Properties

Label 1.45
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 33.57098
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 33.57098962762165661470681143187220\ldots \pm 5 \cdot 10^{-92} \) (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.

\(a_{1}= +1 \) \(a_{2}= -0.57690724 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.86122696 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.66717804 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.55274601 \pm 1 \cdot 10^{-8} \) \(a_{6}= +1.07375531 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.46703151 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.96180708 \pm 1 \cdot 10^{-8} \) \(a_{9}= +2.46416581 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.31888317 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.28556827 \pm 1 \cdot 10^{-8} \) \(a_{12}= +1.24176975 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.10920251 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.26943386 \pm 1 \cdot 10^{-8} \) \(a_{15}= +1.02878577 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.11230457 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.03963813 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.42159509 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.69925159 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.36878000 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.86925164 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.16474640 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.65002928 \pm 1 \cdot 10^{-8} \) \(a_{24}= -1.79014127 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.69447185 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.06299972 \pm 1 \cdot 10^{-8} \) \(a_{27}= -2.72514488 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.31159317 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.77208946 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.59351396 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.05441484 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.02659640 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.53150737 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.02286753 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.25814980 \pm 1 \cdot 10^{-8} \) \(a_{36}= -1.64403731 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +1.56471965 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.40340331 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.20325066 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.53163502 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.15858529 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.50147756 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +1.15711942 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.19052488 \pm 1 \cdot 10^{-8} \) \(a_{45}= -1.36205781 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.37500660 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.63299883 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.20902430 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.78188157 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.40064584 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.07377556 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.07285752 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.06355629 \pm 1 \cdot 10^{-8} \) \(a_{54}= +1.57215581 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.15784672 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.44919421 \pm 1 \cdot 10^{-8} \) \(a_{57}= -1.30146592 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.44542400 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.18112331 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.68638327 \pm 1 \cdot 10^{-8} \)

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