Properties

Label 3.36
Level 33
Weight 00
Character 3.1
Symmetry odd
RR 16.96539
Fricke sign not computed rigorously

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Maass form invariants

Level: 3 3
Weight: 0 0
Character: 3.1
Symmetry: odd
Fricke sign: not computed rigorously
Spectral parameter: 16.9653979482295206395782966382±410616.9653979482295206395782966382 \pm 4 \cdot 10^{-6}

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=0.27140621±3.9103a_{2}= -0.27140621 \pm 3.9 \cdot 10^{-3} a3=±0.57735027±1.0108a_{3}= \pm0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.92633867±7.0103a_{4}= -0.92633867 \pm 7.0 \cdot 10^{-3} a5=+0.88701142±5.3103a_{5}= +0.88701142 \pm 5.3 \cdot 10^{-3} a6=±0.15669645±2.2103a_{6}= \pm0.15669645 \pm 2.2 \cdot 10^{-3}
a7=+0.44233409±4.4103a_{7}= +0.44233409 \pm 4.4 \cdot 10^{-3} a8=+0.52282028±4.7103a_{8}= +0.52282028 \pm 4.7 \cdot 10^{-3} a9=±0.33333333±1.0108a_{9}= \pm0.33333333 \pm 1.0 \cdot 10^{-8}
a10=0.24074041±3.0103a_{10}= -0.24074041 \pm 3.0 \cdot 10^{-3} a11=0.48209419±4.9103a_{11}= -0.48209419 \pm 4.9 \cdot 10^{-3} a12=±0.53482188±4.0103a_{12}= \pm0.53482188 \pm 4.0 \cdot 10^{-3}
a13=+1.36615398±4.7103a_{13}= +1.36615398 \pm 4.7 \cdot 10^{-3} a14=0.12005222±3.0103a_{14}= -0.12005222 \pm 3.0 \cdot 10^{-3} a15=±0.51211628±3.1103a_{15}= \pm0.51211628 \pm 3.1 \cdot 10^{-3}
a16=+0.78444199±5.7103a_{16}= +0.78444199 \pm 5.7 \cdot 10^{-3} a17=1.20406801±3.5103a_{17}= -1.20406801 \pm 3.5 \cdot 10^{-3} a18=±0.09046874±1.3103a_{18}= \pm0.09046874 \pm 1.3 \cdot 10^{-3}
a19=1.58490148±2.9103a_{19}= -1.58490148 \pm 2.9 \cdot 10^{-3} a20=0.82167298±5.0103a_{20}= -0.82167298 \pm 5.0 \cdot 10^{-3} a21=±0.25538170±2.5103a_{21}= \pm0.25538170 \pm 2.5 \cdot 10^{-3}
a22=+0.13084336±2.4103a_{22}= +0.13084336 \pm 2.4 \cdot 10^{-3} a23=0.88938742±1.0102a_{23}= -0.88938742 \pm 1.0 \cdot 10^{-2} a24=±0.30185043±2.7103a_{24}= \pm0.30185043 \pm 2.7 \cdot 10^{-3}
a25=0.21321074±4.4103a_{25}= -0.21321074 \pm 4.4 \cdot 10^{-3} a26=0.37078268±1.6103a_{26}= -0.37078268 \pm 1.6 \cdot 10^{-3} a27=±0.19245009±1.0108a_{27}= \pm0.19245009 \pm 1.0 \cdot 10^{-8}
a28=0.40975117±2.9103a_{28}= -0.40975117 \pm 2.9 \cdot 10^{-3} a29=+1.36067712±1.0102a_{29}= +1.36067712 \pm 1.0 \cdot 10^{-2} a30=±0.13899154±1.7103a_{30}= \pm0.13899154 \pm 1.7 \cdot 10^{-3}
a31=1.05564852±4.5103a_{31}= -1.05564852 \pm 4.5 \cdot 10^{-3} a32=0.73572271±6.3103a_{32}= -0.73572271 \pm 6.3 \cdot 10^{-3} a33=±0.27833721±2.8103a_{33}= \pm0.27833721 \pm 2.8 \cdot 10^{-3}
a34=+0.32679154±4.3103a_{34}= +0.32679154 \pm 4.3 \cdot 10^{-3} a35=+0.39235539±1.9103a_{35}= +0.39235539 \pm 1.9 \cdot 10^{-3} a36=±0.30877956±2.3103a_{36}= \pm0.30877956 \pm 2.3 \cdot 10^{-3}
a37=+0.35776429±5.4103a_{37}= +0.35776429 \pm 5.4 \cdot 10^{-3} a38=+0.43015211±1.3103a_{38}= +0.43015211 \pm 1.3 \cdot 10^{-3} a39=±0.78874937±2.7103a_{39}= \pm0.78874937 \pm 2.7 \cdot 10^{-3}
a40=+0.46374756±2.9103a_{40}= +0.46374756 \pm 2.9 \cdot 10^{-3} a41=1.34131023±1.0102a_{41}= -1.34131023 \pm 1.0 \cdot 10^{-2} a42=±0.06931218±1.7103a_{42}= \pm0.06931218 \pm 1.7 \cdot 10^{-3}
a43=+0.57469831±6.8103a_{43}= +0.57469831 \pm 6.8 \cdot 10^{-3} a44=+0.44658249±4.3103a_{44}= +0.44658249 \pm 4.3 \cdot 10^{-3} a45=±0.29567047±1.7103a_{45}= \pm0.29567047 \pm 1.7 \cdot 10^{-3}
a46=+0.24138527±3.1103a_{46}= +0.24138527 \pm 3.1 \cdot 10^{-3} a47=0.04214236±8.5103a_{47}= -0.04214236 \pm 8.5 \cdot 10^{-3} a48=±0.45289780±3.3103a_{48}= \pm0.45289780 \pm 3.3 \cdot 10^{-3}
a49=0.80434055±7.4103a_{49}= -0.80434055 \pm 7.4 \cdot 10^{-3} a50=+0.05786672±2.1103a_{50}= +0.05786672 \pm 2.1 \cdot 10^{-3} a51=±0.69516899±2.0103a_{51}= \pm0.69516899 \pm 2.0 \cdot 10^{-3}
a52=1.26552126±4.3103a_{52}= -1.26552126 \pm 4.3 \cdot 10^{-3} a53=+1.30030034±4.2103a_{53}= +1.30030034 \pm 4.2 \cdot 10^{-3} a54=±0.05223215±7.5104a_{54}= \pm0.05223215 \pm 7.5 \cdot 10^{-4}
a55=0.42762305±3.4103a_{55}= -0.42762305 \pm 3.4 \cdot 10^{-3} a56=+0.23126123±4.2103a_{56}= +0.23126123 \pm 4.2 \cdot 10^{-3} a57=±0.91504330±1.6103a_{57}= \pm0.91504330 \pm 1.6 \cdot 10^{-3}
a58=0.36929623±4.2103a_{58}= -0.36929623 \pm 4.2 \cdot 10^{-3} a59=0.53475422±6.8103a_{59}= -0.53475422 \pm 6.8 \cdot 10^{-3} a60=±0.47439311±2.8103a_{60}= \pm0.47439311 \pm 2.8 \cdot 10^{-3}

Displaying ana_n with nn up to: 60 180 1000