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: \( 13.9637989662 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-1.558373967\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.172498103\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=-1.101936799\)
\(a_{11}=+1.541334452\) \(a_{12}=+0.288675135\) \(a_{13}=+1.793416423\) \(a_{14}=-0.121974578\) \(a_{15}=-0.899727629\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.468941390\) \(a_{18}=+0.235702260\) \(a_{19}=+0.579362712\) \(a_{20}=-0.779186983\)
\(a_{21}=-0.099591826\) \(a_{22}=+1.089888043\) \(a_{23}=+0.094549040\) \(a_{24}=+0.204124145\) \(a_{25}=+1.428529420\)
\(a_{26}=+1.268136914\) \(a_{27}=+0.192450090\) \(a_{28}=-0.086249051\) \(a_{29}=+0.463195992\) \(a_{30}=-0.636203508\)
\(a_{31}=+1.092537193\) \(a_{32}=+0.176776695\) \(a_{33}=+0.889889861\) \(a_{34}=-0.331591637\) \(a_{35}=+0.268816553\)
\(a_{36}=+0.166666667\) \(a_{37}=-0.164672408\) \(a_{38}=+0.409671303\) \(a_{39}=+1.035429455\) \(a_{40}=-0.550968400\)
\(a_{41}=-0.986764825\) \(a_{42}=-0.070422056\) \(a_{43}=-0.242601655\) \(a_{44}=+0.770667226\) \(a_{45}=-0.519457989\)
\(a_{46}=+0.066856267\) \(a_{47}=+1.208602286\) \(a_{48}=+0.144337567\) \(a_{49}=-0.970244405\) \(a_{50}=+1.010122840\)
\(a_{51}=-0.270743437\) \(a_{52}=+0.896708211\) \(a_{53}=-0.884795800\) \(a_{54}=+0.136082763\) \(a_{55}=-2.401975484\)
\(a_{56}=-0.060987289\) \(a_{57}=+0.334495218\) \(a_{58}=+0.327529027\) \(a_{59}=+1.483806300\) \(a_{60}=-0.449863815\)
\(a_{61}=+0.897345200\) \(a_{62}=+0.772540458\) \(a_{63}=-0.057499368\) \(a_{64}=+0.125000000\) \(a_{65}=-2.794813465\)
\(a_{66}=+0.629247155\) \(a_{67}=+0.851102002\) \(a_{68}=-0.234470695\) \(a_{69}=+0.054587914\) \(a_{70}=+0.190082007\)
\(a_{71}=-0.870054000\) \(a_{72}=+0.117851130\) \(a_{73}=-0.722000122\) \(a_{74}=-0.116440976\) \(a_{75}=+0.824761845\)
\(a_{76}=+0.289681356\) \(a_{77}=-0.265877269\) \(a_{78}=+0.732159189\) \(a_{79}=+1.161600000\) \(a_{80}=-0.389593492\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.697748099\) \(a_{83}=-0.835900009\) \(a_{84}=-0.049795913\) \(a_{85}=+0.730786053\)
\(a_{86}=-0.171545276\) \(a_{87}=+0.267426331\) \(a_{88}=+0.544944022\) \(a_{89}=-1.464000702\) \(a_{90}=-0.367312266\)
\(a_{91}=-0.309360930\) \(a_{92}=+0.047274520\) \(a_{93}=+0.630776642\) \(a_{94}=+0.854610872\) \(a_{95}=-0.902863768\)
\(a_{96}=+0.102062073\)

Showing all 96 available coefficients

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