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: \( 6.99752889314 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.935205268\) \(a_{3}=+0.577350269\) \(a_{4}=+2.745019429\) \(a_{5}=+0.447213596\)
\(a_{6}=-1.117291282\) \(a_{7}=+1.223313246\) \(a_{8}=-3.376970792\) \(a_{9}=+0.333333333\) \(a_{10}=-0.865450106\)
\(a_{11}=+0.337208198\) \(a_{12}=+1.584837706\) \(a_{13}=-0.153205417\) \(a_{14}=-2.367362238\) \(a_{15}=+0.258198890\)
\(a_{16}=+3.790112238\) \(a_{17}=-0.305849880\) \(a_{18}=-0.645068423\) \(a_{19}=+0.540031443\) \(a_{20}=+1.227610009\)
\(a_{21}=+0.706280232\) \(a_{22}=-0.652567081\) \(a_{23}=-0.952181807\) \(a_{24}=-1.949694996\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.296483930\) \(a_{27}=+0.192450090\) \(a_{28}=+3.358018628\) \(a_{29}=+1.458560026\) \(a_{30}=-0.499667852\)
\(a_{31}=+0.679272544\) \(a_{32}=-3.957674377\) \(a_{33}=+0.194687244\) \(a_{34}=+0.591882300\) \(a_{35}=+0.547082315\)
\(a_{36}=+0.915006476\) \(a_{37}=+0.071928609\) \(a_{38}=-1.045071693\) \(a_{39}=-0.088453189\) \(a_{40}=-1.510227250\)
\(a_{41}=-0.093969395\) \(a_{42}=-1.366797225\) \(a_{43}=+0.872586015\) \(a_{44}=+0.925643055\) \(a_{45}=+0.149071198\)
\(a_{46}=+1.842667248\) \(a_{47}=-1.166932413\) \(a_{48}=+2.188222321\) \(a_{49}=+0.496495298\) \(a_{50}=-0.387041054\)
\(a_{51}=-0.176582511\) \(a_{52}=-0.420551846\) \(a_{53}=+1.271412574\) \(a_{54}=-0.372430427\) \(a_{55}=+0.150804091\)
\(a_{56}=-4.131093102\) \(a_{57}=+0.311787299\) \(a_{58}=-2.822613046\) \(a_{59}=+1.340209462\) \(a_{60}=+0.708760969\)
\(a_{61}=+1.322657721\) \(a_{62}=-1.314531806\) \(a_{63}=+0.407771082\) \(a_{64}=+3.868800065\) \(a_{65}=-0.068515545\)
\(a_{66}=-0.376759780\) \(a_{67}=+0.323672046\) \(a_{68}=-0.839563864\) \(a_{69}=-0.549742422\) \(a_{70}=-1.058716578\)
\(a_{71}=+1.155084732\) \(a_{72}=-1.125656931\) \(a_{73}=-1.220123166\) \(a_{74}=-0.139196624\) \(a_{75}=+0.115470054\)
\(a_{76}=+1.482396802\) \(a_{77}=+0.412511255\) \(a_{78}=+0.171175077\) \(a_{79}=-1.689231723\) \(a_{80}=+1.694989721\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.181850068\) \(a_{83}=-0.024366885\) \(a_{84}=+1.938752959\) \(a_{85}=-0.136780225\)
\(a_{86}=-1.688633053\) \(a_{87}=+0.842100024\) \(a_{88}=-1.138742235\) \(a_{89}=+0.669914412\) \(a_{90}=-0.288483369\)
\(a_{91}=-0.187418216\) \(a_{92}=-2.613757559\) \(a_{93}=+0.392178186\) \(a_{94}=+2.258253754\) \(a_{95}=+0.241509403\)
\(a_{96}=-2.284964367\) \(a_{97}=-0.201524537\) \(a_{98}=-0.960820316\) \(a_{99}=+0.112402733\) \(a_{100}=+0.549003886\)

Showing 100 of 228 available coefficients

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