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: \( 19.7518011761 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.176346587\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-0.124695868\) \(a_{7}=-1.867394080\) \(a_{8}=+0.353553391\) \(a_{9}=-0.968901881\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.638315826\) \(a_{12}=-0.088173294\) \(a_{13}=-0.914754632\) \(a_{14}=-1.320447017\) \(a_{15}=+0.078864591\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.923722900\) \(a_{18}=-0.685117090\) \(a_{19}=+0.067455266\) \(a_{20}=-0.223606798\)
\(a_{21}=+0.329308573\) \(a_{22}=-0.451357449\) \(a_{23}=+1.688635832\) \(a_{24}=-0.062347934\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.646829203\) \(a_{27}=+0.347209128\) \(a_{28}=-0.933697040\) \(a_{29}=+0.745850486\) \(a_{30}=+0.055765687\)
\(a_{31}=-0.868893034\) \(a_{32}=+0.176776695\) \(a_{33}=+0.112564818\) \(a_{34}=-0.653170726\) \(a_{35}=+0.835124021\)
\(a_{36}=-0.484450941\) \(a_{37}=+0.120453237\) \(a_{38}=+0.047698076\) \(a_{39}=+0.161313858\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.584524156\) \(a_{42}=+0.232856325\) \(a_{43}=-1.120776485\) \(a_{44}=-0.319157913\) \(a_{45}=+0.433306094\)
\(a_{46}=+1.194045848\) \(a_{47}=+0.691784458\) \(a_{48}=-0.044086647\) \(a_{49}=+2.487160649\) \(a_{50}=+0.141421356\)
\(a_{51}=+0.162895381\) \(a_{52}=-0.457377316\) \(a_{53}=-0.106515967\) \(a_{54}=+0.245513929\) \(a_{55}=+0.285463515\)
\(a_{56}=-0.660223508\) \(a_{57}=-0.011895506\) \(a_{58}=+0.527395936\) \(a_{59}=-0.518133521\) \(a_{60}=+0.039432296\)
\(a_{61}=-1.621748987\) \(a_{62}=-0.614400157\) \(a_{63}=+1.809321637\) \(a_{64}=+0.125000000\) \(a_{65}=+0.409090708\)
\(a_{66}=+0.079595346\) \(a_{67}=-1.915750656\) \(a_{68}=-0.461861450\) \(a_{69}=-0.297785166\) \(a_{70}=+0.590521858\)
\(a_{71}=-1.550361910\) \(a_{72}=-0.342558545\) \(a_{73}=+1.395070455\) \(a_{74}=+0.085173300\) \(a_{75}=-0.035269317\)
\(a_{76}=+0.033727633\) \(a_{77}=+1.191987194\) \(a_{78}=+0.114066123\) \(a_{79}=+1.067313984\) \(a_{80}=-0.111803399\)
\(a_{81}=+0.907672736\) \(a_{82}=+0.413320994\) \(a_{83}=+0.886461433\) \(a_{84}=+0.164654287\) \(a_{85}=+0.413101439\)
\(a_{86}=-0.792508653\) \(a_{87}=-0.131528188\) \(a_{88}=-0.225678724\) \(a_{89}=+0.282673598\) \(a_{90}=+0.306393677\)
\(a_{91}=+1.708207384\) \(a_{92}=+0.844317916\) \(a_{93}=+0.153226321\) \(a_{94}=+0.489165481\) \(a_{95}=-0.030166912\)
\(a_{96}=-0.031173967\) \(a_{97}=-0.936702777\) \(a_{98}=+1.758688161\) \(a_{99}=+0.618465404\) \(a_{100}=+0.099975586\)

Showing 100 of 192 available coefficients

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