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: \( 1.5061266371 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.340029690\) \(a_{3}=+0.620782224\) \(a_{4}=-0.884379810\) \(a_{5}=+0.273602802\)
\(a_{6}=+0.211084388\) \(a_{7}=-0.309831213\) \(a_{8}=-0.640745083\) \(a_{9}=-0.614629430\) \(a_{10}=+0.093033076\)
\(a_{11}=+1.884524757\) \(a_{12}=-0.549007265\) \(a_{13}=+0.830883917\) \(a_{14}=-0.105351812\) \(a_{15}=+0.169847756\)
\(a_{16}=+0.666507457\) \(a_{17}=-1.067371031\) \(a_{18}=-0.208992255\) \(a_{19}=-0.272845464\) \(a_{20}=-0.241968794\)
\(a_{21}=-0.192337710\) \(a_{22}=+0.640794370\) \(a_{23}=+0.208514414\) \(a_{24}=-0.397763158\) \(a_{25}=-0.925141507\)
\(a_{26}=+0.282525201\) \(a_{27}=-1.002333249\) \(a_{28}=+0.274008470\) \(a_{29}=+0.091366569\) \(a_{30}=+0.057753280\)
\(a_{31}=-0.533405117\) \(a_{32}=+0.867377408\) \(a_{33}=+1.169879471\) \(a_{34}=-0.362937841\) \(a_{35}=-0.084770688\)
\(a_{36}=+0.543565858\) \(a_{37}=+1.541523459\) \(a_{38}=-0.092775559\) \(a_{39}=+0.515797966\) \(a_{40}=-0.175309650\)
\(a_{41}=-0.113237434\) \(a_{42}=-0.065400532\) \(a_{43}=-1.002816949\) \(a_{44}=-1.666635646\) \(a_{45}=-0.168164334\)
\(a_{46}=+0.070901092\) \(a_{47}=+1.000941530\) \(a_{48}=+0.413755982\) \(a_{49}=-0.904004619\) \(a_{50}=-0.314575580\)
\(a_{51}=-0.662604963\) \(a_{52}=-0.734816961\) \(a_{53}=+0.805868366\) \(a_{54}=-0.340823064\) \(a_{55}=+0.515611254\)
\(a_{56}=+0.198522827\) \(a_{57}=-0.169377614\) \(a_{58}=+0.031067346\) \(a_{59}=+1.180280525\) \(a_{60}=-0.150209926\)
\(a_{61}=-1.125923806\) \(a_{62}=-0.181373577\) \(a_{63}=+0.190431382\) \(a_{64}=-0.371573386\) \(a_{65}=+0.227332168\)
\(a_{66}=+0.397793754\) \(a_{67}=+1.182844063\) \(a_{68}=+0.943961390\) \(a_{69}=+0.129442042\) \(a_{70}=-0.028824551\)
\(a_{71}=-0.828726473\) \(a_{72}=+0.393820785\) \(a_{73}=-0.355687710\) \(a_{74}=+0.524163745\) \(a_{75}=-0.574311402\)
\(a_{76}=+0.241299019\) \(a_{77}=-0.583884592\) \(a_{78}=+0.175386623\) \(a_{79}=+0.549860719\) \(a_{80}=+0.182358308\)
\(a_{81}=-0.007601234\) \(a_{82}=-0.038504090\) \(a_{83}=-0.137734704\) \(a_{84}=+0.170099587\) \(a_{85}=-0.292035705\)
\(a_{86}=-0.340987537\) \(a_{87}=+0.056718742\) \(a_{88}=-1.207499973\) \(a_{89}=+0.345373383\) \(a_{90}=-0.057180867\)
\(a_{91}=-0.257433772\) \(a_{92}=-0.184405938\) \(a_{93}=-0.331128415\) \(a_{94}=+0.340349839\) \(a_{95}=-0.074651283\)
\(a_{96}=+0.538452477\) \(a_{97}=-0.738395203\) \(a_{98}=-0.307388411\) \(a_{99}=-1.158284377\) \(a_{100}=+0.818176469\)

Showing 100 of 546 available coefficients

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