Properties

Level $3$
Weight $0$
Character 3.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 28.2155159278 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.608977536\) \(a_{3}=-0.577350269\) \(a_{4}=+1.588808711\) \(a_{5}=+0.175527861\)
\(a_{6}=-0.928943614\) \(a_{7}=-1.041360282\) \(a_{8}=+0.947379990\) \(a_{9}=+0.333333333\) \(a_{10}=+0.282420385\)
\(a_{11}=+1.786147348\) \(a_{12}=-0.917299137\) \(a_{13}=-0.795014952\) \(a_{14}=-1.675525301\) \(a_{15}=-0.101341058\)
\(a_{16}=-0.064495590\) \(a_{17}=-0.928665352\) \(a_{18}=+0.536325845\) \(a_{19}=-0.406746794\) \(a_{20}=+0.278880194\)
\(a_{21}=+0.601229639\) \(a_{22}=+2.873870959\) \(a_{23}=-0.644810698\) \(a_{24}=-0.546970092\) \(a_{25}=-0.969189970\)
\(a_{26}=-1.279161199\) \(a_{27}=-0.192450090\) \(a_{28}=-1.654522288\) \(a_{29}=-1.365562072\) \(a_{30}=-0.163055485\)
\(a_{31}=+1.585869261\) \(a_{32}=-1.051151945\) \(a_{33}=-1.031232652\) \(a_{34}=-1.494201690\) \(a_{35}=-0.182787743\)
\(a_{36}=+0.529602904\) \(a_{37}=-0.614531257\) \(a_{38}=-0.654446454\) \(a_{39}=+0.459002097\) \(a_{40}=+0.166291583\)
\(a_{41}=+0.498678515\) \(a_{42}=+0.967364984\) \(a_{43}=-1.431558199\) \(a_{44}=+2.837846466\) \(a_{45}=+0.058509287\)
\(a_{46}=-1.037485928\) \(a_{47}=+0.146786935\) \(a_{48}=+0.037236546\) \(a_{49}=+0.084431238\) \(a_{50}=-1.559404890\)
\(a_{51}=+0.536165191\) \(a_{52}=-1.263126681\) \(a_{53}=-0.878971035\) \(a_{54}=-0.309647871\) \(a_{55}=+0.313518623\)
\(a_{56}=-0.986563893\) \(a_{57}=+0.234835371\) \(a_{58}=-2.197158698\) \(a_{59}=-1.585877234\) \(a_{60}=-0.161011555\)
\(a_{61}=-0.317758044\) \(a_{62}=+2.551628016\) \(a_{63}=-0.347120094\) \(a_{64}=-1.626784277\) \(a_{65}=-0.139547274\)
\(a_{66}=-1.659230172\) \(a_{67}=+0.974702608\) \(a_{68}=-1.475471601\) \(a_{69}=+0.372281630\) \(a_{70}=-0.294101372\)
\(a_{71}=+1.430736081\) \(a_{72}=+0.315793330\) \(a_{73}=+0.054447793\) \(a_{74}=-0.988766988\) \(a_{75}=+0.559562090\)
\(a_{76}=-0.646242849\) \(a_{77}=-1.860022907\) \(a_{78}=+0.738524062\) \(a_{79}=+0.770134891\) \(a_{80}=-0.011320773\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.802362529\) \(a_{83}=-0.819118304\) \(a_{84}=+0.955238888\) \(a_{85}=-0.163006643\)
\(a_{86}=-2.303344984\) \(a_{87}=+0.788407630\) \(a_{88}=+1.692160256\) \(a_{89}=-1.003081402\) \(a_{90}=+0.094140128\)
\(a_{91}=+0.827896995\) \(a_{92}=-1.024480854\) \(a_{93}=-0.915602045\) \(a_{94}=+0.236176881\) \(a_{95}=-0.071395395\)
\(a_{96}=+0.606882858\) \(a_{97}=+1.013599555\) \(a_{98}=+0.135847965\) \(a_{99}=+0.595382449\) \(a_{100}=-1.539857468\)

Showing 100 of 1228 available coefficients

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