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: \( 2.61034478629 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.712480064\) \(a_{3}=+1.292853764\) \(a_{4}=-0.492372158\) \(a_{5}=+0.779633138\)
\(a_{6}=+0.921132533\) \(a_{7}=-1.567473625\) \(a_{8}=-1.063285411\) \(a_{9}=+0.671470856\) \(a_{10}=+0.555473069\)
\(a_{11}=+1.376315943\) \(a_{12}=-0.636565198\) \(a_{13}=+0.465292731\) \(a_{14}=-1.116793709\) \(a_{15}=+1.007951638\)
\(a_{16}=-0.265197500\) \(a_{17}=-0.025275956\) \(a_{18}=+0.478409599\) \(a_{19}=+0.229415734\) \(a_{20}=-0.383869651\)
\(a_{21}=-2.026514174\) \(a_{22}=+0.980597668\) \(a_{23}=+0.355035661\) \(a_{24}=-1.374672545\) \(a_{25}=-0.392172174\)
\(a_{26}=+0.331511803\) \(a_{27}=-0.424740155\) \(a_{28}=+0.771780381\) \(a_{29}=+0.840064476\) \(a_{30}=+0.718145423\)
\(a_{31}=-0.050817207\) \(a_{32}=+0.874337433\) \(a_{33}=+1.779375282\) \(a_{34}=-0.018008581\) \(a_{35}=-1.222054386\)
\(a_{36}=-0.330613558\) \(a_{37}=-1.707940339\) \(a_{38}=+0.163454149\) \(a_{39}=+0.601555464\) \(a_{40}=-0.828972559\)
\(a_{41}=-0.193744836\) \(a_{42}=-1.443850943\) \(a_{43}=+1.280964765\) \(a_{44}=-0.677659659\) \(a_{45}=+0.523500887\)
\(a_{46}=+0.252955832\) \(a_{47}=-0.211741389\) \(a_{48}=-0.342861530\) \(a_{49}=+1.456973480\) \(a_{50}=-0.279414859\)
\(a_{51}=-0.032678091\) \(a_{52}=-0.229097137\) \(a_{53}=-1.356616716\) \(a_{54}=-0.302618929\) \(a_{55}=+1.073021450\)
\(a_{56}=+1.666671834\) \(a_{57}=+0.296600927\) \(a_{58}=+0.598529108\) \(a_{59}=-0.566132172\) \(a_{60}=-0.496287211\)
\(a_{61}=-1.391103643\) \(a_{62}=-0.036206318\) \(a_{63}=-1.052512890\) \(a_{64}=+0.888145502\) \(a_{65}=+0.362757739\)
\(a_{66}=+1.267769434\) \(a_{67}=+1.248986694\) \(a_{68}=+0.012445218\) \(a_{69}=+0.459009138\) \(a_{70}=-0.870689397\)
\(a_{71}=+0.510724512\) \(a_{72}=-0.713965237\) \(a_{73}=+0.754279713\) \(a_{74}=-1.216873446\) \(a_{75}=-0.507021350\)
\(a_{76}=-0.112957821\) \(a_{77}=-2.157338899\) \(a_{78}=+0.428596237\) \(a_{79}=+0.307532497\) \(a_{80}=-0.206756739\)
\(a_{81}=-1.220597690\) \(a_{82}=-0.138039295\) \(a_{83}=-0.161430059\) \(a_{84}=+0.997799167\) \(a_{85}=-0.019705942\)
\(a_{86}=+0.912661868\) \(a_{87}=+1.086080469\) \(a_{88}=-1.463416759\) \(a_{89}=+1.162135952\) \(a_{90}=+0.372984019\)
\(a_{91}=-0.729334048\) \(a_{92}=-0.174809609\) \(a_{93}=-0.065699321\) \(a_{94}=-0.150861582\) \(a_{95}=+0.178860089\)
\(a_{96}=+1.130390582\) \(a_{97}=-0.527949165\) \(a_{98}=+1.038064607\) \(a_{99}=+0.924156045\) \(a_{100}=+0.193094684\)

Showing 100 of 1500 available coefficients

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