Properties

Label 7.2
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 3.190858
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(3.1908587629390006224343617764 \pm 10 \cdot 10^{-14}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.83625991 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.26984682 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.30066936 \pm 1 \cdot 10^{-8} \) \(a_{5}= +1.13127327 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.22566208 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -1.08769764 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.92718269 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.94603848 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.99072323 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.08113467 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.42786634 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.31607654 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= -0.30527050 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.60892858 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.11183765 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.77536572 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +1.44527991 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.34013921 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.10199251 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +0.82850212 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.56069614 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.29351175 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.27977921 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.35780747 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.52004413 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.11364234 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= -1.18936259 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.25528548 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.29775645 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.57847509 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.26734352 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.09352534 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.42758110 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +0.27877543 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +1.02114130 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.20862965 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.11545837 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -1.23048327 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.99343549 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.08529225 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.04182029 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.29788012 \pm 1 \cdot 10^{-8} \) \(a_{45}= -1.04889699 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.46888770 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.28721012 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.16431744 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= +0.23396813 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.03017903 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.12864630 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.02689712 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.43489206 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +1.12077870 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.41111107 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= -0.39000419 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.99461626 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.02583187 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.09178549 \pm 1 \cdot 10^{-8} \)

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