Properties

Label 13.106
Level $13$
Weight $0$
Character 13.1
Symmetry odd
\(R\) 11.15411
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(11.1541136158394570484299428908 \pm 2 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.77908793 \pm 8.2 \cdot 10^{-5} \) \(a_{3}= -0.84954762 \pm 7.9 \cdot 10^{-5} \)
\(a_{4}= -0.39302199 \pm 7.4 \cdot 10^{-5} \) \(a_{5}= +0.29000761 \pm 7.0 \cdot 10^{-5} \) \(a_{6}= +0.66187230 \pm 9.0 \cdot 10^{-5} \)
\(a_{7}= -0.40364812 \pm 7.2 \cdot 10^{-5} \) \(a_{8}= +1.08528662 \pm 6.2 \cdot 10^{-5} \) \(a_{9}= -0.27826883 \pm 7.7 \cdot 10^{-5} \)
\(a_{10}= -0.22594143 \pm 8.0 \cdot 10^{-5} \) \(a_{11}= -1.71813494 \pm 6.6 \cdot 10^{-5} \) \(a_{12}= +0.33389090 \pm 8.0 \cdot 10^{-5} \)
\(a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +0.31447738 \pm 7.8 \cdot 10^{-5} \) \(a_{15}= -0.24637528 \pm 8.6 \cdot 10^{-5} \)
\(a_{16}= -0.45251172 \pm 6.4 \cdot 10^{-5} \) \(a_{17}= -1.52813884 \pm 7.2 \cdot 10^{-5} \) \(a_{18}= +0.21679589 \pm 8.8 \cdot 10^{-5} \)
\(a_{19}= -1.73224163 \pm 5.9 \cdot 10^{-5} \) \(a_{20}= -0.11397937 \pm 7.2 \cdot 10^{-5} \) \(a_{21}= +0.34291830 \pm 6.2 \cdot 10^{-5} \)
\(a_{22}= +1.33857820 \pm 7.3 \cdot 10^{-5} \) \(a_{23}= -1.64203854 \pm 6.0 \cdot 10^{-5} \) \(a_{24}= -0.92200267 \pm 6.0 \cdot 10^{-5} \)
\(a_{25}= -0.91589558 \pm 5.4 \cdot 10^{-5} \) \(a_{26}= -0.21608011 \pm 8.2 \cdot 10^{-5} \) \(a_{27}= +1.08595025 \pm 6.4 \cdot 10^{-5} \)
\(a_{28}= +0.15864259 \pm 6.8 \cdot 10^{-5} \) \(a_{29}= +0.49981393 \pm 5.3 \cdot 10^{-5} \) \(a_{30}= +0.19194801 \pm 1.0 \cdot 10^{-4} \)
\(a_{31}= +0.72295661 \pm 7.7 \cdot 10^{-5} \) \(a_{32}= -0.73274020 \pm 8.3 \cdot 10^{-5} \) \(a_{33}= +1.45963746 \pm 5.7 \cdot 10^{-5} \)
\(a_{34}= +1.19055453 \pm 7.9 \cdot 10^{-5} \) \(a_{35}= -0.11706103 \pm 5.8 \cdot 10^{-5} \) \(a_{36}= +0.10936577 \pm 7.2 \cdot 10^{-5} \)
\(a_{37}= -0.10367080 \pm 8.9 \cdot 10^{-5} \) \(a_{38}= +1.34956855 \pm 5.6 \cdot 10^{-5} \) \(a_{39}= -0.23562212 \pm 7.9 \cdot 10^{-5} \)
\(a_{40}= +0.31474139 \pm 6.1 \cdot 10^{-5} \) \(a_{41}= +0.71053435 \pm 6.5 \cdot 10^{-5} \) \(a_{42}= -0.26716351 \pm 5.1 \cdot 10^{-5} \)
\(a_{43}= -0.86355996 \pm 7.2 \cdot 10^{-5} \) \(a_{44}= +0.67526482 \pm 6.9 \cdot 10^{-5} \) \(a_{45}= -0.08070008 \pm 7.7 \cdot 10^{-5} \)
\(a_{46}= +1.27929241 \pm 7.8 \cdot 10^{-5} \) \(a_{47}= -0.38237666 \pm 7.5 \cdot 10^{-5} \) \(a_{48}= +0.38443026 \pm 7.3 \cdot 10^{-5} \)
\(a_{49}= -0.83706820 \pm 6.5 \cdot 10^{-5} \) \(a_{50}= +0.71356320 \pm 6.5 \cdot 10^{-5} \) \(a_{51}= +1.29822672 \pm 8.4 \cdot 10^{-5} \)
\(a_{52}= -0.10900469 \pm 7.4 \cdot 10^{-5} \) \(a_{53}= +0.99122803 \pm 5.5 \cdot 10^{-5} \) \(a_{54}= -0.84605074 \pm 7.4 \cdot 10^{-5} \)
\(a_{55}= -0.49827222 \pm 4.7 \cdot 10^{-5} \) \(a_{56}= -0.43807391 \pm 5.4 \cdot 10^{-5} \) \(a_{57}= +1.47162177 \pm 5.7 \cdot 10^{-5} \)
\(a_{58}= -0.38939900 \pm 5.2 \cdot 10^{-5} \) \(a_{59}= -0.80597950 \pm 6.6 \cdot 10^{-5} \) \(a_{60}= +0.09683090 \pm 8.6 \cdot 10^{-5} \)

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