Properties

Label 3.50
Level 33
Weight 00
Character 3.1
Symmetry odd
RR 19.17596
Fricke sign 1-1

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Maass form invariants

Level: 3 3
Weight: 0 0
Character: 3.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 19.1759646544262442089015364564±210419.1759646544262442089015364564 \pm 2 \cdot 10^{-4}

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=0.79105220±2.8102a_{2}= -0.79105220 \pm 2.8 \cdot 10^{-2} a3=+0.57735027±1.0108a_{3}= +0.57735027 \pm 1.0 \cdot 10^{-8}
a4=0.37423642±5.1102a_{4}= -0.37423642 \pm 5.1 \cdot 10^{-2} a5=1.37664488±3.9102a_{5}= -1.37664488 \pm 3.9 \cdot 10^{-2} a6=0.45671420±2.8102a_{6}= -0.45671420 \pm 2.8 \cdot 10^{-2}
a7=1.12032810±3.2102a_{7}= -1.12032810 \pm 3.2 \cdot 10^{-2} a8=+1.08709274±3.4102a_{8}= +1.08709274 \pm 3.4 \cdot 10^{-2} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+1.08899796±2.2102a_{10}= +1.08899796 \pm 2.2 \cdot 10^{-2} a11=1.71520147±3.5102a_{11}= -1.71520147 \pm 3.5 \cdot 10^{-2} a12=0.21606550±5.1102a_{12}= -0.21606550 \pm 5.1 \cdot 10^{-2}
a13=0.44729529±3.4102a_{13}= -0.44729529 \pm 3.4 \cdot 10^{-2} a14=+0.88623801±2.2102a_{14}= +0.88623801 \pm 2.2 \cdot 10^{-2} a15=0.79480629±3.9102a_{15}= -0.79480629 \pm 3.9 \cdot 10^{-2}
a16=0.48571068±4.1102a_{16}= -0.48571068 \pm 4.1 \cdot 10^{-2} a17=0.42943391±2.6102a_{17}= -0.42943391 \pm 2.6 \cdot 10^{-2} a18=0.26368407±2.8102a_{18}= -0.26368407 \pm 2.8 \cdot 10^{-2}
a19=0.85596626±2.1102a_{19}= -0.85596626 \pm 2.1 \cdot 10^{-2} a20=+0.51519065±3.6102a_{20}= +0.51519065 \pm 3.6 \cdot 10^{-2} a21=0.64682173±3.2102a_{21}= -0.64682173 \pm 3.2 \cdot 10^{-2}
a22=+1.35681389±1.8102a_{22}= +1.35681389 \pm 1.8 \cdot 10^{-2} a23=+0.71058831±7.8102a_{23}= +0.71058831 \pm 7.8 \cdot 10^{-2} a24=+0.62763329±3.4102a_{24}= +0.62763329 \pm 3.4 \cdot 10^{-2}
a25=+0.89515114±3.2102a_{25}= +0.89515114 \pm 3.2 \cdot 10^{-2} a26=+0.35383392±1.2102a_{26}= +0.35383392 \pm 1.2 \cdot 10^{-2} a27=+0.19245009±9.4108a_{27}= +0.19245009 \pm 9.4 \cdot 10^{-8}
a28=+0.41926758±2.1102a_{28}= +0.41926758 \pm 2.1 \cdot 10^{-2} a29=+1.04035634±7.4102a_{29}= +1.04035634 \pm 7.4 \cdot 10^{-2} a30=+0.62873327±6.7102a_{30}= +0.62873327 \pm 6.7 \cdot 10^{-2}
a31=+0.62799514±3.3102a_{31}= +0.62799514 \pm 3.3 \cdot 10^{-2} a32=0.70287024±4.6102a_{32}= -0.70287024 \pm 4.6 \cdot 10^{-2} a33=0.99027203±3.5102a_{33}= -0.99027203 \pm 3.5 \cdot 10^{-2}
a34=+0.33970463±3.1102a_{34}= +0.33970463 \pm 3.1 \cdot 10^{-2} a35=+1.54229395±1.4102a_{35}= +1.54229395 \pm 1.4 \cdot 10^{-2} a36=0.12474547±5.1102a_{36}= -0.12474547 \pm 5.1 \cdot 10^{-2}
a37=0.22485173±3.9102a_{37}= -0.22485173 \pm 3.9 \cdot 10^{-2} a38=+0.67711399±9.6103a_{38}= +0.67711399 \pm 9.6 \cdot 10^{-3} a39=0.25824606±3.4102a_{39}= -0.25824606 \pm 3.4 \cdot 10^{-2}
a40=1.49654066±2.1102a_{40}= -1.49654066 \pm 2.1 \cdot 10^{-2} a41=+0.31215390±7.5102a_{41}= +0.31215390 \pm 7.5 \cdot 10^{-2} a42=+0.51166975±6.0102a_{42}= +0.51166975 \pm 6.0 \cdot 10^{-2}
a43=+0.28122374±5.0102a_{43}= +0.28122374 \pm 5.0 \cdot 10^{-2} a44=+0.64189086±3.1102a_{44}= +0.64189086 \pm 3.1 \cdot 10^{-2} a45=0.45888163±3.9102a_{45}= -0.45888163 \pm 3.9 \cdot 10^{-2}
a46=0.56211244±2.2102a_{46}= -0.56211244 \pm 2.2 \cdot 10^{-2} a47=+0.73891609±6.2102a_{47}= +0.73891609 \pm 6.2 \cdot 10^{-2} a48=0.28042519±4.1102a_{48}= -0.28042519 \pm 4.1 \cdot 10^{-2}
a49=+0.25513506±5.4102a_{49}= +0.25513506 \pm 5.4 \cdot 10^{-2} a50=0.70811128±1.5102a_{50}= -0.70811128 \pm 1.5 \cdot 10^{-2} a51=0.24793378±2.6102a_{51}= -0.24793378 \pm 2.6 \cdot 10^{-2}
a52=+0.16739419±3.1102a_{52}= +0.16739419 \pm 3.1 \cdot 10^{-2} a53=0.04890870±3.1102a_{53}= -0.04890870 \pm 3.1 \cdot 10^{-2} a54=0.15223807±2.8102a_{54}= -0.15223807 \pm 2.8 \cdot 10^{-2}
a55=+2.36122332±2.4102a_{55}= +2.36122332 \pm 2.4 \cdot 10^{-2} a56=1.21790055±3.0102a_{56}= -1.21790055 \pm 3.0 \cdot 10^{-2} a57=0.49419235±2.1102a_{57}= -0.49419235 \pm 2.1 \cdot 10^{-2}
a58=0.82297617±3.0102a_{58}= -0.82297617 \pm 3.0 \cdot 10^{-2} a59=+1.43856395±5.0102a_{59}= +1.43856395 \pm 5.0 \cdot 10^{-2} a60=+0.29744546±9.0102a_{60}= +0.29744546 \pm 9.0 \cdot 10^{-2}

Displaying ana_n with nn up to: 60 180 1000