Properties

Label 2.11
Level 22
Weight 00
Character 2.1
Symmetry odd
RR 14.09720
Fricke sign 1-1

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Maass form invariants

Level: 2 2
Weight: 0 0
Character: 2.1
Symmetry: odd
Fricke sign: 1-1
Spectral parameter: 14.097203733919118562864404305±210814.097203733919118562864404305 \pm 2 \cdot 10^{-8}

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=+0.70710678±1.0108a_{2}= +0.70710678 \pm 1.0 \cdot 10^{-8} a3=1.52313756±3.0107a_{3}= -1.52313756 \pm 3.0 \cdot 10^{-7}
a4=+0.5a_{4}= +0.5 a5=+0.53848903±2.2107a_{5}= +0.53848903 \pm 2.2 \cdot 10^{-7} a6=1.07702089±3.1107a_{6}= -1.07702089 \pm 3.1 \cdot 10^{-7}
a7=+1.10504771±2.5107a_{7}= +1.10504771 \pm 2.5 \cdot 10^{-7} a8=+0.35355339±4.2108a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} a9=+1.31994801±5.2107a_{9}= +1.31994801 \pm 5.2 \cdot 10^{-7}
a10=+0.38076925±2.3107a_{10}= +0.38076925 \pm 2.3 \cdot 10^{-7} a11=+1.06533591±7.4107a_{11}= +1.06533591 \pm 7.4 \cdot 10^{-7} a12=0.76156878±3.1107a_{12}= -0.76156878 \pm 3.1 \cdot 10^{-7}
a13=+0.53069533±5.8107a_{13}= +0.53069533 \pm 5.8 \cdot 10^{-7} a14=+0.78138673±2.6107a_{14}= +0.78138673 \pm 2.6 \cdot 10^{-7} a15=0.82019287±1.6107a_{15}= -0.82019287 \pm 1.6 \cdot 10^{-7}
a16=+0.25a_{16}= +0.25 a17=0.51927767±4.2107a_{17}= -0.51927767 \pm 4.2 \cdot 10^{-7} a18=+0.93334419±5.3107a_{18}= +0.93334419 \pm 5.3 \cdot 10^{-7}
a19=0.12602366±3.0107a_{19}= -0.12602366 \pm 3.0 \cdot 10^{-7} a20=+0.26924452±2.3107a_{20}= +0.26924452 \pm 2.3 \cdot 10^{-7} a21=1.68313967±1.2107a_{21}= -1.68313967 \pm 1.2 \cdot 10^{-7}
a22=+0.75330624±7.5107a_{22}= +0.75330624 \pm 7.5 \cdot 10^{-7} a23=+1.30256905±3.1107a_{23}= +1.30256905 \pm 3.1 \cdot 10^{-7} a24=0.53851045±3.1107a_{24}= -0.53851045 \pm 3.1 \cdot 10^{-7}
a25=0.71002956±5.8107a_{25}= -0.71002956 \pm 5.8 \cdot 10^{-7} a26=+0.37525827±5.9107a_{26}= +0.37525827 \pm 5.9 \cdot 10^{-7} a27=0.48732484±4.7107a_{27}= -0.48732484 \pm 4.7 \cdot 10^{-7}
a28=+0.55252386±2.6107a_{28}= +0.55252386 \pm 2.6 \cdot 10^{-7} a29=0.03435910±5.2107a_{29}= -0.03435910 \pm 5.2 \cdot 10^{-7} a30=0.57996394±5.4107a_{30}= -0.57996394 \pm 5.4 \cdot 10^{-7}
a31=+1.31299756±6.1107a_{31}= +1.31299756 \pm 6.1 \cdot 10^{-7} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=1.62265313±2.9107a_{33}= -1.62265313 \pm 2.9 \cdot 10^{-7}
a34=0.36718476±4.3107a_{34}= -0.36718476 \pm 4.3 \cdot 10^{-7} a35=+0.59505607±6.5108a_{35}= +0.59505607 \pm 6.5 \cdot 10^{-8} a36=+0.65997401±5.3107a_{36}= +0.65997401 \pm 5.3 \cdot 10^{-7}
a37=+0.46938276±7.6107a_{37}= +0.46938276 \pm 7.6 \cdot 10^{-7} a38=0.08911218±3.1107a_{38}= -0.08911218 \pm 3.1 \cdot 10^{-7} a39=0.80832199±2.3107a_{39}= -0.80832199 \pm 2.3 \cdot 10^{-7}
a40=+0.19038462±2.3107a_{40}= +0.19038462 \pm 2.3 \cdot 10^{-7} a41=+0.12753792±7.7107a_{41}= +0.12753792 \pm 7.7 \cdot 10^{-7} a42=1.19015948±5.7107a_{42}= -1.19015948 \pm 5.7 \cdot 10^{-7}
a43=+0.46916818±1.7107a_{43}= +0.46916818 \pm 1.7 \cdot 10^{-7} a44=+0.53266795±7.5107a_{44}= +0.53266795 \pm 7.5 \cdot 10^{-7} a45=+0.71077753±1.3107a_{45}= +0.71077753 \pm 1.3 \cdot 10^{-7}
a46=+0.92105541±3.2107a_{46}= +0.92105541 \pm 3.2 \cdot 10^{-7} a47=1.68853154±5.5107a_{47}= -1.68853154 \pm 5.5 \cdot 10^{-7} a48=0.38078439±3.1107a_{48}= -0.38078439 \pm 3.1 \cdot 10^{-7}
a49=+0.22113045±5.5107a_{49}= +0.22113045 \pm 5.5 \cdot 10^{-7} a50=0.50206672±5.9107a_{50}= -0.50206672 \pm 5.9 \cdot 10^{-7} a51=+0.79093132±3.1107a_{51}= +0.79093132 \pm 3.1 \cdot 10^{-7}
a52=+0.26534767±5.9107a_{52}= +0.26534767 \pm 5.9 \cdot 10^{-7} a53=0.32758291±6.3107a_{53}= -0.32758291 \pm 6.3 \cdot 10^{-7} a54=0.34459070±4.8107a_{54}= -0.34459070 \pm 4.8 \cdot 10^{-7}
a55=+0.57367170±1.8107a_{55}= +0.57367170 \pm 1.8 \cdot 10^{-7} a56=+0.39069337±2.6107a_{56}= +0.39069337 \pm 2.6 \cdot 10^{-7} a57=+0.19195137±2.6107a_{57}= +0.19195137 \pm 2.6 \cdot 10^{-7}
a58=0.02429555±5.3107a_{58}= -0.02429555 \pm 5.3 \cdot 10^{-7} a59=1.15361851±5.2107a_{59}= -1.15361851 \pm 5.2 \cdot 10^{-7} a60=0.41009643±5.4107a_{60}= -0.41009643 \pm 5.4 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000