Properties

Label 1.21
Level $1$
Weight $0$
Character 1.1
Symmetry even
\(R\) 25.82624
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 25.82624371270915837390410321428202\ldots \pm 7 \cdot 10^{-92} \) (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.

\(a_{1}= +1 \) \(a_{2}= +0.25806619 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.33374147 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.93340184 \pm 1 \cdot 10^{-8} \) \(a_{5}= +1.27636110 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.34419358 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.74356362 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.49894565 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.77886632 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.32938564 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.41901934 \pm 1 \cdot 10^{-8} \) \(a_{12}= -1.24491675 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.84232463 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.19188863 \pm 1 \cdot 10^{-8} \) \(a_{15}= +1.70233573 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.80464084 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.71105546 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.20099906 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +1.21212165 \pm 1 \cdot 10^{-8} \) \(a_{20}= -1.19135780 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.99172164 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.10813473 \pm 1 \cdot 10^{-8} \) \(a_{23}= +0.11544427 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.66546450 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.62909765 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.21737551 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.29493517 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.69404365 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.82572943 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.43931529 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.11688219 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.70659624 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.55886348 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.18349937 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.94905568 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.72699525 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.74236320 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.31280761 \pm 1 \cdot 10^{-8} \) \(a_{39}= +1.12344330 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.63683481 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.22932613 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.25592982 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.79219314 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.39111343 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.99411466 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.02979226 \pm 1 \cdot 10^{-8} \) \(a_{47}= -1.72925190 \pm 1 \cdot 10^{-8} \) \(a_{48}= +1.07318286 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.44711314 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.16234883 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.94836416 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.78622736 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.10836733 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.07611279 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.53481999 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.37099783 \pm 1 \cdot 10^{-8} \) \(a_{57}= +1.61665691 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.21309285 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.52139665 \pm 1 \cdot 10^{-8} \) \(a_{60}= -1.58896330 \pm 1 \cdot 10^{-8} \)

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