Properties

Level $15$
Weight $0$
Character 15.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 7.33539452441 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.588321898\) \(a_{3}=-0.577350269\) \(a_{4}=+1.522766452\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.917018075\) \(a_{7}=+1.710127445\) \(a_{8}=+0.830321403\) \(a_{9}=+0.333333333\) \(a_{10}=-0.710319147\)
\(a_{11}=+1.326127298\) \(a_{12}=-0.879169621\) \(a_{13}=+0.024723328\) \(a_{14}=+2.716232869\) \(a_{15}=+0.258198890\)
\(a_{16}=-0.203948785\) \(a_{17}=+1.250829731\) \(a_{18}=+0.529440633\) \(a_{19}=+0.740083623\) \(a_{20}=-0.681001860\)
\(a_{21}=-0.987342541\) \(a_{22}=+2.106317028\) \(a_{23}=-0.538639665\) \(a_{24}=-0.479386285\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.039268604\) \(a_{27}=-0.192450090\) \(a_{28}=+2.604124701\) \(a_{29}=+0.326858692\) \(a_{30}=+0.410102951\)
\(a_{31}=-1.596020263\) \(a_{32}=-1.154257725\) \(a_{33}=-0.765639953\) \(a_{34}=+1.986720253\) \(a_{35}=-0.764792243\)
\(a_{36}=+0.507588817\) \(a_{37}=-0.030116212\) \(a_{38}=+1.175491025\) \(a_{39}=-0.014274020\) \(a_{40}=-0.371331020\)
\(a_{41}=-0.018090020\) \(a_{42}=-1.568217778\) \(a_{43}=-1.112578581\) \(a_{44}=+2.019382161\) \(a_{45}=-0.149071198\)
\(a_{46}=-0.855533176\) \(a_{47}=-0.646475768\) \(a_{48}=+0.117749886\) \(a_{49}=+1.924535878\) \(a_{50}=+0.317664380\)
\(a_{51}=-0.722166882\) \(a_{52}=+0.037647855\) \(a_{53}=+0.966913894\) \(a_{54}=-0.305672692\) \(a_{55}=-0.593062157\)
\(a_{56}=+1.419955419\) \(a_{57}=-0.427287479\) \(a_{58}=+0.519156818\) \(a_{59}=-0.297768809\) \(a_{60}=+0.393176607\)
\(a_{61}=+0.360267881\) \(a_{62}=-2.534993934\) \(a_{63}=+0.570042482\) \(a_{64}=-1.629384034\) \(a_{65}=-0.011056609\)
\(a_{66}=-1.216082703\) \(a_{67}=-0.211842870\) \(a_{68}=+1.904721552\) \(a_{69}=+0.310983756\) \(a_{70}=-1.214736268\)
\(a_{71}=+1.571610590\) \(a_{72}=+0.276773801\) \(a_{73}=-1.364923887\) \(a_{74}=-0.047834240\) \(a_{75}=-0.115470054\)
\(a_{76}=+1.126974512\) \(a_{77}=+2.267846689\) \(a_{78}=-0.022671739\) \(a_{79}=+1.369902090\) \(a_{80}=+0.091208670\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.028732775\) \(a_{83}=+0.006163781\) \(a_{84}=-1.503492097\) \(a_{85}=-0.559388062\)
\(a_{86}=-1.767132924\) \(a_{87}=-0.188711954\) \(a_{88}=+1.101111878\) \(a_{89}=-1.875494133\) \(a_{90}=-0.236773049\)
\(a_{91}=+0.042280043\) \(a_{92}=-0.820222412\) \(a_{93}=+0.921462729\) \(a_{94}=-1.026811619\) \(a_{95}=-0.330975458\)
\(a_{96}=+0.666411008\) \(a_{97}=+0.282650368\) \(a_{98}=+3.056782479\) \(a_{99}=+0.442042433\) \(a_{100}=+0.304553290\)

Showing 100 of 180 available coefficients

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