Properties

Label 3.37
Level 33
Weight 00
Character 3.1
Symmetry odd
RR 16.99056
Fricke sign 1-1

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Maass form invariants

Level: 3 3
Weight: 0 0
Character: 3.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 16.9905650918938697774436857509±310616.9905650918938697774436857509 \pm 3 \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=+1.59187815±2.6103a_{2}= +1.59187815 \pm 2.6 \cdot 10^{-3} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+1.53407605±4.8103a_{4}= +1.53407605 \pm 4.8 \cdot 10^{-3} a5=+1.84128560±3.6103a_{5}= +1.84128560 \pm 3.6 \cdot 10^{-3} a6=+0.91907128±2.6103a_{6}= +0.91907128 \pm 2.6 \cdot 10^{-3}
a7=0.58632653±3.0103a_{7}= -0.58632653 \pm 3.0 \cdot 10^{-3} a8=+0.85018399±3.2103a_{8}= +0.85018399 \pm 3.2 \cdot 10^{-3} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+2.93110232±2.1103a_{10}= +2.93110232 \pm 2.1 \cdot 10^{-3} a11=0.06533740±3.3103a_{11}= -0.06533740 \pm 3.3 \cdot 10^{-3} a12=+0.88569922±4.8103a_{12}= +0.88569922 \pm 4.8 \cdot 10^{-3}
a13=0.62373348±3.2103a_{13}= -0.62373348 \pm 3.2 \cdot 10^{-3} a14=0.93336040±2.0103a_{14}= -0.93336040 \pm 2.0 \cdot 10^{-3} a15=+1.06306674±3.6103a_{15}= +1.06306674 \pm 3.6 \cdot 10^{-3}
a16=0.18068673±3.9103a_{16}= -0.18068673 \pm 3.9 \cdot 10^{-3} a17=+0.59673171±2.4103a_{17}= +0.59673171 \pm 2.4 \cdot 10^{-3} a18=+0.53062605±2.6103a_{18}= +0.53062605 \pm 2.6 \cdot 10^{-3}
a19=+0.12792492±2.0103a_{19}= +0.12792492 \pm 2.0 \cdot 10^{-3} a20=+2.82467213±3.4103a_{20}= +2.82467213 \pm 3.4 \cdot 10^{-3} a21=0.33851578±3.0103a_{21}= -0.33851578 \pm 3.0 \cdot 10^{-3}
a22=0.10400917±1.7103a_{22}= -0.10400917 \pm 1.7 \cdot 10^{-3} a23=0.25387485±7.4103a_{23}= -0.25387485 \pm 7.4 \cdot 10^{-3} a24=+0.49085395±3.2103a_{24}= +0.49085395 \pm 3.2 \cdot 10^{-3}
a25=+2.39033266±3.0103a_{25}= +2.39033266 \pm 3.0 \cdot 10^{-3} a26=0.99290770±1.1103a_{26}= -0.99290770 \pm 1.1 \cdot 10^{-3} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=0.89946949±2.0103a_{28}= -0.89946949 \pm 2.0 \cdot 10^{-3} a29=0.67260630±6.9103a_{29}= -0.67260630 \pm 6.9 \cdot 10^{-3} a30=+1.69227271±6.3103a_{30}= +1.69227271 \pm 6.3 \cdot 10^{-3}
a31=+0.67027640±3.1103a_{31}= +0.67027640 \pm 3.1 \cdot 10^{-3} a32=1.13781525±4.3103a_{32}= -1.13781525 \pm 4.3 \cdot 10^{-3} a33=0.03772256±3.3103a_{33}= -0.03772256 \pm 3.3 \cdot 10^{-3}
a34=+0.94992417±2.9103a_{34}= +0.94992417 \pm 2.9 \cdot 10^{-3} a35=1.07959460±1.3103a_{35}= -1.07959460 \pm 1.3 \cdot 10^{-3} a36=+0.51135868±4.8103a_{36}= +0.51135868 \pm 4.8 \cdot 10^{-3}
a37=0.53701226±3.7103a_{37}= -0.53701226 \pm 3.7 \cdot 10^{-3} a38=+0.20364089±9.1104a_{38}= +0.20364089 \pm 9.1 \cdot 10^{-4} a39=0.36011269±3.2103a_{39}= -0.36011269 \pm 3.2 \cdot 10^{-3}
a40=+1.56543153±2.0103a_{40}= +1.56543153 \pm 2.0 \cdot 10^{-3} a41=0.93660130±7.1103a_{41}= -0.93660130 \pm 7.1 \cdot 10^{-3} a42=0.53887588±5.7103a_{42}= -0.53887588 \pm 5.7 \cdot 10^{-3}
a43=+0.80999460±4.7103a_{43}= +0.80999460 \pm 4.7 \cdot 10^{-3} a44=0.10023253±2.9103a_{44}= -0.10023253 \pm 2.9 \cdot 10^{-3} a45=+0.61376187±3.6103a_{45}= +0.61376187 \pm 3.6 \cdot 10^{-3}
a46=0.40413783±2.1103a_{46}= -0.40413783 \pm 2.1 \cdot 10^{-3} a47=1.72643484±5.8103a_{47}= -1.72643484 \pm 5.8 \cdot 10^{-3} a48=0.10431953±3.9103a_{48}= -0.10431953 \pm 3.9 \cdot 10^{-3}
a49=0.65622120±5.1103a_{49}= -0.65622120 \pm 5.1 \cdot 10^{-3} a50=+3.80511834±1.5103a_{50}= +3.80511834 \pm 1.5 \cdot 10^{-3} a51=+0.34452321±2.4103a_{51}= +0.34452321 \pm 2.4 \cdot 10^{-3}
a52=0.95685459±3.0103a_{52}= -0.95685459 \pm 3.0 \cdot 10^{-3} a53=1.56262872±2.9103a_{53}= -1.56262872 \pm 2.9 \cdot 10^{-3} a54=+0.30635709±2.6103a_{54}= +0.30635709 \pm 2.6 \cdot 10^{-3}
a55=0.12030481±2.3103a_{55}= -0.12030481 \pm 2.3 \cdot 10^{-3} a56=0.49848543±2.9103a_{56}= -0.49848543 \pm 2.9 \cdot 10^{-3} a57=+0.07385749±2.0103a_{57}= +0.07385749 \pm 2.0 \cdot 10^{-3}
a58=1.07070727±2.8103a_{58}= -1.07070727 \pm 2.8 \cdot 10^{-3} a59=+1.46394498±4.7103a_{59}= +1.46394498 \pm 4.7 \cdot 10^{-3} a60=+1.63082522±8.5103a_{60}= +1.63082522 \pm 8.5 \cdot 10^{-3}

Displaying ana_n with nn up to: 60 180 1000