Properties

Label 7.75
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 13.40120
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: 13.4012029875852052894404796208±710913.4012029875852052894404796208 \pm 7 \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=+0.75715079±4.6106a_{2}= +0.75715079 \pm 4.6 \cdot 10^{-6} a3=+1.40748965±3.1106a_{3}= +1.40748965 \pm 3.1 \cdot 10^{-6}
a4=0.42672267±2.7106a_{4}= -0.42672267 \pm 2.7 \cdot 10^{-6} a5=0.24112059±3.3106a_{5}= -0.24112059 \pm 3.3 \cdot 10^{-6} a6=+1.06568191±3.6106a_{6}= +1.06568191 \pm 3.6 \cdot 10^{-6}
a7=0.37796447±1.0108a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} a8=1.08024421±3.0106a_{8}= -1.08024421 \pm 3.0 \cdot 10^{-6} a9=+0.98102711±2.9106a_{9}= +0.98102711 \pm 2.9 \cdot 10^{-6}
a10=0.18256465±3.3106a_{10}= -0.18256465 \pm 3.3 \cdot 10^{-6} a11=1.64309703±2.8106a_{11}= -1.64309703 \pm 2.8 \cdot 10^{-6} a12=0.60060775±2.4106a_{12}= -0.60060775 \pm 2.4 \cdot 10^{-6}
a13=0.69052028±3.4106a_{13}= -0.69052028 \pm 3.4 \cdot 10^{-6} a14=0.28617610±4.6106a_{14}= -0.28617610 \pm 4.6 \cdot 10^{-6} a15=0.33937474±2.6106a_{15}= -0.33937474 \pm 2.6 \cdot 10^{-6}
a16=0.39118509±3.9106a_{16}= -0.39118509 \pm 3.9 \cdot 10^{-6} a17=0.54110167±2.5106a_{17}= -0.54110167 \pm 2.5 \cdot 10^{-6} a18=+0.74278546±2.8106a_{18}= +0.74278546 \pm 2.8 \cdot 10^{-6}
a19=+1.15400755±3.2106a_{19}= +1.15400755 \pm 3.2 \cdot 10^{-6} a20=+0.10289162±2.1106a_{20}= +0.10289162 \pm 2.1 \cdot 10^{-6} a21=0.53198108±3.1106a_{21}= -0.53198108 \pm 3.1 \cdot 10^{-6}
a22=1.24407222±2.8106a_{22}= -1.24407222 \pm 2.8 \cdot 10^{-6} a23=+1.23431590±4.1106a_{23}= +1.23431590 \pm 4.1 \cdot 10^{-6} a24=1.52043254±2.0106a_{24}= -1.52043254 \pm 2.0 \cdot 10^{-6}
a25=0.94186086±3.1106a_{25}= -0.94186086 \pm 3.1 \cdot 10^{-6} a26=0.52282798±4.1106a_{26}= -0.52282798 \pm 4.1 \cdot 10^{-6} a27=0.02670415±3.4106a_{27}= -0.02670415 \pm 3.4 \cdot 10^{-6}
a28=+0.16128601±2.7106a_{28}= +0.16128601 \pm 2.7 \cdot 10^{-6} a29=0.80175232±3.1106a_{29}= -0.80175232 \pm 3.1 \cdot 10^{-6} a30=0.25695785±2.9106a_{30}= -0.25695785 \pm 2.9 \cdot 10^{-6}
a31=0.78478190±2.5106a_{31}= -0.78478190 \pm 2.5 \cdot 10^{-6} a32=+0.78405811±4.0106a_{32}= +0.78405811 \pm 4.0 \cdot 10^{-6} a33=2.31264206±2.3106a_{33}= -2.31264206 \pm 2.3 \cdot 10^{-6}
a34=0.40969556±3.0106a_{34}= -0.40969556 \pm 3.0 \cdot 10^{-6} a35=+0.09113502±3.3106a_{35}= +0.09113502 \pm 3.3 \cdot 10^{-6} a36=0.41862651±1.6106a_{36}= -0.41862651 \pm 1.6 \cdot 10^{-6}
a37=+0.76331868±3.1106a_{37}= +0.76331868 \pm 3.1 \cdot 10^{-6} a38=+0.87375773±3.2106a_{38}= +0.87375773 \pm 3.2 \cdot 10^{-6} a39=0.97190015±2.5106a_{39}= -0.97190015 \pm 2.5 \cdot 10^{-6}
a40=+0.26046912±3.1106a_{40}= +0.26046912 \pm 3.1 \cdot 10^{-6} a41=+0.06750528±4.0106a_{41}= +0.06750528 \pm 4.0 \cdot 10^{-6} a42=0.40278990±7.7106a_{42}= -0.40278990 \pm 7.7 \cdot 10^{-6}
a43=1.37065808±2.4106a_{43}= -1.37065808 \pm 2.4 \cdot 10^{-6} a44=+0.70114676±2.0106a_{44}= +0.70114676 \pm 2.0 \cdot 10^{-6} a45=0.23654584±2.6106a_{45}= -0.23654584 \pm 2.6 \cdot 10^{-6}
a46=+0.93456326±4.9106a_{46}= +0.93456326 \pm 4.9 \cdot 10^{-6} a47=0.00803099±3.7106a_{47}= -0.00803099 \pm 3.7 \cdot 10^{-6} a48=0.55058896±2.9106a_{48}= -0.55058896 \pm 2.9 \cdot 10^{-6}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=0.71313070±3.8106a_{50}= -0.71313070 \pm 3.8 \cdot 10^{-6} a51=0.76159500±1.8106a_{51}= -0.76159500 \pm 1.8 \cdot 10^{-6}
a52=+0.29466066±2.2106a_{52}= +0.29466066 \pm 2.2 \cdot 10^{-6} a53=+0.93508812±2.5106a_{53}= +0.93508812 \pm 2.5 \cdot 10^{-6} a54=0.02021907±4.2106a_{54}= -0.02021907 \pm 4.2 \cdot 10^{-6}
a55=+0.39618453±2.7106a_{55}= +0.39618453 \pm 2.7 \cdot 10^{-6} a56=+0.40829393±3.0106a_{56}= +0.40829393 \pm 3.0 \cdot 10^{-6} a57=+1.62425368±1.6106a_{57}= +1.62425368 \pm 1.6 \cdot 10^{-6}
a58=0.60704740±3.1106a_{58}= -0.60704740 \pm 3.1 \cdot 10^{-6} a59=1.60116461±5.0106a_{59}= -1.60116461 \pm 5.0 \cdot 10^{-6} a60=+0.14481890±2.1106a_{60}= +0.14481890 \pm 2.1 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000