Properties

Label 7.5
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 4.119009
Fricke sign +1+1

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Maass form invariants

Level: 7 7
Weight: 0 0
Character: 7.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 4.11900929292429020757499481407±310134.11900929292429020757499481407 \pm 3 \cdot 10^{-13}

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=1.02117295±1108a_{2}= -1.02117295 \pm 1 \cdot 10^{-8} a3=0.01772280±1108a_{3}= -0.01772280 \pm 1 \cdot 10^{-8}
a4=+0.04279419±1108a_{4}= +0.04279419 \pm 1 \cdot 10^{-8} a5=0.72350278±1108a_{5}= -0.72350278 \pm 1 \cdot 10^{-8} a6=+0.01809804±1108a_{6}= +0.01809804 \pm 1 \cdot 10^{-8}
a7=0.37796447±1.0108a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} a8=+0.97747268±1108a_{8}= +0.97747268 \pm 1 \cdot 10^{-8} a9=0.99968590±1108a_{9}= -0.99968590 \pm 1 \cdot 10^{-8}
a10=+0.73882147±1108a_{10}= +0.73882147 \pm 1 \cdot 10^{-8} a11=+0.41625717±1108a_{11}= +0.41625717 \pm 1 \cdot 10^{-8} a12=0.00075843±1108a_{12}= -0.00075843 \pm 1 \cdot 10^{-8}
a13=1.41042644±1108a_{13}= -1.41042644 \pm 1 \cdot 10^{-8} a14=+0.38596709±1.0108a_{14}= +0.38596709 \pm 1.0 \cdot 10^{-8} a15=+0.01282249±1108a_{15}= +0.01282249 \pm 1 \cdot 10^{-8}
a16=1.04096284±1108a_{16}= -1.04096284 \pm 1 \cdot 10^{-8} a17=+1.28049790±1108a_{17}= +1.28049790 \pm 1 \cdot 10^{-8} a18=+1.02085220±1108a_{18}= +1.02085220 \pm 1 \cdot 10^{-8}
a19=0.02778868±1108a_{19}= -0.02778868 \pm 1 \cdot 10^{-8} a20=0.03096171±1108a_{20}= -0.03096171 \pm 1 \cdot 10^{-8} a21=+0.00669859±1.0108a_{21}= +0.00669859 \pm 1.0 \cdot 10^{-8}
a22=0.42507056±1108a_{22}= -0.42507056 \pm 1 \cdot 10^{-8} a23=1.52725195±1108a_{23}= -1.52725195 \pm 1 \cdot 10^{-8} a24=0.01732355±1108a_{24}= -0.01732355 \pm 1 \cdot 10^{-8}
a25=0.47654373±1108a_{25}= -0.47654373 \pm 1 \cdot 10^{-8} a26=+1.44028933±1108a_{26}= +1.44028933 \pm 1 \cdot 10^{-8} a27=+0.03544002±1108a_{27}= +0.03544002 \pm 1 \cdot 10^{-8}
a28=0.01617468±1.0108a_{28}= -0.01617468 \pm 1.0 \cdot 10^{-8} a29=+0.67303199±1108a_{29}= +0.67303199 \pm 1 \cdot 10^{-8} a30=0.01309398±1108a_{30}= -0.01309398 \pm 1 \cdot 10^{-8}
a31=+0.21080125±1108a_{31}= +0.21080125 \pm 1 \cdot 10^{-8} a32=+0.08553041±1108a_{32}= +0.08553041 \pm 1 \cdot 10^{-8} a33=0.00737724±1108a_{33}= -0.00737724 \pm 1 \cdot 10^{-8}
a34=1.30760981±1108a_{34}= -1.30760981 \pm 1 \cdot 10^{-8} a35=+0.27345835±1.0108a_{35}= +0.27345835 \pm 1.0 \cdot 10^{-8} a36=0.04278074±1108a_{36}= -0.04278074 \pm 1 \cdot 10^{-8}
a37=+0.03324309±1108a_{37}= +0.03324309 \pm 1 \cdot 10^{-8} a38=+0.02837705±1108a_{38}= +0.02837705 \pm 1 \cdot 10^{-8} a39=+0.02499670±1108a_{39}= +0.02499670 \pm 1 \cdot 10^{-8}
a40=0.70720420±1108a_{40}= -0.70720420 \pm 1 \cdot 10^{-8} a41=+0.94313944±1108a_{41}= +0.94313944 \pm 1 \cdot 10^{-8} a42=0.00684042±1.0108a_{42}= -0.00684042 \pm 1.0 \cdot 10^{-8}
a43=1.23019210±1108a_{43}= -1.23019210 \pm 1 \cdot 10^{-8} a44=+0.01781339±1108a_{44}= +0.01781339 \pm 1 \cdot 10^{-8} a45=+0.72327553±1108a_{45}= +0.72327553 \pm 1 \cdot 10^{-8}
a46=+1.55958837±1108a_{46}= +1.55958837 \pm 1 \cdot 10^{-8} a47=0.59520697±1108a_{47}= -0.59520697 \pm 1 \cdot 10^{-8} a48=+0.01844877±1108a_{48}= +0.01844877 \pm 1 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+0.48663356±1108a_{50}= +0.48663356 \pm 1 \cdot 10^{-8} a51=0.02269400±1108a_{51}= -0.02269400 \pm 1 \cdot 10^{-8}
a52=0.06035805±1108a_{52}= -0.06035805 \pm 1 \cdot 10^{-8} a53=1.17326267±1108a_{53}= -1.17326267 \pm 1 \cdot 10^{-8} a54=0.03619039±1108a_{54}= -0.03619039 \pm 1 \cdot 10^{-8}
a55=0.30116322±1108a_{55}= -0.30116322 \pm 1 \cdot 10^{-8} a56=0.36944995±1.0108a_{56}= -0.36944995 \pm 1.0 \cdot 10^{-8} a57=+0.00049249±1108a_{57}= +0.00049249 \pm 1 \cdot 10^{-8}
a58=0.68728206±1108a_{58}= -0.68728206 \pm 1 \cdot 10^{-8} a59=0.63588462±1108a_{59}= -0.63588462 \pm 1 \cdot 10^{-8} a60=+0.00054873±1108a_{60}= +0.00054873 \pm 1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000