Properties

Label 1.59
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 37.29558
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 37.29558319925431760616644913095425\ldots \pm 4 \cdot 10^{-92} \) (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.

\(a_{1}= +1 \) \(a_{2}= +1.27572529 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.11574304 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.62747503 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.75617457 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.14765632 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.53507827 \pm 1 \cdot 10^{-8} \) \(a_{8}= -0.47523953 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.98660355 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.96467103 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.92574343 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.07262587 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +1.58574944 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.68261288 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.08752194 \pm 1 \cdot 10^{-8} \)
\(a_{16}= -1.23375012 \pm 1 \cdot 10^{-8} \) \(a_{17}= -1.37976027 \pm 1 \cdot 10^{-8} \) \(a_{18}= -1.25863510 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.08946993 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.47448066 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.06193159 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -1.18099432 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.18793566 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.05500567 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.42820002 \pm 1 \cdot 10^{-8} \) \(a_{26}= +2.02298067 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.22993553 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.33574825 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.19215517 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.11165396 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -1.85897939 \pm 1 \cdot 10^{-8} \) \(a_{32}= -1.09868670 \pm 1 \cdot 10^{-8} \) \(a_{33}= +0.10714836 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -1.76019508 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.40461258 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.61906909 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.61665679 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.11413905 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.18353946 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.35936405 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.51997019 \pm 1 \cdot 10^{-8} \) \(a_{42}= +0.07900769 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +1.01583112 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.58088089 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.74604451 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.23975428 \pm 1 \cdot 10^{-8} \) \(a_{47}= +1.24464724 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.14279799 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.71369125 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.54626560 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.15969765 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +0.99501817 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.52275994 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.29333458 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.70002364 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.25429035 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.01035552 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.24513722 \pm 1 \cdot 10^{-8} \) \(a_{59}= -0.23970290 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.05491783 \pm 1 \cdot 10^{-8} \)

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