Properties

Label 11.89
Level 1111
Weight 00
Character 11.1
Symmetry odd
RR 11.26124
Fricke sign +1+1

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Maass form invariants

Level: 11 11
Weight: 0 0
Character: 11.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 11.2612425027035251260082390096±5101011.2612425027035251260082390096 \pm 5 \cdot 10^{-10}

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=0.72164439±4.6106a_{2}= -0.72164439 \pm 4.6 \cdot 10^{-6} a3=1.72027069±3.8106a_{3}= -1.72027069 \pm 3.8 \cdot 10^{-6}
a4=0.47922938±5.4106a_{4}= -0.47922938 \pm 5.4 \cdot 10^{-6} a5=0.98168527±3.9106a_{5}= -0.98168527 \pm 3.9 \cdot 10^{-6} a6=+1.24142368±4.7106a_{6}= +1.24142368 \pm 4.7 \cdot 10^{-6}
a7=1.50765960±3.9106a_{7}= -1.50765960 \pm 3.9 \cdot 10^{-6} a8=+1.06747758±4.5106a_{8}= +1.06747758 \pm 4.5 \cdot 10^{-6} a9=+1.95933124±4.2106a_{9}= +1.95933124 \pm 4.2 \cdot 10^{-6}
a10=+0.70842766±4.8106a_{10}= +0.70842766 \pm 4.8 \cdot 10^{-6} a11=0.30151134±1.0108a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} a12=+0.82440426±5.0106a_{12}= +0.82440426 \pm 5.0 \cdot 10^{-6}
a13=0.52388168±3.1106a_{13}= -0.52388168 \pm 3.1 \cdot 10^{-6} a14=+1.08799409±3.3106a_{14}= +1.08799409 \pm 3.3 \cdot 10^{-6} a15=+1.68876439±3.0106a_{15}= +1.68876439 \pm 3.0 \cdot 10^{-6}
a16=0.29110982±4.0106a_{16}= -0.29110982 \pm 4.0 \cdot 10^{-6} a17=+1.90860392±3.9106a_{17}= +1.90860392 \pm 3.9 \cdot 10^{-6} a18=1.41394039±4.3106a_{18}= -1.41394039 \pm 4.3 \cdot 10^{-6}
a19=0.25340204±2.8106a_{19}= -0.25340204 \pm 2.8 \cdot 10^{-6} a20=+0.47045242±5.2106a_{20}= +0.47045242 \pm 5.2 \cdot 10^{-6} a21=+2.59358262±3.0106a_{21}= +2.59358262 \pm 3.0 \cdot 10^{-6}
a22=+0.21758397±4.6106a_{22}= +0.21758397 \pm 4.6 \cdot 10^{-6} a23=0.42825166±3.7106a_{23}= -0.42825166 \pm 3.7 \cdot 10^{-6} a24=1.83635039±5.3106a_{24}= -1.83635039 \pm 5.3 \cdot 10^{-6}
a25=0.03629403±3.2106a_{25}= -0.03629403 \pm 3.2 \cdot 10^{-6} a26=+0.37805628±2.4106a_{26}= +0.37805628 \pm 2.4 \cdot 10^{-6} a27=1.65030942±3.6106a_{27}= -1.65030942 \pm 3.6 \cdot 10^{-6}
a28=+0.72251478±4.0106a_{28}= +0.72251478 \pm 4.0 \cdot 10^{-6} a29=+0.25659394±3.6106a_{29}= +0.25659394 \pm 3.6 \cdot 10^{-6} a30=1.21868734±2.7106a_{30}= -1.21868734 \pm 2.7 \cdot 10^{-6}
a31=1.16637508±3.8106a_{31}= -1.16637508 \pm 3.8 \cdot 10^{-6} a32=0.85739981±3.3106a_{32}= -0.85739981 \pm 3.3 \cdot 10^{-6} a33=+0.51868113±3.8106a_{33}= +0.51868113 \pm 3.8 \cdot 10^{-6}
a34=1.37733330±4.7106a_{34}= -1.37733330 \pm 4.7 \cdot 10^{-6} a35=+1.48004722±3.7106a_{35}= +1.48004722 \pm 3.7 \cdot 10^{-6} a36=0.93896910±4.5106a_{36}= -0.93896910 \pm 4.5 \cdot 10^{-6}
a37=0.20216591±3.9106a_{37}= -0.20216591 \pm 3.9 \cdot 10^{-6} a38=+0.18286616±3.9106a_{38}= +0.18286616 \pm 3.9 \cdot 10^{-6} a39=+0.90121830±2.3106a_{39}= +0.90121830 \pm 2.3 \cdot 10^{-6}
a40=1.04792701±3.7106a_{40}= -1.04792701 \pm 3.7 \cdot 10^{-6} a41=+0.24774315±2.6106a_{41}= +0.24774315 \pm 2.6 \cdot 10^{-6} a42=1.87164434±3.3106a_{42}= -1.87164434 \pm 3.3 \cdot 10^{-6}
a43=+0.05793280±3.7106a_{43}= +0.05793280 \pm 3.7 \cdot 10^{-6} a44=+0.14449309±5.4106a_{44}= +0.14449309 \pm 5.4 \cdot 10^{-6} a45=1.92344662±4.1106a_{45}= -1.92344662 \pm 4.1 \cdot 10^{-6}
a46=+0.30904540±5.3106a_{46}= +0.30904540 \pm 5.3 \cdot 10^{-6} a47=+1.39770660±3.1106a_{47}= +1.39770660 \pm 3.1 \cdot 10^{-6} a48=+0.50078769±4.1106a_{48}= +0.50078769 \pm 4.1 \cdot 10^{-6}
a49=+1.27303748±3.4106a_{49}= +1.27303748 \pm 3.4 \cdot 10^{-6} a50=+0.02619139±5.0106a_{50}= +0.02619139 \pm 5.0 \cdot 10^{-6} a51=3.28331538±3.8106a_{51}= -3.28331538 \pm 3.8 \cdot 10^{-6}
a52=+0.25105949±3.3106a_{52}= +0.25105949 \pm 3.3 \cdot 10^{-6} a53=+1.33820657±3.0106a_{53}= +1.33820657 \pm 3.0 \cdot 10^{-6} a54=+1.19093653±3.1106a_{54}= +1.19093653 \pm 3.1 \cdot 10^{-6}
a55=+0.29598925±3.9106a_{55}= +0.29598925 \pm 3.9 \cdot 10^{-6} a56=1.60939282±2.7106a_{56}= -1.60939282 \pm 2.7 \cdot 10^{-6} a57=+0.43592010±2.5106a_{57}= +0.43592010 \pm 2.5 \cdot 10^{-6}
a58=0.18516958±3.5106a_{58}= -0.18516958 \pm 3.5 \cdot 10^{-6} a59=0.06959452±4.4106a_{59}= -0.06959452 \pm 4.4 \cdot 10^{-6} a60=0.80930551±2.4106a_{60}= -0.80930551 \pm 2.4 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000