_{66}=+0.000000000\) \(a_{67}=+0.085308500\) \(a_{68}=+0.000000000\) \(a_{69}=-0.138314187\) \(a_{70}=+0.000000000\)
\(a_{71}=+1.048649400\) \(a_{72}=+0.000000000\) \(a_{73}=+0.056097000\) \(a_{74}=+0.000000000\) \(a_{75}=+0.115470054\)
\(a_{76}=+0.000000000\) \(a_{77}=+0.048360472\) \(a_{78}=+0.000000000\) \(a_{79}=-1.231723000\) \(a_{80}=+0.000000000\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.000000000\) \(a_{83}=+1.086229500\) \(a_{84}=+0.000000000\) \(a_{85}=-0.281952785\)
\(a_{86}=+0.000000000\) \(a_{87}=+0.768521093\) \(a_{88}=+0.000000000\) \(a_{89}=+0.941012800\) \(a_{90}=+0.000000000\)
\(a_{91}=+0.616785273\) \(a_{92}=+0.000000000\) \(a_{93}=+0.628416165\) \(a_{94}=+0.000000000\) \(a_{95}=+0.262601142\)
\(a_{96}=+0.000000000\) \(a_{97}=+0.159802400\) \(a_{98}=+0.000000000\) \(a_{99}=-0.044570802\) \(a_{100}=+0.000000000\)

Showing 100 of 490 available coefficients

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