Properties

Label 5.5
Level $5$
Weight $0$
Character 5.1
Symmetry even
\(R\) 5.436180
Fricke sign $-1$

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Maass form invariants

Level: \( 5 \)
Weight: \( 0 \)
Character: 5.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \(5.43618046141585614838569313633 \pm 4 \cdot 10^{-13}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.03471171 \pm 1 \cdot 10^{-8} \) \(a_{3}= -0.87643005 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.99879510 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} \) \(a_{6}= +0.03042239 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.62053822 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.06938160 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.23187037 \pm 1 \cdot 10^{-8} \)
\(a_{10}= -0.01552355 \pm 1.0 \cdot 10^{-8} \) \(a_{11}= +0.76704312 \pm 1 \cdot 10^{-8} \) \(a_{12}= +0.87537403 \pm 1 \cdot 10^{-8} \)
\(a_{13}= -1.78457627 \pm 1 \cdot 10^{-8} \) \(a_{14}= +0.02153994 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.39195143 \pm 1.0 \cdot 10^{-8} \)
\(a_{16}= +0.99638674 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.12779471 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.00804862 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.53834185 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.44667475 \pm 1.0 \cdot 10^{-8} \) \(a_{21}= +0.54385834 \pm 1 \cdot 10^{-8} \)
\(a_{22}= -0.02662538 \pm 1 \cdot 10^{-8} \) \(a_{23}= -1.51251008 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.06080812 \pm 1 \cdot 10^{-8} \)
\(a_{25}= +0.2 \) \(a_{26}= +0.06194570 \pm 1 \cdot 10^{-8} \) \(a_{27}= +1.07964821 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.61979053 \pm 1 \cdot 10^{-8} \) \(a_{29}= -0.66710160 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.01360530 \pm 1.0 \cdot 10^{-8} \)
\(a_{31}= +0.13466564 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.10396789 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.67225963 \pm 1 \cdot 10^{-8} \)
\(a_{34}= +0.00443597 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.27751313 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= +0.23159099 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -0.76811762 \pm 1 \cdot 10^{-8} \) \(a_{38}= -0.01868677 \pm 1 \cdot 10^{-8} \) \(a_{39}= +1.56405626 \pm 1 \cdot 10^{-8} \)
\(a_{40}= +0.03102839 \pm 1.0 \cdot 10^{-8} \) \(a_{41}= -0.14835565 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.01887825 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.97810158 \pm 1 \cdot 10^{-8} \) \(a_{44}= -0.76611890 \pm 1 \cdot 10^{-8} \) \(a_{45}= -0.10369558 \pm 1.0 \cdot 10^{-8} \)
\(a_{46}= +0.05250181 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.41110464 \pm 1 \cdot 10^{-8} \) \(a_{48}= -0.87326328 \pm 1 \cdot 10^{-8} \)
\(a_{49}= -0.61493231 \pm 1 \cdot 10^{-8} \) \(a_{50}= -0.00694234 \pm 1.0 \cdot 10^{-8} \) \(a_{51}= +0.11200313 \pm 1 \cdot 10^{-8} \)
\(a_{52}= +1.78242603 \pm 1 \cdot 10^{-8} \) \(a_{53}= -0.19457851 \pm 1 \cdot 10^{-8} \) \(a_{54}= -0.03747644 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.34303211 \pm 1.0 \cdot 10^{-8} \) \(a_{56}= -0.04305393 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.47181897 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.02315624 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.46708941 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.39147917 \pm 1.0 \cdot 10^{-8} \)

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