Properties

Label 7.28
Level $7$
Weight $0$
Character 7.1
Symmetry even
\(R\) 8.697505
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(8.69750590722918944842957568381 \pm 9 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.09997530 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.83622919 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.20994565 \pm 1 \cdot 10^{-8} \) \(a_{5}= +1.28915647 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.91983145 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.86904027 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.30072075 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -1.41804027 \pm 1 \cdot 10^{-8} \) \(a_{11}= -1.17226841 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.17556268 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +1.14299590 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.41575158 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -1.07803027 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.16586847 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.07216287 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.33078539 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.12773555 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.27065279 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.31606492 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +1.28946629 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.04458376 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.72671684 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.66192441 \pm 1 \cdot 10^{-8} \) \(a_{26}= -1.25726725 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.08770065 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.07935200 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -0.77661892 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.18580667 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.44450152 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.41338625 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.98028506 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.07937737 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.48725535 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -0.06313501 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.20032722 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.14050595 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.95580653 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +1.12032888 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.59498683 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.34766361 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -1.84048437 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.24611265 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.38767610 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +1.14901633 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.04990956 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.97493325 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.72810050 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.06034470 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.23996702 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.20760633 \pm 1 \cdot 10^{-8} \) \(a_{54}= -1.19644385 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -1.51123741 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.32846635 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -0.10681619 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.85426163 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.63214167 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.22632777 \pm 1 \cdot 10^{-8} \)

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