Properties

Label 7.81
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 13.86825
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(13.8682520056691646974949948808 \pm 2 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.70028361 \pm 1.7 \cdot 10^{-4} \) \(a_{3}= -0.04188706 \pm 1.1 \cdot 10^{-4} \)
\(a_{4}= +1.89096436 \pm 1.0 \cdot 10^{-4} \) \(a_{5}= +0.09250928 \pm 1.2 \cdot 10^{-4} \) \(a_{6}= +0.07121988 \pm 1.3 \cdot 10^{-4} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -1.51489210 \pm 1.1 \cdot 10^{-4} \) \(a_{9}= -0.99824547 \pm 1.0 \cdot 10^{-4} \)
\(a_{10}= -0.15729201 \pm 1.2 \cdot 10^{-4} \) \(a_{11}= -0.39723464 \pm 1.0 \cdot 10^{-4} \) \(a_{12}= -0.07920694 \pm 9.0 \cdot 10^{-5} \)
\(a_{13}= +1.27321969 \pm 1.2 \cdot 10^{-4} \) \(a_{14}= +0.64264680 \pm 1.7 \cdot 10^{-4} \) \(a_{15}= -0.00387494 \pm 9.6 \cdot 10^{-5} \)
\(a_{16}= +0.68478186 \pm 1.4 \cdot 10^{-4} \) \(a_{17}= +0.94597499 \pm 9.4 \cdot 10^{-5} \) \(a_{18}= +1.69730042 \pm 1.0 \cdot 10^{-4} \)
\(a_{19}= +0.25405488 \pm 1.2 \cdot 10^{-4} \) \(a_{20}= +0.17493175 \pm 7.9 \cdot 10^{-5} \) \(a_{21}= +0.01583182 \pm 1.1 \cdot 10^{-4} \)
\(a_{22}= +0.67541154 \pm 1.0 \cdot 10^{-4} \) \(a_{23}= +0.98913896 \pm 1.5 \cdot 10^{-4} \) \(a_{24}= +0.06345438 \pm 7.4 \cdot 10^{-5} \)
\(a_{25}= -0.99144203 \pm 1.1 \cdot 10^{-4} \) \(a_{26}= -2.16483457 \pm 1.5 \cdot 10^{-4} \) \(a_{27}= +0.08370063 \pm 1.2 \cdot 10^{-4} \)
\(a_{28}= -0.71471735 \pm 1.0 \cdot 10^{-4} \) \(a_{29}= +0.73323577 \pm 1.1 \cdot 10^{-4} \) \(a_{30}= +0.00658850 \pm 1.0 \cdot 10^{-4} \)
\(a_{31}= -1.46170369 \pm 9.3 \cdot 10^{-5} \) \(a_{32}= +0.35056873 \pm 1.4 \cdot 10^{-4} \) \(a_{33}= +0.01663899 \pm 8.5 \cdot 10^{-5} \)
\(a_{34}= -1.60842577 \pm 1.1 \cdot 10^{-4} \) \(a_{35}= -0.03496522 \pm 1.2 \cdot 10^{-4} \) \(a_{36}= -1.88764662 \pm 6.0 \cdot 10^{-5} \)
\(a_{37}= +0.79073251 \pm 1.1 \cdot 10^{-4} \) \(a_{38}= -0.43196535 \pm 1.1 \cdot 10^{-4} \) \(a_{39}= -0.05333143 \pm 9.3 \cdot 10^{-5} \)
\(a_{40}= -0.14014158 \pm 1.1 \cdot 10^{-4} \) \(a_{41}= +1.19949656 \pm 1.5 \cdot 10^{-4} \) \(a_{42}= -0.02691859 \pm 2.8 \cdot 10^{-4} \)
\(a_{43}= +1.07555288 \pm 9.0 \cdot 10^{-5} \) \(a_{44}= -0.75115654 \pm 7.7 \cdot 10^{-5} \) \(a_{45}= -0.09234697 \pm 9.6 \cdot 10^{-5} \)
\(a_{46}= -1.68181676 \pm 1.8 \cdot 10^{-4} \) \(a_{47}= -1.70807915 \pm 1.3 \cdot 10^{-4} \) \(a_{48}= -0.02868350 \pm 1.0 \cdot 10^{-4} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +1.68573264 \pm 1.4 \cdot 10^{-4} \) \(a_{51}= -0.03962411 \pm 6.9 \cdot 10^{-5} \)
\(a_{52}= +2.40761306 \pm 8.2 \cdot 10^{-5} \) \(a_{53}= -1.78350123 \pm 9.5 \cdot 10^{-5} \) \(a_{54}= -0.14231481 \pm 1.5 \cdot 10^{-4} \)
\(a_{55}= -0.03674789 \pm 1.0 \cdot 10^{-4} \) \(a_{56}= +0.57257540 \pm 1.1 \cdot 10^{-4} \) \(a_{57}= -0.01064161 \pm 6.0 \cdot 10^{-5} \)
\(a_{58}= -1.24670877 \pm 1.1 \cdot 10^{-4} \) \(a_{59}= -0.10895733 \pm 1.8 \cdot 10^{-4} \) \(a_{60}= -0.00732738 \pm 7.7 \cdot 10^{-5} \)

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