Properties

Label 101.5
Level $101$
Weight $0$
Character 101.1
Symmetry even
\(R\) 0.881980
Fricke sign $+1$

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Maass form invariants

Level: \( 101 \)
Weight: \( 0 \)
Character: 101.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(0.881980379496583899111386982194 \pm 3 \cdot 10^{-6}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.25379811 \pm 3.0 \cdot 10^{-4} \) \(a_{3}= +0.02554520 \pm 2.8 \cdot 10^{-4} \)
\(a_{4}= -0.93558652 \pm 3.2 \cdot 10^{-4} \) \(a_{5}= -0.67747235 \pm 2.6 \cdot 10^{-4} \) \(a_{6}= +0.00648332 \pm 3.4 \cdot 10^{-4} \)
\(a_{7}= +0.72802564 \pm 2.6 \cdot 10^{-4} \) \(a_{8}= -0.49124820 \pm 3.2 \cdot 10^{-4} \) \(a_{9}= -0.99934744 \pm 3.0 \cdot 10^{-4} \)
\(a_{10}= -0.17194120 \pm 3.2 \cdot 10^{-4} \) \(a_{11}= +1.64482086 \pm 2.6 \cdot 10^{-4} \) \(a_{12}= -0.02389975 \pm 3.6 \cdot 10^{-4} \)
\(a_{13}= -0.14764973 \pm 2.5 \cdot 10^{-4} \) \(a_{14}= +0.18477153 \pm 3.1 \cdot 10^{-4} \) \(a_{15}= -0.01730617 \pm 2.9 \cdot 10^{-4} \)
\(a_{16}= +0.81090865 \pm 3.2 \cdot 10^{-4} \) \(a_{17}= +0.29992340 \pm 2.5 \cdot 10^{-4} \) \(a_{18}= -0.25363249 \pm 3.7 \cdot 10^{-4} \)
\(a_{19}= +0.03079351 \pm 2.2 \cdot 10^{-4} \) \(a_{20}= +0.63383400 \pm 3.4 \cdot 10^{-4} \) \(a_{21}= +0.01859756 \pm 2.7 \cdot 10^{-4} \)
\(a_{22}= +0.41745243 \pm 2.9 \cdot 10^{-4} \) \(a_{23}= -0.94784463 \pm 2.5 \cdot 10^{-4} \) \(a_{24}= -0.01254904 \pm 3.9 \cdot 10^{-4} \)
\(a_{25}= -0.54103121 \pm 2.6 \cdot 10^{-4} \) \(a_{26}= -0.03747322 \pm 3.1 \cdot 10^{-4} \) \(a_{27}= -0.05107374 \pm 3.0 \cdot 10^{-4} \)
\(a_{28}= -0.68113097 \pm 3.4 \cdot 10^{-4} \) \(a_{29}= +1.21070858 \pm 2.6 \cdot 10^{-4} \) \(a_{30}= -0.00439227 \pm 3.4 \cdot 10^{-4} \)
\(a_{31}= +0.99431624 \pm 2.4 \cdot 10^{-4} \) \(a_{32}= +0.69705528 \pm 3.4 \cdot 10^{-4} \) \(a_{33}= +0.04201728 \pm 2.9 \cdot 10^{-4} \)
\(a_{34}= +0.07611999 \pm 3.0 \cdot 10^{-4} \) \(a_{35}= -0.49321724 \pm 2.7 \cdot 10^{-4} \) \(a_{36}= +0.93497599 \pm 4.0 \cdot 10^{-4} \)
\(a_{37}= -0.02001555 \pm 2.6 \cdot 10^{-4} \) \(a_{38}= +0.00781533 \pm 2.5 \cdot 10^{-4} \) \(a_{39}= -0.00377174 \pm 2.9 \cdot 10^{-4} \)
\(a_{40}= +0.33280708 \pm 3.2 \cdot 10^{-4} \) \(a_{41}= +0.33525195 \pm 2.3 \cdot 10^{-4} \) \(a_{42}= +0.00472003 \pm 3.1 \cdot 10^{-4} \)
\(a_{43}= -1.49523624 \pm 2.3 \cdot 10^{-4} \) \(a_{44}= -1.53887222 \pm 3.1 \cdot 10^{-4} \) \(a_{45}= +0.67703026 \pm 3.2 \cdot 10^{-4} \)
\(a_{46}= -0.24056118 \pm 2.9 \cdot 10^{-4} \) \(a_{47}= -1.77569741 \pm 2.5 \cdot 10^{-4} \) \(a_{48}= +0.02071483 \pm 3.7 \cdot 10^{-4} \)
\(a_{49}= -0.46997867 \pm 2.4 \cdot 10^{-4} \) \(a_{50}= -0.13731270 \pm 3.1 \cdot 10^{-4} \) \(a_{51}= +0.00766160 \pm 2.8 \cdot 10^{-4} \)
\(a_{52}= +0.13813910 \pm 3.2 \cdot 10^{-4} \) \(a_{53}= +1.63645960 \pm 2.5 \cdot 10^{-4} \) \(a_{54}= -0.01296242 \pm 3.5 \cdot 10^{-4} \)
\(a_{55}= -1.11432066 \pm 2.8 \cdot 10^{-4} \) \(a_{56}= -0.35764128 \pm 3.3 \cdot 10^{-4} \) \(a_{57}= +0.00078663 \pm 2.7 \cdot 10^{-4} \)
\(a_{58}= +0.30727555 \pm 3.0 \cdot 10^{-4} \) \(a_{59}= +1.57000893 \pm 2.3 \cdot 10^{-4} \) \(a_{60}= +0.01619142 \pm 3.7 \cdot 10^{-4} \)

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