Properties

Label 29.34
Level $29$
Weight $0$
Character 29.1
Symmetry even
\(R\) 4.213698
Fricke sign $-1$

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Maass form invariants

Level: \( 29 \)
Weight: \( 0 \)
Character: 29.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(4.21369833883085011969053601248 \pm 5 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.15357478 \pm 1.3 \cdot 10^{-8} \) \(a_{3}= +1.52006573 \pm 1.2 \cdot 10^{-8} \)
\(a_{4}= -0.97641479 \pm 1.4 \cdot 10^{-8} \) \(a_{5}= -0.74765597 \pm 1.1 \cdot 10^{-8} \) \(a_{6}= +0.23344376 \pm 1.3 \cdot 10^{-8} \)
\(a_{7}= -1.59208018 \pm 1.1 \cdot 10^{-8} \) \(a_{8}= -0.30352747 \pm 1.6 \cdot 10^{-8} \) \(a_{9}= +1.31059984 \pm 1.1 \cdot 10^{-8} \)
\(a_{10}= -0.11482110 \pm 1.3 \cdot 10^{-8} \) \(a_{11}= +0.17774324 \pm 1.0 \cdot 10^{-8} \) \(a_{12}= -1.48421466 \pm 1.2 \cdot 10^{-8} \)
\(a_{13}= -1.41378406 \pm 1.1 \cdot 10^{-8} \) \(a_{14}= -0.24450336 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -1.13648622 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.92980062 \pm 1.7 \cdot 10^{-8} \) \(a_{17}= +0.11821138 \pm 1.0 \cdot 10^{-8} \) \(a_{18}= +0.20127508 \pm 1.5 \cdot 10^{-8} \)
\(a_{19}= +0.15085212 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.73002235 \pm 1.3 \cdot 10^{-8} \) \(a_{21}= -2.42006653 \pm 1.1 \cdot 10^{-8} \)
\(a_{22}= +0.02729688 \pm 1.2 \cdot 10^{-8} \) \(a_{23}= +1.35186531 \pm 1.1 \cdot 10^{-8} \) \(a_{24}= -0.46138170 \pm 1.4 \cdot 10^{-8} \)
\(a_{25}= -0.44101055 \pm 1.1 \cdot 10^{-8} \) \(a_{26}= -0.21712158 \pm 1.4 \cdot 10^{-8} \) \(a_{27}= +0.47213217 \pm 1.2 \cdot 10^{-8} \)
\(a_{28}= +1.55453063 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.18569534 \pm 1.0 \cdot 10^{-8} \) \(a_{30}= -0.17453562 \pm 1.3 \cdot 10^{-8} \)
\(a_{31}= -1.34303293 \pm 1.1 \cdot 10^{-8} \) \(a_{32}= +0.44632139 \pm 1.8 \cdot 10^{-8} \) \(a_{33}= +0.27018141 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.01815429 \pm 1.4 \cdot 10^{-8} \) \(a_{35}= +1.19032825 \pm 1.2 \cdot 10^{-8} \) \(a_{36}= -1.27968906 \pm 1.4 \cdot 10^{-8} \)
\(a_{37}= +0.24180936 \pm 1.1 \cdot 10^{-8} \) \(a_{38}= +0.02316708 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= -2.14904471 \pm 1.1 \cdot 10^{-8} \)
\(a_{40}= +0.22693412 \pm 1.5 \cdot 10^{-8} \) \(a_{41}= +0.65680179 \pm 1.1 \cdot 10^{-8} \) \(a_{42}= -0.37166118 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -1.79465967 \pm 1.1 \cdot 10^{-8} \) \(a_{44}= -0.17355113 \pm 1.2 \cdot 10^{-8} \) \(a_{45}= -0.97987780 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= +0.20761242 \pm 1.1 \cdot 10^{-8} \) \(a_{47}= +1.05621410 \pm 1.0 \cdot 10^{-8} \) \(a_{48}= +1.41335807 \pm 1.4 \cdot 10^{-8} \)
\(a_{49}= +1.53471930 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.06772810 \pm 1.2 \cdot 10^{-8} \) \(a_{51}= +0.17968907 \pm 1.1 \cdot 10^{-8} \)
\(a_{52}= +1.38043966 \pm 1.6 \cdot 10^{-8} \) \(a_{53}= -1.04944443 \pm 1.2 \cdot 10^{-8} \) \(a_{54}= +0.07250759 \pm 1.5 \cdot 10^{-8} \)
\(a_{55}= -0.13289080 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= +0.48324006 \pm 1.1 \cdot 10^{-8} \) \(a_{57}= +0.22930513 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.02851812 \pm 2.4 \cdot 10^{-8} \) \(a_{59}= -0.12166386 \pm 1.0 \cdot 10^{-8} \) \(a_{60}= +1.10968195 \pm 1.2 \cdot 10^{-8} \)

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