Properties

Level $22$
Weight $0$
Character 22.1
Symmetry odd
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 22 = 2 \cdot 11 \)
Weight: \( 0 \)
Character: 22.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.7113634789 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.586239918\) \(a_{4}=+0.500000000\) \(a_{5}=+0.987389112\)
\(a_{6}=+0.414534221\) \(a_{7}=+1.055407350\) \(a_{8}=+0.353553391\) \(a_{9}=-0.656322759\) \(a_{10}=+0.698189537\)
\(a_{11}=-0.301511345\) \(a_{12}=+0.293119959\) \(a_{13}=-1.539188752\) \(a_{14}=+0.746285694\) \(a_{15}=+0.578846912\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.883977772\) \(a_{18}=-0.464090273\) \(a_{19}=-0.183773855\) \(a_{20}=+0.493694556\)
\(a_{21}=+0.618721918\) \(a_{22}=-0.213200716\) \(a_{23}=+0.068639023\) \(a_{24}=+0.207267111\) \(a_{25}=-0.025062741\)
\(a_{26}=-1.088370804\) \(a_{27}=-0.971002518\) \(a_{28}=+0.527703675\) \(a_{29}=-1.384304187\) \(a_{30}=+0.409306577\)
\(a_{31}=-0.216024426\) \(a_{32}=+0.176776695\) \(a_{33}=-0.176757986\) \(a_{34}=+0.625066677\) \(a_{35}=+1.042097726\)
\(a_{36}=-0.328161379\) \(a_{37}=+1.004428860\) \(a_{38}=-0.129947739\) \(a_{39}=-0.902333888\) \(a_{40}=+0.349094769\)
\(a_{41}=+1.834761537\) \(a_{42}=+0.437502464\) \(a_{43}=-0.584024991\) \(a_{44}=-0.150755673\) \(a_{45}=-0.648045946\)
\(a_{46}=+0.048535120\) \(a_{47}=-1.184721057\) \(a_{48}=+0.146559977\) \(a_{49}=+0.113884674\) \(a_{50}=-0.017722031\)
\(a_{51}=+0.518223057\) \(a_{52}=-0.769594376\) \(a_{53}=-0.433419330\) \(a_{54}=-0.686602473\) \(a_{55}=-0.297709007\)
\(a_{56}=+0.373142864\) \(a_{57}=-0.107735568\) \(a_{58}=-0.978850903\) \(a_{59}=+1.634312119\) \(a_{60}=+0.289423456\)
\(a_{61}=+1.775464385\) \(a_{62}=-0.152752330\) \(a_{63}=-0.692687863\) \(a_{64}=+0.125000006\) \(a_{65}=-1.519778210\)
\(a_{66}=-0.124986784\) \(a_{67}=-0.273837220\) \(a_{68}=+0.441988865\) \(a_{69}=+0.040238937\) \(a_{70}=+0.736874410\)
\(a_{71}=-1.149485359\) \(a_{72}=-0.232045115\) \(a_{73}=+1.706208781\) \(a_{74}=+0.710238409\) \(a_{75}=-0.014692765\)
\(a_{76}=-0.091886968\) \(a_{77}=-0.318217193\) \(a_{78}=-0.638046392\) \(a_{79}=+0.842142633\) \(a_{80}=+0.246847411\)
\(a_{81}=+0.087082198\) \(a_{82}=+1.297372228\) \(a_{83}=-0.920239550\) \(a_{84}=+0.309361187\) \(a_{85}=+0.872830412\)
\(a_{86}=-0.412968331\) \(a_{87}=-0.811534337\) \(a_{88}=-0.106600355\) \(a_{89}=-0.265873949\) \(a_{90}=-0.458237672\)
\(a_{91}=-1.624471128\) \(a_{92}=+0.034319466\) \(a_{93}=-0.126642132\) \(a_{94}=-0.837724272\) \(a_{95}=-0.181456315\)
\(a_{96}=+0.103633609\) \(a_{97}=-0.078687687\) \(a_{98}=+0.080528599\) \(a_{99}=+0.197888732\) \(a_{100}=-0.012531363\)

Showing 100 of 1500 available coefficients

Rows: Cols: