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: \( 6.00033540888 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+0.707106781\) \(a_{3}=+0.577350269\) \(a_{4}=+0.500000000\) \(a_{5}=+1.470842019\)
\(a_{6}=+0.408248290\) \(a_{7}=-0.823288056\) \(a_{8}=+0.353553391\) \(a_{9}=+0.333333333\) \(a_{10}=+1.040042366\)
\(a_{11}=-0.897769071\) \(a_{12}=+0.288675135\) \(a_{13}=-0.411297019\) \(a_{14}=-0.582152568\) \(a_{15}=+0.849191036\)
\(a_{16}=+0.250000000\) \(a_{17}=-0.910505571\) \(a_{18}=+0.235702260\) \(a_{19}=+0.829115324\) \(a_{20}=+0.735421010\)
\(a_{21}=-0.475325581\) \(a_{22}=-0.634818598\) \(a_{23}=-1.447778936\) \(a_{24}=+0.204124145\) \(a_{25}=+1.163376246\)
\(a_{26}=-0.290830911\) \(a_{27}=+0.192450090\) \(a_{28}=-0.411644028\) \(a_{29}=+1.153659039\) \(a_{30}=+0.600468740\)
\(a_{31}=-0.568827399\) \(a_{32}=+0.176776695\) \(a_{33}=-0.518327215\) \(a_{34}=-0.643824664\) \(a_{35}=-1.210926667\)
\(a_{36}=+0.166666667\) \(a_{37}=+0.647923523\) \(a_{38}=+0.586273068\) \(a_{39}=-0.237462444\) \(a_{40}=+0.520021183\)
\(a_{41}=+0.148292161\) \(a_{42}=-0.336105942\) \(a_{43}=+1.248867980\) \(a_{44}=-0.448884536\) \(a_{45}=+0.490280673\)
\(a_{46}=-1.023734304\) \(a_{47}=-0.862836180\) \(a_{48}=+0.144337567\) \(a_{49}=-0.322196776\) \(a_{50}=+0.822631233\)
\(a_{51}=-0.525680637\) \(a_{52}=-0.205648509\) \(a_{53}=+0.937203700\) \(a_{54}=+0.136082763\) \(a_{55}=-1.320476474\)
\(a_{56}=-0.291076284\) \(a_{57}=+0.478689956\) \(a_{58}=+0.815760129\) \(a_{59}=+0.265069000\) \(a_{60}=+0.424595518\)
\(a_{61}=+0.738251999\) \(a_{62}=-0.402221711\) \(a_{63}=-0.274429352\) \(a_{64}=+0.125000000\) \(a_{65}=-0.604952937\)
\(a_{66}=-0.366512689\) \(a_{67}=+0.345900059\) \(a_{68}=-0.455252786\) \(a_{69}=-0.835875559\) \(a_{70}=-0.856254458\)
\(a_{71}=-0.055999994\) \(a_{72}=+0.117851130\) \(a_{73}=+0.779399872\) \(a_{74}=+0.458151117\) \(a_{75}=+0.671675589\)
\(a_{76}=+0.414557662\) \(a_{77}=+0.739122554\) \(a_{78}=-0.167911305\) \(a_{79}=-0.459999084\) \(a_{80}=+0.367710505\)
\(a_{81}=+0.111111111\) \(a_{82}=+0.104858393\) \(a_{83}=-0.750000000\) \(a_{84}=-0.237662790\) \(a_{85}=-1.339209853\)
\(a_{86}=+0.883083017\) \(a_{87}=+0.666065356\) \(a_{88}=-0.317409299\)

Showing all 88 available coefficients

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