Properties

Label 15.65
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 9.824178
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: \(9.82417896066128541274978863687 \pm 9 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.83201443 \pm 3.1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.30775199 \pm 3.3 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.48036376 \pm 4.1 \cdot 10^{-8} \)
\(a_{7}= -1.15946452 \pm 2.1 \cdot 10^{-8} \) \(a_{8}= +1.08806853 \pm 3.3 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.37208816 \pm 4.1 \cdot 10^{-8} \) \(a_{11}= +1.51253669 \pm 1.8 \cdot 10^{-8} \) \(a_{12}= -0.17768069 \pm 4.3 \cdot 10^{-8} \)
\(a_{13}= -1.59511180 \pm 1.9 \cdot 10^{-8} \) \(a_{14}= +0.96469121 \pm 2.1 \cdot 10^{-8} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.59753673 \pm 2.6 \cdot 10^{-8} \) \(a_{17}= -1.25518491 \pm 2.4 \cdot 10^{-8} \) \(a_{18}= -0.27733814 \pm 4.1 \cdot 10^{-8} \)
\(a_{19}= -0.53242184 \pm 2.0 \cdot 10^{-8} \) \(a_{20}= -0.13763087 \pm 4.3 \cdot 10^{-8} \) \(a_{21}= -0.66941715 \pm 3.2 \cdot 10^{-8} \)
\(a_{22}= -1.25845235 \pm 2.0 \cdot 10^{-8} \) \(a_{23}= +0.99607643 \pm 2.7 \cdot 10^{-8} \) \(a_{24}= +0.62819666 \pm 4.4 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +1.32715604 \pm 2.2 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.35682751 \pm 1.9 \cdot 10^{-8} \) \(a_{29}= +0.88766924 \pm 2.7 \cdot 10^{-8} \) \(a_{30}= -0.21482520 \pm 4.1 \cdot 10^{-8} \)
\(a_{31}= -0.35798668 \pm 2.3 \cdot 10^{-8} \) \(a_{32}= -0.59090935 \pm 2.3 \cdot 10^{-8} \) \(a_{33}= +0.87326346 \pm 2.9 \cdot 10^{-8} \)
\(a_{34}= +1.04433196 \pm 3.2 \cdot 10^{-8} \) \(a_{35}= -0.51852829 \pm 3.2 \cdot 10^{-8} \) \(a_{36}= -0.10258400 \pm 4.3 \cdot 10^{-8} \)
\(a_{37}= +1.48711680 \pm 2.2 \cdot 10^{-8} \) \(a_{38}= +0.44298266 \pm 1.9 \cdot 10^{-8} \) \(a_{39}= -0.92093823 \pm 2.9 \cdot 10^{-8} \)
\(a_{40}= +0.48659904 \pm 4.4 \cdot 10^{-8} \) \(a_{41}= +1.49189814 \pm 2.1 \cdot 10^{-8} \) \(a_{42}= +0.55696473 \pm 6.3 \cdot 10^{-8} \)
\(a_{43}= +0.70822630 \pm 2.3 \cdot 10^{-8} \) \(a_{44}= -0.46548617 \pm 1.9 \cdot 10^{-8} \) \(a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= -0.82874996 \pm 4.2 \cdot 10^{-8} \) \(a_{47}= -0.55768184 \pm 1.6 \cdot 10^{-8} \) \(a_{48}= -0.34498799 \pm 3.6 \cdot 10^{-8} \)
\(a_{49}= +0.34435796 \pm 2.4 \cdot 10^{-8} \) \(a_{50}= -0.16640289 \pm 4.1 \cdot 10^{-8} \) \(a_{51}= -0.72468135 \pm 3.4 \cdot 10^{-8} \)
\(a_{52}= +0.49089883 \pm 2.5 \cdot 10^{-8} \) \(a_{53}= +1.60533090 \pm 1.7 \cdot 10^{-8} \) \(a_{54}= -0.16012125 \pm 4.1 \cdot 10^{-8} \)
\(a_{55}= +0.67642697 \pm 2.9 \cdot 10^{-8} \) \(a_{56}= -1.26157684 \pm 2.4 \cdot 10^{-8} \) \(a_{57}= -0.30739390 \pm 3.1 \cdot 10^{-8} \)
\(a_{58}= -0.73855361 \pm 4.0 \cdot 10^{-8} \) \(a_{59}= +1.13460463 \pm 2.5 \cdot 10^{-8} \) \(a_{60}= -0.07946122 \pm 4.3 \cdot 10^{-8} \)

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