Properties

Level $293$
Weight $0$
Character 293.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 293 \)
Weight: \( 0 \)
Character: 293.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 0.743184828643 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.160011255\) \(a_{3}=-1.810788909\) \(a_{4}=-0.974396406\) \(a_{5}=-0.800050971\)
\(a_{6}=-0.289746615\) \(a_{7}=-0.963648957\) \(a_{8}=-0.315925642\) \(a_{9}=+2.278956472\) \(a_{10}=-0.128017157\)
\(a_{11}=+1.232003668\) \(a_{12}=+1.764426193\) \(a_{13}=-1.996565706\) \(a_{14}=-0.154194676\) \(a_{15}=+1.448723411\)
\(a_{16}=+0.923844741\) \(a_{17}=+0.403144590\) \(a_{18}=+0.364658698\) \(a_{19}=-0.678050447\) \(a_{20}=+0.779566789\)
\(a_{21}=+1.744964851\) \(a_{22}=+0.197134454\) \(a_{23}=+0.599182942\) \(a_{24}=+0.572074655\) \(a_{25}=-0.359918429\)
\(a_{26}=-0.319472995\) \(a_{27}=-2.315920203\) \(a_{28}=+0.938976082\) \(a_{29}=-1.527089541\) \(a_{30}=+0.231812047\)
\(a_{31}=-0.178907819\) \(a_{32}=+0.463751196\) \(a_{33}=-2.230898582\) \(a_{34}=+0.064507670\) \(a_{35}=+0.770968274\)
\(a_{36}=-2.220606968\) \(a_{37}=+0.714926774\) \(a_{38}=-0.108495706\) \(a_{39}=+3.615359042\) \(a_{40}=+0.252756601\)
\(a_{41}=-0.797879422\) \(a_{42}=+0.279214028\) \(a_{43}=+0.828974823\) \(a_{44}=-1.200459941\) \(a_{45}=-1.823281312\)
\(a_{46}=+0.095876028\) \(a_{47}=+0.428818316\) \(a_{48}=-1.672887793\) \(a_{49}=-0.071380665\) \(a_{50}=-0.057591020\)
\(a_{51}=-0.730009735\) \(a_{52}=+1.945446411\) \(a_{53}=-0.369096719\) \(a_{54}=-0.370573315\) \(a_{55}=-0.985665721\)
\(a_{56}=+0.304441453\) \(a_{57}=+1.227806240\) \(a_{58}=-0.244351538\) \(a_{59}=-0.519709679\) \(a_{60}=-1.411630891\)
\(a_{61}=+0.338245762\) \(a_{62}=-0.028627254\) \(a_{63}=-2.196114052\) \(a_{64}=-0.849639334\) \(a_{65}=+1.597354326\)
\(a_{66}=-0.356968868\) \(a_{67}=-0.970223074\) \(a_{68}=-0.392822634\) \(a_{69}=-1.084993875\) \(a_{70}=+0.123363624\)
\(a_{71}=+1.621395813\) \(a_{72}=-0.719980844\) \(a_{73}=+0.128063296\) \(a_{74}=+0.114396357\) \(a_{75}=+0.651736311\)
\(a_{76}=+0.660689948\) \(a_{77}=-1.187219058\) \(a_{78}=+0.578498149\) \(a_{79}=+0.885224918\) \(a_{80}=-0.739122883\)
\(a_{81}=+1.914686162\) \(a_{82}=-0.127669677\) \(a_{83}=-0.524457118\) \(a_{84}=-1.700287464\) \(a_{85}=-0.322536194\)
\(a_{86}=+0.132645294\) \(a_{87}=+2.765236813\) \(a_{88}=-0.389221546\) \(a_{89}=-0.786549087\) \(a_{90}=-0.291745523\)
\(a_{91}=+1.923988433\) \(a_{92}=-0.583841703\) \(a_{93}=+0.323964289\) \(a_{94}=+0.068615785\) \(a_{95}=+0.542474895\)
\(a_{96}=-0.839755497\) \(a_{97}=+1.214175776\) \(a_{98}=-0.011421713\) \(a_{99}=+2.807682758\) \(a_{100}=+0.350703187\)

Showing 100 of 918 available coefficients

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