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: \( 3.85551540683 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.639143629\) \(a_{3}=+0.577350269\) \(a_{4}=+1.686791838\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.946360016\) \(a_{7}=+1.493239140\) \(a_{8}=-1.125750466\) \(a_{9}=+0.333333333\) \(a_{10}=+0.733047316\)
\(a_{11}=+0.017359932\) \(a_{12}=+0.973869722\) \(a_{13}=+0.860207965\) \(a_{14}=-2.447633423\) \(a_{15}=-0.258198890\)
\(a_{16}=+0.158474866\) \(a_{17}=+1.747150229\) \(a_{18}=-0.546381210\) \(a_{19}=-0.227424933\) \(a_{20}=-0.754356243\)
\(a_{21}=+0.862122019\) \(a_{22}=-0.028455421\) \(a_{23}=-0.440943476\) \(a_{24}=-0.649952334\) \(a_{25}=+0.199951172\)
\(a_{26}=-1.410004406\) \(a_{27}=+0.192450090\) \(a_{28}=+2.518783593\) \(a_{29}=+0.110711860\) \(a_{30}=+0.423225065\)
\(a_{31}=+0.704733998\) \(a_{32}=+0.865987398\) \(a_{33}=+0.010022761\) \(a_{34}=-2.863830167\) \(a_{35}=-0.667796845\)
\(a_{36}=+0.562263945\) \(a_{37}=-1.142861650\) \(a_{38}=+0.372782129\) \(a_{39}=+0.496641302\) \(a_{40}=+0.503450909\)
\(a_{41}=+0.348079649\) \(a_{42}=-1.413141809\) \(a_{43}=-1.114517240\) \(a_{44}=+0.029282591\) \(a_{45}=-0.149071198\)
\(a_{46}=+0.722769690\) \(a_{47}=+1.207651284\) \(a_{48}=+0.091495507\) \(a_{49}=+1.229763129\) \(a_{50}=-0.327828726\)
\(a_{51}=+1.008717655\) \(a_{52}=+1.450991775\) \(a_{53}=-0.360590079\) \(a_{54}=-0.315453339\) \(a_{55}=-0.007763598\)
\(a_{56}=-1.681014656\) \(a_{57}=-0.131303844\) \(a_{58}=-0.181472641\) \(a_{59}=-0.236460763\) \(a_{60}=-0.435527780\)
\(a_{61}=-0.497236554\) \(a_{62}=-1.155160242\) \(a_{63}=+0.497746382\) \(a_{64}=-1.577952586\) \(a_{65}=-0.384696696\)
\(a_{66}=-0.016428755\) \(a_{67}=+1.435237641\) \(a_{68}=+2.947078752\) \(a_{69}=-0.254578816\) \(a_{70}=+1.094614952\)
\(a_{71}=-1.353412819\) \(a_{72}=-0.375250172\) \(a_{73}=-0.826307093\) \(a_{74}=+1.873314396\) \(a_{75}=+0.115470053\)
\(a_{76}=-0.383618521\) \(a_{77}=+0.025922528\) \(a_{78}=-0.814066422\) \(a_{79}=-0.391912864\) \(a_{80}=-0.070872115\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.570552539\) \(a_{83}=-0.752742473\) \(a_{84}=+1.454220387\) \(a_{85}=-0.781349336\)
\(a_{86}=+1.826853815\) \(a_{87}=+0.063919528\) \(a_{88}=-0.019542949\) \(a_{89}=-0.289472428\) \(a_{90}=+0.244349105\)
\(a_{91}=+1.284496218\) \(a_{92}=-0.743779863\) \(a_{93}=+0.406878331\) \(a_{94}=-1.979513893\) \(a_{95}=+0.101707534\)
\(a_{96}=+0.499978071\) \(a_{97}=+0.938855109\) \(a_{98}=-2.015758410\) \(a_{99}=+0.005786625\) \(a_{100}=+0.337358343\)

Showing 100 of 1500 available coefficients

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