Properties

Label 15.22
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 5.859504
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: \(5.85950414296348633115912355467 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.49233525 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.22706450 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.86160016 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.43506977 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.33885636 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.66739261 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -1.45351474 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.70844602 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= +1.43663049 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.64926995 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.72137721 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.12264391 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.49744508 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= -0.11950906 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.54875993 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.25118765 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +2.16913128 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.50557738 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.19563881 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -2.14393433 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.53385867 \pm 1 \cdot 10^{-8} \) \(a_{29}= -1.46699387 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.38531931 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +0.42825837 \pm 1 \cdot 10^{-8} \) \(a_{32}= +1.41539300 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.83918712 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= -0.18302583 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.19456911 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +0.40902150 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= +0.32724539 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.17834758 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.82943900 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= -0.15154117 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -0.50373965 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.37485618 \pm 1.1 \cdot 10^{-8} \)
\(a_{43}= -1.56281428 \pm 1 \cdot 10^{-8} \) \(a_{44}= -1.78355634 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +2.24682619 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.90218632 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.41648733 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.81071430 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.29846705 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.07080849 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= +1.76283828 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.30016658 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.28720005 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= -0.65003155 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= -0.14742616 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.06899859 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +2.18924666 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.87399392 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.31682669 \pm 1.0 \cdot 10^{-8} \)

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