Properties

Label 47.1
Level $47$
Weight $0$
Character 47.1
Symmetry odd
\(R\) 0.585452
Fricke sign $+1$

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Maass form invariants

Level: \( 47 \)
Weight: \( 0 \)
Character: 47.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(0.585452143018342300656860380573 \pm 4 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.93283958 \pm 1.6 \cdot 10^{-6} \) \(a_{3}= -1.20462161 \pm 1.5 \cdot 10^{-6} \)
\(a_{4}= -0.12981032 \pm 1.6 \cdot 10^{-6} \) \(a_{5}= -0.66984044 \pm 1.4 \cdot 10^{-6} \) \(a_{6}= +1.12371872 \pm 1.6 \cdot 10^{-6} \)
\(a_{7}= -0.76458745 \pm 1.2 \cdot 10^{-6} \) \(a_{8}= +1.05393178 \pm 1.7 \cdot 10^{-6} \) \(a_{9}= +0.45111323 \pm 1.6 \cdot 10^{-6} \)
\(a_{10}= +0.62485368 \pm 1.7 \cdot 10^{-6} \) \(a_{11}= +0.56974287 \pm 1.3 \cdot 10^{-6} \) \(a_{12}= +0.15637231 \pm 1.5 \cdot 10^{-6} \)
\(a_{13}= -0.74185375 \pm 1.3 \cdot 10^{-6} \) \(a_{14}= +0.71323744 \pm 1.4 \cdot 10^{-6} \) \(a_{15}= +0.80690427 \pm 1.5 \cdot 10^{-6} \)
\(a_{16}= -0.85333896 \pm 1.9 \cdot 10^{-6} \) \(a_{17}= -0.95312882 \pm 1.2 \cdot 10^{-6} \) \(a_{18}= -0.42081628 \pm 1.6 \cdot 10^{-6} \)
\(a_{19}= +0.35909695 \pm 1.2 \cdot 10^{-6} \) \(a_{20}= +0.08695220 \pm 1.7 \cdot 10^{-6} \) \(a_{21}= +0.92103857 \pm 1.4 \cdot 10^{-6} \)
\(a_{22}= -0.53147870 \pm 1.6 \cdot 10^{-6} \) \(a_{23}= -1.62062257 \pm 1.2 \cdot 10^{-6} \) \(a_{24}= -1.26958900 \pm 1.6 \cdot 10^{-6} \)
\(a_{25}= -0.55131378 \pm 1.4 \cdot 10^{-6} \) \(a_{26}= +0.69203054 \pm 1.2 \cdot 10^{-6} \) \(a_{27}= +0.66120086 \pm 1.6 \cdot 10^{-6} \)
\(a_{28}= +0.09925134 \pm 1.4 \cdot 10^{-6} \) \(a_{29}= +0.95597535 \pm 1.3 \cdot 10^{-6} \) \(a_{30}= -0.75271224 \pm 1.7 \cdot 10^{-6} \)
\(a_{31}= -0.25474021 \pm 1.2 \cdot 10^{-6} \) \(a_{32}= -0.25790342 \pm 1.9 \cdot 10^{-6} \) \(a_{33}= -0.68632458 \pm 1.3 \cdot 10^{-6} \)
\(a_{34}= +0.88911629 \pm 1.4 \cdot 10^{-6} \) \(a_{35}= +0.51215159 \pm 1.3 \cdot 10^{-6} \) \(a_{36}= -0.05855915 \pm 1.6 \cdot 10^{-6} \)
\(a_{37}= +0.41932881 \pm 1.3 \cdot 10^{-6} \) \(a_{38}= -0.33497985 \pm 1.5 \cdot 10^{-6} \) \(a_{39}= +0.89365306 \pm 1.5 \cdot 10^{-6} \)
\(a_{40}= -0.70596613 \pm 1.7 \cdot 10^{-6} \) \(a_{41}= +0.69571917 \pm 1.3 \cdot 10^{-6} \) \(a_{42}= -0.85918123 \pm 1.7 \cdot 10^{-6} \)
\(a_{43}= +0.96639955 \pm 1.2 \cdot 10^{-6} \) \(a_{44}= -0.07395850 \pm 1.7 \cdot 10^{-6} \) \(a_{45}= -0.30217389 \pm 1.6 \cdot 10^{-6} \)
\(a_{46}= +1.51178088 \pm 1.5 \cdot 10^{-6} \) \(a_{47}= -0.14586499 \pm 1.0 \cdot 10^{-8} \) \(a_{48}= +1.02795056 \pm 1.6 \cdot 10^{-6} \)
\(a_{49}= -0.41540603 \pm 1.2 \cdot 10^{-6} \) \(a_{50}= +0.51428732 \pm 1.8 \cdot 10^{-6} \) \(a_{51}= +1.14815958 \pm 1.4 \cdot 10^{-6} \)
\(a_{52}= +0.09630027 \pm 1.2 \cdot 10^{-6} \) \(a_{53}= -0.55004640 \pm 1.4 \cdot 10^{-6} \) \(a_{54}= -0.61679434 \pm 1.7 \cdot 10^{-6} \)
\(a_{55}= -0.38163682 \pm 1.3 \cdot 10^{-6} \) \(a_{56}= -0.80582301 \pm 1.5 \cdot 10^{-6} \) \(a_{57}= -0.43257595 \pm 1.2 \cdot 10^{-6} \)
\(a_{58}= -0.89177164 \pm 1.5 \cdot 10^{-6} \) \(a_{59}= -0.83023455 \pm 1.3 \cdot 10^{-6} \) \(a_{60}= -0.10474450 \pm 1.7 \cdot 10^{-6} \)

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