Properties

Label 2.11
Level $2$
Weight $0$
Character 2.1
Symmetry odd
\(R\) 14.09720
Fricke sign $-1$

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Maass form invariants

Level: \( 2 \)
Weight: \( 0 \)
Character: 2.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(14.097203733919118562864404305 \pm 2 \cdot 10^{-8}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.52313756 \pm 3.0 \cdot 10^{-7} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.53848903 \pm 2.2 \cdot 10^{-7} \) \(a_{6}= -1.07702089 \pm 3.1 \cdot 10^{-7} \)
\(a_{7}= +1.10504771 \pm 2.5 \cdot 10^{-7} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +1.31994801 \pm 5.2 \cdot 10^{-7} \)
\(a_{10}= +0.38076925 \pm 2.3 \cdot 10^{-7} \) \(a_{11}= +1.06533591 \pm 7.4 \cdot 10^{-7} \) \(a_{12}= -0.76156878 \pm 3.1 \cdot 10^{-7} \)
\(a_{13}= +0.53069533 \pm 5.8 \cdot 10^{-7} \) \(a_{14}= +0.78138673 \pm 2.6 \cdot 10^{-7} \) \(a_{15}= -0.82019287 \pm 1.6 \cdot 10^{-7} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.51927767 \pm 4.2 \cdot 10^{-7} \) \(a_{18}= +0.93334419 \pm 5.3 \cdot 10^{-7} \)
\(a_{19}= -0.12602366 \pm 3.0 \cdot 10^{-7} \) \(a_{20}= +0.26924452 \pm 2.3 \cdot 10^{-7} \) \(a_{21}= -1.68313967 \pm 1.2 \cdot 10^{-7} \)
\(a_{22}= +0.75330624 \pm 7.5 \cdot 10^{-7} \) \(a_{23}= +1.30256905 \pm 3.1 \cdot 10^{-7} \) \(a_{24}= -0.53851045 \pm 3.1 \cdot 10^{-7} \)
\(a_{25}= -0.71002956 \pm 5.8 \cdot 10^{-7} \) \(a_{26}= +0.37525827 \pm 5.9 \cdot 10^{-7} \) \(a_{27}= -0.48732484 \pm 4.7 \cdot 10^{-7} \)
\(a_{28}= +0.55252386 \pm 2.6 \cdot 10^{-7} \) \(a_{29}= -0.03435910 \pm 5.2 \cdot 10^{-7} \) \(a_{30}= -0.57996394 \pm 5.4 \cdot 10^{-7} \)
\(a_{31}= +1.31299756 \pm 6.1 \cdot 10^{-7} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= -1.62265313 \pm 2.9 \cdot 10^{-7} \)
\(a_{34}= -0.36718476 \pm 4.3 \cdot 10^{-7} \) \(a_{35}= +0.59505607 \pm 6.5 \cdot 10^{-8} \) \(a_{36}= +0.65997401 \pm 5.3 \cdot 10^{-7} \)
\(a_{37}= +0.46938276 \pm 7.6 \cdot 10^{-7} \) \(a_{38}= -0.08911218 \pm 3.1 \cdot 10^{-7} \) \(a_{39}= -0.80832199 \pm 2.3 \cdot 10^{-7} \)
\(a_{40}= +0.19038462 \pm 2.3 \cdot 10^{-7} \) \(a_{41}= +0.12753792 \pm 7.7 \cdot 10^{-7} \) \(a_{42}= -1.19015948 \pm 5.7 \cdot 10^{-7} \)
\(a_{43}= +0.46916818 \pm 1.7 \cdot 10^{-7} \) \(a_{44}= +0.53266795 \pm 7.5 \cdot 10^{-7} \) \(a_{45}= +0.71077753 \pm 1.3 \cdot 10^{-7} \)
\(a_{46}= +0.92105541 \pm 3.2 \cdot 10^{-7} \) \(a_{47}= -1.68853154 \pm 5.5 \cdot 10^{-7} \) \(a_{48}= -0.38078439 \pm 3.1 \cdot 10^{-7} \)
\(a_{49}= +0.22113045 \pm 5.5 \cdot 10^{-7} \) \(a_{50}= -0.50206672 \pm 5.9 \cdot 10^{-7} \) \(a_{51}= +0.79093132 \pm 3.1 \cdot 10^{-7} \)
\(a_{52}= +0.26534767 \pm 5.9 \cdot 10^{-7} \) \(a_{53}= -0.32758291 \pm 6.3 \cdot 10^{-7} \) \(a_{54}= -0.34459070 \pm 4.8 \cdot 10^{-7} \)
\(a_{55}= +0.57367170 \pm 1.8 \cdot 10^{-7} \) \(a_{56}= +0.39069337 \pm 2.6 \cdot 10^{-7} \) \(a_{57}= +0.19195137 \pm 2.6 \cdot 10^{-7} \)
\(a_{58}= -0.02429555 \pm 5.3 \cdot 10^{-7} \) \(a_{59}= -1.15361851 \pm 5.2 \cdot 10^{-7} \) \(a_{60}= -0.41009643 \pm 5.4 \cdot 10^{-7} \)

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