Properties

Label 3.33
Level 33
Weight 00
Character 3.1
Symmetry even
RR 15.79949
Fricke sign +1+1

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Maass form invariants

Level: 3 3
Weight: 0 0
Character: 3.1
Symmetry: even
Fricke sign: +1+1
Spectral parameter: 15.7994939260844159351480665632±210715.7994939260844159351480665632 \pm 2 \cdot 10^{-7}

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=+1.88979233±8.0107a_{2}= +1.88979233 \pm 8.0 \cdot 10^{-7} a3=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+2.57131506±4.9107a_{4}= +2.57131506 \pm 4.9 \cdot 10^{-7} a5=+0.58480210±6.9108a_{5}= +0.58480210 \pm 6.9 \cdot 10^{-8} a6=1.09107211±8.1107a_{6}= -1.09107211 \pm 8.1 \cdot 10^{-7}
a7=0.03104569±4.4107a_{7}= -0.03104569 \pm 4.4 \cdot 10^{-7} a8=+2.96945915±1.8107a_{8}= +2.96945915 \pm 1.8 \cdot 10^{-7} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+1.10515453±8.3108a_{10}= +1.10515453 \pm 8.3 \cdot 10^{-8} a11=+0.08493308±2.4107a_{11}= +0.08493308 \pm 2.4 \cdot 10^{-7} a12=1.48454944±5.0107a_{12}= -1.48454944 \pm 5.0 \cdot 10^{-7}
a13=+1.52538435±3.2107a_{13}= +1.52538435 \pm 3.2 \cdot 10^{-7} a14=0.05866991±6.0107a_{14}= -0.05866991 \pm 6.0 \cdot 10^{-7} a15=0.33763565±8.0108a_{15}= -0.33763565 \pm 8.0 \cdot 10^{-8}
a16=+3.04034608±6.8107a_{16}= +3.04034608 \pm 6.8 \cdot 10^{-7} a17=0.67682700±5.7107a_{17}= -0.67682700 \pm 5.7 \cdot 10^{-7} a18=+0.62993078±8.1107a_{18}= +0.62993078 \pm 8.1 \cdot 10^{-7}
a19=+0.04700919±9.1107a_{19}= +0.04700919 \pm 9.1 \cdot 10^{-7} a20=+1.50371045±8.7108a_{20}= +1.50371045 \pm 8.7 \cdot 10^{-8} a21=+0.01792424±4.6107a_{21}= +0.01792424 \pm 4.6 \cdot 10^{-7}
a22=+0.16050589±3.2107a_{22}= +0.16050589 \pm 3.2 \cdot 10^{-7} a23=+0.83713434±2.0107a_{23}= +0.83713434 \pm 2.0 \cdot 10^{-7} a24=1.71441804±1.9107a_{24}= -1.71441804 \pm 1.9 \cdot 10^{-7}
a25=0.65800650±5.8107a_{25}= -0.65800650 \pm 5.8 \cdot 10^{-7} a26=+2.88265965±4.5107a_{26}= +2.88265965 \pm 4.5 \cdot 10^{-7} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.07982825±3.7107a_{28}= -0.07982825 \pm 3.7 \cdot 10^{-7} a29=1.08143461±1.5107a_{29}= -1.08143461 \pm 1.5 \cdot 10^{-7} a30=0.63806127±8.8107a_{30}= -0.63806127 \pm 8.8 \cdot 10^{-7}
a31=0.73514243±6.8107a_{31}= -0.73514243 \pm 6.8 \cdot 10^{-7} a32=+2.77616356±7.6107a_{32}= +2.77616356 \pm 7.6 \cdot 10^{-7} a33=0.04903614±2.5107a_{33}= -0.04903614 \pm 2.5 \cdot 10^{-7}
a34=1.27906248±7.6107a_{34}= -1.27906248 \pm 7.6 \cdot 10^{-7} a35=0.01815559±6.1108a_{35}= -0.01815559 \pm 6.1 \cdot 10^{-8} a36=+0.85710502±5.0107a_{36}= +0.85710502 \pm 5.0 \cdot 10^{-7}
a37=0.82980604±1.5107a_{37}= -0.82980604 \pm 1.5 \cdot 10^{-7} a38=+0.08883762±1.2106a_{38}= +0.08883762 \pm 1.2 \cdot 10^{-6} a39=0.88068107±3.4107a_{39}= -0.88068107 \pm 3.4 \cdot 10^{-7}
a40=+1.73654596±5.3108a_{40}= +1.73654596 \pm 5.3 \cdot 10^{-8} a41=0.61266330±6.5107a_{41}= -0.61266330 \pm 6.5 \cdot 10^{-7} a42=+0.03387309±1.2106a_{42}= +0.03387309 \pm 1.2 \cdot 10^{-6}
a43=0.72099717±1.1107a_{43}= -0.72099717 \pm 1.1 \cdot 10^{-7} a44=+0.21838972±1.9107a_{44}= +0.21838972 \pm 1.9 \cdot 10^{-7} a45=+0.19493403±8.0108a_{45}= +0.19493403 \pm 8.0 \cdot 10^{-8}
a46=+1.58201006±2.9107a_{46}= +1.58201006 \pm 2.9 \cdot 10^{-7} a47=+0.23706617±5.9107a_{47}= +0.23706617 \pm 5.9 \cdot 10^{-7} a48=1.75534463±6.9107a_{48}= -1.75534463 \pm 6.9 \cdot 10^{-7}
a49=0.99903617±2.5107a_{49}= -0.99903617 \pm 2.5 \cdot 10^{-7} a50=1.24349564±7.9107a_{50}= -1.24349564 \pm 7.9 \cdot 10^{-7} a51=+0.39076625±5.8107a_{51}= +0.39076625 \pm 5.8 \cdot 10^{-7}
a52=+3.92224376±3.1107a_{52}= +3.92224376 \pm 3.1 \cdot 10^{-7} a53=0.94364515±1.7107a_{53}= -0.94364515 \pm 1.7 \cdot 10^{-7} a54=0.36369070±8.1107a_{54}= -0.36369070 \pm 8.1 \cdot 10^{-7}
a55=+0.04966905±2.4108a_{55}= +0.04966905 \pm 2.4 \cdot 10^{-8} a56=0.09218891±1.3107a_{56}= -0.09218891 \pm 1.3 \cdot 10^{-7} a57=0.02714077±9.3107a_{57}= -0.02714077 \pm 9.3 \cdot 10^{-7}
a58=2.04368684±2.2107a_{58}= -2.04368684 \pm 2.2 \cdot 10^{-7} a59=+1.03520149±5.5108a_{59}= +1.03520149 \pm 5.5 \cdot 10^{-8} a60=0.86816764±5.7107a_{60}= -0.86816764 \pm 5.7 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000