Properties

Label 15.3
Level $15$
Weight $0$
Character 15.1
Symmetry odd
\(R\) 2.230474
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: \(2.23047412064561808730126364629 \pm 6 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.11250388 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.23766488 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.64230441 \pm 1.8 \cdot 10^{-8} \)
\(a_{7}= +0.41466007 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.84810078 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.49752686 \pm 1.8 \cdot 10^{-8} \) \(a_{11}= +1.62560085 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.13721588 \pm 1.8 \cdot 10^{-8} \)
\(a_{13}= -1.20229706 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.46131094 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -1.18118028 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.86017003 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.37083463 \pm 1.8 \cdot 10^{-8} \)
\(a_{19}= -0.02743998 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.10628696 \pm 1.8 \cdot 10^{-8} \) \(a_{21}= -0.23940411 \pm 1.7 \cdot 10^{-8} \)
\(a_{22}= +1.80848724 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.73407444 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.48965121 \pm 1.6 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -1.33756014 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.09855013 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.34022030 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.28724727 \pm 1.8 \cdot 10^{-8} \)
\(a_{31}= +0.32701002 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.46596686 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.93854109 \pm 1.7 \cdot 10^{-8} \)
\(a_{34}= -0.95694250 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.18544162 \pm 1.7 \cdot 10^{-8} \) \(a_{36}= +0.07922163 \pm 1.8 \cdot 10^{-8} \)
\(a_{37}= +0.37166710 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.03052708 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.69414653 \pm 1.7 \cdot 10^{-8} \)
\(a_{40}= -0.37928220 \pm 1.6 \cdot 10^{-8} \) \(a_{41}= +1.25568310 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.26633800 \pm 2.6 \cdot 10^{-8} \)
\(a_{43}= -0.68976670 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.38634822 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +0.81666066 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.81773971 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.68195475 \pm 1.7 \cdot 10^{-8} \)
\(a_{49}= -0.82805702 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.22250078 \pm 1.8 \cdot 10^{-8} \) \(a_{51}= +0.49661940 \pm 1.6 \cdot 10^{-8} \)
\(a_{52}= -0.28574378 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.09641932 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.21410147 \pm 1.8 \cdot 10^{-8} \)
\(a_{55}= +0.72699080 \pm 1.7 \cdot 10^{-8} \) \(a_{56}= -0.35167353 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.01584248 \pm 1.6 \cdot 10^{-8} \)
\(a_{58}= +0.37849641 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.45939166 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.06136481 \pm 1.8 \cdot 10^{-8} \)

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