Properties

Level $22$
Weight $0$
Character 22.1
Symmetry even
Fricke sign $+1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 5.97205405178 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.981089039\) \(a_{4}=+0.500000000\) \(a_{5}=+0.833265723\)
\(a_{6}=-0.693734712\) \(a_{7}=+0.512482249\) \(a_{8}=-0.353553391\) \(a_{9}=-0.037464298\) \(a_{10}=-0.589207843\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.490544519\) \(a_{13}=+1.152235090\) \(a_{14}=-0.362379674\) \(a_{15}=+0.817507867\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.098835001\) \(a_{18}=+0.026491259\) \(a_{19}=+0.806845572\) \(a_{20}=+0.416632861\)
\(a_{21}=+0.502790717\) \(a_{22}=+0.213200716\) \(a_{23}=+1.420143648\) \(a_{24}=-0.346867356\) \(a_{25}=-0.305668235\)
\(a_{26}=-0.814753246\) \(a_{27}=-1.017844851\) \(a_{28}=+0.256241124\) \(a_{29}=+0.994288702\) \(a_{30}=-0.578065357\)
\(a_{31}=+0.684136338\) \(a_{32}=-0.176776695\) \(a_{33}=-0.295809475\) \(a_{34}=+0.069886899\) \(a_{35}=+0.427033892\)
\(a_{36}=-0.018732149\) \(a_{37}=+0.869803847\) \(a_{38}=-0.570525976\) \(a_{39}=+1.130445217\) \(a_{40}=-0.294603922\)
\(a_{41}=+0.974404681\) \(a_{42}=-0.355526726\) \(a_{43}=+0.311130755\) \(a_{44}=-0.150755672\) \(a_{45}=-0.031217715\)
\(a_{46}=-1.004193204\) \(a_{47}=-1.168164591\) \(a_{48}=+0.245272260\) \(a_{49}=-0.737361944\) \(a_{50}=+0.216140082\)
\(a_{51}=-0.096965936\) \(a_{52}=+0.576117545\) \(a_{53}=-0.329354428\) \(a_{54}=+0.719724996\) \(a_{55}=-0.251239069\)
\(a_{56}=-0.181189837\) \(a_{57}=+0.791587347\) \(a_{58}=-0.703068284\) \(a_{59}=-1.670502371\) \(a_{60}=+0.408753934\)
\(a_{61}=+1.752945923\) \(a_{62}=-0.483757444\) \(a_{63}=-0.019199787\) \(a_{64}=+0.125000000\) \(a_{65}=+0.960118005\)
\(a_{66}=+0.209168886\) \(a_{67}=-0.527720703\) \(a_{68}=-0.049417500\) \(a_{69}=+1.393287367\) \(a_{70}=-0.301958561\)
\(a_{71}=+1.600535727\) \(a_{72}=+0.013245629\) \(a_{73}=-0.610286622\) \(a_{74}=-0.615044199\) \(a_{75}=-0.299887755\)
\(a_{76}=+0.403422786\) \(a_{77}=-0.154519212\) \(a_{78}=-0.799345479\) \(a_{79}=-1.303835996\) \(a_{80}=+0.208316431\)
\(a_{81}=-0.961132129\) \(a_{82}=-0.689008158\) \(a_{83}=-0.208886359\) \(a_{84}=+0.251395359\) \(a_{85}=-0.082355819\)
\(a_{86}=-0.220002666\) \(a_{87}=+0.975485747\) \(a_{88}=+0.106600358\) \(a_{89}=-1.238322035\) \(a_{90}=+0.022074258\)
\(a_{91}=+0.590500030\) \(a_{92}=+0.710071824\) \(a_{93}=+0.671198662\) \(a_{94}=+0.826017104\) \(a_{95}=+0.672316759\)
\(a_{96}=-0.173433678\) \(a_{97}=-0.044374257\) \(a_{98}=+0.521393631\) \(a_{99}=+0.011295911\) \(a_{100}=-0.152834117\)

Showing 100 of 262 available coefficients

Rows: Cols: