Properties

Label 5.5
Level 55
Weight 00
Character 5.1
Symmetry even
RR 5.436180
Fricke sign 1-1

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Maass form invariants

Level: 5 5
Weight: 0 0
Character: 5.1
Symmetry: even
Fricke sign: 1-1
Spectral parameter: 5.43618046141585614838569313633±410135.43618046141585614838569313633 \pm 4 \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=0.03471171±1108a_{2}= -0.03471171 \pm 1 \cdot 10^{-8} a3=0.87643005±1108a_{3}= -0.87643005 \pm 1 \cdot 10^{-8}
a4=0.99879510±1108a_{4}= -0.99879510 \pm 1 \cdot 10^{-8} a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=+0.03042239±1108a_{6}= +0.03042239 \pm 1 \cdot 10^{-8}
a7=0.62053822±1108a_{7}= -0.62053822 \pm 1 \cdot 10^{-8} a8=+0.06938160±1108a_{8}= +0.06938160 \pm 1 \cdot 10^{-8} a9=0.23187037±1108a_{9}= -0.23187037 \pm 1 \cdot 10^{-8}
a10=0.01552355±1.0108a_{10}= -0.01552355 \pm 1.0 \cdot 10^{-8} a11=+0.76704312±1108a_{11}= +0.76704312 \pm 1 \cdot 10^{-8} a12=+0.87537403±1108a_{12}= +0.87537403 \pm 1 \cdot 10^{-8}
a13=1.78457627±1108a_{13}= -1.78457627 \pm 1 \cdot 10^{-8} a14=+0.02153994±1108a_{14}= +0.02153994 \pm 1 \cdot 10^{-8} a15=0.39195143±1.0108a_{15}= -0.39195143 \pm 1.0 \cdot 10^{-8}
a16=+0.99638674±1108a_{16}= +0.99638674 \pm 1 \cdot 10^{-8} a17=0.12779471±1108a_{17}= -0.12779471 \pm 1 \cdot 10^{-8} a18=+0.00804862±1108a_{18}= +0.00804862 \pm 1 \cdot 10^{-8}
a19=+0.53834185±1108a_{19}= +0.53834185 \pm 1 \cdot 10^{-8} a20=0.44667475±1.0108a_{20}= -0.44667475 \pm 1.0 \cdot 10^{-8} a21=+0.54385834±1108a_{21}= +0.54385834 \pm 1 \cdot 10^{-8}
a22=0.02662538±1108a_{22}= -0.02662538 \pm 1 \cdot 10^{-8} a23=1.51251008±1108a_{23}= -1.51251008 \pm 1 \cdot 10^{-8} a24=0.06080812±1108a_{24}= -0.06080812 \pm 1 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=+0.06194570±1108a_{26}= +0.06194570 \pm 1 \cdot 10^{-8} a27=+1.07964821±1108a_{27}= +1.07964821 \pm 1 \cdot 10^{-8}
a28=+0.61979053±1108a_{28}= +0.61979053 \pm 1 \cdot 10^{-8} a29=0.66710160±1108a_{29}= -0.66710160 \pm 1 \cdot 10^{-8} a30=+0.01360530±1.0108a_{30}= +0.01360530 \pm 1.0 \cdot 10^{-8}
a31=+0.13466564±1108a_{31}= +0.13466564 \pm 1 \cdot 10^{-8} a32=0.10396789±1108a_{32}= -0.10396789 \pm 1 \cdot 10^{-8} a33=0.67225963±1108a_{33}= -0.67225963 \pm 1 \cdot 10^{-8}
a34=+0.00443597±1108a_{34}= +0.00443597 \pm 1 \cdot 10^{-8} a35=0.27751313±1.0108a_{35}= -0.27751313 \pm 1.0 \cdot 10^{-8} a36=+0.23159099±1108a_{36}= +0.23159099 \pm 1 \cdot 10^{-8}
a37=0.76811762±1108a_{37}= -0.76811762 \pm 1 \cdot 10^{-8} a38=0.01868677±1108a_{38}= -0.01868677 \pm 1 \cdot 10^{-8} a39=+1.56405626±1108a_{39}= +1.56405626 \pm 1 \cdot 10^{-8}
a40=+0.03102839±1.0108a_{40}= +0.03102839 \pm 1.0 \cdot 10^{-8} a41=0.14835565±1108a_{41}= -0.14835565 \pm 1 \cdot 10^{-8} a42=0.01887825±1108a_{42}= -0.01887825 \pm 1 \cdot 10^{-8}
a43=+0.97810158±1108a_{43}= +0.97810158 \pm 1 \cdot 10^{-8} a44=0.76611890±1108a_{44}= -0.76611890 \pm 1 \cdot 10^{-8} a45=0.10369558±1.0108a_{45}= -0.10369558 \pm 1.0 \cdot 10^{-8}
a46=+0.05250181±1108a_{46}= +0.05250181 \pm 1 \cdot 10^{-8} a47=0.41110464±1108a_{47}= -0.41110464 \pm 1 \cdot 10^{-8} a48=0.87326328±1108a_{48}= -0.87326328 \pm 1 \cdot 10^{-8}
a49=0.61493231±1108a_{49}= -0.61493231 \pm 1 \cdot 10^{-8} a50=0.00694234±1.0108a_{50}= -0.00694234 \pm 1.0 \cdot 10^{-8} a51=+0.11200313±1108a_{51}= +0.11200313 \pm 1 \cdot 10^{-8}
a52=+1.78242603±1108a_{52}= +1.78242603 \pm 1 \cdot 10^{-8} a53=0.19457851±1108a_{53}= -0.19457851 \pm 1 \cdot 10^{-8} a54=0.03747644±1108a_{54}= -0.03747644 \pm 1 \cdot 10^{-8}
a55=+0.34303211±1.0108a_{55}= +0.34303211 \pm 1.0 \cdot 10^{-8} a56=0.04305393±1108a_{56}= -0.04305393 \pm 1 \cdot 10^{-8} a57=0.47181897±1108a_{57}= -0.47181897 \pm 1 \cdot 10^{-8}
a58=+0.02315624±1108a_{58}= +0.02315624 \pm 1 \cdot 10^{-8} a59=+0.46708941±1108a_{59}= +0.46708941 \pm 1 \cdot 10^{-8} a60=+0.39147917±1.0108a_{60}= +0.39147917 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000