Properties

Label 15.8
Level $15$
Weight $0$
Character 15.1
Symmetry even
\(R\) 3.492902
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: \(3.49290270259253829669762604106 \pm 8 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.88183811 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.22236155 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.50912947 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -1.74020519 \pm 1 \cdot 10^{-8} \) \(a_{8}= +1.07792500 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.39436999 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +0.05890722 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.12838050 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= -1.08130549 \pm 1 \cdot 10^{-8} \) \(a_{14}= +1.53457926 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.72819380 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.26911202 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.29394604 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= +0.92144269 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.09944311 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -1.00470793 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.05194663 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.73293349 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.62234029 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.95353639 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.38695472 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.11349613 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.22768962 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -0.69257519 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.43577595 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.03401010 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.23731324 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.77824342 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -0.07412052 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -1.50999645 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.81256328 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.62429201 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= -0.48206271 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= +0.96172487 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.88598975 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -0.36548642 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.01309870 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +0.64632869 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.16451821 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.42042288 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= +2.02831410 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.17636762 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.15537190 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= +0.24044076 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.03521137 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.16970982 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= -0.02634411 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= -1.87581067 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.53199519 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= -0.10008521 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.76396140 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.05741350 \pm 1.0 \cdot 10^{-8} \)

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