Properties

Label 15.33
Level $15$
Weight $0$
Character 15.1
Symmetry odd
\(R\) 7.059654
Fricke sign $-1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(7.05965411929993922610252179018 \pm 7 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.59521575 \pm 9.3 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.64571821 \pm 9.3 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.34364797 \pm 1.0 \cdot 10^{-7} \)
\(a_{7}= -0.23719387 \pm 8.0 \cdot 10^{-8} \) \(a_{8}= -0.97955740 \pm 6.7 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.26618858 \pm 1.0 \cdot 10^{-7} \) \(a_{11}= +1.05269440 \pm 8.1 \cdot 10^{-8} \) \(a_{12}= +0.37280558 \pm 1.0 \cdot 10^{-7} \)
\(a_{13}= +0.95284560 \pm 8.0 \cdot 10^{-8} \) \(a_{14}= -0.14118153 \pm 9.6 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.06267021 \pm 7.8 \cdot 10^{-8} \) \(a_{17}= +0.74091617 \pm 7.1 \cdot 10^{-8} \) \(a_{18}= +0.19840525 \pm 1.0 \cdot 10^{-7} \)
\(a_{19}= +1.73306080 \pm 7.0 \cdot 10^{-8} \) \(a_{20}= -0.28877396 \pm 1.0 \cdot 10^{-7} \) \(a_{21}= +0.13694394 \pm 9.1 \cdot 10^{-8} \)
\(a_{22}= +0.62658029 \pm 9.7 \cdot 10^{-8} \) \(a_{23}= -0.60262529 \pm 6.2 \cdot 10^{-8} \) \(a_{24}= +0.56554773 \pm 7.8 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.56714871 \pm 1.0 \cdot 10^{-7} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.15316040 \pm 1.0 \cdot 10^{-7} \) \(a_{29}= -1.41169978 \pm 5.2 \cdot 10^{-8} \) \(a_{30}= -0.15368405 \pm 1.0 \cdot 10^{-7} \)
\(a_{31}= -0.01183810 \pm 4.2 \cdot 10^{-8} \) \(a_{32}= +1.01685970 \pm 7.1 \cdot 10^{-8} \) \(a_{33}= -0.60777339 \pm 9.2 \cdot 10^{-8} \)
\(a_{34}= +0.44100498 \pm 8.9 \cdot 10^{-8} \) \(a_{35}= -0.10607632 \pm 9.1 \cdot 10^{-8} \) \(a_{36}= -0.21523940 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= +0.82850905 \pm 6.0 \cdot 10^{-8} \) \(a_{38}= +1.03154509 \pm 7.9 \cdot 10^{-8} \) \(a_{39}= -0.55012566 \pm 9.1 \cdot 10^{-8} \)
\(a_{40}= -0.43807139 \pm 7.8 \cdot 10^{-8} \) \(a_{41}= +0.80838959 \pm 7.1 \cdot 10^{-8} \) \(a_{42}= +0.08151119 \pm 1.8 \cdot 10^{-7} \)
\(a_{43}= -0.76281401 \pm 7.7 \cdot 10^{-8} \) \(a_{44}= -0.67974394 \pm 7.6 \cdot 10^{-8} \) \(a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= -0.35869207 \pm 4.6 \cdot 10^{-8} \) \(a_{47}= +1.45089825 \pm 9.4 \cdot 10^{-8} \) \(a_{48}= -0.03618266 \pm 8.9 \cdot 10^{-8} \)
\(a_{49}= -0.94373907 \pm 6.0 \cdot 10^{-8} \) \(a_{50}= +0.11904315 \pm 1.0 \cdot 10^{-7} \) \(a_{51}= -0.42776815 \pm 8.1 \cdot 10^{-8} \)
\(a_{52}= -0.61526975 \pm 8.3 \cdot 10^{-8} \) \(a_{53}= +0.21894781 \pm 1.0 \cdot 10^{-7} \) \(a_{54}= -0.11454932 \pm 1.0 \cdot 10^{-7} \)
\(a_{55}= +0.47077925 \pm 9.2 \cdot 10^{-8} \) \(a_{56}= +0.23234501 \pm 6.9 \cdot 10^{-8} \) \(a_{57}= -1.00058312 \pm 8.1 \cdot 10^{-8} \)
\(a_{58}= -0.84026595 \pm 6.8 \cdot 10^{-8} \) \(a_{59}= +1.52872913 \pm 6.6 \cdot 10^{-8} \) \(a_{60}= +0.16672372 \pm 1.0 \cdot 10^{-7} \)

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