Properties

Level $3$
Weight $0$
Character 3.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 3 \)
Weight: \( 0 \)
Character: 3.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 19.871635671 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.248752433\) \(a_{3}=+0.577350269\) \(a_{4}=+0.559382640\) \(a_{5}=-0.354363697\)
\(a_{6}=+0.720967554\) \(a_{7}=-0.928739859\) \(a_{8}=-0.550222001\) \(a_{9}=+0.333333333\) \(a_{10}=-0.442512528\)
\(a_{11}=-0.268633364\) \(a_{12}=+0.322959718\) \(a_{13}=-1.523250281\) \(a_{14}=-1.159766158\) \(a_{15}=-0.204591976\)
\(a_{16}=-1.246473702\) \(a_{17}=-0.608790843\) \(a_{18}=+0.416250811\) \(a_{19}=+1.763630830\) \(a_{20}=-0.198224900\)
\(a_{21}=-0.536208207\) \(a_{22}=-0.335456567\) \(a_{23}=+0.523162563\) \(a_{24}=-0.317670820\) \(a_{25}=-0.874426371\)
\(a_{26}=-1.902162495\) \(a_{27}=+0.192450090\) \(a_{28}=-0.519520954\) \(a_{29}=-1.149126454\) \(a_{30}=-0.255484727\)
\(a_{31}=+0.455103486\) \(a_{32}=-1.006315068\) \(a_{33}=-0.155095545\) \(a_{34}=-0.760229047\) \(a_{35}=+0.329111689\)
\(a_{36}=+0.186460880\) \(a_{37}=-1.714226696\) \(a_{38}=+2.202338291\) \(a_{39}=-0.879448960\) \(a_{40}=+0.194978702\)
\(a_{41}=+0.176605137\) \(a_{42}=-0.669591304\) \(a_{43}=-0.506931652\) \(a_{44}=-0.150268840\) \(a_{45}=-0.118121232\)
\(a_{46}=+0.653300523\) \(a_{47}=+1.789751835\) \(a_{48}=-0.719651927\) \(a_{49}=-0.137442275\) \(a_{50}=-1.091942058\)
\(a_{51}=-0.351485557\) \(a_{52}=-0.852079763\) \(a_{53}=+1.280825127\) \(a_{54}=+0.240322518\) \(a_{55}=+0.095193912\)
\(a_{56}=+0.511013103\) \(a_{57}=+1.018232735\) \(a_{58}=-1.434974456\) \(a_{59}=-0.515874930\) \(a_{60}=-0.114445199\)
\(a_{61}=-0.081663688\) \(a_{62}=+0.568311586\) \(a_{63}=-0.309579953\) \(a_{64}=-0.010164688\) \(a_{65}=+0.539784600\)
\(a_{66}=-0.193675939\) \(a_{67}=+0.012039186\) \(a_{68}=-0.340547029\) \(a_{69}=+0.302048046\) \(a_{70}=+0.410979023\)
\(a_{71}=+0.151682750\) \(a_{72}=-0.183407334\) \(a_{73}=+0.835969328\) \(a_{74}=-2.140644758\) \(a_{75}=-0.504850300\)
\(a_{76}=+0.986544470\) \(a_{77}=+0.249490512\) \(a_{78}=-1.098214029\) \(a_{79}=+1.369034491\) \(a_{80}=+0.441705029\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.220536095\) \(a_{83}=-0.108979619\) \(a_{84}=-0.299945562\) \(a_{85}=+0.215733374\)
\(a_{86}=-0.633032133\) \(a_{87}=-0.663448468\) \(a_{88}=+0.147807987\) \(a_{89}=-1.245526661\) \(a_{90}=-0.147504176\)
\(a_{91}=+1.414703250\) \(a_{92}=+0.292648055\) \(a_{93}=+0.262754120\) \(a_{94}=+2.234956960\) \(a_{95}=-0.624966740\)
\(a_{96}=-0.580996275\) \(a_{97}=-1.204266926\) \(a_{98}=-0.171631376\) \(a_{99}=-0.089544455\) \(a_{100}=-0.489138931\)

Showing 100 of 1228 available coefficients

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