Properties

Label 11.85
Level 1111
Weight 00
Character 11.1
Symmetry odd
RR 10.98990
Fricke sign +1+1

Related objects

Downloads

Learn more

Maass form invariants

Level: 11 11
Weight: 0 0
Character: 11.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 10.9899047920475420421886097926±4101010.9899047920475420421886097926 \pm 4 \cdot 10^{-10}

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=+1.37799891±5.7107a_{2}= +1.37799891 \pm 5.7 \cdot 10^{-7} a3=1.76401178±4.7107a_{3}= -1.76401178 \pm 4.7 \cdot 10^{-7}
a4=+0.89888100±6.7107a_{4}= +0.89888100 \pm 6.7 \cdot 10^{-7} a5=+0.56444728±4.9107a_{5}= +0.56444728 \pm 4.9 \cdot 10^{-7} a6=2.43080631±5.8107a_{6}= -2.43080631 \pm 5.8 \cdot 10^{-7}
a7=+1.09281904±4.9107a_{7}= +1.09281904 \pm 4.9 \cdot 10^{-7} a8=0.13934188±5.6107a_{8}= -0.13934188 \pm 5.6 \cdot 10^{-7} a9=+2.11173757±5.3107a_{9}= +2.11173757 \pm 5.3 \cdot 10^{-7}
a10=+0.77780773±6.0107a_{10}= +0.77780773 \pm 6.0 \cdot 10^{-7} a11=0.30151134±1.0108a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} a12=1.58563667±6.2107a_{12}= -1.58563667 \pm 6.2 \cdot 10^{-7}
a13=0.16360491±3.9107a_{13}= -0.16360491 \pm 3.9 \cdot 10^{-7} a14=+1.50590345±4.1107a_{14}= +1.50590345 \pm 4.1 \cdot 10^{-7} a15=0.99569165±3.7107a_{15}= -0.99569165 \pm 3.7 \cdot 10^{-7}
a16=1.09089395±4.9107a_{16}= -1.09089395 \pm 4.9 \cdot 10^{-7} a17=1.15982407±4.8107a_{17}= -1.15982407 \pm 4.8 \cdot 10^{-7} a18=+2.90997207±5.4107a_{18}= +2.90997207 \pm 5.4 \cdot 10^{-7}
a19=1.18160512±3.5107a_{19}= -1.18160512 \pm 3.5 \cdot 10^{-7} a20=+0.50737093±6.5107a_{20}= +0.50737093 \pm 6.5 \cdot 10^{-7} a21=1.92774566±3.8107a_{21}= -1.92774566 \pm 3.8 \cdot 10^{-7}
a22=0.41548230±5.8107a_{22}= -0.41548230 \pm 5.8 \cdot 10^{-7} a23=+0.91885496±4.6107a_{23}= +0.91885496 \pm 4.6 \cdot 10^{-7} a24=+0.24580071±6.6107a_{24}= +0.24580071 \pm 6.6 \cdot 10^{-7}
a25=0.68139927±4.0107a_{25}= -0.68139927 \pm 4.0 \cdot 10^{-7} a26=0.22544738±3.0107a_{26}= -0.22544738 \pm 3.0 \cdot 10^{-7} a27=1.96111817±4.5107a_{27}= -1.96111817 \pm 4.5 \cdot 10^{-7}
a28=+0.98231427±4.9107a_{28}= +0.98231427 \pm 4.9 \cdot 10^{-7} a29=1.56124203±4.5107a_{29}= -1.56124203 \pm 4.5 \cdot 10^{-7} a30=1.37206201±3.4107a_{30}= -1.37206201 \pm 3.4 \cdot 10^{-7}
a31=+0.87680398±4.8107a_{31}= +0.87680398 \pm 4.8 \cdot 10^{-7} a32=1.36390880±4.1107a_{32}= -1.36390880 \pm 4.1 \cdot 10^{-7} a33=+0.53186956±4.8107a_{33}= +0.53186956 \pm 4.8 \cdot 10^{-7}
a34=1.59823630±5.8107a_{34}= -1.59823630 \pm 5.8 \cdot 10^{-7} a35=+0.61683873±4.7107a_{35}= +0.61683873 \pm 4.7 \cdot 10^{-7} a36=+1.89820077±5.6107a_{36}= +1.89820077 \pm 5.6 \cdot 10^{-7}
a37=+0.24178608±4.9107a_{37}= +0.24178608 \pm 4.9 \cdot 10^{-7} a38=1.62825057±4.8107a_{38}= -1.62825057 \pm 4.8 \cdot 10^{-7} a39=+0.28860098±2.8107a_{39}= +0.28860098 \pm 2.8 \cdot 10^{-7}
a40=0.07865114±4.6107a_{40}= -0.07865114 \pm 4.6 \cdot 10^{-7} a41=+0.45191683±3.2107a_{41}= +0.45191683 \pm 3.2 \cdot 10^{-7} a42=2.65643142±4.2107a_{42}= -2.65643142 \pm 4.2 \cdot 10^{-7}
a43=1.95279426±4.6107a_{43}= -1.95279426 \pm 4.6 \cdot 10^{-7} a44=0.27102282±6.8107a_{44}= -0.27102282 \pm 6.8 \cdot 10^{-7} a45=+1.19196452±5.2107a_{45}= +1.19196452 \pm 5.2 \cdot 10^{-7}
a46=+1.26618114±6.6107a_{46}= +1.26618114 \pm 6.6 \cdot 10^{-7} a47=0.70127837±3.9107a_{47}= -0.70127837 \pm 3.9 \cdot 10^{-7} a48=+1.92434978±5.1107a_{48}= +1.92434978 \pm 5.1 \cdot 10^{-7}
a49=+0.19425346±4.3107a_{49}= +0.19425346 \pm 4.3 \cdot 10^{-7} a50=0.93896745±6.2107a_{50}= -0.93896745 \pm 6.2 \cdot 10^{-7} a51=+2.04594332±4.8107a_{51}= +2.04594332 \pm 4.8 \cdot 10^{-7}
a52=0.14706134±4.1107a_{52}= -0.14706134 \pm 4.1 \cdot 10^{-7} a53=+0.09587727±3.7107a_{53}= +0.09587727 \pm 3.7 \cdot 10^{-7} a54=2.70241871±3.9107a_{54}= -2.70241871 \pm 3.9 \cdot 10^{-7}
a55=0.17018726±5.0107a_{55}= -0.17018726 \pm 5.0 \cdot 10^{-7} a56=0.15227546±3.3107a_{56}= -0.15227546 \pm 3.3 \cdot 10^{-7} a57=+2.08436536±3.1107a_{57}= +2.08436536 \pm 3.1 \cdot 10^{-7}
a58=2.15138982±4.4107a_{58}= -2.15138982 \pm 4.4 \cdot 10^{-7} a59=1.18938312±5.5107a_{59}= -1.18938312 \pm 5.5 \cdot 10^{-7} a60=0.89500830±3.0107a_{60}= -0.89500830 \pm 3.0 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000