Properties

Level $23$
Weight $0$
Character 23.1
Symmetry even
Fricke sign $-1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: even
Fricke sign: $-1$
Spectral parameter: \( 3.01662095343 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.778668494\) \(a_{3}=+0.165367208\) \(a_{4}=-0.393675377\) \(a_{5}=+0.680260332\)
\(a_{6}=-0.128766235\) \(a_{7}=-1.686284579\) \(a_{8}=+1.085211106\) \(a_{9}=-0.972653687\) \(a_{10}=-0.529697288\)
\(a_{11}=-1.052107362\) \(a_{12}=-0.065100998\) \(a_{13}=+1.495802299\) \(a_{14}=+1.313056673\) \(a_{15}=+0.112492752\)
\(a_{16}=-0.451344320\) \(a_{17}=-0.629981133\) \(a_{18}=+0.757374781\) \(a_{19}=-0.766351232\) \(a_{20}=-0.267801743\)
\(a_{21}=-0.278856173\) \(a_{22}=+0.819242855\) \(a_{23}=+0.208514414\) \(a_{24}=+0.179458331\) \(a_{25}=-0.537245880\)
\(a_{26}=-1.164734123\) \(a_{27}=-0.326212233\) \(a_{28}=+0.663848718\) \(a_{29}=-0.343014962\) \(a_{30}=-0.087594562\)
\(a_{31}=+1.269829435\) \(a_{32}=-0.733763505\) \(a_{33}=-0.173984057\) \(a_{34}=+0.490546461\) \(a_{35}=-1.147112508\)
\(a_{36}=+0.382909806\) \(a_{37}=-0.056530222\) \(a_{38}=+0.596733560\) \(a_{39}=+0.247356652\) \(a_{40}=+0.738226067\)
\(a_{41}=+0.730798298\) \(a_{42}=+0.217136516\) \(a_{43}=-0.529790002\) \(a_{44}=+0.414188767\) \(a_{45}=-0.661657727\)
\(a_{46}=-0.162363608\) \(a_{47}=-1.345723610\) \(a_{48}=-0.074637547\) \(a_{49}=+1.843555691\) \(a_{50}=+0.418336445\)
\(a_{51}=-0.104178230\) \(a_{52}=-0.588860554\) \(a_{53}=+0.385530111\) \(a_{54}=+0.254011209\) \(a_{55}=-0.715706885\)
\(a_{56}=-1.829974770\) \(a_{57}=-0.126729409\) \(a_{58}=+0.267094941\) \(a_{59}=-1.504367146\) \(a_{60}=-0.044285552\)
\(a_{61}=-0.515090712\) \(a_{62}=-0.988776227\) \(a_{63}=+1.640170912\) \(a_{64}=+1.022702896\) \(a_{65}=+1.017535058\)
\(a_{66}=+0.135475881\) \(a_{67}=-0.166985048\) \(a_{68}=+0.248008051\) \(a_{69}=+0.034481445\) \(a_{70}=+0.893220383\)
\(a_{71}=+0.519255166\) \(a_{72}=-1.055534615\) \(a_{73}=-0.337796043\) \(a_{74}=+0.044018314\) \(a_{75}=-0.088842861\)
\(a_{76}=+0.301693598\) \(a_{77}=+1.774152455\) \(a_{78}=-0.192608829\) \(a_{79}=+0.738204326\) \(a_{80}=-0.307031616\)
\(a_{81}=+0.918708887\) \(a_{82}=-0.569049629\) \(a_{83}=-1.230786865\) \(a_{84}=+0.109778788\) \(a_{85}=-0.428551111\)
\(a_{86}=+0.412530850\) \(a_{87}=-0.056723495\) \(a_{88}=-1.141758624\) \(a_{89}=-0.451902922\) \(a_{90}=+0.515211960\)
\(a_{91}=-2.522348314\) \(a_{92}=-0.082086996\) \(a_{93}=+0.209988121\) \(a_{94}=+1.047872529\) \(a_{95}=-0.521318366\)
\(a_{96}=-0.121340416\) \(a_{97}=+0.901572288\) \(a_{98}=-1.435518732\) \(a_{99}=+1.023336169\) \(a_{100}=+0.211500534\)

Showing 100 of 1500 available coefficients

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