Properties

Label 7.22
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 7.719562
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(7.71956232873361348738928840864 \pm 4 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.26399410 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.69965192 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.59768107 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.67343849 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.88435590 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.50852875 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.51048719 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.85122227 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.75008757 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.41816871 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.61692317 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.47774486 \pm 1.2 \cdot 10^{-8} \) \(a_{15}= +0.47117253 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.24045841 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.34219139 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.64525279 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.12099195 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.40250144 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.26444357 \pm 1.1 \cdot 10^{-8} \)
\(a_{22}= -0.94810625 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.91946017 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.35579312 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.54648060 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.77978725 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.05681526 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.22590221 \pm 1.1 \cdot 10^{-8} \) \(a_{29}= -1.66294620 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.59555930 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.34080011 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.05940336 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.52480021 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +1.69652200 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.25453582 \pm 1.1 \cdot 10^{-8} \) \(a_{36}= -0.30510853 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +1.50328805 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.15293311 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.43163148 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.34246283 \pm 1 \cdot 10^{-8} \) \(a_{41}= -1.56381415 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.33425511 \pm 1.3 \cdot 10^{-8} \)
\(a_{43}= -1.25523439 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.44831314 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.34378172 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +1.16219222 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.02006290 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.86788911 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.69074826 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.93906679 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.36872330 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.35240424 \pm 1 \cdot 10^{-8} \) \(a_{54}= +1.33580826 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.50513784 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.19220580 \pm 1.1 \cdot 10^{-8} \) \(a_{57}= +0.08465225 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -2.10195417 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.60986889 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.28161091 \pm 1 \cdot 10^{-8} \)

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