Properties

Label 7.32
Level $7$
Weight $0$
Character 7.1
Symmetry even
\(R\) 9.043174
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(9.04317475934475316020212165607 \pm 8 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.76083825 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.40738712 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +2.10055136 \pm 1 \cdot 10^{-8} \) \(a_{5}= -1.65932682 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.71734283 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -1.93789294 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.83403573 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +2.92180614 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.57027487 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.85573758 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.15350800 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.66553430 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.67598838 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +1.31176465 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.04052070 \pm 1 \cdot 10^{-8} \) \(a_{18}= +1.46860202 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +1.40714906 \pm 1 \cdot 10^{-8} \) \(a_{20}= -3.48550121 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.15397786 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +1.00416181 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.43358674 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.78947263 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +1.75336550 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.27030275 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.74716254 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.79393379 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -0.67197674 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.19030620 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.62738347 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.37191245 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.23232264 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.07135041 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.62716659 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -1.75193489 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +1.35660258 \pm 1 \cdot 10^{-8} \) \(a_{38}= -2.47776189 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.06253718 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +3.21559772 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.78455291 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.27113011 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -1.32726359 \pm 1 \cdot 10^{-8} \) \(a_{44}= -1.19789166 \pm 1 \cdot 10^{-8} \) \(a_{45}= +1.38393786 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.76347612 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.01412394 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.53439603 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -3.08739304 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.01650761 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.32245143 \pm 1 \cdot 10^{-8} \) \(a_{53}= +1.16099364 \pm 1 \cdot 10^{-8} \) \(a_{54}= +1.31563238 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.94627239 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.73245468 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +0.57325441 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +1.18324234 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.52629429 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.41994831 \pm 1 \cdot 10^{-8} \)

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