Properties

Label 15.46
Level $15$
Weight $0$
Character 15.1
Symmetry odd
\(R\) 8.485439
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(8.4854397033297492137005702893 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.17225154 \pm 1.0 \cdot 10^{-6} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.37417368 \pm 1.0 \cdot 10^{-6} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.67679974 \pm 1.0 \cdot 10^{-6} \)
\(a_{7}= -1.42437306 \pm 9.2 \cdot 10^{-7} \) \(a_{8}= +0.73362587 \pm 7.7 \cdot 10^{-7} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.52424683 \pm 1.0 \cdot 10^{-6} \) \(a_{11}= +1.41031972 \pm 9.3 \cdot 10^{-7} \) \(a_{12}= -0.21602928 \pm 1.0 \cdot 10^{-6} \)
\(a_{13}= +1.41020145 \pm 9.2 \cdot 10^{-7} \) \(a_{14}= +1.66972351 \pm 1.0 \cdot 10^{-6} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -1.23416774 \pm 8.9 \cdot 10^{-7} \) \(a_{17}= -1.31860169 \pm 8.1 \cdot 10^{-7} \) \(a_{18}= -0.39075051 \pm 1.0 \cdot 10^{-6} \)
\(a_{19}= +1.11387576 \pm 8.0 \cdot 10^{-7} \) \(a_{20}= -0.16733556 \pm 1.0 \cdot 10^{-6} \) \(a_{21}= +0.82236217 \pm 9.3 \cdot 10^{-7} \)
\(a_{22}= -1.65324947 \pm 1.1 \cdot 10^{-6} \) \(a_{23}= +0.22922865 \pm 7.1 \cdot 10^{-7} \) \(a_{24}= -0.42355909 \pm 7.8 \cdot 10^{-7} \)
\(a_{25}= +0.2 \) \(a_{26}= -1.65311083 \pm 1.1 \cdot 10^{-6} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.53296291 \pm 1.1 \cdot 10^{-6} \) \(a_{29}= -1.61169906 \pm 5.9 \cdot 10^{-7} \) \(a_{30}= -0.30267405 \pm 1.0 \cdot 10^{-6} \)
\(a_{31}= +0.61776986 \pm 4.8 \cdot 10^{-7} \) \(a_{32}= +0.71312917 \pm 8.1 \cdot 10^{-7} \) \(a_{33}= -0.81424847 \pm 9.4 \cdot 10^{-7} \)
\(a_{34}= +1.54573286 \pm 1.0 \cdot 10^{-6} \) \(a_{35}= +0.63699900 \pm 9.3 \cdot 10^{-7} \) \(a_{36}= +0.12472456 \pm 1.0 \cdot 10^{-6} \)
\(a_{37}= +0.07025205 \pm 6.9 \cdot 10^{-7} \) \(a_{38}= -1.30574258 \pm 9.0 \cdot 10^{-7} \) \(a_{39}= -0.81418019 \pm 9.3 \cdot 10^{-7} \)
\(a_{40}= -0.32808746 \pm 7.8 \cdot 10^{-7} \) \(a_{41}= +0.92699518 \pm 8.1 \cdot 10^{-7} \) \(a_{42}= -0.96401532 \pm 2.0 \cdot 10^{-6} \)
\(a_{43}= -0.53247815 \pm 8.8 \cdot 10^{-7} \) \(a_{44}= +0.52770452 \pm 8.7 \cdot 10^{-7} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= -0.26871364 \pm 5.3 \cdot 10^{-7} \) \(a_{47}= -1.32097964 \pm 1.0 \cdot 10^{-6} \) \(a_{48}= +0.71254708 \pm 9.0 \cdot 10^{-7} \)
\(a_{49}= +1.02883860 \pm 6.9 \cdot 10^{-7} \) \(a_{50}= -0.23445031 \pm 1.0 \cdot 10^{-6} \) \(a_{51}= +0.76129504 \pm 8.2 \cdot 10^{-7} \)
\(a_{52}= +0.52766027 \pm 9.5 \cdot 10^{-7} \) \(a_{53}= +0.17515534 \pm 1.1 \cdot 10^{-6} \) \(a_{54}= +0.22559991 \pm 1.0 \cdot 10^{-6} \)
\(a_{55}= -0.63071415 \pm 9.4 \cdot 10^{-7} \) \(a_{56}= -1.04495692 \pm 7.9 \cdot 10^{-7} \) \(a_{57}= -0.64309647 \pm 8.1 \cdot 10^{-7} \)
\(a_{58}= +1.88931671 \pm 7.8 \cdot 10^{-7} \) \(a_{59}= -0.40724118 \pm 7.5 \cdot 10^{-7} \) \(a_{60}= +0.09661123 \pm 1.0 \cdot 10^{-6} \)

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