Properties

Label 1.62
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 38.12090
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 38.12090078958448018880646453420929\ldots \pm 4 \cdot 10^{-92} \) (toggle for full precision) Copy content Toggle raw display

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.00455768 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.76916484 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.99997923 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.56831922 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.00806328 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.43507453 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.00911526 \pm 1 \cdot 10^{-8} \) \(a_{9}= +2.12994423 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.00259022 \pm 1 \cdot 10^{-8} \) \(a_{11}= -1.42070638 \pm 1 \cdot 10^{-8} \) \(a_{12}= -1.76912809 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.35481216 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.00198293 \pm 1 \cdot 10^{-8} \) \(a_{15}= -1.00545039 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.99993768 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.24096470 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.00970760 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.82029209 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.56830742 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.76971856 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.00647512 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.96551554 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.01612640 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.67701326 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.00161712 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.99905760 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.43506549 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.82257965 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.00458252 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.80573499 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.01367266 \pm 1 \cdot 10^{-8} \) \(a_{33}= -2.51346377 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.00109824 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.24726122 \pm 1 \cdot 10^{-8} \) \(a_{36}= -2.12989999 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.31816007 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.00373863 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.62772119 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.00518038 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.66824749 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.00350813 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.46898984 \pm 1 \cdot 10^{-8} \) \(a_{44}= +1.42067686 \pm 1 \cdot 10^{-8} \) \(a_{45}= -1.21048825 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.00440051 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.77250694 \pm 1 \cdot 10^{-8} \) \(a_{48}= +1.76905459 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.81071015 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.00308561 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.42630628 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.35480479 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.19175342 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.00911106 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.80741474 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.00396582 \pm 1 \cdot 10^{-8} \) \(a_{57}= -1.45123192 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.00374905 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.05541877 \pm 1 \cdot 10^{-8} \) \(a_{60}= +1.00542950 \pm 1 \cdot 10^{-8} \)

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