Properties

Label 1.38
Level $1$
Weight $0$
Character 1.1
Symmetry even
\(R\) 31.56627
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 31.56627541175388711218054752214819\ldots \pm 7 \cdot 10^{-92} \) (toggle for full precision) Copy content Toggle raw display

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.53099815 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.84799454 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.71804097 \pm 1 \cdot 10^{-8} \) \(a_{5}= -1.39249860 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.45028353 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.54173033 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.91227657 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.28090526 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.73941418 \pm 1 \cdot 10^{-8} \) \(a_{11}= +1.08788185 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.60889482 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.20656190 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.28765780 \pm 1 \cdot 10^{-8} \) \(a_{15}= +1.18083121 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.23362380 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.62714385 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.14916017 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -1.62551017 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.99987105 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.45938436 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.57766325 \pm 1 \cdot 10^{-8} \) \(a_{23}= +1.58242569 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.77360555 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.93905236 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.10968399 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.08620067 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.38898457 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.64420916 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.62701918 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.31361892 \pm 1 \cdot 10^{-8} \) \(a_{32}= +1.03633038 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.92251787 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.33301222 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.75435872 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.20170148 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.10941795 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.86314289 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.17516336 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +1.27034385 \pm 1 \cdot 10^{-8} \) \(a_{41}= -1.07187534 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.24393224 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.18228096 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.78114374 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.39116018 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.84026511 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.44467169 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.19811171 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.70652825 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.49863506 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.53181456 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.14831991 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.58892866 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.57677054 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -1.51487396 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.49420788 \pm 1 \cdot 10^{-8} \) \(a_{57}= +1.37842375 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.34207387 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.26141505 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.84788519 \pm 1 \cdot 10^{-8} \)

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