Properties

Label 7.5
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 4.119009
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(4.11900929292429020757499481407 \pm 3 \cdot 10^{-13}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.02117295 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.01772280 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.04279419 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.72350278 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.01809804 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.97747268 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.99968590 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.73882147 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.41625717 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.00075843 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -1.41042644 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.38596709 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.01282249 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.04096284 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.28049790 \pm 1 \cdot 10^{-8} \) \(a_{18}= +1.02085220 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.02778868 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.03096171 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.00669859 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.42507056 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.52725195 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.01732355 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.47654373 \pm 1 \cdot 10^{-8} \) \(a_{26}= +1.44028933 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.03544002 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.01617468 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +0.67303199 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.01309398 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.21080125 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.08553041 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.00737724 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -1.30760981 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.27345835 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -0.04278074 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.03324309 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.02837705 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.02499670 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.70720420 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.94313944 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.00684042 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -1.23019210 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.01781339 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.72327553 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +1.55958837 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.59520697 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.01844877 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.48663356 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.02269400 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.06035805 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.17326267 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.03619039 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.30116322 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.36944995 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +0.00049249 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.68728206 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.63588462 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.00054873 \pm 1 \cdot 10^{-8} \)

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