Properties

Label 7.25
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 8.251785
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(8.25178553271231783265150328952 \pm 5 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.78572492 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.62802777 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +2.18881348 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.42588484 \pm 1 \cdot 10^{-8} \) \(a_{6}= +2.90720976 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -2.12289386 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.65047442 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.76051317 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.71786711 \pm 1 \cdot 10^{-8} \) \(a_{12}= -3.56344913 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.28085186 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.67494058 \pm 1.3 \cdot 10^{-8} \) \(a_{15}= -0.69335234 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +1.60209098 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.86758316 \pm 1 \cdot 10^{-8} \) \(a_{18}= -2.94729330 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.54880955 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.93218247 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.61533666 \pm 1.2 \cdot 10^{-8} \)
\(a_{22}= -1.28191319 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.61130430 \pm 1 \cdot 10^{-8} \) \(a_{24}= +3.45613015 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.81862210 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.50152417 \pm 1 \cdot 10^{-8} \) \(a_{27}= -1.05899042 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.82729373 \pm 1.2 \cdot 10^{-8} \) \(a_{29}= +0.67956044 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.23813656 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.74256661 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.73799992 \pm 1 \cdot 10^{-8} \) \(a_{33}= -1.16870760 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -1.54926487 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.16096934 \pm 1.2 \cdot 10^{-8} \) \(a_{36}= +3.61258066 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.39497447 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.98002290 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.45723463 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.90410831 \pm 1 \cdot 10^{-8} \) \(a_{41}= +1.47338145 \pm 1 \cdot 10^{-8} \) \(a_{42}= -1.09882200 \pm 1.5 \cdot 10^{-8} \)
\(a_{43}= -1.11468579 \pm 1 \cdot 10^{-8} \) \(a_{44}= +1.57127722 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.70291203 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +1.09162132 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.97938321 \pm 1 \cdot 10^{-8} \) \(a_{48}= -2.60824860 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +1.46183389 \pm 1 \cdot 10^{-8} \) \(a_{51}= -1.41244948 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.61473234 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.82267831 \pm 1 \cdot 10^{-8} \) \(a_{54}= +1.89106558 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.30572872 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.80237846 \pm 1.2 \cdot 10^{-8} \) \(a_{57}= +0.89347720 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.21350800 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.15214955 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.51761896 \pm 1 \cdot 10^{-8} \)

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