Properties

Label 21.73
Level $21$
Weight $0$
Character 21.1
Symmetry odd
\(R\) 8.557904
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: \(8.55790422191291735607221572644 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.29837478 \pm 2.4 \cdot 10^{-6} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.68577706 \pm 2.8 \cdot 10^{-6} \) \(a_{5}= -0.92976698 \pm 1.9 \cdot 10^{-6} \) \(a_{6}= -0.74961703 \pm 2.4 \cdot 10^{-6} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.40797914 \pm 2.8 \cdot 10^{-6} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +1.20718600 \pm 2.3 \cdot 10^{-6} \) \(a_{11}= -0.20539436 \pm 1.8 \cdot 10^{-6} \) \(a_{12}= +0.39593357 \pm 2.8 \cdot 10^{-6} \)
\(a_{13}= -0.32328544 \pm 2.1 \cdot 10^{-6} \) \(a_{14}= +0.49073954 \pm 2.4 \cdot 10^{-6} \) \(a_{15}= -0.53680122 \pm 1.9 \cdot 10^{-6} \)
\(a_{16}= -1.21548688 \pm 2.3 \cdot 10^{-6} \) \(a_{17}= -1.19487726 \pm 2.1 \cdot 10^{-6} \) \(a_{18}= -0.43279159 \pm 2.4 \cdot 10^{-6} \)
\(a_{19}= -1.03154817 \pm 2.0 \cdot 10^{-6} \) \(a_{20}= -0.63761287 \pm 2.7 \cdot 10^{-6} \) \(a_{21}= -0.21821789 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.26667886 \pm 2.4 \cdot 10^{-6} \) \(a_{23}= +1.32111469 \pm 2.0 \cdot 10^{-6} \) \(a_{24}= +0.23554687 \pm 2.8 \cdot 10^{-6} \)
\(a_{25}= -0.13553336 \pm 1.9 \cdot 10^{-6} \) \(a_{26}= +0.41974566 \pm 2.3 \cdot 10^{-6} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.25919937 \pm 2.8 \cdot 10^{-6} \) \(a_{29}= -1.10371943 \pm 2.1 \cdot 10^{-6} \) \(a_{30}= +0.69696916 \pm 4.3 \cdot 10^{-6} \)
\(a_{31}= -0.75266787 \pm 2.2 \cdot 10^{-6} \) \(a_{32}= +1.17017837 \pm 2.1 \cdot 10^{-6} \) \(a_{33}= -0.11858449 \pm 1.8 \cdot 10^{-6} \)
\(a_{34}= +1.55139849 \pm 1.9 \cdot 10^{-6} \) \(a_{35}= +0.35141889 \pm 1.9 \cdot 10^{-6} \) \(a_{36}= +0.22859235 \pm 2.8 \cdot 10^{-6} \)
\(a_{37}= +0.11839808 \pm 1.9 \cdot 10^{-6} \) \(a_{38}= +1.33933612 \pm 2.4 \cdot 10^{-6} \) \(a_{39}= -0.18664894 \pm 2.1 \cdot 10^{-6} \)
\(a_{40}= -0.37932553 \pm 2.5 \cdot 10^{-6} \) \(a_{41}= +1.33809665 \pm 1.6 \cdot 10^{-6} \) \(a_{42}= +0.28332860 \pm 2.4 \cdot 10^{-6} \)
\(a_{43}= +0.84371741 \pm 2.1 \cdot 10^{-6} \) \(a_{44}= -0.14085474 \pm 2.8 \cdot 10^{-6} \) \(a_{45}= -0.30992233 \pm 1.9 \cdot 10^{-6} \)
\(a_{46}= -1.71530200 \pm 2.4 \cdot 10^{-6} \) \(a_{47}= +1.43222580 \pm 1.9 \cdot 10^{-6} \) \(a_{48}= -0.70176168 \pm 2.3 \cdot 10^{-6} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.17597310 \pm 1.8 \cdot 10^{-6} \) \(a_{51}= -0.68986271 \pm 2.1 \cdot 10^{-6} \)
\(a_{52}= -0.22170174 \pm 2.6 \cdot 10^{-6} \) \(a_{53}= +0.01777122 \pm 2.2 \cdot 10^{-6} \) \(a_{54}= -0.24987234 \pm 2.4 \cdot 10^{-6} \)
\(a_{55}= +0.19096890 \pm 1.7 \cdot 10^{-6} \) \(a_{56}= -0.15420162 \pm 2.8 \cdot 10^{-6} \) \(a_{57}= -0.59556461 \pm 2.0 \cdot 10^{-6} \)
\(a_{58}= +1.43304147 \pm 2.0 \cdot 10^{-6} \) \(a_{59}= +0.91519658 \pm 1.4 \cdot 10^{-6} \) \(a_{60}= -0.36812596 \pm 4.7 \cdot 10^{-6} \)

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