Properties

Label 15.2
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 1.821476
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(1.82147632892265862113987622066 \pm 4 \cdot 10^{-12}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= -1.63846228 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.68455866 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.94596664 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -0.21162199 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.12162354 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.73274261 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +0.52716911 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.97258039 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= +0.19759157 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.34673465 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.15317921 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.34894942 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.54615409 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= +0.53737445 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.75335753 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.12218001 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.86374670 \pm 1 \cdot 10^{-8} \) \(a_{23}= +1.17668744 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.64756965 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.32374634 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.35648965 \pm 1 \cdot 10^{-8} \) \(a_{29}= -1.80361931 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.42304914 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +0.64147283 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.87064518 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.30436123 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +2.21020274 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.09464023 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +0.56151955 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -0.10977070 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.88046777 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.11407955 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= -0.50160530 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= +0.10932670 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.20018734 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -1.35495942 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.88804728 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= -1.92795799 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.58719531 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.08843806 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.95521613 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.32769246 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.77881631 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= +0.33285459 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.90603290 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.31532221 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= +0.23575719 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= +0.23736020 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.31025328 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +2.95516221 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.54171547 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.43495117 \pm 1.0 \cdot 10^{-8} \)

Displaying $a_n$ with $n$ up to: 60 180 1000