Properties

Label 1.49
Level $1$
Weight $0$
Character 1.1
Symmetry odd
\(R\) 34.69531
Fricke sign $+1$

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Maass form invariants

Level: \( 1 \)
Weight: \( 0 \)
Character: 1.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 34.69531040976459391414258000589002\ldots \pm 2 \cdot 10^{-91} \) (toggle for full precision) Copy content Toggle raw display

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= -0.33207778 \pm 1 \cdot 10^{-8} \) \(a_{3}= +0.54863734 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.88972435 \pm 1 \cdot 10^{-8} \) \(a_{5}= -0.06524015 \pm 1 \cdot 10^{-8} \) \(a_{6}= -0.18219027 \pm 1 \cdot 10^{-8} \)
\(a_{7}= +1.03357849 \pm 1 \cdot 10^{-8} \) \(a_{8}= +0.62753546 \pm 1 \cdot 10^{-8} \) \(a_{9}= -0.69899707 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.02166480 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.56114727 \pm 1 \cdot 10^{-8} \) \(a_{12}= -0.48813600 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +1.13607975 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.34322845 \pm 1 \cdot 10^{-8} \) \(a_{15}= -0.03579318 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.68133377 \pm 1 \cdot 10^{-8} \) \(a_{17}= +0.37935820 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.23212139 \pm 1 \cdot 10^{-8} \)
\(a_{19}= -1.39342155 \pm 1 \cdot 10^{-8} \) \(a_{20}= +0.05804575 \pm 1 \cdot 10^{-8} \) \(a_{21}= +0.56705975 \pm 1 \cdot 10^{-8} \)
\(a_{22}= +0.18634454 \pm 1 \cdot 10^{-8} \) \(a_{23}= +1.20972306 \pm 1 \cdot 10^{-8} \) \(a_{24}= +0.34428939 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.99574372 \pm 1 \cdot 10^{-8} \) \(a_{26}= -0.37726684 \pm 1 \cdot 10^{-8} \) \(a_{27}= -0.93213323 \pm 1 \cdot 10^{-8} \)
\(a_{28}= -0.91959994 \pm 1 \cdot 10^{-8} \) \(a_{29}= -1.72598998 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.01188612 \pm 1 \cdot 10^{-8} \)
\(a_{31}= -0.54745549 \pm 1 \cdot 10^{-8} \) \(a_{32}= -0.85379127 \pm 1 \cdot 10^{-8} \) \(a_{33}= -0.30786635 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.12597643 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.06743081 \pm 1 \cdot 10^{-8} \) \(a_{36}= +0.62191471 \pm 1 \cdot 10^{-8} \)
\(a_{37}= -1.52555960 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.46272433 \pm 1 \cdot 10^{-8} \) \(a_{39}= +0.62329577 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.04094051 \pm 1 \cdot 10^{-8} \) \(a_{41}= -0.54573234 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.18830794 \pm 1 \cdot 10^{-8} \)
\(a_{43}= +0.16740289 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.49926639 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.04560267 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.40172215 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.41826514 \pm 1 \cdot 10^{-8} \) \(a_{48}= +0.37380514 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.06828448 \pm 1 \cdot 10^{-8} \) \(a_{50}= +0.33066436 \pm 1 \cdot 10^{-8} \) \(a_{51}= +0.20813007 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -1.01079782 \pm 1 \cdot 10^{-8} \) \(a_{53}= +0.12907159 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.30954073 \pm 1 \cdot 10^{-8} \)
\(a_{55}= +0.03660933 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.64860715 \pm 1 \cdot 10^{-8} \) \(a_{57}= -0.76448309 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.57316292 \pm 1 \cdot 10^{-8} \) \(a_{59}= -1.25918208 \pm 1 \cdot 10^{-8} \) \(a_{60}= +0.03184606 \pm 1 \cdot 10^{-8} \)

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