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: \( 10.6298273272 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=-0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+0.245088370\)
\(a_{6}=-0.408248290\) \(a_{7}=-0.715417088\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+0.173303649\)
\(a_{11}=-0.737454656\) \(a_{12}=-0.288675135\) \(a_{13}=-1.092332745\) \(a_{14}=-0.505876274\) \(a_{15}=-0.141501837\)
\(a_{16}=+0.250000000\) \(a_{17}=-1.785652252\) \(a_{18}=+0.235702260\) \(a_{19}=-1.328834548\) \(a_{20}=+0.122544185\)
\(a_{21}=+0.413046248\) \(a_{22}=-0.521459188\) \(a_{23}=+1.468195495\) \(a_{24}=-0.204124145\) \(a_{25}=-0.939931691\)
\(a_{26}=-0.772395891\) \(a_{27}=-0.192450090\) \(a_{28}=-0.357708544\) \(a_{29}=+0.918555542\) \(a_{30}=-0.100056908\)
\(a_{31}=+0.735394272\) \(a_{32}=+0.176776695\) \(a_{33}=+0.425769644\) \(a_{34}=-1.262646816\) \(a_{35}=-0.175340408\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.530655971\) \(a_{38}=-0.939627920\) \(a_{39}=+0.630658604\) \(a_{40}=+0.086651824\)
\(a_{41}=-1.344205412\) \(a_{42}=+0.292067803\) \(a_{43}=+1.196125861\) \(a_{44}=-0.368727328\) \(a_{45}=+0.081696123\)
\(a_{46}=+1.038170991\) \(a_{47}=-0.231484400\) \(a_{48}=-0.144337567\) \(a_{49}=-0.488178390\) \(a_{50}=-0.664632072\)
\(a_{51}=+1.030946808\) \(a_{52}=-0.546166372\) \(a_{53}=-0.595274200\) \(a_{54}=-0.136082763\) \(a_{55}=-0.180741560\)
\(a_{56}=-0.252938137\) \(a_{57}=+0.767202984\) \(a_{58}=+0.649516853\) \(a_{59}=-0.497349000\) \(a_{60}=-0.070750918\)
\(a_{61}=+0.947536997\) \(a_{62}=+0.520002277\) \(a_{63}=-0.238472363\) \(a_{64}=+0.125000000\) \(a_{65}=-0.267718052\)
\(a_{66}=+0.301064602\) \(a_{67}=-0.586949997\) \(a_{68}=-0.892826126\) \(a_{69}=-0.847663064\) \(a_{70}=-0.123984392\)
\(a_{71}=-0.349998474\) \(a_{72}=+0.117851130\) \(a_{73}=+1.050048828\) \(a_{74}=+0.375230436\) \(a_{75}=+0.542669815\)
\(a_{76}=-0.664417274\) \(a_{77}=+0.527587662\) \(a_{78}=+0.445942976\) \(a_{79}=+0.630004883\) \(a_{80}=+0.061272093\)
\(a_{81}=+0.111111111\) \(a_{82}=-0.950496762\) \(a_{83}=-0.739997864\) \(a_{84}=+0.206523124\) \(a_{85}=-0.437642601\)
\(a_{86}=+0.845788707\) \(a_{87}=-0.530328289\) \(a_{88}=-0.260729594\)

Showing all 88 available coefficients

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