Properties

Label 5.24
Level 55
Weight 00
Character 5.1
Symmetry odd
RR 10.04582
Fricke sign 1-1

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Maass form invariants

Level: 5 5
Weight: 0 0
Character: 5.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 10.0458208250339117398394776953±5101110.0458208250339117398394776953 \pm 5 \cdot 10^{-11}

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=+0.76604997±1.8108a_{2}= +0.76604997 \pm 1.8 \cdot 10^{-8} a3=1.51567547±1.9108a_{3}= -1.51567547 \pm 1.9 \cdot 10^{-8}
a4=0.41316744±1.5108a_{4}= -0.41316744 \pm 1.5 \cdot 10^{-8} a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=1.16108315±1.8108a_{6}= -1.16108315 \pm 1.8 \cdot 10^{-8}
a7=+1.45299570±1108a_{7}= +1.45299570 \pm 1 \cdot 10^{-8} a8=1.08255688±1.6108a_{8}= -1.08255688 \pm 1.6 \cdot 10^{-8} a9=+1.29727213±1108a_{9}= +1.29727213 \pm 1 \cdot 10^{-8}
a10=+0.34258796±2.8108a_{10}= +0.34258796 \pm 2.8 \cdot 10^{-8} a11=+1.18198387±1.0108a_{11}= +1.18198387 \pm 1.0 \cdot 10^{-8} a12=+0.62622775±1.6108a_{12}= +0.62622775 \pm 1.6 \cdot 10^{-8}
a13=0.09958617±1.2108a_{13}= -0.09958617 \pm 1.2 \cdot 10^{-8} a14=+1.11306732±1108a_{14}= +1.11306732 \pm 1 \cdot 10^{-8} a15=0.67783068±3.0108a_{15}= -0.67783068 \pm 3.0 \cdot 10^{-8}
a16=0.41612523±1108a_{16}= -0.41612523 \pm 1 \cdot 10^{-8} a17=+0.99116397±2.0108a_{17}= +0.99116397 \pm 2.0 \cdot 10^{-8} a18=+0.99377528±1108a_{18}= +0.99377528 \pm 1 \cdot 10^{-8}
a19=+0.12942130±1.8108a_{19}= +0.12942130 \pm 1.8 \cdot 10^{-8} a20=0.18477410±2.6108a_{20}= -0.18477410 \pm 2.6 \cdot 10^{-8} a21=2.20226994±1108a_{21}= -2.20226994 \pm 1 \cdot 10^{-8}
a22=+0.90545871±1.0108a_{22}= +0.90545871 \pm 1.0 \cdot 10^{-8} a23=0.40589562±1108a_{23}= -0.40589562 \pm 1 \cdot 10^{-8} a24=+1.64080490±1.7108a_{24}= +1.64080490 \pm 1.7 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=0.07628799±1.5108a_{26}= -0.07628799 \pm 1.5 \cdot 10^{-8} a27=0.45056807±1.5108a_{27}= -0.45056807 \pm 1.5 \cdot 10^{-8}
a28=0.60033052±1108a_{28}= -0.60033052 \pm 1 \cdot 10^{-8} a29=+0.32747491±1108a_{29}= +0.32747491 \pm 1 \cdot 10^{-8} a30=0.51925217±4.8108a_{30}= -0.51925217 \pm 4.8 \cdot 10^{-8}
a31=+0.40756462±1.9108a_{31}= +0.40756462 \pm 1.9 \cdot 10^{-8} a32=+0.76378416±1.9108a_{32}= +0.76378416 \pm 1.9 \cdot 10^{-8} a33=1.79150395±1108a_{33}= -1.79150395 \pm 1 \cdot 10^{-8}
a34=+0.75928113±1.9108a_{34}= +0.75928113 \pm 1.9 \cdot 10^{-8} a35=+0.64979943±1.8108a_{35}= +0.64979943 \pm 1.8 \cdot 10^{-8} a36=0.53599060±1108a_{36}= -0.53599060 \pm 1 \cdot 10^{-8}
a37=+0.87533676±2.4108a_{37}= +0.87533676 \pm 2.4 \cdot 10^{-8} a38=+0.09914318±1.3108a_{38}= +0.09914318 \pm 1.3 \cdot 10^{-8} a39=+0.15094032±1.0108a_{39}= +0.15094032 \pm 1.0 \cdot 10^{-8}
a40=0.48413415±2.7108a_{40}= -0.48413415 \pm 2.7 \cdot 10^{-8} a41=+0.01388687±2.0108a_{41}= +0.01388687 \pm 2.0 \cdot 10^{-8} a42=1.68704883±1108a_{42}= -1.68704883 \pm 1 \cdot 10^{-8}
a43=+1.00022350±2.0108a_{43}= +1.00022350 \pm 2.0 \cdot 10^{-8} a44=0.48835725±1108a_{44}= -0.48835725 \pm 1 \cdot 10^{-8} a45=+0.58015773±2.0108a_{45}= +0.58015773 \pm 2.0 \cdot 10^{-8}
a46=0.31093633±1108a_{46}= -0.31093633 \pm 1 \cdot 10^{-8} a47=0.08342218±1.2108a_{47}= -0.08342218 \pm 1.2 \cdot 10^{-8} a48=+0.63071080±1108a_{48}= +0.63071080 \pm 1 \cdot 10^{-8}
a49=+1.11119651±1.6108a_{49}= +1.11119651 \pm 1.6 \cdot 10^{-8} a50=+0.15320999±2.8108a_{50}= +0.15320999 \pm 2.8 \cdot 10^{-8} a51=1.50228292±1.9108a_{51}= -1.50228292 \pm 1.9 \cdot 10^{-8}
a52=+0.04114576±1.2108a_{52}= +0.04114576 \pm 1.2 \cdot 10^{-8} a53=+1.08201311±1.9108a_{53}= +1.08201311 \pm 1.9 \cdot 10^{-8} a54=0.34515766±1.5108a_{54}= -0.34515766 \pm 1.5 \cdot 10^{-8}
a55=+0.52859925±2.0108a_{55}= +0.52859925 \pm 2.0 \cdot 10^{-8} a56=1.57295049±1108a_{56}= -1.57295049 \pm 1 \cdot 10^{-8} a57=0.19616069±2.1108a_{57}= -0.19616069 \pm 2.1 \cdot 10^{-8}
a58=+0.25086214±1108a_{58}= +0.25086214 \pm 1 \cdot 10^{-8} a59=1.87004361±1.5108a_{59}= -1.87004361 \pm 1.5 \cdot 10^{-8} a60=+0.28005757±4.6108a_{60}= +0.28005757 \pm 4.6 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000