Properties

Label 1.5
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 16.13807
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 16.13807317152103058019829428598600\ldots \pm 2 \cdot 10^{-91} \) (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.

\(a_{1}= +1 \) \(a_{2}= +1.16185559 \pm 1 \cdot 10^{-8} \) \(a_{3}= -1.28197256 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.34990842 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.75680641 \pm 1 \cdot 10^{-8} \) \(a_{6}= -1.48946699 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.29851912 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.75531254 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.64345365 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.87929976 \pm 1 \cdot 10^{-8} \) \(a_{11}= +0.76409070 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.44857299 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.16260232 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.34683611 \pm 1 \cdot 10^{-8} \) \(a_{15}= +0.97020506 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.22747252 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.41641743 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.74760022 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -0.75567638 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.26481293 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.38269332 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.88776306 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.60164449 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.96828995 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.42724405 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.18892041 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.45708264 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.10445435 \pm 1 \cdot 10^{-8} \) \(a_{29}= -1.48437213 \pm 1 \cdot 10^{-8} \) \(a_{30}= +1.12723817 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.95937599 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.67083327 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.97954332 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.48381692 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.22592118 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.22514985 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.40047381 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.87798683 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.20845171 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.57162538 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.39041128 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.44463437 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.15805251 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.26736177 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.48696985 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -1.86087961 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.56173288 \pm 1 \cdot 10^{-8} \) \(a_{48}= +1.57358609 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.91088634 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.49639589 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.53383572 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.05689592 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.42781400 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.53106402 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.57826875 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.22547523 \pm 1 \cdot 10^{-8} \) \(a_{57}= +0.96875639 \pm 1 \cdot 10^{-8} \)
\(a_{58}= -1.72462606 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.22422362 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.33948292 \pm 1 \cdot 10^{-8} \)

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