Properties

Label 7.26
Level $7$
Weight $0$
Character 7.1
Symmetry even
\(R\) 8.421753
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(8.42175366821568324541770516257 \pm 9 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.84543830 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.21737289 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.28523407 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.68370100 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.18377536 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -1.08658612 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.95274903 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.57802702 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.41011161 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.06200215 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -1.07263404 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.31954564 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.14861806 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.63340745 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.12658052 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.80549052 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.71588423 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.19501482 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.08215923 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.34672407 \pm 1 \cdot 10^{-8} \) \(a_{23}= +1.08600269 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.23619436 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.53255294 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.90684591 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.42447469 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.10780835 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +0.84114572 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.12564740 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.88472263 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.55107919 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.08914714 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.10701602 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.25841469 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +0.27175649 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.88165027 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.60523595 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.23316156 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.74290002 \pm 1 \cdot 10^{-8} \) \(a_{41}= -1.43977756 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.06946056 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +1.34393022 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.11697781 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.65139547 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.91814828 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.28876436 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.13768561 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.45024065 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.02751517 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.30595178 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.32288505 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.35886716 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.28039372 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.41069095 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +0.15561382 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.71113681 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.92584662 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.04239093 \pm 1 \cdot 10^{-8} \)

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