Properties

Label 5.22
Level $5$
Weight $0$
Character 5.1
Symmetry even
\(R\) 9.646266
Fricke sign $+1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(9.64626672071141192651290180548 \pm 3 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.06959076 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.32953820 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.14402439 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -1.42206177 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.22509767 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.91554360 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.76767182 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.47833553 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.03376986 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.19148593 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +1.82609312 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.24076239 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.59458756 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -1.12328137 \pm 1 \cdot 10^{-8} \) \(a_{17}= +1.62362468 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.82109469 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.86769390 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.06440967 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.29927595 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.03611993 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.36122841 \pm 1 \cdot 10^{-8} \) \(a_{24}= +1.21725019 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -1.95317232 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.30888918 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.03241956 \pm 1 \cdot 10^{-8} \) \(a_{29}= +1.57893479 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.63596536 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -0.20899072 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.28590777 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.04489832 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -1.73661396 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.10066674 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +0.11056347 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.24550035 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.92807738 \pm 1 \cdot 10^{-8} \) \(a_{39}= +2.42786055 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.40944354 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= +0.36481603 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.32010279 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.62995905 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.00486368 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.34331328 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= +0.38636657 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.34200460 \pm 1 \cdot 10^{-8} \) \(a_{48}= -1.49344549 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.94933104 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.21391815 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= +2.15867103 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.26300196 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.39197389 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.33038502 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.01510234 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= -0.20608673 \pm 1 \cdot 10^{-8} \) \(a_{57}= +1.15363219 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.68881407 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.18299984 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.08563511 \pm 1.0 \cdot 10^{-8} \)

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