Properties

Level $6$
Weight $0$
Character 6.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 6 = 2 \cdot 3 \)
Weight: \( 0 \)
Character: 6.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 5.8716820925 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.710640273\)
\(a_{6}=-0.408248290\) \(a_{7}=+1.376960961\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-0.502498556\)
\(a_{11}=-0.699098980\) \(a_{12}=+0.288675135\) \(a_{13}=+1.629429731\) \(a_{14}=-0.973658433\) \(a_{15}=+0.410288353\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.963856797\) \(a_{18}=-0.235702260\) \(a_{19}=-0.599580556\) \(a_{20}=+0.355320137\)
\(a_{21}=+0.794988781\) \(a_{22}=+0.494337629\) \(a_{23}=+0.537999562\) \(a_{24}=-0.204124145\) \(a_{25}=-0.494990402\)
\(a_{26}=-1.152180812\) \(a_{27}=+0.192450090\) \(a_{28}=+0.688480480\) \(a_{29}=-0.216133390\) \(a_{30}=-0.290117677\)
\(a_{31}=+0.170637549\) \(a_{32}=-0.176776695\) \(a_{33}=-0.403624984\) \(a_{34}=+0.681549677\) \(a_{35}=+0.978523913\)
\(a_{36}=+0.166666667\) \(a_{37}=-1.148269308\) \(a_{38}=+0.423967477\) \(a_{39}=+0.940751694\) \(a_{40}=-0.251249278\)
\(a_{41}=-1.235445330\) \(a_{42}=-0.562141958\) \(a_{43}=-0.021057070\) \(a_{44}=-0.349549490\) \(a_{45}=+0.236880091\)
\(a_{46}=-0.380423139\) \(a_{47}=+1.099547200\) \(a_{48}=+0.144337567\) \(a_{49}=+0.896021488\) \(a_{50}=+0.350011070\)
\(a_{51}=-0.556482981\) \(a_{52}=+0.814714865\) \(a_{53}=-0.573705000\) \(a_{54}=-0.136082763\) \(a_{55}=-0.496807890\)
\(a_{56}=-0.486829216\) \(a_{57}=-0.346167996\) \(a_{58}=+0.152829386\) \(a_{59}=-0.298640000\) \(a_{60}=+0.205144176\)
\(a_{61}=-0.584699988\) \(a_{62}=-0.120658968\) \(a_{63}=+0.458986987\) \(a_{64}=+0.125000000\) \(a_{65}=+1.157938389\)
\(a_{66}=+0.285405963\) \(a_{67}=+0.333000183\) \(a_{68}=-0.481928398\) \(a_{69}=+0.310614192\) \(a_{70}=-0.691920895\)
\(a_{71}=+0.451999664\) \(a_{72}=-0.117851130\) \(a_{73}=-0.690000000\) \(a_{74}=+0.811949014\) \(a_{75}=-0.285782842\)
\(a_{76}=-0.299790278\) \(a_{77}=-0.962632003\) \(a_{78}=-0.665211902\) \(a_{79}=+1.000000000\) \(a_{80}=+0.177660068\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.873591771\) \(a_{83}=-1.300048828\) \(a_{84}=+0.397494391\) \(a_{85}=-0.684955457\)
\(a_{86}=+0.014889597\) \(a_{87}=-0.124784671\) \(a_{88}=+0.247168815\)

Showing all 88 available coefficients

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