Properties

Label 3.51
Level 33
Weight 00
Character 3.1
Symmetry odd
RR 19.56691
Fricke sign +1+1

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Maass form invariants

Level: 3 3
Weight: 0 0
Character: 3.1
Symmetry: odd
Fricke sign: +1+1
Spectral parameter: 19.5669106110084192363326335694±310419.5669106110084192363326335694 \pm 3 \cdot 10^{-4}

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=+1.56540759±1.6102a_{2}= +1.56540759 \pm 1.6 \cdot 10^{-2} a3=0.57735027±1.0108a_{3}= -0.57735027 \pm 1.0 \cdot 10^{-8}
a4=+1.45050094±2.9102a_{4}= +1.45050094 \pm 2.9 \cdot 10^{-2} a5=+0.62263423±2.2102a_{5}= +0.62263423 \pm 2.2 \cdot 10^{-2} a6=0.90378850±1.6102a_{6}= -0.90378850 \pm 1.6 \cdot 10^{-2}
a7=1.93480398±1.8102a_{7}= -1.93480398 \pm 1.8 \cdot 10^{-2} a8=+0.70521759±2.0102a_{8}= +0.70521759 \pm 2.0 \cdot 10^{-2} a9=+0.33333333±4.2108a_{9}= +0.33333333 \pm 4.2 \cdot 10^{-8}
a10=+0.97467635±1.2102a_{10}= +0.97467635 \pm 1.2 \cdot 10^{-2} a11=0.55777999±2.0102a_{11}= -0.55777999 \pm 2.0 \cdot 10^{-2} a12=0.83744711±2.9102a_{12}= -0.83744711 \pm 2.9 \cdot 10^{-2}
a13=+0.10703289±2.0102a_{13}= +0.10703289 \pm 2.0 \cdot 10^{-2} a14=3.02875685±1.2102a_{14}= -3.02875685 \pm 1.2 \cdot 10^{-2} a15=0.35947804±2.2102a_{15}= -0.35947804 \pm 2.2 \cdot 10^{-2}
a16=0.34654797±2.4102a_{16}= -0.34654797 \pm 2.4 \cdot 10^{-2} a17=+0.36348609±1.5102a_{17}= +0.36348609 \pm 1.5 \cdot 10^{-2} a18=+0.52180253±1.6102a_{18}= +0.52180253 \pm 1.6 \cdot 10^{-2}
a19=0.79914212±1.2102a_{19}= -0.79914212 \pm 1.2 \cdot 10^{-2} a20=+0.90313153±2.1102a_{20}= +0.90313153 \pm 2.1 \cdot 10^{-2} a21=+1.11705960±1.8102a_{21}= +1.11705960 \pm 1.8 \cdot 10^{-2}
a22=0.87315303±1.0102a_{22}= -0.87315303 \pm 1.0 \cdot 10^{-2} a23=1.65986030±4.5102a_{23}= -1.65986030 \pm 4.5 \cdot 10^{-2} a24=0.40715756±2.0102a_{24}= -0.40715756 \pm 2.0 \cdot 10^{-2}
a25=0.61232662±1.8102a_{25}= -0.61232662 \pm 1.8 \cdot 10^{-2} a26=+0.16755010±7.0103a_{26}= +0.16755010 \pm 7.0 \cdot 10^{-3} a27=0.19245009±9.4108a_{27}= -0.19245009 \pm 9.4 \cdot 10^{-8}
a28=2.80643499±1.2102a_{28}= -2.80643499 \pm 1.2 \cdot 10^{-2} a29=+0.75651318±4.2102a_{29}= +0.75651318 \pm 4.2 \cdot 10^{-2} a30=0.56272965±3.8102a_{30}= -0.56272965 \pm 3.8 \cdot 10^{-2}
a31=+0.19858530±1.9102a_{31}= +0.19858530 \pm 1.9 \cdot 10^{-2} a32=1.24770641±2.6102a_{32}= -1.24770641 \pm 2.6 \cdot 10^{-2} a33=+0.32203443±2.0102a_{33}= +0.32203443 \pm 2.0 \cdot 10^{-2}
a34=+0.56900389±1.8102a_{34}= +0.56900389 \pm 1.8 \cdot 10^{-2} a35=1.20467519±8.2103a_{35}= -1.20467519 \pm 8.2 \cdot 10^{-3} a36=+0.48350031±2.9102a_{36}= +0.48350031 \pm 2.9 \cdot 10^{-2}
a37=+0.52272516±2.2102a_{37}= +0.52272516 \pm 2.2 \cdot 10^{-2} a38=1.25098314±5.5103a_{38}= -1.25098314 \pm 5.5 \cdot 10^{-3} a39=0.06179547±2.0102a_{39}= -0.06179547 \pm 2.0 \cdot 10^{-2}
a40=+0.43909261±1.2102a_{40}= +0.43909261 \pm 1.2 \cdot 10^{-2} a41=1.19949848±4.3102a_{41}= -1.19949848 \pm 4.3 \cdot 10^{-2} a42=+1.74865358±3.4102a_{42}= +1.74865358 \pm 3.4 \cdot 10^{-2}
a43=+0.93640580±2.8102a_{43}= +0.93640580 \pm 2.8 \cdot 10^{-2} a44=0.80906039±1.8102a_{44}= -0.80906039 \pm 1.8 \cdot 10^{-2} a45=+0.20754474±2.2102a_{45}= +0.20754474 \pm 2.2 \cdot 10^{-2}
a46=2.59835791±1.3102a_{46}= -2.59835791 \pm 1.3 \cdot 10^{-2} a47=+0.22929349±3.6102a_{47}= +0.22929349 \pm 3.6 \cdot 10^{-2} a48=+0.20007956±2.4102a_{48}= +0.20007956 \pm 2.4 \cdot 10^{-2}
a49=+2.74346646±3.1102a_{49}= +2.74346646 \pm 3.1 \cdot 10^{-2} a50=0.95854074±9.1103a_{50}= -0.95854074 \pm 9.1 \cdot 10^{-3} a51=0.20985879±1.5102a_{51}= -0.20985879 \pm 1.5 \cdot 10^{-2}
a52=+0.15525131±1.8102a_{52}= +0.15525131 \pm 1.8 \cdot 10^{-2} a53=+0.06021017±1.8102a_{53}= +0.06021017 \pm 1.8 \cdot 10^{-2} a54=0.30126283±1.6102a_{54}= -0.30126283 \pm 1.6 \cdot 10^{-2}
a55=0.34729291±1.4102a_{55}= -0.34729291 \pm 1.4 \cdot 10^{-2} a56=1.36445780±1.7102a_{56}= -1.36445780 \pm 1.7 \cdot 10^{-2} a57=+0.46138492±1.2102a_{57}= +0.46138492 \pm 1.2 \cdot 10^{-2}
a58=+1.18425147±1.7102a_{58}= +1.18425147 \pm 1.7 \cdot 10^{-2} a59=+0.09877301±2.8102a_{59}= +0.09877301 \pm 2.8 \cdot 10^{-2} a60=0.52142323±5.2102a_{60}= -0.52142323 \pm 5.2 \cdot 10^{-2}

Displaying ana_n with nn up to: 60 180 1000