Properties

Label 23.41
Level $23$
Weight $0$
Character 23.1
Symmetry even
\(R\) 5.406432
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(5.40643263734623575668860722176 \pm 2 \cdot 10^{-10}\)

Maass form coefficients

The coefficients here are shown to at most $8$ digits of precision. Full precision coefficients are available in the downloads.

\(a_{1}= +1 \) \(a_{2}= +1.82488636 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.65571903 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +2.33021024 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.12167101 \pm 1 \cdot 10^{-8} \) \(a_{6}= +3.02149908 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -1.16602567 \pm 1 \cdot 10^{-8} \) \(a_{8}= +2.42748253 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.74140550 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.22203577 \pm 1 \cdot 10^{-8} \) \(a_{11}= -1.65089028 \pm 1 \cdot 10^{-8} \) \(a_{12}= +3.85817343 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -0.26761283 \pm 1 \cdot 10^{-8} \) \(a_{14}= -2.12786435 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.20145301 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +2.09966952 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.76027435 \pm 1 \cdot 10^{-8} \) \(a_{18}= +3.17786715 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.99383604 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.28351903 \pm 1 \cdot 10^{-8} \) \(a_{21}= -1.93061089 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -3.01268716 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.20851441 \pm 1.0 \cdot 10^{-8} \) \(a_{24}= +4.01922901 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.98519617 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.48836300 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.22755919 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -2.71708496 \pm 1 \cdot 10^{-8} \) \(a_{29}= +0.59209996 \pm 1 \cdot 10^{-8} \) \(a_{30}= -0.36762884 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.66766803 \pm 1 \cdot 10^{-8} \) \(a_{32}= +1.40417575 \pm 1 \cdot 10^{-8} \) \(a_{33}= -2.73341045 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +1.38741430 \pm 1 \cdot 10^{-8} \) \(a_{35}= +0.14187152 \pm 1 \cdot 10^{-8} \) \(a_{36}= +4.05784093 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.64801851 \pm 1 \cdot 10^{-8} \) \(a_{38}= +1.81363783 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.44309165 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.29535425 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= +0.06338792 \pm 1 \cdot 10^{-8} \) \(a_{42}= -3.52314549 \pm 1 \cdot 10^{-8} \)
\(a_{43}= -0.08752178 \pm 1 \cdot 10^{-8} \) \(a_{44}= -3.84692144 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.21187857 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.38051511 \pm 1.8 \cdot 10^{-8} \) \(a_{47}= +1.52514343 \pm 1 \cdot 10^{-8} \) \(a_{48}= +3.47646278 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.35961586 \pm 1 \cdot 10^{-8} \) \(a_{50}= -1.79787105 \pm 1 \cdot 10^{-8} \) \(a_{51}= +1.25880071 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.62359415 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.18989208 \pm 1 \cdot 10^{-8} \) \(a_{54}= +2.24015603 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.20086549 \pm 1 \cdot 10^{-8} \) \(a_{56}= -2.83050694 \pm 1 \cdot 10^{-8} \) \(a_{57}= +1.64551324 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +1.08051515 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.54254209 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.46942786 \pm 1 \cdot 10^{-8} \)

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