Properties

Label 7.22
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 7.719562
Fricke sign +1+1

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Maass form invariants

Level: 7 7
Weight: 0 0
Character: 7.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 7.71956232873361348738928840864±410127.71956232873361348738928840864 \pm 4 \cdot 10^{-12}

Maass form coefficients

The coefficients here are shown to at most 88 digits of precision. Full precision coefficients are available in the downloads.

a1=+1a_{1}= +1 a2=+1.26399410±1108a_{2}= +1.26399410 \pm 1 \cdot 10^{-8} a3=0.69965192±1108a_{3}= -0.69965192 \pm 1 \cdot 10^{-8}
a4=+0.59768107±1108a_{4}= +0.59768107 \pm 1 \cdot 10^{-8} a5=0.67343849±1108a_{5}= -0.67343849 \pm 1 \cdot 10^{-8} a6=0.88435590±1108a_{6}= -0.88435590 \pm 1 \cdot 10^{-8}
a7=0.37796447±1.0108a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} a8=0.50852875±1108a_{8}= -0.50852875 \pm 1 \cdot 10^{-8} a9=0.51048719±1108a_{9}= -0.51048719 \pm 1 \cdot 10^{-8}
a10=0.85122227±1108a_{10}= -0.85122227 \pm 1 \cdot 10^{-8} a11=0.75008757±1108a_{11}= -0.75008757 \pm 1 \cdot 10^{-8} a12=0.41816871±1108a_{12}= -0.41816871 \pm 1 \cdot 10^{-8}
a13=+0.61692317±1108a_{13}= +0.61692317 \pm 1 \cdot 10^{-8} a14=0.47774486±1.2108a_{14}= -0.47774486 \pm 1.2 \cdot 10^{-8} a15=+0.47117253±1108a_{15}= +0.47117253 \pm 1 \cdot 10^{-8}
a16=1.24045841±1108a_{16}= -1.24045841 \pm 1 \cdot 10^{-8} a17=+1.34219139±1108a_{17}= +1.34219139 \pm 1 \cdot 10^{-8} a18=0.64525279±1108a_{18}= -0.64525279 \pm 1 \cdot 10^{-8}
a19=0.12099195±1108a_{19}= -0.12099195 \pm 1 \cdot 10^{-8} a20=0.40250144±1108a_{20}= -0.40250144 \pm 1 \cdot 10^{-8} a21=+0.26444357±1.1108a_{21}= +0.26444357 \pm 1.1 \cdot 10^{-8}
a22=0.94810625±1108a_{22}= -0.94810625 \pm 1 \cdot 10^{-8} a23=+0.91946017±1108a_{23}= +0.91946017 \pm 1 \cdot 10^{-8} a24=+0.35579312±1108a_{24}= +0.35579312 \pm 1 \cdot 10^{-8}
a25=0.54648060±1108a_{25}= -0.54648060 \pm 1 \cdot 10^{-8} a26=+0.77978725±1108a_{26}= +0.77978725 \pm 1 \cdot 10^{-8} a27=+1.05681526±1108a_{27}= +1.05681526 \pm 1 \cdot 10^{-8}
a28=0.22590221±1.1108a_{28}= -0.22590221 \pm 1.1 \cdot 10^{-8} a29=1.66294620±1108a_{29}= -1.66294620 \pm 1 \cdot 10^{-8} a30=+0.59555930±1108a_{30}= +0.59555930 \pm 1 \cdot 10^{-8}
a31=1.34080011±1108a_{31}= -1.34080011 \pm 1 \cdot 10^{-8} a32=1.05940336±1108a_{32}= -1.05940336 \pm 1 \cdot 10^{-8} a33=+0.52480021±1108a_{33}= +0.52480021 \pm 1 \cdot 10^{-8}
a34=+1.69652200±1108a_{34}= +1.69652200 \pm 1 \cdot 10^{-8} a35=+0.25453582±1.1108a_{35}= +0.25453582 \pm 1.1 \cdot 10^{-8} a36=0.30510853±1108a_{36}= -0.30510853 \pm 1 \cdot 10^{-8}
a37=+1.50328805±1108a_{37}= +1.50328805 \pm 1 \cdot 10^{-8} a38=0.15293311±1108a_{38}= -0.15293311 \pm 1 \cdot 10^{-8} a39=0.43163148±1108a_{39}= -0.43163148 \pm 1 \cdot 10^{-8}
a40=+0.34246283±1108a_{40}= +0.34246283 \pm 1 \cdot 10^{-8} a41=1.56381415±1108a_{41}= -1.56381415 \pm 1 \cdot 10^{-8} a42=+0.33425511±1.3108a_{42}= +0.33425511 \pm 1.3 \cdot 10^{-8}
a43=1.25523439±1108a_{43}= -1.25523439 \pm 1 \cdot 10^{-8} a44=0.44831314±1108a_{44}= -0.44831314 \pm 1 \cdot 10^{-8} a45=+0.34378172±1108a_{45}= +0.34378172 \pm 1 \cdot 10^{-8}
a46=+1.16219222±1108a_{46}= +1.16219222 \pm 1 \cdot 10^{-8} a47=0.02006290±1108a_{47}= -0.02006290 \pm 1 \cdot 10^{-8} a48=+0.86788911±1108a_{48}= +0.86788911 \pm 1 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=0.69074826±1108a_{50}= -0.69074826 \pm 1 \cdot 10^{-8} a51=0.93906679±1108a_{51}= -0.93906679 \pm 1 \cdot 10^{-8}
a52=+0.36872330±1108a_{52}= +0.36872330 \pm 1 \cdot 10^{-8} a53=0.35240424±1108a_{53}= -0.35240424 \pm 1 \cdot 10^{-8} a54=+1.33580826±1108a_{54}= +1.33580826 \pm 1 \cdot 10^{-8}
a55=+0.50513784±1108a_{55}= +0.50513784 \pm 1 \cdot 10^{-8} a56=+0.19220580±1.1108a_{56}= +0.19220580 \pm 1.1 \cdot 10^{-8} a57=+0.08465225±1108a_{57}= +0.08465225 \pm 1 \cdot 10^{-8}
a58=2.10195417±1108a_{58}= -2.10195417 \pm 1 \cdot 10^{-8} a59=+0.60986889±1108a_{59}= +0.60986889 \pm 1 \cdot 10^{-8} a60=+0.28161091±1108a_{60}= +0.28161091 \pm 1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000