Properties

Label 31.5
Level $31$
Weight $0$
Character 31.1
Symmetry even
\(R\) 1.754642
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(1.75464284976951069759948431403 \pm 3 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.15913305 \pm 1.4 \cdot 10^{-8} \) \(a_{3}= -0.34768590 \pm 1.3 \cdot 10^{-8} \)
\(a_{4}= -0.97467667 \pm 1.4 \cdot 10^{-8} \) \(a_{5}= +1.76902824 \pm 1.2 \cdot 10^{-8} \) \(a_{6}= -0.05532832 \pm 1.4 \cdot 10^{-8} \)
\(a_{7}= +0.71657374 \pm 1.2 \cdot 10^{-8} \) \(a_{8}= -0.31423631 \pm 1.4 \cdot 10^{-8} \) \(a_{9}= -0.87911452 \pm 1.2 \cdot 10^{-8} \)
\(a_{10}= +0.28151085 \pm 1.2 \cdot 10^{-8} \) \(a_{11}= +1.27166694 \pm 1.2 \cdot 10^{-8} \) \(a_{12}= +0.33888133 \pm 1.3 \cdot 10^{-8} \)
\(a_{13}= -0.55465629 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +0.11403056 \pm 1.7 \cdot 10^{-8} \) \(a_{15}= -0.61506617 \pm 1.3 \cdot 10^{-8} \)
\(a_{16}= +0.92467129 \pm 1.5 \cdot 10^{-8} \) \(a_{17}= -1.31842654 \pm 1.1 \cdot 10^{-8} \) \(a_{18}= -0.13989617 \pm 1.1 \cdot 10^{-8} \)
\(a_{19}= +0.30625787 \pm 1.1 \cdot 10^{-8} \) \(a_{20}= -1.72423056 \pm 1.2 \cdot 10^{-8} \) \(a_{21}= -0.24914258 \pm 1.2 \cdot 10^{-8} \)
\(a_{22}= +0.20236423 \pm 1.5 \cdot 10^{-8} \) \(a_{23}= +0.03520067 \pm 1.0 \cdot 10^{-8} \) \(a_{24}= +0.10925553 \pm 1.5 \cdot 10^{-8} \)
\(a_{25}= +2.12946090 \pm 1.3 \cdot 10^{-8} \) \(a_{26}= -0.08826415 \pm 1.1 \cdot 10^{-8} \) \(a_{27}= +0.65334162 \pm 1.3 \cdot 10^{-8} \)
\(a_{28}= -0.69842771 \pm 1.8 \cdot 10^{-8} \) \(a_{29}= -0.42156472 \pm 1.2 \cdot 10^{-8} \) \(a_{30}= -0.09787735 \pm 1.3 \cdot 10^{-8} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.46138207 \pm 1.4 \cdot 10^{-8} \) \(a_{33}= -0.44214066 \pm 1.4 \cdot 10^{-8} \)
\(a_{34}= -0.20980523 \pm 1.2 \cdot 10^{-8} \) \(a_{35}= +1.26763918 \pm 1.3 \cdot 10^{-8} \) \(a_{36}= +0.85685241 \pm 1.1 \cdot 10^{-8} \)
\(a_{37}= +0.24319054 \pm 1.2 \cdot 10^{-8} \) \(a_{38}= +0.04873575 \pm 1.4 \cdot 10^{-8} \) \(a_{39}= +0.19284617 \pm 1.2 \cdot 10^{-8} \)
\(a_{40}= -0.55589291 \pm 1.1 \cdot 10^{-8} \) \(a_{41}= +0.72180000 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.03964682 \pm 1.6 \cdot 10^{-8} \)
\(a_{43}= -0.14271416 \pm 1.2 \cdot 10^{-8} \) \(a_{44}= -1.23946411 \pm 1.5 \cdot 10^{-8} \) \(a_{45}= -1.55517840 \pm 1.3 \cdot 10^{-8} \)
\(a_{46}= +0.00560159 \pm 1.2 \cdot 10^{-8} \) \(a_{47}= -0.89737877 \pm 1.1 \cdot 10^{-8} \) \(a_{48}= -0.32149517 \pm 1.3 \cdot 10^{-8} \)
\(a_{49}= -0.48652208 \pm 1.1 \cdot 10^{-8} \) \(a_{50}= +0.33886760 \pm 1.2 \cdot 10^{-8} \) \(a_{51}= +0.45839831 \pm 1.1 \cdot 10^{-8} \)
\(a_{52}= +0.54061055 \pm 1.1 \cdot 10^{-8} \) \(a_{53}= -1.48016361 \pm 1.2 \cdot 10^{-8} \) \(a_{54}= +0.10396824 \pm 1.4 \cdot 10^{-8} \)
\(a_{55}= +2.24961473 \pm 1.3 \cdot 10^{-8} \) \(a_{56}= -0.22517349 \pm 1.8 \cdot 10^{-8} \) \(a_{57}= -0.10648154 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= -0.06708488 \pm 1.4 \cdot 10^{-8} \) \(a_{59}= +1.12464637 \pm 1.0 \cdot 10^{-8} \) \(a_{60}= +0.59949065 \pm 1.2 \cdot 10^{-8} \)

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