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: \( 4.54845492142 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.360056092\)
\(a_{6}=+0.408248290\) \(a_{7}=+0.182429324\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.961704886\)
\(a_{11}=-1.243401795\) \(a_{12}=-0.288675135\) \(a_{13}=-0.133626634\) \(a_{14}=-0.128997013\) \(a_{15}=+0.785228751\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.990459136\) \(a_{18}=-0.235702251\) \(a_{19}=-1.234469379\) \(a_{20}=-0.680028065\)
\(a_{21}=-0.105325455\) \(a_{22}=+0.879217841\) \(a_{23}=-0.551012060\) \(a_{24}=+0.204124145\) \(a_{25}=+0.849752574\)
\(a_{26}=+0.094488299\) \(a_{27}=-0.192450090\) \(a_{28}=+0.091214662\) \(a_{29}=+0.485979680\) \(a_{30}=-0.555240575\)
\(a_{31}=-0.710888656\) \(a_{32}=-0.176776695\) \(a_{33}=+0.717878361\) \(a_{34}=-0.700360373\) \(a_{35}=-0.248114114\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.206501374\) \(a_{38}=+0.872901657\) \(a_{39}=+0.077149373\) \(a_{40}=+0.480852443\)
\(a_{41}=-0.191872590\) \(a_{42}=+0.074476460\) \(a_{43}=+0.644046859\) \(a_{44}=-0.621700897\) \(a_{45}=-0.453352031\)
\(a_{46}=+0.389624362\) \(a_{47}=-0.173484524\) \(a_{48}=-0.144337566\) \(a_{49}=-0.966719538\) \(a_{50}=-0.600865803\)
\(a_{51}=-0.571841859\) \(a_{52}=-0.066813320\) \(a_{53}=+1.565646699\) \(a_{54}=+0.136082771\) \(a_{55}=+1.691096196\)
\(a_{56}=-0.064498537\) \(a_{57}=+0.712721281\) \(a_{58}=-0.343639515\) \(a_{59}=-1.190794940\) \(a_{60}=+0.392614350\)
\(a_{61}=-1.568816843\) \(a_{62}=+0.502674189\) \(a_{63}=+0.060809775\) \(a_{64}=+0.124999999\) \(a_{65}=+0.181739717\)
\(a_{66}=-0.507616657\) \(a_{67}=-1.100063816\) \(a_{68}=+0.495229569\) \(a_{69}=+0.318126961\) \(a_{70}=+0.175443174\)
\(a_{71}=-0.273204886\) \(a_{72}=-0.117851131\) \(a_{73}=+1.817022570\) \(a_{74}=+0.146018519\) \(a_{75}=-0.490604876\)
\(a_{76}=-0.617234678\) \(a_{77}=-0.226832944\) \(a_{78}=-0.054552848\) \(a_{79}=+1.356900930\) \(a_{80}=-0.340014018\)
\(a_{81}=+0.111111108\) \(a_{82}=+0.135674402\) \(a_{83}=+0.194001291\) \(a_{84}=-0.052662800\) \(a_{85}=-1.347079955\)
\(a_{86}=-0.455409889\) \(a_{87}=-0.280580539\) \(a_{88}=+0.439608900\) \(a_{89}=-0.871984650\) \(a_{90}=+0.320568420\)
\(a_{91}=-0.024377608\) \(a_{92}=-0.275506025\) \(a_{93}=+0.410431533\) \(a_{94}=+0.122672175\) \(a_{95}=+1.678946855\)
\(a_{96}=+0.102061764\) \(a_{97}=-1.356797765\) \(a_{98}=+0.683573521\) \(a_{99}=-0.414467553\) \(a_{100}=+0.424876289\)

Showing 100 of 1000 available coefficients

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