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: \( 1.82147632892 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-1.638462284\) \(a_{3}=+0.577350269\) \(a_{4}=+1.684558656\) \(a_{5}=+0.447213596\)
\(a_{6}=-0.945966641\) \(a_{7}=-0.211621989\) \(a_{8}=-1.121623539\) \(a_{9}=+0.333333333\) \(a_{10}=-0.732742609\)
\(a_{11}=+0.527169108\) \(a_{12}=+0.972580394\) \(a_{13}=+0.197591572\) \(a_{14}=+0.346734648\) \(a_{15}=+0.258198890\)
\(a_{16}=+0.153179210\) \(a_{17}=-1.348949416\) \(a_{18}=-0.546154095\) \(a_{19}=+0.537374448\) \(a_{20}=+0.753357534\)
\(a_{21}=-0.122180012\) \(a_{22}=-0.863746702\) \(a_{23}=+1.176687440\) \(a_{24}=-0.647569652\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.323746339\) \(a_{27}=+0.192450089\) \(a_{28}=-0.356489655\) \(a_{29}=-1.803619309\) \(a_{30}=-0.423049143\)
\(a_{31}=+0.641472829\) \(a_{32}=+0.870645181\) \(a_{33}=+0.304361226\) \(a_{34}=+2.210202741\) \(a_{35}=-0.094640230\)
\(a_{36}=+0.561519552\) \(a_{37}=-0.109770705\) \(a_{38}=-0.880467766\) \(a_{39}=+0.114079548\) \(a_{40}=-0.501605294\)
\(a_{41}=+0.109326694\) \(a_{42}=+0.200187343\) \(a_{43}=-1.354959414\) \(a_{44}=+0.888047281\) \(a_{45}=+0.149071194\)
\(a_{46}=-1.927957988\) \(a_{47}=+0.587195315\) \(a_{48}=+0.088438061\) \(a_{49}=-0.955216146\) \(a_{50}=-0.327692458\)
\(a_{51}=-0.778816295\) \(a_{52}=+0.332854569\) \(a_{53}=+0.906032896\) \(a_{54}=-0.315322182\) \(a_{55}=+0.235757233\)
\(a_{56}=+0.237360188\) \(a_{57}=+0.310253184\) \(a_{58}=+2.955162223\) \(a_{59}=+0.541715468\) \(a_{60}=+0.434951167\)
\(a_{61}=+0.989132859\) \(a_{62}=-1.051029037\) \(a_{63}=-0.070540679\) \(a_{64}=-1.579698540\) \(a_{65}=+0.088365638\)
\(a_{66}=-0.498684395\) \(a_{67}=-0.526669016\) \(a_{68}=-2.272384412\) \(a_{69}=+0.679360841\) \(a_{70}=+0.155064366\)
\(a_{71}=+0.016508054\) \(a_{72}=-0.373873719\) \(a_{73}=+0.017791077\) \(a_{74}=+0.179854993\) \(a_{75}=+0.115469716\)
\(a_{76}=+0.905238448\) \(a_{77}=-0.111559570\) \(a_{78}=-0.186913074\) \(a_{79}=+1.173045293\) \(a_{80}=+0.068505081\)
\(a_{81}=+0.111122667\) \(a_{82}=-0.179125335\) \(a_{83}=-0.968514634\) \(a_{84}=-0.205818747\) \(a_{85}=-0.603240333\)
\(a_{86}=+2.220047476\) \(a_{87}=-1.041327273\) \(a_{88}=-0.591282570\) \(a_{89}=-1.017143354\) \(a_{90}=-0.244249405\)
\(a_{91}=-0.041814876\) \(a_{92}=+1.982178189\) \(a_{93}=+0.370349435\) \(a_{94}=-0.962099061\) \(a_{95}=+0.240322330\)
\(a_{96}=+0.502606297\) \(a_{97}=-0.429176588\) \(a_{98}=+1.565223466\) \(a_{99}=+0.175708953\) \(a_{100}=+0.336810774\)

Showing 100 of 1500 available coefficients

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