Properties

Label 7.12
Level $7$
Weight $0$
Character 7.1
Symmetry even
\(R\) 6.068856
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(6.0688569338471935118674729082 \pm 7 \cdot 10^{-13}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.05589997 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.93840276 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.11492474 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.73245344 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.99085945 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.93455094 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.11940025 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.77339757 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.70752395 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.10784569 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +1.05226162 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.39909267 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.68733634 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.10171704 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.84889411 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.12607472 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +1.85622473 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.08417702 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.35468291 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.74707452 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.97573760 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.87698518 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.46351195 \pm 1 \cdot 10^{-8} \) \(a_{26}= -1.11108301 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.05044829 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.04343747 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -0.37303863 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.72575841 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.00170368 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.22875205 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.66394243 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.89634726 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.27684138 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -0.01372204 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +1.90593475 \pm 1 \cdot 10^{-8} \) \(a_{38}= -1.95998763 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.98744521 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.68451505 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.42788775 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.37450967 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.95891922 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.08131201 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.08745513 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -1.03028130 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.34036766 \pm 1 \cdot 10^{-8} \) \(a_{48}= +1.03385432 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.48942226 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.79660458 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.12093089 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.66534614 \pm 1 \cdot 10^{-8} \) \(a_{54}= -1.10916831 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.51822836 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.35322705 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -1.74188641 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.39389148 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.80345768 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.07899195 \pm 1 \cdot 10^{-8} \)

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