Properties

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

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 10 = 2 \cdot 5 \)
Weight: \( 0 \)
Character: 10.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 31.5872513035 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-1.905217540\) \(a_{4}=+0.500000000\) \(a_{5}=-0.447213595\)
\(a_{6}=-1.347192242\) \(a_{7}=-1.694297219\) \(a_{8}=+0.353553391\) \(a_{9}=+2.629853873\) \(a_{10}=-0.316227766\)
\(a_{11}=-0.627587154\) \(a_{12}=-0.952608770\) \(a_{13}=-0.888615765\) \(a_{14}=-1.198049053\) \(a_{15}=+0.852039186\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.705024174\) \(a_{18}=+1.859587507\) \(a_{19}=+0.933595036\) \(a_{20}=-0.223606798\)
\(a_{21}=+3.228004780\) \(a_{22}=-0.443771132\) \(a_{23}=+0.389155167\) \(a_{24}=-0.673596121\) \(a_{25}=+0.199951172\)
\(a_{26}=-0.628346233\) \(a_{27}=-3.105226187\) \(a_{28}=-0.847148610\) \(a_{29}=+0.150273524\) \(a_{30}=+0.602482686\)
\(a_{31}=-0.669682997\) \(a_{32}=+0.176776695\) \(a_{33}=+1.195690053\) \(a_{34}=-1.205634155\) \(a_{35}=+0.757712751\)
\(a_{36}=+1.314926937\) \(a_{37}=+0.105555443\) \(a_{38}=+0.660151381\) \(a_{39}=+1.693006341\) \(a_{40}=-0.158113883\)
\(a_{41}=+0.573195319\) \(a_{42}=+2.282544069\) \(a_{43}=-0.919532196\) \(a_{44}=-0.313793577\) \(a_{45}=-1.176106406\)
\(a_{46}=+0.275174258\) \(a_{47}=+0.915670802\) \(a_{48}=-0.476304385\) \(a_{49}=+1.870643067\) \(a_{50}=+0.141421356\)
\(a_{51}=+3.248441961\) \(a_{52}=-0.444307882\) \(a_{53}=+0.694519982\) \(a_{54}=-2.195726494\) \(a_{55}=+0.280665508\)
\(a_{56}=-0.599024527\) \(a_{57}=-1.778701638\) \(a_{58}=+0.106259428\) \(a_{59}=-0.591451241\) \(a_{60}=+0.426019593\)
\(a_{61}=+1.463641763\) \(a_{62}=-0.473537388\) \(a_{63}=-4.455754105\) \(a_{64}=+0.125000000\) \(a_{65}=+0.397401051\)
\(a_{66}=+0.845480545\) \(a_{67}=+1.685933640\) \(a_{68}=-0.852512087\) \(a_{69}=-0.741425251\) \(a_{70}=+0.535783825\)
\(a_{71}=+0.482482629\) \(a_{72}=+0.929793754\) \(a_{73}=+0.739425550\) \(a_{74}=+0.074638970\) \(a_{75}=-0.381043508\)
\(a_{76}=+0.466797518\) \(a_{77}=+1.063319169\) \(a_{78}=+1.197136264\) \(a_{79}=-0.824597581\) \(a_{80}=-0.111803399\)
\(a_{81}=+3.286277522\) \(a_{82}=+0.405310297\) \(a_{83}=-0.467809545\) \(a_{84}=+1.614002390\) \(a_{85}=+0.762509991\)
\(a_{86}=-0.650207452\) \(a_{87}=-0.286303754\) \(a_{88}=-0.221885566\) \(a_{89}=+0.682312509\) \(a_{90}=-0.831632815\)
\(a_{91}=+1.505579219\) \(a_{92}=+0.194577584\) \(a_{93}=+1.275891792\) \(a_{94}=+0.647477033\) \(a_{95}=-0.417516393\)
\(a_{96}=-0.336798060\) \(a_{97}=-0.205056842\) \(a_{98}=+1.322744398\) \(a_{99}=-1.650462507\) \(a_{100}=+0.099975586\)

Showing 100 of 250 available coefficients

Rows: Cols: