Properties

Label 2.3
Level $2$
Weight $0$
Character 2.1
Symmetry odd
\(R\) 8.273665
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(8.27366588958609552472525333895 \pm 4 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= +1.19821271 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.21310644 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.84726433 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= -0.94143619 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +0.43571370 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.15068901 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.84862842 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.59910636 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= +0.68598475 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.66569591 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.25534684 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.24707993 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.30809611 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= +0.58731713 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.10655322 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -1.12804081 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.60007091 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +1.67606999 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.42363217 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= -0.95458565 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.48506447 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= -0.67613502 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.47071809 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +0.58885986 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.18055748 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +1.01294005 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -1.01683735 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.17471189 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= +0.20062611 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.21785685 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -0.90102046 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.41529593 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= +0.82195565 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.07534450 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= +0.93939000 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.79764530 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -1.13741790 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.42431421 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= -0.09285339 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +1.18516046 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +0.50068856 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.29955318 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.11369791 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.67499398 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.29605431 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.34299237 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= -0.18007065 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.47809966 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= +0.18084818 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.33284796 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +0.70373085 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.41638680 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= +0.74562420 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.12767342 \pm 1.0 \cdot 10^{-8} \)

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