Properties

Label 13.183
Level $13$
Weight $0$
Character 13.1
Symmetry even
\(R\) 14.39493
Fricke sign $+1$

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Maass form invariants

Level: \( 13 \)
Weight: \( 0 \)
Character: 13.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(14.3949315595531201586695527513 \pm 2 \cdot 10^{-7}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.25797981 \pm 8.2 \cdot 10^{-6} \) \(a_{3}= +0.04706666 \pm 6.2 \cdot 10^{-6} \)
\(a_{4}= +0.58251320 \pm 8.8 \cdot 10^{-6} \) \(a_{5}= -0.93246427 \pm 6.8 \cdot 10^{-6} \) \(a_{6}= -0.05920891 \pm 7.9 \cdot 10^{-6} \)
\(a_{7}= +0.28929489 \pm 6.2 \cdot 10^{-6} \) \(a_{8}= +0.52518997 \pm 8.0 \cdot 10^{-6} \) \(a_{9}= -0.99778473 \pm 5.5 \cdot 10^{-6} \)
\(a_{10}= +1.17302123 \pm 6.2 \cdot 10^{-6} \) \(a_{11}= -0.96241305 \pm 4.6 \cdot 10^{-6} \) \(a_{12}= +0.02741695 \pm 7.8 \cdot 10^{-6} \)
\(a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} \) \(a_{14}= -0.36392712 \pm 8.8 \cdot 10^{-6} \) \(a_{15}= -0.04388798 \pm 5.1 \cdot 10^{-6} \)
\(a_{16}= -1.24319157 \pm 5.6 \cdot 10^{-6} \) \(a_{17}= +1.49466949 \pm 6.1 \cdot 10^{-6} \) \(a_{18}= +1.25519304 \pm 6.5 \cdot 10^{-6} \)
\(a_{19}= +0.37181090 \pm 6.6 \cdot 10^{-6} \) \(a_{20}= -0.54317275 \pm 7.6 \cdot 10^{-6} \) \(a_{21}= +0.01361614 \pm 5.1 \cdot 10^{-6} \)
\(a_{22}= +1.21069618 \pm 4.4 \cdot 10^{-6} \) \(a_{23}= -1.89419078 \pm 4.5 \cdot 10^{-6} \) \(a_{24}= +0.02471894 \pm 7.3 \cdot 10^{-6} \)
\(a_{25}= -0.13051038 \pm 7.6 \cdot 10^{-6} \) \(a_{26}= +0.34890082 \pm 8.2 \cdot 10^{-6} \) \(a_{27}= -0.09402906 \pm 6.7 \cdot 10^{-6} \)
\(a_{28}= +0.16851809 \pm 9.6 \cdot 10^{-6} \) \(a_{29}= -1.79976694 \pm 5.9 \cdot 10^{-6} \) \(a_{30}= +0.05521019 \pm 4.2 \cdot 10^{-6} \)
\(a_{31}= -0.29299591 \pm 4.6 \cdot 10^{-6} \) \(a_{32}= +1.03871993 \pm 6.1 \cdot 10^{-6} \) \(a_{33}= -0.04529757 \pm 5.5 \cdot 10^{-6} \)
\(a_{34}= -1.88026404 \pm 7.7 \cdot 10^{-6} \) \(a_{35}= -0.26975715 \pm 5.6 \cdot 10^{-6} \) \(a_{36}= -0.58122278 \pm 5.4 \cdot 10^{-6} \)
\(a_{37}= -1.03786007 \pm 5.4 \cdot 10^{-6} \) \(a_{38}= -0.46773060 \pm 8.8 \cdot 10^{-6} \) \(a_{39}= -0.01305394 \pm 6.2 \cdot 10^{-6} \)
\(a_{40}= -0.48972088 \pm 7.3 \cdot 10^{-6} \) \(a_{41}= -0.11879255 \pm 9.1 \cdot 10^{-6} \) \(a_{42}= -0.01712883 \pm 7.3 \cdot 10^{-6} \)
\(a_{43}= -0.99232059 \pm 5.1 \cdot 10^{-6} \) \(a_{44}= -0.56061831 \pm 3.6 \cdot 10^{-6} \) \(a_{45}= +0.93039861 \pm 4.7 \cdot 10^{-6} \)
\(a_{46}= +2.38285375 \pm 5.3 \cdot 10^{-6} \) \(a_{47}= -1.40125276 \pm 4.7 \cdot 10^{-6} \) \(a_{48}= -0.05851288 \pm 5.0 \cdot 10^{-6} \)
\(a_{49}= -0.91630847 \pm 4.7 \cdot 10^{-6} \) \(a_{50}= +0.16417942 \pm 6.1 \cdot 10^{-6} \) \(a_{51}= +0.07034910 \pm 6.6 \cdot 10^{-6} \)
\(a_{52}= -0.16156009 \pm 8.8 \cdot 10^{-6} \) \(a_{53}= +0.57104359 \pm 6.5 \cdot 10^{-6} \) \(a_{54}= +0.11828666 \pm 7.1 \cdot 10^{-6} \)
\(a_{55}= +0.89741579 \pm 4.4 \cdot 10^{-6} \) \(a_{56}= +0.15193477 \pm 7.5 \cdot 10^{-6} \) \(a_{57}= +0.01749990 \pm 3.7 \cdot 10^{-6} \)
\(a_{58}= +2.26407047 \pm 9.5 \cdot 10^{-6} \) \(a_{59}= +0.75117561 \pm 5.4 \cdot 10^{-6} \) \(a_{60}= -0.02556533 \pm 4.9 \cdot 10^{-6} \)

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