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: \( 5.90447347445 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.272369331\) \(a_{3}=+0.577350269\) \(a_{4}=-0.925814947\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.157252507\) \(a_{7}=+0.441002867\) \(a_{8}=+0.524532929\) \(a_{9}=+0.333333333\) \(a_{10}=+0.121807268\)
\(a_{11}=+1.563952233\) \(a_{12}=-0.534519509\) \(a_{13}=+0.258039161\) \(a_{14}=-0.120115656\) \(a_{15}=-0.258198890\)
\(a_{16}=+0.782948264\) \(a_{17}=+0.853384358\) \(a_{18}=-0.090789777\) \(a_{19}=+0.598461608\) \(a_{20}=+0.414037031\)
\(a_{21}=+0.254613124\) \(a_{22}=-0.425972624\) \(a_{23}=-1.416231209\) \(a_{24}=+0.302839228\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.070281954\) \(a_{27}=+0.192450090\) \(a_{28}=-0.408287047\) \(a_{29}=-0.343057792\) \(a_{30}=+0.070325459\)
\(a_{31}=+1.303502790\) \(a_{32}=-0.737784024\) \(a_{33}=+0.902948243\) \(a_{34}=-0.232435727\) \(a_{35}=-0.197222478\)
\(a_{36}=-0.308604982\) \(a_{37}=+1.672242877\) \(a_{38}=-0.163002588\) \(a_{39}=+0.148978979\) \(a_{40}=-0.234578257\)
\(a_{41}=-1.024826338\) \(a_{42}=-0.069348806\) \(a_{43}=+0.089987644\) \(a_{44}=-1.447930354\) \(a_{45}=-0.149071198\)
\(a_{46}=+0.385737947\) \(a_{47}=+0.125447228\) \(a_{48}=+0.452035391\) \(a_{49}=-0.805516471\) \(a_{50}=-0.054473866\)
\(a_{51}=+0.492701689\) \(a_{52}=-0.238896512\) \(a_{53}=+1.881090013\) \(a_{54}=-0.052417502\) \(a_{55}=-0.699420701\)
\(a_{56}=+0.231320526\) \(a_{57}=+0.345521971\) \(a_{58}=+0.093438421\) \(a_{59}=-0.997956106\) \(a_{60}=+0.239044392\)
\(a_{61}=+1.973925404\) \(a_{62}=-0.355034183\) \(a_{63}=+0.147000956\) \(a_{64}=-0.581998523\) \(a_{65}=-0.115398621\)
\(a_{66}=-0.245935409\) \(a_{67}=-0.716631052\) \(a_{68}=-0.790075995\) \(a_{69}=-0.817661470\) \(a_{70}=+0.053717354\)
\(a_{71}=-0.019595381\) \(a_{72}=+0.174844310\) \(a_{73}=+1.061251633\) \(a_{74}=-0.455467674\) \(a_{75}=+0.115470054\)
\(a_{76}=-0.554064702\) \(a_{77}=+0.689707419\) \(a_{78}=-0.040577305\) \(a_{79}=+0.424002999\) \(a_{80}=-0.350145108\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.279131264\) \(a_{83}=+0.348934962\) \(a_{84}=-0.235724636\) \(a_{85}=-0.381645087\)
\(a_{86}=-0.024509874\) \(a_{87}=-0.198064508\) \(a_{88}=+0.820344446\) \(a_{89}=-0.457611480\) \(a_{90}=+0.040602423\)
\(a_{91}=+0.113796010\) \(a_{92}=+1.311168023\) \(a_{93}=+0.752577687\) \(a_{94}=-0.034167978\) \(a_{95}=-0.267640168\)
\(a_{96}=-0.425959805\) \(a_{97}=-0.490753170\) \(a_{98}=+0.219397982\) \(a_{99}=+0.521317411\) \(a_{100}=-0.185162989\)

Showing 100 of 148 available coefficients

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