Properties

Level $6$
Weight $0$
Character 6.1
Symmetry even
Fricke sign $+1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: even
Fricke sign: $+1$
Spectral parameter: \( 9.66046617807 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.020321713\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.679120227\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.721476402\)
\(a_{11}=+0.901611086\) \(a_{12}=+0.288675135\) \(a_{13}=+0.980545091\) \(a_{14}=-0.480210517\) \(a_{15}=+0.589083016\)
\(a_{16}=+0.250000000\) \(a_{17}=+1.667781282\) \(a_{18}=+0.235702260\) \(a_{19}=-1.855365742\) \(a_{20}=+0.510160856\)
\(a_{21}=-0.392090246\) \(a_{22}=+0.637535313\) \(a_{23}=+0.069941072\) \(a_{24}=+0.204124145\) \(a_{25}=+0.041056398\)
\(a_{26}=+0.693350083\) \(a_{27}=+0.192450090\) \(a_{28}=-0.339560113\) \(a_{29}=-1.481096637\) \(a_{30}=+0.416544595\)
\(a_{31}=-0.577929056\) \(a_{32}=+0.176776695\) \(a_{33}=+0.520545403\) \(a_{34}=+1.179299454\) \(a_{35}=-0.692921113\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.808654117\) \(a_{38}=-1.311941698\) \(a_{39}=+0.566117972\) \(a_{40}=+0.360738201\)
\(a_{41}=-1.176783380\) \(a_{42}=-0.277249672\) \(a_{43}=-0.148673853\) \(a_{44}=+0.450805543\) \(a_{45}=+0.340107238\)
\(a_{46}=+0.049455806\) \(a_{47}=-0.037485920\) \(a_{48}=+0.144337567\) \(a_{49}=-0.538795718\) \(a_{50}=+0.029031257\)
\(a_{51}=+0.962893972\) \(a_{52}=+0.490272546\) \(a_{53}=-0.756477168\) \(a_{54}=+0.136082763\) \(a_{55}=+0.919933367\)
\(a_{56}=-0.240105259\) \(a_{57}=-1.071195910\) \(a_{58}=-1.047293475\) \(a_{59}=-0.492239165\) \(a_{60}=+0.294541508\)
\(a_{61}=+0.845416325\) \(a_{62}=-0.408657555\) \(a_{63}=-0.226373409\) \(a_{64}=+0.125000000\) \(a_{65}=+1.000471448\)
\(a_{66}=+0.368081184\) \(a_{67}=+0.579268120\) \(a_{68}=+0.833890641\) \(a_{69}=+0.040380494\) \(a_{70}=-0.489969217\)
\(a_{71}=-1.558289925\) \(a_{72}=+0.117851123\) \(a_{73}=-0.652862322\) \(a_{74}=+0.571804810\) \(a_{75}=+0.023703922\)
\(a_{76}=-0.927682871\) \(a_{77}=-0.612302325\) \(a_{78}=+0.400305857\) \(a_{79}=+0.860720626\) \(a_{80}=+0.255080428\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.832111508\) \(a_{83}=+0.410926222\) \(a_{84}=-0.196045123\) \(a_{85}=+1.701673454\)
\(a_{86}=-0.105128290\) \(a_{87}=-0.855111542\) \(a_{88}=+0.318767656\) \(a_{89}=+0.682776377\) \(a_{90}=+0.240492134\)
\(a_{91}=-0.665908004\) \(a_{92}=+0.034970536\) \(a_{93}=-0.333667496\) \(a_{94}=-0.026506548\) \(a_{95}=-1.893069952\)
\(a_{96}=+0.102062073\) \(a_{97}=+0.818422166\) \(a_{98}=-0.380986106\) \(a_{99}=+0.300537029\) \(a_{100}=+0.020528199\)

Showing 100 of 1000 available coefficients

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