Properties

Level $83$
Weight $0$
Character 83.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 83 \)
Weight: \( 0 \)
Character: 83.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 1.87589890769 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.774132166\) \(a_{3}=+1.665589597\) \(a_{4}=-0.400719390\) \(a_{5}=+0.416273130\)
\(a_{6}=+1.289386482\) \(a_{7}=+1.090198784\) \(a_{8}=-1.084341935\) \(a_{9}=+1.774188705\) \(a_{10}=+0.322250420\)
\(a_{11}=-1.520698036\) \(a_{12}=-0.667434047\) \(a_{13}=+0.298643450\) \(a_{14}=+0.843957946\) \(a_{15}=+0.693340195\)
\(a_{16}=-0.438704581\) \(a_{17}=+0.252163506\) \(a_{18}=+1.373456545\) \(a_{19}=-1.245261294\) \(a_{20}=-0.166808715\)
\(a_{21}=+1.815823754\) \(a_{22}=-1.177221264\) \(a_{23}=+0.945735152\) \(a_{24}=-1.806068646\) \(a_{25}=-0.826716681\)
\(a_{26}=+0.231189501\) \(a_{27}=+1.289480653\) \(a_{28}=-0.436863792\) \(a_{29}=-1.018643140\) \(a_{30}=+0.536736946\)
\(a_{31}=-0.765653208\) \(a_{32}=+0.744726608\) \(a_{33}=-2.532858829\) \(a_{34}=+0.195207881\) \(a_{35}=+0.453820460\)
\(a_{36}=-0.710951815\) \(a_{37}=+0.385304868\) \(a_{38}=-0.963996823\) \(a_{39}=+0.497417424\) \(a_{40}=-0.451382411\)
\(a_{41}=+1.720801337\) \(a_{42}=+1.405687575\) \(a_{43}=+1.629211444\) \(a_{44}=+0.609373189\) \(a_{45}=+0.738547085\)
\(a_{46}=+0.732124001\) \(a_{47}=-0.781503071\) \(a_{48}=-0.730701786\) \(a_{49}=+0.188533390\) \(a_{50}=-0.639987975\)
\(a_{51}=+0.420000913\) \(a_{52}=-0.119672221\) \(a_{53}=+0.442920441\) \(a_{54}=+0.998228450\) \(a_{55}=-0.633025731\)
\(a_{56}=-1.182148259\) \(a_{57}=-2.074094257\) \(a_{58}=-0.788564420\) \(a_{59}=+1.481674657\) \(a_{60}=-0.277834860\)
\(a_{61}=+0.254279366\) \(a_{62}=-0.592716776\) \(a_{63}=+1.934218369\) \(a_{64}=+1.015221402\) \(a_{65}=+0.124317244\)
\(a_{66}=-1.960767491\) \(a_{67}=+0.736797378\) \(a_{68}=-0.101046806\) \(a_{69}=+1.575206630\) \(a_{70}=+0.351317016\)
\(a_{71}=+1.499234388\) \(a_{72}=-1.923827213\) \(a_{73}=-0.964080900\) \(a_{74}=+0.298276892\) \(a_{75}=-1.376970704\)
\(a_{76}=+0.499000346\) \(a_{77}=-1.657863151\) \(a_{78}=+0.385066828\) \(a_{79}=-1.550336970\) \(a_{80}=-0.182620929\)
\(a_{81}=+0.373556855\) \(a_{82}=+1.332127666\) \(a_{83}=+0.109764260\) \(a_{84}=-0.727635787\) \(a_{85}=+0.104968892\)
\(a_{86}=+1.261224983\) \(a_{87}=-1.696641416\) \(a_{88}=+1.648956651\) \(a_{89}=+0.727372929\) \(a_{90}=+0.571733055\)
\(a_{91}=+0.325580726\) \(a_{92}=-0.378974413\) \(a_{93}=-1.275264018\) \(a_{94}=-0.604986665\) \(a_{95}=-0.518368817\)
\(a_{96}=+1.240408890\) \(a_{97}=-1.285901387\) \(a_{98}=+0.145949761\) \(a_{99}=-2.698005279\) \(a_{100}=+0.331281404\)

Showing 100 of 546 available coefficients

Rows: Cols: