Properties

Label 13.122
Level $13$
Weight $0$
Character 13.1
Symmetry odd
\(R\) 11.83371
Fricke sign $-1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(11.8337126875639271993663271549 \pm 3 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.80672308 \pm 6.3 \cdot 10^{-6} \) \(a_{3}= -1.21763440 \pm 6.1 \cdot 10^{-6} \)
\(a_{4}= +2.26424828 \pm 5.7 \cdot 10^{-6} \) \(a_{5}= +1.88999499 \pm 5.4 \cdot 10^{-6} \) \(a_{6}= -2.19992817 \pm 6.9 \cdot 10^{-6} \)
\(a_{7}= +0.80009276 \pm 5.5 \cdot 10^{-6} \) \(a_{8}= +2.28414654 \pm 4.8 \cdot 10^{-6} \) \(a_{9}= +0.48263353 \pm 5.9 \cdot 10^{-6} \)
\(a_{10}= +3.41469757 \pm 6.2 \cdot 10^{-6} \) \(a_{11}= -0.66448297 \pm 5.1 \cdot 10^{-6} \) \(a_{12}= -2.75702659 \pm 6.2 \cdot 10^{-6} \)
\(a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= +1.44554606 \pm 6.0 \cdot 10^{-6} \) \(a_{15}= -2.30132291 \pm 6.6 \cdot 10^{-6} \)
\(a_{16}= +1.86257199 \pm 4.9 \cdot 10^{-6} \) \(a_{17}= +0.52529368 \pm 5.6 \cdot 10^{-6} \) \(a_{18}= +0.87198513 \pm 6.8 \cdot 10^{-6} \)
\(a_{19}= -0.91961006 \pm 4.5 \cdot 10^{-6} \) \(a_{20}= +4.27941791 \pm 5.6 \cdot 10^{-6} \) \(a_{21}= -0.97422047 \pm 4.7 \cdot 10^{-6} \)
\(a_{22}= -1.20053672 \pm 5.6 \cdot 10^{-6} \) \(a_{23}= +1.15154304 \pm 4.6 \cdot 10^{-6} \) \(a_{24}= -2.78125540 \pm 4.6 \cdot 10^{-6} \)
\(a_{25}= +2.57208106 \pm 4.2 \cdot 10^{-6} \) \(a_{26}= +0.50109482 \pm 6.3 \cdot 10^{-6} \) \(a_{27}= +0.62996322 \pm 4.9 \cdot 10^{-6} \)
\(a_{28}= +1.81160866 \pm 5.2 \cdot 10^{-6} \) \(a_{29}= +0.04625535 \pm 4.1 \cdot 10^{-6} \) \(a_{30}= -4.15785321 \pm 7.9 \cdot 10^{-6} \)
\(a_{31}= -0.15208597 \pm 5.9 \cdot 10^{-6} \) \(a_{32}= +1.08100526 \pm 6.4 \cdot 10^{-6} \) \(a_{33}= +0.80909732 \pm 4.4 \cdot 10^{-6} \)
\(a_{34}= +0.94906021 \pm 6.1 \cdot 10^{-6} \) \(a_{35}= +1.51217131 \pm 4.5 \cdot 10^{-6} \) \(a_{36}= +1.09280213 \pm 5.5 \cdot 10^{-6} \)
\(a_{37}= +0.18419875 \pm 6.8 \cdot 10^{-6} \) \(a_{38}= -1.66148072 \pm 4.3 \cdot 10^{-6} \) \(a_{39}= -0.33771102 \pm 6.1 \cdot 10^{-6} \)
\(a_{40}= +4.31702552 \pm 4.7 \cdot 10^{-6} \) \(a_{41}= +1.41220945 \pm 5.0 \cdot 10^{-6} \) \(a_{42}= -1.76014660 \pm 3.9 \cdot 10^{-6} \)
\(a_{43}= -0.22158353 \pm 5.5 \cdot 10^{-6} \) \(a_{44}= -1.50455442 \pm 5.3 \cdot 10^{-6} \) \(a_{45}= +0.91217495 \pm 6.0 \cdot 10^{-6} \)
\(a_{46}= +2.08051939 \pm 6.0 \cdot 10^{-6} \) \(a_{47}= -1.51353262 \pm 5.7 \cdot 10^{-6} \) \(a_{48}= -2.26793173 \pm 5.6 \cdot 10^{-6} \)
\(a_{49}= -0.35985157 \pm 5.0 \cdot 10^{-6} \) \(a_{50}= +4.64703821 \pm 5.0 \cdot 10^{-6} \) \(a_{51}= -0.63961565 \pm 6.5 \cdot 10^{-6} \)
\(a_{52}= +0.62798948 \pm 5.7 \cdot 10^{-6} \) \(a_{53}= +0.58417666 \pm 4.2 \cdot 10^{-6} \) \(a_{54}= +1.13816908 \pm 5.7 \cdot 10^{-6} \)
\(a_{55}= -1.25586949 \pm 3.7 \cdot 10^{-6} \) \(a_{56}= +1.82752911 \pm 4.2 \cdot 10^{-6} \) \(a_{57}= +1.11974884 \pm 4.4 \cdot 10^{-6} \)
\(a_{58}= +0.08357061 \pm 4.0 \cdot 10^{-6} \) \(a_{59}= -0.38073459 \pm 5.1 \cdot 10^{-6} \) \(a_{60}= -5.21076644 \pm 6.6 \cdot 10^{-6} \)

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