Properties

Level $19$
Weight $0$
Character 19.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 4.9279077757 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.881662236\) \(a_{3}=-1.219871639\) \(a_{4}=+2.540652769\) \(a_{5}=+1.367185773\)
\(a_{6}=-2.295386394\) \(a_{7}=+0.750375183\) \(a_{8}=+2.898988133\) \(a_{9}=+0.488086815\) \(a_{10}=+2.572581837\)
\(a_{11}=-0.325904197\) \(a_{12}=-3.099270256\) \(a_{13}=+0.192470128\) \(a_{14}=+1.411952644\) \(a_{15}=-1.667791149\)
\(a_{16}=+2.914263722\) \(a_{17}=-1.530990649\) \(a_{18}=+0.918414527\) \(a_{19}=+0.229415734\) \(a_{20}=+3.473544318\)
\(a_{21}=-0.915361404\) \(a_{22}=-0.613241621\) \(a_{23}=-0.409674866\) \(a_{24}=-3.536393403\) \(a_{25}=+0.869196937\)
\(a_{26}=+0.362163770\) \(a_{27}=+0.624468376\) \(a_{28}=+1.906442786\) \(a_{29}=-1.379413183\) \(a_{30}=-3.138219621\)
\(a_{31}=+1.239041092\) \(a_{32}=+2.584671857\) \(a_{33}=+0.397561287\) \(a_{34}=-2.880807288\) \(a_{35}=+1.025902274\)
\(a_{36}=+1.240059117\) \(a_{37}=-1.111390323\) \(a_{38}=+0.431682923\) \(a_{39}=-0.234788850\) \(a_{40}=+3.963455330\)
\(a_{41}=-0.078351469\) \(a_{42}=-1.722400986\) \(a_{43}=-0.939551536\) \(a_{44}=-0.828009402\) \(a_{45}=+0.667305349\)
\(a_{46}=-0.770869724\) \(a_{47}=+0.205607466\) \(a_{48}=-3.555027661\) \(a_{49}=-0.436937085\) \(a_{50}=+1.635535052\)
\(a_{51}=+1.867612072\) \(a_{52}=+0.488999762\) \(a_{53}=+0.461356910\) \(a_{54}=+1.175038561\) \(a_{55}=-0.445571582\)
\(a_{56}=+2.175328750\) \(a_{57}=-0.279857747\) \(a_{58}=-2.595589693\) \(a_{59}=-0.483955418\) \(a_{60}=-4.237278200\)
\(a_{61}=-0.654707300\) \(a_{62}=+2.331456831\) \(a_{63}=+0.366248233\) \(a_{64}=+1.949215702\) \(a_{65}=+0.263142420\)
\(a_{66}=+0.748076061\) \(a_{67}=+1.248989761\) \(a_{68}=-3.889715632\) \(a_{69}=+0.499750750\) \(a_{70}=+1.930401567\)
\(a_{71}=+0.266481720\) \(a_{72}=+1.414957883\) \(a_{73}=+0.453571912\) \(a_{74}=-2.091261199\) \(a_{75}=-1.060308692\)
\(a_{76}=+0.582865719\) \(a_{77}=-0.244550422\) \(a_{78}=-0.441793312\) \(a_{79}=+0.484876483\) \(a_{80}=+3.984339898\)
\(a_{81}=-1.249858076\) \(a_{82}=-0.147431001\) \(a_{83}=+0.730342711\) \(a_{84}=-2.325615485\) \(a_{85}=-2.093148634\)
\(a_{86}=-1.767918644\) \(a_{87}=+1.682707020\) \(a_{88}=-0.944792401\) \(a_{89}=+0.971211304\) \(a_{90}=+1.255643274\)
\(a_{91}=+0.144424807\) \(a_{92}=-1.040841582\) \(a_{93}=-1.511471087\) \(a_{94}=+0.386883803\) \(a_{95}=+0.313653927\)
\(a_{96}=-3.152967893\) \(a_{97}=+0.709745300\) \(a_{98}=-0.822168012\) \(a_{99}=-0.159069542\) \(a_{100}=+2.208327605\)

Showing 100 of 546 available coefficients

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