Properties

Level $23$
Weight $0$
Character 23.1
Symmetry odd
Fricke sign $+1$

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Maass form invariants

Level: \( 23 \)
Weight: \( 0 \)
Character: 23.1
Symmetry: odd
Fricke sign: $+1$
Spectral parameter: \( 4.50005039136 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.674679975\) \(a_{3}=+0.226988521\) \(a_{4}=-0.544806932\) \(a_{5}=+0.234269598\)
\(a_{6}=+0.153144609\) \(a_{7}=-1.191724932\) \(a_{8}=-1.042250302\) \(a_{9}=-0.948476211\) \(a_{10}=+0.158057006\)
\(a_{11}=-0.563214566\) \(a_{12}=-0.123664920\) \(a_{13}=+0.636538639\) \(a_{14}=-0.804032947\) \(a_{15}=+0.053176509\)
\(a_{16}=-0.158378475\) \(a_{17}=+1.271451667\) \(a_{18}=-0.639917906\) \(a_{19}=-0.798776301\) \(a_{20}=-0.127631701\)
\(a_{21}=-0.270507879\) \(a_{22}=-0.379989589\) \(a_{23}=-0.208514414\) \(a_{24}=-0.236578854\) \(a_{25}=-0.945117756\)
\(a_{26}=+0.429459873\) \(a_{27}=-0.442281733\) \(a_{28}=+0.649260004\) \(a_{29}=+1.787546051\) \(a_{30}=+0.035877126\)
\(a_{31}=-0.817640548\) \(a_{32}=+0.935395516\) \(a_{33}=-0.127843241\) \(a_{34}=+0.857822979\) \(a_{35}=-0.279184921\)
\(a_{36}=+0.516736415\) \(a_{37}=-0.639763928\) \(a_{38}=-0.538918374\) \(a_{39}=+0.144486964\) \(a_{40}=-0.244167559\)
\(a_{41}=-1.414163845\) \(a_{42}=-0.182506249\) \(a_{43}=-0.256329533\) \(a_{44}=+0.306843200\) \(a_{45}=-0.222199141\)
\(a_{46}=-0.140680500\) \(a_{47}=+0.931899866\) \(a_{48}=-0.035950096\) \(a_{49}=+0.420208313\) \(a_{50}=-0.637652023\)
\(a_{51}=+0.288604933\) \(a_{52}=-0.346790663\) \(a_{53}=-0.135563610\) \(a_{54}=-0.298398628\) \(a_{55}=-0.131944050\)
\(a_{56}=+1.242075670\) \(a_{57}=-0.181313051\) \(a_{58}=+1.206021524\) \(a_{59}=-0.161940948\) \(a_{60}=-0.028970931\)
\(a_{61}=-0.752412716\) \(a_{62}=-0.551645704\) \(a_{63}=+1.130322749\) \(a_{64}=+0.789471098\) \(a_{65}=+0.149121651\)
\(a_{66}=-0.086253275\) \(a_{67}=-0.589651862\) \(a_{68}=-0.692695682\) \(a_{69}=-0.047330378\) \(a_{70}=-0.188360475\)
\(a_{71}=+0.046333848\) \(a_{72}=+0.988549617\) \(a_{73}=-0.492503736\) \(a_{74}=-0.431635911\) \(a_{75}=-0.214530881\)
\(a_{76}=+0.435178866\) \(a_{77}=+0.671196841\) \(a_{78}=+0.097482461\) \(a_{79}=-1.422728309\) \(a_{80}=-0.037103262\)
\(a_{81}=+0.848083335\) \(a_{82}=-0.954108027\) \(a_{83}=-1.056626565\) \(a_{84}=+0.147374568\) \(a_{85}=+0.297862471\)
\(a_{86}=-0.172940403\) \(a_{87}=+0.405752434\) \(a_{88}=+0.587010551\) \(a_{89}=-0.886507582\) \(a_{90}=-0.149913311\)
\(a_{91}=-0.758578967\) \(a_{92}=+0.113600098\) \(a_{93}=-0.185595019\) \(a_{94}=+0.628734178\) \(a_{95}=-0.187129003\)
\(a_{96}=+0.212324044\) \(a_{97}=+1.863785675\) \(a_{98}=+0.283506134\) \(a_{99}=+0.534195618\) \(a_{100}=+0.514906705\)

Showing 100 of 546 available coefficients

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