Properties

Label 7.25
Level 77
Weight 00
Character 7.1
Symmetry odd
RR 8.251785
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: 8.25178553271231783265150328952±510128.25178553271231783265150328952 \pm 5 \cdot 10^{-12}

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=1.78572492±1108a_{2}= -1.78572492 \pm 1 \cdot 10^{-8} a3=1.62802777±1108a_{3}= -1.62802777 \pm 1 \cdot 10^{-8}
a4=+2.18881348±1108a_{4}= +2.18881348 \pm 1 \cdot 10^{-8} a5=+0.42588484±1108a_{5}= +0.42588484 \pm 1 \cdot 10^{-8} a6=+2.90720976±1108a_{6}= +2.90720976 \pm 1 \cdot 10^{-8}
a7=0.37796447±1.0108a_{7}= -0.37796447 \pm 1.0 \cdot 10^{-8} a8=2.12289386±1108a_{8}= -2.12289386 \pm 1 \cdot 10^{-8} a9=+1.65047442±1108a_{9}= +1.65047442 \pm 1 \cdot 10^{-8}
a10=0.76051317±1108a_{10}= -0.76051317 \pm 1 \cdot 10^{-8} a11=+0.71786711±1108a_{11}= +0.71786711 \pm 1 \cdot 10^{-8} a12=3.56344913±1108a_{12}= -3.56344913 \pm 1 \cdot 10^{-8}
a13=+0.28085186±1108a_{13}= +0.28085186 \pm 1 \cdot 10^{-8} a14=+0.67494058±1.3108a_{14}= +0.67494058 \pm 1.3 \cdot 10^{-8} a15=0.69335234±1108a_{15}= -0.69335234 \pm 1 \cdot 10^{-8}
a16=+1.60209098±1108a_{16}= +1.60209098 \pm 1 \cdot 10^{-8} a17=+0.86758316±1108a_{17}= +0.86758316 \pm 1 \cdot 10^{-8} a18=2.94729330±1108a_{18}= -2.94729330 \pm 1 \cdot 10^{-8}
a19=0.54880955±1108a_{19}= -0.54880955 \pm 1 \cdot 10^{-8} a20=+0.93218247±1108a_{20}= +0.93218247 \pm 1 \cdot 10^{-8} a21=+0.61533666±1.2108a_{21}= +0.61533666 \pm 1.2 \cdot 10^{-8}
a22=1.28191319±1108a_{22}= -1.28191319 \pm 1 \cdot 10^{-8} a23=0.61130430±1108a_{23}= -0.61130430 \pm 1 \cdot 10^{-8} a24=+3.45613015±1108a_{24}= +3.45613015 \pm 1 \cdot 10^{-8}
a25=0.81862210±1108a_{25}= -0.81862210 \pm 1 \cdot 10^{-8} a26=0.50152417±1108a_{26}= -0.50152417 \pm 1 \cdot 10^{-8} a27=1.05899042±1108a_{27}= -1.05899042 \pm 1 \cdot 10^{-8}
a28=0.82729373±1.2108a_{28}= -0.82729373 \pm 1.2 \cdot 10^{-8} a29=+0.67956044±1108a_{29}= +0.67956044 \pm 1 \cdot 10^{-8} a30=+1.23813656±1108a_{30}= +1.23813656 \pm 1 \cdot 10^{-8}
a31=+0.74256661±1108a_{31}= +0.74256661 \pm 1 \cdot 10^{-8} a32=0.73799992±1108a_{32}= -0.73799992 \pm 1 \cdot 10^{-8} a33=1.16870760±1108a_{33}= -1.16870760 \pm 1 \cdot 10^{-8}
a34=1.54926487±1108a_{34}= -1.54926487 \pm 1 \cdot 10^{-8} a35=0.16096934±1.2108a_{35}= -0.16096934 \pm 1.2 \cdot 10^{-8} a36=+3.61258066±1108a_{36}= +3.61258066 \pm 1 \cdot 10^{-8}
a37=1.39497447±1108a_{37}= -1.39497447 \pm 1 \cdot 10^{-8} a38=+0.98002290±1108a_{38}= +0.98002290 \pm 1 \cdot 10^{-8} a39=0.45723463±1108a_{39}= -0.45723463 \pm 1 \cdot 10^{-8}
a40=0.90410831±1108a_{40}= -0.90410831 \pm 1 \cdot 10^{-8} a41=+1.47338145±1108a_{41}= +1.47338145 \pm 1 \cdot 10^{-8} a42=1.09882200±1.5108a_{42}= -1.09882200 \pm 1.5 \cdot 10^{-8}
a43=1.11468579±1108a_{43}= -1.11468579 \pm 1 \cdot 10^{-8} a44=+1.57127722±1108a_{44}= +1.57127722 \pm 1 \cdot 10^{-8} a45=+0.70291203±1108a_{45}= +0.70291203 \pm 1 \cdot 10^{-8}
a46=+1.09162132±1108a_{46}= +1.09162132 \pm 1 \cdot 10^{-8} a47=1.97938321±1108a_{47}= -1.97938321 \pm 1 \cdot 10^{-8} a48=2.60824860±1108a_{48}= -2.60824860 \pm 1 \cdot 10^{-8}
a49=+0.14285714±1.5107a_{49}= +0.14285714 \pm 1.5 \cdot 10^{-7} a50=+1.46183389±1108a_{50}= +1.46183389 \pm 1 \cdot 10^{-8} a51=1.41244948±1108a_{51}= -1.41244948 \pm 1 \cdot 10^{-8}
a52=+0.61473234±1108a_{52}= +0.61473234 \pm 1 \cdot 10^{-8} a53=+0.82267831±1108a_{53}= +0.82267831 \pm 1 \cdot 10^{-8} a54=+1.89106558±1108a_{54}= +1.89106558 \pm 1 \cdot 10^{-8}
a55=+0.30572872±1108a_{55}= +0.30572872 \pm 1 \cdot 10^{-8} a56=+0.80237846±1.2108a_{56}= +0.80237846 \pm 1.2 \cdot 10^{-8} a57=+0.89347720±1108a_{57}= +0.89347720 \pm 1 \cdot 10^{-8}
a58=1.21350800±1108a_{58}= -1.21350800 \pm 1 \cdot 10^{-8} a59=0.15214955±1108a_{59}= -0.15214955 \pm 1 \cdot 10^{-8} a60=1.51761896±1108a_{60}= -1.51761896 \pm 1 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000