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: \( 3.22026652843 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.850039502\) \(a_{3}=-0.577350269\) \(a_{4}=+2.422646161\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.068120805\) \(a_{7}=-0.054710220\) \(a_{8}=+2.631951595\) \(a_{9}=+0.333333333\) \(a_{10}=-0.827362818\)
\(a_{11}=-0.515869390\) \(a_{12}=-1.398715413\) \(a_{13}=-0.753399452\) \(a_{14}=-0.101216069\) \(a_{15}=+0.258198890\)
\(a_{16}=+2.446568259\) \(a_{17}=+0.560762004\) \(a_{18}=+0.616679834\) \(a_{19}=-0.315287600\) \(a_{20}=-1.083440300\)
\(a_{21}=+0.031586960\) \(a_{22}=-0.954378749\) \(a_{23}=+1.852077391\) \(a_{24}=-1.519557962\) \(a_{25}=+0.200000000\)
\(a_{26}=-1.393818747\) \(a_{27}=-0.192450090\) \(a_{28}=-0.132543505\) \(a_{29}=+0.252329440\) \(a_{30}=+0.477678145\)
\(a_{31}=-0.891324757\) \(a_{32}=+1.894296329\) \(a_{33}=+0.297837331\) \(a_{34}=+1.037431860\) \(a_{35}=+0.024467156\)
\(a_{36}=+0.807548720\) \(a_{37}=-1.017790359\) \(a_{38}=-0.583294514\) \(a_{39}=+0.434975376\) \(a_{40}=-1.177044536\)
\(a_{41}=-1.219399856\) \(a_{42}=+0.058437125\) \(a_{43}=+0.747908062\) \(a_{44}=-1.249768997\) \(a_{45}=-0.149071199\)
\(a_{46}=+3.426416334\) \(a_{47}=+1.255667643\) \(a_{48}=-1.412526843\) \(a_{49}=-0.997006792\) \(a_{50}=+0.370007900\)
\(a_{51}=-0.323756094\) \(a_{52}=-1.825220289\) \(a_{53}=+0.084867145\) \(a_{54}=-0.356040269\) \(a_{55}=+0.230703804\)
\(a_{56}=-0.143994651\) \(a_{57}=+0.182031380\) \(a_{58}=+0.466819431\) \(a_{59}=+1.535321579\) \(a_{60}=+0.625524548\)
\(a_{61}=-1.089431199\) \(a_{62}=-1.648986010\) \(a_{63}=-0.018236740\) \(a_{64}=+1.057954784\) \(a_{65}=+0.336930476\)
\(a_{66}=+0.551010822\) \(a_{67}=+1.257468475\) \(a_{68}=+1.358527906\) \(a_{69}=-1.069297365\) \(a_{70}=+0.045265207\)
\(a_{71}=-0.522118773\) \(a_{72}=+0.877317248\) \(a_{73}=-0.066198889\) \(a_{74}=-1.882952428\) \(a_{75}=-0.115470008\)
\(a_{76}=-0.763830257\) \(a_{77}=+0.028223328\) \(a_{78}=+0.804721632\) \(a_{79}=+0.214596407\) \(a_{80}=-1.094138589\)
\(a_{81}=+0.111111111\) \(a_{82}=-2.255937903\) \(a_{83}=-0.869807300\) \(a_{84}=+0.076524039\) \(a_{85}=-0.250780386\)
\(a_{86}=+1.383659456\) \(a_{87}=-0.145682473\) \(a_{88}=-1.357743257\) \(a_{89}=+1.334237666\) \(a_{90}=-0.275787500\)
\(a_{91}=+0.041218661\) \(a_{92}=+4.486928098\) \(a_{93}=+0.514606755\) \(a_{94}=+2.323034855\) \(a_{95}=+0.141001226\)
\(a_{96}=-1.093672587\) \(a_{97}=+0.541756926\) \(a_{98}=-1.844503751\) \(a_{99}=-0.171956220\) \(a_{100}=+0.484528185\)

Showing 100 of 1500 available coefficients

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