Properties

Label 2.1
Level $2$
Weight $0$
Character 2.1
Symmetry odd
\(R\) 5.417334
Fricke sign $-1$

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Maass form of level 2 with the smallest eigenvalue.

Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(5.41733480684467838558658825745 \pm 3 \cdot 10^{-13}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -0.38053857 \pm 1 \cdot 10^{-8} \)
\(a_{4}= +0.5 \) \(a_{5}= -0.25381246 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.26908141 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.39760056 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= -0.85519039 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.17947251 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +1.20183397 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.19026929 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= -0.94870322 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.28114605 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.09658543 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.25 \) \(a_{17}= +0.47280732 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.60471093 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= -0.23125666 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.12690623 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= -0.15130235 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.84982495 \pm 1.0 \cdot 10^{-8} \) \(a_{23}= +0.39807737 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.13454070 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= -0.93557923 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.67083448 \pm 1.0 \cdot 10^{-8} \) \(a_{27}= +0.70597150 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.19880028 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +0.83029958 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.06829621 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= -0.98553380 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -0.45734418 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.33432526 \pm 1.0 \cdot 10^{-8} \) \(a_{35}= -0.10091598 \pm 1 \cdot 10^{-8} \) \(a_{36}= -0.42759520 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= +1.21734592 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.16352316 \pm 1.0 \cdot 10^{-8} \) \(a_{39}= +0.36101817 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.08973626 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -1.21389313 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.10698692 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -0.20850301 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.60091699 \pm 1.0 \cdot 10^{-8} \) \(a_{45}= +0.21705798 \pm 1 \cdot 10^{-8} \)
\(a_{46}= +0.28148321 \pm 1.0 \cdot 10^{-8} \) \(a_{47}= +0.87290539 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.09513464 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.84191379 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.66155442 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= -0.17992142 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.47435161 \pm 1.0 \cdot 10^{-8} \) \(a_{53}= +1.01036754 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.49919724 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= -0.30504044 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.14057303 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +0.08800208 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.58711047 \pm 1.0 \cdot 10^{-8} \) \(a_{59}= -0.82312482 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.04829272 \pm 1.0 \cdot 10^{-8} \)

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