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: \( 7.38627450582 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=-0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=-0.098565809\)
\(a_{6}=-0.408248290\) \(a_{7}=-1.485705533\) \(a_{8}=-0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.069696552\)
\(a_{11}=-0.999230972\) \(a_{12}=+0.288675135\) \(a_{13}=-1.346794650\) \(a_{14}=+1.050552457\) \(a_{15}=-0.056906997\)
\(a_{16}=+0.250000000\) \(a_{17}=+0.734195932\) \(a_{18}=-0.235702260\) \(a_{19}=-1.134102557\) \(a_{20}=-0.049282905\)
\(a_{21}=-0.857772490\) \(a_{22}=+0.706562996\) \(a_{23}=+1.363206909\) \(a_{24}=-0.204124145\) \(a_{25}=-0.990284781\)
\(a_{26}=+0.952327630\) \(a_{27}=+0.192450090\) \(a_{28}=-0.742852767\) \(a_{29}=-0.143589631\) \(a_{30}=+0.040239323\)
\(a_{31}=+0.369734121\) \(a_{32}=-0.176776695\) \(a_{33}=-0.576906271\) \(a_{34}=-0.519154922\) \(a_{35}=+0.146439768\)
\(a_{36}=+0.166666667\) \(a_{37}=+1.256264160\) \(a_{38}=+0.801931609\) \(a_{39}=-0.777572254\) \(a_{40}=+0.034848276\)
\(a_{41}=-0.152586510\) \(a_{42}=+0.606536744\) \(a_{43}=-0.893991745\) \(a_{44}=-0.499615486\) \(a_{45}=-0.032855270\)
\(a_{46}=-0.963932850\) \(a_{47}=-0.277610260\) \(a_{48}=+0.144337567\) \(a_{49}=+1.207320932\) \(a_{50}=+0.700237084\)
\(a_{51}=+0.423888219\) \(a_{52}=-0.673397325\) \(a_{53}=+0.587779300\) \(a_{54}=-0.136082763\) \(a_{55}=+0.098490009\)
\(a_{56}=+0.525276229\) \(a_{57}=-0.654774417\) \(a_{58}=+0.101533201\) \(a_{59}=-1.642981000\) \(a_{60}=-0.028453498\)
\(a_{61}=+0.714139000\) \(a_{62}=-0.261441504\) \(a_{63}=-0.495235178\) \(a_{64}=+0.125000000\) \(a_{65}=+0.132747905\)
\(a_{66}=+0.407934336\) \(a_{67}=-0.162100002\) \(a_{68}=+0.367097966\) \(a_{69}=+0.787047876\) \(a_{70}=-0.103548553\)
\(a_{71}=+0.561699867\) \(a_{72}=-0.117851130\) \(a_{73}=+0.093999863\) \(a_{74}=-0.888312907\) \(a_{75}=-0.571741185\)
\(a_{76}=-0.567051279\) \(a_{77}=+1.484562984\) \(a_{78}=+0.549826613\) \(a_{79}=-1.029998779\) \(a_{80}=-0.024641452\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.107894956\) \(a_{83}=-1.130000000\) \(a_{84}=-0.428886245\) \(a_{85}=-0.072366616\)
\(a_{86}=+0.632147625\) \(a_{87}=-0.082901512\) \(a_{88}=+0.353281498\)

Showing all 88 available coefficients

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