Properties

Label 1.2
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 12.17300
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 12.17300832467967784952795117639554\ldots \pm 4 \cdot 10^{-93} \) (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.

\(a_{1}= +1 \) \(a_{2}= +0.28925187 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.20185876 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.91633335 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.03955271 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.34763990 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.44813310 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.55430301 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.44446448 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.01144069 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.69145078 \pm 1 \cdot 10^{-8} \) \(a_{12}= +1.10130327 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.80278000 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.12962334 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.04753677 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.75600017 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.03767537 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.12856218 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.63717881 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.03624346 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.53859270 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.20000343 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.50879869 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.66619393 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.99843558 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.23220562 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.66767523 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.41063931 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.77999688 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.01375010 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.59801358 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.77297747 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.83102618 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.30014954 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.01772488 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.40727763 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.42921516 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.18430516 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.96482818 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.02192418 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.54852419 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.15578895 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.48935502 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.63359942 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.01757977 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.14717097 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.81686801 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.90860543 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.79917672 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.28879936 \pm 1 \cdot 10^{-8} \) \(a_{51}= +1.24713924 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.73561409 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.97875605 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.19312631 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.02734875 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.24840153 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.76579893 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.22561556 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.34293138 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.04355953 \pm 1 \cdot 10^{-8} \)

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