Properties

Label 7.17
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 7.054070
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(7.05407006402443772681162287093 \pm 3 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.40005431 \pm 7.7 \cdot 10^{-8} \) \(a_{3}= +0.77754554 \pm 5.1 \cdot 10^{-8} \)
\(a_{4}= +0.96015208 \pm 4.6 \cdot 10^{-8} \) \(a_{5}= +0.34215209 \pm 5.4 \cdot 10^{-8} \) \(a_{6}= -1.08860598 \pm 6.1 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.05578925 \pm 5.0 \cdot 10^{-8} \) \(a_{9}= -0.39542294 \pm 4.8 \cdot 10^{-8} \)
\(a_{10}= -0.47903151 \pm 5.6 \cdot 10^{-8} \) \(a_{11}= -1.64843106 \pm 4.6 \cdot 10^{-8} \) \(a_{12}= +0.74656197 \pm 4.0 \cdot 10^{-8} \)
\(a_{13}= +0.36765423 \pm 5.6 \cdot 10^{-8} \) \(a_{14}= +0.52917079 \pm 8.7 \cdot 10^{-8} \) \(a_{15}= +0.26603883 \pm 4.3 \cdot 10^{-8} \)
\(a_{16}= -1.03826006 \pm 6.5 \cdot 10^{-8} \) \(a_{17}= -0.30573775 \pm 4.2 \cdot 10^{-8} \) \(a_{18}= +0.55361359 \pm 4.6 \cdot 10^{-8} \)
\(a_{19}= -1.46294233 \pm 5.4 \cdot 10^{-8} \) \(a_{20}= +0.32851804 \pm 3.5 \cdot 10^{-8} \) \(a_{21}= -0.29388459 \pm 6.2 \cdot 10^{-8} \)
\(a_{22}= +2.30789302 \pm 4.6 \cdot 10^{-8} \) \(a_{23}= +0.15051419 \pm 6.9 \cdot 10^{-8} \) \(a_{24}= +0.04337868 \pm 3.3 \cdot 10^{-8} \)
\(a_{25}= -0.88293195 \pm 5.1 \cdot 10^{-8} \) \(a_{26}= -0.51473589 \pm 6.8 \cdot 10^{-8} \) \(a_{27}= -1.08500488 \pm 5.6 \cdot 10^{-8} \)
\(a_{28}= -0.36290338 \pm 5.6 \cdot 10^{-8} \) \(a_{29}= +1.80198246 \pm 5.1 \cdot 10^{-8} \) \(a_{30}= -0.37246881 \pm 4.9 \cdot 10^{-8} \)
\(a_{31}= -0.35875082 \pm 4.1 \cdot 10^{-8} \) \(a_{32}= +1.39783123 \pm 6.7 \cdot 10^{-8} \) \(a_{33}= -1.28173021 \pm 3.8 \cdot 10^{-8} \)
\(a_{34}= +0.42804945 \pm 5.0 \cdot 10^{-8} \) \(a_{35}= -0.12932133 \pm 6.5 \cdot 10^{-8} \) \(a_{36}= -0.37966616 \pm 2.7 \cdot 10^{-8} \)
\(a_{37}= -0.70779263 \pm 5.2 \cdot 10^{-8} \) \(a_{38}= +2.04819872 \pm 5.3 \cdot 10^{-8} \) \(a_{39}= +0.28586790 \pm 4.2 \cdot 10^{-8} \)
\(a_{40}= +0.01908841 \pm 5.2 \cdot 10^{-8} \) \(a_{41}= -1.22347525 \pm 6.7 \cdot 10^{-8} \) \(a_{42}= +0.41145439 \pm 1.3 \cdot 10^{-7} \)
\(a_{43}= +0.10338373 \pm 4.0 \cdot 10^{-8} \) \(a_{44}= -1.58274452 \pm 3.4 \cdot 10^{-8} \) \(a_{45}= -0.13529478 \pm 4.3 \cdot 10^{-8} \)
\(a_{46}= -0.21072804 \pm 8.2 \cdot 10^{-8} \) \(a_{47}= +1.03833078 \pm 6.2 \cdot 10^{-8} \) \(a_{48}= -0.80729447 \pm 4.9 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +1.23615268 \pm 6.3 \cdot 10^{-8} \) \(a_{51}= -0.23772502 \pm 3.1 \cdot 10^{-8} \)
\(a_{52}= +0.35300397 \pm 3.6 \cdot 10^{-8} \) \(a_{53}= +0.70159950 \pm 4.2 \cdot 10^{-8} \) \(a_{54}= +1.51906576 \pm 7.1 \cdot 10^{-8} \)
\(a_{55}= -0.56401413 \pm 4.5 \cdot 10^{-8} \) \(a_{56}= -0.02108635 \pm 6.1 \cdot 10^{-8} \) \(a_{57}= -1.13750428 \pm 2.7 \cdot 10^{-8} \)
\(a_{58}= -2.52287331 \pm 5.2 \cdot 10^{-8} \) \(a_{59}= +0.56523109 \pm 8.4 \cdot 10^{-8} \) \(a_{60}= +0.25543774 \pm 3.5 \cdot 10^{-8} \)

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