Properties

Level $41$
Weight $0$
Character 41.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 41 \)
Weight: \( 0 \)
Character: 41.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 0.66572483212 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.719265108\) \(a_{3}=-1.407985466\) \(a_{4}=-0.482657707\) \(a_{5}=+0.550170239\)
\(a_{6}=+1.012714817\) \(a_{7}=-0.276631260\) \(a_{8}=+1.066423952\) \(a_{9}=+0.982423066\) \(a_{10}=-0.395718256\)
\(a_{11}=-0.287699414\) \(a_{12}=+0.679575036\) \(a_{13}=-0.811653814\) \(a_{14}=+0.198971217\) \(a_{15}=-0.774631702\)
\(a_{16}=-0.284383831\) \(a_{17}=+1.636040504\) \(a_{18}=-0.706622638\) \(a_{19}=-0.957094116\) \(a_{20}=-0.265543912\)
\(a_{21}=+0.389492816\) \(a_{22}=+0.206932133\) \(a_{23}=-0.474455839\) \(a_{24}=-1.501509411\) \(a_{25}=-0.697312734\)
\(a_{26}=+0.583794256\) \(a_{27}=+0.024748077\) \(a_{28}=+0.133518195\) \(a_{29}=+0.556844934\) \(a_{30}=+0.557165535\)
\(a_{31}=+1.491817444\) \(a_{32}=-0.861876532\) \(a_{33}=+0.405076526\) \(a_{34}=-1.176746830\) \(a_{35}=-0.152194262\)
\(a_{36}=-0.474174120\) \(a_{37}=+1.063777857\) \(a_{38}=+0.688404405\) \(a_{39}=+1.142796766\) \(a_{40}=+0.586714763\)
\(a_{41}=-0.156173840\) \(a_{42}=-0.280148493\) \(a_{43}=-0.222035106\) \(a_{44}=+0.138860370\) \(a_{45}=+0.540499913\)
\(a_{46}=+0.341259505\) \(a_{47}=-0.449021254\) \(a_{48}=+0.400408222\) \(a_{49}=-0.923475193\) \(a_{50}=+0.501552738\)
\(a_{51}=-2.303521285\) \(a_{52}=+0.391750942\) \(a_{53}=-1.042600308\) \(a_{54}=-0.017800414\) \(a_{55}=-0.158283703\)
\(a_{56}=-0.295006171\) \(a_{57}=+1.347574645\) \(a_{58}=-0.400519145\) \(a_{59}=+0.403883604\) \(a_{60}=+0.373882039\)
\(a_{61}=-0.304907169\) \(a_{62}=-1.073012305\) \(a_{63}=-0.271768906\) \(a_{64}=+0.904301652\) \(a_{65}=-0.446547783\)
\(a_{66}=-0.291357477\) \(a_{67}=+0.607720358\) \(a_{68}=-0.789647544\) \(a_{69}=+0.668026864\) \(a_{70}=+0.109468073\)
\(a_{71}=+0.198113907\) \(a_{72}=+1.047679467\) \(a_{73}=-0.893960461\) \(a_{74}=-0.765138240\) \(a_{75}=+0.981806191\)
\(a_{76}=+0.461948794\) \(a_{77}=+0.079586641\) \(a_{78}=-0.821973896\) \(a_{79}=-0.616934506\) \(a_{80}=-0.156459525\)
\(a_{81}=-1.017267987\) \(a_{82}=+0.112330361\) \(a_{83}=+1.229220143\) \(a_{84}=-0.187991654\) \(a_{85}=+0.900100751\)
\(a_{86}=+0.159702080\) \(a_{87}=-0.784029533\) \(a_{88}=-0.306809530\) \(a_{89}=+1.504720905\) \(a_{90}=-0.388762733\)
\(a_{91}=+0.224528799\) \(a_{92}=+0.228999777\) \(a_{93}=-2.100457277\) \(a_{94}=+0.322965311\) \(a_{95}=-0.526564708\)
\(a_{96}=+1.213509701\) \(a_{97}=+0.584082228\) \(a_{98}=+0.664223447\) \(a_{99}=-0.282642539\) \(a_{100}=+0.336563328\)

Showing 100 of 1500 available coefficients

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