Properties

Label 15.16
Level $15$
Weight $0$
Character 15.1
Symmetry odd
\(R\) 5.046391
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: \(5.04639152421925115467652117489 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.12638288 \pm 4.1 \cdot 10^{-8} \) \(a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +0.26873840 \pm 4.1 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= -0.65031746 \pm 5.2 \cdot 10^{-8} \)
\(a_{7}= -1.67990027 \pm 3.6 \cdot 10^{-8} \) \(a_{8}= -0.82368055 \pm 3.0 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.50373374 \pm 5.2 \cdot 10^{-8} \) \(a_{11}= +1.33584752 \pm 3.6 \cdot 10^{-8} \) \(a_{12}= -0.15515618 \pm 5.2 \cdot 10^{-8} \)
\(a_{13}= -0.39969907 \pm 3.5 \cdot 10^{-8} \) \(a_{14}= -1.89221091 \pm 4.2 \cdot 10^{-8} \) \(a_{15}= +0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= -1.19651807 \pm 3.5 \cdot 10^{-8} \) \(a_{17}= +0.92225614 \pm 3.1 \cdot 10^{-8} \) \(a_{18}= +0.37546096 \pm 5.2 \cdot 10^{-8} \)
\(a_{19}= -0.48241875 \pm 3.1 \cdot 10^{-8} \) \(a_{20}= -0.12018346 \pm 5.2 \cdot 10^{-8} \) \(a_{21}= +0.96989087 \pm 4.6 \cdot 10^{-8} \)
\(a_{22}= +1.50467578 \pm 4.3 \cdot 10^{-8} \) \(a_{23}= -1.47555439 \pm 2.7 \cdot 10^{-8} \) \(a_{24}= +0.47555219 \pm 4.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -0.45021419 \pm 4.6 \cdot 10^{-8} \) \(a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= -0.45145370 \pm 4.6 \cdot 10^{-8} \) \(a_{29}= -0.57607064 \pm 2.3 \cdot 10^{-8} \) \(a_{30}= +0.29083081 \pm 5.2 \cdot 10^{-8} \)
\(a_{31}= +0.03412613 \pm 1.8 \cdot 10^{-8} \) \(a_{32}= -0.52405692 \pm 3.1 \cdot 10^{-8} \) \(a_{33}= -0.77125192 \pm 4.6 \cdot 10^{-8} \)
\(a_{34}= +1.03881353 \pm 3.9 \cdot 10^{-8} \) \(a_{35}= +0.75127424 \pm 4.6 \cdot 10^{-8} \) \(a_{36}= +0.08957947 \pm 5.2 \cdot 10^{-8} \)
\(a_{37}= -0.15244083 \pm 2.7 \cdot 10^{-8} \) \(a_{38}= -0.54338823 \pm 3.5 \cdot 10^{-8} \) \(a_{39}= +0.23076637 \pm 4.6 \cdot 10^{-8} \)
\(a_{40}= +0.36836114 \pm 4.0 \cdot 10^{-8} \) \(a_{41}= -0.20874690 \pm 3.1 \cdot 10^{-8} \) \(a_{42}= +1.09246848 \pm 8.8 \cdot 10^{-8} \)
\(a_{43}= -0.32873533 \pm 3.4 \cdot 10^{-8} \) \(a_{44}= +0.35899352 \pm 3.4 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= -1.66203920 \pm 2.0 \cdot 10^{-8} \) \(a_{47}= -0.29840022 \pm 4.1 \cdot 10^{-8} \) \(a_{48}= +0.69081003 \pm 4.5 \cdot 10^{-8} \)
\(a_{49}= +1.82206492 \pm 2.7 \cdot 10^{-8} \) \(a_{50}= +0.22527658 \pm 5.2 \cdot 10^{-8} \) \(a_{51}= -0.53246483 \pm 4.2 \cdot 10^{-8} \)
\(a_{52}= -0.10741449 \pm 3.7 \cdot 10^{-8} \) \(a_{53}= -1.76867867 \pm 4.4 \cdot 10^{-8} \) \(a_{54}= -0.21677249 \pm 5.2 \cdot 10^{-8} \)
\(a_{55}= -0.59740917 \pm 4.6 \cdot 10^{-8} \) \(a_{56}= +1.38370119 \pm 3.1 \cdot 10^{-8} \) \(a_{57}= +0.27852460 \pm 4.2 \cdot 10^{-8} \)
\(a_{58}= -0.64887611 \pm 3.0 \cdot 10^{-8} \) \(a_{59}= -0.26592633 \pm 2.9 \cdot 10^{-8} \) \(a_{60}= +0.06938796 \pm 5.2 \cdot 10^{-8} \)

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