Properties

Label 7.71
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 13.12851
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: 13.1285144686987331488390845984±310913.1285144686987331488390845984 \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=+1.60516468±2.0105a_{2}= +1.60516468 \pm 2.0 \cdot 10^{-5} a3=1.51743928±1.3105a_{3}= -1.51743928 \pm 1.3 \cdot 10^{-5}
a4=+1.57655365±1.2105a_{4}= +1.57655365 \pm 1.2 \cdot 10^{-5} a5=+0.84795194±1.4105a_{5}= +0.84795194 \pm 1.4 \cdot 10^{-5} a6=2.43573993±1.6105a_{6}= -2.43573993 \pm 1.6 \cdot 10^{-5}
a7=0.37796447±1.0108a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} a8=+0.92546356±1.3105a_{8}= +0.92546356 \pm 1.3 \cdot 10^{-5} a9=+1.30262196±1.2105a_{9}= +1.30262196 \pm 1.2 \cdot 10^{-5}
a10=+1.36110251±1.4105a_{10}= +1.36110251 \pm 1.4 \cdot 10^{-5} a11=1.21464606±1.2105a_{11}= -1.21464606 \pm 1.2 \cdot 10^{-5} a12=2.39232444±1.0105a_{12}= -2.39232444 \pm 1.0 \cdot 10^{-5}
a13=+1.11569973±1.4105a_{13}= +1.11569973 \pm 1.4 \cdot 10^{-5} a14=0.60669522±2.0105a_{14}= -0.60669522 \pm 2.0 \cdot 10^{-5} a15=1.28671558±1.1105a_{15}= -1.28671558 \pm 1.1 \cdot 10^{-5}
a16=0.09103223±1.7105a_{16}= -0.09103223 \pm 1.7 \cdot 10^{-5} a17=0.80641098±1.1105a_{17}= -0.80641098 \pm 1.1 \cdot 10^{-5} a18=+2.09092276±1.2105a_{18}= +2.09092276 \pm 1.2 \cdot 10^{-5}
a19=1.68071303±1.4105a_{19}= -1.68071303 \pm 1.4 \cdot 10^{-5} a20=+1.33684173±9.4106a_{20}= +1.33684173 \pm 9.4 \cdot 10^{-6} a21=+0.57353814±1.3105a_{21}= +0.57353814 \pm 1.3 \cdot 10^{-5}
a22=1.94970695±1.2105a_{22}= -1.94970695 \pm 1.2 \cdot 10^{-5} a23=1.25103328±1.8105a_{23}= -1.25103328 \pm 1.8 \cdot 10^{-5} a24=1.40433476±8.9106a_{24}= -1.40433476 \pm 8.9 \cdot 10^{-6}
a25=0.28097751±1.3105a_{25}= -0.28097751 \pm 1.3 \cdot 10^{-5} a26=+1.79088180±1.8105a_{26}= +1.79088180 \pm 1.8 \cdot 10^{-5} a27=0.45921045±1.4105a_{27}= -0.45921045 \pm 1.4 \cdot 10^{-5}
a28=0.59588127±1.2105a_{28}= -0.59588127 \pm 1.2 \cdot 10^{-5} a29=0.42183022±1.3105a_{29}= -0.42183022 \pm 1.3 \cdot 10^{-5} a30=2.06539040±1.3105a_{30}= -2.06539040 \pm 1.3 \cdot 10^{-5}
a31=0.38287997±1.1105a_{31}= -0.38287997 \pm 1.1 \cdot 10^{-5} a32=1.07158528±1.7105a_{32}= -1.07158528 \pm 1.7 \cdot 10^{-5} a33=+1.84315163±1.0105a_{33}= +1.84315163 \pm 1.0 \cdot 10^{-5}
a34=1.29442243±1.3105a_{34}= -1.29442243 \pm 1.3 \cdot 10^{-5} a35=0.32049571±1.4105a_{35}= -0.32049571 \pm 1.4 \cdot 10^{-5} a36=+2.05365341±7.2106a_{36}= +2.05365341 \pm 7.2 \cdot 10^{-6}
a37=+0.35961267±1.3105a_{37}= +0.35961267 \pm 1.3 \cdot 10^{-5} a38=2.69782119±1.4105a_{38}= -2.69782119 \pm 1.4 \cdot 10^{-5} a39=1.69300659±1.1105a_{39}= -1.69300659 \pm 1.1 \cdot 10^{-5}
a40=+0.78474862±1.3105a_{40}= +0.78474862 \pm 1.3 \cdot 10^{-5} a41=+1.79931903±1.7105a_{41}= +1.79931903 \pm 1.7 \cdot 10^{-5} a42=+0.92062316±3.4105a_{42}= +0.92062316 \pm 3.4 \cdot 10^{-5}
a43=+0.15444896±1.0105a_{43}= +0.15444896 \pm 1.0 \cdot 10^{-5} a44=1.91495468±9.2106a_{44}= -1.91495468 \pm 9.2 \cdot 10^{-6} a45=+1.10456082±1.1105a_{45}= +1.10456082 \pm 1.1 \cdot 10^{-5}
a46=2.00811444±2.1105a_{46}= -2.00811444 \pm 2.1 \cdot 10^{-5} a47=+0.00641566±1.6105a_{47}= +0.00641566 \pm 1.6 \cdot 10^{-5} a48=+0.13813588±1.3105a_{48}= +0.13813588 \pm 1.3 \cdot 10^{-5}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=0.45101517±1.6105a_{50}= -0.45101517 \pm 1.6 \cdot 10^{-5} a51=+1.22367970±8.2106a_{51}= +1.22367970 \pm 8.2 \cdot 10^{-6}
a52=+1.75896048±9.7106a_{52}= +1.75896048 \pm 9.7 \cdot 10^{-6} a53=0.75439878±1.1105a_{53}= -0.75439878 \pm 1.1 \cdot 10^{-5} a54=0.73710839±1.8105a_{54}= -0.73710839 \pm 1.8 \cdot 10^{-5}
a55=1.02996148±1.2105a_{55}= -1.02996148 \pm 1.2 \cdot 10^{-5} a56=0.34979235±1.3105a_{56}= -0.34979235 \pm 1.3 \cdot 10^{-5} a57=+2.55037996±7.1106a_{57}= +2.55037996 \pm 7.1 \cdot 10^{-6}
a58=0.67710697±1.3105a_{58}= -0.67710697 \pm 1.3 \cdot 10^{-5} a59=+0.92315829±2.2105a_{59}= +0.92315829 \pm 2.2 \cdot 10^{-5} a60=2.02857615±9.2106a_{60}= -2.02857615 \pm 9.2 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000