Properties

Label 7.44
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 10.64569
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(10.6456998610881626671684696437 \pm 10 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.50376920 \pm 4.6 \cdot 10^{-7} \) \(a_{3}= -1.80106382 \pm 3.0 \cdot 10^{-7} \)
\(a_{4}= -0.74621660 \pm 2.7 \cdot 10^{-7} \) \(a_{5}= +1.49735757 \pm 3.2 \cdot 10^{-7} \) \(a_{6}= +0.90732047 \pm 3.6 \cdot 10^{-7} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.87969013 \pm 3.0 \cdot 10^{-7} \) \(a_{9}= +2.24383089 \pm 2.9 \cdot 10^{-7} \)
\(a_{10}= -0.75432262 \pm 3.3 \cdot 10^{-7} \) \(a_{11}= -0.34690316 \pm 2.7 \cdot 10^{-7} \) \(a_{12}= +1.34398372 \pm 2.4 \cdot 10^{-7} \)
\(a_{13}= +0.18010998 \pm 3.3 \cdot 10^{-7} \) \(a_{14}= +0.19040686 \pm 4.7 \cdot 10^{-7} \) \(a_{15}= -2.69683655 \pm 2.5 \cdot 10^{-7} \)
\(a_{16}= +0.30305581 \pm 3.8 \cdot 10^{-7} \) \(a_{17}= +0.09654488 \pm 2.5 \cdot 10^{-7} \) \(a_{18}= -1.13037288 \pm 2.7 \cdot 10^{-7} \)
\(a_{19}= -0.38277255 \pm 3.2 \cdot 10^{-7} \) \(a_{20}= -1.11735307 \pm 2.1 \cdot 10^{-7} \) \(a_{21}= +0.68073814 \pm 3.1 \cdot 10^{-7} \)
\(a_{22}= +0.17475913 \pm 2.7 \cdot 10^{-7} \) \(a_{23}= -0.11414604 \pm 4.1 \cdot 10^{-7} \) \(a_{24}= -1.58437807 \pm 2.0 \cdot 10^{-7} \)
\(a_{25}= +1.24207970 \pm 3.1 \cdot 10^{-7} \) \(a_{26}= -0.09073386 \pm 4.1 \cdot 10^{-7} \) \(a_{27}= -2.24021881 \pm 3.3 \cdot 10^{-7} \)
\(a_{28}= +0.28204336 \pm 2.8 \cdot 10^{-7} \) \(a_{29}= +0.26151215 \pm 3.0 \cdot 10^{-7} \) \(a_{30}= +1.35858318 \pm 2.9 \cdot 10^{-7} \)
\(a_{31}= +0.52560445 \pm 2.5 \cdot 10^{-7} \) \(a_{32}= -1.03236031 \pm 4.0 \cdot 10^{-7} \) \(a_{33}= +0.62479474 \pm 2.3 \cdot 10^{-7} \)
\(a_{34}= -0.04863634 \pm 2.9 \cdot 10^{-7} \) \(a_{35}= -0.56594797 \pm 3.3 \cdot 10^{-7} \) \(a_{36}= -1.67438385 \pm 1.6 \cdot 10^{-7} \)
\(a_{37}= +1.40023940 \pm 3.1 \cdot 10^{-7} \) \(a_{38}= +0.19282902 \pm 3.2 \cdot 10^{-7} \) \(a_{39}= -0.32438958 \pm 2.5 \cdot 10^{-7} \)
\(a_{40}= +1.31721068 \pm 3.1 \cdot 10^{-7} \) \(a_{41}= -1.71375614 \pm 4.0 \cdot 10^{-7} \) \(a_{42}= -0.34293490 \pm 7.8 \cdot 10^{-7} \)
\(a_{43}= -0.81463946 \pm 2.4 \cdot 10^{-7} \) \(a_{44}= +0.25886490 \pm 2.0 \cdot 10^{-7} \) \(a_{45}= +3.35981718 \pm 2.6 \cdot 10^{-7} \)
\(a_{46}= +0.05750326 \pm 4.9 \cdot 10^{-7} \) \(a_{47}= -0.74773270 \pm 3.7 \cdot 10^{-7} \) \(a_{48}= -0.54582285 \pm 2.9 \cdot 10^{-7} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.62572149 \pm 3.7 \cdot 10^{-7} \) \(a_{51}= -0.17388349 \pm 1.8 \cdot 10^{-7} \)
\(a_{52}= -0.13440106 \pm 2.2 \cdot 10^{-7} \) \(a_{53}= -1.51277851 \pm 2.5 \cdot 10^{-7} \) \(a_{54}= +1.12855323 \pm 4.2 \cdot 10^{-7} \)
\(a_{55}= -0.51943808 \pm 2.7 \cdot 10^{-7} \) \(a_{56}= -0.33249162 \pm 3.1 \cdot 10^{-7} \) \(a_{57}= +0.68939780 \pm 1.6 \cdot 10^{-7} \)
\(a_{58}= -0.13174177 \pm 3.1 \cdot 10^{-7} \) \(a_{59}= +0.97360644 \pm 5.0 \cdot 10^{-7} \) \(a_{60}= +2.01242420 \pm 2.0 \cdot 10^{-7} \)

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