Properties

Label 15.35
Level $15$
Weight $0$
Character 15.1
Symmetry odd
\(R\) 7.198211
Fricke sign $+1$

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Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \(7.19821130416664651903660524395 \pm 8 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.95455596 \pm 9.8 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= -0.08882293 \pm 9.7 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.55111314 \pm 1.0 \cdot 10^{-7} \)
\(a_{7}= +1.27918848 \pm 8.4 \cdot 10^{-8} \) \(a_{8}= +1.03934241 \pm 7.0 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.42689040 \pm 1.0 \cdot 10^{-7} \) \(a_{11}= -0.23540021 \pm 8.5 \cdot 10^{-8} \) \(a_{12}= +0.05128194 \pm 1.0 \cdot 10^{-7} \)
\(a_{13}= -0.11981768 \pm 8.4 \cdot 10^{-8} \) \(a_{14}= -1.22105698 \pm 1.0 \cdot 10^{-7} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -0.90328756 \pm 8.2 \cdot 10^{-8} \) \(a_{17}= +0.19567727 \pm 7.4 \cdot 10^{-8} \) \(a_{18}= -0.31818532 \pm 1.0 \cdot 10^{-7} \)
\(a_{19}= +0.05642835 \pm 7.4 \cdot 10^{-8} \) \(a_{20}= +0.03972282 \pm 1.0 \cdot 10^{-7} \) \(a_{21}= -0.73853981 \pm 9.5 \cdot 10^{-8} \)
\(a_{22}= +0.22470267 \pm 1.0 \cdot 10^{-7} \) \(a_{23}= -1.72550924 \pm 6.5 \cdot 10^{-8} \) \(a_{24}= -0.60006462 \pm 8.1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.11437268 \pm 1.0 \cdot 10^{-7} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.11362126 \pm 1.0 \cdot 10^{-7} \) \(a_{29}= +0.88291175 \pm 5.4 \cdot 10^{-8} \) \(a_{30}= -0.24646529 \pm 1.0 \cdot 10^{-7} \)
\(a_{31}= +1.48437699 \pm 4.4 \cdot 10^{-8} \) \(a_{32}= -0.17710389 \pm 7.4 \cdot 10^{-8} \) \(a_{33}= +0.13590837 \pm 9.5 \cdot 10^{-8} \)
\(a_{34}= -0.18678490 \pm 9.3 \cdot 10^{-8} \) \(a_{35}= -0.57207048 \pm 9.5 \cdot 10^{-8} \) \(a_{36}= -0.02960764 \pm 1.0 \cdot 10^{-7} \)
\(a_{37}= -1.31525248 \pm 6.3 \cdot 10^{-8} \) \(a_{38}= -0.05386401 \pm 8.3 \cdot 10^{-8} \) \(a_{39}= +0.06917677 \pm 9.4 \cdot 10^{-8} \)
\(a_{40}= -0.46480806 \pm 8.1 \cdot 10^{-8} \) \(a_{41}= -1.82572604 \pm 7.5 \cdot 10^{-8} \) \(a_{42}= +0.70497758 \pm 1.9 \cdot 10^{-7} \)
\(a_{43}= +1.75030379 \pm 8.1 \cdot 10^{-8} \) \(a_{44}= +0.02090894 \pm 8.0 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= +1.64709512 \pm 4.8 \cdot 10^{-8} \) \(a_{47}= -1.05488641 \pm 9.8 \cdot 10^{-8} \) \(a_{48}= +0.52151332 \pm 9.2 \cdot 10^{-8} \)
\(a_{49}= +0.63632315 \pm 6.3 \cdot 10^{-8} \) \(a_{50}= -0.19091119 \pm 1.0 \cdot 10^{-7} \) \(a_{51}= -0.11297432 \pm 8.5 \cdot 10^{-8} \)
\(a_{52}= +0.01064256 \pm 8.7 \cdot 10^{-8} \) \(a_{53}= -1.43206537 \pm 1.0 \cdot 10^{-7} \) \(a_{54}= +0.18370438 \pm 1.0 \cdot 10^{-7} \)
\(a_{55}= +0.10527417 \pm 9.5 \cdot 10^{-8} \) \(a_{56}= +1.32951483 \pm 7.2 \cdot 10^{-8} \) \(a_{57}= -0.03257892 \pm 8.4 \cdot 10^{-8} \)
\(a_{58}= -0.84278867 \pm 7.1 \cdot 10^{-8} \) \(a_{59}= -0.12329627 \pm 6.9 \cdot 10^{-8} \) \(a_{60}= -0.02293398 \pm 1.0 \cdot 10^{-7} \)

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