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: \( 5.65655773047 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.780568462\) \(a_{3}=-0.091718122\) \(a_{4}=-0.390712877\) \(a_{5}=-1.842497083\)
\(a_{6}=+0.071592274\) \(a_{7}=-1.027422503\) \(a_{8}=+1.085546611\) \(a_{9}=-0.991587786\) \(a_{10}=+1.438195114\)
\(a_{11}=+0.581812218\) \(a_{12}=+0.035835451\) \(a_{13}=-0.319152366\) \(a_{14}=+0.801973603\) \(a_{15}=+0.168990373\)
\(a_{16}=-0.456630571\) \(a_{17}=+0.257405662\) \(a_{18}=+0.774002153\) \(a_{19}=+0.229415734\) \(a_{20}=+0.719887336\)
\(a_{21}=+0.094233263\) \(a_{22}=-0.454144268\) \(a_{23}=-1.070528576\) \(a_{24}=-0.099564297\) \(a_{25}=+2.394795502\)
\(a_{26}=+0.249120271\) \(a_{27}=+0.182664692\) \(a_{28}=+0.401427202\) \(a_{29}=-1.423530861\) \(a_{30}=-0.131908555\)
\(a_{31}=-1.092636148\) \(a_{32}=-0.729115188\) \(a_{33}=-0.053362724\) \(a_{34}=-0.200922742\) \(a_{35}=+1.893022966\)
\(a_{36}=+0.387426116\) \(a_{37}=-0.268366841\) \(a_{38}=-0.179074686\) \(a_{39}=+0.029272056\) \(a_{40}=-2.000116464\)
\(a_{41}=+1.599810968\) \(a_{42}=-0.073555513\) \(a_{43}=+0.938922647\) \(a_{44}=-0.227321525\) \(a_{45}=+1.826997604\)
\(a_{46}=+0.835620844\) \(a_{47}=-1.030136331\) \(a_{48}=+0.041881299\) \(a_{49}=+0.055597000\) \(a_{50}=-1.869301841\)
\(a_{51}=-0.023608764\) \(a_{52}=+0.124696939\) \(a_{53}=+0.169687696\) \(a_{54}=-0.142582298\) \(a_{55}=-1.071987315\)
\(a_{56}=-1.115315016\) \(a_{57}=-0.021041580\) \(a_{58}=+1.111163294\) \(a_{59}=-1.099692856\) \(a_{60}=-0.066026715\)
\(a_{61}=-0.523716219\) \(a_{62}=+0.852877317\) \(a_{63}=+1.018779605\) \(a_{64}=+1.025754892\) \(a_{65}=+0.588037304\)
\(a_{66}=+0.041653259\) \(a_{67}=+0.701969097\) \(a_{68}=-0.100571707\) \(a_{69}=+0.098186871\) \(a_{70}=-1.477634024\)
\(a_{71}=+0.263870538\) \(a_{72}=-1.076414760\) \(a_{73}=+1.450928531\) \(a_{74}=+0.209478692\) \(a_{75}=-0.219646146\)
\(a_{76}=-0.089635681\) \(a_{77}=-0.597766966\) \(a_{78}=-0.022848843\) \(a_{79}=+0.928588668\) \(a_{80}=+0.841340496\)
\(a_{81}=+0.974834124\) \(a_{82}=-1.248761987\) \(a_{83}=-1.390365156\) \(a_{84}=-0.036818149\) \(a_{85}=-0.474269182\)
\(a_{86}=-0.732893407\) \(a_{87}=+0.130563577\) \(a_{88}=+0.631584281\) \(a_{89}=-0.596886559\) \(a_{90}=-1.426096709\)
\(a_{91}=+0.327904323\) \(a_{92}=+0.418269299\) \(a_{93}=+0.100214536\) \(a_{94}=+0.804091931\) \(a_{95}=-0.422697821\)
\(a_{96}=+0.066873076\) \(a_{97}=+1.566082700\) \(a_{98}=-0.043397265\) \(a_{99}=-0.576917889\) \(a_{100}=-0.935677440\)

Showing 100 of 546 available coefficients

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