Properties

Label 21.71
Level $21$
Weight $0$
Character 21.1
Symmetry odd
\(R\) 8.345437
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(8.34543779151581858717861114593 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.05198079 \pm 5.0 \cdot 10^{-6} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.99729800 \pm 5.9 \cdot 10^{-6} \) \(a_{5}= +0.36911106 \pm 4.0 \cdot 10^{-6} \) \(a_{6}= -0.03001112 \pm 5.1 \cdot 10^{-6} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.10382112 \pm 5.9 \cdot 10^{-6} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.01918668 \pm 4.9 \cdot 10^{-6} \) \(a_{11}= -1.34518328 \pm 3.9 \cdot 10^{-6} \) \(a_{12}= -0.57579027 \pm 5.9 \cdot 10^{-6} \)
\(a_{13}= +0.76668785 \pm 4.5 \cdot 10^{-6} \) \(a_{14}= -0.01964689 \pm 5.1 \cdot 10^{-6} \) \(a_{15}= +0.21310637 \pm 4.0 \cdot 10^{-6} \)
\(a_{16}= +0.99190129 \pm 4.9 \cdot 10^{-6} \) \(a_{17}= +1.44160041 \pm 4.4 \cdot 10^{-6} \) \(a_{18}= -0.01732693 \pm 5.1 \cdot 10^{-6} \)
\(a_{19}= -1.82249494 \pm 4.3 \cdot 10^{-6} \) \(a_{20}= -0.36811372 \pm 5.7 \cdot 10^{-6} \) \(a_{21}= +0.21821789 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.06992369 \pm 5.2 \cdot 10^{-6} \) \(a_{23}= +0.12807244 \pm 4.3 \cdot 10^{-6} \) \(a_{24}= +0.05994115 \pm 5.9 \cdot 10^{-6} \)
\(a_{25}= -0.86375703 \pm 4.0 \cdot 10^{-6} \) \(a_{26}= -0.03985304 \pm 4.9 \cdot 10^{-6} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.37694321 \pm 5.9 \cdot 10^{-6} \) \(a_{29}= -0.90128663 \pm 4.5 \cdot 10^{-6} \) \(a_{30}= -0.01107744 \pm 9.1 \cdot 10^{-6} \)
\(a_{31}= -0.25620466 \pm 4.7 \cdot 10^{-6} \) \(a_{32}= -0.15538093 \pm 4.5 \cdot 10^{-6} \) \(a_{33}= -0.77664193 \pm 3.9 \cdot 10^{-6} \)
\(a_{34}= -0.07493552 \pm 4.1 \cdot 10^{-6} \) \(a_{35}= +0.13951087 \pm 4.0 \cdot 10^{-6} \) \(a_{36}= -0.33243267 \pm 5.9 \cdot 10^{-6} \)
\(a_{37}= -1.85921479 \pm 4.0 \cdot 10^{-6} \) \(a_{38}= +0.09473472 \pm 5.0 \cdot 10^{-6} \) \(a_{39}= +0.44264744 \pm 4.5 \cdot 10^{-6} \)
\(a_{40}= +0.03832152 \pm 5.4 \cdot 10^{-6} \) \(a_{41}= -1.93951865 \pm 3.3 \cdot 10^{-6} \) \(a_{42}= -0.01134314 \pm 5.1 \cdot 10^{-6} \)
\(a_{43}= -0.21804173 \pm 4.5 \cdot 10^{-6} \) \(a_{44}= +1.34154859 \pm 5.8 \cdot 10^{-6} \) \(a_{45}= +0.12303702 \pm 4.0 \cdot 10^{-6} \)
\(a_{46}= -0.00665731 \pm 5.0 \cdot 10^{-6} \) \(a_{47}= -0.83100276 \pm 4.1 \cdot 10^{-6} \) \(a_{48}= +0.57267448 \pm 4.9 \cdot 10^{-6} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.04489877 \pm 3.9 \cdot 10^{-6} \) \(a_{51}= +0.83230838 \pm 4.4 \cdot 10^{-6} \)
\(a_{52}= -0.76461626 \pm 5.6 \cdot 10^{-6} \) \(a_{53}= +0.38903843 \pm 4.6 \cdot 10^{-6} \) \(a_{54}= -0.01000371 \pm 5.1 \cdot 10^{-6} \)
\(a_{55}= -0.49652202 \pm 3.5 \cdot 10^{-6} \) \(a_{56}= +0.03924070 \pm 5.9 \cdot 10^{-6} \) \(a_{57}= -1.05221794 \pm 4.3 \cdot 10^{-6} \)
\(a_{58}= +0.04684959 \pm 4.3 \cdot 10^{-6} \) \(a_{59}= +0.37899847 \pm 3.1 \cdot 10^{-6} \) \(a_{60}= -0.21253056 \pm 9.9 \cdot 10^{-6} \)

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