Properties

Label 7.77
Level $7$
Weight $0$
Character 7.1
Symmetry even
\(R\) 13.60532
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(13.6053245137724225206712525349 \pm 7 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.20114190 \pm 2.6 \cdot 10^{-8} \) \(a_{3}= +1.65214621 \pm 3.0 \cdot 10^{-8} \)
\(a_{4}= +0.44274187 \pm 3.5 \cdot 10^{-8} \) \(a_{5}= -1.10751483 \pm 1.1 \cdot 10^{-8} \) \(a_{6}= -1.98446204 \pm 2.3 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.66934609 \pm 3.0 \cdot 10^{-8} \) \(a_{9}= +1.72958710 \pm 2.6 \cdot 10^{-8} \)
\(a_{10}= +1.33028247 \pm 1.2 \cdot 10^{-8} \) \(a_{11}= -1.13673877 \pm 1.8 \cdot 10^{-8} \) \(a_{12}= +0.73147430 \pm 3.6 \cdot 10^{-8} \)
\(a_{13}= +0.45889837 \pm 1.7 \cdot 10^{-8} \) \(a_{14}= +0.45398897 \pm 3.6 \cdot 10^{-8} \) \(a_{15}= -1.82977644 \pm 1.2 \cdot 10^{-8} \)
\(a_{16}= -1.24672151 \pm 3.1 \cdot 10^{-8} \) \(a_{17}= +1.47601220 \pm 1.8 \cdot 10^{-8} \) \(a_{18}= -2.07747954 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.30127574 \pm 2.3 \cdot 10^{-8} \) \(a_{20}= -0.49034319 \pm 1.1 \cdot 10^{-8} \) \(a_{21}= -0.62445257 \pm 4.0 \cdot 10^{-8} \)
\(a_{22}= +1.36538457 \pm 2.3 \cdot 10^{-8} \) \(a_{23}= -0.74227501 \pm 1.9 \cdot 10^{-8} \) \(a_{24}= +1.10585761 \pm 2.6 \cdot 10^{-8} \)
\(a_{25}= +0.22658911 \pm 2.1 \cdot 10^{-8} \) \(a_{26}= -0.55120206 \pm 1.6 \cdot 10^{-8} \) \(a_{27}= +1.20538457 \pm 2.2 \cdot 10^{-8} \)
\(a_{28}= -0.16734070 \pm 4.6 \cdot 10^{-8} \) \(a_{29}= -0.00275899 \pm 2.0 \cdot 10^{-8} \) \(a_{30}= +2.19782115 \pm 1.3 \cdot 10^{-8} \)
\(a_{31}= +1.97891645 \pm 2.6 \cdot 10^{-8} \) \(a_{32}= +0.82814335 \pm 1.5 \cdot 10^{-8} \) \(a_{33}= -1.87805866 \pm 2.1 \cdot 10^{-8} \)
\(a_{34}= -1.77290010 \pm 1.1 \cdot 10^{-8} \) \(a_{35}= +0.41860126 \pm 2.2 \cdot 10^{-8} \) \(a_{36}= +0.76576062 \pm 2.7 \cdot 10^{-8} \)
\(a_{37}= +1.40261147 \pm 1.8 \cdot 10^{-8} \) \(a_{38}= +0.36187491 \pm 1.9 \cdot 10^{-8} \) \(a_{39}= +0.75816720 \pm 2.2 \cdot 10^{-8} \)
\(a_{40}= -0.74131073 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= +0.38722309 \pm 2.5 \cdot 10^{-8} \) \(a_{42}= +0.75005615 \pm 6.6 \cdot 10^{-8} \)
\(a_{43}= +0.19529846 \pm 2.7 \cdot 10^{-8} \) \(a_{44}= -0.50328185 \pm 3.0 \cdot 10^{-8} \) \(a_{45}= -1.91554337 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.89157761 \pm 1.4 \cdot 10^{-8} \) \(a_{47}= +1.29440898 \pm 1.7 \cdot 10^{-8} \) \(a_{48}= -2.05976621 \pm 3.4 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.27216567 \pm 2.2 \cdot 10^{-8} \) \(a_{51}= +2.43858796 \pm 2.4 \cdot 10^{-8} \)
\(a_{52}= +0.20317352 \pm 1.9 \cdot 10^{-8} \) \(a_{53}= -0.23946491 \pm 2.8 \cdot 10^{-8} \) \(a_{54}= -1.44783791 \pm 2.7 \cdot 10^{-8} \)
\(a_{55}= +1.25895506 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.25298904 \pm 4.1 \cdot 10^{-8} \) \(a_{57}= -0.49775157 \pm 2.4 \cdot 10^{-8} \)
\(a_{58}= +0.00331394 \pm 2.1 \cdot 10^{-8} \) \(a_{59}= +1.34122437 \pm 1.3 \cdot 10^{-8} \) \(a_{60}= -0.81011864 \pm 1.1 \cdot 10^{-8} \)

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