Properties

Label 15.48
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 8.665011
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: \(8.66501125743234703233038713886 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.78430801 \pm 2.2 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.18375508 \pm 2.3 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -1.03017071 \pm 3.2 \cdot 10^{-8} \)
\(a_{7}= -0.86471208 \pm 1.5 \cdot 10^{-8} \) \(a_{8}= -2.11218367 \pm 2.3 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.79796680 \pm 3.2 \cdot 10^{-8} \) \(a_{11}= +1.49839490 \pm 1.2 \cdot 10^{-8} \) \(a_{12}= +1.26079158 \pm 3.3 \cdot 10^{-8} \)
\(a_{13}= -1.32980681 \pm 1.3 \cdot 10^{-8} \) \(a_{14}= +1.54291270 \pm 1.5 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +1.58503116 \pm 1.8 \cdot 10^{-8} \) \(a_{17}= +1.28573655 \pm 1.7 \cdot 10^{-8} \) \(a_{18}= -0.59476934 \pm 3.2 \cdot 10^{-8} \)
\(a_{19}= +0.27539008 \pm 1.4 \cdot 10^{-8} \) \(a_{20}= -0.97660496 \pm 3.3 \cdot 10^{-8} \) \(a_{21}= -0.49924175 \pm 2.5 \cdot 10^{-8} \)
\(a_{22}= -2.67359803 \pm 1.4 \cdot 10^{-8} \) \(a_{23}= +0.54590729 \pm 1.9 \cdot 10^{-8} \) \(a_{24}= -1.21946981 \pm 3.4 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +2.37278494 \pm 1.5 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -1.88831940 \pm 1.3 \cdot 10^{-8} \) \(a_{29}= -1.09434703 \pm 1.9 \cdot 10^{-8} \) \(a_{30}= +0.46070635 \pm 3.2 \cdot 10^{-8} \)
\(a_{31}= +0.59510980 \pm 1.6 \cdot 10^{-8} \) \(a_{32}= -0.71600013 \pm 1.6 \cdot 10^{-8} \) \(a_{33}= +0.86509870 \pm 2.3 \cdot 10^{-8} \)
\(a_{34}= -2.29415002 \pm 2.2 \cdot 10^{-8} \) \(a_{35}= +0.38671100 \pm 2.5 \cdot 10^{-8} \) \(a_{36}= +0.72791836 \pm 3.3 \cdot 10^{-8} \)
\(a_{37}= -1.83037580 \pm 1.5 \cdot 10^{-8} \) \(a_{38}= -0.49138073 \pm 1.3 \cdot 10^{-8} \) \(a_{39}= -0.76776432 \pm 2.3 \cdot 10^{-8} \)
\(a_{40}= +0.94459725 \pm 3.4 \cdot 10^{-8} \) \(a_{41}= -0.61025692 \pm 1.4 \cdot 10^{-8} \) \(a_{42}= +0.89080106 \pm 4.7 \cdot 10^{-8} \)
\(a_{43}= +0.20796810 \pm 1.6 \cdot 10^{-8} \) \(a_{44}= +3.27212748 \pm 1.3 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= -0.97406675 \pm 2.9 \cdot 10^{-8} \) \(a_{47}= -1.16144440 \pm 1.1 \cdot 10^{-8} \) \(a_{48}= +0.91511817 \pm 2.8 \cdot 10^{-8} \)
\(a_{49}= -0.25227301 \pm 1.7 \cdot 10^{-8} \) \(a_{50}= -0.35686160 \pm 3.2 \cdot 10^{-8} \) \(a_{51}= +0.74232034 \pm 2.7 \cdot 10^{-8} \)
\(a_{52}= -2.90397236 \pm 1.7 \cdot 10^{-8} \) \(a_{53}= -0.80364722 \pm 1.2 \cdot 10^{-8} \) \(a_{54}= -0.34339024 \pm 3.2 \cdot 10^{-8} \)
\(a_{55}= -0.67010257 \pm 2.3 \cdot 10^{-8} \) \(a_{56}= +1.82643074 \pm 1.7 \cdot 10^{-8} \) \(a_{57}= +0.15899654 \pm 2.5 \cdot 10^{-8} \)
\(a_{58}= +1.95265216 \pm 2.8 \cdot 10^{-8} \) \(a_{59}= +0.29886782 \pm 1.7 \cdot 10^{-8} \) \(a_{60}= -0.56384314 \pm 3.3 \cdot 10^{-8} \)

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