Properties

Label 21.26
Level $21$
Weight $0$
Character 21.1
Symmetry even
\(R\) 5.106611
Fricke sign $-1$

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Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(5.1066115556010620554847199129 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.83826913 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.29730487 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.89224406 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.48397491 \pm 1.2 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +1.08749062 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.74794064 \pm 1 \cdot 10^{-8} \) \(a_{11}= -1.67712750 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.17164905 \pm 1.2 \cdot 10^{-8} \)
\(a_{13}= -0.66206885 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.31683595 \pm 1.2 \cdot 10^{-8} \) \(a_{15}= +0.51513735 \pm 1.2 \cdot 10^{-8} \)
\(a_{16}= -0.61430494 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.51072932 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.27942304 \pm 1.2 \cdot 10^{-8} \)
\(a_{19}= -0.17154932 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.26526851 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.21821789 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +1.40588420 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.84360349 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.62786300 \pm 1.1 \cdot 10^{-8} \)
\(a_{25}= -0.20390055 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.55499188 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.11237068 \pm 1.2 \cdot 10^{-8} \) \(a_{29}= -1.99220999 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.43182373 \pm 1.3 \cdot 10^{-8} \)
\(a_{31}= +1.67609229 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.57253776 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.96829001 \pm 1.1 \cdot 10^{-8} \)
\(a_{34}= +0.42812862 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.33723655 \pm 1.2 \cdot 10^{-8} \) \(a_{36}= -0.09910162 \pm 1.2 \cdot 10^{-8} \)
\(a_{37}= -0.09746115 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.14380450 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.38224563 \pm 1.1 \cdot 10^{-8} \)
\(a_{40}= +0.97030704 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.08578376 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.18292532 \pm 1.2 \cdot 10^{-8} \)
\(a_{43}= -0.75732056 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.49861818 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.29741469 \pm 1.2 \cdot 10^{-8} \)
\(a_{46}= +0.70716676 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.15226278 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.35466912 \pm 1.1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.17092353 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.29486971 \pm 1.1 \cdot 10^{-8} \)
\(a_{52}= +0.19683630 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.09862576 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.16132497 \pm 1.2 \cdot 10^{-8} \)
\(a_{55}= -1.49640704 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.41103282 \pm 1.1 \cdot 10^{-8} \) \(a_{57}= -0.09904405 \pm 1.1 \cdot 10^{-8} \)
\(a_{58}= +1.67000813 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.38004166 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.15315284 \pm 1.3 \cdot 10^{-8} \)

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