Properties

Label 31.63
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 5.472621
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(5.47262197386512458138123320791 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.36431182 \pm 3.1 \cdot 10^{-6} \) \(a_{3}= +0.00214115 \pm 2.8 \cdot 10^{-6} \)
\(a_{4}= +0.86134674 \pm 3.4 \cdot 10^{-6} \) \(a_{5}= +1.13112098 \pm 2.6 \cdot 10^{-6} \) \(a_{6}= -0.00292120 \pm 3.5 \cdot 10^{-6} \)
\(a_{7}= -1.40913923 \pm 2.5 \cdot 10^{-6} \) \(a_{8}= +0.18916629 \pm 3.5 \cdot 10^{-6} \) \(a_{9}= -0.99999542 \pm 2.6 \cdot 10^{-6} \)
\(a_{10}= -1.54320172 \pm 3.2 \cdot 10^{-6} \) \(a_{11}= +0.31313490 \pm 2.5 \cdot 10^{-6} \) \(a_{12}= +0.00184428 \pm 4.1 \cdot 10^{-6} \)
\(a_{13}= +0.14222769 \pm 2.6 \cdot 10^{-6} \) \(a_{14}= +1.92250531 \pm 2.6 \cdot 10^{-6} \) \(a_{15}= +0.00242190 \pm 2.7 \cdot 10^{-6} \)
\(a_{16}= -1.11942854 \pm 3.1 \cdot 10^{-6} \) \(a_{17}= -0.20667115 \pm 2.4 \cdot 10^{-6} \) \(a_{18}= +1.36430556 \pm 3.4 \cdot 10^{-6} \)
\(a_{19}= -1.03891620 \pm 2.7 \cdot 10^{-6} \) \(a_{20}= +0.97428736 \pm 3.3 \cdot 10^{-6} \) \(a_{21}= -0.00301718 \pm 2.7 \cdot 10^{-6} \)
\(a_{22}= -0.42721364 \pm 2.8 \cdot 10^{-6} \) \(a_{23}= +1.50988969 \pm 2.4 \cdot 10^{-6} \) \(a_{24}= +0.00040503 \pm 4.3 \cdot 10^{-6} \)
\(a_{25}= +0.27943467 \pm 2.5 \cdot 10^{-6} \) \(a_{26}= -0.19404292 \pm 2.7 \cdot 10^{-6} \) \(a_{27}= -0.00428230 \pm 2.3 \cdot 10^{-6} \)
\(a_{28}= -1.21375748 \pm 2.7 \cdot 10^{-6} \) \(a_{29}= +1.53920358 \pm 2.4 \cdot 10^{-6} \) \(a_{30}= -0.00330423 \pm 3.6 \cdot 10^{-6} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +1.33808330 \pm 3.4 \cdot 10^{-6} \) \(a_{33}= +0.00067047 \pm 2.7 \cdot 10^{-6} \)
\(a_{34}= +0.28196389 \pm 3.3 \cdot 10^{-6} \) \(a_{35}= -1.59390695 \pm 2.3 \cdot 10^{-6} \) \(a_{36}= -0.86134279 \pm 3.7 \cdot 10^{-6} \)
\(a_{37}= -0.18935504 \pm 2.3 \cdot 10^{-6} \) \(a_{38}= +1.41740566 \pm 3.2 \cdot 10^{-6} \) \(a_{39}= +0.00030453 \pm 2.6 \cdot 10^{-6} \)
\(a_{40}= +0.21396995 \pm 3.4 \cdot 10^{-6} \) \(a_{41}= +0.72483617 \pm 2.3 \cdot 10^{-6} \) \(a_{42}= +0.00411638 \pm 3.2 \cdot 10^{-6} \)
\(a_{43}= +1.79287708 \pm 2.2 \cdot 10^{-6} \) \(a_{44}= +0.26971772 \pm 2.7 \cdot 10^{-6} \) \(a_{45}= -1.13111579 \pm 2.6 \cdot 10^{-6} \)
\(a_{46}= -2.05996035 \pm 2.3 \cdot 10^{-6} \) \(a_{47}= +0.50682233 \pm 2.2 \cdot 10^{-6} \) \(a_{48}= -0.00239687 \pm 4.0 \cdot 10^{-6} \)
\(a_{49}= +0.98567338 \pm 2.4 \cdot 10^{-6} \) \(a_{50}= -0.38123602 \pm 3.1 \cdot 10^{-6} \) \(a_{51}= -0.00044251 \pm 2.7 \cdot 10^{-6} \)
\(a_{52}= +0.12250736 \pm 2.7 \cdot 10^{-6} \) \(a_{53}= -1.93609179 \pm 2.4 \cdot 10^{-6} \) \(a_{54}= +0.00584239 \pm 3.1 \cdot 10^{-6} \)
\(a_{55}= +0.35419345 \pm 2.7 \cdot 10^{-6} \) \(a_{56}= -0.26656163 \pm 2.6 \cdot 10^{-6} \) \(a_{57}= -0.00222448 \pm 2.6 \cdot 10^{-6} \)
\(a_{58}= -2.09995363 \pm 2.8 \cdot 10^{-6} \) \(a_{59}= +1.55211933 \pm 2.7 \cdot 10^{-6} \) \(a_{60}= +0.00208610 \pm 4.0 \cdot 10^{-6} \)

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