Properties

Level $19$
Weight $0$
Character 19.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 19 \)
Weight: \( 0 \)
Character: 19.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 2.81665576076 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.557239940\) \(a_{3}=-0.646669399\) \(a_{4}=+1.424996232\) \(a_{5}=+1.049917827\)
\(a_{6}=-1.007019417\) \(a_{7}=-0.254770063\) \(a_{8}=+0.661821107\) \(a_{9}=-0.581818687\) \(a_{10}=+1.634973974\)
\(a_{11}=+1.304890079\) \(a_{12}=-0.921501458\) \(a_{13}=-1.622414563\) \(a_{14}=-0.396738118\) \(a_{15}=-0.678949731\)
\(a_{16}=-0.394381970\) \(a_{17}=+1.381840888\) \(a_{18}=-0.906031298\) \(a_{19}=-0.229415733\) \(a_{20}=+1.496128947\)
\(a_{21}=+0.164752004\) \(a_{22}=+2.032026948\) \(a_{23}=+0.431377251\) \(a_{24}=-0.427979456\) \(a_{25}=+0.102327443\)
\(a_{26}=-2.526488757\) \(a_{27}=+1.022913742\) \(a_{28}=-0.363046384\) \(a_{29}=-0.341668604\) \(a_{30}=-1.057287643\)
\(a_{31}=+0.824168379\) \(a_{32}=-1.275968460\) \(a_{33}=-0.843832494\) \(a_{34}=+2.151857841\) \(a_{35}=-0.267487646\)
\(a_{36}=-0.829089444\) \(a_{37}=+0.092497645\) \(a_{38}=-0.357255376\) \(a_{39}=+1.049165849\) \(a_{40}=+0.694857779\)
\(a_{41}=+0.010064416\) \(a_{42}=+0.256558398\) \(a_{43}=-0.714163266\) \(a_{44}=+1.859463440\) \(a_{45}=-0.610861816\)
\(a_{46}=+0.671757889\) \(a_{47}=+0.461103040\) \(a_{48}=+0.255034765\) \(a_{49}=-0.935092236\) \(a_{50}=+0.159348378\)
\(a_{51}=-0.893594197\) \(a_{52}=-2.311934636\) \(a_{53}=-1.518577215\) \(a_{54}=+1.592922141\) \(a_{55}=+1.370027346\)
\(a_{56}=-0.168612202\) \(a_{57}=+0.148356172\) \(a_{58}=-0.532060043\) \(a_{59}=+1.652839206\) \(a_{60}=-0.967500844\)
\(a_{61}=+0.780399500\) \(a_{62}=+1.283427934\) \(a_{63}=+0.148229963\) \(a_{64}=-1.592607069\) \(a_{65}=-1.703401958\)
\(a_{66}=-1.314049636\) \(a_{67}=-0.014290507\) \(a_{68}=+1.969118067\) \(a_{69}=-0.278958479\) \(a_{70}=-0.416542406\)
\(a_{71}=-0.039171796\) \(a_{72}=-0.385059966\) \(a_{73}=+1.113322635\) \(a_{74}=+0.144040967\) \(a_{75}=-0.066172010\)
\(a_{76}=-0.326916585\) \(a_{77}=-0.332446899\) \(a_{78}=+1.633802956\) \(a_{79}=+0.312822779\) \(a_{80}=-0.414068679\)
\(a_{81}=-0.079668364\) \(a_{82}=+0.015672763\) \(a_{83}=+0.365572454\) \(a_{84}=+0.234770989\) \(a_{85}=+1.450819399\)
\(a_{86}=-1.112123669\) \(a_{87}=+0.220946670\) \(a_{88}=+0.863603760\) \(a_{89}=-0.870650460\) \(a_{90}=-0.951258372\)
\(a_{91}=+0.413342661\) \(a_{92}=+0.614711016\) \(a_{93}=-0.532964497\) \(a_{94}=+0.718048045\) \(a_{95}=-0.240867693\)
\(a_{96}=+0.825129699\) \(a_{97}=-1.519795900\) \(a_{98}=-1.456162956\) \(a_{99}=-0.759209403\) \(a_{100}=+0.145816140\)

Showing 100 of 1500 available coefficients

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