Properties

Label 10.44
Level 1010
Weight 00
Character 10.1
Symmetry odd
RR 11.50706
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: 11.5070658355015821787757222496±4101011.5070658355015821787757222496 \pm 4 \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=1.92061742±3.3106a_{3}= -1.92061742 \pm 3.3 \cdot 10^{-6}
a4=+0.5a_{4}= +0.5 a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=1.35808160±3.4106a_{6}= -1.35808160 \pm 3.4 \cdot 10^{-6}
a7=0.28622395±4.2106a_{7}= -0.28622395 \pm 4.2 \cdot 10^{-6} a8=+0.35355339±4.2108a_{8}= +0.35355339 \pm 4.2 \cdot 10^{-8} a9=+2.68877128±3.6106a_{9}= +2.68877128 \pm 3.6 \cdot 10^{-6}
a10=+0.31622777±1.0108a_{10}= +0.31622777 \pm 1.0 \cdot 10^{-8} a11=0.23979952±3.2106a_{11}= -0.23979952 \pm 3.2 \cdot 10^{-6} a12=0.96030871±3.4106a_{12}= -0.96030871 \pm 3.4 \cdot 10^{-6}
a13=+1.37587517±3.7106a_{13}= +1.37587517 \pm 3.7 \cdot 10^{-6} a14=0.20239090±4.2106a_{14}= -0.20239090 \pm 4.2 \cdot 10^{-6} a15=0.85892622±3.4106a_{15}= -0.85892622 \pm 3.4 \cdot 10^{-6}
a16=+0.25a_{16}= +0.25 a17=0.16599162±2.2106a_{17}= -0.16599162 \pm 2.2 \cdot 10^{-6} a18=+1.90124841±3.6106a_{18}= +1.90124841 \pm 3.6 \cdot 10^{-6}
a19=1.75538402±2.9106a_{19}= -1.75538402 \pm 2.9 \cdot 10^{-6} a20=+0.22360680±8.4108a_{20}= +0.22360680 \pm 8.4 \cdot 10^{-8} a21=+0.54972671±3.5106a_{21}= +0.54972671 \pm 3.5 \cdot 10^{-6}
a22=0.16956387±3.2106a_{22}= -0.16956387 \pm 3.2 \cdot 10^{-6} a23=0.43328219±5.1106a_{23}= -0.43328219 \pm 5.1 \cdot 10^{-6} a24=0.67904080±3.4106a_{24}= -0.67904080 \pm 3.4 \cdot 10^{-6}
a25=+0.2a_{25}= +0.2 a26=+0.97289066±3.7106a_{26}= +0.97289066 \pm 3.7 \cdot 10^{-6} a27=3.24348355±4.1106a_{27}= -3.24348355 \pm 4.1 \cdot 10^{-6}
a28=0.14311198±4.2106a_{28}= -0.14311198 \pm 4.2 \cdot 10^{-6} a29=0.18207357±5.3106a_{29}= -0.18207357 \pm 5.3 \cdot 10^{-6} a30=0.60735256±3.4106a_{30}= -0.60735256 \pm 3.4 \cdot 10^{-6}
a31=1.12708452±3.1106a_{31}= -1.12708452 \pm 3.1 \cdot 10^{-6} a32=+0.17677670±1.1107a_{32}= +0.17677670 \pm 1.1 \cdot 10^{-7} a33=+0.46056314±2.6106a_{33}= +0.46056314 \pm 2.6 \cdot 10^{-6}
a34=0.11737380±2.2106a_{34}= -0.11737380 \pm 2.2 \cdot 10^{-6} a35=0.12800324±4.2106a_{35}= -0.12800324 \pm 4.2 \cdot 10^{-6} a36=+1.34438564±3.6106a_{36}= +1.34438564 \pm 3.6 \cdot 10^{-6}
a37=0.19800640±4.0106a_{37}= -0.19800640 \pm 4.0 \cdot 10^{-6} a38=1.24124395±2.9106a_{38}= -1.24124395 \pm 2.9 \cdot 10^{-6} a39=2.64252982±3.0106a_{39}= -2.64252982 \pm 3.0 \cdot 10^{-6}
a40=+0.15811388±1.2107a_{40}= +0.15811388 \pm 1.2 \cdot 10^{-7} a41=0.97725182±2.6106a_{41}= -0.97725182 \pm 2.6 \cdot 10^{-6} a42=+0.38871548±7.6106a_{42}= +0.38871548 \pm 7.6 \cdot 10^{-6}
a43=+1.00649805±3.6106a_{43}= +1.00649805 \pm 3.6 \cdot 10^{-6} a44=0.11989976±3.2106a_{44}= -0.11989976 \pm 3.2 \cdot 10^{-6} a45=+1.20245507±3.6106a_{45}= +1.20245507 \pm 3.6 \cdot 10^{-6}
a46=0.30637677±5.1106a_{46}= -0.30637677 \pm 5.1 \cdot 10^{-6} a47=+0.93662237±2.7106a_{47}= +0.93662237 \pm 2.7 \cdot 10^{-6} a48=0.48015436±3.4106a_{48}= -0.48015436 \pm 3.4 \cdot 10^{-6}
a49=0.91807585±4.2106a_{49}= -0.91807585 \pm 4.2 \cdot 10^{-6} a50=+0.14142136±1.5107a_{50}= +0.14142136 \pm 1.5 \cdot 10^{-7} a51=+0.31880639±2.7106a_{51}= +0.31880639 \pm 2.7 \cdot 10^{-6}
a52=+0.68793758±3.7106a_{52}= +0.68793758 \pm 3.7 \cdot 10^{-6} a53=0.86311544±3.8106a_{53}= -0.86311544 \pm 3.8 \cdot 10^{-6} a54=2.29348921±4.1106a_{54}= -2.29348921 \pm 4.1 \cdot 10^{-6}
a55=0.10724161±3.2106a_{55}= -0.10724161 \pm 3.2 \cdot 10^{-6} a56=0.10119545±4.2106a_{56}= -0.10119545 \pm 4.2 \cdot 10^{-6} a57=+3.37142114±2.5106a_{57}= +3.37142114 \pm 2.5 \cdot 10^{-6}
a58=0.12874546±5.3106a_{58}= -0.12874546 \pm 5.3 \cdot 10^{-6} a59=0.20721015±2.8106a_{59}= -0.20721015 \pm 2.8 \cdot 10^{-6} a60=0.42946311±3.4106a_{60}= -0.42946311 \pm 3.4 \cdot 10^{-6}

Displaying ana_n with nn up to: 60 180 1000