Properties

Label 13.75
Level 1313
Weight 00
Character 13.1
Symmetry odd
RR 9.481478
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: 9.48147888733239185975363636513±310109.48147888733239185975363636513 \pm 3 \cdot 10^{-10}

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=0.38189823±9.8107a_{2}= -0.38189823 \pm 9.8 \cdot 10^{-7} a3=+1.74853633±9.5107a_{3}= +1.74853633 \pm 9.5 \cdot 10^{-7}
a4=0.85415374±8.9107a_{4}= -0.85415374 \pm 8.9 \cdot 10^{-7} a5=0.41535158±8.4107a_{5}= -0.41535158 \pm 8.4 \cdot 10^{-7} a6=0.66776293±1.0106a_{6}= -0.66776293 \pm 1.0 \cdot 10^{-6}
a7=0.31001498±8.7107a_{7}= -0.31001498 \pm 8.7 \cdot 10^{-7} a8=+0.70809803±7.4107a_{8}= +0.70809803 \pm 7.4 \cdot 10^{-7} a9=+2.05737931±9.2107a_{9}= +2.05737931 \pm 9.2 \cdot 10^{-7}
a10=+0.15862203±9.6107a_{10}= +0.15862203 \pm 9.6 \cdot 10^{-7} a11=+0.09183794±8.0107a_{11}= +0.09183794 \pm 8.0 \cdot 10^{-7} a12=1.49351885±9.6107a_{12}= -1.49351885 \pm 9.6 \cdot 10^{-7}
a13=+0.27735010±1.0108a_{13}= +0.27735010 \pm 1.0 \cdot 10^{-8} a14=+0.11839417±9.4107a_{14}= +0.11839417 \pm 9.4 \cdot 10^{-7} a15=0.72625732±1.0106a_{15}= -0.72625732 \pm 1.0 \cdot 10^{-6}
a16=+0.58373236±7.7107a_{16}= +0.58373236 \pm 7.7 \cdot 10^{-7} a17=0.51752466±8.7107a_{17}= -0.51752466 \pm 8.7 \cdot 10^{-7} a18=0.78570952±1.0106a_{18}= -0.78570952 \pm 1.0 \cdot 10^{-6}
a19=+1.51633675±7.1107a_{19}= +1.51633675 \pm 7.1 \cdot 10^{-7} a20=+0.35477410±8.7107a_{20}= +0.35477410 \pm 8.7 \cdot 10^{-7} a21=0.54207245±7.4107a_{21}= -0.54207245 \pm 7.4 \cdot 10^{-7}
a22=0.03507275±8.8107a_{22}= -0.03507275 \pm 8.8 \cdot 10^{-7} a23=+0.91220643±7.2107a_{23}= +0.91220643 \pm 7.2 \cdot 10^{-7} a24=+1.23813514±7.2107a_{24}= +1.23813514 \pm 7.2 \cdot 10^{-7}
a25=0.82748307±6.5107a_{25}= -0.82748307 \pm 6.5 \cdot 10^{-7} a26=0.10591951±9.9107a_{26}= -0.10591951 \pm 9.9 \cdot 10^{-7} a27=+1.84886615±7.7107a_{27}= +1.84886615 \pm 7.7 \cdot 10^{-7}
a28=+0.26480045±8.1107a_{28}= +0.26480045 \pm 8.1 \cdot 10^{-7} a29=+1.54381337±6.4107a_{29}= +1.54381337 \pm 6.4 \cdot 10^{-7} a30=+0.27735639±1.2106a_{30}= +0.27735639 \pm 1.2 \cdot 10^{-6}
a31=0.20517106±9.2107a_{31}= -0.20517106 \pm 9.2 \cdot 10^{-7} a32=0.93102439±1.0106a_{32}= -0.93102439 \pm 1.0 \cdot 10^{-6} a33=+0.16058198±6.9107a_{33}= +0.16058198 \pm 6.9 \cdot 10^{-7}
a34=+0.19764175±9.5107a_{34}= +0.19764175 \pm 9.5 \cdot 10^{-7} a35=+0.12876521±7.0107a_{35}= +0.12876521 \pm 7.0 \cdot 10^{-7} a36=1.75731824±8.7107a_{36}= -1.75731824 \pm 8.7 \cdot 10^{-7}
a37=+1.91501927±1.0106a_{37}= +1.91501927 \pm 1.0 \cdot 10^{-6} a38=0.57908632±6.8107a_{38}= -0.57908632 \pm 6.8 \cdot 10^{-7} a39=+0.48495672±9.6107a_{39}= +0.48495672 \pm 9.6 \cdot 10^{-7}
a40=0.29410963±7.4107a_{40}= -0.29410963 \pm 7.4 \cdot 10^{-7} a41=+1.83331789±7.8107a_{41}= +1.83331789 \pm 7.8 \cdot 10^{-7} a42=+0.20701651±6.2107a_{42}= +0.20701651 \pm 6.2 \cdot 10^{-7}
a43=+0.41048428±8.7107a_{43}= +0.41048428 \pm 8.7 \cdot 10^{-7} a44=0.07844372±8.3107a_{44}= -0.07844372 \pm 8.3 \cdot 10^{-7} a45=0.85453574±9.3107a_{45}= -0.85453574 \pm 9.3 \cdot 10^{-7}
a46=0.34837002±9.3107a_{46}= -0.34837002 \pm 9.3 \cdot 10^{-7} a47=0.09763336±9.0107a_{47}= -0.09763336 \pm 9.0 \cdot 10^{-7} a48=+1.02067724±8.8107a_{48}= +1.02067724 \pm 8.8 \cdot 10^{-7}
a49=0.90389071±7.9107a_{49}= -0.90389071 \pm 7.9 \cdot 10^{-7} a50=+0.31601432±7.8107a_{50}= +0.31601432 \pm 7.8 \cdot 10^{-7} a51=0.90491067±1.0106a_{51}= -0.90491067 \pm 1.0 \cdot 10^{-6}
a52=0.23689962±9.0107a_{52}= -0.23689962 \pm 9.0 \cdot 10^{-7} a53=+0.54767265±6.6107a_{53}= +0.54767265 \pm 6.6 \cdot 10^{-7} a54=0.70607871±8.9107a_{54}= -0.70607871 \pm 8.9 \cdot 10^{-7}
a55=0.03814503±5.7107a_{55}= -0.03814503 \pm 5.7 \cdot 10^{-7} a56=0.21952100±6.5107a_{56}= -0.21952100 \pm 6.5 \cdot 10^{-7} a57=+2.65136990±6.9107a_{57}= +2.65136990 \pm 6.9 \cdot 10^{-7}
a58=0.58957959±6.3107a_{58}= -0.58957959 \pm 6.3 \cdot 10^{-7} a59=0.63026236±8.0107a_{59}= -0.63026236 \pm 8.0 \cdot 10^{-7} a60=+0.62033541±1.0106a_{60}= +0.62033541 \pm 1.0 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000