Properties

Label 7.71
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 13.12851
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(13.1285144686987331488390845984 \pm 3 \cdot 10^{-9}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.60516468 \pm 2.0 \cdot 10^{-5} \) \(a_{3}= -1.51743928 \pm 1.3 \cdot 10^{-5} \)
\(a_{4}= +1.57655365 \pm 1.2 \cdot 10^{-5} \) \(a_{5}= +0.84795194 \pm 1.4 \cdot 10^{-5} \) \(a_{6}= -2.43573993 \pm 1.6 \cdot 10^{-5} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +0.92546356 \pm 1.3 \cdot 10^{-5} \) \(a_{9}= +1.30262196 \pm 1.2 \cdot 10^{-5} \)
\(a_{10}= +1.36110251 \pm 1.4 \cdot 10^{-5} \) \(a_{11}= -1.21464606 \pm 1.2 \cdot 10^{-5} \) \(a_{12}= -2.39232444 \pm 1.0 \cdot 10^{-5} \)
\(a_{13}= +1.11569973 \pm 1.4 \cdot 10^{-5} \) \(a_{14}= -0.60669522 \pm 2.0 \cdot 10^{-5} \) \(a_{15}= -1.28671558 \pm 1.1 \cdot 10^{-5} \)
\(a_{16}= -0.09103223 \pm 1.7 \cdot 10^{-5} \) \(a_{17}= -0.80641098 \pm 1.1 \cdot 10^{-5} \) \(a_{18}= +2.09092276 \pm 1.2 \cdot 10^{-5} \)
\(a_{19}= -1.68071303 \pm 1.4 \cdot 10^{-5} \) \(a_{20}= +1.33684173 \pm 9.4 \cdot 10^{-6} \) \(a_{21}= +0.57353814 \pm 1.3 \cdot 10^{-5} \)
\(a_{22}= -1.94970695 \pm 1.2 \cdot 10^{-5} \) \(a_{23}= -1.25103328 \pm 1.8 \cdot 10^{-5} \) \(a_{24}= -1.40433476 \pm 8.9 \cdot 10^{-6} \)
\(a_{25}= -0.28097751 \pm 1.3 \cdot 10^{-5} \) \(a_{26}= +1.79088180 \pm 1.8 \cdot 10^{-5} \) \(a_{27}= -0.45921045 \pm 1.4 \cdot 10^{-5} \)
\(a_{28}= -0.59588127 \pm 1.2 \cdot 10^{-5} \) \(a_{29}= -0.42183022 \pm 1.3 \cdot 10^{-5} \) \(a_{30}= -2.06539040 \pm 1.3 \cdot 10^{-5} \)
\(a_{31}= -0.38287997 \pm 1.1 \cdot 10^{-5} \) \(a_{32}= -1.07158528 \pm 1.7 \cdot 10^{-5} \) \(a_{33}= +1.84315163 \pm 1.0 \cdot 10^{-5} \)
\(a_{34}= -1.29442243 \pm 1.3 \cdot 10^{-5} \) \(a_{35}= -0.32049571 \pm 1.4 \cdot 10^{-5} \) \(a_{36}= +2.05365341 \pm 7.2 \cdot 10^{-6} \)
\(a_{37}= +0.35961267 \pm 1.3 \cdot 10^{-5} \) \(a_{38}= -2.69782119 \pm 1.4 \cdot 10^{-5} \) \(a_{39}= -1.69300659 \pm 1.1 \cdot 10^{-5} \)
\(a_{40}= +0.78474862 \pm 1.3 \cdot 10^{-5} \) \(a_{41}= +1.79931903 \pm 1.7 \cdot 10^{-5} \) \(a_{42}= +0.92062316 \pm 3.4 \cdot 10^{-5} \)
\(a_{43}= +0.15444896 \pm 1.0 \cdot 10^{-5} \) \(a_{44}= -1.91495468 \pm 9.2 \cdot 10^{-6} \) \(a_{45}= +1.10456082 \pm 1.1 \cdot 10^{-5} \)
\(a_{46}= -2.00811444 \pm 2.1 \cdot 10^{-5} \) \(a_{47}= +0.00641566 \pm 1.6 \cdot 10^{-5} \) \(a_{48}= +0.13813588 \pm 1.3 \cdot 10^{-5} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.45101517 \pm 1.6 \cdot 10^{-5} \) \(a_{51}= +1.22367970 \pm 8.2 \cdot 10^{-6} \)
\(a_{52}= +1.75896048 \pm 9.7 \cdot 10^{-6} \) \(a_{53}= -0.75439878 \pm 1.1 \cdot 10^{-5} \) \(a_{54}= -0.73710839 \pm 1.8 \cdot 10^{-5} \)
\(a_{55}= -1.02996148 \pm 1.2 \cdot 10^{-5} \) \(a_{56}= -0.34979235 \pm 1.3 \cdot 10^{-5} \) \(a_{57}= +2.55037996 \pm 7.1 \cdot 10^{-6} \)
\(a_{58}= -0.67710697 \pm 1.3 \cdot 10^{-5} \) \(a_{59}= +0.92315829 \pm 2.2 \cdot 10^{-5} \) \(a_{60}= -2.02857615 \pm 9.2 \cdot 10^{-6} \)

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