Properties

Label 31.50
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 4.979136
Fricke sign $+1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(4.97913614469592260912157108948 \pm 10 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.43250426 \pm 3.4 \cdot 10^{-5} \) \(a_{3}= -0.97253215 \pm 3.0 \cdot 10^{-5} \)
\(a_{4}= +1.05206845 \pm 3.7 \cdot 10^{-5} \) \(a_{5}= +0.85538327 \pm 2.8 \cdot 10^{-5} \) \(a_{6}= -1.39315645 \pm 3.9 \cdot 10^{-5} \)
\(a_{7}= -0.99174623 \pm 2.8 \cdot 10^{-5} \) \(a_{8}= +0.07458827 \pm 3.9 \cdot 10^{-5} \) \(a_{9}= -0.05418122 \pm 2.9 \cdot 10^{-5} \)
\(a_{10}= +1.22534017 \pm 3.5 \cdot 10^{-5} \) \(a_{11}= -0.73904070 \pm 2.8 \cdot 10^{-5} \) \(a_{12}= -1.02317039 \pm 4.5 \cdot 10^{-5} \)
\(a_{13}= -0.92454602 \pm 2.9 \cdot 10^{-5} \) \(a_{14}= -1.42068070 \pm 2.9 \cdot 10^{-5} \) \(a_{15}= -0.83188773 \pm 2.9 \cdot 10^{-5} \)
\(a_{16}= -0.94522043 \pm 3.4 \cdot 10^{-5} \) \(a_{17}= -0.38308438 \pm 2.6 \cdot 10^{-5} \) \(a_{18}= -0.07761482 \pm 3.7 \cdot 10^{-5} \)
\(a_{19}= +0.20216068 \pm 2.9 \cdot 10^{-5} \) \(a_{20}= +0.89992175 \pm 3.6 \cdot 10^{-5} \) \(a_{21}= +0.96450509 \pm 3.0 \cdot 10^{-5} \)
\(a_{22}= -1.05867895 \pm 3.0 \cdot 10^{-5} \) \(a_{23}= +1.05953261 \pm 2.6 \cdot 10^{-5} \) \(a_{24}= -0.07253949 \pm 4.7 \cdot 10^{-5} \)
\(a_{25}= -0.26831946 \pm 2.7 \cdot 10^{-5} \) \(a_{26}= -1.32441611 \pm 2.9 \cdot 10^{-5} \) \(a_{27}= +1.02522512 \pm 2.5 \cdot 10^{-5} \)
\(a_{28}= -1.04338492 \pm 3.0 \cdot 10^{-5} \) \(a_{29}= -0.04216729 \pm 2.6 \cdot 10^{-5} \) \(a_{30}= -1.19168271 \pm 3.9 \cdot 10^{-5} \)
\(a_{31}= -0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= -1.42862056 \pm 3.7 \cdot 10^{-5} \) \(a_{33}= +0.71874084 \pm 3.0 \cdot 10^{-5} \)
\(a_{34}= -0.54877001 \pm 3.6 \cdot 10^{-5} \) \(a_{35}= -0.84832313 \pm 2.6 \cdot 10^{-5} \) \(a_{36}= -0.05700235 \pm 4.0 \cdot 10^{-5} \)
\(a_{37}= +1.15992607 \pm 2.5 \cdot 10^{-5} \) \(a_{38}= +0.28959603 \pm 3.5 \cdot 10^{-5} \) \(a_{39}= +0.89915073 \pm 2.8 \cdot 10^{-5} \)
\(a_{40}= +0.06380156 \pm 3.7 \cdot 10^{-5} \) \(a_{41}= +1.20367452 \pm 2.5 \cdot 10^{-5} \) \(a_{42}= +1.38165765 \pm 3.5 \cdot 10^{-5} \)
\(a_{43}= -1.63854104 \pm 2.4 \cdot 10^{-5} \) \(a_{44}= -0.77752140 \pm 2.9 \cdot 10^{-5} \) \(a_{45}= -0.04634571 \pm 2.8 \cdot 10^{-5} \)
\(a_{46}= +1.51778497 \pm 2.5 \cdot 10^{-5} \) \(a_{47}= -1.26757375 \pm 2.5 \cdot 10^{-5} \) \(a_{48}= +0.91925726 \pm 4.3 \cdot 10^{-5} \)
\(a_{49}= -0.01643942 \pm 2.6 \cdot 10^{-5} \) \(a_{50}= -0.38436878 \pm 3.4 \cdot 10^{-5} \) \(a_{51}= +0.37256188 \pm 3.0 \cdot 10^{-5} \)
\(a_{52}= -0.97268570 \pm 3.0 \cdot 10^{-5} \) \(a_{53}= -0.19481688 \pm 2.6 \cdot 10^{-5} \) \(a_{54}= +1.46863936 \pm 3.3 \cdot 10^{-5} \)
\(a_{55}= -0.63216305 \pm 3.0 \cdot 10^{-5} \) \(a_{56}= -0.07397264 \pm 2.9 \cdot 10^{-5} \) \(a_{57}= -0.19660776 \pm 2.9 \cdot 10^{-5} \)
\(a_{58}= -0.06040483 \pm 3.1 \cdot 10^{-5} \) \(a_{59}= -1.35560194 \pm 3.0 \cdot 10^{-5} \) \(a_{60}= -0.87520283 \pm 4.4 \cdot 10^{-5} \)

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