Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 27.1088850091 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.347960593\) \(a_{4}=+0.500000000\) \(a_{5}=+0.447213595\)
\(a_{6}=+0.246045295\) \(a_{7}=+0.251312302\) \(a_{8}=-0.353553391\) \(a_{9}=-0.878923426\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.489474086\) \(a_{12}=-0.173980296\) \(a_{13}=-0.654679628\) \(a_{14}=-0.177704633\) \(a_{15}=-0.155612708\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.447171202\) \(a_{18}=+0.621492715\) \(a_{19}=-1.819878228\) \(a_{20}=+0.223606798\)
\(a_{21}=-0.087446778\) \(a_{22}=+0.346110446\) \(a_{23}=-1.630616086\) \(a_{24}=+0.123022647\) \(a_{25}=+0.199951172\)
\(a_{26}=+0.462928404\) \(a_{27}=+0.653791309\) \(a_{28}=+0.125656151\) \(a_{29}=-1.473002546\) \(a_{30}=+0.110034801\)
\(a_{31}=+1.127894808\) \(a_{32}=-0.176776695\) \(a_{33}=+0.170317693\) \(a_{34}=+1.023304570\) \(a_{35}=+0.112390278\)
\(a_{36}=-0.439461713\) \(a_{37}=-1.444416332\) \(a_{38}=+1.286848236\) \(a_{39}=+0.227802711\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.411227107\) \(a_{42}=+0.061834209\) \(a_{43}=+1.366893373\) \(a_{44}=-0.244737043\) \(a_{45}=-0.393066505\)
\(a_{46}=+1.153019692\) \(a_{47}=+1.260231867\) \(a_{48}=-0.086990148\) \(a_{49}=-0.936842127\) \(a_{50}=-0.141421356\)
\(a_{51}=+0.503558549\) \(a_{52}=-0.327339814\) \(a_{53}=-1.496131709\) \(a_{54}=-0.462300268\) \(a_{55}=-0.218899466\)
\(a_{56}=-0.088852317\) \(a_{57}=+0.633245907\) \(a_{58}=+1.041570089\) \(a_{59}=-0.591656235\) \(a_{60}=-0.077806354\)
\(a_{61}=+1.418186111\) \(a_{62}=-0.797542067\) \(a_{63}=-0.220884270\) \(a_{64}=+0.125000000\) \(a_{65}=-0.292781630\)
\(a_{66}=-0.120432796\) \(a_{67}=-0.309781501\) \(a_{68}=-0.723585601\) \(a_{69}=+0.567390140\) \(a_{70}=-0.079471928\)
\(a_{71}=-0.205347934\) \(a_{72}=+0.310746357\) \(a_{73}=+0.567496191\) \(a_{74}=+1.021356583\) \(a_{75}=-0.069592119\)
\(a_{76}=-0.909939114\) \(a_{77}=-0.123010860\) \(a_{78}=-0.161080842\) \(a_{79}=-0.749282451\) \(a_{80}=+0.111803399\)
\(a_{81}=+0.651429815\) \(a_{82}=-0.290781476\) \(a_{83}=-0.665446632\) \(a_{84}=-0.043723389\) \(a_{85}=-0.647194636\)
\(a_{86}=-0.966539573\) \(a_{87}=+0.512546839\) \(a_{88}=+0.173055223\) \(a_{89}=-1.322823201\) \(a_{90}=+0.277939991\)
\(a_{91}=-0.164529045\) \(a_{92}=-0.815308043\) \(a_{93}=-0.392462946\) \(a_{94}=-0.891118499\) \(a_{95}=-0.813874286\)
\(a_{96}=+0.061511324\) \(a_{97}=-0.341846106\) \(a_{98}=+0.662447421\) \(a_{99}=+0.430210241\) \(a_{100}=+0.099975586\)

Showing 100 of 228 available coefficients

Rows: Cols: