Properties

Label 1.61
Level $1$
Weight $0$
Character 1.1
Symmetry even
\(R\) 37.82507
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 37.82507229059302714374892242068118\ldots \pm 4 \cdot 10^{-92} \) (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.

\(a_{1}= +1 \) \(a_{2}= -1.18124490 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57747150 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.39533952 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.76227793 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.68213527 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.16519708 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.71425211 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.66652667 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.90043691 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.17107869 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.22829730 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.20223334 \pm 1 \cdot 10^{-8} \) \(a_{14}= +1.37638311 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.44019378 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.23904618 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.89211660 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.78733123 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -1.30570666 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.30135859 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.67286811 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.20208583 \pm 1 \cdot 10^{-8} \) \(a_{23}= +1.19912274 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.41246024 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.41893236 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.23888710 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.96237165 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.46064845 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.51510393 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.51997666 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +1.05391502 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.74936487 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.09879307 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +2.23505308 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.88820402 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.26350433 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.44377458 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.54235934 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.11678399 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.54445862 \pm 1 \cdot 10^{-8} \) \(a_{41}= +0.17212253 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.79482202 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.28119728 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.06763417 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.50807857 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -1.41645762 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.46070616 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.71551386 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.35768424 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.49486172 \pm 1 \cdot 10^{-8} \) \(a_{51}= -1.09264341 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.07995083 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.01732452 \pm 1 \cdot 10^{-8} \) \(a_{54}= +1.13679661 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.13040951 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.83224448 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.75400839 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.60846389 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.04516818 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.17402600 \pm 1 \cdot 10^{-8} \)

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