Properties

Label 13.191
Level 1313
Weight 00
Character 13.1
Symmetry odd
RR 14.52910
Fricke sign +1+1

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Maass form invariants

Level: 13 13
Weight: 0 0
Character: 13.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 14.5291035368307225057606860365±210714.5291035368307225057606860365 \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=1.35980387±9.6103a_{2}= -1.35980387 \pm 9.6 \cdot 10^{-3} a3=+1.89545750±9.3103a_{3}= +1.89545750 \pm 9.3 \cdot 10^{-3}
a4=+0.84906658±8.7103a_{4}= +0.84906658 \pm 8.7 \cdot 10^{-3} a5=+0.24196165±8.2103a_{5}= +0.24196165 \pm 8.2 \cdot 10^{-3} a6=2.57745045±1.0102a_{6}= -2.57745045 \pm 1.0 \cdot 10^{-2}
a7=1.56763269±8.5103a_{7}= -1.56763269 \pm 8.5 \cdot 10^{-3} a8=+0.20523986±7.3103a_{8}= +0.20523986 \pm 7.3 \cdot 10^{-3} a9=+2.59275914±9.0103a_{9}= +2.59275914 \pm 9.0 \cdot 10^{-3}
a10=0.32902039±9.4103a_{10}= -0.32902039 \pm 9.4 \cdot 10^{-3} a11=+0.24728223±7.8103a_{11}= +0.24728223 \pm 7.8 \cdot 10^{-3} a12=+1.60936961±9.4103a_{12}= +1.60936961 \pm 9.4 \cdot 10^{-3}
a13=0.27735010±1.0108a_{13}= -0.27735010 \pm 1.0 \cdot 10^{-8} a14=+2.13167300±9.2103a_{14}= +2.13167300 \pm 9.2 \cdot 10^{-3} a15=+0.45862802±1.0102a_{15}= +0.45862802 \pm 1.0 \cdot 10^{-2}
a16=1.12815253±7.5103a_{16}= -1.12815253 \pm 7.5 \cdot 10^{-3} a17=0.92142361±8.5103a_{17}= -0.92142361 \pm 8.5 \cdot 10^{-3} a18=3.52564393±1.0102a_{18}= -3.52564393 \pm 1.0 \cdot 10^{-2}
a19=+1.37675535±6.9103a_{19}= +1.37675535 \pm 6.9 \cdot 10^{-3} a20=+0.20544155±8.5103a_{20}= +0.20544155 \pm 8.5 \cdot 10^{-3} a21=2.97138114±7.2103a_{21}= -2.97138114 \pm 7.2 \cdot 10^{-3}
a22=0.33625534±8.6103a_{22}= -0.33625534 \pm 8.6 \cdot 10^{-3} a23=0.97728476±7.1103a_{23}= -0.97728476 \pm 7.1 \cdot 10^{-3} a24=+0.38902342±7.1103a_{24}= +0.38902342 \pm 7.1 \cdot 10^{-3}
a25=0.94145456±6.4103a_{25}= -0.94145456 \pm 6.4 \cdot 10^{-3} a26=+0.37714174±9.6103a_{26}= +0.37714174 \pm 9.6 \cdot 10^{-3} a27=+3.01900727±7.5103a_{27}= +3.01900727 \pm 7.5 \cdot 10^{-3}
a28=1.33102452±7.9103a_{28}= -1.33102452 \pm 7.9 \cdot 10^{-3} a29=0.73056686±6.3103a_{29}= -0.73056686 \pm 6.3 \cdot 10^{-3} a30=0.62364416±1.2102a_{30}= -0.62364416 \pm 1.2 \cdot 10^{-2}
a31=0.28247439±9.0103a_{31}= -0.28247439 \pm 9.0 \cdot 10^{-3} a32=+1.32882632±9.8103a_{32}= +1.32882632 \pm 9.8 \cdot 10^{-3} a33=+0.46871296±6.8103a_{33}= +0.46871296 \pm 6.8 \cdot 10^{-3}
a34=+1.25295539±9.2103a_{34}= +1.25295539 \pm 9.2 \cdot 10^{-3} a35=0.37930699±6.8103a_{35}= -0.37930699 \pm 6.8 \cdot 10^{-3} a36=+2.20142513±8.5103a_{36}= +2.20142513 \pm 8.5 \cdot 10^{-3}
a37=+0.89230613±1.0102a_{37}= +0.89230613 \pm 1.0 \cdot 10^{-2} a38=1.87211726±6.6103a_{38}= -1.87211726 \pm 6.6 \cdot 10^{-3} a39=0.52570532±9.3103a_{39}= -0.52570532 \pm 9.3 \cdot 10^{-3}
a40=+0.04966017±7.2103a_{40}= +0.04966017 \pm 7.2 \cdot 10^{-3} a41=+0.15103577±7.6103a_{41}= +0.15103577 \pm 7.6 \cdot 10^{-3} a42=+4.04049559±6.0103a_{42}= +4.04049559 \pm 6.0 \cdot 10^{-3}
a43=1.20762525±8.5103a_{43}= -1.20762525 \pm 8.5 \cdot 10^{-3} a44=+0.20995908±8.1103a_{44}= +0.20995908 \pm 8.1 \cdot 10^{-3} a45=+0.62734828±9.1103a_{45}= +0.62734828 \pm 9.1 \cdot 10^{-3}
a46=+1.32891560±9.1103a_{46}= +1.32891560 \pm 9.1 \cdot 10^{-3} a47=0.90814642±8.8103a_{47}= -0.90814642 \pm 8.8 \cdot 10^{-3} a48=2.13836517±8.6103a_{48}= -2.13836517 \pm 8.6 \cdot 10^{-3}
a49=+1.45747225±7.7103a_{49}= +1.45747225 \pm 7.7 \cdot 10^{-3} a50=+1.28019356±7.6103a_{50}= +1.28019356 \pm 7.6 \cdot 10^{-3} a51=1.74651929±9.9103a_{51}= -1.74651929 \pm 9.9 \cdot 10^{-3}
a52=0.23548870±8.7103a_{52}= -0.23548870 \pm 8.7 \cdot 10^{-3} a53=0.76158617±6.4103a_{53}= -0.76158617 \pm 6.4 \cdot 10^{-3} a54=4.10525778±8.7103a_{54}= -4.10525778 \pm 8.7 \cdot 10^{-3}
a55=+0.05983282±5.6103a_{55}= +0.05983282 \pm 5.6 \cdot 10^{-3} a56=0.32174071±6.4103a_{56}= -0.32174071 \pm 6.4 \cdot 10^{-3} a57=+2.60958126±6.7103a_{57}= +2.60958126 \pm 6.7 \cdot 10^{-3}
a58=+0.99342765±6.1103a_{58}= +0.99342765 \pm 6.1 \cdot 10^{-3} a59=+0.43979777±7.8103a_{59}= +0.43979777 \pm 7.8 \cdot 10^{-3} a60=+0.38940573±1.0102a_{60}= +0.38940573 \pm 1.0 \cdot 10^{-2}

Displaying ana_n with nn up to: 60 180 1000