Properties

Label 10.49
Level 1010
Weight 00
Character 10.1
Symmetry odd
RR 12.01500
Fricke sign +1+1

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Maass form invariants

Level: 10=25 10 = 2 \cdot 5
Weight: 0 0
Character: 10.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 12.0150070406973263972274387053±7101012.0150070406973263972274387053 \pm 7 \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=0.70710678±1.0108a_{2}= -0.70710678 \pm 1.0 \cdot 10^{-8} a3=1.50507564±1.2106a_{3}= -1.50507564 \pm 1.2 \cdot 10^{-6}
a4=+0.5a_{4}= +0.5 a5=0.44721360±1.0108a_{5}= -0.44721360 \pm 1.0 \cdot 10^{-8} a6=+1.06424919±1.3106a_{6}= +1.06424919 \pm 1.3 \cdot 10^{-6}
a7=1.56407173±1.6106a_{7}= -1.56407173 \pm 1.6 \cdot 10^{-6} a8=0.35355339±4.2108a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} a9=+1.26525268±1.3106a_{9}= +1.26525268 \pm 1.3 \cdot 10^{-6}
a10=+0.31622777±1.0108a_{10}= +0.31622777 \pm 1.0 \cdot 10^{-8} a11=+1.24295679±1.2106a_{11}= +1.24295679 \pm 1.2 \cdot 10^{-6} a12=0.75253782±1.3106a_{12}= -0.75253782 \pm 1.3 \cdot 10^{-6}
a13=+0.02181166±1.4106a_{13}= +0.02181166 \pm 1.4 \cdot 10^{-6} a14=+1.10596573±1.6106a_{14}= +1.10596573 \pm 1.6 \cdot 10^{-6} a15=+0.67309029±1.3106a_{15}= +0.67309029 \pm 1.3 \cdot 10^{-6}
a16=+0.25a_{16}= +0.25 a17=+0.77510394±8.5107a_{17}= +0.77510394 \pm 8.5 \cdot 10^{-7} a18=0.89466875±1.4106a_{18}= -0.89466875 \pm 1.4 \cdot 10^{-6}
a19=+1.54966375±1.1106a_{19}= +1.54966375 \pm 1.1 \cdot 10^{-6} a20=0.22360680±8.4108a_{20}= -0.22360680 \pm 8.4 \cdot 10^{-8} a21=+2.35404626±1.3106a_{21}= +2.35404626 \pm 1.3 \cdot 10^{-6}
a22=0.87890318±1.2106a_{22}= -0.87890318 \pm 1.2 \cdot 10^{-6} a23=0.82473372±1.9106a_{23}= -0.82473372 \pm 1.9 \cdot 10^{-6} a24=+0.53212460±1.3106a_{24}= +0.53212460 \pm 1.3 \cdot 10^{-6}
a25=+0.2a_{25}= +0.2 a26=0.01542317±1.4106a_{26}= -0.01542317 \pm 1.4 \cdot 10^{-6} a27=0.39922534±1.5106a_{27}= -0.39922534 \pm 1.5 \cdot 10^{-6}
a28=0.78203587±1.6106a_{28}= -0.78203587 \pm 1.6 \cdot 10^{-6} a29=1.40588731±2.0106a_{29}= -1.40588731 \pm 2.0 \cdot 10^{-6} a30=0.47594671±1.3106a_{30}= -0.47594671 \pm 1.3 \cdot 10^{-6}
a31=+0.53244342±1.1106a_{31}= +0.53244342 \pm 1.1 \cdot 10^{-6} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=1.87074399±1.0106a_{33}= -1.87074399 \pm 1.0 \cdot 10^{-6}
a34=0.54808125±8.6107a_{34}= -0.54808125 \pm 8.6 \cdot 10^{-7} a35=+0.69947414±1.6106a_{35}= +0.69947414 \pm 1.6 \cdot 10^{-6} a36=+0.63262634±1.4106a_{36}= +0.63262634 \pm 1.4 \cdot 10^{-6}
a37=+0.02700126±1.5106a_{37}= +0.02700126 \pm 1.5 \cdot 10^{-6} a38=1.09577775±1.1106a_{38}= -1.09577775 \pm 1.1 \cdot 10^{-6} a39=0.03282820±1.1106a_{39}= -0.03282820 \pm 1.1 \cdot 10^{-6}
a40=+0.15811388±1.2107a_{40}= +0.15811388 \pm 1.2 \cdot 10^{-7} a41=1.39122423±1.0106a_{41}= -1.39122423 \pm 1.0 \cdot 10^{-6} a42=1.66456208±2.9106a_{42}= -1.66456208 \pm 2.9 \cdot 10^{-6}
a43=+0.85144628±1.3106a_{43}= +0.85144628 \pm 1.3 \cdot 10^{-6} a44=+0.62147840±1.2106a_{44}= +0.62147840 \pm 1.2 \cdot 10^{-6} a45=0.56583820±1.4106a_{45}= -0.56583820 \pm 1.4 \cdot 10^{-6}
a46=+0.58317481±1.9106a_{46}= +0.58317481 \pm 1.9 \cdot 10^{-6} a47=0.66849687±1.0106a_{47}= -0.66849687 \pm 1.0 \cdot 10^{-6} a48=0.37626891±1.3106a_{48}= -0.37626891 \pm 1.3 \cdot 10^{-6}
a49=+1.44632039±1.6106a_{49}= +1.44632039 \pm 1.6 \cdot 10^{-6} a50=0.14142136±1.5107a_{50}= -0.14142136 \pm 1.5 \cdot 10^{-7} a51=1.16659005±1.0106a_{51}= -1.16659005 \pm 1.0 \cdot 10^{-6}
a52=+0.01090583±1.4106a_{52}= +0.01090583 \pm 1.4 \cdot 10^{-6} a53=+1.20679158±1.4106a_{53}= +1.20679158 \pm 1.4 \cdot 10^{-6} a54=+0.28229495±1.5106a_{54}= +0.28229495 \pm 1.5 \cdot 10^{-6}
a55=0.55586718±1.2106a_{55}= -0.55586718 \pm 1.2 \cdot 10^{-6} a56=+0.55298286±1.6106a_{56}= +0.55298286 \pm 1.6 \cdot 10^{-6} a57=2.33236116±9.9107a_{57}= -2.33236116 \pm 9.9 \cdot 10^{-7}
a58=+0.99411245±2.0106a_{58}= +0.99411245 \pm 2.0 \cdot 10^{-6} a59=+0.90224468±1.0106a_{59}= +0.90224468 \pm 1.0 \cdot 10^{-6} a60=+0.33654514±1.3106a_{60}= +0.33654514 \pm 1.3 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000