Properties

Label 10.1
Level 1010
Weight 00
Character 10.1
Symmetry odd
RR 1.446399
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: 1.44639913340300919227740092604±610131.44639913340300919227740092604 \pm 6 \cdot 10^{-13}

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=0.50834095±1108a_{3}= -0.50834095 \pm 1 \cdot 10^{-8}
a4=+0.5a_{4}= +0.5 a5=+0.44721360±1.0108a_{5}= +0.44721360 \pm 1.0 \cdot 10^{-8} a6=+0.35945134±1.0108a_{6}= +0.35945134 \pm 1.0 \cdot 10^{-8}
a7=+0.08483578±1108a_{7}= +0.08483578 \pm 1 \cdot 10^{-8} a8=0.35355339±4.2108a_{8}= -0.35355339 \pm 4.2 \cdot 10^{-8} a9=0.74158947±1108a_{9}= -0.74158947 \pm 1 \cdot 10^{-8}
a10=0.31622777±1.0108a_{10}= -0.31622777 \pm 1.0 \cdot 10^{-8} a11=+0.24526381±1108a_{11}= +0.24526381 \pm 1 \cdot 10^{-8} a12=0.25417048±1.0108a_{12}= -0.25417048 \pm 1.0 \cdot 10^{-8}
a13=+1.03793609±1108a_{13}= +1.03793609 \pm 1 \cdot 10^{-8} a14=0.05998795±1.0108a_{14}= -0.05998795 \pm 1.0 \cdot 10^{-8} a15=0.22733699±1.0108a_{15}= -0.22733699 \pm 1.0 \cdot 10^{-8}
a16=+0.25a_{16}= +0.25 a17=0.05663155±1108a_{17}= -0.05663155 \pm 1 \cdot 10^{-8} a18=+0.52438295±1.0108a_{18}= +0.52438295 \pm 1.0 \cdot 10^{-8}
a19=0.31364879±1108a_{19}= -0.31364879 \pm 1 \cdot 10^{-8} a20=+0.22360680±8.4108a_{20}= +0.22360680 \pm 8.4 \cdot 10^{-8} a21=0.04312550±1108a_{21}= -0.04312550 \pm 1 \cdot 10^{-8}
a22=0.17342771±1.0108a_{22}= -0.17342771 \pm 1.0 \cdot 10^{-8} a23=1.67038673±1108a_{23}= -1.67038673 \pm 1 \cdot 10^{-8} a24=+0.17972567±1.0108a_{24}= +0.17972567 \pm 1.0 \cdot 10^{-8}
a25=+0.2a_{25}= +0.2 a26=0.73393165±1.0108a_{26}= -0.73393165 \pm 1.0 \cdot 10^{-8} a27=+0.88532126±1108a_{27}= +0.88532126 \pm 1 \cdot 10^{-8}
a28=+0.04241789±1.0108a_{28}= +0.04241789 \pm 1.0 \cdot 10^{-8} a29=+1.26525111±1108a_{29}= +1.26525111 \pm 1 \cdot 10^{-8} a30=+0.16075152±1.0108a_{30}= +0.16075152 \pm 1.0 \cdot 10^{-8}
a31=+0.55693258±1108a_{31}= +0.55693258 \pm 1 \cdot 10^{-8} a32=0.17677670±1.1107a_{32}= -0.17677670 \pm 1.1 \cdot 10^{-7} a33=0.12467764±1108a_{33}= -0.12467764 \pm 1 \cdot 10^{-8}
a34=+0.04004456±1.0108a_{34}= +0.04004456 \pm 1.0 \cdot 10^{-8} a35=+0.03793971±1.0108a_{35}= +0.03793971 \pm 1.0 \cdot 10^{-8} a36=0.37079474±1.0108a_{36}= -0.37079474 \pm 1.0 \cdot 10^{-8}
a37=1.24632041±1108a_{37}= -1.24632041 \pm 1 \cdot 10^{-8} a38=+0.22178318±1.0108a_{38}= +0.22178318 \pm 1.0 \cdot 10^{-8} a39=0.52762542±1108a_{39}= -0.52762542 \pm 1 \cdot 10^{-8}
a40=0.15811388±1.2107a_{40}= -0.15811388 \pm 1.2 \cdot 10^{-7} a41=0.40958558±1108a_{41}= -0.40958558 \pm 1 \cdot 10^{-8} a42=+0.03049433±1.0108a_{42}= +0.03049433 \pm 1.0 \cdot 10^{-8}
a43=+0.65627723±1108a_{43}= +0.65627723 \pm 1 \cdot 10^{-8} a44=+0.12263191±1.0108a_{44}= +0.12263191 \pm 1.0 \cdot 10^{-8} a45=0.33164889±1.0108a_{45}= -0.33164889 \pm 1.0 \cdot 10^{-8}
a46=+1.18114179±1.0108a_{46}= +1.18114179 \pm 1.0 \cdot 10^{-8} a47=+0.82107241±1108a_{47}= +0.82107241 \pm 1 \cdot 10^{-8} a48=0.12708524±1.0108a_{48}= -0.12708524 \pm 1.0 \cdot 10^{-8}
a49=0.99280289±1108a_{49}= -0.99280289 \pm 1 \cdot 10^{-8} a50=0.14142136±1.5107a_{50}= -0.14142136 \pm 1.5 \cdot 10^{-7} a51=+0.02878814±1108a_{51}= +0.02878814 \pm 1 \cdot 10^{-8}
a52=+0.51896805±1.0108a_{52}= +0.51896805 \pm 1.0 \cdot 10^{-8} a53=+1.12260378±1108a_{53}= +1.12260378 \pm 1 \cdot 10^{-8} a54=0.62601666±1.0108a_{54}= -0.62601666 \pm 1.0 \cdot 10^{-8}
a55=+0.10968531±1.0108a_{55}= +0.10968531 \pm 1.0 \cdot 10^{-8} a56=0.02999398±1.0108a_{56}= -0.02999398 \pm 1.0 \cdot 10^{-8} a57=+0.15944052±1108a_{57}= +0.15944052 \pm 1 \cdot 10^{-8}
a58=0.89466764±1.0108a_{58}= -0.89466764 \pm 1.0 \cdot 10^{-8} a59=0.24333197±1108a_{59}= -0.24333197 \pm 1 \cdot 10^{-8} a60=0.11366849±1.0108a_{60}= -0.11366849 \pm 1.0 \cdot 10^{-8}

Displaying ana_n with nn up to: 60 180 1000