Properties

Label 7.75
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 13.40120
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(13.4012029875852052894404796208 \pm 7 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.75715079 \pm 4.6 \cdot 10^{-6} \) \(a_{3}= +1.40748965 \pm 3.1 \cdot 10^{-6} \)
\(a_{4}= -0.42672267 \pm 2.7 \cdot 10^{-6} \) \(a_{5}= -0.24112059 \pm 3.3 \cdot 10^{-6} \) \(a_{6}= +1.06568191 \pm 3.6 \cdot 10^{-6} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -1.08024421 \pm 3.0 \cdot 10^{-6} \) \(a_{9}= +0.98102711 \pm 2.9 \cdot 10^{-6} \)
\(a_{10}= -0.18256465 \pm 3.3 \cdot 10^{-6} \) \(a_{11}= -1.64309703 \pm 2.8 \cdot 10^{-6} \) \(a_{12}= -0.60060775 \pm 2.4 \cdot 10^{-6} \)
\(a_{13}= -0.69052028 \pm 3.4 \cdot 10^{-6} \) \(a_{14}= -0.28617610 \pm 4.6 \cdot 10^{-6} \) \(a_{15}= -0.33937474 \pm 2.6 \cdot 10^{-6} \)
\(a_{16}= -0.39118509 \pm 3.9 \cdot 10^{-6} \) \(a_{17}= -0.54110167 \pm 2.5 \cdot 10^{-6} \) \(a_{18}= +0.74278546 \pm 2.8 \cdot 10^{-6} \)
\(a_{19}= +1.15400755 \pm 3.2 \cdot 10^{-6} \) \(a_{20}= +0.10289162 \pm 2.1 \cdot 10^{-6} \) \(a_{21}= -0.53198108 \pm 3.1 \cdot 10^{-6} \)
\(a_{22}= -1.24407222 \pm 2.8 \cdot 10^{-6} \) \(a_{23}= +1.23431590 \pm 4.1 \cdot 10^{-6} \) \(a_{24}= -1.52043254 \pm 2.0 \cdot 10^{-6} \)
\(a_{25}= -0.94186086 \pm 3.1 \cdot 10^{-6} \) \(a_{26}= -0.52282798 \pm 4.1 \cdot 10^{-6} \) \(a_{27}= -0.02670415 \pm 3.4 \cdot 10^{-6} \)
\(a_{28}= +0.16128601 \pm 2.7 \cdot 10^{-6} \) \(a_{29}= -0.80175232 \pm 3.1 \cdot 10^{-6} \) \(a_{30}= -0.25695785 \pm 2.9 \cdot 10^{-6} \)
\(a_{31}= -0.78478190 \pm 2.5 \cdot 10^{-6} \) \(a_{32}= +0.78405811 \pm 4.0 \cdot 10^{-6} \) \(a_{33}= -2.31264206 \pm 2.3 \cdot 10^{-6} \)
\(a_{34}= -0.40969556 \pm 3.0 \cdot 10^{-6} \) \(a_{35}= +0.09113502 \pm 3.3 \cdot 10^{-6} \) \(a_{36}= -0.41862651 \pm 1.6 \cdot 10^{-6} \)
\(a_{37}= +0.76331868 \pm 3.1 \cdot 10^{-6} \) \(a_{38}= +0.87375773 \pm 3.2 \cdot 10^{-6} \) \(a_{39}= -0.97190015 \pm 2.5 \cdot 10^{-6} \)
\(a_{40}= +0.26046912 \pm 3.1 \cdot 10^{-6} \) \(a_{41}= +0.06750528 \pm 4.0 \cdot 10^{-6} \) \(a_{42}= -0.40278990 \pm 7.7 \cdot 10^{-6} \)
\(a_{43}= -1.37065808 \pm 2.4 \cdot 10^{-6} \) \(a_{44}= +0.70114676 \pm 2.0 \cdot 10^{-6} \) \(a_{45}= -0.23654584 \pm 2.6 \cdot 10^{-6} \)
\(a_{46}= +0.93456326 \pm 4.9 \cdot 10^{-6} \) \(a_{47}= -0.00803099 \pm 3.7 \cdot 10^{-6} \) \(a_{48}= -0.55058896 \pm 2.9 \cdot 10^{-6} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.71313070 \pm 3.8 \cdot 10^{-6} \) \(a_{51}= -0.76159500 \pm 1.8 \cdot 10^{-6} \)
\(a_{52}= +0.29466066 \pm 2.2 \cdot 10^{-6} \) \(a_{53}= +0.93508812 \pm 2.5 \cdot 10^{-6} \) \(a_{54}= -0.02021907 \pm 4.2 \cdot 10^{-6} \)
\(a_{55}= +0.39618453 \pm 2.7 \cdot 10^{-6} \) \(a_{56}= +0.40829393 \pm 3.0 \cdot 10^{-6} \) \(a_{57}= +1.62425368 \pm 1.6 \cdot 10^{-6} \)
\(a_{58}= -0.60704740 \pm 3.1 \cdot 10^{-6} \) \(a_{59}= -1.60116461 \pm 5.0 \cdot 10^{-6} \) \(a_{60}= +0.14481890 \pm 2.1 \cdot 10^{-6} \)

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