Properties

Label 15.45
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 8.393886
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: \(8.39388640633562060543200192275 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.87004335 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.24302457 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.50231976 \pm 1.2 \cdot 10^{-8} \)
\(a_{7}= +1.50060735 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.08148526 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.38909522 \pm 1.2 \cdot 10^{-8} \) \(a_{11}= -1.36405327 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.14031030 \pm 1.2 \cdot 10^{-8} \)
\(a_{13}= +0.20552463 \pm 1 \cdot 10^{-8} \) \(a_{14}= +1.30559345 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.69791449 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.75422476 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.29001445 \pm 1.2 \cdot 10^{-8} \)
\(a_{19}= -0.00425440 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.10868389 \pm 1.2 \cdot 10^{-8} \) \(a_{21}= -0.86637606 \pm 1.1 \cdot 10^{-8} \)
\(a_{22}= -1.18678548 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.29879424 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.62439581 \pm 1.2 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.17881534 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.36468445 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.34075076 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.22464423 \pm 1.2 \cdot 10^{-8} \)
\(a_{31}= -1.27716968 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.47426939 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.78753652 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= -1.52625159 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.67109201 \pm 1.1 \cdot 10^{-8} \) \(a_{36}= -0.08100819 \pm 1.2 \cdot 10^{-8} \)
\(a_{37}= -0.81921751 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.00370151 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.11865970 \pm 1.1 \cdot 10^{-8} \)
\(a_{40}= -0.48365491 \pm 1.2 \cdot 10^{-8} \) \(a_{41}= +1.00041861 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.75378473 \pm 1.3 \cdot 10^{-8} \)
\(a_{43}= +1.20126978 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.33149845 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= -1.13000729 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.78380638 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.40294112 \pm 1.1 \cdot 10^{-8} \)
\(a_{49}= +1.25182242 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.17400867 \pm 1.2 \cdot 10^{-8} \) \(a_{51}= +1.01280214 \pm 1.1 \cdot 10^{-8} \)
\(a_{52}= -0.04994753 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.10348909 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.16743992 \pm 1.2 \cdot 10^{-8} \)
\(a_{55}= -0.61002317 \pm 1.1 \cdot 10^{-8} \) \(a_{56}= -1.62288473 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.00245628 \pm 1.1 \cdot 10^{-8} \)
\(a_{58}= -0.29646794 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.29659243 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.06274867 \pm 1.2 \cdot 10^{-8} \)

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