Properties

Level $21$
Weight $0$
Character 21.1
Symmetry even
Fricke sign $-1$

Related objects

Downloads

Learn more

Maass form invariants

Level: \( 21 = 3 \cdot 7 \)
Weight: \( 0 \)
Character: 21.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 6.33284667273 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.094856007\) \(a_{3}=+0.577350269\) \(a_{4}=+0.198709676\) \(a_{5}=-0.826105748\)
\(a_{6}=+0.632115410\) \(a_{7}=-0.377964473\) \(a_{8}=-0.877297525\) \(a_{9}=+0.333333333\) \(a_{10}=-0.904466840\)
\(a_{11}=-1.605545241\) \(a_{12}=+0.114725085\) \(a_{13}=+1.485157490\) \(a_{14}=-0.413816674\) \(a_{15}=-0.476952376\)
\(a_{16}=-1.159224141\) \(a_{17}=-1.742548267\) \(a_{18}=+0.364952002\) \(a_{19}=-0.849654701\) \(a_{20}=-0.164155205\)
\(a_{21}=-0.218217890\) \(a_{22}=-1.757840852\) \(a_{23}=+1.192074845\) \(a_{24}=-0.506507962\) \(a_{25}=-0.317549294\)
\(a_{26}=+1.626033599\) \(a_{27}=+0.192450090\) \(a_{28}=-0.075105198\) \(a_{29}=-0.414994996\) \(a_{30}=-0.522194174\)
\(a_{31}=+1.145690529\) \(a_{32}=-0.391885989\) \(a_{33}=-0.926961977\) \(a_{34}=-1.907839437\) \(a_{35}=+0.312238624\)
\(a_{36}=+0.066236559\) \(a_{37}=-0.240599458\) \(a_{38}=-0.930249553\) \(a_{39}=+0.857456077\) \(a_{40}=+0.724740528\)
\(a_{41}=+0.896383877\) \(a_{42}=-0.238917168\) \(a_{43}=+0.261093028\) \(a_{44}=-0.319037374\) \(a_{45}=-0.275368583\)
\(a_{46}=+1.305150305\) \(a_{47}=-0.601982803\) \(a_{48}=-0.669278370\) \(a_{49}=+0.142857143\) \(a_{50}=-0.347670751\)
\(a_{51}=-1.006060711\) \(a_{52}=+0.295115163\) \(a_{53}=+0.803550305\) \(a_{54}=+0.210705137\) \(a_{55}=+1.326350152\)
\(a_{56}=+0.331587297\) \(a_{57}=-0.490548370\) \(a_{58}=-0.454359764\) \(a_{59}=-1.022935624\) \(a_{60}=-0.094775052\)
\(a_{61}=-0.120871526\) \(a_{62}=+1.254366158\) \(a_{63}=-0.125988158\) \(a_{64}=+0.730165412\) \(a_{65}=-1.226897139\)
\(a_{66}=-1.014889889\) \(a_{67}=+0.211371549\) \(a_{68}=-0.346261201\) \(a_{69}=+0.688244733\) \(a_{70}=+0.341856333\)
\(a_{71}=-0.536392459\) \(a_{72}=-0.292432508\) \(a_{73}=-0.985821707\) \(a_{74}=-0.263421762\) \(a_{75}=-0.183337170\)
\(a_{76}=-0.168834610\) \(a_{77}=+0.606839061\) \(a_{78}=+0.938790936\) \(a_{79}=+0.144511066\) \(a_{80}=+0.957641725\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.981411273\) \(a_{83}=-1.208614169\) \(a_{84}=-0.043362006\) \(a_{85}=+1.439529139\)
\(a_{86}=+0.285859270\) \(a_{87}=-0.239597473\) \(a_{88}=+1.408540866\) \(a_{89}=-1.431772522\) \(a_{90}=-0.301488947\)
\(a_{91}=-0.561336768\) \(a_{92}=+0.236876806\) \(a_{93}=+0.661464736\) \(a_{94}=-0.659084488\) \(a_{95}=+0.701904632\)
\(a_{96}=-0.226255481\) \(a_{97}=-0.902316730\) \(a_{98}=+0.156408001\) \(a_{99}=-0.535181747\) \(a_{100}=-0.063100117\)

Showing 100 of 250 available coefficients

Rows: Cols: