Properties

Label 11.80
Level 1111
Weight 00
Character 11.1
Symmetry odd
RR 10.66941
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: 10.6694194813172660517110241767±2101010.6694194813172660517110241767 \pm 2 \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=+1.83015314±1.1106a_{2}= +1.83015314 \pm 1.1 \cdot 10^{-6} a3=0.06787432±9.0107a_{3}= -0.06787432 \pm 9.0 \cdot 10^{-7}
a4=+2.34946053±1.2106a_{4}= +2.34946053 \pm 1.2 \cdot 10^{-6} a5=0.97667227±9.4107a_{5}= -0.97667227 \pm 9.4 \cdot 10^{-7} a6=0.12422041±1.1106a_{6}= -0.12422041 \pm 1.1 \cdot 10^{-6}
a7=1.64023254±9.4107a_{7}= -1.64023254 \pm 9.4 \cdot 10^{-7} a8=+2.46971943±1.0106a_{8}= +2.46971943 \pm 1.0 \cdot 10^{-6} a9=0.99539308±1.0106a_{9}= -0.99539308 \pm 1.0 \cdot 10^{-6}
a10=1.78745983±1.1106a_{10}= -1.78745983 \pm 1.1 \cdot 10^{-6} a11=0.30151134±1.0108a_{11}= -0.30151134 \pm 1.0 \cdot 10^{-8} a12=0.15946804±1.1106a_{12}= -0.15946804 \pm 1.1 \cdot 10^{-6}
a13=0.38330067±7.4107a_{13}= -0.38330067 \pm 7.4 \cdot 10^{-7} a14=3.00187674±7.8107a_{14}= -3.00187674 \pm 7.8 \cdot 10^{-7} a15=+0.06629097±7.1107a_{15}= +0.06629097 \pm 7.1 \cdot 10^{-7}
a16=+2.17050425±9.5107a_{16}= +2.17050425 \pm 9.5 \cdot 10^{-7} a17=0.73225768±9.3107a_{17}= -0.73225768 \pm 9.3 \cdot 10^{-7} a18=1.82172177±1.0106a_{18}= -1.82172177 \pm 1.0 \cdot 10^{-6}
a19=+1.70042108±6.7107a_{19}= +1.70042108 \pm 6.7 \cdot 10^{-7} a20=2.29465296±1.2106a_{20}= -2.29465296 \pm 1.2 \cdot 10^{-6} a21=+0.11132967±7.2107a_{21}= +0.11132967 \pm 7.2 \cdot 10^{-7}
a22=0.55181194±1.1106a_{22}= -0.55181194 \pm 1.1 \cdot 10^{-6} a23=+0.51786692±8.7107a_{23}= +0.51786692 \pm 8.7 \cdot 10^{-7} a24=0.16763054±1.2106a_{24}= -0.16763054 \pm 1.2 \cdot 10^{-6}
a25=0.04611127±7.7107a_{25}= -0.04611127 \pm 7.7 \cdot 10^{-7} a26=0.70149892±5.8107a_{26}= -0.70149892 \pm 5.8 \cdot 10^{-7} a27=+0.13543596±8.6107a_{27}= +0.13543596 \pm 8.6 \cdot 10^{-7}
a28=3.85366161±9.4107a_{28}= -3.85366161 \pm 9.4 \cdot 10^{-7} a29=0.41268375±8.6107a_{29}= -0.41268375 \pm 8.6 \cdot 10^{-7} a30=+0.12132263±6.6107a_{30}= +0.12132263 \pm 6.6 \cdot 10^{-7}
a31=+0.10945521±9.2107a_{31}= +0.10945521 \pm 9.2 \cdot 10^{-7} a32=+1.50263574±7.8107a_{32}= +1.50263574 \pm 7.8 \cdot 10^{-7} a33=+0.02046488±9.1107a_{33}= +0.02046488 \pm 9.1 \cdot 10^{-7}
a34=1.34014370±1.1106a_{34}= -1.34014370 \pm 1.1 \cdot 10^{-6} a35=+1.60196964±8.9107a_{35}= +1.60196964 \pm 8.9 \cdot 10^{-7} a36=2.33863674±1.0106a_{36}= -2.33863674 \pm 1.0 \cdot 10^{-6}
a37=0.86847304±9.3107a_{37}= -0.86847304 \pm 9.3 \cdot 10^{-7} a38=+3.11203098±9.2107a_{38}= +3.11203098 \pm 9.2 \cdot 10^{-7} a39=+0.02601627±5.4107a_{39}= +0.02601627 \pm 5.4 \cdot 10^{-7}
a40=2.41210649±8.8107a_{40}= -2.41210649 \pm 8.8 \cdot 10^{-7} a41=1.78003002±6.1107a_{41}= -1.78003002 \pm 6.1 \cdot 10^{-7} a42=+0.20375035±8.0107a_{42}= +0.20375035 \pm 8.0 \cdot 10^{-7}
a43=+0.04571231±8.9107a_{43}= +0.04571231 \pm 8.9 \cdot 10^{-7} a44=0.70838900±1.2106a_{44}= -0.70838900 \pm 1.2 \cdot 10^{-6} a45=+0.97217282±9.8107a_{45}= +0.97217282 \pm 9.8 \cdot 10^{-7}
a46=+0.94777577±1.2106a_{46}= +0.94777577 \pm 1.2 \cdot 10^{-6} a47=0.17497620±7.4107a_{47}= -0.17497620 \pm 7.4 \cdot 10^{-7} a48=0.14732151±9.7107a_{48}= -0.14732151 \pm 9.7 \cdot 10^{-7}
a49=+1.69036279±8.2107a_{49}= +1.69036279 \pm 8.2 \cdot 10^{-7} a50=0.08439068±1.1106a_{50}= -0.08439068 \pm 1.1 \cdot 10^{-6} a51=+0.04970150±9.1107a_{51}= +0.04970150 \pm 9.1 \cdot 10^{-7}
a52=0.90054978±7.8107a_{52}= -0.90054978 \pm 7.8 \cdot 10^{-7} a53=+1.14584089±7.2107a_{53}= +1.14584089 \pm 7.2 \cdot 10^{-7} a54=+0.24786854±7.4107a_{54}= +0.24786854 \pm 7.4 \cdot 10^{-7}
a55=+0.29447777±9.5107a_{55}= +0.29447777 \pm 9.5 \cdot 10^{-7} a56=4.05091417±6.4107a_{56}= -4.05091417 \pm 6.4 \cdot 10^{-7} a57=0.11541493±6.0107a_{57}= -0.11541493 \pm 6.0 \cdot 10^{-7}
a58=0.75527446±8.4107a_{58}= -0.75527446 \pm 8.4 \cdot 10^{-7} a59=+0.82636531±1.0106a_{59}= +0.82636531 \pm 1.0 \cdot 10^{-6} a60=+0.15574802±5.7107a_{60}= +0.15574802 \pm 5.7 \cdot 10^{-7}

Displaying ana_n with nn up to: 60 180 1000