Properties

Label 37.1
Level $37$
Weight $0$
Character 37.1
Symmetry odd
\(R\) 0.642305
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 37 \)
Weight: \( 0 \)
Character: 37.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(0.6423059581946939141931947771 \pm 7 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.26097342 \pm 6.5 \cdot 10^{-7} \) \(a_{3}= -1.09228791 \pm 5.8 \cdot 10^{-7} \)
\(a_{4}= +0.59005397 \pm 6.6 \cdot 10^{-7} \) \(a_{5}= -0.22952306 \pm 5.6 \cdot 10^{-7} \) \(a_{6}= -1.37734602 \pm 6.6 \cdot 10^{-7} \)
\(a_{7}= +0.45160974 \pm 5.4 \cdot 10^{-7} \) \(a_{8}= -0.51693105 \pm 6.8 \cdot 10^{-7} \) \(a_{9}= +0.19309287 \pm 5.5 \cdot 10^{-7} \)
\(a_{10}= -0.28942248 \pm 7.2 \cdot 10^{-7} \) \(a_{11}= +0.56017006 \pm 5.0 \cdot 10^{-7} \) \(a_{12}= -0.64450881 \pm 6.2 \cdot 10^{-7} \)
\(a_{13}= +1.61392586 \pm 5.5 \cdot 10^{-7} \) \(a_{14}= +0.56946788 \pm 6.8 \cdot 10^{-7} \) \(a_{15}= +0.25070526 \pm 5.2 \cdot 10^{-7} \)
\(a_{16}= -1.24189028 \pm 6.7 \cdot 10^{-7} \) \(a_{17}= -0.99799068 \pm 5.2 \cdot 10^{-7} \) \(a_{18}= +0.24348498 \pm 6.3 \cdot 10^{-7} \)
\(a_{19}= -0.01164834 \pm 4.9 \cdot 10^{-7} \) \(a_{20}= -0.13543099 \pm 7.2 \cdot 10^{-7} \) \(a_{21}= -0.49328786 \pm 6.2 \cdot 10^{-7} \)
\(a_{22}= +0.70635955 \pm 5.6 \cdot 10^{-7} \) \(a_{23}= +0.66522133 \pm 4.4 \cdot 10^{-7} \) \(a_{24}= +0.56463754 \pm 6.6 \cdot 10^{-7} \)
\(a_{25}= -0.94731917 \pm 5.4 \cdot 10^{-7} \) \(a_{26}= +2.03511762 \pm 6.3 \cdot 10^{-7} \) \(a_{27}= +0.88137490 \pm 5.5 \cdot 10^{-7} \)
\(a_{28}= +0.26647412 \pm 6.6 \cdot 10^{-7} \) \(a_{29}= +0.00508336 \pm 4.7 \cdot 10^{-7} \) \(a_{30}= +0.31613267 \pm 5.7 \cdot 10^{-7} \)
\(a_{31}= -1.19281428 \pm 5.6 \cdot 10^{-7} \) \(a_{32}= -1.04905959 \pm 6.4 \cdot 10^{-7} \) \(a_{33}= -0.61186698 \pm 5.8 \cdot 10^{-7} \)
\(a_{34}= -1.25843972 \pm 6.8 \cdot 10^{-7} \) \(a_{35}= -0.10365485 \pm 5.9 \cdot 10^{-7} \) \(a_{36}= +0.11393522 \pm 6.4 \cdot 10^{-7} \)
\(a_{37}= +0.16439899 \pm 1.0 \cdot 10^{-8} \) \(a_{38}= -0.01468824 \pm 5.3 \cdot 10^{-7} \) \(a_{39}= -1.76287171 \pm 6.8 \cdot 10^{-7} \)
\(a_{40}= +0.11864760 \pm 7.6 \cdot 10^{-7} \) \(a_{41}= +0.27666017 \pm 5.0 \cdot 10^{-7} \) \(a_{42}= -0.62202288 \pm 7.3 \cdot 10^{-7} \)
\(a_{43}= -0.40943865 \pm 5.5 \cdot 10^{-7} \) \(a_{44}= +0.33053056 \pm 6.0 \cdot 10^{-7} \) \(a_{45}= -0.04431927 \pm 5.2 \cdot 10^{-7} \)
\(a_{46}= +0.83882642 \pm 5.2 \cdot 10^{-7} \) \(a_{47}= +0.70757403 \pm 5.4 \cdot 10^{-7} \) \(a_{48}= +1.35650174 \pm 6.4 \cdot 10^{-7} \)
\(a_{49}= -0.79604864 \pm 5.6 \cdot 10^{-7} \) \(a_{50}= -1.19454429 \pm 7.4 \cdot 10^{-7} \) \(a_{51}= +1.09009315 \pm 5.4 \cdot 10^{-7} \)
\(a_{52}= +0.95230336 \pm 5.6 \cdot 10^{-7} \) \(a_{53}= +1.48489557 \pm 5.2 \cdot 10^{-7} \) \(a_{54}= +1.11139032 \pm 6.5 \cdot 10^{-7} \)
\(a_{55}= -0.12857194 \pm 5.0 \cdot 10^{-7} \) \(a_{56}= -0.23345110 \pm 6.6 \cdot 10^{-7} \) \(a_{57}= +0.01272334 \pm 5.6 \cdot 10^{-7} \)
\(a_{58}= +0.00640998 \pm 5.6 \cdot 10^{-7} \) \(a_{59}= -0.37570709 \pm 4.4 \cdot 10^{-7} \) \(a_{60}= +0.14792963 \pm 4.7 \cdot 10^{-7} \)

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