Properties

Label 7.24
Level $7$
Weight $0$
Character 7.1
Symmetry even
\(R\) 8.155725
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(8.15572563068450940971203787557 \pm 6 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.63350875 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.49658529 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.59866666 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.33812669 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.94809987 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +1.01276932 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.23976752 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.21420621 \pm 1 \cdot 10^{-8} \) \(a_{11}= +1.36104718 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.89595572 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.64892398 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.23944380 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.50603542 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.04293156 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.32650352 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.78540357 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.29880379 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.20242518 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.56565607 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.86223530 \pm 1 \cdot 10^{-8} \) \(a_{23}= +1.61484290 \pm 1 \cdot 10^{-8} \) \(a_{24}= +1.51569566 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.88567034 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.41109902 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.35883255 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.22627473 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -1.14056283 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.32057787 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.65087059 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.98557180 \pm 1 \cdot 10^{-8} \) \(a_{33}= +2.03692319 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.84035158 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.12779987 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -0.74220749 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.01768134 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.18929481 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.97117009 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.34244433 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.72958994 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.35834807 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -1.21916879 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.81481358 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.41919848 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -1.02301710 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.81554665 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.06425074 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.56107991 \pm 1 \cdot 10^{-8} \) \(a_{51}= +1.98522565 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.38848916 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.25823884 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.22732356 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.46020637 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.38279082 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -0.44718536 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.72255653 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.07842162 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.30294654 \pm 1 \cdot 10^{-8} \)

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