Properties

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

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 3.61330792232 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.172962255\) \(a_{3}=-0.577350269\) \(a_{4}=-0.970084058\) \(a_{5}=-0.447213596\)
\(a_{6}=-0.099859805\) \(a_{7}=+0.549082103\) \(a_{8}=-0.340750182\) \(a_{9}=+0.333333333\) \(a_{10}=-0.077351072\)
\(a_{11}=-1.142052219\) \(a_{12}=+0.560078292\) \(a_{13}=-1.148428146\) \(a_{14}=+0.094970479\) \(a_{15}=+0.258198890\)
\(a_{16}=+0.911147138\) \(a_{17}=-0.717367403\) \(a_{18}=+0.057654085\) \(a_{19}=+1.459746027\) \(a_{20}=+0.433834780\)
\(a_{21}=-0.317012700\) \(a_{22}=-0.197531928\) \(a_{23}=-1.352527339\) \(a_{24}=+0.196732209\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.198634722\) \(a_{27}=-0.192450090\) \(a_{28}=-0.532655795\) \(a_{29}=+0.421168584\) \(a_{30}=+0.044658662\)
\(a_{31}=-0.803523291\) \(a_{32}=+0.498344246\) \(a_{33}=+0.659364156\) \(a_{34}=-0.124077484\) \(a_{35}=-0.245556982\)
\(a_{36}=-0.323361353\) \(a_{37}=+1.110029914\) \(a_{38}=+0.252480965\) \(a_{39}=+0.663045299\) \(a_{40}=+0.152388114\)
\(a_{41}=-0.106599045\) \(a_{42}=-0.054831232\) \(a_{43}=-0.944211421\) \(a_{44}=+1.107886652\) \(a_{45}=-0.149071198\)
\(a_{46}=-0.233936179\) \(a_{47}=-1.792087701\) \(a_{48}=-0.526051045\) \(a_{49}=-0.698508844\) \(a_{50}=+0.034592451\)
\(a_{51}=+0.414172263\) \(a_{52}=+1.114071837\) \(a_{53}=+0.296765830\) \(a_{54}=-0.033286602\) \(a_{55}=+0.510741279\)
\(a_{56}=-0.187099827\) \(a_{57}=-0.842784761\) \(a_{58}=+0.072846268\) \(a_{59}=-0.441480353\) \(a_{60}=-0.250474628\)
\(a_{61}=+1.658776396\) \(a_{62}=-0.138979200\) \(a_{63}=+0.183027361\) \(a_{64}=-0.824952392\) \(a_{65}=+0.513592688\)
\(a_{66}=+0.114045108\) \(a_{67}=+0.469618082\) \(a_{68}=+0.695906697\) \(a_{69}=+0.780882019\) \(a_{70}=-0.042472111\)
\(a_{71}=+0.066503973\) \(a_{72}=-0.113583396\) \(a_{73}=-1.208420622\) \(a_{74}=+0.191993314\) \(a_{75}=-0.115470091\)
\(a_{76}=-1.416076385\) \(a_{77}=-0.627080435\) \(a_{78}=+0.114681810\) \(a_{79}=-0.093543858\) \(a_{80}=-0.407477388\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.018437611\) \(a_{83}=-0.281577083\) \(a_{84}=+0.307528967\) \(a_{85}=+0.320816455\)
\(a_{86}=-0.163312937\) \(a_{87}=-0.243161795\) \(a_{88}=+0.389154500\) \(a_{89}=+0.821921960\) \(a_{90}=-0.025783693\)
\(a_{91}=-0.630581345\) \(a_{92}=+1.312065212\) \(a_{93}=+0.463914388\) \(a_{94}=-0.309963539\) \(a_{95}=-0.652818262\)
\(a_{96}=-0.287719184\) \(a_{97}=+1.602498071\) \(a_{98}=-0.120815668\) \(a_{99}=-0.380684063\) \(a_{100}=-0.194016809\)

Showing 100 of 1500 available coefficients

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