Properties

Label 31.15
Level $31$
Weight $0$
Character 31.1
Symmetry odd
\(R\) 2.805934
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(2.80593495032754336303823430133 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.15124137 \pm 1.1 \cdot 10^{-6} \) \(a_{3}= +0.20357970 \pm 9.9 \cdot 10^{-7} \)
\(a_{4}= +0.32535668 \pm 1.2 \cdot 10^{-6} \) \(a_{5}= +1.25675200 \pm 9.2 \cdot 10^{-7} \) \(a_{6}= -0.23436937 \pm 1.2 \cdot 10^{-6} \)
\(a_{7}= +1.21792630 \pm 9.0 \cdot 10^{-7} \) \(a_{8}= +0.77667729 \pm 1.2 \cdot 10^{-6} \) \(a_{9}= -0.95855531 \pm 9.4 \cdot 10^{-7} \)
\(a_{10}= -1.44682489 \pm 1.1 \cdot 10^{-6} \) \(a_{11}= -0.28959552 \pm 9.0 \cdot 10^{-7} \) \(a_{12}= +0.06623601 \pm 1.4 \cdot 10^{-6} \)
\(a_{13}= +1.74179425 \pm 9.4 \cdot 10^{-7} \) \(a_{14}= -1.40212714 \pm 9.3 \cdot 10^{-7} \) \(a_{15}= +0.25584919 \pm 9.5 \cdot 10^{-7} \)
\(a_{16}= -1.21949971 \pm 1.1 \cdot 10^{-6} \) \(a_{17}= +0.71098344 \pm 8.5 \cdot 10^{-7} \) \(a_{18}= +1.10352852 \pm 1.2 \cdot 10^{-6} \)
\(a_{19}= +1.12761077 \pm 9.5 \cdot 10^{-7} \) \(a_{20}= +0.40889266 \pm 1.1 \cdot 10^{-6} \) \(a_{21}= +0.24794506 \pm 9.7 \cdot 10^{-7} \)
\(a_{22}= +0.33339435 \pm 9.8 \cdot 10^{-7} \) \(a_{23}= -0.94110053 \pm 8.6 \cdot 10^{-7} \) \(a_{24}= +0.15811573 \pm 1.5 \cdot 10^{-6} \)
\(a_{25}= +0.57942558 \pm 8.7 \cdot 10^{-7} \) \(a_{26}= -2.00522559 \pm 9.5 \cdot 10^{-7} \) \(a_{27}= -0.39872209 \pm 8.3 \cdot 10^{-7} \)
\(a_{28}= +0.39626046 \pm 9.7 \cdot 10^{-7} \) \(a_{29}= +0.04161641 \pm 8.5 \cdot 10^{-7} \) \(a_{30}= -0.29454417 \pm 1.2 \cdot 10^{-6} \)
\(a_{31}= +0.17960530 \pm 1.0 \cdot 10^{-8} \) \(a_{32}= +0.62726122 \pm 1.2 \cdot 10^{-6} \) \(a_{33}= -0.05895577 \pm 9.6 \cdot 10^{-7} \)
\(a_{34}= -0.81851355 \pm 1.1 \cdot 10^{-6} \) \(a_{35}= +1.53063131 \pm 8.3 \cdot 10^{-7} \) \(a_{36}= -0.31187238 \pm 1.3 \cdot 10^{-6} \)
\(a_{37}= -0.62061707 \pm 8.3 \cdot 10^{-7} \) \(a_{38}= -1.29815216 \pm 1.1 \cdot 10^{-6} \) \(a_{39}= +0.35459394 \pm 9.2 \cdot 10^{-7} \)
\(a_{40}= +0.97609074 \pm 1.2 \cdot 10^{-6} \) \(a_{41}= -1.34748366 \pm 8.2 \cdot 10^{-7} \) \(a_{42}= -0.28544461 \pm 1.1 \cdot 10^{-6} \)
\(a_{43}= +1.66415848 \pm 7.8 \cdot 10^{-7} \) \(a_{44}= -0.09422184 \pm 9.6 \cdot 10^{-7} \) \(a_{45}= -1.20466630 \pm 9.1 \cdot 10^{-7} \)
\(a_{46}= +1.08343386 \pm 8.3 \cdot 10^{-7} \) \(a_{47}= +0.34014341 \pm 8.0 \cdot 10^{-7} \) \(a_{48}= -0.24826538 \pm 1.4 \cdot 10^{-6} \)
\(a_{49}= +0.48334447 \pm 8.6 \cdot 10^{-7} \) \(a_{50}= -0.66705870 \pm 1.1 \cdot 10^{-6} \) \(a_{51}= +0.14474179 \pm 9.8 \cdot 10^{-7} \)
\(a_{52}= +0.56670440 \pm 9.7 \cdot 10^{-7} \) \(a_{53}= -0.94488638 \pm 8.6 \cdot 10^{-7} \) \(a_{54}= +0.45902537 \pm 1.0 \cdot 10^{-6} \)
\(a_{55}= -0.36394975 \pm 9.7 \cdot 10^{-7} \) \(a_{56}= +0.94593570 \pm 9.3 \cdot 10^{-7} \) \(a_{57}= +0.22955866 \pm 9.3 \cdot 10^{-7} \)
\(a_{58}= -0.04791053 \pm 1.0 \cdot 10^{-6} \) \(a_{59}= +0.23340959 \pm 9.7 \cdot 10^{-7} \) \(a_{60}= +0.08324224 \pm 1.4 \cdot 10^{-6} \)

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