Properties

Label 15.17
Level $15$
Weight $0$
Character 15.1
Symmetry odd
\(R\) 5.117205
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 15 = 3 \cdot 5 \)
Weight: \( 0 \)
Character: 15.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \(5.1172051641085013418147695668 \pm 2 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +1.69500219 \pm 2.7 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +1.87303244 \pm 2.7 \cdot 10^{-8} \) \(a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.97860997 \pm 3.7 \cdot 10^{-8} \)
\(a_{7}= +1.59196792 \pm 2.3 \cdot 10^{-8} \) \(a_{8}= +1.47979190 \pm 1.9 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= -0.75802803 \pm 3.7 \cdot 10^{-8} \) \(a_{11}= -1.19606076 \pm 2.3 \cdot 10^{-8} \) \(a_{12}= +1.08139578 \pm 3.7 \cdot 10^{-8} \)
\(a_{13}= -0.81830464 \pm 2.3 \cdot 10^{-8} \) \(a_{14}= +2.69838911 \pm 2.8 \cdot 10^{-8} \) \(a_{15}= -0.25819889 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.63521808 \pm 2.3 \cdot 10^{-8} \) \(a_{17}= -0.68412837 \pm 2.0 \cdot 10^{-8} \) \(a_{18}= +0.56500073 \pm 3.7 \cdot 10^{-8} \)
\(a_{19}= +0.04212964 \pm 2.0 \cdot 10^{-8} \) \(a_{20}= -0.83764557 \pm 3.7 \cdot 10^{-8} \) \(a_{21}= +0.91912311 \pm 3.4 \cdot 10^{-8} \)
\(a_{22}= -2.02732561 \pm 2.8 \cdot 10^{-8} \) \(a_{23}= -0.62599567 \pm 1.8 \cdot 10^{-8} \) \(a_{24}= +0.85435825 \pm 3.0 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= -1.38702816 \pm 3.0 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +2.98180755 \pm 3.0 \cdot 10^{-8} \) \(a_{29}= +0.91919391 \pm 1.5 \cdot 10^{-8} \) \(a_{30}= -0.43764768 \pm 3.7 \cdot 10^{-8} \)
\(a_{31}= +0.23469290 \pm 1.2 \cdot 10^{-8} \) \(a_{32}= -0.40309587 \pm 2.0 \cdot 10^{-8} \) \(a_{33}= -0.69054600 \pm 3.4 \cdot 10^{-8} \)
\(a_{34}= -1.15959909 \pm 2.6 \cdot 10^{-8} \) \(a_{35}= -0.71194970 \pm 3.4 \cdot 10^{-8} \) \(a_{36}= +0.62434415 \pm 3.7 \cdot 10^{-8} \)
\(a_{37}= +0.10659028 \pm 1.7 \cdot 10^{-8} \) \(a_{38}= +0.07140983 \pm 2.3 \cdot 10^{-8} \) \(a_{39}= -0.47244840 \pm 3.4 \cdot 10^{-8} \)
\(a_{40}= -0.66178306 \pm 3.0 \cdot 10^{-8} \) \(a_{41}= +1.80174136 \pm 2.0 \cdot 10^{-8} \) \(a_{42}= +1.55791568 \pm 6.1 \cdot 10^{-8} \)
\(a_{43}= +0.80772156 \pm 2.2 \cdot 10^{-8} \) \(a_{44}= -2.24026060 \pm 2.2 \cdot 10^{-8} \) \(a_{45}= -0.14907120 \pm 1.4 \cdot 10^{-7} \)
\(a_{46}= -1.06106403 \pm 1.3 \cdot 10^{-8} \) \(a_{47}= -1.41801684 \pm 2.7 \cdot 10^{-8} \) \(a_{48}= +0.36674333 \pm 3.3 \cdot 10^{-8} \)
\(a_{49}= +1.53436185 \pm 1.7 \cdot 10^{-8} \) \(a_{50}= +0.33900044 \pm 3.7 \cdot 10^{-8} \) \(a_{51}= -0.39498170 \pm 3.1 \cdot 10^{-8} \)
\(a_{52}= -1.53271113 \pm 2.4 \cdot 10^{-8} \) \(a_{53}= +0.32210269 \pm 2.9 \cdot 10^{-8} \) \(a_{54}= +0.32620332 \pm 3.7 \cdot 10^{-8} \)
\(a_{55}= +0.53489463 \pm 3.4 \cdot 10^{-8} \) \(a_{56}= +2.35578123 \pm 2.0 \cdot 10^{-8} \) \(a_{57}= +0.02432356 \pm 3.1 \cdot 10^{-8} \)
\(a_{58}= +1.55803570 \pm 2.0 \cdot 10^{-8} \) \(a_{59}= -1.29832333 \pm 1.9 \cdot 10^{-8} \) \(a_{60}= -0.48361490 \pm 3.7 \cdot 10^{-8} \)

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