Properties

Level $10$
Weight $0$
Character 10.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 31.9163478766 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-1.082237434\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.765257428\) \(a_{7}=-1.009281822\) \(a_{8}=-0.353553391\) \(a_{9}=+0.171237863\) \(a_{10}=-0.316227766\)
\(a_{11}=+1.676917849\) \(a_{12}=-0.541118717\) \(a_{13}=-0.593511074\) \(a_{14}=+0.713670021\) \(a_{15}=-0.483991294\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.012441677\) \(a_{18}=-0.121083454\) \(a_{19}=-0.001798220\) \(a_{20}=+0.223606798\)
\(a_{21}=+1.092282570\) \(a_{22}=-1.185759983\) \(a_{23}=+0.582231036\) \(a_{24}=+0.382628714\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.419675705\) \(a_{27}=+0.896917408\) \(a_{28}=-0.504640911\) \(a_{29}=-0.406883521\) \(a_{30}=+0.342233526\)
\(a_{31}=-0.578588579\) \(a_{32}=-0.176776695\) \(a_{33}=-1.814823270\) \(a_{34}=+0.715904375\) \(a_{35}=-0.451364553\)
\(a_{36}=+0.085618932\) \(a_{37}=-0.602773619\) \(a_{38}=+0.001271534\) \(a_{39}=+0.642319902\) \(a_{40}=-0.158113883\)
\(a_{41}=-0.279568441\) \(a_{42}=-0.772360412\) \(a_{43}=+1.608825334\) \(a_{44}=+0.838458925\) \(a_{45}=+0.076579901\)
\(a_{46}=-0.411699514\) \(a_{47}=+0.544546506\) \(a_{48}=-0.270559358\) \(a_{49}=+0.018649797\) \(a_{50}=-0.141421356\)
\(a_{51}=+1.095702283\) \(a_{52}=-0.296755537\) \(a_{53}=-0.625604364\) \(a_{54}=-0.634216381\) \(a_{55}=+0.749940461\)
\(a_{56}=+0.356835010\) \(a_{57}=+0.001946101\) \(a_{58}=+0.287710097\) \(a_{59}=+1.013272472\) \(a_{60}=-0.241995647\)
\(a_{61}=+0.872054851\) \(a_{62}=+0.409123908\) \(a_{63}=-0.172827263\) \(a_{64}=+0.125000000\) \(a_{65}=-0.265426221\)
\(a_{66}=+1.283273841\) \(a_{67}=+0.601110248\) \(a_{68}=-0.506220839\) \(a_{69}=-0.630112223\) \(a_{70}=+0.319162936\)
\(a_{71}=+0.950517531\) \(a_{72}=-0.060541727\) \(a_{73}=-0.561200314\) \(a_{74}=+0.426225314\) \(a_{75}=-0.216447487\)
\(a_{76}=-0.000899110\) \(a_{77}=-1.692482703\) \(a_{78}=-0.454188758\) \(a_{79}=-1.499545626\) \(a_{80}=+0.111803399\)
\(a_{81}=-1.141915458\) \(a_{82}=+0.197684740\) \(a_{83}=-1.506787465\) \(a_{84}=+0.546141285\) \(a_{85}=-0.452777683\)
\(a_{86}=-1.137611303\) \(a_{87}=+0.440344578\) \(a_{88}=-0.592879991\) \(a_{89}=+1.723573370\) \(a_{90}=-0.054150167\)
\(a_{91}=+0.599019938\) \(a_{92}=+0.291115518\) \(a_{93}=+0.626170219\) \(a_{94}=-0.385052527\) \(a_{95}=-0.000804189\)
\(a_{96}=+0.191314357\) \(a_{97}=-1.734080067\) \(a_{98}=-0.013187398\) \(a_{99}=+0.287151830\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

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