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: \( 4.75479713395 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.951247815\) \(a_{3}=-0.577350269\) \(a_{4}=-0.095127595\) \(a_{5}=-0.447213595\)
\(a_{6}=+0.549203182\) \(a_{7}=+0.071642291\) \(a_{8}=+1.041737732\) \(a_{9}=+0.333333333\) \(a_{10}=+0.425410955\)
\(a_{11}=+0.219873742\) \(a_{12}=+0.054921943\) \(a_{13}=-0.589717332\) \(a_{14}=-0.068149573\) \(a_{15}=+0.258198890\)
\(a_{16}=-0.895823145\) \(a_{17}=+1.835605343\) \(a_{18}=-0.317082605\) \(a_{19}=-0.694758497\) \(a_{20}=+0.042542354\)
\(a_{21}=-0.041362696\) \(a_{22}=-0.209154417\) \(a_{23}=+1.607201507\) \(a_{24}=-0.601447560\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.560967323\) \(a_{27}=-0.192450090\) \(a_{28}=-0.006815159\) \(a_{29}=-1.247986411\) \(a_{30}=-0.245611130\)
\(a_{31}=+0.592755804\) \(a_{32}=-0.189587922\) \(a_{33}=-0.126944164\) \(a_{34}=-1.746115571\) \(a_{35}=-0.032039406\)
\(a_{36}=-0.031709198\) \(a_{37}=+1.391491878\) \(a_{38}=+0.660887502\) \(a_{39}=+0.340473460\) \(a_{40}=-0.465879277\)
\(a_{41}=+1.709282262\) \(a_{42}=+0.039346174\) \(a_{43}=+0.583185023\) \(a_{44}=-0.020916060\) \(a_{45}=-0.149071198\)
\(a_{46}=-1.528846921\) \(a_{47}=-0.114208278\) \(a_{48}=+0.517203734\) \(a_{49}=-0.994867382\) \(a_{50}=-0.190249563\)
\(a_{51}=-1.059787239\) \(a_{52}=+0.056098392\) \(a_{53}=-0.079864251\) \(a_{54}=+0.183067727\) \(a_{55}=-0.098330527\)
\(a_{56}=+0.074632478\) \(a_{57}=+0.401119005\) \(a_{58}=+1.187144346\) \(a_{59}=-0.897200379\) \(a_{60}=-0.024561839\)
\(a_{61}=+0.603195778\) \(a_{62}=-0.563857663\) \(a_{63}=+0.023880764\) \(a_{64}=+1.076168242\) \(a_{65}=+0.263729608\)
\(a_{66}=+0.120755359\) \(a_{67}=+0.079583958\) \(a_{68}=-0.174616722\) \(a_{69}=-0.927918223\) \(a_{70}=+0.030477415\)
\(a_{71}=+1.920131732\) \(a_{72}=+0.347245911\) \(a_{73}=-0.976877452\) \(a_{74}=-1.323653608\) \(a_{75}=-0.115470054\)
\(a_{76}=+0.066090705\) \(a_{77}=+0.015752259\) \(a_{78}=-0.323874635\) \(a_{79}=+0.759275330\) \(a_{80}=+0.400624290\)
\(a_{81}=+0.111111111\) \(a_{82}=-1.625951017\) \(a_{83}=+0.452351070\) \(a_{84}=+0.003934734\) \(a_{85}=-0.820907665\)
\(a_{86}=-0.554753478\) \(a_{87}=+0.720525290\) \(a_{88}=+0.229050774\) \(a_{89}=+0.259583200\) \(a_{90}=+0.141803652\)
\(a_{91}=-0.042248701\) \(a_{92}=-0.152889214\) \(a_{93}=-0.342227723\) \(a_{94}=+0.108640375\) \(a_{95}=+0.310705445\)
\(a_{96}=+0.109458638\) \(a_{97}=-0.414264000\) \(a_{98}=+0.946365423\) \(a_{99}=+0.073291247\) \(a_{100}=-0.019025519\)

Showing 100 of 162 available coefficients

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