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: \( 8.66501125743 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.784308011\) \(a_{3}=+0.577350269\) \(a_{4}=+2.183755077\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.030170710\) \(a_{7}=-0.864712082\) \(a_{8}=-2.112183666\) \(a_{9}=+0.333333333\) \(a_{10}=+0.797966801\)
\(a_{11}=+1.498394903\) \(a_{12}=+1.260791581\) \(a_{13}=-1.329806806\) \(a_{14}=+1.542912695\) \(a_{15}=-0.258198890\)
\(a_{16}=+1.585031158\) \(a_{17}=+1.285736549\) \(a_{18}=-0.594769337\) \(a_{19}=+0.275390083\) \(a_{20}=-0.976604959\)
\(a_{21}=-0.499241753\) \(a_{22}=-2.673598029\) \(a_{23}=+0.545907291\) \(a_{24}=-1.219469808\) \(a_{25}=+0.199951172\)
\(a_{26}=+2.372784937\) \(a_{27}=+0.192450090\) \(a_{28}=-1.888319399\) \(a_{29}=-1.094347026\) \(a_{30}=+0.460706347\)
\(a_{31}=+0.595109800\) \(a_{32}=-0.716000126\) \(a_{33}=+0.865098701\) \(a_{34}=-2.294150024\) \(a_{35}=+0.386710999\)
\(a_{36}=+0.727918359\) \(a_{37}=-1.830375803\) \(a_{38}=-0.491380732\) \(a_{39}=-0.767764317\) \(a_{40}=+0.944597251\)
\(a_{41}=-0.610256922\) \(a_{42}=+0.890801060\) \(a_{43}=+0.207968097\) \(a_{44}=+3.272127476\) \(a_{45}=-0.149071198\)
\(a_{46}=-0.974066752\) \(a_{47}=-1.161444397\) \(a_{48}=+0.915118166\) \(a_{49}=-0.252273015\) \(a_{50}=-0.356861602\)
\(a_{51}=+0.742320343\) \(a_{52}=-2.903972364\) \(a_{53}=-0.803647224\) \(a_{54}=-0.343390237\) \(a_{55}=-0.670102572\)
\(a_{56}=+1.826430736\) \(a_{57}=+0.158996539\) \(a_{58}=+1.952652164\) \(a_{59}=+0.298867815\) \(a_{60}=-0.563843136\)
\(a_{61}=+1.085324975\) \(a_{62}=-1.061859183\) \(a_{63}=-0.288237361\) \(a_{64}=-0.307466397\) \(a_{65}=+0.594707683\)
\(a_{66}=-1.543602542\) \(a_{67}=-1.498608925\) \(a_{68}=+2.807733716\) \(a_{69}=+0.315179721\) \(a_{70}=-0.690011534\)
\(a_{71}=-0.732478176\) \(a_{72}=-0.704061222\) \(a_{73}=-0.925991923\) \(a_{74}=+3.265954207\) \(a_{75}=+0.115470054\)
\(a_{76}=+0.601384493\) \(a_{77}=-1.295680177\) \(a_{78}=+1.369928022\) \(a_{79}=-0.692862373\) \(a_{80}=-0.708847483\)
\(a_{81}=+0.111111111\) \(a_{82}=+1.088886315\) \(a_{83}=+0.838221068\) \(a_{84}=-1.090221714\) \(a_{85}=-0.574998865\)
\(a_{86}=-0.371079141\) \(a_{87}=-0.631821550\) \(a_{88}=-3.164885238\) \(a_{89}=-0.498813812\) \(a_{90}=+0.265988934\)
\(a_{91}=+1.149900015\) \(a_{92}=+1.192127817\) \(a_{93}=+0.343586803\) \(a_{94}=+2.072374544\) \(a_{95}=-0.123158189\)
\(a_{96}=-0.413382866\) \(a_{97}=-1.322362751\) \(a_{98}=+0.450132763\) \(a_{99}=+0.499464968\) \(a_{100}=+0.436751015\)

Showing 100 of 198 available coefficients

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