Properties

Label 1.52
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 35.66639
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 35.66639637099601055643434462491448\ldots \pm 7 \cdot 10^{-92} \) (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.

\(a_{1}= +1 \) \(a_{2}= +0.74299194 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.57366439 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.44796298 \pm 1 \cdot 10^{-8} \) \(a_{5}= +1.11419827 \pm 1 \cdot 10^{-8} \) \(a_{6}= -1.16921996 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +0.60039722 \pm 1 \cdot 10^{-8} \) \(a_{8}= -1.07582482 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.47641963 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.82784034 \pm 1 \cdot 10^{-8} \) \(a_{11}= +1.32621501 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.70494339 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.36656541 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.44609030 \pm 1 \cdot 10^{-8} \) \(a_{15}= -1.75337415 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -0.35136620 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.55961704 \pm 1 \cdot 10^{-8} \) \(a_{18}= +1.09696788 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.59974028 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.49911957 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.94482373 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.98536707 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.42378798 \pm 1 \cdot 10^{-8} \) \(a_{24}= +1.69298722 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.24143779 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.27235514 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.74972460 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.26895573 \pm 1 \cdot 10^{-8} \) \(a_{29}= -1.31332186 \pm 1 \cdot 10^{-8} \) \(a_{30}= -1.30274286 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.11442178 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.81476257 \pm 1 \cdot 10^{-8} \) \(a_{33}= -2.08701735 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.41579095 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.66896155 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.66138133 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.05996078 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.44560219 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.57685093 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -1.19868216 \pm 1 \cdot 10^{-8} \) \(a_{41}= +1.64522448 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.70199642 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.47028414 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.59409522 \pm 1 \cdot 10^{-8} \) \(a_{45}= +1.64502419 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.31487105 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.84179236 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.55293247 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.63952318 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.17938633 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.88064941 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.16420773 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.17662283 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.55703934 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +1.47766647 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.64592223 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.94378992 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -0.97578756 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.27081565 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.78544670 \pm 1 \cdot 10^{-8} \)

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