Properties

Label 7.3
Level $7$
Weight $0$
Character 7.1
Symmetry even
\(R\) 3.454226
Fricke sign $+1$

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Maass form invariants

Level: \( 7 \)
Weight: \( 0 \)
Character: 7.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \(3.45422650357064299269741982252 \pm 9 \cdot 10^{-14}\)

Maass form coefficients

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

\(a_{1}= +1 \) \(a_{2}= +0.05893576 \pm 1 \cdot 10^{-8} \) \(a_{3}= +1.58439467 \pm 1 \cdot 10^{-8} \)
\(a_{4}= -0.99652658 \pm 1 \cdot 10^{-8} \) \(a_{5}= +0.21755483 \pm 1 \cdot 10^{-8} \) \(a_{6}= +0.09337751 \pm 1 \cdot 10^{-8} \)
\(a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} \) \(a_{8}= -0.11766682 \pm 1 \cdot 10^{-8} \) \(a_{9}= +1.51030647 \pm 1 \cdot 10^{-8} \)
\(a_{10}= +0.01282176 \pm 1 \cdot 10^{-8} \) \(a_{11}= -0.66060981 \pm 1 \cdot 10^{-8} \) \(a_{12}= -1.57889139 \pm 1 \cdot 10^{-8} \)
\(a_{13}= +0.73142838 \pm 1 \cdot 10^{-8} \) \(a_{14}= -0.02227563 \pm 1.0 \cdot 10^{-8} \) \(a_{15}= +0.34469271 \pm 1 \cdot 10^{-8} \)
\(a_{16}= +0.98959179 \pm 1 \cdot 10^{-8} \) \(a_{17}= -0.84378109 \pm 1 \cdot 10^{-8} \) \(a_{18}= +0.08901107 \pm 1 \cdot 10^{-8} \)
\(a_{19}= +0.79254676 \pm 1 \cdot 10^{-8} \) \(a_{20}= -0.21679917 \pm 1 \cdot 10^{-8} \) \(a_{21}= -0.59884490 \pm 1.0 \cdot 10^{-8} \)
\(a_{22}= -0.03893354 \pm 1 \cdot 10^{-8} \) \(a_{23}= -0.11033700 \pm 1 \cdot 10^{-8} \) \(a_{24}= -0.18643068 \pm 1 \cdot 10^{-8} \)
\(a_{25}= -0.95266990 \pm 1 \cdot 10^{-8} \) \(a_{26}= +0.04310729 \pm 1 \cdot 10^{-8} \) \(a_{27}= +0.80852684 \pm 1 \cdot 10^{-8} \)
\(a_{28}= +0.37665164 \pm 1.0 \cdot 10^{-8} \) \(a_{29}= +0.96600081 \pm 1 \cdot 10^{-8} \) \(a_{30}= +0.02031473 \pm 1 \cdot 10^{-8} \)
\(a_{31}= +0.10468324 \pm 1 \cdot 10^{-8} \) \(a_{32}= +0.17598917 \pm 1 \cdot 10^{-8} \) \(a_{33}= -1.04666666 \pm 1 \cdot 10^{-8} \)
\(a_{34}= -0.04972888 \pm 1 \cdot 10^{-8} \) \(a_{35}= -0.08222800 \pm 1.0 \cdot 10^{-8} \) \(a_{36}= -1.50506053 \pm 1 \cdot 10^{-8} \)
\(a_{37}= +0.71275243 \pm 1 \cdot 10^{-8} \) \(a_{38}= +0.04670935 \pm 1 \cdot 10^{-8} \) \(a_{39}= +1.15887123 \pm 1 \cdot 10^{-8} \)
\(a_{40}= -0.02559899 \pm 1 \cdot 10^{-8} \) \(a_{41}= -1.48045047 \pm 1 \cdot 10^{-8} \) \(a_{42}= -0.03529338 \pm 1.0 \cdot 10^{-8} \)
\(a_{43}= +0.44689477 \pm 1 \cdot 10^{-8} \) \(a_{44}= +0.65831523 \pm 1 \cdot 10^{-8} \) \(a_{45}= +0.32857447 \pm 1 \cdot 10^{-8} \)
\(a_{46}= -0.00650280 \pm 1 \cdot 10^{-8} \) \(a_{47}= -0.07648718 \pm 1 \cdot 10^{-8} \) \(a_{48}= +1.56790396 \pm 1 \cdot 10^{-8} \)
\(a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} \) \(a_{50}= -0.05614633 \pm 1 \cdot 10^{-8} \) \(a_{51}= -1.33688225 \pm 1 \cdot 10^{-8} \)
\(a_{52}= -0.72888782 \pm 1 \cdot 10^{-8} \) \(a_{53}= -1.44319688 \pm 1 \cdot 10^{-8} \) \(a_{54}= +0.04765115 \pm 1 \cdot 10^{-8} \)
\(a_{55}= -0.14371885 \pm 1 \cdot 10^{-8} \) \(a_{56}= +0.04447388 \pm 1.0 \cdot 10^{-8} \) \(a_{57}= +1.25570687 \pm 1 \cdot 10^{-8} \)
\(a_{58}= +0.05693200 \pm 1 \cdot 10^{-8} \) \(a_{59}= +0.38177751 \pm 1 \cdot 10^{-8} \) \(a_{60}= -0.34349545 \pm 1 \cdot 10^{-8} \)

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