Properties

Label 10.44
Level $10$
Weight $0$
Character 10.1
Symmetry odd
\(R\) 11.50706
Fricke sign $+1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(11.5070658355015821787757222496 \pm 4 \cdot 10^{-10}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} \) \(a_{3}= -1.92061742 \pm 3.3 \cdot 10^{-6} \)
\(a_{4}= +0.5 \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -1.35808160 \pm 3.4 \cdot 10^{-6} \)
\(a_{7}= -0.28622395 \pm 4.2 \cdot 10^{-6} \) \(a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} \) \(a_{9}= +2.68877128 \pm 3.6 \cdot 10^{-6} \)
\(a_{10}= +0.31622777 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= -0.23979952 \pm 3.2 \cdot 10^{-6} \) \(a_{12}= -0.96030871 \pm 3.4 \cdot 10^{-6} \)
\(a_{13}= +1.37587517 \pm 3.7 \cdot 10^{-6} \) \(a_{14}= -0.20239090 \pm 4.2 \cdot 10^{-6} \) \(a_{15}= -0.85892622 \pm 3.4 \cdot 10^{-6} \)
\(a_{16}= +0.25 \) \(a_{17}= -0.16599162 \pm 2.2 \cdot 10^{-6} \) \(a_{18}= +1.90124841 \pm 3.6 \cdot 10^{-6} \)
\(a_{19}= -1.75538402 \pm 2.9 \cdot 10^{-6} \) \(a_{20}= +0.22360680 \pm 8.4 \cdot 10^{-8} \) \(a_{21}= +0.54972671 \pm 3.5 \cdot 10^{-6} \)
\(a_{22}= -0.16956387 \pm 3.2 \cdot 10^{-6} \) \(a_{23}= -0.43328219 \pm 5.1 \cdot 10^{-6} \) \(a_{24}= -0.67904080 \pm 3.4 \cdot 10^{-6} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.97289066 \pm 3.7 \cdot 10^{-6} \) \(a_{27}= -3.24348355 \pm 4.1 \cdot 10^{-6} \)
\(a_{28}= -0.14311198 \pm 4.2 \cdot 10^{-6} \) \(a_{29}= -0.18207357 \pm 5.3 \cdot 10^{-6} \) \(a_{30}= -0.60735256 \pm 3.4 \cdot 10^{-6} \)
\(a_{31}= -1.12708452 \pm 3.1 \cdot 10^{-6} \) \(a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} \) \(a_{33}= +0.46056314 \pm 2.6 \cdot 10^{-6} \)
\(a_{34}= -0.11737380 \pm 2.2 \cdot 10^{-6} \) \(a_{35}= -0.12800324 \pm 4.2 \cdot 10^{-6} \) \(a_{36}= +1.34438564 \pm 3.6 \cdot 10^{-6} \)
\(a_{37}= -0.19800640 \pm 4.0 \cdot 10^{-6} \) \(a_{38}= -1.24124395 \pm 2.9 \cdot 10^{-6} \) \(a_{39}= -2.64252982 \pm 3.0 \cdot 10^{-6} \)
\(a_{40}= +0.15811388 \pm 1.2 \cdot 10^{-7} \) \(a_{41}= -0.97725182 \pm 2.6 \cdot 10^{-6} \) \(a_{42}= +0.38871548 \pm 7.6 \cdot 10^{-6} \)
\(a_{43}= +1.00649805 \pm 3.6 \cdot 10^{-6} \) \(a_{44}= -0.11989976 \pm 3.2 \cdot 10^{-6} \) \(a_{45}= +1.20245507 \pm 3.6 \cdot 10^{-6} \)
\(a_{46}= -0.30637677 \pm 5.1 \cdot 10^{-6} \) \(a_{47}= +0.93662237 \pm 2.7 \cdot 10^{-6} \) \(a_{48}= -0.48015436 \pm 3.4 \cdot 10^{-6} \)
\(a_{49}= -0.91807585 \pm 4.2 \cdot 10^{-6} \) \(a_{50}= +0.14142136 \pm 1.5 \cdot 10^{-7} \) \(a_{51}= +0.31880639 \pm 2.7 \cdot 10^{-6} \)
\(a_{52}= +0.68793758 \pm 3.7 \cdot 10^{-6} \) \(a_{53}= -0.86311544 \pm 3.8 \cdot 10^{-6} \) \(a_{54}= -2.29348921 \pm 4.1 \cdot 10^{-6} \)
\(a_{55}= -0.10724161 \pm 3.2 \cdot 10^{-6} \) \(a_{56}= -0.10119545 \pm 4.2 \cdot 10^{-6} \) \(a_{57}= +3.37142114 \pm 2.5 \cdot 10^{-6} \)
\(a_{58}= -0.12874546 \pm 5.3 \cdot 10^{-6} \) \(a_{59}= -0.20721015 \pm 2.8 \cdot 10^{-6} \) \(a_{60}= -0.42946311 \pm 3.4 \cdot 10^{-6} \)

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