Properties

Label 7.23
Level $7$
Weight $0$
Character 7.1
Symmetry odd
\(R\) 8.071618
Fricke sign $-1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(8.07161868258754741647199140303 \pm 7 \cdot 10^{-12}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.78095261 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.26104362 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.39011303 \pm 1 \cdot 10^{-8} \) \(a_{5}= -1.40488222 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.20386270 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= +1.08561239 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.93185623 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +1.09714643 \pm 1 \cdot 10^{-8} \) \(a_{11}= +1.05965744 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.10183652 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +1.34568407 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.29517234 \pm 1.5 \cdot 10^{-8} \) \(a_{15}= -0.36673555 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.45769880 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.21730688 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.72773555 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.70636310 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.54806285 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.09866522 \pm 1.3 \cdot 10^{-8} \)
\(a_{22}= -0.82754224 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.80915214 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.28339219 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.97369406 \pm 1 \cdot 10^{-8} \) \(a_{26}= -1.05091549 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.50429875 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.14744886 \pm 1.3 \cdot 10^{-8} \) \(a_{29}= +1.74010349 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.28640308 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.27967797 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.72817132 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.27661682 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.16970638 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.53099557 \pm 1.3 \cdot 10^{-8} \) \(a_{36}= +0.36352925 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.41526614 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.55163610 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.35128225 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -1.52515755 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.09704787 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.07705286 \pm 1.8 \cdot 10^{-8} \)
\(a_{43}= +1.05932709 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.41338617 \pm 1 \cdot 10^{-8} \) \(a_{45}= +1.30914825 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.63190947 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.18264642 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.11947935 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.76040891 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.05672658 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.52496889 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.09420467 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.39383342 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -1.48869390 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.41032292 \pm 1.3 \cdot 10^{-8} \) \(a_{57}= +0.18439158 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.35893836 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.50945843 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.14306831 \pm 1 \cdot 10^{-8} \)

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