Properties

Label 21.10
Level $21$
Weight $0$
Character 21.1
Symmetry odd
\(R\) 3.251207
Fricke sign $-1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.25120755731627793275771431396 \pm 6 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.34252536 \pm 4.6 \cdot 10^{-7} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.80237434 \pm 5.3 \cdot 10^{-7} \) \(a_{5}= +1.55320399 \pm 3.6 \cdot 10^{-7} \) \(a_{6}= -0.77510738 \pm 4.7 \cdot 10^{-7} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.26531746 \pm 5.3 \cdot 10^{-7} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -2.08521574 \pm 4.4 \cdot 10^{-7} \) \(a_{11}= +0.95130788 \pm 3.5 \cdot 10^{-7} \) \(a_{12}= +0.46325104 \pm 5.4 \cdot 10^{-7} \)
\(a_{13}= +1.23666557 \pm 4.1 \cdot 10^{-7} \) \(a_{14}= +0.50742689 \pm 4.7 \cdot 10^{-7} \) \(a_{15}= +0.89674274 \pm 3.7 \cdot 10^{-7} \)
\(a_{16}= -1.15856976 \pm 4.4 \cdot 10^{-7} \) \(a_{17}= -0.63940034 \pm 4.0 \cdot 10^{-7} \) \(a_{18}= -0.44750845 \pm 4.7 \cdot 10^{-7} \)
\(a_{19}= -0.14744390 \pm 3.9 \cdot 10^{-7} \) \(a_{20}= +1.24625102 \pm 5.2 \cdot 10^{-7} \) \(a_{21}= -0.21821789 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -1.27715496 \pm 4.7 \cdot 10^{-7} \) \(a_{23}= +0.43647465 \pm 3.8 \cdot 10^{-7} \) \(a_{24}= +0.15318111 \pm 5.4 \cdot 10^{-7} \)
\(a_{25}= +1.41244262 \pm 3.7 \cdot 10^{-7} \) \(a_{26}= -1.66025489 \pm 4.4 \cdot 10^{-7} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.30326900 \pm 5.4 \cdot 10^{-7} \) \(a_{29}= +0.97406121 \pm 4.0 \cdot 10^{-7} \) \(a_{30}= -1.20389987 \pm 8.3 \cdot 10^{-7} \)
\(a_{31}= -1.25035990 \pm 4.2 \cdot 10^{-7} \) \(a_{32}= +1.29009182 \pm 4.1 \cdot 10^{-7} \) \(a_{33}= +0.54923786 \pm 3.6 \cdot 10^{-7} \)
\(a_{34}= +0.85841118 \pm 3.7 \cdot 10^{-7} \) \(a_{35}= -0.58705593 \pm 3.7 \cdot 10^{-7} \) \(a_{36}= +0.26745811 \pm 5.4 \cdot 10^{-7} \)
\(a_{37}= -1.38832542 \pm 3.6 \cdot 10^{-7} \) \(a_{38}= +0.19794718 \pm 4.5 \cdot 10^{-7} \) \(a_{39}= +0.71398920 \pm 4.2 \cdot 10^{-7} \)
\(a_{40}= +0.41209213 \pm 4.8 \cdot 10^{-7} \) \(a_{41}= +0.62741547 \pm 3.0 \cdot 10^{-7} \) \(a_{42}= +0.29296305 \pm 4.7 \cdot 10^{-7} \)
\(a_{43}= +0.43654656 \pm 4.1 \cdot 10^{-7} \) \(a_{44}= +0.76330503 \pm 5.3 \cdot 10^{-7} \) \(a_{45}= +0.51773466 \pm 3.7 \cdot 10^{-7} \)
\(a_{46}= -0.58597828 \pm 4.5 \cdot 10^{-7} \) \(a_{47}= -1.27684306 \pm 3.7 \cdot 10^{-7} \) \(a_{48}= -0.66890056 \pm 4.5 \cdot 10^{-7} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -1.89624004 \pm 3.5 \cdot 10^{-7} \) \(a_{51}= -0.36915796 \pm 4.1 \cdot 10^{-7} \)
\(a_{52}= +0.99226872 \pm 5.0 \cdot 10^{-7} \) \(a_{53}= -1.19393845 \pm 4.1 \cdot 10^{-7} \) \(a_{54}= -0.25836913 \pm 4.7 \cdot 10^{-7} \)
\(a_{55}= +1.47757519 \pm 3.2 \cdot 10^{-7} \) \(a_{56}= -0.10028057 \pm 5.4 \cdot 10^{-7} \) \(a_{57}= -0.08512678 \pm 4.0 \cdot 10^{-7} \)
\(a_{58}= -1.30770188 \pm 3.9 \cdot 10^{-7} \) \(a_{59}= -0.40595360 \pm 2.8 \cdot 10^{-7} \) \(a_{60}= +0.71952336 \pm 9.1 \cdot 10^{-7} \)

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