Properties

Label 13.122
Level 1313
Weight 00
Character 13.1
Symmetry odd
RR 11.83371
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: 11.8337126875639271993663271549±310911.8337126875639271993663271549 \pm 3 \cdot 10^{-9}

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=+1.80672308±6.3106a_{2}= +1.80672308 \pm 6.3 \cdot 10^{-6} a3=1.21763440±6.1106a_{3}= -1.21763440 \pm 6.1 \cdot 10^{-6}
a4=+2.26424828±5.7106a_{4}= +2.26424828 \pm 5.7 \cdot 10^{-6} a5=+1.88999499±5.4106a_{5}= +1.88999499 \pm 5.4 \cdot 10^{-6} a6=2.19992817±6.9106a_{6}= -2.19992817 \pm 6.9 \cdot 10^{-6}
a7=+0.80009276±5.5106a_{7}= +0.80009276 \pm 5.5 \cdot 10^{-6} a8=+2.28414654±4.8106a_{8}= +2.28414654 \pm 4.8 \cdot 10^{-6} a9=+0.48263353±5.9106a_{9}= +0.48263353 \pm 5.9 \cdot 10^{-6}
a10=+3.41469757±6.2106a_{10}= +3.41469757 \pm 6.2 \cdot 10^{-6} a11=0.66448297±5.1106a_{11}= -0.66448297 \pm 5.1 \cdot 10^{-6} a12=2.75702659±6.2106a_{12}= -2.75702659 \pm 6.2 \cdot 10^{-6}
a13=+0.27735010±1.0108a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} a14=+1.44554606±6.0106a_{14}= +1.44554606 \pm 6.0 \cdot 10^{-6} a15=2.30132291±6.6106a_{15}= -2.30132291 \pm 6.6 \cdot 10^{-6}
a16=+1.86257199±4.9106a_{16}= +1.86257199 \pm 4.9 \cdot 10^{-6} a17=+0.52529368±5.6106a_{17}= +0.52529368 \pm 5.6 \cdot 10^{-6} a18=+0.87198513±6.8106a_{18}= +0.87198513 \pm 6.8 \cdot 10^{-6}
a19=0.91961006±4.5106a_{19}= -0.91961006 \pm 4.5 \cdot 10^{-6} a20=+4.27941791±5.6106a_{20}= +4.27941791 \pm 5.6 \cdot 10^{-6} a21=0.97422047±4.7106a_{21}= -0.97422047 \pm 4.7 \cdot 10^{-6}
a22=1.20053672±5.6106a_{22}= -1.20053672 \pm 5.6 \cdot 10^{-6} a23=+1.15154304±4.6106a_{23}= +1.15154304 \pm 4.6 \cdot 10^{-6} a24=2.78125540±4.6106a_{24}= -2.78125540 \pm 4.6 \cdot 10^{-6}
a25=+2.57208106±4.2106a_{25}= +2.57208106 \pm 4.2 \cdot 10^{-6} a26=+0.50109482±6.3106a_{26}= +0.50109482 \pm 6.3 \cdot 10^{-6} a27=+0.62996322±4.9106a_{27}= +0.62996322 \pm 4.9 \cdot 10^{-6}
a28=+1.81160866±5.2106a_{28}= +1.81160866 \pm 5.2 \cdot 10^{-6} a29=+0.04625535±4.1106a_{29}= +0.04625535 \pm 4.1 \cdot 10^{-6} a30=4.15785321±7.9106a_{30}= -4.15785321 \pm 7.9 \cdot 10^{-6}
a31=0.15208597±5.9106a_{31}= -0.15208597 \pm 5.9 \cdot 10^{-6} a32=+1.08100526±6.4106a_{32}= +1.08100526 \pm 6.4 \cdot 10^{-6} a33=+0.80909732±4.4106a_{33}= +0.80909732 \pm 4.4 \cdot 10^{-6}
a34=+0.94906021±6.1106a_{34}= +0.94906021 \pm 6.1 \cdot 10^{-6} a35=+1.51217131±4.5106a_{35}= +1.51217131 \pm 4.5 \cdot 10^{-6} a36=+1.09280213±5.5106a_{36}= +1.09280213 \pm 5.5 \cdot 10^{-6}
a37=+0.18419875±6.8106a_{37}= +0.18419875 \pm 6.8 \cdot 10^{-6} a38=1.66148072±4.3106a_{38}= -1.66148072 \pm 4.3 \cdot 10^{-6} a39=0.33771102±6.1106a_{39}= -0.33771102 \pm 6.1 \cdot 10^{-6}
a40=+4.31702552±4.7106a_{40}= +4.31702552 \pm 4.7 \cdot 10^{-6} a41=+1.41220945±5.0106a_{41}= +1.41220945 \pm 5.0 \cdot 10^{-6} a42=1.76014660±3.9106a_{42}= -1.76014660 \pm 3.9 \cdot 10^{-6}
a43=0.22158353±5.5106a_{43}= -0.22158353 \pm 5.5 \cdot 10^{-6} a44=1.50455442±5.3106a_{44}= -1.50455442 \pm 5.3 \cdot 10^{-6} a45=+0.91217495±6.0106a_{45}= +0.91217495 \pm 6.0 \cdot 10^{-6}
a46=+2.08051939±6.0106a_{46}= +2.08051939 \pm 6.0 \cdot 10^{-6} a47=1.51353262±5.7106a_{47}= -1.51353262 \pm 5.7 \cdot 10^{-6} a48=2.26793173±5.6106a_{48}= -2.26793173 \pm 5.6 \cdot 10^{-6}
a49=0.35985157±5.0106a_{49}= -0.35985157 \pm 5.0 \cdot 10^{-6} a50=+4.64703821±5.0106a_{50}= +4.64703821 \pm 5.0 \cdot 10^{-6} a51=0.63961565±6.5106a_{51}= -0.63961565 \pm 6.5 \cdot 10^{-6}
a52=+0.62798948±5.7106a_{52}= +0.62798948 \pm 5.7 \cdot 10^{-6} a53=+0.58417666±4.2106a_{53}= +0.58417666 \pm 4.2 \cdot 10^{-6} a54=+1.13816908±5.7106a_{54}= +1.13816908 \pm 5.7 \cdot 10^{-6}
a55=1.25586949±3.7106a_{55}= -1.25586949 \pm 3.7 \cdot 10^{-6} a56=+1.82752911±4.2106a_{56}= +1.82752911 \pm 4.2 \cdot 10^{-6} a57=+1.11974884±4.4106a_{57}= +1.11974884 \pm 4.4 \cdot 10^{-6}
a58=+0.08357061±4.0106a_{58}= +0.08357061 \pm 4.0 \cdot 10^{-6} a59=0.38073459±5.1106a_{59}= -0.38073459 \pm 5.1 \cdot 10^{-6} a60=5.21076644±6.6106a_{60}= -5.21076644 \pm 6.6 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000