Properties

Label 3.11
Level $3$
Weight $0$
Character 3.1
Symmetry even
\(R\) 10.23107
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(10.231075689323657356434721872 \pm 4 \cdot 10^{-11}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -1.78019237 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8} \)
\(a_{4}= +2.16908488 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.27577101 \pm 1 \cdot 10^{-8} \) \(a_{6}= -1.02779454 \pm 1.0 \cdot 10^{-8} \)
\(a_{7}= +0.31247325 \pm 1 \cdot 10^{-8} \) \(a_{8}= -2.08119597 \pm 1 \cdot 10^{-8} \) \(a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8} \)
\(a_{10}= +0.49092545 \pm 1 \cdot 10^{-8} \) \(a_{11}= -1.50280572 \pm 1 \cdot 10^{-8} \) \(a_{12}= +1.25232174 \pm 1.0 \cdot 10^{-8} \)
\(a_{13}= -0.50831111 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.55626250 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.15921647 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +1.53584432 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.46120248 \pm 1 \cdot 10^{-8} \) \(a_{18}= -0.59339746 \pm 1.0 \cdot 10^{-8} \)
\(a_{19}= -0.20775181 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.59817073 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.18040652 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= +2.67528328 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.04015381 \pm 1 \cdot 10^{-8} \) \(a_{24}= -1.20157906 \pm 1.0 \cdot 10^{-8} \)
\(a_{25}= -0.92395035 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.90489157 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8} \)
\(a_{28}= +0.67778100 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.55070740 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.28343594 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +0.41310336 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.65290237 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.86764529 \pm 1.0 \cdot 10^{-8} \)
\(a_{34}= +0.82102914 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.08617107 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.72302829 \pm 1.0 \cdot 10^{-8} \)
\(a_{37}= -1.32853091 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.36983819 \pm 1 \cdot 10^{-8} \) \(a_{39}= -0.29347356 \pm 1.0 \cdot 10^{-8} \)
\(a_{40}= +0.57393352 \pm 1 \cdot 10^{-8} \) \(a_{41}= +1.97630462 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.32115830 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= -0.59404577 \pm 1 \cdot 10^{-8} \) \(a_{44}= -3.25971317 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.09192367 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= +1.85167388 \pm 1 \cdot 10^{-8} \) \(a_{47}= +0.46068561 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.88672013 \pm 1.0 \cdot 10^{-8} \)
\(a_{49}= -0.90236047 \pm 1 \cdot 10^{-8} \) \(a_{50}= +1.64480936 \pm 1 \cdot 10^{-8} \) \(a_{51}= -0.26627538 \pm 1.0 \cdot 10^{-8} \)
\(a_{52}= -1.10256995 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.66822974 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.34259818 \pm 1.0 \cdot 10^{-8} \)
\(a_{55}= +0.41443026 \pm 1 \cdot 10^{-8} \) \(a_{56}= -0.65031807 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.11994556 \pm 1.0 \cdot 10^{-8} \)
\(a_{58}= +0.98036511 \pm 1 \cdot 10^{-8} \) \(a_{59}= +1.34566844 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.34535403 \pm 1.0 \cdot 10^{-8} \)

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