Properties

Label 7.81
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 13.86825
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: 13.8682520056691646974949948808±210813.8682520056691646974949948808 \pm 2 \cdot 10^{-8}

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=1.70028361±1.7104a_{2}= -1.70028361 \pm 1.7 \cdot 10^{-4} a3=0.04188706±1.1104a_{3}= -0.04188706 \pm 1.1 \cdot 10^{-4}
a4=+1.89096436±1.0104a_{4}= +1.89096436 \pm 1.0 \cdot 10^{-4} a5=+0.09250928±1.2104a_{5}= +0.09250928 \pm 1.2 \cdot 10^{-4} a6=+0.07121988±1.3104a_{6}= +0.07121988 \pm 1.3 \cdot 10^{-4}
a7=0.37796447±1.0108a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} a8=1.51489210±1.1104a_{8}= -1.51489210 \pm 1.1 \cdot 10^{-4} a9=0.99824547±1.0104a_{9}= -0.99824547 \pm 1.0 \cdot 10^{-4}
a10=0.15729201±1.2104a_{10}= -0.15729201 \pm 1.2 \cdot 10^{-4} a11=0.39723464±1.0104a_{11}= -0.39723464 \pm 1.0 \cdot 10^{-4} a12=0.07920694±9.0105a_{12}= -0.07920694 \pm 9.0 \cdot 10^{-5}
a13=+1.27321969±1.2104a_{13}= +1.27321969 \pm 1.2 \cdot 10^{-4} a14=+0.64264680±1.7104a_{14}= +0.64264680 \pm 1.7 \cdot 10^{-4} a15=0.00387494±9.6105a_{15}= -0.00387494 \pm 9.6 \cdot 10^{-5}
a16=+0.68478186±1.4104a_{16}= +0.68478186 \pm 1.4 \cdot 10^{-4} a17=+0.94597499±9.4105a_{17}= +0.94597499 \pm 9.4 \cdot 10^{-5} a18=+1.69730042±1.0104a_{18}= +1.69730042 \pm 1.0 \cdot 10^{-4}
a19=+0.25405488±1.2104a_{19}= +0.25405488 \pm 1.2 \cdot 10^{-4} a20=+0.17493175±7.9105a_{20}= +0.17493175 \pm 7.9 \cdot 10^{-5} a21=+0.01583182±1.1104a_{21}= +0.01583182 \pm 1.1 \cdot 10^{-4}
a22=+0.67541154±1.0104a_{22}= +0.67541154 \pm 1.0 \cdot 10^{-4} a23=+0.98913896±1.5104a_{23}= +0.98913896 \pm 1.5 \cdot 10^{-4} a24=+0.06345438±7.4105a_{24}= +0.06345438 \pm 7.4 \cdot 10^{-5}
a25=0.99144203±1.1104a_{25}= -0.99144203 \pm 1.1 \cdot 10^{-4} a26=2.16483457±1.5104a_{26}= -2.16483457 \pm 1.5 \cdot 10^{-4} a27=+0.08370063±1.2104a_{27}= +0.08370063 \pm 1.2 \cdot 10^{-4}
a28=0.71471735±1.0104a_{28}= -0.71471735 \pm 1.0 \cdot 10^{-4} a29=+0.73323577±1.1104a_{29}= +0.73323577 \pm 1.1 \cdot 10^{-4} a30=+0.00658850±1.0104a_{30}= +0.00658850 \pm 1.0 \cdot 10^{-4}
a31=1.46170369±9.3105a_{31}= -1.46170369 \pm 9.3 \cdot 10^{-5} a32=+0.35056873±1.4104a_{32}= +0.35056873 \pm 1.4 \cdot 10^{-4} a33=+0.01663899±8.5105a_{33}= +0.01663899 \pm 8.5 \cdot 10^{-5}
a34=1.60842577±1.1104a_{34}= -1.60842577 \pm 1.1 \cdot 10^{-4} a35=0.03496522±1.2104a_{35}= -0.03496522 \pm 1.2 \cdot 10^{-4} a36=1.88764662±6.0105a_{36}= -1.88764662 \pm 6.0 \cdot 10^{-5}
a37=+0.79073251±1.1104a_{37}= +0.79073251 \pm 1.1 \cdot 10^{-4} a38=0.43196535±1.1104a_{38}= -0.43196535 \pm 1.1 \cdot 10^{-4} a39=0.05333143±9.3105a_{39}= -0.05333143 \pm 9.3 \cdot 10^{-5}
a40=0.14014158±1.1104a_{40}= -0.14014158 \pm 1.1 \cdot 10^{-4} a41=+1.19949656±1.5104a_{41}= +1.19949656 \pm 1.5 \cdot 10^{-4} a42=0.02691859±2.8104a_{42}= -0.02691859 \pm 2.8 \cdot 10^{-4}
a43=+1.07555288±9.0105a_{43}= +1.07555288 \pm 9.0 \cdot 10^{-5} a44=0.75115654±7.7105a_{44}= -0.75115654 \pm 7.7 \cdot 10^{-5} a45=0.09234697±9.6105a_{45}= -0.09234697 \pm 9.6 \cdot 10^{-5}
a46=1.68181676±1.8104a_{46}= -1.68181676 \pm 1.8 \cdot 10^{-4} a47=1.70807915±1.3104a_{47}= -1.70807915 \pm 1.3 \cdot 10^{-4} a48=0.02868350±1.0104a_{48}= -0.02868350 \pm 1.0 \cdot 10^{-4}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+1.68573264±1.4104a_{50}= +1.68573264 \pm 1.4 \cdot 10^{-4} a51=0.03962411±6.9105a_{51}= -0.03962411 \pm 6.9 \cdot 10^{-5}
a52=+2.40761306±8.2105a_{52}= +2.40761306 \pm 8.2 \cdot 10^{-5} a53=1.78350123±9.5105a_{53}= -1.78350123 \pm 9.5 \cdot 10^{-5} a54=0.14231481±1.5104a_{54}= -0.14231481 \pm 1.5 \cdot 10^{-4}
a55=0.03674789±1.0104a_{55}= -0.03674789 \pm 1.0 \cdot 10^{-4} a56=+0.57257540±1.1104a_{56}= +0.57257540 \pm 1.1 \cdot 10^{-4} a57=0.01064161±6.0105a_{57}= -0.01064161 \pm 6.0 \cdot 10^{-5}
a58=1.24670877±1.1104a_{58}= -1.24670877 \pm 1.1 \cdot 10^{-4} a59=0.10895733±1.8104a_{59}= -0.10895733 \pm 1.8 \cdot 10^{-4} a60=0.00732738±7.7105a_{60}= -0.00732738 \pm 7.7 \cdot 10^{-5}

Displaying ana_n with nn up to: 60 180 1000